LMFDB - Embedded newform 690.3.k.a.277.12

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:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			277.12
Character	$\chi$	$=$	690.277
Dual form			690.3.k.a.553.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-4.34252 - 2.47842i) q^{5} +2.44949 q^{6} +(-5.93628 - 5.93628i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-4.34252 - 2.47842i) q^{5} +2.44949 q^{6} +(-5.93628 - 5.93628i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-1.86410 - 6.82093i) q^{10} +11.6875 q^{11} +(2.44949 + 2.44949i) q^{12} +(-16.3131 + 16.3131i) q^{13} -11.8726i q^{14} +(-8.35390 + 2.28305i) q^{15} -4.00000 q^{16} +(2.76554 + 2.76554i) q^{17} +(3.00000 - 3.00000i) q^{18} +34.0355i q^{19} +(4.95683 - 8.68503i) q^{20} -14.5409 q^{21} +(11.6875 + 11.6875i) q^{22} +(3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(12.7149 + 21.5251i) q^{25} -32.6263 q^{26} +(-3.67423 - 3.67423i) q^{27} +(11.8726 - 11.8726i) q^{28} +57.1335i q^{29} +(-10.6369 - 6.07086i) q^{30} -27.9492 q^{31} +(-4.00000 - 4.00000i) q^{32} +(14.3142 - 14.3142i) q^{33} +5.53108i q^{34} +(11.0658 + 40.4910i) q^{35} +6.00000 q^{36} +(11.9887 + 11.9887i) q^{37} +(-34.0355 + 34.0355i) q^{38} +39.9589i q^{39} +(13.6419 - 3.72820i) q^{40} -66.6724 q^{41} +(-14.5409 - 14.5409i) q^{42} +(47.1313 - 47.1313i) q^{43} +23.3749i q^{44} +(-7.43525 + 13.0275i) q^{45} +6.78233 q^{46} +(-30.7108 - 30.7108i) q^{47} +(-4.89898 + 4.89898i) q^{48} +21.4788i q^{49} +(-8.81023 + 34.2400i) q^{50} +6.77416 q^{51} +(-32.6263 - 32.6263i) q^{52} +(-31.3399 + 31.3399i) q^{53} -7.34847i q^{54} +(-50.7530 - 28.9664i) q^{55} +23.7451 q^{56} +(41.6848 + 41.6848i) q^{57} +(-57.1335 + 57.1335i) q^{58} +34.2406i q^{59} +(-4.56609 - 16.7078i) q^{60} -59.4597 q^{61} +(-27.9492 - 27.9492i) q^{62} +(-17.8088 + 17.8088i) q^{63} -8.00000i q^{64} +(111.271 - 30.4093i) q^{65} +28.6283 q^{66} +(-14.6139 - 14.6139i) q^{67} +(-5.53108 + 5.53108i) q^{68} -8.30662i q^{69} +(-29.4251 + 51.5568i) q^{70} +75.9585 q^{71} +(6.00000 + 6.00000i) q^{72} +(77.3188 - 77.3188i) q^{73} +23.9774i q^{74} +(41.9353 + 10.7903i) q^{75} -68.0709 q^{76} +(-69.3801 - 69.3801i) q^{77} +(-39.9589 + 39.9589i) q^{78} -141.674i q^{79} +(17.3701 + 9.91367i) q^{80} -9.00000 q^{81} +(-66.6724 - 66.6724i) q^{82} +(-74.9453 + 74.9453i) q^{83} -29.0817i q^{84} +(-5.15524 - 18.8636i) q^{85} +94.2626 q^{86} +(69.9740 + 69.9740i) q^{87} +(-23.3749 + 23.3749i) q^{88} +35.0157i q^{89} +(-20.4628 + 5.59230i) q^{90} +193.679 q^{91} +(6.78233 + 6.78233i) q^{92} +(-34.2306 + 34.2306i) q^{93} -61.4216i q^{94} +(84.3540 - 147.800i) q^{95} -9.79796 q^{96} +(6.39140 + 6.39140i) q^{97} +(-21.4788 + 21.4788i) q^{98} -35.0624i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) $ 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8	$ 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) $ 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8 - 16 * q^10 + 32 * q^11 + 16 * q^13 + 24 * q^15 - 160 * q^16 - 48 * q^17 + 120 * q^18 - 16 * q^20 - 96 * q^21 + 32 * q^22 + 32 * q^26 + 16 * q^28 + 24 * q^30 + 152 * q^31 - 160 * q^32 - 24 * q^33 + 48 * q^35 + 240 * q^36 + 216 * q^37 + 16 * q^38 - 168 * q^41 - 96 * q^42 - 48 * q^43 + 24 * q^45 - 232 * q^47 - 40 * q^50 + 32 * q^52 + 8 * q^53 - 272 * q^55 + 32 * q^56 - 136 * q^58 - 64 * q^61 + 152 * q^62 - 24 * q^63 + 416 * q^65 - 48 * q^66 - 32 * q^67 + 96 * q^68 + 88 * q^70 - 104 * q^71 + 240 * q^72 + 480 * q^73 - 216 * q^75 + 32 * q^76 + 280 * q^77 - 192 * q^78 + 32 * q^80 - 360 * q^81 - 168 * q^82 - 576 * q^83 - 208 * q^85 - 96 * q^86 + 24 * q^87 - 64 * q^88 + 144 * q^91 + 96 * q^93 + 168 * q^95 + 24 * q^97 + 176 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	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
$5$	−4.34252	−	2.47842i	−0.868503	−	0.495683i
$5$	−4.34252	−	2.47842i	−0.868503	−	0.495683i
$6$	2.44949			0.408248
$7$	−5.93628	−	5.93628i	−0.848040	−	0.848040i	0.141849	−	0.989888i	$-0.454695\pi$
$7$	−5.93628	−	5.93628i	−0.848040	−	0.848040i	−0.989888	+	0.141849i	$0.954695\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$	−1.86410	−	6.82093i	−0.186410	−	0.682093i
$11$	11.6875			1.06250			0.531249	−	0.847216i	$-0.321723\pi$
$11$	11.6875			1.06250			0.531249	+	0.847216i	$0.321723\pi$
$12$	2.44949	+	2.44949i	0.204124	+	0.204124i
$13$	−16.3131	+	16.3131i	−1.25486	+	1.25486i	−0.301340	+	0.953517i	$0.597434\pi$
$13$	−16.3131	+	16.3131i	−1.25486	+	1.25486i	−0.953517	+	0.301340i	$0.902566\pi$
$14$		−	11.8726i		−	0.848040i
$15$	−8.35390	+	2.28305i	−0.556927	+	0.152203i
$16$	−4.00000			−0.250000
$17$	2.76554	+	2.76554i	0.162679	+	0.162679i	0.783752	−	0.621074i	$-0.213303\pi$
$17$	2.76554	+	2.76554i	0.162679	+	0.162679i	−0.621074	+	0.783752i	$0.713303\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$			34.0355i			1.79134i	0.444719	+	0.895670i	$0.353303\pi$
$19$			34.0355i			1.79134i	−0.444719	+	0.895670i	$0.646697\pi$
$20$	4.95683	−	8.68503i	0.247842	−	0.434252i
$21$	−14.5409			−0.692422
$22$	11.6875	+	11.6875i	0.531249	+	0.531249i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$24$			4.89898i			0.204124i
$25$	12.7149	+	21.5251i	0.508596	+	0.861005i
$26$	−32.6263			−1.25486
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$	11.8726	−	11.8726i	0.424020	−	0.424020i
$29$			57.1335i			1.97012i	0.172209	+	0.985060i	$0.444910\pi$
$29$			57.1335i			1.97012i	−0.172209	+	0.985060i	$0.555090\pi$
$30$	−10.6369	−	6.07086i	−0.354565	−	0.202362i
$31$	−27.9492			−0.901586			−0.450793	−	0.892628i	$-0.648859\pi$
$31$	−27.9492			−0.901586			−0.450793	+	0.892628i	$0.648859\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	14.3142	−	14.3142i	0.433763	−	0.433763i
$34$			5.53108i			0.162679i
$35$	11.0658	+	40.4910i	0.316166	+	1.15688i
$36$	6.00000			0.166667
$37$	11.9887	+	11.9887i	0.324019	+	0.324019i	0.850307	−	0.526288i	$-0.176416\pi$
$37$	11.9887	+	11.9887i	0.324019	+	0.324019i	−0.526288	+	0.850307i	$0.676416\pi$
$38$	−34.0355	+	34.0355i	−0.895670	+	0.895670i
$39$			39.9589i			1.02459i
$40$	13.6419	−	3.72820i	0.341047	−	0.0932050i
$41$	−66.6724			−1.62616			−0.813078	−	0.582155i	$-0.802210\pi$
$41$	−66.6724			−1.62616			−0.813078	+	0.582155i	$0.802210\pi$
$42$	−14.5409	−	14.5409i	−0.346211	−	0.346211i
$43$	47.1313	−	47.1313i	1.09608	−	1.09608i	0.101211	−	0.994865i	$-0.467728\pi$
$43$	47.1313	−	47.1313i	1.09608	−	1.09608i	0.994865	−	0.101211i	$-0.0322718\pi$
$44$			23.3749i			0.531249i
$45$	−7.43525	+	13.0275i	−0.165228	+	0.289501i
$46$	6.78233			0.147442
$47$	−30.7108	−	30.7108i	−0.653421	−	0.653421i	0.300394	−	0.953815i	$-0.402882\pi$
$47$	−30.7108	−	30.7108i	−0.653421	−	0.653421i	−0.953815	+	0.300394i	$0.902882\pi$
$48$	−4.89898	+	4.89898i	−0.102062	+	0.102062i
$49$			21.4788i			0.438343i
$50$	−8.81023	+	34.2400i	−0.176205	+	0.684801i
$51$	6.77416			0.132827
$52$	−32.6263	−	32.6263i	−0.627428	−	0.627428i
$53$	−31.3399	+	31.3399i	−0.591318	+	0.591318i	−0.937987	−	0.346669i	$-0.887313\pi$
$53$	−31.3399	+	31.3399i	−0.591318	+	0.591318i	0.346669	+	0.937987i	$0.387313\pi$
$54$		−	7.34847i		−	0.136083i
$55$	−50.7530	−	28.9664i	−0.922782	−	0.526662i
$56$	23.7451			0.424020
$57$	41.6848	+	41.6848i	0.731311	+	0.731311i
$58$	−57.1335	+	57.1335i	−0.985060	+	0.985060i
$59$			34.2406i			0.580348i	0.956974	+	0.290174i	$0.0937133\pi$
$59$			34.2406i			0.580348i	−0.956974	+	0.290174i	$0.906287\pi$
$60$	−4.56609	−	16.7078i	−0.0761016	−	0.278463i
$61$	−59.4597			−0.974750			−0.487375	−	0.873193i	$-0.662045\pi$
$61$	−59.4597			−0.974750			−0.487375	+	0.873193i	$0.662045\pi$
$62$	−27.9492	−	27.9492i	−0.450793	−	0.450793i
$63$	−17.8088	+	17.8088i	−0.282680	+	0.282680i
$64$		−	8.00000i		−	0.125000i
$65$	111.271	−	30.4093i	1.71186	−	0.467836i
$66$	28.6283			0.433763
$67$	−14.6139	−	14.6139i	−0.218118	−	0.218118i	0.589587	−	0.807705i	$-0.299291\pi$
$67$	−14.6139	−	14.6139i	−0.218118	−	0.218118i	−0.807705	+	0.589587i	$0.799291\pi$
$68$	−5.53108	+	5.53108i	−0.0813394	+	0.0813394i
$69$		−	8.30662i		−	0.120386i
$70$	−29.4251	+	51.5568i	−0.420359	+	0.736525i
$71$	75.9585			1.06984			0.534919	−	0.844903i	$-0.320342\pi$
$71$	75.9585			1.06984			0.534919	+	0.844903i	$0.320342\pi$
$72$	6.00000	+	6.00000i	0.0833333	+	0.0833333i
