LMFDB - Embedded newform 690.3.k.a.553.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("690.277");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			553.15
Character	$\chi$	$=$	690.553
Dual form			690.3.k.a.277.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(2.64969 + 4.24018i) q^{5} +2.44949 q^{6} +(-5.13413 + 5.13413i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(2.64969 + 4.24018i) q^{5} +2.44949 q^{6} +(-5.13413 + 5.13413i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(6.88987 + 1.59048i) q^{10} -18.8487 q^{11} +(2.44949 - 2.44949i) q^{12} +(-4.85169 - 4.85169i) q^{13} +10.2683i q^{14} +(-1.94794 + 8.43834i) q^{15} -4.00000 q^{16} +(-8.28144 + 8.28144i) q^{17} +(3.00000 + 3.00000i) q^{18} +2.00840i q^{19} +(8.48036 - 5.29939i) q^{20} -12.5760 q^{21} +(-18.8487 + 18.8487i) q^{22} +(-3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(-10.9582 + 22.4704i) q^{25} -9.70339 q^{26} +(-3.67423 + 3.67423i) q^{27} +(10.2683 + 10.2683i) q^{28} -15.3053i q^{29} +(6.49040 + 10.3863i) q^{30} -18.0217 q^{31} +(-4.00000 + 4.00000i) q^{32} +(-23.0848 - 23.0848i) q^{33} +16.5629i q^{34} +(-35.3735 - 8.16576i) q^{35} +6.00000 q^{36} +(7.99013 - 7.99013i) q^{37} +(2.00840 + 2.00840i) q^{38} -11.8842i q^{39} +(3.18097 - 13.7797i) q^{40} -8.60556 q^{41} +(-12.5760 + 12.5760i) q^{42} +(-18.9595 - 18.9595i) q^{43} +37.6973i q^{44} +(-12.7205 + 7.94908i) q^{45} -6.78233 q^{46} +(21.2643 - 21.2643i) q^{47} +(-4.89898 - 4.89898i) q^{48} -3.71868i q^{49} +(11.5121 + 33.4286i) q^{50} -20.2853 q^{51} +(-9.70339 + 9.70339i) q^{52} +(30.6997 + 30.6997i) q^{53} +7.34847i q^{54} +(-49.9432 - 79.9217i) q^{55} +20.5365 q^{56} +(-2.45978 + 2.45978i) q^{57} +(-15.3053 - 15.3053i) q^{58} +37.0580i q^{59} +(16.8767 + 3.89587i) q^{60} +65.9013 q^{61} +(-18.0217 + 18.0217i) q^{62} +(-15.4024 - 15.4024i) q^{63} +8.00000i q^{64} +(7.71654 - 33.4276i) q^{65} -46.1696 q^{66} +(-70.4656 + 70.4656i) q^{67} +(16.5629 + 16.5629i) q^{68} -8.30662i q^{69} +(-43.5393 + 27.2078i) q^{70} -8.38441 q^{71} +(6.00000 - 6.00000i) q^{72} +(78.9935 + 78.9935i) q^{73} -15.9803i q^{74} +(-40.9415 + 14.0994i) q^{75} +4.01680 q^{76} +(96.7715 - 96.7715i) q^{77} +(-11.8842 - 11.8842i) q^{78} +103.875i q^{79} +(-10.5988 - 16.9607i) q^{80} -9.00000 q^{81} +(-8.60556 + 8.60556i) q^{82} +(37.7965 + 37.7965i) q^{83} +25.1520i q^{84} +(-57.0581 - 13.1715i) q^{85} -37.9191 q^{86} +(18.7451 - 18.7451i) q^{87} +(37.6973 + 37.6973i) q^{88} +140.211i q^{89} +(-4.77145 + 20.6696i) q^{90} +49.8185 q^{91} +(-6.78233 + 6.78233i) q^{92} +(-22.0720 - 22.0720i) q^{93} -42.5286i q^{94} +(-8.51597 + 5.32164i) q^{95} -9.79796 q^{96} +(105.406 - 105.406i) q^{97} +(-3.71868 - 3.71868i) q^{98} -56.5460i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) $ 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8	$ 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) $ 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8 - 16 * q^10 + 32 * q^11 + 16 * q^13 + 24 * q^15 - 160 * q^16 - 48 * q^17 + 120 * q^18 - 16 * q^20 - 96 * q^21 + 32 * q^22 + 32 * q^26 + 16 * q^28 + 24 * q^30 + 152 * q^31 - 160 * q^32 - 24 * q^33 + 48 * q^35 + 240 * q^36 + 216 * q^37 + 16 * q^38 - 168 * q^41 - 96 * q^42 - 48 * q^43 + 24 * q^45 - 232 * q^47 - 40 * q^50 + 32 * q^52 + 8 * q^53 - 272 * q^55 + 32 * q^56 - 136 * q^58 - 64 * q^61 + 152 * q^62 - 24 * q^63 + 416 * q^65 - 48 * q^66 - 32 * q^67 + 96 * q^68 + 88 * q^70 - 104 * q^71 + 240 * q^72 + 480 * q^73 - 216 * q^75 + 32 * q^76 + 280 * q^77 - 192 * q^78 + 32 * q^80 - 360 * q^81 - 168 * q^82 - 576 * q^83 - 208 * q^85 - 96 * q^86 + 24 * q^87 - 64 * q^88 + 144 * q^91 + 96 * q^93 + 168 * q^95 + 24 * q^97 + 176 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	2.64969	+	4.24018i	0.529939	+	0.848036i
$5$	2.64969	+	4.24018i	0.529939	+	0.848036i
$6$	2.44949			0.408248
$7$	−5.13413	+	5.13413i	−0.733448	+	0.733448i	−0.971301	−	0.237853i	$-0.923556\pi$
$7$	−5.13413	+	5.13413i	−0.733448	+	0.733448i	0.237853	+	0.971301i	$0.423556\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$			3.00000i			0.333333i
$10$	6.88987	+	1.59048i	0.688987	+	0.159048i
$11$	−18.8487			−1.71351			−0.856757	−	0.515720i	$-0.827524\pi$
$11$	−18.8487			−1.71351			−0.856757	+	0.515720i	$0.827524\pi$
$12$	2.44949	−	2.44949i	0.204124	−	0.204124i
$13$	−4.85169	−	4.85169i	−0.373207	−	0.373207i	0.495437	−	0.868644i	$-0.335008\pi$
$13$	−4.85169	−	4.85169i	−0.373207	−	0.373207i	−0.868644	+	0.495437i	$0.835008\pi$
$14$			10.2683i			0.733448i
$15$	−1.94794	+	8.43834i	−0.129862	+	0.562556i
$16$	−4.00000			−0.250000
$17$	−8.28144	+	8.28144i	−0.487144	+	0.487144i	−0.907404	−	0.420260i	$-0.861939\pi$
$17$	−8.28144	+	8.28144i	−0.487144	+	0.487144i	0.420260	+	0.907404i	$0.361939\pi$
$18$	3.00000	+	3.00000i	0.166667	+	0.166667i
$19$			2.00840i			0.105705i	0.998602	+	0.0528526i	$0.0168313\pi$
$19$			2.00840i			0.105705i	−0.998602	+	0.0528526i	$0.983169\pi$
$20$	8.48036	−	5.29939i	0.424018	−	0.264969i
$21$	−12.5760			−0.598858
$22$	−18.8487	+	18.8487i	−0.856757	+	0.856757i
$23$	−3.39116	−	3.39116i	−0.147442	−	0.147442i
$23$	−3.39116	−	3.39116i	−0.147442	−	0.147442i
$24$		−	4.89898i		−	0.204124i
$25$	−10.9582	+	22.4704i	−0.438329	+	0.898814i
$26$	−9.70339			−0.373207
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	10.2683	+	10.2683i	0.366724	+	0.366724i
$29$		−	15.3053i		−	0.527770i	−0.964554	−	0.263885i	$-0.914996\pi$
$29$		−	15.3053i		−	0.527770i	0.964554	−	0.263885i	$-0.0850040\pi$
$30$	6.49040	+	10.3863i	0.216347	+	0.346209i
$31$	−18.0217			−0.581345			−0.290673	−	0.956823i	$-0.593879\pi$
$31$	−18.0217			−0.581345			−0.290673	+	0.956823i	$0.593879\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	−23.0848	−	23.0848i	−0.699539	−	0.699539i
$34$			16.5629i			0.487144i
$35$	−35.3735	−	8.16576i	−1.01067	−	0.233307i
$36$	6.00000			0.166667
$37$	7.99013	−	7.99013i	0.215950	−	0.215950i	−0.590840	−	0.806789i	$-0.701203\pi$
$37$	7.99013	−	7.99013i	0.215950	−	0.215950i	0.806789	+	0.590840i	$0.201203\pi$
$38$	2.00840	+	2.00840i	0.0528526	+	0.0528526i
$39$		−	11.8842i		−	0.304722i
$40$	3.18097	−	13.7797i	0.0795242	−	0.344494i
$41$	−8.60556			−0.209892			−0.104946	−	0.994478i	$-0.533467\pi$
$41$	−8.60556			−0.209892			−0.104946	+	0.994478i	$0.533467\pi$
$42$	−12.5760	+	12.5760i	−0.299429	+	0.299429i
$43$	−18.9595	−	18.9595i	−0.440920	−	0.440920i	0.451401	−	0.892321i	$-0.350924\pi$
$43$	−18.9595	−	18.9595i	−0.440920	−	0.440920i	−0.892321	+	0.451401i	$0.850924\pi$
$44$			37.6973i			0.856757i
$45$	−12.7205	+	7.94908i	−0.282679	+	0.176646i
$46$	−6.78233			−0.147442
$47$	21.2643	−	21.2643i	0.452431	−	0.452431i	−0.443729	−	0.896161i	$-0.646345\pi$
$47$	21.2643	−	21.2643i	0.452431	−	0.452431i	0.896161	+	0.443729i	$0.146345\pi$
$48$	−4.89898	−	4.89898i	−0.102062	−	0.102062i
$49$		−	3.71868i		−	0.0758913i
$50$	11.5121	+	33.4286i	0.230243	+	0.668572i
$51$	−20.2853			−0.397751
$52$	−9.70339	+	9.70339i	−0.186604	+	0.186604i
$53$	30.6997	+	30.6997i	0.579240	+	0.579240i	0.934694	−	0.355454i	$-0.115674\pi$
$53$	30.6997	+	30.6997i	0.579240	+	0.579240i	−0.355454	+	0.934694i	$0.615674\pi$
$54$			7.34847i			0.136083i
$55$	−49.9432	−	79.9217i	−0.908058	−	1.45312i
$56$	20.5365			0.366724
$57$	−2.45978	+	2.45978i	−0.0431539	+	0.0431539i
$58$	−15.3053	−	15.3053i	−0.263885	−	0.263885i
$59$			37.0580i			0.628102i	0.949406	+	0.314051i	$0.101686\pi$
$59$			37.0580i			0.628102i	−0.949406	+	0.314051i	$0.898314\pi$
$60$	16.8767	+	3.89587i	0.281278	+	0.0649312i
$61$	65.9013			1.08035			0.540175	−	0.841553i	$-0.318358\pi$
$61$	65.9013			1.08035			0.540175	+	0.841553i	$0.318358\pi$
$62$	−18.0217	+	18.0217i	−0.290673	+	0.290673i
$63$	−15.4024	−	15.4024i	−0.244483	−	0.244483i
$64$			8.00000i			0.125000i
$65$	7.71654	−	33.4276i	0.118716	−	0.514270i
$66$	−46.1696			−0.699539
$67$	−70.4656	+	70.4656i	−1.05173	+	1.05173i	−0.0531382	+	0.998587i	$0.516922\pi$
$67$	−70.4656	+	70.4656i	−1.05173	+	1.05173i	−0.998587	+	0.0531382i	$0.983078\pi$
$68$	16.5629	+	16.5629i	0.243572	+	0.243572i
$69$		−	8.30662i		−	0.120386i
$70$	−43.5393	+	27.2078i	−0.621990	+	0.388683i
$71$	−8.38441			−0.118090			−0.0590452	−	0.998255i	$-0.518806\pi$
$71$	−8.38441			−0.118090			−0.0590452	+	0.998255i	$0.518806\pi$
$72$	6.00000	−	6.00000i	0.0833333	−	0.0833333i
$73$	78.9935	+	78.9935i	1.08210	+	1.08210i	0.996313	+	0.0857895i	$0.0273412\pi$
