LMFDB - Embedded newform 690.3.k.b.553.16

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			553.16
Character	$\chi$	$=$	690.553
Dual form			690.3.k.b.277.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(3.93589 + 3.08362i) q^{5} -2.44949 q^{6} +(-1.42240 + 1.42240i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(3.93589 + 3.08362i) q^{5} -2.44949 q^{6} +(-1.42240 + 1.42240i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(-7.01952 + 0.852269i) q^{10} +3.13344 q^{11} +(2.44949 - 2.44949i) q^{12} +(-8.16946 - 8.16946i) q^{13} -2.84480i q^{14} +(1.04381 + 8.59712i) q^{15} -4.00000 q^{16} +(-8.80764 + 8.80764i) q^{17} +(-3.00000 - 3.00000i) q^{18} +33.0294i q^{19} +(6.16725 - 7.87179i) q^{20} -3.48416 q^{21} +(-3.13344 + 3.13344i) q^{22} +(3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(5.98252 + 24.2736i) q^{25} +16.3389 q^{26} +(-3.67423 + 3.67423i) q^{27} +(2.84480 + 2.84480i) q^{28} -8.67288i q^{29} +(-9.64093 - 7.55331i) q^{30} -47.5546 q^{31} +(4.00000 - 4.00000i) q^{32} +(3.83766 + 3.83766i) q^{33} -17.6153i q^{34} +(-9.98457 + 1.21227i) q^{35} +6.00000 q^{36} +(18.6967 - 18.6967i) q^{37} +(-33.0294 - 33.0294i) q^{38} -20.0110i q^{39} +(1.70454 + 14.0390i) q^{40} +21.0080 q^{41} +(3.48416 - 3.48416i) q^{42} +(37.8115 + 37.8115i) q^{43} -6.26687i q^{44} +(-9.25087 + 11.8077i) q^{45} -6.78233 q^{46} +(-4.90320 + 4.90320i) q^{47} +(-4.89898 - 4.89898i) q^{48} +44.9536i q^{49} +(-30.2562 - 18.2911i) q^{50} -21.5742 q^{51} +(-16.3389 + 16.3389i) q^{52} +(6.02763 + 6.02763i) q^{53} -7.34847i q^{54} +(12.3329 + 9.66234i) q^{55} -5.68960 q^{56} +(-40.4526 + 40.4526i) q^{57} +(8.67288 + 8.67288i) q^{58} +91.3726i q^{59} +(17.1942 - 2.08762i) q^{60} -76.7830 q^{61} +(47.5546 - 47.5546i) q^{62} +(-4.26720 - 4.26720i) q^{63} +8.00000i q^{64} +(-6.96258 - 57.3457i) q^{65} -7.67532 q^{66} +(79.6346 - 79.6346i) q^{67} +(17.6153 + 17.6153i) q^{68} +8.30662i q^{69} +(8.77230 - 11.1968i) q^{70} -123.580 q^{71} +(-6.00000 + 6.00000i) q^{72} +(89.3944 + 89.3944i) q^{73} +37.3933i q^{74} +(-22.4020 + 37.0561i) q^{75} +66.0589 q^{76} +(-4.45700 + 4.45700i) q^{77} +(20.0110 + 20.0110i) q^{78} -43.8149i q^{79} +(-15.7436 - 12.3345i) q^{80} -9.00000 q^{81} +(-21.0080 + 21.0080i) q^{82} +(-72.8343 - 72.8343i) q^{83} +6.96831i q^{84} +(-61.8254 + 7.50647i) q^{85} -75.6230 q^{86} +(10.6221 - 10.6221i) q^{87} +(6.26687 + 6.26687i) q^{88} -85.1273i q^{89} +(-2.55681 - 21.0586i) q^{90} +23.2405 q^{91} +(6.78233 - 6.78233i) q^{92} +(-58.2422 - 58.2422i) q^{93} -9.80641i q^{94} +(-101.850 + 130.000i) q^{95} +9.79796 q^{96} +(-104.892 + 104.892i) q^{97} +(-44.9536 - 44.9536i) q^{98} +9.40031i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$4$		−	2.00000i		−	0.500000i
$5$	3.93589	+	3.08362i	0.787179	+	0.616725i
$5$	3.93589	+	3.08362i	0.787179	+	0.616725i
$6$	−2.44949			−0.408248
$7$	−1.42240	+	1.42240i	−0.203200	+	0.203200i	−0.801370	−	0.598170i	$-0.795895\pi$
$7$	−1.42240	+	1.42240i	−0.203200	+	0.203200i	0.598170	+	0.801370i	$0.295895\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$			3.00000i			0.333333i
$10$	−7.01952	+	0.852269i	−0.701952	+	0.0852269i
$11$	3.13344			0.284858			0.142429	−	0.989805i	$-0.454509\pi$
$11$	3.13344			0.284858			0.142429	+	0.989805i	$0.454509\pi$
$12$	2.44949	−	2.44949i	0.204124	−	0.204124i
$13$	−8.16946	−	8.16946i	−0.628420	−	0.628420i	0.319250	−	0.947670i	$-0.396569\pi$
$13$	−8.16946	−	8.16946i	−0.628420	−	0.628420i	−0.947670	+	0.319250i	$0.896569\pi$
$14$		−	2.84480i		−	0.203200i
$15$	1.04381	+	8.59712i	0.0695874	+	0.573141i
$16$	−4.00000			−0.250000
$17$	−8.80764	+	8.80764i	−0.518096	+	0.518096i	−0.916995	−	0.398899i	$-0.869393\pi$
$17$	−8.80764	+	8.80764i	−0.518096	+	0.518096i	0.398899	+	0.916995i	$0.369393\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$			33.0294i			1.73839i	0.494469	+	0.869196i	$0.335363\pi$
$19$			33.0294i			1.73839i	−0.494469	+	0.869196i	$0.664637\pi$
$20$	6.16725	−	7.87179i	0.308362	−	0.393589i
$21$	−3.48416			−0.165912
$22$	−3.13344	+	3.13344i	−0.142429	+	0.142429i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$24$			4.89898i			0.204124i
$25$	5.98252	+	24.2736i	0.239301	+	0.970946i
$26$	16.3389			0.628420
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	2.84480	+	2.84480i	0.101600	+	0.101600i
$29$		−	8.67288i		−	0.299065i	−0.988757	−	0.149532i	$-0.952223\pi$
$29$		−	8.67288i		−	0.299065i	0.988757	−	0.149532i	$-0.0477769\pi$
$30$	−9.64093	−	7.55331i	−0.321364	−	0.251777i
$31$	−47.5546			−1.53402			−0.767010	−	0.641636i	$-0.778256\pi$
$31$	−47.5546			−1.53402			−0.767010	+	0.641636i	$0.778256\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	3.83766	+	3.83766i	0.116293	+	0.116293i
$34$		−	17.6153i		−	0.518096i
$35$	−9.98457	+	1.21227i	−0.285273	+	0.0346362i
$36$	6.00000			0.166667
$37$	18.6967	−	18.6967i	0.505315	−	0.505315i	−0.407770	−	0.913085i	$-0.633693\pi$
$37$	18.6967	−	18.6967i	0.505315	−	0.505315i	0.913085	+	0.407770i	$0.133693\pi$
$38$	−33.0294	−	33.0294i	−0.869196	−	0.869196i
$39$		−	20.0110i		−	0.513103i
$40$	1.70454	+	14.0390i	0.0426134	+	0.350976i
$41$	21.0080			0.512390			0.256195	−	0.966625i	$-0.417531\pi$
$41$	21.0080			0.512390			0.256195	+	0.966625i	$0.417531\pi$
$42$	3.48416	−	3.48416i	0.0829561	−	0.0829561i
$43$	37.8115	+	37.8115i	0.879337	+	0.879337i	0.993466	−	0.114129i	$-0.0364076\pi$
$43$	37.8115	+	37.8115i	0.879337	+	0.879337i	−0.114129	+	0.993466i	$0.536408\pi$
$44$		−	6.26687i		−	0.142429i
$45$	−9.25087	+	11.8077i	−0.205575	+	0.262393i
$46$	−6.78233			−0.147442
$47$	−4.90320	+	4.90320i	−0.104323	+	0.104323i	−0.757342	−	0.653018i	$-0.773502\pi$
$47$	−4.90320	+	4.90320i	−0.104323	+	0.104323i	0.653018	+	0.757342i	$0.273502\pi$
$48$	−4.89898	−	4.89898i	−0.102062	−	0.102062i
$49$			44.9536i			0.917419i
$50$	−30.2562	−	18.2911i	−0.605123	−	0.365822i
$51$	−21.5742			−0.423024
$52$	−16.3389	+	16.3389i	−0.314210	+	0.314210i
$53$	6.02763	+	6.02763i	0.113729	+	0.113729i	0.761681	−	0.647952i	$-0.224374\pi$
$53$	6.02763	+	6.02763i	0.113729	+	0.113729i	−0.647952	+	0.761681i	$0.724374\pi$
$54$		−	7.34847i		−	0.136083i
$55$	12.3329	+	9.66234i	0.224234	+	0.175679i
$56$	−5.68960			−0.101600
$57$	−40.4526	+	40.4526i	−0.709695	+	0.709695i
$58$	8.67288	+	8.67288i	0.149532	+	0.149532i
$59$			91.3726i			1.54869i	0.632765	+	0.774344i	$0.281920\pi$
$59$			91.3726i			1.54869i	−0.632765	+	0.774344i	$0.718080\pi$
$60$	17.1942	−	2.08762i	0.286571	−	0.0347937i
$61$	−76.7830			−1.25874			−0.629369	−	0.777107i	$-0.716687\pi$
$61$	−76.7830			−1.25874			−0.629369	+	0.777107i	$0.716687\pi$
$62$	47.5546	−	47.5546i	0.767010	−	0.767010i
$63$	−4.26720	−	4.26720i	−0.0677334	−	0.0677334i
$64$			8.00000i			0.125000i
$65$	−6.96258	−	57.3457i	−0.107117	−	0.882242i
$66$	−7.67532			−0.116293
$67$	79.6346	−	79.6346i	1.18858	−	1.18858i	0.211114	−	0.977461i	$-0.432291\pi$
$67$	79.6346	−	79.6346i	1.18858	−	1.18858i	0.977461	−	0.211114i	$-0.0677093\pi$
$68$	17.6153	+	17.6153i	0.259048	+	0.259048i
$69$			8.30662i			0.120386i
$70$	8.77230	−	11.1968i	0.125319	−	0.159955i
$71$	−123.580			−1.74057			−0.870283	−	0.492552i	$-0.836064\pi$
$71$	−123.580			−1.74057			−0.870283	+	0.492552i	$0.836064\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	89.3944	+	89.3944i	1.22458	+	1.22458i	0.965986	+	0.258596i	$0.0832598\pi$
$73$	89.3944	+	89.3944i	1.22458	+	1.22458i	0.258596	+	0.965986i	$0.416740\pi$
$74$			37.3933i			0.505315i
$75$	−22.4020	+	37.0561i	−0.298693	+	0.494081i
$76$	66.0589			0.869196
$77$	−4.45700	+	4.45700i	−0.0578831	+	0.0578831i
$78$	20.0110	+	20.0110i	0.256552	+	0.256552i
$79$		−	43.8149i		−	0.554618i	−0.960781	−	0.277309i	$-0.910557\pi$
$79$		−	43.8149i		−	0.554618i	0.960781	−	0.277309i	$-0.0894427\pi$
$80$	−15.7436	−	12.3345i	−0.196795	−	0.154181i
$81$	−9.00000			−0.111111
$82$	−21.0080	+	21.0080i	−0.256195	+	0.256195i
$83$	−72.8343	−	72.8343i	−0.877522	−	0.877522i	0.115756	−	0.993278i	$-0.463071\pi$
$83$	−72.8343	−	72.8343i	−0.877522	−	0.877522i	−0.993278	+	0.115756i	$0.963071\pi$
