LMFDB - Embedded newform 495.2.bj.a.127.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(28,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 15, 18]))

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

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

chi := DirichletCharacter("495.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.bj (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			127.4
Character	$\chi$	$=$	495.127
Dual form			495.2.bj.a.343.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.25897 + 1.15100i) q^{2} +(2.60258 + 3.58214i) q^{4} +(0.867371 + 2.06099i) q^{5} +(0.282837 - 1.78576i) q^{7} +(0.962874 + 6.07934i) q^{8} +O(q^{10})$	\(q+(2.25897 + 1.15100i) q^{2} +(2.60258 + 3.58214i) q^{4} +(0.867371 + 2.06099i) q^{5} +(0.282837 - 1.78576i) q^{7} +(0.962874 + 6.07934i) q^{8} +(-0.412838 + 5.65406i) q^{10} +(-1.72268 - 2.83415i) q^{11} +(-1.02411 + 2.00993i) q^{13} +(2.69434 - 3.70844i) q^{14} +(-2.08573 + 6.41923i) q^{16} +(-1.52724 - 2.99738i) q^{17} +(1.05647 + 0.767569i) q^{19} +(-5.12534 + 8.47092i) q^{20} +(-0.629367 - 8.38507i) q^{22} +(3.16488 - 3.16488i) q^{23} +(-3.49534 + 3.57528i) q^{25} +(-4.62687 + 3.36162i) q^{26} +(7.13295 - 3.63442i) q^{28} +(-2.37569 + 1.72604i) q^{29} +(-1.23925 - 3.81401i) q^{31} +(-3.39552 + 3.39552i) q^{32} -8.52886i q^{34} +(3.92576 - 0.965994i) q^{35} +(3.16942 + 0.501987i) q^{37} +(1.50306 + 2.94992i) q^{38} +(-11.6943 + 7.25752i) q^{40} +(-0.766287 + 1.05470i) q^{41} +(-4.55431 - 4.55431i) q^{43} +(5.66890 - 13.5469i) q^{44} +(10.7922 - 3.50658i) q^{46} +(1.20824 + 7.62854i) q^{47} +(3.54845 + 1.15296i) q^{49} +(-12.0110 + 4.05331i) q^{50} +(-9.86517 + 1.56249i) q^{52} +(-5.67482 - 2.89146i) q^{53} +(4.34694 - 6.00867i) q^{55} +11.1286 q^{56} +(-7.35329 + 1.16465i) q^{58} +(7.28135 + 10.0219i) q^{59} +(-8.85435 - 2.87695i) q^{61} +(1.59052 - 10.0421i) q^{62} +(1.25983 - 0.409344i) q^{64} +(-5.03072 - 0.367324i) q^{65} +(-2.46236 - 2.46236i) q^{67} +(6.76227 - 13.2717i) q^{68} +(9.98004 + 2.33641i) q^{70} +(2.09243 - 6.43984i) q^{71} +(9.32763 + 1.47735i) q^{73} +(6.58185 + 4.78199i) q^{74} +5.78207i q^{76} +(-5.54835 + 2.27469i) q^{77} +(-0.353860 - 1.08907i) q^{79} +(-15.0391 + 1.26918i) q^{80} +(-2.94499 + 1.50055i) q^{82} +(9.32422 - 4.75092i) q^{83} +(4.85288 - 5.74747i) q^{85} +(-5.04603 - 15.5301i) q^{86} +(15.5710 - 13.2017i) q^{88} -3.85743i q^{89} +(3.29960 + 2.39730i) q^{91} +(19.5739 + 3.10019i) q^{92} +(-6.05109 + 18.6233i) q^{94} +(-0.665600 + 2.84313i) q^{95} +(0.353228 - 0.693249i) q^{97} +(6.68878 + 6.68878i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 10 q^{2} + 2 q^{5} + 10 q^{8}+O(q^{10}) $ 32 * q + 10 * q^2 + 2 * q^5 + 10 * q^8	$ 32 q + 10 q^{2} + 2 q^{5} + 10 q^{8} + 24 q^{11} - 10 q^{13} - 8 q^{16} - 16 q^{20} + 10 q^{22} + 24 q^{23} + 16 q^{25} - 20 q^{26} + 50 q^{28} - 28 q^{31} + 10 q^{35} - 8 q^{37} - 10 q^{38} - 50 q^{40} - 40 q^{41} + 60 q^{46} + 28 q^{47} + 50 q^{50} - 50 q^{52} + 24 q^{53} - 64 q^{55} + 