LMFDB - Embedded newform 690.3.k.b.277.7

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			277.7
Character	$\chi$	$=$	690.277
Dual form			690.3.k.b.553.7

$q$-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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$			2.00000i			0.500000i
$5$	4.29808	−	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	0.936532	−	0.350583i	$-0.114017\pi$
$7$	4.10164	+	4.10164i	0.585948	+	0.585948i	−0.350583	+	0.936532i	$0.614017\pi$
$8$	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	−0.933816	−	0.357754i	$-0.883543\pi$
$13$	−7.48881	+	7.48881i	−0.576062	+	0.576062i	0.357754	+	0.933816i	$0.383543\pi$
$14$		−	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	−0.862186	−	0.506591i	$-0.830905\pi$
$17$	−23.2692	−	23.2692i	−1.36878	−	1.36878i	−0.506591	−	0.862186i	$-0.669095\pi$
$18$	−3.00000	+	3.00000i	−0.166667	+	0.166667i
$19$			2.66503i			0.140265i	0.997538	+	0.0701323i	$0.0223421\pi$
$19$			2.66503i			0.140265i	−0.997538	+	0.0701323i	$0.977658\pi$
$20$	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	$-0.927560\pi$
$29$		−	13.0859i		−	0.451237i	0.974216	−	0.225618i	$-0.0724402\pi$
$30$	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	0.683339	−	0.730101i	$-0.260527\pi$
$37$	−1.73017	−	1.73017i	−0.0467614	−	0.0467614i	−0.730101	+	0.683339i	$0.760527\pi$
$38$	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	−0.731154	−	0.682212i	$-0.761018\pi$
$43$	−2.10451	+	2.10451i	−0.0489420	+	0.0489420i	0.682212	+	0.731154i	$0.261018\pi$
$44$		−	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	0.684347	−	0.729157i	$-0.260088\pi$
$47$	−2.10608	−	2.10608i	−0.0448101	−	0.0448101i	−0.729157	+	0.684347i	$0.760088\pi$
$48$	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	−0.783452	−	0.621452i	$-0.786543\pi$
$53$	−8.58604	+	8.58604i	−0.162001	+	0.162001i	0.621452	+	0.783452i	$0.286543\pi$
$54$		−	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	$-0.812326\pi$
$59$		−	65.6109i		−	1.11205i	0.831166	−	0.556025i	$-0.187674\pi$
$60$	−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	0.315457	−	0.948940i	$-0.397842\pi$
$67$	−42.4434	−	42.4434i	−0.633483	−	0.633483i	−0.948940	+	0.315457i	$0.897842\pi$
$68$	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	−0.202519	+	0.979278i	$0.564913\pi$
$73$	−86.2712	+	86.2712i	−1.18180	+	1.18180i	−0.979278	+	0.202519i	$0.935087\pi$
$74$			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	$-0.867324\pi$
$79$		−	63.9660i		−	0.809697i	0.914384	−	0.404848i	$-0.132676\pi$
$80$	−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	0.203814	−	0.979010i	$-0.434666\pi$
$83$	98.1743	−	98.1743i	1.18282	−	1.18282i	0.979010	−	0.203814i	$-0.0653337\pi$
$84$		−	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	$-0.658411\pi$
$89$		−	156.409i		−	1.75740i	0.477373	−	0.878701i	$-0.341589\pi$
$90$	−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	0.913961	−	0.405802i	$-0.133008\pi$
$97$	49.2914	+	49.2914i	0.508158	+	0.508158i	−0.405802	+	0.913961i	$0.633008\pi$
$98$	−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	−0.198028	+	0.980196i	$0.563454\pi$
$103$	−121.357	+	121.357i	−1.17822	+	1.17822i	−0.980196	+	0.198028i	$0.936546\pi$
$104$			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	0.973204	−	0.229943i	$-0.0738540\pi$
$107$	79.5289	+	79.5289i	0.743261	+	0.743261i	−0.229943	+	0.973204i	$0.573854\pi$
$108$	−7.34847	+	7.34847i	−0.0680414	+	0.0680414i
$109$		−	110.939i		−	1.01779i	−0.860828	−	0.508896i	$-0.830054\pi$
$109$		−	110.939i		−	1.01779i	0.860828	−	0.508896i	$-0.169946\pi$
$110$	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	−0.998877	−	0.0473884i	$-0.984910\pi$
