LMFDB - Embedded newform 354.3.b.a.119.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,3,Mod(119,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, 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("354.119");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	354.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:	$9.64580135835$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.7
Character	$\chi$	$=$	354.119
Dual form			354.3.b.a.119.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(-1.23071 - 2.73594i) q^{3} -2.00000 q^{4} -5.41438i q^{5} +(-3.86920 + 1.74048i) q^{6} +0.567729 q^{7} +2.82843i q^{8} +(-5.97072 + 6.73428i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(-1.23071 - 2.73594i) q^{3} -2.00000 q^{4} -5.41438i q^{5} +(-3.86920 + 1.74048i) q^{6} +0.567729 q^{7} +2.82843i q^{8} +(-5.97072 + 6.73428i) q^{9} -7.65709 q^{10} -16.7987i q^{11} +(2.46142 + 5.47188i) q^{12} -7.52630 q^{13} -0.802891i q^{14} +(-14.8134 + 6.66352i) q^{15} +4.00000 q^{16} -2.38099i q^{17} +(9.52371 + 8.44387i) q^{18} -18.4248 q^{19} +10.8288i q^{20} +(-0.698709 - 1.55327i) q^{21} -23.7569 q^{22} +17.2798i q^{23} +(7.73840 - 3.48097i) q^{24} -4.31550 q^{25} +10.6438i q^{26} +(25.7728 + 8.04757i) q^{27} -1.13546 q^{28} +18.4177i q^{29} +(9.42364 + 20.9493i) q^{30} +47.0974 q^{31} -5.65685i q^{32} +(-45.9601 + 20.6743i) q^{33} -3.36724 q^{34} -3.07390i q^{35} +(11.9414 - 13.4686i) q^{36} -0.903411 q^{37} +26.0566i q^{38} +(9.26267 + 20.5915i) q^{39} +15.3142 q^{40} +38.6236i q^{41} +(-2.19666 + 0.988124i) q^{42} -43.2414 q^{43} +33.5973i q^{44} +(36.4620 + 32.3277i) q^{45} +24.4373 q^{46} -15.2019i q^{47} +(-4.92283 - 10.9438i) q^{48} -48.6777 q^{49} +6.10304i q^{50} +(-6.51425 + 2.93031i) q^{51} +15.0526 q^{52} -93.8388i q^{53} +(11.3810 - 36.4482i) q^{54} -90.9543 q^{55} +1.60578i q^{56} +(22.6756 + 50.4092i) q^{57} +26.0466 q^{58} -7.68115i q^{59} +(29.6268 - 13.3270i) q^{60} -44.5707 q^{61} -66.6058i q^{62} +(-3.38975 + 3.82325i) q^{63} -8.00000 q^{64} +40.7502i q^{65} +(29.2378 + 64.9974i) q^{66} +50.8627 q^{67} +4.76199i q^{68} +(47.2764 - 21.2664i) q^{69} -4.34715 q^{70} +2.51506i q^{71} +(-19.0474 - 16.8877i) q^{72} -16.9929 q^{73} +1.27762i q^{74} +(5.31112 + 11.8069i) q^{75} +36.8497 q^{76} -9.53710i q^{77} +(29.1207 - 13.0994i) q^{78} -34.1943 q^{79} -21.6575i q^{80} +(-9.70112 - 80.4170i) q^{81} +54.6220 q^{82} -9.89192i q^{83} +(1.39742 + 3.10655i) q^{84} -12.8916 q^{85} +61.1526i q^{86} +(50.3898 - 22.6668i) q^{87} +47.5138 q^{88} -31.7070i q^{89} +(45.7183 - 51.5650i) q^{90} -4.27290 q^{91} -34.5595i q^{92} +(-57.9632 - 128.856i) q^{93} -21.4987 q^{94} +99.7590i q^{95} +(-15.4768 + 6.96194i) q^{96} -96.7353 q^{97} +68.8406i q^{98} +(113.127 + 100.300i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9}+O(q^{10}) $ 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9	$ 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9} - 16 q^{10} + 34 q^{15} + 160 q^{16} + 16 q^{18} + 24 q^{19} - 18 q^{21} - 16 q^{22} - 16 q^{24} - 216 q^{25} - 30 q^{27} - 16 q^{28} - 64 q^{30} + 96 q^{31} + 76 q^{33} + 80 q^{34} + 48 q^{36} - 200 q^{37} - 28 q^{39} + 32 q^{40} + 48 q^{42} - 104 q^{43} + 58 q^{45} + 32 q^{46} + 288 q^{49} - 176 q^{51} - 40 q^{54} + 360 q^{55} + 214 q^{57} - 128 q^{58} - 68 q^{60} - 32 q^{61} - 132 q^{63} - 320 q^{64} - 112 q^{66} - 344 q^{67} + 88 q^{69} + 192 q^{70} - 32 q^{72} + 40 q^{73} + 28 q^{75} - 48 q^{76} + 96 q^{78} + 32 q^{79} + 336 q^{81} - 80 q^{82} + 36 q^{84} + 168 q^{85} - 162 q^{87} + 32 q^{88} + 112 q^{90} + 88 q^{91} - 316 q^{93} - 400 q^{94} + 32 q^{96} - 184 q^{97} - 148 q^{99}+O(q^{100}) $ 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9 - 16 * q^10 + 34 * q^15 + 160 * q^16 + 16 * q^18 + 24 * q^19 - 18 * q^21 - 16 * q^22 - 16 * q^24 - 216 * q^25 - 30 * q^27 - 16 * q^28 - 64 * q^30 + 96 * q^31 + 76 * q^33 + 80 * q^34 + 48 * q^36 - 200 * q^37 - 28 * q^39 + 32 * q^40 + 48 * q^42 - 104 * q^43 + 58 * q^45 + 32 * q^46 + 288 * q^49 - 176 * q^51 - 40 * q^54 + 360 * q^55 + 214 * q^57 - 128 * q^58 - 68 * q^60 - 32 * q^61 - 132 * q^63 - 320 * q^64 - 112 * q^66 - 344 * q^67 + 88 * q^69 + 192 * q^70 - 32 * q^72 + 40 * q^73 + 28 * q^75 - 48 * q^76 + 96 * q^78 + 32 * q^79 + 336 * q^81 - 80 * q^82 + 36 * q^84 + 168 * q^85 - 162 * q^87 + 32 * q^88 + 112 * q^90 + 88 * q^91 - 316 * q^93 - 400 * q^94 + 32 * q^96 - 184 * q^97 - 148 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	−1.23071	−	2.73594i	−0.410236	−	0.911979i
$3$	−1.23071	−	2.73594i	−0.410236	−	0.911979i
$4$	−2.00000			−0.500000
$5$		−	5.41438i		−	1.08288i	−0.840741	−	0.541438i	$-0.817880\pi$
$5$		−	5.41438i		−	1.08288i	0.840741	−	0.541438i	$-0.182120\pi$
$6$	−3.86920	+	1.74048i	−0.644867	+	0.290081i
$7$	0.567729			0.0811042			0.0405521	−	0.999177i	$-0.487088\pi$
$7$	0.567729			0.0811042			0.0405521	+	0.999177i	$0.487088\pi$
$8$			2.82843i			0.353553i
$9$	−5.97072	+	6.73428i	−0.663413	+	0.748254i
$10$	−7.65709			−0.765709
$11$		−	16.7987i		−	1.52715i	−0.645718	−	0.763576i	$-0.723442\pi$
$11$		−	16.7987i		−	1.52715i	0.645718	−	0.763576i	$-0.276558\pi$
$12$	2.46142	+	5.47188i	0.205118	+	0.455990i
$13$	−7.52630			−0.578946			−0.289473	−	0.957186i	$-0.593480\pi$
$13$	−7.52630			−0.578946			−0.289473	+	0.957186i	$0.593480\pi$
$14$		−	0.802891i		−	0.0573493i
$15$	−14.8134	+	6.66352i	−0.987560	+	0.444235i
$16$	4.00000			0.250000
$17$		−	2.38099i		−	0.140059i	−0.997545	−	0.0700293i	$-0.977691\pi$
$17$		−	2.38099i		−	0.140059i	0.997545	−	0.0700293i	$-0.0223093\pi$
$18$	9.52371	+	8.44387i	0.529095	+	0.469104i
$19$	−18.4248			−0.969728			−0.484864	−	0.874590i	$-0.661131\pi$
$19$	−18.4248			−0.969728			−0.484864	+	0.874590i	$0.661131\pi$
$20$			10.8288i			0.541438i
$21$	−0.698709	−	1.55327i	−0.0332719	−	0.0739654i
$22$	−23.7569			−1.07986
$23$			17.2798i			0.751294i	0.926763	+	0.375647i	$0.122580\pi$
$23$			17.2798i			0.751294i	−0.926763	+	0.375647i	$0.877420\pi$
$24$	7.73840	−	3.48097i	0.322433	−	0.145040i
$25$	−4.31550			−0.172620
$26$			10.6438i			0.409376i
$27$	25.7728	+	8.04757i	0.954548	+	0.298058i
$28$	−1.13546			−0.0405521
$29$			18.4177i			0.635094i	0.948243	+	0.317547i	$0.102859\pi$
$29$			18.4177i			0.635094i	−0.948243	+	0.317547i	$0.897141\pi$
$30$	9.42364	+	20.9493i	0.314121	+	0.698311i
$31$	47.0974			1.51927			0.759636	−	0.650349i	$-0.225377\pi$
$31$	47.0974			1.51927			0.759636	+	0.650349i	$0.225377\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−45.9601	+	20.6743i	−1.39273	+	0.626492i
$34$	−3.36724			−0.0990363
$35$		−	3.07390i		−	0.0878258i
$36$	11.9414	−	13.4686i	0.331706	−	0.374127i
$37$	−0.903411			−0.0244165			−0.0122083	−	0.999925i	$-0.503886\pi$
$37$	−0.903411			−0.0244165			−0.0122083	+	0.999925i	$0.503886\pi$
$38$			26.0566i			0.685701i
$39$	9.26267	+	20.5915i	0.237504	+	0.527987i
$40$	15.3142			0.382854
$41$			38.6236i			0.942039i	0.882123	+	0.471019i	$0.156114\pi$
$41$			38.6236i			0.942039i	−0.882123	+	0.471019i	$0.843886\pi$
$42$	−2.19666	+	0.988124i	−0.0523014	+	0.0235268i
$43$	−43.2414			−1.00561			−0.502807	−	0.864398i	$-0.667699\pi$
$43$	−43.2414			−1.00561			−0.502807	+	0.864398i	$0.667699\pi$
$44$			33.5973i			0.763576i
$45$	36.4620	+	32.3277i	0.810266	+	0.718394i
$46$	24.4373			0.531245
$47$		−	15.2019i		−	0.323444i	−0.986836	−	0.161722i	$-0.948295\pi$
$47$		−	15.2019i		−	0.323444i	0.986836	−	0.161722i	$-0.0517048\pi$
$48$	−4.92283	−	10.9438i	−0.102559	−	0.227995i
$49$	−48.6777			−0.993422
$50$			6.10304i			0.122061i
$51$	−6.51425	+	2.93031i	−0.127730	+	0.0574571i
$52$	15.0526			0.289473