80 q^{56} - 50 q^{58} - 60 q^{61} - 100 q^{62} - 8 q^{67} + 30 q^{68} + 30 q^{70} - 24 q^{71} + 50 q^{73} - 70 q^{77} - 98 q^{80} - 10 q^{82} - 90 q^{83} + 30 q^{85} - 100 q^{86} + 170 q^{88} + 20 q^{91} + 68 q^{92} + 40 q^{95} - 8 q^{97}+O(q^{100}) $ 32 * q + 10 * q^2 + 2 * q^5 + 10 * q^8 + 24 * q^11 - 10 * q^13 - 8 * q^16 - 16 * q^20 + 10 * q^22 + 24 * q^23 + 16 * q^25 - 20 * q^26 + 50 * q^28 - 28 * q^31 + 10 * q^35 - 8 * q^37 - 10 * q^38 - 50 * q^40 - 40 * q^41 + 60 * q^46 + 28 * q^47 + 50 * q^50 - 50 * q^52 + 24 * q^53 - 64 * q^55 + 80 * q^56 - 50 * q^58 - 60 * q^61 - 100 * q^62 - 8 * q^67 + 30 * q^68 + 30 * q^70 - 24 * q^71 + 50 * q^73 - 70 * q^77 - 98 * q^80 - 10 * q^82 - 90 * q^83 + 30 * q^85 - 100 * q^86 + 170 * q^88 + 20 * q^91 + 68 * q^92 + 40 * q^95 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	2.25897	+	1.15100i	1.59733	+	0.813883i	0.999929	+	0.0119437i	$0.00380189\pi$
$2$	2.25897	+	1.15100i	1.59733	+	0.813883i	0.597406	+	0.801939i	$0.296198\pi$
$3$		0			0
$3$		0			0
$4$	2.60258	+	3.58214i	1.30129	+	1.79107i
$5$	0.867371	+	2.06099i	0.387900	+	0.921701i
$5$	0.867371	+	2.06099i	0.387900	+	0.921701i
$6$		0			0
$7$	0.282837	−	1.78576i	0.106902	−	0.674955i	−0.874793	−	0.484497i	$-0.839003\pi$
$7$	0.282837	−	1.78576i	0.106902	−	0.674955i	0.981695	−	0.190458i	$-0.0609972\pi$
$8$	0.962874	+	6.07934i	0.340427	+	2.14937i
$9$		0			0
$10$	−0.412838	+	5.65406i	−0.130551	+	1.78797i
$11$	−1.72268	−	2.83415i	−0.519407	−	0.854527i
$11$	−1.72268	−	2.83415i	−0.519407	−	0.854527i
$12$		0			0
$13$	−1.02411	+	2.00993i	−0.284037	+	0.557454i	−0.988307	−	0.152478i	$-0.951275\pi$
$13$	−1.02411	+	2.00993i	−0.284037	+	0.557454i	0.704270	+	0.709933i	$0.251275\pi$
$14$	2.69434	−	3.70844i	0.720093	−	0.991122i
$15$		0			0
$16$	−2.08573	+	6.41923i	−0.521434	+	1.60481i
$17$	−1.52724	−	2.99738i	−0.370411	−	0.726972i	0.628288	−	0.777981i	$-0.283756\pi$
$17$	−1.52724	−	2.99738i	−0.370411	−	0.726972i	−0.998698	+	0.0510094i	$0.983756\pi$
$18$		0			0
$19$	1.05647	+	0.767569i	0.242370	+	0.176092i	0.702339	−	0.711843i	$-0.252139\pi$
$19$	1.05647	+	0.767569i	0.242370	+	0.176092i	−0.459968	+	0.887935i	$0.652139\pi$
$20$	−5.12534	+	8.47092i	−1.14606	+	1.89415i
$21$		0			0
$22$	−0.629367	−	8.38507i	−0.134181	−	1.78770i
$23$	3.16488	−	3.16488i	0.659922	−	0.659922i	−0.295439	−	0.955362i	$-0.595466\pi$
$23$	3.16488	−	3.16488i	0.659922	−	0.659922i	0.955362	+	0.295439i	$0.0954660\pi$
$24$		0			0
$25$	−3.49534	+	3.57528i	−0.699067	+	0.715056i
$26$	−4.62687	+	3.36162i	−0.907405	+	0.659268i
$27$		0			0
$28$	7.13295	−	3.63442i	1.34800	−	0.686841i
$29$	−2.37569	+	1.72604i	−0.441154	+	0.320517i	−0.786093	−	0.618108i	$-0.787900\pi$
$29$	−2.37569	+	1.72604i	−0.441154	+	0.320517i	0.344939	+	0.938625i	$0.387900\pi$
$30$		0			0
$31$	−1.23925	−	3.81401i	−0.222575	−	0.685016i	−0.998529	−	0.0542261i	$-0.982731\pi$
$31$	−1.23925	−	3.81401i	−0.222575	−	0.685016i	0.775953	−	0.630790i	$-0.217269\pi$
$32$	−3.39552	+	3.39552i	−0.600248	+	0.600248i
$33$		0			0
