LMFDB - Embedded newform 690.3.k.b.553.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(277,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("690.277");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.k (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:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			553.10
Character	$\chi$	$=$	690.553
Dual form			690.3.k.b.277.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-4.46596 + 2.24837i) q^{5} +2.44949 q^{6} +(-8.35401 + 8.35401i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-4.46596 + 2.24837i) q^{5} +2.44949 q^{6} +(-8.35401 + 8.35401i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(2.21759 - 6.71434i) q^{10} +17.4360 q^{11} +(-2.44949 + 2.44949i) q^{12} +(11.0505 + 11.0505i) q^{13} -16.7080i q^{14} +(8.22335 + 2.71598i) q^{15} -4.00000 q^{16} +(-14.9996 + 14.9996i) q^{17} +(-3.00000 - 3.00000i) q^{18} -2.87824i q^{19} +(4.49675 + 8.93192i) q^{20} +20.4631 q^{21} +(-17.4360 + 17.4360i) q^{22} +(3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(14.8896 - 20.0823i) q^{25} -22.1011 q^{26} +(3.67423 - 3.67423i) q^{27} +(16.7080 + 16.7080i) q^{28} +3.12728i q^{29} +(-10.9393 + 5.50737i) q^{30} +18.1414 q^{31} +(4.00000 - 4.00000i) q^{32} +(-21.3546 - 21.3546i) q^{33} -29.9992i q^{34} +(18.5258 - 56.0917i) q^{35} +6.00000 q^{36} +(-11.8822 + 11.8822i) q^{37} +(2.87824 + 2.87824i) q^{38} -27.0682i q^{39} +(-13.4287 - 4.43518i) q^{40} -72.2362 q^{41} +(-20.4631 + 20.4631i) q^{42} +(-43.7755 - 43.7755i) q^{43} -34.8720i q^{44} +(-6.74512 - 13.3979i) q^{45} -6.78233 q^{46} +(-61.4968 + 61.4968i) q^{47} +(4.89898 + 4.89898i) q^{48} -90.5791i q^{49} +(5.19267 + 34.9719i) q^{50} +36.7414 q^{51} +(22.1011 - 22.1011i) q^{52} +(43.0455 + 43.0455i) q^{53} +7.34847i q^{54} +(-77.8685 + 39.2026i) q^{55} -33.4161 q^{56} +(-3.52511 + 3.52511i) q^{57} +(-3.12728 - 3.12728i) q^{58} +60.4399i q^{59} +(5.43196 - 16.4467i) q^{60} +1.37448 q^{61} +(-18.1414 + 18.1414i) q^{62} +(-25.0620 - 25.0620i) q^{63} +8.00000i q^{64} +(-74.1970 - 24.5055i) q^{65} +42.7093 q^{66} +(60.8442 - 60.8442i) q^{67} +(29.9992 + 29.9992i) q^{68} -8.30662i q^{69} +(37.5659 + 74.6174i) q^{70} -89.3191 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-19.0044 - 19.0044i) q^{73} -23.7643i q^{74} +(-42.8317 + 6.35969i) q^{75} -5.75648 q^{76} +(-145.661 + 145.661i) q^{77} +(27.0682 + 27.0682i) q^{78} +44.8163i q^{79} +(17.8638 - 8.99349i) q^{80} -9.00000 q^{81} +(72.2362 - 72.2362i) q^{82} +(-1.63595 - 1.63595i) q^{83} -40.9261i q^{84} +(33.2630 - 100.712i) q^{85} +87.5510 q^{86} +(3.83012 - 3.83012i) q^{87} +(34.8720 + 34.8720i) q^{88} -16.6308i q^{89} +(20.1430 + 6.65277i) q^{90} -184.633 q^{91} +(6.78233 - 6.78233i) q^{92} +(-22.2186 - 22.2186i) q^{93} -122.994i q^{94} +(6.47135 + 12.8541i) q^{95} -9.79796 q^{96} +(53.3660 - 53.3660i) q^{97} +(90.5791 + 90.5791i) q^{98} +52.3080i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$4$		−	2.00000i		−	0.500000i
$5$	−4.46596	+	2.24837i	−0.893192	+	0.449675i
$5$	−4.46596	+	2.24837i	−0.893192	+	0.449675i
$6$	2.44949			0.408248
$7$	−8.35401	+	8.35401i	−1.19343	+	1.19343i	−0.217333	+	0.976098i	$0.569736\pi$
$7$	−8.35401	+	8.35401i	−1.19343	+	1.19343i	−0.976098	+	0.217333i	$0.930264\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$			3.00000i			0.333333i
$10$	2.21759	−	6.71434i	0.221759	−	0.671434i
$11$	17.4360			1.58509			0.792545	−	0.609813i	$-0.208756\pi$
$11$	17.4360			1.58509			0.792545	+	0.609813i	$0.208756\pi$
$12$	−2.44949	+	2.44949i	−0.204124	+	0.204124i
$13$	11.0505	+	11.0505i	0.850041	+	0.850041i	0.990138	−	0.140097i	$-0.0447413\pi$
$13$	11.0505	+	11.0505i	0.850041	+	0.850041i	−0.140097	+	0.990138i	$0.544741\pi$
$14$		−	16.7080i		−	1.19343i
$15$	8.22335	+	2.71598i	0.548223	+	0.181065i
$16$	−4.00000			−0.250000
$17$	−14.9996	+	14.9996i	−0.882330	+	0.882330i	−0.993771	−	0.111441i	$-0.964453\pi$
$17$	−14.9996	+	14.9996i	−0.882330	+	0.882330i	0.111441	+	0.993771i	$0.464453\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$		−	2.87824i		−	0.151486i	−0.997127	−	0.0757431i	$-0.975867\pi$
$19$		−	2.87824i		−	0.151486i	0.997127	−	0.0757431i	$-0.0241329\pi$
$20$	4.49675	+	8.93192i	0.224837	+	0.446596i
$21$	20.4631			0.974432
$22$	−17.4360	+	17.4360i	−0.792545	+	0.792545i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$24$		−	4.89898i		−	0.204124i
$25$	14.8896	−	20.0823i	0.595585	−	0.803292i
$26$	−22.1011			−0.850041
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	16.7080	+	16.7080i	0.596715	+	0.596715i
$29$			3.12728i			0.107837i	0.998545	+	0.0539187i	$0.0171712\pi$
$29$			3.12728i			0.107837i	−0.998545	+	0.0539187i	$0.982829\pi$
$30$	−10.9393	+	5.50737i	−0.364644	+	0.183579i
$31$	18.1414			0.585207			0.292604	−	0.956234i	$-0.405478\pi$
$31$	18.1414			0.585207			0.292604	+	0.956234i	$0.405478\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	−21.3546	−	21.3546i	−0.647110	−	0.647110i
$34$		−	29.9992i		−	0.882330i
$35$	18.5258	−	56.0917i	0.529308	−	1.60262i
$36$	6.00000			0.166667
$37$	−11.8822	+	11.8822i	−0.321139	+	0.321139i	−0.849204	−	0.528065i	$-0.822918\pi$
$37$	−11.8822	+	11.8822i	−0.321139	+	0.321139i	0.528065	+	0.849204i	$0.322918\pi$
$38$	2.87824	+	2.87824i	0.0757431	+	0.0757431i
$39$		−	27.0682i		−	0.694056i
$40$	−13.4287	−	4.43518i	−0.335717	−	0.110879i
$41$	−72.2362			−1.76186			−0.880929	−	0.473248i	$-0.843081\pi$
$41$	−72.2362			−1.76186			−0.880929	+	0.473248i	$0.843081\pi$
$42$	−20.4631	+	20.4631i	−0.487216	+	0.487216i
$43$	−43.7755	−	43.7755i	−1.01803	−	1.01803i	−0.999834	−	0.0181999i	$-0.994206\pi$
$43$	−43.7755	−	43.7755i	−1.01803	−	1.01803i	−0.0181999	−	0.999834i	$-0.505794\pi$
$44$		−	34.8720i		−	0.792545i
$45$	−6.74512	−	13.3979i	−0.149892	−	0.297731i
$46$	−6.78233			−0.147442
$47$	−61.4968	+	61.4968i	−1.30844	+	1.30844i	−0.385902	+	0.922540i	$0.626110\pi$
$47$	−61.4968	+	61.4968i	−1.30844	+	1.30844i	−0.922540	+	0.385902i	$0.873890\pi$
$48$	4.89898	+	4.89898i	0.102062	+	0.102062i
$49$		−	90.5791i		−	1.84855i
$50$	5.19267	+	34.9719i	0.103853	+	0.699439i
$51$	36.7414			0.720420
$52$	22.1011	−	22.1011i	0.425021	−	0.425021i
$53$	43.0455	+	43.0455i	0.812180	+	0.812180i	0.984960	−	0.172781i	$-0.0552752\pi$
$53$	43.0455	+	43.0455i	0.812180	+	0.812180i	−0.172781	+	0.984960i	$0.555275\pi$
$54$			7.34847i			0.136083i
$55$	−77.8685	+	39.2026i	−1.41579	+	0.712775i
$56$	−33.4161			−0.596715
$57$	−3.52511	+	3.52511i	−0.0618440	+	0.0618440i
$58$	−3.12728	−	3.12728i	−0.0539187	−	0.0539187i
$59$			60.4399i			1.02440i	0.858865	+	0.512202i	$0.171170\pi$
$59$			60.4399i			1.02440i	−0.858865	+	0.512202i	$0.828830\pi$
$60$	5.43196	−	16.4467i	0.0905327	−	0.274112i
$61$	1.37448			0.0225324			0.0112662	−	0.999937i	$-0.496414\pi$
$61$	1.37448			0.0225324			0.0112662	+	0.999937i	$0.496414\pi$
$62$	−18.1414	+	18.1414i	−0.292604	+	0.292604i
$63$	−25.0620	−	25.0620i	−0.397810	−	0.397810i
$64$			8.00000i			0.125000i
$65$	−74.1970	−	24.5055i	−1.14149	−	0.377008i
$66$	42.7093			0.647110
$67$	60.8442	−	60.8442i	0.908123	−	0.908123i	−0.0879977	−	0.996121i	$-0.528047\pi$
$67$	60.8442	−	60.8442i	0.908123	−	0.908123i	0.996121	+	0.0879977i	$0.0280468\pi$
$68$	29.9992	+	29.9992i	0.441165	+	0.441165i
$69$		−	8.30662i		−	0.120386i
$70$	37.5659	+	74.6174i	0.536656	+	1.06596i
$71$	−89.3191			−1.25802			−0.629008	−	0.777399i	$-0.716539\pi$
$71$	−89.3191			−1.25802			−0.629008	+	0.777399i	$0.716539\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	−19.0044	−	19.0044i	−0.260334	−	0.260334i	0.564856	−	0.825190i	$-0.308932\pi$
$73$	−19.0044	−	19.0044i	−0.260334	−	0.260334i	−0.825190	+	0.564856i	$0.808932\pi$
$74$		−	23.7643i		−	0.321139i
$75$	−42.8317	+	6.35969i	−0.571089	+	0.0847959i
$76$	−5.75648			−0.0757431
$77$	−145.661	+	145.661i	−1.89170	+	1.89170i
$78$	27.0682	+	27.0682i	0.347028	+	0.347028i
$79$			44.8163i			0.567294i	0.958929	+	0.283647i	$0.0915445\pi$
$79$			44.8163i			0.567294i	−0.958929	+	0.283647i	$0.908456\pi$
$80$	17.8638	−	8.99349i	0.223298	−	0.112419i
$81$	−9.00000			−0.111111