$73$	78.9935	+	78.9935i	1.08210	+	1.08210i	0.0857895	+	0.996313i	$0.472659\pi$
$74$		−	15.9803i		−	0.215950i
$75$	−40.9415	+	14.0994i	−0.545887	+	0.187992i
$76$	4.01680			0.0528526
$77$	96.7715	−	96.7715i	1.25677	−	1.25677i
$78$	−11.8842	−	11.8842i	−0.152361	−	0.152361i
$79$			103.875i			1.31488i	0.753508	+	0.657439i	$0.228360\pi$
$79$			103.875i			1.31488i	−0.753508	+	0.657439i	$0.771640\pi$
$80$	−10.5988	−	16.9607i	−0.132485	−	0.212009i
$81$	−9.00000			−0.111111
$82$	−8.60556	+	8.60556i	−0.104946	+	0.104946i
$83$	37.7965	+	37.7965i	0.455380	+	0.455380i	0.897135	−	0.441756i	$-0.145644\pi$
$83$	37.7965	+	37.7965i	0.455380	+	0.455380i	−0.441756	+	0.897135i	$0.645644\pi$
$84$			25.1520i			0.299429i
$85$	−57.0581	−	13.1715i	−0.671272	−	0.154959i
$86$	−37.9191			−0.440920
$87$	18.7451	−	18.7451i	0.215461	−	0.215461i
$88$	37.6973	+	37.6973i	0.428379	+	0.428379i
$89$			140.211i			1.57541i	0.616055	+	0.787703i	$0.288730\pi$
$89$			140.211i			1.57541i	−0.616055	+	0.787703i	$0.711270\pi$
$90$	−4.77145	+	20.6696i	−0.0530161	+	0.229662i
$91$	49.8185			0.547456
$92$	−6.78233	+	6.78233i	−0.0737210	+	0.0737210i
$93$	−22.0720	−	22.0720i	−0.237333	−	0.237333i
$94$		−	42.5286i		−	0.452431i
$95$	−8.51597	+	5.32164i	−0.0896418	+	0.0560173i
$96$	−9.79796			−0.102062
$97$	105.406	−	105.406i	1.08666	−	1.08666i	0.0907920	−	0.995870i	$-0.471060\pi$
$97$	105.406	−	105.406i	1.08666	−	1.08666i	0.995870	−	0.0907920i	$-0.0289398\pi$
$98$	−3.71868	−	3.71868i	−0.0379457	−	0.0379457i
$99$		−	56.5460i		−	0.571171i
$100$	44.9407	+	21.9165i	0.449407	+	0.219165i
$101$	−166.271			−1.64624			−0.823122	−	0.567865i	$-0.807770\pi$
$101$	−166.271			−1.64624			−0.823122	+	0.567865i	$0.807770\pi$
$102$	−20.2853	+	20.2853i	−0.198876	+	0.198876i
$103$	−10.8622	−	10.8622i	−0.105458	−	0.105458i	0.652409	−	0.757867i	$-0.273759\pi$
$103$	−10.8622	−	10.8622i	−0.105458	−	0.105458i	−0.757867	+	0.652409i	$0.773759\pi$
$104$			19.4068i			0.186604i
$105$	−33.3226	−	53.3245i	−0.317358	−	0.507853i
$106$	61.3995			0.579240
$107$	18.6728	−	18.6728i	0.174512	−	0.174512i	−0.614446	−	0.788959i	$-0.710621\pi$
$107$	18.6728	−	18.6728i	0.174512	−	0.174512i	0.788959	+	0.614446i	$0.210621\pi$
$108$	7.34847	+	7.34847i	0.0680414	+	0.0680414i
$109$			102.811i			0.943220i	0.881807	+	0.471610i	$0.156327\pi$
$109$			102.811i			0.943220i	−0.881807	+	0.471610i	$0.843673\pi$
$110$	−129.865	−	29.9785i	−1.18059	−	0.272532i
$111$	19.5718			0.176322
$112$	20.5365	−	20.5365i	0.183362	−	0.183362i
$113$	18.3180	+	18.3180i	0.162106	+	0.162106i	0.783499	−	0.621393i	$-0.213433\pi$
$113$	18.3180	+	18.3180i	0.162106	+	0.162106i	−0.621393	+	0.783499i	$0.713433\pi$
$114$			4.91955i			0.0431539i
$115$	5.39359	−	23.3647i	0.0469008	−	0.203171i
$116$	−30.6107			−0.263885
$117$	14.5551	−	14.5551i	0.124402	−	0.124402i
$118$	37.0580	+	37.0580i	0.314051	+	0.314051i
$119$		−	85.0361i		−	0.714589i
$120$	20.7725	−	12.9808i	0.173105	−	0.108173i
$121$	234.272			1.93613
$122$	65.9013	−	65.9013i	0.540175	−	0.540175i
$123$	−10.5396	−	10.5396i	−0.0856880	−	0.0856880i
$124$			36.0434i			0.290673i
$125$	−124.314	+	13.0747i	−0.994515	+	0.104598i
$126$	−30.8048			−0.244483
$127$	−71.1197	+	71.1197i	−0.559998	+	0.559998i	−0.929307	−	0.369309i	$-0.879594\pi$
$127$	−71.1197	+	71.1197i	−0.559998	+	0.559998i	0.369309	+	0.929307i	$0.379594\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$		−	46.4412i		−	0.360009i
$130$	−25.7110	−	41.1441i	−0.197777	−	0.316493i
$131$	−135.743			−1.03621			−0.518103	−	0.855318i	$-0.673362\pi$
$131$	−135.743			−1.03621			−0.518103	+	0.855318i	$0.673362\pi$
$132$	−46.1696	+	46.1696i	−0.349770	+	0.349770i
$133$	−10.3114	−	10.3114i	−0.0775292	−	0.0775292i
$134$			140.931i			1.05173i
$135$	−25.3150	−	5.84381i	−0.187519	−	0.0432875i
$136$	33.1258			0.243572
$137$	−60.5881	+	60.5881i	−0.442249	+	0.442249i	−0.892767	−	0.450518i	$-0.851239\pi$
$137$	−60.5881	+	60.5881i	−0.442249	+	0.442249i	0.450518	+	0.892767i	$0.351239\pi$
$138$	−8.30662	−	8.30662i	−0.0601929	−	0.0601929i
$139$		−	227.197i		−	1.63451i	−0.576276	−	0.817255i	$-0.695494\pi$
$139$		−	227.197i		−	1.63451i	0.576276	−	0.817255i	$-0.304506\pi$
$140$	−16.3315	+	70.7471i	−0.116654	+	0.505336i
$141$	52.0866			0.369409
$142$	−8.38441	+	8.38441i	−0.0590452	+	0.0590452i
$143$	91.4479	+	91.4479i	0.639496	+	0.639496i
$144$		−	12.0000i		−	0.0833333i
$145$	64.8973	−	40.5545i	0.447568	−	0.279686i
$146$	157.987			1.08210
$147$	4.55443	−	4.55443i	0.0309825	−	0.0309825i
$148$	−15.9803	−	15.9803i	−0.107975	−	0.107975i
$149$			140.232i			0.941152i	0.882359	+	0.470576i	$0.155954\pi$
$149$			140.232i			0.941152i	−0.882359	+	0.470576i	$0.844046\pi$
$150$	−26.8421	+	55.0409i	−0.178947	+	0.366939i
$151$	214.851			1.42285			0.711427	−	0.702760i	$-0.248049\pi$
$151$	214.851			1.42285			0.711427	+	0.702760i	$0.248049\pi$
$152$	4.01680	−	4.01680i	0.0264263	−	0.0264263i
$153$	−24.8443	−	24.8443i	−0.162381	−	0.162381i
$154$		−	193.543i		−	1.25677i
$155$	−47.7520	−	76.4153i	−0.308078	−	0.493002i
$156$	−23.7683			−0.152361
$157$	119.482	−	119.482i	0.761034	−	0.761034i	−0.215475	−	0.976509i	$-0.569130\pi$
$157$	119.482	−	119.482i	0.761034	−	0.761034i	0.976509	+	0.215475i	$0.0691301\pi$
$158$	103.875	+	103.875i	0.657439	+	0.657439i
$159$			75.1987i			0.472948i
$160$	−27.5595	−	6.36194i	−0.172247	−	0.0397621i
$161$	34.8214			0.216282
$162$	−9.00000	+	9.00000i	−0.0555556	+	0.0555556i
$163$	22.6345	+	22.6345i	0.138862	+	0.138862i	0.773121	−	0.634259i	$-0.218695\pi$
$163$	22.6345	+	22.6345i	0.138862	+	0.138862i	−0.634259	+	0.773121i	$0.718695\pi$
$164$			17.2111i			0.104946i
$165$	36.7160	−	159.051i	0.222521	−	0.963948i
$166$	75.5930			0.455380
$167$	−51.9716	+	51.9716i	−0.311207	+	0.311207i	−0.845377	−	0.534170i	$-0.820624\pi$
$167$	−51.9716	+	51.9716i	−0.311207	+	0.311207i	0.534170	+	0.845377i	$0.320624\pi$
$168$	25.1520	+	25.1520i	0.149714	+	0.149714i
$169$		−	121.922i		−	0.721433i
$170$	−70.2296	+	43.8866i	−0.413115	+	0.258156i
$171$	−6.02519			−0.0352351
$172$	−37.9191	+	37.9191i	−0.220460	+	0.220460i
$173$	−182.504	−	182.504i	−1.05494	−	1.05494i	−0.998401	−	0.0565364i	$-0.981994\pi$
$173$	−182.504	−	182.504i	−1.05494	−	1.05494i	−0.0565364	−	0.998401i	$-0.518006\pi$
$174$		−	37.4903i		−	0.215461i
$175$	−59.1048	−	171.627i	−0.337742	−	0.980725i
$176$	75.3946			0.428379
$177$	−45.3866	+	45.3866i	−0.256422	+	0.256422i
$178$	140.211	+	140.211i	0.787703	+	0.787703i
$179$			23.8205i			0.133076i	0.997784	+	0.0665378i	$0.0211953\pi$
$179$			23.8205i			0.133076i	−0.997784	+	0.0665378i	$0.978805\pi$
$180$	15.8982	+	25.4411i	0.0883232	+	0.141339i
$181$	210.981			1.16564			0.582820	−	0.812601i	$-0.301949\pi$
$181$	210.981			1.16564			0.582820	+	0.812601i	$0.301949\pi$
$182$	49.8185	−	49.8185i	0.273728	−	0.273728i
$183$	80.7123	+	80.7123i	0.441051	+	0.441051i
$184$			13.5647i			0.0737210i
$185$	55.0510	+	12.7082i	0.297573	+	0.0686929i
$186$	−44.1440			−0.237333
$187$	156.094	−	156.094i	0.834728	−	0.834728i
$188$	−42.5286	−	42.5286i	−0.226216	−	0.226216i
$189$		−	37.7280i		−	0.199619i
$190$	−3.19432	+	13.8376i	−0.0168122	+	0.0728295i
$191$	107.185			0.561180			0.280590	−	0.959828i	$-0.409470\pi$
$191$	107.185			0.561180			0.280590	+	0.959828i	$0.409470\pi$
$192$	−9.79796	+	9.79796i	−0.0510310	+	0.0510310i
$193$	−204.925	−	204.925i	−1.06179	−	1.06179i	−0.997961	−	0.0638266i	$-0.979670\pi$
$193$	−204.925	−	204.925i	−1.06179	−	1.06179i	−0.0638266	−	0.997961i	$-0.520330\pi$
$194$		−	210.812i		−	1.08666i
$195$	50.3910	−	31.4894i	0.258415	−	0.161484i
$196$	−7.43735			−0.0379457
$197$	−184.161	+	184.161i	−0.934829	+	0.934829i	−0.998003	−	0.0631740i	$-0.979878\pi$
$197$	−184.161	+	184.161i	−0.934829	+	0.934829i	0.0631740	+	0.998003i	$0.479878\pi$
$198$	−56.5460	−	56.5460i	−0.285586	−	0.285586i
$199$			104.404i			0.524644i	0.964980	+	0.262322i	$0.0844882\pi$
$199$			104.404i			0.524644i	−0.964980	+	0.262322i	$0.915512\pi$
$200$	66.8572	−	23.0243i	0.334286	−	0.115121i
$201$	−172.605			−0.858730
$202$	−166.271	+	166.271i	−0.823122	+	0.823122i
$203$	78.5796	+	78.5796i	0.387092	+	0.387092i
$204$			40.5706i			0.198876i
$205$	−22.8021	−	36.4891i	−0.111230	−	0.177996i
$206$	−21.7244			−0.105458
$207$	10.1735	−	10.1735i	0.0491473	−	0.0491473i
$208$	19.4068	+	19.4068i	0.0933018	+	0.0933018i
$209$		−	37.8556i		−	0.181127i
$210$	−86.6471	−	20.0019i	−0.412605	−	0.0952473i
