LMFDB - Embedded newform 471.2.b.a.313.10

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 15x^{10} + 77x^{8} + 158x^{6} + 111x^{4} + 21x^{2} + 1 $ x^12 + 15x^10 + 77x^8 + 158x^6 + 111x^4 + 21*x^2 + 1
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			313.10
Root			$1.76113i$ of defining polynomial
Character	$\chi$	$=$	471.313
Dual form			471.2.b.a.313.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.76113i q^{2} -1.00000 q^{3} -1.10159 q^{4} -1.19332i q^{5} -1.76113i q^{6} -3.36519i q^{7} +1.58223i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.76113i q^{2} -1.00000 q^{3} -1.10159 q^{4} -1.19332i q^{5} -1.76113i q^{6} -3.36519i q^{7} +1.58223i q^{8} +1.00000 q^{9} +2.10159 q^{10} -3.41368 q^{11} +1.10159 q^{12} +5.92654 q^{13} +5.92654 q^{14} +1.19332i q^{15} -4.98968 q^{16} +5.32449 q^{17} +1.76113i q^{18} +6.59173 q^{19} +1.31454i q^{20} +3.36519i q^{21} -6.01194i q^{22} -5.36122i q^{23} -1.58223i q^{24} +3.57600 q^{25} +10.4374i q^{26} -1.00000 q^{27} +3.70704i q^{28} +4.69962i q^{29} -2.10159 q^{30} -1.97395 q^{31} -5.62303i q^{32} +3.41368 q^{33} +9.37713i q^{34} -4.01573 q^{35} -1.10159 q^{36} -4.07887 q^{37} +11.6089i q^{38} -5.92654 q^{39} +1.88810 q^{40} -3.22214i q^{41} -5.92654 q^{42} -2.11055i q^{43} +3.76046 q^{44} -1.19332i q^{45} +9.44181 q^{46} -1.55088 q^{47} +4.98968 q^{48} -4.32449 q^{49} +6.29781i q^{50} -5.32449 q^{51} -6.52859 q^{52} +9.86204i q^{53} -1.76113i q^{54} +4.07360i q^{55} +5.32449 q^{56} -6.59173 q^{57} -8.27665 q^{58} -3.30751i q^{59} -1.31454i q^{60} -8.66872i q^{61} -3.47639i q^{62} -3.36519i q^{63} -0.0764624 q^{64} -7.07223i q^{65} +6.01194i q^{66} -6.28647 q^{67} -5.86538 q^{68} +5.36122i q^{69} -7.07223i q^{70} +12.3940 q^{71} +1.58223i q^{72} -6.38852i q^{73} -7.18343i q^{74} -3.57600 q^{75} -7.26135 q^{76} +11.4877i q^{77} -10.4374i q^{78} -13.2981i q^{79} +5.95426i q^{80} +1.00000 q^{81} +5.67461 q^{82} +4.86229i q^{83} -3.70704i q^{84} -6.35380i q^{85} +3.71696 q^{86} -4.69962i q^{87} -5.40122i q^{88} -9.74816 q^{89} +2.10159 q^{90} -19.9439i q^{91} +5.90584i q^{92} +1.97395 q^{93} -2.73130i q^{94} -7.86601i q^{95} +5.62303i q^{96} +9.09824i q^{97} -7.61600i q^{98} -3.41368 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{3} - 6 q^{4} + 12 q^{9}+O(q^{10}) $ 12 * q - 12 * q^3 - 6 * q^4 + 12 * q^9	$ 12 q - 12 q^{3} - 6 q^{4} + 12 q^{9} + 18 q^{10} - 2 q^{11} + 6 q^{12} + 4 q^{13} + 4 q^{14} + 10 q^{16} + 2 q^{17} + 4 q^{19} + 12 q^{25} - 12 q^{27} - 18 q^{30} + 2 q^{31} + 2 q^{33} - 4 q^{35} - 6 q^{36} - 2 q^{37} - 4 q^{39} - 40 q^{40} - 4 q^{42} - 36 q^{44} + 34 q^{47} - 10 q^{48} + 10 q^{49} - 2 q^{51} - 6 q^{52} + 2 q^{56} - 4 q^{57} + 24 q^{58} + 28 q^{64} - 38 q^{67} + 32 q^{68} - 26 q^{71} - 12 q^{75} - 28 q^{76} + 12 q^{81} - 50 q^{82} + 6 q^{86} - 4 q^{89} + 18 q^{90} - 2 q^{93} - 2 q^{99}+O(q^{100}) $ 12 * q - 12 * q^3 - 6 * q^4 + 12 * q^9 + 18 * q^10 - 2 * q^11 + 6 * q^12 + 4 * q^13 + 4 * q^14 + 10 * q^16 + 2 * q^17 + 4 * q^19 + 12 * q^25 - 12 * q^27 - 18 * q^30 + 2 * q^31 + 2 * q^33 - 4 * q^35 - 6 * q^36 - 2 * q^37 - 4 * q^39 - 40 * q^40 - 4 * q^42 - 36 * q^44 + 34 * q^47 - 10 * q^48 + 10 * q^49 - 2 * q^51 - 6 * q^52 + 2 * q^56 - 4 * q^57 + 24 * q^58 + 28 * q^64 - 38 * q^67 + 32 * q^68 - 26 * q^71 - 12 * q^75 - 28 * q^76 + 12 * q^81 - 50 * q^82 + 6 * q^86 - 4 * q^89 + 18 * q^90 - 2 * 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 $

$2$			1.76113i			1.24531i	0.782497	+	0.622654i	$0.213946\pi$
$2$			1.76113i			1.24531i	−0.782497	+	0.622654i	$0.786054\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.10159			−0.550793
$5$		−	1.19332i		−	0.533667i	−0.963743	−	0.266833i	$-0.914023\pi$
$5$		−	1.19332i		−	0.533667i	0.963743	−	0.266833i	$-0.0859773\pi$
$6$		−	1.76113i		−	0.718979i
$7$		−	3.36519i		−	1.27192i	−0.771721	−	0.635961i	$-0.780604\pi$
$7$		−	3.36519i		−	1.27192i	0.771721	−	0.635961i	$-0.219396\pi$
$8$			1.58223i			0.559402i
$9$	1.00000			0.333333
$10$	2.10159			0.664580
$11$	−3.41368			−1.02926			−0.514632	−	0.857411i	$-0.672071\pi$
$11$	−3.41368			−1.02926			−0.514632	+	0.857411i	$0.672071\pi$
$12$	1.10159			0.318000
$13$	5.92654			1.64373			0.821863	−	0.569685i	$-0.192935\pi$
$13$	5.92654			1.64373			0.821863	+	0.569685i	$0.192935\pi$
$14$	5.92654			1.58393
$15$			1.19332i			0.308113i
$16$	−4.98968			−1.24742
$17$	5.32449			1.29138			0.645689	−	0.763600i	$-0.276570\pi$
$17$	5.32449			1.29138			0.645689	+	0.763600i	$0.276570\pi$
$18$			1.76113i			0.415103i
$19$	6.59173			1.51225			0.756123	−	0.654429i	$-0.227091\pi$
$19$	6.59173			1.51225			0.756123	+	0.654429i	$0.227091\pi$
$20$			1.31454i			0.293940i
$21$			3.36519i			0.734344i
$22$		−	6.01194i		−	1.28175i
$23$		−	5.36122i		−	1.11789i	−0.829205	−	0.558945i	$-0.811206\pi$
$23$		−	5.36122i		−	1.11789i	0.829205	−	0.558945i	$-0.188794\pi$
$24$		−	1.58223i		−	0.322971i
$25$	3.57600			0.715200
$26$			10.4374i			2.04695i
$27$	−1.00000			−0.192450
$28$			3.70704i			0.700565i
$29$			4.69962i			0.872698i	0.899778	+	0.436349i	$0.143729\pi$
$29$			4.69962i			0.872698i	−0.899778	+	0.436349i	$0.856271\pi$
$30$	−2.10159			−0.383695
$31$	−1.97395			−0.354532			−0.177266	−	0.984163i	$-0.556725\pi$
$31$	−1.97395			−0.354532			−0.177266	+	0.984163i	$0.556725\pi$
$32$		−	5.62303i		−	0.994021i
$33$	3.41368			0.594246
$34$			9.37713i			1.60816i
$35$	−4.01573			−0.678782
$36$	−1.10159			−0.183598
$37$	−4.07887			−0.670562			−0.335281	−	0.942118i	$-0.608831\pi$
$37$	−4.07887			−0.670562			−0.335281	+	0.942118i	$0.608831\pi$
$38$			11.6089i			1.88321i
$39$	−5.92654			−0.949006
$40$	1.88810			0.298534
$41$		−	3.22214i		−	0.503213i	−0.967830	−	0.251607i	$-0.919041\pi$
$41$		−	3.22214i		−	0.503213i	0.967830	−	0.251607i	$-0.0809589\pi$
$42$	−5.92654			−0.914485
$43$		−	2.11055i		−	0.321856i	−0.986966	−	0.160928i	$-0.948551\pi$
$43$		−	2.11055i		−	0.321856i	0.986966	−	0.160928i	$-0.0514487\pi$
$44$	3.76046			0.566911
$45$		−	1.19332i		−	0.177889i
$46$	9.44181			1.39212
$47$	−1.55088			−0.226219			−0.113109	−	0.993583i	$-0.536081\pi$
$47$	−1.55088			−0.226219			−0.113109	+	0.993583i	$0.536081\pi$
$48$	4.98968			0.720198
$49$	−4.32449			−0.617784
$50$			6.29781i			0.890644i
$51$	−5.32449			−0.745578
$52$	−6.52859			−0.905352
$53$			9.86204i			1.35465i	0.735682	+	0.677327i	$0.236862\pi$
$53$			9.86204i			1.35465i	−0.735682	+	0.677327i	$0.763138\pi$
$54$		−	1.76113i		−	0.239660i
$55$			4.07360i			0.549284i
$56$	5.32449			0.711515
$57$	−6.59173			−0.873096
$58$	−8.27665			−1.08678
