LMFDB - Embedded newform 693.2.m.j.631.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (of order $5$, degree $4$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 12 x^{18} - 3 x^{17} + 94 x^{16} - 10 x^{15} + 662 x^{14} - 153 x^{13} + 4638 x^{12} + \cdots + 121 $ x^20 + 12x^18 - 3x^17 + 94x^16 - 10x^15 + 662x^14 - 153x^13 + 4638x^12 - 1174x^11 + 15808x^10 - 3393x^9 + 26062x^8 - 15494x^7 + 11660x^6 - 33295x^5 + 67756x^4 - 43696x^3 + 13084x^2 - 1155x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			631.5
Root			$2.13576 - 1.55172i$ of defining polynomial
Character	$\chi$	$=$	693.631
Dual form			693.2.m.j.190.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.13576 + 1.55172i) q^{2} +(1.53559 + 4.72606i) q^{4} +(2.49476 - 1.81255i) q^{5} +(-0.309017 - 0.951057i) q^{7} +(-2.42230 + 7.45506i) q^{8} +O(q^{10})$	\(q+(2.13576 + 1.55172i) q^{2} +(1.53559 + 4.72606i) q^{4} +(2.49476 - 1.81255i) q^{5} +(-0.309017 - 0.951057i) q^{7} +(-2.42230 + 7.45506i) q^{8} +8.14075 q^{10} +(-1.45539 - 2.98024i) q^{11} +(4.56364 + 3.31568i) q^{13} +(0.815786 - 2.51073i) q^{14} +(-8.70112 + 6.32173i) q^{16} +(-4.53118 + 3.29210i) q^{17} +(0.0379017 - 0.116649i) q^{19} +(12.3971 + 9.00705i) q^{20} +(1.51613 - 8.62342i) q^{22} -1.67325 q^{23} +(1.39340 - 4.28844i) q^{25} +(4.60183 + 14.1630i) q^{26} +(4.02023 - 2.92087i) q^{28} +(-2.73492 - 8.41721i) q^{29} +(-1.29259 - 0.939120i) q^{31} -12.7156 q^{32} -14.7859 q^{34} +(-2.49476 - 1.81255i) q^{35} +(1.28943 + 3.96845i) q^{37} +(0.261956 - 0.190322i) q^{38} +(7.46960 + 22.9891i) q^{40} +(-1.07803 + 3.31785i) q^{41} -5.10698 q^{43} +(11.8499 - 11.4547i) q^{44} +(-3.57364 - 2.59640i) q^{46} +(0.492574 - 1.51599i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(9.63040 - 6.99690i) q^{50} +(-8.66223 + 26.6596i) q^{52} +(-9.59206 - 6.96904i) q^{53} +(-9.03267 - 4.79700i) q^{55} +7.83871 q^{56} +(7.22002 - 22.2209i) q^{58} +(-2.04398 - 6.29072i) q^{59} +(6.86789 - 4.98982i) q^{61} +(-1.30340 - 4.01146i) q^{62} +(-9.75511 - 7.08750i) q^{64} +17.3950 q^{65} -8.04949 q^{67} +(-22.5167 - 16.3593i) q^{68} +(-2.51563 - 7.74231i) q^{70} +(5.05133 - 3.67001i) q^{71} +(1.08466 + 3.33825i) q^{73} +(-3.40401 + 10.4765i) q^{74} +0.609494 q^{76} +(-2.38464 + 2.30511i) q^{77} +(7.60289 + 5.52382i) q^{79} +(-10.2487 + 31.5424i) q^{80} +(-7.45078 + 5.41331i) q^{82} +(-7.63216 + 5.54509i) q^{83} +(-5.33712 + 16.4260i) q^{85} +(-10.9073 - 7.92458i) q^{86} +(25.7433 - 3.63102i) q^{88} +8.45556 q^{89} +(1.74316 - 5.36488i) q^{91} +(-2.56942 - 7.90787i) q^{92} +(3.40440 - 2.47344i) q^{94} +(-0.116877 - 0.359710i) q^{95} +(4.59909 + 3.34143i) q^{97} -2.63994 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8}+O(q^{10}) $ 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8	$ 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8} + 12 q^{10} + q^{11} + 13 q^{13} - 24 q^{16} + q^{17} + 10 q^{19} + 46 q^{20} + 26 q^{22} - 8 q^{25} + 53 q^{26} + 4 q^{28} - 3 q^{29} - 13 q^{31} - 82 q^{32} + 42 q^{34} - 5 q^{35} - 32 q^{37} - 16 q^{38} + 20 q^{40} + 3 q^{41} + 12 q^{43} - 25 q^{44} - 13 q^{46} - 20 q^{47} - 5 q^{49} + 83 q^{50} - 80 q^{52} - 3 q^{53} - 28 q^{55} + 6 q^{56} + 2 q^{58} + 9 q^{59} - 15 q^{61} + 37 q^{62} - 49 q^{64} - 58 q^{65} + 76 q^{67} - 51 q^{68} + 3 q^{70} - 37 q^{71} + 27 q^{73} + 32 q^{74} + 4 q^{76} - 6 q^{77} + 5 q^{79} - 137 q^{80} - 55 q^{82} + 42 q^{83} - 48 q^{85} - 3 q^{86} + 151 q^{88} + 18 q^{89} + 7 q^{91} - 39 q^{92} - 35 q^{94} + 96 q^{95} - 27 q^{97}+O(q^{100}) $ 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8 + 12 * q^10 + q^11 + 13 * q^13 - 24 * q^16 + q^17 + 10 * q^19 + 46 * q^20 + 26 * q^22 - 8 * q^25 + 53 * q^26 + 4 * q^28 - 3 * q^29 - 13 * q^31 - 82 * q^32 + 42 * q^34 - 5 * q^35 - 32 * q^37 - 16 * q^38 + 20 * q^40 + 3 * q^41 + 12 * q^43 - 25 * q^44 - 13 * q^46 - 20 * q^47 - 5 * q^49 + 83 * q^50 - 80 * q^52 - 3 * q^53 - 28 * q^55 + 6 * q^56 + 2 * q^58 + 9 * q^59 - 15 * q^61 + 37 * q^62 - 49 * q^64 - 58 * q^65 + 76 * q^67 - 51 * q^68 + 3 * q^70 - 37 * q^71 + 27 * q^73 + 32 * q^74 + 4 * q^76 - 6 * q^77 + 5 * q^79 - 137 * q^80 - 55 * q^82 + 42 * q^83 - 48 * q^85 - 3 * q^86 + 151 * q^88 + 18 * q^89 + 7 * q^91 - 39 * q^92 - 35 * q^94 + 96 * q^95 - 27 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	2.13576	+	1.55172i	1.51021	+	1.09723i	0.966085	+	0.258224i	$0.0831372\pi$
$2$	2.13576	+	1.55172i	1.51021	+	1.09723i	0.544122	+	0.839006i	$0.316863\pi$
$3$		0			0
$3$		0			0
$4$	1.53559	+	4.72606i	0.767796	+	2.36303i
$5$	2.49476	−	1.81255i	1.11569	−	0.810595i	0.132139	−	0.991231i	$-0.457816\pi$
$5$	2.49476	−	1.81255i	1.11569	−	0.810595i	0.983550	+	0.180636i	$0.0578155\pi$
$6$		0			0
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$	−2.42230	+	7.45506i	−0.856411	+	2.63576i
$9$		0			0
$10$	8.14075			2.57433
$11$	−1.45539	−	2.98024i	−0.438818	−	0.898576i
$11$	−1.45539	−	2.98024i	−0.438818	−	0.898576i
$12$		0			0
$13$	4.56364	+	3.31568i	1.26573	+	0.919604i	0.999024	−	0.0441746i	$-0.0140658\pi$
$13$	4.56364	+	3.31568i	1.26573	+	0.919604i	0.266703	+	0.963779i	$0.414066\pi$
$14$	0.815786	−	2.51073i	0.218028	−	0.671021i
$15$		0			0
$16$	−8.70112	+	6.32173i	−2.17528	+	1.58043i
$17$	−4.53118	+	3.29210i	−1.09897	+	0.798451i	−0.980892	−	0.194553i	$-0.937674\pi$
$17$	−4.53118	+	3.29210i	−1.09897	+	0.798451i	−0.118081	+	0.993004i	$0.537674\pi$
$18$		0			0
$19$	0.0379017	−	0.116649i	0.00869524	−	0.0267612i	−0.946615	−	0.322367i	$-0.895521\pi$
$19$	0.0379017	−	0.116649i	0.00869524	−	0.0267612i	0.955310	+	0.295606i	$0.0955215\pi$
$20$	12.3971	+	9.00705i	2.77208	+	2.01404i
$21$		0			0
$22$	1.51613	−	8.62342i	0.323239	−	1.83852i
$23$	−1.67325			−0.348896			−0.174448	−	0.984666i	$-0.555814\pi$
$23$	−1.67325			−0.348896			−0.174448	+	0.984666i	$0.555814\pi$
$24$		0			0
$25$	1.39340	−	4.28844i	0.278680	−	0.857688i
$26$	4.60183	+	14.1630i	0.902492	+	2.77759i
$27$		0			0
$28$	4.02023	−	2.92087i	0.759752	−	0.551992i
$29$	−2.73492	−	8.41721i	−0.507861	−	1.56304i	−0.795906	−	0.605420i	$-0.793005\pi$
$29$	−2.73492	−	8.41721i	−0.507861	−	1.56304i	0.288045	−	0.957617i	$-0.406995\pi$
$30$		0			0
$31$	−1.29259	−	0.939120i	−0.232156	−	0.168671i	0.465626	−	0.884982i	$-0.345829\pi$
$31$	−1.29259	−	0.939120i	−0.232156	−	0.168671i	−0.697781	+	0.716311i	$0.745829\pi$
$32$	−12.7156			−2.24782
$33$		0			0
$34$	−14.7859			−2.53576
$35$	−2.49476	−	1.81255i	−0.421691	−	0.306376i
$36$		0			0
$37$	1.28943	+	3.96845i	0.211981	+	0.652409i	0.999354	+	0.0359331i	$0.0114403\pi$
$37$	1.28943	+	3.96845i	0.211981	+	0.652409i	−0.787374	+	0.616476i	$0.788560\pi$
$38$	0.261956	−	0.190322i	0.0424948	−	0.0308743i
$39$		0			0
$40$	7.46960	+	22.9891i	1.18105	+	3.63489i
$41$	−1.07803	+	3.31785i	−0.168361	+	0.518161i	−0.999268	−	0.0382497i	$-0.987822\pi$
$41$	−1.07803	+	3.31785i	−0.168361	+	0.518161i	0.830908	+	0.556411i	$0.187822\pi$
$42$		0			0
$43$	−5.10698			−0.778807			−0.389403	−	0.921067i	$-0.627319\pi$
$43$	−5.10698			−0.778807			−0.389403	+	0.921067i	$0.627319\pi$
$44$	11.8499	−	11.4547i	1.78644	−	1.72686i
$45$		0			0
$46$	−3.57364	−	2.59640i	−0.526905	−	0.382819i
$47$	0.492574	−	1.51599i	0.0718494	−	0.221130i	−0.908683	−	0.417486i	$-0.862911\pi$
$47$	0.492574	−	1.51599i	0.0718494	−	0.221130i	0.980532	+	0.196357i	$0.0629111\pi$
$48$		0			0
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	9.63040	−	6.99690i	1.36194	−	0.989511i
$51$		0			0
$52$	−8.66223	+	26.6596i	−1.20123	+	3.69702i
$53$	−9.59206	−	6.96904i	−1.31757	−	0.957271i	−0.999959	−	0.00904978i	$-0.997119\pi$
$53$	−9.59206	−	6.96904i	−1.31757	−	0.957271i	−0.317611	−	0.948221i	$-0.602881\pi$
$54$		0			0
$55$	−9.03267	−	4.79700i	−1.21797	−	0.646828i
$56$	7.83871			1.04749
