LMFDB - Embedded newform 230.3.d.a.91.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,3,Mod(91,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("230.91");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	230.d (of order $2$, degree $1$, 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:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 78x^{14} + 2165x^{12} + 28310x^{10} + 184804x^{8} + 569634x^{6} + 696037x^{4} + 285578x^{2} + 529 $ x^16 + 78x^14 + 2165x^12 + 28310x^10 + 184804x^8 + 569634x^6 + 696037x^4 + 285578*x^2 + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.7
Root			$3.47734i$ of defining polynomial
Character	$\chi$	$=$	230.91
Dual form			230.3.d.a.91.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +4.76369 q^{3} +2.00000 q^{4} -2.23607i q^{5} -6.73687 q^{6} +7.05858i q^{7} -2.82843 q^{8} +13.6927 q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +4.76369 q^{3} +2.00000 q^{4} -2.23607i q^{5} -6.73687 q^{6} +7.05858i q^{7} -2.82843 q^{8} +13.6927 q^{9} +3.16228i q^{10} +10.4520i q^{11} +9.52738 q^{12} +19.0223 q^{13} -9.98235i q^{14} -10.6519i q^{15} +4.00000 q^{16} +12.8329i q^{17} -19.3645 q^{18} -22.7880i q^{19} -4.47214i q^{20} +33.6249i q^{21} -14.7813i q^{22} +(-6.14050 - 22.1652i) q^{23} -13.4737 q^{24} -5.00000 q^{25} -26.9016 q^{26} +22.3548 q^{27} +14.1172i q^{28} -8.61694 q^{29} +15.0641i q^{30} +22.2032 q^{31} -5.65685 q^{32} +49.7900i q^{33} -18.1485i q^{34} +15.7835 q^{35} +27.3855 q^{36} -29.8603i q^{37} +32.2271i q^{38} +90.6164 q^{39} +6.32456i q^{40} -18.7911 q^{41} -47.5528i q^{42} +10.0531i q^{43} +20.9039i q^{44} -30.6179i q^{45} +(8.68398 + 31.3463i) q^{46} +20.6079 q^{47} +19.0548 q^{48} -0.823620 q^{49} +7.07107 q^{50} +61.1320i q^{51} +38.0446 q^{52} +17.3941i q^{53} -31.6144 q^{54} +23.3713 q^{55} -19.9647i q^{56} -108.555i q^{57} +12.1862 q^{58} -103.279 q^{59} -21.3039i q^{60} +74.6163i q^{61} -31.4001 q^{62} +96.6514i q^{63} +8.00000 q^{64} -42.5352i q^{65} -70.4136i q^{66} -101.145i q^{67} +25.6658i q^{68} +(-29.2514 - 105.588i) q^{69} -22.3212 q^{70} -69.4218 q^{71} -38.7289 q^{72} -122.376 q^{73} +42.2289i q^{74} -23.8184 q^{75} -45.5761i q^{76} -73.7761 q^{77} -128.151 q^{78} +140.900i q^{79} -8.94427i q^{80} -16.7435 q^{81} +26.5747 q^{82} -126.423i q^{83} +67.2498i q^{84} +28.6953 q^{85} -14.2173i q^{86} -41.0484 q^{87} -29.5626i q^{88} +11.9403i q^{89} +43.3002i q^{90} +134.271i q^{91} +(-12.2810 - 44.3303i) q^{92} +105.769 q^{93} -29.1440 q^{94} -50.9556 q^{95} -26.9475 q^{96} +57.0325i q^{97} +1.16477 q^{98} +143.116i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9}+O(q^{10}) $ 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9	$ 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9} + 24 q^{13} + 64 q^{16} - 32 q^{18} + 4 q^{23} - 16 q^{24} - 80 q^{25} + 96 q^{26} - 96 q^{27} - 108 q^{29} - 116 q^{31} + 60 q^{35} + 128 q^{36} + 248 q^{39} - 156 q^{41} - 124 q^{46} - 128 q^{47} - 28 q^{49} + 48 q^{52} + 224 q^{54} + 160 q^{58} + 204 q^{59} + 64 q^{62} + 128 q^{64} - 268 q^{69} - 120 q^{70} + 236 q^{71} - 64 q^{72} - 112 q^{73} - 936 q^{77} - 432 q^{78} - 136 q^{81} - 64 q^{82} + 60 q^{85} - 152 q^{87} + 8 q^{92} + 856 q^{93} - 216 q^{94} - 160 q^{95} - 32 q^{96} + 256 q^{98}+O(q^{100}) $ 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9 + 24 * q^13 + 64 * q^16 - 32 * q^18 + 4 * q^23 - 16 * q^24 - 80 * q^25 + 96 * q^26 - 96 * q^27 - 108 * q^29 - 116 * q^31 + 60 * q^35 + 128 * q^36 + 248 * q^39 - 156 * q^41 - 124 * q^46 - 128 * q^47 - 28 * q^49 + 48 * q^52 + 224 * q^54 + 160 * q^58 + 204 * q^59 + 64 * q^62 + 128 * q^64 - 268 * q^69 - 120 * q^70 + 236 * q^71 - 64 * q^72 - 112 * q^73 - 936 * q^77 - 432 * q^78 - 136 * q^81 - 64 * q^82 + 60 * q^85 - 152 * q^87 + 8 * q^92 + 856 * q^93 - 216 * q^94 - 160 * q^95 - 32 * q^96 + 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$-1$

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 $

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$	4.76369			1.58790			0.793948	−	0.607985i	$-0.208022\pi$
$3$	4.76369			1.58790			0.793948	+	0.607985i	$0.208022\pi$
$4$	2.00000			0.500000
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$	−6.73687			−1.12281
$7$			7.05858i			1.00837i	0.863596	+	0.504185i	$0.168207\pi$
$7$			7.05858i			1.00837i	−0.863596	+	0.504185i	$0.831793\pi$
$8$	−2.82843			−0.353553
$9$	13.6927			1.52142
$10$			3.16228i			0.316228i
$11$			10.4520i			0.950179i	0.879937	+	0.475090i	$0.157584\pi$
$11$			10.4520i			0.950179i	−0.879937	+	0.475090i	$0.842416\pi$
$12$	9.52738			0.793948
$13$	19.0223			1.46326			0.731628	−	0.681704i	$-0.238761\pi$
$13$	19.0223			1.46326			0.731628	+	0.681704i	$0.238761\pi$
$14$		−	9.98235i		−	0.713025i
$15$		−	10.6519i		−	0.710129i
$16$	4.00000			0.250000
$17$			12.8329i			0.754877i	0.926035	+	0.377439i	$0.123195\pi$
$17$			12.8329i			0.754877i	−0.926035	+	0.377439i	$0.876805\pi$
$18$	−19.3645			−1.07580
$19$		−	22.7880i		−	1.19937i	−0.800236	−	0.599685i	$-0.795293\pi$
$19$		−	22.7880i		−	1.19937i	0.800236	−	0.599685i	$-0.204707\pi$
$20$		−	4.47214i		−	0.223607i
$21$			33.6249i			1.60119i
$22$		−	14.7813i		−	0.671878i
$23$	−6.14050	−	22.1652i	−0.266978	−	0.963703i
$23$	−6.14050	−	22.1652i	−0.266978	−	0.963703i
$24$	−13.4737			−0.561406
$25$	−5.00000			−0.200000
$26$	−26.9016			−1.03468
$27$	22.3548			0.827954
$28$			14.1172i			0.504185i
$29$	−8.61694			−0.297136			−0.148568	−	0.988902i	$-0.547466\pi$
$29$	−8.61694			−0.297136			−0.148568	+	0.988902i	$0.547466\pi$
$30$			15.0641i			0.502137i
$31$	22.2032			0.716233			0.358116	−	0.933677i	$-0.383419\pi$
$31$	22.2032			0.716233			0.358116	+	0.933677i	$0.383419\pi$
$32$	−5.65685			−0.176777
$33$			49.7900i			1.50879i
$34$		−	18.1485i		−	0.533779i
$35$	15.7835			0.450956
$36$	27.3855			0.760708
$37$		−	29.8603i		−	0.807036i	−0.914972	−	0.403518i	$-0.867787\pi$
$37$		−	29.8603i		−	0.807036i	0.914972	−	0.403518i	$-0.132213\pi$
$38$			32.2271i			0.848083i
$39$	90.6164			2.32350
$40$			6.32456i			0.158114i
$41$	−18.7911			−0.458320			−0.229160	−	0.973389i	$-0.573598\pi$
$41$	−18.7911			−0.458320			−0.229160	+	0.973389i	$0.573598\pi$
$42$		−	47.5528i		−	1.13221i
$43$			10.0531i			0.233794i	0.993144	+	0.116897i	$0.0372948\pi$
$43$			10.0531i			0.233794i	−0.993144	+	0.116897i	$0.962705\pi$
$44$			20.9039i			0.475090i
$45$		−	30.6179i		−	0.680398i
$46$	8.68398	+	31.3463i	0.188782	+	0.681441i
$47$	20.6079			0.438466			0.219233	−	0.975673i	$-0.429645\pi$
$47$	20.6079			0.438466			0.219233	+	0.975673i	$0.429645\pi$
$48$	19.0548			0.396974
$49$	−0.823620			−0.0168086
$50$	7.07107			0.141421
$51$			61.1320i			1.19867i
$52$	38.0446			0.731628
$53$			17.3941i			0.328191i	0.986444	+	0.164096i	$0.0524706\pi$
$53$			17.3941i			0.328191i	−0.986444	+	0.164096i	$0.947529\pi$
