LMFDB - Embedded newform 189.2.f.b.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(64,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("189.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.f (of order $3$, degree $2$, not 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			64.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	189.64
Dual form			189.2.f.b.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.439693 - 0.761570i) q^{2} +(0.613341 - 1.06234i) q^{4} +(0.673648 - 1.16679i) q^{5} +(-0.500000 - 0.866025i) q^{7} -2.83750 q^{8} +O(q^{10})$	\(q+(-0.439693 - 0.761570i) q^{2} +(0.613341 - 1.06234i) q^{4} +(0.673648 - 1.16679i) q^{5} +(-0.500000 - 0.866025i) q^{7} -2.83750 q^{8} -1.18479 q^{10} +(0.826352 + 1.43128i) q^{11} +(1.68479 - 2.91815i) q^{13} +(-0.439693 + 0.761570i) q^{14} +(0.0209445 + 0.0362770i) q^{16} -0.467911 q^{17} -3.22668 q^{19} +(-0.826352 - 1.43128i) q^{20} +(0.726682 - 1.25865i) q^{22} +(4.47178 - 7.74535i) q^{23} +(1.59240 + 2.75811i) q^{25} -2.96316 q^{26} -1.22668 q^{28} +(3.13429 + 5.42874i) q^{29} +(-4.61721 + 7.99724i) q^{31} +(-2.81908 + 4.88279i) q^{32} +(0.205737 + 0.356347i) q^{34} -1.34730 q^{35} +9.23442 q^{37} +(1.41875 + 2.45734i) q^{38} +(-1.91147 + 3.31077i) q^{40} +(1.70574 - 2.95442i) q^{41} +(2.20574 + 3.82045i) q^{43} +2.02734 q^{44} -7.86484 q^{46} +(4.67752 + 8.10170i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(1.40033 - 2.42544i) q^{50} +(-2.06670 - 3.57964i) q^{52} +0.573978 q^{53} +2.22668 q^{55} +(1.41875 + 2.45734i) q^{56} +(2.75624 - 4.77396i) q^{58} +(-5.19846 + 9.00400i) q^{59} +(-3.81908 - 6.61484i) q^{61} +8.12061 q^{62} +5.04189 q^{64} +(-2.26991 - 3.93161i) q^{65} +(-0.298133 + 0.516382i) q^{67} +(-0.286989 + 0.497079i) q^{68} +(0.592396 + 1.02606i) q^{70} +0.554378 q^{71} +2.04963 q^{73} +(-4.06031 - 7.03266i) q^{74} +(-1.97906 + 3.42782i) q^{76} +(0.826352 - 1.43128i) q^{77} +(1.20187 + 2.08169i) q^{79} +0.0564370 q^{80} -3.00000 q^{82} +(-7.52481 - 13.0334i) q^{83} +(-0.315207 + 0.545955i) q^{85} +(1.93969 - 3.35965i) q^{86} +(-2.34477 - 4.06126i) q^{88} -9.08647 q^{89} -3.36959 q^{91} +(-5.48545 - 9.50108i) q^{92} +(4.11334 - 7.12452i) q^{94} +(-2.17365 + 3.76487i) q^{95} +(0.949493 + 1.64457i) q^{97} +0.879385 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 3 q^{7} - 12 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 3 * q^7 - 12 * q^8	$ 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 3 q^{7} - 12 q^{8} + 6 q^{11} + 3 q^{13} + 3 q^{14} - 3 q^{16} - 12 q^{17} - 6 q^{19} - 6 q^{20} - 9 q^{22} + 12 q^{23} + 6 q^{25} + 6 q^{26} + 6 q^{28} + 9 q^{29} + 3 q^{31} - 9 q^{34} - 6 q^{35} - 6 q^{37} + 6 q^{38} + 9 q^{40} + 3 q^{43} - 30 q^{44} + 3 q^{47} - 3 q^{49} - 6 q^{50} + 21 q^{52} - 12 q^{53} + 6 q^{56} + 9 q^{58} - 3 q^{59} - 6 q^{61} + 60 q^{62} + 24 q^{64} + 15 q^{65} + 12 q^{67} + 6 q^{68} - 18 q^{71} - 42 q^{73} - 30 q^{74} - 15 q^{76} + 6 q^{77} + 21 q^{79} + 30 q^{80} - 18 q^{82} - 18 q^{83} - 9 q^{85} + 6 q^{86} - 27 q^{88} - 24 q^{89} - 6 q^{91} + 3 q^{92} + 18 q^{94} - 12 q^{95} + 3 q^{97} - 6 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 3 * q^7 - 12 * q^8 + 6 * q^11 + 3 * q^13 + 3 * q^14 - 3 * q^16 - 12 * q^17 - 6 * q^19 - 6 * q^20 - 9 * q^22 + 12 * q^23 + 6 * q^25 + 6 * q^26 + 6 * q^28 + 9 * q^29 + 3 * q^31 - 9 * q^34 - 6 * q^35 - 6 * q^37 + 6 * q^38 + 9 * q^40 + 3 * q^43 - 30 * q^44 + 3 * q^47 - 3 * q^49 - 6 * q^50 + 21 * q^52 - 12 * q^53 + 6 * q^56 + 9 * q^58 - 3 * q^59 - 6 * q^61 + 60 * q^62 + 24 * q^64 + 15 * q^65 + 12 * q^67 + 6 * q^68 - 18 * q^71 - 42 * q^73 - 30 * q^74 - 15 * q^76 + 6 * q^77 + 21 * q^79 + 30 * q^80 - 18 * q^82 - 18 * q^83 - 9 * q^85 + 6 * q^86 - 27 * q^88 - 24 * q^89 - 6 * q^91 + 3 * q^92 + 18 * q^94 - 12 * q^95 + 3 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.439693	−	0.761570i	−0.310910	−	0.538511i	0.667650	−	0.744475i	$-0.267300\pi$
$2$	−0.439693	−	0.761570i	−0.310910	−	0.538511i	−0.978560	+	0.205964i	$0.933967\pi$
$3$		0			0
$3$		0			0
$4$	0.613341	−	1.06234i	0.306670	−	0.531169i
$5$	0.673648	−	1.16679i	0.301265	−	0.521806i	−0.675158	−	0.737673i	$-0.735925\pi$
$5$	0.673648	−	1.16679i	0.301265	−	0.521806i	0.976423	+	0.215867i	$0.0692579\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	−2.83750			−1.00321
$9$		0			0
$10$	−1.18479			−0.374664
$11$	0.826352	+	1.43128i	0.249154	+	0.431548i	0.963291	−	0.268458i	$-0.0865140\pi$
$11$	0.826352	+	1.43128i	0.249154	+	0.431548i	−0.714137	+	0.700006i	$0.753181\pi$
$12$		0			0
$13$	1.68479	−	2.91815i	0.467277	−	0.809348i	−0.532024	−	0.846729i	$-0.678568\pi$
$13$	1.68479	−	2.91815i	0.467277	−	0.809348i	0.999301	+	0.0373813i	$0.0119016\pi$
$14$	−0.439693	+	0.761570i	−0.117513	+	0.203538i
$15$		0			0
$16$	0.0209445	+	0.0362770i	0.00523613	+	0.00906925i
$17$	−0.467911			−0.113485			−0.0567426	−	0.998389i	$-0.518071\pi$
$17$	−0.467911			−0.113485			−0.0567426	+	0.998389i	$0.518071\pi$
$18$		0			0
$19$	−3.22668			−0.740252			−0.370126	−	0.928982i	$-0.620685\pi$
$19$	−3.22668			−0.740252			−0.370126	+	0.928982i	$0.620685\pi$
$20$	−0.826352	−	1.43128i	−0.184778	−	0.320045i
$21$		0			0
$22$	0.726682	−	1.25865i	0.154929	−	0.268345i
$23$	4.47178	−	7.74535i	0.932431	−	1.61502i	0.153279	−	0.988183i	$-0.451017\pi$
$23$	4.47178	−	7.74535i	0.932431	−	1.61502i	0.779152	−	0.626835i	$-0.215650\pi$
$24$		0			0
$25$	1.59240	+	2.75811i	0.318479	+	0.551622i
$26$	−2.96316			−0.581124
$27$		0			0
$28$	−1.22668			−0.231821
$29$	3.13429	+	5.42874i	0.582022	+	1.00809i	0.995239	+	0.0974595i	$0.0310717\pi$
$29$	3.13429	+	5.42874i	0.582022	+	1.00809i	−0.413217	+	0.910632i	$0.635595\pi$
$30$		0			0
$31$	−4.61721	+	7.99724i	−0.829276	+	1.43635i	0.0693317	+	0.997594i	$0.477913\pi$
$31$	−4.61721	+	7.99724i	−0.829276	+	1.43635i	−0.898607	+	0.438754i	$0.855420\pi$
$32$	−2.81908	+	4.88279i	−0.498347	+	0.863163i
$33$		0			0
$34$	0.205737	+	0.356347i	0.0352836	+	0.0611130i
$35$	−1.34730			−0.227735
$36$		0			0
$37$	9.23442			1.51813			0.759065	−	0.651015i	$-0.225657\pi$
$37$	9.23442			1.51813			0.759065	+	0.651015i	$0.225657\pi$
$38$	1.41875	+	2.45734i	0.230151	+	0.398634i
$39$		0			0
$40$	−1.91147	+	3.31077i	−0.302231	+	0.523479i
$41$	1.70574	−	2.95442i	0.266391	−	0.461403i	−0.701536	−	0.712634i	$-0.747502\pi$
$41$	1.70574	−	2.95442i	0.266391	−	0.461403i	0.967927	+	0.251231i	$0.0808353\pi$
$42$		0			0
$43$	2.20574	+	3.82045i	0.336372	+	0.582613i	0.983747	−	0.179558i	$-0.0574668\pi$
$43$	2.20574	+	3.82045i	0.336372	+	0.582613i	−0.647376	+	0.762171i	$0.724133\pi$
$44$	2.02734			0.305633
$45$		0			0
$46$	−7.86484			−1.15961
$47$	4.67752	+	8.10170i	0.682286	+	1.18175i	0.974281	+	0.225335i	$0.0723475\pi$
$47$	4.67752	+	8.10170i	0.682286	+	1.18175i	−0.291995	+	0.956420i	$0.594319\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	1.40033	−	2.42544i	0.198037	−	0.343009i
$51$		0			0
$52$	−2.06670	−	3.57964i	−0.286600	−	0.496406i
$53$	0.573978			0.0788419			0.0394210	−	0.999223i	$-0.487449\pi$
$53$	0.573978			0.0788419			0.0394210	+	0.999223i	$0.487449\pi$
$54$		0			0
$55$	2.22668			0.300246
$56$	1.41875	+	2.45734i	0.189588	+	0.328376i
$57$		0			0
$58$	2.75624	−	4.77396i	0.361913	−	0.626851i
$59$	−5.19846	+	9.00400i	−0.676782	+	1.17222i	0.299162	+	0.954202i	$0.403293\pi$
$59$	−5.19846	+	9.00400i	−0.676782	+	1.17222i	−0.975945	+	0.218019i	$0.930041\pi$
$60$		0			0
$61$	−3.81908	−	6.61484i	−0.488983	−	0.846943i	0.510937	−	0.859618i	$-0.329299\pi$
$61$	−3.81908	−	6.61484i	−0.488983	−	0.846943i	−0.999920	+	0.0126752i	$0.995965\pi$
$62$	8.12061			1.03132
