LMFDB - Embedded newform 471.2.b.b.313.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(313,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("471.313");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.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:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 24x^{12} + 224x^{10} + 1027x^{8} + 2399x^{6} + 2652x^{4} + 1094x^{2} + 147 $ x^14 + 24x^12 + 224x^10 + 1027x^8 + 2399x^6 + 2652x^4 + 1094x^2 + 147
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			313.9
Root			$0.580612i$ of defining polynomial
Character	$\chi$	$=$	471.313
Dual form			471.2.b.b.313.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.580612i q^{2} +1.00000 q^{3} +1.66289 q^{4} -2.44616i q^{5} +0.580612i q^{6} -1.30605i q^{7} +2.12672i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.580612i q^{2} +1.00000 q^{3} +1.66289 q^{4} -2.44616i q^{5} +0.580612i q^{6} -1.30605i q^{7} +2.12672i q^{8} +1.00000 q^{9} +1.42027 q^{10} -2.31728 q^{11} +1.66289 q^{12} +2.96410 q^{13} +0.758310 q^{14} -2.44616i q^{15} +2.09098 q^{16} -0.119218 q^{17} +0.580612i q^{18} -0.543925 q^{19} -4.06769i q^{20} -1.30605i q^{21} -1.34544i q^{22} -1.90130i q^{23} +2.12672i q^{24} -0.983677 q^{25} +1.72099i q^{26} +1.00000 q^{27} -2.17182i q^{28} -1.94069i q^{29} +1.42027 q^{30} -2.86120 q^{31} +5.46748i q^{32} -2.31728 q^{33} -0.0692195i q^{34} -3.19481 q^{35} +1.66289 q^{36} -2.10289 q^{37} -0.315809i q^{38} +2.96410 q^{39} +5.20228 q^{40} +6.67031i q^{41} +0.758310 q^{42} +5.70782i q^{43} -3.85338 q^{44} -2.44616i q^{45} +1.10392 q^{46} -6.17066 q^{47} +2.09098 q^{48} +5.29423 q^{49} -0.571135i q^{50} -0.119218 q^{51} +4.92897 q^{52} +1.95561i q^{53} +0.580612i q^{54} +5.66843i q^{55} +2.77761 q^{56} -0.543925 q^{57} +1.12679 q^{58} +5.11256i q^{59} -4.06769i q^{60} +4.37193i q^{61} -1.66125i q^{62} -1.30605i q^{63} +1.00747 q^{64} -7.25065i q^{65} -1.34544i q^{66} -1.00850 q^{67} -0.198247 q^{68} -1.90130i q^{69} -1.85494i q^{70} -9.36547 q^{71} +2.12672i q^{72} +14.8637i q^{73} -1.22097i q^{74} -0.983677 q^{75} -0.904487 q^{76} +3.02649i q^{77} +1.72099i q^{78} -9.78715i q^{79} -5.11486i q^{80} +1.00000 q^{81} -3.87287 q^{82} -9.03696i q^{83} -2.17182i q^{84} +0.291626i q^{85} -3.31403 q^{86} -1.94069i q^{87} -4.92820i q^{88} +0.298758 q^{89} +1.42027 q^{90} -3.87127i q^{91} -3.16166i q^{92} -2.86120 q^{93} -3.58276i q^{94} +1.33052i q^{95} +5.46748i q^{96} +5.45493i q^{97} +3.07389i q^{98} -2.31728 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 14 q^{3} - 20 q^{4} + 14 q^{9}+O(q^{10}) $ 14 * q + 14 * q^3 - 20 * q^4 + 14 * q^9	$ 14 q + 14 q^{3} - 20 q^{4} + 14 q^{9} + 6 q^{10} - 2 q^{11} - 20 q^{12} + 24 q^{16} + 18 q^{17} - 12 q^{19} - 18 q^{25} + 14 q^{27} + 6 q^{30} - 14 q^{31} - 2 q^{33} + 16 q^{35} - 20 q^{36} - 14 q^{37} - 36 q^{40} + 24 q^{44} - 8 q^{46} + 22 q^{47} + 24 q^{48} - 48 q^{49} + 18 q^{51} - 50 q^{52} - 62 q^{56} - 12 q^{57} + 20 q^{58} - 34 q^{64} + 42 q^{67} - 56 q^{68} + 38 q^{71} - 18 q^{75} + 52 q^{76} + 14 q^{81} + 10 q^{82} + 34 q^{86} - 48 q^{89} + 6 q^{90} - 14 q^{93} - 2 q^{99}+O(q^{100}) $ 14 * q + 14 * q^3 - 20 * q^4 + 14 * q^9 + 6 * q^10 - 2 * q^11 - 20 * q^12 + 24 * q^16 + 18 * q^17 - 12 * q^19 - 18 * q^25 + 14 * q^27 + 6 * q^30 - 14 * q^31 - 2 * q^33 + 16 * q^35 - 20 * q^36 - 14 * q^37 - 36 * q^40 + 24 * q^44 - 8 * q^46 + 22 * q^47 + 24 * q^48 - 48 * q^49 + 18 * q^51 - 50 * q^52 - 62 * q^56 - 12 * q^57 + 20 * q^58 - 34 * q^64 + 42 * q^67 - 56 * q^68 + 38 * q^71 - 18 * q^75 + 52 * q^76 + 14 * q^81 + 10 * q^82 + 34 * q^86 - 48 * q^89 + 6 * q^90 - 14 * q^93 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$-1$

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 $

$2$			0.580612i			0.410555i	0.978704	+	0.205277i	$0.0658096\pi$
$2$			0.580612i			0.410555i	−0.978704	+	0.205277i	$0.934190\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	1.66289			0.831445
$5$		−	2.44616i		−	1.09395i	−0.837148	−	0.546977i	$-0.815779\pi$
$5$		−	2.44616i		−	1.09395i	0.837148	−	0.546977i	$-0.184221\pi$
$6$			0.580612i			0.237034i
$7$		−	1.30605i		−	0.493642i	−0.969061	−	0.246821i	$-0.920614\pi$
$7$		−	1.30605i		−	0.493642i	0.969061	−	0.246821i	$-0.0793859\pi$
$8$			2.12672i			0.751908i
$9$	1.00000			0.333333
$10$	1.42027			0.449128
$11$	−2.31728			−0.698686			−0.349343	−	0.936995i	$-0.613595\pi$
$11$	−2.31728			−0.698686			−0.349343	+	0.936995i	$0.613595\pi$
$12$	1.66289			0.480035
$13$	2.96410			0.822093			0.411047	−	0.911614i	$-0.365163\pi$
$13$	2.96410			0.822093			0.411047	+	0.911614i	$0.365163\pi$
$14$	0.758310			0.202667
$15$		−	2.44616i		−	0.631595i
$16$	2.09098			0.522745
$17$	−0.119218			−0.0289147			−0.0144573	−	0.999895i	$-0.504602\pi$
$17$	−0.119218			−0.0289147			−0.0144573	+	0.999895i	$0.504602\pi$
$18$			0.580612i			0.136852i
$19$	−0.543925			−0.124785			−0.0623925	−	0.998052i	$-0.519873\pi$
$19$	−0.543925			−0.124785			−0.0623925	+	0.998052i	$0.519873\pi$
$20$		−	4.06769i		−	0.909562i
$21$		−	1.30605i		−	0.285004i
$22$		−	1.34544i		−	0.286849i
$23$		−	1.90130i		−	0.396449i	−0.980157	−	0.198225i	$-0.936482\pi$
$23$		−	1.90130i		−	0.396449i	0.980157	−	0.198225i	$-0.0635175\pi$
$24$			2.12672i			0.434114i
$25$	−0.983677			−0.196735
$26$			1.72099i			0.337514i
$27$	1.00000			0.192450
$28$		−	2.17182i		−	0.410436i
$29$		−	1.94069i		−	0.360377i	−0.983632	−	0.180189i	$-0.942329\pi$
$29$		−	1.94069i		−	0.360377i	0.983632	−	0.180189i	$-0.0576708\pi$
$30$	1.42027			0.259304
$31$	−2.86120			−0.513888			−0.256944	−	0.966426i	$-0.582716\pi$
$31$	−2.86120			−0.513888			−0.256944	+	0.966426i	$0.582716\pi$
$32$			5.46748i			0.966524i
$33$	−2.31728			−0.403387
$34$		−	0.0692195i		−	0.0118711i
$35$	−3.19481			−0.540021
$36$	1.66289			0.277148
$37$	−2.10289			−0.345714			−0.172857	−	0.984947i	$-0.555300\pi$
$37$	−2.10289			−0.345714			−0.172857	+	0.984947i	$0.555300\pi$
$38$		−	0.315809i		−	0.0512310i
$39$	2.96410			0.474636
$40$	5.20228			0.822553
$41$			6.67031i			1.04173i	0.853640	+	0.520864i	$0.174390\pi$
$41$			6.67031i			1.04173i	−0.853640	+	0.520864i	$0.825610\pi$
$42$	0.758310			0.117010
$43$			5.70782i			0.870434i	0.900326	+	0.435217i	$0.143328\pi$
$43$			5.70782i			0.870434i	−0.900326	+	0.435217i	$0.856672\pi$
$44$	−3.85338			−0.580919
$45$		−	2.44616i		−	0.364651i
$46$	1.10392			0.162764
$47$	−6.17066			−0.900083			−0.450042	−	0.893008i	$-0.648591\pi$
$47$	−6.17066			−0.900083			−0.450042	+	0.893008i	$0.648591\pi$
$48$	2.09098			0.301807
$49$	5.29423			0.756318
$50$		−	0.571135i		−	0.0807706i
$51$	−0.119218			−0.0166939
$52$	4.92897			0.683525
$53$			1.95561i			0.268623i	0.990939	+	0.134312i	$0.0428823\pi$
