LMFDB - Embedded newform 690.2.i.f.47.12

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			47.12
Character	$\chi$	$=$	690.47
Dual form			690.2.i.f.323.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.396187 + 1.68613i) q^{3} -1.00000i q^{4} +(-2.10894 + 0.743206i) q^{5} +(1.47242 + 0.912127i) q^{6} +(-2.17056 - 2.17056i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.68607 + 1.33605i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(0.396187 + 1.68613i) 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} +(1.68613 - 0.396187i) q^{12} +(2.60057 - 2.60057i) q^{13} -3.06963 q^{14} +(-2.08868 - 3.26151i) q^{15} -1.00000 q^{16} +(-0.444150 + 0.444150i) q^{17} +(-0.954611 + 2.84407i) 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} +(-3.31694 - 3.99974i) q^{27} +(-2.17056 + 2.17056i) q^{28} -1.70734 q^{29} +(-3.78315 - 0.829313i) q^{30} -5.25582 q^{31} +(-0.707107 + 0.707107i) q^{32} +(8.81518 - 2.07129i) 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} +(-1.21615 - 5.17579i) q^{42} +(7.32093 - 7.32093i) q^{43} -5.22806 q^{44} +(4.67181 - 4.81395i) q^{45} +1.00000 q^{46} +(-6.05572 + 6.05572i) q^{47} +(-0.396187 - 1.68613i) 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} +(5.02409 - 1.18050i) q^{57} +(-1.20727 + 1.20727i) q^{58} -11.1739 q^{59} +(-3.26151 + 2.08868i) q^{60} -1.40994 q^{61} +(-3.71643 + 3.71643i) q^{62} +(8.73023 + 2.93030i) 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} +(2.84407 + 0.954611i) q^{72} +(0.698447 - 0.698447i) q^{73} -3.89665 q^{74} +(6.82888 + 5.32601i) q^{75} -2.97966 q^{76} +(-11.3478 + 11.3478i) q^{77} +(6.20118 - 1.45708i) 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} +(-0.676425 - 2.87879i) q^{87} +(-3.69679 + 3.69679i) q^{88} -3.53601 q^{89} +(-0.100507 - 6.70745i) q^{90} -11.2894 q^{91} +(0.707107 - 0.707107i) q^{92} +(-2.08229 - 8.86201i) 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
$3$	0.396187	+	1.68613i	0.228739	+	0.973488i
$3$	0.396187	+	1.68613i	0.228739	+	0.973488i
$4$		−	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	$-0.711034\pi$
$11$		−	5.22806i		−	1.57632i	0.615472	−	0.788159i	$-0.288966\pi$
$12$	1.68613	−	0.396187i	0.486744	−	0.114369i
$13$	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
$15$	−2.08868	−	3.26151i	−0.539295	−	0.842117i
$16$	−1.00000			−0.250000
$17$	−0.444150	+	0.444150i	−0.107722	+	0.107722i	−0.758914	−	0.651191i	$-0.774270\pi$
$17$	−0.444150	+	0.444150i	−0.107722	+	0.107722i	0.651191	+	0.758914i	$0.274270\pi$
$18$	−0.954611	+	2.84407i	−0.225004	+	0.670353i
$19$		−	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
$27$	−3.31694	−	3.99974i	−0.638345	−	0.769751i
$28$	−2.17056	+	2.17056i	−0.410196	+	0.410196i
$29$	−1.70734			−0.317044			−0.158522	−	0.987355i	$-0.550673\pi$
$29$	−1.70734			−0.317044			−0.158522	+	0.987355i	$0.550673\pi$
$30$	−3.78315	−	0.829313i	−0.690706	−	0.151411i
$31$	−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
$33$	8.81518	−	2.07129i	1.53453	−	0.360565i
$34$			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	$0.183072\pi$
$41$			6.96597i			1.08790i	−0.839117	+	0.543951i	$0.816928\pi$
$42$	−1.21615	−	5.17579i	−0.187656	−	0.798642i
$43$	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
$45$	4.67181	−	4.81395i	0.696433	−	0.717622i
$46$	1.00000			0.147442
$47$	−6.05572	+	6.05572i	−0.883318	+	0.883318i	−0.993870	−	0.110553i	$-0.964738\pi$
$47$	−6.05572	+	6.05572i	−0.883318	+	0.883318i	0.110553	+	0.993870i	$0.464738\pi$
$48$	−0.396187	−	1.68613i	−0.0571847	−	0.243372i
$49$			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	0.686040	−	0.727564i	$-0.259348\pi$
$53$	−0.302305	−	0.302305i	−0.0415247	−	0.0415247i	−0.727564	+	0.686040i	$0.759348\pi$
$54$	−5.17367	−	0.482816i	−0.704048	−	0.0657029i
$55$	3.88553	+	11.0257i	0.523924	+	1.48670i
$56$			3.06963i			0.410196i
$57$	5.02409	−	1.18050i	0.665457	−	0.156361i
$58$	−1.20727	+	1.20727i	−0.158522	+	0.158522i
$59$	−11.1739			−1.45472			−0.727359	−	0.686257i	$-0.759253\pi$
$59$	−11.1739			−1.45472			−0.727359	+	0.686257i	$0.759253\pi$
$60$	−3.26151	+	2.08868i	−0.421059	+	0.269647i
$61$	−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
$63$	8.73023	+	2.93030i	1.09991	+	0.369183i
$64$			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	$-0.911720\pi$
$71$		−	4.61412i		−	0.547596i	0.961787	−	0.273798i	$-0.0882799\pi$
$72$	2.84407	+	0.954611i	0.335177	+	0.112502i
$73$	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
$75$	6.82888	+	5.32601i	0.788531	+	0.614995i
$76$	−2.97966			−0.341790
$77$	−11.3478	+	11.3478i	−1.29320	+	1.29320i
$78$	6.20118	−	1.45708i	0.702145	−	0.164982i
$79$		−	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	$0.00966113\pi$
$83$	9.38271	+	9.38271i	1.02989	+	1.02989i	0.0303467	+	0.999539i	$0.490339\pi$
