LMFDB - Embedded newform 552.2.t.a.19.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(19,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 0, 15]))

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

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

chi := DirichletCharacter("552.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.t (of order $22$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			19.15
Character	$\chi$	$=$	552.19
Dual form			552.2.t.a.523.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.578628 + 1.29042i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-1.33038 + 1.49335i) q^{4} +(-1.60117 - 1.02901i) q^{5} +(0.918744 + 1.07513i) q^{6} +(-0.727375 - 5.05900i) q^{7} +(-2.69685 - 0.852656i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(0.578628 + 1.29042i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-1.33038 + 1.49335i) q^{4} +(-1.60117 - 1.02901i) q^{5} +(0.918744 + 1.07513i) q^{6} +(-0.727375 - 5.05900i) q^{7} +(-2.69685 - 0.852656i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.401374 - 2.66159i) q^{10} +(-4.38108 - 2.00077i) q^{11} +(-0.855764 + 1.80767i) q^{12} +(2.75285 + 0.395800i) q^{13} +(6.10737 - 3.86590i) q^{14} +(-1.82621 - 0.536225i) q^{15} +(-0.460184 - 3.97344i) q^{16} +(2.60879 - 2.26053i) q^{17} +(1.18443 + 0.772742i) q^{18} +(2.96198 + 2.56657i) q^{19} +(3.66683 - 1.02213i) q^{20} +(-2.12320 - 4.64915i) q^{21} +(0.0468245 - 6.81114i) q^{22} +(-4.28462 - 2.15454i) q^{23} +(-2.82783 - 0.0583286i) q^{24} +(-0.572196 - 1.25294i) q^{25} +(1.08213 + 3.78136i) q^{26} +(0.654861 - 0.755750i) q^{27} +(8.52254 + 5.64417i) q^{28} +(-2.71881 + 2.35586i) q^{29} +(-0.364742 - 2.66686i) q^{30} +(-0.621804 + 2.11767i) q^{31} +(4.86114 - 2.89298i) q^{32} +(-4.76730 - 0.685434i) q^{33} +(4.42655 + 2.05843i) q^{34} +(-4.04110 + 8.84878i) q^{35} +(-0.311820 + 1.97554i) q^{36} +(-0.0190901 + 0.0122685i) q^{37} +(-1.59807 + 5.30729i) q^{38} +(2.75285 - 0.395800i) q^{39} +(3.44071 + 4.14032i) q^{40} +(6.31865 + 4.06075i) q^{41} +(4.77083 - 5.42995i) q^{42} +(1.21691 + 4.14440i) q^{43} +(8.81634 - 3.88070i) q^{44} -1.90331 q^{45} +(0.301066 - 6.77564i) q^{46} -5.57574i q^{47} +(-1.56099 - 3.68284i) q^{48} +(-18.3480 + 5.38745i) q^{49} +(1.28573 - 1.46336i) q^{50} +(1.86625 - 2.90394i) q^{51} +(-4.25340 + 3.58440i) q^{52} +(-0.500358 - 3.48007i) q^{53} +(1.35416 + 0.407749i) q^{54} +(4.95603 + 7.71173i) q^{55} +(-2.35197 + 14.2635i) q^{56} +(3.56508 + 1.62812i) q^{57} +(-4.61323 - 2.14524i) q^{58} +(0.962543 - 6.69463i) q^{59} +(3.23033 - 2.01379i) q^{60} +(7.90693 + 2.32169i) q^{61} +(-3.09248 + 0.422954i) q^{62} +(-3.34701 - 3.86266i) q^{63} +(6.54595 + 4.59897i) q^{64} +(-4.00049 - 3.46645i) q^{65} +(-1.87399 - 6.54844i) q^{66} +(8.50756 - 3.88527i) q^{67} +(-0.0949190 + 6.90318i) q^{68} +(-4.71807 - 0.860150i) q^{69} +(-13.7570 - 0.0945748i) q^{70} +(-13.0329 + 5.95194i) q^{71} +(-2.72971 + 0.740725i) q^{72} +(5.60045 - 6.46327i) q^{73} +(-0.0268776 - 0.0175354i) q^{74} +(-0.902011 - 1.04098i) q^{75} +(-7.77334 + 1.00876i) q^{76} +(-6.93522 + 23.6192i) q^{77} +(2.10363 + 3.32332i) q^{78} +(2.32328 - 16.1588i) q^{79} +(-3.35187 + 6.83567i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-1.58393 + 10.5034i) q^{82} +(-0.437726 - 0.681115i) q^{83} +(9.76746 + 3.01446i) q^{84} +(-6.50320 + 0.935019i) q^{85} +(-4.64389 + 3.96839i) q^{86} +(-1.94495 + 3.02641i) q^{87} +(10.1091 + 9.13133i) q^{88} +(1.86816 + 6.36237i) q^{89} +(-1.10131 - 2.45607i) q^{90} -14.2146i q^{91} +(8.91765 - 3.53208i) q^{92} +2.20707i q^{93} +(7.19507 - 3.22628i) q^{94} +(-2.10160 - 7.15740i) q^{95} +(3.84918 - 4.14533i) q^{96} +(5.37204 - 8.35906i) q^{97} +(-17.5687 - 20.5593i) q^{98} +(-4.76730 + 0.685434i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{15}{22}\right)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.578628	+	1.29042i	0.409152	+	0.912466i
$2$	0.578628	+	1.29042i	0.409152	+	0.912466i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$3$	0.959493	−	0.281733i	0.553964	−	0.162658i
$4$	−1.33038	+	1.49335i	−0.665189	+	0.746675i
$5$	−1.60117	−	1.02901i	−0.716064	−	0.460186i	0.131202	−	0.991356i	$-0.458116\pi$
$5$	−1.60117	−	1.02901i	−0.716064	−	0.460186i	−0.847266	+	0.531170i	$0.821753\pi$
$6$	0.918744	+	1.07513i	0.375076	+	0.438921i
$7$	−0.727375	−	5.05900i	−0.274922	−	1.91212i	−0.393767	−	0.919210i	$-0.628828\pi$
$7$	−0.727375	−	5.05900i	−0.274922	−	1.91212i	0.118845	−	0.992913i	$-0.462081\pi$
$8$	−2.69685	−	0.852656i	−0.953479	−	0.301460i
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$	0.401374	−	2.66159i	0.126926	−	0.841670i
$11$	−4.38108	−	2.00077i	−1.32094	−	0.603255i	−0.374832	−	0.927093i	$-0.622300\pi$
$11$	−4.38108	−	2.00077i	−1.32094	−	0.603255i	−0.946113	+	0.323837i	$0.895027\pi$
$12$	−0.855764	+	1.80767i	−0.247038	+	0.521829i
$13$	2.75285	+	0.395800i	0.763504	+	0.109775i	0.513056	−	0.858355i	$-0.328513\pi$
$13$	2.75285	+	0.395800i	0.763504	+	0.109775i	0.250447	+	0.968130i	$0.419422\pi$
$14$	6.10737	−	3.86590i	1.63226	−	1.03321i
$15$	−1.82621	−	0.536225i	−0.471526	−	0.138453i
$16$	−0.460184	−	3.97344i	−0.115046	−	0.993360i
$17$	2.60879	−	2.26053i	0.632723	−	0.548258i	−0.278362	−	0.960476i	$-0.589791\pi$
$17$	2.60879	−	2.26053i	0.632723	−	0.548258i	0.911085	+	0.412218i	$0.135246\pi$
$18$	1.18443	+	0.772742i	0.279172	+	0.182137i
$19$	2.96198	+	2.56657i	0.679524	+	0.588811i	0.924713	−	0.380664i	$-0.124305\pi$
$19$	2.96198	+	2.56657i	0.679524	+	0.588811i	−0.245189	+	0.969475i	$0.578850\pi$
$20$	3.66683	−	1.02213i	0.819927	−	0.228556i
$21$	−2.12320	−	4.64915i	−0.463319	−	1.01453i
$22$	0.0468245	−	6.81114i	0.00998302	−	1.45214i
$23$	−4.28462	−	2.15454i	−0.893405	−	0.449253i
$23$	−4.28462	−	2.15454i	−0.893405	−	0.449253i
$24$	−2.82783	−	0.0583286i	−0.577227	−	0.0119063i
$25$	−0.572196	−	1.25294i	−0.114439	−	0.250587i
$26$	1.08213	+	3.78136i	0.212223	+	0.741586i
$27$	0.654861	−	0.755750i	0.126028	−	0.145444i
$28$	8.52254	+	5.64417i	1.61061	+	1.06665i
$29$	−2.71881	+	2.35586i	−0.504870	+	0.437472i	−0.869685	−	0.493608i	$-0.835678\pi$
$29$	−2.71881	+	2.35586i	−0.504870	+	0.437472i	0.364815	+	0.931080i	$0.381132\pi$
$30$	−0.364742	−	2.66686i	−0.0665925	−	0.486900i
$31$	−0.621804	+	2.11767i	−0.111679	+	0.380345i	−0.996298	−	0.0859709i	$-0.972601\pi$
$31$	−0.621804	+	2.11767i	−0.111679	+	0.380345i	0.884618	+	0.466316i	$0.154419\pi$
$32$	4.86114	−	2.89298i	0.859336	−	0.511411i
$33$	−4.76730	−	0.685434i	−0.829880	−	0.119319i
$34$	4.42655	+	2.05843i	0.759147	+	0.353018i
$35$	−4.04110	+	8.84878i	−0.683071	+	1.49572i
$36$	−0.311820	+	1.97554i	−0.0519701	+	0.329257i
$37$	−0.0190901	+	0.0122685i	−0.00313840	+	0.00201693i	−0.542209	−	0.840244i	$-0.682412\pi$
$37$	−0.0190901	+	0.0122685i	−0.00313840	+	0.00201693i	0.539071	+	0.842261i	$0.318776\pi$
$38$	−1.59807	+	5.30729i	−0.259242	+	0.860956i
$39$	2.75285	−	0.395800i	0.440809	−	0.0633788i
$40$	3.44071	+	4.14032i	0.544024	+	0.654642i
$41$	6.31865	+	4.06075i	0.986808	+	0.634183i	0.931291	−	0.364275i	$-0.118683\pi$
$41$	6.31865	+	4.06075i	0.986808	+	0.634183i	0.0555162	+	0.998458i	$0.482320\pi$
$42$	4.77083	−	5.42995i	0.736155	−	0.837860i
$43$	1.21691	+	4.14440i	0.185576	+	0.632015i	0.998750	+	0.0499932i	$0.0159200\pi$
$43$	1.21691	+	4.14440i	0.185576	+	0.632015i	−0.813173	+	0.582022i	$0.802262\pi$
$44$	8.81634	−	3.88070i	1.32911	−	0.585037i
$45$	−1.90331			−0.283729
$46$	0.301066	−	6.77564i	0.0443897	−	0.999014i
$47$		−	5.57574i		−	0.813306i	−0.913583	−	0.406653i	$-0.866696\pi$
$47$		−	5.57574i		−	0.813306i	0.913583	−	0.406653i	$-0.133304\pi$
$48$	−1.56099	−	3.68284i	−0.225310	−	0.531572i
$49$	−18.3480	+	5.38745i	−2.62114	+	0.769636i
$50$	1.28573	−	1.46336i	0.181829	−	0.206950i
$51$	1.86625	−	2.90394i	0.261327	−	0.406633i
$52$	−4.25340	+	3.58440i	−0.589841	+	0.497067i
$53$	−0.500358	−	3.48007i	−0.0687295	−	0.478024i	−0.994896	−	0.100908i	$-0.967825\pi$
$53$	−0.500358	−	3.48007i	−0.0687295	−	0.478024i	0.926166	−	0.377115i	$-0.123084\pi$
$54$	1.35416	+	0.407749i	0.184277	+	0.0554876i
$55$	4.95603	+	7.71173i	0.668271	+	1.03985i
$56$	−2.35197	+	14.2635i	−0.314296	+	1.90605i
$57$	3.56508	+	1.62812i	0.472207	+	0.215650i
$58$	−4.61323	−	2.14524i	−0.605747	−	0.281684i
$59$	0.962543	−	6.69463i	0.125312	−	0.871567i	−0.826073	−	0.563563i	$-0.809430\pi$
$59$	0.962543	−	6.69463i	0.125312	−	0.871567i	0.951385	−	0.308003i	$-0.0996608\pi$
$60$	3.23033	−	2.01379i	0.417033	−	0.259979i
$61$	7.90693	+	2.32169i	1.01238	+	0.297261i	0.745527	−	0.666476i	$-0.232198\pi$
$61$	7.90693	+	2.32169i	1.01238	+	0.297261i	0.266853	+	0.963737i	$0.414016\pi$
$62$	−3.09248	+	0.422954i	−0.392746	+	0.0537152i
$63$	−3.34701	−	3.86266i	−0.421684	−	0.486649i
$64$	6.54595	+	4.59897i	0.818244	+	0.574871i
$65$	−4.00049	−	3.46645i	−0.496200	−	0.429960i
$66$	−1.87399	−	6.54844i	−0.230673	−	0.806057i
$67$	8.50756	−	3.88527i	1.03936	−	0.474662i	0.178737	−	0.983897i	$-0.442799\pi$
$67$	8.50756	−	3.88527i	1.03936	−	0.474662i	0.860627	+	0.509235i	$0.170072\pi$
$68$	−0.0949190	+	6.90318i	−0.0115106	+	0.837134i
$69$	−4.71807	−	0.860150i	−0.567988	−	0.103550i
$70$	−13.7570	−	0.0945748i	−1.64427	−	0.0113039i
$71$	−13.0329	+	5.95194i	−1.54672	+	0.706365i	−0.992067	−	0.125714i	$-0.959878\pi$
$71$	−13.0329	+	5.95194i	−1.54672	+	0.706365i	−0.554657	+	0.832079i	$0.687151\pi$
