LMFDB - Embedded newform 690.2.j.b.367.3

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			367.3
Character	$\chi$	$=$	690.367
Dual form			690.2.j.b.643.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-0.597287 - 2.15482i) q^{5} +1.00000 q^{6} +(1.47923 - 1.47923i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-0.597287 - 2.15482i) q^{5} +1.00000 q^{6} +(1.47923 - 1.47923i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +(-1.10134 + 1.94603i) q^{10} -0.912381i q^{11} +(-0.707107 - 0.707107i) q^{12} +(-1.90626 + 1.90626i) q^{13} -2.09194 q^{14} +(1.94603 + 1.10134i) q^{15} -1.00000 q^{16} +(2.19207 - 2.19207i) q^{17} +(-0.707107 + 0.707107i) q^{18} -5.16113 q^{19} +(2.15482 - 0.597287i) q^{20} +2.09194i q^{21} +(-0.645151 + 0.645151i) q^{22} +(4.55360 + 1.50490i) q^{23} +1.00000i q^{24} +(-4.28650 + 2.57409i) q^{25} +2.69587 q^{26} +(0.707107 + 0.707107i) q^{27} +(1.47923 + 1.47923i) q^{28} -8.27544i q^{29} +(-0.597287 - 2.15482i) q^{30} -5.45970 q^{31} +(0.707107 + 0.707107i) q^{32} +(0.645151 + 0.645151i) q^{33} -3.10005 q^{34} +(-4.07099 - 2.30394i) q^{35} +1.00000 q^{36} +(3.73458 - 3.73458i) q^{37} +(3.64947 + 3.64947i) q^{38} -2.69587i q^{39} +(-1.94603 - 1.10134i) q^{40} -12.1968 q^{41} +(1.47923 - 1.47923i) q^{42} +(-0.0783063 - 0.0783063i) q^{43} +0.912381 q^{44} +(-2.15482 + 0.597287i) q^{45} +(-2.15576 - 4.28401i) q^{46} +(-4.92197 - 4.92197i) q^{47} +(0.707107 - 0.707107i) q^{48} +2.62378i q^{49} +(4.85117 + 1.21085i) q^{50} +3.10005i q^{51} +(-1.90626 - 1.90626i) q^{52} +(-8.84686 - 8.84686i) q^{53} -1.00000i q^{54} +(-1.96602 + 0.544954i) q^{55} -2.09194i q^{56} +(3.64947 - 3.64947i) q^{57} +(-5.85162 + 5.85162i) q^{58} -5.65776i q^{59} +(-1.10134 + 1.94603i) q^{60} -9.70810i q^{61} +(3.86059 + 3.86059i) q^{62} +(-1.47923 - 1.47923i) q^{63} -1.00000i q^{64} +(5.24624 + 2.96907i) q^{65} -0.912381i q^{66} +(5.22443 - 5.22443i) q^{67} +(2.19207 + 2.19207i) q^{68} +(-4.28401 + 2.15576i) q^{69} +(1.24949 + 4.50776i) q^{70} +10.3196 q^{71} +(-0.707107 - 0.707107i) q^{72} +(-8.97067 + 8.97067i) q^{73} -5.28150 q^{74} +(1.21085 - 4.85117i) q^{75} -5.16113i q^{76} +(-1.34962 - 1.34962i) q^{77} +(-1.90626 + 1.90626i) q^{78} -13.2521 q^{79} +(0.597287 + 2.15482i) q^{80} -1.00000 q^{81} +(8.62442 + 8.62442i) q^{82} +(8.86710 + 8.86710i) q^{83} -2.09194 q^{84} +(-6.03280 - 3.41421i) q^{85} +0.110742i q^{86} +(5.85162 + 5.85162i) q^{87} +(-0.645151 - 0.645151i) q^{88} +0.837888 q^{89} +(1.94603 + 1.10134i) q^{90} +5.63959i q^{91} +(-1.50490 + 4.55360i) q^{92} +(3.86059 - 3.86059i) q^{93} +6.96072i q^{94} +(3.08268 + 11.1213i) q^{95} -1.00000 q^{96} +(0.302433 - 0.302433i) q^{97} +(1.85529 - 1.85529i) q^{98} -0.912381 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
$5$	−0.597287	−	2.15482i	−0.267115	−	0.963665i
$5$	−0.597287	−	2.15482i	−0.267115	−	0.963665i
$6$	1.00000			0.408248
$7$	1.47923	−	1.47923i	0.559095	−	0.559095i	−0.369955	−	0.929050i	$-0.620627\pi$
$7$	1.47923	−	1.47923i	0.559095	−	0.559095i	0.929050	+	0.369955i	$0.120627\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		−	1.00000i		−	0.333333i
$10$	−1.10134	+	1.94603i	−0.348275	+	0.615390i
$11$		−	0.912381i		−	0.275093i	−0.990495	−	0.137547i	$-0.956078\pi$
$11$		−	0.912381i		−	0.275093i	0.990495	−	0.137547i	$-0.0439217\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	−1.90626	+	1.90626i	−0.528703	+	0.528703i	−0.920185	−	0.391483i	$-0.871962\pi$
$13$	−1.90626	+	1.90626i	−0.528703	+	0.528703i	0.391483	+	0.920185i	$0.371962\pi$
$14$	−2.09194			−0.559095
$15$	1.94603	+	1.10134i	0.502464	+	0.284365i
$16$	−1.00000			−0.250000
$17$	2.19207	−	2.19207i	0.531654	−	0.531654i	−0.389410	−	0.921064i	$-0.627321\pi$
$17$	2.19207	−	2.19207i	0.531654	−	0.531654i	0.921064	+	0.389410i	$0.127321\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	−5.16113			−1.18405			−0.592023	−	0.805921i	$-0.701670\pi$
$19$	−5.16113			−1.18405			−0.592023	+	0.805921i	$0.701670\pi$
$20$	2.15482	−	0.597287i	0.481832	−	0.133558i
$21$			2.09194i			0.456499i
$22$	−0.645151	+	0.645151i	−0.137547	+	0.137547i
$23$	4.55360	+	1.50490i	0.949491	+	0.313794i
$23$	4.55360	+	1.50490i	0.949491	+	0.313794i
$24$			1.00000i			0.204124i
$25$	−4.28650	+	2.57409i	−0.857299	+	0.514819i
$26$	2.69587			0.528703
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	1.47923	+	1.47923i	0.279547	+	0.279547i
$29$		−	8.27544i		−	1.53671i	−0.640023	−	0.768355i	$-0.721075\pi$
$29$		−	8.27544i		−	1.53671i	0.640023	−	0.768355i	$-0.278925\pi$
$30$	−0.597287	−	2.15482i	−0.109049	−	0.393414i
$31$	−5.45970			−0.980591			−0.490295	−	0.871556i	$-0.663111\pi$
$31$	−5.45970			−0.980591			−0.490295	+	0.871556i	$0.663111\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	0.645151	+	0.645151i	0.112306	+	0.112306i
$34$	−3.10005			−0.531654
$35$	−4.07099	−	2.30394i	−0.688123	−	0.389437i
$36$	1.00000			0.166667
$37$	3.73458	−	3.73458i	0.613962	−	0.613962i	−0.330014	−	0.943976i	$-0.607054\pi$
$37$	3.73458	−	3.73458i	0.613962	−	0.613962i	0.943976	+	0.330014i	$0.107054\pi$
$38$	3.64947	+	3.64947i	0.592023	+	0.592023i
$39$		−	2.69587i		−	0.431684i
$40$	−1.94603	−	1.10134i	−0.307695	−	0.174137i
$41$	−12.1968			−1.90482			−0.952408	−	0.304826i	$-0.901402\pi$
$41$	−12.1968			−1.90482			−0.952408	+	0.304826i	$0.901402\pi$
$42$	1.47923	−	1.47923i	0.228250	−	0.228250i
$43$	−0.0783063	−	0.0783063i	−0.0119416	−	0.0119416i	0.701111	−	0.713052i	$-0.252688\pi$
$43$	−0.0783063	−	0.0783063i	−0.0119416	−	0.0119416i	−0.713052	+	0.701111i	$0.752688\pi$
$44$	0.912381			0.137547
$45$	−2.15482	+	0.597287i	−0.321222	+	0.0890384i
$46$	−2.15576	−	4.28401i	−0.317849	−	0.631642i
$47$	−4.92197	−	4.92197i	−0.717943	−	0.717943i	0.250241	−	0.968184i	$-0.419490\pi$
$47$	−4.92197	−	4.92197i	−0.717943	−	0.717943i	−0.968184	+	0.250241i	$0.919490\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$			2.62378i			0.374826i
$50$	4.85117	+	1.21085i	0.686059	+	0.171240i
$51$			3.10005i			0.434094i
$52$	−1.90626	−	1.90626i	−0.264351	−	0.264351i
$53$	−8.84686	−	8.84686i	−1.21521	−	1.21521i	−0.969290	−	0.245919i	$-0.920910\pi$
$53$	−8.84686	−	8.84686i	−1.21521	−	1.21521i	−0.245919	−	0.969290i	$-0.579090\pi$
$54$		−	1.00000i		−	0.136083i
$55$	−1.96602	+	0.544954i	−0.265098	+	0.0734816i
$56$		−	2.09194i		−	0.279547i
$57$	3.64947	−	3.64947i	0.483385	−	0.483385i
$58$	−5.85162	+	5.85162i	−0.768355	+	0.768355i
$59$		−	5.65776i		−	0.736577i	−0.929711	−	0.368289i	$-0.879944\pi$
$59$		−	5.65776i		−	0.736577i	0.929711	−	0.368289i	$-0.120056\pi$
$60$	−1.10134	+	1.94603i	−0.142183	+	0.251232i
$61$		−	9.70810i		−	1.24299i	−0.783416	−	0.621497i	$-0.786525\pi$
$61$		−	9.70810i		−	1.24299i	0.783416	−	0.621497i	$-0.213475\pi$
$62$	3.86059	+	3.86059i	0.490295	+	0.490295i
$63$	−1.47923	−	1.47923i	−0.186365	−	0.186365i
$64$		−	1.00000i		−	0.125000i
$65$	5.24624	+	2.96907i	0.650717	+	0.368268i
$66$		−	0.912381i		−	0.112306i
$67$	5.22443	−	5.22443i	0.638265	−	0.638265i	−0.311862	−	0.950127i	$-0.600953\pi$
$67$	5.22443	−	5.22443i	0.638265	−	0.638265i	0.950127	+	0.311862i	$0.100953\pi$
$68$	2.19207	+	2.19207i	0.265827	+	0.265827i
$69$	−4.28401	+	2.15576i	−0.515734	+	0.259522i
$70$	1.24949	+	4.50776i	0.149343	+	0.538780i
$71$	10.3196			1.22472			0.612358	−	0.790580i	$-0.290221\pi$
$71$	10.3196			1.22472			0.612358	+	0.790580i	$0.290221\pi$
$72$	−0.707107	−	0.707107i	−0.0833333	−	0.0833333i
$73$	−8.97067	+	8.97067i	−1.04994	+	1.04994i	−0.0512515	+	0.998686i	$0.516321\pi$
$73$	−8.97067	+	8.97067i	−1.04994	+	1.04994i	−0.998686	+	0.0512515i	$0.983679\pi$
$74$	−5.28150			−0.613962
$75$	1.21085	−	4.85117i	0.139817	−	0.560165i
$76$		−	5.16113i		−	0.592023i
$77$	−1.34962	−	1.34962i	−0.153803	−	0.153803i
$78$	−1.90626	+	1.90626i	−0.215842	+	0.215842i
$79$	−13.2521			−1.49098			−0.745489	−	0.666518i	$-0.767784\pi$
$79$	−13.2521			−1.49098			−0.745489	+	0.666518i	$0.767784\pi$
$80$	0.597287	+	2.15482i	0.0667788	+	0.240916i
$81$	−1.00000			−0.111111
$82$	8.62442	+	8.62442i	0.952408	+	0.952408i
$83$	8.86710	+	8.86710i	0.973290	+	0.973290i	0.999652	−	0.0263622i	$-0.00839232\pi$