$59$		−	3.30751i		−	0.430601i	−0.976548	−	0.215300i	$-0.930927\pi$
$59$		−	3.30751i		−	0.430601i	0.976548	−	0.215300i	$-0.0690730\pi$
$60$		−	1.31454i		−	0.169706i
$61$		−	8.66872i		−	1.10992i	−0.831878	−	0.554958i	$-0.812734\pi$
$61$		−	8.66872i		−	1.10992i	0.831878	−	0.554958i	$-0.187266\pi$
$62$		−	3.47639i		−	0.441502i
$63$		−	3.36519i		−	0.423974i
$64$	−0.0764624			−0.00955780
$65$		−	7.07223i		−	0.877202i
$66$			6.01194i			0.740019i
$67$	−6.28647			−0.768015			−0.384007	−	0.923330i	$-0.625456\pi$
$67$	−6.28647			−0.768015			−0.384007	+	0.923330i	$0.625456\pi$
$68$	−5.86538			−0.711282
$69$			5.36122i			0.645414i
$70$		−	7.07223i		−	0.845293i
$71$	12.3940			1.47089			0.735447	−	0.677583i	$-0.236972\pi$
$71$	12.3940			1.47089			0.735447	+	0.677583i	$0.236972\pi$
$72$			1.58223i			0.186467i
$73$		−	6.38852i		−	0.747720i	−0.927485	−	0.373860i	$-0.878034\pi$
$73$		−	6.38852i		−	0.747720i	0.927485	−	0.373860i	$-0.121966\pi$
$74$		−	7.18343i		−	0.835057i
$75$	−3.57600			−0.412921
$76$	−7.26135			−0.832934
$77$			11.4877i			1.30914i
$78$		−	10.4374i		−	1.18180i
$79$		−	13.2981i		−	1.49615i	−0.663613	−	0.748076i	$-0.730978\pi$
$79$		−	13.2981i		−	1.49615i	0.663613	−	0.748076i	$-0.269022\pi$
$80$			5.95426i			0.665707i
$81$	1.00000			0.111111
$82$	5.67461			0.626655
$83$			4.86229i			0.533705i	0.963737	+	0.266853i	$0.0859837\pi$
$83$			4.86229i			0.533705i	−0.963737	+	0.266853i	$0.914016\pi$
$84$		−	3.70704i		−	0.404471i
$85$		−	6.35380i		−	0.689166i
$86$	3.71696			0.400810
$87$		−	4.69962i		−	0.503852i
$88$		−	5.40122i		−	0.575772i
$89$	−9.74816			−1.03330			−0.516651	−	0.856196i	$-0.672822\pi$
$89$	−9.74816			−1.03330			−0.516651	+	0.856196i	$0.672822\pi$
$90$	2.10159			0.221527
$91$		−	19.9439i		−	2.09069i
$92$			5.90584i			0.615726i
$93$	1.97395			0.204689
$94$		−	2.73130i		−	0.281712i
$95$		−	7.86601i		−	0.807036i
$96$			5.62303i			0.573898i
$97$			9.09824i			0.923786i	0.886936	+	0.461893i	$0.152830\pi$
$97$			9.09824i			0.923786i	−0.886936	+	0.461893i	$0.847170\pi$
$98$		−	7.61600i		−	0.769332i
$99$	−3.41368			−0.343088
$100$	−3.93927			−0.393927
$101$	9.94227			0.989293			0.494646	−	0.869094i	$-0.335298\pi$
$101$	9.94227			0.989293			0.494646	+	0.869094i	$0.335298\pi$
$102$		−	9.37713i		−	0.928474i
$103$			18.0041i			1.77400i	0.461769	+	0.887000i	$0.347215\pi$
$103$			18.0041i			1.77400i	−0.461769	+	0.887000i	$0.652785\pi$
$104$			9.37713i			0.919503i
$105$	4.01573			0.391895
$106$	−17.3683			−1.68696
$107$			16.5983i			1.60462i	0.596906	+	0.802311i	$0.296397\pi$
$107$			16.5983i			1.60462i	−0.596906	+	0.802311i	$0.703603\pi$
$108$	1.10159			0.106000
$109$	7.55371			0.723514			0.361757	−	0.932272i	$-0.382177\pi$
$109$	7.55371			0.723514			0.361757	+	0.932272i	$0.382177\pi$
$110$	−7.17414			−0.684028
$111$	4.07887			0.387149
$112$			16.7912i			1.58662i
$113$	−16.2287			−1.52667			−0.763336	−	0.646002i	$-0.776440\pi$
$113$	−16.2287			−1.52667			−0.763336	+	0.646002i	$0.776440\pi$
$114$		−	11.6089i		−	1.08727i
$115$	−6.39762			−0.596581
$116$		−	5.17703i		−	0.480676i
$117$	5.92654			0.547909
$118$	5.82495			0.536231
$119$		−	17.9179i		−	1.64253i
$120$	−1.88810			−0.172359
$121$	0.653221			0.0593837
$122$	15.2668			1.38219
$123$			3.22214i			0.290530i
$124$	2.17447			0.195274
$125$		−	10.2339i		−	0.915345i
$126$	5.92654			0.527978
$127$	−2.99061			−0.265373			−0.132687	−	0.991158i	$-0.542360\pi$
$127$	−2.99061			−0.265373			−0.132687	+	0.991158i	$0.542360\pi$
$128$		−	11.3807i		−	1.00592i
$129$			2.11055i			0.185824i
$130$	12.4551			1.09239
$131$		−	14.0014i		−	1.22331i	−0.791125	−	0.611654i	$-0.790504\pi$
$131$		−	14.0014i		−	1.22331i	0.791125	−	0.611654i	$-0.209496\pi$
$132$	−3.76046			−0.327306
$133$		−	22.1824i		−	1.92346i
$134$		−	11.0713i		−	0.956415i
$135$			1.19332i			0.102704i
$136$			8.42455i			0.722400i
$137$			8.72640i			0.745547i	0.927922	+	0.372773i	$0.121593\pi$
$137$			8.72640i			0.745547i	−0.927922	+	0.372773i	$0.878407\pi$
$138$	−9.44181			−0.803740
$139$			6.32211i			0.536234i	0.963386	+	0.268117i	$0.0864014\pi$
$139$			6.32211i			0.536234i	−0.963386	+	0.268117i	$0.913599\pi$
$140$	4.42367			0.373868
$141$	1.55088			0.130607
$142$			21.8274i			1.83172i
$143$	−20.2313			−1.69183
$144$	−4.98968			−0.415807
$145$	5.60813			0.465730
$146$	11.2510			0.931142
$147$	4.32449			0.356678
$148$	4.49322			0.369341
$149$		−	18.9631i		−	1.55352i	−0.629799	−	0.776758i	$-0.716863\pi$
$149$		−	18.9631i		−	1.55352i	0.629799	−	0.776758i	$-0.283137\pi$
$150$		−	6.29781i		−	0.514214i
$151$			7.32954i			0.596469i	0.954493	+	0.298235i	$0.0963978\pi$
$151$			7.32954i			0.596469i	−0.954493	+	0.298235i	$0.903602\pi$
$152$			10.4296i			0.845953i
$153$	5.32449			0.430460
$154$	−20.2313			−1.63029
$155$			2.35555i			0.189202i
$156$	6.52859			0.522705
$157$	−8.83735	+	8.88264i	−0.705297	+	0.708912i
$157$	−8.83735	+	8.88264i	−0.705297	+	0.708912i
$158$	23.4197			1.86317
$159$		−	9.86204i		−	0.782110i
$160$	−6.71005			−0.530476
$161$	−18.0415			−1.42187
$162$			1.76113i			0.138368i
$163$		−	1.56480i		−	0.122565i	−0.998120	−	0.0612825i	$-0.980481\pi$
$163$		−	1.56480i		−	0.122565i	0.998120	−	0.0612825i	$-0.0195190\pi$
$164$			3.54946i			0.277166i
$165$		−	4.07360i		−	0.317129i
$166$	−8.56313			−0.664628
$167$	10.0835			0.780285			0.390142	−	0.920755i	$-0.372426\pi$
$167$	10.0835			0.780285			0.390142	+	0.920755i	$0.372426\pi$
$168$	−5.32449			−0.410793
$169$	22.1239			1.70184
$170$	11.1899			0.858224
$171$	6.59173			0.504082
$172$			2.32495i			0.177276i
$173$	−21.8763			−1.66322			−0.831611	−	0.555358i	$-0.812581\pi$
$173$	−21.8763			−1.66322			−0.831611	+	0.555358i	$0.812581\pi$
$174$	8.27665			0.627452
$175$		−	12.0339i		−	0.909678i
$176$	17.0332			1.28392
$177$			3.30751i			0.248607i
$178$		−	17.1678i		−	1.28678i
$179$			9.09296i			0.679640i	0.940491	+	0.339820i	$0.110366\pi$
$179$			9.09296i			0.679640i	−0.940491	+	0.339820i	$0.889634\pi$
$180$			1.31454i			0.0979799i
$181$			23.5230i			1.74845i	0.485519	+	0.874226i	$0.338631\pi$
$181$			23.5230i			1.74845i	−0.485519	+	0.874226i	$0.661369\pi$
$182$	35.1239			2.60355
$183$			8.66872i			0.640810i
$184$	8.48266			0.625350
$185$			4.86738i			0.357857i
$186$			3.47639i			0.254901i
$187$	−18.1761			−1.32917
$188$	1.70842			0.124600
$189$			3.36519i			0.244781i
$190$	13.8531			1.00501
$191$		−	13.0147i		−	0.941714i	−0.882210	−	0.470857i	$-0.843945\pi$
$191$		−	13.0147i		−	0.941714i	0.882210	−	0.470857i	$-0.156055\pi$
$192$	0.0764624			0.00551820
$193$	0.279011			0.0200837			0.0100418	−	0.999950i	$-0.496804\pi$
