LMFDB - Embedded newform 459.2.ba.a.25.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [459,2,Mod(25,459)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(459, base_ring=CyclotomicField(72))

chi = DirichletCharacter(H, H._module([40, 45]))

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

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

chi := DirichletCharacter("459.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	459.ba (of order $72$, degree $24$, 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:	$3.66513345278$
Analytic rank:	$0$
Dimension:	$1248$
Relative dimension:	$52$ over $\Q(\zeta_{72})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{72}]$

Embedding invariants

Embedding label			25.8
Character	$\chi$	$=$	459.25
Dual form			459.2.ba.a.202.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22861 - 1.75463i) q^{2} +(0.00134192 + 1.73205i) q^{3} +(-0.885220 + 2.43212i) q^{4} +(2.58809 - 0.816022i) q^{5} +(3.03746 - 2.13036i) q^{6} +(2.95845 - 2.71092i) q^{7} +(1.21702 - 0.326100i) q^{8} +(-3.00000 + 0.00464853i) q^{9} +(-4.61156 - 3.53858i) q^{10} +(-0.525873 + 1.66786i) q^{11} +(-4.21375 - 1.52998i) q^{12} +(1.62518 - 0.286563i) q^{13} +(-8.39145 - 1.86034i) q^{14} +(1.41686 + 4.48161i) q^{15} +(1.89794 + 1.59256i) q^{16} +(1.02412 - 3.99389i) q^{17} +(3.69397 + 5.25818i) q^{18} +(1.64676 + 6.14578i) q^{19} +(-0.306365 + 7.01691i) q^{20} +(4.69942 + 5.12055i) q^{21} +(3.57257 - 1.12643i) q^{22} +(-0.211394 - 4.84172i) q^{23} +(0.566455 + 2.10751i) q^{24} +(1.93656 - 1.35599i) q^{25} +(-2.49952 - 2.49952i) q^{26} +(-0.0120772 - 5.19614i) q^{27} +(3.97441 + 9.59508i) q^{28} +(-2.02494 + 3.17851i) q^{29} +(6.12280 - 7.99221i) q^{30} +(4.03251 - 4.40072i) q^{31} +(0.682162 - 7.79714i) q^{32} +(-2.88952 - 0.908600i) q^{33} +(-8.26606 + 3.10997i) q^{34} +(5.44457 - 9.43027i) q^{35} +(2.64435 - 7.30047i) q^{36} +(5.95541 - 0.784045i) q^{37} +(8.76037 - 10.4402i) q^{38} +(0.498523 + 2.81451i) q^{39} +(2.88366 - 1.83709i) q^{40} +(-4.02756 - 6.32200i) q^{41} +(3.21094 - 14.5369i) q^{42} +(0.461280 + 5.27246i) q^{43} +(-3.59092 - 2.75541i) q^{44} +(-7.76047 + 2.46009i) q^{45} +(-8.23572 + 6.31949i) q^{46} +(2.23480 + 6.14007i) q^{47} +(-2.75585 + 3.28947i) q^{48} +(0.793252 - 9.06692i) q^{49} +(-4.75853 - 1.73196i) q^{50} +(6.91900 + 1.76847i) q^{51} +(-0.741686 + 4.20631i) q^{52} +(1.89823 - 1.89823i) q^{53} +(-9.10248 + 6.40520i) q^{54} +4.74569i q^{55} +(2.71647 - 4.26400i) q^{56} +(-10.6426 + 2.86051i) q^{57} +(8.06497 - 0.352124i) q^{58} +(7.01689 + 0.613899i) q^{59} +(-12.1541 - 0.521223i) q^{60} +(3.79828 - 3.48048i) q^{61} +(-12.6760 - 1.66883i) q^{62} +(-8.86275 + 8.14651i) q^{63} +(-10.2279 + 5.90509i) q^{64} +(3.97227 - 2.06783i) q^{65} +(1.95582 + 6.18635i) q^{66} +(-2.11370 - 11.9874i) q^{67} +(8.80706 + 6.02626i) q^{68} +(8.38581 - 0.372642i) q^{69} +(-23.2359 + 2.03288i) q^{70} +(-7.26864 + 0.956935i) q^{71} +(-3.64954 + 0.983956i) q^{72} +(-12.0577 + 9.25223i) q^{73} +(-8.69257 - 9.48627i) q^{74} +(2.35124 + 3.35239i) q^{75} +(-16.4050 - 1.43525i) q^{76} +(2.96566 + 6.35988i) q^{77} +(4.32594 - 4.33265i) q^{78} +(7.83817 - 1.73768i) q^{79} +(6.21161 + 2.57293i) q^{80} +(8.99996 - 0.0278911i) q^{81} +(-6.14451 + 14.8341i) q^{82} +(3.56519 + 5.09161i) q^{83} +(-16.6138 + 6.89676i) q^{84} +(-0.608586 - 11.1723i) q^{85} +(8.68450 - 7.28716i) q^{86} +(-5.50806 - 3.50302i) q^{87} +(-0.0961110 + 2.20130i) q^{88} +(-4.39501 - 2.53746i) q^{89} +(13.8511 + 10.5943i) q^{90} +(4.03117 - 5.25352i) q^{91} +(11.9628 + 3.77185i) q^{92} +(7.62767 + 6.97861i) q^{93} +(8.02787 - 11.4650i) q^{94} +(9.27704 + 14.5620i) q^{95} +(13.5060 + 1.17107i) q^{96} +(-0.246246 - 0.473034i) q^{97} +(-16.8837 + 9.74781i) q^{98} +(1.56986 - 5.00601i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1248 q - 24 q^{2} - 24 q^{3} - 24 q^{5} - 24 q^{6} - 24 q^{7} - 12 q^{8} - 24 q^{9} - 12 q^{10} - 36 q^{11} + 12 q^{12} - 24 q^{14} - 24 q^{15} - 48 q^{16} - 12 q^{17} - 48 q^{18} - 12 q^{19} - 24 q^{20}+ \cdots - 168 q^{99}+O(q^{100}) $ 1248 * q - 24 * q^2 - 24 * q^3 - 24 * q^5 - 24 * q^6 - 24 * q^7 - 12 * q^8 - 24 * q^9 - 12 * q^10 - 36 * q^11 + 12 * q^12 - 24 * q^14 - 24 * q^15 - 48 * q^16 - 12 * q^17 - 48 * q^18 - 12 * q^19 - 24 * q^20 - 24 * q^22 + 48 * q^23 - 84 * q^24 - 24 * q^25 - 48 * q^26 - 24 * q^27 - 48 * q^28 - 24 * q^29 - 24 * q^31 - 72 * q^32 - 48 * q^33 - 24 * q^34 - 216 * q^35 - 24 * q^36 - 12 * q^37 - 24 * q^39 - 72 * q^40 - 24 * q^41 + 96 * q^42 + 12 * q^43 - 12 * q^44 - 24 * q^45 - 12 * q^46 - 24 * q^48 - 24 * q^49 - 48 * q^50 - 24 * q^51 - 48 * q^52 - 48 * q^53 - 96 * q^54 + 96 * q^56 - 60 * q^57 - 24 * q^58 + 144 * q^59 - 480 * q^60 - 24 * q^61 - 12 * q^62 + 120 * q^63 - 72 * q^65 - 204 * q^66 - 48 * q^67 - 72 * q^68 + 96 * q^69 + 36 * q^71 - 12 * q^73 - 192 * q^74 - 24 * q^75 - 72 * q^76 - 60 * q^77 + 324 * q^78 - 24 * q^79 - 48 * q^80 - 48 * q^82 - 144 * q^83 - 48 * q^84 - 24 * q^85 + 72 * q^86 - 24 * q^87 + 192 * q^88 - 252 * q^90 - 12 * q^91 - 24 * q^92 - 24 * q^93 - 24 * q^94 + 192 * q^95 + 288 * q^96 - 132 * q^97 - 168 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{8}\right)$

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 $

$2$	−1.22861	−	1.75463i	−0.868756	−	1.24071i	−0.969325	−	0.245782i	$-0.920955\pi$
$2$	−1.22861	−	1.75463i	−0.868756	−	1.24071i	0.100569	−	0.994930i	$-0.467934\pi$
$3$	0.00134192	+	1.73205i	0.000774755	+	1.00000i
$3$	0.00134192	+	1.73205i	0.000774755	+	1.00000i
$4$	−0.885220	+	2.43212i	−0.442610	+	1.21606i
$5$	2.58809	−	0.816022i	1.15743	−	0.364936i	0.339697	−	0.940535i	$-0.389676\pi$
$5$	2.58809	−	0.816022i	1.15743	−	0.364936i	0.817732	+	0.575599i	$0.195231\pi$
$6$	3.03746	−	2.13036i	1.24004	−	0.869717i
$7$	2.95845	−	2.71092i	1.11819	−	1.02463i	0.118693	−	0.992931i	$-0.462130\pi$
$7$	2.95845	−	2.71092i	1.11819	−	1.02463i	0.999497	−	0.0317016i	$-0.0100926\pi$
$8$	1.21702	−	0.326100i	0.430282	−	0.115294i
$9$	−3.00000	+	0.00464853i	−0.999999	+	0.00154951i
$10$	−4.61156	−	3.53858i	−1.45830	−	1.11900i
$11$	−0.525873	+	1.66786i	−0.158557	+	0.502878i	−0.999254	−	0.0386283i	$-0.987701\pi$
$11$	−0.525873	+	1.66786i	−0.158557	+	0.502878i	0.840697	+	0.541506i	$0.182146\pi$
$12$	−4.21375	−	1.52998i	−1.21640	−	0.441668i
$13$	1.62518	−	0.286563i	0.450744	−	0.0794783i	0.0563321	−	0.998412i	$-0.482059\pi$
$13$	1.62518	−	0.286563i	0.450744	−	0.0794783i	0.394412	+	0.918934i	$0.370948\pi$
$14$	−8.39145	−	1.86034i	−2.24271	−	0.497197i
$15$	1.41686	+	4.48161i	0.365833	+	1.15715i
$16$	1.89794	+	1.59256i	0.474485	+	0.398141i
$17$	1.02412	−	3.99389i	0.248386	−	0.968661i
$17$	1.02412	−	3.99389i	0.248386	−	0.968661i
$18$	3.69397	+	5.25818i	0.870678	+	1.23936i
$19$	1.64676	+	6.14578i	0.377792	+	1.40994i	0.849222	+	0.528035i	$0.177071\pi$
$19$	1.64676	+	6.14578i	0.377792	+	1.40994i	−0.471430	+	0.881903i	$0.656262\pi$
$20$	−0.306365	+	7.01691i	−0.0685053	+	1.56903i
$21$	4.69942	+	5.12055i	1.02550	+	1.11740i
$22$	3.57257	−	1.12643i	0.761674	−	0.240155i
$23$	−0.211394	−	4.84172i	−0.0440787	−	1.00957i	−0.884182	−	0.467142i	$-0.845284\pi$
$23$	−0.211394	−	4.84172i	−0.0440787	−	1.00957i	0.840104	−	0.542426i	$-0.182494\pi$
$24$	0.566455	+	2.10751i	0.115627	+	0.430193i
$25$	1.93656	−	1.35599i	0.387311	−	0.271198i
$26$	−2.49952	−	2.49952i	−0.490196	−	0.490196i
$27$	−0.0120772	−	5.19614i	−0.00232426	−	0.999997i
$28$	3.97441	+	9.59508i	0.751094	+	1.81330i
$29$	−2.02494	+	3.17851i	−0.376021	+	0.590235i	−0.978083	−	0.208214i	$-0.933235\pi$
$29$	−2.02494	+	3.17851i	−0.376021	+	0.590235i	0.602062	+	0.798449i	$0.294346\pi$
$30$	6.12280	−	7.99221i	1.11787	−	1.45917i
$31$	4.03251	−	4.40072i	0.724261	−	0.790392i	−0.260283	−	0.965532i	$-0.583816\pi$
$31$	4.03251	−	4.40072i	0.724261	−	0.790392i	0.984543	+	0.175141i	$0.0560380\pi$
$32$	0.682162	−	7.79714i	0.120590	−	1.37835i
$33$	−2.88952	−	0.908600i	−0.503000	−	0.158167i
$34$	−8.26606	+	3.10997i	−1.41762	+	0.533355i
$35$	5.44457	−	9.43027i	0.920300	−	1.59401i
$36$	2.64435	−	7.30047i	0.440725	−	1.21675i
$37$	5.95541	−	0.784045i	0.979063	−	0.128896i	0.376026	−	0.926609i	$-0.377290\pi$
$37$	5.95541	−	0.784045i	0.979063	−	0.128896i	0.603037	+	0.797713i	$0.293957\pi$
$38$	8.76037	−	10.4402i	1.42112	−	1.69362i
$39$	0.498523	+	2.81451i	0.0798275	+	0.450682i
$40$	2.88366	−	1.83709i	0.455946	−	0.290470i
$41$	−4.02756	−	6.32200i	−0.628999	−	0.987331i	−0.998315	−	0.0580272i	$-0.981519\pi$
$41$	−4.02756	−	6.32200i	−0.628999	−	0.987331i	0.369316	−	0.929304i	$-0.379592\pi$
$42$	3.21094	−	14.5369i	0.495459	−	2.24309i
$43$	0.461280	+	5.27246i	0.0703446	+	0.804042i	0.946645	+	0.322278i	$0.104448\pi$
$43$	0.461280	+	5.27246i	0.0703446	+	0.804042i	−0.876301	+	0.481765i	$0.839996\pi$
$44$	−3.59092	−	2.75541i	−0.541351	−	0.415393i
$45$	−7.76047	+	2.46009i	−1.15686	+	0.366729i
$46$	−8.23572	+	6.31949i	−1.21429	+	0.931757i
$47$	2.23480	+	6.14007i	0.325979	+	0.895621i	0.989118	+	0.147124i	$0.0470017\pi$
$47$	2.23480	+	6.14007i	0.325979	+	0.895621i	−0.663139	+	0.748496i	$0.730776\pi$
$48$	−2.75585	+	3.28947i	−0.397773	+	0.474794i
$49$	0.793252	−	9.06692i	0.113322	−	1.29527i
$50$	−4.75853	−	1.73196i	−0.672958	−	0.244937i
$51$	6.91900	+	1.76847i	0.968853	+	0.247635i
$52$	−0.741686	+	4.20631i	−0.102853	+	0.583310i
$53$	1.89823	−	1.89823i	0.260742	−	0.260742i	−0.564613	−	0.825356i	$-0.690975\pi$
$53$	1.89823	−	1.89823i	0.260742	−	0.260742i	0.825356	+	0.564613i	$0.190975\pi$
$54$	−9.10248	+	6.40520i	−1.23869	+	0.871638i
$55$			4.74569i			0.639908i
$56$	2.71647	−	4.26400i	0.363004	−	0.569801i
$57$	−10.6426	+	2.86051i	−1.40965	+	0.378884i
$58$	8.06497	−	0.352124i	1.05898	−	0.0462362i