$82$	72.2362	−	72.2362i	0.880929	−	0.880929i
$83$	−1.63595	−	1.63595i	−0.0197103	−	0.0197103i	0.697183	−	0.716893i	$-0.254437\pi$
$83$	−1.63595	−	1.63595i	−0.0197103	−	0.0197103i	−0.716893	+	0.697183i	$0.754437\pi$
$84$		−	40.9261i		−	0.487216i
$85$	33.2630	−	100.712i	0.391329	−	1.18485i
$86$	87.5510			1.01803
$87$	3.83012	−	3.83012i	0.0440244	−	0.0440244i
$88$	34.8720	+	34.8720i	0.396273	+	0.396273i
$89$		−	16.6308i		−	0.186863i	−0.995626	−	0.0934313i	$-0.970216\pi$
$89$		−	16.6308i		−	0.186863i	0.995626	−	0.0934313i	$-0.0297835\pi$
$90$	20.1430	+	6.65277i	0.223811	+	0.0739196i
$91$	−184.633			−2.02893
$92$	6.78233	−	6.78233i	0.0737210	−	0.0737210i
$93$	−22.2186	−	22.2186i	−0.238910	−	0.238910i
$94$		−	122.994i		−	1.30844i
$95$	6.47135	+	12.8541i	0.0681195	+	0.135306i
$96$	−9.79796			−0.102062
$97$	53.3660	−	53.3660i	0.550164	−	0.550164i	−0.376324	−	0.926488i	$-0.622812\pi$
$97$	53.3660	−	53.3660i	0.550164	−	0.550164i	0.926488	+	0.376324i	$0.122812\pi$
$98$	90.5791	+	90.5791i	0.924276	+	0.924276i
$99$			52.3080i			0.528363i
$100$	−40.1646	−	29.7793i	−0.401646	−	0.297793i
$101$	−35.9808			−0.356246			−0.178123	−	0.984008i	$-0.557002\pi$
$101$	−35.9808			−0.356246			−0.178123	+	0.984008i	$0.557002\pi$
$102$	−36.7414	+	36.7414i	−0.360210	+	0.360210i
$103$	−76.7772	−	76.7772i	−0.745409	−	0.745409i	0.228204	−	0.973613i	$-0.426715\pi$
$103$	−76.7772	−	76.7772i	−0.745409	−	0.745409i	−0.973613	+	0.228204i	$0.926715\pi$
$104$			44.2021i			0.425021i
$105$	−91.3873	+	46.0086i	−0.870355	+	0.438177i
$106$	−86.0910			−0.812180
$107$	111.941	−	111.941i	1.04618	−	1.04618i	0.0472976	−	0.998881i	$-0.484939\pi$
$107$	111.941	−	111.941i	1.04618	−	1.04618i	0.998881	−	0.0472976i	$-0.0150609\pi$
$108$	−7.34847	−	7.34847i	−0.0680414	−	0.0680414i
$109$		−	207.304i		−	1.90187i	−0.309386	−	0.950936i	$-0.600124\pi$
$109$		−	207.304i		−	1.90187i	0.309386	−	0.950936i	$-0.399876\pi$
$110$	38.6659	−	117.071i	0.351508	−	1.06428i
$111$	29.1052			0.262209
$112$	33.4161	−	33.4161i	0.298358	−	0.298358i
$113$	−121.606	−	121.606i	−1.07616	−	1.07616i	−0.996850	−	0.0793109i	$-0.974728\pi$
$113$	−121.606	−	121.606i	−1.07616	−	1.07616i	−0.0793109	−	0.996850i	$-0.525272\pi$
$114$		−	7.05021i		−	0.0618440i
$115$	−22.7694	−	7.52021i	−0.197995	−	0.0653931i
$116$	6.25456			0.0539187
$117$	−33.1516	+	33.1516i	−0.283347	+	0.283347i
$118$	−60.4399	−	60.4399i	−0.512202	−	0.512202i
$119$		−	250.614i		−	2.10600i
$120$	11.0147	+	21.8787i	0.0917895	+	0.182322i
$121$	183.014			1.51251
$122$	−1.37448	+	1.37448i	−0.0112662	+	0.0112662i
$123$	88.4709	+	88.4709i	0.719276	+	0.719276i
$124$		−	36.2829i		−	0.292604i
$125$	−21.3440	+	123.164i	−0.170752	+	0.985314i
$126$	50.1241			0.397810
$127$	−79.3364	+	79.3364i	−0.624696	+	0.624696i	−0.946729	−	0.322033i	$-0.895634\pi$
$127$	−79.3364	+	79.3364i	−0.624696	+	0.624696i	0.322033	+	0.946729i	$0.395634\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$			107.228i			0.831222i
$130$	98.7025	−	49.6915i	0.759250	−	0.382242i
$131$	77.0233			0.587964			0.293982	−	0.955811i	$-0.405019\pi$
$131$	77.0233			0.587964			0.293982	+	0.955811i	$0.405019\pi$
$132$	−42.7093	+	42.7093i	−0.323555	+	0.323555i
$133$	24.0448	+	24.0448i	0.180788	+	0.180788i
$134$			121.688i			0.908123i
$135$	−8.14794	+	24.6700i	−0.0603551	+	0.182741i
$136$	−59.9985			−0.441165
$137$	22.4557	−	22.4557i	0.163910	−	0.163910i	−0.620386	−	0.784296i	$-0.713024\pi$
$137$	22.4557	−	22.4557i	0.163910	−	0.163910i	0.784296	+	0.620386i	$0.213024\pi$
$138$	8.30662	+	8.30662i	0.0601929	+	0.0601929i
$139$			24.4482i			0.175887i	0.996125	+	0.0879433i	$0.0280294\pi$
$139$			24.4482i			0.175887i	−0.996125	+	0.0879433i	$0.971971\pi$
$140$	−112.183	−	37.0515i	−0.801309	−	0.264654i
$141$	150.636			1.06834
$142$	89.3191	−	89.3191i	0.629008	−	0.629008i
$143$	192.677	+	192.677i	1.34739	+	1.34739i
$144$		−	12.0000i		−	0.0833333i
$145$	−7.03130	−	13.9663i	−0.0484917	−	0.0963195i
$146$	38.0087			0.260334
$147$	−110.936	+	110.936i	−0.754669	+	0.754669i
$148$	23.7643	+	23.7643i	0.160570	+	0.160570i
$149$		−	188.531i		−	1.26531i	−0.774435	−	0.632654i	$-0.781966\pi$
$149$		−	188.531i		−	1.26531i	0.774435	−	0.632654i	$-0.218034\pi$
$150$	36.4720	−	49.1914i	0.243147	−	0.327943i
$151$	176.089			1.16615			0.583077	−	0.812417i	$-0.301849\pi$
$151$	176.089			1.16615			0.583077	+	0.812417i	$0.301849\pi$
$152$	5.75648	−	5.75648i	0.0378715	−	0.0378715i
$153$	−44.9989	−	44.9989i	−0.294110	−	0.294110i
$154$		−	291.321i		−	1.89170i
$155$	−81.0189	+	40.7887i	−0.522703	+	0.263153i
$156$	−54.1363			−0.347028
$157$	−32.4124	+	32.4124i	−0.206449	+	0.206449i	−0.802756	−	0.596308i	$-0.796634\pi$
$157$	−32.4124	+	32.4124i	−0.206449	+	0.206449i	0.596308	+	0.802756i	$0.296634\pi$
$158$	−44.8163	−	44.8163i	−0.283647	−	0.283647i
$159$		−	105.440i		−	0.663142i
$160$	−8.87035	+	26.8573i	−0.0554397	+	0.167858i
$161$	−56.6597			−0.351923
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	85.5836	+	85.5836i	0.525053	+	0.525053i	0.919093	−	0.394041i	$-0.128923\pi$
$163$	85.5836	+	85.5836i	0.525053	+	0.525053i	−0.394041	+	0.919093i	$0.628923\pi$
$164$			144.472i			0.880929i
$165$	143.382	+	47.3558i	0.868983	+	0.287005i
$166$	3.27191			0.0197103
$167$	68.9683	−	68.9683i	0.412984	−	0.412984i	−0.469793	−	0.882777i	$-0.655671\pi$
$167$	68.9683	−	68.9683i	0.412984	−	0.412984i	0.882777	+	0.469793i	$0.155671\pi$
$168$	40.9261	+	40.9261i	0.243608	+	0.243608i
$169$			75.2287i			0.445140i
$170$	67.4495	+	133.975i	0.396762	+	0.788091i
$171$	8.63471			0.0504954
$172$	−87.5510	+	87.5510i	−0.509017	+	0.509017i
$173$	27.9513	+	27.9513i	0.161568	+	0.161568i	0.783261	−	0.621693i	$-0.213555\pi$
$173$	27.9513	+	27.9513i	0.161568	+	0.161568i	−0.621693	+	0.783261i	$0.713555\pi$
$174$			7.66025i			0.0440244i
$175$	43.3796	+	292.156i	0.247884	+	1.66946i
$176$	−69.7440			−0.396273
$177$	74.0234	−	74.0234i	0.418211	−	0.418211i
$178$	16.6308	+	16.6308i	0.0934313	+	0.0934313i
$179$			129.232i			0.721969i	0.932572	+	0.360984i	$0.117559\pi$
$179$			129.232i			0.721969i	−0.932572	+	0.360984i	$0.882441\pi$
$180$	−26.7958	+	13.4902i	−0.148865	+	0.0749458i
$181$	43.8532			0.242283			0.121141	−	0.992635i	$-0.461345\pi$
$181$	43.8532			0.242283			0.121141	+	0.992635i	$0.461345\pi$
$182$	184.633	−	184.633i	1.01447	−	1.01447i
$183$	−1.68339	−	1.68339i	−0.00919883	−	0.00919883i
$184$			13.5647i			0.0737210i
$185$	26.3497	−	79.7808i	0.142431	−	0.431248i
$186$	44.4373			0.238910
$187$	−261.533	+	261.533i	−1.39857	+	1.39857i
$188$	122.994	+	122.994i	0.654221	+	0.654221i
$189$			61.3892i			0.324811i
$190$	−19.3255	−	6.38275i	−0.101713	−	0.0335934i
$191$	−371.805			−1.94662			−0.973311	−	0.229490i	$-0.926294\pi$
$191$	−371.805			−1.94662			−0.973311	+	0.229490i	$0.926294\pi$
$192$	9.79796	−	9.79796i	0.0510310	−	0.0510310i
$193$	−135.050	−	135.050i	−0.699740	−	0.699740i	0.264614	−	0.964354i	$-0.414755\pi$
$193$	−135.050	−	135.050i	−0.699740	−	0.699740i	−0.964354	+	0.264614i	$0.914755\pi$
$194$			106.732i			0.550164i
$195$	60.8594	+	120.885i	0.312099	+	0.619925i
$196$	−181.158			−0.924276
$197$	−129.928	+	129.928i	−0.659534	+	0.659534i	−0.955270	−	0.295735i	$-0.904435\pi$
$197$	−129.928	+	129.928i	−0.659534	+	0.659534i	0.295735	+	0.955270i	$0.404435\pi$
$198$	−52.3080	−	52.3080i	−0.264182	−	0.264182i
$199$			191.204i			0.960823i	0.877043	+	0.480411i	$0.159513\pi$
$199$			191.204i			0.960823i	−0.877043	+	0.480411i	$0.840487\pi$
$200$	69.9439	−	10.3853i	0.349719	−	0.0519267i
$201$	−149.037			−0.741479
$202$	35.9808	−	35.9808i	0.178123	−	0.178123i
$203$	−26.1254	−	26.1254i	−0.128696	−	0.128696i
$204$		−	73.4828i		−	0.360210i
$205$	322.604	−	162.414i	1.57368	−	0.792263i
$206$	153.554			0.745409
$207$	−10.1735	+	10.1735i	−0.0491473	+	0.0491473i
$208$	−44.2021	−	44.2021i	−0.212510	−	0.212510i
$209$		−	50.1849i		−	0.240119i
$210$	45.3787	−	137.396i	0.216089	−	0.654266i
$211$	−17.0920			−0.0810047			−0.0405024	−	0.999179i	$-0.512896\pi$
$211$	−17.0920			−0.0810047			−0.0405024	+	0.999179i	$0.512896\pi$
$212$	86.0910	−	86.0910i	0.406090	−	0.406090i