$83$	8.86710	+	8.86710i	0.973290	+	0.973290i	−0.0263622	+	0.999652i	$0.508392\pi$
$84$	−2.09194			−0.228250
$85$	−6.03280	−	3.41421i	−0.654349	−	0.370323i
$86$			0.110742i			0.0119416i
$87$	5.85162	+	5.85162i	0.627360	+	0.627360i
$88$	−0.645151	−	0.645151i	−0.0687733	−	0.0687733i
$89$	0.837888			0.0888160			0.0444080	−	0.999013i	$-0.485860\pi$
$89$	0.837888			0.0888160			0.0444080	+	0.999013i	$0.485860\pi$
$90$	1.94603	+	1.10134i	0.205130	+	0.116092i
$91$			5.63959i			0.591190i
$92$	−1.50490	+	4.55360i	−0.156897	+	0.474746i
$93$	3.86059	−	3.86059i	0.400324	−	0.400324i
$94$			6.96072i			0.717943i
$95$	3.08268	+	11.1213i	0.316276	+	1.14102i
$96$	−1.00000			−0.102062
$97$	0.302433	−	0.302433i	0.0307074	−	0.0307074i	−0.691586	−	0.722294i	$-0.743088\pi$
$97$	0.302433	−	0.302433i	0.0307074	−	0.0307074i	0.722294	+	0.691586i	$0.243088\pi$
$98$	1.85529	−	1.85529i	0.187413	−	0.187413i
$99$	−0.912381			−0.0916978
$100$	−2.57409	−	4.28650i	−0.257409	−	0.428650i
$101$	−7.34962			−0.731314			−0.365657	−	0.930750i	$-0.619156\pi$
$101$	−7.34962			−0.731314			−0.365657	+	0.930750i	$0.619156\pi$
$102$	2.19207	−	2.19207i	0.217047	−	0.217047i
$103$	7.10380	+	7.10380i	0.699959	+	0.699959i	0.964401	−	0.264443i	$-0.0851880\pi$
$103$	7.10380	+	7.10380i	0.699959	+	0.699959i	−0.264443	+	0.964401i	$0.585188\pi$
$104$			2.69587i			0.264351i
$105$	4.50776	−	1.24949i	0.439912	−	0.121938i
$106$			12.5113i			1.21521i
$107$	8.43368	−	8.43368i	0.815315	−	0.815315i	−0.170110	−	0.985425i	$-0.554412\pi$
$107$	8.43368	−	8.43368i	0.815315	−	0.815315i	0.985425	+	0.170110i	$0.0544124\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	−1.62328			−0.155482			−0.0777411	−	0.996974i	$-0.524771\pi$
$109$	−1.62328			−0.155482			−0.0777411	+	0.996974i	$0.524771\pi$
$110$	1.77552	+	1.00484i	0.169290	+	0.0958081i
$111$			5.28150i			0.501298i
$112$	−1.47923	+	1.47923i	−0.139774	+	0.139774i
$113$	−0.871735	−	0.871735i	−0.0820059	−	0.0820059i	0.664914	−	0.746920i	$-0.268468\pi$
$113$	−0.871735	−	0.871735i	−0.0820059	−	0.0820059i	−0.746920	+	0.664914i	$0.768468\pi$
$114$	−5.16113			−0.483385
$115$	0.522984	−	10.7110i	0.0487685	−	0.998810i
$116$	8.27544			0.768355
$117$	1.90626	+	1.90626i	0.176234	+	0.176234i
$118$	−4.00064	+	4.00064i	−0.368289	+	0.368289i
$119$		−	6.48512i		−	0.594490i
$120$	2.15482	−	0.597287i	0.196707	−	0.0545246i
$121$	10.1676			0.924324
$122$	−6.86466	+	6.86466i	−0.621497	+	0.621497i
$123$	8.62442	−	8.62442i	0.777638	−	0.777638i
$124$		−	5.45970i		−	0.490295i
$125$	8.10698	+	7.69915i	0.725110	+	0.688633i
$126$			2.09194i			0.186365i
$127$	8.50911	+	8.50911i	0.755062	+	0.755062i	0.975419	−	0.220357i	$-0.0707224\pi$
$127$	8.50911	+	8.50911i	0.755062	+	0.755062i	−0.220357	+	0.975419i	$0.570722\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	0.110742			0.00975027
$130$	−1.61021	−	5.80910i	−0.141224	−	0.509492i
$131$	−0.782944			−0.0684061			−0.0342030	−	0.999415i	$-0.510889\pi$
$131$	−0.782944			−0.0684061			−0.0342030	+	0.999415i	$0.510889\pi$
$132$	−0.645151	+	0.645151i	−0.0561532	+	0.0561532i
$133$	−7.63448	+	7.63448i	−0.661994	+	0.661994i
$134$	−7.38845			−0.638265
$135$	1.10134	−	1.94603i	0.0947884	−	0.167488i
$136$		−	3.10005i		−	0.265827i
$137$	−7.97847	+	7.97847i	−0.681647	+	0.681647i	−0.960371	−	0.278724i	$-0.910088\pi$
$137$	−7.97847	+	7.97847i	−0.681647	+	0.681647i	0.278724	+	0.960371i	$0.410088\pi$
$138$	4.55360	+	1.50490i	0.387628	+	0.128106i
$139$		−	5.31355i		−	0.450689i	−0.974279	−	0.225345i	$-0.927649\pi$
$139$		−	5.31355i		−	0.450689i	0.974279	−	0.225345i	$-0.0723508\pi$
$140$	2.30394	−	4.07099i	0.194719	−	0.344061i
$141$	6.96072			0.586198
$142$	−7.29709	−	7.29709i	−0.612358	−	0.612358i
$143$	1.73924	+	1.73924i	0.145443	+	0.145443i
$144$			1.00000i			0.0833333i
$145$	−17.8321	+	4.94282i	−1.48087	+	0.410479i
$146$	12.6864			1.04994
$147$	−1.85529	−	1.85529i	−0.153022	−	0.153022i
$148$	3.73458	+	3.73458i	0.306981	+	0.306981i
$149$	−8.12233			−0.665407			−0.332704	−	0.943031i	$-0.607961\pi$
$149$	−8.12233			−0.665407			−0.332704	+	0.943031i	$0.607961\pi$
$150$	−4.28650	+	2.57409i	−0.349991	+	0.210174i
$151$	2.41716			0.196705			0.0983527	−	0.995152i	$-0.468643\pi$
$151$	2.41716			0.196705			0.0983527	+	0.995152i	$0.468643\pi$
$152$	−3.64947	+	3.64947i	−0.296011	+	0.296011i
$153$	−2.19207	−	2.19207i	−0.177218	−	0.177218i
$154$			1.90865i			0.153803i
$155$	3.26101	+	11.7647i	0.261931	+	0.944960i
$156$	2.69587			0.215842
$157$	9.97955	−	9.97955i	0.796455	−	0.796455i	−0.186080	−	0.982535i	$-0.559578\pi$
$157$	9.97955	−	9.97955i	0.796455	−	0.796455i	0.982535	+	0.186080i	$0.0595783\pi$
$158$	9.37065	+	9.37065i	0.745489	+	0.745489i
$159$	12.5113			0.992214
$160$	1.10134	−	1.94603i	0.0870687	−	0.153847i
$161$	8.96189	−	4.50971i	0.706296	−	0.355415i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	11.2043	−	11.2043i	0.877585	−	0.877585i	−0.115699	−	0.993284i	$-0.536911\pi$
$163$	11.2043	−	11.2043i	0.877585	−	0.877585i	0.993284	+	0.115699i	$0.0369108\pi$
$164$		−	12.1968i		−	0.952408i
$165$	1.00484	−	1.77552i	0.0782270	−	0.138224i
$166$		−	12.5400i		−	0.973290i
$167$	13.9061	+	13.9061i	1.07608	+	1.07608i	0.996857	+	0.0792276i	$0.0252454\pi$
$167$	13.9061	+	13.9061i	1.07608	+	1.07608i	0.0792276	+	0.996857i	$0.474755\pi$
$168$	1.47923	+	1.47923i	0.114125	+	0.114125i
$169$			5.73231i			0.440947i
$170$	1.85162	+	6.68005i	0.142013	+	0.512336i
$171$			5.16113i			0.394682i
$172$	0.0783063	−	0.0783063i	0.00597080	−	0.00597080i
$173$	4.89730	−	4.89730i	0.372335	−	0.372335i	−0.495992	−	0.868327i	$-0.665196\pi$
$173$	4.89730	−	4.89730i	0.372335	−	0.372335i	0.868327	+	0.495992i	$0.165196\pi$
$174$		−	8.27544i		−	0.627360i
$175$	−2.53303	+	10.1484i	−0.191479	+	0.767144i
$176$			0.912381i			0.0687733i
$177$	4.00064	+	4.00064i	0.300706	+	0.300706i
$178$	−0.592477	−	0.592477i	−0.0444080	−	0.0444080i
$179$		−	1.76577i		−	0.131980i	−0.997820	−	0.0659899i	$-0.978980\pi$
$179$		−	1.76577i		−	0.131980i	0.997820	−	0.0659899i	$-0.0210205\pi$
$180$	−0.597287	−	2.15482i	−0.0445192	−	0.160611i
$181$		−	4.71006i		−	0.350096i	−0.984560	−	0.175048i	$-0.943992\pi$
$181$		−	4.71006i		−	0.350096i	0.984560	−	0.175048i	$-0.0560080\pi$
$182$	3.98779	−	3.98779i	0.295595	−	0.295595i
$183$	6.86466	+	6.86466i	0.507450	+	0.507450i
$184$	4.28401	−	2.15576i	0.315821	−	0.158924i
$185$	−10.2780	−	5.81673i	−0.755652	−	0.427655i
$186$	−5.45970			−0.400324
$187$	−2.00000	−	2.00000i	−0.146254	−	0.146254i
$188$	4.92197	−	4.92197i	0.358972	−	0.358972i
$189$	2.09194			0.152166
$190$	5.68417	−	10.0437i	0.412373	−	0.728650i
$191$		−	22.1289i		−	1.60119i	−0.599207	−	0.800594i	$-0.704517\pi$
$191$		−	22.1289i		−	1.60119i	0.599207	−	0.800594i	$-0.295483\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	−0.634485	+	0.634485i	−0.0456712	+	0.0456712i	−0.729574	−	0.683902i	$-0.760281\pi$
$193$	−0.634485	+	0.634485i	−0.0456712	+	0.0456712i	0.683902	+	0.729574i	$0.260281\pi$
$194$	−0.427704			−0.0307074
$195$	−5.80910	+	1.61021i	−0.415999	+	0.115309i
$196$	−2.62378			−0.187413
$197$	5.84405	+	5.84405i	0.416371	+	0.416371i	0.883951	−	0.467580i	$-0.154874\pi$
$197$	5.84405	+	5.84405i	0.416371	+	0.416371i	−0.467580	+	0.883951i	$0.654874\pi$
$198$	0.645151	+	0.645151i	0.0458489	+	0.0458489i
$199$	17.5085			1.24114			0.620572	−	0.784150i	$-0.286901\pi$
$199$	17.5085			1.24114			0.620572	+	0.784150i	$0.286901\pi$
$200$	−1.21085	+	4.85117i	−0.0856201	+	0.343029i
$201$			7.38845i			0.521141i
$202$	5.19696	+	5.19696i	0.365657	+	0.365657i
$203$	−12.2412	−	12.2412i	−0.859167	−	0.859167i
$204$	−3.10005			−0.217047
$205$	7.28498	+	26.2818i	0.508805	+	1.83560i
$206$		−	10.0463i		−	0.699959i
$207$	1.50490	−	4.55360i	0.104598	−	0.316497i
$208$	1.90626	−	1.90626i	0.132176	−	0.132176i
$209$			4.70892i			0.325723i
$210$	−4.07099	−	2.30394i	−0.280925	−	0.158987i
$211$	3.92363			0.270113			0.135057	−	0.990838i	$-0.456878\pi$
$211$	3.92363			0.270113			0.135057	+	0.990838i	$0.456878\pi$
$212$	8.84686	−	8.84686i	0.607605	−	0.607605i
$213$	−7.29709	+	7.29709i	−0.499989	+	0.499989i
$214$	−11.9270			−0.815315
$215$	−0.121965	+	0.215507i	−0.00831792	+	0.0146975i
$216$	1.00000			0.0680414