$73$	77.3188	−	77.3188i	1.05916	−	1.05916i	0.0610249	−	0.998136i	$-0.480563\pi$
$73$	77.3188	−	77.3188i	1.05916	−	1.05916i	0.998136	−	0.0610249i	$-0.0194369\pi$
$74$			23.9774i			0.324019i
$75$	41.9353	+	10.7903i	0.559137	+	0.143870i
$76$	−68.0709			−0.895670
$77$	−69.3801	−	69.3801i	−0.901040	−	0.901040i
$78$	−39.9589	+	39.9589i	−0.512293	+	0.512293i
$79$		−	141.674i		−	1.79335i	−0.442692	−	0.896674i	$-0.645977\pi$
$79$		−	141.674i		−	1.79335i	0.442692	−	0.896674i	$-0.354023\pi$
$80$	17.3701	+	9.91367i	0.217126	+	0.123921i
$81$	−9.00000			−0.111111
$82$	−66.6724	−	66.6724i	−0.813078	−	0.813078i
$83$	−74.9453	+	74.9453i	−0.902955	+	0.902955i	−0.995691	−	0.0927358i	$-0.970439\pi$
$83$	−74.9453	+	74.9453i	−0.902955	+	0.902955i	0.0927358	+	0.995691i	$0.470439\pi$
$84$		−	29.0817i		−	0.346211i
$85$	−5.15524	−	18.8636i	−0.0606499	−	0.221924i
$86$	94.2626			1.09608
$87$	69.9740	+	69.9740i	0.804298	+	0.804298i
$88$	−23.3749	+	23.3749i	−0.265624	+	0.265624i
$89$			35.0157i			0.393435i	0.980460	+	0.196718i	$0.0630282\pi$
$89$			35.0157i			0.393435i	−0.980460	+	0.196718i	$0.936972\pi$
$90$	−20.4628	+	5.59230i	−0.227364	+	0.0621367i
$91$	193.679			2.12834
$92$	6.78233	+	6.78233i	0.0737210	+	0.0737210i
$93$	−34.2306	+	34.2306i	−0.368071	+	0.368071i
$94$		−	61.4216i		−	0.653421i
$95$	84.3540	−	147.800i	0.887937	−	1.55578i
$96$	−9.79796			−0.102062
$97$	6.39140	+	6.39140i	0.0658907	+	0.0658907i	0.739284	−	0.673394i	$-0.235164\pi$
$97$	6.39140	+	6.39140i	0.0658907	+	0.0658907i	−0.673394	+	0.739284i	$0.735164\pi$
$98$	−21.4788	+	21.4788i	−0.219171	+	0.219171i
$99$		−	35.0624i		−	0.354166i
$100$	−43.0503	+	25.4298i	−0.430503	+	0.254298i
$101$	−32.1722			−0.318536			−0.159268	−	0.987235i	$-0.550913\pi$
$101$	−32.1722			−0.318536			−0.159268	+	0.987235i	$0.550913\pi$
$102$	6.77416	+	6.77416i	0.0664133	+	0.0664133i
$103$	−68.4939	+	68.4939i	−0.664989	+	0.664989i	−0.956552	−	0.291563i	$-0.905825\pi$
$103$	−68.4939	+	68.4939i	−0.664989	+	0.664989i	0.291563	+	0.956552i	$0.405825\pi$
$104$		−	65.2526i		−	0.627428i
$105$	63.1439	+	36.0383i	0.601370	+	0.343222i
$106$	−62.6797			−0.591318
$107$	22.3110	+	22.3110i	0.208514	+	0.208514i	0.803636	−	0.595122i	$-0.202896\pi$
$107$	22.3110	+	22.3110i	0.208514	+	0.208514i	−0.595122	+	0.803636i	$0.702896\pi$
$108$	7.34847	−	7.34847i	0.0680414	−	0.0680414i
$109$			190.368i			1.74650i	0.487275	+	0.873249i	$0.337991\pi$
$109$			190.368i			1.74650i	−0.487275	+	0.873249i	$0.662009\pi$
$110$	−21.7866	−	79.7195i	−0.198060	−	0.724722i
$111$	29.3662			0.264560
$112$	23.7451	+	23.7451i	0.212010	+	0.212010i
$113$	−61.7629	+	61.7629i	−0.546574	+	0.546574i	−0.925448	−	0.378874i	$-0.876311\pi$
$113$	−61.7629	+	61.7629i	−0.546574	+	0.546574i	0.378874	+	0.925448i	$0.376311\pi$
$114$			83.3695i			0.731311i
$115$	−23.1309	+	6.32147i	−0.201138	+	0.0549693i
$116$	−114.267			−0.985060
$117$	48.9394	+	48.9394i	0.418286	+	0.418286i
$118$	−34.2406	+	34.2406i	−0.290174	+	0.290174i
$119$		−	32.8340i		−	0.275916i
$120$	12.1417	−	21.2739i	0.101181	−	0.177282i
$121$	15.5970			0.128900
$122$	−59.4597	−	59.4597i	−0.487375	−	0.487375i
$123$	−81.6567	+	81.6567i	−0.663875	+	0.663875i
$124$		−	55.8983i		−	0.450793i
$125$	−1.86642	−	124.986i	−0.0149314	−	0.999889i
$126$	−35.6177			−0.282680
$127$	−35.6620	−	35.6620i	−0.280803	−	0.280803i	0.552626	−	0.833429i	$-0.313626\pi$
$127$	−35.6620	−	35.6620i	−0.280803	−	0.280803i	−0.833429	+	0.552626i	$0.813626\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$		−	115.448i		−	0.894942i
$130$	141.680	+	80.8615i	1.08985	+	0.622012i
$131$	−54.4939			−0.415984			−0.207992	−	0.978131i	$-0.566693\pi$
$131$	−54.4939			−0.415984			−0.207992	+	0.978131i	$0.566693\pi$
$132$	28.6283	+	28.6283i	0.216881	+	0.216881i
$133$	202.044	−	202.044i	1.51913	−	1.51913i
$134$		−	29.2279i		−	0.218118i
$135$	6.84914	+	25.0617i	0.0507344	+	0.185642i
$136$	−11.0622			−0.0813394
$137$	−59.6809	−	59.6809i	−0.435627	−	0.435627i	0.454910	−	0.890537i	$-0.349671\pi$
$137$	−59.6809	−	59.6809i	−0.435627	−	0.435627i	−0.890537	+	0.454910i	$0.849671\pi$
$138$	8.30662	−	8.30662i	0.0601929	−	0.0601929i
$139$			75.7410i			0.544899i	0.962170	+	0.272450i	$0.0878338\pi$
$139$			75.7410i			0.544899i	−0.962170	+	0.272450i	$0.912166\pi$
$140$	−80.9819	+	22.1316i	−0.578442	+	0.158083i
$141$	−75.2258			−0.533516
$142$	75.9585	+	75.9585i	0.534919	+	0.534919i
$143$	−190.659	+	190.659i	−1.33328	+	1.33328i
$144$			12.0000i			0.0833333i
$145$	141.601	−	248.103i	0.976556	−	1.71106i
$146$	154.638			1.05916
$147$	26.3060	+	26.3060i	0.178953	+	0.178953i
$148$	−23.9774	+	23.9774i	−0.162010	+	0.162010i
$149$			122.794i			0.824124i	0.911156	+	0.412062i	$0.135191\pi$
$149$			122.794i			0.824124i	−0.911156	+	0.412062i	$0.864809\pi$
$150$	31.1450	+	52.7256i	0.207633	+	0.351504i
$151$	−97.6700			−0.646821			−0.323410	−	0.946259i	$-0.604829\pi$
$151$	−97.6700			−0.646821			−0.323410	+	0.946259i	$0.604829\pi$
$152$	−68.0709	−	68.0709i	−0.447835	−	0.447835i
$153$	8.29661	−	8.29661i	0.0542262	−	0.0542262i
$154$		−	138.760i		−	0.901040i
$155$	121.370	+	69.2697i	0.783031	+	0.446901i
$156$	−79.9177			−0.512293
$157$	−8.25080	−	8.25080i	−0.0525528	−	0.0525528i	0.680342	−	0.732895i	$-0.261831\pi$
$157$	−8.25080	−	8.25080i	−0.0525528	−	0.0525528i	−0.732895	+	0.680342i	$0.761831\pi$
$158$	141.674	−	141.674i	0.896674	−	0.896674i
$159$			76.7667i			0.482809i
$160$	7.45640	+	27.2837i	0.0466025	+	0.170523i
$161$	−40.2618			−0.250073
$162$	−9.00000	−	9.00000i	−0.0555556	−	0.0555556i
$163$	196.824	−	196.824i	1.20751	−	1.20751i	0.235682	−	0.971830i	$-0.424268\pi$
$163$	196.824	−	196.824i	1.20751	−	1.20751i	0.971830	−	0.235682i	$-0.0757323\pi$
$164$		−	133.345i		−	0.813078i
$165$	−97.6360	+	26.6830i	−0.591733	+	0.161715i
$166$	−149.891			−0.902955
$167$	−33.1032	−	33.1032i	−0.198223	−	0.198223i	0.601015	−	0.799238i	$-0.294763\pi$
$167$	−33.1032	−	33.1032i	−0.198223	−	0.198223i	−0.799238	+	0.601015i	$0.794763\pi$
$168$	29.0817	−	29.0817i	0.173105	−	0.173105i
$169$		−	363.237i		−	2.14933i
$170$	13.7083	−	24.0188i	0.0806371	−	0.141287i
$171$	102.106			0.597113
$172$	94.2626	+	94.2626i	0.548038	+	0.548038i
$173$	−129.709	+	129.709i	−0.749764	+	0.749764i	−0.974435	−	0.224670i	$-0.927869\pi$
$173$	−129.709	+	129.709i	−0.749764	+	0.749764i	0.224670	+	0.974435i	$0.427869\pi$
$174$			139.948i			0.804298i
$175$	52.3000	−	203.258i	0.298857	−	1.16148i
$176$	−46.7499			−0.265624
$177$	41.9359	+	41.9359i	0.236926	+	0.236926i
$178$	−35.0157	+	35.0157i	−0.196718	+	0.196718i
$179$			117.226i			0.654893i	0.944870	+	0.327447i	$0.106188\pi$
$179$			117.226i			0.654893i	−0.944870	+	0.327447i	$0.893812\pi$
$180$	−26.0551	−	14.8705i	−0.144751	−	0.0826139i
$181$	−84.0690			−0.464470			−0.232235	−	0.972660i	$-0.574604\pi$
$181$	−84.0690			−0.464470			−0.232235	+	0.972660i	$0.574604\pi$
$182$	193.679	+	193.679i	1.06417	+	1.06417i
$183$	−72.8230	+	72.8230i	−0.397940	+	0.397940i
$184$			13.5647i			0.0737210i
$185$	−22.3481	−	81.7742i	−0.120801	−	0.442022i
$186$	−68.4612			−0.368071
$187$	32.3221	+	32.3221i	0.172846	+	0.172846i
$188$	61.4216	−	61.4216i	0.326711	−	0.326711i
$189$			43.6226i			0.230807i
$190$	232.154	−	63.4455i	1.22186	−	0.333924i
$191$	29.5286			0.154600			0.0772999	−	0.997008i	$-0.475370\pi$
$191$	29.5286			0.154600			0.0772999	+	0.997008i	$0.475370\pi$
$192$	−9.79796	−	9.79796i	−0.0510310	−	0.0510310i
$193$	21.3978	−	21.3978i	0.110869	−	0.110869i	−0.649496	−	0.760365i	$-0.725020\pi$
$193$	21.3978	−	21.3978i	0.110869	−	0.110869i	0.760365	+	0.649496i	$0.225020\pi$
$194$			12.7828i			0.0658907i
$195$	99.0347	−	173.522i	0.507870	−	0.889857i
$196$	−42.9576			−0.219171
$197$	−63.6996	−	63.6996i	−0.323348	−	0.323348i	0.526702	−	0.850050i	$-0.323428\pi$
$197$	−63.6996	−	63.6996i	−0.323348	−	0.323348i	−0.850050	+	0.526702i	$0.823428\pi$
$198$	35.0624	−	35.0624i	0.177083	−	0.177083i
$199$			270.574i			1.35967i	0.733366	+	0.679834i	$0.237948\pi$
$199$			270.574i			1.35967i	−0.733366	+	0.679834i	$0.762052\pi$
$200$	−68.4801	−	17.6205i	−0.342400	−	0.0881023i
$201$	−35.7967			−0.178093
$202$	−32.1722	−	32.1722i	−0.159268	−	0.159268i
$203$	339.160	−	339.160i	1.67074	−	1.67074i
$204$			13.5483i			0.0664133i
$205$	289.526	+	165.242i	1.41232	+	0.806058i
