LMFDB - Embedded newform 690.2.j.a.643.8

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			643.8
Character	$\chi$	$=$	690.643
Dual form			690.2.j.a.367.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-1.57090 - 1.59131i) q^{5} -1.00000 q^{6} +(-1.37926 - 1.37926i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-1.57090 - 1.59131i) q^{5} -1.00000 q^{6} +(-1.37926 - 1.37926i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(-2.23602 - 0.0144369i) q^{10} -0.0288739i q^{11} +(-0.707107 + 0.707107i) q^{12} +(0.711585 + 0.711585i) q^{13} -1.95057 q^{14} +(-0.0144369 + 2.23602i) q^{15} -1.00000 q^{16} +(-0.438634 - 0.438634i) q^{17} +(0.707107 + 0.707107i) q^{18} -7.23057 q^{19} +(-1.59131 + 1.57090i) q^{20} +1.95057i q^{21} +(-0.0204169 - 0.0204169i) q^{22} +(3.06679 + 3.68711i) q^{23} +1.00000i q^{24} +(-0.0645626 + 4.99958i) q^{25} +1.00633 q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.37926 + 1.37926i) q^{28} -3.97284i q^{29} +(1.57090 + 1.59131i) q^{30} -5.20915 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.0204169 + 0.0204169i) q^{33} -0.620322 q^{34} +(-0.0281603 + 4.36152i) q^{35} +1.00000 q^{36} +(1.46265 + 1.46265i) q^{37} +(-5.11278 + 5.11278i) q^{38} -1.00633i q^{39} +(-0.0144369 + 2.23602i) q^{40} -7.17074 q^{41} +(1.37926 + 1.37926i) q^{42} +(-5.83089 + 5.83089i) q^{43} -0.0288739 q^{44} +(1.59131 - 1.57090i) q^{45} +(4.77573 + 0.438634i) q^{46} +(6.90153 - 6.90153i) q^{47} +(0.707107 + 0.707107i) q^{48} -3.19528i q^{49} +(3.48959 + 3.58089i) q^{50} +0.620322i q^{51} +(0.711585 - 0.711585i) q^{52} +(2.73811 - 2.73811i) q^{53} -1.00000i q^{54} +(-0.0459474 + 0.0453579i) q^{55} +1.95057i q^{56} +(5.11278 + 5.11278i) q^{57} +(-2.80922 - 2.80922i) q^{58} -5.73861i q^{59} +(2.23602 + 0.0144369i) q^{60} -5.09237i q^{61} +(-3.68342 + 3.68342i) q^{62} +(1.37926 - 1.37926i) q^{63} +1.00000i q^{64} +(0.0145284 - 2.25018i) q^{65} +0.0288739i q^{66} +(-4.63966 - 4.63966i) q^{67} +(-0.438634 + 0.438634i) q^{68} +(0.438634 - 4.77573i) q^{69} +(3.06415 + 3.10397i) q^{70} -5.47777 q^{71} +(0.707107 - 0.707107i) q^{72} +(-0.908695 - 0.908695i) q^{73} +2.06849 q^{74} +(3.58089 - 3.48959i) q^{75} +7.23057i q^{76} +(-0.0398246 + 0.0398246i) q^{77} +(-0.711585 - 0.711585i) q^{78} -5.20235 q^{79} +(1.57090 + 1.59131i) q^{80} -1.00000 q^{81} +(-5.07048 + 5.07048i) q^{82} +(9.95414 - 9.95414i) q^{83} +1.95057 q^{84} +(-0.00895556 + 1.38705i) q^{85} +8.24612i q^{86} +(-2.80922 + 2.80922i) q^{87} +(-0.0204169 + 0.0204169i) q^{88} +10.5118 q^{89} +(0.0144369 - 2.23602i) q^{90} -1.96292i q^{91} +(3.68711 - 3.06679i) q^{92} +(3.68342 + 3.68342i) q^{93} -9.76024i q^{94} +(11.3585 + 11.5061i) q^{95} +1.00000 q^{96} +(-0.850780 - 0.850780i) q^{97} +(-2.25940 - 2.25940i) q^{98} +0.0288739 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} - 24 q^{16} - 8 q^{23} - 16 q^{25} - 16 q^{26} + 16 q^{31} - 16 q^{35} + 24 q^{36} - 8 q^{46} - 8 q^{47} + 24 q^{50} + 24 q^{55} + 16 q^{58} - 56 q^{62} - 32 q^{70} - 16 q^{71} - 48 q^{73} - 24 q^{81} + 24 q^{82} + 16 q^{87} - 8 q^{92} + 56 q^{93} + 24 q^{95} + 24 q^{96} - 32 q^{98}+O(q^{100}) $ 24 * q - 24 * q^6 - 24 * q^16 - 8 * q^23 - 16 * q^25 - 16 * q^26 + 16 * q^31 - 16 * q^35 + 24 * q^36 - 8 * q^46 - 8 * q^47 + 24 * q^50 + 24 * q^55 + 16 * q^58 - 56 * q^62 - 32 * q^70 - 16 * q^71 - 48 * q^73 - 24 * q^81 + 24 * q^82 + 16 * q^87 - 8 * q^92 + 56 * q^93 + 24 * q^95 + 24 * q^96 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	−1.57090	−	1.59131i	−0.702527	−	0.711657i
$5$	−1.57090	−	1.59131i	−0.702527	−	0.711657i
$6$	−1.00000			−0.408248
$7$	−1.37926	−	1.37926i	−0.521312	−	0.521312i	0.396656	−	0.917967i	$-0.370171\pi$
$7$	−1.37926	−	1.37926i	−0.521312	−	0.521312i	−0.917967	+	0.396656i	$0.870171\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$			1.00000i			0.333333i
$10$	−2.23602	−	0.0144369i	−0.707092	−	0.00456536i
$11$		−	0.0288739i		−	0.00870580i	−0.999991	−	0.00435290i	$-0.998614\pi$
$11$		−	0.0288739i		−	0.00870580i	0.999991	−	0.00435290i	$-0.00138558\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	0.711585	+	0.711585i	0.197358	+	0.197358i	0.798866	−	0.601508i	$-0.205433\pi$
$13$	0.711585	+	0.711585i	0.197358	+	0.197358i	−0.601508	+	0.798866i	$0.705433\pi$
$14$	−1.95057			−0.521312
$15$	−0.0144369	+	2.23602i	−0.00372760	+	0.577338i
$16$	−1.00000			−0.250000
$17$	−0.438634	−	0.438634i	−0.106384	−	0.106384i	0.651911	−	0.758295i	$-0.273968\pi$
$17$	−0.438634	−	0.438634i	−0.106384	−	0.106384i	−0.758295	+	0.651911i	$0.773968\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	−7.23057			−1.65881			−0.829403	−	0.558651i	$-0.811319\pi$
$19$	−7.23057			−1.65881			−0.829403	+	0.558651i	$0.811319\pi$
$20$	−1.59131	+	1.57090i	−0.355829	+	0.351263i
$21$			1.95057i			0.425649i
$22$	−0.0204169	−	0.0204169i	−0.00435290	−	0.00435290i
$23$	3.06679	+	3.68711i	0.639470	+	0.768816i
$23$	3.06679	+	3.68711i	0.639470	+	0.768816i
$24$			1.00000i			0.204124i
$25$	−0.0645626	+	4.99958i	−0.0129125	+	0.999917i
$26$	1.00633			0.197358
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−1.37926	+	1.37926i	−0.260656	+	0.260656i
$29$		−	3.97284i		−	0.737738i	−0.929481	−	0.368869i	$-0.879745\pi$
$29$		−	3.97284i		−	0.737738i	0.929481	−	0.368869i	$-0.120255\pi$
$30$	1.57090	+	1.59131i	0.286805	+	0.290533i
$31$	−5.20915			−0.935591			−0.467795	−	0.883837i	$-0.654952\pi$
$31$	−5.20915			−0.935591			−0.467795	+	0.883837i	$0.654952\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−0.0204169	+	0.0204169i	−0.00355413	+	0.00355413i
$34$	−0.620322			−0.106384
$35$	−0.0281603	+	4.36152i	−0.00475995	+	0.737231i
$36$	1.00000			0.166667
$37$	1.46265	+	1.46265i	0.240457	+	0.240457i	0.817039	−	0.576582i	$-0.195614\pi$
$37$	1.46265	+	1.46265i	0.240457	+	0.240457i	−0.576582	+	0.817039i	$0.695614\pi$
$38$	−5.11278	+	5.11278i	−0.829403	+	0.829403i
$39$		−	1.00633i		−	0.161142i
$40$	−0.0144369	+	2.23602i	−0.00228268	+	0.353546i
$41$	−7.17074			−1.11988			−0.559941	−	0.828533i	$-0.689176\pi$
$41$	−7.17074			−1.11988			−0.559941	+	0.828533i	$0.689176\pi$
$42$	1.37926	+	1.37926i	0.212825	+	0.212825i
$43$	−5.83089	+	5.83089i	−0.889202	+	0.889202i	−0.994446	−	0.105244i	$-0.966438\pi$
$43$	−5.83089	+	5.83089i	−0.889202	+	0.889202i	0.105244	+	0.994446i	$0.466438\pi$
$44$	−0.0288739			−0.00435290
$45$	1.59131	−	1.57090i	0.237219	−	0.234176i
$46$	4.77573	+	0.438634i	0.704143	+	0.0646731i
$47$	6.90153	−	6.90153i	1.00669	−	1.00669i	0.00671393	−	0.999977i	$-0.497863\pi$
$47$	6.90153	−	6.90153i	1.00669	−	1.00669i	0.999977	−	0.00671393i	$-0.00213713\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$		−	3.19528i		−	0.456468i
$50$	3.48959	+	3.58089i	0.493502	+	0.506415i
$51$			0.620322i			0.0868625i
$52$	0.711585	−	0.711585i	0.0986790	−	0.0986790i
$53$	2.73811	−	2.73811i	0.376108	−	0.376108i	−0.493588	−	0.869696i	$-0.664315\pi$
$53$	2.73811	−	2.73811i	0.376108	−	0.376108i	0.869696	+	0.493588i	$0.164315\pi$
$54$		−	1.00000i		−	0.136083i
$55$	−0.0459474	+	0.0453579i	−0.00619555	+	0.00611606i
$56$			1.95057i			0.260656i
$57$	5.11278	+	5.11278i	0.677205	+	0.677205i
$58$	−2.80922	−	2.80922i	−0.368869	−	0.368869i
$59$		−	5.73861i		−	0.747104i	−0.927609	−	0.373552i	$-0.878140\pi$
$59$		−	5.73861i		−	0.747104i	0.927609	−	0.373552i	$-0.121860\pi$
$60$	2.23602	+	0.0144369i	0.288669	+	0.00186380i
$61$		−	5.09237i		−	0.652011i	−0.945368	−	0.326005i	$-0.894297\pi$
$61$		−	5.09237i		−	0.652011i	0.945368	−	0.326005i	$-0.105703\pi$
$62$	−3.68342	+	3.68342i	−0.467795	+	0.467795i
$63$	1.37926	−	1.37926i	0.173771	−	0.173771i
$64$			1.00000i			0.125000i
$65$	0.0145284	−	2.25018i	0.00180202	−	0.279101i
$66$			0.0288739i			0.00355413i
$67$	−4.63966	−	4.63966i	−0.566825	−	0.566825i	0.364413	−	0.931238i	$-0.381270\pi$
$67$	−4.63966	−	4.63966i	−0.566825	−	0.566825i	−0.931238	+	0.364413i	$0.881270\pi$
$68$	−0.438634	+	0.438634i	−0.0531922	+	0.0531922i
$69$	0.438634	−	4.77573i	0.0528053	−	0.574930i
$70$	3.06415	+	3.10397i	0.366235	+	0.370995i
$71$	−5.47777			−0.650092			−0.325046	−	0.945698i	$-0.605380\pi$
$71$	−5.47777			−0.650092			−0.325046	+	0.945698i	$0.605380\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	−0.908695	−	0.908695i	−0.106355	−	0.106355i	0.651927	−	0.758282i	$-0.273961\pi$
$73$	−0.908695	−	0.908695i	−0.106355	−	0.106355i	−0.758282	+	0.651927i	$0.773961\pi$
$74$	2.06849			0.240457