$217$	−8.07613	+	8.07613i	−0.548243	+	0.548243i
$218$	1.14783	+	1.14783i	0.0777411	+	0.0777411i
$219$		−	12.6864i		−	0.857270i
$220$	−0.544954	−	1.96602i	−0.0367408	−	0.132549i
$221$			8.35732i			0.562174i
$222$	3.73458	−	3.73458i	0.250649	−	0.250649i
$223$	8.34970	−	8.34970i	0.559137	−	0.559137i	−0.369925	−	0.929062i	$-0.620617\pi$
$223$	8.34970	−	8.34970i	0.559137	−	0.559137i	0.929062	+	0.369925i	$0.120617\pi$
$224$	2.09194			0.139774
$225$	2.57409	+	4.28650i	0.171606	+	0.285766i
$226$			1.23282i			0.0820059i
$227$	4.73307	−	4.73307i	0.314145	−	0.314145i	−0.532368	−	0.846513i	$-0.678698\pi$
$227$	4.73307	−	4.73307i	0.314145	−	0.314145i	0.846513	+	0.532368i	$0.178698\pi$
$228$	3.64947	+	3.64947i	0.241692	+	0.241692i
$229$	−5.56644			−0.367840			−0.183920	−	0.982941i	$-0.558879\pi$
$229$	−5.56644			−0.367840			−0.183920	+	0.982941i	$0.558879\pi$
$230$	−7.94366	+	7.20405i	−0.523789	+	0.475021i
$231$	1.90865			0.125580
$232$	−5.85162	−	5.85162i	−0.384178	−	0.384178i
$233$	1.86513	−	1.86513i	0.122189	−	0.122189i	−0.643368	−	0.765557i	$-0.722463\pi$
$233$	1.86513	−	1.86513i	0.122189	−	0.122189i	0.765557	+	0.643368i	$0.222463\pi$
$234$		−	2.69587i		−	0.176234i
$235$	−7.66613	+	13.5458i	−0.500083	+	0.883630i
$236$	5.65776			0.368289
$237$	9.37065	−	9.37065i	0.608689	−	0.608689i
$238$	−4.58567	+	4.58567i	−0.297245	+	0.297245i
$239$			19.0304i			1.23097i	0.788148	+	0.615486i	$0.211040\pi$
$239$			19.0304i			1.23097i	−0.788148	+	0.615486i	$0.788960\pi$
$240$	−1.94603	−	1.10134i	−0.125616	−	0.0710913i
$241$			0.615651i			0.0396576i	0.999803	+	0.0198288i	$0.00631211\pi$
$241$			0.615651i			0.0396576i	−0.999803	+	0.0198288i	$0.993688\pi$
$242$	−7.18955	−	7.18955i	−0.462162	−	0.462162i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	9.70810			0.621497
$245$	5.65378	−	1.56715i	0.361206	−	0.100122i
$246$	−12.1968			−0.777638
$247$	9.83849	−	9.83849i	0.626008	−	0.626008i
$248$	−3.86059	+	3.86059i	−0.245148	+	0.245148i
$249$	−12.5400			−0.794688
$250$	−0.288377	−	11.1766i	−0.0182385	−	0.706872i
$251$			18.8785i			1.19160i	0.803133	+	0.595800i	$0.203165\pi$
$251$			18.8785i			1.19160i	−0.803133	+	0.595800i	$0.796835\pi$
$252$	1.47923	−	1.47923i	0.0931825	−	0.0931825i
$253$	1.37304	−	4.15462i	0.0863225	−	0.261199i
$254$		−	12.0337i		−	0.755062i
$255$	6.68005	−	1.85162i	0.418321	−	0.115953i
$256$	1.00000			0.0625000
$257$	−15.0074	−	15.0074i	−0.936134	−	0.936134i	0.0619452	−	0.998080i	$-0.480270\pi$
$257$	−15.0074	−	15.0074i	−0.936134	−	0.936134i	−0.998080	+	0.0619452i	$0.980270\pi$
$258$	−0.0783063	−	0.0783063i	−0.00487514	−	0.00487514i
$259$		−	11.0486i		−	0.686526i
$260$	−2.96907	+	5.24624i	−0.184134	+	0.325358i
$261$	−8.27544			−0.512237
$262$	0.553625	+	0.553625i	0.0342030	+	0.0342030i
$263$	−22.5610	−	22.5610i	−1.39117	−	1.39117i	−0.822705	−	0.568469i	$-0.807536\pi$
$263$	−22.5610	−	22.5610i	−1.39117	−	1.39117i	−0.568469	−	0.822705i	$-0.692464\pi$
$264$	0.912381			0.0561532
$265$	−13.7793	+	24.3475i	−0.846454	+	1.49565i
$266$	10.7968			0.661994
$267$	−0.592477	+	0.592477i	−0.0362590	+	0.0362590i
$268$	5.22443	+	5.22443i	0.319133	+	0.319133i
$269$			26.2246i			1.59894i	0.600705	+	0.799471i	$0.294887\pi$
$269$			26.2246i			1.59894i	−0.600705	+	0.799471i	$0.705113\pi$
$270$	−2.15482	+	0.597287i	−0.131138	+	0.0363498i
$271$	8.26950			0.502337			0.251168	−	0.967943i	$-0.419185\pi$
$271$	8.26950			0.502337			0.251168	+	0.967943i	$0.419185\pi$
$272$	−2.19207	+	2.19207i	−0.132914	+	0.132914i
$273$	−3.98779	−	3.98779i	−0.241352	−	0.241352i
$274$	11.2833			0.681647
$275$	2.34855	+	3.91092i	0.141623	+	0.235837i
$276$	−2.15576	−	4.28401i	−0.129761	−	0.257867i
$277$	11.7278	+	11.7278i	0.704657	+	0.704657i	0.965407	−	0.260749i	$-0.0839696\pi$
$277$	11.7278	+	11.7278i	0.704657	+	0.704657i	−0.260749	+	0.965407i	$0.583970\pi$
$278$	−3.75725	+	3.75725i	−0.225345	+	0.225345i
$279$			5.45970i			0.326864i
$280$	−4.50776	+	1.24949i	−0.269390	+	0.0746713i
$281$		−	29.2523i		−	1.74504i	−0.488574	−	0.872522i	$-0.662483\pi$
$281$		−	29.2523i		−	1.74504i	0.488574	−	0.872522i	$-0.337517\pi$
$282$	−4.92197	−	4.92197i	−0.293099	−	0.293099i
$283$	−7.44353	−	7.44353i	−0.442472	−	0.442472i	0.450370	−	0.892842i	$-0.351292\pi$
$283$	−7.44353	−	7.44353i	−0.442472	−	0.442472i	−0.892842	+	0.450370i	$0.851292\pi$
$284$			10.3196i			0.612358i
$285$	−10.0437	−	5.68417i	−0.594940	−	0.336701i
$286$		−	2.45966i		−	0.145443i
$287$	−18.0418	+	18.0418i	−1.06497	+	1.06497i
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$			7.38969i			0.434688i
$290$	16.1043	+	9.11409i	0.945676	+	0.535198i
$291$			0.427704i			0.0250725i
$292$	−8.97067	−	8.97067i	−0.524969	−	0.524969i
$293$	−10.6547	−	10.6547i	−0.622453	−	0.622453i	0.323705	−	0.946158i	$-0.395072\pi$
$293$	−10.6547	−	10.6547i	−0.622453	−	0.622453i	−0.946158	+	0.323705i	$0.895072\pi$
$294$			2.62378i			0.153022i
$295$	−12.1914	+	3.37931i	−0.709814	+	0.196751i
$296$		−	5.28150i		−	0.306981i
$297$	0.645151	−	0.645151i	0.0374355	−	0.0374355i
$298$	5.74336	+	5.74336i	0.332704	+	0.332704i
$299$	−11.5491	+	5.81163i	−0.667902	+	0.336095i
$300$	4.85117	+	1.21085i	0.280082	+	0.0699085i
$301$	−0.231665			−0.0133530
$302$	−1.70919	−	1.70919i	−0.0983527	−	0.0983527i
$303$	5.19696	−	5.19696i	0.298558	−	0.298558i
$304$	5.16113			0.296011
$305$	−20.9192	+	5.79853i	−1.19783	+	0.332023i
$306$			3.10005i			0.177218i
$307$	4.65466	+	4.65466i	0.265655	+	0.265655i	0.827347	−	0.561692i	$-0.189849\pi$
$307$	4.65466	+	4.65466i	0.265655	+	0.265655i	−0.561692	+	0.827347i	$0.689849\pi$
$308$	1.34962	−	1.34962i	0.0769016	−	0.0769016i
$309$	−10.0463			−0.571514
$310$	6.01299	−	10.6248i	0.341515	−	0.603445i
$311$	10.2005			0.578419			0.289209	−	0.957266i	$-0.406608\pi$
$311$	10.2005			0.578419			0.289209	+	0.957266i	$0.406608\pi$
$312$	−1.90626	−	1.90626i	−0.107921	−	0.107921i
$313$	10.5057	+	10.5057i	0.593820	+	0.593820i	0.938661	−	0.344841i	$-0.112067\pi$
$313$	10.5057	+	10.5057i	0.593820	+	0.593820i	−0.344841	+	0.938661i	$0.612067\pi$
$314$	−14.1132			−0.796455
$315$	−2.30394	+	4.07099i	−0.129812	+	0.229374i
$316$		−	13.2521i		−	0.745489i
$317$	−15.7253	−	15.7253i	−0.883223	−	0.883223i	0.110638	−	0.993861i	$-0.464711\pi$
$317$	−15.7253	−	15.7253i	−0.883223	−	0.883223i	−0.993861	+	0.110638i	$0.964711\pi$
$318$	−8.84686	−	8.84686i	−0.496107	−	0.496107i
$319$	−7.55036			−0.422739
$320$	−2.15482	+	0.597287i	−0.120458	+	0.0333894i
$321$			11.9270i			0.665702i
$322$	−9.52586	−	3.14817i	−0.530856	−	0.175440i
$323$	−11.3135	+	11.3135i	−0.629503	+	0.629503i
$324$		−	1.00000i		−	0.0555556i
$325$	3.26429	−	13.0781i	0.181070	−	0.725442i
$326$	−15.8452			−0.877585
$327$	1.14783	−	1.14783i	0.0634753	−	0.0634753i
$328$	−8.62442	+	8.62442i	−0.476204	+	0.476204i
$329$	−14.5614			−0.802797
$330$	−1.96602	+	0.544954i	−0.108226	+	0.0299987i
$331$	−20.0508			−1.10209			−0.551045	−	0.834475i	$-0.685771\pi$
$331$	−20.0508			−1.10209			−0.551045	+	0.834475i	$0.685771\pi$
$332$	−8.86710	+	8.86710i	−0.486645	+	0.486645i
$333$	−3.73458	−	3.73458i	−0.204654	−	0.204654i
$334$		−	19.6662i		−	1.07608i
$335$	−14.3782	−	8.13721i	−0.785564	−	0.444583i
$336$		−	2.09194i		−	0.114125i
$337$	10.0062	−	10.0062i	0.545074	−	0.545074i	−0.379938	−	0.925012i	$-0.624055\pi$
$337$	10.0062	−	10.0062i	0.545074	−	0.545074i	0.925012	+	0.379938i	$0.124055\pi$
$338$	4.05335	−	4.05335i	0.220473	−	0.220473i
$339$	1.23282			0.0669575
$340$	3.41421	−	6.03280i	0.185162	−	0.327175i
$341$			4.98133i			0.269754i
$342$	3.64947	−	3.64947i	0.197341	−	0.197341i
$343$	14.2357	+	14.2357i	0.768658	+	0.768658i
$344$	−0.110742			−0.00597080
$345$	7.20405	+	7.94366i	0.387853	+	0.427672i
$346$	−6.92582			−0.372335
$347$	−7.67093	−	7.67093i	−0.411797	−	0.411797i	0.470567	−	0.882364i	$-0.344049\pi$
$347$	−7.67093	−	7.67093i	−0.411797	−	0.411797i	−0.882364	+	0.470567i	$0.844049\pi$
$348$	−5.85162	+	5.85162i	−0.313680	+	0.313680i
$349$			24.2192i			1.29643i	0.761459	+	0.648213i	$0.224483\pi$
$349$			24.2192i			1.29643i	−0.761459	+	0.648213i	$0.775517\pi$
$350$	8.96710	−	5.38485i	0.479311	−	0.287832i
$351$	−2.69587			−0.143895