$206$	−136.988			−0.664989
$207$	−10.1735	−	10.1735i	−0.0491473	−	0.0491473i
$208$	65.2526	−	65.2526i	0.313714	−	0.313714i
$209$			397.788i			1.90329i
$210$	27.1056	+	99.1822i	0.129074	+	0.472296i
$211$	−344.189			−1.63123			−0.815614	−	0.578597i	$-0.803600\pi$
$211$	−344.189			−1.63123			−0.815614	+	0.578597i	$0.803600\pi$
$212$	−62.6797	−	62.6797i	−0.295659	−	0.295659i
$213$	93.0298	−	93.0298i	0.436760	−	0.436760i
$214$			44.6219i			0.208514i
$215$	−321.479	+	87.8574i	−1.49525	+	0.408639i
$216$	14.6969			0.0680414
$217$	165.914	+	165.914i	0.764581	+	0.764581i
$218$	−190.368	+	190.368i	−0.873249	+	0.873249i
$219$		−	189.392i		−	0.864801i
$220$	57.9328	−	101.506i	0.263331	−	0.461391i
$221$	−90.2292			−0.408277
$222$	29.3662	+	29.3662i	0.132280	+	0.132280i
$223$	46.6839	−	46.6839i	0.209345	−	0.209345i	−0.594644	−	0.803989i	$-0.702707\pi$
$223$	46.6839	−	46.6839i	0.209345	−	0.209345i	0.803989	+	0.594644i	$0.202707\pi$
$224$			47.4902i			0.212010i
$225$	64.5754	−	38.1447i	0.287002	−	0.169532i
$226$	−123.526			−0.546574
$227$	269.016	+	269.016i	1.18509	+	1.18509i	0.978408	+	0.206684i	$0.0662672\pi$
$227$	269.016	+	269.016i	1.18509	+	1.18509i	0.206684	+	0.978408i	$0.433733\pi$
$228$	−83.3695	+	83.3695i	−0.365656	+	0.365656i
$229$		−	149.901i		−	0.654588i	−0.944923	−	0.327294i	$-0.893863\pi$
$229$		−	149.901i		−	0.654588i	0.944923	−	0.327294i	$-0.106137\pi$
$230$	−29.4524	−	16.8094i	−0.128054	−	0.0730845i
$231$	−169.946			−0.735696
$232$	−114.267	−	114.267i	−0.492530	−	0.492530i
$233$	141.005	−	141.005i	0.605172	−	0.605172i	−0.336508	−	0.941680i	$-0.609246\pi$
$233$	141.005	−	141.005i	0.605172	−	0.605172i	0.941680	+	0.336508i	$0.109246\pi$
$234$			97.8788i			0.418286i
$235$	57.2480	+	209.476i	0.243608	+	0.891388i
$236$	−68.4811			−0.290174
$237$	−173.515	−	173.515i	−0.732131	−	0.732131i
$238$	32.8340	−	32.8340i	0.137958	−	0.137958i
$239$		−	264.006i		−	1.10463i	−0.833636	−	0.552315i	$-0.813745\pi$
$239$		−	264.006i		−	1.10463i	0.833636	−	0.552315i	$-0.186255\pi$
$240$	33.4156	−	9.13219i	0.139232	−	0.0380508i
$241$	193.299			0.802070			0.401035	−	0.916063i	$-0.368651\pi$
$241$	193.299			0.802070			0.401035	+	0.916063i	$0.368651\pi$
$242$	15.5970	+	15.5970i	0.0644502	+	0.0644502i
$243$	−11.0227	+	11.0227i	−0.0453609	+	0.0453609i
$244$		−	118.919i		−	0.487375i
$245$	53.2334	−	93.2720i	0.217279	−	0.380702i
$246$	−163.313			−0.663875
$247$	−555.225	−	555.225i	−2.24788	−	2.24788i
$248$	55.8983	−	55.8983i	0.225397	−	0.225397i
$249$			183.578i			0.737260i
$250$	123.120	−	126.852i	0.492479	−	0.507410i
$251$	408.680			1.62821			0.814104	−	0.580718i	$-0.197228\pi$
$251$	408.680			1.62821			0.814104	+	0.580718i	$0.197228\pi$
$252$	−35.6177	−	35.6177i	−0.141340	−	0.141340i
$253$	39.6341	−	39.6341i	0.156657	−	0.156657i
$254$		−	71.3239i		−	0.280803i
$255$	−29.4169	−	16.7892i	−0.115360	−	0.0658399i
$256$	16.0000			0.0625000
$257$	26.8280	+	26.8280i	0.104389	+	0.104389i	0.757372	−	0.652983i	$-0.226483\pi$
$257$	26.8280	+	26.8280i	0.104389	+	0.104389i	−0.652983	+	0.757372i	$0.726483\pi$
$258$	115.448	−	115.448i	0.447471	−	0.447471i
$259$		−	142.337i		−	0.549562i
$260$	60.8186	+	222.542i	0.233918	+	0.855929i
$261$	171.401			0.656707
$262$	−54.4939	−	54.4939i	−0.207992	−	0.207992i
$263$	−85.7865	+	85.7865i	−0.326185	+	0.326185i	−0.851134	−	0.524949i	$-0.824084\pi$
$263$	−85.7865	+	85.7865i	−0.326185	+	0.326185i	0.524949	+	0.851134i	$0.324084\pi$
$264$			57.2567i			0.216881i
$265$	213.767	−	58.4206i	0.806668	−	0.220455i
$266$	404.088			1.51913
$267$	42.8853	+	42.8853i	0.160619	+	0.160619i
$268$	29.2279	−	29.2279i	0.109059	−	0.109059i
$269$			252.246i			0.937718i	0.883273	+	0.468859i	$0.155335\pi$
$269$			252.246i			0.937718i	−0.883273	+	0.468859i	$0.844665\pi$
$270$	−18.2126	+	31.9108i	−0.0674540	+	0.118188i
$271$	468.292			1.72802			0.864008	−	0.503478i	$-0.167947\pi$
$271$	468.292			1.72802			0.864008	+	0.503478i	$0.167947\pi$
$272$	−11.0622	−	11.0622i	−0.0406697	−	0.0406697i
$273$	237.207	−	237.207i	0.868890	−	0.868890i
$274$		−	119.362i		−	0.435627i
$275$	148.605	+	251.574i	0.540382	+	0.914816i
$276$	16.6132			0.0601929
$277$	338.293	+	338.293i	1.22127	+	1.22127i	0.967180	+	0.254093i	$0.0817771\pi$
$277$	338.293	+	338.293i	1.22127	+	1.22127i	0.254093	+	0.967180i	$0.418223\pi$
$278$	−75.7410	+	75.7410i	−0.272450	+	0.272450i
$279$			83.8475i			0.300529i
$280$	−103.114	−	58.8503i	−0.368263	−	0.210180i
$281$	−49.4745			−0.176066			−0.0880330	−	0.996118i	$-0.528058\pi$
$281$	−49.4745			−0.176066			−0.0880330	+	0.996118i	$0.528058\pi$
$282$	−75.2258	−	75.2258i	−0.266758	−	0.266758i
$283$	−29.5290	+	29.5290i	−0.104343	+	0.104343i	−0.757351	−	0.653008i	$-0.773507\pi$
$283$	−29.5290	+	29.5290i	−0.104343	+	0.104343i	0.653008	+	0.757351i	$0.273507\pi$
$284$			151.917i			0.534919i
$285$	−77.7045	−	284.329i	−0.272647	−	0.997645i
$286$	−381.319			−1.33328
$287$	395.786	+	395.786i	1.37904	+	1.37904i
$288$	−12.0000	+	12.0000i	−0.0416667	+	0.0416667i
$289$		−	273.704i		−	0.947071i
$290$	389.704	−	106.503i	1.34381	−	0.367250i
$291$	15.6557			0.0537995
$292$	154.638	+	154.638i	0.529581	+	0.529581i
$293$	131.570	−	131.570i	0.449045	−	0.449045i	−0.445992	−	0.895037i	$-0.647149\pi$
$293$	131.570	−	131.570i	0.449045	−	0.449045i	0.895037	+	0.445992i	$0.147149\pi$
$294$			52.6121i			0.178953i
$295$	84.8624	−	148.690i	0.287669	−	0.504035i
$296$	−47.9548			−0.162010
$297$	−42.9425	−	42.9425i	−0.144588	−	0.144588i
$298$	−122.794	+	122.794i	−0.412062	+	0.412062i
$299$			110.641i			0.370037i
$300$	−21.5806	+	83.8706i	−0.0719352	+	0.279569i
$301$	−559.569			−1.85903
$302$	−97.6700	−	97.6700i	−0.323410	−	0.323410i
$303$	−39.4027	+	39.4027i	−0.130042	+	0.130042i
$304$		−	136.142i		−	0.447835i
$305$	258.205	+	147.366i	0.846573	+	0.483167i
$306$	16.5932			0.0542262
$307$	−244.537	−	244.537i	−0.796538	−	0.796538i	0.186010	−	0.982548i	$-0.440444\pi$
$307$	−244.537	−	244.537i	−0.796538	−	0.796538i	−0.982548	+	0.186010i	$0.940444\pi$
$308$	138.760	−	138.760i	0.450520	−	0.450520i
$309$			167.775i			0.542961i
$310$	52.1000	+	190.639i	0.168065	+	0.614966i
$311$	292.121			0.939297			0.469648	−	0.882853i	$-0.344381\pi$
$311$	292.121			0.939297			0.469648	+	0.882853i	$0.344381\pi$
$312$	−79.9177	−	79.9177i	−0.256147	−	0.256147i
$313$	221.693	−	221.693i	0.708286	−	0.708286i	−0.257889	−	0.966175i	$-0.583027\pi$
$313$	221.693	−	221.693i	0.708286	−	0.708286i	0.966175	+	0.257889i	$0.0830269\pi$
$314$		−	16.5016i		−	0.0525528i
$315$	121.473	−	33.1974i	0.385628	−	0.105389i
$316$	283.349			0.896674
$317$	−270.588	−	270.588i	−0.853591	−	0.853591i	0.136982	−	0.990573i	$-0.456260\pi$
$317$	−270.588	−	270.588i	−0.853591	−	0.853591i	−0.990573	+	0.136982i	$0.956260\pi$
$318$	−76.7667	+	76.7667i	−0.241405	+	0.241405i
$319$			667.746i			2.09325i
$320$	−19.8273	+	34.7401i	−0.0619604	+	0.108563i
$321$	54.6505			0.170251
$322$	−40.2618	−	40.2618i	−0.125037	−	0.125037i
$323$	−94.1264	+	94.1264i	−0.291413	+	0.291413i
$324$		−	18.0000i		−	0.0555556i
$325$	−558.562	−	143.723i	−1.71865	−	0.442223i
$326$	393.649			1.20751
$327$	233.153	+	233.153i	0.713005	+	0.713005i
$328$	133.345	−	133.345i	0.406539	−	0.406539i
$329$			364.616i			1.10825i
$330$	−124.319	−	70.9530i	−0.376724	−	0.215009i
$331$	−279.894			−0.845601			−0.422801	−	0.906223i	$-0.638953\pi$
$331$	−279.894			−0.845601			−0.422801	+	0.906223i	$0.638953\pi$
$332$	−149.891	−	149.891i	−0.451477	−	0.451477i
$333$	35.9661	−	35.9661i	0.108006	−	0.108006i
$334$		−	66.2064i		−	0.198223i
$335$	27.2418	+	99.6806i	0.0813189	+	0.297554i
$336$	58.1634			0.173105
$337$	291.255	+	291.255i	0.864258	+	0.864258i	0.991829	−	0.127571i	$-0.0407181\pi$
$337$	291.255	+	291.255i	0.864258	+	0.864258i	−0.127571	+	0.991829i	$0.540718\pi$
$338$	363.237	−	363.237i	1.07467	−	1.07467i
$339$			151.288i			0.446276i
$340$	37.7271	−	10.3105i	0.110962	−	0.0303249i
$341$	−326.655			−0.957933
$342$	102.106	+	102.106i	0.298557	+	0.298557i
$343$	−163.374	+	163.374i	−0.476308	+	0.476308i
$344$			188.525i			0.548038i
$345$	−20.5873	+	36.0717i	−0.0596733	+	0.104556i
$346$	−259.418			−0.749764
$347$	−126.085	−	126.085i	−0.363356	−	0.363356i	0.501691	−	0.865047i	$-0.332711\pi$
$347$	−126.085	−	126.085i	−0.363356	−	0.363356i	−0.865047	+	0.501691i	$0.832711\pi$