$84$			6.96831i			0.0829561i
$85$	−61.8254	+	7.50647i	−0.727357	+	0.0883115i
$86$	−75.6230			−0.879337
$87$	10.6221	−	10.6221i	0.122093	−	0.122093i
$88$	6.26687	+	6.26687i	0.0712145	+	0.0712145i
$89$		−	85.1273i		−	0.956487i	−0.878227	−	0.478243i	$-0.841274\pi$
$89$		−	85.1273i		−	0.956487i	0.878227	−	0.478243i	$-0.158726\pi$
$90$	−2.55681	−	21.0586i	−0.0284090	−	0.233984i
$91$	23.2405			0.255390
$92$	6.78233	−	6.78233i	0.0737210	−	0.0737210i
$93$	−58.2422	−	58.2422i	−0.626261	−	0.626261i
$94$		−	9.80641i		−	0.104323i
$95$	−101.850	+	130.000i	−1.07211	+	1.36842i
$96$	9.79796			0.102062
$97$	−104.892	+	104.892i	−1.08136	+	1.08136i	−0.0849800	+	0.996383i	$0.527083\pi$
$97$	−104.892	+	104.892i	−1.08136	+	1.08136i	−0.996383	+	0.0849800i	$0.972917\pi$
$98$	−44.9536	−	44.9536i	−0.458710	−	0.458710i
$99$			9.40031i			0.0949526i
$100$	48.5473	−	11.9650i	0.485473	−	0.119650i
$101$	−161.022			−1.59428			−0.797138	−	0.603798i	$-0.793654\pi$
$101$	−161.022			−1.59428			−0.797138	+	0.603798i	$0.793654\pi$
$102$	21.5742	−	21.5742i	0.211512	−	0.211512i
$103$	51.2006	+	51.2006i	0.497094	+	0.497094i	0.910532	−	0.413438i	$-0.135672\pi$
$103$	51.2006	+	51.2006i	0.497094	+	0.497094i	−0.413438	+	0.910532i	$0.635672\pi$
$104$		−	32.6779i		−	0.314210i
$105$	−13.7133	−	10.7438i	−0.130603	−	0.102322i
$106$	−12.0553			−0.113729
$107$	88.6095	−	88.6095i	0.828127	−	0.828127i	−0.159131	−	0.987257i	$-0.550869\pi$
$107$	88.6095	−	88.6095i	0.828127	−	0.828127i	0.987257	+	0.159131i	$0.0508692\pi$
$108$	7.34847	+	7.34847i	0.0680414	+	0.0680414i
$109$			45.9965i			0.421986i	0.977488	+	0.210993i	$0.0676698\pi$
$109$			45.9965i			0.421986i	−0.977488	+	0.210993i	$0.932330\pi$
$110$	−21.9952	+	2.67053i	−0.199957	+	0.0242775i
$111$	45.7973			0.412588
$112$	5.68960	−	5.68960i	0.0508000	−	0.0508000i
$113$	−100.216	−	100.216i	−0.886871	−	0.886871i	0.107350	−	0.994221i	$-0.465763\pi$
$113$	−100.216	−	100.216i	−0.886871	−	0.886871i	−0.994221	+	0.107350i	$0.965763\pi$
$114$		−	80.9052i		−	0.709695i
$115$	2.89018	+	23.8043i	0.0251320	+	0.206994i
$116$	−17.3458			−0.149532
$117$	24.5084	−	24.5084i	0.209473	−	0.209473i
$118$	−91.3726	−	91.3726i	−0.774344	−	0.774344i
$119$		−	25.0560i		−	0.210554i
$120$	−15.1066	+	19.2819i	−0.125888	+	0.160682i
$121$	−111.182			−0.918856
$122$	76.7830	−	76.7830i	0.629369	−	0.629369i
$123$	25.7294	+	25.7294i	0.209182	+	0.209182i
$124$			95.1092i			0.767010i
$125$	−51.3042	+	113.986i	−0.410434	+	0.911890i
$126$	8.53440			0.0677334
$127$	17.0379	−	17.0379i	0.134157	−	0.134157i	−0.636840	−	0.770996i	$-0.719759\pi$
$127$	17.0379	−	17.0379i	0.134157	−	0.134157i	0.770996	+	0.636840i	$0.219759\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$			92.6189i			0.717976i
$130$	64.3083	+	50.3831i	0.494679	+	0.387563i
$131$	226.477			1.72884			0.864418	−	0.502774i	$-0.167687\pi$
$131$	226.477			1.72884			0.864418	+	0.502774i	$0.167687\pi$
$132$	7.67532	−	7.67532i	0.0581464	−	0.0581464i
$133$	−46.9811	−	46.9811i	−0.353241	−	0.353241i
$134$			159.269i			1.18858i
$135$	−25.7914	+	3.13144i	−0.191047	+	0.0231958i
$136$	−35.2306			−0.259048
$137$	−13.3335	+	13.3335i	−0.0973250	+	0.0973250i	−0.754093	−	0.656768i	$-0.771923\pi$
$137$	−13.3335	+	13.3335i	−0.0973250	+	0.0973250i	0.656768	+	0.754093i	$0.271923\pi$
$138$	−8.30662	−	8.30662i	−0.0601929	−	0.0601929i
$139$			136.577i			0.982566i	0.871000	+	0.491283i	$0.163472\pi$
$139$			136.577i			0.982566i	−0.871000	+	0.491283i	$0.836528\pi$
$140$	2.42453	+	19.9691i	0.0173181	+	0.142637i
$141$	−12.0103			−0.0851798
$142$	123.580	−	123.580i	0.870283	−	0.870283i
$143$	−25.5985	−	25.5985i	−0.179011	−	0.179011i
$144$		−	12.0000i		−	0.0833333i
$145$	26.7439	−	34.1355i	0.184441	−	0.235418i
$146$	−178.789			−1.22458
$147$	−55.0566	+	55.0566i	−0.374535	+	0.374535i
$148$	−37.3933	−	37.3933i	−0.252658	−	0.252658i
$149$			21.6052i			0.145001i	0.997368	+	0.0725006i	$0.0230979\pi$
$149$			21.6052i			0.145001i	−0.997368	+	0.0725006i	$0.976902\pi$
$150$	−14.6541	−	59.4580i	−0.0976941	−	0.396387i
$151$	283.184			1.87539			0.937695	−	0.347459i	$-0.112955\pi$
$151$	283.184			1.87539			0.937695	+	0.347459i	$0.112955\pi$
$152$	−66.0589	+	66.0589i	−0.434598	+	0.434598i
$153$	−26.4229	−	26.4229i	−0.172699	−	0.172699i
$154$		−	8.91400i		−	0.0578831i
$155$	−187.170	−	146.641i	−1.20755	−	0.946068i
$156$	−40.0220			−0.256552
$157$	124.318	−	124.318i	0.791832	−	0.791832i	−0.189960	−	0.981792i	$-0.560836\pi$
$157$	124.318	−	124.318i	0.791832	−	0.791832i	0.981792	+	0.189960i	$0.0608357\pi$
$158$	43.8149	+	43.8149i	0.277309	+	0.277309i
$159$			14.7646i			0.0928592i
$160$	28.0781	−	3.40907i	0.175488	−	0.0213067i
$161$	−9.64719			−0.0599204
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	72.7999	+	72.7999i	0.446625	+	0.446625i	0.894231	−	0.447606i	$-0.147723\pi$
$163$	72.7999	+	72.7999i	0.446625	+	0.446625i	−0.447606	+	0.894231i	$0.647723\pi$
$164$		−	42.0160i		−	0.256195i
$165$	3.27072	+	26.9385i	0.0198225	+	0.163264i
$166$	145.669			0.877522
$167$	60.4809	−	60.4809i	0.362161	−	0.362161i	−0.502447	−	0.864608i	$-0.667567\pi$
$167$	60.4809	−	60.4809i	0.362161	−	0.362161i	0.864608	+	0.502447i	$0.167567\pi$
$168$	−6.96831	−	6.96831i	−0.0414780	−	0.0414780i
$169$		−	35.5197i		−	0.210176i
$170$	54.3189	−	69.3319i	0.319523	−	0.407834i
$171$	−99.0883			−0.579464
$172$	75.6230	−	75.6230i	0.439669	−	0.439669i
$173$	96.5087	+	96.5087i	0.557854	+	0.557854i	0.928696	−	0.370842i	$-0.120931\pi$
$173$	96.5087	+	96.5087i	0.557854	+	0.557854i	−0.370842	+	0.928696i	$0.620931\pi$
$174$			21.2441i			0.122093i
$175$	−43.0364	−	26.0173i	−0.245922	−	0.148670i
$176$	−12.5337			−0.0712145
$177$	−111.908	+	111.908i	−0.632249	+	0.632249i
$178$	85.1273	+	85.1273i	0.478243	+	0.478243i
$179$			115.452i			0.644983i	0.946572	+	0.322491i	$0.104520\pi$
$179$			115.452i			0.644983i	−0.946572	+	0.322491i	$0.895480\pi$
$180$	23.6154	+	18.5017i	0.131196	+	0.102787i
$181$	182.511			1.00835			0.504174	−	0.863602i	$-0.331797\pi$
$181$	182.511			1.00835			0.504174	+	0.863602i	$0.331797\pi$
$182$	−23.2405	+	23.2405i	−0.127695	+	0.127695i
$183$	−94.0396	−	94.0396i	−0.513878	−	0.513878i
$184$			13.5647i			0.0737210i
$185$	131.242	−	15.9346i	0.709414	−	0.0861329i
$186$	116.484			0.626261
$187$	−27.5982	+	27.5982i	−0.147584	+	0.147584i
$188$	9.80641	+	9.80641i	0.0521617	+	0.0521617i
$189$		−	10.4525i		−	0.0553040i
$190$	−28.1499	−	231.851i	−0.148158	−	1.22027i
$191$	−126.245			−0.660969			−0.330485	−	0.943811i	$-0.607212\pi$
$191$	−126.245			−0.660969			−0.330485	+	0.943811i	$0.607212\pi$
$192$	−9.79796	+	9.79796i	−0.0510310	+	0.0510310i
$193$	−104.990	−	104.990i	−0.543989	−	0.543989i	0.380707	−	0.924696i	$-0.375681\pi$
$193$	−104.990	−	104.990i	−0.543989	−	0.543989i	−0.924696	+	0.380707i	$0.875681\pi$
$194$		−	209.784i		−	1.08136i
$195$	61.7065	−	78.7612i	0.316443	−	0.403904i
$196$	89.9071			0.458710
$197$	189.425	−	189.425i	0.961546	−	0.961546i	−0.0377412	−	0.999288i	$-0.512016\pi$
$197$	189.425	−	189.425i	0.961546	−	0.961546i	0.999288	+	0.0377412i	$0.0120163\pi$
$198$	−9.40031	−	9.40031i	−0.0474763	−	0.0474763i
$199$			140.728i			0.707178i	0.935401	+	0.353589i	$0.115039\pi$
$199$			140.728i			0.707178i	−0.935401	+	0.353589i	$0.884961\pi$
$200$	−36.5822	+	60.5123i	−0.182911	+	0.302562i
$201$	195.064			0.970468
$202$	161.022	−	161.022i	0.797138	−	0.797138i
$203$	12.3363	+	12.3363i	0.0607700	+	0.0607700i
$204$			43.1484i			0.211512i
$205$	82.6853	+	64.7808i	0.403343	+	0.316004i
$206$	−102.401			−0.497094
$207$	−10.1735	+	10.1735i	−0.0491473	+	0.0491473i
$208$	32.6779	+	32.6779i	0.157105	+	0.157105i
$209$			103.496i			0.495194i
$210$	24.4571	−	2.96944i	0.116462	−	0.0141402i
$211$	84.3383			0.399707			0.199854	−	0.979826i	$-0.435953\pi$
$211$	84.3383			0.399707			0.199854	+	0.979826i	$0.435953\pi$
$212$	12.0553	−	12.0553i	0.0568644	−	0.0568644i
$213$	−151.354	−	151.354i	−0.710583	−	0.710583i
$214$			177.219i			0.828127i
$215$	32.2256	+	265.419i	0.149886	+	1.23450i
$216$	−14.6969			−0.0680414
