LMFDB - Embedded newform 690.2.j.b.367.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(367,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("690.367");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.j (of order $4$, degree $2$, 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:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			367.11
Character	$\chi$	$=$	690.367
Dual form			690.2.j.b.643.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(1.52094 + 1.63913i) q^{5} +1.00000 q^{6} +(-2.68754 + 2.68754i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(1.52094 + 1.63913i) q^{5} +1.00000 q^{6} +(-2.68754 + 2.68754i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(-0.0835670 + 2.23451i) q^{10} +0.403497i q^{11} +(0.707107 + 0.707107i) q^{12} +(-2.12629 + 2.12629i) q^{13} -3.80076 q^{14} +(2.23451 + 0.0835670i) q^{15} -1.00000 q^{16} +(-4.95666 + 4.95666i) q^{17} +(0.707107 - 0.707107i) q^{18} +5.20795 q^{19} +(-1.63913 + 1.52094i) q^{20} +3.80076i q^{21} +(-0.285316 + 0.285316i) q^{22} +(4.10854 - 2.47384i) q^{23} +1.00000i q^{24} +(-0.373462 + 4.98603i) q^{25} -3.00703 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.68754 - 2.68754i) q^{28} -9.42076i q^{29} +(1.52094 + 1.63913i) q^{30} +3.33683 q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.285316 + 0.285316i) q^{33} -7.00978 q^{34} +(-8.49282 - 0.317618i) q^{35} +1.00000 q^{36} +(2.17130 - 2.17130i) q^{37} +(3.68258 + 3.68258i) q^{38} +3.00703i q^{39} +(-2.23451 - 0.0835670i) q^{40} +5.69885 q^{41} +(-2.68754 + 2.68754i) q^{42} +(-2.56936 - 2.56936i) q^{43} -0.403497 q^{44} +(1.63913 - 1.52094i) q^{45} +(4.65445 + 1.15590i) q^{46} +(8.64413 + 8.64413i) q^{47} +(-0.707107 + 0.707107i) q^{48} -7.44578i q^{49} +(-3.78974 + 3.26158i) q^{50} +7.00978i q^{51} +(-2.12629 - 2.12629i) q^{52} +(-1.47608 - 1.47608i) q^{53} -1.00000i q^{54} +(-0.661382 + 0.613696i) q^{55} -3.80076i q^{56} +(3.68258 - 3.68258i) q^{57} +(6.66148 - 6.66148i) q^{58} +13.4003i q^{59} +(-0.0835670 + 2.23451i) q^{60} -7.51118i q^{61} +(2.35950 + 2.35950i) q^{62} +(2.68754 + 2.68754i) q^{63} -1.00000i q^{64} +(-6.71923 - 0.251289i) q^{65} +0.403497i q^{66} +(4.60755 - 4.60755i) q^{67} +(-4.95666 - 4.95666i) q^{68} +(1.15590 - 4.65445i) q^{69} +(-5.78074 - 6.22992i) q^{70} -5.45281 q^{71} +(0.707107 + 0.707107i) q^{72} +(1.06175 - 1.06175i) q^{73} +3.07068 q^{74} +(3.26158 + 3.78974i) q^{75} +5.20795i q^{76} +(-1.08442 - 1.08442i) q^{77} +(-2.12629 + 2.12629i) q^{78} +0.383565 q^{79} +(-1.52094 - 1.63913i) q^{80} -1.00000 q^{81} +(4.02970 + 4.02970i) q^{82} +(12.3708 + 12.3708i) q^{83} -3.80076 q^{84} +(-15.6634 - 0.585786i) q^{85} -3.63363i q^{86} +(-6.66148 - 6.66148i) q^{87} +(-0.285316 - 0.285316i) q^{88} +6.23158 q^{89} +(2.23451 + 0.0835670i) q^{90} -11.4290i q^{91} +(2.47384 + 4.10854i) q^{92} +(2.35950 - 2.35950i) q^{93} +12.2247i q^{94} +(7.92100 + 8.53649i) q^{95} -1.00000 q^{96} +(8.25631 - 8.25631i) q^{97} +(5.26496 - 5.26496i) q^{98} +0.403497 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{6}+O(q^{10}) $ 24 * q + 24 * q^6	$ 24 q + 24 q^{6} + 16 q^{13} - 24 q^{16} + 16 q^{23} - 16 q^{25} + 16 q^{31} + 24 q^{36} + 8 q^{46} + 40 q^{47} - 8 q^{50} + 16 q^{52} - 56 q^{55} - 16 q^{58} - 8 q^{62} + 32 q^{70} + 64 q^{71} - 16 q^{73} + 32 q^{75} + 16 q^{77} + 16 q^{78} - 24 q^{81} + 24 q^{82} - 48 q^{85} + 16 q^{87} + 16 q^{92} - 8 q^{93} + 24 q^{95} - 24 q^{96}+O(q^{100}) $ 24 * q + 24 * q^6 + 16 * q^13 - 24 * q^16 + 16 * q^23 - 16 * q^25 + 16 * q^31 + 24 * q^36 + 8 * q^46 + 40 * q^47 - 8 * q^50 + 16 * q^52 - 56 * q^55 - 16 * q^58 - 8 * q^62 + 32 * q^70 + 64 * q^71 - 16 * q^73 + 32 * q^75 + 16 * q^77 + 16 * q^78 - 24 * q^81 + 24 * q^82 - 48 * q^85 + 16 * q^87 + 16 * q^92 - 8 * q^93 + 24 * q^95 - 24 * q^96

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$			1.00000i			0.500000i
$5$	1.52094	+	1.63913i	0.680187	+	0.733039i
$5$	1.52094	+	1.63913i	0.680187	+	0.733039i
$6$	1.00000			0.408248
$7$	−2.68754	+	2.68754i	−1.01580	+	1.01580i	−0.0159226	+	0.999873i	$0.505069\pi$
$7$	−2.68754	+	2.68754i	−1.01580	+	1.01580i	−0.999873	+	0.0159226i	$0.994931\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		−	1.00000i		−	0.333333i
$10$	−0.0835670	+	2.23451i	−0.0264262	+	0.706613i
$11$			0.403497i			0.121659i	0.998148	+	0.0608295i	$0.0193746\pi$
$11$			0.403497i			0.121659i	−0.998148	+	0.0608295i	$0.980625\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	−2.12629	+	2.12629i	−0.589728	+	0.589728i	−0.937558	−	0.347830i	$-0.886919\pi$
$13$	−2.12629	+	2.12629i	−0.589728	+	0.589728i	0.347830	+	0.937558i	$0.386919\pi$
$14$	−3.80076			−1.01580
$15$	2.23451	+	0.0835670i	0.576947	+	0.0215769i
$16$	−1.00000			−0.250000
$17$	−4.95666	+	4.95666i	−1.20217	+	1.20217i	−0.228662	+	0.973506i	$0.573435\pi$
$17$	−4.95666	+	4.95666i	−1.20217	+	1.20217i	−0.973506	+	0.228662i	$0.926565\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	5.20795			1.19479			0.597393	−	0.801949i	$-0.296203\pi$
$19$	5.20795			1.19479			0.597393	+	0.801949i	$0.296203\pi$
$20$	−1.63913	+	1.52094i	−0.366520	+	0.340093i
$21$			3.80076i			0.829394i
$22$	−0.285316	+	0.285316i	−0.0608295	+	0.0608295i
$23$	4.10854	−	2.47384i	0.856690	−	0.515832i
$23$	4.10854	−	2.47384i	0.856690	−	0.515832i
$24$			1.00000i			0.204124i
$25$	−0.373462	+	4.98603i	−0.0746924	+	0.997207i
$26$	−3.00703			−0.589728
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−2.68754	−	2.68754i	−0.507898	−	0.507898i
$29$		−	9.42076i		−	1.74939i	−0.484673	−	0.874695i	$-0.661061\pi$
$29$		−	9.42076i		−	1.74939i	0.484673	−	0.874695i	$-0.338939\pi$
$30$	1.52094	+	1.63913i	0.277685	+	0.299262i
$31$	3.33683			0.599312			0.299656	−	0.954047i	$-0.403128\pi$
$31$	3.33683			0.599312			0.299656	+	0.954047i	$0.403128\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	0.285316	+	0.285316i	0.0496671	+	0.0496671i
$34$	−7.00978			−1.20217
$35$	−8.49282	−	0.317618i	−1.43555	−	0.0536873i
$36$	1.00000			0.166667
$37$	2.17130	−	2.17130i	0.356959	−	0.356959i	−0.505732	−	0.862691i	$-0.668777\pi$
$37$	2.17130	−	2.17130i	0.356959	−	0.356959i	0.862691	+	0.505732i	$0.168777\pi$
$38$	3.68258	+	3.68258i	0.597393	+	0.597393i
$39$			3.00703i			0.481511i
$40$	−2.23451	−	0.0835670i	−0.353306	−	0.0132131i
$41$	5.69885			0.890011			0.445006	−	0.895528i	$-0.353202\pi$
$41$	5.69885			0.890011			0.445006	+	0.895528i	$0.353202\pi$
$42$	−2.68754	+	2.68754i	−0.414697	+	0.414697i
$43$	−2.56936	−	2.56936i	−0.391824	−	0.391824i	0.483513	−	0.875337i	$-0.339361\pi$
$43$	−2.56936	−	2.56936i	−0.391824	−	0.391824i	−0.875337	+	0.483513i	$0.839361\pi$
$44$	−0.403497			−0.0608295
$45$	1.63913	−	1.52094i	0.244346	−	0.226729i
$46$	4.65445	+	1.15590i	0.686261	+	0.170429i
