LMFDB - Embedded newform 690.3.k.b.553.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("690.277");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			553.7
Character	$\chi$	$=$	690.553
Dual form			690.3.k.b.277.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(4.29808 + 2.55470i) q^{5} +2.44949 q^{6} +(4.10164 - 4.10164i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(4.29808 + 2.55470i) q^{5} +2.44949 q^{6} +(4.10164 - 4.10164i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(-6.85278 + 1.74338i) q^{10} -12.9366 q^{11} +(-2.44949 + 2.44949i) q^{12} +(-7.48881 - 7.48881i) q^{13} +8.20327i q^{14} +(-2.13519 - 8.39291i) q^{15} -4.00000 q^{16} +(-23.2692 + 23.2692i) q^{17} +(-3.00000 - 3.00000i) q^{18} -2.66503i q^{19} +(5.10941 - 8.59616i) q^{20} -10.0469 q^{21} +(12.9366 - 12.9366i) q^{22} +(-3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(11.9470 + 21.9606i) q^{25} +14.9776 q^{26} +(3.67423 - 3.67423i) q^{27} +(-8.20327 - 8.20327i) q^{28} +13.0859i q^{29} +(10.5281 + 6.25772i) q^{30} +21.6535 q^{31} +(4.00000 - 4.00000i) q^{32} +(15.8440 + 15.8440i) q^{33} -46.5384i q^{34} +(28.1076 - 7.15070i) q^{35} +6.00000 q^{36} +(-1.73017 + 1.73017i) q^{37} +(2.66503 + 2.66503i) q^{38} +18.3438i q^{39} +(3.48675 + 13.7056i) q^{40} -41.1577 q^{41} +(10.0469 - 10.0469i) q^{42} +(-2.10451 - 2.10451i) q^{43} +25.8731i q^{44} +(-7.66411 + 12.8942i) q^{45} +6.78233 q^{46} +(-2.10608 + 2.10608i) q^{47} +(4.89898 + 4.89898i) q^{48} +15.3532i q^{49} +(-33.9076 - 10.0137i) q^{50} +56.9977 q^{51} +(-14.9776 + 14.9776i) q^{52} +(-8.58604 - 8.58604i) q^{53} +7.34847i q^{54} +(-55.6024 - 33.0491i) q^{55} +16.4065 q^{56} +(-3.26398 + 3.26398i) q^{57} +(-13.0859 - 13.0859i) q^{58} +65.6109i q^{59} +(-16.7858 + 4.27038i) q^{60} -39.1540 q^{61} +(-21.6535 + 21.6535i) q^{62} +(12.3049 + 12.3049i) q^{63} +8.00000i q^{64} +(-13.0558 - 51.3192i) q^{65} -31.6880 q^{66} +(-42.4434 + 42.4434i) q^{67} +(46.5384 + 46.5384i) q^{68} +8.30662i q^{69} +(-20.9569 + 35.2583i) q^{70} -119.297 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-86.2712 - 86.2712i) q^{73} -3.46035i q^{74} +(12.2642 - 41.5282i) q^{75} -5.33005 q^{76} +(-53.0611 + 53.0611i) q^{77} +(-18.3438 - 18.3438i) q^{78} +63.9660i q^{79} +(-17.1923 - 10.2188i) q^{80} -9.00000 q^{81} +(41.1577 - 41.1577i) q^{82} +(98.1743 + 98.1743i) q^{83} +20.0938i q^{84} +(-159.459 + 40.5670i) q^{85} +4.20901 q^{86} +(16.0268 - 16.0268i) q^{87} +(-25.8731 - 25.8731i) q^{88} +156.409i q^{89} +(-5.23013 - 20.5583i) q^{90} -61.4328 q^{91} +(-6.78233 + 6.78233i) q^{92} +(-26.5200 - 26.5200i) q^{93} -4.21215i q^{94} +(6.80835 - 11.4545i) q^{95} -9.79796 q^{96} +(49.2914 - 49.2914i) q^{97} +(-15.3532 - 15.3532i) q^{98} -38.8097i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$4$		−	2.00000i		−	0.500000i
$5$	4.29808	+	2.55470i	0.859616	+	0.510941i
$5$	4.29808	+	2.55470i	0.859616	+	0.510941i
$6$	2.44949			0.408248
$7$	4.10164	−	4.10164i	0.585948	−	0.585948i	−0.350583	−	0.936532i	$-0.614017\pi$
$7$	4.10164	−	4.10164i	0.585948	−	0.585948i	0.936532	+	0.350583i	$0.114017\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$			3.00000i			0.333333i
$10$	−6.85278	+	1.74338i	−0.685278	+	0.174338i
$11$	−12.9366			−1.17605			−0.588025	−	0.808842i	$-0.700095\pi$
$11$	−12.9366			−1.17605			−0.588025	+	0.808842i	$0.700095\pi$
$12$	−2.44949	+	2.44949i	−0.204124	+	0.204124i
$13$	−7.48881	−	7.48881i	−0.576062	−	0.576062i	0.357754	−	0.933816i	$-0.383543\pi$
$13$	−7.48881	−	7.48881i	−0.576062	−	0.576062i	−0.933816	+	0.357754i	$0.883543\pi$
$14$			8.20327i			0.585948i
$15$	−2.13519	−	8.39291i	−0.142346	−	0.559527i
$16$	−4.00000			−0.250000
$17$	−23.2692	+	23.2692i	−1.36878	+	1.36878i	−0.506591	+	0.862186i	$0.669095\pi$
$17$	−23.2692	+	23.2692i	−1.36878	+	1.36878i	−0.862186	+	0.506591i	$0.830905\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$		−	2.66503i		−	0.140265i	−0.997538	−	0.0701323i	$-0.977658\pi$
$19$		−	2.66503i		−	0.140265i	0.997538	−	0.0701323i	$-0.0223421\pi$
$20$	5.10941	−	8.59616i	0.255470	−	0.429808i
$21$	−10.0469			−0.478425
$22$	12.9366	−	12.9366i	0.588025	−	0.588025i
$23$	−3.39116	−	3.39116i	−0.147442	−	0.147442i
$23$	−3.39116	−	3.39116i	−0.147442	−	0.147442i
$24$		−	4.89898i		−	0.204124i
$25$	11.9470	+	21.9606i	0.477879	+	0.878425i
$26$	14.9776			0.576062
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	−8.20327	−	8.20327i	−0.292974	−	0.292974i
$29$			13.0859i			0.451237i	0.974216	+	0.225618i	$0.0724402\pi$
$29$			13.0859i			0.451237i	−0.974216	+	0.225618i	$0.927560\pi$
$30$	10.5281	+	6.25772i	0.350937	+	0.208591i
$31$	21.6535			0.698500			0.349250	−	0.937030i	$-0.386436\pi$
$31$	21.6535			0.698500			0.349250	+	0.937030i	$0.386436\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	15.8440	+	15.8440i	0.480121	+	0.480121i
$34$		−	46.5384i		−	1.36878i
$35$	28.1076	−	7.15070i	0.803075	−	0.204306i
$36$	6.00000			0.166667
$37$	−1.73017	+	1.73017i	−0.0467614	+	0.0467614i	−0.730101	−	0.683339i	$-0.760527\pi$
$37$	−1.73017	+	1.73017i	−0.0467614	+	0.0467614i	0.683339	+	0.730101i	$0.260527\pi$
$38$	2.66503	+	2.66503i	0.0701323	+	0.0701323i
$39$			18.3438i			0.470353i
$40$	3.48675	+	13.7056i	0.0871689	+	0.342639i
$41$	−41.1577			−1.00385			−0.501923	−	0.864912i	$-0.667374\pi$
$41$	−41.1577			−1.00385			−0.501923	+	0.864912i	$0.667374\pi$
$42$	10.0469	−	10.0469i	0.239212	−	0.239212i
$43$	−2.10451	−	2.10451i	−0.0489420	−	0.0489420i	0.682212	−	0.731154i	$-0.261018\pi$
$43$	−2.10451	−	2.10451i	−0.0489420	−	0.0489420i	−0.731154	+	0.682212i	$0.761018\pi$
$44$			25.8731i			0.588025i
$45$	−7.66411	+	12.8942i	−0.170314	+	0.286539i
$46$	6.78233			0.147442
$47$	−2.10608	+	2.10608i	−0.0448101	+	0.0448101i	−0.729157	−	0.684347i	$-0.760088\pi$
$47$	−2.10608	+	2.10608i	−0.0448101	+	0.0448101i	0.684347	+	0.729157i	$0.260088\pi$
$48$	4.89898	+	4.89898i	0.102062	+	0.102062i
$49$			15.3532i			0.313330i
$50$	−33.9076	−	10.0137i	−0.678152	−	0.200273i
$51$	56.9977			1.11760
$52$	−14.9776	+	14.9776i	−0.288031	+	0.288031i
$53$	−8.58604	−	8.58604i	−0.162001	−	0.162001i	0.621452	−	0.783452i	$-0.286543\pi$
$53$	−8.58604	−	8.58604i	−0.162001	−	0.162001i	−0.783452	+	0.621452i	$0.786543\pi$
$54$			7.34847i			0.136083i
$55$	−55.6024	−	33.0491i	−1.01095	−	0.600892i
$56$	16.4065			0.292974
$57$	−3.26398	+	3.26398i	−0.0572628	+	0.0572628i
$58$	−13.0859	−	13.0859i	−0.225618	−	0.225618i
$59$			65.6109i			1.11205i	0.831166	+	0.556025i	$0.187674\pi$
$59$			65.6109i			1.11205i	−0.831166	+	0.556025i	$0.812326\pi$
$60$	−16.7858	+	4.27038i	−0.279764	+	0.0711731i
$61$	−39.1540			−0.641869			−0.320935	−	0.947101i	$-0.603997\pi$
$61$	−39.1540			−0.641869			−0.320935	+	0.947101i	$0.603997\pi$
$62$	−21.6535	+	21.6535i	−0.349250	+	0.349250i
$63$	12.3049	+	12.3049i	0.195316	+	0.195316i
$64$			8.00000i			0.125000i
$65$	−13.0558	−	51.3192i	−0.200859	−	0.789526i
$66$	−31.6880			−0.480121
$67$	−42.4434	+	42.4434i	−0.633483	+	0.633483i	−0.948940	−	0.315457i	$-0.897842\pi$
$67$	−42.4434	+	42.4434i	−0.633483	+	0.633483i	0.315457	+	0.948940i	$0.397842\pi$
$68$	46.5384	+	46.5384i	0.684389	+	0.684389i
$69$			8.30662i			0.120386i
$70$	−20.9569	+	35.2583i	−0.299385	+	0.503690i
$71$	−119.297			−1.68023			−0.840117	−	0.542405i	$-0.817514\pi$
$71$	−119.297			−1.68023			−0.840117	+	0.542405i	$0.817514\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	−86.2712	−	86.2712i	−1.18180	−	1.18180i	−0.979278	−	0.202519i	$-0.935087\pi$
$73$	−86.2712	−	86.2712i	−1.18180	−	1.18180i	−0.202519	−	0.979278i	$-0.564913\pi$
$74$		−	3.46035i		−	0.0467614i
$75$	12.2642	−	41.5282i	0.163522	−	0.553709i
$76$	−5.33005			−0.0701323
$77$	−53.0611	+	53.0611i	−0.689105	+	0.689105i
$78$	−18.3438	−	18.3438i	−0.235176	−	0.235176i
$79$			63.9660i			0.809697i	0.914384	+	0.404848i	$0.132676\pi$
$79$			63.9660i			0.809697i	−0.914384	+	0.404848i	$0.867324\pi$
$80$	−17.1923	−	10.2188i	−0.214904	−	0.127735i
$81$	−9.00000			−0.111111
$82$	41.1577	−	41.1577i	0.501923	−	0.501923i