$352$	0.645151	−	0.645151i	0.0343867	−	0.0343867i
$353$	−4.31291	+	4.31291i	−0.229553	+	0.229553i	−0.812506	−	0.582953i	$-0.801897\pi$
$353$	−4.31291	+	4.31291i	−0.229553	+	0.229553i	0.582953	+	0.812506i	$0.301897\pi$
$354$		−	5.65776i		−	0.300706i
$355$	−6.16380	−	22.2370i	−0.327140	−	1.18022i
$356$			0.837888i			0.0444080i
$357$	4.58567	+	4.58567i	0.242700	+	0.242700i
$358$	−1.24859	+	1.24859i	−0.0659899	+	0.0659899i
$359$	24.1751			1.27591			0.637957	−	0.770072i	$-0.279780\pi$
$359$	24.1751			1.27591			0.637957	+	0.770072i	$0.279780\pi$
$360$	−1.10134	+	1.94603i	−0.0580458	+	0.102565i
$361$	7.63731			0.401964
$362$	−3.33051	+	3.33051i	−0.175048	+	0.175048i
$363$	−7.18955	+	7.18955i	−0.377354	+	0.377354i
$364$	−5.63959			−0.295595
$365$	24.6882	+	13.9721i	1.29224	+	0.731333i
$366$		−	9.70810i		−	0.507450i
$367$	9.65448	−	9.65448i	0.503960	−	0.503960i	−0.408706	−	0.912666i	$-0.634020\pi$
$367$	9.65448	−	9.65448i	0.503960	−	0.503960i	0.912666	+	0.408706i	$0.134020\pi$
$368$	−4.55360	−	1.50490i	−0.237373	−	0.0784484i
$369$			12.1968i			0.634939i
$370$	3.15457	+	11.3807i	0.163998	+	0.591653i
$371$	−26.1730			−1.35883
$372$	3.86059	+	3.86059i	0.200162	+	0.200162i
$373$	11.1907	+	11.1907i	0.579430	+	0.579430i	0.934746	−	0.355316i	$-0.115627\pi$
$373$	11.1907	+	11.1907i	0.579430	+	0.579430i	−0.355316	+	0.934746i	$0.615627\pi$
$374$			2.82843i			0.146254i
$375$	−11.1766	+	0.288377i	−0.577158	+	0.0148917i
$376$	−6.96072			−0.358972
$377$	15.7752	+	15.7752i	0.812463	+	0.812463i
$378$	−1.47923	−	1.47923i	−0.0760832	−	0.0760832i
$379$	2.09559			0.107643			0.0538217	−	0.998551i	$-0.482860\pi$
$379$	2.09559			0.107643			0.0538217	+	0.998551i	$0.482860\pi$
$380$	−11.1213	+	3.08268i	−0.570511	+	0.158138i
$381$	−12.0337			−0.616505
$382$	−15.6475	+	15.6475i	−0.800594	+	0.800594i
$383$	−14.3286	−	14.3286i	−0.732155	−	0.732155i	0.238891	−	0.971046i	$-0.423216\pi$
$383$	−14.3286	−	14.3286i	−0.732155	−	0.732155i	−0.971046	+	0.238891i	$0.923216\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−2.10207	+	3.71429i	−0.107132	+	0.189298i
$386$	0.897297			0.0456712
$387$	−0.0783063	+	0.0783063i	−0.00398053	+	0.00398053i
$388$	0.302433	+	0.302433i	0.0153537	+	0.0153537i
$389$	31.8387			1.61429			0.807143	−	0.590356i	$-0.201013\pi$
$389$	31.8387			1.61429			0.807143	+	0.590356i	$0.201013\pi$
$390$	5.24624	+	2.96907i	0.265654	+	0.150345i
$391$	13.2806	−	6.68295i	0.671631	−	0.337971i
$392$	1.85529	+	1.85529i	0.0937065	+	0.0937065i
$393$	0.553625	−	0.553625i	0.0279267	−	0.0279267i
$394$		−	8.26474i		−	0.416371i
$395$	7.91531	+	28.5559i	0.398263	+	1.43680i
$396$		−	0.912381i		−	0.0458489i
$397$	4.21350	+	4.21350i	0.211470	+	0.211470i	0.804892	−	0.593422i	$-0.202223\pi$
$397$	4.21350	+	4.21350i	0.211470	+	0.211470i	−0.593422	+	0.804892i	$0.702223\pi$
$398$	−12.3804	−	12.3804i	−0.620572	−	0.620572i
$399$		−	10.7968i		−	0.540516i
$400$	4.28650	−	2.57409i	0.214325	−	0.128705i
$401$		−	10.3648i		−	0.517594i	−0.965932	−	0.258797i	$-0.916674\pi$
$401$		−	10.3648i		−	0.517594i	0.965932	−	0.258797i	$-0.0833260\pi$
$402$	5.22443	−	5.22443i	0.260571	−	0.260571i
$403$	10.4076	−	10.4076i	0.518441	−	0.518441i
$404$		−	7.34962i		−	0.365657i
$405$	0.597287	+	2.15482i	0.0296795	+	0.107074i
$406$			17.3117i			0.859167i
$407$	−3.40736	−	3.40736i	−0.168897	−	0.168897i
$408$	2.19207	+	2.19207i	0.108523	+	0.108523i
$409$		−	37.4377i		−	1.85118i	−0.378531	−	0.925589i	$-0.623571\pi$
$409$		−	37.4377i		−	1.85118i	0.378531	−	0.925589i	$-0.376429\pi$
$410$	13.4328	−	23.7353i	0.663399	−	1.17220i
$411$		−	11.2833i		−	0.556562i
$412$	−7.10380	+	7.10380i	−0.349979	+	0.349979i
$413$	−8.36910	−	8.36910i	−0.411817	−	0.411817i
$414$	−4.28401	+	2.15576i	−0.210547	+	0.105950i
$415$	13.8108	−	24.4032i	0.677945	−	1.19791i
$416$	−2.69587			−0.132176
$417$	3.75725	+	3.75725i	0.183993	+	0.183993i
$418$	3.32971	−	3.32971i	0.162861	−	0.162861i
$419$	15.3885			0.751778			0.375889	−	0.926665i	$-0.377337\pi$
$419$	15.3885			0.751778			0.375889	+	0.926665i	$0.377337\pi$
$420$	1.24949	+	4.50776i	0.0609689	+	0.219956i
$421$		−	29.0436i		−	1.41550i	−0.706465	−	0.707748i	$-0.749711\pi$
$421$		−	29.0436i		−	1.41550i	0.706465	−	0.707748i	$-0.250289\pi$
$422$	−2.77442	−	2.77442i	−0.135057	−	0.135057i
$423$	−4.92197	+	4.92197i	−0.239314	+	0.239314i
$424$	−12.5113			−0.607605
$425$	−3.75370	+	15.0389i	−0.182081	+	0.729492i
$426$	10.3196			0.499989
$427$	−14.3605	−	14.3605i	−0.694952	−	0.694952i
$428$	8.43368	+	8.43368i	0.407657	+	0.407657i
$429$	−2.45966			−0.118753
$430$	0.238629	−	0.0661447i	0.0115077	−	0.00318978i
$431$			6.36434i			0.306559i	0.988183	+	0.153280i	$0.0489835\pi$
$431$			6.36434i			0.306559i	−0.988183	+	0.153280i	$0.951016\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	−19.6731	−	19.6731i	−0.945429	−	0.945429i	0.0531576	−	0.998586i	$-0.483071\pi$
$433$	−19.6731	−	19.6731i	−0.945429	−	0.945429i	−0.998586	+	0.0531576i	$0.983071\pi$
$434$	11.4214			0.548243
$435$	9.11409	−	16.1043i	0.436987	−	0.772141i
$436$		−	1.62328i		−	0.0777411i
$437$	−23.5017	−	7.76700i	−1.12424	−	0.371546i
$438$	−8.97067	+	8.97067i	−0.428635	+	0.428635i
$439$			7.59434i			0.362458i	0.983441	+	0.181229i	$0.0580075\pi$
$439$			7.59434i			0.362458i	−0.983441	+	0.181229i	$0.941992\pi$
$440$	−1.00484	+	1.77552i	−0.0479040	+	0.0846448i
$441$	2.62378			0.124942
$442$	5.90952	−	5.90952i	0.281087	−	0.281087i
$443$	−4.89201	+	4.89201i	−0.232426	+	0.232426i	−0.813705	−	0.581278i	$-0.802553\pi$
$443$	−4.89201	+	4.89201i	−0.232426	+	0.232426i	0.581278	+	0.813705i	$0.302553\pi$
$444$	−5.28150			−0.250649
$445$	−0.500460	−	1.80550i	−0.0237241	−	0.0855888i
$446$	−11.8083			−0.559137
$447$	5.74336	−	5.74336i	0.271651	−	0.271651i
$448$	−1.47923	−	1.47923i	−0.0698869	−	0.0698869i
$449$		−	6.82441i		−	0.322064i	−0.986949	−	0.161032i	$-0.948518\pi$
$449$		−	6.82441i		−	0.322064i	0.986949	−	0.161032i	$-0.0514822\pi$
$450$	1.21085	−	4.85117i	0.0570801	−	0.228686i
$451$			11.1281i			0.524002i
$452$	0.871735	−	0.871735i	0.0410029	−	0.0410029i
$453$	−1.70919	+	1.70919i	−0.0803046	+	0.0803046i
$454$	−6.69357			−0.314145
$455$	12.1523	−	3.36846i	0.569709	−	0.157916i
$456$		−	5.16113i		−	0.241692i
$457$	−12.7153	+	12.7153i	−0.594797	+	0.594797i	−0.938923	−	0.344126i	$-0.888175\pi$
$457$	−12.7153	+	12.7153i	−0.594797	+	0.594797i	0.344126	+	0.938923i	$0.388175\pi$
$458$	3.93606	+	3.93606i	0.183920	+	0.183920i
$459$	3.10005			0.144698
$460$	10.7110	+	0.522984i	0.499405	+	0.0243842i
$461$	3.97264			0.185024			0.0925121	−	0.995712i	$-0.470510\pi$
$461$	3.97264			0.185024			0.0925121	+	0.995712i	$0.470510\pi$
$462$	−1.34962	−	1.34962i	−0.0627899	−	0.0627899i
$463$	16.0745	−	16.0745i	0.747043	−	0.747043i	−0.226879	−	0.973923i	$-0.572852\pi$
$463$	16.0745	−	16.0745i	0.747043	−	0.747043i	0.973923	+	0.226879i	$0.0728524\pi$
$464$			8.27544i			0.384178i
$465$	−10.6248	−	6.01299i	−0.492711	−	0.278846i
$466$	−2.63770			−0.122189
$467$	−16.4509	+	16.4509i	−0.761258	+	0.761258i	−0.976550	−	0.215292i	$-0.930930\pi$
$467$	−16.4509	+	16.4509i	−0.761258	+	0.761258i	0.215292	+	0.976550i	$0.430930\pi$
$468$	−1.90626	+	1.90626i	−0.0881171	+	0.0881171i
$469$		−	15.4562i		−	0.713702i
$470$	14.9991	−	4.15755i	0.691856	−	0.191773i
$471$			14.1132i			0.650303i
$472$	−4.00064	−	4.00064i	−0.184144	−	0.184144i
$473$	−0.0714452	+	0.0714452i	−0.00328505	+	0.00328505i
$474$	−13.2521			−0.608689
$475$	22.1232	−	13.2852i	1.01508	−	0.609569i
$476$	6.48512			0.297245
$477$	−8.84686	+	8.84686i	−0.405070	+	0.405070i
$478$	13.4565	−	13.4565i	0.615486	−	0.615486i
$479$	16.0301			0.732435			0.366218	−	0.930529i	$-0.380653\pi$
$479$	16.0301			0.732435			0.366218	+	0.930529i	$0.380653\pi$
$480$	0.597287	+	2.15482i	0.0272623	+	0.0983536i
$481$			14.2382i			0.649207i
$482$	0.435331	−	0.435331i	0.0198288	−	0.0198288i
$483$	−3.14817	+	9.52586i	−0.143247	+	0.433442i
$484$			10.1676i			0.462162i
$485$	−0.832327	−	0.471048i	−0.0377940	−	0.0213892i
$486$	−1.00000			−0.0453609
$487$	23.7717	+	23.7717i	1.07720	+	1.07720i	0.996760	+	0.0804367i	$0.0256315\pi$
$487$	23.7717	+	23.7717i	1.07720	+	1.07720i	0.0804367	+	0.996760i	$0.474368\pi$
