LMFDB - Embedded newform 43.7.f.a.2.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,7,Mod(2,43)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([9]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("43.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	43.f (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.89232559565$
Analytic rank:	$0$
Dimension:	$126$
Relative dimension:	$21$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			2.4
Character	$\chi$	$=$	43.2
Dual form			43.7.f.a.22.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.02991 - 10.4447i) q^{2} +(20.6257 - 42.8298i) q^{3} +(-43.8887 + 55.0347i) q^{4} +(127.013 + 28.9898i) q^{5} -551.091 q^{6} -619.099i q^{7} +(72.2435 + 16.4891i) q^{8} +(-954.446 - 1196.84i) q^{9} +O(q^{10})$	\(q+(-5.02991 - 10.4447i) q^{2} +(20.6257 - 42.8298i) q^{3} +(-43.8887 + 55.0347i) q^{4} +(127.013 + 28.9898i) q^{5} -551.091 q^{6} -619.099i q^{7} +(72.2435 + 16.4891i) q^{8} +(-954.446 - 1196.84i) q^{9} +(-336.072 - 1472.43i) q^{10} +(1279.58 + 1604.54i) q^{11} +(1451.89 + 3014.88i) q^{12} +(58.3552 - 255.671i) q^{13} +(-6466.31 + 3114.01i) q^{14} +(3861.36 - 4841.99i) q^{15} +(811.323 + 3554.64i) q^{16} +(-499.657 - 2189.14i) q^{17} +(-7699.85 + 15988.9i) q^{18} +(9757.92 + 7781.68i) q^{19} +(-7169.87 + 5717.78i) q^{20} +(-26515.9 - 12769.4i) q^{21} +(10322.8 - 21435.6i) q^{22} +(5083.42 + 6374.40i) q^{23} +(2196.30 - 2754.07i) q^{24} +(1214.18 + 584.718i) q^{25} +(-2963.93 + 676.497i) q^{26} +(-37160.5 + 8481.65i) q^{27} +(34071.9 + 27171.5i) q^{28} +(8210.48 + 17049.2i) q^{29} +(-69995.5 - 15976.0i) q^{30} +(-5612.02 + 2702.61i) q^{31} +(36754.1 - 29310.4i) q^{32} +(95114.6 - 21709.3i) q^{33} +(-20351.7 + 16230.0i) q^{34} +(17947.6 - 78633.4i) q^{35} +107757. q^{36} +7288.20i q^{37} +(32196.0 - 141060. i) q^{38} +(-9746.70 - 7772.74i) q^{39} +(8697.82 + 4188.65i) q^{40} +(21045.2 - 10134.9i) q^{41} +341180. i q^{42} +(-79504.8 - 585.981i) q^{43} -144465. q^{44} +(-86530.7 - 179683. i) q^{45} +(41009.7 - 85157.5i) q^{46} +(5976.39 - 7494.15i) q^{47} +(168979. + 38568.2i) q^{48} -265635. q^{49} -15622.8i q^{50} +(-104066. - 23752.5i) q^{51} +(11509.6 + 14432.6i) q^{52} +(7862.33 + 34447.1i) q^{53} +(275503. + 345469. i) q^{54} +(116008. + 240892. i) q^{55} +(10208.4 - 44725.9i) q^{56} +(534552. - 257427. i) q^{57} +(136776. - 171512. i) q^{58} +(-63690.5 - 279046. i) q^{59} +(97007.5 + 425018. i) q^{60} +(-56259.6 + 116824. i) q^{61} +(56455.9 + 45022.1i) q^{62} +(-740961. + 590897. i) q^{63} +(-280770. - 135212. i) q^{64} +(14823.7 - 30781.7i) q^{65} +(-705165. - 884249. i) q^{66} +(80047.0 - 100376. i) q^{67} +(142408. + 68580.1i) q^{68} +(377864. - 86244.9i) q^{69} +(-911579. + 208062. i) q^{70} +(-148353. - 118307. i) q^{71} +(-49217.7 - 102202. i) q^{72} +(283332. + 64668.6i) q^{73} +(76123.2 - 36659.0i) q^{74} +(50086.7 - 39942.8i) q^{75} +(-856526. + 195496. i) q^{76} +(993371. - 792187. i) q^{77} +(-32159.0 + 140898. i) q^{78} -223117. q^{79} +475004. i q^{80} +(-154871. + 678535. i) q^{81} +(-211711. - 168834. i) q^{82} +(-167663. - 80742.4i) q^{83} +(1.86651e6 - 898863. i) q^{84} -292534. i q^{85} +(393782. + 833353. i) q^{86} +899563. q^{87} +(65983.9 + 137017. i) q^{88} +(15929.3 - 33077.5i) q^{89} +(-1.44149e6 + 1.80758e6i) q^{90} +(-158285. - 36127.6i) q^{91} -573918. q^{92} +296105. i q^{93} +(-108335. - 24726.8i) q^{94} +(1.01379e6 + 1.27125e6i) q^{95} +(-497279. - 2.17872e6i) q^{96} +(4633.46 + 5810.17i) q^{97} +(1.33612e6 + 2.77448e6i) q^{98} +(699087. - 3.06290e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9}+O(q^{10}) $ 126 * q - 7 * q^2 - 7 * q^3 + 725 * q^4 - 7 * q^5 + 244 * q^6 + 2233 * q^8 + 6312 * q^9	\( 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9} + 1955 q^{10} - 985 q^{11} - 455 q^{12} - 4485 q^{13} - 6771 q^{14} + 5017 q^{15} - 41935 q^{16} - 10409 q^{17} - 5110 q^{18} - 33397 q^{19} - 24507 q^{20} - 5448 q^{21} + 25193 q^{22} - 29017 q^{23} - 1885 q^{24} - 2080 q^{25} + 34713 q^{26} - 7 q^{27} + 28665 q^{28} + 17353 q^{29} - 290052 q^{30} + 13547 q^{31} + 458283 q^{32} - 94801 q^{33} - 191527 q^{34} + 183008 q^{35} + 956352 q^{36} + 304607 q^{38} - 381031 q^{39} + 66419 q^{40} + 313447 q^{41} - 323228 q^{43} + 281588 q^{44} - 1237551 q^{45} + 80948 q^{46} - 180133 q^{47} - 762055 q^{48} - 1861754 q^{49} + 999215 q^{51} + 471797 q^{52} + 1030011 q^{53} - 92099 q^{54} + 324233 q^{55} - 842713 q^{56} + 331037 q^{57} + 849461 q^{58} - 369609 q^{59} + 553323 q^{60} - 594727 q^{61} - 886711 q^{62} + 1914136 q^{63} - 3250219 q^{64} + 1473521 q^{65} - 427559 q^{66} + 122535 q^{67} - 602346 q^{68} + 4320057 q^{69} - 1694994 q^{70} - 770707 q^{71} - 391202 q^{72} + 476945 q^{73} - 3943812 q^{74} + 2061367 q^{75} - 2044462 q^{76} + 3016216 q^{77} + 239350 q^{78} + 5077268 q^{79} + 2388946 q^{81} + 5820437 q^{82} - 1324235 q^{83} + 3759618 q^{84} - 4967947 q^{86} - 3537894 q^{87} - 7289555 q^{88} - 4331495 q^{89} - 12825206 q^{90} + 1802976 q^{91} - 12038260 q^{92} + 6249341 q^{94} - 5313259 q^{95} + 7069598 q^{96} + 788975 q^{97} + 4724783 q^{98} - 2216971 q^{99}+O(q^{100}) \) 126 * q - 7 * q^2 - 7 * q^3 + 725 * q^4 - 7 * q^5 + 244 * q^6 + 2233 * q^8 + 6312 * q^9 + 1955 * q^10 - 985 * q^11 - 455 * q^12 - 4485 * q^13 - 6771 * q^14 + 5017 * q^15 - 41935 * q^16 - 10409 * q^17 - 5110 * q^18 - 33397 * q^19 - 24507 * q^20 - 5448 * q^21 + 25193 * q^22 - 29017 * q^23 - 1885 * q^24 - 2080 * q^25 + 34713 * q^26 - 7 * q^27 + 28665 * q^28 + 17353 * q^29 - 290052 * q^30 + 13547 * q^31 + 458283 * q^32 - 94801 * q^33 - 191527 * q^34 + 183008 * q^35 + 956352 * q^36 + 304607 * q^38 - 381031 * q^39 + 66419 * q^40 + 313447 * q^41 - 323228 * q^43 + 281588 * q^44 - 1237551 * q^45 + 80948 * q^46 - 180133 * q^47 - 762055 * q^48 - 1861754 * q^49 + 999215 * q^51 + 471797 * q^52 + 1030011 * q^53 - 92099 * q^54 + 324233 * q^55 - 842713 * q^56 + 331037 * q^57 + 849461 * q^58 - 369609 * q^59 + 553323 * q^60 - 594727 * q^61 - 886711 * q^62 + 1914136 * q^63 - 3250219 * q^64 + 1473521 * q^65 - 427559 * q^66 + 122535 * q^67 - 602346 * q^68 + 4320057 * q^69 - 1694994 * q^70 - 770707 * q^71 - 391202 * q^72 + 476945 * q^73 - 3943812 * q^74 + 2061367 * q^75 - 2044462 * q^76 + 3016216 * q^77 + 239350 * q^78 + 5077268 * q^79 + 2388946 * q^81 + 5820437 * q^82 - 1324235 * q^83 + 3759618 * q^84 - 4967947 * q^86 - 3537894 * q^87 - 7289555 * q^88 - 4331495 * q^89 - 12825206 * q^90 + 1802976 * q^91 - 12038260 * q^92 + 6249341 * q^94 - 5313259 * q^95 + 7069598 * q^96 + 788975 * q^97 + 4724783 * q^98 - 2216971 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{9}{14}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−5.02991	−	10.4447i	−0.628739	−	1.30559i	−0.935340	−	0.353751i	$-0.884906\pi$
$2$	−5.02991	−	10.4447i	−0.628739	−	1.30559i	0.306601	−	0.951838i	$-0.400808\pi$
$3$	20.6257	−	42.8298i	0.763916	−	1.58629i	−0.0454371	−	0.998967i	$-0.514468\pi$
$3$	20.6257	−	42.8298i	0.763916	−	1.58629i	0.809354	−	0.587322i	$-0.199818\pi$
$4$	−43.8887	+	55.0347i	−0.685761	+	0.859917i
$5$	127.013	+	28.9898i	1.01610	+	0.231919i	0.697969	−	0.716128i	$-0.254087\pi$
$5$	127.013	+	28.9898i	1.01610	+	0.231919i	0.318132	+	0.948046i	$0.396944\pi$
$6$	−551.091			−2.55135
$7$		−	619.099i		−	1.80495i	−0.430739	−	0.902477i	$-0.641747\pi$
$7$		−	619.099i		−	1.80495i	0.430739	−	0.902477i	$-0.358253\pi$
$8$	72.2435	+	16.4891i	0.141101	+	0.0322053i
$9$	−954.446	−	1196.84i	−1.30925	−	1.64175i
$10$	−336.072	−	1472.43i	−0.336072	−	1.47243i
$11$	1279.58	+	1604.54i	0.961368	+	1.20552i	0.978622	+	0.205666i	$0.0659361\pi$
$11$	1279.58	+	1604.54i	0.961368	+	1.20552i	−0.0172542	+	0.999851i	$0.505492\pi$
$12$	1451.89	+	3014.88i	0.840213	+	1.74472i
$13$	58.3552	−	255.671i	0.0265613	−	0.116373i	−0.959909	−	0.280311i	$-0.909563\pi$
$13$	58.3552	−	255.671i	0.0265613	−	0.116373i	0.986471	+	0.163938i	$0.0524197\pi$
$14$	−6466.31	+	3114.01i	−2.35653	+	1.13484i
$15$	3861.36	−	4841.99i	1.14411	−	1.43466i
$16$	811.323	+	3554.64i	0.198077	+	0.867831i
$17$	−499.657	−	2189.14i	−0.101701	−	0.445582i	−0.999981	−	0.00615793i	$-0.998040\pi$
$17$	−499.657	−	2189.14i	−0.101701	−	0.445582i	0.898280	−	0.439424i	$-0.144817\pi$
$18$	−7699.85	+	15988.9i	−1.32028	+	2.74158i
$19$	9757.92	+	7781.68i	1.42265	+	1.13452i	0.970079	+	0.242791i	$0.0780630\pi$
$19$	9757.92	+	7781.68i	1.42265	+	1.13452i	0.452567	+	0.891731i	$0.350508\pi$
$20$	−7169.87	+	5717.78i	−0.896234	+	0.714723i
$21$	−26515.9	−	12769.4i	−2.86318	−	1.37883i
$22$	10322.8	−	21435.6i	0.969461	−	2.01311i
$23$	5083.42	+	6374.40i	0.417803	+	0.523909i	0.945543	−	0.325497i	$-0.105532\pi$
$23$	5083.42	+	6374.40i	0.417803	+	0.523909i	−0.527739	+	0.849406i	$0.676960\pi$
$24$	2196.30	−	2754.07i	0.158876	−	0.199224i
$25$	1214.18	+	584.718i	0.0777075	+	0.0374220i
$26$	−2963.93	+	676.497i	−0.168635	+	0.0384898i
$27$	−37160.5	+	8481.65i	−1.88795	+	0.430912i
$28$	34071.9	+	27171.5i	1.55211	+	1.23777i
$29$	8210.48	+	17049.2i	0.336647	+	0.699055i	0.998730	−	0.0503756i	$-0.0160418\pi$
$29$	8210.48	+	17049.2i	0.336647	+	0.699055i	−0.662083	+	0.749430i	$0.730328\pi$
$30$	−69995.5	−	15976.0i	−2.59243	−	0.591704i
$31$	−5612.02	+	2702.61i	−0.188380	+	0.0907189i	−0.525696	−	0.850672i	$-0.676195\pi$
$31$	−5612.02	+	2702.61i	−0.188380	+	0.0907189i	0.337316	+	0.941391i	$0.390481\pi$
$32$	36754.1	−	29310.4i	1.12165	−	0.894483i
$33$	95114.6	−	21709.3i	2.64670	−	0.604093i
$34$	−20351.7	+	16230.0i	−0.517803	+	0.412934i
$35$	17947.6	−	78633.4i	0.418602	−	1.83402i
$36$	107757.			2.30961
$37$			7288.20i			0.143885i	0.997409	+	0.0719424i	$0.0229198\pi$
$37$			7288.20i			0.143885i	−0.997409	+	0.0719424i	$0.977080\pi$
$38$	32196.0	−	141060.i	0.586747	−	2.57071i
$39$	−9746.70	−	7772.74i	−0.164310	−	0.131033i
$40$	8697.82	+	4188.65i	0.135903	+	0.0654477i
$41$	21045.2	−	10134.9i	0.305353	−	0.147050i	−0.274932	−	0.961464i	$-0.588655\pi$
$41$	21045.2	−	10134.9i	0.305353	−	0.147050i	0.580285	+	0.814413i	$0.302941\pi$
$42$			341180.i			4.60506i
$43$	−79504.8	−	585.981i	−0.999973	−	0.00737018i
$43$	−79504.8	−	585.981i	−0.999973	−	0.00737018i
$44$	−144465.			−1.69591
$45$	−86530.7	−	179683.i	−0.949583	−	1.97183i
