LMFDB - Embedded newform 363.3.b.g.122.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,3,Mod(122,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("363.122");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.b (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:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			122.4
Root			$-1.61803i$ of defining polynomial
Character	$\chi$	$=$	363.122
Dual form			363.3.b.g.122.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-2.00000 + 2.23607i) q^{3} +3.00000 q^{4} -4.38197i q^{5} +(-2.23607 - 2.00000i) q^{6} +2.14590 q^{7} +7.00000i q^{8} +(-1.00000 - 8.94427i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-2.00000 + 2.23607i) q^{3} +3.00000 q^{4} -4.38197i q^{5} +(-2.23607 - 2.00000i) q^{6} +2.14590 q^{7} +7.00000i q^{8} +(-1.00000 - 8.94427i) q^{9} +4.38197 q^{10} +(-6.00000 + 6.70820i) q^{12} +8.76393 q^{13} +2.14590i q^{14} +(9.79837 + 8.76393i) q^{15} +5.00000 q^{16} -6.00000i q^{17} +(8.94427 - 1.00000i) q^{18} +31.1246 q^{19} -13.1459i q^{20} +(-4.29180 + 4.79837i) q^{21} -26.4721i q^{23} +(-15.6525 - 14.0000i) q^{24} +5.79837 q^{25} +8.76393i q^{26} +(22.0000 + 15.6525i) q^{27} +6.43769 q^{28} +47.3951i q^{29} +(-8.76393 + 9.79837i) q^{30} -30.7984 q^{31} +33.0000i q^{32} +6.00000 q^{34} -9.40325i q^{35} +(-3.00000 - 26.8328i) q^{36} +29.5967 q^{37} +31.1246i q^{38} +(-17.5279 + 19.5967i) q^{39} +30.6738 q^{40} +43.5967i q^{41} +(-4.79837 - 4.29180i) q^{42} +39.7082 q^{43} +(-39.1935 + 4.38197i) q^{45} +26.4721 q^{46} -4.29180i q^{47} +(-10.0000 + 11.1803i) q^{48} -44.3951 q^{49} +5.79837i q^{50} +(13.4164 + 12.0000i) q^{51} +26.2918 q^{52} -11.2705i q^{53} +(-15.6525 + 22.0000i) q^{54} +15.0213i q^{56} +(-62.2492 + 69.5967i) q^{57} -47.3951 q^{58} +33.0902i q^{59} +(29.3951 + 26.2918i) q^{60} -27.3738 q^{61} -30.7984i q^{62} +(-2.14590 - 19.1935i) q^{63} -13.0000 q^{64} -38.4033i q^{65} +70.7902 q^{67} -18.0000i q^{68} +(59.1935 + 52.9443i) q^{69} +9.40325 q^{70} -88.1803i q^{71} +(62.6099 - 7.00000i) q^{72} -61.9787 q^{73} +29.5967i q^{74} +(-11.5967 + 12.9656i) q^{75} +93.3738 q^{76} +(-19.5967 - 17.5279i) q^{78} +63.0608 q^{79} -21.9098i q^{80} +(-79.0000 + 17.8885i) q^{81} -43.5967 q^{82} -110.185i q^{83} +(-12.8754 + 14.3951i) q^{84} -26.2918 q^{85} +39.7082i q^{86} +(-105.979 - 94.7902i) q^{87} +9.66563i q^{89} +(-4.38197 - 39.1935i) q^{90} +18.8065 q^{91} -79.4164i q^{92} +(61.5967 - 68.8673i) q^{93} +4.29180 q^{94} -136.387i q^{95} +(-73.7902 - 66.0000i) q^{96} +100.185 q^{97} -44.3951i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{3} + 12 q^{4} + 22 q^{7} - 4 q^{9}+O(q^{10}) $ 4 * q - 8 * q^3 + 12 * q^4 + 22 * q^7 - 4 * q^9	$ 4 q - 8 q^{3} + 12 q^{4} + 22 q^{7} - 4 q^{9} + 22 q^{10} - 24 q^{12} + 44 q^{13} - 10 q^{15} + 20 q^{16} + 44 q^{19} - 44 q^{21} - 26 q^{25} + 88 q^{27} + 66 q^{28} - 44 q^{30} - 74 q^{31} + 24 q^{34} - 12 q^{36} + 20 q^{37} - 88 q^{39} + 154 q^{40} + 30 q^{42} + 132 q^{43} + 40 q^{45} + 88 q^{46} - 40 q^{48} - 30 q^{49} + 132 q^{52} - 88 q^{57} - 42 q^{58} - 30 q^{60} + 132 q^{61} - 22 q^{63} - 52 q^{64} - 12 q^{67} + 40 q^{69} + 136 q^{70} - 154 q^{73} + 52 q^{75} + 132 q^{76} + 20 q^{78} - 110 q^{79} - 316 q^{81} - 76 q^{82} - 132 q^{84} - 132 q^{85} - 330 q^{87} - 22 q^{90} + 272 q^{91} + 148 q^{93} + 44 q^{94} - 42 q^{97}+O(q^{100}) $ 4 * q - 8 * q^3 + 12 * q^4 + 22 * q^7 - 4 * q^9 + 22 * q^10 - 24 * q^12 + 44 * q^13 - 10 * q^15 + 20 * q^16 + 44 * q^19 - 44 * q^21 - 26 * q^25 + 88 * q^27 + 66 * q^28 - 44 * q^30 - 74 * q^31 + 24 * q^34 - 12 * q^36 + 20 * q^37 - 88 * q^39 + 154 * q^40 + 30 * q^42 + 132 * q^43 + 40 * q^45 + 88 * q^46 - 40 * q^48 - 30 * q^49 + 132 * q^52 - 88 * q^57 - 42 * q^58 - 30 * q^60 + 132 * q^61 - 22 * q^63 - 52 * q^64 - 12 * q^67 + 40 * q^69 + 136 * q^70 - 154 * q^73 + 52 * q^75 + 132 * q^76 + 20 * q^78 - 110 * q^79 - 316 * q^81 - 76 * q^82 - 132 * q^84 - 132 * q^85 - 330 * q^87 - 22 * q^90 + 272 * q^91 + 148 * q^93 + 44 * q^94 - 42 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.00000i			0.500000i	0.968246	+	0.250000i	$0.0804306\pi$
$2$			1.00000i			0.500000i	−0.968246	+	0.250000i	$0.919569\pi$
$3$	−2.00000	+	2.23607i	−0.666667	+	0.745356i
$3$	−2.00000	+	2.23607i	−0.666667	+	0.745356i
$4$	3.00000			0.750000
$5$		−	4.38197i		−	0.876393i	−0.898879	−	0.438197i	$-0.855617\pi$
$5$		−	4.38197i		−	0.876393i	0.898879	−	0.438197i	$-0.144383\pi$
$6$	−2.23607	−	2.00000i	−0.372678	−	0.333333i
$7$	2.14590			0.306557			0.153278	−	0.988183i	$-0.451017\pi$
$7$	2.14590			0.306557			0.153278	+	0.988183i	$0.451017\pi$
$8$			7.00000i			0.875000i
$9$	−1.00000	−	8.94427i	−0.111111	−	0.993808i
$10$	4.38197			0.438197
$11$		0			0
$11$		0			0
$12$	−6.00000	+	6.70820i	−0.500000	+	0.559017i
$13$	8.76393			0.674149			0.337074	−	0.941478i	$-0.390563\pi$
$13$	8.76393			0.674149			0.337074	+	0.941478i	$0.390563\pi$
$14$			2.14590i			0.153278i
$15$	9.79837	+	8.76393i	0.653225	+	0.584262i
$16$	5.00000			0.312500
$17$		−	6.00000i		−	0.352941i	−0.984306	−	0.176471i	$-0.943532\pi$
$17$		−	6.00000i		−	0.352941i	0.984306	−	0.176471i	$-0.0564680\pi$
$18$	8.94427	−	1.00000i	0.496904	−	0.0555556i
$19$	31.1246			1.63814			0.819069	−	0.573695i	$-0.194491\pi$
$19$	31.1246			1.63814			0.819069	+	0.573695i	$0.194491\pi$
$20$		−	13.1459i		−	0.657295i
$21$	−4.29180	+	4.79837i	−0.204371	+	0.228494i
$22$		0			0
$23$		−	26.4721i		−	1.15096i	−0.817815	−	0.575481i	$-0.804815\pi$
$23$		−	26.4721i		−	1.15096i	0.817815	−	0.575481i	$-0.195185\pi$
$24$	−15.6525	−	14.0000i	−0.652186	−	0.583333i
$25$	5.79837			0.231935
$26$			8.76393i			0.337074i
$27$	22.0000	+	15.6525i	0.814815	+	0.579721i
$28$	6.43769			0.229918
$29$			47.3951i			1.63431i	0.576415	+	0.817157i	$0.304451\pi$
$29$			47.3951i			1.63431i	−0.576415	+	0.817157i	$0.695549\pi$
$30$	−8.76393	+	9.79837i	−0.292131	+	0.326612i
$31$	−30.7984			−0.993496			−0.496748	−	0.867895i	$-0.665473\pi$
$31$	−30.7984			−0.993496			−0.496748	+	0.867895i	$0.665473\pi$
$32$			33.0000i			1.03125i
$33$		0			0
$34$	6.00000			0.176471
$35$		−	9.40325i		−	0.268664i
$36$	−3.00000	−	26.8328i	−0.0833333	−	0.745356i
$37$	29.5967			0.799912			0.399956	−	0.916534i	$-0.369025\pi$
$37$	29.5967			0.799912			0.399956	+	0.916534i	$0.369025\pi$
$38$			31.1246i			0.819069i
$39$	−17.5279	+	19.5967i	−0.449432	+	0.502481i
$40$	30.6738			0.766844
$41$			43.5967i			1.06334i	0.846953	+	0.531668i	$0.178434\pi$
$41$			43.5967i			1.06334i	−0.846953	+	0.531668i	$0.821566\pi$
$42$	−4.79837	−	4.29180i	−0.114247	−	0.102186i
$43$	39.7082			0.923447			0.461723	−	0.887024i	$-0.347231\pi$
$43$	39.7082			0.923447			0.461723	+	0.887024i	$0.347231\pi$
$44$		0			0
$45$	−39.1935	+	4.38197i	−0.870967	+	0.0973770i
$46$	26.4721			0.575481
$47$		−	4.29180i		−	0.0913148i	−0.998957	−	0.0456574i	$-0.985462\pi$
$47$		−	4.29180i		−	0.0913148i	0.998957	−	0.0456574i	$-0.0145383\pi$
$48$	−10.0000	+	11.1803i	−0.208333	+	0.232924i
$49$	−44.3951			−0.906023
$50$			5.79837i			0.115967i
$51$	13.4164	+	12.0000i	0.263067	+	0.235294i
$52$	26.2918			0.505611
$53$		−	11.2705i		−	0.212651i	−0.994331	−	0.106326i	$-0.966091\pi$
$53$		−	11.2705i		−	0.212651i	0.994331	−	0.106326i	$-0.0339086\pi$
$54$	−15.6525	+	22.0000i	−0.289861	+	0.407407i
$55$		0			0
$56$			15.0213i			0.268237i
$57$	−62.2492	+	69.5967i	−1.09209	+	1.22100i
$58$	−47.3951			−0.817157
$59$			33.0902i			0.560850i	0.959876	+	0.280425i	$0.0904755\pi$