$211$	129.297			0.612783			0.306391	−	0.951906i	$-0.400878\pi$
$211$	129.297			0.612783			0.306391	+	0.951906i	$0.400878\pi$
$212$	61.3995	−	61.3995i	0.289620	−	0.289620i
$213$	−10.2688	−	10.2688i	−0.0482102	−	0.0482102i
$214$		−	37.3457i		−	0.174512i
$215$	30.1548	−	130.629i	0.140255	−	0.607576i
$216$	14.6969			0.0680414
$217$	92.5259	−	92.5259i	0.426387	−	0.426387i
$218$	102.811	+	102.811i	0.471610	+	0.471610i
$219$			193.494i			0.883533i
$220$	−159.843	+	99.8864i	−0.726561	+	0.454029i
$221$	80.3580			0.363611
$222$	19.5718	−	19.5718i	0.0881610	−	0.0881610i
$223$	−18.4366	−	18.4366i	−0.0826755	−	0.0826755i	0.664560	−	0.747235i	$-0.268619\pi$
$223$	−18.4366	−	18.4366i	−0.0826755	−	0.0826755i	−0.747235	+	0.664560i	$0.768619\pi$
$224$		−	41.0731i		−	0.183362i
$225$	−67.4111	−	32.8747i	−0.299605	−	0.146110i
$226$	36.6359			0.162106
$227$	−118.408	+	118.408i	−0.521621	+	0.521621i	−0.918061	−	0.396439i	$-0.870246\pi$
$227$	−118.408	+	118.408i	−0.521621	+	0.521621i	0.396439	+	0.918061i	$0.370246\pi$
$228$	4.91955	+	4.91955i	0.0215770	+	0.0215770i
$229$		−	39.8738i		−	0.174122i	−0.996203	−	0.0870608i	$-0.972253\pi$
$229$		−	39.8738i		−	0.174122i	0.996203	−	0.0870608i	$-0.0277474\pi$
$230$	−17.9711	−	28.7583i	−0.0781352	−	0.125036i
$231$	237.041			1.02615
$232$	−30.6107	+	30.6107i	−0.131943	+	0.131943i
$233$	103.054	+	103.054i	0.442294	+	0.442294i	0.892782	−	0.450489i	$-0.148750\pi$
$233$	103.054	+	103.054i	0.442294	+	0.442294i	−0.450489	+	0.892782i	$0.648750\pi$
$234$		−	29.1102i		−	0.124402i
$235$	146.508	+	33.8205i	0.623439	+	0.143917i
$236$	74.1160			0.314051
$237$	−127.221	+	127.221i	−0.536797	+	0.536797i
$238$	−85.0361	−	85.0361i	−0.357294	−	0.357294i
$239$		−	395.064i		−	1.65299i	−0.562947	−	0.826493i	$-0.690332\pi$
$239$		−	395.064i		−	1.65299i	0.562947	−	0.826493i	$-0.309668\pi$
$240$	7.79175	−	33.7534i	0.0324656	−	0.140639i
$241$	267.186			1.10865			0.554327	−	0.832299i	$-0.312976\pi$
$241$	267.186			1.10865			0.554327	+	0.832299i	$0.312976\pi$
$242$	234.272	−	234.272i	0.968066	−	0.968066i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$		−	131.803i		−	0.540175i
$245$	15.7679	−	9.85336i	0.0643586	−	0.0402178i
$246$	−21.0792			−0.0856880
$247$	9.74413	−	9.74413i	0.0394499	−	0.0394499i
$248$	36.0434	+	36.0434i	0.145336	+	0.145336i
$249$			92.5822i			0.371816i
$250$	−111.240	+	137.389i	−0.444958	+	0.549556i
$251$	−335.484			−1.33659			−0.668294	−	0.743897i	$-0.732975\pi$
$251$	−335.484			−1.33659			−0.668294	+	0.743897i	$0.732975\pi$
$252$	−30.8048	+	30.8048i	−0.122241	+	0.122241i
$253$	63.9189	+	63.9189i	0.252644	+	0.252644i
$254$			142.239i			0.559998i
$255$	−53.7499	−	86.0133i	−0.210784	−	0.337307i
$256$	16.0000			0.0625000
$257$	63.0112	−	63.0112i	0.245180	−	0.245180i	−0.573809	−	0.818989i	$-0.694535\pi$
$257$	63.0112	−	63.0112i	0.245180	−	0.245180i	0.818989	+	0.573809i	$0.194535\pi$
$258$	−46.4412	−	46.4412i	−0.180005	−	0.180005i
$259$			82.0448i			0.316775i
$260$	−66.8551	−	15.4331i	−0.257135	−	0.0593580i
$261$	45.9160			0.175923
$262$	−135.743	+	135.743i	−0.518103	+	0.518103i
$263$	−142.414	−	142.414i	−0.541497	−	0.541497i	0.382471	−	0.923968i	$-0.375073\pi$
$263$	−142.414	−	142.414i	−0.541497	−	0.541497i	−0.923968	+	0.382471i	$0.875073\pi$
$264$			92.3392i			0.349770i
$265$	−48.8274	+	211.517i	−0.184255	+	0.798179i
$266$	−20.6228			−0.0775292
$267$	−171.723	+	171.723i	−0.643157	+	0.643157i
$268$	140.931	+	140.931i	0.525863	+	0.525863i
$269$			207.123i			0.769973i	0.922922	+	0.384987i	$0.125794\pi$
$269$			207.123i			0.769973i	−0.922922	+	0.384987i	$0.874206\pi$
$270$	−31.1588	+	19.4712i	−0.115403	+	0.0721156i
$271$	−380.296			−1.40331			−0.701654	−	0.712518i	$-0.747555\pi$
$271$	−380.296			−1.40331			−0.701654	+	0.712518i	$0.747555\pi$
$272$	33.1258	−	33.1258i	0.121786	−	0.121786i
$273$	61.0149	+	61.0149i	0.223498	+	0.223498i
$274$			121.176i			0.442249i
$275$	206.548	−	423.536i	0.751084	−	1.54013i
$276$	−16.6132			−0.0601929
$277$	202.941	−	202.941i	0.732639	−	0.732639i	−0.238502	−	0.971142i	$-0.576657\pi$
$277$	202.941	−	202.941i	0.732639	−	0.732639i	0.971142	+	0.238502i	$0.0766565\pi$
$278$	−227.197	−	227.197i	−0.817255	−	0.817255i
$279$		−	54.0651i		−	0.193782i
$280$	54.4156	+	87.0786i	0.194341	+	0.310995i
$281$	−215.868			−0.768215			−0.384108	−	0.923288i	$-0.625491\pi$
$281$	−215.868			−0.768215			−0.384108	+	0.923288i	$0.625491\pi$
$282$	52.0866	−	52.0866i	0.184704	−	0.184704i
$283$	−281.977	−	281.977i	−0.996383	−	0.996383i	0.00361003	−	0.999993i	$-0.498851\pi$
$283$	−281.977	−	281.977i	−0.996383	−	0.996383i	−0.999993	+	0.00361003i	$0.998851\pi$
$284$			16.7688i			0.0590452i
$285$	−16.9475	−	3.91223i	−0.0594651	−	0.0137271i
$286$	182.896			0.639496
$287$	44.1821	−	44.1821i	0.153945	−	0.153945i
$288$	−12.0000	−	12.0000i	−0.0416667	−	0.0416667i
$289$			151.835i			0.525382i
$290$	24.3429	−	105.452i	0.0839410	−	0.363627i
$291$	258.191			0.887256
$292$	157.987	−	157.987i	0.541051	−	0.541051i
$293$	−268.608	−	268.608i	−0.916752	−	0.916752i	0.0800393	−	0.996792i	$-0.474495\pi$
$293$	−268.608	−	268.608i	−0.916752	−	0.916752i	−0.996792	+	0.0800393i	$0.974495\pi$
$294$		−	9.10886i		−	0.0309825i
$295$	−157.133	+	98.1924i	−0.532653	+	0.332856i
$296$	−31.9605			−0.107975
$297$	69.2544	−	69.2544i	0.233180	−	0.233180i
$298$	140.232	+	140.232i	0.470576	+	0.470576i
$299$			32.9058i			0.110053i
$300$	28.1988	+	81.8830i	0.0939961	+	0.272943i
$301$	194.682			0.646783
$302$	214.851	−	214.851i	0.711427	−	0.711427i
$303$	−203.639	−	203.639i	−0.672076	−	0.672076i
$304$		−	8.03359i		−	0.0264263i
$305$	174.618	+	279.433i	0.572519	+	0.916175i
$306$	−49.6886			−0.162381
$307$	242.905	−	242.905i	0.791222	−	0.791222i	−0.190471	−	0.981693i	$-0.561001\pi$
$307$	242.905	−	242.905i	0.791222	−	0.791222i	0.981693	+	0.190471i	$0.0610014\pi$
$308$	−193.543	−	193.543i	−0.628387	−	0.628387i
$309$		−	26.6069i		−	0.0861064i
$310$	−124.167	−	28.6632i	−0.400540	−	0.0924621i
$311$	−207.359			−0.666749			−0.333374	−	0.942795i	$-0.608187\pi$
$311$	−207.359			−0.666749			−0.333374	+	0.942795i	$0.608187\pi$
$312$	−23.7683	+	23.7683i	−0.0761806	+	0.0761806i
$313$	−281.476	−	281.476i	−0.899286	−	0.899286i	0.0960873	−	0.995373i	$-0.469367\pi$
$313$	−281.476	−	281.476i	−0.899286	−	0.899286i	−0.995373	+	0.0960873i	$0.969367\pi$
$314$		−	238.965i		−	0.761034i
$315$	24.4973	−	106.121i	0.0777691	−	0.336891i
$316$	207.751			0.657439
$317$	244.685	−	244.685i	0.771877	−	0.771877i	−0.206557	−	0.978435i	$-0.566226\pi$
$317$	244.685	−	244.685i	0.771877	−	0.771877i	0.978435	+	0.206557i	$0.0662260\pi$
$318$	75.1987	+	75.1987i	0.236474	+	0.236474i
$319$			288.485i			0.904342i
$320$	−33.9214	+	21.1976i	−0.106004	+	0.0662424i
$321$	45.7389			0.142489
$322$	34.8214	−	34.8214i	0.108141	−	0.108141i
$323$	−16.6324	−	16.6324i	−0.0514936	−	0.0514936i
$324$			18.0000i			0.0555556i
$325$	162.185	−	55.8533i	0.499032	−	0.171856i
$326$	45.2690			0.138862
$327$	−125.917	+	125.917i	−0.385068	+	0.385068i
$328$	17.2111	+	17.2111i	0.0524729	+	0.0524729i
$329$			218.347i			0.663670i
$330$	−122.335	−	195.767i	−0.370713	−	0.593234i
$331$	638.751			1.92976			0.964881	−	0.262688i	$-0.0846089\pi$
$331$	638.751			1.92976			0.964881	+	0.262688i	$0.0846089\pi$
$332$	75.5930	−	75.5930i	0.227690	−	0.227690i
$333$	23.9704	+	23.9704i	0.0719832	+	0.0719832i
$334$			103.943i			0.311207i
$335$	−485.499	−	112.074i	−1.44925	−	0.334550i
$336$	50.3040			0.149714
$337$	245.749	−	245.749i	0.729225	−	0.729225i	−0.241240	−	0.970465i	$-0.577554\pi$
$337$	245.749	−	245.749i	0.729225	−	0.729225i	0.970465	+	0.241240i	$0.0775542\pi$
$338$	−121.922	−	121.922i	−0.360716	−	0.360716i
$339$			44.8696i			0.132359i
$340$	−26.3430	+	114.116i	−0.0774794	+	0.335636i
$341$	339.685			0.996144
$342$	−6.02519	+	6.02519i	−0.0176175	+	0.0176175i
$343$	−232.480	−	232.480i	−0.677785	−	0.677785i
$344$			75.8382i			0.220460i
$345$	35.2216	−	22.0100i	0.102092	−	0.0637972i
$346$	−365.008			−1.05494
$347$	151.497	−	151.497i	0.436591	−	0.436591i	−0.454272	−	0.890863i	$-0.650100\pi$
$347$	151.497	−	151.497i	0.436591	−	0.436591i	0.890863	+	0.454272i	$0.150100\pi$
$348$	−37.4903	−	37.4903i	−0.107731	−	0.107731i
$349$			247.408i			0.708904i	0.935074	+	0.354452i	$0.115333\pi$
$349$			247.408i			0.708904i	−0.935074	+	0.354452i	$0.884667\pi$
$350$	−230.732	−	112.522i	−0.659233	−	0.321492i
