LMFDB - Embedded newform 690.2.w.b.493.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			493.11
Character	$\chi$	$=$	690.493
Dual form			690.2.w.b.7.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.997452 + 0.0713392i) q^{2} +(0.212565 + 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(1.40256 + 1.74150i) q^{5} +(0.142315 + 0.989821i) q^{6} +(1.87882 + 3.44079i) q^{7} +(0.977147 + 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +O(q^{10})$	\(q+(0.997452 + 0.0713392i) q^{2} +(0.212565 + 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(1.40256 + 1.74150i) q^{5} +(0.142315 + 0.989821i) q^{6} +(1.87882 + 3.44079i) q^{7} +(0.977147 + 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +(1.27475 + 1.83712i) q^{10} +(0.512771 + 0.444318i) q^{11} +(0.0713392 + 0.997452i) q^{12} +(-5.72944 - 3.12851i) q^{13} +(1.62857 + 3.56606i) q^{14} +(-1.40356 + 1.74069i) q^{15} +(0.959493 + 0.281733i) q^{16} +(2.38199 - 3.18196i) q^{17} +(-0.936950 + 0.349464i) q^{18} +(0.239171 - 1.66347i) q^{19} +(1.14044 + 1.92338i) q^{20} +(-2.96279 + 2.56727i) q^{21} +(0.479767 + 0.479767i) q^{22} +(-4.60325 - 1.34539i) q^{23} +1.00000i q^{24} +(-1.06564 + 4.88512i) q^{25} +(-5.49166 - 3.52927i) q^{26} +(-0.599278 - 0.800541i) q^{27} +(1.37002 + 3.67316i) q^{28} +(-2.45679 + 0.353233i) q^{29} +(-1.52417 + 1.63613i) q^{30} +(5.47061 - 3.51575i) q^{31} +(0.936950 + 0.349464i) q^{32} +(-0.325167 + 0.595499i) q^{33} +(2.60292 - 3.00393i) q^{34} +(-3.35699 + 8.09788i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(1.77936 - 4.77064i) q^{37} +(0.357233 - 1.64217i) q^{38} +(1.83913 - 6.26352i) q^{39} +(1.00033 + 1.99984i) q^{40} +(-2.24845 + 4.92341i) q^{41} +(-3.13839 + 2.34937i) q^{42} +(10.7358 - 2.33542i) q^{43} +(0.444318 + 0.512771i) q^{44} +(-1.99926 - 1.00148i) q^{45} +(-4.49554 - 1.67035i) q^{46} +(4.55955 - 4.55955i) q^{47} +(-0.0713392 + 0.997452i) q^{48} +(-4.52463 + 7.04047i) q^{49} +(-1.41143 + 4.79665i) q^{50} +(3.61557 + 1.65118i) q^{51} +(-5.22589 - 3.91205i) q^{52} +(4.09845 - 2.23792i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(-0.0545875 + 1.51617i) q^{55} +(1.10449 + 3.76153i) q^{56} +(1.67630 - 0.119891i) q^{57} +(-2.47573 + 0.177068i) q^{58} +(3.74486 + 12.7538i) q^{59} +(-1.63700 + 1.52323i) q^{60} +(6.18829 + 9.62916i) q^{61} +(5.70748 - 3.11652i) q^{62} +(-3.13839 - 2.34937i) q^{63} +(0.909632 + 0.415415i) q^{64} +(-2.58759 - 14.3657i) q^{65} +(-0.366821 + 0.570784i) q^{66} +(-0.342317 + 4.78621i) q^{67} +(2.81058 - 2.81058i) q^{68} +(0.336152 - 4.78404i) q^{69} +(-3.92613 + 7.83777i) q^{70} +(-7.81093 - 9.01429i) q^{71} +(-0.977147 + 0.212565i) q^{72} +(4.64964 - 3.48068i) q^{73} +(2.11516 - 4.63155i) q^{74} +(-5.00000 - 0.00288011i) q^{75} +(0.473474 - 1.61250i) q^{76} +(-0.565406 + 2.59913i) q^{77} +(2.28128 - 6.11636i) q^{78} +(1.48297 - 0.435439i) q^{79} +(0.855111 + 2.06610i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-2.59395 + 4.75046i) q^{82} +(-11.1767 - 4.16868i) q^{83} +(-3.29799 + 2.11949i) q^{84} +(8.88227 - 0.314670i) q^{85} +(10.8750 - 1.56359i) q^{86} +(-0.867389 - 2.32556i) q^{87} +(0.406606 + 0.543161i) q^{88} +(-1.40078 - 0.900224i) q^{89} +(-1.92272 - 1.14155i) q^{90} -25.5917i q^{91} +(-4.36493 - 1.98681i) q^{92} +(4.59826 + 4.59826i) q^{93} +(4.87320 - 4.22266i) q^{94} +(3.23239 - 1.91661i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(-9.09892 + 3.39372i) q^{97} +(-5.01537 + 6.69975i) q^{98} +(-0.651009 - 0.191153i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{6}+O(q^{10}) $ 240 * q + 24 * q^6	$ 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) $ 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{22}\right)$

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 $

$2$	0.997452	+	0.0713392i	0.705305	+	0.0504444i
$2$	0.997452	+	0.0713392i	0.705305	+	0.0504444i
$3$	0.212565	+	0.977147i	0.122725	+	0.564156i
$3$	0.212565	+	0.977147i	0.122725	+	0.564156i
$4$	0.989821	+	0.142315i	0.494911	+	0.0711574i
$5$	1.40256	+	1.74150i	0.627245	+	0.778822i
$5$	1.40256	+	1.74150i	0.627245	+	0.778822i
$6$	0.142315	+	0.989821i	0.0580998	+	0.404093i
$7$	1.87882	+	3.44079i	0.710126	+	1.30050i	0.944551	+	0.328364i	$0.106497\pi$
$7$	1.87882	+	3.44079i	0.710126	+	1.30050i	−0.234425	+	0.972134i	$0.575321\pi$
$8$	0.977147	+	0.212565i	0.345474	+	0.0751532i
$9$	−0.909632	+	0.415415i	−0.303211	+	0.138472i
$10$	1.27475	+	1.83712i	0.403112	+	0.580948i
$11$	0.512771	+	0.444318i	0.154606	+	0.133967i	0.728729	−	0.684802i	$-0.240111\pi$
$11$	0.512771	+	0.444318i	0.154606	+	0.133967i	−0.574123	+	0.818769i	$0.694657\pi$
$12$	0.0713392	+	0.997452i	0.0205938	+	0.287940i
$13$	−5.72944	−	3.12851i	−1.58906	−	0.867693i	−0.998140	−	0.0609635i	$-0.980583\pi$
$13$	−5.72944	−	3.12851i	−1.58906	−	0.867693i	−0.590921	−	0.806729i	$-0.701236\pi$
$14$	1.62857	+	3.56606i	0.435252	+	0.953070i
$15$	−1.40356	+	1.74069i	−0.362399	+	0.449445i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	2.38199	−	3.18196i	0.577717	−	0.771740i	−0.412548	−	0.910936i	$-0.635361\pi$
$17$	2.38199	−	3.18196i	0.577717	−	0.771740i	0.990265	+	0.139196i	$0.0444519\pi$
$18$	−0.936950	+	0.349464i	−0.220841	+	0.0823695i
$19$	0.239171	−	1.66347i	0.0548697	−	0.381627i	−0.943820	−	0.330459i	$-0.892796\pi$
$19$	0.239171	−	1.66347i	0.0548697	−	0.381627i	0.998690	−	0.0511681i	$-0.0162944\pi$
$20$	1.14044	+	1.92338i	0.255011	+	0.430081i
$21$	−2.96279	+	2.56727i	−0.646534	+	0.560225i
$22$	0.479767	+	0.479767i	0.102287	+	0.102287i
$23$	−4.60325	−	1.34539i	−0.959844	−	0.280533i
$23$	−4.60325	−	1.34539i	−0.959844	−	0.280533i
$24$			1.00000i			0.204124i
$25$	−1.06564	+	4.88512i	−0.213128	+	0.977024i
$26$	−5.49166	−	3.52927i	−1.07700	−	0.692148i
$27$	−0.599278	−	0.800541i	−0.115331	−	0.154064i
$28$	1.37002	+	3.67316i	0.258909	+	0.694161i
$29$	−2.45679	+	0.353233i	−0.456214	+	0.0655937i	−0.366591	−	0.930382i	$-0.619475\pi$
$29$	−2.45679	+	0.353233i	−0.456214	+	0.0655937i	−0.0896229	+	0.995976i	$0.528566\pi$
$30$	−1.52417	+	1.63613i	−0.278274	+	0.298715i
$31$	5.47061	−	3.51575i	0.982551	−	0.631447i	0.0524005	−	0.998626i	$-0.483313\pi$
$31$	5.47061	−	3.51575i	0.982551	−	0.631447i	0.930150	+	0.367179i	$0.119676\pi$
$32$	0.936950	+	0.349464i	0.165631	+	0.0617771i
$33$	−0.325167	+	0.595499i	−0.0566043	+	0.103663i
$34$	2.60292	−	3.00393i	0.446397	−	0.515169i
$35$	−3.35699	+	8.09788i	−0.567434	+	1.36879i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	1.77936	−	4.77064i	0.292525	−	0.784289i	−0.704677	−	0.709528i	$-0.748908\pi$
$37$	1.77936	−	4.77064i	0.292525	−	0.784289i	0.997202	−	0.0747604i	$-0.0238192\pi$
$38$	0.357233	−	1.64217i	0.0579508	−	0.266396i
$39$	1.83913	−	6.26352i	0.294497	−	1.00297i
$40$	1.00033	+	1.99984i	0.158166	+	0.316202i
$41$	−2.24845	+	4.92341i	−0.351148	+	0.768907i	0.648820	+	0.760942i	$0.275263\pi$
$41$	−2.24845	+	4.92341i	−0.351148	+	0.768907i	−0.999968	+	0.00796540i	$0.997465\pi$
$42$	−3.13839	+	2.34937i	−0.484264	+	0.362515i
$43$	10.7358	−	2.33542i	1.63719	−	0.356148i	0.702518	−	0.711666i	$-0.252059\pi$
$43$	10.7358	−	2.33542i	1.63719	−	0.356148i	0.934670	+	0.355517i	$0.115695\pi$
$44$	0.444318	+	0.512771i	0.0669835	+	0.0773031i
$45$	−1.99926	−	1.00148i	−0.298032	−	0.149292i
$46$	−4.49554	−	1.67035i	−0.662832	−	0.246280i
$47$	4.55955	−	4.55955i	0.665078	−	0.665078i	−0.291494	−	0.956573i	$-0.594152\pi$
$47$	4.55955	−	4.55955i	0.665078	−	0.665078i	0.956573	+	0.291494i	$0.0941524\pi$
$48$	−0.0713392	+	0.997452i	−0.0102969	+	0.143970i
$49$	−4.52463	+	7.04047i	−0.646376	+	1.00578i
$50$	−1.41143	+	4.79665i	−0.199606	+	0.678349i
$51$	3.61557	+	1.65118i	0.506282	+	0.231211i
$52$	−5.22589	−	3.91205i	−0.724701	−	0.542504i
$53$	4.09845	−	2.23792i	0.562965	−	0.307402i	−0.172451	−	0.985018i	$-0.555169\pi$
$53$	4.09845	−	2.23792i	0.562965	−	0.307402i	0.735416	+	0.677616i	$0.236987\pi$
$54$	−0.540641	−	0.841254i	−0.0735719	−	0.114480i
$55$	−0.0545875	+	1.51617i	−0.00736058	+	0.204441i
$56$	1.10449	+	3.76153i	0.147593	+	0.502656i
$57$	1.67630	−	0.119891i	0.222031	−	0.0158800i
$58$	−2.47573	+	0.177068i	−0.325079	+	0.0232501i
$59$	3.74486	+	12.7538i	0.487539	+	1.66041i	0.724799	+	0.688960i	$0.241932\pi$
$59$	3.74486	+	12.7538i	0.487539	+	1.66041i	−0.237260	+	0.971446i	$0.576249\pi$
$60$	−1.63700	+	1.52323i	−0.211336	+	0.196648i
$61$	6.18829	+	9.62916i	0.792329	+	1.23289i	0.968619	+	0.248550i	$0.0799539\pi$
$61$	6.18829	+	9.62916i	0.792329	+	1.23289i	−0.176290	+	0.984338i	$0.556410\pi$
$62$	5.70748	−	3.11652i	0.724851	−	0.395799i
$63$	−3.13839	−	2.34937i	−0.395400	−	0.295993i
$64$	0.909632	+	0.415415i	0.113704	+	0.0519269i
$65$	−2.58759	−	14.3657i	−0.320952	−	1.78185i
$66$	−0.366821	+	0.570784i	−0.0451525	+	0.0702587i
$67$	−0.342317	+	4.78621i	−0.0418206	+	0.584729i	0.932732	+	0.360570i	$0.117418\pi$
$67$	−0.342317	+	4.78621i	−0.0418206	+	0.584729i	−0.974553	+	0.224159i	$0.928037\pi$
$68$	2.81058	−	2.81058i	0.340833	−	0.340833i
$69$	0.336152	−	4.78404i	0.0404680	−	0.575930i
$70$	−3.92613	+	7.83777i	−0.469262	+	0.936792i
$71$	−7.81093	−	9.01429i	−0.926987	−	1.06980i	−0.997384	−	0.0722809i	$-0.976972\pi$
$71$	−7.81093	−	9.01429i	−0.926987	−	1.06980i	0.0703974	−	0.997519i	$-0.477573\pi$
$72$	−0.977147	+	0.212565i	−0.115158	+	0.0250511i
$73$	4.64964	−	3.48068i	0.544199	−	0.407383i	−0.291499	−	0.956571i	$-0.594154\pi$
$73$	4.64964	−	3.48068i	0.544199	−	0.407383i	0.835698	+	0.549189i	$0.185063\pi$