$213$	109.393	+	109.393i	0.513582	+	0.513582i
$214$			223.882i			1.04618i
$215$	293.923	+	97.0760i	1.36708	+	0.451516i
$216$	14.6969			0.0680414
$217$	−151.554	+	151.554i	−0.698405	+	0.698405i
$218$	207.304	+	207.304i	0.950936	+	0.950936i
$219$			46.5510i			0.212562i
$220$	78.4052	+	155.737i	0.356387	+	0.707895i
$221$	−331.508			−1.50003
$222$	−29.1052	+	29.1052i	−0.131105	+	0.131105i
$223$	−54.8788	−	54.8788i	−0.246093	−	0.246093i	0.573272	−	0.819365i	$-0.305674\pi$
$223$	−54.8788	−	54.8788i	−0.246093	−	0.246093i	−0.819365	+	0.573272i	$0.805674\pi$
$224$			66.8321i			0.298358i
$225$	60.2469	+	44.6689i	0.267764	+	0.198528i
$226$	243.212			1.07616
$227$	−82.2540	+	82.2540i	−0.362352	+	0.362352i	−0.864678	−	0.502326i	$-0.832478\pi$
$227$	−82.2540	+	82.2540i	−0.362352	+	0.362352i	0.502326	+	0.864678i	$0.332478\pi$
$228$	7.05021	+	7.05021i	0.0309220	+	0.0309220i
$229$		−	429.556i		−	1.87579i	−0.346916	−	0.937896i	$-0.612771\pi$
$229$		−	429.556i		−	1.87579i	0.346916	−	0.937896i	$-0.387229\pi$
$230$	30.2896	−	15.2492i	0.131694	−	0.0663009i
$231$	356.794			1.54456
$232$	−6.25456	+	6.25456i	−0.0269593	+	0.0269593i
$233$	−35.0961	−	35.0961i	−0.150627	−	0.150627i	0.627771	−	0.778398i	$-0.283967\pi$
$233$	−35.0961	−	35.0961i	−0.150627	−	0.150627i	−0.778398	+	0.627771i	$0.783967\pi$
$234$		−	66.3032i		−	0.283347i
$235$	136.375	−	412.910i	0.580317	−	1.75706i
$236$	120.880			0.512202
$237$	54.8885	−	54.8885i	0.231597	−	0.231597i
$238$	250.614	+	250.614i	1.05300	+	1.05300i
$239$			108.716i			0.454880i	0.973792	+	0.227440i	$0.0730355\pi$
$239$			108.716i			0.454880i	−0.973792	+	0.227440i	$0.926965\pi$
$240$	−32.8934	−	10.8639i	−0.137056	−	0.0452663i
$241$	−294.692			−1.22279			−0.611394	−	0.791327i	$-0.709391\pi$
$241$	−294.692			−1.22279			−0.611394	+	0.791327i	$0.709391\pi$
$242$	−183.014	+	183.014i	−0.756256	+	0.756256i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$		−	2.74896i		−	0.0112662i
$245$	203.656	+	404.523i	0.831248	+	1.65111i
$246$	−176.942			−0.719276
$247$	31.8061	−	31.8061i	0.128770	−	0.128770i
$248$	36.2829	+	36.2829i	0.146302	+	0.146302i
$249$			4.00725i			0.0160934i
$250$	−101.820	−	144.508i	−0.407281	−	0.578033i
$251$	451.400			1.79841			0.899203	−	0.437532i	$-0.144147\pi$
$251$	451.400			1.79841			0.899203	+	0.437532i	$0.144147\pi$
$252$	−50.1241	+	50.1241i	−0.198905	+	0.198905i
$253$	59.1283	+	59.1283i	0.233709	+	0.233709i
$254$		−	158.673i		−	0.624696i
$255$	−164.086	+	82.6084i	−0.643473	+	0.323955i
$256$	16.0000			0.0625000
$257$	−185.908	+	185.908i	−0.723378	+	0.723378i	−0.969292	−	0.245914i	$-0.920912\pi$
$257$	−185.908	+	185.908i	−0.723378	+	0.723378i	0.245914	+	0.969292i	$0.420912\pi$
$258$	−107.228	−	107.228i	−0.415611	−	0.415611i
$259$		−	198.527i		−	0.766515i
$260$	−49.0111	+	148.394i	−0.188504	+	0.570746i
$261$	−9.38185			−0.0359458
$262$	−77.0233	+	77.0233i	−0.293982	+	0.293982i
$263$	274.719	+	274.719i	1.04456	+	1.04456i	0.998960	+	0.0456006i	$0.0145202\pi$
$263$	274.719	+	274.719i	1.04456	+	1.04456i	0.0456006	+	0.998960i	$0.485480\pi$
$264$		−	85.4186i		−	0.323555i
$265$	−289.022	−	95.4573i	−1.09065	−	0.360216i
$266$	−48.0897			−0.180788
$267$	−20.3684	+	20.3684i	−0.0762863	+	0.0762863i
$268$	−121.688	−	121.688i	−0.454061	−	0.454061i
$269$			427.490i			1.58918i	0.607146	+	0.794591i	$0.292314\pi$
$269$			427.490i			1.58918i	−0.607146	+	0.794591i	$0.707686\pi$
$270$	−16.5221	−	32.8180i	−0.0611930	−	0.121548i
$271$	101.987			0.376334			0.188167	−	0.982137i	$-0.439745\pi$
$271$	101.987			0.376334			0.188167	+	0.982137i	$0.439745\pi$
$272$	59.9985	−	59.9985i	0.220583	−	0.220583i
$273$	226.128	+	226.128i	0.828307	+	0.828307i
$274$			44.9114i			0.163910i
$275$	259.616	−	350.155i	0.944056	−	1.27329i
$276$	−16.6132			−0.0601929
$277$	−254.686	+	254.686i	−0.919443	+	0.919443i	−0.996989	−	0.0775463i	$-0.975291\pi$
$277$	−254.686	+	254.686i	−0.919443	+	0.919443i	0.0775463	+	0.996989i	$0.475291\pi$
$278$	−24.4482	−	24.4482i	−0.0879433	−	0.0879433i
$279$			54.4243i			0.195069i
$280$	149.235	−	75.1318i	0.532982	−	0.268328i
$281$	−438.626			−1.56094			−0.780472	−	0.625190i	$-0.785021\pi$
$281$	−438.626			−1.56094			−0.780472	+	0.625190i	$0.785021\pi$
$282$	−150.636	+	150.636i	−0.534169	+	0.534169i
$283$	85.3328	+	85.3328i	0.301529	+	0.301529i	0.841612	−	0.540083i	$-0.181607\pi$
$283$	85.3328	+	85.3328i	0.301529	+	0.301529i	−0.540083	+	0.841612i	$0.681607\pi$
$284$			178.638i			0.629008i
$285$	7.81724	−	23.6688i	0.0274289	−	0.0830482i
$286$	−385.354			−1.34739
$287$	603.462	−	603.462i	2.10266	−	2.10266i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$		−	160.977i		−	0.557014i
$290$	20.9976	+	6.93503i	0.0724056	+	0.0239139i
$291$	−130.719			−0.449207
$292$	−38.0087	+	38.0087i	−0.130167	+	0.130167i
$293$	−66.5716	−	66.5716i	−0.227207	−	0.227207i	0.584318	−	0.811525i	$-0.301362\pi$
$293$	−66.5716	−	66.5716i	−0.227207	−	0.227207i	−0.811525	+	0.584318i	$0.801362\pi$
$294$		−	221.873i		−	0.754669i
$295$	−135.891	−	269.922i	−0.460649	−	0.914990i
$296$	−47.5286			−0.160570
$297$	64.0639	−	64.0639i	0.215703	−	0.215703i
$298$	188.531	+	188.531i	0.632654	+	0.632654i
$299$			74.9484i			0.250663i
$300$	12.7194	+	85.6634i	0.0423980	+	0.285545i
$301$	731.402			2.42991
$302$	−176.089	+	176.089i	−0.583077	+	0.583077i
$303$	44.0673	+	44.0673i	0.145437	+	0.145437i
$304$			11.5130i			0.0378715i
$305$	−6.13837	+	3.09034i	−0.0201258	+	0.0101323i
$306$	89.9977			0.294110
$307$	−292.269	+	292.269i	−0.952015	+	0.952015i	−0.998900	−	0.0468849i	$-0.985071\pi$
$307$	−292.269	+	292.269i	−0.952015	+	0.952015i	0.0468849	+	0.998900i	$0.485071\pi$
$308$	291.321	+	291.321i	0.945848	+	0.945848i
$309$			188.065i			0.608624i
$310$	40.2302	−	121.808i	0.129775	−	0.392928i
$311$	−81.4097			−0.261767			−0.130884	−	0.991398i	$-0.541781\pi$
$311$	−81.4097			−0.261767			−0.130884	+	0.991398i	$0.541781\pi$
$312$	54.1363	−	54.1363i	0.173514	−	0.173514i
$313$	147.092	+	147.092i	0.469941	+	0.469941i	0.901895	−	0.431954i	$-0.142176\pi$
$313$	147.092	+	147.092i	0.469941	+	0.469941i	−0.431954	+	0.901895i	$0.642176\pi$
$314$		−	64.8248i		−	0.206449i
$315$	168.275	+	55.5773i	0.534206	+	0.176436i
$316$	89.6325			0.283647
$317$	51.5605	−	51.5605i	0.162651	−	0.162651i	−0.621089	−	0.783740i	$-0.713309\pi$
$317$	51.5605	−	51.5605i	0.162651	−	0.162651i	0.783740	+	0.621089i	$0.213309\pi$
$318$	105.440	+	105.440i	0.331571	+	0.331571i
$319$			54.5273i			0.170932i
$320$	−17.9870	−	35.7277i	−0.0562093	−	0.111649i
$321$	−274.199			−0.854201
$322$	56.6597	−	56.6597i	0.175962	−	0.175962i
$323$	43.1725	+	43.1725i	0.133661	+	0.133661i
$324$			18.0000i			0.0555556i
$325$	386.459	−	57.3818i	1.18910	−	0.176559i
$326$	−171.167			−0.525053
$327$	−253.895	+	253.895i	−0.776436	+	0.776436i
$328$	−144.472	−	144.472i	−0.440465	−	0.440465i
$329$		−	1027.49i		−	3.12307i
$330$	−190.738	+	96.0264i	−0.577994	+	0.290989i
$331$	−445.932			−1.34723			−0.673614	−	0.739084i	$-0.735259\pi$
$331$	−445.932			−1.34723			−0.673614	+	0.739084i	$0.735259\pi$
$332$	−3.27191	+	3.27191i	−0.00985515	+	0.00985515i
$333$	−35.6465	−	35.6465i	−0.107046	−	0.107046i
$334$			137.937i			0.412984i
$335$	−134.927	+	408.529i	−0.402769	+	1.21949i
$336$	−81.8523			−0.243608
$337$	−178.974	+	178.974i	−0.531081	+	0.531081i	−0.920894	−	0.389813i	$-0.872540\pi$
$337$	−178.974	+	178.974i	−0.531081	+	0.531081i	0.389813	+	0.920894i	$0.372540\pi$
$338$	−75.2287	−	75.2287i	−0.222570	−	0.222570i
$339$			297.873i			0.878682i
$340$	−201.425	−	66.5260i	−0.592426	−	0.195665i
$341$	316.314			0.927607
$342$	−8.63471	+	8.63471i	−0.0252477	+	0.0252477i
$343$	347.352	+	347.352i	1.01269	+	1.01269i
$344$		−	175.102i		−	0.509017i
$345$	18.6764	+	37.0971i	0.0541345	+	0.107528i
$346$	−55.9026			−0.161568
$347$	−195.326	+	195.326i	−0.562898	+	0.562898i	−0.930130	−	0.367232i	$-0.880306\pi$
$347$	−195.326	+	195.326i	−0.562898	+	0.562898i	0.367232	+	0.930130i	$0.380306\pi$
$348$	−7.66025	−	7.66025i	−0.0220122	−	0.0220122i
$349$		−	616.027i		−	1.76512i	−0.470200	−	0.882560i	$-0.655818\pi$
