LMFDB - Embedded newform 819.2.fm.e.370.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(370,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 5]))

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

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

chi := DirichletCharacter("819.370");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fm (of order $12$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			370.1
Character	$\chi$	$=$	819.370
Dual form			819.2.fm.e.622.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.687394 - 2.56539i) q^{2} +(-4.37666 + 2.52687i) q^{4} +(1.17771 + 1.17771i) q^{5} +(-1.53750 - 2.15316i) q^{7} +(5.73490 + 5.73490i) q^{8} +O(q^{10})$	\(q+(-0.687394 - 2.56539i) q^{2} +(-4.37666 + 2.52687i) q^{4} +(1.17771 + 1.17771i) q^{5} +(-1.53750 - 2.15316i) q^{7} +(5.73490 + 5.73490i) q^{8} +(2.21174 - 3.83085i) q^{10} +(4.50301 - 1.20658i) q^{11} +(-3.59585 - 0.264293i) q^{13} +(-4.46682 + 5.42436i) q^{14} +(5.71638 - 9.90107i) q^{16} +(-3.15625 - 5.46679i) q^{17} +(-1.09384 + 4.08225i) q^{19} +(-8.13039 - 2.17853i) q^{20} +(-6.19069 - 10.7226i) q^{22} +(-3.67599 - 2.12233i) q^{23} -2.22598i q^{25} +(1.79375 + 9.40643i) q^{26} +(12.1699 + 5.53859i) q^{28} +(0.526889 - 0.912598i) q^{29} +(-5.61834 - 5.61834i) q^{31} +(-13.6615 - 3.66058i) q^{32} +(-11.8549 + 11.8549i) q^{34} +(0.725070 - 4.34654i) q^{35} +(0.572076 - 0.153287i) q^{37} +11.2245 q^{38} +13.5081i q^{40} +(-1.24468 + 0.333510i) q^{41} +(-9.27990 + 5.35775i) q^{43} +(-16.6593 + 16.6593i) q^{44} +(-2.91776 + 10.8892i) q^{46} +(-2.85718 + 2.85718i) q^{47} +(-2.27219 + 6.62096i) q^{49} +(-5.71050 + 1.53012i) q^{50} +(16.4057 - 7.92952i) q^{52} +0.398831 q^{53} +(6.72427 + 3.88226i) q^{55} +(3.53074 - 21.1656i) q^{56} +(-2.70335 - 0.724361i) q^{58} +(8.26243 + 2.21391i) q^{59} +(4.22976 - 2.44205i) q^{61} +(-10.5512 + 18.2752i) q^{62} +14.6977i q^{64} +(-3.92362 - 4.54615i) q^{65} +(-2.76762 - 10.3289i) q^{67} +(27.6277 + 15.9509i) q^{68} +(-11.6490 + 1.12770i) q^{70} +(-4.31760 - 1.15690i) q^{71} +(-0.935407 + 0.935407i) q^{73} +(-0.786484 - 1.36223i) q^{74} +(-5.52795 - 20.6306i) q^{76} +(-9.52134 - 7.84059i) q^{77} -0.927988 q^{79} +(18.3929 - 4.92836i) q^{80} +(1.71117 + 2.96383i) q^{82} +(-7.79378 - 7.79378i) q^{83} +(2.72115 - 10.1555i) q^{85} +(20.1237 + 20.1237i) q^{86} +(32.7439 + 18.9047i) q^{88} +(-1.28296 - 4.78807i) q^{89} +(4.95956 + 8.14879i) q^{91} +21.4514 q^{92} +(9.29378 + 5.36577i) q^{94} +(-6.09595 + 3.51950i) q^{95} +(-1.65635 + 6.18160i) q^{97} +(18.5472 + 1.27783i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8	$ 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 2 q^{10} + 4 q^{11} + 6 q^{13} - 34 q^{14} + 14 q^{16} + 8 q^{17} + 2 q^{19} - 44 q^{20} - 4 q^{22} + 18 q^{23} + 28 q^{26} - 32 q^{28} + 18 q^{29} - 14 q^{31} + 8 q^{32} - 66 q^{34} - 22 q^{35} - 24 q^{37} - 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} + 28 q^{47} + 8 q^{49} - 70 q^{50} + 28 q^{52} + 80 q^{53} + 60 q^{55} + 54 q^{56} - 4 q^{58} + 42 q^{59} + 36 q^{61} - 52 q^{62} - 14 q^{65} + 26 q^{67} + 72 q^{68} - 116 q^{70} + 4 q^{71} + 12 q^{73} + 18 q^{74} - 48 q^{76} - 28 q^{77} - 4 q^{79} + 98 q^{80} + 20 q^{82} + 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} + 54 q^{89} + 148 q^{91} + 4 q^{92} - 60 q^{95} - 40 q^{97} - 36 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8 + 2 * q^10 + 4 * q^11 + 6 * q^13 - 34 * q^14 + 14 * q^16 + 8 * q^17 + 2 * q^19 - 44 * q^20 - 4 * q^22 + 18 * q^23 + 28 * q^26 - 32 * q^28 + 18 * q^29 - 14 * q^31 + 8 * q^32 - 66 * q^34 - 22 * q^35 - 24 * q^37 - 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 + 28 * q^47 + 8 * q^49 - 70 * q^50 + 28 * q^52 + 80 * q^53 + 60 * q^55 + 54 * q^56 - 4 * q^58 + 42 * q^59 + 36 * q^61 - 52 * q^62 - 14 * q^65 + 26 * q^67 + 72 * q^68 - 116 * q^70 + 4 * q^71 + 12 * q^73 + 18 * q^74 - 48 * q^76 - 28 * q^77 - 4 * q^79 + 98 * q^80 + 20 * q^82 + 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 + 54 * q^89 + 148 * q^91 + 4 * q^92 - 60 * q^95 - 40 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$-1$

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 $

$2$	−0.687394	−	2.56539i	−0.486061	−	1.81400i	−0.575235	−	0.817988i	$-0.695089\pi$
$2$	−0.687394	−	2.56539i	−0.486061	−	1.81400i	0.0891737	−	0.996016i	$-0.471577\pi$
$3$		0			0
$3$		0			0
$4$	−4.37666	+	2.52687i	−2.18833	+	1.26343i
$5$	1.17771	+	1.17771i	0.526690	+	0.526690i	0.919584	−	0.392894i	$-0.128526\pi$
$5$	1.17771	+	1.17771i	0.526690	+	0.526690i	−0.392894	+	0.919584i	$0.628526\pi$
$6$		0			0
$7$	−1.53750	−	2.15316i	−0.581120	−	0.813818i
$7$	−1.53750	−	2.15316i	−0.581120	−	0.813818i
$8$	5.73490	+	5.73490i	2.02759	+	2.02759i
$9$		0			0
$10$	2.21174	−	3.83085i	0.699414	−	1.21142i
$11$	4.50301	−	1.20658i	1.35771	−	0.363797i	0.494734	−	0.869044i	$-0.335265\pi$
$11$	4.50301	−	1.20658i	1.35771	−	0.363797i	0.862975	+	0.505247i	$0.168599\pi$
$12$		0			0
$13$	−3.59585	−	0.264293i	−0.997310	−	0.0733017i
$13$	−3.59585	−	0.264293i	−0.997310	−	0.0733017i
$14$	−4.46682	+	5.42436i	−1.19381	+	1.44972i
$15$		0			0
$16$	5.71638	−	9.90107i	1.42910	−	2.47527i
$17$	−3.15625	−	5.46679i	−0.765503	−	1.32589i	−0.939980	−	0.341230i	$-0.889157\pi$
$17$	−3.15625	−	5.46679i	−0.765503	−	1.32589i	0.174476	−	0.984661i	$-0.444177\pi$
$18$		0			0
$19$	−1.09384	+	4.08225i	−0.250943	+	0.936532i	0.719360	+	0.694638i	$0.244435\pi$
$19$	−1.09384	+	4.08225i	−0.250943	+	0.936532i	−0.970303	+	0.241894i	$0.922231\pi$
$20$	−8.13039	−	2.17853i	−1.81801	−	0.487134i
$21$		0			0
$22$	−6.19069	−	10.7226i	−1.31986	−	2.28606i
$23$	−3.67599	−	2.12233i	−0.766496	−	0.442537i	0.0651270	−	0.997877i	$-0.479255\pi$
$23$	−3.67599	−	2.12233i	−0.766496	−	0.442537i	−0.831623	+	0.555340i	$0.812588\pi$
$24$		0			0
$25$		−	2.22598i		−	0.445196i
$26$	1.79375	+	9.40643i	0.351784	+	1.84475i
$27$		0			0
$28$	12.1699	+	5.53859i	2.29989	+	1.04670i
$29$	0.526889	−	0.912598i	0.0978408	−	0.169465i	−0.812950	−	0.582334i	$-0.802140\pi$
$29$	0.526889	−	0.912598i	0.0978408	−	0.169465i	0.910791	+	0.412868i	$0.135473\pi$
$30$		0			0
$31$	−5.61834	−	5.61834i	−1.00908	−	1.00908i	−0.999958	−	0.00912491i	$-0.997095\pi$
$31$	−5.61834	−	5.61834i	−1.00908	−	1.00908i	−0.00912491	−	0.999958i	$-0.502905\pi$
$32$	−13.6615	−	3.66058i	−2.41503	−	0.647105i
$33$		0			0
$34$	−11.8549	+	11.8549i	−2.03309	+	2.03309i
$35$	0.725070	−	4.34654i	0.122559	−	0.734700i
$36$		0			0
$37$	0.572076	−	0.153287i	0.0940488	−	0.0252003i	−0.211488	−	0.977381i	$-0.567831\pi$
$37$	0.572076	−	0.153287i	0.0940488	−	0.0252003i	0.305537	+	0.952180i	$0.401164\pi$
$38$	11.2245			1.82085
$39$		0			0
$40$			13.5081i			2.13583i
$41$	−1.24468	+	0.333510i	−0.194386	+	0.0520856i	−0.354698	−	0.934981i	$-0.615416\pi$
$41$	−1.24468	+	0.333510i	−0.194386	+	0.0520856i	0.160312	+	0.987066i	$0.448750\pi$
$42$		0			0
$43$	−9.27990	+	5.35775i	−1.41517	+	0.817050i	−0.995869	−	0.0907973i	$-0.971058\pi$
$43$	−9.27990	+	5.35775i	−1.41517	+	0.817050i	−0.419302	+	0.907847i	$0.637725\pi$
$44$	−16.6593	+	16.6593i	−2.51148	+	2.51148i
$45$		0			0
$46$	−2.91776	+	10.8892i	−0.430200	+	1.60553i
$47$	−2.85718	+	2.85718i	−0.416762	+	0.416762i	−0.884086	−	0.467324i	$-0.845218\pi$
$47$	−2.85718	+	2.85718i	−0.416762	+	0.416762i	0.467324	+	0.884086i	$0.345218\pi$
$48$		0			0
$49$	−2.27219	+	6.62096i	−0.324598	+	0.945852i
$50$	−5.71050	+	1.53012i	−0.807587	+	0.216392i
$51$		0			0
$52$	16.4057	−	7.92952i	2.27506	−	1.09963i
$53$	0.398831			0.0547836			0.0273918	−	0.999625i	$-0.491280\pi$
$53$	0.398831			0.0547836			0.0273918	+	0.999625i	$0.491280\pi$
$54$		0			0
$55$	6.72427	+	3.88226i	0.906700	+	0.523483i
$56$	3.53074	−	21.1656i	0.471815	−	2.82837i
$57$		0			0
$58$	−2.70335	−	0.724361i	−0.354967	−	0.0951132i