$63$		0			0
$64$	5.04189			0.630236
$65$	−2.26991	−	3.93161i	−0.281548	−	0.487656i
$66$		0			0
$67$	−0.298133	+	0.516382i	−0.0364228	+	0.0630861i	−0.883662	−	0.468125i	$-0.844930\pi$
$67$	−0.298133	+	0.516382i	−0.0364228	+	0.0630861i	0.847239	+	0.531211i	$0.178263\pi$
$68$	−0.286989	+	0.497079i	−0.0348025	+	0.0602797i
$69$		0			0
$70$	0.592396	+	1.02606i	0.0708049	+	0.122638i
$71$	0.554378			0.0657925			0.0328963	−	0.999459i	$-0.489527\pi$
$71$	0.554378			0.0657925			0.0328963	+	0.999459i	$0.489527\pi$
$72$		0			0
$73$	2.04963			0.239891			0.119946	−	0.992780i	$-0.461728\pi$
$73$	2.04963			0.239891			0.119946	+	0.992780i	$0.461728\pi$
$74$	−4.06031	−	7.03266i	−0.472001	−	0.817530i
$75$		0			0
$76$	−1.97906	+	3.42782i	−0.227013	+	0.393198i
$77$	0.826352	−	1.43128i	0.0941715	−	0.163110i
$78$		0			0
$79$	1.20187	+	2.08169i	0.135221	+	0.234209i	0.925682	−	0.378303i	$-0.123492\pi$
$79$	1.20187	+	2.08169i	0.135221	+	0.234209i	−0.790461	+	0.612512i	$0.790159\pi$
$80$	0.0564370			0.00630985
$81$		0			0
$82$	−3.00000			−0.331295
$83$	−7.52481	−	13.0334i	−0.825956	−	1.43060i	−0.901187	−	0.433431i	$-0.857303\pi$
$83$	−7.52481	−	13.0334i	−0.825956	−	1.43060i	0.0752309	−	0.997166i	$-0.476031\pi$
$84$		0			0
$85$	−0.315207	+	0.545955i	−0.0341891	+	0.0592172i
$86$	1.93969	−	3.35965i	0.209162	−	0.362280i
$87$		0			0
$88$	−2.34477	−	4.06126i	−0.249953	−	0.432932i
$89$	−9.08647			−0.963164			−0.481582	−	0.876401i	$-0.659938\pi$
$89$	−9.08647			−0.963164			−0.481582	+	0.876401i	$0.659938\pi$
$90$		0			0
$91$	−3.36959			−0.353228
$92$	−5.48545	−	9.50108i	−0.571898	−	0.990556i
$93$		0			0
$94$	4.11334	−	7.12452i	0.424259	−	0.734838i
$95$	−2.17365	+	3.76487i	−0.223012	+	0.386267i
$96$		0			0
$97$	0.949493	+	1.64457i	0.0964064	+	0.166981i	0.910195	−	0.414181i	$-0.135932\pi$
$97$	0.949493	+	1.64457i	0.0964064	+	0.166981i	−0.813788	+	0.581161i	$0.802598\pi$
$98$	0.879385			0.0888313
$99$		0			0
$100$	3.90673			0.390673
$101$	−0.854570	−	1.48016i	−0.0850329	−	0.147281i	0.820372	−	0.571830i	$-0.193766\pi$
$101$	−0.854570	−	1.48016i	−0.0850329	−	0.147281i	−0.905405	+	0.424548i	$0.860433\pi$
$102$		0			0
$103$	1.81908	−	3.15074i	0.179239	−	0.310451i	−0.762381	−	0.647128i	$-0.775970\pi$
$103$	1.81908	−	3.15074i	0.179239	−	0.310451i	0.941620	+	0.336677i	$0.109303\pi$
$104$	−4.78059	+	8.28023i	−0.468776	+	0.811943i
$105$		0			0
$106$	−0.252374	−	0.437124i	−0.0245127	−	0.0424573i
$107$	−7.12836			−0.689124			−0.344562	−	0.938764i	$-0.611973\pi$
$107$	−7.12836			−0.689124			−0.344562	+	0.938764i	$0.611973\pi$
$108$		0			0
$109$	0.403733			0.0386706			0.0193353	−	0.999813i	$-0.493845\pi$
$109$	0.403733			0.0386706			0.0193353	+	0.999813i	$0.493845\pi$
$110$	−0.979055	−	1.69577i	−0.0933493	−	0.161686i
$111$		0			0
$112$	0.0209445	−	0.0362770i	0.00197907	−	0.00342785i
$113$	7.18479	−	12.4444i	0.675888	−	1.17067i	−0.300320	−	0.953839i	$-0.597093\pi$
$113$	7.18479	−	12.4444i	0.675888	−	1.17067i	0.976208	−	0.216835i	$-0.0695732\pi$
$114$		0			0
$115$	−6.02481	−	10.4353i	−0.561817	−	0.973095i
$116$	7.68954			0.713956
$117$		0			0
$118$	9.14290			0.841672
$119$	0.233956	+	0.405223i	0.0214467	+	0.0371467i
$120$		0			0
$121$	4.13429	−	7.16079i	0.375844	−	0.650981i
$122$	−3.35844	+	5.81699i	−0.304059	+	0.526646i
$123$		0			0
$124$	5.66385	+	9.81007i	0.508629	+	0.880971i
$125$	11.0273			0.986315
$126$		0			0
$127$	−20.7716			−1.84318			−0.921589	−	0.388167i	$-0.873108\pi$
$127$	−20.7716			−1.84318			−0.921589	+	0.388167i	$0.873108\pi$
$128$	3.42127	+	5.92582i	0.302401	+	0.523774i
$129$		0			0
$130$	−1.99613	+	3.45740i	−0.175072	+	0.303234i
$131$	−3.58260	+	6.20524i	−0.313013	+	0.542154i	−0.979013	−	0.203797i	$-0.934672\pi$
$131$	−3.58260	+	6.20524i	−0.313013	+	0.542154i	0.666000	+	0.745952i	$0.268005\pi$
$132$		0			0
$133$	1.61334	+	2.79439i	0.139894	+	0.242304i
$134$	0.524348			0.0452968
$135$		0			0
$136$	1.32770			0.113849
$137$	1.28446	+	2.22475i	0.109739	+	0.190074i	0.915665	−	0.401943i	$-0.131665\pi$
$137$	1.28446	+	2.22475i	0.109739	+	0.190074i	−0.805925	+	0.592017i	$0.798332\pi$
$138$		0			0
$139$	3.06670	−	5.31169i	0.260114	−	0.450531i	−0.706158	−	0.708055i	$-0.749573\pi$
$139$	3.06670	−	5.31169i	0.260114	−	0.450531i	0.966272	+	0.257523i	$0.0829064\pi$
$140$	−0.826352	+	1.43128i	−0.0698395	+	0.120966i
$141$		0			0
$142$	−0.243756	−	0.422197i	−0.0204555	−	0.0354300i
$143$	5.56893			0.465697
$144$		0			0
$145$	8.44562			0.701371
$146$	−0.901207	−	1.56094i	−0.0745844	−	0.129184i
$147$		0			0
$148$	5.66385	−	9.81007i	0.465565	−	0.806383i
$149$	0.215537	−	0.373321i	0.0176575	−	0.0305837i	−0.857062	−	0.515214i	$-0.827712\pi$
$149$	0.215537	−	0.373321i	0.0176575	−	0.0305837i	0.874719	+	0.484630i	$0.161046\pi$
$150$		0			0
$151$	1.23530	+	2.13960i	0.100527	+	0.174118i	0.911902	−	0.410408i	$-0.134614\pi$
$151$	1.23530	+	2.13960i	0.100527	+	0.174118i	−0.811375	+	0.584526i	$0.801280\pi$
$152$	9.15570			0.742625
$153$		0			0
$154$	−1.45336			−0.117115
$155$	6.22075	+	10.7747i	0.499663	+	0.865441i
$156$		0			0
$157$	−5.06670	+	8.77579i	−0.404367	+	0.700384i	−0.994248	−	0.107106i	$-0.965841\pi$
$157$	−5.06670	+	8.77579i	−0.404367	+	0.700384i	0.589881	+	0.807491i	$0.299175\pi$
$158$	1.05690	−	1.83061i	0.0840828	−	0.145636i
$159$		0			0
$160$	3.79813	+	6.57856i	0.300269	+	0.520081i
$161$	−8.94356			−0.704852
$162$		0			0
$163$	−2.59627			−0.203355			−0.101678	−	0.994817i	$-0.532421\pi$
$163$	−2.59627			−0.203355			−0.101678	+	0.994817i	$0.532421\pi$
$164$	−2.09240	−	3.62414i	−0.163389	−	0.282998i
$165$		0			0
$166$	−6.61721	+	11.4613i	−0.513595	+	0.889573i
$167$	−11.5915	+	20.0771i	−0.896979	+	1.55361i	−0.0656422	+	0.997843i	$0.520910\pi$
$167$	−11.5915	+	20.0771i	−0.896979	+	1.55361i	−0.831337	+	0.555769i	$0.812424\pi$
$168$		0			0
$169$	0.822948	+	1.42539i	0.0633037	+	0.109645i
$170$	0.554378			0.0425188
$171$		0			0
$172$	5.41147			0.412621
$173$	−2.37598	−	4.11532i	−0.180643	−	0.312882i	0.761457	−	0.648215i	$-0.224484\pi$
$173$	−2.37598	−	4.11532i	−0.180643	−	0.312882i	−0.942100	+	0.335333i	$0.891151\pi$
$174$		0			0
$175$	1.59240	−	2.75811i	0.120374	−	0.208494i
$176$	−0.0346151	+	0.0599551i	−0.00260921	+	0.00451929i
$177$		0			0
$178$	3.99525	+	6.91998i	0.299457	+	0.518674i
$179$	8.53209			0.637718			0.318859	−	0.947802i	$-0.396700\pi$
$179$	8.53209			0.637718			0.318859	+	0.947802i	$0.396700\pi$
$180$		0			0
$181$	−17.2344			−1.28102			−0.640512	−	0.767948i	$-0.721278\pi$
$181$	−17.2344			−1.28102			−0.640512	+	0.767948i	$0.721278\pi$
$182$	1.48158	+	2.56617i	0.109822	+	0.190218i
$183$		0			0
$184$	−12.6887	+	21.9774i	−0.935421	+	1.62020i
$185$	6.22075	−	10.7747i	0.457359	−	0.792169i
$186$		0			0
$187$	−0.386659	−	0.669713i	−0.0282753	−	0.0489743i
$188$	11.4757			0.836948
$189$		0			0
$190$	3.82295			0.277346
$191$	6.45471	+	11.1799i	0.467046	+	0.808948i	0.999291	−	0.0376425i	$-0.0119848\pi$
$191$	6.45471	+	11.1799i	0.467046	+	0.808948i	−0.532245	+	0.846590i	$0.678651\pi$
$192$		0			0
$193$	0.319078	−	0.552659i	0.0229677	−	0.0397813i	−0.854313	−	0.519759i	$-0.826022\pi$
$193$	0.319078	−	0.552659i	0.0229677	−	0.0397813i	0.877281	+	0.479977i	$0.159355\pi$
$194$	0.834970	−	1.44621i	0.0599473	−	0.103832i
$195$		0			0
$196$	0.613341	+	1.06234i	0.0438101	+	0.0758812i
$197$	−11.4456			−0.815467			−0.407733	−	0.913101i	$-0.633681\pi$
$197$	−11.4456			−0.815467			−0.407733	+	0.913101i	$0.633681\pi$
$198$		0			0
$199$	−3.63816			−0.257902			−0.128951	−	0.991651i	$-0.541161\pi$
$199$	−3.63816			−0.257902			−0.128951	+	0.991651i	$0.541161\pi$