$75$	3.58089	−	3.48959i	0.413486	−	0.402943i
$76$			7.23057i			0.829403i
$77$	−0.0398246	+	0.0398246i	−0.00453844	+	0.00453844i
$78$	−0.711585	−	0.711585i	−0.0805711	−	0.0805711i
$79$	−5.20235			−0.585310			−0.292655	−	0.956218i	$-0.594539\pi$
$79$	−5.20235			−0.585310			−0.292655	+	0.956218i	$0.594539\pi$
$80$	1.57090	+	1.59131i	0.175632	+	0.177914i
$81$	−1.00000			−0.111111
$82$	−5.07048	+	5.07048i	−0.559941	+	0.559941i
$83$	9.95414	−	9.95414i	1.09261	−	1.09261i	0.0973599	−	0.995249i	$-0.468960\pi$
$83$	9.95414	−	9.95414i	1.09261	−	1.09261i	0.995249	−	0.0973599i	$-0.0310398\pi$
$84$	1.95057			0.212825
$85$	−0.00895556	+	1.38705i	−0.000971366	+	0.150447i
$86$			8.24612i			0.889202i
$87$	−2.80922	+	2.80922i	−0.301180	+	0.301180i
$88$	−0.0204169	+	0.0204169i	−0.00217645	+	0.00217645i
$89$	10.5118			1.11425			0.557123	−	0.830430i	$-0.311905\pi$
$89$	10.5118			1.11425			0.557123	+	0.830430i	$0.311905\pi$
$90$	0.0144369	−	2.23602i	0.00152179	−	0.235697i
$91$		−	1.96292i		−	0.205770i
$92$	3.68711	−	3.06679i	0.384408	−	0.319735i
$93$	3.68342	+	3.68342i	0.381953	+	0.381953i
$94$		−	9.76024i		−	1.00669i
$95$	11.3585	+	11.5061i	1.16536	+	1.18050i
$96$	1.00000			0.102062
$97$	−0.850780	−	0.850780i	−0.0863836	−	0.0863836i	0.662595	−	0.748978i	$-0.269455\pi$
$97$	−0.850780	−	0.850780i	−0.0863836	−	0.0863836i	−0.748978	+	0.662595i	$0.769455\pi$
$98$	−2.25940	−	2.25940i	−0.228234	−	0.228234i
$99$	0.0288739			0.00290193
$100$	4.99958	+	0.0645626i	0.499958	+	0.00645626i
$101$	−15.2097			−1.51342			−0.756712	−	0.653748i	$-0.773196\pi$
$101$	−15.2097			−1.51342			−0.756712	+	0.653748i	$0.773196\pi$
$102$	0.438634	+	0.438634i	0.0434313	+	0.0434313i
$103$	−2.54161	+	2.54161i	−0.250432	+	0.250432i	−0.821148	−	0.570715i	$-0.806666\pi$
$103$	−2.54161	+	2.54161i	−0.250432	+	0.250432i	0.570715	+	0.821148i	$0.306666\pi$
$104$		−	1.00633i		−	0.0986790i
$105$	3.10397	−	3.06415i	0.302916	−	0.299030i
$106$		−	3.87227i		−	0.376108i
$107$	−7.38286	−	7.38286i	−0.713728	−	0.713728i	0.253585	−	0.967313i	$-0.418390\pi$
$107$	−7.38286	−	7.38286i	−0.713728	−	0.713728i	−0.967313	+	0.253585i	$0.918390\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	1.23206			0.118010			0.0590049	−	0.998258i	$-0.481207\pi$
$109$	1.23206			0.118010			0.0590049	+	0.998258i	$0.481207\pi$
$110$	−0.000416850		0.0645626i	−3.97451e−5		0.00615580i
$111$		−	2.06849i		−	0.196333i
$112$	1.37926	+	1.37926i	0.130328	+	0.130328i
$113$	10.6065	−	10.6065i	0.997771	−	0.997771i	−0.00222660	−	0.999998i	$-0.500709\pi$
$113$	10.6065	−	10.6065i	0.997771	−	0.997771i	0.999998	+	0.00222660i	$0.000708750\pi$
$114$	7.23057			0.677205
$115$	1.04974	−	10.6723i	0.0978890	−	0.995197i
$116$	−3.97284			−0.368869
$117$	−0.711585	+	0.711585i	−0.0657860	+	0.0657860i
$118$	−4.05781	−	4.05781i	−0.373552	−	0.373552i
$119$			1.20998i			0.110919i
$120$	1.59131	−	1.57090i	0.145266	−	0.143403i
$121$	10.9992			0.999924
$122$	−3.60085	−	3.60085i	−0.326005	−	0.326005i
$123$	5.07048	+	5.07048i	0.457190	+	0.457190i
$124$			5.20915i			0.467795i
$125$	8.05733	−	7.75109i	0.720669	−	0.693279i
$126$		−	1.95057i		−	0.173771i
$127$	−6.45653	+	6.45653i	−0.572925	+	0.572925i	−0.932945	−	0.360020i	$-0.882770\pi$
$127$	−6.45653	+	6.45653i	−0.572925	+	0.572925i	0.360020	+	0.932945i	$0.382770\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	8.24612			0.726030
$130$	−1.58085	−	1.60139i	−0.138649	−	0.140451i
$131$	−14.1312			−1.23465			−0.617323	−	0.786710i	$-0.711783\pi$
$131$	−14.1312			−1.23465			−0.617323	+	0.786710i	$0.711783\pi$
$132$	0.0204169	+	0.0204169i	0.00177706	+	0.00177706i
$133$	9.97284	+	9.97284i	0.864755	+	0.864755i
$134$	−6.56147			−0.566825
$135$	−2.23602	−	0.0144369i	−0.192446	−	0.00124253i
$136$			0.620322i			0.0531922i
$137$	9.99147	+	9.99147i	0.853629	+	0.853629i	0.990578	−	0.136949i	$-0.0437296\pi$
$137$	9.99147	+	9.99147i	0.853629	+	0.853629i	−0.136949	+	0.990578i	$0.543730\pi$
$138$	−3.06679	−	3.68711i	−0.261063	−	0.313868i
$139$		−	11.0483i		−	0.937102i	−0.883436	−	0.468551i	$-0.844776\pi$
$139$		−	11.0483i		−	0.937102i	0.883436	−	0.468551i	$-0.155224\pi$
$140$	4.36152	+	0.0281603i	0.368615	+	0.00237998i
$141$	−9.76024			−0.821960
$142$	−3.87337	+	3.87337i	−0.325046	+	0.325046i
$143$	0.0205462	−	0.0205462i	0.00171816	−	0.00171816i
$144$		−	1.00000i		−	0.0833333i
$145$	−6.32204	+	6.24092i	−0.525017	+	0.518281i
$146$	−1.28509			−0.106355
$147$	−2.25940	+	2.25940i	−0.186352	+	0.186352i
$148$	1.46265	−	1.46265i	0.120229	−	0.120229i
$149$	13.0448			1.06867			0.534336	−	0.845272i	$-0.320562\pi$
$149$	13.0448			1.06867			0.534336	+	0.845272i	$0.320562\pi$
$150$	0.0645626	−	4.99958i	0.00527152	−	0.408214i
$151$	2.16088			0.175850			0.0879250	−	0.996127i	$-0.471976\pi$
$151$	2.16088			0.175850			0.0879250	+	0.996127i	$0.471976\pi$
$152$	5.11278	+	5.11278i	0.414701	+	0.414701i
$153$	0.438634	−	0.438634i	0.0354615	−	0.0354615i
$154$			0.0563205i			0.00453844i
$155$	8.18304	+	8.28939i	0.657277	+	0.665820i
$156$	−1.00633			−0.0805711
$157$	−13.4623	−	13.4623i	−1.07441	−	1.07441i	−0.996999	−	0.0774088i	$-0.975335\pi$
$157$	−13.4623	−	13.4623i	−1.07441	−	1.07441i	−0.0774088	−	0.996999i	$-0.524665\pi$
$158$	−3.67862	+	3.67862i	−0.292655	+	0.292655i
$159$	−3.87227			−0.307091
$160$	2.23602	+	0.0144369i	0.176773	+	0.00114134i
$161$	0.855587	−	9.31540i	0.0674297	−	0.734156i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	−0.576831	−	0.576831i	−0.0451809	−	0.0451809i	0.684155	−	0.729336i	$-0.260171\pi$
$163$	−0.576831	−	0.576831i	−0.0451809	−	0.0451809i	−0.729336	+	0.684155i	$0.760171\pi$
$164$			7.17074i			0.559941i
$165$	0.0645626		0.000416850i	0.00502619		3.24518e-5i
$166$		−	14.0773i		−	1.09261i
$167$	4.06044	−	4.06044i	0.314206	−	0.314206i	−0.532331	−	0.846537i	$-0.678684\pi$
$167$	4.06044	−	4.06044i	0.314206	−	0.314206i	0.846537	+	0.532331i	$0.178684\pi$
$168$	1.37926	−	1.37926i	0.106412	−	0.106412i
$169$		−	11.9873i		−	0.922100i
$170$	0.974463	+	0.987128i	0.0747379	+	0.0757092i
$171$		−	7.23057i		−	0.552935i
$172$	5.83089	+	5.83089i	0.444601	+	0.444601i
$173$	12.1320	+	12.1320i	0.922379	+	0.922379i	0.997197	−	0.0748182i	$-0.0238377\pi$
$173$	12.1320	+	12.1320i	0.922379	+	0.922379i	−0.0748182	+	0.997197i	$0.523838\pi$
$174$			3.97284i			0.301180i
$175$	6.98478	−	6.80668i	0.528000	−	0.514537i
$176$			0.0288739i			0.00217645i
$177$	−4.05781	+	4.05781i	−0.305004	+	0.305004i
$178$	7.43295	−	7.43295i	0.557123	−	0.557123i
$179$		−	16.6646i		−	1.24557i	−0.782393	−	0.622785i	$-0.786001\pi$
$179$		−	16.6646i		−	1.24557i	0.782393	−	0.622785i	$-0.213999\pi$
$180$	−1.57090	−	1.59131i	−0.117088	−	0.118610i
$181$			6.69613i			0.497719i	0.968540	+	0.248860i	$0.0800558\pi$
$181$			6.69613i			0.497719i	−0.968540	+	0.248860i	$0.919944\pi$
$182$	−1.38800	−	1.38800i	−0.102885	−	0.102885i
$183$	−3.60085	+	3.60085i	−0.266182	+	0.266182i
$184$	0.438634	−	4.77573i	0.0323365	−	0.352072i
$185$	0.0298627	−	4.62519i	0.00219555	−	0.340051i
$186$	5.20915			0.381953
$187$	−0.0126651	+	0.0126651i	−0.000926162	+	0.000926162i
$188$	−6.90153	−	6.90153i	−0.503346	−	0.503346i
$189$	−1.95057			−0.141883
$190$	16.1677	+	0.104387i	1.17293	+	0.00757305i
$191$			7.32933i			0.530332i	0.964203	+	0.265166i	$0.0854267\pi$
$191$			7.32933i			0.530332i	−0.964203	+	0.265166i	$0.914573\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	−5.03982	−	5.03982i	−0.362775	−	0.362775i	0.502059	−	0.864833i	$-0.332576\pi$
$193$	−5.03982	−	5.03982i	−0.362775	−	0.362775i	−0.864833	+	0.502059i	$0.832576\pi$
$194$	−1.20318			−0.0863836
$195$	−1.60139	+	1.58085i	−0.114678	+	0.113207i
$196$	−3.19528			−0.228234
$197$	6.17707	−	6.17707i	0.440098	−	0.440098i	−0.451947	−	0.892045i	$-0.649270\pi$
$197$	6.17707	−	6.17707i	0.440098	−	0.440098i	0.892045	+	0.451947i	$0.149270\pi$
$198$	0.0204169	−	0.0204169i	0.00145097	−	0.00145097i
$199$	−20.6272			−1.46222			−0.731111	−	0.682258i	$-0.760998\pi$
$199$	−20.6272			−1.46222			−0.731111	+	0.682258i	$0.760998\pi$
$200$	3.58089	−	3.48959i	0.253207	−	0.246751i
$201$			6.56147i			0.462811i
$202$	−10.7549	+	10.7549i	−0.756712	+	0.756712i
$203$	−5.47959	+	5.47959i	−0.384592	+	0.384592i
$204$	0.620322			0.0434313
$205$	11.2645	+	11.4109i	0.786747	+	0.796972i
$206$			3.59438i			0.250432i
$207$	−3.68711	+	3.06679i	−0.256272	+	0.213157i
$208$	−0.711585	−	0.711585i	−0.0493395	−	0.0493395i
$209$			0.208774i			0.0144412i