$46$	41009.7	−	85157.5i	0.421321	−	0.874882i
$47$	5976.39	−	7494.15i	0.0575632	−	0.0721820i	−0.752216	−	0.658916i	$-0.771015\pi$
$47$	5976.39	−	7494.15i	0.0575632	−	0.0721820i	0.809780	+	0.586734i	$0.199587\pi$
$48$	168979.	+	38568.2i	1.52795	+	0.348744i
$49$	−265635.			−2.25786
$50$		−	15622.8i		−	0.124983i
$51$	−104066.	−	23752.5i	−0.784512	−	0.179060i
$52$	11509.6	+	14432.6i	0.0818561	+	0.102644i
$53$	7862.33	+	34447.1i	0.0528109	+	0.231380i	0.994445	−	0.105259i	$-0.0335671\pi$
$53$	7862.33	+	34447.1i	0.0528109	+	0.231380i	−0.941634	+	0.336639i	$0.890710\pi$
$54$	275503.	+	345469.i	1.74962	+	2.19396i
$55$	116008.	+	240892.i	0.697266	+	1.44789i
$56$	10208.4	−	44725.9i	0.0581290	−	0.254680i
$57$	534552.	−	257427.i	2.88646	−	1.39005i
$58$	136776.	−	171512.i	0.701015	−	0.879045i
$59$	−63690.5	−	279046.i	−0.310112	−	1.35869i	−0.854324	−	0.519741i	$-0.826028\pi$
$59$	−63690.5	−	279046.i	−0.310112	−	1.35869i	0.544212	−	0.838948i	$-0.316829\pi$
$60$	97007.5	+	425018.i	0.449109	+	1.96767i
$61$	−56259.6	+	116824.i	−0.247860	+	0.514688i	−0.987365	−	0.158464i	$-0.949346\pi$
$61$	−56259.6	+	116824.i	−0.247860	+	0.514688i	0.739504	+	0.673152i	$0.235060\pi$
$62$	56455.9	+	45022.1i	0.236883	+	0.188908i
$63$	−740961.	+	590897.i	−2.96329	+	2.36314i
$64$	−280770.	−	135212.i	−1.07105	−	0.515792i
$65$	14823.7	−	30781.7i	0.0539779	−	0.112086i
$66$	−705165.	−	884249.i	−2.45278	−	3.07569i
$67$	80047.0	−	100376.i	0.266146	−	0.333737i	−0.630743	−	0.775992i	$-0.717250\pi$
$67$	80047.0	−	100376.i	0.266146	−	0.333737i	0.896889	+	0.442255i	$0.145821\pi$
$68$	142408.	+	68580.1i	0.452906	+	0.218108i
$69$	377864.	−	86244.9i	1.15024	−	0.262534i
$70$	−911579.	+	208062.i	−2.65766	+	0.606594i
$71$	−148353.	−	118307.i	−0.414496	−	0.330549i	0.393938	−	0.919137i	$-0.371113\pi$
$71$	−148353.	−	118307.i	−0.414496	−	0.330549i	−0.808433	+	0.588588i	$0.799684\pi$
$72$	−49217.7	−	102202.i	−0.131863	−	0.273817i
$73$	283332.	+	64668.6i	0.728328	+	0.166236i	0.570578	−	0.821243i	$-0.306719\pi$
$73$	283332.	+	64668.6i	0.728328	+	0.166236i	0.157749	+	0.987479i	$0.449576\pi$
$74$	76123.2	−	36659.0i	0.187855	−	0.0904660i
$75$	50086.7	−	39942.8i	0.118724	−	0.0946793i
$76$	−856526.	+	195496.i	−1.95119	+	0.445346i
$77$	993371.	−	792187.i	2.17590	−	1.73522i
$78$	−32159.0	+	140898.i	−0.0677670	+	0.296907i
$79$	−223117.			−0.452534			−0.226267	−	0.974065i	$-0.572652\pi$
$79$	−223117.			−0.452534			−0.226267	+	0.974065i	$0.572652\pi$
$80$			475004.i			0.927743i
$81$	−154871.	+	678535.i	−0.291418	+	1.27678i
$82$	−211711.	−	168834.i	−0.383975	−	0.306210i
$83$	−167663.	−	80742.4i	−0.293227	−	0.141211i	0.281487	−	0.959565i	$-0.409172\pi$
$83$	−167663.	−	80742.4i	−0.293227	−	0.141211i	−0.574714	+	0.818354i	$0.694887\pi$
$84$	1.86651e6	−	898863.i	3.14914	−	1.51655i
$85$		−	292534.i		−	0.476343i
$86$	393782.	+	833353.i	0.619099	+	1.31019i
$87$	899563.			1.36607
$88$	65983.9	+	137017.i	0.0968255	+	0.201060i
$89$	15929.3	−	33077.5i	0.0225957	−	0.0469205i	−0.889366	−	0.457197i	$-0.848853\pi$
$89$	15929.3	−	33077.5i	0.0225957	−	0.0469205i	0.911961	+	0.410276i	$0.134568\pi$
$90$	−1.44149e6	+	1.80758e6i	−1.97736	+	2.47953i
$91$	−158285.	−	36127.6i	−0.210047	−	0.0479419i
$92$	−573918.			−0.737032
$93$			296105.i			0.368127i
$94$	−108335.	−	24726.8i	−0.130432	−	0.0297703i
$95$	1.01379e6	+	1.27125e6i	1.18244	+	1.48273i
$96$	−497279.	−	2.17872e6i	−0.562065	−	2.46257i
$97$	4633.46	+	5810.17i	0.00507680	+	0.00636610i	0.784363	−	0.620302i	$-0.212990\pi$
$97$	4633.46	+	5810.17i	0.00507680	+	0.00636610i	−0.779287	+	0.626668i	$0.784418\pi$
$98$	1.33612e6	+	2.77448e6i	1.41960	+	2.94783i
$99$	699087.	−	3.06290e6i	0.720486	−	3.15666i
$100$	−85468.6	+	41159.5i	−0.0854686	+	0.0411595i
$101$	701208.	−	879287.i	0.680586	−	0.853427i	−0.314822	−	0.949151i	$-0.601945\pi$
$101$	701208.	−	879287.i	0.680586	−	0.853427i	0.995408	+	0.0957233i	$0.0305164\pi$
$102$	275357.	+	1.20642e6i	0.259475	+	1.13683i
$103$	338968.	+	1.48512e6i	0.310204	+	1.35909i	0.854174	+	0.519987i	$0.174063\pi$
$103$	338968.	+	1.48512e6i	0.310204	+	1.35909i	−0.543971	+	0.839104i	$0.683080\pi$
$104$	8431.56	−	17508.3i	0.00749563	−	0.0155648i
$105$	−2.99767e6	−	2.39056e6i	−2.58950	−	2.06506i
$106$	320244.	−	255386.i	0.268883	−	0.214427i
$107$	1.43089e6	+	689083.i	1.16804	+	0.562497i	0.914404	−	0.404804i	$-0.132660\pi$
$107$	1.43089e6	+	689083.i	1.16804	+	0.562497i	0.253633	+	0.967301i	$0.418374\pi$
$108$	1.16414e6	−	2.41737e6i	0.924134	−	1.91898i
$109$	109492.	+	137299.i	0.0845480	+	0.106020i	0.822306	−	0.569045i	$-0.192687\pi$
$109$	109492.	+	137299.i	0.0845480	+	0.106020i	−0.737758	+	0.675065i	$0.764116\pi$
$110$	1.93254e6	−	2.42333e6i	1.45195	−	1.82069i
$111$	312152.	+	150325.i	0.228243	+	0.109916i
$112$	2.20067e6	−	502289.i	1.56640	−	0.357519i
$113$	−1.85063e6	+	422394.i	−1.28258	+	0.292740i	−0.808895	−	0.587954i	$-0.799934\pi$
$113$	−1.85063e6	+	422394.i	−1.28258	+	0.292740i	−0.473685	+	0.880694i	$0.657077\pi$
$114$	−5.37750e6	−	4.28841e6i	−3.62966	−	2.89456i
$115$	460866.	+	956997.i	0.303027	+	0.629241i
$116$	−1.29865e6	−	296408.i	−0.831989	−	0.189896i
$117$	−361693.	+	174182.i	−0.225831	+	0.108754i
$118$	−2.59420e6	+	2.06881e6i	−1.57891	+	1.25914i
$119$	−1.35530e6	+	309337.i	−0.804254	+	0.183566i
$120$	358798.	−	286132.i	0.207638	−	0.165586i
$121$	−543024.	+	2.37914e6i	−0.306523	+	1.34296i
$122$	1.50318e6			0.827810
$123$		−	1.11040e6i		−	0.596712i
$124$	97567.3	−	427470.i	0.0511728	−	0.224203i
$125$	−1.45424e6	−	1.15972e6i	−0.744570	−	0.593775i
$126$	9.89872e6	+	4.76697e6i	4.94843	+	2.38304i
$127$	−1.98463e6	+	955747.i	−0.968876	+	0.466586i	−0.850265	−	0.526355i	$-0.823558\pi$
$127$	−1.98463e6	+	955747.i	−0.968876	+	0.466586i	−0.118611	+	0.992941i	$0.537844\pi$
$128$			604011.i			0.288015i
$129$	−1.66494e6	+	3.39309e6i	−0.775587	+	1.58062i
$130$	−396068.			−0.180277
$131$	−244324.	−	507345.i	−0.108681	−	0.225678i	0.839534	−	0.543307i	$-0.182828\pi$
$131$	−244324.	−	507345.i	−0.108681	−	0.225678i	−0.948215	+	0.317628i	$0.897114\pi$
$132$	−2.97969e6	+	6.18740e6i	−1.29554	+	2.69021i
$133$	4.81763e6	−	6.04112e6i	2.04776	−	2.56781i
$134$	−1.45102e6	−	331187.i	−0.603060	−	0.137644i
$135$	−4.96574e6			−2.01829
$136$		−	166390.i		−	0.0661471i
$137$	3.12424e6	+	713088.i	1.21502	+	0.277320i	0.781546	−	0.623847i	$-0.214431\pi$
$137$	3.12424e6	+	713088.i	1.21502	+	0.277320i	0.433472	+	0.901167i	$0.357288\pi$
$138$	−2.80142e6	−	3.51287e6i	−1.06596	−	1.33667i
$139$	−152330.	−	667402.i	−0.0567207	−	0.248510i	0.938617	−	0.344961i	$-0.112108\pi$
$139$	−152330.	−	667402.i	−0.0567207	−	0.248510i	−0.995338	+	0.0964514i	$0.969251\pi$
$140$	3.53987e6	+	4.43886e6i	1.29004	+	1.61766i
$141$	−197706.	−	410540.i	−0.0705280	−	0.146453i
$142$	−489485.	+	2.14457e6i	−0.170952	+	0.748990i
$143$	484905.	−	233518.i	0.165824	−	0.0798568i
$144$	3.47996e6	−	4.36373e6i	1.16543	−	1.46141i
$145$	548581.	+	2.40349e6i	0.179944	+	0.788385i
$146$	−749688.	−	3.28460e6i	−0.240892	−	1.05542i
$147$	−5.47891e6	+	1.13771e7i	−1.72481	+	3.58161i
$148$	−401104.	−	319870.i	−0.123729	−	0.0986707i
$149$	780201.	−	622189.i	0.235856	−	0.188089i	−0.498428	−	0.866931i	$-0.666089\pi$
$149$	780201.	−	622189.i	0.235856	−	0.188089i	0.734285	+	0.678842i	$0.237518\pi$
$150$	−669123.	−	322233.i	−0.198259	−	0.0954764i
$151$	−511682.	+	1.06252e6i	−0.148617	+	0.308607i	−0.961966	−	0.273170i	$-0.911928\pi$
$151$	−511682.	+	1.06252e6i	−0.148617	+	0.308607i	0.813349	+	0.581777i	$0.197642\pi$
$152$	576633.	+	723075.i	0.164198	+	0.205898i
$153$	−2.14315e6	+	2.68743e6i	−0.598382	+	0.750348i
$154$	−1.32707e7	−	6.39085e6i	−3.63356	−	1.74983i
$155$	−791146.	+	180574.i	−0.212452	+	0.0484909i
$156$	855541.	−	195272.i	0.225355	−	0.0514358i
$157$	−4.10926e6	−	3.27703e6i	−1.06185	−	0.846800i	−0.0732458	−	0.997314i	$-0.523336\pi$
$157$	−4.10926e6	−	3.27703e6i	−1.06185	−	0.846800i	−0.988608	+	0.150514i	$0.951907\pi$
$158$	1.12226e6	+	2.33039e6i	0.284526	+	0.590824i
$159$	1.63753e6	+	373756.i	0.407378	+	0.0929815i
$160$	5.51794e6	−	2.65730e6i	1.34715	−	0.648755i
$161$	3.94639e6	−	3.14714e6i	0.945631	−	0.754116i
$162$	7.86610e6	−	1.79539e6i	1.85018	−	0.422292i
$163$	−2.73072e6	+	2.17768e6i	−0.630543	+	0.502841i	−0.885821	−	0.464026i	$-0.846404\pi$
$163$	−2.73072e6	+	2.17768e6i	−0.630543	+	0.502841i	0.255278	+	0.966868i	$0.417833\pi$
$164$	−365880.	+	1.60302e6i	−0.0829482	+	0.363420i
$165$	1.27101e7			2.82942
$166$			2.15732e6i			0.471618i
$167$	1.43726e6	−	6.29703e6i	0.308592	−	1.35203i	−0.548191	−	0.836353i	$-0.684683\pi$
$167$	1.43726e6	−	6.29703e6i	0.308592	−	1.35203i	0.856783	−	0.515677i	$-0.172459\pi$
$168$	−1.70504e6	−	1.35973e6i	−0.359590	−	0.286764i
$169$	4.28684e6	+	2.06443e6i	0.888132	+	0.427702i
$170$	−3.05543e6	+	1.47142e6i	−0.621908	+	0.299495i
$171$		−	1.91059e7i		−	3.82101i
$172$	3.52161e6	−	4.34981e6i	0.692080	−	0.854840i
$173$	−4.80434e6			−0.927888			−0.463944	−	0.885865i	$-0.653566\pi$
$173$	−4.80434e6			−0.927888			−0.463944	+	0.885865i	$0.653566\pi$
$174$	−4.52472e6	−	9.39568e6i	−0.858903	−	1.78353i
$175$	361998.	−	751698.i	0.0675449	−	0.140258i
$176$	−4.66542e6	+	5.85025e6i	−0.855761	+	1.07309i
$177$	−1.32652e7	−	3.02769e6i	−2.39217	−	0.545998i
$178$	−425608.			−0.0754657
$179$			4.15894e6i			0.725142i	0.931956	+	0.362571i	$0.118101\pi$
$179$			4.15894e6i			0.725142i	−0.931956	+	0.362571i	$0.881899\pi$
$180$	1.36865e7	+	3.12386e6i	2.34680	+	0.535641i
$181$	4.98673e6	+	6.25316e6i	0.840969	+	1.05454i	0.997759	+	0.0669103i	$0.0213141\pi$
$181$	4.98673e6	+	6.25316e6i	0.840969	+	1.05454i	−0.156790	+	0.987632i	$0.550114\pi$
$182$	418819.	+	1.83496e6i	0.0694723	+	0.304378i
$183$	3.84317e6	+	4.81918e6i	0.627099	+	0.786357i
$184$	262135.	+	544330.i	0.0420797	+	0.0873793i
$185$	−211284.	+	925694.i	−0.0333696	+	0.146202i
$186$	3.09273e6	−	1.48938e6i	0.480622	−	0.231455i
$187$	2.87322e6	−	3.60291e6i	0.439384	−	0.550970i
$188$	150143.	+	657818.i	0.0225959	+	0.0989993i
$189$	5.25098e6	+	2.30061e7i	0.777777	+	3.40766i
$190$	8.17860e6	−	1.69830e7i	1.19239	−	2.47602i
$191$	6.29267e6	+	5.01824e6i	0.903098	+	0.720197i	0.960537	−	0.278152i	$-0.0897219\pi$
$191$	6.29267e6	+	5.01824e6i	0.903098	+	0.720197i	−0.0574387	+	0.998349i	$0.518293\pi$
