LMFDB - Embedded newform 300.2.w.a.127.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(67,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 13]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("300.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, degree $8$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			127.30
Character	$\chi$	$=$	300.127
Dual form			300.2.w.a.163.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41129 - 0.0909451i) q^{2} +(0.891007 - 0.453990i) q^{3} +(1.98346 - 0.256699i) q^{4} +(-1.83309 + 1.28054i) q^{5} +(1.21618 - 0.721743i) q^{6} +(1.46352 - 1.46352i) q^{7} +(2.77588 - 0.542662i) q^{8} +(0.587785 - 0.809017i) q^{9} +O(q^{10})$	\(q+(1.41129 - 0.0909451i) q^{2} +(0.891007 - 0.453990i) q^{3} +(1.98346 - 0.256699i) q^{4} +(-1.83309 + 1.28054i) q^{5} +(1.21618 - 0.721743i) q^{6} +(1.46352 - 1.46352i) q^{7} +(2.77588 - 0.542662i) q^{8} +(0.587785 - 0.809017i) q^{9} +(-2.47056 + 1.97391i) q^{10} +(-0.716610 - 0.986329i) q^{11} +(1.65074 - 1.12919i) q^{12} +(0.610002 - 0.0966148i) q^{13} +(1.93235 - 2.19855i) q^{14} +(-1.05195 + 1.97317i) q^{15} +(3.86821 - 1.01830i) q^{16} +(-2.23367 + 4.38383i) q^{17} +(0.755957 - 1.19521i) q^{18} +(1.11648 + 3.43617i) q^{19} +(-3.30715 + 3.01044i) q^{20} +(0.639583 - 1.96843i) q^{21} +(-1.10104 - 1.32682i) q^{22} +(-6.81819 - 1.07989i) q^{23} +(2.22697 - 1.74374i) q^{24} +(1.72046 - 4.69468i) q^{25} +(0.852100 - 0.191828i) q^{26} +(0.156434 - 0.987688i) q^{27} +(2.52715 - 3.27852i) q^{28} +(0.953684 + 0.309871i) q^{29} +(-1.30515 + 2.88038i) q^{30} +(-10.1146 + 3.28642i) q^{31} +(5.36654 - 1.78891i) q^{32} +(-1.08629 - 0.553491i) q^{33} +(-2.75367 + 6.38999i) q^{34} +(-0.808681 + 4.55687i) q^{35} +(0.958173 - 1.75554i) q^{36} +(-0.749924 - 4.73483i) q^{37} +(1.88818 + 4.74789i) q^{38} +(0.499653 - 0.363019i) q^{39} +(-4.39355 + 4.54936i) q^{40} +(-4.46659 - 3.24517i) q^{41} +(0.723615 - 2.83619i) q^{42} +(-2.74571 - 2.74571i) q^{43} +(-1.67455 - 1.77239i) q^{44} +(-0.0414904 + 2.23568i) q^{45} +(-9.72062 - 0.903960i) q^{46} +(-0.593032 - 1.16389i) q^{47} +(2.98430 - 2.66345i) q^{48} +2.71620i q^{49} +(2.00110 - 6.78200i) q^{50} +4.92009i q^{51} +(1.18511 - 0.348218i) q^{52} +(2.82569 + 5.54573i) q^{53} +(0.130948 - 1.40814i) q^{54} +(2.57664 + 0.890388i) q^{55} +(3.26837 - 4.85677i) q^{56} +(2.55478 + 2.55478i) q^{57} +(1.37410 + 0.350583i) q^{58} +(10.5976 + 7.69958i) q^{59} +(-1.57998 + 4.18374i) q^{60} +(7.64473 - 5.55422i) q^{61} +(-13.9757 + 5.55795i) q^{62} +(-0.323778 - 2.04425i) q^{63} +(7.41104 - 3.01273i) q^{64} +(-0.994471 + 0.958232i) q^{65} +(-1.58340 - 0.682342i) q^{66} +(7.24032 + 3.68913i) q^{67} +(-3.30507 + 9.26853i) q^{68} +(-6.56531 + 2.13320i) q^{69} +(-0.726856 + 6.50459i) q^{70} +(-12.8093 - 4.16201i) q^{71} +(1.19260 - 2.56470i) q^{72} +(1.08745 - 6.86590i) q^{73} +(-1.48897 - 6.61400i) q^{74} +(-0.598399 - 4.96406i) q^{75} +(3.09656 + 6.52891i) q^{76} +(-2.49229 - 0.394740i) q^{77} +(0.672139 - 0.557765i) q^{78} +(-2.17258 + 6.68651i) q^{79} +(-5.78682 + 6.82003i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(-6.59877 - 4.17364i) q^{82} +(3.19885 - 6.27810i) q^{83} +(0.763291 - 4.06849i) q^{84} +(-1.51912 - 10.8963i) q^{85} +(-4.12469 - 3.62528i) q^{86} +(0.990417 - 0.156867i) q^{87} +(-2.52447 - 2.34905i) q^{88} +(8.41934 + 11.5882i) q^{89} +(0.144770 + 3.15896i) q^{90} +(0.751354 - 1.03415i) q^{91} +(-13.8008 - 0.391703i) q^{92} +(-7.52014 + 7.52014i) q^{93} +(-0.942788 - 1.58865i) q^{94} +(-6.44675 - 4.86913i) q^{95} +(3.96948 - 4.03029i) q^{96} +(3.66823 - 1.86906i) q^{97} +(0.247025 + 3.83333i) q^{98} -1.21917 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{8}+O(q^{10}) $ 240 * q + 12 * q^8	$ 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) $ 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{20}\right)$

Coefficient data

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

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

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

$2$	1.41129	−	0.0909451i	0.997930	−	0.0643079i
$2$	1.41129	−	0.0909451i	0.997930	−	0.0643079i
$3$	0.891007	−	0.453990i	0.514423	−	0.262112i
$3$	0.891007	−	0.453990i	0.514423	−	0.262112i
$4$	1.98346	−	0.256699i	0.991729	−	0.128350i
$5$	−1.83309	+	1.28054i	−0.819784	+	0.572673i
$5$	−1.83309	+	1.28054i	−0.819784	+	0.572673i
$6$	1.21618	−	0.721743i	0.496502	−	0.294650i
$7$	1.46352	−	1.46352i	0.553160	−	0.553160i	−0.374192	−	0.927351i	$-0.622080\pi$
$7$	1.46352	−	1.46352i	0.553160	−	0.553160i	0.927351	+	0.374192i	$0.122080\pi$
$8$	2.77588	−	0.542662i	0.981422	−	0.191860i
$9$	0.587785	−	0.809017i	0.195928	−	0.269672i
$10$	−2.47056	+	1.97391i	−0.781260	+	0.624206i
$11$	−0.716610	−	0.986329i	−0.216066	−	0.297389i	0.687202	−	0.726467i	$-0.258839\pi$
$11$	−0.716610	−	0.986329i	−0.216066	−	0.297389i	−0.903268	+	0.429077i	$0.858839\pi$
$12$	1.65074	−	1.12919i	0.476526	−	0.325970i
$13$	0.610002	−	0.0966148i	0.169184	−	0.0267961i	−0.0712677	−	0.997457i	$-0.522704\pi$
$13$	0.610002	−	0.0966148i	0.169184	−	0.0267961i	0.240452	+	0.970661i	$0.422704\pi$
$14$	1.93235	−	2.19855i	0.516442	−	0.587587i
$15$	−1.05195	+	1.97317i	−0.271612	+	0.509471i
$16$	3.86821	−	1.01830i	0.967053	−	0.254576i
$17$	−2.23367	+	4.38383i	−0.541746	+	1.06324i	0.444162	+	0.895946i	$0.353501\pi$
$17$	−2.23367	+	4.38383i	−0.541746	+	1.06324i	−0.985908	+	0.167289i	$0.946499\pi$
$18$	0.755957	−	1.19521i	0.178181	−	0.281714i
$19$	1.11648	+	3.43617i	0.256138	+	0.788312i	0.993603	+	0.112927i	$0.0360227\pi$
$19$	1.11648	+	3.43617i	0.256138	+	0.788312i	−0.737465	+	0.675385i	$0.763977\pi$
$20$	−3.30715	+	3.01044i	−0.739501	+	0.673155i
$21$	0.639583	−	1.96843i	0.139568	−	0.429548i
$22$	−1.10104	−	1.32682i	−0.234743	−	0.282879i
$23$	−6.81819	−	1.07989i	−1.42169	−	0.225174i	−0.602236	−	0.798318i	$-0.705723\pi$
$23$	−6.81819	−	1.07989i	−1.42169	−	0.225174i	−0.819454	+	0.573145i	$0.805723\pi$
$24$	2.22697	−	1.74374i	0.454577	−	0.355939i
$25$	1.72046	−	4.69468i	0.344092	−	0.938936i
$26$	0.852100	−	0.191828i	0.167111	−	0.0376205i
$27$	0.156434	−	0.987688i	0.0301058	−	0.190081i
$28$	2.52715	−	3.27852i	0.477587	−	0.619582i
$29$	0.953684	+	0.309871i	0.177095	+	0.0575416i	0.396222	−	0.918155i	$-0.370321\pi$
$29$	0.953684	+	0.309871i	0.177095	+	0.0575416i	−0.219127	+	0.975696i	$0.570321\pi$
$30$	−1.30515	+	2.88038i	−0.238286	+	0.525883i
$31$	−10.1146	+	3.28642i	−1.81663	+	0.590259i	−0.816717	+	0.577038i	$0.804209\pi$
$31$	−10.1146	+	3.28642i	−1.81663	+	0.590259i	−0.999913	+	0.0132212i	$0.995791\pi$
$32$	5.36654	−	1.78891i	0.948680	−	0.316238i
$33$	−1.08629	−	0.553491i	−0.189098	−	0.0963505i
$34$	−2.75367	+	6.38999i	−0.472250	+	1.09587i
$35$	−0.808681	+	4.55687i	−0.136692	+	0.770251i
$36$	0.958173	−	1.75554i	0.159696	−	0.292589i
$37$	−0.749924	−	4.73483i	−0.123287	−	0.778402i	−0.969416	−	0.245424i	$-0.921073\pi$
$37$	−0.749924	−	4.73483i	−0.123287	−	0.778402i	0.846129	−	0.532978i	$-0.178927\pi$
$38$	1.88818	+	4.74789i	0.306303	+	0.770209i
$39$	0.499653	−	0.363019i	0.0800085	−	0.0581296i
$40$	−4.39355	+	4.54936i	−0.694681	+	0.719317i
$41$	−4.46659	−	3.24517i	−0.697564	−	0.506810i	0.181574	−	0.983377i	$-0.441881\pi$
$41$	−4.46659	−	3.24517i	−0.697564	−	0.506810i	−0.879138	+	0.476568i	$0.841881\pi$
$42$	0.723615	−	2.83619i	0.111656	−	0.437634i
$43$	−2.74571	−	2.74571i	−0.418717	−	0.418717i	0.466044	−	0.884761i	$-0.345679\pi$
$43$	−2.74571	−	2.74571i	−0.418717	−	0.418717i	−0.884761	+	0.466044i	$0.845679\pi$
$44$	−1.67455	−	1.77239i	−0.252449	−	0.267198i
$45$	−0.0414904	+	2.23568i	−0.00618502	+	0.333276i
$46$	−9.72062	−	0.903960i	−1.43323	−	0.133282i
$47$	−0.593032	−	1.16389i	−0.0865026	−	0.169771i	0.843703	−	0.536811i	$-0.180371\pi$
$47$	−0.593032	−	1.16389i	−0.0865026	−	0.169771i	−0.930205	+	0.367040i	$0.880371\pi$
$48$	2.98430	−	2.66345i	0.430747	−	0.384435i
$49$			2.71620i			0.388028i
$50$	2.00110	−	6.78200i	0.282999	−	0.959120i
$51$			4.92009i			0.688951i
$52$	1.18511	−	0.348218i	0.164345	−	0.0482892i
$53$	2.82569	+	5.54573i	0.388139	+	0.761765i	0.999564	−	0.0295374i	$-0.00940340\pi$
$53$	2.82569	+	5.54573i	0.388139	+	0.761765i	−0.611425	+	0.791302i	$0.709403\pi$
$54$	0.130948	−	1.40814i	0.0178198	−	0.191623i
$55$	2.57664	+	0.890388i	0.347434	+	0.120060i
$56$	3.26837	−	4.85677i	0.436754	−	0.649013i
$57$	2.55478	+	2.55478i	0.338389	+	0.338389i
$58$	1.37410	+	0.350583i	0.180429	+	0.0460339i
$59$	10.5976	+	7.69958i	1.37969	+	1.00240i	0.996909	+	0.0785588i	$0.0250318\pi$
$59$	10.5976	+	7.69958i	1.37969	+	1.00240i	0.382776	+	0.923841i	$0.374968\pi$
$60$	−1.57998	+	4.18374i	−0.203975	+	0.540118i
$61$	7.64473	−	5.55422i	0.978807	−	0.711145i	0.0213655	−	0.999772i	$-0.493199\pi$
$61$	7.64473	−	5.55422i	0.978807	−	0.711145i	0.957442	+	0.288627i	$0.0931986\pi$
$62$	−13.9757	+	5.55795i	−1.77491	+	0.705861i
$63$	−0.323778	−	2.04425i	−0.0407922	−	0.257552i
$64$	7.41104	−	3.01273i	0.926380	−	0.376591i
$65$	−0.994471	+	0.958232i	−0.123349	+	0.118854i
$66$	−1.58340	−	0.682342i	−0.194903	−	0.0839905i
$67$	7.24032	+	3.68913i	0.884546	+	0.450699i	0.836386	−	0.548141i	$-0.184664\pi$
$67$	7.24032	+	3.68913i	0.884546	+	0.450699i	0.0481602	+	0.998840i	$0.484664\pi$
$68$	−3.30507	+	9.26853i	−0.400799	+	1.12397i
$69$	−6.56531	+	2.13320i	−0.790370	+	0.256807i
$70$	−0.726856	+	6.50459i	−0.0868759	+	0.777447i
$71$	−12.8093	−	4.16201i	−1.52019	−	0.493940i	−0.574360	−	0.818603i	$-0.694749\pi$