$59$	8.26243	+	2.21391i	1.07568	+	0.288227i	0.752824	−	0.658222i	$-0.228691\pi$
$59$	8.26243	+	2.21391i	1.07568	+	0.288227i	0.322854	+	0.946449i	$0.395358\pi$
$60$		0			0
$61$	4.22976	−	2.44205i	0.541565	−	0.312673i	−0.204148	−	0.978940i	$-0.565442\pi$
$61$	4.22976	−	2.44205i	0.541565	−	0.312673i	0.745713	+	0.666267i	$0.232109\pi$
$62$	−10.5512	+	18.2752i	−1.34001	+	2.32096i
$63$		0			0
$64$			14.6977i			1.83721i
$65$	−3.92362	−	4.54615i	−0.486666	−	0.563880i
$66$		0			0
$67$	−2.76762	−	10.3289i	−0.338118	−	1.26188i	−0.900449	−	0.434962i	$-0.856762\pi$
$67$	−2.76762	−	10.3289i	−0.338118	−	1.26188i	0.562330	−	0.826913i	$-0.309905\pi$
$68$	27.6277	+	15.9509i	3.35035	+	1.93433i
$69$		0			0
$70$	−11.6490	+	1.12770i	−1.39232	+	0.134786i
$71$	−4.31760	−	1.15690i	−0.512405	−	0.137298i	−0.00665372	−	0.999978i	$-0.502118\pi$
$71$	−4.31760	−	1.15690i	−0.512405	−	0.137298i	−0.505751	+	0.862679i	$0.668785\pi$
$72$		0			0
$73$	−0.935407	+	0.935407i	−0.109481	+	0.109481i	−0.759725	−	0.650244i	$-0.774667\pi$
$73$	−0.935407	+	0.935407i	−0.109481	+	0.109481i	0.650244	+	0.759725i	$0.274667\pi$
$74$	−0.786484	−	1.36223i	−0.0914269	−	0.158356i
$75$		0			0
$76$	−5.52795	−	20.6306i	−0.634100	−	2.36649i
$77$	−9.52134	−	7.84059i	−1.08506	−	0.893518i
$78$		0			0
$79$	−0.927988			−0.104407			−0.0522034	−	0.998636i	$-0.516624\pi$
$79$	−0.927988			−0.104407			−0.0522034	+	0.998636i	$0.516624\pi$
$80$	18.3929	−	4.92836i	2.05639	−	0.551008i
$81$		0			0
$82$	1.71117	+	2.96383i	0.188967	+	0.327300i
$83$	−7.79378	−	7.79378i	−0.855479	−	0.855479i	0.135323	−	0.990802i	$-0.456793\pi$
$83$	−7.79378	−	7.79378i	−0.855479	−	0.855479i	−0.990802	+	0.135323i	$0.956793\pi$
$84$		0			0
$85$	2.72115	−	10.1555i	0.295150	−	1.10152i
$86$	20.1237	+	20.1237i	2.16999	+	2.16999i
$87$		0			0
$88$	32.7439	+	18.9047i	3.49052	+	2.01525i
$89$	−1.28296	−	4.78807i	−0.135993	−	0.507534i	−0.999992	−	0.00403982i	$-0.998714\pi$
$89$	−1.28296	−	4.78807i	−0.135993	−	0.507534i	0.863998	−	0.503495i	$-0.167953\pi$
$90$		0			0
$91$	4.95956	+	8.14879i	0.519903	+	0.854225i
$92$	21.4514			2.23646
$93$		0			0
$94$	9.29378	+	5.36577i	0.958580	+	0.553436i
$95$	−6.09595	+	3.51950i	−0.625431	+	0.361093i
$96$		0			0
$97$	−1.65635	+	6.18160i	−0.168177	+	0.627646i	0.829436	+	0.558601i	$0.188662\pi$
$97$	−1.65635	+	6.18160i	−0.168177	+	0.627646i	−0.997614	+	0.0690447i	$0.978005\pi$
$98$	18.5472	+	1.27783i	1.87355	+	0.129081i
$99$		0			0
$100$	5.62475	+	9.74235i	0.562475	+	0.974235i
$101$	0.472587	−	0.818544i	0.0470241	−	0.0814482i	−0.841555	−	0.540171i	$-0.818360\pi$
$101$	0.472587	−	0.818544i	0.0470241	−	0.0814482i	0.888579	+	0.458723i	$0.151693\pi$
$102$		0			0
$103$	−8.04965			−0.793156			−0.396578	−	0.918001i	$-0.629802\pi$
$103$	−8.04965			−0.793156			−0.396578	+	0.918001i	$0.629802\pi$
$104$	−19.1062	−	22.1375i	−1.87351	−	2.17077i
$105$		0			0
$106$	−0.274154	−	1.02316i	−0.0266282	−	0.0993777i
$107$	8.52440	−	14.7647i	0.824085	−	1.42736i	−0.0785320	−	0.996912i	$-0.525023\pi$
$107$	8.52440	−	14.7647i	0.824085	−	1.42736i	0.902617	−	0.430445i	$-0.141643\pi$
$108$		0			0
$109$	1.56781	−	1.56781i	0.150169	−	0.150169i	−0.628025	−	0.778193i	$-0.716136\pi$
$109$	1.56781	−	1.56781i	0.150169	−	0.150169i	0.778193	+	0.628025i	$0.216136\pi$
$110$	5.33728	−	19.9190i	0.508890	−	1.89920i
$111$		0			0
$112$	−30.1075	+	2.91461i	−2.84489	+	0.275405i
$113$	3.02535	+	5.24006i	0.284601	+	0.492943i	0.972512	−	0.232852i	$-0.0748056\pi$
$113$	3.02535	+	5.24006i	0.284601	+	0.492943i	−0.687911	+	0.725795i	$0.741472\pi$
$114$		0			0
$115$	−1.82976	−	6.82876i	−0.170626	−	0.636786i
$116$			5.32551i			0.494462i
$117$		0			0
$118$		−	22.7182i		−	2.09138i
$119$	−6.91813	+	15.2011i	−0.634184	+	1.39348i
$120$		0			0
$121$	9.29500	−	5.36647i	0.845000	−	0.487861i
$122$	−9.17232	−	9.17232i	−0.830423	−	0.830423i
$123$		0			0
$124$	38.7864	+	10.3928i	3.48312	+	0.933299i
$125$	8.51014	−	8.51014i	0.761170	−	0.761170i
$126$		0			0
$127$	−1.60575	−	0.927079i	−0.142487	−	0.0822650i	0.427062	−	0.904222i	$-0.359549\pi$
$127$	−1.60575	−	0.927079i	−0.142487	−	0.0822650i	−0.569549	+	0.821958i	$0.692882\pi$
$128$	10.3824	−	2.78196i	0.917684	−	0.245893i
$129$		0			0
$130$	−8.96556	+	13.1906i	−0.786332	+	1.15689i
$131$			4.94735i			0.432252i	0.976365	+	0.216126i	$0.0693422\pi$
$131$			4.94735i			0.432252i	−0.976365	+	0.216126i	$0.930658\pi$
$132$		0			0
$133$	10.4715	−	3.92126i	0.907994	−	0.340016i
$134$	−24.5952	+	14.2000i	−2.12470	+	1.22670i
$135$		0			0
$136$	13.2507	−	49.4523i	1.13624	−	4.24050i
$137$	−1.82558	+	6.81316i	−0.155970	+	0.582088i	0.843050	+	0.537834i	$0.180757\pi$
$137$	−1.82558	+	6.81316i	−0.155970	+	0.582088i	−0.999020	+	0.0442531i	$0.985909\pi$
$138$		0			0
$139$	10.4051	−	6.00737i	0.882547	−	0.509539i	0.0110494	−	0.999939i	$-0.496483\pi$
$139$	10.4051	−	6.00737i	0.882547	−	0.509539i	0.871497	+	0.490400i	$0.163149\pi$
$140$	7.80975	+	20.8555i	0.660044	+	1.76261i
$141$		0			0
$142$			11.8716i			0.996240i
$143$	−16.5111	+	3.14856i	−1.38072	+	0.263296i
$144$		0			0
$145$	1.69530	−	0.454256i	0.140787	−	0.0377239i
$146$	3.04268	+	1.75669i	0.251814	+	0.145385i
$147$		0			0
$148$	−2.11645	+	2.11645i	−0.173971	+	0.173971i
$149$	4.76731	+	1.27740i	0.390553	+	0.104648i	0.448752	−	0.893657i	$-0.351869\pi$
$149$	4.76731	+	1.27740i	0.390553	+	0.104648i	−0.0581981	+	0.998305i	$0.518535\pi$
$150$		0			0
$151$	−13.7886	−	13.7886i	−1.12210	−	1.12210i	−0.991425	−	0.130675i	$-0.958286\pi$
$151$	−13.7886	−	13.7886i	−1.12210	−	1.12210i	−0.130675	−	0.991425i	$-0.541714\pi$
$152$	−29.6843	+	17.1383i	−2.40772	+	1.39010i
$153$		0			0
$154$	−13.5692	+	29.8155i	−1.09344	+	2.40260i
$155$		−	13.2336i		−	1.06295i
$156$		0			0
$157$			19.9821i			1.59474i	0.603489	+	0.797371i	$0.293777\pi$
$157$			19.9821i			1.59474i	−0.603489	+	0.797371i	$0.706223\pi$
$158$	0.637894	+	2.38065i	0.0507481	+	0.189394i
$159$		0			0
$160$	−11.7782	−	20.4004i	−0.931147	−	1.61279i
$161$	1.08211	+	11.1781i	0.0852824	+	0.880955i
$162$		0			0
$163$	−1.46606	+	5.47141i	−0.114831	+	0.428554i	−0.999274	−	0.0380934i	$-0.987872\pi$
$163$	−1.46606	+	5.47141i	−0.114831	+	0.428554i	0.884444	+	0.466647i	$0.154538\pi$
$164$	4.60480	−	4.60480i	0.359574	−	0.359574i
$165$		0			0
$166$	−14.6367	+	25.3515i	−1.13603	+	1.96766i
$167$	−1.10228	−	4.11377i	−0.0852972	−	0.318333i	0.910073	−	0.414448i	$-0.136025\pi$
$167$	−1.10228	−	4.11377i	−0.0852972	−	0.318333i	−0.995370	+	0.0961143i	$0.969359\pi$
$168$		0			0
$169$	12.8603	+	1.90072i	0.989254	+	0.146209i
$170$	−27.9233			−2.14162
$171$		0			0
$172$	27.0767	−	46.8982i	2.06458	−	3.57595i
$173$	−0.873930	−	1.51369i	−0.0664437	−	0.115084i	0.830890	−	0.556437i	$-0.187832\pi$
$173$	−0.873930	−	1.51369i	−0.0664437	−	0.115084i	−0.897333	+	0.441353i	$0.854499\pi$
$174$		0			0
$175$	−4.79288	+	3.42244i	−0.362308	+	0.258712i
$176$	13.7945	−	51.4819i	1.03980	−	3.88059i
$177$		0			0
$178$	−11.4014	+	6.58258i	−0.854568	+	0.493385i
$179$	19.7578	+	11.4072i	1.47677	+	0.852613i	0.999656	−	0.0262285i	$-0.00834976\pi$
$179$	19.7578	+	11.4072i	1.47677	+	0.852613i	0.477113	+	0.878842i	$0.341683\pi$
$180$		0			0
$181$	13.7425			1.02147			0.510737	−	0.859737i	$-0.329372\pi$
$181$	13.7425			1.02147			0.510737	+	0.859737i	$0.329372\pi$
$182$	17.4957	−	18.3246i	1.29686	−	1.35831i
$183$		0			0
$184$	−8.91006	−	33.2528i	−0.656858	−	2.45143i
$185$	0.854271	+	0.493214i	0.0628073	+	0.0362618i
$186$		0			0
$187$	−20.8087	−	20.8087i	−1.52169	−	1.52169i
$188$	5.28519	−	19.7246i	0.385462	−	1.43856i
$189$		0			0
$190$	13.2192	+	13.2192i	0.959021	+	0.959021i
$191$	−6.02586	−	10.4371i	−0.436016	−	0.755201i	0.561362	−	0.827570i	$-0.310277\pi$
$191$	−6.02586	−	10.4371i	−0.436016	−	0.755201i	−0.997378	+	0.0723688i	$0.976944\pi$
$192$		0			0
$193$	−4.42174	+	1.18480i	−0.318284	+	0.0852838i	−0.414424	−	0.910084i	$-0.636017\pi$