$217$	67.6417	−	67.6417i	0.311713	−	0.311713i
$218$	−45.9965	−	45.9965i	−0.210993	−	0.210993i
$219$			218.971i			0.999867i
$220$	19.3247	−	24.6657i	0.0878395	−	0.112117i
$221$	143.907			0.651165
$222$	−45.7973	+	45.7973i	−0.206294	+	0.206294i
$223$	178.882	+	178.882i	0.802163	+	0.802163i	0.983433	−	0.181270i	$-0.0580209\pi$
$223$	178.882	+	178.882i	0.802163	+	0.802163i	−0.181270	+	0.983433i	$0.558021\pi$
$224$			11.3792i			0.0508000i
$225$	−72.8209	+	17.9475i	−0.323649	+	0.0797669i
$226$	200.433			0.886871
$227$	159.186	−	159.186i	0.701259	−	0.701259i	−0.263422	−	0.964681i	$-0.584851\pi$
$227$	159.186	−	159.186i	0.701259	−	0.701259i	0.964681	+	0.263422i	$0.0848510\pi$
$228$	80.9052	+	80.9052i	0.354848	+	0.354848i
$229$			139.731i			0.610178i	0.952324	+	0.305089i	$0.0986862\pi$
$229$			139.731i			0.610178i	−0.952324	+	0.305089i	$0.901314\pi$
$230$	−26.6945	−	20.9142i	−0.116063	−	0.0909311i
$231$	−10.9174			−0.0472614
$232$	17.3458	−	17.3458i	0.0747662	−	0.0747662i
$233$	63.6155	+	63.6155i	0.273028	+	0.273028i	0.830318	−	0.557290i	$-0.188159\pi$
$233$	63.6155	+	63.6155i	0.273028	+	0.273028i	−0.557290	+	0.830318i	$0.688159\pi$
$234$			49.0168i			0.209473i
$235$	−34.4181	+	4.17885i	−0.146460	+	0.0177823i
$236$	182.745			0.774344
$237$	53.6620	−	53.6620i	0.226422	−	0.226422i
$238$	25.0560	+	25.0560i	0.105277	+	0.105277i
$239$		−	56.4515i		−	0.236199i	−0.993002	−	0.118099i	$-0.962320\pi$
$239$		−	56.4515i		−	0.236199i	0.993002	−	0.118099i	$-0.0376801\pi$
$240$	−4.17525	−	34.3885i	−0.0173969	−	0.143285i
$241$	88.4572			0.367042			0.183521	−	0.983016i	$-0.441250\pi$
$241$	88.4572			0.367042			0.183521	+	0.983016i	$0.441250\pi$
$242$	111.182	−	111.182i	0.459428	−	0.459428i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$			153.566i			0.629369i
$245$	−138.620	+	176.932i	−0.565795	+	0.722173i
$246$	−51.4589			−0.209182
$247$	269.833	−	269.833i	1.09244	−	1.09244i
$248$	−95.1092	−	95.1092i	−0.383505	−	0.383505i
$249$		−	178.407i		−	0.716493i
$250$	−62.6820	−	165.291i	−0.250728	−	0.661162i
$251$	68.5838			0.273242			0.136621	−	0.990623i	$-0.456376\pi$
$251$	68.5838			0.273242			0.136621	+	0.990623i	$0.456376\pi$
$252$	−8.53440	+	8.53440i	−0.0338667	+	0.0338667i
$253$	10.6260	+	10.6260i	0.0420000	+	0.0420000i
$254$			34.0758i			0.134157i
$255$	−84.9138	−	66.5268i	−0.332995	−	0.260889i
$256$	16.0000			0.0625000
$257$	133.320	−	133.320i	0.518754	−	0.518754i	−0.398440	−	0.917194i	$-0.630448\pi$
$257$	133.320	−	133.320i	0.518754	−	0.518754i	0.917194	+	0.398440i	$0.130448\pi$
$258$	−92.6189	−	92.6189i	−0.358988	−	0.358988i
$259$			53.1883i			0.205360i
$260$	−114.691	+	13.9252i	−0.441121	+	0.0535583i
$261$	26.0186			0.0996883
$262$	−226.477	+	226.477i	−0.864418	+	0.864418i
$263$	269.935	+	269.935i	1.02637	+	1.02637i	0.999643	+	0.0267265i	$0.00850832\pi$
$263$	269.935	+	269.935i	1.02637	+	1.02637i	0.0267265	+	0.999643i	$0.491492\pi$
$264$			15.3506i			0.0581464i
$265$	5.13716	+	42.3110i	0.0193855	+	0.159664i
$266$	93.9621			0.353241
$267$	104.259	−	104.259i	0.390484	−	0.390484i
$268$	−159.269	−	159.269i	−0.594288	−	0.594288i
$269$		−	287.611i		−	1.06919i	−0.845109	−	0.534593i	$-0.820465\pi$
$269$		−	287.611i		−	1.06919i	0.845109	−	0.534593i	$-0.179535\pi$
$270$	22.6599	−	28.9228i	0.0839256	−	0.107121i
$271$	146.523			0.540675			0.270338	−	0.962766i	$-0.412865\pi$
$271$	146.523			0.540675			0.270338	+	0.962766i	$0.412865\pi$
$272$	35.2306	−	35.2306i	0.129524	−	0.129524i
$273$	28.4637	+	28.4637i	0.104263	+	0.104263i
$274$		−	26.6670i		−	0.0973250i
$275$	18.7458	+	76.0599i	0.0681667	+	0.276582i
$276$	16.6132			0.0601929
$277$	75.7854	−	75.7854i	0.273594	−	0.273594i	−0.556951	−	0.830545i	$-0.688029\pi$
$277$	75.7854	−	75.7854i	0.273594	−	0.273594i	0.830545	+	0.556951i	$0.188029\pi$
$278$	−136.577	−	136.577i	−0.491283	−	0.491283i
$279$		−	142.664i		−	0.511340i
$280$	−22.3937	−	17.5446i	−0.0799774	−	0.0626593i
$281$	461.843			1.64357			0.821785	−	0.569798i	$-0.192979\pi$
$281$	461.843			1.64357			0.821785	+	0.569798i	$0.192979\pi$
$282$	12.0103	−	12.0103i	0.0425899	−	0.0425899i
$283$	17.7043	+	17.7043i	0.0625594	+	0.0625594i	0.737694	−	0.675135i	$-0.235915\pi$
$283$	17.7043	+	17.7043i	0.0625594	+	0.0625594i	−0.675135	+	0.737694i	$0.735915\pi$
$284$			247.160i			0.870283i
$285$	−283.958	+	34.4765i	−0.996344	+	0.120970i
$286$	51.1970			0.179011
$287$	−29.8818	+	29.8818i	−0.104118	+	0.104118i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$			133.851i			0.463152i
$290$	7.39163	+	60.8795i	0.0254884	+	0.209929i
$291$	−256.932			−0.882929
$292$	178.789	−	178.789i	0.612291	−	0.612291i
$293$	−135.640	−	135.640i	−0.462934	−	0.462934i	0.436682	−	0.899616i	$-0.356153\pi$
$293$	−135.640	−	135.640i	−0.462934	−	0.462934i	−0.899616	+	0.436682i	$0.856153\pi$
$294$		−	110.113i		−	0.374535i
$295$	−281.759	+	359.633i	−0.955114	+	1.21909i
$296$	74.7866			0.252658
$297$	−11.5130	+	11.5130i	−0.0387643	+	0.0387643i
$298$	−21.6052	−	21.6052i	−0.0725006	−	0.0725006i
$299$		−	55.4080i		−	0.185311i
$300$	74.1121	+	44.8039i	0.247040	+	0.149346i
$301$	−107.566			−0.357363
$302$	−283.184	+	283.184i	−0.937695	+	0.937695i
$303$	−197.211	−	197.211i	−0.650860	−	0.650860i
$304$		−	132.118i		−	0.434598i
$305$	−302.210	−	236.770i	−0.990852	−	0.776295i
$306$	52.8458			0.172699
$307$	−337.020	+	337.020i	−1.09779	+	1.09779i	−0.103116	+	0.994669i	$0.532881\pi$
$307$	−337.020	+	337.020i	−1.09779	+	1.09779i	−0.994669	+	0.103116i	$0.967119\pi$
$308$	8.91400	+	8.91400i	0.0289416	+	0.0289416i
$309$			125.415i			0.405875i
$310$	333.810	−	40.5293i	1.07681	−	0.130740i
$311$	205.353			0.660298			0.330149	−	0.943929i	$-0.392901\pi$
$311$	205.353			0.660298			0.330149	+	0.943929i	$0.392901\pi$
$312$	40.0220	−	40.0220i	0.128276	−	0.128276i
$313$	−51.0361	−	51.0361i	−0.163055	−	0.163055i	0.620864	−	0.783918i	$-0.286782\pi$
$313$	−51.0361	−	51.0361i	−0.163055	−	0.163055i	−0.783918	+	0.620864i	$0.786782\pi$
$314$			248.635i			0.791832i
$315$	−3.63680	−	29.9537i	−0.0115454	−	0.0950911i
$316$	−87.6297			−0.277309
$317$	415.998	−	415.998i	1.31230	−	1.31230i	0.392580	−	0.919718i	$-0.371583\pi$
$317$	415.998	−	415.998i	1.31230	−	1.31230i	0.919718	−	0.392580i	$-0.128417\pi$
$318$	−14.7646	−	14.7646i	−0.0464296	−	0.0464296i
$319$		−	27.1759i		−	0.0851910i
$320$	−24.6690	+	31.4871i	−0.0770906	+	0.0983973i
$321$	217.048			0.676162
$322$	9.64719	−	9.64719i	0.0299602	−	0.0299602i
$323$	−290.911	−	290.911i	−0.900654	−	0.900654i
$324$			18.0000i			0.0555556i
$325$	149.429	−	247.177i	0.459781	−	0.760543i
$326$	−145.600			−0.446625
$327$	−56.3340	+	56.3340i	−0.172275	+	0.172275i
$328$	42.0160	+	42.0160i	0.128098	+	0.128098i
$329$		−	13.9486i		−	0.0423971i
$330$	−30.2092	−	23.6678i	−0.0915432	−	0.0717206i
$331$	624.517			1.88676			0.943379	−	0.331717i	$-0.107628\pi$
$331$	624.517			1.88676			0.943379	+	0.331717i	$0.107628\pi$
$332$	−145.669	+	145.669i	−0.438761	+	0.438761i
$333$	56.0900	+	56.0900i	0.168438	+	0.168438i
$334$			120.962i			0.362161i
$335$	558.996	−	67.8701i	1.66865	−	0.202597i
$336$	13.9366			0.0414780
$337$	−86.5233	+	86.5233i	−0.256746	+	0.256746i	−0.823729	−	0.566984i	$-0.808110\pi$
$337$	−86.5233	+	86.5233i	−0.256746	+	0.256746i	0.566984	+	0.823729i	$0.308110\pi$
$338$	35.5197	+	35.5197i	0.105088	+	0.105088i
$339$		−	245.479i		−	0.724127i
$340$	15.0129	+	123.651i	0.0441557	+	0.363679i
$341$	−149.009			−0.436978
$342$	99.0883	−	99.0883i	0.289732	−	0.289732i
$343$	−133.640	−	133.640i	−0.389620	−	0.389620i
$344$			151.246i			0.439669i
$345$	−25.6145	+	32.6940i	−0.0742450	+	0.0947652i
$346$	−193.017			−0.557854
$347$	382.830	−	382.830i	1.10326	−	1.10326i	0.109242	−	0.994015i	$-0.465158\pi$
$347$	382.830	−	382.830i	1.10326	−	1.10326i	0.994015	−	0.109242i	$-0.0348423\pi$
$348$	−21.2441	−	21.2441i	−0.0610464	−	0.0610464i
$349$		−	392.877i		−	1.12572i	−0.826552	−	0.562861i	$-0.809701\pi$
$349$		−	392.877i		−	1.12572i	0.826552	−	0.562861i	$-0.190299\pi$
$350$	69.0537	−	17.0191i	0.197296	−	0.0486259i
$351$	60.0331			0.171034