$59$	7.01689	+	0.613899i	0.913522	+	0.0799228i	0.534216	−	0.845348i	$-0.320607\pi$
$59$	7.01689	+	0.613899i	0.913522	+	0.0799228i	0.379306	+	0.925271i	$0.376163\pi$
$60$	−12.1541	−	0.521223i	−1.56908	−	0.0672896i
$61$	3.79828	−	3.48048i	0.486320	−	0.445630i	−0.394630	−	0.918840i	$-0.629127\pi$
$61$	3.79828	−	3.48048i	0.486320	−	0.445630i	0.880950	+	0.473210i	$0.156905\pi$
$62$	−12.6760	−	1.66883i	−1.60985	−	0.211941i
$63$	−8.86275	+	8.14651i	−1.11660	+	1.02636i
$64$	−10.2279	+	5.90509i	−1.27849	+	0.738137i
$65$	3.97227	−	2.06783i	0.492700	−	0.256483i
$66$	1.95582	+	6.18635i	0.240745	+	0.761487i
$67$	−2.11370	−	11.9874i	−0.258230	−	1.46450i	−0.787643	−	0.616131i	$-0.788699\pi$
$67$	−2.11370	−	11.9874i	−0.258230	−	1.46450i	0.529413	−	0.848364i	$-0.322412\pi$
$68$	8.80706	+	6.02626i	1.06801	+	0.730791i
$69$	8.38581	−	0.372642i	1.00953	−	0.0448608i
$70$	−23.2359	+	2.03288i	−2.77722	+	0.242975i
$71$	−7.26864	+	0.956935i	−0.862629	+	0.113567i	−0.548842	−	0.835926i	$-0.684931\pi$
$71$	−7.26864	+	0.956935i	−0.862629	+	0.113567i	−0.313787	+	0.949493i	$0.601598\pi$
$72$	−3.64954	+	0.983956i	−0.430103	+	0.115960i
$73$	−12.0577	+	9.25223i	−1.41125	+	1.08289i	−0.427368	+	0.904078i	$0.640559\pi$
$73$	−12.0577	+	9.25223i	−1.41125	+	1.08289i	−0.983883	+	0.178814i	$0.942774\pi$
$74$	−8.69257	−	9.48627i	−1.01049	−	1.10276i
$75$	2.35124	+	3.35239i	0.271498	+	0.387101i
$76$	−16.4050	−	1.43525i	−1.88179	−	0.164635i
$77$	2.96566	+	6.35988i	0.337968	+	0.724775i
$78$	4.32594	−	4.33265i	0.489817	−	0.490576i
$79$	7.83817	−	1.73768i	0.881863	−	0.195504i	0.247824	−	0.968805i	$-0.420285\pi$
$79$	7.83817	−	1.73768i	0.881863	−	0.195504i	0.634039	+	0.773301i	$0.281396\pi$
$80$	6.21161	+	2.57293i	0.694479	+	0.287663i
$81$	8.99996	−	0.0278911i	0.999995	−	0.00309902i
$82$	−6.14451	+	14.8341i	−0.678547	+	1.63816i
$83$	3.56519	+	5.09161i	0.391330	+	0.558877i	0.965681	−	0.259732i	$-0.0836343\pi$
$83$	3.56519	+	5.09161i	0.391330	+	0.558877i	−0.574351	+	0.818609i	$0.694745\pi$
$84$	−16.6138	+	6.89676i	−1.81272	+	0.752498i
$85$	−0.608586	−	11.1723i	−0.0660104	−	1.21180i
$86$	8.68450	−	7.28716i	0.936473	−	0.785794i
$87$	−5.50806	−	3.50302i	−0.590526	−	0.375564i
$88$	−0.0961110	+	2.20130i	−0.0102455	+	0.234660i
$89$	−4.39501	−	2.53746i	−0.465870	−	0.268970i	0.248639	−	0.968596i	$-0.420017\pi$
$89$	−4.39501	−	2.53746i	−0.465870	−	0.268970i	−0.714509	+	0.699626i	$0.753350\pi$
$90$	13.8511	+	10.5943i	1.46004	+	1.11674i
$91$	4.03117	−	5.25352i	0.422581	−	0.550719i
$92$	11.9628	+	3.77185i	1.24721	+	0.393243i
$93$	7.62767	+	6.97861i	0.790953	+	0.723648i
$94$	8.02787	−	11.4650i	0.828011	−	1.18252i
$95$	9.27704	+	14.5620i	0.951805	+	1.49403i
$96$	13.5060	+	1.17107i	1.37845	+	0.119522i
$97$	−0.246246	−	0.473034i	−0.0250025	−	0.0480294i	0.874184	−	0.485594i	$-0.161397\pi$
$97$	−0.246246	−	0.473034i	−0.0250025	−	0.0480294i	−0.899187	+	0.437565i	$0.855841\pi$
$98$	−16.8837	+	9.74781i	−1.70551	+	0.984677i
$99$	1.56986	−	5.00601i	0.157777	−	0.503123i
$100$	1.58366	+	5.91029i	0.158366	+	0.591029i
$101$	−9.36006	+	3.40678i	−0.931361	+	0.338988i	−0.762749	−	0.646695i	$-0.776151\pi$
$101$	−9.36006	+	3.40678i	−0.931361	+	0.338988i	−0.168612	+	0.985682i	$0.553929\pi$
$102$	−5.39771	−	14.3131i	−0.534453	−	1.41720i
$103$	−12.3343	+	10.3497i	−1.21533	+	1.01978i	−0.216276	+	0.976332i	$0.569391\pi$
$103$	−12.3343	+	10.3497i	−1.21533	+	1.01978i	−0.999056	+	0.0434521i	$0.986164\pi$
$104$	1.88443	−	0.878725i	0.184784	−	0.0861661i
$105$	16.3410	+	9.41762i	1.59472	+	0.919065i
$106$	−5.66288	−	0.998519i	−0.550028	−	0.0969848i
$107$	10.1199	+	4.19179i	0.978325	+	0.405236i	0.813805	−	0.581138i	$-0.197392\pi$
$107$	10.1199	+	4.19179i	0.978325	+	0.405236i	0.164520	+	0.986374i	$0.447392\pi$
$108$	12.6483	+	4.57035i	1.21709	+	0.439782i
$109$	−3.26229	+	1.35129i	−0.312471	+	0.129430i	−0.533407	−	0.845858i	$-0.679089\pi$
$109$	−3.26229	+	1.35129i	−0.312471	+	0.129430i	0.220936	+	0.975288i	$0.429089\pi$
$110$	8.32693	−	5.83058i	0.793942	−	0.555924i
$111$	1.36600	+	10.3140i	0.129655	+	0.978963i
$112$	9.93229	−	0.433653i	0.938513	−	0.0409764i
$113$	−6.05284	−	3.15091i	−0.569404	−	0.296413i	0.152616	−	0.988286i	$-0.451230\pi$
$113$	−6.05284	−	3.15091i	−0.569404	−	0.296413i	−0.722019	+	0.691873i	$0.756786\pi$
$114$	18.0947	+	15.1594i	1.69472	+	1.41981i
$115$	−4.49805	−	12.3583i	−0.419446	−	1.15242i
$116$	−5.93802	−	7.73857i	−0.551331	−	0.718508i
$117$	−4.87420	+	0.867243i	−0.450620	+	0.0801767i
$118$	−7.54384	−	13.0663i	−0.694467	−	1.20285i
$119$	−7.79732	−	14.5921i	−0.714779	−	1.33765i
$120$	3.18581	+	4.99217i	0.290823	+	0.455721i
$121$	6.50547	+	4.55518i	0.591406	+	0.414107i
$122$	−10.7736	−	2.38844i	−0.975392	−	0.216239i
$123$	10.9446	−	6.98442i	0.986844	−	0.629764i
$124$	7.13342	+	13.7032i	0.640600	+	1.23058i
$125$	−4.35448	+	5.67486i	−0.389476	+	0.507575i
$126$	25.1830	+	5.54200i	2.24348	+	0.493721i
$127$	5.02309	−	1.34593i	0.445727	−	0.119432i	−0.0289724	−	0.999580i	$-0.509224\pi$
$127$	5.02309	−	1.34593i	0.445727	−	0.119432i	0.474699	+	0.880148i	$0.342557\pi$
$128$	8.74016	+	4.07560i	0.772528	+	0.360236i
$129$	−9.13154	+	0.806036i	−0.803988	+	0.0709675i
$130$	−8.50865	−	4.42932i	−0.746258	−	0.388477i
$131$	1.67643	+	1.53617i	0.146470	+	0.134215i	0.745484	−	0.666523i	$-0.232218\pi$
$131$	1.67643	+	1.53617i	0.146470	+	0.134215i	−0.599014	+	0.800739i	$0.704441\pi$
$132$	4.76769	−	6.22335i	0.414974	−	0.541673i
$133$	21.5326	+	13.7178i	1.86711	+	1.18948i
$134$	−18.4366	+	18.4366i	−1.59268	+	1.59268i
$135$	−4.27142	−	13.4382i	−0.367625	−	1.15658i
$136$	−0.0560312	−	5.19462i	−0.00480464	−	0.445435i
$137$	−0.367865	+	2.08627i	−0.0314288	+	0.178242i	−0.996481	−	0.0838148i	$-0.973290\pi$
$137$	−0.367865	+	2.08627i	−0.0314288	+	0.178242i	0.965053	+	0.262057i	$0.0844007\pi$
$138$	−10.9567	−	14.2562i	−0.932698	−	1.21357i
$139$	−9.96409	+	10.8739i	−0.845143	+	0.922312i	−0.997822	−	0.0659641i	$-0.978988\pi$
$139$	−9.96409	+	10.8739i	−0.845143	+	0.922312i	0.152679	+	0.988276i	$0.451210\pi$
$140$	18.1159	+	21.5897i	1.53108	+	1.82467i
$141$	−10.6319	+	3.87903i	−0.895368	+	0.326673i
$142$	10.6094	+	11.5781i	0.890319	+	0.971613i
$143$	−0.376692	+	2.86126i	−0.0315006	+	0.239271i
$144$	−5.70122	−	4.76886i	−0.475102	−	0.397405i
$145$	−2.64698	+	9.87866i	−0.219820	+	0.820378i
$146$	31.0485	+	9.78955i	2.56959	+	0.810189i
$147$	15.7054	+	1.36179i	1.29536	+	0.112318i
$148$	−3.36496	+	15.1783i	−0.276598	+	1.24765i
$149$	−23.2978	+	4.10802i	−1.90863	+	0.336542i	−0.997191	−	0.0749013i	$-0.976136\pi$
$149$	−23.2978	+	4.10802i	−1.90863	+	0.336542i	−0.911435	+	0.411444i	$0.865025\pi$
$150$	2.99346	−	8.24434i	0.244415	−	0.673148i
$151$	−22.8034	+	1.99504i	−1.85572	+	0.162354i	−0.959582	−	0.281430i	$-0.909191\pi$
$151$	−22.8034	+	1.99504i	−1.85572	+	0.162354i	−0.896134	+	0.443785i	$0.853636\pi$
$152$	4.00828	+	6.94254i	0.325114	+	0.563114i
$153$	−3.05379	+	11.9864i	−0.246884	+	0.969045i
$154$	7.51562	−	13.0174i	0.605626	−	1.04897i
$155$	6.84543	−	14.6801i	0.549838	−	1.17913i
$156$	−7.28654	−	1.27899i	−0.583390	−	0.102401i
$157$	11.9492	+	14.2405i	0.953648	+	1.13651i	0.990544	+	0.137194i	$0.0438085\pi$
$157$	11.9492	+	14.2405i	0.953648	+	1.13651i	−0.0368961	+	0.999319i	$0.511747\pi$
$158$	−12.6790	−	11.6182i	−1.00869	−	0.924293i
$159$	3.29038	+	3.28529i	0.260944	+	0.260540i
$160$	−4.59714	−	20.7364i	−0.363436	−	1.63935i
$161$	−13.7509	−	13.7509i	−1.08372	−	1.08372i
$162$	−11.1063	−	15.7574i	−0.872597	−	1.23801i
$163$	5.00403	−	2.07274i	0.391946	−	0.162349i	−0.178002	−	0.984030i	$-0.556963\pi$
$163$	5.00403	−	2.07274i	0.391946	−	0.162349i	0.569948	+	0.821681i	$0.306963\pi$
$164$	18.9412	−	4.19916i	1.47906	−	0.327899i
$165$	−8.21977	+	0.00636831i	−0.639908	+	0.000495772i
$166$	4.55370	−	12.5112i	0.353436	−	0.971056i
$167$	0.199631	+	0.633150i	0.0154479	+	0.0489946i	0.961126	−	0.276109i	$-0.0890452\pi$
$167$	0.199631	+	0.633150i	0.0154479	+	0.0489946i	−0.945678	+	0.325104i	$0.894601\pi$
$168$	7.38911	+	4.69934i	0.570083	+	0.362562i
$169$	−9.65691	+	3.51483i	−0.742839	+	0.270371i
$170$	−18.8555	+	14.7942i	−1.44615	+	1.13466i
$171$	−4.96883	−	18.4297i	−0.379976	−	1.40935i
$172$	−13.2316	−	3.54540i	−1.00890	−	0.270334i
$173$	−20.2319	+	10.5321i	−1.53820	+	0.800737i	−0.999137	−	0.0415271i	$-0.986778\pi$
$173$	−20.2319	+	10.5321i	−1.53820	+	0.800737i	−0.539065	+	0.842264i	$0.681222\pi$
$174$	0.620719	+	13.9685i	0.0470566	+	1.05895i
$175$	2.05322	−	9.26149i	0.155209	−	0.700103i
$176$	−3.65424	+	2.32801i	−0.275449	+	0.175480i
$177$	−1.05389	+	12.1544i	−0.0792150	+	0.913584i
$178$	0.947428	+	10.8292i	0.0710128	+	0.811680i
$179$	−4.04295	+	15.0885i	−0.302184	+	1.12777i	0.633158	+	0.774022i	$0.281758\pi$
$179$	−4.04295	+	15.0885i	−0.302184	+	1.12777i	−0.935342	+	0.353744i	$0.884908\pi$
$180$	0.886475	−	21.0521i	0.0660740	−	1.56913i
$181$	−15.4787	−	2.03780i	−1.15052	−	0.151469i	−0.468952	−	0.883224i	$-0.655368\pi$
$181$	−15.4787	−	2.03780i	−1.15052	−	0.151469i	−0.681568	+	0.731755i	$0.738702\pi$
$182$	−14.1707	−	0.618707i	−1.05040	−	0.0458616i
$183$	6.03347	+	6.57414i	0.446007	+	0.485974i
$184$	−1.83615	−	5.82354i	−0.135363	−	0.429317i
$185$	14.7733	−	6.88892i	1.08616	−	0.506484i
$186$	2.87348	−	21.9577i	0.210694	−	1.61002i
$187$	6.12268	+	3.80837i	0.447735	+	0.278495i
$188$	−16.9117			−1.23341
$189$	−14.1221	−	15.3398i	−1.02723	−	1.11581i
$190$	14.1532	−	34.1688i	1.02678	−	2.47887i
$191$	19.0071	+	3.35146i	1.37531	+	0.242503i	0.811957	−	0.583717i	$-0.198402\pi$
$191$	19.0071	+	3.35146i	1.37531	+	0.242503i	0.563348	+	0.826220i	$0.309513\pi$
$192$	−10.2416	−	17.7073i	−0.739127	−	1.27792i
$193$	−1.04585	−	23.9539i	−0.0752820	−	1.72424i	−0.542463	−	0.840080i	$-0.682508\pi$