$193$	0.279011			0.0200837			0.0100418	+	0.999950i	$0.496804\pi$
$194$	−16.0232			−1.15040
$195$			7.07223i			0.506453i
$196$	4.76380			0.340271
$197$	−3.80272			−0.270932			−0.135466	−	0.990782i	$-0.543253\pi$
$197$	−3.80272			−0.270932			−0.135466	+	0.990782i	$0.543253\pi$
$198$		−	6.01194i		−	0.427250i
$199$	−22.6962			−1.60889			−0.804444	−	0.594028i	$-0.797537\pi$
$199$	−22.6962			−1.60889			−0.804444	+	0.594028i	$0.797537\pi$
$200$			5.65804i			0.400084i
$201$	6.28647			0.443414
$202$			17.5096i			1.23197i
$203$	15.8151			1.11000
$204$	5.86538			0.410659
$205$	−3.84502			−0.268548
$206$	−31.7077			−2.20918
$207$		−	5.36122i		−	0.372630i
$208$	−29.5715			−2.05042
$209$	−22.5021			−1.55650
$210$			7.07223i			0.488030i
$211$			26.1698i			1.80160i	0.434232	+	0.900801i	$0.357020\pi$
$211$			26.1698i			1.80160i	−0.434232	+	0.900801i	$0.642980\pi$
$212$		−	10.8639i		−	0.746134i
$213$	−12.3940			−0.849221
$214$	−29.2319			−1.99825
$215$	−2.51855			−0.171764
$216$		−	1.58223i		−	0.107657i
$217$			6.64272i			0.450937i
$218$			13.3031i			0.900998i
$219$			6.38852i			0.431696i
$220$		−	4.48741i		−	0.302541i
$221$	31.5558			2.12267
$222$			7.18343i			0.482120i
$223$		−	7.44577i		−	0.498606i	−0.968426	−	0.249303i	$-0.919799\pi$
$223$		−	7.44577i		−	0.498606i	0.968426	−	0.249303i	$-0.0802015\pi$
$224$	−18.9226			−1.26432
$225$	3.57600			0.238400
$226$		−	28.5810i		−	1.90118i
$227$			5.27694i			0.350243i	0.984547	+	0.175121i	$0.0560318\pi$
$227$			5.27694i			0.350243i	−0.984547	+	0.175121i	$0.943968\pi$
$228$	7.26135			0.480895
$229$		−	2.44238i		−	0.161397i	−0.996739	−	0.0806985i	$-0.974285\pi$
$229$		−	2.44238i		−	0.161397i	0.996739	−	0.0806985i	$-0.0257151\pi$
$230$		−	11.2671i		−	0.742927i
$231$		−	11.4877i		−	0.755834i
$232$	−7.43587			−0.488189
$233$	5.52606			0.362024			0.181012	−	0.983481i	$-0.442063\pi$
$233$	5.52606			0.362024			0.181012	+	0.983481i	$0.442063\pi$
$234$			10.4374i			0.682315i
$235$			1.85068i			0.120725i
$236$			3.64350i			0.237172i
$237$			13.2981i			0.863804i
$238$	31.5558			2.04546
$239$	−18.5229			−1.19815			−0.599073	−	0.800694i	$-0.704464\pi$
$239$	−18.5229			−1.19815			−0.599073	+	0.800694i	$0.704464\pi$
$240$		−	5.95426i		−	0.384346i
$241$			24.5719i			1.58281i	0.611291	+	0.791406i	$0.290651\pi$
$241$			24.5719i			1.58281i	−0.611291	+	0.791406i	$0.709349\pi$
$242$			1.15041i			0.0739510i
$243$	−1.00000			−0.0641500
$244$			9.54933i			0.611334i
$245$			5.16048i			0.329691i
$246$	−5.67461			−0.361800
$247$	39.0661			2.48572
$248$		−	3.12324i		−	0.198326i
$249$		−	4.86229i		−	0.308135i
$250$	18.0232			1.13989
$251$		−	5.09471i		−	0.321575i	−0.986989	−	0.160788i	$-0.948597\pi$
$251$		−	5.09471i		−	0.321575i	0.986989	−	0.160788i	$-0.0514034\pi$
$252$			3.70704i			0.233522i
$253$			18.3015i			1.15060i
$254$		−	5.26685i		−	0.330472i
$255$			6.35380i			0.397890i
$256$	19.8900			1.24313
$257$	−5.74473			−0.358346			−0.179173	−	0.983818i	$-0.557342\pi$
$257$	−5.74473			−0.358346			−0.179173	+	0.983818i	$0.557342\pi$
$258$	−3.71696			−0.231408
$259$			13.7262i			0.852902i
$260$			7.79066i			0.483156i
$261$			4.69962i			0.290899i
$262$	24.6583			1.52340
$263$	−16.3700			−1.00942			−0.504708	−	0.863290i	$-0.668400\pi$
$263$	−16.3700			−1.00942			−0.504708	+	0.863290i	$0.668400\pi$
$264$			5.40122i			0.332422i
$265$	11.7685			0.722934
$266$	39.0661			2.39530
$267$	9.74816			0.596578
$268$	6.92509			0.423017
$269$			17.8594i			1.08890i	0.838792	+	0.544452i	$0.183262\pi$
$269$			17.8594i			1.08890i	−0.838792	+	0.544452i	$0.816738\pi$
$270$	−2.10159			−0.127898
$271$			5.64539i			0.342933i	0.985190	+	0.171466i	$0.0548505\pi$
$271$			5.64539i			0.342933i	−0.985190	+	0.171466i	$0.945150\pi$
$272$	−26.5675			−1.61089
$273$			19.9439i			1.20706i
$274$	−15.3683			−0.928436
$275$	−12.2073			−0.736129
$276$		−	5.90584i		−	0.355489i
$277$	28.6867			1.72361			0.861807	−	0.507236i	$-0.169333\pi$
$277$	28.6867			1.72361			0.861807	+	0.507236i	$0.169333\pi$
$278$	−11.1341			−0.667777
$279$	−1.97395			−0.118177
$280$		−	6.35380i		−	0.379712i
$281$	6.26586			0.373790			0.186895	−	0.982380i	$-0.440158\pi$
$281$	6.26586			0.373790			0.186895	+	0.982380i	$0.440158\pi$
$282$			2.73130i			0.162646i
$283$	5.20019			0.309119			0.154560	−	0.987983i	$-0.450604\pi$
$283$	5.20019			0.309119			0.154560	+	0.987983i	$0.450604\pi$
$284$	−13.6530			−0.810157
$285$			7.86601i			0.465942i
$286$		−	35.6300i		−	2.10685i
$287$	−10.8431			−0.640048
$288$		−	5.62303i		−	0.331340i
$289$	11.3502			0.667659
$290$			9.87666i			0.579977i
$291$		−	9.09824i		−	0.533348i
$292$			7.03750i			0.411839i
$293$			8.16250i			0.476858i	0.971160	+	0.238429i	$0.0766324\pi$
$293$			8.16250i			0.476858i	−0.971160	+	0.238429i	$0.923368\pi$
$294$			7.61600i			0.444174i
$295$	−3.94690			−0.229797
$296$		−	6.45370i		−	0.375114i
$297$	3.41368			0.198082
$298$	33.3965			1.93461
$299$		−	31.7735i		−	1.83751i
$300$	3.93927			0.227434
$301$	−7.10240			−0.409375
$302$	−12.9083			−0.742788
$303$	−9.94227			−0.571168
$304$	−32.8906			−1.88641
$305$	−10.3445			−0.592325
$306$			9.37713i			0.536055i
$307$		−	19.5589i		−	1.11629i	−0.829745	−	0.558143i	$-0.811514\pi$
$307$		−	19.5589i		−	1.11629i	0.829745	−	0.558143i	$-0.188486\pi$
$308$		−	12.6547i		−	0.721066i
$309$		−	18.0041i		−	1.02422i
$310$	−4.14843			−0.235615
$311$	6.88852			0.390612			0.195306	−	0.980742i	$-0.437430\pi$
$311$	6.88852			0.390612			0.195306	+	0.980742i	$0.437430\pi$
$312$		−	9.37713i		−	0.530876i
$313$	−18.0153			−1.01828			−0.509141	−	0.860683i	$-0.670037\pi$
$313$	−18.0153			−1.01828			−0.509141	+	0.860683i	$0.670037\pi$
$314$	−15.6435	−	15.5637i	−0.882814	−	0.878313i
$315$	−4.01573			−0.226261
$316$			14.6490i			0.824069i
$317$	9.37679			0.526653			0.263326	−	0.964707i	$-0.415180\pi$
$317$	9.37679			0.526653			0.263326	+	0.964707i	$0.415180\pi$
$318$	17.3683			0.973968
$319$		−	16.0430i		−	0.898236i
$320$			0.0912437i			0.00510068i
$321$		−	16.5983i		−	0.926429i
$322$		−	31.7735i		−	1.77067i
$323$	35.0976			1.95288
$324$	−1.10159			−0.0611992
$325$	21.1933			1.17559
$326$	2.75583			0.152631
$327$	−7.55371			−0.417721
$328$	5.09815			0.281498
$329$			5.21899i			0.287732i
$330$	7.17414			0.394924
$331$	−26.4641			−1.45460			−0.727299	−	0.686321i	$-0.759225\pi$
$331$	−26.4641			−1.45460			−0.727299	+	0.686321i	$0.759225\pi$
$332$		−	5.35622i		−	0.293961i
$333$	−4.07887			−0.223521
$334$			17.7584i			0.971695i
$335$			7.50174i			0.409864i
$336$		−	16.7912i		−	0.916036i
$337$			27.4213i			1.49373i	0.664974	+	0.746867i	$0.268443\pi$