$192$	−1.15822e7	+	9.23649e6i	−1.63639	+	1.30498i
$193$	6.12095e6	+	2.94770e6i	0.851427	+	0.410025i	0.808107	−	0.589036i	$-0.200492\pi$
$193$	6.12095e6	+	2.94770e6i	0.851427	+	0.410025i	0.0433197	+	0.999061i	$0.486207\pi$
$194$	37379.7	−	77619.7i	0.00511954	−	0.0106308i
$195$	−1.01263e6	−	1.26979e6i	−0.136567	−	0.171249i
$196$	1.16584e7	−	1.46191e7i	1.54835	−	1.94157i
$197$	8.86018e6	+	4.26684e6i	1.15889	+	0.558094i	0.911694	−	0.410870i	$-0.134775\pi$
$197$	8.86018e6	+	4.26684e6i	1.15889	+	0.558094i	0.247201	+	0.968964i	$0.420489\pi$
$198$	−3.55075e7	+	8.10435e6i	−4.57430	+	1.04405i
$199$	−7.58231e6	+	1.73061e6i	−0.962149	+	0.219604i	−0.674618	−	0.738167i	$-0.735692\pi$
$199$	−7.58231e6	+	1.73061e6i	−0.962149	+	0.219604i	−0.287531	+	0.957771i	$0.592834\pi$
$200$	78075.1	+	62262.8i	0.00975939	+	0.00778285i
$201$	−2.64804e6	−	5.49872e6i	−0.326090	−	0.677132i
$202$	−1.27109e7	−	2.90118e6i	−1.54214	−	0.351982i
$203$	1.05552e7	−	5.08310e6i	1.26176	−	0.607632i
$204$	5.87455e6	−	4.68480e6i	0.691965	−	0.551823i
$205$	2.96682e6	−	677157.i	0.344373	−	0.0786010i
$206$	1.38066e7	−	1.10104e7i	1.57938	−	1.25951i
$207$	2.77728e6	−	1.21680e7i	0.313118	−	1.37186i
$208$	956161.			0.106253
$209$			2.56143e7i			2.80572i
$210$	−9.89074e6	+	4.33342e7i	−1.06800	+	4.67921i
$211$	−2.73954e6	−	2.18471e6i	−0.291629	−	0.232567i	0.466736	−	0.884397i	$-0.345430\pi$
$211$	−2.73954e6	−	2.18471e6i	−0.291629	−	0.232567i	−0.758365	+	0.651830i	$0.774001\pi$
$212$	−2.24086e6	−	1.07914e6i	−0.235183	−	0.113258i
$213$	−8.12696e6	+	3.91374e6i	−0.840987	+	0.404998i
$214$		−	1.84113e7i		−	1.87864i
$215$	−1.00811e7	−	2.37926e6i	−1.01436	−	0.239401i
$216$	−2.82446e6			−0.280269
$217$	1.67318e6	+	3.47440e6i	0.163743	+	0.340017i
$218$	883310.	−	1.83421e6i	0.0852597	−	0.177044i
$219$	8.61367e6	−	1.08012e7i	0.820080	−	1.02835i
$220$	−1.83489e7	−	4.18801e6i	−1.72322	−	0.393314i
$221$	−588857.			−0.0545548
$222$		−	4.01646e6i		−	0.367100i
$223$	−1.11533e7	−	2.54567e6i	−1.00575	−	0.229556i	−0.312240	−	0.950003i	$-0.601079\pi$
$223$	−1.11533e7	−	2.54567e6i	−1.00575	−	0.229556i	−0.693509	+	0.720448i	$0.743936\pi$
$224$	−1.81461e7	−	2.27544e7i	−1.61450	−	2.02452i
$225$	−459057.	−	2.01126e6i	−0.0403013	−	0.176571i
$226$	1.37203e7	+	1.72047e7i	1.18861	+	1.49047i
$227$	7.24549e6	+	1.50454e7i	0.619427	+	1.28625i	0.940691	+	0.339264i	$0.110178\pi$
$227$	7.24549e6	+	1.50454e7i	0.619427	+	1.28625i	−0.321264	+	0.946990i	$0.604108\pi$
$228$	−9.29341e6	+	4.07171e7i	−0.784098	+	3.43536i
$229$	−1.19954e7	+	5.77666e6i	−0.998866	+	0.481028i	−0.860553	−	0.509360i	$-0.829882\pi$
$229$	−1.19954e7	+	5.77666e6i	−0.998866	+	0.481028i	−0.138312	+	0.990389i	$0.544168\pi$
$230$	7.67745e6	−	9.62722e6i	0.631006	−	0.791257i
$231$	−1.34402e7	−	5.88853e7i	−1.09036	−	4.77718i
$232$	312027.	+	1.36708e6i	0.0249878	+	0.109479i
$233$	3.40253e6	−	7.06543e6i	0.268989	−	0.558562i	−0.722096	−	0.691793i	$-0.756821\pi$
$233$	3.40253e6	−	7.06543e6i	0.268989	−	0.558562i	0.991085	+	0.133231i	$0.0425353\pi$
$234$	3.63857e6	+	2.90166e6i	0.283977	+	0.226464i
$235$	976331.	−	778598.i	0.0752304	−	0.0599943i
$236$	1.81525e7	+	8.74179e6i	1.38102	+	0.665066i
$237$	−4.60195e6	+	9.55605e6i	−0.345698	+	0.717850i
$238$	1.00480e7	+	1.25997e7i	0.745327	+	0.934610i
$239$	−4.24398e6	+	5.32179e6i	−0.310871	+	0.389820i	−0.912582	−	0.408894i	$-0.865915\pi$
$239$	−4.24398e6	+	5.32179e6i	−0.310871	+	0.389820i	0.601711	+	0.798714i	$0.294486\pi$
$240$	2.03443e7	+	9.79732e6i	1.47167	+	0.708718i
$241$	1.88194e7	−	4.29542e6i	1.34448	−	0.306870i	0.511080	−	0.859533i	$-0.329246\pi$
$241$	1.88194e7	−	4.29542e6i	1.34448	−	0.306870i	0.833404	+	0.552664i	$0.186389\pi$
$242$	2.75808e7	−	6.29514e6i	1.94608	−	0.444180i
$243$	4.14268e6	+	3.30368e6i	0.288711	+	0.230239i
$244$	−3.96023e6	−	8.22350e6i	−0.272616	−	0.566092i
$245$	−3.37390e7	−	7.70070e6i	−2.29421	−	0.523639i
$246$	−1.15978e7	+	5.58522e6i	−0.779061	+	0.375176i
$247$	2.55897e6	−	2.04071e6i	0.169815	−	0.135423i
$248$	−449996.	+	102709.i	−0.0295021	+	0.00673367i
$249$	−6.91636e6	+	5.51561e6i	−0.448002	+	0.357269i
$250$	−4.79822e6	+	2.10224e7i	−0.307086	+	1.34543i
$251$	−1.51061e7			−0.955279			−0.477640	−	0.878556i	$-0.658508\pi$
$251$	−1.51061e7			−0.955279			−0.477640	+	0.878556i	$0.658508\pi$
$252$		−	6.67123e7i		−	4.16873i
$253$	−3.72336e6	+	1.63131e7i	−0.229918	+	1.00734i
$254$	1.99650e7	+	1.59216e7i	1.21834	+	0.971593i
$255$	−1.25292e7	−	6.03373e6i	−0.755617	−	0.363886i
$256$	−1.16606e7	+	5.61544e6i	−0.695025	+	0.334706i
$257$			2.20954e6i			0.130167i	0.997880	+	0.0650837i	$0.0207314\pi$
$257$			2.20954e6i			0.130167i	−0.997880	+	0.0650837i	$0.979269\pi$
$258$	4.38144e7	+	322928.i	2.55128	+	0.0188039i
$259$	4.51212e6			0.259706
$260$	1.04347e6	+	2.16679e6i	0.0593690	+	0.123281i
$261$	1.25687e7	−	2.60992e7i	0.706918	−	1.46793i
$262$	−4.07014e6	+	5.10380e6i	−0.226311	+	0.283785i
$263$	2.42175e7	+	5.52748e6i	1.33126	+	0.303850i	0.828214	−	0.560412i	$-0.189357\pi$
$263$	2.42175e7	+	5.52748e6i	1.33126	+	0.303850i	0.503042	+	0.864262i	$0.332214\pi$
$264$	7.22938e6			0.392906
$265$			4.60315e6i			0.247353i
$266$	−8.73300e7	−	1.99325e7i	−4.64001	−	1.05905i
$267$	−1.08815e6	−	1.36450e6i	−0.0571682	−	0.0716866i
$268$	2.01099e6	+	8.81072e6i	0.104473	+	0.457728i
$269$	−1.70409e7	−	2.13686e7i	−0.875458	−	1.09779i	−0.994483	−	0.104899i	$-0.966548\pi$
$269$	−1.70409e7	−	2.13686e7i	−0.875458	−	1.09779i	0.119024	−	0.992891i	$-0.462023\pi$
$270$	2.49772e7	+	5.18658e7i	1.26897	+	2.63505i
$271$	−3.29280e6	+	1.44267e7i	−0.165447	+	0.724869i	0.822332	+	0.569007i	$0.192672\pi$
$271$	−3.29280e6	+	1.44267e7i	−0.165447	+	0.724869i	−0.987779	+	0.155861i	$0.950185\pi$
$272$	7.37622e6	−	3.55220e6i	0.366545	−	0.176519i
$273$	−4.81209e6	+	6.03418e6i	−0.236508	+	0.296572i
$274$	−8.26665e6	−	3.62186e7i	−0.401863	−	1.76068i
$275$	615435.	+	2.69640e6i	0.0295927	+	0.129654i
$276$	−1.18375e7	+	2.45808e7i	−0.563031	+	1.16915i
$277$	2.20498e7	+	1.75841e7i	1.03745	+	0.827335i	0.985219	−	0.171300i	$-0.0547968\pi$
$277$	2.20498e7	+	1.75841e7i	1.03745	+	0.827335i	0.0522264	+	0.998635i	$0.483368\pi$
$278$	−6.20462e6	+	4.94802e6i	−0.288789	+	0.230302i
$279$	8.59096e6	+	4.13719e6i	0.395575	+	0.190499i
$280$	2.59319e6	−	5.38481e6i	0.118130	−	0.245299i
$281$	1.38347e7	+	1.73482e7i	0.623520	+	0.781869i	0.988835	−	0.149015i	$-0.0476101\pi$
$281$	1.38347e7	+	1.73482e7i	0.623520	+	0.781869i	−0.365315	+	0.930884i	$0.619039\pi$
$282$	−3.29353e6	+	4.12996e6i	−0.146864	+	0.184161i
$283$	−2.15885e7	−	1.03965e7i	−0.952495	−	0.458698i	−0.107935	−	0.994158i	$-0.534424\pi$
$283$	−2.15885e7	−	1.03965e7i	−0.952495	−	0.458698i	−0.844560	+	0.535460i	$0.820138\pi$
$284$	1.30220e7	−	2.97219e6i	0.568490	−	0.129754i
$285$	7.53577e7	−	1.71999e7i	3.25532	−	0.743005i
$286$	−4.87805e6	−	3.89012e6i	−0.208520	−	0.166289i
$287$	−6.27448e6	−	1.30291e7i	−0.265419	−	0.551148i
$288$	−7.01597e7	−	1.60135e7i	−2.93704	−	0.670361i
$289$	1.72045e7	−	8.28526e6i	0.712769	−	0.343251i
$290$	2.23445e7	−	1.78191e7i	0.916170	−	0.730621i
$291$	344417.	−	78610.9i	0.0139767	−	0.00319010i
$292$	−1.59941e7	+	1.27549e7i	−0.642408	+	0.512303i
$293$	−1.41603e6	+	6.20402e6i	−0.0562948	+	0.246644i	−0.995244	−	0.0974116i	$-0.968944\pi$
$293$	−1.41603e6	+	6.20402e6i	−0.0562948	+	0.246644i	0.938949	+	0.344055i	$0.111801\pi$
$294$	1.46389e8			5.76057
$295$		−	3.72888e7i		−	1.45249i
$296$	−120176.	+	526525.i	−0.00463385	+	0.0203022i
$297$	−6.11591e7	−	4.87727e7i	−2.33449	−	1.86169i
$298$	−1.04229e7	−	5.01942e6i	−0.393859	−	0.189673i
$299$	1.92639e6	−	927701.i	0.0720661	−	0.0347052i
$300$			4.50955e6i			0.167020i
$301$	−362780.	+	4.92214e7i	−0.0133028	+	1.80490i
$302$	1.36714e7			0.496356
$303$	−2.31968e7	−	4.81685e7i	−0.833872	−	1.73155i
$304$	−1.97442e7	+	4.09993e7i	−0.702780	+	1.45934i
$305$	−1.05324e7	+	1.32072e7i	−0.371217	+	0.465491i
$306$	3.88493e7	+	8.86709e6i	1.35587	+	0.309469i
$307$	1.93216e7			0.667771			0.333886	−	0.942614i	$-0.391640\pi$
$307$	1.93216e7			0.667771			0.333886	+	0.942614i	$0.391640\pi$
$308$			8.94380e7i			3.06105i
$309$	7.05987e7	+	1.61137e7i	2.39288	+	0.546159i
$310$	5.86544e6	+	7.35503e6i	0.196886	+	0.246888i
$311$	−7.93209e6	−	3.47528e7i	−0.263698	−	1.15534i	−0.917205	−	0.398415i	$-0.869560\pi$
$311$	−7.93209e6	−	3.47528e7i	−0.263698	−	1.15534i	0.653507	−	0.756920i	$-0.273297\pi$
$312$	−575970.	−	722244.i	−0.0189643	−	0.0237805i
$313$	−2.87731e6	−	5.97479e6i	−0.0938325	−	0.194845i	0.848770	−	0.528762i	$-0.177344\pi$
$313$	−2.87731e6	−	5.97479e6i	−0.0938325	−	0.194845i	−0.942602	+	0.333917i	$0.891629\pi$
$314$	−1.35584e7	+	5.94032e7i	−0.437945	+	1.91876i
$315$	−1.11241e8	+	5.35711e7i	−3.55906	+	1.71395i
$316$	9.79232e6	−	1.22792e7i	0.310330	−	0.389142i
$317$	−1.31798e7	−	5.77446e7i	−0.413744	−	1.81273i	−0.566019	−	0.824392i	$-0.691517\pi$
$317$	−1.31798e7	−	5.77446e7i	−0.413744	−	1.81273i	0.152275	−	0.988338i	$-0.451340\pi$
$318$	−4.33286e6	−	1.89835e7i	−0.134739	−	0.590330i
$319$	−1.68503e7	+	3.49900e7i	−0.519081	+	1.07788i
$320$	−3.17416e7	−	2.53131e7i	−0.968678	−	0.772495i
$321$	5.90265e7	−	4.70721e7i	1.78456	−	1.42314i
$322$	−5.27209e7	−	2.53891e7i	−1.57912	−	0.760464i
$323$	1.21596e7	−	2.52497e7i	0.360837	−	0.749287i
$324$	−3.05459e7	−	3.83033e7i	−0.898086	−	1.12616i
$325$	220349.	−	276309.i	0.00641890	−	0.00804905i
$326$	3.64805e7	+	1.75681e7i	1.05295	+	0.507075i
$327$	8.13883e6	−	1.85764e6i	0.232766	−	0.0531272i
$328$	1.68750e6	−	385160.i	0.0478213	−	0.0109149i
$329$	−4.63962e6	−	3.69998e6i	−0.130285	−	0.103899i
$330$	−6.39307e7	−	1.32753e8i	−1.77897	−	3.69406i
$331$	5.86943e7	+	1.33966e7i	1.61850	+	0.369411i	0.933343	−	0.358987i	$-0.116878\pi$
$331$	5.86943e7	+	1.33966e7i	1.61850	+	0.369411i	0.685154	+	0.728398i	$0.259735\pi$
$332$	1.18022e7	−	5.68362e6i	0.322513	−	0.155314i
$333$	8.72280e6	−	6.95620e6i	0.236223	−	0.188382i
$334$	−7.29999e7	+	1.66618e7i	−1.95922	+	0.447179i
$335$	1.30769e7	−	1.04284e7i	0.347832	−	0.277386i
$336$	2.38776e7	−	1.04614e8i	0.629466	−	2.75787i
$337$	−7.93483e6			−0.207323			−0.103662	−	0.994613i	$-0.533056\pi$
$337$	−7.93483e6			−0.207323			−0.103662	+	0.994613i	$0.533056\pi$
$338$		−	5.51588e7i		−	1.42845i