$348$	−139.948	+	139.948i	−0.402149	+	0.402149i
$349$		−	370.710i		−	1.06221i	−0.847307	−	0.531104i	$-0.821777\pi$
$349$		−	370.710i		−	1.06221i	0.847307	−	0.531104i	$-0.178223\pi$
$350$	255.558	−	150.958i	0.730167	−	0.431310i
$351$	119.877			0.341529
$352$	−46.7499	−	46.7499i	−0.132812	−	0.132812i
$353$	−115.425	+	115.425i	−0.326984	+	0.326984i	−0.851439	−	0.524454i	$-0.824269\pi$
$353$	−115.425	+	115.425i	−0.326984	+	0.326984i	0.524454	+	0.851439i	$0.324269\pi$
$354$			83.8719i			0.236926i
$355$	−329.851	−	188.257i	−0.929158	−	0.530301i
$356$	−70.0315			−0.196718
$357$	−40.2133	−	40.2133i	−0.112642	−	0.112642i
$358$	−117.226	+	117.226i	−0.327447	+	0.327447i
$359$			201.226i			0.560518i	0.959924	+	0.280259i	$0.0904204\pi$
$359$			201.226i			0.560518i	−0.959924	+	0.280259i	$0.909580\pi$
$360$	−11.1846	−	40.9256i	−0.0310683	−	0.113682i
$361$	−797.412			−2.20890
$362$	−84.0690	−	84.0690i	−0.232235	−	0.232235i
$363$	19.1023	−	19.1023i	0.0526234	−	0.0526234i
$364$			387.357i			1.06417i
$365$	−527.386	+	144.130i	−1.44489	+	0.394876i
$366$	−145.646			−0.397940
$367$	−121.905	−	121.905i	−0.332167	−	0.332167i	0.521242	−	0.853409i	$-0.325469\pi$
$367$	−121.905	−	121.905i	−0.332167	−	0.332167i	−0.853409	+	0.521242i	$0.825469\pi$
$368$	−13.5647	+	13.5647i	−0.0368605	+	0.0368605i
$369$			200.017i			0.542052i
$370$	59.4260	−	104.122i	0.160611	−	0.281412i
$371$	372.084			1.00292
$372$	−68.4612	−	68.4612i	−0.184035	−	0.184035i
$373$	190.337	−	190.337i	0.510288	−	0.510288i	−0.404327	−	0.914615i	$-0.632494\pi$
$373$	190.337	−	190.337i	0.510288	−	0.510288i	0.914615	+	0.404327i	$0.132494\pi$
$374$			64.6443i			0.172846i
$375$	−155.362	−	150.790i	−0.414298	−	0.402107i
$376$	122.843			0.326711
$377$	−932.027	−	932.027i	−2.47222	−	2.47222i
$378$	−43.6226	+	43.6226i	−0.115404	+	0.115404i
$379$			8.74600i			0.0230765i	0.999933	+	0.0115383i	$0.00367282\pi$
$379$			8.74600i			0.0230765i	−0.999933	+	0.0115383i	$0.996327\pi$
$380$	295.599	+	168.708i	0.777892	+	0.443969i
$381$	−87.3536			−0.229275
$382$	29.5286	+	29.5286i	0.0772999	+	0.0772999i
$383$	4.52817	−	4.52817i	0.0118229	−	0.0118229i	−0.701171	−	0.712994i	$-0.747339\pi$
$383$	4.52817	−	4.52817i	0.0118229	−	0.0118229i	0.712994	+	0.701171i	$0.247339\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	129.331	+	473.237i	0.335926	+	1.22919i
$386$	42.7956			0.110869
$387$	−141.394	−	141.394i	−0.365359	−	0.365359i
$388$	−12.7828	+	12.7828i	−0.0329454	+	0.0329454i
$389$		−	647.329i		−	1.66408i	−0.554713	−	0.832042i	$-0.687172\pi$
$389$		−	647.329i		−	1.66408i	0.554713	−	0.832042i	$-0.312828\pi$
$390$	272.557	−	74.4873i	0.698863	−	0.190993i
$391$	18.7568			0.0479713
$392$	−42.9576	−	42.9576i	−0.109586	−	0.109586i
$393$	−66.7412	+	66.7412i	−0.169825	+	0.169825i
$394$		−	127.399i		−	0.323348i
$395$	−351.128	+	615.224i	−0.888932	+	1.55753i
$396$	70.1248			0.177083
$397$	−457.813	−	457.813i	−1.15318	−	1.15318i	−0.985911	−	0.167272i	$-0.946504\pi$
$397$	−457.813	−	457.813i	−1.15318	−	1.15318i	−0.167272	−	0.985911i	$-0.553496\pi$
$398$	−270.574	+	270.574i	−0.679834	+	0.679834i
$399$		−	494.905i		−	1.24036i
$400$	−50.8596	−	86.1005i	−0.127149	−	0.215251i
$401$	−419.534			−1.04622			−0.523109	−	0.852266i	$-0.675228\pi$
$401$	−419.534			−1.04622			−0.523109	+	0.852266i	$0.675228\pi$
$402$	−35.7967	−	35.7967i	−0.0890464	−	0.0890464i
$403$	455.939	−	455.939i	1.13136	−	1.13136i
$404$		−	64.3444i		−	0.159268i
$405$	39.0826	+	22.3058i	0.0965004	+	0.0550759i
$406$	678.321			1.67074
$407$	140.118	+	140.118i	0.344269	+	0.344269i
$408$	−13.5483	+	13.5483i	−0.0332067	+	0.0332067i
$409$			168.996i			0.413194i	0.978426	+	0.206597i	$0.0662389\pi$
$409$			168.996i			0.413194i	−0.978426	+	0.206597i	$0.933761\pi$
$410$	124.284	+	454.768i	0.303132	+	1.10919i
$411$	−146.188			−0.355688
$412$	−136.988	−	136.988i	−0.332494	−	0.332494i
$413$	203.261	−	203.261i	0.492159	−	0.492159i
$414$		−	20.3470i		−	0.0491473i
$415$	511.197	−	139.705i	1.23180	−	0.336640i
$416$	130.505			0.313714
$417$	92.7634	+	92.7634i	0.222454	+	0.222454i
$418$	−397.788	+	397.788i	−0.951647	+	0.951647i
$419$			688.224i			1.64254i	0.570540	+	0.821270i	$0.306734\pi$
$419$			688.224i			1.64254i	−0.570540	+	0.821270i	$0.693266\pi$
$420$	−72.0766	+	126.288i	−0.171611	+	0.300685i
$421$	−4.67524			−0.0111051			−0.00555255	−	0.999985i	$-0.501767\pi$
$421$	−4.67524			−0.0111051			−0.00555255	+	0.999985i	$0.501767\pi$
$422$	−344.189	−	344.189i	−0.815614	−	0.815614i
$423$	−92.1324	+	92.1324i	−0.217807	+	0.217807i
$424$		−	125.359i		−	0.295659i
$425$	−24.3650	+	94.6921i	−0.0573295	+	0.222805i
$426$	186.060			0.436760
$427$	352.969	+	352.969i	0.826626	+	0.826626i
$428$	−44.6219	+	44.6219i	−0.104257	+	0.104257i
$429$			467.018i			1.08862i
$430$	−409.337	−	233.622i	−0.951946	−	0.543307i
$431$	−273.490			−0.634549			−0.317274	−	0.948334i	$-0.602768\pi$
$431$	−273.490			−0.634549			−0.317274	+	0.948334i	$0.602768\pi$
$432$	14.6969	+	14.6969i	0.0340207	+	0.0340207i
$433$	559.711	−	559.711i	1.29264	−	1.29264i	0.359484	−	0.933151i	$-0.382953\pi$
$433$	559.711	−	559.711i	1.29264	−	1.29264i	0.933151	−	0.359484i	$-0.117047\pi$
$434$			331.828i			0.764581i
$435$	−130.438	−	477.288i	−0.299859	−	1.09721i
$436$	−380.736			−0.873249
$437$	115.420	+	115.420i	0.264119	+	0.264119i
$438$	189.392	−	189.392i	0.432401	−	0.432401i
$439$			331.061i			0.754126i	0.926188	+	0.377063i	$0.123066\pi$
$439$			331.061i			0.754126i	−0.926188	+	0.377063i	$0.876934\pi$
$440$	159.439	−	43.5732i	0.362361	−	0.0990300i
$441$	64.4364			0.146114
$442$	−90.2292	−	90.2292i	−0.204138	−	0.204138i
$443$	−302.093	+	302.093i	−0.681926	+	0.681926i	−0.960434	−	0.278508i	$-0.910160\pi$
$443$	−302.093	+	302.093i	−0.681926	+	0.681926i	0.278508	+	0.960434i	$0.410160\pi$
$444$			58.7324i			0.132280i
$445$	86.7836	−	152.056i	0.195019	−	0.341700i
$446$	93.3678			0.209345
$447$	150.392	+	150.392i	0.336447	+	0.336447i
$448$	−47.4902	+	47.4902i	−0.106005	+	0.106005i
$449$			49.8135i			0.110943i	0.998460	+	0.0554716i	$0.0176662\pi$
$449$			49.8135i			0.110943i	−0.998460	+	0.0554716i	$0.982334\pi$
$450$	102.720	+	26.4307i	0.228267	+	0.0587349i
$451$	−779.231			−1.72779
$452$	−123.526	−	123.526i	−0.273287	−	0.273287i
$453$	−119.621	+	119.621i	−0.264064	+	0.264064i
$454$			538.032i			1.18509i
$455$	−841.053	−	480.016i	−1.84847	−	1.05498i
$456$	−166.739			−0.365656
$457$	599.809	+	599.809i	1.31249	+	1.31249i	0.919573	+	0.392919i	$0.128535\pi$
$457$	599.809	+	599.809i	1.31249	+	1.31249i	0.392919	+	0.919573i	$0.371465\pi$
$458$	149.901	−	149.901i	0.327294	−	0.327294i
$459$		−	20.3225i		−	0.0442755i
$460$	−12.6429	−	46.2618i	−0.0274847	−	0.100569i
$461$	−42.9308			−0.0931255			−0.0465627	−	0.998915i	$-0.514827\pi$
$461$	−42.9308			−0.0931255			−0.0465627	+	0.998915i	$0.514827\pi$
$462$	−169.946	−	169.946i	−0.367848	−	0.367848i
$463$	−94.7288	+	94.7288i	−0.204598	+	0.204598i	−0.801967	−	0.597369i	$-0.796213\pi$
$463$	−94.7288	+	94.7288i	−0.204598	+	0.204598i	0.597369	+	0.801967i	$0.296213\pi$
$464$		−	228.534i		−	0.492530i
$465$	233.485	−	63.8093i	0.502118	−	0.137224i
$466$	282.010			0.605172
$467$	242.603	+	242.603i	0.519493	+	0.519493i	0.917418	−	0.397925i	$-0.130270\pi$
$467$	242.603	+	242.603i	0.519493	+	0.519493i	−0.397925	+	0.917418i	$0.630270\pi$
$468$	−97.8788	+	97.8788i	−0.209143	+	0.209143i
$469$			173.505i			0.369946i
$470$	−152.228	+	266.724i	−0.323890	+	0.567498i
$471$	−20.2102			−0.0429092
$472$	−68.4811	−	68.4811i	−0.145087	−	0.145087i
$473$	550.845	−	550.845i	1.16458	−	1.16458i
$474$		−	347.030i		−	0.732131i
$475$	−732.618	+	432.757i	−1.54235	+	0.911068i
$476$	65.6680			0.137958
$477$	94.0196	+	94.0196i	0.197106	+	0.197106i
$478$	264.006	−	264.006i	0.552315	−	0.552315i
$479$			246.825i			0.515291i	0.966239	+	0.257646i	$0.0829467\pi$
$479$			246.825i			0.515291i	−0.966239	+	0.257646i	$0.917053\pi$
$480$	42.5478	+	24.2834i	0.0886412	+	0.0505905i
$481$	−391.147			−0.813195
$482$	193.299	+	193.299i	0.401035	+	0.401035i
$483$	−49.3104	+	49.3104i	−0.102092	+	0.102092i
$484$			31.1939i			0.0644502i
$485$	−11.9142	−	43.5953i	−0.0245654	−	0.0898872i
$486$	−22.0454			−0.0453609
$487$	110.009	+	110.009i	0.225890	+	0.225890i	0.810973	−	0.585083i	$-0.198938\pi$