$72$	−2.72971	+	0.740725i	−0.321700	+	0.0872952i
$73$	5.60045	−	6.46327i	0.655484	−	0.756468i	−0.326549	−	0.945180i	$-0.605886\pi$
$73$	5.60045	−	6.46327i	0.655484	−	0.756468i	0.982032	+	0.188712i	$0.0604312\pi$
$74$	−0.0268776	−	0.0175354i	−0.00312446	−	0.00203845i
$75$	−0.902011	−	1.04098i	−0.104155	−	0.120202i
$76$	−7.77334	+	1.00876i	−0.891663	+	0.115713i
$77$	−6.93522	+	23.6192i	−0.790342	+	2.69166i
$78$	2.10363	+	3.32332i	0.238189	+	0.376292i
$79$	2.32328	−	16.1588i	0.261389	−	1.81800i	−0.261048	−	0.965326i	$-0.584068\pi$
$79$	2.32328	−	16.1588i	0.261389	−	1.81800i	0.522437	−	0.852678i	$-0.325023\pi$
$80$	−3.35187	+	6.83567i	−0.374750	+	0.764252i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	−1.58393	+	10.5034i	−0.174916	+	1.15991i
$83$	−0.437726	−	0.681115i	−0.0480467	−	0.0747621i	0.816399	−	0.577488i	$-0.195967\pi$
$83$	−0.437726	−	0.681115i	−0.0480467	−	0.0747621i	−0.864446	+	0.502726i	$0.832331\pi$
$84$	9.76746	+	3.01446i	1.06572	+	0.328905i
$85$	−6.50320	+	0.935019i	−0.705371	+	0.101417i
$86$	−4.64389	+	3.96839i	−0.500763	+	0.427922i
$87$	−1.94495	+	3.02641i	−0.208521	+	0.324465i
$88$	10.1091	+	9.13133i	1.07764	+	0.973403i
$89$	1.86816	+	6.36237i	0.198025	+	0.674410i	0.997299	+	0.0734441i	$0.0233990\pi$
$89$	1.86816	+	6.36237i	0.198025	+	0.674410i	−0.799275	+	0.600966i	$0.794783\pi$
$90$	−1.10131	−	2.45607i	−0.116088	−	0.258893i
$91$		−	14.2146i		−	1.49009i
$92$	8.91765	−	3.53208i	0.929729	−	0.368244i
$93$			2.20707i			0.228863i
$94$	7.19507	−	3.22628i	0.742114	−	0.332766i
$95$	−2.10160	−	7.15740i	−0.215620	−	0.734334i
$96$	3.84918	−	4.14533i	0.392856	−	0.423081i
$97$	5.37204	−	8.35906i	0.545448	−	0.848734i	−0.453650	−	0.891180i	$-0.649879\pi$
$97$	5.37204	−	8.35906i	0.545448	−	0.848734i	0.999099	+	0.0424455i	$0.0135149\pi$
$98$	−17.5687	−	20.5593i	−1.77471	−	2.07680i
$99$	−4.76730	+	0.685434i	−0.479131	+	0.0688887i
$100$	2.63231	+	0.812390i	0.263231	+	0.0812390i
$101$	9.34541	+	14.5417i	0.929903	+	1.44696i	0.894237	+	0.447593i	$0.147719\pi$
$101$	9.34541	+	14.5417i	0.929903	+	1.44696i	0.0356657	+	0.999364i	$0.488645\pi$
$102$	4.82717	+	0.727947i	0.477961	+	0.0720775i
$103$	1.45531	−	3.18668i	0.143396	−	0.313993i	−0.824283	−	0.566177i	$-0.808422\pi$
$103$	1.45531	−	3.18668i	0.143396	−	0.313993i	0.967679	+	0.252185i	$0.0811490\pi$
$104$	−7.08653	−	3.41465i	−0.694892	−	0.334834i
$105$	−1.38442	+	9.62885i	−0.135106	+	0.939680i
$106$	4.20123	−	2.65934i	0.408060	−	0.258298i
$107$	0.625601	−	2.13060i	0.0604791	−	0.205973i	−0.923710	−	0.383092i	$-0.874859\pi$
$107$	0.625601	−	2.13060i	0.0604791	−	0.205973i	0.984190	+	0.177118i	$0.0566776\pi$
$108$	0.257385	+	1.98337i	0.0247669	+	0.190850i
$109$	2.44017	+	2.81610i	0.233726	+	0.269734i	0.860481	−	0.509482i	$-0.170163\pi$
$109$	2.44017	+	2.81610i	0.233726	+	0.269734i	−0.626756	+	0.779216i	$0.715618\pi$
$110$	−7.08369	+	10.8576i	−0.675403	+	1.03523i
$111$	−0.0148604	+	0.0171498i	−0.00141049	+	0.00162779i
$112$	−19.7669	+	5.21825i	−1.86780	+	0.493079i
$113$	1.68819	−	0.770969i	0.158811	−	0.0725267i	−0.334424	−	0.942423i	$-0.608542\pi$
$113$	1.68819	−	0.770969i	0.158811	−	0.0725267i	0.493235	+	0.869896i	$0.335814\pi$
$114$	−0.0381032	+	5.54254i	−0.00356869	+	0.519106i
$115$	4.64335	+	7.85868i	0.432995	+	0.732826i
$116$	0.0989221	−	7.19432i	0.00918468	−	0.667976i
$117$	2.52983	−	1.15534i	0.233883	−	0.106811i
$118$	9.19585	−	2.63162i	0.846547	−	0.242260i
$119$	−13.3336	−	11.5536i	−1.22229	−	1.05912i
$120$	4.46780	+	3.00325i	0.407852	+	0.274158i
$121$	7.98729	+	9.21783i	0.726118	+	0.837984i
$122$	1.57922	+	11.5467i	0.142976	+	1.04539i
$123$	7.20675	+	2.11609i	0.649811	+	0.190802i
$124$	−2.33519	−	3.74588i	−0.209706	−	0.336390i
$125$	−1.72744	+	12.0146i	−0.154507	+	1.07462i
$126$	3.04778	−	6.55410i	0.271518	−	0.583885i
$127$	5.97856	+	2.73032i	0.530511	+	0.242276i	0.662616	−	0.748959i	$-0.269446\pi$
$127$	5.97856	+	2.73032i	0.530511	+	0.242276i	−0.132105	+	0.991236i	$0.542174\pi$
$128$	−2.14693	+	11.1081i	−0.189764	+	0.981830i
$129$	2.33522	+	3.63368i	0.205605	+	0.319928i
$130$	2.15838	−	7.16811i	0.189303	−	0.628685i
$131$	0.522627	+	3.63495i	0.0456622	+	0.317587i	0.999832	+	0.0183221i	$0.00583243\pi$
$131$	0.522627	+	3.63495i	0.0456622	+	0.317587i	−0.954170	+	0.299265i	$0.903258\pi$
$132$	7.36590	−	6.20735i	0.641119	−	0.540281i
$133$	10.8298	−	16.8515i	0.939063	−	1.46121i
$134$	9.93636	+	8.73022i	0.858370	+	0.754176i
$135$	−1.82621	+	0.536225i	−0.157175	+	0.0461509i
$136$	−8.96294	+	3.87189i	−0.768566	+	0.332012i
$137$		−	16.6950i		−	1.42635i	−0.700988	−	0.713173i	$-0.747257\pi$
$137$		−	16.6950i		−	1.42635i	0.700988	−	0.713173i	$-0.252743\pi$
$138$	−1.62005	−	6.58600i	−0.137908	−	0.560638i
$139$	−20.9662			−1.77833			−0.889165	−	0.457588i	$-0.848714\pi$
$139$	−20.9662			−1.77833			−0.889165	+	0.457588i	$0.848714\pi$
$140$	−7.83812	−	17.8070i	−0.662442	−	1.50497i
$141$	−1.57087	−	5.34989i	−0.132291	−	0.450542i
$142$	−15.2217	−	13.3740i	−1.27738	−	1.12232i
$143$	−11.2686	−	7.24186i	−0.942324	−	0.605595i
$144$	−2.53534	−	3.09388i	−0.211278	−	0.257823i
$145$	6.77746	−	0.974452i	0.562838	−	0.0809238i
$146$	11.5809	+	3.48712i	0.958444	+	0.288596i
$147$	−16.0869	+	10.3384i	−1.32683	+	0.852701i
$148$	0.00707598	−	0.0448300i	0.000581642	−	0.00368500i
$149$	−3.22022	+	7.05129i	−0.263810	+	0.577664i	−0.994463	−	0.105085i	$-0.966489\pi$
$149$	−3.22022	+	7.05129i	−0.263810	+	0.577664i	0.730653	+	0.682749i	$0.239216\pi$
$150$	0.821370	−	1.76631i	0.0670646	−	0.144219i
$151$	21.3230	+	3.06578i	1.73524	+	0.249490i	0.936119	−	0.351683i	$-0.114390\pi$
$151$	21.3230	+	3.06578i	1.73524	+	0.249490i	0.799119	+	0.601173i	$0.205300\pi$
$152$	−5.79960	−	9.44719i	−0.470409	−	0.766268i
$153$	0.972517	−	3.31209i	0.0786234	−	0.267767i
$154$	−34.4916	+	4.71737i	−2.77942	+	0.380136i
$155$	3.17471	−	2.75090i	0.254999	−	0.220958i
$156$	−3.07127	+	4.63753i	−0.245898	+	0.371300i
$157$	−13.3497	+	15.4064i	−1.06542	+	1.22956i	−0.0931633	+	0.995651i	$0.529698\pi$
$157$	−13.3497	+	15.4064i	−1.06542	+	1.22956i	−0.972258	+	0.233911i	$0.924848\pi$
$158$	22.1959	−	6.35191i	1.76581	−	0.505331i
$159$	−1.46054	−	3.19813i	−0.115828	−	0.253628i
$160$	−10.7604	−	0.370012i	−0.850684	−	0.0292520i
$161$	−7.78330	+	23.2431i	−0.613410	+	1.83181i
$162$	1.41418	+	0.00972205i	0.111108	+	0.000763837i
$163$	0.126491	+	0.276977i	0.00990755	+	0.0216945i	0.914521	−	0.404538i	$-0.132568\pi$
$163$	0.126491	+	0.276977i	0.00990755	+	0.0216945i	−0.904614	+	0.426233i	$0.859840\pi$
$164$	−14.4703	+	4.03362i	−1.12994	+	0.314973i
$165$	6.92792	+	6.00308i	0.539338	+	0.467339i
$166$	0.625646	−	0.958964i	0.0485595	−	0.0744300i
$167$	13.6198	−	11.8017i	1.05394	−	0.913240i	0.0575629	−	0.998342i	$-0.481667\pi$
$167$	13.6198	−	11.8017i	1.05394	−	0.913240i	0.996372	+	0.0851019i	$0.0271216\pi$
$168$	1.76180	+	14.3484i	0.135926	+	1.10700i
$169$	−5.05188	−	1.48336i	−0.388606	−	0.114105i
$170$	−4.96950	−	7.85084i	−0.381143	−	0.602132i
$171$	3.87937	+	0.557769i	0.296663	+	0.0426536i
$172$	−7.80798	−	3.69636i	−0.595353	−	0.281845i
$173$	2.60410	+	1.18925i	0.197986	+	0.0904173i	0.511941	−	0.859021i	$-0.328927\pi$
$173$	2.60410	+	1.18925i	0.197986	+	0.0904173i	−0.313955	+	0.949438i	$0.601654\pi$
$174$	−5.03075	−	0.758647i	−0.381380	−	0.0575129i
$175$	−5.92240	+	3.80610i	−0.447692	+	0.287714i
$176$	−5.93384	+	18.3287i	−0.447280	+	1.38158i
$177$	−0.962543	−	6.69463i	−0.0723491	−	0.503199i
$178$	−7.12917	+	6.09216i	−0.534354	+	0.456627i
$179$	7.62422	+	4.89979i	0.569861	+	0.366227i	0.793617	−	0.608418i	$-0.208196\pi$
$179$	7.62422	+	4.89979i	0.569861	+	0.366227i	−0.223756	+	0.974645i	$0.571832\pi$
$180$	2.53212	−	2.84231i	0.188733	−	0.211853i
$181$	0.930650	−	0.273264i	0.0691747	−	0.0203115i	−0.246962	−	0.969025i	$-0.579432\pi$
$181$	0.930650	−	0.273264i	0.0691747	−	0.0203115i	0.316137	+	0.948714i	$0.397614\pi$
$182$	18.3428	−	8.22495i	1.35966	−	0.609674i
$183$	8.24074			0.609173
$184$	9.71787	+	9.46377i	0.716411	+	0.697678i
$185$	0.0431909			0.00317546
$186$	−2.84806	+	1.27707i	−0.208830	+	0.0936397i
$187$	−15.9521	+	4.68395i	−1.16653	+	0.342525i
$188$	8.32653	+	7.41785i	0.607275	+	0.541003i
$189$	−4.29967	−	2.76323i	−0.312755	−	0.200995i
$190$	8.02002	−	6.85343i	0.581834	−	0.497200i
$191$	1.38922	+	9.66223i	0.100520	+	0.699134i	0.976300	+	0.216423i	$0.0694389\pi$
$191$	1.38922	+	9.66223i	0.100520	+	0.699134i	−0.875779	+	0.482711i	$0.839652\pi$
$192$	7.57648	+	2.56847i	0.546785	+	0.185363i
$193$	−1.46161	+	0.939321i	−0.105209	+	0.0676138i	−0.592187	−	0.805800i	$-0.701735\pi$
$193$	−1.46161	+	0.939321i	−0.105209	+	0.0676138i	0.486978	+	0.873414i	$0.338099\pi$
$194$	13.8951	+	2.09541i	0.997613	+	0.150442i
$195$	−4.81506	−	2.19896i	−0.344813	−	0.157471i
$196$	16.3644	−	34.5673i	1.16889	−	2.46909i
$197$	−15.6137	−	2.24491i	−1.11243	−	0.159943i	−0.438495	−	0.898734i	$-0.644488\pi$
$197$	−15.6137	−	2.24491i	−1.11243	−	0.159943i	−0.673936	+	0.738790i	$0.735397\pi$
$198$	−3.64299	−	5.75521i	−0.258896	−	0.409005i
$199$	−20.0209	−	5.87866i	−1.41924	−	0.416727i	−0.519996	−	0.854169i	$-0.674067\pi$
$199$	−20.0209	−	5.87866i	−1.41924	−	0.416727i	−0.899247	+	0.437441i	$0.855885\pi$
$200$	0.474802	+	3.86686i	0.0335736	+	0.273428i
$201$	7.06834	−	6.12475i	0.498562	−	0.432006i
$202$	−13.3575	+	20.4738i	−0.939828	+	1.44053i
$203$	13.8959	+	12.0409i	0.975301	+	0.845103i