$57$		0			0
$58$	7.22002	−	22.2209i	0.948035	−	2.91775i
$59$	−2.04398	−	6.29072i	−0.266103	−	0.818982i	−0.991437	−	0.130584i	$-0.958315\pi$
$59$	−2.04398	−	6.29072i	−0.266103	−	0.818982i	0.725334	−	0.688397i	$-0.241685\pi$
$60$		0			0
$61$	6.86789	−	4.98982i	0.879344	−	0.638880i	−0.0537342	−	0.998555i	$-0.517112\pi$
$61$	6.86789	−	4.98982i	0.879344	−	0.638880i	0.933078	+	0.359675i	$0.117112\pi$
$62$	−1.30340	−	4.01146i	−0.165532	−	0.509456i
$63$		0			0
$64$	−9.75511	−	7.08750i	−1.21939	−	0.885938i
$65$	17.3950			2.15758
$66$		0			0
$67$	−8.04949			−0.983402			−0.491701	−	0.870764i	$-0.663625\pi$
$67$	−8.04949			−0.983402			−0.491701	+	0.870764i	$0.663625\pi$
$68$	−22.5167	−	16.3593i	−2.73055	−	1.98386i
$69$		0			0
$70$	−2.51563	−	7.74231i	−0.300675	−	0.925383i
$71$	5.05133	−	3.67001i	0.599483	−	0.435550i	−0.246213	−	0.969216i	$-0.579186\pi$
$71$	5.05133	−	3.67001i	0.599483	−	0.435550i	0.845695	+	0.533666i	$0.179186\pi$
$72$		0			0
$73$	1.08466	+	3.33825i	0.126950	+	0.390713i	0.994251	−	0.107071i	$-0.0341472\pi$
$73$	1.08466	+	3.33825i	0.126950	+	0.390713i	−0.867301	+	0.497784i	$0.834147\pi$
$74$	−3.40401	+	10.4765i	−0.395708	+	1.21786i
$75$		0			0
$76$	0.609494			0.0699138
$77$	−2.38464	+	2.30511i	−0.271754	+	0.262691i
$78$		0			0
$79$	7.60289	+	5.52382i	0.855392	+	0.621479i	0.926627	−	0.375981i	$-0.122694\pi$
$79$	7.60289	+	5.52382i	0.855392	+	0.621479i	−0.0712355	+	0.997460i	$0.522694\pi$
$80$	−10.2487	+	31.5424i	−1.14584	+	3.52654i
$81$		0			0
$82$	−7.45078	+	5.41331i	−0.822801	+	0.597800i
$83$	−7.63216	+	5.54509i	−0.837738	+	0.608652i	−0.921738	−	0.387814i	$-0.873230\pi$
$83$	−7.63216	+	5.54509i	−0.837738	+	0.608652i	0.0839999	+	0.996466i	$0.473230\pi$
$84$		0			0
$85$	−5.33712	+	16.4260i	−0.578892	+	1.78165i
$86$	−10.9073	−	7.92458i	−1.17616	−	0.854530i
$87$		0			0
$88$	25.7433	−	3.63102i	2.74424	−	0.387068i
$89$	8.45556			0.896288			0.448144	−	0.893961i	$-0.352085\pi$
$89$	8.45556			0.896288			0.448144	+	0.893961i	$0.352085\pi$
$90$		0			0
$91$	1.74316	−	5.36488i	0.182732	−	0.562393i
$92$	−2.56942	−	7.90787i	−0.267881	−	0.824452i
$93$		0			0
$94$	3.40440	−	2.47344i	0.351137	−	0.255116i
$95$	−0.116877	−	0.359710i	−0.0119913	−	0.0369055i
$96$		0			0
$97$	4.59909	+	3.34143i	0.466966	+	0.339271i	0.796258	−	0.604957i	$-0.206810\pi$
$97$	4.59909	+	3.34143i	0.466966	+	0.339271i	−0.329291	+	0.944228i	$0.606810\pi$
$98$	−2.63994			−0.266674
$99$		0			0
$100$	22.4071			2.24071
$101$	13.6542	+	9.92038i	1.35865	+	0.987115i	0.998530	+	0.0542078i	$0.0172634\pi$
$101$	13.6542	+	9.92038i	1.35865	+	0.987115i	0.360117	+	0.932907i	$0.382737\pi$
$102$		0			0
$103$	−4.08433	−	12.5703i	−0.402441	−	1.23859i	−0.923013	−	0.384768i	$-0.874281\pi$
$103$	−4.08433	−	12.5703i	−0.402441	−	1.23859i	0.520572	−	0.853818i	$-0.325719\pi$
$104$	−35.7731	+	25.9907i	−3.50784	+	2.54859i
$105$		0			0
$106$	−9.67231	−	29.7683i	−0.939458	−	2.89135i
$107$	−3.42221	+	10.5325i	−0.330838	+	1.01821i	0.637899	+	0.770120i	$0.279804\pi$
$107$	−3.42221	+	10.5325i	−0.330838	+	1.01821i	−0.968736	+	0.248093i	$0.920196\pi$
$108$		0			0
$109$	−4.87369			−0.466815			−0.233407	−	0.972379i	$-0.574988\pi$
$109$	−4.87369			−0.466815			−0.233407	+	0.972379i	$0.574988\pi$
$110$	−11.8480	−	24.2614i	−1.12966	−	2.31323i
$111$		0			0
$112$	8.70112	+	6.32173i	0.822178	+	0.597347i
$113$	1.63242	−	5.02408i	0.153565	−	0.472626i	−0.844447	−	0.535639i	$-0.820071\pi$
$113$	1.63242	−	5.02408i	0.153565	−	0.472626i	0.998013	+	0.0630130i	$0.0200709\pi$
$114$		0			0
$115$	−4.17434	+	3.03284i	−0.389259	+	0.282813i
$116$	35.5806	−	25.8508i	3.30357	−	2.40019i
$117$		0			0
$118$	5.39598	−	16.6071i	0.496740	−	1.52881i
$119$	4.53118	+	3.29210i	0.415373	+	0.301786i
$120$		0			0
$121$	−6.76366	+	8.67484i	−0.614878	+	0.788622i
$122$	22.4109			2.02899
$123$		0			0
$124$	2.45346	−	7.55096i	0.220327	−	0.678096i
$125$	0.467754	+	1.43960i	0.0418372	+	0.128762i
$126$		0			0
$127$	9.17429	−	6.66551i	0.814086	−	0.591468i	−0.100926	−	0.994894i	$-0.532181\pi$
$127$	9.17429	−	6.66551i	0.814086	−	0.591468i	0.915012	+	0.403426i	$0.132181\pi$
$128$	−1.97808	−	6.08791i	−0.174839	−	0.538100i
$129$		0			0
$130$	37.1515	+	26.9921i	3.25840	+	2.36737i
$131$	0.970284			0.0847741			0.0423870	−	0.999101i	$-0.486504\pi$
$131$	0.970284			0.0847741			0.0423870	+	0.999101i	$0.486504\pi$
$132$		0			0
$133$	−0.122652			−0.0106353
$134$	−17.1918	−	12.4905i	−1.48514	−	1.07902i
$135$		0			0
$136$	−13.5669	−	41.7547i	−1.16335	−	3.58043i
$137$	−0.101208	+	0.0735323i	−0.00864682	+	0.00628229i	−0.592100	−	0.805864i	$-0.701701\pi$
$137$	−0.101208	+	0.0735323i	−0.00864682	+	0.00628229i	0.583453	+	0.812147i	$0.301701\pi$
$138$		0			0
$139$	−0.518637	−	1.59620i	−0.0439902	−	0.135388i	0.926649	−	0.375927i	$-0.122676\pi$
$139$	−0.518637	−	1.59620i	−0.0439902	−	0.135388i	−0.970639	+	0.240539i	$0.922676\pi$
$140$	4.73529	−	14.5737i	0.400205	−	1.23170i
$141$		0			0
$142$	16.4832			1.38324
$143$	3.23963	−	18.4264i	0.270911	−	1.54089i
$144$		0			0
$145$	−22.0795	−	16.0417i	−1.83361	−	1.33219i
$146$	−2.86345	+	8.81278i	−0.236981	+	0.729351i
$147$		0			0
$148$	−16.7751	+	12.1878i	−1.37891	+	1.00183i
$149$	11.4712	−	8.33429i	0.939754	−	0.682771i	−0.00860721	−	0.999963i	$-0.502740\pi$
$149$	11.4712	−	8.33429i	0.939754	−	0.682771i	0.948362	+	0.317191i	$0.102740\pi$
$150$		0			0
$151$	4.90791	−	15.1050i	0.399400	−	1.22923i	−0.526082	−	0.850434i	$-0.676339\pi$
$151$	4.90791	−	15.1050i	0.399400	−	1.22923i	0.925482	−	0.378793i	$-0.123661\pi$
$152$	0.777819	+	0.565119i	0.0630895	+	0.0458372i
$153$		0			0
$154$	−8.66987	+	1.22286i	−0.698638	+	0.0985412i
$155$	−4.92689			−0.395737
$156$		0			0
$157$	−2.84251	+	8.74833i	−0.226857	+	0.698193i	0.771241	+	0.636543i	$0.219636\pi$
$157$	−2.84251	+	8.74833i	−0.226857	+	0.698193i	−0.998098	+	0.0616500i	$0.980364\pi$
$158$	7.66650	+	23.5951i	0.609914	+	1.87712i
$159$		0			0
$160$	−31.7222	+	23.0476i	−2.50786	+	1.82207i
$161$	0.517061	+	1.59135i	0.0407501	+	0.125416i
$162$		0			0
$163$	−7.90363	−	5.74232i	−0.619060	−	0.449773i	0.233533	−	0.972349i	$-0.424971\pi$
$163$	−7.90363	−	5.74232i	−0.619060	−	0.449773i	−0.852593	+	0.522575i	$0.824971\pi$
$164$	−17.3358			−1.35370
$165$		0			0
$166$	−24.9048			−1.93299
$167$	4.93691	+	3.58688i	0.382030	+	0.277561i	0.762182	−	0.647363i	$-0.224128\pi$
$167$	4.93691	+	3.58688i	0.382030	+	0.277561i	−0.380152	+	0.924924i	$0.624128\pi$
$168$		0			0
$169$	5.81587	+	17.8994i	0.447375	+	1.37688i
$170$	−36.8872	+	26.8001i	−2.82912	+	2.05548i
$171$		0			0
$172$	−7.84223	−	24.1359i	−0.597964	−	1.84035i
$173$	−2.08221	+	6.40839i	−0.158308	+	0.487221i	−0.998481	−	0.0550972i	$-0.982453\pi$
$173$	−2.08221	+	6.40839i	−0.158308	+	0.487221i	0.840173	+	0.542318i	$0.182453\pi$
$174$		0			0
$175$	−4.50913			−0.340858
$176$	31.5038	+	16.7308i	2.37469	+	1.26113i
$177$		0			0
$178$	18.0590	+	13.1206i	1.35358	+	0.983433i
$179$	−4.01523	+	12.3576i	−0.300112	+	0.923651i	0.681344	+	0.731964i	$0.261396\pi$
$179$	−4.01523	+	12.3576i	−0.300112	+	0.923651i	−0.981456	+	0.191687i	$0.938604\pi$
$180$		0			0
$181$	3.31550	−	2.40886i	0.246440	−	0.179049i	−0.457708	−	0.889103i	$-0.651329\pi$
$181$	3.31550	−	2.40886i	0.246440	−	0.179049i	0.704147	+	0.710054i	$0.251329\pi$
$182$	12.0477	−	8.75319i	0.893038	−	0.648830i
$183$		0			0
$184$	4.05310	−	12.4741i	0.298798	−	0.919606i
$185$	10.4098	+	7.56317i	0.765344	+	0.556055i
$186$		0			0
$187$	16.4059	+	8.71272i	1.19972	+	0.637137i
$188$	7.92105			0.577702
$189$		0			0
$190$	0.308548	−	0.949613i	0.0223844	−	0.0688922i
$191$	−6.64498	−	20.4511i	−0.480814	−	1.47979i	−0.837953	−	0.545742i	$-0.816248\pi$
$191$	−6.64498	−	20.4511i	−0.480814	−	1.47979i	0.357139	−	0.934051i	$-0.383752\pi$