$487$	110.009	+	110.009i	0.225890	+	0.225890i	−0.585083	+	0.810973i	$0.698938\pi$
$488$	118.919	−	118.919i	0.243687	−	0.243687i
$489$		−	482.119i		−	0.985929i
$490$	146.505	−	40.0386i	0.298991	−	0.0817115i
$491$	−269.756			−0.549400			−0.274700	−	0.961530i	$-0.588579\pi$
$491$	−269.756			−0.549400			−0.274700	+	0.961530i	$0.588579\pi$
$492$	−163.313	−	163.313i	−0.331938	−	0.331938i
$493$	−158.005	+	158.005i	−0.320497	+	0.320497i
$494$		−	1110.45i		−	2.24788i
$495$	−86.8993	+	152.259i	−0.175554	+	0.307594i
$496$	111.797			0.225397
$497$	−450.911	−	450.911i	−0.907266	−	0.907266i
$498$	−183.578	+	183.578i	−0.368630	+	0.368630i
$499$			349.467i			0.700334i	0.936687	+	0.350167i	$0.113875\pi$
$499$			349.467i			0.700334i	−0.936687	+	0.350167i	$0.886125\pi$
$500$	249.972	−	3.73284i	0.499944	−	0.00746568i
$501$	−81.0859			−0.161848
$502$	408.680	+	408.680i	0.814104	+	0.814104i
$503$	−343.643	+	343.643i	−0.683187	+	0.683187i	−0.960717	−	0.277530i	$-0.910484\pi$
$503$	−343.643	+	343.643i	−0.683187	+	0.683187i	0.277530	+	0.960717i	$0.410484\pi$
$504$		−	71.2353i		−	0.141340i
$505$	139.708	+	79.7361i	0.276650	+	0.157893i
$506$	79.2683			0.156657
$507$	−444.873	−	444.873i	−0.877461	−	0.877461i
$508$	71.3239	−	71.3239i	0.140401	−	0.140401i
$509$			603.575i			1.18581i	0.805274	+	0.592903i	$0.202018\pi$
$509$			603.575i			1.18581i	−0.805274	+	0.592903i	$0.797982\pi$
$510$	−12.6277	−	46.2061i	−0.0247602	−	0.0906001i
$511$	−917.971			−1.79642
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	125.054	−	125.054i	0.243770	−	0.243770i
$514$			53.6559i			0.104389i
$515$	467.192	−	127.679i	0.907169	−	0.247921i
$516$	230.895			0.447471
$517$	−358.931	−	358.931i	−0.694258	−	0.694258i
$518$	142.337	−	142.337i	0.274781	−	0.274781i
$519$			317.721i			0.612180i
$520$	−161.723	+	283.360i	−0.311006	+	0.544924i
$521$	−572.281			−1.09843			−0.549214	−	0.835681i	$-0.685073\pi$
$521$	−572.281			−1.09843			−0.549214	+	0.835681i	$0.685073\pi$
$522$	171.401	+	171.401i	0.328353	+	0.328353i
$523$	360.248	−	360.248i	0.688810	−	0.688810i	−0.273159	−	0.961969i	$-0.588069\pi$
$523$	360.248	−	360.248i	0.688810	−	0.688810i	0.961969	+	0.273159i	$0.0880685\pi$
$524$		−	108.988i		−	0.207992i
$525$	−184.885	−	312.994i	−0.352163	−	0.596179i
$526$	−171.573			−0.326185
$527$	−77.2945	−	77.2945i	−0.146669	−	0.146669i
$528$	−57.2567	+	57.2567i	−0.108441	+	0.108441i
$529$		−	23.0000i		−	0.0434783i
$530$	272.188	+	155.346i	0.513562	+	0.293107i
$531$	102.722			0.193449
$532$	404.088	+	404.088i	0.759564	+	0.759564i
$533$	1087.64	−	1087.64i	2.04059	−	2.04059i
$534$			85.7707i			0.160619i
$535$	−41.5899	−	152.182i	−0.0777381	−	0.284452i
$536$	58.4557			0.109059
$537$	143.572	+	143.572i	0.267359	+	0.267359i
$538$	−252.246	+	252.246i	−0.468859	+	0.468859i
$539$			251.033i			0.465738i
$540$	−50.1234	+	13.6983i	−0.0928211	+	0.0253672i
$541$	536.996			0.992598			0.496299	−	0.868152i	$-0.334692\pi$
$541$	536.996			0.992598			0.496299	+	0.868152i	$0.334692\pi$
$542$	468.292	+	468.292i	0.864008	+	0.864008i
$543$	−102.963	+	102.963i	−0.189619	+	0.189619i
$544$		−	22.1243i		−	0.0406697i
$545$	471.812	−	826.677i	0.865710	−	1.51684i
$546$	474.414			0.868890
$547$	332.299	+	332.299i	0.607493	+	0.607493i	0.942290	−	0.334797i	$-0.108668\pi$
$547$	332.299	+	332.299i	0.607493	+	0.607493i	−0.334797	+	0.942290i	$0.608668\pi$
$548$	119.362	−	119.362i	0.217814	−	0.217814i
$549$			178.379i			0.324917i
$550$	−102.969	+	400.179i	−0.187217	+	0.727599i
$551$	−1944.56			−3.52916
$552$	16.6132	+	16.6132i	0.0300965	+	0.0300965i
$553$	−841.019	+	841.019i	−1.52083	+	1.52083i
$554$			676.585i			1.22127i
$555$	−127.523	−	72.7817i	−0.229772	−	0.131138i
$556$	−151.482			−0.272450
$557$	−466.722	−	466.722i	−0.837921	−	0.837921i	0.150664	−	0.988585i	$-0.451859\pi$
$557$	−466.722	−	466.722i	−0.837921	−	0.837921i	−0.988585	+	0.150664i	$0.951859\pi$
$558$	−83.8475	+	83.8475i	−0.150264	+	0.150264i
$559$			1537.72i			2.75084i
$560$	−44.2633	−	161.964i	−0.0790415	−	0.289221i
$561$	79.1728			0.141128
$562$	−49.4745	−	49.4745i	−0.0880330	−	0.0880330i
$563$	−575.407	+	575.407i	−1.02204	+	1.02204i	−0.0222862	+	0.999752i	$0.507095\pi$
$563$	−575.407	+	575.407i	−1.02204	+	1.02204i	−0.999752	+	0.0222862i	$0.992905\pi$
$564$		−	150.452i		−	0.266758i
$565$	421.281	−	115.132i	0.745629	−	0.203774i
$566$	−59.0580			−0.104343
$567$	53.4265	+	53.4265i	0.0942266	+	0.0942266i
$568$	−151.917	+	151.917i	−0.267460	+	0.267460i
$569$		−	90.6448i		−	0.159305i	−0.996823	−	0.0796527i	$-0.974619\pi$
$569$		−	90.6448i		−	0.159305i	0.996823	−	0.0796527i	$-0.0253811\pi$
$570$	206.624	−	362.033i	0.362499	−	0.635146i
$571$	876.900			1.53573			0.767863	−	0.640614i	$-0.221320\pi$
$571$	876.900			1.53573			0.767863	+	0.640614i	$0.221320\pi$
$572$	−381.319	−	381.319i	−0.666641	−	0.666641i
$573$	36.1649	−	36.1649i	0.0631151	−	0.0631151i
$574$			791.572i			1.37904i
$575$	116.114	+	29.8769i	0.201937	+	0.0519599i
$576$	−24.0000			−0.0416667
$577$	−570.461	−	570.461i	−0.988668	−	0.988668i	0.0112686	−	0.999937i	$-0.496413\pi$
$577$	−570.461	−	570.461i	−0.988668	−	0.988668i	−0.999937	+	0.0112686i	$0.996413\pi$
$578$	273.704	−	273.704i	0.473536	−	0.473536i
$579$		−	52.4137i		−	0.0905245i
$580$	496.206	+	283.201i	0.855528	+	0.488278i
$581$	889.792			1.53148
$582$	15.6557	+	15.6557i	0.0268998	+	0.0268998i
$583$	−366.284	+	366.284i	−0.628274	+	0.628274i
$584$			309.275i			0.529581i
$585$	−91.2280	−	333.812i	−0.155945	−	0.570620i
$586$	263.140			0.449045
$587$	−476.810	−	476.810i	−0.812283	−	0.812283i	0.172693	−	0.984976i	$-0.444753\pi$
$587$	−476.810	−	476.810i	−0.812283	−	0.812283i	−0.984976	+	0.172693i	$0.944753\pi$
$588$	−52.6121	+	52.6121i	−0.0894764	+	0.0894764i
$589$		−	951.263i		−	1.61505i
$590$	233.553	−	63.8278i	0.395852	−	0.108183i
$591$	−156.031			−0.264013
$592$	−47.9548	−	47.9548i	−0.0810048	−	0.0810048i
$593$	−464.944	+	464.944i	−0.784053	+	0.784053i	−0.980512	−	0.196459i	$-0.937056\pi$
$593$	−464.944	+	464.944i	−0.784053	+	0.784053i	0.196459	+	0.980512i	$0.437056\pi$
$594$		−	85.8850i		−	0.144588i
$595$	−81.3764	+	142.582i	−0.136767	+	0.239634i
$596$	−245.589			−0.412062
$597$	331.384	+	331.384i	0.555082	+	0.555082i
$598$	−110.641	+	110.641i	−0.185019	+	0.185019i
$599$			1081.33i			1.80523i	0.430445	+	0.902617i	$0.358357\pi$
$599$			1081.33i			1.80523i	−0.430445	+	0.902617i	$0.641643\pi$
$600$	−105.451	+	62.2900i	−0.175752	+	0.103817i
$601$	486.380			0.809285			0.404642	−	0.914475i	$-0.367396\pi$
$601$	486.380			0.809285			0.404642	+	0.914475i	$0.367396\pi$
$602$	−559.569	−	559.569i	−0.929516	−	0.929516i
$603$	−43.8418	+	43.8418i	−0.0727061	+	0.0727061i
$604$		−	195.340i		−	0.323410i
$605$	−67.7300	−	38.6557i	−0.111950	−	0.0638938i
$606$	−78.8054			−0.130042
$607$	476.578	+	476.578i	0.785136	+	0.785136i	0.980693	−	0.195556i	$-0.0626512\pi$
$607$	476.578	+	476.578i	0.785136	+	0.785136i	−0.195556	+	0.980693i	$0.562651\pi$
$608$	136.142	−	136.142i	0.223917	−	0.223917i
$609$		−	830.770i		−	1.36415i
$610$	110.839	+	405.571i	0.181703	+	0.664870i
$611$	1001.98			1.63990
$612$	16.5932	+	16.5932i	0.0271131	+	0.0271131i
$613$	−65.0705	+	65.0705i	−0.106151	+	0.106151i	−0.758187	−	0.652037i	$-0.773915\pi$
$613$	−65.0705	+	65.0705i	−0.106151	+	0.106151i	0.652037	+	0.758187i	$0.273915\pi$
$614$		−	489.074i		−	0.796538i
$615$	556.975	−	152.216i	0.905650	−	0.247506i
$616$	277.520			0.450520
$617$	−573.526	−	573.526i	−0.929539	−	0.929539i	0.0681366	−	0.997676i	$-0.478295\pi$
$617$	−573.526	−	573.526i	−0.929539	−	0.929539i	−0.997676	+	0.0681366i	$0.978295\pi$
$618$	−167.775	+	167.775i	−0.271481	+	0.271481i
$619$		−	59.7320i		−	0.0964976i	−0.998835	−	0.0482488i	$-0.984636\pi$
$619$		−	59.7320i		−	0.0964976i	0.998835	−	0.0482488i	$-0.0153640\pi$
$620$	−138.539	+	242.739i	−0.223451	+	0.391515i
$621$	−24.9199			−0.0401286
$622$	292.121	+	292.121i	0.469648	+	0.469648i
$623$	207.863	−	207.863i	0.333649	−	0.333649i
$624$		−	159.835i		−	0.256147i
$625$	−301.663	+	547.380i	−0.482660	+	0.875808i
$626$	443.387			0.708286
$627$	487.189	+	487.189i	0.777016	+	0.777016i
$628$	16.5016	−	16.5016i	0.0262764	−	0.0262764i
$629$			66.3104i			0.105422i
$630$	154.670	+	88.2754i	0.245508	+	0.140120i