$71$	−12.8093	−	4.16201i	−1.52019	−	0.493940i	−0.945830	+	0.324663i	$0.894749\pi$
$72$	1.19260	−	2.56470i	0.140549	−	0.302253i
$73$	1.08745	−	6.86590i	0.127277	−	0.803592i	−0.838630	−	0.544701i	$-0.816643\pi$
$73$	1.08745	−	6.86590i	0.127277	−	0.803592i	0.965907	−	0.258891i	$-0.0833570\pi$
$74$	−1.48897	−	6.61400i	−0.173089	−	0.768862i
$75$	−0.598399	−	4.96406i	−0.0690972	−	0.573201i
$76$	3.09656	+	6.52891i	0.355199	+	0.748917i
$77$	−2.49229	−	0.394740i	−0.284023	−	0.0449848i
$78$	0.672139	−	0.557765i	0.0761047	−	0.0631545i
$79$	−2.17258	+	6.68651i	−0.244434	+	0.752291i	0.751295	+	0.659967i	$0.229430\pi$
$79$	−2.17258	+	6.68651i	−0.244434	+	0.752291i	−0.995729	+	0.0923241i	$0.970570\pi$
$80$	−5.78682	+	6.82003i	−0.646986	+	0.762502i
$81$	−0.309017	−	0.951057i	−0.0343352	−	0.105673i
$82$	−6.59877	−	4.17364i	−0.728712	−	0.460902i
$83$	3.19885	−	6.27810i	0.351119	−	0.689111i	−0.646130	−	0.763227i	$-0.723614\pi$
$83$	3.19885	−	6.27810i	0.351119	−	0.689111i	0.997250	+	0.0741166i	$0.0236137\pi$
$84$	0.763291	−	4.06849i	0.0832819	−	0.443908i
$85$	−1.51912	−	10.8963i	−0.164772	−	1.18187i
$86$	−4.12469	−	3.62528i	−0.444777	−	0.390924i
$87$	0.990417	−	0.156867i	0.106184	−	0.0168179i
$88$	−2.52447	−	2.34905i	−0.269109	−	0.250410i
$89$	8.41934	+	11.5882i	0.892448	+	1.22835i	0.972815	+	0.231585i	$0.0743910\pi$
$89$	8.41934	+	11.5882i	0.892448	+	1.22835i	−0.0803663	+	0.996765i	$0.525609\pi$
$90$	0.144770	+	3.15896i	0.0152601	+	0.332984i
$91$	0.751354	−	1.03415i	0.0787633	−	0.108408i
$92$	−13.8008	−	0.391703i	−1.43883	−	0.0408378i
$93$	−7.52014	+	7.52014i	−0.779802	+	0.779802i
$94$	−0.942788	−	1.58865i	−0.0972412	−	0.163857i
$95$	−6.44675	−	4.86913i	−0.661423	−	0.499563i
$96$	3.96948	−	4.03029i	0.405133	−	0.411340i
$97$	3.66823	−	1.86906i	0.372453	−	0.189774i	−0.257737	−	0.966215i	$-0.582977\pi$
$97$	3.66823	−	1.86906i	0.372453	−	0.189774i	0.630190	+	0.776441i	$0.282977\pi$
$98$	0.247025	+	3.83333i	0.0249533	+	0.387225i
$99$	−1.21917			−0.122531
$100$	2.20734	−	9.75334i	0.220734	−	0.975334i
$101$	−14.2792			−1.42083			−0.710417	−	0.703781i	$-0.751494\pi$
$101$	−14.2792			−1.42083			−0.710417	+	0.703781i	$0.751494\pi$
$102$	0.447458	+	6.94366i	0.0443050	+	0.687524i
$103$	11.1840	−	5.69852i	1.10199	−	0.561492i	0.194219	−	0.980958i	$-0.437783\pi$
$103$	11.1840	−	5.69852i	1.10199	−	0.561492i	0.907771	+	0.419467i	$0.137783\pi$
$104$	1.64086	−	0.599216i	0.160900	−	0.0587579i
$105$	1.34823	+	4.42733i	0.131574	+	0.432063i
$106$	4.49222	+	7.56963i	0.436323	+	0.735228i
$107$	3.88843	−	3.88843i	0.375909	−	0.375909i	−0.493715	−	0.869624i	$-0.664361\pi$
$107$	3.88843	−	3.88843i	0.375909	−	0.375909i	0.869624	+	0.493715i	$0.164361\pi$
$108$	0.0567424	−	1.99919i	0.00546004	−	0.192373i
$109$	−3.30533	+	4.54940i	−0.316593	+	0.435753i	−0.937423	−	0.348192i	$-0.886796\pi$
$109$	−3.30533	+	4.54940i	−0.316593	+	0.435753i	0.620830	+	0.783945i	$0.286796\pi$
$110$	3.71735	+	1.02226i	0.354436	+	0.0974686i
$111$	−2.81776	−	3.87831i	−0.267450	−	0.368113i
$112$	4.17091	−	7.15153i	0.394114	−	0.675756i
$113$	6.70930	−	1.06265i	0.631158	−	0.0999656i	0.167345	−	0.985898i	$-0.446481\pi$
$113$	6.70930	−	1.06265i	0.631158	−	0.0999656i	0.463813	+	0.885933i	$0.346481\pi$
$114$	3.83787	+	3.37318i	0.359450	+	0.315928i
$115$	13.8812	−	6.75138i	1.29443	−	0.629569i
$116$	1.97114	+	0.369806i	0.183015	+	0.0343356i
$117$	0.280387	−	0.550290i	0.0259218	−	0.0508744i
$118$	15.6564	+	9.90252i	1.44129	+	0.911601i
$119$	3.14681	+	9.68488i	0.288467	+	0.887811i
$120$	−1.84932	+	6.04814i	−0.168819	+	0.552117i
$121$	2.93987	−	9.04800i	0.267261	−	0.822545i
$122$	10.2838	−	8.53385i	0.931049	−	0.772618i
$123$	−5.45303	−	0.863676i	−0.491683	−	0.0778750i
$124$	−19.2182	+	9.11488i	−1.72585	+	0.818541i
$125$	2.85794	+	10.8089i	0.255622	+	0.966777i
$126$	−0.642858	−	2.85558i	−0.0572703	−	0.254395i
$127$	2.16580	−	13.6743i	0.192183	−	1.21340i	−0.683296	−	0.730142i	$-0.739454\pi$
$127$	2.16580	−	13.6743i	0.192183	−	1.21340i	0.875479	−	0.483256i	$-0.160546\pi$
$128$	10.1851	−	4.92582i	0.900244	−	0.435385i
$129$	−3.69297	−	1.19992i	−0.325148	−	0.105647i
$130$	−1.31634	+	1.44278i	−0.115450	+	0.126540i
$131$	1.62756	−	0.528826i	0.142201	−	0.0462038i	−0.237052	−	0.971497i	$-0.576181\pi$
$131$	1.62756	−	0.528826i	0.142201	−	0.0462038i	0.379253	+	0.925293i	$0.376181\pi$
$132$	−2.29669	−	0.818977i	−0.199901	−	0.0712828i
$133$	6.66292	+	3.39493i	0.577748	+	0.294377i
$134$	10.5537	+	4.54795i	0.911699	+	0.392883i
$135$	0.978011	+	2.01084i	0.0841738	+	0.173066i
$136$	−3.82148	+	13.3811i	−0.327689	+	1.14742i
$137$	−0.0719242	−	0.454112i	−0.00614490	−	0.0387974i	0.984425	−	0.175803i	$-0.0562522\pi$
$137$	−0.0719242	−	0.454112i	−0.00614490	−	0.0387974i	−0.990570	+	0.137006i	$0.956252\pi$
$138$	−9.07153	+	3.60764i	−0.772220	+	0.307102i
$139$	3.76808	−	2.73767i	0.319604	−	0.232206i	−0.416402	−	0.909180i	$-0.636709\pi$
$139$	3.76808	−	2.73767i	0.319604	−	0.232206i	0.736007	+	0.676974i	$0.236709\pi$
$140$	−0.434241	+	9.24594i	−0.0367001	+	0.781425i
$141$	−1.05679	−	0.767803i	−0.0889978	−	0.0646607i
$142$	−18.4562	−	4.70884i	−1.54881	−	0.395157i
$143$	−0.532427	−	0.532427i	−0.0445238	−	0.0445238i
$144$	1.44985	−	3.72799i	0.120821	−	0.310666i
$145$	−2.14499	+	0.653204i	−0.178132	+	0.0542456i
$146$	0.910285	−	9.78864i	0.0753357	−	0.810114i
$147$	1.23313	+	2.42015i	0.101707	+	0.199611i
$148$	−2.70287	−	9.19884i	−0.222175	−	0.756140i
$149$		−	19.6344i		−	1.60852i	−0.594281	−	0.804258i	$-0.702563\pi$
$149$		−	19.6344i		−	1.60852i	0.594281	−	0.804258i	$-0.297437\pi$
$150$	−1.29597	−	6.95129i	−0.105815	−	0.567571i
$151$			23.7781i			1.93504i	0.252799	+	0.967519i	$0.418649\pi$
$151$			23.7781i			1.93504i	−0.252799	+	0.967519i	$0.581351\pi$
$152$	4.96390	+	8.93254i	0.402625	+	0.724525i
$153$	2.23367	+	4.38383i	0.180582	+	0.354412i
$154$	−3.55323	−	0.330429i	−0.286328	−	0.0266268i
$155$	14.3326	−	18.9764i	1.15122	−	1.52422i
$156$	0.897854	−	0.848294i	0.0718859	−	0.0679179i
$157$	2.38350	+	2.38350i	0.190224	+	0.190224i	0.795793	−	0.605569i	$-0.207054\pi$
$157$	2.38350	+	2.38350i	0.190224	+	0.190224i	−0.605569	+	0.795793i	$0.707054\pi$
$158$	−2.45802	+	9.63416i	−0.195550	+	0.766453i
$159$	5.03542	+	3.65845i	0.399335	+	0.290134i
$160$	−7.54661	+	10.1513i	−0.596612	+	0.802530i
$161$	−11.5590	+	8.39812i	−0.910979	+	0.661865i
$162$	−0.522605	−	1.31411i	−0.0410598	−	0.103246i
$163$	−0.927372	−	5.85520i	−0.0726374	−	0.458614i	−0.997020	−	0.0771471i	$-0.975419\pi$
$163$	−0.927372	−	5.85520i	−0.0726374	−	0.458614i	0.924382	−	0.381467i	$-0.124581\pi$
$164$	−9.69232	−	5.29008i	−0.756843	−	0.413086i
$165$	2.70003	−	0.376429i	0.210197	−	0.0293049i
$166$	3.94353	−	9.15111i	0.306077	−	0.710264i
$167$	11.9576	+	6.09269i	0.925305	+	0.471467i	0.850644	−	0.525742i	$-0.176212\pi$
$167$	11.9576	+	6.09269i	0.925305	+	0.471467i	0.0746615	+	0.997209i	$0.476212\pi$
$168$	0.707213	−	5.81122i	0.0545626	−	0.448345i
$169$	−12.0010	+	3.89935i	−0.923151	+	0.299950i
$170$	−3.13487	−	15.2396i	−0.240434	−	1.16882i
$171$	3.43617	+	1.11648i	0.262771	+	0.0853794i
$172$	−6.15083	−	4.74118i	−0.468996	−	0.361512i
$173$	2.52253	−	15.9266i	0.191785	−	1.21088i	−0.684473	−	0.729038i	$-0.739968\pi$
$173$	2.52253	−	15.9266i	0.191785	−	1.21088i	0.876258	−	0.481842i	$-0.160032\pi$
$174$	1.38350	−	0.311457i	0.104883	−	0.0236115i
$175$	−4.35284	−	9.38871i	−0.329044	−	0.709720i
$176$	−3.77638	−	3.08560i	−0.284655	−	0.232586i
$177$	12.9380	+	2.04918i	0.972482	+	0.154026i
$178$	12.9360	+	15.5886i	0.969594	+	1.16842i
$179$	−1.87266	+	5.76347i	−0.139970	+	0.430782i	−0.996330	−	0.0855968i	$-0.972720\pi$
$179$	−1.87266	+	5.76347i	−0.139970	+	0.430782i	0.856360	+	0.516379i	$0.172720\pi$
$180$	0.491604	+	4.44503i	0.0366420	+	0.331313i
$181$	7.06640	+	21.7482i	0.525242	+	1.61653i	0.763837	+	0.645409i	$0.223313\pi$
$181$	7.06640	+	21.7482i	0.525242	+	1.61653i	−0.238596	+	0.971119i	$0.576687\pi$
$182$	0.966324	−	1.52781i	0.0716287	−	0.113249i
$183$	4.28994	−	8.41948i	0.317121	−	0.622386i
$184$	−19.5125	+	0.702310i	−1.43848	+	0.0517750i
$185$	7.43780	+	7.71909i	0.546838	+	0.567518i
$186$	−9.92915	+	11.2970i	−0.728041	+	0.828336i
$187$	5.92457	−	0.938360i	0.433248	−	0.0686197i
$188$	−1.47502	−	2.15630i	−0.107577	−	0.157264i
$189$	−1.21656	−	1.67445i	−0.0884917	−	0.121798i
$190$	−9.54104	−	6.28544i	−0.692180	−	0.455994i
$191$	4.71698	−	6.49237i	0.341309	−	0.469771i	−0.603514	−	0.797352i	$-0.706233\pi$
$191$	4.71698	−	6.49237i	0.341309	−	0.469771i	0.944823	+	0.327581i	$0.106233\pi$
$192$	5.23553	−	6.04890i	0.377842	−	0.436542i
$193$	7.12358	−	7.12358i	0.512767	−	0.512767i	−0.402606	−	0.915373i	$-0.631896\pi$
$193$	7.12358	−	7.12358i	0.512767	−	0.512767i	0.915373	+	0.402606i	$0.131896\pi$
$194$	5.00695	−	2.97139i	0.359478	−	0.213333i
$195$	−0.451052	+	1.30527i	−0.0323005	+	0.0934724i
$196$	0.697246	+	5.38747i	0.0498033	+	0.384819i
$197$	13.3419	−	6.79803i	0.950570	−	0.484339i	0.0912781	−	0.995825i	$-0.470905\pi$
$197$	13.3419	−	6.79803i	0.950570	−	0.484339i	0.859292	+	0.511486i	$0.170905\pi$
$198$	−1.72060	+	0.110877i	−0.122277	+	0.00787972i
$199$	−4.76131			−0.337520			−0.168760	−	0.985657i	$-0.553976\pi$
$199$	−4.76131			−0.337520			−0.168760	+	0.985657i	$0.553976\pi$
$200$	2.22817	−	13.9655i	0.157555	−	0.987510i
$201$	8.12601			0.573164
$202$	−20.1520	+	1.29862i	−1.41789	+	0.0913709i
$203$	1.84924	−	0.942236i	0.129791	−	0.0661320i
$204$	1.26298	+	9.75879i	0.0884265	+	0.683252i
$205$	12.3432	+	0.229069i	0.862088	+	0.0159988i