$54$	−31.6144			−0.585452
$55$	23.3713			0.424933
$56$		−	19.9647i		−	0.356512i
$57$		−	108.555i		−	1.90448i
$58$	12.1862			0.210107
$59$	−103.279			−1.75048			−0.875242	−	0.483686i	$-0.839298\pi$
$59$	−103.279			−1.75048			−0.875242	+	0.483686i	$0.839298\pi$
$60$		−	21.3039i		−	0.355064i
$61$			74.6163i			1.22322i	0.791160	+	0.611609i	$0.209477\pi$
$61$			74.6163i			1.22322i	−0.791160	+	0.611609i	$0.790523\pi$
$62$	−31.4001			−0.506453
$63$			96.6514i			1.53415i
$64$	8.00000			0.125000
$65$		−	42.5352i		−	0.654388i
$66$		−	70.4136i		−	1.06687i
$67$		−	101.145i		−	1.50963i	−0.655937	−	0.754816i	$-0.727726\pi$
$67$		−	101.145i		−	1.50963i	0.655937	−	0.754816i	$-0.272274\pi$
$68$			25.6658i			0.377439i
$69$	−29.2514	−	105.588i	−0.423934	−	1.53026i
$70$	−22.3212			−0.318874
$71$	−69.4218			−0.977772			−0.488886	−	0.872348i	$-0.662597\pi$
$71$	−69.4218			−0.977772			−0.488886	+	0.872348i	$0.662597\pi$
$72$	−38.7289			−0.537902
$73$	−122.376			−1.67638			−0.838189	−	0.545380i	$-0.816385\pi$
$73$	−122.376			−1.67638			−0.838189	+	0.545380i	$0.816385\pi$
$74$			42.2289i			0.570661i
$75$	−23.8184			−0.317579
$76$		−	45.5761i		−	0.599685i
$77$	−73.7761			−0.958132
$78$	−128.151			−1.64296
$79$			140.900i			1.78355i	0.452482	+	0.891774i	$0.350539\pi$
$79$			140.900i			1.78355i	−0.452482	+	0.891774i	$0.649461\pi$
$80$		−	8.94427i		−	0.111803i
$81$	−16.7435			−0.206710
$82$	26.5747			0.324082
$83$		−	126.423i		−	1.52317i	−0.648064	−	0.761586i	$-0.724421\pi$
$83$		−	126.423i		−	1.52317i	0.648064	−	0.761586i	$-0.275579\pi$
$84$			67.2498i			0.800593i
$85$	28.6953			0.337591
$86$		−	14.2173i		−	0.165317i
$87$	−41.0484			−0.471821
$88$		−	29.5626i		−	0.335939i
$89$			11.9403i			0.134161i	0.997748	+	0.0670805i	$0.0213684\pi$
$89$			11.9403i			0.134161i	−0.997748	+	0.0670805i	$0.978632\pi$
$90$			43.3002i			0.481114i
$91$			134.271i			1.47550i
$92$	−12.2810	−	44.3303i	−0.133489	−	0.481851i
$93$	105.769			1.13730
$94$	−29.1440			−0.310042
$95$	−50.9556			−0.536374
$96$	−26.9475			−0.280703
$97$			57.0325i			0.587964i	0.955811	+	0.293982i	$0.0949805\pi$
$97$			57.0325i			0.587964i	−0.955811	+	0.293982i	$0.905019\pi$
$98$	1.16477			0.0118855
$99$			143.116i			1.44562i
$100$	−10.0000			−0.100000
$101$	−28.7667			−0.284819			−0.142410	−	0.989808i	$-0.545485\pi$
$101$	−28.7667			−0.284819			−0.142410	+	0.989808i	$0.545485\pi$
$102$		−	86.4538i		−	0.847586i
$103$		−	165.265i		−	1.60452i	−0.596976	−	0.802259i	$-0.703631\pi$
$103$		−	165.265i		−	1.60452i	0.596976	−	0.802259i	$-0.296369\pi$
$104$	−53.8032			−0.517339
$105$	75.1876			0.716072
$106$		−	24.5990i		−	0.232066i
$107$		−	194.859i		−	1.82112i	−0.413381	−	0.910558i	$-0.635652\pi$
$107$		−	194.859i		−	1.82112i	0.413381	−	0.910558i	$-0.364348\pi$
$108$	44.7095			0.413977
$109$			62.2801i			0.571377i	0.958323	+	0.285688i	$0.0922222\pi$
$109$			62.2801i			0.571377i	−0.958323	+	0.285688i	$0.907778\pi$
$110$	−33.0520			−0.300473
$111$		−	142.245i		−	1.28149i
$112$			28.2343i			0.252092i
$113$		−	47.4389i		−	0.419813i	−0.977721	−	0.209907i	$-0.932684\pi$
$113$		−	47.4389i		−	0.419813i	0.977721	−	0.209907i	$-0.0673160\pi$
$114$			153.520i			1.34667i
$115$	−49.5628	+	13.7306i	−0.430981	+	0.119396i
$116$	−17.2339			−0.148568
$117$	260.468			2.22622
$118$	146.058			1.23778
$119$	−90.5822			−0.761195
$120$			30.1282i			0.251069i
$121$	11.7563			0.0971591
$122$		−	105.523i		−	0.864946i
$123$	−89.5152			−0.727766
$124$	44.4064			0.358116
$125$			11.1803i			0.0894427i
$126$		−	136.686i		−	1.08481i
$127$	194.450			1.53110			0.765552	−	0.643374i	$-0.222466\pi$
$127$	194.450			1.53110			0.765552	+	0.643374i	$0.222466\pi$
$128$	−11.3137			−0.0883883
$129$			47.8901i			0.371241i
$130$			60.1539i			0.462722i
$131$	−77.9594			−0.595110			−0.297555	−	0.954705i	$-0.596171\pi$
$131$	−77.9594			−0.595110			−0.297555	+	0.954705i	$0.596171\pi$
$132$			99.5799i			0.754393i
$133$	160.851			1.20941
$134$			143.041i			1.06747i
$135$		−	49.9868i		−	0.370272i
$136$		−	36.2970i		−	0.266889i
$137$			231.913i			1.69279i	0.532553	+	0.846397i	$0.321233\pi$
$137$			231.913i			1.69279i	−0.532553	+	0.846397i	$0.678767\pi$
$138$	41.3678	+	149.324i	0.299766	+	1.08206i
$139$	49.7145			0.357658			0.178829	−	0.983880i	$-0.442769\pi$
$139$	49.7145			0.357658			0.178829	+	0.983880i	$0.442769\pi$
$140$	31.5670			0.225478
$141$	98.1696			0.696238
$142$	98.1773			0.691389
$143$			198.821i			1.39036i
$144$	54.7710			0.380354
$145$			19.2681i			0.132883i
$146$	173.065			1.18538
$147$	−3.92347			−0.0266903
$148$		−	59.7207i		−	0.403518i
$149$		−	179.442i		−	1.20431i	−0.798379	−	0.602156i	$-0.794309\pi$
$149$		−	179.442i		−	1.20431i	0.798379	−	0.602156i	$-0.205691\pi$
$150$	33.6844			0.224562
$151$	−33.4205			−0.221327			−0.110664	−	0.993858i	$-0.535298\pi$
$151$	−33.4205			−0.221327			−0.110664	+	0.993858i	$0.535298\pi$
$152$			64.4543i			0.424041i
$153$			175.718i			1.14848i
$154$	104.335			0.677501
$155$		−	49.6479i		−	0.320309i
$156$	181.233			1.16175
$157$		−	18.9433i		−	0.120658i	−0.998179	−	0.0603291i	$-0.980785\pi$
$157$		−	18.9433i		−	0.120658i	0.998179	−	0.0603291i	$-0.0192150\pi$
$158$		−	199.263i		−	1.26116i
$159$			82.8603i			0.521134i
$160$			12.6491i			0.0790569i
$161$	156.455	−	43.3432i	0.971768	−	0.269213i
$162$	23.6789			0.146166
$163$	−322.188			−1.97661			−0.988307	−	0.152478i	$-0.951275\pi$
$163$	−322.188			−1.97661			−0.988307	+	0.152478i	$0.951275\pi$
$164$	−37.5823			−0.229160
$165$	111.334			0.674750
$166$			178.790i			1.07705i
$167$	−49.4087			−0.295861			−0.147930	−	0.988998i	$-0.547261\pi$
$167$	−49.4087			−0.295861			−0.147930	+	0.988998i	$0.547261\pi$
$168$		−	95.1056i		−	0.566105i
$169$	192.849			1.14112
$170$	−40.5812			−0.238713
$171$		−	312.031i		−	1.82474i
$172$			20.1063i			0.116897i
$173$	218.540			1.26324			0.631619	−	0.775279i	$-0.282391\pi$
$173$	218.540			1.26324			0.631619	+	0.775279i	$0.282391\pi$
$174$	58.0513			0.333628
$175$		−	35.2929i		−	0.201674i
$176$			41.8079i			0.237545i
$177$	−491.987			−2.77959
$178$		−	16.8862i		−	0.0948662i
$179$	−299.137			−1.67116			−0.835579	−	0.549370i	$-0.814868\pi$
$179$	−299.137			−1.67116			−0.835579	+	0.549370i	$0.814868\pi$
$180$		−	61.2358i		−	0.340199i
$181$		−	43.0432i		−	0.237808i	−0.992906	−	0.118904i	$-0.962062\pi$
$181$		−	43.0432i		−	0.237808i	0.992906	−	0.118904i	$-0.0379380\pi$
$182$		−	189.887i		−	1.04334i
$183$			355.449i			1.94234i
$184$	17.3680	+	62.6925i	0.0943910	+	0.340720i
$185$	−66.7698			−0.360918
$186$	−149.580			−0.804195
$187$	−134.129			−0.717269
$188$	41.2158			0.219233
$189$			157.793i			0.834884i
$190$	72.0621			0.379274
$191$			312.014i			1.63358i	0.576933	+	0.816792i	$0.304249\pi$
$191$			312.014i			1.63358i	−0.576933	+	0.816792i	$0.695751\pi$
