LMFDB - Embedded newform 690.2.j.b.643.7

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			643.7
Character	$\chi$	$=$	690.643
Dual form			690.2.j.b.367.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-2.19853 + 0.408021i) q^{5} +1.00000 q^{6} +(-1.64584 - 1.64584i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-2.19853 + 0.408021i) q^{5} +1.00000 q^{6} +(-1.64584 - 1.64584i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(-1.26608 + 1.84311i) q^{10} -6.11317i q^{11} +(0.707107 - 0.707107i) q^{12} +(-0.241478 - 0.241478i) q^{13} -2.32757 q^{14} +(-1.84311 - 1.26608i) q^{15} -1.00000 q^{16} +(-0.327163 - 0.327163i) q^{17} +(0.707107 + 0.707107i) q^{18} +0.759529 q^{19} +(0.408021 + 2.19853i) q^{20} -2.32757i q^{21} +(-4.32266 - 4.32266i) q^{22} +(-4.49658 - 1.66757i) q^{23} -1.00000i q^{24} +(4.66704 - 1.79409i) q^{25} -0.341501 q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.64584 + 1.64584i) q^{28} -7.09541i q^{29} +(-2.19853 + 0.408021i) q^{30} -8.30560 q^{31} +(-0.707107 + 0.707107i) q^{32} +(4.32266 - 4.32266i) q^{33} -0.462678 q^{34} +(4.28997 + 2.94689i) q^{35} +1.00000 q^{36} +(1.92602 + 1.92602i) q^{37} +(0.537068 - 0.537068i) q^{38} -0.341501i q^{39} +(1.84311 + 1.26608i) q^{40} +6.75167 q^{41} +(-1.64584 - 1.64584i) q^{42} +(0.144662 - 0.144662i) q^{43} -6.11317 q^{44} +(-0.408021 - 2.19853i) q^{45} +(-4.35871 + 2.00041i) q^{46} +(1.46451 - 1.46451i) q^{47} +(-0.707107 - 0.707107i) q^{48} -1.58240i q^{49} +(2.03148 - 4.56871i) q^{50} -0.462678i q^{51} +(-0.241478 + 0.241478i) q^{52} +(-1.45249 + 1.45249i) q^{53} +1.00000i q^{54} +(2.49430 + 13.4400i) q^{55} +2.32757i q^{56} +(0.537068 + 0.537068i) q^{57} +(-5.01721 - 5.01721i) q^{58} -1.68540i q^{59} +(-1.26608 + 1.84311i) q^{60} +8.05915i q^{61} +(-5.87295 + 5.87295i) q^{62} +(1.64584 - 1.64584i) q^{63} +1.00000i q^{64} +(0.629423 + 0.432367i) q^{65} -6.11317i q^{66} +(3.13950 + 3.13950i) q^{67} +(-0.327163 + 0.327163i) q^{68} +(-2.00041 - 4.35871i) q^{69} +(5.11723 - 0.949699i) q^{70} +6.24090 q^{71} +(0.707107 - 0.707107i) q^{72} +(6.62866 + 6.62866i) q^{73} +2.72380 q^{74} +(4.56871 + 2.03148i) q^{75} -0.759529i q^{76} +(-10.0613 + 10.0613i) q^{77} +(-0.241478 - 0.241478i) q^{78} +3.83429 q^{79} +(2.19853 - 0.408021i) q^{80} -1.00000 q^{81} +(4.77416 - 4.77416i) q^{82} +(2.14295 - 2.14295i) q^{83} -2.32757 q^{84} +(0.852765 + 0.585786i) q^{85} -0.204583i q^{86} +(5.01721 - 5.01721i) q^{87} +(-4.32266 + 4.32266i) q^{88} -4.64280 q^{89} +(-1.84311 - 1.26608i) q^{90} +0.794868i q^{91} +(-1.66757 + 4.49658i) q^{92} +(-5.87295 - 5.87295i) q^{93} -2.07114i q^{94} +(-1.66985 + 0.309904i) q^{95} -1.00000 q^{96} +(11.2007 + 11.2007i) q^{97} +(-1.11893 - 1.11893i) q^{98} +6.11317 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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

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

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
$5$	−2.19853	+	0.408021i	−0.983211	+	0.182473i
$5$	−2.19853	+	0.408021i	−0.983211	+	0.182473i
$6$	1.00000			0.408248
$7$	−1.64584	−	1.64584i	−0.622070	−	0.622070i	0.323990	−	0.946060i	$-0.394976\pi$
$7$	−1.64584	−	1.64584i	−0.622070	−	0.622070i	−0.946060	+	0.323990i	$0.894976\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$			1.00000i			0.333333i
$10$	−1.26608	+	1.84311i	−0.400369	+	0.582842i
$11$		−	6.11317i		−	1.84319i	−0.388154	−	0.921595i	$-0.626887\pi$
$11$		−	6.11317i		−	1.84319i	0.388154	−	0.921595i	$-0.373113\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	−0.241478	−	0.241478i	−0.0669738	−	0.0669738i	0.672826	−	0.739800i	$-0.265080\pi$
$13$	−0.241478	−	0.241478i	−0.0669738	−	0.0669738i	−0.739800	+	0.672826i	$0.765080\pi$
$14$	−2.32757			−0.622070
$15$	−1.84311	−	1.26608i	−0.475888	−	0.326900i
$16$	−1.00000			−0.250000
$17$	−0.327163	−	0.327163i	−0.0793486	−	0.0793486i	0.666319	−	0.745667i	$-0.267869\pi$
$17$	−0.327163	−	0.327163i	−0.0793486	−	0.0793486i	−0.745667	+	0.666319i	$0.767869\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	0.759529			0.174248			0.0871240	−	0.996197i	$-0.472232\pi$
$19$	0.759529			0.174248			0.0871240	+	0.996197i	$0.472232\pi$
$20$	0.408021	+	2.19853i	0.0912363	+	0.491605i
$21$		−	2.32757i		−	0.507918i
$22$	−4.32266	−	4.32266i	−0.921595	−	0.921595i
$23$	−4.49658	−	1.66757i	−0.937601	−	0.347712i
$23$	−4.49658	−	1.66757i	−0.937601	−	0.347712i
$24$		−	1.00000i		−	0.204124i
$25$	4.66704	−	1.79409i	0.933408	−	0.358818i
$26$	−0.341501			−0.0669738
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−1.64584	+	1.64584i	−0.311035	+	0.311035i
$29$		−	7.09541i		−	1.31758i	−0.752325	−	0.658792i	$-0.771068\pi$
$29$		−	7.09541i		−	1.31758i	0.752325	−	0.658792i	$-0.228932\pi$
$30$	−2.19853	+	0.408021i	−0.401394	+	0.0744941i
$31$	−8.30560			−1.49173			−0.745865	−	0.666097i	$-0.767964\pi$
$31$	−8.30560			−1.49173			−0.745865	+	0.666097i	$0.767964\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	4.32266	−	4.32266i	0.752479	−	0.752479i
$34$	−0.462678			−0.0793486
$35$	4.28997	+	2.94689i	0.725137	+	0.498116i
$36$	1.00000			0.166667
$37$	1.92602	+	1.92602i	0.316636	+	0.316636i	0.847474	−	0.530838i	$-0.178123\pi$
$37$	1.92602	+	1.92602i	0.316636	+	0.316636i	−0.530838	+	0.847474i	$0.678123\pi$
$38$	0.537068	−	0.537068i	0.0871240	−	0.0871240i
$39$		−	0.341501i		−	0.0546839i
$40$	1.84311	+	1.26608i	0.291421	+	0.200185i
$41$	6.75167			1.05443			0.527217	−	0.849731i	$-0.323235\pi$
$41$	6.75167			1.05443			0.527217	+	0.849731i	$0.323235\pi$
$42$	−1.64584	−	1.64584i	−0.253959	−	0.253959i
$43$	0.144662	−	0.144662i	0.0220608	−	0.0220608i	−0.695990	−	0.718051i	$-0.745034\pi$
$43$	0.144662	−	0.144662i	0.0220608	−	0.0220608i	0.718051	+	0.695990i	$0.245034\pi$
$44$	−6.11317			−0.921595
$45$	−0.408021	−	2.19853i	−0.0608242	−	0.327737i
$46$	−4.35871	+	2.00041i	−0.642657	+	0.294945i
$47$	1.46451	−	1.46451i	0.213621	−	0.213621i	−0.592183	−	0.805804i	$-0.701734\pi$
$47$	1.46451	−	1.46451i	0.213621	−	0.213621i	0.805804	+	0.592183i	$0.201734\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$		−	1.58240i		−	0.226057i
$50$	2.03148	−	4.56871i	0.287295	−	0.646113i
$51$		−	0.462678i		−	0.0647879i
$52$	−0.241478	+	0.241478i	−0.0334869	+	0.0334869i
$53$	−1.45249	+	1.45249i	−0.199515	+	0.199515i	−0.799792	−	0.600277i	$-0.795057\pi$
$53$	−1.45249	+	1.45249i	−0.199515	+	0.199515i	0.600277	+	0.799792i	$0.295057\pi$
$54$			1.00000i			0.136083i
$55$	2.49430	+	13.4400i	0.336332	+	1.81224i
$56$			2.32757i			0.311035i
$57$	0.537068	+	0.537068i	0.0711365	+	0.0711365i
$58$	−5.01721	−	5.01721i	−0.658792	−	0.658792i
$59$		−	1.68540i		−	0.219420i	−0.993964	−	0.109710i	$-0.965008\pi$
$59$		−	1.68540i		−	0.219420i	0.993964	−	0.109710i	$-0.0349922\pi$
$60$	−1.26608	+	1.84311i	−0.163450	+	0.237944i
$61$			8.05915i			1.03187i	0.856628	+	0.515934i	$0.172555\pi$
$61$			8.05915i			1.03187i	−0.856628	+	0.515934i	$0.827445\pi$
$62$	−5.87295	+	5.87295i	−0.745865	+	0.745865i
$63$	1.64584	−	1.64584i	0.207357	−	0.207357i
$64$			1.00000i			0.125000i
$65$	0.629423	+	0.432367i	0.0780703	+	0.0536285i
$66$		−	6.11317i		−	0.752479i
$67$	3.13950	+	3.13950i	0.383551	+	0.383551i	0.872380	−	0.488829i	$-0.162576\pi$
$67$	3.13950	+	3.13950i	0.383551	+	0.383551i	−0.488829	+	0.872380i	$0.662576\pi$
$68$	−0.327163	+	0.327163i	−0.0396743	+	0.0396743i
$69$	−2.00041	−	4.35871i	−0.240821	−	0.524727i
$70$	5.11723	−	0.949699i	0.611626	−	0.113511i
$71$	6.24090			0.740658			0.370329	−	0.928901i	$-0.379245\pi$
$71$	6.24090			0.740658			0.370329	+	0.928901i	$0.379245\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	6.62866	+	6.62866i	0.775826	+	0.775826i	0.979118	−	0.203292i	$-0.0651641\pi$
$73$	6.62866	+	6.62866i	0.775826	+	0.775826i	−0.203292	+	0.979118i	$0.565164\pi$
$74$	2.72380			0.316636
$75$	4.56871	+	2.03148i	0.527549	+	0.234575i
$76$		−	0.759529i		−	0.0871240i
$77$	−10.0613	+	10.0613i	−1.14659	+	1.14659i
$78$	−0.241478	−	0.241478i	−0.0273419	−	0.0273419i
$79$	3.83429			0.431391			0.215695	−	0.976461i	$-0.430798\pi$
$79$	3.83429			0.431391			0.215695	+	0.976461i	$0.430798\pi$
$80$	2.19853	−	0.408021i	0.245803	−	0.0456181i
$81$	−1.00000			−0.111111