$339$	−2.00796e7	+	8.79743e7i	−0.515413	+	2.25817i
$340$	1.60995e7	+	1.28389e7i	0.409615	+	0.326657i
$341$	−1.15175e7	−	5.54653e6i	−0.290466	−	0.139881i
$342$	−1.99555e8	+	9.61007e7i	−4.98867	+	2.40242i
$343$			9.16178e7i			2.27037i
$344$	−5.73404e6	−	1.35330e6i	−0.140859	−	0.0332443i
$345$	5.04937e7			1.22965
$346$	2.41654e7	+	5.01800e7i	0.583399	+	1.21144i
$347$	−2.42370e7	+	5.03286e7i	−0.580083	+	1.20455i	0.380038	+	0.924971i	$0.375911\pi$
$347$	−2.42370e7	+	5.03286e7i	−0.580083	+	1.20455i	−0.960121	+	0.279584i	$0.909803\pi$
$348$	−3.94807e7	+	4.95072e7i	−0.936800	+	1.17471i
$349$	−4.01031e7	−	9.15328e6i	−0.943414	−	0.215328i	−0.276966	−	0.960880i	$-0.589329\pi$
$349$	−4.01031e7	−	9.15328e6i	−0.943414	−	0.215328i	−0.666448	+	0.745552i	$0.732186\pi$
$350$	−9.67209e6			−0.225588
$351$			9.99581e6i			0.231151i
$352$	9.40597e7	+	2.14685e7i	2.15663	+	0.492237i
$353$	−2.41691e7	−	3.03071e7i	−0.549461	−	0.689002i	0.427110	−	0.904200i	$-0.359532\pi$
$353$	−2.41691e7	−	3.03071e7i	−0.549461	−	0.689002i	−0.976570	+	0.215198i	$0.930960\pi$
$354$	3.50992e7	+	1.53780e8i	0.791203	+	3.46649i
$355$	−1.54130e7	−	1.93272e7i	−0.344509	−	0.432001i
$356$	1.12129e6	+	2.32839e6i	0.0248525	+	0.0516067i
$357$	−1.47051e7	+	6.44274e7i	−0.323195	+	1.41601i
$358$	4.34389e7	−	2.09191e7i	0.946738	−	0.455925i
$359$	3.54249e7	−	4.44214e7i	0.765641	−	0.960084i	−0.234286	−	0.972168i	$-0.575275\pi$
$359$	3.54249e7	−	4.44214e7i	0.765641	−	0.960084i	0.999927	+	0.0120841i	$0.00384657\pi$
$360$	−3.28847e6	−	1.44077e7i	−0.0704833	−	0.308808i
$361$	2.41938e7	+	1.06000e8i	0.514259	+	2.25312i
$362$	4.02297e7	−	8.35378e7i	0.848049	−	1.76099i
$363$	9.06979e7	+	7.23292e7i	1.89617	+	1.51215i
$364$	8.93522e6	−	7.12560e6i	0.185268	−	0.147747i
$365$	3.41120e7	+	1.64275e7i	0.701502	+	0.337825i
$366$	3.10042e7	−	6.43808e7i	0.632378	−	1.31315i
$367$	−5.25507e7	−	6.58965e7i	−1.06312	−	1.33310i	−0.940176	−	0.340690i	$-0.889339\pi$
$367$	−5.25507e7	−	6.58965e7i	−1.06312	−	1.33310i	−0.122940	−	0.992414i	$-0.539232\pi$
$368$	−1.85344e7	+	2.32414e7i	−0.371907	+	0.466357i
$369$	−3.22163e7	−	1.55146e7i	−0.641205	−	0.308788i
$370$	1.07313e7	−	2.44936e6i	0.211860	−	0.0483557i
$371$	2.13262e7	−	4.86756e6i	0.417630	−	0.0953213i
$372$	−1.62961e7	−	1.29957e7i	−0.316558	−	0.252447i
$373$	−2.00490e7	−	4.16322e7i	−0.386337	−	0.802237i	−0.999921	−	0.0126075i	$-0.995987\pi$
$373$	−2.00490e7	−	4.16322e7i	−0.386337	−	0.802237i	0.613583	−	0.789630i	$-0.289727\pi$
$374$	−5.20834e7	−	1.18877e7i	−0.995599	−	0.227239i
$375$	−7.96652e7	+	3.83647e7i	−1.51069	+	0.727509i
$376$	555327.	−	442858.i	0.0104468	−	0.00833108i
$377$	4.83811e6	−	1.10427e6i	0.0902926	−	0.0206087i
$378$	2.13880e8	−	1.70563e8i	3.95999	−	3.15799i
$379$	−2.22923e7	+	9.76691e7i	−0.409485	+	1.79407i	0.177112	+	0.984191i	$0.443325\pi$
$379$	−2.22923e7	+	9.76691e7i	−0.409485	+	1.79407i	−0.586597	+	0.809879i	$0.699533\pi$
$380$	−1.14457e8			−2.08589
$381$			1.04714e8i			1.89335i
$382$	2.07625e7	−	9.09665e7i	0.372469	−	1.63189i
$383$	8.96127e6	+	7.14637e6i	0.159505	+	0.127201i	0.699990	−	0.714153i	$-0.253188\pi$
$383$	8.96127e6	+	7.14637e6i	0.159505	+	0.127201i	−0.540485	+	0.841354i	$0.681759\pi$
$384$	2.58697e7	+	1.24582e7i	0.456875	+	0.220019i
$385$	1.49136e8	−	7.18202e7i	2.61337	−	1.25853i
$386$		−	7.87583e7i		−	1.36941i
$387$	7.51818e7	+	9.57137e7i	1.29712	+	1.65136i
$388$	−523117.			−0.00895579
$389$	−1.07806e7	−	2.23862e7i	−0.183145	−	0.380305i	0.789102	−	0.614263i	$-0.210547\pi$
$389$	−1.07806e7	−	2.23862e7i	−0.183145	−	0.380305i	−0.972247	+	0.233958i	$0.924832\pi$
$390$	−8.16920e6	+	1.69635e7i	−0.137716	+	0.285971i
$391$	1.14145e7	−	1.43133e7i	0.190953	−	0.239448i
$392$	−1.91904e7	−	4.38008e6i	−0.318585	−	0.0727149i
$393$	−2.67689e7			−0.441014
$394$		−	1.14004e8i		−	1.86394i
$395$	−2.83387e7	−	6.46812e6i	−0.459821	−	0.104951i
$396$	1.37884e8	+	1.72901e8i	2.22038	+	2.78427i
$397$	−2.35349e7	−	1.03113e8i	−0.376132	−	1.64794i	−0.709177	−	0.705030i	$-0.750933\pi$
$397$	−2.35349e7	−	1.03113e8i	−0.376132	−	1.64794i	0.333046	−	0.942911i	$-0.391924\pi$
$398$	5.62141e7	+	7.04902e7i	0.891653	+	1.11810i
$399$	−1.59373e8	−	3.30941e8i	−2.50897	−	5.20993i
$400$	−1.09337e6	+	4.79036e6i	−0.0170839	+	0.0748494i
$401$	−1.88287e7	+	9.06744e6i	−0.292003	+	0.140621i	−0.574151	−	0.818750i	$-0.694668\pi$
$401$	−1.88287e7	+	9.06744e6i	−0.292003	+	0.140621i	0.282147	+	0.959371i	$0.408953\pi$
$402$	−4.41131e7	+	5.53161e7i	−0.679031	+	0.851478i
$403$	363487.	+	1.59254e6i	0.00555359	+	0.0243319i
$404$	1.76162e7	+	7.71816e7i	0.267158	+	1.17049i
$405$	−3.93412e7	+	8.16929e7i	−0.592220	+	1.22976i
$406$	−1.06183e8	−	8.46782e7i	−1.58664	−	1.26530i
$407$	−1.16942e7	+	9.32584e6i	−0.173456	+	0.138326i
$408$	−7.12646e6	−	3.43192e6i	−0.104928	−	0.0505309i
$409$	−3.29472e7	+	6.84156e7i	−0.481558	+	0.999966i	0.508728	+	0.860927i	$0.330116\pi$
$409$	−3.29472e7	+	6.84156e7i	−0.481558	+	0.999966i	−0.990287	+	0.139039i	$0.955599\pi$
$410$	−2.19956e7	−	2.75816e7i	−0.319142	−	0.400191i
$411$	9.49812e7	−	1.19103e8i	1.36808	−	1.71552i
$412$	−9.66098e7	−	4.65248e7i	−1.38143	−	0.665262i
$413$	−1.72757e8	+	3.94307e7i	−2.45237	+	0.559738i
$414$	−1.41061e8	+	3.21963e7i	−1.98796	+	0.453738i
$415$	−1.89547e7	−	1.51158e7i	−0.265199	−	0.211489i
$416$	−5.34902e6	−	1.11074e7i	−0.0743010	−	0.154288i
$417$	−3.17266e7	−	7.24140e6i	−0.437538	−	0.0998652i
$418$	2.67534e8	−	1.28838e8i	3.66311	−	1.76406i
$419$	−5.11876e7	+	4.08207e7i	−0.695861	+	0.554931i	−0.906279	−	0.422681i	$-0.861089\pi$
$419$	−5.11876e7	+	4.08207e7i	−0.695861	+	0.554931i	0.210418	+	0.977612i	$0.432518\pi$
$420$	2.63128e8	−	6.00573e7i	3.55156	−	0.810621i
$421$	6.99991e7	−	5.58224e7i	0.938094	−	0.748105i	−0.0297760	−	0.999557i	$-0.509479\pi$
$421$	6.99991e7	−	5.58224e7i	0.938094	−	0.748105i	0.967870	+	0.251452i	$0.0809080\pi$
$422$	−9.03905e6	+	3.96027e7i	−0.120278	+	0.526972i
$423$	−1.46734e7			−0.193870
$424$			2.61822e6i			0.0343486i
$425$	673357.	−	2.95017e6i	0.00877160	−	0.0384309i
$426$	8.17557e7	+	6.51980e7i	1.05752	+	0.843345i
$427$	7.23258e7	+	3.48303e7i	0.928987	+	0.447377i
$428$	−1.00724e8	+	4.85059e7i	−1.28469	+	0.618676i
$429$		−	2.55849e7i		−	0.324049i
$430$	2.58565e7	+	1.17262e8i	0.325211	+	1.47486i
$431$	1.56042e7			0.194899			0.0974497	−	0.995240i	$-0.468931\pi$
$431$	1.56042e7			0.194899			0.0974497	+	0.995240i	$0.468931\pi$
$432$	−6.02984e7	−	1.25211e8i	−0.747919	−	1.55307i
$433$	5.39374e7	−	1.12002e8i	0.664395	−	1.37963i	−0.247371	−	0.968921i	$-0.579567\pi$
$433$	5.39374e7	−	1.12002e8i	0.664395	−	1.37963i	0.911766	−	0.410710i	$-0.134719\pi$
$434$	2.78731e7	−	3.49518e7i	0.340970	−	0.427563i
$435$	1.14256e8	+	2.60782e7i	1.38807	+	0.316818i
$436$	−1.23617e7			−0.149148
$437$			1.01758e8i			1.21934i
$438$	−1.56142e8	−	3.56383e7i	−1.85822	−	0.424126i
$439$	3.06855e7	+	3.84784e7i	0.362693	+	0.454803i	0.929377	−	0.369132i	$-0.120345\pi$
$439$	3.06855e7	+	3.84784e7i	0.362693	+	0.454803i	−0.566683	+	0.823936i	$0.691774\pi$
$440$	4.40869e6	+	1.93158e7i	0.0517550	+	0.226753i
$441$	2.53534e8	+	3.17922e8i	2.95611	+	3.70684i
$442$	2.96190e6	+	6.15044e6i	0.0343007	+	0.0712262i
$443$	1.04474e7	−	4.57730e7i	0.120170	−	0.526499i	−0.878629	−	0.477505i	$-0.841541\pi$
$443$	1.04474e7	−	4.57730e7i	0.120170	−	0.526499i	0.998799	−	0.0489944i	$-0.0156016\pi$
$444$	−2.19730e7	+	1.05817e7i	−0.251039	+	0.120894i
$445$	2.98213e6	−	3.73947e6i	0.0338413	−	0.0424356i
$446$	2.95114e7	+	1.29298e8i	0.332648	+	1.45743i
$447$	−1.05560e7	−	4.62490e7i	−0.118189	−	0.517821i
$448$	−8.37095e7	+	1.73825e8i	−0.930981	+	1.93320i
$449$	−7.85263e7	−	6.26226e7i	−0.867513	−	0.691819i	0.0849785	−	0.996383i	$-0.472918\pi$
$449$	−7.85263e7	−	6.26226e7i	−0.867513	−	0.691819i	−0.952492	+	0.304564i	$0.901489\pi$
$450$	−1.86980e7	+	1.49112e7i	−0.205191	+	0.163634i
$451$	4.31909e7	+	2.07996e7i	0.470828	+	0.226739i
$452$	5.79755e7	−	1.20387e8i	0.627811	−	1.30366i
$453$	3.49537e7	+	4.38305e7i	0.376009	+	0.471500i
$454$	1.20701e8	−	1.51354e8i	1.28986	−	1.61743i
$455$	−1.90569e7	−	9.17733e6i	−0.202311	−	0.0974277i
$456$	4.28627e7	−	9.78312e6i	0.452048	−	0.103177i
$457$	8.41297e6	−	1.92020e6i	0.0881456	−	0.0201187i	−0.178221	−	0.983991i	$-0.557034\pi$
$457$	8.41297e6	−	1.92020e6i	0.0881456	−	0.0201187i	0.266366	+	0.963872i	$0.414177\pi$
$458$	1.20671e8	+	9.62321e7i	1.25605	+	1.00167i
$459$	3.71351e7	+	7.71118e7i	0.384013	+	0.797412i
$460$	−7.28949e7	−	1.66378e7i	−0.748899	−	0.170931i
$461$	3.15094e7	−	1.51741e7i	0.321616	−	0.154882i	−0.266109	−	0.963943i	$-0.585738\pi$
$461$	3.15094e7	−	1.51741e7i	0.321616	−	0.154882i	0.587725	+	0.809061i	$0.300024\pi$
$462$	−5.47438e8	+	4.36567e8i	−5.55148	+	4.42716i
$463$	−1.26025e8	+	2.87644e7i	−1.26974	+	0.289810i	−0.803743	−	0.594977i	$-0.797161\pi$
$463$	−1.26025e8	+	2.87644e7i	−1.26974	+	0.289810i	−0.465996	+	0.884787i	$0.654304\pi$
$464$	−5.39425e7	+	4.30177e7i	−0.539980	+	0.430619i
$465$	−8.58404e6	+	3.76091e7i	−0.0853754	+	0.374054i
$466$	−9.09109e7			−0.898376
$467$		−	2.11929e7i		−	0.208085i	−0.994573	−	0.104042i	$-0.966822\pi$
$467$		−	2.11929e7i		−	0.208085i	0.994573	−	0.104042i	$-0.0331777\pi$
$468$	6.28818e6	−	2.75503e7i	0.0613462	−	0.268775i
$469$	−6.21425e7	−	4.95570e7i	−0.602380	−	0.480382i
$470$	−1.30431e7	−	6.28122e6i	−0.125628	−	0.0604993i
$471$	−2.25111e8	+	1.08408e8i	−2.15444	+	1.03752i
$472$		−	2.12095e7i		−	0.201699i
$473$	−1.00793e8	−	1.28319e8i	−0.952457	−	1.21257i
$474$	1.22958e8			1.15457
$475$	7.29778e6	+	1.51540e7i	0.0680942	+	0.141399i
$476$	4.24579e7	−	8.81647e7i	0.393675	−	0.817474i
$477$	3.37235e7	−	4.22879e7i	0.310726	−	0.389638i
$478$	7.69314e7	+	1.75591e7i	0.704401	+	0.160775i
$479$	1.12818e7			0.102653			0.0513265	−	0.998682i	$-0.483655\pi$
$479$	1.12818e7			0.102653			0.0513265	+	0.998682i	$0.483655\pi$
$480$		−	2.91141e8i		−	2.63257i
$481$	1.86338e6	+	425304.i	0.0167443	+	0.00382177i
$482$	−1.39524e8	−	1.74958e8i	−1.24597	−	1.56240i
$483$	−5.33941e7	−	2.33935e8i	−0.473862	−	2.07613i
$484$	−1.07103e8	−	1.34303e8i	−0.944636	−	1.18454i
$485$	420072.	+	872288.i	0.00368212	+	0.00764601i
$486$	1.36687e7	−	5.98864e7i	0.119074	−	0.521698i
$487$	−1.52039e8	+	7.32182e7i	−1.31634	+	0.633916i	−0.954469	−	0.298311i	$-0.903577\pi$