$84$	−4.51979	−	2.79989i	−0.493149	−	0.305493i
$85$	0.606592	−	1.26678i	0.0657942	−	0.137402i
$86$		−	10.3534i		−	1.11643i
$87$	−0.676425	−	2.87879i	−0.0725204	−	0.308639i
$88$	−3.69679	+	3.69679i	−0.394080	+	0.394080i
$89$	−3.53601			−0.374816			−0.187408	−	0.982282i	$-0.560009\pi$
$89$	−3.53601			−0.374816			−0.187408	+	0.982282i	$0.560009\pi$
$90$	−0.100507	−	6.70745i	−0.0105944	−	0.707027i
$91$	−11.2894			−1.18345
$92$	0.707107	−	0.707107i	0.0737210	−	0.0737210i
$93$	−2.08229	−	8.86201i	−0.215924	−	0.918947i
$94$			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	$0.182070\pi$
$101$			10.8801i			1.08261i	−0.840825	+	0.541306i	$0.817930\pi$
$102$	−1.05910	+	0.248854i	−0.104866	+	0.0246402i
$103$	−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
$105$	−2.54568	+	11.6129i	−0.248433	+	1.13330i
$106$	−0.427523			−0.0415247
$107$	9.52639	−	9.52639i	0.920950	−	0.920950i	−0.0761462	−	0.997097i	$-0.524262\pi$
$107$	9.52639	−	9.52639i	0.920950	−	0.920950i	0.997097	+	0.0761462i	$0.0242616\pi$
$108$	−3.99974	+	3.31694i	−0.384875	+	0.319172i
$109$			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	0.728094	−	0.685477i	$-0.240406\pi$
$113$	0.453030	+	0.453030i	0.0426174	+	0.0426174i	−0.685477	+	0.728094i	$0.740406\pi$
$114$	2.71783	−	4.38731i	0.254548	−	0.410909i
$115$	−2.01677	−	0.965722i	−0.188065	−	0.0900541i
$116$			1.70734i			0.158522i
$117$	−3.51083	+	10.4598i	−0.324576	+	0.967008i
$118$	−7.90115	+	7.90115i	−0.727359	+	0.727359i
$119$	1.92810			0.176749
$120$	−0.829313	+	3.78315i	−0.0757056	+	0.345353i
$121$	−16.3326			−1.48478
$122$	−0.996981	+	0.996981i	−0.0902625	+	0.0902625i
$123$	−11.7455	+	2.75983i	−1.05906	+	0.248845i
$124$			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	$-0.955484\pi$
$131$		−	3.19088i		−	0.278788i	0.990237	−	0.139394i	$-0.0445155\pi$
$132$	−2.07129	−	8.81518i	−0.180283	−	0.767263i
$133$	−6.46751	+	6.46751i	−0.560804	+	0.560804i
$134$	5.15352			0.445196
$135$	9.96787	+	5.97006i	0.857897	+	0.513821i
$136$	0.628123			0.0538611
$137$	12.8044	−	12.8044i	1.09396	−	1.09396i	0.0988556	−	0.995102i	$-0.468482\pi$
$137$	12.8044	−	12.8044i	1.09396	−	1.09396i	0.995102	−	0.0988556i	$-0.0315182\pi$
$138$	0.396187	+	1.68613i	0.0337257	+	0.143533i
$139$		−	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
$147$	−4.08486	+	0.959812i	−0.336913	+	0.0791640i
$148$	−2.75535	+	2.75535i	−0.226488	+	0.226488i
$149$	−17.1561			−1.40548			−0.702740	−	0.711447i	$-0.748040\pi$
$149$	−17.1561			−1.40548			−0.702740	+	0.711447i	$0.748040\pi$
$150$	8.59481	−	1.06269i	0.701763	−	0.0867682i
$151$	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
$153$	0.599613	−	1.78642i	0.0484759	−	0.144424i
$154$			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
$162$	−1.23565	−	8.91477i	−0.0970821	−	0.700411i
$163$	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
$165$	−17.0513	+	10.9197i	−1.32744	+	0.850100i
$166$	13.2692			1.02989
$167$	11.5545	−	11.5545i	0.894117	−	0.894117i	−0.100791	−	0.994908i	$-0.532137\pi$
$167$	11.5545	−	11.5545i	0.894117	−	0.894117i	0.994908	+	0.100791i	$0.0321372\pi$
$168$	−5.17579	+	1.21615i	−0.399321	+	0.0938279i
$169$		−	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	0.911977	−	0.410242i	$-0.134556\pi$
$173$	6.59928	+	6.59928i	0.501734	+	0.501734i	−0.410242	+	0.911977i	$0.634556\pi$
$174$	−2.51392	−	1.55731i	−0.190580	−	0.118059i
$175$	−15.2591	−	1.65077i	−1.15348	−	0.124786i
$176$			5.22806i			0.394080i
$177$	−4.42696	−	18.8407i	−0.332751	−	1.41615i
$178$	−2.50034	+	2.50034i	−0.187408	+	0.187408i
$179$	18.4232			1.37702			0.688508	−	0.725229i	$-0.258266\pi$
$179$	18.4232			1.37702			0.688508	+	0.725229i	$0.258266\pi$
$180$	−4.81395	−	4.67181i	−0.358811	−	0.348217i
$181$	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
$183$	−0.558602	−	2.37735i	−0.0412931	−	0.175739i
$184$		−	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	$0.0368667\pi$
$191$			3.19418i			0.231123i	−0.993300	+	0.115561i	$0.963133\pi$
$192$	−1.68613	+	0.396187i	−0.121686	+	0.0285924i
$193$	−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
$195$	−13.9135	−	3.05001i	−0.996368	−	0.218416i
$196$	2.42262			0.173044
$197$	16.0842	−	16.0842i	1.14595	−	1.14595i	0.158614	−	0.987341i	$-0.449298\pi$
$197$	16.0842	−	16.0842i	1.14595	−	1.14595i	0.987341	−	0.158614i	$-0.0507025\pi$
$198$	14.8689	+	4.99076i	1.05669	+	0.354678i
$199$		−	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
$207$	−2.84407	−	0.954611i	−0.197676	−	0.0663501i
$208$	−2.60057	+	2.60057i	−0.180317	+	0.180317i
$209$	−15.5778			−1.07754
$210$	6.41147	+	10.0116i	0.442434	+	0.690867i
$211$	−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
$213$	7.78001	−	1.82806i	0.533078	−	0.125256i
$214$		−	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
