LMFDB - Embedded newform 471.2.b.b.313.1

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			313.1
Root			$-2.72109i$ of defining polynomial
Character	$\chi$	$=$	471.313
Dual form			471.2.b.b.313.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.72109i q^{2} +1.00000 q^{3} -5.40431 q^{4} +1.84852i q^{5} -2.72109i q^{6} +5.01715i q^{7} +9.26343i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.72109i q^{2} +1.00000 q^{3} -5.40431 q^{4} +1.84852i q^{5} -2.72109i q^{6} +5.01715i q^{7} +9.26343i q^{8} +1.00000 q^{9} +5.02998 q^{10} -1.38069 q^{11} -5.40431 q^{12} -1.03086 q^{13} +13.6521 q^{14} +1.84852i q^{15} +14.3980 q^{16} +5.75850 q^{17} -2.72109i q^{18} -5.92993 q^{19} -9.98996i q^{20} +5.01715i q^{21} +3.75698i q^{22} +2.89116i q^{23} +9.26343i q^{24} +1.58298 q^{25} +2.80507i q^{26} +1.00000 q^{27} -27.1142i q^{28} +1.63099i q^{29} +5.02998 q^{30} -7.31062 q^{31} -20.6512i q^{32} -1.38069 q^{33} -15.6694i q^{34} -9.27429 q^{35} -5.40431 q^{36} +6.34148 q^{37} +16.1358i q^{38} -1.03086 q^{39} -17.1236 q^{40} +6.98418i q^{41} +13.6521 q^{42} -1.29205i q^{43} +7.46168 q^{44} +1.84852i q^{45} +7.86710 q^{46} +6.08099 q^{47} +14.3980 q^{48} -18.1718 q^{49} -4.30743i q^{50} +5.75850 q^{51} +5.57111 q^{52} +5.57361i q^{53} -2.72109i q^{54} -2.55223i q^{55} -46.4760 q^{56} -5.92993 q^{57} +4.43806 q^{58} -3.41804i q^{59} -9.98996i q^{60} -10.6841i q^{61} +19.8928i q^{62} +5.01715i q^{63} -27.3979 q^{64} -1.90557i q^{65} +3.75698i q^{66} +12.1893 q^{67} -31.1207 q^{68} +2.89116i q^{69} +25.2361i q^{70} -3.19330 q^{71} +9.26343i q^{72} +5.10379i q^{73} -17.2557i q^{74} +1.58298 q^{75} +32.0472 q^{76} -6.92713i q^{77} +2.80507i q^{78} -7.11562i q^{79} +26.6149i q^{80} +1.00000 q^{81} +19.0046 q^{82} -12.9986i q^{83} -27.1142i q^{84} +10.6447i q^{85} -3.51579 q^{86} +1.63099i q^{87} -12.7899i q^{88} -2.52258 q^{89} +5.02998 q^{90} -5.17200i q^{91} -15.6247i q^{92} -7.31062 q^{93} -16.5469i q^{94} -10.9616i q^{95} -20.6512i q^{96} -13.9316i q^{97} +49.4471i q^{98} -1.38069 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	2.72109i		−	1.92410i	−0.272876	−	0.962049i	$-0.587975\pi$
$2$		−	2.72109i		−	1.92410i	0.272876	−	0.962049i	$-0.412025\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−5.40431			−2.70216
$5$			1.84852i			0.826682i	0.910576	+	0.413341i	$0.135638\pi$
$5$			1.84852i			0.826682i	−0.910576	+	0.413341i	$0.864362\pi$
$6$		−	2.72109i		−	1.11088i
$7$			5.01715i			1.89630i	0.317816	+	0.948152i	$0.397051\pi$
$7$			5.01715i			1.89630i	−0.317816	+	0.948152i	$0.602949\pi$
$8$			9.26343i			3.27512i
$9$	1.00000			0.333333
$10$	5.02998			1.59062
$11$	−1.38069			−0.416294			−0.208147	−	0.978098i	$-0.566743\pi$
$11$	−1.38069			−0.416294			−0.208147	+	0.978098i	$0.566743\pi$
$12$	−5.40431			−1.56009
$13$	−1.03086			−0.285910			−0.142955	−	0.989729i	$-0.545660\pi$
$13$	−1.03086			−0.285910			−0.142955	+	0.989729i	$0.545660\pi$
$14$	13.6521			3.64868
$15$			1.84852i			0.477285i
$16$	14.3980			3.59949
$17$	5.75850			1.39664			0.698321	−	0.715785i	$-0.253931\pi$
$17$	5.75850			1.39664			0.698321	+	0.715785i	$0.253931\pi$
$18$		−	2.72109i		−	0.641366i
$19$	−5.92993			−1.36042			−0.680209	−	0.733018i	$-0.738111\pi$
$19$	−5.92993			−1.36042			−0.680209	+	0.733018i	$0.738111\pi$
$20$		−	9.98996i		−	2.23382i
$21$			5.01715i			1.09483i
$22$			3.75698i			0.800990i
$23$			2.89116i			0.602849i	0.953490	+	0.301424i	$0.0974621\pi$
$23$			2.89116i			0.602849i	−0.953490	+	0.301424i	$0.902538\pi$
$24$			9.26343i			1.89089i
$25$	1.58298			0.316597
$26$			2.80507i			0.550120i
$27$	1.00000			0.192450
$28$		−	27.1142i		−	5.12411i
$29$			1.63099i			0.302867i	0.988467	+	0.151433i	$0.0483889\pi$
$29$			1.63099i			0.302867i	−0.988467	+	0.151433i	$0.951611\pi$
$30$	5.02998			0.918344
$31$	−7.31062			−1.31303			−0.656513	−	0.754315i	$-0.727969\pi$
$31$	−7.31062			−1.31303			−0.656513	+	0.754315i	$0.727969\pi$
$32$		−	20.6512i		−	3.65066i
$33$	−1.38069			−0.240347
$34$		−	15.6694i		−	2.68728i
$35$	−9.27429			−1.56764
$36$	−5.40431			−0.900719
$37$	6.34148			1.04253			0.521267	−	0.853394i	$-0.325460\pi$
$37$	6.34148			1.04253			0.521267	+	0.853394i	$0.325460\pi$
$38$			16.1358i			2.61758i
$39$	−1.03086			−0.165070
$40$	−17.1236			−2.70748
$41$			6.98418i			1.09075i	0.838193	+	0.545373i	$0.183612\pi$
$41$			6.98418i			1.09075i	−0.838193	+	0.545373i	$0.816388\pi$
$42$	13.6521			2.10657
$43$		−	1.29205i		−	0.197036i	−0.995135	−	0.0985182i	$-0.968590\pi$
$43$		−	1.29205i		−	0.197036i	0.995135	−	0.0985182i	$-0.0314103\pi$
$44$	7.46168			1.12489
$45$			1.84852i			0.275561i
$46$	7.86710			1.15994
$47$	6.08099			0.887003			0.443502	−	0.896274i	$-0.353736\pi$
$47$	6.08099			0.887003			0.443502	+	0.896274i	$0.353736\pi$
$48$	14.3980			2.07817
$49$	−18.1718			−2.59597
$50$		−	4.30743i		−	0.609163i
$51$	5.75850			0.806351
$52$	5.57111			0.772575
$53$			5.57361i			0.765595i	0.923832	+	0.382797i	$0.125039\pi$
$53$			5.57361i			0.765595i	−0.923832	+	0.382797i	$0.874961\pi$
$54$		−	2.72109i		−	0.370293i
$55$		−	2.55223i		−	0.344143i
$56$	−46.4760			−6.21062
$57$	−5.92993			−0.785438
$58$	4.43806			0.582745
$59$		−	3.41804i		−	0.444991i	−0.974934	−	0.222496i	$-0.928580\pi$
$59$		−	3.41804i		−	0.444991i	0.974934	−	0.222496i	$-0.0714203\pi$
$60$		−	9.98996i		−	1.28970i
$61$		−	10.6841i		−	1.36796i	−0.729501	−	0.683980i	$-0.760248\pi$
$61$		−	10.6841i		−	1.36796i	0.729501	−	0.683980i	$-0.239752\pi$
$62$			19.8928i			2.52639i
$63$			5.01715i			0.632102i
$64$	−27.3979			−3.42474
$65$		−	1.90557i		−	0.236357i
$66$			3.75698i			0.462452i
$67$	12.1893			1.48916			0.744581	−	0.667532i	$-0.232649\pi$
$67$	12.1893			1.48916			0.744581	+	0.667532i	$0.232649\pi$
$68$	−31.1207			−3.77394
$69$			2.89116i			0.348055i
$70$			25.2361i			3.01630i
$71$	−3.19330			−0.378975			−0.189488	−	0.981883i	$-0.560683\pi$
$71$	−3.19330			−0.378975			−0.189488	+	0.981883i	$0.560683\pi$
$72$			9.26343i			1.09171i
$73$			5.10379i			0.597353i	0.954354	+	0.298676i	$0.0965451\pi$
$73$			5.10379i			0.597353i	−0.954354	+	0.298676i	$0.903455\pi$
$74$		−	17.2557i		−	2.00594i
$75$	1.58298			0.182787
$76$	32.0472			3.67606
$77$		−	6.92713i		−	0.789420i
$78$			2.80507i			0.317612i