$59$			33.0902i			0.560850i	−0.959876	+	0.280425i	$0.909525\pi$
$60$	29.3951	+	26.2918i	0.489919	+	0.438197i
$61$	−27.3738			−0.448751			−0.224376	−	0.974503i	$-0.572034\pi$
$61$	−27.3738			−0.448751			−0.224376	+	0.974503i	$0.572034\pi$
$62$		−	30.7984i		−	0.496748i
$63$	−2.14590	−	19.1935i	−0.0340619	−	0.304659i
$64$	−13.0000			−0.203125
$65$		−	38.4033i		−	0.590819i
$66$		0			0
$67$	70.7902			1.05657			0.528285	−	0.849067i	$-0.322835\pi$
$67$	70.7902			1.05657			0.528285	+	0.849067i	$0.322835\pi$
$68$		−	18.0000i		−	0.264706i
$69$	59.1935	+	52.9443i	0.857877	+	0.767308i
$70$	9.40325			0.134332
$71$		−	88.1803i		−	1.24198i	−0.783820	−	0.620988i	$-0.786731\pi$
$71$		−	88.1803i		−	1.24198i	0.783820	−	0.620988i	$-0.213269\pi$
$72$	62.6099	−	7.00000i	0.869582	−	0.0972222i
$73$	−61.9787			−0.849023			−0.424512	−	0.905422i	$-0.639554\pi$
$73$	−61.9787			−0.849023			−0.424512	+	0.905422i	$0.639554\pi$
$74$			29.5967i			0.399956i
$75$	−11.5967	+	12.9656i	−0.154623	+	0.172874i
$76$	93.3738			1.22860
$77$		0			0
$78$	−19.5967	−	17.5279i	−0.251240	−	0.224716i
$79$	63.0608			0.798237			0.399119	−	0.916899i	$-0.369316\pi$
$79$	63.0608			0.798237			0.399119	+	0.916899i	$0.369316\pi$
$80$		−	21.9098i		−	0.273873i
$81$	−79.0000	+	17.8885i	−0.975309	+	0.220846i
$82$	−43.5967			−0.531668
$83$		−	110.185i		−	1.32753i	−0.747939	−	0.663767i	$-0.768957\pi$
$83$		−	110.185i		−	1.32753i	0.747939	−	0.663767i	$-0.231043\pi$
$84$	−12.8754	+	14.3951i	−0.153278	+	0.171370i
$85$	−26.2918			−0.309315
$86$			39.7082i			0.461723i
$87$	−105.979	−	94.7902i	−1.21815	−	1.08954i
$88$		0			0
$89$			9.66563i			0.108603i	0.998525	+	0.0543013i	$0.0172931\pi$
$89$			9.66563i			0.108603i	−0.998525	+	0.0543013i	$0.982707\pi$
$90$	−4.38197	−	39.1935i	−0.0486885	−	0.435483i
$91$	18.8065			0.206665
$92$		−	79.4164i		−	0.863222i
$93$	61.5967	−	68.8673i	0.662331	−	0.740508i
$94$	4.29180			0.0456574
$95$		−	136.387i		−	1.43565i
$96$	−73.7902	−	66.0000i	−0.768648	−	0.687500i
$97$	100.185			1.03284			0.516419	−	0.856336i	$-0.327265\pi$
$97$	100.185			1.03284			0.516419	+	0.856336i	$0.327265\pi$
$98$		−	44.3951i		−	0.453011i
$99$		0			0
$100$	17.3951			0.173951
$101$			13.4114i			0.132786i	0.997794	+	0.0663930i	$0.0211491\pi$
$101$			13.4114i			0.132786i	−0.997794	+	0.0663930i	$0.978851\pi$
$102$	−12.0000	+	13.4164i	−0.117647	+	0.131533i
$103$	0.411383			0.00399401			0.00199700	−	0.999998i	$-0.499364\pi$
$103$	0.411383			0.00399401			0.00199700	+	0.999998i	$0.499364\pi$
$104$			61.3475i			0.589880i
$105$	21.0263	+	18.8065i	0.200251	+	0.179110i
$106$	11.2705			0.106326
$107$		−	204.782i		−	1.91385i	−0.290333	−	0.956926i	$-0.593766\pi$
$107$		−	204.782i		−	1.91385i	0.290333	−	0.956926i	$-0.406234\pi$
$108$	66.0000	+	46.9574i	0.611111	+	0.434791i
$109$	−107.331			−0.984690			−0.492345	−	0.870400i	$-0.663860\pi$
$109$	−107.331			−0.984690			−0.492345	+	0.870400i	$0.663860\pi$
$110$		0			0
$111$	−59.1935	+	66.1803i	−0.533275	+	0.596219i
$112$	10.7295			0.0957990
$113$			75.6656i			0.669607i	0.942288	+	0.334804i	$0.108670\pi$
$113$			75.6656i			0.669607i	−0.942288	+	0.334804i	$0.891330\pi$
$114$	−69.5967	−	62.2492i	−0.610498	−	0.546046i
$115$	−116.000			−1.00870
$116$			142.185i			1.22574i
$117$	−8.76393	−	78.3870i	−0.0749054	−	0.669974i
$118$	−33.0902			−0.280425
$119$		−	12.8754i		−	0.108197i
$120$	−61.3475	+	68.5886i	−0.511229	+	0.571572i
$121$		0			0
$122$		−	27.3738i		−	0.224376i
$123$	−97.4853	−	87.1935i	−0.792563	−	0.708890i
$124$	−92.3951			−0.745122
$125$		−	134.957i		−	1.07966i
$126$	19.1935	−	2.14590i	0.152329	−	0.0170309i
$127$	−74.5836			−0.587272			−0.293636	−	0.955917i	$-0.594865\pi$
$127$	−74.5836			−0.587272			−0.293636	+	0.955917i	$0.594865\pi$
$128$			119.000i			0.929688i
$129$	−79.4164	+	88.7902i	−0.615631	+	0.688296i
$130$	38.4033			0.295410
$131$			8.00813i			0.0611308i	0.999533	+	0.0305654i	$0.00973078\pi$
$131$			8.00813i			0.0611308i	−0.999533	+	0.0305654i	$0.990269\pi$
$132$		0			0
$133$	66.7902			0.502182
$134$			70.7902i			0.528285i
$135$	68.5886	−	96.4033i	0.508064	−	0.714098i
$136$	42.0000			0.308824
$137$		−	32.7477i		−	0.239034i	−0.992832	−	0.119517i	$-0.961865\pi$
$137$		−	32.7477i		−	0.239034i	0.992832	−	0.119517i	$-0.0381346\pi$
$138$	−52.9443	+	59.1935i	−0.383654	+	0.428938i
$139$	−213.580			−1.53655			−0.768275	−	0.640120i	$-0.778885\pi$
$139$	−213.580			−1.53655			−0.768275	+	0.640120i	$0.778885\pi$
$140$		−	28.2098i		−	0.201498i
$141$	9.59675	+	8.58359i	0.0680620	+	0.0608765i
$142$	88.1803			0.620988
$143$		0			0
$144$	−5.00000	−	44.7214i	−0.0347222	−	0.310565i
$145$	207.684			1.43230
$146$		−	61.9787i		−	0.424512i
$147$	88.7902	−	99.2705i	0.604015	−	0.675310i
$148$	88.7902			0.599934
$149$			115.992i			0.778469i	0.921139	+	0.389234i	$0.127260\pi$
$149$			115.992i			0.778469i	−0.921139	+	0.389234i	$0.872740\pi$
$150$	−12.9656	−	11.5967i	−0.0864371	−	0.0773117i
$151$	−0.450850			−0.00298576			−0.00149288	−	0.999999i	$-0.500475\pi$
$151$	−0.450850			−0.00298576			−0.00149288	+	0.999999i	$0.500475\pi$
$152$			217.872i			1.43337i
$153$	−53.6656	+	6.00000i	−0.350756	+	0.0392157i
$154$		0			0
$155$			134.957i			0.870693i
$156$	−52.5836	+	58.7902i	−0.337074	+	0.376861i
$157$	42.0000			0.267516			0.133758	−	0.991014i	$-0.457296\pi$
$157$	42.0000			0.267516			0.133758	+	0.991014i	$0.457296\pi$
$158$			63.0608i			0.399119i
$159$	25.2016	+	22.5410i	0.158501	+	0.141767i
$160$	144.605			0.903780
$161$		−	56.8065i		−	0.352835i
$162$	−17.8885	−	79.0000i	−0.110423	−	0.487654i
$163$	−11.2098			−0.0687715			−0.0343858	−	0.999409i	$-0.510947\pi$
$163$	−11.2098			−0.0687715			−0.0343858	+	0.999409i	$0.510947\pi$
$164$			130.790i			0.797501i
$165$		0			0
$166$	110.185			0.663767
$167$		−	59.1772i		−	0.354355i	−0.984179	−	0.177177i	$-0.943303\pi$
$167$		−	59.1772i		−	0.354355i	0.984179	−	0.177177i	$-0.0566966\pi$
$168$	−33.5886	−	30.0426i	−0.199932	−	0.178825i
$169$	−92.1935			−0.545524
$170$		−	26.2918i		−	0.154658i
$171$	−31.1246	−	278.387i	−0.182015	−	1.62799i
$172$	119.125			0.692585
$173$			35.2016i			0.203478i	0.994811	+	0.101739i	$0.0324406\pi$
$173$			35.2016i			0.203478i	−0.994811	+	0.101739i	$0.967559\pi$
$174$	94.7902	−	105.979i	0.544772	−	0.609073i
$175$	12.4427			0.0711013
$176$		0			0
$177$	−73.9919	−	66.1803i	−0.418033	−	0.373900i
$178$	−9.66563			−0.0543013
$179$			11.1622i			0.0623584i	0.999514	+	0.0311792i	$0.00992626\pi$
$179$			11.1622i			0.0623584i	−0.999514	+	0.0311792i	$0.990074\pi$
$180$	−117.580	+	13.1459i	−0.653225	+	0.0730328i
$181$	−265.967			−1.46943			−0.734717	−	0.678374i	$-0.762685\pi$
$181$	−265.967			−1.46943			−0.734717	+	0.678374i	$0.762685\pi$
$182$			18.8065i			0.103332i
$183$	54.7477	−	61.2098i	0.299168	−	0.334480i
$184$	185.305			1.00709
$185$		−	129.692i		−	0.701038i
$186$	68.8673	+	61.5967i	0.370254	+	0.331165i
$187$		0			0
$188$		−	12.8754i		−	0.0684861i
$189$	47.2098	+	33.5886i	0.249787	+	0.177718i
$190$	136.387			0.717826
$191$			247.915i			1.29798i	0.760795	+	0.648992i	$0.224809\pi$
$191$			247.915i			1.29798i	−0.760795	+	0.648992i	$0.775191\pi$
$192$	26.0000	−	29.0689i	0.135417	−	0.151400i
$193$	24.6869			0.127911			0.0639557	−	0.997953i	$-0.479628\pi$
$193$	24.6869			0.127911			0.0639557	+	0.997953i	$0.479628\pi$
$194$			100.185i			0.516419i
$195$	85.8723	+	76.8065i	0.440371	+	0.393880i
$196$	−133.185			−0.679517
