LMFDB - Embedded newform 287.3.g.a.132.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,3,Mod(132,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("287.132");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	287.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.82018358714$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			132.19
Character	$\chi$	$=$	287.132
Dual form			287.3.g.a.237.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.34555i q^{2} +(-2.45356 + 2.45356i) q^{3} +2.18949 q^{4} +9.16655 q^{5} +(3.30139 + 3.30139i) q^{6} +(-4.09097 - 5.68014i) q^{7} -8.32828i q^{8} -3.03988i q^{9} +O(q^{10})$	\(q-1.34555i q^{2} +(-2.45356 + 2.45356i) q^{3} +2.18949 q^{4} +9.16655 q^{5} +(3.30139 + 3.30139i) q^{6} +(-4.09097 - 5.68014i) q^{7} -8.32828i q^{8} -3.03988i q^{9} -12.3341i q^{10} +(0.297405 + 0.297405i) q^{11} +(-5.37204 + 5.37204i) q^{12} +(7.30132 - 7.30132i) q^{13} +(-7.64292 + 5.50461i) q^{14} +(-22.4907 + 22.4907i) q^{15} -2.44817 q^{16} +(2.47713 + 2.47713i) q^{17} -4.09032 q^{18} +(8.93778 + 8.93778i) q^{19} +20.0701 q^{20} +(23.9740 + 3.89911i) q^{21} +(0.400174 - 0.400174i) q^{22} +0.143695 q^{23} +(20.4339 + 20.4339i) q^{24} +59.0257 q^{25} +(-9.82431 - 9.82431i) q^{26} +(-14.6235 - 14.6235i) q^{27} +(-8.95714 - 12.4366i) q^{28} +(-28.5657 - 28.5657i) q^{29} +(30.2623 + 30.2623i) q^{30} +31.5797i q^{31} -30.0190i q^{32} -1.45940 q^{33} +(3.33310 - 3.33310i) q^{34} +(-37.5001 - 52.0673i) q^{35} -6.65579i q^{36} +48.1626 q^{37} +(12.0262 - 12.0262i) q^{38} +35.8284i q^{39} -76.3416i q^{40} +(40.9598 + 1.81570i) q^{41} +(5.24646 - 32.2582i) q^{42} -47.5814i q^{43} +(0.651166 + 0.651166i) q^{44} -27.8652i q^{45} -0.193349i q^{46} +(38.7736 + 38.7736i) q^{47} +(6.00673 - 6.00673i) q^{48} +(-15.5279 + 46.4745i) q^{49} -79.4221i q^{50} -12.1555 q^{51} +(15.9862 - 15.9862i) q^{52} +(28.9978 + 28.9978i) q^{53} +(-19.6767 + 19.6767i) q^{54} +(2.72618 + 2.72618i) q^{55} +(-47.3058 + 34.0707i) q^{56} -43.8587 q^{57} +(-38.4367 + 38.4367i) q^{58} +47.4282i q^{59} +(-49.2431 + 49.2431i) q^{60} -54.7097 q^{61} +42.4921 q^{62} +(-17.2669 + 12.4361i) q^{63} -50.1848 q^{64} +(66.9280 - 66.9280i) q^{65} +1.96370i q^{66} +(-68.8824 + 68.8824i) q^{67} +(5.42364 + 5.42364i) q^{68} +(-0.352564 + 0.352564i) q^{69} +(-70.0592 + 50.4583i) q^{70} +(-48.9469 - 48.9469i) q^{71} -25.3170 q^{72} -52.4323 q^{73} -64.8053i q^{74} +(-144.823 + 144.823i) q^{75} +(19.5692 + 19.5692i) q^{76} +(0.472627 - 2.90598i) q^{77} +48.2090 q^{78} +(6.48392 + 6.48392i) q^{79} -22.4413 q^{80} +99.1180 q^{81} +(2.44311 - 55.1135i) q^{82} +1.55343i q^{83} +(52.4908 + 8.53707i) q^{84} +(22.7067 + 22.7067i) q^{85} -64.0232 q^{86} +140.175 q^{87} +(2.47688 - 2.47688i) q^{88} +(-112.697 + 112.697i) q^{89} -37.4941 q^{90} +(-71.3420 - 11.6030i) q^{91} +0.314619 q^{92} +(-77.4825 - 77.4825i) q^{93} +(52.1719 - 52.1719i) q^{94} +(81.9286 + 81.9286i) q^{95} +(73.6533 + 73.6533i) q^{96} +(-125.201 - 125.201i) q^{97} +(62.5339 + 20.8936i) q^{98} +(0.904077 - 0.904077i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 216 q^{4} - 2 q^{7}+O(q^{10}) $ 108 * q - 216 * q^4 - 2 * q^7	$ 108 q - 216 q^{4} - 2 q^{7} - 20 q^{11} - 4 q^{14} - 28 q^{15} + 408 q^{16} + 24 q^{18} + 20 q^{22} - 8 q^{23} + 452 q^{25} - 62 q^{28} + 168 q^{29} - 64 q^{30} - 10 q^{35} - 208 q^{37} - 44 q^{42} + 44 q^{44} + 272 q^{51} - 92 q^{53} + 24 q^{56} - 256 q^{57} + 248 q^{58} - 440 q^{60} - 252 q^{63} - 1104 q^{64} - 644 q^{65} - 348 q^{67} - 30 q^{70} - 564 q^{71} + 796 q^{72} + 1924 q^{78} + 196 q^{79} - 468 q^{81} + 32 q^{85} + 152 q^{86} + 840 q^{88} - 428 q^{92} + 32 q^{93} + 4 q^{95} + 108 q^{98} - 484 q^{99}+O(q^{100}) $ 108 * q - 216 * q^4 - 2 * q^7 - 20 * q^11 - 4 * q^14 - 28 * q^15 + 408 * q^16 + 24 * q^18 + 20 * q^22 - 8 * q^23 + 452 * q^25 - 62 * q^28 + 168 * q^29 - 64 * q^30 - 10 * q^35 - 208 * q^37 - 44 * q^42 + 44 * q^44 + 272 * q^51 - 92 * q^53 + 24 * q^56 - 256 * q^57 + 248 * q^58 - 440 * q^60 - 252 * q^63 - 1104 * q^64 - 644 * q^65 - 348 * q^67 - 30 * q^70 - 564 * q^71 + 796 * q^72 + 1924 * q^78 + 196 * q^79 - 468 * q^81 + 32 * q^85 + 152 * q^86 + 840 * q^88 - 428 * q^92 + 32 * q^93 + 4 * q^95 + 108 * q^98 - 484 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	1.34555i		−	0.672776i	−0.941723	−	0.336388i	$-0.890795\pi$
$2$		−	1.34555i		−	0.672776i	0.941723	−	0.336388i	$-0.109205\pi$
$3$	−2.45356	+	2.45356i	−0.817852	+	0.817852i	−0.985796	−	0.167944i	$-0.946287\pi$
$3$	−2.45356	+	2.45356i	−0.817852	+	0.817852i	0.167944	+	0.985796i	$0.446287\pi$
$4$	2.18949			0.547373
$5$	9.16655			1.83331			0.916655	−	0.399679i	$-0.130878\pi$
$5$	9.16655			1.83331			0.916655	+	0.399679i	$0.130878\pi$
$6$	3.30139	+	3.30139i	0.550231	+	0.550231i
$7$	−4.09097	−	5.68014i	−0.584424	−	0.811448i
$7$	−4.09097	−	5.68014i	−0.584424	−	0.811448i
$8$		−	8.32828i		−	1.04104i
$9$		−	3.03988i		−	0.337764i
$10$		−	12.3341i		−	1.23341i
$11$	0.297405	+	0.297405i	0.0270369	+	0.0270369i	0.720496	−	0.693459i	$-0.243914\pi$
$11$	0.297405	+	0.297405i	0.0270369	+	0.0270369i	−0.693459	+	0.720496i	$0.743914\pi$
$12$	−5.37204	+	5.37204i	−0.447670	+	0.447670i
$13$	7.30132	−	7.30132i	0.561640	−	0.561640i	−0.368133	−	0.929773i	$-0.620003\pi$
$13$	7.30132	−	7.30132i	0.561640	−	0.561640i	0.929773	+	0.368133i	$0.120003\pi$
$14$	−7.64292	+	5.50461i	−0.545923	+	0.393187i
$15$	−22.4907	+	22.4907i	−1.49938	+	1.49938i
$16$	−2.44817			−0.153011
$17$	2.47713	+	2.47713i	0.145713	+	0.145713i	0.776200	−	0.630487i	$-0.217145\pi$
$17$	2.47713	+	2.47713i	0.145713	+	0.145713i	−0.630487	+	0.776200i	$0.717145\pi$
$18$	−4.09032			−0.227240
$19$	8.93778	+	8.93778i	0.470409	+	0.470409i	0.902047	−	0.431638i	$-0.142064\pi$
$19$	8.93778	+	8.93778i	0.470409	+	0.470409i	−0.431638	+	0.902047i	$0.642064\pi$
$20$	20.0701			1.00350
$21$	23.9740	+	3.89911i	1.14162	+	0.185672i
$22$	0.400174	−	0.400174i	0.0181897	−	0.0181897i
$23$	0.143695			0.00624761			0.00312381	−	0.999995i	$-0.499006\pi$
$23$	0.143695			0.00624761			0.00312381	+	0.999995i	$0.499006\pi$
$24$	20.4339	+	20.4339i	0.851413	+	0.851413i
$25$	59.0257			2.36103
$26$	−9.82431	−	9.82431i	−0.377858	−	0.377858i
$27$	−14.6235	−	14.6235i	−0.541611	−	0.541611i
$28$	−8.95714	−	12.4366i	−0.319898	−	0.444164i
$29$	−28.5657	−	28.5657i	−0.985026	−	0.985026i	0.0148640	−	0.999890i	$-0.495268\pi$
$29$	−28.5657	−	28.5657i	−0.985026	−	0.985026i	−0.999890	+	0.0148640i	$0.995268\pi$
$30$	30.2623	+	30.2623i	1.00874	+	1.00874i
$31$			31.5797i			1.01870i	0.860560	+	0.509350i	$0.170114\pi$
$31$			31.5797i			1.01870i	−0.860560	+	0.509350i	$0.829886\pi$
$32$		−	30.0190i		−	0.938093i
$33$	−1.45940			−0.0442243
$34$	3.33310	−	3.33310i	0.0980324	−	0.0980324i
$35$	−37.5001	−	52.0673i	−1.07143	−	1.48764i
$36$		−	6.65579i		−	0.184883i
$37$	48.1626			1.30169			0.650846	−	0.759209i	$-0.274414\pi$
$37$	48.1626			1.30169			0.650846	+	0.759209i	$0.274414\pi$
$38$	12.0262	−	12.0262i	0.316480	−	0.316480i
$39$			35.8284i			0.918677i
$40$		−	76.3416i		−	1.90854i
$41$	40.9598	+	1.81570i	0.999019	+	0.0442853i
$41$	40.9598	+	1.81570i	0.999019	+	0.0442853i
$42$	5.24646	−	32.2582i	0.124916	−	0.768053i
$43$		−	47.5814i		−	1.10654i	−0.833001	−	0.553272i	$-0.813379\pi$
$43$		−	47.5814i		−	1.10654i	0.833001	−	0.553272i	$-0.186621\pi$
$44$	0.651166	+	0.651166i	0.0147992	+	0.0147992i
$45$		−	27.8652i		−	0.619227i
$46$		−	0.193349i		−	0.00420324i
$47$	38.7736	+	38.7736i	0.824971	+	0.824971i	0.986816	−	0.161845i	$-0.0517445\pi$
$47$	38.7736	+	38.7736i	0.824971	+	0.824971i	−0.161845	+	0.986816i	$0.551744\pi$
$48$	6.00673	−	6.00673i	0.125140	−	0.125140i
$49$	−15.5279	+	46.4745i	−0.316897	+	0.948460i
$50$		−	79.4221i		−	1.58844i
$51$	−12.1555			−0.238344
$52$	15.9862	−	15.9862i	0.307426	−	0.307426i
$53$	28.9978	+	28.9978i	0.547128	+	0.547128i	0.925609	−	0.378481i	$-0.123554\pi$
$53$	28.9978	+	28.9978i	0.547128	+	0.547128i	−0.378481	+	0.925609i	$0.623554\pi$
$54$	−19.6767	+	19.6767i	−0.364383	+	0.364383i
$55$	2.72618	+	2.72618i	0.0495670	+	0.0495670i
$56$	−47.3058	+	34.0707i	−0.844746	+	0.608406i
$57$	−43.8587			−0.769451
$58$	−38.4367	+	38.4367i	−0.662701	+	0.662701i
$59$			47.4282i			0.803868i	0.915669	+	0.401934i	$0.131662\pi$
$59$			47.4282i			0.803868i	−0.915669	+	0.401934i	$0.868338\pi$
$60$	−49.2431	+	49.2431i	−0.820718	+	0.820718i
$61$	−54.7097			−0.896880			−0.448440	−	0.893813i	$-0.648020\pi$