$79$		−	7.11562i		−	0.800570i	−0.916391	−	0.400285i	$-0.868911\pi$
$79$		−	7.11562i		−	0.800570i	0.916391	−	0.400285i	$-0.131089\pi$
$80$			26.6149i			2.97563i
$81$	1.00000			0.111111
$82$	19.0046			2.09870
$83$		−	12.9986i		−	1.42678i	−0.700767	−	0.713390i	$-0.747159\pi$
$83$		−	12.9986i		−	1.42678i	0.700767	−	0.713390i	$-0.252841\pi$
$84$		−	27.1142i		−	2.95841i
$85$			10.6447i			1.15458i
$86$	−3.51579			−0.379118
$87$			1.63099i			0.174860i
$88$		−	12.7899i		−	1.36341i
$89$	−2.52258			−0.267393			−0.133697	−	0.991022i	$-0.542685\pi$
$89$	−2.52258			−0.267393			−0.133697	+	0.991022i	$0.542685\pi$
$90$	5.02998			0.530206
$91$		−	5.17200i		−	0.542173i
$92$		−	15.6247i		−	1.62899i
$93$	−7.31062			−0.758076
$94$		−	16.5469i		−	1.70668i
$95$		−	10.9616i		−	1.12463i
$96$		−	20.6512i		−	2.10771i
$97$		−	13.9316i		−	1.41454i	−0.706945	−	0.707269i	$-0.749927\pi$
$97$		−	13.9316i		−	1.41454i	0.706945	−	0.707269i	$-0.250073\pi$
$98$			49.4471i			4.99491i
$99$	−1.38069			−0.138765
$100$	−8.55493			−0.855493
$101$	19.3012			1.92054			0.960269	−	0.279077i	$-0.0900283\pi$
$101$	19.3012			1.92054			0.960269	+	0.279077i	$0.0900283\pi$
$102$		−	15.6694i		−	1.55150i
$103$			18.7066i			1.84321i	0.388126	+	0.921606i	$0.373123\pi$
$103$			18.7066i			1.84321i	−0.388126	+	0.921606i	$0.626877\pi$
$104$		−	9.54934i		−	0.936390i
$105$	−9.27429			−0.905078
$106$	15.1663			1.47308
$107$		−	0.788583i		−	0.0762352i	−0.999273	−	0.0381176i	$-0.987864\pi$
$107$		−	0.788583i		−	0.0762352i	0.999273	−	0.0381176i	$-0.0121362\pi$
$108$	−5.40431			−0.520030
$109$	9.66109			0.925365			0.462682	−	0.886524i	$-0.346887\pi$
$109$	9.66109			0.925365			0.462682	+	0.886524i	$0.346887\pi$
$110$	−6.94484			−0.662164
$111$	6.34148			0.601907
$112$			72.2367i			6.82573i
$113$	6.31979			0.594515			0.297258	−	0.954797i	$-0.403928\pi$
$113$	6.31979			0.594515			0.297258	+	0.954797i	$0.403928\pi$
$114$			16.1358i			1.51126i
$115$	−5.34436			−0.498364
$116$		−	8.81436i		−	0.818393i
$117$	−1.03086			−0.0953035
$118$	−9.30079			−0.856207
$119$			28.8913i			2.64846i
$120$	−17.1236			−1.56316
$121$	−9.09370			−0.826700
$122$	−29.0724			−2.63209
$123$			6.98418i			0.629743i
$124$	39.5089			3.54800
$125$			12.1688i			1.08841i
$126$	13.6521			1.21623
$127$	−13.2622			−1.17683			−0.588417	−	0.808558i	$-0.700249\pi$
$127$	−13.2622			−1.17683			−0.588417	+	0.808558i	$0.700249\pi$
$128$			33.2496i			2.93887i
$129$		−	1.29205i		−	0.113759i
$130$	−5.18522			−0.454774
$131$			9.41723i			0.822787i	0.911458	+	0.411393i	$0.134958\pi$
$131$			9.41723i			0.822787i	−0.911458	+	0.411393i	$0.865042\pi$
$132$	7.46168			0.649456
$133$		−	29.7513i		−	2.57977i
$134$		−	33.1682i		−	2.86529i
$135$			1.84852i			0.159095i
$136$			53.3434i			4.57416i
$137$			0.212881i			0.0181876i	0.999959	+	0.00909381i	$0.00289469\pi$
$137$			0.212881i			0.0181876i	−0.999959	+	0.00909381i	$0.997105\pi$
$138$	7.86710			0.669692
$139$		−	17.7997i		−	1.50975i	−0.655867	−	0.754877i	$-0.727697\pi$
$139$		−	17.7997i		−	1.50975i	0.655867	−	0.754877i	$-0.272303\pi$
$140$	50.1212			4.23601
$141$	6.08099			0.512112
$142$			8.68926i			0.729186i
$143$	1.42330			0.119023
$144$	14.3980			1.19983
$145$	−3.01491			−0.250374
$146$	13.8878			1.14937
$147$	−18.1718			−1.49879
$148$	−34.2714			−2.81709
$149$			6.16044i			0.504683i	0.967638	+	0.252341i	$0.0812006\pi$
$149$			6.16044i			0.504683i	−0.967638	+	0.252341i	$0.918799\pi$
$150$		−	4.30743i		−	0.351701i
$151$			11.7964i			0.959981i	0.877274	+	0.479990i	$0.159360\pi$
$151$			11.7964i			0.959981i	−0.877274	+	0.479990i	$0.840640\pi$
$152$		−	54.9315i		−	4.45553i
$153$	5.75850			0.465547
$154$	−18.8493			−1.51892
$155$		−	13.5138i		−	1.08546i
$156$	5.57111			0.446046
$157$	11.5256	+	4.91529i	0.919845	+	0.392283i
$157$	11.5256	+	4.91529i	0.919845	+	0.392283i
$158$	−19.3622			−1.54038
$159$			5.57361i			0.442016i
$160$	38.1742			3.01793
$161$	−14.5054			−1.14319
$162$		−	2.72109i		−	0.213789i
$163$			9.05604i			0.709324i	0.934995	+	0.354662i	$0.115404\pi$
$163$			9.05604i			0.709324i	−0.934995	+	0.354662i	$0.884596\pi$
$164$		−	37.7447i		−	2.94737i
$165$		−	2.55223i		−	0.198691i
$166$	−35.3703			−2.74527
$167$	14.6532			1.13390			0.566949	−	0.823753i	$-0.308123\pi$
$167$	14.6532			1.13390			0.566949	+	0.823753i	$0.308123\pi$
$168$	−46.4760			−3.58570
$169$	−11.9373			−0.918255
$170$	28.9651			2.22152
$171$	−5.92993			−0.453473
$172$			6.98266i			0.532423i
$173$	14.1403			1.07507			0.537533	−	0.843243i	$-0.319356\pi$
$173$	14.1403			1.07507			0.537533	+	0.843243i	$0.319356\pi$
$174$	4.43806			0.336448
$175$			7.94207i			0.600364i
$176$	−19.8791			−1.49844
$177$		−	3.41804i		−	0.256916i
$178$			6.86416i			0.514491i
$179$			10.3657i			0.774769i	0.921918	+	0.387384i	$0.126621\pi$
$179$			10.3657i			0.774769i	−0.921918	+	0.387384i	$0.873379\pi$
$180$		−	9.98996i		−	0.744608i
$181$		−	8.68105i		−	0.645257i	−0.946526	−	0.322629i	$-0.895434\pi$
$181$		−	8.68105i		−	0.645257i	0.946526	−	0.322629i	$-0.104566\pi$
$182$	−14.0735			−1.04319
$183$		−	10.6841i		−	0.789792i
$184$	−26.7821			−1.97440
$185$			11.7223i			0.861844i
$186$			19.8928i			1.45861i
$187$	−7.95070			−0.581413
$188$	−32.8636			−2.39682
$189$			5.01715i			0.364944i
$190$	−29.8274			−2.16391
$191$		−	20.6093i		−	1.49123i	−0.666375	−	0.745617i	$-0.732155\pi$
$191$		−	20.6093i		−	1.49123i	0.666375	−	0.745617i	$-0.267845\pi$
$192$	−27.3979			−1.97727
$193$	−15.9682			−1.14941			−0.574707	−	0.818359i	$-0.694884\pi$
$193$	−15.9682			−1.14941			−0.574707	+	0.818359i	$0.694884\pi$
$194$	−37.9090			−2.72171
$195$		−	1.90557i		−	0.136461i
$196$	98.2061			7.01472
$197$	13.4801			0.960419			0.480210	−	0.877154i	$-0.340561\pi$
$197$	13.4801			0.960419			0.480210	+	0.877154i	$0.340561\pi$
$198$			3.75698i			0.266997i
$199$	2.09562			0.148554			0.0742772	−	0.997238i	$-0.476335\pi$
$199$	2.09562			0.148554			0.0742772	+	0.997238i	$0.476335\pi$
$200$			14.6638i			1.03689i
$201$	12.1893			0.859768
$202$		−	52.5201i		−	3.69530i
$203$	−8.18291			−0.574327
$204$	−31.1207			−2.17889
$205$	−12.9104			−0.901700
$206$	50.9022			3.54652
$207$			2.89116i			0.200950i
$208$	−14.8423			−1.02913
$209$	8.18739			0.566334
$210$			25.2361i			1.74146i