$83$	98.1743	+	98.1743i	1.18282	+	1.18282i	0.979010	+	0.203814i	$0.0653337\pi$
$83$	98.1743	+	98.1743i	1.18282	+	1.18282i	0.203814	+	0.979010i	$0.434666\pi$
$84$			20.0938i			0.239212i
$85$	−159.459	+	40.5670i	−1.87599	+	0.477259i
$86$	4.20901			0.0489420
$87$	16.0268	−	16.0268i	0.184217	−	0.184217i
$88$	−25.8731	−	25.8731i	−0.294013	−	0.294013i
$89$			156.409i			1.75740i	0.477373	+	0.878701i	$0.341589\pi$
$89$			156.409i			1.75740i	−0.477373	+	0.878701i	$0.658411\pi$
$90$	−5.23013	−	20.5583i	−0.0581126	−	0.228426i
$91$	−61.4328			−0.675085
$92$	−6.78233	+	6.78233i	−0.0737210	+	0.0737210i
$93$	−26.5200	−	26.5200i	−0.285161	−	0.285161i
$94$		−	4.21215i		−	0.0448101i
$95$	6.80835	−	11.4545i	0.0716669	−	0.120574i
$96$	−9.79796			−0.102062
$97$	49.2914	−	49.2914i	0.508158	−	0.508158i	−0.405802	−	0.913961i	$-0.633008\pi$
$97$	49.2914	−	49.2914i	0.508158	−	0.508158i	0.913961	+	0.405802i	$0.133008\pi$
$98$	−15.3532	−	15.3532i	−0.156665	−	0.156665i
$99$		−	38.8097i		−	0.392017i
$100$	43.9213	−	23.8940i	0.439213	−	0.238940i
$101$	−41.2318			−0.408236			−0.204118	−	0.978946i	$-0.565433\pi$
$101$	−41.2318			−0.408236			−0.204118	+	0.978946i	$0.565433\pi$
$102$	−56.9977	+	56.9977i	−0.558801	+	0.558801i
$103$	−121.357	−	121.357i	−1.17822	−	1.17822i	−0.980196	−	0.198028i	$-0.936546\pi$
$103$	−121.357	−	121.357i	−1.17822	−	1.17822i	−0.198028	−	0.980196i	$-0.563454\pi$
$104$		−	29.9552i		−	0.288031i
$105$	−43.1825	−	25.6669i	−0.411261	−	0.244447i
$106$	17.1721			0.162001
$107$	79.5289	−	79.5289i	0.743261	−	0.743261i	−0.229943	−	0.973204i	$-0.573854\pi$
$107$	79.5289	−	79.5289i	0.743261	−	0.743261i	0.973204	+	0.229943i	$0.0738540\pi$
$108$	−7.34847	−	7.34847i	−0.0680414	−	0.0680414i
$109$			110.939i			1.01779i	0.860828	+	0.508896i	$0.169946\pi$
$109$			110.939i			1.01779i	−0.860828	+	0.508896i	$0.830054\pi$
$110$	88.6514	−	22.5533i	0.805922	−	0.205030i
$111$	4.23804			0.0381805
$112$	−16.4065	+	16.4065i	−0.146487	+	0.146487i
$113$	−107.518	−	107.518i	−0.951488	−	0.951488i	0.0473884	−	0.998877i	$-0.484910\pi$
$113$	−107.518	−	107.518i	−0.951488	−	0.951488i	−0.998877	+	0.0473884i	$0.984910\pi$
$114$		−	6.52796i		−	0.0572628i
$115$	−5.91208	−	23.2389i	−0.0514094	−	0.202078i
$116$	26.1717			0.225618
$117$	22.4664	−	22.4664i	0.192021	−	0.192021i
$118$	−65.6109	−	65.6109i	−0.556025	−	0.556025i
$119$			190.884i			1.60407i
$120$	12.5154	−	21.0562i	0.104295	−	0.175468i
$121$	46.3546			0.383096
$122$	39.1540	−	39.1540i	0.320935	−	0.320935i
$123$	50.4077	+	50.4077i	0.409818	+	0.409818i
$124$		−	43.3070i		−	0.349250i
$125$	−4.75380	+	124.910i	−0.0380304	+	0.999277i
$126$	−24.6098			−0.195316
$127$	78.0096	−	78.0096i	0.614249	−	0.614249i	−0.329801	−	0.944050i	$-0.606982\pi$
$127$	78.0096	−	78.0096i	0.614249	−	0.614249i	0.944050	+	0.329801i	$0.106982\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$			5.15497i			0.0399610i
$130$	64.3750	+	38.2634i	0.495192	+	0.294334i
$131$	133.553			1.01949			0.509744	−	0.860326i	$-0.329740\pi$
$131$	133.553			1.01949			0.509744	+	0.860326i	$0.329740\pi$
$132$	31.6880	−	31.6880i	0.240060	−	0.240060i
$133$	−10.9310	−	10.9310i	−0.0821878	−	0.0821878i
$134$		−	84.8868i		−	0.633483i
$135$	25.1787	−	6.40558i	0.186509	−	0.0474487i
$136$	−93.0769			−0.684389
$137$	72.6388	−	72.6388i	0.530210	−	0.530210i	−0.390425	−	0.920635i	$-0.627672\pi$
$137$	72.6388	−	72.6388i	0.530210	−	0.530210i	0.920635	+	0.390425i	$0.127672\pi$
$138$	−8.30662	−	8.30662i	−0.0601929	−	0.0601929i
$139$			194.073i			1.39621i	0.715997	+	0.698103i	$0.245972\pi$
$139$			194.073i			1.39621i	−0.715997	+	0.698103i	$0.754028\pi$
$140$	−14.3014	−	56.2153i	−0.102153	−	0.401538i
$141$	5.15881			0.0365873
$142$	119.297	−	119.297i	0.840117	−	0.840117i
$143$	96.8794	+	96.8794i	0.677479	+	0.677479i
$144$		−	12.0000i		−	0.0833333i
$145$	−33.4305	+	56.2441i	−0.230555	+	0.387890i
$146$	172.542			1.18180
$147$	18.8037	−	18.8037i	0.127916	−	0.127916i
$148$	3.46035	+	3.46035i	0.0233807	+	0.0233807i
$149$		−	118.977i		−	0.798506i	−0.916841	−	0.399253i	$-0.869270\pi$
$149$		−	118.977i		−	0.798506i	0.916841	−	0.399253i	$-0.130730\pi$
$150$	29.2640	+	53.7924i	0.195093	+	0.358616i
$151$	−211.993			−1.40392			−0.701962	−	0.712214i	$-0.747692\pi$
$151$	−211.993			−1.40392			−0.701962	+	0.712214i	$0.747692\pi$
$152$	5.33005	−	5.33005i	0.0350661	−	0.0350661i
$153$	−69.8077	−	69.8077i	−0.456259	−	0.456259i
$154$		−	106.122i		−	0.689105i
$155$	93.0685	+	55.3183i	0.600442	+	0.356892i
$156$	36.6875			0.235176
$157$	−161.138	+	161.138i	−1.02636	+	1.02636i	−0.0267147	+	0.999643i	$0.508505\pi$
$157$	−161.138	+	161.138i	−1.02636	+	1.02636i	−0.999643	+	0.0267147i	$0.991495\pi$
$158$	−63.9660	−	63.9660i	−0.404848	−	0.404848i
$159$			21.0314i			0.132273i
$160$	27.4111	−	6.97351i	0.171320	−	0.0435844i
$161$	−27.8187			−0.172787
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	−171.976	−	171.976i	−1.05507	−	1.05507i	−0.998393	−	0.0566742i	$-0.981950\pi$
$163$	−171.976	−	171.976i	−1.05507	−	1.05507i	−0.0566742	−	0.998393i	$-0.518050\pi$
$164$			82.3154i			0.501923i
$165$	27.6220	+	108.575i	0.167406	+	0.658033i
$166$	−196.349			−1.18282
$167$	145.411	−	145.411i	0.870724	−	0.870724i	−0.121828	−	0.992551i	$-0.538876\pi$
$167$	145.411	−	145.411i	0.870724	−	0.870724i	0.992551	+	0.121828i	$0.0388755\pi$
$168$	−20.0938	−	20.0938i	−0.119606	−	0.119606i
$169$		−	56.8354i		−	0.336304i
$170$	118.892	−	200.026i	0.699364	−	1.17662i
$171$	7.99508			0.0467549
$172$	−4.20901	+	4.20901i	−0.0244710	+	0.0244710i
$173$	−98.5498	−	98.5498i	−0.569652	−	0.569652i	0.362379	−	0.932031i	$-0.381965\pi$
$173$	−98.5498	−	98.5498i	−0.569652	−	0.569652i	−0.932031	+	0.362379i	$0.881965\pi$
$174$			32.0537i			0.184217i
$175$	139.077	+	41.0724i	0.794724	+	0.234699i
$176$	51.7462			0.294013
$177$	80.3567	−	80.3567i	0.453992	−	0.453992i
$178$	−156.409	−	156.409i	−0.878701	−	0.878701i
$179$			150.914i			0.843097i	0.906806	+	0.421549i	$0.138513\pi$
$179$			150.914i			0.843097i	−0.906806	+	0.421549i	$0.861487\pi$
$180$	25.7885	+	15.3282i	0.143269	+	0.0851568i
$181$	−113.802			−0.628740			−0.314370	−	0.949301i	$-0.601793\pi$
$181$	−113.802			−0.628740			−0.314370	+	0.949301i	$0.601793\pi$
$182$	61.4328	−	61.4328i	0.337543	−	0.337543i
$183$	47.9537	+	47.9537i	0.262042	+	0.262042i
$184$		−	13.5647i		−	0.0737210i
$185$	−11.8565	+	3.01634i	−0.0640892	+	0.0163046i
$186$	53.0400			0.285161
$187$	301.024	−	301.024i	1.60975	−	1.60975i
$188$	4.21215	+	4.21215i	0.0224051	+	0.0224051i
$189$		−	30.1408i		−	0.159475i
$190$	4.64615	+	18.2629i	0.0244534	+	0.0961203i
$191$	−5.60105			−0.0293249			−0.0146624	−	0.999893i	$-0.504667\pi$
$191$	−5.60105			−0.0293249			−0.0146624	+	0.999893i	$0.504667\pi$
$192$	9.79796	−	9.79796i	0.0510310	−	0.0510310i
$193$	179.654	+	179.654i	0.930848	+	0.930848i	0.997759	−	0.0669105i	$-0.0213142\pi$
$193$	179.654	+	179.654i	0.930848	+	0.930848i	−0.0669105	+	0.997759i	$0.521314\pi$
$194$			98.5827i			0.508158i
$195$	−46.8629	+	78.8430i	−0.240322	+	0.404323i
$196$	30.7063			0.156665
$197$	−107.119	+	107.119i	−0.543749	+	0.543749i	−0.924626	−	0.380876i	$-0.875622\pi$
$197$	−107.119	+	107.119i	−0.543749	+	0.543749i	0.380876	+	0.924626i	$0.375622\pi$
$198$	38.8097	+	38.8097i	0.196008	+	0.196008i
$199$		−	108.814i		−	0.546805i	−0.961900	−	0.273403i	$-0.911851\pi$
$199$		−	108.814i		−	0.546805i	0.961900	−	0.273403i	$-0.0881491\pi$
$200$	−20.0273	+	67.8152i	−0.100137	+	0.339076i
$201$	103.965			0.517237
$202$	41.2318	−	41.2318i	0.204118	−	0.204118i
$203$	53.6734	+	53.6734i	0.264401	+	0.264401i
$204$		−	113.995i		−	0.558801i
$205$	−176.899	−	105.146i	−0.862922	−	0.512906i
$206$	242.714			1.17822
$207$	10.1735	−	10.1735i	0.0491473	−	0.0491473i
$208$	29.9552	+	29.9552i	0.144016	+	0.144016i
$209$			34.4763i			0.164958i
$210$	68.8493	−	17.5156i	0.327854	−	0.0834075i
$211$	208.930			0.990192			0.495096	−	0.868838i	$-0.335133\pi$
$211$	208.930			0.990192			0.495096	+	0.868838i	$0.335133\pi$
$212$	−17.1721	+	17.1721i	−0.0810003	+	0.0810003i
$213$	146.108	+	146.108i	0.685953	+	0.685953i