$193$	−4.42174	+	1.18480i	−0.318284	+	0.0852838i	0.0961404	+	0.995368i	$0.469350\pi$
$194$	16.9968			1.22030
$195$		0			0
$196$	−6.78570	−	34.7192i	−0.484693	−	2.47995i
$197$	−5.05766	−	18.8754i	−0.360343	−	1.34482i	−0.873625	−	0.486599i	$-0.838237\pi$
$197$	−5.05766	−	18.8754i	−0.360343	−	1.34482i	0.513282	−	0.858220i	$-0.328430\pi$
$198$		0			0
$199$	−12.2497	−	21.2170i	−0.868355	−	1.50403i	−0.863677	−	0.504046i	$-0.831844\pi$
$199$	−12.2497	−	21.2170i	−0.868355	−	1.50403i	−0.00467796	−	0.999989i	$-0.501489\pi$
$200$	12.7658	−	12.7658i	0.902676	−	0.902676i
$201$		0			0
$202$	−2.42474	−	0.649707i	−0.170604	−	0.0457132i
$203$	−2.77506	+	0.268644i	−0.194771	+	0.0188551i
$204$		0			0
$205$	−1.85865	−	1.07309i	−0.129814	−	0.0749482i
$206$	5.53328	+	20.6505i	0.385522	+	1.43879i
$207$		0			0
$208$	−23.1721	+	34.0920i	−1.60669	+	2.36385i
$209$			19.7022i			1.36283i
$210$		0			0
$211$	−11.4160	+	19.7731i	−0.785910	+	1.36124i	0.142544	+	0.989788i	$0.454472\pi$
$211$	−11.4160	+	19.7731i	−0.785910	+	1.36124i	−0.928454	+	0.371448i	$0.878862\pi$
$212$	−1.74555	+	1.00779i	−0.119885	+	0.0692154i
$213$		0			0
$214$	−43.7368	−	11.7192i	−2.98979	−	0.801111i
$215$	−17.2390	−	4.61917i	−1.17569	−	0.315025i
$216$		0			0
$217$	−3.45898	+	20.7354i	−0.234811	+	1.40761i
$218$	−5.09973	−	2.94433i	−0.345397	−	0.199415i
$219$		0			0
$220$	−39.2398			−2.64555
$221$	9.90458	+	20.4919i	0.666254	+	1.37844i
$222$		0			0
$223$	−12.2434	+	3.28062i	−0.819881	+	0.219686i	−0.644294	−	0.764778i	$-0.722849\pi$
$223$	−12.2434	+	3.28062i	−0.819881	+	0.219686i	−0.175586	+	0.984464i	$0.556182\pi$
$224$	13.1227	+	35.0434i	0.876797	+	2.34144i
$225$		0			0
$226$	11.3632	−	11.3632i	0.755868	−	0.755868i
$227$	2.99465	−	11.1762i	0.198762	−	0.741790i	−0.792499	−	0.609874i	$-0.791220\pi$
$227$	2.99465	−	11.1762i	0.198762	−	0.741790i	0.991261	−	0.131917i	$-0.0421131\pi$
$228$		0			0
$229$	9.10742	−	9.10742i	0.601835	−	0.601835i	−0.338964	−	0.940799i	$-0.610077\pi$
$229$	9.10742	−	9.10742i	0.601835	−	0.601835i	0.940799	+	0.338964i	$0.110077\pi$
$230$	−16.2607	+	9.38810i	−1.07220	+	0.619033i
$231$		0			0
$232$	8.25532	−	2.21201i	0.541988	−	0.145225i
$233$			1.49633i			0.0980277i	0.998798	+	0.0490139i	$0.0156079\pi$
$233$			1.49633i			0.0980277i	−0.998798	+	0.0490139i	$0.984392\pi$
$234$		0			0
$235$	−6.72988			−0.439009
$236$	−41.7562	+	11.1885i	−2.71809	+	0.728311i
$237$		0			0
$238$	43.7522	+	7.29855i	2.83604	+	0.473095i
$239$	3.19313	−	3.19313i	0.206546	−	0.206546i	−0.596252	−	0.802798i	$-0.703344\pi$
$239$	3.19313	−	3.19313i	0.206546	−	0.206546i	0.802798	+	0.596252i	$0.203344\pi$
$240$		0			0
$241$	9.27435	+	2.48506i	0.597414	+	0.160076i	0.544839	−	0.838541i	$-0.316591\pi$
$241$	9.27435	+	2.48506i	0.597414	+	0.160076i	0.0525744	+	0.998617i	$0.483257\pi$
$242$	−20.1564	−	20.1564i	−1.29570	−	1.29570i
$243$		0			0
$244$	−12.3415	+	21.3761i	−0.790082	+	1.36846i
$245$	−10.4736	+	5.12162i	−0.669133	+	0.327208i
$246$		0			0
$247$	5.01218	−	14.3901i	0.318917	−	0.915618i
$248$		−	64.4412i		−	4.09202i
$249$		0			0
$250$	−27.6816	−	15.9820i	−1.75074	−	1.01079i
$251$	12.9361	+	22.4061i	0.816522	+	1.41426i	0.908230	+	0.418472i	$0.137434\pi$
$251$	12.9361	+	22.4061i	0.816522	+	1.41426i	−0.0917077	+	0.995786i	$0.529233\pi$
$252$		0			0
$253$	−19.1138	−	5.12152i	−1.20167	−	0.321987i
$254$	−1.27454	+	4.75664i	−0.0799716	+	0.298458i
$255$		0			0
$256$	0.424093	+	0.734550i	0.0265058	+	0.0459094i
$257$	11.4386	−	19.8122i	0.713518	−	1.23585i	−0.250011	−	0.968243i	$-0.580434\pi$
$257$	11.4386	−	19.8122i	0.713518	−	1.23585i	0.963528	−	0.267606i	$-0.0862326\pi$
$258$		0			0
$259$	−1.20962	−	0.996092i	−0.0751621	−	0.0618941i
$260$	28.6599	+	9.98248i	1.77741	+	0.619087i
$261$		0			0
$262$	12.6919	−	3.40078i	0.784107	−	0.210101i
$263$	10.9168	−	18.9085i	0.673160	−	1.16595i	−0.303844	−	0.952722i	$-0.598270\pi$
$263$	10.9168	−	18.9085i	0.673160	−	1.16595i	0.977003	−	0.213225i	$-0.0683966\pi$
$264$		0			0
$265$	0.469709	+	0.469709i	0.0288540	+	0.0288540i
$266$	−17.2576	−	24.1680i	−1.05813	−	1.48184i
$267$		0			0
$268$	38.2127	+	38.2127i	2.33421	+	2.33421i
$269$	−5.09171	+	2.93970i	−0.310447	+	0.179237i	−0.647127	−	0.762383i	$-0.724029\pi$
$269$	−5.09171	+	2.93970i	−0.310447	+	0.179237i	0.336679	+	0.941619i	$0.390696\pi$
$270$		0			0
$271$	−1.80033	−	6.71891i	−0.109362	−	0.408145i	0.889441	−	0.457049i	$-0.151094\pi$
$271$	−1.80033	−	6.71891i	−0.109362	−	0.408145i	−0.998803	+	0.0489044i	$0.984427\pi$
$272$	−72.1694			−4.37591
$273$		0			0
$274$	18.7333			1.13172
$275$	−2.68582	−	10.0236i	−0.161961	−	0.604446i
$276$		0			0
$277$	10.7111	−	6.18406i	0.643568	−	0.371564i	−0.142420	−	0.989806i	$-0.545488\pi$
$277$	10.7111	−	6.18406i	0.643568	−	0.371564i	0.785988	+	0.618242i	$0.212155\pi$
$278$	−22.5636	−	22.5636i	−1.35328	−	1.35328i
$279$		0			0
$280$	29.0852	−	20.7688i	1.73817	−	1.24117i
$281$	15.6520	+	15.6520i	0.933721	+	0.933721i	0.997936	−	0.0642154i	$-0.0204545\pi$
$281$	15.6520	+	15.6520i	0.933721	+	0.933721i	−0.0642154	+	0.997936i	$0.520454\pi$
$282$		0			0
$283$	14.3579	−	24.8687i	0.853490	−	1.47829i	−0.0245489	−	0.999699i	$-0.507815\pi$
$283$	14.3579	−	24.8687i	0.853490	−	1.47829i	0.878039	−	0.478589i	$-0.158852\pi$
$284$	21.8200	−	5.84665i	1.29478	−	0.346935i
$285$		0			0
$286$	19.4269	+	40.1930i	1.14874	+	2.37666i
$287$	2.63179	+	2.16722i	0.155350	+	0.127927i
$288$		0			0
$289$	−11.4238	+	19.7867i	−0.671991	+	1.16392i
$290$	−2.33069	−	4.03687i	−0.136863	−	0.237053i
$291$		0			0
$292$	1.73031	−	6.45761i	0.101259	−	0.377903i
$293$	22.3231	+	5.98146i	1.30413	+	0.349441i	0.843011	−	0.537897i	$-0.180781\pi$
$293$	22.3231	+	5.98146i	1.30413	+	0.349441i	0.461120	+	0.887338i	$0.347448\pi$
$294$		0			0
$295$	7.12343	+	12.3381i	0.414742	+	0.718355i
$296$	4.15989	+	2.40171i	0.241789	+	0.139597i
$297$		0			0
$298$		−	13.1081i		−	0.759331i
$299$	12.6574	+	8.60313i	0.731996	+	0.497532i
$300$		0			0
$301$	25.8039	+	11.7436i	1.48731	+	0.676887i
$302$	−25.8949	+	44.8513i	−1.49009	+	2.58090i
$303$		0			0
$304$	34.1658	+	34.1658i	1.95954	+	1.95954i
$305$	7.85749	+	2.10541i	0.449918	+	0.120555i
$306$		0			0
$307$	−5.52660	+	5.52660i	−0.315419	+	0.315419i	−0.847005	−	0.531585i	$-0.821596\pi$
$307$	−5.52660	+	5.52660i	−0.315419	+	0.315419i	0.531585	+	0.847005i	$0.321596\pi$
$308$	61.4838	+	10.2564i	3.50336	+	0.584415i
$309$		0			0
$310$	−33.9493	+	9.09669i	−1.92819	+	0.516658i
$311$	10.3208			0.585239			0.292620	−	0.956229i	$-0.405473\pi$
$311$	10.3208			0.585239			0.292620	+	0.956229i	$0.405473\pi$
$312$		0			0
$313$		−	20.9365i		−	1.18340i	−0.806157	−	0.591701i	$-0.798457\pi$
$313$		−	20.9365i		−	1.18340i	0.806157	−	0.591701i	$-0.201543\pi$
$314$	51.2618	−	13.7356i	2.89287	−	0.775142i
$315$		0			0
$316$	4.06149	−	2.34490i	0.228477	−	0.131911i
$317$	−8.45606	+	8.45606i	−0.474940	+	0.474940i	−0.903509	−	0.428569i	$-0.859018\pi$
$317$	−8.45606	+	8.45606i	−0.474940	+	0.474940i	0.428569	+	0.903509i	$0.359018\pi$
$318$		0			0
$319$	1.27147	−	4.74517i	0.0711884	−	0.265679i
$320$	−17.3097	+	17.3097i	−0.967641	+	0.967641i
$321$		0			0
$322$	27.9323	−	10.4598i	1.55660	−	0.582901i
$323$	25.7692	−	6.90484i	1.43384	−	0.384195i
$324$		0			0
$325$	−0.588311	+	8.00429i	−0.0326336	+	0.443998i
$326$	15.0441			0.833213
$327$		0			0
$328$	−9.05075	−	5.22545i	−0.499744	−	0.288527i
$329$	10.5449	+	1.75905i	0.581357	+	0.0969794i
$330$		0			0
$331$	25.0550	+	6.71347i	1.37715	+	0.369006i	0.870084	−	0.492903i	$-0.164064\pi$
$331$	25.0550	+	6.71347i	1.37715	+	0.369006i	0.507064	+	0.861909i	$0.330731\pi$
$332$	53.8046	+	14.4169i	2.95291	+	0.791230i
$333$		0			0
$334$	−9.79573	+	5.65557i	−0.535999	+	0.309459i
$335$	8.90502	−	15.4240i	0.486533	−	0.842700i
$336$		0			0
$337$			26.1315i			1.42348i	0.702445	+	0.711738i	$0.252092\pi$