$192$		0			0
$193$	−14.3976	+	10.4604i	−1.03636	+	0.752960i	−0.969572	−	0.244808i	$-0.921275\pi$
$193$	−14.3976	+	10.4604i	−1.03636	+	0.752960i	−0.0667882	+	0.997767i	$0.521275\pi$
$194$	4.63757	+	14.2730i	0.332958	+	1.02474i
$195$		0			0
$196$	−4.02023	−	2.92087i	−0.287159	−	0.208633i
$197$	−18.1083			−1.29016			−0.645080	−	0.764115i	$-0.723176\pi$
$197$	−18.1083			−1.29016			−0.645080	+	0.764115i	$0.723176\pi$
$198$		0			0
$199$	2.67139			0.189370			0.0946848	−	0.995507i	$-0.469816\pi$
$199$	2.67139			0.189370			0.0946848	+	0.995507i	$0.469816\pi$
$200$	28.5954	+	20.7757i	2.02200	+	1.46907i
$201$		0			0
$202$	13.7685	+	42.3750i	0.968747	+	2.98150i
$203$	−7.16011	+	5.20212i	−0.502541	+	0.365117i
$204$		0			0
$205$	3.32432	+	10.2312i	0.232181	+	0.714579i
$206$	10.7824	−	33.1848i	0.751244	−	2.31209i
$207$		0			0
$208$	−60.6696			−4.20668
$209$	−0.402805	+	0.0568146i	−0.0278626	+	0.00392995i
$210$		0			0
$211$	6.59710	+	4.79308i	0.454163	+	0.329969i	0.791237	−	0.611509i	$-0.209437\pi$
$211$	6.59710	+	4.79308i	0.454163	+	0.329969i	−0.337074	+	0.941478i	$0.609437\pi$
$212$	18.2066	−	56.0343i	1.25044	−	3.84845i
$213$		0			0
$214$	−23.6524	+	17.1845i	−1.61685	+	1.17471i
$215$	−12.7407	+	9.25663i	−0.868906	+	0.631297i
$216$		0			0
$217$	−0.493725	+	1.51953i	−0.0335162	+	0.103152i
$218$	−10.4090	−	7.56259i	−0.704987	−	0.512203i
$219$		0			0
$220$	8.80045	−	50.0552i	0.593326	−	3.37472i
$221$	−31.5942			−2.12526
$222$		0			0
$223$	2.62282	−	8.07221i	0.175637	−	0.540555i	−0.824025	−	0.566554i	$-0.808276\pi$
$223$	2.62282	−	8.07221i	0.175637	−	0.540555i	0.999662	+	0.0259982i	$0.00827642\pi$
$224$	3.92933	+	12.0932i	0.262539	+	0.808012i
$225$		0			0
$226$	11.2824	−	8.19715i	0.750494	−	0.545266i
$227$	6.84547	+	21.0682i	0.454350	+	1.39835i	0.871897	+	0.489690i	$0.162890\pi$
$227$	6.84547	+	21.0682i	0.454350	+	1.39835i	−0.417546	+	0.908656i	$0.637110\pi$
$228$		0			0
$229$	7.26508	+	5.27839i	0.480090	+	0.348806i	0.801361	−	0.598181i	$-0.204110\pi$
$229$	7.26508	+	5.27839i	0.480090	+	0.348806i	−0.321270	+	0.946988i	$0.604110\pi$
$230$	−13.6215			−0.898173
$231$		0			0
$232$	69.3756			4.55473
$233$	16.0921	+	11.6916i	1.05423	+	0.765940i	0.973011	−	0.230757i	$-0.0741203\pi$
$233$	16.0921	+	11.6916i	1.05423	+	0.765940i	0.0812140	+	0.996697i	$0.474120\pi$
$234$		0			0
$235$	−1.51895	−	4.67483i	−0.0990851	−	0.304953i
$236$	26.5916	−	19.3199i	1.73097	−	1.25762i
$237$		0			0
$238$	4.56910	+	14.0622i	0.296170	+	0.911519i
$239$	2.84906	−	8.76851i	0.184291	−	0.567188i	−0.815645	−	0.578553i	$-0.803618\pi$
$239$	2.84906	−	8.76851i	0.184291	−	0.567188i	0.999935	+	0.0113649i	$0.00361764\pi$
$240$		0			0
$241$	−0.802919			−0.0517206			−0.0258603	−	0.999666i	$-0.508233\pi$
$241$	−0.802919			−0.0517206			−0.0258603	+	0.999666i	$0.508233\pi$
$242$	−27.9064	+	8.03206i	−1.79389	+	0.516320i
$243$		0			0
$244$	34.1285	+	24.7958i	2.18485	+	1.58739i
$245$	−0.952912	+	2.93276i	−0.0608793	+	0.187367i
$246$		0			0
$247$	0.559742	−	0.406676i	0.0356155	−	0.0258762i
$248$	10.1322	−	7.36149i	0.643397	−	0.467455i
$249$		0			0
$250$	−1.23484	+	3.80045i	−0.0780982	+	0.240362i
$251$	0.371563	+	0.269956i	0.0234528	+	0.0170395i	0.599450	−	0.800412i	$-0.295386\pi$
$251$	0.371563	+	0.269956i	0.0234528	+	0.0170395i	−0.575997	+	0.817452i	$0.695386\pi$
$252$		0			0
$253$	2.43523	+	4.98667i	0.153102	+	0.313509i
$254$	29.9370			1.87842
$255$		0			0
$256$	−2.23023	+	6.86394i	−0.139389	+	0.428996i
$257$	7.21782	+	22.2142i	0.450235	+	1.38568i	0.876639	+	0.481149i	$0.159780\pi$
$257$	7.21782	+	22.2142i	0.450235	+	1.38568i	−0.426404	+	0.904533i	$0.640220\pi$
$258$		0			0
$259$	3.37577	−	2.45264i	0.209760	−	0.152399i
$260$	26.7116	+	82.2099i	1.65658	+	5.09844i
$261$		0			0
$262$	2.07229	+	1.50561i	0.128026	+	0.0930166i
$263$	4.96169			0.305951			0.152975	−	0.988230i	$-0.451114\pi$
$263$	4.96169			0.305951			0.152975	+	0.988230i	$0.451114\pi$
$264$		0			0
$265$	−36.5615			−2.24596
$266$	−0.261956	−	0.190322i	−0.0160615	−	0.0116694i
$267$		0			0
$268$	−12.3607	−	38.0424i	−0.755052	−	2.32381i
$269$	0.834929	−	0.606611i	0.0509065	−	0.0369857i	−0.562041	−	0.827109i	$-0.689984\pi$
$269$	0.834929	−	0.606611i	0.0509065	−	0.0369857i	0.612948	+	0.790124i	$0.289984\pi$
$270$		0			0
$271$	4.67936	+	14.4016i	0.284251	+	0.874835i	0.986622	+	0.163024i	$0.0521247\pi$
$271$	4.67936	+	14.4016i	0.284251	+	0.874835i	−0.702371	+	0.711811i	$0.747875\pi$
$272$	18.6146	−	57.2898i	1.12868	−	3.47371i
$273$		0			0
$274$	−0.330258			−0.0199516
$275$	−14.8085	+	2.08871i	−0.892988	+	0.125954i
$276$		0			0
$277$	0.865659	+	0.628938i	0.0520124	+	0.0377892i	0.613488	−	0.789704i	$-0.289766\pi$
$277$	0.865659	+	0.628938i	0.0520124	+	0.0377892i	−0.561475	+	0.827494i	$0.689766\pi$
$278$	1.36917	−	4.21387i	0.0821174	−	0.252731i
$279$		0			0
$280$	19.5557	−	14.2080i	1.16868	−	0.849092i
$281$	−25.3295	+	18.4029i	−1.51103	+	1.09783i	−0.545313	+	0.838232i	$0.683589\pi$
$281$	−25.3295	+	18.4029i	−1.51103	+	1.09783i	−0.965717	+	0.259596i	$0.916411\pi$
$282$		0			0
$283$	9.87775	−	30.4006i	0.587171	−	1.80713i	−0.00320001	−	0.999995i	$-0.501019\pi$
$283$	9.87775	−	30.4006i	0.587171	−	1.80713i	0.590371	−	0.807132i	$-0.298981\pi$
$284$	25.1015	+	18.2373i	1.48950	+	1.08218i
$285$		0			0
$286$	35.5116	−	34.3272i	2.09984	−	2.02981i
$287$	3.48859			0.205925
$288$		0			0
$289$	4.44043	−	13.6662i	0.261202	−	0.803896i
$290$	−22.2643	−	68.5224i	−1.30740	−	4.02377i
$291$		0			0
$292$	−14.1112	+	10.2524i	−0.825795	+	0.599975i
$293$	0.146154	+	0.449814i	0.00853838	+	0.0262784i	0.955235	−	0.295848i	$-0.0956023\pi$
$293$	0.146154	+	0.449814i	0.00853838	+	0.0262784i	−0.946697	+	0.322127i	$0.895602\pi$
$294$		0			0
$295$	−16.5014	−	11.9890i	−0.960751	−	0.698027i
$296$	−32.7084			−1.90114
$297$		0			0
$298$	37.4321			2.16838
$299$	−7.63609	−	5.54795i	−0.441607	−	0.320846i
$300$		0			0
$301$	1.57814	+	4.85702i	0.0909626	+	0.279954i
$302$	33.9208	−	24.6449i	1.95192	−	1.41815i
$303$		0			0
$304$	0.407639	+	1.25458i	0.0233797	+	0.0719553i
$305$	8.08944	−	24.8967i	0.463200	−	1.42558i
$306$		0			0
$307$	−22.3522			−1.27571			−0.637854	−	0.770158i	$-0.720177\pi$
$307$	−22.3522			−1.27571			−0.637854	+	0.770158i	$0.720177\pi$
$308$	−14.5559	−	7.73024i	−0.829400	−	0.440471i
$309$		0			0
$310$	−10.5226	−	7.64514i	−0.597645	−	0.434215i
$311$	−6.79337	+	20.9078i	−0.385216	+	1.18557i	0.551107	+	0.834435i	$0.314206\pi$
$311$	−6.79337	+	20.9078i	−0.385216	+	1.18557i	−0.936323	+	0.351140i	$0.885794\pi$
$312$		0			0
$313$	6.43190	−	4.67305i	0.363553	−	0.264136i	−0.390980	−	0.920399i	$-0.627864\pi$
$313$	6.43190	−	4.67305i	0.363553	−	0.264136i	0.754532	+	0.656263i	$0.227864\pi$
$314$	−19.6458	+	14.2735i	−1.10868	+	0.805502i
$315$		0			0
$316$	−14.4310	+	44.4141i	−0.811808	+	2.49849i
$317$	−12.2345	−	8.88889i	−0.687158	−	0.499250i	0.188566	−	0.982060i	$-0.439616\pi$
$317$	−12.2345	−	8.88889i	−0.687158	−	0.499250i	−0.875725	+	0.482811i	$0.839616\pi$
$318$		0			0
$319$	−21.1049	+	20.4011i	−1.18165	+	1.14224i
$320$	−37.1831			−2.07860
$321$		0			0
$322$	−1.36501	+	4.20107i	−0.0760691	+	0.234116i
$323$	0.212282	+	0.653336i	0.0118117	+	0.0363526i
$324$		0			0
$325$	20.5781	−	14.9508i	1.14147	−	0.829323i
$326$	−7.96976	−	24.5284i	−0.441404	−	1.35850i
$327$		0			0
$328$	−22.1234	−	16.0736i	−1.22156	−	0.887517i
$329$	−1.59400			−0.0878803
$330$		0			0
$331$	−6.02542			−0.331187			−0.165594	−	0.986194i	$-0.552954\pi$
$331$	−6.02542			−0.331187			−0.165594	+	0.986194i	$0.552954\pi$
$332$	−37.9263	−	27.5551i	−2.08148	−	1.51228i
$333$		0			0
$334$	4.97822	+	15.3214i	0.272396	+	0.838349i
$335$	−20.0815	+	14.5901i	−1.09717	+	0.797141i
$336$		0			0
