LMFDB - Embedded newform 690.2.i.f.47.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(47,690)]

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([2, 1, 0]))

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

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

chi := DirichletCharacter("690.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.i (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:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.1
Character	$\chi$	$=$	690.47
Dual form			690.2.i.f.323.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.68613 - 0.396187i) q^{3} -1.00000i q^{4} +(2.10894 - 0.743206i) q^{5} +(1.47242 - 0.912127i) q^{6} +(-2.17056 - 2.17056i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.68607 + 1.33605i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.68613 - 0.396187i) q^{3} -1.00000i q^{4} +(2.10894 - 0.743206i) q^{5} +(1.47242 - 0.912127i) q^{6} +(-2.17056 - 2.17056i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.68607 + 1.33605i) q^{9} +(-0.965722 + 2.01677i) q^{10} +5.22806i q^{11} +(-0.396187 + 1.68613i) q^{12} +(2.60057 - 2.60057i) q^{13} +3.06963 q^{14} +(-3.85040 + 0.417606i) q^{15} -1.00000 q^{16} +(0.444150 - 0.444150i) q^{17} +(-2.84407 + 0.954611i) q^{18} -2.97966i q^{19} +(-0.743206 - 2.10894i) q^{20} +(2.79989 + 4.51979i) q^{21} +(-3.69679 - 3.69679i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(-0.912127 - 1.47242i) q^{24} +(3.89529 - 3.13476i) q^{25} +3.67776i q^{26} +(-3.99974 - 3.31694i) q^{27} +(-2.17056 + 2.17056i) q^{28} +1.70734 q^{29} +(2.42735 - 3.01794i) q^{30} -5.25582 q^{31} +(0.707107 - 0.707107i) q^{32} +(2.07129 - 8.81518i) q^{33} +0.628123i q^{34} +(-6.19075 - 2.96441i) q^{35} +(1.33605 - 2.68607i) q^{36} +(-2.75535 - 2.75535i) q^{37} +(2.10693 + 2.10693i) q^{38} +(-5.41521 + 3.35458i) q^{39} +(2.01677 + 0.965722i) q^{40} -6.96597i q^{41} +(-5.17579 - 1.21615i) q^{42} +(7.32093 - 7.32093i) q^{43} +5.22806 q^{44} +(6.65773 + 0.821342i) q^{45} +1.00000 q^{46} +(6.05572 - 6.05572i) q^{47} +(1.68613 + 0.396187i) q^{48} +2.42262i q^{49} +(-0.537774 + 4.97100i) q^{50} +(-0.924861 + 0.572928i) q^{51} +(-2.60057 - 2.60057i) q^{52} +(0.302305 + 0.302305i) q^{53} +(5.17367 - 0.482816i) q^{54} +(3.88553 + 11.0257i) q^{55} -3.06963i q^{56} +(-1.18050 + 5.02409i) q^{57} +(-1.20727 + 1.20727i) q^{58} +11.1739 q^{59} +(0.417606 + 3.85040i) q^{60} -1.40994 q^{61} +(3.71643 - 3.71643i) q^{62} +(-2.93030 - 8.73023i) q^{63} +1.00000i q^{64} +(3.55169 - 7.41721i) q^{65} +(4.76865 + 7.69790i) q^{66} +(3.64409 + 3.64409i) q^{67} +(-0.444150 - 0.444150i) q^{68} +(0.912127 + 1.47242i) q^{69} +(6.47368 - 2.28137i) q^{70} +4.61412i q^{71} +(0.954611 + 2.84407i) q^{72} +(0.698447 - 0.698447i) q^{73} +3.89665 q^{74} +(-7.80992 + 3.74235i) q^{75} -2.97966 q^{76} +(11.3478 - 11.3478i) q^{77} +(1.45708 - 6.20118i) q^{78} -11.7332i q^{79} +(-2.10894 + 0.743206i) q^{80} +(5.42996 + 7.17743i) q^{81} +(4.92569 + 4.92569i) q^{82} +(-9.38271 - 9.38271i) q^{83} +(4.51979 - 2.79989i) q^{84} +(0.606592 - 1.26678i) q^{85} +10.3534i q^{86} +(-2.87879 - 0.676425i) q^{87} +(-3.69679 + 3.69679i) q^{88} +3.53601 q^{89} +(-5.28850 + 4.12695i) q^{90} -11.2894 q^{91} +(-0.707107 + 0.707107i) q^{92} +(8.86201 + 2.08229i) q^{93} +8.56408i q^{94} +(-2.21450 - 6.28393i) q^{95} +(-1.47242 + 0.912127i) q^{96} +(-13.1840 - 13.1840i) q^{97} +(-1.71305 - 1.71305i) q^{98} +(-6.98493 + 14.0429i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7}+O(q^{10}) $ 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7	$ 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7} - 4 q^{12} - 12 q^{15} - 32 q^{16} + 8 q^{18} - 40 q^{22} + 32 q^{25} + 4 q^{27} + 8 q^{28} - 20 q^{30} + 8 q^{31} + 8 q^{33} + 20 q^{36} - 16 q^{37} + 8 q^{40} - 8 q^{42} - 80 q^{43} - 4 q^{45} + 32 q^{46} - 4 q^{48} + 36 q^{51} + 12 q^{57} - 16 q^{58} - 4 q^{60} + 8 q^{61} + 44 q^{63} + 52 q^{66} + 64 q^{67} + 64 q^{70} - 8 q^{72} - 56 q^{73} - 68 q^{75} - 8 q^{76} + 60 q^{78} - 44 q^{81} - 48 q^{85} - 60 q^{87} - 40 q^{88} - 64 q^{90} + 40 q^{91} + 92 q^{93} - 12 q^{96} - 40 q^{97}+O(q^{100}) $ 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7 - 4 * q^12 - 12 * q^15 - 32 * q^16 + 8 * q^18 - 40 * q^22 + 32 * q^25 + 4 * q^27 + 8 * q^28 - 20 * q^30 + 8 * q^31 + 8 * q^33 + 20 * q^36 - 16 * q^37 + 8 * q^40 - 8 * q^42 - 80 * q^43 - 4 * q^45 + 32 * q^46 - 4 * q^48 + 36 * q^51 + 12 * q^57 - 16 * q^58 - 4 * q^60 + 8 * q^61 + 44 * q^63 + 52 * q^66 + 64 * q^67 + 64 * q^70 - 8 * q^72 - 56 * q^73 - 68 * q^75 - 8 * q^76 + 60 * q^78 - 44 * q^81 - 48 * q^85 - 60 * q^87 - 40 * q^88 - 64 * q^90 + 40 * q^91 + 92 * q^93 - 12 * q^96 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−1.68613	−	0.396187i	−0.973488	−	0.228739i
$3$	−1.68613	−	0.396187i	−0.973488	−	0.228739i
$4$		−	1.00000i		−	0.500000i
$5$	2.10894	−	0.743206i	0.943148	−	0.332372i
$5$	2.10894	−	0.743206i	0.943148	−	0.332372i
$6$	1.47242	−	0.912127i	0.601113	−	0.372374i
$7$	−2.17056	−	2.17056i	−0.820393	−	0.820393i	0.165771	−	0.986164i	$-0.446989\pi$
$7$	−2.17056	−	2.17056i	−0.820393	−	0.820393i	−0.986164	+	0.165771i	$0.946989\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.68607	+	1.33605i	0.895357	+	0.445349i
$10$	−0.965722	+	2.01677i	−0.305388	+	0.637760i
$11$			5.22806i			1.57632i	0.615472	+	0.788159i	$0.288966\pi$
$11$			5.22806i			1.57632i	−0.615472	+	0.788159i	$0.711034\pi$
$12$	−0.396187	+	1.68613i	−0.114369	+	0.486744i
$13$	2.60057	−	2.60057i	0.721268	−	0.721268i	−0.247596	−	0.968863i	$-0.579641\pi$
$13$	2.60057	−	2.60057i	0.721268	−	0.721268i	0.968863	+	0.247596i	$0.0796405\pi$
$14$	3.06963			0.820393
$15$	−3.85040	+	0.417606i	−0.994170	+	0.107825i
$16$	−1.00000			−0.250000
$17$	0.444150	−	0.444150i	0.107722	−	0.107722i	−0.651191	−	0.758914i	$-0.725730\pi$
$17$	0.444150	−	0.444150i	0.107722	−	0.107722i	0.758914	+	0.651191i	$0.225730\pi$
$18$	−2.84407	+	0.954611i	−0.670353	+	0.225004i
$19$		−	2.97966i		−	0.683580i	−0.939776	−	0.341790i	$-0.888967\pi$
$19$		−	2.97966i		−	0.683580i	0.939776	−	0.341790i	$-0.111033\pi$
$20$	−0.743206	−	2.10894i	−0.166186	−	0.471574i
$21$	2.79989	+	4.51979i	0.610987	+	0.986298i
$22$	−3.69679	−	3.69679i	−0.788159	−	0.788159i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$23$	−0.707107	−	0.707107i	−0.147442	−	0.147442i
$24$	−0.912127	−	1.47242i	−0.186187	−	0.300557i
$25$	3.89529	−	3.13476i	0.779058	−	0.626952i
$26$			3.67776i			0.721268i
$27$	−3.99974	−	3.31694i	−0.769751	−	0.638345i
$28$	−2.17056	+	2.17056i	−0.410196	+	0.410196i
$29$	1.70734			0.317044			0.158522	−	0.987355i	$-0.449327\pi$
$29$	1.70734			0.317044			0.158522	+	0.987355i	$0.449327\pi$
$30$	2.42735	−	3.01794i	0.443172	−	0.550998i
$31$	−5.25582			−0.943974			−0.471987	−	0.881606i	$-0.656463\pi$
$31$	−5.25582			−0.943974			−0.471987	+	0.881606i	$0.656463\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	2.07129	−	8.81518i	0.360565	−	1.53453i
$34$			0.628123i			0.107722i
$35$	−6.19075	−	2.96441i	−1.04643	−	0.501077i
$36$	1.33605	−	2.68607i	0.222674	−	0.447679i
$37$	−2.75535	−	2.75535i	−0.452977	−	0.452977i	0.443365	−	0.896341i	$-0.353785\pi$
$37$	−2.75535	−	2.75535i	−0.452977	−	0.452977i	−0.896341	+	0.443365i	$0.853785\pi$
$38$	2.10693	+	2.10693i	0.341790	+	0.341790i
$39$	−5.41521	+	3.35458i	−0.867127	+	0.537163i
$40$	2.01677	+	0.965722i	0.318880	+	0.152694i
$41$		−	6.96597i		−	1.08790i	−0.839117	−	0.543951i	$-0.816928\pi$
$41$		−	6.96597i		−	1.08790i	0.839117	−	0.543951i	$-0.183072\pi$
$42$	−5.17579	−	1.21615i	−0.798642	−	0.187656i
$43$	7.32093	−	7.32093i	1.11643	−	1.11643i	0.124170	−	0.992261i	$-0.460373\pi$
$43$	7.32093	−	7.32093i	1.11643	−	1.11643i	0.992261	−	0.124170i	$-0.0396268\pi$
$44$	5.22806			0.788159
$45$	6.65773	+	0.821342i	0.992476	+	0.122438i
$46$	1.00000			0.147442
$47$	6.05572	−	6.05572i	0.883318	−	0.883318i	−0.110553	−	0.993870i	$-0.535262\pi$
$47$	6.05572	−	6.05572i	0.883318	−	0.883318i	0.993870	+	0.110553i	$0.0352621\pi$
$48$	1.68613	+	0.396187i	0.243372	+	0.0571847i
$49$			2.42262i			0.346089i
$50$	−0.537774	+	4.97100i	−0.0760527	+	0.703005i
$51$	−0.924861	+	0.572928i	−0.129506	+	0.0802260i
$52$	−2.60057	−	2.60057i	−0.360634	−	0.360634i
$53$	0.302305	+	0.302305i	0.0415247	+	0.0415247i	0.727564	−	0.686040i	$-0.240652\pi$
$53$	0.302305	+	0.302305i	0.0415247	+	0.0415247i	−0.686040	+	0.727564i	$0.740652\pi$
$54$	5.17367	−	0.482816i	0.704048	−	0.0657029i
$55$	3.88553	+	11.0257i	0.523924	+	1.48670i
$56$		−	3.06963i		−	0.410196i
$57$	−1.18050	+	5.02409i	−0.156361	+	0.665457i
$58$	−1.20727	+	1.20727i	−0.158522	+	0.158522i
$59$	11.1739			1.45472			0.727359	−	0.686257i	$-0.240747\pi$
$59$	11.1739			1.45472			0.727359	+	0.686257i	$0.240747\pi$
$60$	0.417606	+	3.85040i	0.0539127	+	0.497085i
$61$	−1.40994			−0.180525			−0.0902625	−	0.995918i	$-0.528771\pi$
