LMFDB - Embedded newform 819.2.fm.e.622.5

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			622.5
Character	$\chi$	$=$	819.622
Dual form			819.2.fm.e.370.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.189683 - 0.707908i) q^{2} +(1.26690 + 0.731443i) q^{4} +(1.23329 - 1.23329i) q^{5} +(-2.64473 + 0.0736014i) q^{7} +(1.79455 - 1.79455i) q^{8} +O(q^{10})$	\(q+(0.189683 - 0.707908i) q^{2} +(1.26690 + 0.731443i) q^{4} +(1.23329 - 1.23329i) q^{5} +(-2.64473 + 0.0736014i) q^{7} +(1.79455 - 1.79455i) q^{8} +(-0.639122 - 1.10699i) q^{10} +(3.18977 + 0.854696i) q^{11} +(2.53031 + 2.56856i) q^{13} +(-0.449558 + 1.88618i) q^{14} +(0.532906 + 0.923019i) q^{16} +(0.433708 - 0.751205i) q^{17} +(-1.01858 - 3.80140i) q^{19} +(2.46454 - 0.660371i) q^{20} +(1.21009 - 2.09594i) q^{22} +(3.77196 - 2.17774i) q^{23} +1.95798i q^{25} +(2.29826 - 1.30401i) q^{26} +(-3.40443 - 1.84122i) q^{28} +(-2.65427 - 4.59734i) q^{29} +(0.220754 - 0.220754i) q^{31} +(5.65731 - 1.51587i) q^{32} +(-0.449517 - 0.449517i) q^{34} +(-3.17095 + 3.35249i) q^{35} +(-3.57217 - 0.957160i) q^{37} -2.88425 q^{38} -4.42641i q^{40} +(-1.90334 - 0.509998i) q^{41} +(9.99342 + 5.76970i) q^{43} +(3.41595 + 3.41595i) q^{44} +(-0.826162 - 3.08328i) q^{46} +(-3.68984 - 3.68984i) q^{47} +(6.98917 - 0.389311i) q^{49} +(1.38607 + 0.371397i) q^{50} +(1.32689 + 5.10489i) q^{52} +3.55843 q^{53} +(4.98801 - 2.87983i) q^{55} +(-4.61402 + 4.87818i) q^{56} +(-3.75796 + 1.00694i) q^{58} +(-8.89645 + 2.38380i) q^{59} +(4.78192 + 2.76084i) q^{61} +(-0.114400 - 0.198147i) q^{62} -2.16076i q^{64} +(6.28840 + 0.0471733i) q^{65} +(1.01969 - 3.80552i) q^{67} +(1.09893 - 0.634466i) q^{68} +(1.77178 + 2.88065i) q^{70} +(-11.9487 + 3.20164i) q^{71} +(5.55302 + 5.55302i) q^{73} +(-1.35516 + 2.34721i) q^{74} +(1.49007 - 5.56101i) q^{76} +(-8.49898 - 2.02567i) q^{77} -15.7334 q^{79} +(1.79558 + 0.481124i) q^{80} +(-0.722063 + 1.25065i) q^{82} +(3.80823 - 3.80823i) q^{83} +(-0.391566 - 1.46134i) q^{85} +(5.98000 - 5.98000i) q^{86} +(7.25801 - 4.19041i) q^{88} +(3.26801 - 12.1964i) q^{89} +(-6.88104 - 6.60691i) q^{91} +6.37158 q^{92} +(-3.31197 + 1.91217i) q^{94} +(-5.94444 - 3.43202i) q^{95} +(0.756697 + 2.82403i) q^{97} +(1.05013 - 5.02153i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$-1$

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 $

$2$	0.189683	−	0.707908i	0.134126	−	0.500566i	−0.865874	−	0.500263i	$-0.833237\pi$
$2$	0.189683	−	0.707908i	0.134126	−	0.500566i	1.00000		0.000303559i	$-9.66258e-5\pi$
$3$		0			0
$3$		0			0
$4$	1.26690	+	0.731443i	0.633449	+	0.365722i
$5$	1.23329	−	1.23329i	0.551545	−	0.551545i	−0.375342	−	0.926887i	$-0.622475\pi$
$5$	1.23329	−	1.23329i	0.551545	−	0.551545i	0.926887	+	0.375342i	$0.122475\pi$
$6$		0			0
$7$	−2.64473	+	0.0736014i	−0.999613	+	0.0278187i
$7$	−2.64473	+	0.0736014i	−0.999613	+	0.0278187i
$8$	1.79455	−	1.79455i	0.634470	−	0.634470i
$9$		0			0
$10$	−0.639122	−	1.10699i	−0.202108	−	0.350062i
$11$	3.18977	+	0.854696i	0.961752	+	0.257701i	0.705342	−	0.708867i	$-0.250794\pi$
$11$	3.18977	+	0.854696i	0.961752	+	0.257701i	0.256410	+	0.966568i	$0.417460\pi$
$12$		0			0
$13$	2.53031	+	2.56856i	0.701783	+	0.712391i
$13$	2.53031	+	2.56856i	0.701783	+	0.712391i
$14$	−0.449558	+	1.88618i	−0.120149	+	0.504104i
$15$		0			0
$16$	0.532906	+	0.923019i	0.133226	+	0.230755i
$17$	0.433708	−	0.751205i	0.105190	−	0.182194i	−0.808626	−	0.588323i	$-0.799788\pi$
$17$	0.433708	−	0.751205i	0.105190	−	0.182194i	0.913816	+	0.406129i	$0.133122\pi$
$18$		0			0
$19$	−1.01858	−	3.80140i	−0.233679	−	0.872100i	−0.978740	−	0.205105i	$-0.934247\pi$
$19$	−1.01858	−	3.80140i	−0.233679	−	0.872100i	0.745061	−	0.666996i	$-0.232420\pi$
$20$	2.46454	−	0.660371i	0.551087	−	0.147663i
$21$		0			0
$22$	1.21009	−	2.09594i	0.257993	−	0.446856i
$23$	3.77196	−	2.17774i	0.786508	−	0.454090i	−0.0522240	−	0.998635i	$-0.516631\pi$
$23$	3.77196	−	2.17774i	0.786508	−	0.454090i	0.838732	+	0.544545i	$0.183298\pi$
$24$		0			0
$25$			1.95798i			0.391596i
$26$	2.29826	−	1.30401i	0.450727	−	0.255738i
$27$		0			0
$28$	−3.40443	−	1.84122i	−0.643377	−	0.347958i
$29$	−2.65427	−	4.59734i	−0.492886	−	0.853704i	0.507080	−	0.861899i	$-0.330725\pi$
$29$	−2.65427	−	4.59734i	−0.492886	−	0.853704i	−0.999966	+	0.00819474i	$0.997392\pi$
$30$		0			0
$31$	0.220754	−	0.220754i	0.0396485	−	0.0396485i	−0.687005	−	0.726653i	$-0.741075\pi$
$31$	0.220754	−	0.220754i	0.0396485	−	0.0396485i	0.726653	+	0.687005i	$0.241075\pi$
$32$	5.65731	−	1.51587i	1.00008	−	0.267971i
$33$		0			0
$34$	−0.449517	−	0.449517i	−0.0770915	−	0.0770915i
$35$	−3.17095	+	3.35249i	−0.535988	+	0.566675i
$36$		0			0
$37$	−3.57217	−	0.957160i	−0.587261	−	0.157356i	−0.0470599	−	0.998892i	$-0.514985\pi$
$37$	−3.57217	−	0.957160i	−0.587261	−	0.157356i	−0.540201	+	0.841536i	$0.681652\pi$
$38$	−2.88425			−0.467887
$39$		0			0
$40$		−	4.42641i		−	0.699878i
$41$	−1.90334	−	0.509998i	−0.297251	−	0.0796483i	0.107111	−	0.994247i	$-0.465840\pi$
$41$	−1.90334	−	0.509998i	−0.297251	−	0.0796483i	−0.404363	+	0.914599i	$0.632507\pi$
$42$		0			0
$43$	9.99342	+	5.76970i	1.52398	+	0.879872i	0.999597	+	0.0283909i	$0.00903832\pi$
$43$	9.99342	+	5.76970i	1.52398	+	0.879872i	0.524386	+	0.851481i	$0.324295\pi$
$44$	3.41595	+	3.41595i	0.514974	+	0.514974i
$45$		0			0
$46$	−0.826162	−	3.08328i	−0.121811	−	0.454605i
$47$	−3.68984	−	3.68984i	−0.538219	−	0.538219i	0.384786	−	0.923006i	$-0.374275\pi$
$47$	−3.68984	−	3.68984i	−0.538219	−	0.538219i	−0.923006	+	0.384786i	$0.874275\pi$
$48$		0			0
$49$	6.98917	−	0.389311i	0.998452	−	0.0556159i
$50$	1.38607	+	0.371397i	0.196020	+	0.0525234i
$51$		0			0
$52$	1.32689	+	5.10489i	0.184006	+	0.707920i
$53$	3.55843			0.488788			0.244394	−	0.969676i	$-0.421411\pi$
$53$	3.55843			0.488788			0.244394	+	0.969676i	$0.421411\pi$
$54$		0			0
$55$	4.98801	−	2.87983i	0.672583	−	0.388316i
$56$	−4.61402	+	4.87818i	−0.616575	+	0.651875i
$57$		0			0
$58$	−3.75796	+	1.00694i	−0.493445	+	0.132218i
$59$	−8.89645	+	2.38380i	−1.15822	+	0.310344i	−0.786255	−	0.617903i	$-0.787983\pi$
$59$	−8.89645	+	2.38380i	−1.15822	+	0.310344i	−0.371965	+	0.928247i	$0.621316\pi$
$60$		0			0
$61$	4.78192	+	2.76084i	0.612262	+	0.353490i	0.773850	−	0.633369i	$-0.218328\pi$
$61$	4.78192	+	2.76084i	0.612262	+	0.353490i	−0.161588	+	0.986858i	$0.551662\pi$
$62$	−0.114400	−	0.198147i	−0.0145288	−	0.0251646i
$63$		0			0
$64$		−	2.16076i		−	0.270095i
$65$	6.28840	+	0.0471733i	0.779980	+	0.00585112i
$66$		0			0
$67$	1.01969	−	3.80552i	0.124575	−	0.464919i	−0.875250	−	0.483672i	$-0.839303\pi$
$67$	1.01969	−	3.80552i	0.124575	−	0.464919i	0.999824	+	0.0187529i	$0.00596958\pi$
$68$	1.09893	−	0.634466i	0.133265	−	0.0769403i
$69$		0			0
$70$	1.77178	+	2.88065i	0.211768	+	0.344304i
$71$	−11.9487	+	3.20164i	−1.41805	+	0.379965i	−0.884791	−	0.465987i	$-0.845699\pi$
$71$	−11.9487	+	3.20164i	−1.41805	+	0.379965i	−0.533258	+	0.845952i	$0.679033\pi$
$72$		0			0
$73$	5.55302	+	5.55302i	0.649932	+	0.649932i	0.952977	−	0.303044i	$-0.0980030\pi$
$73$	5.55302	+	5.55302i	0.649932	+	0.649932i	−0.303044	+	0.952977i	$0.598003\pi$
$74$	−1.35516	+	2.34721i	−0.157534	+	0.272858i
$75$		0			0
$76$	1.49007	−	5.56101i	0.170923	−	0.637892i
$77$	−8.49898	−	2.02567i	−0.968549	−	0.230846i
$78$		0			0
$79$	−15.7334			−1.77015			−0.885073	−	0.465453i	$-0.845891\pi$
$79$	−15.7334			−1.77015			−0.885073	+	0.465453i	$0.845891\pi$
$80$	1.79558	+	0.481124i	0.200752	+	0.0537913i
$81$		0			0