$337$	6.44281	+	19.8289i	0.350962	+	1.08015i	0.958314	+	0.285718i	$0.0922320\pi$
$337$	6.44281	+	19.8289i	0.350962	+	1.08015i	−0.607351	+	0.794433i	$0.707768\pi$
$338$	−15.3536	+	47.2534i	−0.835123	+	2.57025i
$339$		0			0
$340$	−85.8258			−4.65456
$341$	−0.917579	+	5.21901i	−0.0496897	+	0.282625i
$342$		0			0
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	12.3706	−	38.0728i	0.666979	−	2.05275i
$345$		0			0
$346$	−14.3911	+	10.4557i	−0.773670	+	0.562104i
$347$	1.20810	−	0.877737i	0.0648543	−	0.0471194i	−0.554886	−	0.831927i	$-0.687238\pi$
$347$	1.20810	−	0.877737i	0.0648543	−	0.0471194i	0.619740	+	0.784807i	$0.287238\pi$
$348$		0			0
$349$	−6.63753	+	20.4282i	−0.355299	+	1.09350i	0.600537	+	0.799597i	$0.294954\pi$
$349$	−6.63753	+	20.4282i	−0.355299	+	1.09350i	−0.955836	+	0.293901i	$0.905046\pi$
$350$	−9.63040	−	6.99690i	−0.514767	−	0.374000i
$351$		0			0
$352$	18.5062	+	37.8954i	0.986381	+	2.01983i
$353$	−11.4760			−0.610808			−0.305404	−	0.952223i	$-0.598792\pi$
$353$	−11.4760			−0.610808			−0.305404	+	0.952223i	$0.598792\pi$
$354$		0			0
$355$	5.94978	−	18.3115i	0.315782	−	0.971876i
$356$	12.9843	+	39.9615i	0.688166	+	2.11796i
$357$		0			0
$358$	−27.7511	+	20.1623i	−1.46669	+	1.06561i
$359$	1.76906	+	5.44462i	0.0933676	+	0.287356i	0.986825	−	0.161792i	$-0.0517275\pi$
$359$	1.76906	+	5.44462i	0.0933676	+	0.287356i	−0.893457	+	0.449148i	$0.851727\pi$
$360$		0			0
$361$	15.3592	+	11.1591i	0.808376	+	0.587320i
$362$	10.8190			0.568632
$363$		0			0
$364$	28.0316			1.46925
$365$	8.75671	+	6.36212i	0.458347	+	0.333009i
$366$		0			0
$367$	5.40752	+	16.6426i	0.282270	+	0.868738i	0.987204	+	0.159465i	$0.0509768\pi$
$367$	5.40752	+	16.6426i	0.282270	+	0.868738i	−0.704933	+	0.709273i	$0.749023\pi$
$368$	14.5591	−	10.5778i	0.758946	−	0.551406i
$369$		0			0
$370$	10.4969	+	32.3062i	0.545708	+	1.67952i
$371$	−3.66384	+	11.2761i	−0.190217	+	0.585428i
$372$		0			0
$373$	−9.54362			−0.494150			−0.247075	−	0.968996i	$-0.579469\pi$
$373$	−9.54362			−0.494150			−0.247075	+	0.968996i	$0.579469\pi$
$374$	21.5193	+	44.0655i	1.11274	+	2.27857i
$375$		0			0
$376$	10.1086	+	7.34434i	0.521312	+	0.378756i
$377$	15.4276	−	47.4813i	0.794562	−	2.44541i
$378$		0			0
$379$	−25.8566	+	18.7859i	−1.32816	+	0.964967i	−0.328372	+	0.944549i	$0.606500\pi$
$379$	−25.8566	+	18.7859i	−1.32816	+	0.964967i	−0.999792	+	0.0204186i	$0.993500\pi$
$380$	1.52054	−	1.10474i	0.0780020	−	0.0566718i
$381$		0			0
$382$	17.5423	−	53.9898i	0.897545	−	2.76236i
$383$	−7.94646	−	5.77344i	−0.406045	−	0.295009i	0.365954	−	0.930633i	$-0.380743\pi$
$383$	−7.94646	−	5.77344i	−0.406045	−	0.295009i	−0.771999	+	0.635624i	$0.780743\pi$
$384$		0			0
$385$	−1.77097	+	10.0729i	−0.0902571	+	0.513365i
$386$	−46.9814			−2.39129
$387$		0			0
$388$	−8.72950	+	26.8666i	−0.443173	+	1.36395i
$389$	−10.2593	−	31.5749i	−0.520167	−	1.60091i	−0.773680	−	0.633577i	$-0.781586\pi$
$389$	−10.2593	−	31.5749i	−0.520167	−	1.60091i	0.253513	−	0.967332i	$-0.418414\pi$
$390$		0			0
$391$	7.58178	−	5.50849i	0.383427	−	0.278576i
$392$	−2.42230	−	7.45506i	−0.122344	−	0.376537i
$393$		0			0
$394$	−38.6748	−	28.0989i	−1.94841	−	1.41560i
$395$	28.9795			1.45812
$396$		0			0
$397$	23.6535			1.18713			0.593566	−	0.804785i	$-0.297719\pi$
$397$	23.6535			1.18713			0.593566	+	0.804785i	$0.297719\pi$
$398$	5.70543	+	4.14524i	0.285987	+	0.207782i
$399$		0			0
$400$	14.9862	+	46.1229i	0.749312	+	2.30615i
$401$	20.4469	−	14.8555i	1.02107	−	0.741849i	0.0545658	−	0.998510i	$-0.482623\pi$
$401$	20.4469	−	14.8555i	1.02107	−	0.741849i	0.966501	+	0.256661i	$0.0826225\pi$
$402$		0			0
$403$	−2.78509	−	8.57162i	−0.138735	−	0.426983i
$404$	−25.9170	+	79.7644i	−1.28942	+	3.96843i
$405$		0			0
$406$	−23.3645			−1.15956
$407$	9.95031	−	9.61846i	0.493219	−	0.476769i
$408$		0			0
$409$	−11.3048	−	8.21344i	−0.558988	−	0.406129i	0.272100	−	0.962269i	$-0.412282\pi$
$409$	−11.3048	−	8.21344i	−0.558988	−	0.406129i	−0.831088	+	0.556140i	$0.812282\pi$
$410$	−8.77601	+	27.0098i	−0.433416	+	1.33392i
$411$		0			0
$412$	53.1361	−	38.6056i	2.61783	−	1.90196i
$413$	−5.35120	+	3.88788i	−0.263315	+	0.191310i
$414$		0			0
$415$	−8.98964	+	27.6673i	−0.441284	+	1.35813i
$416$	−58.0293	−	42.1608i	−2.84512	−	2.06710i
$417$		0			0
$418$	−0.948453	−	0.503697i	−0.0463904	−	0.0246366i
$419$	−29.7445			−1.45311			−0.726556	−	0.687107i	$-0.758880\pi$
$419$	−29.7445			−1.45311			−0.726556	+	0.687107i	$0.758880\pi$
$420$		0			0
$421$	11.2073	−	34.4925i	0.546210	−	1.68106i	−0.171887	−	0.985117i	$-0.554986\pi$
$421$	11.2073	−	34.4925i	0.546210	−	1.68106i	0.718096	−	0.695944i	$-0.245014\pi$
$422$	6.65230	+	20.4737i	0.323829	+	0.996643i
$423$		0			0
$424$	75.1894	−	54.6283i	3.65152	−	2.65298i
$425$	7.80422	+	24.0189i	0.378560	+	1.16509i
$426$		0			0
$427$	−6.86789	−	4.98982i	−0.332361	−	0.241474i
$428$	−55.0323			−2.66009
$429$		0			0
$430$	−41.5746			−2.00491
$431$	28.9682	+	21.0466i	1.39535	+	1.01378i	0.995255	+	0.0973046i	$0.0310221\pi$
$431$	28.9682	+	21.0466i	1.39535	+	1.01378i	0.400093	+	0.916475i	$0.368978\pi$
$432$		0			0
$433$	−7.13701	−	21.9655i	−0.342983	−	1.05559i	−0.962655	−	0.270731i	$-0.912734\pi$
$433$	−7.13701	−	21.9655i	−0.342983	−	1.05559i	0.619672	−	0.784861i	$-0.287266\pi$
$434$	−3.41235	+	2.47922i	−0.163798	+	0.119006i
$435$		0			0
$436$	−7.48400	−	23.0334i	−0.358419	−	1.10310i
$437$	−0.0634188	+	0.195183i	−0.00303373	+	0.00933687i
$438$		0			0
$439$	24.7837			1.18286			0.591431	−	0.806356i	$-0.298563\pi$
$439$	24.7837			1.18286			0.591431	+	0.806356i	$0.298563\pi$
$440$	57.6418	−	55.7194i	2.74796	−	2.65632i
$441$		0			0
$442$	−67.4776	−	49.0253i	−3.20958	−	2.33190i
$443$	−4.10823	+	12.6438i	−0.195188	+	0.600727i	0.804786	+	0.593565i	$0.202280\pi$
$443$	−4.10823	+	12.6438i	−0.195188	+	0.600727i	−0.999974	+	0.00716250i	$0.997720\pi$
$444$		0			0
$445$	21.0946	−	15.3261i	0.999978	−	0.726527i
$446$	18.1275	−	13.1704i	0.858362	−	0.623636i
$447$		0			0
$448$	−3.72612	+	11.4678i	−0.176043	+	0.541804i
$449$	16.8853	+	12.2679i	0.796866	+	0.578957i	0.909993	−	0.414623i	$-0.136087\pi$
$449$	16.8853	+	12.2679i	0.796866	+	0.578957i	−0.113127	+	0.993581i	$0.536087\pi$
$450$		0			0
$451$	11.4569	−	1.61597i	0.539487	−	0.0760932i
$452$	26.2509			1.23474
$453$		0			0
$454$	−18.0716	+	55.6188i	−0.848144	+	2.61032i
$455$	−5.37535	−	16.5436i	−0.252000	−	0.775577i
$456$		0			0
$457$	22.8421	−	16.5958i	1.06851	−	0.776317i	0.0928655	−	0.995679i	$-0.470397\pi$
$457$	22.8421	−	16.5958i	1.06851	−	0.776317i	0.975644	+	0.219361i	$0.0703973\pi$
$458$	7.32587	+	22.5467i	0.342316	+	1.05354i
$459$		0			0
$460$	−20.7435	−	15.0710i	−0.967169	−	0.702689i
$461$	13.5432			0.630770			0.315385	−	0.948964i	$-0.397866\pi$
$461$	13.5432			0.630770			0.315385	+	0.948964i	$0.397866\pi$
$462$		0			0
$463$	−33.9584			−1.57818			−0.789090	−	0.614277i	$-0.789448\pi$
$463$	−33.9584			−1.57818			−0.789090	+	0.614277i	$0.789448\pi$
$464$	77.0082	+	55.9497i	3.57502	+	2.59740i
$465$		0			0
$466$	16.2267	+	49.9406i	0.751687	+	2.31346i
$467$	10.1781	−	7.39484i	0.470987	−	0.342192i	−0.326839	−	0.945080i	$-0.605983\pi$
$467$	10.1781	−	7.39484i	0.470987	−	0.342192i	0.797826	+	0.602888i	$0.205983\pi$
$468$		0			0
$469$	2.48743	+	7.65552i	0.114859	+	0.353499i
$470$	4.00992	−	12.3413i	0.184964	−	0.569261i
$471$		0			0
$472$	51.8488			2.38653
$473$	7.43266	+	15.2200i	0.341754	+	0.699817i
$474$		0			0
$475$	−0.447432	−	0.325078i	−0.0205296	−	0.0149156i
$476$	−8.60062	+	26.4700i	−0.394209	+	1.21325i
$477$		0			0
$478$	19.6912	−	14.3065i	0.900653	−	0.654362i
$479$	23.3738	−	16.9821i	1.06798	−	0.775931i	0.0924293	−	0.995719i	$-0.470537\pi$
$479$	23.3738	−	16.9821i	1.06798	−	0.775931i	0.975548	+	0.219789i	$0.0705368\pi$
$480$		0			0