$210$	0.0281603	−	4.36152i	0.00194324	−	0.300973i
$211$	−25.2880			−1.74090			−0.870448	−	0.492261i	$-0.836171\pi$
$211$	−25.2880			−1.74090			−0.870448	+	0.492261i	$0.836171\pi$
$212$	−2.73811	−	2.73811i	−0.188054	−	0.188054i
$213$	3.87337	+	3.87337i	0.265399	+	0.265399i
$214$	−10.4409			−0.713728
$215$	18.4385	+	0.119049i	1.25750	+	0.00811906i
$216$	−1.00000			−0.0680414
$217$	7.18478	+	7.18478i	0.487735	+	0.487735i
$218$	0.871197	−	0.871197i	0.0590049	−	0.0590049i
$219$			1.28509i			0.0868382i
$220$	0.0453579	+	0.0459474i	0.00305803	+	0.00309777i
$221$		−	0.624251i		−	0.0419916i
$222$	−1.46265	−	1.46265i	−0.0981663	−	0.0981663i
$223$	6.36523	+	6.36523i	0.426247	+	0.426247i	0.887348	−	0.461101i	$-0.152545\pi$
$223$	6.36523	+	6.36523i	0.426247	+	0.426247i	−0.461101	+	0.887348i	$0.652545\pi$
$224$	1.95057			0.130328
$225$	−4.99958	−	0.0645626i	−0.333306	−	0.00430417i
$226$		−	14.9998i		−	0.997771i
$227$	12.2183	+	12.2183i	0.810956	+	0.810956i	0.984777	−	0.173822i	$-0.0556116\pi$
$227$	12.2183	+	12.2183i	0.810956	+	0.810956i	−0.173822	+	0.984777i	$0.555612\pi$
$228$	5.11278	−	5.11278i	0.338602	−	0.338602i
$229$	20.2222			1.33632			0.668162	−	0.744016i	$-0.267081\pi$
$229$	20.2222			1.33632			0.668162	+	0.744016i	$0.267081\pi$
$230$	−6.80418	−	8.28874i	−0.448654	−	0.546543i
$231$	0.0563205			0.00370562
$232$	−2.80922	+	2.80922i	−0.184434	+	0.184434i
$233$	−2.91503	−	2.91503i	−0.190970	−	0.190970i	0.605145	−	0.796115i	$-0.293115\pi$
$233$	−2.91503	−	2.91503i	−0.190970	−	0.190970i	−0.796115	+	0.605145i	$0.793115\pi$
$234$			1.00633i			0.0657860i
$235$	−21.8241	−	0.140908i	−1.42365	−	0.00919182i
$236$	−5.73861			−0.373552
$237$	3.67862	+	3.67862i	0.238952	+	0.238952i
$238$	0.855587	+	0.855587i	0.0554594	+	0.0554594i
$239$			8.30821i			0.537413i	0.963222	+	0.268707i	$0.0865962\pi$
$239$			8.30821i			0.537413i	−0.963222	+	0.268707i	$0.913404\pi$
$240$	0.0144369	−	2.23602i	0.000931900	−	0.144335i
$241$			14.5130i			0.934862i	0.884030	+	0.467431i	$0.154820\pi$
$241$			14.5130i			0.934862i	−0.884030	+	0.467431i	$0.845180\pi$
$242$	7.77759	−	7.77759i	0.499962	−	0.499962i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−5.09237			−0.326005
$245$	−5.08469	+	5.01945i	−0.324849	+	0.320681i
$246$	7.17074			0.457190
$247$	−5.14516	−	5.14516i	−0.327379	−	0.327379i
$248$	3.68342	+	3.68342i	0.233898	+	0.233898i
$249$	−14.0773			−0.892112
$250$	0.216542	−	11.1782i	0.0136953	−	0.706974i
$251$		−	14.3863i		−	0.908054i	−0.890988	−	0.454027i	$-0.849987\pi$
$251$		−	14.3863i		−	0.908054i	0.890988	−	0.454027i	$-0.150013\pi$
$252$	−1.37926	−	1.37926i	−0.0868853	−	0.0868853i
$253$	0.106461	−	0.0885501i	0.00669316	−	0.00556710i
$254$			9.13091i			0.572925i
$255$	0.987128	−	0.974463i	0.0618163	−	0.0610232i
$256$	1.00000			0.0625000
$257$	3.82209	−	3.82209i	0.238416	−	0.238416i	−0.577778	−	0.816194i	$-0.696080\pi$
$257$	3.82209	−	3.82209i	0.238416	−	0.238416i	0.816194	+	0.577778i	$0.196080\pi$
$258$	5.83089	−	5.83089i	0.363015	−	0.363015i
$259$		−	4.03474i		−	0.250707i
$260$	−2.25018	−	0.0145284i	−0.139550	−	0.000901011i
$261$	3.97284			0.245913
$262$	−9.99224	+	9.99224i	−0.617323	+	0.617323i
$263$	−19.6268	+	19.6268i	−1.21024	+	1.21024i	−0.239296	+	0.970947i	$0.576917\pi$
$263$	−19.6268	+	19.6268i	−1.21024	+	1.21024i	−0.970947	+	0.239296i	$0.923083\pi$
$264$	0.0288739			0.00177706
$265$	−8.65847	−	0.0559037i	−0.531886	−	0.00343414i
$266$	14.1037			0.864755
$267$	−7.43295	−	7.43295i	−0.454889	−	0.454889i
$268$	−4.63966	+	4.63966i	−0.283413	+	0.283413i
$269$		−	1.94226i		−	0.118422i	−0.998245	−	0.0592110i	$-0.981142\pi$
$269$		−	1.94226i		−	0.118422i	0.998245	−	0.0592110i	$-0.0188585\pi$
$270$	−1.59131	+	1.57090i	−0.0968443	+	0.0956018i
$271$	5.65568			0.343558			0.171779	−	0.985136i	$-0.445049\pi$
$271$	5.65568			0.343558			0.171779	+	0.985136i	$0.445049\pi$
$272$	0.438634	+	0.438634i	0.0265961	+	0.0265961i
$273$	−1.38800	+	1.38800i	−0.0840053	+	0.0840053i
$274$	14.1301			0.853629
$275$	0.144357	+	0.00186417i	0.00870508	+	0.000112414i
$276$	−4.77573	−	0.438634i	−0.287465	−	0.0264027i
$277$	−6.03861	+	6.03861i	−0.362825	+	0.362825i	−0.864852	−	0.502027i	$-0.832588\pi$
$277$	−6.03861	+	6.03861i	−0.362825	+	0.362825i	0.502027	+	0.864852i	$0.332588\pi$
$278$	−7.81231	−	7.81231i	−0.468551	−	0.468551i
$279$		−	5.20915i		−	0.311864i
$280$	3.10397	−	3.06415i	0.185498	−	0.183118i
$281$			19.0527i			1.13659i	0.822825	+	0.568294i	$0.192396\pi$
$281$			19.0527i			1.13659i	−0.822825	+	0.568294i	$0.807604\pi$
$282$	−6.90153	+	6.90153i	−0.410980	+	0.410980i
$283$	3.82033	−	3.82033i	0.227095	−	0.227095i	−0.584383	−	0.811478i	$-0.698663\pi$
$283$	3.82033	−	3.82033i	0.227095	−	0.227095i	0.811478	+	0.584383i	$0.198663\pi$
$284$			5.47777i			0.325046i
$285$	0.104387	−	16.1677i	0.00618337	−	0.957692i
$286$		−	0.0290567i		−	0.00171816i
$287$	9.89032	+	9.89032i	0.583807	+	0.583807i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$		−	16.6152i		−	0.977365i
$290$	−0.0573557	+	8.88336i	−0.00336804	+	0.521649i
$291$			1.20318i			0.0705319i
$292$	−0.908695	+	0.908695i	−0.0531773	+	0.0531773i
$293$	2.20441	−	2.20441i	0.128783	−	0.128783i	−0.639777	−	0.768560i	$-0.720973\pi$
$293$	2.20441	−	2.20441i	0.128783	−	0.128783i	0.768560	+	0.639777i	$0.220973\pi$
$294$			3.19528i			0.186352i
$295$	−9.13194	+	9.01477i	−0.531682	+	0.524860i
$296$		−	2.06849i		−	0.120229i
$297$	−0.0204169	−	0.0204169i	−0.00118471	−	0.00118471i
$298$	9.22408	−	9.22408i	0.534336	−	0.534336i
$299$	−0.441412	+	4.80597i	−0.0255275	+	0.277937i
$300$	−3.48959	−	3.58089i	−0.201471	−	0.206743i
$301$	16.0846			0.927103
$302$	1.52797	−	1.52797i	0.0879250	−	0.0879250i
$303$	10.7549	+	10.7549i	0.617853	+	0.617853i
$304$	7.23057			0.414701
$305$	−8.10355	+	7.99958i	−0.464008	+	0.458055i
$306$		−	0.620322i		−	0.0354615i
$307$	−13.5388	+	13.5388i	−0.772700	+	0.772700i	−0.978578	−	0.205878i	$-0.933995\pi$
$307$	−13.5388	+	13.5388i	−0.772700	+	0.772700i	0.205878	+	0.978578i	$0.433995\pi$
$308$	0.0398246	+	0.0398246i	0.00226922	+	0.00226922i
$309$	3.59438			0.204477
$310$	11.6478	+	0.0752042i	0.661549	+	0.00427131i
$311$	−32.1959			−1.82566			−0.912831	−	0.408337i	$-0.866109\pi$
$311$	−32.1959			−1.82566			−0.912831	+	0.408337i	$0.866109\pi$
$312$	−0.711585	+	0.711585i	−0.0402855	+	0.0402855i
$313$	19.4438	−	19.4438i	1.09903	−	1.09903i	0.104502	−	0.994525i	$-0.466675\pi$
$313$	19.4438	−	19.4438i	1.09903	−	1.09903i	0.994525	−	0.104502i	$-0.0333247\pi$
$314$	−19.0386			−1.07441
$315$	−4.36152	−	0.0281603i	−0.245744	−	0.00158665i
$316$			5.20235i			0.292655i
$317$	−1.40155	+	1.40155i	−0.0787188	+	0.0787188i	−0.745370	−	0.666651i	$-0.767727\pi$
$317$	−1.40155	+	1.40155i	−0.0787188	+	0.0787188i	0.666651	+	0.745370i	$0.267727\pi$
$318$	−2.73811	+	2.73811i	−0.153545	+	0.153545i
$319$	−0.114711			−0.00642260
$320$	1.59131	−	1.57090i	0.0889572	−	0.0878158i
$321$			10.4409i			0.582756i
$322$	−5.98199	−	7.19197i	−0.333363	−	0.400793i
$323$	3.17157	+	3.17157i	0.176471	+	0.176471i
$324$			1.00000i			0.0555556i
$325$	−3.60357	+	3.51168i	−0.199890	+	0.194793i
$326$	−0.815762			−0.0451809
$327$	−0.871197	−	0.871197i	−0.0481773	−	0.0481773i
$328$	5.07048	+	5.07048i	0.279970	+	0.279970i
$329$	−19.0380			−1.04960
$330$	0.0459474	−	0.0453579i	0.00252932	−	0.00249687i
$331$	29.9547			1.64646			0.823229	−	0.567709i	$-0.192170\pi$
$331$	29.9547			1.64646			0.823229	+	0.567709i	$0.192170\pi$
$332$	−9.95414	−	9.95414i	−0.546305	−	0.546305i
$333$	−1.46265	+	1.46265i	−0.0801525	+	0.0801525i
$334$		−	5.74232i		−	0.314206i
$335$	−0.0947276	+	14.6716i	−0.00517552	+	0.801595i
$336$		−	1.95057i		−	0.106412i
$337$	9.66919	+	9.66919i	0.526714	+	0.526714i	0.919591	−	0.392877i	$-0.128520\pi$
$337$	9.66919	+	9.66919i	0.526714	+	0.526714i	−0.392877	+	0.919591i	$0.628520\pi$
$338$	−8.47630	−	8.47630i	−0.461050	−	0.461050i
$339$	−14.9998			−0.814677
$340$	1.38705	+	0.00895556i	0.0752236	+	0.000485683i
$341$			0.150408i			0.00814507i
$342$	−5.11278	−	5.11278i	−0.276468	−	0.276468i
$343$	−14.0620	+	14.0620i	−0.759274	+	0.759274i
$344$	8.24612			0.444601
$345$	−8.28874	+	6.80418i	−0.446251	+	0.366325i
$346$	17.1572			0.922379
$347$	5.75653	−	5.75653i	0.309026	−	0.309026i	−0.535505	−	0.844532i	$-0.679879\pi$
$347$	5.75653	−	5.75653i	0.309026	−	0.309026i	0.844532	+	0.535505i	$0.179879\pi$
$348$	2.80922	+	2.80922i	0.150590	+	0.150590i
$349$			15.4579i			0.827443i	0.910404	+	0.413721i	$0.135771\pi$
