LMFDB - Embedded newform 690.3.k.b.553.22

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			553.22
Character	$\chi$	$=$	690.553
Dual form			690.3.k.b.277.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(3.98727 - 3.01689i) q^{5} -2.44949 q^{6} +(-6.00383 + 6.00383i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(3.98727 - 3.01689i) q^{5} -2.44949 q^{6} +(-6.00383 + 6.00383i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(-0.970383 + 7.00417i) q^{10} -21.0865 q^{11} +(2.44949 - 2.44949i) q^{12} +(6.18805 + 6.18805i) q^{13} -12.0077i q^{14} +(8.57832 + 1.18847i) q^{15} -4.00000 q^{16} +(-1.00579 + 1.00579i) q^{17} +(-3.00000 - 3.00000i) q^{18} -17.5101i q^{19} +(-6.03378 - 7.97455i) q^{20} -14.7063 q^{21} +(21.0865 - 21.0865i) q^{22} +(3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(6.79672 - 24.0584i) q^{25} -12.3761 q^{26} +(-3.67423 + 3.67423i) q^{27} +(12.0077 + 12.0077i) q^{28} -36.7302i q^{29} +(-9.76679 + 7.38985i) q^{30} -27.5739 q^{31} +(4.00000 - 4.00000i) q^{32} +(-25.8256 - 25.8256i) q^{33} -2.01158i q^{34} +(-5.82601 + 42.0518i) q^{35} +6.00000 q^{36} +(-26.3672 + 26.3672i) q^{37} +(17.5101 + 17.5101i) q^{38} +15.1576i q^{39} +(14.0083 + 1.94077i) q^{40} -26.4885 q^{41} +(14.7063 - 14.7063i) q^{42} +(-22.3435 - 22.3435i) q^{43} +42.1730i q^{44} +(9.05068 + 11.9618i) q^{45} -6.78233 q^{46} +(4.99263 - 4.99263i) q^{47} +(-4.89898 - 4.89898i) q^{48} -23.0919i q^{49} +(17.2616 + 30.8551i) q^{50} -2.46367 q^{51} +(12.3761 - 12.3761i) q^{52} +(-52.5294 - 52.5294i) q^{53} -7.34847i q^{54} +(-84.0776 + 63.6156i) q^{55} -24.0153 q^{56} +(21.4455 - 21.4455i) q^{57} +(36.7302 + 36.7302i) q^{58} +59.1834i q^{59} +(2.37694 - 17.1566i) q^{60} -60.6356 q^{61} +(27.5739 - 27.5739i) q^{62} +(-18.0115 - 18.0115i) q^{63} +8.00000i q^{64} +(43.3421 + 6.00477i) q^{65} +51.6511 q^{66} +(-56.3450 + 56.3450i) q^{67} +(2.01158 + 2.01158i) q^{68} +8.30662i q^{69} +(-36.2258 - 47.8778i) q^{70} -6.19517 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-10.2369 - 10.2369i) q^{73} -52.7344i q^{74} +(37.7896 - 21.1411i) q^{75} -35.0203 q^{76} +(126.600 - 126.600i) q^{77} +(-15.1576 - 15.1576i) q^{78} +44.9126i q^{79} +(-15.9491 + 12.0676i) q^{80} -9.00000 q^{81} +(26.4885 - 26.4885i) q^{82} +(-53.2159 - 53.2159i) q^{83} +29.4126i q^{84} +(-0.976002 + 7.04473i) q^{85} +44.6869 q^{86} +(44.9852 - 44.9852i) q^{87} +(-42.1730 - 42.1730i) q^{88} -117.848i q^{89} +(-21.0125 - 2.91115i) q^{90} -74.3039 q^{91} +(6.78233 - 6.78233i) q^{92} +(-33.7710 - 33.7710i) q^{93} +9.98527i q^{94} +(-52.8262 - 69.8177i) q^{95} +9.79796 q^{96} +(37.7963 - 37.7963i) q^{97} +(23.0919 + 23.0919i) q^{98} -63.2594i 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
$5$	3.98727	−	3.01689i	0.797455	−	0.603378i
$5$	3.98727	−	3.01689i	0.797455	−	0.603378i
$6$	−2.44949			−0.408248
$7$	−6.00383	+	6.00383i	−0.857690	+	0.857690i	−0.991066	−	0.133376i	$-0.957418\pi$
$7$	−6.00383	+	6.00383i	−0.857690	+	0.857690i	0.133376	+	0.991066i	$0.457418\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$			3.00000i			0.333333i
$10$	−0.970383	+	7.00417i	−0.0970383	+	0.700417i
$11$	−21.0865			−1.91695			−0.958476	−	0.285172i	$-0.907949\pi$
$11$	−21.0865			−1.91695			−0.958476	+	0.285172i	$0.907949\pi$
$12$	2.44949	−	2.44949i	0.204124	−	0.204124i
$13$	6.18805	+	6.18805i	0.476004	+	0.476004i	0.903851	−	0.427847i	$-0.140728\pi$
$13$	6.18805	+	6.18805i	0.476004	+	0.476004i	−0.427847	+	0.903851i	$0.640728\pi$
$14$		−	12.0077i		−	0.857690i
$15$	8.57832	+	1.18847i	0.571888	+	0.0792314i
$16$	−4.00000			−0.250000
$17$	−1.00579	+	1.00579i	−0.0591642	+	0.0591642i	−0.736070	−	0.676906i	$-0.763321\pi$
$17$	−1.00579	+	1.00579i	−0.0591642	+	0.0591642i	0.676906	+	0.736070i	$0.263321\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$		−	17.5101i		−	0.921586i	−0.887508	−	0.460793i	$-0.847565\pi$
$19$		−	17.5101i		−	0.921586i	0.887508	−	0.460793i	$-0.152435\pi$
$20$	−6.03378	−	7.97455i	−0.301689	−	0.398727i
$21$	−14.7063			−0.700301
$22$	21.0865	−	21.0865i	0.958476	−	0.958476i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$24$			4.89898i			0.204124i
$25$	6.79672	−	24.0584i	0.271869	−	0.962334i
$26$	−12.3761			−0.476004
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	12.0077	+	12.0077i	0.428845	+	0.428845i
$29$		−	36.7302i		−	1.26656i	−0.773923	−	0.633280i	$-0.781708\pi$
$29$		−	36.7302i		−	1.26656i	0.773923	−	0.633280i	$-0.218292\pi$
$30$	−9.76679	+	7.38985i	−0.325560	+	0.246328i
$31$	−27.5739			−0.889480			−0.444740	−	0.895660i	$-0.646704\pi$
$31$	−27.5739			−0.889480			−0.444740	+	0.895660i	$0.646704\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	−25.8256	−	25.8256i	−0.782593	−	0.782593i
$34$		−	2.01158i		−	0.0591642i
$35$	−5.82601	+	42.0518i	−0.166457	+	1.20148i
$36$	6.00000			0.166667
$37$	−26.3672	+	26.3672i	−0.712627	+	0.712627i	−0.967084	−	0.254457i	$-0.918103\pi$
$37$	−26.3672	+	26.3672i	−0.712627	+	0.712627i	0.254457	+	0.967084i	$0.418103\pi$
$38$	17.5101	+	17.5101i	0.460793	+	0.460793i
$39$			15.1576i			0.388655i
$40$	14.0083	+	1.94077i	0.350208	+	0.0485191i
$41$	−26.4885			−0.646061			−0.323031	−	0.946389i	$-0.604702\pi$
$41$	−26.4885			−0.646061			−0.323031	+	0.946389i	$0.604702\pi$
$42$	14.7063	−	14.7063i	0.350150	−	0.350150i
$43$	−22.3435	−	22.3435i	−0.519615	−	0.519615i	0.397840	−	0.917455i	$-0.369760\pi$
$43$	−22.3435	−	22.3435i	−0.519615	−	0.519615i	−0.917455	+	0.397840i	$0.869760\pi$
$44$			42.1730i			0.958476i
$45$	9.05068	+	11.9618i	0.201126	+	0.265818i
$46$	−6.78233			−0.147442
$47$	4.99263	−	4.99263i	0.106226	−	0.106226i	−0.651996	−	0.758222i	$-0.726068\pi$
$47$	4.99263	−	4.99263i	0.106226	−	0.106226i	0.758222	+	0.651996i	$0.226068\pi$
$48$	−4.89898	−	4.89898i	−0.102062	−	0.102062i
$49$		−	23.0919i		−	0.471263i
$50$	17.2616	+	30.8551i	0.345233	+	0.617102i
$51$	−2.46367			−0.0483073
$52$	12.3761	−	12.3761i	0.238002	−	0.238002i
$53$	−52.5294	−	52.5294i	−0.991120	−	0.991120i	0.00884058	−	0.999961i	$-0.497186\pi$
$53$	−52.5294	−	52.5294i	−0.991120	−	0.991120i	−0.999961	+	0.00884058i	$0.997186\pi$
$54$		−	7.34847i		−	0.136083i
$55$	−84.0776	+	63.6156i	−1.52868	+	1.15665i
$56$	−24.0153			−0.428845
$57$	21.4455	−	21.4455i	0.376236	−	0.376236i
$58$	36.7302	+	36.7302i	0.633280	+	0.633280i
$59$			59.1834i			1.00311i	0.865126	+	0.501554i	$0.167238\pi$
$59$			59.1834i			1.00311i	−0.865126	+	0.501554i	$0.832762\pi$
$60$	2.37694	−	17.1566i	0.0396157	−	0.285944i
$61$	−60.6356			−0.994027			−0.497013	−	0.867743i	$-0.665570\pi$
$61$	−60.6356			−0.994027			−0.497013	+	0.867743i	$0.665570\pi$
$62$	27.5739	−	27.5739i	0.444740	−	0.444740i
$63$	−18.0115	−	18.0115i	−0.285897	−	0.285897i
$64$			8.00000i			0.125000i
$65$	43.3421	+	6.00477i	0.666802	+	0.0923811i
$66$	51.6511			0.782593
$67$	−56.3450	+	56.3450i	−0.840970	+	0.840970i	−0.988985	−	0.148015i	$-0.952711\pi$
$67$	−56.3450	+	56.3450i	−0.840970	+	0.840970i	0.148015	+	0.988985i	$0.452711\pi$
$68$	2.01158	+	2.01158i	0.0295821	+	0.0295821i
$69$			8.30662i			0.120386i
$70$	−36.2258	−	47.8778i	−0.517512	−	0.683969i
$71$	−6.19517			−0.0872560			−0.0436280	−	0.999048i	$-0.513892\pi$
$71$	−6.19517			−0.0872560			−0.0436280	+	0.999048i	$0.513892\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	−10.2369	−	10.2369i	−0.140232	−	0.140232i	0.633506	−	0.773738i	$-0.281615\pi$
$73$	−10.2369	−	10.2369i	−0.140232	−	0.140232i	−0.773738	+	0.633506i	$0.781615\pi$
$74$		−	52.7344i		−	0.712627i
$75$	37.7896	−	21.1411i	0.503861	−	0.281881i
$76$	−35.0203			−0.460793
$77$	126.600	−	126.600i	1.64415	−	1.64415i
$78$	−15.1576	−	15.1576i	−0.194328	−	0.194328i
$79$			44.9126i			0.568514i	0.958748	+	0.284257i	$0.0917469\pi$
$79$			44.9126i			0.568514i	−0.958748	+	0.284257i	$0.908253\pi$
$80$	−15.9491	+	12.0676i	−0.199364	+	0.150845i
$81$	−9.00000			−0.111111
$82$	26.4885	−	26.4885i	0.323031	−	0.323031i
$83$	−53.2159	−	53.2159i	−0.641155	−	0.641155i	0.309684	−	0.950839i	$-0.399777\pi$
$83$	−53.2159	−	53.2159i	−0.641155	−	0.641155i	−0.950839	+	0.309684i	$0.899777\pi$