$481$	−7.27363	+	22.3859i	−0.331649	+	1.02071i
$482$	−1.71484	−	1.24590i	−0.0781088	−	0.0567494i
$483$		0			0
$484$	−51.3841	−	18.6445i	−2.33564	−	0.847476i
$485$	17.5301			0.796001
$486$		0			0
$487$	7.88232	−	24.2593i	0.357182	−	1.09929i	−0.597552	−	0.801830i	$-0.703860\pi$
$487$	7.88232	−	24.2593i	0.357182	−	1.09929i	0.954734	−	0.297462i	$-0.0961403\pi$
$488$	20.5633	+	63.2874i	0.930857	+	2.86488i
$489$		0			0
$490$	−6.58600	+	4.78501i	−0.297525	+	0.216165i
$491$	−1.44187	−	4.43761i	−0.0650705	−	0.200266i	0.913235	−	0.407433i	$-0.133576\pi$
$491$	−1.44187	−	4.43761i	−0.0650705	−	0.200266i	−0.978306	+	0.207166i	$0.933576\pi$
$492$		0			0
$493$	40.1027	+	29.1363i	1.80613	+	1.31223i
$494$	1.82652			0.0821789
$495$		0			0
$496$	17.1838			0.771576
$497$	−5.05133	−	3.67001i	−0.226583	−	0.164622i
$498$		0			0
$499$	−5.71553	−	17.5906i	−0.255862	−	0.787463i	−0.993659	−	0.112440i	$-0.964134\pi$
$499$	−5.71553	−	17.5906i	−0.255862	−	0.787463i	0.737796	−	0.675023i	$-0.235866\pi$
$500$	−6.08535	+	4.42127i	−0.272145	+	0.197725i
$501$		0			0
$502$	0.374672	+	1.15312i	0.0167224	+	0.0514663i
$503$	7.14065	−	21.9767i	0.318386	−	0.979891i	−0.655952	−	0.754802i	$-0.727733\pi$
$503$	7.14065	−	21.9767i	0.318386	−	0.979891i	0.974338	−	0.225089i	$-0.0722673\pi$
$504$		0			0
$505$	52.0451			2.31598
$506$	−2.53685	+	14.4291i	−0.112777	+	0.641452i
$507$		0			0
$508$	45.5896	+	33.1228i	2.02271	+	1.46959i
$509$	8.85461	−	27.2517i	0.392474	−	1.20791i	−0.538438	−	0.842665i	$-0.680985\pi$
$509$	8.85461	−	27.2517i	0.392474	−	1.20791i	0.930912	−	0.365245i	$-0.119015\pi$
$510$		0			0
$511$	2.83969	−	2.06315i	0.125620	−	0.0912685i
$512$	−25.7715	+	18.7241i	−1.13895	+	0.827495i
$513$		0			0
$514$	−19.0546	+	58.6441i	−0.840463	+	2.58668i
$515$	−32.9736	−	23.9567i	−1.45299	−	1.05566i
$516$		0			0
$517$	−5.23490	+	0.738369i	−0.230231	+	0.0324734i
$518$	11.0156			0.483998
$519$		0			0
$520$	−42.1358	+	129.681i	−1.84778	+	5.68688i
$521$	2.46972	+	7.60103i	0.108201	+	0.333007i	0.990468	−	0.137741i	$-0.0439841\pi$
$521$	2.46972	+	7.60103i	0.108201	+	0.333007i	−0.882268	+	0.470748i	$0.843984\pi$
$522$		0			0
$523$	−30.1277	+	21.8891i	−1.31739	+	0.957143i	−0.317433	+	0.948281i	$0.602821\pi$
$523$	−30.1277	+	21.8891i	−1.31739	+	0.957143i	−0.999961	+	0.00886223i	$0.997179\pi$
$524$	1.48996	+	4.58562i	0.0650892	+	0.200324i
$525$		0			0
$526$	10.5970	+	7.69914i	0.462049	+	0.335699i
$527$	8.94863			0.389808
$528$		0			0
$529$	−20.2002			−0.878272
$530$	−78.0865	−	56.7332i	−3.39186	−	2.46433i
$531$		0			0
$532$	−0.188344	−	0.579663i	−0.00816575	−	0.0251316i
$533$	−15.9207	+	11.5671i	−0.689601	+	0.501025i
$534$		0			0
$535$	10.5530	+	32.4789i	0.456247	+	1.40418i
$536$	19.4983	−	60.0095i	0.842196	−	2.59201i
$537$		0			0
$538$	2.72449			0.117461
$539$	2.92918	+	1.55561i	0.126169	+	0.0670047i
$540$		0			0
$541$	18.5985	+	13.5126i	0.799613	+	0.580953i	0.910801	−	0.412846i	$-0.135465\pi$
$541$	18.5985	+	13.5126i	0.799613	+	0.580953i	−0.111187	+	0.993799i	$0.535465\pi$
$542$	−12.3532	+	38.0193i	−0.530617	+	1.63307i
$543$		0			0
$544$	57.6166	−	41.8609i	2.47029	−	1.79477i
$545$	−12.1587	+	8.83379i	−0.520820	+	0.378398i
$546$		0			0
$547$	9.40294	−	28.9393i	0.402041	−	1.23735i	−0.521301	−	0.853373i	$-0.674553\pi$
$547$	9.40294	−	28.9393i	0.402041	−	1.23735i	0.923341	−	0.383981i	$-0.125447\pi$
$548$	−0.502933	−	0.365402i	−0.0214842	−	0.0156092i
$549$		0			0
$550$	−34.8685	−	18.5177i	−1.48680	−	0.789596i
$551$	−1.08552			−0.0462447
$552$		0			0
$553$	2.90405	−	8.93773i	0.123493	−	0.380071i
$554$	0.872902	+	2.68652i	0.0370861	+	0.114139i
$555$		0			0
$556$	6.74734	−	4.90223i	0.286151	−	0.207901i
$557$	13.1274	+	40.4020i	0.556226	+	1.71189i	0.692684	+	0.721241i	$0.256428\pi$
$557$	13.1274	+	40.4020i	0.556226	+	1.71189i	−0.136459	+	0.990646i	$0.543572\pi$
$558$		0			0
$559$	−23.3064	−	16.9331i	−0.985756	−	0.716194i
$560$	33.1656			1.40150
$561$		0			0
$562$	−82.6538			−3.48654
$563$	9.78569	+	7.10972i	0.412418	+	0.299639i	0.774580	−	0.632476i	$-0.217961\pi$
$563$	9.78569	+	7.10972i	0.412418	+	0.299639i	−0.362162	+	0.932115i	$0.617961\pi$
$564$		0			0
$565$	−5.03388	−	15.4927i	−0.211777	−	0.651783i
$566$	68.2696	−	49.6007i	2.86958	−	2.08487i
$567$		0			0
$568$	15.1243	+	46.5478i	0.634602	+	1.95310i
$569$	10.5082	−	32.3410i	0.440528	−	1.35581i	−0.446786	−	0.894641i	$-0.647432\pi$
$569$	10.5082	−	32.3410i	0.440528	−	1.35581i	0.887314	−	0.461165i	$-0.152568\pi$
$570$		0			0
$571$	16.0762			0.672767			0.336383	−	0.941725i	$-0.390796\pi$
$571$	16.0762			0.672767			0.336383	+	0.941725i	$0.390796\pi$
$572$	92.0589	−	12.9847i	3.84918	−	0.542917i
$573$		0			0
$574$	7.45078	+	5.41331i	0.310990	+	0.225947i
$575$	−2.33150	+	7.17561i	−0.0972302	+	0.299244i
$576$		0			0
$577$	−3.18808	+	2.31628i	−0.132722	+	0.0964278i	−0.652165	−	0.758077i	$-0.726139\pi$
$577$	−3.18808	+	2.31628i	−0.132722	+	0.0964278i	0.519444	+	0.854505i	$0.326139\pi$
$578$	30.6898	−	22.2974i	1.27653	−	0.927451i
$579$		0			0
$580$	41.9091	−	128.983i	1.74018	−	5.35572i
$581$	7.63216	+	5.54509i	0.316635	+	0.230049i
$582$		0			0
$583$	−6.80919	+	38.7293i	−0.282008	+	1.60400i
$584$	−27.5142			−1.13855
$585$		0			0
$586$	−0.385836	+	1.18748i	−0.0159388	+	0.0490544i
$587$	−3.06798	−	9.44228i	−0.126629	−	0.389725i	0.867565	−	0.497324i	$-0.165684\pi$
$587$	−3.06798	−	9.44228i	−0.126629	−	0.389725i	−0.994194	+	0.107599i	$0.965684\pi$
$588$		0			0
$589$	−0.158539	+	0.115185i	−0.00653249	+	0.00474613i
$590$	−16.6395	−	51.2111i	−0.685038	−	2.10833i
$591$		0			0
$592$	−36.3069	−	26.3785i	−1.49221	−	1.08415i
$593$	−1.35512			−0.0556480			−0.0278240	−	0.999613i	$-0.508858\pi$
$593$	−1.35512			−0.0556480			−0.0278240	+	0.999613i	$0.508858\pi$
$594$		0			0
$595$	17.2713			0.708053
$596$	57.0034	+	41.4154i	2.33495	+	1.69644i
$597$		0			0
$598$	−7.69999	−	23.6981i	−0.314876	−	0.969088i
$599$	−24.8920	+	18.0851i	−1.01706	+	0.738938i	−0.965678	−	0.259742i	$-0.916363\pi$
$599$	−24.8920	+	18.0851i	−1.01706	+	0.738938i	−0.0513821	+	0.998679i	$0.516363\pi$
$600$		0			0
$601$	−4.08413	−	12.5697i	−0.166595	−	0.512727i	0.832555	−	0.553942i	$-0.186877\pi$
$601$	−4.08413	−	12.5697i	−0.166595	−	0.512727i	−0.999150	+	0.0412149i	$0.986877\pi$
$602$	−4.16620	+	12.8222i	−0.169802	+	0.522596i
$603$		0			0
$604$	78.9237			3.21136
$605$	−1.15013	+	33.9011i	−0.0467593	+	1.37827i
$606$		0			0
$607$	4.71906	+	3.42860i	0.191541	+	0.139162i	0.679423	−	0.733747i	$-0.262230\pi$
$607$	4.71906	+	3.42860i	0.191541	+	0.139162i	−0.487882	+	0.872910i	$0.662230\pi$
$608$	−0.481941	+	1.48326i	−0.0195453	+	0.0601543i
$609$		0			0
$610$	55.9098	−	40.6208i	2.26372	−	1.64469i
$611$	7.27446	−	5.28521i	0.294293	−	0.213817i
$612$		0			0
$613$	2.06340	−	6.35050i	0.0833400	−	0.256494i	−0.900700	−	0.434442i	$-0.856946\pi$
$613$	2.06340	−	6.35050i	0.0833400	−	0.256494i	0.984040	+	0.177947i	$0.0569457\pi$
$614$	−47.7388	−	34.6843i	−1.92658	−	1.39974i
$615$		0			0
$616$	−11.4084	−	23.3612i	−0.459658	−	0.941252i
$617$	−15.1716			−0.610785			−0.305392	−	0.952227i	$-0.598788\pi$
$617$	−15.1716			−0.610785			−0.305392	+	0.952227i	$0.598788\pi$
$618$		0			0
$619$	8.64944	−	26.6202i	0.347650	−	1.06996i	−0.612499	−	0.790471i	$-0.709836\pi$
$619$	8.64944	−	26.6202i	0.347650	−	1.06996i	0.960150	−	0.279487i	$-0.0901642\pi$
$620$	−7.56569	−	23.2848i	−0.303845	−	0.935140i
$621$		0			0
$622$	−46.9520	+	34.1126i	−1.88260	+	1.36779i
$623$	−2.61291	−	8.04172i	−0.104684	−	0.322185i
$624$		0			0
$625$	22.0161	+	15.9956i	0.880644	+	0.639825i
$626$	20.9882			0.838858
$627$		0			0
$628$	−45.7101			−1.82403
$629$	−18.9072	−	13.7369i	−0.753878	−	0.547724i
$630$		0			0
$631$	−1.72442	−	5.30723i	−0.0686482	−	0.211277i	0.910847	−	0.412743i	$-0.135429\pi$
