LMFDB - Embedded newform 60.7.l.a.23.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(23,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

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

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

chi := DirichletCharacter("60.23");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.l (of order $4$, degree $2$, 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:	$13.8032450172$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.8
Character	$\chi$	$=$	60.23
Dual form			60.7.l.a.47.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.60301 - 2.48882i) q^{2} +(-13.5986 + 23.3255i) q^{3} +(51.6115 + 37.8451i) q^{4} +(120.360 + 33.7399i) q^{5} +(161.443 - 143.500i) q^{6} +(184.076 + 184.076i) q^{7} +(-298.214 - 416.188i) q^{8} +(-359.157 - 634.387i) q^{9} +O(q^{10})$	\(q+(-7.60301 - 2.48882i) q^{2} +(-13.5986 + 23.3255i) q^{3} +(51.6115 + 37.8451i) q^{4} +(120.360 + 33.7399i) q^{5} +(161.443 - 143.500i) q^{6} +(184.076 + 184.076i) q^{7} +(-298.214 - 416.188i) q^{8} +(-359.157 - 634.387i) q^{9} +(-831.129 - 556.080i) q^{10} +2353.32 q^{11} +(-1584.60 + 689.226i) q^{12} +(-2270.29 - 2270.29i) q^{13} +(-941.400 - 1857.66i) q^{14} +(-2423.73 + 2348.65i) q^{15} +(1231.50 + 3906.48i) q^{16} +(4696.72 + 4696.72i) q^{17} +(1151.80 + 5717.13i) q^{18} +3860.38 q^{19} +(4935.10 + 6296.41i) q^{20} +(-6796.84 + 1790.49i) q^{21} +(-17892.3 - 5856.99i) q^{22} +(2283.27 + 2283.27i) q^{23} +(13763.1 - 1296.41i) q^{24} +(13348.2 + 8121.89i) q^{25} +(11610.7 + 22911.4i) q^{26} +(19681.4 + 249.237i) q^{27} +(2534.08 + 16466.8i) q^{28} +2697.25 q^{29} +(24273.0 - 11824.6i) q^{30} +22554.7i q^{31} +(359.410 - 32766.0i) q^{32} +(-32001.8 + 54892.3i) q^{33} +(-24019.9 - 47398.5i) q^{34} +(15944.8 + 28366.2i) q^{35} +(5471.75 - 46334.0i) q^{36} +(-66085.2 + 66085.2i) q^{37} +(-29350.5 - 9607.80i) q^{38} +(83828.4 - 22082.9i) q^{39} +(-21850.9 - 60154.3i) q^{40} -37847.2i q^{41} +(56132.6 + 3302.97i) q^{42} +(-64071.0 + 64071.0i) q^{43} +(121458. + 89061.4i) q^{44} +(-21824.2 - 88473.0i) q^{45} +(-11677.1 - 23042.4i) q^{46} +(-54149.4 + 54149.4i) q^{47} +(-107867. - 24397.2i) q^{48} -49881.0i q^{49} +(-81272.9 - 94972.2i) q^{50} +(-173422. + 45684.6i) q^{51} +(-31253.9 - 203093. i) q^{52} +(57084.1 - 57084.1i) q^{53} +(-149018. - 50878.5i) q^{54} +(283246. + 79400.7i) q^{55} +(21716.3 - 131504. i) q^{56} +(-52495.7 + 90045.3i) q^{57} +(-20507.2 - 6712.97i) q^{58} +53317.9i q^{59} +(-213977. + 29491.3i) q^{60} +196822. q^{61} +(56134.6 - 171484. i) q^{62} +(50663.2 - 182888. i) q^{63} +(-84281.4 + 248226. i) q^{64} +(-196654. - 349853. i) q^{65} +(379927. - 337700. i) q^{66} +(171949. + 171949. i) q^{67} +(64657.3 + 420152. i) q^{68} +(-84307.8 + 22209.2i) q^{69} +(-50629.8 - 255352. i) q^{70} +192491. q^{71} +(-156919. + 338660. i) q^{72} +(-133036. - 133036. i) q^{73} +(666921. - 337972. i) q^{74} +(-370964. + 200908. i) q^{75} +(199240. + 146096. i) q^{76} +(433189. + 433189. i) q^{77} +(-692309. - 40737.1i) q^{78} -98211.4 q^{79} +(16419.8 + 511737. i) q^{80} +(-273453. + 455690. i) q^{81} +(-94195.0 + 287753. i) q^{82} +(168484. + 168484. i) q^{83} +(-418557. - 164817. i) q^{84} +(406832. + 723765. i) q^{85} +(646594. - 327671. i) q^{86} +(-36678.8 + 62914.7i) q^{87} +(-701791. - 979423. i) q^{88} -246306. q^{89} +(-54264.1 + 726978. i) q^{90} -835813. i q^{91} +(31432.7 + 204254. i) q^{92} +(-526099. - 306712. i) q^{93} +(546467. - 276930. i) q^{94} +(464637. + 130249. i) q^{95} +(759396. + 453955. i) q^{96} +(374797. - 374797. i) q^{97} +(-124145. + 379246. i) q^{98} +(-845211. - 1.49291e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 4 q^{6}+O(q^{10}) $ 136 * q - 4 * q^6	$ 136 q - 4 q^{6} - 2092 q^{10} - 1460 q^{12} - 8 q^{13} - 932 q^{16} - 12744 q^{18} - 16056 q^{21} + 25444 q^{22} - 8 q^{25} - 52244 q^{28} + 82868 q^{30} - 2920 q^{33} - 69524 q^{36} - 113000 q^{37} + 99944 q^{40} + 19436 q^{42} - 62504 q^{45} + 145936 q^{46} - 82364 q^{48} + 219504 q^{52} - 286152 q^{57} - 351260 q^{58} + 466756 q^{60} + 652976 q^{61} - 61800 q^{66} + 243868 q^{70} - 145560 q^{72} - 316856 q^{73} + 269024 q^{76} + 613272 q^{78} + 1472232 q^{81} - 1652880 q^{82} - 1466984 q^{85} - 1084100 q^{88} + 448368 q^{90} - 2869552 q^{93} - 278860 q^{96} + 2135272 q^{97}+O(q^{100}) $ 136 * q - 4 * q^6 - 2092 * q^10 - 1460 * q^12 - 8 * q^13 - 932 * q^16 - 12744 * q^18 - 16056 * q^21 + 25444 * q^22 - 8 * q^25 - 52244 * q^28 + 82868 * q^30 - 2920 * q^33 - 69524 * q^36 - 113000 * q^37 + 99944 * q^40 + 19436 * q^42 - 62504 * q^45 + 145936 * q^46 - 82364 * q^48 + 219504 * q^52 - 286152 * q^57 - 351260 * q^58 + 466756 * q^60 + 652976 * q^61 - 61800 * q^66 + 243868 * q^70 - 145560 * q^72 - 316856 * q^73 + 269024 * q^76 + 613272 * q^78 + 1472232 * q^81 - 1652880 * q^82 - 1466984 * q^85 - 1084100 * q^88 + 448368 * q^90 - 2869552 * q^93 - 278860 * q^96 + 2135272 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−7.60301	−	2.48882i	−0.950376	−	0.311103i
$2$	−7.60301	−	2.48882i	−0.950376	−	0.311103i
$3$	−13.5986	+	23.3255i	−0.503651	+	0.863907i
$3$	−13.5986	+	23.3255i	−0.503651	+	0.863907i
$4$	51.6115	+	37.8451i	0.806430	+	0.591329i
$5$	120.360	+	33.7399i	0.962883	+	0.269919i
$5$	120.360	+	33.7399i	0.962883	+	0.269919i
$6$	161.443	−	143.500i	0.747422	−	0.664350i
$7$	184.076	+	184.076i	0.536665	+	0.536665i	0.922548	−	0.385883i	$-0.126103\pi$
$7$	184.076	+	184.076i	0.536665	+	0.536665i	−0.385883	+	0.922548i	$0.626103\pi$
$8$	−298.214	−	416.188i	−0.582448	−	0.812868i
$9$	−359.157	−	634.387i	−0.492671	−	0.870215i
$10$	−831.129	−	556.080i	−0.831129	−	0.556080i
$11$	2353.32			1.76808			0.884041	−	0.467409i	$-0.154812\pi$
$11$	2353.32			1.76808			0.884041	+	0.467409i	$0.154812\pi$
$12$	−1584.60	+	689.226i	−0.917013	+	0.398858i
$13$	−2270.29	−	2270.29i	−1.03336	−	1.03336i	−0.999424	−	0.0339359i	$-0.989196\pi$
$13$	−2270.29	−	2270.29i	−1.03336	−	1.03336i	−0.0339359	−	0.999424i	$-0.510804\pi$
$14$	−941.400	−	1857.66i	−0.343076	−	0.676991i
$15$	−2423.73	+	2348.65i	−0.718142	+	0.695897i
$16$	1231.50	+	3906.48i	0.300660	+	0.953731i
$17$	4696.72	+	4696.72i	0.955978	+	0.955978i	0.999071	−	0.0430935i	$-0.0137213\pi$
$17$	4696.72	+	4696.72i	0.955978	+	0.955978i	−0.0430935	+	0.999071i	$0.513721\pi$
$18$	1151.80	+	5717.13i	0.197497	+	0.980304i
$19$	3860.38			0.562820			0.281410	−	0.959588i	$-0.409198\pi$
$19$	3860.38			0.562820			0.281410	+	0.959588i	$0.409198\pi$
$20$	4935.10	+	6296.41i	0.616887	+	0.787052i
$21$	−6796.84	+	1790.49i	−0.733920	+	0.193337i
$22$	−17892.3	−	5856.99i	−1.68034	−	0.550055i
$23$	2283.27	+	2283.27i	0.187661	+	0.187661i	0.794684	−	0.607023i	$-0.207636\pi$
$23$	2283.27	+	2283.27i	0.187661	+	0.187661i	−0.607023	+	0.794684i	$0.707636\pi$
$24$	13763.1	−	1296.41i	0.995593	−	0.0937797i
$25$	13348.2	+	8121.89i	0.854287	+	0.519801i
$26$	11610.7	+	22911.4i	0.660600	+	1.30356i
$27$	19681.4	+	249.237i	0.999920	+	0.0126626i
$28$	2534.08	+	16466.8i	0.115437	+	0.750128i
$29$	2697.25			0.110593			0.0552964	−	0.998470i	$-0.482390\pi$
$29$	2697.25			0.110593			0.0552964	+	0.998470i	$0.482390\pi$
$30$	24273.0	−	11824.6i	0.899000	−	0.437948i
$31$			22554.7i			0.757098i	0.925581	+	0.378549i	$0.123577\pi$
$31$			22554.7i			0.757098i	−0.925581	+	0.378549i	$0.876423\pi$
$32$	359.410	−	32766.0i	0.0109683	−	0.999940i
$33$	−32001.8	+	54892.3i	−0.890496	+	1.52746i
$34$	−24019.9	−	47398.5i	−0.611131	−	1.20595i
$35$	15944.8	+	28366.2i	0.371889	+	0.661602i
$36$	5471.75	−	46334.0i	0.117279	−	0.993099i
$37$	−66085.2	+	66085.2i	−1.30466	+	1.30466i	−0.379454	+	0.925210i	$0.623888\pi$
$37$	−66085.2	+	66085.2i	−1.30466	+	1.30466i	−0.925210	+	0.379454i	$0.876112\pi$
$38$	−29350.5	−	9607.80i	−0.534891	−	0.175095i
$39$	83828.4	−	22082.9i	1.41318	−	0.372274i
$40$	−21850.9	−	60154.3i	−0.341421	−	0.939910i
$41$		−	37847.2i		−	0.549139i	−0.961567	−	0.274570i	$-0.911465\pi$
$41$		−	37847.2i		−	0.549139i	0.961567	−	0.274570i	$-0.0885354\pi$
$42$	56132.6	+	3302.97i	0.757648	+	0.0445818i
$43$	−64071.0	+	64071.0i	−0.805853	+	0.805853i	−0.984003	−	0.178150i	$-0.942989\pi$
$43$	−64071.0	+	64071.0i	−0.805853	+	0.805853i	0.178150	+	0.984003i	$0.442989\pi$
$44$	121458.	+	89061.4i	1.42584	+	1.04552i
$45$	−21824.2	−	88473.0i	−0.239497	−	0.970897i
$46$	−11677.1	−	23042.4i	−0.119967	−	0.236731i
$47$	−54149.4	+	54149.4i	−0.521555	+	0.521555i	−0.918041	−	0.396486i	$-0.870230\pi$
$47$	−54149.4	+	54149.4i	−0.521555	+	0.521555i	0.396486	+	0.918041i	$0.370230\pi$
$48$	−107867.	−	24397.2i	−0.975363	−	0.220606i
$49$		−	49881.0i		−	0.423982i
$50$	−81272.9	−	94972.2i	−0.650183	−	0.759778i
$51$	−173422.	+	45684.6i	−1.30735	+	0.344397i
$52$	−31253.9	−	203093.i	−0.222277	−	1.44439i
$53$	57084.1	−	57084.1i	0.383431	−	0.383431i	−0.488906	−	0.872337i	$-0.662604\pi$
$53$	57084.1	−	57084.1i	0.383431	−	0.383431i	0.872337	+	0.488906i	$0.162604\pi$
$54$	−149018.	−	50878.5i	−0.946361	−	0.323112i
$55$	283246.	+	79400.7i	1.70246	+	0.477239i
$56$	21716.3	−	131504.i	0.123658	−	0.748817i
$57$	−52495.7	+	90045.3i	−0.283465	+	0.486224i
$58$	−20507.2	−	6712.97i	−0.105105	−	0.0344057i
$59$			53317.9i			0.259607i	0.991540	+	0.129804i	$0.0414347\pi$
$59$			53317.9i			0.259607i	−0.991540	+	0.129804i	$0.958565\pi$
$60$	−213977.	+	29491.3i	−0.990635	+	0.136534i
$61$	196822.			0.867130			0.433565	−	0.901122i	$-0.357255\pi$
$61$	196822.			0.867130			0.433565	+	0.901122i	$0.357255\pi$
$62$	56134.6	−	171484.i	0.235535	−	0.719528i
$63$	50663.2	−	182888.i	0.202615	−	0.731413i
$64$	−84281.4	+	248226.i	−0.321508	+	0.946907i
$65$	−196654.	−	349853.i	−0.716081	−	1.27393i
$66$	379927.	−	337700.i	1.32150	−	1.17463i