$61$	−54.7097			−0.896880			−0.448440	+	0.893813i	$0.648020\pi$
$62$	42.4921			0.685356
$63$	−17.2669	+	12.4361i	−0.274078	+	0.197398i
$64$	−50.1848			−0.784137
$65$	66.9280	−	66.9280i	1.02966	−	1.02966i
$66$			1.96370i			0.0297530i
$67$	−68.8824	+	68.8824i	−1.02810	+	1.02810i	−0.0285013	+	0.999594i	$0.509073\pi$
$67$	−68.8824	+	68.8824i	−1.02810	+	1.02810i	−0.999594	+	0.0285013i	$0.990927\pi$
$68$	5.42364	+	5.42364i	0.0797595	+	0.0797595i
$69$	−0.352564	+	0.352564i	−0.00510962	+	0.00510962i
$70$	−70.0592	+	50.4583i	−1.00085	+	0.720833i
$71$	−48.9469	−	48.9469i	−0.689393	−	0.689393i	0.272705	−	0.962098i	$-0.412082\pi$
$71$	−48.9469	−	48.9469i	−0.689393	−	0.689393i	−0.962098	+	0.272705i	$0.912082\pi$
$72$	−25.3170			−0.351625
$73$	−52.4323			−0.718251			−0.359125	−	0.933289i	$-0.616925\pi$
$73$	−52.4323			−0.718251			−0.359125	+	0.933289i	$0.616925\pi$
$74$		−	64.8053i		−	0.875748i
$75$	−144.823	+	144.823i	−1.93097	+	1.93097i
$76$	19.5692	+	19.5692i	0.257489	+	0.257489i
$77$	0.472627	−	2.90598i	0.00613802	−	0.0377400i
$78$	48.2090			0.618064
$79$	6.48392	+	6.48392i	0.0820749	+	0.0820749i	0.746952	−	0.664878i	$-0.231516\pi$
$79$	6.48392	+	6.48392i	0.0820749	+	0.0820749i	−0.664878	+	0.746952i	$0.731516\pi$
$80$	−22.4413			−0.280516
$81$	99.1180			1.22368
$82$	2.44311	−	55.1135i	0.0297941	−	0.672116i
$83$			1.55343i			0.0187161i	0.999956	+	0.00935804i	$0.00297880\pi$
$83$			1.55343i			0.0187161i	−0.999956	+	0.00935804i	$0.997021\pi$
$84$	52.4908	+	8.53707i	0.624890	+	0.101632i
$85$	22.7067	+	22.7067i	0.267138	+	0.267138i
$86$	−64.0232			−0.744456
$87$	140.175			1.61121
$88$	2.47688	−	2.47688i	0.0281463	−	0.0281463i
$89$	−112.697	+	112.697i	−1.26625	+	1.26625i	−0.318247	+	0.948008i	$0.603094\pi$
$89$	−112.697	+	112.697i	−1.26625	+	1.26625i	−0.948008	+	0.318247i	$0.896906\pi$
$90$	−37.4941			−0.416601
$91$	−71.3420	−	11.6030i	−0.783978	−	0.127506i
$92$	0.314619			0.00341977
$93$	−77.4825	−	77.4825i	−0.833146	−	0.833146i
$94$	52.1719	−	52.1719i	0.555021	−	0.555021i
$95$	81.9286	+	81.9286i	0.862407	+	0.862407i
$96$	73.6533	+	73.6533i	0.767221	+	0.767221i
$97$	−125.201	−	125.201i	−1.29074	−	1.29074i	−0.934331	−	0.356406i	$-0.884002\pi$
$97$	−125.201	−	125.201i	−1.29074	−	1.29074i	−0.356406	−	0.934331i	$-0.615998\pi$
$98$	62.5339	+	20.8936i	0.638101	+	0.213200i
$99$	0.904077	−	0.904077i	0.00913209	−	0.00913209i
$100$	129.236			1.29236
$101$	20.0691	+	20.0691i	0.198704	+	0.198704i	0.799444	−	0.600740i	$-0.205127\pi$
$101$	20.0691	+	20.0691i	0.198704	+	0.198704i	−0.600740	+	0.799444i	$0.705127\pi$
$102$			16.3559i			0.160352i
$103$	−38.6332			−0.375079			−0.187540	−	0.982257i	$-0.560051\pi$
$103$	−38.6332			−0.375079			−0.187540	+	0.982257i	$0.560051\pi$
$104$	−60.8075	−	60.8075i	−0.584687	−	0.584687i
$105$	219.759	+	35.7414i	2.09294	+	0.340395i
$106$	39.0180	−	39.0180i	0.368094	−	0.368094i
$107$	−64.7674			−0.605303			−0.302651	−	0.953101i	$-0.597872\pi$
$107$	−64.7674			−0.605303			−0.302651	+	0.953101i	$0.597872\pi$
$108$	−32.0180	−	32.0180i	−0.296463	−	0.296463i
$109$	−20.5614	+	20.5614i	−0.188637	+	0.188637i	−0.795107	−	0.606470i	$-0.792585\pi$
$109$	−20.5614	+	20.5614i	−0.188637	+	0.188637i	0.606470	+	0.795107i	$0.292585\pi$
$110$	3.66822	−	3.66822i	0.0333475	−	0.0333475i
$111$	−118.170	+	118.170i	−1.06459	+	1.06459i
$112$	10.0154	+	13.9060i	0.0894232	+	0.124160i
$113$	134.175			1.18739			0.593693	−	0.804692i	$-0.297669\pi$
$113$	134.175			1.18739			0.593693	+	0.804692i	$0.297669\pi$
$114$			59.0142i			0.517668i
$115$	1.31719			0.0114538
$116$	−62.5444	−	62.5444i	−0.539176	−	0.539176i
$117$	−22.1951	−	22.1951i	−0.189702	−	0.189702i
$118$	63.8172			0.540823
$119$	3.93657	−	24.2043i	0.0330804	−	0.203397i
$120$	187.308	+	187.308i	1.56090	+	1.56090i
$121$		−	120.823i		−	0.998538i
$122$			73.6147i			0.603399i
$123$	−104.952	+	96.0422i	−0.853269	+	0.780831i
$124$			69.1434i			0.557608i
$125$	311.898			2.49519
$126$	16.7334	+	23.2336i	0.132804	+	0.184393i
$127$	−155.797			−1.22675			−0.613373	−	0.789793i	$-0.710188\pi$
$127$	−155.797			−1.22675			−0.613373	+	0.789793i	$0.710188\pi$
$128$		−	52.5497i		−	0.410544i
$129$	116.744	+	116.744i	0.904989	+	0.904989i
$130$	−90.0550	−	90.0550i	−0.692731	−	0.692731i
$131$	−4.82183			−0.0368079			−0.0184039	−	0.999831i	$-0.505858\pi$
$131$	−4.82183			−0.0368079			−0.0184039	+	0.999831i	$0.505858\pi$
$132$	−3.19535			−0.0242072
$133$	14.2036	−	87.3320i	0.106794	−	0.656632i
$134$	92.6848	+	92.6848i	0.691678	+	0.691678i
$135$	−134.047	−	134.047i	−0.992941	−	0.992941i
$136$	20.6302	−	20.6302i	0.151693	−	0.151693i
$137$	9.00825	−	9.00825i	0.0657536	−	0.0657536i	−0.673465	−	0.739219i	$-0.735195\pi$
$137$	9.00825	−	9.00825i	0.0657536	−	0.0657536i	0.739219	+	0.673465i	$0.235195\pi$
$138$	0.474393	+	0.474393i	0.00343763	+	0.00343763i
$139$			160.834i			1.15708i	0.815654	+	0.578540i	$0.196377\pi$
$139$			160.834i			1.15708i	−0.815654	+	0.578540i	$0.803623\pi$
$140$	−82.1061	−	114.001i	−0.586472	−	0.814291i
$141$	−190.267			−1.34941
$142$	−65.8606	+	65.8606i	−0.463807	+	0.463807i
$143$	4.34291			0.0303700
$144$			7.44215i			0.0516816i
$145$	−261.849	−	261.849i	−1.80586	−	1.80586i
$146$			70.5504i			0.483222i
$147$	−75.9293	−	152.127i	−0.516526	−	1.03487i
$148$	105.452			0.712511
$149$	−178.240	+	178.240i	−1.19624	+	1.19624i	−0.220955	+	0.975284i	$0.570917\pi$
$149$	−178.240	+	178.240i	−1.19624	+	1.19624i	−0.975284	+	0.220955i	$0.929083\pi$
$150$	194.867	+	194.867i	1.29911	+	1.29911i
$151$	−134.961	−	134.961i	−0.893781	−	0.893781i	0.101096	−	0.994877i	$-0.467765\pi$
$151$	−134.961	−	134.961i	−0.893781	−	0.893781i	−0.994877	+	0.101096i	$0.967765\pi$
$152$	74.4363	−	74.4363i	0.489713	−	0.489713i
$153$	7.53017	−	7.53017i	0.0492168	−	0.0492168i
$154$	−3.91015	−	0.635944i	−0.0253906	−	0.00412951i
$155$			289.477i			1.86759i
$156$			78.4460i			0.502859i
$157$	−128.374	+	128.374i	−0.817670	+	0.817670i	−0.985770	−	0.168100i	$-0.946237\pi$
$157$	−128.374	+	128.374i	−0.817670	+	0.817670i	0.168100	+	0.985770i	$0.446237\pi$
$158$	8.72445	−	8.72445i	0.0552180	−	0.0552180i
$159$	−142.295			−0.894939
$160$		−	275.171i		−	1.71982i
$161$	−0.587852	−	0.816208i	−0.00365126	−	0.00506962i
$162$		−	133.368i		−	0.823262i
$163$	78.5989			0.482202			0.241101	−	0.970500i	$-0.422492\pi$
$163$	78.5989			0.482202			0.241101	+	0.970500i	$0.422492\pi$
$164$	89.6810	+	3.97545i	0.546835	+	0.0242405i
$165$	−13.3777			−0.0810769
$166$	2.09023			0.0125917
$167$	70.8693	−	70.8693i	0.424367	−	0.424367i	−0.462337	−	0.886704i	$-0.652989\pi$
$167$	70.8693	−	70.8693i	0.424367	−	0.424367i	0.886704	+	0.462337i	$0.152989\pi$
$168$	32.4729	−	199.662i	0.193291	−	1.18846i
$169$			62.3814i			0.369121i
$170$	30.5531	−	30.5531i	0.179724	−	0.179724i
$171$	27.1698	−	27.1698i	0.158888	−	0.158888i
$172$		−	104.179i		−	0.605691i
$173$	29.0124			0.167702			0.0838510	−	0.996478i	$-0.473278\pi$
$173$	29.0124			0.167702			0.0838510	+	0.996478i	$0.473278\pi$
$174$		−	188.613i		−	1.08398i
$175$	−241.472	−	335.274i	−1.37984	−	1.91585i
$176$	−0.728100	−	0.728100i	−0.00413693	−	0.00413693i
$177$	−116.368	−	116.368i	−0.657446	−	0.657446i
$178$	151.639	+	151.639i	0.851906	+	0.851906i
$179$	166.970	−	166.970i	0.932793	−	0.932793i	−0.0650863	−	0.997880i	$-0.520732\pi$
$179$	166.970	−	166.970i	0.932793	−	0.932793i	0.997880	+	0.0650863i	$0.0207323\pi$
$180$		−	61.0106i		−	0.338948i
$181$	−180.202	−	180.202i	−0.995591	−	0.995591i	0.00439926	−	0.999990i	$-0.498600\pi$
$181$	−180.202	−	180.202i	−0.995591	−	0.995591i	−0.999990	+	0.00439926i	$0.998600\pi$
$182$	−15.6125	+	95.9944i	−0.0857828	+	0.527442i
$183$	134.233	−	134.233i	0.733515	−	0.733515i
$184$		−	1.19673i		−	0.00650398i
$185$	441.485			2.38641
$186$	−104.257	+	104.257i	−0.560520	+	0.560520i
$187$			1.47342i			0.00787926i
$188$	84.8945	+	84.8945i	0.451566	+	0.451566i
$189$	−23.2392	+	142.888i	−0.122959	+	0.756020i
$190$	110.239	−	110.239i	0.580207	−	0.580207i
$191$	−204.530	+	204.530i	−1.07084	+	1.07084i	−0.0735444	+	0.997292i	$0.523431\pi$
$191$	−204.530	+	204.530i	−1.07084	+	1.07084i	−0.997292	+	0.0735444i	$0.976569\pi$
$192$	123.131	−	123.131i	0.641308	−	0.641308i
$193$	134.762	+	134.762i	0.698247	+	0.698247i	0.964032	−	0.265785i	$-0.0856312\pi$
$193$	134.762	+	134.762i	0.698247	+	0.698247i	−0.265785	+	0.964032i	$0.585631\pi$
$194$	−168.465	+	168.465i	−0.868377	+	0.868377i
$195$			328.423i			1.68422i