$53$			1.95561i			0.268623i	−0.990939	+	0.134312i	$0.957118\pi$
$54$			0.580612i			0.0790113i
$55$			5.66843i			0.764331i
$56$	2.77761			0.371173
$57$	−0.543925			−0.0720446
$58$	1.12679			0.147955
$59$			5.11256i			0.665599i	0.942998	+	0.332800i	$0.107993\pi$
$59$			5.11256i			0.665599i	−0.942998	+	0.332800i	$0.892007\pi$
$60$		−	4.06769i		−	0.525136i
$61$			4.37193i			0.559768i	0.960034	+	0.279884i	$0.0902961\pi$
$61$			4.37193i			0.559768i	−0.960034	+	0.279884i	$0.909704\pi$
$62$		−	1.66125i		−	0.210979i
$63$		−	1.30605i		−	0.164547i
$64$	1.00747			0.125934
$65$		−	7.25065i		−	0.899332i
$66$		−	1.34544i		−	0.165612i
$67$	−1.00850			−0.123208			−0.0616039	−	0.998101i	$-0.519622\pi$
$67$	−1.00850			−0.123208			−0.0616039	+	0.998101i	$0.519622\pi$
$68$	−0.198247			−0.0240409
$69$		−	1.90130i		−	0.228890i
$70$		−	1.85494i		−	0.221708i
$71$	−9.36547			−1.11148			−0.555738	−	0.831357i	$-0.687564\pi$
$71$	−9.36547			−1.11148			−0.555738	+	0.831357i	$0.687564\pi$
$72$			2.12672i			0.250636i
$73$			14.8637i			1.73966i	0.493350	+	0.869831i	$0.335772\pi$
$73$			14.8637i			1.73966i	−0.493350	+	0.869831i	$0.664228\pi$
$74$		−	1.22097i		−	0.141934i
$75$	−0.983677			−0.113585
$76$	−0.904487			−0.103752
$77$			3.02649i			0.344901i
$78$			1.72099i			0.194864i
$79$		−	9.78715i		−	1.10114i	−0.834789	−	0.550570i	$-0.814410\pi$
$79$		−	9.78715i		−	1.10114i	0.834789	−	0.550570i	$-0.185590\pi$
$80$		−	5.11486i		−	0.571859i
$81$	1.00000			0.111111
$82$	−3.87287			−0.427686
$83$		−	9.03696i		−	0.991935i	−0.868341	−	0.495967i	$-0.834814\pi$
$83$		−	9.03696i		−	0.991935i	0.868341	−	0.495967i	$-0.165186\pi$
$84$		−	2.17182i		−	0.236965i
$85$			0.291626i			0.0316313i
$86$	−3.31403			−0.357361
$87$		−	1.94069i		−	0.208064i
$88$		−	4.92820i		−	0.525348i
$89$	0.298758			0.0316683			0.0158341	−	0.999875i	$-0.494960\pi$
$89$	0.298758			0.0316683			0.0158341	+	0.999875i	$0.494960\pi$
$90$	1.42027			0.149709
$91$		−	3.87127i		−	0.405819i
$92$		−	3.16166i		−	0.329626i
$93$	−2.86120			−0.296693
$94$		−	3.58276i		−	0.369534i
$95$			1.33052i			0.136509i
$96$			5.46748i			0.558023i
$97$			5.45493i			0.553865i	0.960889	+	0.276932i	$0.0893178\pi$
$97$			5.45493i			0.553865i	−0.960889	+	0.276932i	$0.910682\pi$
$98$			3.07389i			0.310510i
$99$	−2.31728			−0.232895
$100$	−1.63575			−0.163575
$101$	−10.1433			−1.00929			−0.504646	−	0.863326i	$-0.668377\pi$
$101$	−10.1433			−1.00929			−0.504646	+	0.863326i	$0.668377\pi$
$102$		−	0.0692195i		−	0.00685375i
$103$		−	1.90751i		−	0.187952i	−0.995574	−	0.0939762i	$-0.970042\pi$
$103$		−	1.90751i		−	0.187952i	0.995574	−	0.0939762i	$-0.0299578\pi$
$104$			6.30380i			0.618139i
$105$	−3.19481			−0.311781
$106$	−1.13545			−0.110285
$107$			0.436061i			0.0421556i	0.999778	+	0.0210778i	$0.00670977\pi$
$107$			0.436061i			0.0421556i	−0.999778	+	0.0210778i	$0.993290\pi$
$108$	1.66289			0.160012
$109$	−12.9081			−1.23637			−0.618187	−	0.786031i	$-0.712132\pi$
$109$	−12.9081			−1.23637			−0.618187	+	0.786031i	$0.712132\pi$
$110$	−3.29116			−0.313800
$111$	−2.10289			−0.199598
$112$		−	2.73093i		−	0.258049i
$113$	−1.23734			−0.116399			−0.0581997	−	0.998305i	$-0.518536\pi$
$113$	−1.23734			−0.116399			−0.0581997	+	0.998305i	$0.518536\pi$
$114$		−	0.315809i		−	0.0295783i
$115$	−4.65088			−0.433697
$116$		−	3.22716i		−	0.299634i
$117$	2.96410			0.274031
$118$	−2.96842			−0.273265
$119$			0.155705i			0.0142735i
$120$	5.20228			0.474901
$121$	−5.63021			−0.511838
$122$	−2.53840			−0.229816
$123$			6.67031i			0.601442i
$124$	−4.75787			−0.427269
$125$		−	9.82455i		−	0.878735i
$126$	0.758310			0.0675556
$127$	−2.53958			−0.225351			−0.112676	−	0.993632i	$-0.535942\pi$
$127$	−2.53958			−0.225351			−0.112676	+	0.993632i	$0.535942\pi$
$128$			11.5199i			1.01823i
$129$			5.70782i			0.502545i
$130$	4.20981			0.369225
$131$			16.7799i			1.46607i	0.680193	+	0.733033i	$0.261896\pi$
$131$			16.7799i			1.46607i	−0.680193	+	0.733033i	$0.738104\pi$
$132$	−3.85338			−0.335394
$133$			0.710395i			0.0615990i
$134$		−	0.585547i		−	0.0505835i
$135$		−	2.44616i		−	0.210532i
$136$		−	0.253543i		−	0.0217412i
$137$		−	7.73905i		−	0.661191i	−0.943773	−	0.330596i	$-0.892750\pi$
$137$		−	7.73905i		−	0.661191i	0.943773	−	0.330596i	$-0.107250\pi$
$138$	1.10392			0.0939719
$139$		−	5.41521i		−	0.459313i	−0.973272	−	0.229656i	$-0.926240\pi$
$139$		−	5.41521i		−	0.459313i	0.973272	−	0.229656i	$-0.0737602\pi$
$140$	−5.31261			−0.448998
$141$	−6.17066			−0.519663
$142$		−	5.43770i		−	0.456322i
$143$	−6.86865			−0.574385
$144$	2.09098			0.174248
$145$	−4.74723			−0.394236
$146$	−8.63003			−0.714226
$147$	5.29423			0.436660
$148$	−3.49688			−0.287442
$149$			2.29122i			0.187704i	0.995586	+	0.0938518i	$0.0299180\pi$
$149$			2.29122i			0.187704i	−0.995586	+	0.0938518i	$0.970082\pi$
$150$		−	0.571135i		−	0.0466329i
$151$		−	3.91880i		−	0.318908i	−0.987205	−	0.159454i	$-0.949027\pi$
$151$		−	3.91880i		−	0.318908i	0.987205	−	0.159454i	$-0.0509733\pi$
$152$		−	1.15677i		−	0.0938268i
$153$	−0.119218			−0.00963822
$154$	−1.75722			−0.141601
$155$			6.99895i			0.562169i
$156$	4.92897			0.394634
$157$	12.3611	+	2.05004i	0.986525	+	0.163611i
$157$	12.3611	+	2.05004i	0.986525	+	0.163611i
$158$	5.68254			0.452078
$159$			1.95561i			0.155090i
$160$	13.3743			1.05733
$161$	−2.48320			−0.195704
$162$			0.580612i			0.0456172i
$163$		−	18.4481i		−	1.44497i	−0.691387	−	0.722485i	$-0.743000\pi$
$163$		−	18.4481i		−	1.44497i	0.691387	−	0.722485i	$-0.257000\pi$
$164$			11.0920i			0.866139i
$165$			5.66843i			0.441286i
$166$	5.24697			0.407244
$167$	10.2808			0.795554			0.397777	−	0.917482i	$-0.369782\pi$
$167$	10.2808			0.795554			0.397777	+	0.917482i	$0.369782\pi$
$168$	2.77761			0.214297
$169$	−4.21411			−0.324162
$170$	−0.169322			−0.0129864
$171$	−0.543925			−0.0415950
$172$			9.49147i			0.723718i
$173$	17.7206			1.34727			0.673635	−	0.739064i	$-0.264732\pi$
$173$	17.7206			1.34727			0.673635	+	0.739064i	$0.264732\pi$
$174$	1.12679			0.0854216
$175$			1.28473i			0.0971167i
$176$	−4.84539			−0.365235
$177$			5.11256i			0.384284i
$178$			0.173462i			0.0130016i
$179$			0.0713724i			0.00533462i	0.999996	+	0.00266731i	$0.000849033\pi$
$179$			0.0713724i			0.00533462i	−0.999996	+	0.00266731i	$0.999151\pi$
$180$		−	4.06769i		−	0.303187i
$181$		−	19.6792i		−	1.46274i	−0.681980	−	0.731371i	$-0.738881\pi$
$181$		−	19.6792i		−	1.46274i	0.681980	−	0.731371i	$-0.261119\pi$
$182$	2.24771			0.166611
$183$			4.37193i			0.323182i
$184$	4.04354			0.298093
$185$			5.14401i			0.378195i
$186$		−	1.66125i		−	0.121809i
$187$	0.276262			0.0202023
$188$	−10.2611			−0.748370
$189$		−	1.30605i		−	0.0950014i