$337$			27.4213i			1.49373i	−0.664974	+	0.746867i	$0.731557\pi$
$338$			38.9631i			2.11931i
$339$	16.2287			0.881424
$340$			6.99925i			0.379587i
$341$	6.73844			0.364907
$342$			11.6089i			0.627738i
$343$		−	9.00359i		−	0.486148i
$344$	3.33937			0.180047
$345$	6.39762			0.344436
$346$		−	38.5270i		−	2.07122i
$347$	−4.21559			−0.226305			−0.113152	−	0.993578i	$-0.536095\pi$
$347$	−4.21559			−0.226305			−0.113152	+	0.993578i	$0.536095\pi$
$348$			5.17703i			0.277518i
$349$	27.1645			1.45408			0.727040	−	0.686595i	$-0.240895\pi$
$349$	27.1645			1.45408			0.727040	+	0.686595i	$0.240895\pi$
$350$	21.1933			1.13283
$351$	−5.92654			−0.316335
$352$			19.1952i			1.02311i
$353$	−20.7333			−1.10352			−0.551762	−	0.834002i	$-0.686044\pi$
$353$	−20.7333			−1.10352			−0.551762	+	0.834002i	$0.686044\pi$
$354$	−5.82495			−0.309593
$355$		−	14.7899i		−	0.784967i
$356$	10.7384			0.569136
$357$			17.9179i			0.948317i
$358$	−16.0139			−0.846361
$359$		−	3.91669i		−	0.206715i	−0.994644	−	0.103358i	$-0.967041\pi$
$359$		−	3.91669i		−	0.206715i	0.994644	−	0.103358i	$-0.0329586\pi$
$360$	1.88810			0.0995114
$361$	24.4509			1.28689
$362$	−41.4271			−2.17736
$363$	−0.653221			−0.0342852
$364$			21.9699i			1.15154i
$365$	−7.62352			−0.399033
$366$	−15.2668			−0.798006
$367$		−	34.6327i		−	1.80781i	−0.427731	−	0.903906i	$-0.640687\pi$
$367$		−	34.6327i		−	1.80781i	0.427731	−	0.903906i	$-0.359313\pi$
$368$			26.7508i			1.39448i
$369$		−	3.22214i		−	0.167738i
$370$	−8.57209			−0.445642
$371$	33.1876			1.72301
$372$	−2.17447			−0.112741
$373$		−	22.2040i		−	1.14968i	−0.818266	−	0.574840i	$-0.805064\pi$
$373$		−	22.2040i		−	1.14968i	0.818266	−	0.574840i	$-0.194936\pi$
$374$		−	32.0105i		−	1.65523i
$375$			10.2339i			0.528475i
$376$		−	2.45384i		−	0.126547i
$377$			27.8525i			1.43448i
$378$	−5.92654			−0.304828
$379$			17.1678i			0.881850i	0.897544	+	0.440925i	$0.145350\pi$
$379$			17.1678i			0.881850i	−0.897544	+	0.440925i	$0.854650\pi$
$380$			8.66508i			0.444509i
$381$	2.99061			0.153213
$382$	22.9207			1.17272
$383$		−	6.05875i		−	0.309587i	−0.987947	−	0.154794i	$-0.950529\pi$
$383$		−	6.05875i		−	0.309587i	0.987947	−	0.154794i	$-0.0494713\pi$
$384$			11.3807i			0.580770i
$385$	13.7084			0.698646
$386$			0.491375i			0.0250103i
$387$		−	2.11055i		−	0.107285i
$388$		−	10.0225i		−	0.508814i
$389$	38.7137			1.96286			0.981431	−	0.191818i	$-0.0614383\pi$
$389$	38.7137			1.96286			0.981431	+	0.191818i	$0.0614383\pi$
$390$	−12.4551			−0.630690
$391$		−	28.5457i		−	1.44362i
$392$		−	6.84233i		−	0.345590i
$393$			14.0014i			0.706278i
$394$		−	6.69708i		−	0.337394i
$395$	−15.8688			−0.798446
$396$	3.76046			0.188970
$397$			5.63368i			0.282746i	0.989956	+	0.141373i	$0.0451517\pi$
$397$			5.63368i			0.282746i	−0.989956	+	0.141373i	$0.954848\pi$
$398$		−	39.9710i		−	2.00356i
$399$			22.1824i			1.11051i
$400$	−17.8431			−0.892155
$401$		−	12.1552i		−	0.607003i	−0.952831	−	0.303502i	$-0.901844\pi$
$401$		−	12.1552i		−	0.607003i	0.952831	−	0.303502i	$-0.0981558\pi$
$402$			11.0713i			0.552187i
$403$	−11.6987			−0.582754
$404$	−10.9523			−0.544895
$405$		−	1.19332i		−	0.0592963i
$406$			27.8525i			1.38230i
$407$	13.9240			0.690185
$408$		−	8.42455i		−	0.417078i
$409$		−	19.9856i		−	0.988226i	−0.869398	−	0.494113i	$-0.835493\pi$
$409$		−	19.9856i		−	0.988226i	0.869398	−	0.494113i	$-0.164507\pi$
$410$		−	6.77159i		−	0.334425i
$411$		−	8.72640i		−	0.430442i
$412$		−	19.8331i		−	0.977106i
$413$	−11.1304			−0.547690
$414$	9.44181			0.464039
$415$	5.80224			0.284821
$416$		−	33.3251i		−	1.63390i
$417$		−	6.32211i		−	0.309595i
$418$		−	39.6291i		−	1.93832i
$419$	−24.4014			−1.19209			−0.596044	−	0.802952i	$-0.703262\pi$
$419$	−24.4014			−1.19209			−0.596044	+	0.802952i	$0.703262\pi$
$420$	−4.42367			−0.215853
$421$		−	18.2634i		−	0.890102i	−0.895505	−	0.445051i	$-0.853186\pi$
$421$		−	18.2634i		−	0.890102i	0.895505	−	0.445051i	$-0.146814\pi$
$422$	−46.0884			−2.24355
$423$	−1.55088			−0.0754062
$424$	−15.6040			−0.757796
$425$	19.0404			0.923594
$426$		−	21.8274i		−	1.05754i
$427$	−29.1719			−1.41173
$428$		−	18.2845i		−	0.883814i
$429$	20.2313			0.976777
$430$		−	4.43550i		−	0.213899i
$431$	9.38076			0.451855			0.225928	−	0.974144i	$-0.427459\pi$
$431$	9.38076			0.451855			0.225928	+	0.974144i	$0.427459\pi$
$432$	4.98968			0.240066
$433$			4.07360i			0.195765i	0.995198	+	0.0978823i	$0.0312069\pi$
$433$			4.07360i			0.195765i	−0.995198	+	0.0978823i	$0.968793\pi$
$434$	−11.6987			−0.561555
$435$	−5.60813			−0.268889
$436$	−8.32106			−0.398506
$437$		−	35.3397i		−	1.69053i
$438$	−11.2510			−0.537595
$439$			18.4986i			0.882892i	0.897288	+	0.441446i	$0.145534\pi$
$439$			18.4986i			0.882892i	−0.897288	+	0.441446i	$0.854466\pi$
$440$	−6.44536			−0.307270
$441$	−4.32449			−0.205928
$442$			55.5739i			2.64338i
$443$			27.9538i			1.32813i	0.747676	+	0.664063i	$0.231170\pi$
$443$			27.9538i			1.32813i	−0.747676	+	0.664063i	$0.768830\pi$
$444$	−4.49322			−0.213239
$445$			11.6326i			0.551439i
$446$	13.1130			0.620918
$447$			18.9631i			0.896923i
$448$			0.257310i			0.0121568i
$449$		−	36.4468i		−	1.72003i	−0.510270	−	0.860014i	$-0.670455\pi$
$449$		−	36.4468i		−	1.72003i	0.510270	−	0.860014i	$-0.329545\pi$
$450$			6.29781i			0.296881i
$451$			10.9993i			0.517939i
$452$	17.8773			0.840879
$453$		−	7.32954i		−	0.344372i
$454$	−9.29338			−0.436160
$455$	−23.7994			−1.11573
$456$		−	10.4296i		−	0.488411i
$457$	−7.41685			−0.346946			−0.173473	−	0.984839i	$-0.555499\pi$
$457$	−7.41685			−0.346946			−0.173473	+	0.984839i	$0.555499\pi$
$458$	4.30135			0.200989
$459$	−5.32449			−0.248526
$460$	7.04752			0.328592
$461$	−6.26586			−0.291830			−0.145915	−	0.989297i	$-0.546613\pi$
$461$	−6.26586			−0.291830			−0.145915	+	0.989297i	$0.546613\pi$
$462$	20.2313			0.941246
$463$			42.0946i			1.95630i	0.207891	+	0.978152i	$0.433340\pi$
$463$			42.0946i			1.95630i	−0.207891	+	0.978152i	$0.566660\pi$
$464$		−	23.4496i		−	1.08862i
$465$		−	2.35555i		−	0.109236i
$466$			9.73213i			0.450832i
$467$	−20.9803			−0.970852			−0.485426	−	0.874278i	$-0.661335\pi$
$467$	−20.9803			−0.970852			−0.485426	+	0.874278i	$0.661335\pi$
$468$	−6.52859			−0.301784
$469$			21.1552i			0.976855i
$470$	−3.25930			−0.150340
$471$	8.83735	−	8.88264i	0.407204	−	0.409290i
$472$	5.23323			0.240879
$473$			7.20474i			0.331274i
$474$	−23.4197			−1.07570
$475$	23.5720			1.08156
$476$			19.7381i			0.904695i
$477$			9.86204i			0.451552i
$478$		−	32.6213i		−	1.49206i
$479$		−	23.3234i		−	1.06567i	−0.846218	−	0.532837i	$-0.821126\pi$