$196$	−33.9983	+	101.756i	−0.173460	+	0.519161i
$197$			47.2488i			0.239842i	0.992783	+	0.119921i	$0.0382641\pi$
$197$			47.2488i			0.239842i	−0.992783	+	0.119921i	$0.961736\pi$
$198$	−1.21648	−	1.21648i	−0.00614385	−	0.00614385i
$199$	−82.2386	−	82.2386i	−0.413259	−	0.413259i	0.469613	−	0.882872i	$-0.344393\pi$
$199$	−82.2386	−	82.2386i	−0.413259	−	0.413259i	−0.882872	+	0.469613i	$0.844393\pi$
$200$		−	491.583i		−	2.45791i
$201$		−	338.014i		−	1.68166i
$202$	27.0041	−	27.0041i	0.133684	−	0.133684i
$203$	−45.3958	+	279.119i	−0.223624	+	1.37497i
$204$	−26.6144			−0.130463
$205$	375.460	+	16.6437i	1.83151	+	0.0811887i
$206$			51.9829i			0.252344i
$207$		−	0.436816i		−	0.00211022i
$208$	−17.8749	+	17.8749i	−0.0859370	+	0.0859370i
$209$			5.31629i			0.0254368i
$210$	48.0920	−	295.697i	0.229009	−	1.40808i
$211$	−133.081	+	133.081i	−0.630716	+	0.630716i	−0.948248	−	0.317531i	$-0.897146\pi$
$211$	−133.081	+	133.081i	−0.630716	+	0.630716i	0.317531	+	0.948248i	$0.397146\pi$
$212$	63.4903	+	63.4903i	0.299483	+	0.299483i
$213$	240.188			1.12764
$214$			87.1479i			0.407233i
$215$		−	436.157i		−	2.02864i
$216$	−121.789	+	121.789i	−0.563836	+	0.563836i
$217$	179.377	−	129.192i	0.826622	−	0.595353i
$218$	27.6664	+	27.6664i	0.126910	+	0.126910i
$219$	128.646	−	128.646i	0.587423	−	0.587423i
$220$	5.96895	+	5.96895i	0.0271316	+	0.0271316i
$221$	36.1726			0.163677
$222$	159.004	+	159.004i	0.716232	+	0.716232i
$223$			16.6605i			0.0747110i	0.999302	+	0.0373555i	$0.0118934\pi$
$223$			16.6605i			0.0747110i	−0.999302	+	0.0373555i	$0.988107\pi$
$224$	−170.512	+	122.807i	−0.761214	+	0.548244i
$225$		−	179.431i		−	0.797471i
$226$		−	180.539i		−	0.798845i
$227$	−226.653	−	226.653i	−0.998473	−	0.998473i	0.00152581	−	0.999999i	$-0.499514\pi$
$227$	−226.653	−	226.653i	−0.998473	−	0.998473i	−0.999999	+	0.00152581i	$0.999514\pi$
$228$	−96.0282			−0.421176
$229$	274.192	+	274.192i	1.19735	+	1.19735i	0.974959	+	0.222386i	$0.0713847\pi$
$229$	274.192	+	274.192i	1.19735	+	1.19735i	0.222386	+	0.974959i	$0.428615\pi$
$230$		−	1.77235i		−	0.00770585i
$231$	5.97037	+	8.28960i	0.0258458	+	0.0358857i
$232$	−237.903	+	237.903i	−1.02545	+	1.02545i
$233$	258.859	+	258.859i	1.11098	+	1.11098i	0.993018	+	0.117963i	$0.0376365\pi$
$233$	258.859	+	258.859i	1.11098	+	1.11098i	0.117963	+	0.993018i	$0.462363\pi$
$234$	−29.8647	+	29.8647i	−0.127627	+	0.127627i
$235$	355.421	+	355.421i	1.51243	+	1.51243i
$236$			103.844i			0.440015i
$237$	−31.8173			−0.134250
$238$	−32.5681	−	5.29686i	−0.136841	−	0.0222557i
$239$	75.7800	+	75.7800i	0.317071	+	0.317071i	0.847641	−	0.530570i	$-0.178022\pi$
$239$	75.7800	+	75.7800i	0.317071	+	0.317071i	−0.530570	+	0.847641i	$0.678022\pi$
$240$	55.0610	−	55.0610i	0.229421	−	0.229421i
$241$	125.083			0.519016			0.259508	−	0.965741i	$-0.416440\pi$
$241$	125.083			0.519016			0.259508	+	0.965741i	$0.416440\pi$
$242$	−162.574			−0.671792
$243$	−111.580	+	111.580i	−0.459178	+	0.459178i
$244$	−119.786			−0.490927
$245$	−142.338	+	426.011i	−0.580970	+	1.73882i
$246$	129.230	+	141.218i	0.525324	+	0.574059i
$247$	130.515			0.528402
$248$	263.004			1.06050
$249$	−3.81144	−	3.81144i	−0.0153070	−	0.0153070i
$250$		−	419.675i		−	1.67870i
$251$	314.303			1.25220			0.626102	−	0.779742i	$-0.284650\pi$
$251$	314.303			1.25220			0.626102	+	0.779742i	$0.284650\pi$
$252$	−37.8058	+	27.2286i	−0.150023	+	0.108050i
$253$	0.0427357	+	0.0427357i	0.000168916	+	0.000168916i
$254$			209.633i			0.825325i
$255$	−111.424			−0.436958
$256$	−271.447			−1.06034
$257$	11.5701	−	11.5701i	0.0450200	−	0.0450200i	−0.684238	−	0.729258i	$-0.739865\pi$
$257$	11.5701	−	11.5701i	0.0450200	−	0.0450200i	0.729258	+	0.684238i	$0.239865\pi$
$258$	157.085	−	157.085i	0.608855	−	0.608855i
$259$	−197.032	−	273.570i	−0.760741	−	1.05626i
$260$	146.538	−	146.538i	0.563608	−	0.563608i
$261$	−86.8364	+	86.8364i	−0.332707	+	0.332707i
$262$			6.48802i			0.0247634i
$263$	340.334	−	340.334i	1.29404	−	1.29404i	0.361780	−	0.932263i	$-0.382169\pi$
$263$	340.334	−	340.334i	1.29404	−	1.29404i	0.932263	−	0.361780i	$-0.117831\pi$
$264$			12.1543i			0.0460390i
$265$	265.810	+	265.810i	1.00305	+	1.00305i
$266$	−117.510	−	19.1117i	−0.441766	−	0.0718486i
$267$		−	553.015i		−	2.07122i
$268$	−150.817	+	150.817i	−0.562751	+	0.562751i
$269$		−	277.825i		−	1.03281i	−0.856345	−	0.516404i	$-0.827270\pi$
$269$		−	277.825i		−	1.03281i	0.856345	−	0.516404i	$-0.172730\pi$
$270$	−180.367	+	180.367i	−0.668027	+	0.668027i
$271$			217.838i			0.803830i	0.915677	+	0.401915i	$0.131655\pi$
$271$			217.838i			0.803830i	−0.915677	+	0.401915i	$0.868345\pi$
$272$	−6.06443	−	6.06443i	−0.0222957	−	0.0222957i
$273$	203.510	−	146.573i	0.745459	−	0.536897i
$274$	−12.1211	−	12.1211i	−0.0442375	−	0.0442375i
$275$	17.5546	+	17.5546i	0.0638348	+	0.0638348i
$276$	−0.771936	+	0.771936i	−0.00279687	+	0.00279687i
$277$	−329.437			−1.18930			−0.594652	−	0.803983i	$-0.702710\pi$
$277$	−329.437			−1.18930			−0.594652	+	0.803983i	$0.702710\pi$
$278$	216.411			0.778456
$279$	95.9984			0.344080
$280$	−433.631	+	312.311i	−1.54868	+	1.11540i
$281$	13.8642	−	13.8642i	0.0493387	−	0.0493387i	−0.682007	−	0.731346i	$-0.738893\pi$
$281$	13.8642	−	13.8642i	0.0493387	−	0.0493387i	0.731346	+	0.682007i	$0.238893\pi$
$282$			256.014i			0.907850i
$283$		−	303.297i		−	1.07172i	−0.844306	−	0.535861i	$-0.819987\pi$
$283$		−	303.297i		−	1.07172i	0.844306	−	0.535861i	$-0.180013\pi$
$284$	−107.169	−	107.169i	−0.377355	−	0.377355i
$285$	−402.033			−1.41064
$286$		−	5.84360i		−	0.0204322i
$287$	−157.252	−	240.085i	−0.547916	−	0.836534i
$288$	−91.2541			−0.316854
$289$		−	276.728i		−	0.957535i
$290$	−352.332	+	352.332i	−1.21494	+	1.21494i
$291$	614.378			2.11126
$292$	−114.800			−0.393151
$293$	25.2044	+	25.2044i	0.0860219	+	0.0860219i	0.748808	−	0.662787i	$-0.230626\pi$
$293$	25.2044	+	25.2044i	0.0860219	+	0.0860219i	−0.662787	+	0.748808i	$0.730626\pi$
$294$	−204.694	+	102.167i	−0.696239	+	0.347506i
$295$			434.753i			1.47374i
$296$		−	401.112i		−	1.35511i
$297$		−	8.69821i		−	0.0292869i
$298$	239.831	+	239.831i	0.804801	+	0.804801i
$299$	1.04916	−	1.04916i	0.00350891	−	0.00350891i
$300$	−317.088	+	317.088i	−1.05696	+	1.05696i
$301$	−270.269	+	194.654i	−0.897903	+	0.646691i
$302$	−181.597	+	181.597i	−0.601314	+	0.601314i
$303$	−98.4816			−0.325022
$304$	−21.8812	−	21.8812i	−0.0719777	−	0.0719777i
$305$	−501.499			−1.64426
$306$	−10.1322	−	10.1322i	−0.0331119	−	0.0331119i
$307$	40.8584			0.133089			0.0665447	−	0.997783i	$-0.478803\pi$
$307$	40.8584			0.133089			0.0665447	+	0.997783i	$0.478803\pi$
$308$	1.03481	−	6.36261i	0.00335978	−	0.0206578i
$309$	94.7887	−	94.7887i	0.306759	−	0.306759i
$310$	389.506			1.25647
$311$	220.065	+	220.065i	0.707603	+	0.707603i	0.966031	−	0.258427i	$-0.0832042\pi$
$311$	220.065	+	220.065i	0.707603	+	0.707603i	−0.258427	+	0.966031i	$0.583204\pi$
$312$	298.389			0.956375
$313$	12.7581	+	12.7581i	0.0407606	+	0.0407606i	0.727193	−	0.686433i	$-0.240824\pi$
$313$	12.7581	+	12.7581i	0.0407606	+	0.0407606i	−0.686433	+	0.727193i	$0.740824\pi$
$314$	172.734	+	172.734i	0.550109	+	0.550109i
$315$	−158.278	+	113.996i	−0.502471	+	0.361891i
$316$	14.1965	+	14.1965i	0.0449255	+	0.0449255i
$317$	186.799	+	186.799i	0.589271	+	0.589271i	0.937434	−	0.348163i	$-0.113194\pi$
$317$	186.799	+	186.799i	0.589271	+	0.589271i	−0.348163	+	0.937434i	$0.613194\pi$
$318$			191.466i			0.602093i
$319$		−	16.9912i		−	0.0532640i
$320$	−460.022			−1.43757
$321$	158.911	−	158.911i	0.495048	−	0.495048i
$322$	−1.09825	+	0.790986i	−0.00341072	+	0.00245648i
$323$			44.2800i			0.137090i
$324$	217.018			0.669809
$325$	430.966	−	430.966i	1.32605	−	1.32605i
$326$		−	105.759i		−	0.324414i
$327$		−	100.897i		−	0.308554i
$328$	15.1216	−	341.124i	0.0461025	−	1.04001i
$329$	61.6178	−	378.861i	0.187288	−	1.15155i
$330$			18.0004i			0.0545466i
$331$	−115.603	−	115.603i	−0.349253	−	0.349253i	0.510578	−	0.859831i	$-0.329431\pi$
$331$	−115.603	−	115.603i	−0.349253	−	0.349253i	−0.859831	+	0.510578i	$0.829431\pi$
$332$			3.40123i			0.0102447i
$333$		−	146.409i		−	0.439666i
$334$	−95.3583	−	95.3583i	−0.285504	−	0.285504i
$335$	−631.414	+	631.414i	−1.88482	+	1.88482i
$336$	−58.6924	−	9.54571i	−0.174680	−	0.0284098i
$337$			410.128i			1.21700i	0.793555	+	0.608499i	$0.208228\pi$
$337$			410.128i			1.21700i	−0.793555	+	0.608499i	$0.791772\pi$
$338$	83.9374			0.248336