$197$		−	219.395i		−	1.11368i	−0.830620	−	0.556840i	$-0.812013\pi$
$197$		−	219.395i		−	1.11368i	0.830620	−	0.556840i	$-0.187987\pi$
$198$		0			0
$199$	19.8146			0.0995710			0.0497855	−	0.998760i	$-0.484146\pi$
$199$	19.8146			0.0995710			0.0497855	+	0.998760i	$0.484146\pi$
$200$			40.5886i			0.202943i
$201$	−141.580	+	158.292i	−0.704381	+	0.787521i
$202$	−13.4114			−0.0663930
$203$			101.705i			0.501010i
$204$	40.2492	+	36.0000i	0.197300	+	0.176471i
$205$	191.039			0.931900
$206$			0.411383i			0.00199700i
$207$	−236.774	+	26.4721i	−1.14384	+	0.127885i
$208$	43.8197			0.210671
$209$		0			0
$210$	−18.8065	+	21.0263i	−0.0895548	+	0.100125i
$211$	−199.262			−0.944371			−0.472186	−	0.881499i	$-0.656535\pi$
$211$	−199.262			−0.944371			−0.472186	+	0.881499i	$0.656535\pi$
$212$		−	33.8115i		−	0.159488i
$213$	197.177	+	176.361i	0.925715	+	0.827984i
$214$	204.782			0.956926
$215$		−	174.000i		−	0.809302i
$216$	−109.567	+	154.000i	−0.507256	+	0.712963i
$217$	−66.0902			−0.304563
$218$		−	107.331i		−	0.492345i
$219$	123.957	−	138.589i	0.566016	−	0.632825i
$220$		0			0
$221$		−	52.5836i		−	0.237935i
$222$	−66.1803	−	59.1935i	−0.298110	−	0.266637i
$223$	−43.0081			−0.192862			−0.0964308	−	0.995340i	$-0.530743\pi$
$223$	−43.0081			−0.192862			−0.0964308	+	0.995340i	$0.530743\pi$
$224$			70.8146i			0.316137i
$225$	−5.79837	−	51.8622i	−0.0257706	−	0.230499i
$226$	−75.6656			−0.334804
$227$		−	76.5724i		−	0.337323i	−0.985674	−	0.168662i	$-0.946056\pi$
$227$		−	76.5724i		−	0.337323i	0.985674	−	0.168662i	$-0.0539445\pi$
$228$	−186.748	+	208.790i	−0.819069	+	0.915747i
$229$	−146.774			−0.640934			−0.320467	−	0.947260i	$-0.603840\pi$
$229$	−146.774			−0.640934			−0.320467	+	0.947260i	$0.603840\pi$
$230$		−	116.000i		−	0.504348i
$231$		0			0
$232$	−331.766			−1.43003
$233$			44.3707i			0.190432i	0.995457	+	0.0952162i	$0.0303542\pi$
$233$			44.3707i			0.190432i	−0.995457	+	0.0952162i	$0.969646\pi$
$234$	78.3870	−	8.76393i	0.334987	−	0.0374527i
$235$	−18.8065			−0.0800277
$236$			99.2705i			0.420638i
$237$	−126.122	+	141.008i	−0.532158	+	0.594971i
$238$	12.8754			0.0540983
$239$			308.790i			1.29201i	0.763333	+	0.646005i	$0.223561\pi$
$239$			308.790i			1.29201i	−0.763333	+	0.646005i	$0.776439\pi$
$240$	48.9919	+	43.8197i	0.204133	+	0.182582i
$241$	5.35565			0.0222226			0.0111113	−	0.999938i	$-0.496463\pi$
$241$	5.35565			0.0222226			0.0111113	+	0.999938i	$0.496463\pi$
$242$		0			0
$243$	118.000	−	212.426i	0.485597	−	0.874183i
$244$	−82.1215			−0.336564
$245$			194.538i			0.794032i
$246$	87.1935	−	97.4853i	0.354445	−	0.396282i
$247$	272.774			1.10435
$248$		−	215.589i		−	0.869309i
$249$	246.382	+	220.371i	0.989486	+	0.885023i
$250$	134.957			0.539830
$251$		−	279.851i		−	1.11494i	−0.830196	−	0.557472i	$-0.811771\pi$
$251$		−	279.851i		−	1.11494i	0.830196	−	0.557472i	$-0.188229\pi$
$252$	−6.43769	−	57.5805i	−0.0255464	−	0.228494i
$253$		0			0
$254$		−	74.5836i		−	0.293636i
$255$	52.5836	−	58.7902i	0.206210	−	0.230550i
$256$	−171.000			−0.667969
$257$		−	116.636i		−	0.453837i	−0.973914	−	0.226919i	$-0.927135\pi$
$257$		−	116.636i		−	0.453837i	0.973914	−	0.226919i	$-0.0728652\pi$
$258$	−88.7902	−	79.4164i	−0.344148	−	0.307816i
$259$	63.5116			0.245219
$260$		−	115.210i		−	0.443114i
$261$	423.915	−	47.3951i	1.62419	−	0.181591i
$262$	−8.00813			−0.0305654
$263$			435.580i			1.65620i	0.560581	+	0.828100i	$0.310578\pi$
$263$			435.580i			1.65620i	−0.560581	+	0.828100i	$0.689422\pi$
$264$		0			0
$265$	−49.3870			−0.186366
$266$			66.7902i			0.251091i
$267$	−21.6130	−	19.3313i	−0.0809476	−	0.0724017i
$268$	212.371			0.792428
$269$			149.745i			0.556671i	0.960484	+	0.278336i	$0.0897827\pi$
$269$			149.745i			0.556671i	−0.960484	+	0.278336i	$0.910217\pi$
$270$	96.4033	+	68.5886i	0.357049	+	0.254032i
$271$	13.7771			0.0508380			0.0254190	−	0.999677i	$-0.491908\pi$
$271$	13.7771			0.0508380			0.0254190	+	0.999677i	$0.491908\pi$
$272$		−	30.0000i		−	0.110294i
$273$	−37.6130	+	42.0526i	−0.137777	+	0.154039i
$274$	32.7477			0.119517
$275$		0			0
$276$	177.580	+	158.833i	0.643408	+	0.575481i
$277$	−109.135			−0.393988			−0.196994	−	0.980405i	$-0.563118\pi$
$277$	−109.135			−0.393988			−0.196994	+	0.980405i	$0.563118\pi$
$278$		−	213.580i		−	0.768275i
$279$	30.7984	+	275.469i	0.110388	+	0.987344i
$280$	65.8228			0.235081
$281$			195.161i			0.694523i	0.937768	+	0.347262i	$0.112888\pi$
$281$			195.161i			0.694523i	−0.937768	+	0.347262i	$0.887112\pi$
$282$	−8.58359	+	9.59675i	−0.0304383	+	0.0340310i
$283$	−152.918			−0.540346			−0.270173	−	0.962812i	$-0.587081\pi$
$283$	−152.918			−0.540346			−0.270173	+	0.962812i	$0.587081\pi$
$284$		−	264.541i		−	0.931482i
$285$	304.971	+	272.774i	1.07007	+	0.957102i
$286$		0			0
$287$			93.5542i			0.325973i
$288$	295.161	−	33.0000i	1.02486	−	0.114583i
$289$	253.000			0.875433
$290$			207.684i			0.716151i
$291$	−200.371	+	224.021i	−0.688559	+	0.769833i
$292$	−185.936			−0.636768
$293$			444.766i			1.51797i	0.651107	+	0.758986i	$0.274305\pi$
$293$			444.766i			1.51797i	−0.651107	+	0.758986i	$0.725695\pi$
$294$	99.2705	+	88.7902i	0.337655	+	0.302008i
$295$	145.000			0.491525
$296$			207.177i			0.699923i
$297$		0			0
$298$	−115.992			−0.389234
$299$		−	232.000i		−	0.775920i
$300$	−34.7902	+	38.8967i	−0.115967	+	0.129656i
$301$	85.2098			0.283089
$302$		−	0.450850i		−	0.00149288i
$303$	−29.9888	−	26.8228i	−0.0989728	−	0.0885240i
$304$	155.623			0.511918
$305$			119.951i			0.393283i
$306$	−6.00000	−	53.6656i	−0.0196078	−	0.175378i
$307$	−345.039			−1.12391			−0.561954	−	0.827169i	$-0.689950\pi$
$307$	−345.039			−1.12391			−0.561954	+	0.827169i	$0.689950\pi$
$308$		0			0
$309$	−0.822766	+	0.919880i	−0.00266267	+	0.00297696i
$310$	−134.957			−0.435347
$311$		−	388.859i		−	1.25035i	−0.780484	−	0.625175i	$-0.785027\pi$
$311$		−	388.859i		−	1.25035i	0.780484	−	0.625175i	$-0.214973\pi$
$312$	−137.177	−	122.695i	−0.439671	−	0.393253i
$313$	195.782			0.625502			0.312751	−	0.949835i	$-0.398749\pi$
$313$	195.782			0.625502			0.312751	+	0.949835i	$0.398749\pi$
$314$			42.0000i			0.133758i
$315$	−84.1052	+	9.40325i	−0.267001	+	0.0298516i
$316$	189.182			0.598678
$317$			554.328i			1.74867i	0.485324	+	0.874335i	$0.338702\pi$
$317$			554.328i			1.74867i	−0.485324	+	0.874335i	$0.661298\pi$
$318$	−22.5410	+	25.2016i	−0.0708837	+	0.0792504i
$319$		0			0
$320$			56.9656i			0.178017i
$321$	457.907	+	409.564i	1.42650	+	1.27590i
$322$	56.8065			0.176418
$323$		−	186.748i		−	0.578166i
$324$	−237.000	+	53.6656i	−0.731481	+	0.165635i
$325$	50.8166			0.156359
$326$		−	11.2098i		−	0.0343858i
$327$	214.663	−	240.000i	0.656460	−	0.733945i
$328$	−305.177			−0.930418
$329$		−	9.20976i		−	0.0279932i
$330$		0			0
$331$	−100.420			−0.303382			−0.151691	−	0.988428i	$-0.548472\pi$
$331$	−100.420			−0.303382			−0.151691	+	0.988428i	$0.548472\pi$
$332$		−	330.556i		−	0.995651i
$333$	−29.5967	−	264.721i	−0.0888791	−	0.794959i
$334$	59.1772			0.177177
$335$		−	310.200i		−	0.925971i
$336$	−21.4590	+	23.9919i	−0.0638660	+	0.0714044i
$337$	−115.698			−0.343318			−0.171659	−	0.985156i	$-0.554913\pi$
$337$	−115.698			−0.343318			−0.171659	+	0.985156i	$0.554913\pi$
$338$		−	92.1935i		−	0.272762i
$339$	−169.193	−	151.331i	−0.499096	−	0.446405i
$340$	−78.8754			−0.231986
$341$		0			0
$342$	278.387	−	31.1246i	0.813997	−	0.0910076i
$343$	−200.416			−0.584304
$344$			277.957i			0.808016i
$345$	232.000	−	259.384i	0.672464	−	0.751837i
