LMFDB - Embedded newform 690.2.w.b.7.11

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			7.11
Character	$\chi$	$=$	690.7
Dual form			690.2.w.b.493.11

$q$-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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{19}{22}\right)$

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	−0.234425	−	0.972134i	$-0.575321\pi$
$7$	1.87882	−	3.44079i	0.710126	−	1.30050i	0.944551	−	0.328364i	$-0.106497\pi$
$8$	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	−0.574123	−	0.818769i	$-0.694657\pi$
$11$	0.512771	−	0.444318i	0.154606	−	0.133967i	0.728729	+	0.684802i	$0.240111\pi$
$12$	0.0713392	−	0.997452i	0.0205938	−	0.287940i
$13$	−5.72944	+	3.12851i	−1.58906	+	0.867693i	−0.590921	+	0.806729i	$0.701236\pi$
$13$	−5.72944	+	3.12851i	−1.58906	+	0.867693i	−0.998140	+	0.0609635i	$0.980583\pi$
$14$	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	0.990265	−	0.139196i	$-0.0444519\pi$
$17$	2.38199	+	3.18196i	0.577717	+	0.771740i	−0.412548	+	0.910936i	$0.635361\pi$
$18$	−0.936950	−	0.349464i	−0.220841	−	0.0823695i
$19$	0.239171	+	1.66347i	0.0548697	+	0.381627i	0.998690	+	0.0511681i	$0.0162944\pi$
$19$	0.239171	+	1.66347i	0.0548697	+	0.381627i	−0.943820	+	0.330459i	$0.892796\pi$
$20$	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	−0.0896229	−	0.995976i	$-0.528566\pi$
$29$	−2.45679	−	0.353233i	−0.456214	−	0.0655937i	−0.366591	+	0.930382i	$0.619475\pi$
$30$	−1.52417	−	1.63613i	−0.278274	−	0.298715i
$31$	5.47061	+	3.51575i	0.982551	+	0.631447i	0.930150	−	0.367179i	$-0.119676\pi$
$31$	5.47061	+	3.51575i	0.982551	+	0.631447i	0.0524005	+	0.998626i	$0.483313\pi$
$32$	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	0.997202	+	0.0747604i	$0.0238192\pi$
$37$	1.77936	+	4.77064i	0.292525	+	0.784289i	−0.704677	+	0.709528i	$0.748908\pi$
$38$	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	−0.999968	−	0.00796540i	$-0.997465\pi$
$41$	−2.24845	−	4.92341i	−0.351148	−	0.768907i	0.648820	−	0.760942i	$-0.275263\pi$
$42$	−3.13839	−	2.34937i	−0.484264	−	0.362515i
$43$	10.7358	+	2.33542i	1.63719	+	0.356148i	0.934670	−	0.355517i	$-0.115695\pi$
$43$	10.7358	+	2.33542i	1.63719	+	0.356148i	0.702518	+	0.711666i	$0.252059\pi$
$44$	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	0.956573	−	0.291494i	$-0.0941524\pi$
$47$	4.55955	+	4.55955i	0.665078	+	0.665078i	−0.291494	+	0.956573i	$0.594152\pi$
$48$	−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	0.735416	−	0.677616i	$-0.236987\pi$
$53$	4.09845	+	2.23792i	0.562965	+	0.307402i	−0.172451	+	0.985018i	$0.555169\pi$
$54$	−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	−0.237260	−	0.971446i	$-0.576249\pi$
$59$	3.74486	−	12.7538i	0.487539	−	1.66041i	0.724799	−	0.688960i	$-0.241932\pi$
$60$	−1.63700	−	1.52323i	−0.211336	−	0.196648i
$61$	6.18829	−	9.62916i	0.792329	−	1.23289i	−0.176290	−	0.984338i	$-0.556410\pi$
$61$	6.18829	−	9.62916i	0.792329	−	1.23289i	0.968619	−	0.248550i	$-0.0799539\pi$
$62$	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	−0.974553	−	0.224159i	$-0.928037\pi$
$67$	−0.342317	−	4.78621i	−0.0418206	−	0.584729i	0.932732	−	0.360570i	$-0.117418\pi$
$68$	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	0.0703974	+	0.997519i	$0.477573\pi$
$71$	−7.81093	+	9.01429i	−0.926987	+	1.06980i	−0.997384	+	0.0722809i	$0.976972\pi$
$72$	−0.977147	−	0.212565i	−0.115158	−	0.0250511i
$73$	4.64964	+	3.48068i	0.544199	+	0.407383i	0.835698	−	0.549189i	$-0.185063\pi$
$73$	4.64964	+	3.48068i	0.544199	+	0.407383i	−0.291499	+	0.956571i	$0.594154\pi$
$74$	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	0.364089	−	0.931364i	$-0.381380\pi$
$79$	1.48297	+	0.435439i	0.166847	+	0.0489907i	−0.197242	+	0.980355i	$0.563198\pi$
$80$	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	−0.877562	−	0.479463i	$-0.840831\pi$
$83$	−11.1767	+	4.16868i	−1.22680	+	0.457572i	−0.349235	+	0.937035i	$0.613559\pi$