$193$	−1.04585	−	23.9539i	−0.0752820	−	1.72424i	0.467181	−	0.884162i	$-0.345270\pi$
$194$	−0.527462	+	1.01324i	−0.0378696	+	0.0727467i
$195$	3.58692	+	6.87740i	0.256865	+	0.492501i
$196$	21.3496	+	9.95550i	1.52497	+	0.711107i
$197$	−2.24514	+	17.0535i	−0.159959	+	1.21501i	0.703537	+	0.710658i	$0.251603\pi$
$197$	−2.24514	+	17.0535i	−0.159959	+	1.21501i	−0.863497	+	0.504354i	$0.831731\pi$
$198$	−10.7124	+	3.39588i	−0.761301	+	0.241335i
$199$	0.314064	+	2.38555i	0.0222634	+	0.169107i	0.998964	−	0.0454970i	$-0.0144872\pi$
$199$	0.314064	+	2.38555i	0.0222634	+	0.169107i	−0.976701	+	0.214604i	$0.931154\pi$
$200$	1.91464	−	2.28178i	0.135386	−	0.161346i
$201$	20.7600	−	3.67713i	1.46429	−	0.259365i
$202$	17.4775	+	12.2379i	1.22971	+	0.861054i
$203$	2.62602	+	14.8929i	0.184311	+	1.04528i
$204$	−10.4260	+	15.2624i	−0.729964	+	1.06858i
$205$	−15.5826	−	13.0753i	−1.08833	−	0.913221i
$206$	33.3139	+	8.92642i	2.32109	+	0.621933i
$207$	0.656688	+	14.5242i	0.0456430	+	1.00950i
$208$	3.54087	+	2.04432i	0.245515	+	0.141748i
$209$	−11.1163	−	0.485347i	−0.768928	−	0.0335721i
$210$	−3.55223	−	40.2430i	−0.245127	−	2.77703i
$211$	10.6178	−	20.3966i	0.730959	−	1.40416i	−0.176620	−	0.984279i	$-0.556516\pi$
$211$	10.6178	−	20.3966i	0.730959	−	1.40416i	0.907579	−	0.419881i	$-0.137928\pi$
$212$	2.93638	+	6.29709i	0.201671	+	0.432486i
$213$	−1.66721	−	12.5884i	−0.114236	−	0.862541i
$214$	−5.07830	−	22.9067i	−0.347145	−	1.56587i
$215$	5.49627	+	13.2692i	0.374843	+	0.904951i
$216$	−1.70916	−	6.31987i	−0.116294	−	0.430013i
$217$		−	23.9511i		−	1.62591i
$218$	6.37909	+	4.06393i	0.432046	+	0.275244i
$219$	−16.0415	−	20.8722i	−1.08398	−	1.41041i
$220$	−11.5421	−	4.20098i	−0.778167	−	0.283230i
$221$	0.519878	−	6.78427i	0.0349708	−	0.456360i
$222$	16.4190	−	15.0687i	1.10197	−	1.01134i
$223$	4.98394	−	10.6881i	0.333749	−	0.715728i	−0.665788	−	0.746141i	$-0.731905\pi$
$223$	4.98394	−	10.6881i	0.333749	−	0.715728i	0.999537	+	0.0304131i	$0.00968229\pi$
$224$	−19.1193	−	24.9168i	−1.27746	−	1.66482i
$225$	−5.80336	+	4.07697i	−0.386891	+	0.271798i
$226$	1.90787	+	14.4917i	0.126910	+	0.963977i
$227$	−1.53536	+	4.86954i	−0.101906	+	0.323203i	−0.990879	−	0.134756i	$-0.956975\pi$
$227$	−1.53536	+	4.86954i	−0.101906	+	0.323203i	0.888973	+	0.457959i	$0.151419\pi$
$228$	2.46392	−	28.4163i	0.163177	−	1.88191i
$229$	−2.62446	+	3.74812i	−0.173429	+	0.247683i	−0.896451	−	0.443142i	$-0.853864\pi$
$229$	−2.62446	+	3.74812i	−0.173429	+	0.247683i	0.723022	+	0.690825i	$0.242752\pi$
$230$	−16.1579	+	23.0759i	−1.06542	+	1.52158i
$231$	−11.0116	+	5.14520i	−0.724513	+	0.338530i
$232$	−1.42788	+	4.52865i	−0.0937448	+	0.297320i
$233$	−2.67711	−	20.3347i	−0.175383	−	1.33217i	−0.822058	−	0.569403i	$-0.807174\pi$
$233$	−2.67711	−	20.3347i	−0.175383	−	1.33217i	0.646675	−	0.762766i	$-0.276159\pi$
$234$	7.51017	+	7.48694i	0.490955	+	0.489436i
$235$	10.7943	+	14.0674i	0.704142	+	0.917656i
$236$	−7.70457	+	16.5225i	−0.501525	+	1.07552i
$237$	3.02027	+	13.5738i	0.196188	+	0.881711i
$238$	−16.0239	+	31.6093i	−1.03867	+	2.04893i
$239$	9.17934	+	3.34101i	0.593762	+	0.216112i	0.621383	−	0.783507i	$-0.286571\pi$
$239$	9.17934	+	3.34101i	0.593762	+	0.216112i	−0.0276213	+	0.999618i	$0.508793\pi$
$240$	−4.44811	+	10.7623i	−0.287124	+	0.694702i
$241$	−17.6811	−	11.2641i	−1.13894	−	0.725583i	−0.173144	−	0.984897i	$-0.555393\pi$
$241$	−17.6811	−	11.2641i	−1.13894	−	0.725583i	−0.965793	+	0.259313i	$0.916504\pi$
$242$		−	17.0112i		−	1.09352i
$243$	0.0603860	+	15.5883i	0.00387377	+	0.999992i
$244$	5.10264	+	12.3189i	0.326663	+	0.788635i
$245$	−5.34579	−	24.1133i	−0.341530	−	1.54054i
$246$	−25.7017	−	10.6227i	−1.63868	−	0.677278i
$247$	4.43743	+	9.51610i	0.282347	+	0.605495i
$248$	3.47258	−	6.67077i	0.220509	−	0.423594i
$249$	−8.81415	+	6.18191i	−0.558574	+	0.391763i
$250$	15.3072	+	0.668329i	0.968115	+	0.0422688i
$251$	15.7035	+	9.06644i	0.991199	+	0.572269i	0.905632	−	0.424064i	$-0.139397\pi$
$251$	15.7035	+	9.06644i	0.991199	+	0.572269i	0.0855663	+	0.996332i	$0.472730\pi$
$252$	−11.9678	−	28.7667i	−0.753902	−	1.81213i
$253$	8.18645	+	2.19355i	0.514678	+	0.137908i
$254$	−8.53301	−	7.16005i	−0.535409	−	0.449261i
$255$	19.3501	−	1.06909i	1.21175	−	0.0669493i
$256$	0.514601	+	2.91845i	0.0321626	+	0.182403i
$257$	11.0705	+	7.75165i	0.690559	+	0.483535i	0.865413	−	0.501060i	$-0.167056\pi$
$257$	11.0705	+	7.75165i	0.690559	+	0.483535i	−0.174853	+	0.984594i	$0.555945\pi$
$258$	12.6334	+	15.0322i	0.786520	+	0.935864i
$259$	15.4933	−	18.4642i	0.962708	−	1.14731i
$260$	1.51289	+	11.4915i	0.0938254	+	0.712675i
$261$	6.06002	−	9.54494i	0.375106	−	0.590817i
$262$	0.635732	−	4.82886i	0.0392757	−	0.298328i
$263$	−6.39058	−	2.97998i	−0.394060	−	0.183753i	0.215480	−	0.976508i	$-0.430868\pi$
$263$	−6.39058	−	2.97998i	−0.394060	−	0.183753i	−0.609541	+	0.792755i	$0.708646\pi$
$264$	−3.81290	−	0.163515i	−0.234668	−	0.0100637i
$265$	3.36380	−	6.46180i	0.206636	−	0.396945i
$266$	−2.38544	−	54.6355i	−0.146261	−	3.34992i
$267$	4.38911	−	7.61577i	0.268609	−	0.466078i
$268$	31.0259	+	5.47071i	1.89521	+	0.334177i
$269$	7.04290	−	17.0031i	0.429413	−	1.03669i	−0.550061	−	0.835125i	$-0.685396\pi$
$269$	7.04290	−	17.0031i	0.429413	−	1.03669i	0.979474	−	0.201570i	$-0.0646045\pi$
$270$	−18.3312	+	24.0051i	−1.11560	+	1.46090i
$271$	−15.5531			−0.944786			−0.472393	−	0.881388i	$-0.656610\pi$
$271$	−15.5531			−0.944786			−0.472393	+	0.881388i	$0.656610\pi$
$272$	8.30424	−	5.94920i	0.503519	−	0.360723i
$273$	9.10478	+	6.97514i	0.551046	+	0.422155i
$274$	4.11259	−	1.91773i	0.248451	−	0.115854i
$275$	1.24322	+	3.94298i	0.0749688	+	0.237770i
$276$	−6.51698	+	20.7252i	−0.392276	+	1.24751i
$277$	−17.0356	−	0.743790i	−1.02357	−	0.0446900i	−0.474324	−	0.880350i	$-0.657307\pi$
$277$	−17.0356	−	0.743790i	−1.02357	−	0.0446900i	−0.549246	+	0.835660i	$0.685085\pi$
$278$	31.3216	+	4.12357i	1.87855	+	0.247315i
$279$	−12.0771	+	13.2209i	−0.723035	+	0.791513i
$280$	3.55095	−	13.2523i	0.212210	−	0.791978i
$281$	−0.509175	−	5.81990i	−0.0303748	−	0.347186i	−0.996141	−	0.0877707i	$-0.972026\pi$
$281$	−0.509175	−	5.81990i	−0.0303748	−	0.347186i	0.965766	−	0.259415i	$-0.0835298\pi$
$282$	19.8687	+	13.8893i	1.18316	+	0.827095i
$283$	7.54077	−	4.80400i	0.448252	−	0.285568i	−0.293854	−	0.955850i	$-0.594938\pi$
$283$	7.54077	−	4.80400i	0.448252	−	0.285568i	0.742106	+	0.670282i	$0.233827\pi$
$284$	4.10697	−	18.5253i	0.243704	−	1.09928i
$285$	−25.2097	+	16.0878i	−1.49330	+	0.952962i
$286$	5.48327	−	2.85441i	0.324233	−	0.168785i
$287$	−29.0538	−	7.78495i	−1.71499	−	0.459531i
$288$	−2.01024	+	23.3946i	−0.118454	+	1.37854i
$289$	−14.9024	−	8.18046i	−0.876609	−	0.481203i
$290$	20.5855	−	7.49252i	1.20882	−	0.439976i
$291$	0.818989	−	0.427145i	0.0480100	−	0.0250397i
$292$	−11.8288	−	37.5161i	−0.692228	−	2.19547i
$293$	−2.64746	+	7.27384i	−0.154666	+	0.424942i	−0.992690	−	0.120692i	$-0.961489\pi$
$293$	−2.64746	+	7.27384i	−0.154666	+	0.424942i	0.838024	+	0.545634i	$0.183711\pi$
$294$	−16.9064	−	29.2303i	−0.985998	−	1.70475i
$295$	18.6613	−	4.13711i	1.08650	−	0.240872i
$296$	6.99219	−	2.89626i	0.406413	−	0.168342i
$297$	8.67276	+	2.71237i	0.503245	+	0.157387i
$298$	35.8318	+	35.8318i	2.07568	+	2.07568i
$299$	−1.73101	−	7.80809i	−0.100107	−	0.451553i
$300$	−10.2348	+	2.75091i	−0.590907	+	0.158824i
$301$	15.6579	+	14.3478i	0.902507	+	0.826995i
$302$	31.5170	+	37.5605i	1.81360	+	2.16136i
$303$	−5.91328	−	16.2075i	−0.339709	−	0.931098i
$304$	−6.66209	+	14.2869i	−0.382097	+	0.819410i
$305$	6.99014	−	12.1073i	0.400254	−	0.693261i
$306$	24.7837	−	9.36832i	1.41679	−	0.535551i
$307$	−2.83052	−	4.90261i	−0.161546	−	0.279807i	0.773877	−	0.633336i	$-0.218315\pi$
$307$	−2.83052	−	4.90261i	−0.161546	−	0.279807i	−0.935423	+	0.353529i	$0.884982\pi$
$308$	−18.0933	+	1.58295i	−1.03096	+	0.0901972i
$309$	−17.9427	−	21.3497i	−1.02073	−	1.21454i
$310$	−34.1685	+	6.02482i	−1.94064	+	0.342187i
$311$	3.57257	−	16.1148i	0.202582	−	0.913789i	−0.761496	−	0.648170i	$-0.775535\pi$
$311$	3.57257	−	16.1148i	0.202582	−	0.913789i	0.964078	−	0.265619i	$-0.0855763\pi$
$312$	1.52452	+	3.26275i	0.0863092	+	0.184717i
$313$	−6.42138	−	2.02465i	−0.362958	−	0.114440i	0.113733	−	0.993511i	$-0.463719\pi$
$313$	−6.42138	−	2.02465i	−0.362958	−	0.114440i	−0.476690	+	0.879071i	$0.658164\pi$
$314$	10.3060	−	38.4624i	0.581599	−	2.17056i
$315$	−16.2899	+	28.3161i	−0.917829	+	1.59543i
$316$	−2.71225	+	20.6016i	−0.152576	+	1.15893i
$317$	18.2346	+	19.8996i	1.02416	+	1.11767i	0.992995	+	0.118157i	$0.0376986\pi$
$317$	18.2346	+	19.8996i	1.02416	+	1.11767i	0.0311623	+	0.999514i	$0.490079\pi$
$318$	1.72189	−	9.80974i	0.0965586	−	0.550103i
$319$	−4.23644	−	5.04879i	−0.237195	−	0.282678i
$320$	−21.6521	+	23.6291i	−1.21039	+	1.32091i
$321$	−7.24681	+	17.5338i	−0.404478	+	0.978639i
$322$	−7.23334	+	41.0223i	−0.403098	+	2.28608i
$323$	26.2321	−	0.282949i	1.45959	−	0.0157437i
$324$	−7.89911	+	21.9137i	−0.438839	+	1.21743i
$325$	2.75868	−	2.75868i	0.153024	−	0.153024i
$326$	−9.78488	−	6.23365i	−0.541934	−	0.345250i
$327$	−2.34487	−	5.64864i	−0.129672	−	0.312371i
$328$	−6.96323	−	6.38063i	−0.384480	−	0.352311i
$329$	23.2568	+	12.1067i	1.28219	+	0.667465i
$330$	10.1100	+	14.4148i	0.556539	+	0.793511i
$331$	−20.3908	−	9.50839i	−1.12078	−	0.522629i	−0.228244	−	0.973604i	$-0.573298\pi$
$331$	−20.3908	−	9.50839i	−1.12078	−	0.522629i	−0.892536	+	0.450975i	$0.851076\pi$
$332$	−15.5394	+	4.16377i	−0.852835	+	0.228517i
$333$	−17.8626	+	2.37981i	−0.978863	+	0.130413i
$334$	0.865677	−	1.12817i	0.0473677	−	0.0617308i
$335$	−15.2524	−	29.2997i	−0.833330	−	1.60081i
$336$	0.764437	+	17.2026i	0.0417035	+	0.938481i
$337$	−13.0771	−	2.89913i	−0.712356	−	0.157926i	−0.154657	−	0.987968i	$-0.549427\pi$