$61$	−1.40994			−0.180525			−0.0902625	+	0.995918i	$0.528771\pi$
$62$	3.71643	−	3.71643i	0.471987	−	0.471987i
$63$	−2.93030	−	8.73023i	−0.369183	−	1.09991i
$64$			1.00000i			0.125000i
$65$	3.55169	−	7.41721i	0.440533	−	0.919991i
$66$	4.76865	+	7.69790i	0.586981	+	0.947546i
$67$	3.64409	+	3.64409i	0.445196	+	0.445196i	0.893754	−	0.448558i	$-0.148062\pi$
$67$	3.64409	+	3.64409i	0.445196	+	0.445196i	−0.448558	+	0.893754i	$0.648062\pi$
$68$	−0.444150	−	0.444150i	−0.0538611	−	0.0538611i
$69$	0.912127	+	1.47242i	0.109807	+	0.177259i
$70$	6.47368	−	2.28137i	0.773752	−	0.272676i
$71$			4.61412i			0.547596i	0.961787	+	0.273798i	$0.0882799\pi$
$71$			4.61412i			0.547596i	−0.961787	+	0.273798i	$0.911720\pi$
$72$	0.954611	+	2.84407i	0.112502	+	0.335177i
$73$	0.698447	−	0.698447i	0.0817471	−	0.0817471i	−0.665051	−	0.746798i	$-0.731590\pi$
$73$	0.698447	−	0.698447i	0.0817471	−	0.0817471i	0.746798	+	0.665051i	$0.231590\pi$
$74$	3.89665			0.452977
$75$	−7.80992	+	3.74235i	−0.901811	+	0.432130i
$76$	−2.97966			−0.341790
$77$	11.3478	−	11.3478i	1.29320	−	1.29320i
$78$	1.45708	−	6.20118i	0.164982	−	0.702145i
$79$		−	11.7332i		−	1.32009i	−0.751225	−	0.660046i	$-0.770537\pi$
$79$		−	11.7332i		−	1.32009i	0.751225	−	0.660046i	$-0.229463\pi$
$80$	−2.10894	+	0.743206i	−0.235787	+	0.0830930i
$81$	5.42996	+	7.17743i	0.603329	+	0.797493i
$82$	4.92569	+	4.92569i	0.543951	+	0.543951i
$83$	−9.38271	−	9.38271i	−1.02989	−	1.02989i	−0.999539	−	0.0303467i	$-0.990339\pi$
$83$	−9.38271	−	9.38271i	−1.02989	−	1.02989i	−0.0303467	−	0.999539i	$-0.509661\pi$
$84$	4.51979	−	2.79989i	0.493149	−	0.305493i
$85$	0.606592	−	1.26678i	0.0657942	−	0.137402i
$86$			10.3534i			1.11643i
$87$	−2.87879	−	0.676425i	−0.308639	−	0.0725204i
$88$	−3.69679	+	3.69679i	−0.394080	+	0.394080i
$89$	3.53601			0.374816			0.187408	−	0.982282i	$-0.439991\pi$
$89$	3.53601			0.374816			0.187408	+	0.982282i	$0.439991\pi$
$90$	−5.28850	+	4.12695i	−0.557457	+	0.435019i
$91$	−11.2894			−1.18345
$92$	−0.707107	+	0.707107i	−0.0737210	+	0.0737210i
$93$	8.86201	+	2.08229i	0.918947	+	0.215924i
$94$			8.56408i			0.883318i
$95$	−2.21450	−	6.28393i	−0.227203	−	0.644717i
$96$	−1.47242	+	0.912127i	−0.150278	+	0.0930936i
$97$	−13.1840	−	13.1840i	−1.33863	−	1.33863i	−0.897391	−	0.441237i	$-0.854540\pi$
$97$	−13.1840	−	13.1840i	−1.33863	−	1.33863i	−0.441237	−	0.897391i	$-0.645460\pi$
$98$	−1.71305	−	1.71305i	−0.173044	−	0.173044i
$99$	−6.98493	+	14.0429i	−0.702012	+	1.41137i
$100$	−3.13476	−	3.89529i	−0.313476	−	0.389529i
$101$		−	10.8801i		−	1.08261i	−0.840825	−	0.541306i	$-0.817930\pi$
$101$		−	10.8801i		−	1.08261i	0.840825	−	0.541306i	$-0.182070\pi$
$102$	0.248854	−	1.05910i	0.0246402	−	0.104866i
$103$	−2.54969	+	2.54969i	−0.251228	+	0.251228i	−0.821474	−	0.570246i	$-0.806848\pi$
$103$	−2.54969	+	2.54969i	−0.251228	+	0.251228i	0.570246	+	0.821474i	$0.306848\pi$
$104$	3.67776			0.360634
$105$	9.26395	+	7.45108i	0.904069	+	0.727151i
$106$	−0.427523			−0.0415247
$107$	−9.52639	+	9.52639i	−0.920950	+	0.920950i	−0.997097	−	0.0761462i	$-0.975738\pi$
$107$	−9.52639	+	9.52639i	−0.920950	+	0.920950i	0.0761462	+	0.997097i	$0.475738\pi$
$108$	−3.31694	+	3.99974i	−0.319172	+	0.384875i
$109$			8.20451i			0.785849i	0.919571	+	0.392925i	$0.128537\pi$
$109$			8.20451i			0.785849i	−0.919571	+	0.392925i	$0.871463\pi$
$110$	−10.5438	−	5.04885i	−1.00531	−	0.481389i
$111$	3.55425	+	5.73752i	0.337354	+	0.544581i
$112$	2.17056	+	2.17056i	0.205098	+	0.205098i
$113$	−0.453030	−	0.453030i	−0.0426174	−	0.0426174i	0.685477	−	0.728094i	$-0.259594\pi$
$113$	−0.453030	−	0.453030i	−0.0426174	−	0.0426174i	−0.728094	+	0.685477i	$0.759594\pi$
$114$	−2.71783	−	4.38731i	−0.254548	−	0.410909i
$115$	−2.01677	−	0.965722i	−0.188065	−	0.0900541i
$116$		−	1.70734i		−	0.158522i
$117$	10.4598	−	3.51083i	0.967008	−	0.324576i
$118$	−7.90115	+	7.90115i	−0.727359	+	0.727359i
$119$	−1.92810			−0.176749
$120$	−3.01794	−	2.42735i	−0.275499	−	0.221586i
$121$	−16.3326			−1.48478
$122$	0.996981	−	0.996981i	0.0902625	−	0.0902625i
$123$	−2.75983	+	11.7455i	−0.248845	+	1.05906i
$124$			5.25582i			0.471987i
$125$	5.88517	−	9.50604i	0.526386	−	0.850246i
$126$	8.24524	+	4.10117i	0.734545	+	0.365361i
$127$	13.0705	+	13.0705i	1.15982	+	1.15982i	0.984514	+	0.175307i	$0.0560919\pi$
$127$	13.0705	+	13.0705i	1.15982	+	1.15982i	0.175307	+	0.984514i	$0.443908\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−15.2445	+	9.44358i	−1.34220	+	0.831461i
$130$	2.73333	+	7.75618i	0.239729	+	0.680262i
$131$			3.19088i			0.278788i	0.990237	+	0.139394i	$0.0445155\pi$
$131$			3.19088i			0.278788i	−0.990237	+	0.139394i	$0.955484\pi$
$132$	−8.81518	−	2.07129i	−0.767263	−	0.180283i
$133$	−6.46751	+	6.46751i	−0.560804	+	0.560804i
$134$	−5.15352			−0.445196
$135$	−10.9004	−	4.02260i	−0.938157	−	0.346210i
$136$	0.628123			0.0538611
$137$	−12.8044	+	12.8044i	−1.09396	+	1.09396i	−0.0988556	+	0.995102i	$0.531518\pi$
$137$	−12.8044	+	12.8044i	−1.09396	+	1.09396i	−0.995102	+	0.0988556i	$0.968482\pi$
$138$	−1.68613	−	0.396187i	−0.143533	−	0.0337257i
$139$		−	11.9592i		−	1.01437i	−0.861839	−	0.507183i	$-0.830687\pi$
$139$		−	11.9592i		−	1.01437i	0.861839	−	0.507183i	$-0.169313\pi$
$140$	−2.96441	+	6.19075i	−0.250538	+	0.523214i
$141$	−12.6099	+	7.81153i	−1.06195	+	0.657850i
$142$	−3.26268	−	3.26268i	−0.273798	−	0.273798i
$143$	13.5959	+	13.5959i	1.13695	+	1.13695i
$144$	−2.68607	−	1.33605i	−0.223839	−	0.111337i
$145$	3.60068	−	1.26890i	0.299020	−	0.105377i
$146$			0.987754i			0.0817471i
$147$	0.959812	−	4.08486i	0.0791640	−	0.336913i
$148$	−2.75535	+	2.75535i	−0.226488	+	0.226488i
$149$	17.1561			1.40548			0.702740	−	0.711447i	$-0.251960\pi$
$149$	17.1561			1.40548			0.702740	+	0.711447i	$0.251960\pi$
$150$	2.87620	−	8.16869i	0.234841	−	0.666971i
$151$	16.9726			1.38121			0.690603	−	0.723234i	$-0.257345\pi$
$151$	16.9726			1.38121			0.690603	+	0.723234i	$0.257345\pi$
$152$	2.10693	−	2.10693i	0.170895	−	0.170895i
$153$	1.78642	−	0.599613i	0.144424	−	0.0484759i
$154$			16.0482i			1.29320i
$155$	−11.0842	+	3.90616i	−0.890308	+	0.313751i
$156$	3.35458	+	5.41521i	0.268582	+	0.433564i
$157$	11.7841	+	11.7841i	0.940473	+	0.940473i	0.998325	−	0.0578517i	$-0.0184251\pi$
$157$	11.7841	+	11.7841i	0.940473	+	0.940473i	−0.0578517	+	0.998325i	$0.518425\pi$
$158$	8.29665	+	8.29665i	0.660046	+	0.660046i
$159$	−0.389956	−	0.629494i	−0.0309255	−	0.0499221i
$160$	0.965722	−	2.01677i	0.0763470	−	0.159440i
$161$			3.06963i			0.241921i
$162$	−8.91477	−	1.23565i	−0.700411	−	0.0970821i
$163$	3.78878	−	3.78878i	0.296760	−	0.296760i	−0.542983	−	0.839743i	$-0.682705\pi$
$163$	3.78878	−	3.78878i	0.296760	−	0.296760i	0.839743	+	0.542983i	$0.182705\pi$
$164$	−6.96597			−0.543951
$165$	−2.18327	−	20.1301i	−0.169967	−	1.56713i
$166$	13.2692			1.02989
$167$	−11.5545	+	11.5545i	−0.894117	+	0.894117i	−0.994908	−	0.100791i	$-0.967863\pi$
$167$	−11.5545	+	11.5545i	−0.894117	+	0.894117i	0.100791	+	0.994908i	$0.467863\pi$
$168$	−1.21615	+	5.17579i	−0.0938279	+	0.399321i
$169$		−	0.525898i		−	0.0404537i
$170$	0.466825	+	1.32468i	0.0358038	+	0.101598i
$171$	3.98096	−	8.00357i	0.304432	−	0.612048i
$172$	−7.32093	−	7.32093i	−0.558215	−	0.558215i
$173$	−6.59928	−	6.59928i	−0.501734	−	0.501734i	0.410242	−	0.911977i	$-0.365444\pi$
$173$	−6.59928	−	6.59928i	−0.501734	−	0.501734i	−0.911977	+	0.410242i	$0.865444\pi$
$174$	2.51392	−	1.55731i	0.190580	−	0.118059i
$175$	−15.2591	−	1.65077i	−1.15348	−	0.124786i
$176$		−	5.22806i		−	0.394080i
$177$	−18.8407	−	4.42696i	−1.41615	−	0.332751i
$178$	−2.50034	+	2.50034i	−0.187408	+	0.187408i
$179$	−18.4232			−1.37702			−0.688508	−	0.725229i	$-0.741734\pi$
$179$	−18.4232			−1.37702			−0.688508	+	0.725229i	$0.741734\pi$
$180$	0.821342	−	6.65773i	0.0612192	−	0.496238i
$181$	4.84965			0.360472			0.180236	−	0.983623i	$-0.442314\pi$
$181$	4.84965			0.360472			0.180236	+	0.983623i	$0.442314\pi$
$182$	7.98278	−	7.98278i	0.591723	−	0.591723i
$183$	2.37735	+	0.558602i	0.175739	+	0.0412931i
$184$		−	1.00000i		−	0.0737210i
$185$	−7.85867	−	3.76309i	−0.577781	−	0.276668i
$186$	−7.73879	+	4.79398i	−0.567435	+	0.351512i
$187$	2.32204	+	2.32204i	0.169804	+	0.169804i
$188$	−6.05572	−	6.05572i	−0.441659	−	0.441659i
$189$	1.48207	+	15.8813i	0.107804	+	1.15519i
$190$	6.00929	+	2.87752i	0.435960	+	0.208757i
$191$		−	3.19418i		−	0.231123i	−0.993300	−	0.115561i	$-0.963133\pi$
$191$		−	3.19418i		−	0.231123i	0.993300	−	0.115561i	$-0.0368667\pi$
$192$	0.396187	−	1.68613i	0.0285924	−	0.121686i
$193$	−1.55053	+	1.55053i	−0.111610	+	0.111610i	−0.760706	−	0.649096i	$-0.775147\pi$
$193$	−1.55053	+	1.55053i	−0.111610	+	0.111610i	0.649096	+	0.760706i	$0.275147\pi$
$194$	18.6449			1.33863
$195$	−8.92722	+	11.0992i	−0.639291	+	0.794833i
$196$	2.42262			0.173044
$197$	−16.0842	+	16.0842i	−1.14595	+	1.14595i	−0.158614	+	0.987341i	$0.550702\pi$