$352$	12.5337	−	12.5337i	0.0356072	−	0.0356072i
$353$	−238.494	−	238.494i	−0.675620	−	0.675620i	0.283386	−	0.959006i	$-0.408542\pi$
$353$	−238.494	−	238.494i	−0.675620	−	0.675620i	−0.959006	+	0.283386i	$0.908542\pi$
$354$		−	223.816i		−	0.632249i
$355$	−486.398	−	381.075i	−1.37014	−	1.07345i
$356$	−170.255			−0.478243
$357$	30.6872	−	30.6872i	0.0859585	−	0.0859585i
$358$	−115.452	−	115.452i	−0.322491	−	0.322491i
$359$			434.304i			1.20976i	0.796316	+	0.604881i	$0.206779\pi$
$359$			434.304i			1.20976i	−0.796316	+	0.604881i	$0.793221\pi$
$360$	−42.1171	+	5.11361i	−0.116992	+	0.0142045i
$361$	−729.943			−2.02200
$362$	−182.511	+	182.511i	−0.504174	+	0.504174i
$363$	−136.169	−	136.169i	−0.375121	−	0.375121i
$364$		−	46.4810i		−	0.127695i
$365$	76.1881	+	627.506i	0.208734	+	1.71919i
$366$	188.079			0.513878
$367$	139.615	−	139.615i	0.380421	−	0.380421i	−0.490832	−	0.871254i	$-0.663307\pi$
$367$	139.615	−	139.615i	0.380421	−	0.380421i	0.871254	+	0.490832i	$0.163307\pi$
$368$	−13.5647	−	13.5647i	−0.0368605	−	0.0368605i
$369$			63.0240i			0.170797i
$370$	−115.307	+	147.176i	−0.311640	+	0.397773i
$371$	−17.1474			−0.0462194
$372$	−116.484	+	116.484i	−0.313130	+	0.313130i
$373$	−78.8131	−	78.8131i	−0.211295	−	0.211295i	0.593522	−	0.804817i	$-0.297737\pi$
$373$	−78.8131	−	78.8131i	−0.211295	−	0.211295i	−0.804817	+	0.593522i	$0.797737\pi$
$374$		−	55.1964i		−	0.147584i
$375$	−202.439	+	76.7695i	−0.539837	+	0.204719i
$376$	−19.6128			−0.0521617
$377$	−70.8528	+	70.8528i	−0.187938	+	0.187938i
$378$	10.4525	+	10.4525i	0.0276520	+	0.0276520i
$379$		−	59.0081i		−	0.155694i	−0.996965	−	0.0778470i	$-0.975195\pi$
$379$		−	59.0081i		−	0.155694i	0.996965	−	0.0778470i	$-0.0248046\pi$
$380$	260.001	+	203.701i	0.684212	+	0.536055i
$381$	41.7342			0.109539
$382$	126.245	−	126.245i	0.330485	−	0.330485i
$383$	101.487	+	101.487i	0.264980	+	0.264980i	0.827074	−	0.562094i	$-0.190004\pi$
$383$	101.487	+	101.487i	0.264980	+	0.264980i	−0.562094	+	0.827074i	$0.690004\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	−31.2860	+	3.79856i	−0.0812624	+	0.00986640i
$386$	209.980			0.543989
$387$	−113.435	+	113.435i	−0.293112	+	0.293112i
$388$	209.784	+	209.784i	0.540681	+	0.540681i
$389$		−	276.824i		−	0.711630i	−0.934556	−	0.355815i	$-0.884203\pi$
$389$		−	276.824i		−	0.711630i	0.934556	−	0.355815i	$-0.115797\pi$
$390$	17.0548	+	140.468i	0.0437302	+	0.360174i
$391$	−59.7363			−0.152778
$392$	−89.9071	+	89.9071i	−0.229355	+	0.229355i
$393$	277.377	+	277.377i	0.705794	+	0.705794i
$394$			378.849i			0.961546i
$395$	135.109	−	172.451i	0.342047	−	0.436584i
$396$	18.8006			0.0474763
$397$	−304.445	+	304.445i	−0.766864	+	0.766864i	−0.977553	−	0.210689i	$-0.932429\pi$
$397$	−304.445	+	304.445i	−0.766864	+	0.766864i	0.210689	+	0.977553i	$0.432429\pi$
$398$	−140.728	−	140.728i	−0.353589	−	0.353589i
$399$		−	115.080i		−	0.288420i
$400$	−23.9301	−	97.0946i	−0.0598252	−	0.242736i
$401$	−506.097			−1.26209			−0.631044	−	0.775747i	$-0.717373\pi$
$401$	−506.097			−1.26209			−0.631044	+	0.775747i	$0.717373\pi$
$402$	−195.064	+	195.064i	−0.485234	+	0.485234i
$403$	388.496	+	388.496i	0.964009	+	0.964009i
$404$			322.044i			0.797138i
$405$	−35.4230	−	27.7526i	−0.0874643	−	0.0685250i
$406$	−24.6726			−0.0607700
$407$	58.5848	−	58.5848i	0.143943	−	0.143943i
$408$	−43.1484	−	43.1484i	−0.105756	−	0.105756i
$409$		−	65.7017i		−	0.160640i	−0.996769	−	0.0803200i	$-0.974406\pi$
$409$		−	65.7017i		−	0.160640i	0.996769	−	0.0803200i	$-0.0255942\pi$
$410$	−147.466	+	17.9045i	−0.359673	+	0.0436694i
$411$	−32.6603			−0.0794655
$412$	102.401	−	102.401i	0.248547	−	0.248547i
$413$	−129.968	−	129.968i	−0.314693	−	0.314693i
$414$		−	20.3470i		−	0.0491473i
$415$	−62.0744	−	511.262i	−0.149577	−	1.23196i
$416$	−65.3557			−0.157105
$417$	−167.272	+	167.272i	−0.401131	+	0.401131i
$418$	−103.496	−	103.496i	−0.247597	−	0.247597i
$419$			496.707i			1.18546i	0.805402	+	0.592729i	$0.201949\pi$
$419$			496.707i			1.18546i	−0.805402	+	0.592729i	$0.798051\pi$
$420$	−21.4877	+	27.4265i	−0.0511611	+	0.0653013i
$421$	−452.792			−1.07552			−0.537758	−	0.843099i	$-0.680728\pi$
$421$	−452.792			−1.07552			−0.537758	+	0.843099i	$0.680728\pi$
$422$	−84.3383	+	84.3383i	−0.199854	+	0.199854i
$423$	−14.7096	−	14.7096i	−0.0347745	−	0.0347745i
$424$			24.1105i			0.0568644i
$425$	−266.485	−	161.102i	−0.627024	−	0.379063i
$426$	302.708			0.710583
$427$	109.216	−	109.216i	0.255776	−	0.255776i
$428$	−177.219	−	177.219i	−0.414063	−	0.414063i
$429$		−	62.7033i		−	0.146161i
$430$	−297.644	−	233.193i	−0.692196	−	0.542309i
$431$	375.766			0.871847			0.435924	−	0.899984i	$-0.356422\pi$
$431$	375.766			0.871847			0.435924	+	0.899984i	$0.356422\pi$
$432$	14.6969	−	14.6969i	0.0340207	−	0.0340207i
$433$	463.698	+	463.698i	1.07090	+	1.07090i	0.997287	+	0.0736079i	$0.0234513\pi$
$433$	463.698	+	463.698i	1.07090	+	1.07090i	0.0736079	+	0.997287i	$0.476549\pi$
$434$			135.283i			0.311713i
$435$	74.5618	−	9.05286i	0.171406	−	0.0208112i
$436$	91.9930			0.210993
$437$	−112.008	+	112.008i	−0.256312	+	0.256312i
$438$	−218.971	−	218.971i	−0.499933	−	0.499933i
$439$			772.787i			1.76033i	0.474664	+	0.880167i	$0.342570\pi$
$439$			772.787i			1.76033i	−0.474664	+	0.880167i	$0.657430\pi$
$440$	5.34106	+	43.9904i	0.0121388	+	0.0999783i
$441$	−134.861			−0.305806
$442$	−143.907	+	143.907i	−0.325582	+	0.325582i
$443$	−314.253	−	314.253i	−0.709374	−	0.709374i	0.257029	−	0.966404i	$-0.417256\pi$
$443$	−314.253	−	314.253i	−0.709374	−	0.709374i	−0.966404	+	0.257029i	$0.917256\pi$
$444$		−	91.5946i		−	0.206294i
$445$	262.501	−	335.052i	0.589889	−	0.752926i
$446$	−357.765			−0.802163
$447$	−26.4608	+	26.4608i	−0.0591965	+	0.0591965i
$448$	−11.3792	−	11.3792i	−0.0254000	−	0.0254000i
$449$			123.814i			0.275756i	0.990449	+	0.137878i	$0.0440281\pi$
$449$			123.814i			0.275756i	−0.990449	+	0.137878i	$0.955972\pi$
$450$	54.8734	−	90.7685i	0.121941	−	0.201708i
$451$	65.8273			0.145958
$452$	−200.433	+	200.433i	−0.443435	+	0.443435i
$453$	346.828	+	346.828i	0.765625	+	0.765625i
$454$			318.372i			0.701259i
$455$	91.4721	+	71.6650i	0.201038	+	0.157505i
$456$	−161.810			−0.354848
$457$	−83.6198	+	83.6198i	−0.182976	+	0.182976i	−0.792651	−	0.609676i	$-0.791300\pi$
$457$	−83.6198	+	83.6198i	−0.182976	+	0.182976i	0.609676	+	0.792651i	$0.291300\pi$
$458$	−139.731	−	139.731i	−0.305089	−	0.305089i
$459$		−	64.7227i		−	0.141008i
$460$	47.6087	−	5.78037i	0.103497	−	0.0125660i
$461$	−350.628			−0.760582			−0.380291	−	0.924867i	$-0.624176\pi$
$461$	−350.628			−0.760582			−0.380291	+	0.924867i	$0.624176\pi$
$462$	10.9174	−	10.9174i	0.0236307	−	0.0236307i
$463$	−486.539	−	486.539i	−1.05084	−	1.05084i	−0.998636	−	0.0522029i	$-0.983376\pi$
$463$	−486.539	−	486.539i	−1.05084	−	1.05084i	−0.0522029	−	0.998636i	$-0.516624\pi$
$464$			34.6915i			0.0747662i
$465$	−49.6380	−	408.833i	−0.106748	−	0.879210i
$466$	−127.231			−0.273028
$467$	−392.159	+	392.159i	−0.839742	+	0.839742i	−0.988825	−	0.149083i	$-0.952368\pi$
$467$	−392.159	+	392.159i	−0.839742	+	0.839742i	0.149083	+	0.988825i	$0.452368\pi$
$468$	−49.0168	−	49.0168i	−0.104737	−	0.104737i
$469$			226.545i			0.483037i
$470$	30.2393	−	38.5970i	0.0643389	−	0.0821212i
$471$	304.515			0.646528
$472$	−182.745	+	182.745i	−0.387172	+	0.387172i
$473$	118.480	+	118.480i	0.250486	+	0.250486i
$474$			107.324i			0.226422i
$475$	−801.744	+	197.599i	−1.68788	+	0.415998i
$476$	−50.1120			−0.105277
$477$	−18.0829	+	18.0829i	−0.0379096	+	0.0379096i
$478$	56.4515	+	56.4515i	0.118099	+	0.118099i
$479$			201.795i			0.421283i	0.977563	+	0.210642i	$0.0675553\pi$
$479$			201.795i			0.421283i	−0.977563	+	0.210642i	$0.932445\pi$
$480$	38.5637	+	30.2132i	0.0803411	+	0.0629442i
$481$	−305.483			−0.635101
$482$	−88.4572	+	88.4572i	−0.183521	+	0.183521i
$483$	−11.8153	−	11.8153i	−0.0244624	−	0.0244624i
$484$			222.363i			0.459428i
$485$	−736.293	+	89.3963i	−1.51813	+	0.184322i
$486$	22.0454			0.0453609
$487$	−406.615	+	406.615i	−0.834939	+	0.834939i	−0.988188	−	0.153249i	$-0.951026\pi$