$200$	−4.51842	−	7.82613i	−0.319500	−	0.553391i
$201$		0			0
$202$	−0.751497	+	1.30163i	−0.0528751	+	0.0915824i
$203$	3.13429	−	5.42874i	0.219984	−	0.381023i
$204$		0			0
$205$	−2.29813	−	3.98048i	−0.160509	−	0.278009i
$206$	−3.19934			−0.222909
$207$		0			0
$208$	0.141149			0.00978691
$209$	−2.66637	−	4.61830i	−0.184437	−	0.319454i
$210$		0			0
$211$	−2.91147	+	5.04282i	−0.200434	+	0.347162i	−0.948668	−	0.316273i	$-0.897569\pi$
$211$	−2.91147	+	5.04282i	−0.200434	+	0.347162i	0.748234	+	0.663435i	$0.230902\pi$
$212$	0.352044	−	0.609758i	0.0241785	−	0.0418784i
$213$		0			0
$214$	3.13429	+	5.42874i	0.214255	+	0.371101i
$215$	5.94356			0.405348
$216$		0			0
$217$	9.23442			0.626873
$218$	−0.177519	−	0.307471i	−0.0120231	−	0.0208246i
$219$		0			0
$220$	1.36571	−	2.36549i	0.0920765	−	0.159481i
$221$	−0.788333	+	1.36543i	−0.0530290	+	0.0918490i
$222$		0			0
$223$	−3.54189	−	6.13473i	−0.237182	−	0.410812i	0.722722	−	0.691139i	$-0.242891\pi$
$223$	−3.54189	−	6.13473i	−0.237182	−	0.410812i	−0.959905	+	0.280327i	$0.909557\pi$
$224$	5.63816			0.376715
$225$		0			0
$226$	−12.6364			−0.840561
$227$	−5.97178	−	10.3434i	−0.396361	−	0.686517i	0.596913	−	0.802306i	$-0.296394\pi$
$227$	−5.97178	−	10.3434i	−0.396361	−	0.686517i	−0.993274	+	0.115789i	$0.963060\pi$
$228$		0			0
$229$	8.77631	−	15.2010i	0.579955	−	1.00451i	−0.415529	−	0.909580i	$-0.636403\pi$
$229$	8.77631	−	15.2010i	0.579955	−	1.00451i	0.995484	−	0.0949315i	$-0.0302632\pi$
$230$	−5.29813	+	9.17664i	−0.349349	+	0.605089i
$231$		0			0
$232$	−8.89352	−	15.4040i	−0.583888	−	1.01132i
$233$	−16.2540			−1.06484			−0.532418	−	0.846481i	$-0.678717\pi$
$233$	−16.2540			−1.06484			−0.532418	+	0.846481i	$0.678717\pi$
$234$		0			0
$235$	12.6040			0.822195
$236$	6.37686	+	11.0450i	0.415098	+	0.718971i
$237$		0			0
$238$	0.205737	−	0.356347i	0.0133360	−	0.0230985i
$239$	−7.54963	+	13.0763i	−0.488345	+	0.845838i	−0.999910	−	0.0134062i	$-0.995733\pi$
$239$	−7.54963	+	13.0763i	−0.488345	+	0.845838i	0.511565	+	0.859244i	$0.329066\pi$
$240$		0			0
$241$	7.81908	+	13.5430i	0.503671	+	0.872384i	0.999991	+	0.00424420i	$0.00135097\pi$
$241$	7.81908	+	13.5430i	0.503671	+	0.872384i	−0.496320	+	0.868140i	$0.665316\pi$
$242$	−7.27126			−0.467414
$243$		0			0
$244$	−9.36959			−0.599826
$245$	0.673648	+	1.16679i	0.0430378	+	0.0745437i
$246$		0			0
$247$	−5.43629	+	9.41593i	−0.345903	+	0.599121i
$248$	13.1013	−	22.6922i	0.831935	−	1.44095i
$249$		0			0
$250$	−4.84864	−	8.39809i	−0.306655	−	0.531142i
$251$	−19.0651			−1.20338			−0.601690	−	0.798730i	$-0.705506\pi$
$251$	−19.0651			−1.20338			−0.601690	+	0.798730i	$0.705506\pi$
$252$		0			0
$253$	14.7811			0.929277
$254$	9.13310	+	15.8190i	0.573062	+	0.992572i
$255$		0			0
$256$	8.05051	−	13.9439i	0.503157	−	0.871493i
$257$	13.2909	−	23.0204i	0.829061	−	1.43598i	−0.0697146	−	0.997567i	$-0.522209\pi$
$257$	13.2909	−	23.0204i	0.829061	−	1.43598i	0.898776	−	0.438409i	$-0.144458\pi$
$258$		0			0
$259$	−4.61721	−	7.99724i	−0.286900	−	0.496925i
$260$	−5.56893			−0.345370
$261$		0			0
$262$	6.30096			0.389275
$263$	−0.367059	−	0.635765i	−0.0226338	−	0.0392029i	0.854487	−	0.519473i	$-0.173872\pi$
$263$	−0.367059	−	0.635765i	−0.0226338	−	0.0392029i	−0.877120	+	0.480270i	$0.840539\pi$
$264$		0			0
$265$	0.386659	−	0.669713i	0.0237523	−	0.0411402i
$266$	1.41875	−	2.45734i	0.0869890	−	0.150669i
$267$		0			0
$268$	0.365715	+	0.633436i	0.0223396	+	0.0386933i
$269$	20.8503			1.27126			0.635632	−	0.771992i	$-0.280739\pi$
$269$	20.8503			1.27126			0.635632	+	0.771992i	$0.280739\pi$
$270$		0			0
$271$	6.95811			0.422675			0.211338	−	0.977413i	$-0.432218\pi$
$271$	6.95811			0.422675			0.211338	+	0.977413i	$0.432218\pi$
$272$	−0.00980018	−	0.0169744i	−0.000594223	−	0.00102922i
$273$		0			0
$274$	1.12954	−	1.95642i	0.0682379	−	0.118191i
$275$	−2.63176	+	4.55834i	−0.158701	+	0.274878i
$276$		0			0
$277$	−8.93629	−	15.4781i	−0.536930	−	0.929989i	−0.999067	−	0.0431811i	$-0.986251\pi$
$277$	−8.93629	−	15.4781i	−0.536930	−	0.929989i	0.462138	−	0.886808i	$-0.347083\pi$
$278$	−5.39363			−0.323488
$279$		0			0
$280$	3.82295			0.228465
$281$	11.1552	+	19.3214i	0.665465	+	1.15262i	0.979159	+	0.203095i	$0.0651001\pi$
$281$	11.1552	+	19.3214i	0.665465	+	1.15262i	−0.313694	+	0.949524i	$0.601567\pi$
$282$		0			0
$283$	9.29726	−	16.1033i	0.552665	−	0.957243i	−0.445417	−	0.895323i	$-0.646944\pi$
$283$	9.29726	−	16.1033i	0.552665	−	0.957243i	0.998081	−	0.0619196i	$-0.0197222\pi$
$284$	0.340022	−	0.588936i	0.0201766	−	0.0349469i
$285$		0			0
$286$	−2.44862	−	4.24113i	−0.144790	−	0.250783i
$287$	−3.41147			−0.201373
$288$		0			0
$289$	−16.7811			−0.987121
$290$	−3.71348	−	6.43193i	−0.218063	−	0.377696i
$291$		0			0
$292$	1.25712	−	2.17740i	0.0735675	−	0.127423i
$293$	6.54576	−	11.3376i	0.382407	−	0.662349i	−0.608998	−	0.793171i	$-0.708428\pi$
$293$	6.54576	−	11.3376i	0.382407	−	0.662349i	0.991406	+	0.130822i	$0.0417618\pi$
$294$		0			0
$295$	7.00387	+	12.1311i	0.407781	+	0.706298i
$296$	−26.2026			−1.52300
$297$		0			0
$298$	−0.379081			−0.0219595
$299$	−15.0680	−	26.0986i	−0.871408	−	1.50932i
$300$		0			0
$301$	2.20574	−	3.82045i	0.127137	−	0.220207i
$302$	1.08630	−	1.88153i	0.0625098	−	0.108270i
$303$		0			0
$304$	−0.0675813	−	0.117054i	−0.00387606	−	0.00671353i
$305$	−10.2909			−0.589253
$306$		0			0
$307$	6.31046			0.360157			0.180078	−	0.983652i	$-0.442365\pi$
$307$	6.31046			0.360157			0.180078	+	0.983652i	$0.442365\pi$
$308$	−1.01367	−	1.75573i	−0.0577592	−	0.100042i
$309$		0			0
$310$	5.47044	−	9.47508i	0.310700	−	0.538148i
$311$	−4.76217	+	8.24833i	−0.270038	+	0.467720i	−0.968871	−	0.247565i	$-0.920370\pi$
$311$	−4.76217	+	8.24833i	−0.270038	+	0.467720i	0.698833	+	0.715285i	$0.253703\pi$
$312$		0			0
$313$	8.81433	+	15.2669i	0.498215	+	0.862934i	0.999998	−	0.00205946i	$-0.000655547\pi$
$313$	8.81433	+	15.2669i	0.498215	+	0.862934i	−0.501782	+	0.864994i	$0.667322\pi$
$314$	8.91117			0.502886
$315$		0			0
$316$	2.94862			0.165873
$317$	4.03849	+	6.99486i	0.226824	+	0.392871i	0.956865	−	0.290533i	$-0.0938325\pi$
$317$	4.03849	+	6.99486i	0.226824	+	0.392871i	−0.730041	+	0.683403i	$0.760499\pi$
$318$		0			0
$319$	−5.18004	+	8.97210i	−0.290027	+	0.502341i
$320$	3.39646	−	5.88284i	0.189868	−	0.328861i
$321$		0			0
$322$	3.93242	+	6.81115i	0.219145	+	0.379570i
$323$	1.50980			0.0840075
$324$		0			0
$325$	10.7314			0.595273
$326$	1.14156	+	1.97724i	0.0632251	+	0.109509i
$327$		0			0
$328$	−4.84002	+	8.38316i	−0.267246	+	0.462883i
$329$	4.67752	−	8.10170i	0.257880	−	0.446661i
$330$		0			0
$331$	−11.5248	−	19.9616i	−0.633461	−	1.09719i	−0.986839	−	0.161706i	$-0.948300\pi$
$331$	−11.5248	−	19.9616i	−0.633461	−	1.09719i	0.353378	−	0.935481i	$-0.385033\pi$
$332$	−18.4611			−1.01318
$333$		0			0
$334$	20.3868			1.11552
$335$	0.401674	+	0.695720i	0.0219458	+	0.0380112i
$336$		0			0
$337$	−14.5116	+	25.1348i	−0.790498	+	1.36918i	0.135161	+	0.990824i	$0.456845\pi$
$337$	−14.5116	+	25.1348i	−0.790498	+	1.36918i	−0.925659	+	0.378359i	$0.876489\pi$
$338$	0.723689	−	1.25347i	0.0393635	−	0.0681795i
$339$		0			0
$340$	0.386659	+	0.669713i	0.0209695	+	0.0363203i
$341$	−15.2618			−0.826471
$342$		0			0
$343$	1.00000			0.0539949
$344$	−6.25877	−	10.8405i	−0.337450	−	0.584481i
$345$		0			0
$346$	−2.08940	+	3.61895i	−0.112327	+	0.194556i
$347$	6.47313	−	11.2118i	0.347496	−	0.601880i	−0.638308	−	0.769781i	$-0.720365\pi$
$347$	6.47313	−	11.2118i	0.347496	−	0.601880i	0.985804	+	0.167901i	$0.0536988\pi$
$348$		0			0
$349$	−0.731429	−	1.26687i	−0.0391525	−	0.0678141i	0.845785	−	0.533524i	$-0.179132\pi$