$337$			26.1315i			1.42348i	−0.702445	+	0.711738i	$0.747908\pi$
$338$	−3.96401	−	34.2982i	−0.215614	−	1.86558i
$339$		0			0
$340$	13.7520	+	51.3231i	0.745806	+	2.78339i
$341$	−32.0784	−	18.5205i	−1.73714	−	1.00294i
$342$		0			0
$343$	17.7495	−	5.28735i	0.958382	−	0.285490i
$344$	−83.9455	−	22.4931i	−4.52604	−	1.21275i
$345$		0			0
$346$	−3.28247	+	3.28247i	−0.176467	+	0.176467i
$347$	−3.74039	−	6.47855i	−0.200795	−	0.347787i	0.747990	−	0.663710i	$-0.231019\pi$
$347$	−3.74039	−	6.47855i	−0.200795	−	0.347787i	−0.948785	+	0.315923i	$0.897686\pi$
$348$		0			0
$349$	0.528661	+	1.97299i	0.0282986	+	0.105612i	0.978631	−	0.205626i	$-0.0659231\pi$
$349$	0.528661	+	1.97299i	0.0282986	+	0.105612i	−0.950332	+	0.311238i	$0.899256\pi$
$350$	12.0745	+	9.94305i	0.645409	+	0.531478i
$351$		0			0
$352$	−65.9345			−3.51432
$353$	12.1175	−	3.24687i	0.644949	−	0.172813i	0.0785047	−	0.996914i	$-0.474985\pi$
$353$	12.1175	−	3.24687i	0.644949	−	0.172813i	0.566444	+	0.824100i	$0.308319\pi$
$354$		0			0
$355$	−3.72241	−	6.44740i	−0.197565	−	0.342192i
$356$	17.7139	+	17.7139i	0.938835	+	0.938835i
$357$		0			0
$358$	15.6825	−	58.5278i	0.828844	−	3.09329i
$359$	6.92976	+	6.92976i	0.365739	+	0.365739i	0.865920	−	0.500182i	$-0.166733\pi$
$359$	6.92976	+	6.92976i	0.365739	+	0.365739i	−0.500182	+	0.865920i	$0.666733\pi$
$360$		0			0
$361$	0.986209	+	0.569388i	0.0519057	+	0.0299678i
$362$	−9.44654	−	35.2550i	−0.496499	−	1.85296i
$363$		0			0
$364$	−42.2972	−	23.1324i	−2.21698	−	1.21247i
$365$	−2.20328			−0.115325
$366$		0			0
$367$	21.7912	+	12.5811i	1.13749	+	0.656730i	0.945808	−	0.324727i	$-0.105272\pi$
$367$	21.7912	+	12.5811i	1.13749	+	0.656730i	0.191682	+	0.981457i	$0.438606\pi$
$368$	−42.0267	+	24.2641i	−2.19079	+	1.26486i
$369$		0			0
$370$	0.678064	−	2.53057i	0.0352509	−	0.131558i
$371$	−0.613202	−	0.858746i	−0.0318359	−	0.0445839i
$372$		0			0
$373$	5.81848	+	10.0779i	0.301270	+	0.521814i	0.976424	−	0.215862i	$-0.0692562\pi$
$373$	5.81848	+	10.0779i	0.301270	+	0.521814i	−0.675154	+	0.737677i	$0.735923\pi$
$374$	−39.0787	+	67.6864i	−2.02071	+	3.49998i
$375$		0			0
$376$	−32.7713			−1.69005
$377$	−2.13581	+	3.14232i	−0.110000	+	0.161837i
$378$		0			0
$379$	−6.70131	−	25.0096i	−0.344223	−	1.28466i	−0.893517	−	0.449029i	$-0.851770\pi$
$379$	−6.70131	−	25.0096i	−0.344223	−	1.28466i	0.549294	−	0.835629i	$-0.314897\pi$
$380$	17.7866	−	30.8073i	0.912434	−	1.58038i
$381$		0			0
$382$	−22.6331	+	22.6331i	−1.15801	+	1.15801i
$383$	−2.62259	+	9.78763i	−0.134008	+	0.500125i	0.865992	+	0.500058i	$0.166688\pi$
$383$	−2.62259	+	9.78763i	−0.134008	+	0.500125i	−1.00000		6.67944e-5i	$0.999979\pi$
$384$		0			0
$385$	−1.97944	−	20.4474i	−0.100882	−	1.04210i
$386$	6.07895	+	10.5291i	0.309410	+	0.535915i
$387$		0			0
$388$	−8.37077	−	31.2401i	−0.424962	−	1.58598i
$389$			25.4046i			1.28806i	0.764999	+	0.644032i	$0.222740\pi$
$389$			25.4046i			1.28806i	−0.764999	+	0.644032i	$0.777260\pi$
$390$		0			0
$391$			26.7945i			1.35505i
$392$	−51.0013	+	24.9398i	−2.57596	+	1.25965i
$393$		0			0
$394$	−44.9463	+	25.9497i	−2.26436	+	1.30733i
$395$	−1.09291	−	1.09291i	−0.0549900	−	0.0549900i
$396$		0			0
$397$	−23.6455	−	6.33580i	−1.18673	−	0.317984i	−0.389140	−	0.921179i	$-0.627228\pi$
$397$	−23.6455	−	6.33580i	−1.18673	−	0.317984i	−0.797594	+	0.603194i	$0.793894\pi$
$398$	−46.0096	+	46.0096i	−2.30625	+	2.30625i
$399$		0			0
$400$	−22.0396	−	12.7245i	−1.10198	−	0.636227i
$401$	−19.0591	+	5.10686i	−0.951765	+	0.255025i	−0.701111	−	0.713052i	$-0.747312\pi$
$401$	−19.0591	+	5.10686i	−0.951765	+	0.255025i	−0.250654	+	0.968077i	$0.580646\pi$
$402$		0			0
$403$	18.7178	+	21.6876i	0.932401	+	1.08034i
$404$			4.77666i			0.237647i
$405$		0			0
$406$	2.59674	+	6.93445i	0.128874	+	0.344151i
$407$	2.39111	−	1.38051i	0.118523	−	0.0684293i
$408$		0			0
$409$	6.62979	−	24.7427i	0.327822	−	1.22345i	−0.583622	−	0.812025i	$-0.698365\pi$
$409$	6.62979	−	24.7427i	0.327822	−	1.22345i	0.911444	−	0.411423i	$-0.134968\pi$
$410$	−1.47528	+	5.50581i	−0.0728588	+	0.271913i
$411$		0			0
$412$	35.2306	−	20.3404i	1.73569	−	1.00210i
$413$	−7.93659	−	21.1942i	−0.390534	−	1.04290i
$414$		0			0
$415$		−	18.3577i		−	0.901144i
$416$	48.1571	+	16.7735i	2.36110	+	0.822390i
$417$		0			0
$418$	50.5438	−	13.5432i	2.47218	−	0.662419i
$419$	−2.48993	−	1.43756i	−0.121641	−	0.0702295i	0.437945	−	0.899002i	$-0.355706\pi$
$419$	−2.48993	−	1.43756i	−0.121641	−	0.0702295i	−0.559586	+	0.828772i	$0.689040\pi$
$420$		0			0
$421$	−13.5970	+	13.5970i	−0.662676	+	0.662676i	−0.956010	−	0.293334i	$-0.905235\pi$
$421$	−13.5970	+	13.5970i	−0.662676	+	0.662676i	0.293334	+	0.956010i	$0.405235\pi$
$422$	58.5730	+	15.6946i	2.85129	+	0.764000i
$423$		0			0
$424$	2.28725	+	2.28725i	0.111079	+	0.111079i
$425$	−12.1689	+	7.02575i	−0.590281	+	0.340799i
$426$		0			0
$427$	−11.7614	−	5.35269i	−0.569173	−	0.259035i
$428$			86.1601i			4.16471i
$429$		0			0
$430$			47.3999i			2.28582i
$431$	−9.48793	−	35.4094i	−0.457017	−	1.70561i	−0.682089	−	0.731269i	$-0.738928\pi$
$431$	−9.48793	−	35.4094i	−0.457017	−	1.70561i	0.225071	−	0.974342i	$-0.427738\pi$
$432$		0			0
$433$	−0.0741930	−	0.128506i	−0.00356549	−	0.00617561i	0.864237	−	0.503085i	$-0.167802\pi$
$433$	−0.0741930	−	0.128506i	−0.00356549	−	0.00617561i	−0.867803	+	0.496909i	$0.834468\pi$
$434$	55.5720	−	5.37974i	2.66754	−	0.258236i
$435$		0			0
$436$	−2.90012	+	10.8234i	−0.138891	+	0.518346i
$437$	12.6848	−	12.6848i	0.606797	−	0.606797i
$438$		0			0
$439$	4.05749	−	7.02778i	0.193654	−	0.335418i	−0.752805	−	0.658244i	$-0.771300\pi$
$439$	4.05749	−	7.02778i	0.193654	−	0.335418i	0.946458	+	0.322826i	$0.104633\pi$
$440$	16.2986	+	60.8274i	0.777007	+	2.89983i
$441$		0			0
$442$	45.7615	−	39.4951i	2.17665	−	1.87859i
$443$	26.1952			1.24457			0.622285	−	0.782790i	$-0.286204\pi$
$443$	26.1952			1.24457			0.622285	+	0.782790i	$0.286204\pi$
$444$		0			0
$445$	4.12802	−	7.14994i	0.195687	−	0.338940i
$446$	16.8321	+	29.1541i	0.797024	+	1.38049i
$447$		0			0
$448$	31.6465	−	22.5977i	1.49516	−	1.06764i
$449$	−0.953576	+	3.55879i	−0.0450020	+	0.167950i	−0.984770	−	0.173864i	$-0.944375\pi$
$449$	−0.953576	+	3.55879i	−0.0450020	+	0.167950i	0.939768	+	0.341814i	$0.111041\pi$
$450$		0			0
$451$	−5.20239	+	3.00360i	−0.244971	+	0.141434i
$452$	−26.4819	−	15.2893i	−1.24560	−	0.719148i
$453$		0			0
$454$	−30.7298			−1.44222
$455$	−3.75601	+	15.4379i	−0.176084	+	0.723739i
$456$		0			0
$457$	2.49719	+	9.31962i	0.116813	+	0.435954i	0.999416	−	0.0341660i	$-0.0108775\pi$
$457$	2.49719	+	9.31962i	0.116813	+	0.435954i	−0.882603	+	0.470119i	$0.844211\pi$
$458$	−29.6245	−	17.1037i	−1.38426	−	0.799203i
$459$		0			0
$460$	25.2636	+	25.2636i	1.17792	+	1.17792i
$461$	1.90787	−	7.12028i	0.0888585	−	0.331624i	−0.907158	−	0.420789i	$-0.861753\pi$
$461$	1.90787	−	7.12028i	0.0888585	−	0.331624i	0.996017	+	0.0891650i	$0.0284198\pi$
$462$		0			0
$463$	10.2671	+	10.2671i	0.477153	+	0.477153i	0.904220	−	0.427067i	$-0.140453\pi$
$463$	10.2671	+	10.2671i	0.477153	+	0.477153i	−0.427067	+	0.904220i	$0.640453\pi$
$464$	−6.02380	−	10.4335i	−0.279648	−	0.484364i
$465$		0			0
$466$	3.83867	−	1.02857i	0.177823	−	0.0476475i
$467$	−34.1823			−1.58177			−0.790883	−	0.611967i	$-0.790379\pi$
$467$	−34.1823			−1.58177			−0.790883	+	0.611967i	$0.790379\pi$
$468$		0			0
$469$	−17.9845	+	21.8398i	−0.830449	+	1.00847i
$470$	4.62608	+	17.2648i	0.213385	+	0.796364i
$471$		0			0
$472$	34.6877	+	60.0808i	1.59663	+	2.76544i
$473$	−35.3229	+	35.3229i	−1.62415	+	1.62415i
$474$		0			0
$475$	9.08699	+	2.43485i	0.416940	+	0.111719i
$476$	−8.13285	−	84.0113i	−0.372769	−	3.85065i
$477$		0			0
$478$	−10.3865	−	5.99668i	−0.475070	−	0.274282i
$479$	−9.19517	−	34.3169i	−0.420138	−	1.56798i	−0.774316	−	0.632799i	$-0.781906\pi$
$479$	−9.19517	−	34.3169i	−0.420138	−	1.56798i	0.354178	−	0.935178i	$-0.384761\pi$