$47$	8.64413	+	8.64413i	1.26088	+	1.26088i	0.950669	+	0.310208i	$0.100399\pi$
$47$	8.64413	+	8.64413i	1.26088	+	1.26088i	0.310208	+	0.950669i	$0.399601\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$		−	7.44578i		−	1.06368i
$50$	−3.78974	+	3.26158i	−0.535950	+	0.461257i
$51$			7.00978i			0.981566i
$52$	−2.12629	−	2.12629i	−0.294864	−	0.294864i
$53$	−1.47608	−	1.47608i	−0.202755	−	0.202755i	0.598424	−	0.801179i	$-0.295794\pi$
$53$	−1.47608	−	1.47608i	−0.202755	−	0.202755i	−0.801179	+	0.598424i	$0.795794\pi$
$54$		−	1.00000i		−	0.136083i
$55$	−0.661382	+	0.613696i	−0.0891808	+	0.0827508i
$56$		−	3.80076i		−	0.507898i
$57$	3.68258	−	3.68258i	0.487769	−	0.487769i
$58$	6.66148	−	6.66148i	0.874695	−	0.874695i
$59$			13.4003i			1.74458i	0.488992	+	0.872288i	$0.337365\pi$
$59$			13.4003i			1.74458i	−0.488992	+	0.872288i	$0.662635\pi$
$60$	−0.0835670	+	2.23451i	−0.0107885	+	0.288473i
$61$		−	7.51118i		−	0.961708i	−0.876801	−	0.480854i	$-0.840327\pi$
$61$		−	7.51118i		−	0.961708i	0.876801	−	0.480854i	$-0.159673\pi$
$62$	2.35950	+	2.35950i	0.299656	+	0.299656i
$63$	2.68754	+	2.68754i	0.338599	+	0.338599i
$64$		−	1.00000i		−	0.125000i
$65$	−6.71923	−	0.251289i	−0.833418	−	0.0311685i
$66$			0.403497i			0.0496671i
$67$	4.60755	−	4.60755i	0.562902	−	0.562902i	−0.367229	−	0.930131i	$-0.619693\pi$
$67$	4.60755	−	4.60755i	0.562902	−	0.562902i	0.930131	+	0.367229i	$0.119693\pi$
$68$	−4.95666	−	4.95666i	−0.601084	−	0.601084i
$69$	1.15590	−	4.65445i	0.139154	−	0.560330i
$70$	−5.78074	−	6.22992i	−0.690931	−	0.744618i
$71$	−5.45281			−0.647129			−0.323565	−	0.946206i	$-0.604881\pi$
$71$	−5.45281			−0.647129			−0.323565	+	0.946206i	$0.604881\pi$
$72$	0.707107	+	0.707107i	0.0833333	+	0.0833333i
$73$	1.06175	−	1.06175i	0.124269	−	0.124269i	−0.642237	−	0.766506i	$-0.721994\pi$
$73$	1.06175	−	1.06175i	0.124269	−	0.124269i	0.766506	+	0.642237i	$0.221994\pi$
$74$	3.07068			0.356959
$75$	3.26158	+	3.78974i	0.376615	+	0.437601i
$76$			5.20795i			0.597393i
$77$	−1.08442	−	1.08442i	−0.123581	−	0.123581i
$78$	−2.12629	+	2.12629i	−0.240755	+	0.240755i
$79$	0.383565			0.0431544			0.0215772	−	0.999767i	$-0.493131\pi$
$79$	0.383565			0.0431544			0.0215772	+	0.999767i	$0.493131\pi$
$80$	−1.52094	−	1.63913i	−0.170047	−	0.183260i
$81$	−1.00000			−0.111111
$82$	4.02970	+	4.02970i	0.445006	+	0.445006i
$83$	12.3708	+	12.3708i	1.35787	+	1.35787i	0.876540	+	0.481328i	$0.159846\pi$
$83$	12.3708	+	12.3708i	1.35787	+	1.35787i	0.481328	+	0.876540i	$0.340154\pi$
$84$	−3.80076			−0.414697
$85$	−15.6634	−	0.585786i	−1.69893	−	0.0635375i
$86$		−	3.63363i		−	0.391824i
$87$	−6.66148	−	6.66148i	−0.714186	−	0.714186i
$88$	−0.285316	−	0.285316i	−0.0304147	−	0.0304147i
$89$	6.23158			0.660546			0.330273	−	0.943885i	$-0.392859\pi$
$89$	6.23158			0.660546			0.330273	+	0.943885i	$0.392859\pi$
$90$	2.23451	+	0.0835670i	0.235538	+	0.00880874i
$91$		−	11.4290i		−	1.19809i
$92$	2.47384	+	4.10854i	0.257916	+	0.428345i
$93$	2.35950	−	2.35950i	0.244668	−	0.244668i
$94$			12.2247i			1.26088i
$95$	7.92100	+	8.53649i	0.812678	+	0.875825i
$96$	−1.00000			−0.102062
$97$	8.25631	−	8.25631i	0.838301	−	0.838301i	−0.150334	−	0.988635i	$-0.548035\pi$
$97$	8.25631	−	8.25631i	0.838301	−	0.838301i	0.988635	+	0.150334i	$0.0480350\pi$
$98$	5.26496	−	5.26496i	0.531841	−	0.531841i
$99$	0.403497			0.0405530
$100$	−4.98603	−	0.373462i	−0.498603	−	0.0373462i
$101$	−7.08442			−0.704926			−0.352463	−	0.935826i	$-0.614656\pi$
$101$	−7.08442			−0.704926			−0.352463	+	0.935826i	$0.614656\pi$
$102$	−4.95666	+	4.95666i	−0.490783	+	0.490783i
$103$	−6.87041	−	6.87041i	−0.676961	−	0.676961i	0.282350	−	0.959311i	$-0.408886\pi$
$103$	−6.87041	−	6.87041i	−0.676961	−	0.676961i	−0.959311	+	0.282350i	$0.908886\pi$
$104$		−	3.00703i		−	0.294864i
$105$	−6.22992	+	5.78074i	−0.607978	+	0.564143i
$106$		−	2.08749i		−	0.202755i
$107$	−3.14660	+	3.14660i	−0.304194	+	0.304194i	−0.842652	−	0.538458i	$-0.819007\pi$
$107$	−3.14660	+	3.14660i	−0.304194	+	0.304194i	0.538458	+	0.842652i	$0.319007\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	−12.6901			−1.21549			−0.607744	−	0.794133i	$-0.707925\pi$
$109$	−12.6901			−1.21549			−0.607744	+	0.794133i	$0.707925\pi$
$110$	−0.901617	−	0.0337191i	−0.0859658	−	0.00321499i
$111$		−	3.07068i		−	0.291456i
$112$	2.68754	−	2.68754i	0.253949	−	0.253949i
$113$	−8.96499	−	8.96499i	−0.843356	−	0.843356i	0.145938	−	0.989294i	$-0.453380\pi$
$113$	−8.96499	−	8.96499i	−0.843356	−	0.843356i	−0.989294	+	0.145938i	$0.953380\pi$
$114$	5.20795			0.487769
$115$	10.3038	+	2.97183i	0.960834	+	0.277125i
$116$	9.42076			0.874695
$117$	2.12629	+	2.12629i	0.196576	+	0.196576i
$118$	−9.47547	+	9.47547i	−0.872288	+	0.872288i
$119$		−	26.6425i		−	2.44231i
$120$	−1.63913	+	1.52094i	−0.149631	+	0.138843i
$121$	10.8372			0.985199
$122$	5.31121	−	5.31121i	0.480854	−	0.480854i
$123$	4.02970	−	4.02970i	0.363346	−	0.363346i
$124$			3.33683i			0.299656i
$125$	−8.74075	+	6.97132i	−0.781796	+	0.623534i
$126$			3.80076i			0.338599i
$127$	−9.84286	−	9.84286i	−0.873413	−	0.873413i	0.119430	−	0.992843i	$-0.461893\pi$
$127$	−9.84286	−	9.84286i	−0.873413	−	0.873413i	−0.992843	+	0.119430i	$0.961893\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−3.63363			−0.319923
$130$	−4.57353	−	4.92890i	−0.401125	−	0.432293i
$131$	−1.09419			−0.0955998			−0.0477999	−	0.998857i	$-0.515221\pi$
$131$	−1.09419			−0.0955998			−0.0477999	+	0.998857i	$0.515221\pi$
$132$	−0.285316	+	0.285316i	−0.0248335	+	0.0248335i
$133$	−13.9966	+	13.9966i	−1.21366	+	1.21366i
$134$	6.51606			0.562902
$135$	0.0835670	−	2.23451i	0.00719230	−	0.192316i
$136$		−	7.00978i		−	0.601084i
$137$	13.9152	−	13.9152i	1.18885	−	1.18885i	0.211471	−	0.977384i	$-0.432175\pi$
$137$	13.9152	−	13.9152i	1.18885	−	1.18885i	0.977384	−	0.211471i	$-0.0678253\pi$
$138$	4.10854	−	2.47384i	0.349742	−	0.210588i
$139$		−	19.8141i		−	1.68061i	−0.542116	−	0.840304i	$-0.682377\pi$
$139$		−	19.8141i		−	1.68061i	0.542116	−	0.840304i	$-0.317623\pi$
$140$	0.317618	−	8.49282i	0.0268436	−	0.717774i
$141$	12.2247			1.02950
$142$	−3.85572	−	3.85572i	−0.323565	−	0.323565i
$143$	−0.857953	−	0.857953i	−0.0717457	−	0.0717457i
$144$			1.00000i			0.0833333i
$145$	15.4418	−	14.3284i	1.28237	−	1.18991i
$146$	1.50154			0.124269
$147$	−5.26496	−	5.26496i	−0.434247	−	0.434247i
$148$	2.17130	+	2.17130i	0.178480	+	0.178480i
$149$	−11.1431			−0.912875			−0.456438	−	0.889755i	$-0.650875\pi$
$149$	−11.1431			−0.912875			−0.456438	+	0.889755i	$0.650875\pi$
$150$	−0.373462	+	4.98603i	−0.0304930	+	0.407108i
$151$	19.9653			1.62475			0.812375	−	0.583135i	$-0.198174\pi$
$151$	19.9653			1.62475			0.812375	+	0.583135i	$0.198174\pi$
$152$	−3.68258	+	3.68258i	−0.298697	+	0.298697i