$190$	−0.772519			−0.0560444
$191$		−	11.4931i		−	0.831610i	−0.909454	−	0.415805i	$-0.863500\pi$
$191$		−	11.4931i		−	0.831610i	0.909454	−	0.415805i	$-0.136500\pi$
$192$	1.00747			0.0727082
$193$	−4.25001			−0.305923			−0.152961	−	0.988232i	$-0.548881\pi$
$193$	−4.25001			−0.305923			−0.152961	+	0.988232i	$0.548881\pi$
$194$	−3.16720			−0.227392
$195$		−	7.25065i		−	0.519230i
$196$	8.80371			0.628837
$197$	15.7933			1.12522			0.562612	−	0.826721i	$-0.309796\pi$
$197$	15.7933			1.12522			0.562612	+	0.826721i	$0.309796\pi$
$198$		−	1.34544i		−	0.0956163i
$199$	−7.63871			−0.541494			−0.270747	−	0.962651i	$-0.587271\pi$
$199$	−7.63871			−0.541494			−0.270747	+	0.962651i	$0.587271\pi$
$200$		−	2.09200i		−	0.147927i
$201$	−1.00850			−0.0711340
$202$		−	5.88930i		−	0.414370i
$203$	−2.53465			−0.177897
$204$	−0.198247			−0.0138800
$205$	16.3166			1.13960
$206$	1.10752			0.0771648
$207$		−	1.90130i		−	0.132150i
$208$	6.19788			0.429745
$209$	1.26043			0.0871855
$210$		−	1.85494i		−	0.128003i
$211$		−	22.3605i		−	1.53936i	−0.638430	−	0.769680i	$-0.720416\pi$
$211$		−	22.3605i		−	1.53936i	0.638430	−	0.769680i	$-0.279584\pi$
$212$			3.25196i			0.223345i
$213$	−9.36547			−0.641711
$214$	−0.253182			−0.0173072
$215$	13.9622			0.952214
$216$			2.12672i			0.144705i
$217$			3.73688i			0.253676i
$218$		−	7.49461i		−	0.507599i
$219$			14.8637i			1.00439i
$220$			9.42597i			0.635499i
$221$	−0.353375			−0.0237706
$222$		−	1.22097i		−	0.0819459i
$223$			8.10302i			0.542618i	0.962492	+	0.271309i	$0.0874566\pi$
$223$			8.10302i			0.542618i	−0.962492	+	0.271309i	$0.912543\pi$
$224$	7.14082			0.477116
$225$	−0.983677			−0.0655784
$226$		−	0.718416i		−	0.0477883i
$227$			15.0129i			0.996441i	0.867050	+	0.498221i	$0.166013\pi$
$227$			15.0129i			0.996441i	−0.867050	+	0.498221i	$0.833987\pi$
$228$	−0.904487			−0.0599011
$229$			18.2556i			1.20636i	0.797603	+	0.603182i	$0.206101\pi$
$229$			18.2556i			1.20636i	−0.797603	+	0.603182i	$0.793899\pi$
$230$		−	2.70036i		−	0.178056i
$231$			3.02649i			0.199128i
$232$	4.12730			0.270971
$233$	18.9841			1.24369			0.621845	−	0.783140i	$-0.286383\pi$
$233$	18.9841			1.24369			0.621845	+	0.783140i	$0.286383\pi$
$234$			1.72099i			0.112505i
$235$			15.0944i			0.984650i
$236$			8.50163i			0.553409i
$237$		−	9.78715i		−	0.635743i
$238$	−0.0904044			−0.00586004
$239$	3.09055			0.199911			0.0999554	−	0.994992i	$-0.468130\pi$
$239$	3.09055			0.199911			0.0999554	+	0.994992i	$0.468130\pi$
$240$		−	5.11486i		−	0.330163i
$241$			0.308856i			0.0198951i	0.999951	+	0.00994757i	$0.00316646\pi$
$241$			0.308856i			0.0198951i	−0.999951	+	0.00994757i	$0.996834\pi$
$242$		−	3.26897i		−	0.210137i
$243$	1.00000			0.0641500
$244$			7.27004i			0.465417i
$245$		−	12.9505i		−	0.827377i
$246$	−3.87287			−0.246925
$247$	−1.61225			−0.102585
$248$		−	6.08498i		−	0.386396i
$249$		−	9.03696i		−	0.572694i
$250$	5.70425			0.360769
$251$		−	2.96368i		−	0.187066i	−0.995616	−	0.0935329i	$-0.970184\pi$
$251$		−	2.96368i		−	0.187066i	0.995616	−	0.0935329i	$-0.0298160\pi$
$252$		−	2.17182i		−	0.136812i
$253$			4.40585i			0.276994i
$254$		−	1.47451i		−	0.0925190i
$255$			0.291626i			0.0182623i
$256$	−4.67366			−0.292104
$257$	30.4836			1.90152			0.950758	−	0.309934i	$-0.100307\pi$
$257$	30.4836			1.90152			0.950758	+	0.309934i	$0.100307\pi$
$258$	−3.31403			−0.206322
$259$			2.74649i			0.170659i
$260$		−	12.0570i		−	0.747745i
$261$		−	1.94069i		−	0.120126i
$262$	−9.74261			−0.601900
$263$	8.20830			0.506146			0.253073	−	0.967447i	$-0.418559\pi$
$263$	8.20830			0.506146			0.253073	+	0.967447i	$0.418559\pi$
$264$		−	4.92820i		−	0.303310i
$265$	4.78372			0.293862
$266$	−0.412464			−0.0252898
$267$	0.298758			0.0182837
$268$	−1.67702			−0.102440
$269$		−	6.27149i		−	0.382379i	−0.981553	−	0.191190i	$-0.938765\pi$
$269$		−	6.27149i		−	0.382379i	0.981553	−	0.191190i	$-0.0612346\pi$
$270$	1.42027			0.0864347
$271$			23.9634i			1.45567i	0.685750	+	0.727837i	$0.259474\pi$
$271$			23.9634i			1.45567i	−0.685750	+	0.727837i	$0.740526\pi$
$272$	−0.249283			−0.0151150
$273$		−	3.87127i		−	0.234300i
$274$	4.49338			0.271455
$275$	2.27945			0.137456
$276$		−	3.16166i		−	0.190309i
$277$	19.4244			1.16710			0.583548	−	0.812078i	$-0.301664\pi$
$277$	19.4244			1.16710			0.583548	+	0.812078i	$0.301664\pi$
$278$	3.14414			0.188573
$279$	−2.86120			−0.171296
$280$		−	6.79446i		−	0.406046i
$281$	16.6474			0.993098			0.496549	−	0.868009i	$-0.334600\pi$
$281$	16.6474			0.993098			0.496549	+	0.868009i	$0.334600\pi$
$282$		−	3.58276i		−	0.213350i
$283$	−26.4673			−1.57332			−0.786659	−	0.617388i	$-0.788191\pi$
$283$	−26.4673			−1.57332			−0.786659	+	0.617388i	$0.788191\pi$
$284$	−15.5737			−0.924132
$285$			1.33052i			0.0788135i
$286$		−	3.98802i		−	0.235817i
$287$	8.71178			0.514240
$288$			5.46748i			0.322175i
$289$	−16.9858			−0.999164
$290$		−	2.75630i		−	0.161856i
$291$			5.45493i			0.319774i
$292$			24.7166i			1.44643i
$293$		−	12.3316i		−	0.720422i	−0.932871	−	0.360211i	$-0.882705\pi$
$293$		−	12.3316i		−	0.720422i	0.932871	−	0.360211i	$-0.117295\pi$
$294$			3.07389i			0.179273i
$295$	12.5061			0.728135
$296$		−	4.47226i		−	0.259945i
$297$	−2.31728			−0.134462
$298$	−1.33031			−0.0770626
$299$		−	5.63565i		−	0.325918i
$300$	−1.63575			−0.0944398
$301$	7.45471			0.429682
$302$	2.27530			0.130929
$303$	−10.1433			−0.582715
$304$	−1.13734			−0.0652307
$305$	10.6944			0.612361
$306$		−	0.0692195i		−	0.00395702i
$307$			13.4829i			0.769512i	0.923018	+	0.384756i	$0.125714\pi$
$307$			13.4829i			0.769512i	−0.923018	+	0.384756i	$0.874286\pi$
$308$			5.03272i			0.286766i
$309$		−	1.90751i		−	0.108514i
$310$	−4.06368			−0.230801
$311$	−12.7177			−0.721154			−0.360577	−	0.932730i	$-0.617420\pi$
$311$	−12.7177			−0.721154			−0.360577	+	0.932730i	$0.617420\pi$
$312$			6.30380i			0.356883i
$313$	−7.79431			−0.440560			−0.220280	−	0.975437i	$-0.570697\pi$
$313$	−7.79431			−0.440560			−0.220280	+	0.975437i	$0.570697\pi$
$314$	−1.19028	+	7.17702i	−0.0671712	+	0.405022i
$315$	−3.19481			−0.180007
$316$		−	16.2749i		−	0.915537i
$317$	25.9237			1.45602			0.728011	−	0.685565i	$-0.240445\pi$
$317$	25.9237			1.45602			0.728011	+	0.685565i	$0.240445\pi$
$318$	−1.13545			−0.0636728
$319$			4.49712i			0.251791i
$320$		−	2.46444i		−	0.137766i
$321$			0.436061i			0.0243385i
$322$		−	1.44178i		−	0.0803471i
$323$	0.0648458			0.00360811
$324$	1.66289			0.0923828
$325$	−2.91572			−0.161735
$326$	10.7112			0.593239
$327$	−12.9081			−0.713820
$328$	−14.1859			−0.783284
$329$			8.05921i			0.444319i
$330$	−3.29116			−0.181172
$331$	−14.6637			−0.805988			−0.402994	−	0.915203i	$-0.632030\pi$