$192$	38.1095			0.198487
$193$	92.5081			0.479317			0.239658	−	0.970857i	$-0.422965\pi$
$193$	92.5081			0.479317			0.239658	+	0.970857i	$0.422965\pi$
$194$		−	80.6561i		−	0.415753i
$195$		−	202.624i		−	1.03910i
$196$	−1.64724			−0.00840428
$197$	49.6153			0.251855			0.125927	−	0.992039i	$-0.459809\pi$
$197$	49.6153			0.251855			0.125927	+	0.992039i	$0.459809\pi$
$198$		−	202.397i		−	1.02221i
$199$		−	169.572i		−	0.852122i	−0.904694	−	0.426061i	$-0.859901\pi$
$199$		−	169.572i		−	0.852122i	0.904694	−	0.426061i	$-0.140099\pi$
$200$	14.1421			0.0707107
$201$		−	481.825i		−	2.39714i
$202$	40.6823			0.201397
$203$		−	60.8234i		−	0.299623i
$204$			122.264i			0.599334i
$205$			42.0183i			0.204967i
$206$			233.721i			1.13457i
$207$	−84.0802	−	303.502i	−0.406185	−	1.46619i
$208$	76.0893			0.365814
$209$	238.180			1.13962
$210$	−106.331			−0.506340
$211$	185.271			0.878061			0.439030	−	0.898472i	$-0.355322\pi$
$211$	185.271			0.878061			0.439030	+	0.898472i	$0.355322\pi$
$212$			34.7883i			0.164096i
$213$	−330.704			−1.55260
$214$			275.573i			1.28772i
$215$	22.4795			0.104556
$216$	−63.2288			−0.292726
$217$			156.723i			0.722227i
$218$		−	88.0773i		−	0.404024i
$219$	−582.959			−2.66191
$220$	46.7426			0.212467
$221$			244.112i			1.10458i
$222$			201.165i			0.906151i
$223$	−6.88625			−0.0308800			−0.0154400	−	0.999881i	$-0.504915\pi$
$223$	−6.88625			−0.0308800			−0.0154400	+	0.999881i	$0.504915\pi$
$224$		−	39.9294i		−	0.178256i
$225$	−68.4637			−0.304283
$226$			67.0887i			0.296853i
$227$		−	168.723i		−	0.743274i	−0.928378	−	0.371637i	$-0.878797\pi$
$227$		−	168.723i		−	0.743274i	0.928378	−	0.371637i	$-0.121203\pi$
$228$		−	217.110i		−	0.952238i
$229$		−	112.037i		−	0.489246i	−0.969618	−	0.244623i	$-0.921336\pi$
$229$		−	112.037i		−	0.489246i	0.969618	−	0.244623i	$-0.0786642\pi$
$230$	70.0924	−	19.4180i	0.304750	−	0.0844259i
$231$	−351.447			−1.52141
$232$	24.3724			0.105053
$233$	−46.2974			−0.198701			−0.0993507	−	0.995052i	$-0.531677\pi$
$233$	−46.2974			−0.198701			−0.0993507	+	0.995052i	$0.531677\pi$
$234$	−368.357			−1.57417
$235$		−	46.0806i		−	0.196088i
$236$	−206.557			−0.875242
$237$			671.205i			2.83209i
$238$	128.103			0.538246
$239$	386.253			1.61612			0.808062	−	0.589098i	$-0.200517\pi$
$239$	386.253			1.61612			0.808062	+	0.589098i	$0.200517\pi$
$240$		−	42.6077i		−	0.177532i
$241$		−	107.193i		−	0.444784i	−0.974957	−	0.222392i	$-0.928613\pi$
$241$		−	107.193i		−	0.444784i	0.974957	−	0.222392i	$-0.0713866\pi$
$242$	−16.6259			−0.0687019
$243$	−280.954			−1.15619
$244$			149.233i			0.611609i
$245$			1.84167i			0.00751702i
$246$	126.594			0.514608
$247$		−	433.481i		−	1.75498i
$248$	−62.8002			−0.253226
$249$		−	602.241i		−	2.41864i
$250$		−	15.8114i		−	0.0632456i
$251$			217.402i			0.866145i	0.901359	+	0.433073i	$0.142571\pi$
$251$			217.402i			0.866145i	−0.901359	+	0.433073i	$0.857429\pi$
$252$			193.303i			0.767074i
$253$	231.670	−	64.1803i	0.915690	−	0.253677i
$254$	−274.994			−1.08265
$255$	136.695			0.536060
$256$	16.0000			0.0625000
$257$	277.660			1.08039			0.540195	−	0.841540i	$-0.318350\pi$
$257$	277.660			1.08039			0.540195	+	0.841540i	$0.318350\pi$
$258$		−	67.7268i		−	0.262507i
$259$	210.772			0.813791
$260$		−	85.0704i		−	0.327194i
$261$	−117.990			−0.452067
$262$	110.251			0.420807
$263$			146.744i			0.557962i	0.960297	+	0.278981i	$0.0899966\pi$
$263$			146.744i			0.557962i	−0.960297	+	0.278981i	$0.910003\pi$
$264$		−	140.827i		−	0.533437i
$265$	38.8945			0.146772
$266$	−227.478			−0.855180
$267$			56.8801i			0.213034i
$268$		−	202.291i		−	0.754816i
$269$	450.903			1.67622			0.838110	−	0.545502i	$-0.183661\pi$
$269$	450.903			1.67622			0.838110	+	0.545502i	$0.183661\pi$
$270$			70.6920i			0.261822i
$271$	482.964			1.78216			0.891078	−	0.453851i	$-0.149950\pi$
$271$	482.964			1.78216			0.891078	+	0.453851i	$0.149950\pi$
$272$			51.3317i			0.188719i
$273$			639.624i			2.34294i
$274$		−	327.974i		−	1.19699i
$275$		−	52.2599i		−	0.190036i
$276$	−58.5029	−	211.176i	−0.211967	−	0.765130i
$277$	339.496			1.22562			0.612809	−	0.790231i	$-0.290040\pi$
$277$	339.496			1.22562			0.612809	+	0.790231i	$0.290040\pi$
$278$	−70.3069			−0.252903
$279$	304.023			1.08969
$280$	−44.6424			−0.159437
$281$			306.804i			1.09183i	0.837841	+	0.545914i	$0.183818\pi$
$281$			306.804i			1.09183i	−0.837841	+	0.545914i	$0.816182\pi$
$282$	−138.833			−0.492315
$283$			440.226i			1.55557i	0.628531	+	0.777784i	$0.283656\pi$
$283$			440.226i			1.55557i	−0.628531	+	0.777784i	$0.716344\pi$
$284$	−138.844			−0.488886
$285$	−242.737			−0.851707
$286$		−	281.175i		−	0.983130i
$287$		−	132.639i		−	0.462156i
$288$	−77.4578			−0.268951
$289$	124.316			0.430160
$290$		−	27.2492i		−	0.0939626i
$291$			271.685i			0.933625i
$292$	−244.751			−0.838189
$293$			105.316i			0.359439i	0.983718	+	0.179719i	$0.0575190\pi$
$293$			105.316i			0.359439i	−0.983718	+	0.179719i	$0.942481\pi$
$294$	5.54862			0.0188729
$295$			230.938i			0.782840i
$296$			84.4578i			0.285330i
$297$			233.651i			0.786705i
$298$			253.770i			0.851577i
$299$	−116.807	−	421.633i	−0.390657	−	1.41014i
$300$	−47.6369			−0.158790
$301$	−70.9610			−0.235751
$302$	47.2637			0.156502
$303$	−137.036			−0.452263
$304$		−	91.1521i		−	0.299842i
$305$	166.847			0.547040
$306$		−	248.503i		−	0.812100i
$307$	−364.046			−1.18582			−0.592909	−	0.805270i	$-0.702021\pi$
$307$	−364.046			−1.18582			−0.592909	+	0.805270i	$0.702021\pi$
$308$	−147.552			−0.479066
$309$		−	787.273i		−	2.54781i
$310$			70.2127i			0.226493i
$311$	−444.626			−1.42967			−0.714833	−	0.699295i	$-0.753497\pi$
$311$	−444.626			−1.42967			−0.714833	+	0.699295i	$0.753497\pi$
$312$	−256.302			−0.821481
$313$		−	78.3010i		−	0.250163i	−0.992146	−	0.125081i	$-0.960081\pi$
$313$		−	78.3010i		−	0.250163i	0.992146	−	0.125081i	$-0.0399192\pi$
$314$			26.7899i			0.0853182i
$315$	216.119			0.686092
$316$			281.800i			0.891774i
$317$	−100.802			−0.317986			−0.158993	−	0.987280i	$-0.550825\pi$
$317$	−100.802			−0.317986			−0.158993	+	0.987280i	$0.550825\pi$
$318$		−	117.182i		−	0.368497i
$319$		−	90.0641i		−	0.282332i
$320$		−	17.8885i		−	0.0559017i
$321$		−	928.250i		−	2.89174i
$322$	−221.260	+	61.2966i	−0.687144	+	0.190362i
$323$	292.437			0.905377
$324$	−33.4870			−0.103355
$325$	−95.1116			−0.292651
$326$	455.643			1.39768
$327$			296.683i			0.907287i
$328$	53.1494			0.162041
$329$			145.463i			0.442135i
$330$	−157.450			−0.477120
$331$	−454.682			−1.37366			−0.686831	−	0.726817i	$-0.740999\pi$
$331$	−454.682			−1.37366			−0.686831	+	0.726817i	$0.740999\pi$
$332$		−	252.847i		−	0.761586i
$333$		−	408.870i		−	1.22784i
$334$	69.8745			0.209205
$335$	−226.168			−0.675128
$336$			134.500i			0.400297i
$337$			656.763i			1.94885i	0.224708	+	0.974426i	$0.427857\pi$