$153$	4.95666	+	4.95666i	0.400723	+	0.400723i
$154$		−	1.53360i		−	0.123581i
$155$	5.07513	+	5.46948i	0.407644	+	0.439319i
$156$	−3.00703			−0.240755
$157$	−2.44491	+	2.44491i	−0.195125	+	0.195125i	−0.797907	−	0.602781i	$-0.794059\pi$
$157$	−2.44491	+	2.44491i	−0.195125	+	0.195125i	0.602781	+	0.797907i	$0.294059\pi$
$158$	0.271221	+	0.271221i	0.0215772	+	0.0215772i
$159$	−2.08749			−0.165549
$160$	0.0835670	−	2.23451i	0.00660655	−	0.176653i
$161$	−4.39331	+	17.6904i	−0.346242	+	1.39420i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	0.238521	−	0.238521i	0.0186824	−	0.0186824i	−0.697704	−	0.716386i	$-0.745795\pi$
$163$	0.238521	−	0.238521i	0.0186824	−	0.0186824i	0.716386	+	0.697704i	$0.245795\pi$
$164$			5.69885i			0.445006i
$165$	−0.0337191	+	0.901617i	−0.00262502	+	0.0701908i
$166$			17.4949i			1.35787i
$167$	6.43688	+	6.43688i	0.498101	+	0.498101i	0.910846	−	0.412746i	$-0.135430\pi$
$167$	6.43688	+	6.43688i	0.498101	+	0.498101i	−0.412746	+	0.910846i	$0.635430\pi$
$168$	−2.68754	−	2.68754i	−0.207348	−	0.207348i
$169$			3.95776i			0.304443i
$170$	−10.6615	−	11.4899i	−0.817698	−	0.881236i
$171$		−	5.20795i		−	0.398262i
$172$	2.56936	−	2.56936i	0.195912	−	0.195912i
$173$	−5.89468	+	5.89468i	−0.448164	+	0.448164i	−0.894744	−	0.446580i	$-0.852642\pi$
$173$	−5.89468	+	5.89468i	−0.448164	+	0.448164i	0.446580	+	0.894744i	$0.352642\pi$
$174$		−	9.42076i		−	0.714186i
$175$	−12.3965	−	14.4039i	−0.937086	−	1.08883i
$176$		−	0.403497i		−	0.0304147i
$177$	9.47547	+	9.47547i	0.712220	+	0.712220i
$178$	4.40639	+	4.40639i	0.330273	+	0.330273i
$179$			2.77575i			0.207469i	0.994605	+	0.103735i	$0.0330792\pi$
$179$			2.77575i			0.207469i	−0.994605	+	0.103735i	$0.966921\pi$
$180$	1.52094	+	1.63913i	0.113364	+	0.122173i
$181$		−	21.2640i		−	1.58054i	−0.612760	−	0.790269i	$-0.709941\pi$
$181$		−	21.2640i		−	1.58054i	0.612760	−	0.790269i	$-0.290059\pi$
$182$	8.08153	−	8.08153i	0.599043	−	0.599043i
$183$	−5.31121	−	5.31121i	−0.392616	−	0.392616i
$184$	−1.15590	+	4.65445i	−0.0852143	+	0.343130i
$185$	6.86145	+	0.256608i	0.504464	+	0.0188662i
$186$	3.33683			0.244668
$187$	−2.00000	−	2.00000i	−0.146254	−	0.146254i
$188$	−8.64413	+	8.64413i	−0.630438	+	0.630438i
$189$	3.80076			0.276465
$190$	−0.435213	+	11.6372i	−0.0315737	+	0.844251i
$191$			15.5937i			1.12832i	0.825666	+	0.564160i	$0.190800\pi$
$191$			15.5937i			1.12832i	−0.825666	+	0.564160i	$0.809200\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	−6.99660	+	6.99660i	−0.503626	+	0.503626i	−0.912563	−	0.408937i	$-0.865900\pi$
$193$	−6.99660	+	6.99660i	−0.503626	+	0.503626i	0.408937	+	0.912563i	$0.365900\pi$
$194$	11.6762			0.838301
$195$	−4.92890	+	4.57353i	−0.352966	+	0.327517i
$196$	7.44578			0.531841
$197$	4.96503	+	4.96503i	0.353744	+	0.353744i	0.861501	−	0.507757i	$-0.169525\pi$
$197$	4.96503	+	4.96503i	0.353744	+	0.353744i	−0.507757	+	0.861501i	$0.669525\pi$
$198$	0.285316	+	0.285316i	0.0202765	+	0.0202765i
$199$	13.2209			0.937202			0.468601	−	0.883410i	$-0.344758\pi$
$199$	13.2209			0.937202			0.468601	+	0.883410i	$0.344758\pi$
$200$	−3.26158	−	3.78974i	−0.230629	−	0.267975i
$201$		−	6.51606i		−	0.459608i
$202$	−5.00944	−	5.00944i	−0.352463	−	0.352463i
$203$	25.3187	+	25.3187i	1.77702	+	1.77702i
$204$	−7.00978			−0.490783
$205$	8.66763	+	9.34113i	0.605374	+	0.652413i
$206$		−	9.71622i		−	0.676961i
$207$	−2.47384	−	4.10854i	−0.171944	−	0.285563i
$208$	2.12629	−	2.12629i	0.147432	−	0.147432i
$209$			2.10139i			0.145356i
$210$	−8.49282	−	0.317618i	−0.586060	−	0.0219177i
$211$	14.3412			0.987286			0.493643	−	0.869665i	$-0.335665\pi$
$211$	14.3412			0.987286			0.493643	+	0.869665i	$0.335665\pi$
$212$	1.47608	−	1.47608i	0.101377	−	0.101377i
$213$	−3.85572	+	3.85572i	−0.264189	+	0.264189i
$214$	−4.44997			−0.304194
$215$	0.303651	−	8.11936i	0.0207088	−	0.553736i
$216$	1.00000			0.0680414
$217$	−8.96787	+	8.96787i	−0.608779	+	0.608779i
$218$	−8.97323	−	8.97323i	−0.607744	−	0.607744i
$219$		−	1.50154i		−	0.101465i
$220$	−0.613696	−	0.661382i	−0.0413754	−	0.0445904i
$221$		−	21.0786i		−	1.41790i
$222$	2.17130	−	2.17130i	0.145728	−	0.145728i
$223$	−10.4795	+	10.4795i	−0.701757	+	0.701757i	−0.964788	−	0.263030i	$-0.915278\pi$
$223$	−10.4795	+	10.4795i	−0.701757	+	0.701757i	0.263030	+	0.964788i	$0.415278\pi$
$224$	3.80076			0.253949
$225$	4.98603	+	0.373462i	0.332402	+	0.0248975i
$226$		−	12.6784i		−	0.843356i
$227$	−0.390578	+	0.390578i	−0.0259236	+	0.0259236i	−0.719950	−	0.694026i	$-0.755835\pi$
$227$	−0.390578	+	0.390578i	−0.0259236	+	0.0259236i	0.694026	+	0.719950i	$0.255835\pi$
$228$	3.68258	+	3.68258i	0.243885	+	0.243885i
$229$	−16.0170			−1.05844			−0.529218	−	0.848486i	$-0.677515\pi$
$229$	−16.0170			−1.05844			−0.529218	+	0.848486i	$0.677515\pi$
$230$	5.18448	+	9.38729i	0.341855	+	0.618979i
$231$	−1.53360			−0.100903
$232$	6.66148	+	6.66148i	0.437348	+	0.437348i
$233$	−13.0826	+	13.0826i	−0.857070	+	0.857070i	−0.990992	−	0.133922i	$-0.957243\pi$
$233$	−13.0826	+	13.0826i	−0.857070	+	0.857070i	0.133922	+	0.990992i	$0.457243\pi$
$234$			3.00703i			0.196576i
$235$	−1.02158	+	27.3161i	−0.0666404	+	1.78190i
$236$	−13.4003			−0.872288
$237$	0.271221	−	0.271221i	0.0176177	−	0.0176177i
$238$	18.8391	−	18.8391i	1.22116	−	1.22116i
$239$		−	14.8384i		−	0.959816i	−0.877319	−	0.479908i	$-0.840670\pi$
$239$		−	14.8384i		−	0.959816i	0.877319	−	0.479908i	$-0.159330\pi$
$240$	−2.23451	−	0.0835670i	−0.144237	−	0.00539423i
$241$		−	9.52147i		−	0.613332i	−0.951817	−	0.306666i	$-0.900787\pi$
$241$		−	9.52147i		−	0.613332i	0.951817	−	0.306666i	$-0.0992135\pi$
$242$	7.66305	+	7.66305i	0.492600	+	0.492600i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	7.51118			0.480854
$245$	12.2046	−	11.3246i	0.779721	−	0.723503i
$246$	5.69885			0.363346
$247$	−11.0736	+	11.0736i	−0.704598	+	0.704598i
$248$	−2.35950	+	2.35950i	−0.149828	+	0.149828i
$249$	17.4949			1.10870
$250$	−11.1101	−	1.25117i	−0.702665	−	0.0791310i
$251$		−	2.75797i		−	0.174082i	−0.996205	−	0.0870409i	$-0.972259\pi$
$251$		−	2.75797i		−	0.174082i	0.996205	−	0.0870409i	$-0.0277411\pi$
$252$	−2.68754	+	2.68754i	−0.169299	+	0.169299i
$253$	0.998189	+	1.65778i	0.0627556	+	0.104224i
$254$		−	13.9199i		−	0.873413i
$255$	−11.4899	+	10.6615i	−0.719526	+	0.667648i
$256$	1.00000			0.0625000
$257$	4.31593	+	4.31593i	0.269220	+	0.269220i	0.828786	−	0.559566i	$-0.189032\pi$
$257$	4.31593	+	4.31593i	0.269220	+	0.269220i	−0.559566	+	0.828786i	$0.689032\pi$
$258$	−2.56936	−	2.56936i	−0.159961	−	0.159961i
$259$			11.6709i			0.725196i
$260$	0.251289	−	6.71923i	0.0155843	−	0.416709i
$261$	−9.42076			−0.583130
$262$	−0.773709	−	0.773709i	−0.0477999	−	0.0477999i
$263$	4.09411	+	4.09411i	0.252453	+	0.252453i	0.821976	−	0.569522i	$-0.192872\pi$