$206$	15.2655	−	9.05937i	1.06360	−	0.631196i
$207$	−4.88128	+	4.88128i	−0.339273	+	0.339273i
$208$	2.26123	−	0.994893i	0.156788	−	0.0689834i
$209$	2.58912	−	3.56361i	0.179093	−	0.246500i
$210$	2.30539	+	6.12562i	0.159087	+	0.422708i
$211$	−0.683337	−	0.940532i	−0.0470428	−	0.0647489i	0.784848	−	0.619689i	$-0.212741\pi$
$211$	−0.683337	−	0.940532i	−0.0470428	−	0.0647489i	−0.831890	+	0.554940i	$0.812741\pi$
$212$	7.02823	+	10.2744i	0.482701	+	0.705647i
$213$	−13.3027	+	2.10694i	−0.911488	+	0.144365i
$214$	5.13406	−	5.84132i	0.350957	−	0.399305i
$215$	8.54912	+	1.51716i	0.583045	+	0.103470i
$216$	−0.101737	−	2.82660i	−0.00692234	−	0.192326i
$217$	−9.99315	+	19.6127i	−0.678379	+	1.33139i
$218$	−4.25102	+	6.72110i	−0.287916	+	0.455211i
$219$	−2.14813	−	6.61125i	−0.145157	−	0.446747i
$220$	5.33922	+	1.10463i	0.359970	+	0.0744739i
$221$	−0.939002	+	2.88995i	−0.0631641	+	0.194399i
$222$	−4.32937	−	5.21714i	−0.290569	−	0.350152i
$223$	−21.2551	−	3.36648i	−1.42335	−	0.225436i	−0.603202	−	0.797589i	$-0.706109\pi$
$223$	−21.2551	−	3.36648i	−1.42335	−	0.225436i	−0.820147	+	0.572152i	$0.806109\pi$
$224$	5.23595	−	10.4722i	0.349841	−	0.699702i
$225$	−2.78681	−	4.15134i	−0.185788	−	0.276756i
$226$	9.37210	−	2.10988i	0.623423	−	0.140347i
$227$	1.05635	−	6.66952i	0.0701123	−	0.442672i	−0.927513	−	0.373792i	$-0.878057\pi$
$227$	1.05635	−	6.66952i	0.0701123	−	0.442672i	0.997625	−	0.0688800i	$-0.0219425\pi$
$228$	5.72311	+	4.41149i	0.379022	+	0.292158i
$229$	−19.0806	−	6.19967i	−1.26088	−	0.409686i	−0.399075	−	0.916918i	$-0.630669\pi$
$229$	−19.0806	−	6.19967i	−1.26088	−	0.409686i	−0.861809	+	0.507232i	$0.830669\pi$
$230$	18.9764	−	10.7906i	1.25126	−	0.711508i
$231$	−2.39985	+	0.779760i	−0.157899	+	0.0513044i
$232$	2.81547	+	0.342637i	0.184845	+	0.0224952i
$233$	−4.84966	−	2.47103i	−0.317712	−	0.161882i	0.287861	−	0.957672i	$-0.407056\pi$
$233$	−4.84966	−	2.47103i	−0.317712	−	0.161882i	−0.605573	+	0.795790i	$0.707056\pi$
$234$	0.345660	−	0.802117i	0.0225965	−	0.0524360i
$235$	2.57749	+	1.37412i	0.168137	+	0.0896378i
$236$	22.9963	+	12.5514i	1.49693	+	0.817027i
$237$	1.09983	+	6.94405i	0.0714416	+	0.451064i
$238$	5.32184	+	13.3819i	0.344964	+	0.867423i
$239$	−11.2896	+	8.20235i	−0.730261	+	0.530566i	−0.889646	−	0.456651i	$-0.849049\pi$
$239$	−11.2896	+	8.20235i	−0.730261	+	0.530566i	0.159385	+	0.987217i	$0.449049\pi$
$240$	−2.05986	+	8.70385i	−0.132964	+	0.561831i
$241$	13.3980	+	9.73420i	0.863040	+	0.627035i	0.928710	−	0.370806i	$-0.120919\pi$
$241$	13.3980	+	9.73420i	0.863040	+	0.627035i	−0.0656704	+	0.997841i	$0.520919\pi$
$242$	3.32613	−	13.0367i	0.213812	−	0.838030i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	13.7372	−	12.9790i	0.879436	−	0.830893i
$245$	−3.47819	−	4.97904i	−0.222213	−	0.318099i
$246$	−7.77434	−	0.722967i	−0.495674	−	0.0460947i
$247$	1.01304	+	1.98820i	0.0644582	+	0.126506i
$248$	−26.2934	+	14.6115i	−1.66963	+	0.927832i
$249$		−	7.04607i		−	0.446527i
$250$	5.01639	+	14.9945i	0.317264	+	0.948337i
$251$			22.8681i			1.44342i	0.692195	+	0.721711i	$0.256644\pi$
$251$			22.8681i			1.44342i	−0.692195	+	0.721711i	$0.743356\pi$
$252$	−1.16696	−	3.97158i	−0.0735114	−	0.250186i
$253$	3.82085	+	7.49883i	0.240215	+	0.471448i
$254$	1.81295	−	19.4953i	0.113754	−	1.22325i
$255$	−6.30035	−	9.01898i	−0.394543	−	0.564791i
$256$	13.9261	−	7.87803i	0.870382	−	0.492377i
$257$	−17.5555	−	17.5555i	−1.09508	−	1.09508i	−0.994977	−	0.100106i	$-0.968082\pi$
$257$	−17.5555	−	17.5555i	−1.09508	−	1.09508i	−0.100106	−	0.994977i	$-0.531918\pi$
$258$	−5.32097	−	1.35757i	−0.331269	−	0.0845188i
$259$	−8.02707	−	5.83201i	−0.498778	−	0.362383i
$260$	−1.72651	+	2.15589i	−0.107074	+	0.133703i
$261$	0.811252	−	0.589409i	0.0502153	−	0.0364835i
$262$	2.24886	−	0.894344i	0.138935	−	0.0552528i
$263$	1.08432	+	6.84611i	0.0668619	+	0.422149i	0.998302	+	0.0582542i	$0.0185534\pi$
$263$	1.08432	+	6.84611i	0.0668619	+	0.422149i	−0.931440	+	0.363895i	$0.881447\pi$
$264$	−3.31576	−	0.946939i	−0.204071	−	0.0582801i
$265$	−12.2813	−	6.54745i	−0.754432	−	0.402206i
$266$	9.71204	+	4.18525i	0.595483	+	0.256614i
$267$	12.7626	+	6.50289i	0.781061	+	0.397970i
$268$	15.3079	+	5.45865i	0.935077	+	0.333440i
$269$	26.2916	−	8.54266i	1.60303	−	0.520855i	0.635174	−	0.772369i	$-0.280928\pi$
$269$	26.2916	−	8.54266i	1.60303	−	0.520855i	0.967854	+	0.251514i	$0.0809284\pi$
$270$	1.56313	+	2.74893i	0.0951290	+	0.167295i
$271$	−14.4397	−	4.69173i	−0.877147	−	0.285002i	−0.164375	−	0.986398i	$-0.552561\pi$
$271$	−14.4397	−	4.69173i	−0.877147	−	0.285002i	−0.712772	+	0.701396i	$0.752561\pi$
$272$	−4.17625	+	19.2322i	−0.253222	+	1.16612i
$273$	0.199967	−	1.26254i	0.0121025	−	0.0764125i
$274$	−0.142805	−	0.634340i	−0.00862716	−	0.0383219i
$275$	−5.86339	+	1.66731i	−0.353576	+	0.100543i
$276$	−12.4744	+	5.91642i	−0.750872	+	0.356127i
$277$	−18.0952	−	2.86600i	−1.08723	−	0.172201i	−0.413009	−	0.910727i	$-0.635522\pi$
$277$	−18.0952	−	2.86600i	−1.08723	−	0.172201i	−0.674225	+	0.738526i	$0.735522\pi$
$278$	5.06886	−	4.20632i	0.304010	−	0.252278i
$279$	−3.28642	+	10.1146i	−0.196753	+	0.605543i
$280$	0.228034	+	13.0882i	0.0136277	+	0.782167i
$281$	−4.45191	−	13.7016i	−0.265579	−	0.817368i	−0.991559	−	0.129653i	$-0.958614\pi$
$281$	−4.45191	−	13.7016i	−0.265579	−	0.817368i	0.725980	−	0.687715i	$-0.241386\pi$
$282$	−1.56126	−	0.987480i	−0.0929718	−	0.0588036i
$283$	−13.2557	+	26.0158i	−0.787971	+	1.54648i	0.0487251	+	0.998812i	$0.484484\pi$
$283$	−13.2557	+	26.0158i	−0.787971	+	1.54648i	−0.836696	+	0.547668i	$0.815516\pi$
$284$	−26.4752	−	4.96702i	−1.57101	−	0.294738i
$285$	−7.95464	−	1.41167i	−0.471192	−	0.0836198i
$286$	−0.799828	−	0.702985i	−0.0472948	−	0.0415684i
$287$	−11.2863	+	1.78758i	−0.666211	+	0.105517i
$288$	1.70711	−	5.39312i	0.100593	−	0.317793i
$289$	−4.23634	−	5.83082i	−0.249197	−	0.342990i
$290$	−2.96779	+	1.11693i	−0.174275	+	0.0655887i
$291$	2.41989	−	3.33069i	0.141856	−	0.195248i
$292$	0.394444	−	13.8974i	0.0230831	−	0.813282i
$293$	3.00790	−	3.00790i	0.175723	−	0.175723i	−0.613765	−	0.789489i	$-0.710346\pi$
$293$	3.00790	−	3.00790i	0.175723	−	0.175723i	0.789489	+	0.613765i	$0.210346\pi$
$294$	1.96040	+	3.30338i	0.114333	+	0.192657i
$295$	−29.2859	−	0.543495i	−1.70509	−	0.0316435i
$296$	−4.65111	−	12.7364i	−0.270340	−	0.740287i
$297$	−1.08629	+	0.553491i	−0.0630328	+	0.0321168i
$298$	−1.78566	−	27.7098i	−0.103440	−	1.60519i
$299$	−4.26344			−0.246561
$300$	−2.46117	−	9.69240i	−0.142096	−	0.559591i
$301$	−8.03683			−0.463235
$302$	2.16251	+	33.5578i	0.124438	+	1.93103i
$303$	−12.7229	+	6.48262i	−0.730909	+	0.372417i
$304$	7.81785	+	12.1549i	0.448385	+	0.697133i
$305$	−6.90112	+	19.9707i	−0.395157	+	1.14352i
$306$	3.55104	+	5.98370i	0.203000	+	0.342065i
$307$	−22.9222	+	22.9222i	−1.30824	+	1.30824i	−0.385554	+	0.922685i	$0.625990\pi$
$307$	−22.9222	+	22.9222i	−1.30824	+	1.30824i	−0.922685	+	0.385554i	$0.874010\pi$
$308$	−5.04468	−	0.143181i	−0.287447	−	0.00815851i
$309$	7.37792	−	10.1548i	0.419715	−	0.577688i
$310$	18.5015	−	28.0846i	1.05082	−	1.59510i
$311$	−5.82470	−	8.01702i	−0.330289	−	0.454603i	0.611285	−	0.791411i	$-0.290653\pi$
$311$	−5.82470	−	8.01702i	−0.330289	−	0.454603i	−0.941574	+	0.336807i	$0.890653\pi$
$312$	1.18998	−	1.27884i	0.0673694	−	0.0724001i
$313$	−12.2798	+	1.94493i	−0.694097	+	0.109934i	−0.493508	−	0.869741i	$-0.664286\pi$
$313$	−12.2798	+	1.94493i	−0.694097	+	0.109934i	−0.200589	+	0.979675i	$0.564286\pi$
$314$	3.58057	+	3.14703i	0.202063	+	0.177597i
$315$	3.21125	+	3.33270i	0.180934	+	0.187776i
$316$	−2.59280	+	13.8201i	−0.145856	+	0.777441i
$317$	1.92273	−	3.77356i	0.107991	−	0.211944i	−0.830687	−	0.556740i	$-0.812052\pi$
$317$	1.92273	−	3.77356i	0.107991	−	0.211944i	0.938678	+	0.344796i	$0.112052\pi$
$318$	7.43914	+	4.70517i	0.417166	+	0.263853i
$319$	−0.377785	−	1.16270i	−0.0211519	−	0.0650988i
$320$	−9.72721	+	15.0127i	−0.543768	+	0.839236i
$321$	1.69931	−	5.22993i	0.0948461	−	0.291906i
$322$	−15.5493	+	12.9034i	−0.866530	+	0.719078i
$323$	−17.5575	−	2.78083i	−0.976924	−	0.154730i
$324$	−0.857058	−	1.80706i	−0.0476143	−	0.100392i
$325$	0.595908	−	3.02998i	0.0330550	−	0.168073i
$326$	−1.84129	−	8.17902i	−0.101980	−	0.452994i
$327$	−0.879688	+	5.55413i	−0.0486468	+	0.307144i
$328$	−14.1597	−	6.58435i	−0.781841	−	0.363560i
$329$	−2.57130	−	0.835465i	−0.141760	−	0.0460607i
$330$	3.77628	−	0.776803i	0.207878	−	0.0427616i
$331$	8.18304	−	2.65883i	0.449781	−	0.146143i	−0.0753630	−	0.997156i	$-0.524012\pi$
$331$	8.18304	−	2.65883i	0.449781	−	0.146143i	0.525144	+	0.851014i	$0.324012\pi$
$332$	4.73320	−	13.2735i	0.259768	−	0.728477i
$333$	−4.27135	−	2.17636i	−0.234069	−	0.119264i
$334$	17.4297	+	7.51105i	0.953709	+	0.410986i
$335$	−17.9962	+	2.50897i	−0.983240	+	0.137080i
$336$	0.469578	−	8.26561i	0.0256176	−	0.450926i
$337$	0.107869	+	0.681059i	0.00587601	+	0.0370997i	0.990452	−	0.137857i	$-0.0440215\pi$
$337$	0.107869	+	0.681059i	0.00587601	+	0.0370997i	−0.984576	+	0.174957i	$0.944021\pi$
$338$	−16.5822	+	6.59453i	−0.901951	+	0.358695i
$339$	5.49560	−	3.99279i	0.298480	−	0.216858i
$340$	−5.81017	−	21.2223i	−0.315101	−	1.15094i
$341$	10.4897	+	7.62121i	0.568049	+	0.412711i
$342$	4.95096	+	1.26317i	0.267717	+	0.0683044i
$343$	14.2199	+	14.2199i	0.767802	+	0.767802i
$344$	−9.11176	−	6.13178i	−0.491273	−	0.330603i
$345$	9.30319	−	12.3175i	0.500867	−	0.663150i
$346$	2.11156	−	22.7065i	0.113518	−	1.22071i