$214$			159.058i			0.743261i
$215$	−3.66895	−	14.4217i	−0.0170649	−	0.0670778i
$216$	14.6969			0.0680414
$217$	88.8148	−	88.8148i	0.409285	−	0.409285i
$218$	−110.939	−	110.939i	−0.508896	−	0.508896i
$219$			211.320i			0.964934i
$220$	−66.0981	+	111.205i	−0.300446	+	0.505476i
$221$	348.518			1.57700
$222$	−4.23804	+	4.23804i	−0.0190903	+	0.0190903i
$223$	−68.2548	−	68.2548i	−0.306075	−	0.306075i	0.537310	−	0.843385i	$-0.319441\pi$
$223$	−68.2548	−	68.2548i	−0.306075	−	0.306075i	−0.843385	+	0.537310i	$0.819441\pi$
$224$		−	32.8131i		−	0.146487i
$225$	−65.8819	+	35.8410i	−0.292808	+	0.159293i
$226$	215.036			0.951488
$227$	−6.98511	+	6.98511i	−0.0307714	+	0.0307714i	−0.722325	−	0.691554i	$-0.756927\pi$
$227$	−6.98511	+	6.98511i	−0.0307714	+	0.0307714i	0.691554	+	0.722325i	$0.256927\pi$
$228$	6.52796	+	6.52796i	0.0286314	+	0.0286314i
$229$			95.6049i			0.417488i	0.977970	+	0.208744i	$0.0669376\pi$
$229$			95.6049i			0.417488i	−0.977970	+	0.208744i	$0.933062\pi$
$230$	29.1510	+	17.3268i	0.126743	+	0.0753341i
$231$	129.973			0.562652
$232$	−26.1717	+	26.1717i	−0.112809	+	0.112809i
$233$	221.116	+	221.116i	0.948996	+	0.948996i	0.998761	−	0.0497647i	$-0.0158471\pi$
$233$	221.116	+	221.116i	0.948996	+	0.948996i	−0.0497647	+	0.998761i	$0.515847\pi$
$234$			44.9329i			0.192021i
$235$	−14.4325	+	3.67168i	−0.0614148	+	0.0156242i
$236$	131.222			0.556025
$237$	78.3421	−	78.3421i	0.330557	−	0.330557i
$238$	−190.884	−	190.884i	−0.802033	−	0.802033i
$239$			210.437i			0.880491i	0.897877	+	0.440246i	$0.145109\pi$
$239$			210.437i			0.880491i	−0.897877	+	0.440246i	$0.854891\pi$
$240$	8.54077	+	33.5716i	0.0355865	+	0.139882i
$241$	300.706			1.24774			0.623872	−	0.781527i	$-0.285559\pi$
$241$	300.706			1.24774			0.623872	+	0.781527i	$0.285559\pi$
$242$	−46.3546	+	46.3546i	−0.191548	+	0.191548i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$			78.3080i			0.320935i
$245$	−39.2227	+	65.9891i	−0.160093	+	0.269343i
$246$	−100.815			−0.409818
$247$	−19.9579	+	19.9579i	−0.0808011	+	0.0808011i
$248$	43.3070	+	43.3070i	0.174625	+	0.174625i
$249$		−	240.477i		−	0.965771i
$250$	−120.156	−	129.663i	−0.480623	−	0.518653i
$251$	−301.201			−1.20000			−0.600002	−	0.799999i	$-0.704833\pi$
$251$	−301.201			−1.20000			−0.600002	+	0.799999i	$0.704833\pi$
$252$	24.6098	−	24.6098i	0.0976580	−	0.0976580i
$253$	43.8700	+	43.8700i	0.173399	+	0.173399i
$254$			156.019i			0.614249i
$255$	244.981	+	145.612i	0.960709	+	0.571028i
$256$	16.0000			0.0625000
$257$	−81.1010	+	81.1010i	−0.315568	+	0.315568i	−0.847062	−	0.531494i	$-0.821631\pi$
$257$	−81.1010	+	81.1010i	−0.315568	+	0.315568i	0.531494	+	0.847062i	$0.321631\pi$
$258$	−5.15497	−	5.15497i	−0.0199805	−	0.0199805i
$259$			14.1931i			0.0547995i
$260$	−102.638	+	26.1116i	−0.394763	+	0.100429i
$261$	−39.2576			−0.150412
$262$	−133.553	+	133.553i	−0.509744	+	0.509744i
$263$	203.519	+	203.519i	0.773838	+	0.773838i	0.978775	−	0.204937i	$-0.0656990\pi$
$263$	203.519	+	203.519i	0.773838	+	0.773838i	−0.204937	+	0.978775i	$0.565699\pi$
$264$			63.3759i			0.240060i
$265$	−14.9687	−	58.8382i	−0.0564857	−	0.222031i
$266$	21.8619			0.0821878
$267$	191.561	−	191.561i	0.717456	−	0.717456i
$268$	84.8868	+	84.8868i	0.316742	+	0.316742i
$269$		−	382.826i		−	1.42315i	−0.702612	−	0.711573i	$-0.747983\pi$
$269$		−	382.826i		−	1.42315i	0.702612	−	0.711573i	$-0.252017\pi$
$270$	−18.7732	+	31.5843i	−0.0695302	+	0.116979i
$271$	261.659			0.965532			0.482766	−	0.875749i	$-0.339632\pi$
$271$	261.659			0.965532			0.482766	+	0.875749i	$0.339632\pi$
$272$	93.0769	−	93.0769i	0.342194	−	0.342194i
$273$	75.2395	+	75.2395i	0.275602	+	0.275602i
$274$			145.278i			0.530210i
$275$	−154.553	−	284.095i	−0.562011	−	1.03307i
$276$	16.6132			0.0601929
$277$	−221.694	+	221.694i	−0.800340	+	0.800340i	−0.983149	−	0.182809i	$-0.941481\pi$
$277$	−221.694	+	221.694i	−0.800340	+	0.800340i	0.182809	+	0.983149i	$0.441481\pi$
$278$	−194.073	−	194.073i	−0.698103	−	0.698103i
$279$			64.9605i			0.232833i
$280$	70.5167	+	41.9139i	0.251845	+	0.149692i
$281$	−4.44209			−0.0158081			−0.00790407	−	0.999969i	$-0.502516\pi$
$281$	−4.44209			−0.0158081			−0.00790407	+	0.999969i	$0.502516\pi$
$282$	−5.15881	+	5.15881i	−0.0182937	+	0.0182937i
$283$	154.746	+	154.746i	0.546804	+	0.546804i	0.925515	−	0.378711i	$-0.123633\pi$
$283$	154.746	+	154.746i	0.546804	+	0.546804i	−0.378711	+	0.925515i	$0.623633\pi$
$284$			238.593i			0.840117i
$285$	−22.3673	+	5.69034i	−0.0784819	+	0.0199661i
$286$	−193.759			−0.677479
$287$	−168.814	+	168.814i	−0.588202	+	0.588202i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$		−	793.913i		−	2.74710i
$290$	−22.8136	−	89.6746i	−0.0786675	−	0.309223i
$291$	−120.739			−0.414910
$292$	−172.542	+	172.542i	−0.590899	+	0.590899i
$293$	−194.221	−	194.221i	−0.662871	−	0.662871i	0.293185	−	0.956056i	$-0.405285\pi$
$293$	−194.221	−	194.221i	−0.662871	−	0.662871i	−0.956056	+	0.293185i	$0.905285\pi$
$294$			37.6074i			0.127916i
$295$	−167.616	+	282.001i	−0.568191	+	0.955936i
$296$	−6.92069			−0.0233807
$297$	−47.5320	+	47.5320i	−0.160040	+	0.160040i
$298$	118.977	+	118.977i	0.399253	+	0.399253i
$299$			50.7916i			0.169872i
$300$	−83.0564	−	24.5283i	−0.276855	−	0.0817611i
$301$	−17.2638			−0.0573550
$302$	211.993	−	211.993i	0.701962	−	0.701962i
$303$	50.4985	+	50.4985i	0.166662	+	0.166662i
$304$			10.6601i			0.0350661i
$305$	−168.287	−	100.027i	−0.551761	−	0.327957i
$306$	139.615			0.456259
$307$	342.709	−	342.709i	1.11632	−	1.11632i	0.124040	−	0.992277i	$-0.460415\pi$
$307$	342.709	−	342.709i	1.11632	−	1.11632i	0.992277	−	0.124040i	$-0.0395851\pi$
$308$	106.122	+	106.122i	0.344552	+	0.344552i
$309$			297.263i			0.962016i
$310$	−148.387	+	37.7502i	−0.478667	+	0.121775i
$311$	44.3383			0.142567			0.0712834	−	0.997456i	$-0.477291\pi$
$311$	44.3383			0.142567			0.0712834	+	0.997456i	$0.477291\pi$
$312$	−36.6875	+	36.6875i	−0.117588	+	0.117588i
$313$	−3.37158	−	3.37158i	−0.0107718	−	0.0107718i	0.701700	−	0.712472i	$-0.252425\pi$
$313$	−3.37158	−	3.37158i	−0.0107718	−	0.0107718i	−0.712472	+	0.701700i	$0.752425\pi$
$314$		−	322.276i		−	1.02636i
$315$	21.4521	+	84.3229i	0.0681019	+	0.267692i
$316$	127.932			0.404848
$317$	65.0482	−	65.0482i	0.205199	−	0.205199i	−0.597024	−	0.802223i	$-0.703650\pi$
$317$	65.0482	−	65.0482i	0.205199	−	0.205199i	0.802223	+	0.597024i	$0.203650\pi$
$318$	−21.0314	−	21.0314i	−0.0661365	−	0.0661365i
$319$		−	169.286i		−	0.530677i
$320$	−20.4376	+	34.3846i	−0.0638676	+	0.107452i
$321$	−194.805			−0.606870
$322$	27.8187	−	27.8187i	0.0863933	−	0.0863933i
$323$	62.0131	+	62.0131i	0.191991	+	0.191991i
$324$			18.0000i			0.0555556i
$325$	74.9903	−	253.928i	0.230739	−	0.781316i
$326$	343.952			1.05507
$327$	135.872	−	135.872i	0.415512	−	0.415512i
$328$	−82.3154	−	82.3154i	−0.250962	−	0.250962i
$329$			17.2767i			0.0525128i
$330$	−136.197	−	80.9534i	−0.412720	−	0.245313i
$331$	−50.7044			−0.153186			−0.0765928	−	0.997062i	$-0.524404\pi$
$331$	−50.7044			−0.153186			−0.0765928	+	0.997062i	$0.524404\pi$
$332$	196.349	−	196.349i	0.591412	−	0.591412i
$333$	−5.19052	−	5.19052i	−0.0155871	−	0.0155871i
$334$			290.822i			0.870724i
$335$	−290.855	+	73.9948i	−0.868225	+	0.220880i
$336$	40.1877			0.119606
$337$	80.1441	−	80.1441i	0.237816	−	0.237816i	−0.578129	−	0.815945i	$-0.696217\pi$
$337$	80.1441	−	80.1441i	0.237816	−	0.237816i	0.815945	+	0.578129i	$0.196217\pi$
$338$	56.8354	+	56.8354i	0.168152	+	0.168152i
$339$			263.365i			0.776887i
$340$	81.1341	+	318.918i	0.238630	+	0.937994i
$341$	−280.122			−0.821472
$342$	−7.99508	+	7.99508i	−0.0233774	+	0.0233774i
$343$	263.953	+	263.953i	0.769543	+	0.769543i
$344$		−	8.41803i		−	0.0244710i
$345$	−21.2210	+	35.7025i	−0.0615100	+	0.103486i
$346$	197.100			0.569652
$347$	312.785	−	312.785i	0.901398	−	0.901398i	−0.0941595	−	0.995557i	$-0.530016\pi$
$347$	312.785	−	312.785i	0.901398	−	0.901398i	0.995557	+	0.0941595i	$0.0300164\pi$
$348$	−32.0537	−	32.0537i	−0.0921083	−	0.0921083i
$349$			12.2678i			0.0351514i	0.999846	+	0.0175757i	$0.00559481\pi$