$263$	4.09411	+	4.09411i	0.252453	+	0.252453i	−0.569522	+	0.821976i	$0.692872\pi$
$264$	−0.403497			−0.0248335
$265$	0.174445	−	4.66451i	0.0107161	−	0.286538i
$266$	−19.7942			−1.21366
$267$	4.40639	−	4.40639i	0.269667	−	0.269667i
$268$	4.60755	+	4.60755i	0.281451	+	0.281451i
$269$		−	30.5379i		−	1.86193i	−0.365111	−	0.930964i	$-0.618969\pi$
$269$		−	30.5379i		−	1.86193i	0.365111	−	0.930964i	$-0.381031\pi$
$270$	1.63913	−	1.52094i	0.0997540	−	0.0925617i
$271$	−14.3414			−0.871178			−0.435589	−	0.900146i	$-0.643460\pi$
$271$	−14.3414			−0.871178			−0.435589	+	0.900146i	$0.643460\pi$
$272$	4.95666	−	4.95666i	0.300542	−	0.300542i
$273$	−8.08153	−	8.08153i	−0.489116	−	0.489116i
$274$	19.6791			1.18885
$275$	−2.01185	−	0.150691i	−0.121319	−	0.00908700i
$276$	4.65445	+	1.15590i	0.280165	+	0.0695772i
$277$	2.49148	+	2.49148i	0.149698	+	0.149698i	0.777983	−	0.628285i	$-0.216243\pi$
$277$	2.49148	+	2.49148i	0.149698	+	0.149698i	−0.628285	+	0.777983i	$0.716243\pi$
$278$	14.0107	−	14.0107i	0.840304	−	0.840304i
$279$		−	3.33683i		−	0.199771i
$280$	6.22992	−	5.78074i	0.372309	−	0.345465i
$281$			24.3745i			1.45406i	0.686604	+	0.727031i	$0.259100\pi$
$281$			24.3745i			1.45406i	−0.686604	+	0.727031i	$0.740900\pi$
$282$	8.64413	+	8.64413i	0.514751	+	0.514751i
$283$	1.55632	+	1.55632i	0.0925135	+	0.0925135i	0.751849	−	0.659335i	$-0.229162\pi$
$283$	1.55632	+	1.55632i	0.0925135	+	0.0925135i	−0.659335	+	0.751849i	$0.729162\pi$
$284$		−	5.45281i		−	0.323565i
$285$	11.6372	+	0.435213i	0.689328	+	0.0257798i
$286$		−	1.21333i		−	0.0717457i
$287$	−15.3159	+	15.3159i	−0.904070	+	0.904070i
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$		−	32.1370i		−	1.89041i
$290$	21.0507	+	0.787264i	1.23614	+	0.0462298i
$291$		−	11.6762i		−	0.684470i
$292$	1.06175	+	1.06175i	0.0621343	+	0.0621343i
$293$	−16.6999	−	16.6999i	−0.975619	−	0.975619i	0.0240909	−	0.999710i	$-0.492331\pi$
$293$	−16.6999	−	16.6999i	−0.975619	−	0.975619i	−0.999710	+	0.0240909i	$0.992331\pi$
$294$		−	7.44578i		−	0.434247i
$295$	−21.9648	+	20.3812i	−1.27884	+	1.18664i
$296$			3.07068i			0.178480i
$297$	0.285316	−	0.285316i	0.0165557	−	0.0165557i
$298$	−7.87934	−	7.87934i	−0.456438	−	0.456438i
$299$	−3.47584	+	13.9961i	−0.201013	+	0.809414i
$300$	−3.78974	+	3.26158i	−0.218800	+	0.188307i
$301$	13.8105			0.796026
$302$	14.1176	+	14.1176i	0.812375	+	0.812375i
$303$	−5.00944	+	5.00944i	−0.287785	+	0.287785i
$304$	−5.20795			−0.298697
$305$	12.3118	−	11.4241i	0.704970	−	0.654141i
$306$			7.00978i			0.400723i
$307$	2.34796	+	2.34796i	0.134005	+	0.134005i	0.770928	−	0.636923i	$-0.219793\pi$
$307$	2.34796	+	2.34796i	0.134005	+	0.134005i	−0.636923	+	0.770928i	$0.719793\pi$
$308$	1.08442	−	1.08442i	0.0617903	−	0.0617903i
$309$	−9.71622			−0.552737
$310$	−0.278849	+	7.45617i	−0.0158376	+	0.423482i
$311$	12.8558			0.728988			0.364494	−	0.931206i	$-0.381242\pi$
$311$	12.8558			0.728988			0.364494	+	0.931206i	$0.381242\pi$
$312$	−2.12629	−	2.12629i	−0.120378	−	0.120378i
$313$	−3.38173	−	3.38173i	−0.191147	−	0.191147i	0.605045	−	0.796192i	$-0.293155\pi$
$313$	−3.38173	−	3.38173i	−0.191147	−	0.191147i	−0.796192	+	0.605045i	$0.793155\pi$
$314$	−3.45763			−0.195125
$315$	−0.317618	+	8.49282i	−0.0178958	+	0.478516i
$316$			0.383565i			0.0215772i
$317$	16.1019	+	16.1019i	0.904375	+	0.904375i	0.995811	−	0.0914360i	$-0.0291457\pi$
$317$	16.1019	+	16.1019i	0.904375	+	0.904375i	−0.0914360	+	0.995811i	$0.529146\pi$
$318$	−1.47608	−	1.47608i	−0.0827743	−	0.0827743i
$319$	3.80125			0.212829
$320$	1.63913	−	1.52094i	0.0916299	−	0.0850233i
$321$			4.44997i			0.248373i
$322$	−15.6156	+	9.40249i	−0.870222	+	0.523980i
$323$	−25.8141	+	25.8141i	−1.43633	+	1.43633i
$324$		−	1.00000i		−	0.0555556i
$325$	−9.80768	−	11.3959i	−0.544032	−	0.632128i
$326$	0.337320			0.0186824
$327$	−8.97323	+	8.97323i	−0.496221	+	0.496221i
$328$	−4.02970	+	4.02970i	−0.222503	+	0.222503i
$329$	−46.4630			−2.56159
$330$	−0.661382	+	0.613696i	−0.0364079	+	0.0337829i
$331$	11.6757			0.641756			0.320878	−	0.947120i	$-0.396022\pi$
$331$	11.6757			0.641756			0.320878	+	0.947120i	$0.396022\pi$
$332$	−12.3708	+	12.3708i	−0.678934	+	0.678934i
$333$	−2.17130	−	2.17130i	−0.118986	−	0.118986i
$334$			9.10312i			0.498101i
$335$	14.5602	+	0.544528i	0.795508	+	0.0297507i
$336$		−	3.80076i		−	0.207348i
$337$	−10.5109	+	10.5109i	−0.572567	+	0.572567i	−0.932845	−	0.360278i	$-0.882682\pi$
$337$	−10.5109	+	10.5109i	−0.572567	+	0.572567i	0.360278	+	0.932845i	$0.382682\pi$
$338$	−2.79856	+	2.79856i	−0.152221	+	0.152221i
$339$	−12.6784			−0.688597
$340$	0.585786	−	15.6634i	0.0317687	−	0.849467i
$341$			1.34640i			0.0729117i
$342$	3.68258	−	3.68258i	0.199131	−	0.199131i
$343$	1.19805	+	1.19805i	0.0646884	+	0.0646884i
$344$	3.63363			0.195912
$345$	9.38729	−	5.18448i	0.505395	−	0.279123i
$346$	−8.33634			−0.448164
$347$	−17.9614	−	17.9614i	−0.964218	−	0.964218i	0.0351639	−	0.999382i	$-0.488805\pi$
$347$	−17.9614	−	17.9614i	−0.964218	−	0.964218i	−0.999382	+	0.0351639i	$0.988805\pi$
$348$	6.66148	−	6.66148i	0.357093	−	0.357093i
$349$			18.2166i			0.975113i	0.873092	+	0.487556i	$0.162112\pi$
$349$			18.2166i			0.975113i	−0.873092	+	0.487556i	$0.837888\pi$
$350$	1.41944	−	18.9507i	0.0758722	−	1.01296i
$351$	3.00703			0.160504
$352$	0.285316	−	0.285316i	0.0152074	−	0.0152074i
$353$	−13.3386	+	13.3386i	−0.709942	+	0.709942i	−0.966523	−	0.256581i	$-0.917404\pi$
$353$	−13.3386	+	13.3386i	−0.709942	+	0.709942i	0.256581	+	0.966523i	$0.417404\pi$
$354$			13.4003i			0.712220i
$355$	−8.29342	−	8.93784i	−0.440169	−	0.474371i
$356$			6.23158i			0.330273i
$357$	−18.8391	−	18.8391i	−0.997070	−	0.997070i
$358$	−1.96275	+	1.96275i	−0.103735	+	0.103735i
$359$	−23.6679			−1.24915			−0.624573	−	0.780967i	$-0.714727\pi$
$359$	−23.6679			−1.24915			−0.624573	+	0.780967i	$0.714727\pi$
$360$	−0.0835670	+	2.23451i	−0.00440437	+	0.117769i
$361$	8.12277			0.427514
$362$	15.0359	−	15.0359i	0.790269	−	0.790269i
$363$	7.66305	−	7.66305i	0.402206	−	0.402206i
$364$	11.4290			0.599043
$365$	3.35521	+	0.125479i	0.175620	+	0.00656789i
$366$		−	7.51118i		−	0.392616i
$367$	−1.82999	+	1.82999i	−0.0955248	+	0.0955248i	−0.753254	−	0.657729i	$-0.771517\pi$
$367$	−1.82999	+	1.82999i	−0.0955248	+	0.0955248i	0.657729	+	0.753254i	$0.271517\pi$
$368$	−4.10854	+	2.47384i	−0.214172	+	0.128958i
$369$		−	5.69885i		−	0.296670i
$370$	4.67033	+	5.03323i	0.242799	+	0.261665i
$371$	7.93404			0.411915
$372$	2.35950	+	2.35950i	0.122334	+	0.122334i
$373$	4.97536	+	4.97536i	0.257615	+	0.257615i	0.824083	−	0.566469i	$-0.191691\pi$
$373$	4.97536	+	4.97536i	0.257615	+	0.257615i	−0.566469	+	0.824083i	$0.691691\pi$
$374$		−	2.82843i		−	0.146254i
$375$	−1.25117	+	11.1101i	−0.0646102	+	0.573724i