$480$		0			0
$481$	−2.09761	+	0.400003i	−0.0956430	+	0.0182386i
$482$		−	25.5005i		−	1.16152i
$483$		0			0
$484$	−27.1207	+	46.9745i	−1.23276	+	2.13520i
$485$	−9.23087	+	5.32944i	−0.419152	+	0.241998i
$486$		0			0
$487$	22.0147	+	5.89883i	0.997583	+	0.267302i	0.720433	−	0.693525i	$-0.243943\pi$
$487$	22.0147	+	5.89883i	0.997583	+	0.267302i	0.277150	+	0.960827i	$0.410610\pi$
$488$	38.2622	+	10.2523i	1.73205	+	0.464101i
$489$		0			0
$490$	20.3384	+	23.3483i	0.918797	+	1.05477i
$491$	−12.8664	−	7.42840i	−0.580651	−	0.335239i	0.180741	−	0.983531i	$-0.442150\pi$
$491$	−12.8664	−	7.42840i	−0.580651	−	0.335239i	−0.761392	+	0.648292i	$0.775484\pi$
$492$		0			0
$493$	−6.65198			−0.299590
$494$	−40.3615	−	2.96655i	−1.81595	−	0.133471i
$495$		0			0
$496$	−87.7441	+	23.5110i	−3.93983	+	1.05567i
$497$	4.14733	+	11.0752i	0.186033	+	0.496791i
$498$		0			0
$499$	−11.2290	+	11.2290i	−0.502679	+	0.502679i	−0.912270	−	0.409590i	$-0.865672\pi$
$499$	−11.2290	+	11.2290i	−0.502679	+	0.502679i	0.409590	+	0.912270i	$0.365672\pi$
$500$	−15.7420	+	58.7500i	−0.704004	+	2.62738i
$501$		0			0
$502$	48.5880	−	48.5880i	2.16859	−	2.16859i
$503$	−13.8096	+	7.97299i	−0.615741	+	0.355498i	−0.775209	−	0.631705i	$-0.782355\pi$
$503$	−13.8096	+	7.97299i	−0.615741	+	0.355498i	0.159468	+	0.987203i	$0.449022\pi$
$504$		0			0
$505$	1.52058	−	0.407439i	0.0676651	−	0.0181308i
$506$			52.5548i			2.33635i
$507$		0			0
$508$	9.37043			0.415745
$509$	21.2058	−	5.68207i	0.939930	−	0.251853i	0.243846	−	0.969814i	$-0.421591\pi$
$509$	21.2058	−	5.68207i	0.939930	−	0.251853i	0.696084	+	0.717961i	$0.254924\pi$
$510$		0			0
$511$	3.45227	+	0.575892i	0.152719	+	0.0254759i
$512$	16.7938	−	16.7938i	0.742187	−	0.742187i
$513$		0			0
$514$	−58.6887	−	15.7256i	−2.58865	−	0.693626i
$515$	−9.48019	−	9.48019i	−0.417747	−	0.417747i
$516$		0			0
$517$	−9.41849	+	16.3133i	−0.414225	+	0.717458i
$518$	−1.72388	+	3.78785i	−0.0757429	+	0.166429i
$519$		0			0
$520$	3.57011	−	48.5733i	0.156560	−	2.13008i
$521$		−	27.9103i		−	1.22277i	−0.791332	−	0.611387i	$-0.790612\pi$
$521$		−	27.9103i		−	1.22277i	0.791332	−	0.611387i	$-0.209388\pi$
$522$		0			0
$523$	14.4506	+	8.34306i	0.631881	+	0.364817i	0.781480	−	0.623930i	$-0.214465\pi$
$523$	14.4506	+	8.34306i	0.631881	+	0.364817i	−0.149599	+	0.988747i	$0.547798\pi$
$524$	−12.5013	−	21.6529i	−0.546122	−	0.945911i
$525$		0			0
$526$	−56.0118	−	15.0083i	−2.44223	−	0.654393i
$527$	−12.9814	+	48.4472i	−0.565478	+	2.11039i
$528$		0			0
$529$	−2.49141	−	4.31525i	−0.108322	−	0.187620i
$530$	0.882111	−	1.52786i	0.0383164	−	0.0663660i
$531$		0			0
$532$	−35.9217	+	43.6221i	−1.55740	+	1.89126i
$533$	4.56382	−	0.870294i	0.197681	−	0.0376966i
$534$		0			0
$535$	27.4279	−	7.34928i	1.18581	−	0.317737i
$536$	43.3632	−	75.1072i	1.87300	−	3.24414i
$537$		0			0
$538$	11.0415	+	11.0415i	0.476032	+	0.476032i
$539$	−2.24297	+	32.5559i	−0.0966117	+	1.40228i
$540$		0			0
$541$	−14.9557	−	14.9557i	−0.642996	−	0.642996i	0.308295	−	0.951291i	$-0.400242\pi$
$541$	−14.9557	−	14.9557i	−0.642996	−	0.642996i	−0.951291	+	0.308295i	$0.900242\pi$
$542$	−15.9991	+	9.23708i	−0.687220	+	0.396767i
$543$		0			0
$544$	23.1074	+	86.2380i	0.990722	+	3.69743i
$545$	3.69285			0.158184
$546$		0			0
$547$	39.1844			1.67540			0.837702	−	0.546127i	$-0.183898\pi$
$547$	39.1844			1.67540			0.837702	+	0.546127i	$0.183898\pi$
$548$	−9.22600	−	34.4319i	−0.394115	−	1.47086i
$549$		0			0
$550$	−23.8682	+	13.7803i	−1.01775	+	0.587595i
$551$	3.14912	+	3.14912i	0.134157	+	0.134157i
$552$		0			0
$553$	1.42678	+	1.99811i	0.0606729	+	0.0849681i
$554$	−23.2273	−	23.2273i	−0.986833	−	0.986833i
$555$		0			0
$556$	−30.3597	+	52.5845i	−1.28754	+	2.23008i
$557$	1.74793	−	0.468357i	0.0740623	−	0.0198449i	−0.221598	−	0.975138i	$-0.571127\pi$
$557$	1.74793	−	0.468357i	0.0740623	−	0.0198449i	0.295660	+	0.955293i	$0.404460\pi$
$558$		0			0
$559$	34.7852	−	16.8131i	1.47126	−	0.711117i
$560$	−38.8906	−	32.0255i	−1.64343	−	1.35332i
$561$		0			0
$562$	29.3944	−	50.9126i	1.23993	−	2.14762i
$563$	3.27798	+	5.67763i	0.138150	+	0.239284i	0.926797	−	0.375564i	$-0.122551\pi$
$563$	3.27798	+	5.67763i	0.138150	+	0.239284i	−0.788646	+	0.614847i	$0.789218\pi$
$564$		0			0
$565$	−2.60829	+	9.73429i	−0.109732	+	0.409524i
$566$	−73.6673	−	19.7391i	−3.09647	−	0.829696i
$567$		0			0
$568$	−18.1263	−	31.3957i	−0.760563	−	1.31733i
$569$	7.73692	+	4.46691i	0.324349	+	0.187263i	0.653329	−	0.757074i	$-0.273372\pi$
$569$	7.73692	+	4.46691i	0.324349	+	0.187263i	−0.328981	+	0.944337i	$0.606705\pi$
$570$		0			0
$571$		−	21.0842i		−	0.882348i	−0.897422	−	0.441174i	$-0.854562\pi$
$571$		−	21.0842i		−	0.882348i	0.897422	−	0.441174i	$-0.145438\pi$
$572$	64.3073	−	55.5014i	2.68882	−	2.32063i
$573$		0			0
$574$	3.75068	−	8.24131i	0.156550	−	0.343986i
$575$	−4.72426	+	8.18267i	−0.197015	+	0.341241i
$576$		0			0
$577$	−4.76619	−	4.76619i	−0.198419	−	0.198419i	0.600903	−	0.799322i	$-0.294808\pi$
$577$	−4.76619	−	4.76619i	−0.198419	−	0.198419i	−0.799322	+	0.600903i	$0.794808\pi$
$578$	58.6133	+	15.7054i	2.43799	+	0.653257i
$579$		0			0
$580$	−6.27193	+	6.27193i	−0.260428	+	0.260428i
$581$	−4.79831	+	28.7642i	−0.199067	+	1.19334i
$582$		0			0
$583$	1.79594	−	0.481220i	0.0743802	−	0.0199301i
$584$	−10.7289			−0.443966
$585$		0			0
$586$		−	61.3791i		−	2.53555i
$587$	−13.3468	+	3.57628i	−0.550883	+	0.147609i	−0.523515	−	0.852017i	$-0.675379\pi$
$587$	−13.3468	+	3.57628i	−0.550883	+	0.147609i	−0.0273686	+	0.999625i	$0.508713\pi$
$588$		0			0
$589$	29.0810	−	16.7899i	1.19826	−	0.691816i
$590$	26.7555	−	26.7555i	1.10151	−	1.10151i
$591$		0			0
$592$	1.75250	−	6.54042i	0.0720273	−	0.268809i
$593$	17.2336	−	17.2336i	0.707698	−	0.707698i	−0.258353	−	0.966051i	$-0.583180\pi$
$593$	17.2336	−	17.2336i	0.707698	−	0.707698i	0.966051	+	0.258353i	$0.0831796\pi$
$594$		0			0
$595$	−26.0501	+	9.75497i	−1.06795	+	0.399915i
$596$	−24.0927	+	6.45563i	−0.986877	+	0.264433i
$597$		0			0
$598$	13.3698	−	38.3849i	0.546730	−	1.56967i
$599$	−35.8803			−1.46603			−0.733015	−	0.680212i	$-0.761888\pi$
$599$	−35.8803			−1.46603			−0.733015	+	0.680212i	$0.761888\pi$
$600$		0			0
$601$	1.74937	+	1.01000i	0.0713582	+	0.0411987i	0.535255	−	0.844691i	$-0.320216\pi$
$601$	1.74937	+	1.01000i	0.0713582	+	0.0411987i	−0.463896	+	0.885889i	$0.653549\pi$
$602$	12.3893	−	74.2696i	0.504951	−	3.02700i
$603$		0			0
$604$	95.1900	+	25.5061i	3.87323	+	1.03783i
$605$	17.2670	+	4.62669i	0.702005	+	0.188102i
$606$		0			0
$607$	−26.9378	+	15.5526i	−1.09337	+	0.631259i	−0.934473	−	0.356035i	$-0.884128\pi$
$607$	−26.9378	+	15.5526i	−1.09337	+	0.631259i	−0.158901	+	0.987295i	$0.550795\pi$
$608$	29.8868	−	51.7654i	1.21207	−	2.09936i
$609$		0			0
$610$		−	21.6048i		−	0.874751i
$611$	11.0291	−	9.51885i	0.446190	−	0.385092i
$612$		0			0
$613$	2.49860	+	9.32490i	0.100917	+	0.376629i	0.997850	−	0.0655381i	$-0.0208764\pi$
$613$	2.49860	+	9.32490i	0.100917	+	0.376629i	−0.896933	+	0.442167i	$0.854210\pi$
$614$	17.9768	+	10.3789i	0.725485	+	0.418859i
$615$		0			0
$616$	−9.63893	−	99.5689i	−0.388364	−	4.01175i
$617$	7.40462	+	1.98406i	0.298099	+	0.0798753i	0.404768	−	0.914419i	$-0.367352\pi$
$617$	7.40462	+	1.98406i	0.298099	+	0.0798753i	−0.106670	+	0.994294i	$0.534019\pi$
$618$		0			0
$619$	−23.5040	+	23.5040i	−0.944707	+	0.944707i	−0.998549	−	0.0538424i	$-0.982853\pi$
$619$	−23.5040	+	23.5040i	−0.944707	+	0.944707i	0.0538424	+	0.998549i	$0.482853\pi$
$620$	33.4395	+	57.9190i	1.34296	+	2.32608i
$621$		0			0
$622$	−7.09446	−	26.4769i	−0.284462	−	1.06163i
$623$	−8.33692	+	10.1241i	−0.334012	+	0.405612i
$624$		0			0
$625$	8.91513			0.356605
$626$	−53.7104	+	14.3916i	−2.14670	+	0.575206i
$627$		0			0
$628$	−50.4920	−	87.4548i	−2.01485	−	3.48983i
$629$	−2.64361	−	2.64361i	−0.105408	−	0.105408i
$630$		0			0