$82$	4.77416	−	4.77416i	0.527217	−	0.527217i
$83$	2.14295	−	2.14295i	0.235219	−	0.235219i	−0.579648	−	0.814867i	$-0.696810\pi$
$83$	2.14295	−	2.14295i	0.235219	−	0.235219i	0.814867	+	0.579648i	$0.196810\pi$
$84$	−2.32757			−0.253959
$85$	0.852765	+	0.585786i	0.0924953	+	0.0635375i
$86$		−	0.204583i		−	0.0220608i
$87$	5.01721	−	5.01721i	0.537901	−	0.537901i
$88$	−4.32266	+	4.32266i	−0.460797	+	0.460797i
$89$	−4.64280			−0.492136			−0.246068	−	0.969253i	$-0.579139\pi$
$89$	−4.64280			−0.492136			−0.246068	+	0.969253i	$0.579139\pi$
$90$	−1.84311	−	1.26608i	−0.194281	−	0.133456i
$91$			0.794868i			0.0833248i
$92$	−1.66757	+	4.49658i	−0.173856	+	0.468801i
$93$	−5.87295	−	5.87295i	−0.608996	−	0.608996i
$94$		−	2.07114i		−	0.213621i
$95$	−1.66985	+	0.309904i	−0.171323	+	0.0317955i
$96$	−1.00000			−0.102062
$97$	11.2007	+	11.2007i	1.13726	+	1.13726i	0.988940	+	0.148317i	$0.0473856\pi$
$97$	11.2007	+	11.2007i	1.13726	+	1.13726i	0.148317	+	0.988940i	$0.452614\pi$
$98$	−1.11893	−	1.11893i	−0.113029	−	0.113029i
$99$	6.11317			0.614396
$100$	−1.79409	−	4.66704i	−0.179409	−	0.466704i
$101$	−16.0613			−1.59816			−0.799080	−	0.601224i	$-0.794680\pi$
$101$	−16.0613			−1.59816			−0.799080	+	0.601224i	$0.794680\pi$
$102$	−0.327163	−	0.327163i	−0.0323939	−	0.0323939i
$103$	1.60298	−	1.60298i	0.157946	−	0.157946i	−0.623710	−	0.781656i	$-0.714375\pi$
$103$	1.60298	−	1.60298i	0.157946	−	0.157946i	0.781656	+	0.623710i	$0.214375\pi$
$104$			0.341501i			0.0334869i
$105$	0.949699	+	5.11723i	0.0926812	+	0.499391i
$106$			2.05413i			0.199515i
$107$	−9.95278	−	9.95278i	−0.962171	−	0.962171i	0.0371390	−	0.999310i	$-0.488176\pi$
$107$	−9.95278	−	9.95278i	−0.962171	−	0.962171i	−0.999310	+	0.0371390i	$0.988176\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$	14.4446			1.38354			0.691771	−	0.722117i	$-0.256831\pi$
$109$	14.4446			1.38354			0.691771	+	0.722117i	$0.256831\pi$
$110$	11.2672	+	7.73975i	1.07429	+	0.737956i
$111$			2.72380i			0.258532i
$112$	1.64584	+	1.64584i	0.155518	+	0.155518i
$113$	0.885110	−	0.885110i	0.0832642	−	0.0832642i	−0.664248	−	0.747512i	$-0.731248\pi$
$113$	0.885110	−	0.885110i	0.0832642	−	0.0832642i	0.747512	+	0.664248i	$0.231248\pi$
$114$	0.759529			0.0711365
$115$	10.5662	+	1.83150i	0.985308	+	0.170788i
$116$	−7.09541			−0.658792
$117$	0.241478	−	0.241478i	0.0223246	−	0.0223246i
$118$	−1.19176	−	1.19176i	−0.109710	−	0.109710i
$119$			1.07692i			0.0987208i
$120$	0.408021	+	2.19853i	0.0372471	+	0.200697i
$121$	−26.3708			−2.39735
$122$	5.69868	+	5.69868i	0.515934	+	0.515934i
$123$	4.77416	+	4.77416i	0.430471	+	0.430471i
$124$			8.30560i			0.745865i
$125$	−9.52858	+	5.84861i	−0.852262	+	0.523115i
$126$		−	2.32757i		−	0.207357i
$127$	−6.44789	+	6.44789i	−0.572158	+	0.572158i	−0.932731	−	0.360573i	$-0.882581\pi$
$127$	−6.44789	+	6.44789i	−0.572158	+	0.572158i	0.360573	+	0.932731i	$0.382581\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	0.204583			0.0180125
$130$	0.750799	−	0.139340i	0.0658494	−	0.0122209i
$131$	10.5482			0.921604			0.460802	−	0.887503i	$-0.347562\pi$
$131$	10.5482			0.921604			0.460802	+	0.887503i	$0.347562\pi$
$132$	−4.32266	−	4.32266i	−0.376239	−	0.376239i
$133$	−1.25007	−	1.25007i	−0.108395	−	0.108395i
$134$	4.43992			0.383551
$135$	1.26608	−	1.84311i	0.108967	−	0.158629i
$136$			0.462678i			0.0396743i
$137$	−15.3962	−	15.3962i	−1.31538	−	1.31538i	−0.917388	−	0.397994i	$-0.869706\pi$
$137$	−15.3962	−	15.3962i	−1.31538	−	1.31538i	−0.397994	−	0.917388i	$-0.630294\pi$
$138$	−4.49658	−	1.66757i	−0.382774	−	0.141953i
$139$		−	5.75151i		−	0.487837i	−0.969796	−	0.243918i	$-0.921567\pi$
$139$		−	5.75151i		−	0.487837i	0.969796	−	0.243918i	$-0.0784329\pi$
$140$	2.94689	−	4.28997i	0.249058	−	0.362569i
$141$	2.07114			0.174421
$142$	4.41298	−	4.41298i	0.370329	−	0.370329i
$143$	−1.47619	+	1.47619i	−0.123445	+	0.123445i
$144$		−	1.00000i		−	0.0833333i
$145$	2.89508	+	15.5994i	0.240423	+	1.29546i
$146$	9.37434			0.775826
$147$	1.11893	−	1.11893i	0.0922874	−	0.0922874i
$148$	1.92602	−	1.92602i	0.158318	−	0.158318i
$149$	17.6985			1.44992			0.724960	−	0.688791i	$-0.241858\pi$
$149$	17.6985			1.44992			0.724960	+	0.688791i	$0.241858\pi$
$150$	4.66704	−	1.79409i	0.381062	−	0.146487i
$151$	−11.9117			−0.969359			−0.484680	−	0.874692i	$-0.661064\pi$
$151$	−11.9117			−0.969359			−0.484680	+	0.874692i	$0.661064\pi$
$152$	−0.537068	−	0.537068i	−0.0435620	−	0.0435620i
$153$	0.327163	−	0.327163i	0.0264495	−	0.0264495i
$154$			14.2288i			1.14659i
$155$	18.2601	−	3.38886i	1.46669	−	0.272200i
$156$	−0.341501			−0.0273419
$157$	5.35896	+	5.35896i	0.427692	+	0.427692i	0.887841	−	0.460150i	$-0.152204\pi$
$157$	5.35896	+	5.35896i	0.427692	+	0.427692i	−0.460150	+	0.887841i	$0.652204\pi$
$158$	2.71125	−	2.71125i	0.215695	−	0.215695i
$159$	−2.05413			−0.162903
$160$	1.26608	−	1.84311i	0.100092	−	0.145710i
$161$	4.65610	+	10.1452i	0.366952	+	0.799555i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	1.79995	+	1.79995i	0.140983	+	0.140983i	0.774076	−	0.633093i	$-0.218215\pi$
$163$	1.79995	+	1.79995i	0.140983	+	0.140983i	−0.633093	+	0.774076i	$0.718215\pi$
$164$		−	6.75167i		−	0.527217i
$165$	−7.73975	+	11.2672i	−0.602539	+	0.877152i
$166$		−	3.03059i		−	0.235219i
$167$	9.84687	−	9.84687i	0.761974	−	0.761974i	−0.214705	−	0.976679i	$-0.568879\pi$
$167$	9.84687	−	9.84687i	0.761974	−	0.761974i	0.976679	+	0.214705i	$0.0688791\pi$
$168$	−1.64584	+	1.64584i	−0.126980	+	0.126980i
$169$		−	12.8834i		−	0.991029i
$170$	1.01721	−	0.188782i	0.0780164	−	0.0144789i
$171$			0.759529i			0.0580827i
$172$	−0.144662	−	0.144662i	−0.0110304	−	0.0110304i
$173$	12.1316	+	12.1316i	0.922351	+	0.922351i	0.997195	−	0.0748442i	$-0.0238459\pi$
$173$	12.1316	+	12.1316i	0.922351	+	0.922351i	−0.0748442	+	0.997195i	$0.523846\pi$
$174$		−	7.09541i		−	0.537901i
$175$	−10.6340	−	4.72842i	−0.803855	−	0.357435i
$176$			6.11317i			0.460797i
$177$	1.19176	−	1.19176i	0.0895778	−	0.0895778i
$178$	−3.28296	+	3.28296i	−0.246068	+	0.246068i
$179$		−	1.62037i		−	0.121112i	−0.998165	−	0.0605561i	$-0.980713\pi$
$179$		−	1.62037i		−	0.121112i	0.998165	−	0.0605561i	$-0.0192874\pi$
$180$	−2.19853	+	0.408021i	−0.163868	+	0.0304121i
$181$		−	20.5841i		−	1.53000i	−0.644030	−	0.765000i	$-0.722739\pi$
$181$		−	20.5841i		−	1.53000i	0.644030	−	0.765000i	$-0.277261\pi$
$182$	0.562057	+	0.562057i	0.0416624	+	0.0416624i
$183$	−5.69868	+	5.69868i	−0.421258	+	0.421258i
$184$	2.00041	+	4.35871i	0.147472	+	0.321328i
$185$	−5.02026	−	3.44855i	−0.369097	−	0.253542i
$186$	−8.30560			−0.608996
$187$	−2.00000	+	2.00000i	−0.146254	+	0.146254i
$188$	−1.46451	−	1.46451i	−0.106811	−	0.106811i
$189$	2.32757			0.169306
$190$	−0.961624	+	1.39989i	−0.0697635	+	0.101559i
$191$		−	20.8203i		−	1.50650i	−0.657734	−	0.753251i	$-0.728485\pi$
$191$		−	20.8203i		−	1.50650i	0.657734	−	0.753251i	$-0.271515\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	5.74993	+	5.74993i	0.413889	+	0.413889i	0.883091	−	0.469202i	$-0.155458\pi$
$193$	5.74993	+	5.74993i	0.413889	+	0.413889i	−0.469202	+	0.883091i	$0.655458\pi$
$194$	15.8402			1.13726
$195$	0.139340	+	0.750799i	0.00997831	+	0.0537658i
$196$	−1.58240			−0.113029
$197$	1.24668	−	1.24668i	0.0888223	−	0.0888223i	−0.661300	−	0.750122i	$-0.729995\pi$
$197$	1.24668	−	1.24668i	0.0888223	−	0.0888223i	0.750122	+	0.661300i	$0.229995\pi$
$198$	4.32266	−	4.32266i	0.307198	−	0.307198i
$199$	4.17076			0.295658			0.147829	−	0.989013i	$-0.452772\pi$
$199$	4.17076			0.295658			0.147829	+	0.989013i	$0.452772\pi$
$200$	−4.56871	−	2.03148i	−0.323056	−	0.143647i
$201$			4.43992i			0.313168i
$202$	−11.3571	+	11.3571i	−0.799080	+	0.799080i
$203$	−11.6779	+	11.6779i	−0.819630	+	0.819630i
$204$	−0.462678			−0.0323939
$205$	−14.8437	+	2.75483i	−1.03673	+	0.192405i
$206$		−	2.26695i		−	0.157946i
$207$	1.66757	−	4.49658i	0.115904	−	0.312534i
$208$	0.241478	+	0.241478i	0.0167435	+	0.0167435i
$209$		−	4.64313i		−	0.321172i
$210$	4.28997	+	2.94689i	0.296036	+	0.203355i
$211$	6.87441			0.473254			0.236627	−	0.971601i	$-0.423958\pi$
$211$	6.87441			0.473254			0.236627	+	0.971601i	$0.423958\pi$
$212$	1.45249	+	1.45249i	0.0997574	+	0.0997574i
$213$	4.41298	+	4.41298i	0.302373	+	0.302373i