$351$	35.6525			0.101574
$352$	75.3946	−	75.3946i	0.214189	−	0.214189i
$353$	−304.079	−	304.079i	−0.861415	−	0.861415i	0.130088	−	0.991503i	$-0.458474\pi$
$353$	−304.079	−	304.079i	−0.861415	−	0.861415i	−0.991503	+	0.130088i	$0.958474\pi$
$354$			90.7732i			0.256422i
$355$	−22.2161	−	35.5514i	−0.0625807	−	0.100145i
$356$	280.422			0.787703
$357$	104.147	−	104.147i	0.291730	−	0.291730i
$358$	23.8205	+	23.8205i	0.0665378	+	0.0665378i
$359$			257.894i			0.718369i	0.933267	+	0.359184i	$0.116945\pi$
$359$			257.894i			0.718369i	−0.933267	+	0.359184i	$0.883055\pi$
$360$	41.3392	+	9.54290i	0.114831	+	0.0265081i
$361$	356.966			0.988826
$362$	210.981	−	210.981i	0.582820	−	0.582820i
$363$	286.923	+	286.923i	0.790422	+	0.790422i
$364$		−	99.6370i		−	0.273728i
$365$	−125.638	+	544.255i	−0.344213	+	1.49111i
$366$	161.425			0.441051
$367$	−293.848	+	293.848i	−0.800675	+	0.800675i	−0.983201	−	0.182526i	$-0.941573\pi$
$367$	−293.848	+	293.848i	−0.800675	+	0.800675i	0.182526	+	0.983201i	$0.441573\pi$
$368$	13.5647	+	13.5647i	0.0368605	+	0.0368605i
$369$		−	25.8167i		−	0.0699639i
$370$	67.7592	−	42.3428i	0.183133	−	0.114440i
$371$	−315.233			−0.849685
$372$	−44.1440	+	44.1440i	−0.118667	+	0.118667i
$373$	414.362	+	414.362i	1.11089	+	1.11089i	0.993030	+	0.117861i	$0.0376037\pi$
$373$	414.362	+	414.362i	1.11089	+	1.11089i	0.117861	+	0.993030i	$0.462396\pi$
$374$		−	312.188i		−	0.834728i
$375$	−168.267	−	136.240i	−0.448711	−	0.363307i
$376$	−85.0571			−0.226216
$377$	−74.2568	+	74.2568i	−0.196968	+	0.196968i
$378$	−37.7280	−	37.7280i	−0.0998096	−	0.0998096i
$379$			308.141i			0.813036i	0.913643	+	0.406518i	$0.133257\pi$
$379$			308.141i			0.813036i	−0.913643	+	0.406518i	$0.866743\pi$
$380$	10.6433	+	17.0319i	0.0280086	+	0.0448209i
$381$	−174.207			−0.457236
$382$	107.185	−	107.185i	0.280590	−	0.280590i
$383$	206.195	+	206.195i	0.538368	+	0.538368i	0.923049	−	0.384682i	$-0.125689\pi$
$383$	206.195	+	206.195i	0.538368	+	0.538368i	−0.384682	+	0.923049i	$0.625689\pi$
$384$			19.5959i			0.0510310i
$385$	666.744	+	153.914i	1.73180	+	0.399776i
$386$	−409.850			−1.06179
$387$	56.8786	−	56.8786i	0.146973	−	0.146973i
$388$	−210.812	−	210.812i	−0.543331	−	0.543331i
$389$			474.840i			1.22067i	0.792144	+	0.610334i	$0.208965\pi$
$389$			474.840i			1.22067i	−0.792144	+	0.610334i	$0.791035\pi$
$390$	18.9016	−	81.8804i	0.0484656	−	0.209950i
$391$	56.1675			0.143651
$392$	−7.43735	+	7.43735i	−0.0189728	+	0.0189728i
$393$	−166.251	−	166.251i	−0.423029	−	0.423029i
$394$			368.322i			0.934829i
$395$	−440.450	+	275.238i	−1.11506	+	0.696805i
$396$	−113.092			−0.285586
$397$	−240.297	+	240.297i	−0.605281	+	0.605281i	−0.941709	−	0.336428i	$-0.890781\pi$
$397$	−240.297	+	240.297i	−0.605281	+	0.605281i	0.336428	+	0.941709i	$0.390781\pi$
$398$	104.404	+	104.404i	0.262322	+	0.262322i
$399$		−	25.2576i		−	0.0633023i
$400$	43.8329	−	89.8814i	0.109582	−	0.224704i
$401$	201.562			0.502648			0.251324	−	0.967903i	$-0.419134\pi$
$401$	201.562			0.502648			0.251324	+	0.967903i	$0.419134\pi$
$402$	−172.605	+	172.605i	−0.429365	+	0.429365i
$403$	87.4358	+	87.4358i	0.216962	+	0.216962i
$404$			332.541i			0.823122i
$405$	−23.8473	−	38.1616i	−0.0588821	−	0.0942262i
$406$	157.159			0.387092
$407$	−150.603	+	150.603i	−0.370033	+	0.370033i
$408$	40.5706	+	40.5706i	0.0994378	+	0.0994378i
$409$			675.609i			1.65186i	0.563775	+	0.825928i	$0.309349\pi$
$409$			675.609i			1.65186i	−0.563775	+	0.825928i	$0.690651\pi$
$410$	−59.2912	−	13.6870i	−0.144613	−	0.0333830i
$411$	−148.410			−0.361095
$412$	−21.7244	+	21.7244i	−0.0527292	+	0.0527292i
$413$	−190.261	−	190.261i	−0.460680	−	0.460680i
$414$		−	20.3470i		−	0.0491473i
$415$	−60.1148	+	260.413i	−0.144855	+	0.627502i
$416$	38.8135			0.0933018
$417$	278.258	−	278.258i	0.667286	−	0.667286i
$418$	−37.8556	−	37.8556i	−0.0905637	−	0.0905637i
$419$			384.622i			0.917952i	0.888449	+	0.458976i	$0.151784\pi$
$419$			384.622i			0.917952i	−0.888449	+	0.458976i	$0.848216\pi$
$420$	−106.649	+	66.6452i	−0.253926	+	0.158679i
$421$	−454.018			−1.07843			−0.539214	−	0.842169i	$-0.681279\pi$
$421$	−454.018			−1.07843			−0.539214	+	0.842169i	$0.681279\pi$
$422$	129.297	−	129.297i	0.306391	−	0.306391i
$423$	63.7928	+	63.7928i	0.150810	+	0.150810i
$424$		−	122.799i		−	0.289620i
$425$	−95.3370	−	276.837i	−0.224322	−	0.651381i
$426$	−20.5375			−0.0482102
$427$	−338.346	+	338.346i	−0.792380	+	0.792380i
$428$	−37.3457	−	37.3457i	−0.0872562	−	0.0872562i
$429$			224.001i			0.522146i
$430$	−100.474	−	160.784i	−0.233660	−	0.373916i
$431$	−241.139			−0.559487			−0.279743	−	0.960075i	$-0.590249\pi$
$431$	−241.139			−0.559487			−0.279743	+	0.960075i	$0.590249\pi$
$432$	14.6969	−	14.6969i	0.0340207	−	0.0340207i
$433$	−278.432	−	278.432i	−0.643031	−	0.643031i	0.308269	−	0.951299i	$-0.400250\pi$
$433$	−278.432	−	278.432i	−0.643031	−	0.643031i	−0.951299	+	0.308269i	$0.900250\pi$
$434$		−	185.052i		−	0.426387i
$435$	129.152	+	29.8138i	0.296900	+	0.0685375i
$436$	205.622			0.471610
$437$	6.81081	−	6.81081i	0.0155854	−	0.0155854i
$438$	193.494	+	193.494i	0.441767	+	0.441767i
$439$			439.356i			1.00081i	0.865791	+	0.500406i	$0.166816\pi$
$439$			439.356i			1.00081i	−0.865791	+	0.500406i	$0.833184\pi$
$440$	−59.9570	+	259.730i	−0.136266	+	0.590295i
$441$	11.1560			0.0252971
$442$	80.3580	−	80.3580i	0.181805	−	0.181805i
$443$	−261.606	−	261.606i	−0.590532	−	0.590532i	0.347243	−	0.937775i	$-0.387118\pi$
$443$	−261.606	−	261.606i	−0.590532	−	0.590532i	−0.937775	+	0.347243i	$0.887118\pi$
$444$		−	39.1435i		−	0.0881610i
$445$	−594.520	+	371.517i	−1.33600	+	0.834869i
$446$	−36.8733			−0.0826755
$447$	−171.748	+	171.748i	−0.384224	+	0.384224i
$448$	−41.0731	−	41.0731i	−0.0916810	−	0.0916810i
$449$			876.612i			1.95237i	0.216948	+	0.976183i	$0.430390\pi$
$449$			876.612i			1.95237i	−0.216948	+	0.976183i	$0.569610\pi$
$450$	−100.286	+	34.5364i	−0.222857	+	0.0767475i
$451$	162.203			0.359653
$452$	36.6359	−	36.6359i	0.0810529	−	0.0810529i
$453$	263.138	+	263.138i	0.580878	+	0.580878i
$454$			236.816i			0.521621i
$455$	132.004	+	211.239i	0.290118	+	0.464262i
$456$	9.83910			0.0215770
$457$	18.0348	−	18.0348i	0.0394635	−	0.0394635i	−0.687100	−	0.726563i	$-0.741116\pi$
$457$	18.0348	−	18.0348i	0.0394635	−	0.0394635i	0.726563	+	0.687100i	$0.241116\pi$
$458$	−39.8738	−	39.8738i	−0.0870608	−	0.0870608i
$459$		−	60.8559i		−	0.132584i
$460$	−46.7294	−	10.7872i	−0.101586	−	0.0234504i
$461$	746.316			1.61891			0.809453	−	0.587185i	$-0.199764\pi$
$461$	746.316			1.61891			0.809453	+	0.587185i	$0.199764\pi$
$462$	237.041	−	237.041i	0.513076	−	0.513076i
$463$	−178.472	−	178.472i	−0.385469	−	0.385469i	0.487599	−	0.873068i	$-0.337873\pi$
$463$	−178.472	−	178.472i	−0.385469	−	0.385469i	−0.873068	+	0.487599i	$0.837873\pi$
$464$			61.2213i			0.131943i
$465$	35.1052	−	152.073i	0.0754950	−	0.327039i
$466$	206.109			0.442294
$467$	−246.803	+	246.803i	−0.528486	+	0.528486i	−0.920121	−	0.391635i	$-0.871910\pi$
$467$	−246.803	+	246.803i	−0.528486	+	0.528486i	0.391635	+	0.920121i	$0.371910\pi$
$468$	−29.1102	−	29.1102i	−0.0622012	−	0.0622012i
$469$		−	723.560i		−	1.54277i
$470$	180.329	−	112.688i	0.383678	−	0.239761i
$471$	292.671			0.621382
$472$	74.1160	−	74.1160i	0.157026	−	0.157026i
$473$	357.362	+	357.362i	0.755522	+	0.755522i
$474$			254.442i			0.536797i
$475$	−45.1294	−	22.0085i	−0.0950093	−	0.0463337i
$476$	−170.072			−0.357294
$477$	−92.0992	+	92.0992i	−0.193080	+	0.193080i
$478$	−395.064	−	395.064i	−0.826493	−	0.826493i
$479$			171.427i			0.357886i	0.983859	+	0.178943i	$0.0572678\pi$
$479$			171.427i			0.357886i	−0.983859	+	0.178943i	$0.942732\pi$
$480$	−25.9616	−	41.5451i	−0.0540867	−	0.0865523i
$481$	−77.5314			−0.161188
$482$	267.186	−	267.186i	0.554327	−	0.554327i
$483$	42.6473	+	42.6473i	0.0882967	+	0.0882967i
$484$		−	468.544i		−	0.968066i
$485$	726.235	+	167.647i	1.49739	+	0.345664i
$486$	−22.0454			−0.0453609
$487$	68.8983	−	68.8983i	0.141475	−	0.141475i	−0.632822	−	0.774297i	$-0.718104\pi$
$487$	68.8983	−	68.8983i	0.141475	−	0.141475i	0.774297	+	0.632822i	$0.218104\pi$
$488$	−131.803	−	131.803i	−0.270087	−	0.270087i
$489$			55.4430i			0.113380i
$490$	5.91449	−	25.6212i	0.0120704	−	0.0522882i
$491$	−716.560			−1.45939			−0.729695	−	0.683773i	$-0.760338\pi$
$491$	−716.560			−1.45939			−0.729695	+	0.683773i	$0.760338\pi$
$492$	−21.0792	+	21.0792i	−0.0428440	+	0.0428440i