$337$	−13.0771	−	2.89913i	−0.712356	−	0.157926i	−0.557700	+	0.830043i	$0.688316\pi$
$338$	18.0318	+	12.6260i	0.980799	+	0.686763i
$339$	5.44941	−	10.4881i	0.295972	−	0.569633i
$340$	27.7110	+	8.40975i	1.50284	+	0.456083i
$341$	5.21917	+	9.03987i	0.282634	+	0.489536i
$342$	−26.2325	+	31.3613i	−1.41849	+	1.69582i
$343$	−5.13358	−	6.69022i	−0.277187	−	0.361238i
$344$	2.28074	+	6.26627i	0.122969	+	0.337855i
$345$	21.3992	−	7.80744i	1.15209	−	0.420338i
$346$	43.3369	+	22.5598i	2.32981	+	1.21282i
$347$	−12.6284	+	0.551368i	−0.677928	+	0.0295990i	−0.379996	−	0.924988i	$-0.624075\pi$
$347$	−12.6284	+	0.551368i	−0.677928	+	0.0295990i	−0.297932	+	0.954587i	$0.596297\pi$
$348$	13.3956	−	10.2953i	0.718081	−	0.551887i
$349$	−1.27797	+	0.894843i	−0.0684081	+	0.0478999i	−0.607280	−	0.794488i	$-0.707739\pi$
$349$	−1.27797	+	0.894843i	−0.0684081	+	0.0478999i	0.538872	+	0.842388i	$0.318851\pi$
$350$	−18.7731	+	7.77608i	−1.00347	+	0.415649i
$351$	−1.50865	−	8.44120i	−0.0805258	−	0.450558i
$352$	12.6458	+	5.23805i	0.674022	+	0.279189i
$353$	4.70103	+	0.828919i	0.250211	+	0.0441189i	0.297347	−	0.954770i	$-0.403898\pi$
$353$	4.70103	+	0.828919i	0.250211	+	0.0441189i	−0.0471360	+	0.998888i	$0.515009\pi$
$354$	22.6214	−	13.0838i	1.20231	−	0.695398i
$355$	−18.0310	+	8.40800i	−0.956987	+	0.446251i
$356$	10.0620	−	8.44298i	0.533282	−	0.447477i
$357$	25.2637	−	13.5249i	1.33710	−	0.715815i
$358$	31.4419	−	11.4439i	1.66176	−	0.604831i
$359$	8.73017	+	32.5814i	0.460761	+	1.71958i	0.670576	+	0.741841i	$0.266047\pi$
$359$	8.73017	+	32.5814i	0.460761	+	1.71958i	−0.209815	+	0.977741i	$0.567286\pi$
$360$	−8.64242	+	5.52467i	−0.455496	+	0.291176i
$361$	−18.6043	+	10.7412i	−0.979175	+	0.565327i
$362$	15.4416	+	29.6630i	0.811592	+	1.55905i
$363$	−7.88107	+	11.2739i	−0.413649	+	0.591727i
$364$	9.20874	+	14.4548i	0.482669	+	0.757639i
$365$	−23.6565	+	33.7850i	−1.23824	+	1.76839i
$366$	4.12244	−	18.6635i	0.215483	−	0.975559i
$367$	26.5449	+	8.36956i	1.38563	+	0.436888i	0.899470	−	0.436982i	$-0.143953\pi$
$367$	26.5449	+	8.36956i	1.38563	+	0.436888i	0.486160	+	0.873870i	$0.338397\pi$
$368$	7.30952	−	9.52596i	0.381035	−	0.496575i
$369$	12.1121	+	18.9473i	0.630528	+	0.986355i
$370$	−30.2382	−	17.4580i	−1.57201	−	0.907598i
$371$	0.469870	−	10.7618i	0.0243944	−	0.558725i
$372$	−23.7250	+	12.3738i	−1.23008	+	0.641553i
$373$	−1.58172	+	1.32722i	−0.0818983	+	0.0687208i	−0.682818	−	0.730589i	$-0.739246\pi$
$373$	−1.58172	+	1.32722i	−0.0818983	+	0.0687208i	0.600919	+	0.799310i	$0.294801\pi$
$374$	−0.840085	−	15.4220i	−0.0434397	−	0.797455i
$375$	−9.83499	−	7.53456i	−0.507877	−	0.389083i
$376$	4.72208	+	6.74382i	0.243523	+	0.347786i
$377$	−2.38004	+	5.74593i	−0.122578	+	0.295930i
$378$	−9.56524	+	43.6256i	−0.491983	+	2.24386i
$379$	5.66628	+	2.34705i	0.291057	+	0.120560i	0.523435	−	0.852066i	$-0.324650\pi$
$379$	5.66628	+	2.34705i	0.291057	+	0.120560i	−0.232377	+	0.972626i	$0.574650\pi$
$380$	−43.6289	+	9.67229i	−2.23811	+	0.496178i
$381$	2.33796	+	8.69843i	0.119777	+	0.445634i
$382$	−17.4717	−	37.4681i	−0.893928	−	1.91703i
$383$	21.1454	+	1.84999i	1.08048	+	0.0945299i	0.613468	−	0.789720i	$-0.289774\pi$
$383$	21.1454	+	1.84999i	1.08048	+	0.0945299i	0.467014	+	0.884250i	$0.345330\pi$
$384$	−7.04742	+	15.1439i	−0.359637	+	0.772807i
$385$	12.8652	+	14.0399i	0.655671	+	0.715539i
$386$	−40.7454	+	31.2650i	−2.07389	+	1.59135i
$387$	−1.40835	−	15.8152i	−0.0715904	−	0.803932i
$388$	1.36846	−	0.180161i	0.0694730	−	0.00914630i
$389$	22.1389	−	1.93690i	1.12248	−	0.0982046i	0.489235	−	0.872152i	$-0.337276\pi$
$389$	22.1389	−	1.93690i	1.12248	−	0.0982046i	0.633250	+	0.773948i	$0.281721\pi$
$390$	7.66039	−	14.7434i	0.387899	−	0.746559i
$391$	−19.5538	−	4.11422i	−0.988878	−	0.208065i
$392$	−1.99132	−	11.2933i	−0.100577	−	0.570398i
$393$	−2.65847	+	2.90572i	−0.134102	+	0.146574i
$394$	32.6810	−	17.0127i	1.64645	−	0.857086i
$395$	18.8679	−	10.8934i	0.949347	−	0.548106i
$396$	10.7855	+	8.24952i	0.541994	+	0.414554i
$397$	−11.5436	−	1.51974i	−0.579354	−	0.0762735i	−0.164847	−	0.986319i	$-0.552713\pi$
$397$	−11.5436	−	1.51974i	−0.579354	−	0.0762735i	−0.414508	+	0.910046i	$0.636046\pi$
$398$	3.79990	−	3.48197i	0.190472	−	0.174535i
$399$	−23.7310	+	37.3139i	−1.18803	+	1.86803i
$400$	5.83497	+	0.510494i	0.291749	+	0.0255247i
$401$	−12.0767	+	0.527280i	−0.603082	+	0.0263311i	−0.343126	−	0.939289i	$-0.611486\pi$
$401$	−12.0767	+	0.527280i	−0.603082	+	0.0263311i	−0.259956	+	0.965620i	$0.583708\pi$
$402$	−31.9578	−	31.9084i	−1.59391	−	1.59144i
$403$	5.29248	−	8.30753i	0.263637	−	0.413827i
$404$		−	25.7806i		−	1.28263i
$405$	23.2699	−	7.41634i	1.15629	−	0.368521i
$406$	22.9053	−	22.9053i	1.13677	−	1.13677i
$407$	−1.82412	+	10.3451i	−0.0904181	+	0.512786i
$408$	8.99727	−	0.104020i	0.445431	−	0.00514974i
$409$	21.6304	+	7.87282i	1.06955	+	0.389286i	0.816010	−	0.578038i	$-0.196182\pi$
$409$	21.6304	+	7.87282i	1.06955	+	0.389286i	0.253544	+	0.967324i	$0.418404\pi$
$410$	−3.79755	+	43.4062i	−0.187547	+	2.14368i
$411$	−3.61401	−	0.634361i	−0.178266	−	0.0312907i
$412$	−14.2531	−	39.1602i	−0.702202	−	1.92928i
$413$	22.4234	−	17.2061i	1.10338	−	0.846655i
$414$	24.6777	−	18.9967i	1.21284	−	0.933638i
$415$	13.3819	+	10.2683i	0.656891	+	0.504050i
$416$	−1.12574	−	12.8672i	−0.0551939	−	0.630869i
$417$	−18.8475	−	17.2437i	−0.922966	−	0.844428i
$418$	12.8059	+	20.1013i	0.626358	+	0.983185i
$419$	−8.57297	+	5.46158i	−0.418817	+	0.266816i	−0.729882	−	0.683573i	$-0.760425\pi$
$419$	−8.57297	+	5.46158i	−0.418817	+	0.266816i	0.311066	+	0.950388i	$0.399314\pi$
$420$	−37.3702	+	31.4067i	−1.82348	+	1.53249i
$421$	11.2228	−	13.3749i	0.546968	−	0.651851i	−0.419767	−	0.907632i	$-0.637888\pi$
$421$	11.2228	−	13.3749i	0.546968	−	0.651851i	0.966735	+	0.255781i	$0.0823327\pi$
$422$	−48.8336	+	6.42907i	−2.37718	+	0.312962i
$423$	−6.73294	−	18.4098i	−0.327367	−	0.895115i
$424$	1.69118	−	2.92920i	0.0821308	−	0.142255i
$425$	−3.43242	−	9.12310i	−0.166497	−	0.442535i
$426$	−20.0396	+	18.3915i	−0.970923	+	0.891072i
$427$	1.80171	−	20.5937i	0.0871910	−	0.996598i
$428$	−19.1533	+	20.9021i	−0.925808	+	1.01034i
$429$	−4.95636	−	0.648611i	−0.239295	−	0.0313152i
$430$	16.5298	−	25.9465i	0.797137	−	1.25125i
$431$	−1.99769	−	4.82284i	−0.0962251	−	0.232308i	0.868436	−	0.495801i	$-0.165125\pi$
$431$	−1.99769	−	4.82284i	−0.0962251	−	0.232308i	−0.964661	+	0.263493i	$0.915125\pi$
$432$	8.25225	−	9.88120i	0.397037	−	0.475410i
$433$	11.6637	+	11.6637i	0.560523	+	0.560523i	0.929456	−	0.368933i	$-0.120277\pi$
$433$	11.6637	+	11.6637i	0.560523	+	0.560523i	−0.368933	+	0.929456i	$0.620277\pi$
$434$	−42.0255	+	29.4265i	−2.01729	+	1.41252i
$435$	−17.1139	−	4.57145i	−0.820548	−	0.219184i
$436$	−0.398645	−	9.13048i	−0.0190917	−	0.437271i
$437$	29.4080	−	9.27231i	1.40678	−	0.443555i
$438$	−16.9143	+	53.7907i	−0.808198	+	2.57022i
$439$	0.740149	−	16.9522i	0.0353254	−	0.809084i	−0.895816	−	0.444425i	$-0.853408\pi$
$439$	0.740149	−	16.9522i	0.0353254	−	0.809084i	0.931141	−	0.364659i	$-0.118814\pi$
$440$	1.54757	+	5.77560i	0.0737774	+	0.275341i
$441$	−2.33761	+	27.2044i	−0.111315	+	1.29545i
$442$	−12.5426	+	7.42301i	−0.596592	+	0.353076i
$443$	−27.9615	−	23.4625i	−1.32849	−	1.11474i	−0.984428	−	0.175791i	$-0.943752\pi$
$443$	−27.9615	−	23.4625i	−1.32849	−	1.11474i	−0.344064	−	0.938946i	$-0.611804\pi$
$444$	−26.2942	−	5.80791i	−1.24787	−	0.275631i
$445$	−13.4453	−	2.98075i	−0.637368	−	0.141301i
$446$	−24.8770	+	4.38648i	−1.17796	+	0.207706i
$447$	−7.14656	−	40.3474i	−0.338021	−	1.90836i
$448$	−14.2506	+	45.1970i	−0.673276	+	2.13536i
$449$	16.1055	+	12.3582i	0.760067	+	0.583220i	0.914406	−	0.404798i	$-0.132658\pi$
$449$	16.1055	+	12.3582i	0.760067	+	0.583220i	−0.154339	+	0.988018i	$0.549325\pi$
$450$	14.2836	+	5.17377i	0.673337	+	0.243894i
$451$	12.6622	−	3.39282i	0.596239	−	0.159762i
$452$	13.0215	−	11.9320i	0.612480	−	0.561234i
$453$	−3.48611	−	39.4940i	−0.163792	−	1.85559i
$454$	10.4306	−	3.28876i	0.489533	−	0.154349i
$455$	6.14604	−	16.8861i	0.288131	−	0.791633i
$456$	−12.0195	+	6.95185i	−0.562862	+	0.325550i
$457$	15.0625	+	21.5115i	0.704594	+	1.00627i	0.998724	+	0.0504996i	$0.0160813\pi$
$457$	15.0625	+	21.5115i	0.704594	+	1.00627i	−0.294130	+	0.955766i	$0.595030\pi$
$458$	9.80100			0.457971
$459$	−20.7652	−	5.27324i	−0.969236	−	0.246134i
$460$	34.0387			1.58706
$461$	2.91571	+	4.16406i	0.135798	+	0.193940i	0.881291	−	0.472574i	$-0.156675\pi$
$461$	2.91571	+	4.16406i	0.135798	+	0.193940i	−0.745493	+	0.666513i	$0.767786\pi$
$462$	22.5569	+	13.0000i	1.04944	+	0.604813i
$463$	−0.510791	+	1.40339i	−0.0237385	+	0.0652209i	−0.950996	−	0.309204i	$-0.899938\pi$
$463$	−0.510791	+	1.40339i	−0.0237385	+	0.0652209i	0.927257	+	0.374425i	$0.122160\pi$
$464$	−8.90519	+	2.80779i	−0.413413	+	0.130349i
$465$	25.4358	+	11.8369i	1.17956	+	0.548924i
$466$	−32.3908	+	29.6807i	−1.50047	+	1.37493i
$467$	19.9533	−	5.34648i	0.923331	−	0.247406i	0.234322	−	0.972159i	$-0.424713\pi$
$467$	19.9533	−	5.34648i	0.923331	−	0.247406i	0.689009	+	0.724753i	$0.258046\pi$
$468$	2.20550	−	12.6224i	0.101949	−	0.583469i
$469$	−38.7502	−	29.7341i	−1.78932	−	1.37299i
$470$	11.4212	−	36.2233i	0.526819	−	1.67086i
$471$	−24.6492	+	20.7157i	−1.13577	+	0.954528i
$472$	8.73991	−	1.54108i	0.402287	−	0.0709340i
$473$	−9.03628	−	2.00329i	−0.415488	−	0.0921116i
$474$	20.1063	−	21.9763i	0.923511	−	1.00940i
$475$	11.5227	+	9.66866i	0.528696	+	0.443629i
$476$	42.3920	−	6.04686i	1.94303	−	0.277157i
$477$	−5.68587	+	5.70352i	−0.260338	+	0.261146i
$478$	−5.41556	−	20.2111i	−0.247702	−	0.924436i
$479$	0.426259	−	9.76294i	0.0194763	−	0.446080i	−0.964095	−	0.265559i	$-0.914444\pi$
$479$	0.426259	−	9.76294i	0.0194763	−	0.446080i	0.983571	−	0.180522i	$-0.0577786\pi$
