LMFDB - Embedded newform 16.7.f.a.3.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,7,Mod(3,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([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("16.3");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	16.f (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:	$3.68086533792$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.10
Character	$\chi$	$=$	16.3
Dual form			16.7.f.a.11.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.25359 + 3.37422i) q^{2} +(14.8973 - 14.8973i) q^{3} +(41.2292 + 48.9505i) q^{4} +(41.0202 - 41.0202i) q^{5} +(158.326 - 57.7921i) q^{6} -67.2599 q^{7} +(133.890 + 494.184i) q^{8} +285.141i q^{9} +O(q^{10})$	\(q+(7.25359 + 3.37422i) q^{2} +(14.8973 - 14.8973i) q^{3} +(41.2292 + 48.9505i) q^{4} +(41.0202 - 41.0202i) q^{5} +(158.326 - 57.7921i) q^{6} -67.2599 q^{7} +(133.890 + 494.184i) q^{8} +285.141i q^{9} +(435.955 - 159.133i) q^{10} +(-959.330 - 959.330i) q^{11} +(1343.43 + 115.026i) q^{12} +(-1152.76 - 1152.76i) q^{13} +(-487.876 - 226.950i) q^{14} -1222.18i q^{15} +(-696.303 + 4036.38i) q^{16} -8749.14 q^{17} +(-962.129 + 2068.30i) q^{18} +(2786.86 - 2786.86i) q^{19} +(3699.19 + 316.728i) q^{20} +(-1001.99 + 1001.99i) q^{21} +(-3721.59 - 10195.6i) q^{22} +18050.6 q^{23} +(9356.60 + 5367.40i) q^{24} +12259.7i q^{25} +(-4471.97 - 12251.3i) q^{26} +(15108.0 + 15108.0i) q^{27} +(-2773.07 - 3292.40i) q^{28} +(14997.1 + 14997.1i) q^{29} +(4123.91 - 8865.20i) q^{30} -33172.8i q^{31} +(-18670.4 + 26928.8i) q^{32} -28582.9 q^{33} +(-63462.7 - 29521.6i) q^{34} +(-2759.01 + 2759.01i) q^{35} +(-13957.8 + 11756.1i) q^{36} +(-4363.03 + 4363.03i) q^{37} +(29618.3 - 10811.3i) q^{38} -34345.9 q^{39} +(25763.7 + 14779.3i) q^{40} -23563.8i q^{41} +(-10649.0 + 3887.09i) q^{42} +(61646.0 + 61646.0i) q^{43} +(7407.25 - 86512.1i) q^{44} +(11696.5 + 11696.5i) q^{45} +(130932. + 60906.8i) q^{46} -135549. i q^{47} +(49758.2 + 70504.2i) q^{48} -113125. q^{49} +(-41366.9 + 88926.8i) q^{50} +(-130339. + 130339. i) q^{51} +(8900.76 - 103955. i) q^{52} +(173023. - 173023. i) q^{53} +(58609.4 + 160565. i) q^{54} -78703.8 q^{55} +(-9005.43 - 33238.7i) q^{56} -83033.5i q^{57} +(58179.5 + 159387. i) q^{58} +(-49138.8 - 49138.8i) q^{59} +(59826.4 - 50389.6i) q^{60} +(190716. + 190716. i) q^{61} +(111933. - 240622. i) q^{62} -19178.5i q^{63} +(-226291. + 132333. i) q^{64} -94572.7 q^{65} +(-207328. - 96444.9i) q^{66} +(-246599. + 246599. i) q^{67} +(-360720. - 428275. i) q^{68} +(268905. - 268905. i) q^{69} +(-29322.3 + 10703.2i) q^{70} -5723.74 q^{71} +(-140912. + 38177.5i) q^{72} +344002. i q^{73} +(-46369.5 + 16925.8i) q^{74} +(182636. + 182636. i) q^{75} +(251319. + 21518.1i) q^{76} +(64524.4 + 64524.4i) q^{77} +(-249132. - 115891. i) q^{78} +78590.7i q^{79} +(137011. + 194136. i) q^{80} +242268. q^{81} +(79509.5 - 170922. i) q^{82} +(472406. - 472406. i) q^{83} +(-90359.2 - 7736.65i) q^{84} +(-358891. + 358891. i) q^{85} +(239148. + 655162. i) q^{86} +446834. q^{87} +(345640. - 602530. i) q^{88} -418087. i q^{89} +(45375.2 + 124309. i) q^{90} +(77534.3 + 77534.3i) q^{91} +(744212. + 883586. i) q^{92} +(-494186. - 494186. i) q^{93} +(457371. - 983214. i) q^{94} -228635. i q^{95} +(123028. + 679304. i) q^{96} -758697. q^{97} +(-820564. - 381709. i) q^{98} +(273544. - 273544. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8}+O(q^{10}) $ 22 * q - 2 * q^2 - 2 * q^3 + 88 * q^4 - 2 * q^5 - 512 * q^6 - 4 * q^7 + 964 * q^8	\( 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8} - 1124 q^{10} + 1358 q^{11} - 2348 q^{12} - 2 q^{13} + 7564 q^{14} - 7976 q^{16} - 4 q^{17} - 1874 q^{18} + 3934 q^{19} - 16564 q^{20} - 1460 q^{21} + 25252 q^{22} - 13124 q^{23} - 32592 q^{24} + 58952 q^{26} + 35776 q^{27} + 45176 q^{28} - 33202 q^{29} + 8452 q^{30} - 39672 q^{32} - 4 q^{33} - 52588 q^{34} - 112420 q^{35} - 138484 q^{36} + 3598 q^{37} - 187280 q^{38} + 254396 q^{39} + 165160 q^{40} + 353496 q^{42} - 267986 q^{43} + 380724 q^{44} + 32706 q^{45} + 248156 q^{46} - 460824 q^{48} + 168066 q^{49} - 719674 q^{50} + 301788 q^{51} - 784892 q^{52} - 221842 q^{53} - 547552 q^{54} - 232708 q^{55} + 366424 q^{56} + 1441912 q^{58} + 39150 q^{59} + 2405600 q^{60} + 326494 q^{61} + 182832 q^{62} - 318656 q^{64} + 186412 q^{65} - 3392732 q^{66} - 122786 q^{67} - 2504400 q^{68} - 543188 q^{69} - 1186816 q^{70} - 267012 q^{71} + 1748596 q^{72} + 3610396 q^{74} - 275278 q^{75} + 4245988 q^{76} + 231180 q^{77} + 3179052 q^{78} - 2898968 q^{80} - 354298 q^{81} - 5004624 q^{82} - 288322 q^{83} - 7602776 q^{84} + 340748 q^{85} - 3240476 q^{86} + 2029884 q^{87} + 3308152 q^{88} + 10273400 q^{90} + 302396 q^{91} + 7253656 q^{92} - 1173344 q^{93} + 3859056 q^{94} - 5689424 q^{96} - 4 q^{97} - 9176950 q^{98} - 271522 q^{99}+O(q^{100}) \) 22 * q - 2 * q^2 - 2 * q^3 + 88 * q^4 - 2 * q^5 - 512 * q^6 - 4 * q^7 + 964 * q^8 - 1124 * q^10 + 1358 * q^11 - 2348 * q^12 - 2 * q^13 + 7564 * q^14 - 7976 * q^16 - 4 * q^17 - 1874 * q^18 + 3934 * q^19 - 16564 * q^20 - 1460 * q^21 + 25252 * q^22 - 13124 * q^23 - 32592 * q^24 + 58952 * q^26 + 35776 * q^27 + 45176 * q^28 - 33202 * q^29 + 8452 * q^30 - 39672 * q^32 - 4 * q^33 - 52588 * q^34 - 112420 * q^35 - 138484 * q^36 + 3598 * q^37 - 187280 * q^38 + 254396 * q^39 + 165160 * q^40 + 353496 * q^42 - 267986 * q^43 + 380724 * q^44 + 32706 * q^45 + 248156 * q^46 - 460824 * q^48 + 168066 * q^49 - 719674 * q^50 + 301788 * q^51 - 784892 * q^52 - 221842 * q^53 - 547552 * q^54 - 232708 * q^55 + 366424 * q^56 + 1441912 * q^58 + 39150 * q^59 + 2405600 * q^60 + 326494 * q^61 + 182832 * q^62 - 318656 * q^64 + 186412 * q^65 - 3392732 * q^66 - 122786 * q^67 - 2504400 * q^68 - 543188 * q^69 - 1186816 * q^70 - 267012 * q^71 + 1748596 * q^72 + 3610396 * q^74 - 275278 * q^75 + 4245988 * q^76 + 231180 * q^77 + 3179052 * q^78 - 2898968 * q^80 - 354298 * q^81 - 5004624 * q^82 - 288322 * q^83 - 7602776 * q^84 + 340748 * q^85 - 3240476 * q^86 + 2029884 * q^87 + 3308152 * q^88 + 10273400 * q^90 + 302396 * q^91 + 7253656 * q^92 - 1173344 * q^93 + 3859056 * q^94 - 5689424 * q^96 - 4 * q^97 - 9176950 * q^98 - 271522 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	7.25359	+	3.37422i	0.906699	+	0.421778i
$2$	7.25359	+	3.37422i	0.906699	+	0.421778i
$3$	14.8973	−	14.8973i	0.551752	−	0.551752i	−0.375194	−	0.926946i	$-0.622424\pi$
$3$	14.8973	−	14.8973i	0.551752	−	0.551752i	0.926946	+	0.375194i	$0.122424\pi$
$4$	41.2292	+	48.9505i	0.644207	+	0.764852i
$5$	41.0202	−	41.0202i	0.328162	−	0.328162i	−0.523725	−	0.851887i	$-0.675458\pi$
$5$	41.0202	−	41.0202i	0.328162	−	0.328162i	0.851887	+	0.523725i	$0.175458\pi$
$6$	158.326	−	57.7921i	0.732990	−	0.267556i
$7$	−67.2599			−0.196093			−0.0980465	−	0.995182i	$-0.531259\pi$
$7$	−67.2599			−0.196093			−0.0980465	+	0.995182i	$0.531259\pi$
$8$	133.890	+	494.184i	0.261504	+	0.965202i
$9$			285.141i			0.391140i
$10$	435.955	−	159.133i	0.435955	−	0.159133i
$11$	−959.330	−	959.330i	−0.720759	−	0.720759i	0.248001	−	0.968760i	$-0.420226\pi$
$11$	−959.330	−	959.330i	−0.720759	−	0.720759i	−0.968760	+	0.248001i	$0.920226\pi$
$12$	1343.43	+	115.026i	0.777450	+	0.0665661i
$13$	−1152.76	−	1152.76i	−0.524696	−	0.524696i	0.394290	−	0.918986i	$-0.370991\pi$
$13$	−1152.76	−	1152.76i	−0.524696	−	0.524696i	−0.918986	+	0.394290i	$0.870991\pi$
$14$	−487.876	−	226.950i	−0.177797	−	0.0827077i
$15$		−	1222.18i		−	0.362128i
$16$	−696.303	+	4036.38i	−0.169996	+	0.985445i
$17$	−8749.14			−1.78081			−0.890407	−	0.455166i	$-0.849580\pi$
$17$	−8749.14			−1.78081			−0.890407	+	0.455166i	$0.849580\pi$
$18$	−962.129	+	2068.30i	−0.164974	+	0.354646i
$19$	2786.86	−	2786.86i	0.406307	−	0.406307i	−0.474141	−	0.880449i	$-0.657241\pi$
$19$	2786.86	−	2786.86i	0.406307	−	0.406307i	0.880449	+	0.474141i	$0.157241\pi$
$20$	3699.19	+	316.728i	0.462399	+	0.0395911i
$21$	−1001.99	+	1001.99i	−0.108195	+	0.108195i
$22$	−3721.59	−	10195.6i	−0.349511	−	0.957511i
$23$	18050.6			1.48357			0.741785	−	0.670638i	$-0.233979\pi$
$23$	18050.6			1.48357			0.741785	+	0.670638i	$0.233979\pi$
$24$	9356.60	+	5367.40i	0.676838	+	0.388267i
$25$			12259.7i			0.784620i
$26$	−4471.97	−	12251.3i	−0.254436	−	0.697047i
$27$	15108.0	+	15108.0i	0.767564	+	0.767564i
$28$	−2773.07	−	3292.40i	−0.126324	−	0.149982i
$29$	14997.1	+	14997.1i	0.614914	+	0.614914i	0.944222	−	0.329308i	$-0.106816\pi$
$29$	14997.1	+	14997.1i	0.614914	+	0.614914i	−0.329308	+	0.944222i	$0.606816\pi$
$30$	4123.91	−	8865.20i	0.152737	−	0.328341i
$31$		−	33172.8i		−	1.11352i	−0.830674	−	0.556760i	$-0.812044\pi$
$31$		−	33172.8i		−	1.11352i	0.830674	−	0.556760i	$-0.187956\pi$
$32$	−18670.4	+	26928.8i	−0.569774	+	0.821801i
$33$	−28582.9			−0.795360
$34$	−63462.7	−	29521.6i	−1.61466	−	0.751108i
$35$	−2759.01	+	2759.01i	−0.0643502	+	0.0643502i
$36$	−13957.8	+	11756.1i	−0.299164	+	0.251975i
$37$	−4363.03	+	4363.03i	−0.0861357	+	0.0861357i	−0.748862	−	0.662726i	$-0.769399\pi$
$37$	−4363.03	+	4363.03i	−0.0861357	+	0.0861357i	0.662726	+	0.748862i	$0.269399\pi$
$38$	29618.3	−	10811.3i	0.539770	−	0.197027i
$39$	−34345.9			−0.579004
$40$	25763.7	+	14779.3i	0.402558	+	0.230927i
$41$		−	23563.8i		−	0.341896i	−0.985280	−	0.170948i	$-0.945317\pi$
$41$		−	23563.8i		−	0.341896i	0.985280	−	0.170948i	$-0.0546830\pi$
$42$	−10649.0	+	3887.09i	−0.143734	+	0.0524659i
$43$	61646.0	+	61646.0i	0.775353	+	0.775353i	0.979037	−	0.203684i	$-0.0652914\pi$
$43$	61646.0	+	61646.0i	0.775353	+	0.775353i	−0.203684	+	0.979037i	$0.565291\pi$
$44$	7407.25	−	86512.1i	0.0869559	−	1.01559i
$45$	11696.5	+	11696.5i	0.128357	+	0.128357i
$46$	130932.	+	60906.8i	1.34515	+	0.625737i
$47$		−	135549.i		−	1.30557i	−0.757541	−	0.652787i	$-0.773600\pi$
$47$		−	135549.i		−	1.30557i	0.757541	−	0.652787i	$-0.226400\pi$