$222$	−1.54381	−	6.57027i	−0.103613	−	0.440967i
$223$	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
$225$	−6.27483	+	13.6245i	−0.418322	+	0.908299i
$226$	0.640680			0.0426174
$227$	9.96258	−	9.96258i	0.661239	−	0.661239i	−0.294433	−	0.955672i	$-0.595131\pi$
$227$	9.96258	−	9.96258i	0.661239	−	0.661239i	0.955672	+	0.294433i	$0.0951307\pi$
$228$	−1.18050	−	5.02409i	−0.0781806	−	0.332728i
$229$			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	0.656217	−	0.754572i	$-0.272156\pi$
$233$	−1.50132	−	1.50132i	−0.0983549	−	0.0983549i	−0.754572	+	0.656217i	$0.772156\pi$
$234$	4.91366	+	9.87872i	0.321216	+	0.645792i
$235$	8.27052	−	17.2718i	0.539509	−	1.12669i
$236$			11.1739i			0.727359i
$237$	19.7838	−	4.64856i	1.28509	−	0.301956i
$238$	1.36338	−	1.36338i	0.0883745	−	0.0883745i
$239$	−24.3097			−1.57246			−0.786232	−	0.617932i	$-0.787971\pi$
$239$	−24.3097			−1.57246			−0.786232	+	0.617932i	$0.787971\pi$
$240$	2.08868	+	3.26151i	0.134824	+	0.210529i
$241$	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
$243$	14.2534	+	6.31201i	0.914354	+	0.404915i
$244$			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	$0.251411\pi$
$251$			22.5045i			1.42047i	−0.703965	+	0.710234i	$0.748589\pi$
$252$	2.93030	−	8.73023i	0.184592	−	0.549953i
$253$	3.69679	−	3.69679i	0.232415	−	0.232415i
$254$	18.4845			1.15982
$255$	2.37628	+	0.520910i	0.148809	+	0.0326207i
$256$	1.00000			0.0625000
$257$	17.0064	−	17.0064i	1.06083	−	1.06083i	0.0628062	−	0.998026i	$-0.479995\pi$
$257$	17.0064	−	17.0064i	1.06083	−	1.06083i	0.998026	−	0.0628062i	$-0.0200050\pi$
$258$	17.4571	−	4.10187i	1.08683	−	0.255371i
$259$			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	$-0.964458\pi$
$263$	−17.9233	−	17.9233i	−1.10520	−	1.10520i	−0.111428	−	0.993773i	$-0.535542\pi$
$264$	−7.69790	−	4.76865i	−0.473773	−	0.293490i
$265$	0.862218	+	0.412869i	0.0529656	+	0.0253623i
$266$			9.14644i			0.560804i
$267$	−1.40092	−	5.96217i	−0.0857350	−	0.364879i
$268$	3.64409	−	3.64409i	0.222598	−	0.222598i
$269$	−17.9945			−1.09714			−0.548571	−	0.836104i	$-0.684828\pi$
$269$	−17.9945			−1.09714			−0.548571	+	0.836104i	$0.684828\pi$
$270$	11.2698	−	2.82688i	0.685859	−	0.172038i
$271$	−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
$273$	−4.47270	−	19.0353i	−0.270700	−	1.15207i
$274$		−	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	$-0.841672\pi$
$281$		−	15.9968i		−	0.954291i	0.878824	−	0.477145i	$-0.158328\pi$
$282$	−14.4402	+	3.39298i	−0.859899	+	0.202049i
$283$	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
$285$	−9.71816	+	6.22355i	−0.575654	+	0.368651i
$286$	−19.2275			−1.13695
$287$	15.1200	−	15.1200i	0.892507	−	0.892507i
$288$	0.954611	−	2.84407i	0.0562510	−	0.167588i
$289$			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	0.816284	−	0.577651i	$-0.196031\pi$
$293$	4.08472	+	4.08472i	0.238632	+	0.238632i	−0.577651	+	0.816284i	$0.696031\pi$
$294$	−2.20974	+	3.56712i	−0.128875	+	0.208039i
$295$	23.5651	−	8.30452i	1.37202	−	0.483508i
$296$			3.89665i			0.226488i
$297$	−20.9109	+	17.3411i	−1.21337	+	1.00623i
$298$	−12.1312	+	12.1312i	−0.702740	+	0.702740i
$299$	3.67776			0.212690
$300$	5.32601	−	6.82888i	0.307497	−	0.394266i
$301$	−31.7810			−1.83182
$302$	12.0014	−	12.0014i	0.690603	−	0.690603i
$303$	−18.3453	+	4.31057i	−1.05391	+	0.247636i
$304$			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	$-0.808102\pi$
$311$		−	19.9984i		−	1.13401i	0.823715	−	0.567004i	$-0.191898\pi$
$312$	−1.45708	−	6.20118i	−0.0824910	−	0.351073i
$313$	−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
$315$	−20.5894	+	0.308520i	−1.16008	+	0.0173831i
$316$	−11.7332			−0.660046
$317$	−17.0015	+	17.0015i	−0.954897	+	0.954897i	−0.999026	−	0.0441291i	$-0.985949\pi$
$317$	−17.0015	+	17.0015i	−0.954897	+	0.954897i	0.0441291	+	0.999026i	$0.485949\pi$
$318$	−0.169379	−	0.720860i	−0.00949832	−	0.0404238i
$319$			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
$327$	−13.8339	+	3.25052i	−0.765015	+	0.179754i
$328$	4.92569	−	4.92569i	0.271975	−	0.271975i
$329$	26.2886			1.44933
$330$	−4.33569	+	19.7785i	−0.238672	+	1.08877i
$331$	−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
$333$	11.0823	+	3.71979i	0.607309	+	0.203843i
$334$		−	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
$342$	8.47434	+	2.84441i	0.458240	+	0.153808i
$343$	−9.93545	+	9.93545i	−0.536464	+	0.536464i
$344$	−10.3534			−0.558215
$345$	0.829313	−	3.78315i	0.0446487	−	0.203678i
$346$	9.33280			0.501734
$347$	−15.1025	+	15.1025i	−0.810743	+	0.810743i	−0.984745	−	0.174003i	$-0.944330\pi$
$347$	−15.1025	+	15.1025i	−0.810743	+	0.810743i	0.174003	+	0.984745i	$0.444330\pi$
$348$	−2.87879	+	0.676425i	−0.154319	+	0.0362602i
$349$			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	0.102056	−	0.994779i	$-0.467458\pi$