$74$	2.11516	−	4.63155i	0.245882	−	0.538407i
$75$	−5.00000	−	0.00288011i	−0.577350	−	0.000332566i
$76$	0.473474	−	1.61250i	0.0543112	−	0.184967i
$77$	−0.565406	+	2.59913i	−0.0644340	+	0.296198i
$78$	2.28128	−	6.11636i	0.258304	−	0.692541i
$79$	1.48297	−	0.435439i	0.166847	−	0.0489907i	−0.197242	−	0.980355i	$-0.563198\pi$
$79$	1.48297	−	0.435439i	0.166847	−	0.0489907i	0.364089	+	0.931364i	$0.381380\pi$
$80$	0.855111	+	2.06610i	0.0956043	+	0.230997i
$81$	0.654861	−	0.755750i	0.0727623	−	0.0839722i
$82$	−2.59395	+	4.75046i	−0.286454	+	0.524601i
$83$	−11.1767	−	4.16868i	−1.22680	−	0.457572i	−0.349235	−	0.937035i	$-0.613559\pi$
$83$	−11.1767	−	4.16868i	−1.22680	−	0.457572i	−0.877562	+	0.479463i	$0.840831\pi$
$84$	−3.29799	+	2.11949i	−0.359841	+	0.231256i
$85$	8.88227	−	0.314670i	0.963418	−	0.0341307i
$86$	10.8750	−	1.56359i	1.17268	−	0.168606i
$87$	−0.867389	−	2.32556i	−0.0929938	−	0.249326i
$88$	0.406606	+	0.543161i	0.0433443	+	0.0579012i
$89$	−1.40078	−	0.900224i	−0.148482	−	0.0954236i	0.464290	−	0.885683i	$-0.346309\pi$
$89$	−1.40078	−	0.900224i	−0.148482	−	0.0954236i	−0.612772	+	0.790259i	$0.709946\pi$
$90$	−1.92272	−	1.14155i	−0.202673	−	0.120330i
$91$		−	25.5917i		−	2.68274i
$92$	−4.36493	−	1.98681i	−0.455075	−	0.207139i
$93$	4.59826	+	4.59826i	0.476818	+	0.476818i
$94$	4.87320	−	4.22266i	0.502633	−	0.435534i
$95$	3.23239	−	1.91661i	0.331636	−	0.196640i
$96$	−0.142315	+	0.989821i	−0.0145249	+	0.101023i
$97$	−9.09892	+	3.39372i	−0.923856	+	0.344580i	−0.765969	−	0.642877i	$-0.777741\pi$
$97$	−9.09892	+	3.39372i	−0.923856	+	0.344580i	−0.157886	+	0.987457i	$0.550468\pi$
$98$	−5.01537	+	6.69975i	−0.506629	+	0.676776i
$99$	−0.651009	−	0.191153i	−0.0654289	−	0.0192116i
$100$	−1.75002	+	4.68374i	−0.175002	+	0.468374i
$101$	2.64440	+	5.79044i	0.263128	+	0.576170i	0.994372	−	0.105946i	$-0.0337871\pi$
$101$	2.64440	+	5.79044i	0.263128	+	0.576170i	−0.731244	+	0.682116i	$0.761060\pi$
$102$	3.48857	+	1.90490i	0.345420	+	0.188613i
$103$	−0.528338	−	7.38713i	−0.0520587	−	0.727876i	−0.954717	−	0.297517i	$-0.903842\pi$
$103$	−0.528338	−	7.38713i	−0.0520587	−	0.727876i	0.902658	−	0.430359i	$-0.141613\pi$
$104$	−4.93349	−	4.27490i	−0.483769	−	0.419188i
$105$	−8.62640	−	1.55894i	−0.841851	−	0.152137i
$106$	4.24766	−	1.93984i	0.412569	−	0.188414i
$107$	−10.1771	−	2.21389i	−0.983857	−	0.214025i	−0.308265	−	0.951301i	$-0.599748\pi$
$107$	−10.1771	−	2.21389i	−0.983857	−	0.214025i	−0.675592	+	0.737276i	$0.736112\pi$
$108$	−0.479249	−	0.877679i	−0.0461158	−	0.0844547i
$109$	1.29119	+	8.98042i	0.123674	+	0.860168i	0.953338	+	0.301906i	$0.0976227\pi$
$109$	1.29119	+	8.98042i	0.123674	+	0.860168i	−0.829664	+	0.558263i	$0.811468\pi$
$110$	−0.162611	+	1.50842i	−0.0155044	+	0.143822i
$111$	5.03985	+	0.724621i	0.478361	+	0.0687780i
$112$	0.833327	+	3.83074i	0.0787420	+	0.361971i
$113$	−3.98860	−	0.285271i	−0.375216	−	0.0268360i	−0.117542	−	0.993068i	$-0.537502\pi$
$113$	−3.98860	−	0.285271i	−0.375216	−	0.0268360i	−0.257674	+	0.966232i	$0.582956\pi$
$114$	1.68058			0.157401
$115$	−4.11335	−	9.90355i	−0.383572	−	0.923511i
$116$	−2.48205			−0.230453
$117$	6.51131	+	0.465698i	0.601971	+	0.0430538i
$118$	2.82547	+	12.9885i	0.260106	+	1.19569i
$119$	15.4238	+	2.21761i	1.41390	+	0.203288i
$120$	−1.74150	+	1.40256i	−0.158976	+	0.128036i
$121$	−1.49995	−	10.4324i	−0.136359	−	0.948397i
$122$	5.48558	+	10.0461i	0.496641	+	0.909531i
$123$	−5.28883	−	1.15052i	−0.476878	−	0.103738i
$124$	5.91527	−	2.70141i	0.531207	−	0.242594i
$125$	−10.0021	+	4.99587i	−0.894612	+	0.446844i
$126$	−2.96279	−	2.56727i	−0.263946	−	0.228711i
$127$	−0.991568	−	13.8639i	−0.0879875	−	1.23023i	−0.829199	−	0.558954i	$-0.811203\pi$
$127$	−0.991568	−	13.8639i	−0.0879875	−	1.23023i	0.741211	−	0.671272i	$-0.234252\pi$
$128$	0.877679	+	0.479249i	0.0775766	+	0.0423600i
$129$	4.56410	+	9.99398i	0.401847	+	0.879921i
$130$	−1.55616	−	14.5137i	−0.136484	−	1.27294i
$131$	−5.52602	−	1.62259i	−0.482811	−	0.141766i	0.0312645	−	0.999511i	$-0.490047\pi$
$131$	−5.52602	−	1.62259i	−0.482811	−	0.141766i	−0.514075	+	0.857745i	$0.671865\pi$
$132$	−0.406606	+	0.543161i	−0.0353905	+	0.0472761i
$133$	6.17303	−	2.30242i	0.535270	−	0.199645i
$134$	−0.682889	+	4.74960i	−0.0589926	+	0.410303i
$135$	0.553618	−	2.16645i	0.0476479	−	0.186458i
$136$	3.00393	−	2.60292i	0.257585	−	0.223198i
$137$	−2.25904	−	2.25904i	−0.193003	−	0.193003i	0.603989	−	0.796992i	$-0.293577\pi$
$137$	−2.25904	−	2.25904i	−0.193003	−	0.193003i	−0.796992	+	0.603989i	$0.793577\pi$
$138$	0.676585	−	4.74787i	0.0575947	−	0.404165i
$139$		−	12.0020i		−	1.01800i	−0.860766	−	0.509000i	$-0.830015\pi$
$139$		−	12.0020i		−	1.01800i	0.860766	−	0.509000i	$-0.169985\pi$
$140$	−4.47527	+	7.53771i	−0.378229	+	0.637053i
$141$	5.42455	+	3.48615i	0.456829	+	0.293586i
$142$	−7.14796	−	9.54855i	−0.599843	−	0.801297i
$143$	−1.54783	−	4.14990i	−0.129436	−	0.347032i
$144$	−0.989821	+	0.142315i	−0.0824851	+	0.0118596i
$145$	−4.06095	−	3.78307i	−0.337244	−	0.314166i
$146$	4.88610	−	3.14011i	0.404377	−	0.259877i
$147$	−7.84135	−	2.92467i	−0.646744	−	0.241223i
$148$	2.44018	−	4.46885i	0.200582	−	0.367338i
$149$	−5.00101	+	5.77147i	−0.409698	+	0.472817i	−0.922671	−	0.385588i	$-0.873999\pi$
$149$	−5.00101	+	5.77147i	−0.409698	+	0.472817i	0.512973	+	0.858405i	$0.328544\pi$
$150$	−4.98705	−	0.359569i	−0.407191	−	0.0293587i
$151$	22.7294	−	6.67394i	1.84969	−	0.543118i	0.849818	−	0.527076i	$-0.176712\pi$
$151$	22.7294	−	6.67394i	1.84969	−	0.543118i	0.999871	−	0.0160417i	$-0.00510645\pi$
$152$	0.587302	−	1.57462i	0.0476365	−	0.127718i
$153$	−0.844897	+	3.88393i	−0.0683059	+	0.313997i
$154$	−0.749386	+	2.55217i	−0.0603872	+	0.205660i
$155$	13.7955	+	4.59601i	1.10808	+	0.369161i
$156$	2.71181	−	5.93803i	0.217118	−	0.475423i
$157$	14.4471	−	10.8150i	1.15301	−	0.863131i	0.160709	−	0.987002i	$-0.448622\pi$
$157$	14.4471	−	10.8150i	1.15301	−	0.863131i	0.992298	+	0.123871i	$0.0395309\pi$
$158$	1.51026	−	0.328536i	0.120149	−	0.0261369i
$159$	3.05797	+	3.52908i	0.242513	+	0.279874i
$160$	0.705538	+	2.12184i	0.0557777	+	0.167746i
$161$	−4.01945	−	18.3666i	−0.316777	−	1.44749i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−0.963591	+	13.4728i	−0.0754743	+	1.05527i	0.808734	+	0.588175i	$0.200153\pi$
$163$	−0.963591	+	13.4728i	−0.0754743	+	1.05527i	−0.884208	+	0.467093i	$0.845301\pi$
$164$	−2.92623	+	4.55331i	−0.228500	+	0.355554i
$165$	−1.49313	+	0.268946i	−0.116240	+	0.0209374i
$166$	−10.8508	−	4.95539i	−0.842184	−	0.384613i
$167$	−9.80590	−	7.34061i	−0.758804	−	0.568033i	0.148299	−	0.988943i	$-0.452620\pi$
$167$	−9.80590	−	7.34061i	−0.758804	−	0.568033i	−0.907103	+	0.420909i	$0.861711\pi$
$168$	−3.44079	+	1.87882i	−0.265463	+	0.144954i
$169$	16.0106	+	24.9129i	1.23158	+	1.91638i
$170$	8.88209	+	0.319786i	0.681225	+	0.0245265i
$171$	0.473474	+	1.61250i	0.0362075	+	0.123311i
$172$	10.9588	−	0.783792i	0.835604	−	0.0597636i
$173$	−11.4469	+	0.818698i	−0.870291	+	0.0622444i	−0.499338	−	0.866407i	$-0.666423\pi$
$173$	−11.4469	+	0.818698i	−0.870291	+	0.0622444i	−0.370953	+	0.928652i	$0.620969\pi$
$174$	−0.699275	−	2.38151i	−0.0530119	−	0.180542i
$175$	−18.8108	+	5.51159i	−1.42197	+	0.416637i
$176$	0.366821	+	0.570784i	0.0276502	+	0.0430245i
$177$	−11.6663	+	6.37030i	−0.876895	+	0.478821i
$178$	−1.33299	−	0.997861i	−0.0999115	−	0.0747928i
$179$	−4.26821	−	1.94923i	−0.319021	−	0.145692i	0.249468	−	0.968383i	$-0.419744\pi$
$179$	−4.26821	−	1.94923i	−0.319021	−	0.145692i	−0.568489	+	0.822691i	$0.692472\pi$
$180$	−1.83639	−	1.27581i	−0.136876	−	0.0950932i
$181$	7.97765	−	12.4135i	0.592974	−	0.922686i	−0.406983	−	0.913436i	$-0.633419\pi$
$181$	7.97765	−	12.4135i	0.592974	−	0.922686i	0.999957	−	0.00924997i	$-0.00294440\pi$
$182$	1.82569	−	25.5265i	0.135329	−	1.89215i
$183$	−8.09369	+	8.09369i	−0.598303	+	0.598303i
$184$	−4.21207	−	2.29314i	−0.310518	−	0.169052i
$185$	10.8037	−	3.59237i	0.794306	−	0.264116i
$186$	4.25851	+	4.91458i	0.312249	+	0.360355i
$187$	2.63522	−	0.573257i	0.192706	−	0.0419207i
$188$	5.16203	−	3.86425i	0.376480	−	0.281829i
$189$	1.62857	−	3.56606i	0.118461	−	0.259393i
$190$	3.36088	−	1.68113i	0.243824	−	0.121962i
$191$	−4.28220	+	14.5838i	−0.309849	+	1.05525i	0.646474	+	0.762936i	$0.276243\pi$
$191$	−4.28220	+	14.5838i	−0.309849	+	1.05525i	−0.956323	+	0.292312i	$0.905575\pi$
$192$	−0.212565	+	0.977147i	−0.0153406	+	0.0705195i
$193$	−7.00614	+	18.7842i	−0.504313	+	1.35211i	0.396551	+	0.918013i	$0.370207\pi$
$193$	−7.00614	+	18.7842i	−0.504313	+	1.35211i	−0.900864	+	0.434102i	$0.857066\pi$
$194$	−9.31785	+	2.73597i	−0.668982	+	0.196431i
$195$	13.4874	−	5.58212i	0.965854	−	0.399744i
$196$	−5.48054	+	6.32488i	−0.391467	+	0.451777i
$197$	−0.507104	+	0.928691i	−0.0361297	+	0.0661665i	−0.895120	−	0.445825i	$-0.852910\pi$
$197$	−0.507104	+	0.928691i	−0.0361297	+	0.0661665i	0.858990	+	0.511992i	$0.171092\pi$
$198$	−0.635714	−	0.237109i	−0.0451782	−	0.0168506i
$199$	0.938963	−	0.603435i	0.0665613	−	0.0427764i	−0.506937	−	0.861983i	$-0.669222\pi$
$199$	0.938963	−	0.603435i	0.0665613	−	0.0427764i	0.573498	+	0.819207i	$0.305586\pi$
$200$	−2.07969	+	4.54696i	−0.147057	+	0.321519i
$201$	−4.74960	+	0.682889i	−0.335011	+	0.0481673i
$202$	2.22458	+	5.96433i	0.156521	+	0.419649i
$203$	−5.83126	−	7.78965i	−0.409274	−	0.546726i
$204$	3.34379	+	2.14892i	0.234112	+	0.150455i
$205$	−11.7277	+	2.98972i	−0.819098	+	0.208811i
$206$		−	7.40600i		−	0.516001i
$207$	4.74616	−	0.688450i	0.329881	−	0.0478506i