$197$	−16.0842	+	16.0842i	−1.14595	+	1.14595i	−0.987341	+	0.158614i	$0.949298\pi$
$198$	−4.99076	−	14.8689i	−0.354678	−	1.05669i
$199$		−	8.97499i		−	0.636220i	−0.948054	−	0.318110i	$-0.896952\pi$
$199$		−	8.97499i		−	0.636220i	0.948054	−	0.318110i	$-0.103048\pi$
$200$	4.97100	+	0.537774i	0.351502	+	0.0380263i
$201$	−4.70067	−	7.58815i	−0.331559	−	0.535227i
$202$	7.69341	+	7.69341i	0.541306	+	0.541306i
$203$	−3.70587	−	3.70587i	−0.260101	−	0.260101i
$204$	0.572928	+	0.924861i	0.0401130	+	0.0647532i
$205$	−5.17715	−	14.6908i	−0.361588	−	1.02605i
$206$		−	3.60580i		−	0.251228i
$207$	−0.954611	−	2.84407i	−0.0663501	−	0.197676i
$208$	−2.60057	+	2.60057i	−0.180317	+	0.180317i
$209$	15.5778			1.07754
$210$	−11.8193	+	1.28190i	−0.815610	+	0.0884592i
$211$	−0.301249			−0.0207388			−0.0103694	−	0.999946i	$-0.503301\pi$
$211$	−0.301249			−0.0207388			−0.0103694	+	0.999946i	$0.503301\pi$
$212$	0.302305	−	0.302305i	0.0207624	−	0.0207624i
$213$	1.82806	−	7.78001i	0.125256	−	0.533078i
$214$		−	13.4723i		−	0.920950i
$215$	9.99846	−	20.8804i	0.681890	−	1.42403i
$216$	−0.482816	−	5.17367i	−0.0328515	−	0.352024i
$217$	11.4081	+	11.4081i	0.774430	+	0.774430i
$218$	−5.80146	−	5.80146i	−0.392925	−	0.392925i
$219$	−1.45439	+	0.900957i	−0.0982785	+	0.0608810i
$220$	11.0257	−	3.88553i	0.743351	−	0.261962i
$221$		−	2.31008i		−	0.155393i
$222$	−6.57027	−	1.54381i	−0.440967	−	0.103613i
$223$	12.8348	−	12.8348i	0.859480	−	0.859480i	−0.131797	−	0.991277i	$-0.542075\pi$
$223$	12.8348	−	12.8348i	0.859480	−	0.859480i	0.991277	+	0.131797i	$0.0420745\pi$
$224$	−3.06963			−0.205098
$225$	14.6512	−	3.21590i	0.976747	−	0.214394i
$226$	0.640680			0.0426174
$227$	−9.96258	+	9.96258i	−0.661239	+	0.661239i	−0.955672	−	0.294433i	$-0.904869\pi$
$227$	−9.96258	+	9.96258i	−0.661239	+	0.661239i	0.294433	+	0.955672i	$0.404869\pi$
$228$	5.02409	+	1.18050i	0.332728	+	0.0781806i
$229$			17.6169i			1.16416i	0.813133	+	0.582079i	$0.197760\pi$
$229$			17.6169i			1.16416i	−0.813133	+	0.582079i	$0.802240\pi$
$230$	2.10894	−	0.743206i	0.139060	−	0.0490056i
$231$	−23.6297	+	14.6380i	−1.55472	+	0.963110i
$232$	1.20727	+	1.20727i	0.0792611	+	0.0792611i
$233$	1.50132	+	1.50132i	0.0983549	+	0.0983549i	0.754572	−	0.656217i	$-0.227844\pi$
$233$	1.50132	+	1.50132i	0.0983549	+	0.0983549i	−0.656217	+	0.754572i	$0.727844\pi$
$234$	−4.91366	+	9.87872i	−0.321216	+	0.645792i
$235$	8.27052	−	17.2718i	0.539509	−	1.12669i
$236$		−	11.1739i		−	0.727359i
$237$	−4.64856	+	19.7838i	−0.301956	+	1.28509i
$238$	1.36338	−	1.36338i	0.0883745	−	0.0883745i
$239$	24.3097			1.57246			0.786232	−	0.617932i	$-0.212029\pi$
$239$	24.3097			1.57246			0.786232	+	0.617932i	$0.212029\pi$
$240$	3.85040	−	0.417606i	0.248542	−	0.0269564i
$241$	23.8969			1.53933			0.769667	−	0.638445i	$-0.220422\pi$
$241$	23.8969			1.53933			0.769667	+	0.638445i	$0.220422\pi$
$242$	11.5489	−	11.5489i	0.742390	−	0.742390i
$243$	−6.31201	−	14.2534i	−0.404915	−	0.914354i
$244$			1.40994i			0.0902625i
$245$	1.80051	+	5.10918i	0.115030	+	0.326413i
$246$	−6.35385	−	10.2568i	−0.405107	−	0.653952i
$247$	−7.74879	−	7.74879i	−0.493044	−	0.493044i
$248$	−3.71643	−	3.71643i	−0.235993	−	0.235993i
$249$	12.1032	+	19.5378i	0.767007	+	1.23816i
$250$	2.56034	+	10.8832i	0.161930	+	0.688316i
$251$		−	22.5045i		−	1.42047i	−0.703965	−	0.710234i	$-0.748589\pi$
$251$		−	22.5045i		−	1.42047i	0.703965	−	0.710234i	$-0.251411\pi$
$252$	−8.73023	+	2.93030i	−0.549953	+	0.184592i
$253$	3.69679	−	3.69679i	0.232415	−	0.232415i
$254$	−18.4845			−1.15982
$255$	−1.52468	+	1.89564i	−0.0954789	+	0.118709i
$256$	1.00000			0.0625000
$257$	−17.0064	+	17.0064i	−1.06083	+	1.06083i	−0.0628062	+	0.998026i	$0.520005\pi$
$257$	−17.0064	+	17.0064i	−1.06083	+	1.06083i	−0.998026	+	0.0628062i	$0.979995\pi$
$258$	4.10187	−	17.4571i	0.255371	−	1.08683i
$259$			11.9613i			0.743238i
$260$	−7.41721	−	3.55169i	−0.459996	−	0.220267i
$261$	4.58603	+	2.28108i	0.283868	+	0.141195i
$262$	−2.25629	−	2.25629i	−0.139394	−	0.139394i
$263$	17.9233	+	17.9233i	1.10520	+	1.10520i	0.993773	+	0.111428i	$0.0355425\pi$
$263$	17.9233	+	17.9233i	1.10520	+	1.10520i	0.111428	+	0.993773i	$0.464458\pi$
$264$	7.69790	−	4.76865i	0.473773	−	0.293490i
$265$	0.862218	+	0.412869i	0.0529656	+	0.0253623i
$266$		−	9.14644i		−	0.560804i
$267$	−5.96217	−	1.40092i	−0.364879	−	0.0857350i
$268$	3.64409	−	3.64409i	0.222598	−	0.222598i
$269$	17.9945			1.09714			0.548571	−	0.836104i	$-0.315172\pi$
$269$	17.9945			1.09714			0.548571	+	0.836104i	$0.315172\pi$
$270$	10.5522	−	4.86334i	0.642184	−	0.295973i
$271$	−14.0280			−0.852139			−0.426070	−	0.904690i	$-0.640102\pi$
$271$	−14.0280			−0.852139			−0.426070	+	0.904690i	$0.640102\pi$
$272$	−0.444150	+	0.444150i	−0.0269305	+	0.0269305i
$273$	19.0353	+	4.47270i	1.15207	+	0.270700i
$274$		−	18.1082i		−	1.09396i
$275$	16.3887	+	20.3648i	0.988276	+	1.22804i
$276$	1.47242	−	0.912127i	0.0886293	−	0.0549036i
$277$	−0.994150	−	0.994150i	−0.0597327	−	0.0597327i	0.676609	−	0.736342i	$-0.263449\pi$
$277$	−0.994150	−	0.994150i	−0.0597327	−	0.0597327i	−0.736342	+	0.676609i	$0.763449\pi$
$278$	8.45642	+	8.45642i	0.507183	+	0.507183i
$279$	−14.1175	−	7.02203i	−0.845194	−	0.420398i
$280$	−2.28137	−	6.47368i	−0.136338	−	0.386876i
$281$			15.9968i			0.954291i	0.878824	+	0.477145i	$0.158328\pi$
$281$			15.9968i			0.954291i	−0.878824	+	0.477145i	$0.841672\pi$
$282$	3.39298	−	14.4402i	0.202049	−	0.859899i
$283$	21.3172	−	21.3172i	1.26718	−	1.26718i	0.319636	−	0.947540i	$-0.396439\pi$
$283$	21.3172	−	21.3172i	1.26718	−	1.26718i	0.947540	−	0.319636i	$-0.103561\pi$
$284$	4.61412			0.273798
$285$	1.24432	+	11.4729i	0.0737073	+	0.679594i
$286$	−19.2275			−1.13695
$287$	−15.1200	+	15.1200i	−0.892507	+	0.892507i
$288$	2.84407	−	0.954611i	0.167588	−	0.0562510i
$289$			16.6055i			0.976792i
$290$	−1.64881	+	3.44331i	−0.0968216	+	0.202198i
$291$	17.0065	+	27.4532i	0.996941	+	1.60933i
$292$	−0.698447	−	0.698447i	−0.0408735	−	0.0408735i
$293$	−4.08472	−	4.08472i	−0.238632	−	0.238632i	0.577651	−	0.816284i	$-0.303969\pi$
$293$	−4.08472	−	4.08472i	−0.238632	−	0.238632i	−0.816284	+	0.577651i	$0.803969\pi$
$294$	2.20974	+	3.56712i	0.128875	+	0.208039i
$295$	23.5651	−	8.30452i	1.37202	−	0.483508i
$296$		−	3.89665i		−	0.226488i
$297$	17.3411	−	20.9109i	1.00623	−	1.21337i
$298$	−12.1312	+	12.1312i	−0.702740	+	0.702740i
$299$	−3.67776			−0.212690
$300$	3.74235	+	7.80992i	0.216065	+	0.450906i
$301$	−31.7810			−1.83182
$302$	−12.0014	+	12.0014i	−0.690603	+	0.690603i
$303$	−4.31057	+	18.3453i	−0.247636	+	1.05391i
$304$			2.97966i			0.170895i
$305$	−2.97349	+	1.04788i	−0.170262	+	0.0600014i
$306$	−0.839202	+	1.68718i	−0.0479740	+	0.0964498i
$307$	15.3903	+	15.3903i	0.878369	+	0.878369i	0.993366	−	0.114997i	$-0.0366858\pi$
$307$	15.3903	+	15.3903i	0.878369	+	0.878369i	−0.114997	+	0.993366i	$0.536686\pi$
$308$	−11.3478	−	11.3478i	−0.646600	−	0.646600i
$309$	5.30926	−	3.28895i	0.302033	−	0.187102i
$310$	5.07567	−	10.5998i	0.288278	−	0.602029i
$311$			19.9984i			1.13401i	0.823715	+	0.567004i	$0.191898\pi$
$311$			19.9984i			1.13401i	−0.823715	+	0.567004i	$0.808102\pi$
$312$	−6.20118	−	1.45708i	−0.351073	−	0.0824910i
$313$	−21.4652	+	21.4652i	−1.21329	+	1.21329i	−0.243348	+	0.969939i	$0.578246\pi$
$313$	−21.4652	+	21.4652i	−1.21329	+	1.21329i	−0.969939	+	0.243348i	$0.921754\pi$
$314$	−16.6652			−0.940473
$315$	−12.6682	−	16.2337i	−0.713773	−	0.914668i
$316$	−11.7332			−0.660046
$317$	17.0015	−	17.0015i	0.954897	−	0.954897i	−0.0441291	−	0.999026i	$-0.514051\pi$
$317$	17.0015	−	17.0015i	0.954897	−	0.954897i	0.999026	+	0.0441291i	$0.0140513\pi$
$318$	0.720860	+	0.169379i	0.0404238	+	0.00949832i
$319$			8.92605i			0.499763i
$320$	0.743206	+	2.10894i	0.0415465	+	0.117894i
$321$	19.8370	−	12.2885i	1.10719	−	0.685877i
$322$	−2.17056	−	2.17056i	−0.120960	−	0.120960i
$323$	−1.32341	−	1.32341i	−0.0736367	−	0.0736367i
$324$	7.17743	−	5.42996i	0.398746	−	0.301664i
$325$	1.97780	−	18.2821i	0.109709	−	1.01411i
$326$			5.35815i			0.296760i
$327$	3.25052	−	13.8339i	0.179754	−	0.765015i
$328$	4.92569	−	4.92569i	0.271975	−	0.271975i
$329$	−26.2886			−1.44933
$330$	15.7780	+	12.6903i	0.868548	+	0.698580i
$331$	−33.1267			−1.82081			−0.910404	−	0.413720i	$-0.864229\pi$
$331$	−33.1267			−1.82081			−0.910404	+	0.413720i	$0.864229\pi$
$332$	−9.38271	+	9.38271i	−0.514943	+	0.514943i
$333$	−3.71979	−	11.0823i	−0.203843	−	0.607309i
$334$		−	16.3406i		−	0.894117i
$335$	10.3935	+	4.97687i	0.567857	+	0.271915i
$336$	−2.79989	−	4.51979i	−0.152747	−	0.246575i
$337$	−0.517894	−	0.517894i	−0.0282115	−	0.0282115i	0.692860	−	0.721072i	$-0.256350\pi$
$337$	−0.517894	−	0.517894i	−0.0282115	−	0.0282115i	−0.721072	+	0.692860i	$0.756350\pi$
$338$	0.371866	+	0.371866i	0.0202269	+	0.0202269i
$339$	0.584382	+	0.943351i	0.0317393	+	0.0512358i
$340$	−1.26678	−	0.606592i	−0.0687009	−	0.0328971i