$82$	−0.722063	+	1.25065i	−0.0797385	+	0.138111i
$83$	3.80823	−	3.80823i	0.418007	−	0.418007i	−0.466509	−	0.884516i	$-0.654488\pi$
$83$	3.80823	−	3.80823i	0.418007	−	0.418007i	0.884516	+	0.466509i	$0.154488\pi$
$84$		0			0
$85$	−0.391566	−	1.46134i	−0.0424713	−	0.158505i
$86$	5.98000	−	5.98000i	0.644841	−	0.644841i
$87$		0			0
$88$	7.25801	−	4.19041i	0.773706	−	0.446700i
$89$	3.26801	−	12.1964i	0.346409	−	1.29282i	−0.544549	−	0.838729i	$-0.683299\pi$
$89$	3.26801	−	12.1964i	0.346409	−	1.29282i	0.890958	−	0.454086i	$-0.150034\pi$
$90$		0			0
$91$	−6.88104	−	6.60691i	−0.721329	−	0.692593i
$92$	6.37158			0.664283
$93$		0			0
$94$	−3.31197	+	1.91217i	−0.341604	+	0.197225i
$95$	−5.94444	−	3.43202i	−0.609887	−	0.352118i
$96$		0			0
$97$	0.756697	+	2.82403i	0.0768309	+	0.286737i	0.993642	−	0.112584i	$-0.0359127\pi$
$97$	0.756697	+	2.82403i	0.0768309	+	0.286737i	−0.916811	+	0.399321i	$0.869246\pi$
$98$	1.05013	−	5.02153i	0.106079	−	0.507251i
$99$		0			0
$100$	−1.43215	+	2.48056i	−0.143215	+	0.248056i
$101$	4.75389	+	8.23397i	0.473029	+	0.819311i	0.999523	−	0.0308679i	$-0.00982712\pi$
$101$	4.75389	+	8.23397i	0.473029	+	0.819311i	−0.526494	+	0.850179i	$0.676494\pi$
$102$		0			0
$103$	−8.04351			−0.792551			−0.396275	−	0.918132i	$-0.629697\pi$
$103$	−8.04351			−0.792551			−0.396275	+	0.918132i	$0.629697\pi$
$104$	9.15020	+	0.0686414i	0.897251	+	0.00673085i
$105$		0			0
$106$	0.674975	−	2.51904i	0.0655594	−	0.244671i
$107$	−5.49111	−	9.51088i	−0.530845	−	0.919451i	−0.999352	−	0.0359912i	$-0.988541\pi$
$107$	−5.49111	−	9.51088i	−0.530845	−	0.919451i	0.468507	−	0.883460i	$-0.344792\pi$
$108$		0			0
$109$	−2.13897	−	2.13897i	−0.204876	−	0.204876i	0.597209	−	0.802086i	$-0.296276\pi$
$109$	−2.13897	−	2.13897i	−0.204876	−	0.204876i	−0.802086	+	0.597209i	$0.796276\pi$
$110$	−1.09251	−	4.07731i	−0.104167	−	0.388756i
$111$		0			0
$112$	−1.47733	−	2.40191i	−0.139594	−	0.226959i
$113$	−7.04028	+	12.1941i	−0.662294	+	1.14713i	0.317718	+	0.948185i	$0.397084\pi$
$113$	−7.04028	+	12.1941i	−0.662294	+	1.14713i	−0.980011	+	0.198941i	$0.936250\pi$
$114$		0			0
$115$	1.96614	−	7.33772i	0.183343	−	0.684246i
$116$		−	7.76581i		−	0.721037i
$117$		0			0
$118$			6.75004i			0.621391i
$119$	−1.09175	+	2.01865i	−0.100081	+	0.185050i
$120$		0			0
$121$	−0.0821489	−	0.0474287i	−0.00746808	−	0.00431170i
$122$	2.86147	−	2.86147i	0.259066	−	0.259066i
$123$		0			0
$124$	0.441141	−	0.118203i	0.0396156	−	0.0106150i
$125$	8.58122	+	8.58122i	0.767528	+	0.767528i
$126$		0			0
$127$	4.95962	−	2.86344i	0.440095	−	0.254089i	−0.263543	−	0.964648i	$-0.584891\pi$
$127$	4.95962	−	2.86344i	0.440095	−	0.254089i	0.703638	+	0.710559i	$0.251558\pi$
$128$	9.78499	+	2.62188i	0.864879	+	0.231744i
$129$		0			0
$130$	1.22620	−	4.44266i	0.107545	−	0.389647i
$131$			21.7908i			1.90387i	0.306294	+	0.951937i	$0.400911\pi$
$131$			21.7908i			1.90387i	−0.306294	+	0.951937i	$0.599089\pi$
$132$		0			0
$133$	2.97366	+	9.97869i	0.257849	+	0.865262i
$134$	−2.50054	−	1.44369i	−0.216014	−	0.124716i
$135$		0			0
$136$	−0.569764	−	2.12639i	−0.0488569	−	0.182336i
$137$	−0.00993599	−	0.0370816i	−0.000848889	−	0.00316810i	0.965500	−	0.260403i	$-0.0838553\pi$
$137$	−0.00993599	−	0.0370816i	−0.000848889	−	0.00316810i	−0.966349	+	0.257235i	$0.917189\pi$
$138$		0			0
$139$	−14.5766	−	8.41579i	−1.23637	−	0.713818i	−0.268018	−	0.963414i	$-0.586369\pi$
$139$	−14.5766	−	8.41579i	−1.23637	−	0.713818i	−0.968350	+	0.249596i	$0.919702\pi$
$140$	−6.46942	+	1.92789i	−0.546766	+	0.162937i
$141$		0			0
$142$			9.06588i			0.760792i
$143$	5.87578	+	10.3558i	0.491357	+	0.865994i
$144$		0			0
$145$	−8.94335	−	2.39636i	−0.742705	−	0.199007i
$146$	4.98435	−	2.87771i	0.412507	−	0.238161i
$147$		0			0
$148$	−3.82546	−	3.82546i	−0.314451	−	0.314451i
$149$	−13.8533	+	3.71198i	−1.13491	+	0.304097i	−0.776901	−	0.629622i	$-0.783210\pi$
$149$	−13.8533	+	3.71198i	−1.13491	+	0.304097i	−0.358005	+	0.933720i	$0.616543\pi$
$150$		0			0
$151$	−16.8022	+	16.8022i	−1.36735	+	1.36735i	−0.503142	+	0.864204i	$0.667823\pi$
$151$	−16.8022	+	16.8022i	−1.36735	+	1.36735i	−0.864204	+	0.503142i	$0.832177\pi$
$152$	−8.64971	−	4.99391i	−0.701584	−	0.405060i
$153$		0			0
$154$	−3.04610	+	5.63226i	−0.245462	+	0.453860i
$155$		−	0.544507i		−	0.0437359i
$156$		0			0
$157$			15.4058i			1.22952i	0.788715	+	0.614758i	$0.210746\pi$
$157$			15.4058i			1.22952i	−0.788715	+	0.614758i	$0.789254\pi$
$158$	−2.98436	+	11.1378i	−0.237423	+	0.886075i
$159$		0			0
$160$	5.10760	−	8.84662i	0.403791	−	0.699387i
$161$	−9.81552	+	6.03715i	−0.773571	+	0.475794i
$162$		0			0
$163$	−0.340861	−	1.27211i	−0.0266983	−	0.0996393i	0.951291	−	0.308294i	$-0.0997581\pi$
$163$	−0.340861	−	1.27211i	−0.0266983	−	0.0996393i	−0.977989	+	0.208655i	$0.933091\pi$
$164$	−2.03830	−	2.03830i	−0.159164	−	0.159164i
$165$		0			0
$166$	−1.97352	−	3.41823i	−0.153175	−	0.265306i
$167$	6.28848	−	23.4689i	0.486617	−	1.81608i	−0.0860480	−	0.996291i	$-0.527424\pi$
$167$	6.28848	−	23.4689i	0.486617	−	1.81608i	0.572665	−	0.819789i	$-0.305909\pi$
$168$		0			0
$169$	−0.195031	+	12.9985i	−0.0150024	+	0.999887i
$170$	−1.10877			−0.0850388
$171$		0			0
$172$	8.44042	+	14.6192i	0.643576	+	1.11471i
$173$	0.316932	−	0.548943i	0.0240959	−	0.0417353i	−0.853726	−	0.520722i	$-0.825663\pi$
$173$	0.316932	−	0.548943i	0.0240959	−	0.0417353i	0.877822	+	0.478987i	$0.158996\pi$
$174$		0			0
$175$	−0.144110	−	5.17833i	−0.0108937	−	0.391445i
$176$	0.910945	+	3.39969i	0.0686651	+	0.256261i
$177$		0			0
$178$	−8.01403	−	4.62691i	−0.600677	−	0.346801i
$179$	−12.6821	+	7.32204i	−0.947908	+	0.547275i	−0.892431	−	0.451185i	$-0.851002\pi$
$179$	−12.6821	+	7.32204i	−0.947908	+	0.547275i	−0.0554778	+	0.998460i	$0.517668\pi$
$180$		0			0
$181$	6.41112			0.476535			0.238267	−	0.971200i	$-0.423421\pi$
$181$	6.41112			0.476535			0.238267	+	0.971200i	$0.423421\pi$
$182$	−5.98230	+	3.61792i	−0.443438	+	0.268178i
$183$		0			0
$184$	2.86091	−	10.6770i	0.210909	−	0.787122i
$185$	−5.58598	+	3.22507i	−0.410690	+	0.237112i
$186$		0			0
$187$	2.02548	−	2.02548i	0.148118	−	0.148118i
$188$	−1.97574	−	7.37357i	−0.144096	−	0.537773i
$189$		0			0
$190$	−3.55712	+	3.55712i	−0.258060	+	0.258060i
$191$	−2.37706	+	4.11718i	−0.171998	+	0.297909i	−0.939118	−	0.343594i	$-0.888356\pi$
$191$	−2.37706	+	4.11718i	−0.171998	+	0.297909i	0.767120	+	0.641503i	$0.221689\pi$
$192$		0			0
$193$	−9.10651	−	2.44008i	−0.655501	−	0.175641i	−0.0842861	−	0.996442i	$-0.526861\pi$
$193$	−9.10651	−	2.44008i	−0.655501	−	0.175641i	−0.571215	+	0.820801i	$0.693528\pi$
$194$	2.14269			0.153836
$195$		0			0
$196$	9.13931	+	4.61896i	0.652808	+	0.329926i
$197$	−2.90812	+	10.8532i	−0.207195	+	0.773262i	0.781574	+	0.623812i	$0.214417\pi$
$197$	−2.90812	+	10.8532i	−0.207195	+	0.773262i	−0.988769	+	0.149450i	$0.952250\pi$
$198$		0			0
$199$	−6.27981	+	10.8770i	−0.445164	+	0.771047i	−0.998064	−	0.0622009i	$-0.980188\pi$
$199$	−6.27981	+	10.8770i	−0.445164	+	0.771047i	0.552899	+	0.833248i	$0.313521\pi$
$200$	3.51370	+	3.51370i	0.248456	+	0.248456i
$201$		0			0
$202$	6.73063	−	1.80347i	0.473565	−	0.126891i
$203$	7.35820	+	11.9633i	0.516445	+	0.839662i
$204$		0			0
$205$	−2.97635	+	1.71839i	−0.207877	+	0.120018i
$206$	−1.52572	+	5.69406i	−0.106302	+	0.396724i
$207$		0			0
$208$	−1.02242	+	3.70433i	−0.0708918	+	0.256849i
$209$		−	12.9962i		−	0.898963i
$210$		0			0
$211$	−5.70417	−	9.87991i	−0.392691	−	0.680161i	0.600112	−	0.799916i	$-0.295123\pi$
$211$	−5.70417	−	9.87991i	−0.392691	−	0.680161i	−0.992804	+	0.119755i	$0.961789\pi$