$53$		−	93.8388i		−	1.77054i	−0.465074	−	0.885272i	$-0.653972\pi$
$53$		−	93.8388i		−	1.77054i	0.465074	−	0.885272i	$-0.346028\pi$
$54$	11.3810	−	36.4482i	0.210759	−	0.674967i
$55$	−90.9543			−1.65372
$56$			1.60578i			0.0286747i
$57$	22.6756	+	50.4092i	0.397817	+	0.884372i
$58$	26.0466			0.449079
$59$		−	7.68115i		−	0.130189i
$59$		−	7.68115i		−	0.130189i
$60$	29.6268	−	13.3270i	0.493780	−	0.222117i
$61$	−44.5707			−0.730667			−0.365334	−	0.930877i	$-0.619045\pi$
$61$	−44.5707			−0.730667			−0.365334	+	0.930877i	$0.619045\pi$
$62$		−	66.6058i		−	1.07429i
$63$	−3.38975	+	3.82325i	−0.0538056	+	0.0606865i
$64$	−8.00000			−0.125000
$65$			40.7502i			0.626926i
$66$	29.2378	+	64.9974i	0.442997	+	0.984809i
$67$	50.8627			0.759144			0.379572	−	0.925162i	$-0.376071\pi$
$67$	50.8627			0.759144			0.379572	+	0.925162i	$0.376071\pi$
$68$			4.76199i			0.0700293i
$69$	47.2764	−	21.2664i	0.685165	−	0.308208i
$70$	−4.34715			−0.0621022
$71$			2.51506i			0.0354233i	0.999843	+	0.0177117i	$0.00563810\pi$
$71$			2.51506i			0.0354233i	−0.999843	+	0.0177117i	$0.994362\pi$
$72$	−19.0474	−	16.8877i	−0.264548	−	0.234552i
$73$	−16.9929			−0.232779			−0.116389	−	0.993204i	$-0.537132\pi$
$73$	−16.9929			−0.232779			−0.116389	+	0.993204i	$0.537132\pi$
$74$			1.27762i			0.0172651i
$75$	5.31112	+	11.8069i	0.0708149	+	0.157426i
$76$	36.8497			0.484864
$77$		−	9.53710i		−	0.123858i
$78$	29.1207	−	13.0994i	0.373343	−	0.167941i
$79$	−34.1943			−0.432839			−0.216420	−	0.976300i	$-0.569438\pi$
$79$	−34.1943			−0.432839			−0.216420	+	0.976300i	$0.569438\pi$
$80$		−	21.6575i		−	0.270719i
$81$	−9.70112	−	80.4170i	−0.119767	−	0.992802i
$82$	54.6220			0.666122
$83$		−	9.89192i		−	0.119180i	−0.998223	−	0.0595899i	$-0.981021\pi$
$83$		−	9.89192i		−	0.119180i	0.998223	−	0.0595899i	$-0.0189793\pi$
$84$	1.39742	+	3.10655i	0.0166359	+	0.0369827i
$85$	−12.8916			−0.151666
$86$			61.1526i			0.711077i
$87$	50.3898	−	22.6668i	0.579193	−	0.260538i
$88$	47.5138			0.539930
$89$		−	31.7070i		−	0.356259i	−0.984007	−	0.178129i	$-0.942995\pi$
$89$		−	31.7070i		−	0.356259i	0.984007	−	0.178129i	$-0.0570045\pi$
$90$	45.7183	−	51.5650i	0.507981	−	0.572944i
$91$	−4.27290			−0.0469549
$92$		−	34.5595i		−	0.375647i
$93$	−57.9632	−	128.856i	−0.623260	−	1.38554i
$94$	−21.4987			−0.228710
$95$			99.7590i			1.05009i
$96$	−15.4768	+	6.96194i	−0.161217	+	0.0725202i
$97$	−96.7353			−0.997271			−0.498636	−	0.866812i	$-0.666165\pi$
$97$	−96.7353			−0.997271			−0.498636	+	0.866812i	$0.666165\pi$
$98$			68.8406i			0.702456i
$99$	113.127	+	100.300i	1.14270	+	1.01313i
$100$	8.63100			0.0863100
$101$		−	148.001i		−	1.46536i	−0.680574	−	0.732680i	$-0.738269\pi$
$101$		−	148.001i		−	1.46536i	0.680574	−	0.732680i	$-0.261731\pi$
$102$	4.14408	+	9.21255i	0.0406283	+	0.0903191i
$103$	−2.63244			−0.0255577			−0.0127789	−	0.999918i	$-0.504068\pi$
$103$	−2.63244			−0.0255577			−0.0127789	+	0.999918i	$0.504068\pi$
$104$		−	21.2876i		−	0.204688i
$105$	−8.41001	+	3.78308i	−0.0800953	+	0.0360293i
$106$	−132.708			−1.25196
$107$		−	136.244i		−	1.27331i	−0.771148	−	0.636655i	$-0.780317\pi$
$107$		−	136.244i		−	1.27331i	0.771148	−	0.636655i	$-0.219683\pi$
$108$	−51.5456	−	16.0951i	−0.477274	−	0.149029i
$109$	−209.093			−1.91828			−0.959140	−	0.282931i	$-0.908693\pi$
$109$	−209.093			−1.91828			−0.959140	+	0.282931i	$0.908693\pi$
$110$			128.629i			1.16935i
$111$	1.11184	+	2.47168i	0.0100165	+	0.0222674i
$112$	2.27092			0.0202761
$113$		−	142.446i		−	1.26058i	−0.776358	−	0.630292i	$-0.782935\pi$
$113$		−	142.446i		−	1.26058i	0.776358	−	0.630292i	$-0.217065\pi$
$114$	71.2894	−	32.0681i	0.625345	−	0.281299i
$115$	93.5592			0.813558
$116$		−	36.8355i		−	0.317547i
$117$	44.9374	−	50.6842i	0.384080	−	0.433198i
$118$	−10.8628			−0.0920575
$119$		−	1.35176i		−	0.0113593i
$120$	−18.8473	−	41.8986i	−0.157061	−	0.349155i
$121$	−161.195			−1.33219
$122$			63.0325i			0.516660i
$123$	105.672	−	47.5344i	0.859120	−	0.386458i
$124$	−94.1948			−0.759636
$125$		−	111.994i		−	0.895950i
$126$	5.40689	+	4.79383i	0.0429118	+	0.0380463i
$127$	85.4223			0.672617			0.336308	−	0.941752i	$-0.390822\pi$
$127$	85.4223			0.672617			0.336308	+	0.941752i	$0.390822\pi$
$128$			11.3137i			0.0883883i
$129$	53.2176	+	118.306i	0.412539	+	0.917100i
$130$	57.6295			0.443304
$131$		−	162.994i		−	1.24423i	−0.782928	−	0.622113i	$-0.786274\pi$
$131$		−	162.994i		−	1.24423i	0.782928	−	0.622113i	$-0.213726\pi$
$132$	91.9202	−	41.3485i	0.696365	−	0.313246i
$133$	−10.4603			−0.0786490
$134$		−	71.9307i		−	0.536796i
$135$	43.5726	−	139.544i	0.322760	−	1.03366i
$136$	6.73447			0.0495182
$137$			217.549i			1.58795i	0.607953	+	0.793973i	$0.291991\pi$
$137$			217.549i			1.58795i	−0.607953	+	0.793973i	$0.708009\pi$
$138$	−30.0752	−	66.8589i	−0.217936	−	0.484485i
$139$	33.6879			0.242359			0.121180	−	0.992631i	$-0.461332\pi$
$139$	33.6879			0.242359			0.121180	+	0.992631i	$0.461332\pi$
$140$			6.14780i			0.0439129i
$141$	−41.5914	+	18.7091i	−0.294975	+	0.132689i
$142$	3.55683			0.0250481
$143$			126.432i			0.884138i
$144$	−23.8829	+	26.9371i	−0.165853	+	0.187063i
$145$	99.7206			0.687728
$146$			24.0315i			0.164600i
$147$	59.9080	+	133.179i	0.407538	+	0.905980i
$148$	1.80682			0.0122083
$149$		−	9.47872i		−	0.0636156i	−0.999494	−	0.0318078i	$-0.989874\pi$
$149$		−	9.47872i		−	0.0636156i	0.999494	−	0.0318078i	$-0.0101264\pi$
$150$	16.6975	−	7.51106i	0.111317	−	0.0500737i
$151$	117.500			0.778148			0.389074	−	0.921206i	$-0.372795\pi$
$151$	117.500			0.778148			0.389074	+	0.921206i	$0.372795\pi$
$152$		−	52.1133i		−	0.342851i
$153$	16.0343	+	14.2162i	0.104799	+	0.0929166i
$154$	−13.4875			−0.0875811
$155$		−	255.003i		−	1.64518i
$156$	−18.5253	−	41.1830i	−0.118752	−	0.263993i
$157$	68.6863			0.437492			0.218746	−	0.975782i	$-0.429803\pi$
$157$	68.6863			0.437492			0.218746	+	0.975782i	$0.429803\pi$
$158$			48.3580i			0.306064i
$159$	−256.737	+	115.488i	−1.61470	+	0.726341i
$160$	−30.6284			−0.191427
$161$			9.81023i			0.0609331i
$162$	−113.727	+	13.7195i	−0.702017	+	0.0846880i
$163$	51.3210			0.314853			0.157426	−	0.987531i	$-0.449680\pi$
$163$	51.3210			0.314853			0.157426	+	0.987531i	$0.449680\pi$
$164$		−	77.2472i		−	0.471019i
$165$	111.938	+	248.845i	0.678414	+	1.50815i
$166$	−13.9893			−0.0842729
$167$			162.935i			0.975659i	0.872939	+	0.487829i	$0.162211\pi$
$167$			162.935i			0.975659i	−0.872939	+	0.487829i	$0.837789\pi$
$168$	4.39332	−	1.97625i	0.0261507	−	0.0117634i
$169$	−112.355			−0.664822
$170$			18.2315i			0.107244i
$171$	110.009	−	124.078i	0.643330	−	0.725602i
$172$	86.4829			0.502807
$173$			323.325i			1.86893i	0.356055	+	0.934465i	$0.384122\pi$
$173$			323.325i			1.86893i	−0.356055	+	0.934465i	$0.615878\pi$
$174$	−32.0558	−	71.2619i	−0.184229	−	0.409551i
$175$	−2.45004			−0.0140002
$176$		−	67.1947i		−	0.381788i
$177$	−21.0151	+	9.45325i	−0.118730	+	0.0534082i
$178$	−44.8405			−0.251913
$179$		−	179.503i		−	1.00281i	−0.865212	−	0.501406i	$-0.832816\pi$
$179$		−	179.503i		−	1.00281i	0.865212	−	0.501406i	$-0.167184\pi$
$180$	−72.9239	−	64.6554i	−0.405133	−	0.359197i
$181$	90.6080			0.500597			0.250298	−	0.968169i	$-0.419471\pi$
$181$	90.6080			0.500597			0.250298	+	0.968169i	$0.419471\pi$
$182$			6.04279i			0.0332022i
$183$	54.8535	+	121.943i	0.299746	+	0.666354i
$184$	−48.8746			−0.265623
$185$			4.89141i			0.0264401i
$186$	−182.229	+	81.9723i	−0.979728	+	0.440711i
$187$	−39.9975			−0.213891
$188$			30.4038i			0.161722i
$189$	14.6320	+	4.56884i	0.0774178	+	0.0241738i
$190$	141.081			0.742529
$191$		−	194.347i		−	1.01752i	−0.860908	−	0.508761i	$-0.830104\pi$
$191$		−	194.347i		−	1.01752i	0.860908	−	0.508761i	$-0.169896\pi$