$353$	−16.7727	−	16.7727i	−0.892723	−	0.892723i	−0.994779	+	0.102056i	$0.967458\pi$
$354$	−16.4527	−	10.1920i	−0.874451	−	0.541700i
$355$	3.42925	+	9.73092i	0.182005	+	0.516464i
$356$			3.53601i			0.187408i
$357$	0.763890	+	3.25103i	0.0404294	+	0.172063i
$358$	13.0272	−	13.0272i	0.688508	−	0.688508i
$359$	−3.97799			−0.209950			−0.104975	−	0.994475i	$-0.533476\pi$
$359$	−3.97799			−0.209950			−0.104975	+	0.994475i	$0.533476\pi$
$360$	−6.70745	+	0.100507i	−0.353514	+	0.00529720i
$361$	10.1217			0.532719
$362$	3.42922	−	3.42922i	0.180236	−	0.180236i
$363$	−6.47076	−	27.5388i	−0.339627	−	1.44541i
$364$			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
$372$	−8.86201	+	2.08229i	−0.459474	+	0.107962i
$373$	−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
$375$	−18.3601	−	6.15699i	−0.948109	−	0.317946i
$376$	8.56408			0.441659
$377$	−4.44004	+	4.44004i	−0.228674	+	0.228674i
$378$	10.1818	+	12.2777i	0.523693	+	0.631498i
$379$		−	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	$-0.945303\pi$
$383$	−22.6285	−	22.6285i	−1.15626	−	1.15626i	−0.170991	−	0.985273i	$-0.554697\pi$
$384$	−0.912127	+	1.47242i	−0.0465468	+	0.0751392i
$385$	15.4981	−	32.3656i	0.789856	−	1.64950i
$386$			2.19279i			0.111610i
$387$	−9.88343	+	29.4456i	−0.502403	+	1.49681i
$388$	−13.1840	+	13.1840i	−0.669314	+	0.669314i
$389$	−28.6741			−1.45384			−0.726918	−	0.686724i	$-0.759048\pi$
$389$	−28.6741			−1.45384			−0.726918	+	0.686724i	$0.759048\pi$
$390$	−11.9950	+	7.68166i	−0.607392	+	0.388976i
$391$	−0.628123			−0.0317655
$392$	1.71305	−	1.71305i	0.0865222	−	0.0865222i
$393$	5.38024	−	1.26419i	0.271397	−	0.0637697i
$394$		−	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	$-0.940560\pi$
$401$		−	7.43533i		−	0.371303i	0.982616	−	0.185651i	$-0.0594395\pi$
$402$	2.04176	+	8.68950i	0.101834	+	0.433393i
$403$	−13.6681	+	13.6681i	−0.680858	+	0.680858i
$404$	10.8801			0.541306
$405$	−6.11716	+	19.1724i	−0.303964	+	0.952683i
$406$	5.24089			0.260101
$407$	−14.4051	+	14.4051i	−0.714036	+	0.714036i
$408$	0.248854	+	1.05910i	0.0123201	+	0.0524331i
$409$		−	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
$417$	20.1648	−	4.73808i	0.987472	−	0.232025i
$418$	−11.0152	+	11.0152i	−0.538770	+	0.538770i
$419$	4.96433			0.242523			0.121262	−	0.992621i	$-0.461306\pi$
$419$	4.96433			0.242523			0.121262	+	0.992621i	$0.461306\pi$
$420$	11.6129	+	2.54568i	0.566650	+	0.124217i
$421$	−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
$423$	8.17537	−	24.3568i	0.397500	−	1.18427i
$424$			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	$-0.762587\pi$
$431$		−	28.1762i		−	1.35720i	0.734508	−	0.678600i	$-0.237413\pi$
$432$	3.31694	+	3.99974i	0.159586	+	0.192438i
$433$	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
$435$	3.56608	+	5.56849i	0.170980	+	0.266988i
$436$	8.20451			0.392925
$437$	2.10693	−	2.10693i	0.100788	−	0.100788i
$438$	1.66548	−	0.391335i	0.0795798	−	0.0186987i
$439$			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	$0.0536919\pi$
$443$	24.2823	+	24.2823i	1.15369	+	1.15369i	0.167879	+	0.985808i	$0.446308\pi$
$444$	−5.73752	−	3.55425i	−0.272290	−	0.168677i
$445$	7.45724	−	2.62798i	0.353507	−	0.124578i
$446$		−	18.1511i		−	0.859480i
$447$	−6.79701	−	28.9274i	−0.321488	−	1.36822i
$448$	2.17056	−	2.17056i	0.102549	−	0.102549i
$449$	15.3176			0.722883			0.361442	−	0.932395i	$-0.382285\pi$
$449$	15.3176			0.722883			0.361442	+	0.932395i	$0.382285\pi$
$450$	5.19699	+	14.0709i	0.244988	+	0.663310i
$451$	36.4185			1.71488
$452$	0.453030	−	0.453030i	0.0213087	−	0.0213087i
$453$	6.72431	+	28.6179i	0.315936	+	1.34459i
$454$		−	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	$-0.754728\pi$
$461$		−	29.9101i		−	1.39305i	0.717531	−	0.696527i	$-0.245272\pi$
$462$	−27.0593	+	6.35809i	−1.25891	+	0.295805i
$463$	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
$465$	10.9777	+	17.1419i	0.509080	+	0.794937i
$466$	−2.12319			−0.0983549
$467$	27.4406	−	27.4406i	1.26980	−	1.26980i	0.323607	−	0.946192i	$-0.395105\pi$
$467$	27.4406	−	27.4406i	1.26980	−	1.26980i	0.946192	−	0.323607i	$-0.104895\pi$
$468$	10.4598	+	3.51083i	0.483504	+	0.162288i
$469$		−	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
$477$	1.21590	+	0.408118i	0.0556724	+	0.0186865i
$478$	−17.1895	+	17.1895i	−0.786232	+	0.786232i
$479$	15.9073			0.726824			0.363412	−	0.931629i	$-0.381612\pi$
$479$	15.9073			0.726824			0.363412	+	0.931629i	$0.381612\pi$
$480$	3.78315	+	0.829313i	0.172676	+	0.0378528i
$481$	−14.3309			−0.653435
$482$	16.8977	−	16.8977i	0.769667	−	0.769667i
$483$	5.17579	−	1.21615i	0.235507	−	0.0553367i
$484$			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	$0.0911283\pi$
$491$			12.5148i			0.564787i	−0.959299	+	0.282393i	$0.908872\pi$
$492$	2.75983	+	11.7455i	0.124423	+	0.529530i