$113$	−107.518	+	107.518i	−0.951488	+	0.951488i	0.0473884	+	0.998877i	$0.484910\pi$
$114$			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	0.944050	−	0.329801i	$-0.106982\pi$
$127$	78.0096	+	78.0096i	0.614249	+	0.614249i	−0.329801	+	0.944050i	$0.606982\pi$
$128$	−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	0.920635	−	0.390425i	$-0.127672\pi$
$137$	72.6388	+	72.6388i	0.530210	+	0.530210i	−0.390425	+	0.920635i	$0.627672\pi$
$138$	−8.30662	+	8.30662i	−0.0601929	+	0.0601929i
$139$		−	194.073i		−	1.39621i	−0.715997	−	0.698103i	$-0.754028\pi$
$139$		−	194.073i		−	1.39621i	0.715997	−	0.698103i	$-0.245972\pi$
$140$	−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	$0.130730\pi$
$149$			118.977i			0.798506i	−0.916841	+	0.399253i	$0.869270\pi$
$150$	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	−0.999643	−	0.0267147i	$-0.991495\pi$
$157$	−161.138	−	161.138i	−1.02636	−	1.02636i	−0.0267147	−	0.999643i	$-0.508505\pi$
$158$	−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	−0.0566742	+	0.998393i	$0.518050\pi$
$163$	−171.976	+	171.976i	−1.05507	+	1.05507i	−0.998393	+	0.0566742i	$0.981950\pi$
$164$		−	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	0.992551	−	0.121828i	$-0.0388755\pi$
$167$	145.411	+	145.411i	0.870724	+	0.870724i	−0.121828	+	0.992551i	$0.538876\pi$
$168$	−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	−0.932031	−	0.362379i	$-0.881965\pi$
$173$	−98.5498	+	98.5498i	−0.569652	+	0.569652i	0.362379	+	0.932031i	$0.381965\pi$
$174$		−	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	$-0.861487\pi$
$179$		−	150.914i		−	0.843097i	0.906806	−	0.421549i	$-0.138513\pi$
$180$	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	−0.0669105	−	0.997759i	$-0.521314\pi$
$193$	179.654	−	179.654i	0.930848	−	0.930848i	0.997759	+	0.0669105i	$0.0213142\pi$
$194$		−	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	0.380876	−	0.924626i	$-0.375622\pi$
$197$	−107.119	−	107.119i	−0.543749	−	0.543749i	−0.924626	+	0.380876i	$0.875622\pi$
$198$	38.8097	−	38.8097i	0.196008	−	0.196008i
$199$			108.814i			0.546805i	0.961900	+	0.273403i	$0.0881491\pi$
$199$			108.814i			0.546805i	−0.961900	+	0.273403i	$0.911851\pi$
$200$	−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	−0.843385	−	0.537310i	$-0.819441\pi$
$223$	−68.2548	+	68.2548i	−0.306075	+	0.306075i	0.537310	+	0.843385i	$0.319441\pi$
$224$			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	0.691554	−	0.722325i	$-0.256927\pi$
$227$	−6.98511	−	6.98511i	−0.0307714	−	0.0307714i	−0.722325	+	0.691554i	$0.756927\pi$
$228$	6.52796	−	6.52796i	0.0286314	−	0.0286314i
$229$		−	95.6049i		−	0.417488i	−0.977970	−	0.208744i	$-0.933062\pi$
$229$		−	95.6049i		−	0.417488i	0.977970	−	0.208744i	$-0.0669376\pi$
$230$	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	−0.0497647	−	0.998761i	$-0.515847\pi$
$233$	221.116	−	221.116i	0.948996	−	0.948996i	0.998761	+	0.0497647i	$0.0158471\pi$
$234$		−	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	$-0.854891\pi$
$239$		−	210.437i		−	0.880491i	0.897877	−	0.440246i	$-0.145109\pi$
$240$	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	0.531494	−	0.847062i	$-0.321631\pi$
$257$	−81.1010	−	81.1010i	−0.315568	−	0.315568i	−0.847062	+	0.531494i	$0.821631\pi$
$258$	−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	−0.204937	−	0.978775i	$-0.565699\pi$
$263$	203.519	−	203.519i	0.773838	−	0.773838i	0.978775	+	0.204937i	$0.0656990\pi$
$264$		−	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	$0.252017\pi$
$269$			382.826i			1.42315i	−0.702612	+	0.711573i	$0.747983\pi$
$270$	−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	0.182809	−	0.983149i	$-0.441481\pi$
$277$	−221.694	−	221.694i	−0.800340	−	0.800340i	−0.983149	+	0.182809i	$0.941481\pi$