$84$	−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	−0.612772	−	0.790259i	$-0.709946\pi$
$89$	−1.40078	+	0.900224i	−0.148482	+	0.0954236i	0.464290	+	0.885683i	$0.346309\pi$
$90$	−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	−0.157886	−	0.987457i	$-0.550468\pi$
$97$	−9.09892	−	3.39372i	−0.923856	−	0.344580i	−0.765969	+	0.642877i	$0.777741\pi$
$98$	−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	−0.731244	−	0.682116i	$-0.761060\pi$
$101$	2.64440	−	5.79044i	0.263128	−	0.576170i	0.994372	+	0.105946i	$0.0337871\pi$
$102$	3.48857	−	1.90490i	0.345420	−	0.188613i
$103$	−0.528338	+	7.38713i	−0.0520587	+	0.727876i	0.902658	+	0.430359i	$0.141613\pi$
$103$	−0.528338	+	7.38713i	−0.0520587	+	0.727876i	−0.954717	+	0.297517i	$0.903842\pi$
$104$	−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	−0.675592	−	0.737276i	$-0.736112\pi$
$107$	−10.1771	+	2.21389i	−0.983857	+	0.214025i	−0.308265	+	0.951301i	$0.599748\pi$
$108$	−0.479249	+	0.877679i	−0.0461158	+	0.0844547i
$109$	1.29119	−	8.98042i	0.123674	−	0.860168i	−0.829664	−	0.558263i	$-0.811468\pi$
$109$	1.29119	−	8.98042i	0.123674	−	0.860168i	0.953338	−	0.301906i	$-0.0976227\pi$
$110$	−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	−0.257674	−	0.966232i	$-0.582956\pi$
$113$	−3.98860	+	0.285271i	−0.375216	+	0.0268360i	−0.117542	+	0.993068i	$0.537502\pi$
$114$	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	0.741211	+	0.671272i	$0.234252\pi$
$127$	−0.991568	+	13.8639i	−0.0879875	+	1.23023i	−0.829199	+	0.558954i	$0.811203\pi$
$128$	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	−0.514075	−	0.857745i	$-0.671865\pi$
$131$	−5.52602	+	1.62259i	−0.482811	+	0.141766i	0.0312645	+	0.999511i	$0.490047\pi$
$132$	−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	−0.796992	−	0.603989i	$-0.793577\pi$
$137$	−2.25904	+	2.25904i	−0.193003	+	0.193003i	0.603989	+	0.796992i	$0.293577\pi$
$138$	0.676585	+	4.74787i	0.0575947	+	0.404165i
$139$			12.0020i			1.01800i	0.860766	+	0.509000i	$0.169985\pi$
$139$			12.0020i			1.01800i	−0.860766	+	0.509000i	$0.830015\pi$
$140$	−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	0.512973	−	0.858405i	$-0.328544\pi$
$149$	−5.00101	−	5.77147i	−0.409698	−	0.472817i	−0.922671	+	0.385588i	$0.873999\pi$
$150$	−4.98705	+	0.359569i	−0.407191	+	0.0293587i
$151$	22.7294	+	6.67394i	1.84969	+	0.543118i	0.999871	+	0.0160417i	$0.00510645\pi$
$151$	22.7294	+	6.67394i	1.84969	+	0.543118i	0.849818	+	0.527076i	$0.176712\pi$
$152$	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	0.992298	−	0.123871i	$-0.0395309\pi$
$157$	14.4471	+	10.8150i	1.15301	+	0.863131i	0.160709	+	0.987002i	$0.448622\pi$
$158$	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	−0.884208	−	0.467093i	$-0.845301\pi$
$163$	−0.963591	−	13.4728i	−0.0754743	−	1.05527i	0.808734	−	0.588175i	$-0.200153\pi$
$164$	−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	−0.907103	−	0.420909i	$-0.861711\pi$
$167$	−9.80590	+	7.34061i	−0.758804	+	0.568033i	0.148299	+	0.988943i	$0.452620\pi$
$168$	−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	−0.370953	−	0.928652i	$-0.620969\pi$
$173$	−11.4469	−	0.818698i	−0.870291	−	0.0622444i	−0.499338	+	0.866407i	$0.666423\pi$
$174$	−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	−0.568489	−	0.822691i	$-0.692472\pi$
$179$	−4.26821	+	1.94923i	−0.319021	+	0.145692i	0.249468	+	0.968383i	$0.419744\pi$
$180$	−1.83639	+	1.27581i	−0.136876	+	0.0950932i
$181$	7.97765	+	12.4135i	0.592974	+	0.922686i	0.999957	+	0.00924997i	$0.00294440\pi$
$181$	7.97765	+	12.4135i	0.592974	+	0.922686i	−0.406983	+	0.913436i	$0.633419\pi$
$182$	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	−0.956323	−	0.292312i	$-0.905575\pi$
$191$	−4.28220	−	14.5838i	−0.309849	−	1.05525i	0.646474	−	0.762936i	$-0.276243\pi$
$192$	−0.212565	−	0.977147i	−0.0153406	−	0.0705195i