$631$	−6.11577	+	22.8244i	−0.243465	+	0.908623i	0.730684	+	0.682716i	$0.239201\pi$
$631$	−6.11577	+	22.8244i	−0.243465	+	0.908623i	−0.974149	+	0.225907i	$0.927465\pi$
$632$	−5.32192	−	5.32192i	−0.211695	−	0.211695i
$633$		0			0
$634$	27.5057	+	15.8804i	1.09239	+	0.630693i
$635$	−0.799278	−	2.98295i	−0.0317184	−	0.118375i
$636$		0			0
$637$	9.92032	−	23.2075i	0.393058	−	0.919514i
$638$	−13.0472			−0.516544
$639$		0			0
$640$	15.5039	+	8.95116i	0.612844	+	0.353826i
$641$	1.08956	−	0.629057i	0.0430350	−	0.0248463i	−0.478328	−	0.878181i	$-0.658757\pi$
$641$	1.08956	−	0.629057i	0.0430350	−	0.0248463i	0.521363	+	0.853335i	$0.325424\pi$
$642$		0			0
$643$	−8.43652	+	31.4855i	−0.332704	+	1.24167i	0.573633	+	0.819113i	$0.305534\pi$
$643$	−8.43652	+	31.4855i	−0.332704	+	1.24167i	−0.906337	+	0.422556i	$0.861133\pi$
$644$	−32.9815	−	46.1883i	−1.29965	−	1.82007i
$645$		0			0
$646$	−35.4272	−	61.3617i	−1.39386	−	2.41424i
$647$	4.65030	−	8.05456i	0.182822	−	0.316657i	−0.760018	−	0.649902i	$-0.774810\pi$
$647$	4.65030	−	8.05456i	0.182822	−	0.316657i	0.942841	+	0.333244i	$0.108143\pi$
$648$		0			0
$649$	39.8771			1.56531
$650$	20.9385	−	3.99285i	0.821276	−	0.156613i
$651$		0			0
$652$	−7.40908	−	27.6510i	−0.290162	−	1.08290i
$653$	13.4181	−	23.2408i	0.525090	−	0.909482i	−0.474483	−	0.880264i	$-0.657365\pi$
$653$	13.4181	−	23.2408i	0.525090	−	0.909482i	0.999573	−	0.0292175i	$-0.00930153\pi$
$654$		0			0
$655$	−5.82657	+	5.82657i	−0.227663	+	0.227663i
$656$	−3.81295	+	14.2301i	−0.148871	+	0.555593i
$657$		0			0
$658$	−2.73584	−	28.2608i	−0.106654	−	1.10172i
$659$	7.95731	+	13.7825i	0.309973	+	0.536889i	0.978356	−	0.206928i	$-0.0663467\pi$
$659$	7.95731	+	13.7825i	0.309973	+	0.536889i	−0.668383	+	0.743817i	$0.733013\pi$
$660$		0			0
$661$	0.555848	+	2.07445i	0.0216200	+	0.0806868i	0.975893	−	0.218250i	$-0.0700348\pi$
$661$	0.555848	+	2.07445i	0.0216200	+	0.0806868i	−0.954273	+	0.298937i	$0.903368\pi$
$662$		−	68.8907i		−	2.67751i
$663$		0			0
$664$		−	89.3931i		−	3.46913i
$665$	16.9506	+	7.71432i	0.657314	+	0.299148i
$666$		0			0
$667$	−3.87367	+	2.23647i	−0.149989	+	0.0865963i
$668$	15.2193	+	15.2193i	0.588852	+	0.588852i
$669$		0			0
$670$	−45.6897	−	12.2425i	−1.76515	−	0.472970i
$671$	16.1001	−	16.1001i	0.621538	−	0.621538i
$672$		0			0
$673$	−33.3114	−	19.2323i	−1.28406	−	0.741352i	−0.306472	−	0.951880i	$-0.599148\pi$
$673$	−33.3114	−	19.2323i	−1.28406	−	0.741352i	−0.977588	+	0.210528i	$0.932482\pi$
$674$	67.0376	−	17.9627i	2.58219	−	0.691896i
$675$		0			0
$676$	−61.0881	+	24.1775i	−2.34954	+	0.929903i
$677$			18.0903i			0.695268i	0.937630	+	0.347634i	$0.113015\pi$
$677$			18.0903i			0.695268i	−0.937630	+	0.347634i	$0.886985\pi$
$678$		0			0
$679$	15.8566	−	5.93781i	0.608521	−	0.227872i
$680$	73.8462	−	42.6351i	2.83187	−	1.63498i
$681$		0			0
$682$	−25.4617	+	95.0245i	−0.974980	+	3.63868i
$683$	9.14504	−	34.1297i	0.349925	−	1.30594i	−0.536827	−	0.843693i	$-0.680377\pi$
$683$	9.14504	−	34.1297i	0.349925	−	1.30594i	0.886752	−	0.462246i	$-0.152956\pi$
$684$		0			0
$685$	−10.1740	+	5.87394i	−0.388727	+	0.224432i
$686$	−25.7650	−	41.8998i	−0.983712	−	1.59974i
$687$		0			0
$688$			122.508i			4.67057i
$689$	−1.43414	−	0.105408i	−0.0546362	−	0.00401573i
$690$		0			0
$691$	−18.6167	+	4.98833i	−0.708213	+	0.189765i	−0.594906	−	0.803795i	$-0.702811\pi$
$691$	−18.6167	+	4.98833i	−0.708213	+	0.189765i	−0.113306	+	0.993560i	$0.536144\pi$
$692$	7.64980	+	4.41661i	0.290802	+	0.167894i
$693$		0			0
$694$	−14.0489	+	14.0489i	−0.533289	+	0.533289i
$695$	19.3292	+	5.17924i	0.733197	+	0.196460i
$696$		0			0
$697$	5.75175	+	5.75175i	0.217863	+	0.217863i
$698$	4.69809	−	2.71244i	0.177825	−	0.102668i
$699$		0			0
$700$	12.3288	−	27.0899i	0.465984	−	1.02390i
$701$		−	30.2993i		−	1.14439i	−0.820118	−	0.572194i	$-0.806092\pi$
$701$		−	30.2993i		−	1.14439i	0.820118	−	0.572194i	$-0.193908\pi$
$702$		0			0
$703$			2.50303i			0.0944035i
$704$	17.7339	+	66.1839i	0.668373	+	2.49440i
$705$		0			0
$706$	−16.6590	−	28.8542i	−0.626969	−	1.08594i
$707$	−2.48906	+	0.240957i	−0.0936106	+	0.00906214i
$708$		0			0
$709$	−4.09223	+	15.2724i	−0.153687	+	0.573567i	0.845527	+	0.533932i	$0.179286\pi$
$709$	−4.09223	+	15.2724i	−0.153687	+	0.573567i	−0.999214	+	0.0396350i	$0.987380\pi$
$710$	−13.9813	+	13.9813i	−0.524710	+	0.524710i
$711$		0			0
$712$	20.1015	−	34.8167i	0.753334	−	1.30481i
$713$	8.72896	+	32.5769i	0.326902	+	1.22002i
$714$		0			0
$715$	−23.1534	−	15.7372i	−0.865888	−	0.588538i
$716$	−115.298			−4.30888
$717$		0			0
$718$	13.0141	−	22.5410i	0.485680	−	0.841223i
$719$	−4.93530	−	8.54819i	−0.184056	−	0.318794i	0.759202	−	0.650855i	$-0.225589\pi$
$719$	−4.93530	−	8.54819i	−0.184056	−	0.318794i	−0.943258	+	0.332061i	$0.892256\pi$
$720$		0			0
$721$	12.3763	+	17.3322i	0.460919	+	0.645484i
$722$	0.782788	−	2.92140i	0.0291324	−	0.108723i
$723$		0			0
$724$	−60.1465	+	34.7256i	−2.23533	+	1.29057i
$725$	−2.03142	−	1.17284i	−0.0754452	−	0.0435583i
$726$		0			0
$727$	24.0371			0.891486			0.445743	−	0.895161i	$-0.352939\pi$
$727$	24.0371			0.891486			0.445743	+	0.895161i	$0.352939\pi$
$728$	−18.2899	+	75.1751i	−0.677870	+	2.78617i
$729$		0			0
$730$	1.51452	+	5.65228i	0.0560551	+	0.209200i
$731$	58.5794	+	33.8208i	2.16664	+	1.25091i
$732$		0			0
$733$	−12.9796	−	12.9796i	−0.479413	−	0.479413i	0.425531	−	0.904944i	$-0.360087\pi$
$733$	−12.9796	−	12.9796i	−0.479413	−	0.479413i	−0.904944	+	0.425531i	$0.860087\pi$
$734$	17.2964	−	64.5510i	0.638422	−	2.38262i
$735$		0			0
$736$	42.4504	+	42.4504i	1.56474	+	1.56474i
$737$	−24.9252	−	43.1718i	−0.918133	−	1.59025i
$738$		0			0
$739$	−27.1236	+	7.26773i	−0.997756	+	0.267348i	−0.720505	−	0.693450i	$-0.756090\pi$
$739$	−27.1236	+	7.26773i	−0.997756	+	0.267348i	−0.277251	+	0.960798i	$0.589423\pi$
$740$	−4.98514			−0.183258
$741$		0			0
$742$	−1.78151	+	2.16340i	−0.0654011	+	0.0794209i
$743$	5.26385	+	19.6449i	0.193112	+	0.720703i	0.992748	+	0.120218i	$0.0383592\pi$
$743$	5.26385	+	19.6449i	0.193112	+	0.720703i	−0.799636	+	0.600485i	$0.794974\pi$
$744$		0			0
$745$	4.11012	+	7.11894i	0.150583	+	0.260818i
$746$	21.8542	−	21.8542i	0.800138	−	0.800138i
$747$		0			0
$748$	143.654	+	38.4919i	5.25250	+	1.40740i
$749$	−44.8970	+	4.34633i	−1.64050	+	0.158811i
$750$		0			0
$751$	−29.4512	−	17.0036i	−1.07469	−	0.620472i	−0.145230	−	0.989398i	$-0.546392\pi$
$751$	−29.4512	−	17.0036i	−1.07469	−	0.620472i	−0.929459	+	0.368926i	$0.879725\pi$
$752$	11.9564	+	44.6218i	0.436004	+	1.62719i
$753$		0			0
$754$	9.52941	+	3.31917i	0.347040	+	0.120877i
$755$		−	32.4781i		−	1.18200i
$756$		0			0
$757$	−12.1464	+	21.0382i	−0.441469	+	0.764646i	−0.997799	−	0.0663153i	$-0.978876\pi$
$757$	−12.1464	+	21.0382i	−0.441469	+	0.764646i	0.556330	+	0.830961i	$0.312209\pi$
$758$	−59.5530	+	34.3830i	−2.16306	+	1.24885i
$759$		0			0
$760$	−55.1436	−	14.7757i	−2.00027	−	0.535971i
$761$	16.6934	+	4.47299i	0.605136	+	0.162146i	0.548362	−	0.836241i	$-0.315252\pi$
$761$	16.6934	+	4.47299i	0.605136	+	0.162146i	0.0567745	+	0.998387i	$0.481918\pi$
$762$		0			0
$763$	−5.78624	−	0.965233i	−0.209476	−	0.0349438i
$764$	52.7463	+	30.4531i	1.90829	+	1.10175i
$765$		0			0
$766$	26.9118			0.972364
$767$	−29.1254	−	10.1446i	−1.05166	−	0.366301i
$768$		0			0
$769$	10.4169	−	2.79121i	0.375644	−	0.100654i	−0.0660568	−	0.997816i	$-0.521042\pi$
$769$	10.4169	−	2.79121i	0.375644	−	0.100654i	0.441701	+	0.897162i	$0.354375\pi$
$770$	−51.0949	+	19.1335i	−1.84133	+	0.689522i
$771$		0			0
$772$	16.3586	−	16.3586i	0.588759	−	0.588759i
$773$	−10.6384	+	39.7032i	−0.382638	+	1.42802i	0.459219	+	0.888323i	$0.348129\pi$
$773$	−10.6384	+	39.7032i	−0.382638	+	1.42802i	−0.841857	+	0.539701i	$0.818537\pi$
$774$		0			0
$775$	−12.5063	+	12.5063i	−0.449239	+	0.449239i
$776$	−44.9499	+	25.9518i	−1.61361	+	0.931616i
$777$		0			0
$778$	65.1727	−	17.4630i	2.33655	−	0.626078i
