LMFDB - Embedded newform 690.3.k.b.553.20

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			553.20
Character	$\chi$	$=$	690.553
Dual form			690.3.k.b.277.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-4.82966 + 1.29396i) q^{5} -2.44949 q^{6} +(5.84802 - 5.84802i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-4.82966 + 1.29396i) q^{5} -2.44949 q^{6} +(5.84802 - 5.84802i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(3.53570 - 6.12363i) q^{10} -1.76345 q^{11} +(2.44949 - 2.44949i) q^{12} +(5.00063 + 5.00063i) q^{13} +11.6960i q^{14} +(-7.49988 - 4.33033i) q^{15} -4.00000 q^{16} +(-8.50993 + 8.50993i) q^{17} +(-3.00000 - 3.00000i) q^{18} -22.3969i q^{19} +(2.58793 + 9.65933i) q^{20} +14.3247 q^{21} +(1.76345 - 1.76345i) q^{22} +(3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(21.6513 - 12.4988i) q^{25} -10.0013 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-11.6960 - 11.6960i) q^{28} -38.8089i q^{29} +(11.8302 - 3.16955i) q^{30} +15.0913 q^{31} +(4.00000 - 4.00000i) q^{32} +(-2.15977 - 2.15977i) q^{33} -17.0199i q^{34} +(-20.6769 + 35.8111i) q^{35} +6.00000 q^{36} +(28.5900 - 28.5900i) q^{37} +(22.3969 + 22.3969i) q^{38} +12.2490i q^{39} +(-12.2473 - 7.07140i) q^{40} +63.9487 q^{41} +(-14.3247 + 14.3247i) q^{42} +(34.7533 + 34.7533i) q^{43} +3.52689i q^{44} +(-3.88189 - 14.4890i) q^{45} -6.78233 q^{46} +(2.22777 - 2.22777i) q^{47} +(-4.89898 - 4.89898i) q^{48} -19.3988i q^{49} +(-9.15250 + 34.1501i) q^{50} -20.8450 q^{51} +(10.0013 - 10.0013i) q^{52} +(67.8328 + 67.8328i) q^{53} -7.34847i q^{54} +(8.51686 - 2.28183i) q^{55} +23.3921 q^{56} +(27.4305 - 27.4305i) q^{57} +(38.8089 + 38.8089i) q^{58} +29.3548i q^{59} +(-8.66066 + 14.9998i) q^{60} +54.6267 q^{61} +(-15.0913 + 15.0913i) q^{62} +(17.5441 + 17.5441i) q^{63} +8.00000i q^{64} +(-30.6220 - 17.6807i) q^{65} +4.31954 q^{66} +(14.0005 - 14.0005i) q^{67} +(17.0199 + 17.0199i) q^{68} +8.30662i q^{69} +(-15.1343 - 56.4880i) q^{70} -36.0984 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-58.7921 - 58.7921i) q^{73} +57.1799i q^{74} +(41.8252 + 11.2095i) q^{75} -44.7938 q^{76} +(-10.3127 + 10.3127i) q^{77} +(-12.2490 - 12.2490i) q^{78} +128.176i q^{79} +(19.3187 - 5.17585i) q^{80} -9.00000 q^{81} +(-63.9487 + 63.9487i) q^{82} +(-68.9222 - 68.9222i) q^{83} -28.6494i q^{84} +(30.0886 - 52.1116i) q^{85} -69.5066 q^{86} +(47.5310 - 47.5310i) q^{87} +(-3.52689 - 3.52689i) q^{88} +19.7288i q^{89} +(18.3709 + 10.6071i) q^{90} +58.4876 q^{91} +(6.78233 - 6.78233i) q^{92} +(18.4829 + 18.4829i) q^{93} +4.45554i q^{94} +(28.9808 + 108.170i) q^{95} +9.79796 q^{96} +(85.9628 - 85.9628i) q^{97} +(19.3988 + 19.3988i) q^{98} -5.29034i 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
$5$	−4.82966	+	1.29396i	−0.965933	+	0.258793i
$5$	−4.82966	+	1.29396i	−0.965933	+	0.258793i
$6$	−2.44949			−0.408248
$7$	5.84802	−	5.84802i	0.835432	−	0.835432i	−0.152822	−	0.988254i	$-0.548836\pi$
$7$	5.84802	−	5.84802i	0.835432	−	0.835432i	0.988254	+	0.152822i	$0.0488360\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$			3.00000i			0.333333i
$10$	3.53570	−	6.12363i	0.353570	−	0.612363i
$11$	−1.76345			−0.160313			−0.0801567	−	0.996782i	$-0.525542\pi$
$11$	−1.76345			−0.160313			−0.0801567	+	0.996782i	$0.525542\pi$
$12$	2.44949	−	2.44949i	0.204124	−	0.204124i
$13$	5.00063	+	5.00063i	0.384664	+	0.384664i	0.872779	−	0.488115i	$-0.162315\pi$
$13$	5.00063	+	5.00063i	0.384664	+	0.384664i	−0.488115	+	0.872779i	$0.662315\pi$
$14$			11.6960i			0.835432i
$15$	−7.49988	−	4.33033i	−0.499992	−	0.288689i
$16$	−4.00000			−0.250000
$17$	−8.50993	+	8.50993i	−0.500584	+	0.500584i	−0.911619	−	0.411035i	$-0.865167\pi$
$17$	−8.50993	+	8.50993i	−0.500584	+	0.500584i	0.411035	+	0.911619i	$0.365167\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$		−	22.3969i		−	1.17879i	−0.807847	−	0.589393i	$-0.799367\pi$
$19$		−	22.3969i		−	1.17879i	0.807847	−	0.589393i	$-0.200633\pi$
$20$	2.58793	+	9.65933i	0.129396	+	0.482966i
$21$	14.3247			0.682127
$22$	1.76345	−	1.76345i	0.0801567	−	0.0801567i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$24$			4.89898i			0.204124i
$25$	21.6513	−	12.4988i	0.866053	−	0.499953i
$26$	−10.0013			−0.384664
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	−11.6960	−	11.6960i	−0.417716	−	0.417716i
$29$		−	38.8089i		−	1.33824i	−0.743155	−	0.669120i	$-0.766671\pi$
$29$		−	38.8089i		−	1.33824i	0.743155	−	0.669120i	$-0.233329\pi$
$30$	11.8302	−	3.16955i	0.394340	−	0.105652i
$31$	15.0913			0.486815			0.243407	−	0.969924i	$-0.421735\pi$
$31$	15.0913			0.486815			0.243407	+	0.969924i	$0.421735\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	−2.15977	−	2.15977i	−0.0654476	−	0.0654476i
$34$		−	17.0199i		−	0.500584i
$35$	−20.6769	+	35.8111i	−0.590768	+	1.02318i
$36$	6.00000			0.166667
$37$	28.5900	−	28.5900i	0.772702	−	0.772702i	−0.205876	−	0.978578i	$-0.566004\pi$
$37$	28.5900	−	28.5900i	0.772702	−	0.772702i	0.978578	+	0.205876i	$0.0660044\pi$
$38$	22.3969	+	22.3969i	0.589393	+	0.589393i
$39$			12.2490i			0.314077i
$40$	−12.2473	−	7.07140i	−0.306181	−	0.176785i
$41$	63.9487			1.55972			0.779862	−	0.625951i	$-0.215289\pi$
$41$	63.9487			1.55972			0.779862	+	0.625951i	$0.215289\pi$
$42$	−14.3247	+	14.3247i	−0.341064	+	0.341064i
$43$	34.7533	+	34.7533i	0.808217	+	0.808217i	0.984364	−	0.176147i	$-0.0563634\pi$
$43$	34.7533	+	34.7533i	0.808217	+	0.808217i	−0.176147	+	0.984364i	$0.556363\pi$
$44$			3.52689i			0.0801567i
$45$	−3.88189	−	14.4890i	−0.0862642	−	0.321978i
$46$	−6.78233			−0.147442
$47$	2.22777	−	2.22777i	0.0473994	−	0.0473994i	−0.683010	−	0.730409i	$-0.739329\pi$
$47$	2.22777	−	2.22777i	0.0473994	−	0.0473994i	0.730409	+	0.683010i	$0.239329\pi$
$48$	−4.89898	−	4.89898i	−0.102062	−	0.102062i
$49$		−	19.3988i		−	0.395894i
$50$	−9.15250	+	34.1501i	−0.183050	+	0.683003i
$51$	−20.8450			−0.408725
$52$	10.0013	−	10.0013i	0.192332	−	0.192332i
$53$	67.8328	+	67.8328i	1.27986	+	1.27986i	0.940743	+	0.339121i	$0.110129\pi$
$53$	67.8328	+	67.8328i	1.27986	+	1.27986i	0.339121	+	0.940743i	$0.389871\pi$
$54$		−	7.34847i		−	0.136083i
$55$	8.51686	−	2.28183i	0.154852	−	0.0414879i
$56$	23.3921			0.417716
$57$	27.4305	−	27.4305i	0.481237	−	0.481237i
$58$	38.8089	+	38.8089i	0.669120	+	0.669120i
$59$			29.3548i			0.497538i	0.968563	+	0.248769i	$0.0800260\pi$
$59$			29.3548i			0.497538i	−0.968563	+	0.248769i	$0.919974\pi$
$60$	−8.66066	+	14.9998i	−0.144344	+	0.249996i
$61$	54.6267			0.895520			0.447760	−	0.894154i	$-0.352222\pi$
$61$	54.6267			0.895520			0.447760	+	0.894154i	$0.352222\pi$
$62$	−15.0913	+	15.0913i	−0.243407	+	0.243407i
$63$	17.5441	+	17.5441i	0.278477	+	0.278477i
$64$			8.00000i			0.125000i
$65$	−30.6220	−	17.6807i	−0.471108	−	0.272011i
$66$	4.31954			0.0654476
$67$	14.0005	−	14.0005i	0.208963	−	0.208963i	−0.594864	−	0.803826i	$-0.702794\pi$
$67$	14.0005	−	14.0005i	0.208963	−	0.208963i	0.803826	+	0.594864i	$0.202794\pi$
$68$	17.0199	+	17.0199i	0.250292	+	0.250292i
$69$			8.30662i			0.120386i
$70$	−15.1343	−	56.4880i	−0.216204	−	0.806971i
$71$	−36.0984			−0.508428			−0.254214	−	0.967148i	$-0.581817\pi$
$71$	−36.0984			−0.508428			−0.254214	+	0.967148i	$0.581817\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	−58.7921	−	58.7921i	−0.805371	−	0.805371i	0.178558	−	0.983929i	$-0.442857\pi$
$73$	−58.7921	−	58.7921i	−0.805371	−	0.805371i	−0.983929	+	0.178558i	$0.942857\pi$
$74$			57.1799i			0.772702i
$75$	41.8252	+	11.2095i	0.557669	+	0.149460i
$76$	−44.7938			−0.589393
$77$	−10.3127	+	10.3127i	−0.133931	+	0.133931i
$78$	−12.2490	−	12.2490i	−0.157038	−	0.157038i
$79$			128.176i			1.62248i	0.584713	+	0.811240i	$0.301207\pi$
$79$			128.176i			1.62248i	−0.584713	+	0.811240i	$0.698793\pi$
$80$	19.3187	−	5.17585i	0.241483	−	0.0646982i
$81$	−9.00000			−0.111111
$82$	−63.9487	+	63.9487i	−0.779862	+	0.779862i
$83$	−68.9222	−	68.9222i	−0.830389	−	0.830389i	0.157181	−	0.987570i	$-0.449759\pi$
$83$	−68.9222	−	68.9222i	−0.830389	−	0.830389i	−0.987570	+	0.157181i	$0.949759\pi$
