LMFDB - Embedded newform 690.3.k.b.277.2

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			277.2
Character	$\chi$	$=$	690.277
Dual form			690.3.k.b.553.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.35673 + 2.45335i) q^{5} +2.44949 q^{6} +(-3.40648 - 3.40648i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.35673 + 2.45335i) q^{5} +2.44949 q^{6} +(-3.40648 - 3.40648i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(6.81008 + 1.90338i) q^{10} -17.0916 q^{11} +(-2.44949 - 2.44949i) q^{12} +(9.51988 - 9.51988i) q^{13} +6.81296i q^{14} +(2.33116 - 8.34061i) q^{15} -4.00000 q^{16} +(-1.23132 - 1.23132i) q^{17} +(-3.00000 + 3.00000i) q^{18} -10.6522i q^{19} +(-4.90669 - 8.71346i) q^{20} +8.34414 q^{21} +(17.0916 + 17.0916i) q^{22} +(-3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(12.9622 - 21.3771i) q^{25} -19.0398 q^{26} +(3.67423 + 3.67423i) q^{27} +(6.81296 - 6.81296i) q^{28} +16.4830i q^{29} +(-10.6718 + 6.00945i) q^{30} -21.1370 q^{31} +(4.00000 + 4.00000i) q^{32} +(20.9328 - 20.9328i) q^{33} +2.46265i q^{34} +(23.1984 + 6.48384i) q^{35} +6.00000 q^{36} +(0.589707 + 0.589707i) q^{37} +(-10.6522 + 10.6522i) q^{38} +23.3188i q^{39} +(-3.80677 + 13.6202i) q^{40} +44.7585 q^{41} +(-8.34414 - 8.34414i) q^{42} +(-49.7416 + 49.7416i) q^{43} -34.1832i q^{44} +(7.36004 + 13.0702i) q^{45} +6.78233 q^{46} +(59.0386 + 59.0386i) q^{47} +(4.89898 - 4.89898i) q^{48} -25.7918i q^{49} +(-34.3393 + 8.41495i) q^{50} +3.01611 q^{51} +(19.0398 + 19.0398i) q^{52} +(-38.1796 + 38.1796i) q^{53} -7.34847i q^{54} +(74.4634 - 41.9316i) q^{55} -13.6259 q^{56} +(13.0463 + 13.0463i) q^{57} +(16.4830 - 16.4830i) q^{58} +16.5016i q^{59} +(16.6812 + 4.66232i) q^{60} +85.3928 q^{61} +(21.1370 + 21.1370i) q^{62} +(-10.2194 + 10.2194i) q^{63} -8.00000i q^{64} +(-18.1200 + 64.8311i) q^{65} -41.8657 q^{66} +(87.1773 + 87.1773i) q^{67} +(2.46265 - 2.46265i) q^{68} -8.30662i q^{69} +(-16.7145 - 29.6822i) q^{70} -18.0891 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-17.4717 + 17.4717i) q^{73} -1.17941i q^{74} +(10.3062 + 42.0569i) q^{75} +21.3045 q^{76} +(58.2221 + 58.2221i) q^{77} +(23.3188 - 23.3188i) q^{78} -67.2838i q^{79} +(17.4269 - 9.81339i) q^{80} -9.00000 q^{81} +(-44.7585 - 44.7585i) q^{82} +(8.41202 - 8.41202i) q^{83} +16.6883i q^{84} +(8.38541 + 2.34368i) q^{85} +99.4833 q^{86} +(-20.1875 - 20.1875i) q^{87} +(-34.1832 + 34.1832i) q^{88} -44.8108i q^{89} +(5.71015 - 20.4302i) q^{90} -64.8586 q^{91} +(-6.78233 - 6.78233i) q^{92} +(25.8875 - 25.8875i) q^{93} -118.077i q^{94} +(26.1336 + 46.4089i) q^{95} -9.79796 q^{96} +(84.0085 + 84.0085i) q^{97} +(-25.7918 + 25.7918i) q^{98} +51.2748i 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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$			2.00000i			0.500000i
$5$	−4.35673	+	2.45335i	−0.871346	+	0.490669i
$5$	−4.35673	+	2.45335i	−0.871346	+	0.490669i
$6$	2.44949			0.408248
$7$	−3.40648	−	3.40648i	−0.486640	−	0.486640i	0.420604	−	0.907244i	$-0.361818\pi$
$7$	−3.40648	−	3.40648i	−0.486640	−	0.486640i	−0.907244	+	0.420604i	$0.861818\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$		−	3.00000i		−	0.333333i
$10$	6.81008	+	1.90338i	0.681008	+	0.190338i
$11$	−17.0916			−1.55378			−0.776890	−	0.629636i	$-0.783204\pi$
$11$	−17.0916			−1.55378			−0.776890	+	0.629636i	$0.783204\pi$
$12$	−2.44949	−	2.44949i	−0.204124	−	0.204124i
$13$	9.51988	−	9.51988i	0.732298	−	0.732298i	−0.238776	−	0.971075i	$-0.576746\pi$
$13$	9.51988	−	9.51988i	0.732298	−	0.732298i	0.971075	+	0.238776i	$0.0767462\pi$
$14$			6.81296i			0.486640i
$15$	2.33116	−	8.34061i	0.155411	−	0.556040i
$16$	−4.00000			−0.250000
$17$	−1.23132	−	1.23132i	−0.0724308	−	0.0724308i	0.669963	−	0.742394i	$-0.266310\pi$
$17$	−1.23132	−	1.23132i	−0.0724308	−	0.0724308i	−0.742394	+	0.669963i	$0.766310\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$		−	10.6522i		−	0.560644i	−0.959906	−	0.280322i	$-0.909559\pi$
$19$		−	10.6522i		−	0.560644i	0.959906	−	0.280322i	$-0.0904413\pi$
$20$	−4.90669	−	8.71346i	−0.245335	−	0.435673i
$21$	8.34414			0.397340
$22$	17.0916	+	17.0916i	0.776890	+	0.776890i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$24$			4.89898i			0.204124i
$25$	12.9622	−	21.3771i	0.518487	−	0.855085i
$26$	−19.0398			−0.732298
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$	6.81296	−	6.81296i	0.243320	−	0.243320i
$29$			16.4830i			0.568380i	0.958768	+	0.284190i	$0.0917247\pi$
$29$			16.4830i			0.568380i	−0.958768	+	0.284190i	$0.908275\pi$
$30$	−10.6718	+	6.00945i	−0.355725	+	0.200315i
$31$	−21.1370			−0.681839			−0.340920	−	0.940092i	$-0.610738\pi$
$31$	−21.1370			−0.681839			−0.340920	+	0.940092i	$0.610738\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	20.9328	−	20.9328i	0.634328	−	0.634328i
$34$			2.46265i			0.0724308i
$35$	23.1984	+	6.48384i	0.662811	+	0.185252i
$36$	6.00000			0.166667
$37$	0.589707	+	0.589707i	0.0159380	+	0.0159380i	0.715031	−	0.699093i	$-0.246413\pi$
$37$	0.589707	+	0.589707i	0.0159380	+	0.0159380i	−0.699093	+	0.715031i	$0.746413\pi$
$38$	−10.6522	+	10.6522i	−0.280322	+	0.280322i
$39$			23.3188i			0.597919i
$40$	−3.80677	+	13.6202i	−0.0951692	+	0.340504i
$41$	44.7585			1.09167			0.545835	−	0.837893i	$-0.316213\pi$
$41$	44.7585			1.09167			0.545835	+	0.837893i	$0.316213\pi$
$42$	−8.34414	−	8.34414i	−0.198670	−	0.198670i
$43$	−49.7416	+	49.7416i	−1.15678	+	1.15678i	−0.171619	+	0.985163i	$0.554900\pi$
$43$	−49.7416	+	49.7416i	−1.15678	+	1.15678i	−0.985163	+	0.171619i	$0.945100\pi$
$44$		−	34.1832i		−	0.776890i
$45$	7.36004	+	13.0702i	0.163556	+	0.290449i
$46$	6.78233			0.147442
$47$	59.0386	+	59.0386i	1.25614	+	1.25614i	0.952920	+	0.303220i	$0.0980619\pi$
$47$	59.0386	+	59.0386i	1.25614	+	1.25614i	0.303220	+	0.952920i	$0.401938\pi$
$48$	4.89898	−	4.89898i	0.102062	−	0.102062i
$49$		−	25.7918i		−	0.526363i
$50$	−34.3393	+	8.41495i	−0.686786	+	0.168299i
$51$	3.01611			0.0591395
$52$	19.0398	+	19.0398i	0.366149	+	0.366149i
$53$	−38.1796	+	38.1796i	−0.720369	+	0.720369i	−0.968680	−	0.248311i	$-0.920124\pi$
$53$	−38.1796	+	38.1796i	−0.720369	+	0.720369i	0.248311	+	0.968680i	$0.420124\pi$
$54$		−	7.34847i		−	0.136083i
$55$	74.4634	−	41.9316i	1.35388	−	0.762392i
$56$	−13.6259			−0.243320
$57$	13.0463	+	13.0463i	0.228882	+	0.228882i
$58$	16.4830	−	16.4830i	0.284190	−	0.284190i
$59$			16.5016i			0.279688i	0.990174	+	0.139844i	$0.0446601\pi$
$59$			16.5016i			0.279688i	−0.990174	+	0.139844i	$0.955340\pi$
$60$	16.6812	+	4.66232i	0.278020	+	0.0777053i
$61$	85.3928			1.39988			0.699941	−	0.714201i	$-0.253210\pi$
$61$	85.3928			1.39988			0.699941	+	0.714201i	$0.253210\pi$
$62$	21.1370	+	21.1370i	0.340920	+	0.340920i
$63$	−10.2194	+	10.2194i	−0.162213	+	0.162213i
$64$		−	8.00000i		−	0.125000i
$65$	−18.1200	+	64.8311i	−0.278769	+	0.997402i
$66$	−41.8657			−0.634328
$67$	87.1773	+	87.1773i	1.30115	+	1.30115i	0.927614	+	0.373540i	$0.121856\pi$
$67$	87.1773	+	87.1773i	1.30115	+	1.30115i	0.373540	+	0.927614i	$0.378144\pi$
$68$	2.46265	−	2.46265i	0.0362154	−	0.0362154i
$69$		−	8.30662i		−	0.120386i
$70$	−16.7145	−	29.6822i	−0.238779	−	0.424032i
$71$	−18.0891			−0.254776			−0.127388	−	0.991853i	$-0.540659\pi$
$71$	−18.0891			−0.254776			−0.127388	+	0.991853i	$0.540659\pi$
$72$	−6.00000	−	6.00000i	−0.0833333	−	0.0833333i
$73$	−17.4717	+	17.4717i	−0.239338	+	0.239338i	−0.816576	−	0.577238i	$-0.804130\pi$
$73$	−17.4717	+	17.4717i	−0.239338	+	0.239338i	0.577238	+	0.816576i	$0.304130\pi$
$74$		−	1.17941i		−	0.0159380i
$75$	10.3062	+	42.0569i	0.137416	+	0.560759i
$76$	21.3045			0.280322
$77$	58.2221	+	58.2221i	0.756132	+	0.756132i
$78$	23.3188	−	23.3188i	0.298960	−	0.298960i
$79$		−	67.2838i		−	0.851693i	−0.904795	−	0.425847i	$-0.859976\pi$
$79$		−	67.2838i		−	0.851693i	0.904795	−	0.425847i	$-0.140024\pi$
$80$	17.4269	−	9.81339i	0.217836	−	0.122667i
$81$	−9.00000			−0.111111
$82$	−44.7585	−	44.7585i	−0.545835	−	0.545835i
$83$	8.41202	−	8.41202i	0.101350	−	0.101350i	−0.654614	−	0.755963i	$-0.727169\pi$