$480$	35.9102	−	7.99030i	1.63907	−	0.364706i
$481$	9.45394	−	2.98082i	0.431063	−	0.135913i
$482$	1.95876	+	44.8629i	0.0892189	+	2.04345i
$483$	23.7988	−	23.8357i	1.08288	−	1.08456i
$484$	−16.8375	+	11.7898i	−0.765342	+	0.535898i
$485$	−1.02331	−	1.02331i	−0.0464663	−	0.0464663i
$486$	27.2776	−	19.2579i	1.23734	−	0.873556i
$487$	2.66960	+	6.44498i	0.120971	+	0.292050i	0.972752	−	0.231848i	$-0.0744772\pi$
$487$	2.66960	+	6.44498i	0.120971	+	0.292050i	−0.851781	+	0.523898i	$0.824477\pi$
$488$	3.48760	−	5.47444i	0.157876	−	0.247816i
$489$	3.59680	+	8.66445i	0.162653	+	0.391820i
$490$	−35.7421	+	39.0057i	−1.61466	+	1.76210i
$491$	0.584886	−	6.68528i	0.0263955	−	0.301702i	−0.971509	−	0.237002i	$-0.923835\pi$
$491$	0.584886	−	6.68528i	0.0263955	−	0.301702i	0.997905	−	0.0647005i	$-0.0206092\pi$
$492$	7.29857	+	32.8014i	0.329045	+	1.47880i
$493$	10.6209	+	11.3426i	0.478339	+	0.510843i
$494$	11.2454	−	19.4776i	0.505955	−	0.876339i
$495$	−0.0220605	−	14.2370i	−0.000991544	−	0.639907i
$496$	14.6619	−	1.93027i	0.658338	−	0.0866719i
$497$	−18.9098	+	22.5358i	−0.848219	+	1.01087i
$498$	21.6761	+	7.87044i	0.971330	+	0.352683i
$499$	11.4116	−	7.27000i	0.510854	−	0.325450i	−0.256639	−	0.966507i	$-0.582615\pi$
$499$	11.4116	−	7.27000i	0.510854	−	0.325450i	0.767493	+	0.641058i	$0.221504\pi$
$500$	−9.94730	−	15.6141i	−0.444857	−	0.698285i
$501$	−1.09638	+	0.346621i	−0.0489826	+	0.0154859i
$502$	−3.38520	−	38.6930i	−0.151089	−	1.72695i
$503$	14.7736	+	11.3362i	0.658723	+	0.505456i	0.883184	−	0.469027i	$-0.155395\pi$
$503$	14.7736	+	11.3362i	0.658723	+	0.505456i	−0.224461	+	0.974483i	$0.572062\pi$
$504$	−8.12958	+	12.8046i	−0.362120	+	0.570363i
$505$	−21.4447	+	16.4551i	−0.954275	+	0.732241i
$506$	−6.20905	−	17.0592i	−0.276026	−	0.758376i
$507$	−6.10082	−	16.7215i	−0.270947	−	0.742630i
$508$	−1.17307	+	13.4082i	−0.0520464	+	0.594893i
$509$	−11.8031	−	4.29598i	−0.523163	−	0.190416i	0.0669200	−	0.997758i	$-0.478683\pi$
$509$	−11.8031	−	4.29598i	−0.523163	−	0.190416i	−0.590083	+	0.807343i	$0.700905\pi$
$510$	−25.6495	−	32.6388i	−1.13578	−	1.44527i
$511$	−10.5902	+	60.0599i	−0.468482	+	2.65689i
$512$	18.1268	−	18.1268i	0.801099	−	0.801099i
$513$	31.9144	−	8.63100i	1.40906	−	0.381068i
$514$		−	28.9484i		−	1.27686i
$515$	−23.4766	+	36.8509i	−1.03450	+	1.62385i
$516$	6.12305	−	22.9226i	0.269552	−	1.00911i
$517$	−11.4160	+	0.498432i	−0.502074	+	0.0219210i
$518$	−51.4331	−	4.49981i	−2.25984	−	0.197711i
$519$	−18.2692	−	35.0285i	−0.801929	−	1.53758i
$520$	4.16002	−	3.81196i	0.182429	−	0.167165i
$521$	−14.2881	−	1.88106i	−0.625973	−	0.0824108i	−0.189135	−	0.981951i	$-0.560568\pi$
$521$	−14.2881	−	1.88106i	−0.625973	−	0.0824108i	−0.436838	+	0.899540i	$0.643902\pi$
$522$	−24.1932	+	1.09386i	−1.05891	+	0.0478770i
$523$	−4.48893	+	2.59169i	−0.196287	+	0.113327i	−0.594923	−	0.803783i	$-0.702817\pi$
$523$	−4.48893	+	2.59169i	−0.196287	+	0.113327i	0.398635	+	0.917110i	$0.369484\pi$
$524$	−5.22015	+	2.71744i	−0.228043	+	0.118712i
$525$	16.0441	+	3.54386i	0.700223	+	0.154667i
$526$	2.62275	+	14.8743i	0.114357	+	0.648552i
$527$	−13.4462	−	20.6123i	−0.585726	−	0.897885i
$528$	−4.03713	−	6.32621i	−0.175694	−	0.275313i
$529$	−0.485062	+	0.0424374i	−0.0210897	+	0.00184511i
$530$	−15.4709	+	2.03678i	−0.672011	+	0.0884720i
$531$	−21.0535	−	1.80908i	−0.913645	−	0.0785072i
$532$	−52.4244	+	40.2266i	−2.27289	+	1.74405i
$533$	−8.35717	−	9.12025i	−0.361989	−	0.395042i
$534$	−18.7554	+	1.65553i	−0.811624	+	0.0716416i
$535$	29.6117	+	2.59069i	1.28023	+	0.112005i
$536$	−6.48152	−	13.8997i	−0.279959	−	0.600374i
$537$	−26.1394	−	6.98234i	−1.12800	−	0.301310i
$538$	−38.4871	+	8.53238i	−1.65930	+	0.367857i
$539$	14.7052	+	6.09108i	0.633396	+	0.262361i
$540$	36.4645	+	1.50717i	1.56918	+	0.0648583i
$541$	−3.30520	+	7.97946i	−0.142102	+	0.343064i	−0.978867	−	0.204498i	$-0.934444\pi$
$541$	−3.30520	+	7.97946i	−0.142102	+	0.343064i	0.836765	+	0.547562i	$0.184444\pi$
$542$	19.1087	+	27.2900i	0.820789	+	1.17221i
$543$	3.50881	−	26.8126i	0.150577	−	1.15064i
$544$	−30.4423	−	10.7097i	−1.30520	−	0.459174i
$545$	−7.34043	+	6.15935i	−0.314429	+	0.263838i
$546$	1.05262	−	24.5452i	0.0450478	−	1.05044i
$547$	0.299136	−	6.85134i	0.0127901	−	0.292942i	−0.981858	−	0.189619i	$-0.939275\pi$
$547$	0.299136	−	6.85134i	0.0127901	−	0.292942i	0.994648	−	0.103323i	$-0.0329475\pi$
$548$	−4.74841	−	2.74150i	−0.202842	−	0.117111i
$549$	−11.3786	+	10.4591i	−0.485629	+	0.446383i
$550$	5.39105	−	7.02576i	0.229875	−	0.299579i
$551$	−22.8690	−	7.21057i	−0.974253	−	0.307181i
$552$	10.0842	−	3.18813i	0.429212	−	0.135696i
$553$	18.4781	−	26.3895i	0.785771	−	1.12220i
$554$	19.6250	+	30.8050i	0.833786	+	1.30878i
$555$	11.9518	+	25.5789i	0.507325	+	1.08576i
$556$	−17.6262	−	33.8597i	−0.747519	−	1.43597i
$557$	−4.03993	+	2.33245i	−0.171177	+	0.0988292i	−0.583141	−	0.812371i	$-0.698176\pi$
$557$	−4.03993	+	2.33245i	−0.171177	+	0.0988292i	0.411964	+	0.911200i	$0.364843\pi$
$558$	38.0357	+	4.94755i	1.61018	+	0.209447i
$559$	2.26056	+	8.43651i	0.0956113	+	0.356826i
$560$	25.3518	−	9.22729i	1.07131	−	0.389924i
$561$	−6.58807	+	10.6099i	−0.278148	+	0.447950i
$562$	−9.58621	+	8.04378i	−0.404370	+	0.339306i
$563$	−12.5577	+	5.85575i	−0.529243	+	0.246790i	−0.668824	−	0.743420i	$-0.733202\pi$
$563$	−12.5577	+	5.85575i	−0.529243	+	0.246790i	0.139581	+	0.990211i	$0.455424\pi$
$564$	−0.0226940	−	29.2919i	−0.000955592	−	1.23341i
$565$	−18.2365	−	3.21559i	−0.767216	−	0.135281i
$566$	−17.6939	−	7.32905i	−0.743730	−	0.308063i
$567$	26.5503	−	24.4807i	1.11501	−	1.02809i
$568$	−8.53404	+	3.53492i	−0.358080	+	0.148322i
$569$	−11.5027	+	8.05429i	−0.482219	+	0.337653i	−0.789277	−	0.614038i	$-0.789544\pi$
$569$	−11.5027	+	8.05429i	−0.482219	+	0.337653i	0.307058	+	0.951691i	$0.400655\pi$
$570$	59.2011	+	24.4682i	2.47966	+	1.02486i
$571$	35.3458	−	1.54323i	1.47918	−	0.0645822i	0.710263	−	0.703936i	$-0.248576\pi$
$571$	35.3458	−	1.54323i	1.47918	−	0.0645822i	0.768913	+	0.639354i	$0.220798\pi$
$572$	−6.62549	−	3.44901i	−0.277026	−	0.144210i
$573$	−5.77940	+	32.9257i	−0.241438	+	1.37549i
$574$	22.0360	+	60.5434i	0.919765	+	2.52703i
$575$	−6.97470	−	9.08961i	−0.290865	−	0.379063i
$576$	30.6563	−	17.7628i	1.27734	−	0.740117i
$577$	−21.1267	−	36.5925i	−0.879516	−	1.52337i	−0.851873	−	0.523748i	$-0.824533\pi$
$577$	−21.1267	−	36.5925i	−0.879516	−	1.52337i	−0.0276421	−	0.999618i	$-0.508800\pi$
$578$	3.95544	+	36.1987i	0.164525	+	1.50567i
$579$	41.4880	−	1.84361i	1.72418	−	0.0766178i
$580$	−21.6830	−	15.1826i	−0.900336	−	0.630422i
$581$	24.3504	+	5.39836i	1.01023	+	0.223962i
$582$	−1.75570	−	0.912231i	−0.0727761	−	0.0378132i
$583$	2.16775	+	4.16421i	0.0897790	+	0.172464i
$584$	−11.6574	+	15.1922i	−0.482386	+	0.628657i
$585$	−11.9072	+	6.22196i	−0.492302	+	0.257246i
$586$	16.0156	−	4.29137i	0.661598	−	0.177275i
$587$	−8.17318	−	3.81122i	−0.337343	−	0.157306i	0.246563	−	0.969127i	$-0.420699\pi$
$587$	−8.17318	−	3.81122i	−0.337343	−	0.157306i	−0.583906	+	0.811821i	$0.698477\pi$
$588$	−17.2148	+	36.9920i	−0.709926	+	1.52553i
$589$	33.6864	+	17.5360i	1.38802	+	0.722559i
$590$	−30.1865	−	27.6609i	−1.24276	−	1.13878i
$591$	−29.5406	−	3.86581i	−1.21514	−	0.159018i
$592$	12.5517	+	7.99629i	0.515870	+	0.328646i
$593$	29.5733	−	29.5733i	1.21443	−	1.21443i	0.244874	−	0.969555i	$-0.421254\pi$
$593$	29.5733	−	29.5733i	1.21443	−	1.21443i	0.969555	−	0.244874i	$-0.0787465\pi$
$594$	−5.89621	−	18.5499i	−0.241924	−	0.761113i
$595$	−32.0876	−	31.4028i	−1.31546	−	1.28739i
$596$	10.6324	−	60.2995i	0.435521	−	2.46996i
$597$	−4.13147	+	0.547175i	−0.169090	+	0.0223944i
$598$	−11.5736	+	12.6304i	−0.473279	+	0.516494i
$599$	3.47172	+	4.13743i	0.141851	+	0.169051i	0.832292	−	0.554337i	$-0.187028\pi$
$599$	3.47172	+	4.13743i	0.141851	+	0.169051i	−0.690442	+	0.723388i	$0.742584\pi$
$600$	3.95473	+	3.31320i	0.161451	+	0.135261i
$601$	10.7307	+	11.7105i	0.437716	+	0.477683i	0.916377	−	0.400317i	$-0.131100\pi$
$601$	10.7307	+	11.7105i	0.437716	+	0.477683i	−0.478661	+	0.878000i	$0.658878\pi$
$602$	5.93775	−	45.1017i	0.242005	−	1.83821i
$603$	6.39683	+	35.9524i	0.260499	+	1.46409i
$604$	15.3339	−	57.2267i	0.623926	−	2.32852i
$605$	20.5539	+	6.48061i	0.835633	+	0.263474i
$606$	−21.1732	+	30.2883i	−0.860101	+	1.23038i
$607$	−7.08873	+	31.9752i	−0.287723	+	1.29783i	0.585564	+	0.810626i	$0.300873\pi$
$607$	−7.08873	+	31.9752i	−0.287723	+	1.29783i	−0.873287	+	0.487206i	$0.838016\pi$
$608$	49.0429	−	8.64758i	1.98895	−	0.350706i
$609$	−25.7918	+	4.56839i	−1.04514	+	0.185121i
$610$	−29.8320	+	2.60996i	−1.20786	+	0.105674i
$611$	5.39147	+	9.33830i	0.218116	+	0.377787i
$612$	−26.4492	−	18.0378i	−1.06914	−	0.729136i
$613$	−3.68934	+	6.39012i	−0.149011	+	0.258094i	−0.930862	−	0.365371i	$-0.880942\pi$
$613$	−3.68934	+	6.39012i	−0.149011	+	0.258094i	0.781851	+	0.623465i	$0.214276\pi$
$614$	−5.12468	+	10.9899i	−0.206815	+	0.443517i
$615$	22.6262	−	27.0074i	0.912378	−	1.08904i
$616$	5.68323	+	6.77301i	0.228984	+	0.272892i
$617$	21.0687	+	19.3059i	0.848195	+	0.777227i	0.976729	−	0.214478i	$-0.0688050\pi$
$617$	21.0687	+	19.3059i	0.848195	+	0.777227i	−0.128534	+	0.991705i	$0.541027\pi$
$618$	−15.4163	+	57.7133i	−0.620135	+	2.32157i
$619$	−4.44690	−	20.0587i	−0.178736	−	0.806227i	−0.978555	−	0.205985i	$-0.933960\pi$
$619$	−4.44690	−	20.0587i	−0.178736	−	0.806227i	0.799819	−	0.600241i	$-0.204929\pi$
$620$	29.6440	+	29.6440i	1.19053	+	1.19053i
$621$	−25.1557	+	1.15691i	−1.00946	+	0.0464251i
$622$	−32.6649	+	13.5302i	−1.30974	+	0.542513i
$623$	−19.8813	+	4.40757i	−0.796526	+	0.176586i
$624$	−3.53612	+	6.13570i	−0.141558	+	0.245625i
$625$	−10.6818	+	29.3480i	−0.427273	+	1.17392i
$626$	4.33683	+	13.7547i	0.173334	+	0.549747i