$487$	−1.52039e8	+	7.32182e7i	−1.31634	+	0.633916i	−0.361872	+	0.932228i	$0.617862\pi$
$488$	−5.99072e6	+	7.51212e6i	−0.0515489	+	0.0646403i
$489$	3.69464e7	+	1.61873e8i	0.315969	+	1.38435i
$490$	8.92724e7	+	3.91128e8i	0.758802	+	3.32453i
$491$	−4.98923e7	+	1.03603e8i	−0.421492	+	0.875237i	0.576804	+	0.816883i	$0.304300\pi$
$491$	−4.98923e7	+	1.03603e8i	−0.421492	+	0.875237i	−0.998296	+	0.0583547i	$0.981415\pi$
$492$	6.11107e7	+	4.87341e7i	0.513123	+	0.409202i
$493$	3.32208e7	−	2.64927e7i	0.277248	−	0.221098i
$494$	−3.41861e7	−	1.64631e7i	−0.283575	−	0.136563i
$495$	1.77586e8	−	3.68761e8i	1.46418	−	3.04039i
$496$	−1.41600e7	−	1.77560e7i	−0.116042	−	0.145513i
$497$	−7.32439e7	+	9.18449e7i	−0.596626	+	0.748145i
$498$	9.23977e7	+	4.44964e7i	0.748123	+	0.360277i
$499$	5.09189e7	−	1.16219e7i	0.409805	−	0.0935353i	−0.0126484	−	0.999920i	$-0.504026\pi$
$499$	5.09189e7	−	1.16219e7i	0.409805	−	0.0935353i	0.422453	+	0.906385i	$0.361169\pi$
$500$	1.27649e8	−	2.91351e7i	1.02119	−	0.233081i
$501$	−2.40056e8	−	1.91438e8i	−1.90897	−	1.52235i
$502$	7.59822e7	+	1.57779e8i	0.600621	+	1.24720i
$503$	1.34476e8	+	3.06932e7i	1.05667	+	0.241179i	0.715349	−	0.698767i	$-0.246268\pi$
$503$	1.34476e8	+	3.06932e7i	1.05667	+	0.241179i	0.341323	+	0.939946i	$0.389125\pi$
$504$	−6.32730e7	+	3.04707e7i	−0.494227	+	0.238007i
$505$	1.14553e8	−	9.13527e7i	0.889470	−	0.709328i
$506$	1.89114e8	−	4.31641e7i	1.45973	−	0.333174i
$507$	1.76839e8	−	1.41024e8i	1.35692	−	1.08211i
$508$	3.45036e7	−	1.51170e8i	0.263192	−	1.15312i
$509$	1.49021e8			1.13004			0.565020	−	0.825077i	$-0.308868\pi$
$509$	1.49021e8			1.13004			0.565020	+	0.825077i	$0.308868\pi$
$510$			1.61213e8i			1.21531i
$511$	4.00363e7	−	1.75410e8i	0.300048	−	1.31460i
$512$	1.47526e8	+	1.17648e8i	1.09916	+	0.876548i
$513$	−4.28611e8	−	2.06408e8i	−3.17476	−	1.52889i
$514$	2.30780e7	−	1.11138e7i	0.169945	−	0.0818412i
$515$			1.98455e8i			1.45292i
$516$	−1.13665e8	−	2.40548e8i	−0.827331	−	1.75087i
$517$	1.96720e7			0.142356
$518$	−2.26955e7	−	4.71278e7i	−0.163287	−	0.339069i
$519$	−9.90931e7	+	2.05769e8i	−0.708829	+	1.47190i
$520$	1.57848e6	−	1.97935e6i	0.0112261	−	0.0140771i
$521$	2.50818e8	+	5.72475e7i	1.77356	+	0.404802i	0.979240	−	0.202704i	$-0.0649728\pi$
$521$	2.50818e8	+	5.72475e7i	1.77356	+	0.404802i	0.794315	+	0.607506i	$0.207830\pi$
$522$	−3.35818e8			−2.36098
$523$			1.79104e7i			0.125199i	0.998039	+	0.0625996i	$0.0199391\pi$
$523$			1.79104e7i			0.125199i	−0.998039	+	0.0625996i	$0.980061\pi$
$524$	3.86447e7	+	8.82040e6i	0.268594	+	0.0613048i
$525$	−2.47286e7	−	3.10086e7i	−0.170892	−	0.214291i
$526$	−6.40787e7	−	2.80747e8i	−0.440308	−	1.92912i
$527$	8.72048e6	+	1.09351e7i	0.0595811	+	0.0747124i
$528$	1.54337e8	+	3.20485e8i	1.04850	+	2.17724i
$529$	1.81492e7	−	7.95169e7i	0.122600	−	0.537146i
$530$	4.80786e7	−	2.31534e7i	0.322942	−	0.155521i
$531$	−2.73184e8	+	3.42562e8i	−1.82462	+	2.28800i
$532$	1.21032e8	+	5.30274e8i	0.803829	+	3.52181i
$533$	−1.36309e6	−	5.97207e6i	−0.00900206	−	0.0394406i
$534$	−8.77847e6	+	1.82287e7i	−0.0576495	+	0.119710i
$535$	1.61765e8	+	1.29004e8i	1.05639	+	0.842443i
$536$	7.43798e6	−	5.93159e6i	0.0483015	−	0.0385192i
$537$	1.78126e8	+	8.57812e7i	1.15029	+	0.553948i
$538$	−1.37475e8	+	2.85469e8i	−0.882828	+	1.83321i
$539$	−3.39901e8	−	4.26222e8i	−2.17063	−	2.72189i
$540$	2.17940e8	−	2.73288e8i	1.38406	−	1.73556i
$541$	−2.65834e8	−	1.28019e8i	−1.67887	−	0.808503i	−0.997031	−	0.0770052i	$-0.975464\pi$
$541$	−2.65834e8	−	1.28019e8i	−1.67887	−	0.808503i	−0.681844	−	0.731498i	$-0.738822\pi$
$542$	1.67245e8	−	3.81727e7i	1.05040	−	0.239748i
$543$	3.70677e8	−	8.46046e7i	2.31524	−	0.528438i
$544$	−8.25292e7	−	6.58148e7i	−0.512638	−	0.408815i
$545$	9.92662e6	+	2.06128e7i	0.0613214	+	0.127335i
$546$	8.72296e7	+	1.99096e7i	0.535903	+	0.122316i
$547$	−5.90605e7	+	2.84420e7i	−0.360857	+	0.173780i	−0.605523	−	0.795828i	$-0.707036\pi$
$547$	−5.90605e7	+	2.84420e7i	−0.360857	+	0.173780i	0.244666	+	0.969607i	$0.421322\pi$
$548$	−1.76364e8	+	1.40645e8i	−1.07168	+	0.854640i
$549$	1.93517e8	−	4.41689e7i	1.16950	−	0.266931i
$550$	2.50675e7	−	1.99907e7i	0.150669	−	0.120154i
$551$	−5.25546e7	+	2.30257e8i	−0.314163	+	1.37644i
$552$	2.87203e7			0.170754
$553$			1.38131e8i			0.816803i
$554$	7.27527e7	−	3.18750e8i	0.427878	−	1.87465i
$555$	3.52894e7	+	2.81424e7i	0.206427	+	0.164620i
$556$	4.34159e7	+	2.09080e7i	0.252595	+	0.121643i
$557$	1.22032e8	−	5.87673e7i	0.706166	−	0.340072i	−0.0460947	−	0.998937i	$-0.514678\pi$
$557$	1.22032e8	−	5.87673e7i	0.706166	−	0.340072i	0.752261	+	0.658865i	$0.228963\pi$
$558$		−	1.10540e8i		−	0.636233i
$559$	−4.78934e6	+	2.02929e7i	−0.0274183	+	0.116174i
$560$	2.94075e8			1.67453
$561$	−9.50494e7	−	1.97372e8i	−0.538345	−	1.11789i
$562$	1.11609e8	−	2.31759e8i	0.628769	−	1.30565i
$563$	1.22188e8	−	1.53219e8i	0.684705	−	0.858593i	−0.311073	−	0.950386i	$-0.600688\pi$
$563$	1.22188e8	−	1.53219e8i	0.684705	−	0.858593i	0.995778	+	0.0917926i	$0.0292597\pi$
$564$	3.12710e7	+	7.13740e6i	0.174303	+	0.0397835i
$565$	−2.47299e8			−1.37112
$566$			2.77779e8i			1.53197i
$567$	4.20081e8	+	9.58807e7i	2.30454	+	0.525995i
$568$	−8.76673e6	−	1.09931e7i	−0.0478401	−	0.0599896i
$569$	7.70575e7	+	3.37611e8i	0.418290	+	1.83265i	0.542061	+	0.840339i	$0.317644\pi$
$569$	7.70575e7	+	3.37611e8i	0.418290	+	1.83265i	−0.123770	+	0.992311i	$0.539499\pi$
$570$	−5.58691e8	−	7.00576e8i	−3.01680	−	3.78295i
$571$	5.48569e7	+	1.13912e8i	0.294661	+	0.611871i	0.994767	−	0.102168i	$-0.0325781\pi$
$571$	5.48569e7	+	1.13912e8i	0.294661	+	0.611871i	−0.700106	+	0.714039i	$0.746864\pi$
$572$	−8.43026e6	+	3.69354e7i	−0.0450457	+	0.197358i
$573$	3.44721e8	−	1.66009e8i	1.83233	−	0.882405i
$574$	−1.04525e8	+	1.31070e8i	−0.552694	+	0.693056i
$575$	2.44495e6	+	1.07120e7i	0.0128608	+	0.0563467i
$576$	1.06154e8	+	4.65089e8i	0.555478	+	2.43371i
$577$	−1.54753e8	+	3.21348e8i	−0.805586	+	1.67282i	−0.0678798	+	0.997694i	$0.521623\pi$
$577$	−1.54753e8	+	3.21348e8i	−0.805586	+	1.67282i	−0.737706	+	0.675122i	$0.764091\pi$
$578$	−1.73074e8	−	1.38022e8i	−0.896291	−	0.714768i
$579$	2.52499e8	−	2.01361e8i	1.30084	−	1.03738i
$580$	−1.56352e8	−	7.52951e7i	−0.801345	−	0.385907i
$581$	−4.99875e7	+	1.03800e8i	−0.254879	+	0.529261i
$582$	−2.55345e6	−	3.20193e6i	−0.0129527	−	0.0162421i
$583$	−4.52114e7	+	5.66934e7i	−0.228162	+	0.286106i
$584$	1.94025e7	+	9.34378e6i	0.0974137	+	0.0469120i
$585$	−5.09891e7	+	1.16379e7i	−0.254689	+	0.0581311i
$586$	7.19217e7	−	1.64157e7i	0.357410	−	0.0815765i
$587$	−8.59886e7	−	6.85736e7i	−0.425135	−	0.339034i	0.387436	−	0.921897i	$-0.373361\pi$
$587$	−8.59886e7	−	6.85736e7i	−0.425135	−	0.339034i	−0.812570	+	0.582863i	$0.801932\pi$
$588$	−3.85672e8	−	8.00856e8i	−1.89708	−	3.93933i
$589$	−7.57925e7	−	1.72992e7i	−0.370920	−	0.0846601i
$590$	−3.89471e8	+	1.87559e8i	−1.89635	+	0.913235i
$591$	3.65496e8	−	2.91473e8i	1.77060	−	1.41200i
$592$	−2.59069e7	+	5.91308e6i	−0.124868	+	0.0285003i
$593$	−2.33595e8	+	1.86286e8i	−1.12021	+	0.893337i	−0.995107	−	0.0988074i	$-0.968497\pi$
$593$	−2.33595e8	+	1.86286e8i	−1.12021	+	0.893337i	−0.125102	+	0.992144i	$0.539926\pi$
$594$	−2.01793e8	+	8.84112e8i	−0.962822	+	4.21840i
$595$	−1.81107e8			−0.859776
$596$			7.02452e7i			0.331801i
$597$	−8.22690e7	+	3.60444e8i	−0.386646	+	1.69401i
$598$	−1.93791e7	−	1.54543e7i	−0.0906214	−	0.0722682i
$599$	−5.14692e7	−	2.47863e7i	−0.239479	−	0.115327i	0.310296	−	0.950640i	$-0.399572\pi$
$599$	−5.14692e7	−	2.47863e7i	−0.239479	−	0.115327i	−0.549774	+	0.835313i	$0.685286\pi$
$600$	4.27706e6	−	2.05972e6i	0.0198012	−	0.00953576i
$601$		−	2.90524e8i		−	1.33831i	−0.743121	−	0.669157i	$-0.766655\pi$
$601$		−	2.90524e8i		−	1.33831i	0.743121	−	0.669157i	$-0.233345\pi$
$602$	5.15928e8	−	2.43790e8i	2.36483	−	1.11745i
$603$	−1.96534e8			−0.896367
$604$	−3.60184e7	−	7.47929e7i	−0.163461	−	0.339429i
$605$	−1.37942e8	+	2.86439e8i	−0.622916	+	1.29350i
$606$	−3.86429e8	+	4.84567e8i	−1.73641	+	2.17739i
$607$	7.41338e7	+	1.69205e7i	0.331474	+	0.0756569i	0.385019	−	0.922909i	$-0.374195\pi$
$607$	7.41338e7	+	1.69205e7i	0.331474	+	0.0756569i	−0.0535448	+	0.998565i	$0.517052\pi$
$608$	5.86728e8			2.61052
$609$		−	5.56919e8i		−	2.46570i
$610$	1.90923e8	+	4.35768e7i	0.841139	+	0.191985i
$611$	−1.56728e6	−	1.96531e6i	−0.00687106	−	0.00861603i
$612$	−5.38416e7	−	2.35896e8i	−0.234890	−	1.02912i
$613$	−1.08503e8	−	1.36059e8i	−0.471045	−	0.590671i	0.488382	−	0.872630i	$-0.337587\pi$
$613$	−1.08503e8	−	1.36059e8i	−0.471045	−	0.590671i	−0.959427	+	0.281959i	$0.909016\pi$
$614$	−9.71858e7	−	2.01808e8i	−0.419853	−	0.871835i
$615$	3.21904e7	−	1.41035e8i	0.138389	−	0.606320i
$616$	8.48271e7	−	4.08506e7i	0.362904	−	0.174766i
$617$	−1.34015e7	+	1.68049e7i	−0.0570554	+	0.0715452i	−0.809540	−	0.587064i	$-0.800284\pi$
$617$	−1.34015e7	+	1.68049e7i	−0.0570554	+	0.0715452i	0.752485	+	0.658609i	$0.228855\pi$
$618$	−1.86802e8	−	8.18433e8i	−0.791437	−	3.46751i
$619$	−6.82136e7	−	2.98863e8i	−0.287607	−	1.26009i	−0.887799	−	0.460231i	$-0.847767\pi$
$619$	−6.82136e7	−	2.98863e8i	−0.287607	−	1.26009i	0.600193	−	0.799856i	$-0.295091\pi$
$620$	2.47846e7	−	5.14657e7i	0.103994	−	0.215945i
$621$	−2.42968e8	−	1.93760e8i	−1.01455	−	0.809078i
$622$	−3.23085e8	+	2.57652e8i	−1.34260	+	1.07068i
$623$	−2.04782e7	−	9.86180e6i	−0.0846893	−	0.0407842i
$624$	1.97215e7	−	4.09522e7i	0.0811684	−	0.168548i
$625$	−1.64216e8	−	2.05920e8i	−0.672627	−	0.843448i
$626$	−4.79324e7	+	6.01053e7i	−0.195392	+	0.245014i
$627$	1.09706e9	+	5.28314e8i	4.45068	+	2.14333i
$628$	3.60700e8	−	8.23275e7i	1.45636	−	0.332404i
$629$	1.59549e7	−	3.64160e6i	0.0641124	−	0.0146332i
$630$	1.11907e9	+	8.92428e8i	4.47544	+	3.56904i
$631$	7.61300e7	+	1.58086e8i	0.303018	+	0.629223i	0.995763	−	0.0919599i	$-0.0293132\pi$
$631$	7.61300e7	+	1.58086e8i	0.303018	+	0.629223i	−0.692745	+	0.721183i	$0.743599\pi$
$632$	−1.61187e7	−	3.67900e6i	−0.0638528	−	0.0145740i
$633$	−1.50076e8	+	7.22728e7i	−0.591698	+	0.284947i
$634$	−5.36832e8	+	4.28109e8i	−2.10654	+	1.67991i
$635$	−2.79780e8	+	6.38579e7i	−1.09269	+	0.249398i
$636$	−9.24387e7	+	7.37174e7i	−0.359321	+	0.286549i
$637$	−1.55011e7	+	6.79150e7i	−0.0599716	+	0.262753i