$193$	−7.00614	−	18.7842i	−0.504313	−	1.35211i	−0.900864	−	0.434102i	$-0.857066\pi$
$193$	−7.00614	−	18.7842i	−0.504313	−	1.35211i	0.396551	−	0.918013i	$-0.370207\pi$
$194$	−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	0.858990	−	0.511992i	$-0.171092\pi$
$197$	−0.507104	−	0.928691i	−0.0361297	−	0.0661665i	−0.895120	+	0.445825i	$0.852910\pi$
$198$	−0.635714	+	0.237109i	−0.0451782	+	0.0168506i
$199$	0.938963	+	0.603435i	0.0665613	+	0.0427764i	0.573498	−	0.819207i	$-0.305586\pi$
$199$	0.938963	+	0.603435i	0.0665613	+	0.0427764i	−0.506937	+	0.861983i	$0.669222\pi$
$200$	−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	0.997063	−	0.0765830i	$-0.0244010\pi$
$211$	0.273262	+	1.90058i	0.0188121	+	0.130841i	−0.978251	+	0.207424i	$0.933492\pi$
$212$	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	−0.966437	−	0.256904i	$-0.917298\pi$
$223$	−3.40209	+	6.23045i	−0.227820	+	0.417222i	0.738617	+	0.674126i	$0.235479\pi$
$224$	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	0.697552	+	0.716534i	$0.254273\pi$
$227$	−3.53495	+	16.2499i	−0.234623	+	1.07854i	−0.932175	+	0.362009i	$0.882091\pi$
$228$	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	−0.604220	−	0.796818i	$-0.706515\pi$
$233$	4.21918	−	19.3953i	0.276408	−	1.27063i	0.880628	−	0.473809i	$-0.157121\pi$
$234$	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	0.996142	−	0.0877542i	$-0.0279690\pi$
$239$	24.4595	+	11.1703i	1.58216	+	0.722547i	0.586014	+	0.810301i	$0.300696\pi$
$240$	−1.83712	−	1.27475i	−0.118586	−	0.0822848i
$241$	−17.8086	+	15.4312i	−1.14715	+	0.994012i	−0.147163	+	0.989112i	$0.547014\pi$
$241$	−17.8086	+	15.4312i	−1.14715	+	0.994012i	−0.999988	+	0.00489987i	$0.998440\pi$
$242$	−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	−0.999430	−	0.0337616i	$-0.989251\pi$
$251$	−18.6168	−	16.1315i	−1.17508	−	1.01821i	−0.175652	−	0.984452i	$-0.556203\pi$
$252$	−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	−0.999900	−	0.0141470i	$-0.995497\pi$
$257$	−11.2959	+	15.0896i	−0.704622	+	0.941264i	0.295278	+	0.955411i	$0.404588\pi$
$258$	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	0.872286	−	0.488997i	$-0.162637\pi$
$263$	−0.173166	−	0.317129i	−0.0106778	−	0.0195550i	−0.882963	+	0.469442i	$0.844455\pi$
$264$	−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	−0.860102	−	0.510122i	$-0.829600\pi$
$269$	−6.76273	−	23.0318i	−0.412331	−	1.40427i	0.447771	−	0.894148i	$-0.352218\pi$
$270$	0.706760	+	2.12144i	0.0430121	+	0.129106i
$271$	4.66151	+	10.2073i	0.283166	+	0.620048i	0.996753	−	0.0805191i	$-0.0256578\pi$
$271$	4.66151	+	10.2073i	0.283166	+	0.620048i	−0.713587	+	0.700567i	$0.752931\pi$
$272$	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	0.125589	−	0.992082i	$-0.459918\pi$
$277$	−14.4213	−	14.4213i	−0.866493	−	0.866493i	−0.992082	+	0.125589i	$0.959918\pi$
$278$	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	−0.365165	−	0.930943i	$-0.618988\pi$
$281$	1.66393	−	0.759890i	0.0992616	−	0.0453313i	0.464427	+	0.885611i	$0.346260\pi$
$282$	5.16203	−	3.86425i	0.307394	−	0.230112i
$283$	−10.1636	−	5.54977i	−0.604166	−	0.329900i	0.147885	−	0.989005i	$-0.452754\pi$
$283$	−10.1636	−	5.54977i	−0.604166	−	0.329900i	−0.752051	+	0.659105i	$0.770935\pi$
$284$	−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	−0.981227	−	0.192857i	$-0.938225\pi$
$293$	−18.3604	+	13.7444i	−1.07263	+	0.802957i	−0.0913986	+	0.995814i	$0.529134\pi$
$294$	−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	0.910748	−	0.412962i	$-0.135506\pi$
$307$	−1.56376	−	7.18847i	−0.0892482	−	0.410268i	−0.999996	+	0.00269472i	$0.999142\pi$
$308$	−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	0.978217	−	0.207584i	$-0.0665599\pi$
$311$	11.1725	+	12.8937i	0.633532	+	0.731135i	−0.344686	+	0.938718i	$0.612014\pi$
$312$	3.12851	+	5.72944i	0.177117	+	0.324366i