$84$			29.4126i			0.350150i
$85$	−0.976002	+	7.04473i	−0.0114824	+	0.0828792i
$86$	44.6869			0.519615
$87$	44.9852	−	44.9852i	0.517071	−	0.517071i
$88$	−42.1730	−	42.1730i	−0.479238	−	0.479238i
$89$		−	117.848i		−	1.32413i	−0.749444	−	0.662067i	$-0.769679\pi$
$89$		−	117.848i		−	1.32413i	0.749444	−	0.662067i	$-0.230321\pi$
$90$	−21.0125	−	2.91115i	−0.233472	−	0.0323461i
$91$	−74.3039			−0.816527
$92$	6.78233	−	6.78233i	0.0737210	−	0.0737210i
$93$	−33.7710	−	33.7710i	−0.363129	−	0.363129i
$94$			9.98527i			0.106226i
$95$	−52.8262	−	69.8177i	−0.556065	−	0.734923i
$96$	9.79796			0.102062
$97$	37.7963	−	37.7963i	0.389652	−	0.389652i	−0.484911	−	0.874563i	$-0.661148\pi$
$97$	37.7963	−	37.7963i	0.389652	−	0.389652i	0.874563	+	0.484911i	$0.161148\pi$
$98$	23.0919	+	23.0919i	0.235632	+	0.235632i
$99$		−	63.2594i		−	0.638984i
$100$	−48.1167	−	13.5934i	−0.481167	−	0.135934i
$101$	0.722362			0.00715210			0.00357605	−	0.999994i	$-0.498862\pi$
$101$	0.722362			0.00715210			0.00357605	+	0.999994i	$0.498862\pi$
$102$	2.46367	−	2.46367i	0.0241537	−	0.0241537i
$103$	51.2106	+	51.2106i	0.497190	+	0.497190i	0.910562	−	0.413372i	$-0.135649\pi$
$103$	51.2106	+	51.2106i	0.497190	+	0.497190i	−0.413372	+	0.910562i	$0.635649\pi$
$104$			24.7522i			0.238002i
$105$	−58.6381	+	44.3674i	−0.558458	+	0.422546i
$106$	105.059			0.991120
$107$	130.522	−	130.522i	1.21983	−	1.21983i	0.252138	−	0.967691i	$-0.418866\pi$
$107$	130.522	−	130.522i	1.21983	−	1.21983i	0.967691	−	0.252138i	$-0.0811336\pi$
$108$	7.34847	+	7.34847i	0.0680414	+	0.0680414i
$109$			59.6898i			0.547613i	0.961785	+	0.273806i	$0.0882828\pi$
$109$			59.6898i			0.547613i	−0.961785	+	0.273806i	$0.911717\pi$
$110$	20.4620	−	147.693i	0.186018	−	1.34267i
$111$	−64.5862			−0.581858
$112$	24.0153	−	24.0153i	0.214422	−	0.214422i
$113$	30.6253	+	30.6253i	0.271020	+	0.271020i	0.829511	−	0.558491i	$-0.188619\pi$
$113$	30.6253	+	30.6253i	0.271020	+	0.271020i	−0.558491	+	0.829511i	$0.688619\pi$
$114$			42.8909i			0.376236i
$115$	23.7523	+	3.29073i	0.206542	+	0.0286150i
$116$	−73.4604			−0.633280
$117$	−18.5641	+	18.5641i	−0.158668	+	0.158668i
$118$	−59.1834	−	59.1834i	−0.501554	−	0.501554i
$119$		−	12.0772i		−	0.101489i
$120$	14.7797	+	19.5336i	0.123164	+	0.162780i
$121$	323.640			2.67471
$122$	60.6356	−	60.6356i	0.497013	−	0.497013i
$123$	−32.4417	−	32.4417i	−0.263753	−	0.263753i
$124$			55.1478i			0.444740i
$125$	−45.4811	−	116.432i	−0.363849	−	0.931458i
$126$	36.0230			0.285897
$127$	−147.054	+	147.054i	−1.15791	+	1.15791i	−0.172984	+	0.984925i	$0.555341\pi$
$127$	−147.054	+	147.054i	−1.15791	+	1.15791i	−0.984925	+	0.172984i	$0.944659\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$		−	54.7301i		−	0.424264i
$130$	−49.3469	+	37.3373i	−0.379591	+	0.287210i
$131$	−135.120			−1.03145			−0.515724	−	0.856755i	$-0.672477\pi$
$131$	−135.120			−1.03145			−0.515724	+	0.856755i	$0.672477\pi$
$132$	−51.6511	+	51.6511i	−0.391296	+	0.391296i
$133$	105.128	+	105.128i	0.790435	+	0.790435i
$134$		−	112.690i		−	0.840970i
$135$	−3.56541	+	25.7350i	−0.0264105	+	0.190629i
$136$	−4.02316			−0.0295821
$137$	97.0197	−	97.0197i	0.708173	−	0.708173i	−0.257978	−	0.966151i	$-0.583056\pi$
$137$	97.0197	−	97.0197i	0.708173	−	0.708173i	0.966151	+	0.257978i	$0.0830561\pi$
$138$	−8.30662	−	8.30662i	−0.0601929	−	0.0601929i
$139$			227.494i			1.63664i	0.574759	+	0.818322i	$0.305096\pi$
$139$			227.494i			1.63664i	−0.574759	+	0.818322i	$0.694904\pi$
$140$	84.1036	+	11.6520i	0.600740	+	0.0832287i
$141$	12.2294			0.0867334
$142$	6.19517	−	6.19517i	0.0436280	−	0.0436280i
$143$	−130.484	−	130.484i	−0.912476	−	0.912476i
$144$		−	12.0000i		−	0.0833333i
$145$	−110.811	−	146.453i	−0.764215	−	1.01002i
$146$	20.4738			0.140232
$147$	28.2817	−	28.2817i	0.192393	−	0.192393i
$148$	52.7344	+	52.7344i	0.356314	+	0.356314i
$149$			122.204i			0.820160i	0.912050	+	0.410080i	$0.134499\pi$
$149$			122.204i			0.820160i	−0.912050	+	0.410080i	$0.865501\pi$
$150$	−16.6485	+	58.9307i	−0.110990	+	0.392871i
$151$	−251.682			−1.66677			−0.833386	−	0.552692i	$-0.813601\pi$
$151$	−251.682			−1.66677			−0.833386	+	0.552692i	$0.813601\pi$
$152$	35.0203	−	35.0203i	0.230397	−	0.230397i
$153$	−3.01737	−	3.01737i	−0.0197214	−	0.0197214i
$154$			253.199i			1.64415i
$155$	−109.945	+	83.1875i	−0.709321	+	0.536693i
$156$	30.3151			0.194328
$157$	−127.807	+	127.807i	−0.814056	+	0.814056i	−0.985239	−	0.171183i	$-0.945241\pi$
$157$	−127.807	+	127.807i	−0.814056	+	0.814056i	0.171183	+	0.985239i	$0.445241\pi$
$158$	−44.9126	−	44.9126i	−0.284257	−	0.284257i
$159$		−	128.670i		−	0.809246i
$160$	3.88153	−	28.0167i	0.0242596	−	0.175104i
$161$	−40.7199			−0.252919
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	−159.010	−	159.010i	−0.975523	−	0.975523i	0.0241846	−	0.999708i	$-0.492301\pi$
$163$	−159.010	−	159.010i	−0.975523	−	0.975523i	−0.999708	+	0.0241846i	$0.992301\pi$
$164$			52.9770i			0.323031i
$165$	−180.887	−	25.0607i	−1.09628	−	0.151883i
$166$	106.432			0.641155
$167$	215.445	−	215.445i	1.29009	−	1.29009i	0.355364	−	0.934728i	$-0.384357\pi$
$167$	215.445	−	215.445i	1.29009	−	1.29009i	0.934728	−	0.355364i	$-0.115643\pi$
$168$	−29.4126	−	29.4126i	−0.175075	−	0.175075i
$169$		−	92.4162i		−	0.546841i
$170$	−6.06873	−	8.02073i	−0.0356984	−	0.0471808i
$171$	52.5304			0.307195
$172$	−44.6869	+	44.6869i	−0.259808	+	0.259808i
$173$	196.009	+	196.009i	1.13300	+	1.13300i	0.989676	+	0.143324i	$0.0457792\pi$
$173$	196.009	+	196.009i	1.13300	+	1.13300i	0.143324	+	0.989676i	$0.454221\pi$
$174$			89.9703i			0.517071i
$175$	103.636	+	185.249i	0.592205	+	1.05856i
$176$	84.3459			0.479238
$177$	−72.4846	+	72.4846i	−0.409517	+	0.409517i
$178$	117.848	+	117.848i	0.662067	+	0.662067i
$179$			199.164i			1.11265i	0.830966	+	0.556324i	$0.187789\pi$
$179$			199.164i			1.11265i	−0.830966	+	0.556324i	$0.812211\pi$
$180$	23.9236	−	18.1014i	0.132909	−	0.100563i
$181$	−93.9000			−0.518785			−0.259392	−	0.965772i	$-0.583522\pi$
$181$	−93.9000			−0.518785			−0.259392	+	0.965772i	$0.583522\pi$
$182$	74.3039	−	74.3039i	0.408263	−	0.408263i
$183$	−74.2632	−	74.2632i	−0.405810	−	0.405810i
$184$			13.5647i			0.0737210i
$185$	−25.5863	+	184.680i	−0.138304	+	0.998272i
$186$	67.5420			0.363129
$187$	21.2086	−	21.2086i	0.113415	−	0.113415i
$188$	−9.98527	−	9.98527i	−0.0531131	−	0.0531131i
$189$		−	44.1189i		−	0.233434i
$190$	122.644	+	16.9915i	0.645494	+	0.0894291i
$191$	56.7646			0.297197			0.148598	−	0.988898i	$-0.452524\pi$
$191$	56.7646			0.297197			0.148598	+	0.988898i	$0.452524\pi$
$192$	−9.79796	+	9.79796i	−0.0510310	+	0.0510310i
$193$	174.217	+	174.217i	0.902676	+	0.902676i	0.995667	−	0.0929907i	$-0.0296427\pi$
$193$	174.217	+	174.217i	0.902676	+	0.902676i	−0.0929907	+	0.995667i	$0.529643\pi$
$194$			75.5926i			0.389652i
$195$	45.7287	+	60.4373i	0.234506	+	0.309935i
$196$	−46.1838			−0.235632
$197$	−44.6214	+	44.6214i	−0.226504	+	0.226504i	−0.811231	−	0.584726i	$-0.801202\pi$
$197$	−44.6214	+	44.6214i	−0.226504	+	0.226504i	0.584726	+	0.811231i	$0.301202\pi$
$198$	63.2594	+	63.2594i	0.319492	+	0.319492i
$199$		−	98.4802i		−	0.494875i	−0.968904	−	0.247438i	$-0.920411\pi$
$199$		−	98.4802i		−	0.494875i	0.968904	−	0.247438i	$-0.0795886\pi$
$200$	61.7102	−	34.5233i	0.308551	−	0.172616i
$201$	−138.016			−0.686649
$202$	−0.722362	+	0.722362i	−0.00357605	+	0.00357605i
$203$	220.522	+	220.522i	1.08632	+	1.08632i
$204$			4.92735i			0.0241537i
$205$	−105.617	+	79.9130i	−0.515205	+	0.389819i
$206$	−102.421			−0.497190
$207$	−10.1735	+	10.1735i	−0.0491473	+	0.0491473i
$208$	−24.7522	−	24.7522i	−0.119001	−	0.119001i
$209$			369.227i			1.76664i
$210$	14.2708	−	103.005i	0.0679560	−	0.490502i
$211$	314.996			1.49287			0.746435	−	0.665458i	$-0.231764\pi$
$211$	314.996			1.49287			0.746435	+	0.665458i	$0.231764\pi$
$212$	−105.059	+	105.059i	−0.495560	+	0.495560i
$213$	−7.58751	−	7.58751i	−0.0356221	−	0.0356221i
$214$			261.043i			1.21983i
$215$	−156.497	−	21.6817i	−0.727895	−	0.100845i
$216$	−14.6969			−0.0680414