$337$			656.763i			1.94885i	−0.224708	+	0.974426i	$0.572143\pi$
$338$	−272.729			−0.806891
$339$		−	225.984i		−	0.666620i
$340$	57.3905			0.168796
$341$			232.067i			0.680549i
$342$			441.278i			1.29029i
$343$			340.057i			0.991420i
$344$		−	28.4346i		−	0.0826587i
$345$	−236.102	+	65.4082i	−0.684353	+	0.189589i
$346$	−309.062			−0.893244
$347$	605.936			1.74621			0.873107	−	0.487528i	$-0.162101\pi$
$347$	605.936			1.74621			0.873107	+	0.487528i	$0.162101\pi$
$348$	−82.0969			−0.235911
$349$	−433.209			−1.24129			−0.620643	−	0.784093i	$-0.713129\pi$
$349$	−433.209			−1.24129			−0.620643	+	0.784093i	$0.713129\pi$
$350$			49.9117i			0.142605i
$351$	425.239			1.21151
$352$		−	59.1253i		−	0.167970i
$353$	64.7160			0.183331			0.0916657	−	0.995790i	$-0.470781\pi$
$353$	64.7160			0.183331			0.0916657	+	0.995790i	$0.470781\pi$
$354$	695.774			1.96546
$355$			155.232i			0.437273i
$356$			23.8807i			0.0670805i
$357$	−431.506			−1.20870
$358$	423.044			1.18169
$359$		−	258.799i		−	0.720889i	−0.932781	−	0.360445i	$-0.882625\pi$
$359$		−	258.799i		−	0.720889i	0.932781	−	0.360445i	$-0.117375\pi$
$360$			86.6005i			0.240557i
$361$	−158.294			−0.438488
$362$			60.8723i			0.168155i
$363$	56.0031			0.154279
$364$			268.541i			0.737751i
$365$			273.640i			0.749699i
$366$		−	502.681i		−	1.37344i
$367$		−	208.595i		−	0.568378i	−0.958768	−	0.284189i	$-0.908276\pi$
$367$		−	208.595i		−	0.568378i	0.958768	−	0.284189i	$-0.0917243\pi$
$368$	−24.5620	−	88.6606i	−0.0667445	−	0.240926i
$369$	−257.302			−0.697296
$370$	94.4267			0.255207
$371$	−122.778			−0.330938
$372$	211.538			0.568652
$373$		−	429.843i		−	1.15240i	−0.817310	−	0.576198i	$-0.804536\pi$
$373$		−	429.843i		−	1.15240i	0.817310	−	0.576198i	$-0.195464\pi$
$374$	189.687			0.507186
$375$			53.2597i			0.142026i
$376$	−58.2879			−0.155021
$377$	−163.914			−0.434786
$378$		−	223.153i		−	0.590352i
$379$			34.7433i			0.0916710i	0.998949	+	0.0458355i	$0.0145950\pi$
$379$			34.7433i			0.0916710i	−0.998949	+	0.0458355i	$0.985405\pi$
$380$	−101.911			−0.268187
$381$	926.301			2.43124
$382$		−	441.255i		−	1.15512i
$383$		−	287.953i		−	0.751835i	−0.926653	−	0.375918i	$-0.877328\pi$
$383$		−	287.953i		−	0.751835i	0.926653	−	0.375918i	$-0.122672\pi$
$384$	−53.8950			−0.140352
$385$			164.968i			0.428490i
$386$	−130.826			−0.338928
$387$			137.655i			0.355698i
$388$			114.065i			0.293982i
$389$		−	35.8847i		−	0.0922485i	−0.998936	−	0.0461242i	$-0.985313\pi$
$389$		−	35.8847i		−	0.0922485i	0.998936	−	0.0461242i	$-0.0146870\pi$
$390$			286.554i			0.734755i
$391$	284.444	−	78.8005i	0.727477	−	0.201536i
$392$	2.32955			0.00594273
$393$	−371.375			−0.944974
$394$	−70.1667			−0.178088
$395$	315.063			0.797627
$396$			286.232i			0.722809i
$397$	366.185			0.922379			0.461190	−	0.887302i	$-0.347423\pi$
$397$	366.185			0.922379			0.461190	+	0.887302i	$0.347423\pi$
$398$			239.811i			0.602541i
$399$	766.245			1.92041
$400$	−20.0000			−0.0500000
$401$		−	204.806i		−	0.510738i	−0.966844	−	0.255369i	$-0.917803\pi$
$401$		−	204.806i		−	0.510738i	0.966844	−	0.255369i	$-0.0821969\pi$
$402$			681.403i			1.69503i
$403$	422.357			1.04803
$404$	−57.5334			−0.142410
$405$			37.4396i			0.0924435i
$406$			86.0173i			0.211865i
$407$	312.100			0.766829
$408$		−	172.908i		−	0.423793i
$409$	−602.537			−1.47320			−0.736598	−	0.676331i	$-0.763569\pi$
$409$	−602.537			−1.47320			−0.736598	+	0.676331i	$0.763569\pi$
$410$		−	59.4228i		−	0.144934i
$411$			1104.76i			2.68798i
$412$		−	330.531i		−	0.802259i
$413$		−	729.000i		−	1.76513i
$414$	118.907	+	429.216i	0.287216	+	1.03675i
$415$	−282.691			−0.681183
$416$	−107.606			−0.258669
$417$	236.824			0.567924
$418$	−336.837			−0.805831
$419$		−	232.219i		−	0.554221i	−0.960838	−	0.277111i	$-0.910623\pi$
$419$		−	232.219i		−	0.554221i	0.960838	−	0.277111i	$-0.0893769\pi$
$420$	150.375			0.358036
$421$			164.906i			0.391702i	0.980634	+	0.195851i	$0.0627468\pi$
$421$			164.906i			0.391702i	−0.980634	+	0.195851i	$0.937253\pi$
$422$	−262.012			−0.620883
$423$	282.179			0.667089
$424$		−	49.1981i		−	0.116033i
$425$		−	64.1646i		−	0.150975i
$426$	467.686			1.09785
$427$	−526.685			−1.23346
$428$		−	389.719i		−	0.910558i
$429$			947.121i			2.20774i
$430$	−31.7908			−0.0739322
$431$			410.913i			0.953394i	0.879068	+	0.476697i	$0.158166\pi$
$431$			410.913i			0.953394i	−0.879068	+	0.476697i	$0.841834\pi$
$432$	89.4191			0.206989
$433$		−	653.473i		−	1.50918i	−0.656199	−	0.754588i	$-0.727837\pi$
$433$		−	653.473i		−	1.50918i	0.656199	−	0.754588i	$-0.272163\pi$
$434$		−	221.640i		−	0.510692i
$435$			91.7871i			0.211005i
$436$			124.560i			0.285688i
$437$	−505.100	+	139.930i	−1.15584	+	0.320206i
$438$	824.429			1.88226
$439$	−433.746			−0.988031			−0.494016	−	0.869453i	$-0.664471\pi$
$439$	−433.746			−0.988031			−0.494016	+	0.869453i	$0.664471\pi$
$440$	−66.1041			−0.150237
$441$	−11.2776			−0.0255728
$442$		−	345.226i		−	0.781055i
$443$	127.713			0.288291			0.144146	−	0.989556i	$-0.453957\pi$
$443$	127.713			0.288291			0.144146	+	0.989556i	$0.453957\pi$
$444$		−	284.491i		−	0.640745i
$445$	26.6994			0.0599987
$446$	9.73863			0.0218355
$447$		−	854.808i		−	1.91232i
$448$			56.4687i			0.126046i
$449$	647.900			1.44298			0.721492	−	0.692422i	$-0.243457\pi$
$449$	647.900			1.44298			0.721492	+	0.692422i	$0.243457\pi$
$450$	96.8223			0.215161
$451$		−	196.404i		−	0.435487i
$452$		−	94.8778i		−	0.209907i
$453$	−159.205			−0.351445
$454$			238.611i			0.525574i
$455$	300.238			0.659864
$456$			307.040i			0.673334i
$457$			504.529i			1.10400i	0.833844	+	0.552001i	$0.186135\pi$
$457$			504.529i			1.10400i	−0.833844	+	0.552001i	$0.813865\pi$
$458$			158.445i			0.345949i
$459$			286.877i			0.625004i
$460$	−99.1256	+	27.4611i	−0.215490	+	0.0596981i
$461$	−106.745			−0.231551			−0.115776	−	0.993275i	$-0.536935\pi$
$461$	−106.745			−0.231551			−0.115776	+	0.993275i	$0.536935\pi$
$462$	497.021			1.07580
$463$	90.1407			0.194688			0.0973442	−	0.995251i	$-0.468965\pi$
$463$	90.1407			0.194688			0.0973442	+	0.995251i	$0.468965\pi$
$464$	−34.4678			−0.0742840
$465$		−	236.507i		−	0.508617i
$466$	65.4744			0.140503
$467$			715.930i			1.53304i	0.642219	+	0.766521i	$0.278014\pi$
$467$			715.930i			1.53304i	−0.642219	+	0.766521i	$0.721986\pi$
$468$	520.935			1.11311
$469$	713.943			1.52227
$470$			65.1679i			0.138655i
$471$		−	90.2402i		−	0.191593i
$472$	292.116			0.618889
$473$	−105.075			−0.222146
$474$		−	949.227i		−	2.00259i
$475$			113.940i			0.239874i
$476$	−181.164			−0.380598
$477$			238.174i			0.499316i
$478$	−546.245			−1.14277
$479$			596.758i			1.24584i	0.782285	+	0.622921i	$0.214054\pi$
$479$			596.758i			1.24584i	−0.782285	+	0.622921i	$0.785946\pi$
$480$			60.2564i			0.125534i
$481$		−	568.013i		−	1.18090i
$482$			151.594i			0.314510i