$339$	−329.205	+	329.205i	−0.971106	+	0.971106i
$340$	49.7161	+	49.7161i	0.146224	+	0.146224i
$341$	−9.39197	+	9.39197i	−0.0275424	+	0.0275424i
$342$	−36.5583	−	36.5583i	−0.106896	−	0.106896i
$343$	327.506	−	101.925i	0.954828	−	0.297158i
$344$	−396.271			−1.15195
$345$	−3.23180	+	3.23180i	−0.00936753	+	0.00936753i
$346$		−	39.0378i		−	0.112826i
$347$	336.525	−	336.525i	0.969814	−	0.969814i	−0.0297436	−	0.999558i	$-0.509469\pi$
$347$	336.525	−	336.525i	0.969814	−	0.969814i	0.999558	+	0.0297436i	$0.00946909\pi$
$348$	306.912			0.881932
$349$	−487.552			−1.39700			−0.698499	−	0.715611i	$-0.746148\pi$
$349$	−487.552			−1.39700			−0.698499	+	0.715611i	$0.746148\pi$
$350$	−451.129	+	324.914i	−1.28894	+	0.928325i
$351$	−213.542			−0.608381
$352$	8.92781	−	8.92781i	0.0253631	−	0.0253631i
$353$			384.262i			1.08856i	0.838904	+	0.544280i	$0.183197\pi$
$353$			384.262i			1.08856i	−0.838904	+	0.544280i	$0.816803\pi$
$354$	−156.579	+	156.579i	−0.442314	+	0.442314i
$355$	−448.674	−	448.674i	−1.26387	−	1.26387i
$356$	−246.748	+	246.748i	−0.693113	+	0.693113i
$357$	49.7279	+	69.0451i	0.139294	+	0.193404i
$358$	−224.667	−	224.667i	−0.627561	−	0.627561i
$359$	203.254			0.566167			0.283084	−	0.959095i	$-0.408643\pi$
$359$	203.254			0.566167			0.283084	+	0.959095i	$0.408643\pi$
$360$	−232.069			−0.644637
$361$		−	201.232i		−	0.557430i
$362$	−242.471	+	242.471i	−0.669810	+	0.669810i
$363$	296.446	+	296.446i	0.816657	+	0.816657i
$364$	−156.203	−	25.4047i	−0.429128	−	0.0697932i
$365$	−480.624			−1.31678
$366$	−180.618	−	180.618i	−0.493491	−	0.493491i
$367$	−85.0064			−0.231625			−0.115813	−	0.993271i	$-0.536947\pi$
$367$	−85.0064			−0.231625			−0.115813	+	0.993271i	$0.536947\pi$
$368$	−0.351791			−0.000955953
$369$	5.51950	−	124.513i	0.0149580	−	0.337433i
$370$		−	594.042i		−	1.60552i
$371$	46.0823	−	283.340i	0.124211	−	0.763720i
$372$	−169.647	−	169.647i	−0.456041	−	0.456041i
$373$	−725.011			−1.94373			−0.971864	−	0.235543i	$-0.924313\pi$
$373$	−725.011			−1.94373			−0.971864	+	0.235543i	$0.924313\pi$
$374$	1.98256			0.00530098
$375$	−765.260	+	765.260i	−2.04069	+	2.04069i
$376$	322.918	−	322.918i	0.858824	−	0.858824i
$377$	−417.135			−1.10646
$378$	192.263	+	31.2695i	0.508632	+	0.0827236i
$379$	502.063			1.32470			0.662352	−	0.749193i	$-0.269559\pi$
$379$	502.063			1.32470			0.662352	+	0.749193i	$0.269559\pi$
$380$	179.382	+	179.382i	0.472058	+	0.472058i
$381$	382.256	−	382.256i	1.00330	−	1.00330i
$382$	275.205	+	275.205i	0.720433	+	0.720433i
$383$	−48.5674	−	48.5674i	−0.126808	−	0.126808i	0.640855	−	0.767662i	$-0.278580\pi$
$383$	−48.5674	−	48.5674i	−0.126808	−	0.126808i	−0.767662	+	0.640855i	$0.778580\pi$
$384$	128.934	+	128.934i	0.335765	+	0.335765i
$385$	4.33236	−	26.6378i	0.0112529	−	0.0691891i
$386$	181.329	−	181.329i	0.469764	−	0.469764i
$387$	−144.642			−0.373751
$388$	−274.127	−	274.127i	−0.706514	−	0.706514i
$389$		−	188.216i		−	0.483845i	−0.970296	−	0.241922i	$-0.922222\pi$
$389$		−	188.216i		−	0.483845i	0.970296	−	0.241922i	$-0.0777779\pi$
$390$	441.910			1.13310
$391$	0.355951	+	0.355951i	0.000910360	+	0.000910360i
$392$	387.053	+	129.321i	0.987380	+	0.329900i
$393$	11.8306	−	11.8306i	0.0301034	−	0.0301034i
$394$	63.5757			0.161360
$395$	59.4352	+	59.4352i	0.150469	+	0.150469i
$396$	1.97947	−	1.97947i	0.00499865	−	0.00499865i
$397$	210.685	−	210.685i	0.530692	−	0.530692i	−0.390086	−	0.920778i	$-0.627555\pi$
$397$	210.685	−	210.685i	0.530692	−	0.530692i	0.920778	+	0.390086i	$0.127555\pi$
$398$	−110.656	+	110.656i	−0.278031	+	0.278031i
$399$	179.425	+	249.123i	0.449686	+	0.624370i
$400$	−144.505			−0.361263
$401$		−	32.5736i		−	0.0812309i	−0.999175	−	0.0406155i	$-0.987068\pi$
$401$		−	32.5736i		−	0.0812309i	0.999175	−	0.0406155i	$-0.0129319\pi$
$402$	−454.815			−1.13138
$403$	230.573	+	230.573i	0.572142	+	0.572142i
$404$	43.9412	+	43.9412i	0.108765	+	0.108765i
$405$	908.571			2.24338
$406$	375.569	+	61.0824i	0.925047	+	0.150449i
$407$	14.3238	+	14.3238i	0.0351937	+	0.0351937i
$408$			101.235i			0.248124i
$409$			551.588i			1.34863i	0.738446	+	0.674313i	$0.235560\pi$
$409$			551.588i			1.34863i	−0.738446	+	0.674313i	$0.764440\pi$
$410$	22.3949	−	505.201i	0.0546218	−	1.23220i
$411$			44.2045i			0.107554i
$412$	−84.5869			−0.205308
$413$	269.399	−	194.027i	0.652298	−	0.469800i
$414$	−0.587758			−0.00141971
$415$			14.2396i			0.0343124i
$416$	−219.178	−	219.178i	−0.526871	−	0.526871i
$417$	−394.616	−	394.616i	−0.946321	−	0.946321i
$418$	7.15334			0.0171133
$419$	447.823			1.06879			0.534395	−	0.845235i	$-0.320540\pi$
$419$	447.823			1.06879			0.534395	+	0.845235i	$0.320540\pi$
$420$	481.159	+	78.2555i	1.14562	+	0.186323i
$421$	96.1046	+	96.1046i	0.228277	+	0.228277i	0.811973	−	0.583696i	$-0.198394\pi$
$421$	96.1046	+	96.1046i	0.228277	+	0.228277i	−0.583696	+	0.811973i	$0.698394\pi$
$422$	179.068	+	179.068i	0.424331	+	0.424331i
$423$	117.867	−	117.867i	0.278646	−	0.278646i
$424$	241.502	−	241.502i	0.569579	−	0.569579i
$425$	146.214	+	146.214i	0.344033	+	0.344033i
$426$		−	323.185i		−	0.758651i
$427$	223.816	+	310.758i	0.524158	+	0.727772i
$428$	−141.808			−0.331326
$429$	−10.6556	+	10.6556i	−0.0248381	+	0.0248381i
$430$	−586.872			−1.36482
$431$			774.781i			1.79764i	0.438322	+	0.898818i	$0.355573\pi$
$431$			774.781i			1.79764i	−0.438322	+	0.898818i	$0.644427\pi$
$432$	35.8008	+	35.8008i	0.0828723	+	0.0828723i
$433$			271.046i			0.625971i	0.949758	+	0.312986i	$0.101329\pi$
$433$			271.046i			0.625971i	−0.949758	+	0.312986i	$0.898671\pi$
$434$	−173.834	−	241.361i	−0.400539	−	0.556131i
$435$	1284.92			2.95385
$436$	−45.0190	+	45.0190i	−0.103255	+	0.103255i
$437$	1.28432	+	1.28432i	0.00293894	+	0.00293894i
$438$	−173.099	−	173.099i	−0.395204	−	0.395204i
$439$	−141.117	+	141.117i	−0.321451	+	0.321451i	−0.849323	−	0.527873i	$-0.822990\pi$
$439$	−141.117	+	141.117i	−0.321451	+	0.321451i	0.527873	+	0.849323i	$0.322990\pi$
$440$	22.7044	−	22.7044i	0.0516009	−	0.0516009i
$441$	141.277	+	47.2030i	0.320356	+	0.107036i
$442$		−	48.6721i		−	0.110118i
$443$			343.264i			0.774862i	0.921899	+	0.387431i	$0.126638\pi$
$443$			343.264i			0.774862i	−0.921899	+	0.387431i	$0.873362\pi$
$444$	−258.732	+	258.732i	−0.582729	+	0.582729i
$445$	−1033.04	+	1033.04i	−2.32144	+	2.32144i
$446$	22.4176			0.0502637
$447$		−	874.642i		−	1.95669i
$448$	205.304	+	285.056i	0.458269	+	0.636287i
$449$		−	627.625i		−	1.39783i	−0.715205	−	0.698914i	$-0.753667\pi$
$449$		−	627.625i		−	1.39783i	0.715205	−	0.698914i	$-0.246333\pi$
$450$	−241.434			−0.536519
$451$	11.6417	+	12.7217i	0.0258130	+	0.0282077i
$452$	293.774			0.649942
$453$	662.268			1.46196
$454$	−304.974	+	304.974i	−0.671749	+	0.671749i
$455$	−653.960	−	106.360i	−1.43728	−	0.233758i
$456$			365.268i			0.801025i
$457$	231.414	−	231.414i	0.506377	−	0.506377i	−0.407035	−	0.913413i	$-0.633437\pi$
$457$	231.414	−	231.414i	0.506377	−	0.506377i	0.913413	+	0.407035i	$0.133437\pi$
$458$	368.940	−	368.940i	0.805545	−	0.805545i
$459$		−	72.4485i		−	0.157840i
$460$	2.88397			0.00626950
$461$		−	60.9597i		−	0.132234i	−0.997812	−	0.0661168i	$-0.978939\pi$
$461$		−	60.9597i		−	0.132234i	0.997812	−	0.0661168i	$-0.0210610\pi$
$462$	11.1541	−	8.03344i	0.0241431	−	0.0173884i
$463$	−471.542	−	471.542i	−1.01845	−	1.01845i	−0.999827	−	0.0186233i	$-0.994072\pi$
$463$	−471.542	−	471.542i	−1.01845	−	1.01845i	−0.0186233	−	0.999827i	$-0.505928\pi$
$464$	69.9339	+	69.9339i	0.150720	+	0.150720i
$465$	−710.248	−	710.248i	−1.52741	−	1.52741i
$466$	348.308	−	348.308i	0.747442	−	0.747442i
$467$			878.028i			1.88015i	0.340973	+	0.940073i	$0.389244\pi$
$467$			878.028i			1.88015i	−0.340973	+	0.940073i	$0.610756\pi$
$468$	−48.5960	−	48.5960i	−0.103838	−	0.103838i
$469$	673.057	+	109.466i	1.43509	+	0.233402i
$470$	478.237	−	478.237i	1.01753	−	1.01753i
$471$		−	629.946i		−	1.33747i
$472$	394.996			0.836855
$473$	14.1510	−	14.1510i	0.0299174	−	0.0299174i
$474$			42.8118i			0.0903203i
$475$	527.559	+	527.559i	1.11065	+	1.11065i
$476$	8.61908	−	52.9950i	0.0181073	−	0.111334i
$477$	88.1497	−	88.1497i	0.184800	−	0.184800i
$478$	101.966	−	101.966i	0.213318	−	0.213318i
$479$	−390.712	+	390.712i	−0.815683	+	0.815683i	−0.985479	−	0.169796i	$-0.945689\pi$
$479$	−390.712	+	390.712i	−0.815683	+	0.815683i	0.169796	+	0.985479i	$0.445689\pi$
$480$	675.147	+	675.147i	1.40656	+	1.40656i
$481$	351.651	−	351.651i	0.731083	−	0.731083i
$482$		−	168.305i		−	0.349181i