$349$	−0.731429	−	1.26687i	−0.0391525	−	0.0678141i	−0.884938	+	0.465710i	$0.845799\pi$
$350$	−2.80066			−0.149702
$351$		0			0
$352$	−9.31820			−0.496662
$353$	7.16637	+	12.4125i	0.381428	+	0.660652i	0.991267	−	0.131873i	$-0.0420992\pi$
$353$	7.16637	+	12.4125i	0.381428	+	0.660652i	−0.609839	+	0.792525i	$0.708766\pi$
$354$		0			0
$355$	0.373455	−	0.646844i	0.0198210	−	0.0343309i
$356$	−5.57310	+	9.65289i	−0.295374	+	0.511602i
$357$		0			0
$358$	−3.75150	−	6.49778i	−0.198273	−	0.343418i
$359$	20.9368			1.10500			0.552500	−	0.833513i	$-0.313674\pi$
$359$	20.9368			1.10500			0.552500	+	0.833513i	$0.313674\pi$
$360$		0			0
$361$	−8.58853			−0.452028
$362$	7.57785	+	13.1252i	0.398283	+	0.689846i
$363$		0			0
$364$	−2.06670	+	3.57964i	−0.108325	+	0.187624i
$365$	1.38073	−	2.39149i	0.0722707	−	0.125176i
$366$		0			0
$367$	6.02869	+	10.4420i	0.314695	+	0.545067i	0.979373	−	0.202063i	$-0.0647645\pi$
$367$	6.02869	+	10.4420i	0.314695	+	0.545067i	−0.664678	+	0.747130i	$0.731431\pi$
$368$	0.374638			0.0195293
$369$		0			0
$370$	−10.9409			−0.568789
$371$	−0.286989	−	0.497079i	−0.0148997	−	0.0258071i
$372$		0			0
$373$	0.390530	−	0.676417i	0.0202209	−	0.0350235i	−0.855738	−	0.517410i	$-0.826896\pi$
$373$	0.390530	−	0.676417i	0.0202209	−	0.0350235i	0.875959	+	0.482386i	$0.160230\pi$
$374$	−0.340022	+	0.588936i	−0.0175821	+	0.0304532i
$375$		0			0
$376$	−13.2724	−	22.9885i	−0.684474	−	1.18554i
$377$	21.1225			1.08786
$378$		0			0
$379$	−6.92396			−0.355660			−0.177830	−	0.984061i	$-0.556908\pi$
$379$	−6.92396			−0.355660			−0.177830	+	0.984061i	$0.556908\pi$
$380$	2.66637	+	4.61830i	0.136782	+	0.236914i
$381$		0			0
$382$	5.67617	−	9.83142i	0.290418	−	0.503019i
$383$	3.86618	−	6.69642i	0.197553	−	0.342171i	−0.750182	−	0.661232i	$-0.770034\pi$
$383$	3.86618	−	6.69642i	0.197553	−	0.342171i	0.947734	+	0.319061i	$0.103367\pi$
$384$		0			0
$385$	−1.11334	−	1.92836i	−0.0567411	−	0.0982785i
$386$	−0.561185			−0.0285636
$387$		0			0
$388$	2.32945			0.118260
$389$	2.69981	+	4.67620i	0.136886	+	0.237093i	0.926316	−	0.376747i	$-0.122957\pi$
$389$	2.69981	+	4.67620i	0.136886	+	0.237093i	−0.789431	+	0.613840i	$0.789624\pi$
$390$		0			0
$391$	−2.09240	+	3.62414i	−0.105817	+	0.183280i
$392$	1.41875	−	2.45734i	0.0716576	−	0.124115i
$393$		0			0
$394$	5.03256	+	8.71664i	0.253536	+	0.439138i
$395$	3.23854			0.162949
$396$		0			0
$397$	−29.2344			−1.46723			−0.733617	−	0.679563i	$-0.762169\pi$
$397$	−29.2344			−1.46723			−0.733617	+	0.679563i	$0.762169\pi$
$398$	1.59967	+	2.77071i	0.0801842	+	0.138883i
$399$		0			0
$400$	−0.0667040	+	0.115535i	−0.00333520	+	0.00577674i
$401$	−13.6989	+	23.7272i	−0.684092	+	1.18488i	0.289629	+	0.957139i	$0.406468\pi$
$401$	−13.6989	+	23.7272i	−0.684092	+	1.18488i	−0.973721	+	0.227743i	$0.926865\pi$
$402$		0			0
$403$	15.5581	+	26.9474i	0.775003	+	1.34235i
$404$	−2.09657			−0.104308
$405$		0			0
$406$	−5.51249			−0.273580
$407$	7.63088	+	13.2171i	0.378249	+	0.655146i
$408$		0			0
$409$	4.51249	−	7.81586i	0.223128	−	0.386469i	−0.732628	−	0.680629i	$-0.761706\pi$
$409$	4.51249	−	7.81586i	0.223128	−	0.386469i	0.955756	+	0.294160i	$0.0950398\pi$
$410$	−2.02094	+	3.50038i	−0.0998073	+	0.172871i
$411$		0			0
$412$	−2.23143	−	3.86495i	−0.109935	−	0.190412i
$413$	10.3969			0.511599
$414$		0			0
$415$	−20.2763			−0.995325
$416$	9.49912	+	16.4530i	0.465733	+	0.806673i
$417$		0			0
$418$	−2.34477	+	4.06126i	−0.114686	+	0.198643i
$419$	0.0876485	−	0.151812i	0.00428191	−	0.00741649i	−0.863877	−	0.503704i	$-0.831970\pi$
$419$	0.0876485	−	0.151812i	0.00428191	−	0.00741649i	0.868158	+	0.496287i	$0.165304\pi$
$420$		0			0
$421$	12.3525	+	21.3952i	0.602025	+	1.04274i	0.992514	+	0.122130i	$0.0389724\pi$
$421$	12.3525	+	21.3952i	0.602025	+	1.04274i	−0.390490	+	0.920607i	$0.627694\pi$
$422$	5.12061			0.249268
$423$		0			0
$424$	−1.62866			−0.0790947
$425$	−0.745100	−	1.29055i	−0.0361427	−	0.0626009i
$426$		0			0
$427$	−3.81908	+	6.61484i	−0.184818	+	0.320114i
$428$	−4.37211	+	7.57272i	−0.211334	+	0.366041i
$429$		0			0
$430$	−2.61334	−	4.52644i	−0.126026	−	0.218284i
$431$	29.3191			1.41225			0.706126	−	0.708086i	$-0.250441\pi$
$431$	29.3191			1.41225			0.706126	+	0.708086i	$0.250441\pi$
$432$		0			0
$433$	19.6554			0.944578			0.472289	−	0.881444i	$-0.343428\pi$
$433$	19.6554			0.944578			0.472289	+	0.881444i	$0.343428\pi$
$434$	−4.06031	−	7.03266i	−0.194901	−	0.337578i
$435$		0			0
$436$	0.247626	−	0.428901i	0.0118591	−	0.0205406i
$437$	−14.4290	+	24.9918i	−0.690233	+	1.19552i
$438$		0			0
$439$	10.9650	+	18.9919i	0.523330	+	0.906434i	0.999631	+	0.0271516i	$0.00864370\pi$
$439$	10.9650	+	18.9919i	0.523330	+	0.906434i	−0.476302	+	0.879282i	$0.658023\pi$
$440$	−6.31820			−0.301208
$441$		0			0
$442$	1.38650			0.0659489
$443$	−9.35504	−	16.2034i	−0.444471	−	0.769847i	0.553544	−	0.832820i	$-0.313275\pi$
$443$	−9.35504	−	16.2034i	−0.444471	−	0.769847i	−0.998015	+	0.0629732i	$0.979942\pi$
$444$		0			0
$445$	−6.12108	+	10.6020i	−0.290167	+	0.502584i
$446$	−3.11468	+	5.39479i	−0.147485	+	0.255451i
$447$		0			0
$448$	−2.52094	−	4.36640i	−0.119103	−	0.206293i
$449$	−6.68004			−0.315251			−0.157625	−	0.987499i	$-0.550384\pi$
$449$	−6.68004			−0.315251			−0.157625	+	0.987499i	$0.550384\pi$
$450$		0			0
$451$	5.63816			0.265490
$452$	−8.81345	−	15.2653i	−0.414550	−	0.718022i
$453$		0			0
$454$	−5.25150	+	9.09586i	−0.246465	+	0.426890i
$455$	−2.26991	+	3.93161i	−0.106415	+	0.184317i
$456$		0			0
$457$	9.71436	+	16.8258i	0.454418	+	0.787076i	0.998655	−	0.0518563i	$-0.0165138\pi$
$457$	9.71436	+	16.8258i	0.454418	+	0.787076i	−0.544236	+	0.838932i	$0.683180\pi$
$458$	−15.4355			−0.721254
$459$		0			0
$460$	−14.7811			−0.689170
$461$	−0.482926	−	0.836452i	−0.0224921	−	0.0389575i	0.854560	−	0.519352i	$-0.173827\pi$
$461$	−0.482926	−	0.836452i	−0.0224921	−	0.0389575i	−0.877052	+	0.480395i	$0.840493\pi$
$462$		0			0
$463$	0.222811	−	0.385920i	0.0103549	−	0.0179352i	−0.860802	−	0.508941i	$-0.830037\pi$
$463$	0.222811	−	0.385920i	0.0103549	−	0.0179352i	0.871156	+	0.491006i	$0.163371\pi$
$464$	−0.131292	+	0.227405i	−0.00609509	+	0.0105570i
$465$		0			0
$466$	7.14677	+	12.3786i	0.331068	+	0.573426i
$467$	34.2148			1.58327			0.791637	−	0.610992i	$-0.209229\pi$
$467$	34.2148			1.58327			0.791637	+	0.610992i	$0.209229\pi$
$468$		0			0
$469$	0.596267			0.0275330
$470$	−5.54189	−	9.59883i	−0.255628	−	0.442761i
$471$		0			0
$472$	14.7506	−	25.5488i	0.678952	−	1.17598i
$473$	−3.64543	+	6.31407i	−0.167617	+	0.290321i
$474$		0			0
$475$	−5.13816	−	8.89955i	−0.235755	−	0.408339i
$476$	0.573978			0.0263082
$477$		0			0
$478$	13.2781			0.607325
$479$	−10.8965	−	18.8732i	−0.497872	−	0.862339i	0.502125	−	0.864795i	$-0.332552\pi$
$479$	−10.8965	−	18.8732i	−0.497872	−	0.862339i	−0.999997	+	0.00245553i	$0.999218\pi$
$480$		0			0
$481$	15.5581	−	26.9474i	0.709388	−	1.22870i
$482$	6.87598	−	11.9095i	0.313192	−	0.542465i
$483$		0			0
$484$	−5.07145	−	8.78401i	−0.230521	−	0.399273i
$485$	2.55850			0.116175
$486$		0			0
$487$	19.3928			0.878772			0.439386	−	0.898298i	$-0.355196\pi$
$487$	19.3928			0.878772			0.439386	+	0.898298i	$0.355196\pi$
$488$	10.8366	+	18.7696i	0.490551	+	0.849659i
$489$		0			0
$490$	0.592396	−	1.02606i	0.0267617	−	0.0463527i
$491$	13.0783	−	22.6523i	0.590216	−	1.02228i	−0.403987	−	0.914765i	$-0.632376\pi$
$491$	13.0783	−	22.6523i	0.590216	−	1.02228i	0.994203	−	0.107519i	$-0.0342908\pi$
$492$		0			0
$493$	−1.46657	−	2.54017i	−0.0660509	−	0.114403i
$494$	9.56118			0.430178
$495$		0			0
$496$	−0.386821			−0.0173688
$497$	−0.277189	−	0.480105i	−0.0124336	−	0.0215357i