$212$	4.50817	+	2.60279i	0.309622	+	0.178760i
$213$		0			0
$214$	−7.77440	+	2.08314i	−0.531447	+	0.142401i
$215$	19.4405	−	5.20908i	1.32583	−	0.355256i
$216$		0			0
$217$	−0.567585	+	0.600081i	−0.0385302	+	0.0407362i
$218$	−1.91992	+	1.10847i	−0.130034	+	0.0750749i
$219$		0			0
$220$	8.42572			0.568062
$221$	3.02693	−	0.786776i	0.203614	−	0.0529243i
$222$		0			0
$223$	7.03645	+	1.88541i	0.471196	+	0.126257i	0.486600	−	0.873625i	$-0.338237\pi$
$223$	7.03645	+	1.88541i	0.471196	+	0.126257i	−0.0154044	+	0.999881i	$0.504904\pi$
$224$	−14.8505	+	4.42545i	−0.992238	+	0.295688i
$225$		0			0
$226$	7.29689	+	7.29689i	0.485382	+	0.485382i
$227$	6.07133	+	22.6585i	0.402968	+	1.50390i	0.807772	+	0.589495i	$0.200673\pi$
$227$	6.07133	+	22.6585i	0.402968	+	1.50390i	−0.404804	+	0.914404i	$0.632660\pi$
$228$		0			0
$229$	16.2331	+	16.2331i	1.07271	+	1.07271i	0.997140	+	0.0755720i	$0.0240783\pi$
$229$	16.2331	+	16.2331i	1.07271	+	1.07271i	0.0755720	+	0.997140i	$0.475922\pi$
$230$	−4.82148	−	2.78368i	−0.317919	−	0.183551i
$231$		0			0
$232$	−13.0134	−	3.48693i	−0.854372	−	0.228928i
$233$			16.5274i			1.08274i	0.840783	+	0.541372i	$0.182095\pi$
$233$			16.5274i			1.08274i	−0.840783	+	0.541372i	$0.817905\pi$
$234$		0			0
$235$	−9.10131			−0.593704
$236$	−13.0145	−	3.48723i	−0.847172	−	0.226999i
$237$		0			0
$238$	1.22193	+	1.15576i	0.0792062	+	0.0749170i
$239$	−18.8339	−	18.8339i	−1.21826	−	1.21826i	−0.968239	−	0.250025i	$-0.919561\pi$
$239$	−18.8339	−	18.8339i	−1.21826	−	1.21826i	−0.250025	−	0.968239i	$-0.580439\pi$
$240$		0			0
$241$	1.11909	−	0.299860i	0.0720871	−	0.0193157i	−0.222595	−	0.974911i	$-0.571453\pi$
$241$	1.11909	−	0.299860i	0.0720871	−	0.0193157i	0.294682	+	0.955595i	$0.404786\pi$
$242$	−0.0491574	+	0.0491574i	−0.00315996	+	0.00315996i
$243$		0			0
$244$	4.03880	+	6.99541i	0.258558	+	0.447835i
$245$	8.13955	−	9.09982i	0.520017	−	0.581366i
$246$		0			0
$247$	7.18680	−	12.2350i	0.457285	−	0.778495i
$248$		−	0.792308i		−	0.0503116i
$249$		0			0
$250$	7.70243	−	4.44700i	0.487144	−	0.281253i
$251$	−6.82617	+	11.8233i	−0.430864	+	0.746278i	−0.996948	−	0.0780693i	$-0.975124\pi$
$251$	−6.82617	+	11.8233i	−0.430864	+	0.746278i	0.566084	+	0.824348i	$0.308458\pi$
$252$		0			0
$253$	13.8930	−	3.72262i	0.873445	−	0.234039i
$254$	−1.08629	−	4.05410i	−0.0681600	−	0.254377i
$255$		0			0
$256$	5.87286	−	10.1721i	0.367054	−	0.635756i
$257$	0.128138	+	0.221941i	0.00799302	+	0.0138443i	0.869994	−	0.493062i	$-0.164122\pi$
$257$	0.128138	+	0.221941i	0.00799302	+	0.0138443i	−0.862001	+	0.506906i	$0.830789\pi$
$258$		0			0
$259$	9.51786	+	2.26851i	0.591411	+	0.140958i
$260$	7.93225	+	4.65937i	0.491938	+	0.288962i
$261$		0			0
$262$	15.4259	+	4.13336i	0.953015	+	0.255360i
$263$	−6.21656	−	10.7674i	−0.383329	−	0.663946i	0.608206	−	0.793779i	$-0.291889\pi$
$263$	−6.21656	−	10.7674i	−0.383329	−	0.663946i	−0.991536	+	0.129833i	$0.958556\pi$
$264$		0			0
$265$	4.38858	−	4.38858i	0.269589	−	0.269589i
$266$	7.62805	−	0.212285i	0.467706	−	0.0130160i
$267$		0			0
$268$	4.07536	−	4.07536i	0.248942	−	0.248942i
$269$	−23.9300	−	13.8160i	−1.45904	−	0.842375i	−0.460072	−	0.887882i	$-0.652176\pi$
$269$	−23.9300	−	13.8160i	−1.45904	−	0.842375i	−0.998964	+	0.0455067i	$0.985510\pi$
$270$		0			0
$271$	7.85980	−	29.3332i	0.477449	−	1.78186i	−0.134442	−	0.990921i	$-0.542924\pi$
$271$	7.85980	−	29.3332i	0.477449	−	1.78186i	0.611891	−	0.790942i	$-0.290409\pi$
$272$	0.924502			0.0560562
$273$		0			0
$274$	−0.0281351			−0.00169970
$275$	−1.67348	+	6.24551i	−0.100915	+	0.376619i
$276$		0			0
$277$	9.29180	+	5.36462i	0.558290	+	0.322329i	0.752459	−	0.658639i	$-0.228868\pi$
$277$	9.29180	+	5.36462i	0.558290	+	0.322329i	−0.194169	+	0.980968i	$0.562201\pi$
$278$	−8.72253	+	8.72253i	−0.523143	+	0.523143i
$279$		0			0
$280$	0.325790	+	11.7067i	0.0194697	+	0.699607i
$281$	17.6179	−	17.6179i	1.05099	−	1.05099i	0.0523655	−	0.998628i	$-0.483324\pi$
$281$	17.6179	−	17.6179i	1.05099	−	1.05099i	0.998628	−	0.0523655i	$-0.0166761\pi$
$282$		0			0
$283$	−4.91523	−	8.51342i	−0.292180	−	0.506070i	0.682145	−	0.731217i	$-0.261047\pi$
$283$	−4.91523	−	8.51342i	−0.292180	−	0.506070i	−0.974325	+	0.225147i	$0.927714\pi$
$284$	−17.4796	−	4.68364i	−1.03722	−	0.277923i
$285$		0			0
$286$	8.44547	−	2.19519i	0.499391	−	0.129804i
$287$	5.07134	+	1.20872i	0.299352	+	0.0713483i
$288$		0			0
$289$	8.12379	+	14.0708i	0.477870	+	0.827696i
$290$	−3.39281	+	5.87652i	−0.199233	+	0.345081i
$291$		0			0
$292$	2.97339	+	11.0968i	0.174004	+	0.649393i
$293$	24.9107	−	6.67480i	1.45530	−	0.389946i	0.557435	−	0.830221i	$-0.311786\pi$
$293$	24.9107	−	6.67480i	1.45530	−	0.389946i	0.897863	+	0.440275i	$0.145119\pi$
$294$		0			0
$295$	−8.03201	+	13.9118i	−0.467641	+	0.809979i
$296$	−8.12812	+	4.69277i	−0.472437	+	0.272762i
$297$		0			0
$298$			10.5110i			0.608883i
$299$	15.1379	+	4.17815i	0.875447	+	0.241628i
$300$		0			0
$301$	−26.8545	−	14.5238i	−1.54787	−	0.837136i
$302$	8.70733	+	15.0815i	0.501050	+	0.867845i
$303$		0			0
$304$	2.96596	−	2.96596i	0.170109	−	0.170109i
$305$	9.30243	−	2.49258i	0.532656	−	0.142725i
$306$		0			0
$307$	−3.13433	−	3.13433i	−0.178886	−	0.178886i	0.611984	−	0.790870i	$-0.290372\pi$
$307$	−3.13433	−	3.13433i	−0.178886	−	0.178886i	−0.790870	+	0.611984i	$0.790372\pi$
$308$	−9.28567	−	8.78284i	−0.529100	−	0.500448i
$309$		0			0
$310$	−0.385461	−	0.103284i	−0.0218927	−	0.00586614i
$311$	−22.3642			−1.26816			−0.634078	−	0.773269i	$-0.718620\pi$
$311$	−22.3642			−1.26816			−0.634078	+	0.773269i	$0.718620\pi$
$312$		0			0
$313$		−	5.32563i		−	0.301022i	−0.988608	−	0.150511i	$-0.951908\pi$
$313$		−	5.32563i		−	0.301022i	0.988608	−	0.150511i	$-0.0480919\pi$
$314$	10.9059	+	2.92222i	0.615455	+	0.164911i
$315$		0			0
$316$	−19.9326	−	11.5081i	−1.12130	−	0.647380i
$317$	−9.55320	−	9.55320i	−0.536561	−	0.536561i	0.385956	−	0.922517i	$-0.373872\pi$
$317$	−9.55320	−	9.55320i	−0.536561	−	0.536561i	−0.922517	+	0.385956i	$0.873872\pi$
$318$		0			0
$319$	−4.53720	−	16.9331i	−0.254034	−	0.948069i
$320$	−2.66485	−	2.66485i	−0.148970	−	0.148970i
$321$		0			0
$322$	2.41191	+	8.09363i	0.134410	+	0.451040i
$323$	−3.29740	−	0.883534i	−0.183472	−	0.0491612i
$324$		0			0
$325$	−5.02920	+	4.95431i	−0.278970	+	0.274816i
$326$	−0.965192			−0.0534571
$327$		0			0
$328$	−4.33086	+	2.50042i	−0.239132	+	0.138063i
$329$	10.0302	+	9.48706i	0.552983	+	0.523038i
$330$		0			0
$331$	9.25799	−	2.48067i	0.508865	−	0.136350i	0.00475394	−	0.999989i	$-0.498487\pi$
$331$	9.25799	−	2.48067i	0.508865	−	0.136350i	0.504111	+	0.863639i	$0.331820\pi$
$332$	7.61014	−	2.03913i	0.417661	−	0.111912i
$333$		0			0
$334$	−15.4210	−	8.90333i	−0.843801	−	0.487169i
$335$	−3.43575	−	5.95089i	−0.187715	−	0.325132i
$336$		0			0
$337$		−	27.7219i		−	1.51011i	−0.655663	−	0.755053i	$-0.727611\pi$
$337$		−	27.7219i		−	1.51011i	0.655663	−	0.755053i	$-0.272389\pi$
$338$	9.16477	+	2.60367i	0.498498	+	0.141621i
$339$		0			0
$340$	0.572817	−	2.13778i	0.0310653	−	0.115937i
$341$	0.892831	−	0.515476i	0.0483495	−	0.0279146i
$342$		0			0
$343$	−18.4558	+	1.54403i	−0.996519	+	0.0833700i
$344$	28.2878	−	7.57968i	1.52517	−	0.408669i
$345$		0			0
$346$	−0.328484	−	0.328484i	−0.0176594	−	0.0176594i
$347$	11.5943	−	20.0819i	0.622413	−	1.07805i	−0.366622	−	0.930370i	$-0.619486\pi$
$347$	11.5943	−	20.0819i	0.622413	−	1.07805i	0.989035	−	0.147681i	$-0.0471808\pi$
$348$		0			0
$349$	4.20372	−	15.6885i	0.225020	−	0.839787i	−0.757376	−	0.652979i	$-0.773519\pi$