$278$	−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	−0.378711	−	0.925515i	$-0.623633\pi$
$283$	154.746	−	154.746i	0.546804	−	0.546804i	0.925515	+	0.378711i	$0.123633\pi$
$284$		−	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	−0.956056	−	0.293185i	$-0.905285\pi$
$293$	−194.221	+	194.221i	−0.662871	+	0.662871i	0.293185	+	0.956056i	$0.405285\pi$
$294$		−	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	0.992277	+	0.124040i	$0.0395851\pi$
$307$	342.709	+	342.709i	1.11632	+	1.11632i	0.124040	+	0.992277i	$0.460415\pi$
$308$	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	−0.712472	−	0.701700i	$-0.752425\pi$
$313$	−3.37158	+	3.37158i	−0.0107718	+	0.0107718i	0.701700	+	0.712472i	$0.252425\pi$
$314$			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	0.802223	−	0.597024i	$-0.203650\pi$
$317$	65.0482	+	65.0482i	0.205199	+	0.205199i	−0.597024	+	0.802223i	$0.703650\pi$
$318$	−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	0.815945	−	0.578129i	$-0.196217\pi$
$337$	80.1441	+	80.1441i	0.237816	+	0.237816i	−0.578129	+	0.815945i	$0.696217\pi$
$338$	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	0.995557	−	0.0941595i	$-0.0300164\pi$
$347$	312.785	+	312.785i	0.901398	+	0.901398i	−0.0941595	+	0.995557i	$0.530016\pi$
$348$	−32.0537	+	32.0537i	−0.0921083	+	0.0921083i
$349$		−	12.2678i		−	0.0351514i	−0.999846	−	0.0175757i	$-0.994405\pi$
$349$		−	12.2678i		−	0.0351514i	0.999846	−	0.0175757i	$-0.00559481\pi$
$350$	−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	−0.126699	+	0.991941i	$0.540438\pi$
$353$	−394.880	+	394.880i	−1.11864	+	1.11864i	−0.991941	+	0.126699i	$0.959562\pi$
$354$		−	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	$0.190772\pi$
$359$			405.015i			1.12818i	−0.825715	+	0.564088i	$0.809228\pi$
$360$	−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	0.729949	−	0.683501i	$-0.239544\pi$
$367$	17.0463	+	17.0463i	0.0464477	+	0.0464477i	−0.683501	+	0.729949i	$0.739544\pi$
$368$	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	−0.994173	−	0.107798i	$-0.965620\pi$
$373$	−330.618	+	330.618i	−0.886375	+	0.886375i	0.107798	+	0.994173i	$0.465620\pi$
$374$		−	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	$0.0719700\pi$
$379$			169.928i			0.448358i	−0.974548	+	0.224179i	$0.928030\pi$
$380$	−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	−0.883528	−	0.468377i	$-0.844839\pi$
$383$	−159.003	+	159.003i	−0.415151	+	0.415151i	0.468377	+	0.883528i	$0.344839\pi$
$384$		−	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	$-0.780629\pi$
$389$		−	494.731i		−	1.27180i	0.771770	−	0.635901i	$-0.219371\pi$
$390$	−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	0.780669	−	0.624944i	$-0.214878\pi$
$397$	61.8230	+	61.8230i	0.155725	+	0.155725i	−0.624944	+	0.780669i	$0.714878\pi$
$398$	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	$-0.825831\pi$
$409$		−	425.582i		−	1.04054i	0.854001	−	0.520271i	$-0.174169\pi$
$410$	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	$-0.902071\pi$
$419$		−	253.765i		−	0.605645i	0.953047	−	0.302822i	$-0.0979289\pi$
$420$	−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	−0.835590	−	0.549353i	$-0.814874\pi$
$433$	−123.940	+	123.940i	−0.286237	+	0.286237i	0.549353	+	0.835590i	$0.314874\pi$
$434$		−	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	$-0.935380\pi$
$439$		−	177.022i		−	0.403238i	0.979464	−	0.201619i	$-0.0646203\pi$
$440$	−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	−0.485699	−	0.874126i	$-0.661435\pi$
$443$	172.073	−	172.073i	0.388428	−	0.388428i	0.874126	+	0.485699i	$0.161435\pi$
$444$			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	$0.263416\pi$