$479$		−	23.3234i		−	1.06567i	0.846218	−	0.532837i	$-0.178874\pi$
$480$	6.71005			0.306270
$481$	−24.1736			−1.10222
$482$	−43.2743			−1.97109
$483$	18.0415			0.820917
$484$	−0.719578			−0.0327081
$485$	10.8571			0.492994
$486$		−	1.76113i		−	0.0798866i
$487$	−16.1725			−0.732845			−0.366422	−	0.930449i	$-0.619417\pi$
$487$	−16.1725			−0.732845			−0.366422	+	0.930449i	$0.619417\pi$
$488$	13.7159			0.620889
$489$			1.56480i			0.0707629i
$490$	−9.08829			−0.410567
$491$			20.0523i			0.904947i	0.891778	+	0.452474i	$0.149458\pi$
$491$			20.0523i			0.904947i	−0.891778	+	0.452474i	$0.850542\pi$
$492$		−	3.54946i		−	0.160022i
$493$			25.0231i			1.12698i
$494$			68.8006i			3.09549i
$495$			4.07360i			0.183095i
$496$	9.84938			0.442250
$497$		−	41.7080i		−	1.87086i
$498$	8.56313			0.383723
$499$		−	12.7852i		−	0.572342i	−0.958179	−	0.286171i	$-0.907617\pi$
$499$		−	12.7852i		−	0.572342i	0.958179	−	0.286171i	$-0.0923825\pi$
$500$			11.2735i			0.504165i
$501$	−10.0835			−0.450497
$502$	8.97245			0.400460
$503$			15.4778i			0.690119i	0.938581	+	0.345060i	$0.112141\pi$
$503$			15.4778i			0.690119i	−0.938581	+	0.345060i	$0.887859\pi$
$504$	5.32449			0.237172
$505$		−	11.8643i		−	0.527953i
$506$	−32.2313			−1.43286
$507$	−22.1239			−0.982556
$508$	3.29441			0.146166
$509$			17.7587i			0.787140i	0.919295	+	0.393570i	$0.128760\pi$
$509$			17.7587i			0.787140i	−0.919295	+	0.393570i	$0.871240\pi$
$510$	−11.1899			−0.495496
$511$	−21.4986			−0.951041
$512$			12.2675i			0.542153i
$513$	−6.59173			−0.291032
$514$		−	10.1172i		−	0.446252i
$515$	21.4846			0.946725
$516$		−	2.32495i		−	0.102350i
$517$	5.29420			0.232839
$518$	−24.1736			−1.06213
$519$	21.8763			0.960262
$520$	11.1899			0.490708
$521$		−	17.0880i		−	0.748639i	−0.927300	−	0.374319i	$-0.877876\pi$
$521$		−	17.0880i		−	0.748639i	0.927300	−	0.374319i	$-0.122124\pi$
$522$	−8.27665			−0.362259
$523$	35.9823			1.57340			0.786698	−	0.617338i	$-0.211789\pi$
$523$	35.9823			1.57340			0.786698	+	0.617338i	$0.211789\pi$
$524$			15.4237i			0.673789i
$525$			12.0339i			0.525203i
$526$		−	28.8297i		−	1.25703i
$527$	−10.5103			−0.457835
$528$	−17.0332			−0.741274
$529$	−5.74263			−0.249679
$530$			20.7259i			0.900276i
$531$		−	3.30751i		−	0.143534i
$532$			24.4358i			1.05943i
$533$		−	19.0961i		−	0.827145i
$534$			17.1678i			0.742923i
$535$	19.8071			0.856334
$536$		−	9.94663i		−	0.429629i
$537$		−	9.09296i		−	0.392390i
$538$	−31.4527			−1.35602
$539$	14.7624			0.635863
$540$		−	1.31454i		−	0.0565687i
$541$			24.7031i			1.06207i	0.847350	+	0.531036i	$0.178197\pi$
$541$			24.7031i			1.06207i	−0.847350	+	0.531036i	$0.821803\pi$
$542$	−9.94227			−0.427057
$543$		−	23.5230i		−	1.00947i
$544$		−	29.9398i		−	1.28366i
$545$		−	9.01396i		−	0.386116i
$546$	−35.1239			−1.50316
$547$	5.26881			0.225278			0.112639	−	0.993636i	$-0.464070\pi$
$547$	5.26881			0.225278			0.112639	+	0.993636i	$0.464070\pi$
$548$		−	9.61288i		−	0.410642i
$549$		−	8.66872i		−	0.369972i
$550$		−	21.4987i		−	0.916708i
$551$			30.9786i			1.31973i
$552$	−8.48266			−0.361046
$553$	−44.7506			−1.90299
$554$			50.5210i			2.14643i
$555$		−	4.86738i		−	0.206609i
$556$		−	6.96434i		−	0.295354i
$557$	31.1668			1.32058			0.660289	−	0.751011i	$-0.270434\pi$
$557$	31.1668			1.32058			0.660289	+	0.751011i	$0.270434\pi$
$558$		−	3.47639i		−	0.147167i
$559$		−	12.5083i		−	0.529043i
$560$	20.0372			0.846727
$561$	18.1761			0.767396
$562$			11.0350i			0.465483i
$563$			7.43930i			0.313529i	0.987636	+	0.156765i	$0.0501064\pi$
$563$			7.43930i			0.313529i	−0.987636	+	0.156765i	$0.949894\pi$
$564$	−1.70842			−0.0719376
$565$			19.3660i			0.814734i
$566$			9.15822i			0.384949i
$567$		−	3.36519i		−	0.141325i
$568$			19.6101i			0.822820i
$569$		−	40.7462i		−	1.70817i	−0.520133	−	0.854085i	$-0.674118\pi$
$569$		−	40.7462i		−	1.70817i	0.520133	−	0.854085i	$-0.325882\pi$
$570$	−13.8531			−0.580242
$571$	−32.3165			−1.35240			−0.676201	−	0.736717i	$-0.736375\pi$
$571$	−32.3165			−1.35240			−0.676201	+	0.736717i	$0.736375\pi$
$572$	22.2865			0.931846
$573$			13.0147i			0.543699i
$574$		−	19.0961i		−	0.797056i
$575$		−	19.1717i		−	0.799515i
$576$	−0.0764624			−0.00318593
$577$	−25.1344			−1.04636			−0.523180	−	0.852222i	$-0.675255\pi$
$577$	−25.1344			−1.04636			−0.523180	+	0.852222i	$0.675255\pi$
$578$			19.9892i			0.831442i
$579$	−0.279011			−0.0115953
$580$	−6.17783			−0.256521
$581$	16.3625			0.678831
$582$	16.0232			0.664183
$583$		−	33.6659i		−	1.39430i
$584$	10.1081			0.418276
$585$		−	7.07223i		−	0.292401i
$586$	−14.3752			−0.593835
$587$			29.2175i			1.20594i	0.797766	+	0.602968i	$0.206015\pi$
$587$			29.2175i			1.20594i	−0.797766	+	0.602968i	$0.793985\pi$
$588$	−4.76380			−0.196456
$589$	−13.0117			−0.536140
$590$		−	6.95101i		−	0.286168i
$591$	3.80272			0.156423
$592$	20.3523			0.836473
$593$	−16.7622			−0.688340			−0.344170	−	0.938907i	$-0.611840\pi$
$593$	−16.7622			−0.688340			−0.344170	+	0.938907i	$0.611840\pi$
$594$			6.01194i			0.246673i
$595$	−21.3817			−0.876565
$596$			20.8895i			0.855665i
$597$	22.6962			0.928892
$598$	55.9572			2.28826
$599$			0.328923i			0.0134394i	0.999977	+	0.00671971i	$0.00213897\pi$
$599$			0.328923i			0.0134394i	−0.999977	+	0.00671971i	$0.997861\pi$
$600$		−	5.65804i		−	0.230989i
$601$	37.1262			1.51441			0.757205	−	0.653177i	$-0.226564\pi$
$601$	37.1262			1.51441			0.757205	+	0.653177i	$0.226564\pi$
$602$		−	12.5083i		−	0.509798i
$603$	−6.28647			−0.256005
$604$		−	8.07411i		−	0.328531i
$605$		−	0.779498i		−	0.0316911i
$606$		−	17.5096i		−	0.711281i
$607$			39.9871i			1.62302i	0.584335	+	0.811512i	$0.301355\pi$
$607$			39.9871i			1.62302i	−0.584335	+	0.811512i	$0.698645\pi$
$608$		−	37.0655i		−	1.50320i
$609$	−15.8151			−0.640861
$610$		−	18.2181i		−	0.737628i
$611$	−9.19133			−0.371841
$612$	−5.86538			−0.237094
$613$		−	3.92962i		−	0.158716i	−0.996846	−	0.0793580i	$-0.974713\pi$
$613$		−	3.92962i		−	0.158716i	0.996846	−	0.0793580i	$-0.0252870\pi$
$614$	34.4458			1.39012
$615$	3.84502			0.155046
$616$	−18.1761			−0.732337
$617$	4.11293			0.165580			0.0827902	−	0.996567i	$-0.473617\pi$
$617$	4.11293			0.165580			0.0827902	+	0.996567i	$0.473617\pi$
$618$	31.7077			1.27547
$619$	14.5546			0.584997			0.292499	−	0.956266i	$-0.405513\pi$
$619$	14.5546			0.584997			0.292499	+	0.956266i	$0.405513\pi$
$620$		−	2.59483i		−	0.104211i
$621$			5.36122i			0.215138i
$622$			12.1316i			0.486433i
$623$			32.8044i			1.31428i
$624$	29.5715			1.18381
$625$	5.66776			0.226711
$626$		−	31.7272i		−	1.26808i
$627$	22.5021			0.898646