$493$	126.750	+	126.750i	0.257100	+	0.257100i
$494$		−	19.4883i		−	0.0394499i
$495$	239.765	−	149.830i	0.484374	−	0.302686i
$496$	72.0868			0.145336
$497$	43.0467	−	43.0467i	0.0866131	−	0.0866131i
$498$	92.5822	+	92.5822i	0.185908	+	0.185908i
$499$		−	103.164i		−	0.206742i	−0.994643	−	0.103371i	$-0.967037\pi$
$499$		−	103.164i		−	0.206742i	0.994643	−	0.103371i	$-0.0329629\pi$
$500$	26.1495	+	248.629i	0.0522989	+	0.497257i
$501$	−127.304			−0.254100
$502$	−335.484	+	335.484i	−0.668294	+	0.668294i
$503$	−213.360	−	213.360i	−0.424176	−	0.424176i	0.462463	−	0.886639i	$-0.346966\pi$
$503$	−213.360	−	213.360i	−0.424176	−	0.424176i	−0.886639	+	0.462463i	$0.846966\pi$
$504$			61.6096i			0.122241i
$505$	−440.566	−	705.017i	−0.872409	−	1.39607i
$506$	127.838			0.252644
$507$	149.324	−	149.324i	0.294524	−	0.294524i
$508$	142.239	+	142.239i	0.279999	+	0.279999i
$509$			65.8915i			0.129453i	0.997903	+	0.0647264i	$0.0206175\pi$
$509$			65.8915i			0.129453i	−0.997903	+	0.0647264i	$0.979383\pi$
$510$	−139.763	−	32.2635i	−0.274045	−	0.0632617i
$511$	−811.127			−1.58733
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	−7.37933	−	7.37933i	−0.0143846	−	0.0143846i
$514$		−	126.022i		−	0.245180i
$515$	17.2762	−	74.8393i	0.0335460	−	0.145319i
$516$	−92.8824			−0.180005
$517$	−400.803	+	400.803i	−0.775248	+	0.775248i
$518$	82.0448	+	82.0448i	0.158388	+	0.158388i
$519$		−	447.042i		−	0.861352i
$520$	−82.2882	+	51.4220i	−0.158247	+	0.0988885i
$521$	898.750			1.72505			0.862524	−	0.506016i	$-0.168882\pi$
$521$	898.750			1.72505			0.862524	+	0.506016i	$0.168882\pi$
$522$	45.9160	−	45.9160i	0.0879617	−	0.0879617i
$523$	380.156	+	380.156i	0.726876	+	0.726876i	0.969996	−	0.243120i	$-0.0781709\pi$
$523$	380.156	+	380.156i	0.726876	+	0.726876i	−0.243120	+	0.969996i	$0.578171\pi$
$524$			271.486i			0.518103i
$525$	137.811	−	282.587i	0.262497	−	0.538262i
$526$	−284.827			−0.541497
$527$	149.246	−	149.246i	0.283199	−	0.283199i
$528$	92.3392	+	92.3392i	0.174885	+	0.174885i
$529$			23.0000i			0.0434783i
$530$	162.690	+	260.345i	0.306962	+	0.491217i
$531$	−111.174			−0.209367
$532$	−20.6228	+	20.6228i	−0.0387646	+	0.0387646i
$533$	41.7516	+	41.7516i	0.0783331	+	0.0783331i
$534$			343.446i			0.643157i
$535$	128.653	+	29.6988i	0.240474	+	0.0555118i
$536$	281.862			0.525863
$537$	−29.1741	+	29.1741i	−0.0543278	+	0.0543278i
$538$	207.123	+	207.123i	0.384987	+	0.384987i
$539$			70.0921i			0.130041i
$540$	−11.6876	+	50.6300i	−0.0216437	+	0.0937593i
$541$	−181.504			−0.335498			−0.167749	−	0.985830i	$-0.553650\pi$
$541$	−181.504			−0.335498			−0.167749	+	0.985830i	$0.553650\pi$
$542$	−380.296	+	380.296i	−0.701654	+	0.701654i
$543$	258.398	+	258.398i	0.475871	+	0.475871i
$544$		−	66.2515i		−	0.121786i
$545$	−435.937	+	272.418i	−0.799884	+	0.499849i
$546$	122.030			0.223498
$547$	−369.884	+	369.884i	−0.676206	+	0.676206i	−0.959139	−	0.282934i	$-0.908692\pi$
$547$	−369.884	+	369.884i	−0.676206	+	0.676206i	0.282934	+	0.959139i	$0.408692\pi$
$548$	121.176	+	121.176i	0.221124	+	0.221124i
$549$			197.704i			0.360117i
$550$	−216.988	−	630.084i	−0.394524	−	1.14561i
$551$	30.7392			0.0557880
$552$	−16.6132	+	16.6132i	−0.0300965	+	0.0300965i
$553$	−533.310	−	533.310i	−0.964394	−	0.964394i
$554$		−	405.882i		−	0.732639i
$555$	51.8592	+	82.9877i	0.0934399	+	0.149527i
$556$	−454.394			−0.817255
$557$	443.307	−	443.307i	0.795884	−	0.795884i	−0.186560	−	0.982444i	$-0.559734\pi$
$557$	443.307	−	443.307i	0.795884	−	0.795884i	0.982444	+	0.186560i	$0.0597338\pi$
$558$	−54.0651	−	54.0651i	−0.0968909	−	0.0968909i
$559$			183.972i			0.329109i
$560$	141.494	+	32.6630i	0.252668	+	0.0583268i
$561$	382.351			0.681552
$562$	−215.868	+	215.868i	−0.384108	+	0.384108i
$563$	204.223	+	204.223i	0.362742	+	0.362742i	0.864821	−	0.502080i	$-0.167432\pi$
$563$	204.223	+	204.223i	0.362742	+	0.362742i	−0.502080	+	0.864821i	$0.667432\pi$
$564$		−	104.173i		−	0.184704i
$565$	−29.1344	+	126.208i	−0.0515653	+	0.223378i
$566$	−563.953			−0.996383
$567$	46.2072	−	46.2072i	0.0814942	−	0.0814942i
$568$	16.7688	+	16.7688i	0.0295226	+	0.0295226i
$569$		−	54.1051i		−	0.0950881i	−0.998869	−	0.0475440i	$-0.984861\pi$
$569$		−	54.1051i		−	0.0950881i	0.998869	−	0.0475440i	$-0.0151394\pi$
$570$	−20.8598	+	13.0353i	−0.0365961	+	0.0228690i
$571$	−1055.98			−1.84935			−0.924674	−	0.380759i	$-0.875663\pi$
$571$	−1055.98			−1.84935			−0.924674	+	0.380759i	$0.875663\pi$
$572$	182.896	−	182.896i	0.319748	−	0.319748i
$573$	131.275	+	131.275i	0.229101	+	0.229101i
$574$		−	88.3642i		−	0.153945i
$575$	113.362	−	39.0395i	0.197151	−	0.0678948i
$576$	−24.0000			−0.0416667
$577$	128.192	−	128.192i	0.222171	−	0.222171i	−0.587241	−	0.809412i	$-0.699786\pi$
$577$	128.192	−	128.192i	0.222171	−	0.222171i	0.809412	+	0.587241i	$0.199786\pi$
$578$	151.835	+	151.835i	0.262691	+	0.262691i
$579$		−	501.962i		−	0.866946i
$580$	−81.1089	−	129.795i	−0.139843	−	0.223784i
$581$	−388.105			−0.667995
$582$	258.191	−	258.191i	0.443628	−	0.443628i
$583$	−578.649	−	578.649i	−0.992537	−	0.992537i
$584$		−	315.974i		−	0.541051i
$585$	100.283	+	23.1496i	0.171423	+	0.0395720i
$586$	−537.217			−0.916752
$587$	−18.1091	+	18.1091i	−0.0308503	+	0.0308503i	−0.722364	−	0.691513i	$-0.756944\pi$
$587$	−18.1091	+	18.1091i	−0.0308503	+	0.0308503i	0.691513	+	0.722364i	$0.256944\pi$
$588$	−9.10886	−	9.10886i	−0.0154913	−	0.0154913i
$589$		−	36.1948i		−	0.0614512i
$590$	−58.9402	+	255.325i	−0.0998986	+	0.432754i
$591$	−451.101			−0.763284
$592$	−31.9605	+	31.9605i	−0.0539874	+	0.0539874i
$593$	−696.941	−	696.941i	−1.17528	−	1.17528i	−0.980933	−	0.194348i	$-0.937741\pi$
$593$	−696.941	−	696.941i	−1.17528	−	1.17528i	−0.194348	−	0.980933i	$-0.562259\pi$
$594$		−	138.509i		−	0.233180i
$595$	360.568	−	225.320i	0.605997	−	0.378688i
$596$	280.463			0.470576
$597$	−127.868	+	127.868i	−0.214185	+	0.214185i
$598$	32.9058	+	32.9058i	0.0550264	+	0.0550264i
$599$			757.584i			1.26475i	0.774663	+	0.632374i	$0.217919\pi$
$599$			757.584i			1.26475i	−0.774663	+	0.632374i	$0.782081\pi$
$600$	110.082	+	53.6842i	0.183470	+	0.0894736i
$601$	642.457			1.06898			0.534490	−	0.845175i	$-0.320504\pi$
$601$	642.457			1.06898			0.534490	+	0.845175i	$0.320504\pi$
$602$	194.682	−	194.682i	0.323391	−	0.323391i
$603$	−211.397	−	211.397i	−0.350575	−	0.350575i
$604$		−	429.702i		−	0.711427i
$605$	620.749	+	993.355i	1.02603	+	1.64191i
$606$	−407.278			−0.672076
$607$	−590.328	+	590.328i	−0.972534	+	0.972534i	−0.999633	−	0.0270991i	$-0.991373\pi$
$607$	−590.328	+	590.328i	−0.972534	+	0.972534i	0.0270991	+	0.999633i	$0.491373\pi$
$608$	−8.03359	−	8.03359i	−0.0132131	−	0.0132131i
$609$			192.480i			0.316059i
$610$	454.052	+	104.815i	0.744347	+	0.171828i
$611$	−206.335			−0.337701
$612$	−49.6886	+	49.6886i	−0.0811906	+	0.0811906i
$613$	411.975	+	411.975i	0.672064	+	0.672064i	0.958191	−	0.286128i	$-0.0923682\pi$
$613$	411.975	+	411.975i	0.672064	+	0.672064i	−0.286128	+	0.958191i	$0.592368\pi$
$614$		−	485.810i		−	0.791222i
$615$	16.7631	−	72.6167i	0.0272571	−	0.118076i
$616$	−387.086			−0.628387
$617$	−401.638	+	401.638i	−0.650953	+	0.650953i	−0.953222	−	0.302270i	$-0.902256\pi$
$617$	−401.638	+	401.638i	−0.650953	+	0.650953i	0.302270	+	0.953222i	$0.402256\pi$
$618$	−26.6069	−	26.6069i	−0.0430532	−	0.0430532i
$619$		−	753.916i		−	1.21796i	−0.793186	−	0.608979i	$-0.791579\pi$
$619$		−	753.916i		−	1.21796i	0.793186	−	0.608979i	$-0.208421\pi$
$620$	−152.831	+	95.5041i	−0.246501	+	0.154039i
$621$	24.9199			0.0401286
$622$	−207.359	+	207.359i	−0.333374	+	0.333374i
$623$	−719.863	−	719.863i	−1.15548	−	1.15548i
$624$			47.5367i			0.0761806i
$625$	−384.834	−	492.471i	−0.615735	−	0.787953i
$626$	−562.953			−0.899286
$627$	46.3635	−	46.3635i	0.0739449	−	0.0739449i
$628$	−238.965	−	238.965i	−0.380517	−	0.380517i
$629$			132.340i			0.210397i
$630$	−81.6233	−	130.618i	−0.129561	−	0.207330i
$631$	737.230			1.16835			0.584176	−	0.811627i	$-0.301418\pi$
$631$	737.230			1.16835			0.584176	+	0.811627i	$0.301418\pi$
$632$	207.751	−	207.751i	0.328719	−	0.328719i
$633$	158.356	+	158.356i	0.250167	+	0.250167i
$634$		−	489.370i		−	0.771877i
$635$	−490.006	−	113.115i	−0.771662	−	0.178133i
$636$	150.397			0.236474
$637$	−18.0419	+	18.0419i	−0.0283232	+	0.0283232i
$638$	288.485	+	288.485i	0.452171	+	0.452171i
$639$		−	25.1532i		−	0.0393634i
$640$	−12.7239	+	55.1190i	−0.0198810	+	0.0861234i