$313$	−17.0596	+	6.36291i	−0.964267	+	0.359653i	−0.781779	−	0.623555i	$-0.785688\pi$
$313$	−17.0596	+	6.36291i	−0.964267	+	0.359653i	−0.182488	+	0.983208i	$0.558415\pi$
$314$	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	−0.426611	−	0.904435i	$-0.640293\pi$
$317$	8.69000	−	23.2988i	0.488079	−	1.30859i	0.914690	−	0.404156i	$-0.132435\pi$
$318$	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	−0.928796	−	0.370592i	$-0.879155\pi$
$331$	−0.736628	+	1.61299i	−0.0404887	+	0.0886580i	0.888307	+	0.459250i	$0.151882\pi$
$332$	−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	0.0780697	−	0.996948i	$-0.475124\pi$
$337$	10.3396	−	2.24923i	0.563232	−	0.122524i	0.485162	+	0.874424i	$0.338761\pi$
$338$	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	0.00207227	−	0.999998i	$-0.499340\pi$
$347$	2.72784	−	0.195099i	0.146438	−	0.0104735i	0.144366	+	0.989524i	$0.453886\pi$
$348$	−0.527598	+	2.42533i	−0.0282822	+	0.130011i
$349$	5.08131	−	0.730582i	0.271996	−	0.0391072i	−0.00496701	−	0.999988i	$-0.501581\pi$
$349$	5.08131	−	0.730582i	0.271996	−	0.0391072i	0.276963	+	0.960881i	$0.410672\pi$
$350$	−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	−0.655137	−	0.755510i	$-0.727389\pi$
$353$	−17.6088	+	3.83056i	−0.937221	+	0.203880i	−0.282084	+	0.959390i	$0.591026\pi$
$354$	−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	−0.813813	−	0.581127i	$-0.802612\pi$
$359$	2.99950	−	6.56798i	0.158307	−	0.346645i	0.972121	+	0.234482i	$0.0753393\pi$
$360$	−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	−0.395671	−	0.918392i	$-0.629488\pi$
$367$	10.0139	−	10.0139i	0.522721	−	0.522721i	0.918392	+	0.395671i	$0.129488\pi$
$368$	−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	−0.998905	−	0.0467949i	$-0.985099\pi$
$373$	−4.12025	+	11.0468i	−0.213339	+	0.571983i	0.785566	+	0.618778i	$0.212372\pi$
$374$	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	0.495515	−	0.868599i	$-0.334979\pi$
$379$	−8.46392	−	9.76789i	−0.434762	−	0.501743i	−0.930277	+	0.366857i	$0.880434\pi$
$380$	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	0.629277	+	0.777181i	$0.283351\pi$
$383$	7.43125	+	34.1609i	0.379719	+	1.74554i	−0.249557	+	0.968360i	$0.580285\pi$
$384$	−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	−0.447003	+	0.894532i	$0.647509\pi$
$389$	−25.0250	+	28.8803i	−1.26882	+	1.46429i	−0.821812	+	0.569759i	$0.807037\pi$
$390$	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	−0.872865	−	0.487962i	$-0.837740\pi$
$397$	−12.9628	+	9.70381i	−0.650583	+	0.487020i	0.222282	+	0.974982i	$0.428649\pi$
$398$	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	−0.196028	−	0.980598i	$-0.562804\pi$
$401$	9.99312	−	34.0334i	0.499033	−	1.69955i	0.695061	−	0.718951i	$-0.255377\pi$
$402$	−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	−0.885596	−	0.464457i	$-0.846250\pi$
$409$	−22.5399	+	10.2936i	−1.11452	+	0.508986i	−0.228929	+	0.973443i	$0.573522\pi$
$410$	−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	0.986814	−	0.161860i	$-0.0517493\pi$
$419$	4.46772	+	9.78295i	0.218263	+	0.477928i	−0.768551	+	0.639788i	$0.779022\pi$
$420$	−8.31674	+	2.77074i	−0.405815	+	0.135198i
$421$	−3.57125	−	12.1626i	−0.174052	−	0.592767i	−0.999596	−	0.0284286i	$-0.990950\pi$
$421$	−3.57125	−	12.1626i	−0.174052	−	0.592767i	0.825544	−	0.564338i	$-0.190869\pi$
$422$	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	0.430456	−	0.902612i	$-0.358353\pi$
$431$	12.2317	+	1.75865i	0.589180	+	0.0847113i	0.158724	+	0.987323i	$0.449262\pi$
$432$	−0.349464	+	0.936950i	−0.0168136	+	0.0450790i
$433$	0.545690	−	0.728957i	0.0262242	−	0.0350314i	−0.787237	−	0.616650i	$-0.788489\pi$
$433$	0.545690	−	0.728957i	0.0262242	−	0.0350314i	0.813462	+	0.581618i	$0.197580\pi$
$434$	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	0.972691	−	0.232102i	$-0.0745604\pi$
$439$	18.4670	+	16.0017i	0.881380	+	0.763720i	−0.0913114	+	0.995822i	$0.529106\pi$