$48$	49758.2	+	70504.2i	0.449926	+	0.637516i
$49$	−113125.			−0.961548
$50$	−41366.9	+	88926.8i	−0.330935	+	0.711414i
$51$	−130339.	+	130339.i	−0.982567	+	0.982567i
$52$	8900.76	−	103955.i	0.0633019	−	0.739327i
$53$	173023.	−	173023.i	1.16218	−	1.16218i	0.178189	−	0.983996i	$-0.442976\pi$
$53$	173023.	−	173023.i	1.16218	−	1.16218i	0.983996	−	0.178189i	$-0.0570237\pi$
$54$	58609.4	+	160565.i	0.372208	+	1.01969i
$55$	−78703.8			−0.473051
$56$	−9005.43	−	33238.7i	−0.0512791	−	0.189269i
$57$		−	83033.5i		−	0.448362i
$58$	58179.5	+	159387.i	0.298185	+	0.816900i
$59$	−49138.8	−	49138.8i	−0.239259	−	0.239259i	0.577284	−	0.816543i	$-0.304113\pi$
$59$	−49138.8	−	49138.8i	−0.239259	−	0.239259i	−0.816543	+	0.577284i	$0.804113\pi$
$60$	59826.4	−	50389.6i	0.276974	−	0.233285i
$61$	190716.	+	190716.i	0.840230	+	0.840230i	0.988889	−	0.148658i	$-0.0474954\pi$
$61$	190716.	+	190716.i	0.840230	+	0.840230i	−0.148658	+	0.988889i	$0.547495\pi$
$62$	111933.	−	240622.i	0.469658	−	1.00963i
$63$		−	19178.5i		−	0.0766997i
$64$	−226291.	+	132333.i	−0.863231	+	0.504809i
$65$	−94572.7			−0.344370
$66$	−207328.	−	96444.9i	−0.721152	−	0.335465i
$67$	−246599.	+	246599.i	−0.819910	+	0.819910i	−0.986095	−	0.166184i	$-0.946855\pi$
$67$	−246599.	+	246599.i	−0.819910	+	0.819910i	0.166184	+	0.986095i	$0.446855\pi$
$68$	−360720.	−	428275.i	−1.14721	−	1.36206i
$69$	268905.	−	268905.i	0.818563	−	0.818563i
$70$	−29322.3	+	10703.2i	−0.0854877	+	0.0312048i
$71$	−5723.74			−0.0159921			−0.00799604	−	0.999968i	$-0.502545\pi$
$71$	−5723.74			−0.0159921			−0.00799604	+	0.999968i	$0.502545\pi$
$72$	−140912.	+	38177.5i	−0.377529	+	0.102285i
$73$			344002.i			0.884285i	0.896945	+	0.442142i	$0.145781\pi$
$73$			344002.i			0.884285i	−0.896945	+	0.442142i	$0.854219\pi$
$74$	−46369.5	+	16925.8i	−0.114429	+	0.0417690i
$75$	182636.	+	182636.i	0.432915	+	0.432915i
$76$	251319.	+	21518.1i	0.572511	+	0.0490189i
$77$	64524.4	+	64524.4i	0.141336	+	0.141336i
$78$	−249132.	−	115891.i	−0.524983	−	0.244211i
$79$			78590.7i			0.159401i	0.996819	+	0.0797003i	$0.0253963\pi$
$79$			78590.7i			0.159401i	−0.996819	+	0.0797003i	$0.974604\pi$
$80$	137011.	+	194136.i	0.267599	+	0.379171i
$81$	242268.			0.455870
$82$	79509.5	−	170922.i	0.144204	−	0.309997i
$83$	472406.	−	472406.i	0.826192	−	0.826192i	−0.160795	−	0.986988i	$-0.551406\pi$
$83$	472406.	−	472406.i	0.826192	−	0.826192i	0.986988	+	0.160795i	$0.0514059\pi$
$84$	−90359.2	−	7736.65i	−0.152453	−	0.0130531i
$85$	−358891.	+	358891.i	−0.584395	+	0.584395i
$86$	239148.	+	655162.i	0.375985	+	1.03004i
$87$	446834.			0.678560
$88$	345640.	−	602530.i	0.507197	−	0.884159i
$89$		−	418087.i		−	0.593058i	−0.955024	−	0.296529i	$-0.904171\pi$
$89$		−	418087.i		−	0.593058i	0.955024	−	0.296529i	$-0.0958291\pi$
$90$	45375.2	+	124309.i	0.0622431	+	0.170519i
$91$	77534.3	+	77534.3i	0.102889	+	0.102889i
$92$	744212.	+	883586.i	0.955726	+	1.13471i
$93$	−494186.	−	494186.i	−0.614386	−	0.614386i
$94$	457371.	−	983214.i	0.550662	−	1.18376i
$95$		−	228635.i		−	0.266669i
$96$	123028.	+	679304.i	0.139057	+	0.767804i
$97$	−758697.			−0.831291			−0.415646	−	0.909527i	$-0.636444\pi$
$97$	−758697.			−0.831291			−0.415646	+	0.909527i	$0.636444\pi$
$98$	−820564.	−	381709.i	−0.871834	−	0.405560i
$99$	273544.	−	273544.i	0.281917	−	0.281917i
$100$	−600118.	+	505457.i	−0.600118	+	0.505457i
$101$	−1.35481e6	+	1.35481e6i	−1.31497	+	1.31497i	−0.397263	+	0.917705i	$0.630040\pi$
$101$	−1.35481e6	+	1.35481e6i	−1.31497	+	1.31497i	−0.917705	+	0.397263i	$0.869960\pi$
$102$	−1.38521e6	+	505631.i	−1.30532	+	0.476468i
$103$	−508750.			−0.465578			−0.232789	−	0.972527i	$-0.574785\pi$
$103$	−508750.			−0.465578			−0.232789	+	0.972527i	$0.574785\pi$
$104$	415331.	−	724017.i	0.369228	−	0.643648i
$105$			82203.7i			0.0710107i
$106$	1.83885e6	−	671218.i	1.54394	−	0.563568i
$107$	−852289.	−	852289.i	−0.695722	−	0.695722i	0.267763	−	0.963485i	$-0.413716\pi$
$107$	−852289.	−	852289.i	−0.695722	−	0.695722i	−0.963485	+	0.267763i	$0.913716\pi$
$108$	−116653.	+	1.36243e6i	−0.0926027	+	1.08154i
$109$	−907976.	−	907976.i	−0.701124	−	0.701124i	0.263528	−	0.964652i	$-0.415114\pi$
$109$	−907976.	−	907976.i	−0.701124	−	0.701124i	−0.964652	+	0.263528i	$0.915114\pi$
$110$	−570886.	−	265564.i	−0.428915	−	0.199522i
$111$			129995.i			0.0950511i
$112$	46833.2	−	271487.i	0.0333350	−	0.193239i
$113$	1.80590e6			1.25158			0.625789	−	0.779992i	$-0.284777\pi$
$113$	1.80590e6			1.25158			0.625789	+	0.779992i	$0.284777\pi$
$114$	280174.	−	602291.i	0.189109	−	0.406529i
$115$	740439.	−	740439.i	0.486851	−	0.486851i
$116$	−115797.	+	1.35244e6i	−0.0741863	+	0.866450i
$117$	328698.	−	328698.i	0.205229	−	0.205229i
$118$	−190628.	−	522239.i	−0.116022	−	0.317851i
$119$	588466.			0.349205
$120$	603982.	−	163638.i	0.349526	−	0.0946978i
$121$			69066.6i			0.0389863i
$122$	739859.	+	2.02690e6i	0.407445	+	1.11623i
$123$	−351037.	−	351037.i	−0.188642	−	0.188642i
$124$	1.62383e6	−	1.36769e6i	0.851677	−	0.717336i
$125$	1.14384e6	+	1.14384e6i	0.585644	+	0.585644i
$126$	64712.7	−	139113.i	0.0323503	−	0.0695436i
$127$			3.85145e6i			1.88024i	0.340848	+	0.940118i	$0.389286\pi$
$127$			3.85145e6i			1.88024i	−0.340848	+	0.940118i	$0.610714\pi$
$128$	−2.08794e6	+	196330.i	−0.995608	+	0.0936174i
$129$	1.83672e6			0.855605
$130$	−685992.	−	319109.i	−0.312240	−	0.145248i
$131$	564224.	−	564224.i	0.250979	−	0.250979i	−0.570393	−	0.821372i	$-0.693209\pi$
$131$	564224.	−	564224.i	0.250979	−	0.250979i	0.821372	+	0.570393i	$0.193209\pi$
$132$	−1.17845e6	−	1.39914e6i	−0.512376	−	0.608332i
$133$	−187444.	+	187444.i	−0.0796740	+	0.0796740i
$134$	−2.62081e6	+	956647.i	−1.08923	+	0.397592i
$135$	1.23946e6			0.503770
$136$	−1.17142e6	−	4.32368e6i	−0.465690	−	1.71885i
$137$			1.47761e6i			0.574641i	0.957834	+	0.287321i	$0.0927645\pi$
$137$			1.47761e6i			0.574641i	−0.957834	+	0.287321i	$0.907235\pi$
$138$	2.85788e6	−	1.04318e6i	1.08744	−	0.396938i
$139$	−476423.	−	476423.i	−0.177398	−	0.177398i	0.612823	−	0.790221i	$-0.290034\pi$
$139$	−476423.	−	476423.i	−0.177398	−	0.177398i	−0.790221	+	0.612823i	$0.790034\pi$
$140$	−248807.	−	21303.1i	−0.0906731	−	0.00776352i
$141$	−2.01931e6	−	2.01931e6i	−0.720353	−	0.720353i
$142$	−41517.7	−	19313.2i	−0.0145000	−	0.00674511i
$143$			2.21175e6i			0.756359i
$144$	−1.15094e6	−	198544.i	−0.385447	−	0.0664921i
$145$	1.23037e6			0.403583
$146$	−1.16074e6	+	2.49525e6i	−0.372972	+	0.801780i
$147$	−1.68526e6	+	1.68526e6i	−0.530536	+	0.530536i
$148$	−393457.	−	33688.2i	−0.121370	−	0.0103918i
$149$	2.43655e6	−	2.43655e6i	0.736574	−	0.736574i	−0.235339	−	0.971913i	$-0.575620\pi$
$149$	2.43655e6	−	2.43655e6i	0.736574	−	0.736574i	0.971913	+	0.235339i	$0.0756200\pi$
$150$	708513.	+	1.94102e6i	0.209930	+	0.575118i
$151$	−2.84256e6			−0.825616			−0.412808	−	0.910818i	$-0.635452\pi$
$151$	−2.84256e6			−0.825616			−0.412808	+	0.910818i	$0.635452\pi$
$152$	1.75036e6	+	1.00409e6i	0.498420	+	0.285918i
$153$		−	2.49474e6i		−	0.696547i
$154$	250314.	+	685754.i	0.0685366	+	0.187761i
$155$	−1.36076e6	−	1.36076e6i	−0.365414	−	0.365414i
$156$	−1.41606e6	−	1.68125e6i	−0.372998	−	0.442852i
$157$	1.11302e6	+	1.11302e6i	0.287610	+	0.287610i	0.836135	−	0.548524i	$-0.184810\pi$
$157$	1.11302e6	+	1.11302e6i	0.287610	+	0.287610i	−0.548524	+	0.836135i	$0.684810\pi$
$158$	−265183.	+	570065.i	−0.0672317	+	0.144528i
$159$		−	5.15514e6i		−	1.28248i
$160$	338763.	+	1.87049e6i	0.0827058	+	0.456662i
$161$	−1.21408e6			−0.290918
$162$	1.75731e6	+	817467.i	0.413337	+	0.192276i
$163$	−1.92618e6	+	1.92618e6i	−0.444768	+	0.444768i	−0.893611	−	0.448843i	$-0.851836\pi$
$163$	−1.92618e6	+	1.92618e6i	−0.444768	+	0.444768i	0.448843	+	0.893611i	$0.351836\pi$
$164$	1.15346e6	−	971517.i	0.261499	−	0.220251i
$165$	−1.17247e6	+	1.17247e6i	−0.261007	+	0.261007i
$166$	5.02065e6	−	1.83264e6i	1.09758	−	0.400638i
$167$	−4.80910e6			−1.03256			−0.516278	−	0.856421i	$-0.672683\pi$
$167$	−4.80910e6			−1.03256			−0.516278	+	0.856421i	$0.672683\pi$
$168$	−629324.	−	361011.i	−0.132723	−	0.0761364i
$169$		−	2.16911e6i		−	0.449388i
$170$	−3.81423e6	+	1.39227e6i	−0.776355	+	0.283385i
$171$	794648.	+	794648.i	0.158923	+	0.158923i
$172$	−475986.	+	5.55922e6i	−0.0935424	+	1.09252i
$173$	2.92099e6	+	2.92099e6i	0.564147	+	0.564147i	0.930483	−	0.366336i	$-0.119388\pi$
$173$	2.92099e6	+	2.92099e6i	0.564147	+	0.564147i	−0.366336	+	0.930483i	$0.619388\pi$
$174$	3.24115e6	+	1.50772e6i	0.615250	+	0.286202i
$175$		−	824585.i		−	0.153858i
$176$	4.54021e6	−	3.20424e6i	0.832794	−	0.587742i
$177$	−1.46407e6			−0.264024
$178$	1.41072e6	−	3.03263e6i	0.250139	−	0.537725i
$179$	1.02489e6	−	1.02489e6i	0.178698	−	0.178698i	−0.612090	−	0.790788i	$-0.709671\pi$
$179$	1.02489e6	−	1.02489e6i	0.178698	−	0.178698i	0.790788	+	0.612090i	$0.209671\pi$
$180$	−90312.2	+	1.05479e6i	−0.0154856	+	0.180863i
$181$	480156.	−	480156.i	0.0809742	−	0.0809742i	−0.665460	−	0.746434i	$-0.731764\pi$
$181$	480156.	−	480156.i	0.0809742	−	0.0809742i	0.746434	+	0.665460i	$0.231764\pi$
$182$	300784.	+	824020.i	0.0498931	+	0.136686i
$183$	5.68232e6			0.927197
$184$	2.41679e6	+	8.92031e6i	0.387959	+	1.43195i
$185$			357945.i			0.0565329i
$186$	−1.91713e6	−	5.25212e6i	−0.297929	−	0.816198i
$187$	8.39331e6	+	8.39331e6i	1.28354	+	1.28354i
$188$	6.63517e6	−	5.58856e6i	0.998570	−	0.841059i
$189$	−1.01616e6	−	1.01616e6i	−0.150514	−	0.150514i
$190$	771467.	−	1.65843e6i	0.112475	−	0.241789i
$191$		−	1.25040e7i		−	1.79452i	−0.441500	−	0.897261i	$-0.645553\pi$
$191$		−	1.25040e7i		−	1.79452i	0.441500	−	0.897261i	$-0.354447\pi$
$192$	−1.39973e6	+	5.34252e6i	−0.197760	+	0.754819i
$193$	−1.08769e7			−1.51298			−0.756489	−	0.654007i	$-0.773087\pi$
$193$	−1.08769e7			−1.51298			−0.756489	+	0.654007i	$0.773087\pi$