$204$	1.85378	+	6.65030i	0.129790	+	0.465614i
$205$	−5.93867	−	13.0039i	−0.414775	−	0.908230i
$206$	4.95424	+	0.0340589i	0.345178	+	0.00237300i
$207$	−4.76928	+	0.503925i	−0.331488	+	0.0350252i
$208$	0.305870	−	11.1204i	0.0212083	−	0.771063i
$209$	−7.84154	−	17.1706i	−0.542411	−	1.18771i
$210$	−13.2263	+	3.78504i	−0.912705	+	0.261193i
$211$	2.05906	−	2.37628i	0.141751	−	0.163590i	−0.680434	−	0.732809i	$-0.738209\pi$
$211$	2.05906	−	2.37628i	0.141751	−	0.163590i	0.822186	+	0.569219i	$0.192754\pi$
$212$	5.86262	+	3.88260i	0.402646	+	0.266658i
$213$	−10.8281	+	9.38264i	−0.741932	+	0.642888i
$214$	3.11137	−	0.425537i	0.212689	−	0.0290891i
$215$	2.31615	−	7.88808i	0.157960	−	0.537963i
$216$	−2.41045	+	1.47977i	−0.164011	+	0.100686i
$217$	11.1656	+	1.60537i	0.757970	+	0.108980i
$218$	−2.22201	+	4.77832i	−0.150494	+	0.323629i
$219$	3.55268	−	7.77929i	0.240068	−	0.525676i
$220$	−18.1097	−	2.85844i	−1.22096	−	0.192716i
$221$	8.07631	−	5.19033i	0.543272	−	0.349139i
$222$	−0.0307292	−	0.00925284i	−0.00206241	−	0.000621010i
$223$	22.0721	−	3.17348i	1.47805	−	0.212512i	0.644353	−	0.764728i	$-0.277127\pi$
$223$	22.0721	−	3.17348i	1.47805	−	0.212512i	0.833701	+	0.552216i	$0.186218\pi$
$224$	−18.1714	−	22.4882i	−1.21413	−	1.50256i
$225$	−1.15875	−	0.744684i	−0.0772500	−	0.0496456i
$226$	1.97171	+	1.73237i	0.131156	+	0.115236i
$227$	−6.69415	−	22.7982i	−0.444306	−	1.51317i	−0.812244	−	0.583317i	$-0.801754\pi$
$227$	−6.69415	−	22.7982i	−0.444306	−	1.51317i	0.367938	−	0.929850i	$-0.380064\pi$
$228$	−7.17426	+	3.15790i	−0.475127	+	0.209137i
$229$	17.4695			1.15442			0.577209	−	0.816597i	$-0.304142\pi$
$229$	17.4695			1.15442			0.577209	+	0.816597i	$0.304142\pi$
$230$	−7.45424	+	10.5391i	−0.491518	+	0.694930i
$231$			24.6163i			1.61964i
$232$	9.34094	−	4.03518i	0.613263	−	0.264923i
$233$	2.22820	−	0.654258i	0.145974	−	0.0428619i	−0.207929	−	0.978144i	$-0.566672\pi$
$233$	2.22820	−	0.654258i	0.145974	−	0.0428619i	0.353903	+	0.935282i	$0.384854\pi$
$234$	2.95470	+	2.59604i	0.193155	+	0.169709i
$235$	−5.73748	+	8.92770i	−0.374272	+	0.582379i
$236$	8.71688	+	10.3438i	0.567420	+	0.673325i
$237$	−2.32328	−	16.1588i	−0.150913	−	1.04962i
$238$	7.19385	−	23.8912i	0.466308	−	1.54863i
$239$	7.67562	+	11.9435i	0.496495	+	0.772561i	0.995573	−	0.0939962i	$-0.0299642\pi$
$239$	7.67562	+	11.9435i	0.496495	+	0.772561i	−0.499078	+	0.866557i	$0.666328\pi$
$240$	−1.29026	+	7.50311i	−0.0832861	+	0.484324i
$241$	−4.35029	−	1.98671i	−0.280227	−	0.127975i	0.270344	−	0.962764i	$-0.412863\pi$
$241$	−4.35029	−	1.98671i	−0.280227	−	0.127975i	−0.550571	+	0.834789i	$0.685590\pi$
$242$	−7.27322	+	15.6407i	−0.467540	+	1.00542i
$243$	0.142315	−	0.989821i	0.00912950	−	0.0634971i
$244$	−13.9863	+	8.71909i	−0.895381	+	0.558183i
$245$	34.9219	+	10.2540i	2.23108	+	0.655104i
$246$	1.43938	+	10.5242i	0.0917712	+	0.670997i
$247$	7.13804	+	8.23773i	0.454182	+	0.524154i
$248$	3.48256	−	5.18085i	0.221143	−	0.328984i
$249$	−0.611888	−	0.530204i	−0.0387768	−	0.0336003i
$250$	−16.5035	+	4.72288i	−1.04377	+	0.298701i
$251$	20.1961	−	9.22325i	1.27477	−	0.582167i	0.341005	−	0.940061i	$-0.389233\pi$
$251$	20.1961	−	9.22325i	1.27477	−	0.582167i	0.933762	+	0.357895i	$0.116505\pi$
$252$	10.2211	+	0.140540i	0.643868	+	0.00885320i
$253$	14.4605	+	18.0118i	0.909124	+	1.13239i
$254$	−0.0638982	+	9.29470i	−0.00400933	+	0.583201i
$255$	−5.97635	+	2.72931i	−0.374253	+	0.170916i
$256$	−15.5765	+	3.65703i	−0.973529	+	0.228564i
$257$	−6.22565	+	7.18478i	−0.388345	+	0.448174i	−0.915936	−	0.401324i	$-0.868550\pi$
$257$	−6.22565	+	7.18478i	−0.388345	+	0.448174i	0.527591	+	0.849499i	$0.323095\pi$
$258$	−3.33775	+	5.11598i	−0.207800	+	0.318507i
$259$	0.0759520	+	0.0876533i	0.00471943	+	0.00544651i
$260$	10.4988	−	1.36245i	0.651107	−	0.0844953i
$261$	−1.01353	+	3.45177i	−0.0627361	+	0.213659i
$262$	−4.38822	+	2.77770i	−0.271105	+	0.171607i
$263$	1.78463	−	12.4124i	0.110045	−	0.765382i	−0.857827	−	0.513939i	$-0.828186\pi$
$263$	1.78463	−	12.4124i	0.110045	−	0.765382i	0.967872	−	0.251443i	$-0.0809051\pi$
$264$	12.2722	+	5.91337i	0.755303	+	0.363943i
$265$	−2.77986	+	6.08704i	−0.170765	+	0.373924i
$266$	28.0120	+	4.22427i	1.71753	+	0.259006i
$267$	3.58497	+	5.57833i	0.219397	+	0.341388i
$268$	−5.51621	+	17.8736i	−0.336956	+	1.09181i
$269$	20.0010	−	2.87571i	1.21948	−	0.175335i	0.497634	−	0.867387i	$-0.334202\pi$
$269$	20.0010	−	2.87571i	1.21948	−	0.175335i	0.721847	+	0.692052i	$0.243293\pi$
$270$	−1.74865	−	2.04631i	−0.106420	−	0.124535i
$271$	7.16595	−	11.1504i	0.435300	−	0.677341i	−0.552421	−	0.833565i	$-0.686296\pi$
$271$	7.16595	−	11.1504i	0.435300	−	0.677341i	0.987722	+	0.156225i	$0.0499324\pi$
$272$	−10.1826	−	9.32559i	−0.617410	−	0.565447i
$273$	−4.00471	−	13.6388i	−0.242376	−	0.825457i
$274$	21.5435	−	9.66017i	1.30149	−	0.583592i
$275$			6.63404i			0.400048i
$276$	7.56132	−	5.90139i	0.455138	−	0.355222i
$277$		−	7.43682i		−	0.446835i	−0.974723	−	0.223418i	$-0.928279\pi$
$277$		−	7.43682i		−	0.446835i	0.974723	−	0.223418i	$-0.0717214\pi$
$278$	−12.1316	−	27.0552i	−0.727607	−	1.62267i
$279$	0.621804	+	2.11767i	0.0372265	+	0.126782i
$280$	18.4432	−	20.4181i	1.10219	−	1.22022i
$281$	−3.34856	+	5.21046i	−0.199758	+	0.310830i	−0.926652	−	0.375920i	$-0.877327\pi$
$281$	−3.34856	+	5.21046i	−0.199758	+	0.310830i	0.726894	+	0.686750i	$0.240963\pi$
$282$	5.99467	−	5.12268i	0.356977	−	0.305051i
$283$	16.6549	−	2.39462i	0.990032	−	0.142345i	0.371776	−	0.928322i	$-0.378749\pi$
$283$	16.6549	−	2.39462i	0.990032	−	0.142345i	0.618256	+	0.785977i	$0.287840\pi$
$284$	8.45041	−	27.3810i	0.501439	−	1.62477i
$285$	−4.03295	−	6.27539i	−0.238891	−	0.371722i
$286$	2.82475	−	18.7315i	0.167031	−	1.10762i
$287$	15.9473	−	34.9198i	0.941341	−	2.06125i
$288$	2.52539	−	5.06186i	0.148810	−	0.298273i
$289$	−0.723567	+	5.03252i	−0.0425627	+	0.296030i
$290$	5.17908	+	8.18194i	0.304126	+	0.480460i
$291$	2.79942	−	9.53394i	0.164105	−	0.558890i
$292$	2.20119	+	16.9620i	0.128815	+	0.992628i
$293$	5.05059	+	5.82869i	0.295058	+	0.340516i	0.883851	−	0.467769i	$-0.154942\pi$
$293$	5.05059	+	5.82869i	0.295058	+	0.340516i	−0.588792	+	0.808284i	$0.700396\pi$
$294$	−22.6493	−	14.7768i	−1.32093	−	0.861802i
$295$	−8.43002	+	9.72876i	−0.490814	+	0.566430i
$296$	0.0619440	−	0.0168089i	0.00360042	−	0.000976997i
$297$	−4.38108	+	2.00077i	−0.254216	+	0.116097i
$298$	−10.9624	−	0.0753634i	−0.635038	−	0.00436569i
$299$	−10.9422	−	7.62698i	−0.632801	−	0.441080i
$300$	2.75456	+	0.0378753i	0.159034	+	0.00218673i
$301$	20.0814	−	9.17086i	1.15747	−	0.528600i
$302$	8.38192	+	29.2896i	0.482325	+	1.68543i
$303$	13.0637	+	11.3198i	0.750492	+	0.650305i
$304$	8.83505	−	12.9503i	0.506725	−	0.742753i
$305$	−10.2713	−	11.8537i	−0.588132	−	0.678741i
$306$	4.83672	−	0.661511i	0.276497	−	0.0378160i
$307$	16.6419	+	4.88650i	0.949804	+	0.278887i	0.719705	−	0.694280i	$-0.244277\pi$
$307$	16.6419	+	4.88650i	0.949804	+	0.278887i	0.230098	+	0.973167i	$0.426095\pi$
$308$	−26.0452	−	41.7792i	−1.48407	−	2.38059i
$309$	0.498566	−	3.46760i	0.0283624	−	0.197265i
$310$	5.38680	+	2.50497i	0.305950	+	0.142273i
$311$	15.6658	+	7.15433i	0.888326	+	0.405685i	0.806688	−	0.590977i	$-0.201258\pi$
$311$	15.6658	+	7.15433i	0.888326	+	0.405685i	0.0816380	+	0.996662i	$0.473985\pi$
$312$	−7.76150	−	1.27982i	−0.439408	−	0.0724558i
$313$	−6.02199	−	9.37040i	−0.340383	−	0.529646i	0.628292	−	0.777978i	$-0.283754\pi$
$313$	−6.02199	−	9.37040i	−0.340383	−	0.529646i	−0.968675	+	0.248331i	$0.920118\pi$
$314$	−27.6052	−	8.31218i	−1.55785	−	0.469083i
$315$	1.38442	+	9.62885i	0.0780032	+	0.542524i
$316$	21.0398	+	24.9668i	1.18358	+	1.40449i
$317$	10.5942	−	16.4849i	0.595031	−	0.925886i	−0.404903	−	0.914360i	$-0.632695\pi$
$317$	10.5942	−	16.4849i	0.595031	−	0.925886i	0.999934	−	0.0115263i	$-0.00366901\pi$
$318$	3.28183	−	3.73524i	0.184036	−	0.209462i
$319$	16.6248	−	4.88150i	0.930813	−	0.273311i
$320$	−5.74879	−	14.0995i	−0.321367	−	0.788189i
$321$		−	2.22055i		−	0.123939i
$322$	−34.4970	+	3.40534i	−1.92244	+	0.189772i
$323$	13.5290			0.752771
$324$	0.805739	+	1.83051i	0.0447633	+	0.101695i
$325$	−1.07926	−	3.67562i	−0.0598666	−	0.203887i
$326$	−0.284226	+	0.323494i	−0.0157418	+	0.0179167i
$327$	3.13471	+	2.01456i	0.173350	+	0.111405i
$328$	−13.5780	−	16.3389i	−0.749720	−	0.902163i
$329$	−28.2077	+	4.05566i	−1.55514	+	0.223596i
$330$	−3.73781	+	12.4135i	−0.205760	+	0.683340i
$331$	−18.8420	+	12.1090i	−1.03565	+	0.665571i	−0.943907	−	0.330211i	$-0.892880\pi$
$331$	−18.8420	+	12.1090i	−1.03565	+	0.665571i	−0.0917423	+	0.995783i	$0.529244\pi$
$332$	1.59948	+	0.252463i	0.0877831	+	0.0138557i
$333$	−0.00942680	+	0.0206418i	−0.000516586	+	0.00113116i
$334$	23.1100	+	10.7466i	1.26452	+	0.588026i
$335$	−17.6200	−	2.53337i	−0.962683	−	0.138413i
$336$	−17.4961	+	10.5759i	−0.954489	+	0.576961i
$337$	−8.61680	+	29.3461i	−0.469387	+	1.59858i	0.296116	+	0.955152i	$0.404308\pi$
$337$	−8.61680	+	29.3461i	−0.469387	+	1.59858i	−0.765503	+	0.643433i	$0.777510\pi$
$338$	−1.00899	−	7.37737i	−0.0548819	−	0.401276i
$339$	1.40260	−	1.21536i	0.0761786	−	0.0660091i
$340$	7.25541	−	10.9555i	0.393480	−	0.594144i
$341$	6.96115	−	8.03360i	0.376967	−	0.435044i
$342$	1.52495	+	5.32876i	0.0824600	+	0.288146i
$343$	25.7386	+	56.3597i	1.38975	+	3.04314i
$344$	0.251943	−	12.2144i	0.0135838	−	0.658557i
$345$	6.66931	+	6.23217i	0.359064	+	0.335529i