$440$	−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	0.982225	−	0.187707i	$-0.0601056\pi$
$443$	11.0583	+	14.7722i	0.525397	+	0.701848i	−0.456828	+	0.889555i	$0.651015\pi$
$444$	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	0.0339625	−	0.999423i	$-0.489187\pi$
$449$	21.7839	−	18.8759i	1.02805	−	0.890807i	0.994084	+	0.108616i	$0.0346419\pi$
$450$	−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	−0.812159	−	0.583437i	$-0.801708\pi$
$457$	3.61228	−	16.6054i	0.168975	−	0.776767i	0.981134	−	0.193330i	$-0.0619288\pi$
$458$	−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	−0.531011	−	0.847365i	$-0.678188\pi$
$463$	6.54177	−	30.0720i	0.304022	−	1.39757i	0.835033	−	0.550201i	$-0.185449\pi$
$464$	−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	−0.878186	−	0.478319i	$-0.841246\pi$
$467$	−0.0219352	+	0.0401712i	−0.00101504	+	0.00185890i	0.877171	+	0.480178i	$0.159428\pi$
$468$	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	0.995518	+	0.0945746i	$0.0301491\pi$
$479$	1.46571	+	10.1943i	0.0669702	+	0.465788i	−0.928548	+	0.371213i	$0.878942\pi$
$480$	−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	−0.636309	−	0.771434i	$-0.719540\pi$
$487$	6.24847	−	8.34698i	0.283145	−	0.378238i	0.919455	+	0.393196i	$0.128631\pi$
$488$	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	0.207300	−	0.978277i	$-0.433532\pi$
$491$	−13.2166	−	8.49379i	−0.596456	−	0.383319i	−0.803757	+	0.594958i	$0.797169\pi$
$492$	−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	−0.743976	−	0.668207i	$-0.767062\pi$
$499$	−10.7082	−	36.4687i	−0.479363	−	1.63256i	0.264612	−	0.964355i	$-0.414756\pi$
$500$	−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	0.672601	−	0.740005i	$-0.265177\pi$
$503$	21.9121	+	4.76668i	0.977011	+	0.212536i	0.304410	+	0.952541i	$0.401541\pi$
$504$	−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	−0.884911	−	0.465760i	$-0.845781\pi$
$509$	−21.2294	−	33.0336i	−0.940976	−	1.46419i	−0.0560650	−	0.998427i	$-0.517855\pi$
$510$	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	−0.859039	−	0.511911i	$-0.828938\pi$
$521$	−0.833831	+	1.29747i	−0.0365308	+	0.0568430i	0.822508	+	0.568754i	$0.192574\pi$
$522$	2.17845	+	1.18952i	0.0953480	+	0.0520639i
$523$	13.1672	−	9.85683i	0.575761	−	0.431009i	−0.271308	−	0.962493i	$-0.587456\pi$
$523$	13.1672	−	9.85683i	0.575761	−	0.431009i	0.847069	+	0.531484i	$0.178365\pi$
$524$	−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	0.909386	−	0.415954i	$-0.136552\pi$
$541$	8.56520	+	9.88477i	0.368247	+	0.424979i	−0.541139	+	0.840933i	$0.682007\pi$
$542$	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	−0.253174	+	0.967421i	$0.581475\pi$
$547$	−16.2632	+	43.6033i	−0.695364	+	1.86434i	−0.442189	+	0.896922i	$0.645798\pi$
$548$	−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	0.441888	−	0.897070i	$-0.354309\pi$
$557$	4.44614	+	1.65833i	0.188389	+	0.0702655i	−0.253499	+	0.967336i	$0.581581\pi$
$558$	−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	−0.994471	−	0.105008i	$-0.966513\pi$
$563$	0.114411	−	1.59967i	0.00482184	−	0.0674182i	0.999293	+	0.0375893i	$0.0119679\pi$
$564$	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	0.899349	+	0.437232i	$0.144041\pi$
$569$	−2.06937	+	14.3928i	−0.0867526	+	0.603377i	−0.986101	+	0.166145i	$0.946868\pi$
$570$	2.35712	−	2.92673i	0.0987287	−	0.122587i
$571$	−32.3897	+	4.65693i	−1.35547	+	0.194886i	−0.781455	−	0.623962i	$-0.785522\pi$
$571$	−32.3897	+	4.65693i	−1.35547	+	0.194886i	−0.574010	+	0.818848i	$0.694613\pi$
$572$	−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	−0.930234	−	0.366968i	$-0.880396\pi$
$577$	−43.2080	+	3.09030i	−1.79877	+	0.128651i	−0.868540	+	0.495619i	$0.834941\pi$
$578$	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	−0.847605	−	0.530628i	$-0.821956\pi$
