LMFDB - Embedded newform 630.2.i.i.121.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(121,630)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0, 2]))

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

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

chi := DirichletCharacter("630.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.i (of order $3$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 2 x^{14} - 4 x^{13} + 5 x^{12} + 2 x^{11} - 35 x^{10} + 81 x^{9} - 66 x^{8} + \cdots + 6561 $ x^16 - x^15 + 2x^14 - 4x^13 + 5x^12 + 2x^11 - 35x^10 + 81x^9 - 66x^8 + 243x^7 - 315x^6 + 54x^5 + 405x^4 - 972x^3 + 1458x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.4
Root			$1.52536 - 0.820531i$ of defining polynomial
Character	$\chi$	$=$	630.121
Dual form			630.2.i.i.151.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.0520808 + 1.73127i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.0520808 - 1.73127i) q^{6} +(0.226513 + 2.63604i) q^{7} -1.00000 q^{8} +(-2.99458 + 0.180332i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.0520808 + 1.73127i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.0520808 - 1.73127i) q^{6} +(0.226513 + 2.63604i) q^{7} -1.00000 q^{8} +(-2.99458 + 0.180332i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-2.57071 + 4.45260i) q^{11} +(0.0520808 + 1.73127i) q^{12} +(1.62366 - 2.81226i) q^{13} +(-0.226513 - 2.63604i) q^{14} +(-1.47328 + 0.910737i) q^{15} +1.00000 q^{16} +(-2.89695 - 5.01766i) q^{17} +(2.99458 - 0.180332i) q^{18} +(-2.34980 + 4.06997i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-4.55189 + 0.529441i) q^{21} +(2.57071 - 4.45260i) q^{22} +(1.33463 + 2.31164i) q^{23} +(-0.0520808 - 1.73127i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.62366 + 2.81226i) q^{26} +(-0.468162 - 5.17502i) q^{27} +(0.226513 + 2.63604i) q^{28} +(0.227646 + 0.394295i) q^{29} +(1.47328 - 0.910737i) q^{30} +7.14142 q^{31} -1.00000 q^{32} +(-7.84252 - 4.21869i) q^{33} +(2.89695 + 5.01766i) q^{34} +(-2.16962 + 1.51418i) q^{35} +(-2.99458 + 0.180332i) q^{36} +(2.00070 - 3.46531i) q^{37} +(2.34980 - 4.06997i) q^{38} +(4.95334 + 2.66453i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-3.71105 + 6.42773i) q^{41} +(4.55189 - 0.529441i) q^{42} +(-1.80497 - 3.12631i) q^{43} +(-2.57071 + 4.45260i) q^{44} +(-1.65346 - 2.50321i) q^{45} +(-1.33463 - 2.31164i) q^{46} -3.15842 q^{47} +(0.0520808 + 1.73127i) q^{48} +(-6.89738 + 1.19419i) q^{49} +(0.500000 - 0.866025i) q^{50} +(8.53604 - 5.27671i) q^{51} +(1.62366 - 2.81226i) q^{52} +(-1.63008 - 2.82338i) q^{53} +(0.468162 + 5.17502i) q^{54} -5.14142 q^{55} +(-0.226513 - 2.63604i) q^{56} +(-7.16858 - 3.85616i) q^{57} +(-0.227646 - 0.394295i) q^{58} -11.1331 q^{59} +(-1.47328 + 0.910737i) q^{60} +5.99566 q^{61} -7.14142 q^{62} +(-1.15367 - 7.85296i) q^{63} +1.00000 q^{64} +3.24732 q^{65} +(7.84252 + 4.21869i) q^{66} -11.7774 q^{67} +(-2.89695 - 5.01766i) q^{68} +(-3.93256 + 2.43099i) q^{69} +(2.16962 - 1.51418i) q^{70} -4.38588 q^{71} +(2.99458 - 0.180332i) q^{72} +(6.94143 + 12.0229i) q^{73} +(-2.00070 + 3.46531i) q^{74} +(-1.52536 - 0.820531i) q^{75} +(-2.34980 + 4.06997i) q^{76} +(-12.3195 - 5.76791i) q^{77} +(-4.95334 - 2.66453i) q^{78} +2.95190 q^{79} +(0.500000 + 0.866025i) q^{80} +(8.93496 - 1.08003i) q^{81} +(3.71105 - 6.42773i) q^{82} +(6.13291 + 10.6225i) q^{83} +(-4.55189 + 0.529441i) q^{84} +(2.89695 - 5.01766i) q^{85} +(1.80497 + 3.12631i) q^{86} +(-0.670774 + 0.414652i) q^{87} +(2.57071 - 4.45260i) q^{88} +(-4.83214 + 8.36951i) q^{89} +(1.65346 + 2.50321i) q^{90} +(7.78102 + 3.64302i) q^{91} +(1.33463 + 2.31164i) q^{92} +(0.371931 + 12.3637i) q^{93} +3.15842 q^{94} -4.69959 q^{95} +(-0.0520808 - 1.73127i) q^{96} +(3.91728 + 6.78493i) q^{97} +(6.89738 - 1.19419i) q^{98} +(6.89523 - 13.7972i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} + 2 q^{3} + 16 q^{4} + 8 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} - 6 q^{9}+O(q^{10}) $ 16 * q - 16 * q^2 + 2 * q^3 + 16 * q^4 + 8 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 - 6 * q^9	\( 16 q - 16 q^{2} + 2 q^{3} + 16 q^{4} + 8 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} - 6 q^{9} - 8 q^{10} + q^{11} + 2 q^{12} + 2 q^{13} - 4 q^{14} + q^{15} + 16 q^{16} + 11 q^{17} + 6 q^{18} - 2 q^{19} + 8 q^{20} - 15 q^{21} - q^{22} + 11 q^{23} - 2 q^{24} - 8 q^{25} - 2 q^{26} - 7 q^{27} + 4 q^{28} + 17 q^{29} - q^{30} + 30 q^{31} - 16 q^{32} + 5 q^{33} - 11 q^{34} - 4 q^{35} - 6 q^{36} - 2 q^{37} + 2 q^{38} - 8 q^{40} + 7 q^{41} + 15 q^{42} - 13 q^{43} + q^{44} + 3 q^{45} - 11 q^{46} + 10 q^{47} + 2 q^{48} - 14 q^{49} + 8 q^{50} - 3 q^{51} + 2 q^{52} + 18 q^{53} + 7 q^{54} + 2 q^{55} - 4 q^{56} - 4 q^{57} - 17 q^{58} - 2 q^{59} + q^{60} + 54 q^{61} - 30 q^{62} + 41 q^{63} + 16 q^{64} + 4 q^{65} - 5 q^{66} + 20 q^{67} + 11 q^{68} - 14 q^{69} + 4 q^{70} - 38 q^{71} + 6 q^{72} - 8 q^{73} + 2 q^{74} - q^{75} - 2 q^{76} - 7 q^{77} + 50 q^{79} + 8 q^{80} - 6 q^{81} - 7 q^{82} + 2 q^{83} - 15 q^{84} - 11 q^{85} + 13 q^{86} - 32 q^{87} - q^{88} - 6 q^{89} - 3 q^{90} + 14 q^{91} + 11 q^{92} - 6 q^{93} - 10 q^{94} - 4 q^{95} - 2 q^{96} + 26 q^{97} + 14 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q - 16 * q^2 + 2 * q^3 + 16 * q^4 + 8 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 - 6 * q^9 - 8 * q^10 + q^11 + 2 * q^12 + 2 * q^13 - 4 * q^14 + q^15 + 16 * q^16 + 11 * q^17 + 6 * q^18 - 2 * q^19 + 8 * q^20 - 15 * q^21 - q^22 + 11 * q^23 - 2 * q^24 - 8 * q^25 - 2 * q^26 - 7 * q^27 + 4 * q^28 + 17 * q^29 - q^30 + 30 * q^31 - 16 * q^32 + 5 * q^33 - 11 * q^34 - 4 * q^35 - 6 * q^36 - 2 * q^37 + 2 * q^38 - 8 * q^40 + 7 * q^41 + 15 * q^42 - 13 * q^43 + q^44 + 3 * q^45 - 11 * q^46 + 10 * q^47 + 2 * q^48 - 14 * q^49 + 8 * q^50 - 3 * q^51 + 2 * q^52 + 18 * q^53 + 7 * q^54 + 2 * q^55 - 4 * q^56 - 4 * q^57 - 17 * q^58 - 2 * q^59 + q^60 + 54 * q^61 - 30 * q^62 + 41 * q^63 + 16 * q^64 + 4 * q^65 - 5 * q^66 + 20 * q^67 + 11 * q^68 - 14 * q^69 + 4 * q^70 - 38 * q^71 + 6 * q^72 - 8 * q^73 + 2 * q^74 - q^75 - 2 * q^76 - 7 * q^77 + 50 * q^79 + 8 * q^80 - 6 * q^81 - 7 * q^82 + 2 * q^83 - 15 * q^84 - 11 * q^85 + 13 * q^86 - 32 * q^87 - q^88 - 6 * q^89 - 3 * q^90 + 14 * q^91 + 11 * q^92 - 6 * q^93 - 10 * q^94 - 4 * q^95 - 2 * q^96 + 26 * q^97 + 14 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.0520808	+	1.73127i	0.0300689	+	0.999548i
$3$	0.0520808	+	1.73127i	0.0300689	+	0.999548i
$4$	1.00000			0.500000
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.0520808	−	1.73127i	−0.0212619	−	0.706787i
$7$	0.226513	+	2.63604i	0.0856138	+	0.996328i
$7$	0.226513	+	2.63604i	0.0856138	+	0.996328i
$8$	−1.00000			−0.353553
$9$	−2.99458	+	0.180332i	−0.998192	+	0.0601105i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−2.57071	+	4.45260i	−0.775097	+	1.34251i	0.159642	+	0.987175i	$0.448966\pi$
$11$	−2.57071	+	4.45260i	−0.775097	+	1.34251i	−0.934740	+	0.355333i	$0.884367\pi$
$12$	0.0520808	+	1.73127i	0.0150344	+	0.499774i
$13$	1.62366	−	2.81226i	0.450323	−	0.779982i	−0.548083	−	0.836424i	$-0.684642\pi$
$13$	1.62366	−	2.81226i	0.450323	−	0.779982i	0.998406	+	0.0564419i	$0.0179756\pi$
$14$	−0.226513	−	2.63604i	−0.0605381	−	0.704511i
$15$	−1.47328	+	0.910737i	−0.380400	+	0.235151i
$16$	1.00000			0.250000
$17$	−2.89695	−	5.01766i	−0.702613	−	1.21696i	−0.967546	−	0.252694i	$-0.918683\pi$
$17$	−2.89695	−	5.01766i	−0.702613	−	1.21696i	0.264933	−	0.964267i	$-0.414650\pi$
$18$	2.99458	−	0.180332i	0.705828	−	0.0425046i
$19$	−2.34980	+	4.06997i	−0.539080	+	0.933715i	0.459873	+	0.887984i	$0.347895\pi$
$19$	−2.34980	+	4.06997i	−0.539080	+	0.933715i	−0.998954	+	0.0457301i	$0.985439\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	−4.55189	+	0.529441i	−0.993304	+	0.115534i
$22$	2.57071	−	4.45260i	0.548077	−	0.949297i
$23$	1.33463	+	2.31164i	0.278289	+	0.482011i	0.970960	−	0.239243i	$-0.0768994\pi$
$23$	1.33463	+	2.31164i	0.278289	+	0.482011i	−0.692671	+	0.721254i	$0.743566\pi$
$24$	−0.0520808	−	1.73127i	−0.0106310	−	0.353394i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.62366	+	2.81226i	−0.318426	+	0.551531i
$27$	−0.468162	−	5.17502i	−0.0900979	−	0.995933i
$28$	0.226513	+	2.63604i	0.0428069	+	0.498164i
$29$	0.227646	+	0.394295i	0.0422728	+	0.0732187i	0.886388	−	0.462944i	$-0.153207\pi$
$29$	0.227646	+	0.394295i	0.0422728	+	0.0732187i	−0.844115	+	0.536162i	$0.819873\pi$
$30$	1.47328	−	0.910737i	0.268983	−	0.166277i
$31$	7.14142			1.28264			0.641318	−	0.767275i	$-0.278388\pi$
$31$	7.14142			1.28264			0.641318	+	0.767275i	$0.278388\pi$
$32$	−1.00000			−0.176777
$33$	−7.84252	−	4.21869i	−1.36521	−	0.734379i
$34$	2.89695	+	5.01766i	0.496822	+	0.860521i
$35$	−2.16962	+	1.51418i	−0.366732	+	0.255944i
$36$	−2.99458	+	0.180332i	−0.499096	+	0.0300553i
$37$	2.00070	−	3.46531i	0.328913	−	0.569694i	−0.653384	−	0.757027i	$-0.726651\pi$
$37$	2.00070	−	3.46531i	0.328913	−	0.569694i	0.982296	+	0.187333i	$0.0599844\pi$
$38$	2.34980	−	4.06997i	0.381187	−	0.660236i
$39$	4.95334	+	2.66453i	0.793170	+	0.426666i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−3.71105	+	6.42773i	−0.579569	+	1.00384i	0.415960	+	0.909383i	$0.363446\pi$
$41$	−3.71105	+	6.42773i	−0.579569	+	1.00384i	−0.995529	+	0.0944596i	$0.969888\pi$
$42$	4.55189	−	0.529441i	0.702372	−	0.0816946i
$43$	−1.80497	−	3.12631i	−0.275256	−	0.476757i	0.694944	−	0.719064i	$-0.255429\pi$
$43$	−1.80497	−	3.12631i	−0.275256	−	0.476757i	−0.970200	+	0.242307i	$0.922096\pi$