$349$			15.4579i			0.827443i	−0.910404	+	0.413721i	$0.864229\pi$
$350$	0.125934	−	9.75204i	0.00673145	−	0.521268i
$351$	1.00633			0.0537141
$352$	0.0204169	+	0.0204169i	0.00108823	+	0.00108823i
$353$	0.0222101	+	0.0222101i	0.00118213	+	0.00118213i	0.707698	−	0.706515i	$-0.249734\pi$
$353$	0.0222101	+	0.0222101i	0.00118213	+	0.00118213i	−0.706515	+	0.707698i	$0.749734\pi$
$354$			5.73861i			0.305004i
$355$	8.60501	+	8.71685i	0.456707	+	0.462643i
$356$		−	10.5118i		−	0.557123i
$357$	0.855587	−	0.855587i	0.0452824	−	0.0452824i
$358$	−11.7837	−	11.7837i	−0.622785	−	0.622785i
$359$	32.6259			1.72193			0.860964	−	0.508666i	$-0.169861\pi$
$359$	32.6259			1.72193			0.860964	+	0.508666i	$0.169861\pi$
$360$	−2.23602	−	0.0144369i	−0.117849	−	0.000760894i
$361$	33.2811			1.75164
$362$	4.73488	+	4.73488i	0.248860	+	0.248860i
$363$	−7.77759	−	7.77759i	−0.408217	−	0.408217i
$364$	−1.96292			−0.102885
$365$	−0.0185527	+	2.87348i	−0.000971095	+	0.150405i
$366$			5.09237i			0.266182i
$367$	15.1093	+	15.1093i	0.788701	+	0.788701i	0.981281	−	0.192580i	$-0.0616854\pi$
$367$	15.1093	+	15.1093i	0.788701	+	0.788701i	−0.192580	+	0.981281i	$0.561685\pi$
$368$	−3.06679	−	3.68711i	−0.159867	−	0.192204i
$369$		−	7.17074i		−	0.373294i
$370$	−3.24939	−	3.29162i	−0.168928	−	0.171123i
$371$	−7.55313			−0.392139
$372$	3.68342	−	3.68342i	0.190977	−	0.190977i
$373$	−9.38306	+	9.38306i	−0.485836	+	0.485836i	−0.906990	−	0.421153i	$-0.861625\pi$
$373$	−9.38306	+	9.38306i	−0.485836	+	0.485836i	0.421153	+	0.906990i	$0.361625\pi$
$374$			0.0179111i			0.000926162i
$375$	−11.1782	−	0.216542i	−0.577242	−	0.0111822i
$376$	−9.76024			−0.503346
$377$	2.82701	−	2.82701i	0.145599	−	0.145599i
$378$	−1.37926	+	1.37926i	−0.0709416	+	0.0709416i
$379$	14.3962			0.739483			0.369741	−	0.929135i	$-0.379446\pi$
$379$	14.3962			0.739483			0.369741	+	0.929135i	$0.379446\pi$
$380$	11.5061	−	11.3585i	0.590251	−	0.582678i
$381$	9.13091			0.467791
$382$	5.18262	+	5.18262i	0.265166	+	0.265166i
$383$	−6.21540	+	6.21540i	−0.317592	+	0.317592i	−0.847842	−	0.530249i	$-0.822098\pi$
$383$	−6.21540	+	6.21540i	−0.317592	+	0.317592i	0.530249	+	0.847842i	$0.322098\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	0.125934		0.000813096i	0.00641819		4.14392e-5i
$386$	−7.12739			−0.362775
$387$	−5.83089	−	5.83089i	−0.296401	−	0.296401i
$388$	−0.850780	+	0.850780i	−0.0431918	+	0.0431918i
$389$	−23.6231			−1.19774			−0.598869	−	0.800847i	$-0.704383\pi$
$389$	−23.6231			−1.19774			−0.598869	+	0.800847i	$0.704383\pi$
$390$	−0.0145284	+	2.25018i	−0.000735672	+	0.113942i
$391$	0.272095	−	2.96249i	0.0137604	−	0.149820i
$392$	−2.25940	+	2.25940i	−0.114117	+	0.114117i
$393$	9.99224	+	9.99224i	0.504042	+	0.504042i
$394$		−	8.73570i		−	0.440098i
$395$	8.17236	+	8.27858i	0.411196	+	0.416540i
$396$		−	0.0288739i		−	0.00145097i
$397$	−4.91069	+	4.91069i	−0.246461	+	0.246461i	−0.819516	−	0.573056i	$-0.805758\pi$
$397$	−4.91069	+	4.91069i	−0.246461	+	0.246461i	0.573056	+	0.819516i	$0.305758\pi$
$398$	−14.5856	+	14.5856i	−0.731111	+	0.731111i
$399$		−	14.1037i		−	0.706069i
$400$	0.0645626	−	4.99958i	0.00322813	−	0.249979i
$401$		−	14.4696i		−	0.722575i	−0.932454	−	0.361288i	$-0.882337\pi$
$401$		−	14.4696i		−	0.722575i	0.932454	−	0.361288i	$-0.117663\pi$
$402$	4.63966	+	4.63966i	0.231405	+	0.231405i
$403$	−3.70675	−	3.70675i	−0.184646	−	0.184646i
$404$			15.2097i			0.756712i
$405$	1.57090	+	1.59131i	0.0780585	+	0.0790730i
$406$			7.74930i			0.384592i
$407$	0.0422322	−	0.0422322i	0.00209337	−	0.00209337i
$408$	0.438634	−	0.438634i	0.0217156	−	0.0217156i
$409$		−	22.5518i		−	1.11512i	−0.830138	−	0.557558i	$-0.811738\pi$
$409$		−	22.5518i		−	1.11512i	0.830138	−	0.557558i	$-0.188262\pi$
$410$	16.0339	+	0.103524i	0.791859	+	0.00511266i
$411$		−	14.1301i		−	0.696985i
$412$	2.54161	+	2.54161i	0.125216	+	0.125216i
$413$	−7.91505	+	7.91505i	−0.389474	+	0.389474i
$414$	−0.438634	+	4.77573i	−0.0215577	+	0.234714i
$415$	−31.4771	−	0.203233i	−1.54515	−	0.00997631i
$416$	−1.00633			−0.0493395
$417$	−7.81231	+	7.81231i	−0.382570	+	0.382570i
$418$	0.147626	+	0.147626i	0.00722062	+	0.00722062i
$419$	−30.0512			−1.46810			−0.734049	−	0.679097i	$-0.762372\pi$
$419$	−30.0512			−1.46810			−0.734049	+	0.679097i	$0.762372\pi$
$420$	−3.06415	−	3.10397i	−0.149515	−	0.151458i
$421$			21.5409i			1.04984i	0.851152	+	0.524919i	$0.175905\pi$
$421$			21.5409i			1.04984i	−0.851152	+	0.524919i	$0.824095\pi$
$422$	−17.8813	+	17.8813i	−0.870448	+	0.870448i
$423$	6.90153	+	6.90153i	0.335564	+	0.335564i
$424$	−3.87227			−0.188054
$425$	2.22131	−	2.16467i	0.107749	−	0.105002i
$426$	5.47777			0.265399
$427$	−7.02370	+	7.02370i	−0.339901	+	0.339901i
$428$	−7.38286	+	7.38286i	−0.356864	+	0.356864i
$429$	−0.0290567			−0.00140287
$430$	13.1222	−	12.9538i	0.632807	−	0.624688i
$431$			15.6022i			0.751529i	0.926715	+	0.375765i	$0.122620\pi$
$431$			15.6022i			0.751529i	−0.926715	+	0.375765i	$0.877380\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	−11.2969	+	11.2969i	−0.542893	+	0.542893i	−0.924376	−	0.381483i	$-0.875414\pi$
$433$	−11.2969	+	11.2969i	−0.542893	+	0.542893i	0.381483	+	0.924376i	$0.375414\pi$
$434$	10.1608			0.487735
$435$	8.88336	+	0.0573557i	0.425924	+	0.00274999i
$436$		−	1.23206i		−	0.0590049i
$437$	−22.1746	−	26.6599i	−1.06076	−	1.27532i
$438$	0.908695	+	0.908695i	0.0434191	+	0.0434191i
$439$		−	3.20333i		−	0.152887i	−0.997074	−	0.0764433i	$-0.975644\pi$
$439$		−	3.20333i		−	0.152887i	0.997074	−	0.0764433i	$-0.0243564\pi$
$440$	0.0645626		0.000416850i	0.00307790		1.98726e-5i
$441$	3.19528			0.152156
$442$	−0.441412	−	0.441412i	−0.0209958	−	0.0209958i
$443$	−15.6087	−	15.6087i	−0.741590	−	0.741590i	0.231294	−	0.972884i	$-0.425704\pi$
$443$	−15.6087	−	15.6087i	−0.741590	−	0.741590i	−0.972884	+	0.231294i	$0.925704\pi$
$444$	−2.06849			−0.0981663
$445$	−16.5129	−	16.7275i	−0.782788	−	0.792961i
$446$	9.00179			0.426247
$447$	−9.22408	−	9.22408i	−0.436284	−	0.436284i
$448$	1.37926	−	1.37926i	0.0651640	−	0.0651640i
$449$			11.2112i			0.529087i	0.964374	+	0.264543i	$0.0852213\pi$
$449$			11.2112i			0.529087i	−0.964374	+	0.264543i	$0.914779\pi$
$450$	−3.58089	+	3.48959i	−0.168805	+	0.164501i
$451$			0.207047i			0.00974947i
$452$	−10.6065	−	10.6065i	−0.498885	−	0.498885i
$453$	−1.52797	−	1.52797i	−0.0717904	−	0.0717904i
$454$	17.2793			0.810956
$455$	−3.12363	+	3.08355i	−0.146438	+	0.144559i
$456$		−	7.23057i		−	0.338602i
$457$	17.6613	+	17.6613i	0.826163	+	0.826163i	0.986984	−	0.160821i	$-0.0514141\pi$
$457$	17.6613	+	17.6613i	0.826163	+	0.826163i	−0.160821	+	0.986984i	$0.551414\pi$
$458$	14.2993	−	14.2993i	0.668162	−	0.668162i
$459$	−0.620322			−0.0289542
$460$	−10.6723	−	1.04974i	−0.497599	−	0.0489445i
$461$	19.3119			0.899444			0.449722	−	0.893169i	$-0.351523\pi$
$461$	19.3119			0.899444			0.449722	+	0.893169i	$0.351523\pi$
$462$	0.0398246	−	0.0398246i	0.00185281	−	0.00185281i
$463$	12.6411	+	12.6411i	0.587484	+	0.587484i	0.936949	−	0.349465i	$-0.113637\pi$
$463$	12.6411	+	12.6411i	0.587484	+	0.587484i	−0.349465	+	0.936949i	$0.613637\pi$
$464$			3.97284i			0.184434i
$465$	0.0752042	−	11.6478i	0.00348751	−	0.540152i
$466$	−4.12247			−0.190970
$467$	−27.3483	−	27.3483i	−1.26553	−	1.26553i	−0.948373	−	0.317157i	$-0.897272\pi$
$467$	−27.3483	−	27.3483i	−1.26553	−	1.26553i	−0.317157	−	0.948373i	$-0.602728\pi$
$468$	0.711585	+	0.711585i	0.0328930	+	0.0328930i
$469$			12.7986i			0.590985i
$470$	−15.5316	+	15.3323i	−0.716419	+	0.707228i
$471$			19.0386i			0.877251i
$472$	−4.05781	+	4.05781i	−0.186776	+	0.186776i
$473$	0.168360	+	0.168360i	0.00774122	+	0.00774122i
$474$	5.20235			0.238952
$475$	0.466824	−	36.1498i	0.0214194	−	1.65867i
$476$	1.20998			0.0554594
$477$	2.73811	+	2.73811i	0.125369	+	0.125369i
$478$	5.87479	+	5.87479i	0.268707	+	0.268707i
$479$	−26.9547			−1.23159			−0.615796	−	0.787906i	$-0.711165\pi$
$479$	−26.9547			−1.23159			−0.615796	+	0.787906i	$0.711165\pi$
$480$	−1.57090	−	1.59131i	−0.0717013	−	0.0726332i
$481$			2.08159i			0.0949124i
$482$	10.2622	+	10.2622i	0.467431	+	0.467431i
$483$	−7.19197	+	5.98199i	−0.327246	+	0.272190i
$484$		−	10.9992i		−	0.499962i
$485$	−0.0173703	+	2.69035i	−0.000788745	+	0.122162i
$486$	1.00000			0.0453609
$487$	28.7208	−	28.7208i	1.30146	−	1.30146i	0.374058	−	0.927405i	$-0.377966\pi$
$487$	28.7208	−	28.7208i	1.30146	−	1.30146i	0.927405	−	0.374058i	$-0.122034\pi$