$483$	3.44494	+	0.560284i	0.00713238	+	0.00116001i
$484$		−	264.541i		−	0.546572i
$485$	−1147.67	−	1147.67i	−2.36632	−	2.36632i
$486$	150.137	+	150.137i	0.308924	+	0.308924i
$487$		−	507.320i		−	1.04172i	−0.853641	−	0.520862i	$-0.825611\pi$
$487$		−	507.320i		−	1.04172i	0.853641	−	0.520862i	$-0.174389\pi$
$488$			455.637i			0.933683i
$489$	−192.847	+	192.847i	−0.394370	+	0.394370i
$490$	573.220	+	191.523i	1.16984	+	0.390863i
$491$	−185.233			−0.377256			−0.188628	−	0.982049i	$-0.560404\pi$
$491$	−185.233			−0.377256			−0.188628	+	0.982049i	$0.560404\pi$
$492$	−229.791	+	210.283i	−0.467056	+	0.427405i
$493$		−	141.522i		−	0.287063i
$494$		−	175.615i		−	0.355496i
$495$	8.28727	−	8.28727i	0.0167420	−	0.0167420i
$496$		−	77.3125i		−	0.155872i
$497$	−77.7849	+	478.265i	−0.156509	+	0.962305i
$498$	−5.12849	+	5.12849i	−0.0102982	+	0.0102982i
$499$	204.116	+	204.116i	0.409051	+	0.409051i	0.881408	−	0.472357i	$-0.156597\pi$
$499$	204.116	+	204.116i	0.409051	+	0.409051i	−0.472357	+	0.881408i	$0.656597\pi$
$500$	682.898			1.36580
$501$			347.764i			0.694139i
$502$		−	422.911i		−	0.842452i
$503$	−152.995	+	152.995i	−0.304164	+	0.304164i	−0.842641	−	0.538476i	$-0.819000\pi$
$503$	−152.995	+	152.995i	−0.304164	+	0.304164i	0.538476	+	0.842641i	$0.319000\pi$
$504$	103.571	+	143.804i	0.205498	+	0.285325i
$505$	183.965	+	183.965i	0.364287	+	0.364287i
$506$	0.0575031	−	0.0575031i	0.000113643	−	0.000113643i
$507$	−153.056	−	153.056i	−0.301886	−	0.301886i
$508$	−341.115			−0.671487
$509$	−119.043	−	119.043i	−0.233876	−	0.233876i	0.580433	−	0.814308i	$-0.302883\pi$
$509$	−119.043	−	119.043i	−0.233876	−	0.233876i	−0.814308	+	0.580433i	$0.802883\pi$
$510$			149.927i			0.293975i
$511$	214.499	+	297.823i	0.419763	+	0.582823i
$512$			155.048i			0.302828i
$513$		−	261.403i		−	0.509558i
$514$	−15.5682	−	15.5682i	−0.0302884	−	0.0302884i
$515$	−354.133			−0.687637
$516$	255.609	+	255.609i	0.495366	+	0.495366i
$517$			23.0630i			0.0446092i
$518$	−368.103	+	265.117i	−0.710624	+	0.511808i
$519$	−71.1837	+	71.1837i	−0.137155	+	0.137155i
$520$	−557.395	−	557.395i	−1.07191	−	1.07191i
$521$	350.206	−	350.206i	0.672180	−	0.672180i	−0.286038	−	0.958218i	$-0.592338\pi$
$521$	350.206	−	350.206i	0.672180	−	0.672180i	0.958218	+	0.286038i	$0.0923385\pi$
$522$	116.843	+	116.843i	0.223837	+	0.223837i
$523$		−	701.858i		−	1.34199i	−0.741464	−	0.670993i	$-0.765868\pi$
$523$		−	701.858i		−	1.34199i	0.741464	−	0.670993i	$-0.234132\pi$
$524$	−10.5573			−0.0201476
$525$	1415.08	+	230.148i	2.69539	+	0.438377i
$526$	−457.936	−	457.936i	−0.870602	−	0.870602i
$527$	−78.2268	+	78.2268i	−0.148438	+	0.148438i
$528$	3.57287			0.00676680
$529$	−528.979			−0.999961
$530$	357.661	−	357.661i	0.674831	−	0.674831i
$531$	144.176			0.271518
$532$	31.0987	−	191.213i	0.0584562	−	0.359422i
$533$	312.317	−	285.804i	0.585962	−	0.536217i
$534$	−744.111			−1.39347
$535$	−593.694			−1.10971
$536$	573.672	+	573.672i	1.07028	+	1.07028i
$537$			819.341i			1.52577i
$538$	−373.829			−0.694849
$539$	−18.4399	+	9.20369i	−0.0342113	+	0.0170755i
$540$	−293.495	−	293.495i	−0.543509	−	0.543509i
$541$		−	457.870i		−	0.846339i	−0.906050	−	0.423170i	$-0.860917\pi$
$541$		−	457.870i		−	0.846339i	0.906050	−	0.423170i	$-0.139083\pi$
$542$	293.112			0.540798
$543$	884.272			1.62849
$544$	74.3608	−	74.3608i	0.136693	−	0.136693i
$545$	−188.477	+	188.477i	−0.345830	+	0.345830i
$546$	−197.222	−	273.834i	−0.361212	−	0.501527i
$547$	284.395	−	284.395i	0.519918	−	0.519918i	−0.397629	−	0.917546i	$-0.630167\pi$
$547$	284.395	−	284.395i	0.519918	−	0.519918i	0.917546	+	0.397629i	$0.130167\pi$
$548$	19.7235	−	19.7235i	0.0359917	−	0.0359917i
$549$			166.311i			0.302934i
$550$	23.6206	−	23.6206i	0.0429465	−	0.0429465i
$551$		−	510.629i		−	0.926731i
$552$	2.93625	+	2.93625i	0.00531930	+	0.00531930i
$553$	10.3040	−	63.3550i	0.0186330	−	0.114566i
$554$			443.275i			0.800135i
$555$	−1083.21	+	1083.21i	−1.95173	+	1.95173i
$556$			352.145i			0.633354i
$557$	114.074	−	114.074i	0.204800	−	0.204800i	−0.597253	−	0.802053i	$-0.703741\pi$
$557$	114.074	−	114.074i	0.204800	−	0.204800i	0.802053	+	0.597253i	$0.203741\pi$
$558$		−	129.171i		−	0.231489i
$559$	−347.407	−	347.407i	−0.621479	−	0.621479i
$560$	91.8067	+	127.470i	0.163941	+	0.227625i
$561$	−3.61512	−	3.61512i	−0.00644407	−	0.00644407i
$562$	−18.6549	−	18.6549i	−0.0331939	−	0.0331939i
$563$	72.1548	−	72.1548i	0.128161	−	0.128161i	−0.640117	−	0.768278i	$-0.721114\pi$
$563$	72.1548	−	72.1548i	0.128161	−	0.128161i	0.768278	+	0.640117i	$0.221114\pi$
$564$	−416.587			−0.738629
$565$	1229.92			2.17685
$566$	−408.102			−0.721029
$567$	−405.489	−	563.004i	−0.715148	−	0.992953i
$568$	−407.643	+	407.643i	−0.717682	+	0.717682i
$569$			223.936i			0.393561i	0.980448	+	0.196781i	$0.0630486\pi$
$569$			223.936i			0.393561i	−0.980448	+	0.196781i	$0.936951\pi$
$570$			540.956i			0.949046i
$571$	115.127	+	115.127i	0.201624	+	0.201624i	0.800696	−	0.599072i	$-0.204464\pi$
$571$	115.127	+	115.127i	0.201624	+	0.201624i	−0.599072	+	0.800696i	$0.704464\pi$
$572$	9.50875			0.0166237
$573$		−	1003.65i		−	1.75157i
$574$	−323.047	+	211.590i	−0.562800	+	0.368624i
$575$	8.48170			0.0147508
$576$			152.556i			0.264854i
$577$	−187.607	+	187.607i	−0.325141	+	0.325141i	−0.850735	−	0.525594i	$-0.823843\pi$
$577$	−187.607	+	187.607i	−0.325141	+	0.325141i	0.525594	+	0.850735i	$0.323843\pi$
$578$	−372.351			−0.644207
$579$	−661.291			−1.14213
$580$	−573.317	−	573.317i	−0.988477	−	0.988477i
$581$	8.82372	−	6.35505i	0.0151871	−	0.0109381i
$582$		−	826.677i		−	1.42041i
$583$			17.2482i			0.0295852i
$584$			436.671i			0.747724i
$585$	−203.453	−	203.453i	−0.347783	−	0.347783i
$586$	33.9138	−	33.9138i	0.0578735	−	0.0578735i
$587$	739.681	−	739.681i	1.26010	−	1.26010i	0.309063	−	0.951042i	$-0.399985\pi$
$587$	739.681	−	739.681i	1.26010	−	1.26010i	0.951042	−	0.309063i	$-0.100015\pi$
$588$	−166.246	−	333.080i	−0.282732	−	0.566462i
$589$	−282.252	+	282.252i	−0.479206	+	0.479206i
$590$	584.983			0.991497
$591$	−115.928	−	115.928i	−0.196155	−	0.196155i
$592$	−117.910			−0.199173
$593$	−203.255	−	203.255i	−0.342757	−	0.342757i	0.514646	−	0.857403i	$-0.327924\pi$
$593$	−203.255	−	203.255i	−0.342757	−	0.342757i	−0.857403	+	0.514646i	$0.827924\pi$
$594$	−11.7039			−0.0197035
$595$	36.0848	−	221.870i	0.0606467	−	0.372890i
$596$	−390.254	+	390.254i	−0.654788	+	0.654788i
$597$	403.554			0.675970
$598$	−1.41171	−	1.41171i	−0.00236071	−	0.00236071i
$599$	976.001			1.62938			0.814692	−	0.579894i	$-0.196906\pi$
$599$	976.001			1.62938			0.814692	+	0.579894i	$0.196906\pi$
$600$	1206.13	+	1206.13i	2.01021	+	2.01021i
$601$	600.611	+	600.611i	0.999353	+	0.999353i	1.00000		0.000647019i	$-0.000205952\pi$
$601$	600.611	+	600.611i	0.999353	+	0.999353i	−0.000647019		1.00000i	$0.500206\pi$
$602$	261.917	+	363.661i	0.435078	+	0.604087i
$603$	209.394	+	209.394i	0.347254	+	0.347254i
$604$	−295.496	−	295.496i	−0.489231	−	0.489231i
$605$		−	1107.53i		−	1.83063i
$606$			132.512i			0.218667i
$607$	−207.231			−0.341402			−0.170701	−	0.985323i	$-0.554603\pi$
$607$	−207.231			−0.341402			−0.170701	+	0.985323i	$0.554603\pi$
$608$	268.303	−	268.303i	0.441288	−	0.441288i
$609$	−573.453	−	796.215i	−0.941631	−	1.30741i
$610$			674.793i			1.10622i
$611$	566.198			0.926674
$612$	16.4872	−	16.4872i	0.0269399	−	0.0269399i
$613$		−	1099.74i		−	1.79403i	−0.442003	−	0.897013i	$-0.645732\pi$
$613$		−	1099.74i		−	1.79403i	0.442003	−	0.897013i	$-0.354268\pi$
$614$		−	54.9771i		−	0.0895393i
$615$	−962.048	+	880.376i	−1.56431	+	1.43151i
$616$	−24.2018	−	3.93617i	−0.0392887	−	0.00638989i
$617$		−	143.862i		−	0.233164i	−0.993181	−	0.116582i	$-0.962806\pi$
$617$		−	143.862i		−	0.233164i	0.993181	−	0.116582i	$-0.0371938\pi$
$618$	−127.543	−	127.543i	−0.206380	−	0.206380i
$619$			625.900i			1.01115i	0.862783	+	0.505574i	$0.168719\pi$
$619$			625.900i			1.01115i	−0.862783	+	0.505574i	$0.831281\pi$
$620$			633.807i			1.02227i
$621$	−2.10132	−	2.10132i	−0.00338378	−	0.00338378i
$622$	296.108	−	296.108i	0.476059	−	0.476059i
$623$	1101.17	+	179.094i	1.76753	+	0.287470i
$624$		−	87.7142i		−	0.140568i
$625$	1383.39			2.21342
$626$	17.1667	−	17.1667i	0.0274228	−	0.0274228i
$627$	−13.0438	−	13.0438i	−0.0208035	−	0.0208035i
$628$	−281.074	+	281.074i	−0.447570	+	0.447570i
$629$	119.305	+	119.305i	0.189674	+	0.189674i
$630$	153.387	+	212.972i	0.243472	+	0.338050i