$331$	−14.6637			−0.805988			−0.402994	+	0.915203i	$0.632030\pi$
$332$		−	15.0275i		−	0.824739i
$333$	−2.10289			−0.115238
$334$			5.96917i			0.326618i
$335$			2.46695i			0.134784i
$336$		−	2.73093i		−	0.148985i
$337$		−	5.23706i		−	0.285281i	−0.989775	−	0.142640i	$-0.954441\pi$
$337$		−	5.23706i		−	0.285281i	0.989775	−	0.142640i	$-0.0455592\pi$
$338$		−	2.44676i		−	0.133086i
$339$	−1.23734			−0.0672033
$340$			0.484942i			0.0262997i
$341$	6.63021			0.359046
$342$		−	0.315809i		−	0.0170770i
$343$		−	16.0569i		−	0.866992i
$344$	−12.1389			−0.654486
$345$	−4.65088			−0.250395
$346$			10.2888i			0.553128i
$347$	8.30840			0.446018			0.223009	−	0.974816i	$-0.428412\pi$
$347$	8.30840			0.446018			0.223009	+	0.974816i	$0.428412\pi$
$348$		−	3.22716i		−	0.172994i
$349$	8.68166			0.464718			0.232359	−	0.972630i	$-0.425356\pi$
$349$	8.68166			0.464718			0.232359	+	0.972630i	$0.425356\pi$
$350$	−0.745932			−0.0398717
$351$	2.96410			0.158212
$352$		−	12.6697i		−	0.675297i
$353$	−25.9874			−1.38317			−0.691585	−	0.722295i	$-0.743087\pi$
$353$	−25.9874			−1.38317			−0.691585	+	0.722295i	$0.743087\pi$
$354$	−2.96842			−0.157770
$355$			22.9094i			1.21590i
$356$	0.496801			0.0263304
$357$			0.155705i			0.00824080i
$358$	−0.0414397			−0.00219015
$359$			1.32916i			0.0701502i	0.999385	+	0.0350751i	$0.0111670\pi$
$359$			1.32916i			0.0701502i	−0.999385	+	0.0350751i	$0.988833\pi$
$360$	5.20228			0.274184
$361$	−18.7041			−0.984429
$362$	11.4260			0.600536
$363$	−5.63021			−0.295510
$364$		−	6.43750i		−	0.337416i
$365$	36.3589			1.90311
$366$	−2.53840			−0.132684
$367$			3.89773i			0.203460i	0.994812	+	0.101730i	$0.0324377\pi$
$367$			3.89773i			0.203460i	−0.994812	+	0.101730i	$0.967562\pi$
$368$		−	3.97559i		−	0.207242i
$369$			6.67031i			0.347243i
$370$	−2.98667			−0.155270
$371$	2.55413			0.132604
$372$	−4.75787			−0.246684
$373$		−	29.5026i		−	1.52759i	−0.645461	−	0.763793i	$-0.723335\pi$
$373$		−	29.5026i		−	1.52759i	0.645461	−	0.763793i	$-0.276665\pi$
$374$			0.160401i			0.00829414i
$375$		−	9.82455i		−	0.507338i
$376$		−	13.1233i		−	0.676780i
$377$		−	5.75240i		−	0.296264i
$378$	0.758310			0.0390033
$379$		−	29.4893i		−	1.51476i	−0.652972	−	0.757382i	$-0.726478\pi$
$379$		−	29.4893i		−	1.51476i	0.652972	−	0.757382i	$-0.273522\pi$
$380$			2.21252i			0.113500i
$381$	−2.53958			−0.130107
$382$	6.67302			0.341421
$383$		−	7.27186i		−	0.371575i	−0.982590	−	0.185787i	$-0.940516\pi$
$383$		−	7.27186i		−	0.371575i	0.982590	−	0.185787i	$-0.0594835\pi$
$384$			11.5199i			0.587874i
$385$	7.40327			0.377305
$386$		−	2.46761i		−	0.125598i
$387$			5.70782i			0.290145i
$388$			9.07095i			0.460508i
$389$	2.85031			0.144517			0.0722583	−	0.997386i	$-0.476979\pi$
$389$	2.85031			0.144517			0.0722583	+	0.997386i	$0.476979\pi$
$390$	4.20981			0.213172
$391$			0.226670i			0.0114632i
$392$			11.2593i			0.568682i
$393$			16.7799i			0.846434i
$394$			9.16977i			0.461966i
$395$	−23.9409			−1.20460
$396$	−3.85338			−0.193640
$397$		−	13.3835i		−	0.671699i	−0.941916	−	0.335850i	$-0.890977\pi$
$397$		−	13.3835i		−	0.671699i	0.941916	−	0.335850i	$-0.109023\pi$
$398$		−	4.43513i		−	0.222313i
$399$			0.710395i			0.0355642i
$400$	−2.05685			−0.102842
$401$		−	17.0474i		−	0.851306i	−0.904886	−	0.425653i	$-0.860044\pi$
$401$		−	17.0474i		−	0.851306i	0.904886	−	0.425653i	$-0.139956\pi$
$402$		−	0.585547i		−	0.0292044i
$403$	−8.48090			−0.422464
$404$	−16.8671			−0.839171
$405$		−	2.44616i		−	0.121550i
$406$		−	1.47165i		−	0.0730365i
$407$	4.87300			0.241545
$408$		−	0.253543i		−	0.0125523i
$409$		−	6.23664i		−	0.308382i	−0.988041	−	0.154191i	$-0.950723\pi$
$409$		−	6.23664i		−	0.308382i	0.988041	−	0.154191i	$-0.0492771\pi$
$410$			9.47363i			0.467869i
$411$		−	7.73905i		−	0.381739i
$412$		−	3.17198i		−	0.156272i
$413$	6.67728			0.328567
$414$	1.10392			0.0542547
$415$	−22.1058			−1.08513
$416$			16.2062i			0.794573i
$417$		−	5.41521i		−	0.265184i
$418$			0.731819i			0.0357944i
$419$	−20.9335			−1.02267			−0.511335	−	0.859382i	$-0.670849\pi$
$419$	−20.9335			−1.02267			−0.511335	+	0.859382i	$0.670849\pi$
$420$	−5.31261			−0.259229
$421$		−	5.04528i		−	0.245892i	−0.992413	−	0.122946i	$-0.960766\pi$
$421$		−	5.04528i		−	0.245892i	0.992413	−	0.122946i	$-0.0392342\pi$
$422$	12.9828			0.631992
$423$	−6.17066			−0.300028
$424$	−4.15902			−0.201980
$425$	0.117272			0.00568854
$426$		−	5.43770i		−	0.263458i
$427$	5.70997			0.276325
$428$			0.725121i			0.0350501i
$429$	−6.86865			−0.331622
$430$			8.10662i			0.390936i
$431$	−9.08167			−0.437449			−0.218724	−	0.975787i	$-0.570190\pi$
$431$	−9.08167			−0.437449			−0.218724	+	0.975787i	$0.570190\pi$
$432$	2.09098			0.100602
$433$			36.9469i			1.77555i	0.460273	+	0.887777i	$0.347751\pi$
$433$			36.9469i			1.77555i	−0.460273	+	0.887777i	$0.652249\pi$
$434$	−2.16968			−0.104148
$435$	−4.74723			−0.227612
$436$	−21.4648			−1.02798
$437$			1.03417i			0.0494709i
$438$	−8.63003			−0.412359
$439$		−	16.8779i		−	0.805540i	−0.915301	−	0.402770i	$-0.868047\pi$
$439$		−	16.8779i		−	0.805540i	0.915301	−	0.402770i	$-0.131953\pi$
$440$	−12.0551			−0.574707
$441$	5.29423			0.252106
$442$		−	0.205174i		−	0.00975911i
$443$			29.7450i			1.41323i	0.707600	+	0.706613i	$0.249778\pi$
$443$			29.7450i			1.41323i	−0.707600	+	0.706613i	$0.750222\pi$
$444$	−3.49688			−0.165955
$445$		−	0.730808i		−	0.0346436i
$446$	−4.70471			−0.222774
$447$			2.29122i			0.108371i
$448$		−	1.31581i		−	0.0621664i
$449$			15.4606i			0.729631i	0.931080	+	0.364815i	$0.118868\pi$
$449$			15.4606i			0.729631i	−0.931080	+	0.364815i	$0.881132\pi$
$450$		−	0.571135i		−	0.0269235i
$451$		−	15.4570i		−	0.727841i
$452$	−2.05756			−0.0967797
$453$		−	3.91880i		−	0.184121i
$454$	−8.71667			−0.409094
$455$	−9.46973			−0.443948
$456$		−	1.15677i		−	0.0541709i
$457$	11.4104			0.533755			0.266877	−	0.963730i	$-0.414008\pi$
$457$	11.4104			0.533755			0.266877	+	0.963730i	$0.414008\pi$
$458$	−10.5994			−0.495279
$459$	−0.119218			−0.00556463
$460$	−7.73391			−0.360595
$461$	−1.63187			−0.0760039			−0.0380020	−	0.999278i	$-0.512099\pi$
$461$	−1.63187			−0.0760039			−0.0380020	+	0.999278i	$0.512099\pi$
$462$	−1.75722			−0.0817531
$463$			33.0233i			1.53472i	0.641215	+	0.767362i	$0.278431\pi$
$463$			33.0233i			1.53472i	−0.641215	+	0.767362i	$0.721569\pi$
$464$		−	4.05795i		−	0.188386i
$465$			6.99895i			0.324569i
$466$			11.0224i			0.510603i
$467$	−4.83358			−0.223671			−0.111836	−	0.993727i	$-0.535673\pi$
$467$	−4.83358			−0.223671			−0.111836	+	0.993727i	$0.535673\pi$
$468$	4.92897			0.227842
$469$			1.31715i			0.0608205i
$470$	−8.76399			−0.404253
$471$	12.3611	+	2.05004i	0.569570	+	0.0944607i
$472$	−10.8730			−0.500470