$194$	−5.50328e6	−	2.56001e6i	−0.753731	−	0.350620i
$195$	−1.40888e6	+	1.40888e6i	−0.190007	+	0.190007i
$196$	−4.66406e6	−	5.53753e6i	−0.619435	−	0.735441i
$197$	−702956.	+	702956.i	−0.0919453	+	0.0919453i	−0.751583	−	0.659638i	$-0.770710\pi$
$197$	−702956.	+	702956.i	−0.0919453	+	0.0919453i	0.659638	+	0.751583i	$0.270710\pi$
$198$	2.90718e6	−	1.06118e6i	0.374521	−	0.136708i
$199$	3.26734e6			0.414605			0.207303	−	0.978277i	$-0.433532\pi$
$199$	3.26734e6			0.414605			0.207303	+	0.978277i	$0.433532\pi$
$200$	−6.05854e6	+	1.64145e6i	−0.757317	+	0.205181i
$201$			7.34731e6i			0.904774i
$202$	−1.43987e7	+	5.25582e6i	−1.74690	+	0.637656i
$203$	−1.00871e6	−	1.00871e6i	−0.120580	−	0.120580i
$204$	−1.17539e7	−	1.00638e6i	−1.38449	−	0.118542i
$205$	−966592.	−	966592.i	−0.112197	−	0.112197i
$206$	−3.69027e6	−	1.71664e6i	−0.422139	−	0.196371i
$207$			5.14696e6i			0.580283i
$208$	5.45564e6	−	3.85030e6i	0.606255	−	0.427863i
$209$	−5.34704e6			−0.585699
$210$	−277374.	+	596272.i	−0.0299507	+	0.0643853i
$211$	4.54501e6	−	4.54501e6i	0.483824	−	0.483824i	−0.422526	−	0.906351i	$-0.638857\pi$
$211$	4.54501e6	−	4.54501e6i	0.483824	−	0.483824i	0.906351	+	0.422526i	$0.138857\pi$
$212$	1.56031e7	+	1.33596e6i	1.63759	+	0.140212i
$213$	−85268.3	+	85268.3i	−0.00882366	+	0.00882366i
$214$	−3.30634e6	−	9.05797e6i	−0.337370	−	0.924251i
$215$	5.05746e6			0.508882
$216$	−5.44330e6	+	9.48891e6i	−0.540134	+	0.941576i
$217$			2.23120e6i			0.218353i
$218$	−3.52237e6	−	9.64980e6i	−0.339990	−	0.931427i
$219$	5.12470e6	+	5.12470e6i	0.487906	+	0.487906i
$220$	−3.24490e6	−	3.85259e6i	−0.304742	−	0.361814i
$221$	1.00856e7	+	1.00856e7i	0.934386	+	0.934386i
$222$	−438632.	+	942929.i	−0.0400905	+	0.0861827i
$223$		−	1.47973e6i		−	0.133434i	−0.997772	−	0.0667170i	$-0.978748\pi$
$223$		−	1.47973e6i		−	0.133434i	0.997772	−	0.0667170i	$-0.0212525\pi$
$224$	1.25577e6	−	1.81123e6i	0.111729	−	0.161149i
$225$	−3.49574e6			−0.306896
$226$	1.30993e7	+	6.09351e6i	1.13481	+	0.527889i
$227$	−4.08883e6	+	4.08883e6i	−0.349560	+	0.349560i	−0.859945	−	0.510386i	$-0.829503\pi$
$227$	−4.08883e6	+	4.08883e6i	−0.349560	+	0.349560i	0.510386	+	0.859945i	$0.329503\pi$
$228$	4.06453e6	−	3.42341e6i	0.342930	−	0.288838i
$229$	1.17316e7	−	1.17316e7i	0.976900	−	0.976900i	−0.0228393	−	0.999739i	$-0.507271\pi$
$229$	1.17316e7	−	1.17316e7i	0.976900	−	0.976900i	0.999739	+	0.0228393i	$0.00727060\pi$
$230$	7.86925e6	−	2.87244e6i	0.646770	−	0.236084i
$231$	1.92248e6			0.155964
$232$	−5.40338e6	+	9.41931e6i	−0.432714	+	0.754319i
$233$			3.16693e6i			0.250363i	0.992134	+	0.125182i	$0.0399514\pi$
$233$			3.16693e6i			0.250363i	−0.992134	+	0.125182i	$0.960049\pi$
$234$	3.49334e6	−	1.27514e6i	0.272643	−	0.0995201i
$235$	−5.56023e6	−	5.56023e6i	−0.428439	−	0.428439i
$236$	379415.	−	4.43133e6i	0.0288654	−	0.337130i
$237$	1.17079e6	+	1.17079e6i	0.0879496	+	0.0879496i
$238$	4.26849e6	+	1.98562e6i	0.316624	+	0.147287i
$239$		−	8.23655e6i		−	0.603326i	−0.953415	−	0.301663i	$-0.902458\pi$
$239$		−	8.23655e6i		−	0.603326i	0.953415	−	0.301663i	$-0.0975417\pi$
$240$	4.93319e6	+	851008.i	0.356857	+	0.0615602i
$241$	2.79082e6			0.199379			0.0996897	−	0.995019i	$-0.468215\pi$
$241$	2.79082e6			0.199379			0.0996897	+	0.995019i	$0.468215\pi$
$242$	−233046.	+	500981.i	−0.0164436	+	0.0353488i
$243$	−7.40456e6	+	7.40456e6i	−0.516037	+	0.516037i
$244$	−1.47257e6	+	1.71987e7i	−0.101370	+	1.18393i
$245$	−4.64042e6	+	4.64042e6i	−0.315543	+	0.315543i
$246$	−1.36180e6	−	3.73076e6i	−0.0914763	−	0.250606i
$247$	−6.42515e6			−0.426376
$248$	1.63935e7	−	4.44151e6i	1.07477	−	0.291190i
$249$		−	1.40752e7i		−	0.911707i
$250$	4.43736e6	+	1.21565e7i	0.283991	+	0.778014i
$251$	−1.03993e7	−	1.03993e7i	−0.657633	−	0.657633i	0.297187	−	0.954819i	$-0.403952\pi$
$251$	−1.03993e7	−	1.03993e7i	−0.657633	−	0.657633i	−0.954819	+	0.297187i	$0.903952\pi$
$252$	938799.	−	790716.i	0.0586639	−	0.0494105i
$253$	−1.73165e7	−	1.73165e7i	−1.06930	−	1.06930i
$254$	−1.29956e7	+	2.79368e7i	−0.793043	+	1.70481i
$255$			1.06930e7i			0.644882i
$256$	−1.58075e7	−	5.62109e6i	−0.942203	−	0.335043i
$257$	1.52480e7			0.898283			0.449141	−	0.893461i	$-0.351730\pi$
$257$	1.52480e7			0.898283			0.449141	+	0.893461i	$0.351730\pi$
$258$	1.33228e7	+	6.19750e6i	0.775776	+	0.360875i
$259$	293457.	−	293457.i	0.0168906	−	0.0168906i
$260$	−3.89916e6	−	4.62938e6i	−0.221846	−	0.263392i
$261$	−4.27630e6	+	4.27630e6i	−0.240517	+	0.240517i
$262$	5.99647e6	−	2.18883e6i	0.333420	−	0.121705i
$263$	−2.87421e7			−1.57998			−0.789988	−	0.613122i	$-0.789913\pi$
$263$	−2.87421e7			−1.57998			−0.789988	+	0.613122i	$0.789913\pi$
$264$	−3.82696e6	−	1.41252e7i	−0.207990	−	0.767683i
$265$		−	1.41948e7i		−	0.762769i
$266$	−1.99212e6	+	727164.i	−0.105845	+	0.0386356i
$267$	−6.22837e6	−	6.22837e6i	−0.327221	−	0.327221i
$268$	−2.22382e7	−	1.90406e6i	−1.15530	−	0.0989181i
$269$	2.82907e6	+	2.82907e6i	0.145341	+	0.145341i	0.776033	−	0.630692i	$-0.217229\pi$
$269$	2.82907e6	+	2.82907e6i	0.145341	+	0.145341i	−0.630692	+	0.776033i	$0.717229\pi$
$270$	8.99056e6	+	4.18223e6i	0.456768	+	0.212479i
$271$			1.96222e7i			0.985915i	0.870053	+	0.492958i	$0.164084\pi$
$271$			1.96222e7i			0.985915i	−0.870053	+	0.492958i	$0.835916\pi$
$272$	6.09205e6	−	3.53149e7i	0.302731	−	1.75489i
$273$	2.31010e6			0.113539
$274$	−4.98577e6	+	1.07179e7i	−0.242371	+	0.521027i
$275$	1.17611e7	−	1.17611e7i	0.565522	−	0.565522i
$276$	2.42498e7	+	2.07629e6i	1.15340	+	0.0987554i
$277$	1.07923e6	−	1.07923e6i	0.0507781	−	0.0507781i	−0.681262	−	0.732040i	$-0.738568\pi$
$277$	1.07923e6	−	1.07923e6i	0.0507781	−	0.0507781i	0.732040	+	0.681262i	$0.238568\pi$
$278$	−1.84822e6	−	5.06334e6i	−0.0860240	−	0.235669i
$279$	9.45893e6			0.435542
$280$	−1.73286e6	−	994055.i	−0.0789388	−	0.0452831i
$281$			2.13021e7i			0.960070i	0.877249	+	0.480035i	$0.159376\pi$
$281$			2.13021e7i			0.960070i	−0.877249	+	0.480035i	$0.840624\pi$
$282$	−7.83364e6	−	2.14608e7i	−0.349314	−	0.956972i
$283$	2.02280e7	+	2.02280e7i	0.892472	+	0.892472i	0.994755	−	0.102283i	$-0.0326149\pi$
$283$	2.02280e7	+	2.02280e7i	0.892472	+	0.892472i	−0.102283	+	0.994755i	$0.532615\pi$
$284$	−235985.	−	280180.i	−0.0103022	−	0.0122316i
$285$	−3.40605e6	−	3.40605e6i	−0.147135	−	0.147135i
$286$	−7.46294e6	+	1.60431e7i	−0.319015	+	0.685790i
$287$			1.58490e6i			0.0670433i
$288$	−7.67850e6	−	5.32368e6i	−0.321439	−	0.222861i
$289$	5.24098e7			2.17130
$290$	8.92462e6	+	4.15155e6i	0.365928	+	0.170222i
$291$	−1.13025e7	+	1.13025e7i	−0.458666	+	0.458666i
$292$	−1.68391e7	+	1.41829e7i	−0.676346	+	0.569662i
$293$	−1.76909e7	+	1.76909e7i	−0.703310	+	0.703310i	−0.965120	−	0.261810i	$-0.915681\pi$
$293$	−1.76909e7	+	1.76909e7i	−0.703310	+	0.703310i	0.261810	+	0.965120i	$0.415681\pi$
$294$	−1.79106e7	+	6.53774e6i	−0.704805	+	0.257268i
$295$	−4.03137e6			−0.157031
$296$	−2.74031e6	−	1.57197e6i	−0.105663	−	0.0606136i
$297$		−	2.89870e7i		−	1.10646i
$298$	2.58952e7	−	9.45228e6i	0.978522	−	0.357180i
$299$	−2.08080e7	−	2.08080e7i	−0.778423	−	0.778423i
$300$	−1.41018e6	+	1.64701e7i	−0.0522291	+	0.610003i
$301$	−4.14630e6	−	4.14630e6i	−0.152041	−	0.152041i
$302$	−2.06187e7	−	9.59142e6i	−0.748585	−	0.348227i
$303$			4.03661e7i			1.45107i
$304$	9.30834e6	+	1.31893e7i	0.331323	+	0.469464i
$305$	1.56464e7			0.551463
$306$	8.41780e6	−	1.80958e7i	0.293788	−	0.631559i
$307$	4.05598e7	−	4.05598e7i	1.40178	−	1.40178i	0.607347	−	0.794437i	$-0.292234\pi$
$307$	4.05598e7	−	4.05598e7i	1.40178	−	1.40178i	0.794437	−	0.607347i	$-0.207766\pi$
$308$	−498211.	+	5.81879e6i	−0.0170514	+	0.199150i
$309$	−7.57900e6	+	7.57900e6i	−0.256884	+	0.256884i
$310$	−5.27888e6	−	1.44619e7i	−0.177197	−	0.485445i
$311$	4.79807e7			1.59509			0.797545	−	0.603259i	$-0.206131\pi$
$311$	4.79807e7			1.59509			0.797545	+	0.603259i	$0.206131\pi$
$312$	−4.59858e6	−	1.69732e7i	−0.151412	−	0.558856i
$313$			3.78269e7i			1.23358i	0.787127	+	0.616791i	$0.211567\pi$
$313$			3.78269e7i			1.23358i	−0.787127	+	0.616791i	$0.788433\pi$
$314$	4.31782e6	+	1.18290e7i	0.139468	+	0.382084i
$315$	−786708.	−	786708.i	−0.0251699	−	0.0251699i
$316$	−3.84705e6	+	3.24023e6i	−0.121918	+	0.102687i
$317$	8.72336e6	+	8.72336e6i	0.273846	+	0.273846i	0.830646	−	0.556801i	$-0.187971\pi$
$317$	8.72336e6	+	8.72336e6i	0.273846	+	0.273846i	−0.556801	+	0.830646i	$0.687971\pi$
$318$	1.73946e7	−	3.73933e7i	0.540920	−	1.16282i
$319$		−	2.87744e7i		−	0.886410i
$320$	−3.85419e6	+	1.47108e7i	−0.117621	+	0.448938i
$321$	−2.53936e7			−0.767732
$322$	−8.80645e6	−	4.09658e6i	−0.263775	−	0.122703i
$323$	−2.43826e7	+	2.43826e7i	−0.723558	+	0.723558i
$324$	9.98852e6	+	1.18591e7i	0.293674	+	0.348673i
$325$	1.41324e7	−	1.41324e7i	0.411687	−	0.411687i
$326$	−2.04711e7	+	7.47235e6i	−0.590864	+	0.215677i
$327$	−2.70528e7			−0.773693
$328$	1.16448e7	−	3.15496e6i	0.329999	−	0.0894071i
$329$			9.11698e6i			0.256014i
$330$	−1.24608e7	+	4.54846e6i	−0.346741	+	0.126568i
$331$	−1.05617e7	−	1.05617e7i	−0.291240	−	0.291240i	0.546330	−	0.837570i	$-0.316024\pi$
$331$	−1.05617e7	−	1.05617e7i	−0.291240	−	0.291240i	−0.837570	+	0.546330i	$0.816024\pi$
$332$	4.26015e7	+	3.64758e6i	1.16415	+	0.0996760i
$333$	−1.24408e6	−	1.24408e6i	−0.0336911	−	0.0336911i
$334$	−3.48832e7	−	1.62270e7i	−0.936218	−	0.435510i
$335$			2.02311e7i			0.538126i
$336$	−3.34673e6	−	4.74210e6i	−0.0882272	−	0.125012i
$337$	−5.84187e7			−1.52638			−0.763189	−	0.646175i	$-0.776368\pi$
$337$	−5.84187e7			−1.52638			−0.763189	+	0.646175i	$0.776368\pi$
$338$	7.31906e6	−	1.57338e7i	0.189542	−	0.407460i
$339$	2.69030e7	−	2.69030e7i	0.690561	−	0.690561i
$340$	−3.23647e7	−	2.77110e6i	−0.823446	−	0.0705043i
$341$	−3.18237e7	+	3.18237e7i	−0.802579	+	0.802579i
$342$	3.08273e6	+	8.44538e6i	0.0770651	+	0.211126i
$343$	1.55218e7			0.384646