$487$	−406.615	+	406.615i	−0.834939	+	0.834939i	0.153249	+	0.988188i	$0.451026\pi$
$488$	−153.566	−	153.566i	−0.314684	−	0.314684i
$489$			178.323i			0.364668i
$490$	−38.3125	−	315.552i	−0.0781888	−	0.643984i
$491$	128.249			0.261199			0.130599	−	0.991435i	$-0.458310\pi$
$491$	128.249			0.261199			0.130599	+	0.991435i	$0.458310\pi$
$492$	51.4589	−	51.4589i	0.104591	−	0.104591i
$493$	76.3876	+	76.3876i	0.154944	+	0.154944i
$494$			539.666i			1.09244i
$495$	−28.9870	+	36.9986i	−0.0585597	+	0.0747447i
$496$	190.218			0.383505
$497$	175.780	−	175.780i	0.353683	−	0.353683i
$498$	178.407	+	178.407i	0.358247	+	0.358247i
$499$			395.030i			0.791644i	0.918327	+	0.395822i	$0.129540\pi$
$499$			395.030i			0.791644i	−0.918327	+	0.395822i	$0.870460\pi$
$500$	227.973	+	102.608i	0.455945	+	0.205217i
$501$	148.147			0.295703
$502$	−68.5838	+	68.5838i	−0.136621	+	0.136621i
$503$	194.782	+	194.782i	0.387241	+	0.387241i	0.873702	−	0.486461i	$-0.161713\pi$
$503$	194.782	+	194.782i	0.387241	+	0.387241i	−0.486461	+	0.873702i	$0.661713\pi$
$504$		−	17.0688i		−	0.0338667i
$505$	−633.765	−	496.531i	−1.25498	−	0.983229i
$506$	−21.2520			−0.0420000
$507$	43.5026	−	43.5026i	0.0858039	−	0.0858039i
$508$	−34.0758	−	34.0758i	−0.0670784	−	0.0670784i
$509$		−	366.809i		−	0.720646i	−0.932828	−	0.360323i	$-0.882666\pi$
$509$		−	366.809i		−	0.720646i	0.932828	−	0.360323i	$-0.117334\pi$
$510$	151.441	−	18.3870i	0.296942	−	0.0360530i
$511$	−254.309			−0.497670
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−121.358	−	121.358i	−0.236565	−	0.236565i
$514$			266.639i			0.518754i
$515$	43.6367	+	359.404i	0.0847315	+	0.697872i
$516$	185.238			0.358988
$517$	−15.3639	+	15.3639i	−0.0297174	+	0.0297174i
$518$	−53.1883	−	53.1883i	−0.102680	−	0.102680i
$519$			236.397i			0.455485i
$520$	100.766	−	128.617i	0.193781	−	0.247340i
$521$	301.749			0.579173			0.289587	−	0.957152i	$-0.406482\pi$
$521$	301.749			0.579173			0.289587	+	0.957152i	$0.406482\pi$
$522$	−26.0186	+	26.0186i	−0.0498442	+	0.0498442i
$523$	−323.972	−	323.972i	−0.619449	−	0.619449i	0.325941	−	0.945390i	$-0.394319\pi$
$523$	−323.972	−	323.972i	−0.619449	−	0.619449i	−0.945390	+	0.325941i	$0.894319\pi$
$524$		−	452.955i		−	0.864418i
$525$	−20.8440	−	84.5731i	−0.0397029	−	0.161092i
$526$	−539.870			−1.02637
$527$	418.844	−	418.844i	0.794770	−	0.794770i
$528$	−15.3506	−	15.3506i	−0.0290732	−	0.0290732i
$529$			23.0000i			0.0434783i
$530$	−47.4482	−	37.1739i	−0.0895249	−	0.0701394i
$531$	−274.118			−0.516229
$532$	−93.9621	+	93.9621i	−0.176621	+	0.176621i
$533$	−171.624	−	171.624i	−0.321996	−	0.321996i
$534$			208.519i			0.390484i
$535$	621.996	−	75.5191i	1.16261	−	0.141157i
$536$	318.538			0.594288
$537$	−141.399	+	141.399i	−0.263313	+	0.263313i
$538$	287.611	+	287.611i	0.534593	+	0.534593i
$539$			140.859i			0.261334i
$540$	6.26287	+	51.5827i	0.0115979	+	0.0955235i
$541$	−38.7881			−0.0716970			−0.0358485	−	0.999357i	$-0.511413\pi$
$541$	−38.7881			−0.0716970			−0.0358485	+	0.999357i	$0.511413\pi$
$542$	−146.523	+	146.523i	−0.270338	+	0.270338i
$543$	223.529	+	223.529i	0.411656	+	0.411656i
$544$			70.4611i			0.129524i
$545$	−141.836	+	181.037i	−0.260250	+	0.332179i
$546$	−56.9274			−0.104263
$547$	539.005	−	539.005i	0.985383	−	0.985383i	−0.0145113	−	0.999895i	$-0.504619\pi$
$547$	539.005	−	539.005i	0.985383	−	0.985383i	0.999895	+	0.0145113i	$0.00461926\pi$
$548$	26.6670	+	26.6670i	0.0486625	+	0.0486625i
$549$		−	230.349i		−	0.419579i
$550$	−94.8058	−	57.3141i	−0.172374	−	0.104207i
$551$	286.460			0.519892
$552$	−16.6132	+	16.6132i	−0.0300965	+	0.0300965i
$553$	62.3223	+	62.3223i	0.112699	+	0.112699i
$554$			151.571i			0.273594i
$555$	180.253	+	141.222i	0.324781	+	0.254453i
$556$	273.153			0.491283
$557$	−239.468	+	239.468i	−0.429925	+	0.429925i	−0.888603	−	0.458678i	$-0.848323\pi$
$557$	−239.468	+	239.468i	−0.429925	+	0.429925i	0.458678	+	0.888603i	$0.348323\pi$
$558$	142.664	+	142.664i	0.255670	+	0.255670i
$559$		−	617.800i		−	1.10519i
$560$	39.9383	−	4.84907i	0.0713183	−	0.00865905i
$561$	−67.6015			−0.120502
$562$	−461.843	+	461.843i	−0.821785	+	0.821785i
$563$	316.131	+	316.131i	0.561512	+	0.561512i	0.929737	−	0.368225i	$-0.120034\pi$
$563$	316.131	+	316.131i	0.561512	+	0.561512i	−0.368225	+	0.929737i	$0.620034\pi$
$564$			24.0207i			0.0425899i
$565$	−85.4113	−	703.471i	−0.151170	−	1.24508i
$566$	−35.4086			−0.0625594
$567$	12.8016	−	12.8016i	0.0225778	−	0.0225778i
$568$	−247.160	−	247.160i	−0.435141	−	0.435141i
$569$		−	235.711i		−	0.414256i	−0.978314	−	0.207128i	$-0.933588\pi$
$569$		−	235.711i		−	0.414256i	0.978314	−	0.207128i	$-0.0664116\pi$
$570$	249.481	−	318.434i	0.437687	−	0.558657i
$571$	930.317			1.62928			0.814638	−	0.579969i	$-0.196935\pi$
$571$	930.317			1.62928			0.814638	+	0.579969i	$0.196935\pi$
$572$	−51.1970	+	51.1970i	−0.0895053	+	0.0895053i
$573$	−154.618	−	154.618i	−0.269840	−	0.269840i
$574$		−	59.7636i		−	0.104118i
$575$	−62.0282	+	102.604i	−0.107875	+	0.178441i
$576$	−24.0000			−0.0416667
$577$	−480.176	+	480.176i	−0.832193	+	0.832193i	−0.987816	−	0.155623i	$-0.950261\pi$
$577$	−480.176	+	480.176i	−0.832193	+	0.832193i	0.155623	+	0.987816i	$0.450261\pi$
$578$	−133.851	−	133.851i	−0.231576	−	0.231576i
$579$		−	257.172i		−	0.444165i
$580$	−68.2711	−	53.4878i	−0.117709	−	0.0922204i
$581$	207.199			0.356625
$582$	256.932	−	256.932i	0.441464	−	0.441464i
$583$	18.8872	+	18.8872i	0.0323966	+	0.0323966i
$584$			357.578i			0.612291i
$585$	172.037	−	20.8877i	0.294081	−	0.0357055i
$586$	271.279			0.462934
$587$	175.266	−	175.266i	0.298579	−	0.298579i	−0.541878	−	0.840457i	$-0.682287\pi$
$587$	175.266	−	175.266i	0.298579	−	0.298579i	0.840457	+	0.541878i	$0.182287\pi$
$588$	110.113	+	110.113i	0.187267	+	0.187267i
$589$		−	1570.70i		−	2.66673i
$590$	−77.8740	−	641.391i	−0.131990	−	1.08710i
$591$	463.994			0.785099
$592$	−74.7866	+	74.7866i	−0.126329	+	0.126329i
$593$	204.328	+	204.328i	0.344567	+	0.344567i	0.858081	−	0.513514i	$-0.171657\pi$
$593$	204.328	+	204.328i	0.344567	+	0.344567i	−0.513514	+	0.858081i	$0.671657\pi$
$594$		−	23.0260i		−	0.0387643i
$595$	77.2632	−	98.6177i	0.129854	−	0.165744i
$596$	43.2103			0.0725006
$597$	−172.356	+	172.356i	−0.288704	+	0.288704i
$598$	55.4080	+	55.4080i	0.0926555	+	0.0926555i
$599$		−	353.006i		−	0.589326i	−0.955601	−	0.294663i	$-0.904793\pi$
$599$		−	353.006i		−	0.589326i	0.955601	−	0.294663i	$-0.0952074\pi$
$600$	−118.916	+	29.3082i	−0.198193	+	0.0488470i
$601$	−377.286			−0.627763			−0.313882	−	0.949462i	$-0.601630\pi$
$601$	−377.286			−0.627763			−0.313882	+	0.949462i	$0.601630\pi$
$602$	107.566	−	107.566i	0.178681	−	0.178681i
$603$	238.904	+	238.904i	0.396192	+	0.396192i
$604$		−	566.368i		−	0.937695i
$605$	−437.599	−	342.842i	−0.723304	−	0.566681i
$606$	394.421			0.650860
$607$	582.145	−	582.145i	0.959053	−	0.959053i	−0.0401409	−	0.999194i	$-0.512781\pi$
$607$	582.145	−	582.145i	0.959053	−	0.959053i	0.999194	+	0.0401409i	$0.0127807\pi$
$608$	132.118	+	132.118i	0.217299	+	0.217299i
$609$			30.2177i			0.0496185i
$610$	538.980	−	65.4397i	0.883573	−	0.107278i
$611$	80.1131			0.131118
$612$	−52.8458	+	52.8458i	−0.0863494	+	0.0863494i
$613$	−88.4721	−	88.4721i	−0.144326	−	0.144326i	0.631252	−	0.775578i	$-0.282542\pi$
$613$	−88.4721	−	88.4721i	−0.144326	−	0.144326i	−0.775578	+	0.631252i	$0.782542\pi$
$614$		−	674.040i		−	1.09779i
$615$	21.9284	+	180.608i	0.0356559	+	0.293672i
$616$	−17.8280			−0.0289416
$617$	604.135	−	604.135i	0.979149	−	0.979149i	−0.0206376	−	0.999787i	$-0.506570\pi$
$617$	604.135	−	604.135i	0.979149	−	0.979149i	0.999787	+	0.0206376i	$0.00656963\pi$
$618$	−125.415	−	125.415i	−0.202938	−	0.202938i
$619$		−	822.499i		−	1.32875i	−0.747397	−	0.664377i	$-0.768697\pi$
$619$		−	822.499i		−	1.32875i	0.747397	−	0.664377i	$-0.231303\pi$
$620$	−293.281	+	374.340i	−0.473034	+	0.603774i
$621$	−24.9199			−0.0401286
$622$	−205.353	+	205.353i	−0.330149	+	0.330149i
$623$	121.085	+	121.085i	0.194358	+	0.194358i
$624$			80.0441i			0.128276i