$341$		−	27.4777i		−	1.48800i
$342$	2.84441	+	8.47434i	0.153808	+	0.458240i
$343$	−9.93545	+	9.93545i	−0.536464	+	0.536464i
$344$	10.3534			0.558215
$345$	3.01794	+	2.42735i	0.162480	+	0.130684i
$346$	9.33280			0.501734
$347$	15.1025	−	15.1025i	0.810743	−	0.810743i	−0.174003	−	0.984745i	$-0.555670\pi$
$347$	15.1025	−	15.1025i	0.810743	−	0.810743i	0.984745	+	0.174003i	$0.0556701\pi$
$348$	−0.676425	+	2.87879i	−0.0362602	+	0.154319i
$349$			1.81851i			0.0973424i	0.998815	+	0.0486712i	$0.0154986\pi$
$349$			1.81851i			0.0973424i	−0.998815	+	0.0486712i	$0.984501\pi$
$350$	11.9571	−	9.62255i	0.639133	−	0.514347i
$351$	−19.0275	+	1.77568i	−1.01561	+	0.0947788i
$352$	3.69679	+	3.69679i	0.197040	+	0.197040i
$353$	16.7727	+	16.7727i	0.892723	+	0.892723i	0.994779	−	0.102056i	$-0.0325420\pi$
$353$	16.7727	+	16.7727i	0.892723	+	0.892723i	−0.102056	+	0.994779i	$0.532542\pi$
$354$	16.4527	−	10.1920i	0.874451	−	0.541700i
$355$	3.42925	+	9.73092i	0.182005	+	0.516464i
$356$		−	3.53601i		−	0.187408i
$357$	3.25103	+	0.763890i	0.172063	+	0.0404294i
$358$	13.0272	−	13.0272i	0.688508	−	0.688508i
$359$	3.97799			0.209950			0.104975	−	0.994475i	$-0.466524\pi$
$359$	3.97799			0.209950			0.104975	+	0.994475i	$0.466524\pi$
$360$	4.12695	+	5.28850i	0.217509	+	0.278729i
$361$	10.1217			0.532719
$362$	−3.42922	+	3.42922i	−0.180236	+	0.180236i
$363$	27.5388	+	6.47076i	1.44541	+	0.339627i
$364$			11.2894i			0.591723i
$365$	0.953896	−	1.99208i	0.0499292	−	0.104270i
$366$	−2.07603	+	1.28605i	−0.108516	+	0.0672229i
$367$	−14.9574	−	14.9574i	−0.780770	−	0.780770i	0.199191	−	0.979961i	$-0.436169\pi$
$367$	−14.9574	−	14.9574i	−0.780770	−	0.780770i	−0.979961	+	0.199191i	$0.936169\pi$
$368$	0.707107	+	0.707107i	0.0368605	+	0.0368605i
$369$	9.30686	−	18.7111i	0.484496	−	0.974061i
$370$	8.21783	−	2.89602i	0.427224	−	0.150557i
$371$		−	1.31234i		−	0.0681332i
$372$	2.08229	−	8.86201i	0.107962	−	0.459474i
$373$	−3.78362	+	3.78362i	−0.195909	+	0.195909i	−0.798243	−	0.602335i	$-0.794237\pi$
$373$	−3.78362	+	3.78362i	−0.195909	+	0.195909i	0.602335	+	0.798243i	$0.294237\pi$
$374$	−3.28386			−0.169804
$375$	−13.6893	+	13.6968i	−0.706914	+	0.707299i
$376$	8.56408			0.441659
$377$	4.44004	−	4.44004i	0.228674	−	0.228674i
$378$	−12.2777	−	10.1818i	−0.631498	−	0.523693i
$379$		−	0.706517i		−	0.0362913i	−0.999835	−	0.0181457i	$-0.994224\pi$
$379$		−	0.706517i		−	0.0362913i	0.999835	−	0.0181457i	$-0.00577626\pi$
$380$	−6.28393	+	2.21450i	−0.322359	+	0.113601i
$381$	−16.8602	−	27.2170i	−0.863776	−	1.39437i
$382$	2.25863	+	2.25863i	0.115561	+	0.115561i
$383$	22.6285	+	22.6285i	1.15626	+	1.15626i	0.985273	+	0.170991i	$0.0546968\pi$
$383$	22.6285	+	22.6285i	1.15626	+	1.15626i	0.170991	+	0.985273i	$0.445303\pi$
$384$	0.912127	+	1.47242i	0.0465468	+	0.0751392i
$385$	15.4981	−	32.3656i	0.789856	−	1.64950i
$386$		−	2.19279i		−	0.111610i
$387$	29.4456	−	9.88343i	1.49681	−	0.502403i
$388$	−13.1840	+	13.1840i	−0.669314	+	0.669314i
$389$	28.6741			1.45384			0.726918	−	0.686724i	$-0.240952\pi$
$389$	28.6741			1.45384			0.726918	+	0.686724i	$0.240952\pi$
$390$	−1.53585	−	14.1608i	−0.0777710	−	0.717062i
$391$	−0.628123			−0.0317655
$392$	−1.71305	+	1.71305i	−0.0865222	+	0.0865222i
$393$	1.26419	−	5.38024i	0.0637697	−	0.271397i
$394$		−	22.7465i		−	1.14595i
$395$	−8.72021	−	24.7447i	−0.438762	−	1.24504i
$396$	14.0429	+	6.98493i	0.705684	+	0.351006i
$397$	−4.16145	−	4.16145i	−0.208857	−	0.208857i	0.594924	−	0.803782i	$-0.297182\pi$
$397$	−4.16145	−	4.16145i	−0.208857	−	0.208857i	−0.803782	+	0.594924i	$0.797182\pi$
$398$	6.34628	+	6.34628i	0.318110	+	0.318110i
$399$	13.4674	−	8.34272i	0.674214	−	0.417658i
$400$	−3.89529	+	3.13476i	−0.194764	+	0.156738i
$401$			7.43533i			0.371303i	0.982616	+	0.185651i	$0.0594395\pi$
$401$			7.43533i			0.371303i	−0.982616	+	0.185651i	$0.940560\pi$
$402$	8.68950	+	2.04176i	0.433393	+	0.101834i
$403$	−13.6681	+	13.6681i	−0.680858	+	0.680858i
$404$	−10.8801			−0.541306
$405$	16.7858	+	11.1012i	0.834093	+	0.551624i
$406$	5.24089			0.260101
$407$	14.4051	−	14.4051i	0.714036	−	0.714036i
$408$	−1.05910	−	0.248854i	−0.0524331	−	0.0123201i
$409$		−	14.4432i		−	0.714170i	−0.934072	−	0.357085i	$-0.883771\pi$
$409$		−	14.4432i		−	0.714170i	0.934072	−	0.357085i	$-0.116229\pi$
$410$	14.0488	+	6.72719i	0.693821	+	0.332232i
$411$	26.6629	−	16.5170i	1.31518	−	0.814724i
$412$	2.54969	+	2.54969i	0.125614	+	0.125614i
$413$	−24.2536	−	24.2536i	−1.19344	−	1.19344i
$414$	2.68607	+	1.33605i	0.132013	+	0.0656631i
$415$	−26.7609	−	12.8143i	−1.31364	−	0.629030i
$416$		−	3.67776i		−	0.180317i
$417$	−4.73808	+	20.1648i	−0.232025	+	0.987472i
$418$	−11.0152	+	11.0152i	−0.538770	+	0.538770i
$419$	−4.96433			−0.242523			−0.121262	−	0.992621i	$-0.538694\pi$
$419$	−4.96433			−0.242523			−0.121262	+	0.992621i	$0.538694\pi$
$420$	7.45108	−	9.26395i	0.363575	−	0.452035i
$421$	−38.1579			−1.85970			−0.929851	−	0.367938i	$-0.880064\pi$
$421$	−38.1579			−1.85970			−0.929851	+	0.367938i	$0.880064\pi$
$422$	0.213015	−	0.213015i	0.0103694	−	0.0103694i
$423$	24.3568	−	8.17537i	1.18427	−	0.397500i
$424$			0.427523i			0.0207624i
$425$	0.337788	−	3.12240i	0.0163851	−	0.151458i
$426$	4.20867	+	6.79393i	0.203911	+	0.329167i
$427$	3.06036	+	3.06036i	0.148101	+	0.148101i
$428$	9.52639	+	9.52639i	0.460475	+	0.460475i
$429$	−17.5380	−	28.3110i	−0.846740	−	1.36687i
$430$	7.69468	+	21.8346i	0.371070	+	1.05296i
$431$			28.1762i			1.35720i	0.734508	+	0.678600i	$0.237413\pi$
$431$			28.1762i			1.35720i	−0.734508	+	0.678600i	$0.762587\pi$
$432$	3.99974	+	3.31694i	0.192438	+	0.159586i
$433$	13.8540	−	13.8540i	0.665781	−	0.665781i	−0.290956	−	0.956737i	$-0.593973\pi$
$433$	13.8540	−	13.8540i	0.665781	−	0.665781i	0.956737	+	0.290956i	$0.0939732\pi$
$434$	−16.1334			−0.774430
$435$	−6.57393	+	0.712994i	−0.315196	+	0.0341855i
$436$	8.20451			0.392925
$437$	−2.10693	+	2.10693i	−0.100788	+	0.100788i
$438$	0.391335	−	1.66548i	0.0186987	−	0.0795798i
$439$			13.6748i			0.652661i	0.945256	+	0.326330i	$0.105812\pi$
$439$			13.6748i			0.652661i	−0.945256	+	0.326330i	$0.894188\pi$
$440$	−5.04885	+	10.5438i	−0.240694	+	0.502657i
$441$	−3.23674	+	6.50734i	−0.154130	+	0.309873i
$442$	1.63348	+	1.63348i	0.0776965	+	0.0776965i
$443$	−24.2823	−	24.2823i	−1.15369	−	1.15369i	−0.985808	−	0.167879i	$-0.946308\pi$
$443$	−24.2823	−	24.2823i	−1.15369	−	1.15369i	−0.167879	−	0.985808i	$-0.553692\pi$
$444$	5.73752	−	3.55425i	0.272290	−	0.168677i
$445$	7.45724	−	2.62798i	0.353507	−	0.124578i
$446$			18.1511i			0.859480i
$447$	−28.9274	−	6.79701i	−1.36822	−	0.321488i
$448$	2.17056	−	2.17056i	0.102549	−	0.102549i
$449$	−15.3176			−0.722883			−0.361442	−	0.932395i	$-0.617715\pi$
$449$	−15.3176			−0.722883			−0.361442	+	0.932395i	$0.617715\pi$
$450$	−8.08598	+	12.6340i	−0.381177	+	0.595570i
$451$	36.4185			1.71488
$452$	−0.453030	+	0.453030i	−0.0213087	+	0.0213087i
$453$	−28.6179	−	6.72431i	−1.34459	−	0.315936i
$454$		−	14.0892i		−	0.661239i
$455$	−23.8086	+	8.39032i	−1.11616	+	0.393344i
$456$	−4.38731	+	2.71783i	−0.205454	+	0.127274i
$457$	0.783829	+	0.783829i	0.0366660	+	0.0366660i	0.725202	−	0.688536i	$-0.241746\pi$
$457$	0.783829	+	0.783829i	0.0366660	+	0.0366660i	−0.688536	+	0.725202i	$0.741746\pi$
$458$	−12.4570	−	12.4570i	−0.582079	−	0.582079i
$459$	−3.24970	+	0.303268i	−0.151683	+	0.0141553i
$460$	−0.965722	+	2.01677i	−0.0450270	+	0.0940326i
$461$			29.9101i			1.39305i	0.717531	+	0.696527i	$0.245272\pi$
$461$			29.9101i			1.39305i	−0.717531	+	0.696527i	$0.754728\pi$
$462$	6.35809	−	27.0593i	0.295805	−	1.25891i
$463$	12.8240	−	12.8240i	0.595982	−	0.595982i	−0.343259	−	0.939241i	$-0.611531\pi$
$463$	12.8240	−	12.8240i	0.595982	−	0.595982i	0.939241	+	0.343259i	$0.111531\pi$
$464$	−1.70734			−0.0792611
$465$	20.2370	−	2.19487i	0.938470	−	0.101784i
$466$	−2.12319			−0.0983549
$467$	−27.4406	+	27.4406i	−1.26980	+	1.26980i	−0.323607	+	0.946192i	$0.604895\pi$
$467$	−27.4406	+	27.4406i	−1.26980	+	1.26980i	−0.946192	+	0.323607i	$0.895105\pi$
$468$	−3.51083	−	10.4598i	−0.162288	−	0.483504i
$469$		−	15.8194i		−	0.730472i
$470$	6.36488	+	18.0612i	0.293590	+	0.833100i
$471$	−15.2008	−	24.5382i	−0.700417	−	1.13066i
$472$	7.90115	+	7.90115i	0.363680	+	0.363680i
$473$	38.2742	+	38.2742i	1.75985	+	1.75985i
$474$	−10.7022	−	17.2763i	−0.491568	−	0.793525i
$475$	−9.34051	−	11.6066i	−0.428572	−	0.532548i
$476$			1.92810i			0.0883745i
$477$	0.408118	+	1.21590i	0.0186865	+	0.0556724i
$478$	−17.1895	+	17.1895i	−0.786232	+	0.786232i
$479$	−15.9073			−0.726824			−0.363412	−	0.931629i	$-0.618388\pi$
$479$	−15.9073			−0.726824			−0.363412	+	0.931629i	$0.618388\pi$
$480$	−2.42735	+	3.01794i	−0.110793	+	0.137749i
$481$	−14.3309			−0.653435
$482$	−16.8977	+	16.8977i	−0.769667	+	0.769667i
$483$	1.21615	−	5.17579i	0.0553367	−	0.235507i
$484$			16.3326i			0.742390i