$376$	−12.2247			−0.630438
$377$	20.0313	+	20.0313i	1.03166	+	1.03166i
$378$	2.68754	+	2.68754i	0.138232	+	0.138232i
$379$	−3.53426			−0.181543			−0.0907714	−	0.995872i	$-0.528933\pi$
$379$	−3.53426			−0.181543			−0.0907714	+	0.995872i	$0.528933\pi$
$380$	−8.53649	+	7.92100i	−0.437912	+	0.406339i
$381$	−13.9199			−0.713138
$382$	−11.0264	+	11.0264i	−0.564160	+	0.564160i
$383$	13.8129	+	13.8129i	0.705805	+	0.705805i	0.965650	−	0.259845i	$-0.0836715\pi$
$383$	13.8129	+	13.8129i	0.705805	+	0.705805i	−0.259845	+	0.965650i	$0.583671\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	0.128158	−	3.42683i	0.00653154	−	0.174647i
$386$	−9.89468			−0.503626
$387$	−2.56936	+	2.56936i	−0.130608	+	0.130608i
$388$	8.25631	+	8.25631i	0.419150	+	0.419150i
$389$	−6.63285			−0.336299			−0.168149	−	0.985762i	$-0.553779\pi$
$389$	−6.63285			−0.336299			−0.168149	+	0.985762i	$0.553779\pi$
$390$	−6.71923	−	0.251289i	−0.340242	−	0.0127245i
$391$	−8.10263	+	32.6267i	−0.409768	+	1.65000i
$392$	5.26496	+	5.26496i	0.265921	+	0.265921i
$393$	−0.773709	+	0.773709i	−0.0390284	+	0.0390284i
$394$			7.02162i			0.353744i
$395$	0.583380	+	0.628711i	0.0293530	+	0.0316339i
$396$			0.403497i			0.0202765i
$397$	−6.61498	−	6.61498i	−0.331996	−	0.331996i	0.521348	−	0.853344i	$-0.325429\pi$
$397$	−6.61498	−	6.61498i	−0.331996	−	0.331996i	−0.853344	+	0.521348i	$0.825429\pi$
$398$	9.34856	+	9.34856i	0.468601	+	0.468601i
$399$			19.7942i			0.990948i
$400$	0.373462	−	4.98603i	0.0186731	−	0.249302i
$401$			9.81654i			0.490215i	0.969496	+	0.245107i	$0.0788232\pi$
$401$			9.81654i			0.490215i	−0.969496	+	0.245107i	$0.921177\pi$
$402$	4.60755	−	4.60755i	0.229804	−	0.229804i
$403$	−7.09508	+	7.09508i	−0.353431	+	0.353431i
$404$		−	7.08442i		−	0.352463i
$405$	−1.52094	−	1.63913i	−0.0755763	−	0.0814488i
$406$			35.8060i			1.77702i
$407$	0.876113	+	0.876113i	0.0434273	+	0.0434273i
$408$	−4.95666	−	4.95666i	−0.245391	−	0.245391i
$409$		−	1.62998i		−	0.0805974i	−0.999188	−	0.0402987i	$-0.987169\pi$
$409$		−	1.62998i		−	0.0805974i	0.999188	−	0.0402987i	$-0.0128309\pi$
$410$	−0.476236	+	12.7341i	−0.0235196	+	0.628893i
$411$		−	19.6791i		−	0.970696i
$412$	6.87041	−	6.87041i	0.338481	−	0.338481i
$413$	−36.0140	−	36.0140i	−1.77213	−	1.77213i
$414$	1.15590	−	4.65445i	0.0568096	−	0.228754i
$415$	−1.46200	+	39.0925i	−0.0717666	+	1.91897i
$416$	3.00703			0.147432
$417$	−14.0107	−	14.0107i	−0.686105	−	0.686105i
$418$	−1.48591	+	1.48591i	−0.0726782	+	0.0726782i
$419$	11.2744			0.550791			0.275395	−	0.961331i	$-0.411191\pi$
$419$	11.2744			0.550791			0.275395	+	0.961331i	$0.411191\pi$
$420$	−5.78074	−	6.22992i	−0.282071	−	0.303989i
$421$			16.1033i			0.784825i	0.919789	+	0.392412i	$0.128359\pi$
$421$			16.1033i			0.784825i	−0.919789	+	0.392412i	$0.871641\pi$
$422$	10.1407	+	10.1407i	0.493643	+	0.493643i
$423$	8.64413	−	8.64413i	0.420292	−	0.420292i
$424$	2.08749			0.101377
$425$	−22.8630	−	26.5652i	−1.10902	−	1.28860i
$426$	−5.45281			−0.264189
$427$	20.1866	+	20.1866i	0.976899	+	0.976899i
$428$	−3.14660	−	3.14660i	−0.152097	−	0.152097i
$429$	−1.21333			−0.0585801
$430$	5.95597	−	5.52654i	0.287222	−	0.266513i
$431$			37.5672i			1.80955i	0.425894	+	0.904773i	$0.359960\pi$
$431$			37.5672i			1.80955i	−0.425894	+	0.904773i	$0.640040\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	19.4771	+	19.4771i	0.936012	+	0.936012i	0.998072	−	0.0620607i	$-0.0197672\pi$
$433$	19.4771	+	19.4771i	0.936012	+	0.936012i	−0.0620607	+	0.998072i	$0.519767\pi$
$434$	−12.6825			−0.608779
$435$	0.787264	−	21.0507i	0.0377464	−	1.00931i
$436$		−	12.6901i		−	0.607744i
$437$	21.3971	−	12.8837i	1.02356	−	0.616309i
$438$	1.06175	−	1.06175i	0.0507324	−	0.0507324i
$439$		−	27.5197i		−	1.31344i	−0.754133	−	0.656721i	$-0.771943\pi$
$439$		−	27.5197i		−	1.31344i	0.754133	−	0.656721i	$-0.228057\pi$
$440$	0.0337191	−	0.901617i	0.00160749	−	0.0429829i
$441$	−7.44578			−0.354561
$442$	14.9048	−	14.9048i	0.708951	−	0.708951i
$443$	21.8369	−	21.8369i	1.03750	−	1.03750i	0.0382321	−	0.999269i	$-0.487827\pi$
$443$	21.8369	−	21.8369i	1.03750	−	1.03750i	0.999269	−	0.0382321i	$-0.0121726\pi$
$444$	3.07068			0.145728
$445$	9.47788	+	10.2143i	0.449295	+	0.484206i
$446$	−14.8202			−0.701757
$447$	−7.87934	+	7.87934i	−0.372680	+	0.372680i
$448$	2.68754	+	2.68754i	0.126974	+	0.126974i
$449$			3.81966i			0.180261i	0.995930	+	0.0901306i	$0.0287284\pi$
$449$			3.81966i			0.180261i	−0.995930	+	0.0901306i	$0.971272\pi$
$450$	3.26158	+	3.78974i	0.153752	+	0.178650i
$451$			2.29947i			0.108278i
$452$	8.96499	−	8.96499i	0.421678	−	0.421678i
$453$	14.1176	−	14.1176i	0.663301	−	0.663301i
$454$	−0.552361			−0.0259236
$455$	18.7336	−	17.3829i	0.878244	−	0.814922i
$456$			5.20795i			0.243885i
$457$	19.1698	−	19.1698i	0.896726	−	0.896726i	−0.0984194	−	0.995145i	$-0.531379\pi$
$457$	19.1698	−	19.1698i	0.896726	−	0.896726i	0.995145	+	0.0984194i	$0.0313787\pi$
$458$	−11.3258	−	11.3258i	−0.529218	−	0.529218i
$459$	7.00978			0.327189
$460$	−2.97183	+	10.3038i	−0.138562	+	0.480417i
$461$	−23.5334			−1.09606			−0.548029	−	0.836459i	$-0.684622\pi$
$461$	−23.5334			−1.09606			−0.548029	+	0.836459i	$0.684622\pi$
$462$	−1.08442	−	1.08442i	−0.0504516	−	0.0504516i
$463$	20.0945	−	20.0945i	0.933869	−	0.933869i	−0.0640760	−	0.997945i	$-0.520410\pi$
$463$	20.0945	−	20.0945i	0.933869	−	0.933869i	0.997945	+	0.0640760i	$0.0204100\pi$
$464$			9.42076i			0.437348i
$465$	7.45617	+	0.278849i	0.345771	+	0.0129313i
$466$	−18.5016			−0.857070
$467$	8.34291	−	8.34291i	0.386064	−	0.386064i	−0.487217	−	0.873281i	$-0.661988\pi$
$467$	8.34291	−	8.34291i	0.386064	−	0.386064i	0.873281	+	0.487217i	$0.161988\pi$
$468$	−2.12629	+	2.12629i	−0.0982879	+	0.0982879i
$469$			24.7660i			1.14359i
$470$	−20.0377	+	18.5930i	−0.924272	+	0.857631i
$471$			3.45763i			0.159319i
$472$	−9.47547	−	9.47547i	−0.436144	−	0.436144i
$473$	1.03673	−	1.03673i	0.0476689	−	0.0476689i
$474$	0.383565			0.0176177
$475$	−1.94497	+	25.9670i	−0.0892414	+	1.19145i
$476$	26.6425			1.22116
$477$	−1.47608	+	1.47608i	−0.0675849	+	0.0675849i
$478$	10.4923	−	10.4923i	0.479908	−	0.479908i
$479$	21.0887			0.963565			0.481783	−	0.876291i	$-0.339989\pi$
$479$	21.0887			0.963565			0.481783	+	0.876291i	$0.339989\pi$
$480$	−1.52094	−	1.63913i	−0.0694213	−	0.0748155i
$481$			9.23364i			0.421018i
$482$	6.73270	−	6.73270i	0.306666	−	0.306666i
$483$	9.40249	+	15.6156i	0.427828	+	0.710533i
$484$			10.8372i			0.492600i
$485$	26.0905	+	0.975743i	1.18471	+	0.0443062i
$486$	−1.00000			−0.0453609
$487$	−0.859666	−	0.859666i	−0.0389552	−	0.0389552i	0.687361	−	0.726316i	$-0.258769\pi$
$487$	−0.859666	−	0.859666i	−0.0389552	−	0.0389552i	−0.726316	+	0.687361i	$0.758769\pi$
$488$	5.31121	+	5.31121i	0.240427	+	0.240427i