$44$	−2.57071	+	4.45260i	−0.387549	+	0.671254i
$45$	−1.65346	−	2.50321i	−0.246483	−	0.373157i
$46$	−1.33463	−	2.31164i	−0.196780	−	0.340833i
$47$	−3.15842			−0.460703			−0.230352	−	0.973107i	$-0.573988\pi$
$47$	−3.15842			−0.460703			−0.230352	+	0.973107i	$0.573988\pi$
$48$	0.0520808	+	1.73127i	0.00751722	+	0.249887i
$49$	−6.89738	+	1.19419i	−0.985341	+	0.170599i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	8.53604	−	5.27671i	1.19528	−	0.738888i
$52$	1.62366	−	2.81226i	0.225161	−	0.389991i
$53$	−1.63008	−	2.82338i	−0.223909	−	0.387821i	0.732083	−	0.681216i	$-0.238548\pi$
$53$	−1.63008	−	2.82338i	−0.223909	−	0.387821i	−0.955991	+	0.293395i	$0.905215\pi$
$54$	0.468162	+	5.17502i	0.0637088	+	0.704231i
$55$	−5.14142			−0.693268
$56$	−0.226513	−	2.63604i	−0.0302691	−	0.352255i
$57$	−7.16858	−	3.85616i	−0.949502	−	0.510761i
$58$	−0.227646	−	0.394295i	−0.0298914	−	0.0517735i
$59$	−11.1331			−1.44941			−0.724705	−	0.689059i	$-0.758024\pi$
$59$	−11.1331			−1.44941			−0.724705	+	0.689059i	$0.758024\pi$
$60$	−1.47328	+	0.910737i	−0.190200	+	0.117576i
$61$	5.99566			0.767665			0.383833	−	0.923403i	$-0.374604\pi$
$61$	5.99566			0.767665			0.383833	+	0.923403i	$0.374604\pi$
$62$	−7.14142			−0.906961
$63$	−1.15367	−	7.85296i	−0.145349	−	0.989380i
$64$	1.00000			0.125000
$65$	3.24732			0.402781
$66$	7.84252	+	4.21869i	0.965347	+	0.519285i
$67$	−11.7774			−1.43883			−0.719417	−	0.694579i	$-0.755591\pi$
$67$	−11.7774			−1.43883			−0.719417	+	0.694579i	$0.755591\pi$
$68$	−2.89695	−	5.01766i	−0.351306	−	0.608481i
$69$	−3.93256	+	2.43099i	−0.473425	+	0.292657i
$70$	2.16962	−	1.51418i	0.259319	−	0.180980i
$71$	−4.38588			−0.520508			−0.260254	−	0.965540i	$-0.583806\pi$
$71$	−4.38588			−0.520508			−0.260254	+	0.965540i	$0.583806\pi$
$72$	2.99458	−	0.180332i	0.352914	−	0.0212523i
$73$	6.94143	+	12.0229i	0.812433	+	1.40718i	0.911157	+	0.412060i	$0.135191\pi$
$73$	6.94143	+	12.0229i	0.812433	+	1.40718i	−0.0987235	+	0.995115i	$0.531476\pi$
$74$	−2.00070	+	3.46531i	−0.232577	+	0.402834i
$75$	−1.52536	−	0.820531i	−0.176134	−	0.0947467i
$76$	−2.34980	+	4.06997i	−0.269540	+	0.466857i
$77$	−12.3195	−	5.76791i	−1.40394	−	0.657314i
$78$	−4.95334	−	2.66453i	−0.560856	−	0.301698i
$79$	2.95190			0.332114			0.166057	−	0.986116i	$-0.446896\pi$
$79$	2.95190			0.332114			0.166057	+	0.986116i	$0.446896\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	8.93496	−	1.08003i	0.992773	−	0.120004i
$82$	3.71105	−	6.42773i	0.409817	−	0.709824i
$83$	6.13291	+	10.6225i	0.673174	+	1.16597i	0.976999	+	0.213244i	$0.0684030\pi$
$83$	6.13291	+	10.6225i	0.673174	+	1.16597i	−0.303824	+	0.952728i	$0.598264\pi$
$84$	−4.55189	+	0.529441i	−0.496652	+	0.0577668i
$85$	2.89695	−	5.01766i	0.314218	−	0.544242i
$86$	1.80497	+	3.12631i	0.194635	+	0.337118i
$87$	−0.670774	+	0.414652i	−0.0719145	+	0.0444553i
$88$	2.57071	−	4.45260i	0.274038	−	0.474648i
$89$	−4.83214	+	8.36951i	−0.512206	+	0.887166i	0.487694	+	0.873014i	$0.337838\pi$
$89$	−4.83214	+	8.36951i	−0.512206	+	0.887166i	−0.999900	+	0.0141515i	$0.995495\pi$
$90$	1.65346	+	2.50321i	0.174290	+	0.263862i
$91$	7.78102	+	3.64302i	0.815672	+	0.381892i
$92$	1.33463	+	2.31164i	0.139144	+	0.241005i
$93$	0.371931	+	12.3637i	0.0385674	+	1.28206i
$94$	3.15842			0.325766
$95$	−4.69959			−0.482168
$96$	−0.0520808	−	1.73127i	−0.00531548	−	0.176697i
$97$	3.91728	+	6.78493i	0.397740	+	0.688905i	0.993447	−	0.114296i	$-0.0364614\pi$
$97$	3.91728	+	6.78493i	0.397740	+	0.688905i	−0.595707	+	0.803202i	$0.703128\pi$
$98$	6.89738	−	1.19419i	0.696741	−	0.120632i
$99$	6.89523	−	13.7972i	0.692997	−	1.38667i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	2.86471	−	4.96182i	0.285049	−	0.493720i	−0.687572	−	0.726116i	$-0.741323\pi$
$101$	2.86471	−	4.96182i	0.285049	−	0.493720i	0.972621	+	0.232397i	$0.0746567\pi$
$102$	−8.53604	+	5.27671i	−0.845193	+	0.522473i
$103$	7.01544	+	12.1511i	0.691252	+	1.19728i	0.971428	+	0.237335i	$0.0762740\pi$
$103$	7.01544	+	12.1511i	0.691252	+	1.19728i	−0.280176	+	0.959949i	$0.590393\pi$
$104$	−1.62366	+	2.81226i	−0.159213	+	0.275765i
$105$	−2.73445	−	3.67733i	−0.266855	−	0.358871i
$106$	1.63008	+	2.82338i	0.158327	+	0.274231i
$107$	7.30355	−	12.6501i	0.706061	−	1.22293i	−0.260247	−	0.965542i	$-0.583804\pi$
$107$	7.30355	−	12.6501i	0.706061	−	1.22293i	0.966307	−	0.257391i	$-0.0828627\pi$
$108$	−0.468162	−	5.17502i	−0.0450489	−	0.497966i
$109$	1.60392	+	2.77806i	0.153627	+	0.266090i	0.932558	−	0.361019i	$-0.117571\pi$
$109$	1.60392	+	2.77806i	0.153627	+	0.266090i	−0.778931	+	0.627110i	$0.784238\pi$
$110$	5.14142			0.490215
$111$	6.10358	+	3.28327i	0.579326	+	0.311634i
$112$	0.226513	+	2.63604i	0.0214035	+	0.249082i
$113$	1.14968	−	1.99131i	0.108153	−	0.187327i	−0.806869	−	0.590731i	$-0.798840\pi$
$113$	1.14968	−	1.99131i	0.108153	−	0.187327i	0.915022	+	0.403404i	$0.132173\pi$
$114$	7.16858	+	3.85616i	0.671399	+	0.361162i
$115$	−1.33463	+	2.31164i	−0.124455	+	0.215562i
$116$	0.227646	+	0.394295i	0.0211364	+	0.0366094i
$117$	−4.35504	+	8.71434i	−0.402623	+	0.805641i
$118$	11.1331			1.02489
$119$	12.5705	−	8.77302i	1.15234	−	0.804222i
$120$	1.47328	−	0.910737i	0.134492	−	0.0831385i
$121$	−7.71707	−	13.3664i	−0.701552	−	1.21512i
$122$	−5.99566			−0.542821
$123$	−11.3214	−	6.09006i	−1.02082	−	0.549122i
$124$	7.14142			0.641318
$125$	−1.00000			−0.0894427
$126$	1.15367	+	7.85296i	0.102777	+	0.699598i
$127$	−2.31880			−0.205760			−0.102880	−	0.994694i	$-0.532806\pi$
$127$	−2.31880			−0.205760			−0.102880	+	0.994694i	$0.532806\pi$
$128$	−1.00000			−0.0883883
$129$	5.31847	−	3.28771i	0.468265	−	0.289467i
$130$	−3.24732			−0.284809
$131$	9.38105	+	16.2485i	0.819626	+	1.41963i	0.905958	+	0.423368i	$0.139152\pi$
$131$	9.38105	+	16.2485i	0.819626	+	1.41963i	−0.0863317	+	0.996266i	$0.527514\pi$
$132$	−7.84252	−	4.21869i	−0.682604	−	0.367190i
$133$	−11.2608	−	5.27225i	−0.976439	−	0.457162i
$134$	11.7774			1.01741
$135$	4.24762	−	2.99295i	0.365577	−	0.257592i
$136$	2.89695	+	5.01766i	0.248411	+	0.430261i
$137$	3.19895	−	5.54075i	0.273305	−	0.473378i	−0.696401	−	0.717653i	$-0.745216\pi$
$137$	3.19895	−	5.54075i	0.273305	−	0.473378i	0.969706	+	0.244275i	$0.0785498\pi$
$138$	3.93256	−	2.43099i	0.334762	−	0.206939i
$139$	10.4744	−	18.1422i	0.888429	−	1.53880i	0.0466966	−	0.998909i	$-0.485131\pi$
$139$	10.4744	−	18.1422i	0.888429	−	1.53880i	0.841732	−	0.539895i	$-0.181536\pi$
$140$	−2.16962	+	1.51418i	−0.183366	+	0.127972i
$141$	−0.164493	−	5.46807i	−0.0138528	−	0.460495i
$142$	4.38588			0.368055
$143$	8.34792	+	14.4590i	0.698088	+	1.20912i
$144$	−2.99458	+	0.180332i	−0.249548	+	0.0150276i
$145$	−0.227646	+	0.394295i	−0.0189050	+	0.0327444i
$146$	−6.94143	−	12.0229i	−0.574477	−	0.995023i
$147$	−2.42669	−	11.8790i	−0.200150	−	0.979765i
$148$	2.00070	−	3.46531i	0.164456	−	0.284847i
$149$	6.17989	+	10.7039i	0.506276	+	0.876896i	0.999974	+	0.00726207i	$0.00231161\pi$
$149$	6.17989	+	10.7039i	0.506276	+	0.876896i	−0.493698	+	0.869634i	$0.664355\pi$
$150$	1.52536	+	0.820531i	0.124545	+	0.0669960i
$151$	−9.70783	+	16.8145i	−0.790012	+	1.36834i	0.135947	+	0.990716i	$0.456592\pi$
$151$	−9.70783	+	16.8145i	−0.790012	+	1.36834i	−0.925959	+	0.377625i	$0.876741\pi$
$152$	2.34980	−	4.06997i	0.190594	−	0.330118i
$153$	9.57997	+	14.5033i	0.774494	+	1.17253i
$154$	12.3195	+	5.76791i	0.992734	+	0.464791i
$155$	3.57071	+	6.18465i	0.286806	+	0.496763i
$156$	4.95334	+	2.66453i	0.396585	+	0.213333i
$157$	−2.46099			−0.196409			−0.0982043	−	0.995166i	$-0.531310\pi$
$157$	−2.46099			−0.196409			−0.0982043	+	0.995166i	$0.531310\pi$
$158$	−2.95190			−0.234840
$159$	4.80313	−	2.96915i	0.380913	−	0.235469i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−5.79126	+	4.04174i	−0.456415	+	0.318534i
$162$	−8.93496	+	1.08003i	−0.701997	+	0.0848554i
$163$	4.96118	−	8.59301i	0.388589	−	0.673057i	−0.603671	−	0.797234i	$-0.706296\pi$
$163$	4.96118	−	8.59301i	0.388589	−	0.673057i	0.992260	+	0.124177i	$0.0396291\pi$
$164$	−3.71105	+	6.42773i	−0.289784	+	0.501921i
$165$	−0.267769	−	8.90117i	−0.0208458	−	0.692955i
$166$	−6.13291	−	10.6225i	−0.476006	−	0.824467i
$167$	−3.26841	+	5.66106i	−0.252917	+	0.438066i	−0.964328	−	0.264711i	$-0.914723\pi$
$167$	−3.26841	+	5.66106i	−0.252917	+	0.438066i	0.711410	+	0.702777i	$0.248057\pi$
$168$	4.55189	−	0.529441i	0.351186	−	0.0408473i
$169$	1.22744	+	2.12600i	0.0944188	+	0.163538i
$170$	−2.89695	+	5.01766i	−0.222186	+	0.384837i
$171$	6.30270	−	12.6116i	0.481979	−	0.964431i
$172$	−1.80497	−	3.12631i	−0.137628	−	0.238379i
$173$	12.7290			0.967765			0.483883	−	0.875133i	$-0.339226\pi$
$173$	12.7290			0.967765			0.483883	+	0.875133i	$0.339226\pi$
$174$	0.670774	−	0.414652i	0.0508512	−	0.0314347i
$175$	−2.39613	−	1.12185i	−0.181131	−	0.0848041i
$176$	−2.57071	+	4.45260i	−0.193774	+	0.335627i
$177$	−0.579822	−	19.2744i	−0.0435821	−	1.44875i
$178$	4.83214	−	8.36951i	0.362184	−	0.627321i
$179$	11.6182	+	20.1233i	0.868386	+	1.50409i	0.863646	+	0.504100i	$0.168176\pi$
$179$	11.6182	+	20.1233i	0.868386	+	1.50409i	0.00474023	+	0.999989i	$0.498491\pi$
$180$	−1.65346	−	2.50321i	−0.123242	−	0.186578i
$181$	−19.0687			−1.41737			−0.708683	−	0.705527i	$-0.750710\pi$
$181$	−19.0687			−1.41737			−0.708683	+	0.705527i	$0.750710\pi$
$182$	−7.78102	−	3.64302i	−0.576767	−	0.270039i
$183$	0.312259	+	10.3801i	0.0230828	+	0.767318i
$184$	−1.33463	−	2.31164i	−0.0983900	−	0.170416i
$185$	4.00140			0.294189