$485$	−37.6026	−	18.0058i	−1.70745	−	0.817602i
$486$	14.5419	+	5.61539i	0.659635	+	0.254719i
$487$	17.8486	+	17.8486i	0.808797	+	0.808797i	0.984452	−	0.175655i	$-0.0562042\pi$
$487$	17.8486	+	17.8486i	0.808797	+	0.808797i	−0.175655	+	0.984452i	$0.556204\pi$
$488$	−0.996981	−	0.996981i	−0.0451312	−	0.0451312i
$489$	−7.88945	+	4.88731i	−0.356773	+	0.221012i
$490$	−4.88588	−	2.33958i	−0.220722	−	0.105691i
$491$		−	12.5148i		−	0.564787i	−0.959299	−	0.282393i	$-0.908872\pi$
$491$		−	12.5148i		−	0.564787i	0.959299	−	0.282393i	$-0.0911283\pi$
$492$	11.7455	+	2.75983i	0.529530	+	0.124423i
$493$	0.758313	−	0.758313i	0.0341527	−	0.0341527i
$494$	10.9584			0.493044
$495$	−4.29402	+	34.8070i	−0.193002	+	1.56446i
$496$	5.25582			0.235993
$497$	10.0152	−	10.0152i	0.449243	−	0.449243i
$498$	−22.3735	−	5.25707i	−1.00258	−	0.235575i
$499$		−	26.3804i		−	1.18095i	−0.807056	−	0.590474i	$-0.798941\pi$
$499$		−	26.3804i		−	1.18095i	0.807056	−	0.590474i	$-0.201059\pi$
$500$	−9.50604	−	5.88517i	−0.425123	−	0.263193i
$501$	24.0602	−	14.9047i	1.07493	−	0.665893i
$502$	15.9131	+	15.9131i	0.710234	+	0.710234i
$503$	9.48821	+	9.48821i	0.423059	+	0.423059i	0.886255	−	0.463197i	$-0.153298\pi$
$503$	9.48821	+	9.48821i	0.423059	+	0.423059i	−0.463197	+	0.886255i	$0.653298\pi$
$504$	4.10117	−	8.24524i	0.182681	−	0.367272i
$505$	−8.08618	−	22.9456i	−0.359830	−	1.02106i
$506$			5.22806i			0.232415i
$507$	−0.208354	+	0.886733i	−0.00925334	+	0.0393812i
$508$	13.0705	−	13.0705i	0.579911	−	0.579911i
$509$	−14.3787			−0.637323			−0.318662	−	0.947869i	$-0.603233\pi$
$509$	−14.3787			−0.637323			−0.318662	+	0.947869i	$0.603233\pi$
$510$	−0.262308	−	2.41853i	−0.0116152	−	0.107094i
$511$	−3.03204			−0.134129
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−9.88333	+	11.9179i	−0.436360	+	0.526186i
$514$		−	24.0507i		−	1.06083i
$515$	−3.48221	+	7.27210i	−0.153444	+	0.320447i
$516$	9.44358	+	15.2445i	0.415730	+	0.671101i
$517$	31.6596	+	31.6596i	1.39239	+	1.39239i
$518$	−8.45790	−	8.45790i	−0.371619	−	0.371619i
$519$	8.51270	+	13.7418i	0.373666	+	0.603198i
$520$	7.75618	−	2.73333i	0.340131	−	0.119865i
$521$		−	12.6632i		−	0.554784i	−0.960757	−	0.277392i	$-0.910530\pi$
$521$		−	12.6632i		−	0.554784i	0.960757	−	0.277392i	$-0.0894701\pi$
$522$	−4.85578	+	1.62984i	−0.212532	+	0.0713363i
$523$	−9.41837	+	9.41837i	−0.411836	+	0.411836i	−0.882378	−	0.470541i	$-0.844059\pi$
$523$	−9.41837	+	9.41837i	−0.411836	+	0.411836i	0.470541	+	0.882378i	$0.344059\pi$
$524$	3.19088			0.139394
$525$	25.0748	+	8.82887i	1.09436	+	0.385324i
$526$	−25.3474			−1.10520
$527$	−2.33437	+	2.33437i	−0.101687	+	0.101687i
$528$	−2.07129	+	8.81518i	−0.0901413	+	0.383632i
$529$			1.00000i			0.0434783i
$530$	−0.901622	+	0.317738i	−0.0391640	+	0.0138017i
$531$	30.0139	+	14.9289i	1.30249	+	0.647858i
$532$	6.46751	+	6.46751i	0.280402	+	0.280402i
$533$	−18.1155	−	18.1155i	−0.784668	−	0.784668i
$534$	5.20649	−	3.22529i	0.225307	−	0.139572i
$535$	−13.0105	+	27.1707i	−0.562495	+	1.17469i
$536$			5.15352i			0.222598i
$537$	31.0639	+	7.29904i	1.34051	+	0.314977i
$538$	−12.7240	+	12.7240i	−0.548571	+	0.548571i
$539$	−12.6656			−0.545546
$540$	−4.02260	+	10.9004i	−0.173105	+	0.469078i
$541$	9.84624			0.423323			0.211661	−	0.977343i	$-0.432113\pi$
$541$	9.84624			0.423323			0.211661	+	0.977343i	$0.432113\pi$
$542$	9.91928	−	9.91928i	0.426070	−	0.426070i
$543$	−8.17714	−	1.92137i	−0.350915	−	0.0824538i
$544$		−	0.628123i		−	0.0269305i
$545$	6.09764	+	17.3028i	0.261194	+	0.741173i
$546$	−16.6227	+	10.2973i	−0.711385	+	0.440685i
$547$	−24.2038	−	24.2038i	−1.03488	−	1.03488i	−0.999369	−	0.0355120i	$-0.988694\pi$
$547$	−24.2038	−	24.2038i	−1.03488	−	1.03488i	−0.0355120	−	0.999369i	$-0.511306\pi$
$548$	12.8044	+	12.8044i	0.546979	+	0.546979i
$549$	−3.78721	−	1.88375i	−0.161634	−	0.0803966i
$550$	−25.9886	−	2.81151i	−1.10816	−	0.119883i
$551$		−	5.08727i		−	0.216725i
$552$	−0.396187	+	1.68613i	−0.0168629	+	0.0717665i
$553$	−25.4676	+	25.4676i	−1.08299	+	1.08299i
$554$	1.40594			0.0597327
$555$	11.7599	+	9.45856i	0.499178	+	0.401494i
$556$	−11.9592			−0.507183
$557$	19.7073	−	19.7073i	0.835026	−	0.835026i	−0.153174	−	0.988199i	$-0.548949\pi$
$557$	19.7073	−	19.7073i	0.835026	−	0.835026i	0.988199	+	0.153174i	$0.0489494\pi$
$558$	14.9479	−	5.01727i	0.632796	−	0.212398i
$559$		−	38.0771i		−	1.61049i
$560$	6.19075	+	2.96441i	0.261607	+	0.125269i
$561$	−2.99530	−	4.83523i	−0.126462	−	0.204143i
$562$	−11.3115	−	11.3115i	−0.477145	−	0.477145i
$563$	−6.01209	−	6.01209i	−0.253379	−	0.253379i	0.568975	−	0.822355i	$-0.307340\pi$
$563$	−6.01209	−	6.01209i	−0.253379	−	0.253379i	−0.822355	+	0.568975i	$0.807340\pi$
$564$	7.81153	+	12.6099i	0.328925	+	0.530974i
$565$	−1.29211	−	0.618719i	−0.0543594	−	0.0260297i
$566$			30.1471i			1.26718i
$567$	3.79300	−	27.3650i	0.159291	−	1.14922i
$568$	−3.26268	+	3.26268i	−0.136899	+	0.136899i
$569$	1.31647			0.0551895			0.0275947	−	0.999619i	$-0.491215\pi$
$569$	1.31647			0.0551895			0.0275947	+	0.999619i	$0.491215\pi$
$570$	−8.99242	−	7.23268i	−0.376651	−	0.302944i
$571$	17.5617			0.734934			0.367467	−	0.930036i	$-0.380225\pi$
$571$	17.5617			0.734934			0.367467	+	0.930036i	$0.380225\pi$
$572$	13.5959	−	13.5959i	0.568474	−	0.568474i
$573$	−1.26549	+	5.38581i	−0.0528668	+	0.224995i
$574$		−	21.3829i		−	0.892507i
$575$	−4.97100	−	0.537774i	−0.207305	−	0.0224267i
$576$	−1.33605	+	2.68607i	−0.0556686	+	0.111920i
$577$	16.0820	+	16.0820i	0.669504	+	0.669504i	0.957601	−	0.288097i	$-0.0930225\pi$
$577$	16.0820	+	16.0820i	0.669504	+	0.669504i	−0.288097	+	0.957601i	$0.593023\pi$
$578$	−11.7418	−	11.7418i	−0.488396	−	0.488396i
$579$	3.22871	−	2.00010i	0.134180	−	0.0831214i
$580$	−1.26890	−	3.60068i	−0.0526883	−	0.149510i
$581$			40.7314i			1.68982i
$582$	−31.4378	−	7.38688i	−1.30314	−	0.306196i
$583$	−1.58046	+	1.58046i	−0.0654562	+	0.0654562i
$584$	0.987754			0.0408735
$585$	19.4498	−	15.1779i	0.804152	−	0.627530i
$586$	5.77667			0.238632
$587$	9.61314	−	9.61314i	0.396777	−	0.396777i	−0.480318	−	0.877095i	$-0.659479\pi$
$587$	9.61314	−	9.61314i	0.396777	−	0.396777i	0.877095	+	0.480318i	$0.159479\pi$
$588$	−4.08486	−	0.959812i	−0.168457	−	0.0395820i
$589$			15.6605i			0.645282i
$590$	−10.7909	+	22.5353i	−0.444254	+	0.927762i
$591$	33.4925	−	20.7478i	1.37770	−	0.853448i
$592$	2.75535	+	2.75535i	0.113244	+	0.113244i
$593$	−12.3638	−	12.3638i	−0.507719	−	0.507719i	0.406106	−	0.913826i	$-0.366886\pi$
$593$	−12.3638	−	12.3638i	−0.507719	−	0.507719i	−0.913826	+	0.406106i	$0.866886\pi$
$594$	2.52419	+	27.0483i	0.103569	+	1.10980i
$595$	−4.06626	+	1.43298i	−0.166701	+	0.0587464i
$596$		−	17.1561i		−	0.702740i
$597$	−3.55578	+	15.1330i	−0.145528	+	0.619353i
$598$	2.60057	−	2.60057i	0.106345	−	0.106345i
$599$	−48.6613			−1.98825			−0.994123	−	0.108255i	$-0.965474\pi$
$599$	−48.6613			−1.98825			−0.994123	+	0.108255i	$0.965474\pi$
$600$	−8.16869	−	2.87620i	−0.333485	−	0.117420i
$601$	−28.4823			−1.16182			−0.580909	−	0.813969i	$-0.697303\pi$
$601$	−28.4823			−1.16182			−0.580909	+	0.813969i	$0.697303\pi$
$602$	22.4725	−	22.4725i	0.915912	−	0.915912i
$603$	4.91961	+	14.6570i	0.200342	+	0.596877i
$604$		−	16.9726i		−	0.690603i
$605$	−34.4445	+	12.1385i	−1.40037	+	0.493499i
$606$	−9.92406	−	16.0201i	−0.403137	−	0.650773i
$607$	10.2267	+	10.2267i	0.415088	+	0.415088i	0.883507	−	0.468419i	$-0.155176\pi$
$607$	10.2267	+	10.2267i	0.415088	+	0.415088i	−0.468419	+	0.883507i	$0.655176\pi$
$608$	−2.10693	−	2.10693i	−0.0854475	−	0.0854475i
$609$	4.78036	+	7.71679i	0.193710	+	0.312700i
$610$	1.36161	−	2.84354i	0.0551302	−	0.115132i
$611$		−	31.4966i		−	1.27422i
$612$	−0.599613	−	1.78642i	−0.0242379	−	0.0722119i
$613$	4.21128	−	4.21128i	0.170092	−	0.170092i	−0.616928	−	0.787020i	$-0.711623\pi$
$613$	4.21128	−	4.21128i	0.170092	−	0.170092i	0.787020	+	0.616928i	$0.211623\pi$
$614$	−21.7651			−0.878369
$615$	2.90903	+	26.8218i	0.117304	+	1.08156i
$616$	16.0482			0.646600
$617$	−1.18781	+	1.18781i	−0.0478194	+	0.0478194i	−0.730612	−	0.682793i	$-0.760765\pi$
$617$	−1.18781	+	1.18781i	−0.0478194	+	0.0478194i	0.682793	+	0.730612i	$0.260765\pi$
$618$	−1.42857	+	6.07986i	−0.0574657	+	0.244568i
$619$			9.65709i			0.388151i	0.980987	+	0.194076i	$0.0621707\pi$
$619$			9.65709i			0.388151i	−0.980987	+	0.194076i	$0.937829\pi$
$620$	3.90616	+	11.0842i	0.156875	+	0.445154i
$621$	0.482816	+	5.17367i	0.0193747	+	0.207612i
$622$	−14.1410	−	14.1410i	−0.567004	−	0.567004i
$623$	−7.67510	−	7.67510i	−0.307497	−	0.307497i
$624$	5.41521	−	3.35458i	0.216782	−	0.134291i
$625$	5.34654	−	24.4216i	0.213862	−	0.976864i
$626$		−	30.3564i		−	1.21329i
$627$	−26.2662	−	6.17173i	−1.04897	−	0.246475i
$628$	11.7841	−	11.7841i	0.470237	−	0.470237i
$629$	−2.44758			−0.0975913
$630$	20.4368	+	2.52122i	0.814220	+	0.100448i
$631$	−20.1398			−0.801754			−0.400877	−	0.916132i	$-0.631295\pi$