$473$		−	13.2266i		−	0.608160i
$474$	5.68254			0.261007
$475$	0.535046			0.0245496
$476$			0.258921i			0.0118676i
$477$			1.95561i			0.0895411i
$478$			1.79441i			0.0820743i
$479$			29.4324i			1.34480i	0.740188	+	0.672400i	$0.234737\pi$
$479$			29.4324i			1.34480i	−0.740188	+	0.672400i	$0.765263\pi$
$480$	13.3743			0.610451
$481$	−6.23319			−0.284209
$482$	−0.179325			−0.00816805
$483$	−2.48320			−0.112990
$484$	−9.36242			−0.425565
$485$	13.3436			0.605902
$486$			0.580612i			0.0263371i
$487$	−6.58332			−0.298319			−0.149159	−	0.988813i	$-0.547657\pi$
$487$	−6.58332			−0.298319			−0.149159	+	0.988813i	$0.547657\pi$
$488$	−9.29786			−0.420895
$489$		−	18.4481i		−	0.834254i
$490$	7.51922			0.339684
$491$			12.8842i			0.581457i	0.956806	+	0.290729i	$0.0938977\pi$
$491$			12.8842i			0.581457i	−0.956806	+	0.290729i	$0.906102\pi$
$492$			11.0920i			0.500066i
$493$			0.231366i			0.0104202i
$494$		−	0.936091i		−	0.0421167i
$495$			5.66843i			0.254777i
$496$	−5.98273			−0.268632
$497$			12.2318i			0.548671i
$498$	5.24697			0.235122
$499$		−	19.9026i		−	0.890961i	−0.895292	−	0.445480i	$-0.853033\pi$
$499$		−	19.9026i		−	0.890961i	0.895292	−	0.445480i	$-0.146967\pi$
$500$		−	16.3371i		−	0.730619i
$501$	10.2808			0.459313
$502$	1.72075			0.0768008
$503$			4.99386i			0.222665i	0.993783	+	0.111333i	$0.0355119\pi$
$503$			4.99386i			0.222665i	−0.993783	+	0.111333i	$0.964488\pi$
$504$	2.77761			0.123724
$505$			24.8120i			1.10412i
$506$	−2.55809			−0.113721
$507$	−4.21411			−0.187155
$508$	−4.22304			−0.187367
$509$		−	37.2194i		−	1.64972i	−0.565337	−	0.824860i	$-0.691254\pi$
$509$		−	37.2194i		−	1.64972i	0.565337	−	0.824860i	$-0.308746\pi$
$510$	−0.169322			−0.00749769
$511$	19.4127			0.858769
$512$			20.3263i			0.898302i
$513$	−0.543925			−0.0240149
$514$			17.6992i			0.780676i
$515$	−4.66606			−0.205611
$516$			9.49147i			0.417839i
$517$	14.2991			0.628876
$518$	−1.59465			−0.0700647
$519$	17.7206			0.777847
$520$	15.4201			0.676216
$521$		−	35.3199i		−	1.54739i	−0.633557	−	0.773696i	$-0.718406\pi$
$521$		−	35.3199i		−	1.54739i	0.633557	−	0.773696i	$-0.281594\pi$
$522$	1.12679			0.0493182
$523$	−8.92898			−0.390437			−0.195219	−	0.980760i	$-0.562542\pi$
$523$	−8.92898			−0.390437			−0.195219	+	0.980760i	$0.562542\pi$
$524$			27.9031i			1.21895i
$525$			1.28473i			0.0560704i
$526$			4.76584i			0.207800i
$527$	0.341108			0.0148589
$528$	−4.84539			−0.210868
$529$	19.3850			0.842828
$530$			2.77748i			0.120646i
$531$			5.11256i			0.221866i
$532$			1.18131i			0.0512162i
$533$			19.7715i			0.856398i
$534$			0.173462i			0.00750645i
$535$	1.06667			0.0461163
$536$		−	2.14479i		−	0.0926410i
$537$			0.0713724i			0.00307995i
$538$	3.64130			0.156988
$539$	−12.2682			−0.528429
$540$		−	4.06769i		−	0.175045i
$541$		−	20.5833i		−	0.884943i	−0.896783	−	0.442472i	$-0.854102\pi$
$541$		−	20.5833i		−	0.884943i	0.896783	−	0.442472i	$-0.145898\pi$
$542$	−13.9135			−0.597634
$543$		−	19.6792i		−	0.844514i
$544$		−	0.651824i		−	0.0279467i
$545$			31.5753i			1.35254i
$546$	2.24771			0.0961930
$547$	23.9148			1.02252			0.511262	−	0.859425i	$-0.329178\pi$
$547$	23.9148			1.02252			0.511262	+	0.859425i	$0.329178\pi$
$548$		−	12.8692i		−	0.549744i
$549$			4.37193i			0.186589i
$550$			1.32348i			0.0564333i
$551$			1.05559i			0.0449697i
$552$	4.04354			0.172104
$553$	−12.7825			−0.543568
$554$			11.2780i			0.479157i
$555$			5.14401i			0.218351i
$556$		−	9.00490i		−	0.381893i
$557$	26.1072			1.10620			0.553099	−	0.833116i	$-0.313445\pi$
$557$	26.1072			1.10620			0.553099	+	0.833116i	$0.313445\pi$
$558$		−	1.66125i		−	0.0703263i
$559$			16.9185i			0.715578i
$560$	−6.68028			−0.282294
$561$	0.276262			0.0116638
$562$			9.66566i			0.407721i
$563$		−	27.7914i		−	1.17127i	−0.810575	−	0.585634i	$-0.800845\pi$
$563$		−	27.7914i		−	1.17127i	0.810575	−	0.585634i	$-0.199155\pi$
$564$	−10.2611			−0.432071
$565$			3.02673i			0.127336i
$566$		−	15.3672i		−	0.645933i
$567$		−	1.30605i		−	0.0548491i
$568$		−	19.9177i		−	0.835729i
$569$		−	10.5628i		−	0.442815i	−0.975181	−	0.221407i	$-0.928935\pi$
$569$		−	10.5628i		−	0.442815i	0.975181	−	0.221407i	$-0.0710651\pi$
$570$	−0.772519			−0.0323573
$571$	20.7825			0.869722			0.434861	−	0.900498i	$-0.356798\pi$
$571$	20.7825			0.869722			0.434861	+	0.900498i	$0.356798\pi$
$572$	−11.4218			−0.477570
$573$		−	11.4931i		−	0.480130i
$574$			5.05817i			0.211124i
$575$			1.87027i			0.0779956i
$576$	1.00747			0.0419781
$577$	−33.3584			−1.38873			−0.694365	−	0.719623i	$-0.744315\pi$
$577$	−33.3584			−1.38873			−0.694365	+	0.719623i	$0.744315\pi$
$578$		−	9.86215i		−	0.410211i
$579$	−4.25001			−0.176624
$580$	−7.89412			−0.327786
$581$	−11.8027			−0.489660
$582$	−3.16720			−0.131285
$583$		−	4.53169i		−	0.187683i
$584$	−31.6108			−1.30807
$585$		−	7.25065i		−	0.299777i
$586$	7.15990			0.295773
$587$		−	44.6687i		−	1.84368i	−0.387575	−	0.921838i	$-0.626687\pi$
$587$		−	44.6687i		−	1.84368i	0.387575	−	0.921838i	$-0.373313\pi$
$588$	8.80371			0.363059
$589$	1.55628			0.0641254
$590$			7.26121i			0.298939i
$591$	15.7933			0.649648
$592$	−4.39711			−0.180720
$593$	−7.51248			−0.308501			−0.154250	−	0.988032i	$-0.549296\pi$
$593$	−7.51248			−0.308501			−0.154250	+	0.988032i	$0.549296\pi$
$594$		−	1.34544i		−	0.0552041i
$595$	0.380879			0.0156145
$596$			3.81004i			0.156065i
$597$	−7.63871			−0.312632
$598$	3.27213			0.133807
$599$		−	34.9640i		−	1.42859i	−0.699845	−	0.714295i	$-0.746747\pi$
$599$		−	34.9640i		−	1.42859i	0.699845	−	0.714295i	$-0.253253\pi$
$600$		−	2.09200i		−	0.0854057i
$601$	41.4097			1.68914			0.844569	−	0.535447i	$-0.179857\pi$
$601$	41.4097			1.68914			0.844569	+	0.535447i	$0.179857\pi$
$602$			4.32829i			0.176408i
$603$	−1.00850			−0.0410693
$604$		−	6.51653i		−	0.265154i
$605$			13.7724i			0.559927i
$606$		−	5.88930i		−	0.239236i
$607$		−	23.4482i		−	0.951735i	−0.879517	−	0.475867i	$-0.842134\pi$
$607$		−	23.4482i		−	0.951735i	0.879517	−	0.475867i	$-0.157866\pi$
$608$		−	2.97390i		−	0.120608i
$609$	−2.53465			−0.102709
$610$			6.20931i			0.251408i
$611$	−18.2905			−0.739953
$612$	−0.198247			−0.00801365
$613$			8.45058i			0.341316i	0.985330	+	0.170658i	$0.0545893\pi$
$613$			8.45058i			0.341316i	−0.985330	+	0.170658i	$0.945411\pi$
$614$	−7.82835			−0.315927
$615$	16.3166			0.657950
$616$	−6.43649			−0.259334
$617$	16.3517			0.658297			0.329148	−	0.944278i	$-0.393238\pi$
$617$	16.3517			0.658297			0.329148	+	0.944278i	$0.393238\pi$
$618$	1.10752			0.0445511
$619$	−5.12290			−0.205907			−0.102953	−	0.994686i	$-0.532829\pi$
$619$	−5.12290			−0.205907			−0.102953	+	0.994686i	$0.532829\pi$
$620$			11.6385i			0.467413i
$621$		−	1.90130i		−	0.0762967i