$186$	−0.371931	−	12.3637i	−0.0272713	−	0.906551i
$187$	29.7888			2.17837
$188$	−3.15842			−0.230352
$189$	13.5355	−	2.40630i	0.984563	−	0.175033i
$190$	4.69959			0.340944
$191$	26.2989			1.90292			0.951462	−	0.307767i	$-0.0995817\pi$
$191$	26.2989			1.90292			0.951462	+	0.307767i	$0.0995817\pi$
$192$	0.0520808	+	1.73127i	0.00375861	+	0.124943i
$193$	4.68862			0.337494			0.168747	−	0.985659i	$-0.446028\pi$
$193$	4.68862			0.337494			0.168747	+	0.985659i	$0.446028\pi$
$194$	−3.91728	−	6.78493i	−0.281244	−	0.487130i
$195$	0.169123	+	5.62199i	0.0121112	+	0.402599i
$196$	−6.89738	+	1.19419i	−0.492670	+	0.0852995i
$197$	10.4576			0.745076			0.372538	−	0.928017i	$-0.378488\pi$
$197$	10.4576			0.745076			0.372538	+	0.928017i	$0.378488\pi$
$198$	−6.89523	+	13.7972i	−0.490023	+	0.980525i
$199$	−8.16053	−	14.1345i	−0.578485	−	1.00197i	−0.995653	−	0.0931362i	$-0.970311\pi$
$199$	−8.16053	−	14.1345i	−0.578485	−	1.00197i	0.417168	−	0.908829i	$-0.363023\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	−0.613374	−	20.3898i	−0.0432641	−	1.43818i
$202$	−2.86471	+	4.96182i	−0.201560	+	0.349113i
$203$	−0.987811	+	0.689397i	−0.0693307	+	0.0483862i
$204$	8.53604	−	5.27671i	0.597642	−	0.369444i
$205$	−7.42210			−0.518382
$206$	−7.01544	−	12.1511i	−0.488789	−	0.846608i
$207$	−4.41350	−	6.68171i	−0.306760	−	0.464411i
$208$	1.62366	−	2.81226i	0.112581	−	0.194995i
$209$	−12.0813	−	20.9254i	−0.835680	−	1.44744i
$210$	2.73445	+	3.67733i	0.188695	+	0.253760i
$211$	−2.17495	+	3.76713i	−0.149730	+	0.259340i	−0.931128	−	0.364693i	$-0.881174\pi$
$211$	−2.17495	+	3.76713i	−0.149730	+	0.259340i	0.781398	+	0.624033i	$0.214507\pi$
$212$	−1.63008	−	2.82338i	−0.111954	−	0.193911i
$213$	−0.228420	−	7.59313i	−0.0156511	−	0.520273i
$214$	−7.30355	+	12.6501i	−0.499260	+	0.864744i
$215$	1.80497	−	3.12631i	0.123098	−	0.213212i
$216$	0.468162	+	5.17502i	0.0318544	+	0.352115i
$217$	1.61762	+	18.8250i	0.109811	+	1.27793i
$218$	−1.60392	−	2.77806i	−0.108631	−	0.188154i
$219$	−20.4534	+	12.6436i	−1.38211	+	0.854378i
$220$	−5.14142			−0.346634
$221$	−18.8146			−1.26561
$222$	−6.10358	−	3.28327i	−0.409646	−	0.220359i
$223$	1.72717	+	2.99154i	0.115660	+	0.200328i	0.918043	−	0.396480i	$-0.129768\pi$
$223$	1.72717	+	2.99154i	0.115660	+	0.200328i	−0.802384	+	0.596809i	$0.796435\pi$
$224$	−0.226513	−	2.63604i	−0.0151345	−	0.176128i
$225$	1.34112	−	2.68354i	0.0894077	−	0.178903i
$226$	−1.14968	+	1.99131i	−0.0764758	+	0.132460i
$227$	9.60477	−	16.6359i	0.637491	−	1.10417i	−0.348491	−	0.937312i	$-0.613306\pi$
$227$	9.60477	−	16.6359i	0.637491	−	1.10417i	0.985982	−	0.166854i	$-0.0533610\pi$
$228$	−7.16858	−	3.85616i	−0.474751	−	0.255380i
$229$	10.8311	+	18.7600i	0.715739	+	1.23970i	0.962674	+	0.270665i	$0.0872435\pi$
$229$	10.8311	+	18.7600i	0.715739	+	1.23970i	−0.246934	+	0.969032i	$0.579423\pi$
$230$	1.33463	−	2.31164i	0.0880027	−	0.152425i
$231$	9.34419	−	21.6288i	0.614802	−	1.42307i
$232$	−0.227646	−	0.394295i	−0.0149457	−	0.0258867i
$233$	−1.36959	+	2.37220i	−0.0897248	+	0.155408i	−0.907395	−	0.420279i	$-0.861932\pi$
$233$	−1.36959	+	2.37220i	−0.0897248	+	0.155408i	0.817670	+	0.575687i	$0.195265\pi$
$234$	4.35504	−	8.71434i	0.284698	−	0.569674i
$235$	−1.57921	−	2.73527i	−0.103016	−	0.178430i
$236$	−11.1331			−0.724705
$237$	0.153737	+	5.11052i	0.00998630	+	0.331964i
$238$	−12.5705	+	8.77302i	−0.814827	+	0.568671i
$239$	11.2181	−	19.4304i	0.725641	−	1.25685i	−0.233068	−	0.972460i	$-0.574877\pi$
$239$	11.2181	−	19.4304i	0.725641	−	1.25685i	0.958710	−	0.284387i	$-0.0917901\pi$
$240$	−1.47328	+	0.910737i	−0.0950999	+	0.0587878i
$241$	−10.9177	+	18.9101i	−0.703273	+	1.21810i	0.264038	+	0.964512i	$0.414945\pi$
$241$	−10.9177	+	18.9101i	−0.703273	+	1.21810i	−0.967311	+	0.253592i	$0.918388\pi$
$242$	7.71707	+	13.3664i	0.496072	+	0.859222i
$243$	2.33517	+	15.4126i	0.149801	+	0.988716i
$244$	5.99566			0.383833
$245$	−4.48289	−	5.37621i	−0.286402	−	0.343474i
$246$	11.3214	+	6.09006i	0.721826	+	0.388288i
$247$	7.63055	+	13.2165i	0.485520	+	0.840946i
$248$	−7.14142			−0.453480
$249$	−18.0710	+	11.1709i	−1.14520	+	0.707930i
$250$	1.00000			0.0632456
$251$	−5.65826			−0.357146			−0.178573	−	0.983927i	$-0.557148\pi$
$251$	−5.65826			−0.357146			−0.178573	+	0.983927i	$0.557148\pi$
$252$	−1.15367	−	7.85296i	−0.0726744	−	0.494690i
$253$	−13.7237			−0.862804
$254$	2.31880			0.145494
$255$	8.83779	+	4.75407i	0.553444	+	0.297711i
$256$	1.00000			0.0625000
$257$	−3.88139	−	6.72276i	−0.242114	−	0.419354i	0.719202	−	0.694801i	$-0.244508\pi$
$257$	−3.88139	−	6.72276i	−0.242114	−	0.419354i	−0.961316	+	0.275447i	$0.911174\pi$
$258$	−5.31847	+	3.28771i	−0.331113	+	0.204684i
$259$	9.58788	+	4.48898i	0.595762	+	0.278932i
$260$	3.24732			0.201390
$261$	−0.752808	−	1.13969i	−0.0465976	−	0.0705453i
$262$	−9.38105	−	16.2485i	−0.579563	−	1.00383i
$263$	−4.59133	+	7.95241i	−0.283113	+	0.490367i	−0.972150	−	0.234360i	$-0.924701\pi$
$263$	−4.59133	+	7.95241i	−0.283113	+	0.490367i	0.689037	+	0.724727i	$0.258034\pi$
$264$	7.84252	+	4.21869i	0.482674	+	0.259642i
$265$	1.63008	−	2.82338i	0.100135	−	0.173439i
$266$	11.2608	+	5.27225i	0.690447	+	0.323262i
$267$	−14.7415	−	7.92983i	−0.902166	−	0.485298i
$268$	−11.7774			−0.719417
$269$	9.03012	+	15.6406i	0.550576	+	0.953626i	0.998233	+	0.0594206i	$0.0189253\pi$
$269$	9.03012	+	15.6406i	0.550576	+	0.953626i	−0.447657	+	0.894205i	$0.647741\pi$
$270$	−4.24762	+	2.99295i	−0.258502	+	0.182145i
$271$	−12.2464	+	21.2114i	−0.743917	+	1.28850i	0.206782	+	0.978387i	$0.433701\pi$
$271$	−12.2464	+	21.2114i	−0.743917	+	1.28850i	−0.950699	+	0.310115i	$0.899632\pi$
$272$	−2.89695	−	5.01766i	−0.175653	−	0.304240i
$273$	−5.90180	+	13.6608i	−0.357193	+	0.826786i
$274$	−3.19895	+	5.54075i	−0.193256	+	0.334729i
$275$	−2.57071	−	4.45260i	−0.155019	−	0.268502i
$276$	−3.93256	+	2.43099i	−0.236712	+	0.146328i
$277$	6.55834	−	11.3594i	0.394052	−	0.682518i	−0.598927	−	0.800803i	$-0.704406\pi$
$277$	6.55834	−	11.3594i	0.394052	−	0.682518i	0.992980	+	0.118285i	$0.0377396\pi$
$278$	−10.4744	+	18.1422i	−0.628214	+	1.08810i
$279$	−21.3855	+	1.28782i	−1.28032	+	0.0770999i
$280$	2.16962	−	1.51418i	0.129660	−	0.0904898i
$281$	1.06057	+	1.83696i	0.0632684	+	0.109584i	0.895925	−	0.444206i	$-0.146514\pi$
$281$	1.06057	+	1.83696i	0.0632684	+	0.109584i	−0.832656	+	0.553790i	$0.813181\pi$
$282$	0.164493	+	5.46807i	0.00979543	+	0.325619i
$283$	−11.2536			−0.668957			−0.334478	−	0.942403i	$-0.608560\pi$
$283$	−11.2536			−0.668957			−0.334478	+	0.942403i	$0.608560\pi$
$284$	−4.38588			−0.260254
$285$	−0.244759	−	8.13625i	−0.0144982	−	0.481950i
$286$	−8.34792	−	14.4590i	−0.493623	−	0.854980i
$287$	−17.7843	−	8.32650i	−1.04978	−	0.491498i
$288$	2.99458	−	0.180332i	0.176457	−	0.0106261i
$289$	−8.28460	+	14.3493i	−0.487329	+	0.844079i
$290$	0.227646	−	0.394295i	0.0133678	−	0.0231538i
$291$	−11.5425	+	7.13523i	−0.676634	+	0.418274i
$292$	6.94143	+	12.0229i	0.406217	+	0.703588i
$293$	4.80935	−	8.33003i	0.280965	−	0.486646i	−0.690658	−	0.723182i	$-0.742679\pi$
$293$	4.80935	−	8.33003i	0.280965	−	0.486646i	0.971623	+	0.236536i	$0.0760121\pi$
$294$	2.42669	+	11.8790i	0.141527	+	0.692799i
$295$	−5.56657	−	9.64157i	−0.324098	−	0.561354i
$296$	−2.00070	+	3.46531i	−0.116288	+	0.201417i
$297$	24.2458	+	11.2189i	1.40688	+	0.650988i
$298$	−6.17989	−	10.7039i	−0.357991	−	0.620059i
$299$	8.66793			0.501279
$300$	−1.52536	−	0.820531i	−0.0880668	−	0.0473734i
$301$	7.83221	−	5.46613i	0.451441	−	0.315062i
$302$	9.70783	−	16.8145i	0.558623	−	0.967563i
$303$	8.73944	+	4.70116i	0.502068	+	0.270075i
$304$	−2.34980	+	4.06997i	−0.134770	+	0.233429i
$305$	2.99783	+	5.19239i	0.171655	+	0.297315i
$306$	−9.57997	−	14.5033i	−0.547650	−	0.829101i
$307$	−9.13535			−0.521382			−0.260691	−	0.965422i	$-0.583950\pi$
$307$	−9.13535			−0.521382			−0.260691	+	0.965422i	$0.583950\pi$
$308$	−12.3195	−	5.76791i	−0.701969	−	0.328657i
$309$	−20.6714	+	12.7784i	−1.17596	+	0.726941i
$310$	−3.57071	−	6.18465i	−0.202803	−	0.351264i
$311$	20.5948			1.16782			0.583911	−	0.811818i	$-0.301522\pi$
$311$	20.5948			1.16782			0.583911	+	0.811818i	$0.301522\pi$
$312$	−4.95334	−	2.66453i	−0.280428	−	0.150849i
$313$	−0.550854			−0.0311361			−0.0155680	−	0.999879i	$-0.504956\pi$
$313$	−0.550854			−0.0311361			−0.0155680	+	0.999879i	$0.504956\pi$
$314$	2.46099			0.138882
$315$	6.22403	−	4.92559i	0.350684	−	0.277526i
$316$	2.95190			0.166057
$317$	−26.9744			−1.51503			−0.757517	−	0.652815i	$-0.773588\pi$
$317$	−26.9744			−1.51503			−0.757517	+	0.652815i	$0.773588\pi$
$318$	−4.80313	+	2.96915i	−0.269346	+	0.166502i
$319$	−2.34085			−0.131062
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	22.2811	+	11.9856i	1.24361	+	0.668969i
$322$	5.79126	−	4.04174i	0.322734	−	0.225238i
$323$	27.2289			1.51506
$324$	8.93496	−	1.08003i	0.496387	−	0.0600018i
$325$	1.62366	+	2.81226i	0.0900646	+	0.155996i
$326$	−4.96118	+	8.59301i	−0.274774	+	0.475923i
$327$	−4.72604	+	2.92149i	−0.261350	+	0.161559i
$328$	3.71105	−	6.42773i	0.204908	−	0.354912i
$329$	−0.715423	−	8.32572i	−0.0394426	−	0.459012i
$330$	0.267769	+	8.90117i	0.0147402	+	0.489993i
$331$	−16.8877			−0.928231			−0.464115	−	0.885775i	$-0.653628\pi$
$331$	−16.8877			−0.928231			−0.464115	+	0.885775i	$0.653628\pi$
$332$	6.13291	+	10.6225i	0.336587	+	0.582986i
$333$	−5.36634	+	10.7379i	−0.294074	+	0.588435i
$334$	3.26841	−	5.66106i	0.178840	−	0.309759i
$335$	−5.88868	−	10.1995i	−0.321733	−	0.557258i
$336$	−4.55189	+	0.529441i	−0.248326	+	0.0288834i