$631$	202.943			0.321621			0.160811	−	0.986985i	$-0.448589\pi$
$631$	202.943			0.321621			0.160811	+	0.986985i	$0.448589\pi$
$632$	53.9999	−	53.9999i	0.0854428	−	0.0854428i
$633$		−	653.044i		−	1.03167i
$634$	251.348	−	251.348i	0.396447	−	0.396447i
$635$	−1428.12			−2.24901
$636$	−311.554			−0.489865
$637$	225.951	+	452.700i	0.354711	+	0.710675i
$638$	−22.8626			−0.0358347
$639$	−148.793	+	148.793i	−0.232852	+	0.232852i
$640$		−	481.699i		−	0.752655i
$641$	657.614	−	657.614i	1.02592	−	1.02592i	0.0262644	−	0.999655i	$-0.491639\pi$
$641$	657.614	−	657.614i	1.02592	−	1.02592i	0.999655	−	0.0262644i	$-0.00836117\pi$
$642$	−213.822	−	213.822i	−0.333057	−	0.333057i
$643$	383.961	−	383.961i	0.597140	−	0.597140i	−0.342410	−	0.939550i	$-0.611243\pi$
$643$	383.961	−	383.961i	0.597140	−	0.597140i	0.939550	+	0.342410i	$0.111243\pi$
$644$	−1.28710	−	1.78708i	−0.00199860	−	0.00277497i
$645$	1070.14	+	1070.14i	1.65913	+	1.65913i
$646$	59.5811			0.0922307
$647$	−1282.52			−1.98226			−0.991131	−	0.132890i	$-0.957574\pi$
$647$	−1282.52			−1.98226			−0.991131	+	0.132890i	$0.957574\pi$
$648$		−	825.483i		−	1.27389i
$649$	−14.1054	+	14.1054i	−0.0217341	+	0.0217341i
$650$	−579.887	−	579.887i	−0.892133	−	0.892133i
$651$	−123.133	+	757.090i	−0.189144	+	1.16296i
$652$	172.092			0.263944
$653$	355.025	+	355.025i	0.543684	+	0.543684i	0.924607	−	0.380923i	$-0.124394\pi$
$653$	355.025	+	355.025i	0.543684	+	0.543684i	−0.380923	+	0.924607i	$0.624394\pi$
$654$	−135.762			−0.207588
$655$	−44.1995			−0.0674802
$656$	−100.277	−	4.44514i	−0.152861	−	0.00677613i
$657$			159.388i			0.242600i
$658$	−509.778	−	82.9100i	−0.774738	−	0.126003i
$659$	357.736	+	357.736i	0.542847	+	0.542847i	0.924362	−	0.381516i	$-0.124598\pi$
$659$	357.736	+	357.736i	0.542847	+	0.542847i	−0.381516	+	0.924362i	$0.624598\pi$
$660$	−29.2903			−0.0443793
$661$	−868.911			−1.31454			−0.657270	−	0.753655i	$-0.728289\pi$
$661$	−868.911			−1.31454			−0.657270	+	0.753655i	$0.728289\pi$
$662$	−155.549	+	155.549i	−0.234969	+	0.234969i
$663$	−88.7515	+	88.7515i	−0.133863	+	0.133863i
$664$	12.9374			0.0194841
$665$	130.198	−	800.534i	0.195787	−	1.20381i
$666$	−197.000			−0.295796
$667$	−4.10476	−	4.10476i	−0.00615406	−	0.00615406i
$668$	155.168	−	155.168i	0.232287	−	0.232287i
$669$	−40.8776	−	40.8776i	−0.0611025	−	0.0611025i
$670$	849.600	+	849.600i	1.26806	+	1.26806i
$671$	−16.2710	−	16.2710i	−0.0242488	−	0.0242488i
$672$	117.047	−	719.674i	0.174178	−	1.07094i
$673$	179.379	−	179.379i	0.266536	−	0.266536i	−0.561167	−	0.827703i	$-0.689647\pi$
$673$	179.379	−	179.379i	0.266536	−	0.266536i	0.827703	+	0.561167i	$0.189647\pi$
$674$	551.849			0.818766
$675$	−863.162	−	863.162i	−1.27876	−	1.27876i
$676$			136.583i			0.202047i
$677$	−711.377			−1.05078			−0.525389	−	0.850862i	$-0.676080\pi$
$677$	−711.377			−1.05078			−0.525389	+	0.850862i	$0.676080\pi$
$678$	442.962	+	442.962i	0.653337	+	0.653337i
$679$	−198.966	+	1223.36i	−0.293028	+	1.80170i
$680$	189.108	−	189.108i	0.278100	−	0.278100i
$681$	1112.21			1.63321
$682$	12.6374	+	12.6374i	0.0185299	+	0.0185299i
$683$	−459.523	+	459.523i	−0.672802	+	0.672802i	−0.958361	−	0.285559i	$-0.907821\pi$
$683$	−459.523	+	459.523i	−0.672802	+	0.672802i	0.285559	+	0.958361i	$0.407821\pi$
$684$	59.4880	−	59.4880i	0.0869707	−	0.0869707i
$685$	82.5746	−	82.5746i	0.120547	−	0.120547i
$686$	−137.146	−	440.676i	−0.199921	−	0.642386i
$687$	−1345.49			−1.95850
$688$			116.487i			0.169313i
$689$	423.444			0.614578
$690$	4.34855	+	4.34855i	0.00630225	+	0.00630225i
$691$	861.767	+	861.767i	1.24713	+	1.24713i	0.956982	+	0.290148i	$0.0937047\pi$
$691$	861.767	+	861.767i	1.24713	+	1.24713i	0.290148	+	0.956982i	$0.406295\pi$
$692$	63.5225			0.0917955
$693$	−8.83383	−	1.43673i	−0.0127472	−	0.00207320i
$694$	−452.812	−	452.812i	−0.652467	−	0.652467i
$695$			1474.30i			2.12129i
$696$		−	1167.42i		−	1.67733i
$697$	96.9648	+	105.960i	0.139117	+	0.152023i
$698$			656.027i			0.939867i
$699$	−1270.25			−1.81724
$700$	−528.701	−	734.079i	−0.755288	−	1.04868i
$701$	−111.987			−0.159753			−0.0798767	−	0.996805i	$-0.525453\pi$
$701$	−111.987			−0.159753			−0.0798767	+	0.996805i	$0.525453\pi$
$702$			287.331i			0.409304i
$703$	430.467	+	430.467i	0.612329	+	0.612329i
$704$	−14.9252	−	14.9252i	−0.0212006	−	0.0212006i
$705$	−1744.09			−2.47389
$706$	517.044			0.732357
$707$	31.8932	−	196.098i	0.0451107	−	0.277366i
$708$	−254.786	−	254.786i	−0.359868	−	0.359868i
$709$	526.248	+	526.248i	0.742240	+	0.742240i	0.973009	−	0.230769i	$-0.0741240\pi$
$709$	526.248	+	526.248i	0.742240	+	0.742240i	−0.230769	+	0.973009i	$0.574124\pi$
$710$	−603.715	+	603.715i	−0.850302	+	0.850302i
$711$	19.7103	−	19.7103i	0.0277220	−	0.0277220i
$712$	938.570	+	938.570i	1.31822	+	1.31822i
$713$			4.53785i			0.00636444i
$714$	92.9038	−	66.9115i	0.130117	−	0.0937136i
$715$	39.8095			0.0556776
$716$	365.579	−	365.579i	0.510585	−	0.510585i
$717$	−371.861			−0.518635
$718$		−	273.489i		−	0.380904i
$719$	440.064	+	440.064i	0.612049	+	0.612049i	0.943480	−	0.331430i	$-0.107531\pi$
$719$	440.064	+	440.064i	0.612049	+	0.612049i	−0.331430	+	0.943480i	$0.607531\pi$
$720$			68.2189i			0.0947485i
$721$	158.047	+	219.442i	0.219205	+	0.304357i
$722$	−270.768			−0.375025
$723$	−306.898	+	306.898i	−0.424478	+	0.424478i
$724$	−394.550	−	394.550i	−0.544959	−	0.544959i
$725$	−1686.11	−	1686.11i	−2.32567	−	2.32567i
$726$	398.884	−	398.884i	0.549427	−	0.549427i
$727$	287.328	−	287.328i	0.395225	−	0.395225i	−0.481320	−	0.876545i	$-0.659843\pi$
$727$	287.328	−	287.328i	0.395225	−	0.395225i	0.876545	+	0.481320i	$0.159843\pi$
$728$	−96.6333	+	594.156i	−0.132738	+	0.816149i
$729$			344.525i			0.472600i
$730$			646.704i			0.885896i
$731$	117.865	−	117.865i	0.161238	−	0.161238i
$732$	293.902	−	293.902i	0.401506	−	0.401506i
$733$	−950.256			−1.29639			−0.648197	−	0.761473i	$-0.724476\pi$
$733$	−950.256			−1.29639			−0.648197	+	0.761473i	$0.724476\pi$
$734$			114.381i			0.155832i
$735$	−696.010	−	1394.48i	−0.946952	−	1.89725i
$736$		−	4.31358i		−	0.00586084i
$737$	−40.9720			−0.0555929
$738$	−167.538	−	7.42677i	−0.227017	−	0.0100634i
$739$	883.528			1.19557			0.597786	−	0.801656i	$-0.296047\pi$
$739$	883.528			1.19557			0.597786	+	0.801656i	$0.296047\pi$
$740$	966.628			1.30625
$741$	−320.226	+	320.226i	−0.432155	+	0.432155i
$742$	−381.249	−	62.0062i	−0.513813	−	0.0835663i
$743$		−	970.959i		−	1.30681i	−0.757009	−	0.653404i	$-0.773340\pi$
$743$		−	970.959i		−	1.30681i	0.757009	−	0.653404i	$-0.226660\pi$
$744$	−645.296	+	645.296i	−0.867334	+	0.867334i
$745$	−1633.84	+	1633.84i	−2.19308	+	2.19308i
$746$			975.539i			1.30769i
$747$	4.72225			0.00632162
$748$			3.22604i			0.00431289i
$749$	264.962	+	367.888i	0.353754	+	0.491172i
$750$	1029.70	+	1029.70i	1.37293	+	1.37293i
$751$	−849.506	−	849.506i	−1.13117	−	1.13117i	−0.989984	−	0.141183i	$-0.954909\pi$
$751$	−849.506	−	849.506i	−1.13117	−	1.13117i	−0.141183	−	0.989984i	$-0.545091\pi$
$752$	−94.9246	−	94.9246i	−0.126230	−	0.126230i
$753$	−771.160	+	771.160i	−1.02412	+	1.02412i
$754$			561.277i			0.744400i
$755$	−1237.13	−	1237.13i	−1.63858	−	1.63858i
$756$	−50.8820	+	312.851i	−0.0673042	+	0.413824i
$757$	−252.158	+	252.158i	−0.333102	+	0.333102i	−0.853763	−	0.520661i	$-0.825685\pi$
$757$	−252.158	+	252.158i	−0.333102	+	0.333102i	0.520661	+	0.853763i	$0.325685\pi$
$758$		−	675.551i		−	0.891228i
$759$	−0.209709			−0.000276296
$760$	682.325	−	682.325i	0.897796	−	0.897796i
$761$		−	1092.59i		−	1.43573i	−0.696182	−	0.717866i	$-0.745119\pi$
$761$		−	1092.59i		−	1.43573i	0.696182	−	0.717866i	$-0.254881\pi$
$762$	−514.345	−	514.345i	−0.674994	−	0.674994i
$763$	200.908	+	32.6755i	0.263313	+	0.0428251i
$764$	−447.816	+	447.816i	−0.586146	+	0.586146i
$765$	69.0257	−	69.0257i	0.0902296	−	0.0902296i
$766$	−65.3499	+	65.3499i	−0.0853132	+	0.0853132i
$767$	346.289	+	346.289i	0.451485	+	0.451485i
$768$	666.012	−	666.012i	0.867203	−	0.867203i
$769$		−	53.2502i		−	0.0692461i	−0.999400	−	0.0346230i	$-0.988977\pi$
$769$		−	53.2502i		−	0.0692461i	0.999400	−	0.0346230i	$-0.0110231\pi$
$770$	−35.8426	−	5.82942i	−0.0465488	−	0.00757067i
$771$			56.7760i			0.0736394i
$772$	295.059	+	295.059i	0.382201	+	0.382201i
$773$	−250.064	−	250.064i	−0.323499	−	0.323499i	0.526609	−	0.850108i	$-0.323463\pi$
$773$	−250.064	−	250.064i	−0.323499	−	0.323499i	−0.850108	+	0.526609i	$0.823463\pi$
$774$			194.623i			0.251451i