$627$	0.825727	−	19.2546i	0.0329764	−	0.768954i
$628$	−45.2122	+	16.4559i	−1.80416	+	0.656662i
$629$	2.96767	−	24.5882i	0.118329	−	0.980397i
$630$	69.6982	−	6.20664i	2.77684	−	0.247278i
$631$	0.563670	+	0.151035i	0.0224394	+	0.00601261i	0.270021	−	0.962854i	$-0.412969\pi$
$631$	0.563670	+	0.151035i	0.0224394	+	0.00601261i	−0.247582	+	0.968867i	$0.579636\pi$
$632$	8.97257	−	4.67082i	0.356910	−	0.185795i
$633$	35.3422	+	18.3632i	1.40473	+	0.729871i
$634$	12.5133	−	56.4438i	0.496966	−	2.24167i
$635$	11.9019	−	7.58234i	0.472312	−	0.300896i
$636$	−10.9029	+	5.09441i	−0.432329	+	0.202006i
$637$	−1.30907	−	14.9627i	−0.0518671	−	0.592843i
$638$	−3.65386	+	13.6364i	−0.144658	+	0.539870i
$639$	21.8015	−	2.90459i	0.862452	−	0.114904i
$640$	25.9461	+	3.41587i	1.02561	+	0.135024i
$641$	−13.4702	−	0.588123i	−0.532042	−	0.0232295i	−0.223976	−	0.974595i	$-0.571904\pi$
$641$	−13.4702	−	0.588123i	−0.532042	−	0.0232295i	−0.308066	+	0.951365i	$0.599682\pi$
$642$	39.6688	−	8.82661i	1.56560	−	0.348358i
$643$	5.42761	+	17.2142i	0.214044	+	0.678861i	0.998292	+	0.0584137i	$0.0186043\pi$
$643$	5.42761	+	17.2142i	0.214044	+	0.678861i	−0.784249	+	0.620447i	$0.786951\pi$
$644$	45.6165	−	21.2713i	1.79754	−	0.838208i
$645$	−22.9755	+	9.53763i	−0.904660	+	0.375544i
$646$	−32.7254	−	45.6800i	−1.28756	−	1.79726i
$647$	−32.7101			−1.28597			−0.642983	−	0.765880i	$-0.722304\pi$
$647$	−32.7101			−1.28597			−0.642983	+	0.765880i	$0.722304\pi$
$648$	10.9440	−	2.96883i	0.429923	−	0.116627i
$649$	−4.71389	+	11.3803i	−0.185036	+	0.446717i
$650$	−8.22980	−	1.45113i	−0.322799	−	0.0569182i
$651$	41.4846	−	0.0321404i	1.62591	−	0.00125968i
$652$	0.611482	+	14.0052i	0.0239475	+	0.548488i
$653$	18.8615	−	36.2326i	0.738107	−	1.41789i	−0.164036	−	0.986454i	$-0.552451\pi$
$653$	18.8615	−	36.2326i	0.738107	−	1.41789i	0.902143	−	0.431437i	$-0.141993\pi$
$654$	−7.03037	+	11.0544i	−0.274909	+	0.432259i
$655$	5.59230	+	2.60773i	0.218509	+	0.101892i
$656$	2.42411	−	18.4129i	0.0946456	−	0.718904i
$657$	36.1302	−	27.8127i	1.40957	−	1.08508i
$658$	−7.33061	−	55.6815i	−0.285777	−	2.17069i
$659$	−23.4999	+	28.0061i	−0.915426	+	1.09096i	0.0801291	+	0.996784i	$0.474467\pi$
$659$	−23.4999	+	28.0061i	−0.915426	+	1.09096i	−0.995555	+	0.0941780i	$0.969978\pi$
$660$	7.26081	−	19.9971i	0.282627	−	0.778387i
$661$	−25.3426	−	17.7450i	−0.985711	−	0.690202i	−0.0347125	−	0.999397i	$-0.511052\pi$
$661$	−25.3426	−	17.7450i	−0.985711	−	0.690202i	−0.950999	+	0.309195i	$0.899940\pi$
$662$	8.36856	+	47.4605i	0.325253	+	1.84460i
$663$	11.7514	+	0.891352i	0.456386	+	0.0346172i
$664$	5.99928	+	5.03400i	0.232817	+	0.195357i
$665$	66.9223	+	17.9318i	2.59513	+	0.695364i
$666$	26.1218	+	28.4184i	1.01220	+	1.10119i
$667$	15.8175	+	9.13225i	0.612457	+	0.353602i
$668$	−1.71662	−	0.0749490i	−0.0664178	−	0.00289987i
$669$	18.5190	+	8.61809i	0.715986	+	0.333195i
$670$	−32.6709	+	62.7602i	−1.26219	+	2.42464i
$671$	3.80753	+	8.16527i	0.146988	+	0.315217i
$672$	43.1314	−	33.1490i	1.66383	−	1.27875i
$673$	−6.72679	−	30.3426i	−0.259299	−	1.16962i	−0.911410	−	0.411498i	$-0.865006\pi$
$673$	−6.72679	−	30.3426i	−0.259299	−	1.16962i	0.652112	−	0.758123i	$-0.273883\pi$
$674$	10.9797	+	26.5074i	0.422924	+	1.02103i
$675$	−7.06931	−	10.0462i	−0.272098	−	0.386680i
$676$		−	26.5982i		−	1.02301i
$677$	29.5859	+	18.8483i	1.13708	+	0.724398i	0.965405	−	0.260756i	$-0.0839717\pi$
$677$	29.5859	+	18.8483i	1.13708	+	0.724398i	0.171673	+	0.985154i	$0.445083\pi$
$678$	−25.0979	+	3.32398i	−0.963878	+	0.127657i
$679$	−2.01087	−	0.731896i	−0.0771700	−	0.0280876i
$680$	−4.38394	−	13.3984i	−0.168116	−	0.513806i
$681$	−8.43636	−	2.65279i	−0.323282	−	0.101655i
$682$	9.44934	−	20.2642i	0.361834	−	0.775955i
$683$	13.3217	+	17.3611i	0.509739	+	0.664305i	0.975345	−	0.220687i	$-0.0708300\pi$
$683$	13.3217	+	17.3611i	0.509739	+	0.664305i	−0.465605	+	0.884992i	$0.654163\pi$
$684$	49.2217	+	4.22950i	1.88204	+	0.161719i
$685$	0.750370	+	5.69963i	0.0286702	+	0.217772i
$686$	−5.43171	+	17.2272i	−0.207384	+	0.657737i
$687$	−6.49545	−	4.54067i	−0.247817	−	0.173237i
$688$	−7.52123	+	10.7414i	−0.286744	+	0.409513i
$689$	2.54101	−	3.62894i	0.0968047	−	0.138251i
$690$	−39.9903	−	27.9554i	−1.52241	−	1.06424i
$691$	−5.99126	+	19.0018i	−0.227918	+	0.722864i	0.768618	+	0.639708i	$0.220945\pi$
$691$	−5.99126	+	19.0018i	−0.227918	+	0.722864i	−0.996537	+	0.0831565i	$0.973500\pi$
$692$	−7.70557	−	58.5296i	−0.292922	−	2.22496i
$693$	−8.92653	−	19.0658i	−0.339091	−	0.724251i
$694$	16.4828	+	21.4808i	0.625678	+	0.815399i
$695$	−16.9146	+	36.2735i	−0.641608	+	1.37593i
$696$	−7.84576	−	2.46708i	−0.297393	−	0.0935144i
$697$	−29.3741	+	9.61115i	−1.11262	+	0.364048i
$698$	3.14024	+	1.14295i	0.118860	+	0.0432615i
$699$	35.2171	−	4.66418i	1.33203	−	0.176415i
$700$	20.7075	+	13.1922i	0.782671	+	0.498617i
$701$		−	15.7351i		−	0.594308i	−0.954830	−	0.297154i	$-0.903962\pi$
$701$		−	15.7351i		−	0.594308i	0.954830	−	0.297154i	$-0.0960375\pi$
$702$	−12.9577	+	13.0180i	−0.489056	+	0.491334i
$703$	14.6257	+	35.3095i	0.551618	+	1.33172i
$704$	−4.47026	−	20.1640i	−0.168479	−	0.759960i
$705$	−24.3510	+	18.7151i	−0.917110	+	0.704853i
$706$	−4.32127	−	9.26700i	−0.162633	−	0.348768i
$707$	−18.4558	+	35.4532i	−0.694101	+	1.33336i
$708$	−28.6282	−	13.3225i	−1.07591	−	0.500692i
$709$	41.2453	+	1.80081i	1.54900	+	0.0676309i	0.802054	−	0.597252i	$-0.203741\pi$
$709$	41.2453	+	1.80081i	1.54900	+	0.0676309i	0.746948	+	0.664883i	$0.231519\pi$
$710$	36.9060	+	21.3077i	1.38506	+	0.799663i
$711$	−23.5064	+	5.24947i	−0.881559	+	0.196871i
$712$	−6.17628	−	1.65493i	−0.231466	−	0.0620211i
$713$	−22.1595	−	18.5940i	−0.829879	−	0.696351i
$714$	−54.7705	−	27.7117i	−2.04973	−	1.03708i
$715$	1.35994	+	7.71260i	0.0508588	+	0.288435i
$716$	−33.1182	−	23.1896i	−1.23768	−	0.866635i
$717$	−5.77447	+	15.9036i	−0.215652	+	0.593929i
$718$	46.4425	−	55.3480i	1.73322	−	2.06557i
$719$	−1.01735	−	7.72751i	−0.0379406	−	0.288187i	−0.999888	−	0.0149534i	$-0.995240\pi$
$719$	−1.01735	−	7.72751i	−0.0379406	−	0.288187i	0.961948	−	0.273234i	$-0.0880933\pi$
$720$	−18.6468	−	7.68991i	−0.694924	−	0.286586i
$721$	−8.43317	+	64.0563i	−0.314068	+	2.38558i
$722$	41.7043	+	19.4470i	1.55207	+	0.723743i
$723$	19.4862	−	30.6396i	0.724700	−	1.13950i
$724$	18.6582	−	35.8421i	0.693427	−	1.33206i
$725$	0.388633	+	8.90116i	0.0144335	+	0.330581i
$726$	29.4643	−	0.0228276i	1.09352	−	0.000847213i
$727$	−38.8277	−	6.84637i	−1.44004	−	0.253918i	−0.601550	−	0.798835i	$-0.705450\pi$
$727$	−38.8277	−	6.84637i	−1.44004	−	0.253918i	−0.838490	+	0.544917i	$0.816561\pi$
$728$	3.19285	−	7.70822i	0.118335	−	0.285686i
$729$	−26.9997	+	0.125510i	−0.999989	+	0.00464852i
$730$	88.3447			3.26978
$731$	21.5300	+	3.55733i	0.796317	+	0.131573i
$732$	−21.3301	+	8.85457i	−0.788382	+	0.327274i
$733$	−21.2073	+	9.88914i	−0.783311	+	0.365264i	−0.772775	−	0.634681i	$-0.781132\pi$
$733$	−21.2073	+	9.88914i	−0.783311	+	0.365264i	−0.0105364	+	0.999944i	$0.503354\pi$
$734$	−17.9277	−	56.8594i	−0.661723	−	2.09872i
$735$	41.7583	−	9.29154i	1.54028	−	0.342723i
$736$	−37.8958	−	1.65456i	−1.39686	−	0.0609881i
$737$	21.1048	+	2.77850i	0.777406	+	0.102347i
$738$	18.3645	−	44.5310i	0.676008	−	1.63921i
$739$	−6.34305	+	23.6726i	−0.233333	+	0.870810i	0.745560	+	0.666438i	$0.232182\pi$
$739$	−6.34305	+	23.6726i	−0.233333	+	0.870810i	−0.978893	+	0.204372i	$0.934485\pi$
$740$	3.67704	+	42.0288i	0.135171	+	1.54501i
$741$	−16.4764	+	7.69862i	−0.605276	+	0.282816i
$742$	−19.4603	+	12.3976i	−0.714410	+	0.455129i
$743$	8.59926	−	38.7888i	0.315476	−	1.42302i	−0.510772	−	0.859716i	$-0.670640\pi$
$743$	8.59926	−	38.7888i	0.315476	−	1.42302i	0.826249	−	0.563306i	$-0.190471\pi$
$744$	11.5588	+	6.00573i	0.423765	+	0.220181i
$745$	−56.9444	+	29.6434i	−2.08628	+	1.08605i
$746$	4.27209	+	1.14470i	0.156412	+	0.0419106i
$747$	−10.7192	−	15.2582i	−0.392195	−	0.558270i
$748$	−14.6823	+	11.5199i	−0.536839	+	0.421208i
$749$	41.3028	−	15.0330i	1.50917	−	0.549293i
$750$	−1.13704	+	26.5138i	−0.0415188	+	0.968148i
$751$	−10.2744	−	32.5861i	−0.374917	−	1.18908i	−0.933177	−	0.359418i	$-0.882975\pi$
$751$	−10.2744	−	32.5861i	−0.374917	−	1.18908i	0.558260	−	0.829666i	$-0.311469\pi$
$752$	−5.53691	+	15.2125i	−0.201911	+	0.554745i
$753$	−15.6825	+	27.2115i	−0.571501	+	0.991642i
$754$	13.0061	−	2.88339i	0.473655	−	0.105007i
$755$	−57.3893	+	23.7714i	−2.08861	+	0.865130i
$756$	49.8094	−	20.7675i	1.81155	−	0.755306i
$757$	−30.7063	−	30.7063i	−1.11604	−	1.11604i	−0.992317	−	0.123722i	$-0.960517\pi$
$757$	−30.7063	−	30.7063i	−1.11604	−	1.11604i	−0.123722	−	0.992317i	$-0.539483\pi$
$758$	−2.84342	−	12.8258i	−0.103278	−	0.465855i
$759$	−3.78836	+	14.1823i	−0.137509	+	0.514785i
$760$	16.0390	+	14.6971i	0.581797	+	0.533119i
$761$	−20.4558	−	24.3782i	−0.741521	−	0.883710i	0.255010	−	0.966938i	$-0.417921\pi$
$761$	−20.4558	−	24.3782i	−0.741521	−	0.883710i	−0.996530	+	0.0832285i	$0.973477\pi$
$762$	12.3901	−	14.7892i	0.448847	−	0.535757i
$763$	−5.98811	+	12.8415i	−0.216784	+	0.464895i
$764$	−24.9766	+	43.2608i	−0.903623	+	1.56512i
$765$	1.87769	+	33.5139i	0.0678881	+	1.21170i
$766$	−22.7334	−	39.3754i	−0.821391	−	1.42269i
$767$	11.5796	−	1.01309i	0.418117	−	0.0365805i
$768$	−5.05421	+	0.895232i	−0.182378	+	0.0323039i
$769$	15.9119	−	2.80570i	0.573797	−	0.101176i	0.120783	−	0.992679i	$-0.461460\pi$
$769$	15.9119	−	2.80570i	0.573797	−	0.101176i	0.453015	+	0.891503i	$0.350348\pi$
$770$	8.82859	−	39.8232i	0.318160	−	1.43513i
$771$	−13.4114	+	19.1851i	−0.483000	+	0.690934i
$772$	59.1847	+	18.6609i	2.13010	+	0.671619i
$773$	6.54038	−	24.4090i	0.235241	−	0.877932i	−0.742799	−	0.669515i	$-0.766502\pi$
$773$	6.54038	−	24.4090i	0.235241	−	0.877932i	0.978040	−	0.208418i	$-0.0668313\pi$