$349$	4.20372	−	15.6885i	0.225020	−	0.839787i	0.982396	−	0.186808i	$-0.0598142\pi$
$350$	−3.69312	−	0.880226i	−0.197405	−	0.0470501i
$351$		0			0
$352$	19.3411			1.03088
$353$	−12.1897	−	3.26621i	−0.648790	−	0.173843i	−0.0806085	−	0.996746i	$-0.525686\pi$
$353$	−12.1897	−	3.26621i	−0.648790	−	0.173843i	−0.568182	+	0.822903i	$0.692353\pi$
$354$		0			0
$355$	−10.7877	+	18.6848i	−0.572550	+	0.991686i
$356$	13.0612	−	13.0612i	0.692243	−	0.692243i
$357$		0			0
$358$	2.77774	+	10.3667i	0.146808	+	0.547895i
$359$	2.03793	−	2.03793i	0.107558	−	0.107558i	−0.651280	−	0.758838i	$-0.725768\pi$
$359$	2.03793	−	2.03793i	0.107558	−	0.107558i	0.758838	+	0.651280i	$0.225768\pi$
$360$		0			0
$361$	3.04137	−	1.75593i	0.160072	−	0.0924176i
$362$	1.21608	−	4.53848i	0.0639159	−	0.238537i
$363$		0			0
$364$	−3.88498	−	13.4034i	−0.203628	−	0.702527i
$365$	13.6970			0.716934
$366$		0			0
$367$	−24.3990	+	14.0868i	−1.27362	+	0.735325i	−0.975667	−	0.219256i	$-0.929637\pi$
$367$	−24.3990	+	14.0868i	−1.27362	+	0.735325i	−0.297953	+	0.954581i	$0.596304\pi$
$368$	4.02019	+	2.32106i	0.209567	+	0.120994i
$369$		0			0
$370$	1.22348	+	4.56610i	0.0636059	+	0.237380i
$371$	−9.41108	+	0.261906i	−0.488599	+	0.0135975i
$372$		0			0
$373$	12.9669	−	22.4593i	0.671400	−	1.16290i	−0.306107	−	0.951997i	$-0.599026\pi$
$373$	12.9669	−	22.4593i	0.671400	−	1.16290i	0.977507	−	0.210902i	$-0.0676402\pi$
$374$	−1.04965	−	1.81805i	−0.0542763	−	0.0940094i
$375$		0			0
$376$	−13.2432			−0.682968
$377$	5.09241	−	18.4504i	0.262272	−	0.950243i
$378$		0			0
$379$	−8.41204	+	31.3942i	−0.432097	+	1.61261i	0.315821	+	0.948819i	$0.397720\pi$
$379$	−8.41204	+	31.3942i	−0.432097	+	1.61261i	−0.747918	+	0.663791i	$0.768946\pi$
$380$	−5.02066	−	8.69604i	−0.257555	−	0.446098i
$381$		0			0
$382$	2.46370	+	2.46370i	0.126054	+	0.126054i
$383$	1.42917	+	5.33373i	0.0730271	+	0.272541i	0.992779	−	0.119960i	$-0.0382767\pi$
$383$	1.42917	+	5.33373i	0.0730271	+	0.272541i	−0.919752	+	0.392501i	$0.871610\pi$
$384$		0			0
$385$	−12.9800	+	7.98348i	−0.661520	+	0.406876i
$386$	−3.45471	+	5.98373i	−0.175840	+	0.304564i
$387$		0			0
$388$	−1.10696	+	4.13124i	−0.0561975	+	0.209732i
$389$			24.3224i			1.23319i	0.787279	+	0.616597i	$0.211489\pi$
$389$			24.3224i			1.23319i	−0.787279	+	0.616597i	$0.788511\pi$
$390$		0			0
$391$		−	3.77802i		−	0.191063i
$392$	11.8438	−	13.2411i	0.598202	−	0.668775i
$393$		0			0
$394$	7.13148	+	4.11736i	0.359279	+	0.207430i
$395$	−19.4039	+	19.4039i	−0.976315	+	0.976315i
$396$		0			0
$397$	−10.3563	+	2.77495i	−0.519765	+	0.139271i	−0.509158	−	0.860673i	$-0.670043\pi$
$397$	−10.3563	+	2.77495i	−0.519765	+	0.139271i	−0.0106073	+	0.999944i	$0.503376\pi$
$398$	6.50871	+	6.50871i	0.326252	+	0.326252i
$399$		0			0
$400$	−1.80726	+	1.04342i	−0.0903628	+	0.0521710i
$401$	−25.6010	−	6.85977i	−1.27845	−	0.342561i	−0.445190	−	0.895436i	$-0.646864\pi$
$401$	−25.6010	−	6.85977i	−1.27845	−	0.342561i	−0.833264	+	0.552875i	$0.813531\pi$
$402$		0			0
$403$	1.12560	+	0.00844380i	0.0560699	+	0.000420616i
$404$			13.9088i			0.691988i
$405$		0			0
$406$	9.86468	−	2.93968i	0.489576	−	0.145894i
$407$	−10.5763	−	6.10624i	−0.524249	−	0.302675i
$408$		0			0
$409$	0.225314	+	0.840884i	0.0111411	+	0.0415790i	0.971273	−	0.237970i	$-0.0764819\pi$
$409$	0.225314	+	0.840884i	0.0111411	+	0.0415790i	−0.960132	+	0.279549i	$0.909815\pi$
$410$	0.651902	+	2.43293i	0.0321951	+	0.120154i
$411$		0			0
$412$	−10.1903	−	5.88337i	−0.502040	−	0.289853i
$413$	23.3532	−	6.95929i	1.14914	−	0.342444i
$414$		0			0
$415$		−	9.39332i		−	0.461100i
$416$	18.2084	+	10.6955i	0.892738	+	0.524391i
$417$		0			0
$418$	−9.20009	−	2.46516i	−0.449991	−	0.120575i
$419$	24.0763	−	13.9005i	1.17621	−	0.679083i	0.221072	−	0.975257i	$-0.429044\pi$
$419$	24.0763	−	13.9005i	1.17621	−	0.679083i	0.955134	+	0.296174i	$0.0957110\pi$
$420$		0			0
$421$	6.14872	+	6.14872i	0.299670	+	0.299670i	0.840885	−	0.541214i	$-0.182035\pi$
$421$	6.14872	+	6.14872i	0.299670	+	0.299670i	−0.541214	+	0.840885i	$0.682035\pi$
$422$	−8.07605	+	2.16397i	−0.393136	+	0.105340i
$423$		0			0
$424$	6.38579	−	6.38579i	0.310122	−	0.310122i
$425$	1.47085	+	0.849193i	0.0713465	+	0.0411919i
$426$		0			0
$427$	−12.8501	−	6.94972i	−0.621859	−	0.336321i
$428$		−	16.0657i		−	0.776567i
$429$		0			0
$430$		−	14.7502i		−	0.711317i
$431$	7.07164	−	26.3917i	0.340629	−	1.27124i	−0.557007	−	0.830507i	$-0.688051\pi$
$431$	7.07164	−	26.3917i	0.340629	−	1.27124i	0.897636	−	0.440737i	$-0.145283\pi$
$432$		0			0
$433$	11.5716	−	20.0425i	0.556094	−	0.963182i	−0.441724	−	0.897151i	$-0.645633\pi$
$433$	11.5716	−	20.0425i	0.556094	−	0.963182i	0.997818	−	0.0660314i	$-0.0210338\pi$
$434$	0.317141	+	0.515624i	0.0152232	+	0.0247507i
$435$		0			0
$436$	−1.14532	−	4.27440i	−0.0548509	−	0.204706i
$437$	−12.1205	−	12.1205i	−0.579802	−	0.579802i
$438$		0			0
$439$	20.4076	+	35.3470i	0.974003	+	1.68702i	0.683188	+	0.730242i	$0.260593\pi$
$439$	20.4076	+	35.3470i	0.974003	+	1.68702i	0.290814	+	0.956779i	$0.406074\pi$
$440$	3.78324	−	14.1192i	0.180359	−	0.673109i
$441$		0			0
$442$	0.0171940	−	2.29203i	0.000817833	−	0.109021i
$443$	6.05837			0.287842			0.143921	−	0.989589i	$-0.454029\pi$
$443$	6.05837			0.287842			0.143921	+	0.989589i	$0.454029\pi$
$444$		0			0
$445$	−11.0113	−	19.0721i	−0.521986	−	0.904106i
$446$	2.66940	−	4.62353i	0.126400	−	0.218930i
$447$		0			0
$448$	0.159035	+	5.71463i	0.00751371	+	0.269991i
$449$	1.65796	+	6.18758i	0.0782438	+	0.292010i	0.993949	−	0.109840i	$-0.0350340\pi$
$449$	1.65796	+	6.18758i	0.0782438	+	0.292010i	−0.915705	+	0.401850i	$0.868367\pi$
$450$		0			0
$451$	−5.63532	−	3.25355i	−0.265357	−	0.153204i
$452$	−17.8386	+	10.2991i	−0.839058	+	0.484430i
$453$		0			0
$454$	17.1918			0.806850
$455$	−16.6346	+	0.338075i	−0.779841	+	0.0158492i
$456$		0			0
$457$	−7.61312	+	28.4126i	−0.356127	+	1.32908i	0.522934	+	0.852373i	$0.324837\pi$
$457$	−7.61312	+	28.4126i	−0.356127	+	1.32908i	−0.879061	+	0.476710i	$0.841829\pi$
$458$	14.5707	−	8.41238i	0.680843	−	0.393085i
$459$		0			0
$460$	7.85801	−	7.85801i	0.366382	−	0.366382i
$461$	3.01129	+	11.2383i	0.140250	+	0.523419i	0.999921	+	0.0125715i	$0.00400175\pi$
$461$	3.01129	+	11.2383i	0.140250	+	0.523419i	−0.859671	+	0.510848i	$0.829332\pi$
$462$		0			0
$463$	8.42591	−	8.42591i	0.391585	−	0.391585i	−0.483667	−	0.875252i	$-0.660695\pi$
$463$	8.42591	−	8.42591i	0.391585	−	0.391585i	0.875252	+	0.483667i	$0.160695\pi$
$464$	2.82895	−	4.89989i	0.131331	−	0.227472i
$465$		0			0
$466$	11.6999	+	3.13497i	0.541985	+	0.145225i
$467$	21.2254			0.982195			0.491097	−	0.871105i	$-0.336596\pi$
$467$	21.2254			0.982195			0.491097	+	0.871105i	$0.336596\pi$
$468$		0			0
$469$	−2.41670	+	10.1396i	−0.111593	+	0.468204i
$470$	−1.72637	+	6.44289i	−0.0796314	+	0.297188i
$471$		0			0
$472$	−11.6873	+	20.2430i	−0.537952	+	0.931760i
$473$	26.9454	+	26.9454i	1.23895	+	1.23895i
$474$		0			0
$475$	7.44307	−	1.99436i	0.341511	−	0.0915077i
$476$	−2.85967	+	1.75887i	−0.131073	+	0.0806178i
$477$		0			0
$478$	−16.9052	+	9.76019i	−0.773224	+	0.446421i
$479$	5.66017	−	21.1241i	0.258620	−	0.965183i	−0.707421	−	0.706793i	$-0.750141\pi$
$479$	5.66017	−	21.1241i	0.258620	−	0.965183i	0.966041	−	0.258390i	$-0.0831920\pi$
$480$		0			0
$481$	−6.58018	−	11.5973i	−0.300030	−	0.528789i
$482$		−	0.849093i		−	0.0386751i
$483$		0			0
$484$	−0.0693828	−	0.120174i	−0.00315376	−	0.00546248i
$485$	4.41608	+	2.54963i	0.200524	+	0.115773i
$486$		0			0