$488$	−6.86466	−	6.86466i	−0.310749	−	0.310749i
$489$			15.8452i			0.716546i
$490$	−5.10597	−	2.88968i	−0.230664	−	0.130542i
$491$	−6.01407			−0.271411			−0.135706	−	0.990749i	$-0.543330\pi$
$491$	−6.01407			−0.271411			−0.135706	+	0.990749i	$0.543330\pi$
$492$	8.62442	+	8.62442i	0.388819	+	0.388819i
$493$	−18.1403	−	18.1403i	−0.816999	−	0.816999i
$494$	−13.9137			−0.626008
$495$	0.544954	+	1.96602i	0.0244939	+	0.0883659i
$496$	5.45970			0.245148
$497$	15.2651	−	15.2651i	0.684733	−	0.684733i
$498$	8.86710	+	8.86710i	0.397344	+	0.397344i
$499$		−	28.8110i		−	1.28976i	−0.764285	−	0.644879i	$-0.776908\pi$
$499$		−	28.8110i		−	1.28976i	0.764285	−	0.644879i	$-0.223092\pi$
$500$	−7.69915	+	8.10698i	−0.344316	+	0.362555i
$501$	−19.6662			−0.878619
$502$	13.3491	−	13.3491i	0.595800	−	0.595800i
$503$	11.9638	+	11.9638i	0.533439	+	0.533439i	0.921594	−	0.388155i	$-0.126888\pi$
$503$	11.9638	+	11.9638i	0.533439	+	0.533439i	−0.388155	+	0.921594i	$0.626888\pi$
$504$	−2.09194			−0.0931825
$505$	4.38983	+	15.8371i	0.195345	+	0.704742i
$506$	−3.90865	+	1.96687i	−0.173761	+	0.0874381i
$507$	−4.05335	−	4.05335i	−0.180016	−	0.180016i
$508$	−8.50911	+	8.50911i	−0.377531	+	0.377531i
$509$		−	0.392000i		−	0.0173751i	−0.999962	−	0.00868754i	$-0.997235\pi$
$509$		−	0.392000i		−	0.0173751i	0.999962	−	0.00868754i	$-0.00276536\pi$
$510$	−6.03280	−	3.41421i	−0.267137	−	0.151184i
$511$			26.5393i			1.17403i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−3.64947	−	3.64947i	−0.161128	−	0.161128i
$514$			21.2236i			0.936134i
$515$	11.0644	−	19.5504i	0.487556	−	0.861495i
$516$			0.110742i			0.00487514i
$517$	−4.49071	+	4.49071i	−0.197501	+	0.197501i
$518$	−7.81253	+	7.81253i	−0.343263	+	0.343263i
$519$			6.92582i			0.304010i
$520$	5.80910	−	1.61021i	0.254746	−	0.0706122i
$521$		−	34.1983i		−	1.49826i	−0.662426	−	0.749128i	$-0.730473\pi$
$521$		−	34.1983i		−	1.49826i	0.662426	−	0.749128i	$-0.269527\pi$
$522$	5.85162	+	5.85162i	0.256118	+	0.256118i
$523$	23.0752	+	23.0752i	1.00901	+	1.00901i	0.999959	+	0.00905061i	$0.00288094\pi$
$523$	23.0752	+	23.0752i	1.00901	+	1.00901i	0.00905061	+	0.999959i	$0.497119\pi$
$524$		−	0.782944i		−	0.0342030i
$525$	−5.38485	−	8.96710i	−0.235014	−	0.391356i
$526$			31.9061i			1.39117i
$527$	−11.9680	+	11.9680i	−0.521335	+	0.521335i
$528$	−0.645151	−	0.645151i	−0.0280766	−	0.0280766i
$529$	18.4705	+	13.7054i	0.803067	+	0.595889i
$530$	26.9597	−	7.47287i	1.17105	−	0.324601i
$531$	−5.65776			−0.245526
$532$	−7.63448	−	7.63448i	−0.330997	−	0.330997i
$533$	23.2503	−	23.2503i	1.00708	−	1.00708i
$534$	0.837888			0.0362590
$535$	−23.2104	−	13.1357i	−1.00347	−	0.567907i
$536$		−	7.38845i		−	0.319133i
$537$	1.24859	+	1.24859i	0.0538805	+	0.0538805i
$538$	18.5436	−	18.5436i	0.799471	−	0.799471i
$539$	2.39389			0.103112
$540$	1.94603	+	1.10134i	0.0837440	+	0.0473942i
$541$	10.0462			0.431921			0.215961	−	0.976402i	$-0.430712\pi$
$541$	10.0462			0.431921			0.215961	+	0.976402i	$0.430712\pi$
$542$	−5.84742	−	5.84742i	−0.251168	−	0.251168i
$543$	3.33051	+	3.33051i	0.142926	+	0.142926i
$544$	3.10005			0.132914
$545$	0.969565	+	3.49788i	0.0415316	+	0.149833i
$546$			5.63959i			0.241352i
$547$	5.55946	+	5.55946i	0.237705	+	0.237705i	0.815899	−	0.578194i	$-0.196242\pi$
$547$	5.55946	+	5.55946i	0.237705	+	0.237705i	−0.578194	+	0.815899i	$0.696242\pi$
$548$	−7.97847	−	7.97847i	−0.340824	−	0.340824i
$549$	−9.70810			−0.414332
$550$	1.10476	−	4.42612i	0.0471070	−	0.188730i
$551$			42.7107i			1.81954i
$552$	−1.50490	+	4.55360i	−0.0640529	+	0.193814i
$553$	−19.6028	+	19.6028i	−0.833598	+	0.833598i
$554$		−	16.5857i		−	0.704657i
$555$	11.3807	−	3.15457i	0.483083	−	0.133904i
$556$	5.31355			0.225345
$557$	−28.4426	+	28.4426i	−1.20515	+	1.20515i	−0.232575	+	0.972578i	$0.574715\pi$
$557$	−28.4426	+	28.4426i	−1.20515	+	1.20515i	−0.972578	+	0.232575i	$0.925285\pi$
$558$	3.86059	−	3.86059i	0.163432	−	0.163432i
$559$	0.298545			0.0126271
$560$	4.07099	+	2.30394i	0.172031	+	0.0973593i
$561$	2.82843			0.119416
$562$	−20.6845	+	20.6845i	−0.872522	+	0.872522i
$563$	−19.7106	−	19.7106i	−0.830701	−	0.830701i	0.156912	−	0.987613i	$-0.449846\pi$
$563$	−19.7106	−	19.7106i	−0.830701	−	0.830701i	−0.987613	+	0.156912i	$0.949846\pi$
$564$			6.96072i			0.293099i
$565$	−1.35775	+	2.39911i	−0.0571212	+	0.100931i
$566$			10.5267i			0.442472i
$567$	−1.47923	+	1.47923i	−0.0621216	+	0.0621216i
$568$	7.29709	−	7.29709i	0.306179	−	0.306179i
$569$	36.0611			1.51176			0.755880	−	0.654710i	$-0.227209\pi$
$569$	36.0611			1.51176			0.755880	+	0.654710i	$0.227209\pi$
$570$	3.08268	+	11.1213i	0.129119	+	0.465821i
$571$		−	26.1960i		−	1.09627i	−0.836390	−	0.548134i	$-0.815338\pi$
$571$		−	26.1960i		−	1.09627i	0.836390	−	0.548134i	$-0.184662\pi$
$572$	−1.73924	+	1.73924i	−0.0727213	+	0.0727213i
$573$	15.6475	+	15.6475i	0.653682	+	0.653682i
$574$	25.5149			1.06497
$575$	−23.3927	+	5.27064i	−0.975545	+	0.219801i
$576$	−1.00000			−0.0416667
$577$	−12.1729	−	12.1729i	−0.506763	−	0.506763i	0.406768	−	0.913531i	$-0.366656\pi$
$577$	−12.1729	−	12.1729i	−0.506763	−	0.506763i	−0.913531	+	0.406768i	$0.866656\pi$
$578$	5.22530	−	5.22530i	0.217344	−	0.217344i
$579$		−	0.897297i		−	0.0372904i
$580$	−4.94282	−	17.8321i	−0.205239	−	0.740437i
$581$	26.2329			1.08832
$582$	0.302433	−	0.302433i	0.0125362	−	0.0125362i
$583$	−8.07171	+	8.07171i	−0.334296	+	0.334296i
$584$			12.6864i			0.524969i
$585$	2.96907	−	5.24624i	0.122756	−	0.216906i
$586$			15.0680i			0.622453i
$587$	−21.6269	−	21.6269i	−0.892636	−	0.892636i	0.102134	−	0.994771i	$-0.467433\pi$
$587$	−21.6269	−	21.6269i	−0.892636	−	0.892636i	−0.994771	+	0.102134i	$0.967433\pi$
$588$	1.85529	−	1.85529i	0.0765110	−	0.0765110i
$589$	28.1782			1.16106
$590$	11.0102	+	6.23112i	0.453282	+	0.256531i
$591$	−8.26474			−0.339966
$592$	−3.73458	+	3.73458i	−0.153490	+	0.153490i
$593$	10.4088	−	10.4088i	0.427438	−	0.427438i	−0.460317	−	0.887755i	$-0.652264\pi$
$593$	10.4088	−	10.4088i	0.427438	−	0.427438i	0.887755	+	0.460317i	$0.152264\pi$
$594$	−0.912381			−0.0374355
$595$	−13.9743	+	3.87348i	−0.572889	+	0.158797i
$596$		−	8.12233i		−	0.332704i
$597$	−12.3804	+	12.3804i	−0.506695	+	0.506695i
$598$	12.2759	+	4.05701i	0.501999	+	0.165904i
$599$			20.6812i			0.845013i	0.906360	+	0.422506i	$0.138850\pi$
$599$			20.6812i			0.845013i	−0.906360	+	0.422506i	$0.861150\pi$
$600$	−2.57409	−	4.28650i	−0.105087	−	0.174995i
$601$	34.8691			1.42234			0.711171	−	0.703019i	$-0.248165\pi$
$601$	34.8691			1.42234			0.711171	+	0.703019i	$0.248165\pi$
$602$	0.163812	+	0.163812i	0.00667649	+	0.00667649i
$603$	−5.22443	−	5.22443i	−0.212755	−	0.212755i
$604$			2.41716i			0.0983527i
$605$	−6.07296	−	21.9093i	−0.246901	−	0.890738i
$606$	−7.34962			−0.298558
$607$	15.1745	+	15.1745i	0.615913	+	0.615913i	0.944481	−	0.328567i	$-0.106566\pi$
$607$	15.1745	+	15.1745i	0.615913	+	0.615913i	−0.328567	+	0.944481i	$0.606566\pi$
$608$	−3.64947	−	3.64947i	−0.148006	−	0.148006i
$609$	17.3117			0.701507
$610$	18.8923	+	10.6919i	0.764926	+	0.432904i
$611$	18.7652			0.759157
$612$	2.19207	−	2.19207i	0.0886090	−	0.0886090i
$613$	−20.4989	−	20.4989i	−0.827943	−	0.827943i	0.159289	−	0.987232i	$-0.449080\pi$
$613$	−20.4989	−	20.4989i	−0.827943	−	0.827943i	−0.987232	+	0.159289i	$0.949080\pi$
$614$		−	6.58268i		−	0.265655i
$615$	−23.7353	−	13.4328i	−0.957101	−	0.541663i
$616$	−1.90865			−0.0769016
$617$	−17.4461	+	17.4461i	−0.702354	+	0.702354i	−0.964915	−	0.262561i	$-0.915433\pi$
$617$	−17.4461	+	17.4461i	−0.702354	+	0.702354i	0.262561	+	0.964915i	$0.415433\pi$
$618$	7.10380	+	7.10380i	0.285757	+	0.285757i
$619$	1.36779			0.0549760			0.0274880	−	0.999622i	$-0.491249\pi$
$619$	1.36779			0.0549760			0.0274880	+	0.999622i	$0.491249\pi$
$620$	−11.7647	+	3.26101i	−0.472480	+	0.130965i
$621$	2.15576	+	4.28401i	0.0865075	+	0.171911i
$622$	−7.21286	−	7.21286i	−0.289209	−	0.289209i
$623$	1.23943	−	1.23943i	0.0496566	−	0.0496566i
$624$			2.69587i			0.107921i
$625$	11.7481	−	22.0677i	0.469923	−	0.882707i
$626$		−	14.8574i		−	0.593820i
$627$	−3.32971	−	3.32971i	−0.132976	−	0.132976i
$628$	9.97955	+	9.97955i	0.398227	+	0.398227i