$483$	745.301	−	206.474i	1.54307	−	0.427482i
$484$	23.5125			0.0485796
$485$	127.528			0.262945
$486$	397.329			0.817549
$487$	−74.0657			−0.152086			−0.0760428	−	0.997105i	$-0.524229\pi$
$487$	−74.0657			−0.152086			−0.0760428	+	0.997105i	$0.524229\pi$
$488$		−	211.047i		−	0.432473i
$489$	−1534.80			−3.13866
$490$		−	2.60451i		−	0.00531534i
$491$	299.500			0.609980			0.304990	−	0.952356i	$-0.401347\pi$
$491$	299.500			0.609980			0.304990	+	0.952356i	$0.401347\pi$
$492$	−179.030			−0.363883
$493$		−	110.581i		−	0.224301i
$494$			613.035i			1.24096i
$495$	320.017			0.646500
$496$	88.8128			0.179058
$497$		−	490.020i		−	0.985955i
$498$			851.698i			1.71024i
$499$	−298.145			−0.597484			−0.298742	−	0.954334i	$-0.596567\pi$
$499$	−298.145			−0.597484			−0.298742	+	0.954334i	$0.596567\pi$
$500$			22.3607i			0.0447214i
$501$	−235.368			−0.469796
$502$		−	307.453i		−	0.612457i
$503$		−	125.936i		−	0.250371i	−0.992133	−	0.125185i	$-0.960047\pi$
$503$		−	125.936i		−	0.250371i	0.992133	−	0.125185i	$-0.0399525\pi$
$504$		−	273.371i		−	0.542404i
$505$			64.3244i			0.127375i
$506$	−327.630	+	90.7647i	−0.647491	+	0.179377i
$507$	918.671			1.81197
$508$	388.901			0.765552
$509$	143.424			0.281777			0.140888	−	0.990025i	$-0.455004\pi$
$509$	143.424			0.281777			0.140888	+	0.990025i	$0.455004\pi$
$510$	−193.316			−0.379052
$511$		−	863.798i		−	1.69041i
$512$	−22.6274			−0.0441942
$513$		−	509.421i		−	0.993023i
$514$	−392.671			−0.763951
$515$	−369.545			−0.717563
$516$			95.7801i			0.185620i
$517$			215.393i			0.416621i
$518$	−298.076			−0.575437
$519$	1041.06			2.00589
$520$			120.308i			0.231361i
$521$			149.956i			0.287824i	0.989591	+	0.143912i	$0.0459682\pi$
$521$			149.956i			0.287824i	−0.989591	+	0.143912i	$0.954032\pi$
$522$	166.862			0.319660
$523$		−	308.927i		−	0.590683i	−0.955392	−	0.295342i	$-0.904567\pi$
$523$		−	308.927i		−	0.590683i	0.955392	−	0.295342i	$-0.0954335\pi$
$524$	−155.919			−0.297555
$525$		−	168.125i		−	0.320237i
$526$		−	207.527i		−	0.394538i
$527$			284.932i			0.540668i
$528$			199.160i			0.377197i
$529$	−453.589	+	272.210i	−0.857445	+	0.514575i
$530$	−55.0051			−0.103783
$531$	−1414.17			−2.66321
$532$	321.702			0.604704
$533$	−357.451			−0.670640
$534$		−	80.4405i		−	0.150638i
$535$	−435.719			−0.814428
$536$			286.082i			0.533735i
$537$	−1425.00			−2.65363
$538$	−637.673			−1.18527
$539$		−	8.60845i		−	0.0159712i
$540$		−	99.9735i		−	0.185136i
$541$	−365.240			−0.675120			−0.337560	−	0.941304i	$-0.609602\pi$
$541$	−365.240			−0.675120			−0.337560	+	0.941304i	$0.609602\pi$
$542$	−683.014			−1.26017
$543$		−	205.044i		−	0.377614i
$544$		−	72.5939i		−	0.133445i
$545$	139.262			0.255528
$546$		−	904.565i		−	1.65671i
$547$	788.355			1.44123			0.720617	−	0.693334i	$-0.243859\pi$
$547$	788.355			1.44123			0.720617	+	0.693334i	$0.243859\pi$
$548$			463.825i			0.846397i
$549$			1021.70i			1.86102i
$550$			73.9066i			0.134376i
$551$			196.363i			0.356376i
$552$	82.7355	+	298.648i	0.149883	+	0.541029i
$553$	−994.556			−1.79847
$554$	−480.120			−0.866642
$555$	−318.070			−0.573100
$556$	99.4290			0.178829
$557$		−	316.183i		−	0.567654i	−0.958876	−	0.283827i	$-0.908396\pi$
$557$		−	316.183i		−	0.567654i	0.958876	−	0.283827i	$-0.0916041\pi$
$558$	−429.953			−0.770525
$559$			191.234i			0.342100i
$560$	63.1339			0.112739
$561$	−638.950			−1.13895
$562$		−	433.886i		−	0.772039i
$563$		−	849.606i		−	1.50907i	−0.656260	−	0.754535i	$-0.727863\pi$
$563$		−	849.606i		−	1.50907i	0.656260	−	0.754535i	$-0.272137\pi$
$564$	196.339			0.348119
$565$	−106.077			−0.187746
$566$		−	622.573i		−	1.09995i
$567$		−	118.185i		−	0.208440i
$568$	196.355			0.345695
$569$		−	251.184i		−	0.441448i	−0.975336	−	0.220724i	$-0.929158\pi$
$569$		−	251.184i		−	0.441448i	0.975336	−	0.220724i	$-0.0708420\pi$
$570$	343.281			0.602248
$571$			731.800i			1.28161i	0.767704	+	0.640805i	$0.221399\pi$
$571$			731.800i			1.28161i	−0.767704	+	0.640805i	$0.778601\pi$
$572$			397.642i			0.695178i
$573$			1486.34i			2.59396i
$574$			187.580i			0.326794i
$575$	30.7025	+	110.826i	0.0533956	+	0.192741i
$576$	109.542			0.190177
$577$	−232.889			−0.403620			−0.201810	−	0.979425i	$-0.564682\pi$
$577$	−232.889			−0.403620			−0.201810	+	0.979425i	$0.564682\pi$
$578$	−175.810			−0.304169
$579$	440.680			0.761105
$580$			38.5361i			0.0664416i
$581$	892.369			1.53592
$582$		−	384.221i		−	0.660173i
$583$	−181.803			−0.311841
$584$	346.130			0.592689
$585$		−	582.423i		−	0.995596i
$586$		−	148.939i		−	0.254162i
$587$	−257.843			−0.439255			−0.219628	−	0.975584i	$-0.570484\pi$
$587$	−257.843			−0.439255			−0.219628	+	0.975584i	$0.570484\pi$
$588$	−7.84694			−0.0133451
$589$		−	505.967i		−	0.859028i
$590$		−	326.595i		−	0.553551i
$591$	236.352			0.399919
$592$		−	119.441i		−	0.201759i
$593$	86.9783			0.146675			0.0733375	−	0.997307i	$-0.476635\pi$
$593$	86.9783			0.146675			0.0733375	+	0.997307i	$0.476635\pi$
$594$		−	330.433i		−	0.556284i
$595$			202.548i			0.340417i
$596$		−	358.885i		−	0.602156i
$597$		−	807.790i		−	1.35308i
$598$	165.189	+	596.279i	0.276236	+	0.997122i
$599$	−382.075			−0.637854			−0.318927	−	0.947779i	$-0.603323\pi$
$599$	−382.075			−0.637854			−0.318927	+	0.947779i	$0.603323\pi$
$600$	67.3687			0.112281
$601$	−109.548			−0.182277			−0.0911384	−	0.995838i	$-0.529051\pi$
$601$	−109.548			−0.182277			−0.0911384	+	0.995838i	$0.529051\pi$
$602$	100.354			0.166701
$603$		−	1384.96i		−	2.29678i
$604$	−66.8409			−0.110664
$605$		−	26.2878i		−	0.0434509i
$606$	193.798			0.319798
$607$	−936.232			−1.54239			−0.771196	−	0.636597i	$-0.780341\pi$
$607$	−936.232			−1.54239			−0.771196	+	0.636597i	$0.780341\pi$
$608$			128.909i			0.212021i
$609$		−	289.744i		−	0.475770i
$610$	−235.957			−0.386815
$611$	392.010			0.641587
$612$			351.436i			0.574241i
$613$			85.4745i			0.139436i	0.997567	+	0.0697182i	$0.0222100\pi$
$613$			85.4745i			0.139436i	−0.997567	+	0.0697182i	$0.977790\pi$
$614$	514.839			0.838500
$615$			200.162i			0.325467i
$616$	208.670			0.338751
$617$			476.428i			0.772169i	0.922463	+	0.386085i	$0.126173\pi$
$617$			476.428i			0.772169i	−0.922463	+	0.386085i	$0.873827\pi$
$618$			1113.37i			1.80157i
$619$			207.565i			0.335323i	0.985845	+	0.167662i	$0.0536216\pi$
$619$			207.565i			0.335323i	−0.985845	+	0.167662i	$0.946378\pi$
$620$		−	99.2958i		−	0.160154i
$621$	−137.269	−	495.497i	−0.221046	−	0.797902i
$622$	628.796			1.01093
$623$	−84.2819			−0.135284
$624$	362.466			0.580875
$625$	25.0000			0.0400000
$626$			110.734i			0.176892i
$627$	1134.61			1.80959
$628$		−	37.8867i		−	0.0603291i
$629$	383.195			0.609214
$630$	−305.638			−0.485140
$631$		−	406.573i		−	0.644331i	−0.946683	−	0.322166i	$-0.895589\pi$
$631$		−	406.573i		−	0.644331i	0.946683	−	0.322166i	$-0.104411\pi$
$632$		−	398.526i		−	0.630579i