$349$			12.2678i			0.0351514i	−0.999846	+	0.0175757i	$0.994405\pi$
$350$	−180.149	+	98.0044i	−0.514712	+	0.280013i
$351$	−55.0313			−0.156784
$352$	−51.7462	+	51.7462i	−0.147006	+	0.147006i
$353$	−394.880	−	394.880i	−1.11864	−	1.11864i	−0.991941	−	0.126699i	$-0.959562\pi$
$353$	−394.880	−	394.880i	−1.11864	−	1.11864i	−0.126699	−	0.991941i	$-0.540438\pi$
$354$			160.713i			0.453992i
$355$	−512.746	−	304.767i	−1.44436	−	0.858500i
$356$	312.817			0.878701
$357$	233.784	−	233.784i	0.654857	−	0.654857i
$358$	−150.914	−	150.914i	−0.421549	−	0.421549i
$359$		−	405.015i		−	1.12818i	−0.825715	−	0.564088i	$-0.809228\pi$
$359$		−	405.015i		−	1.12818i	0.825715	−	0.564088i	$-0.190772\pi$
$360$	−41.1167	+	10.4603i	−0.114213	+	0.0290563i
$361$	353.898			0.980326
$362$	113.802	−	113.802i	0.314370	−	0.314370i
$363$	−56.7725	−	56.7725i	−0.156398	−	0.156398i
$364$			122.866i			0.337543i
$365$	−150.403	−	591.198i	−0.412064	−	1.61972i
$366$	−95.9074			−0.262042
$367$	17.0463	−	17.0463i	0.0464477	−	0.0464477i	−0.683501	−	0.729949i	$-0.739544\pi$
$367$	17.0463	−	17.0463i	0.0464477	−	0.0464477i	0.729949	+	0.683501i	$0.239544\pi$
$368$	13.5647	+	13.5647i	0.0368605	+	0.0368605i
$369$		−	123.473i		−	0.334615i
$370$	8.84016	−	14.8728i	0.0238923	−	0.0401969i
$371$	−70.4336			−0.189848
$372$	−53.0400	+	53.0400i	−0.142581	+	0.142581i
$373$	−330.618	−	330.618i	−0.886375	−	0.886375i	0.107798	−	0.994173i	$-0.465620\pi$
$373$	−330.618	−	330.618i	−0.886375	−	0.886375i	−0.994173	+	0.107798i	$0.965620\pi$
$374$			602.047i			1.60975i
$375$	158.805	−	147.160i	0.423479	−	0.392427i
$376$	−8.42430			−0.0224051
$377$	97.9975	−	97.9975i	0.259940	−	0.259940i
$378$	30.1408	+	30.1408i	0.0797374	+	0.0797374i
$379$		−	169.928i		−	0.448358i	−0.974548	−	0.224179i	$-0.928030\pi$
$379$		−	169.928i		−	0.448358i	0.974548	−	0.224179i	$-0.0719700\pi$
$380$	−22.9090	−	13.6167i	−0.0602868	−	0.0358334i
$381$	−191.084			−0.501532
$382$	5.60105	−	5.60105i	0.0146624	−	0.0146624i
$383$	−159.003	−	159.003i	−0.415151	−	0.415151i	0.468377	−	0.883528i	$-0.344839\pi$
$383$	−159.003	−	159.003i	−0.415151	−	0.415151i	−0.883528	+	0.468377i	$0.844839\pi$
$384$			19.5959i			0.0510310i
$385$	−363.616	+	92.5055i	−0.944457	+	0.240274i
$386$	−359.308			−0.930848
$387$	6.31352	−	6.31352i	0.0163140	−	0.0163140i
$388$	−98.5827	−	98.5827i	−0.254079	−	0.254079i
$389$			494.731i			1.27180i	0.771770	+	0.635901i	$0.219371\pi$
$389$			494.731i			1.27180i	−0.771770	+	0.635901i	$0.780629\pi$
$390$	−31.9801	−	125.706i	−0.0820003	−	0.322323i
$391$	157.820			0.403631
$392$	−30.7063	+	30.7063i	−0.0783324	+	0.0783324i
$393$	−163.568	−	163.568i	−0.416204	−	0.416204i
$394$		−	214.237i		−	0.543749i
$395$	−163.414	+	274.931i	−0.413707	+	0.696028i
$396$	−77.6194			−0.196008
$397$	61.8230	−	61.8230i	0.155725	−	0.155725i	−0.624944	−	0.780669i	$-0.714878\pi$
$397$	61.8230	−	61.8230i	0.155725	−	0.155725i	0.780669	+	0.624944i	$0.214878\pi$
$398$	108.814	+	108.814i	0.273403	+	0.273403i
$399$			26.7753i			0.0671060i
$400$	−47.7879	−	87.8425i	−0.119470	−	0.219606i
$401$	−301.250			−0.751248			−0.375624	−	0.926772i	$-0.622572\pi$
$401$	−301.250			−0.751248			−0.375624	+	0.926772i	$0.622572\pi$
$402$	−103.965	+	103.965i	−0.258619	+	0.258619i
$403$	−162.159	−	162.159i	−0.402380	−	0.402380i
$404$			82.4637i			0.204118i
$405$	−38.6827	−	22.9923i	−0.0955129	−	0.0567712i
$406$	−107.347			−0.264401
$407$	22.3825	−	22.3825i	0.0549938	−	0.0549938i
$408$	113.995	+	113.995i	0.279401	+	0.279401i
$409$			425.582i			1.04054i	0.854001	+	0.520271i	$0.174169\pi$
$409$			425.582i			1.04054i	−0.854001	+	0.520271i	$0.825831\pi$
$410$	282.045	−	71.7534i	0.687914	−	0.175008i
$411$	−177.928			−0.432915
$412$	−242.714	+	242.714i	−0.589112	+	0.589112i
$413$	269.112	+	269.112i	0.651604	+	0.651604i
$414$			20.3470i			0.0491473i
$415$	171.155	+	672.767i	0.412421	+	1.62113i
$416$	−59.9105			−0.144016
$417$	237.689	−	237.689i	0.569999	−	0.569999i
$418$	−34.4763	−	34.4763i	−0.0824791	−	0.0824791i
$419$			253.765i			0.605645i	0.953047	+	0.302822i	$0.0979289\pi$
$419$			253.765i			0.605645i	−0.953047	+	0.302822i	$0.902071\pi$
$420$	−51.3338	+	86.3649i	−0.122223	+	0.205631i
$421$	239.342			0.568508			0.284254	−	0.958749i	$-0.408254\pi$
$421$	239.342			0.568508			0.284254	+	0.958749i	$0.408254\pi$
$422$	−208.930	+	208.930i	−0.495096	+	0.495096i
$423$	−6.31823	−	6.31823i	−0.0149367	−	0.0149367i
$424$		−	34.3441i		−	0.0810003i
$425$	−789.004	−	233.010i	−1.85648	−	0.548258i
$426$	−292.216			−0.685953
$427$	−160.596	+	160.596i	−0.376102	+	0.376102i
$428$	−159.058	−	159.058i	−0.371630	−	0.371630i
$429$		−	237.305i		−	0.553159i
$430$	18.0907	+	10.7528i	0.0420714	+	0.0250065i
$431$	515.995			1.19720			0.598602	−	0.801047i	$-0.295723\pi$
$431$	515.995			1.19720			0.598602	+	0.801047i	$0.295723\pi$
$432$	−14.6969	+	14.6969i	−0.0340207	+	0.0340207i
$433$	−123.940	−	123.940i	−0.286237	−	0.286237i	0.549353	−	0.835590i	$-0.314874\pi$
$433$	−123.940	−	123.940i	−0.286237	−	0.286237i	−0.835590	+	0.549353i	$0.814874\pi$
$434$			177.630i			0.409285i
$435$	109.828	−	27.9408i	0.252479	−	0.0642318i
$436$	221.879			0.508896
$437$	−9.03755	+	9.03755i	−0.0206809	+	0.0206809i
$438$	−211.320	−	211.320i	−0.482467	−	0.482467i
$439$			177.022i			0.403238i	0.979464	+	0.201619i	$0.0646203\pi$
$439$			177.022i			0.403238i	−0.979464	+	0.201619i	$0.935380\pi$
$440$	−45.1066	−	177.303i	−0.102515	−	0.402961i
$441$	−46.0595			−0.104443
$442$	−348.518	+	348.518i	−0.788501	+	0.788501i
$443$	172.073	+	172.073i	0.388428	+	0.388428i	0.874126	−	0.485699i	$-0.161435\pi$
$443$	172.073	+	172.073i	0.388428	+	0.388428i	−0.485699	+	0.874126i	$0.661435\pi$
$444$		−	8.47608i		−	0.0190903i
$445$	−399.578	+	672.257i	−0.897928	+	1.51069i
$446$	136.510			0.306075
$447$	−145.717	+	145.717i	−0.325989	+	0.325989i
$448$	32.8131	+	32.8131i	0.0732435	+	0.0732435i
$449$		−	661.173i		−	1.47254i	−0.676685	−	0.736272i	$-0.736584\pi$
$449$		−	661.173i		−	1.47254i	0.676685	−	0.736272i	$-0.263416\pi$
$450$	30.0410	−	101.723i	0.0667577	−	0.226051i
$451$	532.439			1.18057
$452$	−215.036	+	215.036i	−0.475744	+	0.475744i
$453$	259.637	+	259.637i	0.573150	+	0.573150i
$454$		−	13.9702i		−	0.0307714i
$455$	−264.043	−	156.942i	−0.580314	−	0.344928i
$456$	−13.0559			−0.0286314
$457$	397.994	−	397.994i	0.870885	−	0.870885i	−0.121684	−	0.992569i	$-0.538829\pi$
$457$	397.994	−	397.994i	0.870885	−	0.870885i	0.992569	+	0.121684i	$0.0388295\pi$
$458$	−95.6049	−	95.6049i	−0.208744	−	0.208744i
$459$			170.993i			0.372534i
$460$	−46.4778	+	11.8242i	−0.101039	+	0.0257047i
$461$	23.4186			0.0507996			0.0253998	−	0.999677i	$-0.491914\pi$
$461$	23.4186			0.0507996			0.0253998	+	0.999677i	$0.491914\pi$
$462$	−129.973	+	129.973i	−0.281326	+	0.281326i
$463$	109.823	+	109.823i	0.237199	+	0.237199i	0.815689	−	0.578490i	$-0.196358\pi$
$463$	109.823	+	109.823i	0.237199	+	0.237199i	−0.578490	+	0.815689i	$0.696358\pi$
$464$		−	52.3434i		−	0.112809i
$465$	−46.2344	−	181.736i	−0.0994288	−	0.390830i
$466$	−442.232			−0.948996
$467$	−585.760	+	585.760i	−1.25430	+	1.25430i	−0.300534	+	0.953771i	$0.597165\pi$
$467$	−585.760	+	585.760i	−1.25430	+	1.25430i	−0.953771	+	0.300534i	$0.902835\pi$
$468$	−44.9329	−	44.9329i	−0.0960104	−	0.0960104i
$469$			348.175i			0.742377i
$470$	10.7608	−	18.1042i	0.0228953	−	0.0385195i
$471$	394.706			0.838018
$472$	−131.222	+	131.222i	−0.278012	+	0.278012i
$473$	27.2251	+	27.2251i	0.0575583	+	0.0575583i
$474$			156.684i			0.330557i
$475$	58.5257	−	31.8390i	0.123212	−	0.0670296i
$476$	381.768			0.802033
$477$	25.7581	−	25.7581i	0.0540002	−	0.0540002i
$478$	−210.437	−	210.437i	−0.440246	−	0.440246i
$479$		−	654.854i		−	1.36713i	−0.729891	−	0.683564i	$-0.760429\pi$
$479$		−	654.854i		−	1.36713i	0.729891	−	0.683564i	$-0.239571\pi$
$480$	−42.1124	−	25.0309i	−0.0877342	−	0.0521477i
$481$	25.9139			0.0538750
$482$	−300.706	+	300.706i	−0.623872	+	0.623872i
$483$	34.0708	+	34.0708i	0.0705399	+	0.0705399i
$484$		−	92.7092i		−	0.191548i
$485$	337.783	−	85.9334i	0.696460	−	0.177182i