$346$	−35.2016			−0.101739
$347$			248.024i			0.714768i	0.933958	+	0.357384i	$0.116331\pi$
$347$			248.024i			0.714768i	−0.933958	+	0.357384i	$0.883669\pi$
$348$	−317.936	−	284.371i	−0.913610	−	0.817157i
$349$	−508.200			−1.45616			−0.728081	−	0.685491i	$-0.759587\pi$
$349$	−508.200			−1.45616			−0.728081	+	0.685491i	$0.759587\pi$
$350$			12.4427i			0.0355506i
$351$	192.807	+	137.177i	0.549306	+	0.390818i
$352$		0			0
$353$		−	308.577i		−	0.874157i	−0.899423	−	0.437078i	$-0.856013\pi$
$353$		−	308.577i		−	0.874157i	0.899423	−	0.437078i	$-0.143987\pi$
$354$	66.1803	−	73.9919i	0.186950	−	0.209017i
$355$	−386.403			−1.08846
$356$			28.9969i			0.0814520i
$357$	28.7902	+	25.7508i	0.0806449	+	0.0721310i
$358$	−11.1622			−0.0311792
$359$		−	10.7902i		−	0.0300564i	−0.999887	−	0.0150282i	$-0.995216\pi$
$359$		−	10.7902i		−	0.0300564i	0.999887	−	0.0150282i	$-0.00478380\pi$
$360$	−30.6738	−	274.354i	−0.0852049	−	0.762096i
$361$	607.741			1.68349
$362$		−	265.967i		−	0.734717i
$363$		0			0
$364$	56.4195			0.154999
$365$			271.589i			0.744078i
$366$	61.2098	+	54.7477i	0.167240	+	0.149584i
$367$	−494.976			−1.34871			−0.674354	−	0.738408i	$-0.735578\pi$
$367$	−494.976			−1.34871			−0.674354	+	0.738408i	$0.735578\pi$
$368$		−	132.361i		−	0.359676i
$369$	389.941	−	43.5967i	1.05675	−	0.118148i
$370$	129.692			0.350519
$371$		−	24.1854i		−	0.0651897i
$372$	184.790	−	206.602i	0.496748	−	0.555381i
$373$	−356.472			−0.955689			−0.477845	−	0.878444i	$-0.658582\pi$
$373$	−356.472			−0.955689			−0.477845	+	0.878444i	$0.658582\pi$
$374$		0			0
$375$	301.774	+	269.915i	0.804731	+	0.719773i
$376$	30.0426			0.0799005
$377$			415.368i			1.10177i
$378$	−33.5886	+	47.2098i	−0.0888588	+	0.124894i
$379$	214.354			0.565579			0.282790	−	0.959182i	$-0.408740\pi$
$379$	214.354			0.565579			0.282790	+	0.959182i	$0.408740\pi$
$380$		−	409.161i		−	1.07674i
$381$	149.167	−	166.774i	0.391515	−	0.437727i
$382$	−247.915			−0.648992
$383$		−	37.5441i		−	0.0980264i	−0.998798	−	0.0490132i	$-0.984392\pi$
$383$		−	37.5441i		−	0.0980264i	0.998798	−	0.0490132i	$-0.0156076\pi$
$384$	−266.092	−	238.000i	−0.692948	−	0.619792i
$385$		0			0
$386$			24.6869i			0.0639557i
$387$	−39.7082	−	355.161i	−0.102605	−	0.917729i
$388$	300.556			0.774629
$389$		−	386.551i		−	0.993705i	−0.867835	−	0.496852i	$-0.834489\pi$
$389$		−	386.551i		−	0.993705i	0.867835	−	0.496852i	$-0.165511\pi$
$390$	−76.8065	+	85.8723i	−0.196940	+	0.220185i
$391$	−158.833			−0.406222
$392$		−	310.766i		−	0.792770i
$393$	−17.9067	−	16.0163i	−0.0455642	−	0.0407538i
$394$	219.395			0.556840
$395$		−	276.330i		−	0.699570i
$396$		0			0
$397$	−718.741			−1.81043			−0.905216	−	0.424952i	$-0.860291\pi$
$397$	−718.741			−1.81043			−0.905216	+	0.424952i	$0.860291\pi$
$398$			19.8146i			0.0497855i
$399$	−133.580	+	149.348i	−0.334788	+	0.374305i
$400$	28.9919			0.0724797
$401$		−	331.082i		−	0.825641i	−0.910812	−	0.412820i	$-0.864544\pi$
$401$		−	331.082i		−	0.825641i	0.910812	−	0.412820i	$-0.135456\pi$
$402$	−158.292	−	141.580i	−0.393761	−	0.352190i
$403$	−269.915			−0.669764
$404$			40.2341i			0.0995895i
$405$	78.3870	+	346.175i	0.193548	+	0.854754i
$406$	−101.705			−0.250505
$407$		0			0
$408$	−84.0000	+	93.9149i	−0.205882	+	0.230183i
$409$	−544.175			−1.33050			−0.665251	−	0.746620i	$-0.731675\pi$
$409$	−544.175			−1.33050			−0.665251	+	0.746620i	$0.731675\pi$
$410$			191.039i			0.465950i
$411$	73.2260	+	65.4953i	0.178165	+	0.159356i
$412$	1.23415			0.00299551
$413$			71.0081i			0.171933i
$414$	−26.4721	−	236.774i	−0.0639424	−	0.571918i
$415$	−482.829			−1.16344
$416$			289.210i			0.695216i
$417$	427.161	−	477.580i	1.02437	−	1.14528i
$418$		0			0
$419$		−	117.592i		−	0.280649i	−0.990106	−	0.140324i	$-0.955186\pi$
$419$		−	117.592i		−	0.280649i	0.990106	−	0.140324i	$-0.0448145\pi$
$420$	63.0789	+	56.4195i	0.150188	+	0.134332i
$421$	194.033			0.460885			0.230442	−	0.973086i	$-0.425983\pi$
$421$	194.033			0.460885			0.230442	+	0.973086i	$0.425983\pi$
$422$		−	199.262i		−	0.472186i
$423$	−38.3870	+	4.29180i	−0.0907494	+	0.0101461i
$424$	78.8936			0.186070
$425$		−	34.7902i		−	0.0818594i
$426$	−176.361	+	197.177i	−0.413992	+	0.462857i
$427$	−58.7415			−0.137568
$428$		−	614.346i		−	1.43539i
$429$		0			0
$430$	174.000			0.404651
$431$			355.613i			0.825088i	0.910938	+	0.412544i	$0.135360\pi$
$431$			355.613i			0.825088i	−0.910938	+	0.412544i	$0.864640\pi$
$432$	110.000	+	78.2624i	0.254630	+	0.181163i
$433$	−604.379			−1.39579			−0.697897	−	0.716198i	$-0.745881\pi$
$433$	−604.379			−1.39579			−0.697897	+	0.716198i	$0.745881\pi$
$434$		−	66.0902i		−	0.152281i
$435$	−415.368	+	464.395i	−0.954868	+	1.06757i
$436$	−321.994			−0.738518
$437$		−	823.935i		−	1.88543i
$438$	138.589	+	123.957i	0.316412	+	0.283008i
$439$	−28.9424			−0.0659279			−0.0329640	−	0.999457i	$-0.510495\pi$
$439$	−28.9424			−0.0659279			−0.0329640	+	0.999457i	$0.510495\pi$
$440$		0			0
$441$	44.3951	+	397.082i	0.100669	+	0.900413i
$442$	52.5836			0.118967
$443$		−	65.2968i		−	0.147397i	−0.997281	−	0.0736984i	$-0.976520\pi$
$443$		−	65.2968i		−	0.147397i	0.997281	−	0.0736984i	$-0.0234802\pi$
$444$	−177.580	+	198.541i	−0.399956	+	0.447164i
$445$	42.3545			0.0951786
$446$		−	43.0081i		−	0.0964308i
$447$	−259.366	−	231.984i	−0.580236	−	0.518979i
$448$	−27.8967			−0.0622694
$449$			283.331i			0.631027i	0.948921	+	0.315514i	$0.102177\pi$
$449$			283.331i			0.631027i	−0.948921	+	0.315514i	$0.897823\pi$
$450$	51.8622	−	5.79837i	0.115249	−	0.0128853i
$451$		0			0
$452$			226.997i			0.502206i
$453$	0.901699	−	1.00813i	0.00199051	−	0.00222545i
$454$	76.5724			0.168662
$455$		−	82.4095i		−	0.181120i
$456$	−487.177	−	435.745i	−1.06837	−	0.955580i
$457$	706.507			1.54597			0.772984	−	0.634426i	$-0.218763\pi$
$457$	706.507			1.54597			0.772984	+	0.634426i	$0.218763\pi$
$458$		−	146.774i		−	0.320467i
$459$	93.9149	−	132.000i	0.204608	−	0.287582i
$460$	−348.000			−0.756522
$461$			356.322i			0.772933i	0.922304	+	0.386466i	$0.126304\pi$
$461$			356.322i			0.772933i	−0.922304	+	0.386466i	$0.873696\pi$
$462$		0			0
$463$	801.137			1.73032			0.865158	−	0.501499i	$-0.167218\pi$
$463$	801.137			1.73032			0.865158	+	0.501499i	$0.167218\pi$
$464$			236.976i			0.510723i
$465$	−301.774	−	269.915i	−0.648976	−	0.580462i
$466$	−44.3707			−0.0952162
$467$			501.690i			1.07428i	0.843492	+	0.537141i	$0.180496\pi$
$467$			501.690i			1.07428i	−0.843492	+	0.537141i	$0.819504\pi$
$468$	−26.2918	−	235.161i	−0.0561791	−	0.502481i
$469$	151.909			0.323899
$470$		−	18.8065i		−	0.0400138i
$471$	−84.0000	+	93.9149i	−0.178344	+	0.199395i
$472$	−231.631			−0.490744
$473$		0			0
$474$	−141.008	−	126.122i	−0.297486	−	0.266079i
$475$	180.472			0.379941
$476$		−	38.6262i		−	0.0811474i
$477$	−100.807	+	11.2705i	−0.211334	+	0.0236279i
$478$	−308.790			−0.646005
$479$		−	419.177i		−	0.875109i	−0.899192	−	0.437555i	$-0.855845\pi$
$479$		−	419.177i		−	0.875109i	0.899192	−	0.437555i	$-0.144155\pi$
$480$	−289.210	+	323.346i	−0.602520	+	0.673638i
$481$	259.384			0.539260
$482$			5.35565i			0.0111113i
$483$	127.023	+	113.613i	0.262988	+	0.235224i
$484$		0			0
$485$		−	439.009i		−	0.905173i
$486$	212.426	+	118.000i	0.437091	+	0.242798i
$487$	−65.9756			−0.135474			−0.0677368	−	0.997703i	$-0.521578\pi$
$487$	−65.9756			−0.135474			−0.0677368	+	0.997703i	$0.521578\pi$
$488$		−	191.617i		−	0.392657i
$489$	22.4195	−	25.0658i	0.0458477	−	0.0512593i