$208$	−4.61595	−	4.61595i	−0.320059	−	0.320059i
$209$	0.861752	−	0.746712i	0.0596086	−	0.0516512i
$210$	−8.49321	−	2.17037i	−0.586087	−	0.149770i
$211$	0.273262	−	1.90058i	0.0188121	−	0.130841i	−0.978251	−	0.207424i	$-0.933492\pi$
$211$	0.273262	−	1.90058i	0.0188121	−	0.130841i	0.997063	+	0.0765830i	$0.0244010\pi$
$212$	4.37522	−	1.63187i	0.300492	−	0.112078i
$213$	7.14796	−	9.54855i	0.489770	−	0.654256i
$214$	−9.99323	−	2.93428i	−0.683123	−	0.200583i
$215$	19.1247	+	15.4207i	1.30429	+	1.05169i
$216$	−0.415415	−	0.909632i	−0.0282654	−	0.0618926i
$217$	22.3752	+	12.2178i	1.51893	+	0.829399i
$218$	0.647244	+	9.04965i	0.0438369	+	0.612920i
$219$	4.38949	+	3.80351i	0.296614	+	0.257017i
$220$	−0.269806	+	1.49297i	−0.0181903	+	0.100656i
$221$	−23.6023	+	10.7788i	−1.58766	+	0.725060i
$222$	4.97531	+	1.08231i	0.333921	+	0.0726401i
$223$	−3.40209	−	6.23045i	−0.227820	−	0.417222i	0.738617	−	0.674126i	$-0.235479\pi$
$223$	−3.40209	−	6.23045i	−0.227820	−	0.417222i	−0.966437	+	0.256904i	$0.917298\pi$
$224$	0.557922	+	3.88043i	0.0372777	+	0.259272i
$225$	−1.06001	−	4.88635i	−0.0706675	−	0.325756i
$226$	−3.95809	−	0.569087i	−0.263288	−	0.0378551i
$227$	−3.53495	−	16.2499i	−0.234623	−	1.07854i	−0.932175	−	0.362009i	$-0.882091\pi$
$227$	−3.53495	−	16.2499i	−0.234623	−	1.07854i	0.697552	−	0.716534i	$-0.254273\pi$
$228$	1.67630	+	0.119891i	0.111016	+	0.00793999i
$229$	−18.7338			−1.23797			−0.618983	−	0.785404i	$-0.712455\pi$
$229$	−18.7338			−1.23797			−0.618983	+	0.785404i	$0.712455\pi$
$230$	−3.39636	−	10.1718i	−0.223949	−	0.670706i
$231$	−2.65992			−0.175010
$232$	−2.47573	−	0.177068i	−0.162540	−	0.0116251i
$233$	4.21918	+	19.3953i	0.276408	+	1.27063i	0.880628	+	0.473809i	$0.157121\pi$
$233$	4.21918	+	19.3953i	0.276408	+	1.27063i	−0.604220	+	0.796818i	$0.706515\pi$
$234$	6.46150	+	0.929024i	0.422402	+	0.0607322i
$235$	14.3355	+	1.54540i	0.935145	+	0.100811i
$236$	1.89168	+	13.1570i	0.123138	+	0.856445i
$237$	0.740716	+	1.35652i	0.0481147	+	0.0881155i
$238$	15.2263	+	3.31228i	0.986975	+	0.214703i
$239$	24.4595	−	11.1703i	1.58216	−	0.722547i	0.586014	−	0.810301i	$-0.300696\pi$
$239$	24.4595	−	11.1703i	1.58216	−	0.722547i	0.996142	+	0.0877542i	$0.0279690\pi$
$240$	−1.83712	+	1.27475i	−0.118586	+	0.0822848i
$241$	−17.8086	−	15.4312i	−1.14715	−	0.994012i	−0.999988	−	0.00489987i	$-0.998440\pi$
$241$	−17.8086	−	15.4312i	−1.14715	−	0.994012i	−0.147163	−	0.989112i	$-0.547014\pi$
$242$	−0.751890	−	10.5128i	−0.0483333	−	0.675788i
$243$	0.877679	+	0.479249i	0.0563031	+	0.0307438i
$244$	4.75493	+	10.4118i	0.304403	+	0.666550i
$245$	−18.6070	+	1.99504i	−1.18876	+	0.127459i
$246$	−5.19328	−	1.52489i	−0.331112	−	0.0972231i
$247$	−6.57451	+	8.78252i	−0.418326	+	0.558819i
$248$	6.09292	−	2.27254i	0.386901	−	0.144306i
$249$	1.69764	−	11.8073i	0.107584	−	0.748260i
$250$	−10.3330	+	4.26960i	−0.653515	+	0.270033i
$251$	−18.6168	+	16.1315i	−1.17508	+	1.01821i	−0.175652	+	0.984452i	$0.556203\pi$
$251$	−18.6168	+	16.1315i	−1.17508	+	1.01821i	−0.999430	+	0.0337616i	$0.989251\pi$
$252$	−2.77209	−	2.77209i	−0.174626	−	0.174626i
$253$	−1.76263	−	2.73518i	−0.110816	−	0.171960i
$254$		−	13.8994i		−	0.872123i
$255$	2.19554	+	8.61240i	0.137490	+	0.539329i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	−11.2959	−	15.0896i	−0.704622	−	0.941264i	0.295278	−	0.955411i	$-0.404588\pi$
$257$	−11.2959	−	15.0896i	−0.704622	−	0.941264i	−0.999900	+	0.0141470i	$0.995497\pi$
$258$	3.83951	+	10.2941i	0.239037	+	0.640884i
$259$	19.7579	−	2.84076i	1.22770	−	0.176516i
$260$	−0.516797	−	14.5878i	−0.0320504	−	0.904696i
$261$	2.08804	−	1.34190i	0.129246	−	0.0830615i
$262$	−5.39619	−	2.01267i	−0.333377	−	0.124343i
$263$	−0.173166	+	0.317129i	−0.0106778	+	0.0195550i	−0.882963	−	0.469442i	$-0.844455\pi$
$263$	−0.173166	+	0.317129i	−0.0106778	+	0.0195550i	0.872286	+	0.488997i	$0.162637\pi$
$264$	−0.444318	+	0.512771i	−0.0273459	+	0.0315588i
$265$	9.64567	+	3.99862i	0.592529	+	0.245633i
$266$	6.32155	−	1.85618i	0.387599	−	0.113809i
$267$	0.581895	−	1.56012i	0.0356114	−	0.0954778i
$268$	−1.01998	+	4.68878i	−0.0623053	+	0.286413i
$269$	−6.76273	+	23.0318i	−0.412331	+	1.40427i	0.447771	+	0.894148i	$0.352218\pi$
$269$	−6.76273	+	23.0318i	−0.412331	+	1.40427i	−0.860102	+	0.510122i	$0.829600\pi$
$270$	0.706760	−	2.12144i	0.0430121	−	0.129106i
$271$	4.66151	−	10.2073i	0.283166	−	0.620048i	−0.713587	−	0.700567i	$-0.752931\pi$
$271$	4.66151	−	10.2073i	0.283166	−	0.620048i	0.996753	+	0.0805191i	$0.0256578\pi$
$272$	3.18196	−	2.38199i	0.192935	−	0.144429i
$273$	25.0069	−	5.43991i	1.51349	−	0.329239i
$274$	−2.09213	−	2.41444i	−0.126390	−	0.145862i
$275$	−2.71698	+	2.03146i	−0.163840	+	0.122502i
$276$	1.01357	−	4.68750i	0.0610097	−	0.282154i
$277$	−14.4213	+	14.4213i	−0.866493	+	0.866493i	−0.992082	−	0.125589i	$-0.959918\pi$
$277$	−14.4213	+	14.4213i	−0.866493	+	0.866493i	0.125589	+	0.992082i	$0.459918\pi$
$278$	0.856216	−	11.9715i	0.0513524	−	0.718001i
$279$	−3.51575	+	5.47061i	−0.210482	+	0.327517i
$280$	−5.00160	+	7.19924i	−0.298903	+	0.430237i
$281$	1.66393	+	0.759890i	0.0992616	+	0.0453313i	0.464427	−	0.885611i	$-0.346260\pi$
$281$	1.66393	+	0.759890i	0.0992616	+	0.0453313i	−0.365165	+	0.930943i	$0.618988\pi$
$282$	5.16203	+	3.86425i	0.307394	+	0.230112i
$283$	−10.1636	+	5.54977i	−0.604166	+	0.329900i	−0.752051	−	0.659105i	$-0.770935\pi$
$283$	−10.1636	+	5.54977i	−0.604166	+	0.329900i	0.147885	+	0.989005i	$0.452754\pi$
$284$	−6.44856	−	10.0342i	−0.382652	−	0.595417i
$285$	2.55990	+	2.75112i	0.151635	+	0.162962i
$286$	−1.24784	−	4.24975i	−0.0737863	−	0.251293i
$287$	−21.1649	+	1.51374i	−1.24932	+	0.0893533i
$288$	−0.997452	+	0.0713392i	−0.0587754	+	0.00420370i
$289$	0.338428	+	1.15258i	0.0199075	+	0.0677988i
$290$	−3.78073	−	4.06313i	−0.222012	−	0.238595i
$291$	−5.25028	−	8.16960i	−0.307777	−	0.478910i
$292$	5.09767	−	2.78354i	0.298318	−	0.162894i
$293$	−18.3604	−	13.7444i	−1.07263	−	0.802957i	−0.0913986	−	0.995814i	$-0.529134\pi$
$293$	−18.3604	−	13.7444i	−1.07263	−	0.802957i	−0.981227	+	0.192857i	$0.938225\pi$
$294$	−7.61273	−	3.47662i	−0.443983	−	0.202760i
$295$	−16.9584	+	24.4097i	−0.987355	+	1.42119i
$296$	2.75277	−	4.28339i	0.160001	−	0.248967i
$297$	0.0484031	−	0.676764i	0.00280863	−	0.0392698i
$298$	−5.40000	+	5.40000i	−0.312813	+	0.312813i
$299$	22.1650	+	22.1097i	1.28183	+	1.27863i
$300$	−4.94870	−	0.714425i	−0.285713	−	0.0412473i
$301$	28.2062	+	32.5517i	1.62578	+	1.87625i
$302$	23.1476	−	5.03544i	1.33199	−	0.289757i
$303$	−5.09600	+	3.81482i	−0.292757	+	0.219155i
$304$	0.698138	−	1.52871i	0.0400410	−	0.0876775i
$305$	−8.08973	+	24.2824i	−0.463216	+	1.39041i
$306$	−1.11982	+	3.81376i	−0.0640159	+	0.218018i
$307$	−1.56376	+	7.18847i	−0.0892482	+	0.410268i	−0.999996	−	0.00269472i	$-0.999142\pi$
$307$	−1.56376	+	7.18847i	−0.0892482	+	0.410268i	0.910748	+	0.412962i	$0.135506\pi$
$308$	−0.929546	+	2.49221i	−0.0529658	+	0.142007i
$309$	7.10601	−	2.08651i	0.404247	−	0.118698i
$310$	13.4325	+	5.56846i	0.762916	+	0.316268i
$311$	11.1725	−	12.8937i	0.633532	−	0.731135i	−0.344686	−	0.938718i	$-0.612014\pi$
$311$	11.1725	−	12.8937i	0.633532	−	0.731135i	0.978217	+	0.207584i	$0.0665599\pi$
$312$	3.12851	−	5.72944i	0.177117	−	0.324366i
$313$	−17.0596	−	6.36291i	−0.964267	−	0.359653i	−0.182488	−	0.983208i	$-0.558415\pi$
$313$	−17.0596	−	6.36291i	−0.964267	−	0.359653i	−0.781779	+	0.623555i	$0.785688\pi$
$314$	15.1819	−	9.75680i	0.856762	−	0.550608i
$315$	−0.310361	−	8.76064i	−0.0174868	−	0.493606i
$316$	1.52984	−	0.219958i	0.0860605	−	0.0123736i
$317$	8.69000	+	23.2988i	0.488079	+	1.30859i	0.914690	+	0.404156i	$0.132435\pi$
$317$	8.69000	+	23.2988i	0.488079	+	1.30859i	−0.426611	+	0.904435i	$0.640293\pi$
$318$	2.79841	+	3.73824i	0.156927	+	0.209630i
$319$	−1.41672	−	0.910469i	−0.0793209	−	0.0509765i
$320$	0.552370	+	2.16677i	0.0308784	+	0.121126i
$321$		−	10.4151i		−	0.581315i
$322$	−2.69895	−	18.6065i	−0.150407	−	1.03690i
$323$	−4.72341	−	4.72341i	−0.262818	−	0.262818i
$324$	0.755750	−	0.654861i	0.0419861	−	0.0363812i
$325$	21.3887	−	24.6551i	1.18643	−	1.36762i
$326$	−1.92227	+	13.3697i	−0.106465	+	0.740479i
$327$	−8.50073	+	3.17061i	−0.470091	+	0.175335i
$328$	−3.24361	+	4.33295i	−0.179098	+	0.239247i
$329$	24.2550	+	7.12191i	1.33722	+	0.392644i
$330$	−1.50851	+	0.161742i	−0.0830407	+	0.00890361i
$331$	−0.736628	−	1.61299i	−0.0404887	−	0.0886580i	0.888307	−	0.459250i	$-0.151882\pi$
$331$	−0.736628	−	1.61299i	−0.0404887	−	0.0886580i	−0.928796	+	0.370592i	$0.879155\pi$
$332$	−10.4696	−	5.71685i	−0.574595	−	0.313753i
$333$	0.363236	+	5.07870i	0.0199052	+	0.278311i
$334$	−9.25725	−	8.02145i	−0.506534	−	0.438914i
$335$	−8.81530	+	6.11681i	−0.481632	+	0.334197i
$336$	−3.56606	+	1.62857i	−0.194545	+	0.0888455i
$337$	10.3396	+	2.24923i	0.563232	+	0.122524i	0.485162	−	0.874424i	$-0.338761\pi$
$337$	10.3396	+	2.24923i	0.563232	+	0.122524i	0.0780697	+	0.996948i	$0.475124\pi$
$338$	14.1925	+	25.9917i	0.771971	+	1.41376i
$339$	−0.569087	−	3.95809i	−0.0309086	−	0.214974i
$340$	8.83665	+	0.952612i	0.479234	+	0.0516627i
$341$	4.36728	+	0.627920i	0.236501	+	0.0340038i
$342$	0.357233	+	1.64217i	0.0193169	+	0.0887985i
$343$	−5.35334	−	0.382878i	−0.289053	−	0.0206735i
$344$	10.9868			0.592371
$345$	8.80287	−	6.12450i	0.473931	−	0.329732i
$346$	−11.4761			−0.616960
$347$	2.72784	+	0.195099i	0.146438	+	0.0104735i	0.144366	−	0.989524i	$-0.453886\pi$
$347$	2.72784	+	0.195099i	0.146438	+	0.0104735i	0.00207227	+	0.999998i	$0.499340\pi$