$192$	9.84566	+	21.8875i	0.0512795	+	0.113997i
$193$	−142.480			−0.738237			−0.369119	−	0.929382i	$-0.620340\pi$
$193$	−142.480			−0.738237			−0.369119	+	0.929382i	$0.620340\pi$
$194$			136.804i			0.705177i
$195$	111.490	−	50.1516i	0.571744	−	0.257188i
$196$	97.3554			0.496711
$197$		−	326.787i		−	1.65882i	−0.558642	−	0.829409i	$-0.688677\pi$
$197$		−	326.787i		−	1.65882i	0.558642	−	0.829409i	$-0.311323\pi$
$198$	141.846	−	159.986i	0.716392	−	0.808008i
$199$	277.021			1.39206			0.696032	−	0.718011i	$-0.254947\pi$
$199$	277.021			1.39206			0.696032	+	0.718011i	$0.254947\pi$
$200$		−	12.2061i		−	0.0610304i
$201$	−62.5971	−	139.157i	−0.311428	−	0.692324i
$202$	−209.305			−1.03617
$203$			10.4563i			0.0515088i
$204$	13.0285	−	5.86062i	0.0638652	−	0.0287285i
$205$	209.123			1.02011
$206$			3.72284i			0.0180720i
$207$	−116.367	−	103.173i	−0.562159	−	0.498418i
$208$	−30.1052			−0.144736
$209$			309.513i			1.48092i
$210$	5.35008	+	11.8935i	0.0254766	+	0.0566359i
$211$	68.3015			0.323704			0.161852	−	0.986815i	$-0.448253\pi$
$211$	68.3015			0.323704			0.161852	+	0.986815i	$0.448253\pi$
$212$			187.678i			0.885272i
$213$	6.88104	−	3.09530i	0.0323054	−	0.0145319i
$214$	−192.678			−0.900367
$215$			234.126i			1.08896i
$216$	−22.7620	+	72.8965i	−0.105379	+	0.337484i
$217$	26.7386			0.123219
$218$			295.702i			1.35643i
$219$	20.9132	+	46.4914i	0.0954943	+	0.212290i
$220$	181.909			0.826858
$221$			17.9201i			0.0810863i
$222$	3.49548	−	1.57237i	0.0157454	−	0.00708276i
$223$	278.221			1.24763			0.623813	−	0.781574i	$-0.285583\pi$
$223$	278.221			1.24763			0.623813	+	0.781574i	$0.285583\pi$
$224$		−	3.21156i		−	0.0143373i
$225$	25.7666	−	29.0618i	0.114518	−	0.129163i
$226$	−201.449			−0.891368
$227$			131.781i			0.580534i	0.956946	+	0.290267i	$0.0937441\pi$
$227$			131.781i			0.580534i	−0.956946	+	0.290267i	$0.906256\pi$
$228$	−45.3512	−	100.818i	−0.198909	−	0.442186i
$229$	−329.027			−1.43680			−0.718399	−	0.695631i	$-0.755125\pi$
$229$	−329.027			−1.43680			−0.718399	+	0.695631i	$0.755125\pi$
$230$		−	132.313i		−	0.575273i
$231$	−26.0929	+	11.7374i	−0.112956	+	0.0508112i
$232$	−52.0932			−0.224540
$233$			96.0787i			0.412355i	0.978515	+	0.206177i	$0.0661024\pi$
$233$			96.0787i			0.412355i	−0.978515	+	0.206177i	$0.933898\pi$
$234$	−71.6783	−	63.5510i	−0.306317	−	0.271586i
$235$	−82.3087			−0.350250
$236$			15.3623i			0.0650945i
$237$	42.0832	+	93.5535i	0.177566	+	0.394740i
$238$	−1.91168			−0.00803226
$239$		−	199.643i		−	0.835328i	−0.908602	−	0.417664i	$-0.862849\pi$
$239$		−	199.643i		−	0.835328i	0.908602	−	0.417664i	$-0.137151\pi$
$240$	−59.2536	+	26.6541i	−0.246890	+	0.111059i
$241$	−333.879			−1.38539			−0.692695	−	0.721231i	$-0.743577\pi$
$241$	−333.879			−1.38539			−0.692695	+	0.721231i	$0.743577\pi$
$242$			227.964i			0.942001i
$243$	−208.077	+	125.511i	−0.856282	+	0.516508i
$244$	89.1414			0.365334
$245$			263.559i			1.07575i
$246$	−67.2237	−	149.442i	−0.273267	−	0.607490i
$247$	138.671			0.561420
$248$			133.212i			0.537144i
$249$	−27.0637	+	12.1741i	−0.108690	+	0.0488919i
$250$	−158.383			−0.633532
$251$			393.676i			1.56843i	0.620489	+	0.784215i	$0.286934\pi$
$251$			393.676i			1.56843i	−0.620489	+	0.784215i	$0.713066\pi$
$252$	6.77950	−	7.64650i	0.0269028	−	0.0303433i
$253$	290.277			1.14734
$254$		−	120.805i		−	0.475612i
$255$	15.8658	+	35.2706i	0.0622189	+	0.138316i
$256$	16.0000			0.0625000
$257$		−	269.563i		−	1.04888i	−0.851447	−	0.524441i	$-0.824274\pi$
$257$		−	269.563i		−	1.04888i	0.851447	−	0.524441i	$-0.175726\pi$
$258$	167.310	−	75.2610i	0.648488	−	0.291709i
$259$	−0.512893			−0.00198028
$260$		−	81.5004i		−	0.313463i
$261$	−124.030	−	109.967i	−0.475211	−	0.421330i
$262$	−230.508			−0.879800
$263$			390.523i			1.48488i	0.669914	+	0.742439i	$0.266331\pi$
$263$			390.523i			1.48488i	−0.669914	+	0.742439i	$0.733669\pi$
$264$	−58.4756	−	129.995i	−0.221499	−	0.492405i
$265$	−508.079			−1.91728
$266$			14.7931i			0.0556132i
$267$	−86.7485	+	39.0221i	−0.324901	+	0.146150i
$268$	−101.725			−0.379572
$269$			237.530i			0.883013i	0.897258	+	0.441506i	$0.145556\pi$
$269$			237.530i			0.883013i	−0.897258	+	0.441506i	$0.854444\pi$
$270$	−197.345	−	61.6210i	−0.730906	−	0.228226i
$271$	−168.525			−0.621864			−0.310932	−	0.950432i	$-0.600641\pi$
$271$	−168.525			−0.621864			−0.310932	+	0.950432i	$0.600641\pi$
$272$		−	9.52398i		−	0.0350146i
$273$	5.25869	+	11.6904i	0.0192626	+	0.0428219i
$274$	307.660			1.12285
$275$			72.4946i			0.263617i
$276$	−94.5528	+	42.5327i	−0.342582	+	0.154104i
$277$	−118.529			−0.427901			−0.213951	−	0.976844i	$-0.568633\pi$
$277$	−118.529			−0.427901			−0.213951	+	0.976844i	$0.568633\pi$
$278$		−	47.6419i		−	0.171374i
$279$	−281.205	+	317.167i	−1.00790	+	1.13680i
$280$	8.69431			0.0310511
$281$		−	118.979i		−	0.423412i	−0.977333	−	0.211706i	$-0.932098\pi$
$281$		−	118.979i		−	0.423412i	0.977333	−	0.211706i	$-0.0679019\pi$
$282$	26.4586	+	58.8191i	0.0938249	+	0.208578i
$283$	505.422			1.78594			0.892972	−	0.450112i	$-0.148616\pi$
$283$	505.422			1.78594			0.892972	+	0.450112i	$0.148616\pi$
$284$		−	5.03012i		−	0.0177117i
$285$	272.934	−	122.774i	0.957665	−	0.430787i
$286$	178.801			0.625180
$287$			21.9278i			0.0764033i
$288$	38.0949	+	33.7755i	0.132274	+	0.117276i
$289$	283.331			0.980384
$290$		−	141.026i		−	0.486297i
$291$	119.053	+	264.662i	0.409117	+	0.909491i
$292$	33.9857			0.116389
$293$		−	7.68630i		−	0.0262331i	−0.999914	−	0.0131166i	$-0.995825\pi$
$293$		−	7.68630i		−	0.0262331i	0.999914	−	0.0131166i	$-0.00417525\pi$
$294$	188.344	−	84.7227i	0.640625	−	0.288173i
$295$	−41.5886			−0.140978
$296$		−	2.55523i		−	0.00863254i
$297$	135.188	−	432.948i	0.455180	−	1.45774i
$298$	−13.4049			−0.0449830
$299$		−	130.053i		−	0.434959i
$300$	−10.6222	−	23.6139i	−0.0354075	−	0.0787129i
$301$	−24.5494			−0.0815596
$302$		−	166.171i		−	0.550234i
$303$	−404.922	+	182.146i	−1.33638	+	0.601143i
$304$	−73.6993			−0.242432
$305$			241.323i			0.791222i
$306$	20.1048	−	22.6759i	0.0657020	−	0.0741043i
$307$	440.471			1.43476			0.717380	−	0.696683i	$-0.245341\pi$
$307$	440.471			1.43476			0.717380	+	0.696683i	$0.245341\pi$
$308$			19.0742i			0.0619292i
$309$	3.23977	+	7.20220i	0.0104847	+	0.0233081i
$310$	−360.629			−1.16332
$311$		−	106.347i		−	0.341952i	−0.985275	−	0.170976i	$-0.945308\pi$
$311$		−	106.347i		−	0.341952i	0.985275	−	0.170976i	$-0.0546920\pi$
$312$	−58.2415	+	26.1988i	−0.186671	+	0.0839705i
$313$	487.886			1.55874			0.779371	−	0.626563i	$-0.215539\pi$
$313$	487.886			1.55874			0.779371	+	0.626563i	$0.215539\pi$
$314$		−	97.1371i		−	0.309354i
$315$	20.7005	+	18.3534i	0.0657160	+	0.0582647i
$316$	68.3886			0.216420
$317$		−	235.119i		−	0.741701i	−0.928693	−	0.370850i	$-0.879066\pi$
$317$		−	235.119i		−	0.741701i	0.928693	−	0.370850i	$-0.120934\pi$
$318$	163.325	+	363.081i	0.513600	+	1.14176i
$319$	309.393			0.969885
$320$			43.3150i			0.135359i
$321$	−372.756	+	167.677i	−1.16123	+	0.522358i
$322$	13.8738			0.0430862
$323$			43.8694i			0.135819i
$324$	19.4022	+	160.834i	0.0598835	+	0.496401i
$325$	32.4797			0.0999376
$326$		−	72.5788i		−	0.222634i
$327$	257.332	+	572.064i	0.786948	+	1.74943i
$328$	−109.244			−0.333061
$329$		−	8.63056i		−	0.0262327i
$330$	351.921	−	158.305i	1.06643	−	0.479711i
$331$	−362.206			−1.09428			−0.547139	−	0.837042i	$-0.684283\pi$
$331$	−362.206			−1.09428			−0.547139	+	0.837042i	$0.684283\pi$
$332$			19.7838i			0.0595899i
$333$	5.39401	−	6.08383i	0.0161982	−	0.0182697i
$334$	230.425			0.689895
$335$		−	275.390i		−	0.822059i
$336$	−2.79484	−	6.21309i	−0.00831797	−	0.0184913i