$337$	12.8294	−	22.2212i	0.698863	−	1.21047i	−0.269998	−	0.962861i	$-0.587023\pi$
$337$	12.8294	−	22.2212i	0.698863	−	1.21047i	0.968861	−	0.247606i	$-0.0796437\pi$
$338$	−1.22744	−	2.12600i	−0.0667642	−	0.115639i
$339$	3.50737	+	1.88670i	0.190494	+	0.102472i
$340$	2.89695	−	5.01766i	0.157109	−	0.272121i
$341$	−18.3585	+	31.7978i	−0.994168	+	1.72195i
$342$	−6.30270	+	12.6116i	−0.340811	+	0.681955i
$343$	−4.71028	−	17.9113i	−0.254331	−	0.967117i
$344$	1.80497	+	3.12631i	0.0973176	+	0.168559i
$345$	−4.07158	−	2.19020i	−0.219206	−	0.117917i
$346$	−12.7290			−0.684313
$347$	−17.0235			−0.913871			−0.456936	−	0.889500i	$-0.651053\pi$
$347$	−17.0235			−0.913871			−0.456936	+	0.889500i	$0.651053\pi$
$348$	−0.670774	+	0.414652i	−0.0359573	+	0.0222277i
$349$	−11.3156	−	19.5992i	−0.605709	−	1.04912i	−0.991939	−	0.126716i	$-0.959556\pi$
$349$	−11.3156	−	19.5992i	−0.605709	−	1.04912i	0.386230	−	0.922403i	$-0.373777\pi$
$350$	2.39613	+	1.12185i	0.128079	+	0.0599655i
$351$	−15.3137	−	7.08589i	−0.817383	−	0.378217i
$352$	2.57071	−	4.45260i	0.137019	−	0.237324i
$353$	4.37421	−	7.57635i	0.232815	−	0.403248i	−0.725820	−	0.687885i	$-0.758540\pi$
$353$	4.37421	−	7.57635i	0.232815	−	0.403248i	0.958636	+	0.284636i	$0.0918729\pi$
$354$	0.579822	+	19.2744i	0.0308172	+	1.02442i
$355$	−2.19294	−	3.79828i	−0.116389	−	0.201592i
$356$	−4.83214	+	8.36951i	−0.256103	+	0.443583i
$357$	15.8431	+	21.3061i	0.838508	+	1.12764i
$358$	−11.6182	−	20.1233i	−0.614041	−	1.06355i
$359$	13.0119	−	22.5373i	0.686741	−	1.18947i	−0.286145	−	0.958186i	$-0.592374\pi$
$359$	13.0119	−	22.5373i	0.686741	−	1.18947i	0.972886	−	0.231284i	$-0.0742928\pi$
$360$	1.65346	+	2.50321i	0.0871450	+	0.131931i
$361$	−1.54309	−	2.67271i	−0.0812152	−	0.140669i
$362$	19.0687			1.00223
$363$	22.7388	−	14.0565i	1.19348	−	0.737772i
$364$	7.78102	+	3.64302i	0.407836	+	0.190946i
$365$	−6.94143	+	12.0229i	−0.363331	+	0.629308i
$366$	−0.312259	−	10.3801i	−0.0163220	−	0.542576i
$367$	−17.2794	+	29.9288i	−0.901976	+	1.56227i	−0.0770508	+	0.997027i	$0.524550\pi$
$367$	−17.2794	+	29.9288i	−0.901976	+	1.56227i	−0.824925	+	0.565242i	$0.808783\pi$
$368$	1.33463	+	2.31164i	0.0695722	+	0.120503i
$369$	9.95390	−	19.9175i	0.518179	−	1.03687i
$370$	−4.00140			−0.208023
$371$	7.07330	−	4.93648i	0.367227	−	0.256289i
$372$	0.371931	+	12.3637i	0.0192837	+	0.641028i
$373$	−4.48949	−	7.77603i	−0.232457	−	0.402627i	0.726074	−	0.687617i	$-0.241343\pi$
$373$	−4.48949	−	7.77603i	−0.232457	−	0.402627i	−0.958531	+	0.284990i	$0.908010\pi$
$374$	−29.7888			−1.54034
$375$	−0.0520808	−	1.73127i	−0.00268944	−	0.0894023i
$376$	3.15842			0.162883
$377$	1.47848			0.0761457
$378$	−13.5355	+	2.40630i	−0.696191	+	0.123767i
$379$	−21.2288			−1.09045			−0.545225	−	0.838290i	$-0.683556\pi$
$379$	−21.2288			−1.09045			−0.545225	+	0.838290i	$0.683556\pi$
$380$	−4.69959			−0.241084
$381$	−0.120765	−	4.01446i	−0.00618697	−	0.205667i
$382$	−26.2989			−1.34557
$383$	−0.108153	−	0.187326i	−0.00552634	−	0.00957190i	0.863249	−	0.504778i	$-0.168426\pi$
$383$	−0.108153	−	0.187326i	−0.00552634	−	0.00957190i	−0.868775	+	0.495206i	$0.835092\pi$
$384$	−0.0520808	−	1.73127i	−0.00265774	−	0.0883484i
$385$	−1.16460	−	13.5530i	−0.0593534	−	0.690723i
$386$	−4.68862			−0.238645
$387$	5.96890	+	9.03646i	0.303416	+	0.459349i
$388$	3.91728	+	6.78493i	0.198870	+	0.344453i
$389$	5.81312	−	10.0686i	0.294737	−	0.510499i	−0.680187	−	0.733039i	$-0.738101\pi$
$389$	5.81312	−	10.0686i	0.294737	−	0.510499i	0.974924	+	0.222540i	$0.0714347\pi$
$390$	−0.169123	−	5.62199i	−0.00856389	−	0.284680i
$391$	7.73269	−	13.3934i	0.391059	−	0.677334i
$392$	6.89738	−	1.19419i	0.348370	−	0.0603159i
$393$	−27.6419	+	17.0873i	−1.39435	+	0.861942i
$394$	−10.4576			−0.526848
$395$	1.47595	+	2.55642i	0.0742630	+	0.128627i
$396$	6.89523	−	13.7972i	0.346498	−	0.693336i
$397$	−14.1667	+	24.5375i	−0.711007	+	1.23150i	0.253472	+	0.967343i	$0.418427\pi$
$397$	−14.1667	+	24.5375i	−0.711007	+	1.23150i	−0.964479	+	0.264158i	$0.914906\pi$
$398$	8.16053	+	14.1345i	0.409051	+	0.708496i
$399$	8.54120	−	19.7701i	0.427595	−	0.989744i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	3.41125	+	5.90845i	0.170349	+	0.295054i	0.938542	−	0.345165i	$-0.112177\pi$
$401$	3.41125	+	5.90845i	0.170349	+	0.295054i	−0.768193	+	0.640219i	$0.778844\pi$
$402$	0.613374	+	20.3898i	0.0305923	+	1.01695i
$403$	11.5952	−	20.0836i	0.577600	−	1.00043i
$404$	2.86471	−	4.96182i	0.142525	−	0.246860i
$405$	5.40282	+	7.19789i	0.268468	+	0.357666i
$406$	0.987811	−	0.689397i	0.0490242	−	0.0342142i
$407$	10.2864	+	17.8166i	0.509879	+	0.883137i
$408$	−8.53604	+	5.27671i	−0.422597	+	0.261236i
$409$	11.1738			0.552511			0.276255	−	0.961084i	$-0.410906\pi$
$409$	11.1738			0.552511			0.276255	+	0.961084i	$0.410906\pi$
$410$	7.42210			0.366551
$411$	9.75913	+	5.24968i	0.481382	+	0.258948i
$412$	7.01544	+	12.1511i	0.345626	+	0.598642i
$413$	−2.52180	−	29.3473i	−0.124090	−	1.44409i
$414$	4.41350	+	6.68171i	0.216912	+	0.328388i
$415$	−6.13291	+	10.6225i	−0.301053	+	0.521439i
$416$	−1.62366	+	2.81226i	−0.0796066	+	0.137883i
$417$	31.9546	+	17.1892i	1.56482	+	0.841757i
$418$	12.0813	+	20.9254i	0.590915	+	1.02349i
$419$	−2.78160	+	4.81787i	−0.135890	+	0.235368i	−0.925937	−	0.377678i	$-0.876723\pi$
$419$	−2.78160	+	4.81787i	−0.135890	+	0.235368i	0.790047	+	0.613046i	$0.210056\pi$
$420$	−2.73445	−	3.67733i	−0.133428	−	0.179435i
$421$	−17.2899	−	29.9470i	−0.842658	−	1.45953i	−0.887640	−	0.460539i	$-0.847656\pi$
$421$	−17.2899	−	29.9470i	−0.842658	−	1.45953i	0.0449814	−	0.998988i	$-0.485677\pi$
$422$	2.17495	−	3.76713i	0.105875	−	0.183381i
$423$	9.45813	−	0.569563i	0.459870	−	0.0276931i
$424$	1.63008	+	2.82338i	0.0791636	+	0.137115i
$425$	5.79389			0.281045
$426$	0.228420	+	7.59313i	0.0110670	+	0.367889i
$427$	1.35809	+	15.8048i	0.0657228	+	0.764847i
$428$	7.30355	−	12.6501i	0.353030	−	0.611466i
$429$	−24.5977	+	15.2055i	−1.18759	+	0.734129i
$430$	−1.80497	+	3.12631i	−0.0870435	+	0.150764i
$431$	19.2277	+	33.3034i	0.926167	+	1.60417i	0.789673	+	0.613528i	$0.210250\pi$
$431$	19.2277	+	33.3034i	0.926167	+	1.60417i	0.136495	+	0.990641i	$0.456416\pi$
$432$	−0.468162	−	5.17502i	−0.0225245	−	0.248983i
$433$	30.9550			1.48760			0.743800	−	0.668402i	$-0.233021\pi$
$433$	30.9550			1.48760			0.743800	+	0.668402i	$0.233021\pi$
$434$	−1.61762	−	18.8250i	−0.0776484	−	0.903631i
$435$	−0.694486	−	0.373581i	−0.0332981	−	0.0179119i
$436$	1.60392	+	2.77806i	0.0768136	+	0.133045i
$437$	−12.5444			−0.600080
$438$	20.4534	−	12.6436i	0.977299	−	0.604136i
$439$	26.8388			1.28095			0.640474	−	0.767980i	$-0.278738\pi$
$439$	26.8388			1.28095			0.640474	+	0.767980i	$0.278738\pi$
$440$	5.14142			0.245107
$441$	20.4394	−	4.81992i	0.973304	−	0.229520i
$442$	18.8146			0.894922
$443$	−32.2517			−1.53232			−0.766162	−	0.642647i	$-0.777836\pi$
$443$	−32.2517			−1.53232			−0.766162	+	0.642647i	$0.777836\pi$
$444$	6.10358	+	3.28327i	0.289663	+	0.155817i
$445$	−9.66427			−0.458131
$446$	−1.72717	−	2.99154i	−0.0817838	−	0.141654i
$447$	−18.2094	+	11.2565i	−0.861276	+	0.532414i
$448$	0.226513	+	2.63604i	0.0107017	+	0.124541i
$449$	−9.45029			−0.445987			−0.222993	−	0.974820i	$-0.571583\pi$
$449$	−9.45029			−0.445987			−0.222993	+	0.974820i	$0.571583\pi$
$450$	−1.34112	+	2.68354i	−0.0632208	+	0.126503i
$451$	−19.0801	−	33.0476i	−0.898445	−	1.55615i
$452$	1.14968	−	1.99131i	0.0540766	−	0.0936634i
$453$	−29.6159	−	15.9311i	−1.39148	−	0.748510i
$454$	−9.60477	+	16.6359i	−0.450774	+	0.780764i
$455$	0.735561	+	8.56007i	0.0344836	+	0.401302i
$456$	7.16858	+	3.85616i	0.335700	+	0.180581i
$457$	25.3313			1.18495			0.592474	−	0.805589i	$-0.298151\pi$
$457$	25.3313			1.18495			0.592474	+	0.805589i	$0.298151\pi$
$458$	−10.8311	−	18.7600i	−0.506104	−	0.876598i
$459$	−24.6102	+	17.3408i	−1.14871	+	0.809401i
$460$	−1.33463	+	2.31164i	−0.0622273	+	0.107781i
$461$	0.0688453	+	0.119244i	0.00320645	+	0.00555373i	0.867624	−	0.497221i	$-0.165646\pi$
$461$	0.0688453	+	0.119244i	0.00320645	+	0.00555373i	−0.864418	+	0.502774i	$0.832313\pi$
$462$	−9.34419	+	21.6288i	−0.434731	+	1.00626i
$463$	−8.01422	+	13.8810i	−0.372452	+	0.645106i	−0.989942	−	0.141473i	$-0.954816\pi$
$463$	−8.01422	+	13.8810i	−0.372452	+	0.645106i	0.617490	+	0.786579i	$0.288150\pi$
$464$	0.227646	+	0.394295i	0.0105682	+	0.0183047i
$465$	−10.5213	+	6.50395i	−0.487914	+	0.301614i
$466$	1.36959	−	2.37220i	0.0634450	−	0.109890i
$467$	10.9032	−	18.8849i	0.504540	−	0.873888i	−0.495447	−	0.868638i	$-0.664996\pi$
$467$	10.9032	−	18.8849i	0.504540	−	0.873888i	0.999986	−	0.00524984i	$-0.00167108\pi$
$468$	−4.35504	+	8.71434i	−0.201312	+	0.402820i
$469$	−2.66772	−	31.0456i	−0.123184	−	1.43355i
$470$	1.57921	+	2.73527i	0.0728436	+	0.126169i
$471$	−0.128170	−	4.26064i	−0.00590578	−	0.196320i
$472$	11.1331			0.512444
$473$	18.5602			0.853400
$474$	−0.153737	−	5.11052i	−0.00706138	−	0.234734i
$475$	−2.34980	−	4.06997i	−0.107816	−	0.186743i
$476$	12.5705	−	8.77302i	0.576170	−	0.402111i
$477$	5.39054	+	8.16087i	0.246816	+	0.373661i
$478$	−11.2181	+	19.4304i	−0.513106	+	0.888725i
$479$	8.13300	−	14.0868i	0.371606	−	0.643641i	−0.618206	−	0.786016i	$-0.712140\pi$
$479$	8.13300	−	14.0868i	0.371606	−	0.643641i	0.989813	+	0.142375i	$0.0454738\pi$
$480$	1.47328	−	0.910737i	0.0672458	−	0.0415693i
$481$	−6.49692	−	11.2530i	−0.296234	−	0.513092i
$482$	10.9177	−	18.9101i	0.497289	−	0.861330i
$483$	−7.29895	−	9.81573i	−0.332114	−	0.446631i