$486$	−22.0454			−0.0453609
$487$	168.359	−	168.359i	0.345706	−	0.345706i	−0.512801	−	0.858507i	$-0.671392\pi$
$487$	168.359	−	168.359i	0.345706	−	0.345706i	0.858507	+	0.512801i	$0.171392\pi$
$488$	−78.3080	−	78.3080i	−0.160467	−	0.160467i
$489$			421.253i			0.861459i
$490$	−26.7663	−	105.212i	−0.0546252	−	0.214718i
$491$	−705.190			−1.43623			−0.718117	−	0.695923i	$-0.754996\pi$
$491$	−705.190			−1.43623			−0.718117	+	0.695923i	$0.754996\pi$
$492$	100.815	−	100.815i	0.204909	−	0.204909i
$493$	−304.498	−	304.498i	−0.617642	−	0.617642i
$494$		−	39.9158i		−	0.0808011i
$495$	99.1472	−	166.807i	0.200297	−	0.336984i
$496$	−86.6140			−0.174625
$497$	−489.311	+	489.311i	−0.984530	+	0.984530i
$498$	240.477	+	240.477i	0.482886	+	0.482886i
$499$			199.214i			0.399227i	0.979875	+	0.199614i	$0.0639687\pi$
$499$			199.214i			0.399227i	−0.979875	+	0.199614i	$0.936031\pi$
$500$	249.819	+	9.50760i	0.499638	+	0.0190152i
$501$	−356.182			−0.710943
$502$	301.201	−	301.201i	0.600002	−	0.600002i
$503$	10.4047	+	10.4047i	0.0206852	+	0.0206852i	0.717374	−	0.696689i	$-0.245344\pi$
$503$	10.4047	+	10.4047i	0.0206852	+	0.0206852i	−0.696689	+	0.717374i	$0.745344\pi$
$504$			49.2196i			0.0976580i
$505$	−177.218	−	105.335i	−0.350926	−	0.208584i
$506$	−87.7400			−0.173399
$507$	−69.6089	+	69.6089i	−0.137296	+	0.137296i
$508$	−156.019	−	156.019i	−0.307124	−	0.307124i
$509$			691.773i			1.35908i	0.733637	+	0.679541i	$0.237821\pi$
$509$			691.773i			1.35908i	−0.733637	+	0.679541i	$0.762179\pi$
$510$	−390.593	+	99.3685i	−0.765869	+	0.194840i
$511$	−707.706			−1.38494
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−9.79193	−	9.79193i	−0.0190876	−	0.0190876i
$514$		−	162.202i		−	0.315568i
$515$	−211.571	−	831.634i	−0.410818	−	1.61482i
$516$	10.3099			0.0199805
$517$	27.2454	−	27.2454i	0.0526990	−	0.0526990i
$518$	−14.1931	−	14.1931i	−0.0273998	−	0.0273998i
$519$			241.397i			0.465119i
$520$	76.5267	−	128.750i	0.147167	−	0.247596i
$521$	928.776			1.78268			0.891340	−	0.453336i	$-0.149766\pi$
$521$	928.776			1.78268			0.891340	+	0.453336i	$0.149766\pi$
$522$	39.2576	−	39.2576i	0.0752061	−	0.0752061i
$523$	167.034	+	167.034i	0.319377	+	0.319377i	0.848528	−	0.529151i	$-0.177490\pi$
$523$	167.034	+	167.034i	0.319377	+	0.319377i	−0.529151	+	0.848528i	$0.677490\pi$
$524$		−	267.106i		−	0.509744i
$525$	−120.030	−	220.637i	−0.228629	−	0.420260i
$526$	−407.039			−0.773838
$527$	−503.860	+	503.860i	−0.956091	+	0.956091i
$528$	−63.3759	−	63.3759i	−0.120030	−	0.120030i
$529$			23.0000i			0.0434783i
$530$	73.8069	+	43.8695i	0.139258	+	0.0827727i
$531$	−196.833			−0.370683
$532$	−21.8619	+	21.8619i	−0.0410939	+	0.0410939i
$533$	308.222	+	308.222i	0.578278	+	0.578278i
$534$			383.122i			0.717456i
$535$	544.994	−	138.649i	1.01868	−	0.259157i
$536$	−169.774			−0.316742
$537$	184.832	−	184.832i	0.344193	−	0.344193i
$538$	382.826	+	382.826i	0.711573	+	0.711573i
$539$		−	198.617i		−	0.368492i
$540$	−12.8112	−	50.3575i	−0.0237244	−	0.0932546i
$541$	−233.251			−0.431148			−0.215574	−	0.976488i	$-0.569162\pi$
$541$	−233.251			−0.431148			−0.215574	+	0.976488i	$0.569162\pi$
$542$	−261.659	+	261.659i	−0.482766	+	0.482766i
$543$	139.378	+	139.378i	0.256682	+	0.256682i
$544$			186.154i			0.342194i
$545$	−283.417	+	476.826i	−0.520031	+	0.874911i
$546$	−150.479			−0.275602
$547$	−65.6316	+	65.6316i	−0.119985	+	0.119985i	−0.764550	−	0.644565i	$-0.777039\pi$
$547$	−65.6316	+	65.6316i	−0.119985	+	0.119985i	0.644565	+	0.764550i	$0.277039\pi$
$548$	−145.278	−	145.278i	−0.265105	−	0.265105i
$549$		−	117.462i		−	0.213956i
$550$	438.648	+	129.542i	0.797542	+	0.235531i
$551$	34.8742			0.0632925
$552$	−16.6132	+	16.6132i	−0.0300965	+	0.0300965i
$553$	262.365	+	262.365i	0.474440	+	0.474440i
$554$		−	443.388i		−	0.800340i
$555$	18.2154	+	10.8269i	0.0328206	+	0.0195080i
$556$	388.145			0.698103
$557$	−41.4036	+	41.4036i	−0.0743332	+	0.0743332i	−0.743296	−	0.668963i	$-0.766739\pi$
$557$	−41.4036	+	41.4036i	−0.0743332	+	0.0743332i	0.668963	+	0.743296i	$0.266739\pi$
$558$	−64.9605	−	64.9605i	−0.116417	−	0.116417i
$559$			31.5205i			0.0563873i
$560$	−112.431	+	28.6028i	−0.200769	+	0.0510764i
$561$	−737.354			−1.31436
$562$	4.44209	−	4.44209i	0.00790407	−	0.00790407i
$563$	−715.121	−	715.121i	−1.27020	−	1.27020i	−0.945984	−	0.324213i	$-0.894901\pi$
$563$	−715.121	−	715.121i	−1.27020	−	1.27020i	−0.324213	−	0.945984i	$-0.605099\pi$
$564$		−	10.3176i		−	0.0182937i
$565$	−187.445	−	736.799i	−0.331761	−	1.30407i
$566$	−309.491			−0.546804
$567$	−36.9147	+	36.9147i	−0.0651053	+	0.0651053i
$568$	−238.593	−	238.593i	−0.420059	−	0.420059i
$569$			332.987i			0.585215i	0.956233	+	0.292608i	$0.0945229\pi$
$569$			332.987i			0.585215i	−0.956233	+	0.292608i	$0.905477\pi$
$570$	16.6770	−	28.0577i	0.0292579	−	0.0492240i
$571$	−42.8085			−0.0749712			−0.0374856	−	0.999297i	$-0.511935\pi$
$571$	−42.8085			−0.0749712			−0.0374856	+	0.999297i	$0.511935\pi$
$572$	193.759	−	193.759i	0.338739	−	0.338739i
$573$	6.85986	+	6.85986i	0.0119718	+	0.0119718i
$574$		−	337.628i		−	0.588202i
$575$	33.9579	−	114.986i	0.0590573	−	0.199976i
$576$	−24.0000			−0.0416667
$577$	186.404	−	186.404i	0.323057	−	0.323057i	−0.526882	−	0.849939i	$-0.676639\pi$
$577$	186.404	−	186.404i	0.323057	−	0.323057i	0.849939	+	0.526882i	$0.176639\pi$
$578$	793.913	+	793.913i	1.37355	+	1.37355i
$579$		−	440.060i		−	0.760035i
$580$	112.488	+	66.8610i	0.193945	+	0.115278i
$581$	805.351			1.38615
$582$	120.739	−	120.739i	0.207455	−	0.207455i
$583$	111.074	+	111.074i	0.190521	+	0.190521i
$584$		−	345.085i		−	0.590899i
$585$	153.958	−	39.1675i	0.263175	−	0.0669529i
$586$	388.443			0.662871
$587$	692.061	−	692.061i	1.17898	−	1.17898i	0.198976	−	0.980004i	$-0.436238\pi$
$587$	692.061	−	692.061i	1.17898	−	1.17898i	0.980004	−	0.198976i	$-0.0637616\pi$
$588$	−37.6074	−	37.6074i	−0.0639581	−	0.0639581i
$589$		−	57.7072i		−	0.0979748i
$590$	−114.385	−	449.618i	−0.193872	−	0.762064i
$591$	262.386			0.443970
$592$	6.92069	−	6.92069i	0.0116904	−	0.0116904i
$593$	453.459	+	453.459i	0.764686	+	0.764686i	0.977165	−	0.212480i	$-0.0681539\pi$
$593$	453.459	+	453.459i	0.764686	+	0.764686i	−0.212480	+	0.977165i	$0.568154\pi$
$594$		−	95.0639i		−	0.160040i
$595$	−487.651	+	820.434i	−0.819582	+	1.37888i
$596$	−237.955			−0.399253
$597$	−133.270	+	133.270i	−0.223232	+	0.223232i
$598$	−50.7916	−	50.7916i	−0.0849358	−	0.0849358i
$599$		−	644.669i		−	1.07624i	−0.842868	−	0.538121i	$-0.819134\pi$
$599$		−	644.669i		−	1.07624i	0.842868	−	0.538121i	$-0.180866\pi$
$600$	107.585	−	58.5280i	0.179308	−	0.0975467i
$601$	−147.557			−0.245519			−0.122760	−	0.992436i	$-0.539174\pi$
$601$	−147.557			−0.245519			−0.122760	+	0.992436i	$0.539174\pi$
$602$	17.2638	−	17.2638i	0.0286775	−	0.0286775i
$603$	−127.330	−	127.330i	−0.211161	−	0.211161i
$604$			423.985i			0.701962i
$605$	199.236	+	118.422i	0.329315	+	0.195739i
$606$	−100.997			−0.166662
$607$	280.715	−	280.715i	0.462462	−	0.462462i	−0.436999	−	0.899462i	$-0.643959\pi$
$607$	280.715	−	280.715i	0.462462	−	0.462462i	0.899462	+	0.436999i	$0.143959\pi$
$608$	−10.6601	−	10.6601i	−0.0175331	−	0.0175331i
$609$		−	131.473i		−	0.215883i
$610$	268.314	−	68.2602i	0.439859	−	0.111902i
$611$	31.5440			0.0516268
$612$	−139.615	+	139.615i	−0.228130	+	0.228130i
$613$	534.330	+	534.330i	0.871665	+	0.871665i	0.992654	−	0.120989i	$-0.0386066\pi$
$613$	534.330	+	534.330i	0.871665	+	0.871665i	−0.120989	+	0.992654i	$0.538607\pi$
$614$			685.419i			1.11632i
$615$	87.8796	+	345.433i	0.142894	+	0.561679i
$616$	−212.244			−0.344552
$617$	−747.441	+	747.441i	−1.21141	+	1.21141i	−0.240848	+	0.970563i	$0.577426\pi$
$617$	−747.441	+	747.441i	−1.21141	+	1.21141i	−0.970563	+	0.240848i	$0.922574\pi$
$618$	−297.263	−	297.263i	−0.481008	−	0.481008i
$619$			627.150i			1.01317i	0.862191	+	0.506583i	$0.169092\pi$
$619$			627.150i			1.01317i	−0.862191	+	0.506583i	$0.830908\pi$
$620$	110.637	−	186.137i	0.178446	−	0.300221i
$621$	−24.9199			−0.0401286
$622$	−44.3383	+	44.3383i	−0.0712834	+	0.0712834i