$622$		−	7.38404i		−	0.296073i
$623$		−	0.390193i		−	0.0156328i
$624$	6.19788			0.248114
$625$	−28.9508			−1.15803
$626$		−	4.52547i		−	0.180874i
$627$	1.26043			0.0503366
$628$	20.5552	+	3.40899i	0.820241	+	0.136033i
$629$	0.250703			0.00999620
$630$		−	1.85494i		−	0.0739027i
$631$	15.9095			0.633349			0.316674	−	0.948534i	$-0.397434\pi$
$631$	15.9095			0.633349			0.316674	+	0.948534i	$0.397434\pi$
$632$	20.8145			0.827956
$633$		−	22.3605i		−	0.888750i
$634$			15.0516i			0.597777i
$635$			6.21220i			0.246524i
$636$			3.25196i			0.128949i
$637$	15.6926			0.621764
$638$	−2.61109			−0.103374
$639$	−9.36547			−0.370492
$640$	28.1795			1.11389
$641$	−6.99732			−0.276378			−0.138189	−	0.990406i	$-0.544128\pi$
$641$	−6.99732			−0.276378			−0.138189	+	0.990406i	$0.544128\pi$
$642$	−0.253182			−0.00999230
$643$			39.1966i			1.54576i	0.634550	+	0.772882i	$0.281186\pi$
$643$			39.1966i			1.54576i	−0.634550	+	0.772882i	$0.718814\pi$
$644$	−4.12929			−0.162717
$645$	13.9622			0.549761
$646$			0.0376502i			0.00148133i
$647$	−20.9475			−0.823531			−0.411765	−	0.911290i	$-0.635088\pi$
$647$	−20.9475			−0.823531			−0.411765	+	0.911290i	$0.635088\pi$
$648$			2.12672i			0.0835454i
$649$		−	11.8472i		−	0.465045i
$650$		−	1.69290i		−	0.0664010i
$651$			3.73688i			0.146460i
$652$		−	30.6772i		−	1.20141i
$653$	3.89383			0.152377			0.0761887	−	0.997093i	$-0.475725\pi$
$653$	3.89383			0.152377			0.0761887	+	0.997093i	$0.475725\pi$
$654$		−	7.49461i		−	0.293062i
$655$	41.0462			1.60381
$656$			13.9475i			0.544558i
$657$			14.8637i			0.579887i
$658$	−4.67927			−0.182417
$659$	−17.0679			−0.664869			−0.332435	−	0.943126i	$-0.607870\pi$
$659$	−17.0679			−0.664869			−0.332435	+	0.943126i	$0.607870\pi$
$660$			9.42597i			0.366905i
$661$	−0.264648			−0.0102936			−0.00514681	−	0.999987i	$-0.501638\pi$
$661$	−0.264648			−0.0102936			−0.00514681	+	0.999987i	$0.501638\pi$
$662$		−	8.51390i		−	0.330902i
$663$	−0.353375			−0.0137239
$664$	19.2191			0.745844
$665$	1.73774			0.0673865
$666$		−	1.22097i		−	0.0473115i
$667$	−3.68984			−0.142871
$668$	17.0959			0.661459
$669$			8.10302i			0.313281i
$670$	−1.43234			−0.0553361
$671$		−	10.1310i		−	0.391102i
$672$	7.14082			0.275463
$673$		−	40.8630i		−	1.57515i	−0.616217	−	0.787577i	$-0.711335\pi$
$673$		−	40.8630i		−	1.57515i	0.616217	−	0.787577i	$-0.288665\pi$
$674$	3.04070			0.117123
$675$	−0.983677			−0.0378617
$676$	−7.00760			−0.269523
$677$	20.3190			0.780923			0.390461	−	0.920619i	$-0.372315\pi$
$677$	20.3190			0.780923			0.390461	+	0.920619i	$0.372315\pi$
$678$		−	0.718416i		−	0.0275906i
$679$	7.12443			0.273411
$680$	−0.620207			−0.0237838
$681$			15.0129i			0.575296i
$682$			3.84958i			0.147408i
$683$			5.04472i			0.193031i	0.995331	+	0.0965155i	$0.0307697\pi$
$683$			5.04472i			0.193031i	−0.995331	+	0.0965155i	$0.969230\pi$
$684$	−0.904487			−0.0345839
$685$	−18.9309			−0.723313
$686$	9.32284			0.355947
$687$			18.2556i			0.696495i
$688$			11.9349i			0.455015i
$689$			5.79661i			0.220833i
$690$		−	2.70036i		−	0.102801i
$691$		−	3.91884i		−	0.149080i	−0.997218	−	0.0745398i	$-0.976251\pi$
$691$		−	3.91884i		−	0.149080i	0.997218	−	0.0745398i	$-0.0237488\pi$
$692$	29.4674			1.12018
$693$			3.02649i			0.114967i
$694$			4.82396i			0.183115i
$695$	−13.2465			−0.502467
$696$	4.12730			0.156445
$697$		−	0.795223i		−	0.0301212i
$698$			5.04067i			0.190792i
$699$	18.9841			0.718045
$700$			2.13637i			0.0807472i
$701$			41.8989i			1.58250i	0.611494	+	0.791249i	$0.290569\pi$
$701$			41.8989i			1.58250i	−0.611494	+	0.791249i	$0.709431\pi$
$702$			1.72099i			0.0649547i
$703$	1.14382			0.0431399
$704$	−2.33460			−0.0879886
$705$			15.0944i			0.568488i
$706$		−	15.0886i		−	0.567867i
$707$			13.2476i			0.498229i
$708$			8.50163i			0.319511i
$709$	13.8580			0.520448			0.260224	−	0.965548i	$-0.416204\pi$
$709$	13.8580			0.520448			0.260224	+	0.965548i	$0.416204\pi$
$710$	−13.3015			−0.499195
$711$		−	9.78715i		−	0.367047i
$712$			0.635374i			0.0238116i
$713$			5.44002i			0.203730i
$714$	−0.0904044			−0.00338330
$715$			16.8018i			0.628351i
$716$			0.118684i			0.00443544i
$717$	3.09055			0.115419
$718$	−0.771725			−0.0288005
$719$			14.6393i			0.545954i	0.962021	+	0.272977i	$0.0880084\pi$
$719$			14.6393i			0.545954i	−0.962021	+	0.272977i	$0.911992\pi$
$720$		−	5.11486i		−	0.190620i
$721$	−2.49131			−0.0927811
$722$		−	10.8599i		−	0.404162i
$723$			0.308856i			0.0114865i
$724$		−	32.7243i		−	1.21619i
$725$			1.90901i			0.0708990i
$726$		−	3.26897i		−	0.121323i
$727$	36.4791			1.35293			0.676467	−	0.736473i	$-0.263510\pi$
$727$	36.4791			1.35293			0.676467	+	0.736473i	$0.263510\pi$
$728$	8.23310			0.305139
$729$	1.00000			0.0370370
$730$			21.1104i			0.781331i
$731$		−	0.680475i		−	0.0251683i
$732$			7.27004i			0.268708i
$733$	2.05871			0.0760402			0.0380201	−	0.999277i	$-0.487895\pi$
$733$	2.05871			0.0760402			0.0380201	+	0.999277i	$0.487895\pi$
$734$	−2.26307			−0.0835313
$735$		−	12.9505i		−	0.477686i
$736$	10.3953			0.383178
$737$	2.33698			0.0860836
$738$	−3.87287			−0.142562
$739$	−52.2228			−1.92105			−0.960523	−	0.278201i	$-0.910262\pi$
$739$	−52.2228			−1.92105			−0.960523	+	0.278201i	$0.910262\pi$
$740$			8.55392i			0.314448i
$741$	−1.61225			−0.0592274
$742$			1.48296i			0.0544410i
$743$	−25.8755			−0.949279			−0.474640	−	0.880180i	$-0.657422\pi$
$743$	−25.8755			−0.949279			−0.474640	+	0.880180i	$0.657422\pi$
$744$		−	6.08498i		−	0.223086i
$745$	5.60467			0.205339
$746$	17.1296			0.627158
$747$		−	9.03696i		−	0.330645i
$748$	0.459393			0.0167971
$749$	0.569519			0.0208098
$750$	5.70425			0.208290
$751$		−	16.8668i		−	0.615478i	−0.951471	−	0.307739i	$-0.900428\pi$
$751$		−	16.8668i		−	0.615478i	0.951471	−	0.307739i	$-0.0995723\pi$
$752$	−12.9027			−0.470514
$753$		−	2.96368i		−	0.108003i
$754$	3.33991			0.121633
$755$	−9.58600			−0.348870
$756$		−	2.17182i		−	0.0789884i
$757$		−	33.3186i		−	1.21098i	−0.795851	−	0.605492i	$-0.792976\pi$
$757$		−	33.3186i		−	1.21098i	0.795851	−	0.605492i	$-0.207024\pi$
$758$	17.1219			0.621894
$759$			4.40585i			0.159922i
$760$	−2.82965			−0.102642
$761$			32.6421i			1.18327i	0.806205	+	0.591637i	$0.201518\pi$
$761$			32.6421i			1.18327i	−0.806205	+	0.591637i	$0.798482\pi$
$762$		−	1.47451i		−	0.0534159i
$763$			16.8587i			0.610325i
$764$		−	19.1117i		−	0.691438i
$765$			0.291626i			0.0105438i
$766$	4.22213			0.152552
$767$			15.1542i			0.547185i
$768$	−4.67366			−0.168646
$769$	−22.3868			−0.807290			−0.403645	−	0.914916i	$-0.632257\pi$
$769$	−22.3868			−0.807290			−0.403645	+	0.914916i	$0.632257\pi$
$770$			4.29843i			0.154904i
$771$	30.4836			1.09784
$772$	−7.06730			−0.254358