$84$		−	28.6494i		−	0.341064i
$85$	30.0886	−	52.1116i	0.353983	−	0.613078i
$86$	−69.5066			−0.808217
$87$	47.5310	−	47.5310i	0.546334	−	0.546334i
$88$	−3.52689	−	3.52689i	−0.0400783	−	0.0400783i
$89$			19.7288i			0.221672i	0.993839	+	0.110836i	$0.0353529\pi$
$89$			19.7288i			0.221672i	−0.993839	+	0.110836i	$0.964647\pi$
$90$	18.3709	+	10.6071i	0.204121	+	0.117857i
$91$	58.4876			0.642721
$92$	6.78233	−	6.78233i	0.0737210	−	0.0737210i
$93$	18.4829	+	18.4829i	0.198741	+	0.198741i
$94$			4.45554i			0.0473994i
$95$	28.9808	+	108.170i	0.305061	+	1.13863i
$96$	9.79796			0.102062
$97$	85.9628	−	85.9628i	0.886215	−	0.886215i	−0.107942	−	0.994157i	$-0.534426\pi$
$97$	85.9628	−	85.9628i	0.886215	−	0.886215i	0.994157	+	0.107942i	$0.0344262\pi$
$98$	19.3988	+	19.3988i	0.197947	+	0.197947i
$99$		−	5.29034i		−	0.0534378i
$100$	−24.9976	−	43.3026i	−0.249976	−	0.433026i
$101$	−9.56680			−0.0947207			−0.0473604	−	0.998878i	$-0.515081\pi$
$101$	−9.56680			−0.0947207			−0.0473604	+	0.998878i	$0.515081\pi$
$102$	20.8450	−	20.8450i	0.204363	−	0.204363i
$103$	52.1473	+	52.1473i	0.506284	+	0.506284i	0.913384	−	0.407100i	$-0.133460\pi$
$103$	52.1473	+	52.1473i	0.506284	+	0.506284i	−0.407100	+	0.913384i	$0.633460\pi$
$104$			20.0025i			0.192332i
$105$	−69.1834	+	18.5356i	−0.658889	+	0.176530i
$106$	−135.666			−1.27986
$107$	125.340	−	125.340i	1.17140	−	1.17140i	0.189525	−	0.981876i	$-0.439305\pi$
$107$	125.340	−	125.340i	1.17140	−	1.17140i	0.981876	−	0.189525i	$-0.0606947\pi$
$108$	7.34847	+	7.34847i	0.0680414	+	0.0680414i
$109$			65.7207i			0.602942i	0.953475	+	0.301471i	$0.0974777\pi$
$109$			65.7207i			0.602942i	−0.953475	+	0.301471i	$0.902522\pi$
$110$	−6.23502	+	10.7987i	−0.0566820	+	0.0981699i
$111$	70.0308			0.630908
$112$	−23.3921	+	23.3921i	−0.208858	+	0.208858i
$113$	50.2423	+	50.2423i	0.444622	+	0.444622i	0.893562	−	0.448940i	$-0.148198\pi$
$113$	50.2423	+	50.2423i	0.444622	+	0.444622i	−0.448940	+	0.893562i	$0.648198\pi$
$114$			54.8610i			0.481237i
$115$	−20.7662	−	11.9901i	−0.180576	−	0.104262i
$116$	−77.6179			−0.669120
$117$	−15.0019	+	15.0019i	−0.128221	+	0.128221i
$118$	−29.3548	−	29.3548i	−0.248769	−	0.248769i
$119$			99.5325i			0.836408i
$120$	−6.33910	−	23.6604i	−0.0528258	−	0.197170i
$121$	−117.890			−0.974300
$122$	−54.6267	+	54.6267i	−0.447760	+	0.447760i
$123$	78.3209	+	78.3209i	0.636755	+	0.636755i
$124$		−	30.1825i		−	0.243407i
$125$	−88.3956	+	88.3811i	−0.707165	+	0.707049i
$126$	−35.0881			−0.278477
$127$	87.1032	−	87.1032i	0.685852	−	0.685852i	−0.275461	−	0.961312i	$-0.588830\pi$
$127$	87.1032	−	87.1032i	0.685852	−	0.685852i	0.961312	+	0.275461i	$0.0888304\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$			85.1279i			0.659906i
$130$	48.3027	−	12.9413i	0.371560	−	0.0995482i
$131$	151.951			1.15993			0.579966	−	0.814641i	$-0.303066\pi$
$131$	151.951			1.15993			0.579966	+	0.814641i	$0.303066\pi$
$132$	−4.31954	+	4.31954i	−0.0327238	+	0.0327238i
$133$	−130.978	−	130.978i	−0.984795	−	0.984795i
$134$			28.0010i			0.208963i
$135$	12.9910	−	22.4996i	0.0962296	−	0.166664i
$136$	−34.0397			−0.250292
$137$	67.2320	−	67.2320i	0.490745	−	0.490745i	−0.417796	−	0.908541i	$-0.637197\pi$
$137$	67.2320	−	67.2320i	0.490745	−	0.490745i	0.908541	+	0.417796i	$0.137197\pi$
$138$	−8.30662	−	8.30662i	−0.0601929	−	0.0601929i
$139$			147.787i			1.06322i	0.846990	+	0.531610i	$0.178413\pi$
$139$			147.787i			1.06322i	−0.846990	+	0.531610i	$0.821587\pi$
$140$	71.6223	+	41.3537i	0.511588	+	0.295384i
$141$	5.45691			0.0387015
$142$	36.0984	−	36.0984i	0.254214	−	0.254214i
$143$	−8.81835	−	8.81835i	−0.0616668	−	0.0616668i
$144$		−	12.0000i		−	0.0833333i
$145$	50.2173	+	187.434i	0.346326	+	1.29265i
$146$	117.584			0.805371
$147$	23.7586	−	23.7586i	0.161623	−	0.161623i
$148$	−57.1799	−	57.1799i	−0.386351	−	0.386351i
$149$		−	34.3711i		−	0.230678i	−0.993326	−	0.115339i	$-0.963205\pi$
$149$		−	34.3711i		−	0.230678i	0.993326	−	0.115339i	$-0.0367955\pi$
$150$	−53.0347	+	30.6157i	−0.353565	+	0.204105i
$151$	−187.555			−1.24208			−0.621042	−	0.783777i	$-0.713290\pi$
$151$	−187.555			−1.24208			−0.621042	+	0.783777i	$0.713290\pi$
$152$	44.7938	−	44.7938i	0.294696	−	0.294696i
$153$	−25.5298	−	25.5298i	−0.166861	−	0.166861i
$154$		−	20.6254i		−	0.133931i
$155$	−72.8857	+	19.5275i	−0.470230	+	0.125984i
$156$	24.4980			0.157038
$157$	173.198	−	173.198i	1.10317	−	1.10317i	0.109147	−	0.994026i	$-0.465188\pi$
$157$	173.198	−	173.198i	1.10317	−	1.10317i	0.994026	−	0.109147i	$-0.0348120\pi$
$158$	−128.176	−	128.176i	−0.811240	−	0.811240i
$159$			166.156i			1.04500i
$160$	−14.1428	+	24.4945i	−0.0883925	+	0.153091i
$161$	39.6632			0.246355
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	−12.3280	−	12.3280i	−0.0756321	−	0.0756321i	0.668279	−	0.743911i	$-0.267031\pi$
$163$	−12.3280	−	12.3280i	−0.0756321	−	0.0756321i	−0.743911	+	0.668279i	$0.767031\pi$
$164$		−	127.897i		−	0.779862i
$165$	13.2256	+	7.63631i	0.0801554	+	0.0462807i
$166$	137.844			0.830389
$167$	67.8791	−	67.8791i	0.406461	−	0.406461i	−0.474041	−	0.880503i	$-0.657205\pi$
$167$	67.8791	−	67.8791i	0.406461	−	0.406461i	0.880503	+	0.474041i	$0.157205\pi$
$168$	28.6494	+	28.6494i	0.170532	+	0.170532i
$169$		−	118.987i		−	0.704067i
$170$	22.0231	+	82.2002i	0.129547	+	0.483531i
$171$	67.1908			0.392928
$172$	69.5066	−	69.5066i	0.404108	−	0.404108i
$173$	36.4436	+	36.4436i	0.210656	+	0.210656i	0.804546	−	0.593890i	$-0.202409\pi$
$173$	36.4436	+	36.4436i	0.210656	+	0.210656i	−0.593890	+	0.804546i	$0.702409\pi$
$174$			95.0621i			0.546334i
$175$	53.5241	−	199.711i	0.305852	−	1.14120i
$176$	7.05379			0.0400783
$177$	−35.9521	+	35.9521i	−0.203119	+	0.203119i
$178$	−19.7288	−	19.7288i	−0.110836	−	0.110836i
$179$			96.1704i			0.537265i	0.963243	+	0.268633i	$0.0865717\pi$
$179$			96.1704i			0.537265i	−0.963243	+	0.268633i	$0.913428\pi$
$180$	−28.9780	+	7.76378i	−0.160989	+	0.0431321i
$181$	204.330			1.12889			0.564447	−	0.825469i	$-0.309089\pi$
$181$	204.330			1.12889			0.564447	+	0.825469i	$0.309089\pi$
$182$	−58.4876	+	58.4876i	−0.321361	+	0.321361i
$183$	66.9038	+	66.9038i	0.365594	+	0.365594i
$184$			13.5647i			0.0737210i
$185$	−101.086	+	175.074i	−0.546409	+	0.946348i
$186$	−36.9659			−0.198741
$187$	15.0068	−	15.0068i	0.0802503	−	0.0802503i
$188$	−4.45554	−	4.45554i	−0.0236997	−	0.0236997i
$189$			42.9740i			0.227376i
$190$	−137.150	−	79.1888i	−0.721844	−	0.416783i
$191$	−103.300			−0.540835			−0.270418	−	0.962743i	$-0.587162\pi$
$191$	−103.300			−0.540835			−0.270418	+	0.962743i	$0.587162\pi$
$192$	−9.79796	+	9.79796i	−0.0510310	+	0.0510310i
$193$	21.4091	+	21.4091i	0.110928	+	0.110928i	0.760392	−	0.649464i	$-0.225007\pi$
$193$	21.4091	+	21.4091i	0.110928	+	0.110928i	−0.649464	+	0.760392i	$0.725007\pi$
$194$			171.926i			0.886215i
$195$	−15.8497	−	59.1585i	−0.0812807	−	0.303377i
$196$	−38.7976			−0.197947
$197$	5.19419	−	5.19419i	0.0263664	−	0.0263664i	−0.693801	−	0.720167i	$-0.744065\pi$
$197$	5.19419	−	5.19419i	0.0263664	−	0.0263664i	0.720167	+	0.693801i	$0.244065\pi$
$198$	5.29034	+	5.29034i	0.0267189	+	0.0267189i
$199$		−	343.482i		−	1.72604i	−0.505168	−	0.863021i	$-0.668570\pi$
$199$		−	343.482i		−	1.72604i	0.505168	−	0.863021i	$-0.331430\pi$
$200$	68.3003	+	18.3050i	0.341501	+	0.0915250i
$201$	34.2941			0.170617
$202$	9.56680	−	9.56680i	0.0473604	−	0.0473604i
$203$	−226.956	−	226.956i	−1.11801	−	1.11801i
$204$			41.6900i			0.204363i
$205$	−308.851	+	82.7473i	−1.50659	+	0.403645i
$206$	−104.295			−0.506284
$207$	−10.1735	+	10.1735i	−0.0491473	+	0.0491473i
$208$	−20.0025	−	20.0025i	−0.0961660	−	0.0961660i
$209$			39.4958i			0.188975i
$210$	50.6478	−	87.7190i	0.241180	−	0.417709i
$211$	−203.788			−0.965819			−0.482910	−	0.875670i	$-0.660420\pi$
$211$	−203.788			−0.965819			−0.482910	+	0.875670i	$0.660420\pi$
$212$	135.666	−	135.666i	0.639932	−	0.639932i
$213$	−44.2113	−	44.2113i	−0.207565	−	0.207565i
$214$			250.680i			1.17140i
$215$	−212.816	−	122.877i	−0.989844	−	0.571523i
$216$	−14.6969			−0.0680414
$217$	88.2540	−	88.2540i	0.406701	−	0.406701i