$779$		−	5.44589i		−	0.195119i
$780$		0			0
$781$	−20.8381			−0.745646
$782$	68.7382	−	18.4184i	2.45807	−	0.658639i
$783$		0			0
$784$	52.5659	+	60.3450i	1.87735	+	2.15518i
$785$	−23.5332	+	23.5332i	−0.839935	+	0.839935i
$786$		0			0
$787$	−26.7623	−	7.17094i	−0.953973	−	0.255616i	−0.251926	−	0.967747i	$-0.581064\pi$
$787$	−26.7623	−	7.17094i	−0.953973	−	0.255616i	−0.702047	+	0.712130i	$0.747731\pi$
$788$	69.8314	+	69.8314i	2.48764	+	2.48764i
$789$		0			0
$790$	−2.05247	+	3.55498i	−0.0730236	+	0.126481i
$791$	6.63120	−	14.5706i	0.235778	−	0.518072i
$792$		0			0
$793$	−15.8550	+	7.66336i	−0.563027	+	0.272134i
$794$			65.0151i			2.30730i
$795$		0			0
$796$	107.225	+	61.9065i	3.80050	+	2.19422i
$797$	26.4182	+	45.7577i	0.935781	+	1.62082i	0.773235	+	0.634119i	$0.218637\pi$
$797$	26.4182	+	45.7577i	0.935781	+	1.62082i	0.162546	+	0.986701i	$0.448029\pi$
$798$		0			0
$799$	24.6376	+	6.60161i	0.871614	+	0.233548i
$800$	−8.14837	+	30.4101i	−0.288088	+	1.07516i
$801$		0			0
$802$	26.2022	+	45.3835i	0.925232	+	1.60255i
$803$	−3.08351	+	5.34079i	−0.108815	+	0.188472i
$804$		0			0
$805$	−11.8902	+	14.4390i	−0.419073	+	0.508908i
$806$	42.7706	−	62.9264i	1.50653	−	2.21649i
$807$		0			0
$808$	7.40451	−	1.98403i	0.260490	−	0.0697980i
$809$	−12.7930	+	22.1581i	−0.449776	+	0.779036i	−0.998371	−	0.0570528i	$-0.981830\pi$
$809$	−12.7930	+	22.1581i	−0.449776	+	0.779036i	0.548595	+	0.836088i	$0.315163\pi$
$810$		0			0
$811$	−34.1937	−	34.1937i	−1.20070	−	1.20070i	−0.973953	−	0.226749i	$-0.927190\pi$
$811$	−34.1937	−	34.1937i	−1.20070	−	1.20070i	−0.226749	−	0.973953i	$-0.572810\pi$
$812$	11.4667	−	8.18798i	0.402402	−	0.287342i
$813$		0			0
$814$	−5.18518	−	5.18518i	−0.181741	−	0.181741i
$815$	−8.17035	+	4.71716i	−0.286195	+	0.165235i
$816$		0			0
$817$	−11.7210	−	43.7433i	−0.410066	−	1.53039i
$818$	−68.0320			−2.37868
$819$		0			0
$820$	10.8463			0.378768
$821$	5.38960	+	20.1142i	0.188098	+	0.701992i	0.993946	+	0.109869i	$0.0350432\pi$
$821$	5.38960	+	20.1142i	0.188098	+	0.701992i	−0.805848	+	0.592123i	$0.798290\pi$
$822$		0			0
$823$	−1.66588	+	0.961795i	−0.0580689	+	0.0335261i	−0.528753	−	0.848776i	$-0.677340\pi$
$823$	−1.66588	+	0.961795i	−0.0580689	+	0.0335261i	0.470684	+	0.882302i	$0.344007\pi$
$824$	−46.1639	−	46.1639i	−1.60820	−	1.60820i
$825$		0			0
$826$	−48.9159	+	34.9292i	−1.70200	+	1.21534i
$827$	−22.0447	−	22.0447i	−0.766570	−	0.766570i	0.210931	−	0.977501i	$-0.432351\pi$
$827$	−22.0447	−	22.0447i	−0.766570	−	0.766570i	−0.977501	+	0.210931i	$0.932351\pi$
$828$		0			0
$829$	−1.67430	+	2.89997i	−0.0581508	+	0.100720i	−0.893635	−	0.448794i	$-0.851854\pi$
$829$	−1.67430	+	2.89997i	−0.0581508	+	0.100720i	0.835485	+	0.549514i	$0.185187\pi$
$830$	−47.0946	+	12.6190i	−1.63468	+	0.438011i
$831$		0			0
$832$	3.88450	−	52.8508i	0.134671	−	1.83227i
$833$	43.3670	−	8.47586i	1.50258	−	0.293671i
$834$		0			0
$835$	3.54668	−	6.14303i	0.122738	−	0.212588i
$836$	−49.7849	−	86.2299i	−1.72185	−	2.98232i
$837$		0			0
$838$	−1.97634	+	7.37582i	−0.0682717	+	0.254793i
$839$	−52.8531	−	14.1619i	−1.82469	−	0.488925i	−0.827343	−	0.561696i	$-0.810149\pi$
$839$	−52.8531	−	14.1619i	−1.82469	−	0.488925i	−0.997349	+	0.0727716i	$0.976816\pi$
$840$		0			0
$841$	13.9448	+	24.1531i	0.480854	+	0.832864i
$842$	44.2280	+	25.5351i	1.52420	+	0.879996i
$843$		0			0
$844$		−	115.387i		−	3.97178i
$845$	12.9073	+	17.3843i	0.444023	+	0.598037i
$846$		0			0
$847$	−25.8459	−	11.7627i	−0.888077	−	0.404170i
$848$	2.27987	−	3.94885i	0.0782910	−	0.135604i
$849$		0			0
$850$	26.3886	+	26.3886i	0.905123	+	0.905123i
$851$	−2.42827	−	0.650654i	−0.0832401	−	0.0223041i
$852$		0			0
$853$	21.1183	−	21.1183i	0.723077	−	0.723077i	−0.246154	−	0.969231i	$-0.579167\pi$
$853$	21.1183	−	21.1183i	0.723077	−	0.723077i	0.969231	+	0.246154i	$0.0791669\pi$
$854$	−5.64702	+	33.8519i	−0.193237	+	1.15839i
$855$		0			0
$856$	133.561	−	35.7875i	4.56501	−	1.22319i
$857$	30.2671			1.03390			0.516951	−	0.856015i	$-0.327067\pi$
$857$	30.2671			1.03390			0.516951	+	0.856015i	$0.327067\pi$
$858$		0			0
$859$		−	2.18372i		−	0.0745075i	−0.999306	−	0.0372537i	$-0.988139\pi$
$859$		−	2.18372i		−	0.0745075i	0.999306	−	0.0372537i	$-0.0118610\pi$
$860$	87.1212	−	23.3441i	2.97081	−	0.796026i
$861$		0			0
$862$	−84.3170	+	48.6805i	−2.87185	+	1.65806i
$863$	−22.7673	+	22.7673i	−0.775006	+	0.775006i	−0.978977	−	0.203971i	$-0.934615\pi$
$863$	−22.7673	+	22.7673i	−0.775006	+	0.775006i	0.203971	+	0.978977i	$0.434615\pi$
$864$		0			0
$865$	0.753456	−	2.81194i	0.0256183	−	0.0956087i
$866$	−0.278668	+	0.278668i	−0.00946954	+	0.00946954i
$867$		0			0
$868$	−37.2567	−	99.4921i	−1.26458	−	3.37698i
$869$	−4.17874	+	1.11969i	−0.141754	+	0.0379829i
$870$		0			0
$871$	7.22209	+	37.8726i	0.244711	+	1.28327i
$872$	17.9824			0.608961
$873$		0			0
$874$	−41.2609	−	23.8220i	−1.39567	−	0.805792i
$875$	−31.4080	−	5.23934i	−1.06178	−	0.177122i
$876$		0			0
$877$	−4.78095	−	1.28105i	−0.161441	−	0.0432580i	0.177193	−	0.984176i	$-0.443298\pi$
$877$	−4.78095	−	1.28105i	−0.161441	−	0.0432580i	−0.338634	+	0.940918i	$0.609965\pi$
$878$	−20.8181	−	5.57819i	−0.702577	−	0.188255i
$879$		0			0
$880$	76.8770	−	44.3849i	2.59152	−	1.49622i
$881$	−17.8019	+	30.8338i	−0.599762	+	1.03882i	0.393094	+	0.919498i	$0.371405\pi$
$881$	−17.8019	+	30.8338i	−0.599762	+	1.03882i	−0.992856	+	0.119320i	$0.961929\pi$
$882$		0			0
$883$			16.6669i			0.560886i	0.959871	+	0.280443i	$0.0904814\pi$
$883$			16.6669i			0.560886i	−0.959871	+	0.280443i	$0.909519\pi$
$884$	−95.1294	−	64.6587i	−3.19955	−	2.17471i
$885$		0			0
$886$	−18.0064	−	67.2009i	−0.604937	−	2.25766i
$887$	−24.7682	−	14.2999i	−0.831635	−	0.480145i	0.0227770	−	0.999741i	$-0.492749\pi$
$887$	−24.7682	−	14.2999i	−0.831635	−	0.480145i	−0.854412	+	0.519596i	$0.826083\pi$
$888$		0			0
$889$	0.472689	+	4.88282i	0.0158535	+	0.163764i
$890$	−21.1800	−	5.67515i	−0.709954	−	0.190231i
$891$		0			0
$892$	45.2957	−	45.2957i	1.51661	−	1.51661i
$893$	−8.53842	−	14.7890i	−0.285727	−	0.494894i
$894$		0			0
$895$	9.83467	+	36.7035i	0.328737	+	1.22686i
$896$	−21.9529	−	18.0777i	−0.733396	−	0.603934i
$897$		0			0
$898$	9.78518			0.326536
$899$	−8.08753	+	2.16705i	−0.269734	+	0.0722750i
$900$		0			0
$901$	−1.25881	−	2.18032i	−0.0419370	−	0.0726371i
$902$	11.2815	+	11.2815i	0.375633	+	0.375633i
$903$		0			0
$904$	−12.7011	+	47.4013i	−0.422433	+	1.57654i
$905$	16.1848	+	16.1848i	0.538000	+	0.538000i
$906$		0			0
$907$	31.1299	+	17.9728i	1.03365	+	0.596778i	0.918028	−	0.396515i	$-0.129780\pi$
$907$	31.1299	+	17.9728i	1.03365	+	0.596778i	0.115622	+	0.993293i	$0.463114\pi$
$908$	15.1342	+	56.4815i	0.502245	+	1.87441i
$909$		0			0
$910$	42.1861	−	0.976294i	1.39845	−	0.0323638i
$911$	−23.0425			−0.763432			−0.381716	−	0.924280i	$-0.624667\pi$
$911$	−23.0425			−0.763432			−0.381716	+	0.924280i	$0.624667\pi$
$912$		0			0
$913$	−44.4993	−	25.6917i	−1.47271	−	0.850270i
$914$	22.1919	−	12.8125i	0.734043	−	0.423800i
$915$		0			0
$916$	−16.8469	+	62.8733i	−0.556636	+	2.07739i
$917$	10.6524	−	7.60655i	0.351774	−	0.251190i
$918$		0			0
$919$	−19.2005	−	33.2563i	−0.633367	−	1.09702i	−0.986859	−	0.161586i	$-0.948339\pi$
$919$	−19.2005	−	33.2563i	−0.633367	−	1.09702i	0.353492	−	0.935438i	$-0.384994\pi$
$920$	28.6688	−	49.6558i	0.945182	−	1.63710i
$921$		0			0
$922$	−19.5777			−0.644759
$923$	15.2197	+	5.30114i	0.500962	+	0.174489i
$924$		0			0
$925$	−0.341214	−	1.27343i	−0.0112191	−	0.0418701i
$926$	19.2816	−	33.3967i	0.633633	−	1.09748i
$927$		0			0
$928$	−10.5387	+	10.5387i	−0.345950	+	0.345950i
$929$	0.718418	−	2.68117i	0.0235705	−	0.0879664i	−0.953139	−	0.302534i	$-0.902167\pi$
$929$	0.718418	−	2.68117i	0.0235705	−	0.0879664i	0.976709	+	0.214567i	$0.0688342\pi$
$930$		0			0
$931$	−24.5430	−	16.5179i	−0.804365	−	0.541351i
$932$	−3.78102	−	6.54892i	−0.123852	−	0.214517i