$488$	−3.60085	+	3.60085i	−0.163003	+	0.163003i
$489$			0.815762i			0.0368900i
$490$	−0.0461300	+	7.14470i	−0.00208394	+	0.322765i
$491$	2.65360			0.119755			0.0598777	−	0.998206i	$-0.480929\pi$
$491$	2.65360			0.119755			0.0598777	+	0.998206i	$0.480929\pi$
$492$	5.07048	−	5.07048i	0.228595	−	0.228595i
$493$	−1.74262	+	1.74262i	−0.0784838	+	0.0784838i
$494$	−7.27635			−0.327379
$495$	−0.0453579	−	0.0459474i	−0.00203869	−	0.00206518i
$496$	5.20915			0.233898
$497$	7.55528	+	7.55528i	0.338900	+	0.338900i
$498$	−9.95414	+	9.95414i	−0.446056	+	0.446056i
$499$			9.11525i			0.408055i	0.978965	+	0.204027i	$0.0654032\pi$
$499$			9.11525i			0.408055i	−0.978965	+	0.204027i	$0.934597\pi$
$500$	−7.75109	−	8.05733i	−0.346639	−	0.360335i
$501$	−5.74232			−0.256548
$502$	−10.1726	−	10.1726i	−0.454027	−	0.454027i
$503$	17.5461	−	17.5461i	0.782343	−	0.782343i	−0.197883	−	0.980226i	$-0.563407\pi$
$503$	17.5461	−	17.5461i	0.782343	−	0.782343i	0.980226	+	0.197883i	$0.0634065\pi$
$504$	−1.95057			−0.0868853
$505$	23.8929	+	24.2035i	1.06322	+	1.07704i
$506$	0.0126651	−	0.137894i	0.000563031	−	0.00613013i
$507$	−8.47630	+	8.47630i	−0.376446	+	0.376446i
$508$	6.45653	+	6.45653i	0.286462	+	0.286462i
$509$		−	23.7897i		−	1.05446i	−0.849722	−	0.527231i	$-0.823230\pi$
$509$		−	23.7897i		−	1.05446i	0.849722	−	0.527231i	$-0.176770\pi$
$510$	0.00895556	−	1.38705i	0.000396559	−	0.0614198i
$511$			2.50666i			0.110888i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−5.11278	+	5.11278i	−0.225735	+	0.225735i
$514$		−	5.40526i		−	0.238416i
$515$	8.03712	+	0.0518919i	0.354158	+	0.00228663i
$516$		−	8.24612i		−	0.363015i
$517$	−0.199274	−	0.199274i	−0.00876406	−	0.00876406i
$518$	−2.85299	−	2.85299i	−0.125353	−	0.125353i
$519$		−	17.1572i		−	0.753119i
$520$	−1.60139	+	1.58085i	−0.0702257	+	0.0693246i
$521$		−	34.3911i		−	1.50670i	−0.657619	−	0.753351i	$-0.728436\pi$
$521$		−	34.3911i		−	1.50670i	0.657619	−	0.753351i	$-0.271564\pi$
$522$	2.80922	−	2.80922i	0.122956	−	0.122956i
$523$	7.14069	−	7.14069i	0.312240	−	0.312240i	−0.533537	−	0.845777i	$-0.679137\pi$
$523$	7.14069	−	7.14069i	0.312240	−	0.312240i	0.845777	+	0.533537i	$0.179137\pi$
$524$			14.1312i			0.617323i
$525$	−9.75204	−	0.125934i	−0.425614	−	0.00549621i
$526$			27.7565i			1.21024i
$527$	2.28491	+	2.28491i	0.0995323	+	0.0995323i
$528$	0.0204169	−	0.0204169i	0.000888532	−	0.000888532i
$529$	−4.18960	+	22.6152i	−0.182156	+	0.983270i
$530$	−6.16199	+	6.08293i	−0.267660	+	0.264226i
$531$	5.73861			0.249035
$532$	9.97284	−	9.97284i	0.432377	−	0.432377i
$533$	−5.10259	−	5.10259i	−0.221018	−	0.221018i
$534$	−10.5118			−0.454889
$535$	−0.150735	+	23.3462i	−0.00651685	+	1.00934i
$536$			6.56147i			0.283413i
$537$	−11.7837	+	11.7837i	−0.508502	+	0.508502i
$538$	−1.37339	−	1.37339i	−0.0592110	−	0.0592110i
$539$	−0.0922600			−0.00397392
$540$	−0.0144369	+	2.23602i	−0.000621267	+	0.0962230i
$541$	8.24675			0.354555			0.177278	−	0.984161i	$-0.443271\pi$
$541$	8.24675			0.354555			0.177278	+	0.984161i	$0.443271\pi$
$542$	3.99917	−	3.99917i	0.171779	−	0.171779i
$543$	4.73488	−	4.73488i	0.203193	−	0.203193i
$544$	0.620322			0.0265961
$545$	−1.93544	−	1.96059i	−0.0829050	−	0.0839825i
$546$			1.96292i			0.0840053i
$547$	11.4282	−	11.4282i	0.488633	−	0.488633i	−0.419242	−	0.907875i	$-0.637704\pi$
$547$	11.4282	−	11.4282i	0.488633	−	0.488633i	0.907875	+	0.419242i	$0.137704\pi$
$548$	9.99147	−	9.99147i	0.426815	−	0.426815i
$549$	5.09237			0.217337
$550$	0.103394	−	0.100758i	0.00440875	−	0.00429633i
$551$			28.7259i			1.22376i
$552$	−3.68711	+	3.06679i	−0.156934	+	0.130531i
$553$	7.17540	+	7.17540i	0.305129	+	0.305129i
$554$			8.53988i			0.362825i
$555$	−3.29162	+	3.24939i	−0.139722	+	0.137929i
$556$	−11.0483			−0.468551
$557$	−28.6684	−	28.6684i	−1.21472	−	1.21472i	−0.969456	−	0.245264i	$-0.921125\pi$
$557$	−28.6684	−	28.6684i	−1.21472	−	1.21472i	−0.245264	−	0.969456i	$-0.578875\pi$
$558$	−3.68342	−	3.68342i	−0.155932	−	0.155932i
$559$	−8.29834			−0.350982
$560$	0.0281603	−	4.36152i	0.00118999	−	0.184308i
$561$	0.0179111			0.000756208
$562$	13.4723	+	13.4723i	0.568294	+	0.568294i
$563$	6.96259	−	6.96259i	0.293438	−	0.293438i	−0.544999	−	0.838437i	$-0.683470\pi$
$563$	6.96259	−	6.96259i	0.293438	−	0.293438i	0.838437	+	0.544999i	$0.183470\pi$
$564$			9.76024i			0.410980i
$565$	−33.5398	−	0.216551i	−1.41103	−	0.00911037i
$566$		−	5.40276i		−	0.227095i
$567$	1.37926	+	1.37926i	0.0579235	+	0.0579235i
$568$	3.87337	+	3.87337i	0.162523	+	0.162523i
$569$	14.2217			0.596204			0.298102	−	0.954534i	$-0.403647\pi$
$569$	14.2217			0.596204			0.298102	+	0.954534i	$0.403647\pi$
$570$	−11.3585	−	11.5061i	−0.475754	−	0.481938i
$571$		−	35.8009i		−	1.49822i	−0.662444	−	0.749111i	$-0.730481\pi$
$571$		−	35.8009i		−	1.49822i	0.662444	−	0.749111i	$-0.269519\pi$
$572$	−0.0205462	−	0.0205462i	−0.000859080	−	0.000859080i
$573$	5.18262	−	5.18262i	0.216507	−	0.216507i
$574$	13.9870			0.583807
$575$	−18.6320	+	15.0946i	−0.777009	+	0.629489i
$576$	−1.00000			−0.0416667
$577$	−27.3402	+	27.3402i	−1.13819	+	1.13819i	−0.149414	+	0.988775i	$0.547739\pi$
$577$	−27.3402	+	27.3402i	−1.13819	+	1.13819i	−0.988775	+	0.149414i	$0.952261\pi$
$578$	−11.7487	−	11.7487i	−0.488682	−	0.488682i
$579$			7.12739i			0.296204i
$580$	6.24092	+	6.32204i	0.259140	+	0.262508i
$581$	−27.4587			−1.13918
$582$	0.850780	+	0.850780i	0.0352660	+	0.0352660i
$583$	−0.0790597	−	0.0790597i	−0.00327432	−	0.00327432i
$584$			1.28509i			0.0531773i
$585$	2.25018	+	0.0145284i	0.0930335	+	0.000600674i
$586$		−	3.11750i		−	0.128783i
$587$	20.3799	−	20.3799i	0.841168	−	0.841168i	−0.147843	−	0.989011i	$-0.547233\pi$
$587$	20.3799	−	20.3799i	0.841168	−	0.841168i	0.989011	+	0.147843i	$0.0472330\pi$
$588$	2.25940	+	2.25940i	0.0931761	+	0.0931761i
$589$	37.6651			1.55196
$590$	−0.0828480	+	12.8317i	−0.00341080	+	0.528271i
$591$	−8.73570			−0.359339
$592$	−1.46265	−	1.46265i	−0.0601144	−	0.0601144i
$593$	25.3498	+	25.3498i	1.04099	+	1.04099i	0.999123	+	0.0418694i	$0.0133313\pi$
$593$	25.3498	+	25.3498i	1.04099	+	1.04099i	0.0418694	+	0.999123i	$0.486669\pi$
$594$	−0.0288739			−0.00118471
$595$	1.92546	−	1.90076i	0.0789363	−	0.0779235i
$596$		−	13.0448i		−	0.534336i
$597$	14.5856	+	14.5856i	0.596950	+	0.596950i
$598$	3.08621	+	3.71046i	0.126205	+	0.151732i
$599$			10.3371i			0.422363i	0.977447	+	0.211182i	$0.0677311\pi$
$599$			10.3371i			0.422363i	−0.977447	+	0.211182i	$0.932269\pi$
$600$	−4.99958	−	0.0645626i	−0.204107	−	0.00263576i
$601$	−4.83569			−0.197252			−0.0986259	−	0.995125i	$-0.531445\pi$
$601$	−4.83569			−0.197252			−0.0986259	+	0.995125i	$0.531445\pi$
$602$	11.3736	−	11.3736i	0.463552	−	0.463552i
$603$	4.63966	−	4.63966i	0.188942	−	0.188942i
$604$		−	2.16088i		−	0.0879250i
$605$	−17.2786	−	17.5031i	−0.702473	−	0.711603i
$606$	15.2097			0.617853
$607$	25.7553	−	25.7553i	1.04538	−	1.04538i	0.0464558	−	0.998920i	$-0.485207\pi$
$607$	25.7553	−	25.7553i	1.04538	−	1.04538i	0.998920	−	0.0464558i	$-0.0147927\pi$
$608$	5.11278	−	5.11278i	0.207351	−	0.207351i
$609$	7.74930			0.314018
$610$	−0.0735182	+	11.3866i	−0.00297666	+	0.461031i
$611$	9.82204			0.397357
$612$	−0.438634	−	0.438634i	−0.0177307	−	0.0177307i
$613$	16.7564	−	16.7564i	0.676784	−	0.676784i	−0.282487	−	0.959271i	$-0.591159\pi$
$613$	16.7564	−	16.7564i	0.676784	−	0.676784i	0.959271	+	0.282487i	$0.0911593\pi$
$614$			19.1467i			0.772700i
$615$	0.103524	−	16.0339i	0.00417447	−	0.646550i
$616$	0.0563205			0.00226922
$617$	3.44309	+	3.44309i	0.138614	+	0.138614i	0.773009	−	0.634395i	$-0.218751\pi$
$617$	3.44309	+	3.44309i	0.138614	+	0.138614i	−0.634395	+	0.773009i	$0.718751\pi$
$618$	2.54161	−	2.54161i	0.102239	−	0.102239i
$619$	41.6136			1.67259			0.836296	−	0.548278i	$-0.184716\pi$
$619$	41.6136			1.67259			0.836296	+	0.548278i	$0.184716\pi$
$620$	8.28939	−	8.18304i	0.332910	−	0.328639i
$621$	4.77573	+	0.438634i	0.191643	+	0.0176018i
$622$	−22.7659	+	22.7659i	−0.912831	+	0.912831i
$623$	−14.4985	−	14.4985i	−0.580870	−	0.580870i
$624$			1.00633i			0.0402855i
$625$	−24.9917	−	0.645572i	−0.999667	−	0.0258229i
$626$		−	27.4976i		−	1.09903i
$627$	0.147626	−	0.147626i	0.00589561	−	0.00589561i
$628$	−13.4623	+	13.4623i	−0.537204	+	0.537204i
$629$		−	1.28313i		−	0.0511618i
$630$	−3.10397	+	3.06415i	−0.123665	+	0.122078i
$631$			6.27086i			0.249639i	0.992179	+	0.124820i	$0.0398352\pi$