$631$	−20.1398			−0.801754			−0.400877	+	0.916132i	$0.631295\pi$
$632$	8.29665	−	8.29665i	0.330023	−	0.330023i
$633$	0.507945	+	0.119351i	0.0201890	+	0.00474377i
$634$			24.0437i			0.954897i
$635$	37.2791	+	17.8509i	1.47938	+	0.708391i
$636$	−0.629494	+	0.389956i	−0.0249611	+	0.0154627i
$637$	6.30019	+	6.30019i	0.249623	+	0.249623i
$638$	−6.31167	−	6.31167i	−0.249881	−	0.249881i
$639$	−6.16468	+	12.3939i	−0.243871	+	0.490294i
$640$	−2.01677	−	0.965722i	−0.0797200	−	0.0381735i
$641$		−	7.77971i		−	0.307280i	−0.988127	−	0.153640i	$-0.950900\pi$
$641$		−	7.77971i		−	0.307280i	0.988127	−	0.153640i	$-0.0490996\pi$
$642$	−5.33757	+	22.7161i	−0.210657	+	0.896534i
$643$	−22.1643	+	22.1643i	−0.874075	+	0.874075i	−0.992914	−	0.118838i	$-0.962083\pi$
$643$	−22.1643	+	22.1643i	−0.874075	+	0.874075i	0.118838	+	0.992914i	$0.462083\pi$
$644$	3.06963			0.120960
$645$	−25.1313	+	31.2458i	−0.989542	+	1.23030i
$646$	1.87159			0.0736367
$647$	−7.24949	+	7.24949i	−0.285007	+	0.285007i	−0.835102	−	0.550095i	$-0.814591\pi$
$647$	−7.24949	+	7.24949i	−0.285007	+	0.285007i	0.550095	+	0.835102i	$0.314591\pi$
$648$	−1.23565	+	8.91477i	−0.0485410	+	0.350205i
$649$			58.4178i			2.29310i
$650$	11.5289	+	14.3259i	0.452200	+	0.561909i
$651$	−14.7157	−	23.7552i	−0.576756	−	0.931040i
$652$	−3.78878	−	3.78878i	−0.148380	−	0.148380i
$653$	−18.2696	−	18.2696i	−0.714944	−	0.714944i	0.252621	−	0.967565i	$-0.418707\pi$
$653$	−18.2696	−	18.2696i	−0.714944	−	0.714944i	−0.967565	+	0.252621i	$0.918707\pi$
$654$	7.48356	+	12.0805i	0.292630	+	0.472385i
$655$	2.37148	+	6.72938i	0.0926615	+	0.262939i
$656$			6.96597i			0.271975i
$657$	2.80924	−	0.942921i	0.109599	−	0.0367868i
$658$	18.5888	−	18.5888i	0.724667	−	0.724667i
$659$	−23.0114			−0.896399			−0.448199	−	0.893934i	$-0.647934\pi$
$659$	−23.0114			−0.896399			−0.448199	+	0.893934i	$0.647934\pi$
$660$	−20.1301	+	2.18327i	−0.783564	+	0.0849836i
$661$	−21.2264			−0.825611			−0.412806	−	0.910819i	$-0.635451\pi$
$661$	−21.2264			−0.825611			−0.412806	+	0.910819i	$0.635451\pi$
$662$	23.4241	−	23.4241i	0.910404	−	0.910404i
$663$	−0.915226	+	3.89510i	−0.0355444	+	0.151273i
$664$		−	13.2692i		−	0.514943i
$665$	−8.83292	+	18.4463i	−0.342526	+	0.715317i
$666$	10.4667	+	5.20611i	0.405576	+	0.201733i
$667$	−1.20727	−	1.20727i	−0.0467456	−	0.0467456i
$668$	11.5545	+	11.5545i	0.447058	+	0.447058i
$669$	−26.7261	+	16.5561i	−1.03329	+	0.640097i
$670$	−10.8685	+	3.83013i	−0.419886	+	0.147971i
$671$		−	7.37127i		−	0.284565i
$672$	5.17579	+	1.21615i	0.199661	+	0.0469139i
$673$	−2.23113	+	2.23113i	−0.0860038	+	0.0860038i	−0.748800	−	0.662796i	$-0.769370\pi$
$673$	−2.23113	+	2.23113i	−0.0860038	+	0.0860038i	0.662796	+	0.748800i	$0.269370\pi$
$674$	0.732413			0.0282115
$675$	−25.9780	−	0.382189i	−0.999892	−	0.0147105i
$676$	−0.525898			−0.0202269
$677$	8.73195	−	8.73195i	0.335596	−	0.335596i	−0.519111	−	0.854707i	$-0.673737\pi$
$677$	8.73195	−	8.73195i	0.335596	−	0.335596i	0.854707	+	0.519111i	$0.173737\pi$
$678$	−1.08027	−	0.253829i	−0.0414876	−	0.00974826i
$679$			57.2330i			2.19640i
$680$	1.32468	−	0.466825i	0.0507990	−	0.0179019i
$681$	20.7453	−	12.8512i	0.794960	−	0.492457i
$682$	19.4297	+	19.4297i	0.744002	+	0.744002i
$683$	−7.60796	−	7.60796i	−0.291110	−	0.291110i	0.546408	−	0.837519i	$-0.315995\pi$
$683$	−7.60796	−	7.60796i	−0.291110	−	0.291110i	−0.837519	+	0.546408i	$0.815995\pi$
$684$	−8.00357	−	3.98096i	−0.306024	−	0.152216i
$685$	−17.4875	+	36.5202i	−0.668163	+	1.39536i
$686$		−	14.0509i		−	0.536464i
$687$	6.97959	−	29.7044i	0.266288	−	1.13329i
$688$	−7.32093	+	7.32093i	−0.279108	+	0.279108i
$689$	1.57233			0.0599009
$690$	−3.85040	+	0.417606i	−0.146582	+	0.0158980i
$691$	48.5623			1.84740			0.923698	−	0.383120i	$-0.125151\pi$
$691$	48.5623			1.84740			0.923698	+	0.383120i	$0.125151\pi$
$692$	−6.59928	+	6.59928i	−0.250867	+	0.250867i
$693$	45.6421	−	15.3198i	1.73380	−	0.581951i
$694$			21.3581i			0.810743i
$695$	−8.88815	−	25.2213i	−0.337147	−	0.956697i
$696$	−1.55731	−	2.51392i	−0.0590296	−	0.0952898i
$697$	−3.09394	−	3.09394i	−0.117191	−	0.117191i
$698$	−1.28588	−	1.28588i	−0.0486712	−	0.0486712i
$699$	−1.93662	−	3.12623i	−0.0732497	−	0.118245i
$700$	−1.65077	+	15.2591i	−0.0623931	+	0.576740i
$701$		−	18.5789i		−	0.701715i	−0.936429	−	0.350858i	$-0.885890\pi$
$701$		−	18.5789i		−	0.701715i	0.936429	−	0.350858i	$-0.114110\pi$
$702$	12.1989	−	14.7101i	0.460417	−	0.555196i
$703$	−8.21000	+	8.21000i	−0.309646	+	0.309646i
$704$	−5.22806			−0.197040
$705$	−20.7881	+	25.8459i	−0.782924	+	0.973412i
$706$	−23.7202			−0.892723
$707$	−23.6159	+	23.6159i	−0.888168	+	0.888168i
$708$	−4.42696	+	18.8407i	−0.166375	+	0.708076i
$709$		−	40.6579i		−	1.52694i	−0.645844	−	0.763469i	$-0.723495\pi$
$709$		−	40.6579i		−	1.52694i	0.645844	−	0.763469i	$-0.276505\pi$
$710$	−9.30564	−	4.45596i	−0.349235	−	0.167229i
$711$	15.6761	−	31.5163i	0.587901	−	1.18195i
$712$	2.50034	+	2.50034i	0.0937041	+	0.0937041i
$713$	3.71643	+	3.71643i	0.139181	+	0.139181i
$714$	−2.83898	+	1.75868i	−0.106246	+	0.0658168i
$715$	38.7776	+	18.5684i	1.45020	+	0.694420i
$716$			18.4232i			0.688508i
$717$	−40.9893	−	9.63119i	−1.53077	−	0.359683i
$718$	−2.81286	+	2.81286i	−0.104975	+	0.104975i
$719$	20.2760			0.756166			0.378083	−	0.925772i	$-0.376583\pi$
$719$	20.2760			0.756166			0.378083	+	0.925772i	$0.376583\pi$
$720$	−6.65773	−	0.821342i	−0.248119	−	0.0306096i
$721$	11.0685			0.412212
$722$	−7.15709	+	7.15709i	−0.266359	+	0.266359i
$723$	−40.2933	−	9.46765i	−1.49852	−	0.352106i
$724$		−	4.84965i		−	0.180236i
$725$	6.65057	−	5.35209i	0.246996	−	0.198772i
$726$	−24.0484	+	14.8974i	−0.892520	+	0.552894i
$727$	36.0659	+	36.0659i	1.33761	+	1.33761i	0.898370	+	0.439239i	$0.144752\pi$
$727$	36.0659	+	36.0659i	1.33761	+	1.33761i	0.439239	+	0.898370i	$0.355248\pi$
$728$	−7.98278	−	7.98278i	−0.295861	−	0.295861i
$729$	4.99586	+	26.5338i	0.185032	+	0.982733i
$730$	0.734105	+	2.08312i	0.0271704	+	0.0770996i
$731$		−	6.50318i		−	0.240529i
$732$	0.558602	−	2.37735i	0.0206465	−	0.0878694i
$733$	−13.8202	+	13.8202i	−0.510462	+	0.510462i	−0.914668	−	0.404206i	$-0.867548\pi$
$733$	−13.8202	+	13.8202i	−0.510462	+	0.510462i	0.404206	+	0.914668i	$0.367548\pi$
$734$	21.1530			0.780770
$735$	−1.01170	−	9.32807i	−0.0373172	−	0.344071i
$736$	−1.00000			−0.0368605
$737$	−19.0515	+	19.0515i	−0.701771	+	0.701771i
$738$	6.64980	+	19.8117i	0.244782	+	0.729278i
$739$		−	18.0843i		−	0.665240i	−0.943061	−	0.332620i	$-0.892067\pi$
$739$		−	18.0843i		−	0.665240i	0.943061	−	0.332620i	$-0.107933\pi$
$740$	−3.76309	+	7.85867i	−0.138334	+	0.288891i
$741$	9.99550	+	16.1354i	0.367194	+	0.592751i
$742$	0.927963	+	0.927963i	0.0340666	+	0.0340666i
$743$	14.2366	+	14.2366i	0.522291	+	0.522291i	0.918263	−	0.395972i	$-0.129592\pi$
$743$	14.2366	+	14.2366i	0.522291	+	0.522291i	−0.395972	+	0.918263i	$0.629592\pi$
$744$	4.79398	+	7.73879i	0.175756	+	0.283718i
$745$	36.1812	−	12.7505i	1.32558	−	0.467142i
$746$		−	5.35085i		−	0.195909i
$747$	−12.6669	−	37.7384i	−0.463457	−	1.38077i
$748$	2.32204	−	2.32204i	0.0849022	−	0.0849022i
$749$	41.3551			1.51108
$750$	−0.00527343	−	19.3649i	−0.000192558	−	0.707107i
$751$	9.75271			0.355882			0.177941	−	0.984041i	$-0.443056\pi$
$751$	9.75271			0.355882			0.177941	+	0.984041i	$0.443056\pi$
$752$	−6.05572	+	6.05572i	−0.220829	+	0.220829i
$753$	−8.91598	+	37.9454i	−0.324916	+	1.38281i
$754$			6.27917i			0.228674i
$755$	35.7942	−	12.6141i	1.30268	−	0.459074i
$756$	15.8813	−	1.48207i	0.577596	−	0.0539022i
$757$	20.1653	+	20.1653i	0.732920	+	0.732920i	0.971197	−	0.238277i	$-0.0765827\pi$
$757$	20.1653	+	20.1653i	0.732920	+	0.732920i	−0.238277	+	0.971197i	$0.576583\pi$
$758$	0.499583	+	0.499583i	0.0181457	+	0.0181457i
$759$	−7.69790	+	4.76865i	−0.279416	+	0.173091i
$760$	2.87752	−	6.00929i	0.104379	−	0.217980i
$761$		−	1.55390i		−	0.0563288i	−0.999603	−	0.0281644i	$-0.991034\pi$
$761$		−	1.55390i		−	0.0563288i	0.999603	−	0.0281644i	$-0.00896620\pi$
$762$	31.1673	+	7.32333i	1.12907	+	0.265296i
$763$	17.8083	−	17.8083i	0.644705	−	0.644705i
$764$	−3.19418			−0.115561
$765$	3.32183	−	2.59223i	0.120101	−	0.0937223i
$766$	−32.0016			−1.15626
$767$	29.0585	−	29.0585i	1.04924	−	1.04924i
$768$	−1.68613	−	0.396187i	−0.0608430	−	0.0142962i
$769$		−	26.7080i		−	0.963116i	−0.876414	−	0.481558i	$-0.840071\pi$
$769$		−	26.7080i		−	0.963116i	0.876414	−	0.481558i	$-0.159929\pi$
$770$	11.9271	+	33.8447i	0.429824	+	1.21968i
$771$	35.4128	−	21.9373i	1.27536	−	0.790053i
$772$	1.55053	+	1.55053i	0.0558050	+	0.0558050i
$773$	4.61426	+	4.61426i	0.165963	+	0.165963i	0.785202	−	0.619239i	$-0.212559\pi$
$773$	4.61426	+	4.61426i	0.165963	+	0.165963i	−0.619239	+	0.785202i	$0.712559\pi$
$774$	−13.8326	+	27.8098i	−0.497201	+	0.999604i
$775$	−20.4730	+	16.4758i	−0.735410	+	0.591827i
$776$		−	18.6449i		−	0.669314i