$498$		0			0
$499$	7.15064	−	12.3853i	0.320107	−	0.554441i	−0.660403	−	0.750911i	$-0.729615\pi$
$499$	7.15064	−	12.3853i	0.320107	−	0.554441i	0.980510	+	0.196470i	$0.0629479\pi$
$500$	6.76352	−	11.7148i	0.302474	−	0.523900i
$501$		0			0
$502$	8.38279	+	14.5194i	0.374142	+	0.648033i
$503$	−18.7033			−0.833937			−0.416969	−	0.908921i	$-0.636908\pi$
$503$	−18.7033			−0.833937			−0.416969	+	0.908921i	$0.636908\pi$
$504$		0			0
$505$	−2.30272			−0.102470
$506$	−6.49912	−	11.2568i	−0.288921	−	0.500426i
$507$		0			0
$508$	−12.7400	+	22.0664i	−0.565248	+	0.979039i
$509$	−12.8045	+	22.1781i	−0.567551	+	0.983027i	0.429257	+	0.903183i	$0.358776\pi$
$509$	−12.8045	+	22.1781i	−0.567551	+	0.983027i	−0.996807	+	0.0798442i	$0.974558\pi$
$510$		0			0
$511$	−1.02481	−	1.77503i	−0.0453351	−	0.0785228i
$512$	−0.473897			−0.0209435
$513$		0			0
$514$	−23.3756			−1.03105
$515$	−2.45084	−	4.24497i	−0.107997	−	0.187056i
$516$		0			0
$517$	−7.73055	+	13.3897i	−0.339989	+	0.588879i
$518$	−4.06031	+	7.03266i	−0.178400	+	0.308997i
$519$		0			0
$520$	6.44087	+	11.1559i	0.282451	+	0.489220i
$521$	21.2121			0.929320			0.464660	−	0.885489i	$-0.346176\pi$
$521$	21.2121			0.929320			0.464660	+	0.885489i	$0.346176\pi$
$522$		0			0
$523$	20.8057			0.909770			0.454885	−	0.890550i	$-0.349680\pi$
$523$	20.8057			0.909770			0.454885	+	0.890550i	$0.349680\pi$
$524$	4.39470	+	7.61185i	0.191984	+	0.332525i
$525$		0			0
$526$	−0.322786	+	0.559082i	−0.0140741	+	0.0243771i
$527$	2.16044	−	3.74200i	0.0941104	−	0.163004i
$528$		0			0
$529$	−28.4937	−	49.3525i	−1.23885	−	2.14576i
$530$	−0.680045			−0.0295393
$531$		0			0
$532$	3.95811			0.171606
$533$	−5.74763	−	9.95518i	−0.248957	−	0.431207i
$534$		0			0
$535$	−4.80200	+	8.31731i	−0.207609	+	0.359589i
$536$	0.845952	−	1.46523i	0.0365396	−	0.0632884i
$537$		0			0
$538$	−9.16772	−	15.8790i	−0.395248	−	0.684590i
$539$	−1.65270			−0.0711870
$540$		0			0
$541$	26.7297			1.14920			0.574599	−	0.818435i	$-0.305158\pi$
$541$	26.7297			1.14920			0.574599	+	0.818435i	$0.305158\pi$
$542$	−3.05943	−	5.29909i	−0.131414	−	0.227615i
$543$		0			0
$544$	1.31908	−	2.28471i	0.0565550	−	0.0979561i
$545$	0.271974	−	0.471073i	0.0116501	−	0.0201786i
$546$		0			0
$547$	−18.3812	−	31.8372i	−0.785923	−	1.36126i	−0.928446	−	0.371467i	$-0.878855\pi$
$547$	−18.3812	−	31.8372i	−0.785923	−	1.36126i	0.142523	−	0.989792i	$-0.454479\pi$
$548$	3.15125			0.134615
$549$		0			0
$550$	4.62866			0.197367
$551$	−10.1133	−	17.5168i	−0.430843	−	0.746242i
$552$		0			0
$553$	1.20187	−	2.08169i	0.0511086	−	0.0885226i
$554$	−7.85844	+	13.6112i	−0.333873	+	0.578285i
$555$		0			0
$556$	−3.76187	−	6.51575i	−0.159539	−	0.276329i
$557$	−32.3387			−1.37024			−0.685118	−	0.728432i	$-0.740249\pi$
$557$	−32.3387			−1.37024			−0.685118	+	0.728432i	$0.740249\pi$
$558$		0			0
$559$	14.8648			0.628716
$560$	−0.0282185	−	0.0488759i	−0.00119245	−	0.00206538i
$561$		0			0
$562$	9.80974	−	16.9910i	0.413799	−	0.716721i
$563$	−8.87093	+	15.3649i	−0.373865	+	0.647553i	−0.990156	−	0.139965i	$-0.955301\pi$
$563$	−8.87093	+	15.3649i	−0.373865	+	0.647553i	0.616291	+	0.787518i	$0.288634\pi$
$564$		0			0
$565$	−9.68004	−	16.7663i	−0.407243	−	0.705365i
$566$	−16.3517			−0.687315
$567$		0			0
$568$	−1.57304			−0.0660035
$569$	−13.3007	−	23.0374i	−0.557593	−	0.965779i	−0.997697	−	0.0678320i	$-0.978392\pi$
$569$	−13.3007	−	23.0374i	−0.557593	−	0.965779i	0.440104	−	0.897947i	$-0.354942\pi$
$570$		0			0
$571$	5.00862	−	8.67518i	0.209604	−	0.363045i	−0.741986	−	0.670416i	$-0.766116\pi$
$571$	5.00862	−	8.67518i	0.209604	−	0.363045i	0.951590	+	0.307371i	$0.0994491\pi$
$572$	3.41565	−	5.91608i	0.142815	−	0.247364i
$573$		0			0
$574$	1.50000	+	2.59808i	0.0626088	+	0.108442i
$575$	28.4834			1.18784
$576$		0			0
$577$	−32.9145			−1.37025			−0.685124	−	0.728427i	$-0.740252\pi$
$577$	−32.9145			−1.37025			−0.685124	+	0.728427i	$0.740252\pi$
$578$	7.37851	+	12.7800i	0.306905	+	0.531576i
$579$		0			0
$580$	5.18004	−	8.97210i	0.215090	−	0.372546i
$581$	−7.52481	+	13.0334i	−0.312182	+	0.540715i
$582$		0			0
$583$	0.474308	+	0.821525i	0.0196438	+	0.0340241i
$584$	−5.81582			−0.240660
$585$		0			0
$586$	−11.5125			−0.475577
$587$	−7.53643	−	13.0535i	−0.311062	−	0.538774i	0.667531	−	0.744582i	$-0.267351\pi$
$587$	−7.53643	−	13.0535i	−0.311062	−	0.538774i	−0.978592	+	0.205808i	$0.934018\pi$
$588$		0			0
$589$	14.8983	−	25.8046i	0.613873	−	1.06326i
$590$	6.15910	−	10.6679i	0.253566	−	0.439189i
$591$		0			0
$592$	0.193411	+	0.334997i	0.00794913	+	0.0137683i
$593$	−41.0009			−1.68371			−0.841853	−	0.539706i	$-0.818535\pi$
$593$	−41.0009			−1.68371			−0.841853	+	0.539706i	$0.818535\pi$
$594$		0			0
$595$	0.630415			0.0258445
$596$	−0.264396	−	0.457947i	−0.0108301	−	0.0187582i
$597$		0			0
$598$	−13.2506	+	22.9507i	−0.541858	+	0.938526i
$599$	3.03684	−	5.25996i	0.124082	−	0.214916i	−0.797292	−	0.603594i	$-0.793735\pi$
$599$	3.03684	−	5.25996i	0.124082	−	0.214916i	0.921374	+	0.388678i	$0.127068\pi$
$600$		0			0
$601$	7.06758	+	12.2414i	0.288293	+	0.499338i	0.973402	−	0.229102i	$-0.0735791\pi$
$601$	7.06758	+	12.2414i	0.288293	+	0.499338i	−0.685110	+	0.728440i	$0.740246\pi$
$602$	−3.87939			−0.158112
$603$		0			0
$604$	3.03064			0.123315
$605$	−5.57011	−	9.64771i	−0.226457	−	0.392235i
$606$		0			0
$607$	−23.0449	+	39.9149i	−0.935363	+	1.62010i	−0.161377	+	0.986893i	$0.551594\pi$
$607$	−23.0449	+	39.9149i	−0.935363	+	1.62010i	−0.773986	+	0.633203i	$0.781740\pi$
$608$	9.09627	−	15.7552i	0.368902	−	0.638958i
$609$		0			0
$610$	4.52481	+	7.83721i	0.183204	+	0.317319i
$611$	31.5226			1.27527
$612$		0			0
$613$	−26.4938			−1.07008			−0.535038	−	0.844828i	$-0.679703\pi$
$613$	−26.4938			−1.07008			−0.535038	+	0.844828i	$0.679703\pi$
$614$	−2.77466	−	4.80586i	−0.111976	−	0.193949i
$615$		0			0
$616$	−2.34477	+	4.06126i	−0.0944735	+	0.163633i
$617$	−1.12495	+	1.94847i	−0.0452889	+	0.0784426i	−0.887781	−	0.460266i	$-0.847754\pi$
$617$	−1.12495	+	1.94847i	−0.0452889	+	0.0784426i	0.842492	+	0.538708i	$0.181087\pi$
$618$		0			0
$619$	−3.09539	−	5.36137i	−0.124414	−	0.215492i	0.797090	−	0.603861i	$-0.206372\pi$
$619$	−3.09539	−	5.36137i	−0.124414	−	0.215492i	−0.921504	+	0.388369i	$0.873038\pi$
$620$	15.2618			0.612927
$621$		0			0
$622$	8.37557			0.335830
$623$	4.54323	+	7.86911i	0.182021	+	0.315269i
$624$		0			0
$625$	−0.533433	+	0.923933i	−0.0213373	+	0.0369573i
$626$	7.75119	−	13.4255i	0.309800	−	0.536589i
$627$		0			0
$628$	6.21523	+	10.7651i	0.248015	+	0.429574i
$629$	−4.32089			−0.172285
$630$		0			0
$631$	26.1661			1.04166			0.520829	−	0.853661i	$-0.325623\pi$
$631$	26.1661			1.04166			0.520829	+	0.853661i	$0.325623\pi$
$632$	−3.41029	−	5.90680i	−0.135654	−	0.234960i
$633$		0			0
$634$	3.55138	−	6.15118i	0.141043	−	0.244295i
$635$	−13.9927	+	24.2361i	−0.555284	+	0.961781i
$636$		0			0
$637$	1.68479	+	2.91815i	0.0667539	+	0.115621i
$638$	9.11051			0.360689
$639$		0			0
$640$	9.21894			0.364411
$641$	2.44444	+	4.23389i	0.0965496	+	0.167229i	0.910254	−	0.414050i	$-0.135886\pi$
$641$	2.44444	+	4.23389i	0.0965496	+	0.167229i	−0.813705	+	0.581278i	$0.802553\pi$
$642$		0			0
$643$	20.1839	−	34.9596i	0.795976	−	1.37867i	−0.126242	−	0.992000i	$-0.540291\pi$
$643$	20.1839	−	34.9596i	0.795976	−	1.37867i	0.922218	−	0.386671i	$-0.126375\pi$
$644$	−5.48545	+	9.50108i	−0.216157	+	0.374395i
$645$		0			0
$646$	−0.663848	−	1.14982i	−0.0261188	−	0.0452390i
$647$	2.28075			0.0896657			0.0448329	−	0.998995i	$-0.485724\pi$
$647$	2.28075			0.0896657			0.0448329	+	0.998995i	$0.485724\pi$
$648$		0			0
$649$	−17.1830			−0.674493