$349$		−	616.027i		−	1.76512i	0.470200	−	0.882560i	$-0.344182\pi$
$350$	−335.536	−	248.776i	−0.958673	−	0.710790i
$351$	81.2045			0.231352
$352$	69.7440	−	69.7440i	0.198136	−	0.198136i
$353$	−242.640	−	242.640i	−0.687366	−	0.687366i	0.274283	−	0.961649i	$-0.411560\pi$
$353$	−242.640	−	242.640i	−0.687366	−	0.687366i	−0.961649	+	0.274283i	$0.911560\pi$
$354$			148.047i			0.418211i
$355$	398.896	−	200.823i	1.12365	−	0.565698i
$356$	−33.2615			−0.0934313
$357$	−306.938	+	306.938i	−0.859771	+	0.859771i
$358$	−129.232	−	129.232i	−0.360984	−	0.360984i
$359$			309.086i			0.860963i	0.902599	+	0.430482i	$0.141656\pi$
$359$			309.086i			0.860963i	−0.902599	+	0.430482i	$0.858344\pi$
$360$	13.3055	−	40.2860i	0.0369598	−	0.111906i
$361$	352.716			0.977052
$362$	−43.8532	+	43.8532i	−0.121141	+	0.121141i
$363$	−224.145	−	224.145i	−0.617480	−	0.617480i
$364$			369.265i			1.01447i
$365$	127.602	+	42.1439i	0.349594	+	0.115463i
$366$	3.36677			0.00919883
$367$	320.182	−	320.182i	0.872429	−	0.872429i	−0.120307	−	0.992737i	$-0.538388\pi$
$367$	320.182	−	320.182i	0.872429	−	0.872429i	0.992737	+	0.120307i	$0.0383880\pi$
$368$	−13.5647	−	13.5647i	−0.0368605	−	0.0368605i
$369$		−	216.709i		−	0.587286i
$370$	53.4311	+	106.131i	0.144408	+	0.286839i
$371$	−719.206			−1.93856
$372$	−44.4373	+	44.4373i	−0.119455	+	0.119455i
$373$	40.8847	+	40.8847i	0.109610	+	0.109610i	0.759785	−	0.650175i	$-0.225304\pi$
$373$	40.8847	+	40.8847i	0.109610	+	0.109610i	−0.650175	+	0.759785i	$0.725304\pi$
$374$		−	523.066i		−	1.39857i
$375$	176.986	−	124.704i	0.471962	−	0.332543i
$376$	−245.987			−0.654221
$377$	−34.5581	+	34.5581i	−0.0916662	+	0.0916662i
$378$	−61.3892	−	61.3892i	−0.162405	−	0.162405i
$379$		−	235.010i		−	0.620079i	−0.950724	−	0.310040i	$-0.899658\pi$
$379$		−	235.010i		−	0.620079i	0.950724	−	0.310040i	$-0.100342\pi$
$380$	25.7082	−	12.9427i	0.0676532	−	0.0340598i
$381$	194.334			0.510062
$382$	371.805	−	371.805i	0.973311	−	0.973311i
$383$	−344.365	−	344.365i	−0.899125	−	0.899125i	0.0962334	−	0.995359i	$-0.469320\pi$
$383$	−344.365	−	344.365i	−0.899125	−	0.899125i	−0.995359	+	0.0962334i	$0.969320\pi$
$384$			19.5959i			0.0510310i
$385$	323.015	−	978.014i	0.839000	−	2.54030i
$386$	270.100			0.699740
$387$	131.326	−	131.326i	0.339345	−	0.339345i
$388$	−106.732	−	106.732i	−0.275082	−	0.275082i
$389$		−	522.732i		−	1.34378i	−0.740649	−	0.671892i	$-0.765482\pi$
$389$		−	522.732i		−	1.34378i	0.740649	−	0.671892i	$-0.234518\pi$
$390$	−181.745	−	60.0261i	−0.466012	−	0.153913i
$391$	−101.732			−0.260185
$392$	181.158	−	181.158i	0.462138	−	0.462138i
$393$	−94.3339	−	94.3339i	−0.240035	−	0.240035i
$394$		−	259.857i		−	0.659534i
$395$	−100.764	−	200.148i	−0.255098	−	0.506703i
$396$	104.616			0.264182
$397$	−130.039	+	130.039i	−0.327554	+	0.327554i	−0.851656	−	0.524101i	$-0.824401\pi$
$397$	−130.039	+	130.039i	−0.327554	+	0.327554i	0.524101	+	0.851656i	$0.324401\pi$
$398$	−191.204	−	191.204i	−0.480411	−	0.480411i
$399$		−	58.8976i		−	0.147613i
$400$	−59.5585	+	80.3292i	−0.148896	+	0.200823i
$401$	711.927			1.77538			0.887690	−	0.460442i	$-0.152309\pi$
$401$	711.927			1.77538			0.887690	+	0.460442i	$0.152309\pi$
$402$	149.037	−	149.037i	0.370740	−	0.370740i
$403$	200.473	+	200.473i	0.497450	+	0.497450i
$404$			71.9617i			0.178123i
$405$	40.1937	−	20.2354i	0.0992436	−	0.0499639i
$406$	52.2507			0.128696
$407$	−207.177	+	207.177i	−0.509035	+	0.509035i
$408$	73.4828	+	73.4828i	0.180105	+	0.180105i
$409$		−	225.265i		−	0.550770i	−0.961334	−	0.275385i	$-0.911195\pi$
$409$		−	225.265i		−	0.550770i	0.961334	−	0.275385i	$-0.0888054\pi$
$410$	−160.190	+	485.018i	−0.390708	+	1.18297i
$411$	−55.0050			−0.133832
$412$	−153.554	+	153.554i	−0.372705	+	0.372705i
$413$	−504.916	−	504.916i	−1.22256	−	1.22256i
$414$		−	20.3470i		−	0.0491473i
$415$	10.9843	+	3.62787i	0.0264683	+	0.00874187i
$416$	88.4043			0.212510
$417$	29.9428	−	29.9428i	0.0718054	−	0.0718054i
$418$	50.1849	+	50.1849i	0.120060	+	0.120060i
$419$			727.460i			1.73618i	0.496406	+	0.868090i	$0.334653\pi$
$419$			727.460i			1.73618i	−0.496406	+	0.868090i	$0.665347\pi$
$420$	92.0173	+	182.775i	0.219089	+	0.435178i
$421$	188.423			0.447562			0.223781	−	0.974640i	$-0.428160\pi$
$421$	188.423			0.447562			0.223781	+	0.974640i	$0.428160\pi$
$422$	17.0920	−	17.0920i	0.0405024	−	0.0405024i
$423$	−184.490	−	184.490i	−0.436147	−	0.436147i
$424$			172.182i			0.406090i
$425$	77.8880	+	524.566i	0.183266	+	1.23427i
$426$	−218.786			−0.513582
$427$	−11.4824	+	11.4824i	−0.0268909	+	0.0268909i
$428$	−223.882	−	223.882i	−0.523089	−	0.523089i
$429$		−	471.960i		−	1.10014i
$430$	−390.999	+	196.847i	−0.909301	+	0.457784i
$431$	624.307			1.44851			0.724254	−	0.689534i	$-0.242185\pi$
$431$	624.307			1.44851			0.724254	+	0.689534i	$0.242185\pi$
$432$	−14.6969	+	14.6969i	−0.0340207	+	0.0340207i
$433$	208.628	+	208.628i	0.481821	+	0.481821i	0.905713	−	0.423892i	$-0.139336\pi$
$433$	208.628	+	208.628i	0.481821	+	0.481821i	−0.423892	+	0.905713i	$0.639336\pi$
$434$		−	303.108i		−	0.698405i
$435$	−8.49364	+	25.7167i	−0.0195256	+	0.0591189i
$436$	−414.608			−0.950936
$437$	9.76058	−	9.76058i	0.0223354	−	0.0223354i
$438$	−46.5510	−	46.5510i	−0.106281	−	0.106281i
$439$			555.867i			1.26621i	0.774065	+	0.633106i	$0.218220\pi$
$439$			555.867i			1.26621i	−0.774065	+	0.633106i	$0.781780\pi$
$440$	−234.142	−	77.3317i	−0.532141	−	0.175754i
$441$	271.737			0.616184
$442$	331.508	−	331.508i	0.750017	−	0.750017i
$443$	−479.179	−	479.179i	−1.08167	−	1.08167i	−0.996354	−	0.0853137i	$-0.972811\pi$
$443$	−479.179	−	479.179i	−1.08167	−	1.08167i	−0.0853137	−	0.996354i	$-0.527189\pi$
$444$		−	58.2104i		−	0.131105i
$445$	37.3922	+	74.2724i	0.0840273	+	0.166904i
$446$	109.758			0.246093
$447$	−230.902	+	230.902i	−0.516560	+	0.516560i
$448$	−66.8321	−	66.8321i	−0.149179	−	0.149179i
$449$		−	526.390i		−	1.17236i	−0.810180	−	0.586181i	$-0.800631\pi$
$449$		−	526.390i		−	1.17236i	0.810180	−	0.586181i	$-0.199369\pi$
$450$	−104.916	+	15.5780i	−0.233146	+	0.0346178i
$451$	−1259.51			−2.79270
$452$	−243.212	+	243.212i	−0.538080	+	0.538080i
$453$	−215.664	−	215.664i	−0.476080	−	0.476080i
$454$		−	164.508i		−	0.362352i
$455$	824.562	−	415.123i	1.81223	−	0.912359i
$456$	−14.1004			−0.0309220
$457$	190.661	−	190.661i	0.417201	−	0.417201i	−0.467037	−	0.884238i	$-0.654678\pi$
$457$	190.661	−	190.661i	0.417201	−	0.417201i	0.884238	+	0.467037i	$0.154678\pi$
$458$	429.556	+	429.556i	0.937896	+	0.937896i
$459$			110.224i			0.240140i
$460$	−15.0404	+	45.5388i	−0.0326966	+	0.0989975i
$461$	−138.301			−0.300003			−0.150001	−	0.988686i	$-0.547928\pi$
$461$	−138.301			−0.300003			−0.150001	+	0.988686i	$0.547928\pi$
$462$	−356.794	+	356.794i	−0.772281	+	0.772281i
$463$	377.857	+	377.857i	0.816106	+	0.816106i	0.985541	−	0.169435i	$-0.0541943\pi$
$463$	377.857	+	377.857i	0.816106	+	0.816106i	−0.169435	+	0.985541i	$0.554194\pi$
$464$		−	12.5091i		−	0.0269593i
$465$	149.183	+	49.2718i	0.320824	+	0.105961i
$466$	70.1921			0.150627
$467$	−121.247	+	121.247i	−0.259629	+	0.259629i	−0.824903	−	0.565274i	$-0.808770\pi$
$467$	−121.247	+	121.247i	−0.259629	+	0.259629i	0.565274	+	0.824903i	$0.308770\pi$
$468$	66.3032	+	66.3032i	0.141674	+	0.141674i
$469$			1016.59i			2.16756i
$470$	276.535	+	549.284i	0.588373	+	1.16869i
$471$	79.3939			0.168565
$472$	−120.880	+	120.880i	−0.256101	+	0.256101i
$473$	−763.269	−	763.269i	−1.61368	−	1.61368i
$474$			109.777i			0.231597i
$475$	−57.8016	−	42.8559i	−0.121688	−	0.0902230i
$476$	−501.228			−1.05300
$477$	−129.137	+	129.137i	−0.270727	+	0.270727i
$478$	−108.716	−	108.716i	−0.227440	−	0.227440i
$479$			687.235i			1.43473i	0.696698	+	0.717364i	$0.254652\pi$
$479$			687.235i			1.43473i	−0.696698	+	0.717364i	$0.745348\pi$
$480$	43.7573	−	22.0295i	0.0911611	−	0.0458947i
$481$	−262.608			−0.545963
$482$	294.692	−	294.692i	0.611394	−	0.611394i
$483$	69.3937	+	69.3937i	0.143672	+	0.143672i
$484$		−	366.028i		−	0.756256i
$485$	−118.344	+	358.317i	−0.244008	+	0.738798i
$486$	−22.0454			−0.0453609