$83$	8.41202	−	8.41202i	0.101350	−	0.101350i	0.755963	+	0.654614i	$0.227169\pi$
$84$			16.6883i			0.198670i
$85$	8.38541	+	2.34368i	0.0986518	+	0.0275727i
$86$	99.4833			1.15678
$87$	−20.1875	−	20.1875i	−0.232040	−	0.232040i
$88$	−34.1832	+	34.1832i	−0.388445	+	0.388445i
$89$		−	44.8108i		−	0.503492i	−0.967793	−	0.251746i	$-0.918995\pi$
$89$		−	44.8108i		−	0.503492i	0.967793	−	0.251746i	$-0.0810047\pi$
$90$	5.71015	−	20.4302i	0.0634461	−	0.227003i
$91$	−64.8586			−0.712731
$92$	−6.78233	−	6.78233i	−0.0737210	−	0.0737210i
$93$	25.8875	−	25.8875i	0.278360	−	0.278360i
$94$		−	118.077i		−	1.25614i
$95$	26.1336	+	46.4089i	0.275091	+	0.488515i
$96$	−9.79796			−0.102062
$97$	84.0085	+	84.0085i	0.866067	+	0.866067i	0.992034	−	0.125967i	$-0.0402034\pi$
$97$	84.0085	+	84.0085i	0.866067	+	0.866067i	−0.125967	+	0.992034i	$0.540203\pi$
$98$	−25.7918	+	25.7918i	−0.263182	+	0.263182i
$99$			51.2748i			0.517927i
$100$	42.7543	+	25.9244i	0.427543	+	0.259244i
$101$	110.266			1.09174			0.545871	−	0.837869i	$-0.316199\pi$
$101$	110.266			1.09174			0.545871	+	0.837869i	$0.316199\pi$
$102$	−3.01611	−	3.01611i	−0.0295697	−	0.0295697i
$103$	103.363	−	103.363i	1.00352	−	1.00352i	0.00352878	−	0.999994i	$-0.498877\pi$
$103$	103.363	−	103.363i	1.00352	−	1.00352i	0.999994	−	0.00352878i	$-0.00112325\pi$
$104$		−	38.0795i		−	0.366149i
$105$	−36.3531	+	20.4711i	−0.346220	+	0.194962i
$106$	76.3591			0.720369
$107$	−39.1624	−	39.1624i	−0.366004	−	0.366004i	0.500014	−	0.866018i	$-0.333328\pi$
$107$	−39.1624	−	39.1624i	−0.366004	−	0.366004i	−0.866018	+	0.500014i	$0.833328\pi$
$108$	−7.34847	+	7.34847i	−0.0680414	+	0.0680414i
$109$		−	167.451i		−	1.53625i	−0.640299	−	0.768126i	$-0.721190\pi$
$109$		−	167.451i		−	1.53625i	0.640299	−	0.768126i	$-0.278810\pi$
$110$	−116.395	−	32.5318i	−1.05814	−	0.295744i
$111$	−1.44448			−0.0130133
$112$	13.6259	+	13.6259i	0.121660	+	0.121660i
$113$	−58.3978	+	58.3978i	−0.516794	+	0.516794i	−0.916600	−	0.399806i	$-0.869078\pi$
$113$	−58.3978	+	58.3978i	−0.516794	+	0.516794i	0.399806	+	0.916600i	$0.369078\pi$
$114$		−	26.0925i		−	0.228882i
$115$	6.45469	−	23.0941i	0.0561277	−	0.200818i
$116$	−32.9661			−0.284190
$117$	−28.5596	−	28.5596i	−0.244099	−	0.244099i
$118$	16.5016	−	16.5016i	0.139844	−	0.139844i
$119$			8.38896i			0.0704954i
$120$	−12.0189	−	21.3435i	−0.100157	−	0.177863i
$121$	171.122			1.41423
$122$	−85.3928	−	85.3928i	−0.699941	−	0.699941i
$123$	−54.8177	+	54.8177i	−0.445672	+	0.445672i
$124$		−	42.2740i		−	0.340920i
$125$	−4.02721	+	124.935i	−0.0322177	+	0.999481i
$126$	20.4389			0.162213
$127$	38.7338	+	38.7338i	0.304990	+	0.304990i	0.842963	−	0.537972i	$-0.180809\pi$
$127$	38.7338	+	38.7338i	0.304990	+	0.304990i	−0.537972	+	0.842963i	$0.680809\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$		−	121.842i		−	0.944509i
$130$	82.9511	−	46.7111i	0.638085	−	0.359316i
$131$	53.9132			0.411551			0.205776	−	0.978599i	$-0.434028\pi$
$131$	53.9132			0.411551			0.205776	+	0.978599i	$0.434028\pi$
$132$	41.8657	+	41.8657i	0.317164	+	0.317164i
$133$	−36.2866	+	36.2866i	−0.272832	+	0.272832i
$134$		−	174.355i		−	1.30115i
$135$	−25.0218	−	6.99348i	−0.185347	−	0.0518035i
$136$	−4.92529			−0.0362154
$137$	−77.4818	−	77.4818i	−0.565561	−	0.565561i	0.365321	−	0.930882i	$-0.380959\pi$
$137$	−77.4818	−	77.4818i	−0.565561	−	0.565561i	−0.930882	+	0.365321i	$0.880959\pi$
$138$	−8.30662	+	8.30662i	−0.0601929	+	0.0601929i
$139$		−	39.5073i		−	0.284225i	−0.989850	−	0.142113i	$-0.954610\pi$
$139$		−	39.5073i		−	0.284225i	0.989850	−	0.142113i	$-0.0453895\pi$
$140$	−12.9677	+	46.3968i	−0.0926262	+	0.331405i
$141$	−144.614			−1.02563
$142$	18.0891	+	18.0891i	0.127388	+	0.127388i
$143$	−162.710	+	162.710i	−1.13783	+	1.13783i
$144$			12.0000i			0.0833333i
$145$	−40.4386	−	71.8121i	−0.278887	−	0.495256i
$146$	34.9433			0.239338
$147$	31.5884	+	31.5884i	0.214887	+	0.214887i
$148$	−1.17941	+	1.17941i	−0.00796901	+	0.00796901i
$149$			124.537i			0.835817i	0.908489	+	0.417909i	$0.137237\pi$
$149$			124.537i			0.835817i	−0.908489	+	0.417909i	$0.862763\pi$
$150$	31.7507	−	52.3631i	0.211672	−	0.349087i
$151$	100.260			0.663973			0.331986	−	0.943284i	$-0.392281\pi$
$151$	100.260			0.663973			0.331986	+	0.943284i	$0.392281\pi$
$152$	−21.3045	−	21.3045i	−0.140161	−	0.140161i
$153$	−3.69397	+	3.69397i	−0.0241436	+	0.0241436i
$154$		−	116.444i		−	0.756132i
$155$	92.0883	−	51.8564i	0.594118	−	0.334558i
$156$	−46.6377			−0.298960
$157$	169.452	+	169.452i	1.07931	+	1.07931i	0.996571	+	0.0827379i	$0.0263664\pi$
$157$	169.452	+	169.452i	1.07931	+	1.07931i	0.0827379	+	0.996571i	$0.473634\pi$
$158$	−67.2838	+	67.2838i	−0.425847	+	0.425847i
$159$		−	93.5205i		−	0.588179i
$160$	−27.2403	−	7.61353i	−0.170252	−	0.0475846i
$161$	23.1039			0.143502
$162$	9.00000	+	9.00000i	0.0555556	+	0.0555556i
$163$	125.349	−	125.349i	0.769014	−	0.769014i	−0.208919	−	0.977933i	$-0.566994\pi$
$163$	125.349	−	125.349i	0.769014	−	0.769014i	0.977933	+	0.208919i	$0.0669944\pi$
$164$			89.5169i			0.545835i
$165$	−39.8432	+	142.554i	−0.241474	+	0.863965i
$166$	−16.8240			−0.101350
$167$	148.841	+	148.841i	0.891262	+	0.891262i	0.994642	−	0.103380i	$-0.0329657\pi$
$167$	148.841	+	148.841i	0.891262	+	0.891262i	−0.103380	+	0.994642i	$0.532966\pi$
$168$	16.6883	−	16.6883i	0.0993350	−	0.0993350i
$169$		−	12.2562i		−	0.0725222i
$170$	−6.04173	−	10.7291i	−0.0355396	−	0.0631123i
$171$	−31.9567			−0.186881
$172$	−99.4833	−	99.4833i	−0.578391	−	0.578391i
$173$	89.4157	−	89.4157i	0.516854	−	0.516854i	−0.399764	−	0.916618i	$-0.630908\pi$
$173$	89.4157	−	89.4157i	0.516854	−	0.516854i	0.916618	+	0.399764i	$0.130908\pi$
$174$			40.3750i			0.232040i
$175$	−116.976	+	28.6654i	−0.668435	+	0.163802i
$176$	68.3663			0.388445
$177$	−20.2103	−	20.2103i	−0.114182	−	0.114182i
$178$	−44.8108	+	44.8108i	−0.251746	+	0.251746i
$179$			82.4024i			0.460349i	0.973149	+	0.230174i	$0.0739296\pi$
$179$			82.4024i			0.460349i	−0.973149	+	0.230174i	$0.926070\pi$
$180$	−26.1404	+	14.7201i	−0.145224	+	0.0817782i
$181$	−345.572			−1.90924			−0.954620	−	0.297828i	$-0.903738\pi$
$181$	−345.572			−1.90924			−0.954620	+	0.297828i	$0.903738\pi$
$182$	64.8586	+	64.8586i	0.356366	+	0.356366i
$183$	−104.584	+	104.584i	−0.571499	+	0.571499i
$184$			13.5647i			0.0737210i
$185$	−4.01595	−	1.12244i	−0.0217078	−	0.00606723i
$186$	−51.7749			−0.278360
$187$	21.0453	+	21.0453i	0.112542	+	0.112542i
$188$	−118.077	+	118.077i	−0.628070	+	0.628070i
$189$		−	25.0324i		−	0.132447i
$190$	20.2753	−	72.5425i	0.106712	−	0.381803i
$191$	−263.122			−1.37760			−0.688801	−	0.724950i	$-0.741863\pi$
$191$	−263.122			−1.37760			−0.688801	+	0.724950i	$0.741863\pi$
$192$	9.79796	+	9.79796i	0.0510310	+	0.0510310i
$193$	140.875	−	140.875i	0.729920	−	0.729920i	−0.240684	−	0.970604i	$-0.577372\pi$
$193$	140.875	−	140.875i	0.729920	−	0.729920i	0.970604	+	0.240684i	$0.0773717\pi$
$194$		−	168.017i		−	0.866067i
$195$	−57.2092	−	101.594i	−0.293381	−	0.520994i
$196$	51.5836			0.263182
$197$	−85.4790	−	85.4790i	−0.433903	−	0.433903i	0.456051	−	0.889954i	$-0.349264\pi$
$197$	−85.4790	−	85.4790i	−0.433903	−	0.433903i	−0.889954	+	0.456051i	$0.849264\pi$
$198$	51.2748	−	51.2748i	0.258963	−	0.258963i
$199$			234.435i			1.17806i	0.808110	+	0.589032i	$0.200491\pi$
$199$			234.435i			1.17806i	−0.808110	+	0.589032i	$0.799509\pi$
$200$	−16.8299	−	68.6786i	−0.0841495	−	0.343393i
$201$	−213.540			−1.06239
$202$	−110.266	−	110.266i	−0.545871	−	0.545871i
$203$	56.1491	−	56.1491i	0.276597	−	0.276597i
$204$			6.03223i			0.0295697i
$205$	−195.001	+	109.808i	−0.951222	+	0.535649i
$206$	−206.726			−1.00352
$207$	10.1735	+	10.1735i	0.0491473	+	0.0491473i
$208$	−38.0795	+	38.0795i	−0.183075	+	0.183075i
$209$			182.064i			0.871118i
$210$	56.8242	+	15.8821i	0.270591	+	0.0756290i
$211$	−145.969			−0.691795			−0.345897	−	0.938272i	$-0.612426\pi$
$211$	−145.969			−0.691795			−0.345897	+	0.938272i	$0.612426\pi$
$212$	−76.3591	−	76.3591i	−0.360185	−	0.360185i
$213$	22.1545	−	22.1545i	0.104012	−	0.104012i
$214$			78.3249i			0.366004i