$217$	165.549	−	165.549i	0.762898	−	0.762898i
$218$	−59.6898	−	59.6898i	−0.273806	−	0.273806i
$219$		−	25.0752i		−	0.114499i
$220$	127.231	+	168.155i	0.578324	+	0.764342i
$221$	−12.4478			−0.0563247
$222$	64.5862	−	64.5862i	0.290929	−	0.290929i
$223$	75.6348	+	75.6348i	0.339170	+	0.339170i	0.856055	−	0.516885i	$-0.172909\pi$
$223$	75.6348	+	75.6348i	0.339170	+	0.339170i	−0.516885	+	0.856055i	$0.672909\pi$
$224$			48.0306i			0.214422i
$225$	72.1751	+	20.3902i	0.320778	+	0.0906230i
$226$	−61.2506			−0.271020
$227$	−193.730	+	193.730i	−0.853438	+	0.853438i	−0.990555	−	0.137117i	$-0.956216\pi$
$227$	−193.730	+	193.730i	−0.853438	+	0.853438i	0.137117	+	0.990555i	$0.456216\pi$
$228$	−42.8909	−	42.8909i	−0.188118	−	0.188118i
$229$		−	32.5190i		−	0.142004i	−0.997476	−	0.0710021i	$-0.977380\pi$
$229$		−	32.5190i		−	0.142004i	0.997476	−	0.0710021i	$-0.0226197\pi$
$230$	−27.0430	+	20.4616i	−0.117578	+	0.0889633i
$231$	310.104			1.34244
$232$	73.4604	−	73.4604i	0.316640	−	0.316640i
$233$	67.8411	+	67.8411i	0.291164	+	0.291164i	0.837540	−	0.546376i	$-0.183993\pi$
$233$	67.8411	+	67.8411i	0.291164	+	0.291164i	−0.546376	+	0.837540i	$0.683993\pi$
$234$		−	37.1283i		−	0.158668i
$235$	4.84476	−	34.9692i	0.0206160	−	0.148805i
$236$	118.367			0.501554
$237$	−55.0065	+	55.0065i	−0.232095	+	0.232095i
$238$	12.0772	+	12.0772i	0.0507445	+	0.0507445i
$239$			199.800i			0.835981i	0.908451	+	0.417991i	$0.137266\pi$
$239$			199.800i			0.835981i	−0.908451	+	0.417991i	$0.862734\pi$
$240$	−34.3133	−	4.75388i	−0.142972	−	0.0198079i
$241$	−39.9680			−0.165842			−0.0829212	−	0.996556i	$-0.526425\pi$
$241$	−39.9680			−0.165842			−0.0829212	+	0.996556i	$0.526425\pi$
$242$	−323.640	+	323.640i	−1.33735	+	1.33735i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$			121.271i			0.497013i
$245$	−69.6658	−	92.0738i	−0.284350	−	0.375811i
$246$	64.8833			0.263753
$247$	108.354	−	108.354i	0.438678	−	0.438678i
$248$	−55.1478	−	55.1478i	−0.222370	−	0.222370i
$249$		−	130.352i		−	0.523501i
$250$	161.913	+	70.9512i	0.647653	+	0.283805i
$251$	449.793			1.79200			0.896002	−	0.444051i	$-0.146459\pi$
$251$	449.793			1.79200			0.896002	+	0.444051i	$0.146459\pi$
$252$	−36.0230	+	36.0230i	−0.142948	+	0.142948i
$253$	−71.5077	−	71.5077i	−0.282639	−	0.282639i
$254$		−	294.109i		−	1.15791i
$255$	−9.82335	+	7.43264i	−0.0385229	+	0.0291476i
$256$	16.0000			0.0625000
$257$	192.890	−	192.890i	0.750543	−	0.750543i	−0.224037	−	0.974581i	$-0.571924\pi$
$257$	192.890	−	192.890i	0.750543	−	0.750543i	0.974581	+	0.224037i	$0.0719237\pi$
$258$	54.7301	+	54.7301i	0.212132	+	0.212132i
$259$		−	316.608i		−	1.22243i
$260$	12.0095	−	86.6842i	0.0461906	−	0.333401i
$261$	110.191			0.422186
$262$	135.120	−	135.120i	0.515724	−	0.515724i
$263$	−221.543	−	221.543i	−0.842371	−	0.842371i	0.146796	−	0.989167i	$-0.453104\pi$
$263$	−221.543	−	221.543i	−0.842371	−	0.842371i	−0.989167	+	0.146796i	$0.953104\pi$
$264$		−	103.302i		−	0.391296i
$265$	−367.925	−	50.9736i	−1.38839	−	0.192353i
$266$	−210.256			−0.790435
$267$	144.334	−	144.334i	0.540576	−	0.540576i
$268$	112.690	+	112.690i	0.420485	+	0.420485i
$269$		−	27.1359i		−	0.100877i	−0.998727	−	0.0504385i	$-0.983938\pi$
$269$		−	27.1359i		−	0.100877i	0.998727	−	0.0504385i	$-0.0160619\pi$
$270$	−22.1695	−	29.3004i	−0.0821094	−	0.108520i
$271$	58.8552			0.217178			0.108589	−	0.994087i	$-0.465367\pi$
$271$	58.8552			0.217178			0.108589	+	0.994087i	$0.465367\pi$
$272$	4.02316	−	4.02316i	0.0147910	−	0.0147910i
$273$	−91.0034	−	91.0034i	−0.333346	−	0.333346i
$274$			194.039i			0.708173i
$275$	−143.319	+	507.306i	−0.521160	+	1.84475i
$276$	16.6132			0.0601929
$277$	−125.315	+	125.315i	−0.452399	+	0.452399i	−0.896150	−	0.443751i	$-0.853648\pi$
$277$	−125.315	+	125.315i	−0.452399	+	0.452399i	0.443751	+	0.896150i	$0.353648\pi$
$278$	−227.494	−	227.494i	−0.818322	−	0.818322i
$279$		−	82.7217i		−	0.296493i
$280$	−95.7557	+	72.4516i	−0.341984	+	0.258756i
$281$	−248.499			−0.884338			−0.442169	−	0.896932i	$-0.645791\pi$
$281$	−248.499			−0.884338			−0.442169	+	0.896932i	$0.645791\pi$
$282$	−12.2294	+	12.2294i	−0.0433667	+	0.0433667i
$283$	−7.52411	−	7.52411i	−0.0265870	−	0.0265870i	0.693688	−	0.720275i	$-0.255985\pi$
$283$	−7.52411	−	7.52411i	−0.0265870	−	0.0265870i	−0.720275	+	0.693688i	$0.755985\pi$
$284$			12.3903i			0.0436280i
$285$	20.8103	−	150.208i	0.0730186	−	0.527044i
$286$	260.968			0.912476
$287$	159.032	−	159.032i	0.554120	−	0.554120i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$			286.977i			0.992999i
$290$	257.265	+	35.6424i	0.887119	+	0.122905i
$291$	92.5816			0.318150
$292$	−20.4738	+	20.4738i	−0.0701158	+	0.0701158i
$293$	134.027	+	134.027i	0.457429	+	0.457429i	0.897811	−	0.440382i	$-0.145157\pi$
$293$	134.027	+	134.027i	0.457429	+	0.457429i	−0.440382	+	0.897811i	$0.645157\pi$
$294$			56.5634i			0.192393i
$295$	178.550	+	235.981i	0.605254	+	0.799934i
$296$	−105.469			−0.356314
$297$	77.4767	−	77.4767i	0.260864	−	0.260864i
$298$	−122.204	−	122.204i	−0.410080	−	0.410080i
$299$			41.9694i			0.140366i
$300$	−42.2822	−	75.5792i	−0.140941	−	0.251931i
$301$	268.293			0.891338
$302$	251.682	−	251.682i	0.833386	−	0.833386i
$303$	0.884709	+	0.884709i	0.00291983	+	0.00291983i
$304$			70.0406i			0.230397i
$305$	−241.771	+	182.931i	−0.792692	+	0.599774i
$306$	6.03475			0.0197214
$307$	−40.5810	+	40.5810i	−0.132186	+	0.132186i	−0.770104	−	0.637918i	$-0.779796\pi$
$307$	−40.5810	+	40.5810i	−0.132186	+	0.132186i	0.637918	+	0.770104i	$0.279796\pi$
$308$	−253.199	−	253.199i	−0.822075	−	0.822075i
$309$			125.440i			0.405954i
$310$	26.7572	−	193.132i	0.0863136	−	0.623007i
$311$	167.030			0.537075			0.268537	−	0.963269i	$-0.413460\pi$
$311$	167.030			0.537075			0.268537	+	0.963269i	$0.413460\pi$
$312$	−30.3151	+	30.3151i	−0.0971638	+	0.0971638i
$313$	−124.961	−	124.961i	−0.399238	−	0.399238i	0.478726	−	0.877964i	$-0.341099\pi$
$313$	−124.961	−	124.961i	−0.399238	−	0.399238i	−0.877964	+	0.478726i	$0.841099\pi$
$314$		−	255.614i		−	0.814056i
$315$	−126.155	−	17.4780i	−0.400494	−	0.0554858i
$316$	89.8252			0.284257
$317$	253.126	−	253.126i	0.798505	−	0.798505i	−0.184355	−	0.982860i	$-0.559019\pi$
$317$	253.126	−	253.126i	0.798505	−	0.798505i	0.982860	+	0.184355i	$0.0590195\pi$
$318$	128.670	+	128.670i	0.404623	+	0.404623i
$319$			774.511i			2.42793i
$320$	24.1351	+	31.8982i	0.0754223	+	0.0996819i
$321$	319.712			0.995986
$322$	40.7199	−	40.7199i	0.126459	−	0.126459i
$323$	17.6115	+	17.6115i	0.0545249	+	0.0545249i
$324$			18.0000i			0.0555556i
$325$	190.933	−	106.816i	0.587485	−	0.328664i
$326$	318.020			0.975523
$327$	−73.1048	+	73.1048i	−0.223562	+	0.223562i
$328$	−52.9770	−	52.9770i	−0.161515	−	0.161515i
$329$			59.9498i			0.182218i
$330$	205.947	−	155.826i	0.624082	−	0.472200i
$331$	−578.658			−1.74821			−0.874106	−	0.485735i	$-0.838552\pi$
$331$	−578.658			−1.74821			−0.874106	+	0.485735i	$0.838552\pi$
$332$	−106.432	+	106.432i	−0.320578	+	0.320578i
$333$	−79.1016	−	79.1016i	−0.237542	−	0.237542i
$334$			430.891i			1.29009i
$335$	−54.6762	+	394.650i	−0.163212	+	1.17806i
$336$	58.8253			0.175075
$337$	84.2588	−	84.2588i	0.250026	−	0.250026i	−0.570955	−	0.820981i	$-0.693427\pi$
$337$	84.2588	−	84.2588i	0.250026	−	0.250026i	0.820981	+	0.570955i	$0.193427\pi$
$338$	92.4162	+	92.4162i	0.273421	+	0.273421i
$339$			75.0163i			0.221287i
$340$	14.0895	+	1.95200i	0.0414396	+	0.00574119i
$341$	581.436			1.70509
$342$	−52.5304	+	52.5304i	−0.153598	+	0.153598i
$343$	−155.548	−	155.548i	−0.453492	−	0.453492i
$344$		−	89.3738i		−	0.259808i
$345$	25.0602	+	33.1208i	0.0726382	+	0.0960023i
$346$	−392.018			−1.13300
$347$	−472.033	+	472.033i	−1.36033	+	1.36033i	−0.486830	+	0.873497i	$0.661847\pi$
$347$	−472.033	+	472.033i	−1.36033	+	1.36033i	−0.873497	+	0.486830i	$0.838153\pi$
$348$	−89.9703	−	89.9703i	−0.258535	−	0.258535i
$349$			224.162i			0.642297i	0.947029	+	0.321148i	$0.104069\pi$
$349$			224.162i			0.642297i	−0.947029	+	0.321148i	$0.895931\pi$
$350$	−288.885	−	81.6127i	−0.825384	−	0.233179i
$351$	−45.4727			−0.129552