$775$			1864.01i			2.40518i
$776$	−1042.71	+	1042.71i	−1.34370	+	1.34370i
$777$	1154.65	+	187.792i	1.48604	+	0.241688i
$778$	−253.254			−0.325519
$779$	349.861	+	382.318i	0.449116	+	0.490780i
$780$			719.079i			0.921896i
$781$		−	29.1141i		−	0.0372780i
$782$	0.478950	−	0.478950i	0.000612469	−	0.000612469i
$783$			835.462i			1.06700i
$784$	38.0151	−	113.778i	0.0484886	−	0.145125i
$785$	−1176.75	+	1176.75i	−1.49904	+	1.49904i
$786$	−15.9187	−	15.9187i	−0.0202528	−	0.0202528i
$787$	316.064			0.401606			0.200803	−	0.979632i	$-0.435645\pi$
$787$	316.064			0.401606			0.200803	+	0.979632i	$0.435645\pi$
$788$			103.451i			0.131283i
$789$			1670.06i			2.11667i
$790$	79.9731	−	79.9731i	0.101232	−	0.101232i
$791$	−548.904	−	762.130i	−0.693937	−	0.963502i
$792$	−7.52940	−	7.52940i	−0.00950682	−	0.00950682i
$793$	−399.453	+	399.453i	−0.503724	+	0.503724i
$794$	−283.487	−	283.487i	−0.357037	−	0.357037i
$795$	−1304.36			−1.64070
$796$	−180.060	−	180.060i	−0.226207	−	0.226207i
$797$			290.331i			0.364280i	0.983273	+	0.182140i	$0.0583025\pi$
$797$			290.331i			0.364280i	−0.983273	+	0.182140i	$0.941698\pi$
$798$	335.209	−	241.425i	0.420061	−	0.302538i
$799$			192.094i			0.240419i
$800$		−	1771.89i		−	2.21486i
$801$	342.584	+	342.584i	0.427696	+	0.427696i
$802$	−43.8295			−0.0546502
$803$	−15.5937	−	15.5937i	−0.0194192	−	0.0194192i
$804$		−	740.077i		−	0.920494i
$805$	−5.38858	−	7.48181i	−0.00669389	−	0.00929418i
$806$	310.249	−	310.249i	0.384924	−	0.384924i
$807$	681.661	+	681.661i	0.844685	+	0.844685i
$808$	167.141	−	167.141i	0.206858	−	0.206858i
$809$	−3.10193	−	3.10193i	−0.00383428	−	0.00383428i	0.705187	−	0.709021i	$-0.250863\pi$
$809$	−3.10193	−	3.10193i	−0.00383428	−	0.00383428i	−0.709021	+	0.705187i	$0.750863\pi$
$810$		−	1222.53i		−	1.50930i
$811$	1109.41			1.36796			0.683979	−	0.729501i	$-0.260248\pi$
$811$	1109.41			1.36796			0.683979	+	0.729501i	$0.260248\pi$
$812$	−99.3936	+	611.128i	−0.122406	+	0.752621i
$813$	−534.478	−	534.478i	−0.657414	−	0.657414i
$814$	19.2735	−	19.2735i	0.0236775	−	0.0236775i
$815$	720.481			0.884026
$816$	29.7589			0.0364692
$817$	425.272	−	425.272i	0.520528	−	0.520528i
$818$	742.190			0.907323
$819$	−35.2718	+	216.871i	−0.0430669	+	0.264800i
$820$	822.066	+	36.4412i	1.00252	+	0.0444405i
$821$	1212.58			1.47696			0.738479	−	0.674276i	$-0.235544\pi$
$821$	1212.58			1.47696			0.738479	+	0.674276i	$0.235544\pi$
$822$	59.4794			0.0723594
$823$	82.6858	+	82.6858i	0.100469	+	0.100469i	0.755555	−	0.655086i	$-0.227368\pi$
$823$	82.6858	+	82.6858i	0.100469	+	0.100469i	−0.655086	+	0.755555i	$0.727368\pi$
$824$			321.748i			0.390471i
$825$	−86.1422			−0.104415
$826$	−261.074	−	362.490i	−0.316070	−	0.438850i
$827$	−233.024	−	233.024i	−0.281770	−	0.281770i	0.552044	−	0.833815i	$-0.313848\pi$
$827$	−233.024	−	233.024i	−0.281770	−	0.281770i	−0.833815	+	0.552044i	$0.813848\pi$
$828$		−	0.956404i		−	0.00115508i
$829$	−1249.19			−1.50687			−0.753433	−	0.657525i	$-0.771603\pi$
$829$	−1249.19			−1.50687			−0.753433	+	0.657525i	$0.771603\pi$
$830$	19.1602			0.0230845
$831$	808.293	−	808.293i	0.972675	−	0.972675i
$832$	−366.415	+	366.415i	−0.440403	+	0.440403i
$833$	−153.588	+	76.6587i	−0.184379	+	0.0920272i
$834$	−530.976	+	530.976i	−0.636662	+	0.636662i
$835$	649.627	−	649.627i	0.777997	−	0.777997i
$836$			11.6400i			0.0139234i
$837$	461.805	−	461.805i	0.551739	−	0.551739i
$838$		−	602.569i		−	0.719056i
$839$	78.1360	+	78.1360i	0.0931300	+	0.0931300i	0.752137	−	0.659007i	$-0.229023\pi$
$839$	78.1360	+	78.1360i	0.0931300	+	0.0931300i	−0.659007	+	0.752137i	$0.729023\pi$
$840$	297.665	−	1830.21i	0.354363	−	2.17882i
$841$			791.003i			0.940551i
$842$	129.314	−	129.314i	0.153579	−	0.153579i
$843$			68.0330i			0.0807035i
$844$	−291.380	+	291.380i	−0.345237	+	0.345237i
$845$			571.822i			0.676713i
$846$	−158.596	−	158.596i	−0.187466	−	0.187466i
$847$	−686.292	+	494.284i	−0.810262	+	0.583570i
$848$	−70.9916	−	70.9916i	−0.0837165	−	0.0837165i
$849$	744.157	+	744.157i	0.876510	+	0.876510i
$850$	196.739	−	196.739i	0.231457	−	0.231457i
$851$	6.92074			0.00813248
$852$	525.889			0.617241
$853$	558.257			0.654463			0.327232	−	0.944944i	$-0.393884\pi$
$853$	558.257			0.654463			0.327232	+	0.944944i	$0.393884\pi$
$854$	418.142	−	301.156i	0.489627	−	0.352641i
$855$	249.053	−	249.053i	0.291290	−	0.291290i
$856$			539.401i			0.630142i
$857$			1240.00i			1.44691i	0.690372	+	0.723455i	$0.257447\pi$
$857$			1240.00i			1.44691i	−0.690372	+	0.723455i	$0.742553\pi$
$858$	14.3376	+	14.3376i	0.0167105	+	0.0167105i
$859$	−507.234			−0.590494			−0.295247	−	0.955421i	$-0.595402\pi$
$859$	−507.234			−0.590494			−0.295247	+	0.955421i	$0.595402\pi$
$860$		−	954.962i		−	1.11042i
$861$	974.889	+	203.236i	1.13227	+	0.236047i
$862$	1042.51			1.20941
$863$		−	325.768i		−	0.377483i	−0.982027	−	0.188741i	$-0.939559\pi$
$863$		−	325.768i		−	0.377483i	0.982027	−	0.188741i	$-0.0604408\pi$
$864$	−438.982	+	438.982i	−0.508081	+	0.508081i
$865$	265.944			0.307450
$866$	364.706			0.421138
$867$	678.967	+	678.967i	0.783122	+	0.783122i
$868$	392.744	−	282.864i	0.452470	−	0.325880i
$869$			3.85670i			0.00443809i
$870$		−	1728.93i		−	1.98728i
$871$			1005.86i			1.15484i
$872$	171.241	+	171.241i	0.196377	+	0.196377i
$873$	−380.597	+	380.597i	−0.435965	+	0.435965i
$874$	1.72811	−	1.72811i	0.00197725	−	0.00197725i
$875$	−1275.97	−	1771.63i	−1.45825	−	2.02472i
$876$	281.668	−	281.668i	0.321539	−	0.321539i
$877$	−449.855			−0.512947			−0.256474	−	0.966551i	$-0.582561\pi$
$877$	−449.855			−0.512947			−0.256474	+	0.966551i	$0.582561\pi$
$878$	189.880	+	189.880i	0.216264	+	0.216264i
$879$	−123.681			−0.140706
$880$	−6.67417	−	6.67417i	−0.00758428	−	0.00758428i
$881$	370.648			0.420712			0.210356	−	0.977625i	$-0.432538\pi$
$881$	370.648			0.420712			0.210356	+	0.977625i	$0.432538\pi$
$882$	63.5142	−	190.096i	0.0720115	−	0.215528i
$883$	−212.518	+	212.518i	−0.240677	+	0.240677i	−0.817130	−	0.576453i	$-0.804436\pi$
$883$	−212.518	+	212.518i	−0.240677	+	0.240677i	0.576453	+	0.817130i	$0.304436\pi$
$884$	79.1995			0.0895922
$885$	−1066.69	−	1066.69i	−1.20530	−	1.20530i
$886$	461.880			0.521309
$887$	−77.5651	−	77.5651i	−0.0874465	−	0.0874465i	0.662030	−	0.749477i	$-0.269695\pi$
$887$	−77.5651	−	77.5651i	−0.0874465	−	0.0874465i	−0.749477	+	0.662030i	$0.769695\pi$
$888$	984.151	+	984.151i	1.10828	+	1.10828i
$889$	637.360	+	884.947i	0.716940	+	0.995441i
$890$	1390.01	+	1390.01i	1.56181	+	1.56181i
$891$	29.4782	+	29.4782i	0.0330844	+	0.0330844i
$892$			36.4781i			0.0408947i
$893$			693.101i			0.776148i
$894$	−1176.88			−1.31642
$895$	1530.54	−	1530.54i	1.71010	−	1.71010i
$896$	−298.489	+	214.979i	−0.333135	+	0.239932i
$897$			5.14837i			0.00573954i
$898$	−844.502			−0.940425
$899$	902.097	−	902.097i	1.00344	−	1.00344i
$900$		−	392.862i		−	0.436514i
$901$			143.662i			0.159448i
$902$	17.1176	−	15.6645i	0.0189774	−	0.0173664i
$903$	185.525	−	1140.71i	0.205454	−	1.26325i
$904$		−	1117.44i		−	1.23611i
$905$	−1651.83	−	1651.83i	−1.82523	−	1.82523i
$906$		−	891.117i		−	0.983572i
$907$		−	813.975i		−	0.897437i	−0.893673	−	0.448718i	$-0.851881\pi$
$907$		−	813.975i		−	0.897437i	0.893673	−	0.448718i	$-0.148119\pi$
$908$	−496.255	−	496.255i	−0.546537	−	0.546537i
$909$	61.0078	−	61.0078i	0.0671153	−	0.0671153i
$910$	−143.113	+	879.937i	−0.157267	+	0.966964i
$911$		−	1082.56i		−	1.18833i	−0.804345	−	0.594163i	$-0.797483\pi$
$911$		−	1082.56i		−	1.18833i	0.804345	−	0.594163i	$-0.202517\pi$
$912$	107.374			0.117734
$913$	−0.462000	+	0.462000i	−0.000506024	+	0.000506024i
$914$	−311.380	−	311.380i	−0.340679	−	0.340679i
$915$	1230.46	−	1230.46i	1.34476	−	1.34476i
$916$	600.341	+	600.341i	0.655394	+	0.655394i
$917$	19.7260	+	27.3887i	0.0215114	+	0.0298677i
$918$	−97.4832			−0.106191
$919$	752.749	−	752.749i	0.819096	−	0.819096i	−0.166881	−	0.985977i	$-0.553370\pi$
$919$	752.749	−	752.749i	0.819096	−	0.819096i	0.985977	+	0.166881i	$0.0533696\pi$
$920$		−	10.9699i		−	0.0119238i
$921$	−100.248	+	100.248i	−0.108847	+	0.108847i
$922$	−82.0244			−0.0889636
$923$	−714.754			−0.774382
$924$	13.0721	+	18.1500i	0.0141473	+	0.0196429i
$925$	2842.83			3.07333
$926$	−634.485	+	634.485i	−0.685189	+	0.685189i
$927$			117.440i			0.126688i
$928$	−857.514	+	857.514i	−0.924046	+	0.924046i
$929$	−1250.93	−	1250.93i	−1.34653	−	1.34653i	−0.889401	−	0.457128i	$-0.848878\pi$