$490$	−194.538			−0.397016
$491$		−	405.226i		−	0.825308i	−0.910888	−	0.412654i	$-0.864602\pi$
$491$		−	405.226i		−	0.825308i	0.910888	−	0.412654i	$-0.135398\pi$
$492$	−292.456	−	261.580i	−0.594423	−	0.531668i
$493$	284.371			0.576817
$494$			272.774i			0.552174i
$495$		0			0
$496$	−153.992			−0.310467
$497$		−	189.226i		−	0.380736i
$498$	−220.371	+	246.382i	−0.442512	+	0.494743i
$499$	−300.741			−0.602688			−0.301344	−	0.953515i	$-0.597435\pi$
$499$	−300.741			−0.602688			−0.301344	+	0.953515i	$0.597435\pi$
$500$		−	404.872i		−	0.809745i
$501$	132.324	+	118.354i	0.264120	+	0.236236i
$502$	279.851			0.557472
$503$			429.935i			0.854741i	0.904076	+	0.427371i	$0.140560\pi$
$503$			429.935i			0.854741i	−0.904076	+	0.427371i	$0.859440\pi$
$504$	134.354	−	15.0213i	0.266576	−	0.0298041i
$505$	58.7682			0.116373
$506$		0			0
$507$	184.387	−	206.151i	0.363682	−	0.406609i
$508$	−223.751			−0.440454
$509$		−	893.110i		−	1.75464i	−0.479909	−	0.877319i	$-0.659330\pi$
$509$		−	893.110i		−	1.75464i	0.479909	−	0.877319i	$-0.340670\pi$
$510$	58.7902	+	52.5836i	0.115275	+	0.103105i
$511$	−133.000			−0.260274
$512$			305.000i			0.595703i
$513$	684.741	+	487.177i	1.33478	+	0.949663i
$514$	116.636			0.226919
$515$		−	1.80267i		−	0.00350032i
$516$	−238.249	+	266.371i	−0.461723	+	0.516222i
$517$		0			0
$518$			63.5116i			0.122609i
$519$	−78.7132	−	70.4033i	−0.151663	−	0.135652i
$520$	268.823			0.516967
$521$			755.611i			1.45031i	0.688587	+	0.725154i	$0.258232\pi$
$521$			755.611i			1.45031i	−0.688587	+	0.725154i	$0.741768\pi$
$522$	47.3951	+	423.915i	0.0907953	+	0.812097i
$523$	622.997			1.19120			0.595599	−	0.803282i	$-0.296915\pi$
$523$	622.997			1.19120			0.595599	+	0.803282i	$0.296915\pi$
$524$			24.0244i			0.0458481i
$525$	−24.8854	+	27.8228i	−0.0474008	+	0.0529957i
$526$	−435.580			−0.828100
$527$			184.790i			0.350646i
$528$		0			0
$529$	−171.774			−0.324715
$530$		−	49.3870i		−	0.0931830i
$531$	295.967	−	33.0902i	0.557378	−	0.0623167i
$532$	200.371			0.376637
$533$			382.079i			0.716846i
$534$	19.3313	−	21.6130i	0.0362009	−	0.0404738i
$535$	−897.348			−1.67729
$536$			495.532i			0.924499i
$537$	−24.9593	−	22.3243i	−0.0464792	−	0.0415723i
$538$	−149.745			−0.278336
$539$		0			0
$540$	205.766	−	289.210i	0.381048	−	0.535574i
$541$	1048.17			1.93748			0.968738	−	0.248087i	$-0.0798020\pi$
$541$	1048.17			1.93748			0.968738	+	0.248087i	$0.0798020\pi$
$542$			13.7771i			0.0254190i
$543$	531.935	−	594.721i	0.979622	−	1.09525i
$544$	198.000			0.363971
$545$			470.322i			0.862976i
$546$	−42.0526	−	37.6130i	−0.0770195	−	0.0688883i
$547$	33.9737			0.0621091			0.0310546	−	0.999518i	$-0.490113\pi$
$547$	33.9737			0.0621091			0.0310546	+	0.999518i	$0.490113\pi$
$548$		−	98.2430i		−	0.179276i
$549$	27.3738	+	244.839i	0.0498613	+	0.445973i
$550$		0			0
$551$			1475.15i			2.67723i
$552$	−370.610	+	414.354i	−0.671395	+	0.750642i
$553$	135.322			0.244705
$554$		−	109.135i		−	0.196994i
$555$	290.000	+	259.384i	0.522523	+	0.467358i
$556$	−640.741			−1.15241
$557$			510.395i			0.916329i	0.888867	+	0.458164i	$0.151493\pi$
$557$			510.395i			0.916329i	−0.888867	+	0.458164i	$0.848507\pi$
$558$	−275.469	+	30.7984i	−0.493672	+	0.0551942i
$559$	348.000			0.622540
$560$		−	47.0163i		−	0.0839576i
$561$		0			0
$562$	−195.161			−0.347262
$563$		−	936.354i		−	1.66315i	−0.555411	−	0.831576i	$-0.687439\pi$
$563$		−	936.354i		−	1.66315i	0.555411	−	0.831576i	$-0.312561\pi$
$564$	28.7902	+	25.7508i	0.0510465	+	0.0456574i
$565$	331.564			0.586839
$566$		−	152.918i		−	0.270173i
$567$	−169.526	+	38.3870i	−0.298988	+	0.0677019i
$568$	617.262			1.08673
$569$		−	474.387i		−	0.833721i	−0.908971	−	0.416860i	$-0.863130\pi$
$569$		−	474.387i		−	0.833721i	0.908971	−	0.416860i	$-0.136870\pi$
$570$	−272.774	+	304.971i	−0.478551	+	0.535036i
$571$	1032.88			1.80890			0.904451	−	0.426577i	$-0.140281\pi$
$571$	1032.88			1.80890			0.904451	+	0.426577i	$0.140281\pi$
$572$		0			0
$573$	−554.354	−	495.830i	−0.967460	−	0.865322i
$574$	−93.5542			−0.162986
$575$		−	153.495i		−	0.266948i
$576$	13.0000	+	116.276i	0.0225694	+	0.201867i
$577$	38.8146			0.0672697			0.0336349	−	0.999434i	$-0.489292\pi$
$577$	38.8146			0.0672697			0.0336349	+	0.999434i	$0.489292\pi$
$578$			253.000i			0.437716i
$579$	−49.3738	+	55.2016i	−0.0852743	+	0.0953396i
$580$	623.051			1.07423
$581$		−	236.447i		−	0.406965i
$582$	−224.021	−	200.371i	−0.384916	−	0.344280i
$583$		0			0
$584$		−	433.851i		−	0.742896i
$585$	−343.489	+	38.4033i	−0.587161	+	0.0656466i
$586$	−444.766			−0.758986
$587$		−	314.258i		−	0.535363i	−0.963507	−	0.267682i	$-0.913743\pi$
$587$		−	314.258i		−	0.535363i	0.963507	−	0.267682i	$-0.0862575\pi$
$588$	266.371	−	297.812i	0.453011	−	0.506482i
$589$	−958.587			−1.62748
$590$			145.000i			0.245763i
$591$	490.582	+	438.790i	0.830089	+	0.742454i
$592$	147.984			0.249973
$593$			231.984i			0.391204i	0.980683	+	0.195602i	$0.0626660\pi$
$593$			231.984i			0.391204i	−0.980683	+	0.195602i	$0.937334\pi$
$594$		0			0
$595$	−56.4195			−0.0948227
$596$			347.976i			0.583852i
$597$	−39.6293	+	44.3069i	−0.0663807	+	0.0742159i
$598$	232.000			0.387960
$599$			591.368i			0.987258i	0.869673	+	0.493629i	$0.164330\pi$
$599$			591.368i			0.987258i	−0.869673	+	0.493629i	$0.835670\pi$
$600$	−90.7589	−	81.1772i	−0.151265	−	0.135295i
$601$	545.870			0.908270			0.454135	−	0.890933i	$-0.349948\pi$
$601$	545.870			0.908270			0.454135	+	0.890933i	$0.349948\pi$
$602$			85.2098i			0.141544i
$603$	−70.7902	−	633.167i	−0.117397	−	1.05003i
$604$	−1.35255			−0.00223932
$605$		0			0
$606$	26.8228	−	29.9888i	0.0442620	−	0.0494864i
$607$	−1086.66			−1.79021			−0.895104	−	0.445857i	$-0.852899\pi$
$607$	−1086.66			−1.79021			−0.895104	+	0.445857i	$0.852899\pi$
$608$			1027.11i			1.68933i
$609$	−227.420	−	203.410i	−0.373431	−	0.334007i
$610$	−119.951			−0.196641
$611$		−	37.6130i		−	0.0615598i
$612$	−160.997	+	18.0000i	−0.263067	+	0.0294118i
$613$	167.921			0.273933			0.136967	−	0.990576i	$-0.456265\pi$
$613$	167.921			0.273933			0.136967	+	0.990576i	$0.456265\pi$
$614$		−	345.039i		−	0.561954i
$615$	−382.079	+	427.177i	−0.621267	+	0.694597i
$616$		0			0
$617$		−	700.754i		−	1.13574i	−0.823117	−	0.567872i	$-0.807767\pi$
$617$		−	700.754i		−	1.13574i	0.823117	−	0.567872i	$-0.192233\pi$
$618$	−0.919880	−	0.822766i	−0.00148848	−	0.00133134i
$619$	−330.790			−0.534395			−0.267197	−	0.963642i	$-0.586098\pi$
$619$	−330.790			−0.534395			−0.267197	+	0.963642i	$0.586098\pi$
$620$			404.872i			0.653020i
$621$	414.354	−	582.387i	0.667237	−	0.937821i
$622$	388.859			0.625175
$623$			20.7415i			0.0332929i
$624$	−87.6393	+	97.9837i	−0.140448	+	0.157025i
$625$	−446.420			−0.714271
$626$			195.782i			0.312751i
$627$		0			0
$628$	126.000			0.200637
$629$		−	177.580i		−	0.282322i
$630$	−9.40325	−	84.1052i	−0.0149258	−	0.133500i
$631$	746.169			1.18252			0.591259	−	0.806482i	$-0.298631\pi$
$631$	746.169			1.18252			0.591259	+	0.806482i	$0.298631\pi$
$632$			441.425i			0.698458i
$633$	398.525	−	445.564i	0.629581	−	0.703893i
$634$	−554.328			−0.874335
$635$			326.823i			0.514682i
$636$	75.6049	+	67.6231i	0.118876	+	0.106326i
$637$	−389.076			−0.610794
$638$		0			0
$639$	−788.709	+	88.1803i	−1.23429	+	0.137997i
$640$	521.454			0.814772
$641$			149.672i			0.233497i	0.993161	+	0.116749i	$0.0372472\pi$
$641$			149.672i			0.233497i	−0.993161	+	0.116749i	$0.962753\pi$
$642$	−409.564	+	457.907i	−0.637951	+	0.713250i