$347$	11.6804	+	22.9240i	0.627035	+	1.23063i	0.957942	+	0.286962i	$0.0926455\pi$
$347$	11.6804	+	22.9240i	0.627035	+	1.23063i	−0.330907	+	0.943663i	$0.607355\pi$
$348$	1.92418	−	0.565378i	0.103147	−	0.0303074i
$349$			29.6548i			1.58739i	0.608318	+	0.793694i	$0.291845\pi$
$349$			29.6548i			1.58739i	−0.608318	+	0.793694i	$0.708155\pi$
$350$	−6.99696	−	12.8543i	−0.374003	−	0.687090i
$351$		−	0.617605i		−	0.0329653i
$352$	−5.61017	−	4.01122i	−0.299023	−	0.213799i
$353$	−15.1420	−	29.7179i	−0.805928	−	1.58172i	−0.813368	−	0.581750i	$-0.802368\pi$
$353$	−15.1420	−	29.7179i	−0.805928	−	1.58172i	0.00744012	−	0.999972i	$-0.497632\pi$
$354$	18.4456	+	1.71533i	0.980374	+	0.0911689i
$355$	28.8103	−	8.77347i	1.52909	−	0.465647i
$356$	19.6741	+	20.8235i	1.04273	+	1.10364i
$357$	7.20067	+	7.20067i	0.381100	+	0.381100i
$358$	−2.11871	+	8.30421i	−0.111977	+	0.438891i
$359$	−5.20850	−	3.78419i	−0.274894	−	0.199722i	0.441793	−	0.897117i	$-0.354342\pi$
$359$	−5.20850	−	3.78419i	−0.274894	−	0.199722i	−0.716687	+	0.697395i	$0.754342\pi$
$360$	1.09805	+	6.22851i	0.0578722	+	0.328271i
$361$	4.81056	−	3.49508i	0.253187	−	0.183951i
$362$	11.9506	+	30.0502i	0.628110	+	1.57940i
$363$	−1.48826	−	9.39650i	−0.0781133	−	0.493188i
$364$	1.22481	−	2.24406i	0.0641976	−	0.117621i
$365$	6.79862	+	13.9783i	0.355856	+	0.731660i
$366$	5.28862	−	12.2724i	0.276441	−	0.641491i
$367$	8.78476	+	4.47606i	0.458561	+	0.233648i	0.667982	−	0.744177i	$-0.267158\pi$
$367$	8.78476	+	4.47606i	0.458561	+	0.233648i	−0.209422	+	0.977825i	$0.567158\pi$
$368$	−27.4738	+	2.76573i	−1.43217	+	0.144173i
$369$	−5.25079	+	1.70608i	−0.273345	+	0.0888152i
$370$	11.1989	+	10.2174i	0.582202	+	0.531178i
$371$	12.2518	+	3.98084i	0.636081	+	0.206675i
$372$	−12.9855	+	16.8463i	−0.673265	+	0.873440i
$373$	−1.58263	+	9.99236i	−0.0819457	+	0.517385i	0.912236	+	0.409666i	$0.134355\pi$
$373$	−1.58263	+	9.99236i	−0.0819457	+	0.517385i	−0.994181	+	0.107719i	$0.965645\pi$
$374$	8.27593	−	1.86311i	0.427938	−	0.0963389i
$375$	7.45358	+	8.33332i	0.384901	+	0.430331i
$376$	−2.27779	−	2.90901i	−0.117468	−	0.150021i
$377$	0.611687	+	0.0968817i	0.0315035	+	0.00498966i
$378$	−1.86920	−	2.25249i	−0.0961411	−	0.115856i
$379$	5.72788	−	17.6286i	0.294221	−	0.905521i	−0.689260	−	0.724514i	$-0.742064\pi$
$379$	5.72788	−	17.6286i	0.294221	−	0.905521i	0.983482	−	0.181007i	$-0.0579356\pi$
$380$	−14.0368	−	8.00285i	−0.720071	−	0.410537i
$381$	−4.27826	−	13.1671i	−0.219182	−	0.674573i
$382$	6.06656	−	9.59158i	0.310392	−	0.490748i
$383$	−4.71055	+	9.24497i	−0.240698	+	0.472396i	−0.979478	−	0.201550i	$-0.935402\pi$
$383$	−4.71055	+	9.24497i	−0.240698	+	0.472396i	0.738781	+	0.673946i	$0.235402\pi$
$384$	6.83871	−	9.01288i	0.348987	−	0.459937i
$385$	5.07408	−	2.46787i	0.258599	−	0.125774i
$386$	9.40556	−	10.7013i	0.478730	−	0.544680i
$387$	−3.83522	+	0.607439i	−0.194955	+	0.0308778i
$388$	6.79600	−	4.64883i	0.345015	−	0.236009i
$389$	16.6111	+	22.8633i	0.842217	+	1.15921i	0.985524	+	0.169535i	$0.0542264\pi$
$389$	16.6111	+	22.8633i	0.842217	+	1.15921i	−0.143307	+	0.989678i	$0.545774\pi$
$390$	−0.517855	+	1.88313i	−0.0262226	+	0.0953561i
$391$	19.9637	−	27.4777i	1.00961	−	1.38960i
$392$	1.47398	+	7.53985i	0.0744471	+	0.380820i
$393$	1.21008	−	1.21008i	0.0610407	−	0.0610407i
$394$	18.2110	−	10.8073i	0.917455	−	0.544466i
$395$	−4.57977	−	15.0390i	−0.230433	−	0.756697i
$396$	−2.41817	+	0.312960i	−0.121518	+	0.0157268i
$397$	−13.0371	+	6.64271i	−0.654311	+	0.333388i	−0.749436	−	0.662077i	$-0.769675\pi$
$397$	−13.0371	+	6.64271i	−0.654311	+	0.333388i	0.0951247	+	0.995465i	$0.469675\pi$
$398$	−6.71957	+	0.433018i	−0.336822	+	0.0217052i
$399$	7.47797			0.374367
$400$	1.87449	−	19.9120i	0.0937245	−	0.995598i
$401$	−18.3995			−0.918829			−0.459415	−	0.888222i	$-0.651941\pi$
$401$	−18.3995			−0.918829			−0.459415	+	0.888222i	$0.651941\pi$
$402$	11.4681	−	0.739020i	0.571978	−	0.0368590i
$403$	−5.85239	+	2.98194i	−0.291528	+	0.148541i
$404$	−28.3222	+	3.66546i	−1.40908	+	0.182363i
$405$	1.78432	+	1.34767i	0.0886635	+	0.0669662i
$406$	2.52412	−	1.49794i	0.125270	−	0.0743417i
$407$	−4.13270	+	4.13270i	−0.204850	+	0.204850i
$408$	2.66995	+	13.6576i	0.132182	+	0.676151i
$409$	1.04712	−	1.44123i	0.0517766	−	0.0712643i	−0.782344	−	0.622847i	$-0.785976\pi$
$409$	1.04712	−	1.44123i	0.0517766	−	0.0712643i	0.834120	+	0.551583i	$0.185976\pi$
$410$	17.4406	−	0.799274i	0.861332	−	0.0394733i
$411$	−0.270247	−	0.371963i	−0.0133303	−	0.0183476i
$412$	20.7201	−	14.1737i	1.02081	−	0.698287i
$413$	26.7783	−	4.24127i	1.31767	−	0.208699i
$414$	−6.44496	+	7.33281i	−0.316752	+	0.360388i
$415$	2.17553	+	15.6046i	0.106793	+	0.765998i
$416$	3.10076	−	1.60973i	0.152027	−	0.0789234i
$417$	2.11451	−	4.14995i	0.103548	−	0.203224i
$418$	3.32989	−	5.26474i	0.162870	−	0.257507i
$419$	−12.5557	−	38.6425i	−0.613386	−	1.88781i	−0.423108	−	0.906079i	$-0.639061\pi$
$419$	−12.5557	−	38.6425i	−0.613386	−	1.88781i	−0.190279	−	0.981730i	$-0.560939\pi$
$420$	3.81066	+	8.43534i	0.185941	+	0.411602i
$421$	2.89797	−	8.91902i	0.141238	−	0.434687i	−0.855270	−	0.518183i	$-0.826609\pi$
$421$	2.89797	−	8.91902i	0.141238	−	0.434687i	0.996508	+	0.0834962i	$0.0266087\pi$
$422$	−1.04992	−	1.26521i	−0.0511093	−	0.0615897i
$423$	−1.29018	−	0.204345i	−0.0627308	−	0.00993559i
$424$	10.8532	+	13.8609i	0.527080	+	0.673145i
$425$	16.7377	+	18.0286i	0.811900	+	0.874515i
$426$	−18.5823	+	4.18332i	−0.900317	+	0.202682i
$427$	3.05951	−	19.3170i	0.148060	−	0.934814i
$428$	6.71438	−	8.71070i	0.324552	−	0.421047i
$429$	−0.716113	−	0.232679i	−0.0345742	−	0.0112339i
$430$	12.2032	+	1.36365i	0.588493	+	0.0657612i
$431$	−3.54339	+	1.15132i	−0.170679	+	0.0554571i	−0.393110	−	0.919491i	$-0.628601\pi$
$431$	−3.54339	+	1.15132i	−0.170679	+	0.0554571i	0.222431	+	0.974948i	$0.428601\pi$
$432$	−0.400646	−	3.97988i	−0.0192761	−	0.191482i
$433$	−5.53878	−	2.82215i	−0.266177	−	0.135624i	0.315809	−	0.948823i	$-0.397724\pi$
$433$	−5.53878	−	2.82215i	−0.266177	−	0.135624i	−0.581986	+	0.813199i	$0.697724\pi$
$434$	−12.3195	+	28.5879i	−0.591356	+	1.37226i
$435$	−1.61465	+	1.55582i	−0.0774167	+	0.0745956i
$436$	−5.38816	+	9.87201i	−0.258046	+	0.472784i
$437$	−3.90167	−	24.6342i	−0.186642	−	1.17841i
$438$	−3.63288	−	9.13501i	−0.173586	−	0.436488i
$439$	0.813614	−	0.591125i	0.0388317	−	0.0282129i	−0.568200	−	0.822890i	$-0.692360\pi$
$439$	0.813614	−	0.591125i	0.0388317	−	0.0282129i	0.607032	+	0.794678i	$0.292360\pi$
$440$	7.63563	+	1.07337i	0.364014	+	0.0511708i
$441$	2.19745	+	1.59654i	0.104641	+	0.0760258i
$442$	−1.06237	+	4.16395i	−0.0505320	+	0.198059i
$443$	10.2940	+	10.2940i	0.489083	+	0.489083i	0.908017	−	0.418934i	$-0.137596\pi$
$443$	10.2940	+	10.2940i	0.489083	+	0.489083i	−0.418934	+	0.908017i	$0.637596\pi$
$444$	−6.58446	−	6.96915i	−0.312485	−	0.330741i
$445$	−30.2726	−	10.4610i	−1.43506	−	0.495901i
$446$	−30.3032	−	2.81802i	−1.43490	−	0.133437i
$447$	−8.91385	−	17.4944i	−0.421610	−	0.827457i
$448$	6.43702	−	15.2554i	0.304121	−	0.720751i
$449$			18.2346i			0.860542i	0.902700	+	0.430271i	$0.141582\pi$
$449$			18.2346i			0.860542i	−0.902700	+	0.430271i	$0.858418\pi$
$450$	−4.31054	−	5.60529i	−0.203201	−	0.264236i
$451$			6.73104i			0.316952i
$452$	13.0348	−	3.82999i	0.613107	−	0.180148i
$453$	10.7950	+	21.1865i	0.507196	+	0.995428i
$454$	0.884250	−	9.50868i	0.0414999	−	0.446264i
$455$	−0.0530363	+	2.85783i	−0.00248638	+	0.133977i
$456$	8.47816	+	5.70539i	0.397026	+	0.267179i
$457$	20.4576	+	20.4576i	0.956967	+	0.956967i	0.999112	−	0.0421448i	$-0.0134191\pi$
$457$	20.4576	+	20.4576i	0.956967	+	0.956967i	−0.0421448	+	0.999112i	$0.513419\pi$
$458$	−27.4921	−	7.01422i	−1.28462	−	0.327753i
$459$	3.98044	+	2.89196i	0.185791	+	0.134985i
$460$	25.7997	−	16.9544i	1.20292	−	0.790502i
$461$	1.26163	−	0.916631i	0.0587602	−	0.0426918i	−0.558017	−	0.829829i	$-0.688438\pi$
$461$	1.26163	−	0.916631i	0.0587602	−	0.0426918i	0.616778	+	0.787137i	$0.288438\pi$
$462$	−3.31597	+	1.31872i	−0.154273	+	0.0613524i
$463$	−1.78849	−	11.2921i	−0.0831181	−	0.524787i	−0.993755	−	0.111581i	$-0.964409\pi$
$463$	−1.78849	−	11.2921i	−0.0831181	−	0.524787i	0.910637	−	0.413207i	$-0.135591\pi$
$464$	4.00459	+	0.227505i	0.185909	+	0.0105617i
$465$	4.15531	−	23.4149i	0.192698	−	1.08584i
$466$	−7.06899	−	3.04627i	−0.327465	−	0.141116i
$467$	24.5198	+	12.4935i	1.13464	+	0.578129i	0.917391	−	0.397987i	$-0.130291\pi$
$467$	24.5198	+	12.4935i	1.13464	+	0.578129i	0.217251	+	0.976116i	$0.430291\pi$
$468$	0.414877	−	1.16345i	0.0191777	−	0.0537806i
$469$	15.9955	−	5.19726i	0.738604	−	0.239987i
$470$	3.76254	+	1.70487i	0.173553	+	0.0786398i
$471$	3.20580	+	1.04163i	0.147716	+	0.0479957i
$472$	33.5959	+	15.6222i	1.54637	+	0.719071i
$473$	−0.740570	+	4.67578i	−0.0340515	+	0.214992i
$474$	2.18370	+	9.70002i	0.100301	+	0.445537i
$475$	18.0526	+	0.670280i	0.828310	+	0.0307546i
$476$	8.72766	+	18.4018i	0.400032	+	0.843443i
$477$	6.14749	+	0.973667i	0.281474	+	0.0445812i
$478$	−15.1868	+	12.6026i	−0.694630	+	0.576429i
$479$	0.100925	−	0.310615i	0.00461137	−	0.0141923i	−0.948724	−	0.316105i	$-0.897625\pi$
$479$	0.100925	−	0.310615i	0.00461137	−	0.0141923i	0.953336	+	0.301912i	$0.0976250\pi$
$480$	−2.11549	+	12.4710i	−0.0965583	+	0.569219i
$481$	−0.914910	−	2.81580i	−0.0417163	−	0.128390i
$482$	19.7937	+	12.5193i	0.901577	+	0.570237i
$483$	−6.48650	+	12.7305i	−0.295146	+	0.579256i
$484$	3.50850	−	18.7010i	0.159477	−	0.850045i
$485$	−4.33082	+	8.12346i	−0.196652	+	0.368867i
$486$	−1.06224	−	0.933622i	−0.0481841	−	0.0423500i