$484$	−7.71707	−	13.3664i	−0.350776	−	0.607562i
$485$	−3.91728	+	6.78493i	−0.177875	+	0.308088i
$486$	−2.33517	−	15.4126i	−0.105925	−	0.699128i
$487$	−17.0685	−	29.5636i	−0.773449	−	1.33965i	−0.935662	−	0.352897i	$-0.885196\pi$
$487$	−17.0685	−	29.5636i	−0.773449	−	1.33965i	0.162213	−	0.986756i	$-0.448137\pi$
$488$	−5.99566			−0.271411
$489$	15.1352	+	8.14159i	0.684437	+	0.368176i
$490$	4.48289	+	5.37621i	0.202516	+	0.242873i
$491$	21.6539	−	37.5057i	0.977228	−	1.69261i	0.304849	−	0.952401i	$-0.401394\pi$
$491$	21.6539	−	37.5057i	0.977228	−	1.69261i	0.672379	−	0.740207i	$-0.265273\pi$
$492$	−11.3214	−	6.09006i	−0.510408	−	0.274561i
$493$	1.31896	−	2.28450i	0.0594029	−	0.102889i
$494$	−7.63055	−	13.2165i	−0.343315	−	0.594639i
$495$	15.3964	−	0.927160i	0.692015	−	0.0416727i
$496$	7.14142			0.320659
$497$	−0.993459	−	11.5613i	−0.0445627	−	0.518597i
$498$	18.0710	−	11.1709i	0.809781	−	0.500582i
$499$	−3.32314	−	5.75585i	−0.148764	−	0.257667i	0.782007	−	0.623270i	$-0.214196\pi$
$499$	−3.32314	−	5.75585i	−0.148764	−	0.257667i	−0.930771	+	0.365603i	$0.880863\pi$
$500$	−1.00000			−0.0447214
$501$	−9.97103	−	5.36367i	−0.445473	−	0.239631i
$502$	5.65826			0.252540
$503$	35.8333			1.59773			0.798865	−	0.601510i	$-0.205434\pi$
$503$	35.8333			1.59773			0.798865	+	0.601510i	$0.205434\pi$
$504$	1.15367	+	7.85296i	0.0513886	+	0.349799i
$505$	5.72942			0.254956
$506$	13.7237			0.610095
$507$	−3.61674	+	2.23576i	−0.160625	+	0.0992935i
$508$	−2.31880			−0.102880
$509$	−6.93730	−	12.0158i	−0.307490	−	0.532589i	0.670322	−	0.742070i	$-0.266156\pi$
$509$	−6.93730	−	12.0158i	−0.307490	−	0.532589i	−0.977813	+	0.209481i	$0.932823\pi$
$510$	−8.83779	−	4.75407i	−0.391344	−	0.210514i
$511$	−30.1205	+	21.0212i	−1.33245	+	0.929924i
$512$	−1.00000			−0.0441942
$513$	22.1622	+	10.2548i	0.978487	+	0.452762i
$514$	3.88139	+	6.72276i	0.171201	+	0.296528i
$515$	−7.01544	+	12.1511i	−0.309137	+	0.535442i
$516$	5.31847	−	3.28771i	0.234132	−	0.144733i
$517$	8.11938	−	14.0632i	0.357090	−	0.618498i
$518$	−9.58788	−	4.48898i	−0.421267	−	0.197234i
$519$	0.662935	+	22.0372i	0.0290996	+	0.967328i
$520$	−3.24732			−0.142405
$521$	−5.15160	−	8.92284i	−0.225696	−	0.390917i	0.730832	−	0.682557i	$-0.239132\pi$
$521$	−5.15160	−	8.92284i	−0.225696	−	0.390917i	−0.956528	+	0.291641i	$0.905799\pi$
$522$	0.752808	+	1.13969i	0.0329495	+	0.0498830i
$523$	6.16132	−	10.6717i	0.269416	−	0.466642i	−0.699295	−	0.714833i	$-0.746503\pi$
$523$	6.16132	−	10.6717i	0.269416	−	0.466642i	0.968711	+	0.248191i	$0.0798360\pi$
$524$	9.38105	+	16.2485i	0.409813	+	0.709817i
$525$	1.81743	−	4.20677i	0.0793194	−	0.183599i
$526$	4.59133	−	7.95241i	0.200191	−	0.346742i
$527$	−20.6883	−	35.8332i	−0.901196	−	1.56092i
$528$	−7.84252	−	4.21869i	−0.341302	−	0.183595i
$529$	7.93754	−	13.7482i	0.345111	−	0.597749i
$530$	−1.63008	+	2.82338i	−0.0708061	+	0.122640i
$531$	33.3390	−	2.00766i	1.44679	−	0.0871248i
$532$	−11.2608	−	5.27225i	−0.488220	−	0.228581i
$533$	12.0510	+	20.8729i	0.521986	+	0.904106i
$534$	14.7415	+	7.92983i	0.637928	+	0.343157i
$535$	14.6071			0.631520
$536$	11.7774			0.508704
$537$	−34.2338	+	21.1623i	−1.47730	+	0.913219i
$538$	−9.03012	−	15.6406i	−0.389316	−	0.674315i
$539$	12.4139	−	33.7812i	0.534704	−	1.45506i
$540$	4.24762	−	2.99295i	0.182788	−	0.128796i
$541$	13.9275	−	24.1231i	0.598789	−	1.03713i	−0.394211	−	0.919020i	$-0.628982\pi$
$541$	13.9275	−	24.1231i	0.598789	−	1.03713i	0.993000	−	0.118113i	$-0.0376847\pi$
$542$	12.2464	−	21.2114i	0.526029	−	0.911109i
$543$	−0.993114	−	33.0130i	−0.0426186	−	1.41673i
$544$	2.89695	+	5.01766i	0.124206	+	0.215130i
$545$	−1.60392	+	2.77806i	−0.0687042	+	0.118999i
$546$	5.90180	−	13.6608i	0.252574	−	0.584626i
$547$	4.11573	+	7.12866i	0.175976	+	0.304799i	0.940499	−	0.339798i	$-0.110359\pi$
$547$	4.11573	+	7.12866i	0.175976	+	0.304799i	−0.764523	+	0.644597i	$0.777025\pi$
$548$	3.19895	−	5.54075i	0.136653	−	0.236689i
$549$	−17.9544	+	1.08121i	−0.766277	+	0.0461448i
$550$	2.57071	+	4.45260i	0.109615	+	0.189859i
$551$	−2.13969			−0.0911538
$552$	3.93256	−	2.43099i	0.167381	−	0.103470i
$553$	0.668643	+	7.78131i	0.0284336	+	0.330895i
$554$	−6.55834	+	11.3594i	−0.278637	+	0.482613i
$555$	0.208396	+	6.92749i	0.00884592	+	0.294056i
$556$	10.4744	−	18.1422i	0.444214	−	0.769402i
$557$	12.5376	+	21.7157i	0.531234	+	0.920125i	0.999335	+	0.0364501i	$0.0116050\pi$
$557$	12.5376	+	21.7157i	0.531234	+	0.920125i	−0.468101	+	0.883675i	$0.655062\pi$
$558$	21.3855	−	1.28782i	0.905321	−	0.0545179i
$559$	−11.7227			−0.495816
$560$	−2.16962	+	1.51418i	−0.0916831	+	0.0639860i
$561$	1.55143	+	51.5724i	0.0655012	+	2.17739i
$562$	−1.06057	−	1.83696i	−0.0447375	−	0.0774877i
$563$	16.4091			0.691561			0.345780	−	0.938315i	$-0.387614\pi$
$563$	16.4091			0.691561			0.345780	+	0.938315i	$0.387614\pi$
$564$	−0.164493	−	5.46807i	−0.00692641	−	0.230247i
$565$	2.29937			0.0967351
$566$	11.2536			0.473024
$567$	4.87089	+	23.3082i	0.204558	+	0.978854i
$568$	4.38588			0.184027
$569$	−31.7805			−1.33231			−0.666154	−	0.745814i	$-0.732061\pi$
$569$	−31.7805			−1.33231			−0.666154	+	0.745814i	$0.732061\pi$
$570$	0.244759	+	8.13625i	0.0102518	+	0.340790i
$571$	26.1756			1.09542			0.547708	−	0.836670i	$-0.315501\pi$
$571$	26.1756			1.09542			0.547708	+	0.836670i	$0.315501\pi$
$572$	8.34792	+	14.4590i	0.349044	+	0.604562i
$573$	1.36967	+	45.5305i	0.0572188	+	1.90206i
$574$	17.7843	+	8.32650i	0.742304	+	0.347542i
$575$	−2.66925			−0.111316
$576$	−2.99458	+	0.180332i	−0.124774	+	0.00751382i
$577$	21.3065	+	36.9039i	0.887000	+	1.53633i	0.843405	+	0.537279i	$0.180548\pi$
$577$	21.3065	+	36.9039i	0.887000	+	1.53633i	0.0435950	+	0.999049i	$0.486119\pi$
$578$	8.28460	−	14.3493i	0.344594	−	0.596854i
$579$	0.244187	+	8.11726i	0.0101481	+	0.337342i
$580$	−0.227646	+	0.394295i	−0.00945250	+	0.0163722i
$581$	−26.6122	+	18.5727i	−1.10406	+	0.770526i
$582$	11.5425	−	7.13523i	0.478453	−	0.295765i
$583$	16.7618			0.694204
$584$	−6.94143	−	12.0229i	−0.287238	−	0.497512i
$585$	−9.72436	+	0.585595i	−0.402053	+	0.0242114i
$586$	−4.80935	+	8.33003i	−0.198672	+	0.344111i
$587$	9.85073	+	17.0620i	0.406583	+	0.704223i	0.994504	−	0.104695i	$-0.0333868\pi$
$587$	9.85073	+	17.0620i	0.406583	+	0.704223i	−0.587921	+	0.808918i	$0.700053\pi$
$588$	−2.42669	−	11.8790i	−0.100075	−	0.489883i
$589$	−16.7809	+	29.0653i	−0.691444	+	1.19762i
$590$	5.56657	+	9.64157i	0.229172	+	0.396937i
$591$	0.544642	+	18.1050i	0.0224036	+	0.744739i
$592$	2.00070	−	3.46531i	0.0822282	−	0.142423i
$593$	−11.4796	+	19.8832i	−0.471411	+	0.816507i	−0.999465	−	0.0327034i	$-0.989588\pi$
$593$	−11.4796	+	19.8832i	−0.471411	+	0.816507i	0.528055	+	0.849210i	$0.322922\pi$
$594$	−24.2458	−	11.2189i	−0.994816	−	0.460318i
$595$	13.8829	+	6.49989i	0.569145	+	0.266470i
$596$	6.17989	+	10.7039i	0.253138	+	0.438448i
$597$	24.0455	−	14.8642i	0.984118	−	0.608351i
$598$	−8.66793			−0.354458
$599$	−8.63254			−0.352716			−0.176358	−	0.984326i	$-0.556432\pi$
$599$	−8.63254			−0.352716			−0.176358	+	0.984326i	$0.556432\pi$
$600$	1.52536	+	0.820531i	0.0622726	+	0.0334980i
$601$	10.2828	+	17.8104i	0.419445	+	0.726500i	0.995884	−	0.0906402i	$-0.0288913\pi$
$601$	10.2828	+	17.8104i	0.419445	+	0.726500i	−0.576439	+	0.817140i	$0.695558\pi$
$602$	−7.83221	+	5.46613i	−0.319217	+	0.222783i
$603$	35.2682	−	2.12383i	1.43623	−	0.0864890i
$604$	−9.70783	+	16.8145i	−0.395006	+	0.684171i
$605$	7.71707	−	13.3664i	0.313744	−	0.543420i
$606$	−8.73944	−	4.70116i	−0.355015	−	0.190972i
$607$	7.70623	+	13.3476i	0.312786	+	0.541762i	0.978964	−	0.204031i	$-0.0654043\pi$
$607$	7.70623	+	13.3476i	0.312786	+	0.541762i	−0.666178	+	0.745793i	$0.732071\pi$
$608$	2.34980	−	4.06997i	0.0952968	−	0.165059i
$609$	−1.24498	−	1.67426i	−0.0504490	−	0.0678445i
$610$	−2.99783	−	5.19239i	−0.121379	−	0.210234i
$611$	−5.12821	+	8.88232i	−0.207465	+	0.359340i
$612$	9.57997	+	14.5033i	0.387247	+	0.586263i
$613$	−3.08756	−	5.34781i	−0.124705	−	0.215996i	0.796912	−	0.604095i	$-0.206465\pi$
$613$	−3.08756	−	5.34781i	−0.124705	−	0.215996i	−0.921618	+	0.388099i	$0.873132\pi$
$614$	9.13535			0.368673
$615$	−0.386549	−	12.8496i	−0.0155872	−	0.518148i
$616$	12.3195	+	5.76791i	0.496367	+	0.232396i
$617$	6.63619	−	11.4942i	0.267163	−	0.462740i	−0.700965	−	0.713196i	$-0.747247\pi$
$617$	6.63619	−	11.4942i	0.267163	−	0.462740i	0.968128	+	0.250456i	$0.0805804\pi$
$618$	20.6714	−	12.7784i	0.831527	−	0.514025i
$619$	−12.5689	+	21.7700i	−0.505187	+	0.875010i	0.494795	+	0.869010i	$0.335243\pi$
$619$	−12.5689	+	21.7700i	−0.505187	+	0.875010i	−0.999982	+	0.00600015i	$0.998090\pi$
$620$	3.57071	+	6.18465i	0.143403	+	0.248381i
$621$	11.3380	−	7.98894i	0.454977	−	0.320585i
$622$	−20.5948			−0.825775
$623$	−23.1569	−	10.8419i	−0.927761	−	0.434371i
$624$	4.95334	+	2.66453i	0.198292	+	0.106666i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	0.550854			0.0220165
$627$	35.5982	−	22.0057i	1.42166	−	0.878825i
$628$	−2.46099			−0.0982043
$629$	−23.1837			−0.924394
$630$	−6.22403	+	4.92559i	−0.247971	+	0.196240i
$631$	−22.4313			−0.892978			−0.446489	−	0.894789i	$-0.647326\pi$
$631$	−22.4313			−0.892978			−0.446489	+	0.894789i	$0.647326\pi$
$632$	−2.95190			−0.117420
$633$	−6.63519	−	3.56923i	−0.263725	−	0.141864i
$634$	26.9744			1.07129
$635$	−1.15940	−	2.00814i	−0.0460093	−	0.0796905i
$636$	4.80313	−	2.96915i	0.190457	−	0.117734i
$637$	−7.84063	+	21.3362i	−0.310657	+	0.845372i
$638$	2.34085			0.0926750