$774$	−26.0196	+	21.9018i	−0.935254	+	0.787244i
$775$	1.84186	−	13.9903i	0.0661614	−	0.502546i
$776$	−0.453943	−	0.495392i	−0.0162956	−	0.0177835i
$777$	32.0017	+	26.8104i	1.14806	+	0.961819i
$778$	−30.5985	−	36.4659i	−1.09701	−	1.30736i
$779$	32.2212	−	35.1633i	1.15445	−	1.25986i
$780$	−19.9019	+	2.63582i	−0.712602	+	0.0943776i
$781$	2.22635	−	12.6263i	0.0796652	−	0.451804i
$782$	16.8050	+	39.3645i	0.600945	+	1.40767i
$783$	16.5404	+	10.4835i	0.591107	+	0.374648i
$784$	15.9452	−	15.9452i	0.569470	−	0.569470i
$785$	42.5461	+	27.1048i	1.51853	+	0.967413i
$786$	8.36469	+	1.09464i	0.298359	+	0.0390445i
$787$	−3.14037	−	2.87762i	−0.111942	−	0.102576i	0.617670	−	0.786438i	$-0.288077\pi$
$787$	−3.14037	−	2.87762i	−0.111942	−	0.102576i	−0.729612	+	0.683862i	$0.760299\pi$
$788$	−39.4888	−	20.5566i	−1.40673	−	0.732297i
$789$	5.15290	−	11.0728i	0.183448	−	0.394202i
$790$	−42.2951	−	19.7225i	−1.50479	−	0.701697i
$791$	−26.4489	+	7.08697i	−0.940416	+	0.251984i
$792$	0.278100	−	6.60435i	0.00988185	−	0.234675i
$793$	5.17551	−	6.74486i	0.183788	−	0.239517i
$794$	11.5159	+	22.1219i	0.408684	+	0.785075i
$795$	11.1967	+	5.81760i	0.397105	+	0.206329i
$796$	−6.07997	−	1.34790i	−0.215499	−	0.0477749i
$797$	−16.0286	−	11.2233i	−0.567762	−	0.397551i	0.254151	−	0.967165i	$-0.418204\pi$
$797$	−16.0286	−	11.2233i	−0.567762	−	0.397551i	−0.821913	+	0.569614i	$0.807093\pi$
$798$	94.6283	−	4.20502i	3.34981	−	0.148856i
$799$	26.8115	−	2.63739i	0.948522	−	0.0933041i
$800$	−9.25181	−	16.0246i	−0.327101	−	0.566556i
$801$	13.1968	+	7.59193i	0.466286	+	0.268248i
$802$	15.7627	+	20.5424i	0.556601	+	0.725376i
$803$	−9.09054	−	24.9761i	−0.320798	−	0.881386i
$804$	−9.43391	+	53.7458i	−0.332708	+	1.89547i
$805$	−46.8097	−	24.3676i	−1.64982	−	0.858844i
$806$	−21.0790	+	0.920330i	−0.742477	+	0.0324173i
$807$	29.4596	+	12.1758i	1.03703	+	0.428610i
$808$	−10.2804	+	7.19845i	−0.361665	+	0.253240i
$809$	−26.9541	+	11.1648i	−0.947657	+	0.392532i	−0.802350	−	0.596854i	$-0.796417\pi$
$809$	−26.9541	+	11.1648i	−0.947657	+	0.392532i	−0.145307	+	0.989387i	$0.546417\pi$
$810$	−41.6026	−	31.7184i	−1.46177	−	1.11447i
$811$	−7.65981	−	3.17280i	−0.268972	−	0.111412i	0.244121	−	0.969745i	$-0.421501\pi$
$811$	−7.65981	−	3.17280i	−0.268972	−	0.111412i	−0.513093	+	0.858333i	$0.671501\pi$
$812$	−38.5460	−	6.79670i	−1.35270	−	0.238518i
$813$	−0.0208710	−	26.9388i	−0.000731978	−	0.944786i
$814$	20.3929	−	9.50938i	0.714772	−	0.333304i
$815$	11.2595	−	9.44783i	0.394402	−	0.330943i
$816$	10.3155	+	14.3754i	0.361113	+	0.503239i
$817$	−31.6438	+	11.5174i	−1.10707	+	0.402942i
$818$	−12.7613	−	47.6260i	−0.446190	−	1.66520i
$819$	−12.0691	+	15.7793i	−0.421728	+	0.551373i
$820$	45.5948	−	26.3242i	1.59224	−	0.919281i
$821$	−17.8350	−	34.2607i	−0.622445	−	1.19571i	−0.966478	−	0.256748i	$-0.917349\pi$
$821$	−17.8350	−	34.2607i	−0.622445	−	1.19571i	0.344034	−	0.938957i	$-0.388207\pi$
$822$	3.32713	+	7.12064i	0.116047	+	0.248361i
$823$	−7.81432	−	12.2660i	−0.272390	−	0.427567i	0.679652	−	0.733535i	$-0.262131\pi$
$823$	−7.81432	−	12.2660i	−0.272390	−	0.427567i	−0.952042	+	0.305968i	$0.901020\pi$
$824$	−11.6360	+	16.6180i	−0.405361	+	0.578915i
$825$	−6.82777	+	2.15860i	−0.237712	+	0.0751529i
$826$	−57.7399	−	18.2053i	−2.00903	−	0.633444i
$827$	−28.8026	+	37.5363i	−1.00157	+	1.30527i	−0.0496954	+	0.998764i	$0.515825\pi$
$827$	−28.8026	+	37.5363i	−1.00157	+	1.30527i	−0.951870	+	0.306501i	$0.900842\pi$
$828$	−35.9058	−	11.2599i	−1.24781	−	0.391310i
$829$	−22.6565	−	13.0807i	−0.786891	−	0.454312i	0.0519758	−	0.998648i	$-0.483448\pi$
$829$	−22.6565	−	13.0807i	−0.786891	−	0.454312i	−0.838867	+	0.544337i	$0.816781\pi$
$830$	1.57598	−	36.0960i	0.0547032	−	1.25291i
$831$	1.26542	−	29.5075i	0.0438970	−	1.02360i
$832$	−14.9300	+	12.5278i	−0.517606	+	0.434323i
$833$	−35.3999	−	12.4538i	−1.22653	−	0.431498i
$834$	−7.10020	+	54.2562i	−0.245860	+	1.87874i
$835$	1.03333	+	1.47574i	0.0357598	+	0.0510702i
$836$	11.0208	−	26.6065i	0.381161	−	0.920204i
$837$	−22.9154	−	20.9003i	−0.792073	−	0.722422i
$838$	20.1159	+	8.33227i	0.694892	+	0.287834i
$839$	18.2985	−	4.05667i	0.631733	−	0.140052i	0.111068	−	0.993813i	$-0.464573\pi$
$839$	18.2985	−	4.05667i	0.631733	−	0.140052i	0.520665	+	0.853761i	$0.325684\pi$
$840$	22.9585	+	6.13264i	0.792142	+	0.211596i
$841$	6.25336	+	13.4104i	0.215633	+	0.462426i
$842$	−37.2564	−	3.25951i	−1.28394	−	0.112330i
$843$	10.0797	−	0.889727i	0.347162	−	0.0306438i
$844$	40.2079	+	43.8793i	1.38401	+	1.51039i
$845$	−22.1248	+	16.9769i	−0.761115	+	0.584024i
$846$	−24.0303	+	34.4322i	−0.826178	+	1.18380i
$847$	31.5949	−	4.15954i	1.08561	−	0.142924i
$848$	6.62579	−	0.579681i	0.227531	−	0.0199063i
$849$	8.33089	+	13.0545i	0.285915	+	0.448031i
$850$	−11.7906	+	17.2313i	−0.404414	+	0.591030i
$851$	−5.05506	−	28.6687i	−0.173285	−	0.982749i
$852$	32.0923	+	7.08861i	1.09946	+	0.242852i
$853$	36.7696	−	19.1411i	1.25897	−	0.655378i	0.304166	−	0.952619i	$-0.401622\pi$
$853$	36.7696	−	19.1411i	1.25897	−	0.655378i	0.954802	+	0.297241i	$0.0960666\pi$
$854$	−38.3479	+	22.1402i	−1.31224	+	0.757622i
$855$	−27.8988	−	43.6429i	−0.954118	−	1.49256i
$856$	13.6831	+	1.80141i	0.467677	+	0.0615709i
$857$	−5.30618	+	4.86222i	−0.181256	+	0.166090i	−0.761095	−	0.648641i	$-0.775338\pi$
$857$	−5.30618	+	4.86222i	−0.181256	+	0.166090i	0.579839	+	0.814731i	$0.303115\pi$
$858$	4.95134	+	9.49347i	0.169036	+	0.324102i
$859$	−13.7794	−	1.20554i	−0.470147	−	0.0411326i	−0.150379	−	0.988628i	$-0.548049\pi$
$859$	−13.7794	−	1.20554i	−0.470147	−	0.0411326i	−0.319768	+	0.947496i	$0.603605\pi$
$860$	−37.1377	+	1.62147i	−1.26638	+	0.0552915i
$861$	13.4449	−	50.3331i	0.458202	−	1.71535i
$862$	−6.00794	+	9.43058i	−0.204631	+	0.321207i
$863$			38.4607i			1.30922i	0.755968	+	0.654608i	$0.227166\pi$
$863$			38.4607i			1.30922i	−0.755968	+	0.654608i	$0.772834\pi$
$864$	−40.5233	−	3.45044i	−1.37863	−	0.117386i
$865$	−43.7676	+	43.7676i	−1.48814	+	1.48814i
$866$	6.13542	−	34.7957i	0.208490	−	1.18241i
$867$	14.1490	−	25.8226i	0.480524	−	0.876982i
$868$	58.2521	+	21.2020i	1.97721	+	0.719644i
$869$	−1.22368	+	13.9867i	−0.0415105	+	0.474468i
$870$	13.0050	+	35.6451i	0.440912	+	1.20848i
$871$	−6.87030	−	18.8760i	−0.232791	−	0.639589i
$872$	−3.52963	+	2.70838i	−0.119528	+	0.0917173i
$873$	0.740936	+	1.41796i	0.0250769	+	0.0479906i
$874$	−52.4004	−	40.2082i	−1.77247	−	1.36006i
$875$	2.50160	+	28.5935i	0.0845697	+	0.966636i
$876$	64.9640	−	20.5384i	2.19493	−	0.693929i
$877$	−7.25651	−	11.3904i	−0.245035	−	0.384628i	0.698655	−	0.715459i	$-0.253782\pi$
$877$	−7.25651	−	11.3904i	−0.245035	−	0.384628i	−0.943690	+	0.330831i	$0.892671\pi$
$878$	−30.6542	+	19.5289i	−1.03453	+	0.659068i
$879$	−12.6022	−	4.57577i	−0.425062	−	0.154337i
$880$	−7.55780	+	9.00703i	−0.254773	+	0.303627i
$881$	11.9725	−	1.57621i	0.403363	−	0.0531038i	0.0738845	−	0.997267i	$-0.476460\pi$
$881$	11.9725	−	1.57621i	0.403363	−	0.0531038i	0.329479	+	0.944163i	$0.393127\pi$
$882$	50.6057	−	29.3219i	1.70398	−	0.987319i
$883$	2.92284	−	5.06251i	0.0983615	−	0.170367i	−0.812645	−	0.582759i	$-0.801973\pi$
$883$	2.92284	−	5.06251i	0.0983615	−	0.170367i	0.911007	+	0.412392i	$0.135307\pi$
$884$	16.0400	+	7.26998i	0.539483	+	0.244516i
$885$	7.19073	+	32.3168i	0.241714	+	1.08632i
$886$	−6.81435	+	77.8884i	−0.228933	+	2.61671i
$887$	33.8379	−	36.9276i	1.13617	−	1.23991i	0.169040	−	0.985609i	$-0.445933\pi$
$887$	33.8379	−	36.9276i	1.13617	−	1.23991i	0.967126	−	0.254298i	$-0.0818444\pi$
$888$	5.02585	+	12.1069i	0.168656	+	0.406282i
$889$	11.2118	−	17.5991i	0.376033	−	0.590254i
$890$	11.2889	+	27.2537i	0.378403	+	0.913546i
$891$	−4.68632	+	15.0253i	−0.156998	+	0.503367i
$892$	21.5829	+	21.5829i	0.722648	+	0.722648i
$893$	−34.0553	+	23.8458i	−1.13962	+	0.797969i
$894$	−62.0145	+	62.1106i	−2.07407	+	2.07729i
$895$	1.84902	+	42.3495i	0.0618059	+	1.41559i
$896$	36.9060	−	11.6364i	1.23294	−	0.388745i
$897$	13.5217	−	3.00868i	0.451476	−	0.100457i
$898$	1.89675	−	43.4427i	0.0632953	−	1.44970i
$899$	5.82215	+	21.7286i	0.194179	+	0.724688i
$900$	−4.77844	−	17.7235i	−0.159281	−	0.590783i
$901$	−5.63732	−	9.52536i	−0.187806	−	0.317336i
$902$	−21.5100	−	18.0490i	−0.716205	−	0.600967i
$903$	−24.8301	+	27.1395i	−0.826295	+	0.903147i
$904$	−8.39395	−	1.86089i	−0.279179	−	0.0618924i
$905$	−41.7231	+	7.35690i	−1.38692	+	0.244552i
$906$	−65.0144	+	54.6394i	−2.15996	+	1.81527i
$907$	4.53679	−	14.3889i	0.150642	−	0.477775i	−0.847993	−	0.530007i	$-0.822189\pi$
$907$	4.53679	−	14.3889i	0.150642	−	0.477775i	0.998635	+	0.0522325i	$0.0166337\pi$
$908$	−10.4842	−	8.04481i	−0.347930	−	0.266976i
$909$	28.0643	−	10.2638i	0.930835	−	0.340430i
$910$	−37.1800	+	9.96235i	−1.23250	+	0.330249i
$911$	22.5354	−	20.6499i	0.746633	−	0.684163i	−0.209266	−	0.977859i	$-0.567108\pi$
$911$	22.5354	−	20.6499i	0.746633	−	0.684163i	0.955899	+	0.293696i	$0.0948853\pi$
$912$	−24.7546	−	11.5199i	−0.819705	−	0.381462i
$913$	−10.3669	+	3.26868i	−0.343095	+	0.108177i
$914$	19.2389	−	52.8583i	0.636365	−	1.74840i
$915$	20.9798	+	12.0910i	0.693570	+	0.399717i
$916$	−6.79266	−	9.70092i	−0.224436	−	0.320527i
$917$	9.12407			0.301303
$918$	16.2597	+	42.9140i	0.536649	+	1.41637i
$919$	9.80152			0.323322			0.161661	−	0.986846i	$-0.448315\pi$
$919$	9.80152			0.323322			0.161661	+	0.986846i	$0.448315\pi$
$920$	−9.50427	−	13.5735i	−0.313346	−	0.447505i
$921$	8.48777	−	4.90919i	0.279681	−	0.161763i
$922$	3.72414	−	10.2320i	0.122648	−	0.336973i
$923$	−11.5386	+	3.63812i	−0.379799	+	0.119750i
$924$	−2.76604	−	31.3363i	−0.0909959	−	1.03089i
$925$	10.4698	−	9.59383i	0.344246	−	0.315443i
$926$	3.08999	−	0.827960i	0.101543	−	0.0272084i
$927$	36.9547	−	31.1063i	1.21375	−	1.02167i