$348$	−0.527598	−	2.42533i	−0.0282822	−	0.130011i
$349$	5.08131	+	0.730582i	0.271996	+	0.0391072i	0.276963	−	0.960881i	$-0.410672\pi$
$349$	5.08131	+	0.730582i	0.271996	+	0.0391072i	−0.00496701	+	0.999988i	$0.501581\pi$
$350$	−19.1561	+	4.15560i	−1.02394	+	0.222126i
$351$	0.929024	+	6.46150i	0.0495876	+	0.344889i
$352$	0.325167	+	0.595499i	0.0173315	+	0.0317402i
$353$	−17.6088	−	3.83056i	−0.937221	−	0.203880i	−0.282084	−	0.959390i	$-0.591026\pi$
$353$	−17.6088	−	3.83056i	−0.937221	−	0.203880i	−0.655137	+	0.755510i	$0.727389\pi$
$354$	−12.0911	+	5.52180i	−0.642632	+	0.293480i
$355$	4.74308	−	26.2458i	0.251736	−	1.39298i
$356$	−1.25840	−	1.09041i	−0.0666952	−	0.0577917i
$357$	1.11164	+	15.5427i	0.0588340	+	0.822607i
$358$	−4.11828	−	2.24875i	−0.217658	−	0.118850i
$359$	2.99950	+	6.56798i	0.158307	+	0.346645i	0.972121	−	0.234482i	$-0.0753393\pi$
$359$	2.99950	+	6.56798i	0.158307	+	0.346645i	−0.813813	+	0.581127i	$0.802612\pi$
$360$	−1.74069	−	1.40356i	−0.0917425	−	0.0739744i
$361$	15.5204	+	4.55721i	0.816864	+	0.239853i
$362$	8.84289	−	11.8127i	0.464772	−	0.620863i
$363$	9.87512	−	3.68323i	0.518309	−	0.193319i
$364$	3.64208	−	25.3312i	0.190897	−	1.32772i
$365$	12.5830	+	3.21548i	0.658625	+	0.168306i
$366$	−8.65047	+	7.49567i	−0.452167	+	0.391805i
$367$	10.0139	+	10.0139i	0.522721	+	0.522721i	0.918392	−	0.395671i	$-0.129488\pi$
$367$	10.0139	+	10.0139i	0.522721	+	0.522721i	−0.395671	+	0.918392i	$0.629488\pi$
$368$	−4.03775	−	2.58778i	−0.210482	−	0.134897i
$369$		−	5.41253i		−	0.281765i
$370$	11.0325	−	2.81249i	0.573551	−	0.146214i
$371$	15.4005	+	9.89728i	0.799552	+	0.513841i
$372$	3.89706	+	5.20586i	0.202053	+	0.269911i
$373$	−4.12025	−	11.0468i	−0.213339	−	0.571983i	0.785566	−	0.618778i	$-0.212372\pi$
$373$	−4.12025	−	11.0468i	−0.213339	−	0.571983i	−0.998905	+	0.0467949i	$0.985099\pi$
$374$	2.66940	−	0.383802i	0.138031	−	0.0198459i
$375$	−7.00779	−	8.71154i	−0.361881	−	0.449862i
$376$	5.42455	−	3.48615i	0.279750	−	0.179784i
$377$	15.1811	+	5.66227i	0.781867	+	0.291621i
$378$	1.87882	−	3.44079i	0.0966359	−	0.176975i
$379$	−8.46392	+	9.76789i	−0.434762	+	0.501743i	−0.930277	−	0.366857i	$-0.880434\pi$
$379$	−8.46392	+	9.76789i	−0.434762	+	0.501743i	0.495515	+	0.868599i	$0.334979\pi$
$380$	3.47225	−	1.43708i	0.178123	−	0.0737208i
$381$	13.3363	−	3.91590i	0.683241	−	0.200618i
$382$	−5.31168	+	14.2412i	−0.271769	+	0.728642i
$383$	7.43125	−	34.1609i	0.379719	−	1.74554i	−0.249557	−	0.968360i	$-0.580285\pi$
$383$	7.43125	−	34.1609i	0.379719	−	1.74554i	0.629277	−	0.777181i	$-0.283351\pi$
$384$	−0.281733	+	0.959493i	−0.0143771	+	0.0489639i
$385$	−5.31940	+	2.66079i	−0.271102	+	0.135606i
$386$	−8.32833	+	18.2365i	−0.423901	+	0.928214i
$387$	−8.79542	+	6.58417i	−0.447096	+	0.334692i
$388$	−9.48929	+	2.06427i	−0.481746	+	0.104797i
$389$	−25.0250	−	28.8803i	−1.26882	−	1.46429i	−0.821812	−	0.569759i	$-0.807037\pi$
$389$	−25.0250	−	28.8803i	−1.26882	−	1.46429i	−0.447003	−	0.894532i	$-0.647509\pi$
$390$	13.8513	−	4.60572i	0.701386	−	0.233219i
$391$	−15.2459	+	11.4427i	−0.771017	+	0.578681i
$392$	−5.91779	+	5.91779i	−0.298894	+	0.298894i
$393$	0.410865	−	5.74464i	0.0207254	−	0.289779i
$394$	−0.572064	+	0.890149i	−0.0288202	+	0.0448450i
$395$	2.83827	+	1.97186i	0.142809	+	0.0992151i
$396$	−0.617179	−	0.281856i	−0.0310144	−	0.0141638i
$397$	−12.9628	−	9.70381i	−0.650583	−	0.487020i	0.222282	−	0.974982i	$-0.428649\pi$
$397$	−12.9628	−	9.70381i	−0.650583	−	0.487020i	−0.872865	+	0.487962i	$0.837740\pi$
$398$	0.979619	−	0.534912i	0.0491039	−	0.0268127i
$399$	3.56198	+	5.54254i	0.178322	+	0.277474i
$400$	−2.39877	+	4.38701i	−0.119939	+	0.219351i
$401$	9.99312	+	34.0334i	0.499033	+	1.69955i	0.695061	+	0.718951i	$0.255377\pi$
$401$	9.99312	+	34.0334i	0.499033	+	1.69955i	−0.196028	+	0.980598i	$0.562804\pi$
$402$	−4.78621	+	0.342317i	−0.238715	+	0.0170732i
$403$	−42.3426	+	3.02840i	−2.10924	+	0.150855i
$404$	1.79342	+	6.10784i	0.0892261	+	0.303876i
$405$	2.23462	+	0.0804541i	0.111039	+	0.00399780i
$406$	−5.26069	−	8.18580i	−0.261084	−	0.406254i
$407$	3.03209	−	1.65564i	0.150295	−	0.0820672i
$408$	3.18196	+	2.38199i	0.157531	+	0.117926i
$409$	−22.5399	−	10.2936i	−1.11452	−	0.508986i	−0.228929	−	0.973443i	$-0.573522\pi$
$409$	−22.5399	−	10.2936i	−1.11452	−	0.508986i	−0.885596	+	0.464457i	$0.846250\pi$
$410$	−11.9111	+	2.14546i	−0.588247	+	0.105957i
$411$	1.72722	−	2.68761i	0.0851976	−	0.132570i
$412$	0.528338	−	7.38713i	0.0260294	−	0.363938i
$413$	−36.8474	+	36.8474i	−1.81314	+	1.81314i
$414$	4.78318	−	0.348109i	0.235081	−	0.0171086i
$415$	−8.41620	−	25.3110i	−0.413135	−	1.24247i
$416$	−4.27490	−	4.93349i	−0.209594	−	0.241884i
$417$	11.7278	−	2.55122i	0.574311	−	0.124934i
$418$	0.912826	−	0.683333i	0.0446478	−	0.0334229i
$419$	4.46772	−	9.78295i	0.218263	−	0.477928i	−0.768551	−	0.639788i	$-0.779022\pi$
$419$	4.46772	−	9.78295i	0.218263	−	0.477928i	0.986814	+	0.161860i	$0.0517493\pi$
$420$	−8.31674	−	2.77074i	−0.405815	−	0.135198i
$421$	−3.57125	+	12.1626i	−0.174052	+	0.592767i	0.825544	+	0.564338i	$0.190869\pi$
$421$	−3.57125	+	12.1626i	−0.174052	+	0.592767i	−0.999596	+	0.0284286i	$0.990950\pi$
$422$	0.408152	−	1.87624i	0.0198685	−	0.0913341i
$423$	−2.25341	+	6.04161i	−0.109564	+	0.293753i
$424$	4.48049	−	1.31559i	0.217592	−	0.0638908i
$425$	13.0059	+	15.0271i	0.630881	+	0.728923i
$426$	7.81093	−	9.01429i	0.378441	−	0.436744i
$427$	−21.5053	+	39.3841i	−1.04072	+	1.90593i
$428$	−9.75844	−	3.63971i	−0.471692	−	0.175932i
$429$	3.72605	−	2.39459i	0.179895	−	0.115612i
$430$	17.9759	+	16.7458i	0.866873	+	0.807554i
$431$	12.2317	−	1.75865i	0.589180	−	0.0847113i	0.158724	−	0.987323i	$-0.449262\pi$
$431$	12.2317	−	1.75865i	0.589180	−	0.0847113i	0.430456	+	0.902612i	$0.358353\pi$
$432$	−0.349464	−	0.936950i	−0.0168136	−	0.0450790i
$433$	0.545690	+	0.728957i	0.0262242	+	0.0350314i	0.813462	−	0.581618i	$-0.197580\pi$
$433$	0.545690	+	0.728957i	0.0262242	+	0.0350314i	−0.787237	+	0.616650i	$0.788489\pi$
$434$	21.4466	+	13.7829i	1.02947	+	0.661601i
$435$	2.83339	−	4.77230i	0.135851	−	0.228814i
$436$			9.07277i			0.434507i
$437$	−3.33899	+	7.33561i	−0.159725	+	0.350910i
$438$	4.10696	+	4.10696i	0.196238	+	0.196238i
$439$	18.4670	−	16.0017i	0.881380	−	0.763720i	−0.0913114	−	0.995822i	$-0.529106\pi$
$439$	18.4670	−	16.0017i	0.881380	−	0.763720i	0.972691	+	0.232102i	$0.0745604\pi$
$440$	−0.375626	+	1.46992i	−0.0179073	+	0.0700757i
$441$	1.19104	−	8.28383i	0.0567160	−	0.394468i
$442$	−24.3111	+	9.06757i	−1.15636	+	0.431300i
$443$	11.0583	−	14.7722i	0.525397	−	0.701848i	−0.456828	−	0.889555i	$-0.651015\pi$
$443$	11.0583	−	14.7722i	0.525397	−	0.701848i	0.982225	+	0.187707i	$0.0601056\pi$
$444$	4.88542	+	1.43449i	0.231852	+	0.0680779i
$445$	−0.396935	−	3.70207i	−0.0188165	−	0.175495i
$446$	−2.94894	−	6.45728i	−0.139636	−	0.305761i
$447$	−6.70261	−	3.65990i	−0.317023	−	0.173107i
$448$	0.279673	+	3.91035i	0.0132133	+	0.184746i
$449$	21.7839	+	18.8759i	1.02805	+	0.890807i	0.994084	−	0.108616i	$-0.0346419\pi$
$449$	21.7839	+	18.8759i	1.02805	+	0.890807i	0.0339625	+	0.999423i	$0.489187\pi$
$450$	−0.708723	−	4.94952i	−0.0334095	−	0.233322i
$451$	−3.34050	+	1.52555i	−0.157298	+	0.0718355i
$452$	−3.90741	−	0.850004i	−0.183789	−	0.0399808i
$453$	11.3529	+	20.7913i	0.533406	+	0.976859i
$454$	−2.36669	−	16.4607i	−0.111074	−	0.772537i
$455$	44.5680	−	35.8940i	2.08938	−	1.68274i
$456$	1.66347	+	0.239171i	0.0778993	+	0.0112002i
$457$	3.61228	+	16.6054i	0.168975	+	0.776767i	0.981134	+	0.193330i	$0.0619288\pi$
$457$	3.61228	+	16.6054i	0.168975	+	0.776767i	−0.812159	+	0.583437i	$0.801708\pi$
$458$	−18.6861	−	1.33646i	−0.873144	−	0.0624485i
$459$	−3.97477			−0.185526
$460$	−2.66206	−	10.3881i	−0.124119	−	0.484350i
$461$	16.2965			0.759003			0.379502	−	0.925191i	$-0.376095\pi$
$461$	16.2965			0.759003			0.379502	+	0.925191i	$0.376095\pi$
$462$	−2.65314	−	0.189756i	−0.123435	−	0.00882827i
$463$	6.54177	+	30.0720i	0.304022	+	1.39757i	0.835033	+	0.550201i	$0.185449\pi$
$463$	6.54177	+	30.0720i	0.304022	+	1.39757i	−0.531011	+	0.847365i	$0.678188\pi$
$464$	−2.45679	−	0.353233i	−0.114054	−	0.0163984i
$465$	−1.55852	+	14.4572i	−0.0722748	+	0.670438i
$466$	2.82479	+	19.6469i	0.130856	+	0.910123i
$467$	−0.0219352	−	0.0401712i	−0.00101504	−	0.00185890i	0.877171	−	0.480178i	$-0.159428\pi$
$467$	−0.0219352	−	0.0401712i	−0.00101504	−	0.00185890i	−0.878186	+	0.478319i	$0.841246\pi$
$468$	6.37876	+	1.38761i	0.294858	+	0.0641425i
$469$	−17.1115	+	7.81457i	−0.790137	+	0.360843i
$470$	14.1887	+	2.56415i	0.654477	+	0.118275i
$471$	13.6388	+	11.8181i	0.628443	+	0.544549i
$472$	0.948258	+	13.2584i	0.0436471	+	0.610267i
$473$	6.54265	+	3.57256i	0.300831	+	0.164266i
$474$	0.642056	+	1.40591i	0.0294906	+	0.0645754i
$475$	7.87140	+	2.94105i	0.361165	+	0.134944i
$476$	14.9512	+	4.39007i	0.685288	+	0.201219i
$477$	−2.79841	+	3.73824i	−0.128131	+	0.171162i
$478$	25.1941	−	9.39691i	1.15235	−	0.429805i
$479$	1.46571	−	10.1943i	0.0669702	−	0.465788i	−0.928548	−	0.371213i	$-0.878942\pi$
$479$	1.46571	−	10.1943i	0.0669702	−	0.465788i	0.995518	−	0.0945746i	$-0.0301491\pi$
$480$	−1.92338	+	1.14044i	−0.0877898	+	0.0520539i
$481$	−25.1197	+	21.7664i	−1.14536	+	0.992461i
$482$	−16.6623	−	16.6623i	−0.758949	−	0.758949i
$483$	17.0925	−	7.83169i	0.777734	−	0.356354i
$484$		−	10.5396i		−	0.479075i
$485$	−18.6720	−	11.0859i	−0.847850	−	0.503383i
$486$	0.841254	+	0.540641i	0.0381600	+	0.0245240i