$623$	641.532	+	641.532i	1.02975	+	1.02975i
$624$		−	73.3751i		−	0.117588i
$625$	−339.539	+	524.727i	−0.543263	+	0.839563i
$626$	6.74316			0.0107718
$627$	42.2246	−	42.2246i	0.0673439	−	0.0673439i
$628$	322.276	+	322.276i	0.513179	+	0.513179i
$629$		−	80.5195i		−	0.128012i
$630$	−105.775	−	62.8708i	−0.167897	−	0.0997949i
$631$	23.8992			0.0378750			0.0189375	−	0.999821i	$-0.493972\pi$
$631$	23.8992			0.0378750			0.0189375	+	0.999821i	$0.493972\pi$
$632$	−127.932	+	127.932i	−0.202424	+	0.202424i
$633$	−255.887	−	255.887i	−0.404244	−	0.404244i
$634$			130.096i			0.205199i
$635$	534.583	−	136.000i	0.841863	−	0.214173i
$636$	42.0628			0.0661365
$637$	114.977	−	114.977i	0.180497	−	0.180497i
$638$	169.286	+	169.286i	0.265339	+	0.265339i
$639$		−	357.890i		−	0.560078i
$640$	−13.9470	−	54.8223i	−0.0217922	−	0.0856598i
$641$	−406.130			−0.633588			−0.316794	−	0.948494i	$-0.602606\pi$
$641$	−406.130			−0.633588			−0.316794	+	0.948494i	$0.602606\pi$
$642$	194.805	−	194.805i	0.303435	−	0.303435i
$643$	−37.4307	−	37.4307i	−0.0582126	−	0.0582126i	0.677401	−	0.735614i	$-0.263106\pi$
$643$	−37.4307	−	37.4307i	−0.0582126	−	0.0582126i	−0.735614	+	0.677401i	$0.763106\pi$
$644$			55.6373i			0.0863933i
$645$	−13.1694	+	22.1565i	−0.0204177	+	0.0343511i
$646$	−124.026			−0.191991
$647$	361.519	−	361.519i	0.558762	−	0.558762i	−0.370193	−	0.928955i	$-0.620708\pi$
$647$	361.519	−	361.519i	0.558762	−	0.558762i	0.928955	+	0.370193i	$0.120708\pi$
$648$	−18.0000	−	18.0000i	−0.0277778	−	0.0277778i
$649$		−	848.780i		−	1.30783i
$650$	178.937	+	328.918i	0.275288	+	0.506028i
$651$	−217.551			−0.334180
$652$	−343.952	+	343.952i	−0.527533	+	0.527533i
$653$	−613.695	−	613.695i	−0.939809	−	0.939809i	0.0584794	−	0.998289i	$-0.481375\pi$
$653$	−613.695	−	613.695i	−0.939809	−	0.939809i	−0.998289	+	0.0584794i	$0.981375\pi$
$654$			271.745i			0.415512i
$655$	574.021	+	341.188i	0.876368	+	0.520897i
$656$	164.631			0.250962
$657$	258.814	−	258.814i	0.393933	−	0.393933i
$658$	−17.2767	−	17.2767i	−0.0262564	−	0.0262564i
$659$			43.1767i			0.0655185i	0.999463	+	0.0327592i	$0.0104295\pi$
$659$			43.1767i			0.0655185i	−0.999463	+	0.0327592i	$0.989571\pi$
$660$	217.151	−	55.2441i	0.329016	−	0.0837032i
$661$	121.963			0.184513			0.0922564	−	0.995735i	$-0.470592\pi$
$661$	121.963			0.184513			0.0922564	+	0.995735i	$0.470592\pi$
$662$	50.7044	−	50.7044i	0.0765928	−	0.0765928i
$663$	−426.845	−	426.845i	−0.643809	−	0.643809i
$664$			392.697i			0.591412i
$665$	−19.0568	−	74.9076i	−0.0286569	−	0.112643i
$666$	10.3810			0.0155871
$667$	44.3763	−	44.3763i	0.0665312	−	0.0665312i
$668$	−290.822	−	290.822i	−0.435362	−	0.435362i
$669$			167.189i			0.249909i
$670$	216.860	−	364.850i	0.323672	−	0.544552i
$671$	506.518			0.754871
$672$	−40.1877	+	40.1877i	−0.0598031	+	0.0598031i
$673$	320.935	+	320.935i	0.476873	+	0.476873i	0.904130	−	0.427257i	$-0.140520\pi$
$673$	320.935	+	320.935i	0.476873	+	0.476873i	−0.427257	+	0.904130i	$0.640520\pi$
$674$			160.288i			0.237816i
$675$	124.585	+	36.7925i	0.184570	+	0.0545074i
$676$	−113.671			−0.168152
$677$	−827.103	+	827.103i	−1.22172	+	1.22172i	−0.254696	+	0.967021i	$0.581976\pi$
$677$	−827.103	+	827.103i	−1.22172	+	1.22172i	−0.967021	+	0.254696i	$0.918024\pi$
$678$	−263.365	−	263.365i	−0.388443	−	0.388443i
$679$		−	404.351i		−	0.595509i
$680$	−400.052	−	237.784i	−0.588312	−	0.349682i
$681$	17.1100			0.0251248
$682$	280.122	−	280.122i	0.410736	−	0.410736i
$683$	400.994	+	400.994i	0.587107	+	0.587107i	0.936847	−	0.349740i	$-0.113730\pi$
$683$	400.994	+	400.994i	0.587107	+	0.587107i	−0.349740	+	0.936847i	$0.613730\pi$
$684$		−	15.9902i		−	0.0233774i
$685$	497.778	−	126.637i	0.726683	−	0.184871i
$686$	−527.907			−0.769543
$687$	117.092	−	117.092i	0.170439	−	0.170439i
$688$	8.41803	+	8.41803i	0.0122355	+	0.0122355i
$689$			128.598i			0.186645i
$690$	−14.4816	−	56.9235i	−0.0209878	−	0.0824978i
$691$	802.239			1.16098			0.580491	−	0.814267i	$-0.302861\pi$
$691$	802.239			1.16098			0.580491	+	0.814267i	$0.302861\pi$
$692$	−197.100	+	197.100i	−0.284826	+	0.284826i
$693$	−159.183	−	159.183i	−0.229702	−	0.229702i
$694$			625.570i			0.901398i
$695$	−495.798	+	834.140i	−0.713378	+	1.20020i
$696$	64.1074			0.0921083
$697$	957.707	−	957.707i	1.37404	−	1.37404i
$698$	−12.2678	−	12.2678i	−0.0175757	−	0.0175757i
$699$		−	541.622i		−	0.774852i
$700$	82.1447	−	278.153i	0.117350	−	0.397362i
$701$	896.380			1.27872			0.639358	−	0.768909i	$-0.279200\pi$
$701$	896.380			1.27872			0.639358	+	0.768909i	$0.279200\pi$
$702$	55.0313	−	55.0313i	0.0783922	−	0.0783922i
$703$	4.61096	+	4.61096i	0.00655897	+	0.00655897i
$704$		−	103.492i		−	0.147006i
$705$	22.1730	+	13.1792i	0.0314510	+	0.0186939i
$706$	789.760			1.11864
$707$	−169.118	+	169.118i	−0.239205	+	0.239205i
$708$	−160.713	−	160.713i	−0.226996	−	0.226996i
$709$		−	266.000i		−	0.375176i	−0.982248	−	0.187588i	$-0.939933\pi$
$709$		−	266.000i		−	0.375176i	0.982248	−	0.187588i	$-0.0600670\pi$
$710$	817.514	−	207.979i	1.15143	−	0.292928i
$711$	−191.898			−0.269899
$712$	−312.817	+	312.817i	−0.439350	+	0.439350i
$713$	−73.4306	−	73.4306i	−0.102988	−	0.102988i
$714$			467.568i			0.654857i
$715$	168.897	+	663.894i	0.236220	+	0.928523i
$716$	301.829			0.421549
$717$	257.732	−	257.732i	0.359459	−	0.359459i
$718$	405.015	+	405.015i	0.564088	+	0.564088i
$719$		−	1262.51i		−	1.75592i	−0.478734	−	0.877960i	$-0.658904\pi$
$719$		−	1262.51i		−	1.75592i	0.478734	−	0.877960i	$-0.341096\pi$
$720$	30.6564	−	51.5770i	0.0425784	−	0.0716347i
$721$	−995.525			−1.38076
$722$	−353.898	+	353.898i	−0.490163	+	0.490163i
$723$	−368.288	−	368.288i	−0.509389	−	0.509389i
$724$			227.604i			0.314370i
$725$	−287.374	+	156.337i	−0.396378	+	0.215637i
$726$	113.545			0.156398
$727$	−530.129	+	530.129i	−0.729201	+	0.729201i	−0.970461	−	0.241259i	$-0.922440\pi$
$727$	−530.129	+	530.129i	−0.729201	+	0.729201i	0.241259	+	0.970461i	$0.422440\pi$
$728$	−122.866	−	122.866i	−0.168771	−	0.168771i
$729$		−	27.0000i		−	0.0370370i
$730$	741.601	+	440.795i	1.01589	+	0.603828i
$731$	97.9405			0.133982
$732$	95.9074	−	95.9074i	0.131021	−	0.131021i
$733$	−468.474	−	468.474i	−0.639119	−	0.639119i	0.311220	−	0.950338i	$-0.399263\pi$
$733$	−468.474	−	468.474i	−0.639119	−	0.639119i	−0.950338	+	0.311220i	$0.899263\pi$
$734$			34.0926i			0.0464477i
$735$	128.858	−	32.7819i	0.175317	−	0.0446013i
$736$	−27.1293			−0.0368605
$737$	549.071	−	549.071i	0.745009	−	0.745009i
$738$	123.473	+	123.473i	0.167308	+	0.167308i
$739$			1042.62i			1.41085i	0.708785	+	0.705424i	$0.249243\pi$
$739$			1042.62i			1.41085i	−0.708785	+	0.705424i	$0.750757\pi$
$740$	6.03269	+	23.7130i	0.00815228	+	0.0320446i
$741$	48.8866			0.0659739
$742$	70.4336	−	70.4336i	0.0949240	−	0.0949240i
$743$	1013.36	+	1013.36i	1.36387	+	1.36387i	0.868923	+	0.494948i	$0.164813\pi$
$743$	1013.36	+	1013.36i	1.36387	+	1.36387i	0.494948	+	0.868923i	$0.335187\pi$
$744$		−	106.080i		−	0.142581i
$745$	303.952	−	511.374i	0.407989	−	0.686408i
$746$	661.235			0.886375
$747$	−294.523	+	294.523i	−0.394274	+	0.394274i
$748$	−602.047	−	602.047i	−0.804876	−	0.804876i
$749$		−	652.398i		−	0.871025i
$750$	−11.6444	+	305.965i	−0.0155259	+	0.407953i
$751$	−639.972			−0.852160			−0.426080	−	0.904686i	$-0.640106\pi$
$751$	−639.972			−0.852160			−0.426080	+	0.904686i	$0.640106\pi$
$752$	8.42430	−	8.42430i	0.0112025	−	0.0112025i
$753$	368.894	+	368.894i	0.489899	+	0.489899i
$754$			195.995i			0.259940i
$755$	−911.161	−	541.578i	−1.20684	−	0.717322i
$756$	−60.2815			−0.0797374
$757$	53.7428	−	53.7428i	0.0709945	−	0.0709945i	−0.670718	−	0.741712i	$-0.734014\pi$
$757$	53.7428	−	53.7428i	0.0709945	−	0.0709945i	0.741712	+	0.670718i	$0.234014\pi$
$758$	169.928	+	169.928i	0.224179	+	0.224179i
$759$		−	107.459i		−	0.141580i
$760$	36.5257	−	9.29229i	0.0480601	−	0.0122267i
$761$	−595.415			−0.782411			−0.391205	−	0.920303i	$-0.627942\pi$
$761$	−595.415			−0.782411			−0.391205	+	0.920303i	$0.627942\pi$
$762$	191.084	−	191.084i	0.250766	−	0.250766i
$763$	455.033	+	455.033i	0.596373	+	0.596373i
$764$			11.2021i			0.0146624i