$631$			6.27086i			0.249639i	−0.992179	+	0.124820i	$0.960165\pi$
$632$	3.67862	+	3.67862i	0.146328	+	0.146328i
$633$	17.8813	+	17.8813i	0.710718	+	0.710718i
$634$			1.98209i			0.0787188i
$635$	20.4169	+	0.131822i	0.810221	+	0.00523121i
$636$			3.87227i			0.153545i
$637$	2.27371	−	2.27371i	0.0900876	−	0.0900876i
$638$	−0.0811132	+	0.0811132i	−0.00321130	+	0.00321130i
$639$		−	5.47777i		−	0.216697i
$640$	0.0144369	−	2.23602i	0.000570670	−	0.0883865i
$641$			21.1913i			0.837007i	0.908215	+	0.418504i	$0.137445\pi$
$641$			21.1913i			0.837007i	−0.908215	+	0.418504i	$0.862555\pi$
$642$	7.38286	+	7.38286i	0.291378	+	0.291378i
$643$	25.8131	−	25.8131i	1.01797	−	1.01797i	0.0181324	−	0.999836i	$-0.494228\pi$
$643$	25.8131	−	25.8131i	1.01797	−	1.01797i	0.999836	−	0.0181324i	$-0.00577205\pi$
$644$	−9.31540	−	0.855587i	−0.367078	−	0.0337148i
$645$	−12.9538	−	13.1222i	−0.510056	−	0.516685i
$646$	4.48528			0.176471
$647$	33.5677	−	33.5677i	1.31968	−	1.31968i	0.405654	−	0.914027i	$-0.367044\pi$
$647$	33.5677	−	33.5677i	1.31968	−	1.31968i	0.914027	−	0.405654i	$-0.132956\pi$
$648$	0.707107	+	0.707107i	0.0277778	+	0.0277778i
$649$	−0.165696			−0.00650414
$650$	−0.0649715	+	5.03124i	−0.00254839	+	0.197342i
$651$		−	10.1608i		−	0.398234i
$652$	−0.576831	+	0.576831i	−0.0225904	+	0.0225904i
$653$	−13.1083	−	13.1083i	−0.512967	−	0.512967i	0.402467	−	0.915434i	$-0.368153\pi$
$653$	−13.1083	−	13.1083i	−0.512967	−	0.512967i	−0.915434	+	0.402467i	$0.868153\pi$
$654$	−1.23206			−0.0481773
$655$	22.1986	+	22.4871i	0.867372	+	0.878645i
$656$	7.17074			0.279970
$657$	0.908695	−	0.908695i	0.0354516	−	0.0354516i
$658$	−13.4619	+	13.4619i	−0.524800	+	0.524800i
$659$	13.3409			0.519688			0.259844	−	0.965651i	$-0.416329\pi$
$659$	13.3409			0.519688			0.259844	+	0.965651i	$0.416329\pi$
$660$	0.000416850	−	0.0645626i	1.62259e−5	−	0.00251310i
$661$		−	42.1609i		−	1.63987i	−0.572459	−	0.819934i	$-0.694010\pi$
$661$		−	42.1609i		−	1.63987i	0.572459	−	0.819934i	$-0.305990\pi$
$662$	21.1812	−	21.1812i	0.823229	−	0.823229i
$663$	−0.441412	+	0.441412i	−0.0171430	+	0.0171430i
$664$	−14.0773			−0.546305
$665$	0.203615	−	31.5362i	0.00789584	−	1.22292i
$666$			2.06849i			0.0801525i
$667$	14.6483	−	12.1839i	0.567185	−	0.471761i
$668$	−4.06044	−	4.06044i	−0.157103	−	0.157103i
$669$		−	9.00179i		−	0.348029i
$670$	10.3074	+	10.4414i	0.398210	+	0.403385i
$671$	−0.147036			−0.00567627
$672$	−1.37926	−	1.37926i	−0.0532062	−	0.0532062i
$673$	−8.80148	−	8.80148i	−0.339272	−	0.339272i	0.516821	−	0.856093i	$-0.327115\pi$
$673$	−8.80148	−	8.80148i	−0.339272	−	0.339272i	−0.856093	+	0.516821i	$0.827115\pi$
$674$	13.6743			0.526714
$675$	3.48959	+	3.58089i	0.134314	+	0.137829i
$676$	−11.9873			−0.461050
$677$	1.46521	+	1.46521i	0.0563127	+	0.0563127i	0.734702	−	0.678390i	$-0.237322\pi$
$677$	1.46521	+	1.46521i	0.0563127	+	0.0563127i	−0.678390	+	0.734702i	$0.737322\pi$
$678$	−10.6065	+	10.6065i	−0.407338	+	0.407338i
$679$			2.34690i			0.0900656i
$680$	0.987128	−	0.974463i	0.0378546	−	0.0373689i
$681$		−	17.2793i		−	0.662142i
$682$	0.106355	+	0.106355i	0.00407253	+	0.00407253i
$683$	−8.63814	−	8.63814i	−0.330529	−	0.330529i	0.522258	−	0.852787i	$-0.325090\pi$
$683$	−8.63814	−	8.63814i	−0.330529	−	0.330529i	−0.852787	+	0.522258i	$0.825090\pi$
$684$	−7.23057			−0.276468
$685$	0.203995	−	31.5952i	0.00779425	−	1.20719i
$686$			19.8866i			0.759274i
$687$	−14.2993	−	14.2993i	−0.545552	−	0.545552i
$688$	5.83089	−	5.83089i	0.222300	−	0.222300i
$689$	3.89679			0.148456
$690$	−1.04974	+	10.6723i	−0.0399630	+	0.406288i
$691$	−3.45873			−0.131576			−0.0657882	−	0.997834i	$-0.520956\pi$
$691$	−3.45873			−0.131576			−0.0657882	+	0.997834i	$0.520956\pi$
$692$	12.1320	−	12.1320i	0.461189	−	0.461189i
$693$	−0.0398246	−	0.0398246i	−0.00151281	−	0.00151281i
$694$		−	8.14096i		−	0.309026i
$695$	−17.5813	+	17.3557i	−0.666895	+	0.658339i
$696$	3.97284			0.150590
$697$	3.14533	+	3.14533i	0.119138	+	0.119138i
$698$	10.9304	+	10.9304i	0.413721	+	0.413721i
$699$			4.12247i			0.155926i
$700$	−6.80668	−	6.98478i	−0.257268	−	0.264000i
$701$		−	27.3257i		−	1.03208i	−0.856565	−	0.516039i	$-0.827406\pi$
$701$		−	27.3257i		−	1.03208i	0.856565	−	0.516039i	$-0.172594\pi$
$702$	0.711585	−	0.711585i	0.0268570	−	0.0268570i
$703$	−10.5758	−	10.5758i	−0.398872	−	0.398872i
$704$	0.0288739			0.00108823
$705$	15.3323	+	15.5316i	0.577449	+	0.584954i
$706$	0.0314099			0.00118213
$707$	20.9782	+	20.9782i	0.788966	+	0.788966i
$708$	4.05781	+	4.05781i	0.152502	+	0.152502i
$709$	−16.0144			−0.601435			−0.300717	−	0.953713i	$-0.597226\pi$
$709$	−16.0144			−0.601435			−0.300717	+	0.953713i	$0.597226\pi$
$710$	12.2484	+	0.0790822i	0.459675	+	0.00296790i
$711$		−	5.20235i		−	0.195103i
$712$	−7.43295	−	7.43295i	−0.278562	−	0.278562i
$713$	−15.9754	−	19.2067i	−0.598282	−	0.719297i
$714$		−	1.20998i		−	0.0452824i
$715$	−0.0649715		0.000419490i	−0.00242979		1.56880e-5i
$716$	−16.6646			−0.622785
$717$	5.87479	−	5.87479i	0.219398	−	0.219398i
$718$	23.0700	−	23.0700i	0.860964	−	0.860964i
$719$			19.1306i			0.713451i	0.934209	+	0.356726i	$0.116107\pi$
$719$			19.1306i			0.713451i	−0.934209	+	0.356726i	$0.883893\pi$
$720$	−1.59131	+	1.57090i	−0.0593048	+	0.0585439i
$721$	7.01110			0.261107
$722$	23.5333	−	23.5333i	0.875818	−	0.875818i
$723$	10.2622	−	10.2622i	0.381656	−	0.381656i
$724$	6.69613			0.248860
$725$	19.8625	+	0.256497i	0.737676	+	0.00952606i
$726$	−10.9992			−0.408217
$727$	19.9934	+	19.9934i	0.741513	+	0.741513i	0.972869	−	0.231356i	$-0.0743162\pi$
$727$	19.9934	+	19.9934i	0.741513	+	0.741513i	−0.231356	+	0.972869i	$0.574316\pi$
$728$	−1.38800	+	1.38800i	−0.0514425	+	0.0514425i
$729$		−	1.00000i		−	0.0370370i
$730$	2.01874	+	2.04498i	0.0747170	+	0.0756881i
$731$	5.11525			0.189194
$732$	3.60085	+	3.60085i	0.133091	+	0.133091i
$733$	24.0119	−	24.0119i	0.886899	−	0.886899i	−0.107325	−	0.994224i	$-0.534229\pi$
$733$	24.0119	−	24.0119i	0.886899	−	0.886899i	0.994224	+	0.107325i	$0.0342286\pi$
$734$	21.3678			0.788701
$735$	7.14470	+	0.0461300i	0.263536	+	0.00170153i
$736$	−4.77573	−	0.438634i	−0.176036	−	0.0161683i
$737$	−0.133965	+	0.133965i	−0.00493467	+	0.00493467i
$738$	−5.07048	−	5.07048i	−0.186647	−	0.186647i
$739$			34.2178i			1.25872i	0.777114	+	0.629360i	$0.216683\pi$
$739$			34.2178i			1.25872i	−0.777114	+	0.629360i	$0.783317\pi$
$740$	−4.62519	−	0.0298627i	−0.170026	−	0.00109777i
$741$			7.27635i			0.267304i
$742$	−5.34087	+	5.34087i	−0.196069	+	0.196069i
$743$	4.18125	−	4.18125i	0.153395	−	0.153395i	−0.626237	−	0.779633i	$-0.715406\pi$
$743$	4.18125	−	4.18125i	0.153395	−	0.153395i	0.779633	+	0.626237i	$0.215406\pi$
$744$		−	5.20915i		−	0.190977i
$745$	−20.4921	−	20.7584i	−0.750771	−	0.760529i
$746$			13.2696i			0.485836i
$747$	9.95414	+	9.95414i	0.364203	+	0.364203i
$748$	0.0126651	+	0.0126651i	0.000463081	+	0.000463081i
$749$			20.3658i			0.744150i
$750$	−8.05733	+	7.75109i	−0.294212	+	0.283030i
$751$		−	27.8901i		−	1.01772i	−0.860848	−	0.508861i	$-0.830067\pi$
$751$		−	27.8901i		−	1.01772i	0.860848	−	0.508861i	$-0.169933\pi$
$752$	−6.90153	+	6.90153i	−0.251673	+	0.251673i
$753$	−10.1726	+	10.1726i	−0.370712	+	0.370712i
$754$		−	3.99800i		−	0.145599i
$755$	−3.39452	−	3.43864i	−0.123539	−	0.125145i
$756$			1.95057i			0.0709416i
$757$	24.9495	+	24.9495i	0.906806	+	0.906806i	0.996013	−	0.0892070i	$-0.0284333\pi$
$757$	24.9495	+	24.9495i	0.906806	+	0.906806i	−0.0892070	+	0.996013i	$0.528433\pi$
$758$	10.1796	−	10.1796i	0.369741	−	0.369741i
$759$	−0.137894	−	0.0126651i	−0.00500523	−	0.000459713i
$760$	0.104387	−	16.1677i	0.00378652	−	0.586464i
$761$	13.0514			0.473115			0.236557	−	0.971618i	$-0.423981\pi$
$761$	13.0514			0.473115			0.236557	+	0.971618i	$0.423981\pi$
$762$	6.45653	−	6.45653i	0.233895	−	0.233895i
$763$	−1.69933	−	1.69933i	−0.0615199	−	0.0615199i
$764$	7.32933			0.265166
$765$	−1.38705	−	0.00895556i	−0.0501490	−	0.000323789i
$766$			8.78991i			0.317592i
$767$	4.08351	−	4.08351i	0.147447	−	0.147447i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−50.0583			−1.80515			−0.902574	−	0.430536i	$-0.858325\pi$
$769$	−50.0583			−1.80515			−0.902574	+	0.430536i	$0.858325\pi$
$770$	0.0896237	−	0.0884738i	0.00322981	−	0.00318837i
$771$	−5.40526			−0.194666
$772$	−5.03982	+	5.03982i	−0.181387	+	0.181387i
$773$	4.59947	−	4.59947i	0.165431	−	0.165431i	−0.619537	−	0.784968i	$-0.712679\pi$
$773$	4.59947	−	4.59947i	0.165431	−	0.165431i	0.784968	+	0.619537i	$0.212679\pi$