$487$	6.24847	+	8.34698i	0.283145	+	0.378238i	0.919455	−	0.393196i	$-0.128631\pi$
$487$	6.24847	+	8.34698i	0.283145	+	0.378238i	−0.636309	+	0.771434i	$0.719540\pi$
$488$	4.00004	+	10.7245i	0.181073	+	0.485476i
$489$	−13.3697	+	1.92227i	−0.604598	+	0.0869281i
$490$	−18.7020	+	0.662549i	−0.844869	+	0.0299309i
$491$	−13.2166	+	8.49379i	−0.596456	+	0.383319i	−0.803757	−	0.594958i	$-0.797169\pi$
$491$	−13.2166	+	8.49379i	−0.596456	+	0.383319i	0.207300	+	0.978277i	$0.433532\pi$
$492$	−5.07127	−	1.89148i	−0.228630	−	0.0852747i
$493$	−4.72807	+	8.65881i	−0.212941	+	0.389973i
$494$	−7.18430	+	8.29113i	−0.323237	+	0.373035i
$495$	−0.580187	−	1.40184i	−0.0260775	−	0.0630079i
$496$	6.23951	−	1.83209i	0.280162	−	0.0822631i
$497$	16.3410	−	43.8120i	0.732996	−	1.96524i
$498$	2.53564	−	11.6562i	0.113625	−	0.522325i
$499$	−10.7082	+	36.4687i	−0.479363	+	1.63256i	0.264612	+	0.964355i	$0.414756\pi$
$499$	−10.7082	+	36.4687i	−0.479363	+	1.63256i	−0.743976	+	0.668207i	$0.767062\pi$
$500$	−10.6112	+	3.52158i	−0.474549	+	0.157490i
$501$	5.08846	−	11.1422i	0.227335	−	0.497795i
$502$	−19.7202	+	14.7623i	−0.880154	+	0.658875i
$503$	21.9121	−	4.76668i	0.977011	−	0.212536i	0.304410	−	0.952541i	$-0.401541\pi$
$503$	21.9121	−	4.76668i	0.977011	−	0.212536i	0.672601	+	0.740005i	$0.265177\pi$
$504$	−2.56727	−	2.96279i	−0.114355	−	0.131973i
$505$	−6.37510	+	12.7267i	−0.283688	+	0.566330i
$506$	−1.56301	−	2.85396i	−0.0694844	−	0.126874i
$507$	−20.9403	+	20.9403i	−0.929992	+	0.929992i
$508$	0.991568	−	13.8639i	0.0439937	−	0.615113i
$509$	−21.2294	+	33.0336i	−0.940976	+	1.46419i	−0.0560650	+	0.998427i	$0.517855\pi$
$509$	−21.2294	+	33.0336i	−0.940976	+	1.46419i	−0.884911	+	0.465760i	$0.845781\pi$
$510$	1.57555	+	8.74708i	0.0697664	+	0.387327i
$511$	20.7121	+	9.45891i	0.916250	+	0.418437i
$512$	0.800541	+	0.599278i	0.0353793	+	0.0264846i
$513$	−1.47501	+	0.805416i	−0.0651232	+	0.0355600i
$514$	−10.1907	−	15.8570i	−0.449492	−	0.699423i
$515$	12.1237	−	11.2810i	0.534232	−	0.497101i
$516$	3.09535	+	10.5418i	0.136265	+	0.464077i
$517$	4.36389	−	0.312112i	0.191924	−	0.0137267i
$518$	19.9102	−	1.42401i	0.874804	−	0.0625672i
$519$	−3.23320	−	11.0113i	−0.141922	−	0.483341i
$520$	0.525200	−	14.5875i	0.0230315	−	0.639703i
$521$	−0.833831	−	1.29747i	−0.0365308	−	0.0568430i	0.822508	−	0.568754i	$-0.192574\pi$
$521$	−0.833831	−	1.29747i	−0.0365308	−	0.0568430i	−0.859039	+	0.511911i	$0.828938\pi$
$522$	2.17845	−	1.18952i	0.0953480	−	0.0520639i
$523$	13.1672	+	9.85683i	0.575761	+	0.431009i	0.847069	−	0.531484i	$-0.178365\pi$
$523$	13.1672	+	9.85683i	0.575761	+	0.431009i	−0.271308	+	0.962493i	$0.587456\pi$
$524$	−5.23885	−	2.39250i	−0.228860	−	0.104517i
$525$	−9.38417	−	17.2094i	−0.409559	−	0.751079i
$526$	−0.195348	+	0.303967i	−0.00851758	+	0.0132536i
$527$	1.84395	−	25.7818i	0.0803236	−	1.12307i
$528$	−0.479767	+	0.479767i	−0.0208792	+	0.0208792i
$529$	19.3799	+	12.3863i	0.842602	+	0.538536i
$530$	9.33584	+	4.67655i	0.405523	+	0.203136i
$531$	−8.70457	−	10.0456i	−0.377746	−	0.435943i
$532$	6.43787	−	1.40047i	0.279117	−	0.0607182i
$533$	28.2853	−	21.1741i	1.22517	−	0.917152i
$534$	0.691710	−	1.51463i	0.0299332	−	0.0655446i
$535$	−10.4185	−	20.8285i	−0.450432	−	0.900496i
$536$	−1.35188	+	4.60407i	−0.0583921	+	0.198865i
$537$	0.997408	−	4.58501i	0.0430413	−	0.197858i
$538$	−8.38857	+	22.4906i	−0.361657	+	0.969640i
$539$	−5.44831	+	1.59977i	−0.234675	+	0.0689068i
$540$	0.856301	−	2.06561i	0.0368493	−	0.0888897i
$541$	8.56520	−	9.88477i	0.368247	−	0.424979i	−0.541139	−	0.840933i	$-0.682007\pi$
$541$	8.56520	−	9.88477i	0.368247	−	0.424979i	0.909386	+	0.415954i	$0.136552\pi$
$542$	5.37781	−	9.84872i	0.230997	−	0.423039i
$543$	13.8256	+	5.15666i	0.593311	+	0.221294i
$544$	3.34379	−	2.14892i	0.143364	−	0.0921342i
$545$	−13.8284	+	14.8442i	−0.592344	+	0.635856i
$546$	25.3312	−	3.64208i	1.08408	−	0.155867i
$547$	−16.2632	−	43.6033i	−0.695364	−	1.86434i	−0.442189	−	0.896922i	$-0.645798\pi$
$547$	−16.2632	−	43.6033i	−0.695364	−	1.86434i	−0.253174	−	0.967421i	$-0.581475\pi$
$548$	−1.91455	−	2.55754i	−0.0817857	−	0.109253i
$549$	−9.62916	−	6.18829i	−0.410963	−	0.264110i
$550$	−2.85498	+	1.83246i	−0.121737	+	0.0781364i
$551$			4.17129i			0.177703i
$552$	1.34539	−	4.60325i	0.0572636	−	0.195927i
$553$	4.28448	+	4.28448i	0.182195	+	0.182195i
$554$	−15.4134	+	13.3558i	−0.654852	+	0.567432i
$555$	5.80677	+	9.79322i	0.246484	+	0.415699i
$556$	1.70807	−	11.8799i	0.0724383	−	0.503819i
$557$	4.44614	−	1.65833i	0.188389	−	0.0702655i	−0.253499	−	0.967336i	$-0.581581\pi$
$557$	4.44614	−	1.65833i	0.188389	−	0.0702655i	0.441888	+	0.897070i	$0.354309\pi$
$558$	−3.89706	+	5.20586i	−0.164976	+	0.220382i
$559$	−68.8163	−	20.2063i	−2.91062	−	0.854635i
$560$	−5.50244	+	6.82409i	−0.232521	+	0.288370i
$561$	1.12031	+	2.45314i	0.0472996	+	0.103572i
$562$	1.60548	+	0.876658i	0.0677230	+	0.0369796i
$563$	0.114411	+	1.59967i	0.00482184	+	0.0674182i	0.999293	−	0.0375893i	$-0.0119679\pi$
$563$	0.114411	+	1.59967i	0.00482184	+	0.0674182i	−0.994471	+	0.105008i	$0.966513\pi$
$564$	4.87320	+	4.22266i	0.205199	+	0.177806i
$565$	−5.09746	−	7.34626i	−0.214452	−	0.309060i
$566$	−10.5337	+	4.81057i	−0.442763	+	0.202203i
$567$	3.83074	+	0.833327i	0.160876	+	0.0349964i
$568$	−5.71630	−	10.4686i	−0.239851	−	0.439254i
$569$	−2.06937	−	14.3928i	−0.0867526	−	0.603377i	−0.986101	−	0.166145i	$-0.946868\pi$
$569$	−2.06937	−	14.3928i	−0.0867526	−	0.603377i	0.899349	−	0.437232i	$-0.144041\pi$
$570$	2.35712	+	2.92673i	0.0987287	+	0.122587i
$571$	−32.3897	−	4.65693i	−1.35547	−	0.194886i	−0.574010	−	0.818848i	$-0.694613\pi$
$571$	−32.3897	−	4.65693i	−1.35547	−	0.194886i	−0.781455	+	0.623962i	$0.785522\pi$
$572$	−0.941486	−	4.32794i	−0.0393655	−	0.180960i
$573$	−15.1608	−	1.08432i	−0.633351	−	0.0452981i
$574$	−21.2189			−0.885660
$575$	11.4778	−	21.0537i	0.478658	−	0.878002i
$576$	−1.00000			−0.0416667
$577$	−43.2080	−	3.09030i	−1.79877	−	0.128651i	−0.868540	−	0.495619i	$-0.834941\pi$
$577$	−43.2080	−	3.09030i	−1.79877	−	0.128651i	−0.930234	+	0.366968i	$0.880396\pi$
$578$	0.255342	+	1.17379i	0.0106208	+	0.0488231i
$579$	−19.8442	−	2.85316i	−0.824695	−	0.118573i
$580$	−3.48123	−	4.32249i	−0.144550	−	0.179482i
$581$	−6.65532	−	46.2888i	−0.276109	−	1.92038i
$582$	−4.65409	−	8.52333i	−0.192918	−	0.353304i
$583$	3.09591	+	0.673475i	0.128220	+	0.0278925i
$584$	5.28325	−	2.41278i	0.218623	−	0.0998416i
$585$	8.32151	+	11.9926i	0.344052	+	0.495834i
$586$	−17.3331	−	15.0192i	−0.716024	−	0.620438i
$587$	1.62059	+	22.6588i	0.0668888	+	0.935228i	0.914494	+	0.404600i	$0.132589\pi$
$587$	1.62059	+	22.6588i	0.0668888	+	0.935228i	−0.847605	+	0.530628i	$0.821956\pi$
$588$	−7.34531	−	4.01084i	−0.302916	−	0.165404i
$589$	−4.53994	−	9.94108i	−0.187065	−	0.409615i
$590$	−18.6565	+	23.1377i	−0.768077	+	0.952564i
$591$	−1.01526	−	0.298107i	−0.0417622	−	0.0122625i
$592$	3.05133	−	4.07609i	0.125409	−	0.167526i
$593$	27.3373	−	10.1963i	1.12261	−	0.418711i	0.281491	−	0.959564i	$-0.409171\pi$
$593$	27.3373	−	10.1963i	1.12261	−	0.418711i	0.841117	+	0.540853i	$0.181898\pi$
$594$	0.0965596	−	0.671587i	0.00396189	−	0.0275555i
$595$	17.7709	+	29.9709i	0.728535	+	1.22869i
$596$	−5.77147	+	5.00101i	−0.236409	+	0.204849i
$597$	0.789235	+	0.789235i	0.0323012	+	0.0323012i
$598$	20.5312	+	23.6346i	0.839584	+	0.966489i
$599$		−	24.6520i		−	1.00725i	−0.863921	−	0.503627i	$-0.831998\pi$
$599$		−	24.6520i		−	1.00725i	0.863921	−	0.503627i	$-0.168002\pi$
$600$	−4.88512	−	1.06564i	−0.199434	−	0.0435046i
$601$	11.9445	+	7.67624i	0.487225	+	0.313120i	0.761088	−	0.648648i	$-0.224665\pi$
$601$	11.9445	+	7.67624i	0.487225	+	0.313120i	−0.273864	+	0.961769i	$0.588302\pi$
$602$	25.8121	+	34.4810i	1.05202	+	1.40534i
$603$	−1.67688	−	4.49589i	−0.0682879	−	0.183087i
$604$	23.4478	−	3.37129i	0.954078	−	0.137176i
$605$	16.0642	−	17.2442i	0.653102	−	0.701077i
$606$	−5.35516	+	3.44155i	−0.217539	+	0.139804i
$607$	0.639270	+	0.238435i	0.0259472	+	0.00967780i	0.362404	−	0.932021i	$-0.381956\pi$
$607$	0.639270	+	0.238435i	0.0259472	+	0.00967780i	−0.336457	+	0.941699i	$0.609229\pi$
$608$	0.805416	−	1.47501i	0.0326639	−	0.0598195i
$609$	6.37211	−	7.35380i	0.258211	−	0.297991i
$610$	−9.80140	+	23.6434i	−0.396847	+	0.957294i
$611$	−40.3882	+	11.8591i	−1.63393	+	0.479766i
$612$	−1.38904	+	3.72416i	−0.0561485	+	0.150540i
$613$	9.62258	−	44.2343i	0.388652	−	1.78661i	−0.201685	−	0.979450i	$-0.564642\pi$
$613$	9.62258	−	44.2343i	0.388652	−	1.78661i	0.590338	−	0.807156i	$-0.298995\pi$
$614$	−2.07259	+	7.05860i	−0.0836430	+	0.284862i
$615$	−5.41430	−	10.8242i	−0.218325	−	0.436473i
$616$	−1.10497	+	2.41955i	−0.0445205	+	0.0974863i
$617$	−9.71374	+	7.27161i	−0.391060	+	0.292744i	−0.776657	−	0.629923i	$-0.783086\pi$
$617$	−9.71374	+	7.27161i	−0.391060	+	0.292744i	0.385597	+	0.922667i	$0.373995\pi$
$618$	7.23675	−	1.57426i	0.291105	−	0.0633260i
$619$	−12.0048	−	13.8542i	−0.482512	−	0.556848i	0.461337	−	0.887225i	$-0.347370\pi$
$619$	−12.0048	−	13.8542i	−0.482512	−	0.556848i	−0.943849	+	0.330377i	$0.892824\pi$
$620$	13.0010	+	6.51254i	0.522134	+	0.261550i
$621$	1.68159	+	4.49135i	0.0674797	+	0.180232i
$622$	12.0638	−	12.0638i	0.483715	−	0.483715i
$623$	0.465686	−	6.51114i	0.0186573	−	0.260863i
$624$	3.52927	−	5.49166i	0.141284	−	0.219842i
$625$	−22.7288	−	10.4116i	−0.909153	−	0.416463i
$626$	−16.5622	−	7.56372i	−0.661960	−	0.302307i
$627$	0.912826	+	0.683333i	0.0364548	+	0.0272897i