$344$	−2.22107e7	+	3.87182e7i	−0.545615	+	0.951131i
$345$		−	2.20611e7i		−	0.537242i
$346$	1.13316e7	+	3.10438e7i	0.273567	+	0.749457i
$347$	−1.11618e7	−	1.11618e7i	−0.267145	−	0.267145i	0.560804	−	0.827949i	$-0.310492\pi$
$347$	−1.11618e7	−	1.11618e7i	−0.267145	−	0.267145i	−0.827949	+	0.560804i	$0.810492\pi$
$348$	1.84226e7	+	2.18727e7i	0.437133	+	0.518998i
$349$	−5.53114e7	−	5.53114e7i	−1.30118	−	1.30118i	−0.927595	−	0.373588i	$-0.878128\pi$
$349$	−5.53114e7	−	5.53114e7i	−1.30118	−	1.30118i	−0.373588	−	0.927595i	$-0.621872\pi$
$350$	2.78233e6	−	5.98120e6i	0.0648941	−	0.139503i
$351$		−	3.48316e7i		−	0.805476i
$352$	4.37446e7	−	7.92256e6i	1.00299	−	0.181651i
$353$	−2.61242e7			−0.593907			−0.296954	−	0.954892i	$-0.595971\pi$
$353$	−2.61242e7			−0.593907			−0.296954	+	0.954892i	$0.595971\pi$
$354$	−1.06198e7	−	4.94011e6i	−0.239390	−	0.111359i
$355$	−234789.	+	234789.i	−0.00524799	+	0.00524799i
$356$	2.04656e7	−	1.72374e7i	0.453601	−	0.382052i
$357$	8.76655e6	−	8.76655e6i	0.192674	−	0.192674i
$358$	1.08924e7	−	3.97594e6i	0.237396	−	0.0866545i
$359$	2.91485e7			0.629988			0.314994	−	0.949094i	$-0.397997\pi$
$359$	2.91485e7			0.629988			0.314994	+	0.949094i	$0.397997\pi$
$360$	−4.21419e6	+	7.34629e6i	−0.0903247	+	0.157456i
$361$			3.15127e7i			0.669829i
$362$	5.10301e6	−	1.86270e6i	0.107572	−	0.0392661i
$363$	1.02891e6	+	1.02891e6i	0.0215108	+	0.0215108i
$364$	−598664.	+	6.99202e6i	−0.0124131	+	0.144977i
$365$	1.41110e7	+	1.41110e7i	0.290188	+	0.290188i
$366$	4.12172e7	+	1.91734e7i	0.840689	+	0.391071i
$367$		−	1.29099e7i		−	0.261170i	−0.991437	−	0.130585i	$-0.958314\pi$
$367$		−	1.29099e7i		−	0.261170i	0.991437	−	0.130585i	$-0.0416856\pi$
$368$	−1.25687e7	+	7.28591e7i	−0.252201	+	1.46198i
$369$	6.71900e6			0.133729
$370$	−1.20779e6	+	2.59639e6i	−0.0238443	+	0.0512583i
$371$	−1.16375e7	+	1.16375e7i	−0.227896	+	0.227896i
$372$	3.81575e6	−	4.45655e7i	0.0741226	−	0.865706i
$373$	1.90086e7	−	1.90086e7i	0.366289	−	0.366289i	−0.499833	−	0.866122i	$-0.666605\pi$
$373$	1.90086e7	−	1.90086e7i	0.366289	−	0.366289i	0.866122	+	0.499833i	$0.166605\pi$
$374$	3.25607e7	+	8.92025e7i	0.622414	+	1.70515i
$375$	3.40801e7			0.646260
$376$	6.69859e7	−	1.81486e7i	1.26014	−	0.341413i
$377$		−	3.45761e7i		−	0.645286i
$378$	−3.94206e6	−	1.07996e7i	−0.0729873	−	0.199954i
$379$	6.64849e7	+	6.64849e7i	1.22125	+	1.22125i	0.967187	+	0.254066i	$0.0817681\pi$
$379$	6.64849e7	+	6.64849e7i	1.22125	+	1.22125i	0.254066	+	0.967187i	$0.418232\pi$
$380$	1.11918e7	−	9.42646e6i	0.203962	−	0.171790i
$381$	5.73761e7	+	5.73761e7i	1.03742	+	1.03742i
$382$	4.21913e7	−	9.06990e7i	0.756890	−	1.62709i
$383$		−	4.04403e7i		−	0.719811i	−0.932989	−	0.359906i	$-0.882809\pi$
$383$		−	4.04403e7i		−	0.719811i	0.932989	−	0.359906i	$-0.117191\pi$
$384$	−2.81799e7	+	3.40295e7i	−0.497675	+	0.600982i
$385$	5.29361e6			0.0927619
$386$	−7.88965e7	−	3.67010e7i	−1.37182	−	0.638141i
$387$	−1.75778e7	+	1.75778e7i	−0.303271	+	0.303271i
$388$	−3.12805e7	−	3.71386e7i	−0.535523	−	0.635814i
$389$	2.76812e7	−	2.76812e7i	0.470259	−	0.470259i	−0.431740	−	0.901998i	$-0.642100\pi$
$389$	2.76812e7	−	2.76812e7i	0.470259	−	0.470259i	0.901998	+	0.431740i	$0.142100\pi$
$390$	−1.49733e7	+	5.46556e6i	−0.252420	+	0.0921384i
$391$	−1.57927e8			−2.64196
$392$	−1.51463e7	−	5.59046e7i	−0.251449	−	0.928088i
$393$		−	1.68108e7i		−	0.276956i
$394$	−7.47089e6	+	2.72703e6i	−0.122147	+	0.0445862i
$395$	3.22381e6	+	3.22381e6i	0.0523092	+	0.0523092i
$396$	2.46681e7	+	2.11211e6i	0.397238	+	0.0340119i
$397$	4.04918e7	+	4.04918e7i	0.647135	+	0.647135i	0.952300	−	0.305164i	$-0.0987114\pi$
$397$	4.04918e7	+	4.04918e7i	0.647135	+	0.647135i	−0.305164	+	0.952300i	$0.598711\pi$
$398$	2.36999e7	+	1.10247e7i	0.375922	+	0.174871i
$399$			5.58482e6i			0.0879206i
$400$	−4.94848e7	−	8.53645e6i	−0.773200	−	0.133382i
$401$	3.49325e7			0.541747			0.270873	−	0.962615i	$-0.412688\pi$
$401$	3.49325e7			0.541747			0.270873	+	0.962615i	$0.412688\pi$
$402$	−2.47915e7	+	5.32944e7i	−0.381614	+	0.820358i
$403$	−3.82402e7	+	3.82402e7i	−0.584259	+	0.584259i
$404$	−1.22177e8	−	1.04609e7i	−1.85287	−	0.158644i
$405$	9.93788e6	−	9.93788e6i	0.149599	−	0.149599i
$406$	−3.91314e6	−	1.07203e7i	−0.0584719	−	0.160188i
$407$	8.37117e6			0.124166
$408$	−8.18622e7	−	4.69601e7i	−1.20532	−	0.691431i
$409$			6.75168e7i			0.986829i	0.869794	+	0.493414i	$0.164251\pi$
$409$			6.75168e7i			0.986829i	−0.869794	+	0.493414i	$0.835749\pi$
$410$	−3.74977e6	−	1.02728e7i	−0.0544067	−	0.149051i
$411$	2.20123e7	+	2.20123e7i	0.317059	+	0.317059i
$412$	−2.09754e7	−	2.49036e7i	−0.299929	−	0.356098i
$413$	3.30507e6	+	3.30507e6i	0.0469171	+	0.0469171i
$414$	−1.73670e7	+	3.73340e7i	−0.244751	+	0.526142i
$415$		−	3.87564e7i		−	0.542249i
$416$	5.25647e7	−	9.51997e6i	0.730154	−	0.132238i
$417$	−1.41948e7			−0.195759
$418$	−3.87853e7	−	1.80421e7i	−0.531053	−	0.247035i
$419$	−7.56911e7	+	7.56911e7i	−1.02897	+	1.02897i	−0.0294018	+	0.999568i	$0.509360\pi$
$419$	−7.56911e7	+	7.56911e7i	−1.02897	+	1.02897i	−0.999568	+	0.0294018i	$0.990640\pi$
$420$	−4.02391e6	+	3.38920e6i	−0.0543126	+	0.0457455i
$421$	3.66497e7	−	3.66497e7i	0.491162	−	0.491162i	−0.417510	−	0.908672i	$-0.637097\pi$
$421$	3.66497e7	−	3.66497e7i	0.491162	−	0.491162i	0.908672	+	0.417510i	$0.137097\pi$
$422$	4.83035e7	−	1.76318e7i	0.642749	−	0.234617i
$423$	3.86504e7			0.510662
$424$	1.08671e8	+	6.23389e7i	1.42566	+	0.817828i
$425$		−	1.07262e8i		−	1.39726i
$426$	−906216.	+	330787.i	−0.0117220	+	0.00427878i
$427$	−1.28276e7	−	1.28276e7i	−0.164763	−	0.164763i
$428$	6.58076e6	−	7.68592e7i	0.0839353	−	0.980313i
$429$	3.29491e7	+	3.29491e7i	0.417322	+	0.417322i
$430$	3.66848e7	+	1.70650e7i	0.461403	+	0.214635i
$431$		−	1.35146e7i		−	0.168800i	−0.996432	−	0.0843999i	$-0.973103\pi$
$431$		−	1.35146e7i		−	0.168800i	0.996432	−	0.0843999i	$-0.0268973\pi$
$432$	−7.15012e7	+	5.04618e7i	−0.886875	+	0.625909i
$433$	−3.45830e7			−0.425989			−0.212995	−	0.977053i	$-0.568322\pi$
$433$	−3.45830e7			−0.425989			−0.212995	+	0.977053i	$0.568322\pi$
$434$	−7.52857e6	+	1.61842e7i	−0.0920966	+	0.197981i
$435$	1.83292e7	−	1.83292e7i	0.222677	−	0.222677i
$436$	7.01073e6	−	8.18810e7i	0.0845871	−	0.987925i
$437$	5.03045e7	−	5.03045e7i	0.602786	−	0.602786i
$438$	1.98806e7	+	5.44643e7i	0.236596	+	0.648172i
$439$	8.85153e6			0.104622			0.0523112	−	0.998631i	$-0.483341\pi$
$439$	8.85153e6			0.104622			0.0523112	+	0.998631i	$0.483341\pi$
$440$	−1.05377e7	−	3.88941e7i	−0.123705	−	0.456590i
$441$		−	3.22566e7i		−	0.376099i
$442$	3.91259e7	+	1.07188e8i	0.453103	+	1.24131i
$443$	7.32715e7	+	7.32715e7i	0.842799	+	0.842799i	0.989222	−	0.146423i	$-0.0467761\pi$
$443$	7.32715e7	+	7.32715e7i	0.842799	+	0.842799i	−0.146423	+	0.989222i	$0.546776\pi$
$444$	−6.36331e6	+	5.35958e6i	−0.0727000	+	0.0612325i
$445$	−1.71500e7	−	1.71500e7i	−0.194619	−	0.194619i
$446$	4.99293e6	−	1.07333e7i	0.0562795	−	0.120985i
$447$		−	7.25961e7i		−	0.812813i
$448$	1.52203e7	−	8.90067e6i	0.169274	−	0.0989894i
$449$	−3.25457e7			−0.359547			−0.179773	−	0.983708i	$-0.557536\pi$
$449$	−3.25457e7			−0.359547			−0.179773	+	0.983708i	$0.557536\pi$
$450$	−2.53567e7	−	1.17954e7i	−0.278262	−	0.129442i
$451$	−2.26055e7	+	2.26055e7i	−0.246424	+	0.246424i
$452$	7.44558e7	+	8.83997e7i	0.806275	+	0.957272i
$453$	−4.23464e7	+	4.23464e7i	−0.455535	+	0.455535i
$454$	−4.34553e7	+	1.58621e7i	−0.464382	+	0.169509i
$455$	6.36095e6			0.0675286
$456$	4.10338e7	−	1.11174e7i	0.432760	−	0.117248i
$457$			1.65930e8i			1.73851i	0.494368	+	0.869253i	$0.335399\pi$
$457$			1.65930e8i			1.73851i	−0.494368	+	0.869253i	$0.664601\pi$
$458$	1.24681e8	−	4.55111e7i	1.29779	−	0.473719i
$459$	−1.32182e8	−	1.32182e8i	−1.36689	−	1.36689i
$460$	6.67726e7	+	5.71714e6i	0.686001	+	0.0587361i
$461$	−6.52136e7	−	6.52136e7i	−0.665634	−	0.665634i	0.291068	−	0.956702i	$-0.405989\pi$
$461$	−6.52136e7	−	6.52136e7i	−0.665634	−	0.665634i	−0.956702	+	0.291068i	$0.905989\pi$
$462$	1.39449e7	+	6.48687e6i	0.141413	+	0.0657824i
$463$			1.95649e8i			1.97122i	0.169044	+	0.985608i	$0.445932\pi$
$463$			1.95649e8i			1.97122i	−0.169044	+	0.985608i	$0.554068\pi$
$464$	−7.09768e7	+	5.00917e7i	−0.710497	+	0.501431i
$465$	−4.05432e7			−0.403236
$466$	−1.06859e7	+	2.29716e7i	−0.105598	+	0.227004i
$467$	9.73782e7	−	9.73782e7i	0.956117	−	0.956117i	−0.0429599	−	0.999077i	$-0.513679\pi$
$467$	9.73782e7	−	9.73782e7i	0.956117	−	0.956117i	0.999077	+	0.0429599i	$0.0136788\pi$
$468$	2.96419e7	+	2.53797e6i	0.289180	+	0.0247599i
$469$	1.65862e7	−	1.65862e7i	0.160779	−	0.160779i
$470$	−2.15702e7	−	5.90931e7i	−0.207759	−	0.569172i
$471$	3.31620e7			0.317379
$472$	1.77044e7	−	3.08628e7i	0.168366	−	0.293501i
$473$		−	1.18278e8i		−	1.11768i
$474$	4.54192e6	+	1.24429e7i	0.0426486	+	0.116839i
$475$	3.41661e7	+	3.41661e7i	0.318797	+	0.318797i
$476$	2.42620e7	+	2.88057e7i	0.224960	+	0.267090i
$477$	4.93358e7	+	4.93358e7i	0.454577	+	0.454577i
$478$	2.77920e7	−	5.97446e7i	0.254469	−	0.547035i
$479$		−	6.72495e7i		−	0.611903i	−0.952047	−	0.305951i	$-0.901025\pi$
$479$		−	6.72495e7i		−	0.611903i	0.952047	−	0.305951i	$-0.0989745\pi$
$480$	3.29119e7	+	2.28185e7i	0.297597	+	0.206331i
$481$	1.00590e7			0.0903901
$482$	2.02435e7	+	9.41684e6i	0.180777	+	0.0840939i
$483$	−1.80865e7	+	1.80865e7i	−0.160514	+	0.160514i
$484$	−3.38084e6	+	2.84756e6i	−0.0298187	+	0.0251152i
$485$	−3.11219e7	+	3.11219e7i	−0.272798	+	0.272798i
$486$	−7.86944e7	+	2.87250e7i	−0.685543	+	0.250237i
$487$	−1.41878e8			−1.22837			−0.614183	−	0.789164i	$-0.710514\pi$
$487$	−1.41878e8			−1.22837			−0.614183	+	0.789164i	$0.710514\pi$
$488$	−6.87139e7	+	1.19784e8i	−0.591269	+	1.03072i
$489$			5.73897e7i			0.490803i
$490$	−4.93175e7	+	1.80019e7i	−0.419192	+	0.153013i
$491$	−9.32669e7	−	9.32669e7i	−0.787922	−	0.787922i	0.193231	−	0.981153i	$-0.438103\pi$