$487$	−5.27724	+	0.835833i	−0.239135	+	0.0378752i	−0.274851	−	0.961487i	$-0.588629\pi$
$487$	−5.27724	+	0.835833i	−0.239135	+	0.0378752i	0.0357166	+	0.999362i	$0.488629\pi$
$488$	18.2068	−	19.5664i	0.824183	−	0.885727i
$489$	−3.48450	−	4.79600i	−0.157574	−	0.216883i
$490$	−5.36154	−	6.71053i	−0.242210	−	0.303151i
$491$	21.9210	−	30.1717i	0.989282	−	1.36163i	0.0576063	−	0.998339i	$-0.481653\pi$
$491$	21.9210	−	30.1717i	0.989282	−	1.36163i	0.931676	−	0.363291i	$-0.118347\pi$
$492$	−11.0376	−	0.313275i	−0.497612	−	0.0141235i
$493$	−3.48864	+	3.48864i	−0.157121	+	0.157121i
$494$	1.61051	+	2.71379i	0.0724601	+	0.122099i
$495$	2.23485	−	1.56119i	0.100449	−	0.0701702i
$496$	−35.7787	+	23.0123i	−1.60651	+	1.03328i
$497$	−24.8380	+	12.6556i	−1.11414	+	0.567680i
$498$	−0.640806	−	9.94402i	−0.0287152	−	0.445602i
$499$	−13.5542			−0.606769			−0.303385	−	0.952868i	$-0.598117\pi$
$499$	−13.5542			−0.606769			−0.303385	+	0.952868i	$0.598117\pi$
$500$	8.44324	+	20.7054i	0.377593	+	0.925972i
$501$	13.4203			0.599575
$502$	2.07974	+	32.2734i	0.0928234	+	1.44043i
$503$	31.6307	−	16.1167i	1.41034	−	0.718606i	0.427668	−	0.903936i	$-0.359335\pi$
$503$	31.6307	−	16.1167i	1.41034	−	0.718606i	0.982676	+	0.185330i	$0.0593353\pi$
$504$	−2.00811	−	5.49890i	−0.0894482	−	0.244941i
$505$	26.1751	−	18.2850i	1.16478	−	0.813673i
$506$	6.07429	+	10.2355i	0.270035	+	0.455024i
$507$	−8.92267	+	8.92267i	−0.396270	+	0.396270i
$508$	0.785584	−	27.6784i	0.0348547	−	1.22803i
$509$	5.94794	−	8.18664i	0.263638	−	0.362866i	−0.656591	−	0.754247i	$-0.728002\pi$
$509$	5.94794	−	8.18664i	0.263638	−	0.362866i	0.920229	+	0.391380i	$0.128002\pi$
$510$	−9.71183	−	12.1554i	−0.430047	−	0.538249i
$511$	−8.45689	−	11.6399i	−0.374111	−	0.514919i
$512$	18.9373	−	12.3847i	0.836917	−	0.547330i
$513$	3.56853	−	0.565199i	0.157554	−	0.0249541i
$514$	−26.3724	−	23.1793i	−1.16324	−	1.02239i
$515$	−13.2041	+	24.7674i	−0.581842	+	1.09138i
$516$	−7.63288	−	1.43201i	−0.336019	−	0.0630406i
$517$	−0.723006	+	1.41898i	−0.0317978	+	0.0624067i
$518$	−11.8589	−	7.50061i	−0.521050	−	0.329558i
$519$	−4.98295	−	15.3359i	−0.218727	−	0.673173i
$520$	−2.24054	+	3.19960i	−0.0982541	+	0.140312i
$521$	−11.1158	+	34.2110i	−0.486994	+	1.49881i	0.342079	+	0.939671i	$0.388869\pi$
$521$	−11.1158	+	34.2110i	−0.486994	+	1.49881i	−0.829072	+	0.559141i	$0.811131\pi$
$522$	1.09131	−	0.905605i	0.0477651	−	0.0396372i
$523$	22.2065	+	3.51717i	0.971023	+	0.153795i	0.621741	−	0.783223i	$-0.286426\pi$
$523$	22.2065	+	3.51717i	0.971023	+	0.153795i	0.349282	+	0.937018i	$0.386426\pi$
$524$	3.09245	−	1.46670i	0.135094	−	0.0640730i
$525$	−8.14079	−	6.38925i	−0.355293	−	0.278850i
$526$	2.15290	+	9.56321i	0.0938710	+	0.416976i
$527$	8.18553	−	51.6814i	0.356567	−	2.25128i
$528$	−4.76561	−	1.03485i	−0.207397	−	0.0450360i
$529$	23.4472	+	7.61845i	1.01944	+	0.331237i
$530$	−17.9278	−	8.12340i	−0.778735	−	0.352858i
$531$	12.4582	−	4.04791i	0.540639	−	0.175664i
$532$	14.0871	+	5.02333i	0.610753	+	0.217789i
$533$	−3.03816	−	1.54802i	−0.131597	−	0.0670521i
$534$	18.6031	+	8.01674i	0.805036	+	0.346918i
$535$	−2.14858	+	12.1071i	−0.0928914	+	0.523437i
$536$	22.1002	+	6.31154i	0.954585	+	0.272617i
$537$	0.948004	+	5.98546i	0.0409094	+	0.258292i
$538$	36.3281	−	14.4472i	1.56621	−	0.622865i
$539$	2.67906	−	1.94645i	0.115395	−	0.0838397i
$540$	2.45603	+	3.73737i	0.105690	+	0.160831i
$541$	16.8088	+	12.2123i	0.722666	+	0.525048i	0.887235	−	0.461318i	$-0.152623\pi$
$541$	16.8088	+	12.2123i	0.722666	+	0.525048i	−0.164569	+	0.986366i	$0.552623\pi$
$542$	−20.8052	−	5.30816i	−0.893659	−	0.228005i
$543$	16.1697	+	16.1697i	0.693907	+	0.693907i
$544$	−4.14481	+	27.5219i	−0.177707	+	1.17999i
$545$	0.233316	−	12.5721i	0.00999414	−	0.538528i
$546$	0.167389	−	1.79999i	0.00716357	−	0.0770326i
$547$	−1.88617	−	3.70181i	−0.0806466	−	0.158278i	0.847162	−	0.531335i	$-0.178310\pi$
$547$	−1.88617	−	3.70181i	−0.0806466	−	0.158278i	−0.927808	+	0.373057i	$0.878310\pi$
$548$	−0.259229	−	0.882248i	−0.0110737	−	0.0376878i
$549$		−	9.44940i		−	0.403291i
$550$	−8.12329	+	2.88630i	−0.346378	+	0.123072i
$551$			3.62299i			0.154345i
$552$	−17.0669	+	9.48425i	−0.726416	+	0.403676i
$553$	6.60624	+	12.9655i	0.280926	+	0.551348i
$554$	−25.7981	−	2.39907i	−1.09606	−	0.101927i
$555$	10.1315	+	3.50107i	0.430059	+	0.148612i
$556$	6.77107	−	6.39731i	0.287157	−	0.271306i
$557$	−12.9204	−	12.9204i	−0.547455	−	0.547455i	0.378249	−	0.925704i	$-0.376526\pi$
$557$	−12.9204	−	12.9204i	−0.547455	−	0.547455i	−0.925704	+	0.378249i	$0.876526\pi$
$558$	−3.71821	+	14.5734i	−0.157404	+	0.616943i
$559$	−1.94016	−	1.40961i	−0.0820602	−	0.0596202i
$560$	1.51213	+	18.4504i	0.0638990	+	0.779672i
$561$	4.85283	−	3.52578i	0.204886	−	0.148859i
$562$	−7.52902	−	18.9320i	−0.317592	−	0.798597i
$563$	−0.508973	−	3.21353i	−0.0214506	−	0.135434i	0.974639	−	0.223783i	$-0.0718408\pi$
$563$	−0.508973	−	3.21353i	−0.0214506	−	0.135434i	−0.996090	+	0.0883493i	$0.971841\pi$
$564$	−2.29319	−	1.25163i	−0.0965609	−	0.0527031i
$565$	−10.9380	+	10.5394i	−0.460166	+	0.443397i
$566$	−16.3416	+	37.9213i	−0.686889	+	1.59395i
$567$	−1.84415	−	0.939640i	−0.0774469	−	0.0394612i
$568$	−37.8158	−	4.60210i	−1.58672	−	0.193100i
$569$	−18.5217	+	6.01805i	−0.776468	+	0.252290i	−0.670332	−	0.742062i	$-0.733848\pi$
$569$	−18.5217	+	6.01805i	−0.776468	+	0.252290i	−0.106137	+	0.994352i	$0.533848\pi$
$570$	−11.3547	−	1.26883i	−0.475594	−	0.0531453i
$571$	39.3841	+	12.7967i	1.64817	+	0.535525i	0.978343	−	0.206989i	$-0.0663663\pi$
$571$	39.3841	+	12.7967i	1.64817	+	0.535525i	0.669832	+	0.742513i	$0.266366\pi$
$572$	−1.19272	−	0.919373i	−0.0498701	−	0.0384409i
$573$	1.25539	−	7.92621i	0.0524446	−	0.331122i
$574$	−15.7657	+	3.54922i	−0.658046	+	0.148142i
$575$	−16.8002	+	30.1513i	−0.700616	+	1.25740i
$576$	1.91875	−	7.76649i	0.0799478	−	0.323604i
$577$	24.3357	+	3.85440i	1.01311	+	0.160461i	0.640849	−	0.767667i	$-0.278583\pi$
$577$	24.3357	+	3.85440i	1.01311	+	0.160461i	0.372261	+	0.928128i	$0.378583\pi$
$578$	−6.50898	−	7.84369i	−0.270738	−	0.326254i
$579$	3.11312	−	9.58120i	0.129377	−	0.398181i
$580$	−4.08682	+	1.84622i	−0.169696	+	0.0766601i
$581$	−4.50655	−	13.8697i	−0.186963	−	0.575413i
$582$	3.11224	−	4.92063i	0.129007	−	0.203967i
$583$	3.44500	−	6.76119i	0.142677	−	0.280020i
$584$	−0.707225	−	19.6490i	−0.0292652	−	0.813083i
$585$	0.190691	+	1.36778i	0.00788409	+	0.0565507i
$586$	3.97145	−	4.51856i	0.164059	−	0.186660i
$587$	−38.9053	+	6.16199i	−1.60579	+	0.254333i	−0.894003	−	0.448060i	$-0.852115\pi$
$587$	−38.9053	+	6.16199i	−1.60579	+	0.254333i	−0.711789	+	0.702393i	$0.752115\pi$
$588$	3.06711	+	4.48372i	0.126485	+	0.184906i
$589$	−22.5854	−	31.0862i	−0.930617	−	1.28088i
$590$	−41.3802	+	1.89638i	−1.70360	+	0.0780728i
$591$	8.80146	−	12.1142i	0.362044	−	0.498311i
$592$	−7.72236	−	17.5517i	−0.317387	−	0.721370i
$593$	−22.6547	+	22.6547i	−0.930317	+	0.930317i	−0.997725	−	0.0674081i	$-0.978527\pi$
$593$	−22.6547	+	22.6547i	−0.930317	+	0.930317i	0.0674081	+	0.997725i	$0.478527\pi$
$594$	−1.48273	+	0.879927i	−0.0608370	+	0.0361038i
$595$	−18.1702	−	13.7237i	−0.744906	−	0.562616i
$596$	−5.04014	−	38.9441i	−0.206452	−	1.59521i
$597$	−4.24236	+	2.16159i	−0.173628	+	0.0884680i
$598$	−6.01693	+	0.387739i	−0.246051	+	0.0158558i
$599$	33.3301			1.36183			0.680916	−	0.732361i	$-0.261582\pi$
$599$	33.3301			1.36183			0.680916	+	0.732361i	$0.261582\pi$
$600$	−4.35489	−	13.4549i	−0.177788	−	0.549295i
$601$	−30.1376			−1.22934			−0.614669	−	0.788785i	$-0.710710\pi$
$601$	−30.1376			−1.22934			−0.614669	+	0.788785i	$0.710710\pi$
$602$	−11.3423	+	0.730910i	−0.462276	+	0.0297897i
$603$	7.24032	−	3.68913i	0.294849	−	0.150233i
$604$	6.10383	+	47.1629i	0.248361	+	1.91903i
$605$	6.19722	+	20.3504i	0.251953	+	0.827363i
$606$	−17.3660	+	10.3059i	−0.705447	+	0.418649i
$607$	−16.1185	+	16.1185i	−0.654230	+	0.654230i	−0.954009	−	0.299779i	$-0.903087\pi$
$607$	−16.1185	+	16.1185i	−0.654230	+	0.654230i	0.299779	+	0.954009i	$0.403087\pi$
$608$	12.1387	+	16.4431i	0.492288	+	0.666855i
$609$	1.21992	−	1.67908i	0.0494337	−	0.0680396i
$610$	−7.92322	+	28.8121i	−0.320802	+	1.16657i
$611$	−0.474199	−	0.652680i	−0.0191841	−	0.0264046i
$612$	5.55573	+	8.12177i	0.224577	+	0.328303i
$613$	−41.4745	+	6.56892i	−1.67514	+	0.265316i	−0.920478	−	0.390795i	$-0.872200\pi$
$613$	−41.4745	+	6.56892i	−1.67514	+	0.265316i	−0.754664	+	0.656112i	$0.772200\pi$
$614$	−30.2651	+	34.4345i	−1.22140	+	1.38966i
$615$	11.1019	−	5.39960i	0.447671	−	0.217733i
$616$	−7.13251	+	0.256719i	−0.287377	+	0.0103435i
$617$	10.3229	−	20.2599i	0.415585	−	0.815632i	−0.584406	−	0.811461i	$-0.698673\pi$
$617$	10.3229	−	20.2599i	0.415585	−	0.815632i	0.999991	−	0.00417035i	$-0.00132747\pi$
$618$	9.48882	−	15.0024i	0.381696	−	0.603483i
$619$	4.80555	+	14.7900i	0.193151	+	0.594459i	0.999993	+	0.00369144i	$0.00117503\pi$
$619$	4.80555	+	14.7900i	0.193151	+	0.594459i	−0.806842	+	0.590768i	$0.798825\pi$
$620$	23.5568	−	41.3180i	0.946065	−	1.65937i
$621$	−2.13320	+	6.56531i	−0.0856023	+	0.263457i
$622$	−8.94943	−	10.7846i	−0.358840	−	0.432422i
$623$	29.2815	+	4.63774i	1.17314	+	0.185807i
$624$	1.56310	−	1.91303i	0.0625741	−	0.0765827i
$625$	−19.0800	−	16.1540i	−0.763201	−	0.646161i
$626$	−17.1535	+	3.86165i	−0.685591	+	0.154343i
$627$	0.689073	−	4.35064i	0.0275189	−	0.173748i
$628$	5.33942	+	4.11573i	0.213066	+	0.164236i
$629$	22.4318	+	7.28854i	0.894415	+	0.290613i
$630$	4.83509	+	4.41134i	0.192635	+	0.175752i