$628$	15.8392	−	8.64887i	0.632054	−	0.345128i
$629$	−10.9416	−	17.0255i	−0.436270	−	0.678850i
$630$	0.315407	−	8.76046i	0.0125661	−	0.349025i
$631$	9.36759	+	31.9031i	0.372918	+	1.27004i	0.905747	+	0.423819i	$0.139311\pi$
$631$	9.36759	+	31.9031i	0.372918	+	1.27004i	−0.532829	+	0.846223i	$0.678871\pi$
$632$	1.54164	−	0.110260i	0.0613231	−	0.00438591i
$633$	1.91523	−	0.136980i	0.0761236	−	0.00544447i
$634$	7.00574	+	23.8594i	0.278234	+	0.947577i
$635$	22.7533	−	21.1718i	0.902937	−	0.840179i
$636$	2.52460	+	3.92836i	0.100107	+	0.155769i
$637$	47.9498	−	26.1826i	1.89984	−	1.03739i
$638$	−1.34816	−	1.00922i	−0.0533740	−	0.0399553i
$639$	10.8497	+	4.95491i	0.429209	+	0.196013i
$640$	0.396387	+	2.20065i	0.0156686	+	0.0869885i
$641$	14.6239	−	22.7552i	0.577608	−	0.898776i	−0.422363	−	0.906427i	$-0.638799\pi$
$641$	14.6239	−	22.7552i	0.577608	−	0.898776i	0.999971	+	0.00765135i	$0.00243552\pi$
$642$	0.743006	−	10.3886i	0.0293241	−	0.410004i
$643$	18.8269	−	18.8269i	0.742460	−	0.742460i	−0.230591	−	0.973051i	$-0.574066\pi$
$643$	18.8269	−	18.8269i	0.742460	−	0.742460i	0.973051	+	0.230591i	$0.0740660\pi$
$644$	−1.36470	−	18.7517i	−0.0537768	−	0.738919i
$645$	−11.0031	+	21.9656i	−0.433246	+	0.864893i
$646$	−4.37441	−	5.04834i	−0.172109	−	0.198624i
$647$	−3.85047	+	0.837618i	−0.151377	+	0.0329301i	−0.287615	−	0.957746i	$-0.592862\pi$
$647$	−3.85047	+	0.837618i	−0.151377	+	0.0329301i	0.136238	+	0.990676i	$0.456499\pi$
$648$	0.800541	−	0.599278i	0.0314482	−	0.0235419i
$649$	−3.74650	+	8.20369i	−0.147063	+	0.322023i
$650$	23.0931	−	23.0665i	0.905785	−	0.904742i
$651$	−7.18239	+	24.4610i	−0.281500	+	0.958701i
$652$	−2.87116	+	13.1985i	−0.112443	+	0.516893i
$653$	0.710338	−	1.90449i	0.0277977	−	0.0745284i	−0.922310	−	0.386452i	$-0.873701\pi$
$653$	0.710338	−	1.90449i	0.0277977	−	0.0745284i	0.950107	+	0.311923i	$0.100973\pi$
$654$	−8.70526	+	2.55609i	−0.340402	+	0.0999512i
$655$	−4.92485	−	11.8993i	−0.192430	−	0.464946i
$656$	−3.54445	+	4.09052i	−0.138388	+	0.159708i
$657$	−2.78354	+	5.09767i	−0.108596	+	0.198879i
$658$	23.6851	+	8.83410i	0.923343	+	0.344389i
$659$	3.28397	−	2.11048i	0.127925	−	0.0822127i	−0.475113	−	0.879925i	$-0.657593\pi$
$659$	3.28397	−	2.11048i	0.127925	−	0.0822127i	0.603039	+	0.797712i	$0.293956\pi$
$660$	−1.51620	+	0.0537141i	−0.0590182	+	0.00209082i
$661$	13.4896	−	1.93951i	0.524684	−	0.0754381i	0.125117	−	0.992142i	$-0.460070\pi$
$661$	13.4896	−	1.93951i	0.524684	−	0.0754381i	0.399567	+	0.916704i	$0.369160\pi$
$662$	−0.619682	−	1.66143i	−0.0240846	−	0.0645733i
$663$	−15.5495	−	20.7717i	−0.603892	−	0.806705i
$664$	−10.0351	−	6.44918i	−0.389438	−	0.250277i
$665$	12.6677	+	7.52104i	0.491233	+	0.291653i
$666$			5.09167i			0.197298i
$667$	11.7845	+	1.67932i	0.456296	+	0.0650235i
$668$	−8.66142	−	8.66142i	−0.335120	−	0.335120i
$669$	5.36490	−	4.64872i	0.207419	−	0.179730i
$670$	−9.22921	+	5.47235i	−0.356556	+	0.211415i
$671$	−1.10524	+	7.68712i	−0.0426674	+	0.296758i
$672$	−3.67316	+	1.37002i	−0.141695	+	0.0528495i
$673$	14.0067	−	18.7107i	0.539918	−	0.721245i	−0.444756	−	0.895652i	$-0.646710\pi$
$673$	14.0067	−	18.7107i	0.539918	−	0.721245i	0.984674	+	0.174406i	$0.0558006\pi$
$674$	10.1528	+	2.98112i	0.391069	+	0.114828i
$675$	4.54936	−	2.07445i	0.175105	−	0.0798458i
$676$	12.3021	+	26.9379i	0.473159	+	1.03607i
$677$	23.2692	+	12.7060i	0.894309	+	0.488330i	0.859542	−	0.511066i	$-0.170749\pi$
$677$	23.2692	+	12.7060i	0.894309	+	0.488330i	0.0347672	+	0.999395i	$0.488931\pi$
$678$	−0.285271	−	3.98860i	−0.0109558	−	0.153181i
$679$	−28.7723	−	24.9313i	−1.10418	−	0.956777i
$680$	8.74617	+	1.58058i	0.335400	+	0.0606127i
$681$	15.1271	−	6.90832i	0.579672	−	0.264727i
$682$	4.31136	+	0.937878i	0.165090	+	0.0359132i
$683$	8.72266	+	15.9744i	0.333763	+	0.611242i	0.989631	−	0.143634i	$-0.0458789\pi$
$683$	8.72266	+	15.9744i	0.333763	+	0.611242i	−0.655868	+	0.754876i	$0.727697\pi$
$684$	0.239171	+	1.66347i	0.00914495	+	0.0636045i
$685$	0.765674	−	7.10257i	0.0292549	−	0.271375i
$686$	−5.31238	−	0.763806i	−0.202828	−	0.0291622i
$687$	−3.98216	−	18.3057i	−0.151929	−	0.698407i
$688$	10.9588	+	0.783792i	0.417802	+	0.0298818i
$689$	−30.4832			−1.16132
$690$	9.21736	−	5.48090i	0.350899	−	0.208654i
$691$	−9.47636			−0.360498			−0.180249	−	0.983621i	$-0.557690\pi$
$691$	−9.47636			−0.360498			−0.180249	+	0.983621i	$0.557690\pi$
$692$	−11.4469	−	0.818698i	−0.435145	−	0.0311222i
$693$	−0.565406	−	2.59913i	−0.0214780	−	0.0987328i
$694$	2.70697	+	0.389203i	0.102755	+	0.0147740i
$695$	20.9016	−	16.8336i	0.792841	−	0.638535i
$696$	−0.353233	−	2.45679i	−0.0133893	−	0.0931243i
$697$	10.3103	+	18.8820i	0.390532	+	0.715206i
$698$	5.01624	+	1.09122i	0.189868	+	0.0413032i
$699$	−18.0552	+	8.24553i	−0.682910	+	0.311874i
$700$	−19.4038	+	2.77843i	−0.733393	+	0.105015i
$701$	−33.0736	−	28.6584i	−1.24917	−	1.08241i	−0.993283	−	0.115709i	$-0.963086\pi$
$701$	−33.0736	−	28.6584i	−1.24917	−	1.08241i	−0.255890	−	0.966706i	$-0.582368\pi$
$702$	0.465698	+	6.51131i	0.0175767	+	0.245754i
$703$	−7.51027	−	4.10092i	−0.283255	−	0.154669i
$704$	0.281856	+	0.617179i	0.0106228	+	0.0232608i
$705$	1.53714	+	14.3364i	0.0578922	+	0.539939i
$706$	−17.2907	−	5.07699i	−0.650742	−	0.191075i
$707$	−14.9554	+	19.9780i	−0.562454	+	0.751351i
$708$	−12.4542	+	4.64517i	−0.468056	+	0.174576i
$709$	−3.89851	+	27.1147i	−0.146412	+	1.01831i	0.775620	+	0.631200i	$0.217437\pi$
$709$	−3.89851	+	27.1147i	−0.146412	+	1.01831i	−0.922032	+	0.387114i	$0.873472\pi$
$710$	6.60335	−	25.8406i	0.247819	−	0.969780i
$711$	−1.16807	+	1.01214i	−0.0438060	+	0.0379581i
$712$	−1.17741	−	1.17741i	−0.0441252	−	0.0441252i
$713$	−29.9127	+	8.82377i	−1.12024	+	0.330453i
$714$			15.5824i			0.583157i
$715$	5.05612	−	8.51605i	0.189088	−	0.318482i
$716$	−3.94736	−	2.53682i	−0.147520	−	0.0948053i
$717$	16.1143	+	21.5261i	0.601799	+	0.803909i
$718$	2.52330	+	6.76523i	0.0941687	+	0.252476i
$719$	−0.877403	+	0.126151i	−0.0327216	+	0.00470466i	−0.158656	−	0.987334i	$-0.550716\pi$
$719$	−0.877403	+	0.126151i	−0.0327216	+	0.00470466i	0.125935	+	0.992039i	$0.459807\pi$
$720$	−1.63613	−	1.52417i	−0.0609749	−	0.0568024i
$721$	24.4250	−	15.6970i	0.909633	−	0.584586i
$722$	15.1558	+	5.65281i	0.564039	+	0.210376i
$723$	11.2931	−	20.6817i	0.419994	−	0.769162i
$724$	9.66307	−	11.1518i	0.359125	−	0.414453i
$725$	0.892468	−	12.3781i	0.0331454	−	0.459712i
$726$	10.1127	−	2.96936i	0.375318	−	0.110203i
$727$	9.18577	−	24.6280i	0.340681	−	0.913402i	−0.647766	−	0.761839i	$-0.724297\pi$
$727$	9.18577	−	24.6280i	0.340681	−	0.913402i	0.988448	−	0.151563i	$-0.0484306\pi$
$728$	5.43991	−	25.0069i	0.201617	−	0.926817i
$729$	−0.281733	+	0.959493i	−0.0104345	+	0.0355368i
$730$	12.3216	+	4.10495i	0.456041	+	0.151931i
$731$	18.1412	−	39.7237i	0.670977	−	1.46924i
$732$	−9.16316	+	6.85946i	−0.338680	+	0.253533i
$733$	8.98213	−	1.95394i	0.331763	−	0.0721705i	−0.0435987	−	0.999049i	$-0.513882\pi$
$733$	8.98213	−	1.95394i	0.331763	−	0.0721705i	0.375361	+	0.926879i	$0.377519\pi$
$734$	9.27400	+	10.7028i	0.342310	+	0.395046i
$735$	−5.90466	−	17.7577i	−0.217797	−	0.655004i
$736$	−3.84285	−	2.86923i	−0.141649	−	0.105761i
$737$	−2.30213	+	2.30213i	−0.0848001	+	0.0848001i
$738$	0.386125	−	5.39874i	0.0142135	−	0.198730i
$739$	−7.41168	+	11.5328i	−0.272643	+	0.424241i	−0.950393	−	0.311051i	$-0.899319\pi$
$739$	−7.41168	+	11.5328i	−0.272643	+	0.424241i	0.677750	+	0.735293i	$0.262955\pi$
$740$	11.2050	−	2.01827i	0.411904	−	0.0741932i
$741$	−9.97933	−	4.55741i	−0.366600	−	0.167421i
$742$	14.6552	+	10.9707i	0.538008	+	0.402748i
$743$	−36.0453	+	19.6822i	−1.32237	+	0.722070i	−0.976358	−	0.216159i	$-0.930647\pi$
$743$	−36.0453	+	19.6822i	−1.32237	+	0.722070i	−0.346014	+	0.938229i	$0.612465\pi$
$744$	3.51575	+	5.47061i	0.128894	+	0.200562i
$745$	−17.0652	−	0.614407i	−0.625222	−	0.0225101i
$746$	−3.32169	−	11.3126i	−0.121616	−	0.414184i
$747$	11.8984	−	0.850988i	0.435339	−	0.0311360i
$748$	2.68998	−	0.192391i	0.0983553	−	0.00703451i
$749$	−11.5033	−	39.1768i	−0.420323	−	1.43149i
$750$	−6.36846	−	9.18927i	−0.232543	−	0.335545i
$751$	−1.84076	−	2.86428i	−0.0671704	−	0.104519i	0.806044	−	0.591856i	$-0.201605\pi$
$751$	−1.84076	−	2.86428i	−0.0671704	−	0.104519i	−0.873214	+	0.487337i	$0.837968\pi$
$752$	5.65943	−	3.09028i	0.206378	−	0.112691i
$753$	−19.7202	−	14.7623i	−0.718643	−	0.537969i
$754$	14.7385	+	6.73085i	0.536744	+	0.245123i
$755$	43.5020	+	30.2226i	1.58320	+	1.09991i
$756$	2.11949	−	3.29799i	0.0770852	−	0.119947i
$757$	−1.49149	+	20.8537i	−0.0542090	+	0.757941i	0.895550	+	0.444960i	$0.146782\pi$
$757$	−1.49149	+	20.8537i	−0.0542090	+	0.757941i	−0.949759	+	0.312981i	$0.898672\pi$
$758$	−9.13919	+	9.13919i	−0.331950	+	0.331950i
$759$	2.29800	−	2.30375i	0.0834122	−	0.0836210i
$760$	3.56592	−	1.18571i	0.129350	−	0.0430103i
$761$	0.996455	+	1.14997i	0.0361215	+	0.0416864i	0.773523	−	0.633768i	$-0.218493\pi$
$761$	0.996455	+	1.14997i	0.0361215	+	0.0416864i	−0.737401	+	0.675455i	$0.763947\pi$
$762$	13.5817	−	2.95452i	0.492013	−	0.107031i
$763$	−28.4739	+	21.3153i	−1.03082	+	0.771665i
$764$	−6.31411	+	13.8260i	−0.228436	+	0.500206i
$765$	−7.94888	+	3.97606i	−0.287392	+	0.143755i
$766$	9.84933	−	33.5437i	0.355871	−	1.21198i
$767$	18.4445	−	84.7881i	0.665993	−	3.06152i
$768$	−0.349464	+	0.936950i	−0.0126102	+	0.0338093i
$769$	27.3934	−	8.04344i	0.987832	−	0.290054i	0.252378	−	0.967629i	$-0.418787\pi$
$769$	27.3934	−	8.04344i	0.987832	−	0.290054i	0.735454	+	0.677575i	$0.236969\pi$