$633$	882.573			1.39427
$634$	142.555			0.224850
$635$		−	434.804i		−	0.684731i
$636$			165.721i			0.260567i
$637$	−15.6672			−0.0245952
$638$			127.370i			0.199639i
$639$	−950.575			−1.48760
$640$			25.2982i			0.0395285i
$641$			356.666i			0.556421i	0.960520	+	0.278210i	$0.0897412\pi$
$641$			356.666i			0.556421i	−0.960520	+	0.278210i	$0.910259\pi$
$642$			1312.74i			2.04477i
$643$			311.622i			0.484637i	0.970197	+	0.242318i	$0.0779079\pi$
$643$			311.622i			0.484637i	−0.970197	+	0.242318i	$0.922092\pi$
$644$	312.909	−	86.6865i	0.485884	−	0.134606i
$645$	107.085			0.166024
$646$	−413.568			−0.640198
$647$	−512.625			−0.792310			−0.396155	−	0.918184i	$-0.629656\pi$
$647$	−512.625			−0.792310			−0.396155	+	0.918184i	$0.629656\pi$
$648$	47.3578			0.0730830
$649$		−	1079.46i		−	1.66327i
$650$	134.508			0.206936
$651$			746.581i			1.14682i
$652$	−644.376			−0.988307
$653$	1018.05			1.55903			0.779515	−	0.626384i	$-0.215466\pi$
$653$	1018.05			1.55903			0.779515	+	0.626384i	$0.215466\pi$
$654$		−	419.573i		−	0.641549i
$655$			174.323i			0.266141i
$656$	−75.1646			−0.114580
$657$	−1675.66			−2.55047
$658$		−	205.715i		−	0.312637i
$659$		−	396.548i		−	0.601742i	−0.953665	−	0.300871i	$-0.902723\pi$
$659$		−	396.548i		−	0.601742i	0.953665	−	0.300871i	$-0.0972773\pi$
$660$	222.667			0.337375
$661$			71.0934i			0.107554i	0.998553	+	0.0537772i	$0.0171261\pi$
$661$			71.0934i			0.107554i	−0.998553	+	0.0537772i	$0.982874\pi$
$662$	643.017			0.971325
$663$			1162.87i			1.75396i
$664$			357.579i			0.538523i
$665$		−	359.674i		−	0.540864i
$666$			578.230i			0.868212i
$667$	52.9123	+	190.996i	0.0793288	+	0.286351i
$668$	−98.8174			−0.147930
$669$	−32.8040			−0.0490343
$670$	319.850			0.477387
$671$	−779.888			−1.16228
$672$		−	190.211i		−	0.283052i
$673$	−889.230			−1.32129			−0.660646	−	0.750697i	$-0.729718\pi$
$673$	−889.230			−1.32129			−0.660646	+	0.750697i	$0.729718\pi$
$674$		−	928.804i		−	1.37805i
$675$	−111.774			−0.165591
$676$	385.697			0.570558
$677$			1106.29i			1.63411i	0.576561	+	0.817054i	$0.304394\pi$
$677$			1106.29i			1.63411i	−0.576561	+	0.817054i	$0.695606\pi$
$678$			319.590i			0.471372i
$679$	−402.569			−0.592884
$680$	−81.1625			−0.119357
$681$		−	803.746i		−	1.18024i
$682$		−	328.193i		−	0.481221i
$683$	769.950			1.12731			0.563653	−	0.826012i	$-0.309396\pi$
$683$	769.950			1.12731			0.563653	+	0.826012i	$0.309396\pi$
$684$		−	624.061i		−	0.912370i
$685$	518.573			0.757040
$686$		−	480.913i		−	0.701040i
$687$		−	533.711i		−	0.776872i
$688$			40.2126i			0.0584485i
$689$			330.877i			0.480228i
$690$	333.898	−	92.5011i	0.483911	−	0.134060i
$691$	−314.516			−0.455160			−0.227580	−	0.973759i	$-0.573081\pi$
$691$	−314.516			−0.455160			−0.227580	+	0.973759i	$0.573081\pi$
$692$	437.080			0.631619
$693$	−1010.20			−1.45772
$694$	−856.923			−1.23476
$695$		−	111.165i		−	0.159950i
$696$	116.103			0.166814
$697$		−	241.145i		−	0.345976i
$698$	612.650			0.877722
$699$	−220.547			−0.315517
$700$		−	70.5858i		−	0.100837i
$701$			853.482i			1.21752i	0.793354	+	0.608760i	$0.208333\pi$
$701$			853.482i			1.21752i	−0.793354	+	0.608760i	$0.791667\pi$
$702$	−601.379			−0.856666
$703$	−680.458			−0.967935
$704$			83.6158i			0.118772i
$705$		−	219.514i		−	0.311367i
$706$	−91.5222			−0.129635
$707$		−	203.052i		−	0.287203i
$708$	−983.974			−1.38979
$709$			1121.84i			1.58229i	0.611631	+	0.791143i	$0.290514\pi$
$709$			1121.84i			1.58229i	−0.611631	+	0.791143i	$0.709486\pi$
$710$		−	219.531i		−	0.309199i
$711$			1929.31i			2.71352i
$712$		−	33.7724i		−	0.0474331i
$713$	−136.339	−	492.138i	−0.191218	−	0.690235i
$714$	610.241			0.854680
$715$	444.577			0.621786
$716$	−598.275			−0.835579
$717$	1839.99			2.56624
$718$			365.997i			0.509746i
$719$	−1026.36			−1.42748			−0.713739	−	0.700411i	$-0.753000\pi$
$719$	−1026.36			−1.42748			−0.713739	+	0.700411i	$0.753000\pi$
$720$		−	122.472i		−	0.170099i
$721$	1166.54			1.61795
$722$	223.862			0.310058
$723$		−	510.635i		−	0.706272i
$724$		−	86.0864i		−	0.118904i
$725$	43.0847			0.0594272
$726$	−79.2004			−0.109091
$727$			86.2743i			0.118672i	0.998238	+	0.0593358i	$0.0188983\pi$
$727$			86.2743i			0.118672i	−0.998238	+	0.0593358i	$0.981102\pi$
$728$		−	379.775i		−	0.521669i
$729$	−1187.68			−1.62920
$730$		−	386.985i		−	0.530117i
$731$	−129.011			−0.176486
$732$			710.898i			0.971172i
$733$			224.013i			0.305611i	0.988256	+	0.152806i	$0.0488308\pi$
$733$			224.013i			0.305611i	−0.988256	+	0.152806i	$0.951169\pi$
$734$			294.998i			0.401904i
$735$			8.77315i			0.0119363i
$736$	34.7359	+	125.385i	0.0471955	+	0.170360i
$737$	1057.17			1.43442
$738$	363.880			0.493063
$739$	865.320			1.17093			0.585467	−	0.810696i	$-0.300911\pi$
$739$	865.320			1.17093			0.585467	+	0.810696i	$0.300911\pi$
$740$	−133.540			−0.180459
$741$		−	2064.97i		−	2.78673i
$742$	173.634			0.234009
$743$			1204.15i			1.62066i	0.585975	+	0.810329i	$0.300712\pi$
$743$			1204.15i			1.62066i	−0.585975	+	0.810329i	$0.699288\pi$
$744$	−299.160			−0.402097
$745$	−401.245			−0.538584
$746$			607.890i			0.814867i
$747$		−	1731.08i		−	2.31738i
$748$	−268.259			−0.358635
$749$	1375.43			1.83636
$750$		−	75.3206i		−	0.100427i
$751$		−	1410.90i		−	1.87870i	−0.342967	−	0.939348i	$-0.611432\pi$
$751$		−	1410.90i		−	1.87870i	0.342967	−	0.939348i	$-0.388568\pi$
$752$	82.4316			0.109616
$753$			1035.64i			1.37535i
$754$	231.810			0.307440
$755$			74.7304i			0.0989807i
$756$			315.586i			0.417442i
$757$		−	1113.96i		−	1.47155i	−0.677226	−	0.735775i	$-0.736818\pi$
$757$		−	1113.96i		−	1.47155i	0.677226	−	0.735775i	$-0.263182\pi$
$758$		−	49.1345i		−	0.0648212i
$759$	1103.60	−	305.735i	1.45402	−	0.402813i
$760$	144.124			0.189637
$761$	308.718			0.405674			0.202837	−	0.979212i	$-0.434984\pi$
$761$	308.718			0.405674			0.202837	+	0.979212i	$0.434984\pi$
$762$	−1309.99			−1.71914
$763$	−439.609			−0.576159
$764$			624.029i			0.816792i
$765$	392.917			0.513617
$766$			407.227i			0.531628i
$767$	−1964.60			−2.56140
$768$	76.2190			0.0992435
$769$			630.246i			0.819566i	0.912183	+	0.409783i	$0.134396\pi$
$769$			630.246i			0.819566i	−0.912183	+	0.409783i	$0.865604\pi$
$770$		−	233.301i		−	0.302988i
$771$	1322.69			1.71555
$772$	185.016			0.239658
$773$			408.103i			0.527947i	0.964530	+	0.263974i	$0.0850332\pi$
$773$			408.103i			0.527947i	−0.964530	+	0.263974i	$0.914967\pi$
$774$		−	194.674i		−	0.251516i
$775$	−111.016			−0.143247
$776$		−	161.312i		−	0.207877i
$777$	1004.05			1.29222
$778$			50.7486i			0.0652295i
$779$			428.213i			0.549696i
$780$		−	405.249i		−	0.519550i
$781$		−	725.595i		−	0.929059i
$782$	−402.264	+	111.441i	−0.514404	+	0.142507i
$783$	−192.630			−0.246015
$784$	−3.29448			−0.00420214
$785$	−42.3586			−0.0539600
$786$	525.203			0.668197
$787$		−	220.127i		−	0.279703i	−0.990172	−	0.139852i	$-0.955337\pi$