$631$	−9.56990	+	3.10945i	−0.380972	+	0.123785i	−0.493241	−	0.869893i	$-0.664188\pi$
$631$	−9.56990	+	3.10945i	−0.380972	+	0.123785i	0.112270	+	0.993678i	$0.464188\pi$
$632$	−2.40231	+	19.7399i	−0.0955586	+	0.785212i
$633$	−1.03585	−	0.527792i	−0.0411714	−	0.0209779i
$634$	2.37033	−	5.50044i	0.0941379	−	0.218450i
$635$	13.5403	+	27.8396i	0.537331	+	1.10478i
$636$	10.9267	+	5.96379i	0.433270	+	0.236480i
$637$	0.262425	+	1.65689i	0.0103977	+	0.0656482i
$638$	−0.638905	−	1.60655i	−0.0252945	−	0.0636038i
$639$	−10.8963	+	7.91661i	−0.431050	+	0.313176i
$640$	−12.3625	+	22.0719i	−0.488673	+	0.872467i
$641$	−2.79699	−	2.03213i	−0.110474	−	0.0802644i	0.531176	−	0.847261i	$-0.321750\pi$
$641$	−2.79699	−	2.03213i	−0.110474	−	0.0802644i	−0.641651	+	0.766997i	$0.721750\pi$
$642$	1.92257	−	7.53547i	0.0758779	−	0.297401i
$643$	−17.1130	−	17.1130i	−0.674871	−	0.674871i	0.283964	−	0.958835i	$-0.408350\pi$
$643$	−17.1130	−	17.1130i	−0.674871	−	0.674871i	−0.958835	+	0.283964i	$0.908350\pi$
$644$	−20.7710	+	19.6245i	−0.818494	+	0.773314i
$645$	8.30610	−	2.52942i	0.327053	−	0.0995957i
$646$	−25.0315	−	2.32778i	−0.984852	−	0.0915853i
$647$	−16.5566	−	32.4942i	−0.650909	−	1.27748i	−0.946666	−	0.322217i	$-0.895572\pi$
$647$	−16.5566	−	32.4942i	−0.650909	−	1.27748i	0.295757	−	0.955263i	$-0.404428\pi$
$648$	−1.37390	−	2.47233i	−0.0539718	−	0.0971222i
$649$		−	15.9703i		−	0.626888i
$650$	0.565434	−	4.33037i	0.0221782	−	0.169851i
$651$			22.0118i			0.862711i
$652$	−3.34243	−	11.3755i	−0.130900	−	0.445498i
$653$	−18.6301	−	36.5636i	−0.729051	−	1.43084i	−0.895623	−	0.444813i	$-0.853270\pi$
$653$	−18.6301	−	36.5636i	−0.729051	−	1.43084i	0.166573	−	0.986029i	$-0.446730\pi$
$654$	−0.736370	+	7.91847i	−0.0287944	+	0.309637i
$655$	−2.30629	+	3.05354i	−0.0901141	+	0.119312i
$656$	−20.5823	−	8.00464i	−0.803603	−	0.312529i
$657$	−4.91544	−	4.91544i	−0.191770	−	0.191770i
$658$	−3.70482	−	0.945234i	−0.144429	−	0.0368490i
$659$	−25.5515	−	18.5642i	−0.995344	−	0.723160i	−0.0342591	−	0.999413i	$-0.510907\pi$
$659$	−25.5515	−	18.5642i	−0.995344	−	0.723160i	−0.961085	+	0.276253i	$0.910907\pi$
$660$	5.25877	−	1.43973i	0.204697	−	0.0560413i
$661$	−6.57518	+	4.77715i	−0.255745	+	0.185810i	−0.708269	−	0.705943i	$-0.750524\pi$
$661$	−6.57518	+	4.77715i	−0.255745	+	0.185810i	0.452524	+	0.891752i	$0.350524\pi$
$662$	11.3068	−	4.49658i	0.439452	−	0.174765i
$663$	0.475353	+	3.00126i	0.0184612	+	0.116559i
$664$	5.47274	−	19.1631i	0.212384	−	0.743674i
$665$	−16.5611	+	2.30888i	−0.642211	+	0.0895347i
$666$	−6.22603	−	2.68301i	−0.241254	−	0.103965i
$667$	−6.16777	−	3.14263i	−0.238817	−	0.121683i
$668$	25.2813	+	9.01510i	0.978165	+	0.348805i
$669$	−20.4668	+	6.65007i	−0.791293	+	0.257107i
$670$	−25.1697	+	5.17755i	−0.972389	+	0.200026i
$671$	−10.9566	−	3.56001i	−0.422974	−	0.137433i
$672$	−0.0890083	−	11.7078i	−0.00343357	−	0.451640i
$673$	−4.92681	+	31.1067i	−0.189915	+	1.19907i	0.689952	+	0.723855i	$0.257631\pi$
$673$	−4.92681	+	31.1067i	−0.189915	+	1.19907i	−0.879867	+	0.475220i	$0.842369\pi$
$674$	0.214173	+	0.951360i	0.00824965	+	0.0366450i
$675$	−4.36774	−	2.43369i	−0.168114	−	0.0936727i
$676$	−22.8025	+	10.8148i	−0.877017	+	0.415955i
$677$	−4.81004	−	0.761836i	−0.184865	−	0.0292797i	0.0633155	−	0.997994i	$-0.479833\pi$
$677$	−4.81004	−	0.761836i	−0.184865	−	0.0292797i	−0.248180	+	0.968714i	$0.579833\pi$
$678$	7.39274	−	6.13476i	0.283916	−	0.235604i
$679$	2.63314	−	8.10396i	0.101050	−	0.311001i
$680$	−10.1299	−	29.4224i	−0.388463	−	1.12830i
$681$	−2.08669	−	6.42216i	−0.0799620	−	0.246098i
$682$	15.4971	+	9.80172i	0.593413	+	0.375327i
$683$	−3.12436	+	6.13190i	−0.119550	+	0.234631i	−0.943025	−	0.332723i	$-0.892033\pi$
$683$	−3.12436	+	6.13190i	−0.119550	+	0.234631i	0.823474	+	0.567353i	$0.192033\pi$
$684$	7.10211	+	1.33243i	0.271556	+	0.0509467i
$685$	0.713350	+	0.740327i	0.0272557	+	0.0282865i
$686$	21.3616	+	18.7751i	0.815588	+	0.716837i
$687$	−19.8156	+	3.13848i	−0.756011	+	0.119740i
$688$	−13.4170	−	7.82502i	−0.511517	−	0.298326i
$689$	2.25948	+	3.10990i	0.0860792	+	0.118478i
$690$	12.0092	−	18.2295i	0.457184	−	0.693987i
$691$	−6.99922	+	9.63360i	−0.266263	+	0.366480i	−0.921124	−	0.389270i	$-0.872727\pi$
$691$	−6.99922	+	9.63360i	−0.266263	+	0.366480i	0.654861	+	0.755750i	$0.272727\pi$
$692$	0.914981	−	32.2374i	0.0347823	−	1.22548i
$693$	−1.78428	+	1.78428i	−0.0677793	+	0.0677793i
$694$	18.5692	+	31.2901i	0.704876	+	1.18776i
$695$	−3.40156	+	9.84356i	−0.129028	+	0.373387i
$696$	2.66416	−	0.972905i	0.100985	−	0.0368779i
$697$	24.2032	−	12.3321i	0.916760	−	0.467113i
$698$	2.69696	+	41.8515i	0.102082	+	1.58410i
$699$	−5.44290			−0.205869
$700$	−11.0437	−	17.5047i	−0.417414	−	0.661617i
$701$	33.9745			1.28320			0.641600	−	0.767040i	$-0.278271\pi$
$701$	33.9745			1.28320			0.641600	+	0.767040i	$0.278271\pi$
$702$	−0.0561682	−	0.871618i	−0.00211993	−	0.0328971i
$703$	15.4324	−	7.86322i	0.582045	−	0.296567i
$704$	−8.28236	−	5.15077i	−0.312153	−	0.194127i
$705$	2.92039	+	0.0541974i	0.109988	+	0.00204119i
$706$	−24.0724	−	40.5633i	−0.905977	−	1.52662i
$707$	−20.8979	+	20.8979i	−0.785948	+	0.785948i
$708$	26.1881	+	0.743286i	0.984208	+	0.0279344i
$709$	−9.76306	+	13.4377i	−0.366659	+	0.504663i	−0.951989	−	0.306132i	$-0.900965\pi$
$709$	−9.76306	+	13.4377i	−0.366659	+	0.504663i	0.585330	+	0.810795i	$0.300965\pi$
$710$	39.8617	−	15.0020i	1.49598	−	0.563016i
$711$	4.13249	+	5.68788i	0.154980	+	0.213312i
$712$	29.6596	+	27.5987i	1.11154	+	1.03430i
$713$	72.5120	−	11.4848i	2.71560	−	0.430108i
$714$	10.8171	+	9.50734i	0.404819	+	0.355803i
$715$	1.65778	+	0.294197i	0.0619974	+	0.0110023i
$716$	−2.23487	+	11.9123i	−0.0835211	+	0.445184i
$717$	−6.33529	+	12.4337i	−0.236596	+	0.464345i
$718$	−7.69483	−	4.86689i	−0.287169	−	0.181631i
$719$	11.5947	+	35.6849i	0.432410	+	1.33082i	0.895717	+	0.444624i	$0.146663\pi$
$719$	11.5947	+	35.6849i	0.432410	+	1.33082i	−0.463307	+	0.886198i	$0.653337\pi$
$720$	2.11611	+	8.69034i	0.0788628	+	0.323870i
$721$	8.02809	−	24.7079i	0.298982	−	0.920171i
$722$	6.47122	−	5.37005i	0.240834	−	0.199853i
$723$	16.3569	+	2.59068i	0.608321	+	0.0963485i
$724$	19.5987	+	41.3226i	0.728378	+	1.53574i
$725$	3.09552	−	3.94412i	0.114965	−	0.146481i
$726$	−2.95493	−	13.1258i	−0.109668	−	0.487144i
$727$	5.20051	−	32.8348i	0.192876	−	1.21777i	−0.681241	−	0.732059i	$-0.738559\pi$
$727$	5.20051	−	32.8348i	0.192876	−	1.21777i	0.874118	−	0.485715i	$-0.161441\pi$
$728$	1.52448	−	3.27841i	0.0565008	−	0.121506i
$729$	−0.951057	−	0.309017i	−0.0352243	−	0.0114451i
$730$	10.8661	+	19.1091i	0.402171	+	0.707261i
$731$	18.1698	−	5.90372i	0.672033	−	0.218357i
$732$	6.34764	−	17.8009i	0.234616	−	0.657941i
$733$	28.4963	+	14.5196i	1.05254	+	0.536294i	0.892607	−	0.450835i	$-0.148874\pi$
$733$	28.4963	+	14.5196i	1.05254	+	0.536294i	0.159928	+	0.987129i	$0.448874\pi$
$734$	12.8049	+	5.51807i	0.472637	+	0.203676i
$735$	−5.35953	−	2.85730i	−0.197689	−	0.105393i
$736$	−38.5219	+	6.40184i	−1.41994	+	0.235975i
$737$	−1.54979	−	9.78500i	−0.0570873	−	0.360435i
$738$	−7.25521	+	2.88531i	−0.267068	+	0.106210i
$739$	14.5373	−	10.5619i	0.534762	−	0.388527i	−0.287374	−	0.957818i	$-0.592782\pi$
$739$	14.5373	−	10.5619i	0.534762	−	0.388527i	0.822136	+	0.569291i	$0.192782\pi$
$740$	16.7340	+	13.4012i	0.615156	+	0.492638i
$741$	1.80525	+	1.31159i	0.0663175	+	0.0481825i
$742$	17.6528	+	4.50387i	0.648055	+	0.165342i
$743$	13.7539	+	13.7539i	0.504581	+	0.504581i	0.912858	−	0.408277i	$-0.133870\pi$
$743$	13.7539	+	13.7539i	0.504581	+	0.504581i	−0.408277	+	0.912858i	$0.633870\pi$
$744$	−16.7941	+	24.9559i	−0.615703	+	0.914928i
$745$	25.1426	+	35.9917i	0.921153	+	1.31864i
$746$	−1.32479	+	14.2460i	−0.0485041	+	0.521584i
$747$	−3.19885	−	6.27810i	−0.117040	−	0.229704i
$748$	11.5103	−	3.38203i	0.420857	−	0.123659i
$749$		−	11.3816i		−	0.415875i
$750$	11.2770	+	11.0828i	0.411778	+	0.404688i
$751$		−	1.95838i		−	0.0714623i	−0.999361	−	0.0357311i	$-0.988624\pi$
$751$		−	1.95838i		−	0.0714623i	0.999361	−	0.0357311i	$-0.0113760\pi$
$752$	−3.47917	−	3.89829i	−0.126872	−	0.142156i
$753$	10.3819	+	20.3756i	0.378337	+	0.742529i
$754$	0.872076	+	0.0810979i	0.0317591	+	0.00295341i
$755$	−30.4487	−	43.5875i	−1.10814	−	1.58631i
$756$	−2.84282	−	3.00891i	−0.103393	−	0.109433i
$757$	−17.8464	−	17.8464i	−0.648640	−	0.648640i	0.304025	−	0.952664i	$-0.401670\pi$
$757$	−17.8464	−	17.8464i	−0.648640	−	0.648640i	−0.952664	+	0.304025i	$0.901670\pi$
$758$	6.48044	−	25.3999i	0.235380	−	0.922567i
$759$	6.80880	+	4.94688i	0.247144	+	0.179560i
$760$	−20.5377	−	10.0177i	−0.744981	−	0.363381i
$761$	−9.56396	+	6.94862i	−0.346693	+	0.251887i	−0.747481	−	0.664284i	$-0.768737\pi$
$761$	−9.56396	+	6.94862i	−0.346693	+	0.251887i	0.400787	+	0.916171i	$0.368737\pi$
$762$	−7.23534	−	18.1935i	−0.262109	−	0.659082i
$763$	1.82072	+	11.4956i	0.0659145	+	0.416168i
$764$	7.68935	−	14.0882i	0.278191	−	0.509693i
$765$	−9.70819	−	5.17568i	−0.351000	−	0.187127i
$766$	−5.80714	+	13.4757i	−0.209821	+	0.486897i
$767$	7.20842	+	3.67288i	0.260281	+	0.132620i
$768$	8.83171	−	13.3417i	0.318687	−	0.481427i
$769$	19.4145	−	6.30814i	0.700103	−	0.227477i	0.0627276	−	0.998031i	$-0.480020\pi$
$769$	19.4145	−	6.30814i	0.700103	−	0.227477i	0.637375	+	0.770553i	$0.280020\pi$
$770$	6.93654	−	3.94433i	0.249975	−	0.142144i
$771$	−23.6121	−	7.67204i	−0.850370	−	0.276302i
$772$	12.3007	−	15.9579i	0.442712	−	0.574339i
$773$	−3.16880	+	20.0070i	−0.113974	+	0.719603i	0.862834	+	0.505487i	$0.168687\pi$