$631$	394.424			0.625077			0.312539	−	0.949905i	$-0.398821\pi$
$631$	394.424			0.625077			0.312539	+	0.949905i	$0.398821\pi$
$632$	283.349	+	283.349i	0.448337	+	0.448337i
$633$	−421.544	+	421.544i	−0.665946	+	0.665946i
$634$		−	541.177i		−	0.853591i
$635$	66.4775	+	243.248i	0.104689	+	0.383067i
$636$	−153.533			−0.241405
$637$	−350.387	−	350.387i	−0.550058	−	0.550058i
$638$	−667.746	+	667.746i	−1.04662	+	1.04662i
$639$		−	227.876i		−	0.356613i
$640$	−54.5675	+	14.9128i	−0.0852617	+	0.0233012i
$641$	1137.01			1.77381			0.886905	−	0.461951i	$-0.152850\pi$
$641$	1137.01			1.77381			0.886905	+	0.461951i	$0.152850\pi$
$642$	54.6505	+	54.6505i	0.0851254	+	0.0851254i
$643$	−208.084	+	208.084i	−0.323614	+	0.323614i	−0.850152	−	0.526538i	$-0.823490\pi$
$643$	−208.084	+	208.084i	−0.323614	+	0.323614i	0.526538	+	0.850152i	$0.323490\pi$
$644$		−	80.5236i		−	0.125037i
$645$	−286.127	+	501.333i	−0.443608	+	0.777261i
$646$	−188.253			−0.291413
$647$	336.574	+	336.574i	0.520207	+	0.520207i	0.917634	−	0.397427i	$-0.130097\pi$
$647$	336.574	+	336.574i	0.520207	+	0.520207i	−0.397427	+	0.917634i	$0.630097\pi$
$648$	18.0000	−	18.0000i	0.0277778	−	0.0277778i
$649$			400.185i			0.616619i
$650$	−414.840	−	702.285i	−0.638215	−	1.08044i
$651$	406.405			0.624278
$652$	393.649	+	393.649i	0.603756	+	0.603756i
$653$	−29.6916	+	29.6916i	−0.0454695	+	0.0454695i	−0.729476	−	0.684006i	$-0.760236\pi$
$653$	−29.6916	+	29.6916i	−0.0454695	+	0.0454695i	0.684006	+	0.729476i	$0.260236\pi$
$654$			466.305i			0.713005i
$655$	236.641	+	135.059i	0.361284	+	0.206196i
$656$	266.690			0.406539
$657$	−231.956	−	231.956i	−0.353054	−	0.353054i
$658$	−364.616	+	364.616i	−0.554127	+	0.554127i
$659$			1060.05i			1.60858i	0.594240	+	0.804288i	$0.297453\pi$
$659$			1060.05i			1.60858i	−0.594240	+	0.804288i	$0.702547\pi$
$660$	−53.3661	−	195.272i	−0.0808577	−	0.295867i
$661$	339.496			0.513609			0.256805	−	0.966463i	$-0.417330\pi$
$661$	339.496			0.513609			0.256805	+	0.966463i	$0.417330\pi$
$662$	−279.894	−	279.894i	−0.422801	−	0.422801i
$663$	−110.508	+	110.508i	−0.166678	+	0.166678i
$664$		−	299.781i		−	0.451477i
$665$	−1378.13	+	376.630i	−2.07237	+	0.566361i
$666$	71.9322			0.108006
$667$	193.749	+	193.749i	0.290478	+	0.290478i
$668$	66.2064	−	66.2064i	0.0991113	−	0.0991113i
$669$		−	114.352i		−	0.170929i
$670$	−72.4388	+	126.922i	−0.108118	+	0.189436i
$671$	−694.934			−1.03567
$672$	58.1634	+	58.1634i	0.0865527	+	0.0865527i
$673$	−652.029	+	652.029i	−0.968839	+	0.968839i	−0.999529	−	0.0306899i	$-0.990230\pi$
$673$	−652.029	+	652.029i	−0.968839	+	0.968839i	0.0306899	+	0.999529i	$0.490230\pi$
$674$			582.510i			0.864258i
$675$	32.3709	−	125.806i	0.0479568	−	0.186379i
$676$	726.474			1.07467
$677$	784.901	+	784.901i	1.15938	+	1.15938i	0.984609	+	0.174771i	$0.0559187\pi$
$677$	784.901	+	784.901i	1.15938	+	1.15938i	0.174771	+	0.984609i	$0.444081\pi$
$678$	−151.288	+	151.288i	−0.223138	+	0.223138i
$679$		−	75.8822i		−	0.111756i
$680$	48.0376	+	27.4166i	0.0706435	+	0.0403186i
$681$	658.952			0.967623
$682$	−326.655	−	326.655i	−0.478966	−	0.478966i
$683$	726.204	−	726.204i	1.06326	−	1.06326i	0.0653967	−	0.997859i	$-0.479169\pi$
$683$	726.204	−	726.204i	1.06326	−	1.06326i	0.997859	−	0.0653967i	$-0.0208313\pi$
$684$			204.213i			0.298557i
$685$	111.251	+	407.080i	0.162410	+	0.594277i
$686$	−326.747			−0.476308
$687$	−183.590	−	183.590i	−0.267234	−	0.267234i
$688$	−188.525	+	188.525i	−0.274019	+	0.274019i
$689$		−	1022.50i		−	1.48404i
$690$	−56.6589	+	15.4844i	−0.0821144	+	0.0224411i
$691$	−41.6811			−0.0603199			−0.0301600	−	0.999545i	$-0.509602\pi$
$691$	−41.6811			−0.0603199			−0.0301600	+	0.999545i	$0.509602\pi$
$692$	−259.418	−	259.418i	−0.374882	−	0.374882i
$693$	−208.140	+	208.140i	−0.300347	+	0.300347i
$694$		−	252.169i		−	0.363356i
$695$	187.718	−	328.906i	0.270097	−	0.473247i
$696$	−279.896			−0.402149
$697$	−184.385	−	184.385i	−0.264541	−	0.264541i
$698$	370.710	−	370.710i	0.531104	−	0.531104i
$699$		−	345.390i		−	0.494121i
$700$	406.517	+	104.600i	0.580738	+	0.149429i
$701$	376.669			0.537331			0.268666	−	0.963234i	$-0.413417\pi$
$701$	376.669			0.537331			0.268666	+	0.963234i	$0.413417\pi$
$702$	119.877	+	119.877i	0.170764	+	0.170764i
$703$	−408.041	+	408.041i	−0.580428	+	0.580428i
$704$		−	93.4998i		−	0.132812i
$705$	326.669	+	186.441i	0.463360	+	0.264455i
$706$	−230.851			−0.326984
$707$	190.983	+	190.983i	0.270132	+	0.270132i
$708$	−83.8719	+	83.8719i	−0.118463	+	0.118463i
$709$		−	34.6689i		−	0.0488983i	−0.999701	−	0.0244491i	$-0.992217\pi$
$709$		−	34.6689i		−	0.0488983i	0.999701	−	0.0244491i	$-0.00778318\pi$
$710$	−141.594	−	518.108i	−0.199429	−	0.729730i
$711$	−425.023			−0.597782
$712$	−70.0315	−	70.0315i	−0.0983588	−	0.0983588i
$713$	−94.7802	+	94.7802i	−0.132932	+	0.132932i
$714$		−	80.4266i		−	0.112642i
$715$	1300.47	−	355.408i	1.81885	−	0.497074i
$716$	−234.452			−0.327447
$717$	−323.340	−	323.340i	−0.450963	−	0.450963i
$718$	−201.226	+	201.226i	−0.280259	+	0.280259i
$719$		−	299.243i		−	0.416194i	−0.978108	−	0.208097i	$-0.933273\pi$
$719$		−	299.243i		−	0.416194i	0.978108	−	0.208097i	$-0.0667270\pi$
$720$	29.7410	−	52.1102i	0.0413069	−	0.0723753i
$721$	813.197			1.12787
$722$	−797.412	−	797.412i	−1.10445	−	1.10445i
$723$	236.742	−	236.742i	0.327444	−	0.327444i
$724$		−	168.138i		−	0.232235i
$725$	−1229.81	+	726.447i	−1.69628	+	1.00200i
$726$	38.2046			0.0526234
$727$	434.804	+	434.804i	0.598079	+	0.598079i	0.939801	−	0.341722i	$-0.111010\pi$
$727$	434.804	+	434.804i	0.598079	+	0.598079i	−0.341722	+	0.939801i	$0.611010\pi$
$728$	−387.357	+	387.357i	−0.532084	+	0.532084i
$729$			27.0000i			0.0370370i
$730$	−671.516	−	383.256i	−0.919885	−	0.525009i
$731$	260.687			0.356617
$732$	−145.646	−	145.646i	−0.198970	−	0.198970i
$733$	215.359	−	215.359i	0.293806	−	0.293806i	−0.544776	−	0.838582i	$-0.683385\pi$
$733$	215.359	−	215.359i	0.293806	−	0.293806i	0.838582	+	0.544776i	$0.183385\pi$
$734$		−	243.811i		−	0.332167i
$735$	−49.0371	−	179.432i	−0.0667171	−	0.244125i
$736$	−27.1293			−0.0368605
$737$	−170.800	−	170.800i	−0.231750	−	0.231750i
$738$	−200.017	+	200.017i	−0.271026	+	0.271026i
$739$		−	21.9856i		−	0.0297504i	−0.999889	−	0.0148752i	$-0.995265\pi$
$739$		−	21.9856i		−	0.0297504i	0.999889	−	0.0148752i	$-0.00473510\pi$
$740$	163.548	−	44.6963i	0.221011	−	0.0604004i
$741$	−1360.02			−1.83538
$742$	372.084	+	372.084i	0.501461	+	0.501461i
$743$	229.362	−	229.362i	0.308697	−	0.308697i	−0.535707	−	0.844404i	$-0.679955\pi$
$743$	229.362	−	229.362i	0.308697	−	0.308697i	0.844404	+	0.535707i	$0.179955\pi$
$744$		−	136.922i		−	0.184035i
$745$	304.336	−	533.237i	0.408504	−	0.715754i
$746$	380.675			0.510288
$747$	224.836	+	224.836i	0.300985	+	0.300985i
$748$	−64.6443	+	64.6443i	−0.0864228	+	0.0864228i
$749$		−	264.888i		−	0.353656i
$750$	−4.57177	−	306.152i	−0.00609570	−	0.408203i
$751$	−433.258			−0.576908			−0.288454	−	0.957494i	$-0.593141\pi$
$751$	−433.258			−0.576908			−0.288454	+	0.957494i	$0.593141\pi$
$752$	122.843	+	122.843i	0.163355	+	0.163355i
$753$	500.529	−	500.529i	0.664714	−	0.664714i
$754$		−	1864.05i		−	2.47222i
$755$	424.133	+	242.067i	0.561766	+	0.320618i
$756$	−87.2451			−0.115404
$757$	−707.838	−	707.838i	−0.935057	−	0.935057i	0.0629594	−	0.998016i	$-0.479946\pi$
$757$	−707.838	−	707.838i	−0.935057	−	0.935057i	−0.998016	+	0.0629594i	$0.979946\pi$
$758$	−8.74600	+	8.74600i	−0.0115383	+	0.0115383i
$759$		−	97.0834i		−	0.127910i
$760$	126.891	+	464.307i	0.166962	+	0.610930i
$761$	211.795			0.278311			0.139155	−	0.990271i	$-0.455561\pi$
$761$	211.795			0.278311			0.139155	+	0.990271i	$0.455561\pi$
$762$	−87.3536	−	87.3536i	−0.114637	−	0.114637i
$763$	1130.08	−	1130.08i	1.48110	−	1.48110i
$764$			59.0571i			0.0772999i
$765$	−56.5907	+	15.4657i	−0.0739747	+	0.0202166i
$766$	9.05634			0.0118229
$767$	−558.571	−	558.571i	−0.728254	−	0.728254i
$768$	19.5959	−	19.5959i	0.0255155	−	0.0255155i
$769$			67.3997i			0.0876459i	0.999039	+	0.0438230i	$0.0139538\pi$
$769$			67.3997i			0.0876459i	−0.999039	+	0.0438230i	$0.986046\pi$
$770$	−343.905	+	602.568i	−0.446630	+	0.782556i
$771$	65.7148			0.0852332
$772$	42.7956	+	42.7956i	0.0554347	+	0.0554347i
$773$	994.512	−	994.512i	1.28656	−	1.28656i	0.349699	−	0.936862i	$-0.386284\pi$