$629$		−	16.3729i		−	0.652831i
$630$	4.50776	−	1.24949i	0.179593	−	0.0497809i
$631$			29.9727i			1.19320i	0.802540	+	0.596598i	$0.203481\pi$
$631$			29.9727i			1.19320i	−0.802540	+	0.596598i	$0.796519\pi$
$632$	−9.37065	+	9.37065i	−0.372744	+	0.372744i
$633$	−2.77442	+	2.77442i	−0.110273	+	0.110273i
$634$			22.2390i			0.883223i
$635$	13.2532	−	23.4180i	0.525938	−	0.929315i
$636$			12.5113i			0.496107i
$637$	−5.00162	−	5.00162i	−0.198171	−	0.198171i
$638$	5.33891	+	5.33891i	0.211369	+	0.211369i
$639$		−	10.3196i		−	0.408239i
$640$	1.94603	+	1.10134i	0.0769237	+	0.0435343i
$641$		−	6.35878i		−	0.251157i	−0.992084	−	0.125578i	$-0.959921\pi$
$641$		−	6.35878i		−	0.251157i	0.992084	−	0.125578i	$-0.0400786\pi$
$642$	8.43368	−	8.43368i	0.332851	−	0.332851i
$643$	31.9508	+	31.9508i	1.26002	+	1.26002i	0.951083	+	0.308934i	$0.0999724\pi$
$643$	31.9508	+	31.9508i	1.26002	+	1.26002i	0.308934	+	0.951083i	$0.400028\pi$
$644$	4.50971	+	8.96189i	0.177708	+	0.353148i
$645$	−0.0661447	−	0.238629i	−0.00260445	−	0.00939599i
$646$	15.9998			0.629503
$647$	6.63244	+	6.63244i	0.260748	+	0.260748i	0.825358	−	0.564610i	$-0.190973\pi$
$647$	6.63244	+	6.63244i	0.260748	+	0.260748i	−0.564610	+	0.825358i	$0.690973\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$	−5.16203			−0.202627
$650$	−11.5558	+	6.93941i	−0.453256	+	0.272186i
$651$		−	11.4214i		−	0.447639i
$652$	11.2043	+	11.2043i	0.438793	+	0.438793i
$653$	33.4213	−	33.4213i	1.30788	−	1.30788i	0.384932	−	0.922945i	$-0.374225\pi$
$653$	33.4213	−	33.4213i	1.30788	−	1.30788i	0.922945	−	0.384932i	$-0.125775\pi$
$654$	−1.62328			−0.0634753
$655$	0.467642	+	1.68710i	0.0182723	+	0.0659205i
$656$	12.1968			0.476204
$657$	8.97067	+	8.97067i	0.349979	+	0.349979i
$658$	10.2965	+	10.2965i	0.401398	+	0.401398i
$659$	−17.4038			−0.677955			−0.338978	−	0.940794i	$-0.610081\pi$
$659$	−17.4038			−0.677955			−0.338978	+	0.940794i	$0.610081\pi$
$660$	1.77552	+	1.00484i	0.0691122	+	0.0391135i
$661$		−	13.4061i		−	0.521436i	−0.965415	−	0.260718i	$-0.916041\pi$
$661$		−	13.4061i		−	0.521436i	0.965415	−	0.260718i	$-0.0839592\pi$
$662$	14.1780	+	14.1780i	0.551045	+	0.551045i
$663$	−5.90952	−	5.90952i	−0.229507	−	0.229507i
$664$	12.5400			0.486645
$665$	21.0109	+	11.8910i	0.814768	+	0.461111i
$666$			5.28150i			0.204654i
$667$	12.4537	−	37.6830i	0.482210	−	1.45909i
$668$	−13.9061	+	13.9061i	−0.538042	+	0.538042i
$669$			11.8083i			0.456534i
$670$	4.41303	+	15.9208i	0.170490	+	0.615074i
$671$	−8.85749			−0.341940
$672$	−1.47923	+	1.47923i	−0.0570624	+	0.0570624i
$673$	10.3552	−	10.3552i	0.399163	−	0.399163i	−0.478775	−	0.877938i	$-0.658919\pi$
$673$	10.3552	−	10.3552i	0.399163	−	0.399163i	0.877938	+	0.478775i	$0.158919\pi$
$674$	−14.1509			−0.545074
$675$	−4.85117	−	1.21085i	−0.186722	−	0.0466057i
$676$	−5.73231			−0.220473
$677$	31.9860	−	31.9860i	1.22932	−	1.22932i	0.265099	−	0.964221i	$-0.414595\pi$
$677$	31.9860	−	31.9860i	1.22932	−	1.22932i	0.964221	−	0.265099i	$-0.0854047\pi$
$678$	−0.871735	−	0.871735i	−0.0334788	−	0.0334788i
$679$		−	0.894732i		−	0.0343367i
$680$	−6.68005	+	1.85162i	−0.256168	+	0.0710064i
$681$			6.69357i			0.256498i
$682$	3.52233	−	3.52233i	0.134877	−	0.134877i
$683$	10.0450	−	10.0450i	0.384360	−	0.384360i	−0.488310	−	0.872670i	$-0.662387\pi$
$683$	10.0450	−	10.0450i	0.384360	−	0.384360i	0.872670	+	0.488310i	$0.162387\pi$
$684$	−5.16113			−0.197341
$685$	21.9576	+	12.4267i	0.838957	+	0.474801i
$686$		−	20.1324i		−	0.768658i
$687$	3.93606	−	3.93606i	0.150170	−	0.150170i
$688$	0.0783063	+	0.0783063i	0.00298540	+	0.00298540i
$689$	33.7289			1.28497
$690$	0.522984	−	10.7110i	0.0199096	−	0.407763i
$691$	−38.3889			−1.46038			−0.730192	−	0.683242i	$-0.760569\pi$
$691$	−38.3889			−1.46038			−0.730192	+	0.683242i	$0.760569\pi$
$692$	4.89730	+	4.89730i	0.186167	+	0.186167i
$693$	−1.34962	+	1.34962i	−0.0512677	+	0.0512677i
$694$			10.8483i			0.411797i
$695$	−11.4497	+	3.17372i	−0.434313	+	0.120386i
$696$	8.27544			0.313680
$697$	−26.7361	+	26.7361i	−1.01270	+	1.01270i
$698$	17.1256	−	17.1256i	0.648213	−	0.648213i
$699$			2.63770i			0.0997669i
$700$	−10.1484	−	2.53303i	−0.383572	−	0.0957395i
$701$			30.4867i			1.15147i	0.817638	+	0.575733i	$0.195283\pi$
$701$			30.4867i			1.15147i	−0.817638	+	0.575733i	$0.804717\pi$
$702$	1.90626	+	1.90626i	0.0719473	+	0.0719473i
$703$	−19.2747	+	19.2747i	−0.726959	+	0.726959i
$704$	−0.912381			−0.0343867
$705$	−4.15755	−	14.9991i	−0.156582	−	0.564898i
$706$	6.09938			0.229553
$707$	−10.8717	+	10.8717i	−0.408874	+	0.408874i
$708$	−4.00064	+	4.00064i	−0.150353	+	0.150353i
$709$	−51.1949			−1.92267			−0.961333	−	0.275388i	$-0.911194\pi$
$709$	−51.1949			−1.92267			−0.961333	+	0.275388i	$0.911194\pi$
$710$	−11.3655	+	20.0824i	−0.426538	+	0.753678i
$711$			13.2521i			0.496993i
$712$	0.592477	−	0.592477i	0.0222040	−	0.0222040i
$713$	−24.8613	−	8.21631i	−0.931062	−	0.307703i
$714$		−	6.48512i		−	0.242700i
$715$	2.70892	−	4.78658i	0.101308	−	0.179008i
$716$	1.76577			0.0659899
$717$	−13.4565	−	13.4565i	−0.502543	−	0.502543i
$718$	−17.0944	−	17.0944i	−0.637957	−	0.637957i
$719$			41.9754i			1.56542i	0.622387	+	0.782709i	$0.286163\pi$
$719$			41.9754i			1.56542i	−0.622387	+	0.782709i	$0.713837\pi$
$720$	2.15482	−	0.597287i	0.0803054	−	0.0222596i
$721$	21.0163			0.782686
$722$	−5.40040	−	5.40040i	−0.200982	−	0.200982i
$723$	−0.435331	−	0.435331i	−0.0161901	−	0.0161901i
$724$	4.71006			0.175048
$725$	21.3018	+	35.4726i	0.791127	+	1.31742i
$726$	10.1676			0.377354
$727$	13.4172	−	13.4172i	0.497617	−	0.497617i	−0.413079	−	0.910695i	$-0.635546\pi$
$727$	13.4172	−	13.4172i	0.497617	−	0.497617i	0.910695	+	0.413079i	$0.135546\pi$
$728$	3.98779	+	3.98779i	0.147797	+	0.147797i
$729$			1.00000i			0.0370370i
$730$	−7.57745	−	27.3370i	−0.280454	−	1.01179i
$731$	−0.343305			−0.0126976
$732$	−6.86466	+	6.86466i	−0.253725	+	0.253725i
$733$	8.19187	+	8.19187i	0.302574	+	0.302574i	0.842020	−	0.539446i	$-0.181366\pi$
$733$	8.19187	+	8.19187i	0.302574	+	0.302574i	−0.539446	+	0.842020i	$0.681366\pi$
$734$	−13.6535			−0.503960
$735$	−2.88968	+	5.10597i	−0.106587	+	0.188336i
$736$	2.15576	+	4.28401i	0.0794622	+	0.157911i
$737$	−4.76667	−	4.76667i	−0.175582	−	0.175582i
$738$	8.62442	−	8.62442i	0.317469	−	0.317469i
$739$			28.3966i			1.04459i	0.852766	+	0.522294i	$0.174924\pi$
$739$			28.3966i			1.04459i	−0.852766	+	0.522294i	$0.825076\pi$
$740$	5.81673	−	10.2780i	0.213827	−	0.377826i
$741$			13.9137i			0.511134i
$742$	18.5071	+	18.5071i	0.679417	+	0.679417i
$743$	−20.2499	−	20.2499i	−0.742898	−	0.742898i	0.230237	−	0.973135i	$-0.426050\pi$
$743$	−20.2499	−	20.2499i	−0.742898	−	0.742898i	−0.973135	+	0.230237i	$0.926050\pi$
$744$		−	5.45970i		−	0.200162i
$745$	4.85137	+	17.5022i	0.177740	+	0.641229i
$746$		−	15.8260i		−	0.579430i
$747$	8.86710	−	8.86710i	0.324430	−	0.324430i
$748$	2.00000	−	2.00000i	0.0731272	−	0.0731272i
$749$		−	24.9506i		−	0.911677i
$750$	8.10698	+	7.69915i	0.296025	+	0.281133i
$751$			24.6848i			0.900762i	0.892836	+	0.450381i	$0.148712\pi$
$751$			24.6848i			0.900762i	−0.892836	+	0.450381i	$0.851288\pi$
$752$	4.92197	+	4.92197i	0.179486	+	0.179486i
$753$	−13.3491	−	13.3491i	−0.486469	−	0.486469i
$754$		−	22.3095i		−	0.812463i
$755$	−1.44374	−	5.20854i	−0.0525430	−	0.189558i
$756$			2.09194i			0.0760832i
$757$	11.7787	−	11.7787i	0.428104	−	0.428104i	−0.459878	−	0.887982i	$-0.652107\pi$
$757$	11.7787	−	11.7787i	0.428104	−	0.428104i	0.887982	+	0.459878i	$0.152107\pi$
$758$	−1.48181	−	1.48181i	−0.0538217	−	0.0538217i
$759$	1.96687	+	3.90865i	0.0713929	+	0.141875i
$760$	10.0437	+	5.68417i	0.364325	+	0.206187i
$761$	−0.392492			−0.0142278			−0.00711391	−	0.999975i	$-0.502264\pi$
$761$	−0.392492			−0.0142278			−0.00711391	+	0.999975i	$0.502264\pi$
$762$	8.50911	+	8.50911i	0.308253	+	0.308253i
$763$	−2.40120	+	2.40120i	−0.0869293	+	0.0869293i
$764$	22.1289			0.800594
$765$	−3.41421	+	6.03280i	−0.123441	+	0.218116i
$766$			20.2636i			0.732155i
$767$	10.7852	+	10.7852i	0.389430	+	0.389430i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	−45.5745			−1.64346			−0.821729	−	0.569879i	$-0.806990\pi$