$777$	4.73891	−	20.1683i	0.170007	−	0.723533i
$778$	−20.2757	+	20.2757i	−0.726918	+	0.726918i
$779$	−20.7562			−0.743668
$780$	11.0992	+	8.92722i	0.397417	+	0.319646i
$781$	−24.1229			−0.863185
$782$	0.444150	−	0.444150i	0.0158828	−	0.0158828i
$783$	−6.82890	−	5.66313i	−0.244045	−	0.202384i
$784$		−	2.42262i		−	0.0865222i
$785$	33.6100	+	16.0940i	1.19959	+	0.574419i
$786$	2.91049	+	4.69832i	0.103814	+	0.167583i
$787$	−30.6924	−	30.6924i	−1.09407	−	1.09407i	−0.995090	−	0.0989765i	$-0.968443\pi$
$787$	−30.6924	−	30.6924i	−1.09407	−	1.09407i	−0.0989765	−	0.995090i	$-0.531557\pi$
$788$	16.0842	+	16.0842i	0.572977	+	0.572977i
$789$	−23.1201	−	37.3221i	−0.823097	−	1.32870i
$790$	23.6633	+	11.3310i	0.841902	+	0.403140i
$791$			1.96665i			0.0699261i
$792$	−14.8689	+	4.99076i	−0.528345	+	0.177339i
$793$	−3.66666	+	3.66666i	−0.130207	+	0.130207i
$794$	5.88519			0.208857
$795$	−1.29024	−	1.03775i	−0.0457600	−	0.0368052i
$796$	−8.97499			−0.318110
$797$	−27.3624	+	27.3624i	−0.969225	+	0.969225i	−0.999540	−	0.0303157i	$-0.990349\pi$
$797$	−27.3624	+	27.3624i	−0.969225	+	0.969225i	0.0303157	+	0.999540i	$0.490349\pi$
$798$	−3.62370	+	15.4221i	−0.128278	+	0.545936i
$799$		−	5.37930i		−	0.190306i
$800$	0.537774	−	4.97100i	0.0190132	−	0.175751i
$801$	9.49797	+	4.72427i	0.335594	+	0.166924i
$802$	−5.25757	−	5.25757i	−0.185651	−	0.185651i
$803$	3.65152	+	3.65152i	0.128859	+	0.128859i
$804$	−7.58815	+	4.70067i	−0.267613	+	0.165780i
$805$	2.28137	+	6.47368i	0.0804077	+	0.228167i
$806$		−	19.3296i		−	0.680858i
$807$	−30.3410	−	7.12918i	−1.06805	−	0.250959i
$808$	7.69341	−	7.69341i	0.270653	−	0.270653i
$809$	9.73699			0.342334			0.171167	−	0.985242i	$-0.445246\pi$
$809$	9.73699			0.342334			0.171167	+	0.985242i	$0.445246\pi$
$810$	−19.7191	+	4.01959i	−0.692859	+	0.141234i
$811$	50.7236			1.78115			0.890573	−	0.454840i	$-0.150303\pi$
$811$	50.7236			1.78115			0.890573	+	0.454840i	$0.150303\pi$
$812$	−3.70587	+	3.70587i	−0.130050	+	0.130050i
$813$	23.6530	+	5.55771i	0.829547	+	0.194917i
$814$			20.3719i			0.714036i
$815$	5.17448	−	10.8062i	0.181254	−	0.378524i
$816$	0.924861	−	0.572928i	0.0323766	−	0.0200565i
$817$	−21.8138	−	21.8138i	−0.763170	−	0.763170i
$818$	10.2129	+	10.2129i	0.357085	+	0.357085i
$819$	−30.3240	−	15.0831i	−1.05961	−	0.527046i
$820$	−14.6908	+	5.17715i	−0.513026	+	0.180794i
$821$			16.7113i			0.583228i	0.956536	+	0.291614i	$0.0941922\pi$
$821$			16.7113i			0.583228i	−0.956536	+	0.291614i	$0.905808\pi$
$822$	−7.17425	+	30.5328i	−0.250231	+	1.06495i
$823$	15.4051	−	15.4051i	0.536987	−	0.536987i	−0.385656	−	0.922643i	$-0.626025\pi$
$823$	15.4051	−	15.4051i	0.536987	−	0.536987i	0.922643	+	0.385656i	$0.126025\pi$
$824$	−3.60580			−0.125614
$825$	−19.5652	−	40.8307i	−0.681174	−	1.42154i
$826$	34.2998			1.19344
$827$	5.54156	−	5.54156i	0.192699	−	0.192699i	−0.604162	−	0.796861i	$-0.706492\pi$
$827$	5.54156	−	5.54156i	0.192699	−	0.192699i	0.796861	+	0.604162i	$0.206492\pi$
$828$	−2.84407	+	0.954611i	−0.0988382	+	0.0331750i
$829$		−	46.0012i		−	1.59769i	−0.601538	−	0.798844i	$-0.705445\pi$
$829$		−	46.0012i		−	1.59769i	0.601538	−	0.798844i	$-0.294555\pi$
$830$	27.9839	−	9.86172i	0.971335	−	0.342305i
$831$	1.28240	+	2.07014i	0.0444858	+	0.0718122i
$832$	2.60057	+	2.60057i	0.0901584	+	0.0901584i
$833$	1.07601	+	1.07601i	0.0372815	+	0.0372815i
$834$	−10.9083	−	17.6090i	−0.377724	−	0.609748i
$835$	−15.7805	+	32.9553i	−0.546105	+	1.14046i
$836$		−	15.5778i		−	0.538770i
$837$	21.0219	+	17.4332i	0.726625	+	0.602581i
$838$	3.51031	−	3.51031i	0.121262	−	0.121262i
$839$	−31.5440			−1.08902			−0.544510	−	0.838755i	$-0.683284\pi$
$839$	−31.5440			−1.08902			−0.544510	+	0.838755i	$0.683284\pi$
$840$	1.28190	+	11.8193i	0.0442296	+	0.407805i
$841$	−26.0850			−0.899483
$842$	26.9817	−	26.9817i	0.929851	−	0.929851i
$843$	6.33774	−	26.9727i	0.218283	−	0.928990i
$844$			0.301249i			0.0103694i
$845$	−0.390851	−	1.10909i	−0.0134457	−	0.0381539i
$846$	−11.4420	+	23.0037i	−0.393385	+	0.790885i
$847$	35.4507	+	35.4507i	1.21810	+	1.21810i
$848$	−0.302305	−	0.302305i	−0.0103812	−	0.0103812i
$849$	−44.3892	+	27.4980i	−1.52343	+	0.943729i
$850$	1.96902	+	2.44672i	0.0675367	+	0.0839218i
$851$			3.89665i			0.133576i
$852$	−7.78001	−	1.82806i	−0.266539	−	0.0626282i
$853$	−9.47742	+	9.47742i	−0.324501	+	0.324501i	−0.850491	−	0.525990i	$-0.823695\pi$
$853$	−9.47742	+	9.47742i	−0.324501	+	0.324501i	0.525990	+	0.850491i	$0.323695\pi$
$854$	−4.32801			−0.148101
$855$	2.44732	−	19.8377i	0.0836965	−	0.678437i
$856$	−13.4723			−0.460475
$857$	6.58621	−	6.58621i	0.224981	−	0.224981i	−0.585611	−	0.810592i	$-0.699146\pi$
$857$	6.58621	−	6.58621i	0.224981	−	0.224981i	0.810592	+	0.585611i	$0.199146\pi$
$858$	32.4201	+	7.61770i	1.10680	+	0.260064i
$859$			22.0094i			0.750952i	0.926832	+	0.375476i	$0.122521\pi$
$859$			22.0094i			0.750952i	−0.926832	+	0.375476i	$0.877479\pi$
$860$	−20.8804	−	9.99846i	−0.712015	−	0.340945i
$861$	31.4847	−	19.5040i	1.07300	−	0.664694i
$862$	−19.9236	−	19.9236i	−0.678600	−	0.678600i
$863$	19.0130	+	19.0130i	0.647209	+	0.647209i	0.952318	−	0.305108i	$-0.0986927\pi$
$863$	19.0130	+	19.0130i	0.647209	+	0.647209i	−0.305108	+	0.952318i	$0.598693\pi$
$864$	−5.17367	+	0.482816i	−0.176012	+	0.0164257i
$865$	−18.8222	−	9.01289i	−0.639972	−	0.306447i
$866$			19.5925i			0.665781i
$867$	6.57887	−	27.9990i	0.223430	−	0.950895i
$868$	11.4081	−	11.4081i	0.387215	−	0.387215i
$869$	61.3420			2.08088
$870$	4.14431	−	5.15264i	0.140505	−	0.174691i
$871$	18.9534			0.642211
$872$	−5.80146	+	5.80146i	−0.196462	+	0.196462i
$873$	−17.7987	−	53.0274i	−0.602393	−	1.79471i
$874$		−	2.97966i		−	0.100788i
$875$	−33.4075	+	7.85930i	−1.12938	+	0.265693i
$876$	0.900957	+	1.45439i	0.0304405	+	0.0491393i
$877$	−27.4105	−	27.4105i	−0.925587	−	0.925587i	0.0718296	−	0.997417i	$-0.477116\pi$
$877$	−27.4105	−	27.4105i	−0.925587	−	0.925587i	−0.997417	+	0.0718296i	$0.977116\pi$
$878$	−9.66951	−	9.66951i	−0.326330	−	0.326330i
$879$	5.26906	+	8.50569i	0.177721	+	0.286890i
$880$	−3.88553	−	11.0257i	−0.130981	−	0.371675i
$881$		−	20.1555i		−	0.679057i	−0.940596	−	0.339529i	$-0.889732\pi$
$881$		−	20.1555i		−	0.679057i	0.940596	−	0.339529i	$-0.110268\pi$
$882$	−2.31266	−	6.89010i	−0.0778714	−	0.232002i
$883$	12.8350	−	12.8350i	0.431932	−	0.431932i	−0.457353	−	0.889285i	$-0.651202\pi$
$883$	12.8350	−	12.8350i	0.431932	−	0.431932i	0.889285	+	0.457353i	$0.151202\pi$
$884$	−2.31008			−0.0776965
$885$	−43.0240	+	4.66629i	−1.44624	+	0.156856i
$886$	34.3404			1.15369
$887$	30.6618	−	30.6618i	1.02952	−	1.02952i	0.0299723	−	0.999551i	$-0.490458\pi$
$887$	30.6618	−	30.6618i	1.02952	−	1.02952i	0.999551	−	0.0299723i	$-0.00954192\pi$
$888$	−1.54381	+	6.57027i	−0.0518067	+	0.220484i
$889$		−	56.7406i		−	1.90302i
$890$	−3.41480	+	7.13133i	−0.114464	+	0.239043i
$891$	−37.5240	+	28.3881i	−1.25710	+	0.951038i
$892$	−12.8348	−	12.8348i	−0.429740	−	0.429740i
$893$	−18.0440	−	18.0440i	−0.603818	−	0.603818i
$894$	25.2609	−	15.6485i	0.844852	−	0.523365i
$895$	−38.8535	+	13.6922i	−1.29873	+	0.457681i
$896$			3.06963i			0.102549i
$897$	6.20118	+	1.45708i	0.207051	+	0.0486505i
$898$	10.8312	−	10.8312i	0.361442	−	0.361442i
$899$	−8.97346			−0.299282
$900$	−3.21590	−	14.6512i	−0.107197	−	0.488374i
$901$	0.268537			0.00894627
$902$	−25.7518	+	25.7518i	−0.857440	+	0.857440i
$903$	53.5868	+	12.5912i	1.78326	+	0.419009i
$904$		−	0.640680i		−	0.0213087i
$905$	10.2276	−	3.60429i	0.339978	−	0.119811i
$906$	24.9907	−	15.4811i	0.830262	−	0.514326i
$907$	2.56656	+	2.56656i	0.0852212	+	0.0852212i	0.748432	−	0.663211i	$-0.230807\pi$
$907$	2.56656	+	2.56656i	0.0852212	+	0.0852212i	−0.663211	+	0.748432i	$0.730807\pi$
$908$	9.96258	+	9.96258i	0.330620	+	0.330620i
$909$	14.5364	−	29.2248i	0.482140	−	0.969325i
$910$	10.9024	−	22.7681i	0.361410	−	0.754754i
$911$			25.6942i			0.851287i	0.904891	+	0.425643i	$0.139952\pi$
$911$			25.6942i			0.851287i	−0.904891	+	0.425643i	$0.860048\pi$
$912$	1.18050	−	5.02409i	0.0390903	−	0.166364i
$913$	49.0533	−	49.0533i	1.62343	−	1.62343i
$914$	−1.10850			−0.0366660
$915$	5.42886	−	0.588802i	0.179472	−	0.0194652i
$916$	17.6169			0.582079
$917$	6.92598	−	6.92598i	0.228716	−	0.228716i
$918$	2.08344	−	2.51233i	0.0687639	−	0.0829192i
$919$		−	8.00741i		−	0.264140i	−0.991240	−	0.132070i	$-0.957838\pi$
$919$		−	8.00741i		−	0.264140i	0.991240	−	0.132070i	$-0.0421624\pi$
$920$	−0.743206	−	2.10894i	−0.0245028	−	0.0695298i
$921$	−19.8526	−	32.0474i	−0.654164	−	1.05600i
$922$	−21.1496	−	21.1496i	−0.696527	−	0.696527i
$923$	11.9993	+	11.9993i	0.394963	+	0.394963i
$924$	14.6380	+	23.6297i	0.481555	+	0.777360i
$925$	−19.3703	−	2.09552i	−0.636890	−	0.0689002i
$926$			18.1359i			0.595982i
$927$	−10.2551	+	3.44214i	−0.336823	+	0.113055i
$928$	1.20727	−	1.20727i	0.0396305	−	0.0396305i
$929$	−19.2717			−0.632283			−0.316142	−	0.948712i	$-0.602387\pi$