$214$	−14.0754			−0.962171
$215$	−0.259018	+	0.377069i	−0.0176649	+	0.0257159i
$216$	1.00000			0.0680414
$217$	13.6697	+	13.6697i	0.927961	+	0.927961i
$218$	10.2139	−	10.2139i	0.691771	−	0.691771i
$219$			9.37434i			0.633459i
$220$	13.4400	−	2.49430i	0.906122	−	0.168166i
$221$			0.158005i			0.0106286i
$222$	1.92602	+	1.92602i	0.129266	+	0.129266i
$223$	11.2802	+	11.2802i	0.755379	+	0.755379i	0.975478	−	0.220098i	$-0.0706379\pi$
$223$	11.2802	+	11.2802i	0.755379	+	0.755379i	−0.220098	+	0.975478i	$0.570638\pi$
$224$	2.32757			0.155518
$225$	1.79409	+	4.66704i	0.119606	+	0.311136i
$226$		−	1.25173i		−	0.0832642i
$227$	2.22998	+	2.22998i	0.148009	+	0.148009i	0.777228	−	0.629219i	$-0.216625\pi$
$227$	2.22998	+	2.22998i	0.148009	+	0.148009i	−0.629219	+	0.777228i	$0.716625\pi$
$228$	0.537068	−	0.537068i	0.0355682	−	0.0355682i
$229$	5.86090			0.387299			0.193650	−	0.981071i	$-0.437968\pi$
$229$	5.86090			0.387299			0.193650	+	0.981071i	$0.437968\pi$
$230$	8.76653	−	6.17640i	0.578048	−	0.407260i
$231$	−14.2288			−0.936190
$232$	−5.01721	+	5.01721i	−0.329396	+	0.329396i
$233$	13.1762	+	13.1762i	0.863199	+	0.863199i	0.991708	−	0.128510i	$-0.0410193\pi$
$233$	13.1762	+	13.1762i	0.863199	+	0.863199i	−0.128510	+	0.991708i	$0.541019\pi$
$234$		−	0.341501i		−	0.0223246i
$235$	−2.62222	+	3.81733i	−0.171055	+	0.249015i
$236$	−1.68540			−0.109710
$237$	2.71125	+	2.71125i	0.176115	+	0.176115i
$238$	0.761495	+	0.761495i	0.0493604	+	0.0493604i
$239$		−	22.8269i		−	1.47655i	−0.674499	−	0.738276i	$-0.735640\pi$
$239$		−	22.8269i		−	1.47655i	0.674499	−	0.738276i	$-0.264360\pi$
$240$	1.84311	+	1.26608i	0.118972	+	0.0817250i
$241$		−	18.6517i		−	1.20146i	−0.799451	−	0.600731i	$-0.794876\pi$
$241$		−	18.6517i		−	1.20146i	0.799451	−	0.600731i	$-0.205124\pi$
$242$	−18.6470	+	18.6470i	−1.19867	+	1.19867i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	8.05915			0.515934
$245$	0.645653	+	3.47895i	0.0412492	+	0.222262i
$246$	6.75167			0.430471
$247$	−0.183409	−	0.183409i	−0.0116701	−	0.0116701i
$248$	5.87295	+	5.87295i	0.372933	+	0.372933i
$249$	3.03059			0.192056
$250$	−2.60213	+	10.8733i	−0.164573	+	0.687689i
$251$		−	24.1095i		−	1.52178i	−0.648880	−	0.760890i	$-0.724762\pi$
$251$		−	24.1095i		−	1.52178i	0.648880	−	0.760890i	$-0.275238\pi$
$252$	−1.64584	−	1.64584i	−0.103678	−	0.103678i
$253$	−10.1941	+	27.4883i	−0.640900	+	1.72818i
$254$			9.11869i			0.572158i
$255$	0.188782	+	1.01721i	0.0118220	+	0.0637001i
$256$	1.00000			0.0625000
$257$	−16.3759	+	16.3759i	−1.02150	+	1.02150i	−0.0217381	+	0.999764i	$0.506920\pi$
$257$	−16.3759	+	16.3759i	−1.02150	+	1.02150i	−0.999764	+	0.0217381i	$0.993080\pi$
$258$	0.144662	−	0.144662i	0.00900627	−	0.00900627i
$259$		−	6.33986i		−	0.393939i
$260$	0.432367	−	0.629423i	0.0268143	−	0.0390351i
$261$	7.09541			0.439195
$262$	7.45873	−	7.45873i	0.460802	−	0.460802i
$263$	16.2523	−	16.2523i	1.00216	−	1.00216i	0.00216013	−	0.999998i	$-0.499312\pi$
$263$	16.2523	−	16.2523i	1.00216	−	1.00216i	0.999998	−	0.00216013i	$-0.000687592\pi$
$264$	−6.11317			−0.376239
$265$	2.60069	−	3.78598i	0.159759	−	0.232571i
$266$	−1.76786			−0.108395
$267$	−3.28296	−	3.28296i	−0.200914	−	0.200914i
$268$	3.13950	−	3.13950i	0.191775	−	0.191775i
$269$		−	27.3620i		−	1.66829i	−0.551546	−	0.834144i	$-0.685962\pi$
$269$		−	27.3620i		−	1.66829i	0.551546	−	0.834144i	$-0.314038\pi$
$270$	−0.408021	−	2.19853i	−0.0248314	−	0.133798i
$271$	−30.7037			−1.86512			−0.932559	−	0.361017i	$-0.882430\pi$
$271$	−30.7037			−1.86512			−0.932559	+	0.361017i	$0.882430\pi$
$272$	0.327163	+	0.327163i	0.0198371	+	0.0198371i
$273$	−0.562057	+	0.562057i	−0.0340172	+	0.0340172i
$274$	−21.7734			−1.31538
$275$	−10.9676	−	28.5304i	−0.661370	−	1.72045i
$276$	−4.35871	+	2.00041i	−0.262364	+	0.120411i
$277$	2.21937	−	2.21937i	0.133349	−	0.133349i	−0.637282	−	0.770631i	$-0.719941\pi$
$277$	2.21937	−	2.21937i	0.133349	−	0.133349i	0.770631	+	0.637282i	$0.219941\pi$
$278$	−4.06693	−	4.06693i	−0.243918	−	0.243918i
$279$		−	8.30560i		−	0.497243i
$280$	−0.949699	−	5.11723i	−0.0567554	−	0.305813i
$281$			26.0473i			1.55385i	0.629592	+	0.776926i	$0.283222\pi$
$281$			26.0473i			1.55385i	−0.629592	+	0.776926i	$0.716778\pi$
$282$	1.46451	−	1.46451i	0.0872106	−	0.0872106i
$283$	5.48295	−	5.48295i	0.325928	−	0.325928i	−0.525108	−	0.851036i	$-0.675975\pi$
$283$	5.48295	−	5.48295i	0.325928	−	0.325928i	0.851036	+	0.525108i	$0.175975\pi$
$284$		−	6.24090i		−	0.370329i
$285$	−1.39989	−	0.961624i	−0.0829226	−	0.0569617i
$286$			2.08765i			0.123445i
$287$	−11.1122	−	11.1122i	−0.655932	−	0.655932i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$		−	16.7859i		−	0.987408i
$290$	13.0776	+	8.98334i	0.767943	+	0.527520i
$291$			15.8402i			0.928566i
$292$	6.62866	−	6.62866i	0.387913	−	0.387913i
$293$	−18.5543	+	18.5543i	−1.08395	+	1.08395i	−0.0878182	+	0.996137i	$0.527989\pi$
$293$	−18.5543	+	18.5543i	−1.08395	+	1.08395i	−0.996137	+	0.0878182i	$0.972011\pi$
$294$		−	1.58240i		−	0.0922874i
$295$	0.687677	+	3.70539i	0.0400381	+	0.215736i
$296$		−	2.72380i		−	0.158318i
$297$	4.32266	+	4.32266i	0.250826	+	0.250826i
$298$	12.5148	−	12.5148i	0.724960	−	0.724960i
$299$	0.683142	+	1.48850i	0.0395071	+	0.0860824i
$300$	2.03148	−	4.56871i	0.117288	−	0.263774i
$301$	−0.476182			−0.0274467
$302$	−8.42283	+	8.42283i	−0.484680	+	0.484680i
$303$	−11.3571	−	11.3571i	−0.652446	−	0.652446i
$304$	−0.759529			−0.0435620
$305$	−3.28830	−	17.7183i	−0.188288	−	1.01454i
$306$		−	0.462678i		−	0.0264495i
$307$	20.3743	−	20.3743i	1.16282	−	1.16282i	0.178966	−	0.983855i	$-0.442725\pi$
$307$	20.3743	−	20.3743i	1.16282	−	1.16282i	0.983855	−	0.178966i	$-0.0572752\pi$
$308$	10.0613	+	10.0613i	0.573297	+	0.573297i
$309$	2.26695			0.128962
$310$	10.5155	−	15.3081i	0.597243	−	0.869443i
$311$	16.5017			0.935724			0.467862	−	0.883801i	$-0.345024\pi$
$311$	16.5017			0.935724			0.467862	+	0.883801i	$0.345024\pi$
$312$	−0.241478	+	0.241478i	−0.0136710	+	0.0136710i
$313$	4.53498	−	4.53498i	0.256332	−	0.256332i	−0.567228	−	0.823561i	$-0.691984\pi$
$313$	4.53498	−	4.53498i	0.256332	−	0.256332i	0.823561	+	0.567228i	$0.191984\pi$
$314$	7.57872			0.427692
$315$	−2.94689	+	4.28997i	−0.166039	+	0.241712i
$316$		−	3.83429i		−	0.215695i
$317$	−12.5140	+	12.5140i	−0.702856	+	0.702856i	−0.965023	−	0.262167i	$-0.915563\pi$
$317$	−12.5140	+	12.5140i	−0.702856	+	0.702856i	0.262167	+	0.965023i	$0.415563\pi$
$318$	−1.45249	+	1.45249i	−0.0814516	+	0.0814516i
$319$	−43.3754			−2.42856
$320$	−0.408021	−	2.19853i	−0.0228091	−	0.122901i
$321$		−	14.0754i		−	0.785609i
$322$	10.4661	+	3.88139i	0.583254	+	0.216301i
$323$	−0.248490	−	0.248490i	−0.0138263	−	0.0138263i
$324$			1.00000i			0.0555556i
$325$	−1.56022	−	0.693752i	−0.0865453	−	0.0384824i
$326$	2.54552			0.140983
$327$	10.2139	+	10.2139i	0.564828	+	0.564828i
$328$	−4.77416	−	4.77416i	−0.263609	−	0.263609i
$329$	−4.82072			−0.265775
$330$	2.49430	+	13.4400i	0.137307	+	0.739846i
$331$	24.3710			1.33955			0.669775	−	0.742564i	$-0.266390\pi$
$331$	24.3710			1.33955			0.669775	+	0.742564i	$0.266390\pi$
$332$	−2.14295	−	2.14295i	−0.117610	−	0.117610i
$333$	−1.92602	+	1.92602i	−0.105545	+	0.105545i
$334$		−	13.9256i		−	0.761974i
$335$	−8.18325	−	5.62129i	−0.447099	−	0.307124i
$336$			2.32757i			0.126980i
$337$	−15.7870	−	15.7870i	−0.859971	−	0.859971i	0.131363	−	0.991334i	$-0.458065\pi$
$337$	−15.7870	−	15.7870i	−0.859971	−	0.859971i	−0.991334	+	0.131363i	$0.958065\pi$
$338$	−9.10992	−	9.10992i	−0.495515	−	0.495515i
$339$	1.25173			0.0679849
$340$	0.585786	−	0.852765i	0.0317687	−	0.0462477i
$341$			50.7735i			2.74954i
$342$	0.537068	+	0.537068i	0.0290413	+	0.0290413i
$343$	−14.1253	+	14.1253i	−0.762694	+	0.762694i
$344$	−0.204583			−0.0110304
$345$	6.17640	+	8.76653i	0.332526	+	0.471974i
$346$	17.1567			0.922351
$347$	−11.4749	+	11.4749i	−0.616007	+	0.616007i	−0.944505	−	0.328498i	$-0.893458\pi$
$347$	−11.4749	+	11.4749i	−0.616007	+	0.616007i	0.328498	+	0.944505i	$0.393458\pi$
$348$	−5.01721	−	5.01721i	−0.268951	−	0.268951i
$349$			5.86005i			0.313682i	0.987624	+	0.156841i	$0.0501309\pi$
$349$			5.86005i			0.313682i	−0.987624	+	0.156841i	$0.949869\pi$