$587$	1.62059	−	22.6588i	0.0668888	−	0.935228i	0.914494	−	0.404600i	$-0.132589\pi$
$588$	−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	0.841117	−	0.540853i	$-0.181898\pi$
$593$	27.3373	+	10.1963i	1.12261	+	0.418711i	0.281491	+	0.959564i	$0.409171\pi$
$594$	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	$0.168002\pi$
$599$			24.6520i			1.00725i	−0.863921	+	0.503627i	$0.831998\pi$
$600$	−4.88512	+	1.06564i	−0.199434	+	0.0435046i
$601$	11.9445	−	7.67624i	0.487225	−	0.313120i	−0.273864	−	0.961769i	$-0.588302\pi$
$601$	11.9445	−	7.67624i	0.487225	−	0.313120i	0.761088	+	0.648648i	$0.224665\pi$
$602$	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	−0.336457	−	0.941699i	$-0.609229\pi$
$607$	0.639270	−	0.238435i	0.0259472	−	0.00967780i	0.362404	+	0.932021i	$0.381956\pi$
$608$	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	0.590338	+	0.807156i	$0.298995\pi$
$613$	9.62258	+	44.2343i	0.388652	+	1.78661i	−0.201685	+	0.979450i	$0.564642\pi$
$614$	−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	0.385597	−	0.922667i	$-0.373995\pi$
$617$	−9.71374	−	7.27161i	−0.391060	−	0.292744i	−0.776657	+	0.629923i	$0.783086\pi$
$618$	7.23675	+	1.57426i	0.291105	+	0.0633260i
$619$	−12.0048	+	13.8542i	−0.482512	+	0.556848i	−0.943849	−	0.330377i	$-0.892824\pi$
$619$	−12.0048	+	13.8542i	−0.482512	+	0.556848i	0.461337	+	0.887225i	$0.347370\pi$
$620$	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	−0.532829	−	0.846223i	$-0.678871\pi$
$631$	9.36759	−	31.9031i	0.372918	−	1.27004i	0.905747	−	0.423819i	$-0.139311\pi$
$632$	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	0.999971	−	0.00765135i	$-0.00243552\pi$
$641$	14.6239	+	22.7552i	0.577608	+	0.898776i	−0.422363	+	0.906427i	$0.638799\pi$
$642$	0.743006	+	10.3886i	0.0293241	+	0.410004i
$643$	18.8269	+	18.8269i	0.742460	+	0.742460i	0.973051	−	0.230591i	$-0.0740660\pi$
$643$	18.8269	+	18.8269i	0.742460	+	0.742460i	−0.230591	+	0.973051i	$0.574066\pi$
$644$	−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	0.136238	−	0.990676i	$-0.456499\pi$
$647$	−3.85047	−	0.837618i	−0.151377	−	0.0329301i	−0.287615	+	0.957746i	$0.592862\pi$
$648$	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	0.950107	−	0.311923i	$-0.100973\pi$
$653$	0.710338	+	1.90449i	0.0277977	+	0.0745284i	−0.922310	+	0.386452i	$0.873701\pi$
$654$	−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	0.603039	−	0.797712i	$-0.293956\pi$
$659$	3.28397	+	2.11048i	0.127925	+	0.0822127i	−0.475113	+	0.879925i	$0.657593\pi$
$660$	−1.51620	−	0.0537141i	−0.0590182	−	0.00209082i
$661$	13.4896	+	1.93951i	0.524684	+	0.0754381i	0.399567	−	0.916704i	$-0.369160\pi$
$661$	13.4896	+	1.93951i	0.524684	+	0.0754381i	0.125117	+	0.992142i	$0.460070\pi$
$662$	−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	0.984674	−	0.174406i	$-0.0558006\pi$
$673$	14.0067	+	18.7107i	0.539918	+	0.721245i	−0.444756	+	0.895652i	$0.646710\pi$
$674$	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	0.0347672	−	0.999395i	$-0.488931\pi$
$677$	23.2692	−	12.7060i	0.894309	−	0.488330i	0.859542	+	0.511066i	$0.170749\pi$
$678$	−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	−0.655868	−	0.754876i	$-0.727697\pi$
$683$	8.72266	−	15.9744i	0.333763	−	0.611242i	0.989631	+	0.143634i	$0.0458789\pi$
$684$	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	−0.255890	+	0.966706i	$0.582368\pi$
$701$	−33.0736	+	28.6584i	−1.24917	+	1.08241i	−0.993283	+	0.115709i	$0.963086\pi$
$702$	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	−0.922032	−	0.387114i	$-0.873472\pi$
$709$	−3.89851	−	27.1147i	−0.146412	−	1.01831i	0.775620	−	0.631200i	$-0.217437\pi$
$710$	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	0.125935	−	0.992039i	$-0.459807\pi$
$719$	−0.877403	−	0.126151i	−0.0327216	−	0.00470466i	−0.158656	+	0.987334i	$0.550716\pi$
$720$	−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	0.988448	+	0.151563i	$0.0484306\pi$