$773$	−3.16880	+	20.0070i	−0.113974	+	0.719603i	−0.976808	+	0.214116i	$0.931313\pi$
$774$	−5.35734	+	1.20606i	−0.192566	+	0.0433511i
$775$	−1.97301	+	53.1388i	−0.0708725	+	1.90880i
$776$	9.16832	−	7.17890i	0.329123	−	0.257707i
$777$	−9.79985	−	1.55214i	−0.351568	−	0.0556828i
$778$	25.5224	+	30.7559i	0.915021	+	1.10265i
$779$	6.16410	−	18.9711i	0.220852	−	0.679711i
$780$	−0.559580	+	2.70474i	−0.0200362	+	0.0968451i
$781$	5.07419	+	15.6168i	0.181569	+	0.558812i
$782$	25.6755	−	40.5944i	0.918155	−	1.45165i
$783$	0.455245	−	0.893468i	0.0162691	−	0.0319300i
$784$	2.76592	+	10.5068i	0.0987827	+	0.375244i
$785$	−7.42134	−	1.31702i	−0.264879	−	0.0470065i
$786$	1.59772	−	1.81783i	0.0569889	−	0.0648397i
$787$	−49.0348	+	7.76635i	−1.74790	+	0.276841i	−0.946832	−	0.321729i	$-0.895736\pi$
$787$	−49.0348	+	7.76635i	−1.74790	+	0.276841i	−0.801071	+	0.598570i	$0.795736\pi$
$788$	24.7180	−	16.9085i	0.880543	−	0.602339i
$789$	4.07420	+	5.60766i	0.145046	+	0.199638i
$790$	−7.83109	−	20.8079i	−0.278618	−	0.740312i
$791$	8.26401	−	11.3744i	0.293834	−	0.404428i
$792$	−3.38427	+	0.661597i	−0.120255	+	0.0235088i
$793$	4.12668	−	4.12668i	0.146543	−	0.146543i
$794$	−17.7949	+	10.5604i	−0.631517	+	0.374775i
$795$	−13.9152	−	0.258241i	−0.493520	−	0.00915887i
$796$	−9.44386	+	1.22222i	−0.334729	+	0.0433206i
$797$	10.0858	−	5.13896i	0.357257	−	0.182031i	−0.266145	−	0.963933i	$-0.585750\pi$
$797$	10.0858	−	5.13896i	0.357257	−	0.182031i	0.623402	+	0.781902i	$0.285750\pi$
$798$	10.5536	−	0.680085i	0.373592	−	0.0240747i
$799$	6.42694			0.227369
$800$	0.834546	−	28.2720i	0.0295057	−	0.999565i
$801$	14.3238			0.506108
$802$	−25.9670	+	1.67335i	−0.916927	+	0.0590880i
$803$	−7.55131	+	3.84758i	−0.266480	+	0.135778i
$804$	16.1176	−	2.08594i	0.568424	−	0.0735654i
$805$	10.4347	−	30.1963i	0.367774	−	1.06428i
$806$	−7.98820	+	4.74062i	−0.281372	+	0.166981i
$807$	19.5477	−	19.5477i	0.688112	−	0.688112i
$808$	−39.6374	+	7.74878i	−1.39444	+	0.272601i
$809$	−9.99015	+	13.7503i	−0.351235	+	0.483434i	−0.947681	−	0.319220i	$-0.896579\pi$
$809$	−9.99015	+	13.7503i	−0.351235	+	0.483434i	0.596446	+	0.802653i	$0.296579\pi$
$810$	2.64075	+	1.73967i	0.0927864	+	0.0611258i
$811$	−13.4786	−	18.5517i	−0.473299	−	0.651440i	0.503901	−	0.863761i	$-0.331898\pi$
$811$	−13.4786	−	18.5517i	−0.473299	−	0.651440i	−0.977200	+	0.212322i	$0.931898\pi$
$812$	3.42602	−	2.34358i	0.120230	−	0.0822437i
$813$	−14.9958	+	2.37511i	−0.525927	+	0.0832986i
$814$	−5.45657	+	6.20827i	−0.191253	+	0.217600i
$815$	9.19774	+	9.54559i	0.322183	+	0.334367i
$816$	5.01015	+	19.0320i	0.175390	+	0.666252i
$817$	6.36921	−	12.5003i	0.222830	−	0.437329i
$818$	1.34671	−	2.12922i	0.0470865	−	0.0744465i
$819$	−0.395010	−	1.21572i	−0.0138028	−	0.0424805i
$820$	24.5411	−	2.71415i	0.857011	−	0.0947821i
$821$	6.99281	−	21.5217i	0.244051	−	0.751111i	−0.751740	−	0.659459i	$-0.770785\pi$
$821$	6.99281	−	21.5217i	0.244051	−	0.751111i	0.995791	−	0.0916520i	$-0.0292147\pi$
$822$	−0.415225	−	0.500369i	−0.0144826	−	0.0174524i
$823$	53.8434	+	8.52795i	1.87686	+	0.297266i	0.987216	−	0.159386i	$-0.0509514\pi$
$823$	53.8434	+	8.52795i	1.87686	+	0.297266i	0.889646	+	0.456652i	$0.150951\pi$
$824$	27.9530	−	21.8875i	0.973789	−	0.762488i
$825$	−4.46738	+	4.14751i	−0.155534	+	0.144398i
$826$	37.4061	−	8.42100i	1.30153	−	0.293004i
$827$	−2.96544	+	18.7231i	−0.103119	+	0.651065i	0.880941	+	0.473226i	$0.156911\pi$
$827$	−2.96544	+	18.7231i	−0.103119	+	0.651065i	−0.984060	+	0.177839i	$0.943089\pi$
$828$	−8.42880	+	10.9348i	−0.292921	+	0.380012i
$829$	−3.94785	−	1.28273i	−0.137114	−	0.0445512i	0.239656	−	0.970858i	$-0.422965\pi$
$829$	−3.94785	−	1.28273i	−0.137114	−	0.0445512i	−0.376770	+	0.926307i	$0.622965\pi$
$830$	4.48946	+	21.8247i	0.155831	+	0.757545i
$831$	−17.4241	+	5.66142i	−0.604434	+	0.196393i
$832$	4.22967	−	2.55379i	0.146637	−	0.0885366i
$833$	−11.9074	−	6.06710i	−0.412566	−	0.210213i
$834$	2.60676	−	6.04907i	0.0902646	−	0.209462i
$835$	−29.7213	+	4.14363i	−1.02855	+	0.143396i
$836$	4.22063	−	7.73290i	0.145973	−	0.267448i
$837$	1.66369	+	10.5042i	0.0575057	+	0.363077i
$838$	−21.2340	−	53.3937i	−0.733518	−	1.84446i
$839$	2.92007	−	2.12156i	0.100812	−	0.0732443i	−0.536237	−	0.844067i	$-0.680155\pi$
$839$	2.92007	−	2.12156i	0.100812	−	0.0732443i	0.637049	+	0.770823i	$0.280155\pi$
$840$	6.14508	+	11.5581i	0.212025	+	0.398793i
$841$	−22.6480	−	16.4547i	−0.780965	−	0.567405i
$842$	3.27872	−	12.8509i	0.112992	−	0.442870i
$843$	−10.1871	−	10.1871i	−0.350861	−	0.350861i
$844$	−1.59680	−	1.69009i	−0.0549643	−	0.0581755i
$845$	17.0056	−	22.5155i	0.585012	−	0.774558i
$846$	−1.83940	−	0.171053i	−0.0632399	−	0.00588093i
$847$	−8.93938	−	17.5445i	−0.307161	−	0.602837i
$848$	16.5776	+	18.5747i	0.569278	+	0.637856i
$849$			29.1982i			1.00208i
$850$	25.2614	+	23.9213i	0.866458	+	0.820494i
$851$			33.0928i			1.13441i
$852$	−25.8445	+	7.59383i	−0.885419	+	0.260160i
$853$	−2.88314	−	5.65849i	−0.0987169	−	0.193743i	0.836366	−	0.548171i	$-0.184676\pi$
$853$	−2.88314	−	5.65849i	−0.0987169	−	0.193743i	−0.935083	+	0.354428i	$0.884676\pi$
$854$	2.56106	−	27.5400i	0.0876376	−	0.942400i
$855$	−7.72852	+	2.35353i	−0.264310	+	0.0804890i
$856$	8.68372	−	12.9039i	0.296803	−	0.441047i
$857$	0.669915	+	0.669915i	0.0228838	+	0.0228838i	0.718456	−	0.695572i	$-0.244849\pi$
$857$	0.669915	+	0.669915i	0.0228838	+	0.0228838i	−0.695572	+	0.718456i	$0.744849\pi$
$858$	−1.03180	−	0.263250i	−0.0352251	−	0.00898720i
$859$	−6.89179	−	5.00718i	−0.235145	−	0.170843i	0.463973	−	0.885849i	$-0.346424\pi$
$859$	−6.89179	−	5.00718i	−0.235145	−	0.170843i	−0.699117	+	0.715007i	$0.746424\pi$
$860$	17.3463	+	0.814679i	0.591503	+	0.0277803i
$861$	−9.24465	+	6.71663i	−0.315057	+	0.228902i
$862$	−4.89604	+	1.94709i	−0.166760	+	0.0663183i
$863$	1.83066	+	11.5583i	0.0623164	+	0.393451i	0.999057	+	0.0434252i	$0.0138270\pi$
$863$	1.83066	+	11.5583i	0.0623164	+	0.393451i	−0.936740	+	0.350025i	$0.886173\pi$
$864$	−0.927377	−	5.58032i	−0.0315500	−	0.189846i
$865$	15.7706	+	32.4252i	0.536216	+	1.10249i
$866$	−8.07346	−	3.47913i	−0.274347	−	0.118226i
$867$	−6.42175	−	3.27204i	−0.218094	−	0.111124i
$868$	−14.7864	+	41.4661i	−0.501884	+	1.40745i
$869$	8.15198	−	2.64874i	0.276537	−	0.0898523i
$870$	−2.13724	+	2.34255i	−0.0724594	+	0.0794197i
$871$	4.77303	+	1.55085i	0.161728	+	0.0525486i
$872$	−6.70642	+	14.4223i	−0.227108	+	0.488399i
$873$	0.644034	−	4.06627i	0.0217972	−	0.137622i
$874$	−7.74672	−	34.4110i	−0.262037	−	1.16397i
$875$	20.0017	+	11.6364i	0.676182	+	0.393382i
$876$	−5.95782	−	12.5617i	−0.201296	−	0.424421i
$877$	27.8979	+	4.41859i	0.942044	+	0.149205i	0.608522	−	0.793537i	$-0.291763\pi$
$877$	27.8979	+	4.41859i	0.942044	+	0.149205i	0.333522	+	0.942742i	$0.391763\pi$
$878$	1.09448	−	0.908241i	0.0369370	−	0.0306517i
$879$	1.31450	−	4.04561i	0.0443370	−	0.136455i
$880$	10.8737	+	0.820406i	0.366552	+	0.0276559i
$881$	7.87708	+	24.2432i	0.265386	+	0.816773i	0.991604	+	0.129309i	$0.0412759\pi$
$881$	7.87708	+	24.2432i	0.265386	+	0.816773i	−0.726219	+	0.687464i	$0.758724\pi$
$882$	3.24643	+	2.05333i	0.109313	+	0.0691392i
$883$	7.98248	−	15.6665i	0.268632	−	0.527219i	−0.716803	−	0.697276i	$-0.754395\pi$
$883$	7.98248	−	15.6665i	0.268632	−	0.527219i	0.985434	+	0.170057i	$0.0543951\pi$
$884$	−1.12062	+	5.97314i	−0.0376906	+	0.200898i
$885$	−26.3407	+	12.8113i	−0.885432	+	0.430646i
$886$	15.4640	+	13.5916i	0.519522	+	0.456619i
$887$	24.9107	−	3.94547i	0.836421	−	0.132476i	0.276491	−	0.961016i	$-0.410828\pi$
$887$	24.9107	−	3.94547i	0.836421	−	0.132476i	0.559929	+	0.828540i	$0.310828\pi$
$888$	−9.92637	−	9.23664i	−0.333107	−	0.309961i
$889$	−16.8430	−	23.1823i	−0.564895	−	0.777511i
$890$	−43.6746	−	12.0104i	−1.46398	−	0.402589i
$891$	−0.716610	+	0.986329i	−0.0240073	+	0.0330432i
$892$	−43.0228	−	1.22110i	−1.44051	−	0.0408855i
$893$	3.33722	−	3.33722i	0.111676	−	0.111676i
$894$	−14.1710	−	23.8789i	−0.473950	−	0.798631i
$895$	−3.94756	−	12.9630i	−0.131952	−	0.433305i
$896$	7.69708	−	22.1152i	0.257141	−	0.738817i
$897$	−3.79875	+	1.93556i	−0.126837	+	0.0646265i
$898$	1.65834	+	25.7342i	0.0553397	+	0.858761i
$899$	−10.6645			−0.355680
$900$	−6.59318	−	7.51864i	−0.219773	−	0.250621i
$901$	−30.6232			−1.02021
$902$	0.612155	+	9.49942i	0.0203825	+	0.316296i
$903$	−7.16086	+	3.64864i	−0.238299	+	0.121419i
$904$	18.0476	−	6.59067i	0.600253	−	0.219202i
$905$	−40.8027	−	30.8176i	−1.35633	−	1.02441i
$906$	17.1617	+	28.9184i	0.570160	+	0.960750i
$907$	−20.9210	+	20.9210i	−0.694669	+	0.694669i	−0.963256	−	0.268586i	$-0.913444\pi$
$907$	−20.9210	+	20.9210i	−0.694669	+	0.694669i	0.268586	+	0.963256i	$0.413444\pi$
$908$	0.383162	−	13.4999i	0.0127157	−	0.448009i
$909$	−8.39311	+	11.5521i	−0.278382	+	0.383160i
$910$	0.185056	+	4.03804i	0.00613455	+	0.133860i
$911$	−16.8211	−	23.1523i	−0.557309	−	0.767070i	0.433672	−	0.901071i	$-0.357218\pi$
$911$	−16.8211	−	23.1523i	−0.557309	−	0.767070i	−0.990981	+	0.134000i	$0.957218\pi$
$912$	12.4840	+	7.28089i	0.413386	+	0.241094i
$913$	−8.48459	+	1.34383i	−0.280799	+	0.0444742i
$914$	30.7321	+	27.0110i	1.01653	+	0.893445i
$915$	2.91758	+	20.9271i	0.0964523	+	0.691829i
$916$	−39.4371	−	7.39881i	−1.30304	−	0.244464i
$917$	1.60802	−	3.15592i	0.0531016	−	0.104218i
$918$	5.88055	+	3.71938i	0.194087	+	0.122758i
$919$	7.46481	+	22.9743i	0.246241	+	0.757853i	0.995430	+	0.0954962i	$0.0304438\pi$
$919$	7.46481	+	22.9743i	0.246241	+	0.757853i	−0.749188	+	0.662357i	$0.769556\pi$