$350$	−10.8629	+	4.17588i	−0.580645	+	0.223210i
$351$	0.341501			0.0182280
$352$	4.32266	+	4.32266i	0.230399	+	0.230399i
$353$	3.94327	+	3.94327i	0.209879	+	0.209879i	0.804216	−	0.594337i	$-0.202586\pi$
$353$	3.94327	+	3.94327i	0.209879	+	0.209879i	−0.594337	+	0.804216i	$0.702586\pi$
$354$		−	1.68540i		−	0.0895778i
$355$	−13.7208	+	2.54642i	−0.728224	+	0.135150i
$356$			4.64280i			0.246068i
$357$	−0.761495	+	0.761495i	−0.0403026	+	0.0403026i
$358$	−1.14577	−	1.14577i	−0.0605561	−	0.0605561i
$359$	−32.6374			−1.72254			−0.861269	−	0.508150i	$-0.830330\pi$
$359$	−32.6374			−1.72254			−0.861269	+	0.508150i	$0.830330\pi$
$360$	−1.26608	+	1.84311i	−0.0667282	+	0.0971403i
$361$	−18.4231			−0.969638
$362$	−14.5551	−	14.5551i	−0.765000	−	0.765000i
$363$	−18.6470	−	18.6470i	−0.978713	−	0.978713i
$364$	0.794868			0.0416624
$365$	−17.2779	−	11.8687i	−0.904368	−	0.621234i
$366$			8.05915i			0.421258i
$367$	−22.9985	−	22.9985i	−1.20051	−	1.20051i	−0.974011	−	0.226499i	$-0.927272\pi$
$367$	−22.9985	−	22.9985i	−1.20051	−	1.20051i	−0.226499	−	0.974011i	$-0.572728\pi$
$368$	4.49658	+	1.66757i	0.234400	+	0.0869281i
$369$			6.75167i			0.351478i
$370$	−5.98836	+	1.11137i	−0.311320	+	0.0577774i
$371$	4.78114			0.248224
$372$	−5.87295	+	5.87295i	−0.304498	+	0.304498i
$373$	−15.4627	+	15.4627i	−0.800629	+	0.800629i	−0.983194	−	0.182564i	$-0.941560\pi$
$373$	−15.4627	+	15.4627i	−0.800629	+	0.800629i	0.182564	+	0.983194i	$0.441560\pi$
$374$			2.82843i			0.146254i
$375$	−10.8733	−	2.60213i	−0.561495	−	0.134374i
$376$	−2.07114			−0.106811
$377$	−1.71338	+	1.71338i	−0.0882436	+	0.0882436i
$378$	1.64584	−	1.64584i	0.0846530	−	0.0846530i
$379$	11.0986			0.570095			0.285048	−	0.958513i	$-0.407991\pi$
$379$	11.0986			0.570095			0.285048	+	0.958513i	$0.407991\pi$
$380$	0.309904	+	1.66985i	0.0158977	+	0.0856613i
$381$	−9.11869			−0.467165
$382$	−14.7221	−	14.7221i	−0.753251	−	0.753251i
$383$	−18.4090	+	18.4090i	−0.940653	+	0.940653i	−0.998335	−	0.0576815i	$-0.981629\pi$
$383$	−18.4090	+	18.4090i	−0.940653	+	0.940653i	0.0576815	+	0.998335i	$0.481629\pi$
$384$			1.00000i			0.0510310i
$385$	18.0148	−	26.2253i	0.918121	−	1.33656i
$386$	8.13163			0.413889
$387$	0.144662	+	0.144662i	0.00735359	+	0.00735359i
$388$	11.2007	−	11.2007i	0.568628	−	0.568628i
$389$	21.2944			1.07967			0.539833	−	0.841772i	$-0.318487\pi$
$389$	21.2944			1.07967			0.539833	+	0.841772i	$0.318487\pi$
$390$	0.629423	+	0.432367i	0.0318721	+	0.0218937i
$391$	0.925546	+	2.01668i	0.0468069	+	0.101988i
$392$	−1.11893	+	1.11893i	−0.0565143	+	0.0565143i
$393$	7.45873	+	7.45873i	0.376243	+	0.376243i
$394$		−	1.76307i		−	0.0888223i
$395$	−8.42978	+	1.56447i	−0.424148	+	0.0787170i
$396$		−	6.11317i		−	0.307198i
$397$	−17.4767	+	17.4767i	−0.877130	+	0.877130i	−0.993237	−	0.116107i	$-0.962959\pi$
$397$	−17.4767	+	17.4767i	−0.877130	+	0.877130i	0.116107	+	0.993237i	$0.462959\pi$
$398$	2.94918	−	2.94918i	0.147829	−	0.147829i
$399$		−	1.76786i		−	0.0885037i
$400$	−4.66704	+	1.79409i	−0.233352	+	0.0897045i
$401$			9.34370i			0.466602i	0.972405	+	0.233301i	$0.0749528\pi$
$401$			9.34370i			0.466602i	−0.972405	+	0.233301i	$0.925047\pi$
$402$	3.13950	+	3.13950i	0.156584	+	0.156584i
$403$	2.00562	+	2.00562i	0.0999069	+	0.0999069i
$404$			16.0613i			0.799080i
$405$	2.19853	−	0.408021i	0.109246	−	0.0202747i
$406$			16.5151i			0.819630i
$407$	11.7741	−	11.7741i	0.583620	−	0.583620i
$408$	−0.327163	+	0.327163i	−0.0161970	+	0.0161970i
$409$			15.8867i			0.785545i	0.919636	+	0.392773i	$0.128484\pi$
$409$			15.8867i			0.785545i	−0.919636	+	0.392773i	$0.871516\pi$
$410$	−8.54815	+	12.4441i	−0.422163	+	0.614568i
$411$		−	21.7734i		−	1.07401i
$412$	−1.60298	−	1.60298i	−0.0789730	−	0.0789730i
$413$	−2.77390	+	2.77390i	−0.136495	+	0.136495i
$414$	−2.00041	−	4.35871i	−0.0983148	−	0.214219i
$415$	−3.83697	+	5.58570i	−0.188349	+	0.274191i
$416$	0.341501			0.0167435
$417$	4.06693	−	4.06693i	0.199159	−	0.199159i
$418$	−3.28319	−	3.28319i	−0.160586	−	0.160586i
$419$	5.11030			0.249654			0.124827	−	0.992178i	$-0.460162\pi$
$419$	5.11030			0.249654			0.124827	+	0.992178i	$0.460162\pi$
$420$	5.11723	−	0.949699i	0.249695	−	0.0463406i
$421$			5.71253i			0.278412i	0.990263	+	0.139206i	$0.0444550\pi$
$421$			5.71253i			0.278412i	−0.990263	+	0.139206i	$0.955545\pi$
$422$	4.86094	−	4.86094i	0.236627	−	0.236627i
$423$	1.46451	+	1.46451i	0.0712071	+	0.0712071i
$424$	2.05413			0.0997574
$425$	−2.11384	−	0.939921i	−0.102536	−	0.0455929i
$426$	6.24090			0.302373
$427$	13.2641	−	13.2641i	0.641895	−	0.641895i
$428$	−9.95278	+	9.95278i	−0.481086	+	0.481086i
$429$	−2.08765			−0.100793
$430$	0.0834743	+	0.449782i	0.00402549	+	0.0216904i
$431$		−	3.28744i		−	0.158351i	−0.996861	−	0.0791753i	$-0.974771\pi$
$431$		−	3.28744i		−	0.158351i	0.996861	−	0.0791753i	$-0.0252287\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	11.6374	−	11.6374i	0.559256	−	0.559256i	−0.369840	−	0.929096i	$-0.620587\pi$
$433$	11.6374	−	11.6374i	0.559256	−	0.559256i	0.929096	+	0.369840i	$0.120587\pi$
$434$	19.3319			0.927961
$435$	−8.98334	+	13.0776i	−0.430718	+	0.627023i
$436$		−	14.4446i		−	0.691771i
$437$	−3.41528	−	1.26657i	−0.163375	−	0.0605882i
$438$	6.62866	+	6.62866i	0.316730	+	0.316730i
$439$		−	12.3751i		−	0.590631i	−0.955400	−	0.295316i	$-0.904575\pi$
$439$		−	12.3751i		−	0.590631i	0.955400	−	0.295316i	$-0.0954248\pi$
$440$	7.73975	−	11.2672i	0.368978	−	0.537144i
$441$	1.58240			0.0753524
$442$	0.111726	+	0.111726i	0.00531428	+	0.00531428i
$443$	24.4511	+	24.4511i	1.16171	+	1.16171i	0.984102	+	0.177606i	$0.0568354\pi$
$443$	24.4511	+	24.4511i	1.16171	+	1.16171i	0.177606	+	0.984102i	$0.443165\pi$
$444$	2.72380			0.129266
$445$	10.2073	−	1.89436i	0.483873	−	0.0898013i
$446$	15.9526			0.755379
$447$	12.5148	+	12.5148i	0.591927	+	0.591927i
$448$	1.64584	−	1.64584i	0.0777588	−	0.0777588i
$449$		−	41.0277i		−	1.93622i	−0.250534	−	0.968108i	$-0.580606\pi$
$449$		−	41.0277i		−	1.93622i	0.250534	−	0.968108i	$-0.419394\pi$
$450$	4.56871	+	2.03148i	0.215371	+	0.0957649i
$451$		−	41.2741i		−	1.94352i
$452$	−0.885110	−	0.885110i	−0.0416321	−	0.0416321i
$453$	−8.42283	−	8.42283i	−0.395739	−	0.395739i
$454$	3.15367			0.148009
$455$	−0.324323	−	1.74754i	−0.0152045	−	0.0819259i
$456$		−	0.759529i		−	0.0355682i
$457$	−18.5456	−	18.5456i	−0.867526	−	0.867526i	0.124672	−	0.992198i	$-0.460212\pi$
$457$	−18.5456	−	18.5456i	−0.867526	−	0.867526i	−0.992198	+	0.124672i	$0.960212\pi$
$458$	4.14428	−	4.14428i	0.193650	−	0.193650i
$459$	0.462678			0.0215960
$460$	1.83150	−	10.5662i	0.0853940	−	0.492654i
$461$	21.4962			1.00118			0.500588	−	0.865686i	$-0.333117\pi$
$461$	21.4962			1.00118			0.500588	+	0.865686i	$0.333117\pi$
$462$	−10.0613	+	10.0613i	−0.468095	+	0.468095i
$463$	−14.7714	−	14.7714i	−0.686485	−	0.686485i	0.274968	−	0.961453i	$-0.411333\pi$
$463$	−14.7714	−	14.7714i	−0.686485	−	0.686485i	−0.961453	+	0.274968i	$0.911333\pi$
$464$			7.09541i			0.329396i
$465$	15.3081	+	10.5155i	0.709897	+	0.487647i
$466$	18.6339			0.863199
$467$	23.9052	+	23.9052i	1.10620	+	1.10620i	0.993646	+	0.112554i	$0.0359030\pi$
$467$	23.9052	+	23.9052i	1.10620	+	1.10620i	0.112554	+	0.993646i	$0.464097\pi$
$468$	−0.241478	−	0.241478i	−0.0111623	−	0.0111623i
$469$		−	10.3342i		−	0.477191i
$470$	0.845067	+	4.55345i	0.0389800	+	0.210035i
$471$			7.57872i			0.349209i
$472$	−1.19176	+	1.19176i	−0.0548550	+	0.0548550i
$473$	−0.884344	−	0.884344i	−0.0406622	−	0.0406622i
$474$	3.83429			0.176115
$475$	3.54475	−	1.36266i	0.162644	−	0.0625233i
$476$	1.07692			0.0493604
$477$	−1.45249	−	1.45249i	−0.0665049	−	0.0665049i
$478$	−16.1411	−	16.1411i	−0.738276	−	0.738276i
$479$	11.0131			0.503199			0.251600	−	0.967831i	$-0.419043\pi$
$479$	11.0131			0.503199			0.251600	+	0.967831i	$0.419043\pi$
$480$	2.19853	−	0.408021i	0.100349	−	0.0186235i
$481$		−	0.930181i		−	0.0424126i
$482$	−13.1887	−	13.1887i	−0.600731	−	0.600731i
$483$	−3.88139	+	10.4661i	−0.176609	+	0.476225i
$484$			26.3708i			1.19867i
$485$	−29.1951	−	20.0549i	−1.32568	−	0.910645i
$486$	−1.00000			−0.0453609
$487$	25.8202	−	25.8202i	1.17002	−	1.17002i	0.187820	−	0.982203i	$-0.439858\pi$
$487$	25.8202	−	25.8202i	1.17002	−	1.17002i	0.982203	−	0.187820i	$-0.0601422\pi$