$487$	437.113	−	437.113i	0.897563	−	0.897563i	−0.0976574	−	0.995220i	$-0.531135\pi$
$487$	437.113	−	437.113i	0.897563	−	0.897563i	0.995220	+	0.0976574i	$0.0311349\pi$
$488$	2.74896	+	2.74896i	0.00563311	+	0.00563311i
$489$		−	209.636i		−	0.428704i
$490$	−608.178	−	200.867i	−1.24118	−	0.409933i
$491$	−129.408			−0.263559			−0.131780	−	0.991279i	$-0.542069\pi$
$491$	−129.408			−0.263559			−0.131780	+	0.991279i	$0.542069\pi$
$492$	176.942	−	176.942i	0.359638	−	0.359638i
$493$	−46.9080	−	46.9080i	−0.0951482	−	0.0951482i
$494$			63.6121i			0.128770i
$495$	−117.608	−	233.605i	−0.237592	−	0.471930i
$496$	−72.5657			−0.146302
$497$	746.173	−	746.173i	1.50135	−	1.50135i
$498$	−4.00725	−	4.00725i	−0.00804670	−	0.00804670i
$499$			958.920i			1.92168i	0.277098	+	0.960842i	$0.410627\pi$
$499$			958.920i			1.92168i	−0.277098	+	0.960842i	$0.589373\pi$
$500$	246.329	+	42.6880i	0.492657	+	0.0853761i
$501$	−168.937			−0.337200
$502$	−451.400	+	451.400i	−0.899203	+	0.899203i
$503$	−135.406	−	135.406i	−0.269197	−	0.269197i	0.559580	−	0.828777i	$-0.310963\pi$
$503$	−135.406	−	135.406i	−0.269197	−	0.269197i	−0.828777	+	0.559580i	$0.810963\pi$
$504$		−	100.248i		−	0.198905i
$505$	160.689	−	80.8984i	0.318196	−	0.160195i
$506$	−118.257			−0.233709
$507$	92.1359	−	92.1359i	0.181728	−	0.181728i
$508$	158.673	+	158.673i	0.312348	+	0.312348i
$509$		−	642.984i		−	1.26323i	−0.775282	−	0.631615i	$-0.782392\pi$
$509$		−	642.984i		−	1.26323i	0.775282	−	0.631615i	$-0.217608\pi$
$510$	81.4773	−	246.694i	0.159759	−	0.483714i
$511$	317.526			0.621381
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−10.5753	−	10.5753i	−0.0206147	−	0.0206147i
$514$		−	371.816i		−	0.723378i
$515$	515.508	+	170.260i	1.00099	+	0.330602i
$516$	214.455			0.415611
$517$	−1072.26	+	1072.26i	−2.07400	+	2.07400i
$518$	198.527	+	198.527i	0.383258	+	0.383258i
$519$		−	68.4664i		−	0.131920i
$520$	−99.3829	−	197.405i	−0.191121	−	0.379625i
$521$	343.522			0.659351			0.329676	−	0.944094i	$-0.393061\pi$
$521$	343.522			0.659351			0.329676	+	0.944094i	$0.393061\pi$
$522$	9.38185	−	9.38185i	0.0179729	−	0.0179729i
$523$	−44.8371	−	44.8371i	−0.0857306	−	0.0857306i	0.662941	−	0.748672i	$-0.269308\pi$
$523$	−44.8371	−	44.8371i	−0.0857306	−	0.0857306i	−0.748672	+	0.662941i	$0.769308\pi$
$524$		−	154.047i		−	0.293982i
$525$	304.688	−	410.946i	0.580357	−	0.782753i
$526$	−549.439			−1.04456
$527$	−272.115	+	272.115i	−0.516346	+	0.516346i
$528$	85.4186	+	85.4186i	0.161778	+	0.161778i
$529$			23.0000i			0.0434783i
$530$	384.479	−	193.565i	0.725433	−	0.365217i
$531$	−181.320			−0.341468
$532$	48.0897	−	48.0897i	0.0903941	−	0.0903941i
$533$	−798.249	−	798.249i	−1.49765	−	1.49765i
$534$		−	40.7369i		−	0.0762863i
$535$	−248.239	+	751.610i	−0.463999	+	1.40488i
$536$	243.377			0.454061
$537$	158.277	−	158.277i	0.294742	−	0.294742i
$538$	−427.490	−	427.490i	−0.794591	−	0.794591i
$539$		−	1579.34i		−	2.93012i
$540$	49.3401	+	16.2959i	0.0913705	+	0.0301776i
$541$	−425.664			−0.786809			−0.393404	−	0.919366i	$-0.628703\pi$
$541$	−425.664			−0.786809			−0.393404	+	0.919366i	$0.628703\pi$
$542$	−101.987	+	101.987i	−0.188167	+	0.188167i
$543$	−53.7089	−	53.7089i	−0.0989115	−	0.0989115i
$544$			119.997i			0.220583i
$545$	466.097	+	925.812i	0.855224	+	1.69874i
$546$	−452.256			−0.828307
$547$	−561.015	+	561.015i	−1.02562	+	1.02562i	−0.0259585	+	0.999663i	$0.508264\pi$
$547$	−561.015	+	561.015i	−1.02562	+	1.02562i	−0.999663	+	0.0259585i	$0.991736\pi$
$548$	−44.9114	−	44.9114i	−0.0819551	−	0.0819551i
$549$			4.12344i			0.00751082i
$550$	90.5393	+	609.770i	0.164617	+	1.10867i
$551$	9.00106			0.0163359
$552$	16.6132	−	16.6132i	0.0300965	−	0.0300965i
$553$	−374.396	−	374.396i	−0.677026	−	0.677026i
$554$		−	509.371i		−	0.919443i
$555$	−129.983	+	65.4394i	−0.234203	+	0.117909i
$556$	48.8964			0.0879433
$557$	567.369	−	567.369i	1.01862	−	1.01862i	0.0187923	−	0.999823i	$-0.494018\pi$
$557$	567.369	−	567.369i	1.01862	−	1.01862i	0.999823	−	0.0187923i	$-0.00598211\pi$
$558$	−54.4243	−	54.4243i	−0.0975346	−	0.0975346i
$559$		−	967.485i		−	1.73074i
$560$	−74.1031	+	224.367i	−0.132327	+	0.400655i
$561$	640.623			1.14193
$562$	438.626	−	438.626i	0.780472	−	0.780472i
$563$	−156.606	−	156.606i	−0.278164	−	0.278164i	0.554212	−	0.832376i	$-0.313020\pi$
$563$	−156.606	−	156.606i	−0.278164	−	0.278164i	−0.832376	+	0.554212i	$0.813020\pi$
$564$		−	301.271i		−	0.534169i
$565$	816.505	+	269.672i	1.44514	+	0.477296i
$566$	−170.666			−0.301529
$567$	75.1861	−	75.1861i	0.132603	−	0.132603i
$568$	−178.638	−	178.638i	−0.314504	−	0.314504i
$569$			331.356i			0.582347i	0.956670	+	0.291174i	$0.0940458\pi$
$569$			331.356i			0.582347i	−0.956670	+	0.291174i	$0.905954\pi$
$570$	15.8515	+	31.4860i	0.0278097	+	0.0552386i
$571$	−859.490			−1.50524			−0.752618	−	0.658457i	$-0.771209\pi$
$571$	−859.490			−1.50524			−0.752618	+	0.658457i	$0.771209\pi$
$572$	385.354	−	385.354i	0.673696	−	0.673696i
$573$	455.366	+	455.366i	0.794705	+	0.794705i
$574$			1206.92i			2.10266i
$575$	118.596	−	17.6092i	0.206253	−	0.0306247i
$576$	−24.0000			−0.0416667
$577$	20.7204	−	20.7204i	0.0359106	−	0.0359106i	−0.688923	−	0.724834i	$-0.741916\pi$
$577$	20.7204	−	20.7204i	0.0359106	−	0.0359106i	0.724834	+	0.688923i	$0.241916\pi$
$578$	160.977	+	160.977i	0.278507	+	0.278507i
$579$			330.803i			0.571336i
$580$	−27.9326	+	14.0626i	−0.0481597	+	0.0242459i
$581$	27.3336			0.0470457
$582$	130.719	−	130.719i	0.224604	−	0.224604i
$583$	750.541	+	750.541i	1.28738	+	1.28738i
$584$		−	76.0175i		−	0.130167i
$585$	73.5166	−	222.591i	0.125669	−	0.380497i
$586$	133.143			0.227207
$587$	−103.084	+	103.084i	−0.175612	+	0.175612i	−0.789440	−	0.613828i	$-0.789629\pi$
$587$	−103.084	+	103.084i	−0.175612	+	0.175612i	0.613828	+	0.789440i	$0.289629\pi$
$588$	221.873	+	221.873i	0.377334	+	0.377334i
$589$		−	52.2154i		−	0.0886509i
$590$	405.814	+	134.031i	0.687820	+	0.227171i
$591$	318.258			0.538508
$592$	47.5286	−	47.5286i	0.0802849	−	0.0802849i
$593$	489.343	+	489.343i	0.825199	+	0.825199i	0.986848	−	0.161649i	$-0.0516814\pi$
$593$	489.343	+	489.343i	0.825199	+	0.825199i	−0.161649	+	0.986848i	$0.551681\pi$
$594$			128.128i			0.215703i
$595$	563.474	+	1119.23i	0.947015	+	1.88106i
$596$	−377.062			−0.632654
$597$	234.176	−	234.176i	0.392254	−	0.392254i
$598$	−74.9484	−	74.9484i	−0.125332	−	0.125332i
$599$			351.503i			0.586816i	0.955987	+	0.293408i	$0.0947894\pi$
$599$			351.503i			0.586816i	−0.955987	+	0.293408i	$0.905211\pi$
$600$	−98.3828	−	72.9440i	−0.163971	−	0.121573i
$601$	−985.264			−1.63937			−0.819687	−	0.572811i	$-0.805853\pi$
$601$	−985.264			−1.63937			−0.819687	+	0.572811i	$0.805853\pi$
$602$	−731.402	+	731.402i	−1.21495	+	1.21495i
$603$	182.533	+	182.533i	0.302708	+	0.302708i
$604$		−	352.178i		−	0.583077i
$605$	−817.333	+	411.483i	−1.35096	+	0.680138i
$606$	−88.1347			−0.145437
$607$	167.150	−	167.150i	0.275371	−	0.275371i	−0.555887	−	0.831258i	$-0.687621\pi$
$607$	167.150	−	167.150i	0.275371	−	0.275371i	0.831258	+	0.555887i	$0.187621\pi$
$608$	−11.5130	−	11.5130i	−0.0189358	−	0.0189358i
$609$			63.9938i			0.105080i
$610$	3.04803	−	9.22871i	0.00499677	−	0.0151290i
$611$	−1359.14			−2.22446
$612$	−89.9977	+	89.9977i	−0.147055	+	0.147055i
$613$	50.3714	+	50.3714i	0.0821719	+	0.0821719i	0.746998	−	0.664826i	$-0.231494\pi$
$613$	50.3714	+	50.3714i	0.0821719	+	0.0821719i	−0.664826	+	0.746998i	$0.731494\pi$
$614$		−	584.537i		−	0.952015i
$615$	−594.023	−	196.192i	−0.965892	−	0.319012i
$616$	−582.642			−0.945848
$617$	−318.895	+	318.895i	−0.516848	+	0.516848i	−0.916616	−	0.399768i	$-0.869091\pi$
$617$	−318.895	+	318.895i	−0.516848	+	0.516848i	0.399768	+	0.916616i	$0.369091\pi$
$618$	−188.065	−	188.065i	−0.304312	−	0.304312i
$619$		−	316.148i		−	0.510741i	−0.966843	−	0.255370i	$-0.917803\pi$
$619$		−	316.148i		−	0.510741i	0.966843	−	0.255370i	$-0.0821974\pi$
$620$	81.5774	+	162.038i	0.131577	+	0.261351i
$621$	24.9199			0.0401286
$622$	81.4097	−	81.4097i	0.130884	−	0.130884i
$623$	138.934	+	138.934i	0.223007	+	0.223007i
$624$			108.273i			0.173514i
$625$	−181.598	−	598.036i	−0.290556	−	0.956858i