$643$	455.161			0.707871			0.353935	−	0.935270i	$-0.384843\pi$
$643$	455.161			0.707871			0.353935	+	0.935270i	$0.384843\pi$
$644$		−	170.420i		−	0.264627i
$645$	389.076	+	348.000i	0.603218	+	0.539535i
$646$	186.748			0.289083
$647$		−	1250.14i		−	1.93221i	−0.258144	−	0.966106i	$-0.583111\pi$
$647$		−	1250.14i		−	1.93221i	0.258144	−	0.966106i	$-0.416889\pi$
$648$	−125.220	−	553.000i	−0.193240	−	0.853395i
$649$		0			0
$650$			50.8166i			0.0781793i
$651$	132.180	−	147.782i	0.203042	−	0.227008i
$652$	−33.6293			−0.0515786
$653$			849.687i			1.30121i	0.759418	+	0.650603i	$0.225484\pi$
$653$			849.687i			1.30121i	−0.759418	+	0.650603i	$0.774516\pi$
$654$	240.000	+	214.663i	0.366972	+	0.328230i
$655$	35.0914			0.0535746
$656$			217.984i			0.332292i
$657$	61.9787	+	554.354i	0.0943359	+	0.843766i
$658$	9.20976			0.0139966
$659$		−	511.766i		−	0.776579i	−0.921537	−	0.388290i	$-0.873066\pi$
$659$		−	511.766i		−	0.776579i	0.921537	−	0.388290i	$-0.126934\pi$
$660$		0			0
$661$	945.854			1.43094			0.715472	−	0.698642i	$-0.246212\pi$
$661$	945.854			1.43094			0.715472	+	0.698642i	$0.246212\pi$
$662$		−	100.420i		−	0.151691i
$663$	117.580	+	105.167i	0.177346	+	0.158623i
$664$	771.298			1.16159
$665$		−	292.673i		−	0.440109i
$666$	264.721	−	29.5967i	0.397480	−	0.0444396i
$667$	1254.65			1.88103
$668$		−	177.532i		−	0.265766i
$669$	86.0163	−	96.1691i	0.128574	−	0.143751i
$670$	310.200			0.462986
$671$		0			0
$672$	−158.346	−	141.629i	−0.235634	−	0.210758i
$673$	1169.55			1.73782			0.868910	−	0.494970i	$-0.164821\pi$
$673$	1169.55			1.73782			0.868910	+	0.494970i	$0.164821\pi$
$674$		−	115.698i		−	0.171659i
$675$	127.564	+	90.7589i	0.188984	+	0.134458i
$676$	−276.580			−0.409143
$677$		−	807.137i		−	1.19223i	−0.802901	−	0.596113i	$-0.796711\pi$
$677$		−	807.137i		−	1.19223i	0.802901	−	0.596113i	$-0.203289\pi$
$678$	151.331	−	169.193i	0.223202	−	0.249548i
$679$	214.988			0.316624
$680$		−	184.043i		−	0.270651i
$681$	171.221	+	153.145i	0.251426	+	0.224882i
$682$		0			0
$683$			305.746i			0.447652i	0.974629	+	0.223826i	$0.0718548\pi$
$683$			305.746i			0.447652i	−0.974629	+	0.223826i	$0.928145\pi$
$684$	−93.3738	−	835.161i	−0.136511	−	1.22100i
$685$	−143.499			−0.209488
$686$		−	200.416i		−	0.292152i
$687$	293.548	−	328.197i	0.427290	−	0.477724i
$688$	198.541			0.288577
$689$		−	98.7740i		−	0.143358i
$690$	259.384	+	232.000i	0.375919	+	0.336232i
$691$	−551.193			−0.797675			−0.398838	−	0.917022i	$-0.630586\pi$
$691$	−551.193			−0.797675			−0.398838	+	0.917022i	$0.630586\pi$
$692$			105.605i			0.152608i
$693$		0			0
$694$	−248.024			−0.357384
$695$			935.902i			1.34662i
$696$	663.532	−	741.851i	0.953350	−	1.06588i
$697$	261.580			0.375295
$698$		−	508.200i		−	0.728081i
$699$	−99.2160	−	88.7415i	−0.141940	−	0.126955i
$700$	37.3282			0.0533259
$701$			537.161i			0.766278i	0.923691	+	0.383139i	$0.125157\pi$
$701$			537.161i			0.766278i	−0.923691	+	0.383139i	$0.874843\pi$
$702$	−137.177	+	192.807i	−0.195409	+	0.274653i
$703$	921.187			1.31037
$704$		0			0
$705$	37.6130	−	42.0526i	0.0533518	−	0.0596491i
$706$	308.577			0.437078
$707$			28.7795i			0.0407064i
$708$	−221.976	−	198.541i	−0.313525	−	0.280425i
$709$	−1034.66			−1.45932			−0.729662	−	0.683808i	$-0.760322\pi$
$709$	−1034.66			−1.45932			−0.729662	+	0.683808i	$0.760322\pi$
$710$		−	386.403i		−	0.544230i
$711$	−63.0608	−	564.033i	−0.0886930	−	0.793295i
$712$	−67.6594			−0.0950273
$713$			815.299i			1.14348i
$714$	−25.7508	+	28.7902i	−0.0360655	+	0.0403225i
$715$		0			0
$716$			33.4865i			0.0467688i
$717$	−690.476	−	617.580i	−0.963007	−	0.861340i
$718$	10.7902			0.0150282
$719$			424.348i			0.590192i	0.955468	+	0.295096i	$0.0953517\pi$
$719$			424.348i			0.590192i	−0.955468	+	0.295096i	$0.904648\pi$
$720$	−195.967	+	21.9098i	−0.272177	+	0.0304303i
$721$	0.882786			0.00122439
$722$			607.741i			0.841747i
$723$	−10.7113	+	11.9756i	−0.0148151	+	0.0165638i
$724$	−797.902			−1.10208
$725$			274.815i			0.379055i
$726$		0			0
$727$	−359.580			−0.494609			−0.247304	−	0.968938i	$-0.579545\pi$
$727$	−359.580			−0.494609			−0.247304	+	0.968938i	$0.579545\pi$
$728$			131.646i			0.180832i
$729$	239.000	+	688.709i	0.327846	+	0.944731i
$730$	−271.589			−0.372039
$731$		−	238.249i		−	0.325922i
$732$	164.243	−	183.629i	0.224376	−	0.250860i
$733$	−1082.08			−1.47623			−0.738115	−	0.674675i	$-0.764284\pi$
$733$	−1082.08			−1.47623			−0.738115	+	0.674675i	$0.764284\pi$
$734$		−	494.976i		−	0.674354i
$735$	−435.000	−	389.076i	−0.591837	−	0.529355i
$736$	873.580			1.18693
$737$		0			0
$738$	43.5967	+	389.941i	0.0590742	+	0.528376i
$739$	27.9149			0.0377738			0.0188869	−	0.999822i	$-0.493988\pi$
$739$	27.9149			0.0377738			0.0188869	+	0.999822i	$0.493988\pi$
$740$		−	389.076i		−	0.525778i
$741$	−545.548	+	609.941i	−0.736232	+	0.823132i
$742$	24.1854			0.0325948
$743$			773.145i			1.04057i	0.853992	+	0.520286i	$0.174175\pi$
$743$			773.145i			1.04057i	−0.853992	+	0.520286i	$0.825825\pi$
$744$	482.071	+	431.177i	0.647945	+	0.579539i
$745$	508.272			0.682245
$746$		−	356.472i		−	0.477845i
$747$	−985.528	+	110.185i	−1.31931	+	0.147504i
$748$		0			0
$749$		−	439.442i		−	0.586704i
$750$	−269.915	+	301.774i	−0.359886	+	0.402365i
$751$	−1016.32			−1.35329			−0.676646	−	0.736309i	$-0.736567\pi$
$751$	−1016.32			−1.35329			−0.676646	+	0.736309i	$0.736567\pi$
$752$		−	21.4590i		−	0.0285359i
$753$	625.766	+	559.702i	0.831030	+	0.743296i
$754$	−415.368			−0.550885
$755$			1.97561i			0.00261670i
$756$	141.629	+	100.766i	0.187340	+	0.133288i
$757$	1012.27			1.33722			0.668608	−	0.743615i	$-0.266890\pi$
$757$	1012.27			1.33722			0.668608	+	0.743615i	$0.266890\pi$
$758$			214.354i			0.282790i
$759$		0			0
$760$	954.709			1.25620
$761$			1114.74i			1.46484i	0.680854	+	0.732419i	$0.261609\pi$
$761$			1114.74i			1.46484i	−0.680854	+	0.732419i	$0.738391\pi$
$762$	166.774	+	149.167i	0.218863	+	0.195757i
$763$	−230.322			−0.301864
$764$			743.745i			0.973488i
$765$	26.2918	+	235.161i	0.0343684	+	0.307400i
$766$	37.5441			0.0490132
$767$			290.000i			0.378096i
$768$	342.000	−	382.368i	0.445312	−	0.497875i
$769$	−261.746			−0.340372			−0.170186	−	0.985412i	$-0.554437\pi$
$769$	−261.746			−0.340372			−0.170186	+	0.985412i	$0.554437\pi$
$770$		0			0
$771$	260.807	+	233.272i	0.338270	+	0.302558i
$772$	74.0608			0.0959336
$773$		−	362.080i		−	0.468409i	−0.972187	−	0.234204i	$-0.924751\pi$
$773$		−	362.080i		−	0.468409i	0.972187	−	0.234204i	$-0.0752485\pi$
$774$	355.161	−	39.7082i	0.458864	−	0.0513026i
$775$	−178.580			−0.230426
$776$			701.298i			0.903734i
$777$	−127.023	+	142.016i	−0.163479	+	0.182775i
$778$	386.551			0.496852
$779$			1356.93i			1.74189i
$780$	257.617	+	230.420i	0.330278	+	0.295410i
$781$		0			0
$782$		−	158.833i		−	0.203111i
$783$	−741.851	+	1042.69i	−0.947447	+	1.33166i
$784$	−221.976			−0.283132
$785$		−	184.043i		−	0.234449i
$786$	16.0163	−	17.9067i	0.0203769	−	0.0227821i
$787$	−809.745			−1.02890			−0.514450	−	0.857520i	$-0.672004\pi$
$787$	−809.745			−1.02890			−0.514450	+	0.857520i	$0.672004\pi$
$788$		−	658.185i		−	0.835261i
$789$	−973.988	−	871.161i	−1.23446	−	1.10413i
$790$	276.330			0.349785
$791$			162.371i			0.205273i
$792$		0			0
$793$	−239.902			−0.302525
$794$		−	718.741i		−	0.905216i
$795$	98.7740	−	110.433i	0.124244	−	0.138909i
$796$	59.4439			0.0746783
$797$			773.337i			0.970310i	0.874428	+	0.485155i	$0.161237\pi$