$488$	5.69868	−	5.69868i	0.257967	−	0.257967i
$489$			2.54552i			0.115112i
$490$	2.91653	+	2.00344i	0.131756	+	0.0905063i
$491$	−21.1318			−0.953665			−0.476832	−	0.878994i	$-0.658215\pi$
$491$	−21.1318			−0.953665			−0.476832	+	0.878994i	$0.658215\pi$
$492$	4.77416	−	4.77416i	0.215236	−	0.215236i
$493$	−2.32135	+	2.32135i	−0.104548	+	0.104548i
$494$	−0.259380			−0.0116701
$495$	−13.4400	+	2.49430i	−0.604081	+	0.112111i
$496$	8.30560			0.372933
$497$	−10.2715	−	10.2715i	−0.460742	−	0.460742i
$498$	2.14295	−	2.14295i	0.0960279	−	0.0960279i
$499$			25.7570i			1.15304i	0.817083	+	0.576520i	$0.195590\pi$
$499$			25.7570i			1.15304i	−0.817083	+	0.576520i	$0.804410\pi$
$500$	5.84861	+	9.52858i	0.261558	+	0.426131i
$501$	13.9256			0.622149
$502$	−17.0480	−	17.0480i	−0.760890	−	0.760890i
$503$	−2.42325	+	2.42325i	−0.108048	+	0.108048i	−0.759064	−	0.651016i	$-0.774343\pi$
$503$	−2.42325	+	2.42325i	−0.108048	+	0.108048i	0.651016	+	0.759064i	$0.274343\pi$
$504$	−2.32757			−0.103678
$505$	35.3112	−	6.55336i	1.57133	−	0.291621i
$506$	12.2288	+	26.6455i	0.543639	+	1.18454i
$507$	9.10992	−	9.10992i	0.404586	−	0.404586i
$508$	6.44789	+	6.44789i	0.286079	+	0.286079i
$509$			37.8408i			1.67726i	0.544698	+	0.838632i	$0.316644\pi$
$509$			37.8408i			1.67726i	−0.544698	+	0.838632i	$0.683356\pi$
$510$	0.852765	+	0.585786i	0.0377611	+	0.0259391i
$511$		−	21.8195i		−	0.965237i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−0.537068	+	0.537068i	−0.0237122	+	0.0237122i
$514$			23.1590i			1.02150i
$515$	−2.87014	+	4.17824i	−0.126473	+	0.184115i
$516$		−	0.204583i		−	0.00900627i
$517$	−8.95282	−	8.95282i	−0.393745	−	0.393745i
$518$	−4.48296	−	4.48296i	−0.196970	−	0.196970i
$519$			17.1567i			0.753096i
$520$	−0.139340	−	0.750799i	−0.00611044	−	0.0329247i
$521$			8.64661i			0.378815i	0.981899	+	0.189407i	$0.0606567\pi$
$521$			8.64661i			0.378815i	−0.981899	+	0.189407i	$0.939343\pi$
$522$	5.01721	−	5.01721i	0.219597	−	0.219597i
$523$	22.1099	−	22.1099i	0.966800	−	0.966800i	−0.0326665	−	0.999466i	$-0.510400\pi$
$523$	22.1099	−	22.1099i	0.966800	−	0.966800i	0.999466	+	0.0326665i	$0.0103999\pi$
$524$		−	10.5482i		−	0.460802i
$525$	−4.17588	−	10.8629i	−0.182250	−	0.474095i
$526$		−	22.9842i		−	1.00216i
$527$	2.71728	+	2.71728i	0.118367	+	0.118367i
$528$	−4.32266	+	4.32266i	−0.188120	+	0.188120i
$529$	17.4384	+	14.9967i	0.758192	+	0.652031i
$530$	−0.838129	−	4.51606i	−0.0364060	−	0.196165i
$531$	1.68540			0.0731400
$532$	−1.25007	+	1.25007i	−0.0541973	+	0.0541973i
$533$	−1.63038	−	1.63038i	−0.0706195	−	0.0706195i
$534$	−4.64280			−0.200914
$535$	25.9424	+	17.8205i	1.12159	+	0.770447i
$536$		−	4.43992i		−	0.191775i
$537$	1.14577	−	1.14577i	0.0494438	−	0.0494438i
$538$	−19.3478	−	19.3478i	−0.834144	−	0.834144i
$539$	−9.67348			−0.416666
$540$	−1.84311	−	1.26608i	−0.0793147	−	0.0544833i
$541$	31.2535			1.34369			0.671846	−	0.740691i	$-0.265502\pi$
$541$	31.2535			1.34369			0.671846	+	0.740691i	$0.265502\pi$
$542$	−21.7108	+	21.7108i	−0.932559	+	0.932559i
$543$	14.5551	−	14.5551i	0.624620	−	0.624620i
$544$	0.462678			0.0198371
$545$	−31.7568	+	5.89370i	−1.36031	+	0.252458i
$546$			0.794868i			0.0340172i
$547$	12.6714	−	12.6714i	0.541792	−	0.541792i	−0.382262	−	0.924054i	$-0.624855\pi$
$547$	12.6714	−	12.6714i	0.541792	−	0.541792i	0.924054	+	0.382262i	$0.124855\pi$
$548$	−15.3962	+	15.3962i	−0.657691	+	0.657691i
$549$	−8.05915			−0.343956
$550$	−27.9293	−	12.4188i	−1.19091	−	0.529539i
$551$		−	5.38917i		−	0.229586i
$552$	−1.66757	+	4.49658i	−0.0709765	+	0.191387i
$553$	−6.31063	−	6.31063i	−0.268355	−	0.268355i
$554$		−	3.13866i		−	0.133349i
$555$	−1.11137	−	5.98836i	−0.0471750	−	0.254192i
$556$	−5.75151			−0.243918
$557$	2.52234	+	2.52234i	0.106875	+	0.106875i	0.758522	−	0.651647i	$-0.225922\pi$
$557$	2.52234	+	2.52234i	0.106875	+	0.106875i	−0.651647	+	0.758522i	$0.725922\pi$
$558$	−5.87295	−	5.87295i	−0.248622	−	0.248622i
$559$	−0.0698653			−0.00295499
$560$	−4.28997	−	2.94689i	−0.181284	−	0.124529i
$561$	−2.82843			−0.119416
$562$	18.4182	+	18.4182i	0.776926	+	0.776926i
$563$	26.8499	−	26.8499i	1.13159	−	1.13159i	0.141675	−	0.989913i	$-0.454751\pi$
$563$	26.8499	−	26.8499i	1.13159	−	1.13159i	0.989913	−	0.141675i	$-0.0452489\pi$
$564$		−	2.07114i		−	0.0872106i
$565$	−1.58479	+	2.30708i	−0.0666728	+	0.0970597i
$566$		−	7.75406i		−	0.325928i
$567$	1.64584	+	1.64584i	0.0691189	+	0.0691189i
$568$	−4.41298	−	4.41298i	−0.185165	−	0.185165i
$569$	−17.2543			−0.723337			−0.361668	−	0.932307i	$-0.617793\pi$
$569$	−17.2543			−0.723337			−0.361668	+	0.932307i	$0.617793\pi$
$570$	−1.66985	+	0.309904i	−0.0699421	+	0.0129805i
$571$			43.9751i			1.84030i	0.391565	+	0.920151i	$0.371934\pi$
$571$			43.9751i			1.84030i	−0.391565	+	0.920151i	$0.628066\pi$
$572$	1.47619	+	1.47619i	0.0617227	+	0.0617227i
$573$	14.7221	−	14.7221i	0.615027	−	0.615027i
$574$	−15.7150			−0.655932
$575$	−23.9775	+	0.284659i	−0.999930	+	0.0118711i
$576$	−1.00000			−0.0416667
$577$	3.00797	−	3.00797i	0.125223	−	0.125223i	−0.641718	−	0.766941i	$-0.721778\pi$
$577$	3.00797	−	3.00797i	0.125223	−	0.125223i	0.766941	+	0.641718i	$0.221778\pi$
$578$	−11.8694	−	11.8694i	−0.493704	−	0.493704i
$579$			8.13163i			0.337939i
$580$	15.5994	−	2.89508i	0.647731	−	0.120211i
$581$	−7.05392			−0.292646
$582$	11.2007	+	11.2007i	0.464283	+	0.464283i
$583$	8.87931	+	8.87931i	0.367744	+	0.367744i
$584$		−	9.37434i		−	0.387913i
$585$	−0.432367	+	0.629423i	−0.0178762	+	0.0260234i
$586$			26.2398i			1.08395i
$587$	−22.9088	+	22.9088i	−0.945548	+	0.945548i	−0.998592	−	0.0530437i	$-0.983108\pi$
$587$	−22.9088	+	22.9088i	−0.945548	+	0.945548i	0.0530437	+	0.998592i	$0.483108\pi$
$588$	−1.11893	−	1.11893i	−0.0461437	−	0.0461437i
$589$	−6.30835			−0.259931
$590$	3.10637	+	2.13384i	0.127887	+	0.0878490i
$591$	1.76307			0.0725231
$592$	−1.92602	−	1.92602i	−0.0791590	−	0.0791590i
$593$	−11.7866	−	11.7866i	−0.484017	−	0.484017i	0.422395	−	0.906412i	$-0.361190\pi$
$593$	−11.7866	−	11.7866i	−0.484017	−	0.484017i	−0.906412	+	0.422395i	$0.861190\pi$
$594$	6.11317			0.250826
$595$	−0.439405	−	2.36763i	−0.0180138	−	0.0970634i
$596$		−	17.6985i		−	0.724960i
$597$	2.94918	+	2.94918i	0.120702	+	0.120702i
$598$	1.53558	+	0.569476i	0.0627947	+	0.0232876i
$599$			46.9341i			1.91767i	0.283957	+	0.958837i	$0.408353\pi$
$599$			46.9341i			1.91767i	−0.283957	+	0.958837i	$0.591647\pi$
$600$	−1.79409	−	4.66704i	−0.0732434	−	0.190531i
$601$	−2.50913			−0.102350			−0.0511748	−	0.998690i	$-0.516297\pi$
$601$	−2.50913			−0.102350			−0.0511748	+	0.998690i	$0.516297\pi$
$602$	−0.336712	+	0.336712i	−0.0137234	+	0.0137234i
$603$	−3.13950	+	3.13950i	−0.127850	+	0.127850i
$604$			11.9117i			0.484680i
$605$	57.9769	−	10.7599i	2.35710	−	0.437450i
$606$	−16.0613			−0.652446
$607$	−4.62585	+	4.62585i	−0.187758	+	0.187758i	−0.794726	−	0.606968i	$-0.792385\pi$
$607$	−4.62585	+	4.62585i	−0.187758	+	0.187758i	0.606968	+	0.794726i	$0.292385\pi$
$608$	−0.537068	+	0.537068i	−0.0217810	+	0.0217810i
$609$	−16.5151			−0.669225
$610$	−14.8539	−	10.2035i	−0.601416	−	0.413128i
$611$	−0.707295			−0.0286141
$612$	−0.327163	−	0.327163i	−0.0132248	−	0.0132248i
$613$	−4.93150	+	4.93150i	−0.199181	+	0.199181i	−0.799649	−	0.600468i	$-0.794981\pi$
$613$	−4.93150	+	4.93150i	−0.199181	+	0.199181i	0.600468	+	0.799649i	$0.294981\pi$
$614$		−	28.8136i		−	1.16282i
$615$	−12.4441	−	8.54815i	−0.501793	−	0.344695i
$616$	14.2288			0.573297
$617$	27.5512	+	27.5512i	1.10917	+	1.10917i	0.993260	+	0.115911i	$0.0369787\pi$
$617$	27.5512	+	27.5512i	1.10917	+	1.10917i	0.115911	+	0.993260i	$0.463021\pi$
$618$	1.60298	−	1.60298i	0.0644812	−	0.0644812i
$619$	14.2298			0.571945			0.285972	−	0.958238i	$-0.407683\pi$
$619$	14.2298			0.571945			0.285972	+	0.958238i	$0.407683\pi$
$620$	−3.38886	−	18.2601i	−0.136100	−	0.733343i
$621$	4.35871	−	2.00041i	0.174909	−	0.0802737i
$622$	11.6684	−	11.6684i	0.467862	−	0.467862i
$623$	7.64132	+	7.64132i	0.306143	+	0.306143i
$624$			0.341501i			0.0136710i
$625$	18.5625	−	16.7462i	0.742499	−	0.669847i
$626$		−	6.41343i		−	0.256332i
$627$	3.28319	−	3.28319i	0.131118	−	0.131118i
$628$	5.35896	−	5.35896i	0.213846	−	0.213846i