$491$	−9.32669e7	−	9.32669e7i	−0.787922	−	0.787922i	−0.981153	+	0.193231i	$0.938103\pi$
$492$	2.71045e6	−	3.16564e7i	0.0227587	−	0.265807i
$493$	−1.31212e8	−	1.31212e8i	−1.09505	−	1.09505i
$494$	−4.66054e7	−	2.16799e7i	−0.386595	−	0.179836i
$495$		−	2.24417e7i		−	0.185029i
$496$	1.33898e8	+	2.30983e7i	1.09731	+	0.189294i
$497$	384978.			0.00313593
$498$	4.74927e7	−	1.02095e8i	0.384538	−	0.826643i
$499$	1.20593e8	−	1.20593e8i	0.970555	−	0.970555i	−0.0290238	−	0.999579i	$-0.509240\pi$
$499$	1.20593e8	−	1.20593e8i	0.970555	−	0.970555i	0.999579	+	0.0290238i	$0.00923987\pi$
$500$	−8.83187e6	+	1.03151e8i	−0.0706550	+	0.825206i
$501$	−7.16425e7	+	7.16425e7i	−0.569715	+	0.569715i
$502$	−4.03428e7	−	1.10522e8i	−0.318900	−	0.873650i
$503$	2.01027e8			1.57961			0.789806	−	0.613357i	$-0.210181\pi$
$503$	2.01027e8			1.57961			0.789806	+	0.613357i	$0.210181\pi$
$504$	9.47772e6	−	2.56781e6i	0.0740308	−	0.0200573i
$505$			1.11149e8i			0.863044i
$506$	−6.71770e7	−	1.84036e8i	−0.518524	−	1.42054i
$507$	−3.23139e7	−	3.23139e7i	−0.247951	−	0.247951i
$508$	−1.88530e8	+	1.58792e8i	−1.43810	+	1.21126i
$509$	−2.03126e6	−	2.03126e6i	−0.0154032	−	0.0154032i	0.699363	−	0.714766i	$-0.253467\pi$
$509$	−2.03126e6	−	2.03126e6i	−0.0154032	−	0.0154032i	−0.714766	+	0.699363i	$0.753467\pi$
$510$	−3.60807e7	+	7.75629e7i	−0.271997	+	0.584714i
$511$		−	2.31375e7i		−	0.173402i
$512$	−9.56947e7	−	9.41113e7i	−0.712981	−	0.701184i
$513$	8.42076e7			0.623734
$514$	1.10603e8	+	5.14501e7i	0.814472	+	0.378876i
$515$	−2.08690e7	+	2.08690e7i	−0.152785	+	0.152785i
$516$	7.57264e7	+	8.99083e7i	0.551186	+	0.654411i
$517$	−1.30036e8	+	1.30036e8i	−0.941004	+	0.941004i
$518$	3.11881e6	−	1.13843e6i	0.0224388	−	0.00819061i
$519$	8.70299e7			0.622539
$520$	−1.26623e7	−	4.67363e7i	−0.0900542	−	0.332387i
$521$		−	6.91304e7i		−	0.488828i	−0.969671	−	0.244414i	$-0.921404\pi$
$521$		−	6.91304e7i		−	0.488828i	0.969671	−	0.244414i	$-0.0785956\pi$
$522$	−4.54477e7	+	1.65893e7i	−0.319522	+	0.116632i
$523$	7.28429e7	+	7.28429e7i	0.509193	+	0.509193i	0.914279	−	0.405086i	$-0.132758\pi$
$523$	7.28429e7	+	7.28429e7i	0.509193	+	0.509193i	−0.405086	+	0.914279i	$0.632758\pi$
$524$	5.08816e7	+	4.35653e6i	0.353644	+	0.0302794i
$525$	−1.22841e7	−	1.22841e7i	−0.0848916	−	0.0848916i
$526$	−2.08483e8	−	9.69821e7i	−1.43256	−	0.666399i
$527$			2.90234e8i			1.98297i
$528$	1.99023e7	−	1.15371e8i	0.135208	−	0.783783i
$529$	1.77788e8			1.20098
$530$	4.78966e7	−	1.02964e8i	0.321719	−	0.691602i
$531$	1.40115e7	−	1.40115e7i	0.0935838	−	0.0935838i
$532$	−1.69036e7	−	1.44731e6i	−0.112265	−	0.00961227i
$533$	−2.71633e7	+	2.71633e7i	−0.179391	+	0.179391i
$534$	−2.41621e7	−	6.61940e7i	−0.158676	−	0.434705i
$535$	−6.99222e7			−0.456619
$536$	−1.54882e8	−	8.88479e7i	−1.00579	−	0.576970i
$537$		−	3.05363e7i		−	0.197194i
$538$	1.09750e7	+	3.00669e7i	0.0704788	+	0.193082i
$539$	1.08524e8	+	1.08524e8i	0.693044	+	0.693044i
$540$	5.11021e7	+	6.06724e7i	0.324532	+	0.385309i
$541$	9.62645e7	+	9.62645e7i	0.607959	+	0.607959i	0.942412	−	0.334453i	$-0.108552\pi$
$541$	9.62645e7	+	9.62645e7i	0.607959	+	0.607959i	−0.334453	+	0.942412i	$0.608552\pi$
$542$	−6.62097e7	+	1.42331e8i	−0.415837	+	0.893928i
$543$		−	1.43061e7i		−	0.0893553i
$544$	1.63349e8	−	2.35604e8i	1.01466	−	1.46348i
$545$	−7.44907e7			−0.460164
$546$	1.67566e7	+	7.79481e6i	0.102945	+	0.0478881i
$547$	1.66783e8	−	1.66783e8i	1.01904	−	1.01904i	0.0192202	−	0.999815i	$-0.493882\pi$
$547$	1.66783e8	−	1.66783e8i	1.01904	−	1.01904i	0.999815	−	0.0192202i	$-0.00611834\pi$
$548$	−7.23295e7	+	6.09205e7i	−0.439515	+	0.370188i
$549$	−5.43810e7	+	5.43810e7i	−0.328647	+	0.328647i
$550$	1.24995e8	−	4.56256e7i	0.751282	−	0.274233i
$551$	8.35900e7			0.499689
$552$	1.68892e8	+	9.68848e7i	1.00414	+	0.576021i
$553$		−	5.28600e6i		−	0.0312573i
$554$	1.14699e7	−	4.18674e6i	0.0674575	−	0.0246234i
$555$	5.33241e6	+	5.33241e6i	0.0311921	+	0.0311921i
$556$	3.67860e6	−	4.29637e7i	0.0214022	−	0.249964i
$557$	2.35415e7	+	2.35415e7i	0.136229	+	0.136229i	0.771933	−	0.635704i	$-0.219290\pi$
$557$	2.35415e7	+	2.35415e7i	0.136229	+	0.136229i	−0.635704	+	0.771933i	$0.719290\pi$
$558$	6.86113e7	+	3.19166e7i	0.394905	+	0.183702i
$559$		−	1.42126e8i		−	0.813649i
$560$	−9.21533e6	−	1.30575e7i	−0.0524743	−	0.0743528i
$561$	2.50075e8			1.41639
$562$	−7.18779e7	+	1.54516e8i	−0.404936	+	0.870494i
$563$	−4.12906e7	+	4.12906e7i	−0.231380	+	0.231380i	−0.813269	−	0.581889i	$-0.802314\pi$
$563$	−4.12906e7	+	4.12906e7i	−0.231380	+	0.231380i	0.581889	+	0.813269i	$0.302314\pi$
$564$	1.55916e7	−	1.82101e8i	0.0869069	−	1.01502i
$565$	7.40784e7	−	7.40784e7i	0.410720	−	0.410720i
$566$	7.84720e7	+	2.14980e8i	0.432778	+	1.18563i
$567$	−1.62949e7			−0.0893929
$568$	−766352.	−	2.82858e6i	−0.00418199	−	0.0154356i
$569$		−	1.01604e8i		−	0.551536i	−0.961224	−	0.275768i	$-0.911068\pi$
$569$		−	1.01604e8i		−	0.551536i	0.961224	−	0.275768i	$-0.0889321\pi$
$570$	−1.32133e7	−	3.61989e7i	−0.0713489	−	0.195466i
$571$	−1.56232e8	−	1.56232e8i	−0.839190	−	0.839190i	0.149562	−	0.988752i	$-0.452214\pi$
$571$	−1.56232e8	−	1.56232e8i	−0.839190	−	0.839190i	−0.988752	+	0.149562i	$0.952214\pi$
$572$	−1.08266e8	+	9.11887e7i	−0.578502	+	0.487251i
$573$	−1.86276e8	−	1.86276e8i	−0.990131	−	0.990131i
$574$	−5.34780e6	+	1.14962e7i	−0.0282774	+	0.0607881i
$575$			2.21295e8i			1.16404i
$576$	−3.77334e7	−	6.45248e7i	−0.197451	−	0.337644i
$577$	335155.			0.00174469			0.000872345	−	1.00000i	$-0.499722\pi$
$577$	335155.			0.00174469			0.000872345		1.00000i	$0.499722\pi$
$578$	3.80160e8	+	1.76843e8i	1.96871	+	0.915805i
$579$	−1.62036e8	+	1.62036e8i	−0.834788	+	0.834788i
$580$	5.07273e7	+	6.02273e7i	0.259991	+	0.308681i
$581$	−3.17740e7	+	3.17740e7i	−0.162010	+	0.162010i
$582$	−1.20121e8	+	4.38467e7i	−0.609328	+	0.222417i
$583$	−3.31972e8			−1.67531
$584$	−1.70000e8	+	4.60584e7i	−0.853514	+	0.231244i
$585$		−	2.69665e7i		−	0.134697i
$586$	−1.88015e8	+	6.86295e7i	−0.934331	+	0.341050i
$587$	−1.00455e8	−	1.00455e8i	−0.496660	−	0.496660i	0.413737	−	0.910397i	$-0.364223\pi$
$587$	−1.00455e8	−	1.00455e8i	−0.496660	−	0.496660i	−0.910397	+	0.413737i	$0.864223\pi$
$588$	−1.51976e8	−	1.30124e7i	−0.747556	−	0.0640065i
$589$	−9.24482e7	−	9.24482e7i	−0.452431	−	0.452431i
$590$	−2.92419e7	−	1.36028e7i	−0.142380	−	0.0662324i
$591$			2.09443e7i			0.101462i
$592$	−1.45729e7	−	2.06489e7i	−0.0702393	−	0.0995247i
$593$	−6.10833e7			−0.292926			−0.146463	−	0.989216i	$-0.546789\pi$
$593$	−6.10833e7			−0.292926			−0.146463	+	0.989216i	$0.546789\pi$
$594$	9.78088e7	−	2.10260e8i	0.466679	−	1.00322i
$595$	2.41390e7	−	2.41390e7i	0.114596	−	0.114596i
$596$	2.19727e8	+	1.88133e7i	1.03788	+	0.0888640i
$597$	4.86745e7	−	4.86745e7i	0.228759	−	0.228759i
$598$	−8.07217e7	−	2.21143e8i	−0.377474	−	1.03412i
$599$	−1.52111e8			−0.707750			−0.353875	−	0.935293i	$-0.615136\pi$
$599$	−1.52111e8			−0.707750			−0.353875	+	0.935293i	$0.615136\pi$
$600$	−6.58027e7	+	1.14709e8i	−0.304642	+	0.531060i
$601$		−	4.87716e6i		−	0.0224669i	−0.999937	−	0.0112335i	$-0.996424\pi$
$601$		−	4.87716e6i		−	0.0224669i	0.999937	−	0.0112335i	$-0.00357580\pi$
$602$	−1.60850e7	−	4.40661e7i	−0.0737280	−	0.201983i
$603$	−7.03154e7	−	7.03154e7i	−0.320700	−	0.320700i
$604$	−1.17196e8	−	1.39145e8i	−0.531867	−	0.631474i
$605$	2.83313e6	+	2.83313e6i	0.0127938	+	0.0127938i
$606$	−1.36204e8	+	2.92799e8i	−0.612030	+	1.31569i
$607$		−	1.52473e8i		−	0.681754i	−0.940108	−	0.340877i	$-0.889276\pi$
$607$		−	1.52473e8i		−	0.681754i	0.940108	−	0.340877i	$-0.110724\pi$
$608$	2.30151e7	+	1.27079e8i	0.102401	+	0.565407i
$609$	−3.00540e7			−0.133061
$610$	1.13493e8	+	5.27946e7i	0.500011	+	0.232595i
$611$	−1.56255e8	+	1.56255e8i	−0.685030	+	0.685030i
$612$	1.22119e8	−	1.02856e8i	0.532755	−	0.448720i
$613$	2.90273e8	−	2.90273e8i	1.26016	−	1.26016i	0.309146	−	0.951015i	$-0.399957\pi$
$613$	2.90273e8	−	2.90273e8i	1.26016	−	1.26016i	0.951015	−	0.309146i	$-0.100043\pi$
$614$	4.31062e8	−	1.57347e8i	1.86224	−	0.679754i
$615$	−2.87992e7			−0.123810
$616$	−2.32477e7	+	4.05261e7i	−0.0994577	+	0.173377i
$617$			1.52743e8i			0.650287i	0.945665	+	0.325143i	$0.105413\pi$
$617$			1.52743e8i			0.650287i	−0.945665	+	0.325143i	$0.894587\pi$
$618$	−8.05482e7	+	2.94017e7i	−0.341264	+	0.124568i
$619$	−4.88917e7	−	4.88917e7i	−0.206140	−	0.206140i	0.596484	−	0.802625i	$-0.296564\pi$
$619$	−4.88917e7	−	4.88917e7i	−0.206140	−	0.206140i	−0.802625	+	0.596484i	$0.796564\pi$
$620$	1.05068e7	−	1.22713e8i	0.0440854	−	0.514890i
$621$	2.72708e8	+	2.72708e8i	1.13873	+	1.13873i
$622$	3.48032e8	+	1.61898e8i	1.44627	+	0.672774i
$623$			2.81205e7i			0.116294i
$624$	2.39152e7	−	1.38633e8i	0.0984282	−	0.570577i
$625$	−9.77168e7			−0.400248
$626$	−1.27636e8	+	2.74381e8i	−0.520298	+	1.11849i
$627$	−7.96565e7	+	7.96565e7i	−0.323161	+	0.323161i
$628$	−8.59395e6	+	1.00372e8i	−0.0346987	+	0.405260i
$629$	3.81728e7	−	3.81728e7i	0.153392	−	0.153392i
$630$	−3.05193e6	−	8.36098e6i	−0.0122054	−	0.0334377i
$631$	3.24666e8			1.29226			0.646129	−	0.763228i	$-0.276387\pi$
$631$	3.24666e8			1.29226			0.646129	+	0.763228i	$0.276387\pi$
$632$	−3.88382e7	+	1.05225e7i	−0.153854	+	0.0416839i
$633$		−	1.35417e8i		−	0.533902i
$634$	3.38411e7	+	9.27103e7i	0.132794	+	0.363798i
$635$	1.57987e8	+	1.57987e8i	0.617022	+	0.617022i
$636$	2.52347e8	−	2.12542e8i	0.980903	−	0.826179i
$637$	1.30406e8	+	1.30406e8i	0.504520	+	0.504520i
$638$	9.70913e7	−	2.08718e8i	0.373868	−	0.803707i
$639$		−	1.63207e6i		−	0.00625514i
$640$	−7.75943e7	+	9.37013e7i	−0.295999	+	0.357442i
$641$	−8.42699e7			−0.319962			−0.159981	−	0.987120i	$-0.551143\pi$
$641$	−8.42699e7			−0.319962			−0.159981	+	0.987120i	$0.551143\pi$
$642$	−1.84195e8	−	8.56838e7i	−0.696102	−	0.323812i