$797$			773.337i			0.970310i	−0.874428	+	0.485155i	$0.838763\pi$
$798$	−149.348	−	133.580i	−0.187152	−	0.167394i
$799$	−25.7508			−0.0322288
$800$			191.346i			0.239183i
$801$	86.4520	−	9.66563i	0.107930	−	0.0120670i
$802$	331.082			0.412820
$803$		0			0
$804$	−424.741	+	474.875i	−0.528285	+	0.590641i
$805$	−248.924			−0.309223
$806$		−	269.915i		−	0.334882i
$807$	−334.839	−	299.489i	−0.414918	−	0.371114i
$808$	−93.8797			−0.116188
$809$			391.662i			0.484131i	0.970260	+	0.242065i	$0.0778249\pi$
$809$			391.662i			0.484131i	−0.970260	+	0.242065i	$0.922175\pi$
$810$	−346.175	+	78.3870i	−0.427377	+	0.0967741i
$811$	−18.3219			−0.0225918			−0.0112959	−	0.999936i	$-0.503596\pi$
$811$	−18.3219			−0.0225918			−0.0112959	+	0.999936i	$0.503596\pi$
$812$			305.115i			0.375758i
$813$	−27.5542	+	30.8065i	−0.0338920	+	0.0378924i
$814$		0			0
$815$			49.1208i			0.0602709i
$816$	67.0820	+	60.0000i	0.0822084	+	0.0735294i
$817$	1235.90			1.51273
$818$		−	544.175i		−	0.665251i
$819$	−18.8065	−	168.210i	−0.0229628	−	0.205385i
$820$	573.118			0.698925
$821$			480.831i			0.585665i	0.956164	+	0.292832i	$0.0945978\pi$
$821$			480.831i			0.585665i	−0.956164	+	0.292832i	$0.905402\pi$
$822$	−65.4953	+	73.2260i	−0.0796780	+	0.0890827i
$823$	−1104.83			−1.34244			−0.671221	−	0.741258i	$-0.734230\pi$
$823$	−1104.83			−1.34244			−0.671221	+	0.741258i	$0.734230\pi$
$824$			2.87968i			0.00349476i
$825$		0			0
$826$	−71.0081			−0.0859663
$827$		−	726.363i		−	0.878310i	−0.898411	−	0.439155i	$-0.855278\pi$
$827$		−	726.363i		−	0.878310i	0.898411	−	0.439155i	$-0.144722\pi$
$828$	−710.322	+	79.4164i	−0.857877	+	0.0959135i
$829$	−77.5805			−0.0935832			−0.0467916	−	0.998905i	$-0.514900\pi$
$829$	−77.5805			−0.0935832			−0.0467916	+	0.998905i	$0.514900\pi$
$830$		−	482.829i		−	0.581721i
$831$	218.269	−	244.033i	0.262659	−	0.293661i
$832$	−113.931			−0.136936
$833$			266.371i			0.319773i
$834$	477.580	+	427.161i	0.572638	+	0.512183i
$835$	−259.313			−0.310554
$836$		0			0
$837$	−677.564	−	482.071i	−0.809515	−	0.575951i
$838$	117.592			0.140324
$839$			283.909i			0.338389i	0.985583	+	0.169195i	$0.0541167\pi$
$839$			283.909i			0.338389i	−0.985583	+	0.169195i	$0.945883\pi$
$840$	−131.646	+	147.184i	−0.156721	+	0.175219i
$841$	−1405.30			−1.67098
$842$			194.033i			0.230442i
$843$	−436.393	−	390.322i	−0.517667	−	0.463015i
$844$	−597.787			−0.708279
$845$			403.989i			0.478093i
$846$	−4.29180	−	38.3870i	−0.00507304	−	0.0453747i
$847$		0			0
$848$		−	56.3525i		−	0.0664535i
$849$	305.836	−	341.935i	0.360231	−	0.402750i
$850$	34.7902			0.0409297
$851$		−	783.489i		−	0.920669i
$852$	591.532	+	529.082i	0.694286	+	0.620988i
$853$	489.447			0.573794			0.286897	−	0.957961i	$-0.407376\pi$
$853$	489.447			0.573794			0.286897	+	0.957961i	$0.407376\pi$
$854$		−	58.7415i		−	0.0687839i
$855$	−1219.88	+	136.387i	−1.42676	+	0.159517i
$856$	1433.47			1.67462
$857$		−	995.112i		−	1.16116i	−0.814204	−	0.580579i	$-0.802826\pi$
$857$		−	995.112i		−	1.16116i	0.814204	−	0.580579i	$-0.197174\pi$
$858$		0			0
$859$	1179.53			1.37315			0.686573	−	0.727061i	$-0.259114\pi$
$859$	1179.53			1.37315			0.686573	+	0.727061i	$0.259114\pi$
$860$		−	522.000i		−	0.606977i
$861$	−209.193	−	187.108i	−0.242966	−	0.217315i
$862$	−355.613			−0.412544
$863$		−	812.486i		−	0.941467i	−0.882275	−	0.470734i	$-0.843989\pi$
$863$		−	812.486i		−	0.941467i	0.882275	−	0.470734i	$-0.156011\pi$
$864$	−516.532	+	726.000i	−0.597838	+	0.840278i
$865$	154.252			0.178326
$866$		−	604.379i		−	0.697897i
$867$	−506.000	+	565.725i	−0.583622	+	0.652509i
$868$	−198.271			−0.228422
$869$		0			0
$870$	−464.395	−	415.368i	−0.533787	−	0.477434i
$871$	620.401			0.712286
$872$		−	751.319i		−	0.861604i
$873$	−100.185	−	896.085i	−0.114760	−	1.02644i
$874$	823.935			0.942717
$875$		−	289.605i		−	0.330977i
$876$	371.872	−	415.766i	0.424512	−	0.474619i
$877$	−1063.14			−1.21225			−0.606124	−	0.795370i	$-0.707276\pi$
$877$	−1063.14			−1.21225			−0.606124	+	0.795370i	$0.707276\pi$
$878$		−	28.9424i		−	0.0329640i
$879$	−994.527	−	889.532i	−1.13143	−	1.01198i
$880$		0			0
$881$			542.138i			0.615366i	0.951489	+	0.307683i	$0.0995537\pi$
$881$			542.138i			0.615366i	−0.951489	+	0.307683i	$0.900446\pi$
$882$	−397.082	+	44.3951i	−0.450206	+	0.0503346i
$883$	596.807			0.675885			0.337943	−	0.941167i	$-0.390269\pi$
$883$	596.807			0.675885			0.337943	+	0.941167i	$0.390269\pi$
$884$		−	157.751i		−	0.178451i
$885$	−290.000	+	324.230i	−0.327684	+	0.366361i
$886$	65.2968			0.0736984
$887$		−	458.741i		−	0.517183i	−0.965987	−	0.258592i	$-0.916742\pi$
$887$		−	458.741i		−	0.517183i	0.965987	−	0.258592i	$-0.0832584\pi$
$888$	−463.262	−	414.354i	−0.521692	−	0.466615i
$889$	−160.049			−0.180032
$890$			42.3545i			0.0475893i
$891$		0			0
$892$	−129.024			−0.144646
$893$		−	133.580i		−	0.149586i
$894$	231.984	−	259.366i	0.259490	−	0.290118i
$895$	48.9122			0.0546505
$896$			255.362i			0.285002i
$897$	518.768	+	464.000i	0.578336	+	0.517280i
$898$	−283.331			−0.315514
$899$		−	1459.69i		−	1.62368i
$900$	−17.3951	−	155.587i	−0.0193279	−	0.172874i
$901$	−67.6231			−0.0750533
$902$		0			0
$903$	−170.420	+	190.535i	−0.188726	+	0.211002i
$904$	−529.659			−0.585906
$905$			1165.46i			1.28780i
$906$	1.00813	+	0.901699i	0.00111273	+	0.000995253i
$907$	49.9512			0.0550730			0.0275365	−	0.999621i	$-0.491234\pi$
$907$	49.9512			0.0550730			0.0275365	+	0.999621i	$0.491234\pi$
$908$		−	229.717i		−	0.252992i
$909$	119.955	−	13.4114i	0.131964	−	0.0147540i
$910$	82.4095			0.0905598
$911$		−	346.591i		−	0.380451i	−0.981740	−	0.190226i	$-0.939078\pi$
$911$		−	346.591i		−	0.380451i	0.981740	−	0.190226i	$-0.0609220\pi$
$912$	−311.246	+	347.984i	−0.341279	+	0.381561i
$913$		0			0
$914$			706.507i			0.772984i
$915$	−268.219	−	239.902i	−0.293136	−	0.262188i
$916$	−440.322			−0.480701
$917$			17.1846i			0.0187401i
$918$	132.000	+	93.9149i	0.143791	+	0.102304i
$919$	837.065			0.910843			0.455421	−	0.890276i	$-0.349489\pi$
$919$	837.065			0.910843			0.455421	+	0.890276i	$0.349489\pi$
$920$		−	812.000i		−	0.882609i
$921$	690.079	−	771.532i	0.749271	−	0.837711i
$922$	−356.322			−0.386466
$923$		−	772.807i		−	0.837277i
$924$		0			0
$925$	171.613			0.185528
$926$			801.137i			0.865158i
$927$	−0.411383	−	3.67952i	−0.000443779	−	0.00396928i
$928$	−1564.04			−1.68539
$929$		−	998.656i		−	1.07498i	−0.843270	−	0.537490i	$-0.819373\pi$
$929$		−	998.656i		−	1.07498i	0.843270	−	0.537490i	$-0.180627\pi$
$930$	269.915	−	301.774i	0.290231	−	0.324488i
$931$	−1381.78			−1.48419
$932$			133.112i			0.142824i
$933$	869.515	+	777.718i	0.931957	+	0.833567i
$934$	−501.690			−0.537141
$935$		0			0
$936$	548.709	−	61.3475i	0.586227	−	0.0655422i
$937$	1026.70			1.09573			0.547864	−	0.836567i	$-0.315441\pi$
$937$	1026.70			1.09573			0.547864	+	0.836567i	$0.315441\pi$
$938$			151.909i			0.161950i
$939$	−391.564	+	437.782i	−0.417001	+	0.466222i
$940$	−56.4195			−0.0600208
$941$		−	1571.48i		−	1.67001i	−0.550240	−	0.835007i	$-0.685464\pi$
$941$		−	1571.48i		−	1.67001i	0.550240	−	0.835007i	$-0.314536\pi$
$942$	−93.9149	−	84.0000i	−0.0996973	−	0.0891720i
$943$	1154.10			1.22386
$944$			165.451i			0.175266i
$945$	147.184	−	206.872i	0.155750	−	0.218912i
$946$		0			0
$947$		−	1622.14i		−	1.71292i	−0.516209	−	0.856462i	$-0.672657\pi$
$947$		−	1622.14i		−	1.71292i	0.516209	−	0.856462i	$-0.327343\pi$
$948$	−378.365	+	423.024i	−0.399119	+	0.446228i
$949$	−543.177			−0.572368