$346$	−0.0278324	+	4.04853i	−0.00149628	+	0.217650i
$347$	2.36149	+	5.17094i	0.126771	+	0.277591i	0.962366	−	0.271755i	$-0.0876042\pi$
$347$	2.36149	+	5.17094i	0.126771	+	0.277591i	−0.835595	+	0.549346i	$0.814877\pi$
$348$	−1.93196	−	6.93077i	−0.103564	−	0.371528i
$349$	−15.4645	−	13.4001i	−0.827796	−	0.717290i	0.134022	−	0.990978i	$-0.457211\pi$
$349$	−15.4645	−	13.4001i	−0.827796	−	0.717290i	−0.961818	+	0.273689i	$0.911756\pi$
$350$	−8.33834	−	5.44008i	−0.445703	−	0.290785i
$351$	2.10186	−	1.82127i	0.112189	−	0.0972123i
$352$	−27.0852	+	2.94833i	−1.44365	+	0.157146i
$353$	17.3888	+	5.10583i	0.925515	+	0.271756i	0.709558	−	0.704647i	$-0.248895\pi$
$353$	17.3888	+	5.10583i	0.925515	+	0.271756i	0.215957	+	0.976403i	$0.430713\pi$
$354$	8.08195	−	5.11579i	0.429551	−	0.271901i
$355$	26.9925	+	3.88093i	1.43261	+	0.205978i
$356$	−11.9866	−	5.67455i	−0.635289	−	0.300750i
$357$	−16.0485	−	7.32910i	−0.849376	−	0.387897i
$358$	−1.91121	+	12.6736i	−0.101010	+	0.669821i
$359$	−8.93913	+	5.74483i	−0.471789	+	0.303200i	−0.754845	−	0.655903i	$-0.772288\pi$
$359$	−8.93913	+	5.74483i	−0.471789	+	0.303200i	0.283056	+	0.959103i	$0.408652\pi$
$360$	5.13293	+	1.62287i	0.270529	+	0.0855328i
$361$	−0.517942	−	3.60237i	−0.0272601	−	0.189598i
$362$	0.891126	+	1.04281i	0.0468365	+	0.0548091i
$363$	10.2607	+	6.59416i	0.538548	+	0.346104i
$364$	21.2273	+	18.9108i	1.11261	+	0.991194i
$365$	−15.6180	+	4.58586i	−0.817484	+	0.240035i
$366$	4.76833	+	10.6340i	0.249244	+	0.555850i
$367$	−23.2232			−1.21224			−0.606121	−	0.795373i	$-0.707275\pi$
$367$	−23.2232			−1.21224			−0.606121	+	0.795373i	$0.707275\pi$
$368$	−6.58922	+	18.0162i	−0.343487	+	0.939157i
$369$	7.51100			0.391007
$370$	0.0249915	+	0.0557344i	0.00129924	+	0.00289750i
$371$	−17.2417	+	5.06262i	−0.895145	+	0.262838i
$372$	−3.29593	−	2.93624i	−0.170886	−	0.152237i
$373$	1.63651	+	1.05172i	0.0847351	+	0.0544559i	0.582322	−	0.812958i	$-0.302144\pi$
$373$	1.63651	+	1.05172i	0.0847351	+	0.0544559i	−0.497587	+	0.867414i	$0.665781\pi$
$374$	−15.2746	−	17.8747i	−0.789831	−	0.924276i
$375$	1.72744	+	12.0146i	0.0892049	+	0.620433i
$376$	−4.75419	+	15.0369i	−0.245179	+	0.775470i
$377$	−8.41692	+	5.40923i	−0.433494	+	0.278589i
$378$	1.07782	−	7.14727i	0.0554372	−	0.367616i
$379$	−21.9865	−	10.0409i	−1.12937	−	0.515767i	−0.239008	−	0.971018i	$-0.576822\pi$
$379$	−21.9865	−	10.0409i	−1.12937	−	0.515767i	−0.890363	+	0.455251i	$0.849549\pi$
$380$	13.4844	+	6.38363i	0.691737	+	0.327473i
$381$	6.50560	+	0.935364i	0.333292	+	0.0479202i
$382$	−11.6645	+	7.38351i	−0.596808	+	0.377773i
$383$	−12.5581	−	3.68738i	−0.641688	−	0.188416i	−0.0553292	−	0.998468i	$-0.517621\pi$
$383$	−12.5581	−	3.68738i	−0.641688	−	0.188416i	−0.586359	+	0.810052i	$0.699439\pi$
$384$	1.06956	+	11.2630i	0.0545805	+	0.574765i
$385$	35.4088	−	30.6819i	1.80460	−	1.56369i
$386$	−2.05785	−	1.34258i	−0.104742	−	0.0683355i
$387$	3.26436	+	2.82858i	0.165937	+	0.143785i
$388$	5.33615	+	19.1431i	0.270902	+	0.971841i
$389$	−4.70087	−	10.2935i	−0.238343	−	0.521899i	0.752227	−	0.658904i	$-0.228980\pi$
$389$	−4.70087	−	10.2935i	−0.238343	−	0.521899i	−0.990570	+	0.137005i	$0.956252\pi$
$390$	0.0514628	−	7.48584i	0.00260592	−	0.379060i
$391$	−16.0480	+	4.06476i	−0.811584	+	0.205564i
$392$	54.0753	+	1.11539i	2.73122	+	0.0563359i
$393$	1.52554	+	3.34047i	0.0769534	+	0.168504i
$394$	−6.13765	−	21.4472i	−0.309210	−	1.08050i
$395$	−20.3475	+	23.4822i	−1.02379	+	1.18152i
$396$	5.31872	−	8.03112i	0.267276	−	0.403579i
$397$	−7.74960	+	6.71507i	−0.388941	+	0.337019i	−0.827279	−	0.561791i	$-0.810113\pi$
$397$	−7.74960	+	6.71507i	−0.388941	+	0.337019i	0.438338	+	0.898810i	$0.355567\pi$
$398$	−3.99869	−	29.2370i	−0.200436	−	1.46552i
$399$	5.64351	−	19.2200i	0.282529	−	0.962204i
$400$	−4.71515	+	2.85017i	−0.235757	+	0.142508i
$401$	32.7035	+	4.70206i	1.63314	+	0.234809i	0.897002	−	0.442027i	$-0.145740\pi$
$401$	32.7035	+	4.70206i	1.63314	+	0.234809i	0.736134	+	0.676836i	$0.236649\pi$
$402$	11.9935	+	5.57719i	0.598179	+	0.278165i
$403$	−2.54991	+	5.58352i	−0.127020	+	0.278135i
$404$	−34.1488	−	5.39006i	−1.69897	−	0.268166i
$405$	−1.60117	+	1.02901i	−0.0795626	+	0.0511318i
$406$	−7.49724	+	24.8988i	−0.372082	+	1.23570i
$407$	0.108182	−	0.0155542i	0.00536237	−	0.000770993i
$408$	−7.50904	+	6.24020i	−0.371753	+	0.308936i
$409$	22.7702	+	14.6335i	1.12591	+	0.723581i	0.964703	−	0.263339i	$-0.0848238\pi$
$409$	22.7702	+	14.6335i	1.12591	+	0.723581i	0.161210	+	0.986920i	$0.448460\pi$
$410$	13.3442	−	15.1878i	0.659024	−	0.750072i
$411$	−4.70351	−	16.0187i	−0.232007	−	0.790144i
$412$	2.82271	+	6.41277i	0.139065	+	0.315935i
$413$	−34.5683			−1.70099
$414$	−3.40992	−	5.86280i	−0.167588	−	0.288141i
$415$			1.54100i			0.0756448i
$416$	14.5270	−	6.03989i	0.712247	−	0.296130i
$417$	−20.1169	+	5.90686i	−0.985129	+	0.289260i
$418$	17.6200	−	20.0543i	0.861820	−	0.980887i
$419$	−1.64328	+	2.55699i	−0.0802794	+	0.124917i	−0.879071	−	0.476690i	$-0.841836\pi$
$419$	−1.64328	+	2.55699i	−0.0802794	+	0.124917i	0.798792	+	0.601607i	$0.205473\pi$
$420$	−12.5374	−	14.8774i	−0.611764	−	0.725945i
$421$	−1.96039	−	13.6348i	−0.0955436	−	0.664520i	−0.980161	−	0.198203i	$-0.936490\pi$
$421$	−1.96039	−	13.6348i	−0.0955436	−	0.664520i	0.884617	−	0.466318i	$-0.154420\pi$
$422$	4.25784	+	1.28207i	0.207268	+	0.0624103i
$423$	−3.01448	−	4.69062i	−0.146569	−	0.228066i
$424$	−1.61791	+	9.81184i	−0.0785728	+	0.476505i
$425$	−4.32503	−	1.97517i	−0.209795	−	0.0958101i
$426$	−18.3730	−	8.54382i	−0.890177	−	0.413949i
$427$	5.99411	−	41.6899i	0.290075	−	2.01752i
$428$	2.34945	+	3.76875i	0.113565	+	0.182169i
$429$	−12.8524	−	3.77379i	−0.620518	−	0.182201i
$430$	11.5191	−	1.57545i	0.555502	−	0.0759752i
$431$	−0.454945	−	0.525035i	−0.0219139	−	0.0252900i	0.744687	−	0.667414i	$-0.232599\pi$
$431$	−0.454945	−	0.525035i	−0.0219139	−	0.0252900i	−0.766601	+	0.642124i	$0.778053\pi$
$432$	−3.30428	−	2.25427i	−0.158977	−	0.108458i
$433$	−15.7014	−	13.6054i	−0.754563	−	0.653832i	0.190141	−	0.981757i	$-0.439105\pi$
$433$	−15.7014	−	13.6054i	−0.754563	−	0.653832i	−0.944704	+	0.327924i	$0.893651\pi$
$434$	4.38912	+	15.3372i	0.210685	+	0.736211i
$435$	6.22839	−	2.84441i	0.298629	−	0.136379i
$436$	−7.45177	−	0.102462i	−0.356875	−	0.00490704i
$437$	−7.16117	−	17.3785i	−0.342565	−	0.831325i
$438$	12.0943	+	0.0831443i	0.577886	+	0.00397279i
$439$	−22.0573	+	10.0732i	−1.05274	+	0.480770i	−0.865168	−	0.501481i	$-0.832789\pi$
$439$	−22.0573	+	10.0732i	−1.05274	+	0.480770i	−0.187570	+	0.982251i	$0.560061\pi$
$440$	−6.79019	−	25.0231i	−0.323709	−	1.19293i
$441$	−12.5226	+	14.4519i	−0.596316	+	0.688185i
$442$	11.3709	+	7.41858i	0.540859	+	0.352866i
$443$	−3.54065	−	4.08613i	−0.168221	−	0.194138i	0.665379	−	0.746506i	$-0.268270\pi$
$443$	−3.54065	−	4.08613i	−0.168221	−	0.194138i	−0.833601	+	0.552368i	$0.813724\pi$
$444$	−0.00584071	−	0.0450076i	−0.000277188	−	0.00213597i
$445$	3.55569	−	12.1096i	0.168556	−	0.574048i
$446$	16.8667	+	26.6460i	0.798659	+	1.26173i
$447$	−1.10320	+	7.67290i	−0.0521794	+	0.362916i
$448$	18.5048	−	36.4612i	0.874270	−	1.72263i
$449$	8.93461	−	19.5641i	0.421650	−	0.923285i	−0.572958	−	0.819585i	$-0.694204\pi$
$449$	8.93461	−	19.5641i	0.421650	−	0.923285i	0.994609	−	0.103701i	$-0.0330684\pi$
$450$	0.290471	−	1.92617i	0.0136929	−	0.0908006i
$451$	−19.5579	−	30.4326i	−0.920944	−	1.43302i
$452$	−1.09460	+	3.54673i	−0.0514857	+	0.166824i
$453$	21.3230	−	3.06578i	1.00184	−	0.144043i
$454$	25.5458	−	21.8299i	1.19893	−	1.02453i
$455$	−14.6269	+	22.7599i	−0.685720	+	1.06700i
$456$	−8.22625	−	7.43058i	−0.385230	−	0.347969i
$457$	4.06357	+	13.8393i	0.190086	+	0.647373i	0.998289	+	0.0584695i	$0.0186220\pi$
$457$	4.06357	+	13.8393i	0.190086	+	0.647373i	−0.808203	+	0.588904i	$0.799560\pi$
$458$	10.1083	+	22.5430i	0.472332	+	1.05337i
$459$		−	3.45192i		−	0.161122i
$460$	−17.9132	−	3.52088i	−0.835206	−	0.164162i
$461$		−	22.6957i		−	1.05704i	−0.848920	−	0.528522i	$-0.822746\pi$
$461$		−	22.6957i		−	1.05704i	0.848920	−	0.528522i	$-0.177254\pi$
$462$	−31.7655	+	14.2437i	−1.47786	+	0.662677i
$463$	9.44402	+	32.1634i	0.438901	+	1.49476i	0.821157	+	0.570703i	$0.193329\pi$
$463$	9.44402	+	32.1634i	0.438901	+	1.49476i	−0.382256	+	0.924057i	$0.624853\pi$
$464$	10.6120	+	9.71889i	0.492651	+	0.451188i
$465$	2.27109	−	3.53389i	0.105319	−	0.163880i
$466$	2.13357	+	2.49674i	0.0988356	+	0.115659i
$467$	−38.7988	+	5.57842i	−1.79539	+	0.258139i	−0.957652	−	0.287928i	$-0.907034\pi$
$467$	−38.7988	+	5.57842i	−1.79539	+	0.258139i	−0.837742	+	0.546066i	$0.816125\pi$
$468$	−1.64032	+	5.31496i	−0.0758236	+	0.245684i
$469$	−25.8438	−	40.2137i	−1.19336	−	1.85690i
$470$	−14.8404	−	2.23796i	−0.684535	−	0.103229i
$471$	−8.46846	+	18.5433i	−0.390206	+	0.854432i
$472$	−8.30405	+	17.2337i	−0.382225	+	0.793244i
$473$	2.96064	−	20.5917i	0.136130	−	0.946807i
$474$	19.5073	−	12.3479i	0.896001	−	0.567159i
$475$	1.52091	−	5.17975i	0.0697842	−	0.237663i
$476$	34.9923	−	4.54100i	1.60387	−	0.208137i
$477$	−2.30239	−	2.65710i	−0.105419	−	0.121660i
$478$	−10.9708	+	16.8156i	−0.501794	+	0.769130i
$479$	21.9128	−	25.2887i	1.00122	−	1.15547i	0.0133937	−	0.999910i	$-0.495737\pi$
$479$	21.9128	−	25.2887i	1.00122	−	1.15547i	0.987827	−	0.155559i	$-0.0497180\pi$
$480$	−10.4288	+	2.67653i	−0.476006	+	0.122166i
$481$	−0.0574082	+	0.0262174i	−0.00261759	+	0.00119541i
$482$	0.0464954	−	6.76327i	0.00211781	−	0.308059i