$638$	4.50215e8			1.73364
$639$			2.90472e8i			1.11327i
$640$	−1.75102e7	+	7.67170e7i	−0.0667960	+	0.292652i
$641$	1.70131e8	+	1.35675e8i	0.645967	+	0.515141i	0.890783	−	0.454428i	$-0.150156\pi$
$641$	1.70131e8	+	1.35675e8i	0.645967	+	0.515141i	−0.244817	+	0.969569i	$0.578728\pi$
$642$	−7.88553e8	−	3.79747e8i	−2.98006	−	1.43512i
$643$	−4.70684e7	+	2.26669e7i	−0.177050	+	0.0852629i	−0.520309	−	0.853978i	$-0.674183\pi$
$643$	−4.70684e7	+	2.26669e7i	−0.177050	+	0.0852629i	0.343259	+	0.939241i	$0.388469\pi$
$644$			3.55312e8i			1.33031i
$645$	−3.09834e8	+	3.82699e8i	−1.15465	+	1.42619i
$646$	−3.24887e8			−1.20513
$647$	2.45204e6	+	5.09171e6i	0.00905346	+	0.0187997i	0.905447	−	0.424460i	$-0.139536\pi$
$647$	2.45204e6	+	5.09171e6i	0.00905346	+	0.0187997i	−0.896393	+	0.443260i	$0.853822\pi$
$648$	−2.23769e7	+	4.64661e7i	−0.0822384	+	0.170770i
$649$	3.66245e8	−	4.59256e8i	1.33979	−	1.68005i
$650$	−3.99430e6	−	911673.i	−0.0145446	−	0.00331970i
$651$	1.83318e8			0.664451
$652$		−	2.45860e8i		−	0.887044i
$653$	−4.38109e8	−	9.99956e7i	−1.57341	−	0.359122i	−0.655278	−	0.755387i	$-0.727449\pi$
$653$	−4.38109e8	−	9.99956e7i	−1.57341	−	0.359122i	−0.918136	+	0.396266i	$0.870306\pi$
$654$	−6.03400e7	−	7.56640e7i	−0.215711	−	0.270493i
$655$	−1.63245e7	−	7.15222e7i	−0.0580919	−	0.254517i
$656$	5.31002e7	+	6.65856e7i	0.188098	+	0.235868i
$657$	−1.93027e8	−	4.00825e8i	−0.680648	−	1.41338i
$658$	−1.53083e7	+	6.70701e7i	−0.0537340	+	0.235424i
$659$	2.99646e7	−	1.44302e7i	0.104701	−	0.0504215i	−0.380800	−	0.924657i	$-0.624351\pi$
$659$	2.99646e7	−	1.44302e7i	0.104701	−	0.0504215i	0.485501	+	0.874236i	$0.338637\pi$
$660$	−5.57830e8	+	6.99497e8i	−1.94031	+	2.43307i
$661$	−7.48865e7	−	3.28099e8i	−0.259298	−	1.13606i	−0.922005	−	0.387179i	$-0.873450\pi$
$661$	−7.48865e7	−	3.28099e8i	−0.259298	−	1.13606i	0.662707	−	0.748879i	$-0.269408\pi$
$662$	−1.55303e8	−	6.80429e8i	−0.535312	−	2.34535i
$663$	−1.21456e7	+	2.52206e7i	−0.0416753	+	0.0865397i
$664$	−1.07812e7	−	8.59773e6i	−0.0368267	−	0.0293683i
$665$	7.87032e8	−	6.27637e8i	2.67625	−	2.13424i
$666$	−1.16530e8	−	5.61181e7i	−0.394472	−	0.189968i
$667$	−6.69414e7	+	1.39005e8i	−0.225589	+	0.468440i
$668$	2.83476e8	+	3.55467e8i	0.951013	+	1.19253i
$669$	−3.39076e8	+	4.25188e8i	−1.13245	+	1.42005i
$670$	−1.74698e8	−	8.41299e7i	−0.580848	−	0.279722i
$671$	−2.59438e8	+	5.92151e7i	−0.858750	+	0.196004i
$672$	−1.34884e9	+	3.07865e8i	−4.44482	+	1.01450i
$673$	9.90632e7	+	7.90003e7i	0.324988	+	0.259169i	0.772369	−	0.635174i	$-0.219072\pi$
$673$	9.90632e7	+	7.90003e7i	0.324988	+	0.259169i	−0.447381	+	0.894344i	$0.647643\pi$
$674$	3.99115e7	+	8.28771e7i	0.130352	+	0.270679i
$675$	−5.00790e7	−	1.14302e7i	−0.162834	−	0.0371657i
$676$	−3.01760e8	+	1.45320e8i	−0.976834	+	0.470419i
$677$	9.60702e7	−	7.66134e7i	0.309615	−	0.246910i	−0.456337	−	0.889807i	$-0.650839\pi$
$677$	9.60702e7	−	7.66134e7i	0.309615	−	0.246910i	0.765953	+	0.642897i	$0.222268\pi$
$678$	1.01987e9	−	2.32778e8i	3.27230	−	0.746882i
$679$	3.59707e6	−	2.86857e6i	0.0114905	−	0.00916338i
$680$	4.82362e6	−	2.11337e7i	0.0153407	−	0.0672122i
$681$	7.93836e8			2.51356
$682$			1.48195e8i			0.467177i
$683$	−1.13933e8	+	4.99174e8i	−0.357593	+	1.56672i	0.401579	+	0.915824i	$0.368462\pi$
$683$	−1.13933e8	+	4.99174e8i	−0.357593	+	1.56672i	−0.759171	+	0.650891i	$0.774396\pi$
$684$	1.05149e9	+	8.38531e8i	3.28575	+	2.62030i
$685$	3.76146e8	+	1.81142e8i	1.17027	+	0.563571i
$686$	9.56921e8	−	4.60829e8i	2.96417	−	1.42747i
$687$			6.32907e8i			1.95195i
$688$	−6.24211e7	−	2.83086e8i	−0.191675	−	0.869268i
$689$	9.26593e6			0.0283290
$690$	−2.53979e8	−	5.27392e8i	−0.773126	−	1.60541i
$691$	2.82374e7	−	5.86356e7i	0.0855836	−	0.177716i	−0.853785	−	0.520627i	$-0.825698\pi$
$691$	2.82374e7	−	5.86356e7i	0.0855836	−	0.177716i	0.939368	+	0.342910i	$0.111413\pi$
$692$	2.10856e8	−	2.64405e8i	0.636309	−	0.797907i
$693$	−1.89624e9	−	4.32804e8i	−5.69762	−	1.30044i
$694$	6.47578e8			1.93737
$695$		−	8.91846e7i		−	0.265666i
$696$	6.49876e7	+	1.48330e7i	0.192754	+	0.0439948i
$697$	−3.27020e7	−	4.10071e7i	−0.0965776	−	0.121105i
$698$	1.06112e8	+	4.64906e8i	0.312031	+	1.36710i
$699$	−2.32431e8	−	2.91460e8i	−0.680555	−	0.853389i
$700$	2.54818e7	+	5.29135e7i	0.0742910	+	0.154267i
$701$	−5.22539e7	+	2.28939e8i	−0.151693	+	0.664610i	0.840700	+	0.541501i	$0.182144\pi$
$701$	−5.22539e7	+	2.28939e8i	−0.151693	+	0.664610i	−0.992393	+	0.123109i	$0.960714\pi$
$702$	1.04403e8	−	5.02780e7i	0.301789	−	0.145334i
$703$	−5.67145e7	+	7.11177e7i	−0.163241	+	0.204697i
$704$	−1.42315e8	−	6.23523e8i	−0.407880	−	1.78704i
$705$	−1.32096e7	−	5.78752e7i	−0.0376985	−	0.165168i
$706$	−1.94981e8	+	4.04882e8i	−0.554086	+	1.15057i
$707$	−5.44366e8	−	4.34117e8i	−1.54040	−	1.22843i
$708$	7.48819e8	−	5.97163e8i	2.10997	−	1.68265i
$709$	4.04567e8	+	1.94829e8i	1.13514	+	0.546657i	0.904539	−	0.426390i	$-0.140215\pi$
$709$	4.04567e8	+	1.94829e8i	1.13514	+	0.546657i	0.230606	+	0.973047i	$0.425929\pi$
$710$	−1.24342e8	+	2.58198e8i	−0.347410	+	0.721403i
$711$	2.12953e8	+	2.67035e8i	0.592482	+	0.742949i
$712$	1.69620e6	−	2.12697e6i	0.00469935	−	0.00589280i
$713$	−4.57558e7	−	2.20348e7i	−0.126234	−	0.0607912i
$714$	7.46891e8	−	1.70473e8i	2.05193	−	0.468340i
$715$	6.83587e7	−	1.56024e7i	0.187015	−	0.0426849i
$716$	−2.28886e8	−	1.82530e8i	−0.623562	−	0.497274i
$717$	1.40396e8	+	2.91535e8i	0.380887	+	0.790921i
$718$	−6.42153e8	−	1.46567e8i	−1.73486	−	0.395971i
$719$	−4.72740e8	+	2.27660e8i	−1.27185	+	0.612491i	−0.943283	−	0.331990i	$-0.892280\pi$
$719$	−4.72740e8	+	2.27660e8i	−1.27185	+	0.612491i	−0.328567	+	0.944481i	$0.606566\pi$
$720$	5.68503e8	−	4.53366e8i	1.52312	−	1.21465i
$721$	9.19433e8	−	2.09855e8i	2.45310	−	0.559903i
$722$	9.85445e8	−	7.85866e8i	2.61831	−	2.08803i
$723$	2.04193e8	−	8.94629e8i	0.540290	−	2.36716i
$724$	−5.63002e8			−1.48352
$725$			2.55017e7i			0.0669198i
$726$	2.99255e8	−	1.31112e9i	0.782045	−	3.42636i
$727$	1.48768e8	+	1.18639e8i	0.387175	+	0.308762i	0.797662	−	0.603105i	$-0.206070\pi$
$727$	1.48768e8	+	1.18639e8i	0.387175	+	0.308762i	−0.410487	+	0.911866i	$0.634641\pi$
$728$	−1.08394e7	−	5.21997e6i	−0.0280938	−	0.0135293i
$729$	−2.30186e8	+	1.10852e8i	−0.594149	+	0.286127i
$730$		−	4.38919e8i		−	1.12828i
$731$	3.84424e7	+	1.74340e8i	0.0984143	+	0.446319i
$732$	−4.33894e8			−1.10624
$733$	1.77821e8	+	3.69250e8i	0.451515	+	0.937581i	0.995160	+	0.0982655i	$0.0313294\pi$
$733$	1.77821e8	+	3.69250e8i	0.451515	+	0.937581i	−0.543645	+	0.839315i	$0.682956\pi$
$734$	−4.23945e8	+	8.80330e8i	−1.07207	+	2.22617i
$735$	−1.02571e9	+	1.28620e9i	−2.58323	+	3.23927i
$736$	3.73673e8	+	8.52884e7i	0.937256	+	0.213923i
$737$	2.63484e8			0.658190
$738$			4.14527e8i			1.03130i
$739$	−6.90781e8	−	1.57666e8i	−1.71162	−	0.390666i	−0.749223	−	0.662318i	$-0.769573\pi$
$739$	−6.90781e8	−	1.57666e8i	−1.71162	−	0.390666i	−0.962396	+	0.271652i	$0.912430\pi$
$740$	−4.16723e7	−	5.22555e7i	−0.102838	−	0.128955i
$741$	−3.46226e7	−	1.51692e8i	−0.0850952	−	0.372827i
$742$	−1.58109e8	−	1.98263e8i	−0.387030	−	0.485321i
$743$	4.68689e7	+	9.73242e7i	0.114266	+	0.237276i	0.950257	−	0.311468i	$-0.100821\pi$
$743$	4.68689e7	+	9.73242e7i	0.114266	+	0.237276i	−0.835991	+	0.548744i	$0.815106\pi$
$744$	−4.88251e6	+	2.13917e7i	−0.0118556	+	0.0519429i
$745$	1.17133e8	−	5.64081e7i	0.283275	−	0.136418i
$746$	−3.33992e8	+	4.18812e8i	−0.804487	+	1.00880i
$747$	6.33901e7	+	2.77730e8i	0.152076	+	0.666287i
$748$	7.21829e7	+	3.16254e8i	0.172476	+	0.755668i
$749$	4.26610e8	−	8.85866e8i	1.01528	−	2.10825i
$750$	8.01418e8	+	6.39109e8i	1.89966	+	1.51493i
$751$	3.52963e8	−	2.81479e8i	0.833316	−	0.664548i	−0.110915	−	0.993830i	$-0.535378\pi$
$751$	3.52963e8	−	2.81479e8i	0.833316	−	0.664548i	0.944232	+	0.329282i	$0.106807\pi$
$752$	3.14878e7	+	1.51637e7i	0.0740438	+	0.0356576i
$753$	−3.11574e8	+	6.46990e8i	−0.729754	+	1.51535i
$754$	−3.58690e7	−	4.49784e7i	−0.0836769	−	0.104928i
$755$	−9.57924e7	+	1.20120e8i	−0.222582	+	0.279109i
$756$	−1.49659e9	−	7.20720e8i	−3.46368	−	1.66802i
$757$	1.59052e8	−	3.63025e7i	0.366649	−	0.0836854i	−0.0352268	−	0.999379i	$-0.511215\pi$
$757$	1.59052e8	−	3.63025e7i	0.366649	−	0.0836854i	0.401876	+	0.915694i	$0.368358\pi$
$758$	1.13225e9	−	2.58430e8i	2.59978	−	0.593382i
$759$	6.21891e8	+	4.95941e8i	1.42229	+	1.13424i
$760$	5.22779e7	+	1.08556e8i	0.119091	+	0.247294i
$761$	−3.25671e8	−	7.43324e7i	−0.738968	−	0.168665i	−0.163563	−	0.986533i	$-0.552299\pi$
$761$	−3.25671e8	−	7.43324e7i	−0.738968	−	0.168665i	−0.575405	+	0.817868i	$0.695156\pi$
$762$	1.09371e9	−	5.26703e8i	2.47194	−	1.19042i
$763$	8.50015e7	−	6.77864e7i	0.191361	−	0.152605i
$764$	−5.52355e8	+	1.26071e8i	−1.23862	+	0.282707i
$765$	−3.50116e8	+	2.79208e8i	−0.782037	+	0.623654i
$766$	2.95674e7	−	1.29543e8i	0.0657851	−	0.288223i
$767$	−7.50606e7			−0.166351
$768$			6.15243e8i			1.35820i
$769$	−2.35541e7	+	1.03197e8i	−0.0517949	+	0.226928i	−0.994200	−	0.107545i	$-0.965701\pi$
$769$	−2.35541e7	+	1.03197e8i	−0.0517949	+	0.226928i	0.942405	+	0.334473i	$0.108558\pi$
$770$	−1.50028e9	−	1.19644e9i	−3.28625	−	2.62070i
$771$	9.46341e7	+	4.55734e7i	0.206483	+	0.0994370i
$772$	−4.30866e8	+	2.07494e8i	−0.936463	+	0.450977i
$773$			6.26711e8i			1.35684i	0.734674	+	0.678421i	$0.237335\pi$
$773$			6.26711e8i			1.35684i	−0.734674	+	0.678421i	$0.762665\pi$
$774$	6.21545e8	−	1.26668e9i	1.34045	−	2.73178i
$775$	−8.39427e6			−0.0180334
$776$	238932.	+	496148.i	0.000511317	+	0.00106176i
$777$	9.30658e7	−	1.93253e8i	0.198393	−	0.411968i
$778$	−1.79592e8	+	2.25201e8i	−0.381372	+	0.478225i
$779$	2.84224e8	+	6.48723e7i	0.601241	+	0.137229i
$780$	1.14325e8			0.240912
$781$		−	3.89422e8i		−	0.817461i
$782$	−2.06913e8	−	4.72265e7i	−0.432680	−	0.0987564i
$783$	−4.49712e8	−	5.63921e8i	−0.936804	−	1.17472i
$784$	−2.15515e8	−	9.44235e8i	−0.447229	−	1.95944i
$785$	−4.26928e8	−	5.35351e8i	−0.882563	−	1.10670i
$786$	1.34645e8	+	2.79593e8i	0.277282	+	0.575783i
$787$	−1.50497e8	+	6.59372e8i	−0.308748	+	1.35272i	0.547783	+	0.836620i	$0.315472\pi$
$787$	−1.50497e8	+	6.59372e8i	−0.308748	+	1.35272i	−0.856532	+	0.516095i	$0.827385\pi$
$788$	−6.23686e8	+	3.00352e8i	−1.27464	+	0.613834i
$789$	7.36244e8	−	9.23221e8i	1.49896	−	1.87964i