$34$		−	8.52886i		−	1.46269i
$35$	3.92576	−	0.965994i	0.663574	−	0.163283i
$36$		0			0
$37$	3.16942	+	0.501987i	0.521050	+	0.0825262i	0.411419	−	0.911446i	$-0.365033\pi$
$37$	3.16942	+	0.501987i	0.521050	+	0.0825262i	0.109631	+	0.993972i	$0.465033\pi$
$38$	1.50306	+	2.94992i	0.243828	+	0.478539i
$39$		0			0
$40$	−11.6943	+	7.25752i	−1.84903	+	1.14751i
$41$	−0.766287	+	1.05470i	−0.119674	+	0.164717i	−0.864651	−	0.502373i	$-0.832460\pi$
$41$	−0.766287	+	1.05470i	−0.119674	+	0.164717i	0.744977	+	0.667090i	$0.232460\pi$
$42$		0			0
$43$	−4.55431	−	4.55431i	−0.694526	−	0.694526i	0.268698	−	0.963224i	$-0.413407\pi$
$43$	−4.55431	−	4.55431i	−0.694526	−	0.694526i	−0.963224	+	0.268698i	$0.913407\pi$
$44$	5.66890	−	13.5469i	0.854620	−	2.04228i
$45$		0			0
$46$	10.7922	−	3.50658i	1.59122	−	0.517017i
$47$	1.20824	+	7.62854i	0.176240	+	1.11274i	0.904198	+	0.427114i	$0.140470\pi$
$47$	1.20824	+	7.62854i	0.176240	+	1.11274i	−0.727957	+	0.685622i	$0.759530\pi$
$48$		0			0
$49$	3.54845	+	1.15296i	0.506921	+	0.164709i
$50$	−12.0110	+	4.05331i	−1.69862	+	0.573225i
$51$		0			0
$52$	−9.86517	+	1.56249i	−1.36805	+	0.216678i
$53$	−5.67482	−	2.89146i	−0.779496	−	0.397173i	0.0185052	−	0.999829i	$-0.494109\pi$
$53$	−5.67482	−	2.89146i	−0.779496	−	0.397173i	−0.798001	+	0.602656i	$0.794109\pi$
$54$		0			0
$55$	4.34694	−	6.00867i	0.586141	−	0.810209i
$56$	11.1286			1.48712
$57$		0			0
$58$	−7.35329	+	1.16465i	−0.965535	+	0.152926i
$59$	7.28135	+	10.0219i	0.947952	+	1.30474i	0.952431	+	0.304753i	$0.0985740\pi$
$59$	7.28135	+	10.0219i	0.947952	+	1.30474i	−0.00447977	+	0.999990i	$0.501426\pi$
$60$		0			0
$61$	−8.85435	−	2.87695i	−1.13368	−	0.368356i	−0.318709	−	0.947853i	$-0.603249\pi$
$61$	−8.85435	−	2.87695i	−1.13368	−	0.368356i	−0.814975	+	0.579496i	$0.803249\pi$
$62$	1.59052	−	10.0421i	0.201996	−	1.27535i
$63$		0			0
$64$	1.25983	−	0.409344i	0.157479	−	0.0511679i
$65$	−5.03072	−	0.367324i	−0.623984	−	0.0455609i
$66$		0			0
$67$	−2.46236	−	2.46236i	−0.300825	−	0.300825i	0.540512	−	0.841336i	$-0.318231\pi$
$67$	−2.46236	−	2.46236i	−0.300825	−	0.300825i	−0.841336	+	0.540512i	$0.818231\pi$
$68$	6.76227	−	13.2717i	0.820046	−	1.60943i
$69$		0			0
$70$	9.98004	+	2.33641i	1.19284	+	0.279254i
$71$	2.09243	−	6.43984i	0.248326	−	0.764268i	−0.746746	−	0.665110i	$-0.768385\pi$
$71$	2.09243	−	6.43984i	0.248326	−	0.764268i	0.995072	−	0.0991588i	$-0.0316152\pi$
$72$		0			0
$73$	9.32763	+	1.47735i	1.09172	+	0.172911i	0.676232	−	0.736689i	$-0.263612\pi$
$73$	9.32763	+	1.47735i	1.09172	+	0.172911i	0.415485	+	0.909600i	$0.363612\pi$
$74$	6.58185	+	4.78199i	0.765125	+	0.555896i
$75$		0			0
$76$			5.78207i			0.663249i
$77$	−5.54835	+	2.27469i	−0.632293	+	0.259225i
$78$		0			0
$79$	−0.353860	−	1.08907i	−0.0398123	−	0.122530i	0.929175	−	0.369640i	$-0.120519\pi$
$79$	−0.353860	−	1.08907i	−0.0398123	−	0.122530i	−0.968987	+	0.247110i	$0.920519\pi$
$80$	−15.0391	+	1.26918i	−1.68142	+	0.141899i
$81$		0			0
$82$	−2.94499	+	1.50055i	−0.325220	+	0.165708i