$773$	−23.1885			−0.834032			−0.417016	−	0.908899i	$-0.636924\pi$
$773$	−23.1885			−0.834032			−0.417016	+	0.908899i	$0.636924\pi$
$774$	−3.31403			−0.119120
$775$	2.81450			0.101100
$776$	−11.6011			−0.416455
$777$			2.74649i			0.0985298i
$778$			1.65493i			0.0593320i
$779$		−	3.62815i		−	0.129992i
$780$		−	12.0570i		−	0.431711i
$781$	21.7024			0.776573
$782$	−0.131607			−0.00470627
$783$		−	1.94069i		−	0.0693546i
$784$	11.0701			0.395362
$785$	5.01471	−	30.2372i	0.178983	−	1.07921i
$786$	−9.74261			−0.347507
$787$		−	50.3287i		−	1.79402i	−0.442007	−	0.897012i	$-0.645733\pi$
$787$		−	50.3287i		−	1.79402i	0.442007	−	0.897012i	$-0.354267\pi$
$788$	26.2625			0.935562
$789$	8.20830			0.292223
$790$		−	13.9004i		−	0.494553i
$791$			1.61604i			0.0574596i
$792$		−	4.92820i		−	0.175116i
$793$			12.9588i			0.460182i
$794$	7.77063			0.275769
$795$	4.78372			0.169661
$796$	−12.7023			−0.450222
$797$	50.6257			1.79325			0.896627	−	0.442787i	$-0.146010\pi$
$797$	50.6257			1.79325			0.896627	+	0.442787i	$0.146010\pi$
$798$	−0.412464			−0.0146011
$799$	0.735655			0.0260256
$800$		−	5.37824i		−	0.190149i
$801$	0.298758			0.0105561
$802$	9.89792			0.349508
$803$		−	34.4433i		−	1.21548i
$804$	−1.67702			−0.0591440
$805$			6.07430i			0.214091i
$806$		−	4.92411i		−	0.173444i
$807$		−	6.27149i		−	0.220767i
$808$		−	21.5719i		−	0.758895i
$809$		−	22.9311i		−	0.806214i	−0.915153	−	0.403107i	$-0.867930\pi$
$809$		−	22.9311i		−	0.806214i	0.915153	−	0.403107i	$-0.132070\pi$
$810$	1.42027			0.0499031
$811$			35.5162i			1.24714i	0.781767	+	0.623571i	$0.214319\pi$
$811$			35.5162i			1.24714i	−0.781767	+	0.623571i	$0.785681\pi$
$812$	−4.21484			−0.147912
$813$			23.9634i			0.840434i
$814$			2.82932i			0.0991676i
$815$	−45.1270			−1.58073
$816$	−0.249283			−0.00872665
$817$		−	3.10462i		−	0.108617i
$818$	3.62107			0.126608
$819$		−	3.87127i		−	0.135273i
$820$	27.1327			0.947517
$821$	7.83820			0.273555			0.136778	−	0.990602i	$-0.456325\pi$
$821$	7.83820			0.273555			0.136778	+	0.990602i	$0.456325\pi$
$822$	4.49338			0.156725
$823$			13.2582i			0.462151i	0.972936	+	0.231076i	$0.0742245\pi$
$823$			13.2582i			0.462151i	−0.972936	+	0.231076i	$0.925776\pi$
$824$	4.05673			0.141323
$825$	2.27945			0.0793604
$826$			3.87691i			0.134895i
$827$	5.43350			0.188941			0.0944706	−	0.995528i	$-0.469884\pi$
$827$	5.43350			0.188941			0.0944706	+	0.995528i	$0.469884\pi$
$828$		−	3.16166i		−	0.109875i
$829$	−39.0323			−1.35565			−0.677824	−	0.735224i	$-0.737077\pi$
$829$	−39.0323			−1.35565			−0.677824	+	0.735224i	$0.737077\pi$
$830$		−	12.8349i		−	0.445506i
$831$	19.4244			0.673823
$832$	2.98626			0.103530
$833$	−0.631168			−0.0218687
$834$	3.14414			0.108873
$835$		−	25.1485i		−	0.870299i
$836$	2.09595			0.0724899
$837$	−2.86120			−0.0988977
$838$		−	12.1543i		−	0.419862i
$839$		−	25.4805i		−	0.879686i	−0.898075	−	0.439843i	$-0.855034\pi$
$839$		−	25.4805i		−	0.879686i	0.898075	−	0.439843i	$-0.144966\pi$
$840$		−	6.79446i		−	0.234431i
$841$	25.2337			0.870128
$842$	2.92935			0.100952
$843$	16.6474			0.573365
$844$		−	37.1830i		−	1.27989i
$845$			10.3084i			0.354619i
$846$		−	3.58276i		−	0.123178i
$847$			7.35336i			0.252664i
$848$			4.08914i			0.140422i
$849$	−26.4673			−0.908355
$850$			0.0680896i			0.00233546i
$851$			3.99824i			0.137058i
$852$	−15.5737			−0.533548
$853$	15.4470			0.528897			0.264448	−	0.964400i	$-0.414810\pi$
$853$	15.4470			0.528897			0.264448	+	0.964400i	$0.414810\pi$
$854$			3.31528i			0.113447i
$855$			1.33052i			0.0455030i
$856$	−0.927378			−0.0316971
$857$			34.4084i			1.17537i	0.809090	+	0.587685i	$0.199960\pi$
$857$			34.4084i			1.17537i	−0.809090	+	0.587685i	$0.800040\pi$
$858$		−	3.98802i		−	0.136149i
$859$		−	5.98087i		−	0.204065i	−0.994781	−	0.102032i	$-0.967465\pi$
$859$		−	5.98087i		−	0.204065i	0.994781	−	0.102032i	$-0.0325345\pi$
$860$	23.2176			0.791714
$861$	8.71178			0.296897
$862$		−	5.27293i		−	0.179597i
$863$			43.8044i			1.49112i	0.666439	+	0.745560i	$0.267818\pi$
$863$			43.8044i			1.49112i	−0.666439	+	0.745560i	$0.732182\pi$
$864$			5.46748i			0.186008i
$865$		−	43.3473i		−	1.47385i
$866$	−21.4518			−0.728962
$867$	−16.9858			−0.576868
$868$			6.21403i			0.210918i
$869$			22.6796i			0.769351i
$870$		−	2.75630i		−	0.0934473i
$871$	−2.98929			−0.101288
$872$		−	27.4519i		−	0.929639i
$873$			5.45493i			0.184622i
$874$	−0.600449			−0.0203105
$875$	−12.8314			−0.433780
$876$			24.7166i			0.835098i
$877$			5.85926i			0.197853i	0.995095	+	0.0989265i	$0.0315409\pi$
$877$			5.85926i			0.197853i	−0.995095	+	0.0989265i	$0.968459\pi$
$878$	9.79954			0.330718
$879$		−	12.3316i		−	0.415936i
$880$			11.8526i			0.399550i
$881$			24.9571i			0.840826i	0.907333	+	0.420413i	$0.138115\pi$
$881$			24.9571i			0.840826i	−0.907333	+	0.420413i	$0.861885\pi$
$882$			3.07389i			0.103503i
$883$		−	3.88991i		−	0.130906i	−0.997856	−	0.0654530i	$-0.979151\pi$
$883$		−	3.88991i		−	0.130906i	0.997856	−	0.0654530i	$-0.0208492\pi$
$884$	−0.587623			−0.0197639
$885$	12.5061			0.420389
$886$	−17.2703			−0.580207
$887$		−	37.3546i		−	1.25424i	−0.778921	−	0.627122i	$-0.784233\pi$
$887$		−	37.3546i		−	1.25424i	0.778921	−	0.627122i	$-0.215767\pi$
$888$		−	4.47226i		−	0.150079i
$889$			3.31682i			0.111243i
$890$	0.424316			0.0142231
$891$	−2.31728			−0.0776318
$892$			13.4744i			0.451157i
$893$	3.35638			0.112317
$894$	−1.33031			−0.0444921
$895$	0.174588			0.00583583
$896$	15.0456			0.502639
$897$		−	5.63565i		−	0.188169i
$898$	−8.97661			−0.299553
$899$			5.55272i			0.185193i
$900$	−1.63575			−0.0545249
$901$		−	0.233144i		−	0.00776715i
$902$	8.97451			0.298819
$903$	7.45471			0.248077
$904$		−	2.63148i		−	0.0875217i
$905$	−48.1383			−1.60017
$906$	2.27530			0.0755919
$907$	29.8711			0.991852			0.495926	−	0.868365i	$-0.334829\pi$
$907$	29.8711			0.991852			0.495926	+	0.868365i	$0.334829\pi$
$908$			24.9648i			0.828486i
$909$	−10.1433			−0.336431
$910$		−	5.49824i		−	0.182265i
$911$	−26.8419			−0.889312			−0.444656	−	0.895702i	$-0.646674\pi$
$911$	−26.8419			−0.889312			−0.444656	+	0.895702i	$0.646674\pi$
$912$	−1.13734			−0.0376610
$913$			20.9412i			0.693051i
$914$			6.62500i			0.219136i
$915$	10.6944			0.353547
$916$			30.3571i			1.00303i
$917$	21.9154			0.723711
$918$		−	0.0692195i		−	0.00228458i
$919$			57.2643i			1.88898i	0.328546	+	0.944488i	$0.393441\pi$
$919$			57.2643i			1.88898i	−0.328546	+	0.944488i	$0.606559\pi$
$920$		−	9.89112i		−	0.326100i
$921$			13.4829i			0.444278i
$922$		−	0.947485i		−	0.0312038i
$923$	−27.7602			−0.913738
$924$			5.03272i			0.165564i
$925$	2.06857			0.0680141
$926$	−19.1737			−0.630088
$927$		−	1.90751i		−	0.0626508i
$928$	10.6107			0.348313