$483$	−0.919698	+	24.4944i	−0.0418477	+	1.11453i
$484$	−24.3916	−	0.335385i	−1.10871	−	0.0152448i
$485$	−17.2031	+	7.85638i	−0.781151	+	0.356740i
$486$	1.35963	−	0.389092i	0.0616743	−	0.0176496i
$487$	31.2445	+	27.0735i	1.41582	+	1.22682i	0.937198	+	0.348799i	$0.113410\pi$
$487$	31.2445	+	27.0735i	1.41582	+	1.22682i	0.478625	+	0.878019i	$0.341135\pi$
$488$	−19.3442	−	13.0031i	−0.875670	−	0.588624i
$489$	0.199401	+	0.230121i	0.00901722	+	0.0104064i
$490$	6.97481	+	50.9972i	0.315090	+	2.30382i
$491$	−37.2533	−	10.9386i	−1.68122	−	0.493650i	−0.704777	−	0.709429i	$-0.748953\pi$
$491$	−37.2533	−	10.9386i	−1.68122	−	0.493650i	−0.976442	+	0.215779i	$0.930771\pi$
$492$	−12.7478	+	7.94699i	−0.574714	+	0.358278i
$493$	−1.76730	+	12.2919i	−0.0795954	+	0.553598i
$494$	−6.49989	+	13.9777i	−0.292444	+	0.628885i
$495$	8.33855	+	3.80809i	0.374790	+	0.171161i
$496$	8.70059	+	1.49618i	0.390668	+	0.0671807i
$497$	39.5907	+	61.6043i	1.77588	+	2.76333i
$498$	0.330131	−	1.09638i	0.0147935	−	0.0491301i
$499$	−5.19460	−	36.1293i	−0.232542	−	1.61737i	−0.687040	−	0.726620i	$-0.741090\pi$
$499$	−5.19460	−	36.1293i	−0.232542	−	1.61737i	0.454497	−	0.890748i	$-0.349819\pi$
$500$	−15.6439	−	18.5637i	−0.699616	−	0.830194i
$501$	9.74323	−	15.1608i	0.435296	−	0.677333i
$502$	23.5879	+	20.7247i	1.05278	+	0.924987i
$503$	−32.9960	+	9.68850i	−1.47122	+	0.431989i	−0.916495	−	0.400046i	$-0.868994\pi$
$503$	−32.9960	+	9.68850i	−1.47122	+	0.431989i	−0.554724	+	0.832035i	$0.687176\pi$
$504$	5.73285	+	13.2708i	0.255361	+	0.591130i
$505$		−	32.9002i		−	1.46404i
$506$	−14.8755	+	29.0823i	−0.661297	+	1.29286i
$507$	−5.26515			−0.233834
$508$	−12.0311	+	5.29572i	−0.533792	+	0.234960i
$509$	−2.80657	−	9.55830i	−0.124399	−	0.423664i	0.873618	−	0.486613i	$-0.161768\pi$
$509$	−2.80657	−	9.55830i	−0.124399	−	0.423664i	−0.998017	+	0.0629487i	$0.979950\pi$
$510$	−6.98004	−	6.13276i	−0.309081	−	0.271563i
$511$	−36.7713	−	23.6315i	−1.62667	−	1.04540i
$512$	−13.7321	−	17.9842i	−0.606878	−	0.794795i
$513$	3.87937	−	0.557769i	0.171278	−	0.0246261i
$514$	−12.8737	−	3.87640i	−0.567836	−	0.170981i
$515$	−5.60931	+	3.60488i	−0.247176	+	0.158850i
$516$	−8.53309	−	1.34687i	−0.375648	−	0.0592925i
$517$	−11.1558	+	24.4278i	−0.490631	+	1.07433i
$518$	−0.0691618	+	0.148729i	−0.00303879	+	0.00653477i
$519$	2.83367	+	0.407420i	0.124384	+	0.0178838i
$520$	7.83302	+	12.7595i	0.343501	+	0.559542i
$521$	5.96439	−	20.3128i	0.261305	−	0.889921i	−0.719428	−	0.694567i	$-0.755596\pi$
$521$	5.96439	−	20.3128i	0.261305	−	0.889921i	0.980733	−	0.195355i	$-0.0625858\pi$
$522$	−5.04070	+	0.689409i	−0.220626	+	0.0301746i
$523$	−16.7891	+	14.5479i	−0.734138	+	0.636134i	−0.939499	−	0.342552i	$-0.888709\pi$
$523$	−16.7891	+	14.5479i	−0.734138	+	0.636134i	0.205361	+	0.978686i	$0.434163\pi$
$524$	−6.12355	−	4.05540i	−0.267508	−	0.177161i
$525$	−4.61020	+	5.32046i	−0.201206	+	0.232204i
$526$	17.0499	−	4.87924i	0.743410	−	0.212745i
$527$	3.16490	+	6.93015i	0.137865	+	0.301882i
$528$	−0.529696	+	19.2580i	−0.0230521	+	0.838097i
$529$	13.7159	+	18.4628i	0.596344	+	0.802729i
$530$	−9.46335	−	0.0650576i	−0.411062	−	0.00282592i
$531$	−2.80965	−	6.15227i	−0.121928	−	0.266986i
$532$	10.7574	+	38.5916i	0.466394	+	1.67316i
$533$	15.7871	+	13.6796i	0.683814	+	0.592528i
$534$	−5.12403	+	7.85391i	−0.221739	+	0.339872i
$535$	−3.19410	+	2.76770i	−0.138093	+	0.119658i
$536$	−26.2564	+	3.22395i	−1.13410	+	0.139254i
$537$	8.69581	+	2.55332i	0.375252	+	0.110184i
$538$	15.2840	+	24.1457i	0.658940	+	1.04100i
$539$	91.1630	+	13.1073i	3.92667	+	0.564570i
$540$	1.62878	−	3.44056i	0.0700917	−	0.148058i
$541$	−29.3535	−	13.4053i	−1.26200	−	0.576338i	−0.331789	−	0.943353i	$-0.607652\pi$
$541$	−29.3535	−	13.4053i	−1.26200	−	0.576338i	−0.930215	+	0.367015i	$0.880380\pi$
$542$	18.5352	+	2.79514i	0.796154	+	0.120062i
$543$	0.815965	−	0.524389i	0.0350164	−	0.0225037i
$544$	6.14202	−	18.5359i	0.263337	−	0.794719i
$545$	−1.00932	−	7.02000i	−0.0432347	−	0.300704i
$546$	15.2826	−	13.0596i	0.654033	−	0.558897i
$547$	25.7590	+	16.5543i	1.10138	+	0.707811i	0.959397	−	0.282058i	$-0.0910172\pi$
$547$	25.7590	+	16.5543i	1.10138	+	0.707811i	0.141979	+	0.989870i	$0.454654\pi$
$548$	24.9314	+	22.2106i	1.06502	+	0.948790i
$549$	7.90693	−	2.32169i	0.337460	−	0.0990871i
$550$	−8.56072	+	3.83864i	−0.365030	+	0.163680i
$551$	−14.0995			−0.600660
$552$	11.9905	+	6.34258i	0.510349	+	0.269958i
$553$	−83.4371			−3.54811
$554$	9.59664	−	4.30315i	0.407722	−	0.182824i
$555$	0.0414413	−	0.0121683i	0.00175909	−	0.000516514i
$556$	27.8930	−	31.3098i	1.18293	−	1.32783i
$557$	37.5773	+	24.1495i	1.59220	+	1.02325i	0.970841	+	0.239723i	$0.0770567\pi$
$557$	37.5773	+	24.1495i	1.59220	+	1.02325i	0.621362	+	0.783524i	$0.286580\pi$
$558$	−2.37290	+	2.02773i	−0.100453	+	0.0858408i
$559$	1.70961	+	11.8906i	0.0723086	+	0.502917i
$560$	37.0198	+	11.9850i	1.56437	+	0.506459i
$561$	−13.9863	+	8.98844i	−0.590502	+	0.379492i
$562$	−8.66126	−	1.30614i	−0.365353	−	0.0550960i
$563$	−10.3604	−	4.73144i	−0.436639	−	0.199406i	0.184953	−	0.982747i	$-0.440787\pi$
$563$	−10.3604	−	4.73144i	−0.436639	−	0.199406i	−0.621592	+	0.783341i	$0.713514\pi$
$564$	10.0791	+	4.77152i	0.424407	+	0.200917i
$565$	−3.49640	−	0.502707i	−0.147095	−	0.0211490i
$566$	12.7271	+	20.1063i	0.534959	+	0.845130i
$567$	−4.90399	−	1.43994i	−0.205948	−	0.0604719i
$568$	40.2227	−	4.93885i	1.68771	−	0.207230i
$569$	19.5036	−	16.8999i	0.817632	−	0.708482i	−0.141961	−	0.989872i	$-0.545341\pi$
$569$	19.5036	−	16.8999i	0.817632	−	0.708482i	0.959594	+	0.281390i	$0.0907954\pi$
$570$	5.76432	−	8.83532i	0.241441	−	0.370071i
$571$	33.8634	+	29.3428i	1.41714	+	1.22796i	0.936324	+	0.351138i	$0.114205\pi$
$571$	33.8634	+	29.3428i	1.41714	+	1.22796i	0.480817	+	0.876821i	$0.340340\pi$
$572$	25.8061	−	7.19347i	1.07901	−	0.300774i
$573$	4.05511	+	8.87945i	0.169405	+	0.370944i
$574$	54.2888	+	0.373219i	2.26597	+	0.0155779i
$575$	−0.247856	+	6.60117i	−0.0103363	+	0.275288i
$576$	7.99320	+	0.329886i	0.333050	+	0.0137453i
$577$	2.82404	+	6.18379i	0.117566	+	0.257434i	0.959262	−	0.282518i	$-0.0911696\pi$
$577$	2.82404	+	6.18379i	0.117566	+	0.257434i	−0.841696	+	0.539952i	$0.818442\pi$
$578$	−6.91275	+	1.97825i	−0.287532	+	0.0822843i
$579$	−1.13777	+	1.31306i	−0.0472841	+	0.0545687i
$580$	−7.56140	+	11.4175i	−0.313970	+	0.474086i
$581$	−3.12737	+	2.70988i	−0.129745	+	0.112425i
$582$	13.9226	−	1.90418i	0.577112	−	0.0789306i
$583$	−4.77071	+	16.2475i	−0.197583	+	0.672905i
$584$	−20.6145	+	12.6552i	−0.853034	+	0.523675i
$585$	−5.23953	−	0.753331i	−0.216628	−	0.0311464i
$586$	−4.59906	+	9.89003i	−0.189985	+	0.408554i
$587$	−13.4390	+	29.4273i	−0.554686	+	1.21459i	0.399873	+	0.916571i	$0.369054\pi$
$587$	−13.4390	+	29.4273i	−0.554686	+	1.21459i	−0.954559	+	0.298023i	$0.903673\pi$
$588$	5.96281	−	37.7775i	0.245902	−	1.55792i
$589$	−7.27692	+	4.67659i	−0.299840	+	0.192696i
$590$	−17.4320	−	5.24895i	−0.717666	−	0.216096i
$591$	−15.6137	+	2.24491i	−0.642262	+	0.0923434i
$592$	0.0575331	+	0.0702078i	0.00236460	+	0.00288552i
$593$	14.7867	+	9.50285i	0.607218	+	0.390235i	0.807813	−	0.589439i	$-0.200651\pi$
$593$	14.7867	+	9.50285i	0.607218	+	0.390235i	−0.200595	+	0.979674i	$0.564287\pi$
$594$	−5.11686	−	4.49574i	−0.209947	−	0.184462i
$595$	9.46052	+	32.2196i	0.387844	+	1.32087i
$596$	−6.24593	−	14.1898i	−0.255843	−	0.581237i
$597$	−20.8661			−0.853993
$598$	3.51059	−	18.5332i	0.143559	−	0.757878i
$599$			11.4905i			0.469491i	0.972057	+	0.234745i	$0.0754256\pi$
$599$			11.4905i			0.469491i	−0.972057	+	0.234745i	$0.924574\pi$
$600$	1.54499	+	3.57646i	0.0630739	+	0.146008i
$601$	−14.6997	+	4.31623i	−0.599615	+	0.176063i	−0.567433	−	0.823419i	$-0.692064\pi$
$601$	−14.6997	+	4.31623i	−0.599615	+	0.176063i	−0.0321814	+	0.999482i	$0.510245\pi$
$602$	23.4539	+	20.6069i	0.955911	+	0.839876i
$603$	5.05648	−	7.86803i	0.205916	−	0.320411i
$604$	−32.9459	+	27.7640i	−1.34055	+	1.12970i
$605$	−3.30378	−	22.9783i	−0.134318	−	0.934199i
$606$	−7.04826	+	23.4077i	−0.286316	+	0.950872i
$607$	−21.6392	−	33.6713i	−0.878309	−	1.36668i	−0.929825	−	0.368003i	$-0.880042\pi$
$607$	−21.6392	−	33.6713i	−0.878309	−	1.36668i	0.0515155	−	0.998672i	$-0.483595\pi$
$608$	21.8236	+	3.90752i	0.885064	+	0.158471i
$609$	16.7253	+	7.63820i	0.677744	+	0.309515i
$610$	9.35302	−	20.1132i	0.378693	−	0.814359i
$611$	2.20688	−	15.3492i	0.0892809	−	0.620962i
$612$	3.65229	+	5.85864i	0.147635	+	0.236822i
$613$	−10.0009	−	2.93652i	−0.403931	−	0.118605i	0.0734550	−	0.997299i	$-0.476597\pi$
$613$	−10.0009	−	2.93652i	−0.403931	−	0.118605i	−0.477386	+	0.878694i	$0.658416\pi$
$614$	3.32382	+	24.3025i	0.134138	+	0.980771i
$615$	−9.36173	−	10.8040i	−0.377501	−	0.435660i
$616$	38.8423	−	57.7840i	1.56500	−	2.32818i
$617$	−19.8097	−	17.1652i	−0.797509	−	0.691045i	0.157534	−	0.987514i	$-0.449646\pi$
$617$	−19.8097	−	17.1652i	−0.797509	−	0.691045i	−0.955043	+	0.296468i	$0.904191\pi$
$618$	4.76316	−	1.36309i	0.191602	−	0.0548316i
$619$	−34.3687	+	15.6957i	−1.38139	+	0.630862i	−0.961017	−	0.276488i	$-0.910830\pi$
$619$	−34.3687	+	15.6957i	−1.38139	+	0.630862i	−0.420377	+	0.907349i	$0.638102\pi$
$620$	−0.115510	+	8.40070i	−0.00463899	+	0.337380i
$621$	−4.43412	+	1.82717i	−0.177935	+	0.0733220i
$622$	−0.167435	+	24.3552i	−0.00671351	+	0.976555i
$623$	30.8284	−	14.0789i	1.23511	−	0.564057i
$624$	−2.83951	−	10.7562i	−0.113671	−	0.430591i