$628$	9.73509	−	9.78498i	0.388473	−	0.390463i
$629$	−21.7179			−0.865950
$630$		−	7.07223i		−	0.281764i
$631$	26.9175			1.07157			0.535784	−	0.844355i	$-0.320016\pi$
$631$	26.9175			1.07157			0.535784	+	0.844355i	$0.320016\pi$
$632$	21.0406			0.836950
$633$		−	26.1698i		−	1.04016i
$634$			16.5138i			0.655845i
$635$			3.56874i			0.141621i
$636$			10.8639i			0.430781i
$637$	−25.6293			−1.01547
$638$	28.2539			1.11858
$639$	12.3940			0.490298
$640$	−13.5808			−0.536828
$641$	−22.1007			−0.872926			−0.436463	−	0.899722i	$-0.643769\pi$
$641$	−22.1007			−0.872926			−0.436463	+	0.899722i	$0.643769\pi$
$642$	29.2319			1.15369
$643$		−	3.64111i		−	0.143591i	−0.997419	−	0.0717957i	$-0.977127\pi$
$643$		−	3.64111i		−	0.143591i	0.997419	−	0.0717957i	$-0.0228730\pi$
$644$	19.8742			0.783155
$645$	2.51855			0.0991678
$646$			61.8115i			2.43194i
$647$	48.1442			1.89274			0.946371	−	0.323082i	$-0.104719\pi$
$647$	48.1442			1.89274			0.946371	+	0.323082i	$0.104719\pi$
$648$			1.58223i			0.0621557i
$649$			11.2908i			0.443202i
$650$			37.3242i			1.46398i
$651$		−	6.64272i		−	0.260349i
$652$			1.72377i			0.0675079i
$653$	12.3156			0.481946			0.240973	−	0.970532i	$-0.422534\pi$
$653$	12.3156			0.481946			0.240973	+	0.970532i	$0.422534\pi$
$654$		−	13.3031i		−	0.520192i
$655$	−16.7081			−0.652839
$656$			16.0774i			0.627718i
$657$		−	6.38852i		−	0.249240i
$658$	−9.19133			−0.358315
$659$	−10.8998			−0.424594			−0.212297	−	0.977205i	$-0.568094\pi$
$659$	−10.8998			−0.424594			−0.212297	+	0.977205i	$0.568094\pi$
$660$			4.48741i			0.174672i
$661$	13.0120			0.506107			0.253053	−	0.967452i	$-0.418565\pi$
$661$	13.0120			0.506107			0.253053	+	0.967452i	$0.418565\pi$
$662$		−	46.6068i		−	1.81142i
$663$	−31.5558			−1.22553
$664$	−7.69324			−0.298556
$665$	−26.4706			−1.02649
$666$		−	7.18343i		−	0.278352i
$667$	25.1957			0.975581
$668$	−11.1078			−0.429775
$669$			7.44577i			0.287870i
$670$	−13.2116			−0.510407
$671$			29.5923i			1.14240i
$672$	18.9226			0.729953
$673$		−	29.9513i		−	1.15454i	−0.816554	−	0.577270i	$-0.804118\pi$
$673$		−	29.9513i		−	1.15454i	0.816554	−	0.577270i	$-0.195882\pi$
$674$	−48.2925			−1.86016
$675$	−3.57600			−0.137640
$676$	−24.3713			−0.937359
$677$	11.6844			0.449069			0.224534	−	0.974466i	$-0.427914\pi$
$677$	11.6844			0.449069			0.224534	+	0.974466i	$0.427914\pi$
$678$			28.5810i			1.09764i
$679$	30.6173			1.17498
$680$	10.0531			0.385521
$681$		−	5.27694i		−	0.202213i
$682$			11.8673i			0.454422i
$683$		−	13.9640i		−	0.534317i	−0.963653	−	0.267158i	$-0.913915\pi$
$683$		−	13.9640i		−	0.534317i	0.963653	−	0.267158i	$-0.0860847\pi$
$684$	−7.26135			−0.277645
$685$	10.4133			0.397874
$686$	15.8565			0.605404
$687$			2.44238i			0.0931825i
$688$			10.5310i			0.401489i
$689$			58.4478i			2.22668i
$690$			11.2671i			0.428929i
$691$			37.0605i			1.40985i	0.709284	+	0.704923i	$0.249019\pi$
$691$			37.0605i			1.40985i	−0.709284	+	0.704923i	$0.750981\pi$
$692$	24.0986			0.916090
$693$			11.4877i			0.436381i
$694$		−	7.42421i		−	0.281819i
$695$	7.54427			0.286170
$696$	7.43587			0.281856
$697$		−	17.1562i		−	0.649839i
$698$			47.8402i			1.81078i
$699$	−5.52606			−0.209015
$700$			13.2564i			0.501044i
$701$		−	39.0283i		−	1.47408i	−0.675850	−	0.737039i	$-0.736223\pi$
$701$		−	39.0283i		−	1.47408i	0.675850	−	0.737039i	$-0.263777\pi$
$702$		−	10.4374i		−	0.393935i
$703$	−26.8868			−1.01406
$704$	0.261018			0.00983749
$705$		−	1.85068i		−	0.0697008i
$706$		−	36.5141i		−	1.37423i
$707$		−	33.4576i		−	1.25830i
$708$		−	3.64350i		−	0.136931i
$709$	−14.9952			−0.563157			−0.281579	−	0.959538i	$-0.590858\pi$
$709$	−14.9952			−0.563157			−0.281579	+	0.959538i	$0.590858\pi$
$710$	26.0470			0.977526
$711$		−	13.2981i		−	0.498717i
$712$		−	15.4238i		−	0.578031i
$713$			10.5828i			0.396328i
$714$	−31.5558			−1.18095
$715$			24.1423i			0.902872i
$716$		−	10.0167i		−	0.374341i
$717$	18.5229			0.691750
$718$	6.89781			0.257424
$719$		−	44.3677i		−	1.65463i	−0.561735	−	0.827317i	$-0.689866\pi$
$719$		−	44.3677i		−	1.65463i	0.561735	−	0.827317i	$-0.310134\pi$
$720$			5.95426i			0.221902i
$721$	60.5873			2.25639
$722$			43.0612i			1.60257i
$723$		−	24.5719i		−	0.913837i
$724$		−	25.9126i		−	0.963035i
$725$			16.8058i			0.624153i
$726$		−	1.15041i		−	0.0426956i
$727$	4.35364			0.161467			0.0807337	−	0.996736i	$-0.474274\pi$
$727$	4.35364			0.161467			0.0807337	+	0.996736i	$0.474274\pi$
$728$	31.5558			1.16954
$729$	1.00000			0.0370370
$730$		−	13.4260i		−	0.496919i
$731$		−	11.2376i		−	0.415638i
$732$		−	9.54933i		−	0.352954i
$733$	7.12151			0.263039			0.131519	−	0.991314i	$-0.458014\pi$
$733$	7.12151			0.263039			0.131519	+	0.991314i	$0.458014\pi$
$734$	60.9927			2.25128
$735$		−	5.16048i		−	0.190347i
$736$	−30.1463			−1.11121
$737$	21.4600			0.790490
$738$	5.67461			0.208885
$739$	−3.81982			−0.140514			−0.0702572	−	0.997529i	$-0.522382\pi$
$739$	−3.81982			−0.140514			−0.0702572	+	0.997529i	$0.522382\pi$
$740$		−	5.36183i		−	0.197105i
$741$	−39.0661			−1.43513
$742$			58.4478i			2.14568i
$743$	−2.84073			−0.104216			−0.0521082	−	0.998641i	$-0.516594\pi$
$743$	−2.84073			−0.104216			−0.0521082	+	0.998641i	$0.516594\pi$
$744$			3.12324i			0.114503i
$745$	−22.6289			−0.829060
$746$	39.1042			1.43170
$747$			4.86229i			0.177902i
$748$	20.0225			0.732097
$749$	55.8566			2.04095
$750$	−18.0232			−0.658114
$751$		−	15.7318i		−	0.574062i	−0.957921	−	0.287031i	$-0.907332\pi$
$751$		−	15.7318i		−	0.574062i	0.957921	−	0.287031i	$-0.0926682\pi$
$752$	7.73838			0.282190
$753$			5.09471i			0.185662i
$754$	−49.0519			−1.78637
$755$	8.74645			0.318316
$756$		−	3.70704i		−	0.134824i
$757$			32.8009i			1.19217i	0.802921	+	0.596085i	$0.203278\pi$
$757$			32.8009i			1.19217i	−0.802921	+	0.596085i	$0.796722\pi$
$758$	−30.2347			−1.09818
$759$		−	18.3015i		−	0.664302i
$760$	12.4458			0.451457
$761$			22.9776i			0.832936i	0.909150	+	0.416468i	$0.136732\pi$
$761$			22.9776i			0.832936i	−0.909150	+	0.416468i	$0.863268\pi$
$762$			5.26685i			0.190798i
$763$		−	25.4197i		−	0.920253i
$764$			14.3368i			0.518689i
$765$		−	6.35380i		−	0.229722i
$766$	10.6702			0.385532
$767$		−	19.6021i		−	0.707790i
$768$	−19.8900			−0.717720
$769$	−40.6847			−1.46713			−0.733563	−	0.679621i	$-0.762144\pi$
$769$	−40.6847			−1.46713			−0.733563	+	0.679621i	$0.762144\pi$
$770$			24.1423i			0.870029i
$771$	5.74473			0.206891
$772$	−0.307354			−0.0110619
$773$	−18.6276			−0.669987			−0.334993	−	0.942220i	$-0.608734\pi$
$773$	−18.6276			−0.669987			−0.334993	+	0.942220i	$0.608734\pi$
$774$	3.71696			0.133603