$67$	171949.	+	171949.i	0.571710	+	0.571710i	0.932606	−	0.360896i	$-0.117529\pi$
$67$	171949.	+	171949.i	0.571710	+	0.571710i	−0.360896	+	0.932606i	$0.617529\pi$
$68$	64657.3	+	420152.i	0.205632	+	1.33623i
$69$	−84307.8	+	22209.2i	−0.256638	+	0.0676061i
$70$	−50629.8	−	255352.i	−0.147609	−	0.744466i
$71$	192491.			0.537819			0.268909	−	0.963166i	$-0.413337\pi$
$71$	192491.			0.537819			0.268909	+	0.963166i	$0.413337\pi$
$72$	−156919.	+	338660.i	−0.420414	+	0.907332i
$73$	−133036.	−	133036.i	−0.341979	−	0.341979i	0.515132	−	0.857111i	$-0.327743\pi$
$73$	−133036.	−	133036.i	−0.341979	−	0.341979i	−0.857111	+	0.515132i	$0.827743\pi$
$74$	666921.	−	337972.i	1.64581	−	0.834038i
$75$	−370964.	+	200908.i	−0.879323	+	0.476227i
$76$	199240.	+	146096.i	0.453875	+	0.332812i
$77$	433189.	+	433189.i	0.948868	+	0.948868i
$78$	−692309.	−	40737.1i	−1.45887	−	0.0858432i
$79$	−98211.4			−0.199196			−0.0995980	−	0.995028i	$-0.531756\pi$
$79$	−98211.4			−0.199196			−0.0995980	+	0.995028i	$0.531756\pi$
$80$	16419.8	+	511737.i	0.0320699	+	0.999486i
$81$	−273453.	+	455690.i	−0.514550	+	0.857460i
$82$	−94195.0	+	287753.i	−0.170839	+	0.521889i
$83$	168484.	+	168484.i	0.294662	+	0.294662i	0.838919	−	0.544257i	$-0.183188\pi$
$83$	168484.	+	168484.i	0.294662	+	0.294662i	−0.544257	+	0.838919i	$0.683188\pi$
$84$	−418557.	−	164817.i	−0.706181	−	0.278076i
$85$	406832.	+	723765.i	0.662458	+	1.17853i
$86$	646594.	−	327671.i	1.01657	−	0.515161i
$87$	−36678.8	+	62914.7i	−0.0557002	+	0.0955420i
$88$	−701791.	−	979423.i	−1.02982	−	1.43722i
$89$	−246306.			−0.349386			−0.174693	−	0.984623i	$-0.555893\pi$
$89$	−246306.			−0.349386			−0.174693	+	0.984623i	$0.555893\pi$
$90$	−54264.1	+	726978.i	−0.0744363	+	0.997226i
$91$		−	835813.i		−	1.10914i
$92$	31432.7	+	204254.i	0.0403662	+	0.262305i
$93$	−526099.	−	306712.i	−0.654062	−	0.381313i
$94$	546467.	−	276930.i	0.657931	−	0.333417i
$95$	464637.	+	130249.i	0.541930	+	0.151916i
$96$	759396.	+	453955.i	0.858331	+	0.513096i
$97$	374797.	−	374797.i	0.410659	−	0.410659i	−0.471309	−	0.881968i	$-0.656218\pi$
$97$	374797.	−	374797.i	0.410659	−	0.410659i	0.881968	+	0.471309i	$0.156218\pi$
$98$	−124145.	+	379246.i	−0.131902	+	0.402942i
$99$	−845211.	−	1.49291e6i	−0.871083	−	1.53861i
$100$	381550.	+	924348.i	0.381550	+	0.924348i
$101$			352462.i			0.342096i	0.985263	+	0.171048i	$0.0547154\pi$
$101$			352462.i			0.342096i	−0.985263	+	0.171048i	$0.945285\pi$
$102$	1.43223e6	+	84275.7i	1.34962	+	0.0794149i
$103$	−935719.	+	935719.i	−0.856315	+	0.856315i	−0.990902	−	0.134587i	$-0.957029\pi$
$103$	−935719.	+	935719.i	−0.856315	+	0.856315i	0.134587	+	0.990902i	$0.457029\pi$
$104$	−267837.	+	1.62190e6i	−0.238106	+	1.44186i
$105$	−878481.	−	13820.2i	−0.758865	−	0.0119384i
$106$	−576083.	+	291939.i	−0.483690	+	0.245117i
$107$	605327.	−	605327.i	0.494128	−	0.494128i	−0.415476	−	0.909604i	$-0.636385\pi$
$107$	605327.	−	605327.i	0.494128	−	0.494128i	0.909604	+	0.415476i	$0.136385\pi$
$108$	1.00636e6	+	757708.i	0.798878	+	0.601493i
$109$		−	1.84769e6i		−	1.42676i	−0.700778	−	0.713380i	$-0.747164\pi$
$109$		−	1.84769e6i		−	1.42676i	0.700778	−	0.713380i	$-0.252836\pi$
$110$	−1.95591e6	−	1.30863e6i	−1.46950	−	0.983195i
$111$	−642805.	−	2.44013e6i	−0.470014	−	1.78421i
$112$	−492400.	+	945780.i	−0.350481	+	0.673188i
$113$	1.09348e6	−	1.09348e6i	0.757838	−	0.757838i	−0.218090	−	0.975929i	$-0.569983\pi$
$113$	1.09348e6	−	1.09348e6i	0.757838	−	0.757838i	0.975929	+	0.218090i	$0.0699827\pi$
$114$	623232.	−	553963.i	0.420664	−	0.373909i
$115$	197778.	+	351853.i	0.130042	+	0.231349i
$116$	139209.	+	102078.i	0.0891855	+	0.0653968i
$117$	−624852.	+	2.25564e6i	−0.390139	+	1.40835i
$118$	132699.	−	405376.i	0.0807645	−	0.246724i
$119$			1.72911e6i			1.02608i
$120$	1.70027e6	+	308328.i	0.983952	+	0.178431i
$121$	3.76654e6			2.12611
$122$	−1.49644e6	−	489855.i	−0.824100	−	0.269766i
$123$	882805.	+	514668.i	0.474405	+	0.276575i
$124$	−853584.	+	1.16408e6i	−0.447694	+	0.610547i
$125$	1.33257e6	+	1.42792e6i	0.682274	+	0.731096i
$126$	−840368.	+	1.26441e6i	−0.420105	+	0.632084i
$127$	−1.31238e6	−	1.31238e6i	−0.640690	−	0.640690i	0.310035	−	0.950725i	$-0.399659\pi$
$127$	−1.31238e6	−	1.31238e6i	−0.640690	−	0.640690i	−0.950725	+	0.310035i	$0.899659\pi$
$128$	1.25858e6	−	1.67750e6i	0.600139	−	0.799896i
$129$	−623213.	−	2.36576e6i	−0.290314	−	1.10205i
$130$	624440.	+	3.14937e6i	0.284224	+	1.43349i
$131$	−18487.3			−0.00822358			−0.00411179	−	0.999992i	$-0.501309\pi$
$131$	−18487.3			−0.00822358			−0.00411179	+	0.999992i	$0.501309\pi$
$132$	−3.72906e6	+	1.62197e6i	−1.62135	+	0.705213i
$133$	710604.	+	710604.i	0.302046	+	0.302046i
$134$	−879381.	−	1.73528e6i	−0.365479	−	0.721200i
$135$	2.36045e6	+	694047.i	0.959388	+	0.282090i
$136$	554094.	−	3.35534e6i	0.220276	−	1.33389i
$137$	−2.17005e6	−	2.17005e6i	−0.843931	−	0.843931i	0.145436	−	0.989368i	$-0.453541\pi$
$137$	−2.17005e6	−	2.17005e6i	−0.843931	−	0.843931i	−0.989368	+	0.145436i	$0.953541\pi$
$138$	696268.	+	40970.0i	0.264935	+	0.0155894i
$139$	−1.97714e6			−0.736196			−0.368098	−	0.929787i	$-0.619991\pi$
$139$	−1.97714e6			−0.736196			−0.368098	+	0.929787i	$0.619991\pi$
$140$	−250586.	+	2.06745e6i	−0.0913214	+	0.753445i
$141$	−526707.	−	1.99942e6i	−0.187894	−	0.713257i
$142$	−1.46351e6	−	479076.i	−0.511130	−	0.167317i
$143$	−5.34272e6	−	5.34272e6i	−1.82707	−	1.82707i
$144$	2.03592e6	−	2.18429e6i	0.681825	−	0.731515i
$145$	324642.	+	91004.9i	0.106488	+	0.0298511i
$146$	680370.	+	1.34257e6i	0.218618	+	0.431399i
$147$	1.16350e6	+	678311.i	0.366281	+	0.213539i
$148$	−5.91176e6	+	909761.i	−1.82361	+	0.280635i
$149$	−1.46263e6			−0.442157			−0.221079	−	0.975256i	$-0.570958\pi$
$149$	−1.46263e6			−0.442157			−0.221079	+	0.975256i	$0.570958\pi$
$150$	3.32047e6	−	604243.i	0.983843	−	0.179035i
$151$			3.38297e6i			0.982577i	0.870997	+	0.491289i	$0.163474\pi$
$151$			3.38297e6i			0.982577i	−0.870997	+	0.491289i	$0.836526\pi$
$152$	−1.15122e6	−	1.60665e6i	−0.327814	−	0.457498i
$153$	1.29268e6	−	4.66640e6i	0.360924	−	1.30289i
$154$	−2.21541e6	−	4.37167e6i	−0.606586	−	1.19698i
$155$	−760993.	+	2.71469e6i	−0.204355	+	0.728997i
$156$	5.16224e6	+	2.03276e6i	1.35977	+	0.535441i
$157$	585930.	−	585930.i	0.151407	−	0.151407i	−0.627339	−	0.778746i	$-0.715856\pi$
$157$	585930.	−	585930.i	0.151407	−	0.151407i	0.778746	+	0.627339i	$0.215856\pi$
$158$	746702.	+	244431.i	0.189311	+	0.0619704i
$159$	555252.	+	2.10778e6i	0.138133	+	0.524364i
$160$	1.14878e6	−	3.93161e6i	0.280464	−	0.959865i
$161$			840592.i			0.201422i
$162$	3.21320e6	−	2.78404e6i	0.755774	−	0.654832i
$163$	1.88922e6	−	1.88922e6i	0.436234	−	0.436234i	−0.454508	−	0.890742i	$-0.650185\pi$
$163$	1.88922e6	−	1.88922e6i	0.436234	−	0.436234i	0.890742	+	0.454508i	$0.150185\pi$
$164$	1.43233e6	−	1.95335e6i	0.324722	−	0.442843i
$165$	−5.70381e6	+	5.52712e6i	−1.26973	+	1.23040i
$166$	−861660.	−	1.70031e6i	−0.188370	−	0.371710i
$167$	5.02155e6	−	5.02155e6i	1.07817	−	1.07817i	0.0815004	−	0.996673i	$-0.474029\pi$
$167$	5.02155e6	−	5.02155e6i	1.07817	−	1.07817i	0.996673	−	0.0815004i	$-0.0259712\pi$
$168$	2.77209e6	+	2.29481e6i	0.584628	+	0.483971i
$169$			5.48164e6i			1.13567i
$170$	−1.29183e6	−	6.51533e6i	−0.262940	−	1.32614i
$171$	−1.38648e6	−	2.44898e6i	−0.277285	−	0.489775i
$172$	−5.73157e6	+	882032.i	−1.12639	+	0.173340i
$173$	−1.87442e6	+	1.87442e6i	−0.362016	+	0.362016i	−0.864555	−	0.502538i	$-0.832400\pi$
$173$	−1.87442e6	+	1.87442e6i	−0.362016	+	0.362016i	0.502538	+	0.864555i	$0.332400\pi$
$174$	435452.	−	387054.i	0.0826595	−	0.0734724i
$175$	962045.	+	3.95214e6i	0.179507	+	0.737425i
$176$	2.89812e6	+	9.19320e6i	0.531591	+	1.68628i
$177$	−1.24367e6	−	725047.i	−0.224276	−	0.130751i
$178$	1.87267e6	+	613012.i	0.332048	+	0.108695i
$179$			4.65406e6i			0.811470i	0.913991	+	0.405735i	$0.132984\pi$
$179$			4.65406e6i			0.811470i	−0.913991	+	0.405735i	$0.867016\pi$
$180$	2.22189e6	−	5.39216e6i	0.380982	−	0.924582i
$181$	5.34208e6			0.900897			0.450448	−	0.892803i	$-0.351264\pi$
$181$	5.34208e6			0.900897			0.450448	+	0.892803i	$0.351264\pi$
$182$	−2.08019e6	+	6.35469e6i	−0.345055	+	1.05410i
$183$	−2.67650e6	+	4.59097e6i	−0.436731	+	0.749120i
$184$	269369.	−	1.63118e6i	0.0432408	−	0.261847i
$185$	−1.01837e7	+	5.72433e6i	−1.60839	+	0.904086i
$186$	3.23659e6	+	3.64130e6i	0.502978	+	0.565871i
$187$	1.10529e7	+	1.10529e7i	1.69025	+	1.69025i
$188$	−4.84402e6	+	745447.i	−0.729009	+	0.112187i
$189$	3.57700e6	+	3.66876e6i	0.529826	+	0.543417i
$190$	−3.20847e6	−	2.14668e6i	−0.467776	−	0.312973i
$191$	−5.28213e6			−0.758070			−0.379035	−	0.925382i	$-0.623744\pi$
$191$	−5.28213e6			−0.758070			−0.379035	+	0.925382i	$0.623744\pi$
$192$	−4.64389e6	−	5.34142e6i	−0.656112	−	0.754664i
$193$	−1.36792e6	−	1.36792e6i	−0.190278	−	0.190278i	0.605538	−	0.795816i	$-0.292958\pi$
$193$	−1.36792e6	−	1.36792e6i	−0.190278	−	0.190278i	−0.795816	+	0.605538i	$0.792958\pi$
$194$	−3.78239e6	+	1.91678e6i	−0.518037	+	0.262523i
$195$	1.08347e7	+	170451.i	1.46121	+	0.0229877i
$196$	1.88775e6	−	2.57444e6i	0.250713	−	0.341912i
$197$	6.46113e6	+	6.46113e6i	0.845104	+	0.845104i	0.989517	−	0.144414i	$-0.0461296\pi$
$197$	6.46113e6	+	6.46113e6i	0.845104	+	0.845104i	−0.144414	+	0.989517i	$0.546130\pi$
$198$	2.71056e6	+	1.34542e7i	0.349191	+	1.73326i
$199$	1.70321e6			0.216127			0.108063	−	0.994144i	$-0.465535\pi$
$199$	1.70321e6			0.216127			0.108063	+	0.994144i	$0.465535\pi$
$200$	−600389.	−	7.97744e6i	−0.0750486	−	0.997180i
$201$	−6.34907e6	+	1.67254e6i	−0.781847	+	0.205962i
$202$	877215.	−	2.67977e6i	0.106427	−	0.325120i
$203$	496499.	+	496499.i	0.0593513	+	0.0593513i
$204$	−1.06795e7	−	4.20531e6i	−1.25794	−	0.495345i
$205$	1.27696e6	−	4.55531e6i	0.148223	−	0.528757i