$629$		−	1.26024i		−	0.0502492i
$630$	0.949699	+	5.11723i	0.0378369	+	0.203875i
$631$			19.7938i			0.787979i	0.919115	+	0.393990i	$0.128905\pi$
$631$			19.7938i			0.787979i	−0.919115	+	0.393990i	$0.871095\pi$
$632$	−2.71125	−	2.71125i	−0.107848	−	0.107848i
$633$	4.86094	+	4.86094i	0.193205	+	0.193205i
$634$			17.6975i			0.702856i
$635$	11.5450	−	16.8067i	0.458149	−	0.666955i
$636$			2.05413i			0.0814516i
$637$	−0.382114	+	0.382114i	−0.0151399	+	0.0151399i
$638$	−30.6710	+	30.6710i	−1.21428	+	1.21428i
$639$			6.24090i			0.246886i
$640$	−1.84311	−	1.26608i	−0.0728552	−	0.0500461i
$641$			31.1566i			1.23061i	0.788289	+	0.615306i	$0.210967\pi$
$641$			31.1566i			1.23061i	−0.788289	+	0.615306i	$0.789033\pi$
$642$	−9.95278	−	9.95278i	−0.392805	−	0.392805i
$643$	21.5814	−	21.5814i	0.851087	−	0.851087i	−0.139180	−	0.990267i	$-0.544447\pi$
$643$	21.5814	−	21.5814i	0.851087	−	0.851087i	0.990267	+	0.139180i	$0.0444468\pi$
$644$	10.1452	−	4.65610i	0.399778	−	0.183476i
$645$	−0.449782	+	0.0834743i	−0.0177101	+	0.00328680i
$646$	−0.351417			−0.0138263
$647$	1.34183	−	1.34183i	0.0527528	−	0.0527528i	−0.680238	−	0.732991i	$-0.738124\pi$
$647$	1.34183	−	1.34183i	0.0527528	−	0.0527528i	0.732991	+	0.680238i	$0.238124\pi$
$648$	0.707107	+	0.707107i	0.0277778	+	0.0277778i
$649$	−10.3031			−0.404432
$650$	−1.59380	+	0.612683i	−0.0625139	+	0.0240314i
$651$			19.3319i			0.757677i
$652$	1.79995	−	1.79995i	0.0704916	−	0.0704916i
$653$	−25.9393	−	25.9393i	−1.01508	−	1.01508i	−0.999885	−	0.0151973i	$-0.995162\pi$
$653$	−25.9393	−	25.9393i	−1.01508	−	1.01508i	−0.0151973	−	0.999885i	$-0.504838\pi$
$654$	14.4446			0.564828
$655$	−23.1906	+	4.30391i	−0.906131	+	0.168168i
$656$	−6.75167			−0.263609
$657$	−6.62866	+	6.62866i	−0.258609	+	0.258609i
$658$	−3.40877	+	3.40877i	−0.132888	+	0.132888i
$659$	−3.80748			−0.148318			−0.0741592	−	0.997246i	$-0.523627\pi$
$659$	−3.80748			−0.148318			−0.0741592	+	0.997246i	$0.523627\pi$
$660$	11.2672	+	7.73975i	0.438576	+	0.301269i
$661$		−	4.54043i		−	0.176602i	−0.996094	−	0.0883010i	$-0.971856\pi$
$661$		−	4.54043i		−	0.176602i	0.996094	−	0.0883010i	$-0.0281438\pi$
$662$	17.2329	−	17.2329i	0.669775	−	0.669775i
$663$	−0.111726	+	0.111726i	−0.00433909	+	0.00433909i
$664$	−3.03059			−0.117610
$665$	3.25836	+	2.23825i	0.126354	+	0.0867956i
$666$			2.72380i			0.105545i
$667$	−11.8321	+	31.9050i	−0.458140	+	1.23537i
$668$	−9.84687	−	9.84687i	−0.380987	−	0.380987i
$669$			15.9526i			0.616765i
$670$	−9.76128	+	1.81158i	−0.377111	+	0.0699875i
$671$	49.2669			1.90193
$672$	1.64584	+	1.64584i	0.0634898	+	0.0634898i
$673$	22.6605	+	22.6605i	0.873499	+	0.873499i	0.992852	−	0.119353i	$-0.0380821\pi$
$673$	22.6605	+	22.6605i	0.873499	+	0.873499i	−0.119353	+	0.992852i	$0.538082\pi$
$674$	−22.3261			−0.859971
$675$	−2.03148	+	4.56871i	−0.0781917	+	0.175850i
$676$	−12.8834			−0.495515
$677$	33.2731	+	33.2731i	1.27879	+	1.27879i	0.941347	+	0.337440i	$0.109561\pi$
$677$	33.2731	+	33.2731i	1.27879	+	1.27879i	0.337440	+	0.941347i	$0.390439\pi$
$678$	0.885110	−	0.885110i	0.0339925	−	0.0339925i
$679$		−	36.8691i		−	1.41491i
$680$	−0.188782	−	1.01721i	−0.00723947	−	0.0390082i
$681$			3.15367i			0.120849i
$682$	35.9023	+	35.9023i	1.37477	+	1.37477i
$683$	16.5376	+	16.5376i	0.632793	+	0.632793i	0.948768	−	0.315975i	$-0.102332\pi$
$683$	16.5376	+	16.5376i	0.632793	+	0.632793i	−0.315975	+	0.948768i	$0.602332\pi$
$684$	0.759529			0.0290413
$685$	40.1308	+	27.5669i	1.53332	+	1.05328i
$686$			19.9762i			0.762694i
$687$	4.14428	+	4.14428i	0.158114	+	0.158114i
$688$	−0.144662	+	0.144662i	−0.00551519	+	0.00551519i
$689$	0.701487			0.0267245
$690$	10.5662	+	1.83150i	0.402250	+	0.0697239i
$691$	−38.2075			−1.45348			−0.726741	−	0.686912i	$-0.758966\pi$
$691$	−38.2075			−1.45348			−0.726741	+	0.686912i	$0.758966\pi$
$692$	12.1316	−	12.1316i	0.461176	−	0.461176i
$693$	−10.0613	−	10.0613i	−0.382198	−	0.382198i
$694$			16.2280i			0.616007i
$695$	2.34674	+	12.6448i	0.0890168	+	0.479646i
$696$	−7.09541			−0.268951
$697$	−2.20890	−	2.20890i	−0.0836679	−	0.0836679i
$698$	4.14368	+	4.14368i	0.156841	+	0.156841i
$699$			18.6339i			0.704799i
$700$	−4.72842	+	10.6340i	−0.178717	+	0.401928i
$701$		−	5.54946i		−	0.209600i	−0.994493	−	0.104800i	$-0.966580\pi$
$701$		−	5.54946i		−	0.209600i	0.994493	−	0.104800i	$-0.0334203\pi$
$702$	0.241478	−	0.241478i	0.00911398	−	0.00911398i
$703$	1.46287	+	1.46287i	0.0551732	+	0.0551732i
$704$	6.11317			0.230399
$705$	−4.55345	+	0.845067i	−0.171493	+	0.0318271i
$706$	5.57662			0.209879
$707$	26.4344	+	26.4344i	0.994168	+	0.994168i
$708$	−1.19176	−	1.19176i	−0.0447889	−	0.0447889i
$709$	41.0934			1.54329			0.771647	−	0.636051i	$-0.219433\pi$
$709$	41.0934			1.54329			0.771647	+	0.636051i	$0.219433\pi$
$710$	−7.90147	+	11.5026i	−0.296537	+	0.431687i
$711$			3.83429i			0.143797i
$712$	3.28296	+	3.28296i	0.123034	+	0.123034i
$713$	37.3468	+	13.8502i	1.39865	+	0.518693i
$714$			1.07692i			0.0403026i
$715$	2.64313	−	3.84777i	0.0988475	−	0.143898i
$716$	−1.62037			−0.0605561
$717$	16.1411	−	16.1411i	0.602800	−	0.602800i
$718$	−23.0781	+	23.0781i	−0.861269	+	0.861269i
$719$			1.72658i			0.0643905i	0.999482	+	0.0321952i	$0.0102498\pi$
$719$			1.72658i			0.0643905i	−0.999482	+	0.0321952i	$0.989750\pi$
$720$	0.408021	+	2.19853i	0.0152060	+	0.0819342i
$721$	−5.27650			−0.196507
$722$	−13.0271	+	13.0271i	−0.484819	+	0.484819i
$723$	13.1887	−	13.1887i	0.490495	−	0.490495i
$724$	−20.5841			−0.765000
$725$	−12.7298	−	33.1145i	−0.472773	−	1.22984i
$726$	−26.3708			−0.978713
$727$	3.72425	+	3.72425i	0.138125	+	0.138125i	0.772788	−	0.634664i	$-0.218861\pi$
$727$	3.72425	+	3.72425i	0.138125	+	0.138125i	−0.634664	+	0.772788i	$0.718861\pi$
$728$	0.562057	−	0.562057i	0.0208312	−	0.0208312i
$729$		−	1.00000i		−	0.0370370i
$730$	−20.6097	+	3.82493i	−0.762801	+	0.141567i
$731$	−0.0946561			−0.00350098
$732$	5.69868	+	5.69868i	0.210629	+	0.210629i
$733$	6.33773	−	6.33773i	0.234089	−	0.234089i	−0.580308	−	0.814397i	$-0.697068\pi$
$733$	6.33773	−	6.33773i	0.234089	−	0.234089i	0.814397	+	0.580308i	$0.197068\pi$
$734$	−32.5248			−1.20051
$735$	−2.00344	+	2.91653i	−0.0738981	+	0.107578i
$736$	4.35871	−	2.00041i	0.160664	−	0.0737361i
$737$	19.1923	−	19.1923i	0.706956	−	0.706956i
$738$	4.77416	+	4.77416i	0.175739	+	0.175739i
$739$			27.5093i			1.01195i	0.862549	+	0.505973i	$0.168867\pi$
$739$			27.5093i			1.01195i	−0.862549	+	0.505973i	$0.831133\pi$
$740$	−3.44855	+	5.02026i	−0.126771	+	0.184549i
$741$		−	0.259380i		−	0.00952856i
$742$	3.38078	−	3.38078i	0.124112	−	0.124112i
$743$	−20.8781	+	20.8781i	−0.765942	+	0.765942i	−0.977389	−	0.211448i	$-0.932182\pi$
$743$	−20.8781	+	20.8781i	−0.765942	+	0.765942i	0.211448	+	0.977389i	$0.432182\pi$
$744$			8.30560i			0.304498i
$745$	−38.9107	+	7.22137i	−1.42558	+	0.264571i
$746$			21.8676i			0.800629i
$747$	2.14295	+	2.14295i	0.0784065	+	0.0784065i
$748$	2.00000	+	2.00000i	0.0731272	+	0.0731272i
$749$			32.7614i			1.19708i
$750$	−9.52858	+	5.84861i	−0.347935	+	0.213561i
$751$			12.1937i			0.444954i	0.974938	+	0.222477i	$0.0714142\pi$
$751$			12.1937i			0.444954i	−0.974938	+	0.222477i	$0.928586\pi$
$752$	−1.46451	+	1.46451i	−0.0534053	+	0.0534053i
$753$	17.0480	−	17.0480i	0.621264	−	0.621264i
$754$			2.42309i			0.0882436i
$755$	26.1882	−	4.86022i	0.953085	−	0.176881i
$756$		−	2.32757i		−	0.0846530i
$757$	−13.7127	−	13.7127i	−0.498396	−	0.498396i	0.412543	−	0.910938i	$-0.364641\pi$
$757$	−13.7127	−	13.7127i	−0.498396	−	0.498396i	−0.910938	+	0.412543i	$0.864641\pi$
$758$	7.84787	−	7.84787i	0.285048	−	0.285048i
$759$	−26.6455	+	12.2288i	−0.967171	+	0.443879i
$760$	1.39989	+	0.961624i	0.0507795	+	0.0348818i
$761$	15.5354			0.563159			0.281580	−	0.959538i	$-0.409142\pi$
$761$	15.5354			0.563159			0.281580	+	0.959538i	$0.409142\pi$
$762$	−6.44789	+	6.44789i	−0.233582	+	0.233582i
$763$	−23.7735	−	23.7735i	−0.860660	−	0.860660i
$764$	−20.8203			−0.753251
$765$	−0.585786	+	0.852765i	−0.0211792	+	0.0308318i
$766$			26.0342i			0.940653i
$767$	−0.406985	+	0.406985i	−0.0146954	+	0.0146954i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	−30.1885			−1.08863			−0.544313	−	0.838882i	$-0.683210\pi$