$83$	9.32422	−	4.75092i	1.02347	−	0.521482i	0.140086	−	0.990139i	$-0.455262\pi$
$83$	9.32422	−	4.75092i	1.02347	−	0.521482i	0.883380	+	0.468658i	$0.155262\pi$
$84$		0			0
$85$	4.85288	−	5.74747i	0.526369	−	0.623400i
$86$	−5.04603	−	15.5301i	−0.544128	−	1.67465i
$87$		0			0
$88$	15.5710	−	13.2017i	1.65988	−	1.40730i
$89$		−	3.85743i		−	0.408887i	−0.978878	−	0.204443i	$-0.934462\pi$
$89$		−	3.85743i		−	0.408887i	0.978878	−	0.204443i	$-0.0655384\pi$
$90$		0			0
$91$	3.29960	+	2.39730i	0.345892	+	0.251305i
$92$	19.5739	+	3.10019i	2.04072	+	0.323218i
$93$		0			0
$94$	−6.05109	+	18.6233i	−0.624123	+	1.92085i
$95$	−0.665600	+	2.84313i	−0.0682891	+	0.291699i
$96$		0			0
$97$	0.353228	−	0.693249i	0.0358649	−	0.0703888i	−0.872379	−	0.488831i	$-0.837424\pi$
$97$	0.353228	−	0.693249i	0.0358649	−	0.0703888i	0.908244	+	0.418442i	$0.137424\pi$
$98$	6.68878	+	6.68878i	0.675669	+	0.675669i
$99$		0			0
$100$	−21.9040	−	3.21584i	−2.19040	−	0.321584i
$101$	−9.28960	+	3.01837i	−0.924350	+	0.300339i	−0.732250	−	0.681036i	$-0.761530\pi$
$101$	−9.28960	+	3.01837i	−0.924350	+	0.300339i	−0.192100	+	0.981375i	$0.561530\pi$
$102$		0			0
$103$	0.730841	−	4.61435i	0.0720119	−	0.454665i	−0.925164	−	0.379567i	$-0.876073\pi$
$103$	0.730841	−	4.61435i	0.0720119	−	0.454665i	0.997176	−	0.0750982i	$-0.0239270\pi$
$104$	−13.2051	−	4.29061i	−1.29487	−	0.420729i
$105$		0			0
$106$	−9.49117	−	13.0635i	−0.921864	−	1.26884i
$107$	−15.1133	+	2.39372i	−1.46106	+	0.231410i	−0.835813	−	0.549015i	$-0.815003\pi$
$107$	−15.1133	+	2.39372i	−1.46106	+	0.231410i	−0.625250	+	0.780424i	$0.715003\pi$
$108$		0			0
$109$	−17.8837			−1.71295			−0.856476	−	0.516187i	$-0.827351\pi$
$109$	−17.8837			−1.71295			−0.856476	+	0.516187i	$0.827351\pi$
$110$	16.7356	−	8.57008i	1.59568	−	0.817125i
$111$		0			0
$112$	10.8733	+	5.54022i	1.02743	+	0.523502i
$113$	−7.37759	+	1.16850i	−0.694025	+	0.109923i	−0.493474	−	0.869760i	$-0.664273\pi$
$113$	−7.37759	+	1.16850i	−0.694025	+	0.109923i	−0.200551	+	0.979683i	$0.564273\pi$
$114$		0			0
$115$	9.26789	+	3.77765i	0.864235	+	0.352268i
$116$	−12.3658	−	4.01790i	−1.14814	−	0.373053i
$117$		0			0
$118$	4.91310	+	31.0201i	0.452288	+	2.85563i
$119$	−5.78457	+	1.87952i	−0.530271	+	0.172295i
$120$		0			0
$121$	−5.06477	+	9.76464i	−0.460433	+	0.887694i
$122$	−16.6904	−	16.6904i	−1.51107	−	1.51107i
$123$		0			0
$124$	10.4371	−	14.3654i	0.937277	−	1.29005i
$125$	−10.4004	−	4.10275i	−0.930236	−	0.366961i
$126$		0			0
$127$	−0.0936079	−	0.183716i	−0.00830635	−	0.0163021i	0.886816	−	0.462123i	$-0.152912\pi$
$127$	−0.0936079	−	0.183716i	−0.00830635	−	0.0163021i	−0.895122	+	0.445820i	$0.852912\pi$
$128$	12.8028	+	2.02777i	1.13162	+	0.179231i
$129$		0			0
$130$	−10.9415	−	6.62016i	−0.959631	−	0.580626i
$131$			0.551708i			0.0482029i	0.999710	+	0.0241015i	$0.00767248\pi$
$131$			0.551708i			0.0482029i	−0.999710	+	0.0241015i	$0.992328\pi$
$132$		0			0
$133$	1.66950	−	1.66950i	0.144764	−	0.144764i
$134$	−2.72821	−	8.39658i	−0.235682	−	0.725354i
$135$		0			0
$136$	16.7516	−	12.1707i	1.43644	−	1.04363i