$352$	−84.3459	+	84.3459i	−0.239619	+	0.239619i
$353$	−173.495	−	173.495i	−0.491489	−	0.491489i	0.417286	−	0.908775i	$-0.362981\pi$
$353$	−173.495	−	173.495i	−0.491489	−	0.491489i	−0.908775	+	0.417286i	$0.862981\pi$
$354$		−	144.969i		−	0.409517i
$355$	−24.7019	+	18.6902i	−0.0695827	+	0.0526484i
$356$	−235.696			−0.662067
$357$	14.7915	−	14.7915i	0.0414327	−	0.0414327i
$358$	−199.164	−	199.164i	−0.556324	−	0.556324i
$359$			330.215i			0.919818i	0.887966	+	0.459909i	$0.152118\pi$
$359$			330.215i			0.919818i	−0.887966	+	0.459909i	$0.847882\pi$
$360$	−5.82230	+	42.0250i	−0.0161730	+	0.116736i
$361$	54.3951			0.150679
$362$	93.9000	−	93.9000i	0.259392	−	0.259392i
$363$	396.376	+	396.376i	1.09195	+	1.09195i
$364$			148.608i			0.408263i
$365$	−71.7010	−	9.93371i	−0.196441	−	0.0272157i
$366$	148.526			0.405810
$367$	248.568	−	248.568i	0.677296	−	0.677296i	−0.282091	−	0.959388i	$-0.591028\pi$
$367$	248.568	−	248.568i	0.677296	−	0.677296i	0.959388	+	0.282091i	$0.0910281\pi$
$368$	−13.5647	−	13.5647i	−0.0368605	−	0.0368605i
$369$		−	79.4655i		−	0.215354i
$370$	−159.094	−	210.267i	−0.429984	−	0.568288i
$371$	630.755			1.70015
$372$	−67.5420	+	67.5420i	−0.181564	+	0.181564i
$373$	324.805	+	324.805i	0.870790	+	0.870790i	0.992558	−	0.121769i	$-0.0388567\pi$
$373$	324.805	+	324.805i	0.870790	+	0.870790i	−0.121769	+	0.992558i	$0.538857\pi$
$374$			42.4172i			0.113415i
$375$	86.8971	−	198.303i	0.231726	−	0.528807i
$376$	19.9705			0.0531131
$377$	227.288	−	227.288i	0.602887	−	0.602887i
$378$	44.1189	+	44.1189i	0.116717	+	0.116717i
$379$			594.997i			1.56991i	0.619550	+	0.784957i	$0.287315\pi$
$379$			594.997i			1.56991i	−0.619550	+	0.784957i	$0.712685\pi$
$380$	−139.635	+	105.652i	−0.367462	+	0.278033i
$381$	−360.208			−0.945429
$382$	−56.7646	+	56.7646i	−0.148598	+	0.148598i
$383$	−432.810	−	432.810i	−1.13005	−	1.13005i	−0.990168	−	0.139883i	$-0.955327\pi$
$383$	−432.810	−	432.810i	−1.13005	−	1.13005i	−0.139883	−	0.990168i	$-0.544673\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	122.850	−	886.725i	0.319091	−	2.30318i
$386$	−348.433			−0.902676
$387$	67.0304	−	67.0304i	0.173205	−	0.173205i
$388$	−75.5926	−	75.5926i	−0.194826	−	0.194826i
$389$		−	72.4398i		−	0.186221i	−0.995656	−	0.0931103i	$-0.970319\pi$
$389$		−	72.4398i		−	0.186221i	0.995656	−	0.0931103i	$-0.0296809\pi$
$390$	−106.166	−	14.7086i	−0.272221	−	0.0377144i
$391$	−6.82161			−0.0174466
$392$	46.1838	−	46.1838i	0.117816	−	0.117816i
$393$	−165.487	−	165.487i	−0.421087	−	0.421087i
$394$		−	89.2428i		−	0.226504i
$395$	135.497	+	179.079i	0.343029	+	0.453364i
$396$	−126.519			−0.319492
$397$	455.021	−	455.021i	1.14615	−	1.14615i	0.158844	−	0.987304i	$-0.449223\pi$
$397$	455.021	−	455.021i	1.14615	−	1.14615i	0.987304	−	0.158844i	$-0.0507766\pi$
$398$	98.4802	+	98.4802i	0.247438	+	0.247438i
$399$			257.510i			0.645388i
$400$	−27.1869	+	96.2334i	−0.0679672	+	0.240584i
$401$	−411.151			−1.02532			−0.512658	−	0.858593i	$-0.671339\pi$
$401$	−411.151			−1.02532			−0.512658	+	0.858593i	$0.671339\pi$
$402$	138.016	−	138.016i	0.343324	−	0.343324i
$403$	−170.629	−	170.629i	−0.423396	−	0.423396i
$404$		−	1.44472i		−	0.00357605i
$405$	−35.8855	+	27.1520i	−0.0886061	+	0.0670421i
$406$	−441.044			−1.08632
$407$	555.992	−	555.992i	1.36607	−	1.36607i
$408$	−4.92735	−	4.92735i	−0.0120768	−	0.0120768i
$409$			126.323i			0.308858i	0.988004	+	0.154429i	$0.0493538\pi$
$409$			126.323i			0.308858i	−0.988004	+	0.154429i	$0.950646\pi$
$410$	25.7040	−	185.530i	0.0626927	−	0.452512i
$411$	237.649			0.578221
$412$	102.421	−	102.421i	0.248595	−	0.248595i
$413$	−355.327	−	355.327i	−0.860356	−	0.860356i
$414$		−	20.3470i		−	0.0491473i
$415$	−372.733	−	51.6398i	−0.898152	−	0.124433i
$416$	49.5044			0.119001
$417$	−278.622	+	278.622i	−0.668157	+	0.668157i
$418$	−369.227	−	369.227i	−0.883319	−	0.883319i
$419$		−	81.1655i		−	0.193712i	−0.995298	−	0.0968562i	$-0.969121\pi$
$419$		−	81.1655i		−	0.193712i	0.995298	−	0.0968562i	$-0.0308787\pi$
$420$	88.7347	+	117.276i	0.211273	+	0.279229i
$421$	−453.518			−1.07724			−0.538620	−	0.842549i	$-0.681054\pi$
$421$	−453.518			−1.07724			−0.538620	+	0.842549i	$0.681054\pi$
$422$	−314.996	+	314.996i	−0.746435	+	0.746435i
$423$	14.9779	+	14.9779i	0.0354087	+	0.0354087i
$424$		−	210.118i		−	0.495560i
$425$	17.3616	+	31.0338i	0.0408508	+	0.0730206i
$426$	15.1750			0.0356221
$427$	364.046	−	364.046i	0.852567	−	0.852567i
$428$	−261.043	−	261.043i	−0.609915	−	0.609915i
$429$		−	319.620i		−	0.745034i
$430$	178.179	−	134.816i	0.414370	−	0.313525i
$431$	−455.025			−1.05574			−0.527872	−	0.849324i	$-0.677010\pi$
$431$	−455.025			−1.05574			−0.527872	+	0.849324i	$0.677010\pi$
$432$	14.6969	−	14.6969i	0.0340207	−	0.0340207i
$433$	−133.773	−	133.773i	−0.308945	−	0.308945i	0.535555	−	0.844500i	$-0.320102\pi$
$433$	−133.773	−	133.773i	−0.308945	−	0.308945i	−0.844500	+	0.535555i	$0.820102\pi$
$434$			331.098i			0.762898i
$435$	43.6528	−	315.084i	0.100351	−	0.724330i
$436$	119.380			0.273806
$437$	59.3798	−	59.3798i	0.135880	−	0.135880i
$438$	25.0752	+	25.0752i	0.0572493	+	0.0572493i
$439$		−	544.847i		−	1.24111i	−0.784163	−	0.620555i	$-0.786907\pi$
$439$		−	544.847i		−	1.24111i	0.784163	−	0.620555i	$-0.213093\pi$
$440$	−295.386	−	40.9239i	−0.671333	−	0.0930089i
$441$	69.2757			0.157088
$442$	12.4478	−	12.4478i	0.0281624	−	0.0281624i
$443$	−213.869	−	213.869i	−0.482774	−	0.482774i	0.423243	−	0.906016i	$-0.360892\pi$
$443$	−213.869	−	213.869i	−0.482774	−	0.482774i	−0.906016	+	0.423243i	$0.860892\pi$
$444$			129.172i			0.290929i
$445$	−355.535	−	469.892i	−0.798954	−	1.05594i
$446$	−151.270			−0.339170
$447$	−149.668	+	149.668i	−0.334829	+	0.334829i
$448$	−48.0306	−	48.0306i	−0.107211	−	0.107211i
$449$		−	892.075i		−	1.98680i	−0.114688	−	0.993402i	$-0.536587\pi$
$449$		−	892.075i		−	1.98680i	0.114688	−	0.993402i	$-0.463413\pi$
$450$	−92.5652	+	51.7849i	−0.205701	+	0.115078i
$451$	558.550			1.23847
$452$	61.2506	−	61.2506i	0.135510	−	0.135510i
$453$	−308.247	−	308.247i	−0.680457	−	0.680457i
$454$		−	387.461i		−	0.853438i
$455$	−296.270	+	224.167i	−0.651143	+	0.492675i
$456$	85.7818			0.188118
$457$	−621.138	+	621.138i	−1.35916	+	1.35916i	−0.484217	+	0.874948i	$0.660895\pi$
$457$	−621.138	+	621.138i	−1.35916	+	1.35916i	−0.874948	+	0.484217i	$0.839105\pi$
$458$	32.5190	+	32.5190i	0.0710021	+	0.0710021i
$459$		−	7.39102i		−	0.0161024i
$460$	6.58145	−	47.5046i	0.0143075	−	0.103271i
$461$	591.449			1.28297			0.641484	−	0.767136i	$-0.278319\pi$
$461$	591.449			1.28297			0.641484	+	0.767136i	$0.278319\pi$
$462$	−310.104	+	310.104i	−0.671222	+	0.671222i
$463$	253.139	+	253.139i	0.546736	+	0.546736i	0.925495	−	0.378759i	$-0.123649\pi$
$463$	253.139	+	253.139i	0.546736	+	0.546736i	−0.378759	+	0.925495i	$0.623649\pi$
$464$			146.921i			0.316640i
$465$	−236.538	−	32.7708i	−0.508683	−	0.0704748i
$466$	−135.682			−0.291164
$467$	12.5041	−	12.5041i	0.0267754	−	0.0267754i	−0.693592	−	0.720368i	$-0.743973\pi$
$467$	12.5041	−	12.5041i	0.0267754	−	0.0267754i	0.720368	+	0.693592i	$0.243973\pi$
$468$	37.1283	+	37.1283i	0.0793339	+	0.0793339i
$469$		−	676.571i		−	1.44258i
$470$	30.1245	+	39.8140i	0.0640946	+	0.0847106i
$471$	−313.061			−0.664674
$472$	−118.367	+	118.367i	−0.250777	+	0.250777i
$473$	471.145	+	471.145i	0.996078	+	0.996078i
$474$		−	110.013i		−	0.232095i
$475$	−421.265	−	119.012i	−0.886874	−	0.250551i
$476$	−24.1544			−0.0507445
$477$	157.588	−	157.588i	0.330373	−	0.330373i
$478$	−199.800	−	199.800i	−0.417991	−	0.417991i
$479$			456.156i			0.952308i	0.879362	+	0.476154i	$0.157970\pi$
$479$			456.156i			0.952308i	−0.879362	+	0.476154i	$0.842030\pi$
$480$	39.0672	−	29.5594i	0.0813899	−	0.0615821i
$481$	−326.323			−0.678426
$482$	39.9680	−	39.9680i	0.0829212	−	0.0829212i
$483$	−49.8715	−	49.8715i	−0.103254	−	0.103254i
$484$		−	647.279i		−	1.33735i
$485$	36.6769	−	264.731i	0.0756224	−	0.545838i
$486$	22.0454			0.0453609
$487$	194.257	−	194.257i	0.398886	−	0.398886i	−0.478954	−	0.877840i	$-0.658984\pi$