$211$		−	14.3161i		−	0.985562i	−0.870153	−	0.492781i	$-0.835980\pi$
$211$		−	14.3161i		−	0.985562i	0.870153	−	0.492781i	$-0.164020\pi$
$212$		−	30.1215i		−	2.06876i
$213$	−3.19330			−0.218802
$214$	−2.14580			−0.146684
$215$	2.38838			0.162886
$216$			9.26343i			0.630296i
$217$		−	36.6785i		−	2.48990i
$218$		−	26.2887i		−	1.78049i
$219$			5.10379i			0.344882i
$220$			13.7930i			0.929927i
$221$	−5.93623			−0.399314
$222$		−	17.2557i		−	1.15813i
$223$		−	8.93897i		−	0.598598i	−0.954159	−	0.299299i	$-0.903247\pi$
$223$		−	8.93897i		−	0.598598i	0.954159	−	0.299299i	$-0.0967527\pi$
$224$	103.610			6.92276
$225$	1.58298			0.105532
$226$		−	17.1967i		−	1.14391i
$227$		−	1.44082i		−	0.0956307i	−0.998856	−	0.0478154i	$-0.984774\pi$
$227$		−	1.44082i		−	0.0956307i	0.998856	−	0.0478154i	$-0.0152259\pi$
$228$	32.0472			2.12238
$229$			13.1727i			0.870475i	0.900316	+	0.435238i	$0.143336\pi$
$229$			13.1727i			0.870475i	−0.900316	+	0.435238i	$0.856664\pi$
$230$			14.5425i			0.958902i
$231$		−	6.92713i		−	0.455772i
$232$	−15.1085			−0.991923
$233$	−16.0713			−1.05286			−0.526432	−	0.850217i	$-0.676471\pi$
$233$	−16.0713			−1.05286			−0.526432	+	0.850217i	$0.676471\pi$
$234$			2.80507i			0.183373i
$235$			11.2408i			0.733270i
$236$			18.4722i			1.20244i
$237$		−	7.11562i		−	0.462209i
$238$	78.6156			5.09589
$239$	22.0281			1.42488			0.712441	−	0.701732i	$-0.247590\pi$
$239$	22.0281			1.42488			0.712441	+	0.701732i	$0.247590\pi$
$240$			26.6149i			1.71798i
$241$			5.40237i			0.347997i	0.984746	+	0.173998i	$0.0556688\pi$
$241$			5.40237i			0.347997i	−0.984746	+	0.173998i	$0.944331\pi$
$242$			24.7447i			1.59065i
$243$	1.00000			0.0641500
$244$			57.7402i			3.69644i
$245$		−	33.5909i		−	2.14604i
$246$	19.0046			1.21169
$247$	6.11295			0.388958
$248$		−	67.7214i		−	4.30031i
$249$		−	12.9986i		−	0.823752i
$250$	33.1122			2.09420
$251$		−	23.6203i		−	1.49090i	−0.666560	−	0.745451i	$-0.732234\pi$
$251$		−	23.6203i		−	1.49090i	0.666560	−	0.745451i	$-0.267766\pi$
$252$		−	27.1142i		−	1.70804i
$253$		−	3.99180i		−	0.250962i
$254$			36.0877i			2.26434i
$255$			10.6447i			0.666596i
$256$	35.6791			2.22995
$257$	14.5867			0.909893			0.454947	−	0.890519i	$-0.349658\pi$
$257$	14.5867			0.909893			0.454947	+	0.890519i	$0.349658\pi$
$258$	−3.51579			−0.218884
$259$			31.8162i			1.97696i
$260$			10.2983i			0.638674i
$261$			1.63099i			0.100956i
$262$	25.6251			1.58312
$263$	−26.4962			−1.63383			−0.816914	−	0.576760i	$-0.804317\pi$
$263$	−26.4962			−1.63383			−0.816914	+	0.576760i	$0.804317\pi$
$264$		−	12.7899i		−	0.787165i
$265$	−10.3029			−0.632904
$266$	−80.9560			−4.96373
$267$	−2.52258			−0.154380
$268$	−65.8748			−4.02395
$269$		−	14.3366i		−	0.874119i	−0.899433	−	0.437060i	$-0.856020\pi$
$269$		−	14.3366i		−	0.874119i	0.899433	−	0.437060i	$-0.143980\pi$
$270$	5.02998			0.306115
$271$			11.8806i			0.721697i	0.932624	+	0.360848i	$0.117513\pi$
$271$			11.8806i			0.721697i	−0.932624	+	0.360848i	$0.882487\pi$
$272$	82.9107			5.02720
$273$		−	5.17200i		−	0.313024i
$274$	0.579266			0.0349948
$275$	−2.18561			−0.131797
$276$		−	15.6247i		−	0.940499i
$277$	−5.86311			−0.352280			−0.176140	−	0.984365i	$-0.556361\pi$
$277$	−5.86311			−0.352280			−0.176140	+	0.984365i	$0.556361\pi$
$278$	−48.4346			−2.90491
$279$	−7.31062			−0.437675
$280$		−	85.9117i		−	5.13421i
$281$	18.6946			1.11523			0.557613	−	0.830101i	$-0.311717\pi$
$281$	18.6946			1.11523			0.557613	+	0.830101i	$0.311717\pi$
$282$		−	16.5469i		−	0.985353i
$283$	−8.00372			−0.475772			−0.237886	−	0.971293i	$-0.576454\pi$
$283$	−8.00372			−0.475772			−0.237886	+	0.971293i	$0.576454\pi$
$284$	17.2576			1.02405
$285$		−	10.9616i		−	0.649308i
$286$		−	3.87293i		−	0.229011i
$287$	−35.0407			−2.06839
$288$		−	20.6512i		−	1.21689i
$289$	16.1603			0.950607
$290$			8.20382i			0.481745i
$291$		−	13.9316i		−	0.816684i
$292$		−	27.5824i		−	1.61414i
$293$		−	11.9902i		−	0.700476i	−0.936661	−	0.350238i	$-0.886101\pi$
$293$		−	11.9902i		−	0.700476i	0.936661	−	0.350238i	$-0.113899\pi$
$294$			49.4471i			2.88381i
$295$	6.31831			0.367866
$296$			58.7439i			3.41442i
$297$	−1.38069			−0.0801157
$298$	16.7631			0.971059
$299$		−	2.98040i		−	0.172361i
$300$	−8.55493			−0.493919
$301$	6.48243			0.373641
$302$	32.0991			1.84710
$303$	19.3012			1.10882
$304$	−85.3789			−4.89681
$305$	19.7498			1.13087
$306$		−	15.6694i		−	0.895759i
$307$		−	0.116307i		−	0.00663797i	−0.999994	−	0.00331898i	$-0.998944\pi$
$307$		−	0.116307i		−	0.00663797i	0.999994	−	0.00331898i	$-0.00105647\pi$
$308$			37.4364i			2.13313i
$309$			18.7066i			1.06418i
$310$	−36.7722			−2.08852
$311$	1.55267			0.0880436			0.0440218	−	0.999031i	$-0.485983\pi$
$311$	1.55267			0.0880436			0.0440218	+	0.999031i	$0.485983\pi$
$312$		−	9.54934i		−	0.540625i
$313$	10.3868			0.587097			0.293548	−	0.955944i	$-0.405164\pi$
$313$	10.3868			0.587097			0.293548	+	0.955944i	$0.405164\pi$
$314$	13.3749	−	31.3622i	0.754791	−	1.76987i
$315$	−9.27429			−0.522547
$316$			38.4550i			2.16327i
$317$	−9.75427			−0.547854			−0.273927	−	0.961750i	$-0.588323\pi$
$317$	−9.75427			−0.547854			−0.273927	+	0.961750i	$0.588323\pi$
$318$	15.1663			0.850483
$319$		−	2.25189i		−	0.126081i
$320$		−	50.6455i		−	2.83117i
$321$		−	0.788583i		−	0.0440144i
$322$			39.4704i			2.19960i
$323$	−34.1475			−1.90002
$324$	−5.40431			−0.300240
$325$	−1.63184			−0.0905183
$326$	24.6423			1.36481
$327$	9.66109			0.534260
$328$	−64.6975			−3.57232
$329$			30.5092i			1.68203i
$330$	−6.94484			−0.382301
$331$	−14.9741			−0.823051			−0.411525	−	0.911398i	$-0.635004\pi$
$331$	−14.9741			−0.823051			−0.411525	+	0.911398i	$0.635004\pi$
$332$			70.2484i			3.85538i
$333$	6.34148			0.347511
$334$		−	39.8726i		−	2.18173i
$335$			22.5322i			1.23106i
$336$			72.2367i			3.94084i
$337$		−	18.1923i		−	0.990997i	−0.868609	−	0.495498i	$-0.834985\pi$
$337$		−	18.1923i		−	0.990997i	0.868609	−	0.495498i	$-0.165015\pi$
$338$			32.4825i			1.76681i
$339$	6.31979			0.343244
$340$		−	57.5272i		−	3.11985i
$341$	10.0937			0.546604
$342$			16.1358i			0.872527i
$343$		−	56.0506i		−	3.02645i
$344$	11.9688			0.645317
$345$	−5.34436			−0.287731
$346$		−	38.4770i		−	2.06853i
$347$	−7.93622			−0.426038			−0.213019	−	0.977048i	$-0.568330\pi$