$206$	9.44311e6	−	4.78544e6i	1.08022	−	0.547420i
$207$	628425.	−	2.26853e6i	0.0708504	−	0.255761i
$208$	6.07299e6	−	1.16647e7i	0.674858	−	1.29624i
$209$	9.08471e6			0.995112
$210$	6.64470e6	+	2.29146e6i	0.717493	+	0.247431i
$211$			1.02333e6i			0.108936i	0.998516	+	0.0544678i	$0.0173462\pi$
$211$			1.02333e6i			0.108936i	−0.998516	+	0.0544678i	$0.982654\pi$
$212$	5.10655e6	−	785847.i	0.535945	−	0.0824765i
$213$	−2.61761e6	+	4.48995e6i	−0.270873	+	0.464625i
$214$	−6.10886e6	+	3.09576e6i	−0.623331	+	0.315883i
$215$	−9.87336e6	+	5.54986e6i	−0.993458	+	0.558427i
$216$	−5.76554e6	−	8.26550e6i	−0.572109	−	0.820178i
$217$	−4.15178e6	+	4.15178e6i	−0.406308	+	0.406308i
$218$	−4.59858e6	+	1.40480e7i	−0.443868	+	1.35596i
$219$	4.91222e6	−	1.29403e6i	0.467676	−	0.123200i
$220$	1.16138e7	+	1.48175e7i	1.09071	+	1.39157i
$221$		−	2.13258e7i		−	1.97574i
$222$	−1.18580e6	+	2.01522e7i	−0.108381	+	1.84189i
$223$	7.87690e6	−	7.87690e6i	0.710298	−	0.710298i	−0.256300	−	0.966597i	$-0.582503\pi$
$223$	7.87690e6	−	7.87690e6i	0.710298	−	0.710298i	0.966597	+	0.256300i	$0.0825034\pi$
$224$	6.09760e6	−	5.96528e6i	0.542519	−	0.530746i
$225$	358305.	−	1.13850e7i	0.0314561	−	0.999505i
$226$	−1.10352e7	+	5.59228e6i	−0.955997	+	0.484466i
$227$	1.50071e7	−	1.50071e7i	1.28298	−	1.28298i	0.344013	−	0.938965i	$-0.388213\pi$
$227$	1.50071e7	−	1.50071e7i	1.28298	−	1.28298i	0.938965	−	0.344013i	$-0.111787\pi$
$228$	−6.11716e6	+	2.66068e6i	−0.516113	+	0.224485i
$229$		−	5.29136e6i		−	0.440616i	−0.975430	−	0.220308i	$-0.929294\pi$
$229$		−	5.29136e6i		−	0.440616i	0.975430	−	0.220308i	$-0.0707063\pi$
$230$	−628011.	−	3.16738e6i	−0.0516159	−	0.260325i
$231$	−1.59951e7	+	4.21360e6i	−1.29763	+	0.341835i
$232$	−804356.	−	1.12256e6i	−0.0644146	−	0.0898974i
$233$	811098.	−	811098.i	0.0641218	−	0.0641218i	−0.674319	−	0.738440i	$-0.735563\pi$
$233$	811098.	−	811098.i	0.0641218	−	0.0641218i	0.738440	+	0.674319i	$0.235563\pi$
$234$	1.03646e7	−	1.55945e7i	0.808921	−	1.21709i
$235$	−8.34444e6	+	4.69045e6i	−0.642974	+	0.361419i
$236$	−2.01782e6	+	2.75182e6i	−0.153513	+	0.209355i
$237$	1.33554e6	−	2.29083e6i	0.100325	−	0.172087i
$238$	4.30344e6	−	1.31464e7i	0.319216	−	0.975161i
$239$			1.56676e7i			1.14765i	0.818978	+	0.573825i	$0.194541\pi$
$239$			1.56676e7i			1.14765i	−0.818978	+	0.573825i	$0.805459\pi$
$240$	−1.21598e7	−	6.57589e6i	−0.879615	−	0.475687i
$241$	−5.28746e6			−0.377743			−0.188871	−	0.982002i	$-0.560483\pi$
$241$	−5.28746e6			−0.377743			−0.188871	+	0.982002i	$0.560483\pi$
$242$	−2.86371e7	−	9.37425e6i	−2.02061	−	0.661440i
$243$	−6.91062e6	−	1.25752e7i	−0.481613	−	0.876384i
$244$	1.01583e7	+	7.44874e6i	0.699280	+	0.512759i
$245$	1.68298e6	−	6.00370e6i	0.114441	−	0.408245i
$246$	−5.43106e6	−	6.11017e6i	−0.364821	−	0.410439i
$247$	−8.76419e6	−	8.76419e6i	−0.581596	−	0.581596i
$248$	9.38700e6	−	6.72612e6i	0.615420	−	0.440970i
$249$	−6.22112e6	+	1.63883e6i	−0.402968	+	0.106154i
$250$	−6.57768e6	−	1.41730e7i	−0.420972	−	0.907074i
$251$	10433.5			0.000659796			0.000329898	−	1.00000i	$-0.499895\pi$
$251$	10433.5			0.000659796			0.000329898		1.00000i	$0.499895\pi$
$252$	9.53620e6	−	7.52177e6i	0.595901	−	0.470022i
$253$	5.37327e6	+	5.37327e6i	0.331801	+	0.331801i
$254$	6.71175e6	+	1.32443e7i	0.409576	+	0.808217i
$255$	−2.24145e7	−	352624.i	−1.35179	−	0.0212663i
$256$	−1.37440e7	+	9.62169e6i	−0.819207	+	0.573497i
$257$	1.41249e7	+	1.41249e7i	0.832119	+	0.832119i	0.987806	−	0.155687i	$-0.0497591\pi$
$257$	1.41249e7	+	1.41249e7i	0.832119	+	0.832119i	−0.155687	+	0.987806i	$0.549759\pi$
$258$	−1.14966e6	+	1.95380e7i	−0.0669438	+	1.13768i
$259$	−2.43294e7			−1.40034
$260$	3.09059e6	−	2.54988e7i	0.175841	−	1.45077i
$261$	−968737.	−	1.71110e6i	−0.0544859	−	0.0962396i
$262$	140560.	+	46011.7i	0.00781549	+	0.00255838i
$263$	−1.01250e7	−	1.01250e7i	−0.556581	−	0.556581i	0.371751	−	0.928332i	$-0.378757\pi$
$263$	−1.01250e7	−	1.01250e7i	−0.556581	−	0.556581i	−0.928332	+	0.371751i	$0.878757\pi$
$264$	3.23889e7	−	3.05086e6i	1.76029	−	0.165810i
$265$	8.79667e6	−	4.94465e6i	0.472695	−	0.265704i
$266$	−3.63416e6	−	7.17129e6i	−0.193090	−	0.381024i
$267$	3.34941e6	−	5.74521e6i	0.175968	−	0.301837i
$268$	2.36714e6	+	1.53820e7i	0.122976	+	0.799113i
$269$	−2.33761e7			−1.20092			−0.600462	−	0.799653i	$-0.705017\pi$
$269$	−2.33761e7			−1.20092			−0.600462	+	0.799653i	$0.705017\pi$
$270$	−1.62192e7	−	1.11516e7i	−0.824021	−	0.566560i
$271$		−	2.65528e7i		−	1.33414i	−0.744994	−	0.667071i	$-0.767548\pi$
$271$		−	2.65528e7i		−	1.33414i	0.744994	−	0.667071i	$-0.232452\pi$
$272$	−1.25636e7	+	2.41317e7i	−0.624322	+	1.19917i
$273$	1.94957e7	+	1.13659e7i	0.958190	+	0.558617i
$274$	1.10980e7	+	2.18997e7i	0.539503	+	1.06460i
$275$	3.14126e7	+	1.91134e7i	1.51045	+	0.919051i
$276$	−5.19176e6	−	2.04438e6i	−0.246938	−	0.0972377i
$277$	5.65965e6	−	5.65965e6i	0.266287	−	0.266287i	−0.561315	−	0.827602i	$-0.689704\pi$
$277$	5.65965e6	−	5.65965e6i	0.266287	−	0.266287i	0.827602	+	0.561315i	$0.189704\pi$
$278$	1.50322e7	+	4.92075e6i	0.699663	+	0.229032i
$279$	1.43084e7	−	8.10069e6i	0.658838	−	0.373000i
$280$	7.05072e6	−	1.50952e7i	0.321188	−	0.687646i
$281$		−	1.40720e7i		−	0.634215i	−0.948390	−	0.317107i	$-0.897288\pi$
$281$		−	1.40720e7i		−	0.634215i	0.948390	−	0.317107i	$-0.102712\pi$
$282$	−971632.	+	1.65125e7i	−0.0433266	+	0.736317i
$283$	7.02592e6	−	7.02592e6i	0.309987	−	0.309987i	−0.534917	−	0.844904i	$-0.679657\pi$
$283$	7.02592e6	−	7.02592e6i	0.309987	−	0.309987i	0.844904	+	0.534917i	$0.179657\pi$
$284$	9.93477e6	+	7.28484e6i	0.433713	+	0.318028i
$285$	−9.35652e6	+	9.06669e6i	−0.404185	+	0.391664i
$286$	2.73237e7	+	5.39178e7i	1.16799	+	2.30480i
$287$	6.96677e6	−	6.96677e6i	0.294704	−	0.294704i
$288$	−2.09154e7	+	1.15402e7i	−0.875567	+	0.483097i
$289$			1.99807e7i			0.827786i
$290$	−2.24176e6	−	1.49989e6i	−0.0919169	−	0.0614985i
$291$	3.64562e6	+	1.38390e7i	0.147942	+	0.561599i
$292$	−1.83143e6	−	1.19009e7i	−0.0735601	−	0.478004i
$293$	1.00254e6	−	1.00254e6i	0.0398566	−	0.0398566i	−0.686898	−	0.726754i	$-0.741028\pi$
$293$	1.00254e6	−	1.00254e6i	0.0398566	−	0.0398566i	0.726754	+	0.686898i	$0.241028\pi$
$294$	−7.15791e6	−	8.05295e6i	−0.281672	−	0.316893i
$295$	−1.79894e6	+	6.41736e6i	−0.0700729	+	0.249971i
$296$	4.72114e7	+	7.79638e6i	1.82042	+	0.300620i
$297$	4.63166e7	+	586534.i	1.76794	+	0.0223884i
$298$	1.11204e7	+	3.64023e6i	0.420216	+	0.137556i
$299$		−	1.03674e7i		−	0.387843i
$300$	−2.67494e7	−	3.66999e6i	−0.990719	−	0.135925i
$301$	−2.35879e7			−0.864946
$302$	8.41959e6	−	2.57207e7i	0.305682	−	0.933818i
$303$	−8.22135e6	−	4.79298e6i	−0.295539	−	0.172297i
$304$	4.75407e6	+	1.50805e7i	0.169217	+	0.536779i
$305$	2.36896e7	+	6.64076e6i	0.834945	+	0.234055i
$306$	−2.14421e7	+	3.22614e7i	−0.748346	+	1.12595i
$307$	−3.58358e7	−	3.58358e7i	−1.23852	−	1.23852i	−0.960607	−	0.277911i	$-0.910358\pi$
$307$	−3.58358e7	−	3.58358e7i	−1.23852	−	1.23852i	−0.277911	−	0.960607i	$-0.589642\pi$
$308$	5.96349e6	+	3.87516e7i	0.204103	+	1.32629i
$309$	−9.10166e6	−	3.45505e7i	−0.308493	−	1.17106i
$310$	1.25422e7	−	1.87459e7i	0.421007	−	0.629246i
$311$	−3.94772e7			−1.31240			−0.656199	−	0.754588i	$-0.727837\pi$
$311$	−3.94772e7			−1.31240			−0.656199	+	0.754588i	$0.727837\pi$
$312$	−3.41894e7	−	2.83030e7i	−1.12571	−	0.931898i
$313$	−2.68047e7	−	2.68047e7i	−0.874133	−	0.874133i	0.118787	−	0.992920i	$-0.462099\pi$
$313$	−2.68047e7	−	2.68047e7i	−0.874133	−	0.874133i	−0.992920	+	0.118787i	$0.962099\pi$
$314$	−5.91311e6	+	2.99656e6i	−0.190997	+	0.0967907i
$315$	1.22685e7	−	2.03031e7i	0.392517	−	0.649576i
$316$	−5.06884e6	−	3.71682e6i	−0.160638	−	0.117790i
$317$	1.99404e6	+	1.99404e6i	0.0625974	+	0.0625974i	0.737712	−	0.675115i	$-0.235906\pi$
$317$	1.99404e6	+	1.99404e6i	0.0625974	+	0.0625974i	−0.675115	+	0.737712i	$0.735906\pi$
$318$	1.02429e6	−	1.74074e7i	0.0318524	−	0.541317i
$319$	6.34749e6			0.195537
$320$	−1.85193e7	+	2.70329e7i	−0.565163	+	0.824979i
$321$	5.88797e6	+	2.23512e7i	0.178013	+	0.675748i
$322$	2.09208e6	−	6.39103e6i	0.0626630	−	0.191427i
$323$	1.81311e7	+	1.81311e7i	0.538043	+	0.538043i
$324$	−3.13589e7	+	1.31700e7i	−0.921990	+	0.387214i
$325$	−1.18653e7	−	4.87435e7i	−0.345645	−	1.41993i
$326$	−1.90657e7	+	9.66183e6i	−0.550300	+	0.278873i
$327$	4.30984e7	+	2.51260e7i	1.23259	+	0.718589i
$328$	−1.57516e7	+	1.12866e7i	−0.446378	+	0.319845i
$329$	−1.99352e7			−0.559801
$330$	5.71221e7	−	2.78270e7i	1.58951	−	0.774328i
$331$			6.09636e7i			1.68107i	0.541754	+	0.840537i	$0.317760\pi$
$331$			6.09636e7i			1.68107i	−0.541754	+	0.840537i	$0.682240\pi$
$332$	2.31943e6	+	1.50720e7i	0.0633822	+	0.411867i
$333$	6.56586e7	+	1.81886e7i	1.77811	+	0.492569i
$334$	−5.06767e7	+	2.56812e7i	−1.36009	+	0.689248i
$335$	1.48943e7	+	2.64974e7i	0.396174	+	0.704805i
$336$	−1.53649e7	−	2.43467e7i	−0.405052	−	0.641834i
$337$	−4.57529e7	+	4.57529e7i	−1.19544	+	1.19544i	−0.219926	+	0.975516i	$0.570582\pi$
$337$	−4.57529e7	+	4.57529e7i	−1.19544	+	1.19544i	−0.975516	+	0.219926i	$0.929418\pi$
$338$	1.36428e7	−	4.16770e7i	0.353308	−	1.07931i
$339$	1.06362e7	+	4.03758e7i	0.273016	+	1.03639i
$340$	−6.39372e6	+	5.27512e7i	−0.162674	+	1.34213i
$341$			5.30784e7i			1.33861i
$342$	4.44640e6	+	2.20703e7i	0.111155	+	0.551734i
$343$	3.08383e7	−	3.08383e7i	0.764201	−	0.764201i
$344$	4.57724e7	+	7.55876e6i	1.12442	+	0.185684i
$345$	−1.08967e7	−	171426.i	−0.265360	−	0.00417463i
$346$	1.89163e7	−	9.58613e6i	0.456676	−	0.231428i
$347$	3.11634e7	−	3.11634e7i	0.745859	−	0.745859i	−0.227840	−	0.973699i	$-0.573166\pi$
$347$	3.11634e7	−	3.11634e7i	0.745859	−	0.745859i	0.973699	+	0.227840i	$0.0731663\pi$
$348$	−4.27406e6	+	1.85901e6i	−0.101415	+	0.0441108i
$349$			1.66436e7i			0.391535i	0.980650	+	0.195768i	$0.0627199\pi$