$774$	−8.24612			−0.296401
$775$	0.336316	−	26.0436i	0.0120808	−	0.935513i
$776$			1.20318i			0.0431918i
$777$	−2.85299	+	2.85299i	−0.102351	+	0.102351i
$778$	−16.7040	+	16.7040i	−0.598869	+	0.598869i
$779$	51.8485			1.85767
$780$	1.58085	+	1.60139i	0.0566033	+	0.0573390i
$781$			0.158164i			0.00565957i
$782$	−1.90240	−	2.28720i	−0.0680296	−	0.0817900i
$783$	−2.80922	−	2.80922i	−0.100393	−	0.100393i
$784$			3.19528i			0.114117i
$785$	−0.274859	+	42.5706i	−0.00981012	+	1.51941i
$786$	14.1312			0.504042
$787$	−34.0252	−	34.0252i	−1.21287	−	1.21287i	−0.970080	−	0.242787i	$-0.921938\pi$
$787$	−34.0252	−	34.0252i	−1.21287	−	1.21287i	−0.242787	−	0.970080i	$-0.578062\pi$
$788$	−6.17707	−	6.17707i	−0.220049	−	0.220049i
$789$	27.7565			0.988159
$790$	11.6326	+	0.0751060i	0.413868	+	0.00267215i
$791$	−29.2581			−1.04030
$792$	−0.0204169	−	0.0204169i	−0.000725484	−	0.000725484i
$793$	3.62365	−	3.62365i	0.128680	−	0.128680i
$794$			6.94477i			0.246461i
$795$	6.08293	+	6.16199i	0.215739	+	0.218543i
$796$			20.6272i			0.731111i
$797$	−1.37656	−	1.37656i	−0.0487602	−	0.0487602i	0.682306	−	0.731066i	$-0.260977\pi$
$797$	−1.37656	−	1.37656i	−0.0487602	−	0.0487602i	−0.731066	+	0.682306i	$0.760977\pi$
$798$	−9.97284	−	9.97284i	−0.353035	−	0.353035i
$799$	−6.05449			−0.214193
$800$	−3.48959	−	3.58089i	−0.123376	−	0.126604i
$801$			10.5118i			0.371415i
$802$	−10.2315	−	10.2315i	−0.361288	−	0.361288i
$803$	−0.0262375	+	0.0262375i	−0.000925903	+	0.000925903i
$804$	6.56147			0.231405
$805$	−16.1678	+	13.2720i	−0.569839	+	0.467777i
$806$	−5.24214			−0.184646
$807$	−1.37339	+	1.37339i	−0.0483456	+	0.0483456i
$808$	10.7549	+	10.7549i	0.378356	+	0.378356i
$809$			22.8770i			0.804313i	0.915571	+	0.402156i	$0.131739\pi$
$809$			22.8770i			0.804313i	−0.915571	+	0.402156i	$0.868261\pi$
$810$	2.23602	+	0.0144369i	0.0785658	+	0.000507262i
$811$	13.7863			0.484103			0.242052	−	0.970263i	$-0.422180\pi$
$811$	13.7863			0.484103			0.242052	+	0.970263i	$0.422180\pi$
$812$	5.47959	+	5.47959i	0.192296	+	0.192296i
$813$	−3.99917	−	3.99917i	−0.140257	−	0.140257i
$814$		−	0.0597254i		−	0.00209337i
$815$	−0.0117771	+	1.82406i	−0.000412534	+	0.0638941i
$816$		−	0.620322i		−	0.0217156i
$817$	42.1606	−	42.1606i	1.47501	−	1.47501i
$818$	−15.9466	−	15.9466i	−0.557558	−	0.557558i
$819$	1.96292			0.0685901
$820$	11.4109	−	11.2645i	0.398486	−	0.393373i
$821$	22.3491			0.779988			0.389994	−	0.920817i	$-0.372477\pi$
$821$	22.3491			0.779988			0.389994	+	0.920817i	$0.372477\pi$
$822$	−9.99147	−	9.99147i	−0.348493	−	0.348493i
$823$	26.7332	+	26.7332i	0.931861	+	0.931861i	0.997822	−	0.0659610i	$-0.0210113\pi$
$823$	26.7332	+	26.7332i	0.931861	+	0.931861i	−0.0659610	+	0.997822i	$0.521011\pi$
$824$	3.59438			0.125216
$825$	−0.100758	−	0.103394i	−0.00350794	−	0.00359973i
$826$			11.1936i			0.389474i
$827$	15.5121	+	15.5121i	0.539409	+	0.539409i	0.923355	−	0.383947i	$-0.125435\pi$
$827$	15.5121	+	15.5121i	0.539409	+	0.539409i	−0.383947	+	0.923355i	$0.625435\pi$
$828$	3.06679	+	3.68711i	0.106578	+	0.128136i
$829$			32.8637i			1.14140i	0.821157	+	0.570702i	$0.193329\pi$
$829$			32.8637i			1.14140i	−0.821157	+	0.570702i	$0.806671\pi$
$830$	−22.4014	+	22.1140i	−0.777563	+	0.767587i
$831$	8.53988			0.296245
$832$	−0.711585	+	0.711585i	−0.0246698	+	0.0246698i
$833$	−1.40156	+	1.40156i	−0.0485611	+	0.0485611i
$834$			11.0483i			0.382570i
$835$	−12.8400	−	0.0829016i	−0.444345	−	0.00286893i
$836$	0.208774			0.00722062
$837$	−3.68342	+	3.68342i	−0.127318	+	0.127318i
$838$	−21.2494	+	21.2494i	−0.734049	+	0.734049i
$839$	−1.16009			−0.0400506			−0.0200253	−	0.999799i	$-0.506375\pi$
$839$	−1.16009			−0.0400506			−0.0200253	+	0.999799i	$0.506375\pi$
$840$	−4.36152	−	0.0281603i	−0.150487	−	0.000971621i
$841$	13.2165			0.455743
$842$	15.2317	+	15.2317i	0.524919	+	0.524919i
$843$	13.4723	−	13.4723i	0.464010	−	0.464010i
$844$			25.2880i			0.870448i
$845$	−19.0756	+	18.8308i	−0.656219	+	0.647800i
$846$	9.76024			0.335564
$847$	−15.1707	−	15.1707i	−0.521272	−	0.521272i
$848$	−2.73811	+	2.73811i	−0.0940269	+	0.0940269i
$849$	−5.40276			−0.185422
$850$	0.0400496	−	3.10135i	0.00137369	−	0.106376i
$851$	−0.907312	+	9.87856i	−0.0311022	+	0.338633i
$852$	3.87337	−	3.87337i	0.132699	−	0.132699i
$853$	−23.7980	−	23.7980i	−0.814828	−	0.814828i	0.170525	−	0.985353i	$-0.445454\pi$
$853$	−23.7980	−	23.7980i	−0.814828	−	0.814828i	−0.985353	+	0.170525i	$0.945454\pi$
$854$			9.93302i			0.339901i
$855$	−11.5061	+	11.3585i	−0.393500	+	0.388452i
$856$			10.4409i			0.356864i
$857$	−5.14887	+	5.14887i	−0.175882	+	0.175882i	−0.789558	−	0.613676i	$-0.789690\pi$
$857$	−5.14887	+	5.14887i	−0.175882	+	0.175882i	0.613676	+	0.789558i	$0.289690\pi$
$858$	−0.0205462	+	0.0205462i	−0.000701436	+	0.000701436i
$859$			45.5119i			1.55285i	0.630212	+	0.776423i	$0.282968\pi$
$859$			45.5119i			1.55285i	−0.630212	+	0.776423i	$0.717032\pi$
$860$	0.119049	−	18.4385i	0.00405953	−	0.628748i
$861$		−	13.9870i		−	0.476677i
$862$	11.0324	+	11.0324i	0.375765	+	0.375765i
$863$	−17.4151	−	17.4151i	−0.592816	−	0.592816i	0.345575	−	0.938391i	$-0.387684\pi$
$863$	−17.4151	−	17.4151i	−0.592816	−	0.592816i	−0.938391	+	0.345575i	$0.887684\pi$
$864$			1.00000i			0.0340207i
$865$	0.247698	−	38.3640i	0.00842199	−	1.30441i
$866$			15.9762i			0.542893i
$867$	−11.7487	+	11.7487i	−0.399007	+	0.399007i
$868$	7.18478	−	7.18478i	0.243867	−	0.243867i
$869$			0.150212i			0.00509560i
$870$	6.32204	−	6.24092i	0.214337	−	0.211587i
$871$		−	6.60302i		−	0.223735i
$872$	−0.871197	−	0.871197i	−0.0295024	−	0.0295024i
$873$	0.850780	−	0.850780i	0.0287945	−	0.0287945i
$874$	−34.5312	−	3.17157i	−1.16804	−	0.107280i
$875$	−21.8039	−	0.422381i	−0.737108	−	0.0142791i
$876$	1.28509			0.0434191
$877$	3.53043	−	3.53043i	0.119214	−	0.119214i	−0.644983	−	0.764197i	$-0.723136\pi$
$877$	3.53043	−	3.53043i	0.119214	−	0.119214i	0.764197	+	0.644983i	$0.223136\pi$
$878$	−2.26510	−	2.26510i	−0.0764433	−	0.0764433i
$879$	−3.11750			−0.105151
$880$	0.0459474	−	0.0453579i	0.00154889	−	0.00152901i
$881$		−	47.1248i		−	1.58768i	−0.608130	−	0.793838i	$-0.708080\pi$
$881$		−	47.1248i		−	1.58768i	0.608130	−	0.793838i	$-0.291920\pi$
$882$	2.25940	−	2.25940i	0.0760780	−	0.0760780i
$883$	−4.17195	−	4.17195i	−0.140397	−	0.140397i	0.633415	−	0.773812i	$-0.281653\pi$
$883$	−4.17195	−	4.17195i	−0.140397	−	0.140397i	−0.773812	+	0.633415i	$0.781653\pi$
$884$	−0.624251			−0.0209958
$885$	12.8317	+	0.0828480i	0.431332	+	0.00278491i
$886$	−22.0740			−0.741590
$887$	−28.7906	+	28.7906i	−0.966694	+	0.966694i	−0.999463	−	0.0327690i	$-0.989567\pi$
$887$	−28.7906	+	28.7906i	−0.966694	+	0.966694i	0.0327690	+	0.999463i	$0.489567\pi$
$888$	−1.46265	+	1.46265i	−0.0490832	+	0.0490832i
$889$	17.8105			0.597345
$890$	−23.5046	−	0.151758i	−0.787874	−	0.00508694i
$891$			0.0288739i			0.000967311i
$892$	6.36523	−	6.36523i	0.213124	−	0.213124i
$893$	−49.9020	+	49.9020i	−1.66991	+	1.66991i
$894$	−13.0448			−0.436284
$895$	−26.5186	+	26.1784i	−0.886420	+	0.875047i
$896$		−	1.95057i		−	0.0651640i
$897$	3.71046	−	3.08621i	0.123889	−	0.103046i
$898$	7.92748	+	7.92748i	0.264543	+	0.264543i
$899$			20.6951i			0.690221i
$900$	−0.0645626	+	4.99958i	−0.00215209	+	0.166653i
$901$	−2.40205			−0.0800240
$902$	0.146404	+	0.146404i	0.00487473	+	0.00487473i
$903$	−11.3736	−	11.3736i	−0.378488	−	0.378488i
$904$	−14.9998			−0.498885
$905$	10.6556	−	10.5189i	0.354206	−	0.349661i
$906$	−2.16088			−0.0717904
$907$	−25.5309	−	25.5309i	−0.847738	−	0.847738i	0.142112	−	0.989851i	$-0.454611\pi$
$907$	−25.5309	−	25.5309i	−0.847738	−	0.847738i	−0.989851	+	0.142112i	$0.954611\pi$
$908$	12.2183	−	12.2183i	0.405478	−	0.405478i
$909$		−	15.2097i		−	0.504475i
$910$	−0.0283386	+	4.38914i	−0.000939415	+	0.145498i
$911$			60.0473i			1.98946i	0.102548	+	0.994728i	$0.467300\pi$
$911$			60.0473i			1.98946i	−0.102548	+	0.994728i	$0.532700\pi$
$912$	−5.11278	−	5.11278i	−0.169301	−	0.169301i
$913$	−0.287415	−	0.287415i	−0.00951204	−	0.00951204i
$914$	24.9769			0.826163
$915$	11.3866	+	0.0735182i	0.376431	+	0.00243044i
$916$		−	20.2222i		−	0.668162i
$917$	19.4906	+	19.4906i	0.643635	+	0.643635i
$918$	−0.438634	+	0.438634i	−0.0144771	+	0.0144771i
$919$	12.2350			0.403596			0.201798	−	0.979427i	$-0.435322\pi$
$919$	12.2350			0.403596			0.201798	+	0.979427i	$0.435322\pi$
$920$	−8.28874	+	6.80418i	−0.273272	+	0.224327i