$347$	−7.93622			−0.426038			−0.213019	+	0.977048i	$0.568330\pi$
$348$		−	8.81436i		−	0.472499i
$349$	5.77121			0.308926			0.154463	−	0.987999i	$-0.450635\pi$
$349$	5.77121			0.308926			0.154463	+	0.987999i	$0.450635\pi$
$350$	21.6110			1.15516
$351$	−1.03086			−0.0550235
$352$			28.5130i			1.51975i
$353$	18.2517			0.971439			0.485720	−	0.874115i	$-0.338558\pi$
$353$	18.2517			0.971439			0.485720	+	0.874115i	$0.338558\pi$
$354$	−9.30079			−0.494332
$355$		−	5.90288i		−	0.313292i
$356$	13.6328			0.722538
$357$			28.8913i			1.52909i
$358$	28.2060			1.49073
$359$			6.91660i			0.365044i	0.983202	+	0.182522i	$0.0584261\pi$
$359$			6.91660i			0.365044i	−0.983202	+	0.182522i	$0.941574\pi$
$360$	−17.1236			−0.902493
$361$	16.1641			0.850740
$362$	−23.6219			−1.24154
$363$	−9.09370			−0.477295
$364$			27.9511i			1.46504i
$365$	−9.43444			−0.493821
$366$	−29.0724			−1.51964
$367$			19.7721i			1.03210i	0.856559	+	0.516049i	$0.172598\pi$
$367$			19.7721i			1.03210i	−0.856559	+	0.516049i	$0.827402\pi$
$368$			41.6268i			2.16995i
$369$			6.98418i			0.363582i
$370$	31.8975			1.65827
$371$	−27.9637			−1.45180
$372$	39.5089			2.04844
$373$			4.96273i			0.256961i	0.991712	+	0.128480i	$0.0410099\pi$
$373$			4.96273i			0.256961i	−0.991712	+	0.128480i	$0.958990\pi$
$374$			21.6345i			1.11870i
$375$			12.1688i			0.628392i
$376$			56.3308i			2.90504i
$377$		−	1.68133i		−	0.0865927i
$378$	13.6521			0.702188
$379$			14.2935i			0.734206i	0.930180	+	0.367103i	$0.119650\pi$
$379$			14.2935i			0.734206i	−0.930180	+	0.367103i	$0.880350\pi$
$380$			59.2398i			3.03894i
$381$	−13.2622			−0.679445
$382$	−56.0796			−2.86928
$383$			8.16527i			0.417226i	0.977998	+	0.208613i	$0.0668949\pi$
$383$			8.16527i			0.417226i	−0.977998	+	0.208613i	$0.933105\pi$
$384$			33.2496i			1.69676i
$385$	12.8049			0.652599
$386$			43.4508i			2.21159i
$387$		−	1.29205i		−	0.0656788i
$388$			75.2906i			3.82230i
$389$	18.6550			0.945844			0.472922	−	0.881104i	$-0.343199\pi$
$389$	18.6550			0.945844			0.472922	+	0.881104i	$0.343199\pi$
$390$	−5.18522			−0.262564
$391$			16.6488i			0.841964i
$392$		−	168.333i		−	8.50211i
$393$			9.41723i			0.475036i
$394$		−	36.6806i		−	1.84794i
$395$	13.1534			0.661817
$396$	7.46168			0.374963
$397$		−	0.00176308i		−	8.84863e-5i	−1.00000		4.42432e-5i	$-0.999986\pi$
$397$		−	0.00176308i		−	8.84863e-5i	1.00000		4.42432e-5i	$-1.40830e-5\pi$
$398$		−	5.70235i		−	0.285833i
$399$		−	29.7513i		−	1.48943i
$400$	22.7917			1.13959
$401$		−	3.76477i		−	0.188004i	−0.995572	−	0.0940019i	$-0.970034\pi$
$401$		−	3.76477i		−	0.188004i	0.995572	−	0.0940019i	$-0.0299660\pi$
$402$		−	33.1682i		−	1.65428i
$403$	7.53626			0.375408
$404$	−104.310			−5.18959
$405$			1.84852i			0.0918536i
$406$			22.2664i			1.10506i
$407$	−8.75562			−0.434000
$408$			53.3434i			2.64089i
$409$			16.8841i			0.834866i	0.908708	+	0.417433i	$0.137070\pi$
$409$			16.8841i			0.834866i	−0.908708	+	0.417433i	$0.862930\pi$
$410$			35.1303i			1.73496i
$411$			0.212881i			0.0105006i
$412$		−	101.096i		−	4.98065i
$413$	17.1488			0.843839
$414$	7.86710			0.386647
$415$	24.0281			1.17949
$416$			21.2886i			1.04376i
$417$		−	17.7997i		−	0.871656i
$418$		−	22.2786i		−	1.08968i
$419$	29.6161			1.44684			0.723421	−	0.690407i	$-0.242569\pi$
$419$	29.6161			1.44684			0.723421	+	0.690407i	$0.242569\pi$
$420$	50.1212			2.44566
$421$			21.5006i			1.04788i	0.851756	+	0.523938i	$0.175538\pi$
$421$			21.5006i			1.04788i	−0.851756	+	0.523938i	$0.824462\pi$
$422$	−38.9554			−1.89632
$423$	6.08099			0.295668
$424$	−51.6308			−2.50741
$425$	9.11561			0.442172
$426$			8.68926i			0.420996i
$427$	53.6038			2.59407
$428$			4.26175i			0.206000i
$429$	1.42330			0.0687178
$430$		−	6.49900i		−	0.313410i
$431$	−12.7112			−0.612278			−0.306139	−	0.951987i	$-0.599037\pi$
$431$	−12.7112			−0.612278			−0.306139	+	0.951987i	$0.599037\pi$
$432$	14.3980			0.692722
$433$			0.514855i			0.0247423i	0.999923	+	0.0123712i	$0.00393797\pi$
$433$			0.514855i			0.0247423i	−0.999923	+	0.0123712i	$0.996062\pi$
$434$	−99.8053			−4.79081
$435$	−3.01491			−0.144554
$436$	−52.2115			−2.50048
$437$		−	17.1444i		−	0.820127i
$438$	13.8878			0.663587
$439$		−	27.1773i		−	1.29710i	−0.761171	−	0.648552i	$-0.775375\pi$
$439$		−	27.1773i		−	1.29710i	0.761171	−	0.648552i	$-0.224625\pi$
$440$	23.6424			1.12711
$441$	−18.1718			−0.865324
$442$			16.1530i			0.768320i
$443$			16.8235i			0.799311i	0.916665	+	0.399655i	$0.130870\pi$
$443$			16.8235i			0.799311i	−0.916665	+	0.399655i	$0.869130\pi$
$444$	−34.2714			−1.62645
$445$		−	4.66304i		−	0.221049i
$446$	−24.3237			−1.15176
$447$			6.16044i			0.291379i
$448$		−	137.459i		−	6.49435i
$449$		−	8.47216i		−	0.399826i	−0.979814	−	0.199913i	$-0.935934\pi$
$449$		−	8.47216i		−	0.399826i	0.979814	−	0.199913i	$-0.0640659\pi$
$450$		−	4.30743i		−	0.203054i
$451$		−	9.64299i		−	0.454071i
$452$	−34.1541			−1.60647
$453$			11.7964i			0.554245i
$454$	−3.92060			−0.184003
$455$	9.56054			0.448205
$456$		−	54.9315i		−	2.57240i
$457$	9.18634			0.429719			0.214859	−	0.976645i	$-0.431071\pi$
$457$	9.18634			0.429719			0.214859	+	0.976645i	$0.431071\pi$
$458$	35.8440			1.67488
$459$	5.75850			0.268784
$460$	28.8826			1.34666
$461$	17.2800			0.804809			0.402405	−	0.915462i	$-0.368175\pi$
$461$	17.2800			0.804809			0.402405	+	0.915462i	$0.368175\pi$
$462$	−18.8493			−0.876950
$463$			7.42263i			0.344959i	0.985013	+	0.172480i	$0.0551779\pi$
$463$			7.42263i			0.344959i	−0.985013	+	0.172480i	$0.944822\pi$
$464$			23.4829i			1.09017i
$465$		−	13.5138i		−	0.626688i
$466$			43.7313i			2.02581i
$467$	30.1493			1.39514			0.697571	−	0.716516i	$-0.254264\pi$
$467$	30.1493			1.39514			0.697571	+	0.716516i	$0.254264\pi$
$468$	5.57111			0.257525
$469$			61.1556i			2.82390i
$470$	30.5872			1.41088
$471$	11.5256	+	4.91529i	0.531073	+	0.226485i
$472$	31.6628			1.45740
$473$			1.78393i			0.0820250i
$474$	−19.3622			−0.889337
$475$	−9.38698			−0.430704
$476$		−	156.137i		−	7.15655i
$477$			5.57361i			0.255198i
$478$		−	59.9405i		−	2.74161i
$479$		−	0.308663i		−	0.0141032i	−0.999975	−	0.00705158i	$-0.997755\pi$
$479$		−	0.308663i		−	0.0141032i	0.999975	−	0.00705158i	$-0.00224461\pi$
$480$	38.1742			1.74241
$481$	−6.53721			−0.298071
$482$	14.7003			0.669580
$483$	−14.5054			−0.660018