$641$	−310.531			−0.484448			−0.242224	−	0.970220i	$-0.577877\pi$
$641$	−310.531			−0.484448			−0.242224	+	0.970220i	$0.577877\pi$
$642$	45.7389	−	45.7389i	0.0712444	−	0.0712444i
$643$	433.442	+	433.442i	0.674093	+	0.674093i	0.958657	−	0.284564i	$-0.0918487\pi$
$643$	433.442	+	433.442i	0.674093	+	0.674093i	−0.284564	+	0.958657i	$0.591849\pi$
$644$		−	69.6428i		−	0.108141i
$645$	196.919	−	123.055i	0.305301	−	0.190783i
$646$	−33.2649			−0.0514936
$647$	−123.580	+	123.580i	−0.191005	+	0.191005i	−0.796130	−	0.605125i	$-0.793123\pi$
$647$	−123.580	+	123.580i	−0.191005	+	0.191005i	0.605125	+	0.796130i	$0.293123\pi$
$648$	18.0000	+	18.0000i	0.0277778	+	0.0277778i
$649$		−	698.494i		−	1.07626i
$650$	106.332	−	218.039i	0.163588	−	0.335444i
$651$	226.641			0.348143
$652$	45.2690	−	45.2690i	0.0694310	−	0.0694310i
$653$	−14.9705	−	14.9705i	−0.0229257	−	0.0229257i	0.695551	−	0.718477i	$-0.255160\pi$
$653$	−14.9705	−	14.9705i	−0.0229257	−	0.0229257i	−0.718477	+	0.695551i	$0.755160\pi$
$654$			251.834i			0.385068i
$655$	−359.678	−	575.575i	−0.549126	−	0.878740i
$656$	34.4223			0.0524729
$657$	−236.981	+	236.981i	−0.360701	+	0.360701i
$658$	218.347	+	218.347i	0.331835	+	0.331835i
$659$			340.257i			0.516324i	0.966102	+	0.258162i	$0.0831168\pi$
$659$			340.257i			0.516324i	−0.966102	+	0.258162i	$0.916883\pi$
$660$	−318.103	−	73.4320i	−0.481974	−	0.111261i
$661$	694.682			1.05096			0.525478	−	0.850807i	$-0.323886\pi$
$661$	694.682			1.05096			0.525478	+	0.850807i	$0.323886\pi$
$662$	638.751	−	638.751i	0.964881	−	0.964881i
$663$	98.4181	+	98.4181i	0.148444	+	0.148444i
$664$		−	151.186i		−	0.227690i
$665$	16.4001	−	71.0441i	0.0246618	−	0.106833i
$666$	47.9408			0.0719832
$667$	−51.9029	+	51.9029i	−0.0778155	+	0.0778155i
$668$	103.943	+	103.943i	0.155604	+	0.155604i
$669$		−	45.1604i		−	0.0675043i
$670$	−597.573	+	373.425i	−0.891901	+	0.557350i
$671$	−1242.15			−1.85119
$672$	50.3040	−	50.3040i	0.0748572	−	0.0748572i
$673$	−625.021	−	625.021i	−0.928709	−	0.928709i	0.0689133	−	0.997623i	$-0.478047\pi$
$673$	−625.021	−	625.021i	−0.928709	−	0.928709i	−0.997623	+	0.0689133i	$0.978047\pi$
$674$		−	491.498i		−	0.729225i
$675$	−42.2983	−	122.824i	−0.0626641	−	0.181962i
$676$	−243.844			−0.360716
$677$	−144.970	+	144.970i	−0.214135	+	0.214135i	−0.806021	−	0.591886i	$-0.798383\pi$
$677$	−144.970	+	144.970i	−0.214135	+	0.214135i	0.591886	+	0.806021i	$0.298383\pi$
$678$	44.8696	+	44.8696i	0.0661794	+	0.0661794i
$679$			1082.34i			1.59402i
$680$	87.7732	+	140.459i	0.129078	+	0.206558i
$681$	−290.039			−0.425902
$682$	339.685	−	339.685i	0.498072	−	0.498072i
$683$	−31.1325	−	31.1325i	−0.0455820	−	0.0455820i	0.683948	−	0.729530i	$-0.260261\pi$
$683$	−31.1325	−	31.1325i	−0.0455820	−	0.0455820i	−0.729530	+	0.683948i	$0.760261\pi$
$684$			12.0504i			0.0176175i
$685$	−417.444	−	96.3644i	−0.609408	−	0.140678i
$686$	−464.961			−0.677785
$687$	48.8353	−	48.8353i	0.0710848	−	0.0710848i
$688$	75.8382	+	75.8382i	0.110230	+	0.110230i
$689$		−	297.891i		−	0.432353i
$690$	13.2116	−	57.2316i	0.0191472	−	0.0829443i
$691$	287.872			0.416603			0.208301	−	0.978065i	$-0.433207\pi$
$691$	287.872			0.416603			0.208301	+	0.978065i	$0.433207\pi$
$692$	−365.008	+	365.008i	−0.527468	+	0.527468i
$693$	290.315	+	290.315i	0.418924	+	0.418924i
$694$		−	302.994i		−	0.436591i
$695$	963.356	−	602.003i	1.38612	−	0.866191i
$696$	−74.9805			−0.107731
$697$	71.2665	−	71.2665i	0.102247	−	0.102247i
$698$	247.408	+	247.408i	0.354452	+	0.354452i
$699$			252.431i			0.361131i
$700$	−343.254	+	118.210i	−0.490363	+	0.168871i
$701$	366.250			0.522468			0.261234	−	0.965276i	$-0.415871\pi$
$701$	366.250			0.522468			0.261234	+	0.965276i	$0.415871\pi$
$702$	35.6525	−	35.6525i	0.0507871	−	0.0507871i
$703$	16.0474	+	16.0474i	0.0228270	+	0.0228270i
$704$		−	150.789i		−	0.214189i
$705$	138.014	+	220.857i	0.195764	+	0.313272i
$706$	−608.159			−0.861415
$707$	853.656	−	853.656i	1.20743	−	1.20743i
$708$	90.7732	+	90.7732i	0.128211	+	0.128211i
$709$			113.568i			0.160180i	0.996788	+	0.0800902i	$0.0255208\pi$
$709$			113.568i			0.160180i	−0.996788	+	0.0800902i	$0.974479\pi$
$710$	−57.7675	−	13.3353i	−0.0813627	−	0.0187821i
$711$	−311.626			−0.438293
$712$	280.422	−	280.422i	0.393852	−	0.393852i
$713$	61.1146	+	61.1146i	0.0857147	+	0.0857147i
$714$		−	208.295i		−	0.291730i
$715$	−145.446	+	630.065i	−0.203422	+	0.881209i
$716$	47.6410			0.0665378
$717$	483.852	−	483.852i	0.674829	−	0.674829i
$718$	257.894	+	257.894i	0.359184	+	0.359184i
$719$			597.111i			0.830475i	0.909713	+	0.415237i	$0.136301\pi$
$719$			597.111i			0.830475i	−0.909713	+	0.415237i	$0.863699\pi$
$720$	50.8821	−	31.7963i	0.0706696	−	0.0441616i
$721$	111.536			0.154696
$722$	356.966	−	356.966i	0.494413	−	0.494413i
$723$	327.234	+	327.234i	0.452606	+	0.452606i
$724$		−	421.962i		−	0.582820i
$725$	343.916	+	167.719i	0.474367	+	0.231337i
$726$	573.847			0.790422
$727$	−648.585	+	648.585i	−0.892138	+	0.892138i	−0.994724	−	0.102586i	$-0.967288\pi$
$727$	−648.585	+	648.585i	−0.892138	+	0.892138i	0.102586	+	0.994724i	$0.467288\pi$
$728$	−99.6370	−	99.6370i	−0.136864	−	0.136864i
$729$		−	27.0000i		−	0.0370370i
$730$	418.617	+	669.893i	0.573448	+	0.917662i
$731$	314.025			0.429582
$732$	161.425	−	161.425i	0.220525	−	0.220525i
$733$	998.046	+	998.046i	1.36159	+	1.36159i	0.871892	+	0.489699i	$0.162893\pi$
$733$	998.046	+	998.046i	1.36159	+	1.36159i	0.489699	+	0.871892i	$0.337107\pi$
$734$			587.695i			0.800675i
$735$	31.3794	+	7.24375i	0.0426931	+	0.00985544i
$736$	27.1293			0.0368605
$737$	1328.18	−	1328.18i	1.80215	−	1.80215i
$738$	−25.8167	−	25.8167i	−0.0349820	−	0.0349820i
$739$		−	1236.71i		−	1.67349i	−0.547592	−	0.836745i	$-0.684456\pi$
$739$		−	1236.71i		−	1.67349i	0.547592	−	0.836745i	$-0.315544\pi$
$740$	25.4164	−	110.102i	0.0343464	−	0.148787i
$741$	23.8681			0.0322107
$742$	−315.233	+	315.233i	−0.424843	+	0.424843i
$743$	666.268	+	666.268i	0.896727	+	0.896727i	0.995145	−	0.0984183i	$-0.0313783\pi$
$743$	666.268	+	666.268i	0.896727	+	0.896727i	−0.0984183	+	0.995145i	$0.531378\pi$
$744$			88.2880i			0.118667i
$745$	−594.607	+	371.571i	−0.798131	+	0.498753i
$746$	828.725			1.11089
$747$	−113.390	+	113.390i	−0.151793	+	0.151793i
$748$	−312.188	−	312.188i	−0.417364	−	0.417364i
$749$			191.738i			0.255992i
$750$	−304.507	+	32.0264i	−0.406009	+	0.0427019i
$751$	546.487			0.727679			0.363840	−	0.931462i	$-0.381466\pi$
$751$	546.487			0.727679			0.363840	+	0.931462i	$0.381466\pi$
$752$	−85.0571	+	85.0571i	−0.113108	+	0.113108i
$753$	−410.882	−	410.882i	−0.545660	−	0.545660i
$754$			148.514i			0.196968i
$755$	569.290	+	911.007i	0.754026	+	1.20663i
$756$	−75.4561			−0.0998096
$757$	395.410	−	395.410i	0.522338	−	0.522338i	−0.395939	−	0.918277i	$-0.629581\pi$
$757$	395.410	−	395.410i	0.522338	−	0.522338i	0.918277	+	0.395939i	$0.129581\pi$
$758$	308.141	+	308.141i	0.406518	+	0.406518i
$759$			156.569i			0.206283i
$760$	27.6752	+	6.38865i	0.0364148	+	0.00840612i
$761$	61.4799			0.0807883			0.0403941	−	0.999184i	$-0.487139\pi$
$761$	61.4799			0.0807883			0.0403941	+	0.999184i	$0.487139\pi$
$762$	−174.207	+	174.207i	−0.228618	+	0.228618i
$763$	−527.845	−	527.845i	−0.691802	−	0.691802i
$764$		−	214.371i		−	0.280590i
$765$	39.5145	−	171.174i	0.0516529	−	0.223757i
$766$	412.390			0.538368
$767$	179.794	−	179.794i	0.234412	−	0.234412i
$768$	19.5959	+	19.5959i	0.0255155	+	0.0255155i
$769$		−	430.433i		−	0.559731i	−0.960039	−	0.279865i	$-0.909710\pi$
$769$		−	430.433i		−	0.559731i	0.960039	−	0.279865i	$-0.0902899\pi$
$770$	820.657	−	512.830i	1.06579	−	0.666013i
$771$	154.345			0.200188
$772$	−409.850	+	409.850i	−0.530894	+	0.530894i
$773$	171.075	+	171.075i	0.221313	+	0.221313i	0.809051	−	0.587738i	$-0.199981\pi$
$773$	171.075	+	171.075i	0.221313	+	0.221313i	−0.587738	+	0.809051i	$0.699981\pi$
$774$		−	113.757i		−	0.146973i
$775$	197.486	−	404.954i	0.254821	−	0.522522i
$776$	−421.625			−0.543331
$777$	−100.484	+	100.484i	−0.129323	+	0.129323i
$778$	474.840	+	474.840i	0.610334	+	0.610334i
$779$		−	17.2834i		−	0.0221866i
$780$	−62.9789	−	100.782i	−0.0807421	−	0.129208i
$781$	158.035			0.202349
$782$	56.1675	−	56.1675i	0.0718254	−	0.0718254i
$783$	56.2354	+	56.2354i	0.0718204	+	0.0718204i
$784$			14.8747i			0.0189728i
$785$	823.218	+	190.035i	1.04869	+	0.242082i
$786$	−332.501			−0.423029