$349$			1.66436e7i			0.391535i	−0.980650	+	0.195768i	$0.937280\pi$
$350$	2.52172e6	−	3.24425e7i	0.0588156	−	0.756676i
$351$	−4.41167e7	−	4.52484e7i	−1.02019	−	1.04636i
$352$	845806.	−	7.71089e7i	0.0193929	−	1.76798i
$353$	1.88956e7	−	1.88956e7i	0.429572	−	0.429572i	−0.458911	−	0.888482i	$-0.651760\pi$
$353$	1.88956e7	−	1.88956e7i	0.429572	−	0.429572i	0.888482	+	0.458911i	$0.151760\pi$
$354$	7.65109e6	+	8.60780e6i	0.172470	+	0.194036i
$355$	2.31683e7	+	6.49463e6i	0.517856	+	0.145168i
$356$	−1.27122e7	−	9.32147e6i	−0.281755	−	0.206602i
$357$	−4.03323e7	−	2.35134e7i	−0.886437	−	0.516786i
$358$	1.15831e7	−	3.53848e7i	0.252450	−	0.771202i
$359$			5.67728e6i			0.122704i	0.998116	+	0.0613518i	$0.0195411\pi$
$359$			5.67728e6i			0.122704i	−0.998116	+	0.0613518i	$0.980459\pi$
$360$	−3.03132e7	+	3.54668e7i	−0.649716	+	0.760177i
$361$	−3.21433e7			−0.683234
$362$	−4.06159e7	−	1.32955e7i	−0.856191	−	0.280271i
$363$	−5.12196e7	+	8.78565e7i	−1.07082	+	1.83677i
$364$	3.16314e7	−	4.31376e7i	0.655864	−	0.894441i
$365$	−1.15236e7	−	2.05008e7i	−0.236979	−	0.421592i
$366$	3.17756e7	−	2.82439e7i	0.648112	−	0.576078i
$367$	4.01203e6	+	4.01203e6i	0.0811645	+	0.0811645i	0.746524	−	0.665359i	$-0.231722\pi$
$367$	4.01203e6	+	4.01203e6i	0.0811645	+	0.0811645i	−0.665359	+	0.746524i	$0.731722\pi$
$368$	−6.10772e6	+	1.17314e7i	−0.122556	+	0.235401i
$369$	−2.40098e7	+	1.35931e7i	−0.477869	+	0.270545i
$370$	9.16740e7	−	1.81766e7i	1.80984	−	0.358846i
$371$	2.10156e7			0.411548
$372$	−1.55453e7	−	3.57401e7i	−0.301974	−	0.694268i
$373$	1.07248e7	+	1.07248e7i	0.206663	+	0.206663i	0.802847	−	0.596185i	$-0.203317\pi$
$373$	1.07248e7	+	1.07248e7i	0.206663	+	0.206663i	−0.596185	+	0.802847i	$0.703317\pi$
$374$	−5.65265e7	−	1.11544e8i	−1.08053	−	2.13221i
$375$	−5.14280e7	+	1.16651e7i	−0.975227	+	0.221204i
$376$	3.86845e7	+	6.38827e6i	0.727734	+	0.120176i
$377$	−6.12354e6	−	6.12354e6i	−0.114282	−	0.114282i
$378$	−1.80651e7	−	3.67961e7i	−0.334476	−	0.681281i
$379$	6.22464e7			1.14340			0.571698	−	0.820464i	$-0.306285\pi$
$379$	6.22464e7			1.14340			0.571698	+	0.820464i	$0.306285\pi$
$380$	1.90514e7	+	2.43066e7i	0.347196	+	0.442968i
$381$	4.84583e7	−	1.27654e7i	0.876180	−	0.230812i
$382$	4.01601e7	+	1.31463e7i	0.720451	+	0.235837i
$383$	−7.87666e7	−	7.87666e7i	−1.40199	−	1.40199i	−0.793752	−	0.608242i	$-0.791875\pi$
$383$	−7.87666e7	−	7.87666e7i	−1.40199	−	1.40199i	−0.608242	−	0.793752i	$-0.708125\pi$
$384$	2.20137e7	+	5.21687e7i	0.388775	+	0.921333i
$385$	3.75231e7	+	6.67546e7i	0.657531	+	1.16977i
$386$	6.99579e6	+	1.38048e7i	0.121639	+	0.240031i
$387$	6.36574e7	+	1.76342e7i	1.09829	+	0.304245i
$388$	3.35281e7	−	5.15964e6i	0.574002	−	0.0883332i
$389$	−1.97424e7			−0.335391			−0.167696	−	0.985839i	$-0.553633\pi$
$389$	−1.97424e7			−0.335391			−0.167696	+	0.985839i	$0.553633\pi$
$390$	−8.19521e7	−	2.82616e7i	−1.38155	−	0.476433i
$391$			2.14478e7i			0.358800i
$392$	−2.07599e7	+	1.48752e7i	−0.344641	+	0.246947i
$393$	251402.	−	431227.i	0.00414181	−	0.00710441i
$394$	−3.30435e7	−	6.52047e7i	−0.540253	−	1.06608i
$395$	−1.18208e7	−	3.31364e6i	−0.191802	−	0.0537668i
$396$	1.28768e7	−	1.09039e8i	0.207358	−	1.75588i
$397$	−1.58649e7	+	1.58649e7i	−0.253551	+	0.253551i	−0.822425	−	0.568874i	$-0.807379\pi$
$397$	−1.58649e7	+	1.58649e7i	−0.253551	+	0.253551i	0.568874	+	0.822425i	$0.307379\pi$
$398$	−1.29495e7	−	4.23898e6i	−0.205402	−	0.0672376i
$399$	−2.62384e7	+	6.91199e6i	−0.413065	+	0.108814i
$400$	−1.52897e7	+	6.21468e7i	−0.238901	+	0.971044i
$401$		−	1.11278e8i		−	1.72574i	−0.505424	−	0.862871i	$-0.668664\pi$
$401$		−	1.11278e8i		−	1.72574i	0.505424	−	0.862871i	$-0.331336\pi$
$402$	5.24347e7	+	3.08538e6i	0.807124	+	0.0474930i
$403$	5.12057e7	−	5.12057e7i	0.782354	−	0.782354i
$404$	−1.33389e7	+	1.81911e7i	−0.202291	+	0.275877i
$405$	−4.82878e7	+	4.56207e7i	−0.726896	+	0.686747i
$406$	−2.53919e6	−	5.01059e6i	−0.0379417	−	0.0748704i
$407$	−1.55519e8	+	1.55519e8i	−2.30675	+	2.30675i
$408$	7.07302e7	+	5.85524e7i	1.04142	+	0.862113i
$409$		−	1.64808e7i		−	0.240884i	−0.992720	−	0.120442i	$-0.961569\pi$
$409$		−	1.64808e7i		−	0.240884i	0.992720	−	0.120442i	$-0.0384312\pi$
$410$	−2.10461e7	+	3.14559e7i	−0.305365	+	0.456405i
$411$	8.01269e7	−	2.11079e7i	1.15413	−	0.304032i
$412$	−8.37062e7	+	1.28816e7i	−1.19692	+	0.184194i
$413$	−9.81454e6	+	9.81454e6i	−0.139322	+	0.139322i
$414$	−1.04239e7	+	1.56837e7i	−0.146902	+	0.221028i
$415$	1.45942e7	+	2.59634e7i	0.204190	+	0.363260i
$416$	−7.52044e7	+	7.35725e7i	−1.04463	+	1.02196i
$417$	2.68863e7	−	4.61178e7i	0.370786	−	0.636005i
$418$	−6.90711e7	−	2.26102e7i	−0.945731	−	0.309582i
$419$		−	8.45800e7i		−	1.14981i	−0.818221	−	0.574904i	$-0.805039\pi$
$419$		−	8.45800e7i		−	1.14981i	0.818221	−	0.574904i	$-0.194961\pi$
$420$	−4.48167e7	−	3.39594e7i	−0.604912	−	0.458366i
$421$	−2.05928e7			−0.275975			−0.137987	−	0.990434i	$-0.544063\pi$
$421$	−2.05928e7			−0.275975			−0.137987	+	0.990434i	$0.544063\pi$
$422$	2.54689e6	−	7.78041e6i	0.0338901	−	0.103530i
$423$	5.37999e7	+	1.49035e7i	0.710821	+	0.196910i
$424$	−4.07810e7	−	6.73448e6i	−0.535008	−	0.0883500i
$425$	2.45467e7	+	1.00839e8i	0.319761	+	1.31360i
$426$	3.10764e7	−	2.76224e7i	0.401977	−	0.357300i
$427$	3.62302e7	+	3.62302e7i	0.465358	+	0.465358i
$428$	5.41505e7	−	8.33323e6i	0.690671	−	0.106287i
$429$	1.97275e8	−	5.19682e7i	2.49862	−	0.658212i
$430$	8.88798e7	−	1.76226e7i	1.11789	−	0.221649i
$431$	2.37282e6			0.0296369			0.0148185	−	0.999890i	$-0.495283\pi$
$431$	2.37282e6			0.0296369			0.0148185	+	0.999890i	$0.495283\pi$
$432$	2.32641e7	+	7.71921e7i	0.288559	+	0.957462i
$433$	−9.53949e7	−	9.53949e7i	−1.17506	−	1.17506i	−0.980986	−	0.194078i	$-0.937828\pi$
$433$	−9.53949e7	−	9.53949e7i	−1.17506	−	1.17506i	−0.194078	−	0.980986i	$-0.562172\pi$
$434$	4.18991e7	−	2.12330e7i	0.512549	−	0.259742i
$435$	−6.53740e6	+	6.33490e6i	−0.0794214	+	0.0769612i
$436$	6.99261e7	−	9.53624e7i	0.843684	−	1.15058i
$437$	8.81431e6	+	8.81431e6i	0.105620	+	0.105620i
$438$	−4.05682e7	−	2.38713e6i	−0.482796	−	0.0284089i
$439$	−1.53091e8			−1.80950			−0.904748	−	0.425948i	$-0.859941\pi$
$439$	−1.53091e8			−1.80950			−0.904748	+	0.425948i	$0.859941\pi$
$440$	−5.14222e7	−	1.41562e8i	−0.603660	−	1.66184i
$441$	−3.16439e7	+	1.79151e7i	−0.368955	+	0.208884i
$442$	−5.30762e7	+	1.62141e8i	−0.614657	+	1.87769i
$443$	6.96612e7	+	6.96612e7i	0.801272	+	0.801272i	0.983294	−	0.182023i	$-0.0582644\pi$
$443$	6.96612e7	+	6.96612e7i	0.801272	+	0.801272i	−0.182023	+	0.983294i	$0.558264\pi$
$444$	5.91709e7	−	1.50266e8i	0.676019	−	1.71677i
$445$	−2.96455e7	−	8.31034e6i	−0.336417	−	0.0943059i
$446$	−7.94923e7	+	4.02839e7i	−0.896026	+	0.454075i
$447$	1.98897e7	−	3.41166e7i	0.222693	−	0.381983i
$448$	−6.12066e7	+	3.01783e7i	−0.680714	+	0.335630i
$449$	−3.67936e7			−0.406475			−0.203237	−	0.979130i	$-0.565146\pi$
$449$	−3.67936e7			−0.406475			−0.203237	+	0.979130i	$0.565146\pi$
$450$	−3.10594e7	+	8.56684e7i	−0.340844	+	0.940120i
$451$		−	8.90665e7i		−	0.970923i
$452$	9.78193e7	−	1.50534e7i	1.05928	−	0.163012i
$453$	−7.89093e7	−	4.60035e7i	−0.848856	−	0.494876i
$454$	−1.51449e8	+	7.67492e7i	−1.61845	+	0.820174i
$455$	2.82002e7	−	1.00599e8i	0.299377	−	1.06797i
$456$	5.31307e7	−	5.00464e6i	0.560340	−	0.0527811i
$457$	7.62570e7	−	7.62570e7i	0.798972	−	0.798972i	−0.183962	−	0.982933i	$-0.558892\pi$
$457$	7.62570e7	−	7.62570e7i	0.798972	−	0.798972i	0.982933	+	0.183962i	$0.0588923\pi$
$458$	−1.31692e7	+	4.02302e7i	−0.137077	+	0.418751i
$459$	9.12675e7	+	9.36087e7i	0.943796	+	0.968006i
$460$	−3.10826e6	+	2.56446e7i	−0.0319333	+	0.263465i
$461$			3.58091e7i			0.365502i	0.983159	+	0.182751i	$0.0585003\pi$
$461$			3.58091e7i			0.365502i	−0.983159	+	0.182751i	$0.941500\pi$
$462$	1.32098e8	+	7.77295e6i	1.33958	+	0.0788243i
$463$	−7.00005e7	+	7.00005e7i	−0.705274	+	0.705274i	−0.965538	−	0.260263i	$-0.916191\pi$
$463$	−7.00005e7	+	7.00005e7i	−0.705274	+	0.705274i	0.260263	+	0.965538i	$0.416191\pi$
$464$	3.32167e6	+	1.05368e7i	0.0332508	+	0.105476i
$465$	−5.29731e7	−	5.46665e7i	−0.526862	−	0.543704i
$466$	−8.18547e6	+	4.14811e6i	−0.0808883	+	0.0409914i
$467$	7.61982e7	−	7.61982e7i	0.748159	−	0.748159i	−0.225974	−	0.974133i	$-0.572557\pi$
$467$	7.61982e7	−	7.61982e7i	0.748159	−	0.748159i	0.974133	+	0.225974i	$0.0725565\pi$
$468$	−1.17614e8	+	9.27693e7i	−1.14742	+	0.905038i
$469$			6.33035e7i			0.613633i
$470$	7.51166e7	−	1.48937e7i	0.723506	−	0.143453i
$471$	5.69929e6	+	2.16349e7i	0.0545454	+	0.207058i
$472$	2.21903e7	−	1.59001e7i	0.211026	−	0.151208i
$473$	−1.50779e8	+	1.50779e8i	−1.42482	+	1.42482i
$474$	−1.58556e7	+	1.40933e7i	−0.148883	+	0.132336i
$475$	5.15293e7	+	3.13536e7i	0.480810	+	0.292554i
$476$	−6.54381e7	+	8.92418e7i	−0.606750	+	0.827461i
$477$	−5.67156e7	−	1.57112e7i	−0.522573	−	0.144762i
$478$	3.89939e7	−	1.19121e8i	0.357037	−	1.09070i
$479$		−	5.34280e7i		−	0.486141i	−0.970009	−	0.243071i	$-0.921845\pi$
$479$		−	5.34280e7i		−	0.486141i	0.970009	−	0.243071i	$-0.0781547\pi$
$480$	7.60848e7	+	8.02601e7i	0.687978	+	0.725732i
$481$	3.00065e8			2.69638
$482$	4.02006e7	+	1.31595e7i	0.358998	+	0.117517i
$483$	−1.96072e7	−	1.14309e7i	−0.174010	−	0.101447i
$484$	1.94397e8	+	1.42545e8i	1.71456	+	1.25723i
$485$	5.77563e7	−	3.24651e7i	0.506261	−	0.284572i
$486$	2.12442e7	+	1.12808e8i	0.185068	+	0.982726i
$487$	−8.64937e7	−	8.64937e7i	−0.748855	−	0.748855i	0.225409	−	0.974264i	$-0.427628\pi$
$487$	−8.64937e7	−	8.64937e7i	−0.748855	−	0.748855i	−0.974264	+	0.225409i	$0.927628\pi$
$488$	−5.86950e7	−	8.19150e7i	−0.505059	−	0.704862i
$489$	1.83763e7	+	6.97577e7i	0.157156	+	0.596575i
$490$	−2.77378e7	+	4.14575e7i	−0.235768	+	0.352383i
$491$	1.94012e8			1.63902			0.819512	−	0.573063i	$-0.194245\pi$