$484$	49.1452			2.23387
$485$	25.7528			1.16937
$486$		−	2.72109i		−	0.123431i
$487$	34.7710			1.57563			0.787813	−	0.615914i	$-0.211213\pi$
$487$	34.7710			1.57563			0.787813	+	0.615914i	$0.211213\pi$
$488$	98.9714			4.48023
$489$			9.05604i			0.409528i
$490$	−91.4037			−4.12920
$491$			8.72961i			0.393962i	0.980407	+	0.196981i	$0.0631137\pi$
$491$			8.72961i			0.393962i	−0.980407	+	0.196981i	$0.936886\pi$
$492$		−	37.7447i		−	1.70166i
$493$			9.39204i			0.422996i
$494$		−	16.6339i		−	0.748394i
$495$		−	2.55223i		−	0.114714i
$496$	−105.258			−4.72622
$497$		−	16.0213i		−	0.718653i
$498$	−35.3703			−1.58498
$499$			26.0801i			1.16751i	0.811931	+	0.583753i	$0.198416\pi$
$499$			26.0801i			1.16751i	−0.811931	+	0.583753i	$0.801584\pi$
$500$		−	65.7638i		−	2.94105i
$501$	14.6532			0.654657
$502$	−64.2730			−2.86864
$503$		−	1.16370i		−	0.0518870i	−0.999663	−	0.0259435i	$-0.991741\pi$
$503$		−	1.16370i		−	0.0518870i	0.999663	−	0.0259435i	$-0.00825900\pi$
$504$	−46.4760			−2.07021
$505$			35.6785i			1.58767i
$506$	−10.8620			−0.482876
$507$	−11.9373			−0.530155
$508$	71.6733			3.17999
$509$		−	40.3149i		−	1.78693i	−0.449136	−	0.893463i	$-0.648268\pi$
$509$		−	40.3149i		−	1.78693i	0.449136	−	0.893463i	$-0.351732\pi$
$510$	28.9651			1.28260
$511$	−25.6065			−1.13276
$512$		−	30.5869i		−	1.35176i
$513$	−5.92993			−0.261813
$514$		−	39.6917i		−	1.75072i
$515$	−34.5794			−1.52375
$516$			6.98266i			0.307395i
$517$	−8.39596			−0.369254
$518$	86.5746			3.80387
$519$	14.1403			0.620690
$520$	17.6521			0.774097
$521$		−	33.9367i		−	1.48679i	−0.668851	−	0.743397i	$-0.733213\pi$
$521$		−	33.9367i		−	1.48679i	0.668851	−	0.743397i	$-0.266787\pi$
$522$	4.43806			0.194248
$523$	−13.8746			−0.606694			−0.303347	−	0.952880i	$-0.598104\pi$
$523$	−13.8746			−0.606694			−0.303347	+	0.952880i	$0.598104\pi$
$524$		−	50.8936i		−	2.22330i
$525$			7.94207i			0.346620i
$526$			72.0985i			3.14365i
$527$	−42.0982			−1.83383
$528$	−19.8791			−0.865127
$529$	14.6412			0.636573
$530$			28.0351i			1.21777i
$531$		−	3.41804i		−	0.148330i
$532$			160.786i			6.97094i
$533$		−	7.19975i		−	0.311856i
$534$			6.86416i			0.297041i
$535$	1.45771			0.0630223
$536$			112.915i			4.87718i
$537$			10.3657i			0.447313i
$538$	−39.0112			−1.68189
$539$	25.0896			1.08069
$540$		−	9.98996i		−	0.429900i
$541$		−	4.00154i		−	0.172040i	−0.996293	−	0.0860199i	$-0.972585\pi$
$541$		−	4.00154i		−	0.172040i	0.996293	−	0.0860199i	$-0.0274149\pi$
$542$	32.3282			1.38862
$543$		−	8.68105i		−	0.372539i
$544$		−	118.920i		−	5.09866i
$545$			17.8587i			0.764983i
$546$	−14.0735			−0.602289
$547$	−26.7406			−1.14334			−0.571672	−	0.820482i	$-0.693705\pi$
$547$	−26.7406			−1.14334			−0.571672	+	0.820482i	$0.693705\pi$
$548$		−	1.15047i		−	0.0491458i
$549$		−	10.6841i		−	0.455986i
$550$			5.94723i			0.253591i
$551$		−	9.67163i		−	0.412025i
$552$	−26.7821			−1.13992
$553$	35.7002			1.51813
$554$			15.9540i			0.677821i
$555$			11.7223i			0.497586i
$556$			96.1953i			4.07959i
$557$	−17.9020			−0.758533			−0.379267	−	0.925287i	$-0.623824\pi$
$557$	−17.9020			−0.758533			−0.379267	+	0.925287i	$0.623824\pi$
$558$			19.8928i			0.842130i
$559$			1.33193i			0.0563348i
$560$	−133.531			−5.64271
$561$	−7.95070			−0.335679
$562$		−	50.8696i		−	2.14581i
$563$			15.9147i			0.670724i	0.942089	+	0.335362i	$0.108859\pi$
$563$			15.9147i			0.670724i	−0.942089	+	0.335362i	$0.891141\pi$
$564$	−32.8636			−1.38381
$565$			11.6822i			0.491475i
$566$			21.7788i			0.915432i
$567$			5.01715i			0.210701i
$568$		−	29.5809i		−	1.24119i
$569$			34.4482i			1.44415i	0.691817	+	0.722073i	$0.256810\pi$
$569$			34.4482i			1.44415i	−0.691817	+	0.722073i	$0.743190\pi$
$570$	−29.8274			−1.24933
$571$	−27.7002			−1.15922			−0.579608	−	0.814896i	$-0.696794\pi$
$571$	−27.7002			−1.15922			−0.579608	+	0.814896i	$0.696794\pi$
$572$	−7.69198			−0.321618
$573$		−	20.6093i		−	0.860964i
$574$			95.3488i			3.97978i
$575$			4.57666i			0.190860i
$576$	−27.3979			−1.14158
$577$	−12.0085			−0.499922			−0.249961	−	0.968256i	$-0.580418\pi$
$577$	−12.0085			−0.499922			−0.249961	+	0.968256i	$0.580418\pi$
$578$		−	43.9736i		−	1.82906i
$579$	−15.9682			−0.663615
$580$	16.2935			0.676551
$581$	65.2159			2.70561
$582$	−37.9090			−1.57138
$583$		−	7.69543i		−	0.318712i
$584$	−47.2785			−1.95640
$585$		−	1.90557i		−	0.0787857i
$586$	−32.6264			−1.34778
$587$			8.03151i			0.331496i	0.986168	+	0.165748i	$0.0530038\pi$
$587$			8.03151i			0.331496i	−0.986168	+	0.165748i	$0.946996\pi$
$588$	98.2061			4.04995
$589$	43.3514			1.78627
$590$		−	17.1927i		−	0.707811i
$591$	13.4801			0.554498
$592$	91.3044			3.75259
$593$	7.21839			0.296424			0.148212	−	0.988956i	$-0.452648\pi$
$593$	7.21839			0.296424			0.148212	+	0.988956i	$0.452648\pi$
$594$			3.75698i			0.154151i
$595$	−53.4060			−2.18943
$596$		−	33.2929i		−	1.36373i
$597$	2.09562			0.0857679
$598$	−8.10992			−0.331639
$599$		−	5.79165i		−	0.236640i	−0.992976	−	0.118320i	$-0.962249\pi$
$599$		−	5.79165i		−	0.236640i	0.992976	−	0.118320i	$-0.0377509\pi$
$600$			14.6638i			0.598649i
$601$	−7.99200			−0.326000			−0.163000	−	0.986626i	$-0.552117\pi$
$601$	−7.99200			−0.326000			−0.163000	+	0.986626i	$0.552117\pi$
$602$		−	17.6393i		−	0.718922i
$603$	12.1893			0.496387
$604$		−	63.7517i		−	2.59402i
$605$		−	16.8099i		−	0.683418i
$606$		−	52.5201i		−	2.13348i
$607$		−	6.60676i		−	0.268160i	−0.990970	−	0.134080i	$-0.957192\pi$
$607$		−	6.60676i		−	0.268160i	0.990970	−	0.134080i	$-0.0428080\pi$
$608$			122.460i			4.96642i
$609$	−8.18291			−0.331588
$610$		−	53.7408i		−	2.17590i
$611$	−6.26868			−0.253603
$612$	−31.1207			−1.25798
$613$		−	8.32627i		−	0.336295i	−0.985762	−	0.168147i	$-0.946222\pi$
$613$		−	8.32627i		−	0.336295i	0.985762	−	0.168147i	$-0.0537785\pi$
$614$	−0.316480			−0.0127721
$615$	−12.9104			−0.520597
$616$	64.1689			2.58544
$617$	−21.8159			−0.878273			−0.439137	−	0.898420i	$-0.644716\pi$
$617$	−21.8159			−0.878273			−0.439137	+	0.898420i	$0.644716\pi$
$618$	50.9022			2.04759
$619$	25.5088			1.02529			0.512643	−	0.858602i	$-0.328667\pi$
$619$	25.5088			1.02529			0.512643	+	0.858602i	$0.328667\pi$
$620$			73.0328i			2.93307i
$621$			2.89116i			0.116018i
$622$		−	4.22494i		−	0.169405i