$626$	−294.183			−0.469941
$627$	−61.4637	+	61.4637i	−0.0980283	+	0.0980283i
$628$	64.8248	+	64.8248i	0.103224	+	0.103224i
$629$		−	356.456i		−	0.566702i
$630$	−223.852	+	112.698i	−0.355321	+	0.178885i
$631$	605.041			0.958861			0.479430	−	0.877580i	$-0.340843\pi$
$631$	605.041			0.958861			0.479430	+	0.877580i	$0.340843\pi$
$632$	−89.6325	+	89.6325i	−0.141824	+	0.141824i
$633$	20.9333	+	20.9333i	0.0330700	+	0.0330700i
$634$			103.121i			0.162651i
$635$	175.935	−	532.691i	0.277064	−	0.838884i
$636$	−210.879			−0.331571
$637$	1000.95	−	1000.95i	1.57135	−	1.57135i
$638$	−54.5273	−	54.5273i	−0.0854659	−	0.0854659i
$639$		−	267.957i		−	0.419338i
$640$	53.7147	+	17.7407i	0.0839292	+	0.0277199i
$641$	−465.040			−0.725491			−0.362745	−	0.931888i	$-0.618161\pi$
$641$	−465.040			−0.725491			−0.362745	+	0.931888i	$0.618161\pi$
$642$	274.199	−	274.199i	0.427101	−	0.427101i
$643$	−348.885	−	348.885i	−0.542590	−	0.542590i	0.381697	−	0.924287i	$-0.375340\pi$
$643$	−348.885	−	348.885i	−0.542590	−	0.542590i	−0.924287	+	0.381697i	$0.875340\pi$
$644$			113.319i			0.175962i
$645$	−241.088	−	478.874i	−0.373779	−	0.742441i
$646$	−86.3449			−0.133661
$647$	−190.931	+	190.931i	−0.295102	+	0.295102i	−0.839092	−	0.543990i	$-0.816913\pi$
$647$	−190.931	+	190.931i	−0.295102	+	0.295102i	0.543990	+	0.839092i	$0.316913\pi$
$648$	−18.0000	−	18.0000i	−0.0277778	−	0.0277778i
$649$			1053.83i			1.62377i
$650$	−329.077	+	443.840i	−0.506272	+	0.682831i
$651$	371.229			0.570245
$652$	171.167	−	171.167i	0.262526	−	0.262526i
$653$	−149.378	−	149.378i	−0.228756	−	0.228756i	0.583417	−	0.812173i	$-0.301715\pi$
$653$	−149.378	−	149.378i	−0.228756	−	0.228756i	−0.812173	+	0.583417i	$0.801715\pi$
$654$		−	507.789i		−	0.776436i
$655$	−343.983	+	173.177i	−0.525165	+	0.264393i
$656$	288.945			0.440465
$657$	57.0131	−	57.0131i	0.0867780	−	0.0867780i
$658$	1027.49	+	1027.49i	1.56153	+	1.56153i
$659$			577.391i			0.876163i	0.898935	+	0.438081i	$0.144342\pi$
$659$			577.391i			0.876163i	−0.898935	+	0.438081i	$0.855658\pi$
$660$	94.7116	−	286.764i	0.143502	−	0.434492i
$661$	734.430			1.11109			0.555545	−	0.831487i	$-0.312510\pi$
$661$	734.430			1.11109			0.555545	+	0.831487i	$0.312510\pi$
$662$	445.932	−	445.932i	0.673614	−	0.673614i
$663$	406.012	+	406.012i	0.612386	+	0.612386i
$664$		−	6.54382i		−	0.00985515i
$665$	−161.445	−	53.3216i	−0.242775	−	0.0801828i
$666$	71.2929			0.107046
$667$	−10.6051	+	10.6051i	−0.0158997	+	0.0158997i
$668$	−137.937	−	137.937i	−0.206492	−	0.206492i
$669$			134.425i			0.200934i
$670$	−273.601	−	543.456i	−0.408360	−	0.811129i
$671$	23.9654			0.0357160
$672$	81.8523	−	81.8523i	0.121804	−	0.121804i
$673$	−310.291	−	310.291i	−0.461057	−	0.461057i	0.437945	−	0.899002i	$-0.355706\pi$
$673$	−310.291	−	310.291i	−0.461057	−	0.461057i	−0.899002	+	0.437945i	$0.855706\pi$
$674$		−	357.949i		−	0.531081i
$675$	−19.0791	−	128.495i	−0.0282653	−	0.190363i
$676$	150.457			0.222570
$677$	474.216	−	474.216i	0.700467	−	0.700467i	−0.264044	−	0.964511i	$-0.585056\pi$
$677$	474.216	−	474.216i	0.700467	−	0.700467i	0.964511	+	0.264044i	$0.0850564\pi$
$678$	−297.873	−	297.873i	−0.439341	−	0.439341i
$679$			891.640i			1.31317i
$680$	267.951	−	134.899i	0.394045	−	0.198381i
$681$	201.480			0.295860
$682$	−316.314	+	316.314i	−0.463803	+	0.463803i
$683$	−640.291	−	640.291i	−0.937469	−	0.937469i	0.0606878	−	0.998157i	$-0.480671\pi$
$683$	−640.291	−	640.291i	−0.937469	−	0.937469i	−0.998157	+	0.0606878i	$0.980671\pi$
$684$		−	17.2694i		−	0.0252477i
$685$	−49.7975	+	150.775i	−0.0726971	+	0.220110i
$686$	−694.705			−1.01269
$687$	−526.097	+	526.097i	−0.765789	+	0.765789i
$688$	175.102	+	175.102i	0.254509	+	0.254509i
$689$			951.352i			1.38077i
$690$	−55.7735	−	18.4207i	−0.0808311	−	0.0266966i
$691$	270.091			0.390870			0.195435	−	0.980717i	$-0.437388\pi$
$691$	270.091			0.390870			0.195435	+	0.980717i	$0.437388\pi$
$692$	55.9026	−	55.9026i	0.0807841	−	0.0807841i
$693$	−436.982	−	436.982i	−0.630565	−	0.630565i
$694$		−	390.651i		−	0.562898i
$695$	−54.9687	−	109.185i	−0.0790917	−	0.157100i
$696$	15.3205			0.0220122
$697$	1083.52	−	1083.52i	1.55454	−	1.55454i
$698$	616.027	+	616.027i	0.882560	+	0.882560i
$699$			85.9674i			0.122986i
$700$	584.312	−	86.7593i	0.834732	−	0.123942i
$701$	−713.112			−1.01728			−0.508639	−	0.860980i	$-0.669851\pi$
$701$	−713.112			−1.01728			−0.508639	+	0.860980i	$0.669851\pi$
$702$	−81.2045	+	81.2045i	−0.115676	+	0.115676i
$703$	34.1997	+	34.1997i	0.0486482	+	0.0486482i
$704$			139.488i			0.198136i
$705$	−672.733	+	338.685i	−0.954232	+	0.480405i
$706$	485.281			0.687366
$707$	300.584	−	300.584i	0.425155	−	0.425155i
$708$	−148.047	−	148.047i	−0.209106	−	0.209106i
$709$			1353.88i			1.90956i	0.297314	+	0.954780i	$0.403909\pi$
$709$			1353.88i			1.90956i	−0.297314	+	0.954780i	$0.596091\pi$
$710$	−198.073	+	599.718i	−0.278976	+	0.844674i
$711$	−134.449			−0.189098
$712$	33.2615	−	33.2615i	0.0467156	−	0.0467156i
$713$	61.5206	+	61.5206i	0.0862841	+	0.0862841i
$714$		−	613.876i		−	0.859771i
$715$	−1293.70	−	427.278i	−1.80937	−	0.597592i
$716$	258.465			0.360984
$717$	133.150	−	133.150i	0.185704	−	0.185704i
$718$	−309.086	−	309.086i	−0.430482	−	0.430482i
$719$			652.637i			0.907701i	0.891078	+	0.453850i	$0.149950\pi$
$719$			652.637i			0.907701i	−0.891078	+	0.453850i	$0.850050\pi$
$720$	26.9805	+	53.5915i	0.0374729	+	0.0744327i
$721$	1282.79			1.77919
$722$	−352.716	+	352.716i	−0.488526	+	0.488526i
$723$	360.922	+	360.922i	0.499201	+	0.499201i
$724$		−	87.7063i		−	0.121141i
$725$	62.8030	+	46.5641i	0.0866249	+	0.0642263i
$726$	448.291			0.617480
$727$	532.109	−	532.109i	0.731924	−	0.731924i	−0.239076	−	0.971001i	$-0.576845\pi$
$727$	532.109	−	532.109i	0.731924	−	0.731924i	0.971001	+	0.239076i	$0.0768446\pi$
$728$	−369.265	−	369.265i	−0.507233	−	0.507233i
$729$		−	27.0000i		−	0.0370370i
$730$	−169.746	+	85.4579i	−0.232528	+	0.117066i
$731$	1313.23			1.79649
$732$	−3.36677	+	3.36677i	−0.00459942	+	0.00459942i
$733$	−486.414	−	486.414i	−0.663594	−	0.663594i	0.292631	−	0.956225i	$-0.405469\pi$
$733$	−486.414	−	486.414i	−0.663594	−	0.663594i	−0.956225	+	0.292631i	$0.905469\pi$
$734$			640.363i			0.872429i
$735$	246.011	−	744.863i	0.334709	−	1.01342i
$736$	27.1293			0.0368605
$737$	1060.88	−	1060.88i	1.43946	−	1.43946i
$738$	216.709	+	216.709i	0.293643	+	0.293643i
$739$			161.727i			0.218846i	0.993995	+	0.109423i	$0.0349003\pi$
$739$			161.727i			0.218846i	−0.993995	+	0.109423i	$0.965100\pi$
$740$	−159.562	−	52.6995i	−0.215624	−	0.0712155i
$741$	−77.9086			−0.105140
$742$	719.206	−	719.206i	0.969280	−	0.969280i
$743$	−993.064	−	993.064i	−1.33656	−	1.33656i	−0.899368	−	0.437192i	$-0.855973\pi$
$743$	−993.064	−	993.064i	−1.33656	−	1.33656i	−0.437192	−	0.899368i	$-0.644027\pi$
$744$		−	88.8745i		−	0.119455i
$745$	423.888	+	841.971i	0.568977	+	1.13016i
$746$	−81.7694			−0.109610
$747$	4.90786	−	4.90786i	0.00657010	−	0.00657010i
$748$	523.066	+	523.066i	0.699287	+	0.699287i
$749$			1870.31i			2.49708i
$750$	−52.2820	+	301.690i	−0.0697093	+	0.402253i
$751$	158.149			0.210585			0.105292	−	0.994441i	$-0.466422\pi$
$751$	158.149			0.210585			0.105292	+	0.994441i	$0.466422\pi$
$752$	245.987	−	245.987i	0.327110	−	0.327110i
$753$	−552.850	−	552.850i	−0.734196	−	0.734196i
$754$		−	69.1163i		−	0.0916662i
$755$	−786.408	+	395.914i	−1.04160	+	0.524390i
$756$	122.778			0.162405
$757$	−121.557	+	121.557i	−0.160577	+	0.160577i	−0.782822	−	0.622245i	$-0.786221\pi$
$757$	−121.557	+	121.557i	−0.160577	+	0.160577i	0.622245	+	0.782822i	$0.286221\pi$
$758$	235.010	+	235.010i	0.310040	+	0.310040i
$759$		−	144.834i		−	0.190822i
$760$	−12.7655	+	38.6509i	−0.0167967	+	0.0508565i
$761$	−15.5981			−0.0204969			−0.0102484	−	0.999947i	$-0.503262\pi$
$761$	−15.5981			−0.0204969			−0.0102484	+	0.999947i	$0.503262\pi$
$762$	−194.334	+	194.334i	−0.255031	+	0.255031i
$763$	1731.82	+	1731.82i	2.26975	+	2.26975i
$764$			743.610i			0.973311i
$765$	302.137	+	99.7889i	0.394951	+	0.130443i
$766$	688.730			0.899125
$767$	−667.893	+	667.893i	−0.870786	+	0.870786i