$625$	−553.419	+	290.435i	−0.885470	+	0.464696i
$626$	102.072			0.163055
$627$	−126.756	+	126.756i	−0.202162	+	0.202162i
$628$	−248.635	−	248.635i	−0.395916	−	0.395916i
$629$			329.347i			0.523604i
$630$	33.5905	+	26.3169i	0.0533183	+	0.0417728i
$631$	−190.298			−0.301582			−0.150791	−	0.988566i	$-0.548182\pi$
$631$	−190.298			−0.301582			−0.150791	+	0.988566i	$0.548182\pi$
$632$	87.6297	−	87.6297i	0.138655	−	0.138655i
$633$	103.293	+	103.293i	0.163180	+	0.163180i
$634$			831.997i			1.31230i
$635$	119.598	−	14.5209i	0.188343	−	0.0228675i
$636$	29.5292			0.0464296
$637$	367.246	−	367.246i	0.576525	−	0.576525i
$638$	27.1759	+	27.1759i	0.0425955	+	0.0425955i
$639$		−	370.740i		−	0.580189i
$640$	−6.81815	−	56.1561i	−0.0106534	−	0.0877440i
$641$	490.787			0.765658			0.382829	−	0.923819i	$-0.374950\pi$
$641$	490.787			0.765658			0.382829	+	0.923819i	$0.374950\pi$
$642$	−217.048	+	217.048i	−0.338081	+	0.338081i
$643$	159.376	+	159.376i	0.247863	+	0.247863i	0.820093	−	0.572230i	$-0.193921\pi$
$643$	159.376	+	159.376i	0.247863	+	0.247863i	−0.572230	+	0.820093i	$0.693921\pi$
$644$			19.2944i			0.0299602i
$645$	−285.602	+	364.538i	−0.442794	+	0.565175i
$646$	581.823			0.900654
$647$	518.536	−	518.536i	0.801446	−	0.801446i	−0.181875	−	0.983322i	$-0.558217\pi$
$647$	518.536	−	518.536i	0.801446	−	0.801446i	0.983322	+	0.181875i	$0.0582167\pi$
$648$	−18.0000	−	18.0000i	−0.0277778	−	0.0277778i
$649$			286.310i			0.441156i
$650$	97.7479	+	396.605i	0.150381	+	0.610162i
$651$	165.688			0.254512
$652$	145.600	−	145.600i	0.223313	−	0.223313i
$653$	33.5738	+	33.5738i	0.0514148	+	0.0514148i	0.732347	−	0.680932i	$-0.238425\pi$
$653$	33.5738	+	33.5738i	0.0514148	+	0.0514148i	−0.680932	+	0.732347i	$0.738425\pi$
$654$		−	112.668i		−	0.172275i
$655$	891.391	+	698.372i	1.36090	+	1.06622i
$656$	−84.0320			−0.128098
$657$	−268.183	+	268.183i	−0.408194	+	0.408194i
$658$	13.9486	+	13.9486i	0.0211985	+	0.0211985i
$659$			69.0686i			0.104808i	0.998626	+	0.0524041i	$0.0166884\pi$
$659$			69.0686i			0.104808i	−0.998626	+	0.0524041i	$0.983312\pi$
$660$	53.8771	−	6.54144i	0.0816319	−	0.00991127i
$661$	−1025.91			−1.55205			−0.776026	−	0.630701i	$-0.782768\pi$
$661$	−1025.91			−1.55205			−0.776026	+	0.630701i	$0.782768\pi$
$662$	−624.517	+	624.517i	−0.943379	+	0.943379i
$663$	176.250	+	176.250i	0.265837	+	0.265837i
$664$		−	291.337i		−	0.438761i
$665$	−40.0405	−	329.785i	−0.0602113	−	0.495917i
$666$	−112.180			−0.168438
$667$	29.4112	−	29.4112i	0.0440947	−	0.0440947i
$668$	−120.962	−	120.962i	−0.181081	−	0.181081i
$669$			438.170i			0.654963i
$670$	−491.126	+	626.866i	−0.733024	+	0.935622i
$671$	−240.595			−0.358561
$672$	−13.9366	+	13.9366i	−0.0207390	+	0.0207390i
$673$	36.3139	+	36.3139i	0.0539583	+	0.0539583i	0.733571	−	0.679613i	$-0.237852\pi$
$673$	36.3139	+	36.3139i	0.0539583	+	0.0539583i	−0.679613	+	0.733571i	$0.737852\pi$
$674$		−	173.047i		−	0.256746i
$675$	−111.168	−	67.2059i	−0.164694	−	0.0995643i
$676$	−71.0394			−0.105088
$677$	564.145	−	564.145i	0.833302	−	0.833302i	−0.154665	−	0.987967i	$-0.549430\pi$
$677$	564.145	−	564.145i	0.833302	−	0.833302i	0.987967	+	0.154665i	$0.0494299\pi$
$678$	245.479	+	245.479i	0.362063	+	0.362063i
$679$		−	298.397i		−	0.439466i
$680$	−138.664	−	108.638i	−0.203917	−	0.159761i
$681$	389.924			0.572576
$682$	149.009	−	149.009i	0.218489	−	0.218489i
$683$	120.894	+	120.894i	0.177005	+	0.177005i	0.790049	−	0.613044i	$-0.210055\pi$
$683$	120.894	+	120.894i	0.177005	+	0.177005i	−0.613044	+	0.790049i	$0.710055\pi$
$684$			198.177i			0.289732i
$685$	−93.5949	+	11.3637i	−0.136635	+	0.0165894i
$686$	267.279			0.389620
$687$	−171.135	+	171.135i	−0.249104	+	0.249104i
$688$	−151.246	−	151.246i	−0.219834	−	0.219834i
$689$		−	98.4850i		−	0.142939i
$690$	−7.07948	−	58.3085i	−0.0102601	−	0.0845051i
$691$	−979.008			−1.41680			−0.708400	−	0.705812i	$-0.750582\pi$
$691$	−979.008			−1.41680			−0.708400	+	0.705812i	$0.750582\pi$
$692$	193.017	−	193.017i	0.278927	−	0.278927i
$693$	−13.3710	−	13.3710i	−0.0192944	−	0.0192944i
$694$			765.660i			1.10326i
$695$	−421.151	+	537.551i	−0.605973	+	0.773455i
$696$	42.4883			0.0610464
$697$	−185.031	+	185.031i	−0.265468	+	0.265468i
$698$	392.877	+	392.877i	0.562861	+	0.562861i
$699$			155.825i			0.222926i
$700$	−52.0346	+	86.0727i	−0.0743351	+	0.122961i
$701$	−941.739			−1.34342			−0.671711	−	0.740813i	$-0.734440\pi$
$701$	−941.739			−1.34342			−0.671711	+	0.740813i	$0.734440\pi$
$702$	−60.0331	+	60.0331i	−0.0855172	+	0.0855172i
$703$	617.540	+	617.540i	0.878435	+	0.878435i
$704$			25.0675i			0.0356072i
$705$	−47.2714	−	37.0354i	−0.0670517	−	0.0525325i
$706$	476.988			0.675620
$707$	229.037	−	229.037i	0.323957	−	0.323957i
$708$	223.816	+	223.816i	0.316124	+	0.316124i
$709$			754.542i			1.06423i	0.846671	+	0.532117i	$0.178603\pi$
$709$			754.542i			1.06423i	−0.846671	+	0.532117i	$0.821397\pi$
$710$	867.473	−	105.323i	1.22179	−	0.148343i
$711$	131.445			0.184873
$712$	170.255	−	170.255i	0.239122	−	0.239122i
$713$	−161.265	−	161.265i	−0.226179	−	0.226179i
$714$			61.3744i			0.0859585i
$715$	−21.8168	−	179.689i	−0.0305130	−	0.251314i
$716$	230.904			0.322491
$717$	69.1386	−	69.1386i	0.0964277	−	0.0964277i
$718$	−434.304	−	434.304i	−0.604881	−	0.604881i
$719$			266.966i			0.371302i	0.982616	+	0.185651i	$0.0594394\pi$
$719$			266.966i			0.371302i	−0.982616	+	0.185651i	$0.940561\pi$
$720$	37.0035	−	47.2307i	0.0513937	−	0.0655982i
$721$	−145.656			−0.202019
$722$	729.943	−	729.943i	1.01100	−	1.01100i
$723$	108.337	+	108.337i	0.149844	+	0.149844i
$724$		−	365.022i		−	0.504174i
$725$	210.522	−	51.8857i	0.290376	−	0.0715664i
$726$	272.338			0.375121
$727$	−767.189	+	767.189i	−1.05528	+	1.05528i	−0.0569010	+	0.998380i	$0.518122\pi$
$727$	−767.189	+	767.189i	−1.05528	+	1.05528i	−0.998380	+	0.0569010i	$0.981878\pi$
$728$	46.4810	+	46.4810i	0.0638475	+	0.0638475i
$729$		−	27.0000i		−	0.0370370i
$730$	−703.694	−	551.318i	−0.963964	−	0.755230i
$731$	−666.060			−0.911163
$732$	−188.079	+	188.079i	−0.256939	+	0.256939i
$733$	633.411	+	633.411i	0.864135	+	0.864135i	0.991815	−	0.127680i	$-0.0407531\pi$
$733$	633.411	+	633.411i	0.864135	+	0.864135i	−0.127680	+	0.991815i	$0.540753\pi$
$734$			279.229i			0.380421i
$735$	−386.471	+	46.9230i	−0.525811	+	0.0638409i
$736$	27.1293			0.0368605
$737$	249.530	−	249.530i	0.338575	−	0.338575i
$738$	−63.0240	−	63.0240i	−0.0853984	−	0.0853984i
$739$		−	228.825i		−	0.309641i	−0.987943	−	0.154820i	$-0.950520\pi$
$739$		−	228.825i		−	0.309641i	0.987943	−	0.154820i	$-0.0494799\pi$
$740$	−31.8692	−	262.483i	−0.0430664	−	0.354707i
$741$	660.953			0.891974
$742$	17.1474	−	17.1474i	0.0231097	−	0.0231097i
$743$	−391.292	−	391.292i	−0.526638	−	0.526638i	0.392931	−	0.919568i	$-0.371461\pi$
$743$	−391.292	−	391.292i	−0.526638	−	0.526638i	−0.919568	+	0.392931i	$0.871461\pi$
$744$		−	232.969i		−	0.313130i
$745$	−66.6222	+	85.0356i	−0.0894258	+	0.114142i
$746$	157.626			0.211295
$747$	218.503	−	218.503i	0.292507	−	0.292507i
$748$	55.1964	+	55.1964i	0.0737919	+	0.0737919i
$749$			252.076i			0.336551i
$750$	125.669	−	279.208i	0.167559	−	0.372278i
$751$	430.557			0.573312			0.286656	−	0.958034i	$-0.407456\pi$
$751$	430.557			0.573312			0.286656	+	0.958034i	$0.407456\pi$
$752$	19.6128	−	19.6128i	0.0260809	−	0.0260809i
$753$	83.9976	+	83.9976i	0.111551	+	0.111551i
$754$		−	141.706i		−	0.187938i
$755$	1114.58	+	873.233i	1.47627	+	1.15660i
$756$	−20.9049			−0.0276520
$757$	−788.836	+	788.836i	−1.04206	+	1.04206i	−0.0429790	+	0.999076i	$0.513685\pi$
$757$	−788.836	+	788.836i	−1.04206	+	1.04206i	−0.999076	+	0.0429790i	$0.986315\pi$
$758$	59.0081	+	59.0081i	0.0778470	+	0.0778470i
$759$			26.0283i			0.0342929i
$760$	−463.701	+	56.2999i	−0.610133	+	0.0740788i
$761$	1041.88			1.36909			0.684546	−	0.728969i	$-0.260000\pi$
$761$	1041.88			1.36909			0.684546	+	0.728969i	$0.260000\pi$
$762$	−41.7342	+	41.7342i	−0.0547693	+	0.0547693i
$763$	−65.4255	−	65.4255i	−0.0857477	−	0.0857477i
$764$			252.490i			0.330485i
$765$	−22.5194	−	185.476i	−0.0294372	−	0.242452i