$727$	9.18577	+	24.6280i	0.340681	+	0.913402i	−0.647766	+	0.761839i	$0.724297\pi$
$728$	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	0.375361	−	0.926879i	$-0.377519\pi$
$733$	8.98213	+	1.95394i	0.331763	+	0.0721705i	−0.0435987	+	0.999049i	$0.513882\pi$
$734$	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	0.677750	−	0.735293i	$-0.262955\pi$
$739$	−7.41168	−	11.5328i	−0.272643	−	0.424241i	−0.950393	+	0.311051i	$0.899319\pi$
$740$	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	−0.346014	−	0.938229i	$-0.612465\pi$
$743$	−36.0453	−	19.6822i	−1.32237	−	0.722070i	−0.976358	+	0.216159i	$0.930647\pi$
$744$	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	−0.873214	−	0.487337i	$-0.837968\pi$
$751$	−1.84076	+	2.86428i	−0.0671704	+	0.104519i	0.806044	+	0.591856i	$0.201605\pi$
$752$	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	−0.949759	−	0.312981i	$-0.898672\pi$
$757$	−1.49149	−	20.8537i	−0.0542090	−	0.757941i	0.895550	−	0.444960i	$-0.146782\pi$
$758$	−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	−0.737401	−	0.675455i	$-0.763947\pi$
$761$	0.996455	−	1.14997i	0.0361215	−	0.0416864i	0.773523	+	0.633768i	$0.218493\pi$
$762$	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	0.735454	−	0.677575i	$-0.236969\pi$
$769$	27.3934	+	8.04344i	0.987832	+	0.290054i	0.252378	+	0.967629i	$0.418787\pi$
$770$	−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	0.0401879	−	0.999192i	$-0.487204\pi$
$773$	20.1541	−	7.51708i	0.724892	−	0.270371i	0.684704	+	0.728822i	$0.259932\pi$
$774$	−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	−0.272563	−	0.962138i	$-0.587871\pi$
$787$	−31.1007	−	11.5999i	−1.10862	−	0.413494i	−0.836056	+	0.548644i	$0.815144\pi$
$788$	−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	−0.160709	−	0.987002i	$-0.551378\pi$
$797$	2.91123	−	0.633300i	0.103121	−	0.0224326i	0.263830	+	0.964569i	$0.415014\pi$
$798$	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	−0.780285	−	0.625424i	$-0.784926\pi$
$809$	−38.4765	+	5.53208i	−1.35276	+	0.194498i	−0.572475	+	0.819922i	$0.694017\pi$
$810$	2.22319	−	0.239665i	0.0781148	−	0.00842097i
$811$	5.87520	−	40.8629i	0.206306	−	1.43489i	−0.578769	−	0.815492i	$-0.696467\pi$
$811$	5.87520	−	40.8629i	0.206306	−	1.43489i	0.785075	−	0.619400i	$-0.212624\pi$
$812$	−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	−0.441960	−	0.897035i	$-0.645717\pi$
$821$	−9.42076	+	2.76619i	−0.328787	+	0.0965405i	0.113173	+	0.993575i	$0.463899\pi$
$822$	1.91455	+	2.55754i	0.0667777	+	0.0892046i
$823$	−3.20047	−	1.19371i	−0.111561	−	0.0416103i	0.293064	−	0.956093i	$-0.405325\pi$
$823$	−3.20047	−	1.19371i	−0.111561	−	0.0416103i	−0.404625	+	0.914483i	$0.632598\pi$
$824$	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	0.331233	−	0.943549i	$-0.392535\pi$
$827$	36.6597	−	36.6597i	1.27478	−	1.27478i	0.943549	−	0.331233i	$-0.107465\pi$
$828$	4.79583	+	0.00599354i	0.166667	+	0.000208290i
$829$			14.5303i			0.504658i	0.967642	+	0.252329i	$0.0811965\pi$
$829$			14.5303i			0.504658i	−0.967642	+	0.252329i	$0.918803\pi$
$830$	−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	0.831226	−	0.555934i	$-0.187639\pi$
$839$	4.71139	+	5.43724i	0.162655	+	0.187714i	−0.668571	+	0.743648i	$0.733094\pi$
$840$	−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	0.993474	+	0.114057i	$0.0363848\pi$
$853$	0.769413	+	10.7578i	0.0263442	+	0.368340i	−0.967130	+	0.254283i	$0.918161\pi$
$854$	−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	−0.534353	−	0.845261i	$-0.679445\pi$
$857$	3.69225	−	2.76398i	0.126125	−	0.0944159i	0.660478	+	0.750846i	$0.270354\pi$
$858$	3.88738	+	2.12267i	0.132713	+	0.0724668i
$859$	28.6372	−	44.5603i	0.977088	−	1.52038i	0.128240	−	0.991743i	$-0.459067\pi$
$859$	28.6372	−	44.5603i	0.977088	−	1.52038i	0.848849	−	0.528636i	$-0.177296\pi$