$449$			661.173i			1.47254i	−0.676685	+	0.736272i	$0.736584\pi$
$450$	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	0.992569	−	0.121684i	$-0.0388295\pi$
$457$	397.994	+	397.994i	0.870885	+	0.870885i	−0.121684	+	0.992569i	$0.538829\pi$
$458$	−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	−0.578490	−	0.815689i	$-0.696358\pi$
$463$	109.823	−	109.823i	0.237199	−	0.237199i	0.815689	+	0.578490i	$0.196358\pi$
$464$			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	−0.953771	−	0.300534i	$-0.902835\pi$
$467$	−585.760	−	585.760i	−1.25430	−	1.25430i	−0.300534	−	0.953771i	$-0.597165\pi$
$468$	−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	$0.239571\pi$
$479$			654.854i			1.36713i	−0.729891	+	0.683564i	$0.760429\pi$
$480$	−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	0.858507	−	0.512801i	$-0.171392\pi$
$487$	168.359	+	168.359i	0.345706	+	0.345706i	−0.512801	+	0.858507i	$0.671392\pi$
$488$	−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	$-0.936031\pi$
$499$		−	199.214i		−	0.399227i	0.979875	−	0.199614i	$-0.0639687\pi$
$500$	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	−0.696689	−	0.717374i	$-0.745344\pi$
$503$	10.4047	−	10.4047i	0.0206852	−	0.0206852i	0.717374	+	0.696689i	$0.245344\pi$
$504$		−	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	$-0.762179\pi$
$509$		−	691.773i		−	1.35908i	0.733637	−	0.679541i	$-0.237821\pi$
$510$	−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	−0.529151	−	0.848528i	$-0.677490\pi$
$523$	167.034	−	167.034i	0.319377	−	0.319377i	0.848528	+	0.529151i	$0.177490\pi$
$524$			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	0.644565	−	0.764550i	$-0.277039\pi$
$547$	−65.6316	−	65.6316i	−0.119985	−	0.119985i	−0.764550	+	0.644565i	$0.777039\pi$
$548$	−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	0.668963	−	0.743296i	$-0.266739\pi$
$557$	−41.4036	−	41.4036i	−0.0743332	−	0.0743332i	−0.743296	+	0.668963i	$0.766739\pi$
$558$	−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	−0.324213	+	0.945984i	$0.605099\pi$
$563$	−715.121	+	715.121i	−1.27020	+	1.27020i	−0.945984	+	0.324213i	$0.894901\pi$
$564$			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	$-0.905477\pi$
$569$		−	332.987i		−	0.585215i	0.956233	−	0.292608i	$-0.0945229\pi$
$570$	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	0.849939	−	0.526882i	$-0.176639\pi$
$577$	186.404	+	186.404i	0.323057	+	0.323057i	−0.526882	+	0.849939i	$0.676639\pi$
$578$	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	0.980004	+	0.198976i	$0.0637616\pi$
$587$	692.061	+	692.061i	1.17898	+	1.17898i	0.198976	+	0.980004i	$0.436238\pi$
$588$	−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	−0.212480	−	0.977165i	$-0.568154\pi$
$593$	453.459	−	453.459i	0.764686	−	0.764686i	0.977165	+	0.212480i	$0.0681539\pi$
$594$			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	$0.180866\pi$
$599$			644.669i			1.07624i	−0.842868	+	0.538121i	$0.819134\pi$
$600$	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	0.899462	−	0.436999i	$-0.143959\pi$
$607$	280.715	+	280.715i	0.462462	+	0.462462i	−0.436999	+	0.899462i	$0.643959\pi$
$608$	−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	−0.120989	−	0.992654i	$-0.538607\pi$
$613$	534.330	−	534.330i	0.871665	−	0.871665i	0.992654	+	0.120989i	$0.0386066\pi$
$614$		−	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	−0.970563	−	0.240848i	$-0.922574\pi$
$617$	−747.441	−	747.441i	−1.21141	−	1.21141i	−0.240848	−	0.970563i	$-0.577426\pi$
$618$	−297.263	+	297.263i	−0.481008	+	0.481008i
$619$		−	627.150i		−	1.01317i	−0.862191	−	0.506583i	$-0.830908\pi$
$619$		−	627.150i		−	1.01317i	0.862191	−	0.506583i	$-0.169092\pi$