$766$	−202.975			−0.264980
$767$	746.465	−	746.465i	0.973227	−	0.973227i
$768$	19.5959	+	19.5959i	0.0255155	+	0.0255155i
$769$		−	920.965i		−	1.19761i	−0.800893	−	0.598807i	$-0.795642\pi$
$769$		−	920.965i		−	1.19761i	0.800893	−	0.598807i	$-0.204358\pi$
$770$	27.4874	−	35.0846i	0.0356980	−	0.0455644i
$771$	326.565			0.423561
$772$	−209.980	+	209.980i	−0.271994	+	0.271994i
$773$	95.8217	+	95.8217i	0.123961	+	0.123961i	0.766366	−	0.642405i	$-0.222063\pi$
$773$	95.8217	+	95.8217i	0.123961	+	0.123961i	−0.642405	+	0.766366i	$0.722063\pi$
$774$		−	226.869i		−	0.293112i
$775$	−284.496	−	1154.32i	−0.367092	−	1.48945i
$776$	−419.569			−0.540681
$777$	−65.1421	+	65.1421i	−0.0838379	+	0.0838379i
$778$	276.824	+	276.824i	0.355815	+	0.355815i
$779$			693.882i			0.890735i
$780$	−157.522	−	123.413i	−0.201952	−	0.158222i
$781$	−387.231			−0.495814
$782$	59.7363	−	59.7363i	0.0763891	−	0.0763891i
$783$	31.8662	+	31.8662i	0.0406976	+	0.0406976i
$784$		−	179.814i		−	0.229355i
$785$	872.650	−	105.952i	1.11166	−	0.134971i
$786$	−554.754			−0.705794
$787$	552.775	−	552.775i	0.702382	−	0.702382i	−0.262539	−	0.964921i	$-0.584560\pi$
$787$	552.775	−	552.775i	0.702382	−	0.702382i	0.964921	+	0.262539i	$0.0845598\pi$
$788$	−378.849	−	378.849i	−0.480773	−	0.480773i
$789$			661.203i			0.838027i
$790$	37.3420	+	307.559i	0.0472684	+	0.389315i
$791$	285.096			0.360424
$792$	−18.8006	+	18.8006i	−0.0237382	+	0.0237382i
$793$	627.276	+	627.276i	0.791016	+	0.791016i
$794$		−	608.890i		−	0.766864i
$795$	−45.5285	+	58.1119i	−0.0572686	+	0.0730968i
$796$	281.457			0.353589
$797$	−844.895	+	844.895i	−1.06009	+	1.06009i	−0.0620189	+	0.998075i	$0.519754\pi$
$797$	−844.895	+	844.895i	−1.06009	+	1.06009i	−0.998075	+	0.0620189i	$0.980246\pi$
$798$	115.080	+	115.080i	0.144210	+	0.144210i
$799$		−	86.3713i		−	0.108099i
$800$	121.025	+	73.1645i	0.151281	+	0.0914556i
$801$	255.382			0.318829
$802$	506.097	−	506.097i	0.631044	−	0.631044i
$803$	280.112	+	280.112i	0.348832	+	0.348832i
$804$		−	390.128i		−	0.485234i
$805$	−37.9703	−	29.7483i	−0.0471681	−	0.0369544i
$806$	−776.991			−0.964009
$807$	352.250	−	352.250i	0.436494	−	0.436494i
$808$	−322.044	−	322.044i	−0.398569	−	0.398569i
$809$		−	1058.13i		−	1.30795i	−0.756518	−	0.653973i	$-0.773101\pi$
$809$		−	1058.13i		−	1.30795i	0.756518	−	0.653973i	$-0.226899\pi$
$810$	63.1757	−	7.67042i	0.0779946	−	0.00946965i
$811$	−1149.17			−1.41697			−0.708487	−	0.705723i	$-0.750622\pi$
$811$	−1149.17			−1.41697			−0.708487	+	0.705723i	$0.750622\pi$
$812$	24.6726	−	24.6726i	0.0303850	−	0.0303850i
$813$	179.453	+	179.453i	0.220730	+	0.220730i
$814$			117.170i			0.143943i
$815$	62.0451	+	511.020i	0.0761290	+	0.627019i
$816$	86.2969			0.105756
$817$	−1248.89	+	1248.89i	−1.52863	+	1.52863i
$818$	65.7017	+	65.7017i	0.0803200	+	0.0803200i
$819$			69.7215i			0.0851300i
$820$	129.562	−	165.371i	0.158002	−	0.201671i
$821$	−741.536			−0.903211			−0.451606	−	0.892218i	$-0.649149\pi$
$821$	−741.536			−0.903211			−0.451606	+	0.892218i	$0.649149\pi$
$822$	32.6603	−	32.6603i	0.0397327	−	0.0397327i
$823$	937.263	+	937.263i	1.13884	+	1.13884i	0.988659	+	0.150178i	$0.0479846\pi$
$823$	937.263	+	937.263i	1.13884	+	1.13884i	0.150178	+	0.988659i	$0.452015\pi$
$824$			204.803i			0.248547i
$825$	−70.1951	+	116.113i	−0.0850850	+	0.140743i
$826$	259.937			0.314693
$827$	−205.141	+	205.141i	−0.248055	+	0.248055i	−0.820172	−	0.572117i	$-0.806122\pi$
$827$	−205.141	+	205.141i	−0.248055	+	0.248055i	0.572117	+	0.820172i	$0.306122\pi$
$828$	20.3470	+	20.3470i	0.0245737	+	0.0245737i
$829$		−	83.5409i		−	0.100773i	−0.998730	−	0.0503866i	$-0.983955\pi$
$829$		−	83.5409i		−	0.100773i	0.998730	−	0.0503866i	$-0.0160453\pi$
$830$	573.336	+	449.187i	0.690766	+	0.541190i
$831$	185.636			0.223388
$832$	65.3557	−	65.3557i	0.0785525	−	0.0785525i
$833$	−395.935	−	395.935i	−0.475312	−	0.475312i
$834$		−	334.543i		−	0.401131i
$835$	424.547	−	51.5460i	0.508439	−	0.0617317i
$836$	206.991			0.247597
$837$	174.727	−	174.727i	0.208754	−	0.208754i
$838$	−496.707	−	496.707i	−0.592729	−	0.592729i
$839$		−	1253.41i		−	1.49393i	−0.664865	−	0.746964i	$-0.731511\pi$
$839$		−	1253.41i		−	1.49393i	0.664865	−	0.746964i	$-0.268489\pi$
$840$	−5.93887	−	48.9142i	−0.00707009	−	0.0582312i
$841$	765.781			0.910560
$842$	452.792	−	452.792i	0.537758	−	0.537758i
$843$	565.640	+	565.640i	0.670984	+	0.670984i
$844$		−	168.677i		−	0.199854i
$845$	109.529	−	139.802i	0.129621	−	0.165446i
$846$	29.4192			0.0347745
$847$	158.145	−	158.145i	0.186712	−	0.186712i
$848$	−24.1105	−	24.1105i	−0.0284322	−	0.0284322i
$849$			43.3665i			0.0510795i
$850$	427.587	−	105.384i	0.503043	−	0.123981i
$851$	126.807			0.149009
$852$	−302.708	+	302.708i	−0.355291	+	0.355291i
$853$	−337.158	−	337.158i	−0.395262	−	0.395262i	0.481296	−	0.876558i	$-0.340166\pi$
$853$	−337.158	−	337.158i	−0.395262	−	0.395262i	−0.876558	+	0.481296i	$0.840166\pi$
$854$			218.432i			0.255776i
$855$	−390.001	−	305.551i	−0.456141	−	0.357370i
$856$	354.438			0.414063
$857$	208.941	−	208.941i	0.243806	−	0.243806i	−0.574617	−	0.818423i	$-0.694849\pi$
$857$	208.941	−	208.941i	0.243806	−	0.243806i	0.818423	+	0.574617i	$0.194849\pi$
$858$	62.7033	+	62.7033i	0.0730807	+	0.0730807i
$859$			562.758i			0.655132i	0.944828	+	0.327566i	$0.106228\pi$
$859$			562.758i			0.655132i	−0.944828	+	0.327566i	$0.893772\pi$
$860$	530.837	−	64.4511i	0.617252	−	0.0749432i
$861$	−73.1951			−0.0850118
$862$	−375.766	+	375.766i	−0.435924	+	0.435924i
$863$	489.121	+	489.121i	0.566768	+	0.566768i	0.931222	−	0.364453i	$-0.118744\pi$
$863$	489.121	+	489.121i	0.566768	+	0.566768i	−0.364453	+	0.931222i	$0.618744\pi$
$864$			29.3939i			0.0340207i
$865$	82.2513	+	677.444i	0.0950882	+	0.783173i
$866$	−927.395			−1.07090
$867$	−163.933	+	163.933i	−0.189081	+	0.189081i
$868$	−135.283	−	135.283i	−0.155856	−	0.155856i
$869$		−	137.291i		−	0.157987i
$870$	−65.5090	+	83.6147i	−0.0752976	+	0.0961088i
$871$	−1301.14			−1.49385
$872$	−91.9930	+	91.9930i	−0.105497	+	0.105497i
$873$	−314.677	−	314.677i	−0.360454	−	0.360454i
$874$		−	224.016i		−	0.256312i
$875$	−89.1590	−	235.109i	−0.101896	−	0.268696i
$876$	437.942			0.499933
$877$	208.653	−	208.653i	0.237916	−	0.237916i	−0.578071	−	0.815987i	$-0.696194\pi$
$877$	208.653	−	208.653i	0.237916	−	0.237916i	0.815987	+	0.578071i	$0.196194\pi$
$878$	−772.787	−	772.787i	−0.880167	−	0.880167i
$879$		−	332.248i		−	0.377984i
$880$	−49.3315	−	38.6494i	−0.0560585	−	0.0439197i
$881$	−1167.86			−1.32561			−0.662804	−	0.748793i	$-0.730634\pi$
$881$	−1167.86			−1.32561			−0.662804	+	0.748793i	$0.730634\pi$
$882$	134.861	−	134.861i	0.152903	−	0.152903i
$883$	903.097	+	903.097i	1.02276	+	1.02276i	0.999735	+	0.0230253i	$0.00732981\pi$
$883$	903.097	+	903.097i	1.02276	+	1.02276i	0.0230253	+	0.999735i	$0.492670\pi$
$884$		−	287.815i		−	0.325582i
$885$	−785.541	+	95.3757i	−0.887617	+	0.107769i
$886$	628.506			0.709374
$887$	505.164	−	505.164i	0.569520	−	0.569520i	−0.362474	−	0.931994i	$-0.618068\pi$
$887$	505.164	−	505.164i	0.569520	−	0.569520i	0.931994	+	0.362474i	$0.118068\pi$
$888$	91.5946	+	91.5946i	0.103147	+	0.103147i
$889$			48.4695i			0.0545214i
$890$	72.5514	+	597.553i	0.0815184	+	0.671408i
$891$	−28.2009			−0.0316509
$892$	357.765	−	357.765i	0.401082	−	0.401082i
$893$	−161.950	−	161.950i	−0.181355	−	0.181355i
$894$		−	52.9216i		−	0.0591965i
$895$	−356.010	+	454.406i	−0.397777	+	0.507717i
$896$	22.7584			0.0254000
$897$	67.8607	−	67.8607i	0.0756529	−	0.0756529i
$898$	−123.814	−	123.814i	−0.137878	−	0.137878i
$899$			412.435i			0.458771i
$900$	35.8951	+	145.642i	0.0398834	+	0.161824i
$901$	−106.178			−0.117845
$902$	−65.8273	+	65.8273i	−0.0729792	+	0.0729792i
$903$	−131.741	−	131.741i	−0.145893	−	0.145893i
$904$		−	400.866i		−	0.443435i
$905$	718.344	+	562.795i	0.793750	+	0.621873i
$906$	−693.656			−0.765625
$907$	84.5950	−	84.5950i	0.0932690	−	0.0932690i	−0.658933	−	0.752202i	$-0.728992\pi$
$907$	84.5950	−	84.5950i	0.0932690	−	0.0932690i	0.752202	+	0.658933i	$0.228992\pi$