$487$	28.6992	−	7.68994i	1.30049	−	0.348464i	0.458852	−	0.888512i	$-0.348261\pi$
$487$	28.6992	−	7.68994i	1.30049	−	0.348464i	0.841634	+	0.540048i	$0.181594\pi$
$488$	13.5359	−	3.62693i	0.612741	−	0.164183i
$489$		0			0
$490$	−4.89789	−	7.48813i	−0.221264	−	0.338279i
$491$	23.9204	−	13.8105i	1.07951	−	0.623258i	0.148749	−	0.988875i	$-0.452475\pi$
$491$	23.9204	−	13.8105i	1.07951	−	0.623258i	0.930765	+	0.365617i	$0.119142\pi$
$492$		0			0
$493$	−4.60472			−0.207386
$494$	−7.29805	−	7.40837i	−0.328355	−	0.333318i
$495$		0			0
$496$	0.321401	+	0.0861191i	0.0144313	+	0.00386686i
$497$	31.3654	−	9.34692i	1.40693	−	0.419267i
$498$		0			0
$499$	5.32994	+	5.32994i	0.238601	+	0.238601i	0.816271	−	0.577670i	$-0.196038\pi$
$499$	5.32994	+	5.32994i	0.238601	+	0.238601i	−0.577670	+	0.816271i	$0.696038\pi$
$500$	4.59485	+	17.1482i	0.205488	+	0.766891i
$501$		0			0
$502$	7.07498	+	7.07498i	0.315772	+	0.315772i
$503$	−16.3880	−	9.46160i	−0.730703	−	0.421872i	0.0879761	−	0.996123i	$-0.471960\pi$
$503$	−16.3880	−	9.46160i	−0.730703	−	0.421872i	−0.818679	+	0.574251i	$0.805293\pi$
$504$		0			0
$505$	16.0178	+	4.29196i	0.712784	+	0.190990i
$506$		−	10.5411i		−	0.468608i
$507$		0			0
$508$	8.37777			0.371703
$509$	−19.9100	−	5.33488i	−0.882497	−	0.236464i	−0.211013	−	0.977483i	$-0.567676\pi$
$509$	−19.9100	−	5.33488i	−0.882497	−	0.236464i	−0.671484	+	0.741019i	$0.734343\pi$
$510$		0			0
$511$	−15.0949	−	14.2775i	−0.667761	−	0.631600i
$512$	8.23930	+	8.23930i	0.364129	+	0.364129i
$513$		0			0
$514$	0.181420	−	0.0486112i	0.00800208	−	0.00214415i
$515$	−9.91999	+	9.91999i	−0.437127	+	0.437127i
$516$		0			0
$517$	−8.61606	−	14.9235i	−0.378934	−	0.656333i
$518$	3.41128	−	6.30747i	0.149883	−	0.277134i
$519$		0			0
$520$	11.3695	−	11.2002i	0.498587	−	0.491162i
$521$			8.90519i			0.390144i	0.980789	+	0.195072i	$0.0624940\pi$
$521$			8.90519i			0.390144i	−0.980789	+	0.195072i	$0.937506\pi$
$522$		0			0
$523$	36.0214	−	20.7970i	1.57511	−	0.909387i	0.579577	−	0.814917i	$-0.303218\pi$
$523$	36.0214	−	20.7970i	1.57511	−	0.909387i	0.995528	−	0.0944702i	$-0.0301157\pi$
$524$	−15.9388	+	27.6067i	−0.696288	+	1.20601i
$525$		0			0
$526$	−8.80150	+	2.35835i	−0.383764	+	0.102829i
$527$	−0.0700885	−	0.261574i	−0.00305310	−	0.0113943i
$528$		0			0
$529$	−2.01489	+	3.48989i	−0.0876038	+	0.151734i
$530$	−2.27427	−	3.93915i	−0.0987881	−	0.171106i
$531$		0			0
$532$	−3.53153	+	14.8170i	−0.153111	+	0.642400i
$533$	−3.50608	−	6.17930i	−0.151865	−	0.267655i
$534$		0			0
$535$	−18.5018	−	4.95755i	−0.799904	−	0.214334i
$536$	−4.99933	−	8.65909i	−0.215938	−	0.374016i
$537$		0			0
$538$	−14.3196	+	14.3196i	−0.617360	+	0.617360i
$539$	22.6266	+	4.73180i	0.974596	+	0.203813i
$540$		0			0
$541$	22.8055	−	22.8055i	0.980484	−	0.980484i	−0.0193293	−	0.999813i	$-0.506153\pi$
$541$	22.8055	−	22.8055i	0.980484	−	0.980484i	0.999813	+	0.0193293i	$0.00615308\pi$
$542$	−19.2743	−	11.1280i	−0.827903	−	0.477990i
$543$		0			0
$544$	1.31489	−	4.90724i	0.0563755	−	0.210396i
$545$	−5.27596			−0.225997
$546$		0			0
$547$	15.4775			0.661769			0.330884	−	0.943671i	$-0.392653\pi$
$547$	15.4775			0.661769			0.330884	+	0.943671i	$0.392653\pi$
$548$	0.0145352	−	0.0542462i	0.000620914	−	0.00231728i
$549$		0			0
$550$	4.10382	+	2.36934i	0.174987	+	0.101029i
$551$	−14.7727	+	14.7727i	−0.629339	+	0.629339i
$552$		0			0
$553$	41.6105	−	1.15800i	1.76946	−	0.0492432i
$554$	5.56016	−	5.56016i	0.236228	−	0.236228i
$555$		0			0
$556$	−12.3113	−	21.3239i	−0.522117	−	0.904333i
$557$	16.8975	+	4.52767i	0.715969	+	0.191843i	0.598373	−	0.801218i	$-0.295814\pi$
$557$	16.8975	+	4.52767i	0.715969	+	0.191843i	0.117597	+	0.993061i	$0.462481\pi$
$558$		0			0
$559$	10.4666	+	40.2679i	0.442692	+	1.70315i
$560$	−4.78423	−	1.14029i	−0.202171	−	0.0481859i
$561$		0			0
$562$	−9.13001	−	15.8136i	−0.385126	−	0.667058i
$563$	−13.0176	+	22.5472i	−0.548628	+	0.950251i	0.449741	+	0.893159i	$0.351516\pi$
$563$	−13.0176	+	22.5472i	−0.548628	+	0.950251i	−0.998369	+	0.0570920i	$0.981817\pi$
$564$		0			0
$565$	6.35619	+	23.7216i	0.267407	+	0.997977i
$566$	−6.95905	+	1.86467i	−0.292511	+	0.0783780i
$567$		0			0
$568$	−15.6971	+	27.1881i	−0.658634	+	1.14079i
$569$	5.70128	−	3.29163i	0.239010	−	0.137992i	−0.375712	−	0.926737i	$-0.622602\pi$
$569$	5.70128	−	3.29163i	0.239010	−	0.137992i	0.614722	+	0.788744i	$0.289268\pi$
$570$		0			0
$571$		−	9.46828i		−	0.396235i	−0.980178	−	0.198118i	$-0.936517\pi$
$571$		−	9.46828i		−	0.396235i	0.980178	−	0.198118i	$-0.0634828\pi$
$572$	−0.130660	+	17.4175i	−0.00546315	+	0.728262i
$573$		0			0
$574$	1.81761	−	3.36077i	0.0758656	−	0.140276i
$575$	4.26398	+	7.38543i	0.177820	+	0.307994i
$576$		0			0
$577$	14.5583	−	14.5583i	0.606069	−	0.606069i	−0.335847	−	0.941916i	$-0.609023\pi$
$577$	14.5583	−	14.5583i	0.606069	−	0.606069i	0.941916	+	0.335847i	$0.109023\pi$
$578$	11.5018	−	3.08190i	0.478412	−	0.128190i
$579$		0			0
$580$	−9.57750	−	9.57750i	−0.397684	−	0.397684i
$581$	−9.79144	+	10.3520i	−0.406217	+	0.429474i
$582$		0			0
$583$	11.3506	+	3.04138i	0.470093	+	0.125961i
$584$	19.9304			0.824725
$585$		0			0
$586$		−	18.9006i		−	0.780775i
$587$	−28.3013	−	7.58332i	−1.16812	−	0.312997i	−0.377916	−	0.925840i	$-0.623359\pi$
$587$	−28.3013	−	7.58332i	−1.16812	−	0.312997i	−0.790205	+	0.612843i	$0.790026\pi$
$588$		0			0
$589$	−1.06403	−	0.614317i	−0.0438425	−	0.0253125i
$590$	8.32476	+	8.32476i	0.342725	+	0.342725i
$591$		0			0
$592$	−1.02015	−	3.80726i	−0.0419280	−	0.156477i
$593$	−21.9121	−	21.9121i	−0.899821	−	0.899821i	0.0955990	−	0.995420i	$-0.469523\pi$
$593$	−21.9121	−	21.9121i	−0.899821	−	0.899821i	−0.995420	+	0.0955990i	$0.969523\pi$
$594$		0			0
$595$	1.14314	+	3.83604i	0.0468643	+	0.157262i
$596$	−20.2658	−	5.43021i	−0.830120	−	0.222430i
$597$		0			0
$598$	5.82915	−	9.92371i	0.238372	−	0.405811i
$599$	−15.8653			−0.648240			−0.324120	−	0.946016i	$-0.605068\pi$
$599$	−15.8653			−0.648240			−0.324120	+	0.946016i	$0.605068\pi$
$600$		0			0
$601$	−0.177063	+	0.102227i	−0.00722256	+	0.00416995i	−0.503607	−	0.863933i	$-0.667994\pi$
$601$	−0.177063	+	0.102227i	−0.00722256	+	0.00416995i	0.496384	+	0.868103i	$0.334661\pi$
$602$	−15.3753	+	16.2556i	−0.626652	+	0.662530i
$603$		0			0
$604$	−33.5766	+	8.99681i	−1.36621	+	0.366075i
$605$	−0.159807	+	0.0428201i	−0.00649707	+	0.00174089i
$606$		0			0
$607$	24.0567	+	13.8891i	0.976430	+	0.563742i	0.901190	−	0.433423i	$-0.142695\pi$
$607$	24.0567	+	13.8891i	0.976430	+	0.563742i	0.0752394	+	0.997165i	$0.476028\pi$
$608$	−11.5249	−	19.9616i	−0.467394	−	0.809551i
$609$		0			0
$610$		−	7.05806i		−	0.285773i
$611$	0.141136	−	18.8141i	0.00570976	−	0.761135i
$612$		0			0
$613$	1.20950	−	4.51392i	0.0488513	−	0.182315i	−0.937189	−	0.348822i	$-0.886582\pi$
$613$	1.20950	−	4.51392i	0.0488513	−	0.182315i	0.986040	+	0.166506i	$0.0532486\pi$
$614$	−2.81335	+	1.62429i	−0.113537	+	0.0655508i
$615$		0			0
$616$	−18.8870	+	11.6167i	−0.760980	+	0.468050i
$617$	−0.205999	+	0.0551971i	−0.00829319	+	0.00222215i	−0.262963	−	0.964806i	$-0.584700\pi$
$617$	−0.205999	+	0.0551971i	−0.00829319	+	0.00222215i	0.254670	+	0.967028i	$0.418033\pi$
$618$		0			0
$619$	−10.1547	−	10.1547i	−0.408152	−	0.408152i	0.472941	−	0.881094i	$-0.343192\pi$
$619$	−10.1547	−	10.1547i	−0.408152	−	0.408152i	−0.881094	+	0.472941i	$0.843192\pi$
$620$	0.398276	−	0.689835i	0.0159952	−	0.0277044i
$621$		0			0
$622$	−4.24211	+	15.8318i	−0.170093	+	0.634797i
$623$	−7.74533	+	32.4967i	−0.310310	+	1.30195i
$624$		0			0