$215$	94.6774	−	338.744i	0.440360	−	1.57556i
$216$	14.6969			0.0680414
$217$	72.0028	+	72.0028i	0.331810	+	0.331810i
$218$	−167.451	+	167.451i	−0.768126	+	0.768126i
$219$		−	42.7967i		−	0.195419i
$220$	83.8632	+	148.927i	0.381196	+	0.676940i
$221$	−23.4441			−0.106082
$222$	1.44448	+	1.44448i	0.00650667	+	0.00650667i
$223$	−227.734	+	227.734i	−1.02123	+	1.02123i	−0.0214593	+	0.999770i	$0.506831\pi$
$223$	−227.734	+	227.734i	−1.02123	+	1.02123i	−0.999770	+	0.0214593i	$0.993169\pi$
$224$		−	27.2518i		−	0.121660i
$225$	−64.1314	−	38.8865i	−0.285028	−	0.172829i
$226$	116.796			0.516794
$227$	−63.6156	−	63.6156i	−0.280245	−	0.280245i	0.552962	−	0.833207i	$-0.313498\pi$
$227$	−63.6156	−	63.6156i	−0.280245	−	0.280245i	−0.833207	+	0.552962i	$0.813498\pi$
$228$	−26.0925	+	26.0925i	−0.114441	+	0.114441i
$229$		−	173.353i		−	0.757000i	−0.925601	−	0.378500i	$-0.876440\pi$
$229$		−	173.353i		−	0.757000i	0.925601	−	0.378500i	$-0.123560\pi$
$230$	−29.5488	+	16.6394i	−0.128473	+	0.0723452i
$231$	−142.615			−0.617379
$232$	32.9661	+	32.9661i	0.142095	+	0.142095i
$233$	128.901	−	128.901i	0.553225	−	0.553225i	−0.374145	−	0.927370i	$-0.622064\pi$
$233$	128.901	−	128.901i	0.553225	−	0.553225i	0.927370	+	0.374145i	$0.122064\pi$
$234$			57.1193i			0.244099i
$235$	−402.057	−	112.373i	−1.71088	−	0.478183i
$236$	−33.0032			−0.139844
$237$	82.4054	+	82.4054i	0.347702	+	0.347702i
$238$	8.38896	−	8.38896i	0.0352477	−	0.0352477i
$239$		−	198.218i		−	0.829366i	−0.909966	−	0.414683i	$-0.863892\pi$
$239$		−	198.218i		−	0.829366i	0.909966	−	0.414683i	$-0.136108\pi$
$240$	−9.32463	+	33.3624i	−0.0388526	+	0.139010i
$241$	134.329			0.557381			0.278690	−	0.960381i	$-0.410100\pi$
$241$	134.329			0.557381			0.278690	+	0.960381i	$0.410100\pi$
$242$	−171.122	−	171.122i	−0.707117	−	0.707117i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$			170.786i			0.699941i
$245$	63.2762	+	112.368i	0.258270	+	0.458644i
$246$	109.635			0.445672
$247$	−101.408	−	101.408i	−0.410559	−	0.410559i
$248$	−42.2740	+	42.2740i	−0.170460	+	0.170460i
$249$			20.6052i			0.0827517i
$250$	128.962	−	120.908i	0.515849	−	0.483632i
$251$	−85.1879			−0.339394			−0.169697	−	0.985496i	$-0.554279\pi$
$251$	−85.1879			−0.339394			−0.169697	+	0.985496i	$0.554279\pi$
$252$	−20.4389	−	20.4389i	−0.0811067	−	0.0811067i
$253$	57.9604	−	57.9604i	0.229092	−	0.229092i
$254$		−	77.4676i		−	0.304990i
$255$	−13.1404	+	7.39957i	−0.0515310	+	0.0290179i
$256$	16.0000			0.0625000
$257$	−89.1736	−	89.1736i	−0.346979	−	0.346979i	0.512004	−	0.858983i	$-0.328903\pi$
$257$	−89.1736	−	89.1736i	−0.346979	−	0.346979i	−0.858983	+	0.512004i	$0.828903\pi$
$258$	−121.842	+	121.842i	−0.472254	+	0.472254i
$259$		−	4.01765i		−	0.0155121i
$260$	−129.662	−	36.2400i	−0.498701	−	0.139384i
$261$	49.4491			0.189460
$262$	−53.9132	−	53.9132i	−0.205776	−	0.205776i
$263$	123.208	−	123.208i	0.468473	−	0.468473i	−0.432947	−	0.901420i	$-0.642526\pi$
$263$	123.208	−	123.208i	0.468473	−	0.468473i	0.901420	+	0.432947i	$0.142526\pi$
$264$		−	83.7313i		−	0.317164i
$265$	72.6703	−	260.006i	0.274228	−	0.981154i
$266$	72.5733			0.272832
$267$	54.8818	+	54.8818i	0.205550	+	0.205550i
$268$	−174.355	+	174.355i	−0.650577	+	0.650577i
$269$		−	159.070i		−	0.591340i	−0.955290	−	0.295670i	$-0.904457\pi$
$269$		−	159.070i		−	0.591340i	0.955290	−	0.295670i	$-0.0955429\pi$
$270$	18.0283	+	32.0153i	0.0667716	+	0.118575i
$271$	262.498			0.968627			0.484313	−	0.874895i	$-0.339069\pi$
$271$	262.498			0.968627			0.484313	+	0.874895i	$0.339069\pi$
$272$	4.92529	+	4.92529i	0.0181077	+	0.0181077i
$273$	79.4352	−	79.4352i	0.290971	−	0.290971i
$274$			154.964i			0.565561i
$275$	−221.544	+	365.369i	−0.805615	+	1.32861i
$276$	16.6132			0.0601929
$277$	249.767	+	249.767i	0.901686	+	0.901686i	0.995582	−	0.0938960i	$-0.0299321\pi$
$277$	249.767	+	249.767i	0.901686	+	0.901686i	−0.0938960	+	0.995582i	$0.529932\pi$
$278$	−39.5073	+	39.5073i	−0.142113	+	0.142113i
$279$			63.4111i			0.227280i
$280$	59.3644	−	33.4291i	0.212016	−	0.119390i
$281$	312.983			1.11382			0.556910	−	0.830573i	$-0.311987\pi$
$281$	312.983			1.11382			0.556910	+	0.830573i	$0.311987\pi$
$282$	144.614	+	144.614i	0.512817	+	0.512817i
$283$	−304.788	+	304.788i	−1.07699	+	1.07699i	−0.0802130	+	0.996778i	$0.525560\pi$
$283$	−304.788	+	304.788i	−1.07699	+	1.07699i	−0.996778	+	0.0802130i	$0.974440\pi$
$284$		−	36.1782i		−	0.127388i
$285$	−88.8461	−	24.8321i	−0.311741	−	0.0871300i
$286$	325.420			1.13783
$287$	−152.469	−	152.469i	−0.531250	−	0.531250i
$288$	12.0000	−	12.0000i	0.0416667	−	0.0416667i
$289$		−	285.968i		−	0.989508i
$290$	−31.3735	+	112.251i	−0.108185	+	0.387071i
$291$	−205.778			−0.707141
$292$	−34.9433	−	34.9433i	−0.119669	−	0.119669i
$293$	−342.482	+	342.482i	−1.16888	+	1.16888i	−0.186408	+	0.982472i	$0.559685\pi$
$293$	−342.482	+	342.482i	−1.16888	+	1.16888i	−0.982472	+	0.186408i	$0.940315\pi$
$294$		−	63.1767i		−	0.214887i
$295$	−40.4841	−	71.8930i	−0.137234	−	0.243705i
$296$	2.35883			0.00796901
$297$	−62.7985	−	62.7985i	−0.211443	−	0.211443i
$298$	124.537	−	124.537i	0.417909	−	0.417909i
$299$			64.5670i			0.215943i
$300$	−84.1138	+	20.6123i	−0.280379	+	0.0687078i
$301$	338.888			1.12587
$302$	−100.260	−	100.260i	−0.331986	−	0.331986i
$303$	−135.048	+	135.048i	−0.445702	+	0.445702i
$304$			42.6090i			0.140161i
$305$	−372.033	+	209.498i	−1.21978	+	0.686879i
$306$	7.38794			0.0241436
$307$	242.539	+	242.539i	0.790030	+	0.790030i	0.981499	−	0.191469i	$-0.0613250\pi$
$307$	242.539	+	242.539i	0.790030	+	0.790030i	−0.191469	+	0.981499i	$0.561325\pi$
$308$	−116.444	+	116.444i	−0.378066	+	0.378066i
$309$			253.186i			0.819373i
$310$	−143.945	−	40.2319i	−0.464338	−	0.129780i
$311$	−486.480			−1.56424			−0.782122	−	0.623125i	$-0.785863\pi$
$311$	−486.480			−1.56424			−0.782122	+	0.623125i	$0.785863\pi$
$312$	46.6377	+	46.6377i	0.149480	+	0.149480i
$313$	58.2031	−	58.2031i	0.185953	−	0.185953i	−0.607991	−	0.793944i	$-0.708024\pi$
$313$	58.2031	−	58.2031i	0.185953	−	0.185953i	0.793944	+	0.607991i	$0.208024\pi$
$314$		−	338.903i		−	1.07931i
$315$	19.4515	−	69.5952i	0.0617508	−	0.220937i
$316$	134.568			0.425847
$317$	331.965	+	331.965i	1.04721	+	1.04721i	0.998829	+	0.0483793i	$0.0154056\pi$
$317$	331.965	+	331.965i	1.04721	+	1.04721i	0.0483793	+	0.998829i	$0.484594\pi$
$318$	−93.5205	+	93.5205i	−0.294089	+	0.294089i
$319$		−	281.721i		−	0.883138i
$320$	19.6268	+	34.8538i	0.0613337	+	0.108918i
$321$	95.9280			0.298841
$322$	−23.1039	−	23.1039i	−0.0717511	−	0.0717511i
$323$	−13.1164	+	13.1164i	−0.0406079	+	0.0406079i
$324$		−	18.0000i		−	0.0555556i
$325$	−80.1093	−	326.906i	−0.246490	−	1.00587i
$326$	−250.699			−0.769014
$327$	205.085	+	205.085i	0.627172	+	0.627172i
$328$	89.5169	−	89.5169i	0.272917	−	0.272917i
$329$		−	402.228i		−	1.22258i
$330$	182.397	−	102.711i	0.552719	−	0.311245i
$331$	57.4084			0.173439			0.0867196	−	0.996233i	$-0.472362\pi$
$331$	57.4084			0.173439			0.0867196	+	0.996233i	$0.472362\pi$
$332$	16.8240	+	16.8240i	0.0506748	+	0.0506748i
$333$	1.76912	−	1.76912i	0.00531267	−	0.00531267i
$334$		−	297.682i		−	0.891262i
$335$	−593.684	−	165.932i	−1.77219	−	0.495319i
$336$	−33.3765			−0.0993350
$337$	17.5680	+	17.5680i	0.0521307	+	0.0521307i	0.732692	−	0.680561i	$-0.238264\pi$
$337$	17.5680	+	17.5680i	0.0521307	+	0.0521307i	−0.680561	+	0.732692i	$0.738264\pi$
$338$	−12.2562	+	12.2562i	−0.0362611	+	0.0362611i
$339$		−	143.045i		−	0.421961i
$340$	−4.68736	+	16.7708i	−0.0137864	+	0.0493259i
$341$	361.265			1.05943
$342$	31.9567	+	31.9567i	0.0934407	+	0.0934407i
$343$	−254.777	+	254.777i	−0.742789	+	0.742789i
$344$			198.967i			0.578391i
$345$	20.3790	+	36.1897i	0.0590696	+	0.104898i
$346$	−178.831			−0.516854
$347$	71.5458	+	71.5458i	0.206184	+	0.206184i	0.802643	−	0.596459i	$-0.203426\pi$
$347$	71.5458	+	71.5458i	0.206184	+	0.206184i	−0.596459	+	0.802643i	$0.703426\pi$
$348$	40.3750	−	40.3750i	0.116020	−	0.116020i
$349$			21.0922i			0.0604360i	0.999543	+	0.0302180i	$0.00962015\pi$
$349$			21.0922i			0.0604360i	−0.999543	+	0.0302180i	$0.990380\pi$