$337$	441.041			1.30873			0.654363	−	0.756180i	$-0.272937\pi$
$337$	441.041			1.30873			0.654363	+	0.756180i	$0.272937\pi$
$338$			158.894i			0.470100i
$339$	−389.724	+	175.310i	−1.14963	+	0.517137i
$340$	25.7832			0.0758330
$341$		−	791.174i		−	2.32016i
$342$	−175.473	−	155.577i	−0.513078	−	0.454903i
$343$	−55.4545			−0.161675
$344$		−	122.305i		−	0.355539i
$345$	−115.144	−	255.972i	−0.333751	−	0.741949i
$346$	457.250			1.32153
$347$			36.0053i			0.103762i	0.998653	+	0.0518809i	$0.0165216\pi$
$347$			36.0053i			0.103762i	−0.998653	+	0.0518809i	$0.983478\pi$
$348$	−100.780	+	45.3337i	−0.289596	+	0.130269i
$349$	−298.446			−0.855147			−0.427573	−	0.903981i	$-0.640631\pi$
$349$	−298.446			−0.855147			−0.427573	+	0.903981i	$0.640631\pi$
$350$			3.46487i			0.00989964i
$351$	−193.974	−	60.5684i	−0.552631	−	0.172560i
$352$	−95.0276			−0.269965
$353$		−	165.081i		−	0.467652i	−0.972278	−	0.233826i	$-0.924875\pi$
$353$		−	165.081i		−	0.467652i	0.972278	−	0.233826i	$-0.0751247\pi$
$354$	13.3689	+	29.7199i	0.0377653	+	0.0839545i
$355$	13.6175			0.0383591
$356$			63.4140i			0.178129i
$357$	−3.69833	+	1.66362i	−0.0103595	+	0.00466001i
$358$	−253.856			−0.709095
$359$		−	705.133i		−	1.96416i	−0.188468	−	0.982079i	$-0.560352\pi$
$359$		−	705.133i		−	1.96416i	0.188468	−	0.982079i	$-0.439648\pi$
$360$	−91.4366	+	103.130i	−0.253991	+	0.286472i
$361$	−21.5257			−0.0596279
$362$		−	128.139i		−	0.353975i
$363$	198.384	+	441.020i	0.546513	+	1.21493i
$364$	8.54580			0.0234775
$365$			92.0058i			0.252071i
$366$	172.453	−	77.5746i	0.471183	−	0.211952i
$367$	−522.266			−1.42307			−0.711534	−	0.702652i	$-0.751999\pi$
$367$	−522.266			−1.42307			−0.711534	+	0.702652i	$0.751999\pi$
$368$			69.1191i			0.187824i
$369$	−260.102	−	230.610i	−0.704884	−	0.624961i
$370$	6.91750			0.0186959
$371$		−	53.2750i		−	0.143599i
$372$	115.926	+	257.711i	0.311630	+	0.692772i
$373$	−297.231			−0.796865			−0.398433	−	0.917198i	$-0.630446\pi$
$373$	−297.231			−0.796865			−0.398433	+	0.917198i	$0.630446\pi$
$374$			56.5651i			0.151243i
$375$	−306.408	+	137.832i	−0.817088	+	0.367551i
$376$	42.9974			0.114355
$377$		−	138.617i		−	0.367685i
$378$	6.46132	−	20.6927i	0.0170934	−	0.0547427i
$379$	426.001			1.12401			0.562007	−	0.827132i	$-0.310029\pi$
$379$	426.001			1.12401			0.562007	+	0.827132i	$0.310029\pi$
$380$		−	199.518i		−	0.525047i
$381$	−105.130	−	233.710i	−0.275932	−	0.613413i
$382$	−274.848			−0.719496
$383$		−	50.1260i		−	0.130877i	−0.997857	−	0.0654386i	$-0.979155\pi$
$383$		−	50.1260i		−	0.130877i	0.997857	−	0.0654386i	$-0.0208447\pi$
$384$	30.9536	−	13.9239i	0.0806084	−	0.0362601i
$385$	−51.6375			−0.134123
$386$			201.497i			0.522013i
$387$	258.182	−	291.200i	0.667138	−	0.752455i
$388$	193.471			0.498636
$389$		−	353.735i		−	0.909345i	−0.890659	−	0.454672i	$-0.849756\pi$
$389$		−	353.735i		−	0.909345i	0.890659	−	0.454672i	$-0.150244\pi$
$390$	−70.9251	−	157.671i	−0.181859	−	0.404284i
$391$	41.1430			0.105225
$392$		−	137.681i		−	0.351228i
$393$	−445.940	+	200.598i	−1.13471	+	0.510426i
$394$	−462.147			−1.17296
$395$			185.141i			0.468711i
$396$	−226.254	−	200.600i	−0.571348	−	0.506566i
$397$	414.405			1.04384			0.521920	−	0.852994i	$-0.325216\pi$
$397$	414.405			1.04384			0.521920	+	0.852994i	$0.325216\pi$
$398$		−	391.766i		−	0.984337i
$399$	12.8736	+	28.6188i	0.0322647	+	0.0717263i
$400$	−17.2620			−0.0431550
$401$		−	273.394i		−	0.681780i	−0.940103	−	0.340890i	$-0.889272\pi$
$401$		−	273.394i		−	0.681780i	0.940103	−	0.340890i	$-0.110728\pi$
$402$	−196.798	+	88.5257i	−0.489547	+	0.220213i
$403$	−354.469			−0.879576
$404$			296.003i			0.732680i
$405$	−435.408	+	52.5256i	−1.07508	+	0.129693i
$406$	14.7874			0.0364222
$407$			15.1761i			0.0372877i
$408$	−8.28817	−	18.4251i	−0.0203141	−	0.0451595i
$409$	−227.128			−0.555326			−0.277663	−	0.960679i	$-0.589560\pi$
$409$	−227.128			−0.555326			−0.277663	+	0.960679i	$0.589560\pi$
$410$		−	295.744i		−	0.721327i
$411$	595.200	−	267.739i	1.44817	−	0.651433i
$412$	5.26489			0.0127789
$413$		−	4.36081i		−	0.0105589i
$414$	−145.908	+	164.568i	−0.352435	+	0.397506i
$415$	−53.5586			−0.129057
$416$			42.5752i			0.102344i
$417$	−41.4600	−	92.1681i	−0.0994244	−	0.221027i
$418$	437.717			1.04717
$419$			579.629i			1.38336i	0.722203	+	0.691681i	$0.243130\pi$
$419$			579.629i			1.38336i	−0.722203	+	0.691681i	$0.756870\pi$
$420$	16.8200	−	7.56615i	0.0400477	−	0.0180147i
$421$	615.030			1.46088			0.730440	−	0.682977i	$-0.239315\pi$
$421$	615.030			1.46088			0.730440	+	0.682977i	$0.239315\pi$
$422$		−	96.5929i		−	0.228893i
$423$	102.374	+	90.7661i	0.242018	+	0.214577i
$424$	265.416			0.625982
$425$			10.2752i			0.0241769i
$426$	−4.37742	−	9.73126i	−0.0102756	−	0.0228433i
$427$	−25.3041			−0.0592602
$428$			272.488i			0.636655i
$429$	345.909	−	155.601i	0.806315	−	0.362705i
$430$	331.103			0.770008
$431$		−	241.063i		−	0.559311i	−0.960100	−	0.279655i	$-0.909780\pi$
$431$		−	241.063i		−	0.559311i	0.960100	−	0.279655i	$-0.0902202\pi$
$432$	103.091	+	32.1903i	0.238637	+	0.0745145i
$433$	776.713			1.79379			0.896897	−	0.442240i	$-0.145816\pi$
$433$	776.713			1.79379			0.896897	+	0.442240i	$0.145816\pi$
$434$		−	37.8141i		−	0.0871292i
$435$	−122.727	−	272.829i	−0.282131	−	0.627194i
$436$	418.185			0.959140
$437$		−	318.377i		−	0.728551i
$438$	65.7488	−	29.5758i	0.150111	−	0.0675246i
$439$	−128.081			−0.291757			−0.145878	−	0.989303i	$-0.546601\pi$
$439$	−128.081			−0.291757			−0.145878	+	0.989303i	$0.546601\pi$
$440$		−	257.258i		−	0.584677i
$441$	290.641	−	327.809i	0.659049	−	0.743332i
$442$	25.3428			0.0573367
$443$			369.478i			0.834036i	0.908898	+	0.417018i	$0.136925\pi$
$443$			369.478i			0.834036i	−0.908898	+	0.417018i	$0.863075\pi$
$444$	−2.22367	−	4.94335i	−0.00500827	−	0.0111337i
$445$	−171.674			−0.385784
$446$		−	393.463i		−	0.882205i
$447$	−25.9332	+	11.6655i	−0.0580161	+	0.0260974i
$448$	−4.54184			−0.0101380
$449$		−	517.701i		−	1.15301i	−0.817094	−	0.576504i	$-0.804416\pi$
$449$		−	517.701i		−	1.15301i	0.817094	−	0.576504i	$-0.195584\pi$
$450$	−41.0996	−	36.4395i	−0.0913324	−	0.0809766i
$451$	648.825			1.43864
$452$			284.892i			0.630292i
$453$	−144.609	−	321.474i	−0.319224	−	0.709655i
$454$	186.367			0.410499
$455$			23.1351i			0.0508464i
$456$	−142.579	+	64.1362i	−0.312673	+	0.140650i
$457$	403.089			0.882032			0.441016	−	0.897499i	$-0.354618\pi$
$457$	403.089			0.882032			0.441016	+	0.897499i	$0.354618\pi$
$458$			465.314i			1.01597i
$459$	19.1612	−	61.3649i	0.0417456	−	0.133693i
$460$	−187.118			−0.406779
$461$			74.7615i			0.162172i	0.996707	+	0.0810862i	$0.0258389\pi$
$461$			74.7615i			0.162172i	−0.996707	+	0.0810862i	$0.974161\pi$
$462$	16.5992	+	36.9009i	0.0359289	+	0.0798722i
$463$	−403.795			−0.872126			−0.436063	−	0.899916i	$-0.643628\pi$
$463$	−403.795			−0.872126			−0.436063	+	0.899916i	$0.643628\pi$
$464$			73.6709i			0.158774i
$465$	−697.673	+	313.835i	−1.50037	+	0.674913i
$466$	135.876			0.291579
$467$		−	406.126i		−	0.869649i	−0.900515	−	0.434825i	$-0.856810\pi$
$467$		−	406.126i		−	0.869649i	0.900515	−	0.434825i	$-0.143190\pi$
$468$	−89.8747	+	101.368i	−0.192040	+	0.216599i
$469$	28.8762			0.0615698
$470$			116.402i			0.247664i
$471$	−84.5328	−	187.921i	−0.179475	−	0.398984i
$472$	21.7256			0.0460287
$473$			726.398i			1.53573i
$474$	132.305	−	59.5146i	0.279124	−	0.125558i
$475$	79.5123			0.167394
$476$			2.70352i			0.00567967i
$477$	631.937	+	560.285i	1.32482	+	1.17460i
$478$	−282.338			−0.590666
$479$		−	660.213i		−	1.37832i	−0.724611	−	0.689158i	$-0.757981\pi$
$479$		−	660.213i		−	1.37832i	0.724611	−	0.689158i	$-0.242019\pi$