$489$		−	0.337320i		−	0.0152541i
$490$	16.6376	+	0.622221i	0.751612	+	0.0281091i
$491$	−27.6182			−1.24639			−0.623197	−	0.782065i	$-0.714166\pi$
$491$	−27.6182			−1.24639			−0.623197	+	0.782065i	$0.714166\pi$
$492$	4.02970	+	4.02970i	0.181673	+	0.181673i
$493$	46.6955	+	46.6955i	2.10306	+	2.10306i
$494$	−15.6605			−0.704598
$495$	0.613696	+	0.661382i	0.0275836	+	0.0297269i
$496$	−3.33683			−0.149828
$497$	14.6547	−	14.6547i	0.657351	−	0.657351i
$498$	12.3708	+	12.3708i	0.554348	+	0.554348i
$499$			18.6771i			0.836101i	0.908424	+	0.418051i	$0.137287\pi$
$499$			18.6771i			0.836101i	−0.908424	+	0.418051i	$0.862713\pi$
$500$	−6.97132	−	8.74075i	−0.311767	−	0.390898i
$501$	9.10312			0.406697
$502$	1.95018	−	1.95018i	0.0870409	−	0.0870409i
$503$	−2.24840	−	2.24840i	−0.100251	−	0.100251i	0.655202	−	0.755453i	$-0.272583\pi$
$503$	−2.24840	−	2.24840i	−0.100251	−	0.100251i	−0.755453	+	0.655202i	$0.772583\pi$
$504$	−3.80076			−0.169299
$505$	−10.7750	−	11.6122i	−0.479481	−	0.516738i
$506$	−0.466404	+	1.87806i	−0.0207342	+	0.0834898i
$507$	2.79856	+	2.79856i	0.124288	+	0.124288i
$508$	9.84286	−	9.84286i	0.436706	−	0.436706i
$509$		−	10.9101i		−	0.483582i	−0.970328	−	0.241791i	$-0.922265\pi$
$509$		−	10.9101i		−	0.483582i	0.970328	−	0.241791i	$-0.0777348\pi$
$510$	−15.6634	−	0.585786i	−0.693587	−	0.0259391i
$511$			5.70700i			0.252463i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−3.68258	−	3.68258i	−0.162590	−	0.162590i
$514$			6.10364i			0.269220i
$515$	0.811956	−	21.7110i	0.0357790	−	0.956699i
$516$		−	3.63363i		−	0.159961i
$517$	−3.48788	+	3.48788i	−0.153397	+	0.153397i
$518$	−8.25259	+	8.25259i	−0.362598	+	0.362598i
$519$			8.33634i			0.365925i
$520$	4.92890	−	4.57353i	0.216147	−	0.200562i
$521$		−	31.7519i		−	1.39108i	−0.718489	−	0.695539i	$-0.755166\pi$
$521$		−	31.7519i		−	1.39108i	0.718489	−	0.695539i	$-0.244834\pi$
$522$	−6.66148	−	6.66148i	−0.291565	−	0.291565i
$523$	−17.6479	−	17.6479i	−0.771687	−	0.771687i	0.206714	−	0.978401i	$-0.433723\pi$
$523$	−17.6479	−	17.6479i	−0.771687	−	0.771687i	−0.978401	+	0.206714i	$0.933723\pi$
$524$		−	1.09419i		−	0.0477999i
$525$	−18.9507	−	1.41944i	−0.827077	−	0.0619494i
$526$			5.78994i			0.252453i
$527$	−16.5395	+	16.5395i	−0.720474	+	0.720474i
$528$	−0.285316	−	0.285316i	−0.0124168	−	0.0124168i
$529$	10.7602	−	20.3278i	0.467834	−	0.883816i
$530$	3.42165	−	3.17495i	0.148627	−	0.137911i
$531$	13.4003			0.581525
$532$	−13.9966	−	13.9966i	−0.606829	−	0.606829i
$533$	−12.1174	+	12.1174i	−0.524864	+	0.524864i
$534$	6.23158			0.269667
$535$	−9.94348	−	0.371871i	−0.429894	−	0.0160774i
$536$			6.51606i			0.281451i
$537$	1.96275	+	1.96275i	0.0846989	+	0.0846989i
$538$	21.5936	−	21.5936i	0.930964	−	0.930964i
$539$	3.00435			0.129407
$540$	2.23451	+	0.0835670i	0.0961578	+	0.00359615i
$541$	33.4617			1.43863			0.719315	−	0.694684i	$-0.244456\pi$
$541$	33.4617			1.43863			0.719315	+	0.694684i	$0.244456\pi$
$542$	−10.1409	−	10.1409i	−0.435589	−	0.435589i
$543$	−15.0359	−	15.0359i	−0.645252	−	0.645252i
$544$	7.00978			0.300542
$545$	−19.3009	−	20.8006i	−0.826758	−	0.890999i
$546$		−	11.4290i		−	0.489116i
$547$	−12.8216	−	12.8216i	−0.548213	−	0.548213i	0.377711	−	0.925924i	$-0.376711\pi$
$547$	−12.8216	−	12.8216i	−0.548213	−	0.548213i	−0.925924	+	0.377711i	$0.876711\pi$
$548$	13.9152	+	13.9152i	0.594427	+	0.594427i
$549$	−7.51118			−0.320569
$550$	−1.31604	−	1.52915i	−0.0561161	−	0.0652031i
$551$		−	49.0629i		−	2.09015i
$552$	2.47384	+	4.10854i	0.105294	+	0.174871i
$553$	−1.03085	+	1.03085i	−0.0438361	+	0.0438361i
$554$			3.52348i			0.149698i
$555$	5.03323	−	4.67033i	0.213649	−	0.198245i
$556$	19.8141			0.840304
$557$	−14.8590	+	14.8590i	−0.629594	+	0.629594i	−0.947966	−	0.318372i	$-0.896864\pi$
$557$	−14.8590	+	14.8590i	−0.629594	+	0.629594i	0.318372	+	0.947966i	$0.396864\pi$
$558$	2.35950	−	2.35950i	0.0998854	−	0.0998854i
$559$	10.9264			0.462139
$560$	8.49282	+	0.317618i	0.358887	+	0.0134218i
$561$	−2.82843			−0.119416
$562$	−17.2354	+	17.2354i	−0.727031	+	0.727031i
$563$	−2.14137	−	2.14137i	−0.0902478	−	0.0902478i	0.660542	−	0.750789i	$-0.270327\pi$
$563$	−2.14137	−	2.14137i	−0.0902478	−	0.0902478i	−0.750789	+	0.660542i	$0.770327\pi$
$564$			12.2247i			0.514751i
$565$	1.05950	−	28.3300i	0.0445734	−	1.19185i
$566$			2.20097i			0.0925135i
$567$	2.68754	−	2.68754i	0.112866	−	0.112866i
$568$	3.85572	−	3.85572i	0.161782	−	0.161782i
$569$	44.6987			1.87387			0.936934	−	0.349506i	$-0.113650\pi$
$569$	44.6987			1.87387			0.936934	+	0.349506i	$0.113650\pi$
$570$	7.92100	+	8.53649i	0.331774	+	0.357554i
$571$			26.7672i			1.12017i	0.828435	+	0.560085i	$0.189232\pi$
$571$			26.7672i			1.12017i	−0.828435	+	0.560085i	$0.810768\pi$
$572$	0.857953	−	0.857953i	0.0358728	−	0.0358728i
$573$	11.0264	+	11.0264i	0.460635	+	0.460635i
$574$	−21.6600			−0.904070
$575$	10.8003	+	21.4092i	0.450403	+	0.892825i
$576$	−1.00000			−0.0416667
$577$	−14.2226	−	14.2226i	−0.592095	−	0.592095i	0.346102	−	0.938197i	$-0.387505\pi$
$577$	−14.2226	−	14.2226i	−0.592095	−	0.592095i	−0.938197	+	0.346102i	$0.887505\pi$
$578$	22.7243	−	22.7243i	0.945207	−	0.945207i
$579$			9.89468i			0.411209i
$580$	14.3284	+	15.4418i	0.594956	+	0.641186i
$581$	−66.4940			−2.75863
$582$	8.25631	−	8.25631i	0.342235	−	0.342235i
$583$	0.595593	−	0.595593i	0.0246669	−	0.0246669i
$584$			1.50154i			0.0621343i
$585$	−0.251289	+	6.71923i	−0.0103895	+	0.277806i
$586$		−	23.6172i		−	0.975619i
$587$	−7.01819	−	7.01819i	−0.289672	−	0.289672i	0.547279	−	0.836950i	$-0.315664\pi$
$587$	−7.01819	−	7.01819i	−0.289672	−	0.289672i	−0.836950	+	0.547279i	$0.815664\pi$
$588$	5.26496	−	5.26496i	0.217123	−	0.217123i
$589$	17.3781			0.716050
$590$	−29.9431	−	1.11983i	−1.23274	−	0.0461025i
$591$	7.02162			0.288831
$592$	−2.17130	+	2.17130i	−0.0892398	+	0.0892398i
$593$	−22.3974	+	22.3974i	−0.919752	+	0.919752i	−0.997011	−	0.0772588i	$-0.975383\pi$
$593$	−22.3974	+	22.3974i	−0.919752	+	0.919752i	0.0772588	+	0.997011i	$0.475383\pi$
$594$	0.403497			0.0165557
$595$	43.6704	−	40.5217i	1.79031	−	1.66123i
$596$		−	11.1431i		−	0.456438i
$597$	9.34856	−	9.34856i	0.382611	−	0.382611i
$598$	−12.3545	+	7.43893i	−0.505214	+	0.304201i
$599$			2.54190i			0.103859i	0.998651	+	0.0519296i	$0.0165371\pi$
$599$			2.54190i			0.103859i	−0.998651	+	0.0519296i	$0.983463\pi$
$600$	−4.98603	−	0.373462i	−0.203554	−	0.0152465i
$601$	−15.8155			−0.645130			−0.322565	−	0.946547i	$-0.604545\pi$
$601$	−15.8155			−0.645130			−0.322565	+	0.946547i	$0.604545\pi$
$602$	9.76553	+	9.76553i	0.398013	+	0.398013i
$603$	−4.60755	−	4.60755i	−0.187634	−	0.187634i
$604$			19.9653i			0.812375i
$605$	16.4828	+	17.7635i	0.670119	+	0.722189i
$606$	−7.08442			−0.287785