$491$	1.94012e8			1.63902			0.819512	+	0.573063i	$0.194245\pi$
$492$	2.60853e7	+	5.99727e7i	0.219028	+	0.503568i
$493$	1.26682e7	+	1.26682e7i	0.105724	+	0.105724i
$494$	4.48218e7	+	8.84468e7i	0.371799	+	0.733671i
$495$	−5.13592e7	−	2.08205e8i	−0.423450	−	1.71663i
$496$	−8.81096e7	+	2.77762e7i	−0.722068	+	0.227629i
$497$	3.54330e7	+	3.54330e7i	0.288628	+	0.288628i
$498$	5.13780e7	+	3.02320e6i	0.415996	+	0.0244782i
$499$	−2.03492e8			−1.63774			−0.818872	−	0.573976i	$-0.805400\pi$
$499$	−2.03492e8			−1.63774			−0.818872	+	0.573976i	$0.805400\pi$
$500$	1.47360e7	+	1.24128e8i	0.117888	+	0.993027i
$501$	4.88442e7	+	1.85416e8i	0.388419	+	1.47447i
$502$	−79326.2	−	25967.2i	−0.000627055	−	0.000205264i
$503$	−1.69271e7	−	1.69271e7i	−0.133008	−	0.133008i	0.637468	−	0.770477i	$-0.279982\pi$
$503$	−1.69271e7	−	1.69271e7i	−0.133008	−	0.133008i	−0.770477	+	0.637468i	$0.779982\pi$
$504$	−9.12242e7	+	3.34542e7i	−0.712555	+	0.261312i
$505$	−1.18920e7	+	4.24225e7i	−0.0923383	+	0.329399i
$506$	−2.74799e7	−	5.42261e7i	−0.212111	−	0.418559i
$507$	−1.27862e8	−	7.45425e7i	−0.981109	−	0.571979i
$508$	−1.80668e7	−	1.17401e8i	−0.137813	−	0.895530i
$509$	1.50025e8			1.13766			0.568829	−	0.822456i	$-0.307397\pi$
$509$	1.50025e8			1.13766			0.568829	+	0.822456i	$0.307397\pi$
$510$	1.69540e8	+	5.84667e7i	1.27809	+	0.440756i
$511$		−	4.89774e7i		−	0.367056i
$512$	1.28443e8	−	3.89474e7i	0.956972	−	0.290181i
$513$	7.59778e7	+	962151.i	0.562775	+	0.00712674i
$514$	−7.22374e7	−	1.42546e8i	−0.531952	−	1.04970i
$515$	−1.44194e8	+	8.10524e7i	−1.05567	+	0.593395i
$516$	5.73674e7	−	1.45686e8i	0.417557	−	1.06040i
$517$	−1.27431e8	+	1.27431e8i	−0.922153	+	0.922153i
$518$	1.84977e8	+	6.05515e7i	1.33085	+	0.435648i
$519$	−1.82323e7	−	6.92112e7i	−0.130419	−	0.495078i
$520$	−8.69597e7	+	1.86176e8i	−0.618455	+	1.32408i
$521$		−	1.52845e8i		−	1.08078i	−0.841414	−	0.540391i	$-0.818276\pi$
$521$		−	1.52845e8i		−	1.08078i	0.841414	−	0.540391i	$-0.181724\pi$
$522$	3.10670e6	+	1.54205e7i	0.0218418	+	0.108415i
$523$	−8.64864e7	+	8.64864e7i	−0.604564	+	0.604564i	−0.941520	−	0.336956i	$-0.890603\pi$
$523$	−8.64864e7	+	8.64864e7i	−0.604564	+	0.604564i	0.336956	+	0.941520i	$0.390603\pi$
$524$	−954161.	−	699655.i	−0.00663174	−	0.00486284i
$525$	−1.05268e8	−	3.13033e7i	−0.727476	−	0.216327i
$526$	5.17813e7	+	1.02180e8i	0.355808	+	0.702115i
$527$	−1.05933e8	+	1.05933e8i	−0.723768	+	0.723768i
$528$	−2.53846e8	−	5.74144e7i	−1.72452	−	0.390049i
$529$		−	1.37609e8i		−	0.929567i
$530$	−7.91875e7	+	1.57009e7i	−0.531899	+	0.105462i
$531$	3.38242e7	−	1.91495e7i	0.225914	−	0.127901i
$532$	9.78252e6	+	6.35682e7i	0.0649704	+	0.422187i
$533$	−8.59242e7	+	8.59242e7i	−0.567458	+	0.567458i
$534$	−3.97644e7	+	3.53448e7i	−0.261138	+	0.232114i
$535$	9.32811e7	−	5.24338e7i	0.609161	−	0.342412i
$536$	2.02857e7	−	1.22841e8i	0.131733	−	0.797716i
$537$	−1.08558e8	−	6.32885e7i	−0.701035	−	0.408698i
$538$	1.77729e8	+	5.81790e7i	1.14133	+	0.373611i
$539$		−	1.17386e8i		−	0.749635i
$540$	9.55604e7	+	1.25152e8i	0.606871	+	0.794800i
$541$	2.09862e8			1.32539			0.662694	−	0.748891i	$-0.269413\pi$
$541$	2.09862e8			1.32539			0.662694	+	0.748891i	$0.269413\pi$
$542$	−6.60851e7	+	2.01881e8i	−0.415055	+	1.26794i
$543$	−7.26447e7	+	1.24607e8i	−0.453737	+	0.778291i
$544$	1.55581e8	−	1.52205e8i	0.966405	−	0.945435i
$545$	6.23410e7	−	2.22389e8i	0.385110	−	1.37380i
$546$	−1.19939e8	−	1.34936e8i	−0.736854	−	0.828992i
$547$	2.57843e7	+	2.57843e7i	0.157541	+	0.157541i	0.781476	−	0.623935i	$-0.214467\pi$
$547$	2.57843e7	+	2.57843e7i	0.157541	+	0.157541i	−0.623935	+	0.781476i	$0.714467\pi$
$548$	−2.98739e7	−	1.94125e8i	−0.181531	−	1.17961i
$549$	−7.06901e7	−	1.24861e8i	−0.427210	−	0.754590i
$550$	−1.91261e8	−	2.23500e8i	−1.14958	−	1.34335i
$551$	1.04124e7			0.0622439
$552$	3.43849e7	+	2.84648e7i	0.204433	+	0.169235i
$553$	−1.80784e7	−	1.80784e7i	−0.106902	−	0.106902i
$554$	−5.71162e7	+	2.89445e7i	−0.335916	+	0.170230i
$555$	4.96160e6	−	3.15384e8i	0.0290230	−	1.84485i
$556$	−1.02043e8	−	7.48250e7i	−0.593691	−	0.435334i
$557$	−1.34757e8	−	1.34757e8i	−0.779806	−	0.779806i	0.199991	−	0.979798i	$-0.435909\pi$
$557$	−1.34757e8	−	1.34757e8i	−0.779806	−	0.779806i	−0.979798	+	0.199991i	$0.935909\pi$
$558$	−1.28948e8	+	2.59785e7i	−0.742186	+	0.149524i
$559$	2.90920e8			1.66547
$560$	−9.11760e7	+	9.72209e7i	−0.519178	+	0.553600i
$561$	−4.08117e8	+	1.07510e8i	−2.31151	+	0.608922i
$562$	−3.50226e7	+	1.06989e8i	−0.197306	+	0.602743i
$563$	1.94639e8	+	1.94639e8i	1.09070	+	1.09070i	0.995454	+	0.0952475i	$0.0303642\pi$
$563$	1.94639e8	+	1.94639e8i	1.09070	+	1.09070i	0.0952475	+	0.995454i	$0.469636\pi$
$564$	4.84839e7	−	1.23126e8i	0.270247	−	0.686299i
$565$	1.68506e8	−	9.47180e7i	0.934265	−	0.525155i
$566$	−7.09044e7	+	3.59319e7i	−0.391042	+	0.198167i
$567$	−1.34218e8	+	3.35454e7i	−0.736310	+	0.184028i
$568$	−5.74035e7	−	8.01126e7i	−0.313252	−	0.437175i
$569$	9.18882e7			0.498796			0.249398	−	0.968401i	$-0.419767\pi$
$569$	9.18882e7			0.498796			0.249398	+	0.968401i	$0.419767\pi$
$570$	9.37031e7	−	4.56474e7i	0.505975	−	0.246486i
$571$			1.04992e8i			0.563959i	0.959420	+	0.281980i	$0.0909911\pi$
$571$			1.04992e8i			0.563959i	−0.959420	+	0.281980i	$0.909009\pi$
$572$	−7.35504e7	−	4.77941e8i	−0.393004	−	2.55380i
$573$	7.18295e7	−	1.23208e8i	0.381802	−	0.654902i
$574$	−7.03074e7	+	3.56294e7i	−0.371763	+	0.188396i
$575$	1.19332e7	+	4.90222e7i	0.0627701	+	0.257863i
$576$	1.87742e8	−	3.56852e7i	0.982411	−	0.186733i
$577$	2.36441e8	−	2.36441e8i	1.23082	−	1.23082i	0.267177	−	0.963648i	$-0.413909\pi$
$577$	2.36441e8	−	2.36441e8i	1.23082	−	1.23082i	0.963648	−	0.267177i	$-0.0860908\pi$
$578$	4.97285e7	−	1.51914e8i	0.257526	−	0.786708i
$579$	5.05091e7	−	1.33056e7i	0.260216	−	0.0685487i
$580$	1.33112e7	+	1.69830e7i	0.0682233	+	0.0870423i
$581$			6.20278e7i			0.316270i
$582$	6.72518e6	−	1.14292e8i	0.0341142	−	0.579756i
$583$	1.34337e8	−	1.34337e8i	0.677938	−	0.677938i
$584$	−1.56948e7	+	9.50409e7i	−0.0787986	+	0.477169i
$585$	−1.51312e8	+	2.50407e8i	−0.755799	+	1.25077i
$586$	−1.01175e7	+	5.12720e6i	−0.0502783	+	0.0254793i
$587$	−1.97974e8	+	1.97974e8i	−0.978799	+	0.978799i	−0.999780	−	0.0209809i	$-0.993321\pi$
$587$	−1.97974e8	+	1.97974e8i	−0.978799	+	0.978799i	0.0209809	+	0.999780i	$0.493321\pi$
$588$	3.43793e7	+	7.90414e7i	0.169108	+	0.388797i
$589$			8.70698e7i			0.426110i
$590$	2.96490e7	−	4.43140e7i	0.144362	−	0.215767i
$591$	−2.38571e8	+	6.28469e7i	−1.15573	+	0.304454i
$592$	−3.39545e8	−	1.76777e8i	−1.63656	−	0.852040i
$593$	2.49887e8	−	2.49887e8i	1.19834	−	1.19834i	0.223674	−	0.974664i	$-0.428195\pi$
$593$	2.49887e8	−	2.49887e8i	1.19834	−	1.19834i	0.974664	−	0.223674i	$-0.0718049\pi$
$594$	−3.50686e8	−	1.19733e8i	−1.67324	−	0.571288i
$595$	−5.83399e7	+	2.08116e8i	−0.276958	+	0.987994i
$596$	−7.54888e7	−	5.53535e7i	−0.356569	−	0.261460i
$597$	−2.31612e7	+	3.97282e7i	−0.108852	+	0.186713i
$598$	−2.58026e7	+	7.88234e7i	−0.120659	+	0.368597i
$599$			1.27518e7i			0.0593324i	0.999560	+	0.0296662i	$0.00944443\pi$
$599$			1.27518e7i			0.0593324i	−0.999560	+	0.0296662i	$0.990556\pi$
$600$	1.94242e8	+	9.44774e7i	0.899269	+	0.437396i
$601$	−3.76383e8			−1.73383			−0.866915	−	0.498455i	$-0.833901\pi$
$601$	−3.76383e8			−1.73383			−0.866915	+	0.498455i	$0.833901\pi$
$602$	1.79339e8	+	5.87060e7i	0.822025	+	0.269087i
$603$	4.73255e7	−	1.70839e8i	0.215846	−	0.779176i
$604$	−1.28029e8	+	1.74600e8i	−0.581026	+	0.792380i
$605$	4.53342e8	+	1.27083e8i	2.04720	+	0.573879i
$606$	5.05782e7	+	5.69026e7i	0.227272	+	0.255690i
$607$	1.18191e8	+	1.18191e8i	0.528467	+	0.528467i	0.920115	−	0.391648i	$-0.128095\pi$
$607$	1.18191e8	+	1.18191e8i	0.528467	+	0.528467i	−0.391648	+	0.920115i	$0.628095\pi$
$608$	1.38746e6	−	1.26489e8i	0.00617319	−	0.562786i
$609$	−1.83328e7	+	4.82941e6i	−0.0811664	+	0.0213817i
$610$	−1.63584e8	−	1.09449e8i	−0.720697	−	0.482194i
$611$	2.45870e8			1.07791
$612$	2.43317e8	−	1.91919e8i	1.06150	−	0.837265i
$613$	1.46116e8	+	1.46116e8i	0.634330	+	0.634330i	0.949151	−	0.314821i	$-0.101945\pi$
$613$	1.46116e8	+	1.46116e8i	0.634330	+	0.634330i	−0.314821	+	0.949151i	$0.601945\pi$
$614$	1.83271e8	+	3.61649e8i	0.791752	+	1.56236i
$615$	8.88899e7	+	9.17314e7i	0.382144	+	0.394360i
$616$	5.11054e7	−	3.09471e8i	0.218638	−	1.32397i
$617$	−2.19601e7	−	2.19601e7i	−0.0934930	−	0.0934930i	0.658813	−	0.752306i	$-0.271059\pi$
$617$	−2.19601e7	−	2.19601e7i	−0.0934930	−	0.0934930i	−0.752306	+	0.658813i	$0.771059\pi$
$618$	−1.67901e7	+	2.85341e8i	−0.0711357	+	1.20892i
$619$	1.05583e8			0.445164			0.222582	−	0.974914i	$-0.428551\pi$
$619$	1.05583e8			0.445164			0.222582	+	0.974914i	$0.428551\pi$
$620$	−1.42014e8	+	1.11310e8i	−0.595875	+	0.467044i
$621$	4.43690e7	+	4.55072e7i	0.185270	+	0.190022i
$622$	3.00146e8	+	9.82518e7i	1.24727	+	0.408291i
$623$	−4.53390e7	−	4.53390e7i	−0.187503	−	0.187503i
$624$	1.89502e8	+	3.00279e8i	0.779936	+	1.23587i
$625$	1.12210e8	+	2.16826e8i	0.459614	+	0.888119i
$626$	1.37084e8	+	2.70508e8i	0.558810	+	1.10270i
$627$	−1.23539e8	+	2.11905e8i	−0.501189	+	0.859684i
$628$	5.24153e7	−	8.06619e6i	0.211631	−	0.0325679i
$629$	−6.20767e8			−2.49446
$630$	−1.43808e8	+	1.23830e8i	−0.575123	+	0.495229i
$631$			1.95633e8i			0.778672i	0.921096	+	0.389336i	$0.127295\pi$
$631$			1.95633e8i			0.778672i	−0.921096	+	0.389336i	$0.872705\pi$
$632$	2.92880e7	+	4.08744e7i	0.116021	+	0.161920i
$633$	−2.38697e7	−	1.39159e7i	−0.0941102	−	0.0548655i
$634$	−1.01979e7	−	2.01235e7i	−0.0400169	−	0.0789653i
$635$	−1.13679e8	−	2.02238e8i	−0.443975	−	0.789844i
$636$	−5.11115e7	+	1.29799e8i	−0.198677	+	0.504546i
$637$	−1.13244e8	+	1.13244e8i	−0.438126	+	0.438126i
$638$	−4.82600e7	−	1.57978e7i	−0.185834	−	0.0608322i