$773$	994.512	−	994.512i	1.28656	−	1.28656i	0.936862	−	0.349699i	$-0.113716\pi$
$774$		−	282.788i		−	0.365359i
$775$	−355.371	−	601.610i	−0.458543	−	0.776270i
$776$	−25.5656			−0.0329454
$777$	−174.326	−	174.326i	−0.224358	−	0.224358i
$778$	647.329	−	647.329i	0.832042	−	0.832042i
$779$		−	2269.22i		−	2.91300i
$780$	347.044	+	198.069i	0.444928	+	0.253935i
$781$	887.763			1.13670
$782$	18.7568	+	18.7568i	0.0239857	+	0.0239857i
$783$	209.922	−	209.922i	0.268099	−	0.268099i
$784$		−	85.9152i		−	0.109586i
$785$	15.3803	+	56.2781i	0.0195928	+	0.0716919i
$786$	−133.482			−0.169825
$787$	−470.208	−	470.208i	−0.597469	−	0.597469i	0.342170	−	0.939638i	$-0.388838\pi$
$787$	−470.208	−	470.208i	−0.597469	−	0.597469i	−0.939638	+	0.342170i	$0.888838\pi$
$788$	127.399	−	127.399i	0.161674	−	0.161674i
$789$			210.133i			0.266329i
$790$	−966.352	+	264.095i	−1.22323	+	0.334298i
$791$	733.284			0.927034
$792$	70.1248	+	70.1248i	0.0885414	+	0.0885414i
$793$	969.975	−	969.975i	1.22317	−	1.22317i
$794$		−	915.627i		−	1.15318i
$795$	190.260	−	333.360i	0.239320	−	0.419321i
$796$	−541.148			−0.679834
$797$	441.537	+	441.537i	0.553999	+	0.553999i	0.927593	−	0.373593i	$-0.121874\pi$
$797$	441.537	+	441.537i	0.553999	+	0.553999i	−0.373593	+	0.927593i	$0.621874\pi$
$798$	494.905	−	494.905i	0.620181	−	0.620181i
$799$		−	169.864i		−	0.212595i
$800$	35.2409	−	136.960i	0.0440512	−	0.171200i
$801$	105.047			0.131145
$802$	−419.534	−	419.534i	−0.523109	−	0.523109i
$803$	903.661	−	903.661i	1.12536	−	1.12536i
$804$		−	71.5933i		−	0.0890464i
$805$	174.838	+	99.7855i	0.217189	+	0.123957i
$806$	911.877			1.13136
$807$	308.937	+	308.937i	0.382822	+	0.382822i
$808$	64.3444	−	64.3444i	0.0796341	−	0.0796341i
$809$			604.080i			0.746699i	0.927691	+	0.373350i	$0.121791\pi$
$809$			604.080i			0.746699i	−0.927691	+	0.373350i	$0.878209\pi$
$810$	16.7769	+	61.3884i	0.0207122	+	0.0757881i
$811$	−1490.76			−1.83818			−0.919089	−	0.394051i	$-0.871073\pi$
$811$	−1490.76			−1.83818			−0.919089	+	0.394051i	$0.871073\pi$
$812$	678.321	+	678.321i	0.835370	+	0.835370i
$813$	573.539	−	573.539i	0.705459	−	0.705459i
$814$			280.235i			0.344269i
$815$	−1342.53	+	366.900i	−1.64727	+	0.450185i
$816$	−27.0966			−0.0332067
$817$	1604.13	+	1604.13i	1.96345	+	1.96345i
$818$	−168.996	+	168.996i	−0.206597	+	0.206597i
$819$		−	581.036i		−	0.709446i
$820$	−330.484	+	579.052i	−0.403029	+	0.706161i
$821$	353.858			0.431009			0.215504	−	0.976503i	$-0.430860\pi$
$821$	353.858			0.431009			0.215504	+	0.976503i	$0.430860\pi$
$822$	−146.188	−	146.188i	−0.177844	−	0.177844i
$823$	148.584	−	148.584i	0.180539	−	0.180539i	−0.611052	−	0.791591i	$-0.709253\pi$
$823$	148.584	−	148.584i	0.180539	−	0.180539i	0.791591	+	0.611052i	$0.209253\pi$
$824$		−	273.975i		−	0.332494i
$825$	490.118	+	126.111i	0.594082	+	0.152862i
$826$	406.523			0.492159
$827$	9.96921	+	9.96921i	0.0120547	+	0.0120547i	0.713108	−	0.701054i	$-0.247287\pi$
$827$	9.96921	+	9.96921i	0.0120547	+	0.0120547i	−0.701054	+	0.713108i	$0.747287\pi$
$828$	20.3470	−	20.3470i	0.0245737	−	0.0245737i
$829$		−	371.379i		−	0.447984i	−0.974591	−	0.223992i	$-0.928091\pi$
$829$		−	371.379i		−	0.447984i	0.974591	−	0.223992i	$-0.0719090\pi$
$830$	650.902	+	371.491i	0.784219	+	0.447580i
$831$	828.644			0.997165
$832$	130.505	+	130.505i	0.156857	+	0.156857i
$833$	−59.4004	+	59.4004i	−0.0713090	+	0.0713090i
$834$			185.527i			0.222454i
$835$	61.7076	+	225.795i	0.0739014	+	0.270413i
$836$	−795.577			−0.951647
$837$	102.692	+	102.692i	0.122690	+	0.122690i
$838$	−688.224	+	688.224i	−0.821270	+	0.821270i
$839$		−	182.592i		−	0.217631i	−0.994062	−	0.108815i	$-0.965294\pi$
$839$		−	182.592i		−	0.217631i	0.994062	−	0.108815i	$-0.0347057\pi$
$840$	−198.364	+	54.2112i	−0.236148	+	0.0645371i
$841$	−2423.24			−2.88138
$842$	−4.67524	−	4.67524i	−0.00555255	−	0.00555255i
$843$	−60.5937	+	60.5937i	−0.0718786	+	0.0718786i
$844$		−	688.378i		−	0.815614i
$845$	−900.253	+	1577.36i	−1.06539	+	1.86670i
$846$	−184.265			−0.217807
$847$	−92.5878	−	92.5878i	−0.109313	−	0.109313i
$848$	125.359	−	125.359i	0.147830	−	0.147830i
$849$			72.3309i			0.0851954i
$850$	−119.057	+	70.3271i	−0.140067	+	0.0827377i
$851$	81.3113			0.0955480
$852$	186.060	+	186.060i	0.218380	+	0.218380i
$853$	−64.0810	+	64.0810i	−0.0751243	+	0.0751243i	−0.743671	−	0.668546i	$-0.766917\pi$
$853$	−64.0810	+	64.0810i	−0.0751243	+	0.0751243i	0.668546	+	0.743671i	$0.266917\pi$
$854$			705.939i			0.826626i
$855$	−443.399	−	253.062i	−0.518595	−	0.295979i
$856$	−89.2439			−0.104257
$857$	−432.784	−	432.784i	−0.504998	−	0.504998i	0.407989	−	0.912987i	$-0.366230\pi$
$857$	−432.784	−	432.784i	−0.504998	−	0.504998i	−0.912987	+	0.407989i	$0.866230\pi$
$858$	−467.018	+	467.018i	−0.544310	+	0.544310i
$859$		−	598.759i		−	0.697041i	−0.937301	−	0.348521i	$-0.886684\pi$
$859$		−	598.759i		−	0.697041i	0.937301	−	0.348521i	$-0.113316\pi$
$860$	−175.715	−	642.959i	−0.204320	−	0.747626i
$861$	969.473			1.12599
$862$	−273.490	−	273.490i	−0.317274	−	0.317274i
$863$	356.204	−	356.204i	0.412751	−	0.412751i	−0.469945	−	0.882696i	$-0.655726\pi$
$863$	356.204	−	356.204i	0.412751	−	0.412751i	0.882696	+	0.469945i	$0.155726\pi$
$864$			29.3939i			0.0340207i
$865$	884.738	−	241.791i	1.02282	−	0.279527i
$866$	1119.42			1.29264
$867$	−335.217	−	335.217i	−0.386640	−	0.386640i
$868$	−331.828	+	331.828i	−0.382290	+	0.382290i
$869$		−	1655.82i		−	1.90543i
$870$	346.849	−	607.726i	0.398677	−	0.698536i
$871$	476.798			0.547414
$872$	−380.736	−	380.736i	−0.436624	−	0.436624i
$873$	19.1742	−	19.1742i	0.0219636	−	0.0219636i
$874$			230.840i			0.264119i
$875$	−730.872	+	753.032i	−0.835283	+	0.860608i
$876$	378.783			0.432401
$877$	120.060	+	120.060i	0.136898	+	0.136898i	0.772235	−	0.635337i	$-0.219139\pi$
$877$	120.060	+	120.060i	0.136898	+	0.136898i	−0.635337	+	0.772235i	$0.719139\pi$
$878$	−331.061	+	331.061i	−0.377063	+	0.377063i
$879$		−	322.280i		−	0.366644i
$880$	203.012	+	115.866i	0.230696	+	0.131666i
$881$	964.844			1.09517			0.547585	−	0.836750i	$-0.315547\pi$
$881$	964.844			1.09517			0.547585	+	0.836750i	$0.315547\pi$
$882$	64.4364	+	64.4364i	0.0730571	+	0.0730571i
$883$	−766.730	+	766.730i	−0.868324	+	0.868324i	−0.992287	−	0.123963i	$-0.960440\pi$
$883$	−766.730	+	766.730i	−0.868324	+	0.868324i	0.123963	+	0.992287i	$0.460440\pi$
$884$		−	180.458i		−	0.204138i
$885$	−78.1728	−	286.042i	−0.0883308	−	0.323212i
$886$	−604.186			−0.681926
$887$	149.812	+	149.812i	0.168898	+	0.168898i	0.786495	−	0.617597i	$-0.211894\pi$
$887$	149.812	+	149.812i	0.168898	+	0.168898i	−0.617597	+	0.786495i	$0.711894\pi$
$888$	−58.7324	+	58.7324i	−0.0661401	+	0.0661401i
$889$			423.399i			0.476264i
$890$	238.840	−	65.2728i	0.268360	−	0.0733402i
$891$	−105.187			−0.118055
$892$	93.3678	+	93.3678i	0.104672	+	0.104672i
$893$	1045.26	−	1045.26i	1.17050	−	1.17050i
$894$			300.784i			0.336447i
$895$	290.535	−	509.055i	0.324620	−	0.568777i
$896$	−94.9805			−0.106005
$897$	135.507	+	135.507i	0.151067	+	0.151067i
$898$	−49.8135	+	49.8135i	−0.0554716	+	0.0554716i
$899$		−	1596.83i		−	1.77623i
$900$	76.2894	+	129.151i	0.0847660	+	0.143501i
$901$	−173.343			−0.192390
$902$	−779.231	−	779.231i	−0.863893	−	0.863893i
$903$	−685.329	+	685.329i	−0.758947	+	0.758947i
$904$		−	247.052i		−	0.273287i
$905$	365.071	+	208.358i	0.403393	+	0.230230i
$906$	−239.242			−0.264064
$907$	−190.969	−	190.969i	−0.210550	−	0.210550i	0.593951	−	0.804501i	$-0.297567\pi$
$907$	−190.969	−	190.969i	−0.210550	−	0.210550i	−0.804501	+	0.593951i	$0.797567\pi$
$908$	−538.032	+	538.032i	−0.592546	+	0.592546i
$909$			96.5165i			0.106179i
$910$	−361.036	−	1321.07i	−0.396743	−	1.45172i
$911$	1664.60			1.82723			0.913614	−	0.406584i	$-0.133280\pi$
$911$	1664.60			1.82723			0.913614	+	0.406584i	$0.133280\pi$
$912$	−166.739	−	166.739i	−0.182828	−	0.182828i
$913$	−875.920	+	875.920i	−0.959387	+	0.959387i
$914$			1199.62i			1.31249i
$915$	496.721	−	135.749i	0.542864	−	0.148360i
$916$	299.801			0.327294
$917$	323.491	+	323.491i	0.352771	+	0.352771i
$918$	20.3225	−	20.3225i	0.0221378	−	0.0221378i
$919$		−	276.770i		−	0.301165i	−0.988597	−	0.150582i	$-0.951885\pi$
$919$		−	276.770i		−	0.301165i	0.988597	−	0.150582i	$-0.0481148\pi$
$920$	33.6189	−	58.9048i	0.0365423	−	0.0640269i