$487$	194.257	−	194.257i	0.398886	−	0.398886i	0.877840	+	0.478954i	$0.158984\pi$
$488$	−121.271	−	121.271i	−0.248507	−	0.248507i
$489$		−	389.494i		−	0.796511i
$490$	161.740	+	22.4080i	0.330081	+	0.0457306i
$491$	140.529			0.286210			0.143105	−	0.989708i	$-0.454291\pi$
$491$	140.529			0.286210			0.143105	+	0.989708i	$0.454291\pi$
$492$	−64.8833	+	64.8833i	−0.131877	+	0.131877i
$493$	36.9429	+	36.9429i	0.0749349	+	0.0749349i
$494$			216.707i			0.438678i
$495$	−190.847	−	252.233i	−0.385549	−	0.509561i
$496$	110.296			0.222370
$497$	37.1948	−	37.1948i	0.0748385	−	0.0748385i
$498$	130.352	+	130.352i	0.261750	+	0.261750i
$499$		−	756.268i		−	1.51557i	−0.652507	−	0.757783i	$-0.726283\pi$
$499$		−	756.268i		−	1.51557i	0.652507	−	0.757783i	$-0.273717\pi$
$500$	−232.865	+	90.9622i	−0.465729	+	0.181924i
$501$	527.731			1.05336
$502$	−449.793	+	449.793i	−0.896002	+	0.896002i
$503$	193.496	+	193.496i	0.384684	+	0.384684i	0.872786	−	0.488102i	$-0.162311\pi$
$503$	193.496	+	193.496i	0.384684	+	0.384684i	−0.488102	+	0.872786i	$0.662311\pi$
$504$		−	72.0459i		−	0.142948i
$505$	2.88026	−	2.17929i	0.00570348	−	0.00431542i
$506$	143.015			0.282639
$507$	113.186	−	113.186i	0.223247	−	0.223247i
$508$	294.109	+	294.109i	0.578954	+	0.578954i
$509$			63.6342i			0.125018i	0.998044	+	0.0625090i	$0.0199102\pi$
$509$			63.6342i			0.125018i	−0.998044	+	0.0625090i	$0.980090\pi$
$510$	2.39071	−	17.2560i	0.00468766	−	0.0338353i
$511$	122.921			0.240550
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	64.3364	+	64.3364i	0.125412	+	0.125412i
$514$			385.779i			0.750543i
$515$	358.687	+	49.6939i	0.696481	+	0.0964929i
$516$	−109.460			−0.212132
$517$	−105.277	+	105.277i	−0.203631	+	0.203631i
$518$	316.608	+	316.608i	0.611213	+	0.611213i
$519$			480.122i			0.925091i
$520$	74.6747	+	98.6938i	0.143605	+	0.189796i
$521$	−337.644			−0.648069			−0.324034	−	0.946045i	$-0.605039\pi$
$521$	−337.644			−0.648069			−0.324034	+	0.946045i	$0.605039\pi$
$522$	−110.191	+	110.191i	−0.211093	+	0.211093i
$523$	557.233	+	557.233i	1.06545	+	1.06545i	0.997702	+	0.0677522i	$0.0215827\pi$
$523$	557.233	+	557.233i	1.06545	+	1.06545i	0.0677522	+	0.997702i	$0.478417\pi$
$524$			270.239i			0.515724i
$525$	−99.9547	+	353.810i	−0.190390	+	0.673923i
$526$	443.087			0.842371
$527$	27.7336	−	27.7336i	0.0526254	−	0.0526254i
$528$	103.302	+	103.302i	0.195648	+	0.195648i
$529$			23.0000i			0.0434783i
$530$	418.898	−	316.951i	0.790374	−	0.598021i
$531$	−177.550			−0.334370
$532$	210.256	−	210.256i	0.395218	−	0.395218i
$533$	−163.912	−	163.912i	−0.307527	−	0.307527i
$534$			288.667i			0.540576i
$535$	126.656	−	914.196i	0.236740	−	1.70878i
$536$	−225.380			−0.420485
$537$	−243.925	+	243.925i	−0.454236	+	0.454236i
$538$	27.1359	+	27.1359i	0.0504385	+	0.0504385i
$539$			486.927i			0.903390i
$540$	51.4699	+	7.13083i	0.0953146	+	0.0132052i
$541$	544.600			1.00665			0.503327	−	0.864096i	$-0.332109\pi$
$541$	544.600			1.00665			0.503327	+	0.864096i	$0.332109\pi$
$542$	−58.8552	+	58.8552i	−0.108589	+	0.108589i
$543$	−115.004	−	115.004i	−0.211793	−	0.211793i
$544$			8.04633i			0.0147910i
$545$	180.078	+	238.000i	0.330418	+	0.436697i
$546$	182.007			0.333346
$547$	−520.109	+	520.109i	−0.950839	+	0.950839i	−0.998847	−	0.0480075i	$-0.984713\pi$
$547$	−520.109	+	520.109i	−0.950839	+	0.950839i	0.0480075	+	0.998847i	$0.484713\pi$
$548$	−194.039	−	194.039i	−0.354087	−	0.354087i
$549$		−	181.907i		−	0.331342i
$550$	−363.987	−	650.625i	−0.661795	−	1.18295i
$551$	−643.151			−1.16724
$552$	−16.6132	+	16.6132i	−0.0300965	+	0.0300965i
$553$	−269.648	−	269.648i	−0.487609	−	0.487609i
$554$		−	250.629i		−	0.452399i
$555$	−257.523	+	194.850i	−0.464005	+	0.351080i
$556$	454.987			0.818322
$557$	−208.117	+	208.117i	−0.373639	+	0.373639i	−0.868801	−	0.495162i	$-0.835109\pi$
$557$	−208.117	+	208.117i	−0.373639	+	0.373639i	0.495162	+	0.868801i	$0.335109\pi$
$558$	82.7217	+	82.7217i	0.148247	+	0.148247i
$559$		−	276.525i		−	0.494678i
$560$	23.3040	−	168.207i	0.0416144	−	0.300370i
$561$	51.9502			0.0926029
$562$	248.499	−	248.499i	0.442169	−	0.442169i
$563$	−453.569	−	453.569i	−0.805630	−	0.805630i	0.178339	−	0.983969i	$-0.442927\pi$
$563$	−453.569	−	453.569i	−0.805630	−	0.805630i	−0.983969	+	0.178339i	$0.942927\pi$
$564$		−	24.4588i		−	0.0433667i
$565$	214.505	+	29.7182i	0.379654	+	0.0525987i
$566$	15.0482			0.0265870
$567$	54.0345	−	54.0345i	0.0952989	−	0.0952989i
$568$	−12.3903	−	12.3903i	−0.0218140	−	0.0218140i
$569$		−	555.627i		−	0.976498i	−0.872704	−	0.488249i	$-0.837636\pi$
$569$		−	555.627i		−	0.976498i	0.872704	−	0.488249i	$-0.162364\pi$
$570$	129.397	+	171.018i	0.227013	+	0.300031i
$571$	−404.365			−0.708170			−0.354085	−	0.935213i	$-0.615208\pi$
$571$	−404.365			−0.708170			−0.354085	+	0.935213i	$0.615208\pi$
$572$	−260.968	+	260.968i	−0.456238	+	0.456238i
$573$	69.5221	+	69.5221i	0.121330	+	0.121330i
$574$			318.065i			0.554120i
$575$	104.635	−	58.5371i	0.181973	−	0.101804i
$576$	−24.0000			−0.0416667
$577$	84.1526	−	84.1526i	0.145845	−	0.145845i	−0.630414	−	0.776259i	$-0.717115\pi$
$577$	84.1526	−	84.1526i	0.145845	−	0.145845i	0.776259	+	0.630414i	$0.217115\pi$
$578$	−286.977	−	286.977i	−0.496500	−	0.496500i
$579$			426.742i			0.737032i
$580$	−292.907	+	221.622i	−0.505012	+	0.382107i
$581$	638.998			1.09982
$582$	−92.5816	+	92.5816i	−0.159075	+	0.159075i
$583$	1107.66	+	1107.66i	1.89993	+	1.89993i
$584$		−	40.9476i		−	0.0701158i
$585$	−18.0143	+	130.026i	−0.0307937	+	0.222267i
$586$	−268.053			−0.457429
$587$	−721.467	+	721.467i	−1.22907	+	1.22907i	−0.264760	+	0.964314i	$0.585293\pi$
$587$	−721.467	+	721.467i	−1.22907	+	1.22907i	−0.964314	+	0.264760i	$0.914707\pi$
$588$	−56.5634	−	56.5634i	−0.0961963	−	0.0961963i
$589$			482.823i			0.819733i
$590$	−414.531	−	57.4306i	−0.702594	−	0.0973399i
$591$	−109.300			−0.184940
$592$	105.469	−	105.469i	0.178157	−	0.178157i
$593$	419.636	+	419.636i	0.707649	+	0.707649i	0.966040	−	0.258392i	$-0.0831925\pi$
$593$	419.636	+	419.636i	0.707649	+	0.707649i	−0.258392	+	0.966040i	$0.583192\pi$
$594$			154.953i			0.260864i
$595$	−36.4356	−	48.1551i	−0.0612363	−	0.0809329i
$596$	244.408			0.410080
$597$	120.613	−	120.613i	0.202032	−	0.202032i
$598$	−41.9694	−	41.9694i	−0.0701829	−	0.0701829i
$599$		−	873.314i		−	1.45795i	−0.684539	−	0.728977i	$-0.739996\pi$
$599$		−	873.314i		−	1.45795i	0.684539	−	0.728977i	$-0.260004\pi$
$600$	117.861	+	33.2970i	0.196436	+	0.0554950i
$601$	−542.017			−0.901859			−0.450929	−	0.892560i	$-0.648907\pi$
$601$	−542.017			−0.901859			−0.450929	+	0.892560i	$0.648907\pi$
$602$	−268.293	+	268.293i	−0.445669	+	0.445669i
$603$	−169.035	−	169.035i	−0.280323	−	0.280323i
$604$			503.365i			0.833386i
$605$	1290.44	−	976.386i	2.13296	−	1.61386i
$606$	−1.76942			−0.00291983
$607$	213.463	−	213.463i	0.351670	−	0.351670i	−0.509061	−	0.860730i	$-0.670007\pi$
$607$	213.463	−	213.463i	0.351670	−	0.351670i	0.860730	+	0.509061i	$0.170007\pi$
$608$	−70.0406	−	70.0406i	−0.115198	−	0.115198i
$609$			540.166i			0.886972i
$610$	58.8398	−	424.702i	0.0964586	−	0.696233i
$611$	61.7893			0.101128
$612$	−6.03475	+	6.03475i	−0.00986070	+	0.00986070i
$613$	94.5924	+	94.5924i	0.154311	+	0.154311i	0.780040	−	0.625729i	$-0.215199\pi$
$613$	94.5924	+	94.5924i	0.154311	+	0.154311i	−0.625729	+	0.780040i	$0.715199\pi$
$614$		−	81.1621i		−	0.132186i
$615$	−227.227	−	31.4808i	−0.369475	−	0.0511883i
$616$	506.398			0.822075
$617$	−418.711	+	418.711i	−0.678623	+	0.678623i	−0.959689	−	0.281065i	$-0.909312\pi$
$617$	−418.711	+	418.711i	−0.678623	+	0.678623i	0.281065	+	0.959689i	$0.409312\pi$
$618$	−125.440	−	125.440i	−0.202977	−	0.202977i
$619$		−	702.475i		−	1.13485i	−0.823423	−	0.567427i	$-0.807939\pi$
$619$		−	702.475i		−	1.13485i	0.823423	−	0.567427i	$-0.192061\pi$
$620$	166.375	+	219.889i	0.268347	+	0.354660i
$621$	−24.9199			−0.0401286
$622$	−167.030	+	167.030i	−0.268537	+	0.268537i
$623$	707.539	+	707.539i	1.13570	+	1.13570i
$624$		−	60.6302i		−	0.0971638i
$625$	−532.609	−	327.036i	−0.852175	−	0.523257i
$626$	249.923			0.399238
$627$	−452.209	+	452.209i	−0.721227	+	0.721227i