$639$	−6.91346e7	−	1.22114e8i	−0.264968	−	0.468018i
$640$	2.08082e8	−	1.59441e8i	0.793771	−	0.608217i
$641$			1.24792e8i			0.473821i	0.971531	+	0.236911i	$0.0761348\pi$
$641$			1.24792e8i			0.473821i	−0.971531	+	0.236911i	$0.923865\pi$
$642$	1.08617e7	−	1.84590e8i	0.0410481	−	0.697595i
$643$	−2.83424e7	+	2.83424e7i	−0.106611	+	0.106611i	−0.758400	−	0.651789i	$-0.774019\pi$
$643$	−2.83424e7	+	2.83424e7i	−0.106611	+	0.106611i	0.651789	+	0.758400i	$0.274019\pi$
$644$	−3.18123e7	+	4.33843e7i	−0.119107	+	0.162433i
$645$	4.81037e6	−	3.05771e8i	0.0179267	−	1.13951i
$646$	−9.27260e7	−	1.82976e8i	−0.343957	−	0.678730i
$647$	4.66370e7	−	4.66370e7i	0.172194	−	0.172194i	−0.615749	−	0.787943i	$-0.711146\pi$
$647$	4.66370e7	−	4.66370e7i	0.172194	−	0.172194i	0.787943	+	0.615749i	$0.211146\pi$
$648$	2.71200e8	−	2.20849e7i	0.996701	−	0.0811654i
$649$			1.25474e8i			0.459007i
$650$	−3.11015e7	+	4.00128e8i	−0.113251	+	1.45700i
$651$	−4.03840e7	−	1.53301e8i	−0.146375	−	0.555649i
$652$	1.69003e8	−	2.60079e7i	0.609750	−	0.0938345i
$653$	−3.65600e8	+	3.65600e8i	−1.31301	+	1.31301i	−0.393817	+	0.919189i	$0.628846\pi$
$653$	−3.65600e8	+	3.65600e8i	−1.31301	+	1.31301i	−0.919189	+	0.393817i	$0.871154\pi$
$654$	−2.65143e8	−	2.98298e8i	−0.947867	−	1.06639i
$655$	−2.22514e6	−	623761.i	−0.00791834	−	0.00221970i
$656$	1.47850e8	−	4.66090e7i	0.523731	−	0.165104i
$657$	−3.66154e7	+	1.32177e8i	−0.129112	+	0.466079i
$658$	1.51568e8	+	4.96152e7i	0.532021	+	0.174155i
$659$			7.73465e7i			0.270262i	0.990828	+	0.135131i	$0.0431455\pi$
$659$			7.73465e7i			0.270262i	−0.990828	+	0.135131i	$0.956855\pi$
$660$	−5.03556e8	+	6.94024e7i	−1.75152	+	0.241403i
$661$	−3.12065e8			−1.08054			−0.540269	−	0.841492i	$-0.681677\pi$
$661$	−3.12065e8			−1.08054			−0.540269	+	0.841492i	$0.681677\pi$
$662$	1.51728e8	−	4.63507e8i	0.522986	−	1.59765i
$663$	4.97436e8	+	2.90001e8i	1.70685	+	0.995082i
$664$	1.98769e7	−	1.20365e8i	0.0678959	−	0.411147i
$665$	6.15528e7	+	1.09504e8i	0.209307	+	0.372363i
$666$	−4.53935e8	−	3.01701e8i	−1.53663	−	1.02130i
$667$	6.15856e6	+	6.15856e6i	0.0207540	+	0.0207540i
$668$	4.49211e8	−	6.91291e7i	1.50703	−	0.231917i
$669$	7.66179e7	+	2.90847e8i	0.255889	+	0.971374i
$670$	−4.72944e7	−	2.38529e8i	−0.157248	−	0.793081i
$671$	4.63185e8			1.53316
$672$	5.62245e7	+	2.23349e8i	0.185275	+	0.735997i
$673$	2.54495e8	+	2.54495e8i	0.834899	+	0.834899i	0.988182	−	0.153283i	$-0.0489846\pi$
$673$	2.54495e8	+	2.54495e8i	0.834899	+	0.834899i	−0.153283	+	0.988182i	$0.548985\pi$
$674$	4.61730e8	−	2.33989e8i	1.50803	−	0.764215i
$675$	2.60688e8	+	1.63177e8i	0.847637	+	0.530577i
$676$	−2.07453e8	+	2.82916e8i	−0.671552	+	0.915835i
$677$	1.89507e8	+	1.89507e8i	0.610744	+	0.610744i	0.943140	−	0.332396i	$-0.107857\pi$
$677$	1.89507e8	+	1.89507e8i	0.610744	+	0.610744i	−0.332396	+	0.943140i	$0.607857\pi$
$678$	1.96209e7	−	3.33450e8i	0.0629551	−	1.06989i
$679$	1.37982e8			0.440772
$680$	1.79900e8	−	3.85155e8i	0.572142	−	1.22492i
$681$	1.45973e8	+	5.54123e8i	0.462201	+	1.75455i
$682$	1.32103e8	−	4.03555e8i	0.416445	−	1.27218i
$683$	−1.63202e8	−	1.63202e8i	−0.512230	−	0.512230i	0.402979	−	0.915209i	$-0.367975\pi$
$683$	−1.63202e8	−	1.63202e8i	−0.512230	−	0.512230i	−0.915209	+	0.402979i	$0.867975\pi$
$684$	2.11230e7	−	1.78867e8i	0.0660067	−	0.558936i
$685$	−1.87970e8	−	3.34405e8i	−0.584814	−	1.04040i
$686$	−3.11215e8	+	1.57713e8i	−0.964023	+	0.488534i
$687$	1.23423e8	+	7.19549e7i	0.380652	+	0.221917i
$688$	−3.29196e8	−	1.71389e8i	−1.01086	−	0.526280i
$689$	−2.59195e8			−0.792445
$690$	8.24207e7	+	2.84232e7i	0.250893	+	0.0865217i
$691$			5.63141e8i			1.70680i	0.521255	+	0.853401i	$0.325464\pi$
$691$			5.63141e8i			1.70680i	−0.521255	+	0.853401i	$0.674536\pi$
$692$	−1.67679e8	+	2.58041e7i	−0.506012	+	0.0778702i
$693$	1.19227e8	−	4.30393e8i	0.358239	−	1.29320i
$694$	−3.14496e8	+	1.59376e8i	−0.940885	+	0.476808i
$695$	−2.37969e8	−	6.67085e7i	−0.708870	−	0.198713i
$696$	3.71225e7	−	3.49674e6i	0.110106	−	0.0103714i
$697$	1.77758e8	−	1.77758e8i	0.524965	−	0.524965i
$698$	4.14229e7	−	1.26542e8i	0.121808	−	0.372106i
$699$	7.88949e6	+	2.99491e7i	0.0231003	+	0.0876903i
$700$	−9.99162e7	+	2.40385e8i	−0.291301	+	0.700830i
$701$		−	6.60129e8i		−	1.91635i	−0.286185	−	0.958174i	$-0.592387\pi$
$701$		−	6.60129e8i		−	1.91635i	0.286185	−	0.958174i	$-0.407613\pi$
$702$	2.22805e8	+	4.53823e8i	0.644040	+	1.31182i
$703$	−2.55114e8	+	2.55114e8i	−0.734291	+	0.734291i
$704$	−1.98341e8	+	5.84154e8i	−0.568452	+	1.67421i
$705$	4.06548e6	−	2.58422e8i	0.0116023	−	0.737499i
$706$	−1.90691e8	+	9.66355e7i	−0.541896	+	0.274614i
$707$	−6.48798e7	+	6.48798e7i	−0.183591	+	0.183591i
$708$	−3.67480e7	−	8.44874e7i	−0.103546	−	0.238063i
$709$		−	3.05146e8i		−	0.856186i	−0.903735	−	0.428093i	$-0.859185\pi$
$709$		−	3.05146e8i		−	0.856186i	0.903735	−	0.428093i	$-0.140815\pi$
$710$	−1.59985e8	−	1.07041e8i	−0.446996	−	0.299070i
$711$	3.52734e7	+	6.23041e7i	0.0981382	+	0.173343i
$712$	7.34518e7	+	1.02510e8i	0.203499	+	0.284004i
$713$	−5.14986e7	+	5.14986e7i	−0.142078	+	0.142078i
$714$	2.48126e8	+	2.79152e8i	0.681675	+	0.766914i
$715$	−4.62789e8	−	8.23314e8i	−1.26609	−	2.25241i
$716$	−1.76133e8	+	2.40203e8i	−0.479846	+	0.654394i
$717$	−3.65455e8	−	2.13057e8i	−0.991463	−	0.578015i
$718$	1.41297e7	−	4.31644e7i	0.0381734	−	0.116615i
$719$		−	1.91177e8i		−	0.514338i	−0.966367	−	0.257169i	$-0.917210\pi$
$719$		−	1.91177e8i		−	0.514338i	0.966367	−	0.257169i	$-0.0827896\pi$
$720$	3.18742e8	−	1.94210e8i	0.853968	−	0.520326i
$721$	−3.44487e8			−0.919108
$722$	2.44386e8	+	7.99990e7i	0.649329	+	0.212556i
$723$	7.19020e7	−	1.23333e8i	0.190251	−	0.326335i
$724$	2.75713e8	+	2.02171e8i	0.726510	+	0.532726i
$725$	3.60035e7	+	2.19068e7i	0.0944781	+	0.0574863i
$726$	6.08082e8	−	5.40497e8i	1.58910	−	1.41248i
$727$	−3.35230e8	−	3.35230e8i	−0.872448	−	0.872448i	0.120291	−	0.992739i	$-0.461617\pi$
$727$	−3.35230e8	−	3.35230e8i	−0.872448	−	0.872448i	−0.992739	+	0.120291i	$0.961617\pi$
$728$	−3.47855e8	+	2.49251e8i	−0.901581	+	0.646014i
$729$	3.87296e8	+	9.81068e6i	0.999679	+	0.0253231i
$730$	3.65913e7	+	1.84548e8i	0.0940608	+	0.474396i
$731$	−6.01847e8			−1.54076
$732$	−3.11884e8	+	1.35655e8i	−0.795170	+	0.345861i
$733$	1.07643e8	+	1.07643e8i	0.273322	+	0.273322i	0.830436	−	0.557114i	$-0.188091\pi$
$733$	1.07643e8	+	1.07643e8i	0.273322	+	0.273322i	−0.557114	+	0.830436i	$0.688091\pi$
$734$	−2.05183e7	−	4.04887e7i	−0.0518863	−	0.102387i
$735$	1.17153e8	+	1.20898e8i	0.295047	+	0.304479i
$736$	7.56345e7	−	7.39932e7i	0.189708	−	0.185592i
$737$	4.04651e8	+	4.04651e8i	1.01083	+	1.01083i
$738$	2.16378e8	−	4.35925e7i	0.538323	−	0.108453i
$739$	3.92894e8			0.973515			0.486757	−	0.873537i	$-0.338180\pi$
$739$	3.92894e8			0.973515			0.486757	+	0.873537i	$0.338180\pi$
$740$	−7.42236e8	−	8.99629e7i	−1.83167	−	0.222008i
$741$	3.23610e8	−	8.52486e7i	0.795366	−	0.209523i
$742$	−1.59782e8	−	5.23041e7i	−0.391126	−	0.128034i
$743$	−6.39279e7	−	6.39279e7i	−0.155856	−	0.155856i	0.624872	−	0.780728i	$-0.285151\pi$
$743$	−6.39279e7	−	6.39279e7i	−0.155856	−	0.155856i	−0.780728	+	0.624872i	$0.785151\pi$
$744$	2.92401e7	+	3.10422e8i	0.0710004	+	0.753761i
$745$	−1.76043e8	−	4.93491e7i	−0.425746	−	0.119347i
$746$	−5.48485e7	−	1.08233e8i	−0.132114	−	0.260700i
$747$	4.63718e7	−	1.67396e8i	0.111248	−	0.401591i
$748$	1.52159e8	+	9.88752e8i	0.363574	+	2.36256i
$749$	2.22853e8			0.530362
$750$	4.20040e8	+	3.93054e7i	0.995650	+	0.0931683i
$751$		−	5.80286e8i		−	1.37000i	−0.728541	−	0.685002i	$-0.759801\pi$
$751$		−	5.80286e8i		−	1.37000i	0.728541	−	0.685002i	$-0.240199\pi$
$752$	−2.78219e8	−	1.44849e8i	−0.654234	−	0.340613i
$753$	−141881.	+	243367.i	−0.000332307	+	0.000570003i
$754$	3.13170e7	+	6.17978e7i	0.0730576	+	0.144165i
$755$	−1.14141e8	+	4.07175e8i	−0.265216	+	0.946107i
$756$	4.57701e7	+	3.24722e8i	0.105929	+	0.751530i
$757$	1.51692e8	−	1.51692e8i	0.349684	−	0.349684i	−0.510308	−	0.859992i	$-0.670469\pi$
$757$	1.51692e8	−	1.51692e8i	0.349684	−	0.349684i	0.859992	+	0.510308i	$0.170469\pi$
$758$	−4.73260e8	−	1.54920e8i	−1.08666	−	0.355713i
$759$	−1.98403e8	+	5.22654e7i	−0.453757	+	0.119533i
$760$	−8.43530e7	−	2.32218e8i	−0.192159	−	0.529000i
$761$		−	5.97761e8i		−	1.35635i	−0.734898	−	0.678177i	$-0.762770\pi$
$761$		−	5.97761e8i		−	1.35635i	0.734898	−	0.678177i	$-0.237230\pi$
$762$	−4.00200e8	−	2.35487e7i	−0.904508	−	0.0532233i
$763$	3.40116e8	−	3.40116e8i	0.765692	−	0.765692i
$764$	−2.72619e8	−	1.99903e8i	−0.611330	−	0.448269i
$765$	3.13031e8	−	5.18035e8i	0.699202	−	1.15711i
$766$	4.02828e8	+	7.94900e8i	0.896258	+	1.76859i
$767$	1.21047e8	−	1.21047e8i	0.268268	−	0.268268i
$768$	−3.75316e7	−	4.51427e8i	−0.0828540	−	0.996562i
$769$			5.59750e8i			1.23088i	0.788184	+	0.615440i	$0.211021\pi$
$769$			5.59750e8i			1.23088i	−0.788184	+	0.615440i	$0.788979\pi$
$770$	−1.19148e8	−	6.00924e8i	−0.260985	−	1.31628i
$771$	−5.21548e8	+	1.37392e8i	−1.13797	+	0.299776i
$772$	−1.88314e7	−	1.22369e8i	−0.0409290	−	0.265962i
$773$	−5.23600e8	+	5.23600e8i	−1.13360	+	1.13360i	−0.144031	+	0.989573i	$0.546007\pi$
$773$	−5.23600e8	+	5.23600e8i	−1.13360	+	1.13360i	−0.989573	+	0.144031i	$0.953993\pi$
$774$	−4.40099e8	−	2.92505e8i	−0.949135	−	0.630827i
$775$	−1.83187e8	+	3.01066e8i	−0.393540	+	0.646779i
$776$	−2.67756e8	−	4.42166e7i	−0.572998	−	0.0946237i
$777$	3.30845e8	−	5.67495e8i	0.705280	−	1.20976i
$778$	1.50102e8	+	4.91354e7i	0.318748	+	0.104341i
$779$		−	1.46105e8i		−	0.309067i
$780$	5.52745e8	+	4.18837e8i	1.16477	+	0.882594i
$781$	4.52993e8			0.950907
$782$	5.33797e7	−	1.63068e8i	0.111624	−	0.340995i
$783$	5.30857e7	+	672255.i	0.110584	+	0.00140039i
$784$	1.94859e8	−	6.14286e7i	0.404365	−	0.127474i
$785$	9.02919e7	−	5.07535e7i	0.186655	−	0.104920i