$787$	76.7505	−	76.7505i	0.0975229	−	0.0975229i	−0.656662	−	0.754185i	$-0.728032\pi$
$787$	76.7505	−	76.7505i	0.0975229	−	0.0975229i	0.754185	+	0.656662i	$0.228032\pi$
$788$	368.322	+	368.322i	0.467414	+	0.467414i
$789$		−	348.841i		−	0.442130i
$790$	−165.212	+	715.688i	−0.209129	+	0.905934i
$791$	−188.094			−0.237792
$792$	−113.092	+	113.092i	−0.142793	+	0.142793i
$793$	−319.733	−	319.733i	−0.403194	−	0.403194i
$794$			480.593i			0.605281i
$795$	−318.856	+	199.254i	−0.401077	+	0.250633i
$796$	208.808			0.262322
$797$	661.678	−	661.678i	0.830211	−	0.830211i	−0.157334	−	0.987545i	$-0.550290\pi$
$797$	661.678	−	661.678i	0.830211	−	0.830211i	0.987545	+	0.157334i	$0.0502900\pi$
$798$	−25.2576	−	25.2576i	−0.0316512	−	0.0316512i
$799$			352.198i			0.440798i
$800$	−46.0485	−	133.714i	−0.0575606	−	0.167143i
$801$	−420.634			−0.525136
$802$	201.562	−	201.562i	0.251324	−	0.251324i
$803$	−1488.92	−	1488.92i	−1.85420	−	1.85420i
$804$			345.210i			0.429365i
$805$	92.2661	+	147.649i	0.114616	+	0.183415i
$806$	174.872			0.216962
$807$	−253.673	+	253.673i	−0.314340	+	0.314340i
$808$	332.541	+	332.541i	0.411561	+	0.411561i
$809$			891.779i			1.10232i	0.834399	+	0.551161i	$0.185815\pi$
$809$			891.779i			1.10232i	−0.834399	+	0.551161i	$0.814185\pi$
$810$	−62.0089	−	14.3144i	−0.0765542	−	0.0176720i
$811$	1023.79			1.26238			0.631191	−	0.775627i	$-0.282566\pi$
$811$	1023.79			1.26238			0.631191	+	0.775627i	$0.282566\pi$
$812$	157.159	−	157.159i	0.193546	−	0.193546i
$813$	−465.766	−	465.766i	−0.572898	−	0.572898i
$814$			301.207i			0.370033i
$815$	−35.9998	+	155.949i	−0.0441715	+	0.191348i
$816$	81.1412			0.0994378
$817$	38.0783	−	38.0783i	0.0466075	−	0.0466075i
$818$	675.609	+	675.609i	0.825928	+	0.825928i
$819$			149.455i			0.182485i
$820$	−72.9783	+	45.6042i	−0.0889979	+	0.0556149i
$821$	649.979			0.791692			0.395846	−	0.918317i	$-0.370451\pi$
$821$	649.979			0.791692			0.395846	+	0.918317i	$0.370451\pi$
$822$	−148.410	+	148.410i	−0.180547	+	0.180547i
$823$	−512.246	−	512.246i	−0.622413	−	0.622413i	0.323735	−	0.946148i	$-0.395061\pi$
$823$	−512.246	−	512.246i	−0.622413	−	0.622413i	−0.946148	+	0.323735i	$0.895061\pi$
$824$			43.4489i			0.0527292i
$825$	771.692	−	265.755i	0.935385	−	0.322127i
$826$	−380.522			−0.460680
$827$	223.488	−	223.488i	0.270240	−	0.270240i	−0.558957	−	0.829197i	$-0.688798\pi$
$827$	223.488	−	223.488i	0.270240	−	0.270240i	0.829197	+	0.558957i	$0.188798\pi$
$828$	−20.3470	−	20.3470i	−0.0245737	−	0.0245737i
$829$			947.232i			1.14262i	0.820734	+	0.571310i	$0.193565\pi$
$829$			947.232i			1.14262i	−0.820734	+	0.571310i	$0.806435\pi$
$830$	200.298	+	320.528i	0.241323	+	0.386178i
$831$	497.102			0.598198
$832$	38.8135	−	38.8135i	0.0466509	−	0.0466509i
$833$	30.7960	+	30.7960i	0.0369700	+	0.0369700i
$834$		−	556.517i		−	0.667286i
$835$	−358.078	−	82.6600i	−0.428836	−	0.0989941i
$836$	−75.7112			−0.0905637
$837$	66.2160	−	66.2160i	0.0791111	−	0.0791111i
$838$	384.622	+	384.622i	0.458976	+	0.458976i
$839$		−	200.541i		−	0.239024i	−0.992833	−	0.119512i	$-0.961867\pi$
$839$		−	200.541i		−	0.239024i	0.992833	−	0.119512i	$-0.0381330\pi$
$840$	−40.0039	+	173.294i	−0.0476237	+	0.206303i
$841$	606.747			0.721459
$842$	−454.018	+	454.018i	−0.539214	+	0.539214i
$843$	−264.384	−	264.384i	−0.313623	−	0.313623i
$844$		−	258.594i		−	0.306391i
$845$	516.972	−	323.056i	0.611801	−	0.382315i
$846$	127.586			0.150810
$847$	−1202.78	+	1202.78i	−1.42005	+	1.42005i
$848$	−122.799	−	122.799i	−0.144810	−	0.144810i
$849$		−	690.699i		−	0.813544i
$850$	−372.174	−	181.500i	−0.437852	−	0.213529i
$851$	−54.1917			−0.0636801
$852$	−20.5375	+	20.5375i	−0.0241051	+	0.0241051i
$853$	−595.648	−	595.648i	−0.698298	−	0.698298i	0.265745	−	0.964043i	$-0.414382\pi$
$853$	−595.648	−	595.648i	−0.698298	−	0.698298i	−0.964043	+	0.265745i	$0.914382\pi$
$854$			676.693i			0.792380i
$855$	−15.9649	−	25.5479i	−0.0186724	−	0.0298806i
$856$	−74.6913			−0.0872562
$857$	252.861	−	252.861i	0.295054	−	0.295054i	−0.544019	−	0.839073i	$-0.683098\pi$
$857$	252.861	−	252.861i	0.295054	−	0.295054i	0.839073	+	0.544019i	$0.183098\pi$
$858$	224.001	+	224.001i	0.261073	+	0.261073i
$859$			377.138i			0.439043i	0.975608	+	0.219522i	$0.0704497\pi$
$859$			377.138i			0.439043i	−0.975608	+	0.219522i	$0.929550\pi$
$860$	−261.258	−	60.3097i	−0.303788	−	0.0701275i
$861$	108.224			0.125695
$862$	−241.139	+	241.139i	−0.279743	+	0.279743i
$863$	−131.835	−	131.835i	−0.152764	−	0.152764i	0.626587	−	0.779351i	$-0.284451\pi$
$863$	−131.835	−	131.835i	−0.152764	−	0.152764i	−0.779351	+	0.626587i	$0.784451\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	290.270	−	1257.43i	0.335572	−	1.45368i
$866$	−556.865			−0.643031
$867$	−185.960	+	185.960i	−0.214486	+	0.214486i
$868$	−185.052	−	185.052i	−0.213193	−	0.213193i
$869$		−	1957.91i		−	2.25306i
$870$	158.965	−	99.3377i	0.182719	−	0.114181i
$871$	683.755			0.785023
$872$	205.622	−	205.622i	0.235805	−	0.235805i
$873$	316.219	+	316.219i	0.362221	+	0.362221i
$874$		−	13.6216i		−	0.0155854i
$875$	571.119	−	705.374i	0.652707	−	0.806142i
$876$	386.988			0.441767
$877$	−21.3642	+	21.3642i	−0.0243606	+	0.0243606i	−0.719182	−	0.694822i	$-0.755483\pi$
$877$	−21.3642	+	21.3642i	−0.0243606	+	0.0243606i	0.694822	+	0.719182i	$0.255483\pi$
$878$	439.356	+	439.356i	0.500406	+	0.500406i
$879$		−	657.954i		−	0.748525i
$880$	199.773	+	319.687i	0.227015	+	0.363280i
$881$	1643.48			1.86547			0.932737	−	0.360556i	$-0.117413\pi$
$881$	1643.48			1.86547			0.932737	+	0.360556i	$0.117413\pi$
$882$	11.1560	−	11.1560i	0.0126486	−	0.0126486i
$883$	−784.243	−	784.243i	−0.888158	−	0.888158i	0.106188	−	0.994346i	$-0.466135\pi$
$883$	−784.243	−	784.243i	−0.888158	−	0.888158i	−0.994346	+	0.106188i	$0.966135\pi$
$884$		−	160.716i		−	0.181805i
$885$	−312.708	−	72.1867i	−0.353342	−	0.0815669i
$886$	−523.212			−0.590532
$887$	473.986	−	473.986i	0.534369	−	0.534369i	−0.387500	−	0.921870i	$-0.626661\pi$
$887$	473.986	−	473.986i	0.534369	−	0.534369i	0.921870	+	0.387500i	$0.126661\pi$
$888$	−39.1435	−	39.1435i	−0.0440805	−	0.0440805i
$889$		−	730.276i		−	0.821458i
$890$	−223.004	+	966.037i	−0.250566	+	1.08544i
$891$	169.638			0.190390
$892$	−36.8733	+	36.8733i	−0.0413378	+	0.0413378i
$893$	42.7071	+	42.7071i	0.0478243	+	0.0478243i
$894$			343.496i			0.384224i
$895$	−101.003	+	63.1171i	−0.112853	+	0.0705219i
$896$	−82.1462			−0.0916810
$897$	−40.3012	+	40.3012i	−0.0449289	+	0.0449289i
$898$	876.612	+	876.612i	0.976183	+	0.976183i
$899$			275.828i			0.306817i
$900$	−65.7494	+	134.822i	−0.0730549	+	0.149802i
$901$	−508.476			−0.564346
$902$	162.203	−	162.203i	0.179826	−	0.179826i
$903$	238.435	+	238.435i	0.264048	+	0.264048i
$904$		−	73.2718i		−	0.0810529i
$905$	559.035	+	894.597i	0.617718	+	0.988505i
$906$	526.275			0.580878
$907$	676.741	−	676.741i	0.746131	−	0.746131i	−0.227619	−	0.973750i	$-0.573094\pi$
$907$	676.741	−	676.741i	0.746131	−	0.746131i	0.973750	+	0.227619i	$0.0730941\pi$
$908$	236.816	+	236.816i	0.260811	+	0.260811i
$909$		−	498.812i		−	0.548748i
$910$	343.243	+	79.2355i	0.377190	+	0.0870720i
$911$	−273.437			−0.300151			−0.150075	−	0.988675i	$-0.547952\pi$
$911$	−273.437			−0.300151			−0.150075	+	0.988675i	$0.547952\pi$
$912$	9.83910	−	9.83910i	0.0107885	−	0.0107885i
$913$	−712.414	−	712.414i	−0.780300	−	0.780300i
$914$		−	36.0696i		−	0.0394635i
$915$	−128.372	+	556.098i	−0.140297	+	0.607757i
$916$	−79.7477			−0.0870608
$917$	696.923	−	696.923i	0.760003	−	0.760003i
$918$	−60.8559	−	60.8559i	−0.0662918	−	0.0662918i
$919$		−	404.328i		−	0.439965i	−0.975504	−	0.219983i	$-0.929400\pi$
$919$		−	404.328i		−	0.439965i	0.975504	−	0.219983i	$-0.0706001\pi$
$920$	−57.5166	+	35.9422i	−0.0625180	+	0.0390676i
$921$	594.994			0.646030
$922$	746.316	−	746.316i	0.809453	−	0.809453i
$923$	40.6786	+	40.6786i	0.0440722	+	0.0440722i
$924$		−	474.082i		−	0.513076i
$925$	91.9834	+	267.099i	0.0994416	+	0.288756i
$926$	−356.944			−0.385469
$927$	32.5866	−	32.5866i	0.0351528	−	0.0351528i
$928$	61.2213	+	61.2213i	0.0659713	+	0.0659713i
$929$		−	274.030i		−	0.294973i	−0.989064	−	0.147487i	$-0.952882\pi$
$929$		−	274.030i		−	0.294973i	0.989064	−	0.147487i	$-0.0471183\pi$
$930$	−116.968	−	187.178i	−0.125772	−	0.201267i
$931$	7.46858			0.00802211
$932$	206.109	−	206.109i	0.221147	−	0.221147i
$933$	−253.962	−	253.962i	−0.272199	−	0.272199i
$934$			493.606i			0.528486i
$935$	1075.47	+	248.265i	1.15023	+	0.265524i