$770$	−5.49567	+	2.27453i	−0.198050	+	0.0819682i
$771$	12.3436	−	14.2453i	0.444545	−	0.513033i
$772$	−9.60809	+	17.5959i	−0.345803	+	0.633291i
$773$	20.1541	+	7.51708i	0.724892	+	0.270371i	0.684704	−	0.728822i	$-0.259932\pi$
$773$	20.1541	+	7.51708i	0.724892	+	0.270371i	0.0401879	+	0.999192i	$0.487204\pi$
$774$	−9.24272	+	5.93994i	−0.332223	+	0.213507i
$775$	11.3452	+	30.4711i	0.407530	+	1.09455i
$776$	−9.61237	+	1.38205i	−0.345064	+	0.0496127i
$777$	6.97568	+	18.7025i	0.250251	+	0.670949i
$778$	−22.9009	−	30.5920i	−0.821037	−	1.09678i
$779$	7.65220	+	4.91777i	0.274168	+	0.176197i
$780$	14.1445	−	3.60584i	0.506456	−	0.129110i
$781$		−	8.09280i		−	0.289583i
$782$	−16.0233	+	10.3259i	−0.572993	+	0.369253i
$783$	1.75508	+	1.75508i	0.0627213	+	0.0627213i
$784$	−6.32488	+	5.48054i	−0.225889	+	0.195734i
$785$	39.0973	+	9.99099i	1.39544	+	0.356594i
$786$	0.819636	−	5.70069i	0.0292354	−	0.203337i
$787$	−31.1007	+	11.5999i	−1.10862	+	0.413494i	−0.836056	−	0.548644i	$-0.815144\pi$
$787$	−31.1007	+	11.5999i	−1.10862	+	0.413494i	−0.272563	+	0.962138i	$0.587871\pi$
$788$	−0.634109	+	0.847070i	−0.0225892	+	0.0301756i
$789$	−0.346691	−	0.101798i	−0.0123425	−	0.00362409i
$790$	2.69037	+	2.16932i	0.0957191	+	0.0771808i
$791$	−6.51230	−	14.2599i	−0.231551	−	0.507025i
$792$	−0.595499	−	0.325167i	−0.0211601	−	0.0115543i
$793$	−5.33048	−	74.5298i	−0.189291	−	2.64663i
$794$	−12.2375	−	10.6038i	−0.434292	−	0.376316i
$795$	−1.85691	+	10.2752i	−0.0658577	+	0.364424i
$796$	1.01528	−	0.463664i	0.0359858	−	0.0164341i
$797$	2.91123	+	0.633300i	0.103121	+	0.0224326i	0.263830	−	0.964569i	$-0.415014\pi$
$797$	2.91123	+	0.633300i	0.103121	+	0.0224326i	−0.160709	+	0.987002i	$0.551378\pi$
$798$	3.15750	+	5.78253i	0.111774	+	0.204699i
$799$	−3.64753	−	25.3691i	−0.129040	−	0.897494i
$800$	−2.70563	+	4.20471i	−0.0956583	+	0.148659i
$801$	1.64816	+	0.236969i	0.0582348	+	0.00837290i
$802$	7.53974	+	34.6596i	0.266238	+	1.22387i
$803$	3.93073	+	0.281131i	0.138712	+	0.00992091i
$804$	−4.79844			−0.169228
$805$	26.3479	−	32.7601i	0.928640	−	1.15464i
$806$	−42.4508			−1.49526
$807$	−23.9429	−	1.71243i	−0.842831	−	0.0602805i
$808$	1.35312	+	6.22022i	0.0476028	+	0.218826i
$809$	−38.4765	−	5.53208i	−1.35276	−	0.194498i	−0.572475	−	0.819922i	$-0.694017\pi$
$809$	−38.4765	−	5.53208i	−1.35276	−	0.194498i	−0.780285	+	0.625424i	$0.784926\pi$
$810$	2.22319	+	0.239665i	0.0781148	+	0.00842097i
$811$	5.87520	+	40.8629i	0.206306	+	1.43489i	0.785075	+	0.619400i	$0.212624\pi$
$811$	5.87520	+	40.8629i	0.206306	+	1.43489i	−0.578769	+	0.815492i	$0.696467\pi$
$812$	−4.66332	−	8.54023i	−0.163650	−	0.299703i
$813$	10.9649	+	2.38526i	0.384555	+	0.0836549i
$814$	3.14247	−	1.43512i	0.110144	−	0.0503009i
$815$	−24.8143	+	17.2183i	−0.869207	+	0.603130i
$816$	3.00393	+	2.60292i	0.105158	+	0.0911204i
$817$	−1.31723	−	18.4172i	−0.0460839	−	0.644337i
$818$	−21.7481	−	11.8754i	−0.760405	−	0.415212i
$819$	10.6312	+	23.2791i	0.371484	+	0.813436i
$820$	−12.0338	+	1.29026i	−0.420239	+	0.0450579i
$821$	−9.42076	−	2.76619i	−0.328787	−	0.0965405i	0.113173	−	0.993575i	$-0.463899\pi$
$821$	−9.42076	−	2.76619i	−0.328787	−	0.0965405i	−0.441960	+	0.897035i	$0.645717\pi$
$822$	1.91455	−	2.55754i	0.0667777	−	0.0892046i
$823$	−3.20047	+	1.19371i	−0.111561	+	0.0416103i	−0.404625	−	0.914483i	$-0.632598\pi$
$823$	−3.20047	+	1.19371i	−0.111561	+	0.0416103i	0.293064	+	0.956093i	$0.405325\pi$
$824$	1.05398	−	7.33062i	0.0367173	−	0.255374i
$825$	−2.56257	−	2.22307i	−0.0892173	−	0.0773973i
$826$	−39.3822	+	34.1248i	−1.37028	+	1.18736i
$827$	36.6597	+	36.6597i	1.27478	+	1.27478i	0.943549	+	0.331233i	$0.107465\pi$
$827$	36.6597	+	36.6597i	1.27478	+	1.27478i	0.331233	+	0.943549i	$0.392535\pi$
$828$	4.79583	−	0.00599354i	0.166667	−	0.000208290i
$829$		−	14.5303i		−	0.504658i	−0.967642	−	0.252329i	$-0.918803\pi$
$829$		−	14.5303i		−	0.504658i	0.967642	−	0.252329i	$-0.0811965\pi$
$830$	−6.58909	−	25.8469i	−0.228711	−	0.897158i
$831$	−17.1572	−	11.0263i	−0.595177	−	0.382497i
$832$	−3.91205	−	5.22589i	−0.135626	−	0.181175i
$833$	11.6249	+	31.1675i	0.402778	+	1.07989i
$834$	11.8799	−	1.70807i	0.411367	−	0.0591456i
$835$	−0.969722	−	27.3726i	−0.0335586	−	0.947269i
$836$	0.959248	−	0.616472i	0.0331763	−	0.0213211i
$837$	−6.09292	−	2.27254i	−0.210602	−	0.0785505i
$838$	5.15425	−	9.43930i	0.178051	−	0.326075i
$839$	4.71139	−	5.43724i	0.162655	−	0.187714i	−0.668571	−	0.743648i	$-0.733094\pi$
$839$	4.71139	−	5.43724i	0.162655	−	0.187714i	0.831226	+	0.555934i	$0.187639\pi$
$840$	−8.09788	−	3.35699i	−0.279404	−	0.115827i
$841$	−21.9143	+	6.43461i	−0.755664	+	0.221883i
$842$	−4.42982	+	11.8768i	−0.152662	+	0.409301i
$843$	−0.388831	+	1.78743i	−0.0133921	+	0.0615623i
$844$	0.540962	−	1.84235i	0.0186207	−	0.0634162i
$845$	−20.9301	+	62.8244i	−0.720016	+	2.16122i
$846$	−2.67867	+	5.86546i	−0.0920945	+	0.201659i
$847$	33.0775	−	24.7615i	1.13656	−	0.850816i
$848$	4.56293	−	0.992605i	0.156692	−	0.0340862i
$849$	−7.58338	−	8.75169i	−0.260261	−	0.300357i
$850$	11.9008	+	15.9167i	0.408193	+	0.545938i
$851$	−14.6092	+	19.5665i	−0.500797	+	0.670732i
$852$	8.43410	−	8.43410i	0.288948	−	0.288948i
$853$	0.769413	−	10.7578i	0.0263442	−	0.368340i	−0.967130	−	0.254283i	$-0.918161\pi$
$853$	0.769413	−	10.7578i	0.0263442	−	0.368340i	0.993474	−	0.114057i	$-0.0363848\pi$
$854$	−24.2602	+	37.7495i	−0.830165	+	1.29176i
$855$	−2.14410	+	3.08619i	−0.0733266	+	0.105546i
$856$	−9.47392	−	4.32660i	−0.323812	−	0.147880i
$857$	3.69225	+	2.76398i	0.126125	+	0.0944159i	0.660478	−	0.750846i	$-0.270354\pi$
$857$	3.69225	+	2.76398i	0.126125	+	0.0944159i	−0.534353	+	0.845261i	$0.679445\pi$
$858$	3.88738	−	2.12267i	0.132713	−	0.0724668i
$859$	28.6372	+	44.5603i	0.977088	+	1.52038i	0.848849	+	0.528636i	$0.177296\pi$
$859$	28.6372	+	44.5603i	0.977088	+	1.52038i	0.128240	+	0.991743i	$0.459067\pi$
$860$	16.7354	+	17.9855i	0.570674	+	0.613301i
$861$	−5.97806	−	20.3594i	−0.203732	−	0.693847i
$862$	12.3260	−	0.881572i	0.419825	−	0.0300265i
$863$	−17.7862	+	1.27210i	−0.605450	+	0.0433026i	−0.370699	−	0.928753i	$-0.620882\pi$
$863$	−17.7862	+	1.27210i	−0.605450	+	0.0433026i	−0.234751	+	0.972056i	$0.575427\pi$
$864$	−0.281733	−	0.959493i	−0.00958474	−	0.0326426i
$865$	−17.4807	−	18.7865i	−0.594363	−	0.638759i
$866$	0.492297	+	0.766029i	0.0167289	+	0.0260307i
$867$	−1.05430	+	0.575692i	−0.0358060	+	0.0195515i
$868$	20.4087	+	15.2778i	0.692717	+	0.518561i
$869$	0.953897	+	0.435630i	0.0323587	+	0.0147777i
$870$	3.16663	−	4.55801i	0.107359	−	0.154531i
$871$	16.9350	−	26.3514i	0.573821	−	0.892882i
$872$	−0.647244	+	9.04965i	−0.0219184	+	0.306460i
$873$	6.86687	−	6.86687i	0.232408	−	0.232408i
$874$	−3.85380	+	7.07872i	−0.130357	+	0.239441i
$875$	−35.9818	−	25.0287i	−1.21641	−	0.846125i
$876$	3.80351	+	4.38949i	0.128509	+	0.148307i
$877$	−10.9435	+	2.38062i	−0.369537	+	0.0803879i	−0.393499	−	0.919325i	$-0.628736\pi$
$877$	−10.9435	+	2.38062i	−0.369537	+	0.0803879i	0.0239619	+	0.999713i	$0.492372\pi$
$878$	19.5615	−	14.6435i	0.660167	−	0.494195i
$879$	9.52753	−	20.8624i	0.321356	−	0.703671i
$880$	−0.479532	+	1.43938i	−0.0161650	+	0.0485214i
$881$	−9.92788	+	33.8113i	−0.334479	+	1.13913i	0.604915	+	0.796290i	$0.293207\pi$
$881$	−9.92788	+	33.8113i	−0.334479	+	1.13913i	−0.939394	+	0.342840i	$0.888611\pi$
$882$	1.77896	−	8.17776i	0.0599008	−	0.275360i
$883$	−9.39737	+	25.1953i	−0.316247	+	0.847890i	0.677428	+	0.735589i	$0.263095\pi$
$883$	−9.39737	+	25.1953i	−0.316247	+	0.847890i	−0.993674	+	0.112301i	$0.964178\pi$
$884$	−24.8960	+	7.31013i	−0.837344	+	0.245866i
$885$	−27.4566	−	11.3822i	−0.922944	−	0.382607i
$886$	12.0840	−	13.9457i	0.405969	−	0.468514i
$887$	−5.90910	+	10.8217i	−0.198408	+	0.363358i	−0.957874	−	0.287190i	$-0.907279\pi$
$887$	−5.90910	+	10.8217i	−0.198408	+	0.363358i	0.759465	+	0.650548i	$0.225461\pi$
$888$	4.77064	+	1.77936i	0.160092	+	0.0597113i
$889$	45.8400	−	29.4596i	1.53742	−	0.988042i
$890$	−0.131821	−	3.72096i	−0.00441866	−	0.124727i
$891$	0.671587	−	0.0965596i	0.0224990	−	0.00323487i
$892$	−2.48077	−	6.65120i	−0.0830624	−	0.222699i
$893$	−6.49417	−	8.67520i	−0.217319	−	0.290304i
$894$	−6.42444	−	4.12874i	−0.214865	−	0.138086i
$895$	−2.59185	−	10.1670i	−0.0866361	−	0.339845i
$896$			3.92033i			0.130969i
$897$	−16.8929	+	26.3582i	−0.564037	+	0.880075i
$898$	20.3818	+	20.3818i	0.680150	+	0.680150i
$899$	−12.1983	+	10.5699i	−0.406835	+	0.352524i
$900$	−0.353823	−	4.98747i	−0.0117941	−	0.166249i
$901$	2.64147	−	18.3718i	0.0880001	−	0.612054i
$902$	−3.44082	+	1.28336i	−0.114567	+	0.0427312i
$903$	−25.8121	+	34.4810i	−0.858974	+	1.14746i
$904$	−3.83681	−	1.12659i	−0.127611	−	0.0374698i
$905$	32.8072	−	3.51758i	1.09055	−	0.116928i
$906$	9.84074	+	21.5482i	0.326937	+	0.715891i
$907$	−39.7685	−	21.7152i	−1.32049	−	0.721042i	−0.344486	−	0.938792i	$-0.611947\pi$
$907$	−39.7685	−	21.7152i	−1.32049	−	0.721042i	−0.976005	+	0.217749i	$0.930129\pi$
$908$	−1.18637	−	16.5876i	−0.0393709	−	0.550477i
$909$	−4.81087	−	4.16864i	−0.159566	−	0.138265i
$910$	47.0151	−	32.6231i	1.55853	−	1.08144i
$911$	−38.4689	+	17.5682i	−1.27453	+	0.582059i	−0.933697	−	0.358064i	$-0.883437\pi$
$911$	−38.4689	+	17.5682i	−1.27453	+	0.582059i	−0.340835	+	0.940123i	$0.610710\pi$
$912$	1.64217	+	0.357233i	0.0543778	+	0.0118292i
$913$	−3.87884	−	7.10357i	−0.128371	−	0.235094i
$914$	2.41846	+	16.8208i	0.0799956	+	0.556381i
$915$	−25.4471	−	2.74326i	−0.841254	−	0.0906893i