$786$	−2.98465e6	+	2.65293e6i	−0.00614648	+	0.00546333i
$787$	−3.04572e8	−	3.04572e8i	−0.624836	−	0.624836i	0.321928	−	0.946764i	$-0.395669\pi$
$787$	−3.04572e8	−	3.04572e8i	−0.624836	−	0.624836i	−0.946764	+	0.321928i	$0.895669\pi$
$788$	8.89471e7	+	5.77991e8i	0.181783	+	1.18125i
$789$	3.73857e8	−	9.84852e7i	0.761157	−	0.200512i
$790$	8.16263e7	+	5.46134e7i	0.165558	+	0.110769i
$791$	4.02568e8			0.813410
$792$	−3.69280e8	+	7.96974e8i	−0.743327	+	1.60424i
$793$	−4.46844e8	−	4.46844e8i	−0.896058	−	0.896058i
$794$	1.60106e8	−	8.11362e7i	0.319850	−	0.162089i
$795$	−4.28581e6	+	2.72427e8i	−0.00852965	+	0.542187i
$796$	8.79052e7	+	6.44580e7i	0.174291	+	0.127802i
$797$	−3.25095e8	−	3.25095e8i	−0.642149	−	0.642149i	0.308935	−	0.951083i	$-0.400028\pi$
$797$	−3.25095e8	−	3.25095e8i	−0.642149	−	0.642149i	−0.951083	+	0.308935i	$0.900028\pi$
$798$	2.16693e8	+	1.27507e7i	0.426420	+	0.0250915i
$799$	−5.08649e8			−0.997190
$800$	2.70920e8	−	4.34450e8i	0.529140	−	0.848535i
$801$	8.84626e7	+	1.56253e8i	0.172132	+	0.304041i
$802$	−2.76951e8	+	8.46047e8i	−0.536883	+	1.64010i
$803$	−3.13075e8	−	3.13075e8i	−0.604647	−	0.604647i
$804$	−3.90982e8	−	1.53959e8i	−0.752296	−	0.296235i
$805$	−2.83615e7	+	1.01174e8i	−0.0543678	+	0.193946i
$806$	−5.16760e8	+	2.61876e8i	−0.986924	+	0.500139i
$807$	3.17882e8	−	5.45260e8i	0.604847	−	1.03749i
$808$	1.46691e8	−	1.05109e8i	0.278079	−	0.199253i
$809$	3.78866e8			0.715549			0.357775	−	0.933808i	$-0.383536\pi$
$809$	3.78866e8			0.715549			0.357775	+	0.933808i	$0.383536\pi$
$810$	4.80675e8	−	2.26675e8i	0.904474	−	0.426529i
$811$		−	5.26403e8i		−	0.986861i	−0.869785	−	0.493431i	$-0.835743\pi$
$811$		−	5.26403e8i		−	0.986861i	0.869785	−	0.493431i	$-0.164257\pi$
$812$	6.83505e6	+	4.44151e7i	0.0127665	+	0.0829589i
$813$	6.19357e8	+	3.61080e8i	1.15257	+	0.671942i
$814$	1.56948e9	−	7.95356e8i	2.90992	−	1.47465i
$815$	2.91129e8	−	1.63645e8i	0.537790	−	0.302294i
$816$	−3.92036e8	−	6.21209e8i	−0.721531	−	1.14332i
$817$	−2.47339e8	+	2.47339e8i	−0.453550	+	0.453550i
$818$	−4.10178e7	+	1.25304e8i	−0.0749398	+	0.228931i
$819$	−5.30229e8	+	3.00188e8i	−0.965187	+	0.546439i
$820$	2.38302e8	−	1.86780e8i	0.432201	−	0.338757i
$821$			1.26078e8i			0.227829i	0.993491	+	0.113915i	$0.0363390\pi$
$821$			1.26078e8i			0.227829i	−0.993491	+	0.113915i	$0.963661\pi$
$822$	−6.61740e8	−	3.89383e7i	−1.19144	−	0.0701070i
$823$	−4.94298e8	+	4.94298e8i	−0.886727	+	0.886727i	−0.994207	−	0.107481i	$-0.965722\pi$
$823$	−4.94298e8	+	4.94298e8i	−0.886727	+	0.886727i	0.107481	+	0.994207i	$0.465722\pi$
$824$	6.68479e8	+	1.10391e8i	1.19483	+	0.197312i
$825$	−8.72997e8	+	4.72801e8i	−1.55471	+	0.842008i
$826$	9.90467e7	−	5.01934e7i	0.175752	−	0.0890649i
$827$	4.36084e8	−	4.36084e8i	0.770998	−	0.770998i	−0.207283	−	0.978281i	$-0.566462\pi$
$827$	4.36084e8	−	4.36084e8i	0.770998	−	0.770998i	0.978281	+	0.207283i	$0.0664620\pi$
$828$	1.18287e8	−	9.32998e7i	0.208375	−	0.164358i
$829$		−	5.61020e8i		−	0.984725i	−0.870390	−	0.492362i	$-0.836134\pi$
$829$		−	5.61020e8i		−	0.984725i	0.870390	−	0.492362i	$-0.163866\pi$
$830$	−4.63413e7	−	2.33723e8i	−0.0810464	−	0.408758i
$831$	5.50510e7	+	2.08977e8i	0.0959316	+	0.364163i
$832$	7.54889e8	−	3.72202e8i	1.31073	−	0.646262i
$833$	2.34277e8	−	2.34277e8i	0.405317	−	0.405317i
$834$	−3.19196e8	+	2.83719e8i	−0.550249	+	0.489092i
$835$	7.73823e8	−	4.34969e8i	1.32917	−	0.747135i
$836$	4.68876e8	+	3.43811e8i	0.802489	+	0.588439i
$837$	−5.62147e6	+	4.43909e8i	−0.00958680	+	0.757037i
$838$	−2.10504e8	+	6.43062e8i	−0.357708	+	1.09275i
$839$			1.04747e9i			1.77359i	0.462159	+	0.886797i	$0.347075\pi$
$839$			1.04747e9i			1.77359i	−0.462159	+	0.886797i	$0.652925\pi$
$840$	2.56223e8	+	3.69735e8i	0.432295	+	0.623810i
$841$	−5.87548e8			−0.987769
$842$	1.56567e8	+	5.12518e7i	0.262280	+	0.0858565i
$843$	3.28236e8	+	1.91359e8i	0.547903	+	0.319423i
$844$	−3.87281e7	+	5.28158e7i	−0.0644168	+	0.0878489i
$845$	−1.84950e8	+	6.59772e8i	−0.306538	+	1.09351i
$846$	−3.71949e8	−	2.47210e8i	−0.614288	−	0.408277i
$847$	6.93330e8	+	6.93330e8i	1.14101	+	1.14101i
$848$	2.93297e8	+	1.52699e8i	0.480973	+	0.250408i
$849$	6.83405e7	+	2.59426e8i	0.111675	+	0.423926i
$850$	6.43419e7	−	8.27773e8i	0.104770	−	1.34789i
$851$	−3.01781e8			−0.489670
$852$	−3.05021e8	+	1.32670e8i	−0.493187	+	0.214513i
$853$	−2.12238e8	−	2.12238e8i	−0.341961	−	0.341961i	0.515143	−	0.857104i	$-0.327739\pi$
$853$	−2.12238e8	−	2.12238e8i	−0.341961	−	0.341961i	−0.857104	+	0.515143i	$0.827739\pi$
$854$	−1.85288e8	−	3.65629e8i	−0.297491	−	0.587040i
$855$	−8.42496e7	−	3.41540e8i	−0.134794	−	0.546440i
$856$	−4.32447e8	−	7.14133e7i	−0.689464	−	0.113857i
$857$	2.74441e8	+	2.74441e8i	0.436020	+	0.436020i	0.890670	−	0.454650i	$-0.150236\pi$
$857$	2.74441e8	+	2.74441e8i	0.436020	+	0.436020i	−0.454650	+	0.890670i	$0.650236\pi$
$858$	−1.62922e9	−	9.58672e7i	−2.57940	−	0.151778i
$859$	−2.19773e8			−0.346733			−0.173367	−	0.984857i	$-0.555465\pi$
$859$	−2.19773e8			−0.346733			−0.173367	+	0.984857i	$0.555465\pi$
$860$	−7.19614e8	−	8.72210e7i	−1.13137	−	0.137128i
$861$	6.77652e7	+	2.57241e8i	0.106169	+	0.403025i
$862$	−1.80406e7	−	5.90553e6i	−0.0281663	−	0.00922013i
$863$	−5.65360e8	−	5.65360e8i	−0.879616	−	0.879616i	0.113879	−	0.993495i	$-0.463672\pi$
$863$	−5.65360e8	−	5.65360e8i	−0.879616	−	0.879616i	−0.993495	+	0.113879i	$0.963672\pi$
$864$	1.52402e7	−	6.44792e8i	0.0236292	−	0.999721i
$865$	−2.88848e8	+	1.62363e8i	−0.446295	+	0.250864i
$866$	4.87868e8	+	9.62710e8i	0.751188	+	1.48232i
$867$	−4.66061e8	−	2.71710e8i	−0.715130	−	0.416915i
$868$	−3.71404e8	+	5.71554e7i	−0.567920	+	0.0873973i
$869$	−2.31123e8			−0.352195
$870$	6.54704e7	−	3.18939e7i	0.0994231	−	0.0484339i
$871$		−	7.80750e8i		−	1.18156i
$872$	−7.68989e8	+	5.51008e8i	−1.15977	+	0.831014i
$873$	−3.72377e8	−	1.03155e8i	−0.559681	−	0.155042i
$874$	−4.50781e7	−	8.89526e7i	−0.0675198	−	0.133237i
$875$	−1.75526e7	+	5.08140e8i	−0.0262009	+	0.758506i
$876$	3.02500e8	+	1.19116e8i	0.450000	+	0.177198i
$877$	−5.04171e8	+	5.04171e8i	−0.747445	+	0.747445i	−0.973999	−	0.226554i	$-0.927254\pi$
$877$	−5.04171e8	+	5.04171e8i	−0.747445	+	0.747445i	0.226554	+	0.973999i	$0.427254\pi$
$878$	1.16396e9	+	3.81017e8i	1.71970	+	0.562939i
$879$	9.75166e6	+	3.70180e7i	0.0143586	+	0.0545062i
$880$	3.86409e7	+	1.20428e9i	0.0567022	+	1.76717i
$881$		−	6.03989e8i		−	0.883285i	−0.897191	−	0.441643i	$-0.854396\pi$
$881$		−	6.03989e8i		−	0.883285i	0.897191	−	0.441643i	$-0.145604\pi$
$882$	2.85176e8	−	5.74531e7i	0.415631	−	0.0837351i
$883$	−4.35887e7	+	4.35887e7i	−0.0633128	+	0.0633128i	−0.738054	−	0.674741i	$-0.764255\pi$
$883$	−4.35887e7	+	4.35887e7i	−0.0633128	+	0.0633128i	0.674741	+	0.738054i	$0.264255\pi$
$884$	8.07078e8	−	1.10066e9i	1.16831	−	1.59329i
$885$	−1.25225e8	−	1.29228e8i	−0.180660	−	0.186435i
$886$	−3.56261e8	−	7.03009e8i	−0.512232	−	1.01079i
$887$	5.74846e8	−	5.74846e8i	0.823722	−	0.823722i	−0.162917	−	0.986640i	$-0.552090\pi$
$887$	5.74846e8	−	5.74846e8i	0.823722	−	0.823722i	0.986640	+	0.162917i	$0.0520904\pi$
$888$	−8.23862e8	+	9.95209e8i	−1.17656	+	1.42127i
$889$		−	4.83155e8i		−	0.687671i
$890$	2.04712e8	+	1.36966e8i	0.290384	+	0.194286i
$891$	−6.43522e8	+	1.07238e9i	−0.909767	+	1.51606i
$892$	7.04640e8	−	1.08437e8i	0.992826	−	0.152786i
$893$	−2.09038e8	+	2.09038e8i	−0.293542	+	0.293542i
$894$	−2.36132e8	+	2.09887e8i	−0.330478	+	0.293747i
$895$	−1.57027e8	+	5.60164e8i	−0.219031	+	0.781351i
$896$	5.40463e8	−	7.71134e7i	0.751349	−	0.107203i
$897$	2.41825e8	+	1.40982e8i	0.335061	+	0.195338i
$898$	2.79742e8	+	9.15727e7i	0.386304	+	0.126455i
$899$			6.08357e7i			0.0837296i
$900$	4.49358e8	−	5.74037e8i	0.616404	−	0.787430i
$901$	5.36216e8			0.733103
$902$	−2.21671e8	+	6.77174e8i	−0.302057	+	0.922743i
$903$	3.20761e8	−	5.50199e8i	0.435631	−	0.747233i
$904$	−7.81186e8	−	1.29003e8i	−1.05742	−	0.174621i
$905$	6.42975e8	+	1.80241e8i	0.867458	+	0.243169i
$906$	4.85454e8	+	5.46156e8i	0.652775	+	0.734400i
$907$	6.92793e8	+	6.92793e8i	0.928499	+	0.928499i	0.997609	−	0.0691099i	$-0.0220159\pi$
$907$	6.92793e8	+	6.92793e8i	0.928499	+	0.928499i	−0.0691099	+	0.997609i	$0.522016\pi$
$908$	1.34248e9	−	2.06595e8i	1.79329	−	0.275970i
$909$	2.23597e8	−	1.26589e8i	0.297697	−	0.168541i
$910$	−4.64779e8	+	6.94668e8i	−0.616768	+	0.921835i
$911$	1.19806e9			1.58461			0.792306	−	0.610124i	$-0.208880\pi$
$911$	1.19806e9			1.58461			0.792306	+	0.610124i	$0.208880\pi$
$912$	−4.16409e8	−	9.41826e7i	−0.548954	−	0.124161i
$913$	3.96497e8	+	3.96497e8i	0.520987	+	0.520987i
$914$	−7.69573e8	+	3.89993e8i	−1.00789	+	0.510762i
$915$	−4.77044e8	+	4.62266e8i	−0.622723	+	0.603433i
$916$	2.00252e8	−	2.73095e8i	0.260549	−	0.355326i
$917$	−3.40308e6	−	3.40308e6i	−0.00441330	−	0.00441330i
$918$	−4.60932e8	−	9.38856e8i	−0.595812	−	1.21359i
$919$	6.39010e8			0.823305			0.411653	−	0.911341i	$-0.364952\pi$
$919$	6.39010e8			0.823305			0.411653	+	0.911341i	$0.364952\pi$
$920$	8.74570e7	−	1.87240e8i	0.112313	−	0.240456i
$921$	1.32320e9	−	3.48572e8i	1.69374	−	0.446184i
$922$	8.91223e7	−	2.72257e8i	0.113709	−	0.347365i
$923$	−4.37011e8	−	4.37011e8i	−0.555760	−	0.555760i
$924$	−9.84996e8	−	3.87866e8i	−1.24859	−	0.491661i
$925$	−1.41886e9	+	3.45384e8i	−1.79272	+	0.436392i
$926$	7.06433e8	−	3.57996e8i	0.889689	−	0.450863i
$927$	9.29678e8	+	2.57537e8i	1.16706	+	0.323297i
$928$	969418.	−	8.83782e7i	0.00121302	−	0.110586i
$929$	−1.01678e9			−1.26818			−0.634089	−	0.773260i	$-0.718625\pi$
$929$	−1.01678e9			−1.26818			−0.634089	+	0.773260i	$0.718625\pi$
$930$	2.66700e8	+	5.47470e8i	0.331569	+	0.680631i
$931$		−	1.92560e8i		−	0.238625i
$932$	7.25581e7	−	1.11660e7i	0.0896269	−	0.0137927i
$933$	5.36834e8	−	9.20826e8i	0.660991	−	1.13379i