$493$	0.758313	−	0.758313i	0.0341527	−	0.0341527i
$494$	−10.9584			−0.493044
$495$	−25.1676	−	24.4245i	−1.13120	−	1.09780i
$496$	5.25582			0.235993
$497$	−10.0152	+	10.0152i	−0.449243	+	0.449243i
$498$	5.25707	+	22.3735i	0.235575	+	1.00258i
$499$		−	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	0.463197	−	0.886255i	$-0.346702\pi$
$503$	−9.48821	−	9.48821i	−0.423059	−	0.423059i	−0.886255	+	0.463197i	$0.846702\pi$
$504$	−4.10117	−	8.24524i	−0.182681	−	0.367272i
$505$	−8.08618	−	22.9456i	−0.359830	−	1.02106i
$506$		−	5.22806i		−	0.232415i
$507$	0.886733	−	0.208354i	0.0393812	−	0.00925334i
$508$	13.0705	−	13.0705i	0.579911	−	0.579911i
$509$	14.3787			0.637323			0.318662	−	0.947869i	$-0.396767\pi$
$509$	14.3787			0.637323			0.318662	+	0.947869i	$0.396767\pi$
$510$	2.04863	−	1.31195i	0.0907147	−	0.0580940i
$511$	−3.03204			−0.134129
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−11.9179	+	9.88333i	−0.526186	+	0.436360i
$514$		−	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	$0.0894701\pi$
$521$			12.6632i			0.554784i	−0.960757	+	0.277392i	$0.910530\pi$
$522$	1.62984	−	4.85578i	0.0713363	−	0.212532i
$523$	−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
$525$	−3.26206	−	26.3829i	−0.142368	−	1.15144i
$526$	−25.3474			−1.10520
$527$	2.33437	−	2.33437i	0.101687	−	0.101687i
$528$	−8.81518	+	2.07129i	−0.383632	+	0.0901413i
$529$			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
$537$	7.29904	+	31.0639i	0.314977	+	1.34051i
$538$	−12.7240	+	12.7240i	−0.548571	+	0.548571i
$539$	12.6656			0.545546
$540$	5.97006	−	9.96787i	0.256911	−	0.428949i
$541$	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
$543$	1.92137	+	8.17714i	0.0824538	+	0.350915i
$544$		−	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
$552$	1.68613	−	0.396187i	0.0717665	−	0.0168629i
$553$	−25.4676	+	25.4676i	−1.08299	+	1.08299i
$554$	−1.40594			−0.0597327
$555$	−3.23155	+	14.7416i	−0.137171	+	0.625748i
$556$	−11.9592			−0.507183
$557$	−19.7073	+	19.7073i	−0.835026	+	0.835026i	−0.988199	−	0.153174i	$-0.951051\pi$
$557$	−19.7073	+	19.7073i	−0.835026	+	0.835026i	0.153174	+	0.988199i	$0.451051\pi$
$558$	5.01727	−	14.9479i	0.212398	−	0.632796i
$559$		−	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	0.822355	−	0.568975i	$-0.192660\pi$
$563$	6.01209	+	6.01209i	0.253379	+	0.253379i	−0.568975	+	0.822355i	$0.692660\pi$
$564$	−7.81153	+	12.6099i	−0.328925	+	0.530974i
$565$	−1.29211	−	0.618719i	−0.0543594	−	0.0260297i
$566$		−	30.1471i		−	1.26718i
$567$	−27.3650	+	3.79300i	−1.14922	+	0.159291i
$568$	−3.26268	+	3.26268i	−0.136899	+	0.136899i
$569$	−1.31647			−0.0551895			−0.0275947	−	0.999619i	$-0.508785\pi$
$569$	−1.31647			−0.0551895			−0.0275947	+	0.999619i	$0.508785\pi$
$570$	−2.47107	+	11.2725i	−0.103502	+	0.472153i
$571$	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
$573$	−5.38581	+	1.26549i	−0.224995	+	0.0528668i
$574$		−	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
$582$	−7.38688	−	31.4378i	−0.306196	−	1.30314i
$583$	−1.58046	+	1.58046i	−0.0654562	+	0.0654562i
$584$	−0.987754			−0.0408735
$585$	−0.369642	−	24.6684i	−0.0152828	−	1.01991i
$586$	5.77667			0.238632
$587$	−9.61314	+	9.61314i	−0.396777	+	0.396777i	−0.877095	−	0.480318i	$-0.840521\pi$
$587$	−9.61314	+	9.61314i	−0.396777	+	0.396777i	0.480318	+	0.877095i	$0.340521\pi$
$588$	0.959812	+	4.08486i	0.0395820	+	0.168457i
$589$			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	0.913826	−	0.406106i	$-0.133114\pi$
$593$	12.3638	+	12.3638i	0.507719	+	0.507719i	−0.406106	+	0.913826i	$0.633114\pi$
$594$	−2.52419	+	27.0483i	−0.103569	+	1.10980i
$595$	−4.06626	+	1.43298i	−0.166701	+	0.0587464i
$596$			17.1561i			0.702740i
$597$	15.1330	−	3.55578i	0.619353	−	0.145528i
$598$	2.60057	−	2.60057i	0.106345	−	0.106345i
$599$	48.6613			1.98825			0.994123	−	0.108255i	$-0.0345263\pi$
$599$	48.6613			1.98825			0.994123	+	0.108255i	$0.0345263\pi$
$600$	−1.06269	−	8.59481i	−0.0433841	−	0.350881i
$601$	−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
$603$	−14.6570	−	4.91961i	−0.596877	−	0.200342i
$604$		−	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
$612$	−1.78642	−	0.599613i	−0.0722119	−	0.0242379i
$613$	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
$615$	22.7196	−	14.5497i	0.916141	−	0.586700i
$616$	16.0482			0.646600
$617$	1.18781	−	1.18781i	0.0478194	−	0.0478194i	−0.682793	−	0.730612i	$-0.739235\pi$
$617$	1.18781	−	1.18781i	0.0478194	−	0.0478194i	0.730612	+	0.682793i	$0.239235\pi$
$618$	−6.07986	+	1.42857i	−0.244568	+	0.0574657i
$619$			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
$627$	−6.17173	−	26.2662i	−0.246475	−	1.04897i
$628$	11.7841	−	11.7841i	0.470237	−	0.470237i
$629$	2.44758			0.0975913
$630$	−14.3407	+	14.7771i	−0.571349	+	0.588732i