$916$	−18.5432	−	2.66610i	−0.612683	−	0.0880905i
$917$	−4.79939	−	22.0624i	−0.158490	−	0.728566i
$918$	−3.96464	−	0.283557i	−0.130853	−	0.00935876i
$919$	6.41720			0.211684			0.105842	−	0.994383i	$-0.466246\pi$
$919$	6.41720			0.211684			0.105842	+	0.994383i	$0.466246\pi$
$920$	−1.91419	−	10.5516i	−0.0631091	−	0.347875i
$921$	−7.35659			−0.242408
$922$	16.2550	+	1.16258i	0.535329	+	0.0382875i
$923$	16.5509	+	76.0835i	0.544781	+	2.50432i
$924$	−2.63284	−	0.378546i	−0.0866142	−	0.0124532i
$925$	21.4090	+	13.7762i	0.703924	+	0.452958i
$926$	4.37979	+	30.4621i	0.143929	+	1.00105i
$927$	3.54932	+	6.50009i	0.116575	+	0.213491i
$928$	−2.42533	−	0.527598i	−0.0796154	−	0.0173193i
$929$	−4.96255	+	2.26632i	−0.162816	+	0.0743555i	−0.495156	−	0.868804i	$-0.664889\pi$
$929$	−4.96255	+	2.26632i	−0.162816	+	0.0743555i	0.332340	+	0.943160i	$0.392162\pi$
$930$	−2.58592	+	14.3092i	−0.0847957	+	0.469217i
$931$	10.6295	+	9.21049i	0.348367	+	0.301861i
$932$	1.41600	+	19.7983i	0.0463827	+	0.648515i
$933$	14.9739	+	8.17638i	0.490224	+	0.267683i
$934$	−0.0190135	−	0.0416337i	−0.000622140	−	0.00136230i
$935$	4.69438	+	3.78520i	0.153523	+	0.123789i
$936$	6.26352	+	1.83913i	0.204729	+	0.0601140i
$937$	2.25936	−	3.01815i	0.0738100	−	0.0985986i	−0.762117	−	0.647440i	$-0.775840\pi$
$937$	2.25936	−	3.01815i	0.0738100	−	0.0985986i	0.835927	+	0.548841i	$0.184931\pi$
$938$	−17.6254	+	6.57394i	−0.575490	+	0.214647i
$939$	2.59121	−	18.0223i	0.0845611	−	0.588135i
$940$	13.9696	+	3.56983i	0.455640	+	0.116435i
$941$	−36.7322	+	31.8286i	−1.19744	+	1.03758i	−0.199096	+	0.979980i	$0.563801\pi$
$941$	−36.7322	+	31.8286i	−1.19744	+	1.03758i	−0.998340	+	0.0576041i	$0.981654\pi$
$942$	12.7610	+	12.7610i	0.415775	+	0.415775i
$943$	16.9741	−	19.6387i	0.552752	−	0.639523i
$944$			13.2923i			0.432626i
$945$	8.49446	−	2.16548i	0.276325	−	0.0704429i
$946$	6.27112	+	4.03020i	0.203892	+	0.131033i
$947$	27.7615	+	37.0851i	0.902128	+	1.20510i	0.978130	+	0.207995i	$0.0666936\pi$
$947$	27.7615	+	37.0851i	0.902128	+	1.20510i	−0.0760017	+	0.997108i	$0.524215\pi$
$948$	0.540124	+	1.44813i	0.0175424	+	0.0470330i
$949$	−37.5292	+	5.39588i	−1.21825	+	0.175158i
$950$	7.64153	+	3.49509i	0.247924	+	0.113396i
$951$	−20.9192	+	13.4439i	−0.678350	+	0.435949i
$952$	14.5999	+	5.44549i	0.473187	+	0.176489i
$953$	−3.72315	+	6.81843i	−0.120605	+	0.220871i	−0.931006	−	0.365005i	$-0.881067\pi$
$953$	−3.72315	+	6.81843i	−0.120605	+	0.220871i	0.810401	+	0.585875i	$0.199249\pi$
$954$	−3.05797	+	3.52908i	−0.0990054	+	0.114258i
$955$	−31.4038	+	12.9973i	−1.01620	+	0.420582i
$956$	25.8003	−	7.57565i	0.834441	−	0.245014i
$957$	0.588517	−	1.57787i	0.0190240	−	0.0510054i
$958$	2.18923	−	10.0637i	0.0707308	−	0.325144i
$959$	3.52858	−	12.0172i	0.113944	−	0.388056i
$960$	−1.99984	+	1.00033i	−0.0645445	+	0.0322854i
$961$	4.68923	−	10.2680i	0.151266	−	0.331225i
$962$	−26.6085	+	19.9189i	−0.857893	+	0.642211i
$963$	10.1771	−	2.21389i	0.327952	−	0.0713417i
$964$	−15.4312	−	17.8086i	−0.497006	−	0.573576i
$965$	−42.5392	+	14.1448i	−1.36938	+	0.455337i
$966$	17.6076	−	6.59238i	0.566516	−	0.212106i
$967$	14.1429	−	14.1429i	0.454805	−	0.454805i	−0.442141	−	0.896946i	$-0.645781\pi$
$967$	14.1429	−	14.1429i	0.454805	−	0.454805i	0.896946	+	0.442141i	$0.145781\pi$
$968$	0.751890	−	10.5128i	0.0241667	−	0.337894i
$969$	3.61143	−	5.61950i	0.116016	−	0.180524i
$970$	−17.8335	−	12.3897i	−0.572600	−	0.397808i
$971$	23.3313	+	10.6550i	0.748736	+	0.341936i	0.752970	−	0.658055i	$-0.228620\pi$
$971$	23.3313	+	10.6550i	0.748736	+	0.341936i	−0.00423381	+	0.999991i	$0.501348\pi$
$972$	0.800541	+	0.599278i	0.0256774	+	0.0192218i
$973$	41.2966	−	22.5496i	1.32391	−	0.722908i
$974$	5.63708	+	8.77147i	0.180624	+	0.281056i
$975$	28.6382	+	15.6591i	0.917156	+	0.501491i
$976$	3.22477	+	10.9826i	0.103222	+	0.351543i
$977$	13.0171	−	0.931001i	0.416454	−	0.0297853i	0.138459	−	0.990368i	$-0.455785\pi$
$977$	13.0171	−	0.931001i	0.416454	−	0.0297853i	0.277994	+	0.960583i	$0.410330\pi$
$978$	−13.4728	+	0.963591i	−0.430811	+	0.0308122i
$979$	−0.318291	−	1.08400i	−0.0101726	−	0.0346448i
$980$	−18.7016	−	0.673322i	−0.597400	−	0.0215085i
$981$	−4.90511	−	7.63250i	−0.156608	−	0.243687i
$982$	−13.7889	+	7.52928i	−0.440020	+	0.240269i
$983$	16.0792	+	12.0367i	0.512845	+	0.383911i	0.824126	−	0.566407i	$-0.191667\pi$
$983$	16.0792	+	12.0367i	0.512845	+	0.383911i	−0.311280	+	0.950318i	$0.600758\pi$
$984$	−4.92341	−	2.24845i	−0.156953	−	0.0716778i
$985$	−2.32856	+	0.419426i	−0.0741941	+	0.0133640i
$986$	−5.33373	+	8.29945i	−0.169861	+	0.264308i
$987$	−1.80338	+	25.2146i	−0.0574023	+	0.802589i
$988$	−7.75748	+	7.75748i	−0.246798	+	0.246798i
$989$	−52.5615	−	3.69325i	−1.67136	−	0.117439i
$990$	−0.478703	−	1.43965i	−0.0152142	−	0.0457552i
$991$	23.4452	+	27.0572i	0.744762	+	0.859501i	0.994050	−	0.108928i	$-0.0347419\pi$
$991$	23.4452	+	27.0572i	0.744762	+	0.859501i	−0.249288	+	0.968429i	$0.580196\pi$
$992$	6.35432	−	1.38230i	0.201750	−	0.0438880i
$993$	1.41955	−	1.06266i	0.0450480	−	0.0337225i
$994$	19.4249	−	42.5346i	0.616121	−	1.34912i
$995$	2.36783	+	0.788849i	0.0750654	+	0.0250082i
$996$	3.36072	−	11.4456i	0.106489	−	0.362667i
$997$	−11.8798	+	54.6106i	−0.376237	+	1.72954i	0.266846	+	0.963739i	$0.414019\pi$
$997$	−11.8798	+	54.6106i	−0.376237	+	1.72954i	−0.643083	+	0.765796i	$0.722345\pi$
$998$	−13.2825	+	35.6118i	−0.420451	+	1.12727i
$999$	−4.88542	+	1.43449i	−0.154568	+	0.0453853i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.b.493.11	yes	240
5.2	odd	4	inner	690.2.w.b.217.6	yes	240
23.7	odd	22	inner	690.2.w.b.283.6	yes	240
115.7	even	44	inner	690.2.w.b.7.11	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.7.11	✓	240	115.7	even	44	inner
690.2.w.b.217.6	yes	240	5.2	odd	4	inner
690.2.w.b.283.6	yes	240	23.7	odd	22	inner
690.2.w.b.493.11	yes	240	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.997452 + 0.0713392i) q^{2} +(0.212565 + 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(1.40256 + 1.74150i) q^{5} +(0.142315 + 0.989821i) q^{6} +(1.87882 + 3.44079i) q^{7} +(0.977147 + 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +O(q^{10})\)	\(q+(0.997452 + 0.0713392i) q^{2} +(0.212565 + 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(1.40256 + 1.74150i) q^{5} +(0.142315 + 0.989821i) q^{6} +(1.87882 + 3.44079i) q^{7} +(0.977147 + 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +(1.27475 + 1.83712i) q^{10} +(0.512771 + 0.444318i) q^{11} +(0.0713392 + 0.997452i) q^{12} +(-5.72944 - 3.12851i) q^{13} +(1.62857 + 3.56606i) q^{14} +(-1.40356 + 1.74069i) q^{15} +(0.959493 + 0.281733i) q^{16} +(2.38199 - 3.18196i) q^{17} +(-0.936950 + 0.349464i) q^{18} +(0.239171 - 1.66347i) q^{19} +(1.14044 + 1.92338i) q^{20} +(-2.96279 + 2.56727i) q^{21} +(0.479767 + 0.479767i) q^{22} +(-4.60325 - 1.34539i) q^{23} +1.00000i q^{24} +(-1.06564 + 4.88512i) q^{25} +(-5.49166 - 3.52927i) q^{26} +(-0.599278 - 0.800541i) q^{27} +(1.37002 + 3.67316i) q^{28} +(-2.45679 + 0.353233i) q^{29} +(-1.52417 + 1.63613i) q^{30} +(5.47061 - 3.51575i) q^{31} +(0.936950 + 0.349464i) q^{32} +(-0.325167 + 0.595499i) q^{33} +(2.60292 - 3.00393i) q^{34} +(-3.35699 + 8.09788i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(1.77936 - 4.77064i) q^{37} +(0.357233 - 1.64217i) q^{38} +(1.83913 - 6.26352i) q^{39} +(1.00033 + 1.99984i) q^{40} +(-2.24845 + 4.92341i) q^{41} +(-3.13839 + 2.34937i) q^{42} +(10.7358 - 2.33542i) q^{43} +(0.444318 + 0.512771i) q^{44} +(-1.99926 - 1.00148i) q^{45} +(-4.49554 - 1.67035i) q^{46} +(4.55955 - 4.55955i) q^{47} +(-0.0713392 + 0.997452i) q^{48} +(-4.52463 + 7.04047i) q^{49} +(-1.41143 + 4.79665i) q^{50} +(3.61557 + 1.65118i) q^{51} +(-5.22589 - 3.91205i) q^{52} +(4.09845 - 2.23792i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(-0.0545875 + 1.51617i) q^{55} +(1.10449 + 3.76153i) q^{56} +(1.67630 - 0.119891i) q^{57} +(-2.47573 + 0.177068i) q^{58} +(3.74486 + 12.7538i) q^{59} +(-1.63700 + 1.52323i) q^{60} +(6.18829 + 9.62916i) q^{61} +(5.70748 - 3.11652i) q^{62} +(-3.13839 - 2.34937i) q^{63} +(0.909632 + 0.415415i) q^{64} +(-2.58759 - 14.3657i) q^{65} +(-0.366821 + 0.570784i) q^{66} +(-0.342317 + 4.78621i) q^{67} +(2.81058 - 2.81058i) q^{68} +(0.336152 - 4.78404i) q^{69} +(-3.92613 + 7.83777i) q^{70} +(-7.81093 - 9.01429i) q^{71} +(-0.977147 + 0.212565i) q^{72} +(4.64964 - 3.48068i) q^{73} +(2.11516 - 4.63155i) q^{74} +(-5.00000 - 0.00288011i) q^{75} +(0.473474 - 1.61250i) q^{76} +(-0.565406 + 2.59913i) q^{77} +(2.28128 - 6.11636i) q^{78} +(1.48297 - 0.435439i) q^{79} +(0.855111 + 2.06610i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-2.59395 + 4.75046i) q^{82} +(-11.1767 - 4.16868i) q^{83} +(-3.29799 + 2.11949i) q^{84} +(8.88227 - 0.314670i) q^{85} +(10.8750 - 1.56359i) q^{86} +(-0.867389 - 2.32556i) q^{87} +(0.406606 + 0.543161i) q^{88} +(-1.40078 - 0.900224i) q^{89} +(-1.92272 - 1.14155i) q^{90} -25.5917i q^{91} +(-4.36493 - 1.98681i) q^{92} +(4.59826 + 4.59826i) q^{93} +(4.87320 - 4.22266i) q^{94} +(3.23239 - 1.91661i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(-9.09892 + 3.39372i) q^{97} +(-5.01537 + 6.69975i) q^{98} +(-0.651009 - 0.191153i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{6}+O(q^{10}) \) 240 * q + 24 * q^6	\( 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) \) 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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