$768$	−19.5959	−	19.5959i	−0.0255155	−	0.0255155i
$769$			744.420i			0.968037i	0.875058	+	0.484018i	$0.160823\pi$
$769$			744.420i			0.968037i	−0.875058	+	0.484018i	$0.839177\pi$
$770$	654.999	+	1301.03i	0.850647	+	1.68965i
$771$	455.380			0.590635
$772$	−270.100	+	270.100i	−0.349870	+	0.349870i
$773$	157.930	+	157.930i	0.204308	+	0.204308i	0.801843	−	0.597535i	$-0.203853\pi$
$773$	157.930	+	157.930i	0.204308	+	0.204308i	−0.597535	+	0.801843i	$0.703853\pi$
$774$			262.653i			0.339345i
$775$	270.119	−	364.322i	0.348541	−	0.470093i
$776$	213.464			0.275082
$777$	−243.145	+	243.145i	−0.312929	+	0.312929i
$778$	522.732	+	522.732i	0.671892	+	0.671892i
$779$			207.913i			0.266897i
$780$	241.771	−	121.719i	0.309963	−	0.156050i
$781$	−1557.37			−1.99407
$782$	101.732	−	101.732i	0.130093	−	0.130093i
$783$	11.4904	+	11.4904i	0.0146748	+	0.0146748i
$784$			362.316i			0.462138i
$785$	71.8774	−	217.628i	0.0915636	−	0.277233i
$786$	188.668			0.240035
$787$	−828.951	+	828.951i	−1.05330	+	1.05330i	−0.0548078	+	0.998497i	$0.517455\pi$
$787$	−828.951	+	828.951i	−1.05330	+	1.05330i	−0.998497	+	0.0548078i	$0.982545\pi$
$788$	259.857	+	259.857i	0.329767	+	0.329767i
$789$		−	672.922i		−	0.852880i
$790$	300.911	+	99.3840i	0.380900	+	0.125803i
$791$	2031.80			2.56865
$792$	−104.616	+	104.616i	−0.132091	+	0.132091i
$793$	15.1887	+	15.1887i	0.0191535	+	0.0191535i
$794$		−	260.078i		−	0.327554i
$795$	237.068	+	470.889i	0.298198	+	0.592313i
$796$	382.407			0.480411
$797$	−727.382	+	727.382i	−0.912650	+	0.912650i	−0.996480	−	0.0838299i	$-0.973285\pi$
$797$	−727.382	+	727.382i	−0.912650	+	0.912650i	0.0838299	+	0.996480i	$0.473285\pi$
$798$	58.8976	+	58.8976i	0.0738065	+	0.0738065i
$799$		−	1844.86i		−	2.30896i
$800$	−20.7707	−	139.888i	−0.0259633	−	0.174860i
$801$	49.8923			0.0622875
$802$	−711.927	+	711.927i	−0.887690	+	0.887690i
$803$	−331.360	−	331.360i	−0.412653	−	0.412653i
$804$			298.075i			0.370740i
$805$	253.040	−	127.392i	0.314335	−	0.158251i
$806$	−400.945			−0.497450
$807$	523.566	−	523.566i	0.648780	−	0.648780i
$808$	−71.9617	−	71.9617i	−0.0890615	−	0.0890615i
$809$			864.574i			1.06870i	0.845265	+	0.534348i	$0.179443\pi$
$809$			864.574i			1.06870i	−0.845265	+	0.534348i	$0.820557\pi$
$810$	−19.9583	+	60.4290i	−0.0246399	+	0.0746037i
$811$	840.459			1.03632			0.518162	−	0.855282i	$-0.326616\pi$
$811$	840.459			1.03632			0.518162	+	0.855282i	$0.326616\pi$
$812$	−52.2507	+	52.2507i	−0.0643482	+	0.0643482i
$813$	−124.908	−	124.908i	−0.153638	−	0.153638i
$814$		−	414.354i		−	0.509035i
$815$	−574.637	−	189.789i	−0.705076	−	0.232870i
$816$	−146.966			−0.180105
$817$	−125.996	+	125.996i	−0.154218	+	0.154218i
$818$	225.265	+	225.265i	0.275385	+	0.275385i
$819$		−	553.898i		−	0.676310i
$820$	−324.828	−	645.208i	−0.396132	−	0.786839i
$821$	−451.960			−0.550499			−0.275250	−	0.961373i	$-0.588761\pi$
$821$	−451.960			−0.550499			−0.275250	+	0.961373i	$0.588761\pi$
$822$	55.0050	−	55.0050i	0.0669160	−	0.0669160i
$823$	216.013	+	216.013i	0.262470	+	0.262470i	0.826057	−	0.563587i	$-0.190579\pi$
$823$	216.013	+	216.013i	0.262470	+	0.262470i	−0.563587	+	0.826057i	$0.690579\pi$
$824$		−	307.109i		−	0.372705i
$825$	−746.813	+	110.888i	−0.905228	+	0.134409i
$826$	1009.83			1.22256
$827$	1019.71	−	1019.71i	1.23303	−	1.23303i	0.270232	−	0.962795i	$-0.412900\pi$
$827$	1019.71	−	1019.71i	1.23303	−	1.23303i	0.962795	−	0.270232i	$-0.0871004\pi$
$828$	20.3470	+	20.3470i	0.0245737	+	0.0245737i
$829$		−	306.072i		−	0.369206i	−0.982813	−	0.184603i	$-0.940900\pi$
$829$		−	306.072i		−	0.369206i	0.982813	−	0.184603i	$-0.0590999\pi$
$830$	−14.6122	+	7.35648i	−0.0176051	+	0.00886322i
$831$	623.850			0.750722
$832$	−88.4043	+	88.4043i	−0.106255	+	0.106255i
$833$	1358.65	+	1358.65i	1.63103	+	1.63103i
$834$			59.8857i			0.0718054i
$835$	−152.943	+	463.076i	−0.183166	+	0.554582i
$836$	−100.370			−0.120060
$837$	66.6559	−	66.6559i	0.0796367	−	0.0796367i
$838$	−727.460	−	727.460i	−0.868090	−	0.868090i
$839$			827.673i			0.986499i	0.869888	+	0.493250i	$0.164191\pi$
$839$			827.673i			0.986499i	−0.869888	+	0.493250i	$0.835809\pi$
$840$	−274.792	−	90.7573i	−0.327133	−	0.108044i
$841$	831.220			0.988371
$842$	−188.423	+	188.423i	−0.223781	+	0.223781i
$843$	537.204	+	537.204i	0.637253	+	0.637253i
$844$			34.1840i			0.0405024i
$845$	−169.142	−	335.968i	−0.200168	−	0.397596i
$846$	368.981			0.436147
$847$	−1528.90	+	1528.90i	−1.80508	+	1.80508i
$848$	−172.182	−	172.182i	−0.203045	−	0.203045i
$849$		−	209.022i		−	0.246198i
$850$	−602.454	−	446.678i	−0.708769	−	0.525503i
$851$	−80.5887			−0.0946988
$852$	218.786	−	218.786i	0.256791	−	0.256791i
$853$	−438.820	−	438.820i	−0.514443	−	0.514443i	0.401442	−	0.915885i	$-0.368509\pi$
$853$	−438.820	−	438.820i	−0.514443	−	0.514443i	−0.915885	+	0.401442i	$0.868509\pi$
$854$		−	22.9648i		−	0.0268909i
$855$	−38.5623	+	19.4141i	−0.0451021	+	0.0227065i
$856$	447.764			0.523089
$857$	940.789	−	940.789i	1.09777	−	1.09777i	0.103098	−	0.994671i	$-0.467124\pi$
$857$	940.789	−	940.789i	1.09777	−	1.09777i	0.994671	−	0.103098i	$-0.0328757\pi$
$858$	471.960	+	471.960i	0.550070	+	0.550070i
$859$			37.9823i			0.0442169i	0.999756	+	0.0221084i	$0.00703790\pi$
$859$			37.9823i			0.0442169i	−0.999756	+	0.0221084i	$0.992962\pi$
$860$	194.152	−	587.846i	0.225758	−	0.683542i
$861$	−1478.17			−1.71681
$862$	−624.307	+	624.307i	−0.724254	+	0.724254i
$863$	995.920	+	995.920i	1.15402	+	1.15402i	0.985739	+	0.168282i	$0.0538221\pi$
$863$	995.920	+	995.920i	1.15402	+	1.15402i	0.168282	+	0.985739i	$0.446178\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	−187.674	−	61.9844i	−0.216965	−	0.0716583i
$866$	−417.257			−0.481821
$867$	−197.156	+	197.156i	−0.227400	+	0.227400i
$868$	303.108	+	303.108i	0.349202	+	0.349202i
$869$			781.416i			0.899213i
$870$	−17.2231	−	34.2104i	−0.0197967	−	0.0393223i
$871$	1344.72			1.54388
$872$	414.608	−	414.608i	0.475468	−	0.475468i
$873$	160.098	+	160.098i	0.183388	+	0.183388i
$874$			19.5212i			0.0223354i
$875$	−850.608	−	1207.22i	−0.972123	−	1.37968i
$876$	93.1020			0.106281
$877$	475.448	−	475.448i	0.542130	−	0.542130i	−0.382023	−	0.924153i	$-0.624773\pi$
$877$	475.448	−	475.448i	0.542130	−	0.542130i	0.924153	+	0.382023i	$0.124773\pi$
$878$	−555.867	−	555.867i	−0.633106	−	0.633106i
$879$			163.066i			0.185514i
$880$	311.474	−	156.810i	0.353948	−	0.178194i
$881$	1268.64			1.44001			0.720003	−	0.693971i	$-0.244141\pi$
$881$	1268.64			1.44001			0.720003	+	0.693971i	$0.244141\pi$
$882$	−271.737	+	271.737i	−0.308092	+	0.308092i
$883$	−336.031	−	336.031i	−0.380556	−	0.380556i	0.490746	−	0.871302i	$-0.336724\pi$
$883$	−336.031	−	336.031i	−0.380556	−	0.380556i	−0.871302	+	0.490746i	$0.836724\pi$
$884$			663.015i			0.750017i
$885$	−164.153	+	497.018i	−0.185484	+	0.561602i
$886$	958.358			1.08167
$887$	−222.340	+	222.340i	−0.250665	+	0.250665i	−0.821243	−	0.570578i	$-0.806719\pi$
$887$	−222.340	+	222.340i	−0.250665	+	0.250665i	0.570578	+	0.821243i	$0.306719\pi$
$888$	58.2104	+	58.2104i	0.0655523	+	0.0655523i
$889$		−	1325.55i		−	1.49106i
$890$	−111.665	−	36.8802i	−0.125466	−	0.0414384i
$891$	−156.924			−0.176121
$892$	−109.758	+	109.758i	−0.123047	+	0.123047i
$893$	177.002	+	177.002i	0.198211	+	0.198211i
$894$		−	461.804i		−	0.516560i
$895$	−290.563	−	577.147i	−0.324651	−	0.644857i
$896$	133.664			0.149179
$897$	91.7926	−	91.7926i	0.102333	−	0.102333i
$898$	526.390	+	526.390i	0.586181	+	0.586181i
$899$			56.7334i			0.0631072i
$900$	89.3378	−	120.494i	0.0992642	−	0.133882i
$901$	−1291.33			−1.43322
$902$	1259.51	−	1259.51i	1.39635	−	1.39635i
$903$	−895.781	−	895.781i	−0.992005	−	0.992005i
$904$		−	486.425i		−	0.538080i
$905$	−195.847	+	98.5983i	−0.216405	+	0.108948i
$906$	431.329			0.476080
$907$	194.442	−	194.442i	0.214379	−	0.214379i	−0.591746	−	0.806125i	$-0.701561\pi$
$907$	194.442	−	194.442i	0.214379	−	0.214379i	0.806125	+	0.591746i	$0.201561\pi$
$908$	164.508	+	164.508i	0.181176	+	0.181176i
$909$		−	107.943i		−	0.118749i
$910$	−409.439	+	1239.69i	−0.449933	+	1.36229i