$350$	145.642	+	88.3108i	0.416119	+	0.252317i
$351$	69.9565			0.199306
$352$	−68.3663	−	68.3663i	−0.194223	−	0.194223i
$353$	267.728	−	267.728i	0.758436	−	0.758436i	−0.217601	−	0.976038i	$-0.569823\pi$
$353$	267.728	−	267.728i	0.758436	−	0.758436i	0.976038	+	0.217601i	$0.0698232\pi$
$354$			40.4205i			0.114182i
$355$	78.8093	−	44.3788i	0.221998	−	0.125011i
$356$	89.6216			0.251746
$357$	−10.2743	−	10.2743i	−0.0287796	−	0.0287796i
$358$	82.4024	−	82.4024i	0.230174	−	0.230174i
$359$		−	184.468i		−	0.513837i	−0.966433	−	0.256919i	$-0.917293\pi$
$359$		−	184.468i		−	0.513837i	0.966433	−	0.256919i	$-0.0827073\pi$
$360$	40.8605	+	11.4203i	0.113501	+	0.0317231i
$361$	247.530			0.685678
$362$	345.572	+	345.572i	0.954620	+	0.954620i
$363$	−209.581	+	209.581i	−0.577358	+	0.577358i
$364$		−	129.717i		−	0.356366i
$365$	33.2553	−	118.983i	0.0911103	−	0.325982i
$366$	209.169			0.571499
$367$	−370.206	−	370.206i	−1.00874	−	1.00874i	−0.999962	−	0.00877369i	$-0.997207\pi$
$367$	−370.206	−	370.206i	−1.00874	−	1.00874i	−0.00877369	−	0.999962i	$-0.502793\pi$
$368$	13.5647	−	13.5647i	0.0368605	−	0.0368605i
$369$		−	134.275i		−	0.363890i
$370$	2.89351	+	5.13838i	0.00782029	+	0.0138875i
$371$	260.116			0.701121
$372$	51.7749	+	51.7749i	0.139180	+	0.139180i
$373$	479.170	−	479.170i	1.28464	−	1.28464i	0.346638	−	0.937999i	$-0.387323\pi$
$373$	479.170	−	479.170i	1.28464	−	1.28464i	0.937999	−	0.346638i	$-0.112677\pi$
$374$		−	42.0905i		−	0.112542i
$375$	−148.081	−	157.946i	−0.394884	−	0.421189i
$376$	236.154			0.628070
$377$	156.916	+	156.916i	0.416224	+	0.416224i
$378$	−25.0324	+	25.0324i	−0.0662233	+	0.0662233i
$379$			415.235i			1.09561i	0.836607	+	0.547804i	$0.184536\pi$
$379$			415.235i			1.09561i	−0.836607	+	0.547804i	$0.815464\pi$
$380$	−92.8178	+	52.2673i	−0.244257	+	0.137545i
$381$	−94.8780			−0.249024
$382$	263.122	+	263.122i	0.688801	+	0.688801i
$383$	445.768	−	445.768i	1.16389	−	1.16389i	0.180268	−	0.983617i	$-0.442303\pi$
$383$	445.768	−	445.768i	1.16389	−	1.16389i	0.983617	−	0.180268i	$-0.0576966\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	−396.497	−	110.819i	−1.02986	−	0.287842i
$386$	−281.749			−0.729920
$387$	149.225	+	149.225i	0.385594	+	0.385594i
$388$	−168.017	+	168.017i	−0.433034	+	0.433034i
$389$			274.994i			0.706925i	0.935449	+	0.353462i	$0.114996\pi$
$389$			274.994i			0.706925i	−0.935449	+	0.353462i	$0.885004\pi$
$390$	−44.3847	+	158.803i	−0.113807	+	0.407188i
$391$	8.35124			0.0213587
$392$	−51.5836	−	51.5836i	−0.131591	−	0.131591i
$393$	−66.0299	+	66.0299i	−0.168015	+	0.168015i
$394$			170.958i			0.433903i
$395$	165.070	+	293.137i	0.417900	+	0.742119i
$396$	−102.550			−0.258963
$397$	23.6184	+	23.6184i	0.0594921	+	0.0594921i	0.736227	−	0.676735i	$-0.236606\pi$
$397$	23.6184	+	23.6184i	0.0594921	+	0.0594921i	−0.676735	+	0.736227i	$0.736606\pi$
$398$	234.435	−	234.435i	0.589032	−	0.589032i
$399$		−	88.8837i		−	0.222766i
$400$	−51.8487	+	85.5085i	−0.129622	+	0.213771i
$401$	673.867			1.68047			0.840233	−	0.542225i	$-0.182418\pi$
$401$	673.867			1.68047			0.840233	+	0.542225i	$0.182418\pi$
$402$	213.540	+	213.540i	0.531194	+	0.531194i
$403$	−201.222	+	201.222i	−0.499310	+	0.499310i
$404$			220.532i			0.545871i
$405$	39.2106	−	22.0801i	0.0968162	−	0.0545188i
$406$	−112.298			−0.276597
$407$	−10.0790	−	10.0790i	−0.0247642	−	0.0247642i
$408$	6.03223	−	6.03223i	0.0147849	−	0.0147849i
$409$			37.4601i			0.0915894i	0.998951	+	0.0457947i	$0.0145820\pi$
$409$			37.4601i			0.0915894i	−0.998951	+	0.0457947i	$0.985418\pi$
$410$	304.809	+	85.1925i	0.743435	+	0.207787i
$411$	189.791			0.461778
$412$	206.726	+	206.726i	0.501761	+	0.501761i
$413$	56.2124	−	56.2124i	0.136107	−	0.136107i
$414$		−	20.3470i		−	0.0491473i
$415$	−16.0113	+	57.2865i	−0.0385815	+	0.138040i
$416$	76.1590			0.183075
$417$	48.3864	+	48.3864i	0.116035	+	0.116035i
$418$	182.064	−	182.064i	0.435559	−	0.435559i
$419$		−	251.336i		−	0.599846i	−0.953963	−	0.299923i	$-0.903039\pi$
$419$		−	251.336i		−	0.599846i	0.953963	−	0.299923i	$-0.0969610\pi$
$420$	−40.9421	−	72.7063i	−0.0974812	−	0.173110i
$421$	555.687			1.31992			0.659961	−	0.751300i	$-0.270573\pi$
$421$	555.687			1.31992			0.659961	+	0.751300i	$0.270573\pi$
$422$	145.969	+	145.969i	0.345897	+	0.345897i
$423$	177.116	−	177.116i	0.418714	−	0.418714i
$424$			152.718i			0.360185i
$425$	−42.2828	+	10.3615i	−0.0994890	+	0.0243801i
$426$	−44.3090			−0.104012
$427$	−290.889	−	290.889i	−0.681238	−	0.681238i
$428$	78.3249	−	78.3249i	0.183002	−	0.183002i
$429$		−	398.556i		−	0.929035i
$430$	−433.422	+	244.067i	−1.00796	+	0.567598i
$431$	−61.4001			−0.142460			−0.0712298	−	0.997460i	$-0.522692\pi$
$431$	−61.4001			−0.142460			−0.0712298	+	0.997460i	$0.522692\pi$
$432$	−14.6969	−	14.6969i	−0.0340207	−	0.0340207i
$433$	449.062	−	449.062i	1.03709	−	1.03709i	0.0378095	−	0.999285i	$-0.487962\pi$
$433$	449.062	−	449.062i	1.03709	−	1.03709i	0.999285	−	0.0378095i	$-0.0120380\pi$
$434$		−	144.006i		−	0.331810i
$435$	137.478	+	38.4246i	0.316042	+	0.0883323i
$436$	334.903			0.768126
$437$	36.1235	+	36.1235i	0.0826625	+	0.0826625i
$438$	−42.7967	+	42.7967i	−0.0977093	+	0.0977093i
$439$		−	522.143i		−	1.18939i	−0.803951	−	0.594695i	$-0.797273\pi$
$439$		−	522.143i		−	1.18939i	0.803951	−	0.594695i	$-0.202727\pi$
$440$	65.0637	−	232.790i	0.147872	−	0.529068i
$441$	−77.3754			−0.175454
$442$	23.4441	+	23.4441i	0.0530410	+	0.0530410i
$443$	−170.957	+	170.957i	−0.385907	+	0.385907i	−0.873225	−	0.487318i	$-0.837975\pi$
$443$	−170.957	+	170.957i	−0.385907	+	0.385907i	0.487318	+	0.873225i	$0.337975\pi$
$444$		−	2.88896i		−	0.00650667i
$445$	109.936	+	195.228i	0.247048	+	0.438716i
$446$	455.468			1.02123
$447$	−152.526	−	152.526i	−0.341221	−	0.341221i
$448$	−27.2518	+	27.2518i	−0.0608300	+	0.0608300i
$449$		−	129.721i		−	0.288912i	−0.989511	−	0.144456i	$-0.953857\pi$
$449$		−	129.721i		−	0.288912i	0.989511	−	0.144456i	$-0.0461432\pi$
$450$	25.2448	+	103.018i	0.0560997	+	0.228929i
$451$	−764.993			−1.69622
$452$	−116.796	−	116.796i	−0.258397	−	0.258397i
$453$	−122.793	+	122.793i	−0.271066	+	0.271066i
$454$			127.231i			0.280245i
$455$	282.571	−	159.121i	0.621036	−	0.349715i
$456$	52.1851			0.114441
$457$	487.821	+	487.821i	1.06744	+	1.06744i	0.997555	+	0.0698870i	$0.0222639\pi$
$457$	487.821	+	487.821i	1.06744	+	1.06744i	0.0698870	+	0.997555i	$0.477736\pi$
$458$	−173.353	+	173.353i	−0.378500	+	0.378500i
$459$		−	9.04834i		−	0.0197132i
$460$	46.1882	+	12.9094i	0.100409	+	0.0280639i
$461$	10.8881			0.0236185			0.0118093	−	0.999930i	$-0.496241\pi$
$461$	10.8881			0.0236185			0.0118093	+	0.999930i	$0.496241\pi$
$462$	142.615	+	142.615i	0.308689	+	0.308689i
$463$	−400.834	+	400.834i	−0.865732	+	0.865732i	−0.991997	−	0.126265i	$-0.959701\pi$
$463$	−400.834	+	400.834i	−0.865732	+	0.865732i	0.126265	+	0.991997i	$0.459701\pi$
$464$		−	65.9321i		−	0.142095i
$465$	−49.2738	+	176.296i	−0.105965	+	0.379130i
$466$	−257.803			−0.553225
$467$	108.014	+	108.014i	0.231293	+	0.231293i	0.813232	−	0.581939i	$-0.197706\pi$
$467$	108.014	+	108.014i	0.231293	+	0.231293i	−0.581939	+	0.813232i	$0.697706\pi$
$468$	57.1193	−	57.1193i	0.122050	−	0.122050i
$469$		−	593.935i		−	1.26639i
$470$	289.684	+	514.431i	0.616350	+	1.09453i
$471$	−415.070			−0.881252
$472$	33.0032	+	33.0032i	0.0699220	+	0.0699220i
$473$	850.163	−	850.163i	1.79739	−	1.79739i
$474$		−	164.811i		−	0.347702i
$475$	−227.714	−	138.076i	−0.479399	−	0.290687i
$476$	−16.7779			−0.0352477
$477$	114.539	+	114.539i	0.240123	+	0.240123i
$478$	−198.218	+	198.218i	−0.414683	+	0.414683i
$479$		−	517.840i		−	1.08109i	−0.841316	−	0.540543i	$-0.818219\pi$
$479$		−	517.840i		−	1.08109i	0.841316	−	0.540543i	$-0.181781\pi$
$480$	42.6871	−	24.0378i	0.0889314	−	0.0500787i
$481$	11.2279			0.0233428
$482$	−134.329	−	134.329i	−0.278690	−	0.278690i
$483$	−28.2963	+	28.2963i	−0.0585846	+	0.0585846i
$484$			342.244i			0.707117i
$485$	−572.105	−	159.900i	−1.17960	−	0.329692i
$486$	−22.0454			−0.0453609