$218$	−65.7207	−	65.7207i	−0.301471	−	0.301471i
$219$		−	144.011i		−	0.657583i
$220$	−4.56367	−	17.0337i	−0.0207440	−	0.0774260i
$221$	−85.1100			−0.385113
$222$	−70.0308	+	70.0308i	−0.315454	+	0.315454i
$223$	−232.124	−	232.124i	−1.04091	−	1.04091i	−0.999126	−	0.0417883i	$-0.986694\pi$
$223$	−232.124	−	232.124i	−1.04091	−	1.04091i	−0.0417883	−	0.999126i	$-0.513306\pi$
$224$		−	46.7842i		−	0.208858i
$225$	37.4964	+	64.9540i	0.166651	+	0.288684i
$226$	−100.485			−0.444622
$227$	−184.343	+	184.343i	−0.812082	+	0.812082i	−0.984946	−	0.172863i	$-0.944698\pi$
$227$	−184.343	+	184.343i	−0.812082	+	0.812082i	0.172863	+	0.984946i	$0.444698\pi$
$228$	−54.8610	−	54.8610i	−0.240619	−	0.240619i
$229$		−	223.254i		−	0.974908i	−0.873149	−	0.487454i	$-0.837926\pi$
$229$		−	223.254i		−	0.974908i	0.873149	−	0.487454i	$-0.162074\pi$
$230$	32.7564	−	8.77608i	0.142419	−	0.0381569i
$231$	−25.2608			−0.109354
$232$	77.6179	−	77.6179i	0.334560	−	0.334560i
$233$	−296.194	−	296.194i	−1.27122	−	1.27122i	−0.945449	−	0.325769i	$-0.894377\pi$
$233$	−296.194	−	296.194i	−1.27122	−	1.27122i	−0.325769	−	0.945449i	$-0.605623\pi$
$234$		−	30.0038i		−	0.128221i
$235$	−7.87674	+	13.6420i	−0.0335180	+	0.0580513i
$236$	58.7095			0.248769
$237$	−156.983	+	156.983i	−0.662375	+	0.662375i
$238$	−99.5325	−	99.5325i	−0.418204	−	0.418204i
$239$			2.15755i			0.00902741i	0.999990	+	0.00451370i	$0.00143676\pi$
$239$			2.15755i			0.00902741i	−0.999990	+	0.00451370i	$0.998563\pi$
$240$	29.9995	+	17.3213i	0.124998	+	0.0721722i
$241$	−136.072			−0.564612			−0.282306	−	0.959324i	$-0.591099\pi$
$241$	−136.072			−0.564612			−0.282306	+	0.959324i	$0.591099\pi$
$242$	117.890	−	117.890i	0.487150	−	0.487150i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$		−	109.253i		−	0.447760i
$245$	25.1013	+	93.6896i	0.102454	+	0.382407i
$246$	−156.642			−0.636755
$247$	111.999	−	111.999i	0.453436	−	0.453436i
$248$	30.1825	+	30.1825i	0.121704	+	0.121704i
$249$		−	168.824i		−	0.678009i
$250$	0.0145100	−	176.777i	5.80400e−5	−	0.707107i
$251$	191.977			0.764848			0.382424	−	0.923987i	$-0.375089\pi$
$251$	191.977			0.764848			0.382424	+	0.923987i	$0.375089\pi$
$252$	35.0881	−	35.0881i	0.139239	−	0.139239i
$253$	−5.98014	−	5.98014i	−0.0236369	−	0.0236369i
$254$			174.206i			0.685852i
$255$	100.674	−	26.9726i	0.394801	−	0.105775i
$256$	16.0000			0.0625000
$257$	100.820	−	100.820i	0.392294	−	0.392294i	−0.483210	−	0.875504i	$-0.660529\pi$
$257$	100.820	−	100.820i	0.392294	−	0.392294i	0.875504	+	0.483210i	$0.160529\pi$
$258$	−85.1279	−	85.1279i	−0.329953	−	0.329953i
$259$		−	334.390i		−	1.29108i
$260$	−35.3615	+	61.2440i	−0.136006	+	0.235554i
$261$	116.427			0.446080
$262$	−151.951	+	151.951i	−0.579966	+	0.579966i
$263$	−162.391	−	162.391i	−0.617455	−	0.617455i	0.327423	−	0.944878i	$-0.393820\pi$
$263$	−162.391	−	162.391i	−0.617455	−	0.617455i	−0.944878	+	0.327423i	$0.893820\pi$
$264$		−	8.63909i		−	0.0327238i
$265$	−415.383	−	239.836i	−1.56748	−	0.905043i
$266$	261.955			0.984795
$267$	−24.1628	+	24.1628i	−0.0904973	+	0.0904973i
$268$	−28.0010	−	28.0010i	−0.104481	−	0.104481i
$269$			166.072i			0.617366i	0.951165	+	0.308683i	$0.0998883\pi$
$269$			166.072i			0.617366i	−0.951165	+	0.308683i	$0.900112\pi$
$270$	9.50865	+	35.4906i	0.0352172	+	0.131447i
$271$	−309.336			−1.14146			−0.570731	−	0.821137i	$-0.693340\pi$
$271$	−309.336			−1.14146			−0.570731	+	0.821137i	$0.693340\pi$
$272$	34.0397	−	34.0397i	0.125146	−	0.125146i
$273$	71.6324	+	71.6324i	0.262390	+	0.262390i
$274$			134.464i			0.490745i
$275$	−38.1809	+	22.0410i	−0.138840	+	0.0801491i
$276$	16.6132			0.0601929
$277$	−265.998	+	265.998i	−0.960281	+	0.960281i	−0.999241	−	0.0389595i	$-0.987596\pi$
$277$	−265.998	+	265.998i	−0.960281	+	0.960281i	0.0389595	+	0.999241i	$0.487596\pi$
$278$	−147.787	−	147.787i	−0.531610	−	0.531610i
$279$			45.2738i			0.162272i
$280$	−112.976	+	30.2685i	−0.403486	+	0.108102i
$281$	57.9240			0.206135			0.103068	−	0.994674i	$-0.467134\pi$
$281$	57.9240			0.206135			0.103068	+	0.994674i	$0.467134\pi$
$282$	−5.45691	+	5.45691i	−0.0193507	+	0.0193507i
$283$	−116.179	−	116.179i	−0.410525	−	0.410525i	0.471396	−	0.881922i	$-0.343750\pi$
$283$	−116.179	−	116.179i	−0.410525	−	0.410525i	−0.881922	+	0.471396i	$0.843750\pi$
$284$			72.1968i			0.254214i
$285$	−96.9861	+	167.974i	−0.340302	+	0.589383i
$286$	17.6367			0.0616668
$287$	373.974	−	373.974i	1.30304	−	1.30304i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$			144.162i			0.498831i
$290$	−237.651	−	137.217i	−0.819488	−	0.473161i
$291$	210.565			0.723591
$292$	−117.584	+	117.584i	−0.402686	+	0.402686i
$293$	189.001	+	189.001i	0.645056	+	0.645056i	0.951794	−	0.306738i	$-0.0992376\pi$
$293$	189.001	+	189.001i	0.645056	+	0.645056i	−0.306738	+	0.951794i	$0.599238\pi$
$294$			47.5171i			0.161623i
$295$	−37.9840	−	141.774i	−0.128759	−	0.480588i
$296$	114.360			0.386351
$297$	6.47932	−	6.47932i	0.0218159	−	0.0218159i
$298$	34.3711	+	34.3711i	0.115339	+	0.115339i
$299$			33.9159i			0.113431i
$300$	22.4190	−	83.6504i	0.0747299	−	0.278835i
$301$	406.477			1.35042
$302$	187.555	−	187.555i	0.621042	−	0.621042i
$303$	−11.7169	−	11.7169i	−0.0386696	−	0.0386696i
$304$			89.5877i			0.294696i
$305$	−263.829	+	70.6849i	−0.865012	+	0.231754i
$306$	51.0596			0.166861
$307$	307.822	−	307.822i	1.00268	−	1.00268i	0.00268029	−	0.999996i	$-0.499147\pi$
$307$	307.822	−	307.822i	1.00268	−	1.00268i	0.999996	−	0.00268029i	$-0.000853164\pi$
$308$	20.6254	+	20.6254i	0.0669655	+	0.0669655i
$309$			127.734i			0.413379i
$310$	53.3582	−	92.4132i	0.172123	−	0.298107i
$311$	−529.789			−1.70350			−0.851750	−	0.523948i	$-0.824459\pi$
$311$	−529.789			−1.70350			−0.851750	+	0.523948i	$0.824459\pi$
$312$	−24.4980	+	24.4980i	−0.0785192	+	0.0785192i
$313$	64.3377	+	64.3377i	0.205552	+	0.205552i	0.802374	−	0.596822i	$-0.203570\pi$
$313$	64.3377	+	64.3377i	0.205552	+	0.205552i	−0.596822	+	0.802374i	$0.703570\pi$
$314$			346.396i			1.10317i
$315$	−107.433	−	62.0306i	−0.341058	−	0.196923i
$316$	256.352			0.811240
$317$	−393.031	+	393.031i	−1.23985	+	1.23985i	−0.279781	+	0.960064i	$0.590262\pi$
$317$	−393.031	+	393.031i	−1.23985	+	1.23985i	−0.960064	+	0.279781i	$0.909738\pi$
$318$	−166.156	−	166.156i	−0.522502	−	0.522502i
$319$			68.4375i			0.214538i
$320$	−10.3517	−	38.6373i	−0.0323491	−	0.120742i
$321$	307.019			0.956445
$322$	−39.6632	+	39.6632i	−0.123178	+	0.123178i
$323$	190.596	+	190.596i	0.590081	+	0.590081i
$324$			18.0000i			0.0555556i
$325$	170.772	+	45.7683i	0.525453	+	0.140826i
$326$	24.6561			0.0756321
$327$	−80.4911	+	80.4911i	−0.246150	+	0.246150i
$328$	127.897	+	127.897i	0.389931	+	0.389931i
$329$		−	26.0561i		−	0.0791980i
$330$	−20.8620	+	5.58933i	−0.0632180	+	0.0169374i
$331$	179.754			0.543064			0.271532	−	0.962429i	$-0.412470\pi$
$331$	179.754			0.543064			0.271532	+	0.962429i	$0.412470\pi$
$332$	−137.844	+	137.844i	−0.415194	+	0.415194i
$333$	85.7699	+	85.7699i	0.257567	+	0.257567i
$334$			135.758i			0.406461i
$335$	−49.5016	+	85.7338i	−0.147766	+	0.255922i
$336$	−57.2987			−0.170532
$337$	−118.371	+	118.371i	−0.351251	+	0.351251i	−0.860575	−	0.509324i	$-0.829895\pi$
$337$	−118.371	+	118.371i	−0.351251	+	0.351251i	0.509324	+	0.860575i	$0.329895\pi$
$338$	118.987	+	118.987i	0.352034	+	0.352034i
$339$			123.068i			0.363033i
$340$	−104.223	−	60.1771i	−0.306539	−	0.176992i
$341$	−26.6126			−0.0780429
$342$	−67.1908	+	67.1908i	−0.196464	+	0.196464i
$343$	173.109	+	173.109i	0.504690	+	0.504690i
$344$			139.013i			0.404108i
$345$	−10.7485	−	40.1182i	−0.0311550	−	0.116285i
$346$	−72.8871			−0.210656
$347$	379.530	−	379.530i	1.09375	−	1.09375i	0.0986223	−	0.995125i	$-0.468556\pi$
$347$	379.530	−	379.530i	1.09375	−	1.09375i	0.995125	−	0.0986223i	$-0.0314436\pi$
$348$	−95.0621	−	95.0621i	−0.273167	−	0.273167i
$349$			540.641i			1.54912i	0.632503	+	0.774558i	$0.282027\pi$
$349$			540.641i			1.54912i	−0.632503	+	0.774558i	$0.717973\pi$
$350$	146.187	+	253.235i	0.417676	+	0.723528i
$351$	−36.7470			−0.104692