$911$	−822.549			−0.902908			−0.451454	−	0.892294i	$-0.649094\pi$
$911$	−822.549			−0.902908			−0.451454	+	0.892294i	$0.649094\pi$
$912$	14.1004	−	14.1004i	0.0154610	−	0.0154610i
$913$	−28.5245	−	28.5245i	−0.0312426	−	0.0312426i
$914$			381.322i			0.417201i
$915$	11.3028	+	3.73306i	0.0123528	+	0.00407984i
$916$	−859.113			−0.937896
$917$	−643.454	+	643.454i	−0.701695	+	0.701695i
$918$	−110.224	−	110.224i	−0.120070	−	0.120070i
$919$		−	107.710i		−	0.117204i	−0.998281	−	0.0586020i	$-0.981336\pi$
$919$		−	107.710i		−	0.117204i	0.998281	−	0.0586020i	$-0.0186643\pi$
$920$	−30.4984	−	60.5793i	−0.0331505	−	0.0658470i
$921$	715.909			0.777317
$922$	138.301	−	138.301i	0.150001	−	0.150001i
$923$	−987.024	−	987.024i	−1.06936	−	1.06936i
$924$		−	713.588i		−	0.772281i
$925$	61.7001	+	415.542i	0.0667028	+	0.449235i
$926$	−755.714			−0.816106
$927$	230.331	−	230.331i	0.248470	−	0.248470i
$928$	12.5091	+	12.5091i	0.0134797	+	0.0134797i
$929$		−	1205.01i		−	1.29710i	−0.761172	−	0.648550i	$-0.775376\pi$
$929$		−	1205.01i		−	1.29710i	0.761172	−	0.648550i	$-0.224624\pi$
$930$	−198.455	+	99.9115i	−0.213393	+	0.107432i
$931$	−260.708			−0.280030
$932$	−70.1921	+	70.1921i	−0.0753134	+	0.0753134i
$933$	99.7061	+	99.7061i	0.106866	+	0.106866i
$934$		−	242.494i		−	0.259629i
$935$	579.973	−	1756.02i	0.620292	−	1.87810i
$936$	−132.606			−0.141674
$937$	−71.0492	+	71.0492i	−0.0758263	+	0.0758263i	−0.744003	−	0.668177i	$-0.767075\pi$
$937$	−71.0492	+	71.0492i	−0.0758263	+	0.0758263i	0.668177	+	0.744003i	$0.267075\pi$
$938$	−1016.59	−	1016.59i	−1.08378	−	1.08378i
$939$		−	360.299i		−	0.383705i
$940$	−825.820	−	272.749i	−0.878532	−	0.290159i
$941$	−163.158			−0.173387			−0.0866937	−	0.996235i	$-0.527630\pi$
$941$	−163.158			−0.173387			−0.0866937	+	0.996235i	$0.527630\pi$
$942$	−79.3939	+	79.3939i	−0.0842823	+	0.0842823i
$943$	−244.965	−	244.965i	−0.259772	−	0.259772i
$944$		−	241.759i		−	0.256101i
$945$	−138.026	−	274.162i	−0.146059	−	0.290118i
$946$	1526.54			1.61368
$947$	1019.92	−	1019.92i	1.07700	−	1.07700i	0.0802243	−	0.996777i	$-0.474436\pi$
$947$	1019.92	−	1019.92i	1.07700	−	1.07700i	0.996777	−	0.0802243i	$-0.0255636\pi$
$948$	−109.777	−	109.777i	−0.115798	−	0.115798i
$949$		−	420.017i		−	0.442589i
$950$	100.658	−	14.9457i	0.105955	−	0.0157324i
$951$	−126.297			−0.132804
$952$	501.228	−	501.228i	0.526500	−	0.526500i
$953$	−369.650	−	369.650i	−0.387880	−	0.387880i	0.486050	−	0.873931i	$-0.338437\pi$
$953$	−369.650	−	369.650i	−0.387880	−	0.387880i	−0.873931	+	0.486050i	$0.838437\pi$
$954$		−	258.273i		−	0.270727i
$955$	1660.47	−	835.956i	1.73871	−	0.875347i
$956$	217.432			0.227440
$957$	66.7820	−	66.7820i	0.0697827	−	0.0697827i
$958$	−687.235	−	687.235i	−0.717364	−	0.717364i
$959$			375.190i			0.391231i
$960$	−21.7278	+	65.7868i	−0.0226332	+	0.0685279i
$961$	−631.888			−0.657532
$962$	262.608	−	262.608i	0.272982	−	0.272982i
$963$	335.823	+	335.823i	0.348726	+	0.348726i
$964$			589.383i			0.611394i
$965$	906.770	+	299.485i	0.939658	+	0.310347i
$966$	−138.787			−0.143672
$967$	281.202	−	281.202i	0.290799	−	0.290799i	−0.546597	−	0.837396i	$-0.684077\pi$
$967$	281.202	−	281.202i	0.290799	−	0.290799i	0.837396	+	0.546597i	$0.184077\pi$
$968$	366.028	+	366.028i	0.378128	+	0.378128i
$969$		−	105.751i		−	0.109134i
$970$	−239.973	−	476.661i	−0.247395	−	0.491403i
$971$	−1264.29			−1.30205			−0.651023	−	0.759058i	$-0.725660\pi$
$971$	−1264.29			−1.30205			−0.651023	+	0.759058i	$0.725660\pi$
$972$	22.0454	−	22.0454i	0.0226805	−	0.0226805i
$973$	−204.241	−	204.241i	−0.209908	−	0.209908i
$974$			874.226i			0.897563i
$975$	−543.591	−	403.035i	−0.557529	−	0.413369i
$976$	−5.49792			−0.00563311
$977$	−396.137	+	396.137i	−0.405463	+	0.405463i	−0.880153	−	0.474690i	$-0.842560\pi$
$977$	−396.137	+	396.137i	−0.405463	+	0.405463i	0.474690	+	0.880153i	$0.342560\pi$
$978$	209.636	+	209.636i	0.214352	+	0.214352i
$979$		−	289.974i		−	0.296194i
$980$	809.046	−	407.311i	0.825557	−	0.415624i
$981$	621.912			0.633958
$982$	129.408	−	129.408i	0.131780	−	0.131780i
$983$	−1050.18	−	1050.18i	−1.06834	−	1.06834i	−0.997487	−	0.0708503i	$-0.977429\pi$
$983$	−1050.18	−	1050.18i	−1.06834	−	1.06834i	−0.0708503	−	0.997487i	$-0.522571\pi$
$984$			353.884i			0.359638i
$985$	288.127	−	872.382i	0.292515	−	0.885667i
$986$	93.8161			0.0951482
$987$	−1258.41	+	1258.41i	−1.27499	+	1.27499i
$988$	−63.6121	−	63.6121i	−0.0643848	−	0.0643848i
$989$		−	296.900i		−	0.300202i
$990$	351.213	+	115.998i	0.354761	+	0.117169i
$991$	291.520			0.294167			0.147084	−	0.989124i	$-0.453011\pi$
$991$	291.520			0.294167			0.147084	+	0.989124i	$0.453011\pi$
$992$	72.5657	−	72.5657i	0.0731509	−	0.0731509i
$993$	546.153	+	546.153i	0.550003	+	0.550003i
$994$			1492.35i			1.50135i
$995$	−429.897	−	853.909i	−0.432058	−	0.858200i
$996$	8.01451			0.00804670
$997$	−1233.91	+	1233.91i	−1.23762	+	1.23762i	−0.276655	+	0.960969i	$0.589226\pi$
$997$	−1233.91	+	1233.91i	−1.23762	+	1.23762i	−0.960969	+	0.276655i	$0.910774\pi$
$998$	−958.920	−	958.920i	−0.960842	−	0.960842i
$999$			87.3157i			0.0874031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.b.553.10	yes	48
5.2	odd	4	inner	690.3.k.b.277.10	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.b.277.10	✓	48	5.2	odd	4	inner
690.3.k.b.553.10	yes	48	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-4.46596 + 2.24837i) q^{5} +2.44949 q^{6} +(-8.35401 + 8.35401i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-4.46596 + 2.24837i) q^{5} +2.44949 q^{6} +(-8.35401 + 8.35401i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(2.21759 - 6.71434i) q^{10} +17.4360 q^{11} +(-2.44949 + 2.44949i) q^{12} +(11.0505 + 11.0505i) q^{13} -16.7080i q^{14} +(8.22335 + 2.71598i) q^{15} -4.00000 q^{16} +(-14.9996 + 14.9996i) q^{17} +(-3.00000 - 3.00000i) q^{18} -2.87824i q^{19} +(4.49675 + 8.93192i) q^{20} +20.4631 q^{21} +(-17.4360 + 17.4360i) q^{22} +(3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(14.8896 - 20.0823i) q^{25} -22.1011 q^{26} +(3.67423 - 3.67423i) q^{27} +(16.7080 + 16.7080i) q^{28} +3.12728i q^{29} +(-10.9393 + 5.50737i) q^{30} +18.1414 q^{31} +(4.00000 - 4.00000i) q^{32} +(-21.3546 - 21.3546i) q^{33} -29.9992i q^{34} +(18.5258 - 56.0917i) q^{35} +6.00000 q^{36} +(-11.8822 + 11.8822i) q^{37} +(2.87824 + 2.87824i) q^{38} -27.0682i q^{39} +(-13.4287 - 4.43518i) q^{40} -72.2362 q^{41} +(-20.4631 + 20.4631i) q^{42} +(-43.7755 - 43.7755i) q^{43} -34.8720i q^{44} +(-6.74512 - 13.3979i) q^{45} -6.78233 q^{46} +(-61.4968 + 61.4968i) q^{47} +(4.89898 + 4.89898i) q^{48} -90.5791i q^{49} +(5.19267 + 34.9719i) q^{50} +36.7414 q^{51} +(22.1011 - 22.1011i) q^{52} +(43.0455 + 43.0455i) q^{53} +7.34847i q^{54} +(-77.8685 + 39.2026i) q^{55} -33.4161 q^{56} +(-3.52511 + 3.52511i) q^{57} +(-3.12728 - 3.12728i) q^{58} +60.4399i q^{59} +(5.43196 - 16.4467i) q^{60} +1.37448 q^{61} +(-18.1414 + 18.1414i) q^{62} +(-25.0620 - 25.0620i) q^{63} +8.00000i q^{64} +(-74.1970 - 24.5055i) q^{65} +42.7093 q^{66} +(60.8442 - 60.8442i) q^{67} +(29.9992 + 29.9992i) q^{68} -8.30662i q^{69} +(37.5659 + 74.6174i) q^{70} -89.3191 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-19.0044 - 19.0044i) q^{73} -23.7643i q^{74} +(-42.8317 + 6.35969i) q^{75} -5.75648 q^{76} +(-145.661 + 145.661i) q^{77} +(27.0682 + 27.0682i) q^{78} +44.8163i q^{79} +(17.8638 - 8.99349i) q^{80} -9.00000 q^{81} +(72.2362 - 72.2362i) q^{82} +(-1.63595 - 1.63595i) q^{83} -40.9261i q^{84} +(33.2630 - 100.712i) q^{85} +87.5510 q^{86} +(3.83012 - 3.83012i) q^{87} +(34.8720 + 34.8720i) q^{88} -16.6308i q^{89} +(20.1430 + 6.65277i) q^{90} -184.633 q^{91} +(6.78233 - 6.78233i) q^{92} +(-22.2186 - 22.2186i) q^{93} -122.994i q^{94} +(6.47135 + 12.8541i) q^{95} -9.79796 q^{96} +(53.3660 - 53.3660i) q^{97} +(90.5791 + 90.5791i) q^{98} +52.3080i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) \) 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	\( 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) \) 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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