$787$		−	220.127i		−	0.279703i	0.990172	−	0.139852i	$-0.0446626\pi$
$788$	99.2307			0.125927
$789$			699.042i			0.885985i
$790$	−445.566			−0.564007
$791$	334.852			0.423327
$792$		−	404.794i		−	0.511103i
$793$			1419.38i			1.78988i
$794$	−517.863			−0.652221
$795$	185.281			0.233058
$796$		−	339.145i		−	0.426061i
$797$			523.296i			0.656582i	0.944577	+	0.328291i	$0.106473\pi$
$797$			523.296i			0.656582i	−0.944577	+	0.328291i	$0.893527\pi$
$798$	−1083.63			−1.35794
$799$			264.459i			0.330988i
$800$	28.2843			0.0353553
$801$			163.496i			0.204115i
$802$			289.639i			0.361146i
$803$		−	1279.07i		−	1.59286i
$804$		−	963.650i		−	1.19857i
$805$	−96.9184	−	349.843i	−0.120396	−	0.434588i
$806$	−597.302			−0.741070
$807$	2147.96			2.66166
$808$	81.3646			0.100699
$809$	271.141			0.335156			0.167578	−	0.985859i	$-0.446405\pi$
$809$	271.141			0.335156			0.167578	+	0.985859i	$0.446405\pi$
$810$		−	52.9476i		−	0.0653674i
$811$	954.104			1.17645			0.588227	−	0.808696i	$-0.299826\pi$
$811$	954.104			1.17645			0.588227	+	0.808696i	$0.299826\pi$
$812$		−	121.647i		−	0.149811i
$813$	2300.69			2.82988
$814$	−441.375			−0.542230
$815$			720.434i			0.883969i
$816$			244.528i			0.299667i
$817$	229.091			0.280406
$818$	852.116			1.04171
$819$			1838.53i			2.24485i
$820$			84.0365i			0.102484i
$821$	167.223			0.203682			0.101841	−	0.994801i	$-0.467527\pi$
$821$	167.223			0.203682			0.101841	+	0.994801i	$0.467527\pi$
$822$		−	1562.37i		−	1.90069i
$823$	119.120			0.144738			0.0723691	−	0.997378i	$-0.476944\pi$
$823$	119.120			0.144738			0.0723691	+	0.997378i	$0.476944\pi$
$824$			467.441i			0.567283i
$825$		−	248.950i		−	0.301757i
$826$			1030.96i			1.24814i
$827$			291.492i			0.352469i	0.984348	+	0.176234i	$0.0563917\pi$
$827$			291.492i			0.352469i	−0.984348	+	0.176234i	$0.943608\pi$
$828$	−168.160	−	607.004i	−0.203092	−	0.733096i
$829$	456.755			0.550971			0.275486	−	0.961305i	$-0.411161\pi$
$829$	456.755			0.550971			0.275486	+	0.961305i	$0.411161\pi$
$830$	399.786			0.481669
$831$	1617.25			1.94615
$832$	152.179			0.182907
$833$		−	10.5694i		−	0.0126884i
$834$	−334.920			−0.401583
$835$			110.481i			0.132313i
$836$	476.360			0.569808
$837$	496.347			0.593008
$838$			328.407i			0.391894i
$839$		−	666.692i		−	0.794626i	−0.917683	−	0.397313i	$-0.869943\pi$
$839$		−	666.692i		−	0.794626i	0.917683	−	0.397313i	$-0.130057\pi$
$840$	−212.663			−0.253170
$841$	−766.748			−0.911710
$842$		−	233.213i		−	0.276975i
$843$			1461.52i			1.73371i
$844$	370.542			0.439030
$845$		−	431.223i		−	0.510323i
$846$	−399.061			−0.471703
$847$			82.9825i			0.0979723i
$848$			69.5766i			0.0820479i
$849$			2097.10i			2.47008i
$850$			90.7424i			0.106756i
$851$	−661.859	+	183.357i	−0.777743	+	0.215461i
$852$	−661.408			−0.776300
$853$	1286.39			1.50807			0.754037	−	0.656832i	$-0.228104\pi$
$853$	1286.39			1.50807			0.754037	+	0.656832i	$0.228104\pi$
$854$	744.846			0.872185
$855$	−697.722			−0.816049
$856$			551.146i			0.643862i
$857$	721.485			0.841873			0.420936	−	0.907090i	$-0.361702\pi$
$857$	721.485			0.841873			0.420936	+	0.907090i	$0.361702\pi$
$858$		−	1339.43i		−	1.56111i
$859$	997.400			1.16112			0.580559	−	0.814218i	$-0.302834\pi$
$859$	997.400			1.16112			0.580559	+	0.814218i	$0.302834\pi$
$860$	44.9590			0.0522780
$861$		−	631.850i		−	0.733856i
$862$		−	581.118i		−	0.674151i
$863$	−668.668			−0.774818			−0.387409	−	0.921908i	$-0.626630\pi$
$863$	−668.668			−0.774818			−0.387409	+	0.921908i	$0.626630\pi$
$864$	−126.458			−0.146363
$865$		−	488.671i		−	0.564937i
$866$			924.150i			1.06715i
$867$	592.204			0.683050
$868$			313.446i			0.361113i
$869$	−1472.69			−1.69469
$870$		−	129.807i		−	0.149203i
$871$		−	1924.02i		−	2.20898i
$872$		−	176.155i		−	0.202012i
$873$			780.931i			0.894537i
$874$	714.320	−	197.891i	0.817299	−	0.226420i
$875$	−78.9174			−0.0901913
$876$	−1165.92			−1.33096
$877$	−1093.37			−1.24671			−0.623355	−	0.781939i	$-0.714231\pi$
$877$	−1093.37			−1.24671			−0.623355	+	0.781939i	$0.714231\pi$
$878$	613.409			0.698644
$879$			501.691i			0.570752i
$880$	93.4853			0.106233
$881$			185.451i			0.210501i	0.994446	+	0.105250i	$0.0335644\pi$
$881$			185.451i			0.210501i	−0.994446	+	0.105250i	$0.966436\pi$
$882$	15.9490			0.0180827
$883$	774.941			0.877623			0.438812	−	0.898579i	$-0.355400\pi$
$883$	774.941			0.877623			0.438812	+	0.898579i	$0.355400\pi$
$884$			488.224i			0.552289i
$885$			1100.12i			1.24307i
$886$	−180.614			−0.203853
$887$	1409.90			1.58951			0.794757	−	0.606928i	$-0.207598\pi$
$887$	1409.90			1.58951			0.794757	+	0.606928i	$0.207598\pi$
$888$			402.331i			0.453075i
$889$			1372.54i			1.54392i
$890$	−37.7587			−0.0424255
$891$		−	175.003i		−	0.196412i
$892$	−13.7725			−0.0154400
$893$		−	469.613i		−	0.525883i
$894$			1208.88i			1.35222i
$895$			668.892i			0.747365i
$896$		−	79.8588i		−	0.0891281i
$897$	−556.430	−	2008.53i	−0.620323	−	2.23916i
$898$	−916.269			−1.02034
$899$	−191.324			−0.212818
$900$	−136.927			−0.152142
$901$	−223.218			−0.247744
$902$			277.758i			0.307936i
$903$	−338.036			−0.374348
$904$			134.177i			0.148426i
$905$	−96.2475			−0.106351
$906$	225.149			0.248509
$907$		−	917.836i		−	1.01195i	−0.862549	−	0.505974i	$-0.831133\pi$
$907$		−	917.836i		−	1.01195i	0.862549	−	0.505974i	$-0.168867\pi$
$908$		−	337.447i		−	0.371637i
$909$	−393.895			−0.433328
$910$	−424.601			−0.466595
$911$			984.687i			1.08089i	0.841381	+	0.540443i	$0.181743\pi$
$911$			984.687i			1.08089i	−0.841381	+	0.540443i	$0.818257\pi$
$912$		−	434.220i		−	0.476119i
$913$	1321.37			1.44729
$914$		−	713.511i		−	0.780647i
$915$	794.808			0.868643
$916$		−	224.075i		−	0.244623i
$917$		−	550.283i		−	0.600091i
$918$		−	405.705i		−	0.441945i
$919$			690.455i			0.751311i	0.926759	+	0.375656i	$0.122582\pi$
$919$			690.455i			0.751311i	−0.926759	+	0.375656i	$0.877418\pi$
$920$	140.185	−	38.8359i	0.152375	−	0.0422130i
$921$	−1734.20			−1.88296
$922$	150.960			0.163731
$923$	−1320.56			−1.43073
$924$	−702.893			−0.760707
$925$			149.302i			0.161407i
$926$	−127.478			−0.137665
$927$		−	2262.94i		−	2.44114i
$928$	48.7448			0.0525267
$929$	8.38853			0.00902963			0.00451482	−	0.999990i	$-0.498563\pi$
$929$	8.38853			0.00902963			0.00451482	+	0.999990i	$0.498563\pi$
$930$			334.472i			0.359647i
$931$			18.7687i			0.0201597i
$932$	−92.5948			−0.0993507
$933$	−2118.06			−2.27016
$934$		−	1012.48i		−	1.08402i
$935$			299.922i			0.320772i
$936$	−736.714			−0.787087
$937$			1419.17i			1.51459i	0.653076	+	0.757293i	$0.273478\pi$
$937$			1419.17i			1.51459i	−0.653076	+	0.757293i	$0.726522\pi$
$938$	−1009.67			−1.07640
$939$		−	373.002i		−	0.397233i
$940$		−	92.1613i		−	0.0980439i
$941$		−	1521.23i		−	1.61661i	−0.588763	−	0.808306i	$-0.700385\pi$