$487$	389.872	+	389.872i	0.800559	+	0.800559i	0.983183	−	0.182623i	$-0.0584589\pi$
$487$	389.872	+	389.872i	0.800559	+	0.800559i	−0.182623	+	0.983183i	$0.558459\pi$
$488$	170.786	−	170.786i	0.349970	−	0.349970i
$489$			307.042i			0.627897i
$490$	49.0917	−	175.644i	0.100187	−	0.358457i
$491$	559.841			1.14021			0.570103	−	0.821573i	$-0.306903\pi$
$491$	559.841			1.14021			0.570103	+	0.821573i	$0.306903\pi$
$492$	−109.635	−	109.635i	−0.222836	−	0.222836i
$493$	20.2959	−	20.2959i	0.0411682	−	0.0411682i
$494$			202.816i			0.410559i
$495$	−125.795	−	223.390i	−0.254131	−	0.451293i
$496$	84.5481			0.170460
$497$	61.6201	+	61.6201i	0.123984	+	0.123984i
$498$	20.6052	−	20.6052i	0.0413758	−	0.0413758i
$499$			528.700i			1.05952i	0.848148	+	0.529760i	$0.177718\pi$
$499$			528.700i			1.05952i	−0.848148	+	0.529760i	$0.822282\pi$
$500$	−249.870	−	8.05443i	−0.499740	−	0.0161089i
$501$	−364.584			−0.727713
$502$	85.1879	+	85.1879i	0.169697	+	0.169697i
$503$	424.981	−	424.981i	0.844892	−	0.844892i	−0.144599	−	0.989490i	$-0.546189\pi$
$503$	424.981	−	424.981i	0.844892	−	0.844892i	0.989490	+	0.144599i	$0.0461891\pi$
$504$			40.8778i			0.0811067i
$505$	−480.399	+	270.521i	−0.951285	+	0.535684i
$506$	−115.921			−0.229092
$507$	15.0108	+	15.0108i	0.0296071	+	0.0296071i
$508$	−77.4676	+	77.4676i	−0.152495	+	0.152495i
$509$		−	273.415i		−	0.537161i	−0.963257	−	0.268580i	$-0.913445\pi$
$509$		−	273.415i		−	0.537161i	0.963257	−	0.268580i	$-0.0865545\pi$
$510$	20.5400	+	5.74082i	0.0402744	+	0.0112565i
$511$	119.034			0.232943
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	39.1388	−	39.1388i	0.0762940	−	0.0762940i
$514$			178.347i			0.346979i
$515$	−196.739	+	703.909i	−0.382018	+	1.36681i
$516$	243.683			0.472254
$517$	−1009.06	−	1009.06i	−1.95177	−	1.95177i
$518$	−4.01765	+	4.01765i	−0.00775607	+	0.00775607i
$519$			219.023i			0.422009i
$520$	93.4223	+	165.902i	0.179658	+	0.319043i
$521$	−17.9068			−0.0343701			−0.0171850	−	0.999852i	$-0.505470\pi$
$521$	−17.9068			−0.0343701			−0.0171850	+	0.999852i	$0.505470\pi$
$522$	−49.4491	−	49.4491i	−0.0947300	−	0.0947300i
$523$	−709.418	+	709.418i	−1.35644	+	1.35644i	−0.478176	+	0.878264i	$0.658702\pi$
$523$	−709.418	+	709.418i	−1.35644	+	1.35644i	−0.878264	+	0.478176i	$0.841298\pi$
$524$			107.826i			0.205776i
$525$	108.158	−	178.374i	0.206016	−	0.339759i
$526$	−246.417			−0.468473
$527$	26.0265	+	26.0265i	0.0493862	+	0.0493862i
$528$	−83.7313	+	83.7313i	−0.158582	+	0.158582i
$529$		−	23.0000i		−	0.0434783i
$530$	−332.676	+	187.335i	−0.627691	+	0.353463i
$531$	49.5048			0.0932294
$532$	−72.5733	−	72.5733i	−0.136416	−	0.136416i
$533$	426.095	−	426.095i	0.799428	−	0.799428i
$534$		−	109.764i		−	0.205550i
$535$	266.699	+	74.5411i	0.498503	+	0.139329i
$536$	348.709			0.650577
$537$	−100.922	−	100.922i	−0.187937	−	0.187937i
$538$	−159.070	+	159.070i	−0.295670	+	0.295670i
$539$			440.823i			0.817853i
$540$	13.9870	−	50.0436i	0.0259018	−	0.0926734i
$541$	−755.019			−1.39560			−0.697799	−	0.716293i	$-0.745837\pi$
$541$	−755.019			−1.39560			−0.697799	+	0.716293i	$0.745837\pi$
$542$	−262.498	−	262.498i	−0.484313	−	0.484313i
$543$	423.238	−	423.238i	0.779444	−	0.779444i
$544$		−	9.85059i		−	0.0181077i
$545$	410.816	+	729.540i	0.753791	+	1.33861i
$546$	−158.870			−0.290971
$547$	−90.7385	−	90.7385i	−0.165884	−	0.165884i	0.619283	−	0.785167i	$-0.287423\pi$
$547$	−90.7385	−	90.7385i	−0.165884	−	0.165884i	−0.785167	+	0.619283i	$0.787423\pi$
$548$	154.964	−	154.964i	0.282780	−	0.282780i
$549$		−	256.178i		−	0.466627i
$550$	586.913	−	143.825i	1.06712	−	0.261500i
$551$	175.581			0.318659
$552$	−16.6132	−	16.6132i	−0.0300965	−	0.0300965i
$553$	−229.201	+	229.201i	−0.414468	+	0.414468i
$554$		−	499.534i		−	0.901686i
$555$	6.29321	−	3.54381i	0.0113391	−	0.00638524i
$556$	79.0147			0.142113
$557$	305.442	+	305.442i	0.548370	+	0.548370i	0.925969	−	0.377599i	$-0.123250\pi$
$557$	305.442	+	305.442i	0.548370	+	0.548370i	−0.377599	+	0.925969i	$0.623250\pi$
$558$	63.4111	−	63.4111i	0.113640	−	0.113640i
$559$			947.069i			1.69422i
$560$	−92.7935	−	25.9353i	−0.165703	−	0.0463131i
$561$	−51.5502			−0.0918898
$562$	−312.983	−	312.983i	−0.556910	−	0.556910i
$563$	357.189	−	357.189i	0.634438	−	0.634438i	−0.314740	−	0.949178i	$-0.601917\pi$
$563$	357.189	−	357.189i	0.634438	−	0.634438i	0.949178	+	0.314740i	$0.101917\pi$
$564$		−	289.229i		−	0.512817i
$565$	111.153	−	397.693i	0.196732	−	0.703882i
$566$	609.577			1.07699
$567$	30.6583	+	30.6583i	0.0540711	+	0.0540711i
$568$	−36.1782	+	36.1782i	−0.0636940	+	0.0636940i
$569$			661.718i			1.16295i	0.813565	+	0.581474i	$0.197524\pi$
$569$			661.718i			1.16295i	−0.813565	+	0.581474i	$0.802476\pi$
$570$	64.0141	+	113.678i	0.112305	+	0.199435i
$571$	806.448			1.41234			0.706172	−	0.708041i	$-0.250421\pi$
$571$	806.448			1.41234			0.706172	+	0.708041i	$0.250421\pi$
$572$	−325.420	−	325.420i	−0.568916	−	0.568916i
$573$	322.257	−	322.257i	0.562404	−	0.562404i
$574$			304.938i			0.531250i
$575$	28.5365	+	116.450i	0.0496287	+	0.202522i
$576$	−24.0000			−0.0416667
$577$	308.495	+	308.495i	0.534654	+	0.534654i	0.921954	−	0.387300i	$-0.126592\pi$
$577$	308.495	+	308.495i	0.534654	+	0.534654i	−0.387300	+	0.921954i	$0.626592\pi$
$578$	−285.968	+	285.968i	−0.494754	+	0.494754i
$579$			345.071i			0.595977i
$580$	143.624	−	80.8772i	0.247628	−	0.139443i
$581$	−57.3108			−0.0986416
$582$	205.778	+	205.778i	0.353571	+	0.353571i
$583$	652.549	−	652.549i	1.11930	−	1.11930i
$584$			69.8867i			0.119669i
$585$	194.493	+	54.3599i	0.332467	+	0.0929230i
$586$	684.964			1.16888
$587$	266.598	+	266.598i	0.454170	+	0.454170i	0.896736	−	0.442566i	$-0.145932\pi$
$587$	266.598	+	266.598i	0.454170	+	0.454170i	−0.442566	+	0.896736i	$0.645932\pi$
$588$	−63.1767	+	63.1767i	−0.107443	+	0.107443i
$589$			225.157i			0.382269i
$590$	−31.4089	+	112.377i	−0.0532354	+	0.190470i
$591$	209.380			0.354281
$592$	−2.35883	−	2.35883i	−0.00398450	−	0.00398450i
$593$	−167.862	+	167.862i	−0.283073	+	0.283073i	−0.834333	−	0.551260i	$-0.814147\pi$
$593$	−167.862	+	167.862i	−0.283073	+	0.283073i	0.551260	+	0.834333i	$0.314147\pi$
$594$			125.597i			0.211443i
$595$	−20.5810	−	36.5484i	−0.0345899	−	0.0614259i
$596$	−249.074			−0.417909
$597$	−287.123	−	287.123i	−0.480942	−	0.480942i
$598$	64.5670	−	64.5670i	0.107972	−	0.107972i
$599$			356.744i			0.595566i	0.954634	+	0.297783i	$0.0962472\pi$
$599$			356.744i			0.595566i	−0.954634	+	0.297783i	$0.903753\pi$
$600$	104.726	+	63.5015i	0.174544	+	0.105836i
$601$	−18.7334			−0.0311704			−0.0155852	−	0.999879i	$-0.504961\pi$
$601$	−18.7334			−0.0311704			−0.0155852	+	0.999879i	$0.504961\pi$
$602$	−338.888	−	338.888i	−0.562936	−	0.562936i
$603$	261.532	−	261.532i	0.433718	−	0.433718i
$604$			200.520i			0.331986i
$605$	−745.533	+	419.822i	−1.23229	+	0.693921i
$606$	270.095			0.445702
$607$	325.300	+	325.300i	0.535914	+	0.535914i	0.922326	−	0.386412i	$-0.126286\pi$
$607$	325.300	+	325.300i	0.535914	+	0.535914i	−0.386412	+	0.922326i	$0.626286\pi$
$608$	42.6090	−	42.6090i	0.0700805	−	0.0700805i
$609$			137.537i			0.225840i
$610$	581.531	+	162.535i	0.953330	+	0.266451i
$611$	1124.08			1.83974
$612$	−7.38794	−	7.38794i	−0.0120718	−	0.0120718i
$613$	−572.991	+	572.991i	−0.934733	+	0.934733i	−0.997997	−	0.0632636i	$-0.979849\pi$
$613$	−572.991	+	572.991i	−0.934733	+	0.934733i	0.0632636	+	0.997997i	$0.479849\pi$
$614$		−	485.079i		−	0.790030i
$615$	104.339	−	373.313i	0.169657	−	0.607013i
$616$	232.889			0.378066
$617$	−136.873	−	136.873i	−0.221836	−	0.221836i	0.587435	−	0.809271i	$-0.300138\pi$
$617$	−136.873	−	136.873i	−0.221836	−	0.221836i	−0.809271	+	0.587435i	$0.800138\pi$
$618$	253.186	−	253.186i	0.409686	−	0.409686i
$619$			1159.59i			1.87333i	0.350221	+	0.936667i	$0.386106\pi$
$619$			1159.59i			1.87333i	−0.350221	+	0.936667i	$0.613894\pi$
$620$	103.713	+	184.177i	0.167279	+	0.297059i
$621$	−24.9199			−0.0401286
$622$	486.480	+	486.480i	0.782122	+	0.782122i
$623$	−152.647	+	152.647i	−0.245019	+	0.245019i
$624$		−	93.2754i		−	0.149480i