$639$	13.1338	−	0.790913i	0.519567	−	0.0312880i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	19.5729	−	33.9012i	0.773082	−	1.33902i	−0.162784	−	0.986662i	$-0.552047\pi$
$641$	19.5729	−	33.9012i	0.773082	−	1.33902i	0.935866	−	0.352356i	$-0.114619\pi$
$642$	−22.2811	−	11.9856i	−0.879365	−	0.473033i
$643$	−17.4010	+	30.1395i	−0.686230	+	1.18859i	0.286818	+	0.957985i	$0.407402\pi$
$643$	−17.4010	+	30.1395i	−0.686230	+	1.18859i	−0.973048	+	0.230601i	$0.925931\pi$
$644$	−5.79126	+	4.04174i	−0.228208	+	0.159267i
$645$	5.50648	+	2.96207i	0.216817	+	0.116631i
$646$	−27.2289			−1.07131
$647$	15.2199	+	26.3617i	0.598357	+	1.03638i	0.993064	+	0.117578i	$0.0375129\pi$
$647$	15.2199	+	26.3617i	0.598357	+	1.03638i	−0.394707	+	0.918807i	$0.629154\pi$
$648$	−8.93496	+	1.08003i	−0.350998	+	0.0424277i
$649$	28.6200	−	49.5713i	1.12343	−	1.94585i
$650$	−1.62366	−	2.81226i	−0.0636853	−	0.110306i
$651$	−32.5069	+	3.78096i	−1.27405	+	0.148188i
$652$	4.96118	−	8.59301i	0.194295	−	0.336528i
$653$	6.76613	+	11.7193i	0.264779	+	0.458611i	0.967506	−	0.252849i	$-0.0813676\pi$
$653$	6.76613	+	11.7193i	0.264779	+	0.458611i	−0.702727	+	0.711460i	$0.748034\pi$
$654$	4.72604	−	2.92149i	0.184803	−	0.114239i
$655$	−9.38105	+	16.2485i	−0.366548	+	0.634880i
$656$	−3.71105	+	6.42773i	−0.144892	+	0.250961i
$657$	−22.9547	−	34.7518i	−0.895550	−	1.35579i
$658$	0.715423	+	8.32572i	0.0278901	+	0.324570i
$659$	4.39992	+	7.62088i	0.171397	+	0.296867i	0.938908	−	0.344167i	$-0.111839\pi$
$659$	4.39992	+	7.62088i	0.171397	+	0.296867i	−0.767512	+	0.641035i	$0.778505\pi$
$660$	−0.267769	−	8.90117i	−0.0104229	−	0.346477i
$661$	−35.9086			−1.39668			−0.698342	−	0.715764i	$-0.746079\pi$
$661$	−35.9086			−1.39668			−0.698342	+	0.715764i	$0.746079\pi$
$662$	16.8877			0.656358
$663$	−0.979882	−	32.5732i	−0.0380555	−	1.26504i
$664$	−6.13291	−	10.6225i	−0.238003	−	0.412234i
$665$	−1.06452	−	12.3883i	−0.0412803	−	0.480398i
$666$	5.36634	−	10.7379i	0.207941	−	0.416086i
$667$	−0.607646	+	1.05247i	−0.0235281	+	0.0407519i
$668$	−3.26841	+	5.66106i	−0.126459	+	0.219033i
$669$	−5.08921	+	3.14599i	−0.196760	+	0.121631i
$670$	5.88868	+	10.1995i	0.227500	+	0.394041i
$671$	−15.4131	+	26.6962i	−0.595015	+	1.03060i
$672$	4.55189	−	0.529441i	0.175593	−	0.0204236i
$673$	−11.4811	−	19.8858i	−0.442563	−	0.766541i	0.555316	−	0.831639i	$-0.312597\pi$
$673$	−11.4811	−	19.8858i	−0.442563	−	0.766541i	−0.997879	+	0.0650982i	$0.979264\pi$
$674$	−12.8294	+	22.2212i	−0.494171	+	0.855929i
$675$	4.71578	+	2.18207i	0.181510	+	0.0839879i
$676$	1.22744	+	2.12600i	0.0472094	+	0.0817691i
$677$	−32.5662			−1.25162			−0.625810	−	0.779975i	$-0.715232\pi$
$677$	−32.5662			−1.25162			−0.625810	+	0.779975i	$0.715232\pi$
$678$	−3.50737	−	1.88670i	−0.134700	−	0.0724583i
$679$	−16.9980	+	11.8630i	−0.652324	+	0.455259i
$680$	−2.89695	+	5.01766i	−0.111093	+	0.192418i
$681$	29.3015	+	15.7620i	1.12284	+	0.604002i
$682$	18.3585	−	31.7978i	0.702983	−	1.21760i
$683$	−25.6672	−	44.4569i	−0.982128	−	1.70110i	−0.654062	−	0.756441i	$-0.726936\pi$
$683$	−25.6672	−	44.4569i	−0.982128	−	1.70110i	−0.328066	−	0.944655i	$-0.606397\pi$
$684$	6.30270	−	12.6116i	0.240990	−	0.482215i
$685$	6.39791			0.244452
$686$	4.71028	+	17.9113i	0.179839	+	0.683855i
$687$	−31.9145	+	19.7286i	−1.21761	+	0.752692i
$688$	−1.80497	−	3.12631i	−0.0688140	−	0.119189i
$689$	−10.5868			−0.403325
$690$	4.07158	+	2.19020i	0.155002	+	0.0833796i
$691$	39.2794			1.49426			0.747130	−	0.664678i	$-0.231431\pi$
$691$	39.2794			1.49426			0.747130	+	0.664678i	$0.231431\pi$
$692$	12.7290			0.483883
$693$	37.9318	+	15.0508i	1.44091	+	0.571734i
$694$	17.0235			0.646204
$695$	20.9488			0.794635
$696$	0.670774	−	0.414652i	0.0254256	−	0.0157173i
$697$	43.0029			1.62885
$698$	11.3156	+	19.5992i	0.428301	+	0.741839i
$699$	−4.17824	−	2.24758i	−0.158036	−	0.0850113i
$700$	−2.39613	−	1.12185i	−0.0905653	−	0.0424020i
$701$	−40.2576			−1.52051			−0.760254	−	0.649626i	$-0.774926\pi$
$701$	−40.2576			−1.52051			−0.760254	+	0.649626i	$0.774926\pi$
$702$	15.3137	+	7.08589i	0.577977	+	0.267440i
$703$	9.40247	+	16.2856i	0.354621	+	0.614222i
$704$	−2.57071	+	4.45260i	−0.0968872	+	0.167814i
$705$	4.65324	−	2.87649i	0.175251	−	0.108335i
$706$	−4.37421	+	7.57635i	−0.164625	+	0.285140i
$707$	13.7284	+	6.42756i	0.516311	+	0.241733i
$708$	−0.579822	−	19.2744i	−0.0217911	−	0.724377i
$709$	13.2431			0.497355			0.248678	−	0.968586i	$-0.420004\pi$
$709$	13.2431			0.497355			0.248678	+	0.968586i	$0.420004\pi$
$710$	2.19294	+	3.79828i	0.0822996	+	0.142547i
$711$	−8.83968	+	0.532320i	−0.331514	+	0.0199636i
$712$	4.83214	−	8.36951i	0.181092	−	0.313661i
$713$	9.53112	+	16.5084i	0.356943	+	0.618244i
$714$	−15.8431	−	21.3061i	−0.592914	−	0.797359i
$715$	−8.34792	+	14.4590i	−0.312194	+	0.540737i
$716$	11.6182	+	20.1233i	0.434193	+	0.752044i
$717$	34.2235	+	18.4097i	1.27810	+	0.687521i
$718$	−13.0119	+	22.5373i	−0.485599	+	0.841083i
$719$	−22.7520	+	39.4076i	−0.848507	+	1.46966i	0.0340340	+	0.999421i	$0.489165\pi$
$719$	−22.7520	+	39.4076i	−0.848507	+	1.46966i	−0.882541	+	0.470236i	$0.844169\pi$
$720$	−1.65346	−	2.50321i	−0.0616208	−	0.0932892i
$721$	−30.4417	+	21.2454i	−1.13371	+	0.791218i
$722$	1.54309	+	2.67271i	0.0574278	+	0.0994679i
$723$	−33.3070	−	17.9167i	−1.23870	−	0.666328i
$724$	−19.0687			−0.708683
$725$	−0.455293			−0.0169091
$726$	−22.7388	+	14.0565i	−0.843918	+	0.521684i
$727$	0.0908081	+	0.157284i	0.00336789	+	0.00583335i	0.867704	−	0.497080i	$-0.165595\pi$
$727$	0.0908081	+	0.157284i	0.00336789	+	0.00583335i	−0.864337	+	0.502914i	$0.832261\pi$
$728$	−7.78102	−	3.64302i	−0.288384	−	0.135019i
$729$	−26.5616	+	4.84550i	−0.983765	+	0.179463i
$730$	6.94143	−	12.0229i	0.256914	−	0.444988i
$731$	−10.4578	+	18.1135i	−0.386797	+	0.669951i
$732$	0.312259	+	10.3801i	0.0115414	+	0.383659i
$733$	−23.0613	−	39.9434i	−0.851790	−	1.47534i	−0.879591	−	0.475730i	$-0.842184\pi$
$733$	−23.0613	−	39.9434i	−0.851790	−	1.47534i	0.0278011	−	0.999613i	$-0.491149\pi$
$734$	17.2794	−	29.9288i	0.637794	−	1.10469i
$735$	9.07419	−	8.04109i	0.334707	−	0.296600i
$736$	−1.33463	−	2.31164i	−0.0491950	−	0.0852082i
$737$	30.2761	−	52.4398i	1.11524	−	1.93165i
$738$	−9.95390	+	19.9175i	−0.366408	+	0.733175i
$739$	−8.94515	−	15.4935i	−0.329053	−	0.569936i	0.653271	−	0.757124i	$-0.273396\pi$
$739$	−8.94515	−	15.4935i	−0.329053	−	0.569936i	−0.982324	+	0.187188i	$0.940063\pi$
$740$	4.00140			0.147094
$741$	−22.4839	+	13.8989i	−0.825967	+	0.510587i
$742$	−7.07330	+	4.93648i	−0.259669	+	0.181224i
$743$	−8.34901	+	14.4609i	−0.306295	+	0.530519i	−0.977549	−	0.210709i	$-0.932423\pi$
$743$	−8.34901	+	14.4609i	−0.306295	+	0.530519i	0.671253	+	0.741228i	$0.265756\pi$
$744$	−0.371931	−	12.3637i	−0.0136356	−	0.453275i
$745$	−6.17989	+	10.7039i	−0.226413	+	0.392160i
$746$	4.48949	+	7.77603i	0.164372	+	0.284701i
$747$	−20.2810	−	30.7040i	−0.742044	−	1.12340i
$748$	29.7888			1.08919
$749$	35.0005	+	16.3870i	1.27889	+	0.598768i
$750$	0.0520808	+	1.73127i	0.00190172	+	0.0632170i
$751$	−15.6276	−	27.0678i	−0.570260	−	0.987719i	−0.996539	−	0.0831273i	$-0.973509\pi$
$751$	−15.6276	−	27.0678i	−0.570260	−	0.987719i	0.426279	−	0.904592i	$-0.359824\pi$
$752$	−3.15842			−0.115176
$753$	−0.294687	−	9.79596i	−0.0107390	−	0.356984i
$754$	−1.47848			−0.0538431
$755$	−19.4157			−0.706608
$756$	13.5355	−	2.40630i	0.492281	−	0.0875163i
$757$	23.1959			0.843069			0.421534	−	0.906812i	$-0.361492\pi$
$757$	23.1959			0.843069			0.421534	+	0.906812i	$0.361492\pi$
$758$	21.2288			0.771064
$759$	−0.714744	−	23.7595i	−0.0259435	−	0.862414i
$760$	4.69959			0.170472
$761$	−13.2425	−	22.9366i	−0.480039	−	0.831452i	0.519699	−	0.854349i	$-0.326044\pi$
$761$	−13.2425	−	22.9366i	−0.480039	−	0.831452i	−0.999738	+	0.0228979i	$0.992711\pi$
$762$	0.120765	+	4.01446i	0.00437485	+	0.145428i
$763$	−6.95977	+	4.85725i	−0.251961	+	0.175844i
$764$	26.2989			0.951462
$765$	−7.77028	+	15.5482i	−0.280935	+	0.562145i
$766$	0.108153	+	0.187326i	0.00390771	+	0.00676835i
$767$	−18.0764	+	31.3093i	−0.652702	+	1.13051i
$768$	0.0520808	+	1.73127i	0.00187930	+	0.0624717i
$769$	20.5798	−	35.6452i	0.742126	−	1.28540i	−0.209399	−	0.977830i	$-0.567151\pi$
$769$	20.5798	−	35.6452i	0.742126	−	1.28540i	0.951525	−	0.307570i	$-0.0995159\pi$
$770$	1.16460	+	13.5530i	0.0419692	+	0.488415i
$771$	11.4367	−	7.06985i	0.411884	−	0.254614i
$772$	4.68862			0.168747
$773$	−13.2736	−	22.9905i	−0.477418	−	0.826912i	0.522247	−	0.852794i	$-0.325094\pi$
$773$	−13.2736	−	22.9905i	−0.477418	−	0.826912i	−0.999665	+	0.0258823i	$0.991761\pi$
$774$	−5.96890	−	9.03646i	−0.214548	−	0.324809i
$775$	−3.57071	+	6.18465i	−0.128264	+	0.222159i
$776$	−3.91728	−	6.78493i	−0.140622	−	0.243565i
$777$	−7.27228	+	16.8330i	−0.260892	+	0.603879i
$778$	−5.81312	+	10.0686i	−0.208410	+	0.360977i
$779$	−17.4404	−	30.2077i	−0.624868	−	1.08230i
$780$	0.169123	+	5.62199i	0.00605558	+	0.201299i
$781$	11.2748	−	19.5286i	0.403445	−	0.698787i
$782$	−7.73269	+	13.3934i	−0.276520	+	0.478947i
$783$	1.93391	−	1.36267i	0.0691122	−	0.0486978i
$784$	−6.89738	+	1.19419i	−0.246335	+	0.0426497i
$785$	−1.23050	−	2.13128i	−0.0439183	−	0.0760687i
$786$	27.6419	−	17.0873i	0.985952	−	0.609485i
$787$	24.2171			0.863248			0.431624	−	0.902054i	$-0.357941\pi$
$787$	24.2171			0.863248			0.431624	+	0.902054i	$0.357941\pi$
$788$	10.4576			0.372538
$789$	−14.0069	−	7.53465i	−0.498658	−	0.268241i
$790$	−1.47595	−	2.55642i	−0.0525119	−	0.0909533i
$791$	5.50959	+	2.57955i	0.195898	+	0.0917183i