$628$	255.614	+	255.614i	0.407028	+	0.407028i
$629$		−	53.0398i		−	0.0843240i
$630$	143.633	−	108.677i	0.227990	−	0.172504i
$631$	268.944			0.426218			0.213109	−	0.977028i	$-0.431641\pi$
$631$	268.944			0.426218			0.213109	+	0.977028i	$0.431641\pi$
$632$	−89.8252	+	89.8252i	−0.142129	+	0.142129i
$633$	385.789	+	385.789i	0.609462	+	0.609462i
$634$			506.252i			0.798505i
$635$	−142.699	+	1029.99i	−0.224723	+	1.62204i
$636$	−257.340			−0.404623
$637$	142.894	−	142.894i	0.224323	−	0.224323i
$638$	−774.511	−	774.511i	−1.21397	−	1.21397i
$639$		−	18.5855i		−	0.0290853i
$640$	−56.0333	−	7.76306i	−0.0875521	−	0.0121298i
$641$	−1020.93			−1.59272			−0.796359	−	0.604825i	$-0.793243\pi$
$641$	−1020.93			−1.59272			−0.796359	+	0.604825i	$0.793243\pi$
$642$	−319.712	+	319.712i	−0.497993	+	0.497993i
$643$	194.700	+	194.700i	0.302800	+	0.302800i	0.842108	−	0.539308i	$-0.181314\pi$
$643$	194.700	+	194.700i	0.302800	+	0.302800i	−0.539308	+	0.842108i	$0.681314\pi$
$644$			81.4399i			0.126459i
$645$	−165.115	−	218.224i	−0.255992	−	0.338332i
$646$	−35.2231			−0.0545249
$647$	200.168	−	200.168i	0.309378	−	0.309378i	−0.535290	−	0.844668i	$-0.679798\pi$
$647$	200.168	−	200.168i	0.309378	−	0.309378i	0.844668	+	0.535290i	$0.179798\pi$
$648$	−18.0000	−	18.0000i	−0.0277778	−	0.0277778i
$649$		−	1247.97i		−	1.92291i
$650$	−84.1169	+	297.748i	−0.129411	+	0.458075i
$651$	405.510			0.622904
$652$	−318.020	+	318.020i	−0.487761	+	0.487761i
$653$	515.342	+	515.342i	0.789191	+	0.789191i	0.981362	−	0.192170i	$-0.0615526\pi$
$653$	515.342	+	515.342i	0.789191	+	0.789191i	−0.192170	+	0.981362i	$0.561553\pi$
$654$		−	146.210i		−	0.223562i
$655$	−538.760	+	407.642i	−0.822534	+	0.622354i
$656$	105.954			0.161515
$657$	30.7107	−	30.7107i	0.0467439	−	0.0467439i
$658$	−59.9498	−	59.9498i	−0.0911092	−	0.0911092i
$659$			643.550i			0.976555i	0.872688	+	0.488277i	$0.162375\pi$
$659$			643.550i			0.976555i	−0.872688	+	0.488277i	$0.837625\pi$
$660$	−50.1213	+	361.773i	−0.0759414	+	0.548141i
$661$	1164.55			1.76179			0.880897	−	0.473309i	$-0.156940\pi$
$661$	1164.55			1.76179			0.880897	+	0.473309i	$0.156940\pi$
$662$	578.658	−	578.658i	0.874106	−	0.874106i
$663$	−15.2453	−	15.2453i	−0.0229945	−	0.0229945i
$664$		−	212.864i		−	0.320578i
$665$	736.333	+	102.014i	1.10727	+	0.153405i
$666$	158.203			0.237542
$667$	124.558	−	124.558i	0.186744	−	0.186744i
$668$	−430.891	−	430.891i	−0.645046	−	0.645046i
$669$			185.267i			0.276931i
$670$	−339.973	−	449.326i	−0.507423	−	0.670635i
$671$	1278.59			1.90550
$672$	−58.8253	+	58.8253i	−0.0875376	+	0.0875376i
$673$	471.464	+	471.464i	0.700541	+	0.700541i	0.964527	−	0.263985i	$-0.0850371\pi$
$673$	471.464	+	471.464i	0.700541	+	0.700541i	−0.263985	+	0.964527i	$0.585037\pi$
$674$			168.518i			0.250026i
$675$	63.4233	+	113.369i	0.0939604	+	0.167954i
$676$	−184.832			−0.273421
$677$	666.889	−	666.889i	0.985066	−	0.985066i	−0.0148244	−	0.999890i	$-0.504719\pi$
$677$	666.889	−	666.889i	0.985066	−	0.985066i	0.999890	+	0.0148244i	$0.00471893\pi$
$678$	−75.0163	−	75.0163i	−0.110644	−	0.110644i
$679$			453.845i			0.668402i
$680$	−16.0415	+	12.1375i	−0.0235904	+	0.0178492i
$681$	−474.540			−0.696829
$682$	−581.436	+	581.436i	−0.852546	+	0.852546i
$683$	262.581	+	262.581i	0.384452	+	0.384452i	0.872703	−	0.488251i	$-0.162365\pi$
$683$	262.581	+	262.581i	0.384452	+	0.384452i	−0.488251	+	0.872703i	$0.662365\pi$
$684$		−	105.061i		−	0.153598i
$685$	94.1462	−	679.542i	0.137440	−	0.992033i
$686$	311.095			0.453492
$687$	39.8274	−	39.8274i	0.0579730	−	0.0579730i
$688$	89.3738	+	89.3738i	0.129904	+	0.129904i
$689$		−	650.109i		−	0.943554i
$690$	−58.1810	−	8.06060i	−0.0843203	−	0.0116820i
$691$	−924.888			−1.33848			−0.669239	−	0.743047i	$-0.733380\pi$
$691$	−924.888			−1.33848			−0.669239	+	0.743047i	$0.733380\pi$
$692$	392.018	−	392.018i	0.566500	−	0.566500i
$693$	379.799	+	379.799i	0.548050	+	0.548050i
$694$		−	944.067i		−	1.36033i
$695$	686.324	+	907.080i	0.987516	+	1.30515i
$696$	179.941			0.258535
$697$	26.6419	−	26.6419i	0.0382237	−	0.0382237i
$698$	−224.162	−	224.162i	−0.321148	−	0.321148i
$699$			166.176i			0.237734i
$700$	370.497	−	207.272i	0.529282	−	0.296103i
$701$	−886.720			−1.26494			−0.632468	−	0.774587i	$-0.717958\pi$
$701$	−886.720			−1.26494			−0.632468	+	0.774587i	$0.717958\pi$
$702$	45.4727	−	45.4727i	0.0647759	−	0.0647759i
$703$	461.693	+	461.693i	0.656747	+	0.656747i
$704$		−	168.692i		−	0.239619i
$705$	48.7620	−	36.8948i	0.0691660	−	0.0523330i
$706$	346.991			0.491489
$707$	−4.33694	+	4.33694i	−0.00613428	+	0.00613428i
$708$	144.969	+	144.969i	0.204759	+	0.204759i
$709$			289.073i			0.407720i	0.979000	+	0.203860i	$0.0653487\pi$
$709$			289.073i			0.407720i	−0.979000	+	0.203860i	$0.934651\pi$
$710$	6.01169	−	43.3920i	0.00846717	−	0.0611155i
$711$	−134.738			−0.189505
$712$	235.696	−	235.696i	0.331034	−	0.331034i
$713$	−93.5076	−	93.5076i	−0.131147	−	0.131147i
$714$			29.5830i			0.0414327i
$715$	−913.933	−	126.620i	−1.27823	−	0.177090i
$716$	398.328			0.556324
$717$	−244.703	+	244.703i	−0.341288	+	0.341288i
$718$	−330.215	−	330.215i	−0.459909	−	0.459909i
$719$			976.697i			1.35841i	0.733949	+	0.679205i	$0.237675\pi$
$719$			976.697i			1.35841i	−0.733949	+	0.679205i	$0.762325\pi$
$720$	−36.2027	−	47.8473i	−0.0502815	−	0.0664546i
$721$	−614.919			−0.852870
$722$	−54.3951	+	54.3951i	−0.0753394	+	0.0753394i
$723$	−48.9507	−	48.9507i	−0.0677049	−	0.0677049i
$724$			187.800i			0.259392i
$725$	−883.669	−	249.645i	−1.21885	−	0.344338i
$726$	−792.752			−1.09195
$727$	556.759	−	556.759i	0.765831	−	0.765831i	−0.211539	−	0.977370i	$-0.567848\pi$
$727$	556.759	−	556.759i	0.765831	−	0.765831i	0.977370	+	0.211539i	$0.0678475\pi$
$728$	−148.608	−	148.608i	−0.204132	−	0.204132i
$729$		−	27.0000i		−	0.0370370i
$730$	81.6347	−	61.7673i	0.111828	−	0.0846127i
$731$	44.9457			0.0614852
$732$	−148.526	+	148.526i	−0.202905	+	0.202905i
$733$	55.7405	+	55.7405i	0.0760444	+	0.0760444i	0.744106	−	0.668062i	$-0.232876\pi$
$733$	55.7405	+	55.7405i	0.0760444	+	0.0760444i	−0.668062	+	0.744106i	$0.732876\pi$
$734$			497.135i			0.677296i
$735$	27.4441	−	198.090i	0.0373389	−	0.269510i
$736$	27.1293			0.0368605
$737$	1188.12	−	1188.12i	1.61210	−	1.61210i
$738$	79.4655	+	79.4655i	0.107677	+	0.107677i
$739$		−	277.120i		−	0.374993i	−0.982265	−	0.187497i	$-0.939963\pi$
$739$		−	277.120i		−	0.374993i	0.982265	−	0.187497i	$-0.0600374\pi$
$740$	369.361	+	51.1726i	0.499136	+	0.0691521i
$741$	265.411			0.358179
$742$	−630.755	+	630.755i	−0.850074	+	0.850074i
$743$	−262.220	−	262.220i	−0.352921	−	0.352921i	0.508274	−	0.861195i	$-0.330284\pi$
$743$	−262.220	−	262.220i	−0.352921	−	0.352921i	−0.861195	+	0.508274i	$0.830284\pi$
$744$		−	135.084i		−	0.181564i
$745$	368.676	+	487.260i	0.494867	+	0.654040i
$746$	−649.609			−0.870790
$747$	159.648	−	159.648i	0.213718	−	0.213718i
$748$	−42.4172	−	42.4172i	−0.0567075	−	0.0567075i
$749$			1567.26i			2.09247i
$750$	111.405	+	285.200i	0.148541	+	0.380266i
$751$	547.599			0.729159			0.364580	−	0.931172i	$-0.381213\pi$
$751$	547.599			0.729159			0.364580	+	0.931172i	$0.381213\pi$
$752$	−19.9705	+	19.9705i	−0.0265566	+	0.0265566i
$753$	550.881	+	550.881i	0.731582	+	0.731582i
$754$			454.577i			0.602887i
$755$	−1003.53	+	759.299i	−1.32918	+	1.00569i
$756$	−88.2379			−0.116717
$757$	−199.963	+	199.963i	−0.264152	+	0.264152i	−0.826738	−	0.562587i	$-0.809806\pi$
$757$	−199.963	+	199.963i	−0.264152	+	0.264152i	0.562587	+	0.826738i	$0.309806\pi$
$758$	−594.997	−	594.997i	−0.784957	−	0.784957i
$759$		−	175.157i		−	0.230774i
$760$	33.9831	−	245.288i	0.0447146	−	0.322747i
$761$	−1228.05			−1.61373			−0.806864	−	0.590738i	$-0.798837\pi$
$761$	−1228.05			−1.61373			−0.806864	+	0.590738i	$0.798837\pi$
$762$	360.208	−	360.208i	0.472714	−	0.472714i
$763$	−358.367	−	358.367i	−0.469682	−	0.469682i
$764$		−	113.529i		−	0.148598i
$765$	−21.1342	−	2.92801i	−0.0276264	−	0.00382746i
$766$	865.619			1.13005
$767$	−366.230	+	366.230i	−0.477483	+	0.477483i