$352$	−7.05379	+	7.05379i	−0.0200392	+	0.0200392i
$353$	51.2669	+	51.2669i	0.145232	+	0.145232i	0.775984	−	0.630752i	$-0.217254\pi$
$353$	51.2669	+	51.2669i	0.145232	+	0.145232i	−0.630752	+	0.775984i	$0.717254\pi$
$354$		−	71.9042i		−	0.203119i
$355$	174.343	−	46.7100i	0.491107	−	0.131577i
$356$	39.4577			0.110836
$357$	−121.902	+	121.902i	−0.341462	+	0.341462i
$358$	−96.1704	−	96.1704i	−0.268633	−	0.268633i
$359$		−	217.517i		−	0.605898i	−0.953007	−	0.302949i	$-0.902029\pi$
$359$		−	217.517i		−	0.605898i	0.953007	−	0.302949i	$-0.0979712\pi$
$360$	21.2142	−	36.7418i	0.0589284	−	0.102060i
$361$	−140.622			−0.389534
$362$	−204.330	+	204.330i	−0.564447	+	0.564447i
$363$	−144.385	−	144.385i	−0.397756	−	0.397756i
$364$		−	116.975i		−	0.321361i
$365$	360.021	+	207.871i	0.986358	+	0.569510i
$366$	−133.808			−0.365594
$367$	−391.093	+	391.093i	−1.06565	+	1.06565i	−0.0679602	+	0.997688i	$0.521649\pi$
$367$	−391.093	+	391.093i	−1.06565	+	1.06565i	−0.997688	+	0.0679602i	$0.978351\pi$
$368$	−13.5647	−	13.5647i	−0.0368605	−	0.0368605i
$369$			191.846i			0.519908i
$370$	−73.9887	−	276.160i	−0.199970	−	0.746378i
$371$	793.375			2.13848
$372$	36.9659	−	36.9659i	0.0993706	−	0.0993706i
$373$	281.397	+	281.397i	0.754414	+	0.754414i	0.975300	−	0.220885i	$-0.0708947\pi$
$373$	281.397	+	281.397i	0.754414	+	0.754414i	−0.220885	+	0.975300i	$0.570895\pi$
$374$			30.0136i			0.0802503i
$375$	−216.506	−	0.0177710i	−0.577350	−	4.73894e-5i
$376$	8.91109			0.0236997
$377$	194.069	−	194.069i	0.514772	−	0.514772i
$378$	−42.9740	−	42.9740i	−0.113688	−	0.113688i
$379$			450.647i			1.18904i	0.804080	+	0.594521i	$0.202658\pi$
$379$			450.647i			1.18904i	−0.804080	+	0.594521i	$0.797342\pi$
$380$	216.339	−	57.9616i	0.569314	−	0.152530i
$381$	213.358			0.559996
$382$	103.300	−	103.300i	0.270418	−	0.270418i
$383$	−120.781	−	120.781i	−0.315354	−	0.315354i	0.531625	−	0.846980i	$-0.321581\pi$
$383$	−120.781	−	120.781i	−0.315354	−	0.315354i	−0.846980	+	0.531625i	$0.821581\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	36.4626	−	63.1510i	0.0947079	−	0.164029i
$386$	−42.8181			−0.110928
$387$	−104.260	+	104.260i	−0.269406	+	0.269406i
$388$	−171.926	−	171.926i	−0.443107	−	0.443107i
$389$		−	136.553i		−	0.351035i	−0.984476	−	0.175518i	$-0.943840\pi$
$389$		−	136.553i		−	0.351035i	0.984476	−	0.175518i	$-0.0561599\pi$
$390$	75.0083	+	43.3088i	0.192329	+	0.111048i
$391$	−57.7171			−0.147614
$392$	38.7976	−	38.7976i	0.0989734	−	0.0989734i
$393$	186.101	+	186.101i	0.473540	+	0.473540i
$394$			10.3884i			0.0263664i
$395$	−165.855	−	619.047i	−0.419886	−	1.56721i
$396$	−10.5807			−0.0267189
$397$	−11.6153	+	11.6153i	−0.0292576	+	0.0292576i	−0.721584	−	0.692327i	$-0.756586\pi$
$397$	−11.6153	+	11.6153i	−0.0292576	+	0.0292576i	0.692327	+	0.721584i	$0.256586\pi$
$398$	343.482	+	343.482i	0.863021	+	0.863021i
$399$		−	320.829i		−	0.804082i
$400$	−86.6053	+	49.9953i	−0.216513	+	0.124988i
$401$	−325.917			−0.812760			−0.406380	−	0.913704i	$-0.633209\pi$
$401$	−325.917			−0.812760			−0.406380	+	0.913704i	$0.633209\pi$
$402$	−34.2941	+	34.2941i	−0.0853086	+	0.0853086i
$403$	75.4658	+	75.4658i	0.187260	+	0.187260i
$404$			19.1336i			0.0473604i
$405$	43.4670	−	11.6457i	0.107326	−	0.0287547i
$406$	453.911			1.11801
$407$	−50.4169	+	50.4169i	−0.123874	+	0.123874i
$408$	−41.6900	−	41.6900i	−0.102181	−	0.102181i
$409$			447.168i			1.09332i	0.837354	+	0.546661i	$0.184101\pi$
$409$			447.168i			1.09332i	−0.837354	+	0.546661i	$0.815899\pi$
$410$	226.104	−	391.598i	0.551472	−	0.955117i
$411$	164.684			0.400691
$412$	104.295	−	104.295i	0.253142	−	0.253142i
$413$	171.667	+	171.667i	0.415659	+	0.415659i
$414$		−	20.3470i		−	0.0491473i
$415$	422.054	+	243.688i	1.01700	+	0.587201i
$416$	40.0050			0.0961660
$417$	−181.002	+	181.002i	−0.434057	+	0.434057i
$418$	−39.4958	−	39.4958i	−0.0944875	−	0.0944875i
$419$		−	356.216i		−	0.850157i	−0.905157	−	0.425078i	$-0.860247\pi$
$419$		−	356.216i		−	0.850157i	0.905157	−	0.425078i	$-0.139753\pi$
$420$	37.0712	+	138.367i	0.0882648	+	0.329445i
$421$	415.752			0.987534			0.493767	−	0.869594i	$-0.335620\pi$
$421$	415.752			0.987534			0.493767	+	0.869594i	$0.335620\pi$
$422$	203.788	−	203.788i	0.482910	−	0.482910i
$423$	6.68332	+	6.68332i	0.0157998	+	0.0157998i
$424$			271.331i			0.639932i
$425$	−77.8872	+	290.615i	−0.183264	+	0.683801i
$426$	88.4227			0.207565
$427$	319.458	−	319.458i	0.748146	−	0.748146i
$428$	−250.680	−	250.680i	−0.585700	−	0.585700i
$429$		−	21.6004i		−	0.0503507i
$430$	335.694	−	89.9390i	0.780683	−	0.209161i
$431$	−456.460			−1.05907			−0.529536	−	0.848287i	$-0.677634\pi$
$431$	−456.460			−1.05907			−0.529536	+	0.848287i	$0.677634\pi$
$432$	14.6969	−	14.6969i	0.0340207	−	0.0340207i
$433$	−56.6111	−	56.6111i	−0.130741	−	0.130741i	0.638708	−	0.769449i	$-0.279469\pi$
$433$	−56.6111	−	56.6111i	−0.130741	−	0.130741i	−0.769449	+	0.638708i	$0.779469\pi$
$434$			176.508i			0.406701i
$435$	−168.056	+	291.062i	−0.386335	+	0.669109i
$436$	131.441			0.301471
$437$	75.9516	−	75.9516i	0.173802	−	0.173802i
$438$	144.011	+	144.011i	0.328791	+	0.328791i
$439$			533.763i			1.21586i	0.793990	+	0.607931i	$0.208000\pi$
$439$			533.763i			1.21586i	−0.793990	+	0.607931i	$0.792000\pi$
$440$	21.5974	+	12.4700i	0.0490850	+	0.0283410i
$441$	58.1964			0.131965
$442$	85.1100	−	85.1100i	0.192557	−	0.192557i
$443$	−308.316	−	308.316i	−0.695973	−	0.695973i	0.267567	−	0.963539i	$-0.413780\pi$
$443$	−308.316	−	308.316i	−0.695973	−	0.695973i	−0.963539	+	0.267567i	$0.913780\pi$
$444$		−	140.062i		−	0.315454i
$445$	−25.5284	−	95.2836i	−0.0573671	−	0.214121i
$446$	464.248			1.04091
$447$	42.0958	−	42.0958i	0.0941740	−	0.0941740i
$448$	46.7842	+	46.7842i	0.104429	+	0.104429i
$449$		−	479.262i		−	1.06740i	−0.845674	−	0.533699i	$-0.820801\pi$
$449$		−	479.262i		−	1.06740i	0.845674	−	0.533699i	$-0.179199\pi$
$450$	−102.450	−	27.4575i	−0.227668	−	0.0610167i
$451$	−112.770			−0.250045
$452$	100.485	−	100.485i	0.222311	−	0.222311i
$453$	−229.707	−	229.707i	−0.507079	−	0.507079i
$454$		−	368.685i		−	0.812082i
$455$	−282.476	+	75.6808i	−0.620825	+	0.166331i
$456$	109.722			0.240619
$457$	121.058	−	121.058i	0.264898	−	0.264898i	−0.562142	−	0.827040i	$-0.690023\pi$
$457$	121.058	−	121.058i	0.264898	−	0.264898i	0.827040	+	0.562142i	$0.190023\pi$
$458$	223.254	+	223.254i	0.487454	+	0.487454i
$459$		−	62.5350i		−	0.136242i
$460$	−23.9803	+	41.5325i	−0.0521311	+	0.0902880i
$461$	−130.197			−0.282423			−0.141211	−	0.989979i	$-0.545100\pi$
$461$	−130.197			−0.282423			−0.141211	+	0.989979i	$0.545100\pi$
$462$	25.2608	−	25.2608i	0.0546771	−	0.0546771i
$463$	−84.8852	−	84.8852i	−0.183337	−	0.183337i	0.609471	−	0.792808i	$-0.291382\pi$
$463$	−84.8852	−	84.8852i	−0.183337	−	0.183337i	−0.792808	+	0.609471i	$0.791382\pi$
$464$			155.236i			0.334560i
$465$	−113.183	−	65.3501i	−0.243403	−	0.140538i
$466$	592.388			1.27122
$467$	93.2186	−	93.2186i	0.199612	−	0.199612i	−0.600222	−	0.799834i	$-0.704921\pi$
$467$	93.2186	−	93.2186i	0.199612	−	0.199612i	0.799834	+	0.600222i	$0.204921\pi$
$468$	30.0038	+	30.0038i	0.0641107	+	0.0641107i
$469$		−	163.751i		−	0.349148i
$470$	−5.76531	−	21.5188i	−0.0122666	−	0.0457846i
$471$	424.247			0.900737
$472$	−58.7095	+	58.7095i	−0.124385	+	0.124385i
$473$	−61.2856	−	61.2856i	−0.129568	−	0.129568i
$474$		−	313.966i		−	0.662375i
$475$	−279.935	−	484.923i	−0.589337	−	1.02089i
$476$	199.065			0.418204
$477$	−203.498	+	203.498i	−0.426621	+	0.426621i
$478$	−2.15755	−	2.15755i	−0.00451370	−	0.00451370i
$479$		−	376.346i		−	0.785690i	−0.919605	−	0.392845i	$-0.871491\pi$
$479$		−	376.346i		−	0.785690i	0.919605	−	0.392845i	$-0.128509\pi$
$480$	−47.3209	+	12.6782i	−0.0985851	+	0.0264129i
$481$	285.936			0.594461
$482$	136.072	−	136.072i	0.282306	−	0.282306i
$483$	48.5773	+	48.5773i	0.100574	+	0.100574i
$484$			235.781i			0.487150i
$485$	−303.939	+	526.404i	−0.626678	+	1.08537i
$486$	22.0454			0.0453609
$487$	−331.105	+	331.105i	−0.679887	+	0.679887i	−0.959974	−	0.280088i	$-0.909636\pi$