$631$	−1.72442	−	5.30723i	−0.0686482	−	0.211277i	−0.979495	+	0.201466i	$0.935429\pi$
$632$	−59.5969	+	43.2997i	−2.37064	+	1.72237i
$633$		0			0
$634$	−12.3369	−	37.9690i	−0.489960	−	1.50794i
$635$	10.8061	−	33.2576i	0.428826	−	1.31979i
$636$		0			0
$637$	−5.64097			−0.223503
$638$	−76.7317	+	10.8228i	−3.03784	+	0.428479i
$639$		0			0
$640$	−15.9694	−	11.6025i	−0.631248	−	0.458628i
$641$	−3.38889	+	10.4299i	−0.133853	+	0.411958i	−0.995410	−	0.0957036i	$-0.969490\pi$
$641$	−3.38889	+	10.4299i	−0.133853	+	0.411958i	0.861557	+	0.507661i	$0.169490\pi$
$642$		0			0
$643$	−0.322913	+	0.234610i	−0.0127344	+	0.00925212i	−0.594134	−	0.804366i	$-0.702505\pi$
$643$	−0.322913	+	0.234610i	−0.0127344	+	0.00925212i	0.581400	+	0.813618i	$0.302505\pi$
$644$	−6.72683	+	4.88733i	−0.265074	+	0.192588i
$645$		0			0
$646$	−0.560411	+	1.72477i	−0.0220491	+	0.0678600i
$647$	25.3186	+	18.3951i	0.995378	+	0.723185i	0.961092	−	0.276227i	$-0.0890843\pi$
$647$	25.3186	+	18.3951i	0.995378	+	0.723185i	0.0342860	+	0.999412i	$0.489084\pi$
$648$		0			0
$649$	−15.7731	+	15.2470i	−0.619146	+	0.598498i
$650$	67.1492			2.63381
$651$		0			0
$652$	15.0018	−	46.1709i	0.587518	−	1.80819i
$653$	8.08970	+	24.8975i	0.316574	+	0.974316i	0.975102	+	0.221759i	$0.0711798\pi$
$653$	8.08970	+	24.8975i	0.316574	+	0.974316i	−0.658527	+	0.752557i	$0.728820\pi$
$654$		0			0
$655$	2.42062	−	1.75868i	0.0945815	−	0.0687175i
$656$	−11.5944	−	35.6840i	−0.452687	−	1.39323i
$657$		0			0
$658$	−3.40440	−	2.47344i	−0.132717	−	0.0964249i
$659$	5.84482			0.227682			0.113841	−	0.993499i	$-0.463685\pi$
$659$	5.84482			0.227682			0.113841	+	0.993499i	$0.463685\pi$
$660$		0			0
$661$	−6.32811			−0.246135			−0.123067	−	0.992398i	$-0.539273\pi$
$661$	−6.32811			−0.246135			−0.123067	+	0.992398i	$0.539273\pi$
$662$	−12.8688	−	9.34975i	−0.500161	−	0.363388i
$663$		0			0
$664$	−22.8516	−	70.3300i	−0.886814	−	2.72933i
$665$	−0.305988	+	0.222313i	−0.0118657	+	0.00862094i
$666$		0			0
$667$	4.57619	+	14.0841i	0.177191	+	0.545337i
$668$	−9.37073	+	28.8401i	−0.362565	+	1.11586i
$669$		0			0
$670$	−65.5289			−2.53160
$671$	−24.8663	−	13.2058i	−0.959954	−	0.509805i
$672$		0			0
$673$	−3.41334	−	2.47994i	−0.131575	−	0.0955946i	0.520051	−	0.854135i	$-0.325913\pi$
$673$	−3.41334	−	2.47994i	−0.131575	−	0.0955946i	−0.651626	+	0.758540i	$0.725913\pi$
$674$	−17.0086	+	52.3472i	−0.655148	+	2.01634i
$675$		0			0
$676$	−75.6630	+	54.9724i	−2.91012	+	2.11432i
$677$	14.5014	−	10.5359i	0.557333	−	0.404926i	−0.273149	−	0.961972i	$-0.588065\pi$
$677$	14.5014	−	10.5359i	0.557333	−	0.404926i	0.830482	+	0.557045i	$0.188065\pi$
$678$		0			0
$679$	1.75669	−	5.40655i	0.0674157	−	0.207484i
$680$	−109.528	−	79.5771i	−4.20022	−	3.05164i
$681$		0			0
$682$	−10.0582	+	9.72271i	−0.385147	+	0.372302i
$683$	5.96513			0.228249			0.114125	−	0.993466i	$-0.463594\pi$
$683$	5.96513			0.228249			0.114125	+	0.993466i	$0.463594\pi$
$684$		0			0
$685$	−0.119210	+	0.366890i	−0.00455477	+	0.0140182i
$686$	0.815786	+	2.51073i	0.0311469	+	0.0958602i
$687$		0			0
$688$	44.4364	−	32.2849i	1.69412	−	1.23085i
$689$	−20.6676	−	63.6084i	−0.787373	−	2.42329i
$690$		0			0
$691$	31.8821	+	23.1637i	1.21285	+	0.881188i	0.995487	−	0.0949021i	$-0.0302538\pi$
$691$	31.8821	+	23.1637i	1.21285	+	0.881188i	0.217365	+	0.976090i	$0.430254\pi$
$692$	−33.4839			−1.27287
$693$		0			0
$694$	3.94221			0.149644
$695$	−4.18706	−	3.04208i	−0.158824	−	0.115393i
$696$		0			0
$697$	−6.03791	−	18.5828i	−0.228702	−	0.703873i
$698$	−45.8750	+	33.3301i	−1.73639	+	1.26156i
$699$		0			0
$700$	−6.92419	−	21.3105i	−0.261710	−	0.805459i
$701$	7.85780	−	24.1838i	0.296785	−	0.913410i	−0.685831	−	0.727761i	$-0.740561\pi$
$701$	7.85780	−	24.1838i	0.296785	−	0.913410i	0.982616	−	0.185650i	$-0.0594389\pi$
$702$		0			0
$703$	0.511789			0.0193025
$704$	−6.92494	+	39.3877i	−0.260993	+	1.48448i
$705$		0			0
$706$	−24.5100	−	17.8076i	−0.922447	−	0.670197i
$707$	5.21545	−	16.0515i	0.196147	−	0.603679i
$708$		0			0
$709$	−5.72839	+	4.16192i	−0.215134	+	0.156304i	−0.690134	−	0.723682i	$-0.742448\pi$
$709$	−5.72839	+	4.16192i	−0.215134	+	0.156304i	0.474999	+	0.879986i	$0.342448\pi$
$710$	41.1216	−	29.8766i	1.54327	−	1.12125i
$711$		0			0
$712$	−20.4819	+	63.0367i	−0.767590	+	2.36240i
$713$	2.16282	+	1.57138i	0.0809981	+	0.0588486i
$714$		0			0
$715$	−25.3166	−	51.8413i	−0.946786	−	1.93875i
$716$	−64.5686			−2.41304
$717$		0			0
$718$	−4.67022	+	14.3735i	−0.174291	+	0.536413i
$719$	6.66894	+	20.5249i	0.248709	+	0.765449i	0.995004	+	0.0998332i	$0.0318309\pi$
$719$	6.66894	+	20.5249i	0.248709	+	0.765449i	−0.746295	+	0.665616i	$0.768169\pi$
$720$		0			0
$721$	−10.6929	+	7.76886i	−0.398225	+	0.289327i
$722$	15.4877	+	47.6661i	0.576391	+	1.77395i
$723$		0			0
$724$	16.4757	+	11.9703i	0.612313	+	0.444872i
$725$	−39.9075			−1.48213
$726$		0			0
$727$	35.7114			1.32446			0.662231	−	0.749300i	$-0.269610\pi$
$727$	35.7114			1.32446			0.662231	+	0.749300i	$0.269610\pi$
$728$	35.7731	+	25.9907i	1.32584	+	0.963278i
$729$		0			0
$730$	8.82998	+	27.1759i	0.326812	+	1.00582i
$731$	23.1406	−	16.8127i	0.855888	−	0.621839i
$732$		0			0
$733$	1.96072	+	6.03446i	0.0724207	+	0.222888i	0.980715	−	0.195444i	$-0.0626148\pi$
$733$	1.96072	+	6.03446i	0.0724207	+	0.222888i	−0.908294	+	0.418332i	$0.862615\pi$
$734$	−14.2755	+	43.9355i	−0.526919	+	1.62169i
$735$		0			0
$736$	21.2763			0.784254
$737$	11.7152	+	23.9894i	0.431534	+	0.883662i
$738$		0			0
$739$	−8.88336	−	6.45414i	−0.326780	−	0.237419i	0.412283	−	0.911056i	$-0.364731\pi$
$739$	−8.88336	−	6.45414i	−0.326780	−	0.237419i	−0.739063	+	0.673636i	$0.764731\pi$
$740$	−19.7588	+	60.8114i	−0.726348	+	2.23547i
$741$		0			0
$742$	−25.3224	+	18.3978i	−0.929616	+	0.675406i
$743$	−14.9009	+	10.8262i	−0.546662	+	0.397173i	−0.826553	−	0.562859i	$-0.809702\pi$
$743$	−14.9009	+	10.8262i	−0.546662	+	0.397173i	0.279891	+	0.960032i	$0.409702\pi$
$744$		0			0
$745$	13.5115	−	41.5840i	0.495022	−	1.52352i
$746$	−20.3828	−	14.8090i	−0.746268	−	0.542196i
$747$		0			0
$748$	−15.9841	+	90.9145i	−0.584437	+	3.32416i
$749$	11.0745			0.404654
$750$		0			0
$751$	1.53447	−	4.72263i	0.0559938	−	0.172331i	−0.919148	−	0.393912i	$-0.871122\pi$
$751$	1.53447	−	4.72263i	0.0559938	−	0.172331i	0.975142	+	0.221581i	$0.0711216\pi$
$752$	5.29772	+	16.3047i	0.193188	+	0.594572i
$753$		0			0
$754$	106.627	−	77.4691i	3.88313	−	2.82126i
$755$	−15.1345	−	46.5791i	−0.550799	−	1.69519i
$756$		0			0
$757$	0.842244	+	0.611926i	0.0306119	+	0.0222408i	0.602986	−	0.797752i	$-0.293977\pi$
$757$	0.842244	+	0.611926i	0.0306119	+	0.0222408i	−0.572374	+	0.819993i	$0.693977\pi$
$758$	−84.3737			−3.06459
$759$		0			0
$760$	2.96477			0.107544
$761$	−34.0015	−	24.7035i	−1.23255	−	0.895502i	−0.235474	−	0.971881i	$-0.575664\pi$
$761$	−34.0015	−	24.7035i	−1.23255	−	0.895502i	−0.997079	+	0.0763782i	$0.975664\pi$
$762$		0			0
$763$	1.50605	+	4.63516i	0.0545228	+	0.167804i
$764$	86.4495	−	62.8092i	3.12763	−	2.27236i
$765$		0			0
$766$	−8.01295	−	24.6613i	−0.289520	−	0.891050i
$767$	11.5300	−	35.4858i	0.416325	−	1.28132i
$768$		0			0
$769$	44.1300			1.59137			0.795684	−	0.605712i	$-0.207112\pi$
$769$	44.1300			1.59137			0.795684	+	0.605712i	$0.207112\pi$
$770$	−19.4127	+	18.7653i	−0.699586	+	0.676254i
$771$		0			0
$772$	−71.5455	−	51.9809i	−2.57498	−	1.87083i
$773$	11.5272	−	35.4770i	0.414603	−	1.27602i	−0.498002	−	0.867176i	$-0.665933\pi$
$773$	11.5272	−	35.4770i	0.414603	−	1.27602i	0.912605	−	0.408842i	$-0.134067\pi$
$774$		0			0
$775$	−5.82845	+	4.23462i	−0.209364	+	0.152112i
$776$	−36.0509	+	26.1925i	−1.29415	+	0.940257i
$777$		0			0
$778$	27.0839	−	83.3557i	0.971005	−	2.98845i
$779$	0.346166	+	0.251504i	0.0124027	+	0.00901107i
$780$		0			0