$769$	−30.1885			−1.08863			−0.544313	+	0.838882i	$0.683210\pi$
$770$	−5.80567	−	31.2825i	−0.209222	−	1.12734i
$771$	−23.1590			−0.834053
$772$	5.74993	−	5.74993i	0.206945	−	0.206945i
$773$	−8.94529	+	8.94529i	−0.321740	+	0.321740i	−0.849434	−	0.527694i	$-0.823057\pi$
$773$	−8.94529	+	8.94529i	−0.321740	+	0.321740i	0.527694	+	0.849434i	$0.323057\pi$
$774$	0.204583			0.00735359
$775$	−38.7626	+	14.9010i	−1.39239	+	0.535260i
$776$		−	15.8402i		−	0.568628i
$777$	4.48296	−	4.48296i	0.160825	−	0.160825i
$778$	15.0574	−	15.0574i	0.539833	−	0.539833i
$779$	5.12810			0.183733
$780$	0.750799	−	0.139340i	0.0268829	−	0.00498916i
$781$		−	38.1517i		−	1.36517i
$782$	2.08047	+	0.771547i	0.0743973	+	0.0275905i
$783$	5.01721	+	5.01721i	0.179300	+	0.179300i
$784$			1.58240i			0.0565143i
$785$	−13.9684	−	9.59525i	−0.498553	−	0.342469i
$786$	10.5482			0.376243
$787$	37.6119	+	37.6119i	1.34072	+	1.34072i	0.895344	+	0.445375i	$0.146930\pi$
$787$	37.6119	+	37.6119i	1.34072	+	1.34072i	0.445375	+	0.895344i	$0.353070\pi$
$788$	−1.24668	−	1.24668i	−0.0444111	−	0.0444111i
$789$	22.9842			0.818258
$790$	−4.85451	+	7.06700i	−0.172716	+	0.251433i
$791$	−2.91351			−0.103592
$792$	−4.32266	−	4.32266i	−0.153599	−	0.153599i
$793$	1.94610	−	1.94610i	0.0691082	−	0.0691082i
$794$			24.7158i			0.877130i
$795$	4.51606	−	0.838129i	0.160168	−	0.0297254i
$796$		−	4.17076i		−	0.147829i
$797$	−16.1680	−	16.1680i	−0.572700	−	0.572700i	0.360182	−	0.932882i	$-0.382715\pi$
$797$	−16.1680	−	16.1680i	−0.572700	−	0.572700i	−0.932882	+	0.360182i	$0.882715\pi$
$798$	−1.25007	−	1.25007i	−0.0442519	−	0.0442519i
$799$	−0.958269			−0.0339011
$800$	−2.03148	+	4.56871i	−0.0718237	+	0.161528i
$801$		−	4.64280i		−	0.164045i
$802$	6.60699	+	6.60699i	0.233301	+	0.233301i
$803$	40.5221	−	40.5221i	1.42999	−	1.42999i
$804$	4.43992			0.156584
$805$	−14.3760	−	20.4047i	−0.506689	−	0.719173i
$806$	2.83637			0.0999069
$807$	19.3478	−	19.3478i	0.681076	−	0.681076i
$808$	11.3571	+	11.3571i	0.399540	+	0.399540i
$809$		−	11.0745i		−	0.389357i	−0.980867	−	0.194679i	$-0.937634\pi$
$809$		−	11.0745i		−	0.389357i	0.980867	−	0.194679i	$-0.0623664\pi$
$810$	1.26608	−	1.84311i	0.0444855	−	0.0647602i
$811$	−5.55602			−0.195098			−0.0975491	−	0.995231i	$-0.531100\pi$
$811$	−5.55602			−0.195098			−0.0975491	+	0.995231i	$0.531100\pi$
$812$	11.6779	+	11.6779i	0.409815	+	0.409815i
$813$	−21.7108	−	21.7108i	−0.761431	−	0.761431i
$814$		−	16.6511i		−	0.583620i
$815$	−4.69166	−	3.22283i	−0.164342	−	0.112891i
$816$			0.462678i			0.0161970i
$817$	0.109875	−	0.109875i	0.00384405	−	0.00384405i
$818$	11.2336	+	11.2336i	0.392773	+	0.392773i
$819$	−0.794868			−0.0277749
$820$	2.75483	+	14.8437i	0.0962027	+	0.518366i
$821$	11.9158			0.415863			0.207931	−	0.978143i	$-0.433327\pi$
$821$	11.9158			0.415863			0.207931	+	0.978143i	$0.433327\pi$
$822$	−15.3962	−	15.3962i	−0.537003	−	0.537003i
$823$	−18.2633	−	18.2633i	−0.636619	−	0.636619i	0.313101	−	0.949720i	$-0.398632\pi$
$823$	−18.2633	−	18.2633i	−0.636619	−	0.636619i	−0.949720	+	0.313101i	$0.898632\pi$
$824$	−2.26695			−0.0789730
$825$	12.4188	−	27.9293i	0.432366	−	0.972373i
$826$			3.92288i			0.136495i
$827$	−19.7059	−	19.7059i	−0.685241	−	0.685241i	0.275936	−	0.961176i	$-0.411012\pi$
$827$	−19.7059	−	19.7059i	−0.685241	−	0.685241i	−0.961176	+	0.275936i	$0.911012\pi$
$828$	−4.49658	−	1.66757i	−0.156267	−	0.0579520i
$829$			3.61941i			0.125707i	0.998023	+	0.0628537i	$0.0200201\pi$
$829$			3.61941i			0.125707i	−0.998023	+	0.0628537i	$0.979980\pi$
$830$	1.23654	+	6.66283i	0.0429211	+	0.231270i
$831$	3.13866			0.108879
$832$	0.241478	−	0.241478i	0.00837173	−	0.00837173i
$833$	−0.517702	+	0.517702i	−0.0179373	+	0.0179373i
$834$		−	5.75151i		−	0.199159i
$835$	−17.6309	+	25.6663i	−0.610141	+	0.888220i
$836$	−4.64313			−0.160586
$837$	5.87295	−	5.87295i	0.202999	−	0.202999i
$838$	3.61353	−	3.61353i	0.124827	−	0.124827i
$839$	50.9017			1.75732			0.878660	−	0.477447i	$-0.158438\pi$
$839$	50.9017			1.75732			0.878660	+	0.477447i	$0.158438\pi$
$840$	2.94689	−	4.28997i	0.101677	−	0.148018i
$841$	−21.3448			−0.736027
$842$	4.03937	+	4.03937i	0.139206	+	0.139206i
$843$	−18.4182	+	18.4182i	−0.634357	+	0.634357i
$844$		−	6.87441i		−	0.236627i
$845$	5.25669	+	28.3244i	0.180836	+	0.974391i
$846$	2.07114			0.0712071
$847$	43.4022	+	43.4022i	1.49132	+	1.49132i
$848$	1.45249	−	1.45249i	0.0498787	−	0.0498787i
$849$	7.75406			0.266119
$850$	−2.15933	+	0.830086i	−0.0740646	+	0.0284717i
$851$	−5.44873	−	11.8723i	−0.186780	−	0.406976i
$852$	4.41298	−	4.41298i	0.151186	−	0.151186i
$853$	6.62856	+	6.62856i	0.226958	+	0.226958i	0.811420	−	0.584463i	$-0.198695\pi$
$853$	6.62856	+	6.62856i	0.226958	+	0.226958i	−0.584463	+	0.811420i	$0.698695\pi$
$854$		−	18.7583i		−	0.641895i
$855$	−0.309904	−	1.66985i	−0.0105985	−	0.0571075i
$856$			14.0754i			0.481086i
$857$	−8.37639	+	8.37639i	−0.286132	+	0.286132i	−0.835549	−	0.549417i	$-0.814850\pi$
$857$	−8.37639	+	8.37639i	−0.286132	+	0.286132i	0.549417	+	0.835549i	$0.314850\pi$
$858$	−1.47619	+	1.47619i	−0.0503964	+	0.0503964i
$859$			5.10209i			0.174081i	0.996205	+	0.0870405i	$0.0277409\pi$
$859$			5.10209i			0.174081i	−0.996205	+	0.0870405i	$0.972259\pi$
$860$	0.377069	+	0.259018i	0.0128579	+	0.00883245i
$861$		−	15.7150i		−	0.535567i
$862$	−2.32457	−	2.32457i	−0.0791753	−	0.0791753i
$863$	−6.91979	−	6.91979i	−0.235553	−	0.235553i	0.579453	−	0.815006i	$-0.303266\pi$
$863$	−6.91979	−	6.91979i	−0.235553	−	0.235553i	−0.815006	+	0.579453i	$0.803266\pi$
$864$		−	1.00000i		−	0.0340207i
$865$	−31.6217	−	21.7218i	−1.07517	−	0.738562i
$866$		−	16.4577i		−	0.559256i
$867$	11.8694	−	11.8694i	0.403107	−	0.403107i
$868$	13.6697	−	13.6697i	0.463980	−	0.463980i
$869$		−	23.4396i		−	0.795135i
$870$	2.89508	+	15.5994i	0.0981522	+	0.528870i
$871$		−	1.51624i		−	0.0513757i
$872$	−10.2139	−	10.2139i	−0.345885	−	0.345885i
$873$	−11.2007	+	11.2007i	−0.379086	+	0.379086i
$874$	−3.31057	+	1.51937i	−0.111982	+	0.0513935i
$875$	25.3084	+	6.05666i	0.855581	+	0.204752i
$876$	9.37434			0.316730
$877$	−11.0291	+	11.0291i	−0.372427	+	0.372427i	−0.868360	−	0.495934i	$-0.834826\pi$
$877$	−11.0291	+	11.0291i	−0.372427	+	0.372427i	0.495934	+	0.868360i	$0.334826\pi$
$878$	−8.75052	−	8.75052i	−0.295316	−	0.295316i
$879$	−26.2398			−0.885045
$880$	−2.49430	−	13.4400i	−0.0840829	−	0.453061i
$881$		−	53.9458i		−	1.81748i	−0.417361	−	0.908741i	$-0.637045\pi$
$881$		−	53.9458i		−	1.81748i	0.417361	−	0.908741i	$-0.362955\pi$
$882$	1.11893	−	1.11893i	0.0376762	−	0.0376762i
$883$	−21.6479	−	21.6479i	−0.728511	−	0.728511i	0.241812	−	0.970323i	$-0.422258\pi$
$883$	−21.6479	−	21.6479i	−0.728511	−	0.728511i	−0.970323	+	0.241812i	$0.922258\pi$
$884$	0.158005			0.00531428
$885$	−2.13384	+	3.10637i	−0.0717284	+	0.104419i
$886$	34.5791			1.16171
$887$	27.1450	−	27.1450i	0.911441	−	0.911441i	−0.0849443	−	0.996386i	$-0.527071\pi$
$887$	27.1450	−	27.1450i	0.911441	−	0.911441i	0.996386	+	0.0849443i	$0.0270712\pi$
$888$	1.92602	−	1.92602i	0.0646330	−	0.0646330i
$889$	21.2244			0.711845
$890$	5.87815	−	8.55718i	0.197036	−	0.286837i
$891$			6.11317i			0.204799i
$892$	11.2802	−	11.2802i	0.377690	−	0.377690i
$893$	1.11234	−	1.11234i	0.0372231	−	0.0372231i
$894$	17.6985			0.591927
$895$	0.661145	+	3.56243i	0.0220996	+	0.119079i
$896$		−	2.32757i		−	0.0777588i
$897$	−0.569476	+	1.53558i	−0.0190143	+	0.0512717i
$898$	−29.0109	−	29.0109i	−0.968108	−	0.968108i
$899$			58.9316i			1.96548i
$900$	4.66704	−	1.79409i	0.155568	−	0.0598030i
$901$	0.950401			0.0316624
$902$	−29.1852	−	29.1852i	−0.971761	−	0.971761i
$903$	−0.336712	−	0.336712i	−0.0112051	−	0.0112051i
$904$	−1.25173			−0.0416321
$905$	8.39873	+	45.2546i	0.279183	+	1.50431i
$906$	−11.9117			−0.395739
$907$	−30.5493	−	30.5493i	−1.01437	−	1.01437i	−0.999895	−	0.0144762i	$-0.995392\pi$
$907$	−30.5493	−	30.5493i	−1.01437	−	1.01437i	−0.0144762	−	0.999895i	$-0.504608\pi$
$908$	2.22998	−	2.22998i	0.0740046	−	0.0740046i
$909$		−	16.0613i		−	0.532720i
$910$	−1.46503	−	1.00637i	−0.0485652	−	0.0333607i
$911$		−	42.0891i		−	1.39447i	−0.716840	−	0.697237i	$-0.754412\pi$
$911$		−	42.0891i		−	1.39447i	0.716840	−	0.697237i	$-0.245588\pi$