$487$	−331.105	+	331.105i	−0.679887	+	0.679887i	0.280088	+	0.959974i	$0.409636\pi$
$488$	109.253	+	109.253i	0.223880	+	0.223880i
$489$		−	30.1974i		−	0.0617533i
$490$	−118.791	−	68.5883i	−0.242430	−	0.139976i
$491$	95.5294			0.194561			0.0972805	−	0.995257i	$-0.468986\pi$
$491$	95.5294			0.194561			0.0972805	+	0.995257i	$0.468986\pi$
$492$	156.642	−	156.642i	0.318377	−	0.318377i
$493$	330.261	+	330.261i	0.669901	+	0.669901i
$494$			223.997i			0.453436i
$495$	6.84550	+	25.5506i	0.0138293	+	0.0516173i
$496$	−60.3650			−0.121704
$497$	−211.104	+	211.104i	−0.424757	+	0.424757i
$498$	168.824	+	168.824i	0.339005	+	0.339005i
$499$			134.022i			0.268581i	0.990942	+	0.134291i	$0.0428756\pi$
$499$			134.022i			0.268581i	−0.990942	+	0.134291i	$0.957124\pi$
$500$	176.762	+	176.791i	0.353524	+	0.353582i
$501$	166.269			0.331874
$502$	−191.977	+	191.977i	−0.382424	+	0.382424i
$503$	−474.271	−	474.271i	−0.942885	−	0.942885i	0.0555696	−	0.998455i	$-0.482303\pi$
$503$	−474.271	−	474.271i	−0.942885	−	0.942885i	−0.998455	+	0.0555696i	$0.982303\pi$
$504$			70.1763i			0.139239i
$505$	46.2044	−	12.3791i	0.0914939	−	0.0245130i
$506$	11.9603			0.0236369
$507$	145.729	−	145.729i	0.287434	−	0.287434i
$508$	−174.206	−	174.206i	−0.342926	−	0.342926i
$509$			447.848i			0.879859i	0.898032	+	0.439930i	$0.144997\pi$
$509$			447.848i			0.879859i	−0.898032	+	0.439930i	$0.855003\pi$
$510$	−73.7016	+	127.647i	−0.144513	+	0.250288i
$511$	−687.635			−1.34567
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	82.2915	+	82.2915i	0.160412	+	0.160412i
$514$			201.639i			0.392294i
$515$	−319.330	−	184.377i	−0.620059	−	0.358014i
$516$	170.256			0.329953
$517$	−3.92856	+	3.92856i	−0.00759876	+	0.00759876i
$518$	334.390	+	334.390i	0.645540	+	0.645540i
$519$			89.2681i			0.172000i
$520$	−25.8825	−	96.6055i	−0.0497741	−	0.185780i
$521$	348.685			0.669261			0.334631	−	0.942349i	$-0.391388\pi$
$521$	348.685			0.669261			0.334631	+	0.942349i	$0.391388\pi$
$522$	−116.427	+	116.427i	−0.223040	+	0.223040i
$523$	550.982	+	550.982i	1.05350	+	1.05350i	0.998485	+	0.0550166i	$0.0175212\pi$
$523$	550.982	+	550.982i	1.05350	+	1.05350i	0.0550166	+	0.998485i	$0.482479\pi$
$524$		−	303.902i		−	0.579966i
$525$	310.148	−	179.041i	0.590758	−	0.341031i
$526$	324.781			0.617455
$527$	−128.426	+	128.426i	−0.243692	+	0.243692i
$528$	8.63909	+	8.63909i	0.0163619	+	0.0163619i
$529$			23.0000i			0.0434783i
$530$	655.219	−	175.546i	1.23626	−	0.331219i
$531$	−88.0643			−0.165846
$532$	−261.955	+	261.955i	−0.492397	+	0.492397i
$533$	319.784	+	319.784i	0.599970	+	0.599970i
$534$		−	48.3256i		−	0.0904973i
$535$	−443.164	+	767.535i	−0.828345	+	1.43464i
$536$	56.0020			0.104481
$537$	−117.784	+	117.784i	−0.219338	+	0.219338i
$538$	−166.072	−	166.072i	−0.308683	−	0.308683i
$539$			34.2087i			0.0634670i
$540$	−44.9993	−	25.9820i	−0.0833320	−	0.0481148i
$541$	353.593			0.653591			0.326795	−	0.945095i	$-0.394031\pi$
$541$	353.593			0.653591			0.326795	+	0.945095i	$0.394031\pi$
$542$	309.336	−	309.336i	0.570731	−	0.570731i
$543$	250.252	+	250.252i	0.460869	+	0.460869i
$544$			68.0794i			0.125146i
$545$	−85.0401	−	317.409i	−0.156037	−	0.582402i
$546$	−143.265			−0.262390
$547$	−39.6840	+	39.6840i	−0.0725485	+	0.0725485i	−0.742450	−	0.669901i	$-0.766336\pi$
$547$	−39.6840	+	39.6840i	−0.0725485	+	0.0725485i	0.669901	+	0.742450i	$0.266336\pi$
$548$	−134.464	−	134.464i	−0.245372	−	0.245372i
$549$			163.880i			0.298507i
$550$	16.1400	−	60.2219i	0.0293454	−	0.109494i
$551$	−869.201			−1.57750
$552$	−16.6132	+	16.6132i	−0.0300965	+	0.0300965i
$553$	749.576	+	749.576i	1.35547	+	1.35547i
$554$		−	531.996i		−	0.960281i
$555$	−338.225	+	90.6173i	−0.609415	+	0.163274i
$556$	295.575			0.531610
$557$	−162.116	+	162.116i	−0.291052	+	0.291052i	−0.837496	−	0.546444i	$-0.815981\pi$
$557$	−162.116	+	162.116i	−0.291052	+	0.291052i	0.546444	+	0.837496i	$0.315981\pi$
$558$	−45.2738	−	45.2738i	−0.0811358	−	0.0811358i
$559$			347.577i			0.621784i
$560$	82.7075	−	143.245i	0.147692	−	0.255794i
$561$	36.7590			0.0655241
$562$	−57.9240	+	57.9240i	−0.103068	+	0.103068i
$563$	99.3830	+	99.3830i	0.176524	+	0.176524i	0.789839	−	0.613315i	$-0.210164\pi$
$563$	99.3830	+	99.3830i	0.176524	+	0.176524i	−0.613315	+	0.789839i	$0.710164\pi$
$564$		−	10.9138i		−	0.0193507i
$565$	−307.665	−	177.642i	−0.544540	−	0.314410i
$566$	232.357			0.410525
$567$	−52.6322	+	52.6322i	−0.0928258	+	0.0928258i
$568$	−72.1968	−	72.1968i	−0.127107	−	0.127107i
$569$			1021.63i			1.79548i	0.440530	+	0.897738i	$0.354790\pi$
$569$			1021.63i			1.79548i	−0.440530	+	0.897738i	$0.645210\pi$
$570$	−70.9881	−	264.960i	−0.124541	−	0.464843i
$571$	−454.037			−0.795161			−0.397580	−	0.917567i	$-0.630150\pi$
$571$	−454.037			−0.795161			−0.397580	+	0.917567i	$0.630150\pi$
$572$	−17.6367	+	17.6367i	−0.0308334	+	0.0308334i
$573$	−126.516	−	126.516i	−0.220795	−	0.220795i
$574$			747.947i			1.30304i
$575$	115.809	+	31.0377i	0.201407	+	0.0539785i
$576$	−24.0000			−0.0416667
$577$	112.620	−	112.620i	0.195182	−	0.195182i	−0.602749	−	0.797931i	$-0.705928\pi$
$577$	112.620	−	112.620i	0.195182	−	0.195182i	0.797931	+	0.602749i	$0.205928\pi$
$578$	−144.162	−	144.162i	−0.249416	−	0.249416i
$579$			52.4413i			0.0905721i
$580$	374.868	−	100.435i	0.646325	−	0.173163i
$581$	−806.118			−1.38747
$582$	−210.565	+	210.565i	−0.361796	+	0.361796i
$583$	−119.619	−	119.619i	−0.205179	−	0.205179i
$584$		−	235.168i		−	0.402686i
$585$	53.0422	−	91.8660i	0.0906704	−	0.157036i
$586$	−378.003			−0.645056
$587$	760.222	−	760.222i	1.29510	−	1.29510i	0.363505	−	0.931592i	$-0.381580\pi$
$587$	760.222	−	760.222i	1.29510	−	1.29510i	0.931592	−	0.363505i	$-0.118420\pi$
$588$	−47.5171	−	47.5171i	−0.0808114	−	0.0808114i
$589$		−	337.998i		−	0.573850i
$590$	179.758	+	103.790i	0.304674	+	0.175915i
$591$	12.7231			0.0215281
$592$	−114.360	+	114.360i	−0.193175	+	0.193175i
$593$	−623.009	−	623.009i	−1.05061	−	1.05061i	−0.998649	−	0.0519559i	$-0.983454\pi$
$593$	−623.009	−	623.009i	−1.05061	−	1.05061i	−0.0519559	−	0.998649i	$-0.516546\pi$
$594$			12.9586i			0.0218159i
$595$	−128.791	−	480.709i	−0.216456	−	0.807914i
$596$	−68.7421			−0.115339
$597$	420.678	−	420.678i	0.704653	−	0.704653i
$598$	−33.9159	−	33.9159i	−0.0567156	−	0.0567156i
$599$			320.986i			0.535870i	0.963437	+	0.267935i	$0.0863412\pi$
$599$			320.986i			0.535870i	−0.963437	+	0.267935i	$0.913659\pi$
$600$	61.2314	+	106.069i	0.102052	+	0.176782i
$601$	−7.35941			−0.0122453			−0.00612264	−	0.999981i	$-0.501949\pi$
$601$	−7.35941			−0.0122453			−0.00612264	+	0.999981i	$0.501949\pi$
$602$	−406.477	+	406.477i	−0.675210	+	0.675210i
$603$	42.0015	+	42.0015i	0.0696542	+	0.0696542i
$604$			375.109i			0.621042i
$605$	569.370	−	152.546i	0.941108	−	0.252142i
$606$	23.4338			0.0386696
$607$	−360.752	+	360.752i	−0.594319	+	0.594319i	−0.938795	−	0.344476i	$-0.888057\pi$
$607$	−360.752	+	360.752i	−0.594319	+	0.594319i	0.344476	+	0.938795i	$0.388057\pi$
$608$	−89.5877	−	89.5877i	−0.147348	−	0.147348i
$609$		−	555.925i		−	0.912850i
$610$	193.144	−	334.514i	0.316629	−	0.548383i
$611$	22.2805			0.0364657
$612$	−51.0596	+	51.0596i	−0.0834307	+	0.0834307i
$613$	649.344	+	649.344i	1.05929	+	1.05929i	0.998128	+	0.0611606i	$0.0194802\pi$
$613$	649.344	+	649.344i	1.05929	+	1.05929i	0.0611606	+	0.998128i	$0.480520\pi$
$614$			615.643i			1.00268i
$615$	−479.608	−	276.919i	−0.779850	−	0.450275i
$616$	−41.2507			−0.0669655
$617$	686.962	−	686.962i	1.11339	−	1.11339i	0.120701	−	0.992689i	$-0.461486\pi$
$617$	686.962	−	686.962i	1.11339	−	1.11339i	0.992689	−	0.120701i	$-0.0385143\pi$
$618$	−127.734	−	127.734i	−0.206690	−	0.206690i
$619$			246.527i			0.398267i	0.979972	+	0.199133i	$0.0638127\pi$
$619$			246.527i			0.398267i	−0.979972	+	0.199133i	$0.936187\pi$
$620$	39.0551	+	145.771i	0.0629920	+	0.235115i
$621$	−24.9199			−0.0401286
$622$	529.789	−	529.789i	0.851750	−	0.851750i
$623$	115.375	+	115.375i	0.185192	+	0.185192i
$624$		−	48.9960i		−	0.0785192i
$625$	312.559	−	541.232i	0.500095	−	0.865971i
$626$	−128.675			−0.205552