$625$	11.3764			0.455056
$626$	−3.77005	−	1.01018i	−0.150682	−	0.0403750i
$627$		0			0
$628$	−11.2685	+	19.5176i	−0.449661	+	0.778836i
$629$	−2.26830	+	2.26830i	−0.0904431	+	0.0904431i
$630$		0			0
$631$	−2.58932	−	9.66347i	−0.103079	−	0.384697i	0.895041	−	0.445984i	$-0.147146\pi$
$631$	−2.58932	−	9.66347i	−0.103079	−	0.384697i	−0.998120	+	0.0612871i	$0.980479\pi$
$632$	−28.2344	+	28.2344i	−1.12310	+	1.12310i
$633$		0			0
$634$	−8.57487	+	4.95070i	−0.340551	+	0.196617i
$635$	2.58520	−	9.64811i	0.102591	−	0.382873i
$636$		0			0
$637$	18.6847	+	16.9670i	0.740317	+	0.672258i
$638$	−12.8477			−0.508644
$639$		0			0
$640$	15.3013	−	8.83420i	0.604837	−	0.349203i
$641$	19.6180	+	11.3265i	0.774866	+	0.447369i	0.834608	−	0.550845i	$-0.185694\pi$
$641$	19.6180	+	11.3265i	0.774866	+	0.447369i	−0.0597418	+	0.998214i	$0.519028\pi$
$642$		0			0
$643$	−4.29092	−	16.0139i	−0.169217	−	0.631527i	−0.997465	−	0.0711645i	$-0.977328\pi$
$643$	−4.29092	−	16.0139i	−0.169217	−	0.631527i	0.828247	−	0.560363i	$-0.189338\pi$
$644$	−16.8511	+	0.468957i	−0.664026	+	0.0184795i
$645$		0			0
$646$	−1.25092	+	2.16666i	−0.0492169	+	0.0852461i
$647$	−12.5163	−	21.6789i	−0.492068	−	0.852287i	0.507890	−	0.861422i	$-0.330426\pi$
$647$	−12.5163	−	21.6789i	−0.492068	−	0.852287i	−0.999958	+	0.00913503i	$0.997092\pi$
$648$		0			0
$649$	−30.4151			−1.19390
$650$	2.55324	+	4.49996i	0.100146	+	0.176503i
$651$		0			0
$652$	0.498641	−	1.86095i	0.0195283	−	0.0728805i
$653$	9.18955	+	15.9168i	0.359615	+	0.622871i	0.987896	−	0.155115i	$-0.0495747\pi$
$653$	9.18955	+	15.9168i	0.359615	+	0.622871i	−0.628282	+	0.777986i	$0.716241\pi$
$654$		0			0
$655$	26.8745	+	26.8745i	1.05007	+	1.05007i
$656$	−0.543561	−	2.02860i	−0.0212225	−	0.0792034i
$657$		0			0
$658$	8.61853	−	5.30093i	0.335985	−	0.206652i
$659$	2.47281	−	4.28303i	0.0963269	−	0.166843i	−0.813835	−	0.581096i	$-0.802624\pi$
$659$	2.47281	−	4.28303i	0.0963269	−	0.166843i	0.910162	+	0.414253i	$0.135957\pi$
$660$		0			0
$661$	−0.736202	+	2.74754i	−0.0286349	+	0.106867i	−0.978764	−	0.204989i	$-0.934284\pi$
$661$	−0.736202	+	2.74754i	−0.0286349	+	0.106867i	0.950129	+	0.311856i	$0.100951\pi$
$662$		−	7.02435i		−	0.273009i
$663$		0			0
$664$		−	13.6681i		−	0.530426i
$665$	15.9740	+	8.63925i	0.619446	+	0.335016i
$666$		0			0
$667$	−20.0236	−	11.5606i	−0.775318	−	0.447630i
$668$	25.1331	−	25.1331i	0.972427	−	0.972427i
$669$		0			0
$670$	−4.86439	+	1.30341i	−0.187928	+	0.0503551i
$671$	12.8935	+	12.8935i	0.497750	+	0.497750i
$672$		0			0
$673$	−23.4111	+	13.5164i	−0.902431	+	0.521019i	−0.877988	−	0.478682i	$-0.841115\pi$
$673$	−23.4111	+	13.5164i	−0.902431	+	0.521019i	−0.0244432	+	0.999701i	$0.507781\pi$
$674$	−19.6245	−	5.25838i	−0.755909	−	0.202545i
$675$		0			0
$676$	−9.75478	+	16.3252i	−0.375184	+	0.627891i
$677$			1.97396i			0.0758653i	0.999280	+	0.0379327i	$0.0120772\pi$
$677$			1.97396i			0.0758653i	−0.999280	+	0.0379327i	$0.987923\pi$
$678$		0			0
$679$	−2.20911	−	7.41310i	−0.0847779	−	0.284489i
$680$	−3.32514	−	1.91977i	−0.127513	−	0.0736199i
$681$		0			0
$682$	−0.195554	−	0.729819i	−0.00748817	−	0.0279462i
$683$	0.854547	+	3.18921i	0.0326983	+	0.122032i	0.980346	−	0.197286i	$-0.0632128\pi$
$683$	0.854547	+	3.18921i	0.0326983	+	0.122032i	−0.947648	+	0.319318i	$0.896546\pi$
$684$		0			0
$685$	−0.0579865	−	0.0334785i	−0.00221555	−	0.00127915i
$686$	−2.40772	+	13.3579i	−0.0919272	+	0.510006i
$687$		0			0
$688$			12.2988i			0.468889i
$689$	9.00395	+	9.14006i	0.343023	+	0.348208i
$690$		0			0
$691$	43.3678	+	11.6204i	1.64979	+	0.442060i	0.959554	−	0.281525i	$-0.0908402\pi$
$691$	43.3678	+	11.6204i	1.64979	+	0.442060i	0.690236	+	0.723585i	$0.257507\pi$
$692$	0.803041	−	0.463636i	0.0305270	−	0.0176248i
$693$		0			0
$694$	−12.0169	−	12.0169i	−0.456154	−	0.456154i
$695$	−28.3563	+	7.59804i	−1.07562	+	0.288210i
$696$		0			0
$697$	−1.20861	+	1.20861i	−0.0457792	+	0.0457792i
$698$	−10.3086	−	5.95170i	−0.390188	−	0.225275i
$699$		0			0
$700$	3.60508	−	6.66582i	0.136259	−	0.251944i
$701$		−	23.5928i		−	0.891086i	−0.895260	−	0.445543i	$-0.853011\pi$
$701$		−	23.5928i		−	0.891086i	0.895260	−	0.445543i	$-0.146989\pi$
$702$		0			0
$703$			14.5542i			0.548921i
$704$	1.84680	−	6.89234i	0.0696038	−	0.259765i
$705$		0			0
$706$	−4.62435	+	8.00961i	−0.174040	+	0.301446i
$707$	−13.1788	−	21.4267i	−0.495638	−	0.805835i
$708$		0			0
$709$	9.42663	+	35.1807i	0.354025	+	1.32124i	0.881708	+	0.471796i	$0.156394\pi$
$709$	9.42663	+	35.1807i	0.354025	+	1.32124i	−0.527683	+	0.849441i	$0.676939\pi$
$710$	11.1809	+	11.1809i	0.419611	+	0.419611i
$711$		0			0
$712$	−16.0224	−	27.7517i	−0.600467	−	1.04004i
$713$	0.351929	−	1.31342i	0.0131799	−	0.0491879i
$714$		0			0
$715$	20.0182	+	5.52515i	0.748640	+	0.206629i
$716$	−21.4226			−0.800602
$717$		0			0
$718$	−1.05610	−	1.82922i	−0.0394134	−	0.0682660i
$719$	26.2044	−	45.3874i	0.977260	−	1.69266i	0.304994	−	0.952354i	$-0.401346\pi$
$719$	26.2044	−	45.3874i	0.977260	−	1.69266i	0.672266	−	0.740309i	$-0.265321\pi$
$720$		0			0
$721$	21.2729	−	0.592014i	0.792244	−	0.0220477i
$722$	−0.666143	−	2.48608i	−0.0247913	−	0.0925223i
$723$		0			0
$724$	8.12223	+	4.68937i	0.301860	+	0.174279i
$725$	9.00151	−	5.19702i	0.334308	−	0.193013i
$726$		0			0
$727$	−27.7907			−1.03070			−0.515350	−	0.856980i	$-0.672338\pi$
$727$	−27.7907			−1.03070			−0.515350	+	0.856980i	$0.672338\pi$
$728$	−24.2048	+	0.491930i	−0.897091	+	0.0182321i
$729$		0			0
$730$	2.59809	−	9.69621i	0.0961597	−	0.358873i
$731$	8.66846	−	5.00474i	0.320615	−	0.185107i
$732$		0			0
$733$	5.10977	−	5.10977i	0.188734	−	0.188734i	−0.606415	−	0.795149i	$-0.707393\pi$
$733$	5.10977	−	5.10977i	0.188734	−	0.188734i	0.795149	+	0.606415i	$0.207393\pi$
$734$	5.34406	+	19.9443i	0.197253	+	0.736158i
$735$		0			0
$736$	18.0379	−	18.0379i	0.664887	−	0.664887i
$737$	6.50513	−	11.2672i	0.239620	−	0.415034i
$738$		0			0
$739$	0.0573095	+	0.0153560i	0.00210816	+	0.000564880i	0.259873	−	0.965643i	$-0.416319\pi$
$739$	0.0573095	+	0.0153560i	0.00210816	+	0.000564880i	−0.257765	+	0.966208i	$0.582986\pi$
$740$	−9.43582			−0.346868
$741$		0			0
$742$	−1.59972	+	6.71186i	−0.0587276	+	0.246400i
$743$	−9.83505	+	36.7049i	−0.360813	+	1.34657i	0.512196	+	0.858868i	$0.328832\pi$
$743$	−9.83505	+	36.7049i	−0.360813	+	1.34657i	−0.873009	+	0.487704i	$0.837835\pi$
$744$		0			0
$745$	−12.5072	+	21.6631i	−0.458228	+	0.793675i
$746$	−13.4395	−	13.4395i	−0.492056	−	0.492056i
$747$		0			0
$748$	4.04760	−	1.08455i	0.147995	−	0.0396551i
$749$	15.2225	+	24.7495i	0.556218	+	0.904328i
$750$		0			0
$751$	−9.18336	+	5.30202i	−0.335106	+	0.193473i	−0.658106	−	0.752926i	$-0.728642\pi$
$751$	−9.18336	+	5.30202i	−0.335106	+	0.193473i	0.323000	+	0.946399i	$0.395309\pi$
$752$	1.43946	−	5.37214i	0.0524917	−	0.195902i
$753$		0			0
$754$	−12.0952	−	7.10468i	−0.440482	−	0.258737i
$755$			41.4441i			1.50831i
$756$		0			0
$757$	−7.44655	−	12.8978i	−0.270649	−	0.468778i	0.698379	−	0.715728i	$-0.253905\pi$
$757$	−7.44655	−	12.8978i	−0.270649	−	0.468778i	−0.969028	+	0.246950i	$0.920572\pi$
$758$	20.6285	+	11.9099i	0.749263	+	0.432587i
$759$		0			0
$760$	−16.8266	+	4.50866i	−0.610364	+	0.163546i
$761$	44.9797	−	12.0523i	1.63051	−	0.436895i	0.676448	−	0.736490i	$-0.263518\pi$
$761$	44.9797	−	12.0523i	1.63051	−	0.436895i	0.954066	+	0.299595i	$0.0968517\pi$
$762$		0			0
$763$	5.81443	+	5.49957i	0.210497	+	0.199098i
$764$	−6.02297	+	3.47737i	−0.217904	+	0.125807i
$765$		0			0
$766$	4.04688			0.146220