$792$	−6.89523	+	13.7972i	−0.245011	+	0.490263i
$793$	9.73492	−	16.8614i	0.345697	−	0.598765i
$794$	14.1667	−	24.5375i	0.502758	−	0.870802i
$795$	4.97292	+	2.67506i	0.176371	+	0.0948746i
$796$	−8.16053	−	14.1345i	−0.289242	−	0.500983i
$797$	3.05746	−	5.29567i	0.108301	−	0.187582i	−0.806781	−	0.590850i	$-0.798792\pi$
$797$	3.05746	−	5.29567i	0.108301	−	0.187582i	0.915082	+	0.403268i	$0.132126\pi$
$798$	−8.54120	+	19.7701i	−0.302355	+	0.699855i
$799$	9.14978	+	15.8479i	0.323696	+	0.560658i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	12.9609	−	25.9345i	0.457951	−	0.916351i
$802$	−3.41125	−	5.90845i	−0.120455	−	0.208635i
$803$	−71.3776			−2.51886
$804$	−0.613374	−	20.3898i	−0.0216320	−	0.719091i
$805$	−6.39588	−	2.99451i	−0.225425	−	0.105543i
$806$	−11.5952	+	20.0836i	−0.408425	+	0.707413i
$807$	−26.6078	+	16.4481i	−0.936640	+	0.579002i
$808$	−2.86471	+	4.96182i	−0.100780	+	0.174556i
$809$	10.3380	+	17.9059i	0.363464	+	0.629538i	0.988528	−	0.151035i	$-0.0482607\pi$
$809$	10.3380	+	17.9059i	0.363464	+	0.629538i	−0.625065	+	0.780573i	$0.714927\pi$
$810$	−5.40282	−	7.19789i	−0.189836	−	0.252908i
$811$	15.2973			0.537160			0.268580	−	0.963257i	$-0.413446\pi$
$811$	15.2973			0.537160			0.268580	+	0.963257i	$0.413446\pi$
$812$	−0.987811	+	0.689397i	−0.0346654	+	0.0241931i
$813$	−37.3605	−	20.0971i	−1.31029	−	0.704837i
$814$	−10.2864	−	17.8166i	−0.360539	−	0.624472i
$815$	9.92235			0.347565
$816$	8.53604	−	5.27671i	0.298821	−	0.184722i
$817$	16.9653			0.593540
$818$	−11.1738			−0.390684
$819$	−23.9578	−	9.50613i	−0.837153	−	0.332171i
$820$	−7.42210			−0.259191
$821$	6.75181			0.235640			0.117820	−	0.993035i	$-0.462409\pi$
$821$	6.75181			0.235640			0.117820	+	0.993035i	$0.462409\pi$
$822$	−9.75913	−	5.24968i	−0.340389	−	0.183104i
$823$	22.6740			0.790365			0.395183	−	0.918603i	$-0.370681\pi$
$823$	22.6740			0.790365			0.395183	+	0.918603i	$0.370681\pi$
$824$	−7.01544	−	12.1511i	−0.244395	−	0.423304i
$825$	7.57475	−	4.68248i	0.263719	−	0.163023i
$826$	2.52180	+	29.3473i	0.0877446	+	1.02112i
$827$	−26.0867			−0.907122			−0.453561	−	0.891225i	$-0.649847\pi$
$827$	−26.0867			−0.907122			−0.453561	+	0.891225i	$0.649847\pi$
$828$	−4.41350	−	6.68171i	−0.153380	−	0.232205i
$829$	−1.68725	−	2.92240i	−0.0586005	−	0.101499i	0.835237	−	0.549890i	$-0.185330\pi$
$829$	−1.68725	−	2.92240i	−0.0586005	−	0.101499i	−0.893837	+	0.448391i	$0.851997\pi$
$830$	6.13291	−	10.6225i	0.212876	−	0.368713i
$831$	20.0077	+	10.7626i	0.694059	+	0.373351i
$832$	1.62366	−	2.81226i	0.0562903	−	0.0974977i
$833$	25.9734	+	31.1492i	0.899925	+	1.07926i
$834$	−31.9546	−	17.1892i	−1.10650	−	0.595212i
$835$	−6.53683			−0.226216
$836$	−12.0813	−	20.9254i	−0.417840	−	0.723720i
$837$	−3.34334	−	36.9570i	−0.115563	−	1.27742i
$838$	2.78160	−	4.81787i	0.0960887	−	0.166430i
$839$	−11.2557	−	19.4955i	−0.388590	−	0.673058i	0.603670	−	0.797234i	$-0.293704\pi$
$839$	−11.2557	−	19.4955i	−0.388590	−	0.673058i	−0.992260	+	0.124176i	$0.960371\pi$
$840$	2.73445	+	3.67733i	0.0943476	+	0.126880i
$841$	14.3964	−	24.9352i	0.496426	−	0.859835i
$842$	17.2899	+	29.9470i	0.595849	+	1.03204i
$843$	−3.12504	+	1.93180i	−0.107632	+	0.0665349i
$844$	−2.17495	+	3.76713i	−0.0748650	+	0.129670i
$845$	−1.22744	+	2.12600i	−0.0422254	+	0.0731365i
$846$	−9.45813	+	0.569563i	−0.325177	+	0.0195820i
$847$	33.4862	−	23.3701i	1.15060	−	0.803008i
$848$	−1.63008	−	2.82338i	−0.0559771	−	0.0969553i
$849$	−0.586096	−	19.4830i	−0.0201148	−	0.668654i
$850$	−5.79389			−0.198729
$851$	10.6807			0.366131
$852$	−0.228420	−	7.59313i	−0.00782555	−	0.260136i
$853$	12.9138	+	22.3673i	0.442159	+	0.765842i	0.997849	−	0.0655473i	$-0.0208793\pi$
$853$	12.9138	+	22.3673i	0.442159	+	0.765842i	−0.555690	+	0.831389i	$0.687546\pi$
$854$	−1.35809	−	15.8048i	−0.0464730	−	0.540828i
$855$	14.0733	−	0.847485i	0.481296	−	0.0289834i
$856$	−7.30355	+	12.6501i	−0.249630	+	0.432372i
$857$	−12.2157	+	21.1583i	−0.417281	+	0.722752i	−0.995665	−	0.0930126i	$-0.970350\pi$
$857$	−12.2157	+	21.1583i	−0.417281	+	0.722752i	0.578384	+	0.815765i	$0.303684\pi$
$858$	24.5977	−	15.2055i	0.839751	−	0.519108i
$859$	−9.45204	−	16.3714i	−0.322500	−	0.558586i	0.658504	−	0.752578i	$-0.271190\pi$
$859$	−9.45204	−	16.3714i	−0.322500	−	0.558586i	−0.981003	+	0.193992i	$0.937856\pi$
$860$	1.80497	−	3.12631i	0.0615491	−	0.106606i
$861$	13.4892	−	31.2231i	0.459710	−	1.06408i
$862$	−19.2277	−	33.3034i	−0.654899	−	1.13432i
$863$	1.64446	−	2.84828i	0.0559779	−	0.0969566i	−0.836679	−	0.547694i	$-0.815506\pi$
$863$	1.64446	−	2.84828i	0.0559779	−	0.0969566i	0.892656	+	0.450738i	$0.148839\pi$
$864$	0.468162	+	5.17502i	0.0159272	+	0.176058i
$865$	6.36448	+	11.0236i	0.216399	+	0.374814i
$866$	−30.9550			−1.05189
$867$	−25.2740	−	13.5955i	−0.858351	−	0.461729i
$868$	1.61762	+	18.8250i	0.0549057	+	0.638963i
$869$	−7.58846	+	13.1436i	−0.257421	+	0.445866i
$870$	0.694486	+	0.373581i	0.0235453	+	0.0126656i
$871$	−19.1224	+	33.1211i	−0.647939	+	1.12226i
$872$	−1.60392	−	2.77806i	−0.0543154	−	0.0940771i
$873$	−12.9541	−	19.6116i	−0.438431	−	0.663751i
$874$	12.5444			0.424321
$875$	−0.226513	−	2.63604i	−0.00765753	−	0.0891143i
$876$	−20.4534	+	12.6436i	−0.691055	+	0.427189i
$877$	13.3996	+	23.2088i	0.452473	+	0.783706i	0.998539	−	0.0540359i	$-0.0172085\pi$
$877$	13.3996	+	23.2088i	0.452473	+	0.783706i	−0.546066	+	0.837742i	$0.683875\pi$
$878$	−26.8388			−0.905767
$879$	14.6720	+	7.89243i	0.494874	+	0.266205i
$880$	−5.14142			−0.173317
$881$	20.9761			0.706703			0.353352	−	0.935491i	$-0.385042\pi$
$881$	20.9761			0.706703			0.353352	+	0.935491i	$0.385042\pi$
$882$	−20.4394	+	4.81992i	−0.688230	+	0.162295i
$883$	−24.9042			−0.838093			−0.419047	−	0.907965i	$-0.637636\pi$
$883$	−24.9042			−0.838093			−0.419047	+	0.907965i	$0.637636\pi$
$884$	−18.8146			−0.632805
$885$	16.4022	−	10.1394i	0.551355	−	0.340831i
$886$	32.2517			1.08352
$887$	−11.0910	−	19.2102i	−0.372399	−	0.645014i	0.617535	−	0.786544i	$-0.288131\pi$
$887$	−11.0910	−	19.2102i	−0.372399	−	0.645014i	−0.989934	+	0.141529i	$0.954798\pi$
$888$	−6.10358	−	3.28327i	−0.204823	−	0.110179i
$889$	−0.525237	−	6.11243i	−0.0176159	−	0.205004i
$890$	9.66427			0.323947
$891$	−18.1602	+	42.5602i	−0.608390	+	1.42582i
$892$	1.72717	+	2.99154i	0.0578298	+	0.100164i
$893$	7.42165	−	12.8547i	0.248356	−	0.430165i
$894$	18.2094	−	11.2565i	0.609014	−	0.376474i
$895$	−11.6182	+	20.1233i	−0.388354	+	0.672649i
$896$	−0.226513	−	2.63604i	−0.00756727	−	0.0880638i
$897$	0.451433	+	15.0065i	0.0150729	+	0.501053i
$898$	9.45029			0.315360
$899$	1.62572	+	2.81582i	0.0542207	+	0.0939130i
$900$	1.34112	−	2.68354i	0.0447039	−	0.0894515i
$901$	−9.44451	+	16.3584i	−0.314642	+	0.544976i
$902$	19.0801	+	33.0476i	0.635296	+	1.10037i
$903$	9.87123	+	13.2750i	0.328494	+	0.441763i
$904$	−1.14968	+	1.99131i	−0.0382379	+	0.0662300i
$905$	−9.53436	−	16.5140i	−0.316933	−	0.548944i
$906$	29.6159	+	15.9311i	0.983923	+	0.529277i
$907$	−28.3365	+	49.0802i	−0.940897	+	1.62968i	−0.177131	+	0.984187i	$0.556682\pi$
$907$	−28.3365	+	49.0802i	−0.940897	+	1.62968i	−0.763766	+	0.645494i	$0.776652\pi$
$908$	9.60477	−	16.6359i	0.318745	−	0.552083i
$909$	−7.68382	+	15.3751i	−0.254856	+	0.509962i
$910$	−0.735561	−	8.56007i	−0.0243836	−	0.283763i
$911$	22.6917	+	39.3032i	0.751809	+	1.30217i	0.946945	+	0.321396i	$0.104152\pi$
$911$	22.6917	+	39.3032i	0.751809	+	1.30217i	−0.195136	+	0.980776i	$0.562515\pi$
$912$	−7.16858	−	3.85616i	−0.237375	−	0.127690i
$913$	−63.0637			−2.08710
$914$	−25.3313			−0.837885
$915$	−8.83329	+	5.46047i	−0.292020	+	0.180517i
$916$	10.8311	+	18.7600i	0.357870	+	0.619848i
$917$	−40.7066	+	28.4093i	−1.34425	+	0.938157i
$918$	24.6102	−	17.3408i	0.812259	−	0.572333i
$919$	−5.64196	+	9.77216i	−0.186111	+	0.322354i	−0.943950	−	0.330087i	$-0.892922\pi$
$919$	−5.64196	+	9.77216i	−0.186111	+	0.322354i	0.757839	+	0.652441i	$0.226255\pi$
$920$	1.33463	−	2.31164i	0.0440013	−	0.0762126i
$921$	−0.475776	−	15.8157i	−0.0156774	−	0.521146i
$922$	−0.0688453	−	0.119244i	−0.00226730	−	0.00392708i
$923$	−7.12119	+	12.3343i	−0.234397	+	0.405987i
$924$	9.34419	−	21.6288i	0.307401	−	0.711534i
$925$	2.00070	+	3.46531i	0.0657826	+	0.113939i
$926$	8.01422	−	13.8810i	0.263364	−	0.456159i
$927$	−23.1995	−	35.1223i	−0.761972	−	1.15357i
$928$	−0.227646	−	0.394295i	−0.00747285	−	0.0129434i
$929$	−8.70979			−0.285759			−0.142879	−	0.989740i	$-0.545636\pi$
$929$	−8.70979			−0.285759			−0.142879	+	0.989740i	$0.545636\pi$
$930$	10.5213	−	6.50395i	0.345007	−	0.213273i
$931$	11.3471	−	30.8782i	0.371887	−	1.01199i
$932$	−1.36959	+	2.37220i	−0.0448624	+	0.0777040i
$933$	1.07259	+	35.6550i	0.0351151	+	1.16729i
$934$	−10.9032	+	18.8849i	−0.356763	+	0.617932i
$935$	14.8944	+	25.7979i	0.487099	+	0.843680i
$936$	4.35504	−	8.71434i	0.142349	−	0.284837i
$937$	−12.4809			−0.407735			−0.203867	−	0.978999i	$-0.565351\pi$
$937$	−12.4809			−0.407735			−0.203867	+	0.978999i	$0.565351\pi$
$938$	2.66772	+	31.0456i	0.0871043	+	1.01367i
$939$	−0.0286889	−	0.953675i	−0.000936227	−	0.0311220i
$940$	−1.57921	−	2.73527i	−0.0515082	−	0.0892148i
$941$	23.5970			0.769241			0.384620	−	0.923075i	$-0.374332\pi$
$941$	23.5970			0.769241			0.384620	+	0.923075i	$0.374332\pi$
$942$	0.128170	+	4.26064i	0.00417602	+	0.138819i
$943$	−19.8115			−0.645150
$944$	−11.1331			−0.362353
$945$	8.85167	+	10.5189i	0.287945	+	0.342181i
$946$	−18.5602			−0.603445
$947$	−15.7374			−0.511396			−0.255698	−	0.966757i	$-0.582305\pi$