$920$	34.8689	−	26.2738i	1.14959	−	0.866222i
$921$	−10.0174	+	30.8303i	−0.330084	+	1.01589i
$922$	1.69716	−	1.40837i	0.0558931	−	0.0463821i
$923$	−8.21583	−	1.30126i	−0.270427	−	0.0428315i
$924$	−4.55985	+	2.16266i	−0.150008	+	0.0711464i
$925$	−23.5187	−	4.62544i	−0.773291	−	0.152083i
$926$	−3.55103	−	15.7737i	−0.116694	−	0.518356i
$927$	1.96358	−	12.3975i	0.0644923	−	0.407188i
$928$	5.67232	−	0.0431235i	0.186203	−	0.00141560i
$929$	−29.1865	−	9.48327i	−0.957579	−	0.311136i	−0.211787	−	0.977316i	$-0.567928\pi$
$929$	−29.1865	−	9.48327i	−0.957579	−	0.311136i	−0.745791	+	0.666180i	$0.767928\pi$
$930$	3.73486	−	33.4231i	0.122471	−	1.09599i
$931$	−9.33333	+	3.03258i	−0.305888	+	0.0993889i
$932$	−10.2534	−	3.65627i	−0.335862	−	0.119765i
$933$	−8.82950	−	4.49885i	−0.289065	−	0.147286i
$934$	35.7407	+	15.4019i	1.16947	+	0.503966i
$935$	−9.65869	+	9.30672i	−0.315873	+	0.304362i
$936$	0.479699	−	1.67970i	0.0156795	−	0.0549026i
$937$	−5.74987	−	36.3032i	−0.187840	−	1.18598i	−0.883790	−	0.467885i	$-0.845016\pi$
$937$	−5.74987	−	36.3032i	−0.187840	−	1.18598i	0.695950	−	0.718091i	$-0.254984\pi$
$938$	22.1016	−	8.78953i	0.721642	−	0.286988i
$939$	−10.0584	+	7.30788i	−0.328244	+	0.238484i
$940$	5.46507	+	2.06387i	0.178251	+	0.0673162i
$941$	−17.5281	−	12.7349i	−0.571401	−	0.415147i	0.264213	−	0.964464i	$-0.414888\pi$
$941$	−17.5281	−	12.7349i	−0.571401	−	0.415147i	−0.835614	+	0.549317i	$0.814888\pi$
$942$	4.61903	+	1.17848i	0.150496	+	0.0383971i
$943$	26.9496	+	26.9496i	0.877599	+	0.877599i
$944$	48.8341	+	18.9921i	1.58942	+	0.618139i
$945$	4.37426	+	1.51158i	0.142295	+	0.0491716i
$946$	−0.619918	+	6.66621i	−0.0201553	+	0.216737i
$947$	−15.1008	−	29.6371i	−0.490711	−	0.963075i	−0.995032	−	0.0995587i	$-0.968257\pi$
$947$	−15.1008	−	29.6371i	−0.490711	−	0.963075i	0.504320	−	0.863517i	$-0.331743\pi$
$948$	3.96400	+	13.4909i	0.128745	+	0.438164i
$949$		−	4.29327i		−	0.139366i
$950$	25.5383	−	0.695838i	0.828573	−	0.0225760i
$951$		−	4.23517i		−	0.137335i
$952$	13.9908	+	25.1764i	0.453444	+	0.815972i
$953$	12.4971	+	24.5269i	0.404819	+	0.794503i	0.999958	−	0.00911989i	$-0.00290299\pi$
$953$	12.4971	+	24.5269i	0.404819	+	0.794503i	−0.595139	+	0.803623i	$0.702903\pi$
$954$	8.76442	+	0.815039i	0.283759	+	0.0263879i
$955$	−0.332961	+	17.9414i	−0.0107744	+	0.580569i
$956$	−20.2868	+	19.1670i	−0.656123	+	0.619906i
$957$	−0.864465	−	0.864465i	−0.0279442	−	0.0279442i
$958$	0.114185	−	0.447545i	0.00368915	−	0.0144595i
$959$	−0.769866	−	0.559340i	−0.0248603	−	0.0180620i
$960$	−1.85138	+	17.7925i	−0.0597531	+	0.574250i
$961$	66.4244	−	48.2601i	2.14272	−	1.55678i
$962$	−1.54728	−	3.89070i	−0.0498864	−	0.125441i
$963$	−0.860244	−	5.43137i	−0.0277210	−	0.175023i
$964$	29.0731	+	15.8681i	0.936381	+	0.511078i
$965$	−3.93619	+	22.1802i	−0.126711	+	0.714006i
$966$	−7.99653	+	18.5563i	−0.257284	+	0.597038i
$967$	35.2063	+	17.9385i	1.13216	+	0.576863i	0.916671	−	0.399644i	$-0.130866\pi$
$967$	35.2063	+	17.9385i	1.13216	+	0.576863i	0.215487	+	0.976507i	$0.430866\pi$
$968$	3.25073	−	26.7115i	0.104483	−	0.858541i
$969$	−16.9063	+	5.49319i	−0.543108	+	0.176467i
$970$	−5.37324	+	11.8584i	−0.172524	+	0.380750i
$971$	15.6458	+	5.08364i	0.502099	+	0.163142i	0.549106	−	0.835753i	$-0.314968\pi$
$971$	15.6458	+	5.08364i	0.502099	+	0.163142i	−0.0470070	+	0.998895i	$0.514968\pi$
$972$	−1.58403	−	1.22100i	−0.0508078	−	0.0391637i
$973$	1.50803	−	9.52131i	0.0483451	−	0.305239i
$974$	−7.37169	+	1.65954i	−0.236204	+	0.0531751i
$975$	−0.844626	−	2.97027i	−0.0270497	−	0.0951248i
$976$	23.9155	−	29.2696i	0.765518	−	0.936896i
$977$	−1.13863	−	0.180341i	−0.0364279	−	0.00576961i	0.138194	−	0.990405i	$-0.455870\pi$
$977$	−1.13863	−	0.180341i	−0.0364279	−	0.00576961i	−0.174622	+	0.984636i	$0.555870\pi$
$978$	−5.35380	−	6.45163i	−0.171196	−	0.206300i
$979$	5.39642	−	16.6085i	0.172470	−	0.530809i
$980$	−8.17696	−	8.98288i	−0.261203	−	0.286948i
$981$	1.73771	+	5.34814i	0.0554810	+	0.170753i
$982$	28.1929	−	44.5745i	0.899671	−	1.42243i
$983$	0.911754	−	1.78942i	0.0290804	−	0.0570735i	−0.876009	−	0.482294i	$-0.839804\pi$
$983$	0.911754	−	1.78942i	0.0290804	−	0.0570735i	0.905090	+	0.425221i	$0.139804\pi$
$984$	−15.6057	+	0.561692i	−0.497490	+	0.0179061i
$985$	−15.7518	+	29.5462i	−0.501894	+	0.941419i
$986$	−4.60620	+	5.24075i	−0.146691	+	0.166899i
$987$	−2.67034	+	0.422940i	−0.0849977	+	0.0134623i
$988$	2.51969	+	3.68347i	0.0801621	+	0.117187i
$989$	15.7557	+	21.6858i	0.501002	+	0.689570i
$990$	3.01203	−	2.40653i	0.0957286	−	0.0764846i
$991$	14.2213	−	19.5739i	0.451754	−	0.621786i	−0.521019	−	0.853545i	$-0.674448\pi$
$991$	14.2213	−	19.5739i	0.451754	−	0.621786i	0.972773	+	0.231759i	$0.0744480\pi$
$992$	−48.4011	+	35.7308i	−1.53674	+	1.13445i
$993$	6.08406	−	6.08406i	0.193072	−	0.193072i
$994$	−33.9025	+	20.1195i	−1.07532	+	0.638153i
$995$	8.72793	−	6.09703i	0.276694	−	0.193289i
$996$	−1.80872	−	13.9756i	−0.0573115	−	0.442833i
$997$	38.9735	−	19.8580i	1.23430	−	0.628909i	0.289699	−	0.957118i	$-0.406445\pi$
$997$	38.9735	−	19.8580i	1.23430	−	0.628909i	0.944605	+	0.328209i	$0.106445\pi$
$998$	−19.1288	+	1.23269i	−0.605513	+	0.0390200i
$999$	−4.79385			−0.151671

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.127.30	yes	240
3.2	odd	2		900.2.bj.f.127.1		240
4.3	odd	2	inner	300.2.w.a.127.26	✓	240
12.11	even	2		900.2.bj.f.127.5		240
25.13	odd	20	inner	300.2.w.a.163.26	yes	240
75.38	even	20		900.2.bj.f.163.5		240
100.63	even	20	inner	300.2.w.a.163.30	yes	240
300.263	odd	20		900.2.bj.f.163.1		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.127.26	✓	240	4.3	odd	2	inner
300.2.w.a.127.30	yes	240	1.1	even	1	trivial
300.2.w.a.163.26	yes	240	25.13	odd	20	inner
300.2.w.a.163.30	yes	240	100.63	even	20	inner
900.2.bj.f.127.1		240	3.2	odd	2
900.2.bj.f.127.5		240	12.11	even	2
900.2.bj.f.163.1		240	300.263	odd	20
900.2.bj.f.163.5		240	75.38	even	20

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41129 - 0.0909451i) q^{2} +(0.891007 - 0.453990i) q^{3} +(1.98346 - 0.256699i) q^{4} +(-1.83309 + 1.28054i) q^{5} +(1.21618 - 0.721743i) q^{6} +(1.46352 - 1.46352i) q^{7} +(2.77588 - 0.542662i) q^{8} +(0.587785 - 0.809017i) q^{9} +O(q^{10})\)	\(q+(1.41129 - 0.0909451i) q^{2} +(0.891007 - 0.453990i) q^{3} +(1.98346 - 0.256699i) q^{4} +(-1.83309 + 1.28054i) q^{5} +(1.21618 - 0.721743i) q^{6} +(1.46352 - 1.46352i) q^{7} +(2.77588 - 0.542662i) q^{8} +(0.587785 - 0.809017i) q^{9} +(-2.47056 + 1.97391i) q^{10} +(-0.716610 - 0.986329i) q^{11} +(1.65074 - 1.12919i) q^{12} +(0.610002 - 0.0966148i) q^{13} +(1.93235 - 2.19855i) q^{14} +(-1.05195 + 1.97317i) q^{15} +(3.86821 - 1.01830i) q^{16} +(-2.23367 + 4.38383i) q^{17} +(0.755957 - 1.19521i) q^{18} +(1.11648 + 3.43617i) q^{19} +(-3.30715 + 3.01044i) q^{20} +(0.639583 - 1.96843i) q^{21} +(-1.10104 - 1.32682i) q^{22} +(-6.81819 - 1.07989i) q^{23} +(2.22697 - 1.74374i) q^{24} +(1.72046 - 4.69468i) q^{25} +(0.852100 - 0.191828i) q^{26} +(0.156434 - 0.987688i) q^{27} +(2.52715 - 3.27852i) q^{28} +(0.953684 + 0.309871i) q^{29} +(-1.30515 + 2.88038i) q^{30} +(-10.1146 + 3.28642i) q^{31} +(5.36654 - 1.78891i) q^{32} +(-1.08629 - 0.553491i) q^{33} +(-2.75367 + 6.38999i) q^{34} +(-0.808681 + 4.55687i) q^{35} +(0.958173 - 1.75554i) q^{36} +(-0.749924 - 4.73483i) q^{37} +(1.88818 + 4.74789i) q^{38} +(0.499653 - 0.363019i) q^{39} +(-4.39355 + 4.54936i) q^{40} +(-4.46659 - 3.24517i) q^{41} +(0.723615 - 2.83619i) q^{42} +(-2.74571 - 2.74571i) q^{43} +(-1.67455 - 1.77239i) q^{44} +(-0.0414904 + 2.23568i) q^{45} +(-9.72062 - 0.903960i) q^{46} +(-0.593032 - 1.16389i) q^{47} +(2.98430 - 2.66345i) q^{48} +2.71620i q^{49} +(2.00110 - 6.78200i) q^{50} +4.92009i q^{51} +(1.18511 - 0.348218i) q^{52} +(2.82569 + 5.54573i) q^{53} +(0.130948 - 1.40814i) q^{54} +(2.57664 + 0.890388i) q^{55} +(3.26837 - 4.85677i) q^{56} +(2.55478 + 2.55478i) q^{57} +(1.37410 + 0.350583i) q^{58} +(10.5976 + 7.69958i) q^{59} +(-1.57998 + 4.18374i) q^{60} +(7.64473 - 5.55422i) q^{61} +(-13.9757 + 5.55795i) q^{62} +(-0.323778 - 2.04425i) q^{63} +(7.41104 - 3.01273i) q^{64} +(-0.994471 + 0.958232i) q^{65} +(-1.58340 - 0.682342i) q^{66} +(7.24032 + 3.68913i) q^{67} +(-3.30507 + 9.26853i) q^{68} +(-6.56531 + 2.13320i) q^{69} +(-0.726856 + 6.50459i) q^{70} +(-12.8093 - 4.16201i) q^{71} +(1.19260 - 2.56470i) q^{72} +(1.08745 - 6.86590i) q^{73} +(-1.48897 - 6.61400i) q^{74} +(-0.598399 - 4.96406i) q^{75} +(3.09656 + 6.52891i) q^{76} +(-2.49229 - 0.394740i) q^{77} +(0.672139 - 0.557765i) q^{78} +(-2.17258 + 6.68651i) q^{79} +(-5.78682 + 6.82003i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(-6.59877 - 4.17364i) q^{82} +(3.19885 - 6.27810i) q^{83} +(0.763291 - 4.06849i) q^{84} +(-1.51912 - 10.8963i) q^{85} +(-4.12469 - 3.62528i) q^{86} +(0.990417 - 0.156867i) q^{87} +(-2.52447 - 2.34905i) q^{88} +(8.41934 + 11.5882i) q^{89} +(0.144770 + 3.15896i) q^{90} +(0.751354 - 1.03415i) q^{91} +(-13.8008 - 0.391703i) q^{92} +(-7.52014 + 7.52014i) q^{93} +(-0.942788 - 1.58865i) q^{94} +(-6.44675 - 4.86913i) q^{95} +(3.96948 - 4.03029i) q^{96} +(3.66823 - 1.86906i) q^{97} +(0.247025 + 3.83333i) q^{98} -1.21917 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{8}+O(q^{10}) \) 240 * q + 12 * q^8	\( 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) \) 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Introduction

L-functions

Modular forms

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