$625$	10.6190	−	12.2550i	0.424761	−	0.490200i
$626$	8.60728	−	13.1929i	0.344016	−	0.527294i
$627$	−12.3614	−	14.2658i	−0.493667	−	0.569722i
$628$	−5.24694	−	40.4321i	−0.209376	−	1.61341i
$629$	−0.0220688	+	0.0751596i	−0.000879943	+	0.00299681i
$630$	−11.6242	+	7.35801i	−0.463120	+	0.293150i
$631$	−0.800227	+	5.56570i	−0.0318565	+	0.221567i	−0.999531	−	0.0306371i	$-0.990246\pi$
$631$	−0.800227	+	5.56570i	−0.0318565	+	0.221567i	0.967674	+	0.252204i	$0.0811555\pi$
$632$	−20.0434	+	41.5967i	−0.797284	+	1.65463i
$633$	1.30618	−	2.86013i	0.0519159	−	0.113680i
$634$	27.4026	+	4.13237i	1.08830	+	0.164118i
$635$	−6.76315	−	10.5237i	−0.268387	−	0.417619i
$636$	6.71900	+	2.07363i	0.266426	+	0.0822249i
$637$	−52.6416	+	7.56872i	−2.08574	+	0.299884i
$638$	15.9188	+	18.6285i	0.630231	+	0.737509i
$639$	−7.74613	+	12.0532i	−0.306432	+	0.476818i
$640$	14.8680	−	15.5768i	0.587707	−	0.615726i
$641$	−0.569210	−	1.93855i	−0.0224824	−	0.0765682i	0.947488	−	0.319792i	$-0.103613\pi$
$641$	−0.569210	−	1.93855i	−0.0224824	−	0.0765682i	−0.969970	+	0.243224i	$0.921795\pi$
$642$	2.86545	−	1.28487i	0.113090	−	0.0507099i
$643$			20.8117i			0.820733i	0.911921	+	0.410367i	$0.134599\pi$
$643$			20.8117i			0.820733i	−0.911921	+	0.410367i	$0.865401\pi$
$644$	−24.3553	−	42.5453i	−0.959732	−	1.67652i
$645$		−	8.22109i		−	0.323705i
$646$	7.82824	+	17.4581i	0.307998	+	0.686878i
$647$	1.86452	+	6.34997i	0.0733018	+	0.249643i	0.987990	−	0.154517i	$-0.0493821\pi$
$647$	1.86452	+	6.34997i	0.0733018	+	0.249643i	−0.914688	+	0.404160i	$0.867564\pi$
$648$	−1.89591	+	2.09893i	−0.0744785	+	0.0824538i
$649$	−17.6114	+	27.4039i	−0.691308	+	1.07570i
$650$	4.11861	−	3.51952i	0.161545	−	0.138047i
$651$	11.1656	−	1.60537i	0.437614	−	0.0629194i
$652$	−0.581905	−	0.179589i	−0.0227891	−	0.00703324i
$653$	11.3466	+	17.6556i	0.444026	+	0.690919i	0.989063	−	0.147494i	$-0.0471206\pi$
$653$	11.3466	+	17.6556i	0.444026	+	0.690919i	−0.545037	+	0.838412i	$0.683484\pi$
$654$	−0.785796	+	5.21078i	−0.0307271	+	0.203758i
$655$	2.90358	−	6.35795i	0.113452	−	0.248426i
$656$	13.2274	−	26.9755i	0.516444	−	1.05322i
$657$	1.21710	−	8.46508i	0.0474834	−	0.330254i
$658$	−21.5553	−	34.0531i	−0.840312	−	1.32753i
$659$	−7.93414	+	27.0212i	−0.309070	+	1.05260i	0.647734	+	0.761866i	$0.275717\pi$
$659$	−7.93414	+	27.0212i	−0.309070	+	1.05260i	−0.956805	+	0.290731i	$0.906102\pi$
$660$	−18.1814	+	2.35944i	−0.707712	+	0.0918410i
$661$	−20.9820	−	24.2146i	−0.816107	−	0.941837i	0.183041	−	0.983105i	$-0.441406\pi$
$661$	−20.9820	−	24.2146i	−0.816107	−	0.941837i	−0.999148	+	0.0412678i	$0.986860\pi$
$662$	−26.5282	−	17.3075i	−1.03105	−	0.672675i
$663$	6.28688	−	7.25545i	0.244162	−	0.281778i
$664$	0.599723	+	2.21009i	0.0232738	+	0.0857682i
$665$	−34.6807	+	15.8381i	−1.34486	+	0.614176i
$666$	−0.0320913		0.000220618i	−0.00124351		8.54876e-6i
$667$	16.7249	−	4.23618i	0.647589	−	0.164026i
$668$	−0.495549	+	36.0399i	−0.0191734	+	1.39442i
$669$	20.2839	−	9.26335i	0.784221	−	0.358142i
$670$	−6.92631	−	24.2031i	−0.267587	−	0.935048i
$671$	−29.9957	−	25.9915i	−1.15797	−	1.00339i
$672$	−23.7710	−	16.4578i	−0.916988	−	0.634874i
$673$	−11.7899	−	13.6063i	−0.454469	−	0.524485i	0.481558	−	0.876414i	$-0.340071\pi$
$673$	−11.7899	−	13.6063i	−0.454469	−	0.524485i	−0.936027	+	0.351929i	$0.885526\pi$
$674$	−42.8548	+	5.86118i	−1.65070	+	0.225764i
$675$	−1.32161	−	0.388061i	−0.0508690	−	0.0149365i
$676$	8.93609	−	5.57078i	0.343696	−	0.214261i
$677$	−2.63848	+	18.3510i	−0.101405	+	0.705288i	0.874170	+	0.485620i	$0.161406\pi$
$677$	−2.63848	+	18.3510i	−0.101405	+	0.705288i	−0.975575	+	0.219667i	$0.929503\pi$
$678$	2.37991	+	1.10670i	0.0913997	+	0.0425026i
$679$	−46.1960	−	21.0970i	−1.77284	−	0.809629i
$680$	18.3354	+	3.02339i	0.703129	+	0.115942i
$681$	−12.8460	−	19.9887i	−0.492259	−	0.765969i
$682$	14.3946	+	4.33436i	0.551200	+	0.165971i
$683$	−5.99859	−	41.7211i	−0.229530	−	1.59641i	−0.700096	−	0.714049i	$-0.746859\pi$
$683$	−5.99859	−	41.7211i	−0.229530	−	1.59641i	0.470566	−	0.882365i	$-0.344050\pi$
$684$	−5.99397	+	5.05121i	−0.229185	+	0.193138i
$685$	−17.1792	+	26.7314i	−0.656385	+	1.02135i
$686$	−57.8347	+	65.8250i	−2.20814	+	2.51321i
$687$	16.7619	−	4.92173i	0.639505	−	0.187776i
$688$	15.9075	−	6.74249i	0.606469	−	0.257055i
$689$		−	9.77815i		−	0.372518i
$690$	−4.18308	+	12.2123i	−0.159247	+	0.464916i
$691$	36.0367			1.37090			0.685450	−	0.728120i	$-0.259606\pi$
$691$	36.0367			1.37090			0.685450	+	0.728120i	$0.259606\pi$
$692$	−5.24041	+	2.30668i	−0.199211	+	0.0876867i
$693$	6.93522	+	23.6192i	0.263447	+	0.897219i
$694$	−5.30627	+	6.03937i	−0.201423	+	0.229251i
$695$	33.5704	+	21.5744i	1.27340	+	0.818362i
$696$	7.82573	−	6.50338i	0.296633	−	0.246510i
$697$	25.6634	−	3.68984i	0.972072	−	0.139763i
$698$	8.34355	−	27.7094i	0.315808	−	1.04882i
$699$	1.95361	−	1.25551i	0.0738925	−	0.0474878i
$700$	2.19521	−	13.9078i	0.0829710	−	0.525664i
$701$	3.66720	−	8.03006i	0.138508	−	0.303291i	−0.827648	−	0.561247i	$-0.810322\pi$
$701$	3.66720	−	8.03006i	0.138508	−	0.303291i	0.966157	+	0.257956i	$0.0830490\pi$
$702$	3.56641	+	1.65845i	0.134605	+	0.0625941i
$703$	−0.0880325	−	0.0126572i	−0.00332021	−	0.000477374i
$704$	−19.4769	−	33.2454i	−0.734062	−	1.25298i
$705$	−2.98985	+	10.1825i	−0.112604	+	0.383495i
$706$	3.47301	+	25.3933i	0.130708	+	0.955691i
$707$	66.7691	−	57.8557i	2.51111	−	2.17589i
$708$	11.2780	+	7.46898i	0.423852	+	0.280702i
$709$	−7.39785	+	8.53758i	−0.277832	+	0.320635i	−0.877466	−	0.479639i	$-0.840768\pi$
$709$	−7.39785	+	8.53758i	−0.277832	+	0.320635i	0.599634	+	0.800275i	$0.295313\pi$
$710$	10.6106	+	37.0773i	0.398207	+	1.39149i
$711$	−6.78162	−	14.8497i	−0.254331	−	0.556907i
$712$	0.386775	−	18.7512i	0.0144950	−	0.702732i
$713$	7.22680	−	7.73371i	0.270646	−	0.289630i
$714$	0.171525	−	24.9501i	0.00641915	−	0.933736i
$715$	10.5909	+	23.1908i	0.396077	+	0.867288i
$716$	−17.4602	+	4.86705i	−0.652518	+	0.181890i
$717$	10.7296	+	9.29723i	0.400704	+	0.347212i
$718$	−12.5857	−	8.21113i	−0.469694	−	0.306437i
$719$	6.95317	−	6.02495i	0.259309	−	0.224693i	−0.515497	−	0.856891i	$-0.672393\pi$
$719$	6.95317	−	6.02495i	0.259309	−	0.224693i	0.774807	+	0.632198i	$0.217847\pi$
$720$	0.875873	+	7.56269i	0.0326419	+	0.281845i
$721$	−17.1800	−	5.04449i	−0.639816	−	0.187867i
$722$	4.34888	−	2.75280i	0.161849	−	0.102448i
$723$	−4.73379	−	0.680616i	−0.176052	−	0.0253124i
$724$	−0.830040	+	1.75333i	−0.0308482	+	0.0651620i
$725$	4.50743	+	2.05848i	0.167402	+	0.0764499i
$726$	−2.57211	+	17.0562i	−0.0954601	+	0.633016i
$727$	3.42076	−	2.19839i	0.126869	−	0.0815337i	−0.475667	−	0.879625i	$-0.657793\pi$
$727$	3.42076	−	2.19839i	0.126869	−	0.0815337i	0.602536	+	0.798092i	$0.294157\pi$
$728$	−12.1202	+	38.3345i	−0.449203	+	1.42077i
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$	−14.9547	−	17.5003i	−0.553499	−	0.647716i
$731$	12.5432	+	8.06100i	0.463926	+	0.298147i
$732$	−10.9633	+	12.3063i	−0.405216	+	0.454854i
$733$	15.8874	−	4.66495i	0.586813	−	0.172304i	0.0251696	−	0.999683i	$-0.491987\pi$
$733$	15.8874	−	4.66495i	0.586813	−	0.172304i	0.561644	+	0.827379i	$0.310169\pi$
$734$	−13.4376	−	29.9677i	−0.495991	−	1.10613i
$735$	36.3962			1.34249
$736$	−27.0612	+	1.92178i	−0.997488	+	0.0708377i
$737$	−45.0458			−1.65928
$738$	4.34607	+	9.69236i	0.159981	+	0.356781i
$739$	9.65269	−	2.83429i	0.355080	−	0.104261i	−0.0993276	−	0.995055i	$-0.531669\pi$
$739$	9.65269	−	2.83429i	0.355080	−	0.104261i	0.454408	+	0.890794i	$0.349851\pi$
$740$	−0.0574602	+	0.0644990i	−0.00211228	+	0.00237103i
$741$	9.16973	+	5.89303i	0.336859	+	0.216486i
$742$	−16.5095	−	19.3197i	−0.606082	−	0.709249i
$743$	4.03502	+	28.0642i	0.148030	+	1.02957i	0.919439	+	0.393233i	$0.128644\pi$
$743$	4.03502	+	28.0642i	0.148030	+	1.02957i	−0.771408	+	0.636341i	$0.780447\pi$
$744$	1.88188	−	5.95214i	0.0689929	−	0.218216i
$745$	12.4119	−	7.97666i	0.454738	−	0.292242i
$746$	−0.410233	+	2.72034i	−0.0150197	+	0.0995987i
$747$	−0.736477	−	0.336338i	−0.0269463	−	0.0123060i
$748$	14.2275	−	30.0535i	0.520210	−	1.09886i
$749$	−11.2338	−	1.61517i	−0.410473	−	0.0590171i
$750$	−14.5044	+	9.18114i	−0.529626	+	0.335248i
$751$	−13.6474	−	4.00724i	−0.498001	−	0.146226i	0.0230797	−	0.999734i	$-0.492653\pi$
$751$	−13.6474	−	4.00724i	−0.498001	−	0.146226i	−0.521081	+	0.853507i	$0.674471\pi$
$752$	−22.1549	+	2.56587i	−0.807906	+	0.0935676i
$753$	16.7795	−	14.5395i	0.611480	−	0.529851i
$754$	−11.8505	−	7.73145i	−0.431568	−	0.281563i
$755$	−30.9869	−	26.8503i	−1.12773	−	0.977183i
$756$	9.84665	−	2.74476i	0.358119	−	0.0998261i
$757$	−18.2932	−	40.0565i	−0.664877	−	1.45588i	−0.877907	−	0.478831i	$-0.841061\pi$
$757$	−18.2932	−	40.0565i	−0.664877	−	1.45588i	0.213030	−	0.977046i	$-0.431667\pi$
$758$	0.234990	−	34.1818i	0.00853520	−	1.24154i
$759$	18.9493	+	13.2082i	0.687814	+	0.479426i
$760$	−0.435106	+	21.0944i	−0.0157830	+	0.765173i
$761$	−6.63808	−	14.5354i	−0.240630	−	0.526906i	0.750330	−	0.661063i	$-0.229895\pi$
$761$	−6.63808	−	14.5354i	−0.240630	−	0.526906i	−0.990960	+	0.134157i	$0.957167\pi$
$762$	2.55731	+	8.93620i	0.0926415	+	0.323724i
$763$	12.4718	−	14.3932i	0.451508	−	0.521068i
$764$	−16.2773	−	10.7798i	−0.588891	−	0.390001i
$765$	−4.96533	+	4.30248i	−0.179522	+	0.155557i
$766$	−2.50817	−	18.3388i	−0.0906240	−	0.662609i
$767$	5.29947	−	18.0483i	0.191353	−	0.651688i
$768$	−13.9152	+	7.89729i	−0.502122	+	0.284969i