$921$	19.1467			0.630907
$922$	13.6556	−	13.6556i	0.449722	−	0.449722i
$923$	−3.89790	−	3.89790i	−0.128301	−	0.128301i
$924$		−	0.0563205i		−	0.00185281i
$925$	−7.40705	+	7.21818i	−0.243542	+	0.237332i
$926$	17.8773			0.587484
$927$	−2.54161	−	2.54161i	−0.0834775	−	0.0834775i
$928$	2.80922	+	2.80922i	0.0922172	+	0.0922172i
$929$			48.6994i			1.59777i	0.601481	+	0.798887i	$0.294578\pi$
$929$			48.6994i			1.59777i	−0.601481	+	0.798887i	$0.705422\pi$
$930$	−8.18304	−	8.28939i	−0.268332	−	0.271820i
$931$			23.1037i			0.757192i
$932$	−2.91503	+	2.91503i	−0.0954849	+	0.0954849i
$933$	22.7659	+	22.7659i	0.745323	+	0.745323i
$934$	−38.6764			−1.26553
$935$	0.0400496		0.000258582i	0.00130976		8.45652e-6i
$936$	1.00633			0.0328930
$937$	−40.3568	−	40.3568i	−1.31840	−	1.31840i	−0.915042	−	0.403359i	$-0.867843\pi$
$937$	−40.3568	−	40.3568i	−1.31840	−	1.31840i	−0.403359	−	0.915042i	$-0.632157\pi$
$938$	9.04999	+	9.04999i	0.295493	+	0.295493i
$939$	−27.4976			−0.897351
$940$	−0.140908	+	21.8241i	−0.00459591	+	0.711823i
$941$			1.28193i			0.0417897i	0.999782	+	0.0208949i	$0.00665152\pi$
$941$			1.28193i			0.0417897i	−0.999782	+	0.0208949i	$0.993348\pi$
$942$	13.4623	+	13.4623i	0.438625	+	0.438625i
$943$	−21.9912	−	26.4393i	−0.716130	−	0.860983i
$944$			5.73861i			0.186776i
$945$	3.06415	+	3.10397i	0.0996767	+	0.100972i
$946$	0.238097			0.00774122
$947$	24.0315	−	24.0315i	0.780919	−	0.780919i	−0.199067	−	0.979986i	$-0.563791\pi$
$947$	24.0315	−	24.0315i	0.780919	−	0.780919i	0.979986	+	0.199067i	$0.0637912\pi$
$948$	3.67862	−	3.67862i	0.119476	−	0.119476i
$949$		−	1.29323i		−	0.0419799i
$950$	−25.2317	−	25.8919i	−0.818624	−	0.840043i
$951$	1.98209			0.0642736
$952$	0.855587	−	0.855587i	0.0277297	−	0.0277297i
$953$	1.28685	−	1.28685i	0.0416850	−	0.0416850i	−0.685957	−	0.727642i	$-0.740616\pi$
$953$	1.28685	−	1.28685i	0.0416850	−	0.0416850i	0.727642	+	0.685957i	$0.240616\pi$
$954$	3.87227			0.125369
$955$	11.6633	−	11.5136i	0.377414	−	0.372572i
$956$	8.30821			0.268707
$957$	0.0811132	+	0.0811132i	0.00262202	+	0.00262202i
$958$	−19.0598	+	19.0598i	−0.615796	+	0.615796i
$959$		−	27.5617i		−	0.890014i
$960$	−2.23602	−	0.0144369i	−0.0721673	−	0.000465950i
$961$	−3.86477			−0.124670
$962$	1.47191	+	1.47191i	0.0474562	+	0.0474562i
$963$	7.38286	−	7.38286i	0.237909	−	0.237909i
$964$	14.5130			0.467431
$965$	−0.102898	+	15.9370i	−0.00331239	+	0.513030i
$966$	−0.855587	+	9.31540i	−0.0275281	+	0.299718i
$967$	34.5037	−	34.5037i	1.10956	−	1.10956i	0.116356	−	0.993208i	$-0.462879\pi$
$967$	34.5037	−	34.5037i	1.10956	−	1.10956i	0.993208	−	0.116356i	$-0.0371214\pi$
$968$	−7.77759	−	7.77759i	−0.249981	−	0.249981i
$969$		−	4.48528i		−	0.144088i
$970$	1.89008	+	1.91464i	0.0606868	+	0.0614755i
$971$			14.6826i			0.471188i	0.971852	+	0.235594i	$0.0757035\pi$
$971$			14.6826i			0.471188i	−0.971852	+	0.235594i	$0.924297\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	−15.2385	+	15.2385i	−0.488522	+	0.488522i
$974$		−	40.6173i		−	1.30146i
$975$	5.03124	+	0.0649715i	0.161129	+	0.00208075i
$976$			5.09237i			0.163003i
$977$	−40.9702	−	40.9702i	−1.31075	−	1.31075i	−0.920859	−	0.389895i	$-0.872511\pi$
$977$	−40.9702	−	40.9702i	−1.31075	−	1.31075i	−0.389895	−	0.920859i	$-0.627489\pi$
$978$	0.576831	+	0.576831i	0.0184450	+	0.0184450i
$979$		−	0.303516i		−	0.00970041i
$980$	5.01945	+	5.08469i	0.160340	+	0.162424i
$981$			1.23206i			0.0393366i
$982$	1.87638	−	1.87638i	0.0598777	−	0.0598777i
$983$	−30.5500	+	30.5500i	−0.974393	+	0.974393i	−0.999680	−	0.0252874i	$-0.991950\pi$
$983$	−30.5500	+	30.5500i	−0.974393	+	0.974393i	0.0252874	+	0.999680i	$0.491950\pi$
$984$		−	7.17074i		−	0.228595i
$985$	−19.5332	−	0.126117i	−0.622380	−	0.00401841i
$986$			2.46444i			0.0784838i
$987$	13.4619	+	13.4619i	0.428498	+	0.428498i
$988$	−5.14516	+	5.14516i	−0.163689	+	0.163689i
$989$	−39.3812	−	3.61703i	−1.25225	−	0.115015i
$990$	−0.0645626		0.000416850i	−0.00205193		1.32484e-5i
$991$	−33.7746			−1.07289			−0.536443	−	0.843936i	$-0.680232\pi$
$991$	−33.7746			−1.07289			−0.536443	+	0.843936i	$0.680232\pi$
$992$	3.68342	−	3.68342i	0.116949	−	0.116949i
$993$	−21.1812	−	21.1812i	−0.672164	−	0.672164i
$994$	10.6848			0.338900
$995$	32.4032	+	32.8243i	1.02725	+	1.04060i
$996$			14.0773i			0.446056i
$997$	2.06252	−	2.06252i	0.0653208	−	0.0653208i	−0.673692	−	0.739012i	$-0.735292\pi$
$997$	2.06252	−	2.06252i	0.0653208	−	0.0653208i	0.739012	+	0.673692i	$0.235292\pi$
$998$	6.44546	+	6.44546i	0.204027	+	0.204027i
$999$	2.06849			0.0654442

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.j.a.643.8	yes	24
5.2	odd	4	inner	690.2.j.a.367.11	yes	24
23.22	odd	2	inner	690.2.j.a.643.11	yes	24
115.22	even	4	inner	690.2.j.a.367.8	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.j.a.367.8	✓	24	115.22	even	4	inner
690.2.j.a.367.11	yes	24	5.2	odd	4	inner
690.2.j.a.643.8	yes	24	1.1	even	1	trivial
690.2.j.a.643.11	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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-1.57090 - 1.59131i) q^{5} -1.00000 q^{6} +(-1.37926 - 1.37926i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-1.57090 - 1.59131i) q^{5} -1.00000 q^{6} +(-1.37926 - 1.37926i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(-2.23602 - 0.0144369i) q^{10} -0.0288739i q^{11} +(-0.707107 + 0.707107i) q^{12} +(0.711585 + 0.711585i) q^{13} -1.95057 q^{14} +(-0.0144369 + 2.23602i) q^{15} -1.00000 q^{16} +(-0.438634 - 0.438634i) q^{17} +(0.707107 + 0.707107i) q^{18} -7.23057 q^{19} +(-1.59131 + 1.57090i) q^{20} +1.95057i q^{21} +(-0.0204169 - 0.0204169i) q^{22} +(3.06679 + 3.68711i) q^{23} +1.00000i q^{24} +(-0.0645626 + 4.99958i) q^{25} +1.00633 q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.37926 + 1.37926i) q^{28} -3.97284i q^{29} +(1.57090 + 1.59131i) q^{30} -5.20915 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.0204169 + 0.0204169i) q^{33} -0.620322 q^{34} +(-0.0281603 + 4.36152i) q^{35} +1.00000 q^{36} +(1.46265 + 1.46265i) q^{37} +(-5.11278 + 5.11278i) q^{38} -1.00633i q^{39} +(-0.0144369 + 2.23602i) q^{40} -7.17074 q^{41} +(1.37926 + 1.37926i) q^{42} +(-5.83089 + 5.83089i) q^{43} -0.0288739 q^{44} +(1.59131 - 1.57090i) q^{45} +(4.77573 + 0.438634i) q^{46} +(6.90153 - 6.90153i) q^{47} +(0.707107 + 0.707107i) q^{48} -3.19528i q^{49} +(3.48959 + 3.58089i) q^{50} +0.620322i q^{51} +(0.711585 - 0.711585i) q^{52} +(2.73811 - 2.73811i) q^{53} -1.00000i q^{54} +(-0.0459474 + 0.0453579i) q^{55} +1.95057i q^{56} +(5.11278 + 5.11278i) q^{57} +(-2.80922 - 2.80922i) q^{58} -5.73861i q^{59} +(2.23602 + 0.0144369i) q^{60} -5.09237i q^{61} +(-3.68342 + 3.68342i) q^{62} +(1.37926 - 1.37926i) q^{63} +1.00000i q^{64} +(0.0145284 - 2.25018i) q^{65} +0.0288739i q^{66} +(-4.63966 - 4.63966i) q^{67} +(-0.438634 + 0.438634i) q^{68} +(0.438634 - 4.77573i) q^{69} +(3.06415 + 3.10397i) q^{70} -5.47777 q^{71} +(0.707107 - 0.707107i) q^{72} +(-0.908695 - 0.908695i) q^{73} +2.06849 q^{74} +(3.58089 - 3.48959i) q^{75} +7.23057i q^{76} +(-0.0398246 + 0.0398246i) q^{77} +(-0.711585 - 0.711585i) q^{78} -5.20235 q^{79} +(1.57090 + 1.59131i) q^{80} -1.00000 q^{81} +(-5.07048 + 5.07048i) q^{82} +(9.95414 - 9.95414i) q^{83} +1.95057 q^{84} +(-0.00895556 + 1.38705i) q^{85} +8.24612i q^{86} +(-2.80922 + 2.80922i) q^{87} +(-0.0204169 + 0.0204169i) q^{88} +10.5118 q^{89} +(0.0144369 - 2.23602i) q^{90} -1.96292i q^{91} +(3.68711 - 3.06679i) q^{92} +(3.68342 + 3.68342i) q^{93} -9.76024i q^{94} +(11.3585 + 11.5061i) q^{95} +1.00000 q^{96} +(-0.850780 - 0.850780i) q^{97} +(-2.25940 - 2.25940i) q^{98} +0.0288739 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{6}+O(q^{10}) \) 24 * q - 24 * q^6	\( 24 q - 24 q^{6} - 24 q^{16} - 8 q^{23} - 16 q^{25} - 16 q^{26} + 16 q^{31} - 16 q^{35} + 24 q^{36} - 8 q^{46} - 8 q^{47} + 24 q^{50} + 24 q^{55} + 16 q^{58} - 56 q^{62} - 32 q^{70} - 16 q^{71} - 48 q^{73} - 24 q^{81} + 24 q^{82} + 16 q^{87} - 8 q^{92} + 56 q^{93} + 24 q^{95} + 24 q^{96} - 32 q^{98}+O(q^{100}) \) 24 * q - 24 * q^6 - 24 * q^16 - 8 * q^23 - 16 * q^25 - 16 * q^26 + 16 * q^31 - 16 * q^35 + 24 * q^36 - 8 * q^46 - 8 * q^47 + 24 * q^50 + 24 * q^55 + 16 * q^58 - 56 * q^62 - 32 * q^70 - 16 * q^71 - 48 * q^73 - 24 * q^81 + 24 * q^82 + 16 * q^87 - 8 * q^92 + 56 * q^93 + 24 * q^95 + 24 * q^96 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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