$627$	−48.3722	+	48.3722i	−0.0771487	+	0.0771487i
$628$	−346.396	−	346.396i	−0.551586	−	0.551586i
$629$			486.597i			0.773605i
$630$	169.464	−	45.4028i	0.268990	−	0.0720679i
$631$	807.068			1.27903			0.639515	−	0.768778i	$-0.279135\pi$
$631$	807.068			1.27903			0.639515	+	0.768778i	$0.279135\pi$
$632$	−256.352	+	256.352i	−0.405620	+	0.405620i
$633$	−249.588	−	249.588i	−0.394294	−	0.394294i
$634$		−	786.062i		−	1.23985i
$635$	−307.971	+	533.387i	−0.484993	+	0.839980i
$636$	332.311			0.522502
$637$	97.0062	−	97.0062i	0.152286	−	0.152286i
$638$	−68.4375	−	68.4375i	−0.107269	−	0.107269i
$639$		−	108.295i		−	0.169476i
$640$	48.9890	+	28.2856i	0.0765453	+	0.0441963i
$641$	−926.142			−1.44484			−0.722420	−	0.691455i	$-0.756970\pi$
$641$	−926.142			−1.44484			−0.722420	+	0.691455i	$0.756970\pi$
$642$	−307.019	+	307.019i	−0.478222	+	0.478222i
$643$	387.838	+	387.838i	0.603170	+	0.603170i	0.941152	−	0.337982i	$-0.109744\pi$
$643$	387.838	+	387.838i	0.603170	+	0.603170i	−0.337982	+	0.941152i	$0.609744\pi$
$644$		−	79.3265i		−	0.123178i
$645$	−110.152	−	411.139i	−0.170779	−	0.637425i
$646$	−381.192			−0.590081
$647$	873.903	−	873.903i	1.35070	−	1.35070i	0.465822	−	0.884878i	$-0.345759\pi$
$647$	873.903	−	873.903i	1.35070	−	1.35070i	0.884878	−	0.465822i	$-0.154241\pi$
$648$	−18.0000	−	18.0000i	−0.0277778	−	0.0277778i
$649$		−	51.7655i		−	0.0797620i
$650$	−216.541	+	125.004i	−0.333139	+	0.192314i
$651$	216.177			0.332070
$652$	−24.6561	+	24.6561i	−0.0378160	+	0.0378160i
$653$	−697.096	−	697.096i	−1.06753	−	1.06753i	−0.997548	−	0.0699794i	$-0.977707\pi$
$653$	−697.096	−	697.096i	−1.06753	−	1.06753i	−0.0699794	−	0.997548i	$-0.522293\pi$
$654$		−	160.982i		−	0.246150i
$655$	−733.872	+	196.619i	−1.12042	+	0.300182i
$656$	−255.795			−0.389931
$657$	176.376	−	176.376i	0.268457	−	0.268457i
$658$	26.0561	+	26.0561i	0.0395990	+	0.0395990i
$659$			1089.85i			1.65380i	0.562352	+	0.826898i	$0.309897\pi$
$659$			1089.85i			1.65380i	−0.562352	+	0.826898i	$0.690103\pi$
$660$	15.2726	−	26.4513i	0.0231403	−	0.0400777i
$661$	−374.443			−0.566480			−0.283240	−	0.959049i	$-0.591409\pi$
$661$	−374.443			−0.566480			−0.283240	+	0.959049i	$0.591409\pi$
$662$	−179.754	+	179.754i	−0.271532	+	0.271532i
$663$	−104.238	−	104.238i	−0.157222	−	0.157222i
$664$		−	275.689i		−	0.415194i
$665$	802.059	+	463.098i	1.20610	+	0.696388i
$666$	−171.540			−0.257567
$667$	131.608	−	131.608i	0.197313	−	0.197313i
$668$	−135.758	−	135.758i	−0.203231	−	0.203231i
$669$		−	568.585i		−	0.849903i
$670$	−36.2323	−	135.235i	−0.0540780	−	0.201844i
$671$	−96.3313			−0.143564
$672$	57.2987	−	57.2987i	0.0852659	−	0.0852659i
$673$	356.156	+	356.156i	0.529206	+	0.529206i	0.920336	−	0.391130i	$-0.127916\pi$
$673$	356.156	+	356.156i	0.529206	+	0.529206i	−0.391130	+	0.920336i	$0.627916\pi$
$674$		−	236.743i		−	0.351251i
$675$	−33.6284	+	125.476i	−0.0498199	+	0.185890i
$676$	−237.975			−0.352034
$677$	−372.658	+	372.658i	−0.550455	+	0.550455i	−0.926572	−	0.376117i	$-0.877259\pi$
$677$	−372.658	+	372.658i	−0.550455	+	0.550455i	0.376117	+	0.926572i	$0.377259\pi$
$678$	−123.068	−	123.068i	−0.181516	−	0.181516i
$679$		−	1005.43i		−	1.48074i
$680$	164.400	−	44.0461i	0.241765	−	0.0647737i
$681$	−451.546			−0.663062
$682$	26.6126	−	26.6126i	0.0390214	−	0.0390214i
$683$	282.250	+	282.250i	0.413250	+	0.413250i	0.882869	−	0.469619i	$-0.155609\pi$
$683$	282.250	+	282.250i	0.413250	+	0.413250i	−0.469619	+	0.882869i	$0.655609\pi$
$684$		−	134.382i		−	0.196464i
$685$	−237.712	+	411.704i	−0.347025	+	0.601028i
$686$	−346.217			−0.504690
$687$	273.429	−	273.429i	0.398005	−	0.398005i
$688$	−139.013	−	139.013i	−0.202054	−	0.202054i
$689$			678.413i			0.984635i
$690$	50.8667	+	29.3697i	0.0737198	+	0.0425648i
$691$	−560.128			−0.810605			−0.405303	−	0.914183i	$-0.632834\pi$
$691$	−560.128			−0.810605			−0.405303	+	0.914183i	$0.632834\pi$
$692$	72.8871	−	72.8871i	0.105328	−	0.105328i
$693$	−30.9380	−	30.9380i	−0.0446436	−	0.0446436i
$694$			759.061i			1.09375i
$695$	−191.232	−	713.764i	−0.275153	−	1.02700i
$696$	190.124			0.273167
$697$	−544.199	+	544.199i	−0.780773	+	0.780773i
$698$	−540.641	−	540.641i	−0.774558	−	0.774558i
$699$		−	725.524i		−	1.03795i
$700$	−399.422	−	107.048i	−0.570602	−	0.152926i
$701$	149.533			0.213314			0.106657	−	0.994296i	$-0.465985\pi$
$701$	149.533			0.213314			0.106657	+	0.994296i	$0.465985\pi$
$702$	36.7470	−	36.7470i	0.0523461	−	0.0523461i
$703$	−640.327	−	640.327i	−0.910850	−	0.910850i
$704$		−	14.1076i		−	0.0200392i
$705$	−26.3550	+	7.06103i	−0.0373830	+	0.0100157i
$706$	−102.534			−0.145232
$707$	−55.9469	+	55.9469i	−0.0791328	+	0.0791328i
$708$	71.9042	+	71.9042i	0.101560	+	0.101560i
$709$		−	790.988i		−	1.11564i	−0.829963	−	0.557819i	$-0.811638\pi$
$709$		−	790.988i		−	1.11564i	0.829963	−	0.557819i	$-0.188362\pi$
$710$	−127.633	+	221.053i	−0.179765	+	0.311342i
$711$	−384.528			−0.540827
$712$	−39.4577	+	39.4577i	−0.0554181	+	0.0554181i
$713$	51.1769	+	51.1769i	0.0717769	+	0.0717769i
$714$		−	243.804i		−	0.341462i
$715$	54.0003	+	31.1790i	0.0755248	+	0.0436070i
$716$	192.341			0.268633
$717$	−2.64245	+	2.64245i	−0.00368542	+	0.00368542i
$718$	217.517	+	217.517i	0.302949	+	0.302949i
$719$			279.928i			0.389330i	0.980870	+	0.194665i	$0.0623620\pi$
$719$			279.928i			0.389330i	−0.980870	+	0.194665i	$0.937638\pi$
$720$	15.5276	+	57.9560i	0.0215661	+	0.0804944i
$721$	609.917			0.845932
$722$	140.622	−	140.622i	0.194767	−	0.194767i
$723$	−166.653	−	166.653i	−0.230502	−	0.230502i
$724$		−	408.660i		−	0.564447i
$725$	−485.066	−	840.265i	−0.669056	−	1.15899i
$726$	288.771			0.397756
$727$	738.912	−	738.912i	1.01639	−	1.01639i	0.0165221	−	0.999864i	$-0.494741\pi$
$727$	738.912	−	738.912i	1.01639	−	1.01639i	0.999864	−	0.0165221i	$-0.00525940\pi$
$728$	116.975	+	116.975i	0.160680	+	0.160680i
$729$		−	27.0000i		−	0.0370370i
$730$	−567.892	+	152.150i	−0.777934	+	0.208424i
$731$	−591.497			−0.809161
$732$	133.808	−	133.808i	0.182797	−	0.182797i
$733$	709.411	+	709.411i	0.967819	+	0.967819i	0.999498	−	0.0316790i	$-0.0100854\pi$
$733$	709.411	+	709.411i	0.967819	+	0.967819i	−0.0316790	+	0.999498i	$0.510085\pi$
$734$		−	782.186i		−	1.06565i
$735$	−84.0032	+	145.489i	−0.114290	+	0.197944i
$736$	27.1293			0.0368605
$737$	−24.6891	+	24.6891i	−0.0334995	+	0.0334995i
$738$	−191.846	−	191.846i	−0.259954	−	0.259954i
$739$		−	233.841i		−	0.316429i	−0.987405	−	0.158214i	$-0.949426\pi$
$739$		−	233.841i		−	0.316429i	0.987405	−	0.158214i	$-0.0505737\pi$
$740$	350.149	+	202.171i	0.473174	+	0.273204i
$741$	274.340			0.370229
$742$	−793.375	+	793.375i	−1.06924	+	1.06924i
$743$	−201.785	−	201.785i	−0.271581	−	0.271581i	0.558155	−	0.829736i	$-0.311509\pi$
$743$	−201.785	−	201.785i	−0.271581	−	0.271581i	−0.829736	+	0.558155i	$0.811509\pi$
$744$			73.9317i			0.0993706i
$745$	44.4749	+	166.001i	0.0596978	+	0.222820i
$746$	−562.793			−0.754414
$747$	206.767	−	206.767i	0.276796	−	0.276796i
$748$	−30.0136	−	30.0136i	−0.0401251	−	0.0401251i
$749$		−	1465.98i		−	1.95725i
$750$	216.524	−	216.489i	0.288699	−	0.288651i
$751$	76.6521			0.102067			0.0510333	−	0.998697i	$-0.483749\pi$
$751$	76.6521			0.102067			0.0510333	+	0.998697i	$0.483749\pi$
$752$	−8.91109	+	8.91109i	−0.0118499	+	0.0118499i
$753$	235.123	+	235.123i	0.312248	+	0.312248i
$754$			388.138i			0.514772i
$755$	905.826	−	242.689i	1.19977	−	0.321442i
$756$	85.9481			0.113688
$757$	−971.333	+	971.333i	−1.28314	+	1.28314i	−0.344262	+	0.938874i	$0.611871\pi$
$757$	−971.333	+	971.333i	−1.28314	+	1.28314i	−0.938874	+	0.344262i	$0.888129\pi$
$758$	−450.647	−	450.647i	−0.594521	−	0.594521i
$759$		−	14.6483i		−	0.0192995i
$760$	−158.378	+	274.301i	−0.208392	+	0.360922i
$761$	806.466			1.05975			0.529873	−	0.848077i	$-0.322240\pi$
$761$	806.466			1.05975			0.529873	+	0.848077i	$0.322240\pi$
$762$	−213.358	+	213.358i	−0.279998	+	0.279998i
$763$	384.336	+	384.336i	0.503717	+	0.503717i
$764$			206.599i			0.270418i
$765$	156.335	+	90.2657i	0.204359	+	0.117994i
$766$	241.562			0.315354