$941$		−	1521.23i		−	1.61661i	0.588763	−	0.808306i	$-0.299615\pi$
$942$			127.619i			0.135477i
$943$	115.387	+	416.509i	0.122362	+	0.441685i
$944$	−413.114			−0.437621
$945$	352.836			0.373371
$946$	148.599			0.157081
$947$	−121.592			−0.128398			−0.0641988	−	0.997937i	$-0.520449\pi$
$947$	−121.592			−0.128398			−0.0641988	+	0.997937i	$0.520449\pi$
$948$			1342.41i			1.41604i
$949$	−2327.87			−2.45297
$950$		−	161.136i		−	0.169617i
$951$	−480.188			−0.504929
$952$	256.205			0.269123
$953$		−	1607.12i		−	1.68638i	−0.537619	−	0.843188i	$-0.680676\pi$
$953$		−	1607.12i		−	1.68638i	0.537619	−	0.843188i	$-0.319324\pi$
$954$		−	336.828i		−	0.353069i
$955$	697.685			0.730561
$956$	772.507			0.808062
$957$		−	429.037i		−	0.448315i
$958$		−	843.943i		−	0.880943i
$959$	−1636.98			−1.70696
$960$		−	85.2155i		−	0.0887661i
$961$	−468.018			−0.487011
$962$			803.292i			0.835023i
$963$		−	2668.16i		−	2.77067i
$964$		−	214.386i		−	0.222392i
$965$		−	206.854i		−	0.214357i
$966$	−1054.02	+	291.998i	−1.09111	+	0.302275i
$967$	−294.286			−0.304329			−0.152165	−	0.988355i	$-0.548624\pi$
$967$	−294.286			−0.304329			−0.152165	+	0.988355i	$0.548624\pi$
$968$	−33.2517			−0.0343509
$969$	1393.08			1.43765
$970$	−180.353			−0.185930
$971$			99.3755i			0.102343i	0.998690	+	0.0511717i	$0.0162956\pi$
$971$			99.3755i			0.102343i	−0.998690	+	0.0511717i	$0.983704\pi$
$972$	−561.908			−0.578094
$973$			350.914i			0.360652i
$974$	104.745			0.107541
$975$	−453.082			−0.464700
$976$			298.465i			0.305804i
$977$			481.190i			0.492518i	0.969204	+	0.246259i	$0.0792014\pi$
$977$			481.190i			0.492518i	−0.969204	+	0.246259i	$0.920799\pi$
$978$	2170.54			2.21937
$979$	−124.800			−0.127477
$980$			3.68334i			0.00375851i
$981$			852.785i			0.869302i
$982$	−423.557			−0.431321
$983$		−	1525.36i		−	1.55174i	−0.630890	−	0.775872i	$-0.717310\pi$
$983$		−	1525.36i		−	1.55174i	0.630890	−	0.775872i	$-0.282690\pi$
$984$	253.187			0.257304
$985$		−	110.943i		−	0.112633i
$986$			156.384i			0.158605i
$987$			692.939i			0.702065i
$988$		−	866.962i		−	0.877492i
$989$	222.830	−	61.7313i	0.225308	−	0.0624179i
$990$	−452.573			−0.457144
$991$	−621.962			−0.627610			−0.313805	−	0.949487i	$-0.601604\pi$
$991$	−621.962			−0.627610			−0.313805	+	0.949487i	$0.601604\pi$
$992$	−125.600			−0.126613
$993$	−2165.96			−2.18123
$994$			692.993i			0.697176i
$995$	−379.175			−0.381081
$996$		−	1204.48i		−	1.20932i
$997$	−909.755			−0.912492			−0.456246	−	0.889854i	$-0.650806\pi$
$997$	−909.755			−0.912492			−0.456246	+	0.889854i	$0.650806\pi$
$998$	421.640			0.422485
$999$		−	667.521i		−	0.668189i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.d.a.91.7	✓	16
3.2	odd	2		2070.3.c.a.91.14		16
4.3	odd	2		1840.3.k.d.321.1		16
5.2	odd	4		1150.3.c.c.1149.5		32
5.3	odd	4		1150.3.c.c.1149.28		32
5.4	even	2		1150.3.d.b.551.9		16
23.22	odd	2	inner	230.3.d.a.91.8	yes	16
69.68	even	2		2070.3.c.a.91.11		16
92.91	even	2		1840.3.k.d.321.2		16
115.22	even	4		1150.3.c.c.1149.27		32
115.68	even	4		1150.3.c.c.1149.6		32
115.114	odd	2		1150.3.d.b.551.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.d.a.91.7	✓	16	1.1	even	1	trivial
230.3.d.a.91.8	yes	16	23.22	odd	2	inner
1150.3.c.c.1149.5		32	5.2	odd	4
1150.3.c.c.1149.6		32	115.68	even	4
1150.3.c.c.1149.27		32	115.22	even	4
1150.3.c.c.1149.28		32	5.3	odd	4
1150.3.d.b.551.9		16	5.4	even	2
1150.3.d.b.551.10		16	115.114	odd	2
1840.3.k.d.321.1		16	4.3	odd	2
1840.3.k.d.321.2		16	92.91	even	2
2070.3.c.a.91.11		16	69.68	even	2
2070.3.c.a.91.14		16	3.2	odd	2

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	230.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +4.76369 q^{3} +2.00000 q^{4} -2.23607i q^{5} -6.73687 q^{6} +7.05858i q^{7} -2.82843 q^{8} +13.6927 q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +4.76369 q^{3} +2.00000 q^{4} -2.23607i q^{5} -6.73687 q^{6} +7.05858i q^{7} -2.82843 q^{8} +13.6927 q^{9} +3.16228i q^{10} +10.4520i q^{11} +9.52738 q^{12} +19.0223 q^{13} -9.98235i q^{14} -10.6519i q^{15} +4.00000 q^{16} +12.8329i q^{17} -19.3645 q^{18} -22.7880i q^{19} -4.47214i q^{20} +33.6249i q^{21} -14.7813i q^{22} +(-6.14050 - 22.1652i) q^{23} -13.4737 q^{24} -5.00000 q^{25} -26.9016 q^{26} +22.3548 q^{27} +14.1172i q^{28} -8.61694 q^{29} +15.0641i q^{30} +22.2032 q^{31} -5.65685 q^{32} +49.7900i q^{33} -18.1485i q^{34} +15.7835 q^{35} +27.3855 q^{36} -29.8603i q^{37} +32.2271i q^{38} +90.6164 q^{39} +6.32456i q^{40} -18.7911 q^{41} -47.5528i q^{42} +10.0531i q^{43} +20.9039i q^{44} -30.6179i q^{45} +(8.68398 + 31.3463i) q^{46} +20.6079 q^{47} +19.0548 q^{48} -0.823620 q^{49} +7.07107 q^{50} +61.1320i q^{51} +38.0446 q^{52} +17.3941i q^{53} -31.6144 q^{54} +23.3713 q^{55} -19.9647i q^{56} -108.555i q^{57} +12.1862 q^{58} -103.279 q^{59} -21.3039i q^{60} +74.6163i q^{61} -31.4001 q^{62} +96.6514i q^{63} +8.00000 q^{64} -42.5352i q^{65} -70.4136i q^{66} -101.145i q^{67} +25.6658i q^{68} +(-29.2514 - 105.588i) q^{69} -22.3212 q^{70} -69.4218 q^{71} -38.7289 q^{72} -122.376 q^{73} +42.2289i q^{74} -23.8184 q^{75} -45.5761i q^{76} -73.7761 q^{77} -128.151 q^{78} +140.900i q^{79} -8.94427i q^{80} -16.7435 q^{81} +26.5747 q^{82} -126.423i q^{83} +67.2498i q^{84} +28.6953 q^{85} -14.2173i q^{86} -41.0484 q^{87} -29.5626i q^{88} +11.9403i q^{89} +43.3002i q^{90} +134.271i q^{91} +(-12.2810 - 44.3303i) q^{92} +105.769 q^{93} -29.1440 q^{94} -50.9556 q^{95} -26.9475 q^{96} +57.0325i q^{97} +1.16477 q^{98} +143.116i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9}+O(q^{10}) \) 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9	\( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9} + 24 q^{13} + 64 q^{16} - 32 q^{18} + 4 q^{23} - 16 q^{24} - 80 q^{25} + 96 q^{26} - 96 q^{27} - 108 q^{29} - 116 q^{31} + 60 q^{35} + 128 q^{36} + 248 q^{39} - 156 q^{41} - 124 q^{46} - 128 q^{47} - 28 q^{49} + 48 q^{52} + 224 q^{54} + 160 q^{58} + 204 q^{59} + 64 q^{62} + 128 q^{64} - 268 q^{69} - 120 q^{70} + 236 q^{71} - 64 q^{72} - 112 q^{73} - 936 q^{77} - 432 q^{78} - 136 q^{81} - 64 q^{82} + 60 q^{85} - 152 q^{87} + 8 q^{92} + 856 q^{93} - 216 q^{94} - 160 q^{95} - 32 q^{96} + 256 q^{98}+O(q^{100}) \) 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9 + 24 * q^13 + 64 * q^16 - 32 * q^18 + 4 * q^23 - 16 * q^24 - 80 * q^25 + 96 * q^26 - 96 * q^27 - 108 * q^29 - 116 * q^31 + 60 * q^35 + 128 * q^36 + 248 * q^39 - 156 * q^41 - 124 * q^46 - 128 * q^47 - 28 * q^49 + 48 * q^52 + 224 * q^54 + 160 * q^58 + 204 * q^59 + 64 * q^62 + 128 * q^64 - 268 * q^69 - 120 * q^70 + 236 * q^71 - 64 * q^72 - 112 * q^73 - 936 * q^77 - 432 * q^78 - 136 * q^81 - 64 * q^82 + 60 * q^85 - 152 * q^87 + 8 * q^92 + 856 * q^93 - 216 * q^94 - 160 * q^95 - 32 * q^96 + 256 * q^98

Introduction

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