$775$	−7.05885			−0.253561
$776$	−14.3955			−0.516767
$777$		−	13.7262i		−	0.492423i
$778$			68.1799i			2.44437i
$779$		−	21.2394i		−	0.760982i
$780$		−	7.79066i		−	0.278950i
$781$	−42.3091			−1.51394
$782$	50.2728			1.79775
$783$		−	4.69962i		−	0.167951i
$784$	21.5778			0.770637
$785$	10.5998	+	10.5457i	0.378323	+	0.376394i
$786$	−24.6583			−0.879533
$787$		−	37.8633i		−	1.34968i	−0.737964	−	0.674840i	$-0.764213\pi$
$787$		−	37.8633i		−	1.34968i	0.737964	−	0.674840i	$-0.235787\pi$
$788$	4.18902			0.149228
$789$	16.3700			0.582786
$790$		−	27.9471i		−	0.994312i
$791$			54.6128i			1.94181i
$792$		−	5.40122i		−	0.191924i
$793$		−	51.3755i		−	1.82440i
$794$	−9.92165			−0.352106
$795$	−11.7685			−0.417386
$796$	25.0018			0.886164
$797$	−19.8882			−0.704476			−0.352238	−	0.935911i	$-0.614579\pi$
$797$	−19.8882			−0.704476			−0.352238	+	0.935911i	$0.614579\pi$
$798$	−39.0661			−1.38293
$799$	−8.25763			−0.292134
$800$		−	20.1080i		−	0.710924i
$801$	−9.74816			−0.344434
$802$	21.4070			0.755906
$803$			21.8084i			0.769601i
$804$	−6.92509			−0.244229
$805$			21.5292i			0.758804i
$806$		−	20.6029i		−	0.725708i
$807$		−	17.8594i		−	0.628679i
$808$			15.7309i			0.553412i
$809$		−	3.98133i		−	0.139976i	−0.997548	−	0.0699881i	$-0.977704\pi$
$809$		−	3.98133i		−	0.139976i	0.997548	−	0.0699881i	$-0.0222961\pi$
$810$	2.10159			0.0738422
$811$			6.78019i			0.238085i	0.992889	+	0.119042i	$0.0379824\pi$
$811$			6.78019i			0.238085i	−0.992889	+	0.119042i	$0.962018\pi$
$812$	−17.4217			−0.611382
$813$		−	5.64539i		−	0.197992i
$814$			24.5219i			0.859493i
$815$	−1.86730			−0.0654088
$816$	26.5675			0.930049
$817$		−	13.9122i		−	0.486725i
$818$	35.1973			1.23065
$819$		−	19.9439i		−	0.696897i
$820$	4.23562			0.147914
$821$	22.0487			0.769505			0.384753	−	0.923020i	$-0.374287\pi$
$821$	22.0487			0.769505			0.384753	+	0.923020i	$0.374287\pi$
$822$	15.3683			0.536033
$823$			26.8682i			0.936565i	0.883579	+	0.468283i	$0.155127\pi$
$823$			26.8682i			0.936565i	−0.883579	+	0.468283i	$0.844873\pi$
$824$	−28.4866			−0.992379
$825$	12.2073			0.425004
$826$		−	19.6021i		−	0.682043i
$827$	35.1099			1.22089			0.610445	−	0.792059i	$-0.290991\pi$
$827$	35.1099			1.22089			0.610445	+	0.792059i	$0.290991\pi$
$828$			5.90584i			0.205242i
$829$	−40.3043			−1.39983			−0.699913	−	0.714228i	$-0.746778\pi$
$829$	−40.3043			−1.39983			−0.699913	+	0.714228i	$0.746778\pi$
$830$			10.2185i			0.354690i
$831$	−28.6867			−0.995129
$832$	−0.453157			−0.0157104
$833$	−23.0257			−0.797794
$834$	11.1341			0.385541
$835$		−	12.0328i		−	0.416412i
$836$	24.7879			0.857309
$837$	1.97395			0.0682297
$838$		−	42.9741i		−	1.48452i
$839$			31.9246i			1.10216i	0.834453	+	0.551080i	$0.185784\pi$
$839$			31.9246i			1.10216i	−0.834453	+	0.551080i	$0.814216\pi$
$840$			6.35380i			0.219227i
$841$	6.91355			0.238398
$842$	32.1642			1.10845
$843$	−6.26586			−0.215808
$844$		−	28.8282i		−	0.992309i
$845$		−	26.4008i		−	0.908214i
$846$		−	2.73130i		−	0.0939039i
$847$		−	2.19821i		−	0.0755314i
$848$		−	49.2084i		−	1.68982i
$849$	−5.20019			−0.178470
$850$			33.5326i			1.15016i
$851$			21.8677i			0.749615i
$852$	13.6530			0.467744
$853$	6.92344			0.237054			0.118527	−	0.992951i	$-0.462183\pi$
$853$	6.92344			0.237054			0.118527	+	0.992951i	$0.462183\pi$
$854$		−	51.3755i		−	1.75803i
$855$		−	7.86601i		−	0.269012i
$856$	−26.2623			−0.897629
$857$		−	26.0752i		−	0.890711i	−0.895354	−	0.445355i	$-0.853077\pi$
$857$		−	26.0752i		−	0.890711i	0.895354	−	0.445355i	$-0.146923\pi$
$858$			35.6300i			1.21639i
$859$		−	32.0750i		−	1.09439i	−0.837006	−	0.547193i	$-0.815696\pi$
$859$		−	32.0750i		−	1.09439i	0.837006	−	0.547193i	$-0.184304\pi$
$860$	2.77440			0.0946062
$861$	10.8431			0.369532
$862$			16.5208i			0.562699i
$863$		−	12.4655i		−	0.424330i	−0.977234	−	0.212165i	$-0.931949\pi$
$863$		−	12.4655i		−	0.424330i	0.977234	−	0.212165i	$-0.0680514\pi$
$864$			5.62303i			0.191299i
$865$			26.1053i			0.887606i
$866$	−7.17414			−0.243787
$867$	−11.3502			−0.385473
$868$		−	7.31752i		−	0.248373i
$869$			45.3954i			1.53993i
$870$		−	9.87666i		−	0.334850i
$871$	−37.2570			−1.26241
$872$			11.9517i			0.404735i
$873$			9.09824i			0.307929i
$874$	62.2378			2.10523
$875$	−34.4389			−1.16425
$876$		−	7.03750i		−	0.237775i
$877$			45.1259i			1.52379i	0.647698	+	0.761897i	$0.275732\pi$
$877$			45.1259i			1.52379i	−0.647698	+	0.761897i	$0.724268\pi$
$878$	−32.5785			−1.09947
$879$		−	8.16250i		−	0.275314i
$880$		−	20.3260i		−	0.685188i
$881$			25.6172i			0.863064i	0.902098	+	0.431532i	$0.142027\pi$
$881$			25.6172i			0.863064i	−0.902098	+	0.431532i	$0.857973\pi$
$882$		−	7.61600i		−	0.256444i
$883$			26.1479i			0.879946i	0.898011	+	0.439973i	$0.145012\pi$
$883$			26.1479i			0.879946i	−0.898011	+	0.439973i	$0.854988\pi$
$884$	−34.7614			−1.16915
$885$	3.94690			0.132674
$886$	−49.2304			−1.65393
$887$			50.2869i			1.68847i	0.535975	+	0.844234i	$0.319944\pi$
$887$			50.2869i			1.68847i	−0.535975	+	0.844234i	$0.680056\pi$
$888$			6.45370i			0.216572i
$889$			10.0640i			0.337534i
$890$	−20.4866			−0.686712
$891$	−3.41368			−0.114363
$892$			8.20215i			0.274628i
$893$	−10.2230			−0.342098
$894$	−33.3965			−1.11695
$895$	10.8508			0.362701
$896$	−38.2983			−1.27946
$897$			31.7735i			1.06088i
$898$	64.1875			2.14197
$899$		−	9.27682i		−	0.309399i
$900$	−3.93927			−0.131309
$901$			52.5103i			1.74937i
$902$	−19.3713			−0.644994
$903$	7.10240			0.236353
$904$		−	25.6776i		−	0.854023i
$905$	28.0704			0.933091
$906$	12.9083			0.428849
$907$	−47.0430			−1.56204			−0.781018	−	0.624509i	$-0.785299\pi$
$907$	−47.0430			−1.56204			−0.781018	+	0.624509i	$0.785299\pi$
$908$		−	5.81300i		−	0.192911i
$909$	9.94227			0.329764
$910$		−	41.9138i		−	1.38943i
$911$	−14.6401			−0.485049			−0.242524	−	0.970145i	$-0.577975\pi$
$911$	−14.6401			−0.485049			−0.242524	+	0.970145i	$0.577975\pi$
$912$	32.8906			1.08912
$913$		−	16.5983i		−	0.549323i
$914$		−	13.0621i		−	0.432055i
$915$	10.3445			0.341979
$916$			2.69049i			0.0888962i
$917$	−47.1174			−1.55595
$918$		−	9.37713i		−	0.309491i
$919$		−	16.8329i		−	0.555267i	−0.960687	−	0.277633i	$-0.910450\pi$
$919$		−	16.8329i		−	0.555267i	0.960687	−	0.277633i	$-0.0895501\pi$
$920$		−	10.1225i		−	0.333728i
$921$			19.5589i			0.644488i
$922$		−	11.0350i		−	0.363418i
$923$	73.4534			2.41775
$924$			12.6547i			0.416308i
$925$	−14.5860			−0.479586
$926$	−74.1342			−2.43620
$927$			18.0041i			0.591334i
$928$	26.4261			0.867480
$929$	−37.8735			−1.24259			−0.621294	−	0.783577i	$-0.713393\pi$