$480$	37.6946	+	83.7973i	0.0785303	+	0.174578i
$481$	6.79934			0.0141358
$482$			472.176i			0.979619i
$483$	26.8402	−	12.0735i	0.0555698	−	0.0249970i
$484$	322.390			0.666096
$485$			523.761i			1.07992i
$486$	177.500	+	294.265i	0.365226	+	0.605483i
$487$	300.220			0.616468			0.308234	−	0.951311i	$-0.400262\pi$
$487$	300.220			0.616468			0.308234	+	0.951311i	$0.400262\pi$
$488$		−	126.065i		−	0.258330i
$489$	−63.1611	−	140.411i	−0.129164	−	0.287139i
$490$	372.729			0.760672
$491$		−	704.055i		−	1.43392i	−0.697114	−	0.716961i	$-0.745533\pi$
$491$		−	704.055i		−	1.43392i	0.697114	−	0.716961i	$-0.254467\pi$
$492$	−211.344	+	95.0687i	−0.429560	+	0.193229i
$493$	43.8525			0.0889503
$494$		−	196.110i		−	0.396984i
$495$	543.062	−	612.512i	1.09710	−	1.23740i
$496$	188.390			0.379818
$497$			1.42787i			0.00287298i
$498$	17.2167	+	38.2738i	0.0345718	+	0.0768551i
$499$	−670.812			−1.34431			−0.672156	−	0.740410i	$-0.734632\pi$
$499$	−670.812			−1.34431			−0.672156	+	0.740410i	$0.734632\pi$
$500$			223.987i			0.447975i
$501$	445.780	−	200.525i	0.889781	−	0.400250i
$502$	556.742			1.10905
$503$		−	365.392i		−	0.726426i	−0.931706	−	0.363213i	$-0.881680\pi$
$503$		−	365.392i		−	0.726426i	0.931706	−	0.363213i	$-0.118320\pi$
$504$	−10.8138	−	9.58766i	−0.0214559	−	0.0190231i
$505$	−801.335			−1.58680
$506$		−	410.514i		−	0.811292i
$507$	138.276	+	307.396i	0.272734	+	0.606304i
$508$	−170.845			−0.336308
$509$			640.800i			1.25894i	0.777025	+	0.629470i	$0.216728\pi$
$509$			640.800i			1.25894i	−0.777025	+	0.629470i	$0.783272\pi$
$510$	49.8802	−	22.4376i	0.0978044	−	0.0439954i
$511$	−9.64734			−0.0188793
$512$		−	22.6274i		−	0.0441942i
$513$	−474.859	−	148.275i	−0.925652	−	0.289035i
$514$	−381.219			−0.741671
$515$			14.2530i			0.0276758i
$516$	−106.435	−	236.612i	−0.206270	−	0.458550i
$517$	−255.371			−0.493948
$518$			0.725340i			0.00140027i
$519$	884.597	−	397.919i	1.70443	−	0.766702i
$520$	−115.259			−0.221652
$521$			132.848i			0.254986i	0.991839	+	0.127493i	$0.0406930\pi$
$521$			132.848i			0.254986i	−0.991839	+	0.127493i	$0.959307\pi$
$522$	−155.517	+	175.405i	−0.297925	+	0.336025i
$523$	244.702			0.467882			0.233941	−	0.972251i	$-0.424838\pi$
$523$	244.702			0.467882			0.233941	+	0.972251i	$0.424838\pi$
$524$			325.987i			0.622113i
$525$	3.01528	+	6.70314i	0.00574339	+	0.0127679i
$526$	552.283			1.04997
$527$		−	112.139i		−	0.212787i
$528$	−183.840	+	82.6970i	−0.348183	+	0.156623i
$529$	230.410			0.435557
$530$			718.532i			1.35572i
$531$	51.7270	+	45.8619i	0.0974143	+	0.0863690i
$532$	20.9206			0.0393245
$533$		−	290.693i		−	0.545389i
$534$	55.1856	+	122.681i	0.103344	+	0.229739i
$535$	−737.678			−1.37884
$536$			143.861i			0.268398i
$537$	−491.110	+	220.916i	−0.914544	+	0.411390i
$538$	335.919			0.624384
$539$			817.720i			1.51711i
$540$	−87.1452	+	279.087i	−0.161380	+	0.516828i
$541$	−132.343			−0.244626			−0.122313	−	0.992492i	$-0.539031\pi$
$541$	−132.343			−0.244626			−0.122313	+	0.992492i	$0.539031\pi$
$542$			238.331i			0.439725i
$543$	−111.512	−	247.898i	−0.205363	−	0.456534i
$544$	−13.4689			−0.0247591
$545$			1132.11i			2.07726i
$546$	16.5327	−	7.43691i	0.0302797	−	0.0136207i
$547$	−35.6101			−0.0651007			−0.0325503	−	0.999470i	$-0.510363\pi$
$547$	−35.6101			−0.0651007			−0.0325503	+	0.999470i	$0.510363\pi$
$548$		−	435.097i		−	0.793973i
$549$	266.119	−	300.152i	0.484734	−	0.546724i
$550$	102.523			0.186405
$551$		−	339.344i		−	0.615868i
$552$	60.1503	+	133.718i	0.108968	+	0.242242i
$553$	−19.4131			−0.0351051
$554$			167.625i			0.302572i
$555$	13.3826	−	6.01990i	0.0241128	−	0.0108467i
$556$	−67.3758			−0.121180
$557$		−	667.191i		−	1.19783i	−0.800813	−	0.598914i	$-0.795599\pi$
$557$		−	667.191i		−	1.19783i	0.800813	−	0.598914i	$-0.204401\pi$
$558$	448.542	+	397.684i	0.803839	+	0.712696i
$559$	325.448			0.582196
$560$		−	12.2956i		−	0.0219564i
$561$	49.2253	+	109.431i	0.0877456	+	0.195064i
$562$	−168.261			−0.299398
$563$			534.879i			0.950051i	0.879972	+	0.475025i	$0.157561\pi$
$563$			534.879i			0.950051i	−0.879972	+	0.475025i	$0.842439\pi$
$564$	83.1828	−	37.4182i	0.147487	−	0.0663443i
$565$	−771.257			−1.36506
$566$		−	714.775i		−	1.26285i
$567$	−5.50761	−	45.6551i	−0.00971360	−	0.0805204i
$568$	−7.11366			−0.0125240
$569$			216.331i			0.380195i	0.981765	+	0.190097i	$0.0608804\pi$
$569$			216.331i			0.380195i	−0.981765	+	0.190097i	$0.939120\pi$
$570$	−173.629	−	385.988i	−0.304612	−	0.677171i
$571$	145.733			0.255224			0.127612	−	0.991824i	$-0.459269\pi$
$571$	145.733			0.255224			0.127612	+	0.991824i	$0.459269\pi$
$572$		−	252.863i		−	0.442069i
$573$	−531.720	+	239.184i	−0.927958	+	0.417424i
$574$	31.0105			0.0540253
$575$		−	74.5708i		−	0.129688i
$576$	47.7657	−	53.8743i	0.0829266	−	0.0935317i
$577$	574.283			0.995290			0.497645	−	0.867381i	$-0.334198\pi$
$577$	574.283			0.995290			0.497645	+	0.867381i	$0.334198\pi$
$578$		−	400.690i		−	0.693236i
$579$	175.351	+	389.816i	0.302852	+	0.673257i
$580$	−199.441			−0.343864
$581$		−	5.61594i		−	0.00966598i
$582$	374.288	−	168.366i	0.643107	−	0.289289i
$583$	−1576.37			−2.70389
$584$		−	48.0631i		−	0.0822998i
$585$	−274.423	−	243.308i	−0.469100	−	0.415911i
$586$	−10.8701			−0.0185496
$587$			160.327i			0.273129i	0.990631	+	0.136565i	$0.0436061\pi$
$587$			160.327i			0.273129i	−0.990631	+	0.136565i	$0.956394\pi$
$588$	−119.816	−	266.358i	−0.203769	−	0.452990i
$589$	−867.762			−1.47328
$590$			58.8152i			0.0996868i
$591$	−894.069	+	402.180i	−1.51281	+	0.680507i
$592$	−3.61364			−0.00610413
$593$			1171.13i			1.97492i	0.157881	+	0.987458i	$0.449534\pi$
$593$			1171.13i			1.97492i	−0.157881	+	0.987458i	$0.550466\pi$
$594$	−612.282	−	191.185i	−1.03078	−	0.321861i
$595$	−7.31895			−0.0123007
$596$			18.9574i			0.0318078i
$597$	−340.931	−	757.911i	−0.571074	−	1.26953i
$598$	−183.922			−0.307562
$599$			1086.98i			1.81466i	0.420422	+	0.907329i	$0.361882\pi$
$599$			1086.98i			1.81466i	−0.420422	+	0.907329i	$0.638118\pi$
$600$	−33.3951	+	15.0221i	−0.0556584	+	0.0250369i
$601$	−499.604			−0.831287			−0.415644	−	0.909528i	$-0.636444\pi$
$601$	−499.604			−0.831287			−0.415644	+	0.909528i	$0.636444\pi$
$602$			34.7181i			0.0576713i
$603$	−303.686	+	342.524i	−0.503626	+	0.568032i
$604$	−235.001			−0.389074
$605$			872.771i			1.44260i
$606$	257.594	+	572.647i	0.425072	+	0.944962i
$607$	128.397			0.211527			0.105764	−	0.994391i	$-0.466271\pi$
$607$	128.397			0.211527			0.105764	+	0.994391i	$0.466271\pi$
$608$			104.227i			0.171425i
$609$	28.6078	−	12.8686i	0.0469750	−	0.0211308i
$610$	341.282			0.559478
$611$			114.414i			0.187257i
$612$	−32.0686	−	28.4325i	−0.0523996	−	0.0464583i
$613$	−440.167			−0.718054			−0.359027	−	0.933327i	$-0.616891\pi$
$613$	−440.167			−0.718054			−0.359027	+	0.933327i	$0.616891\pi$
$614$		−	622.920i		−	1.01453i
$615$	−257.369	−	572.147i	−0.418486	−	0.930320i
$616$	26.9750			0.0437906
$617$			514.943i			0.834591i	0.908771	+	0.417296i	$0.137022\pi$
$617$			514.943i			0.834591i	−0.908771	+	0.417296i	$0.862978\pi$
$618$	10.1855	−	4.58173i	0.0164813	−	0.00741380i
$619$	−555.138			−0.896830			−0.448415	−	0.893825i	$-0.648011\pi$
$619$	−555.138			−0.896830			−0.448415	+	0.893825i	$0.648011\pi$
$620$			510.006i			0.822591i
$621$	−139.060	+	445.348i	−0.223929	+	0.717146i
$622$	−150.397			−0.241796
$623$		−	18.0010i		−	0.0288941i
$624$	37.0507	+	82.3659i	0.0593761	+	0.131997i
$625$	−714.264			−1.14282
$626$		−	689.975i		−	1.10220i
$627$	846.807	−	380.920i	1.35057	−	0.607527i
$628$	−137.373			−0.218746
$629$			2.15102i			0.00341974i
$630$	25.9556	−	29.2750i	0.0411994	−	0.0464682i
$631$	−455.631			−0.722078			−0.361039	−	0.932551i	$-0.617578\pi$