$607$	−3.60929	−	3.60929i	−0.146497	−	0.146497i	0.630054	−	0.776551i	$-0.283033\pi$
$607$	−3.60929	−	3.60929i	−0.146497	−	0.146497i	−0.776551	+	0.630054i	$0.783033\pi$
$608$	−3.68258	−	3.68258i	−0.149348	−	0.149348i
$609$	35.8060			1.45093
$610$	16.7838	+	0.627687i	0.679556	+	0.0254143i
$611$	−36.7599			−1.48715
$612$	−4.95666	+	4.95666i	−0.200361	+	0.200361i
$613$	−14.0673	−	14.0673i	−0.568173	−	0.568173i	0.363444	−	0.931616i	$-0.381601\pi$
$613$	−14.0673	−	14.0673i	−0.568173	−	0.568173i	−0.931616	+	0.363444i	$0.881601\pi$
$614$			3.32051i			0.134005i
$615$	12.7341	+	0.476236i	0.513489	+	0.0192037i
$616$	1.53360			0.0617903
$617$	−31.3443	+	31.3443i	−1.26187	+	1.26187i	−0.311688	+	0.950185i	$0.600894\pi$
$617$	−31.3443	+	31.3443i	−1.26187	+	1.26187i	−0.950185	+	0.311688i	$0.899106\pi$
$618$	−6.87041	−	6.87041i	−0.276368	−	0.276368i
$619$	20.0495			0.805857			0.402928	−	0.915232i	$-0.367992\pi$
$619$	20.0495			0.805857			0.402928	+	0.915232i	$0.367992\pi$
$620$	−5.46948	+	5.07513i	−0.219660	+	0.203822i
$621$	−4.65445	−	1.15590i	−0.186777	−	0.0463848i
$622$	9.09045	+	9.09045i	0.364494	+	0.364494i
$623$	−16.7476	+	16.7476i	−0.670980	+	0.670980i
$624$		−	3.00703i		−	0.120378i
$625$	−24.7211	−	3.72419i	−0.988842	−	0.148967i
$626$		−	4.78249i		−	0.191147i
$627$	1.48591	+	1.48591i	0.0593415	+	0.0593415i
$628$	−2.44491	−	2.44491i	−0.0975627	−	0.0975627i
$629$			21.5248i			0.858250i
$630$	−6.22992	+	5.78074i	−0.248206	+	0.230310i
$631$		−	13.0006i		−	0.517544i	−0.965938	−	0.258772i	$-0.916682\pi$
$631$		−	13.0006i		−	0.517544i	0.965938	−	0.258772i	$-0.0833178\pi$
$632$	−0.271221	+	0.271221i	−0.0107886	+	0.0107886i
$633$	10.1407	−	10.1407i	0.403058	−	0.403058i
$634$			22.7716i			0.904375i
$635$	1.16324	−	31.1041i	0.0461620	−	1.23433i
$636$		−	2.08749i		−	0.0827743i
$637$	15.8319	+	15.8319i	0.627283	+	0.627283i
$638$	2.68789	+	2.68789i	0.106415	+	0.106415i
$639$			5.45281i			0.215710i
$640$	2.23451	+	0.0835670i	0.0883266	+	0.00330328i
$641$		−	14.0108i		−	0.553393i	−0.960957	−	0.276696i	$-0.910760\pi$
$641$		−	14.0108i		−	0.553393i	0.960957	−	0.276696i	$-0.0892396\pi$
$642$	−3.14660	+	3.14660i	−0.124187	+	0.124187i
$643$	10.2908	+	10.2908i	0.405829	+	0.405829i	0.880281	−	0.474452i	$-0.157354\pi$
$643$	10.2908	+	10.2908i	0.405829	+	0.405829i	−0.474452	+	0.880281i	$0.657354\pi$
$644$	−17.6904	−	4.39331i	−0.697101	−	0.173121i
$645$	−5.52654	−	5.95597i	−0.217607	−	0.234516i
$646$	−36.5066			−1.43633
$647$	−11.8108	−	11.8108i	−0.464329	−	0.464329i	0.435743	−	0.900071i	$-0.356486\pi$
$647$	−11.8108	−	11.8108i	−0.464329	−	0.464329i	−0.900071	+	0.435743i	$0.856486\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	−5.40700			−0.212243
$650$	1.12301	−	14.9932i	0.0440482	−	0.588080i
$651$			12.6825i			0.497066i
$652$	0.238521	+	0.238521i	0.00934121	+	0.00934121i
$653$	−7.33870	+	7.33870i	−0.287185	+	0.287185i	−0.835966	−	0.548781i	$-0.815092\pi$
$653$	−7.33870	+	7.33870i	−0.287185	+	0.287185i	0.548781	+	0.835966i	$0.315092\pi$
$654$	−12.6901			−0.496221
$655$	−1.66420	−	1.79351i	−0.0650257	−	0.0700784i
$656$	−5.69885			−0.222503
$657$	−1.06175	−	1.06175i	−0.0414229	−	0.0414229i
$658$	−32.8543	−	32.8543i	−1.28079	−	1.28079i
$659$	29.6115			1.15350			0.576750	−	0.816921i	$-0.304321\pi$
$659$	29.6115			1.15350			0.576750	+	0.816921i	$0.304321\pi$
$660$	−0.901617	−	0.0337191i	−0.0350954	−	0.00131251i
$661$			0.177775i			0.00691465i	0.999994	+	0.00345732i	$0.00110050\pi$
$661$			0.177775i			0.00691465i	−0.999994	+	0.00345732i	$0.998899\pi$
$662$	8.25599	+	8.25599i	0.320878	+	0.320878i
$663$	−14.9048	−	14.9048i	−0.578856	−	0.578856i
$664$	−17.4949			−0.678934
$665$	−44.2302	−	1.65414i	−1.71517	−	0.0641448i
$666$		−	3.07068i		−	0.118986i
$667$	−23.3055	−	38.7055i	−0.902392	−	1.49868i
$668$	−6.43688	+	6.43688i	−0.249050	+	0.249050i
$669$			14.8202i			0.572982i
$670$	9.91057	+	10.6806i	0.382879	+	0.412629i
$671$	3.03074			0.117000
$672$	2.68754	−	2.68754i	0.103674	−	0.103674i
$673$	3.91098	−	3.91098i	0.150757	−	0.150757i	−0.627699	−	0.778456i	$-0.716003\pi$
$673$	3.91098	−	3.91098i	0.150757	−	0.150757i	0.778456	+	0.627699i	$0.216003\pi$
$674$	−14.8647			−0.572567
$675$	3.78974	−	3.26158i	0.145867	−	0.125538i
$676$	−3.95776			−0.152221
$677$	31.1105	−	31.1105i	1.19567	−	1.19567i	0.220223	−	0.975450i	$-0.429322\pi$
$677$	31.1105	−	31.1105i	1.19567	−	1.19567i	0.975450	−	0.220223i	$-0.0706784\pi$
$678$	−8.96499	−	8.96499i	−0.344299	−	0.344299i
$679$			44.3784i			1.70309i
$680$	11.4899	−	10.6615i	0.440618	−	0.408849i
$681$			0.552361i			0.0211665i
$682$	−0.952050	+	0.952050i	−0.0364559	+	0.0364559i
$683$	27.1997	−	27.1997i	1.04077	−	1.04077i	0.0416348	−	0.999133i	$-0.486743\pi$
$683$	27.1997	−	27.1997i	1.04077	−	1.04077i	0.999133	−	0.0416348i	$-0.0132566\pi$
$684$	5.20795			0.199131
$685$	43.9730	+	1.64452i	1.68012	+	0.0628339i
$686$			1.69429i			0.0646884i
$687$	−11.3258	+	11.3258i	−0.432104	+	0.432104i
$688$	2.56936	+	2.56936i	0.0979560	+	0.0979560i
$689$	6.27715			0.239140
$690$	10.3038	+	2.97183i	0.392259	+	0.113136i
$691$	31.8947			1.21333			0.606666	−	0.794957i	$-0.292507\pi$
$691$	31.8947			1.21333			0.606666	+	0.794957i	$0.292507\pi$
$692$	−5.89468	−	5.89468i	−0.224082	−	0.224082i
$693$	−1.08442	+	1.08442i	−0.0411936	+	0.0411936i
$694$		−	25.4012i		−	0.964218i
$695$	32.4777	−	30.1361i	1.23195	−	1.14313i
$696$	9.42076			0.357093
$697$	−28.2473	+	28.2473i	−1.06994	+	1.06994i
$698$	−12.8811	+	12.8811i	−0.487556	+	0.487556i
$699$			18.5016i			0.699795i
$700$	14.4039	−	12.3965i	0.544415	−	0.468543i
$701$		−	39.2405i		−	1.48209i	−0.671454	−	0.741046i	$-0.734330\pi$
$701$		−	39.2405i		−	1.48209i	0.671454	−	0.741046i	$-0.265670\pi$
$702$	2.12629	+	2.12629i	0.0802518	+	0.0802518i
$703$	11.3080	−	11.3080i	0.426490	−	0.426490i
$704$	0.403497			0.0152074
$705$	18.5930	+	20.0377i	0.700253	+	0.754665i
$706$	−18.8636			−0.709942
$707$	19.0397	−	19.0397i	0.716061	−	0.716061i
$708$	−9.47547	+	9.47547i	−0.356110	+	0.356110i
$709$	−19.6493			−0.737944			−0.368972	−	0.929440i	$-0.620290\pi$
$709$	−19.6493			−0.737944			−0.368972	+	0.929440i	$0.620290\pi$
$710$	0.455675	−	12.1843i	0.0171012	−	0.457270i
$711$		−	0.383565i		−	0.0143848i
$712$	−4.40639	+	4.40639i	−0.165137	+	0.165137i
$713$	13.7095	−	8.25480i	0.513425	−	0.309145i
$714$		−	26.6425i		−	0.997070i
$715$	0.101394	−	2.71119i	0.00379193	−	0.101393i
$716$	−2.77575			−0.103735
$717$	−10.4923	−	10.4923i	−0.391843	−	0.391843i
$718$	−16.7358	−	16.7358i	−0.624573	−	0.624573i
$719$			42.4908i			1.58464i	0.610105	+	0.792321i	$0.291127\pi$
$719$			42.4908i			1.58464i	−0.610105	+	0.792321i	$0.708873\pi$
$720$	−1.63913	+	1.52094i	−0.0610866	+	0.0566822i
$721$	36.9290			1.37531
$722$	5.74366	+	5.74366i	0.213757	+	0.213757i