$769$	−45.5745			−1.64346			−0.821729	+	0.569879i	$0.806990\pi$
$770$	4.11279	−	1.14001i	0.148215	−	0.0410832i
$771$	21.2236			0.764351
$772$	−0.634485	−	0.634485i	−0.0228356	−	0.0228356i
$773$	24.9331	+	24.9331i	0.896780	+	0.896780i	0.995150	−	0.0983701i	$-0.0313629\pi$
$773$	24.9331	+	24.9331i	0.896780	+	0.896780i	−0.0983701	+	0.995150i	$0.531363\pi$
$774$	0.110742			0.00398053
$775$	23.4030	−	14.0538i	0.840659	−	0.504826i
$776$		−	0.427704i		−	0.0153537i
$777$	7.81253	+	7.81253i	0.280273	+	0.280273i
$778$	−22.5134	−	22.5134i	−0.807143	−	0.807143i
$779$	62.9492			2.25539
$780$	−1.61021	−	5.80910i	−0.0576546	−	0.207999i
$781$		−	9.41545i		−	0.336911i
$782$	−14.1164	−	4.66527i	−0.504801	−	0.166830i
$783$	5.85162	−	5.85162i	0.209120	−	0.209120i
$784$		−	2.62378i		−	0.0937065i
$785$	−27.4648	−	15.5435i	−0.980261	−	0.554770i
$786$	−0.782944			−0.0279267
$787$	−3.78084	+	3.78084i	−0.134772	+	0.134772i	−0.771275	−	0.636502i	$-0.780381\pi$
$787$	−3.78084	+	3.78084i	−0.134772	+	0.134772i	0.636502	+	0.771275i	$0.280381\pi$
$788$	−5.84405	+	5.84405i	−0.208186	+	0.208186i
$789$	31.9061			1.13589
$790$	14.5951	−	25.7890i	0.519270	−	0.917533i
$791$	−2.57898			−0.0916981
$792$	−0.645151	+	0.645151i	−0.0229244	+	0.0229244i
$793$	18.5062	+	18.5062i	0.657175	+	0.657175i
$794$		−	5.95879i		−	0.211470i
$795$	−7.47287	−	26.9597i	−0.265035	−	0.956162i
$796$			17.5085i			0.620572i
$797$	−31.9057	+	31.9057i	−1.13016	+	1.13016i	−0.140006	+	0.990151i	$0.544712\pi$
$797$	−31.9057	+	31.9057i	−1.13016	+	1.13016i	−0.990151	+	0.140006i	$0.955288\pi$
$798$	−7.63448	+	7.63448i	−0.270258	+	0.270258i
$799$	−21.5786			−0.763395
$800$	−4.85117	−	1.21085i	−0.171515	−	0.0428100i
$801$		−	0.837888i		−	0.0296053i
$802$	−7.32903	+	7.32903i	−0.258797	+	0.258797i
$803$	8.18467	+	8.18467i	0.288831	+	0.288831i
$804$	−7.38845			−0.260571
$805$	−15.0704	−	16.6177i	−0.531163	−	0.585696i
$806$	−14.7186			−0.518441
$807$	−18.5436	−	18.5436i	−0.652765	−	0.652765i
$808$	−5.19696	+	5.19696i	−0.182829	+	0.182829i
$809$		−	1.28064i		−	0.0450248i	−0.999747	−	0.0225124i	$-0.992833\pi$
$809$		−	1.28064i		−	0.0450248i	0.999747	−	0.0225124i	$-0.00716652\pi$
$810$	1.10134	−	1.94603i	0.0386972	−	0.0683767i
$811$	−24.2852			−0.852769			−0.426385	−	0.904542i	$-0.640213\pi$
$811$	−24.2852			−0.852769			−0.426385	+	0.904542i	$0.640213\pi$
$812$	12.2412	−	12.2412i	0.429584	−	0.429584i
$813$	−5.84742	+	5.84742i	−0.205078	+	0.205078i
$814$			4.81874i			0.168897i
$815$	−30.8353	−	17.4510i	−1.08011	−	0.611282i
$816$		−	3.10005i		−	0.108523i
$817$	0.404149	+	0.404149i	0.0141394	+	0.0141394i
$818$	−26.4725	+	26.4725i	−0.925589	+	0.925589i
$819$	5.63959			0.197063
$820$	−26.2818	+	7.28498i	−0.917802	+	0.254402i
$821$	−35.2773			−1.23118			−0.615592	−	0.788065i	$-0.711083\pi$
$821$	−35.2773			−1.23118			−0.615592	+	0.788065i	$0.711083\pi$
$822$	−7.97847	+	7.97847i	−0.278281	+	0.278281i
$823$	−31.4312	+	31.4312i	−1.09562	+	1.09562i	−0.100706	+	0.994916i	$0.532110\pi$
$823$	−31.4312	+	31.4312i	−1.09562	+	1.09562i	−0.994916	+	0.100706i	$0.967890\pi$
$824$	10.0463			0.349979
$825$	−4.42612	−	1.10476i	−0.154098	−	0.0384627i
$826$			11.8357i			0.411817i
$827$	−1.02870	+	1.02870i	−0.0357714	+	0.0357714i	−0.724766	−	0.688995i	$-0.758052\pi$
$827$	−1.02870	+	1.02870i	−0.0357714	+	0.0357714i	0.688995	+	0.724766i	$0.258052\pi$
$828$	4.55360	+	1.50490i	0.158249	+	0.0522989i
$829$		−	11.5672i		−	0.401744i	−0.979618	−	0.200872i	$-0.935623\pi$
$829$		−	11.5672i		−	0.401744i	0.979618	−	0.200872i	$-0.0643775\pi$
$830$	−27.0214	+	7.48997i	−0.937925	+	0.259980i
$831$	−16.5857			−0.575350
$832$	1.90626	+	1.90626i	0.0660878	+	0.0660878i
$833$	5.75150	+	5.75150i	0.199278	+	0.199278i
$834$		−	5.31355i		−	0.183993i
$835$	21.6592	−	38.2710i	0.749546	−	1.32442i
$836$	−4.70892			−0.162861
$837$	−3.86059	−	3.86059i	−0.133441	−	0.133441i
$838$	−10.8813	−	10.8813i	−0.375889	−	0.375889i
$839$	−40.2056			−1.38805			−0.694026	−	0.719950i	$-0.744165\pi$
$839$	−40.2056			−1.38805			−0.694026	+	0.719950i	$0.744165\pi$
$840$	2.30394	−	4.07099i	0.0794936	−	0.140462i
$841$	−39.4829			−1.36148
$842$	−20.5369	+	20.5369i	−0.707748	+	0.707748i
$843$	20.6845	+	20.6845i	0.712412	+	0.712412i
$844$			3.92363i			0.135057i
$845$	12.3521	−	3.42384i	0.424925	−	0.117784i
$846$	6.96072			0.239314
$847$	15.0401	−	15.0401i	0.516785	−	0.516785i
$848$	8.84686	+	8.84686i	0.303802	+	0.303802i
$849$	10.5267			0.361277
$850$	13.2883	−	7.97982i	0.455787	−	0.273705i
$851$	22.6260	−	11.3856i	0.775609	−	0.390294i
$852$	−7.29709	−	7.29709i	−0.249994	−	0.249994i
$853$	−19.3976	+	19.3976i	−0.664162	+	0.664162i	−0.956358	−	0.292196i	$-0.905614\pi$
$853$	−19.3976	+	19.3976i	−0.664162	+	0.664162i	0.292196	+	0.956358i	$0.405614\pi$
$854$			20.3088i			0.694952i
$855$	11.1213	−	3.08268i	0.380341	−	0.105425i
$856$		−	11.9270i		−	0.407657i
$857$	−10.7351	−	10.7351i	−0.366705	−	0.366705i	0.499569	−	0.866274i	$-0.333492\pi$
$857$	−10.7351	−	10.7351i	−0.366705	−	0.366705i	−0.866274	+	0.499569i	$0.833492\pi$
$858$	1.73924	+	1.73924i	0.0593767	+	0.0593767i
$859$		−	1.48602i		−	0.0507025i	−0.999679	−	0.0253512i	$-0.991930\pi$
$859$		−	1.48602i		−	0.0507025i	0.999679	−	0.0253512i	$-0.00807041\pi$
$860$	−0.215507	−	0.121965i	−0.00734874	−	0.00415896i
$861$		−	25.5149i		−	0.869547i
$862$	4.50027	−	4.50027i	0.153280	−	0.153280i
$863$	27.1906	−	27.1906i	0.925577	−	0.925577i	−0.0718388	−	0.997416i	$-0.522887\pi$
$863$	27.1906	−	27.1906i	0.925577	−	0.925577i	0.997416	+	0.0718388i	$0.0228867\pi$
$864$			1.00000i			0.0340207i
$865$	−13.4779	−	7.62770i	−0.458262	−	0.259349i
$866$			27.8220i			0.945429i
$867$	−5.22530	−	5.22530i	−0.177461	−	0.177461i
$868$	−8.07613	−	8.07613i	−0.274122	−	0.274122i
$869$			12.0910i			0.410158i
$870$	−17.8321	+	4.94282i	−0.604564	+	0.167577i
$871$			19.9183i			0.674905i
$872$	−1.14783	+	1.14783i	−0.0388705	+	0.0388705i
$873$	−0.302433	−	0.302433i	−0.0102358	−	0.0102358i
$874$	11.1261	+	22.1103i	0.376347	+	0.747893i
$875$	23.3808	−	0.603267i	0.790416	−	0.0203941i
$876$	12.6864			0.428635
$877$	−36.6805	−	36.6805i	−1.23861	−	1.23861i	−0.960569	−	0.278042i	$-0.910314\pi$
$877$	−36.6805	−	36.6805i	−1.23861	−	1.23861i	−0.278042	−	0.960569i	$-0.589686\pi$
$878$	5.37001	−	5.37001i	0.181229	−	0.181229i
$879$	15.0680			0.508231
$880$	1.96602	−	0.544954i	0.0662744	−	0.0183704i
$881$		−	15.7381i		−	0.530229i	−0.964217	−	0.265114i	$-0.914590\pi$
$881$		−	15.7381i		−	0.530229i	0.964217	−	0.265114i	$-0.0854097\pi$
$882$	−1.85529	−	1.85529i	−0.0624710	−	0.0624710i
$883$	26.7699	−	26.7699i	0.900880	−	0.900880i	−0.0946326	−	0.995512i	$-0.530168\pi$
$883$	26.7699	−	26.7699i	0.900880	−	0.900880i	0.995512	+	0.0946326i	$0.0301676\pi$
$884$	−8.35732			−0.281087
$885$	6.23112	−	11.0102i	0.209457	−	0.370103i
$886$	6.91834			0.232426
$887$	13.4886	+	13.4886i	0.452904	+	0.452904i	0.896317	−	0.443413i	$-0.146233\pi$
$887$	13.4886	+	13.4886i	0.452904	+	0.452904i	−0.443413	+	0.896317i	$0.646233\pi$
$888$	3.73458	+	3.73458i	0.125324	+	0.125324i
$889$	25.1738			0.844302
$890$	−0.922801	+	1.63056i	−0.0309324	+	0.0546565i
$891$			0.912381i			0.0305659i
$892$	8.34970	+	8.34970i	0.279569	+	0.279569i
$893$	25.4030	+	25.4030i	0.850077	+	0.850077i
$894$	−8.12233			−0.271651
$895$	−3.80491	+	1.05467i	−0.127184	+	0.0352538i
$896$			2.09194i			0.0698869i
$897$	4.05701	−	12.2759i	0.135460	−	0.409880i
$898$	−4.82559	+	4.82559i	−0.161032	+	0.161032i
$899$			45.1814i			1.50688i
$900$	−4.28650	+	2.57409i	−0.142883	+	0.0858031i
$901$	−38.7858			−1.29214
$902$	7.86876	−	7.86876i	0.262001	−	0.262001i
$903$	0.163812	−	0.163812i	0.00545133	−	0.00545133i
$904$	−1.23282			−0.0410029
$905$	−10.1493	+	2.81326i	−0.337375	+	0.0935159i
$906$	2.41716			0.0803046
$907$	1.75120	−	1.75120i	0.0581475	−	0.0581475i	−0.677435	−	0.735583i	$-0.736909\pi$
$907$	1.75120	−	1.75120i	0.0581475	−	0.0581475i	0.735583	+	0.677435i	$0.236909\pi$
$908$	4.73307	+	4.73307i	0.157072	+	0.157072i
$909$			7.34962i			0.243771i
$910$	−10.9748	−	6.21112i	−0.363812	−	0.205897i
$911$		−	23.6824i		−	0.784633i	−0.919830	−	0.392317i	$-0.871674\pi$