$625$	−288.964	−	554.189i	−0.462342	−	0.886702i
$626$	−116.406			−0.185953
$627$	−222.981	−	222.981i	−0.355632	−	0.355632i
$628$	−338.903	+	338.903i	−0.539655	+	0.539655i
$629$		−	1.45224i		−	0.00230881i
$630$	−89.0467	+	50.1436i	−0.141344	+	0.0795931i
$631$	−625.005			−0.990500			−0.495250	−	0.868751i	$-0.664924\pi$
$631$	−625.005			−0.990500			−0.495250	+	0.868751i	$0.664924\pi$
$632$	−134.568	−	134.568i	−0.212923	−	0.212923i
$633$	178.774	−	178.774i	0.282424	−	0.282424i
$634$		−	663.930i		−	1.04721i
$635$	−263.780	−	73.7252i	−0.415402	−	0.116103i
$636$	187.041			0.294089
$637$	−245.535	−	245.535i	−0.385455	−	0.385455i
$638$	−281.721	+	281.721i	−0.441569	+	0.441569i
$639$			54.2673i			0.0849253i
$640$	15.2271	−	54.4806i	0.0237923	−	0.0851259i
$641$	−73.3454			−0.114423			−0.0572117	−	0.998362i	$-0.518221\pi$
$641$	−73.3454			−0.114423			−0.0572117	+	0.998362i	$0.518221\pi$
$642$	−95.9280	−	95.9280i	−0.149421	−	0.149421i
$643$	−268.941	+	268.941i	−0.418260	+	0.418260i	−0.884604	−	0.466343i	$-0.845571\pi$
$643$	−268.941	+	268.941i	−0.418260	+	0.418260i	0.466343	+	0.884604i	$0.345571\pi$
$644$			46.2077i			0.0717511i
$645$	298.920	+	530.831i	0.463441	+	0.822994i
$646$	26.2327			0.0406079
$647$	−529.742	−	529.742i	−0.818767	−	0.818767i	0.167162	−	0.985929i	$-0.446540\pi$
$647$	−529.742	−	529.742i	−0.818767	−	0.818767i	−0.985929	+	0.167162i	$0.946540\pi$
$648$	−18.0000	+	18.0000i	−0.0277778	+	0.0277778i
$649$		−	282.039i		−	0.434574i
$650$	−246.797	+	407.015i	−0.379687	+	0.626178i
$651$	−176.370			−0.270922
$652$	250.699	+	250.699i	0.384507	+	0.384507i
$653$	−541.919	+	541.919i	−0.829891	+	0.829891i	−0.987501	−	0.157610i	$-0.949621\pi$
$653$	−541.919	+	541.919i	−0.829891	+	0.829891i	0.157610	+	0.987501i	$0.449621\pi$
$654$		−	410.170i		−	0.627172i
$655$	−234.885	+	132.268i	−0.358604	+	0.201936i
$656$	−179.034			−0.272917
$657$	52.4150	+	52.4150i	0.0797793	+	0.0797793i
$658$	−402.228	+	402.228i	−0.611288	+	0.611288i
$659$			631.568i			0.958374i	0.877713	+	0.479187i	$0.159068\pi$
$659$			631.568i			0.958374i	−0.877713	+	0.479187i	$0.840932\pi$
$660$	−285.108	−	79.6864i	−0.431982	−	0.120737i
$661$	−556.971			−0.842618			−0.421309	−	0.906917i	$-0.638429\pi$
$661$	−556.971			−0.842618			−0.421309	+	0.906917i	$0.638429\pi$
$662$	−57.4084	−	57.4084i	−0.0867196	−	0.0867196i
$663$	28.7130	−	28.7130i	0.0433078	−	0.0433078i
$664$		−	33.6481i		−	0.0506748i
$665$	69.0674	−	247.115i	0.103861	−	0.371601i
$666$	−3.53824			−0.00531267
$667$	−55.8967	−	55.8967i	−0.0838031	−	0.0838031i
$668$	−297.682	+	297.682i	−0.445631	+	0.445631i
$669$		−	557.832i		−	0.833830i
$670$	427.752	+	759.616i	0.638436	+	1.13376i
$671$	−1459.50			−2.17511
$672$	33.3765	+	33.3765i	0.0496675	+	0.0496675i
$673$	−52.4456	+	52.4456i	−0.0779280	+	0.0779280i	−0.744996	−	0.667068i	$-0.767549\pi$
$673$	−52.4456	+	52.4456i	−0.0779280	+	0.0779280i	0.667068	+	0.744996i	$0.267549\pi$
$674$		−	35.1361i		−	0.0521307i
$675$	126.171	−	30.9185i	0.186920	−	0.0458052i
$676$	24.5125			0.0362611
$677$	−82.3557	−	82.3557i	−0.121648	−	0.121648i	0.643662	−	0.765310i	$-0.277414\pi$
$677$	−82.3557	−	82.3557i	−0.121648	−	0.121648i	−0.765310	+	0.643662i	$0.777414\pi$
$678$	−143.045	+	143.045i	−0.210980	+	0.210980i
$679$		−	572.347i		−	0.842926i
$680$	21.4582	−	12.0835i	0.0315561	−	0.0177698i
$681$	155.826			0.228819
$682$	−361.265	−	361.265i	−0.529714	−	0.529714i
$683$	532.493	−	532.493i	0.779639	−	0.779639i	−0.200131	−	0.979769i	$-0.564137\pi$
$683$	532.493	−	532.493i	0.779639	−	0.779639i	0.979769	+	0.200131i	$0.0641367\pi$
$684$		−	63.9134i		−	0.0934407i
$685$	527.657	+	147.478i	0.770302	+	0.215296i
$686$	509.553			0.742789
$687$	212.313	+	212.313i	0.309044	+	0.309044i
$688$	198.967	−	198.967i	0.289196	−	0.289196i
$689$			726.930i			1.05505i
$690$	15.8107	−	56.5687i	0.0229140	−	0.0819837i
$691$	−1042.26			−1.50834			−0.754171	−	0.656678i	$-0.771961\pi$
$691$	−1042.26			−1.50834			−0.754171	+	0.656678i	$0.771961\pi$
$692$	178.831	+	178.831i	0.258427	+	0.258427i
$693$	174.666	−	174.666i	0.252044	−	0.252044i
$694$		−	143.092i		−	0.206184i
$695$	96.9252	+	172.123i	0.139461	+	0.247659i
$696$	−80.7500			−0.116020
$697$	−55.1121	−	55.1121i	−0.0790705	−	0.0790705i
$698$	21.0922	−	21.0922i	0.0302180	−	0.0302180i
$699$			315.743i			0.451707i
$700$	−57.3307	−	233.952i	−0.0819010	−	0.334218i
$701$	910.607			1.29901			0.649506	−	0.760357i	$-0.274976\pi$
$701$	910.607			1.29901			0.649506	+	0.760357i	$0.274976\pi$
$702$	−69.9565	−	69.9565i	−0.0996532	−	0.0996532i
$703$	6.28169	−	6.28169i	0.00893555	−	0.00893555i
$704$			136.733i			0.194223i
$705$	630.046	−	354.789i	0.893683	−	0.503247i
$706$	−535.456			−0.758436
$707$	−375.619	−	375.619i	−0.531285	−	0.531285i
$708$	40.4205	−	40.4205i	0.0570911	−	0.0570911i
$709$		−	1061.58i		−	1.49729i	−0.662970	−	0.748646i	$-0.730704\pi$
$709$		−	1061.58i		−	1.49729i	0.662970	−	0.748646i	$-0.269296\pi$
$710$	−123.188	−	34.4305i	−0.173504	−	0.0484936i
$711$	−201.851			−0.283898
$712$	−89.6216	−	89.6216i	−0.125873	−	0.125873i
$713$	71.6791	−	71.6791i	0.100532	−	0.100532i
$714$			20.5487i			0.0287796i
$715$	309.699	−	1108.07i	0.433146	−	1.54974i
$716$	−164.805			−0.230174
$717$	242.767	+	242.767i	0.338587	+	0.338587i
$718$	−184.468	+	184.468i	−0.256919	+	0.256919i
$719$		−	126.651i		−	0.176149i	−0.996114	−	0.0880745i	$-0.971929\pi$
$719$		−	126.651i		−	0.176149i	0.996114	−	0.0880745i	$-0.0280714\pi$
$720$	−29.4402	−	52.2808i	−0.0408891	−	0.0726122i
$721$	−704.207			−0.976708
$722$	−247.530	−	247.530i	−0.342839	−	0.342839i
$723$	−164.518	+	164.518i	−0.227550	+	0.227550i
$724$		−	691.145i		−	0.954620i
$725$	352.360	+	213.656i	0.486014	+	0.294698i
$726$	419.162			0.577358
$727$	−629.310	−	629.310i	−0.865626	−	0.865626i	0.126358	−	0.991985i	$-0.459671\pi$
$727$	−629.310	−	629.310i	−0.865626	−	0.865626i	−0.991985	+	0.126358i	$0.959671\pi$
$728$	−129.717	+	129.717i	−0.178183	+	0.178183i
$729$			27.0000i			0.0370370i
$730$	−152.239	+	85.7281i	−0.208546	+	0.117436i
$731$	122.496			0.167573
$732$	−209.169	−	209.169i	−0.285750	−	0.285750i
$733$	−618.111	+	618.111i	−0.843262	+	0.843262i	−0.989282	−	0.146020i	$-0.953354\pi$
$733$	−618.111	+	618.111i	−0.843262	+	0.843262i	0.146020	+	0.989282i	$0.453354\pi$
$734$			740.412i			1.00874i
$735$	−215.119	−	60.1248i	−0.292679	−	0.0818024i
$736$	−27.1293			−0.0368605
$737$	−1490.00	−	1490.00i	−2.02171	−	2.02171i
$738$	−134.275	+	134.275i	−0.181945	+	0.181945i
$739$		−	736.343i		−	0.996405i	−0.867061	−	0.498202i	$-0.833994\pi$
$739$		−	736.343i		−	0.996405i	0.867061	−	0.498202i	$-0.166006\pi$
$740$	2.24487	−	8.03189i	0.00303361	−	0.0108539i
$741$	248.398			0.335220
$742$	−260.116	−	260.116i	−0.350560	−	0.350560i
$743$	−276.121	+	276.121i	−0.371630	+	0.371630i	−0.868071	−	0.496441i	$-0.834640\pi$
$743$	−276.121	+	276.121i	−0.371630	+	0.371630i	0.496441	+	0.868071i	$0.334640\pi$
$744$		−	103.550i		−	0.139180i
$745$	−305.532	−	542.573i	−0.410110	−	0.728286i
$746$	−958.339			−1.28464
$747$	−25.2361	−	25.2361i	−0.0337832	−	0.0337832i
$748$	−42.0905	+	42.0905i	−0.0562708	+	0.0562708i
$749$			266.812i			0.356224i
$750$	−9.86462	+	306.027i	−0.0131528	+	0.408036i
$751$	189.510			0.252343			0.126172	−	0.992008i	$-0.459731\pi$
$751$	189.510			0.252343			0.126172	+	0.992008i	$0.459731\pi$
$752$	−236.154	−	236.154i	−0.314035	−	0.314035i
$753$	104.333	−	104.333i	0.138557	−	0.138557i
$754$		−	313.833i		−	0.416224i
$755$	−436.805	+	245.972i	−0.578550	+	0.325791i
$756$	50.0648			0.0662233
$757$	12.7982	+	12.7982i	0.0169065	+	0.0169065i	0.715509	−	0.698603i	$-0.246195\pi$
$757$	12.7982	+	12.7982i	0.0169065	+	0.0169065i	−0.698603	+	0.715509i	$0.746195\pi$
$758$	415.235	−	415.235i	0.547804	−	0.547804i
$759$			141.973i			0.187053i
$760$	145.085	+	40.5506i	0.190901	+	0.0533560i
$761$	−565.864			−0.743579			−0.371790	−	0.928317i	$-0.621256\pi$
$761$	−565.864			−0.743579			−0.371790	+	0.928317i	$0.621256\pi$
$762$	94.8780	+	94.8780i	0.124512	+	0.124512i
$763$	−570.420	+	570.420i	−0.747601	+	0.747601i