$643$	1.07390e8	−	1.07390e8i	0.403953	−	0.403953i	−0.475671	−	0.879623i	$-0.657795\pi$
$643$	1.07390e8	−	1.07390e8i	0.403953	−	0.403953i	0.879623	+	0.475671i	$0.157795\pi$
$644$	−5.00556e7	−	5.94299e7i	−0.187411	−	0.222509i
$645$	7.53426e7	−	7.53426e7i	0.280777	−	0.280777i
$646$	−2.59134e8	+	9.45893e7i	−0.961230	+	0.350868i
$647$	−7.50814e7			−0.277217			−0.138608	−	0.990347i	$-0.544263\pi$
$647$	−7.50814e7			−0.277217			−0.138608	+	0.990347i	$0.544263\pi$
$648$	3.24373e7	+	1.19725e8i	0.119212	+	0.440007i
$649$			9.42807e7i			0.344896i
$650$	1.50197e8	−	5.48250e7i	0.546917	−	0.199636i
$651$	3.32389e7	+	3.32389e7i	0.120477	+	0.120477i
$652$	−1.73702e8	−	1.48725e7i	−0.626704	−	0.0536590i
$653$	−4.28294e7	−	4.28294e7i	−0.153816	−	0.153816i	0.626004	−	0.779820i	$-0.284689\pi$
$653$	−4.28294e7	−	4.28294e7i	−0.153816	−	0.153816i	−0.779820	+	0.626004i	$0.784689\pi$
$654$	−1.96230e8	−	9.12822e7i	−0.701507	−	0.326327i
$655$		−	4.62892e7i		−	0.164723i
$656$	9.51125e7	+	1.64075e7i	0.336919	+	0.0581208i
$657$	−9.80890e7			−0.345879
$658$	−3.07627e7	+	6.61309e7i	−0.107981	+	0.232127i
$659$	−3.09676e7	+	3.09676e7i	−0.108206	+	0.108206i	−0.759137	−	0.650931i	$-0.774379\pi$
$659$	−3.09676e7	+	3.09676e7i	−0.108206	+	0.108206i	0.650931	+	0.759137i	$0.274379\pi$
$660$	−1.05733e8	−	9.05300e6i	−0.367774	−	0.0314891i
$661$	8.79901e6	−	8.79901e6i	0.0304670	−	0.0304670i	−0.691709	−	0.722176i	$-0.743142\pi$
$661$	8.79901e6	−	8.79901e6i	0.0304670	−	0.0304670i	0.722176	+	0.691709i	$0.243142\pi$
$662$	−4.09728e7	−	1.12248e8i	−0.141228	−	0.386905i
$663$	3.00497e8			1.03110
$664$	2.96706e8	+	1.70205e8i	1.01350	+	0.581390i
$665$			1.53780e7i			0.0522919i
$666$	−4.82624e6	−	1.32218e7i	−0.0163375	−	0.0447579i
$667$	2.70707e8	+	2.70707e8i	0.912268	+	0.912268i
$668$	−1.98275e8	−	2.35408e8i	−0.665180	−	0.789753i
$669$	−2.20439e7	−	2.20439e7i	−0.0736225	−	0.0736225i
$670$	−6.82641e7	+	1.46748e8i	−0.226970	+	0.487919i
$671$		−	3.65920e8i		−	1.21121i
$672$	−8.27487e6	−	4.56899e7i	−0.0272680	−	0.150561i
$673$	−1.72641e8			−0.566369			−0.283184	−	0.959066i	$-0.591391\pi$
$673$	−1.72641e8			−0.566369			−0.283184	+	0.959066i	$0.591391\pi$
$674$	−4.23745e8	−	1.97118e8i	−1.38397	−	0.643793i
$675$	−1.85219e8	+	1.85219e8i	−0.602246	+	0.602246i
$676$	1.06179e8	−	8.94307e7i	0.343715	−	0.289499i
$677$	−1.64521e8	+	1.64521e8i	−0.530220	+	0.530220i	−0.920638	−	0.390418i	$-0.872331\pi$
$677$	−1.64521e8	+	1.64521e8i	−0.530220	+	0.530220i	0.390418	+	0.920638i	$0.372331\pi$
$678$	2.85920e8	−	1.04367e8i	0.917395	−	0.334868i
$679$	5.10298e7			0.163010
$680$	−2.25410e8	−	1.29306e8i	−0.716881	−	0.411238i
$681$			1.21825e8i			0.385740i
$682$	−3.38216e8	+	1.23456e8i	−1.06621	+	0.389187i
$683$	2.87275e8	+	2.87275e8i	0.901646	+	0.901646i	0.995579	−	0.0939321i	$-0.0299437\pi$
$683$	2.87275e8	+	2.87275e8i	0.901646	+	0.901646i	−0.0939321	+	0.995579i	$0.529944\pi$
$684$	−6.13570e6	+	7.16612e7i	−0.0191733	+	0.223932i
$685$	6.06117e7	+	6.06117e7i	0.188575	+	0.188575i
$686$	1.12589e8	+	5.23742e7i	0.348758	+	0.162235i
$687$		−	3.49538e8i		−	1.07801i
$688$	−2.91751e8	+	2.05903e8i	−0.895874	+	0.632261i
$689$	−3.98906e8			−1.21959
$690$	7.44391e7	−	1.60022e8i	0.226597	−	0.487117i
$691$	1.44188e8	−	1.44188e8i	0.437014	−	0.437014i	−0.453992	−	0.891006i	$-0.650000\pi$
$691$	1.44188e8	−	1.44188e8i	0.437014	−	0.437014i	0.891006	+	0.453992i	$0.150000\pi$
$692$	−2.25538e7	+	2.63414e8i	−0.0680615	+	0.794916i
$693$	−1.83985e7	+	1.83985e7i	−0.0552820	+	0.0552820i
$694$	−4.33008e7	−	1.18626e8i	−0.129544	−	0.354895i
$695$	−3.90860e7			−0.116430
$696$	5.98266e7	+	2.20818e8i	0.177446	+	0.654948i
$697$			2.06163e8i			0.608853i
$698$	−2.14573e8	−	5.87839e8i	−0.630971	−	1.72859i
$699$	4.71787e7	+	4.71787e7i	0.138138	+	0.138138i
$700$	4.03638e7	−	3.39970e7i	0.117679	−	0.0991166i
$701$	2.70339e8	+	2.70339e8i	0.784793	+	0.784793i	0.980635	−	0.195843i	$-0.0627442\pi$
$701$	2.70339e8	+	2.70339e8i	0.784793	+	0.784793i	−0.195843	+	0.980635i	$0.562744\pi$
$702$	1.17530e8	−	2.52654e8i	0.339732	−	0.730324i
$703$			2.43183e7i			0.0699952i
$704$	3.44038e8	+	9.01371e7i	0.986027	+	0.258336i
$705$	−1.65665e8			−0.472784
$706$	−1.89494e8	−	8.81488e7i	−0.538495	−	0.250497i
$707$	9.11245e7	−	9.11245e7i	0.257856	−	0.257856i
$708$	−6.03626e7	−	7.16671e7i	−0.170086	−	0.201939i
$709$	−3.87984e7	+	3.87984e7i	−0.108862	+	0.108862i	−0.759440	−	0.650578i	$-0.774527\pi$
$709$	−3.87984e7	+	3.87984e7i	−0.108862	+	0.108862i	0.650578	+	0.759440i	$0.274527\pi$
$710$	−2.49530e6	+	910833.i	−0.00697183	+	0.00254486i
$711$	−2.24094e7			−0.0623479
$712$	2.06612e8	−	5.59777e7i	0.572421	−	0.155087i
$713$		−	5.98790e8i		−	1.65198i
$714$	9.31693e7	−	3.40087e7i	0.255964	−	0.0934319i
$715$	9.07264e7	+	9.07264e7i	0.248208	+	0.248208i
$716$	9.24247e7	+	7.91350e6i	0.251796	+	0.0215590i
$717$	−1.22702e8	−	1.22702e8i	−0.332886	−	0.332886i
$718$	2.11431e8	+	9.83535e7i	0.571210	+	0.265715i
$719$		−	1.18685e8i		−	0.319307i	−0.987173	−	0.159654i	$-0.948962\pi$
$719$		−	1.18685e8i		−	0.319307i	0.987173	−	0.159654i	$-0.0510378\pi$
$720$	−5.53560e7	+	3.90674e7i	−0.148309	+	0.104669i
$721$	3.42185e7			0.0912966
$722$	−1.06331e8	+	2.28580e8i	−0.282519	+	0.607333i
$723$	4.15756e7	−	4.15756e7i	0.110008	−	0.110008i
$724$	4.33003e7	+	3.70742e6i	0.114097	+	0.00976913i
$725$	−1.83860e8	+	1.83860e8i	−0.482474	+	0.482474i
$726$	3.99150e6	+	1.09350e7i	0.0104310	+	0.0285765i
$727$	−4.98987e8			−1.29863			−0.649316	−	0.760519i	$-0.724945\pi$
$727$	−4.98987e8			−1.29863			−0.649316	+	0.760519i	$0.724945\pi$
$728$	−2.79351e7	+	4.86973e7i	−0.0724030	+	0.126215i
$729$			3.97229e8i			1.02532i
$730$	5.47419e7	+	1.49969e8i	0.140718	+	0.385509i
$731$	−5.39349e8	−	5.39349e8i	−1.38076	−	1.38076i
$732$	2.34278e8	+	2.78152e8i	0.597307	+	0.709168i
$733$	−2.73484e8	−	2.73484e8i	−0.694418	−	0.694418i	0.268783	−	0.963201i	$-0.413378\pi$
$733$	−2.73484e8	−	2.73484e8i	−0.694418	−	0.694418i	−0.963201	+	0.268783i	$0.913378\pi$
$734$	4.35608e7	−	9.36430e7i	0.110156	−	0.236803i
$735$			1.38259e8i			0.348203i
$736$	−3.37011e8	+	4.86081e8i	−0.845300	+	1.21920i
$737$	4.73139e8			1.18192
$738$	4.87369e7	+	2.26714e7i	0.121252	+	0.0564040i
$739$	1.90615e7	−	1.90615e7i	0.0472307	−	0.0472307i	−0.683097	−	0.730328i	$-0.739367\pi$
$739$	1.90615e7	−	1.90615e7i	0.0472307	−	0.0472307i	0.730328	+	0.683097i	$0.239367\pi$
$740$	−1.75216e7	+	1.47578e7i	−0.0432393	+	0.0364189i
$741$	−9.57174e7	+	9.57174e7i	−0.235254	+	0.235254i
$742$	−1.23681e8	+	4.51461e7i	−0.302755	+	0.110512i
$743$	5.59609e8			1.36433			0.682163	−	0.731200i	$-0.261040\pi$
$743$	5.59609e8			1.36433			0.682163	+	0.731200i	$0.261040\pi$
$744$	1.78052e8	−	3.10385e8i	0.432343	−	0.753671i
$745$		−	1.99896e8i		−	0.483431i
$746$	2.02020e8	−	7.37414e7i	0.486607	−	0.177621i
$747$	1.34702e8	+	1.34702e8i	0.323157	+	0.323157i
$748$	−6.48071e7	+	7.56906e8i	−0.154852	+	1.80858i
$749$	5.73249e7	+	5.73249e7i	0.136426	+	0.136426i
$750$	2.47203e8	+	1.14994e8i	0.585964	+	0.272578i
$751$		−	4.03825e8i		−	0.953395i	−0.879067	−	0.476698i	$-0.841834\pi$
$751$		−	4.03825e8i		−	0.953395i	0.879067	−	0.476698i	$-0.158166\pi$
$752$	5.47126e8	+	9.43829e7i	1.28657	+	0.221942i
$753$	−3.09843e8			−0.725700
$754$	1.16668e8	−	2.50801e8i	0.272168	−	0.585081i
$755$	−1.16602e8	+	1.16602e8i	−0.270936	+	0.270936i
$756$	7.84605e6	−	9.16370e7i	0.0181587	−	0.212083i
$757$	2.91929e8	−	2.91929e8i	0.672960	−	0.672960i	−0.285438	−	0.958397i	$-0.592139\pi$
$757$	2.91929e8	−	2.91929e8i	0.672960	−	0.672960i	0.958397	+	0.285438i	$0.0921390\pi$
$758$	2.57920e8	+	7.06590e8i	0.592211	+	1.62241i
$759$	−5.15938e8			−1.17997
$760$	1.12988e8	−	3.06120e7i	0.257390	−	0.0697350i
$761$			2.29299e8i			0.520293i	0.965569	+	0.260146i	$0.0837708\pi$
$761$			2.29299e8i			0.520293i	−0.965569	+	0.260146i	$0.916229\pi$
$762$	2.22583e8	+	6.09783e8i	0.503069	+	1.37819i
$763$	6.10703e7	+	6.10703e7i	0.137485	+	0.137485i
$764$	6.12077e8	−	5.15530e8i	1.37254	−	1.15604i
$765$	−1.02335e8	−	1.02335e8i	−0.228580	−	0.228580i
$766$	1.36455e8	−	2.93338e8i	0.303600	−	0.652652i
$767$			1.13290e8i			0.251077i
$768$	−3.19229e8	+	1.51751e8i	−0.704723	+	0.335002i
$769$	1.10606e8			0.243221			0.121610	−	0.992578i	$-0.461194\pi$
$769$	1.10606e8			0.243221			0.121610	+	0.992578i	$0.461194\pi$
$770$	3.83977e7	+	1.78618e7i	0.0841071	+	0.0391249i
$771$	2.27154e8	−	2.27154e8i	0.495629	−	0.495629i
$772$	−4.48445e8	−	5.32429e8i	−0.974670	−	1.15720i
$773$	3.54952e8	−	3.54952e8i	0.768477	−	0.768477i	−0.209361	−	0.977838i	$-0.567138\pi$
$773$	3.54952e8	−	3.54952e8i	0.768477	−	0.768477i	0.977838	+	0.209361i	$0.0671385\pi$
$774$	−1.86814e8	+	6.81907e7i	−0.402889	+	0.147063i
$775$	4.06689e8			0.873689
$776$	−1.01582e8	−	3.74936e8i	−0.217386	−	0.802364i
$777$		−	8.74343e6i		−	0.0186388i
$778$	2.94191e8	−	1.07386e8i	0.624728	−	0.228038i
$779$	−6.56691e7	−	6.56691e7i	−0.138915	−	0.138915i
$780$	−1.27052e8	−	1.08783e7i	−0.267731	−	0.0229234i
$781$	5.49096e6	+	5.49096e6i	0.0115264	+	0.0115264i
$782$	−1.14554e9	−	5.32882e8i	−2.39546	−	1.11432i
$783$			4.53153e8i			0.943972i
$784$	7.87693e7	−	4.56616e8i	0.163459	−	0.947552i
$785$	9.13128e7			0.188765
$786$	5.67235e7	−	1.21939e8i	0.116814	−	0.251116i
$787$	−4.21298e8	+	4.21298e8i	−0.864302	+	0.864302i	−0.991834	−	0.127533i	$-0.959294\pi$
$787$	−4.21298e8	+	4.21298e8i	−0.864302	+	0.864302i	0.127533	+	0.991834i	$0.459294\pi$
$788$	−6.33924e7	−	5.42772e6i	−0.129556	−	0.0110927i
$789$	−4.28179e8	+	4.28179e8i	−0.871755	+	0.871755i
$790$	1.25063e7	+	3.42620e7i	0.0253658	+	0.0694915i
$791$	−1.21465e8			−0.245426
$792$	1.71806e8	+	9.85562e7i	0.345830	+	0.198385i
$793$		−	4.39699e8i		−	0.881731i
$794$	1.57082e8	+	4.30339e8i	0.313810	+	0.859705i
$795$	−2.11465e8	−	2.11465e8i	−0.420859	−	0.420859i
$796$	1.34710e8	+	1.59938e8i	0.267092	+	0.317112i