$631$	−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
$633$	−0.119351	−	0.507945i	−0.00474377	−	0.0201890i
$634$			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	$0.0490996\pi$
$641$			7.77971i			0.307280i	−0.988127	+	0.153640i	$0.950900\pi$
$642$	22.7161	−	5.33757i	0.896534	−	0.210657i
$643$	−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
$645$	−39.1683	−	8.58617i	−1.54225	−	0.338080i
$646$	1.87159			0.0736367
$647$	7.24949	−	7.24949i	0.285007	−	0.285007i	−0.550095	−	0.835102i	$-0.685409\pi$
$647$	7.24949	−	7.24949i	0.285007	−	0.285007i	0.835102	+	0.550095i	$0.185409\pi$
$648$	−8.91477	+	1.23565i	−0.350205	+	0.0485410i
$649$			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	0.967565	−	0.252621i	$-0.0812926\pi$
$653$	18.2696	+	18.2696i	0.714944	+	0.714944i	−0.252621	+	0.967565i	$0.581293\pi$
$654$	−7.48356	+	12.0805i	−0.292630	+	0.472385i
$655$	2.37148	+	6.72938i	0.0926615	+	0.262939i
$656$		−	6.96597i		−	0.271975i
$657$	−0.942921	+	2.80924i	−0.0367868	+	0.109599i
$658$	18.5888	−	18.5888i	0.724667	−	0.724667i
$659$	23.0114			0.896399			0.448199	−	0.893934i	$-0.352066\pi$
$659$	23.0114			0.896399			0.448199	+	0.893934i	$0.352066\pi$
$660$	10.9197	+	17.0513i	0.425050	+	0.663722i
$661$	−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
$663$	−3.89510	+	0.915226i	−0.151273	+	0.0355444i
$664$		−	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
$672$	1.21615	+	5.17579i	0.0469139	+	0.199661i
$673$	−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
$675$	−25.4587	−	5.18234i	−0.979904	−	0.199468i
$676$	−0.525898			−0.0202269
$677$	−8.73195	+	8.73195i	−0.335596	+	0.335596i	−0.854707	−	0.519111i	$-0.826263\pi$
$677$	−8.73195	+	8.73195i	−0.335596	+	0.335596i	0.519111	+	0.854707i	$0.326263\pi$
$678$	0.253829	+	1.08027i	0.00974826	+	0.0414876i
$679$			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	0.837519	−	0.546408i	$-0.184005\pi$
$683$	7.60796	+	7.60796i	0.291110	+	0.291110i	−0.546408	+	0.837519i	$0.684005\pi$
$684$	8.00357	−	3.98096i	0.306024	−	0.152216i
$685$	−17.4875	+	36.5202i	−0.668163	+	1.39536i
$686$			14.0509i			0.536464i
$687$	−29.7044	+	6.97959i	−1.13329	+	0.266288i
$688$	−7.32093	+	7.32093i	−0.279108	+	0.279108i
$689$	−1.57233			−0.0599009
$690$	−2.08868	−	3.26151i	−0.0795147	−	0.124163i
$691$	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
$693$	15.3198	−	45.6421i	0.581951	−	1.73380i
$694$			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	$0.114110\pi$
$701$			18.5789i			0.701715i	−0.936429	+	0.350858i	$0.885890\pi$
$702$	−14.7101	+	12.1989i	−0.555196	+	0.460417i
$703$	−8.21000	+	8.21000i	−0.309646	+	0.309646i
$704$	5.22806			0.197040
$705$	32.3992	+	7.10230i	1.22023	+	0.267488i
$706$	−23.7202			−0.892723
$707$	23.6159	−	23.6159i	0.888168	−	0.888168i
$708$	−18.8407	+	4.42696i	−0.708076	+	0.166375i
$709$		−	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
$717$	−9.63119	−	40.9893i	−0.359683	−	1.53077i
$718$	−2.81286	+	2.81286i	−0.104975	+	0.104975i
$719$	−20.2760			−0.756166			−0.378083	−	0.925772i	$-0.623417\pi$
$719$	−20.2760			−0.756166			−0.378083	+	0.925772i	$0.623417\pi$
$720$	−4.67181	+	4.81395i	−0.174108	+	0.179405i
$721$	11.0685			0.412212
$722$	7.15709	−	7.15709i	0.266359	−	0.266359i
$723$	9.46765	+	40.2933i	0.352106	+	1.49852i
$724$		−	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
$732$	−2.37735	+	0.558602i	−0.0878694	+	0.0206465i
$733$	−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
$735$	7.90140	−	5.06008i	0.291447	−	0.186644i
$736$	−1.00000			−0.0368605
$737$	19.0515	−	19.0515i	0.701771	−	0.701771i
$738$	−19.8117	−	6.64980i	−0.729278	−	0.244782i
$739$		−	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	0.395972	−	0.918263i	$-0.370408\pi$
$743$	−14.2366	−	14.2366i	−0.522291	−	0.522291i	−0.918263	+	0.395972i	$0.870408\pi$
$744$	−4.79398	+	7.73879i	−0.175756	+	0.283718i
$745$	36.1812	−	12.7505i	1.32558	−	0.467142i
$746$			5.35085i			0.195909i
$747$	−37.7384	−	12.6669i	−1.38077	−	0.463457i
$748$	2.32204	−	2.32204i	0.0849022	−	0.0849022i
$749$	−41.3551			−1.51108
$750$	−17.3362	+	8.62887i	−0.633027	+	0.315082i
$751$	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
$753$	−37.9454	+	8.91598i	−1.38281	+	0.324916i
$754$			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	$0.00896620\pi$
$761$			1.55390i			0.0563288i	−0.999603	+	0.0281644i	$0.991034\pi$
$762$	7.32333	+	31.1673i	0.265296	+	1.12907i
$763$	17.8083	−	17.8083i	0.644705	−	0.644705i
$764$	3.19418			0.115561
$765$	0.0631309	+	4.21310i	0.00228250	+	0.152325i
$766$	−32.0016			−1.15626
$767$	−29.0585	+	29.0585i	−1.04924	+	1.04924i
$768$	0.396187	+	1.68613i	0.0142962	+	0.0608430i
$769$		−	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	0.619239	−	0.785202i	$-0.287441\pi$
$773$	−4.61426	−	4.61426i	−0.165963	−	0.165963i	−0.785202	+	0.619239i	$0.787441\pi$