$929$	−19.2717			−0.632283			−0.316142	+	0.948712i	$0.602387\pi$
$930$	−12.7577	+	15.8618i	−0.418343	+	0.520127i
$931$	7.21858			0.236579
$932$	1.50132	−	1.50132i	0.0491774	−	0.0491774i
$933$	7.92313	−	33.7200i	0.259392	−	1.10394i
$934$		−	38.8068i		−	1.26980i
$935$	6.62281	+	3.17130i	0.216589	+	0.103713i
$936$	9.87872	+	4.91366i	0.322896	+	0.160608i
$937$	14.3103	+	14.3103i	0.467498	+	0.467498i	0.901103	−	0.433605i	$-0.142759\pi$
$937$	14.3103	+	14.3103i	0.467498	+	0.467498i	−0.433605	+	0.901103i	$0.642759\pi$
$938$	11.1860	+	11.1860i	0.365236	+	0.365236i
$939$	44.6975	−	27.6889i	1.45865	−	0.903595i
$940$	−17.2718	−	8.27052i	−0.563345	−	0.269755i
$941$			17.7133i			0.577438i	0.957414	+	0.288719i	$0.0932293\pi$
$941$			17.7133i			0.577438i	−0.957414	+	0.288719i	$0.906771\pi$
$942$	28.0998	+	6.60255i	0.915539	+	0.215123i
$943$	−4.92569	+	4.92569i	−0.160402	+	0.160402i
$944$	−11.1739			−0.363680
$945$	14.9286	+	32.3912i	0.485629	+	1.05369i
$946$	−54.1279			−1.75985
$947$	16.1225	−	16.1225i	0.523912	−	0.523912i	−0.394838	−	0.918751i	$-0.629199\pi$
$947$	16.1225	−	16.1225i	0.523912	−	0.523912i	0.918751	+	0.394838i	$0.129199\pi$
$948$	19.7838	+	4.64856i	0.642547	+	0.150978i
$949$		−	3.63272i		−	0.117923i
$950$	14.8119	+	1.60238i	0.480560	+	0.0519881i
$951$	−35.4024	+	21.9309i	−1.14800	+	0.711158i
$952$	−1.36338	−	1.36338i	−0.0441873	−	0.0441873i
$953$	−0.285911	−	0.285911i	−0.00926156	−	0.00926156i	0.702461	−	0.711722i	$-0.252085\pi$
$953$	−0.285911	−	0.285911i	−0.00926156	−	0.00926156i	−0.711722	+	0.702461i	$0.752085\pi$
$954$	−1.14836	−	0.571191i	−0.0371795	−	0.0184930i
$955$	−2.37394	−	6.73635i	−0.0768188	−	0.217983i
$956$		−	24.3097i		−	0.786232i
$957$	3.53639	−	15.0505i	0.114315	−	0.486513i
$958$	11.2482	−	11.2482i	0.363412	−	0.363412i
$959$	55.5855			1.79495
$960$	−0.417606	−	3.85040i	−0.0134782	−	0.124271i
$961$	−3.37631			−0.108913
$962$	10.1335	−	10.1335i	0.326718	−	0.326718i
$963$	−38.3162	+	12.8609i	−1.23472	+	0.414435i
$964$		−	23.8969i		−	0.769667i
$965$	−2.11762	+	4.42236i	−0.0681687	+	0.142361i
$966$	2.79989	+	4.51979i	0.0900851	+	0.145422i
$967$	29.6833	+	29.6833i	0.954550	+	0.954550i	0.999011	−	0.0444613i	$-0.0141571\pi$
$967$	29.6833	+	29.6833i	0.954550	+	0.954550i	−0.0444613	+	0.999011i	$0.514157\pi$
$968$	−11.5489	−	11.5489i	−0.371195	−	0.371195i
$969$	1.70713	+	2.75577i	0.0548409	+	0.0885280i
$970$	39.3211	−	13.8570i	1.26252	−	0.444922i
$971$			0.190623i			0.00611738i	0.999995	+	0.00305869i	$0.000973613\pi$
$971$			0.190623i			0.00611738i	−0.999995	+	0.00305869i	$0.999026\pi$
$972$	−14.2534	+	6.31201i	−0.457177	+	0.202458i
$973$	−25.9581	+	25.9581i	−0.832178	+	0.832178i
$974$	−25.2417			−0.808797
$975$	−10.5780	+	30.0425i	−0.338766	+	0.962128i
$976$	1.40994			0.0451312
$977$	−41.7362	+	41.7362i	−1.33526	+	1.33526i	−0.434670	+	0.900590i	$0.643135\pi$
$977$	−41.7362	+	41.7362i	−1.33526	+	1.33526i	−0.900590	+	0.434670i	$0.856865\pi$
$978$	2.12283	−	9.03453i	0.0678806	−	0.288892i
$979$			18.4865i			0.590830i
$980$	5.10918	−	1.80051i	0.163207	−	0.0575151i
$981$	−10.9616	+	22.0379i	−0.349977	+	0.703616i
$982$	8.84932	+	8.84932i	0.282393	+	0.282393i
$983$	−38.1690	−	38.1690i	−1.21740	−	1.21740i	−0.968538	−	0.248865i	$-0.919943\pi$
$983$	−38.1690	−	38.1690i	−1.21740	−	1.21740i	−0.248865	−	0.968538i	$-0.580057\pi$
$984$	−10.2568	+	6.35385i	−0.326976	+	0.202553i
$985$	−21.9668	+	45.8747i	−0.699922	+	1.46169i
$986$			1.07242i			0.0341527i
$987$	44.3259	+	10.4152i	1.41091	+	0.331519i
$988$	−7.74879	+	7.74879i	−0.246522	+	0.246522i
$989$	−10.3534			−0.329217
$990$	−21.5759	−	27.6486i	−0.685728	−	0.878730i
$991$	14.4306			0.458402			0.229201	−	0.973379i	$-0.426389\pi$
$991$	14.4306			0.458402			0.229201	+	0.973379i	$0.426389\pi$
$992$	−3.71643	+	3.71643i	−0.117997	+	0.117997i
$993$	55.8559	+	13.1244i	1.77253	+	0.416490i
$994$			14.1636i			0.449243i
$995$	−6.67027	−	18.9278i	−0.211462	−	0.600050i
$996$	19.5378	−	12.1032i	0.619078	−	0.383503i
$997$	44.1045	+	44.1045i	1.39680	+	1.39680i	0.809011	+	0.587793i	$0.200003\pi$
$997$	44.1045	+	44.1045i	1.39680	+	1.39680i	0.587793	+	0.809011i	$0.299997\pi$
$998$	18.6538	+	18.6538i	0.590474	+	0.590474i
$999$	1.88137	+	20.1600i	0.0595238	+	0.637835i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.i.f.47.1	✓	32
3.2	odd	2	inner	690.2.i.f.47.12	yes	32
5.3	odd	4	inner	690.2.i.f.323.12	yes	32
15.8	even	4	inner	690.2.i.f.323.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.i.f.47.1	✓	32	1.1	even	1	trivial
690.2.i.f.47.12	yes	32	3.2	odd	2	inner
690.2.i.f.323.1	yes	32	15.8	even	4	inner
690.2.i.f.323.12	yes	32	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.68613 - 0.396187i) q^{3} -1.00000i q^{4} +(2.10894 - 0.743206i) q^{5} +(1.47242 - 0.912127i) q^{6} +(-2.17056 - 2.17056i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.68607 + 1.33605i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.68613 - 0.396187i) q^{3} -1.00000i q^{4} +(2.10894 - 0.743206i) q^{5} +(1.47242 - 0.912127i) q^{6} +(-2.17056 - 2.17056i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.68607 + 1.33605i) q^{9} +(-0.965722 + 2.01677i) q^{10} +5.22806i q^{11} +(-0.396187 + 1.68613i) q^{12} +(2.60057 - 2.60057i) q^{13} +3.06963 q^{14} +(-3.85040 + 0.417606i) q^{15} -1.00000 q^{16} +(0.444150 - 0.444150i) q^{17} +(-2.84407 + 0.954611i) q^{18} -2.97966i q^{19} +(-0.743206 - 2.10894i) q^{20} +(2.79989 + 4.51979i) q^{21} +(-3.69679 - 3.69679i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(-0.912127 - 1.47242i) q^{24} +(3.89529 - 3.13476i) q^{25} +3.67776i q^{26} +(-3.99974 - 3.31694i) q^{27} +(-2.17056 + 2.17056i) q^{28} +1.70734 q^{29} +(2.42735 - 3.01794i) q^{30} -5.25582 q^{31} +(0.707107 - 0.707107i) q^{32} +(2.07129 - 8.81518i) q^{33} +0.628123i q^{34} +(-6.19075 - 2.96441i) q^{35} +(1.33605 - 2.68607i) q^{36} +(-2.75535 - 2.75535i) q^{37} +(2.10693 + 2.10693i) q^{38} +(-5.41521 + 3.35458i) q^{39} +(2.01677 + 0.965722i) q^{40} -6.96597i q^{41} +(-5.17579 - 1.21615i) q^{42} +(7.32093 - 7.32093i) q^{43} +5.22806 q^{44} +(6.65773 + 0.821342i) q^{45} +1.00000 q^{46} +(6.05572 - 6.05572i) q^{47} +(1.68613 + 0.396187i) q^{48} +2.42262i q^{49} +(-0.537774 + 4.97100i) q^{50} +(-0.924861 + 0.572928i) q^{51} +(-2.60057 - 2.60057i) q^{52} +(0.302305 + 0.302305i) q^{53} +(5.17367 - 0.482816i) q^{54} +(3.88553 + 11.0257i) q^{55} -3.06963i q^{56} +(-1.18050 + 5.02409i) q^{57} +(-1.20727 + 1.20727i) q^{58} +11.1739 q^{59} +(0.417606 + 3.85040i) q^{60} -1.40994 q^{61} +(3.71643 - 3.71643i) q^{62} +(-2.93030 - 8.73023i) q^{63} +1.00000i q^{64} +(3.55169 - 7.41721i) q^{65} +(4.76865 + 7.69790i) q^{66} +(3.64409 + 3.64409i) q^{67} +(-0.444150 - 0.444150i) q^{68} +(0.912127 + 1.47242i) q^{69} +(6.47368 - 2.28137i) q^{70} +4.61412i q^{71} +(0.954611 + 2.84407i) q^{72} +(0.698447 - 0.698447i) q^{73} +3.89665 q^{74} +(-7.80992 + 3.74235i) q^{75} -2.97966 q^{76} +(11.3478 - 11.3478i) q^{77} +(1.45708 - 6.20118i) q^{78} -11.7332i q^{79} +(-2.10894 + 0.743206i) q^{80} +(5.42996 + 7.17743i) q^{81} +(4.92569 + 4.92569i) q^{82} +(-9.38271 - 9.38271i) q^{83} +(4.51979 - 2.79989i) q^{84} +(0.606592 - 1.26678i) q^{85} +10.3534i q^{86} +(-2.87879 - 0.676425i) q^{87} +(-3.69679 + 3.69679i) q^{88} +3.53601 q^{89} +(-5.28850 + 4.12695i) q^{90} -11.2894 q^{91} +(-0.707107 + 0.707107i) q^{92} +(8.86201 + 2.08229i) q^{93} +8.56408i q^{94} +(-2.21450 - 6.28393i) q^{95} +(-1.47242 + 0.912127i) q^{96} +(-13.1840 - 13.1840i) q^{97} +(-1.71305 - 1.71305i) q^{98} +(-6.98493 + 14.0429i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7}+O(q^{10}) \) 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7	\( 32 q + 4 q^{3} + 12 q^{6} + 8 q^{7} - 4 q^{12} - 12 q^{15} - 32 q^{16} + 8 q^{18} - 40 q^{22} + 32 q^{25} + 4 q^{27} + 8 q^{28} - 20 q^{30} + 8 q^{31} + 8 q^{33} + 20 q^{36} - 16 q^{37} + 8 q^{40} - 8 q^{42} - 80 q^{43} - 4 q^{45} + 32 q^{46} - 4 q^{48} + 36 q^{51} + 12 q^{57} - 16 q^{58} - 4 q^{60} + 8 q^{61} + 44 q^{63} + 52 q^{66} + 64 q^{67} + 64 q^{70} - 8 q^{72} - 56 q^{73} - 68 q^{75} - 8 q^{76} + 60 q^{78} - 44 q^{81} - 48 q^{85} - 60 q^{87} - 40 q^{88} - 64 q^{90} + 40 q^{91} + 92 q^{93} - 12 q^{96} - 40 q^{97}+O(q^{100}) \) 32 * q + 4 * q^3 + 12 * q^6 + 8 * q^7 - 4 * q^12 - 12 * q^15 - 32 * q^16 + 8 * q^18 - 40 * q^22 + 32 * q^25 + 4 * q^27 + 8 * q^28 - 20 * q^30 + 8 * q^31 + 8 * q^33 + 20 * q^36 - 16 * q^37 + 8 * q^40 - 8 * q^42 - 80 * q^43 - 4 * q^45 + 32 * q^46 - 4 * q^48 + 36 * q^51 + 12 * q^57 - 16 * q^58 - 4 * q^60 + 8 * q^61 + 44 * q^63 + 52 * q^66 + 64 * q^67 + 64 * q^70 - 8 * q^72 - 56 * q^73 - 68 * q^75 - 8 * q^76 + 60 * q^78 - 44 * q^81 - 48 * q^85 - 60 * q^87 - 40 * q^88 - 64 * q^90 + 40 * q^91 + 92 * q^93 - 12 * q^96 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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