$921$	−598.991			−0.650370
$922$	−42.9308	−	42.9308i	−0.0465627	−	0.0465627i
$923$	−1239.12	+	1239.12i	−1.34249	+	1.34249i
$924$		−	339.892i		−	0.367848i
$925$	−105.623	+	410.494i	−0.114187	+	0.443777i
$926$	−189.458			−0.204598
$927$	205.482	+	205.482i	0.221663	+	0.221663i
$928$	228.534	−	228.534i	0.246265	−	0.246265i
$929$			1696.36i			1.82600i	0.407957	+	0.913001i	$0.366241\pi$
$929$			1696.36i			1.82600i	−0.407957	+	0.913001i	$0.633759\pi$
$930$	297.294	+	169.675i	0.319671	+	0.182447i
$931$	−731.041			−0.785221
$932$	282.010	+	282.010i	0.302586	+	0.302586i
$933$	357.774	−	357.774i	0.383466	−	0.383466i
$934$			485.206i			0.519493i
$935$	−60.2517	−	220.467i	−0.0644403	−	0.235794i
$936$	−195.758			−0.209143
$937$	713.370	+	713.370i	0.761334	+	0.761334i	0.976563	−	0.215230i	$-0.0690500\pi$
$937$	713.370	+	713.370i	0.761334	+	0.761334i	−0.215230	+	0.976563i	$0.569050\pi$
$938$	−173.505	+	173.505i	−0.184973	+	0.184973i
$939$		−	543.036i		−	0.578313i
$940$	−418.952	+	114.496i	−0.445694	+	0.121804i
$941$	400.763			0.425891			0.212945	−	0.977064i	$-0.431694\pi$
$941$	400.763			0.425891			0.212945	+	0.977064i	$0.431694\pi$
$942$	−20.2102	−	20.2102i	−0.0214546	−	0.0214546i
$943$	−226.097	+	226.097i	−0.239764	+	0.239764i
$944$		−	136.962i		−	0.145087i
$945$	108.115	−	189.432i	0.114407	−	0.200457i
$946$	1101.69			1.16458
$947$	878.152	+	878.152i	0.927299	+	0.927299i	0.997531	−	0.0702314i	$-0.0223738\pi$
$947$	878.152	+	878.152i	0.927299	+	0.927299i	−0.0702314	+	0.997531i	$0.522374\pi$
$948$	347.030	−	347.030i	0.366065	−	0.366065i
$949$			2522.62i			2.65819i
$950$	−1165.38	−	299.860i	−1.22671	−	0.315642i
$951$	−662.803			−0.696954
$952$	65.6680	+	65.6680i	0.0689790	+	0.0689790i
$953$	885.585	−	885.585i	0.929260	−	0.929260i	−0.0683984	−	0.997658i	$-0.521789\pi$
$953$	885.585	−	885.585i	0.929260	−	0.929260i	0.997658	+	0.0683984i	$0.0217889\pi$
$954$			188.039i			0.197106i
$955$	−128.228	−	73.1841i	−0.134270	−	0.0766325i
$956$	528.013			0.552315
$957$	817.819	+	817.819i	0.854565	+	0.854565i
$958$	−246.825	+	246.825i	−0.257646	+	0.257646i
$959$			708.565i			0.738858i
$960$	18.2644	+	66.8312i	0.0190254	+	0.0696159i
$961$	−179.844			−0.187142
$962$	−391.147	−	391.147i	−0.406598	−	0.406598i
$963$	66.9329	−	66.9329i	0.0695046	−	0.0695046i
$964$			386.598i			0.401035i
$965$	−145.953	+	39.8876i	−0.151247	+	0.0413343i
$966$	−98.6209			−0.102092
$967$	995.798	+	995.798i	1.02978	+	1.02978i	0.999543	+	0.0302380i	$0.00962652\pi$
$967$	995.798	+	995.798i	1.02978	+	1.02978i	0.0302380	+	0.999543i	$0.490373\pi$
$968$	−31.1939	+	31.1939i	−0.0322251	+	0.0322251i
$969$			230.562i			0.237938i
$970$	31.6811	−	55.5095i	0.0326609	−	0.0572263i
$971$	−1481.62			−1.52587			−0.762933	−	0.646478i	$-0.776241\pi$
$971$	−1481.62			−1.52587			−0.762933	+	0.646478i	$0.776241\pi$
$972$	−22.0454	−	22.0454i	−0.0226805	−	0.0226805i
$973$	449.620	−	449.620i	0.462096	−	0.462096i
$974$			220.017i			0.225890i
$975$	−860.120	+	508.073i	−0.882174	+	0.521101i
$976$	237.839			0.243687
$977$	−525.657	−	525.657i	−0.538032	−	0.538032i	0.384919	−	0.922950i	$-0.374229\pi$
$977$	−525.657	−	525.657i	−0.538032	−	0.538032i	−0.922950	+	0.384919i	$0.874229\pi$
$978$	482.119	−	482.119i	0.492965	−	0.492965i
$979$			409.245i			0.418024i
$980$	186.544	+	106.467i	0.190351	+	0.108640i
$981$	571.105			0.582166
$982$	−269.756	−	269.756i	−0.274700	−	0.274700i
$983$	158.749	−	158.749i	0.161494	−	0.161494i	−0.621734	−	0.783228i	$-0.713572\pi$
$983$	158.749	−	158.749i	0.161494	−	0.161494i	0.783228	+	0.621734i	$0.213572\pi$
$984$		−	326.627i		−	0.331938i
$985$	118.742	+	434.491i	0.120551	+	0.441107i
$986$	−316.010			−0.320497
$987$	446.561	+	446.561i	0.452443	+	0.452443i
$988$	1110.45	−	1110.45i	1.12394	−	1.12394i
$989$		−	319.660i		−	0.323215i
$990$	−239.158	+	65.3598i	−0.241574	+	0.0660200i
$991$	930.608			0.939060			0.469530	−	0.882917i	$-0.344423\pi$
$991$	930.608			0.939060			0.469530	+	0.882917i	$0.344423\pi$
$992$	111.797	+	111.797i	0.112698	+	0.112698i
$993$	−342.799	+	342.799i	−0.345215	+	0.345215i
$994$		−	901.822i		−	0.907266i
$995$	670.595	−	1174.97i	0.673965	−	1.18088i
$996$	−367.155			−0.368630
$997$	−353.185	−	353.185i	−0.354248	−	0.354248i	0.507440	−	0.861687i	$-0.330592\pi$
$997$	−353.185	−	353.185i	−0.354248	−	0.354248i	−0.861687	+	0.507440i	$0.830592\pi$
$998$	−349.467	+	349.467i	−0.350167	+	0.350167i
$999$		−	88.0986i		−	0.0881868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.a.277.12	✓	40
5.3	odd	4	inner	690.3.k.a.553.12	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.a.277.12	✓	40	1.1	even	1	trivial
690.3.k.a.553.12	yes	40	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-4.34252 - 2.47842i) q^{5} +2.44949 q^{6} +(-5.93628 - 5.93628i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.22474 - 1.22474i) q^{3} +2.00000i q^{4} +(-4.34252 - 2.47842i) q^{5} +2.44949 q^{6} +(-5.93628 - 5.93628i) q^{7} +(-2.00000 + 2.00000i) q^{8} -3.00000i q^{9} +(-1.86410 - 6.82093i) q^{10} +11.6875 q^{11} +(2.44949 + 2.44949i) q^{12} +(-16.3131 + 16.3131i) q^{13} -11.8726i q^{14} +(-8.35390 + 2.28305i) q^{15} -4.00000 q^{16} +(2.76554 + 2.76554i) q^{17} +(3.00000 - 3.00000i) q^{18} +34.0355i q^{19} +(4.95683 - 8.68503i) q^{20} -14.5409 q^{21} +(11.6875 + 11.6875i) q^{22} +(3.39116 - 3.39116i) q^{23} +4.89898i q^{24} +(12.7149 + 21.5251i) q^{25} -32.6263 q^{26} +(-3.67423 - 3.67423i) q^{27} +(11.8726 - 11.8726i) q^{28} +57.1335i q^{29} +(-10.6369 - 6.07086i) q^{30} -27.9492 q^{31} +(-4.00000 - 4.00000i) q^{32} +(14.3142 - 14.3142i) q^{33} +5.53108i q^{34} +(11.0658 + 40.4910i) q^{35} +6.00000 q^{36} +(11.9887 + 11.9887i) q^{37} +(-34.0355 + 34.0355i) q^{38} +39.9589i q^{39} +(13.6419 - 3.72820i) q^{40} -66.6724 q^{41} +(-14.5409 - 14.5409i) q^{42} +(47.1313 - 47.1313i) q^{43} +23.3749i q^{44} +(-7.43525 + 13.0275i) q^{45} +6.78233 q^{46} +(-30.7108 - 30.7108i) q^{47} +(-4.89898 + 4.89898i) q^{48} +21.4788i q^{49} +(-8.81023 + 34.2400i) q^{50} +6.77416 q^{51} +(-32.6263 - 32.6263i) q^{52} +(-31.3399 + 31.3399i) q^{53} -7.34847i q^{54} +(-50.7530 - 28.9664i) q^{55} +23.7451 q^{56} +(41.6848 + 41.6848i) q^{57} +(-57.1335 + 57.1335i) q^{58} +34.2406i q^{59} +(-4.56609 - 16.7078i) q^{60} -59.4597 q^{61} +(-27.9492 - 27.9492i) q^{62} +(-17.8088 + 17.8088i) q^{63} -8.00000i q^{64} +(111.271 - 30.4093i) q^{65} +28.6283 q^{66} +(-14.6139 - 14.6139i) q^{67} +(-5.53108 + 5.53108i) q^{68} -8.30662i q^{69} +(-29.4251 + 51.5568i) q^{70} +75.9585 q^{71} +(6.00000 + 6.00000i) q^{72} +(77.3188 - 77.3188i) q^{73} +23.9774i q^{74} +(41.9353 + 10.7903i) q^{75} -68.0709 q^{76} +(-69.3801 - 69.3801i) q^{77} +(-39.9589 + 39.9589i) q^{78} -141.674i q^{79} +(17.3701 + 9.91367i) q^{80} -9.00000 q^{81} +(-66.6724 - 66.6724i) q^{82} +(-74.9453 + 74.9453i) q^{83} -29.0817i q^{84} +(-5.15524 - 18.8636i) q^{85} +94.2626 q^{86} +(69.9740 + 69.9740i) q^{87} +(-23.3749 + 23.3749i) q^{88} +35.0157i q^{89} +(-20.4628 + 5.59230i) q^{90} +193.679 q^{91} +(6.78233 + 6.78233i) q^{92} +(-34.2306 + 34.2306i) q^{93} -61.4216i q^{94} +(84.3540 - 147.800i) q^{95} -9.79796 q^{96} +(6.39140 + 6.39140i) q^{97} +(-21.4788 + 21.4788i) q^{98} -35.0624i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) \) 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8	\( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) \) 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8 - 16 * q^10 + 32 * q^11 + 16 * q^13 + 24 * q^15 - 160 * q^16 - 48 * q^17 + 120 * q^18 - 16 * q^20 - 96 * q^21 + 32 * q^22 + 32 * q^26 + 16 * q^28 + 24 * q^30 + 152 * q^31 - 160 * q^32 - 24 * q^33 + 48 * q^35 + 240 * q^36 + 216 * q^37 + 16 * q^38 - 168 * q^41 - 96 * q^42 - 48 * q^43 + 24 * q^45 - 232 * q^47 - 40 * q^50 + 32 * q^52 + 8 * q^53 - 272 * q^55 + 32 * q^56 - 136 * q^58 - 64 * q^61 + 152 * q^62 - 24 * q^63 + 416 * q^65 - 48 * q^66 - 32 * q^67 + 96 * q^68 + 88 * q^70 - 104 * q^71 + 240 * q^72 + 480 * q^73 - 216 * q^75 + 32 * q^76 + 280 * q^77 - 192 * q^78 + 32 * q^80 - 360 * q^81 - 168 * q^82 - 576 * q^83 - 208 * q^85 - 96 * q^86 + 24 * q^87 - 64 * q^88 + 144 * q^91 + 96 * q^93 + 168 * q^95 + 24 * q^97 + 176 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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