$928$	23.4020	+	17.9570i	0.768207	+	0.589466i
$929$	2.73481	−	8.67370i	0.0897261	−	0.284575i	−0.898180	−	0.439628i	$-0.855110\pi$
$929$	2.73481	−	8.67370i	0.0897261	−	0.284575i	0.987906	+	0.155053i	$0.0495548\pi$
$930$	−10.4811	−	59.1734i	−0.343690	−	1.94037i
$931$	57.0296	−	10.0559i	1.86907	−	0.329567i
$932$	51.8263	+	11.4896i	1.69763	+	0.376355i
$933$	27.9165	+	6.16625i	0.913945	+	0.201874i
$934$	−33.8959	−	28.4421i	−1.10911	−	0.930653i
$935$	18.9538	+	4.86015i	0.619854	+	0.158944i
$936$	−5.64920	+	2.64493i	−0.184650	+	0.0864523i
$937$	−1.49447	−	5.57745i	−0.0488223	−	0.182207i	0.937209	−	0.348769i	$-0.113400\pi$
$937$	−1.49447	−	5.57745i	−0.0488223	−	0.182207i	−0.986031	+	0.166562i	$0.946734\pi$
$938$	−4.56361	+	104.524i	−0.149007	+	3.41283i
$939$	3.49818	−	11.1249i	0.114159	−	0.363046i
$940$	−43.7690	+	13.8003i	−1.42759	+	0.450116i
$941$	−0.478464	−	10.9586i	−0.0155975	−	0.357241i	−0.990749	−	0.135704i	$-0.956670\pi$
$941$	−0.478464	−	10.9586i	−0.0155975	−	0.357241i	0.975152	−	0.221537i	$-0.0711074\pi$
$942$	66.6326	+	17.7988i	2.17101	+	0.579917i
$943$	−29.7580	+	20.8367i	−0.969052	+	0.678538i
$944$	12.3400	+	12.3400i	0.401632	+	0.401632i
$945$	−49.0668	−	28.1769i	−1.59614	−	0.916593i
$946$	7.58699	+	18.3166i	0.246674	+	0.595524i
$947$	15.2986	−	24.0139i	0.497136	−	0.780348i	−0.499144	−	0.866519i	$-0.666352\pi$
$947$	15.2986	−	24.0139i	0.497136	−	0.780348i	0.996280	+	0.0861713i	$0.0274632\pi$
$948$	−35.6867	−	4.67012i	−1.15905	−	0.151678i
$949$	−16.9447	+	18.4918i	−0.550047	+	0.600271i
$950$	2.80813	−	32.0970i	0.0911076	−	1.04137i
$951$	−34.4426	+	31.6099i	−1.11688	+	1.02502i
$952$	−14.2480	−	15.2161i	−0.461780	−	0.493158i
$953$	20.3308	−	35.2139i	0.658578	−	1.14069i	−0.322406	−	0.946602i	$-0.604492\pi$
$953$	20.3308	−	35.2139i	0.658578	−	1.14069i	0.980984	−	0.194089i	$-0.0621752\pi$
$954$	16.9933	+	2.96923i	0.550177	+	0.0961324i
$955$	51.9269	−	6.83631i	1.68032	−	0.221218i
$956$	−16.2515	+	19.3677i	−0.525610	+	0.626398i
$957$	8.73908	−	7.34450i	0.282494	−	0.237414i
$958$	−17.6541	+	11.2469i	−0.570377	+	0.363370i
$959$	4.56739	+	7.16937i	0.147489	+	0.231511i
$960$	−40.9559	−	37.4708i	−1.32184	−	1.20937i
$961$	−0.403309	−	4.60984i	−0.0130100	−	0.148705i
$962$	−16.8454	−	12.9259i	−0.543118	−	0.416749i
$963$	−30.3791	−	12.5283i	−0.978952	−	0.403719i
$964$	43.0473	−	33.0313i	1.38646	−	1.06387i
$965$	−22.2537	−	61.1415i	−0.716371	−	1.96821i
$966$	−71.0624	−	12.4735i	−2.28639	−	0.401327i
$967$	4.69794	−	53.6977i	0.151076	−	1.72680i	−0.421396	−	0.906877i	$-0.638460\pi$
$967$	4.69794	−	53.6977i	0.151076	−	1.72680i	0.572471	−	0.819925i	$-0.305985\pi$
$968$	9.40274	+	3.42232i	0.302216	+	0.109997i
$969$	0.525284	+	45.4349i	0.0168745	+	1.45958i
$970$	−0.538289	+	3.05279i	−0.0172834	+	0.0980191i
$971$	−6.69918	+	6.69918i	−0.214987	+	0.214987i	−0.806382	−	0.591395i	$-0.798577\pi$
$971$	−6.69918	+	6.69918i	−0.214987	+	0.214987i	0.591395	+	0.806382i	$0.298577\pi$
$972$	−37.9662	−	13.6522i	−1.21777	−	0.437896i
$973$			59.1818i			1.89728i
$974$	8.02869	−	12.6025i	0.257256	−	0.403811i
$975$	4.78187	+	4.77447i	0.153142	+	0.152905i
$976$	12.7518	−	0.556755i	0.408175	−	0.0178213i
$977$	16.1577	+	1.41362i	0.516931	+	0.0452256i	0.342637	−	0.939468i	$-0.388680\pi$
$977$	16.1577	+	1.41362i	0.516931	+	0.0452256i	0.174294	+	0.984694i	$0.444236\pi$
$978$	10.7839	−	16.9563i	0.344830	−	0.542202i
$979$	6.54333	−	5.99586i	0.209126	−	0.191628i
$980$	63.3787	+	8.34396i	2.02456	+	0.266538i
$981$	9.78059	−	4.06902i	0.312270	−	0.129914i
$982$	−12.4488	+	7.18732i	−0.397257	+	0.229357i
$983$	−18.1078	+	9.42633i	−0.577550	+	0.300653i	−0.725368	−	0.688361i	$-0.758330\pi$
$983$	−18.1078	+	9.42633i	−0.577550	+	0.300653i	0.147818	+	0.989015i	$0.452775\pi$
$984$	11.0422	−	12.0692i	0.352013	−	0.384753i
$985$	8.10542	+	45.9681i	0.258260	+	1.46467i
$986$	6.85316	−	32.5712i	0.218249	−	1.03728i
$987$	−20.9382	+	40.2982i	−0.666472	+	1.28271i
$988$	−27.0724	+	2.36853i	−0.861289	+	0.0753530i
$989$	25.4302	−	3.34795i	0.808635	−	0.106459i
$990$	−24.9537	+	17.5304i	−0.793080	+	0.557154i
$991$	26.0725	−	20.0061i	0.828220	−	0.635515i	−0.105140	−	0.994457i	$-0.533529\pi$
$991$	26.0725	−	20.0061i	0.828220	−	0.635515i	0.933360	+	0.358942i	$0.116862\pi$
$992$	−31.5622	−	34.4441i	−1.00210	−	1.09360i
$993$	16.4417	−	35.3307i	0.521760	−	1.12119i
$994$	62.7747	+	5.49207i	1.99109	+	0.174198i
$995$	2.75949	+	5.91774i	0.0874816	+	0.187605i
$996$	−7.23271	−	26.9094i	−0.229177	−	0.852658i
$997$	3.76793	−	0.835330i	0.119332	−	0.0264552i	−0.156369	−	0.987699i	$-0.549979\pi$
$997$	3.76793	−	0.835330i	0.119332	−	0.0264552i	0.275701	+	0.961243i	$0.411090\pi$
$998$	−26.7766	−	11.0912i	−0.847597	−	0.351086i
$999$	−4.14593	−	30.9357i	−0.131171	−	0.978761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.2.ba.a.25.8	✓	1248
17.15	even	8	inner	459.2.ba.a.457.45	yes	1248
27.13	even	9	inner	459.2.ba.a.229.45	yes	1248
459.202	even	72	inner	459.2.ba.a.202.8	yes	1248

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
459.2.ba.a.25.8	✓	1248	1.1	even	1	trivial
459.2.ba.a.202.8	yes	1248	459.202	even	72	inner
459.2.ba.a.229.45	yes	1248	27.13	even	9	inner
459.2.ba.a.457.45	yes	1248	17.15	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	459.ba (of order \(72\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22861 - 1.75463i) q^{2} +(0.00134192 + 1.73205i) q^{3} +(-0.885220 + 2.43212i) q^{4} +(2.58809 - 0.816022i) q^{5} +(3.03746 - 2.13036i) q^{6} +(2.95845 - 2.71092i) q^{7} +(1.21702 - 0.326100i) q^{8} +(-3.00000 + 0.00464853i) q^{9} +(-4.61156 - 3.53858i) q^{10} +(-0.525873 + 1.66786i) q^{11} +(-4.21375 - 1.52998i) q^{12} +(1.62518 - 0.286563i) q^{13} +(-8.39145 - 1.86034i) q^{14} +(1.41686 + 4.48161i) q^{15} +(1.89794 + 1.59256i) q^{16} +(1.02412 - 3.99389i) q^{17} +(3.69397 + 5.25818i) q^{18} +(1.64676 + 6.14578i) q^{19} +(-0.306365 + 7.01691i) q^{20} +(4.69942 + 5.12055i) q^{21} +(3.57257 - 1.12643i) q^{22} +(-0.211394 - 4.84172i) q^{23} +(0.566455 + 2.10751i) q^{24} +(1.93656 - 1.35599i) q^{25} +(-2.49952 - 2.49952i) q^{26} +(-0.0120772 - 5.19614i) q^{27} +(3.97441 + 9.59508i) q^{28} +(-2.02494 + 3.17851i) q^{29} +(6.12280 - 7.99221i) q^{30} +(4.03251 - 4.40072i) q^{31} +(0.682162 - 7.79714i) q^{32} +(-2.88952 - 0.908600i) q^{33} +(-8.26606 + 3.10997i) q^{34} +(5.44457 - 9.43027i) q^{35} +(2.64435 - 7.30047i) q^{36} +(5.95541 - 0.784045i) q^{37} +(8.76037 - 10.4402i) q^{38} +(0.498523 + 2.81451i) q^{39} +(2.88366 - 1.83709i) q^{40} +(-4.02756 - 6.32200i) q^{41} +(3.21094 - 14.5369i) q^{42} +(0.461280 + 5.27246i) q^{43} +(-3.59092 - 2.75541i) q^{44} +(-7.76047 + 2.46009i) q^{45} +(-8.23572 + 6.31949i) q^{46} +(2.23480 + 6.14007i) q^{47} +(-2.75585 + 3.28947i) q^{48} +(0.793252 - 9.06692i) q^{49} +(-4.75853 - 1.73196i) q^{50} +(6.91900 + 1.76847i) q^{51} +(-0.741686 + 4.20631i) q^{52} +(1.89823 - 1.89823i) q^{53} +(-9.10248 + 6.40520i) q^{54} +4.74569i q^{55} +(2.71647 - 4.26400i) q^{56} +(-10.6426 + 2.86051i) q^{57} +(8.06497 - 0.352124i) q^{58} +(7.01689 + 0.613899i) q^{59} +(-12.1541 - 0.521223i) q^{60} +(3.79828 - 3.48048i) q^{61} +(-12.6760 - 1.66883i) q^{62} +(-8.86275 + 8.14651i) q^{63} +(-10.2279 + 5.90509i) q^{64} +(3.97227 - 2.06783i) q^{65} +(1.95582 + 6.18635i) q^{66} +(-2.11370 - 11.9874i) q^{67} +(8.80706 + 6.02626i) q^{68} +(8.38581 - 0.372642i) q^{69} +(-23.2359 + 2.03288i) q^{70} +(-7.26864 + 0.956935i) q^{71} +(-3.64954 + 0.983956i) q^{72} +(-12.0577 + 9.25223i) q^{73} +(-8.69257 - 9.48627i) q^{74} +(2.35124 + 3.35239i) q^{75} +(-16.4050 - 1.43525i) q^{76} +(2.96566 + 6.35988i) q^{77} +(4.32594 - 4.33265i) q^{78} +(7.83817 - 1.73768i) q^{79} +(6.21161 + 2.57293i) q^{80} +(8.99996 - 0.0278911i) q^{81} +(-6.14451 + 14.8341i) q^{82} +(3.56519 + 5.09161i) q^{83} +(-16.6138 + 6.89676i) q^{84} +(-0.608586 - 11.1723i) q^{85} +(8.68450 - 7.28716i) q^{86} +(-5.50806 - 3.50302i) q^{87} +(-0.0961110 + 2.20130i) q^{88} +(-4.39501 - 2.53746i) q^{89} +(13.8511 + 10.5943i) q^{90} +(4.03117 - 5.25352i) q^{91} +(11.9628 + 3.77185i) q^{92} +(7.62767 + 6.97861i) q^{93} +(8.02787 - 11.4650i) q^{94} +(9.27704 + 14.5620i) q^{95} +(13.5060 + 1.17107i) q^{96} +(-0.246246 - 0.473034i) q^{97} +(-16.8837 + 9.74781i) q^{98} +(1.56986 - 5.00601i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1248 q - 24 q^{2} - 24 q^{3} - 24 q^{5} - 24 q^{6} - 24 q^{7} - 12 q^{8} - 24 q^{9} - 12 q^{10} - 36 q^{11} + 12 q^{12} - 24 q^{14} - 24 q^{15} - 48 q^{16} - 12 q^{17} - 48 q^{18} - 12 q^{19} - 24 q^{20}+ \cdots - 168 q^{99}+O(q^{100}) \) 1248 * q - 24 * q^2 - 24 * q^3 - 24 * q^5 - 24 * q^6 - 24 * q^7 - 12 * q^8 - 24 * q^9 - 12 * q^10 - 36 * q^11 + 12 * q^12 - 24 * q^14 - 24 * q^15 - 48 * q^16 - 12 * q^17 - 48 * q^18 - 12 * q^19 - 24 * q^20 - 24 * q^22 + 48 * q^23 - 84 * q^24 - 24 * q^25 - 48 * q^26 - 24 * q^27 - 48 * q^28 - 24 * q^29 - 24 * q^31 - 72 * q^32 - 48 * q^33 - 24 * q^34 - 216 * q^35 - 24 * q^36 - 12 * q^37 - 24 * q^39 - 72 * q^40 - 24 * q^41 + 96 * q^42 + 12 * q^43 - 12 * q^44 - 24 * q^45 - 12 * q^46 - 24 * q^48 - 24 * q^49 - 48 * q^50 - 24 * q^51 - 48 * q^52 - 48 * q^53 - 96 * q^54 + 96 * q^56 - 60 * q^57 - 24 * q^58 + 144 * q^59 - 480 * q^60 - 24 * q^61 - 12 * q^62 + 120 * q^63 - 72 * q^65 - 204 * q^66 - 48 * q^67 - 72 * q^68 + 96 * q^69 + 36 * q^71 - 12 * q^73 - 192 * q^74 - 24 * q^75 - 72 * q^76 - 60 * q^77 + 324 * q^78 - 24 * q^79 - 48 * q^80 - 48 * q^82 - 144 * q^83 - 48 * q^84 - 24 * q^85 + 72 * q^86 - 24 * q^87 + 192 * q^88 - 252 * q^90 - 12 * q^91 - 24 * q^92 - 24 * q^93 - 24 * q^94 + 192 * q^95 + 288 * q^96 - 132 * q^97 - 168 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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