$860$	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	−0.234751	−	0.972056i	$-0.575427\pi$
$863$	−17.7862	−	1.27210i	−0.605450	−	0.0433026i	−0.370699	+	0.928753i	$0.620882\pi$
$864$	−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	0.0239619	−	0.999713i	$-0.492372\pi$
$877$	−10.9435	−	2.38062i	−0.369537	−	0.0803879i	−0.393499	+	0.919325i	$0.628736\pi$
$878$	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	−0.939394	−	0.342840i	$-0.888611\pi$
$881$	−9.92788	−	33.8113i	−0.334479	−	1.13913i	0.604915	−	0.796290i	$-0.293207\pi$
$882$	1.77896	+	8.17776i	0.0599008	+	0.275360i
$883$	−9.39737	−	25.1953i	−0.316247	−	0.847890i	−0.993674	−	0.112301i	$-0.964178\pi$
$883$	−9.39737	−	25.1953i	−0.316247	−	0.847890i	0.677428	−	0.735589i	$-0.263095\pi$
$884$	−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	0.759465	−	0.650548i	$-0.225461\pi$
$887$	−5.90910	−	10.8217i	−0.198408	−	0.363358i	−0.957874	+	0.287190i	$0.907279\pi$
$888$	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	−0.976005	−	0.217749i	$-0.930129\pi$
$907$	−39.7685	+	21.7152i	−1.32049	+	0.721042i	−0.344486	+	0.938792i	$0.611947\pi$
$908$	−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	−0.340835	−	0.940123i	$-0.610710\pi$
$911$	−38.4689	−	17.5682i	−1.27453	−	0.582059i	−0.933697	+	0.358064i	$0.883437\pi$
$912$	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	0.332340	−	0.943160i	$-0.392162\pi$
$929$	−4.96255	−	2.26632i	−0.162816	−	0.0743555i	−0.495156	+	0.868804i	$0.664889\pi$
$930$	−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	0.835927	−	0.548841i	$-0.184931\pi$
$937$	2.25936	+	3.01815i	0.0738100	+	0.0985986i	−0.762117	+	0.647440i	$0.775840\pi$
$938$	−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	−0.998340	−	0.0576041i	$-0.981654\pi$
$941$	−36.7322	−	31.8286i	−1.19744	−	1.03758i	−0.199096	−	0.979980i	$-0.563801\pi$
$942$	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	−0.0760017	−	0.997108i	$-0.524215\pi$
$947$	27.7615	−	37.0851i	0.902128	−	1.20510i	0.978130	−	0.207995i	$-0.0666936\pi$
$948$	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	0.810401	−	0.585875i	$-0.199249\pi$
$953$	−3.72315	−	6.81843i	−0.120605	−	0.220871i	−0.931006	+	0.365005i	$0.881067\pi$
$954$	−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	0.896946	−	0.442141i	$-0.145781\pi$
$967$	14.1429	+	14.1429i	0.454805	+	0.454805i	−0.442141	+	0.896946i	$0.645781\pi$
$968$	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	−0.00423381	−	0.999991i	$-0.501348\pi$
$971$	23.3313	−	10.6550i	0.748736	−	0.341936i	0.752970	+	0.658055i	$0.228620\pi$
$972$	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	0.277994	−	0.960583i	$-0.410330\pi$
$977$	13.0171	+	0.931001i	0.416454	+	0.0297853i	0.138459	+	0.990368i	$0.455785\pi$
$978$	−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	−0.311280	−	0.950318i	$-0.600758\pi$
$983$	16.0792	−	12.0367i	0.512845	−	0.383911i	0.824126	+	0.566407i	$0.191667\pi$
$984$	−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	−0.249288	−	0.968429i	$-0.580196\pi$
$991$	23.4452	−	27.0572i	0.744762	−	0.859501i	0.994050	+	0.108928i	$0.0347419\pi$
$992$	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	−0.643083	−	0.765796i	$-0.722345\pi$
$997$	−11.8798	−	54.6106i	−0.376237	−	1.72954i	0.266846	−	0.963739i	$-0.414019\pi$
$998$	−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.7.11	✓	240
5.3	odd	4	inner	690.2.w.b.283.6	yes	240
23.10	odd	22	inner	690.2.w.b.217.6	yes	240
115.33	even	44	inner	690.2.w.b.493.11	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.7.11	✓	240	1.1	even	1	trivial
690.2.w.b.217.6	yes	240	23.10	odd	22	inner
690.2.w.b.283.6	yes	240	5.3	odd	4	inner
690.2.w.b.493.11	yes	240	115.33	even	44	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
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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