$137$	13.7896	−	7.02615i	1.17812	−	0.600284i	0.248442	−	0.968647i	$-0.420081\pi$
$137$	13.7896	−	7.02615i	1.17812	−	0.600284i	0.929682	+	0.368362i	$0.120081\pi$
$138$		0			0
$139$	−1.15101	+	0.836256i	−0.0976272	+	0.0709303i	−0.635528	−	0.772078i	$-0.719218\pi$
$139$	−1.15101	+	0.836256i	−0.0976272	+	0.0709303i	0.537901	+	0.843008i	$0.319218\pi$
$140$	13.6774	+	11.5485i	1.15595	+	0.976029i
$141$		0			0
$142$	12.1390	−	12.1390i	1.01868	−	1.01868i
$143$	7.46065	−	0.559982i	0.623891	−	0.0468280i
$144$		0			0
$145$	−5.61795	−	3.39915i	−0.466545	−	0.282284i
$146$	19.3704	+	14.0734i	1.60311	+	1.16473i
$147$		0			0
$148$	6.45048	+	12.6598i	0.530226	+	1.04063i
$149$	−7.35615	+	22.6399i	−0.602639	+	1.85473i	−0.0903702	+	0.995908i	$0.528805\pi$
$149$	−7.35615	+	22.6399i	−0.602639	+	1.85473i	−0.512269	+	0.858825i	$0.671195\pi$
$150$		0			0
$151$	−8.45592	+	11.6386i	−0.688133	+	0.947134i	−0.999996	−	0.00299311i	$-0.999047\pi$
$151$	−8.45592	+	11.6386i	−0.688133	+	0.947134i	0.311862	+	0.950127i	$0.399047\pi$
$152$	−3.64907	+	7.16170i	−0.295979	+	0.580891i
$153$		0			0
$154$	−15.1517	−	1.24771i	−1.22096	−	0.100543i
$155$	6.78574	−	5.86223i	0.545044	−	0.470866i
$156$		0			0
$157$	2.11091	+	13.3277i	0.168469	+	1.06367i	0.916508	+	0.400016i	$0.130995\pi$
$157$	2.11091	+	13.3277i	0.168469	+	1.06367i	−0.748040	+	0.663654i	$0.769005\pi$
$158$	0.454163	−	2.86747i	0.0361312	−	0.228124i
$159$		0			0
$160$	−9.94329	−	4.05295i	−0.786086	−	0.320413i
$161$	−4.75657	−	6.54686i	−0.374870	−	0.515965i
$162$		0			0
$163$	0.956239	+	0.487228i	0.0748984	+	0.0381626i	0.491039	−	0.871138i	$-0.336617\pi$
$163$	0.956239	+	0.487228i	0.0748984	+	0.0381626i	−0.416140	+	0.909300i	$0.636617\pi$
$164$	−5.77242			−0.450750
$165$		0			0
$166$	26.5315			2.05924
$167$	1.68563	+	0.858874i	0.130438	+	0.0664616i	0.517992	−	0.855386i	$-0.326680\pi$
$167$	1.68563	+	0.858874i	0.130438	+	0.0664616i	−0.387554	+	0.921847i	$0.626680\pi$
$168$		0			0
$169$	4.65019	+	6.40044i	0.357707	+	0.492342i
$170$	17.5779	−	7.39769i	1.34816	−	0.567377i
$171$		0			0
$172$	4.46123	−	28.1671i	0.340166	−	2.14772i
$173$	2.96401	+	18.7140i	0.225350	+	1.42280i	0.797830	+	0.602883i	$0.205981\pi$
$173$	2.96401	+	18.7140i	0.225350	+	1.42280i	−0.572480	+	0.819919i	$0.694019\pi$
$174$		0			0
$175$	5.39599	+	7.25306i	0.407898	+	0.548280i
$176$	21.7861	−	5.14699i	1.64219	−	0.387969i
$177$		0			0
$178$	4.43992	−	8.71383i	0.332786	−	0.653129i
$179$	−9.62961	+	13.2540i	−0.719751	+	0.990652i	0.279781	+	0.960064i	$0.409738\pi$
$179$	−9.62961	+	13.2540i	−0.719751	+	0.990652i	−0.999532	+	0.0305880i	$0.990262\pi$
$180$		0			0
$181$	4.59306	−	14.1360i	0.341400	−	1.05072i	−0.622084	−	0.782951i	$-0.713714\pi$
$181$	4.59306	−	14.1360i	0.341400	−	1.05072i	0.963483	−	0.267769i	$-0.0862864\pi$
$182$	4.69440	+	9.21329i	0.347972	+	0.682934i
$183$		0			0
$184$	22.2878	+	16.1930i	1.64307	+	1.19376i
$185$	1.71448	+	6.96755i	0.126051	+	0.512265i
$186$		0			0
$187$	−5.86407	+	9.49195i	−0.428823	+	0.694120i
$188$	−24.1819	+	24.1819i	−1.76365	+	1.76365i