$650$	−4.71853	−	8.17273i	−0.185076	−	0.320561i
$651$		0			0
$652$	−1.59240	+	2.75811i	−0.0623631	+	0.108016i
$653$	11.7396	−	20.3336i	0.459407	−	0.795717i	−0.539522	−	0.841971i	$-0.681395\pi$
$653$	11.7396	−	20.3336i	0.459407	−	0.795717i	0.998930	+	0.0462542i	$0.0147284\pi$
$654$		0			0
$655$	4.82682	+	8.36030i	0.188599	+	0.326664i
$656$	0.142903			0.00557944
$657$		0			0
$658$	−8.22668			−0.320709
$659$	−23.9812	−	41.5366i	−0.934174	−	1.61804i	−0.776101	−	0.630609i	$-0.782805\pi$
$659$	−23.9812	−	41.5366i	−0.934174	−	1.61804i	−0.158073	−	0.987427i	$-0.550528\pi$
$660$		0			0
$661$	−14.6545	+	25.3824i	−0.569995	+	0.987260i	0.426571	+	0.904454i	$0.359721\pi$
$661$	−14.6545	+	25.3824i	−0.569995	+	0.987260i	−0.996566	+	0.0828055i	$0.973612\pi$
$662$	−10.1348	+	17.5539i	−0.393898	+	0.682252i
$663$		0			0
$664$	21.3516	+	36.9821i	0.828604	+	1.43518i
$665$	4.34730			0.168581
$666$		0			0
$667$	56.0634			2.17078
$668$	14.2191	+	24.6282i	0.550154	+	0.952894i
$669$		0			0
$670$	0.353226	−	0.611806i	0.0136463	−	0.0236361i
$671$	6.31180	−	10.9324i	0.243664	−	0.422039i
$672$		0			0
$673$	−13.1591	−	22.7922i	−0.507246	−	0.878576i	−0.999965	−	0.00838731i	$-0.997330\pi$
$673$	−13.1591	−	22.7922i	−0.507246	−	0.878576i	0.492719	−	0.870189i	$-0.336003\pi$
$674$	25.5226			0.983094
$675$		0			0
$676$	2.01899			0.0776535
$677$	17.9454	+	31.0823i	0.689697	+	1.19459i	0.971936	+	0.235246i	$0.0755895\pi$
$677$	17.9454	+	31.0823i	0.689697	+	1.19459i	−0.282239	+	0.959344i	$0.591077\pi$
$678$		0			0
$679$	0.949493	−	1.64457i	0.0364382	−	0.0631128i
$680$	0.894400	−	1.54915i	0.0342987	−	0.0594070i
$681$		0			0
$682$	6.71048	+	11.6229i	0.256958	+	0.445064i
$683$	−35.0642			−1.34169			−0.670847	−	0.741596i	$-0.734069\pi$
$683$	−35.0642			−1.34169			−0.670847	+	0.741596i	$0.734069\pi$
$684$		0			0
$685$	3.46110			0.132242
$686$	−0.439693	−	0.761570i	−0.0167875	−	0.0290769i
$687$		0			0
$688$	−0.0923963	+	0.160035i	−0.00352257	+	0.00610128i
$689$	0.967034	−	1.67495i	0.0368411	−	0.0638106i
$690$		0			0
$691$	−1.03343	−	1.78996i	−0.0393136	−	0.0680932i	0.845699	−	0.533660i	$-0.179184\pi$
$691$	−1.03343	−	1.78996i	−0.0393136	−	0.0680932i	−0.885013	+	0.465567i	$0.845850\pi$
$692$	−5.82915			−0.221591
$693$		0			0
$694$	−11.3847			−0.432159
$695$	−4.13176	−	7.15642i	−0.156727	−	0.271458i
$696$		0			0
$697$	−0.798133	+	1.38241i	−0.0302315	+	0.0523624i
$698$	−0.643208	+	1.11407i	−0.0243458	+	0.0421681i
$699$		0			0
$700$	−1.95336	−	3.38332i	−0.0738302	−	0.127878i
$701$	7.36009			0.277987			0.138993	−	0.990293i	$-0.455613\pi$
$701$	7.36009			0.277987			0.138993	+	0.990293i	$0.455613\pi$
$702$		0			0
$703$	−29.7965			−1.12380
$704$	4.16637	+	7.21637i	0.157026	+	0.271977i
$705$		0			0
$706$	6.30200	−	10.9154i	0.237179	−	0.410806i
$707$	−0.854570	+	1.48016i	−0.0321394	+	0.0556671i
$708$		0			0
$709$	−4.55438	−	7.88841i	−0.171043	−	0.296256i	0.767742	−	0.640760i	$-0.221380\pi$
$709$	−4.55438	−	7.88841i	−0.171043	−	0.296256i	−0.938785	+	0.344504i	$0.888047\pi$
$710$	−0.656822			−0.0246501
$711$		0			0
$712$	25.7828			0.966252
$713$	41.2943	+	71.5239i	1.54648	+	2.67859i
$714$		0			0
$715$	3.75150	−	6.49778i	0.140298	−	0.243003i
$716$	5.23308	−	9.06396i	0.195569	−	0.338736i
$717$		0			0
$718$	−9.20574	−	15.9448i	−0.343555	−	0.595055i
$719$	25.9537			0.967908			0.483954	−	0.875093i	$-0.339200\pi$
$719$	25.9537			0.967908			0.483954	+	0.875093i	$0.339200\pi$
$720$		0			0
$721$	−3.63816			−0.135492
$722$	3.77631	+	6.54076i	0.140540	+	0.243422i
$723$		0			0
$724$	−10.5706	+	18.3088i	−0.392852	+	0.680440i
$725$	−9.98205	+	17.2894i	−0.370724	+	0.642113i
$726$		0			0
$727$	5.08007	+	8.79894i	0.188409	+	0.326335i	0.944720	−	0.327878i	$-0.106333\pi$
$727$	5.08007	+	8.79894i	0.188409	+	0.326335i	−0.756311	+	0.654213i	$0.773000\pi$
$728$	9.56118			0.354361
$729$		0			0
$730$	−2.42839			−0.0898786
$731$	−1.03209	−	1.78763i	−0.0381732	−	0.0661179i
$732$		0			0
$733$	−20.3307	+	35.2138i	−0.750931	+	1.30065i	0.196441	+	0.980516i	$0.437062\pi$
$733$	−20.3307	+	35.2138i	−0.750931	+	1.30065i	−0.947372	+	0.320135i	$0.896272\pi$
$734$	5.30154	−	9.18253i	0.195683	−	0.338933i
$735$		0			0
$736$	25.2126	+	43.6695i	0.929349	+	1.60968i
$737$	−0.985452			−0.0362996
$738$		0			0
$739$	−25.3618			−0.932951			−0.466475	−	0.884534i	$-0.654476\pi$
$739$	−25.3618			−0.932951			−0.466475	+	0.884534i	$0.654476\pi$
$740$	−7.63088	−	13.2171i	−0.280517	−	0.485869i
$741$		0			0
$742$	−0.252374	+	0.437124i	−0.00926494	+	0.0160473i
$743$	−11.2221	+	19.4372i	−0.411699	+	0.713083i	−0.995076	−	0.0991184i	$-0.968398\pi$
$743$	−11.2221	+	19.4372i	−0.411699	+	0.713083i	0.583377	+	0.812202i	$0.301731\pi$
$744$		0			0
$745$	−0.290393	−	0.502975i	−0.0106392	−	0.0184276i
$746$	−0.686852			−0.0251474
$747$		0			0
$748$	−0.948615			−0.0346848
$749$	3.56418	+	6.17334i	0.130232	+	0.225569i
$750$		0			0
$751$	−12.1086	+	20.9727i	−0.441849	+	0.765305i	−0.997827	−	0.0658924i	$-0.979011\pi$
$751$	−12.1086	+	20.9727i	−0.441849	+	0.765305i	0.555978	+	0.831197i	$0.312344\pi$
$752$	−0.195937	+	0.339373i	−0.00714508	+	0.0123756i
$753$		0			0
$754$	−9.28740	−	16.0862i	−0.338227	−	0.585827i
$755$	3.32863			0.121141
$756$		0			0
$757$	9.11793			0.331397			0.165698	−	0.986176i	$-0.447012\pi$
$757$	9.11793			0.331397			0.165698	+	0.986176i	$0.447012\pi$
$758$	3.04442	+	5.27308i	0.110578	+	0.191527i
$759$		0			0
$760$	6.16772	−	10.6828i	0.223727	−	0.387506i
$761$	−9.13610	+	15.8242i	−0.331183	+	0.573626i	−0.982744	−	0.184970i	$-0.940781\pi$
$761$	−9.13610	+	15.8242i	−0.331183	+	0.573626i	0.651561	+	0.758596i	$0.274114\pi$
$762$		0			0
$763$	−0.201867	−	0.349643i	−0.00730806	−	0.0126579i
$764$	15.8357			0.572917
$765$		0			0
$766$	−6.79973			−0.245684
$767$	17.5167	+	30.3398i	0.632490	+	1.09550i
$768$		0			0
$769$	−9.26470	+	16.0469i	−0.334094	+	0.578667i	−0.983310	−	0.181936i	$-0.941764\pi$
$769$	−9.26470	+	16.0469i	−0.334094	+	0.578667i	0.649217	+	0.760604i	$0.275097\pi$
$770$	−0.979055	+	1.69577i	−0.0352827	+	0.0611114i
$771$		0			0
$772$	−0.391407	−	0.677937i	−0.0140870	−	0.0243995i
$773$	2.96080			0.106493			0.0532463	−	0.998581i	$-0.483043\pi$
$773$	2.96080			0.106493			0.0532463	+	0.998581i	$0.483043\pi$
$774$		0			0
$775$	−29.4097			−1.05643
$776$	−2.69418	−	4.66646i	−0.0967155	−	0.167516i
$777$		0			0
$778$	2.37417	−	4.11218i	0.0851181	−	0.147429i
$779$	−5.50387	+	9.53298i	−0.197197	+	0.341555i
$780$		0			0
$781$	0.458111	+	0.793471i	0.0163925	+	0.0283926i
$782$	3.68004			0.131598
$783$		0			0
$784$	−0.0418891			−0.00149604
$785$	6.82635	+	11.8236i	0.243643	+	0.422002i
$786$		0			0
$787$	16.7010	−	28.9270i	0.595326	−	1.03113i	−0.398175	−	0.917310i	$-0.630356\pi$
$787$	16.7010	−	28.9270i	0.595326	−	1.03113i	0.993501	−	0.113825i	$-0.0363104\pi$
$788$	−7.02007	+	12.1591i	−0.250080	+	0.433150i
$789$		0			0
$790$	−1.42396	−	2.46638i	−0.0506623	−	0.0877497i
$791$	−14.3696			−0.510924
$792$		0			0
$793$	−25.7374			−0.913962
$794$	12.8542	+	22.2641i	0.456177	+	0.790122i
$795$		0			0
$796$	−2.23143	+	3.86495i	−0.0790909	+	0.136989i
$797$	24.6755	−	42.7391i	0.874050	−	1.51390i	0.0162779	−	0.999868i	$-0.494818\pi$
$797$	24.6755	−	42.7391i	0.874050	−	1.51390i	0.857772	−	0.514031i	$-0.171848\pi$
$798$		0			0
$799$	−2.18866	−	3.79088i	−0.0774293	−	0.134112i
$800$	−17.9564			−0.634853
$801$		0			0
$802$	24.0933			0.850763
$803$	1.69372	+	2.93360i	0.0597699	+	0.103525i
$804$		0			0
$805$	−6.02481	+	10.4353i	−0.212347	+	0.367795i
$806$	13.6816	−	23.6971i	0.481912	−	0.834696i
$807$		0			0
$808$	2.42484	+	4.19995i	0.0853056	+	0.147754i