$774$	13.8326	+	27.8098i	0.497201	+	0.999604i
$775$	−20.4730	+	16.4758i	−0.735410	+	0.591827i
$776$			18.6449i			0.669314i
$777$	−20.1683	+	4.73891i	−0.723533	+	0.170007i
$778$	−20.2757	+	20.2757i	−0.726918	+	0.726918i
$779$	20.7562			0.743668
$780$	−3.05001	+	13.9135i	−0.109208	+	0.498184i
$781$	−24.1229			−0.863185
$782$	−0.444150	+	0.444150i	−0.0158828	+	0.0158828i
$783$	5.66313	+	6.82890i	0.202384	+	0.244045i
$784$		−	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
$792$	4.99076	−	14.8689i	0.177339	−	0.528345i
$793$	−3.66666	+	3.66666i	−0.130207	+	0.130207i
$794$	−5.88519			−0.208857
$795$	−0.354550	+	1.61739i	−0.0125746	+	0.0573627i
$796$	−8.97499			−0.318110
$797$	27.3624	−	27.3624i	0.969225	−	0.969225i	−0.0303157	−	0.999540i	$-0.509651\pi$
$797$	27.3624	−	27.3624i	0.969225	−	0.969225i	0.999540	+	0.0303157i	$0.00965125\pi$
$798$	−15.4221	+	3.62370i	−0.545936	+	0.128278i
$799$		−	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
$807$	−7.12918	−	30.3410i	−0.250959	−	1.06805i
$808$	7.69341	−	7.69341i	0.270653	−	0.270653i
$809$	−9.73699			−0.342334			−0.171167	−	0.985242i	$-0.554754\pi$
$809$	−9.73699			−0.342334			−0.171167	+	0.985242i	$0.554754\pi$
$810$	9.23144	+	17.8824i	0.324360	+	0.628324i
$811$	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
$813$	−5.55771	−	23.6530i	−0.194917	−	0.829547i
$814$			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	$-0.905808\pi$
$821$		−	16.7113i		−	0.583228i	0.956536	−	0.291614i	$-0.0941922\pi$
$822$	30.5328	−	7.17425i	1.06495	−	0.250231i
$823$	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
$825$	27.8447	−	35.7018i	0.969427	−	1.24298i
$826$	34.2998			1.19344
$827$	−5.54156	+	5.54156i	−0.192699	+	0.192699i	−0.796861	−	0.604162i	$-0.793508\pi$
$827$	−5.54156	+	5.54156i	−0.192699	+	0.192699i	0.604162	+	0.796861i	$0.293508\pi$
$828$	−0.954611	+	2.84407i	−0.0331750	+	0.0988382i
$829$		−	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
$837$	17.4332	+	21.0219i	0.602581	+	0.726625i
$838$	3.51031	−	3.51031i	0.121262	−	0.121262i
$839$	31.5440			1.08902			0.544510	−	0.838755i	$-0.316716\pi$
$839$	31.5440			1.08902			0.544510	+	0.838755i	$0.316716\pi$
$840$	10.0116	−	6.41147i	0.345433	−	0.221217i
$841$	−26.0850			−0.899483
$842$	−26.9817	+	26.9817i	−0.929851	+	0.929851i
$843$	26.9727	−	6.33774i	0.928990	−	0.218283i
$844$			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
$852$	−1.82806	−	7.78001i	−0.0626282	−	0.266539i
$853$	−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
$855$	−14.3439	−	13.9204i	−0.490552	−	0.476068i
$856$	−13.4723			−0.460475
$857$	−6.58621	+	6.58621i	−0.224981	+	0.224981i	−0.810592	−	0.585611i	$-0.800854\pi$
$857$	−6.58621	+	6.58621i	−0.224981	+	0.224981i	0.585611	+	0.810592i	$0.300854\pi$
$858$	−7.61770	−	32.4201i	−0.260064	−	1.10680i
$859$			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	0.305108	−	0.952318i	$-0.401307\pi$
$863$	−19.0130	−	19.0130i	−0.647209	−	0.647209i	−0.952318	+	0.305108i	$0.901307\pi$
$864$	5.17367	+	0.482816i	0.176012	+	0.0164257i
$865$	−18.8222	−	9.01289i	−0.639972	−	0.306447i
$866$		−	19.5925i		−	0.665781i
$867$	−27.9990	+	6.57887i	−0.950895	+	0.223430i
$868$	11.4081	−	11.4081i	0.387215	−	0.387215i
$869$	−61.3420			−2.08088
$870$	6.45911	+	1.41592i	0.218984	+	0.0480040i
$871$	18.9534			0.642211
$872$	5.80146	−	5.80146i	0.196462	−	0.196462i
$873$	53.0274	+	17.7987i	1.79471	+	0.602393i
$874$		−	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	$0.110268\pi$
$881$			20.1555i			0.679057i	−0.940596	+	0.339529i	$0.889732\pi$
$882$	−6.89010	−	2.31266i	−0.232002	−	0.0778714i
$883$	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
$885$	23.3387	+	36.4438i	0.784522	+	1.22504i
$886$	34.3404			1.15369
$887$	−30.6618	+	30.6618i	−1.02952	+	1.02952i	−0.0299723	+	0.999551i	$0.509542\pi$
$887$	−30.6618	+	30.6618i	−1.02952	+	1.02952i	−0.999551	+	0.0299723i	$0.990458\pi$
$888$	−6.57027	+	1.54381i	−0.220484	+	0.0518067i
$889$		−	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
$897$	1.45708	+	6.20118i	0.0486505	+	0.207051i
$898$	10.8312	−	10.8312i	0.361442	−	0.361442i
$899$	8.97346			0.299282
$900$	13.6245	+	6.27483i	0.454149	+	0.209161i
$901$	0.268537			0.00894627
$902$	25.7518	−	25.7518i	0.857440	−	0.857440i
$903$	−12.5912	−	53.5868i	−0.419009	−	1.78326i
$904$		−	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	$-0.860048\pi$
$911$		−	25.6942i		−	0.851287i	0.904891	−	0.425643i	$-0.139952\pi$
$912$	−5.02409	+	1.18050i	−0.166364	+	0.0390903i
$913$	49.0533	−	49.0533i	1.62343	−	1.62343i
$914$	1.10850			0.0366660
$915$	2.94492	+	4.59854i	0.0973561	+	0.152023i
$916$	17.6169			0.582079
$917$	−6.92598	+	6.92598i	−0.228716	+	0.228716i
$918$	2.51233	−	2.08344i	0.0829192	−	0.0687639i