$933$		0			0
$934$	23.4967	+	87.6908i	0.768835	+	2.86933i
$935$		−	49.0135i		−	1.60291i
$936$		0			0
$937$			34.9632i			1.14220i	0.820881	+	0.571100i	$0.193483\pi$
$937$			34.9632i			1.14220i	−0.820881	+	0.571100i	$0.806517\pi$
$938$	68.3901	+	31.1248i	2.23301	+	1.01626i
$939$		0			0
$940$	29.4544	−	17.0055i	0.960697	−	0.554658i
$941$	−5.49420	−	5.49420i	−0.179106	−	0.179106i	0.611860	−	0.790966i	$-0.290422\pi$
$941$	−5.49420	−	5.49420i	−0.179106	−	0.179106i	−0.790966	+	0.611860i	$0.790422\pi$
$942$		0			0
$943$	5.28324	+	1.41564i	0.172046	+	0.0460996i
$944$	69.1513	−	69.1513i	2.25068	−	2.25068i
$945$		0			0
$946$	114.898	+	66.3363i	3.73565	+	2.15678i
$947$	−19.3584	+	5.18706i	−0.629063	+	0.168557i	−0.559244	−	0.829003i	$-0.688909\pi$
$947$	−19.3584	+	5.18706i	−0.629063	+	0.168557i	−0.0698185	+	0.997560i	$0.522242\pi$
$948$		0			0
$949$	3.61081	−	3.11636i	0.117212	−	0.101161i
$950$		−	24.9854i		−	0.810633i
$951$		0			0
$952$	−126.852	+	47.5020i	−4.11128	+	1.53955i
$953$	10.4017	−	6.00540i	0.336943	−	0.194534i	−0.321977	−	0.946748i	$-0.604347\pi$
$953$	10.4017	−	6.00540i	0.336943	−	0.194534i	0.658919	+	0.752214i	$0.271014\pi$
$954$		0			0
$955$	5.19517	−	19.3887i	0.168112	−	0.627402i
$956$	−5.90663	+	22.0438i	−0.191034	+	0.712949i
$957$		0			0
$958$	−81.7154	+	47.1784i	−2.64010	+	1.52427i
$959$	17.4766	−	6.54447i	0.564350	−	0.211332i
$960$		0			0
$961$			32.1314i			1.03650i
$962$	2.46805	+	5.10624i	0.0795732	+	0.164632i
$963$		0			0
$964$	−46.8701	+	12.5588i	−1.50959	+	0.404492i
$965$	−6.60290	−	3.81219i	−0.212555	−	0.122719i
$966$		0			0
$967$	−2.97257	+	2.97257i	−0.0955913	+	0.0955913i	−0.753285	−	0.657694i	$-0.771532\pi$
$967$	−2.97257	+	2.97257i	−0.0955913	+	0.0955913i	0.657694	+	0.753285i	$0.271532\pi$
$968$	84.0821	+	22.5297i	2.70250	+	0.724133i
$969$		0			0
$970$	20.0173	+	20.0173i	0.642718	+	0.642718i
$971$	25.0492	−	14.4622i	0.803867	−	0.464113i	−0.0409543	−	0.999161i	$-0.513040\pi$
$971$	25.0492	−	14.4622i	0.803867	−	0.464113i	0.844822	+	0.535048i	$0.179706\pi$
$972$		0			0
$973$	−28.9326	−	13.1674i	−0.927537	−	0.422129i
$974$		−	60.5312i		−	1.93954i
$975$		0			0
$976$		−	55.8388i		−	1.78736i
$977$	15.0612	+	56.2091i	0.481850	+	1.79829i	0.593845	+	0.804579i	$0.297609\pi$
$977$	15.0612	+	56.2091i	0.481850	+	1.79829i	−0.111995	+	0.993709i	$0.535724\pi$
$978$		0			0
$979$	−11.5544	−	20.0127i	−0.369279	−	0.639610i
$980$	32.8977	−	48.8810i	1.05088	−	1.56145i
$981$		0			0
$982$	−10.2125	+	38.1135i	−0.325893	+	1.21625i
$983$	26.9928	−	26.9928i	0.860937	−	0.860937i	−0.130510	−	0.991447i	$-0.541661\pi$
$983$	26.9928	−	26.9928i	0.860937	−	0.860937i	0.991447	+	0.130510i	$0.0416615\pi$
$984$		0			0
$985$	16.2734	−	28.1864i	0.518514	−	0.898092i
$986$	4.57253	+	17.0649i	0.145619	+	0.543458i
$987$		0			0
$988$	14.4252	+	75.6456i	0.458926	+	2.40661i
$989$	45.4837			1.44630
$990$		0			0
$991$	−2.29062	+	3.96747i	−0.0727640	+	0.126031i	−0.900112	−	0.435659i	$-0.856515\pi$
$991$	−2.29062	+	3.96747i	−0.0727640	+	0.126031i	0.827348	+	0.561690i	$0.189849\pi$
$992$	56.1883	+	97.3211i	1.78398	+	3.08995i
$993$		0			0
$994$	25.5614	−	18.2525i	0.810758	−	0.578936i
$995$	10.5610	−	39.4142i	0.334806	−	1.24951i
$996$		0			0
$997$	46.4148	−	26.7976i	1.46997	−	0.848689i	0.470540	−	0.882379i	$-0.344059\pi$
$997$	46.4148	−	26.7976i	1.46997	−	0.848689i	0.999432	+	0.0336896i	$0.0107258\pi$
$998$	36.5255	+	21.0880i	1.15619	+	0.667529i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fm.e.370.1		32
3.2	odd	2		273.2.by.d.97.8	yes	32
7.6	odd	2		819.2.fm.f.370.1		32
13.11	odd	12		819.2.fm.f.622.1		32
21.20	even	2		273.2.by.c.97.8	yes	32
39.11	even	12		273.2.by.c.76.8	✓	32
91.76	even	12	inner	819.2.fm.e.622.1		32
273.167	odd	12		273.2.by.d.76.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.76.8	✓	32	39.11	even	12
273.2.by.c.97.8	yes	32	21.20	even	2
273.2.by.d.76.8	yes	32	273.167	odd	12
273.2.by.d.97.8	yes	32	3.2	odd	2
819.2.fm.e.370.1		32	1.1	even	1	trivial
819.2.fm.e.622.1		32	91.76	even	12	inner
819.2.fm.f.370.1		32	7.6	odd	2
819.2.fm.f.622.1		32	13.11	odd	12

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fm (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.687394 - 2.56539i) q^{2} +(-4.37666 + 2.52687i) q^{4} +(1.17771 + 1.17771i) q^{5} +(-1.53750 - 2.15316i) q^{7} +(5.73490 + 5.73490i) q^{8} +O(q^{10})\)	\(q+(-0.687394 - 2.56539i) q^{2} +(-4.37666 + 2.52687i) q^{4} +(1.17771 + 1.17771i) q^{5} +(-1.53750 - 2.15316i) q^{7} +(5.73490 + 5.73490i) q^{8} +(2.21174 - 3.83085i) q^{10} +(4.50301 - 1.20658i) q^{11} +(-3.59585 - 0.264293i) q^{13} +(-4.46682 + 5.42436i) q^{14} +(5.71638 - 9.90107i) q^{16} +(-3.15625 - 5.46679i) q^{17} +(-1.09384 + 4.08225i) q^{19} +(-8.13039 - 2.17853i) q^{20} +(-6.19069 - 10.7226i) q^{22} +(-3.67599 - 2.12233i) q^{23} -2.22598i q^{25} +(1.79375 + 9.40643i) q^{26} +(12.1699 + 5.53859i) q^{28} +(0.526889 - 0.912598i) q^{29} +(-5.61834 - 5.61834i) q^{31} +(-13.6615 - 3.66058i) q^{32} +(-11.8549 + 11.8549i) q^{34} +(0.725070 - 4.34654i) q^{35} +(0.572076 - 0.153287i) q^{37} +11.2245 q^{38} +13.5081i q^{40} +(-1.24468 + 0.333510i) q^{41} +(-9.27990 + 5.35775i) q^{43} +(-16.6593 + 16.6593i) q^{44} +(-2.91776 + 10.8892i) q^{46} +(-2.85718 + 2.85718i) q^{47} +(-2.27219 + 6.62096i) q^{49} +(-5.71050 + 1.53012i) q^{50} +(16.4057 - 7.92952i) q^{52} +0.398831 q^{53} +(6.72427 + 3.88226i) q^{55} +(3.53074 - 21.1656i) q^{56} +(-2.70335 - 0.724361i) q^{58} +(8.26243 + 2.21391i) q^{59} +(4.22976 - 2.44205i) q^{61} +(-10.5512 + 18.2752i) q^{62} +14.6977i q^{64} +(-3.92362 - 4.54615i) q^{65} +(-2.76762 - 10.3289i) q^{67} +(27.6277 + 15.9509i) q^{68} +(-11.6490 + 1.12770i) q^{70} +(-4.31760 - 1.15690i) q^{71} +(-0.935407 + 0.935407i) q^{73} +(-0.786484 - 1.36223i) q^{74} +(-5.52795 - 20.6306i) q^{76} +(-9.52134 - 7.84059i) q^{77} -0.927988 q^{79} +(18.3929 - 4.92836i) q^{80} +(1.71117 + 2.96383i) q^{82} +(-7.79378 - 7.79378i) q^{83} +(2.72115 - 10.1555i) q^{85} +(20.1237 + 20.1237i) q^{86} +(32.7439 + 18.9047i) q^{88} +(-1.28296 - 4.78807i) q^{89} +(4.95956 + 8.14879i) q^{91} +21.4514 q^{92} +(9.29378 + 5.36577i) q^{94} +(-6.09595 + 3.51950i) q^{95} +(-1.65635 + 6.18160i) q^{97} +(18.5472 + 1.27783i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8	\( 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 2 q^{10} + 4 q^{11} + 6 q^{13} - 34 q^{14} + 14 q^{16} + 8 q^{17} + 2 q^{19} - 44 q^{20} - 4 q^{22} + 18 q^{23} + 28 q^{26} - 32 q^{28} + 18 q^{29} - 14 q^{31} + 8 q^{32} - 66 q^{34} - 22 q^{35} - 24 q^{37} - 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} + 28 q^{47} + 8 q^{49} - 70 q^{50} + 28 q^{52} + 80 q^{53} + 60 q^{55} + 54 q^{56} - 4 q^{58} + 42 q^{59} + 36 q^{61} - 52 q^{62} - 14 q^{65} + 26 q^{67} + 72 q^{68} - 116 q^{70} + 4 q^{71} + 12 q^{73} + 18 q^{74} - 48 q^{76} - 28 q^{77} - 4 q^{79} + 98 q^{80} + 20 q^{82} + 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} + 54 q^{89} + 148 q^{91} + 4 q^{92} - 60 q^{95} - 40 q^{97} - 36 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8 + 2 * q^10 + 4 * q^11 + 6 * q^13 - 34 * q^14 + 14 * q^16 + 8 * q^17 + 2 * q^19 - 44 * q^20 - 4 * q^22 + 18 * q^23 + 28 * q^26 - 32 * q^28 + 18 * q^29 - 14 * q^31 + 8 * q^32 - 66 * q^34 - 22 * q^35 - 24 * q^37 - 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 + 28 * q^47 + 8 * q^49 - 70 * q^50 + 28 * q^52 + 80 * q^53 + 60 * q^55 + 54 * q^56 - 4 * q^58 + 42 * q^59 + 36 * q^61 - 52 * q^62 - 14 * q^65 + 26 * q^67 + 72 * q^68 - 116 * q^70 + 4 * q^71 + 12 * q^73 + 18 * q^74 - 48 * q^76 - 28 * q^77 - 4 * q^79 + 98 * q^80 + 20 * q^82 + 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 + 54 * q^89 + 148 * q^91 + 4 * q^92 - 60 * q^95 - 40 * q^97 - 36 * q^98

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