$809$	−19.8280			−0.697115			−0.348558	−	0.937287i	$-0.613328\pi$
$809$	−19.8280			−0.697115			−0.348558	+	0.937287i	$0.613328\pi$
$810$		0			0
$811$	−23.8557			−0.837686			−0.418843	−	0.908059i	$-0.637564\pi$
$811$	−23.8557			−0.837686			−0.418843	+	0.908059i	$0.637564\pi$
$812$	−3.84477	−	6.65934i	−0.134925	−	0.233697i
$813$		0			0
$814$	6.71048	−	11.6229i	0.235202	−	0.407382i
$815$	−1.74897	+	3.02931i	−0.0612638	+	0.106112i
$816$		0			0
$817$	−7.11721	−	12.3274i	−0.249000	−	0.431280i
$818$	−7.93643			−0.277491
$819$		0			0
$820$	−5.63816			−0.196893
$821$	−25.4714	−	44.1177i	−0.888957	−	1.53972i	−0.841110	−	0.540864i	$-0.818097\pi$
$821$	−25.4714	−	44.1177i	−0.888957	−	1.53972i	−0.0478469	−	0.998855i	$-0.515236\pi$
$822$		0			0
$823$	−6.80747	+	11.7909i	−0.237293	+	0.411004i	−0.959937	−	0.280217i	$-0.909594\pi$
$823$	−6.80747	+	11.7909i	−0.237293	+	0.411004i	0.722643	+	0.691221i	$0.242927\pi$
$824$	−5.16163	+	8.94020i	−0.179814	+	0.311447i
$825$		0			0
$826$	−4.57145	−	7.91799i	−0.159061	−	0.275502i
$827$	−36.2158			−1.25935			−0.629673	−	0.776861i	$-0.716811\pi$
$827$	−36.2158			−1.25935			−0.629673	+	0.776861i	$0.716811\pi$
$828$		0			0
$829$	25.3259			0.879606			0.439803	−	0.898094i	$-0.355048\pi$
$829$	25.3259			0.879606			0.439803	+	0.898094i	$0.355048\pi$
$830$	8.91534	+	15.4418i	0.309456	+	0.535994i
$831$		0			0
$832$	8.49454	−	14.7130i	0.294495	−	0.510080i
$833$	0.233956	−	0.405223i	0.00810608	−	0.0140401i
$834$		0			0
$835$	15.6172	+	27.0498i	0.540456	+	0.936097i
$836$	−6.54158			−0.226245
$837$		0			0
$838$	−0.154154			−0.00532515
$839$	4.35710	+	7.54671i	0.150424	+	0.260541i	0.931383	−	0.364040i	$-0.118603\pi$
$839$	4.35710	+	7.54671i	0.150424	+	0.260541i	−0.780960	+	0.624582i	$0.785270\pi$
$840$		0			0
$841$	−5.14749	+	8.91571i	−0.177500	+	0.307438i
$842$	10.8626	−	18.8146i	0.374350	−	0.648394i
$843$		0			0
$844$	3.57145	+	6.18594i	0.122934	+	0.212929i
$845$	2.21751			0.0762847
$846$		0			0
$847$	−8.26857			−0.284111
$848$	0.0120217	+	0.0208222i	0.000412827	+	0.000715037i
$849$		0			0
$850$	−0.655230	+	1.13489i	−0.0224742	+	0.0389265i
$851$	41.2943	−	71.5239i	1.41555	−	2.45181i
$852$		0			0
$853$	5.99067	+	10.3761i	0.205117	+	0.355272i	0.950170	−	0.311733i	$-0.100909\pi$
$853$	5.99067	+	10.3761i	0.205117	+	0.355272i	−0.745053	+	0.667005i	$0.767576\pi$
$854$	6.71688			0.229847
$855$		0			0
$856$	20.2267			0.691334
$857$	3.25015	+	5.62943i	0.111023	+	0.192298i	0.916183	−	0.400760i	$-0.131254\pi$
$857$	3.25015	+	5.62943i	0.111023	+	0.192298i	−0.805160	+	0.593058i	$0.797921\pi$
$858$		0			0
$859$	26.7763	−	46.3779i	0.913596	−	1.58239i	0.104652	−	0.994509i	$-0.466627\pi$
$859$	26.7763	−	46.3779i	0.913596	−	1.58239i	0.808944	−	0.587886i	$-0.200040\pi$
$860$	3.64543	−	6.31407i	0.124308	−	0.215308i
$861$		0			0
$862$	−12.8914	−	22.3286i	−0.439083	−	0.760514i
$863$	−3.69965			−0.125937			−0.0629687	−	0.998016i	$-0.520057\pi$
$863$	−3.69965			−0.125937			−0.0629687	+	0.998016i	$0.520057\pi$
$864$		0			0
$865$	−6.40230			−0.217685
$866$	−8.64233	−	14.9690i	−0.293678	−	0.508666i
$867$		0			0
$868$	5.66385	−	9.81007i	0.192244	−	0.332976i
$869$	−1.98633	+	3.44042i	−0.0673816	+	0.116708i
$870$		0			0
$871$	1.00459	+	1.73999i	0.0340391	+	0.0589574i
$872$	−1.14559			−0.0387946
$873$		0			0
$874$	25.3773			0.858401
$875$	−5.51367	−	9.54996i	−0.186396	−	0.322847i
$876$		0			0
$877$	5.89440	−	10.2094i	0.199040	−	0.344747i	−0.749178	−	0.662369i	$-0.769551\pi$
$877$	5.89440	−	10.2094i	0.199040	−	0.344747i	0.948217	+	0.317622i	$0.102884\pi$
$878$	9.64244	−	16.7012i	0.325416	−	0.563638i
$879$		0			0
$880$	0.0466368	+	0.0807773i	0.00157213	+	0.00272300i
$881$	−49.4858			−1.66722			−0.833609	−	0.552355i	$-0.813729\pi$
$881$	−49.4858			−1.66722			−0.833609	+	0.552355i	$0.813729\pi$
$882$		0			0
$883$	−21.5357			−0.724734			−0.362367	−	0.932035i	$-0.618031\pi$
$883$	−21.5357			−0.724734			−0.362367	+	0.932035i	$0.618031\pi$
$884$	0.967034	+	1.67495i	0.0325249	+	0.0563347i
$885$		0			0
$886$	−8.22668	+	14.2490i	−0.276381	+	0.478706i
$887$	5.94238	−	10.2925i	0.199526	−	0.345589i	−0.748849	−	0.662741i	$-0.769393\pi$
$887$	5.94238	−	10.2925i	0.199526	−	0.345589i	0.948375	+	0.317152i	$0.102727\pi$
$888$		0			0
$889$	10.3858	+	17.9887i	0.348328	+	0.603322i
$890$	10.7656			0.360863
$891$		0			0
$892$	−8.68954			−0.290947
$893$	−15.0929	−	26.1416i	−0.505063	−	0.874795i
$894$		0			0
$895$	5.74763	−	9.95518i	0.192122	−	0.332765i
$896$	3.42127	−	5.92582i	0.114297	−	0.197968i
$897$		0			0
$898$	2.93717	+	5.08732i	0.0980145	+	0.169766i
$899$	−57.8866			−1.93063
$900$		0			0
$901$	−0.268571			−0.00894739
$902$	−2.47906	−	4.29385i	−0.0825435	−	0.142970i
$903$		0			0
$904$	−20.3868	+	35.3110i	−0.678056	+	1.17443i
$905$	−11.6099	+	20.1090i	−0.385927	+	0.668446i
$906$		0			0
$907$	13.0107	+	22.5353i	0.432014	+	0.748271i	0.997047	−	0.0767980i	$-0.0244697\pi$
$907$	13.0107	+	22.5353i	0.432014	+	0.748271i	−0.565032	+	0.825069i	$0.691136\pi$
$908$	−14.6509			−0.486209
$909$		0			0
$910$	3.99226			0.132342
$911$	−2.01636	−	3.49244i	−0.0668050	−	0.115710i	0.830688	−	0.556738i	$-0.187947\pi$
$911$	−2.01636	−	3.49244i	−0.0668050	−	0.115710i	−0.897493	+	0.441028i	$0.854614\pi$
$912$		0			0
$913$	12.4363	−	21.5403i	0.411581	−	0.712879i
$914$	8.54266	−	14.7963i	0.282566	−	0.489419i
$915$		0			0
$916$	−10.7657	−	18.6468i	−0.355710	−	0.616108i
$917$	7.16519			0.236615
$918$		0			0
$919$	27.4270			0.904732			0.452366	−	0.891832i	$-0.350580\pi$
$919$	27.4270			0.904732			0.452366	+	0.891832i	$0.350580\pi$
$920$	17.0954	+	29.6101i	0.563618	+	0.976216i
$921$		0			0
$922$	−0.424678	+	0.735564i	−0.0139860	+	0.0242245i
$923$	0.934011	−	1.61775i	0.0307434	−	0.0532491i
$924$		0			0
$925$	14.7049	+	25.4696i	0.483493	+	0.837434i
$926$	−0.391874			−0.0128778
$927$		0			0
$928$	−35.3432			−1.16020
$929$	3.83837	+	6.64826i	0.125933	+	0.218122i	0.922097	−	0.386958i	$-0.126474\pi$
$929$	3.83837	+	6.64826i	0.125933	+	0.218122i	−0.796164	+	0.605081i	$0.793141\pi$
$930$		0			0
$931$	1.61334	−	2.79439i	0.0528751	−	0.0915824i
$932$	−9.96926	+	17.2673i	−0.326554	+	0.565608i
$933$		0			0
$934$	−15.0440	−	26.0570i	−0.492255	−	0.852610i
$935$	−1.04189			−0.0340734
$936$		0			0
$937$	−2.02465			−0.0661425			−0.0330713	−	0.999453i	$-0.510529\pi$
$937$	−2.02465			−0.0661425			−0.0330713	+	0.999453i	$0.510529\pi$
$938$	−0.262174	−	0.454099i	−0.00856029	−	0.0148269i
$939$		0			0
$940$	7.73055	−	13.3897i	0.252143	−	0.436724i
$941$	−3.06964	+	5.31677i	−0.100067	+	0.173322i	−0.911712	−	0.410829i	$-0.865239\pi$
$941$	−3.06964	+	5.31677i	−0.100067	+	0.173322i	0.811645	+	0.584151i	$0.198573\pi$
$942$		0			0
$943$	−15.2554	−	26.4231i	−0.496783	−	0.860454i
$944$	−0.435518			−0.0141749
$945$		0			0
$946$	6.41147			0.208455
$947$	2.78224	+	4.81898i	0.0904107	+	0.156596i	0.907684	−	0.419654i	$-0.137849\pi$
$947$	2.78224	+	4.81898i	0.0904107	+	0.156596i	−0.817273	+	0.576250i	$0.804515\pi$
$948$		0			0
$949$	3.45320	−	5.98112i	0.112096	−	0.194155i
$950$	−4.51842	+	7.82613i	−0.146597	+	0.253913i
$951$		0			0
$952$	−0.663848	−	1.14982i	−0.0215154	−	0.0372658i
$953$	8.72018			0.282474			0.141237	−	0.989976i	$-0.454892\pi$
$953$	8.72018			0.282474			0.141237	+	0.989976i	$0.454892\pi$
$954$		0			0
$955$	17.3928			0.562818
$956$	9.26099	+	16.0405i	0.299522	+	0.518787i
$957$		0			0
$958$	−9.58219	+	16.5968i	−0.309586	+	0.536219i
$959$	1.28446	−	2.22475i	0.0414775	−	0.0718411i
$960$		0			0
$961$	−27.1373	−	47.0031i	−0.875396	−	1.51623i
$962$	−27.3631			−0.882222
$963$		0			0