$797$	−2.64378e8	−	2.64378e8i	−0.522216	−	0.522216i	0.396024	−	0.918240i	$-0.370390\pi$
$797$	−2.64378e8	−	2.64378e8i	−0.522216	−	0.522216i	−0.918240	+	0.396024i	$0.870390\pi$
$798$	−1.88444e7	+	4.05100e7i	−0.0370830	+	0.0797175i
$799$			1.18593e9i			2.32498i
$800$	−3.30138e8	−	2.28893e8i	−0.644802	−	0.447056i
$801$	1.19214e8			0.231968
$802$	2.53386e8	+	1.17870e8i	0.491201	+	0.228497i
$803$	3.30011e8	−	3.30011e8i	0.637356	−	0.637356i
$804$	−3.59655e8	+	3.02924e8i	−0.692018	+	0.582862i
$805$	−4.98018e7	+	4.98018e7i	−0.0954680	+	0.0954680i
$806$	−4.06410e8	+	1.48348e8i	−0.776175	+	0.283320i
$807$	8.42911e7			0.160384
$808$	−8.50922e8	−	4.88130e8i	−1.61308	−	0.925341i
$809$			3.90918e8i			0.738312i	0.929367	+	0.369156i	$0.120353\pi$
$809$			3.90918e8i			0.738312i	−0.929367	+	0.369156i	$0.879647\pi$
$810$	1.05618e8	−	3.85527e7i	0.198739	−	0.0725437i
$811$	−4.03676e8	−	4.03676e8i	−0.756781	−	0.756781i	0.218954	−	0.975735i	$-0.429736\pi$
$811$	−4.03676e8	−	4.03676e8i	−0.756781	−	0.756781i	−0.975735	+	0.218954i	$0.929736\pi$
$812$	7.78850e6	−	9.09648e7i	0.0145474	−	0.169905i
$813$	2.92318e8	+	2.92318e8i	0.543981	+	0.543981i
$814$	6.07211e7	+	2.82462e7i	0.112581	+	0.0523705i
$815$			1.58024e8i			0.291912i
$816$	−4.35341e8	−	6.16851e8i	−0.801234	−	1.13530i
$817$	3.43598e8			0.630063
$818$	−2.27817e8	+	4.89739e8i	−0.416223	+	0.894757i
$819$	−2.21082e7	+	2.21082e7i	−0.0402440	+	0.0402440i
$820$	7.46332e6	−	8.71670e7i	0.0135360	−	0.158092i
$821$	8.57163e6	−	8.57163e6i	0.0154894	−	0.0154894i	−0.699320	−	0.714809i	$-0.746514\pi$
$821$	8.57163e6	−	8.57163e6i	0.0154894	−	0.0154894i	0.714809	+	0.699320i	$0.246514\pi$
$822$	8.53940e7	+	2.33943e8i	0.153749	+	0.421206i
$823$	1.09346e8			0.196157			0.0980785	−	0.995179i	$-0.468730\pi$
$823$	1.09346e8			0.196157			0.0980785	+	0.995179i	$0.468730\pi$
$824$	−6.81166e7	−	2.51416e8i	−0.121751	−	0.449377i
$825$		−	3.50417e8i		−	0.624055i
$826$	1.28216e7	+	3.51257e7i	0.0227511	+	0.0623282i
$827$	−3.14775e8	−	3.14775e8i	−0.556524	−	0.556524i	0.371792	−	0.928316i	$-0.378744\pi$
$827$	−3.14775e8	−	3.14775e8i	−0.556524	−	0.556524i	−0.928316	+	0.371792i	$0.878744\pi$
$828$	−2.51946e8	+	2.12205e8i	−0.443831	+	0.373822i
$829$	6.09042e7	+	6.09042e7i	0.106902	+	0.106902i	0.758534	−	0.651633i	$-0.225916\pi$
$829$	6.09042e7	+	6.09042e7i	0.106902	+	0.106902i	−0.651633	+	0.758534i	$0.725916\pi$
$830$	1.30773e8	−	2.81123e8i	0.228709	−	0.491657i
$831$		−	3.21553e7i		−	0.0560338i
$832$	4.13406e8	+	1.08311e8i	0.717805	+	0.188063i
$833$	9.89747e8			1.71234
$834$	−1.02964e8	−	4.78966e7i	−0.177495	−	0.0825670i
$835$	−1.97270e8	+	1.97270e8i	−0.338846	+	0.338846i
$836$	−2.20454e8	−	2.61740e8i	−0.377311	−	0.447973i
$837$	5.01174e8	−	5.01174e8i	0.854697	−	0.854697i
$838$	−8.04431e8	+	2.93634e8i	−1.36696	+	0.498969i
$839$	−5.98148e8			−1.01280			−0.506399	−	0.862299i	$-0.669024\pi$
$839$	−5.98148e8			−1.01280			−0.506399	+	0.862299i	$0.669024\pi$
$840$	−4.06237e7	+	1.10063e7i	−0.0685397	+	0.0185696i
$841$		−	1.44995e8i		−	0.243761i
$842$	3.89507e8	−	1.42178e8i	0.652497	−	0.238175i
$843$	3.17343e8	+	3.17343e8i	0.529720	+	0.529720i
$844$	4.09868e8	+	3.50933e7i	0.681736	+	0.0583710i
$845$	−8.89773e7	−	8.89773e7i	−0.147472	−	0.147472i
$846$	2.80355e8	+	1.30415e8i	0.463017	+	0.215386i
$847$		−	4.64541e6i		−	0.00764493i
$848$	5.77909e8	+	8.18861e8i	0.947703	+	1.34284i
$849$	6.02686e8			0.984846
$850$	3.61925e8	−	7.78032e8i	0.589334	−	1.26690i
$851$	−7.87553e7	+	7.87553e7i	−0.127788	+	0.127788i
$852$	−7.68947e6	−	658380.i	−0.0124330	−	0.00106453i
$853$	−4.03828e8	+	4.03828e8i	−0.650653	+	0.650653i	−0.953150	−	0.302497i	$-0.902180\pi$
$853$	−4.03828e8	+	4.03828e8i	−0.650653	+	0.650653i	0.302497	+	0.953150i	$0.402180\pi$
$854$	−4.97628e7	−	1.36329e8i	−0.0798972	−	0.218884i
$855$	6.51933e7			0.104305
$856$	3.07074e8	−	5.35300e8i	0.489578	−	0.853446i
$857$			8.52095e8i			1.35377i	0.736088	+	0.676886i	$0.236671\pi$
$857$			8.52095e8i			1.35377i	−0.736088	+	0.676886i	$0.763329\pi$
$858$	1.27822e8	+	3.50177e8i	0.202368	+	0.554403i
$859$	1.39728e8	+	1.39728e8i	0.220447	+	0.220447i	0.808686	−	0.588240i	$-0.200179\pi$
$859$	1.39728e8	+	1.39728e8i	0.220447	+	0.220447i	−0.588240	+	0.808686i	$0.700179\pi$
$860$	2.08515e8	+	2.47565e8i	0.327825	+	0.389219i
$861$	2.36107e7	+	2.36107e7i	0.0369913	+	0.0369913i
$862$	4.56014e7	−	9.80296e7i	0.0711961	−	0.153051i
$863$			1.37736e8i			0.214297i	0.994243	+	0.107149i	$0.0341721\pi$
$863$			1.37736e8i			0.214297i	−0.994243	+	0.107149i	$0.965828\pi$
$864$	−6.88910e8	+	1.24768e8i	−1.06812	+	0.193447i
$865$	2.39640e8			0.370263
$866$	−2.50851e8	−	1.16691e8i	−0.386244	−	0.179673i
$867$	7.80765e8	−	7.80765e8i	1.19802	−	1.19802i
$868$	−1.09218e8	+	9.19907e7i	−0.167008	+	0.140665i
$869$	7.53944e7	−	7.53944e7i	0.114889	−	0.114889i
$870$	1.94800e8	−	7.11058e7i	0.295822	−	0.107981i
$871$	5.68537e8			0.860408
$872$	3.27138e8	−	5.70276e8i	0.493380	−	0.860073i
$873$		−	2.16335e8i		−	0.325151i
$874$	5.34627e8	−	1.95150e8i	0.800787	−	0.292303i
$875$	−7.69342e7	−	7.69342e7i	−0.114841	−	0.114841i
$876$	−3.95692e7	+	4.62144e8i	−0.0588634	+	0.687488i
$877$	−2.31068e8	−	2.31068e8i	−0.342563	−	0.342563i	0.514767	−	0.857330i	$-0.327878\pi$
$877$	−2.31068e8	−	2.31068e8i	−0.342563	−	0.342563i	−0.857330	+	0.514767i	$0.827878\pi$
$878$	6.42054e7	+	2.98671e7i	0.0948611	+	0.0441275i
$879$			5.27093e8i			0.776105i
$880$	5.48017e7	−	3.17679e8i	0.0804166	−	0.466165i
$881$	1.47181e8			0.215240			0.107620	−	0.994192i	$-0.465677\pi$
$881$	1.47181e8			0.215240			0.107620	+	0.994192i	$0.465677\pi$
$882$	1.08841e8	−	2.33976e8i	0.158630	−	0.341009i
$883$	−3.76152e8	+	3.76152e8i	−0.546364	+	0.546364i	−0.925387	−	0.379023i	$-0.876260\pi$
$883$	−3.76152e8	+	3.76152e8i	−0.546364	+	0.546364i	0.379023	+	0.925387i	$0.376260\pi$
$884$	−7.78740e7	+	9.09519e8i	−0.112729	+	1.31660i
$885$	−6.00565e7	+	6.00565e7i	−0.0866424	+	0.0866424i
$886$	2.84247e8	+	7.78716e8i	0.408691	+	1.11964i
$887$	−6.99846e8			−1.00284			−0.501420	−	0.865204i	$-0.667189\pi$
$887$	−6.99846e8			−1.00284			−0.501420	+	0.865204i	$0.667189\pi$
$888$	−6.42413e7	+	1.74050e7i	−0.0917435	+	0.0248562i
$889$		−	2.59048e8i		−	0.368701i
$890$	−6.65313e7	−	1.82267e8i	−0.0943747	−	0.258547i
$891$	−2.32415e8	−	2.32415e8i	−0.328572	−	0.328572i
$892$	7.24333e7	−	6.10079e7i	0.102057	−	0.0859591i
$893$	−3.77755e8	−	3.77755e8i	−0.530464	−	0.530464i
$894$	2.44955e8	−	5.26582e8i	0.342827	−	0.736977i
$895$		−	8.40828e7i		−	0.117284i
$896$	1.40435e8	−	1.32051e7i	0.195232	−	0.0183577i
$897$	−6.19965e8			−0.858993
$898$	−2.36074e8	−	1.09817e8i	−0.326001	−	0.151649i
$899$	4.97498e8	−	4.97498e8i	0.684719	−	0.684719i
$900$	−1.44127e8	−	1.71118e8i	−0.197704	−	0.234730i
$901$	−1.51380e9	+	1.51380e9i	−2.06963	+	2.06963i
$902$	−2.40247e8	+	8.76949e7i	−0.327369	+	0.119496i
$903$	−1.23537e8			−0.167778
$904$	2.41792e8	+	8.92446e8i	0.327293	+	1.20803i
$905$		−	3.93922e7i		−	0.0531453i
$906$	−4.50050e8	+	1.64277e8i	−0.605168	+	0.220899i
$907$	1.61947e8	+	1.61947e8i	0.217046	+	0.217046i	0.807252	−	0.590206i	$-0.200954\pi$
$907$	1.61947e8	+	1.61947e8i	0.217046	+	0.217046i	−0.590206	+	0.807252i	$0.700954\pi$
$908$	−3.68729e8	−	3.15710e7i	−0.492550	−	0.0421726i
$909$	−3.86312e8	−	3.86312e8i	−0.514336	−	0.514336i
$910$	4.61397e7	+	2.14633e7i	0.0612281	+	0.0284821i
$911$		−	1.37997e9i		−	1.82522i	−0.408833	−	0.912609i	$-0.634064\pi$
$911$		−	1.37997e9i		−	1.82522i	0.408833	−	0.912609i	$-0.365936\pi$
$912$	3.35155e8	+	5.78164e7i	0.441836	+	0.0762196i
$913$	−9.06387e8			−1.19097
$914$	−5.59885e8	+	1.20359e9i	−0.733263	+	1.57630i
$915$	2.33090e8	−	2.33090e8i	0.304271	−	0.304271i
$916$	1.05795e9	+	9.05828e7i	1.37651	+	0.117858i
$917$	−3.79496e7	+	3.79496e7i	−0.0492152	+	0.0492152i
$918$	−5.12781e8	−	1.40480e9i	−0.662833	−	1.81588i
$919$	−1.35976e8			−0.175192			−0.0875962	−	0.996156i	$-0.527919\pi$
$919$	−1.35976e8			−0.175192			−0.0875962	+	0.996156i	$0.527919\pi$
$920$	4.65050e8	+	2.66776e8i	0.597223	+	0.342596i
$921$		−	1.20846e9i		−	1.54687i
$922$	−2.52988e8	−	6.93078e8i	−0.322780	−	0.884280i
$923$	6.59808e6	+	6.59808e6i	0.00839098	+	0.00839098i
$924$	7.92623e7	+	9.41063e7i	0.100473	+	0.119290i
$925$	−5.34894e7	−	5.34894e7i	−0.0675838	−	0.0675838i
$926$	−6.60163e8	+	1.41916e9i	−0.831416	+	1.78730i
$927$		−	1.45065e8i		−	0.182106i
$928$	−6.83857e8	+	1.23853e8i	−0.855700	+	0.154975i
$929$	−1.18881e9			−1.48274			−0.741370	−	0.671096i	$-0.765824\pi$
$929$	−1.18881e9			−1.48274			−0.741370	+	0.671096i	$0.765824\pi$
$930$	−2.94084e8	−	1.36802e8i	−0.365614	−	0.170076i
$931$	−3.15264e8	+	3.15264e8i	−0.390684	+	0.390684i
$932$	−1.55023e8	+	1.30570e8i	−0.191491	+	0.161286i
$933$	7.14783e8	−	7.14783e8i	0.880094	−	0.880094i
$934$	1.03492e9	−	3.77766e8i	1.27018	−	0.463641i
$935$	6.88591e8			0.842415
$936$	2.06447e8	+	1.18428e8i	0.251756	+	0.144420i
$937$			1.27672e8i			0.155194i	0.996985	+	0.0775972i	$0.0247248\pi$
$937$			1.27672e8i			0.155194i	−0.996985	+	0.0775972i	$0.975275\pi$
$938$	1.76275e8	−	6.43440e7i	0.213591	−	0.0779649i
$939$	5.63519e8	+	5.63519e8i	0.680631	+	0.680631i
$940$	4.29321e7	−	5.01420e8i	0.0516890	−	0.603696i
$941$	9.12612e8	+	9.12612e8i	1.09526	+	1.09526i	0.994957	+	0.100303i	$0.0319812\pi$
$941$	9.12612e8	+	9.12612e8i	1.09526	+	1.09526i	0.100303	+	0.994957i	$0.468019\pi$
$942$	2.40544e8	+	1.11896e8i	0.287767	+	0.133864i
$943$		−	4.25341e8i		−	0.507226i
$944$	2.32559e8	−	1.64128e8i	0.276450	−	0.195104i
$945$	−8.33662e7			−0.0987858
$946$	3.99095e8	−	8.57938e8i	0.471415	−	1.01340i
$947$	−2.43554e8	+	2.43554e8i	−0.286777	+	0.286777i	−0.835804	−	0.549027i	$-0.814998\pi$
$947$	−2.43554e8	+	2.43554e8i	−0.286777	+	0.286777i	0.549027	+	0.835804i	$0.314998\pi$
$948$	−9.03999e6	+	1.05581e8i	−0.0106107	+	0.123926i