$723$	−6.73270	−	6.73270i	−0.250392	−	0.250392i
$724$	21.2640			0.790269
$725$	46.9722	+	3.51829i	1.74450	+	0.130666i
$726$	10.8372			0.402206
$727$	28.3443	−	28.3443i	1.05123	−	1.05123i	0.0526167	−	0.998615i	$-0.483244\pi$
$727$	28.3443	−	28.3443i	1.05123	−	1.05123i	0.998615	−	0.0526167i	$-0.0167562\pi$
$728$	8.08153	+	8.08153i	0.299521	+	0.299521i
$729$			1.00000i			0.0370370i
$730$	2.28376	+	2.46122i	0.0845258	+	0.0910937i
$731$	25.4709			0.942076
$732$	5.31121	−	5.31121i	0.196308	−	0.196308i
$733$	−35.1881	−	35.1881i	−1.29970	−	1.29970i	−0.928587	−	0.371114i	$-0.878976\pi$
$733$	−35.1881	−	35.1881i	−1.29970	−	1.29970i	−0.371114	−	0.928587i	$-0.621024\pi$
$734$	−2.58800			−0.0955248
$735$	0.622221	−	16.6376i	0.0229510	−	0.613688i
$736$	−4.65445	−	1.15590i	−0.171565	−	0.0426072i
$737$	1.85913	+	1.85913i	0.0684821	+	0.0684821i
$738$	4.02970	−	4.02970i	0.148335	−	0.148335i
$739$		−	7.24476i		−	0.266503i	−0.991082	−	0.133251i	$-0.957458\pi$
$739$		−	7.24476i		−	0.266503i	0.991082	−	0.133251i	$-0.0425417\pi$
$740$	−0.256608	+	6.86145i	−0.00943308	+	0.252232i
$741$			15.6605i			0.575302i
$742$	5.61022	+	5.61022i	0.205957	+	0.205957i
$743$	−38.2888	−	38.2888i	−1.40468	−	1.40468i	−0.784309	−	0.620370i	$-0.786983\pi$
$743$	−38.2888	−	38.2888i	−1.40468	−	1.40468i	−0.620370	−	0.784309i	$-0.713017\pi$
$744$			3.33683i			0.122334i
$745$	−16.9480	−	18.2649i	−0.620926	−	0.669173i
$746$			7.03623i			0.257615i
$747$	12.3708	−	12.3708i	0.452623	−	0.452623i
$748$	2.00000	−	2.00000i	0.0731272	−	0.0731272i
$749$		−	16.9133i		−	0.617997i
$750$	−8.74075	+	6.97132i	−0.319167	+	0.254557i
$751$		−	24.3210i		−	0.887484i	−0.896155	−	0.443742i	$-0.853651\pi$
$751$		−	24.3210i		−	0.887484i	0.896155	−	0.443742i	$-0.146349\pi$
$752$	−8.64413	−	8.64413i	−0.315219	−	0.315219i
$753$	−1.95018	−	1.95018i	−0.0710686	−	0.0710686i
$754$			28.3285i			1.03166i
$755$	30.3660	+	32.7256i	1.10513	+	1.19101i
$756$			3.80076i			0.138232i
$757$	26.9257	−	26.9257i	0.978630	−	0.978630i	−0.0211465	−	0.999776i	$-0.506732\pi$
$757$	26.9257	−	26.9257i	0.978630	−	0.978630i	0.999776	+	0.0211465i	$0.00673165\pi$
$758$	−2.49910	−	2.49910i	−0.0907714	−	0.0907714i
$759$	1.87806	+	0.466404i	0.0681691	+	0.0169294i
$760$	−11.6372	−	0.435213i	−0.422126	−	0.0157868i
$761$	−6.15795			−0.223226			−0.111613	−	0.993752i	$-0.535602\pi$
$761$	−6.15795			−0.223226			−0.111613	+	0.993752i	$0.535602\pi$
$762$	−9.84286	−	9.84286i	−0.356569	−	0.356569i
$763$	34.1051	−	34.1051i	1.23469	−	1.23469i
$764$	−15.5937			−0.564160
$765$	−0.585786	+	15.6634i	−0.0211792	+	0.566311i
$766$			19.5344i			0.705805i
$767$	−28.4931	−	28.4931i	−1.02882	−	1.02882i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	23.1519			0.834877			0.417439	−	0.908705i	$-0.362928\pi$
$769$	23.1519			0.834877			0.417439	+	0.908705i	$0.362928\pi$
$770$	2.51376	−	2.33251i	0.0905895	−	0.0840579i
$771$	6.10364			0.219817
$772$	−6.99660	−	6.99660i	−0.251813	−	0.251813i
$773$	7.51233	+	7.51233i	0.270200	+	0.270200i	0.829181	−	0.558981i	$-0.188807\pi$
$773$	7.51233	+	7.51233i	0.270200	+	0.270200i	−0.558981	+	0.829181i	$0.688807\pi$
$774$	−3.63363			−0.130608
$775$	−1.24618	+	16.6375i	−0.0447641

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.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(1.52094 + 1.63913i) q^{5} +1.00000 q^{6} +(-2.68754 + 2.68754i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(1.52094 + 1.63913i) q^{5} +1.00000 q^{6} +(-2.68754 + 2.68754i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(-0.0835670 + 2.23451i) q^{10} +0.403497i q^{11} +(0.707107 + 0.707107i) q^{12} +(-2.12629 + 2.12629i) q^{13} -3.80076 q^{14} +(2.23451 + 0.0835670i) q^{15} -1.00000 q^{16} +(-4.95666 + 4.95666i) q^{17} +(0.707107 - 0.707107i) q^{18} +5.20795 q^{19} +(-1.63913 + 1.52094i) q^{20} +3.80076i q^{21} +(-0.285316 + 0.285316i) q^{22} +(4.10854 - 2.47384i) q^{23} +1.00000i q^{24} +(-0.373462 + 4.98603i) q^{25} -3.00703 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.68754 - 2.68754i) q^{28} -9.42076i q^{29} +(1.52094 + 1.63913i) q^{30} +3.33683 q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.285316 + 0.285316i) q^{33} -7.00978 q^{34} +(-8.49282 - 0.317618i) q^{35} +1.00000 q^{36} +(2.17130 - 2.17130i) q^{37} +(3.68258 + 3.68258i) q^{38} +3.00703i q^{39} +(-2.23451 - 0.0835670i) q^{40} +5.69885 q^{41} +(-2.68754 + 2.68754i) q^{42} +(-2.56936 - 2.56936i) q^{43} -0.403497 q^{44} +(1.63913 - 1.52094i) q^{45} +(4.65445 + 1.15590i) q^{46} +(8.64413 + 8.64413i) q^{47} +(-0.707107 + 0.707107i) q^{48} -7.44578i q^{49} +(-3.78974 + 3.26158i) q^{50} +7.00978i q^{51} +(-2.12629 - 2.12629i) q^{52} +(-1.47608 - 1.47608i) q^{53} -1.00000i q^{54} +(-0.661382 + 0.613696i) q^{55} -3.80076i q^{56} +(3.68258 - 3.68258i) q^{57} +(6.66148 - 6.66148i) q^{58} +13.4003i q^{59} +(-0.0835670 + 2.23451i) q^{60} -7.51118i q^{61} +(2.35950 + 2.35950i) q^{62} +(2.68754 + 2.68754i) q^{63} -1.00000i q^{64} +(-6.71923 - 0.251289i) q^{65} +0.403497i q^{66} +(4.60755 - 4.60755i) q^{67} +(-4.95666 - 4.95666i) q^{68} +(1.15590 - 4.65445i) q^{69} +(-5.78074 - 6.22992i) q^{70} -5.45281 q^{71} +(0.707107 + 0.707107i) q^{72} +(1.06175 - 1.06175i) q^{73} +3.07068 q^{74} +(3.26158 + 3.78974i) q^{75} +5.20795i q^{76} +(-1.08442 - 1.08442i) q^{77} +(-2.12629 + 2.12629i) q^{78} +0.383565 q^{79} +(-1.52094 - 1.63913i) q^{80} -1.00000 q^{81} +(4.02970 + 4.02970i) q^{82} +(12.3708 + 12.3708i) q^{83} -3.80076 q^{84} +(-15.6634 - 0.585786i) q^{85} -3.63363i q^{86} +(-6.66148 - 6.66148i) q^{87} +(-0.285316 - 0.285316i) q^{88} +6.23158 q^{89} +(2.23451 + 0.0835670i) q^{90} -11.4290i q^{91} +(2.47384 + 4.10854i) q^{92} +(2.35950 - 2.35950i) q^{93} +12.2247i q^{94} +(7.92100 + 8.53649i) q^{95} -1.00000 q^{96} +(8.25631 - 8.25631i) q^{97} +(5.26496 - 5.26496i) q^{98} +0.403497 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{6}+O(q^{10}) \) 24 * q + 24 * q^6	\( 24 q + 24 q^{6} + 16 q^{13} - 24 q^{16} + 16 q^{23} - 16 q^{25} + 16 q^{31} + 24 q^{36} + 8 q^{46} + 40 q^{47} - 8 q^{50} + 16 q^{52} - 56 q^{55} - 16 q^{58} - 8 q^{62} + 32 q^{70} + 64 q^{71} - 16 q^{73} + 32 q^{75} + 16 q^{77} + 16 q^{78} - 24 q^{81} + 24 q^{82} - 48 q^{85} + 16 q^{87} + 16 q^{92} - 8 q^{93} + 24 q^{95} - 24 q^{96}+O(q^{100}) \) 24 * q + 24 * q^6 + 16 * q^13 - 24 * q^16 + 16 * q^23 - 16 * q^25 + 16 * q^31 + 24 * q^36 + 8 * q^46 + 40 * q^47 - 8 * q^50 + 16 * q^52 - 56 * q^55 - 16 * q^58 - 8 * q^62 + 32 * q^70 + 64 * q^71 - 16 * q^73 + 32 * q^75 + 16 * q^77 + 16 * q^78 - 24 * q^81 + 24 * q^82 - 48 * q^85 + 16 * q^87 + 16 * q^92 - 8 * q^93 + 24 * q^95 - 24 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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