$767$	−28.6337	−	16.8193i	−1.03390	−	0.607311i
$768$		0			0
$769$	−6.79488	−	1.82068i	−0.245030	−	0.0656555i	0.134214	−	0.990952i	$-0.457149\pi$
$769$	−6.79488	−	1.82068i	−0.245030	−	0.0656555i	−0.379244	+	0.925297i	$0.623816\pi$
$770$	3.18949	+	10.7030i	0.114941	+	0.385708i
$771$		0			0
$772$	−9.75223	−	9.75223i	−0.350990	−	0.350990i
$773$	−2.05344	−	7.66353i	−0.0738570	−	0.275638i	0.919115	−	0.393990i	$-0.128906\pi$
$773$	−2.05344	−	7.66353i	−0.0738570	−	0.275638i	−0.992972	+	0.118352i	$0.962239\pi$
$774$		0			0
$775$	0.432232	+	0.432232i	0.0155262	+	0.0155262i
$776$	6.42581	+	3.70994i	0.230673	+	0.133179i
$777$		0			0
$778$	17.2180	+	4.61355i	0.617295	+	0.165404i
$779$			7.75482i			0.277845i
$780$		0			0
$781$	−40.8500			−1.46173
$782$	−2.67449	−	0.716627i	−0.0956395	−	0.0256265i
$783$		0			0
$784$	4.08391	+	6.24367i	0.145854	+	0.222988i
$785$	18.9999	+	18.9999i	0.678134	+	0.678134i
$786$		0			0
$787$	1.90514	−	0.510480i	0.0679109	−	0.0181967i	−0.224704	−	0.974427i	$-0.572141\pi$
$787$	1.90514	−	0.510480i	0.0679109	−	0.0181967i	0.292615	+	0.956230i	$0.405475\pi$
$788$	−11.6228	+	11.6228i	−0.414046	+	0.414046i
$789$		0			0
$790$	10.0556	+	17.4167i	0.357761	+	0.619660i
$791$	17.7221	−	32.7683i	0.630126	−	1.16511i
$792$		0			0
$793$	5.00836	+	19.2685i	0.177852	+	0.684243i
$794$			7.85763i			0.278857i
$795$		0			0
$796$	−15.9118	+	9.18666i	−0.563977	+	0.325612i
$797$	−25.3033	+	43.8266i	−0.896290	+	1.55242i	−0.0640896	+	0.997944i	$0.520414\pi$
$797$	−25.3033	+	43.8266i	−0.896290	+	1.55242i	−0.832200	+	0.554475i	$0.812919\pi$
$798$		0			0
$799$	−4.37215	+	1.17151i	−0.154675	+	0.0414451i
$800$	2.96805	+	11.0769i	0.104936	+	0.391628i
$801$		0			0
$802$	−9.71217	+	16.8220i	−0.342949	+	0.594005i
$803$	12.9667	+	22.4590i	0.457586	+	0.792562i
$804$		0			0
$805$	−4.65982	+	19.5510i	−0.164237	+	0.689081i
$806$	0.219484	−	0.795216i	0.00773100	−	0.0280103i
$807$		0			0
$808$	23.3074	+	6.24520i	0.819951	+	0.219705i
$809$	17.4409	+	30.2085i	0.613189	+	1.06207i	0.990699	+	0.136069i	$0.0434470\pi$
$809$	17.4409	+	30.2085i	0.613189	+	1.06207i	−0.377510	+	0.926005i	$0.623220\pi$
$810$		0			0
$811$	−30.6128	+	30.6128i	−1.07496	+	1.07496i	−0.0780073	+	0.996953i	$0.524856\pi$
$811$	−30.6128	+	30.6128i	−1.07496	+	1.07496i	−0.996953	+	0.0780073i	$0.975144\pi$
$812$	0.571574	+	20.5384i	0.0200583	+	0.720758i
$813$		0			0
$814$	−6.32881	+	6.32881i	−0.221825	+	0.221825i
$815$	−1.98926	−	1.14850i	−0.0696809	−	0.0402303i
$816$		0			0
$817$	11.7538	−	43.8659i	0.411214	−	1.53467i
$818$	0.638006			0.0223074
$819$		0			0
$820$	−5.02763			−0.175573
$821$	9.42147	−	35.1614i	0.328812	−	1.22714i	−0.581613	−	0.813466i	$-0.697578\pi$
$821$	9.42147	−	35.1614i	0.328812	−	1.22714i	0.910424	−	0.413676i	$-0.135755\pi$
$822$		0			0
$823$	23.5446	+	13.5935i	0.820713	+	0.473839i	0.850662	−	0.525712i	$-0.176201\pi$
$823$	23.5446	+	13.5935i	0.820713	+	0.473839i	−0.0299490	+	0.999551i	$0.509534\pi$
$824$	−14.4345	+	14.4345i	−0.502850	+	0.502850i
$825$		0			0
$826$	−0.496812	−	17.8520i	−0.0172863	−	0.621151i
$827$	−14.3232	+	14.3232i	−0.498066	+	0.498066i	−0.910835	−	0.412770i	$-0.864561\pi$
$827$	−14.3232	+	14.3232i	−0.498066	+	0.498066i	0.412770	+	0.910835i	$0.364561\pi$
$828$		0			0
$829$	−19.9234	−	34.5083i	−0.691968	−	1.19852i	−0.971192	−	0.238298i	$-0.923411\pi$
$829$	−19.9234	−	34.5083i	−0.691968	−	1.19852i	0.279224	−	0.960226i	$-0.409923\pi$
$830$	−6.64960	−	1.78176i	−0.230811	−	0.0618456i
$831$		0			0
$832$	5.55006	−	5.46741i	0.192414	−	0.189548i
$833$	2.73881	−	5.41914i	0.0948940	−	0.187762i
$834$		0			0
$835$	−21.1885	−	36.6996i	−0.733259	−	1.27004i
$836$	9.50596	−	16.4648i	0.328770	−	0.569447i
$837$		0			0
$838$	−5.27338	−	19.6805i	−0.182166	−	0.679852i
$839$	−13.8941	+	3.72291i	−0.479677	+	0.128529i	−0.490552	−	0.871412i	$-0.663205\pi$
$839$	−13.8941	+	3.72291i	−0.479677	+	0.128529i	0.0108750	+	0.999941i	$0.496538\pi$
$840$		0			0
$841$	0.409656	−	0.709546i	0.0141261	−	0.0244671i
$842$	5.51904	−	3.18642i	0.190199	−	0.109811i
$843$		0			0
$844$		−	16.6891i		−	0.574463i
$845$	15.7905	+	16.2715i	0.543208	+	0.559757i
$846$		0			0
$847$	0.220752	+	0.119390i	0.00758513	+	0.00410228i
$848$	1.89631	+	3.28450i	0.0651195	+	0.112790i
$849$		0			0
$850$	0.880145	−	0.880145i	0.0301887	−	0.0301887i
$851$	−15.5585	+	4.16889i	−0.533339	+	0.142908i
$852$		0			0
$853$	−37.5030	−	37.5030i	−1.28408	−	1.28408i	−0.938326	−	0.345753i	$-0.887624\pi$
$853$	−37.5030	−	37.5030i	−1.28408	−	1.28408i	−0.345753	−	0.938326i	$-0.612376\pi$
$854$	−7.35721	+	7.77843i	−0.251758	+	0.266172i
$855$		0			0
$856$	−26.9219	−	7.21369i	−0.920170	−	0.246559i
$857$	−1.29908			−0.0443757			−0.0221879	−	0.999754i	$-0.507063\pi$
$857$	−1.29908			−0.0443757			−0.0221879	+	0.999754i	$0.507063\pi$
$858$		0			0
$859$			28.7112i			0.979614i	0.871831	+	0.489807i	$0.162933\pi$
$859$			28.7112i			0.979614i	−0.871831	+	0.489807i	$0.837067\pi$
$860$	28.4393	+	7.62029i	0.969772	+	0.259850i
$861$		0			0
$862$	−17.3415	−	10.0121i	−0.590655	−	0.341015i
$863$	25.6877	+	25.6877i	0.874419	+	0.874419i	0.992950	−	0.118531i	$-0.0378186\pi$
$863$	25.6877	+	25.6877i	0.874419	+	0.874419i	−0.118531	+	0.992950i	$0.537819\pi$
$864$		0			0
$865$	−0.286137	−	1.06788i	−0.00972894	−	0.0363089i
$866$	−11.9933	−	11.9933i	−0.407550	−	0.407550i
$867$		0			0
$868$	−1.15800	+	0.345084i	−0.0393050	+	0.0117129i
$869$	−50.1859	−	13.4473i	−1.70244	−	0.456168i
$870$		0			0
$871$	12.3549	−	7.01004i	0.418628	−	0.237526i
$872$	−7.67700			−0.259976
$873$		0			0
$874$	−10.8793	+	6.28114i	−0.367996	+	0.212463i
$875$	−23.3266	−	22.0634i	−0.788583	−	0.745879i
$876$		0			0
$877$	−27.9815	+	7.49761i	−0.944867	+	0.253176i	−0.698183	−	0.715920i	$-0.746008\pi$
$877$	−27.9815	+	7.49761i	−0.944867	+	0.253176i	−0.246684	+	0.969096i	$0.579341\pi$
$878$	28.8934	−	7.74197i	0.975106	−	0.261279i
$879$		0			0
$880$	5.31627	+	3.06935i	0.179212	+	0.103468i
$881$	2.10988	+	3.65442i	0.0710838	+	0.123121i	0.899377	−	0.437175i	$-0.144021\pi$
$881$	2.10988	+	3.65442i	0.0710838	+	0.123121i	−0.828293	+	0.560296i	$0.810688\pi$
$882$		0			0
$883$		−	0.594702i		−	0.0200133i	−0.999950	−	0.0100066i	$-0.996815\pi$
$883$		−	0.594702i		−	0.0200133i	0.999950	−	0.0100066i	$-0.00318527\pi$
$884$	4.41030	+	1.21727i	0.148334	+	0.0409411i
$885$		0			0
$886$	1.14917	−	4.28877i	0.0386072	−	0.144084i
$887$	26.7001	−	15.4153i	0.896502	−	0.517596i	0.0204385	−	0.999791i	$-0.493494\pi$
$887$	26.7001	−	15.4153i	0.896502	−	0.517596i	0.876064	+	0.482195i	$0.160160\pi$
$888$		0			0
$889$	−12.9061	+	7.93804i	−0.432856	+	0.266233i
$890$	−15.5900	+	4.17732i	−0.522577	+	0.140024i
$891$		0			0
$892$	7.53539	+	7.53539i	0.252304	+	0.252304i
$893$	−10.2682	+	17.7850i	−0.343611	+	0.595151i
$894$		0			0
$895$	−6.61058	+	24.6710i	−0.220967	+	0.824661i
$896$	−26.0716	−	6.21397i	−0.870991	−	0.207594i
$897$		0			0
$898$	4.69472			0.156665
$899$	−1.60082	−	0.428938i	−0.0533903	−	0.0143059i
$900$		0			0
$901$	1.54332	−	2.67311i	0.0514155	−	0.0890542i
$902$	−3.37214	+	3.37214i	−0.112280	+	0.112280i
$903$		0			0
$904$	9.24884	+	34.5172i	0.307612	+	1.14802i
$905$	7.90678	−	7.90678i	0.262830	−	0.262830i
$906$		0			0
$907$	−19.4291	+	11.2174i	−0.645133	+	0.372468i	−0.786589	−	0.617477i	$-0.788155\pi$
$907$	−19.4291	+	11.2174i	−0.645133	+	0.372468i	0.141456	+	0.989945i	$0.454822\pi$
$908$	−8.88167	+	33.1468i	−0.294749	+	1.10002i
$909$		0			0
$910$	−2.91598	+	11.8399i	−0.0966637	+	0.392488i