$623$		−	12.6562i		−	0.507059i
$624$	−14.8423			−0.594169
$625$	−14.5792			−0.583170
$626$		−	28.2634i		−	1.12963i
$627$	8.18739			0.326973
$628$	−62.2880	−	26.5638i	−2.48556	−	1.06001i
$629$	36.5174			1.45605
$630$			25.2361i			1.00543i
$631$	−18.9445			−0.754170			−0.377085	−	0.926179i	$-0.623074\pi$
$631$	−18.9445			−0.754170			−0.377085	+	0.926179i	$0.623074\pi$
$632$	65.9151			2.62196
$633$		−	14.3161i		−	0.569015i
$634$			26.5422i			1.05413i
$635$		−	24.5155i		−	0.972868i
$636$		−	30.1215i		−	1.19440i
$637$	18.7327			0.742215
$638$	−6.12758			−0.242593
$639$	−3.19330			−0.126325
$640$	−61.4624			−2.42951
$641$	−14.2433			−0.562575			−0.281288	−	0.959624i	$-0.590761\pi$
$641$	−14.2433			−0.562575			−0.281288	+	0.959624i	$0.590761\pi$
$642$	−2.14580			−0.0846881
$643$			24.2635i			0.956861i	0.878125	+	0.478430i	$0.158794\pi$
$643$			24.2635i			0.956861i	−0.878125	+	0.478430i	$0.841206\pi$
$644$	78.3917			3.08906
$645$	2.38838			0.0940426
$646$			92.9183i			3.65582i
$647$	−23.4744			−0.922873			−0.461437	−	0.887173i	$-0.652666\pi$
$647$	−23.4744			−0.922873			−0.461437	+	0.887173i	$0.652666\pi$
$648$			9.26343i			0.363902i
$649$			4.71926i			0.185247i
$650$			4.44038i			0.174166i
$651$		−	36.6785i		−	1.43754i
$652$		−	48.9417i		−	1.91670i
$653$	18.0462			0.706202			0.353101	−	0.935585i	$-0.385127\pi$
$653$	18.0462			0.706202			0.353101	+	0.935585i	$0.385127\pi$
$654$		−	26.2887i		−	1.02797i
$655$	−17.4079			−0.680183
$656$			100.558i			3.92613i
$657$			5.10379i			0.199118i
$658$	83.0183			3.23639
$659$	−1.64758			−0.0641807			−0.0320903	−	0.999485i	$-0.510216\pi$
$659$	−1.64758			−0.0641807			−0.0320903	+	0.999485i	$0.510216\pi$
$660$			13.7930i			0.536893i
$661$	27.6941			1.07717			0.538587	−	0.842570i	$-0.318958\pi$
$661$	27.6941			1.07717			0.538587	+	0.842570i	$0.318958\pi$
$662$			40.7458i			1.58363i
$663$	−5.93623			−0.230544
$664$	120.411			4.67287
$665$	54.9959			2.13265
$666$		−	17.2557i		−	0.668646i
$667$	−4.71545			−0.182583
$668$	−79.1905			−3.06397
$669$		−	8.93897i		−	0.345600i
$670$	61.3119			2.36869
$671$			14.7514i			0.569473i
$672$	103.610			3.99686
$673$		−	49.1616i		−	1.89504i	−0.319696	−	0.947520i	$-0.603581\pi$
$673$		−	49.1616i		−	1.89504i	0.319696	−	0.947520i	$-0.396419\pi$
$674$	−49.5028			−1.90678
$675$	1.58298			0.0609290
$676$	64.5130			2.48127
$677$	−47.3997			−1.82172			−0.910859	−	0.412717i	$-0.864580\pi$
$677$	−47.3997			−1.82172			−0.910859	+	0.412717i	$0.864580\pi$
$678$		−	17.1967i		−	0.660435i
$679$	69.8968			2.68239
$680$	−98.6063			−3.78138
$681$		−	1.44082i		−	0.0552124i
$682$		−	27.4658i		−	1.05172i
$683$		−	16.8027i		−	0.642936i	−0.946920	−	0.321468i	$-0.895824\pi$
$683$		−	16.8027i		−	0.642936i	0.946920	−	0.321468i	$-0.104176\pi$
$684$	32.0472			1.22535
$685$	−0.393513			−0.0150354
$686$	−152.519			−5.82319
$687$			13.1727i			0.502569i
$688$		−	18.6029i		−	0.709231i
$689$		−	5.74564i		−	0.218892i
$690$			14.5425i			0.553622i
$691$			9.00161i			0.342437i	0.985233	+	0.171219i	$0.0547705\pi$
$691$			9.00161i			0.342437i	−0.985233	+	0.171219i	$0.945230\pi$
$692$	−76.4185			−2.90500
$693$		−	6.92713i		−	0.263140i
$694$			21.5951i			0.819740i
$695$	32.9031			1.24809
$696$	−15.1085			−0.572687
$697$			40.2184i			1.52338i
$698$		−	15.7040i		−	0.594404i
$699$	−16.0713			−0.607871
$700$		−	42.9214i		−	1.62228i
$701$		−	40.7444i		−	1.53890i	−0.638709	−	0.769448i	$-0.720531\pi$
$701$		−	40.7444i		−	1.53890i	0.638709	−	0.769448i	$-0.279469\pi$
$702$			2.80507i			0.105871i
$703$	−37.6045			−1.41828
$704$	37.8280			1.42570
$705$			11.2408i			0.423353i
$706$		−	49.6644i		−	1.86915i
$707$			96.8369i			3.64192i
$708$			18.4722i			0.694227i
$709$	−16.1857			−0.607867			−0.303934	−	0.952693i	$-0.598300\pi$
$709$	−16.1857			−0.607867			−0.303934	+	0.952693i	$0.598300\pi$
$710$	−16.0622			−0.602805
$711$		−	7.11562i		−	0.266857i
$712$		−	23.3678i		−	0.875743i
$713$		−	21.1362i		−	0.791556i
$714$	78.6156			2.94212
$715$			2.63100i			0.0983939i
$716$		−	56.0195i		−	2.09355i
$717$	22.0281			0.822656
$718$	18.8207			0.702381
$719$			1.79177i			0.0668219i	0.999442	+	0.0334110i	$0.0106370\pi$
$719$			1.79177i			0.0668219i	−0.999442	+	0.0334110i	$0.989363\pi$
$720$			26.6149i			0.991878i
$721$	−93.8537			−3.49529
$722$		−	43.9838i		−	1.63691i
$723$			5.40237i			0.200916i
$724$			46.9151i			1.74359i
$725$			2.58182i			0.0958865i
$726$			24.7447i			0.918363i
$727$	−0.0625208			−0.00231877			−0.00115938	−	0.999999i	$-0.500369\pi$
$727$	−0.0625208			−0.00231877			−0.00115938	+	0.999999i	$0.500369\pi$
$728$	47.9105			1.77568
$729$	1.00000			0.0370370
$730$			25.6719i			0.950160i
$731$		−	7.44029i		−	0.275189i
$732$			57.7402i			2.13414i
$733$	20.7532			0.766536			0.383268	−	0.923637i	$-0.374798\pi$
$733$	20.7532			0.766536			0.383268	+	0.923637i	$0.374798\pi$
$734$	53.8017			1.98586
$735$		−	33.5909i		−	1.23902i
$736$	59.7061			2.20080
$737$	−16.8297			−0.619928
$738$	19.0046			0.699568
$739$	4.41240			0.162313			0.0811564	−	0.996701i	$-0.474139\pi$
$739$	4.41240			0.162313			0.0811564	+	0.996701i	$0.474139\pi$
$740$		−	63.3512i		−	2.32884i
$741$	6.11295			0.224565
$742$			76.0915i			2.79341i
$743$	−5.86977			−0.215341			−0.107670	−	0.994187i	$-0.534339\pi$
$743$	−5.86977			−0.215341			−0.107670	+	0.994187i	$0.534339\pi$
$744$		−	67.7214i		−	2.48279i
$745$	−11.3877			−0.417212
$746$	13.5040			0.494418
$747$		−	12.9986i		−	0.475594i
$748$	42.9681			1.57107
$749$	3.95644			0.144565
$750$	33.1122			1.20909
$751$		−	43.8183i		−	1.59895i	−0.600697	−	0.799477i	$-0.705110\pi$
$751$		−	43.8183i		−	1.59895i	0.600697	−	0.799477i	$-0.294890\pi$
$752$	87.5538			3.19276
$753$		−	23.6203i		−	0.860773i
$754$	−4.57503			−0.166613
$755$	−21.8059			−0.793599
$756$		−	27.1142i		−	0.986136i
$757$			24.4656i			0.889219i	0.895725	+	0.444609i	$0.146657\pi$
$757$			24.4656i			0.889219i	−0.895725	+	0.444609i	$0.853343\pi$
$758$	38.8937			1.41268
$759$		−	3.99180i		−	0.144893i
$760$	101.542			3.68331
$761$			13.0748i			0.473963i	0.971514	+	0.236981i	$0.0761581\pi$
$761$			13.0748i			0.473963i	−0.971514	+	0.236981i	$0.923842\pi$
$762$			36.0877i			1.30732i
$763$			48.4712i			1.75477i
$764$			111.379i			4.02954i
$765$			10.6447i			0.384860i