$790$	7.49833e7	+	3.28524e8i	0.152084	+	0.666324i
$791$	2.61504e8	+	1.14572e9i	0.528383	+	2.31500i
$792$	1.01009e8	−	2.09747e8i	0.203322	−	0.422203i
$793$	2.65855e7	+	2.12012e7i	0.0533121	+	0.0425149i
$794$	−9.58607e8	+	7.64463e8i	−1.91505	+	1.52720i
$795$	1.97152e8	+	9.49434e7i	0.392374	+	0.188957i
$796$	2.37534e8	−	4.93245e8i	0.470963	−	0.977965i
$797$	−6.53447e7	−	8.19396e7i	−0.129073	−	0.161852i	0.713095	−	0.701067i	$-0.247293\pi$
$797$	−6.53447e7	−	8.19396e7i	−0.129073	−	0.161852i	−0.842168	+	0.539215i	$0.818721\pi$
$798$	−2.65495e9	+	3.32921e9i	−5.22454	+	6.55137i
$799$	−1.93919e7	−	9.33865e6i	−0.0380172	−	0.0183081i
$800$	6.17645e7	−	1.40973e7i	0.120634	−	0.0275339i
$801$	−5.47920e7	+	1.25059e7i	−0.106615	+	0.0243343i
$802$	1.89414e8	+	1.51052e8i	0.367188	+	0.292822i
$803$	2.58782e8	+	5.37367e8i	0.499790	+	1.03783i
$804$	4.18840e8	+	9.55974e7i	0.805897	+	0.183941i
$805$	5.92476e8	−	2.85321e8i	1.13575	−	0.546949i
$806$	1.48053e7	−	1.18069e7i	0.0282757	−	0.0225491i
$807$	−1.26669e9	+	2.89115e8i	−2.41019	+	0.550110i
$808$	6.51564e7	−	5.19605e7i	0.123516	−	0.0985006i
$809$	−7.05628e6	+	3.09156e7i	−0.0133269	+	0.0583891i	−0.981154	−	0.193227i	$-0.938105\pi$
$809$	−7.05628e6	+	3.09156e7i	−0.0133269	+	0.0583891i	0.967827	+	0.251616i	$0.0809619\pi$
$810$	1.05114e9			1.97791
$811$		−	8.30787e8i		−	1.55750i	−0.627337	−	0.778748i	$-0.715855\pi$
$811$		−	8.30787e8i		−	1.55750i	0.627337	−	0.778748i	$-0.284145\pi$
$812$	−1.83506e8	+	8.03992e8i	−0.342753	+	1.50170i
$813$	5.49977e8	+	4.38592e8i	1.02346	+	0.816185i
$814$	1.56227e8	+	7.52348e7i	0.289656	+	0.139491i
$815$	−4.09967e8	+	1.97430e8i	−0.757314	+	0.364703i
$816$		−	3.89189e8i		−	0.716292i
$817$	−7.71242e8	−	6.24400e8i	−1.41424	−	1.14498i
$818$	8.80303e8			1.60832
$819$	1.07836e8	+	2.23924e8i	0.196296	+	0.407614i
$820$	−9.29428e7	+	1.92998e8i	−0.168568	+	0.350034i
$821$	4.84869e8	−	6.08006e8i	0.876183	−	1.09870i	−0.118214	−	0.992988i	$-0.537717\pi$
$821$	4.84869e8	−	6.08006e8i	0.876183	−	1.09870i	0.994397	−	0.105710i	$-0.0337116\pi$
$822$	−1.72174e9	−	3.92976e8i	−3.09993	−	0.707539i
$823$	−2.44023e8			−0.437755			−0.218878	−	0.975752i	$-0.570240\pi$
$823$	−2.44023e8			−0.437755			−0.218878	+	0.975752i	$0.570240\pi$
$824$			1.12879e8i			0.201759i
$825$	1.28180e8	+	2.92563e7i	0.228275	+	0.0521023i
$826$	1.28080e9	+	1.60607e9i	2.27269	+	2.84986i
$827$	−8.03889e7	−	3.52207e8i	−0.142128	−	0.622703i	−0.994939	−	0.100483i	$-0.967961\pi$
$827$	−8.03889e7	−	3.52207e8i	−0.142128	−	0.622703i	0.852811	−	0.522220i	$-0.174896\pi$
$828$	5.47774e8	+	6.86887e8i	0.964962	+	1.21002i
$829$	1.92052e8	+	3.98799e8i	0.337097	+	0.699988i	0.998759	−	0.0498141i	$-0.0158629\pi$
$829$	1.92052e8	+	3.98799e8i	0.337097	+	0.699988i	−0.661662	+	0.749802i	$0.730149\pi$
$830$	−6.25404e7	+	2.74007e8i	−0.109377	+	0.479212i
$831$	1.20792e9	−	5.81703e8i	2.10491	−	1.01367i
$832$	−5.09541e7	+	6.38944e7i	−0.0884727	+	0.110941i
$833$	1.32726e8	+	5.81512e8i	0.229626	+	1.00606i
$834$	8.39478e7	+	3.67799e8i	0.144714	+	0.634034i
$835$	3.65099e8	−	7.58137e8i	0.627121	−	1.30223i
$836$	−1.40968e9	−	1.12418e9i	−2.41268	−	1.92405i
$837$	1.85623e8	−	1.48030e8i	0.316560	−	0.252448i
$838$	6.83830e8	+	3.29315e8i	1.16203	+	0.559602i
$839$	−1.04716e7	+	2.17445e7i	−0.0177307	+	0.0368183i	−0.909646	−	0.415384i	$-0.863647\pi$
$839$	−1.04716e7	+	2.17445e7i	−0.0177307	+	0.0368183i	0.891915	+	0.452202i	$0.149361\pi$
$840$	−1.77144e8	−	2.22132e8i	−0.298874	−	0.374777i
$841$	1.47602e8	−	1.85087e8i	0.248144	−	0.311162i
$842$	−9.35139e8	−	4.50339e8i	−1.56653	−	0.754403i
$843$	1.02837e9	−	2.34718e8i	1.71659	−	0.391800i
$844$	2.40470e8	−	5.48858e7i	0.399976	−	0.0912919i
$845$	4.84636e8	+	3.86484e8i	0.803240	+	0.640563i
$846$	7.38060e7	+	1.53260e8i	0.121894	+	0.253115i
$847$	1.47292e9	+	3.36185e8i	2.42399	+	0.553259i
$848$	−1.16068e8	+	5.58955e7i	−0.190338	+	0.0916620i
$849$	−8.90557e8	+	7.10196e8i	−1.45525	+	1.16053i
$850$	−3.42006e7	+	7.80607e6i	−0.0556900	+	0.0127109i
$851$	−4.64579e7	+	3.70489e7i	−0.0753826	+	0.0601156i
$852$	1.41290e8	−	6.19034e8i	0.228451	−	1.00091i
$853$	−1.75920e8			−0.283444			−0.141722	−	0.989906i	$-0.545264\pi$
$853$	−1.75920e8			−0.283444			−0.141722	+	0.989906i	$0.545264\pi$
$854$		−	9.30616e8i		−	1.49416i
$855$	5.53875e8	−	2.42669e9i	0.886163	−	3.88253i
$856$	9.20105e7	+	7.33759e7i	0.146695	+	0.116986i
$857$	5.44307e8	+	2.62124e8i	0.864771	+	0.416452i	0.813039	−	0.582209i	$-0.197812\pi$
$857$	5.44307e8	+	2.62124e8i	0.864771	+	0.416452i	0.0517321	+	0.998661i	$0.483526\pi$
$858$	−2.67227e8	+	1.28690e8i	−0.423075	+	0.203742i
$859$		−	8.69472e8i		−	1.37175i	−0.727718	−	0.685877i	$-0.759419\pi$
$859$		−	8.69472e8i		−	1.37175i	0.727718	−	0.685877i	$-0.240581\pi$
$860$	5.73390e8	−	4.50390e8i	0.901477	−	0.708098i
$861$	−6.87449e8			−1.07704
$862$	−7.84879e7	−	1.62982e8i	−0.122541	−	0.254459i
$863$	−1.71842e8	+	3.56834e8i	−0.267361	+	0.555181i	−0.990820	−	0.135186i	$-0.956837\pi$
$863$	−1.71842e8	+	3.56834e8i	−0.267361	+	0.555181i	0.723459	+	0.690367i	$0.242551\pi$
$864$	−1.11720e9	+	1.40093e9i	−1.73217	+	2.17207i
$865$	−6.10212e8	−	1.39277e8i	−0.942828	−	0.215194i
$866$	−1.44113e9			−2.21896
$867$		−	9.07755e8i		−	1.39287i
$868$	−2.64646e8	−	6.04038e7i	−0.404675	−	0.0923645i
$869$	−2.85496e8	−	3.58001e8i	−0.435052	−	0.545538i
$870$	−3.02318e8	−	1.32454e9i	−0.459099	−	2.01144i
$871$	−2.09920e7	−	2.63231e7i	−0.0317687	−	0.0398366i
$872$	5.64615e6	+	1.17244e7i	0.00851537	+	0.0176823i
$873$	2.53145e6	−	1.10910e7i	0.00380475	−	0.0166697i
$874$	1.06284e9	−	5.11836e8i	1.59196	−	0.766649i
$875$	−7.17980e8	+	9.00318e8i	−1.07174	+	1.34391i
$876$	2.16398e8	+	9.48102e8i	0.321915	+	1.41040i
$877$	−3.29060e7	−	1.44171e8i	−0.0487839	−	0.213736i	0.944661	−	0.328048i	$-0.106391\pi$
$877$	−3.29060e7	−	1.44171e8i	−0.0487839	−	0.213736i	−0.993445	+	0.114312i	$0.963534\pi$
$878$	2.47551e8	−	5.14044e8i	0.365747	−	0.759481i
$879$	2.36510e8	+	1.88611e8i	0.348244	+	0.277715i
$880$	−7.62165e8	+	6.07806e8i	−1.11841	+	0.891902i
$881$	1.46459e8	+	7.05311e7i	0.214185	+	0.103146i	0.537900	−	0.843008i	$-0.319218\pi$
$881$	1.46459e8	+	7.05311e7i	0.214185	+	0.103146i	−0.323715	+	0.946155i	$0.604932\pi$
$882$	2.04535e9	−	4.24721e9i	2.98100	−	6.19010i
$883$	5.79290e8	+	7.26406e8i	0.841422	+	1.05511i	0.997726	+	0.0674004i	$0.0214705\pi$
$883$	5.79290e8	+	7.26406e8i	0.841422	+	1.05511i	−0.156304	+	0.987709i	$0.549958\pi$
$884$	2.58442e7	−	3.24076e7i	0.0374116	−	0.0469126i
$885$	−1.59707e9	−	7.69109e8i	−2.30406	−	1.10958i
$886$	−5.30635e8	+	1.21114e8i	−0.762948	+	0.174138i
$887$	−6.62735e8	+	1.51265e8i	−0.949662	+	0.216754i	−0.669176	−	0.743104i	$-0.733353\pi$
$887$	−6.62735e8	+	1.51265e8i	−0.949662	+	0.216754i	−0.280486	+	0.959858i	$0.590496\pi$
$888$	2.00722e7	+	1.60071e7i	0.0286653	+	0.0228598i
$889$	5.91702e8	+	1.22868e9i	0.842166	+	1.74878i
$890$	−5.40576e7	−	1.23383e7i	−0.0766808	−	0.0175019i
$891$	−1.28691e9	+	6.19743e8i	−1.81935	+	0.876150i
$892$	6.29606e8	−	5.02094e8i	0.887103	−	0.707441i
$893$	1.16634e8	−	2.66210e7i	0.163784	−	0.0373827i
$894$	−4.29961e8	+	3.42883e8i	−0.601751	+	0.479881i
$895$	−1.20567e8	+	5.28238e8i	−0.168174	+	0.736818i
$896$	3.73942e8			0.519853
$897$		−	1.01641e8i		−	0.140829i
$898$	−2.59095e8	+	1.13517e9i	−0.357792	+	1.56759i
$899$	−9.21548e7	−	7.34910e7i	−0.126835	−	0.101148i
$900$	1.30836e8	+	6.30075e7i	0.179474	+	0.0864301i
$901$	7.14812e7	−	3.44235e7i	0.0977277	−	0.0470632i
$902$		−	5.55737e8i		−	0.757268i
$903$	2.10066e9	+	1.03077e9i	2.85294	+	1.39990i
$904$	−1.40661e8			−0.190401
$905$	4.52100e8	+	9.38796e8i	0.609943	+	1.26656i
$906$	2.81983e8	−	5.85544e8i	0.379174	−	0.787364i
$907$	1.40625e8	−	1.76338e8i	0.188469	−	0.236332i	−0.678616	−	0.734494i	$-0.737420\pi$
$907$	1.40625e8	−	1.76338e8i	0.188469	−	0.236332i	0.867084	+	0.498161i	$0.165991\pi$
$908$	−1.14602e9	−	2.61570e8i	−1.53085	−	0.349407i
$909$	−1.72163e9			−2.29218
$910$			2.45205e8i			0.325391i
$911$	2.97197e8	+	6.78332e7i	0.393087	+	0.0897195i	0.414496	−	0.910051i	$-0.363958\pi$
$911$	2.97197e8	+	6.78332e7i	0.393087	+	0.0897195i	−0.0214087	+	0.999771i	$0.506815\pi$
$912$	1.34875e9	+	1.69128e9i	1.77807	+	2.22963i
$913$	−8.49841e7	−	3.72340e8i	−0.111667	−	0.489245i
$914$	−6.23725e7	−	7.82126e7i	−0.0816872	−	0.102433i
$915$	3.48424e8	+	7.23509e8i	0.454825	+	0.944454i
$916$	2.08544e8	−	9.13692e8i	0.271339	−	1.18881i
$917$	−3.14097e8	+	1.51261e8i	−0.407339	+	0.196164i
$918$	6.18624e8	−	7.75731e8i	0.799648	−	1.00273i
$919$	−1.22500e8	−	5.36707e8i	−0.157830	−	0.691498i	−0.990475	−	0.137691i	$-0.956032\pi$
$919$	−1.22500e8	−	5.36707e8i	−0.157830	−	0.691498i	0.832645	−	0.553807i	$-0.186825\pi$
$920$	1.75145e7	+	7.67361e7i	0.0224923	+	0.0985453i
$921$	3.98522e8	−	8.27540e8i	0.510121	−	1.05928i
$922$	−3.16979e8	−	2.52782e8i	−0.404425	−	0.322518i
$923$	−3.89048e7	+	3.10256e7i	−0.0494764	+	0.0394561i
$924$	3.83061e9	+	1.84473e9i	4.85570	+	2.33838i
$925$	−4.26154e6	+	8.84919e6i	−0.00538445	+	0.0111809i
$926$	9.34332e8	+	1.17162e9i	1.17671	+	1.47554i
$927$	1.45392e9	−	1.82315e9i	1.82516	−	2.28867i
$928$	8.01490e8	+	3.85977e8i	1.00289	+	0.482967i
$929$	−2.04630e8	+	4.67054e7i	−0.255224	+	0.0582533i	−0.348219	−	0.937413i	$-0.613213\pi$
$929$	−2.04630e8	+	4.67054e7i	−0.255224	+	0.0582533i	0.0929944	+	0.995667i	$0.470356\pi$
$930$	4.35993e8	−	9.95126e7i	0.542040	−	0.123717i
$931$	−2.59204e9	−	2.06708e9i	−3.21213	−	2.56159i
$932$	2.39511e8	+	4.97350e8i	0.295855	+	0.614348i
$933$	−1.65206e9	−	3.77072e8i	−2.03414	−	0.464279i
$934$	−2.21354e8	+	1.06598e8i	−0.271673	+	0.130831i
$935$	4.69383e8	−	3.74321e8i	0.574239	−	0.457940i
$936$	−2.90021e7	+	6.61954e6i	−0.0353673	+	0.00807235i
$937$	3.14768e8	−	2.51019e8i	0.382623	−	0.305132i	−0.413224	−	0.910630i	$-0.635597\pi$
$937$	3.14768e8	−	2.51019e8i	0.382623	−	0.305132i	0.795847	+	0.605497i	$0.207026\pi$
$938$	−2.05038e8	+	8.98328e8i	−0.248442	+	1.08850i
$939$	−3.15246e8			−0.380761
$940$			8.79038e7i			0.105834i
$941$	−1.56543e8	+	6.85861e8i	−0.187874	+	0.823128i	0.789861	+	0.613285i	$0.210152\pi$
$941$	−1.56543e8	+	6.85861e8i	−0.187874	+	0.823128i	−0.977735	+	0.209843i	$0.932705\pi$
$942$	2.26457e9	+	1.80594e9i	2.70916	+	2.16048i