$908$	−318.372	−	318.372i	−0.350630	−	0.350630i
$909$		−	483.065i		−	0.531425i
$910$	−163.137	+	19.8071i	−0.179272	+	0.0217661i
$911$	669.856			0.735297			0.367649	−	0.929965i	$-0.380163\pi$
$911$	669.856			0.735297			0.367649	+	0.929965i	$0.380163\pi$
$912$	161.810	−	161.810i	0.177424	−	0.177424i
$913$	−228.222	−	228.222i	−0.249969	−	0.249969i
$914$		−	167.240i		−	0.182976i
$915$	−80.1470	−	660.113i	−0.0875923	−	0.721435i
$916$	279.462			0.305089
$917$	−322.142	+	322.142i	−0.351299	+	0.351299i
$918$	64.7227	+	64.7227i	0.0705040	+	0.0705040i
$919$		−	1375.28i		−	1.49650i	−0.663419	−	0.748248i	$-0.730895\pi$
$919$		−	1375.28i		−	1.49650i	0.663419	−	0.748248i	$-0.269105\pi$
$920$	−41.8283	+	53.3891i	−0.0454656	+	0.0580316i
$921$	−825.528			−0.896338
$922$	350.628	−	350.628i	0.380291	−	0.380291i
$923$	1009.58	+	1009.58i	1.09381	+	1.09381i
$924$			21.8348i			0.0236307i
$925$	565.689	+	341.983i	0.611556	+	0.369711i
$926$	973.077			1.05084
$927$	−153.602	+	153.602i	−0.165698	+	0.165698i
$928$	−34.6915	−	34.6915i	−0.0373831	−	0.0373831i
$929$		−	713.121i		−	0.767622i	−0.923412	−	0.383811i	$-0.874611\pi$
$929$		−	713.121i		−	0.767622i	0.923412	−	0.383811i	$-0.125389\pi$
$930$	458.471	+	359.194i	0.492979	+	0.386231i
$931$	−1484.79			−1.59483
$932$	127.231	−	127.231i	0.136514	−	0.136514i
$933$	251.505	+	251.505i	0.269566	+	0.269566i
$934$		−	784.319i		−	0.839742i
$935$	−193.726	+	23.5211i	−0.207194	+	0.0251562i
$936$	98.0336			0.104737
$937$	38.9789	−	38.9789i	0.0415997	−	0.0415997i	−0.686001	−	0.727601i	$-0.740635\pi$
$937$	38.9789	−	38.9789i	0.0415997	−	0.0415997i	0.727601	+	0.686001i	$0.240635\pi$
$938$	−226.545	−	226.545i	−0.241519	−	0.241519i
$939$		−	125.012i		−	0.133134i
$940$	8.35769	+	68.8362i	0.00889116	+	0.0732301i
$941$	−220.600			−0.234432			−0.117216	−	0.993106i	$-0.537397\pi$
$941$	−220.600			−0.234432			−0.117216	+	0.993106i	$0.537397\pi$
$942$	−304.515	+	304.515i	−0.323264	+	0.323264i
$943$	71.2416	+	71.2416i	0.0755478	+	0.0755478i
$944$		−	365.490i		−	0.387172i
$945$	32.2315	−	41.1398i	0.0341074	−	0.0435342i
$946$	−236.960			−0.250486
$947$	266.506	−	266.506i	0.281422	−	0.281422i	−0.552254	−	0.833676i	$-0.686232\pi$
$947$	266.506	−	266.506i	0.281422	−	0.281422i	0.833676	+	0.552254i	$0.186232\pi$
$948$	−107.324	−	107.324i	−0.113211	−	0.113211i
$949$		−	1460.61i		−	1.53910i
$950$	604.145	−	999.344i	0.635942	−	1.05194i
$951$	1018.98			1.07149
$952$	50.1120	−	50.1120i	0.0526386	−	0.0526386i
$953$	258.995	+	258.995i	0.271768	+	0.271768i	0.829812	−	0.558043i	$-0.188448\pi$
$953$	258.995	+	258.995i	0.271768	+	0.271768i	−0.558043	+	0.829812i	$0.688448\pi$
$954$		−	36.1658i		−	0.0379096i
$955$	−496.887	−	389.293i	−0.520301	−	0.407636i
$956$	−112.903			−0.118099
$957$	33.2836	−	33.2836i	0.0347791	−	0.0347791i
$958$	−201.795	−	201.795i	−0.210642	−	0.210642i
$959$		−	37.9312i		−	0.0395529i
$960$	−68.7770	+	8.35049i	−0.0716427	+	0.00869843i
$961$	1300.44			1.35322
$962$	305.483	−	305.483i	0.317550	−	0.317550i
$963$	265.829	+	265.829i	0.276042	+	0.276042i
$964$		−	176.914i		−	0.183521i
$965$	−89.4796	−	736.978i	−0.0927249	−	0.763708i
$966$	23.6307			0.0244624
$967$	−648.945	+	648.945i	−0.671091	+	0.671091i	−0.957967	−	0.286877i	$-0.907383\pi$
$967$	−648.945	+	648.945i	−0.671091	+	0.671091i	0.286877	+	0.957967i	$0.407383\pi$
$968$	−222.363	−	222.363i	−0.229714	−	0.229714i
$969$		−	712.584i		−	0.735381i
$970$	646.896	−	825.689i	0.666903	−	0.851226i
$971$	−1081.55			−1.11385			−0.556924	−	0.830563i	$-0.688019\pi$
$971$	−1081.55			−1.11385			−0.556924	+	0.830563i	$0.688019\pi$
$972$	−22.0454	+	22.0454i	−0.0226805	+	0.0226805i
$973$	−194.267	−	194.267i	−0.199658	−	0.199658i
$974$		−	813.231i		−	0.834939i
$975$	485.740	−	119.716i	0.498195	−	0.122786i
$976$	307.132			0.314684
$977$	−987.221	+	987.221i	−1.01046	+	1.01046i	−0.0105173	+	0.999945i	$0.503348\pi$
$977$	−987.221	+	987.221i	−1.01046	+	1.01046i	−0.999945	+	0.0105173i	$0.996652\pi$
$978$	−178.323	−	178.323i	−0.182334	−	0.182334i
$979$		−	266.741i		−	0.272463i
$980$	353.865	+	277.240i	0.361087	+	0.282898i
$981$	−137.990			−0.140662
$982$	−128.249	+	128.249i	−0.130599	+	0.130599i
$983$	−1025.65	−	1025.65i	−1.04338	−	1.04338i	−0.999015	−	0.0443674i	$-0.985873\pi$
$983$	−1025.65	−	1025.65i	−1.04338	−	1.04338i	−0.0443674	−	0.999015i	$-0.514127\pi$
$984$			102.918i			0.104591i
$985$	1329.67	−	161.441i	1.34992	−	0.163899i
$986$	−152.775			−0.154944
$987$	17.0835	−	17.0835i	0.0173085	−	0.0173085i
$988$	−539.666	−	539.666i	−0.546220	−	0.546220i
$989$			256.450i			0.259302i
$990$	−8.01159	−	65.9857i	−0.00809252	−	0.0666522i
$991$	−596.884			−0.602304			−0.301152	−	0.953576i	$-0.597371\pi$
$991$	−596.884			−0.602304			−0.301152	+	0.953576i	$0.597371\pi$
$992$	−190.218	+	190.218i	−0.191752	+	0.191752i
$993$	764.874	+	764.874i	0.770266	+	0.770266i
$994$			351.561i			0.353683i
$995$	−433.954	+	553.892i	−0.436134	+	0.556676i
$996$	−356.814			−0.358247
$997$	22.8112	−	22.8112i	0.0228799	−	0.0228799i	−0.695574	−	0.718454i	$-0.744850\pi$
$997$	22.8112	−	22.8112i	0.0228799	−	0.0228799i	0.718454	+	0.695574i	$0.244850\pi$
$998$	−395.030	−	395.030i	−0.395822	−	0.395822i
$999$			137.392i			0.137529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.b.553.16	yes	48
5.2	odd	4	inner	690.3.k.b.277.16	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.b.277.16	✓	48	5.2	odd	4	inner
690.3.k.b.553.16	yes	48	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(3.93589 + 3.08362i) q^{5} -2.44949 q^{6} +(-1.42240 + 1.42240i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(3.93589 + 3.08362i) q^{5} -2.44949 q^{6} +(-1.42240 + 1.42240i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(-7.01952 + 0.852269i) q^{10} +3.13344 q^{11} +(2.44949 - 2.44949i) q^{12} +(-8.16946 - 8.16946i) q^{13} -2.84480i q^{14} +(1.04381 + 8.59712i) q^{15} -4.00000 q^{16} +(-8.80764 + 8.80764i) q^{17} +(-3.00000 - 3.00000i) q^{18} +33.0294i q^{19} +(6.16725 - 7.87179i) q^{20} -3.48416 q^{21} +(-3.13344 + 3.13344i) q^{22} +(3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(5.98252 + 24.2736i) q^{25} +16.3389 q^{26} +(-3.67423 + 3.67423i) q^{27} +(2.84480 + 2.84480i) q^{28} -8.67288i q^{29} +(-9.64093 - 7.55331i) q^{30} -47.5546 q^{31} +(4.00000 - 4.00000i) q^{32} +(3.83766 + 3.83766i) q^{33} -17.6153i q^{34} +(-9.98457 + 1.21227i) q^{35} +6.00000 q^{36} +(18.6967 - 18.6967i) q^{37} +(-33.0294 - 33.0294i) q^{38} -20.0110i q^{39} +(1.70454 + 14.0390i) q^{40} +21.0080 q^{41} +(3.48416 - 3.48416i) q^{42} +(37.8115 + 37.8115i) q^{43} -6.26687i q^{44} +(-9.25087 + 11.8077i) q^{45} -6.78233 q^{46} +(-4.90320 + 4.90320i) q^{47} +(-4.89898 - 4.89898i) q^{48} +44.9536i q^{49} +(-30.2562 - 18.2911i) q^{50} -21.5742 q^{51} +(-16.3389 + 16.3389i) q^{52} +(6.02763 + 6.02763i) q^{53} -7.34847i q^{54} +(12.3329 + 9.66234i) q^{55} -5.68960 q^{56} +(-40.4526 + 40.4526i) q^{57} +(8.67288 + 8.67288i) q^{58} +91.3726i q^{59} +(17.1942 - 2.08762i) q^{60} -76.7830 q^{61} +(47.5546 - 47.5546i) q^{62} +(-4.26720 - 4.26720i) q^{63} +8.00000i q^{64} +(-6.96258 - 57.3457i) q^{65} -7.67532 q^{66} +(79.6346 - 79.6346i) q^{67} +(17.6153 + 17.6153i) q^{68} +8.30662i q^{69} +(8.77230 - 11.1968i) q^{70} -123.580 q^{71} +(-6.00000 + 6.00000i) q^{72} +(89.3944 + 89.3944i) q^{73} +37.3933i q^{74} +(-22.4020 + 37.0561i) q^{75} +66.0589 q^{76} +(-4.45700 + 4.45700i) q^{77} +(20.0110 + 20.0110i) q^{78} -43.8149i q^{79} +(-15.7436 - 12.3345i) q^{80} -9.00000 q^{81} +(-21.0080 + 21.0080i) q^{82} +(-72.8343 - 72.8343i) q^{83} +6.96831i q^{84} +(-61.8254 + 7.50647i) q^{85} -75.6230 q^{86} +(10.6221 - 10.6221i) q^{87} +(6.26687 + 6.26687i) q^{88} -85.1273i q^{89} +(-2.55681 - 21.0586i) q^{90} +23.2405 q^{91} +(6.78233 - 6.78233i) q^{92} +(-58.2422 - 58.2422i) q^{93} -9.80641i q^{94} +(-101.850 + 130.000i) q^{95} +9.79796 q^{96} +(-104.892 + 104.892i) q^{97} +(-44.9536 - 44.9536i) q^{98} +9.40031i 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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