$768$	19.5959	+	19.5959i	0.0255155	+	0.0255155i
$769$		−	648.884i		−	0.843802i	−0.906642	−	0.421901i	$-0.861363\pi$
$769$		−	648.884i		−	0.843802i	0.906642	−	0.421901i	$-0.138637\pi$
$770$	763.875	+	1009.57i	0.992045	+	1.31114i
$771$	472.481			0.612816
$772$	348.433	−	348.433i	0.451338	−	0.451338i
$773$	−126.006	−	126.006i	−0.163009	−	0.163009i	0.620889	−	0.783898i	$-0.286772\pi$
$773$	−126.006	−	126.006i	−0.163009	−	0.163009i	−0.783898	+	0.620889i	$0.786772\pi$
$774$			134.061i			0.173205i
$775$	−187.412	+	663.383i	−0.241822	+	0.855978i
$776$	151.185			0.194826
$777$	387.764	−	387.764i	0.499053	−	0.499053i
$778$	72.4398	+	72.4398i	0.0931103	+	0.0931103i
$779$			463.817i			0.595401i
$780$	120.875	−	91.4574i	0.154968	−	0.117253i
$781$	130.634			0.167266
$782$	6.82161	−	6.82161i	0.00872328	−	0.00872328i
$783$	134.955	+	134.955i	0.172357	+	0.172357i
$784$			92.3676i			0.117816i
$785$	−124.021	+	895.180i	−0.157989	+	1.14036i
$786$	330.974			0.421087
$787$	250.285	−	250.285i	0.318024	−	0.318024i	−0.529984	−	0.848008i	$-0.677802\pi$
$787$	250.285	−	250.285i	0.318024	−	0.318024i	0.848008	+	0.529984i	$0.177802\pi$
$788$	89.2428	+	89.2428i	0.113252	+	0.113252i
$789$		−	542.668i		−	0.687793i
$790$	−314.576	−	43.5824i	−0.398197	−	0.0551676i
$791$	−367.738			−0.464902
$792$	126.519	−	126.519i	0.159746	−	0.159746i
$793$	−375.216	−	375.216i	−0.473160	−	0.473160i
$794$			910.041i			1.14615i
$795$	−388.184	−	513.043i	−0.488282	−	0.645338i
$796$	−196.960			−0.247438
$797$	−253.137	+	253.137i	−0.317612	+	0.317612i	−0.847849	−	0.530237i	$-0.822103\pi$
$797$	−253.137	+	253.137i	−0.317612	+	0.317612i	0.530237	+	0.847849i	$0.322103\pi$
$798$	−257.510	−	257.510i	−0.322694	−	0.322694i
$799$			10.0431i			0.0125696i
$800$	−69.0465	−	123.420i	−0.0863082	−	0.154275i
$801$	353.544			0.441378
$802$	411.151	−	411.151i	0.512658	−	0.512658i
$803$	215.860	+	215.860i	0.268817	+	0.268817i
$804$			276.033i			0.343324i
$805$	−162.362	+	122.848i	−0.201691	+	0.152606i
$806$	341.257			0.423396
$807$	33.2346	−	33.2346i	0.0411829	−	0.0411829i
$808$	1.44472	+	1.44472i	0.00178802	+	0.00178802i
$809$		−	584.572i		−	0.722586i	−0.932452	−	0.361293i	$-0.882335\pi$
$809$		−	584.572i		−	0.722586i	0.932452	−	0.361293i	$-0.117665\pi$
$810$	8.73344	−	63.0375i	0.0107820	−	0.0778241i
$811$	−1095.85			−1.35123			−0.675614	−	0.737256i	$-0.736121\pi$
$811$	−1095.85			−1.35123			−0.675614	+	0.737256i	$0.736121\pi$
$812$	441.044	−	441.044i	0.543158	−	0.543158i
$813$	72.0826	+	72.0826i	0.0886625	+	0.0886625i
$814$			1111.98i			1.36607i
$815$	−1113.73	−	154.301i	−1.36655	−	0.189326i
$816$	9.85470			0.0120768
$817$	−391.237	+	391.237i	−0.478870	+	0.478870i
$818$	−126.323	−	126.323i	−0.154429	−	0.154429i
$819$		−	222.912i		−	0.272176i
$820$	159.826	+	211.234i	0.194910	+	0.257602i
$821$	−101.782			−0.123973			−0.0619864	−	0.998077i	$-0.519744\pi$
$821$	−101.782			−0.123973			−0.0619864	+	0.998077i	$0.519744\pi$
$822$	−237.649	+	237.649i	−0.289110	+	0.289110i
$823$	597.597	+	597.597i	0.726121	+	0.726121i	0.969845	−	0.243724i	$-0.0783691\pi$
$823$	597.597	+	597.597i	0.726121	+	0.726121i	−0.243724	+	0.969845i	$0.578369\pi$
$824$			204.842i			0.248595i
$825$	−796.850	+	445.791i	−0.965878	+	0.540353i
$826$	710.654			0.860356
$827$	−754.273	+	754.273i	−0.912059	+	0.912059i	−0.996434	−	0.0843749i	$-0.973111\pi$
$827$	−754.273	+	754.273i	−0.912059	+	0.912059i	0.0843749	+	0.996434i	$0.473111\pi$
$828$	20.3470	+	20.3470i	0.0245737	+	0.0245737i
$829$		−	1339.48i		−	1.61578i	−0.589336	−	0.807888i	$-0.700610\pi$
$829$		−	1339.48i		−	1.61578i	0.589336	−	0.807888i	$-0.299390\pi$
$830$	424.373	−	321.093i	0.511292	−	0.386859i
$831$	−306.957			−0.369383
$832$	−49.5044	+	49.5044i	−0.0595005	+	0.0595005i
$833$	23.2256	+	23.2256i	0.0278819	+	0.0278819i
$834$		−	557.243i		−	0.668157i
$835$	209.064	−	1509.02i	0.250377	−	1.80720i
$836$	738.454			0.883319
$837$	101.313	−	101.313i	0.121043	−	0.121043i
$838$	81.1655	+	81.1655i	0.0968562	+	0.0968562i
$839$		−	861.265i		−	1.02654i	−0.858228	−	0.513269i	$-0.828434\pi$
$839$		−	861.265i		−	1.02654i	0.858228	−	0.513269i	$-0.171566\pi$
$840$	−206.011	−	28.5415i	−0.245251	−	0.0339780i
$841$	−508.109			−0.604173
$842$	453.518	−	453.518i	0.538620	−	0.538620i
$843$	−304.348	−	304.348i	−0.361030	−	0.361030i
$844$		−	629.991i		−	0.746435i
$845$	−278.810	−	368.489i	−0.329952	−	0.436081i
$846$	−29.9558			−0.0354087
$847$	−1943.08	+	1943.08i	−2.29407	+	2.29407i
$848$	210.118	+	210.118i	0.247780	+	0.247780i
$849$		−	18.4302i		−	0.0217082i
$850$	−48.3954	−	13.6722i	−0.0569357	−	0.0160849i
$851$	−178.831			−0.210142
$852$	−15.1750	+	15.1750i	−0.0178110	+	0.0178110i
$853$	−732.016	−	732.016i	−0.858166	−	0.858166i	0.132956	−	0.991122i	$-0.457553\pi$
$853$	−732.016	−	732.016i	−0.858166	−	0.858166i	−0.991122	+	0.132956i	$0.957553\pi$
$854$			728.092i			0.852567i
$855$	209.453	−	158.479i	0.244974	−	0.185355i
$856$	522.087			0.609915
$857$	345.306	−	345.306i	0.402924	−	0.402924i	−0.476338	−	0.879262i	$-0.658036\pi$
$857$	345.306	−	345.306i	0.402924	−	0.402924i	0.879262	+	0.476338i	$0.158036\pi$
$858$	319.620	+	319.620i	0.372517	+	0.372517i
$859$			73.9194i			0.0860529i	0.999074	+	0.0430265i	$0.0137000\pi$
$859$			73.9194i			0.0860529i	−0.999074	+	0.0430265i	$0.986300\pi$
$860$	−43.3634	+	312.995i	−0.0504226	+	0.363947i
$861$	389.548			0.452437
$862$	455.025	−	455.025i	0.527872	−	0.527872i
$863$	565.608	+	565.608i	0.655397	+	0.655397i	0.954287	−	0.298890i	$-0.0966164\pi$
$863$	565.608	+	565.608i	0.655397	+	0.655397i	−0.298890	+	0.954287i	$0.596616\pi$
$864$			29.3939i			0.0340207i
$865$	1372.88	+	190.204i	1.58714	+	0.219889i
$866$	267.546			0.308945
$867$	−351.473	+	351.473i	−0.405390	+	0.405390i
$868$	−331.098	−	331.098i	−0.381449	−	0.381449i
$869$		−	947.049i		−	1.08981i
$870$	271.431	+	358.736i	0.311989	+	0.412341i
$871$	−697.331			−0.800609
$872$	−119.380	+	119.380i	−0.136903	+	0.136903i
$873$	113.389	+	113.389i	0.129884	+	0.129884i
$874$			118.760i			0.135880i
$875$	972.100	+	425.979i	1.11097	+	0.486833i
$876$	−50.1504			−0.0572493
$877$	−614.360	+	614.360i	−0.700525	+	0.700525i	−0.964523	−	0.263998i	$-0.914959\pi$
$877$	−614.360	+	614.360i	−0.700525	+	0.700525i	0.263998	+	0.964523i	$0.414959\pi$
$878$	544.847	+	544.847i	0.620555	+	0.620555i
$879$			328.297i			0.373489i
$880$	336.310	−	254.463i	0.382171	−	0.289162i
$881$	−478.192			−0.542783			−0.271392	−	0.962469i	$-0.587484\pi$
$881$	−478.192			−0.542783			−0.271392	+	0.962469i	$0.587484\pi$
$882$	−69.2757	+	69.2757i	−0.0785439	+	0.0785439i
$883$	248.230	+	248.230i	0.281121	+	0.281121i	0.833556	−	0.552435i	$-0.186301\pi$
$883$	248.230	+	248.230i	0.281121	+	0.281121i	−0.552435	+	0.833556i	$0.686301\pi$
$884$			24.8955i			0.0281624i
$885$	−70.3378	+	507.694i	−0.0794777	+	0.573666i
$886$	427.738			0.482774
$887$	1082.04	−	1082.04i	1.21988	−	1.21988i	0.252210	−	0.967673i	$-0.418843\pi$
$887$	1082.04	−	1082.04i	1.21988	−	1.21988i	0.967673	−	0.252210i	$-0.0811573\pi$
$888$	−129.172	−	129.172i	−0.145464	−	0.145464i
$889$		−	1765.78i		−	1.98625i
$890$	825.427	+	114.358i	0.927446	+	0.128492i
$891$	189.778			0.212995
$892$	151.270	−	151.270i	0.169585	−	0.169585i
$893$	−87.4217	−	87.4217i	−0.0978966	−	0.0978966i
$894$		−	299.337i		−	0.334829i
$895$	600.856	+	794.121i	0.671348	+	0.887286i
$896$	96.0613			0.107211
$897$	−51.4018	+	51.4018i	−0.0573041	+	0.0573041i
$898$	892.075	+	892.075i	0.993402	+	0.993402i
$899$			1012.80i			1.12658i
$900$	40.7803	−	144.350i	0.0453115	−	0.160389i
$901$	105.667			0.117278
$902$	−558.550	+	558.550i	−0.619234	+	0.619234i
$903$	328.590	+	328.590i	0.363887	+	0.363887i
$904$			122.501i			0.135510i
$905$	−374.405	+	283.286i	−0.413707	+	0.313023i
$906$	616.494			0.680457
$907$	1052.56	−	1052.56i	1.16048	−	1.16048i	0.176111	−	0.984370i	$-0.443648\pi$
$907$	1052.56	−	1052.56i	1.16048	−	1.16048i	0.984370	−	0.176111i	$-0.0563519\pi$
$908$	387.461	+	387.461i	0.426719	+	0.426719i
$909$			2.16709i			0.00238403i
$910$	72.1033	−	520.437i	0.0792343	−	0.571909i