$947$	−15.7374			−0.511396			−0.255698	+	0.966757i	$0.582305\pi$
$948$	0.153737	+	5.11052i	0.00499315	+	0.165982i
$949$	45.0821			1.46343
$950$	2.34980	+	4.06997i	0.0762375	+	0.132047i
$951$	−1.40485	−	46.6999i	−0.0455554	−	1.51435i
$952$	−12.5705	+	8.77302i	−0.407414	+	0.284335i
$953$	−3.60070			−0.116638			−0.0583191	−	0.998298i	$-0.518574\pi$
$953$	−3.60070			−0.116638			−0.0583191	+	0.998298i	$0.518574\pi$
$954$	−5.39054	−	8.16087i	−0.174525	−	0.264218i
$955$	13.1495	+	22.7755i	0.425507	+	0.736999i
$956$	11.2181	−	19.4304i	0.362821	−	0.628424i
$957$	−0.121913	−	4.05263i	−0.00394090	−	0.131003i
$958$	−8.13300	+	14.0868i	−0.262765	+	0.455123i
$959$	15.3302	+	7.17751i	0.495039	+	0.231774i
$960$	−1.47328	+	0.910737i	−0.0475500	+	0.0293939i
$961$	19.9998			0.645155
$962$	6.49692	+	11.2530i	0.209469	+	0.362811i
$963$	−19.5898	+	39.1988i	−0.631273	+	1.26316i
$964$	−10.9177	+	18.9101i	−0.351636	+	0.609052i
$965$	2.34431	+	4.06047i	0.0754660	+	0.130711i
$966$	7.29895	+	9.81573i	0.234840	+	0.315816i
$967$	17.9234	−	31.0443i	0.576379	−	0.998317i	−0.419511	−	0.907750i	$-0.637799\pi$
$967$	17.9234	−	31.0443i	0.576379	−	0.998317i	0.995890	−	0.0905674i	$-0.0288681\pi$
$968$	7.71707	+	13.3664i	0.248036	+	0.429611i
$969$	1.41811	+	47.1406i	0.0455561	+	1.51437i
$970$	3.91728	−	6.78493i	0.125776	−	0.217851i
$971$	−4.25320	+	7.36675i	−0.136492	+	0.236410i	−0.926166	−	0.377115i	$-0.876916\pi$
$971$	−4.25320	+	7.36675i	−0.136492	+	0.236410i	0.789675	+	0.613526i	$0.210249\pi$
$972$	2.33517	+	15.4126i	0.0749005	+	0.494358i
$973$	50.1962	+	23.5015i	1.60922	+	0.753424i
$974$	17.0685	+	29.5636i	0.546911	+	0.947278i
$975$	−4.78422	+	2.95746i	−0.153218	+	0.0947145i
$976$	5.99566			0.191916
$977$	35.5608			1.13769			0.568845	−	0.822445i	$-0.307390\pi$
$977$	35.5608			1.13769			0.568845	+	0.822445i	$0.307390\pi$
$978$	−15.1352	−	8.14159i	−0.483970	−	0.260339i
$979$	−24.8440	−	43.0311i	−0.794018	−	1.37528i
$980$	−4.48289	−	5.37621i	−0.143201	−	0.171737i
$981$	−5.30402	−	8.02988i	−0.169344	−	0.256374i
$982$	−21.6539	+	37.5057i	−0.691004	+	1.19685i
$983$	30.7054	−	53.1834i	0.979351	−	1.69629i	0.314594	−	0.949226i	$-0.398132\pi$
$983$	30.7054	−	53.1834i	0.979351	−	1.69629i	0.664757	−	0.747059i	$-0.268535\pi$
$984$	11.3214	+	6.09006i	0.360913	+	0.194144i
$985$	5.22882	+	9.05658i	0.166604	+	0.288567i
$986$	−1.31896	+	2.28450i	−0.0420042	+	0.0727534i
$987$	14.3768	−	1.67220i	0.457618	−	0.0532267i
$988$	7.63055	+	13.2165i	0.242760	+	0.420473i
$989$	4.81793	−	8.34490i	0.153201	−	0.265352i
$990$	−15.3964	+	0.927160i	−0.489328	+	0.0294671i
$991$	−12.6801	−	21.9626i	−0.402796	−	0.697664i	0.591266	−	0.806477i	$-0.298628\pi$
$991$	−12.6801	−	21.9626i	−0.402796	−	0.697664i	−0.994062	+	0.108813i	$0.965295\pi$
$992$	−7.14142			−0.226740
$993$	−0.879524	−	29.2371i	−0.0279108	−	0.927811i
$994$	0.993459	+	11.5613i	0.0315106	+	0.366704i
$995$	8.16053	−	14.1345i	0.258706	−	0.448093i
$996$	−18.0710	+	11.1709i	−0.572602	+	0.353965i
$997$	0.665689	−	1.15301i	0.0210826	−	0.0365161i	−0.855292	−	0.518147i	$-0.826622\pi$
$997$	0.665689	−	1.15301i	0.0210826	−	0.0365161i	0.876374	+	0.481631i	$0.159955\pi$
$998$	3.32314	+	5.75585i	0.105192	+	0.182198i
$999$	−18.8697	−	8.73133i	−0.597011	−	0.276247i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.i.121.4	✓	16
3.2	odd	2		1890.2.i.i.1171.4		16
7.4	even	3		630.2.l.i.571.7	yes	16
9.2	odd	6		1890.2.l.i.1801.7		16
9.7	even	3		630.2.l.i.331.7	yes	16
21.11	odd	6		1890.2.l.i.361.7		16
63.11	odd	6		1890.2.i.i.991.4		16
63.25	even	3	inner	630.2.i.i.151.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.i.121.4	✓	16	1.1	even	1	trivial
630.2.i.i.151.4	yes	16	63.25	even	3	inner
630.2.l.i.331.7	yes	16	9.7	even	3
630.2.l.i.571.7	yes	16	7.4	even	3
1890.2.i.i.991.4		16	63.11	odd	6
1890.2.i.i.1171.4		16	3.2	odd	2
1890.2.l.i.361.7		16	21.11	odd	6
1890.2.l.i.1801.7		16	9.2	odd	6

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.0520808 + 1.73127i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.0520808 - 1.73127i) q^{6} +(0.226513 + 2.63604i) q^{7} -1.00000 q^{8} +(-2.99458 + 0.180332i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.0520808 + 1.73127i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.0520808 - 1.73127i) q^{6} +(0.226513 + 2.63604i) q^{7} -1.00000 q^{8} +(-2.99458 + 0.180332i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-2.57071 + 4.45260i) q^{11} +(0.0520808 + 1.73127i) q^{12} +(1.62366 - 2.81226i) q^{13} +(-0.226513 - 2.63604i) q^{14} +(-1.47328 + 0.910737i) q^{15} +1.00000 q^{16} +(-2.89695 - 5.01766i) q^{17} +(2.99458 - 0.180332i) q^{18} +(-2.34980 + 4.06997i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-4.55189 + 0.529441i) q^{21} +(2.57071 - 4.45260i) q^{22} +(1.33463 + 2.31164i) q^{23} +(-0.0520808 - 1.73127i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.62366 + 2.81226i) q^{26} +(-0.468162 - 5.17502i) q^{27} +(0.226513 + 2.63604i) q^{28} +(0.227646 + 0.394295i) q^{29} +(1.47328 - 0.910737i) q^{30} +7.14142 q^{31} -1.00000 q^{32} +(-7.84252 - 4.21869i) q^{33} +(2.89695 + 5.01766i) q^{34} +(-2.16962 + 1.51418i) q^{35} +(-2.99458 + 0.180332i) q^{36} +(2.00070 - 3.46531i) q^{37} +(2.34980 - 4.06997i) q^{38} +(4.95334 + 2.66453i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-3.71105 + 6.42773i) q^{41} +(4.55189 - 0.529441i) q^{42} +(-1.80497 - 3.12631i) q^{43} +(-2.57071 + 4.45260i) q^{44} +(-1.65346 - 2.50321i) q^{45} +(-1.33463 - 2.31164i) q^{46} -3.15842 q^{47} +(0.0520808 + 1.73127i) q^{48} +(-6.89738 + 1.19419i) q^{49} +(0.500000 - 0.866025i) q^{50} +(8.53604 - 5.27671i) q^{51} +(1.62366 - 2.81226i) q^{52} +(-1.63008 - 2.82338i) q^{53} +(0.468162 + 5.17502i) q^{54} -5.14142 q^{55} +(-0.226513 - 2.63604i) q^{56} +(-7.16858 - 3.85616i) q^{57} +(-0.227646 - 0.394295i) q^{58} -11.1331 q^{59} +(-1.47328 + 0.910737i) q^{60} +5.99566 q^{61} -7.14142 q^{62} +(-1.15367 - 7.85296i) q^{63} +1.00000 q^{64} +3.24732 q^{65} +(7.84252 + 4.21869i) q^{66} -11.7774 q^{67} +(-2.89695 - 5.01766i) q^{68} +(-3.93256 + 2.43099i) q^{69} +(2.16962 - 1.51418i) q^{70} -4.38588 q^{71} +(2.99458 - 0.180332i) q^{72} +(6.94143 + 12.0229i) q^{73} +(-2.00070 + 3.46531i) q^{74} +(-1.52536 - 0.820531i) q^{75} +(-2.34980 + 4.06997i) q^{76} +(-12.3195 - 5.76791i) q^{77} +(-4.95334 - 2.66453i) q^{78} +2.95190 q^{79} +(0.500000 + 0.866025i) q^{80} +(8.93496 - 1.08003i) q^{81} +(3.71105 - 6.42773i) q^{82} +(6.13291 + 10.6225i) q^{83} +(-4.55189 + 0.529441i) q^{84} +(2.89695 - 5.01766i) q^{85} +(1.80497 + 3.12631i) q^{86} +(-0.670774 + 0.414652i) q^{87} +(2.57071 - 4.45260i) q^{88} +(-4.83214 + 8.36951i) q^{89} +(1.65346 + 2.50321i) q^{90} +(7.78102 + 3.64302i) q^{91} +(1.33463 + 2.31164i) q^{92} +(0.371931 + 12.3637i) q^{93} +3.15842 q^{94} -4.69959 q^{95} +(-0.0520808 - 1.73127i) q^{96} +(3.91728 + 6.78493i) q^{97} +(6.89738 - 1.19419i) q^{98} +(6.89523 - 13.7972i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} + 2 q^{3} + 16 q^{4} + 8 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} - 6 q^{9}+O(q^{10}) \) 16 * q - 16 * q^2 + 2 * q^3 + 16 * q^4 + 8 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 - 6 * q^9	\( 16 q - 16 q^{2} + 2 q^{3} + 16 q^{4} + 8 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} - 6 q^{9} - 8 q^{10} + q^{11} + 2 q^{12} + 2 q^{13} - 4 q^{14} + q^{15} + 16 q^{16} + 11 q^{17} + 6 q^{18} - 2 q^{19} + 8 q^{20} - 15 q^{21} - q^{22} + 11 q^{23} - 2 q^{24} - 8 q^{25} - 2 q^{26} - 7 q^{27} + 4 q^{28} + 17 q^{29} - q^{30} + 30 q^{31} - 16 q^{32} + 5 q^{33} - 11 q^{34} - 4 q^{35} - 6 q^{36} - 2 q^{37} + 2 q^{38} - 8 q^{40} + 7 q^{41} + 15 q^{42} - 13 q^{43} + q^{44} + 3 q^{45} - 11 q^{46} + 10 q^{47} + 2 q^{48} - 14 q^{49} + 8 q^{50} - 3 q^{51} + 2 q^{52} + 18 q^{53} + 7 q^{54} + 2 q^{55} - 4 q^{56} - 4 q^{57} - 17 q^{58} - 2 q^{59} + q^{60} + 54 q^{61} - 30 q^{62} + 41 q^{63} + 16 q^{64} + 4 q^{65} - 5 q^{66} + 20 q^{67} + 11 q^{68} - 14 q^{69} + 4 q^{70} - 38 q^{71} + 6 q^{72} - 8 q^{73} + 2 q^{74} - q^{75} - 2 q^{76} - 7 q^{77} + 50 q^{79} + 8 q^{80} - 6 q^{81} - 7 q^{82} + 2 q^{83} - 15 q^{84} - 11 q^{85} + 13 q^{86} - 32 q^{87} - q^{88} - 6 q^{89} - 3 q^{90} + 14 q^{91} + 11 q^{92} - 6 q^{93} - 10 q^{94} - 4 q^{95} - 2 q^{96} + 26 q^{97} + 14 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q - 16 * q^2 + 2 * q^3 + 16 * q^4 + 8 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 - 6 * q^9 - 8 * q^10 + q^11 + 2 * q^12 + 2 * q^13 - 4 * q^14 + q^15 + 16 * q^16 + 11 * q^17 + 6 * q^18 - 2 * q^19 + 8 * q^20 - 15 * q^21 - q^22 + 11 * q^23 - 2 * q^24 - 8 * q^25 - 2 * q^26 - 7 * q^27 + 4 * q^28 + 17 * q^29 - q^30 + 30 * q^31 - 16 * q^32 + 5 * q^33 - 11 * q^34 - 4 * q^35 - 6 * q^36 - 2 * q^37 + 2 * q^38 - 8 * q^40 + 7 * q^41 + 15 * q^42 - 13 * q^43 + q^44 + 3 * q^45 - 11 * q^46 + 10 * q^47 + 2 * q^48 - 14 * q^49 + 8 * q^50 - 3 * q^51 + 2 * q^52 + 18 * q^53 + 7 * q^54 + 2 * q^55 - 4 * q^56 - 4 * q^57 - 17 * q^58 - 2 * q^59 + q^60 + 54 * q^61 - 30 * q^62 + 41 * q^63 + 16 * q^64 + 4 * q^65 - 5 * q^66 + 20 * q^67 + 11 * q^68 - 14 * q^69 + 4 * q^70 - 38 * q^71 + 6 * q^72 - 8 * q^73 + 2 * q^74 - q^75 - 2 * q^76 - 7 * q^77 + 50 * q^79 + 8 * q^80 - 6 * q^81 - 7 * q^82 + 2 * q^83 - 15 * q^84 - 11 * q^85 + 13 * q^86 - 32 * q^87 - q^88 - 6 * q^89 - 3 * q^90 + 14 * q^91 + 11 * q^92 - 6 * q^93 - 10 * q^94 - 4 * q^95 - 2 * q^96 + 26 * q^97 + 14 * q^98 - 5 * q^99

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