$769$	2.11220	+	0.303689i	0.0761679	+	0.0109513i	0.180293	−	0.983613i	$-0.442295\pi$
$769$	2.11220	+	0.303689i	0.0761679	+	0.0109513i	−0.104126	+	0.994564i	$0.533204\pi$
$770$	60.0811	+	27.9389i	2.16517	+	1.00685i
$771$	−3.94928	+	8.64771i	−0.142230	+	0.311440i
$772$	0.541764	−	3.43235i	0.0194985	−	0.123533i
$773$	18.7028	−	12.0196i	0.672694	−	0.432314i	−0.159202	−	0.987246i	$-0.550892\pi$
$773$	18.7028	−	12.0196i	0.672694	−	0.432314i	0.831896	+	0.554932i	$0.187256\pi$
$774$	−1.76122	+	5.84910i	−0.0633056	+	0.210241i
$775$	3.00910	−	0.432643i	0.108090	−	0.0155410i
$776$	−21.6150	+	17.9626i	−0.775933	+	0.644820i
$777$	0.0975702	+	0.0627046i	0.00350031	+	0.00224951i
$778$	10.5629	−	12.0222i	0.378697	−	0.431016i
$779$	8.29351	+	28.2451i	0.297146	+	1.01199i
$780$	9.68967	−	4.26511i	0.346946	−	0.152715i
$781$	69.0067			2.46925
$782$	−14.5311	−	18.3568i	−0.519631	−	0.656437i
$783$			3.59750i			0.128564i
$784$	29.8502	+	70.4254i	1.06608	+	2.51519i
$785$	37.2283	−	10.9312i	1.32874	−	0.390152i
$786$	−3.42790	+	3.90148i	−0.122269	+	0.139161i
$787$	−1.07005	+	1.66503i	−0.0381431	+	0.0593518i	−0.859801	−	0.510628i	$-0.829413\pi$
$787$	−1.07005	+	1.66503i	−0.0381431	+	0.0593518i	0.821658	+	0.569980i	$0.193049\pi$
$788$	24.1246	−	20.3301i	0.859403	−	0.724231i
$789$	−1.78463	−	12.4124i	−0.0635347	−	0.441893i
$790$	−42.0756	−	12.6693i	−1.49698	−	0.450755i
$791$	−5.12828	−	7.97976i	−0.182341	−	0.283728i
$792$	13.4411	+	2.21636i	0.477609	+	0.0787548i
$793$	20.8477	+	9.52082i	0.740323	+	0.338094i
$794$	−13.1494	−	6.11473i	−0.466655	−	0.217004i
$795$	−0.952337	+	6.62365i	−0.0337759	+	0.234917i
$796$	35.4143	−	22.0773i	1.25523	−	0.782510i
$797$	−11.2679	−	3.30854i	−0.399128	−	0.117195i	0.0760072	−	0.997107i	$-0.475783\pi$
$797$	−11.2679	−	3.30854i	−0.399128	−	0.117195i	−0.475136	+	0.879913i	$0.657601\pi$
$798$	28.0674	−	3.83874i	0.993576	−	0.135890i
$799$	−12.6041	−	14.5459i	−0.445901	−	0.514598i
$800$	−6.40624	−	4.43534i	−0.226495	−	0.156813i
$801$	5.01135	+	4.34236i	0.177067	+	0.153430i
$802$	12.8555	+	44.9221i	0.453945	+	1.58625i
$803$	−37.4676	+	17.1109i	−1.32220	+	0.603829i
$804$	−0.257177	+	18.7037i	−0.00906993	+	0.659630i
$805$	36.3796	−	29.2069i	1.28221	−	1.02941i
$806$	−8.68055	−	0.0596761i	−0.305759	−	0.00210200i
$807$	18.3806	−	8.39415i	0.647028	−	0.295488i
$808$	−12.8040	−	47.1852i	−0.450444	−	1.65997i
$809$	−1.95488	+	2.25605i	−0.0687299	+	0.0793186i	−0.789073	−	0.614299i	$-0.789439\pi$
$809$	−1.95488	+	2.25605i	−0.0687299	+	0.0793186i	0.720343	+	0.693618i	$0.243984\pi$
$810$	−2.25433	−	1.47077i	−0.0792092	−	0.0516775i
$811$	8.56313	+	9.88238i	0.300692	+	0.347017i	0.885909	−	0.463860i	$-0.153536\pi$
$811$	8.56313	+	9.88238i	0.300692	+	0.347017i	−0.585216	+	0.810877i	$0.698990\pi$
$812$	−36.4680	+	4.73252i	−1.27978	+	0.166079i
$813$	3.73424	−	12.7176i	0.130965	−	0.446027i
$814$	0.0826685	+	0.130600i	0.00289753	+	0.00457753i
$815$	0.0824779	−	0.573647i	0.00288908	−	0.0200940i
$816$	−12.3974	−	6.07908i	−0.433997	−	0.212810i
$817$	−7.03244	+	15.3989i	−0.246034	+	0.538739i
$818$	−5.70794	+	37.8505i	−0.199573	+	1.32341i
$819$	−7.68498	−	11.9581i	−0.268535	−	0.417849i
$820$	27.3200	+	8.43157i	0.954056	+	0.294443i
$821$	−5.18438	+	0.745402i	−0.180936	+	0.0260147i	−0.232187	−	0.972671i	$-0.574588\pi$
$821$	−5.18438	+	0.745402i	−0.180936	+	0.0260147i	0.0512510	+	0.998686i	$0.483679\pi$
$822$	17.9493	−	15.3384i	0.626053	−	0.534987i
$823$	−6.67009	+	10.3789i	−0.232505	+	0.361784i	−0.937827	−	0.347102i	$-0.887166\pi$
$823$	−6.67009	+	10.3789i	−0.232505	+	0.361784i	0.705323	+	0.708886i	$0.250802\pi$
$824$	−6.64188	+	7.35310i	−0.231381	+	0.256158i
$825$	1.86903	+	6.36532i	0.0650711	+	0.221612i
$826$	−20.0022	−	44.6077i	−0.695965	−	1.55210i
$827$		−	19.2059i		−	0.667853i	−0.942599	−	0.333927i	$-0.891626\pi$
$827$		−	19.2059i		−	0.667853i	0.942599	−	0.333927i	$-0.108374\pi$
$828$	5.59242	−	7.79262i	0.194350	−	0.270812i
$829$		−	12.1643i		−	0.422485i	−0.977434	−	0.211243i	$-0.932249\pi$
$829$		−	12.1643i		−	0.422485i	0.977434	−	0.211243i	$-0.0677510\pi$
$830$	−1.98854	+	0.891667i	−0.0690234	+	0.0309502i
$831$	−2.09519	−	7.13558i	−0.0726815	−	0.247530i
$832$	16.1998	+	15.2512i	0.561626	+	0.528739i
$833$	−35.6875	+	55.5308i	−1.23650	+	1.92403i
$834$	−19.2626	−	22.5414i	−0.667008	−	0.780546i
$835$	−33.9516	+	4.88151i	−1.17494	+	0.168932i
$836$	36.0739	+	11.1332i	1.24764	+	0.385050i
$837$	1.19323	+	1.85671i	0.0412442	+	0.0641772i
$838$	−4.25045	−	0.640976i	−0.146829	−	0.0221422i
$839$	−8.85409	+	19.3878i	−0.305677	+	0.669340i	−0.998667	−	0.0516073i	$-0.983566\pi$
$839$	−8.85409	+	19.3878i	−0.305677	+	0.669340i	0.692990	+	0.720947i	$0.256293\pi$
$840$	11.9437	−	24.7871i	0.412096	−	0.855236i
$841$	−2.28529	+	15.8946i	−0.0788032	+	0.548088i
$842$	16.4603	−	10.4192i	0.567261	−	0.359070i
$843$	−1.74496	+	5.94279i	−0.0600997	+	0.204681i
$844$	0.809289	+	6.23625i	0.0278569	+	0.214661i
$845$	6.56250	+	7.57353i	0.225757	+	0.260537i
$846$	4.30861	−	6.60407i	0.148133	−	0.227053i
$847$	40.8233	−	47.1125i	1.40270	−	1.61881i
$848$	−13.5976	+	3.58961i	−0.466943	+	0.123268i
$849$	15.3056	−	6.98985i	0.525288	−	0.239891i
$850$	0.0462255	−	6.72401i	0.00158552	−	0.230631i
$851$	0.108227	−	0.0114353i	0.00370997	−	0.000391998i
$852$	0.393975	−	28.6527i	0.0134974	−	0.981624i
$853$	−17.4470	+	7.96779i	−0.597375	+	0.272812i	−0.691069	−	0.722789i	$-0.742860\pi$
$853$	−17.4470	+	7.96779i	−0.597375	+	0.272812i	0.0936940	+	0.995601i	$0.470132\pi$
$854$	57.2660	−	16.3880i	1.95960	−	0.560787i
$855$	−5.63756	−	4.88498i	−0.192801	−	0.167063i
$856$	−3.50382	+	5.21248i	−0.119758	+	0.178159i
$857$	5.74085	+	6.62529i	0.196104	+	0.226316i	0.845282	−	0.534321i	$-0.179433\pi$
$857$	5.74085	+	6.62529i	0.196104	+	0.226316i	−0.649178	+	0.760636i	$0.724887\pi$
$858$	−2.56695	−	18.7686i	−0.0876343	−	0.640749i
$859$	−12.2997	−	3.61151i	−0.419659	−	0.123223i	0.0650836	−	0.997880i	$-0.479269\pi$
$859$	−12.2997	−	3.61151i	−0.419659	−	0.123223i	−0.484743	+	0.874657i	$0.661087\pi$
$860$	8.69830	+	13.9530i	0.296610	+	0.475792i
$861$	5.46331	−	37.9981i	0.186189	−	1.29497i
$862$	0.414272	−	0.890871i	0.0141102	−	0.0303432i
$863$	32.5789	+	14.8783i	1.10900	+	0.506462i	0.883807	−	0.467852i	$-0.154972\pi$
$863$	32.5789	+	14.8783i	1.10900	+	0.506462i	0.225191	+	0.974315i	$0.427699\pi$
$864$	0.997004	−	5.56830i	0.0339188	−	0.189437i
$865$	−2.94585	−	4.58383i	−0.100162	−	0.155855i
$866$	8.47138	−	28.1339i	0.287869	−	0.956030i
$867$	0.723567	+	5.03252i	0.0245736	+	0.170913i
$868$	−17.2518	+	14.5384i	−0.585566	+	0.493465i
$869$	−42.5085	+	66.1445i	−1.44200	+	2.24380i
$870$	7.27442	+	6.39140i	0.246626	+	0.216689i
$871$	24.9578	−	7.32828i	0.845664	−	0.248309i
$872$	−4.17959	−	9.67522i	−0.141539	−	0.327644i
$873$		−	9.93644i		−	0.336297i
$874$	18.2819	−	19.2966i	0.618395	−	0.652717i
$875$	62.0386			2.09729
$876$	6.89078	+	15.6548i	0.232818	+	0.528927i
$877$	8.47076	+	28.8488i	0.286037	+	0.974154i	0.969688	+	0.244345i	$0.0785729\pi$
$877$	8.47076	+	28.8488i	0.286037	+	0.974154i	−0.683651	+	0.729809i	$0.739609\pi$
$878$	−25.7617	−	22.6346i	−0.869416	−	0.763881i
$879$	6.48813	+	4.16967i	0.218839	+	0.140640i
$880$	28.3614	−	23.2413i	0.956063	−	0.783464i
$881$	23.8373	−	3.42728i	0.803098	−	0.115468i	0.271471	−	0.962447i	$-0.412490\pi$
$881$	23.8373	−	3.42728i	0.803098	−	0.115468i	0.531627	+	0.846979i	$0.321581\pi$
$882$	−25.8950	−	7.79721i	−0.871929	−	0.262546i
$883$	−21.5156	+	13.8272i	−0.724058	+	0.465324i	−0.850046	−	0.526708i	$-0.823426\pi$
$883$	−21.5156	+	13.8272i	−0.724058	+	0.465324i	0.125988	+	0.992032i	$0.459790\pi$
$884$	−2.99358	+	18.9659i	−0.100685	+	0.637891i
$885$	−5.34763	+	11.7097i	−0.179759	+	0.393617i
$886$	3.22411	−	6.93329i	0.108316	−	0.232928i
$887$	9.82175	+	1.41215i	0.329782	+	0.0474155i	0.305217	−	0.952283i	$-0.401271\pi$
$887$	9.82175	+	1.41215i	0.329782	+	0.0474155i	0.0245647	+	0.999698i	$0.492180\pi$
$888$	0.0546992	−	0.0335796i	0.00183558	−	0.00112686i
$889$	9.46402	−	32.2315i	0.317413	−	1.08101i
$890$	17.6839	−	2.41860i	0.592765	−	0.0810715i
$891$	−3.63993	+	3.15402i	−0.121942	+	0.105664i
$892$	−24.6251	+	37.1832i	−0.824509	+	1.24499i
$893$	14.3105	−	16.5152i	0.478884	−	0.552661i
$894$	−10.5396	+	3.01617i	−0.352498	+	0.100876i
$895$	−7.16573	−	15.6907i	−0.239524	−	0.524484i
$896$	57.7577	+	2.78157i	1.92955	+	0.0929257i
$897$	−12.6477	−	4.23528i	−0.422294	−	0.141412i
$898$	30.4157	+	0.209099i	1.01499	+	0.00697771i
$899$	−3.29837	−	7.22243i	−0.110007	−	0.240881i
$900$	2.65365	−	0.739708i	0.0884550	−	0.0246569i
$901$	−9.17210	−	7.94767i	−0.305567	−	0.264775i
$902$	27.9542	−	42.8471i	0.930774	−	1.42665i
$903$	16.6842	−	14.4570i	0.555216	−	0.481097i
$904$	−5.21015	+	0.639741i	−0.173287	+	0.0212775i
$905$	−1.77132	−	0.520105i	−0.0588806	−	0.0172889i
$906$	16.2942	+	25.7417i	0.541339	+	0.855210i
$907$	−39.4479	−	5.67175i	−1.30985	−	0.188327i	−0.548214	−	0.836338i	$-0.684692\pi$
$907$	−39.4479	−	5.67175i	−1.30985	−	0.188327i	−0.761631	+	0.648011i	$0.775601\pi$
$908$	42.9514	+	20.3335i	1.42539	+	0.674791i
$909$	15.7237	+	7.18078i	0.521523	+	0.238171i
$910$	−37.8334	−	5.70536i	−1.25417	−	0.189131i
$911$	24.8755	−	15.9865i	0.824163	−	0.529657i	−0.0592554	−	0.998243i	$-0.518873\pi$
$911$	24.8755	−	15.9865i	0.824163	−	0.529657i	0.883418	+	0.468586i	$0.155236\pi$
$912$	4.82864	−	14.9149i	0.159892	−	0.493881i