$929$	−1250.93	−	1250.93i	−1.34653	−	1.34653i	−0.457128	−	0.889401i	$-0.651122\pi$
$930$	−955.675	+	955.675i	−1.02761	+	1.02761i
$931$	−554.165	+	276.594i	−0.595236	+	0.297093i
$932$	566.768	+	566.768i	0.608121	+	0.608121i
$933$	−1079.88			−1.15743
$934$	1181.43			1.26492
$935$			13.5062i			0.0144451i
$936$	−184.847	+	184.847i	−0.197486	+	0.197486i
$937$	−238.479	−	238.479i	−0.254514	−	0.254514i	0.568305	−	0.822818i	$-0.307600\pi$
$937$	−238.479	−	238.479i	−0.254514	−	0.254514i	−0.822818	+	0.568305i	$0.807600\pi$
$938$	147.292	−	905.633i	0.157027	−	0.965494i
$939$	−62.6054			−0.0666724
$940$	778.190	+	778.190i	0.827862	+	0.827862i
$941$	1666.37			1.77085			0.885426	−	0.464781i	$-0.153867\pi$
$941$	1666.37			1.77085			0.885426	+	0.464781i	$0.153867\pi$
$942$	−847.626			−0.899815
$943$	5.88572	+	0.260907i	0.00624148	+	0.000276677i
$944$		−	116.113i		−	0.123001i
$945$	−213.023	+	1309.79i	−0.225421	+	1.38602i
$946$	−19.0408	−	19.0408i	−0.0201277	−	0.0201277i
$947$	−537.711			−0.567805			−0.283902	−	0.958853i	$-0.591629\pi$
$947$	−537.711			−0.567805			−0.283902	+	0.958853i	$0.591629\pi$
$948$	−69.6637			−0.0734849
$949$	−382.825	+	382.825i	−0.403398	+	0.403398i
$950$	709.858	−	709.858i	0.747219	−	0.747219i
$951$	−916.643			−0.963873
$952$	−201.580	−	32.7849i	−0.211744	−	0.0344379i
$953$	−1035.58			−1.08665			−0.543325	−	0.839522i	$-0.682835\pi$
$953$	−1035.58			−1.08665			−0.543325	+	0.839522i	$0.682835\pi$
$954$	−118.610	−	118.610i	−0.124329	−	0.124329i
$955$	−1874.83	+	1874.83i	−1.96318	+	1.96318i
$956$	165.920	+	165.920i	0.173556	+	0.173556i
$957$	41.6889	+	41.6889i	0.0435621	+	0.0435621i
$958$	525.724	+	525.724i	0.548772	+	0.548772i
$959$	−88.0206	−	14.3156i	−0.0917837	−	0.0149277i
$960$	1128.69	−	1128.69i	1.17572	−	1.17572i
$961$	−36.2762			−0.0377484
$962$	−473.165	−	473.165i	−0.491855	−	0.491855i
$963$			196.885i			0.204450i
$964$	273.868			0.284095
$965$	1235.30	+	1235.30i	1.28010	+	1.28010i
$966$	0.753891	−	4.63535i	0.000780425	−	0.00479850i
$967$	−100.193	+	100.193i	−0.103612	+	0.103612i	−0.757013	−	0.653400i	$-0.773342\pi$
$967$	−100.193	+	100.193i	−0.103612	+	0.103612i	0.653400	+	0.757013i	$0.273342\pi$
$968$	−1006.25			−1.03951
$969$	−108.644	−	108.644i	−0.112119	−	0.112119i
$970$	−1544.24	+	1544.24i	−1.59200	+	1.59200i
$971$	1173.83	−	1173.83i	1.20889	−	1.20889i	0.237501	−	0.971387i	$-0.423672\pi$
$971$	1173.83	−	1173.83i	1.20889	−	1.20889i	0.971387	−	0.237501i	$-0.0763283\pi$
$972$	−244.304	+	244.304i	−0.251342	+	0.251342i
$973$	913.561	−	657.968i	0.938911	−	0.676226i
$974$	−682.625			−0.700847
$975$			2114.80i			2.16902i
$976$	133.939			0.137232
$977$	−1047.58	−	1047.58i	−1.07224	−	1.07224i	−0.997179	−	0.0750583i	$-0.976086\pi$
$977$	−1047.58	−	1047.58i	−1.07224	−	1.07224i	−0.0750583	−	0.997179i	$-0.523914\pi$
$978$	259.485	+	259.485i	0.265323	+	0.265323i
$979$	−67.0332			−0.0684711
$980$	−311.647	+	932.748i	−0.318007	+	0.951783i
$981$	62.5042	+	62.5042i	0.0637148	+	0.0637148i
$982$			249.240i			0.253809i
$983$		−	481.073i		−	0.489392i	−0.969600	−	0.244696i	$-0.921312\pi$
$983$		−	481.073i		−	0.489392i	0.969600	−	0.244696i	$-0.0786882\pi$
$984$	799.866	+	874.070i	0.812872	+	0.888283i
$985$			433.109i			0.439704i
$986$	−190.425			−0.193129
$987$	778.375	+	1080.74i	0.788627	+	1.09498i
$988$	285.762			0.289233
$989$		−	6.83721i		−	0.00691326i
$990$	−11.1509	−	11.1509i	−0.0112636	−	0.0112636i
$991$	1131.88	+	1131.88i	1.14216	+	1.14216i	0.988054	+	0.154105i	$0.0492496\pi$
$991$	1131.88	+	1131.88i	1.14216	+	1.14216i	0.154105	+	0.988054i	$0.450750\pi$
$992$	947.990			0.955635
$993$	567.276			0.571275
$994$	643.531	+	104.664i	0.647415	+	0.105295i
$995$	−753.844	−	753.844i	−0.757632	−	0.757632i
$996$	−8.34511	−	8.34511i	−0.00837862	−	0.00837862i
$997$	485.014	−	485.014i	0.486473	−	0.486473i	−0.420718	−	0.907191i	$-0.638222\pi$
$997$	485.014	−	485.014i	0.486473	−	0.486473i	0.907191	+	0.420718i	$0.138222\pi$
$998$	274.649	−	274.649i	0.275200	−	0.275200i
$999$	−704.306	−	704.306i	−0.705011	−	0.705011i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.g.a.132.19	✓	108
7.6	odd	2	inner	287.3.g.a.132.20	yes	108
41.32	even	4	inner	287.3.g.a.237.36	yes	108
287.237	odd	4	inner	287.3.g.a.237.35	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.g.a.132.19	✓	108	1.1	even	1	trivial
287.3.g.a.132.20	yes	108	7.6	odd	2	inner
287.3.g.a.237.35	yes	108	287.237	odd	4	inner
287.3.g.a.237.36	yes	108	41.32	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.34555i q^{2} +(-2.45356 + 2.45356i) q^{3} +2.18949 q^{4} +9.16655 q^{5} +(3.30139 + 3.30139i) q^{6} +(-4.09097 - 5.68014i) q^{7} -8.32828i q^{8} -3.03988i q^{9} +O(q^{10})\)	\(q-1.34555i q^{2} +(-2.45356 + 2.45356i) q^{3} +2.18949 q^{4} +9.16655 q^{5} +(3.30139 + 3.30139i) q^{6} +(-4.09097 - 5.68014i) q^{7} -8.32828i q^{8} -3.03988i q^{9} -12.3341i q^{10} +(0.297405 + 0.297405i) q^{11} +(-5.37204 + 5.37204i) q^{12} +(7.30132 - 7.30132i) q^{13} +(-7.64292 + 5.50461i) q^{14} +(-22.4907 + 22.4907i) q^{15} -2.44817 q^{16} +(2.47713 + 2.47713i) q^{17} -4.09032 q^{18} +(8.93778 + 8.93778i) q^{19} +20.0701 q^{20} +(23.9740 + 3.89911i) q^{21} +(0.400174 - 0.400174i) q^{22} +0.143695 q^{23} +(20.4339 + 20.4339i) q^{24} +59.0257 q^{25} +(-9.82431 - 9.82431i) q^{26} +(-14.6235 - 14.6235i) q^{27} +(-8.95714 - 12.4366i) q^{28} +(-28.5657 - 28.5657i) q^{29} +(30.2623 + 30.2623i) q^{30} +31.5797i q^{31} -30.0190i q^{32} -1.45940 q^{33} +(3.33310 - 3.33310i) q^{34} +(-37.5001 - 52.0673i) q^{35} -6.65579i q^{36} +48.1626 q^{37} +(12.0262 - 12.0262i) q^{38} +35.8284i q^{39} -76.3416i q^{40} +(40.9598 + 1.81570i) q^{41} +(5.24646 - 32.2582i) q^{42} -47.5814i q^{43} +(0.651166 + 0.651166i) q^{44} -27.8652i q^{45} -0.193349i q^{46} +(38.7736 + 38.7736i) q^{47} +(6.00673 - 6.00673i) q^{48} +(-15.5279 + 46.4745i) q^{49} -79.4221i q^{50} -12.1555 q^{51} +(15.9862 - 15.9862i) q^{52} +(28.9978 + 28.9978i) q^{53} +(-19.6767 + 19.6767i) q^{54} +(2.72618 + 2.72618i) q^{55} +(-47.3058 + 34.0707i) q^{56} -43.8587 q^{57} +(-38.4367 + 38.4367i) q^{58} +47.4282i q^{59} +(-49.2431 + 49.2431i) q^{60} -54.7097 q^{61} +42.4921 q^{62} +(-17.2669 + 12.4361i) q^{63} -50.1848 q^{64} +(66.9280 - 66.9280i) q^{65} +1.96370i q^{66} +(-68.8824 + 68.8824i) q^{67} +(5.42364 + 5.42364i) q^{68} +(-0.352564 + 0.352564i) q^{69} +(-70.0592 + 50.4583i) q^{70} +(-48.9469 - 48.9469i) q^{71} -25.3170 q^{72} -52.4323 q^{73} -64.8053i q^{74} +(-144.823 + 144.823i) q^{75} +(19.5692 + 19.5692i) q^{76} +(0.472627 - 2.90598i) q^{77} +48.2090 q^{78} +(6.48392 + 6.48392i) q^{79} -22.4413 q^{80} +99.1180 q^{81} +(2.44311 - 55.1135i) q^{82} +1.55343i q^{83} +(52.4908 + 8.53707i) q^{84} +(22.7067 + 22.7067i) q^{85} -64.0232 q^{86} +140.175 q^{87} +(2.47688 - 2.47688i) q^{88} +(-112.697 + 112.697i) q^{89} -37.4941 q^{90} +(-71.3420 - 11.6030i) q^{91} +0.314619 q^{92} +(-77.4825 - 77.4825i) q^{93} +(52.1719 - 52.1719i) q^{94} +(81.9286 + 81.9286i) q^{95} +(73.6533 + 73.6533i) q^{96} +(-125.201 - 125.201i) q^{97} +(62.5339 + 20.8936i) q^{98} +(0.904077 - 0.904077i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 216 q^{4} - 2 q^{7}+O(q^{10}) \) 108 * q - 216 * q^4 - 2 * q^7	\( 108 q - 216 q^{4} - 2 q^{7} - 20 q^{11} - 4 q^{14} - 28 q^{15} + 408 q^{16} + 24 q^{18} + 20 q^{22} - 8 q^{23} + 452 q^{25} - 62 q^{28} + 168 q^{29} - 64 q^{30} - 10 q^{35} - 208 q^{37} - 44 q^{42} + 44 q^{44} + 272 q^{51} - 92 q^{53} + 24 q^{56} - 256 q^{57} + 248 q^{58} - 440 q^{60} - 252 q^{63} - 1104 q^{64} - 644 q^{65} - 348 q^{67} - 30 q^{70} - 564 q^{71} + 796 q^{72} + 1924 q^{78} + 196 q^{79} - 468 q^{81} + 32 q^{85} + 152 q^{86} + 840 q^{88} - 428 q^{92} + 32 q^{93} + 4 q^{95} + 108 q^{98} - 484 q^{99}+O(q^{100}) \) 108 * q - 216 * q^4 - 2 * q^7 - 20 * q^11 - 4 * q^14 - 28 * q^15 + 408 * q^16 + 24 * q^18 + 20 * q^22 - 8 * q^23 + 452 * q^25 - 62 * q^28 + 168 * q^29 - 64 * q^30 - 10 * q^35 - 208 * q^37 - 44 * q^42 + 44 * q^44 + 272 * q^51 - 92 * q^53 + 24 * q^56 - 256 * q^57 + 248 * q^58 - 440 * q^60 - 252 * q^63 - 1104 * q^64 - 644 * q^65 - 348 * q^67 - 30 * q^70 - 564 * q^71 + 796 * q^72 + 1924 * q^78 + 196 * q^79 - 468 * q^81 + 32 * q^85 + 152 * q^86 + 840 * q^88 - 428 * q^92 + 32 * q^93 + 4 * q^95 + 108 * q^98 - 484 * q^99

Introduction

L-functions

Modular forms

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Database

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