$943$	1.71585e8	+	8.26311e7i	0.204619	+	0.0985391i
$944$	9.40234e8	−	4.52793e8i	1.11769	−	0.538250i
$945$			3.07429e9i			3.64291i
$946$	−8.33275e8	+	1.69818e9i	−0.984272	+	2.00591i
$947$	1.44301e9			1.69911			0.849553	−	0.527503i	$-0.176872\pi$
$947$	1.44301e9			1.69911			0.849553	+	0.527503i	$0.176872\pi$
$948$	−3.23941e8	−	6.72670e8i	−0.380225	−	0.789545i
$949$	3.30677e7	−	6.86659e7i	0.0386906	−	0.0803419i
$950$	1.21572e8	−	1.52446e8i	0.141796	−	0.177806i
$951$	−2.74503e9	−	6.26535e8i	−3.19158	−	0.728457i
$952$	−1.03012e8			−0.119392
$953$		−	8.89623e8i		−	1.02784i	−0.857837	−	0.513922i	$-0.828192\pi$
$953$		−	8.89623e8i		−	1.02784i	0.857837	−	0.513922i	$-0.171808\pi$
$954$	−6.11311e8	−	1.39528e8i	−0.704072	−	0.160700i
$955$	6.53772e8	+	8.19804e8i	0.750613	+	0.941239i
$956$	−1.06620e8	−	4.67133e8i	−0.122030	−	0.534647i
$957$	1.15106e9	+	1.44339e9i	1.31330	+	1.64682i
$958$	−5.67464e7	−	1.17835e8i	−0.0645419	−	0.134023i
$959$	4.41472e8	−	1.93421e9i	0.500550	−	2.19305i
$960$	−1.73885e9	+	8.37386e8i	−1.96539	+	0.946481i
$961$	−5.29159e8	+	6.63544e8i	−0.596233	+	0.747652i
$962$	−4.93045e6	−	2.16017e7i	−0.00553810	−	0.0242640i
$963$	−5.40992e8	−	2.37024e9i	−0.605776	−	2.65408i
$964$	−5.89564e8	+	1.22424e9i	−0.658112	+	1.36658i
$965$	6.91986e8	+	5.51840e8i	0.770044	+	0.614089i
$966$	−2.17482e9	+	1.73436e9i	−2.41263	+	1.92401i
$967$	−6.32857e8	−	3.04768e8i	−0.699884	−	0.337047i	0.0498765	−	0.998755i	$-0.484117\pi$
$967$	−6.32857e8	−	3.04768e8i	−0.699884	−	0.337047i	−0.749761	+	0.661709i	$0.769832\pi$
$968$	−7.84598e7	+	1.62924e8i	−0.0865010	+	0.179621i
$969$	−8.30637e8	−	1.04159e9i	−0.912935	−	1.14478i
$970$	6.99788e6	−	8.77506e6i	0.00766745	−	0.00961468i
$971$	−1.08001e9	−	5.20107e8i	−1.17970	−	0.568113i	−0.261876	−	0.965102i	$-0.584341\pi$
$971$	−1.08001e9	−	5.20107e8i	−1.17970	−	0.568113i	−0.917824	+	0.396989i	$0.870055\pi$
$972$	−3.63634e8	+	8.29971e7i	−0.395973	+	0.0903783i
$973$	−4.13188e8	+	9.43075e7i	−0.448548	+	0.102378i
$974$	1.52949e9	+	1.21972e9i	1.65527	+	1.32003i
$975$	−7.28939e6	−	1.51366e7i	−0.00786461	−	0.0163310i
$976$	−4.60913e8	−	1.05200e8i	−0.495757	−	0.113153i
$977$	−5.75138e8	+	2.76972e8i	−0.616721	+	0.296997i	−0.716041	−	0.698059i	$-0.754047\pi$
$977$	−5.75138e8	+	2.76972e8i	−0.616721	+	0.296997i	0.0993201	+	0.995056i	$0.468333\pi$
$978$	1.50488e9	−	1.20010e9i	1.60873	−	1.28292i
$979$	7.34570e7	−	1.67661e7i	0.0782862	−	0.0178683i
$980$	1.90457e9	−	1.51884e9i	2.02357	−	1.61374i
$981$	5.98200e7	−	2.62088e8i	0.0633635	−	0.277614i
$982$	1.33305e9			1.40771
$983$		−	8.22935e8i		−	0.866374i	−0.901304	−	0.433187i	$-0.857389\pi$
$983$		−	8.22935e8i		−	0.866374i	0.901304	−	0.433187i	$-0.142611\pi$
$984$	1.83095e7	−	8.02193e7i	0.0192173	−	0.0841964i
$985$	1.00166e9	+	7.98798e8i	1.04812	+	0.835850i
$986$	−4.43806e8	−	2.13726e8i	−0.462980	−	0.222960i
$987$	−2.54165e8	+	1.22399e8i	−0.264341	+	0.127300i
$988$			2.30397e8i			0.238894i
$989$	−4.00421e8	−	5.09775e8i	−0.413931	−	0.526974i
$990$	−4.74484e9			−4.89009
$991$	9.13220e7	+	1.89632e8i	0.0938327	+	0.194846i	0.942603	−	0.333917i	$-0.108370\pi$
$991$	9.13220e7	+	1.89632e8i	0.0938327	+	0.194846i	−0.848770	+	0.528763i	$0.822656\pi$
$992$	−1.27050e8	+	2.63823e8i	−0.130149	+	0.270257i
$993$	1.78439e9	−	2.23755e9i	1.82239	−	2.28520i
$994$	1.32770e9	+	3.03040e8i	1.35189	+	0.308561i
$995$	−1.01322e9			−1.02857
$996$		−	6.22713e8i		−	0.630246i
$997$	−2.95604e8	−	6.74697e7i	−0.298281	−	0.0680806i	0.0707616	−	0.997493i	$-0.477457\pi$
$997$	−2.95604e8	−	6.74697e7i	−0.298281	−	0.0680806i	−0.369042	+	0.929413i	$0.620314\pi$
$998$	−3.77505e8	−	4.73376e8i	−0.379779	−	0.476227i
$999$	−6.18160e7	−	2.70833e8i	−0.0620018	−	0.271648i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.f.a.2.4	✓	126
43.22	odd	14	inner	43.7.f.a.22.4	yes	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.f.a.2.4	✓	126	1.1	even	1	trivial
43.7.f.a.22.4	yes	126	43.22	odd	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	43.f (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.02991 - 10.4447i) q^{2} +(20.6257 - 42.8298i) q^{3} +(-43.8887 + 55.0347i) q^{4} +(127.013 + 28.9898i) q^{5} -551.091 q^{6} -619.099i q^{7} +(72.2435 + 16.4891i) q^{8} +(-954.446 - 1196.84i) q^{9} +O(q^{10})\)	\(q+(-5.02991 - 10.4447i) q^{2} +(20.6257 - 42.8298i) q^{3} +(-43.8887 + 55.0347i) q^{4} +(127.013 + 28.9898i) q^{5} -551.091 q^{6} -619.099i q^{7} +(72.2435 + 16.4891i) q^{8} +(-954.446 - 1196.84i) q^{9} +(-336.072 - 1472.43i) q^{10} +(1279.58 + 1604.54i) q^{11} +(1451.89 + 3014.88i) q^{12} +(58.3552 - 255.671i) q^{13} +(-6466.31 + 3114.01i) q^{14} +(3861.36 - 4841.99i) q^{15} +(811.323 + 3554.64i) q^{16} +(-499.657 - 2189.14i) q^{17} +(-7699.85 + 15988.9i) q^{18} +(9757.92 + 7781.68i) q^{19} +(-7169.87 + 5717.78i) q^{20} +(-26515.9 - 12769.4i) q^{21} +(10322.8 - 21435.6i) q^{22} +(5083.42 + 6374.40i) q^{23} +(2196.30 - 2754.07i) q^{24} +(1214.18 + 584.718i) q^{25} +(-2963.93 + 676.497i) q^{26} +(-37160.5 + 8481.65i) q^{27} +(34071.9 + 27171.5i) q^{28} +(8210.48 + 17049.2i) q^{29} +(-69995.5 - 15976.0i) q^{30} +(-5612.02 + 2702.61i) q^{31} +(36754.1 - 29310.4i) q^{32} +(95114.6 - 21709.3i) q^{33} +(-20351.7 + 16230.0i) q^{34} +(17947.6 - 78633.4i) q^{35} +107757. q^{36} +7288.20i q^{37} +(32196.0 - 141060. i) q^{38} +(-9746.70 - 7772.74i) q^{39} +(8697.82 + 4188.65i) q^{40} +(21045.2 - 10134.9i) q^{41} +341180. i q^{42} +(-79504.8 - 585.981i) q^{43} -144465. q^{44} +(-86530.7 - 179683. i) q^{45} +(41009.7 - 85157.5i) q^{46} +(5976.39 - 7494.15i) q^{47} +(168979. + 38568.2i) q^{48} -265635. q^{49} -15622.8i q^{50} +(-104066. - 23752.5i) q^{51} +(11509.6 + 14432.6i) q^{52} +(7862.33 + 34447.1i) q^{53} +(275503. + 345469. i) q^{54} +(116008. + 240892. i) q^{55} +(10208.4 - 44725.9i) q^{56} +(534552. - 257427. i) q^{57} +(136776. - 171512. i) q^{58} +(-63690.5 - 279046. i) q^{59} +(97007.5 + 425018. i) q^{60} +(-56259.6 + 116824. i) q^{61} +(56455.9 + 45022.1i) q^{62} +(-740961. + 590897. i) q^{63} +(-280770. - 135212. i) q^{64} +(14823.7 - 30781.7i) q^{65} +(-705165. - 884249. i) q^{66} +(80047.0 - 100376. i) q^{67} +(142408. + 68580.1i) q^{68} +(377864. - 86244.9i) q^{69} +(-911579. + 208062. i) q^{70} +(-148353. - 118307. i) q^{71} +(-49217.7 - 102202. i) q^{72} +(283332. + 64668.6i) q^{73} +(76123.2 - 36659.0i) q^{74} +(50086.7 - 39942.8i) q^{75} +(-856526. + 195496. i) q^{76} +(993371. - 792187. i) q^{77} +(-32159.0 + 140898. i) q^{78} -223117. q^{79} +475004. i q^{80} +(-154871. + 678535. i) q^{81} +(-211711. - 168834. i) q^{82} +(-167663. - 80742.4i) q^{83} +(1.86651e6 - 898863. i) q^{84} -292534. i q^{85} +(393782. + 833353. i) q^{86} +899563. q^{87} +(65983.9 + 137017. i) q^{88} +(15929.3 - 33077.5i) q^{89} +(-1.44149e6 + 1.80758e6i) q^{90} +(-158285. - 36127.6i) q^{91} -573918. q^{92} +296105. i q^{93} +(-108335. - 24726.8i) q^{94} +(1.01379e6 + 1.27125e6i) q^{95} +(-497279. - 2.17872e6i) q^{96} +(4633.46 + 5810.17i) q^{97} +(1.33612e6 + 2.77448e6i) q^{98} +(699087. - 3.06290e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9}+O(q^{10}) \) 126 * q - 7 * q^2 - 7 * q^3 + 725 * q^4 - 7 * q^5 + 244 * q^6 + 2233 * q^8 + 6312 * q^9	\( 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9} + 1955 q^{10} - 985 q^{11} - 455 q^{12} - 4485 q^{13} - 6771 q^{14} + 5017 q^{15} - 41935 q^{16} - 10409 q^{17} - 5110 q^{18} - 33397 q^{19} - 24507 q^{20} - 5448 q^{21} + 25193 q^{22} - 29017 q^{23} - 1885 q^{24} - 2080 q^{25} + 34713 q^{26} - 7 q^{27} + 28665 q^{28} + 17353 q^{29} - 290052 q^{30} + 13547 q^{31} + 458283 q^{32} - 94801 q^{33} - 191527 q^{34} + 183008 q^{35} + 956352 q^{36} + 304607 q^{38} - 381031 q^{39} + 66419 q^{40} + 313447 q^{41} - 323228 q^{43} + 281588 q^{44} - 1237551 q^{45} + 80948 q^{46} - 180133 q^{47} - 762055 q^{48} - 1861754 q^{49} + 999215 q^{51} + 471797 q^{52} + 1030011 q^{53} - 92099 q^{54} + 324233 q^{55} - 842713 q^{56} + 331037 q^{57} + 849461 q^{58} - 369609 q^{59} + 553323 q^{60} - 594727 q^{61} - 886711 q^{62} + 1914136 q^{63} - 3250219 q^{64} + 1473521 q^{65} - 427559 q^{66} + 122535 q^{67} - 602346 q^{68} + 4320057 q^{69} - 1694994 q^{70} - 770707 q^{71} - 391202 q^{72} + 476945 q^{73} - 3943812 q^{74} + 2061367 q^{75} - 2044462 q^{76} + 3016216 q^{77} + 239350 q^{78} + 5077268 q^{79} + 2388946 q^{81} + 5820437 q^{82} - 1324235 q^{83} + 3759618 q^{84} - 4967947 q^{86} - 3537894 q^{87} - 7289555 q^{88} - 4331495 q^{89} - 12825206 q^{90} + 1802976 q^{91} - 12038260 q^{92} + 6249341 q^{94} - 5313259 q^{95} + 7069598 q^{96} + 788975 q^{97} + 4724783 q^{98} - 2216971 q^{99}+O(q^{100}) \) 126 * q - 7 * q^2 - 7 * q^3 + 725 * q^4 - 7 * q^5 + 244 * q^6 + 2233 * q^8 + 6312 * q^9 + 1955 * q^10 - 985 * q^11 - 455 * q^12 - 4485 * q^13 - 6771 * q^14 + 5017 * q^15 - 41935 * q^16 - 10409 * q^17 - 5110 * q^18 - 33397 * q^19 - 24507 * q^20 - 5448 * q^21 + 25193 * q^22 - 29017 * q^23 - 1885 * q^24 - 2080 * q^25 + 34713 * q^26 - 7 * q^27 + 28665 * q^28 + 17353 * q^29 - 290052 * q^30 + 13547 * q^31 + 458283 * q^32 - 94801 * q^33 - 191527 * q^34 + 183008 * q^35 + 956352 * q^36 + 304607 * q^38 - 381031 * q^39 + 66419 * q^40 + 313447 * q^41 - 323228 * q^43 + 281588 * q^44 - 1237551 * q^45 + 80948 * q^46 - 180133 * q^47 - 762055 * q^48 - 1861754 * q^49 + 999215 * q^51 + 471797 * q^52 + 1030011 * q^53 - 92099 * q^54 + 324233 * q^55 - 842713 * q^56 + 331037 * q^57 + 849461 * q^58 - 369609 * q^59 + 553323 * q^60 - 594727 * q^61 - 886711 * q^62 + 1914136 * q^63 - 3250219 * q^64 + 1473521 * q^65 - 427559 * q^66 + 122535 * q^67 - 602346 * q^68 + 4320057 * q^69 - 1694994 * q^70 - 770707 * q^71 - 391202 * q^72 + 476945 * q^73 - 3943812 * q^74 + 2061367 * q^75 - 2044462 * q^76 + 3016216 * q^77 + 239350 * q^78 + 5077268 * q^79 + 2388946 * q^81 + 5820437 * q^82 - 1324235 * q^83 + 3759618 * q^84 - 4967947 * q^86 - 3537894 * q^87 - 7289555 * q^88 - 4331495 * q^89 - 12825206 * q^90 + 1802976 * q^91 - 12038260 * q^92 + 6249341 * q^94 - 5313259 * q^95 + 7069598 * q^96 + 788975 * q^97 + 4724783 * q^98 - 2216971 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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