$764$		−	526.244i		−	0.688801i
$765$	7.03104	−	25.1562i	0.00919090	−	0.0328839i
$766$	−891.537			−1.16389
$767$	157.093	+	157.093i	0.204815	+	0.204815i
$768$	−19.5959	+	19.5959i	−0.0255155	+	0.0255155i
$769$			973.731i			1.26623i	0.774058	+	0.633115i	$0.218224\pi$
$769$			973.731i			1.26623i	−0.774058	+	0.633115i	$0.781776\pi$
$770$	285.678	+	507.316i	0.371011	+	0.658852i
$771$	218.430			0.283307
$772$	281.749	+	281.749i	0.364960	+	0.364960i
$773$	554.230	−	554.230i	0.716986	−	0.716986i	−0.251001	−	0.967987i	$-0.580760\pi$
$773$	554.230	−	554.230i	0.716986	−	0.716986i	0.967987	+	0.251001i	$0.0807596\pi$
$774$		−	298.450i		−	0.385594i
$775$	−273.982	+	451.849i	−0.353525	+	0.583031i
$776$	336.034			0.433034
$777$	4.92059	+	4.92059i	0.00633281	+	0.00633281i
$778$	274.994	−	274.994i	0.353462	−	0.353462i
$779$		−	476.778i		−	0.612038i
$780$	203.188	−	114.418i	0.260497	−	0.146690i
$781$	309.171			0.395866
$782$	−8.35124	−	8.35124i	−0.0106793	−	0.0106793i
$783$	−60.5625	+	60.5625i	−0.0773468	+	0.0773468i
$784$			103.167i			0.131591i
$785$	−1153.98	−	322.531i	−1.47004	−	0.410868i
$786$	132.060			0.168015
$787$	918.531	+	918.531i	1.16713	+	1.16713i	0.982880	+	0.184249i	$0.0589854\pi$
$787$	918.531	+	918.531i	1.16713	+	1.16713i	0.184249	+	0.982880i	$0.441015\pi$
$788$	170.958	−	170.958i	0.216952	−	0.216952i
$789$			301.798i			0.382506i
$790$	128.067	−	458.208i	0.162110	−	0.580010i
$791$	397.862			0.502986
$792$	102.550	+	102.550i	0.129482	+	0.129482i
$793$	812.929	−	812.929i	1.02513	−	1.02513i
$794$		−	47.2368i		−	0.0594921i
$795$	229.438	+	407.443i	0.288601	+	0.512507i
$796$	−468.869			−0.589032
$797$	268.841	+	268.841i	0.337316	+	0.337316i	0.855356	−	0.518040i	$-0.173338\pi$
$797$	268.841	+	268.841i	0.337316	+	0.337316i	−0.518040	+	0.855356i	$0.673338\pi$
$798$	−88.8837	+	88.8837i	−0.111383	+	0.111383i
$799$		−	145.391i		−	0.181967i
$800$	137.357	−	33.6598i	0.171697	−	0.0420747i
$801$	−134.432			−0.167831
$802$	−673.867	−	673.867i	−0.840233	−	0.840233i
$803$	298.618	−	298.618i	0.371879	−	0.371879i
$804$		−	427.080i		−	0.531194i
$805$	−100.657	+	56.6818i	−0.125040	+	0.0704122i
$806$	402.444			0.499310
$807$	194.821	+	194.821i	0.241414	+	0.241414i
$808$	220.532	−	220.532i	0.272936	−	0.272936i
$809$			533.951i			0.660013i	0.943979	+	0.330007i	$0.107051\pi$
$809$			533.951i			0.660013i	−0.943979	+	0.330007i	$0.892949\pi$
$810$	−61.2907	−	17.1304i	−0.0756675	−	0.0211487i
$811$	−915.450			−1.12879			−0.564396	−	0.825504i	$-0.690891\pi$
$811$	−915.450			−1.12879			−0.564396	+	0.825504i	$0.690891\pi$
$812$	112.298	+	112.298i	0.138298	+	0.138298i
$813$	−321.493	+	321.493i	−0.395440	+	0.395440i
$814$			20.1580i			0.0247642i
$815$	−238.588	+	853.638i	−0.292746	+	1.04741i
$816$	−12.0645			−0.0147849
$817$	529.860	+	529.860i	0.648543	+	0.648543i
$818$	37.4601	−	37.4601i	0.0457947	−	0.0457947i
$819$			194.576i			0.237577i
$820$	−219.616	−	390.001i	−0.267824	−	0.475611i
$821$	288.533			0.351441			0.175720	−	0.984440i	$-0.443775\pi$
$821$	288.533			0.351441			0.175720	+	0.984440i	$0.443775\pi$
$822$	−189.791	−	189.791i	−0.230889	−	0.230889i
$823$	−65.0196	+	65.0196i	−0.0790031	+	0.0790031i	−0.745504	−	0.666501i	$-0.767791\pi$
$823$	−65.0196	+	65.0196i	−0.0790031	+	0.0790031i	0.666501	+	0.745504i	$0.267791\pi$
$824$		−	413.451i		−	0.501761i
$825$	−176.149	−	718.819i	−0.213514	−	0.871296i
$826$	−112.425			−0.136107
$827$	−5.39396	−	5.39396i	−0.00652232	−	0.00652232i	0.703838	−	0.710360i	$-0.251468\pi$
$827$	−5.39396	−	5.39396i	−0.00652232	−	0.00652232i	−0.710360	+	0.703838i	$0.751468\pi$
$828$	−20.3470	+	20.3470i	−0.0245737	+	0.0245737i
$829$			75.7343i			0.0913563i	0.998956	+	0.0456781i	$0.0145449\pi$
$829$			75.7343i			0.0913563i	−0.998956	+	0.0456781i	$0.985455\pi$
$830$	73.2978	−	41.2752i	0.0883106	−	0.0497292i
$831$	−611.802			−0.736224
$832$	−76.1590	−	76.1590i	−0.0915373	−	0.0915373i
$833$	−31.7580	+	31.7580i	−0.0381249	+	0.0381249i
$834$		−	96.7728i		−	0.116035i
$835$	−1013.62	−	283.301i	−1.21391	−	0.339283i
$836$	−364.127			−0.435559
$837$	−77.6624	−	77.6624i	−0.0927866	−	0.0927866i
$838$	−251.336	+	251.336i	−0.299923	+	0.299923i
$839$			121.963i			0.145367i	0.997355	+	0.0726837i	$0.0231563\pi$
$839$			121.963i			0.145367i	−0.997355	+	0.0726837i	$0.976844\pi$
$840$	−31.7642	+	113.648i	−0.0378145	+	0.135296i
$841$	569.310			0.676944
$842$	−555.687	−	555.687i	−0.659961	−	0.659961i
$843$	−383.325	+	383.325i	−0.454715	+	0.454715i
$844$		−	291.937i		−	0.345897i
$845$	30.0688	+	53.3971i	0.0355844	+	0.0631919i
$846$	−354.232			−0.418714
$847$	−582.924	−	582.924i	−0.688222	−	0.688222i
$848$	152.718	−	152.718i	0.180092	−	0.180092i
$849$		−	746.576i		−	0.879359i
$850$	52.6443	+	31.9213i	0.0619345	+	0.0375544i
$851$	−3.99958			−0.00469986
$852$	44.3090	+	44.3090i	0.0520059	+	0.0520059i
$853$	−744.108	+	744.108i	−0.872343	+	0.872343i	−0.992727	−	0.120385i	$-0.961587\pi$
$853$	−744.108	+	744.108i	−0.872343	+	0.872343i	0.120385	+	0.992727i	$0.461587\pi$
$854$			581.777i			0.681238i
$855$	139.227	−	78.4009i	0.162838	−	0.0916969i
$856$	−156.650			−0.183002
$857$	−426.217	−	426.217i	−0.497336	−	0.497336i	0.413272	−	0.910608i	$-0.364386\pi$
$857$	−426.217	−	426.217i	−0.497336	−	0.497336i	−0.910608	+	0.413272i	$0.864386\pi$
$858$	−398.556	+	398.556i	−0.464518	+	0.464518i
$859$			1528.65i			1.77957i	0.456380	+	0.889785i	$0.349146\pi$
$859$			1528.65i			1.77957i	−0.456380	+	0.889785i	$0.650854\pi$
$860$	677.489	+	189.355i	0.787778	+	0.220180i
$861$	373.471			0.433764
$862$	61.4001	+	61.4001i	0.0712298	+	0.0712298i
$863$	1016.16	−	1016.16i	1.17747	−	1.17747i	0.197089	−	0.980386i	$-0.436851\pi$
$863$	1016.16	−	1016.16i	1.17747	−	1.17747i	0.980386	−	0.197089i	$-0.0631489\pi$
$864$			29.3939i			0.0340207i
$865$	−170.192	+	608.928i	−0.196754	+	0.703963i
$866$	−898.124			−1.03709
$867$	350.237	+	350.237i	0.403965	+	0.403965i
$868$	−144.006	+	144.006i	−0.165905	+	0.165905i
$869$			1149.99i			1.32334i
$870$	−99.0539	−	175.903i	−0.113855	−	0.202187i
$871$	1659.84			1.90567
$872$	−334.903	−	334.903i	−0.384063	−	0.384063i
$873$	252.026	−	252.026i	0.288689	−	0.288689i
$874$		−	72.2470i		−	0.0826625i
$875$	439.308	−	411.870i	0.502066	−	0.470709i
$876$	85.5933			0.0977093
$877$	266.773	+	266.773i	0.304188	+	0.304188i	0.842650	−	0.538462i	$-0.180995\pi$
$877$	266.773	+	266.773i	0.304188	+	0.304188i	−0.538462	+	0.842650i	$0.680995\pi$
$878$	−522.143	+	522.143i	−0.594695	+	0.594695i
$879$		−	838.906i		−	0.954387i
$880$	−297.854	+	167.726i	−0.338470	+	0.190598i
$881$	−1409.54			−1.59993			−0.799963	−	0.600049i	$-0.795148\pi$
$881$	−1409.54			−1.59993			−0.799963	+	0.600049i	$0.795148\pi$
$882$	77.3754	+	77.3754i	0.0877272	+	0.0877272i
$883$	647.075	−	647.075i	0.732815	−	0.732815i	−0.238362	−	0.971176i	$-0.576610\pi$
$883$	647.075	−	647.075i	0.732815	−	0.732815i	0.971176	+	0.238362i	$0.0766104\pi$
$884$		−	46.8882i		−	0.0530410i
$885$	137.633	+	38.4679i	0.155518	+	0.0434665i
$886$	341.913			0.385907
$887$	−415.654	−	415.654i	−0.468606	−	0.468606i	0.432857	−	0.901463i	$-0.357506\pi$
$887$	−415.654	−	415.654i	−0.468606	−	0.468606i	−0.901463	+	0.432857i	$0.857506\pi$
$888$	−2.88896	+	2.88896i	−0.00325333	+	0.00325333i
$889$		−	263.892i		−	0.296841i
$890$	85.2921	−	305.165i	0.0958338	−	0.342882i
$891$	153.824			0.172642
$892$	−455.468	−	455.468i	−0.510615	−	0.510615i
$893$	628.893	−	628.893i	0.704248	−	0.704248i
$894$			305.052i			0.341221i
$895$	−202.162	−	359.005i	−0.225879	−	0.401123i
$896$	54.5037			0.0608300
$897$	−79.0781	−	79.0781i	−0.0881584	−	0.0881584i
$898$	−129.721	+	129.721i	−0.144456	+	0.144456i
$899$		−	348.402i		−	0.387544i
$900$	77.7731	−	128.263i	0.0864146	−	0.142514i
$901$	94.0228			0.104354
$902$	764.993	+	764.993i	0.848108	+	0.848108i
$903$	−415.051	+	415.051i	−0.459636	+	0.459636i
$904$			233.591i			0.258397i
$905$	1505.57	−	847.809i	1.66361	−	0.936805i
$906$	245.585			0.271066
$907$	104.950	+	104.950i	0.115711	+	0.115711i	0.762591	−	0.646881i	$-0.223927\pi$