$631$	−455.631			−0.722078			−0.361039	+	0.932551i	$0.617578\pi$
$632$		−	96.7161i		−	0.153032i
$633$	−84.0592	−	186.869i	−0.132795	−	0.295211i
$634$	−332.509			−0.524462
$635$		−	462.509i		−	0.728361i
$636$	513.474	−	230.976i	0.807350	−	0.363170i
$637$	366.363			0.575138
$638$		−	437.548i		−	0.685812i
$639$	−16.9371	−	15.0167i	−0.0265056	−	0.0235003i
$640$	61.2567			0.0957136
$641$		−	373.560i		−	0.582777i	−0.956605	−	0.291388i	$-0.905883\pi$
$641$		−	373.560i		−	0.582777i	0.956605	−	0.291388i	$-0.0941172\pi$
$642$	237.131	+	527.156i	0.369363	+	0.821116i
$643$	241.873			0.376163			0.188082	−	0.982153i	$-0.439773\pi$
$643$	241.873			0.376163			0.188082	+	0.982153i	$0.439773\pi$
$644$		−	19.6205i		−	0.0304666i
$645$	640.553	−	288.140i	0.993105	−	0.446729i
$646$	62.0407			0.0960383
$647$		−	244.555i		−	0.377983i	−0.981979	−	0.188991i	$-0.939478\pi$
$647$		−	244.555i		−	0.377983i	0.981979	−	0.188991i	$-0.0605218\pi$
$648$	227.454	−	27.4389i	0.351009	−	0.0423440i
$649$	−129.033			−0.198818
$650$		−	45.9332i		−	0.0706665i
$651$	−32.9074	−	73.1551i	−0.0505490	−	0.112373i
$652$	−102.642			−0.157426
$653$			885.880i			1.35663i	0.734771	+	0.678315i	$0.237290\pi$
$653$			885.880i			1.35663i	−0.734771	+	0.678315i	$0.762710\pi$
$654$	809.021	−	363.922i	1.23704	−	0.556456i
$655$	−882.509			−1.34734
$656$			154.494i			0.235510i
$657$	101.460	−	114.435i	0.154428	−	0.174178i
$658$	−12.2054			−0.0185493
$659$		−	578.182i		−	0.877362i	−0.898643	−	0.438681i	$-0.855446\pi$
$659$		−	578.182i		−	0.877362i	0.898643	−	0.438681i	$-0.144554\pi$
$660$	−223.876	−	497.691i	−0.339207	−	0.754077i
$661$	1017.15			1.53881			0.769404	−	0.638763i	$-0.220553\pi$
$661$	1017.15			1.53881			0.769404	+	0.638763i	$0.220553\pi$
$662$			512.237i			0.773772i
$663$	49.0282	−	22.0544i	0.0739490	−	0.0332645i
$664$	27.9786			0.0421364
$665$			56.6361i			0.0851671i
$666$	−8.60383	−	7.62828i	−0.0129187	−	0.0114539i
$667$	−318.254			−0.477143
$668$		−	325.870i		−	0.487829i
$669$	−342.408	−	761.194i	−0.511821	−	1.13781i
$670$	−389.460			−0.581283
$671$			748.728i			1.11584i
$672$	−8.78664	+	3.95250i	−0.0130754	+	0.00588169i
$673$	1114.39			1.65585			0.827926	−	0.560838i	$-0.189521\pi$
$673$	1114.39			1.65585			0.827926	+	0.560838i	$0.189521\pi$
$674$		−	623.726i		−	0.925409i
$675$	−111.222	−	34.7293i	−0.164774	−	0.0514508i
$676$	224.710			0.332411
$677$			98.4172i			0.145372i	0.997355	+	0.0726862i	$0.0231572\pi$
$677$			98.4172i			0.145372i	−0.997355	+	0.0726862i	$0.976843\pi$
$678$	247.925	+	551.152i	0.365671	+	0.812909i
$679$	−54.9195			−0.0808829
$680$		−	36.4630i		−	0.0536220i
$681$	360.545	−	162.184i	0.529435	−	0.238156i
$682$	−1118.89			−1.64060
$683$			471.285i			0.690021i	0.938599	+	0.345011i	$0.112125\pi$
$683$			471.285i			0.690021i	−0.938599	+	0.345011i	$0.887875\pi$
$684$	−220.019	+	248.156i	−0.321665	+	0.362801i
$685$	1177.89			1.71955
$686$			78.4245i			0.114321i
$687$	404.936	+	900.197i	0.589426	+	1.31033i
$688$	−172.966			−0.251404
$689$			706.259i			1.02505i
$690$	−361.999	+	162.838i	−0.524637	+	0.235998i
$691$	343.929			0.497727			0.248864	−	0.968539i	$-0.419943\pi$
$691$	343.929			0.497727			0.248864	+	0.968539i	$0.419943\pi$
$692$		−	646.650i		−	0.934465i
$693$	64.2255	+	56.9433i	0.0926775	+	0.0821692i
$694$	50.9192			0.0733706
$695$		−	182.399i		−	0.262445i
$696$	64.1115	+	142.524i	0.0921143	+	0.204776i
$697$	91.9626			0.131941
$698$			422.067i			0.604680i
$699$	262.865	−	118.245i	0.376059	−	0.169163i
$700$	4.90007			0.00700010
$701$			679.280i			0.969016i	0.874787	+	0.484508i	$0.161001\pi$
$701$			679.280i			0.969016i	−0.874787	+	0.484508i	$0.838999\pi$
$702$	−85.6566	+	274.320i	−0.122018	+	0.390769i
$703$	16.6452			0.0236774
$704$			134.389i			0.190894i
$705$	101.298	+	225.192i	0.143685	+	0.319421i
$706$	−233.460			−0.330680
$707$		−	84.0247i		−	0.118847i
$708$	42.0303	−	18.9065i	0.0593648	−	0.0267041i
$709$	−726.751			−1.02504			−0.512518	−	0.858676i	$-0.671287\pi$
$709$	−726.751			−1.02504			−0.512518	+	0.858676i	$0.671287\pi$
$710$		−	19.2580i		−	0.0271240i
$711$	204.164	−	230.274i	0.287151	−	0.323874i
$712$	89.6810			0.125956
$713$			813.832i			1.14142i
$714$	2.35272	+	5.23023i	0.00329512	+	0.00732526i
$715$	684.549			0.957411
$716$			359.007i			0.501406i
$717$	−546.212	+	245.703i	−0.761802	+	0.342682i
$718$	−997.208			−1.38887
$719$		−	1390.63i		−	1.93412i	−0.254556	−	0.967058i	$-0.581929\pi$
$719$		−	1390.63i		−	1.93412i	0.254556	−	0.967058i	$-0.418071\pi$
$720$	145.848	+	129.311i	0.202566	+	0.179598i
$721$	−1.49452			−0.00207284
$722$			30.4419i			0.0421633i
$723$	410.908	+	913.472i	0.568337	+	1.26345i
$724$	−181.216			−0.250298
$725$		−	79.4817i		−	0.109630i
$726$	623.696	−	280.558i	0.859086	−	0.386443i
$727$	−382.472			−0.526097			−0.263048	−	0.964783i	$-0.584728\pi$
$727$	−382.472			−0.526097			−0.263048	+	0.964783i	$0.584728\pi$
$728$		−	12.0856i		−	0.0166011i
$729$	599.473	+	414.817i	0.822323	+	0.569021i
$730$	130.116			0.178241
$731$			102.958i			0.140845i
$732$	−109.707	−	243.885i	−0.149873	−	0.333177i
$733$	−1027.97			−1.40242			−0.701209	−	0.712956i	$-0.747356\pi$
$733$	−1027.97			−1.40242			−0.701209	+	0.712956i	$0.747356\pi$
$734$			738.595i			1.00626i
$735$	721.082	−	324.365i	0.981064	−	0.441313i
$736$	97.7491			0.132811
$737$		−	854.425i		−	1.15933i
$738$	−326.132	+	367.840i	−0.441914	+	0.498428i
$739$	430.060			0.581948			0.290974	−	0.956731i	$-0.406021\pi$
$739$	430.060			0.581948			0.290974	+	0.956731i	$0.406021\pi$
$740$		−	9.78282i		−	0.0132200i
$741$	−170.663	−	379.394i	−0.230315	−	0.512003i
$742$	−75.3423			−0.101539
$743$		−	1335.86i		−	1.79793i	−0.438017	−	0.898967i	$-0.644319\pi$
$743$		−	1335.86i		−	1.79793i	0.438017	−	0.898967i	$-0.355681\pi$
$744$	364.459	−	163.945i	0.489864	−	0.220356i
$745$	−51.3214			−0.0688878
$746$			420.348i			0.563469i
$747$	66.6150	+	59.0619i	0.0891767	+	0.0790654i
$748$	79.9951			0.106945
$749$		−	77.3499i		−	0.103271i
$750$	194.923	+	433.326i	0.259898	+	0.577768i
$751$	1016.30			1.35326			0.676628	−	0.736325i	$-0.263441\pi$
$751$	1016.30			1.35326			0.676628	+	0.736325i	$0.263441\pi$
$752$		−	60.8075i		−	0.0808611i
$753$	1077.07	−	484.500i	1.43038	−	0.643427i
$754$	−196.034			−0.259993
$755$		−	636.191i		−	0.842638i
$756$	−29.2639	−	9.13769i	−0.0387089	−	0.0120869i
$757$	756.668			0.999561			0.499780	−	0.866152i	$-0.333414\pi$
$757$	756.668			0.999561			0.499780	+	0.866152i	$0.333414\pi$
$758$		−	602.457i		−	0.794798i
$759$	−357.246	−	794.180i	−0.470680	−	1.04635i
$760$	−282.161			−0.371265
$761$			1012.55i			1.33055i	0.746599	+	0.665274i	$0.231685\pi$
$761$			1012.55i			1.33055i	−0.746599	+	0.665274i	$0.768315\pi$
$762$	−330.516	+	148.676i	−0.433748	+	0.195113i
$763$	−118.708			−0.155581
$764$			388.693i			0.508761i
$765$	76.9721	−	86.8157i	0.100617	−	0.113485i
$766$	−70.8889			−0.0925442
$767$			57.8106i			0.0753723i
$768$	−19.6913	−	43.7750i	−0.0256398	−	0.0569987i
$769$	−1239.20			−1.61144			−0.805719	−	0.592298i	$-0.798221\pi$
$769$	−1239.20			−1.61144			−0.805719	+	0.592298i	$0.798221\pi$
$770$			73.0264i			0.0948395i
$771$	−737.506	+	331.753i	−0.956558	+	0.430289i
$772$	284.960			0.369119
$773$			219.444i			0.283886i	0.989875	+	0.141943i	$0.0453350\pi$
$773$			219.444i			0.283886i	−0.989875	+	0.141943i	$0.954665\pi$
$774$	−411.819	−	365.125i	−0.532066	−	0.471738i
$775$	−203.249			−0.262256
$776$		−	273.609i		−	0.352589i
$777$	0.631222	+	1.40324i	0.000812383	+	0.00180598i
$778$	−500.257			−0.643004
$779$		−	711.633i		−	0.913521i
$780$	−222.980	+	100.303i	−0.285872	+	0.128594i
$781$	42.2496			0.0540968