$911$		−	23.6824i		−	0.784633i	0.919830	−	0.392317i	$-0.128326\pi$
$912$	−3.64947	+	3.64947i	−0.120846	+	0.120846i
$913$	8.09017	−	8.09017i	0.267746	−	0.267746i
$914$	17.9822			0.594797
$915$	10.6919	−	18.8923i	0.353464	−	0.624560i
$916$		−	5.56644i		−	0.183920i
$917$	−1.15815	+	1.15815i	−0.0382455	+	0.0382455i
$918$	−2.19207	−	2.19207i	−0.0723490	−	0.0723490i
$919$	−3.33655			−0.110062			−0.0550312	−	0.998485i	$-0.517526\pi$
$919$	−3.33655			−0.110062			−0.0550312	+	0.998485i	$0.517526\pi$
$920$	−7.20405	−	7.94366i	−0.237510	−	0.261895i
$921$	−6.58268			−0.216907
$922$	−2.80908	−	2.80908i	−0.0925121	−	0.0925121i
$923$	−19.6720	+	19.6720i	−0.647511	+	0.647511i
$924$			1.90865i			0.0627899i
$925$	−6.39511	+	25.6214i	−0.210270	+	0.842428i
$926$	−22.7327			−0.747043
$927$	7.10380	−	7.10380i	0.233320	−	0.233320i
$928$	5.85162	−	5.85162i	0.192089	−	0.192089i
$929$		−	44.5358i		−	1.46117i	−0.682820	−	0.730586i	$-0.739247\pi$
$929$		−	44.5358i		−	1.46117i	0.682820	−	0.730586i	$-0.260753\pi$
$930$	3.26101	+	11.7647i	0.106933	+	0.385778i
$931$		−	13.5417i		−	0.443811i
$932$	1.86513	+	1.86513i	0.0610945	+	0.0610945i
$933$	−7.21286	+	7.21286i	−0.236139	+	0.236139i
$934$	23.2651			0.761258
$935$	−3.11506	+	5.50421i	−0.101873	+	0.180007i
$936$	2.69587			0.0881171
$937$	−5.08001	+	5.08001i	−0.165957	+	0.165957i	−0.785200	−	0.619243i	$-0.787440\pi$
$937$	−5.08001	+	5.08001i	−0.165957	+	0.165957i	0.619243	+	0.785200i	$0.287440\pi$
$938$	−10.9292	+	10.9292i	−0.356851	+	0.356851i
$939$	−14.8574			−0.484852
$940$	−13.5458	−	7.66613i	−0.441815	−	0.250041i
$941$			35.0322i			1.14202i	0.820944	+	0.571009i	$0.193448\pi$
$941$			35.0322i			1.14202i	−0.820944	+	0.571009i	$0.806552\pi$
$942$	9.97955	−	9.97955i	0.325151	−	0.325151i
$943$	−55.5392	−	18.3549i	−1.80861	−	0.597719i
$944$			5.65776i			0.184144i
$945$	−1.24949	−	4.50776i	−0.0406459	−	0.146637i
$946$	0.101039			0.00328505
$947$	−17.6881	−	17.6881i	−0.574786	−	0.574786i	0.358676	−	0.933462i	$-0.383228\pi$
$947$	−17.6881	−	17.6881i	−0.574786	−	0.574786i	−0.933462	+	0.358676i	$0.883228\pi$
$948$	9.37065	+	9.37065i	0.304345	+	0.304345i
$949$		−	34.2009i		−	1.11021i
$950$	−25.0375	−	6.24937i	−0.812325	−	0.202756i
$951$	22.2390			0.721149
$952$	−4.58567	−	4.58567i	−0.148623	−	0.148623i
$953$	−20.3972	−	20.3972i	−0.660729	−	0.660729i	0.294823	−	0.955552i	$-0.404739\pi$
$953$	−20.3972	−	20.3972i	−0.660729	−	0.660729i	−0.955552	+	0.294823i	$0.904739\pi$
$954$	12.5113			0.405070
$955$	−47.6837	+	13.2173i	−1.54301	+	0.427702i
$956$	−19.0304			−0.615486
$957$	5.33891	−	5.33891i	0.172582	−	0.172582i
$958$	−11.3350	−	11.3350i	−0.366218	−	0.366218i
$959$			23.6039i			0.762211i
$960$	1.10134	−	1.94603i	0.0355456	−	0.0628080i
$961$	−1.19171			−0.0384422
$962$	10.0679	−	10.0679i	0.324603	−	0.324603i
$963$	−8.43368	−	8.43368i	−0.271772	−	0.271772i
$964$	−0.615651			−0.0198288
$965$	1.74617	+	0.988230i	0.0562112	+	0.0318123i
$966$	8.96189	−	4.50971i	0.288344	−	0.145098i
$967$	4.51597	+	4.51597i	0.145224	+	0.145224i	0.775981	−	0.630757i	$-0.217255\pi$
$967$	4.51597	+	4.51597i	0.145224	+	0.145224i	−0.630757	+	0.775981i	$0.717255\pi$
$968$	7.18955	−	7.18955i	0.231081	−	0.231081i
$969$		−	15.9998i		−	0.513987i
$970$	0.255462	+	0.921625i	0.00820240	+	0.0295916i
$971$		−	2.43261i		−	0.0780662i	−0.999238	−	0.0390331i	$-0.987572\pi$
$971$		−	2.43261i		−	0.0780662i	0.999238	−	0.0390331i	$-0.0124278\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	−7.85994	−	7.85994i	−0.251978	−	0.251978i
$974$		−	33.6182i		−	1.07720i
$975$	6.93941	+	11.5558i	0.222239	+	0.370082i
$976$			9.70810i			0.310749i
$977$	7.37436	−	7.37436i	0.235927	−	0.235927i	−0.579234	−	0.815161i	$-0.696648\pi$
$977$	7.37436	−	7.37436i	0.235927	−	0.235927i	0.815161	+	0.579234i	$0.196648\pi$
$978$	11.2043	−	11.2043i	0.358273	−	0.358273i
$979$		−	0.764474i		−	0.0244327i
$980$	1.56715	+	5.65378i	0.0500608	+	0.180603i
$981$			1.62328i			0.0518274i
$982$	4.25259	+	4.25259i	0.135706	+	0.135706i
$983$	36.0967	+	36.0967i	1.15131	+	1.15131i	0.986291	+	0.165014i	$0.0527669\pi$
$983$	36.0967	+	36.0967i	1.15131	+	1.15131i	0.165014	+	0.986291i	$0.447233\pi$
$984$		−	12.1968i		−	0.388819i
$985$	9.10230	−	16.0835i	0.290023	−	0.512462i
$986$			25.6543i			0.816999i
$987$	10.2965	−	10.2965i	0.327740	−	0.327740i
$988$	9.83849	+	9.83849i	0.313004	+	0.313004i
$989$	−0.238732	−	0.474419i	−0.00759124	−	0.0150856i
$990$	1.00484	−	1.77552i	0.0319360	−	0.0564299i
$991$	17.4425			0.554080			0.277040	−	0.960858i	$-0.410647\pi$
$991$	17.4425			0.554080			0.277040	+	0.960858i	$0.410647\pi$
$992$	−3.86059	−	3.86059i	−0.122574	−	0.122574i
$993$	14.1780	−	14.1780i	0.449927	−	0.449927i
$994$	−21.5881			−0.684733
$995$	−10.4576	−	37.7276i	−0.331528	−	1.19605i
$996$		−	12.5400i		−	0.397344i
$997$	8.37860	+	8.37860i	0.265353	+	0.265353i	0.827225	−	0.561872i	$-0.189918\pi$
$997$	8.37860	+	8.37860i	0.265353	+	0.265353i	−0.561872	+	0.827225i	$0.689918\pi$
$998$	−20.3725	+	20.3725i	−0.644879	+	0.644879i
$999$	5.28150			0.167099

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.j.b.367.3	✓	24
5.3	odd	4	inner	690.2.j.b.643.4	yes	24
23.22	odd	2	inner	690.2.j.b.367.4	yes	24
115.68	even	4	inner	690.2.j.b.643.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.j.b.367.3	✓	24	1.1	even	1	trivial
690.2.j.b.367.4	yes	24	23.22	odd	2	inner
690.2.j.b.643.3	yes	24	115.68	even	4	inner
690.2.j.b.643.4	yes	24	5.3	odd	4	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.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-0.597287 - 2.15482i) q^{5} +1.00000 q^{6} +(1.47923 - 1.47923i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-0.597287 - 2.15482i) q^{5} +1.00000 q^{6} +(1.47923 - 1.47923i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +(-1.10134 + 1.94603i) q^{10} -0.912381i q^{11} +(-0.707107 - 0.707107i) q^{12} +(-1.90626 + 1.90626i) q^{13} -2.09194 q^{14} +(1.94603 + 1.10134i) q^{15} -1.00000 q^{16} +(2.19207 - 2.19207i) q^{17} +(-0.707107 + 0.707107i) q^{18} -5.16113 q^{19} +(2.15482 - 0.597287i) q^{20} +2.09194i q^{21} +(-0.645151 + 0.645151i) q^{22} +(4.55360 + 1.50490i) q^{23} +1.00000i q^{24} +(-4.28650 + 2.57409i) q^{25} +2.69587 q^{26} +(0.707107 + 0.707107i) q^{27} +(1.47923 + 1.47923i) q^{28} -8.27544i q^{29} +(-0.597287 - 2.15482i) q^{30} -5.45970 q^{31} +(0.707107 + 0.707107i) q^{32} +(0.645151 + 0.645151i) q^{33} -3.10005 q^{34} +(-4.07099 - 2.30394i) q^{35} +1.00000 q^{36} +(3.73458 - 3.73458i) q^{37} +(3.64947 + 3.64947i) q^{38} -2.69587i q^{39} +(-1.94603 - 1.10134i) q^{40} -12.1968 q^{41} +(1.47923 - 1.47923i) q^{42} +(-0.0783063 - 0.0783063i) q^{43} +0.912381 q^{44} +(-2.15482 + 0.597287i) q^{45} +(-2.15576 - 4.28401i) q^{46} +(-4.92197 - 4.92197i) q^{47} +(0.707107 - 0.707107i) q^{48} +2.62378i q^{49} +(4.85117 + 1.21085i) q^{50} +3.10005i q^{51} +(-1.90626 - 1.90626i) q^{52} +(-8.84686 - 8.84686i) q^{53} -1.00000i q^{54} +(-1.96602 + 0.544954i) q^{55} -2.09194i q^{56} +(3.64947 - 3.64947i) q^{57} +(-5.85162 + 5.85162i) q^{58} -5.65776i q^{59} +(-1.10134 + 1.94603i) q^{60} -9.70810i q^{61} +(3.86059 + 3.86059i) q^{62} +(-1.47923 - 1.47923i) q^{63} -1.00000i q^{64} +(5.24624 + 2.96907i) q^{65} -0.912381i q^{66} +(5.22443 - 5.22443i) q^{67} +(2.19207 + 2.19207i) q^{68} +(-4.28401 + 2.15576i) q^{69} +(1.24949 + 4.50776i) q^{70} +10.3196 q^{71} +(-0.707107 - 0.707107i) q^{72} +(-8.97067 + 8.97067i) q^{73} -5.28150 q^{74} +(1.21085 - 4.85117i) q^{75} -5.16113i q^{76} +(-1.34962 - 1.34962i) q^{77} +(-1.90626 + 1.90626i) q^{78} -13.2521 q^{79} +(0.597287 + 2.15482i) q^{80} -1.00000 q^{81} +(8.62442 + 8.62442i) q^{82} +(8.86710 + 8.86710i) q^{83} -2.09194 q^{84} +(-6.03280 - 3.41421i) q^{85} +0.110742i q^{86} +(5.85162 + 5.85162i) q^{87} +(-0.645151 - 0.645151i) q^{88} +0.837888 q^{89} +(1.94603 + 1.10134i) q^{90} +5.63959i q^{91} +(-1.50490 + 4.55360i) q^{92} +(3.86059 - 3.86059i) q^{93} +6.96072i q^{94} +(3.08268 + 11.1213i) q^{95} -1.00000 q^{96} +(0.302433 - 0.302433i) q^{97} +(1.85529 - 1.85529i) q^{98} -0.912381 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

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