$765$	−121.701	−	478.377i	−0.159086	−	0.625329i
$766$	318.006			0.415151
$767$	491.348	−	491.348i	0.640610	−	0.640610i
$768$	−19.5959	−	19.5959i	−0.0255155	−	0.0255155i
$769$			825.742i			1.07379i	0.843650	+	0.536893i	$0.180402\pi$
$769$			825.742i			1.07379i	−0.843650	+	0.536893i	$0.819598\pi$
$770$	271.111	−	456.121i	0.352092	−	0.592366i
$771$	198.656			0.257660
$772$	359.308	−	359.308i	0.465424	−	0.465424i
$773$	248.538	+	248.538i	0.321523	+	0.321523i	0.849351	−	0.527828i	$-0.176993\pi$
$773$	248.538	+	248.538i	0.321523	+	0.321523i	−0.527828	+	0.849351i	$0.676993\pi$
$774$			12.6270i			0.0163140i
$775$	258.694	+	475.525i	0.333799	+	0.613580i
$776$	197.165			0.254079
$777$	17.3829	−	17.3829i	0.0223718	−	0.0223718i
$778$	−494.731	−	494.731i	−0.635901	−	0.635901i
$779$			109.686i			0.140804i
$780$	157.686	+	93.7257i	0.202161	+	0.120161i
$781$	1543.29			1.97604
$782$	−157.820	+	157.820i	−0.201815	+	0.201815i
$783$	48.0805	+	48.0805i	0.0614055	+	0.0614055i
$784$		−	61.4126i		−	0.0783324i
$785$	−1104.25	+	280.925i	−1.40668	+	0.357866i
$786$	327.136			0.416204
$787$	715.492	−	715.492i	0.909138	−	0.909138i	−0.0870647	−	0.996203i	$-0.527749\pi$
$787$	715.492	−	715.492i	0.909138	−	0.909138i	0.996203	+	0.0870647i	$0.0277487\pi$
$788$	214.237	+	214.237i	0.271875	+	0.271875i
$789$		−	498.519i		−	0.631836i
$790$	−111.517	−	438.345i	−0.141161	−	0.554868i
$791$	−882.001			−1.11505
$792$	77.6194	−	77.6194i	0.0980042	−	0.0980042i
$793$	293.217	+	293.217i	0.369757	+	0.369757i
$794$			123.646i			0.155725i
$795$	−53.7290	+	90.3947i	−0.0675836	+	0.113704i
$796$	−217.628			−0.273403
$797$	−589.624	+	589.624i	−0.739804	+	0.739804i	−0.972540	−	0.232736i	$-0.925232\pi$
$797$	−589.624	+	589.624i	−0.739804	+	0.739804i	0.232736	+	0.972540i	$0.425232\pi$
$798$	−26.7753	−	26.7753i	−0.0335530	−	0.0335530i
$799$		−	98.0135i		−	0.122670i
$800$	135.630	+	40.0546i	0.169538	+	0.0500683i
$801$	−469.226			−0.585800
$802$	301.250	−	301.250i	0.375624	−	0.375624i
$803$	1116.05	+	1116.05i	1.38985	+	1.38985i
$804$		−	207.929i		−	0.258619i
$805$	−119.567	−	71.0684i	−0.148530	−	0.0882837i
$806$	324.318			0.402380
$807$	−468.864	+	468.864i	−0.580997	+	0.580997i
$808$	−82.4637	−	82.4637i	−0.102059	−	0.102059i
$809$		−	378.673i		−	0.468076i	−0.972227	−	0.234038i	$-0.924806\pi$
$809$		−	378.673i		−	0.468076i	0.972227	−	0.234038i	$-0.0751940\pi$
$810$	61.6750	−	15.6904i	0.0761420	−	0.0193709i
$811$	979.837			1.20818			0.604092	−	0.796914i	$-0.293536\pi$
$811$	979.837			1.20818			0.604092	+	0.796914i	$0.293536\pi$
$812$	107.347	−	107.347i	0.132201	−	0.132201i
$813$	−320.466	−	320.466i	−0.394177	−	0.394177i
$814$			44.7650i			0.0549938i
$815$	−299.819	−	1178.51i	−0.367876	−	1.44603i
$816$	−227.991			−0.279401
$817$	−5.60857	+	5.60857i	−0.00686483	+	0.00686483i
$818$	−425.582	−	425.582i	−0.520271	−	0.520271i
$819$		−	184.298i		−	0.225028i
$820$	−210.291	+	353.798i	−0.256453	+	0.431461i
$821$	−1601.36			−1.95050			−0.975249	−	0.221109i	$-0.929032\pi$
$821$	−1601.36			−1.95050			−0.975249	+	0.221109i	$0.929032\pi$
$822$	177.928	−	177.928i	0.216457	−	0.216457i
$823$	712.866	+	712.866i	0.866180	+	0.866180i	0.992047	−	0.125867i	$-0.0401714\pi$
$823$	712.866	+	712.866i	0.866180	+	0.866180i	−0.125867	+	0.992047i	$0.540171\pi$
$824$		−	485.428i		−	0.589112i
$825$	−158.656	+	537.232i	−0.192310	+	0.651190i
$826$	−538.225			−0.651604
$827$	−216.313	+	216.313i	−0.261563	+	0.261563i	−0.825689	−	0.564126i	$-0.809213\pi$
$827$	−216.313	+	216.313i	−0.261563	+	0.261563i	0.564126	+	0.825689i	$0.309213\pi$
$828$	−20.3470	−	20.3470i	−0.0245737	−	0.0245737i
$829$		−	558.498i		−	0.673701i	−0.941558	−	0.336851i	$-0.890638\pi$
$829$		−	558.498i		−	0.673701i	0.941558	−	0.336851i	$-0.109362\pi$
$830$	−843.922	−	501.613i	−1.01677	−	0.604352i
$831$	543.037			0.653475
$832$	59.9105	−	59.9105i	0.0720078	−	0.0720078i
$833$	−357.256	−	357.256i	−0.428879	−	0.428879i
$834$			475.379i			0.569999i
$835$	996.469	−	253.506i	1.19338	−	0.303600i
$836$	68.9526			0.0824791
$837$	79.5600	−	79.5600i	0.0950538	−	0.0950538i
$838$	−253.765	−	253.765i	−0.302822	−	0.302822i
$839$		−	346.694i		−	0.413223i	−0.978423	−	0.206611i	$-0.933756\pi$
$839$		−	346.694i		−	0.413223i	0.978423	−	0.206611i	$-0.0662435\pi$
$840$	−35.0311	−	137.699i	−0.0417037	−	0.163927i
$841$	669.760			0.796386
$842$	−239.342	+	239.342i	−0.284254	+	0.284254i
$843$	5.44042	+	5.44042i	0.00645364	+	0.00645364i
$844$		−	417.861i		−	0.495096i
$845$	145.198	−	244.283i	0.171832	−	0.289093i
$846$	12.6365			0.0149367
$847$	190.130	−	190.130i	0.224474	−	0.224474i
$848$	34.3441	+	34.3441i	0.0405002	+	0.0405002i
$849$		−	379.048i		−	0.446464i
$850$	1022.01	−	555.994i	1.20237	−	0.654111i
$851$	11.7346			0.0137892
$852$	292.216	−	292.216i	0.342976	−	0.342976i
$853$	−1031.39	−	1031.39i	−1.20913	−	1.20913i	−0.971308	−	0.237827i	$-0.923565\pi$
$853$	−1031.39	−	1031.39i	−1.20913	−	1.20913i	−0.237827	−	0.971308i	$-0.576435\pi$
$854$		−	321.191i		−	0.376102i
$855$	34.3635	+	20.4251i	0.0401912	+	0.0238890i
$856$	318.116			0.371630
$857$	−454.070	+	454.070i	−0.529837	+	0.529837i	−0.920524	−	0.390687i	$-0.872238\pi$
$857$	−454.070	+	454.070i	−0.529837	+	0.529837i	0.390687	+	0.920524i	$0.372238\pi$
$858$	237.305	+	237.305i	0.276580	+	0.276580i
$859$			58.2086i			0.0677632i	0.999426	+	0.0338816i	$0.0107869\pi$
$859$			58.2086i			0.0677632i	−0.999426	+	0.0338816i	$0.989213\pi$
$860$	−28.8435	+	7.33790i	−0.0335389	+	0.00853244i
$861$	413.508			0.480265
$862$	−515.995	+	515.995i	−0.598602	+	0.598602i
$863$	−1006.29	−	1006.29i	−1.16604	−	1.16604i	−0.983130	−	0.182909i	$-0.941449\pi$
$863$	−1006.29	−	1006.29i	−1.16604	−	1.16604i	−0.182909	−	0.983130i	$-0.558551\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	−171.810	−	675.341i	−0.198624	−	0.780741i
$866$	247.881			0.286237
$867$	−972.341	+	972.341i	−1.12150	+	1.12150i
$868$	−177.630	−	177.630i	−0.204642	−	0.204642i
$869$		−	827.500i		−	0.952244i
$870$	−81.8876	+	137.769i	−0.0941237	+	0.158355i
$871$	635.701			0.729852
$872$	−221.879	+	221.879i	−0.254448	+	0.254448i
$873$	147.874	+	147.874i	0.169386	+	0.169386i
$874$		−	18.0751i		−	0.0206809i
$875$	492.835	+	531.832i	0.563240	+	0.607808i
$876$	422.641			0.482467
$877$	−292.199	+	292.199i	−0.333180	+	0.333180i	−0.853793	−	0.520613i	$-0.825704\pi$
$877$	−292.199	+	292.199i	−0.333180	+	0.333180i	0.520613	+	0.853793i	$0.325704\pi$
$878$	−177.022	−	177.022i	−0.201619	−	0.201619i
$879$			475.743i			0.541232i
$880$	222.409	+	132.196i	0.252738	+	0.150223i
$881$	426.082			0.483634			0.241817	−	0.970322i	$-0.422257\pi$
$881$	426.082			0.483634			0.241817	+	0.970322i	$0.422257\pi$
$882$	46.0595	−	46.0595i	0.0522216	−	0.0522216i
$883$	378.863	+	378.863i	0.429064	+	0.429064i	0.888309	−	0.459246i	$-0.151880\pi$
$883$	378.863	+	378.863i	0.429064	+	0.429064i	−0.459246	+	0.888309i	$0.651880\pi$
$884$		−	697.035i		−	0.788501i
$885$	550.667	−	140.092i	0.622222	−	0.158296i
$886$	−344.147			−0.388428
$887$	−419.684	+	419.684i	−0.473149	+	0.473149i	−0.902932	−	0.429783i	$-0.858590\pi$
$887$	−419.684	+	419.684i	−0.473149	+	0.473149i	0.429783	+	0.902932i	$0.358590\pi$
$888$	8.47608	+	8.47608i	0.00954514	+	0.00954514i
$889$		−	639.934i		−	0.719836i
$890$	−272.679	−	1071.84i	−0.306381	−	1.20431i
$891$	116.429			0.130672
$892$	−136.510	+	136.510i	−0.153038	+	0.153038i
$893$	5.61275	+	5.61275i	0.00628527	+	0.00628527i
$894$		−	291.434i		−	0.325989i
$895$	−385.541	+	648.642i	−0.430772	+	0.724740i
$896$	−65.6262			−0.0732435
$897$	62.2067	−	62.2067i	0.0693498	−	0.0693498i
$898$	661.173	+	661.173i	0.736272	+	0.736272i
$899$			283.355i			0.315189i
$900$	71.6819	+	131.764i	0.0796466	+	0.146404i
$901$	399.581			0.443486
$902$	−532.439	+	532.439i	−0.590287	+	0.590287i
$903$	21.1438	+	21.1438i	0.0234151	+	0.0234151i
$904$		−	430.073i		−	0.475744i
$905$	−489.130	−	290.730i	−0.540475	−	0.321249i
$906$	−519.274			−0.573150
$907$	−700.991	+	700.991i	−0.772867	+	0.772867i	−0.978607	−	0.205739i	$-0.934040\pi$