$189$		0			0
$190$	−4.77603	+	5.65645i	−0.346490	+	0.410362i
$191$	−1.54488	+	1.12242i	−0.111784	+	0.0812156i	−0.642273	−	0.766476i	$-0.722008\pi$
$191$	−1.54488	+	1.12242i	−0.111784	+	0.0812156i	0.530489	+	0.847692i	$0.322008\pi$
$192$		0			0
$193$	10.1423	−	5.16774i	0.730056	−	0.371982i	−0.0491153	−	0.998793i	$-0.515640\pi$
$193$	10.1423	−	5.16774i	0.730056	−	0.371982i	0.779171	+	0.626811i	$0.215640\pi$
$194$	1.59586	−	1.15946i	0.114576	−	0.0832446i
$195$		0			0
$196$	5.10504	+	15.7117i	0.364646	+	1.12226i
$197$	13.8092	−	13.8092i	0.983863	−	0.983863i	−0.0160086	−	0.999872i	$-0.505096\pi$
$197$	13.8092	−	13.8092i	0.983863	−	0.983863i	0.999872	+	0.0160086i	$0.00509592\pi$
$198$		0			0
$199$			22.3508i			1.58441i	0.610258	+	0.792203i	$0.291066\pi$
$199$			22.3508i			1.58441i	−0.610258	+	0.792203i	$0.708934\pi$
$200$	−25.1009	−	17.8068i	−1.77490	−	1.25913i
$201$		0			0
$202$	−24.4591	−	3.87394i	−1.72094	−	0.272570i
$203$	2.41036	+	4.73060i	0.169174	+	0.332023i
$204$		0			0
$205$	−2.83839	−	0.664489i	−0.198242	−	0.0464099i
$206$	6.96208	−	9.58248i	0.485071	−	0.667643i
$207$		0			0
$208$	−10.7662	−	10.7662i	−0.746501	−	0.746501i
$209$	0.355449	−	4.31646i	0.0245869	−	0.298576i
$210$		0			0
$211$	−0.358113	+	0.116358i	−0.0246535	+	0.00801042i	−0.321318	−	0.946971i	$-0.604126\pi$
$211$	−0.358113	+	0.116358i	−0.0246535	+	0.00801042i	0.296664	+	0.954982i	$0.404126\pi$
$212$	−4.41152	−	27.8532i	−0.302984	−	1.91297i
$213$		0			0
$214$	−36.8958	−	11.9882i	−2.52215	−	0.819495i
$215$	5.43610	−	13.3367i	0.370739	−	0.909552i
$216$		0			0
$217$	−7.16142	+	1.13426i	−0.486149	+	0.0769984i
$218$	−40.3989	−	20.5843i	−2.73616	−	1.39414i
$219$		0			0
$220$	32.8371	−	0.0666851i	2.21388	−	0.00449591i
$221$	7.58859			0.510464
$222$		0			0
$223$	7.51570	−	1.19037i	0.503289	−	0.0797131i	0.100372	−	0.994950i	$-0.467997\pi$
$223$	7.51570	−	1.19037i	0.503289	−	0.0797131i	0.402916	+	0.915237i	$0.367997\pi$
$224$	5.10321	+	7.02396i	0.340972	+	0.469308i
$225$		0			0
$226$	−18.0107	−	5.85204i	−1.19806	−	0.389272i
$227$	−1.28318	+	8.10167i	−0.0851676	+	0.537727i	0.907806	+	0.419390i	$0.137756\pi$
$227$	−1.28318	+	8.10167i	−0.0851676	+	0.537727i	−0.992974	+	0.118336i	$0.962244\pi$
$228$		0			0
$229$	−7.21772	+	2.34518i	−0.476960	+	0.154974i	−0.537624	−	0.843184i	$-0.680678\pi$
$229$	−7.21772	+	2.34518i	−0.476960	+	0.154974i	0.0606641	+	0.998158i	$0.480678\pi$
$230$	16.5878	+	19.2010i	1.09377	+	1.26608i
$231$		0			0
$232$	−12.7807	−	12.7807i	−0.839092	−	0.839092i
$233$	11.9023	−	23.3597i	0.779749	−	1.53034i	−0.0666396	−	0.997777i	$-0.521228\pi$
$233$	11.9023	−	23.3597i	0.779749	−	1.53034i	0.846388	−	0.532566i	$-0.178772\pi$
$234$		0			0
$235$	−14.6743	+	9.10694i	−0.957247	+	0.594071i
$236$	−16.9496	+	52.1656i	−1.10333	+	3.39569i
$237$		0			0
$238$	−15.2305	−	2.41228i	−0.987248	−	0.156365i
$239$	−1.84133	−	1.33781i	−0.119106	−	0.0865356i	0.526638	−	0.850090i	$-0.323452\pi$
$239$	−1.84133	−	1.33781i	−0.119106	−	0.0865356i	−0.645744	+	0.763554i	$0.723452\pi$