$913$	0.554957	+	3.85981i	0.0183664	+	0.127741i
$914$	−15.5072	+	13.2515i	−0.512932	+	0.438321i
$915$	−13.1948	−	8.47978i	−0.436207	−	0.280333i
$916$	−23.2411	+	26.0881i	−0.767906	+	0.861974i
$917$	18.0091	−	5.28794i	0.594712	−	0.174623i
$918$	4.45443	−	1.99738i	0.147018	−	0.0659233i
$919$	−33.9674			−1.12048			−0.560240	−	0.828330i	$-0.689291\pi$
$919$	−33.9674			−1.12048			−0.560240	+	0.828330i	$0.689291\pi$
$920$	−5.82164	−	25.1528i	−0.191934	−	0.829264i
$921$	17.3445			0.571520
$922$	29.2870	−	13.1324i	0.964517	−	0.432491i
$923$	−38.2335	+	11.2264i	−1.25847	+	0.369520i
$924$	−36.7608	−	32.7490i	−1.20934	−	1.07736i
$925$	0.0262949	+	0.0168987i	0.000864572	+	0.000555627i
$926$	−36.0398	+	30.7974i	−1.18434	+	1.01207i
$927$	−0.498566	−	3.46760i	−0.0163751	−	0.113891i
$928$	−6.40106	+	19.3176i	−0.210125	+	0.634132i
$929$	−7.11824	+	4.57461i	−0.233542	+	0.150088i	−0.652178	−	0.758066i	$-0.726145\pi$
$929$	−7.11824	+	4.57461i	−0.233542	+	0.150088i	0.418636	+	0.908154i	$0.362508\pi$
$930$	5.87433	+	0.885861i	0.192627	+	0.0290485i
$931$	−68.1736	−	31.1338i	−2.23430	−	1.02037i
$932$	−1.98731	+	4.19789i	−0.0650966	+	0.137506i
$933$	17.0468	+	2.45097i	0.558089	+	0.0802410i
$934$	−29.6486	−	46.8390i	−0.970132	−	1.53262i
$935$	30.3618	+	8.91502i	0.992936	+	0.291552i
$936$	−7.80767	+	0.958684i	−0.255202	+	0.0313356i
$937$	13.3415	−	11.5605i	0.435849	−	0.377665i	−0.409120	−	0.912481i	$-0.634164\pi$
$937$	13.3415	−	11.5605i	0.435849	−	0.377665i	0.844969	+	0.534815i	$0.179619\pi$
$938$	36.9387	−	56.6182i	1.20609	−	1.84865i
$939$	−8.41801	−	7.29424i	−0.274711	−	0.238039i
$940$	−5.69914	−	20.4453i	−0.185886	−	0.666852i
$941$	−2.61693	−	5.73028i	−0.0853095	−	0.186802i	0.862169	−	0.506620i	$-0.169105\pi$
$941$	−2.61693	−	5.73028i	−0.0853095	−	0.186802i	−0.947479	+	0.319818i	$0.896378\pi$
$942$	−28.8288	−	0.198189i	−0.939294	−	0.00645736i
$943$	−18.3240	−	31.0126i	−0.596710	−	1.00991i
$944$	−27.0437	−	0.743843i	−0.880196	−	0.0242100i
$945$	4.04110	+	8.84878i	0.131457	+	0.287851i
$946$	28.2851	−	8.09446i	0.919627	−	0.263174i
$947$	−3.22548	+	3.72240i	−0.104814	+	0.120962i	−0.805733	−	0.592279i	$-0.798228\pi$
$947$	−3.22548	+	3.72240i	−0.104814	+	0.120962i	0.700919	+	0.713241i	$0.252774\pi$
$948$	27.2215	+	18.0278i	0.884114	+	0.585516i
$949$	17.9754	−	15.5758i	0.583506	−	0.505610i
$950$	7.56410	−	1.03453i	0.245412	−	0.0335646i
$951$	5.52074	−	18.8019i	0.179022	−	0.609694i
$952$	26.1073	+	42.5272i	0.846143	+	1.37832i
$953$	2.94967	+	0.424098i	0.0955491	+	0.0137379i	0.189924	−	0.981799i	$-0.439176\pi$
$953$	2.94967	+	0.424098i	0.0955491	+	0.0137379i	−0.0943744	+	0.995537i	$0.530085\pi$
$954$	2.09656	−	4.50854i	0.0678785	−	0.145969i
$955$	7.71813	−	16.9004i	0.249753	−	0.546883i
$956$	−28.0473	−	4.42700i	−0.907115	−	0.143179i
$957$	14.5761	−	9.36752i	0.471180	−	0.302809i
$958$	45.3124	+	13.6440i	1.46398	+	0.440817i
$959$	−84.4598	+	12.1435i	−2.72735	+	0.392134i
$960$	−9.48823	−	11.9088i	−0.306231	−	0.384355i
$961$	21.9810	+	14.1263i	0.709063	+	0.455687i
$962$	−0.0670496	−	0.0589107i	−0.00216176	−	0.00189936i
$963$	−0.625601	−	2.13060i	−0.0201597	−	0.0686577i
$964$	8.75438	−	3.85342i	0.281960	−	0.124110i
$965$	3.30685			0.106451
$966$	−32.1402	+	12.9863i	−1.03409	+	0.417828i
$967$		−	20.5497i		−	0.660834i	−0.943835	−	0.330417i	$-0.892811\pi$
$967$		−	20.5497i		−	0.660834i	0.943835	−	0.330417i	$-0.107189\pi$
$968$	−13.6809	−	31.6695i	−0.439719	−	1.01790i
$969$	12.9809	−	3.81155i	0.417008	−	0.122445i
$970$	−20.0922	−	17.6533i	−0.645123	−	0.566813i
$971$	−13.9951	+	21.7768i	−0.449123	+	0.698849i	−0.989813	−	0.142373i	$-0.954527\pi$
$971$	−13.9951	+	21.7768i	−0.449123	+	0.698849i	0.540690	+	0.841222i	$0.318163\pi$
$972$	1.28882	+	1.52936i	0.0413388	+	0.0490544i
$973$	15.2503	+	106.068i	0.488901	+	3.40038i
$974$	−16.8573	+	55.9841i	−0.540143	+	1.79385i
$975$	−2.07108	−	3.22267i	−0.0663278	−	0.103208i
$976$	5.58643	−	32.4861i	0.178817	−	1.03986i
$977$	−6.35344	−	2.90152i	−0.203264	−	0.0928278i	0.311182	−	0.950350i	$-0.399275\pi$
$977$	−6.35344	−	2.90152i	−0.203264	−	0.0928278i	−0.514446	+	0.857523i	$0.672002\pi$
$978$	−0.181574	+	0.390466i	−0.00580610	+	0.0124857i
$979$	4.54509	−	31.6118i	0.145262	−	1.01032i
$980$	−61.7722	+	38.5089i	−1.97324	+	1.23012i
$981$	3.57530	+	1.04980i	0.114151	+	0.0335176i
$982$	−7.44046	−	54.4019i	−0.237435	−	1.73603i
$983$	32.8337	+	37.8921i	1.04723	+	1.20857i	0.977485	+	0.211004i	$0.0676735\pi$
$983$	32.8337	+	37.8921i	1.04723	+	1.20857i	0.0697461	+	0.997565i	$0.477781\pi$
$984$	−17.6312	−	11.8517i	−0.562062	−	0.377817i
$985$	22.6901	+	19.6611i	0.722967	+	0.626455i
$986$	−16.8843	+	4.83185i	−0.537706	+	0.153878i
$987$	−25.9225	+	11.8384i	−0.825122	+	0.376821i
$988$	−21.7981	−	0.299725i	−0.693490	−	0.00953551i
$989$	3.71530	−	20.3790i	0.118140	−	0.648016i
$990$	−0.0891216	+	12.9637i	−0.00283247	+	0.412014i
$991$	7.95030	−	3.63078i	0.252549	−	0.115335i	−0.285118	−	0.958492i	$-0.592033\pi$
$991$	7.95030	−	3.63078i	0.252549	−	0.115335i	0.537668	+	0.843157i	$0.319306\pi$
$992$	3.10369	+	12.0932i	0.0985424	+	0.383958i
$993$	−14.6673	+	16.9269i	−0.465451	+	0.537159i
$994$	−56.5873	+	86.7347i	−1.79484	+	2.75106i
$995$	26.0076	+	30.0144i	0.824496	+	0.951519i
$996$	1.60582	−	0.208390i	0.0508824	−	0.00660310i
$997$	9.30210	−	31.6800i	0.294600	−	1.00332i	−0.670603	−	0.741817i	$-0.733965\pi$
$997$	9.30210	−	31.6800i	0.294600	−	1.00332i	0.965203	−	0.261500i	$-0.0842173\pi$
$998$	43.6163	−	27.6086i	1.38065	−	0.873936i
$999$	−0.00322948	+	0.0224615i	−0.000102176	+	0.000710651i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.t.a.19.15	✓	240
8.3	odd	2	inner	552.2.t.a.19.16	yes	240
23.17	odd	22	inner	552.2.t.a.523.16	yes	240
184.155	even	22	inner	552.2.t.a.523.15	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.t.a.19.15	✓	240	1.1	even	1	trivial
552.2.t.a.19.16	yes	240	8.3	odd	2	inner
552.2.t.a.523.15	yes	240	184.155	even	22	inner
552.2.t.a.523.16	yes	240	23.17	odd	22	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.578628 + 1.29042i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-1.33038 + 1.49335i) q^{4} +(-1.60117 - 1.02901i) q^{5} +(0.918744 + 1.07513i) q^{6} +(-0.727375 - 5.05900i) q^{7} +(-2.69685 - 0.852656i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.578628 + 1.29042i) q^{2} +(0.959493 - 0.281733i) q^{3} +(-1.33038 + 1.49335i) q^{4} +(-1.60117 - 1.02901i) q^{5} +(0.918744 + 1.07513i) q^{6} +(-0.727375 - 5.05900i) q^{7} +(-2.69685 - 0.852656i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.401374 - 2.66159i) q^{10} +(-4.38108 - 2.00077i) q^{11} +(-0.855764 + 1.80767i) q^{12} +(2.75285 + 0.395800i) q^{13} +(6.10737 - 3.86590i) q^{14} +(-1.82621 - 0.536225i) q^{15} +(-0.460184 - 3.97344i) q^{16} +(2.60879 - 2.26053i) q^{17} +(1.18443 + 0.772742i) q^{18} +(2.96198 + 2.56657i) q^{19} +(3.66683 - 1.02213i) q^{20} +(-2.12320 - 4.64915i) q^{21} +(0.0468245 - 6.81114i) q^{22} +(-4.28462 - 2.15454i) q^{23} +(-2.82783 - 0.0583286i) q^{24} +(-0.572196 - 1.25294i) q^{25} +(1.08213 + 3.78136i) q^{26} +(0.654861 - 0.755750i) q^{27} +(8.52254 + 5.64417i) q^{28} +(-2.71881 + 2.35586i) q^{29} +(-0.364742 - 2.66686i) q^{30} +(-0.621804 + 2.11767i) q^{31} +(4.86114 - 2.89298i) q^{32} +(-4.76730 - 0.685434i) q^{33} +(4.42655 + 2.05843i) q^{34} +(-4.04110 + 8.84878i) q^{35} +(-0.311820 + 1.97554i) q^{36} +(-0.0190901 + 0.0122685i) q^{37} +(-1.59807 + 5.30729i) q^{38} +(2.75285 - 0.395800i) q^{39} +(3.44071 + 4.14032i) q^{40} +(6.31865 + 4.06075i) q^{41} +(4.77083 - 5.42995i) q^{42} +(1.21691 + 4.14440i) q^{43} +(8.81634 - 3.88070i) q^{44} -1.90331 q^{45} +(0.301066 - 6.77564i) q^{46} -5.57574i q^{47} +(-1.56099 - 3.68284i) q^{48} +(-18.3480 + 5.38745i) q^{49} +(1.28573 - 1.46336i) q^{50} +(1.86625 - 2.90394i) q^{51} +(-4.25340 + 3.58440i) q^{52} +(-0.500358 - 3.48007i) q^{53} +(1.35416 + 0.407749i) q^{54} +(4.95603 + 7.71173i) q^{55} +(-2.35197 + 14.2635i) q^{56} +(3.56508 + 1.62812i) q^{57} +(-4.61323 - 2.14524i) q^{58} +(0.962543 - 6.69463i) q^{59} +(3.23033 - 2.01379i) q^{60} +(7.90693 + 2.32169i) q^{61} +(-3.09248 + 0.422954i) q^{62} +(-3.34701 - 3.86266i) q^{63} +(6.54595 + 4.59897i) q^{64} +(-4.00049 - 3.46645i) q^{65} +(-1.87399 - 6.54844i) q^{66} +(8.50756 - 3.88527i) q^{67} +(-0.0949190 + 6.90318i) q^{68} +(-4.71807 - 0.860150i) q^{69} +(-13.7570 - 0.0945748i) q^{70} +(-13.0329 + 5.95194i) q^{71} +(-2.72971 + 0.740725i) q^{72} +(5.60045 - 6.46327i) q^{73} +(-0.0268776 - 0.0175354i) q^{74} +(-0.902011 - 1.04098i) q^{75} +(-7.77334 + 1.00876i) q^{76} +(-6.93522 + 23.6192i) q^{77} +(2.10363 + 3.32332i) q^{78} +(2.32328 - 16.1588i) q^{79} +(-3.35187 + 6.83567i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-1.58393 + 10.5034i) q^{82} +(-0.437726 - 0.681115i) q^{83} +(9.76746 + 3.01446i) q^{84} +(-6.50320 + 0.935019i) q^{85} +(-4.64389 + 3.96839i) q^{86} +(-1.94495 + 3.02641i) q^{87} +(10.1091 + 9.13133i) q^{88} +(1.86816 + 6.36237i) q^{89} +(-1.10131 - 2.45607i) q^{90} -14.2146i q^{91} +(8.91765 - 3.53208i) q^{92} +2.20707i q^{93} +(7.19507 - 3.22628i) q^{94} +(-2.10160 - 7.15740i) q^{95} +(3.84918 - 4.14533i) q^{96} +(5.37204 - 8.35906i) q^{97} +(-17.5687 - 20.5593i) q^{98} +(-4.76730 + 0.685434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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