$907$	−700.991	+	700.991i	−0.772867	+	0.772867i	0.205739	+	0.978607i	$0.434040\pi$
$908$	13.9702	+	13.9702i	0.0153857	+	0.0153857i
$909$		−	123.695i		−	0.136079i
$910$	420.985	−	107.100i	0.462621	−	0.117693i
$911$	−36.4634			−0.0400257			−0.0200129	−	0.999800i	$-0.506371\pi$
$911$	−36.4634			−0.0400257			−0.0200129	+	0.999800i	$0.506371\pi$
$912$	13.0559	−	13.0559i	0.0143157	−	0.0143157i
$913$	−1270.04	−	1270.04i	−1.39106	−	1.39106i
$914$			795.989i			0.870885i
$915$	83.6014	+	328.616i	0.0913676	+	0.359143i
$916$	191.210			0.208744
$917$	547.785	−	547.785i	0.597367	−	0.597367i
$918$	−170.993	−	170.993i	−0.186267	−	0.186267i
$919$		−	533.827i		−	0.580878i	−0.956893	−	0.290439i	$-0.906199\pi$
$919$		−	533.827i		−	0.580878i	0.956893	−	0.290439i	$-0.0938014\pi$
$920$	34.6537	−	58.3020i	0.0376670	−	0.0633717i
$921$	−839.463			−0.911469
$922$	−23.4186	+	23.4186i	−0.0253998	+	0.0253998i
$923$	893.390	+	893.390i	0.967920	+	0.967920i
$924$		−	259.945i		−	0.281326i
$925$	−58.6660	−	17.3253i	−0.0634228	−	0.0187301i
$926$	−219.646			−0.237199
$927$	364.071	−	364.071i	0.392741	−	0.392741i
$928$	52.3434	+	52.3434i	0.0564046	+	0.0564046i
$929$			1605.45i			1.72815i	0.503366	+	0.864073i	$0.332095\pi$
$929$			1605.45i			1.72815i	−0.503366	+	0.864073i	$0.667905\pi$
$930$	227.970	+	135.502i	0.245129	+	0.145701i
$931$	40.9166			0.0439491
$932$	442.232	−	442.232i	0.474498	−	0.474498i
$933$	−54.3031	−	54.3031i	−0.0582026	−	0.0582026i
$934$		−	1171.52i		−	1.25430i
$935$	2062.85	−	524.798i	2.20626	−	0.561281i
$936$	89.8657			0.0960104
$937$	424.617	−	424.617i	0.453166	−	0.453166i	−0.443238	−	0.896404i	$-0.646170\pi$
$937$	424.617	−	424.617i	0.453166	−	0.453166i	0.896404	+	0.443238i	$0.146170\pi$
$938$	−348.175	−	348.175i	−0.371188	−	0.371188i
$939$			8.25865i			0.00879515i
$940$	7.34337	+	28.8650i	0.00781209	+	0.0307074i
$941$	1367.24			1.45297			0.726484	−	0.687183i	$-0.241153\pi$
$941$	1367.24			1.45297			0.726484	+	0.687183i	$0.241153\pi$
$942$	−394.706	+	394.706i	−0.419009	+	0.419009i
$943$	139.573	+	139.573i	0.148009	+	0.148009i
$944$		−	262.444i		−	0.278012i
$945$	77.0007	−	129.547i	0.0814822	−	0.137087i
$946$	−54.4502			−0.0575583
$947$	−523.311	+	523.311i	−0.552599	+	0.552599i	−0.927190	−	0.374591i	$-0.877783\pi$
$947$	−523.311	+	523.311i	−0.552599	+	0.552599i	0.374591	+	0.927190i	$0.377783\pi$
$948$	−156.684	−	156.684i	−0.165279	−	0.165279i
$949$			1292.14i			1.36158i
$950$	−26.6866	+	90.3647i	−0.0280912	+	0.0951208i
$951$	−159.335			−0.167544
$952$	−381.768	+	381.768i	−0.401016	+	0.401016i
$953$	1162.80	+	1162.80i	1.22014	+	1.22014i	0.967580	+	0.252563i	$0.0812736\pi$
$953$	1162.80	+	1162.80i	1.22014	+	1.22014i	0.252563	+	0.967580i	$0.418726\pi$
$954$			51.5162i			0.0540002i
$955$	−24.0738	−	14.3090i	−0.0252081	−	0.0149833i
$956$	420.875			0.440246
$957$	−207.332	+	207.332i	−0.216648	+	0.216648i
$958$	654.854	+	654.854i	0.683564	+	0.683564i
$959$		−	595.876i		−	0.621351i
$960$	67.1433	−	17.0815i	0.0699409	−	0.0177933i
$961$	−492.126			−0.512098
$962$	−25.9139	+	25.9139i	−0.0269375	+	0.0269375i
$963$	238.587	+	238.587i	0.247754	+	0.247754i
$964$		−	601.413i		−	0.623872i
$965$	313.204	+	1231.13i	0.324564	+	1.27578i
$966$	−68.1415			−0.0705399
$967$	44.9952	−	44.9952i	0.0465307	−	0.0465307i	−0.683459	−	0.729989i	$-0.739525\pi$
$967$	44.9952	−	44.9952i	0.0465307	−	0.0465307i	0.729989	+	0.683459i	$0.239525\pi$
$968$	92.7092	+	92.7092i	0.0957739	+	0.0957739i
$969$		−	151.900i		−	0.156760i
$970$	−251.850	+	423.717i	−0.259639	+	0.436821i
$971$	822.343			0.846903			0.423452	−	0.905919i	$-0.360818\pi$
$971$	822.343			0.846903			0.423452	+	0.905919i	$0.360818\pi$
$972$	22.0454	−	22.0454i	0.0226805	−	0.0226805i
$973$	796.015	+	796.015i	0.818104	+	0.818104i
$974$			336.718i			0.345706i
$975$	−402.841	+	219.153i	−0.413170	+	0.224772i
$976$	156.616			0.160467
$977$	−232.284	+	232.284i	−0.237753	+	0.237753i	−0.815919	−	0.578166i	$-0.803769\pi$
$977$	−232.284	+	232.284i	−0.237753	+	0.237753i	0.578166	+	0.815919i	$0.303769\pi$
$978$	−421.253	−	421.253i	−0.430729	−	0.430729i
$979$		−	2023.39i		−	2.06679i
$980$	131.978	+	78.4455i	0.134672	+	0.0800464i
$981$	−332.818			−0.339264
$982$	705.190	−	705.190i	0.718117	−	0.718117i
$983$	−159.482	−	159.482i	−0.162240	−	0.162240i	0.621318	−	0.783558i	$-0.286597\pi$
$983$	−159.482	−	159.482i	−0.162240	−	0.162240i	−0.783558	+	0.621318i	$0.786597\pi$
$984$			201.631i			0.204909i
$985$	−734.061	+	186.748i	−0.745239	+	0.189592i
$986$	608.995			0.617642
$987$	21.1596	−	21.1596i	0.0214383	−	0.0214383i
$988$	39.9158	+	39.9158i	0.0404006	+	0.0404006i
$989$			14.2735i			0.0144322i
$990$	67.6599	+	265.954i	0.0683433	+	0.268641i
$991$	−797.656			−0.804900			−0.402450	−	0.915442i	$-0.631841\pi$
$991$	−797.656			−0.804900			−0.402450	+	0.915442i	$0.631841\pi$
$992$	86.6140	−	86.6140i	0.0873125	−	0.0873125i
$993$	62.1000	+	62.1000i	0.0625377	+	0.0625377i
$994$		−	978.623i		−	0.984530i
$995$	277.988	−	467.692i	0.279385	−	0.470043i
$996$	−480.954			−0.482886
$997$	−938.091	+	938.091i	−0.940914	+	0.940914i	−0.998349	−	0.0574351i	$-0.981708\pi$
$997$	−938.091	+	938.091i	−0.940914	+	0.940914i	0.0574351	+	0.998349i	$0.481708\pi$
$998$	−199.214	−	199.214i	−0.199614	−	0.199614i
$999$			12.7141i			0.0127268i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.b.553.7	yes	48
5.2	odd	4	inner	690.3.k.b.277.7	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.b.277.7	✓	48	5.2	odd	4	inner
690.3.k.b.553.7	yes	48	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(4.29808 + 2.55470i) q^{5} +2.44949 q^{6} +(4.10164 - 4.10164i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(4.29808 + 2.55470i) q^{5} +2.44949 q^{6} +(4.10164 - 4.10164i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(-6.85278 + 1.74338i) q^{10} -12.9366 q^{11} +(-2.44949 + 2.44949i) q^{12} +(-7.48881 - 7.48881i) q^{13} +8.20327i q^{14} +(-2.13519 - 8.39291i) q^{15} -4.00000 q^{16} +(-23.2692 + 23.2692i) q^{17} +(-3.00000 - 3.00000i) q^{18} -2.66503i q^{19} +(5.10941 - 8.59616i) q^{20} -10.0469 q^{21} +(12.9366 - 12.9366i) q^{22} +(-3.39116 - 3.39116i) q^{23} -4.89898i q^{24} +(11.9470 + 21.9606i) q^{25} +14.9776 q^{26} +(3.67423 - 3.67423i) q^{27} +(-8.20327 - 8.20327i) q^{28} +13.0859i q^{29} +(10.5281 + 6.25772i) q^{30} +21.6535 q^{31} +(4.00000 - 4.00000i) q^{32} +(15.8440 + 15.8440i) q^{33} -46.5384i q^{34} +(28.1076 - 7.15070i) q^{35} +6.00000 q^{36} +(-1.73017 + 1.73017i) q^{37} +(2.66503 + 2.66503i) q^{38} +18.3438i q^{39} +(3.48675 + 13.7056i) q^{40} -41.1577 q^{41} +(10.0469 - 10.0469i) q^{42} +(-2.10451 - 2.10451i) q^{43} +25.8731i q^{44} +(-7.66411 + 12.8942i) q^{45} +6.78233 q^{46} +(-2.10608 + 2.10608i) q^{47} +(4.89898 + 4.89898i) q^{48} +15.3532i q^{49} +(-33.9076 - 10.0137i) q^{50} +56.9977 q^{51} +(-14.9776 + 14.9776i) q^{52} +(-8.58604 - 8.58604i) q^{53} +7.34847i q^{54} +(-55.6024 - 33.0491i) q^{55} +16.4065 q^{56} +(-3.26398 + 3.26398i) q^{57} +(-13.0859 - 13.0859i) q^{58} +65.6109i q^{59} +(-16.7858 + 4.27038i) q^{60} -39.1540 q^{61} +(-21.6535 + 21.6535i) q^{62} +(12.3049 + 12.3049i) q^{63} +8.00000i q^{64} +(-13.0558 - 51.3192i) q^{65} -31.6880 q^{66} +(-42.4434 + 42.4434i) q^{67} +(46.5384 + 46.5384i) q^{68} +8.30662i q^{69} +(-20.9569 + 35.2583i) q^{70} -119.297 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-86.2712 - 86.2712i) q^{73} -3.46035i q^{74} +(12.2642 - 41.5282i) q^{75} -5.33005 q^{76} +(-53.0611 + 53.0611i) q^{77} +(-18.3438 - 18.3438i) q^{78} +63.9660i q^{79} +(-17.1923 - 10.2188i) q^{80} -9.00000 q^{81} +(41.1577 - 41.1577i) q^{82} +(98.1743 + 98.1743i) q^{83} +20.0938i q^{84} +(-159.459 + 40.5670i) q^{85} +4.20901 q^{86} +(16.0268 - 16.0268i) q^{87} +(-25.8731 - 25.8731i) q^{88} +156.409i q^{89} +(-5.23013 - 20.5583i) q^{90} -61.4328 q^{91} +(-6.78233 + 6.78233i) q^{92} +(-26.5200 - 26.5200i) q^{93} -4.21215i q^{94} +(6.80835 - 11.4545i) q^{95} -9.79796 q^{96} +(49.2914 - 49.2914i) q^{97} +(-15.3532 - 15.3532i) q^{98} -38.8097i 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