$782$		−	58.1851i		−	0.0744054i
$783$	−148.218	+	474.676i	−0.189295	+	0.606228i
$784$	−194.711			−0.248356
$785$		−	371.894i		−	0.473750i
$786$	283.688	+	630.655i	0.360926	+	0.802360i
$787$	−1448.84			−1.84096			−0.920480	−	0.390789i	$-0.872202\pi$
$787$	−1448.84			−1.84096			−0.920480	+	0.390789i	$0.872202\pi$
$788$			653.574i			0.829409i
$789$	1068.45	−	480.620i	1.35418	−	0.609150i
$790$	261.829			0.331429
$791$		−	80.8708i		−	0.102239i
$792$	−283.691	+	319.971i	−0.358196	+	0.404004i
$793$	335.452			0.423017
$794$		−	586.057i		−	0.738107i
$795$	625.297	+	1390.07i	0.786537	+	1.74852i
$796$	−554.041			−0.696032
$797$		−	1096.69i		−	1.37602i	−0.725700	−	0.688011i	$-0.758484\pi$
$797$		−	1096.69i		−	1.37602i	0.725700	−	0.688011i	$-0.241516\pi$
$798$	40.4731	−	18.2060i	0.0507181	−	0.0228146i
$799$	−36.1956			−0.0453011
$800$			24.4121i			0.0305152i
$801$	213.524	+	189.314i	0.266572	+	0.236347i
$802$	−386.637			−0.482091
$803$			285.457i			0.355489i
$804$	125.194	+	278.314i	0.155714	+	0.346162i
$805$	53.1163			0.0659830
$806$			501.295i			0.621954i
$807$	649.869	−	292.331i	0.805289	−	0.362244i
$808$	418.611			0.518083
$809$			546.846i			0.675953i	0.941155	+	0.337976i	$0.109742\pi$
$809$			546.846i			0.675953i	−0.941155	+	0.337976i	$0.890258\pi$
$810$	74.2824	+	615.760i	0.0917066	+	0.760197i
$811$	293.428			0.361811			0.180905	−	0.983501i	$-0.442097\pi$
$811$	293.428			0.361811			0.180905	+	0.983501i	$0.442097\pi$
$812$		−	20.9126i		−	0.0257544i
$813$	207.405	+	461.075i	0.255111	+	0.567128i
$814$	21.4622			0.0263664
$815$		−	277.871i		−	0.340946i
$816$	−26.0570	+	11.7212i	−0.0319326	+	0.0143643i
$817$	796.716			0.975173
$818$			321.208i			0.392674i
$819$	25.5123	−	28.7749i	0.0311505	−	0.0351342i
$820$	−418.246			−0.510055
$821$			69.8215i			0.0850445i	0.999096	+	0.0425222i	$0.0135393\pi$
$821$			69.8215i			0.0850445i	−0.999096	+	0.0425222i	$0.986461\pi$
$822$	−378.640	−	841.740i	−0.460633	−	1.02401i
$823$	1132.07			1.37554			0.687772	−	0.725927i	$-0.258589\pi$
$823$	1132.07			1.37554			0.687772	+	0.725927i	$0.258589\pi$
$824$		−	7.44567i		−	0.00903601i
$825$	198.341	−	89.2197i	0.240413	−	0.108145i
$826$	−6.16712			−0.00746625
$827$		−	365.852i		−	0.442384i	−0.975230	−	0.221192i	$-0.929005\pi$
$827$		−	365.852i		−	0.442384i	0.975230	−	0.221192i	$-0.0709948\pi$
$828$	232.734	+	206.345i	0.281079	+	0.249209i
$829$	493.942			0.595829			0.297915	−	0.954593i	$-0.403709\pi$
$829$	493.942			0.595829			0.297915	+	0.954593i	$0.403709\pi$
$830$			75.7433i			0.0912570i
$831$	145.874	+	324.287i	0.175540	+	0.390237i
$832$	60.2104			0.0723682
$833$			115.901i			0.139137i
$834$	−130.345	+	58.6333i	−0.156289	+	0.0703037i
$835$	882.192			1.05652
$836$		−	619.025i		−	0.740461i
$837$	1213.83	+	379.020i	1.45022	+	0.452831i
$838$	819.719			0.978185
$839$			229.180i			0.273158i	0.990629	+	0.136579i	$0.0436108\pi$
$839$			229.180i			0.273158i	−0.990629	+	0.136579i	$0.956389\pi$
$840$	−10.7002	−	23.7871i	−0.0127383	−	0.0283180i
$841$	501.787			0.596655
$842$		−	869.784i		−	1.03300i
$843$	−325.519	+	146.428i	−0.386143	+	0.173699i
$844$	−136.603			−0.161852
$845$			608.332i			0.719919i
$846$	128.363	−	144.778i	0.151729	−	0.171133i
$847$	−91.5152			−0.108046
$848$		−	375.355i		−	0.442636i
$849$	−622.027	−	1382.80i	−0.732659	−	1.62874i
$850$	14.5313			0.0170956
$851$		−	15.6107i		−	0.0183440i
$852$	−13.7621	+	6.19060i	−0.0161527	+	0.00726597i
$853$	−702.287			−0.823315			−0.411657	−	0.911339i	$-0.635050\pi$
$853$	−702.287			−0.823315			−0.411657	+	0.911339i	$0.635050\pi$
$854$			35.7854i			0.0419033i
$855$	−671.805	−	595.633i	−0.785737	−	0.696646i
$856$	385.357			0.450183
$857$			914.239i			1.06679i	0.845866	+	0.533395i	$0.179084\pi$
$857$			914.239i			1.06679i	−0.845866	+	0.533395i	$0.820916\pi$
$858$	−220.052	−	489.190i	−0.256471	−	0.570151i
$859$	629.880			0.733271			0.366636	−	0.930365i	$-0.380510\pi$
$859$	629.880			0.733271			0.366636	+	0.930365i	$0.380510\pi$
$860$		−	468.251i		−	0.544478i
$861$	59.9930	−	26.9867i	0.0696782	−	0.0313434i
$862$	−340.915			−0.395493
$863$			545.531i			0.632133i	0.948737	+	0.316067i	$0.102362\pi$
$863$			545.531i			0.632133i	−0.948737	+	0.316067i	$0.897638\pi$
$864$	45.5239	−	145.793i	0.0526897	−	0.168742i
$865$	1750.60			2.02382
$866$		−	1098.44i		−	1.26840i
$867$	−348.698	−	775.176i	−0.402189	−	0.894090i
$868$	−53.4772			−0.0616097
$869$			574.419i			0.661011i
$870$	−385.839	+	173.562i	−0.443493	+	0.199497i
$871$	−382.807			−0.439503
$872$		−	591.403i		−	0.678215i
$873$	577.579	−	651.443i	0.661602	−	0.746212i
$874$	−450.253			−0.515163
$875$		−	63.5821i		−	0.0726653i
$876$	−41.8265	−	92.9828i	−0.0477471	−	0.106145i
$877$	214.492			0.244575			0.122287	−	0.992495i	$-0.460977\pi$
$877$	214.492			0.244575			0.122287	+	0.992495i	$0.460977\pi$
$878$			181.134i			0.206303i
$879$	−21.0293	+	9.45960i	−0.0239241	+	0.0107618i
$880$	−363.817			−0.413429
$881$			350.025i			0.397305i	0.980070	+	0.198652i	$0.0636564\pi$
$881$			350.025i			0.397305i	−0.980070	+	0.198652i	$0.936344\pi$
$882$	−463.592	−	411.028i	−0.525615	−	0.466018i
$883$	332.489			0.376545			0.188272	−	0.982117i	$-0.439711\pi$
$883$	332.489			0.376545			0.188272	+	0.982117i	$0.439711\pi$
$884$		−	35.8401i		−	0.0405431i
$885$	51.1835	+	113.784i	0.0578344	+	0.128569i
$886$	522.521			0.589752
$887$		−	973.809i		−	1.09787i	−0.835866	−	0.548934i	$-0.815034\pi$
$887$		−	973.809i		−	1.09787i	0.835866	−	0.548934i	$-0.184966\pi$
$888$	−6.99096	+	3.14475i	−0.00787270	+	0.00354138i
$889$	48.4968			0.0545521
$890$			242.783i			0.272790i
$891$	−1350.90	+	162.966i	−1.51616	+	0.182902i
$892$	−556.441			−0.623813
$893$			280.092i			0.313653i
$894$	16.4976	+	36.6751i	0.0184537	+	0.0410236i
$895$	−971.899			−1.08592
$896$			6.42313i			0.00716867i
$897$	−355.816	+	160.057i	−0.396673	+	0.178436i
$898$	−732.140			−0.815300
$899$			867.427i			0.964880i
$900$	−51.5332	+	58.1236i	−0.0572591	+	0.0645817i
$901$	−223.430			−0.247980
$902$		−	917.577i		−	1.01727i
$903$	30.2132	+	67.1657i	0.0334587	+	0.0743807i
$904$	402.898			0.445684
$905$		−	490.586i		−	0.542084i
$906$	−454.633	+	204.508i	−0.501802	+	0.225726i
$907$	1336.37			1.47340			0.736698	−	0.676222i	$-0.236384\pi$
$907$	1336.37			1.47340			0.736698	+	0.676222i	$0.236384\pi$
$908$		−	263.562i		−	0.290267i
$909$	996.683	+	883.674i	1.09646	+	0.972138i
$910$	32.7180			0.0359538
$911$		−	1227.32i		−	1.34722i	−0.739087	−	0.673610i	$-0.764743\pi$
$911$		−	1227.32i		−	1.34722i	0.739087	−	0.673610i	$-0.235257\pi$
$912$	90.7023	+	201.637i	0.0994543	+	0.221093i
$913$	−166.171			−0.182006
$914$		−	570.054i		−	0.623691i
$915$	660.244	−	296.998i	0.721578	−	0.324588i
$916$	658.053			0.718399
$917$		−	92.5363i		−	0.100912i
$918$	−86.7830	−	27.0981i	−0.0945349	−	0.0295186i
$919$	−375.828			−0.408953			−0.204477	−	0.978871i	$-0.565549\pi$
$919$	−375.828			−0.408953			−0.204477	+	0.978871i	$0.565549\pi$
$920$			264.625i			0.287636i
$921$	−542.091	−	1205.10i	−0.588590	−	1.30847i
$922$	105.729			0.114673
$923$		−	18.9291i		−	0.0205082i
$924$	52.1858	−	23.4748i	0.0564782	−	0.0254056i
$925$	3.89867			0.00421478
$926$			571.052i			0.616686i
$927$	15.7176	−	17.7276i	0.0169553	−	0.0191236i
$928$	104.186			0.112270
$929$			518.388i			0.558006i	0.960290	+	0.279003i	$0.0900040\pi$
$929$			518.388i			0.558006i	−0.960290	+	0.279003i	$0.909996\pi$
$930$	443.829	+	986.659i	0.477236	+	1.06092i
$931$	896.878			0.963349
$932$		−	192.157i		−	0.206177i
$933$	−290.959	+	130.882i	−0.311853	+	0.140281i
$934$	−574.349			−0.614935
$935$			216.562i			0.231617i
$936$	143.357	+	127.102i	0.153159	+	0.135793i