$240$		0			0
$241$			6.29531i			0.405517i	0.979229	+	0.202758i	$0.0649906\pi$
$241$			6.29531i			0.405517i	−0.979229	+	0.202758i	$0.935009\pi$
$242$	−22.6803	+	16.2285i	−1.45795	+	1.04321i
$243$		0			0
$244$	−12.7385	−	39.2050i	−0.815498	−	2.50984i
$245$	0.701583	+	8.31335i	0.0448225	+	0.531120i
$246$		0			0
$247$	−2.62470	+	1.33735i	−0.167006	+	0.0850936i
$248$	21.9934	−	11.2062i	1.39658	−	0.711596i
$249$		0			0
$250$	−18.7718	−	21.2389i	−1.18724	−	1.34326i
$251$	8.21826	+	25.2932i	0.518732	+	1.59649i	0.776387	+	0.630256i	$0.217050\pi$
$251$	8.21826	+	25.2932i	0.518732	+	1.59649i	−0.257655	+	0.966237i	$0.582950\pi$
$252$		0			0
$253$	−14.4218	−	3.51766i	−0.906690	−	0.221153i
$254$		−	0.522752i		−	0.0328004i
$255$		0			0
$256$	24.4439	+	17.7595i	1.52774	+	1.10997i
$257$	−19.5307	−	3.09337i	−1.21829	−	0.192959i	−0.486007	−	0.873955i	$-0.661547\pi$
$257$	−19.5307	−	3.09337i	−1.21829	−	0.192959i	−0.732287	+	0.680996i	$0.761547\pi$
$258$		0			0
$259$	1.79286	−	5.51786i	0.111403	−	0.342863i
$260$	−11.7770	−	18.9767i	−0.730380	−	1.17689i
$261$		0			0
$262$	−0.635018	+	1.24629i	−0.0392315	+	0.0769962i
$263$	−5.91748	−	5.91748i	−0.364888	−	0.364888i	0.500721	−	0.865609i	$-0.333068\pi$
$263$	−5.91748	−	5.91748i	−0.364888	−	0.364888i	−0.865609	+	0.500721i	$0.833068\pi$
$264$		0			0
$265$	1.03710	−	14.2037i	0.0637085	−	0.872526i
$266$	5.69297	−	1.84976i	0.349058	−	0.113416i
$267$		0			0
$268$	2.41203	−	15.2290i	0.147338	−	0.930258i
$269$	−9.23539	−	3.00076i	−0.563092	−	0.182960i	0.0136201	−	0.999907i	$-0.495664\pi$
$269$	−9.23539	−	3.00076i	−0.563092	−	0.182960i	−0.576712	+	0.816948i	$0.695664\pi$
$270$		0			0
$271$	1.79360	+	2.46868i	0.108954	+	0.149962i	0.860012	−	0.510274i	$-0.170456\pi$
$271$	1.79360	+	2.46868i	0.108954	+	0.149962i	−0.751058	+	0.660236i	$0.770456\pi$
$272$	22.4263	−	3.55198i	1.35979	−	0.215370i
$273$		0			0
$274$	39.2374			2.37042
$275$	16.1542	+	3.74724i	0.974135	+	0.225967i
$276$		0			0
$277$	−2.12073	−	1.08057i	−0.127422	−	0.0649249i	0.389117	−	0.921188i	$-0.372780\pi$
$277$	−2.12073	−	1.08057i	−0.127422	−	0.0649249i	−0.516540	+	0.856263i	$0.672780\pi$
$278$	−3.56263	+	0.564265i	−0.213672	+	0.0338424i
$279$		0			0
$280$	9.65262	+	22.9359i	0.576854	+	1.37068i
$281$	−26.8503	−	8.72419i	−1.60175	−	0.520442i	−0.634214	−	0.773157i	$-0.718676\pi$
$281$	−26.8503	−	8.72419i	−1.60175	−	0.520442i	−0.967541	+	0.252716i	$0.918676\pi$
$282$		0			0
$283$	−2.66149	−	16.8040i	−0.158209	−	0.998893i	−0.931209	−	0.364486i	$-0.881245\pi$
$283$	−2.66149	−	16.8040i	−0.158209	−	0.998893i	0.773000	−	0.634406i	$-0.218755\pi$
$284$	28.5141	−	9.26479i	1.69200	−	0.549764i
$285$		0			0
$286$	17.4979	+	7.32225i	1.03467	+	0.432974i
$287$	1.66672	+	1.66672i	0.0983831	+	0.0983831i
$288$		0			0
$289$	3.34052	−	4.59783i	0.196501	−	0.270461i
$290$	−8.77835	−	14.1449i	−0.515483	−	0.830615i
$291$		0			0
$292$	18.9838	+	37.2578i	1.11094	+	2.18035i
$293$	−10.5533	−	1.67148i	−0.616533	−	0.0976492i	−0.159646	−	0.987174i	$-0.551035\pi$