$950$			180.472i			0.189971i
$951$	−1239.52	−	1108.66i	−1.30338	−	1.16578i
$952$	90.1277			0.0946720
$953$		−	319.629i		−	0.335393i	−0.985839	−	0.167696i	$-0.946367\pi$
$953$		−	319.629i		−	0.335393i	0.985839	−	0.167696i	$-0.0536328\pi$
$954$	−11.2705	−	100.807i	−0.0118140	−	0.105667i
$955$	1086.35			1.13754
$956$			926.371i			0.969007i
$957$		0			0
$958$	419.177			0.437555
$959$		−	70.2732i		−	0.0732775i
$960$	−127.379	−	113.931i	−0.132686	−	0.118678i
$961$	−12.4602			−0.0129658
$962$			259.384i			0.269630i
$963$	−1831.63	+	204.782i	−1.90200	+	0.212650i
$964$	16.0670			0.0166670
$965$		−	108.177i		−	0.112101i
$966$	−113.613	+	127.023i	−0.117612	+	0.131494i
$967$	−458.267			−0.473906			−0.236953	−	0.971521i	$-0.576149\pi$
$967$	−458.267			−0.473906			−0.236953	+	0.971521i	$0.576149\pi$
$968$		0			0
$969$	417.580	+	373.495i	0.430940	+	0.385444i
$970$	439.009			0.452586
$971$			1406.56i			1.44857i	0.689502	+	0.724284i	$0.257829\pi$
$971$			1406.56i			1.44857i	−0.689502	+	0.724284i	$0.742171\pi$
$972$	354.000	−	637.279i	0.364198	−	0.655637i
$973$	−458.322			−0.471040
$974$		−	65.9756i		−	0.0677368i
$975$	−101.633	+	113.629i	−0.104239	+	0.116543i
$976$	−136.869			−0.140235
$977$		−	940.699i		−	0.962844i	−0.876489	−	0.481422i	$-0.840120\pi$
$977$		−	940.699i		−	0.962844i	0.876489	−	0.481422i	$-0.159880\pi$
$978$	25.0658	+	22.4195i	0.0256296	+	0.0229238i
$979$		0			0
$980$			583.614i			0.595524i
$981$	107.331	+	960.000i	0.109410	+	0.978593i
$982$	405.226			0.412654
$983$			200.597i			0.204067i	0.994781	+	0.102033i	$0.0325348\pi$
$983$			200.597i			0.204067i	−0.994781	+	0.102033i	$0.967465\pi$
$984$	610.354	−	682.397i	0.620279	−	0.693493i
$985$	−961.382			−0.976022
$986$			284.371i			0.288408i
$987$	20.5936	+	18.4195i	0.0208649	+	0.0186621i
$988$	818.322			0.828261
$989$		−	1051.16i		−	1.06285i
$990$		0			0
$991$	184.894			0.186573			0.0932867	−	0.995639i	$-0.470263\pi$
$991$	184.894			0.186573			0.0932867	+	0.995639i	$0.470263\pi$
$992$		−	1016.35i		−	1.02454i
$993$	200.839	−	224.545i	0.202255	−	0.226128i
$994$	189.226			0.190368
$995$		−	86.8271i		−	0.0872634i
$996$	739.146	+	661.112i	0.742114	+	0.663767i
$997$	−222.993			−0.223664			−0.111832	−	0.993727i	$-0.535672\pi$
$997$	−222.993			−0.223664			−0.111832	+	0.993727i	$0.535672\pi$
$998$		−	300.741i		−	0.301344i
$999$	651.128	+	463.262i	0.651780	+	0.463726i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.b.g.122.4		4
3.2	odd	2	inner	363.3.b.g.122.1		4
11.2	odd	10		363.3.h.h.323.1		8
11.3	even	5		363.3.h.g.251.2		8
11.4	even	5		363.3.h.g.269.1		8
11.5	even	5		363.3.h.i.245.1		8
11.6	odd	10		363.3.h.h.245.2		8
11.7	odd	10		33.3.h.a.5.2	yes	8
11.8	odd	10		33.3.h.a.20.1	yes	8
11.9	even	5		363.3.h.i.323.2		8
11.10	odd	2		363.3.b.f.122.2		4
33.2	even	10		363.3.h.h.323.2		8
33.5	odd	10		363.3.h.i.245.2		8
33.8	even	10		33.3.h.a.20.2	yes	8
33.14	odd	10		363.3.h.g.251.1		8
33.17	even	10		363.3.h.h.245.1		8
33.20	odd	10		363.3.h.i.323.1		8
33.26	odd	10		363.3.h.g.269.2		8
33.29	even	10		33.3.h.a.5.1	✓	8
33.32	even	2		363.3.b.f.122.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.h.a.5.1	✓	8	33.29	even	10
33.3.h.a.5.2	yes	8	11.7	odd	10
33.3.h.a.20.1	yes	8	11.8	odd	10
33.3.h.a.20.2	yes	8	33.8	even	10
363.3.b.f.122.2		4	11.10	odd	2
363.3.b.f.122.3		4	33.32	even	2
363.3.b.g.122.1		4	3.2	odd	2	inner
363.3.b.g.122.4		4	1.1	even	1	trivial
363.3.h.g.251.1		8	33.14	odd	10
363.3.h.g.251.2		8	11.3	even	5
363.3.h.g.269.1		8	11.4	even	5
363.3.h.g.269.2		8	33.26	odd	10
363.3.h.h.245.1		8	33.17	even	10
363.3.h.h.245.2		8	11.6	odd	10
363.3.h.h.323.1		8	11.2	odd	10
363.3.h.h.323.2		8	33.2	even	10
363.3.h.i.245.1		8	11.5	even	5
363.3.h.i.245.2		8	33.5	odd	10
363.3.h.i.323.1		8	33.20	odd	10
363.3.h.i.323.2		8	11.9	even	5

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-2.00000 + 2.23607i) q^{3} +3.00000 q^{4} -4.38197i q^{5} +(-2.23607 - 2.00000i) q^{6} +2.14590 q^{7} +7.00000i q^{8} +(-1.00000 - 8.94427i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-2.00000 + 2.23607i) q^{3} +3.00000 q^{4} -4.38197i q^{5} +(-2.23607 - 2.00000i) q^{6} +2.14590 q^{7} +7.00000i q^{8} +(-1.00000 - 8.94427i) q^{9} +4.38197 q^{10} +(-6.00000 + 6.70820i) q^{12} +8.76393 q^{13} +2.14590i q^{14} +(9.79837 + 8.76393i) q^{15} +5.00000 q^{16} -6.00000i q^{17} +(8.94427 - 1.00000i) q^{18} +31.1246 q^{19} -13.1459i q^{20} +(-4.29180 + 4.79837i) q^{21} -26.4721i q^{23} +(-15.6525 - 14.0000i) q^{24} +5.79837 q^{25} +8.76393i q^{26} +(22.0000 + 15.6525i) q^{27} +6.43769 q^{28} +47.3951i q^{29} +(-8.76393 + 9.79837i) q^{30} -30.7984 q^{31} +33.0000i q^{32} +6.00000 q^{34} -9.40325i q^{35} +(-3.00000 - 26.8328i) q^{36} +29.5967 q^{37} +31.1246i q^{38} +(-17.5279 + 19.5967i) q^{39} +30.6738 q^{40} +43.5967i q^{41} +(-4.79837 - 4.29180i) q^{42} +39.7082 q^{43} +(-39.1935 + 4.38197i) q^{45} +26.4721 q^{46} -4.29180i q^{47} +(-10.0000 + 11.1803i) q^{48} -44.3951 q^{49} +5.79837i q^{50} +(13.4164 + 12.0000i) q^{51} +26.2918 q^{52} -11.2705i q^{53} +(-15.6525 + 22.0000i) q^{54} +15.0213i q^{56} +(-62.2492 + 69.5967i) q^{57} -47.3951 q^{58} +33.0902i q^{59} +(29.3951 + 26.2918i) q^{60} -27.3738 q^{61} -30.7984i q^{62} +(-2.14590 - 19.1935i) q^{63} -13.0000 q^{64} -38.4033i q^{65} +70.7902 q^{67} -18.0000i q^{68} +(59.1935 + 52.9443i) q^{69} +9.40325 q^{70} -88.1803i q^{71} +(62.6099 - 7.00000i) q^{72} -61.9787 q^{73} +29.5967i q^{74} +(-11.5967 + 12.9656i) q^{75} +93.3738 q^{76} +(-19.5967 - 17.5279i) q^{78} +63.0608 q^{79} -21.9098i q^{80} +(-79.0000 + 17.8885i) q^{81} -43.5967 q^{82} -110.185i q^{83} +(-12.8754 + 14.3951i) q^{84} -26.2918 q^{85} +39.7082i q^{86} +(-105.979 - 94.7902i) q^{87} +9.66563i q^{89} +(-4.38197 - 39.1935i) q^{90} +18.8065 q^{91} -79.4164i q^{92} +(61.5967 - 68.8673i) q^{93} +4.29180 q^{94} -136.387i q^{95} +(-73.7902 - 66.0000i) q^{96} +100.185 q^{97} -44.3951i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{3} + 12 q^{4} + 22 q^{7} - 4 q^{9}+O(q^{10}) \) 4 * q - 8 * q^3 + 12 * q^4 + 22 * q^7 - 4 * q^9	\( 4 q - 8 q^{3} + 12 q^{4} + 22 q^{7} - 4 q^{9} + 22 q^{10} - 24 q^{12} + 44 q^{13} - 10 q^{15} + 20 q^{16} + 44 q^{19} - 44 q^{21} - 26 q^{25} + 88 q^{27} + 66 q^{28} - 44 q^{30} - 74 q^{31} + 24 q^{34} - 12 q^{36} + 20 q^{37} - 88 q^{39} + 154 q^{40} + 30 q^{42} + 132 q^{43} + 40 q^{45} + 88 q^{46} - 40 q^{48} - 30 q^{49} + 132 q^{52} - 88 q^{57} - 42 q^{58} - 30 q^{60} + 132 q^{61} - 22 q^{63} - 52 q^{64} - 12 q^{67} + 40 q^{69} + 136 q^{70} - 154 q^{73} + 52 q^{75} + 132 q^{76} + 20 q^{78} - 110 q^{79} - 316 q^{81} - 76 q^{82} - 132 q^{84} - 132 q^{85} - 330 q^{87} - 22 q^{90} + 272 q^{91} + 148 q^{93} + 44 q^{94} - 42 q^{97}+O(q^{100}) \) 4 * q - 8 * q^3 + 12 * q^4 + 22 * q^7 - 4 * q^9 + 22 * q^10 - 24 * q^12 + 44 * q^13 - 10 * q^15 + 20 * q^16 + 44 * q^19 - 44 * q^21 - 26 * q^25 + 88 * q^27 + 66 * q^28 - 44 * q^30 - 74 * q^31 + 24 * q^34 - 12 * q^36 + 20 * q^37 - 88 * q^39 + 154 * q^40 + 30 * q^42 + 132 * q^43 + 40 * q^45 + 88 * q^46 - 40 * q^48 - 30 * q^49 + 132 * q^52 - 88 * q^57 - 42 * q^58 - 30 * q^60 + 132 * q^61 - 22 * q^63 - 52 * q^64 - 12 * q^67 + 40 * q^69 + 136 * q^70 - 154 * q^73 + 52 * q^75 + 132 * q^76 + 20 * q^78 - 110 * q^79 - 316 * q^81 - 76 * q^82 - 132 * q^84 - 132 * q^85 - 330 * q^87 - 22 * q^90 + 272 * q^91 + 148 * q^93 + 44 * q^94 - 42 * q^97

Introduction

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