$937$	−1303.18			−1.39080			−0.695402	−	0.718621i	$-0.744774\pi$
$937$	−1303.18			−1.39080			−0.695402	+	0.718621i	$0.744774\pi$
$938$		−	40.8372i		−	0.0435364i
$939$	−600.445	−	1334.83i	−0.639452	−	1.42154i
$940$	164.617			0.175125
$941$		−	890.005i		−	0.945808i	−0.881114	−	0.472904i	$-0.843206\pi$
$941$		−	890.005i		−	0.945808i	0.881114	−	0.472904i	$-0.156794\pi$
$942$	−265.761	+	119.547i	−0.282124	+	0.126908i
$943$	−667.407			−0.707748
$944$		−	30.7246i		−	0.0325472i
$945$	24.7374	−	79.2230i	0.0261772	−	0.0838339i
$946$	1027.28			1.08592
$947$		−	796.675i		−	0.841262i	−0.907232	−	0.420631i	$-0.861809\pi$
$947$		−	796.675i		−	0.841262i	0.907232	−	0.420631i	$-0.138191\pi$
$948$	−84.1664	−	187.107i	−0.0887831	−	0.197370i
$949$	127.893			0.134766
$950$		−	112.447i		−	0.118366i
$951$	−643.272	+	289.363i	−0.676416	+	0.304272i
$952$	3.82336			0.00401613
$953$		−	1385.61i		−	1.45395i	−0.686664	−	0.726975i	$-0.740926\pi$
$953$		−	1385.61i		−	1.45395i	0.686664	−	0.726975i	$-0.259074\pi$
$954$	792.362	−	893.694i	0.830568	−	0.936786i
$955$	−1052.27			−1.10185
$956$			399.287i			0.417664i
$957$	−380.773	−	846.481i	−0.397882	−	0.884515i
$958$	−933.682			−0.974616
$959$			123.509i			0.128789i
$960$	118.507	−	53.3082i	0.123445	−	0.0555293i
$961$	1257.17			1.30819
$962$		−	9.61572i		−	0.00999555i
$963$	917.507	+	813.476i	0.952759	+	0.844731i
$964$	667.758			0.692695
$965$			771.440i			0.799419i
$966$	−17.0746	−	37.9578i	−0.0176755	−	0.0392938i
$967$	544.472			0.563052			0.281526	−	0.959554i	$-0.409159\pi$
$967$	544.472			0.563052			0.281526	+	0.959554i	$0.409159\pi$
$968$		−	455.929i		−	0.471001i
$969$	120.024	−	53.9905i	0.123864	−	0.0557177i
$970$	740.711			0.763619
$971$			258.738i			0.266466i	0.991085	+	0.133233i	$0.0425358\pi$
$971$			258.738i			0.266466i	−0.991085	+	0.133233i	$0.957464\pi$
$972$	416.153	−	251.023i	0.428141	−	0.258254i
$973$	19.1256			0.0196563
$974$		−	424.575i		−	0.435909i
$975$	−39.9730	−	88.8625i	−0.0409980	−	0.0911410i
$976$	−178.283			−0.182667
$977$		−	1050.46i		−	1.07519i	−0.843203	−	0.537595i	$-0.819333\pi$
$977$		−	1050.46i		−	1.07519i	0.843203	−	0.537595i	$-0.180667\pi$
$978$	−198.571	+	89.3233i	−0.203038	+	0.0913326i
$979$	−532.636			−0.544061
$980$		−	527.119i		−	0.537876i
$981$	1248.43	−	1408.09i	1.27261	−	1.43536i
$982$	−995.685			−1.01394
$983$			655.905i			0.667248i	0.942706	+	0.333624i	$0.108272\pi$
$983$			655.905i			0.667248i	−0.942706	+	0.333624i	$0.891728\pi$
$984$	134.447	+	298.885i	0.136634	+	0.303745i
$985$	−1769.35			−1.79629
$986$		−	62.0168i		−	0.0628974i
$987$	−23.6127	+	10.6217i	−0.0239237	+	0.0107616i
$988$	−277.341			−0.280710
$989$		−	747.202i		−	0.755513i
$990$	−866.223	−	768.006i	−0.874973	−	0.775764i
$991$	−1391.25			−1.40389			−0.701945	−	0.712231i	$-0.747685\pi$
$991$	−1391.25			−1.40389			−0.701945	+	0.712231i	$0.747685\pi$
$992$		−	266.423i		−	0.268572i
$993$	445.770	+	990.973i	0.448912	+	0.997959i
$994$	2.01932			0.00203151
$995$		−	1499.89i		−	1.50743i
$996$	54.1274	−	24.3481i	0.0543448	−	0.0244459i
$997$	−275.690			−0.276519			−0.138260	−	0.990396i	$-0.544151\pi$
$997$	−275.690			−0.276519			−0.138260	+	0.990396i	$0.544151\pi$
$998$			948.671i			0.950572i
$999$	−23.2834	−	7.27027i	−0.0233067	−	0.00727754i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.3.b.a.119.7	✓	40
3.2	odd	2	inner	354.3.b.a.119.27	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.3.b.a.119.7	✓	40	1.1	even	1	trivial
354.3.b.a.119.27	yes	40	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	354.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(-1.23071 - 2.73594i) q^{3} -2.00000 q^{4} -5.41438i q^{5} +(-3.86920 + 1.74048i) q^{6} +0.567729 q^{7} +2.82843i q^{8} +(-5.97072 + 6.73428i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(-1.23071 - 2.73594i) q^{3} -2.00000 q^{4} -5.41438i q^{5} +(-3.86920 + 1.74048i) q^{6} +0.567729 q^{7} +2.82843i q^{8} +(-5.97072 + 6.73428i) q^{9} -7.65709 q^{10} -16.7987i q^{11} +(2.46142 + 5.47188i) q^{12} -7.52630 q^{13} -0.802891i q^{14} +(-14.8134 + 6.66352i) q^{15} +4.00000 q^{16} -2.38099i q^{17} +(9.52371 + 8.44387i) q^{18} -18.4248 q^{19} +10.8288i q^{20} +(-0.698709 - 1.55327i) q^{21} -23.7569 q^{22} +17.2798i q^{23} +(7.73840 - 3.48097i) q^{24} -4.31550 q^{25} +10.6438i q^{26} +(25.7728 + 8.04757i) q^{27} -1.13546 q^{28} +18.4177i q^{29} +(9.42364 + 20.9493i) q^{30} +47.0974 q^{31} -5.65685i q^{32} +(-45.9601 + 20.6743i) q^{33} -3.36724 q^{34} -3.07390i q^{35} +(11.9414 - 13.4686i) q^{36} -0.903411 q^{37} +26.0566i q^{38} +(9.26267 + 20.5915i) q^{39} +15.3142 q^{40} +38.6236i q^{41} +(-2.19666 + 0.988124i) q^{42} -43.2414 q^{43} +33.5973i q^{44} +(36.4620 + 32.3277i) q^{45} +24.4373 q^{46} -15.2019i q^{47} +(-4.92283 - 10.9438i) q^{48} -48.6777 q^{49} +6.10304i q^{50} +(-6.51425 + 2.93031i) q^{51} +15.0526 q^{52} -93.8388i q^{53} +(11.3810 - 36.4482i) q^{54} -90.9543 q^{55} +1.60578i q^{56} +(22.6756 + 50.4092i) q^{57} +26.0466 q^{58} -7.68115i q^{59} +(29.6268 - 13.3270i) q^{60} -44.5707 q^{61} -66.6058i q^{62} +(-3.38975 + 3.82325i) q^{63} -8.00000 q^{64} +40.7502i q^{65} +(29.2378 + 64.9974i) q^{66} +50.8627 q^{67} +4.76199i q^{68} +(47.2764 - 21.2664i) q^{69} -4.34715 q^{70} +2.51506i q^{71} +(-19.0474 - 16.8877i) q^{72} -16.9929 q^{73} +1.27762i q^{74} +(5.31112 + 11.8069i) q^{75} +36.8497 q^{76} -9.53710i q^{77} +(29.1207 - 13.0994i) q^{78} -34.1943 q^{79} -21.6575i q^{80} +(-9.70112 - 80.4170i) q^{81} +54.6220 q^{82} -9.89192i q^{83} +(1.39742 + 3.10655i) q^{84} -12.8916 q^{85} +61.1526i q^{86} +(50.3898 - 22.6668i) q^{87} +47.5138 q^{88} -31.7070i q^{89} +(45.7183 - 51.5650i) q^{90} -4.27290 q^{91} -34.5595i q^{92} +(-57.9632 - 128.856i) q^{93} -21.4987 q^{94} +99.7590i q^{95} +(-15.4768 + 6.96194i) q^{96} -96.7353 q^{97} +68.8406i q^{98} +(113.127 + 100.300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9}+O(q^{10}) \) 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9	\( 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9} - 16 q^{10} + 34 q^{15} + 160 q^{16} + 16 q^{18} + 24 q^{19} - 18 q^{21} - 16 q^{22} - 16 q^{24} - 216 q^{25} - 30 q^{27} - 16 q^{28} - 64 q^{30} + 96 q^{31} + 76 q^{33} + 80 q^{34} + 48 q^{36} - 200 q^{37} - 28 q^{39} + 32 q^{40} + 48 q^{42} - 104 q^{43} + 58 q^{45} + 32 q^{46} + 288 q^{49} - 176 q^{51} - 40 q^{54} + 360 q^{55} + 214 q^{57} - 128 q^{58} - 68 q^{60} - 32 q^{61} - 132 q^{63} - 320 q^{64} - 112 q^{66} - 344 q^{67} + 88 q^{69} + 192 q^{70} - 32 q^{72} + 40 q^{73} + 28 q^{75} - 48 q^{76} + 96 q^{78} + 32 q^{79} + 336 q^{81} - 80 q^{82} + 36 q^{84} + 168 q^{85} - 162 q^{87} + 32 q^{88} + 112 q^{90} + 88 q^{91} - 316 q^{93} - 400 q^{94} + 32 q^{96} - 184 q^{97} - 148 q^{99}+O(q^{100}) \) 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9 - 16 * q^10 + 34 * q^15 + 160 * q^16 + 16 * q^18 + 24 * q^19 - 18 * q^21 - 16 * q^22 - 16 * q^24 - 216 * q^25 - 30 * q^27 - 16 * q^28 - 64 * q^30 + 96 * q^31 + 76 * q^33 + 80 * q^34 + 48 * q^36 - 200 * q^37 - 28 * q^39 + 32 * q^40 + 48 * q^42 - 104 * q^43 + 58 * q^45 + 32 * q^46 + 288 * q^49 - 176 * q^51 - 40 * q^54 + 360 * q^55 + 214 * q^57 - 128 * q^58 - 68 * q^60 - 32 * q^61 - 132 * q^63 - 320 * q^64 - 112 * q^66 - 344 * q^67 + 88 * q^69 + 192 * q^70 - 32 * q^72 + 40 * q^73 + 28 * q^75 - 48 * q^76 + 96 * q^78 + 32 * q^79 + 336 * q^81 - 80 * q^82 + 36 * q^84 + 168 * q^85 - 162 * q^87 + 32 * q^88 + 112 * q^90 + 88 * q^91 - 316 * q^93 - 400 * q^94 + 32 * q^96 - 184 * q^97 - 148 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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