$929$	−49.3558			−1.61931			−0.809656	−	0.586905i	$-0.800346\pi$
$929$	−49.3558			−1.61931			−0.809656	+	0.586905i	$0.800346\pi$
$930$	−4.06368			−0.133253
$931$	−2.87966			−0.0943771
$932$	31.5685			1.03406
$933$	−12.7177			−0.416358
$934$		−	2.80644i		−	0.0918294i
$935$		−	0.675780i		−	0.0221004i
$936$			6.30380i			0.206046i
$937$			15.3261i			0.500682i	0.968158	+	0.250341i	$0.0805428\pi$
$937$			15.3261i			0.500682i	−0.968158	+	0.250341i	$0.919457\pi$
$938$	−0.764755			−0.0249701
$939$	−7.79431			−0.254358
$940$			25.1003i			0.818682i
$941$	−24.4704			−0.797711			−0.398856	−	0.917014i	$-0.630593\pi$
$941$	−24.4704			−0.797711			−0.398856	+	0.917014i	$0.630593\pi$
$942$	−1.19028	+	7.17702i	−0.0387813	+	0.233840i
$943$	12.6823			0.412992
$944$			10.6903i			0.347939i
$945$	−3.19481			−0.103927
$946$	7.67953			0.249683
$947$		−	21.6522i		−	0.703602i	−0.936075	−	0.351801i	$-0.885569\pi$
$947$		−	21.6522i		−	0.703602i	0.936075	−	0.351801i	$-0.114431\pi$
$948$		−	16.2749i		−	0.528586i
$949$			44.0574i			1.43016i
$950$			0.310654i			0.0100790i
$951$	25.9237			0.840635
$952$	−0.331141			−0.0107323
$953$	−35.5414			−1.15130			−0.575650	−	0.817696i	$-0.695251\pi$
$953$	−35.5414			−1.15130			−0.575650	+	0.817696i	$0.695251\pi$
$954$	−1.13545			−0.0367615
$955$	−28.1138			−0.909743
$956$	5.13924			0.166215
$957$			4.49712i			0.145371i
$958$	−17.0888			−0.552114
$959$	−10.1076			−0.326391
$960$		−	2.46444i		−	0.0795394i
$961$	−22.8135			−0.735920
$962$		−	3.61907i		−	0.116683i
$963$			0.436061i			0.0140519i
$964$			0.513593i			0.0165417i
$965$			10.3962i			0.334665i
$966$		−	1.44178i		−	0.0463884i
$967$	−6.57992			−0.211596			−0.105798	−	0.994388i	$-0.533740\pi$
$967$	−6.57992			−0.211596			−0.105798	+	0.994388i	$0.533740\pi$
$968$		−	11.9739i		−	0.384855i
$969$	0.0648458			0.00208315
$970$			7.74747i			0.248756i
$971$			57.9524i			1.85978i	0.367835	+	0.929891i	$0.380099\pi$
$971$			57.9524i			1.85978i	−0.367835	+	0.929891i	$0.619901\pi$
$972$	1.66289			0.0533372
$973$	−7.07256			−0.226736
$974$		−	3.82236i		−	0.122476i
$975$	−2.91572			−0.0933776
$976$			9.14162i			0.292616i
$977$	−11.3036			−0.361634			−0.180817	−	0.983517i	$-0.557874\pi$
$977$	−11.3036			−0.361634			−0.180817	+	0.983517i	$0.557874\pi$
$978$	10.7112			0.342507
$979$	−0.692305			−0.0221262
$980$		−	21.5353i		−	0.687918i
$981$	−12.9081			−0.412124
$982$	−7.48074			−0.238720
$983$		−	7.94833i		−	0.253512i	−0.991934	−	0.126756i	$-0.959543\pi$
$983$		−	7.94833i		−	0.253512i	0.991934	−	0.126756i	$-0.0404566\pi$
$984$	−14.1859			−0.452229
$985$		−	38.6328i		−	1.23094i
$986$	−0.134334			−0.00427806
$987$			8.05921i			0.256527i
$988$	−2.68099			−0.0852937
$989$	10.8523			0.345083
$990$	−3.29116			−0.104600
$991$	−4.98674			−0.158409			−0.0792044	−	0.996858i	$-0.525238\pi$
$991$	−4.98674			−0.158409			−0.0792044	+	0.996858i	$0.525238\pi$
$992$		−	15.6436i		−	0.496685i
$993$	−14.6637			−0.465338
$994$	−7.10193			−0.225260
$995$			18.6855i			0.592369i
$996$		−	15.0275i		−	0.476163i
$997$			43.9516i			1.39196i	0.718060	+	0.695981i	$0.245030\pi$
$997$			43.9516i			1.39196i	−0.718060	+	0.695981i	$0.754970\pi$
$998$	11.5557			0.365788
$999$	−2.10289			−0.0665327

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.b.b.313.9	yes	14
3.2	odd	2		1413.2.b.e.784.6		14
157.156	even	2	inner	471.2.b.b.313.6	✓	14
471.470	odd	2		1413.2.b.e.784.9		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.b.b.313.6	✓	14	157.156	even	2	inner
471.2.b.b.313.9	yes	14	1.1	even	1	trivial
1413.2.b.e.784.6		14	3.2	odd	2
1413.2.b.e.784.9		14	471.470	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.580612i q^{2} +1.00000 q^{3} +1.66289 q^{4} -2.44616i q^{5} +0.580612i q^{6} -1.30605i q^{7} +2.12672i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.580612i q^{2} +1.00000 q^{3} +1.66289 q^{4} -2.44616i q^{5} +0.580612i q^{6} -1.30605i q^{7} +2.12672i q^{8} +1.00000 q^{9} +1.42027 q^{10} -2.31728 q^{11} +1.66289 q^{12} +2.96410 q^{13} +0.758310 q^{14} -2.44616i q^{15} +2.09098 q^{16} -0.119218 q^{17} +0.580612i q^{18} -0.543925 q^{19} -4.06769i q^{20} -1.30605i q^{21} -1.34544i q^{22} -1.90130i q^{23} +2.12672i q^{24} -0.983677 q^{25} +1.72099i q^{26} +1.00000 q^{27} -2.17182i q^{28} -1.94069i q^{29} +1.42027 q^{30} -2.86120 q^{31} +5.46748i q^{32} -2.31728 q^{33} -0.0692195i q^{34} -3.19481 q^{35} +1.66289 q^{36} -2.10289 q^{37} -0.315809i q^{38} +2.96410 q^{39} +5.20228 q^{40} +6.67031i q^{41} +0.758310 q^{42} +5.70782i q^{43} -3.85338 q^{44} -2.44616i q^{45} +1.10392 q^{46} -6.17066 q^{47} +2.09098 q^{48} +5.29423 q^{49} -0.571135i q^{50} -0.119218 q^{51} +4.92897 q^{52} +1.95561i q^{53} +0.580612i q^{54} +5.66843i q^{55} +2.77761 q^{56} -0.543925 q^{57} +1.12679 q^{58} +5.11256i q^{59} -4.06769i q^{60} +4.37193i q^{61} -1.66125i q^{62} -1.30605i q^{63} +1.00747 q^{64} -7.25065i q^{65} -1.34544i q^{66} -1.00850 q^{67} -0.198247 q^{68} -1.90130i q^{69} -1.85494i q^{70} -9.36547 q^{71} +2.12672i q^{72} +14.8637i q^{73} -1.22097i q^{74} -0.983677 q^{75} -0.904487 q^{76} +3.02649i q^{77} +1.72099i q^{78} -9.78715i q^{79} -5.11486i q^{80} +1.00000 q^{81} -3.87287 q^{82} -9.03696i q^{83} -2.17182i q^{84} +0.291626i q^{85} -3.31403 q^{86} -1.94069i q^{87} -4.92820i q^{88} +0.298758 q^{89} +1.42027 q^{90} -3.87127i q^{91} -3.16166i q^{92} -2.86120 q^{93} -3.58276i q^{94} +1.33052i q^{95} +5.46748i q^{96} +5.45493i q^{97} +3.07389i q^{98} -2.31728 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{3} - 20 q^{4} + 14 q^{9}+O(q^{10}) \) 14 * q + 14 * q^3 - 20 * q^4 + 14 * q^9	\( 14 q + 14 q^{3} - 20 q^{4} + 14 q^{9} + 6 q^{10} - 2 q^{11} - 20 q^{12} + 24 q^{16} + 18 q^{17} - 12 q^{19} - 18 q^{25} + 14 q^{27} + 6 q^{30} - 14 q^{31} - 2 q^{33} + 16 q^{35} - 20 q^{36} - 14 q^{37} - 36 q^{40} + 24 q^{44} - 8 q^{46} + 22 q^{47} + 24 q^{48} - 48 q^{49} + 18 q^{51} - 50 q^{52} - 62 q^{56} - 12 q^{57} + 20 q^{58} - 34 q^{64} + 42 q^{67} - 56 q^{68} + 38 q^{71} - 18 q^{75} + 52 q^{76} + 14 q^{81} + 10 q^{82} + 34 q^{86} - 48 q^{89} + 6 q^{90} - 14 q^{93} - 2 q^{99}+O(q^{100}) \) 14 * q + 14 * q^3 - 20 * q^4 + 14 * q^9 + 6 * q^10 - 2 * q^11 - 20 * q^12 + 24 * q^16 + 18 * q^17 - 12 * q^19 - 18 * q^25 + 14 * q^27 + 6 * q^30 - 14 * q^31 - 2 * q^33 + 16 * q^35 - 20 * q^36 - 14 * q^37 - 36 * q^40 + 24 * q^44 - 8 * q^46 + 22 * q^47 + 24 * q^48 - 48 * q^49 + 18 * q^51 - 50 * q^52 - 62 * q^56 - 12 * q^57 + 20 * q^58 - 34 * q^64 + 42 * q^67 - 56 * q^68 + 38 * q^71 - 18 * q^75 + 52 * q^76 + 14 * q^81 + 10 * q^82 + 34 * q^86 - 48 * q^89 + 6 * q^90 - 14 * q^93 - 2 * q^99

Introduction

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