$911$	−265.488			−0.291424			−0.145712	−	0.989327i	$-0.546547\pi$
$911$	−265.488			−0.291424			−0.145712	+	0.989327i	$0.546547\pi$
$912$	−85.7818	+	85.7818i	−0.0940590	+	0.0940590i
$913$	1122.14	+	1122.14i	1.22906	+	1.22906i
$914$		−	1242.28i		−	1.35916i
$915$	−520.152	−	72.0637i	−0.568472	−	0.0787581i
$916$	−65.0379			−0.0710021
$917$	811.236	−	811.236i	0.884663	−	0.884663i
$918$	7.39102	+	7.39102i	0.00805122	+	0.00805122i
$919$		−	1362.18i		−	1.48224i	−0.671371	−	0.741121i	$-0.734294\pi$
$919$		−	1362.18i		−	1.48224i	0.671371	−	0.741121i	$-0.265706\pi$
$920$	40.9231	+	54.0860i	0.0444817	+	0.0587892i
$921$	−99.4029			−0.107929
$922$	−591.449	+	591.449i	−0.641484	+	0.641484i
$923$	−38.3360	−	38.3360i	−0.0415341	−	0.0415341i
$924$		−	620.209i		−	0.671222i
$925$	455.141	+	813.562i	0.492044	+	0.879527i
$926$	−506.278			−0.546736
$927$	−153.632	+	153.632i	−0.165730	+	0.165730i
$928$	−146.921	−	146.921i	−0.158320	−	0.158320i
$929$			1275.14i			1.37259i	0.727323	+	0.686296i	$0.240764\pi$
$929$			1275.14i			1.37259i	−0.727323	+	0.686296i	$0.759236\pi$
$930$	269.308	−	203.767i	0.289579	−	0.219104i
$931$	−404.343			−0.434310
$932$	135.682	−	135.682i	0.145582	−	0.145582i
$933$	204.569	+	204.569i	0.219260	+	0.219260i
$934$			25.0082i			0.0267754i
$935$	20.5804	−	148.549i	0.0220112	−	0.158875i
$936$	−74.2566			−0.0793339
$937$	−712.758	+	712.758i	−0.760681	+	0.760681i	−0.976445	−	0.215764i	$-0.930776\pi$
$937$	−712.758	+	712.758i	−0.760681	+	0.760681i	0.215764	+	0.976445i	$0.430776\pi$
$938$	676.571	+	676.571i	0.721291	+	0.721291i
$939$		−	306.092i		−	0.325976i
$940$	−69.9385	−	9.68953i	−0.0744026	−	0.0103080i
$941$	−1189.76			−1.26436			−0.632178	−	0.774823i	$-0.717839\pi$
$941$	−1189.76			−1.26436			−0.632178	+	0.774823i	$0.717839\pi$
$942$	313.061	−	313.061i	0.332337	−	0.332337i
$943$	−89.8269	−	89.8269i	−0.0952565	−	0.0952565i
$944$		−	236.734i		−	0.250777i
$945$	−133.102	−	175.914i	−0.140849	−	0.186153i
$946$	−942.290			−0.996078
$947$	1268.89	−	1268.89i	1.33991	−	1.33991i	0.443763	−	0.896144i	$-0.353643\pi$
$947$	1268.89	−	1268.89i	1.33991	−	1.33991i	0.896144	−	0.443763i	$-0.146357\pi$
$948$	110.013	+	110.013i	0.116047	+	0.116047i
$949$		−	126.693i		−	0.133501i
$950$	540.277	−	302.254i	0.568712	−	0.318162i
$951$	620.030			0.651977
$952$	24.1544	−	24.1544i	0.0253723	−	0.0253723i
$953$	−338.756	−	338.756i	−0.355463	−	0.355463i	0.506675	−	0.862137i	$-0.330875\pi$
$953$	−338.756	−	338.756i	−0.355463	−	0.355463i	−0.862137	+	0.506675i	$0.830875\pi$
$954$			315.176i			0.330373i
$955$	226.336	−	171.253i	0.237001	−	0.179322i
$956$	399.599			0.417991
$957$	−948.579	+	948.579i	−0.991200	+	0.991200i
$958$	−456.156	−	456.156i	−0.476154	−	0.476154i
$959$			1164.98i			1.21479i
$960$	−9.50777	+	68.6265i	−0.00990393	+	0.0714860i
$961$	−200.680			−0.208824
$962$	326.323	−	326.323i	0.339213	−	0.339213i
$963$	391.565	+	391.565i	0.406610	+	0.406610i
$964$			79.9361i			0.0829212i
$965$	1220.24	+	169.057i	1.26450	+	0.175188i
$966$	99.7431			0.103254
$967$	1118.45	−	1118.45i	1.15661	−	1.15661i	0.171415	−	0.985199i	$-0.445166\pi$
$967$	1118.45	−	1118.45i	1.15661	−	1.15661i	0.985199	−	0.171415i	$-0.0548339\pi$
$968$	647.279	+	647.279i	0.668677	+	0.668677i
$969$			43.1393i			0.0445194i
$970$	228.055	+	301.408i	0.235108	+	0.310730i
$971$	237.547			0.244642			0.122321	−	0.992491i	$-0.460966\pi$
$971$	237.547			0.244642			0.122321	+	0.992491i	$0.460966\pi$
$972$	−22.0454	+	22.0454i	−0.0226805	+	0.0226805i
$973$	−1365.83	−	1365.83i	−1.40373	−	1.40373i
$974$			388.515i			0.398886i
$975$	364.666	+	103.022i	0.374016	+	0.105663i
$976$	242.543			0.248507
$977$	1066.78	−	1066.78i	1.09189	−	1.09189i	0.0965651	−	0.995327i	$-0.469214\pi$
$977$	1066.78	−	1066.78i	1.09189	−	1.09189i	0.995327	−	0.0965651i	$-0.0307856\pi$
$978$	389.494	+	389.494i	0.398256	+	0.398256i
$979$			2485.00i			2.53830i
$980$	−184.148	+	139.332i	−0.187906	+	0.142175i
$981$	−179.069			−0.182538
$982$	−140.529	+	140.529i	−0.143105	+	0.143105i
$983$	−274.569	−	274.569i	−0.279317	−	0.279317i	0.553519	−	0.832836i	$-0.313285\pi$
$983$	−274.569	−	274.569i	−0.279317	−	0.279317i	−0.832836	+	0.553519i	$0.813285\pi$
$984$		−	129.767i		−	0.131877i
$985$	−43.2998	+	312.536i	−0.0439592	+	0.317295i
$986$	−73.8858			−0.0749349
$987$	−73.4232	+	73.4232i	−0.0743903	+	0.0743903i
$988$	−216.707	−	216.707i	−0.219339	−	0.219339i
$989$		−	151.541i		−	0.153226i
$990$	443.080	+	61.3859i	0.447555	+	0.0620059i
$991$	−2.38335			−0.00240500			−0.00120250	−	0.999999i	$-0.500383\pi$
$991$	−2.38335			−0.00240500			−0.00120250	+	0.999999i	$0.500383\pi$
$992$	−110.296	+	110.296i	−0.111185	+	0.111185i
$993$	−708.709	−	708.709i	−0.713705	−	0.713705i
$994$			74.3895i			0.0748385i
$995$	−297.104	−	392.668i	−0.298597	−	0.394641i
$996$	−260.703			−0.261750
$997$	−267.354	+	267.354i	−0.268158	+	0.268158i	−0.828358	−	0.560199i	$-0.810724\pi$
$997$	−267.354	+	267.354i	−0.268158	+	0.268158i	0.560199	+	0.828358i	$0.310724\pi$
$998$	756.268	+	756.268i	0.757783	+	0.757783i
$999$		−	193.759i		−	0.193953i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.b.553.22	yes	48
5.2	odd	4	inner	690.3.k.b.277.22	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.b.277.22	✓	48	5.2	odd	4	inner
690.3.k.b.553.22	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)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(3.98727 - 3.01689i) q^{5} -2.44949 q^{6} +(-6.00383 + 6.00383i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(3.98727 - 3.01689i) q^{5} -2.44949 q^{6} +(-6.00383 + 6.00383i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(-0.970383 + 7.00417i) q^{10} -21.0865 q^{11} +(2.44949 - 2.44949i) q^{12} +(6.18805 + 6.18805i) q^{13} -12.0077i q^{14} +(8.57832 + 1.18847i) q^{15} -4.00000 q^{16} +(-1.00579 + 1.00579i) q^{17} +(-3.00000 - 3.00000i) q^{18} -17.5101i q^{19} +(-6.03378 - 7.97455i) q^{20} -14.7063 q^{21} +(21.0865 - 21.0865i) q^{22} +(3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(6.79672 - 24.0584i) q^{25} -12.3761 q^{26} +(-3.67423 + 3.67423i) q^{27} +(12.0077 + 12.0077i) q^{28} -36.7302i q^{29} +(-9.76679 + 7.38985i) q^{30} -27.5739 q^{31} +(4.00000 - 4.00000i) q^{32} +(-25.8256 - 25.8256i) q^{33} -2.01158i q^{34} +(-5.82601 + 42.0518i) q^{35} +6.00000 q^{36} +(-26.3672 + 26.3672i) q^{37} +(17.5101 + 17.5101i) q^{38} +15.1576i q^{39} +(14.0083 + 1.94077i) q^{40} -26.4885 q^{41} +(14.7063 - 14.7063i) q^{42} +(-22.3435 - 22.3435i) q^{43} +42.1730i q^{44} +(9.05068 + 11.9618i) q^{45} -6.78233 q^{46} +(4.99263 - 4.99263i) q^{47} +(-4.89898 - 4.89898i) q^{48} -23.0919i q^{49} +(17.2616 + 30.8551i) q^{50} -2.46367 q^{51} +(12.3761 - 12.3761i) q^{52} +(-52.5294 - 52.5294i) q^{53} -7.34847i q^{54} +(-84.0776 + 63.6156i) q^{55} -24.0153 q^{56} +(21.4455 - 21.4455i) q^{57} +(36.7302 + 36.7302i) q^{58} +59.1834i q^{59} +(2.37694 - 17.1566i) q^{60} -60.6356 q^{61} +(27.5739 - 27.5739i) q^{62} +(-18.0115 - 18.0115i) q^{63} +8.00000i q^{64} +(43.3421 + 6.00477i) q^{65} +51.6511 q^{66} +(-56.3450 + 56.3450i) q^{67} +(2.01158 + 2.01158i) q^{68} +8.30662i q^{69} +(-36.2258 - 47.8778i) q^{70} -6.19517 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-10.2369 - 10.2369i) q^{73} -52.7344i q^{74} +(37.7896 - 21.1411i) q^{75} -35.0203 q^{76} +(126.600 - 126.600i) q^{77} +(-15.1576 - 15.1576i) q^{78} +44.9126i q^{79} +(-15.9491 + 12.0676i) q^{80} -9.00000 q^{81} +(26.4885 - 26.4885i) q^{82} +(-53.2159 - 53.2159i) q^{83} +29.4126i q^{84} +(-0.976002 + 7.04473i) q^{85} +44.6869 q^{86} +(44.9852 - 44.9852i) q^{87} +(-42.1730 - 42.1730i) q^{88} -117.848i q^{89} +(-21.0125 - 2.91115i) q^{90} -74.3039 q^{91} +(6.78233 - 6.78233i) q^{92} +(-33.7710 - 33.7710i) q^{93} +9.98527i q^{94} +(-52.8262 - 69.8177i) q^{95} +9.79796 q^{96} +(37.7963 - 37.7963i) q^{97} +(23.0919 + 23.0919i) q^{98} -63.2594i 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

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Representations

Groups

Database

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