$936$	−58.2203			−0.0622012
$937$	39.3211	−	39.3211i	0.0419649	−	0.0419649i	−0.685813	−	0.727778i	$-0.740553\pi$
$937$	39.3211	−	39.3211i	0.0419649	−	0.0419649i	0.727778	+	0.685813i	$0.240553\pi$
$938$	−723.560	−	723.560i	−0.771386	−	0.771386i
$939$		−	689.474i		−	0.734264i
$940$	67.6410	−	293.016i	0.0719585	−	0.311720i
$941$	−1723.79			−1.83187			−0.915935	−	0.401327i	$-0.868549\pi$
$941$	−1723.79			−1.83187			−0.915935	+	0.401327i	$0.868549\pi$
$942$	292.671	−	292.671i	0.310691	−	0.310691i
$943$	29.1829	+	29.1829i	0.0309469	+	0.0309469i
$944$		−	148.232i		−	0.157026i
$945$	159.974	−	99.9678i	0.169284	−	0.105786i
$946$	714.724			0.755522
$947$	205.982	−	205.982i	0.217510	−	0.217510i	−0.589938	−	0.807448i	$-0.700848\pi$
$947$	205.982	−	205.982i	0.217510	−	0.217510i	0.807448	+	0.589938i	$0.200848\pi$
$948$	254.442	+	254.442i	0.268398	+	0.268398i
$949$		−	766.504i		−	0.807697i
$950$	−67.1379	+	23.1209i	−0.0706715	+	0.0243378i
$951$	599.354			0.630235
$952$	−170.072	+	170.072i	−0.178647	+	0.178647i
$953$	−820.248	−	820.248i	−0.860701	−	0.860701i	0.130719	−	0.991419i	$-0.458271\pi$
$953$	−820.248	−	820.248i	−0.860701	−	0.860701i	−0.991419	+	0.130719i	$0.958271\pi$
$954$			184.198i			0.193080i
$955$	284.009	+	454.486i	0.297391	+	0.475901i
$956$	−790.127			−0.826493
$957$	−353.321	+	353.321i	−0.369196	+	0.369196i
$958$	171.427	+	171.427i	0.178943	+	0.178943i
$959$		−	622.135i		−	0.648733i
$960$	−67.5067	−	15.5835i	−0.0703195	−	0.0162328i
$961$	−636.218			−0.662037
$962$	−77.5314	+	77.5314i	−0.0805939	+	0.0805939i
$963$	56.0185	+	56.0185i	0.0581708	+	0.0581708i
$964$		−	534.371i		−	0.554327i
$965$	325.930	−	1411.91i	0.337751	−	1.46312i
$966$	85.2946			0.0882967
$967$	524.926	−	524.926i	0.542839	−	0.542839i	−0.381521	−	0.924360i	$-0.624600\pi$
$967$	524.926	−	524.926i	0.542839	−	0.542839i	0.924360	+	0.381521i	$0.124600\pi$
$968$	−468.544	−	468.544i	−0.484033	−	0.484033i
$969$		−	40.7410i		−	0.0420443i
$970$	893.882	−	558.589i	0.921528	−	0.575865i
$971$	−1740.45			−1.79243			−0.896215	−	0.443621i	$-0.853694\pi$
$971$	−1740.45			−1.79243			−0.896215	+	0.443621i	$0.853694\pi$
$972$	−22.0454	+	22.0454i	−0.0226805	+	0.0226805i
$973$	1166.46	+	1166.46i	1.19883	+	1.19883i
$974$		−	137.797i		−	0.141475i
$975$	267.042	+	130.230i	0.273889	+	0.133569i
$976$	−263.605			−0.270087
$977$	−1092.92	+	1092.92i	−1.11865	+	1.11865i	−0.126706	+	0.991940i	$0.540441\pi$
$977$	−1092.92	+	1092.92i	−1.11865	+	1.11865i	−0.991940	+	0.126706i	$0.959559\pi$
$978$	55.4430	+	55.4430i	0.0566902	+	0.0566902i
$979$		−	2642.79i		−	2.69948i
$980$	−19.7067	−	31.5357i	−0.0201089	−	0.0321793i
$981$	−308.433			−0.314407
$982$	−716.560	+	716.560i	−0.729695	+	0.729695i
$983$	677.549	+	677.549i	0.689266	+	0.689266i	0.962070	−	0.272804i	$-0.0879509\pi$
$983$	677.549	+	677.549i	0.689266	+	0.689266i	−0.272804	+	0.962070i	$0.587951\pi$
$984$			42.1585i			0.0428440i
$985$	−1268.85	−	292.905i	−1.28817	−	0.297366i
$986$	253.500			0.257100
$987$	−267.420	+	267.420i	−0.270942	+	0.270942i
$988$	−19.4883	−	19.4883i	−0.0197250	−	0.0197250i
$989$			128.590i			0.130020i
$990$	89.9355	−	389.595i	0.0908439	−	0.393530i
$991$	−1816.56			−1.83305			−0.916527	−	0.399973i	$-0.869019\pi$
$991$	−1816.56			−1.83305			−0.916527	+	0.399973i	$0.869019\pi$
$992$	72.0868	−	72.0868i	0.0726682	−	0.0726682i
$993$	782.307	+	782.307i	0.787822	+	0.787822i
$994$		−	86.0934i		−	0.0866131i
$995$	−442.692	+	276.639i	−0.444917	+	0.278029i
$996$	185.164			0.185908
$997$	−369.067	+	369.067i	−0.370178	+	0.370178i	−0.867542	−	0.497364i	$-0.834301\pi$
$997$	−369.067	+	369.067i	−0.370178	+	0.370178i	0.497364	+	0.867542i	$0.334301\pi$
$998$	−103.164	−	103.164i	−0.103371	−	0.103371i
$999$			58.7153i			0.0587740i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.a.553.15	yes	40
5.2	odd	4	inner	690.3.k.a.277.15	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.a.277.15	✓	40	5.2	odd	4	inner
690.3.k.a.553.15	yes	40	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)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(2.64969 + 4.24018i) q^{5} +2.44949 q^{6} +(-5.13413 + 5.13413i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(2.64969 + 4.24018i) q^{5} +2.44949 q^{6} +(-5.13413 + 5.13413i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(6.88987 + 1.59048i) q^{10} -18.8487 q^{11} +(2.44949 - 2.44949i) q^{12} +(-4.85169 - 4.85169i) q^{13} +10.2683i q^{14} +(-1.94794 + 8.43834i) q^{15} -4.00000 q^{16} +(-8.28144 + 8.28144i) q^{17} +(3.00000 + 3.00000i) q^{18} +2.00840i q^{19} +(8.48036 - 5.29939i) q^{20} -12.5760 q^{21} +(-18.8487 + 18.8487i) q^{22} +(-3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(-10.9582 + 22.4704i) q^{25} -9.70339 q^{26} +(-3.67423 + 3.67423i) q^{27} +(10.2683 + 10.2683i) q^{28} -15.3053i q^{29} +(6.49040 + 10.3863i) q^{30} -18.0217 q^{31} +(-4.00000 + 4.00000i) q^{32} +(-23.0848 - 23.0848i) q^{33} +16.5629i q^{34} +(-35.3735 - 8.16576i) q^{35} +6.00000 q^{36} +(7.99013 - 7.99013i) q^{37} +(2.00840 + 2.00840i) q^{38} -11.8842i q^{39} +(3.18097 - 13.7797i) q^{40} -8.60556 q^{41} +(-12.5760 + 12.5760i) q^{42} +(-18.9595 - 18.9595i) q^{43} +37.6973i q^{44} +(-12.7205 + 7.94908i) q^{45} -6.78233 q^{46} +(21.2643 - 21.2643i) q^{47} +(-4.89898 - 4.89898i) q^{48} -3.71868i q^{49} +(11.5121 + 33.4286i) q^{50} -20.2853 q^{51} +(-9.70339 + 9.70339i) q^{52} +(30.6997 + 30.6997i) q^{53} +7.34847i q^{54} +(-49.9432 - 79.9217i) q^{55} +20.5365 q^{56} +(-2.45978 + 2.45978i) q^{57} +(-15.3053 - 15.3053i) q^{58} +37.0580i q^{59} +(16.8767 + 3.89587i) q^{60} +65.9013 q^{61} +(-18.0217 + 18.0217i) q^{62} +(-15.4024 - 15.4024i) q^{63} +8.00000i q^{64} +(7.71654 - 33.4276i) q^{65} -46.1696 q^{66} +(-70.4656 + 70.4656i) q^{67} +(16.5629 + 16.5629i) q^{68} -8.30662i q^{69} +(-43.5393 + 27.2078i) q^{70} -8.38441 q^{71} +(6.00000 - 6.00000i) q^{72} +(78.9935 + 78.9935i) q^{73} -15.9803i q^{74} +(-40.9415 + 14.0994i) q^{75} +4.01680 q^{76} +(96.7715 - 96.7715i) q^{77} +(-11.8842 - 11.8842i) q^{78} +103.875i q^{79} +(-10.5988 - 16.9607i) q^{80} -9.00000 q^{81} +(-8.60556 + 8.60556i) q^{82} +(37.7965 + 37.7965i) q^{83} +25.1520i q^{84} +(-57.0581 - 13.1715i) q^{85} -37.9191 q^{86} +(18.7451 - 18.7451i) q^{87} +(37.6973 + 37.6973i) q^{88} +140.211i q^{89} +(-4.77145 + 20.6696i) q^{90} +49.8185 q^{91} +(-6.78233 + 6.78233i) q^{92} +(-22.0720 - 22.0720i) q^{93} -42.5286i q^{94} +(-8.51597 + 5.32164i) q^{95} -9.79796 q^{96} +(105.406 - 105.406i) q^{97} +(-3.71868 - 3.71868i) q^{98} -56.5460i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8}+O(q^{10}) \) 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8	\( 40 q + 40 q^{2} - 8 q^{5} - 8 q^{7} - 80 q^{8} - 16 q^{10} + 32 q^{11} + 16 q^{13} + 24 q^{15} - 160 q^{16} - 48 q^{17} + 120 q^{18} - 16 q^{20} - 96 q^{21} + 32 q^{22} + 32 q^{26} + 16 q^{28} + 24 q^{30} + 152 q^{31} - 160 q^{32} - 24 q^{33} + 48 q^{35} + 240 q^{36} + 216 q^{37} + 16 q^{38} - 168 q^{41} - 96 q^{42} - 48 q^{43} + 24 q^{45} - 232 q^{47} - 40 q^{50} + 32 q^{52} + 8 q^{53} - 272 q^{55} + 32 q^{56} - 136 q^{58} - 64 q^{61} + 152 q^{62} - 24 q^{63} + 416 q^{65} - 48 q^{66} - 32 q^{67} + 96 q^{68} + 88 q^{70} - 104 q^{71} + 240 q^{72} + 480 q^{73} - 216 q^{75} + 32 q^{76} + 280 q^{77} - 192 q^{78} + 32 q^{80} - 360 q^{81} - 168 q^{82} - 576 q^{83} - 208 q^{85} - 96 q^{86} + 24 q^{87} - 64 q^{88} + 144 q^{91} + 96 q^{93} + 168 q^{95} + 24 q^{97} + 176 q^{98}+O(q^{100}) \) 40 * q + 40 * q^2 - 8 * q^5 - 8 * q^7 - 80 * q^8 - 16 * q^10 + 32 * q^11 + 16 * q^13 + 24 * q^15 - 160 * q^16 - 48 * q^17 + 120 * q^18 - 16 * q^20 - 96 * q^21 + 32 * q^22 + 32 * q^26 + 16 * q^28 + 24 * q^30 + 152 * q^31 - 160 * q^32 - 24 * q^33 + 48 * q^35 + 240 * q^36 + 216 * q^37 + 16 * q^38 - 168 * q^41 - 96 * q^42 - 48 * q^43 + 24 * q^45 - 232 * q^47 - 40 * q^50 + 32 * q^52 + 8 * q^53 - 272 * q^55 + 32 * q^56 - 136 * q^58 - 64 * q^61 + 152 * q^62 - 24 * q^63 + 416 * q^65 - 48 * q^66 - 32 * q^67 + 96 * q^68 + 88 * q^70 - 104 * q^71 + 240 * q^72 + 480 * q^73 - 216 * q^75 + 32 * q^76 + 280 * q^77 - 192 * q^78 + 32 * q^80 - 360 * q^81 - 168 * q^82 - 576 * q^83 - 208 * q^85 - 96 * q^86 + 24 * q^87 - 64 * q^88 + 144 * q^91 + 96 * q^93 + 168 * q^95 + 24 * q^97 + 176 * q^98

Introduction

L-functions

Modular forms

Varieties

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