$934$	−7.68979e8	+	3.89692e8i	−0.943787	+	0.478278i
$935$	9.57405e8	+	1.70325e9i	1.17128	+	2.08374i
$936$	1.12511e9	−	4.12605e8i	1.37204	−	0.503161i
$937$	1.17504e8	−	1.17504e8i	0.142835	−	0.142835i	−0.632073	−	0.774909i	$-0.717796\pi$
$937$	1.17504e8	−	1.17504e8i	0.142835	−	0.142835i	0.774909	+	0.632073i	$0.217796\pi$
$938$	1.57551e8	−	4.81297e8i	0.190903	−	0.583183i
$939$	9.89737e8	−	2.60727e8i	1.19543	−	0.314912i
$940$	−6.08180e8	−	7.37146e7i	−0.732232	−	0.0887503i
$941$			2.81076e8i			0.337330i	0.985673	+	0.168665i	$0.0539456\pi$
$941$			2.81076e8i			0.337330i	−0.985673	+	0.168665i	$0.946054\pi$
$942$	1.05137e7	−	1.78675e8i	0.0125777	−	0.213752i
$943$	8.64156e7	−	8.64156e7i	0.103052	−	0.103052i
$944$	−2.08285e8	+	6.56611e7i	−0.247595	+	0.0780534i
$945$	3.06746e8	+	5.62261e8i	0.363482	+	0.666258i
$946$	1.52164e9	−	7.71114e8i	1.79737	−	0.910847i
$947$	−9.35022e8	+	9.35022e8i	−1.10096	+	1.10096i	−0.106666	+	0.994295i	$0.534017\pi$
$947$	−9.35022e8	+	9.35022e8i	−1.10096	+	1.10096i	−0.994295	+	0.106666i	$0.965983\pi$
$948$	1.55626e8	−	6.76898e7i	0.182665	−	0.0794508i
$949$			6.04060e8i			0.706775i
$950$	−3.13744e8	−	3.66629e8i	−0.365936	−	0.427618i
$951$	−7.36282e7	+	1.93959e7i	−0.0856056	+	0.0225511i
$952$	7.19634e8	−	5.15643e8i	0.834067	−	0.597638i
$953$	4.77607e8	−	4.77607e8i	0.551813	−	0.551813i	−0.375151	−	0.926964i	$-0.622409\pi$
$953$	4.77607e8	−	4.77607e8i	0.551813	−	0.551813i	0.926964	+	0.375151i	$0.122409\pi$
$954$	3.92107e8	+	2.60608e8i	0.451605	+	0.300152i
$955$	−6.35759e8	−	1.78219e8i	−0.729932	−	0.204617i
$956$	−5.92942e8	+	8.08630e8i	−0.678639	+	0.925500i
$957$	−8.63168e7	+	1.48058e8i	−0.0984826	+	0.168926i
$958$	−1.32973e8	+	4.06214e8i	−0.151240	+	0.462017i
$959$		−	7.98907e8i		−	0.905817i
$960$	−3.78721e8	−	7.99580e8i	−0.428061	−	0.903750i
$961$	3.78789e8			0.426803
$962$	−2.28140e9	−	7.46809e8i	−2.56257	−	0.838850i
$963$	−6.01420e8	−	1.66604e8i	−0.673440	−	0.186555i
$964$	−2.72894e8	−	2.00104e8i	−0.304623	−	0.223370i
$965$	−1.18490e8	−	2.10796e8i	−0.131856	−	0.234575i
$966$	1.20625e8	+	1.35708e8i	0.133815	+	0.150547i
$967$	7.56057e8	+	7.56057e8i	0.836133	+	0.836133i	0.988347	−	0.152214i	$-0.0486404\pi$
$967$	7.56057e8	+	7.56057e8i	0.836133	+	0.836133i	−0.152214	+	0.988347i	$0.548640\pi$
$968$	−1.12323e9	−	1.56759e9i	−1.23835	−	1.72825i
$969$	−6.69475e8	+	1.76360e8i	−0.735805	+	0.193833i
$970$	−5.19922e8	+	1.03087e8i	−0.569669	+	0.112951i
$971$	−1.51345e9			−1.65314			−0.826569	−	0.562836i	$-0.809710\pi$
$971$	−1.51345e9			−1.65314			−0.826569	+	0.562836i	$0.809710\pi$
$972$	1.19240e8	−	9.10556e8i	0.129844	−	0.991534i
$973$	−3.63944e8	−	3.63944e8i	−0.395090	−	0.395090i
$974$	4.42345e8	+	8.72880e8i	0.478723	+	0.944665i
$975$	1.29832e9	+	3.86077e8i	1.40077	+	0.416543i
$976$	2.42387e8	+	7.68882e8i	0.260711	+	0.827009i
$977$	3.11589e7	+	3.11589e7i	0.0334117	+	0.0334117i	0.723615	−	0.690204i	$-0.242479\pi$
$977$	3.11589e7	+	3.11589e7i	0.0334117	+	0.0334117i	−0.690204	+	0.723615i	$0.742479\pi$
$978$	3.38993e7	−	5.76104e8i	0.0362388	−	0.615863i
$979$	−5.79636e8			−0.617743
$980$	3.14072e8	−	2.46168e8i	0.333696	−	0.261549i
$981$	−1.17215e9	+	6.63613e8i	−1.24159	+	0.702923i
$982$	−1.47508e9	−	4.82862e8i	−1.55769	−	0.509904i
$983$	9.23426e8	+	9.23426e8i	0.972169	+	0.972169i	0.999623	−	0.0274541i	$-0.00873999\pi$
$983$	9.23426e8	+	9.23426e8i	0.972169	+	0.972169i	−0.0274541	+	0.999623i	$0.508740\pi$
$984$	−4.90655e7	−	5.20894e8i	−0.0514981	−	0.546719i
$985$	5.59666e8	+	9.95662e8i	0.585626	+	1.04185i
$986$	−6.47877e7	−	1.27846e8i	−0.0675868	−	0.133369i
$987$	2.71091e8	−	4.64999e8i	0.281944	−	0.483616i
$988$	−1.20652e8	−	7.84015e8i	−0.125102	−	0.812931i
$989$	−2.92583e8			−0.302455
$990$	−1.27701e8	+	1.71081e9i	−0.131609	+	1.76318i
$991$		−	6.77247e8i		−	0.695866i	−0.937519	−	0.347933i	$-0.886884\pi$
$991$		−	6.77247e8i		−	0.695866i	0.937519	−	0.347933i	$-0.113116\pi$
$992$	7.39028e8	+	8.10638e6i	0.757052	+	0.00830409i
$993$	−1.42201e9	−	8.29019e8i	−1.45229	−	0.846675i
$994$	−1.81211e8	−	3.57584e8i	−0.184513	−	0.364099i
$995$	2.04999e8	+	5.74660e7i	0.208105	+	0.0583367i
$996$	−3.83103e8	−	1.50856e8i	−0.387737	−	0.152681i
$997$	2.98449e8	−	2.98449e8i	0.301151	−	0.301151i	−0.540313	−	0.841464i	$-0.681694\pi$
$997$	2.98449e8	−	2.98449e8i	0.301151	−	0.301151i	0.841464	+	0.540313i	$0.181694\pi$
$998$	1.54715e9	+	5.06456e8i	1.55647	+	0.509507i
$999$	−1.31712e9	+	1.28418e9i	−1.32108	+	1.28804i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.l.a.23.8	✓	136
3.2	odd	2	inner	60.7.l.a.23.61	yes	136
4.3	odd	2	inner	60.7.l.a.23.27	yes	136
5.2	odd	4	inner	60.7.l.a.47.42	yes	136
12.11	even	2	inner	60.7.l.a.23.42	yes	136
15.2	even	4	inner	60.7.l.a.47.27	yes	136
20.7	even	4	inner	60.7.l.a.47.61	yes	136
60.47	odd	4	inner	60.7.l.a.47.8	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.l.a.23.8	✓	136	1.1	even	1	trivial
60.7.l.a.23.27	yes	136	4.3	odd	2	inner
60.7.l.a.23.42	yes	136	12.11	even	2	inner
60.7.l.a.23.61	yes	136	3.2	odd	2	inner
60.7.l.a.47.8	yes	136	60.47	odd	4	inner
60.7.l.a.47.27	yes	136	15.2	even	4	inner
60.7.l.a.47.42	yes	136	5.2	odd	4	inner
60.7.l.a.47.61	yes	136	20.7	even	4	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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.60301 - 2.48882i) q^{2} +(-13.5986 + 23.3255i) q^{3} +(51.6115 + 37.8451i) q^{4} +(120.360 + 33.7399i) q^{5} +(161.443 - 143.500i) q^{6} +(184.076 + 184.076i) q^{7} +(-298.214 - 416.188i) q^{8} +(-359.157 - 634.387i) q^{9} +O(q^{10})\)	\(q+(-7.60301 - 2.48882i) q^{2} +(-13.5986 + 23.3255i) q^{3} +(51.6115 + 37.8451i) q^{4} +(120.360 + 33.7399i) q^{5} +(161.443 - 143.500i) q^{6} +(184.076 + 184.076i) q^{7} +(-298.214 - 416.188i) q^{8} +(-359.157 - 634.387i) q^{9} +(-831.129 - 556.080i) q^{10} +2353.32 q^{11} +(-1584.60 + 689.226i) q^{12} +(-2270.29 - 2270.29i) q^{13} +(-941.400 - 1857.66i) q^{14} +(-2423.73 + 2348.65i) q^{15} +(1231.50 + 3906.48i) q^{16} +(4696.72 + 4696.72i) q^{17} +(1151.80 + 5717.13i) q^{18} +3860.38 q^{19} +(4935.10 + 6296.41i) q^{20} +(-6796.84 + 1790.49i) q^{21} +(-17892.3 - 5856.99i) q^{22} +(2283.27 + 2283.27i) q^{23} +(13763.1 - 1296.41i) q^{24} +(13348.2 + 8121.89i) q^{25} +(11610.7 + 22911.4i) q^{26} +(19681.4 + 249.237i) q^{27} +(2534.08 + 16466.8i) q^{28} +2697.25 q^{29} +(24273.0 - 11824.6i) q^{30} +22554.7i q^{31} +(359.410 - 32766.0i) q^{32} +(-32001.8 + 54892.3i) q^{33} +(-24019.9 - 47398.5i) q^{34} +(15944.8 + 28366.2i) q^{35} +(5471.75 - 46334.0i) q^{36} +(-66085.2 + 66085.2i) q^{37} +(-29350.5 - 9607.80i) q^{38} +(83828.4 - 22082.9i) q^{39} +(-21850.9 - 60154.3i) q^{40} -37847.2i q^{41} +(56132.6 + 3302.97i) q^{42} +(-64071.0 + 64071.0i) q^{43} +(121458. + 89061.4i) q^{44} +(-21824.2 - 88473.0i) q^{45} +(-11677.1 - 23042.4i) q^{46} +(-54149.4 + 54149.4i) q^{47} +(-107867. - 24397.2i) q^{48} -49881.0i q^{49} +(-81272.9 - 94972.2i) q^{50} +(-173422. + 45684.6i) q^{51} +(-31253.9 - 203093. i) q^{52} +(57084.1 - 57084.1i) q^{53} +(-149018. - 50878.5i) q^{54} +(283246. + 79400.7i) q^{55} +(21716.3 - 131504. i) q^{56} +(-52495.7 + 90045.3i) q^{57} +(-20507.2 - 6712.97i) q^{58} +53317.9i q^{59} +(-213977. + 29491.3i) q^{60} +196822. q^{61} +(56134.6 - 171484. i) q^{62} +(50663.2 - 182888. i) q^{63} +(-84281.4 + 248226. i) q^{64} +(-196654. - 349853. i) q^{65} +(379927. - 337700. i) q^{66} +(171949. + 171949. i) q^{67} +(64657.3 + 420152. i) q^{68} +(-84307.8 + 22209.2i) q^{69} +(-50629.8 - 255352. i) q^{70} +192491. q^{71} +(-156919. + 338660. i) q^{72} +(-133036. - 133036. i) q^{73} +(666921. - 337972. i) q^{74} +(-370964. + 200908. i) q^{75} +(199240. + 146096. i) q^{76} +(433189. + 433189. i) q^{77} +(-692309. - 40737.1i) q^{78} -98211.4 q^{79} +(16419.8 + 511737. i) q^{80} +(-273453. + 455690. i) q^{81} +(-94195.0 + 287753. i) q^{82} +(168484. + 168484. i) q^{83} +(-418557. - 164817. i) q^{84} +(406832. + 723765. i) q^{85} +(646594. - 327671. i) q^{86} +(-36678.8 + 62914.7i) q^{87} +(-701791. - 979423. i) q^{88} -246306. q^{89} +(-54264.1 + 726978. i) q^{90} -835813. i q^{91} +(31432.7 + 204254. i) q^{92} +(-526099. - 306712. i) q^{93} +(546467. - 276930. i) q^{94} +(464637. + 130249. i) q^{95} +(759396. + 453955. i) q^{96} +(374797. - 374797. i) q^{97} +(-124145. + 379246. i) q^{98} +(-845211. - 1.49291e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 4 q^{6}+O(q^{10}) \) 136 * q - 4 * q^6	\( 136 q - 4 q^{6} - 2092 q^{10} - 1460 q^{12} - 8 q^{13} - 932 q^{16} - 12744 q^{18} - 16056 q^{21} + 25444 q^{22} - 8 q^{25} - 52244 q^{28} + 82868 q^{30} - 2920 q^{33} - 69524 q^{36} - 113000 q^{37} + 99944 q^{40} + 19436 q^{42} - 62504 q^{45} + 145936 q^{46} - 82364 q^{48} + 219504 q^{52} - 286152 q^{57} - 351260 q^{58} + 466756 q^{60} + 652976 q^{61} - 61800 q^{66} + 243868 q^{70} - 145560 q^{72} - 316856 q^{73} + 269024 q^{76} + 613272 q^{78} + 1472232 q^{81} - 1652880 q^{82} - 1466984 q^{85} - 1084100 q^{88} + 448368 q^{90} - 2869552 q^{93} - 278860 q^{96} + 2135272 q^{97}+O(q^{100}) \) 136 * q - 4 * q^6 - 2092 * q^10 - 1460 * q^12 - 8 * q^13 - 932 * q^16 - 12744 * q^18 - 16056 * q^21 + 25444 * q^22 - 8 * q^25 - 52244 * q^28 + 82868 * q^30 - 2920 * q^33 - 69524 * q^36 - 113000 * q^37 + 99944 * q^40 + 19436 * q^42 - 62504 * q^45 + 145936 * q^46 - 82364 * q^48 + 219504 * q^52 - 286152 * q^57 - 351260 * q^58 + 466756 * q^60 + 652976 * q^61 - 61800 * q^66 + 243868 * q^70 - 145560 * q^72 - 316856 * q^73 + 269024 * q^76 + 613272 * q^78 + 1472232 * q^81 - 1652880 * q^82 - 1466984 * q^85 - 1084100 * q^88 + 448368 * q^90 - 2869552 * q^93 - 278860 * q^96 + 2135272 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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