$767$	−146.792	+	146.792i	−0.191385	+	0.191385i
$768$	19.5959	+	19.5959i	0.0255155	+	0.0255155i
$769$		−	919.455i		−	1.19565i	−0.801626	−	0.597825i	$-0.796032\pi$
$769$		−	919.455i		−	1.19565i	0.801626	−	0.597825i	$-0.203968\pi$
$770$	26.6885	+	99.6136i	0.0346603	+	0.129368i
$771$	246.956			0.320307
$772$	42.8181	−	42.8181i	0.0554639	−	0.0554639i
$773$	604.542	+	604.542i	0.782073	+	0.782073i	0.980180	−	0.198107i	$-0.0634794\pi$
$773$	604.542	+	604.542i	0.782073	+	0.782073i	−0.198107	+	0.980180i	$0.563479\pi$
$774$		−	208.520i		−	0.269406i
$775$	326.746	−	188.623i	0.421607	−	0.243384i
$776$	343.851			0.443107
$777$	409.542	−	409.542i	0.527081	−	0.527081i
$778$	136.553	+	136.553i	0.175518	+	0.175518i
$779$		−	1432.25i		−	1.83858i
$780$	−118.317	+	31.6995i	−0.151689	+	0.0406404i
$781$	63.6576			0.0815078
$782$	57.7171	−	57.7171i	0.0738071	−	0.0738071i
$783$	142.593	+	142.593i	0.182111	+	0.182111i
$784$			77.5951i			0.0989734i
$785$	−612.377	+	1060.60i	−0.780098	+	1.35108i
$786$	−372.202			−0.473540
$787$	−586.515	+	586.515i	−0.745254	+	0.745254i	−0.973584	−	0.228330i	$-0.926673\pi$
$787$	−586.515	+	586.515i	−0.745254	+	0.745254i	0.228330	+	0.973584i	$0.426673\pi$
$788$	−10.3884	−	10.3884i	−0.0131832	−	0.0131832i
$789$		−	397.774i		−	0.504150i
$790$	784.901	+	453.192i	0.993546	+	0.573660i
$791$	587.637			0.742904
$792$	10.5807	−	10.5807i	0.0133594	−	0.0133594i
$793$	273.168	+	273.168i	0.344474	+	0.344474i
$794$		−	23.2306i		−	0.0292576i
$795$	−214.999	−	802.476i	−0.270439	−	1.00940i
$796$	−686.965			−0.863021
$797$	−619.264	+	619.264i	−0.776993	+	0.776993i	−0.979318	−	0.202325i	$-0.935150\pi$
$797$	−619.264	+	619.264i	−0.776993	+	0.776993i	0.202325	+	0.979318i	$0.435150\pi$
$798$	320.829	+	320.829i	0.402041	+	0.402041i
$799$			37.9164i			0.0474548i
$800$	36.6100	−	136.601i	0.0457625	−	0.170751i
$801$	−59.1865			−0.0738908
$802$	325.917	−	325.917i	0.406380	−	0.406380i
$803$	103.677	+	103.677i	0.129112	+	0.129112i
$804$		−	68.5881i		−	0.0853086i
$805$	−191.560	+	51.3228i	−0.237963	+	0.0637550i
$806$	−150.932			−0.187260
$807$	−203.395	+	203.395i	−0.252039	+	0.252039i
$808$	−19.1336	−	19.1336i	−0.0236802	−	0.0236802i
$809$			1363.50i			1.68541i	0.538375	+	0.842705i	$0.319038\pi$
$809$			1363.50i			1.68541i	−0.538375	+	0.842705i	$0.680962\pi$
$810$	−31.8213	+	55.1126i	−0.0392856	+	0.0680403i
$811$	1102.47			1.35940			0.679698	−	0.733492i	$-0.262111\pi$
$811$	1102.47			1.35940			0.679698	+	0.733492i	$0.262111\pi$
$812$	−453.911	+	453.911i	−0.559004	+	0.559004i
$813$	−378.858	−	378.858i	−0.466000	−	0.466000i
$814$		−	100.834i		−	0.123874i
$815$	75.4922	+	43.5882i	0.0926285	+	0.0534825i
$816$	83.3799			0.102181
$817$	778.367	−	778.367i	0.952714	−	0.952714i
$818$	−447.168	−	447.168i	−0.546661	−	0.546661i
$819$			175.463i			0.214240i
$820$	165.495	+	617.702i	0.201823	+	0.753295i
$821$	−1282.68			−1.56234			−0.781169	−	0.624319i	$-0.785376\pi$
$821$	−1282.68			−1.56234			−0.781169	+	0.624319i	$0.785376\pi$
$822$	−164.684	+	164.684i	−0.200346	+	0.200346i
$823$	−151.442	−	151.442i	−0.184013	−	0.184013i	0.609089	−	0.793102i	$-0.291535\pi$
$823$	−151.442	−	151.442i	−0.184013	−	0.184013i	−0.793102	+	0.609089i	$0.791535\pi$
$824$			208.589i			0.253142i
$825$	−73.7565	−	19.7673i	−0.0894018	−	0.0239604i
$826$	−343.335			−0.415659
$827$	424.578	−	424.578i	0.513396	−	0.513396i	−0.402169	−	0.915565i	$-0.631744\pi$
$827$	424.578	−	424.578i	0.513396	−	0.513396i	0.915565	+	0.402169i	$0.131744\pi$
$828$	20.3470	+	20.3470i	0.0245737	+	0.0245737i
$829$			171.099i			0.206392i	0.994661	+	0.103196i	$0.0329069\pi$
$829$			171.099i			0.206392i	−0.994661	+	0.103196i	$0.967093\pi$
$830$	−665.743	+	178.366i	−0.802100	+	0.214898i
$831$	−651.559			−0.784066
$832$	−40.0050	+	40.0050i	−0.0480830	+	0.0480830i
$833$	165.082	+	165.082i	0.198178	+	0.198178i
$834$		−	362.004i		−	0.434057i
$835$	−240.000	+	415.666i	−0.287425	+	0.497804i
$836$	78.9915			0.0944875
$837$	−55.4488	+	55.4488i	−0.0662471	+	0.0662471i
$838$	356.216	+	356.216i	0.425078	+	0.425078i
$839$		−	1019.44i		−	1.21507i	−0.794294	−	0.607533i	$-0.792159\pi$
$839$		−	1019.44i		−	1.21507i	0.794294	−	0.607533i	$-0.207841\pi$
$840$	−175.438	−	101.296i	−0.208855	−	0.120590i
$841$	−665.134			−0.790884
$842$	−415.752	+	415.752i	−0.493767	+	0.493767i
$843$	70.9421	+	70.9421i	0.0841544	+	0.0841544i
$844$			407.576i			0.482910i
$845$	153.965	+	574.669i	0.182207	+	0.680082i
$846$	−13.3666			−0.0157998
$847$	−689.425	+	689.425i	−0.813961	+	0.813961i
$848$	−271.331	−	271.331i	−0.319966	−	0.319966i
$849$		−	284.578i		−	0.335192i
$850$	−212.728	−	368.502i	−0.250268	−	0.433532i
$851$	193.907			0.227857
$852$	−88.4227	+	88.4227i	−0.103782	+	0.103782i
$853$	435.813	+	435.813i	0.510918	+	0.510918i	0.914808	−	0.403890i	$-0.132342\pi$
$853$	435.813	+	435.813i	0.510918	+	0.510918i	−0.403890	+	0.914808i	$0.632342\pi$
$854$			638.917i			0.748146i
$855$	−324.509	+	86.9424i	−0.379542	+	0.101687i
$856$	501.360			0.585700
$857$	−601.838	+	601.838i	−0.702261	+	0.702261i	−0.964896	−	0.262634i	$-0.915409\pi$
$857$	−601.838	+	601.838i	−0.702261	+	0.702261i	0.262634	+	0.964896i	$0.415409\pi$
$858$	21.6004	+	21.6004i	0.0251753	+	0.0251753i
$859$		−	1343.67i		−	1.56422i	−0.623138	−	0.782112i	$-0.714142\pi$
$859$		−	1343.67i		−	1.56422i	0.623138	−	0.782112i	$-0.285858\pi$
$860$	−245.755	+	425.633i	−0.285761	+	0.494922i
$861$	916.045			1.06393
$862$	456.460	−	456.460i	0.529536	−	0.529536i
$863$	−645.537	−	645.537i	−0.748015	−	0.748015i	0.226091	−	0.974106i	$-0.427405\pi$
$863$	−645.537	−	645.537i	−0.748015	−	0.748015i	−0.974106	+	0.226091i	$0.927405\pi$
$864$			29.3939i			0.0340207i
$865$	−223.167	−	128.854i	−0.257996	−	0.148964i
$866$	113.222			0.130741
$867$	−176.562	+	176.562i	−0.203647	+	0.203647i
$868$	−176.508	−	176.508i	−0.203350	−	0.203350i
$869$		−	226.031i		−	0.260105i
$870$	−123.007	−	459.118i	−0.141387	−	0.527722i
$871$	140.023			0.160761
$872$	−131.441	+	131.441i	−0.150736	+	0.150736i
$873$	257.889	+	257.889i	0.295405	+	0.295405i
$874$			151.903i			0.173802i
$875$	−0.0848548	+	1033.79i	−9.69769e−5	+	1.18148i
$876$	−288.021			−0.328791
$877$	−1132.84	+	1132.84i	−1.29172	+	1.29172i	−0.358004	+	0.933720i	$0.616543\pi$
$877$	−1132.84	+	1132.84i	−1.29172	+	1.29172i	−0.933720	+	0.358004i	$0.883457\pi$
$878$	−533.763	−	533.763i	−0.607931	−	0.607931i
$879$			462.957i			0.526686i
$880$	−34.0674	+	9.12734i	−0.0387130	+	0.0103720i
$881$	1591.02			1.80592			0.902960	−	0.429725i	$-0.141389\pi$
$881$	1591.02			1.80592			0.902960	+	0.429725i	$0.141389\pi$
$882$	−58.1964	+	58.1964i	−0.0659823	+	0.0659823i
$883$	−129.734	−	129.734i	−0.146924	−	0.146924i	0.629819	−	0.776742i	$-0.283129\pi$
$883$	−129.734	−	129.734i	−0.146924	−	0.146924i	−0.776742	+	0.629819i	$0.783129\pi$
$884$			170.220i			0.192557i
$885$	127.116	−	220.157i	0.143634	−	0.248765i
$886$	616.632			0.695973
$887$	488.248	−	488.248i	0.550449	−	0.550449i	−0.376122	−	0.926570i	$-0.622743\pi$
$887$	488.248	−	488.248i	0.550449	−	0.550449i	0.926570	+	0.376122i	$0.122743\pi$
$888$	140.062	+	140.062i	0.157727	+	0.157727i
$889$		−	1018.76i		−	1.14597i
$890$	120.812	+	69.7553i	0.135744	+	0.0783767i
$891$	15.8710			0.0178126
$892$	−464.248	+	464.248i	−0.520457	+	0.520457i
$893$	−49.8952	−	49.8952i	−0.0558737	−	0.0558737i
$894$			84.1915i			0.0941740i
$895$	−124.441	−	464.471i	−0.139040	−	0.518962i
$896$	−93.5684			−0.104429
$897$	−41.5384	+	41.5384i	−0.0463081	+	0.0463081i
$898$	479.262	+	479.262i	0.533699	+	0.533699i
$899$		−	585.676i		−	0.651474i
$900$	129.908	−	74.9929i	0.144342	−	0.0833254i
$901$	−1154.50			−1.28136
$902$	112.770	−	112.770i	0.125022	−	0.125022i
$903$	497.830	+	497.830i	0.551307	+	0.551307i
$904$			200.969i			0.222311i
$905$	−986.845	+	264.395i	−1.09044	+	0.292150i
$906$	459.413			0.507079
$907$	717.440	−	717.440i	0.791003	−	0.791003i	−0.190654	−	0.981657i	$-0.561061\pi$
$907$	717.440	−	717.440i	0.791003	−	0.791003i	0.981657	+	0.190654i	$0.0610609\pi$
$908$	368.685	+	368.685i	0.406041	+	0.406041i