$620$	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	−0.735614	−	0.677401i	$-0.763106\pi$
$643$	−37.4307	+	37.4307i	−0.0582126	+	0.0582126i	0.677401	+	0.735614i	$0.263106\pi$
$644$		−	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	0.928955	−	0.370193i	$-0.120708\pi$
$647$	361.519	+	361.519i	0.558762	+	0.558762i	−0.370193	+	0.928955i	$0.620708\pi$
$648$	−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	−0.998289	−	0.0584794i	$-0.981375\pi$
$653$	−613.695	+	613.695i	−0.939809	+	0.939809i	0.0584794	+	0.998289i	$0.481375\pi$
$654$		−	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	$-0.989571\pi$
$659$		−	43.1767i		−	0.0655185i	0.999463	−	0.0327592i	$-0.0104295\pi$
$660$	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	−0.427257	−	0.904130i	$-0.640520\pi$
$673$	320.935	−	320.935i	0.476873	−	0.476873i	0.904130	+	0.427257i	$0.140520\pi$
$674$		−	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	−0.967021	−	0.254696i	$-0.918024\pi$
$677$	−827.103	−	827.103i	−1.22172	−	1.22172i	−0.254696	−	0.967021i	$-0.581976\pi$
$678$	−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	−0.349740	−	0.936847i	$-0.613730\pi$
$683$	400.994	−	400.994i	0.587107	−	0.587107i	0.936847	+	0.349740i	$0.113730\pi$
$684$			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	$0.0600670\pi$
$709$			266.000i			0.375176i	−0.982248	+	0.187588i	$0.939933\pi$
$710$	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	$0.341096\pi$
$719$			1262.51i			1.75592i	−0.478734	+	0.877960i	$0.658904\pi$
$720$	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	0.241259	−	0.970461i	$-0.422440\pi$
$727$	−530.129	−	530.129i	−0.729201	−	0.729201i	−0.970461	+	0.241259i	$0.922440\pi$
$728$	−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	−0.950338	−	0.311220i	$-0.899263\pi$
$733$	−468.474	+	468.474i	−0.639119	+	0.639119i	0.311220	+	0.950338i	$0.399263\pi$
$734$		−	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	$-0.750757\pi$
$739$		−	1042.62i		−	1.41085i	0.708785	−	0.705424i	$-0.249243\pi$
$740$	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	0.494948	−	0.868923i	$-0.335187\pi$
$743$	1013.36	−	1013.36i	1.36387	−	1.36387i	0.868923	−	0.494948i	$-0.164813\pi$
$744$			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	0.741712	−	0.670718i	$-0.234014\pi$
$757$	53.7428	+	53.7428i	0.0709945	+	0.0709945i	−0.670718	+	0.741712i	$0.734014\pi$
$758$	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	$-0.819598\pi$
$769$		−	825.742i		−	1.07379i	0.843650	−	0.536893i	$-0.180402\pi$
$770$	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	−0.527828	−	0.849351i	$-0.676993\pi$
$773$	248.538	−	248.538i	0.321523	−	0.321523i	0.849351	+	0.527828i	$0.176993\pi$
$774$		−	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	0.996203	−	0.0870647i	$-0.0277487\pi$
$787$	715.492	+	715.492i	0.909138	+	0.909138i	−0.0870647	+	0.996203i	$0.527749\pi$
$788$	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	0.232736	−	0.972540i	$-0.425232\pi$
$797$	−589.624	−	589.624i	−0.739804	−	0.739804i	−0.972540	+	0.232736i	$0.925232\pi$
$798$	−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	$0.0751940\pi$
$809$			378.673i			0.468076i	−0.972227	+	0.234038i	$0.924806\pi$
$810$	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	−0.125867	−	0.992047i	$-0.540171\pi$
$823$	712.866	−	712.866i	0.866180	−	0.866180i	0.992047	+	0.125867i	$0.0401714\pi$
$824$			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	0.564126	−	0.825689i	$-0.309213\pi$
$827$	−216.313	−	216.313i	−0.261563	−	0.261563i	−0.825689	+	0.564126i	$0.809213\pi$
$828$	−20.3470	+	20.3470i	−0.0245737	+	0.0245737i
$829$			558.498i			0.673701i	0.941558	+	0.336851i	$0.109362\pi$