$912$	−0.537068	−	0.537068i	−0.0177841	−	0.0177841i
$913$	−13.1002	−	13.1002i	−0.433554	−	0.433554i
$914$	−26.2274			−0.867526
$915$	10.2035	−	14.8539i	0.337318	−	0.491054i
$916$		−	5.86090i		−	0.193650i
$917$	−17.3608	−	17.3608i	−0.573303	−	0.573303i
$918$	0.327163	−	0.327163i	0.0107980	−	0.0107980i
$919$	−6.51121			−0.214785			−0.107393	−	0.994217i	$-0.534250\pi$
$919$	−6.51121			−0.214785			−0.107393	+	0.994217i	$0.534250\pi$
$920$	−6.17640	−	8.76653i	−0.203630	−	0.289024i
$921$	28.8136			0.949440
$922$	15.2001	−	15.2001i	0.500588	−	0.500588i
$923$	−1.50704	−	1.50704i	−0.0496047	−	0.0496047i
$924$			14.2288i			0.468095i
$925$	12.4443	+	5.53336i	0.409165	+	0.181936i
$926$	−20.8899			−0.686485
$927$	1.60298	+	1.60298i	0.0526487	+	0.0526487i
$928$	5.01721	+	5.01721i	0.164698	+	0.164698i
$929$			39.0887i			1.28246i	0.767349	+	0.641229i	$0.221575\pi$
$929$			39.0887i			1.28246i	−0.767349	+	0.641229i	$0.778425\pi$
$930$	18.2601	−	3.38886i	0.598772	−	0.111125i
$931$		−	1.20188i		−	0.0393900i
$932$	13.1762	−	13.1762i	0.431599	−	0.431599i
$933$	11.6684	+	11.6684i	0.382008	+	0.382008i
$934$	33.8070			1.10620
$935$	3.58101	−	5.21310i	0.117112	−	0.170486i
$936$	−0.341501			−0.0111623
$937$	−3.08761	−	3.08761i	−0.100868	−	0.100868i	0.654872	−	0.755740i	$-0.272722\pi$
$937$	−3.08761	−	3.08761i	−0.100868	−	0.100868i	−0.755740	+	0.654872i	$0.772722\pi$
$938$	−7.30741	−	7.30741i	−0.238595	−	0.238595i
$939$	6.41343			0.209294
$940$	3.81733	+	2.62222i	0.124507	+	0.0855274i
$941$		−	21.4791i		−	0.700197i	−0.936713	−	0.350099i	$-0.886148\pi$
$941$		−	21.4791i		−	0.700197i	0.936713	−	0.350099i	$-0.113852\pi$
$942$	5.35896	+	5.35896i	0.174604	+	0.174604i
$943$	−30.3594	−	11.2589i	−0.988639	−	0.366640i
$944$			1.68540i			0.0548550i
$945$	−5.11723	+	0.949699i	−0.166464	+	0.0308937i
$946$	−1.25065			−0.0406622
$947$	−8.49336	+	8.49336i	−0.275997	+	0.275997i	−0.831509	−	0.555512i	$-0.812522\pi$
$947$	−8.49336	+	8.49336i	−0.275997	+	0.275997i	0.555512	+	0.831509i	$0.312522\pi$
$948$	2.71125	−	2.71125i	0.0880573	−	0.0880573i
$949$		−	3.20135i		−	0.103920i
$950$	1.54297	−	3.47007i	0.0500605	−	0.112584i
$951$	−17.6975			−0.573879
$952$	0.761495	−	0.761495i	0.0246802	−	0.0246802i
$953$	−36.6128	+	36.6128i	−1.18601	+	1.18601i	−0.207843	+	0.978162i	$0.566644\pi$
$953$	−36.6128	+	36.6128i	−1.18601	+	1.18601i	−0.978162	+	0.207843i	$0.933356\pi$
$954$	−2.05413			−0.0665049
$955$	8.49511	+	45.7739i	0.274895	+	1.48121i
$956$	−22.8269			−0.738276
$957$	−30.6710	−	30.6710i	−0.991454	−	0.991454i
$958$	7.78741	−	7.78741i	0.251600	−	0.251600i
$959$			50.6793i			1.63652i
$960$	1.26608	−	1.84311i	0.0408625	−	0.0594860i
$961$	37.9830			1.22526
$962$	−0.657738	−	0.657738i	−0.0212063	−	0.0212063i
$963$	9.95278	−	9.95278i	0.320724	−	0.320724i
$964$	−18.6517			−0.600731
$965$	−14.9875	−	10.2953i	−0.482464	−	0.331417i
$966$	4.65610	+	10.1452i	0.149808	+	0.326417i
$967$	16.2892	−	16.2892i	0.523824	−	0.523824i	−0.394900	−	0.918724i	$-0.629221\pi$
$967$	16.2892	−	16.2892i	0.523824	−	0.523824i	0.918724	+	0.394900i	$0.129221\pi$
$968$	18.6470	+	18.6470i	0.599337	+	0.599337i
$969$		−	0.351417i		−	0.0112892i
$970$	−34.8250	+	6.46312i	−1.11816	+	0.207518i
$971$			18.4126i			0.590889i	0.955360	+	0.295444i	$0.0954677\pi$
$971$			18.4126i			0.590889i	−0.955360	+	0.295444i	$0.904532\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	−9.46608	+	9.46608i	−0.303469	+	0.303469i
$974$		−	36.5152i		−	1.17002i
$975$	−0.612683	−	1.59380i	−0.0196216	−	0.0510424i
$976$		−	8.05915i		−	0.257967i
$977$	−30.7089	−	30.7089i	−0.982464	−	0.982464i	0.0173847	−	0.999849i	$-0.494466\pi$
$977$	−30.7089	−	30.7089i	−0.982464	−	0.982464i	−0.999849	+	0.0173847i	$0.994466\pi$
$978$	1.79995	+	1.79995i	0.0575562	+	0.0575562i
$979$			28.3822i			0.907100i
$980$	3.47895	−	0.645653i	0.111131	−	0.0206246i
$981$			14.4446i			0.461180i
$982$	−14.9424	+	14.9424i	−0.476832	+	0.476832i
$983$	−16.1127	+	16.1127i	−0.513916	+	0.513916i	−0.915724	−	0.401808i	$-0.868382\pi$
$983$	−16.1127	+	16.1127i	−0.513916	+	0.513916i	0.401808	+	0.915724i	$0.368382\pi$
$984$		−	6.75167i		−	0.215236i
$985$	−2.23219	+	3.24953i	−0.0711234	+	0.103539i
$986$			3.28289i			0.104548i
$987$	−3.40877	−	3.40877i	−0.108502	−	0.108502i
$988$	−0.183409	+	0.183409i	−0.00583503	+	0.00583503i
$989$	−0.891719	+	0.409250i	−0.0283550	+	0.0130134i
$990$	−7.73975	+	11.2672i	−0.245985	+	0.358096i
$991$	−11.5298			−0.366256			−0.183128	−	0.983089i	$-0.558622\pi$
$991$	−11.5298			−0.366256			−0.183128	+	0.983089i	$0.558622\pi$
$992$	5.87295	−	5.87295i	0.186466	−	0.186466i
$993$	17.2329	+	17.2329i	0.546869	+	0.546869i
$994$	−14.5262			−0.460742
$995$	−9.16953	+	1.70176i	−0.290694	+	0.0539494i
$996$		−	3.03059i		−	0.0960279i
$997$	−5.05273	+	5.05273i	−0.160021	+	0.160021i	−0.782576	−	0.622555i	$-0.786095\pi$
$997$	−5.05273	+	5.05273i	−0.160021	+	0.160021i	0.622555	+	0.782576i	$0.286095\pi$
$998$	18.2129	+	18.2129i	0.576520	+	0.576520i
$999$	−2.72380			−0.0861774

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.j.b.643.7	yes	24
5.2	odd	4	inner	690.2.j.b.367.12	yes	24
23.22	odd	2	inner	690.2.j.b.643.12	yes	24
115.22	even	4	inner	690.2.j.b.367.7	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.j.b.367.7	✓	24	115.22	even	4	inner
690.2.j.b.367.12	yes	24	5.2	odd	4	inner
690.2.j.b.643.7	yes	24	1.1	even	1	trivial
690.2.j.b.643.12	yes	24	23.22	odd	2	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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-2.19853 + 0.408021i) q^{5} +1.00000 q^{6} +(-1.64584 - 1.64584i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-2.19853 + 0.408021i) q^{5} +1.00000 q^{6} +(-1.64584 - 1.64584i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(-1.26608 + 1.84311i) q^{10} -6.11317i q^{11} +(0.707107 - 0.707107i) q^{12} +(-0.241478 - 0.241478i) q^{13} -2.32757 q^{14} +(-1.84311 - 1.26608i) q^{15} -1.00000 q^{16} +(-0.327163 - 0.327163i) q^{17} +(0.707107 + 0.707107i) q^{18} +0.759529 q^{19} +(0.408021 + 2.19853i) q^{20} -2.32757i q^{21} +(-4.32266 - 4.32266i) q^{22} +(-4.49658 - 1.66757i) q^{23} -1.00000i q^{24} +(4.66704 - 1.79409i) q^{25} -0.341501 q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.64584 + 1.64584i) q^{28} -7.09541i q^{29} +(-2.19853 + 0.408021i) q^{30} -8.30560 q^{31} +(-0.707107 + 0.707107i) q^{32} +(4.32266 - 4.32266i) q^{33} -0.462678 q^{34} +(4.28997 + 2.94689i) q^{35} +1.00000 q^{36} +(1.92602 + 1.92602i) q^{37} +(0.537068 - 0.537068i) q^{38} -0.341501i q^{39} +(1.84311 + 1.26608i) q^{40} +6.75167 q^{41} +(-1.64584 - 1.64584i) q^{42} +(0.144662 - 0.144662i) q^{43} -6.11317 q^{44} +(-0.408021 - 2.19853i) q^{45} +(-4.35871 + 2.00041i) q^{46} +(1.46451 - 1.46451i) q^{47} +(-0.707107 - 0.707107i) q^{48} -1.58240i q^{49} +(2.03148 - 4.56871i) q^{50} -0.462678i q^{51} +(-0.241478 + 0.241478i) q^{52} +(-1.45249 + 1.45249i) q^{53} +1.00000i q^{54} +(2.49430 + 13.4400i) q^{55} +2.32757i q^{56} +(0.537068 + 0.537068i) q^{57} +(-5.01721 - 5.01721i) q^{58} -1.68540i q^{59} +(-1.26608 + 1.84311i) q^{60} +8.05915i q^{61} +(-5.87295 + 5.87295i) q^{62} +(1.64584 - 1.64584i) q^{63} +1.00000i q^{64} +(0.629423 + 0.432367i) q^{65} -6.11317i q^{66} +(3.13950 + 3.13950i) q^{67} +(-0.327163 + 0.327163i) q^{68} +(-2.00041 - 4.35871i) q^{69} +(5.11723 - 0.949699i) q^{70} +6.24090 q^{71} +(0.707107 - 0.707107i) q^{72} +(6.62866 + 6.62866i) q^{73} +2.72380 q^{74} +(4.56871 + 2.03148i) q^{75} -0.759529i q^{76} +(-10.0613 + 10.0613i) q^{77} +(-0.241478 - 0.241478i) q^{78} +3.83429 q^{79} +(2.19853 - 0.408021i) q^{80} -1.00000 q^{81} +(4.77416 - 4.77416i) q^{82} +(2.14295 - 2.14295i) q^{83} -2.32757 q^{84} +(0.852765 + 0.585786i) q^{85} -0.204583i q^{86} +(5.01721 - 5.01721i) q^{87} +(-4.32266 + 4.32266i) q^{88} -4.64280 q^{89} +(-1.84311 - 1.26608i) q^{90} +0.794868i q^{91} +(-1.66757 + 4.49658i) q^{92} +(-5.87295 - 5.87295i) q^{93} -2.07114i q^{94} +(-1.66985 + 0.309904i) q^{95} -1.00000 q^{96} +(11.2007 + 11.2007i) q^{97} +(-1.11893 - 1.11893i) q^{98} +6.11317 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

Groups

Database

Properties

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