$909$		−	28.7004i		−	0.0315736i
$910$	206.795	−	358.156i	0.227247	−	0.393578i
$911$	−1469.66			−1.61324			−0.806618	−	0.591073i	$-0.798704\pi$
$911$	−1469.66			−1.61324			−0.806618	+	0.591073i	$0.798704\pi$
$912$	−109.722	+	109.722i	−0.120309	+	0.120309i
$913$	121.541	+	121.541i	0.133122	+	0.133122i
$914$			242.117i			0.264898i
$915$	−409.694	−	236.552i	−0.447753	−	0.258527i
$916$	−446.508			−0.487454
$917$	888.613	−	888.613i	0.969044	−	0.969044i
$918$	62.5350	+	62.5350i	0.0681209	+	0.0681209i
$919$			1596.20i			1.73689i	0.495786	+	0.868445i	$0.334880\pi$
$919$			1596.20i			1.73689i	−0.495786	+	0.868445i	$0.665120\pi$
$920$	−17.5522	−	65.5128i	−0.0190784	−	0.0712095i
$921$	754.006			0.818682
$922$	130.197	−	130.197i	0.141211	−	0.141211i
$923$	−180.515	−	180.515i	−0.195574	−	0.195574i
$924$			50.5216i			0.0546771i
$925$	261.670	−	976.351i	0.282886	−	1.05552i
$926$	169.770			0.183337
$927$	−156.442	+	156.442i	−0.168761	+	0.168761i
$928$	−155.236	−	155.236i	−0.167280	−	0.167280i
$929$		−	1330.70i		−	1.43240i	−0.697895	−	0.716200i	$-0.745880\pi$
$929$		−	1330.70i		−	1.43240i	0.697895	−	0.716200i	$-0.254120\pi$
$930$	178.533	−	47.8325i	0.191971	−	0.0514328i
$931$	−434.473			−0.466673
$932$	−592.388	+	592.388i	−0.635609	+	0.635609i
$933$	−648.856	−	648.856i	−0.695451	−	0.695451i
$934$			186.437i			0.199612i
$935$	−53.0596	+	91.8961i	−0.0567482	+	0.0982846i
$936$	−60.0076			−0.0641107
$937$	1149.86	−	1149.86i	1.22717	−	1.22717i	0.262138	−	0.965030i	$-0.415572\pi$
$937$	1149.86	−	1149.86i	1.22717	−	1.22717i	0.965030	−	0.262138i	$-0.0844276\pi$
$938$	163.751	+	163.751i	0.174574	+	0.174574i
$939$			157.594i			0.167832i
$940$	27.2841	+	15.7535i	0.0290256	+	0.0167590i
$941$	−1043.38			−1.10880			−0.554399	−	0.832251i	$-0.687052\pi$
$941$	−1043.38			−1.10880			−0.554399	+	0.832251i	$0.687052\pi$
$942$	−424.247	+	424.247i	−0.450368	+	0.450368i
$943$	216.861	+	216.861i	0.229969	+	0.229969i
$944$		−	117.419i		−	0.124385i
$945$	−55.6068	−	207.550i	−0.0588432	−	0.219630i
$946$	122.571			0.129568
$947$	235.405	−	235.405i	0.248580	−	0.248580i	−0.571808	−	0.820388i	$-0.693758\pi$
$947$	235.405	−	235.405i	0.248580	−	0.248580i	0.820388	+	0.571808i	$0.193758\pi$
$948$	313.966	+	313.966i	0.331187	+	0.331187i
$949$		−	587.995i		−	0.619594i
$950$	764.858	+	204.988i	0.805113	+	0.215777i
$951$	−962.725			−1.01233
$952$	−199.065	+	199.065i	−0.209102	+	0.209102i
$953$	614.995	+	614.995i	0.645325	+	0.645325i	0.951860	−	0.306534i	$-0.0991695\pi$
$953$	614.995	+	614.995i	0.645325	+	0.645325i	−0.306534	+	0.951860i	$0.599169\pi$
$954$		−	406.997i		−	0.426621i
$955$	498.902	−	133.666i	0.522410	−	0.139964i
$956$	4.31510			0.00451370
$957$	−83.8185	+	83.8185i	−0.0875846	+	0.0875846i
$958$	376.346	+	376.346i	0.392845	+	0.392845i
$959$		−	786.349i		−	0.819968i
$960$	34.6427	−	59.9991i	0.0360861	−	0.0624990i
$961$	−733.254			−0.763011
$962$	−285.936	+	285.936i	−0.297231	+	0.297231i
$963$	376.020	+	376.020i	0.390467	+	0.390467i
$964$			272.143i			0.282306i
$965$	−131.101	−	75.6960i	−0.135856	−	0.0784415i
$966$	−97.1547			−0.100574
$967$	−567.252	+	567.252i	−0.586610	+	0.586610i	−0.936712	−	0.350101i	$-0.886147\pi$
$967$	−567.252	+	567.252i	−0.586610	+	0.586610i	0.350101	+	0.936712i	$0.386147\pi$
$968$	−235.781	−	235.781i	−0.243575	−	0.243575i
$969$			466.863i			0.481799i
$970$	−222.465	−	830.343i	−0.229346	−	0.856024i
$971$	−315.250			−0.324666			−0.162333	−	0.986736i	$-0.551902\pi$
$971$	−315.250			−0.324666			−0.162333	+	0.986736i	$0.551902\pi$
$972$	−22.0454	+	22.0454i	−0.0226805	+	0.0226805i
$973$	864.265	+	864.265i	0.888247	+	0.888247i
$974$		−	662.210i		−	0.679887i
$975$	153.098	+	265.207i	0.157023	+	0.272007i
$976$	−218.507			−0.223880
$977$	−570.296	+	570.296i	−0.583722	+	0.583722i	−0.935924	−	0.352202i	$-0.885433\pi$
$977$	−570.296	+	570.296i	−0.583722	+	0.583722i	0.352202	+	0.935924i	$0.385433\pi$
$978$	30.1974	+	30.1974i	0.0308767	+	0.0308767i
$979$		−	34.7907i		−	0.0355370i
$980$	187.379	−	50.2026i	0.191203	−	0.0512272i
$981$	−197.162			−0.200981
$982$	−95.5294	+	95.5294i	−0.0972805	+	0.0972805i
$983$	246.193	+	246.193i	0.250451	+	0.250451i	0.821156	−	0.570704i	$-0.193330\pi$
$983$	246.193	+	246.193i	0.250451	+	0.250451i	−0.570704	+	0.821156i	$0.693330\pi$
$984$			313.283i			0.318377i
$985$	−18.3651	+	31.8073i	−0.0186448	+	0.0322916i
$986$	−660.523			−0.669901
$987$	31.9121	−	31.9121i	0.0323324	−	0.0323324i
$988$	−223.997	−	223.997i	−0.226718	−	0.226718i
$989$			235.709i			0.238330i
$990$	−32.3961	−	18.7051i	−0.0327233	−	0.0188940i
$991$	1027.66			1.03699			0.518495	−	0.855080i	$-0.326492\pi$
$991$	1027.66			1.03699			0.518495	+	0.855080i	$0.326492\pi$
$992$	60.3650	−	60.3650i	0.0608518	−	0.0608518i
$993$	220.153	+	220.153i	0.221705	+	0.221705i
$994$		−	422.209i		−	0.424757i
$995$	444.453	+	1658.90i	0.446687	+	1.66724i
$996$	−337.649			−0.339005
$997$	−121.459	+	121.459i	−0.121825	+	0.121825i	−0.765391	−	0.643566i	$-0.777454\pi$
$997$	−121.459	+	121.459i	−0.121825	+	0.121825i	0.643566	+	0.765391i	$0.277454\pi$
$998$	−134.022	−	134.022i	−0.134291	−	0.134291i
$999$			210.093i			0.210303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.b.553.20	yes	48
5.2	odd	4	inner	690.3.k.b.277.20	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.b.277.20	✓	48	5.2	odd	4	inner
690.3.k.b.553.20	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)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-4.82966 + 1.29396i) q^{5} -2.44949 q^{6} +(5.84802 - 5.84802i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-4.82966 + 1.29396i) q^{5} -2.44949 q^{6} +(5.84802 - 5.84802i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(3.53570 - 6.12363i) q^{10} -1.76345 q^{11} +(2.44949 - 2.44949i) q^{12} +(5.00063 + 5.00063i) q^{13} +11.6960i q^{14} +(-7.49988 - 4.33033i) q^{15} -4.00000 q^{16} +(-8.50993 + 8.50993i) q^{17} +(-3.00000 - 3.00000i) q^{18} -22.3969i q^{19} +(2.58793 + 9.65933i) q^{20} +14.3247 q^{21} +(1.76345 - 1.76345i) q^{22} +(3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(21.6513 - 12.4988i) q^{25} -10.0013 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-11.6960 - 11.6960i) q^{28} -38.8089i q^{29} +(11.8302 - 3.16955i) q^{30} +15.0913 q^{31} +(4.00000 - 4.00000i) q^{32} +(-2.15977 - 2.15977i) q^{33} -17.0199i q^{34} +(-20.6769 + 35.8111i) q^{35} +6.00000 q^{36} +(28.5900 - 28.5900i) q^{37} +(22.3969 + 22.3969i) q^{38} +12.2490i q^{39} +(-12.2473 - 7.07140i) q^{40} +63.9487 q^{41} +(-14.3247 + 14.3247i) q^{42} +(34.7533 + 34.7533i) q^{43} +3.52689i q^{44} +(-3.88189 - 14.4890i) q^{45} -6.78233 q^{46} +(2.22777 - 2.22777i) q^{47} +(-4.89898 - 4.89898i) q^{48} -19.3988i q^{49} +(-9.15250 + 34.1501i) q^{50} -20.8450 q^{51} +(10.0013 - 10.0013i) q^{52} +(67.8328 + 67.8328i) q^{53} -7.34847i q^{54} +(8.51686 - 2.28183i) q^{55} +23.3921 q^{56} +(27.4305 - 27.4305i) q^{57} +(38.8089 + 38.8089i) q^{58} +29.3548i q^{59} +(-8.66066 + 14.9998i) q^{60} +54.6267 q^{61} +(-15.0913 + 15.0913i) q^{62} +(17.5441 + 17.5441i) q^{63} +8.00000i q^{64} +(-30.6220 - 17.6807i) q^{65} +4.31954 q^{66} +(14.0005 - 14.0005i) q^{67} +(17.0199 + 17.0199i) q^{68} +8.30662i q^{69} +(-15.1343 - 56.4880i) q^{70} -36.0984 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-58.7921 - 58.7921i) q^{73} +57.1799i q^{74} +(41.8252 + 11.2095i) q^{75} -44.7938 q^{76} +(-10.3127 + 10.3127i) q^{77} +(-12.2490 - 12.2490i) q^{78} +128.176i q^{79} +(19.3187 - 5.17585i) q^{80} -9.00000 q^{81} +(-63.9487 + 63.9487i) q^{82} +(-68.9222 - 68.9222i) q^{83} -28.6494i q^{84} +(30.0886 - 52.1116i) q^{85} -69.5066 q^{86} +(47.5310 - 47.5310i) q^{87} +(-3.52689 - 3.52689i) q^{88} +19.7288i q^{89} +(18.3709 + 10.6071i) q^{90} +58.4876 q^{91} +(6.78233 - 6.78233i) q^{92} +(18.4829 + 18.4829i) q^{93} +4.45554i q^{94} +(28.9808 + 108.170i) q^{95} +9.79796 q^{96} +(85.9628 - 85.9628i) q^{97} +(19.3988 + 19.3988i) q^{98} -5.29034i 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

Related objects

Downloads

Learn more