$829$			558.498i			0.673701i	−0.941558	+	0.336851i	$0.890638\pi$
$830$	−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	$0.0662435\pi$
$839$			346.694i			0.413223i	−0.978423	+	0.206611i	$0.933756\pi$
$840$	−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	−0.237827	+	0.971308i	$0.576435\pi$
$853$	−1031.39	+	1031.39i	−1.20913	+	1.20913i	−0.971308	+	0.237827i	$0.923565\pi$
$854$			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	0.390687	−	0.920524i	$-0.372238\pi$
$857$	−454.070	−	454.070i	−0.529837	−	0.529837i	−0.920524	+	0.390687i	$0.872238\pi$
$858$	237.305	−	237.305i	0.276580	−	0.276580i
$859$		−	58.2086i		−	0.0677632i	−0.999426	−	0.0338816i	$-0.989213\pi$
$859$		−	58.2086i		−	0.0677632i	0.999426	−	0.0338816i	$-0.0107869\pi$
$860$	−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	−0.182909	+	0.983130i	$0.558551\pi$
$863$	−1006.29	+	1006.29i	−1.16604	+	1.16604i	−0.983130	+	0.182909i	$0.941449\pi$
$864$			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	0.520613	−	0.853793i	$-0.325704\pi$
$877$	−292.199	−	292.199i	−0.333180	−	0.333180i	−0.853793	+	0.520613i	$0.825704\pi$
$878$	−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	−0.459246	−	0.888309i	$-0.651880\pi$
$883$	378.863	−	378.863i	0.429064	−	0.429064i	0.888309	+	0.459246i	$0.151880\pi$
$884$			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	0.429783	−	0.902932i	$-0.358590\pi$
$887$	−419.684	−	419.684i	−0.473149	−	0.473149i	−0.902932	+	0.429783i	$0.858590\pi$
$888$	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	0.205739	−	0.978607i	$-0.434040\pi$
$907$	−700.991	−	700.991i	−0.772867	−	0.772867i	−0.978607	+	0.205739i	$0.934040\pi$
$908$	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	$0.0938014\pi$
$919$			533.827i			0.580878i	−0.956893	+	0.290439i	$0.906199\pi$
$920$	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	$-0.667905\pi$
$929$		−	1605.45i		−	1.72815i	0.503366	−	0.864073i	$-0.332095\pi$
$930$	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	0.896404	−	0.443238i	$-0.146170\pi$
$937$	424.617	+	424.617i	0.453166	+	0.453166i	−0.443238	+	0.896404i	$0.646170\pi$
$938$	−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	0.374591	−	0.927190i	$-0.377783\pi$
$947$	−523.311	−	523.311i	−0.552599	−	0.552599i	−0.927190	+	0.374591i	$0.877783\pi$
$948$	−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	0.252563	−	0.967580i	$-0.418726\pi$
$953$	1162.80	−	1162.80i	1.22014	−	1.22014i	0.967580	−	0.252563i	$-0.0812736\pi$
$954$		−	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	0.729989	−	0.683459i	$-0.239525\pi$
$967$	44.9952	+	44.9952i	0.0465307	+	0.0465307i	−0.683459	+	0.729989i	$0.739525\pi$
$968$	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	0.578166	−	0.815919i	$-0.303769\pi$
$977$	−232.284	−	232.284i	−0.237753	−	0.237753i	−0.815919	+	0.578166i	$0.803769\pi$
$978$	−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	−0.783558	−	0.621318i	$-0.786597\pi$
$983$	−159.482	+	159.482i	−0.162240	+	0.162240i	0.621318	+	0.783558i	$0.286597\pi$
$984$		−	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	0.0574351	−	0.998349i	$-0.481708\pi$
$997$	−938.091	−	938.091i	−0.940914	−	0.940914i	−0.998349	+	0.0574351i	$0.981708\pi$
$998$	−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.277.7	✓	48
5.3	odd	4	inner	690.3.k.b.553.7	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.b.277.7	✓	48	1.1	even	1	trivial
690.3.k.b.553.7	yes	48	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.29808 - 2.55470i) q^{5} +2.44949 q^{6} +(4.10164 + 4.10164i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(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

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