$781$	−18.2892	−	9.71287i	−0.654438	−	0.347554i
$782$	24.7404			0.884717
$783$		0			0
$784$	3.32353	−	10.2288i	0.118698	−	0.365313i
$785$	8.76540	+	26.9771i	0.312851	+	0.962855i
$786$		0			0
$787$	−5.95282	+	4.32498i	−0.212195	+	0.154169i	−0.688806	−	0.724945i	$-0.741865\pi$
$787$	−5.95282	+	4.32498i	−0.212195	+	0.154169i	0.476611	+	0.879114i	$0.341865\pi$
$788$	−27.8069	−	85.5808i	−0.990579	−	3.04869i
$789$		0			0
$790$	61.8932	+	44.9681i	2.20206	+	1.59989i
$791$	−5.28263			−0.187829
$792$		0			0
$793$	47.8872			1.70053
$794$	50.5180	+	36.7035i	1.79282	+	1.30256i
$795$		0			0
$796$	4.10216	+	12.6251i	0.145397	+	0.447486i
$797$	4.85553	−	3.52775i	0.171992	−	0.124959i	−0.498459	−	0.866913i	$-0.666101\pi$
$797$	4.85553	−	3.52775i	0.171992	−	0.124959i	0.670451	+	0.741954i	$0.266101\pi$
$798$		0			0
$799$	2.75884	+	8.49082i	0.0976006	+	0.300384i
$800$	−17.7179	+	54.5299i	−0.626421	+	1.92792i
$801$		0			0
$802$	66.7210			2.35600
$803$	8.37018	−	8.09103i	0.295377	−	0.285526i
$804$		0			0
$805$	4.17434	+	3.03284i	0.147126	+	0.106893i
$806$	7.35246	−	22.6285i	0.258979	−	0.797056i
$807$		0			0
$808$	−107.032	+	77.7630i	−3.76536	+	2.73569i
$809$	−22.9712	+	16.6895i	−0.807624	+	0.586773i	−0.913141	−	0.407645i	$-0.866350\pi$
$809$	−22.9712	+	16.6895i	−0.807624	+	0.586773i	0.105517	+	0.994418i	$0.466350\pi$
$810$		0			0
$811$	9.85967	−	30.3450i	0.346220	−	1.06556i	−0.614707	−	0.788755i	$-0.710726\pi$
$811$	9.85967	−	30.3450i	0.346220	−	1.06556i	0.960927	−	0.276800i	$-0.0892741\pi$
$812$	−35.5806	−	25.8508i	−1.24863	−	0.907185i
$813$		0			0
$814$	36.1766	−	5.10261i	1.26799	−	0.178847i
$815$	−30.1259			−1.05526
$816$		0			0
$817$	−0.193563	+	0.595726i	−0.00677191	+	0.0208418i
$818$	−11.3994	−	35.0838i	−0.398571	−	1.22668i
$819$		0			0
$820$	−43.2486	+	31.4219i	−1.51031	+	1.09730i
$821$	1.40894	+	4.33626i	0.0491722	+	0.151337i	0.972628	−	0.232369i	$-0.0746477\pi$
$821$	1.40894	+	4.33626i	0.0491722	+	0.151337i	−0.923455	+	0.383706i	$0.874648\pi$
$822$		0			0
$823$	−37.6947	−	27.3868i	−1.31396	−	0.954644i	−0.999986	−	0.00521085i	$-0.998341\pi$
$823$	−37.6947	−	27.3868i	−1.31396	−	0.954644i	−0.313969	−	0.949433i	$-0.601659\pi$
$824$	103.606			3.60927
$825$		0			0
$826$	−17.4617			−0.607572
$827$	−0.811006	−	0.589230i	−0.0282014	−	0.0204895i	0.573595	−	0.819139i	$-0.305548\pi$
$827$	−0.811006	−	0.589230i	−0.0282014	−	0.0204895i	−0.601797	+	0.798649i	$0.705548\pi$
$828$		0			0
$829$	−15.6006	−	48.0136i	−0.541830	−	1.66758i	−0.728410	−	0.685141i	$-0.759740\pi$
$829$	−15.6006	−	48.0136i	−0.541830	−	1.66758i	0.186580	−	0.982440i	$-0.440260\pi$
$830$	−62.1315	+	45.1411i	−2.15661	+	1.56687i
$831$		0			0
$832$	−21.0189	−	64.6897i	−0.728701	−	2.24271i
$833$	1.73076	−	5.32673i	0.0599672	−	0.184560i
$834$		0			0
$835$	18.8178			0.651216
$836$	−0.887054	−	1.81644i	−0.0306794	−	0.0628228i
$837$		0			0
$838$	−63.5269	−	46.1550i	−2.19450	−	1.59440i
$839$	8.05341	−	24.7858i	0.278035	−	0.855703i	−0.710366	−	0.703833i	$-0.751471\pi$
$839$	8.05341	−	24.7858i	0.278035	−	0.855703i	0.988400	−	0.151870i	$-0.0485295\pi$
$840$		0			0
$841$	−39.9082	+	28.9950i	−1.37614	+	0.999827i
$842$	77.4586	−	56.2770i	2.66940	−	1.93943i
$843$		0			0
$844$	−12.5219	+	38.5385i	−0.431023	+	1.32655i
$845$	46.9527	+	34.1131i	1.61522	+	1.17353i
$846$		0			0
$847$	10.3404	+	3.75195i	0.355299	+	0.128918i
$848$	127.518			4.37898
$849$		0			0
$850$	−20.6027	+	63.4085i	−0.706665	+	2.17489i
$851$	−2.15753	−	6.64019i	−0.0739592	−	0.227623i
$852$		0			0
$853$	24.4232	−	17.7445i	0.836235	−	0.607560i	−0.0850814	−	0.996374i	$-0.527115\pi$
$853$	24.4232	−	17.7445i	0.836235	−	0.607560i	0.921316	+	0.388814i	$0.127115\pi$
$854$	−6.92536	−	21.3141i	−0.236981	−	0.729352i
$855$		0			0
$856$	−70.2307	−	51.0256i	−2.40044	−	1.74402i
$857$	25.3151			0.864748			0.432374	−	0.901694i	$-0.357676\pi$
$857$	25.3151			0.864748			0.432374	+	0.901694i	$0.357676\pi$
$858$		0			0
$859$	−10.7680			−0.367399			−0.183699	−	0.982982i	$-0.558807\pi$
$859$	−10.7680			−0.367399			−0.183699	+	0.982982i	$0.558807\pi$
$860$	−63.3119	−	45.9988i	−2.15892	−	1.56855i
$861$		0			0
$862$	29.2105	+	89.9008i	0.994915	+	3.06203i
$863$	−28.5585	+	20.7490i	−0.972143	+	0.706303i	−0.955939	−	0.293566i	$-0.905158\pi$
$863$	−28.5585	+	20.7490i	−0.972143	+	0.706303i	−0.0162040	+	0.999869i	$0.505158\pi$
$864$		0			0
$865$	6.42089	+	19.7615i	0.218317	+	0.671910i
$866$	18.8413	−	57.9875i	0.640252	−	1.97049i
$867$		0			0
$868$	−7.93955			−0.269486
$869$	5.39712	−	30.6978i	0.183085	−	1.04135i
$870$		0			0
$871$	−36.7350	−	26.6896i	−1.24472	−	0.904341i
$872$	11.8055	−	36.3337i	0.399785	−	1.23041i
$873$		0			0
$874$	−0.438316	+	0.318455i	−0.0148263	+	0.0107719i
$875$	1.22459	−	0.889720i	0.0413989	−	0.0300780i
$876$		0			0
$877$	−1.28769	+	3.96311i	−0.0434823	+	0.133825i	−0.970441	−	0.241339i	$-0.922413\pi$
$877$	−1.28769	+	3.96311i	−0.0434823	+	0.133825i	0.926959	+	0.375164i	$0.122413\pi$
$878$	52.9319	+	38.4573i	1.78637	+	1.29787i
$879$		0			0
$880$	108.920	−	15.3629i	3.67168	−	0.517882i
$881$	40.6561			1.36974			0.684870	−	0.728665i	$-0.259859\pi$
$881$	40.6561			1.36974			0.684870	+	0.728665i	$0.259859\pi$
$882$		0			0
$883$	−5.92377	+	18.2315i	−0.199351	+	0.613539i	0.800547	+	0.599269i	$0.204542\pi$
$883$	−5.92377	+	18.2315i	−0.199351	+	0.613539i	−0.999898	+	0.0142692i	$0.995458\pi$
$884$	−48.5158	−	149.316i	−1.63176	−	5.02205i
$885$		0			0
$886$	−28.3939	+	20.6293i	−0.953910	+	0.693056i
$887$	11.4454	+	35.2253i	0.384298	+	1.18275i	0.936988	+	0.349362i	$0.113602\pi$
$887$	11.4454	+	35.2253i	0.384298	+	1.18275i	−0.552690	+	0.833387i	$0.686398\pi$
$888$		0			0
$889$	−9.17429	−	6.66551i	−0.307696	−	0.223554i
$890$	68.8346			2.30734
$891$		0			0
$892$	42.1774			1.41220
$893$	−0.158170	−	0.114917i	−0.00529295	−	0.00384555i
$894$		0			0
$895$	12.3817	+	38.1070i	0.413875	+	1.27378i
$896$	−5.17868	+	3.76253i	−0.173008	+	0.125697i
$897$		0			0
$898$	17.0266	+	52.4024i	0.568184	+	1.74869i
$899$	−4.36965	+	13.4484i	−0.145736	+	0.448529i
$900$		0			0
$901$	66.4061			2.21231
$902$	26.9768	+	14.3266i	0.898228	+	0.477024i
$903$		0			0
$904$	33.5006	+	24.3396i	1.11421	+	0.809523i
$905$	3.90521	−	12.0190i	0.129814	−	0.399525i
$906$		0			0
$907$	23.2660	−	16.9037i	0.772534	−	0.561279i	−0.130195	−	0.991488i	$-0.541560\pi$
$907$	23.2660	−	16.9037i	0.772534	−	0.561279i	0.902729	+	0.430209i	$0.141560\pi$
$908$	−89.0578	+	64.7043i	−2.95549	+	2.14729i
$909$		0			0
$910$	14.1906	−	43.6742i	0.470414	−	1.44778i
$911$	36.2210	+	26.3161i	1.20006	+	0.871892i	0.994290	−	0.106710i	$-0.0340316\pi$
$911$	36.2210	+	26.3161i	1.20006	+	0.871892i	0.205765	+	0.978601i	$0.434032\pi$
$912$		0			0
$913$	27.6335	+	14.6754i	0.914535	+	0.485684i
$914$	74.5371			2.46547
$915$		0			0
$916$	−13.7898	+	42.4407i	−0.455629	+	1.40228i
$917$	−0.299834	−	0.922795i	−0.00990140	−	0.0304734i
$918$		0			0
$919$	−15.6458	+	11.3673i	−0.516107	+	0.374973i	−0.815135	−	0.579271i	$-0.803337\pi$
$919$	−15.6458	+	11.3673i	−0.516107	+	0.374973i	0.299029	+	0.954244i	$0.403337\pi$
$920$	−12.4985	−	38.4664i	−0.412063	−	1.26820i
$921$		0			0
$922$	28.9250	+	21.0152i	0.952594	+	0.692100i
$923$	35.2210			1.15931
$924$		0			0
$925$	18.8152			0.618638
$926$	−72.5268	−	52.6938i	−2.38338	−	1.73163i
$927$		0			0
$928$	34.7760	+	107.030i	1.14158	+	3.51342i
$929$	−21.7730	+	15.8190i	−0.714350	+	0.519006i	−0.884574	−	0.466400i	$-0.845551\pi$
$929$	−21.7730	+	15.8190i	−0.714350	+	0.519006i	0.170224	+	0.985405i	$0.445551\pi$
$930$		0			0
$931$	0.0379017	+	0.116649i	0.00124218	+	0.00382303i
$932$	−30.5443	+	94.0055i	−1.00051	+	3.07925i
$933$		0			0
$934$	33.2127			1.08675
$935$	56.7209	−	8.00034i	1.85497	−	0.261639i
$936$		0			0