$911$	−40.9352			−1.35625			−0.678123	−	0.734949i	$-0.737206\pi$
$911$	−40.9352			−1.35625			−0.678123	+	0.734949i	$0.737206\pi$
$912$		0			0
$913$	15.4023	−	8.89250i	0.509740	−	0.294299i
$914$	18.6694	+	10.7788i	0.617528	+	0.356530i
$915$		0			0
$916$	8.69206	+	32.4392i	0.287194	+	1.07182i
$917$	−1.60384	−	57.6308i	−0.0529633	−	1.90314i
$918$		0			0
$919$	−9.05289	+	15.6801i	−0.298627	+	0.517238i	−0.975822	−	0.218566i	$-0.929862\pi$
$919$	−9.05289	+	15.6801i	−0.298627	+	0.517238i	0.677195	+	0.735804i	$0.263195\pi$
$920$	−9.63958	−	16.6963i	−0.317808	−	0.550459i
$921$		0			0
$922$	8.52686			0.280817
$923$	−38.4576	−	22.5898i	−1.26585	−	0.743553i
$924$		0			0
$925$	1.87410	−	6.99424i	0.0616201	−	0.229969i
$926$	−4.36651	−	7.56302i	−0.143493	−	0.248536i
$927$		0			0
$928$	−21.9850	−	21.9850i	−0.721693	−	0.721693i
$929$	5.79612	+	21.6314i	0.190165	+	0.709704i	0.993466	+	0.114131i	$0.0364083\pi$
$929$	5.79612	+	21.6314i	0.190165	+	0.709704i	−0.803301	+	0.595573i	$0.796925\pi$
$930$		0			0
$931$	−8.59896	−	26.1721i	−0.281820	−	0.857754i
$932$	−12.0888	+	20.9385i	−0.395983	+	0.685863i
$933$		0			0
$934$	4.02611	−	15.0256i	0.131738	−	0.491654i
$935$		−	4.99602i		−	0.163387i
$936$		0			0
$937$			37.1911i			1.21498i	0.794328	+	0.607490i	$0.207823\pi$
$937$			37.1911i			1.21498i	−0.794328	+	0.607490i	$0.792177\pi$
$938$	6.71951	+	3.63412i	0.219400	+	0.118658i
$939$		0			0
$940$	−11.5304	−	6.65709i	−0.376081	−	0.217130i
$941$	−10.1073	+	10.1073i	−0.329488	+	0.329488i	−0.852392	−	0.522904i	$-0.824849\pi$
$941$	−10.1073	+	10.1073i	−0.329488	+	0.329488i	0.522904	+	0.852392i	$0.324849\pi$
$942$		0			0
$943$	−8.28995	+	2.22129i	−0.269958	+	0.0723350i
$944$	−6.94126	−	6.94126i	−0.225919	−	0.225919i
$945$		0			0
$946$	24.1859	−	13.9638i	0.786353	−	0.454001i
$947$	32.0858	+	8.59736i	1.04265	+	0.279377i	0.739210	−	0.673474i	$-0.235199\pi$
$947$	32.0858	+	8.59736i	1.04265	+	0.279377i	0.303438	+	0.952851i	$0.401866\pi$
$948$		0			0
$949$	−0.212403	+	28.3142i	−0.00689488	+	0.919117i
$950$		−	5.64730i		−	0.183223i
$951$		0			0
$952$	1.66338	+	5.58178i	0.0539103	+	0.180907i
$953$	31.7109	+	18.3083i	1.02722	+	0.593063i	0.916186	−	0.400754i	$-0.131252\pi$
$953$	31.7109	+	18.3083i	1.02722	+	0.593063i	0.111030	+	0.993817i	$0.464585\pi$
$954$		0			0
$955$	2.14608	+	8.00930i	0.0694457	+	0.259175i
$956$	−10.0847	−	37.6366i	−0.326162	−	1.21725i
$957$		0			0
$958$	−13.8802	−	8.01376i	−0.448450	−	0.258913i
$959$	0.0290073	+	0.0973395i	0.000936693	+	0.00314326i
$960$		0			0
$961$			30.9025i			0.996856i
$962$	−9.45794	+	2.45836i	−0.304936	+	0.0792606i
$963$		0			0
$964$	1.63711	+	0.438661i	0.0527276	+	0.0141283i
$965$	−14.2403	+	8.22165i	−0.458412	+	0.264664i
$966$		0			0
$967$	−8.31570	−	8.31570i	−0.267415	−	0.267415i	0.560643	−	0.828058i	$-0.310554\pi$
$967$	−8.31570	−	8.31570i	−0.267415	−	0.267415i	−0.828058	+	0.560643i	$0.810554\pi$
$968$	−0.232534	+	0.0623072i	−0.00747392	+	0.00200263i
$969$		0			0
$970$	2.64256	−	2.64256i	0.0848474	−	0.0848474i
$971$	−12.9298	−	7.46501i	−0.414936	−	0.239564i	0.277972	−	0.960589i	$-0.410338\pi$
$971$	−12.9298	−	7.46501i	−0.414936	−	0.239564i	−0.692909	+	0.721026i	$0.743671\pi$
$972$		0			0
$973$	39.1705	+	21.1846i	1.25575	+	0.679147i
$974$		−	21.7751i		−	0.697718i
$975$		0			0
$976$			5.88508i			0.188377i
$977$	5.67268	−	21.1707i	0.181485	−	0.677312i	−0.813871	−	0.581046i	$-0.802644\pi$
$977$	5.67268	−	21.1707i	0.181485	−	0.677312i	0.995356	−	0.0962656i	$-0.0306898\pi$
$978$		0			0
$979$	20.8484	−	36.1105i	0.666319	−	1.15410i
$980$	16.9680	−	5.57491i	0.542022	−	0.178084i
$981$		0			0
$982$	−5.23923	−	19.5531i	−0.167191	−	0.623964i
$983$	−16.7042	−	16.7042i	−0.532782	−	0.532782i	0.388617	−	0.921399i	$-0.372953\pi$
$983$	−16.7042	−	16.7042i	−0.532782	−	0.532782i	−0.921399	+	0.388617i	$0.872953\pi$
$984$		0			0
$985$	9.79866	+	16.9718i	0.312211	+	0.540766i
$986$	−0.873439	+	3.25972i	−0.0278160	+	0.103811i
$987$		0			0
$988$	18.0542	−	10.2438i	0.574379	−	0.325898i
$989$	50.2597			1.59817
$990$		0			0
$991$	−22.3070	−	38.6368i	−0.708604	−	1.22734i	−0.965375	−	0.260866i	$-0.915992\pi$
$991$	−22.3070	−	38.6368i	−0.708604	−	1.22734i	0.256771	−	0.966472i	$-0.417341\pi$
$992$	0.914237	−	1.58350i	0.0290271	−	0.0502763i
$993$		0			0
$994$	−0.667261	−	23.9768i	−0.0211642	−	0.760497i
$995$	5.66962	+	21.1593i	0.179739	+	0.670795i
$996$		0			0
$997$	−23.6130	−	13.6330i	−0.747831	−	0.431760i	0.0770787	−	0.997025i	$-0.475441\pi$
$997$	−23.6130	−	13.6330i	−0.747831	−	0.431760i	−0.824910	+	0.565265i	$0.808774\pi$
$998$	4.78411	−	2.76211i	0.151438	−	0.0874330i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fm.e.622.5		32
3.2	odd	2		273.2.by.d.76.4	yes	32
7.6	odd	2		819.2.fm.f.622.5		32
13.6	odd	12		819.2.fm.f.370.5		32
21.20	even	2		273.2.by.c.76.4	✓	32
39.32	even	12		273.2.by.c.97.4	yes	32
91.6	even	12	inner	819.2.fm.e.370.5		32
273.188	odd	12		273.2.by.d.97.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.76.4	✓	32	21.20	even	2
273.2.by.c.97.4	yes	32	39.32	even	12
273.2.by.d.76.4	yes	32	3.2	odd	2
273.2.by.d.97.4	yes	32	273.188	odd	12
819.2.fm.e.370.5		32	91.6	even	12	inner
819.2.fm.e.622.5		32	1.1	even	1	trivial
819.2.fm.f.370.5		32	13.6	odd	12
819.2.fm.f.622.5		32	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.189683 - 0.707908i) q^{2} +(1.26690 + 0.731443i) q^{4} +(1.23329 - 1.23329i) q^{5} +(-2.64473 + 0.0736014i) q^{7} +(1.79455 - 1.79455i) q^{8} +O(q^{10})\)	\(q+(0.189683 - 0.707908i) q^{2} +(1.26690 + 0.731443i) q^{4} +(1.23329 - 1.23329i) q^{5} +(-2.64473 + 0.0736014i) q^{7} +(1.79455 - 1.79455i) q^{8} +(-0.639122 - 1.10699i) q^{10} +(3.18977 + 0.854696i) q^{11} +(2.53031 + 2.56856i) q^{13} +(-0.449558 + 1.88618i) q^{14} +(0.532906 + 0.923019i) q^{16} +(0.433708 - 0.751205i) q^{17} +(-1.01858 - 3.80140i) q^{19} +(2.46454 - 0.660371i) q^{20} +(1.21009 - 2.09594i) q^{22} +(3.77196 - 2.17774i) q^{23} +1.95798i q^{25} +(2.29826 - 1.30401i) q^{26} +(-3.40443 - 1.84122i) q^{28} +(-2.65427 - 4.59734i) q^{29} +(0.220754 - 0.220754i) q^{31} +(5.65731 - 1.51587i) q^{32} +(-0.449517 - 0.449517i) q^{34} +(-3.17095 + 3.35249i) q^{35} +(-3.57217 - 0.957160i) q^{37} -2.88425 q^{38} -4.42641i q^{40} +(-1.90334 - 0.509998i) q^{41} +(9.99342 + 5.76970i) q^{43} +(3.41595 + 3.41595i) q^{44} +(-0.826162 - 3.08328i) q^{46} +(-3.68984 - 3.68984i) q^{47} +(6.98917 - 0.389311i) q^{49} +(1.38607 + 0.371397i) q^{50} +(1.32689 + 5.10489i) q^{52} +3.55843 q^{53} +(4.98801 - 2.87983i) q^{55} +(-4.61402 + 4.87818i) q^{56} +(-3.75796 + 1.00694i) q^{58} +(-8.89645 + 2.38380i) q^{59} +(4.78192 + 2.76084i) q^{61} +(-0.114400 - 0.198147i) q^{62} -2.16076i q^{64} +(6.28840 + 0.0471733i) q^{65} +(1.01969 - 3.80552i) q^{67} +(1.09893 - 0.634466i) q^{68} +(1.77178 + 2.88065i) q^{70} +(-11.9487 + 3.20164i) q^{71} +(5.55302 + 5.55302i) q^{73} +(-1.35516 + 2.34721i) q^{74} +(1.49007 - 5.56101i) q^{76} +(-8.49898 - 2.02567i) q^{77} -15.7334 q^{79} +(1.79558 + 0.481124i) q^{80} +(-0.722063 + 1.25065i) q^{82} +(3.80823 - 3.80823i) q^{83} +(-0.391566 - 1.46134i) q^{85} +(5.98000 - 5.98000i) q^{86} +(7.25801 - 4.19041i) q^{88} +(3.26801 - 12.1964i) q^{89} +(-6.88104 - 6.60691i) q^{91} +6.37158 q^{92} +(-3.31197 + 1.91217i) q^{94} +(-5.94444 - 3.43202i) q^{95} +(0.756697 + 2.82403i) q^{97} +(1.05013 - 5.02153i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) \) 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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