$929$	−37.8735			−1.24259			−0.621294	+	0.783577i	$0.713393\pi$
$930$	4.14843			0.136032
$931$	−28.5059			−0.934242
$932$	−6.08743			−0.199400
$933$	−6.88852			−0.225520
$934$		−	36.9491i		−	1.20901i
$935$			21.6898i			0.709333i
$936$			9.37713i			0.306501i
$937$			22.7466i			0.743099i	0.928413	+	0.371549i	$0.121173\pi$
$937$			22.7466i			0.743099i	−0.928413	+	0.371549i	$0.878827\pi$
$938$	−37.2570			−1.21649
$939$	18.0153			0.587906
$940$		−	2.03869i		−	0.0664946i
$941$	17.0524			0.555893			0.277947	−	0.960597i	$-0.410346\pi$
$941$	17.0524			0.555893			0.277947	+	0.960597i	$0.410346\pi$
$942$	15.6435	+	15.5637i	0.509693	+	0.507094i
$943$	−17.2746			−0.562537
$944$			16.5034i			0.537140i
$945$	4.01573			0.130632
$946$	−12.6885			−0.412539
$947$		−	40.0286i		−	1.30076i	−0.759611	−	0.650378i	$-0.774610\pi$
$947$		−	40.0286i		−	1.30076i	0.759611	−	0.650378i	$-0.225390\pi$
$948$		−	14.6490i		−	0.475777i
$949$		−	37.8618i		−	1.22905i
$950$			41.5134i			1.34687i
$951$	−9.37679			−0.304063
$952$	28.3502			0.918836
$953$	−43.2919			−1.40236			−0.701181	−	0.712983i	$-0.747344\pi$
$953$	−43.2919			−1.40236			−0.701181	+	0.712983i	$0.747344\pi$
$954$	−17.3683			−0.562321
$955$	−15.5307			−0.502561
$956$	20.4045			0.659930
$957$			16.0430i			0.518597i
$958$	41.0756			1.32709
$959$	29.3660			0.948277
$960$		−	0.0912437i		−	0.00294488i
$961$	−27.1035			−0.874307
$962$		−	42.5729i		−	1.37260i
$963$			16.5983i			0.534874i
$964$		−	27.0680i		−	0.871801i
$965$		−	0.332948i		−	0.0107180i
$966$			31.7735i			1.02229i
$967$	−56.4353			−1.81484			−0.907418	−	0.420228i	$-0.861950\pi$
$967$	−56.4353			−1.81484			−0.907418	+	0.420228i	$0.861950\pi$
$968$			1.03354i			0.0332193i
$969$	−35.0976			−1.12750
$970$			19.1207i			0.613929i
$971$			10.4240i			0.334522i	0.985913	+	0.167261i	$0.0534923\pi$
$971$			10.4240i			0.334522i	−0.985913	+	0.167261i	$0.946508\pi$
$972$	1.10159			0.0353334
$973$	21.2751			0.682048
$974$		−	28.4819i		−	0.912617i
$975$	−21.1933			−0.678729
$976$			43.2542i			1.38453i
$977$	−4.54718			−0.145477			−0.0727386	−	0.997351i	$-0.523174\pi$
$977$	−4.54718			−0.145477			−0.0727386	+	0.997351i	$0.523174\pi$
$978$	−2.75583			−0.0881216
$979$	33.2771			1.06354
$980$		−	5.68471i		−	0.181591i
$981$	7.55371			0.241171
$982$	−35.3147			−1.12694
$983$		−	5.29765i		−	0.168969i	−0.996425	−	0.0844844i	$-0.973076\pi$
$983$		−	5.29765i		−	0.168969i	0.996425	−	0.0844844i	$-0.0269243\pi$
$984$	−5.09815			−0.162523
$985$			4.53784i			0.144588i
$986$	−44.0690			−1.40344
$987$		−	5.21899i		−	0.166122i
$988$	−43.0347			−1.36912
$989$	−11.3151			−0.359800
$990$	−7.17414			−0.228009
$991$	38.4590			1.22169			0.610845	−	0.791750i	$-0.290830\pi$
$991$	38.4590			1.22169			0.610845	+	0.791750i	$0.290830\pi$
$992$			11.0996i			0.352412i
$993$	26.4641			0.839813
$994$	73.4534			2.32980
$995$			27.0837i			0.858611i
$996$			5.35622i			0.169718i
$997$		−	8.46578i		−	0.268114i	−0.990974	−	0.134057i	$-0.957199\pi$
$997$		−	8.46578i		−	0.268114i	0.990974	−	0.134057i	$-0.0428005\pi$
$998$	22.5163			0.712742
$999$	4.07887			0.129050

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.b.a.313.10	yes	12
3.2	odd	2		1413.2.b.c.784.3		12
157.156	even	2	inner	471.2.b.a.313.3	✓	12
471.470	odd	2		1413.2.b.c.784.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.b.a.313.3	✓	12	157.156	even	2	inner
471.2.b.a.313.10	yes	12	1.1	even	1	trivial
1413.2.b.c.784.3		12	3.2	odd	2
1413.2.b.c.784.10		12	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)

\(f(q)\)	\(=\)	\(q+1.76113i q^{2} -1.00000 q^{3} -1.10159 q^{4} -1.19332i q^{5} -1.76113i q^{6} -3.36519i q^{7} +1.58223i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.76113i q^{2} -1.00000 q^{3} -1.10159 q^{4} -1.19332i q^{5} -1.76113i q^{6} -3.36519i q^{7} +1.58223i q^{8} +1.00000 q^{9} +2.10159 q^{10} -3.41368 q^{11} +1.10159 q^{12} +5.92654 q^{13} +5.92654 q^{14} +1.19332i q^{15} -4.98968 q^{16} +5.32449 q^{17} +1.76113i q^{18} +6.59173 q^{19} +1.31454i q^{20} +3.36519i q^{21} -6.01194i q^{22} -5.36122i q^{23} -1.58223i q^{24} +3.57600 q^{25} +10.4374i q^{26} -1.00000 q^{27} +3.70704i q^{28} +4.69962i q^{29} -2.10159 q^{30} -1.97395 q^{31} -5.62303i q^{32} +3.41368 q^{33} +9.37713i q^{34} -4.01573 q^{35} -1.10159 q^{36} -4.07887 q^{37} +11.6089i q^{38} -5.92654 q^{39} +1.88810 q^{40} -3.22214i q^{41} -5.92654 q^{42} -2.11055i q^{43} +3.76046 q^{44} -1.19332i q^{45} +9.44181 q^{46} -1.55088 q^{47} +4.98968 q^{48} -4.32449 q^{49} +6.29781i q^{50} -5.32449 q^{51} -6.52859 q^{52} +9.86204i q^{53} -1.76113i q^{54} +4.07360i q^{55} +5.32449 q^{56} -6.59173 q^{57} -8.27665 q^{58} -3.30751i q^{59} -1.31454i q^{60} -8.66872i q^{61} -3.47639i q^{62} -3.36519i q^{63} -0.0764624 q^{64} -7.07223i q^{65} +6.01194i q^{66} -6.28647 q^{67} -5.86538 q^{68} +5.36122i q^{69} -7.07223i q^{70} +12.3940 q^{71} +1.58223i q^{72} -6.38852i q^{73} -7.18343i q^{74} -3.57600 q^{75} -7.26135 q^{76} +11.4877i q^{77} -10.4374i q^{78} -13.2981i q^{79} +5.95426i q^{80} +1.00000 q^{81} +5.67461 q^{82} +4.86229i q^{83} -3.70704i q^{84} -6.35380i q^{85} +3.71696 q^{86} -4.69962i q^{87} -5.40122i q^{88} -9.74816 q^{89} +2.10159 q^{90} -19.9439i q^{91} +5.90584i q^{92} +1.97395 q^{93} -2.73130i q^{94} -7.86601i q^{95} +5.62303i q^{96} +9.09824i q^{97} -7.61600i q^{98} -3.41368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{3} - 6 q^{4} + 12 q^{9}+O(q^{10}) \) 12 * q - 12 * q^3 - 6 * q^4 + 12 * q^9	\( 12 q - 12 q^{3} - 6 q^{4} + 12 q^{9} + 18 q^{10} - 2 q^{11} + 6 q^{12} + 4 q^{13} + 4 q^{14} + 10 q^{16} + 2 q^{17} + 4 q^{19} + 12 q^{25} - 12 q^{27} - 18 q^{30} + 2 q^{31} + 2 q^{33} - 4 q^{35} - 6 q^{36} - 2 q^{37} - 4 q^{39} - 40 q^{40} - 4 q^{42} - 36 q^{44} + 34 q^{47} - 10 q^{48} + 10 q^{49} - 2 q^{51} - 6 q^{52} + 2 q^{56} - 4 q^{57} + 24 q^{58} + 28 q^{64} - 38 q^{67} + 32 q^{68} - 26 q^{71} - 12 q^{75} - 28 q^{76} + 12 q^{81} - 50 q^{82} + 6 q^{86} - 4 q^{89} + 18 q^{90} - 2 q^{93} - 2 q^{99}+O(q^{100}) \) 12 * q - 12 * q^3 - 6 * q^4 + 12 * q^9 + 18 * q^10 - 2 * q^11 + 6 * q^12 + 4 * q^13 + 4 * q^14 + 10 * q^16 + 2 * q^17 + 4 * q^19 + 12 * q^25 - 12 * q^27 - 18 * q^30 + 2 * q^31 + 2 * q^33 - 4 * q^35 - 6 * q^36 - 2 * q^37 - 4 * q^39 - 40 * q^40 - 4 * q^42 - 36 * q^44 + 34 * q^47 - 10 * q^48 + 10 * q^49 - 2 * q^51 - 6 * q^52 + 2 * q^56 - 4 * q^57 + 24 * q^58 + 28 * q^64 - 38 * q^67 + 32 * q^68 - 26 * q^71 - 12 * q^75 - 28 * q^76 + 12 * q^81 - 50 * q^82 + 6 * q^86 - 4 * q^89 + 18 * q^90 - 2 * q^93 - 2 * q^99

Introduction

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