$937$	−34.4115	−	25.0014i	−1.12417	−	0.816760i	−0.139338	−	0.990245i	$-0.544497\pi$
$937$	−34.4115	−	25.0014i	−1.12417	−	0.816760i	−0.984837	+	0.173484i	$0.944497\pi$
$938$	−6.56667	+	20.2101i	−0.214409	+	0.659884i
$939$		0			0
$940$	19.7611	−	14.3573i	0.644536	−	0.468283i
$941$	−39.4561	+	28.6665i	−1.28623	+	0.934502i	−0.999722	−	0.0235760i	$-0.992495\pi$
$941$	−39.4561	+	28.6665i	−1.28623	+	0.934502i	−0.286509	+	0.958078i	$0.592495\pi$
$942$		0			0
$943$	1.80382	−	5.55158i	0.0587403	−	0.180784i
$944$	57.5531	+	41.8148i	1.87319	+	1.36096i
$945$		0			0
$946$	−7.74282	+	44.0396i	−0.251741	+	1.43185i
$947$	−0.641845			−0.0208572			−0.0104286	−	0.999946i	$-0.503320\pi$
$947$	−0.641845			−0.0208572			−0.0104286	+	0.999946i	$0.503320\pi$
$948$		0			0
$949$	−6.11856	+	18.8310i	−0.198617	+	0.611280i
$950$	−0.451175	−	1.38858i	−0.0146381	−	0.0450513i
$951$		0			0
$952$	−35.5186	+	25.8058i	−1.15117	+	0.836371i
$953$	−2.36690	−	7.28456i	−0.0766713	−	0.235970i	0.905374	−	0.424615i	$-0.139591\pi$
$953$	−2.36690	−	7.28456i	−0.0766713	−	0.235970i	−0.982045	+	0.188645i	$0.939591\pi$
$954$		0			0
$955$	−53.6463	−	38.9763i	−1.73595	−	1.26124i
$956$	45.8156			1.48178
$957$		0			0
$958$	76.2721			2.46424
$959$	0.101208	+	0.0735323i	0.00326819	+	0.00237448i
$960$		0			0
$961$	−8.79069	−	27.0550i	−0.283571	−	0.872741i
$962$	−50.2713	+	36.5242i	−1.62081	+	1.17759i
$963$		0			0
$964$	−1.23296	−	3.79465i	−0.0397108	−	0.122217i
$965$	−16.9584	+	52.1925i	−0.545910	+	1.68014i
$966$		0			0
$967$	−29.7387			−0.956333			−0.478166	−	0.878269i	$-0.658698\pi$
$967$	−29.7387			−0.956333			−0.478166	+	0.878269i	$0.658698\pi$
$968$	−48.2879	−	71.4365i	−1.55203	−	2.29606i
$969$		0			0
$970$	37.4400	+	27.2018i	1.20213	+	0.873396i
$971$	10.7905	−	33.2097i	0.346284	−	1.06575i	−0.614609	−	0.788832i	$-0.710686\pi$
$971$	10.7905	−	33.2097i	0.346284	−	1.06575i	0.960893	−	0.276920i	$-0.0893136\pi$
$972$		0			0
$973$	−1.35781	+	0.986507i	−0.0435294	+	0.0316259i
$974$	54.4782	−	39.5808i	1.74560	−	1.26825i
$975$		0			0
$976$	−28.2141	+	86.8339i	−0.903110	+	2.77949i
$977$	25.8353	+	18.7704i	0.826543	+	0.600519i	0.918579	−	0.395237i	$-0.129338\pi$
$977$	25.8353	+	18.7704i	0.826543	+	0.600519i	−0.0920361	+	0.995756i	$0.529338\pi$
$978$		0			0
$979$	−12.3062	−	25.1996i	−0.393307	−	0.805383i
$980$	−15.3237			−0.489498
$981$		0			0
$982$	3.80644	−	11.7150i	0.121468	−	0.373841i
$983$	10.4791	+	32.2513i	0.334231	+	1.02866i	0.967100	+	0.254398i	$0.0818774\pi$
$983$	10.4791	+	32.2513i	0.334231	+	1.02866i	−0.632868	+	0.774259i	$0.718123\pi$
$984$		0			0
$985$	−45.1757	+	32.8221i	−1.43942	+	1.04580i
$986$	40.4382	+	124.456i	1.28782	+	3.96349i
$987$		0			0
$988$	2.78151	+	2.02089i	0.0884917	+	0.0642930i
$989$	8.54523			0.271722
$990$		0			0
$991$	−13.3101			−0.422809			−0.211404	−	0.977399i	$-0.567804\pi$
$991$	−13.3101			−0.422809			−0.211404	+	0.977399i	$0.567804\pi$
$992$	16.4360	+	11.9414i	0.521843	+	0.379141i
$993$		0			0
$994$	−5.09359	−	15.6765i	−0.161559	−	0.497228i
$995$	6.66446	−	4.84201i	0.211278	−	0.153502i
$996$		0			0
$997$	−0.912394	−	2.80806i	−0.0288958	−	0.0889322i	0.935569	−	0.353145i	$-0.114888\pi$
$997$	−0.912394	−	2.80806i	−0.0288958	−	0.0889322i	−0.964464	+	0.264213i	$0.914888\pi$
$998$	15.0886	−	46.4381i	0.477623	−	1.46997i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.j.631.5		20
3.2	odd	2		231.2.j.g.169.1	✓	20
11.3	even	5	inner	693.2.m.j.190.5		20
11.5	even	5		7623.2.a.cx.1.2		10
11.6	odd	10		7623.2.a.cy.1.9		10
33.5	odd	10		2541.2.a.bq.1.9		10
33.14	odd	10		231.2.j.g.190.1	yes	20
33.17	even	10		2541.2.a.br.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.g.169.1	✓	20	3.2	odd	2
231.2.j.g.190.1	yes	20	33.14	odd	10
693.2.m.j.190.5		20	11.3	even	5	inner
693.2.m.j.631.5		20	1.1	even	1	trivial
2541.2.a.bq.1.9		10	33.5	odd	10
2541.2.a.br.1.2		10	33.17	even	10
7623.2.a.cx.1.2		10	11.5	even	5
7623.2.a.cy.1.9		10	11.6	odd	10

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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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.13576 + 1.55172i) q^{2} +(1.53559 + 4.72606i) q^{4} +(2.49476 - 1.81255i) q^{5} +(-0.309017 - 0.951057i) q^{7} +(-2.42230 + 7.45506i) q^{8} +O(q^{10})\)	\(q+(2.13576 + 1.55172i) q^{2} +(1.53559 + 4.72606i) q^{4} +(2.49476 - 1.81255i) q^{5} +(-0.309017 - 0.951057i) q^{7} +(-2.42230 + 7.45506i) q^{8} +8.14075 q^{10} +(-1.45539 - 2.98024i) q^{11} +(4.56364 + 3.31568i) q^{13} +(0.815786 - 2.51073i) q^{14} +(-8.70112 + 6.32173i) q^{16} +(-4.53118 + 3.29210i) q^{17} +(0.0379017 - 0.116649i) q^{19} +(12.3971 + 9.00705i) q^{20} +(1.51613 - 8.62342i) q^{22} -1.67325 q^{23} +(1.39340 - 4.28844i) q^{25} +(4.60183 + 14.1630i) q^{26} +(4.02023 - 2.92087i) q^{28} +(-2.73492 - 8.41721i) q^{29} +(-1.29259 - 0.939120i) q^{31} -12.7156 q^{32} -14.7859 q^{34} +(-2.49476 - 1.81255i) q^{35} +(1.28943 + 3.96845i) q^{37} +(0.261956 - 0.190322i) q^{38} +(7.46960 + 22.9891i) q^{40} +(-1.07803 + 3.31785i) q^{41} -5.10698 q^{43} +(11.8499 - 11.4547i) q^{44} +(-3.57364 - 2.59640i) q^{46} +(0.492574 - 1.51599i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(9.63040 - 6.99690i) q^{50} +(-8.66223 + 26.6596i) q^{52} +(-9.59206 - 6.96904i) q^{53} +(-9.03267 - 4.79700i) q^{55} +7.83871 q^{56} +(7.22002 - 22.2209i) q^{58} +(-2.04398 - 6.29072i) q^{59} +(6.86789 - 4.98982i) q^{61} +(-1.30340 - 4.01146i) q^{62} +(-9.75511 - 7.08750i) q^{64} +17.3950 q^{65} -8.04949 q^{67} +(-22.5167 - 16.3593i) q^{68} +(-2.51563 - 7.74231i) q^{70} +(5.05133 - 3.67001i) q^{71} +(1.08466 + 3.33825i) q^{73} +(-3.40401 + 10.4765i) q^{74} +0.609494 q^{76} +(-2.38464 + 2.30511i) q^{77} +(7.60289 + 5.52382i) q^{79} +(-10.2487 + 31.5424i) q^{80} +(-7.45078 + 5.41331i) q^{82} +(-7.63216 + 5.54509i) q^{83} +(-5.33712 + 16.4260i) q^{85} +(-10.9073 - 7.92458i) q^{86} +(25.7433 - 3.63102i) q^{88} +8.45556 q^{89} +(1.74316 - 5.36488i) q^{91} +(-2.56942 - 7.90787i) q^{92} +(3.40440 - 2.47344i) q^{94} +(-0.116877 - 0.359710i) q^{95} +(4.59909 + 3.34143i) q^{97} -2.63994 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8}+O(q^{10}) \) 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8	\( 20 q - 14 q^{4} + 5 q^{5} + 5 q^{7} + 9 q^{8} + 12 q^{10} + q^{11} + 13 q^{13} - 24 q^{16} + q^{17} + 10 q^{19} + 46 q^{20} + 26 q^{22} - 8 q^{25} + 53 q^{26} + 4 q^{28} - 3 q^{29} - 13 q^{31} - 82 q^{32} + 42 q^{34} - 5 q^{35} - 32 q^{37} - 16 q^{38} + 20 q^{40} + 3 q^{41} + 12 q^{43} - 25 q^{44} - 13 q^{46} - 20 q^{47} - 5 q^{49} + 83 q^{50} - 80 q^{52} - 3 q^{53} - 28 q^{55} + 6 q^{56} + 2 q^{58} + 9 q^{59} - 15 q^{61} + 37 q^{62} - 49 q^{64} - 58 q^{65} + 76 q^{67} - 51 q^{68} + 3 q^{70} - 37 q^{71} + 27 q^{73} + 32 q^{74} + 4 q^{76} - 6 q^{77} + 5 q^{79} - 137 q^{80} - 55 q^{82} + 42 q^{83} - 48 q^{85} - 3 q^{86} + 151 q^{88} + 18 q^{89} + 7 q^{91} - 39 q^{92} - 35 q^{94} + 96 q^{95} - 27 q^{97}+O(q^{100}) \) 20 * q - 14 * q^4 + 5 * q^5 + 5 * q^7 + 9 * q^8 + 12 * q^10 + q^11 + 13 * q^13 - 24 * q^16 + q^17 + 10 * q^19 + 46 * q^20 + 26 * q^22 - 8 * q^25 + 53 * q^26 + 4 * q^28 - 3 * q^29 - 13 * q^31 - 82 * q^32 + 42 * q^34 - 5 * q^35 - 32 * q^37 - 16 * q^38 + 20 * q^40 + 3 * q^41 + 12 * q^43 - 25 * q^44 - 13 * q^46 - 20 * q^47 - 5 * q^49 + 83 * q^50 - 80 * q^52 - 3 * q^53 - 28 * q^55 + 6 * q^56 + 2 * q^58 + 9 * q^59 - 15 * q^61 + 37 * q^62 - 49 * q^64 - 58 * q^65 + 76 * q^67 - 51 * q^68 + 3 * q^70 - 37 * q^71 + 27 * q^73 + 32 * q^74 + 4 * q^76 - 6 * q^77 + 5 * q^79 - 137 * q^80 - 55 * q^82 + 42 * q^83 - 48 * q^85 - 3 * q^86 + 151 * q^88 + 18 * q^89 + 7 * q^91 - 39 * q^92 - 35 * q^94 + 96 * q^95 - 27 * q^97

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