$907$	104.950	+	104.950i	0.115711	+	0.115711i	−0.646881	+	0.762591i	$0.723927\pi$
$908$	127.231	−	127.231i	0.140122	−	0.140122i
$909$		−	330.798i		−	0.363914i
$910$	−441.692	−	123.451i	−0.485375	−	0.135660i
$911$	−487.776			−0.535430			−0.267715	−	0.963498i	$-0.586268\pi$
$911$	−487.776			−0.535430			−0.267715	+	0.963498i	$0.586268\pi$
$912$	−52.1851	−	52.1851i	−0.0572205	−	0.0572205i
$913$	−143.775	+	143.775i	−0.157475	+	0.157475i
$914$		−	975.642i		−	1.06744i
$915$	199.064	−	712.227i	0.217556	−	0.778390i
$916$	346.706			0.378500
$917$	−183.654	−	183.654i	−0.200277	−	0.200277i
$918$	−9.04834	+	9.04834i	−0.00985658	+	0.00985658i
$919$		−	1682.30i		−	1.83058i	−0.402795	−	0.915290i	$-0.631961\pi$
$919$		−	1682.30i		−	1.83058i	0.402795	−	0.915290i	$-0.368039\pi$
$920$	−33.2788	−	59.0976i	−0.0361726	−	0.0642365i
$921$	−594.097			−0.645057
$922$	−10.8881	−	10.8881i	−0.0118093	−	0.0118093i
$923$	−172.206	+	172.206i	−0.186572	+	0.186572i
$924$		−	285.229i		−	0.308689i
$925$	20.2501	−	4.96235i	0.0218920	−	0.00536470i
$926$	801.668			0.865732
$927$	−310.088	−	310.088i	−0.334508	−	0.334508i
$928$	−65.9321	+	65.9321i	−0.0710475	+	0.0710475i
$929$			1307.03i			1.40692i	0.710734	+	0.703461i	$0.248363\pi$
$929$			1307.03i			1.40692i	−0.710734	+	0.703461i	$0.751637\pi$
$930$	225.569	−	127.022i	0.242548	−	0.136583i
$931$	−274.740			−0.295102
$932$	257.803	+	257.803i	0.276613	+	0.276613i
$933$	595.814	−	595.814i	0.638600	−	0.638600i
$934$		−	216.028i		−	0.231293i
$935$	−143.320	−	40.0572i	−0.153283	−	0.0428419i
$936$	−114.239			−0.122050
$937$	753.154	+	753.154i	0.803792	+	0.803792i	0.983686	−	0.179894i	$-0.0575753\pi$
$937$	753.154	+	753.154i	0.803792	+	0.803792i	−0.179894	+	0.983686i	$0.557575\pi$
$938$	−593.935	+	593.935i	−0.633193	+	0.633193i
$939$			142.568i			0.151830i
$940$	224.746	−	804.115i	0.239092	−	0.855441i
$941$	1343.56			1.42780			0.713901	−	0.700247i	$-0.246927\pi$
$941$	1343.56			1.42780			0.713901	+	0.700247i	$0.246927\pi$
$942$	415.070	+	415.070i	0.440626	+	0.440626i
$943$	−151.783	+	151.783i	−0.160958	+	0.160958i
$944$		−	66.0064i		−	0.0699220i
$945$	61.4132	+	109.059i	0.0649875	+	0.115407i
$946$	−1700.33			−1.79739
$947$	523.662	+	523.662i	0.552970	+	0.552970i	0.927297	−	0.374327i	$-0.122126\pi$
$947$	523.662	+	523.662i	0.552970	+	0.552970i	−0.374327	+	0.927297i	$0.622126\pi$
$948$	−164.811	+	164.811i	−0.173851	+	0.173851i
$949$			332.656i			0.350534i
$950$	89.6380	+	365.791i	0.0943558	+	0.385043i
$951$	−813.145			−0.855042
$952$	16.7779	+	16.7779i	0.0176239	+	0.0176239i
$953$	367.314	−	367.314i	0.385430	−	0.385430i	−0.487624	−	0.873054i	$-0.662136\pi$
$953$	367.314	−	367.314i	0.385430	−	0.385430i	0.873054	+	0.487624i	$0.162136\pi$
$954$		−	229.077i		−	0.240123i
$955$	1146.35	−	645.529i	1.20037	−	0.675947i
$956$	396.437			0.414683
$957$	345.036	+	345.036i	0.360540	+	0.360540i
$958$	−517.840	+	517.840i	−0.540543	+	0.540543i
$959$			527.880i			0.550449i
$960$	−66.7248	−	18.6493i	−0.0695050	−	0.0194263i
$961$	−514.226			−0.535095
$962$	−11.2279	−	11.2279i	−0.0116714	−	0.0116714i
$963$	−117.487	+	117.487i	−0.122001	+	0.122001i
$964$			268.657i			0.278690i
$965$	−268.138	+	959.366i	−0.277863	+	0.994162i
$966$	56.5927			0.0585846
$967$	712.118	+	712.118i	0.736420	+	0.736420i	0.971883	−	0.235463i	$-0.0756608\pi$
$967$	712.118	+	712.118i	0.736420	+	0.736420i	−0.235463	+	0.971883i	$0.575661\pi$
$968$	342.244	−	342.244i	0.353558	−	0.353558i
$969$		−	32.1284i		−	0.0331562i
$970$	412.204	+	732.005i	0.424953	+	0.754644i
$971$	614.628			0.632984			0.316492	−	0.948595i	$-0.397495\pi$
$971$	614.628			0.632984			0.316492	+	0.948595i	$0.397495\pi$
$972$	22.0454	+	22.0454i	0.0226805	+	0.0226805i
$973$	−134.581	+	134.581i	−0.138315	+	0.138315i
$974$		−	779.745i		−	0.800559i
$975$	498.490	+	302.263i	0.511272	+	0.310014i
$976$	−341.571			−0.349970
$977$	−620.888	−	620.888i	−0.635505	−	0.635505i	0.313938	−	0.949443i	$-0.398351\pi$
$977$	−620.888	−	620.888i	−0.635505	−	0.635505i	−0.949443	+	0.313938i	$0.898351\pi$
$978$	307.042	−	307.042i	0.313949	−	0.313949i
$979$			765.887i			0.782316i
$980$	−224.736	+	126.552i	−0.229322	+	0.129135i
$981$	−502.354			−0.512084
$982$	−559.841	−	559.841i	−0.570103	−	0.570103i
$983$	522.578	−	522.578i	0.531615	−	0.531615i	−0.389438	−	0.921053i	$-0.627331\pi$
$983$	522.578	−	522.578i	0.531615	−	0.531615i	0.921053	+	0.389438i	$0.127331\pi$
$984$			219.271i			0.222836i
$985$	582.118	+	162.699i	0.590983	+	0.165177i
$986$	−40.5919			−0.0411682
$987$	492.626	+	492.626i	0.499115	+	0.499115i
$988$	202.816	−	202.816i	0.205279	−	0.205279i
$989$		−	337.364i		−	0.341116i
$990$	−97.5955	+	349.185i	−0.0985813	+	0.352712i
$991$	51.4856			0.0519532			0.0259766	−	0.999663i	$-0.491730\pi$
$991$	51.4856			0.0519532			0.0259766	+	0.999663i	$0.491730\pi$
$992$	−84.5481	−	84.5481i	−0.0852299	−	0.0852299i
$993$	−70.3106	+	70.3106i	−0.0708063	+	0.0708063i
$994$		−	123.240i		−	0.123984i
$995$	−575.149	−	1021.37i	−0.578039	−	1.02650i
$996$	−41.2103			−0.0413758
$997$	−342.034	−	342.034i	−0.343063	−	0.343063i	0.514455	−	0.857518i	$-0.327994\pi$
$997$	−342.034	−	342.034i	−0.343063	−	0.343063i	−0.857518	+	0.514455i	$0.827994\pi$
$998$	528.700	−	528.700i	0.529760	−	0.529760i
$999$			4.33344i			0.00433778i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.b.277.2	✓	48
5.3	odd	4	inner	690.3.k.b.553.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.b.277.2	✓	48	1.1	even	1	trivial
690.3.k.b.553.2	yes	48	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.35673 + 2.45335i) q^{5} +2.44949 q^{6} +(-3.40648 - 3.40648i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(-4.35673 + 2.45335i) q^{5} +2.44949 q^{6} +(-3.40648 - 3.40648i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(6.81008 + 1.90338i) q^{10} -17.0916 q^{11} +(-2.44949 - 2.44949i) q^{12} +(9.51988 - 9.51988i) q^{13} +6.81296i q^{14} +(2.33116 - 8.34061i) q^{15} -4.00000 q^{16} +(-1.23132 - 1.23132i) q^{17} +(-3.00000 + 3.00000i) q^{18} -10.6522i q^{19} +(-4.90669 - 8.71346i) q^{20} +8.34414 q^{21} +(17.0916 + 17.0916i) q^{22} +(-3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(12.9622 - 21.3771i) q^{25} -19.0398 q^{26} +(3.67423 + 3.67423i) q^{27} +(6.81296 - 6.81296i) q^{28} +16.4830i q^{29} +(-10.6718 + 6.00945i) q^{30} -21.1370 q^{31} +(4.00000 + 4.00000i) q^{32} +(20.9328 - 20.9328i) q^{33} +2.46265i q^{34} +(23.1984 + 6.48384i) q^{35} +6.00000 q^{36} +(0.589707 + 0.589707i) q^{37} +(-10.6522 + 10.6522i) q^{38} +23.3188i q^{39} +(-3.80677 + 13.6202i) q^{40} +44.7585 q^{41} +(-8.34414 - 8.34414i) q^{42} +(-49.7416 + 49.7416i) q^{43} -34.1832i q^{44} +(7.36004 + 13.0702i) q^{45} +6.78233 q^{46} +(59.0386 + 59.0386i) q^{47} +(4.89898 - 4.89898i) q^{48} -25.7918i q^{49} +(-34.3393 + 8.41495i) q^{50} +3.01611 q^{51} +(19.0398 + 19.0398i) q^{52} +(-38.1796 + 38.1796i) q^{53} -7.34847i q^{54} +(74.4634 - 41.9316i) q^{55} -13.6259 q^{56} +(13.0463 + 13.0463i) q^{57} +(16.4830 - 16.4830i) q^{58} +16.5016i q^{59} +(16.6812 + 4.66232i) q^{60} +85.3928 q^{61} +(21.1370 + 21.1370i) q^{62} +(-10.2194 + 10.2194i) q^{63} -8.00000i q^{64} +(-18.1200 + 64.8311i) q^{65} -41.8657 q^{66} +(87.1773 + 87.1773i) q^{67} +(2.46265 - 2.46265i) q^{68} -8.30662i q^{69} +(-16.7145 - 29.6822i) q^{70} -18.0891 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-17.4717 + 17.4717i) q^{73} -1.17941i q^{74} +(10.3062 + 42.0569i) q^{75} +21.3045 q^{76} +(58.2221 + 58.2221i) q^{77} +(23.3188 - 23.3188i) q^{78} -67.2838i q^{79} +(17.4269 - 9.81339i) q^{80} -9.00000 q^{81} +(-44.7585 - 44.7585i) q^{82} +(8.41202 - 8.41202i) q^{83} +16.6883i q^{84} +(8.38541 + 2.34368i) q^{85} +99.4833 q^{86} +(-20.1875 - 20.1875i) q^{87} +(-34.1832 + 34.1832i) q^{88} -44.8108i q^{89} +(5.71015 - 20.4302i) q^{90} -64.8586 q^{91} +(-6.78233 - 6.78233i) q^{92} +(25.8875 - 25.8875i) q^{93} -118.077i q^{94} +(26.1336 + 46.4089i) q^{95} -9.79796 q^{96} +(84.0085 + 84.0085i) q^{97} +(-25.7918 + 25.7918i) q^{98} +51.2748i 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