$766$	22.2184			0.802784
$767$			3.52354i			0.127228i
$768$	35.6791			1.28746
$769$	−4.19740			−0.151362			−0.0756810	−	0.997132i	$-0.524113\pi$
$769$	−4.19740			−0.151362			−0.0756810	+	0.997132i	$0.524113\pi$
$770$		−	34.8433i		−	1.25567i
$771$	14.5867			0.525327
$772$	86.2970			3.10590
$773$	2.85388			0.102647			0.0513234	−	0.998682i	$-0.483656\pi$
$773$	2.85388			0.102647			0.0513234	+	0.998682i	$0.483656\pi$
$774$	−3.51579			−0.126373
$775$	−11.5726			−0.415700
$776$	129.054			4.63277
$777$			31.8162i			1.14140i
$778$		−	50.7618i		−	1.81990i
$779$		−	41.4157i		−	1.48387i
$780$			10.2983i			0.368738i
$781$	4.40896			0.157765
$782$	45.3027			1.62002
$783$			1.63099i			0.0582867i
$784$	−261.637			−9.34418
$785$	−9.08600	+	21.3053i	−0.324293	+	0.760419i
$786$	25.6251			0.914016
$787$		−	28.4285i		−	1.01337i	−0.862132	−	0.506683i	$-0.830871\pi$
$787$		−	28.4285i		−	1.01337i	0.862132	−	0.506683i	$-0.169129\pi$
$788$	−72.8508			−2.59520
$789$	−26.4962			−0.943291
$790$		−	35.7914i		−	1.27340i
$791$			31.7073i			1.12738i
$792$		−	12.7899i		−	0.454470i
$793$			11.0139i			0.391114i
$794$	−0.00479749			−0.000170256
$795$	−10.3029			−0.365407
$796$	−11.3254			−0.401417
$797$	−35.8264			−1.26904			−0.634518	−	0.772908i	$-0.718802\pi$
$797$	−35.8264			−1.26904			−0.634518	+	0.772908i	$0.718802\pi$
$798$	−80.9560			−2.86581
$799$	35.0174			1.23883
$800$		−	32.6906i		−	1.15579i
$801$	−2.52258			−0.0891310
$802$	−10.2443			−0.361738
$803$		−	7.04674i		−	0.248674i
$804$	−65.8748			−2.32323
$805$		−	26.8135i		−	0.945051i
$806$		−	20.5068i		−	0.722322i
$807$		−	14.3366i		−	0.504673i
$808$			178.795i			6.28998i
$809$			28.8958i			1.01592i	0.861380	+	0.507961i	$0.169601\pi$
$809$			28.8958i			1.01592i	−0.861380	+	0.507961i	$0.830399\pi$
$810$	5.02998			0.176735
$811$		−	20.0772i		−	0.705005i	−0.935811	−	0.352502i	$-0.885331\pi$
$811$		−	20.0772i		−	0.705005i	0.935811	−	0.352502i	$-0.114669\pi$
$812$	44.2230			1.55192
$813$			11.8806i			0.416672i
$814$			23.8248i			0.835059i
$815$	−16.7403			−0.586385
$816$	82.9107			2.90245
$817$			7.66179i			0.268052i
$818$	45.9431			1.60636
$819$		−	5.17200i		−	0.180724i
$820$	69.7717			2.43653
$821$	−22.8568			−0.797707			−0.398854	−	0.917015i	$-0.630592\pi$
$821$	−22.8568			−0.797707			−0.398854	+	0.917015i	$0.630592\pi$
$822$	0.579266			0.0202042
$823$		−	15.2866i		−	0.532858i	−0.963855	−	0.266429i	$-0.914156\pi$
$823$		−	15.2866i		−	0.532858i	0.963855	−	0.266429i	$-0.0858438\pi$
$824$	−173.287			−6.03674
$825$	−2.18561			−0.0760931
$826$		−	46.6635i		−	1.62363i
$827$	43.6182			1.51676			0.758378	−	0.651816i	$-0.225992\pi$
$827$	43.6182			1.51676			0.758378	+	0.651816i	$0.225992\pi$
$828$		−	15.6247i		−	0.542997i
$829$	4.73438			0.164432			0.0822159	−	0.996615i	$-0.473800\pi$
$829$	4.73438			0.164432			0.0822159	+	0.996615i	$0.473800\pi$
$830$		−	65.3826i		−	2.26946i
$831$	−5.86311			−0.203389
$832$	28.2435			0.979168
$833$	−104.642			−3.62564
$834$	−48.4346			−1.67715
$835$			27.0867i			0.937374i
$836$	−44.2472			−1.53032
$837$	−7.31062			−0.252692
$838$		−	80.5880i		−	2.78387i
$839$			26.2758i			0.907141i	0.891220	+	0.453571i	$0.149850\pi$
$839$			26.2758i			0.907141i	−0.891220	+	0.453571i	$0.850150\pi$
$840$		−	85.9117i		−	2.96424i
$841$	26.3399			0.908272
$842$	58.5051			2.01622
$843$	18.6946			0.643877
$844$			77.3688i			2.66314i
$845$		−	22.0663i		−	0.759105i
$846$		−	16.5469i		−	0.568894i
$847$		−	45.6244i		−	1.56767i
$848$			80.2487i			2.75575i
$849$	−8.00372			−0.274687
$850$		−	24.8044i		−	0.850782i
$851$			18.3343i			0.628490i
$852$	17.2576			0.591236
$853$	−39.2737			−1.34471			−0.672353	−	0.740231i	$-0.734716\pi$
$853$	−39.2737			−1.34471			−0.672353	+	0.740231i	$0.734716\pi$
$854$		−	145.860i		−	4.99124i
$855$		−	10.9616i		−	0.374878i
$856$	7.30498			0.249679
$857$		−	51.0234i		−	1.74293i	−0.490460	−	0.871463i	$-0.663171\pi$
$857$		−	51.0234i		−	1.74293i	0.490460	−	0.871463i	$-0.336829\pi$
$858$		−	3.87293i		−	0.132220i
$859$			1.26561i			0.0431821i	0.999767	+	0.0215911i	$0.00687318\pi$
$859$			1.26561i			0.0431821i	−0.999767	+	0.0215911i	$0.993127\pi$
$860$	−12.9076			−0.440145
$861$	−35.0407			−1.19418
$862$			34.5884i			1.17808i
$863$			10.7422i			0.365670i	0.983144	+	0.182835i	$0.0585274\pi$
$863$			10.7422i			0.365670i	−0.983144	+	0.182835i	$0.941473\pi$
$864$		−	20.6512i		−	0.702570i
$865$			26.1386i			0.888738i
$866$	1.40096			0.0476067
$867$	16.1603			0.548833
$868$			198.222i			6.72809i
$869$			9.82447i			0.333272i
$870$			8.20382i			0.278136i
$871$	−12.5655			−0.425767
$872$			89.4948i			3.03068i
$873$		−	13.9316i		−	0.471512i
$874$	−46.6513			−1.57801
$875$	−61.0525			−2.06395
$876$		−	27.5824i		−	0.931925i
$877$			5.92577i			0.200099i	0.994982	+	0.100049i	$0.0319001\pi$
$877$			5.92577i			0.200099i	−0.994982	+	0.100049i	$0.968100\pi$
$878$	−73.9519			−2.49575
$879$		−	11.9902i		−	0.404420i
$880$		−	36.7469i		−	1.23874i
$881$		−	30.5956i		−	1.03079i	−0.856952	−	0.515396i	$-0.827645\pi$
$881$		−	30.5956i		−	1.03079i	0.856952	−	0.515396i	$-0.172355\pi$
$882$			49.4471i			1.66497i
$883$		−	5.00928i		−	0.168576i	−0.996441	−	0.0842878i	$-0.973138\pi$
$883$		−	5.00928i		−	0.168576i	0.996441	−	0.0842878i	$-0.0268615\pi$
$884$	32.0813			1.07901
$885$	6.31831			0.212388
$886$	45.7783			1.53795
$887$			38.2443i			1.28412i	0.766655	+	0.642059i	$0.221920\pi$
$887$			38.2443i			1.28412i	−0.766655	+	0.642059i	$0.778080\pi$
$888$			58.7439i			1.97131i
$889$		−	66.5387i		−	2.23164i
$890$	−12.6885			−0.425320
$891$	−1.38069			−0.0462548
$892$			48.3090i			1.61750i
$893$	−36.0598			−1.20670
$894$	16.7631			0.560641
$895$	−19.1612			−0.640487
$896$	−166.818			−5.57300
$897$		−	2.98040i		−	0.0995125i
$898$	−23.0535			−0.769304
$899$		−	11.9235i		−	0.397672i
$900$	−8.55493			−0.285164
$901$			32.0957i			1.06926i
$902$	−26.2394			−0.873677
$903$	6.48243			0.215722
$904$			58.5429i			1.94711i
$905$	16.0471			0.533422
$906$	32.0991			1.06642
$907$	11.0729			0.367668			0.183834	−	0.982957i	$-0.441149\pi$
$907$	11.0729			0.367668			0.183834	+	0.982957i	$0.441149\pi$
$908$			7.78665i			0.258409i
$909$	19.3012			0.640179
$910$		−	26.0151i		−	0.862391i
$911$	−25.3441			−0.839687			−0.419844	−	0.907596i	$-0.637915\pi$