$919$		−	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
$927$	3.44214	−	10.2551i	0.113055	−	0.336823i
$928$	1.20727	−	1.20727i	0.0396305	−	0.0396305i
$929$	19.2717			0.632283			0.316142	−	0.948712i	$-0.397613\pi$
$929$	19.2717			0.632283			0.316142	+	0.948712i	$0.397613\pi$
$930$	19.8836	+	4.35872i	0.652008	+	0.142928i
$931$	7.21858			0.236579
$932$	−1.50132	+	1.50132i	−0.0491774	+	0.0491774i
$933$	33.7200	−	7.92313i	1.10394	−	0.259392i
$934$		−	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	$-0.906771\pi$
$941$		−	17.7133i		−	0.577438i	0.957414	−	0.288719i	$-0.0932293\pi$
$942$	6.60255	+	28.0998i	0.215123	+	0.915539i
$943$	−4.92569	+	4.92569i	−0.160402	+	0.160402i
$944$	11.1739			0.363680
$945$	−8.67746	−	34.5942i	−0.282278	−	1.12535i
$946$	−54.1279			−1.75985
$947$	−16.1225	+	16.1225i	−0.523912	+	0.523912i	−0.918751	−	0.394838i	$-0.870801\pi$
$947$	−16.1225	+	16.1225i	−0.523912	+	0.523912i	0.394838	+	0.918751i	$0.370801\pi$
$948$	−4.64856	−	19.7838i	−0.150978	−	0.642547i
$949$		−	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	0.711722	−	0.702461i	$-0.247915\pi$
$953$	0.285911	+	0.285911i	0.00926156	+	0.00926156i	−0.702461	+	0.711722i	$0.747915\pi$
$954$	1.14836	−	0.571191i	0.0371795	−	0.0184930i
$955$	−2.37394	−	6.73635i	−0.0768188	−	0.217983i
$956$			24.3097i			0.786232i
$957$	−15.0505	+	3.53639i	−0.486513	+	0.114315i
$958$	11.2482	−	11.2482i	0.363412	−	0.363412i
$959$	−55.5855			−1.79495
$960$	3.26151	−	2.08868i	0.105265	−	0.0674119i
$961$	−3.37631			−0.108913
$962$	−10.1335	+	10.1335i	−0.326718	+	0.326718i
$963$	−12.8609	+	38.3162i	−0.414435	+	1.23472i
$964$		−	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	$-0.999026\pi$
$971$		−	0.190623i		−	0.00611738i	0.999995	−	0.00305869i	$-0.000973613\pi$
$972$	6.31201	−	14.2534i	0.202458	−	0.457177i
$973$	−25.9581	+	25.9581i	−0.832178	+	0.832178i
$974$	25.2417			0.808797
$975$	31.6096	−	3.90831i	1.01232	−	0.125166i
$976$	1.40994			0.0451312
$977$	41.7362	−	41.7362i	1.33526	−	1.33526i	0.434670	−	0.900590i	$-0.356865\pi$
$977$	41.7362	−	41.7362i	1.33526	−	1.33526i	0.900590	−	0.434670i	$-0.143135\pi$
$978$	9.03453	−	2.12283i	0.288892	−	0.0678806i
$979$			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	$0.0800574\pi$
$983$	38.1690	+	38.1690i	1.21740	+	1.21740i	0.248865	+	0.968538i	$0.419943\pi$
$984$	10.2568	+	6.35385i	0.326976	+	0.202553i
$985$	−21.9668	+	45.8747i	−0.699922	+	1.46169i
$986$		−	1.07242i		−	0.0341527i
$987$	10.4152	+	44.3259i	0.331519	+	1.41091i
$988$	−7.74879	+	7.74879i	−0.246522	+	0.246522i
$989$	10.3534			0.329217
$990$	−35.0669	+	0.525458i	−1.11450	+	0.0167001i
$991$	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
$993$	−13.1244	−	55.8559i	−0.416490	−	1.77253i
$994$			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.47.12	yes	32
3.2	odd	2	inner	690.2.i.f.47.1	✓	32
5.3	odd	4	inner	690.2.i.f.323.1	yes	32
15.8	even	4	inner	690.2.i.f.323.12	yes	32

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

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.396187 + 1.68613i) q^{3} -1.00000i q^{4} +(-2.10894 + 0.743206i) q^{5} +(1.47242 + 0.912127i) q^{6} +(-2.17056 - 2.17056i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.68607 + 1.33605i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.396187 + 1.68613i) 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} +(1.68613 - 0.396187i) q^{12} +(2.60057 - 2.60057i) q^{13} -3.06963 q^{14} +(-2.08868 - 3.26151i) q^{15} -1.00000 q^{16} +(-0.444150 + 0.444150i) q^{17} +(-0.954611 + 2.84407i) 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} +(-3.31694 - 3.99974i) q^{27} +(-2.17056 + 2.17056i) q^{28} -1.70734 q^{29} +(-3.78315 - 0.829313i) q^{30} -5.25582 q^{31} +(-0.707107 + 0.707107i) q^{32} +(8.81518 - 2.07129i) 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} +(-1.21615 - 5.17579i) q^{42} +(7.32093 - 7.32093i) q^{43} -5.22806 q^{44} +(4.67181 - 4.81395i) q^{45} +1.00000 q^{46} +(-6.05572 + 6.05572i) q^{47} +(-0.396187 - 1.68613i) 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} +(5.02409 - 1.18050i) q^{57} +(-1.20727 + 1.20727i) q^{58} -11.1739 q^{59} +(-3.26151 + 2.08868i) q^{60} -1.40994 q^{61} +(-3.71643 + 3.71643i) q^{62} +(8.73023 + 2.93030i) 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} +(2.84407 + 0.954611i) q^{72} +(0.698447 - 0.698447i) q^{73} -3.89665 q^{74} +(6.82888 + 5.32601i) q^{75} -2.97966 q^{76} +(-11.3478 + 11.3478i) q^{77} +(6.20118 - 1.45708i) 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} +(-0.676425 - 2.87879i) q^{87} +(-3.69679 + 3.69679i) q^{88} -3.53601 q^{89} +(-0.100507 - 6.70745i) q^{90} -11.2894 q^{91} +(0.707107 - 0.707107i) q^{92} +(-2.08229 - 8.86201i) 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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