$964$	19.1830			0.617844
$965$	−0.429892	−	0.744596i	−0.0138387	−	0.0239694i
$966$		0			0
$967$	28.8849	−	50.0301i	0.928876	−	1.60886i	0.143670	−	0.989626i	$-0.454110\pi$
$967$	28.8849	−	50.0301i	0.928876	−	1.60886i	0.785206	−	0.619235i	$-0.212557\pi$
$968$	−11.7310	+	20.3187i	−0.377049	+	0.653068i
$969$		0			0
$970$	−1.12495	−	1.94847i	−0.0361200	−	0.0625617i
$971$	30.7192			0.985828			0.492914	−	0.870078i	$-0.335932\pi$
$971$	30.7192			0.985828			0.492914	+	0.870078i	$0.335932\pi$
$972$		0			0
$973$	−6.13341			−0.196628
$974$	−8.52687	−	14.7690i	−0.273219	−	0.473229i
$975$		0			0
$976$	0.159978	−	0.277089i	0.00512076	−	0.00886941i
$977$	5.15002	−	8.92009i	0.164764	−	0.285379i	−0.771808	−	0.635856i	$-0.780647\pi$
$977$	5.15002	−	8.92009i	0.164764	−	0.285379i	0.936571	+	0.350477i	$0.113981\pi$
$978$		0			0
$979$	−7.50862	−	13.0053i	−0.239976	−	0.415651i
$980$	1.65270			0.0527937
$981$		0			0
$982$	−23.0018			−0.734015
$983$	6.84817	+	11.8614i	0.218423	+	0.378319i	0.954326	−	0.298767i	$-0.0965755\pi$
$983$	6.84817	+	11.8614i	0.218423	+	0.378319i	−0.735903	+	0.677087i	$0.763242\pi$
$984$		0			0
$985$	−7.71032	+	13.3547i	−0.245671	+	0.425515i
$986$	−1.28968	+	2.23379i	−0.0410717	+	0.0711383i
$987$		0			0
$988$	6.66860	+	11.5503i	0.212156	+	0.367465i
$989$	39.4543			1.25457
$990$		0			0
$991$	57.9813			1.84184			0.920919	−	0.389754i	$-0.127440\pi$
$991$	57.9813			1.84184			0.920919	+	0.389754i	$0.127440\pi$
$992$	−26.0326	−	45.0897i	−0.826534	−	1.43160i
$993$		0			0
$994$	−0.243756	+	0.422197i	−0.00773146	+	0.0133913i
$995$	−2.45084	+	4.24497i	−0.0776968	+	0.134575i
$996$		0			0
$997$	−8.10876	−	14.0448i	−0.256807	−	0.444803i	0.708578	−	0.705633i	$-0.249337\pi$
$997$	−8.10876	−	14.0448i	−0.256807	−	0.444803i	−0.965385	+	0.260830i	$0.916004\pi$
$998$	−12.5763			−0.398097
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.f.b.64.1		6
3.2	odd	2		63.2.f.a.22.3	✓	6
4.3	odd	2		3024.2.r.k.1009.2		6
7.2	even	3		1323.2.g.d.361.1		6
7.3	odd	6		1323.2.h.b.226.3		6
7.4	even	3		1323.2.h.c.226.3		6
7.5	odd	6		1323.2.g.e.361.1		6
7.6	odd	2		1323.2.f.d.442.1		6
9.2	odd	6		63.2.f.a.43.3	yes	6
9.4	even	3		567.2.a.c.1.3		3
9.5	odd	6		567.2.a.h.1.1		3
9.7	even	3	inner	189.2.f.b.127.1		6
12.11	even	2		1008.2.r.h.337.2		6
21.2	odd	6		441.2.g.c.67.3		6
21.5	even	6		441.2.g.b.67.3		6
21.11	odd	6		441.2.h.d.373.1		6
21.17	even	6		441.2.h.e.373.1		6
21.20	even	2		441.2.f.c.148.3		6
36.7	odd	6		3024.2.r.k.2017.2		6
36.11	even	6		1008.2.r.h.673.2		6
36.23	even	6		9072.2.a.ca.1.2		3
36.31	odd	6		9072.2.a.bs.1.2		3
63.2	odd	6		441.2.h.d.214.1		6
63.11	odd	6		441.2.g.c.79.3		6
63.13	odd	6		3969.2.a.l.1.3		3
63.16	even	3		1323.2.h.c.802.3		6
63.20	even	6		441.2.f.c.295.3		6
63.25	even	3		1323.2.g.d.667.1		6
63.34	odd	6		1323.2.f.d.883.1		6
63.38	even	6		441.2.g.b.79.3		6
63.41	even	6		3969.2.a.q.1.1		3
63.47	even	6		441.2.h.e.214.1		6
63.52	odd	6		1323.2.g.e.667.1		6
63.61	odd	6		1323.2.h.b.802.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.3	✓	6	3.2	odd	2
63.2.f.a.43.3	yes	6	9.2	odd	6
189.2.f.b.64.1		6	1.1	even	1	trivial
189.2.f.b.127.1		6	9.7	even	3	inner
441.2.f.c.148.3		6	21.20	even	2
441.2.f.c.295.3		6	63.20	even	6
441.2.g.b.67.3		6	21.5	even	6
441.2.g.b.79.3		6	63.38	even	6
441.2.g.c.67.3		6	21.2	odd	6
441.2.g.c.79.3		6	63.11	odd	6
441.2.h.d.214.1		6	63.2	odd	6
441.2.h.d.373.1		6	21.11	odd	6
441.2.h.e.214.1		6	63.47	even	6
441.2.h.e.373.1		6	21.17	even	6
567.2.a.c.1.3		3	9.4	even	3
567.2.a.h.1.1		3	9.5	odd	6
1008.2.r.h.337.2		6	12.11	even	2
1008.2.r.h.673.2		6	36.11	even	6
1323.2.f.d.442.1		6	7.6	odd	2
1323.2.f.d.883.1		6	63.34	odd	6
1323.2.g.d.361.1		6	7.2	even	3
1323.2.g.d.667.1		6	63.25	even	3
1323.2.g.e.361.1		6	7.5	odd	6
1323.2.g.e.667.1		6	63.52	odd	6
1323.2.h.b.226.3		6	7.3	odd	6
1323.2.h.b.802.3		6	63.61	odd	6
1323.2.h.c.226.3		6	7.4	even	3
1323.2.h.c.802.3		6	63.16	even	3
3024.2.r.k.1009.2		6	4.3	odd	2
3024.2.r.k.2017.2		6	36.7	odd	6
3969.2.a.l.1.3		3	63.13	odd	6
3969.2.a.q.1.1		3	63.41	even	6
9072.2.a.bs.1.2		3	36.31	odd	6
9072.2.a.ca.1.2		3	36.23	even	6

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.439693 - 0.761570i) q^{2} +(0.613341 - 1.06234i) q^{4} +(0.673648 - 1.16679i) q^{5} +(-0.500000 - 0.866025i) q^{7} -2.83750 q^{8} +O(q^{10})\)	\(q+(-0.439693 - 0.761570i) q^{2} +(0.613341 - 1.06234i) q^{4} +(0.673648 - 1.16679i) q^{5} +(-0.500000 - 0.866025i) q^{7} -2.83750 q^{8} -1.18479 q^{10} +(0.826352 + 1.43128i) q^{11} +(1.68479 - 2.91815i) q^{13} +(-0.439693 + 0.761570i) q^{14} +(0.0209445 + 0.0362770i) q^{16} -0.467911 q^{17} -3.22668 q^{19} +(-0.826352 - 1.43128i) q^{20} +(0.726682 - 1.25865i) q^{22} +(4.47178 - 7.74535i) q^{23} +(1.59240 + 2.75811i) q^{25} -2.96316 q^{26} -1.22668 q^{28} +(3.13429 + 5.42874i) q^{29} +(-4.61721 + 7.99724i) q^{31} +(-2.81908 + 4.88279i) q^{32} +(0.205737 + 0.356347i) q^{34} -1.34730 q^{35} +9.23442 q^{37} +(1.41875 + 2.45734i) q^{38} +(-1.91147 + 3.31077i) q^{40} +(1.70574 - 2.95442i) q^{41} +(2.20574 + 3.82045i) q^{43} +2.02734 q^{44} -7.86484 q^{46} +(4.67752 + 8.10170i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(1.40033 - 2.42544i) q^{50} +(-2.06670 - 3.57964i) q^{52} +0.573978 q^{53} +2.22668 q^{55} +(1.41875 + 2.45734i) q^{56} +(2.75624 - 4.77396i) q^{58} +(-5.19846 + 9.00400i) q^{59} +(-3.81908 - 6.61484i) q^{61} +8.12061 q^{62} +5.04189 q^{64} +(-2.26991 - 3.93161i) q^{65} +(-0.298133 + 0.516382i) q^{67} +(-0.286989 + 0.497079i) q^{68} +(0.592396 + 1.02606i) q^{70} +0.554378 q^{71} +2.04963 q^{73} +(-4.06031 - 7.03266i) q^{74} +(-1.97906 + 3.42782i) q^{76} +(0.826352 - 1.43128i) q^{77} +(1.20187 + 2.08169i) q^{79} +0.0564370 q^{80} -3.00000 q^{82} +(-7.52481 - 13.0334i) q^{83} +(-0.315207 + 0.545955i) q^{85} +(1.93969 - 3.35965i) q^{86} +(-2.34477 - 4.06126i) q^{88} -9.08647 q^{89} -3.36959 q^{91} +(-5.48545 - 9.50108i) q^{92} +(4.11334 - 7.12452i) q^{94} +(-2.17365 + 3.76487i) q^{95} +(0.949493 + 1.64457i) q^{97} +0.879385 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 3 q^{7} - 12 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 3 * q^7 - 12 * q^8	\( 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 3 q^{7} - 12 q^{8} + 6 q^{11} + 3 q^{13} + 3 q^{14} - 3 q^{16} - 12 q^{17} - 6 q^{19} - 6 q^{20} - 9 q^{22} + 12 q^{23} + 6 q^{25} + 6 q^{26} + 6 q^{28} + 9 q^{29} + 3 q^{31} - 9 q^{34} - 6 q^{35} - 6 q^{37} + 6 q^{38} + 9 q^{40} + 3 q^{43} - 30 q^{44} + 3 q^{47} - 3 q^{49} - 6 q^{50} + 21 q^{52} - 12 q^{53} + 6 q^{56} + 9 q^{58} - 3 q^{59} - 6 q^{61} + 60 q^{62} + 24 q^{64} + 15 q^{65} + 12 q^{67} + 6 q^{68} - 18 q^{71} - 42 q^{73} - 30 q^{74} - 15 q^{76} + 6 q^{77} + 21 q^{79} + 30 q^{80} - 18 q^{82} - 18 q^{83} - 9 q^{85} + 6 q^{86} - 27 q^{88} - 24 q^{89} - 6 q^{91} + 3 q^{92} + 18 q^{94} - 12 q^{95} + 3 q^{97} - 6 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 3 * q^7 - 12 * q^8 + 6 * q^11 + 3 * q^13 + 3 * q^14 - 3 * q^16 - 12 * q^17 - 6 * q^19 - 6 * q^20 - 9 * q^22 + 12 * q^23 + 6 * q^25 + 6 * q^26 + 6 * q^28 + 9 * q^29 + 3 * q^31 - 9 * q^34 - 6 * q^35 - 6 * q^37 + 6 * q^38 + 9 * q^40 + 3 * q^43 - 30 * q^44 + 3 * q^47 - 3 * q^49 - 6 * q^50 + 21 * q^52 - 12 * q^53 + 6 * q^56 + 9 * q^58 - 3 * q^59 - 6 * q^61 + 60 * q^62 + 24 * q^64 + 15 * q^65 + 12 * q^67 + 6 * q^68 - 18 * q^71 - 42 * q^73 - 30 * q^74 - 15 * q^76 + 6 * q^77 + 21 * q^79 + 30 * q^80 - 18 * q^82 - 18 * q^83 - 9 * q^85 + 6 * q^86 - 27 * q^88 - 24 * q^89 - 6 * q^91 + 3 * q^92 + 18 * q^94 - 12 * q^95 + 3 * q^97 - 6 * q^98

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