$949$	3.96551e8	−	3.96551e8i	0.463981	−	0.463981i
$950$	1.32543e8	+	3.63111e8i	0.154591	+	0.423514i
$951$	2.59909e8			0.302190
$952$	7.87897e7	+	2.90810e8i	0.0913185	+	0.337053i
$953$			1.27469e9i			1.47273i	0.676582	+	0.736367i	$0.263460\pi$
$953$			1.27469e9i			1.47273i	−0.676582	+	0.736367i	$0.736540\pi$
$954$	1.91392e8	+	5.24332e8i	0.220434	+	0.603895i
$955$	−5.12917e8	−	5.12917e8i	−0.588894	−	0.588894i
$956$	4.03183e8	−	3.39587e8i	0.461455	−	0.388666i
$957$	−4.28661e8	−	4.28661e8i	−0.489078	−	0.489078i
$958$	2.26915e8	−	4.87800e8i	0.258087	−	0.554812i
$959$		−	9.93836e7i		−	0.112683i
$960$	1.61734e8	+	2.76568e8i	0.182805	+	0.312600i
$961$	−2.12934e8			−0.239925
$962$	7.29641e7	+	3.39414e7i	0.0819567	+	0.0381246i
$963$	2.43022e8	−	2.43022e8i	0.272124	−	0.272124i
$964$	1.15063e8	+	1.36612e8i	0.128442	+	0.152496i
$965$	−4.46172e8	+	4.46172e8i	−0.496501	+	0.496501i
$966$	−1.92220e8	+	7.01643e7i	−0.213240	+	0.0778368i
$967$	1.54082e9			1.70401			0.852004	−	0.523536i	$-0.175387\pi$
$967$	1.54082e9			1.70401			0.852004	+	0.523536i	$0.175387\pi$
$968$	−3.41316e7	+	9.24732e6i	−0.0376296	+	0.0101951i
$969$			7.26471e8i			0.798449i
$970$	−3.30758e8	+	1.20733e8i	−0.362406	+	0.132285i
$971$	7.16389e8	+	7.16389e8i	0.782513	+	0.782513i	0.980254	−	0.197742i	$-0.0633607\pi$
$971$	7.16389e8	+	7.16389e8i	0.782513	+	0.782513i	−0.197742	+	0.980254i	$0.563361\pi$
$972$	−6.67742e8	−	5.71727e7i	−0.727126	−	0.0622572i
$973$	3.20442e7	+	3.20442e7i	0.0347865	+	0.0347865i
$974$	−1.02912e9	−	4.78727e8i	−1.11376	−	0.518097i
$975$		−	4.21070e8i		−	0.454298i
$976$	−9.02600e8	+	6.37008e8i	−0.970836	+	0.685165i
$977$	4.36986e8			0.468580			0.234290	−	0.972167i	$-0.424723\pi$
$977$	4.36986e8			0.468580			0.234290	+	0.972167i	$0.424723\pi$
$978$	−1.93646e8	+	4.16281e8i	−0.207010	+	0.445011i
$979$	−4.01084e8	+	4.01084e8i	−0.427451	+	0.427451i
$980$	−4.18471e8	−	3.58299e7i	−0.444619	−	0.0380687i
$981$	2.58901e8	−	2.58901e8i	0.274238	−	0.274238i
$982$	−3.61817e8	−	9.91224e8i	−0.382080	−	1.04674i
$983$	−8.29023e8			−0.872782			−0.436391	−	0.899757i	$-0.643744\pi$
$983$	−8.29023e8			−0.872782			−0.436391	+	0.899757i	$0.643744\pi$
$984$	1.26476e8	−	2.20477e8i	0.132747	−	0.231408i
$985$			5.76708e7i			0.0603458i
$986$	−5.09020e8	−	1.39450e9i	−0.531012	−	1.45475i
$987$	1.35818e8	+	1.35818e8i	0.141256	+	0.141256i
$988$	−2.64904e8	−	3.14514e8i	−0.274674	−	0.326114i
$989$	1.11275e9	+	1.11275e9i	1.15029	+	1.15029i
$990$	7.57233e7	−	1.62783e8i	0.0780412	−	0.167766i
$991$			9.19609e8i			0.944892i	0.881360	+	0.472446i	$0.156629\pi$
$991$			9.19609e8i			0.944892i	−0.881360	+	0.472446i	$0.843371\pi$
$992$	8.93305e8	+	6.19349e8i	0.915092	+	0.634454i
$993$	−3.14682e8			−0.321384
$994$	2.79247e6	+	1.29900e6i	0.00284335	+	0.00132267i
$995$	1.34027e8	−	1.34027e8i	0.136058	−	0.136058i
$996$	6.88986e8	−	5.80308e8i	0.697320	−	0.587327i
$997$	1.02484e9	−	1.02484e9i	1.03412	−	1.03412i	0.0347213	−	0.999397i	$-0.488946\pi$
$997$	1.02484e9	−	1.02484e9i	1.03412	−	1.03412i	0.999397	−	0.0347213i	$-0.0110544\pi$
$998$	1.28164e9	−	4.67824e8i	1.28936	−	0.470643i
$999$	−1.31833e8			−0.132229

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.7.f.a.3.10	✓	22
4.3	odd	2		64.7.f.a.47.4		22
8.3	odd	2		128.7.f.a.95.8		22
8.5	even	2		128.7.f.b.95.4		22
16.3	odd	4		128.7.f.b.31.4		22
16.5	even	4		64.7.f.a.15.4		22
16.11	odd	4	inner	16.7.f.a.11.10	yes	22
16.13	even	4		128.7.f.a.31.8		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.7.f.a.3.10	✓	22	1.1	even	1	trivial
16.7.f.a.11.10	yes	22	16.11	odd	4	inner
64.7.f.a.15.4		22	16.5	even	4
64.7.f.a.47.4		22	4.3	odd	2
128.7.f.a.31.8		22	16.13	even	4
128.7.f.a.95.8		22	8.3	odd	2
128.7.f.b.31.4		22	16.3	odd	4
128.7.f.b.95.4		22	8.5	even	2

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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	16.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(7.25359 + 3.37422i) q^{2} +(14.8973 - 14.8973i) q^{3} +(41.2292 + 48.9505i) q^{4} +(41.0202 - 41.0202i) q^{5} +(158.326 - 57.7921i) q^{6} -67.2599 q^{7} +(133.890 + 494.184i) q^{8} +285.141i q^{9} +O(q^{10})\)	\(q+(7.25359 + 3.37422i) q^{2} +(14.8973 - 14.8973i) q^{3} +(41.2292 + 48.9505i) q^{4} +(41.0202 - 41.0202i) q^{5} +(158.326 - 57.7921i) q^{6} -67.2599 q^{7} +(133.890 + 494.184i) q^{8} +285.141i q^{9} +(435.955 - 159.133i) q^{10} +(-959.330 - 959.330i) q^{11} +(1343.43 + 115.026i) q^{12} +(-1152.76 - 1152.76i) q^{13} +(-487.876 - 226.950i) q^{14} -1222.18i q^{15} +(-696.303 + 4036.38i) q^{16} -8749.14 q^{17} +(-962.129 + 2068.30i) q^{18} +(2786.86 - 2786.86i) q^{19} +(3699.19 + 316.728i) q^{20} +(-1001.99 + 1001.99i) q^{21} +(-3721.59 - 10195.6i) q^{22} +18050.6 q^{23} +(9356.60 + 5367.40i) q^{24} +12259.7i q^{25} +(-4471.97 - 12251.3i) q^{26} +(15108.0 + 15108.0i) q^{27} +(-2773.07 - 3292.40i) q^{28} +(14997.1 + 14997.1i) q^{29} +(4123.91 - 8865.20i) q^{30} -33172.8i q^{31} +(-18670.4 + 26928.8i) q^{32} -28582.9 q^{33} +(-63462.7 - 29521.6i) q^{34} +(-2759.01 + 2759.01i) q^{35} +(-13957.8 + 11756.1i) q^{36} +(-4363.03 + 4363.03i) q^{37} +(29618.3 - 10811.3i) q^{38} -34345.9 q^{39} +(25763.7 + 14779.3i) q^{40} -23563.8i q^{41} +(-10649.0 + 3887.09i) q^{42} +(61646.0 + 61646.0i) q^{43} +(7407.25 - 86512.1i) q^{44} +(11696.5 + 11696.5i) q^{45} +(130932. + 60906.8i) q^{46} -135549. i q^{47} +(49758.2 + 70504.2i) q^{48} -113125. q^{49} +(-41366.9 + 88926.8i) q^{50} +(-130339. + 130339. i) q^{51} +(8900.76 - 103955. i) q^{52} +(173023. - 173023. i) q^{53} +(58609.4 + 160565. i) q^{54} -78703.8 q^{55} +(-9005.43 - 33238.7i) q^{56} -83033.5i q^{57} +(58179.5 + 159387. i) q^{58} +(-49138.8 - 49138.8i) q^{59} +(59826.4 - 50389.6i) q^{60} +(190716. + 190716. i) q^{61} +(111933. - 240622. i) q^{62} -19178.5i q^{63} +(-226291. + 132333. i) q^{64} -94572.7 q^{65} +(-207328. - 96444.9i) q^{66} +(-246599. + 246599. i) q^{67} +(-360720. - 428275. i) q^{68} +(268905. - 268905. i) q^{69} +(-29322.3 + 10703.2i) q^{70} -5723.74 q^{71} +(-140912. + 38177.5i) q^{72} +344002. i q^{73} +(-46369.5 + 16925.8i) q^{74} +(182636. + 182636. i) q^{75} +(251319. + 21518.1i) q^{76} +(64524.4 + 64524.4i) q^{77} +(-249132. - 115891. i) q^{78} +78590.7i q^{79} +(137011. + 194136. i) q^{80} +242268. q^{81} +(79509.5 - 170922. i) q^{82} +(472406. - 472406. i) q^{83} +(-90359.2 - 7736.65i) q^{84} +(-358891. + 358891. i) q^{85} +(239148. + 655162. i) q^{86} +446834. q^{87} +(345640. - 602530. i) q^{88} -418087. i q^{89} +(45375.2 + 124309. i) q^{90} +(77534.3 + 77534.3i) q^{91} +(744212. + 883586. i) q^{92} +(-494186. - 494186. i) q^{93} +(457371. - 983214. i) q^{94} -228635. i q^{95} +(123028. + 679304. i) q^{96} -758697. q^{97} +(-820564. - 381709. i) q^{98} +(273544. - 273544. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8}+O(q^{10}) \) 22 * q - 2 * q^2 - 2 * q^3 + 88 * q^4 - 2 * q^5 - 512 * q^6 - 4 * q^7 + 964 * q^8	\( 22 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 2 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8} - 1124 q^{10} + 1358 q^{11} - 2348 q^{12} - 2 q^{13} + 7564 q^{14} - 7976 q^{16} - 4 q^{17} - 1874 q^{18} + 3934 q^{19} - 16564 q^{20} - 1460 q^{21} + 25252 q^{22} - 13124 q^{23} - 32592 q^{24} + 58952 q^{26} + 35776 q^{27} + 45176 q^{28} - 33202 q^{29} + 8452 q^{30} - 39672 q^{32} - 4 q^{33} - 52588 q^{34} - 112420 q^{35} - 138484 q^{36} + 3598 q^{37} - 187280 q^{38} + 254396 q^{39} + 165160 q^{40} + 353496 q^{42} - 267986 q^{43} + 380724 q^{44} + 32706 q^{45} + 248156 q^{46} - 460824 q^{48} + 168066 q^{49} - 719674 q^{50} + 301788 q^{51} - 784892 q^{52} - 221842 q^{53} - 547552 q^{54} - 232708 q^{55} + 366424 q^{56} + 1441912 q^{58} + 39150 q^{59} + 2405600 q^{60} + 326494 q^{61} + 182832 q^{62} - 318656 q^{64} + 186412 q^{65} - 3392732 q^{66} - 122786 q^{67} - 2504400 q^{68} - 543188 q^{69} - 1186816 q^{70} - 267012 q^{71} + 1748596 q^{72} + 3610396 q^{74} - 275278 q^{75} + 4245988 q^{76} + 231180 q^{77} + 3179052 q^{78} - 2898968 q^{80} - 354298 q^{81} - 5004624 q^{82} - 288322 q^{83} - 7602776 q^{84} + 340748 q^{85} - 3240476 q^{86} + 2029884 q^{87} + 3308152 q^{88} + 10273400 q^{90} + 302396 q^{91} + 7253656 q^{92} - 1173344 q^{93} + 3859056 q^{94} - 5689424 q^{96} - 4 q^{97} - 9176950 q^{98} - 271522 q^{99}+O(q^{100}) \) 22 * q - 2 * q^2 - 2 * q^3 + 88 * q^4 - 2 * q^5 - 512 * q^6 - 4 * q^7 + 964 * q^8 - 1124 * q^10 + 1358 * q^11 - 2348 * q^12 - 2 * q^13 + 7564 * q^14 - 7976 * q^16 - 4 * q^17 - 1874 * q^18 + 3934 * q^19 - 16564 * q^20 - 1460 * q^21 + 25252 * q^22 - 13124 * q^23 - 32592 * q^24 + 58952 * q^26 + 35776 * q^27 + 45176 * q^28 - 33202 * q^29 + 8452 * q^30 - 39672 * q^32 - 4 * q^33 - 52588 * q^34 - 112420 * q^35 - 138484 * q^36 + 3598 * q^37 - 187280 * q^38 + 254396 * q^39 + 165160 * q^40 + 353496 * q^42 - 267986 * q^43 + 380724 * q^44 + 32706 * q^45 + 248156 * q^46 - 460824 * q^48 + 168066 * q^49 - 719674 * q^50 + 301788 * q^51 - 784892 * q^52 - 221842 * q^53 - 547552 * q^54 - 232708 * q^55 + 366424 * q^56 + 1441912 * q^58 + 39150 * q^59 + 2405600 * q^60 + 326494 * q^61 + 182832 * q^62 - 318656 * q^64 + 186412 * q^65 - 3392732 * q^66 - 122786 * q^67 - 2504400 * q^68 - 543188 * q^69 - 1186816 * q^70 - 267012 * q^71 + 1748596 * q^72 + 3610396 * q^74 - 275278 * q^75 + 4245988 * q^76 + 231180 * q^77 + 3179052 * q^78 - 2898968 * q^80 - 354298 * q^81 - 5004624 * q^82 - 288322 * q^83 - 7602776 * q^84 + 340748 * q^85 - 3240476 * q^86 + 2029884 * q^87 + 3308152 * q^88 + 10273400 * q^90 + 302396 * q^91 + 7253656 * q^92 - 1173344 * q^93 + 3859056 * q^94 - 5689424 * q^96 - 4 * q^97 - 9176950 * q^98 - 271522 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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