$911$	−25.3441			−0.839687			−0.419844	+	0.907596i	$0.637915\pi$
$912$	−85.3789			−2.82718
$913$			17.9470i			0.593960i
$914$		−	24.9968i		−	0.826821i
$915$	19.7498			0.652907
$916$		−	71.1893i		−	2.35216i
$917$	−47.2476			−1.56025
$918$		−	15.6694i		−	0.517166i
$919$			5.21683i			0.172087i	0.996291	+	0.0860437i	$0.0274225\pi$
$919$			5.21683i			0.172087i	−0.996291	+	0.0860437i	$0.972578\pi$
$920$		−	49.5071i		−	1.63220i
$921$		−	0.116307i		−	0.00383243i
$922$		−	47.0203i		−	1.54853i
$923$	3.29186			0.108353
$924$			37.4364i			1.23157i
$925$	10.0385			0.330063
$926$	20.1976			0.663735
$927$			18.7066i			0.614404i
$928$	33.6819			1.10566
$929$	−22.6369			−0.742692			−0.371346	−	0.928495i	$-0.621104\pi$
$929$	−22.6369			−0.742692			−0.371346	+	0.928495i	$0.621104\pi$
$930$	−36.7722			−1.20581
$931$	107.758			3.53161
$932$	86.8542			2.84500
$933$	1.55267			0.0508320
$934$		−	82.0388i		−	2.68439i
$935$		−	14.6970i		−	0.480644i
$936$		−	9.54934i		−	0.312130i
$937$		−	25.5423i		−	0.834429i	−0.908808	−	0.417215i	$-0.863006\pi$
$937$		−	25.5423i		−	0.834429i	0.908808	−	0.417215i	$-0.136994\pi$
$938$	166.410			5.43347
$939$	10.3868			0.338961
$940$		−	60.7489i		−	1.98141i
$941$	−6.64743			−0.216700			−0.108350	−	0.994113i	$-0.534557\pi$
$941$	−6.64743			−0.216700			−0.108350	+	0.994113i	$0.534557\pi$
$942$	13.3749	−	31.3622i	0.435779	−	1.02184i
$943$	−20.1924			−0.657555
$944$		−	49.2129i		−	1.60174i
$945$	−9.27429			−0.301693
$946$	4.85422			0.157824
$947$			44.0485i			1.43139i	0.698415	+	0.715693i	$0.253889\pi$
$947$			44.0485i			1.43139i	−0.698415	+	0.715693i	$0.746111\pi$
$948$			38.4550i			1.24896i
$949$		−	5.26131i		−	0.170789i
$950$			25.5428i			0.828717i
$951$	−9.75427			−0.316304
$952$	−267.632			−8.67401
$953$	26.2698			0.850964			0.425482	−	0.904967i	$-0.360105\pi$
$953$	26.2698			0.850964			0.425482	+	0.904967i	$0.360105\pi$
$954$	15.1663			0.491027
$955$	38.0966			1.23278
$956$	−119.047			−3.85025
$957$		−	2.25189i		−	0.0727932i
$958$	−0.839898			−0.0271359
$959$	−1.06805			−0.0344893
$960$		−	50.6455i		−	1.63458i
$961$	22.4451			0.724037
$962$			17.7883i			0.573518i
$963$		−	0.788583i		−	0.0254117i
$964$		−	29.1961i		−	0.940342i
$965$		−	29.5175i		−	0.950201i
$966$			39.4704i			1.26994i
$967$	−53.5552			−1.72222			−0.861110	−	0.508418i	$-0.830230\pi$
$967$	−53.5552			−1.72222			−0.861110	+	0.508418i	$0.830230\pi$
$968$		−	84.2388i		−	2.70754i
$969$	−34.1475			−1.09698
$970$		−	70.0755i		−	2.24999i
$971$			8.74815i			0.280741i	0.990099	+	0.140371i	$0.0448294\pi$
$971$			8.74815i			0.280741i	−0.990099	+	0.140371i	$0.955171\pi$
$972$	−5.40431			−0.173343
$973$	89.3039			2.86295
$974$		−	94.6150i		−	3.03166i
$975$	−1.63184			−0.0522608
$976$		−	153.829i		−	4.92396i
$977$	29.6738			0.949349			0.474674	−	0.880162i	$-0.342566\pi$
$977$	29.6738			0.949349			0.474674	+	0.880162i	$0.342566\pi$
$978$	24.6423			0.787973
$979$	3.48290			0.111314
$980$			181.536i			5.79894i
$981$	9.66109			0.308455
$982$	23.7540			0.758021
$983$			44.6089i			1.42280i	0.702785	+	0.711402i	$0.251939\pi$
$983$			44.6089i			1.42280i	−0.702785	+	0.711402i	$0.748061\pi$
$984$	−64.6975			−2.06248
$985$			24.9182i			0.793961i
$986$	25.5565			0.813886
$987$			30.5092i			0.971120i
$988$	−33.0363			−1.05103
$989$	3.73554			0.118783
$990$	−6.94484			−0.220721
$991$	29.0031			0.921314			0.460657	−	0.887578i	$-0.347614\pi$
$991$	29.0031			0.921314			0.460657	+	0.887578i	$0.347614\pi$
$992$			150.973i			4.79341i
$993$	−14.9741			−0.475189
$994$	−43.5953			−1.38276
$995$			3.87378i			0.122807i
$996$			70.2484i			2.22591i
$997$		−	36.4178i		−	1.15336i	−0.816969	−	0.576681i	$-0.804347\pi$
$997$		−	36.4178i		−	1.15336i	0.816969	−	0.576681i	$-0.195653\pi$
$998$	70.9662			2.24640
$999$	6.34148			0.200636

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.b.b.313.1	✓	14
3.2	odd	2		1413.2.b.e.784.14		14
157.156	even	2	inner	471.2.b.b.313.14	yes	14
471.470	odd	2		1413.2.b.e.784.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.b.b.313.1	✓	14	1.1	even	1	trivial
471.2.b.b.313.14	yes	14	157.156	even	2	inner
1413.2.b.e.784.1		14	471.470	odd	2
1413.2.b.e.784.14		14	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.72109i q^{2} +1.00000 q^{3} -5.40431 q^{4} +1.84852i q^{5} -2.72109i q^{6} +5.01715i q^{7} +9.26343i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.72109i q^{2} +1.00000 q^{3} -5.40431 q^{4} +1.84852i q^{5} -2.72109i q^{6} +5.01715i q^{7} +9.26343i q^{8} +1.00000 q^{9} +5.02998 q^{10} -1.38069 q^{11} -5.40431 q^{12} -1.03086 q^{13} +13.6521 q^{14} +1.84852i q^{15} +14.3980 q^{16} +5.75850 q^{17} -2.72109i q^{18} -5.92993 q^{19} -9.98996i q^{20} +5.01715i q^{21} +3.75698i q^{22} +2.89116i q^{23} +9.26343i q^{24} +1.58298 q^{25} +2.80507i q^{26} +1.00000 q^{27} -27.1142i q^{28} +1.63099i q^{29} +5.02998 q^{30} -7.31062 q^{31} -20.6512i q^{32} -1.38069 q^{33} -15.6694i q^{34} -9.27429 q^{35} -5.40431 q^{36} +6.34148 q^{37} +16.1358i q^{38} -1.03086 q^{39} -17.1236 q^{40} +6.98418i q^{41} +13.6521 q^{42} -1.29205i q^{43} +7.46168 q^{44} +1.84852i q^{45} +7.86710 q^{46} +6.08099 q^{47} +14.3980 q^{48} -18.1718 q^{49} -4.30743i q^{50} +5.75850 q^{51} +5.57111 q^{52} +5.57361i q^{53} -2.72109i q^{54} -2.55223i q^{55} -46.4760 q^{56} -5.92993 q^{57} +4.43806 q^{58} -3.41804i q^{59} -9.98996i q^{60} -10.6841i q^{61} +19.8928i q^{62} +5.01715i q^{63} -27.3979 q^{64} -1.90557i q^{65} +3.75698i q^{66} +12.1893 q^{67} -31.1207 q^{68} +2.89116i q^{69} +25.2361i q^{70} -3.19330 q^{71} +9.26343i q^{72} +5.10379i q^{73} -17.2557i q^{74} +1.58298 q^{75} +32.0472 q^{76} -6.92713i q^{77} +2.80507i q^{78} -7.11562i q^{79} +26.6149i q^{80} +1.00000 q^{81} +19.0046 q^{82} -12.9986i q^{83} -27.1142i q^{84} +10.6447i q^{85} -3.51579 q^{86} +1.63099i q^{87} -12.7899i q^{88} -2.52258 q^{89} +5.02998 q^{90} -5.17200i q^{91} -15.6247i q^{92} -7.31062 q^{93} -16.5469i q^{94} -10.9616i q^{95} -20.6512i q^{96} -13.9316i q^{97} +49.4471i q^{98} -1.38069 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{3} - 20 q^{4} + 14 q^{9}+O(q^{10}) \) 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

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