$293$	−10.5533	−	1.67148i	−0.616533	−	0.0976492i	−0.456886	+	0.889525i	$0.651035\pi$
$294$		0			0
$295$	−14.3394	+	23.6995i	−0.834873	+	1.37984i
$296$			19.7514i			1.14803i
$297$		0			0
$298$	−42.6760	+	42.6760i	−2.47215	+	2.47215i
$299$	3.12000	+	9.60236i	0.180434	+	0.555319i
$300$		0			0
$301$	−9.42104	+	6.84479i	−0.543020	+	0.394527i
$302$	−32.4977	+	16.5584i	−1.87004	+	0.952831i
$303$		0			0
$304$	−7.13071	+	5.18077i	−0.408975	+	0.297137i
$305$	−1.75064	−	20.7441i	−0.100241	−	1.18780i
$306$		0			0
$307$	22.9923	−	22.9923i	1.31224	−	1.31224i	0.392474	−	0.919763i	$-0.371619\pi$
$307$	22.9923	−	22.9923i	1.31224	−	1.31224i	0.919763	−	0.392474i	$-0.128381\pi$
$308$	−22.5882	−	13.9549i	−1.28708	−	0.795154i
$309$		0			0
$310$	22.0762	−	5.43221i	1.25385	−	0.308529i
$311$	11.2361	+	8.16354i	0.637143	+	0.462912i	0.858868	−	0.512198i	$-0.171168\pi$
$311$	11.2361	+	8.16354i	0.637143	+	0.462912i	−0.221724	+	0.975109i	$0.571168\pi$
$312$		0			0
$313$	7.89399	+	15.4928i	0.446195	+	0.875707i	0.999098	+	0.0424612i	$0.0135199\pi$
$313$	7.89399	+	15.4928i	0.446195	+	0.875707i	−0.552903	+	0.833245i	$0.686480\pi$
$314$	−10.5718	+	32.5367i	−0.596601	+	1.83615i
$315$		0			0
$316$	2.98025	−	4.10196i	0.167652	−	0.230753i
$317$	7.33513	−	14.3960i	0.411982	−	0.808560i	−0.588018	−	0.808848i	$-0.700092\pi$
$317$	7.33513	−	14.3960i	0.411982	−	0.808560i	1.00000		0.000287853i	$9.16265e-5\pi$
$318$		0			0
$319$	8.98439	+	3.75964i	0.503029	+	0.210500i
$320$	1.93639	+	2.24144i	0.108248	+	0.125300i
$321$		0			0
$322$	−3.20950	−	20.2640i	−0.178859	−	1.12927i
$323$	0.687214	−	4.33890i	0.0382376	−	0.241423i
$324$		0			0
$325$	−3.60645	−	10.6869i	−0.200050	−	0.592800i
$326$	1.59932	+	2.20127i	0.0885779	+	0.121917i
$327$		0			0
$328$	−7.14975	−	3.64298i	−0.394779	−	0.201150i
$329$	13.9645			0.769887
$330$		0			0
$331$	14.6837			0.807090			0.403545	−	0.914960i	$-0.367778\pi$
$331$	14.6837			0.807090			0.403545	+	0.914960i	$0.367778\pi$
$332$	41.2854	+	21.0360i	2.26583	+	1.15450i
$333$		0			0
$334$	2.81924	+	3.88034i	0.154262	+	0.212323i
$335$	2.93911	−	7.21066i	0.160581	−	0.393961i
$336$		0			0
$337$	2.11047	−	13.3250i	0.114965	−	0.725859i	−0.861109	−	0.508420i	$-0.830230\pi$
$337$	2.11047	−	13.3250i	0.114965	−	0.725859i	0.976074	−	0.217439i	$-0.0697703\pi$
$338$	3.13772	+	19.8108i	0.170670	+	1.07757i
$339$		0			0
$340$	33.2182	+	2.42547i	1.80151	+	0.131539i
$341$	−8.67464	+	10.0825i	−0.469758	+	0.545999i
$342$		0			0
$343$	8.80832	−	17.2873i	0.475604	−	0.933426i
$344$	23.3020	−	32.0725i	1.25636	−	1.72923i
$345$		0			0
$346$	−14.8443	+	45.6861i	−0.798035	+	2.45610i
$347$	−5.55495	−	10.9022i	−0.298205	−	0.585261i	0.692479	−	0.721438i	$-0.256518\pi$
$347$	−5.55495	−	10.9022i	−0.298205	−	0.585261i	−0.990685	+	0.136177i	$0.956518\pi$
$348$		0			0
$349$	16.4807	+	11.9739i	0.882193	+	0.640951i	0.933831	−	0.357715i	$-0.116444\pi$
$349$	16.4807	+	11.9739i	0.882193	+	0.640951i	−0.0516378	+	0.998666i	$0.516444\pi$
$350$	3.84109	+	22.5953i	0.205315	+	1.20777i
$351$		0			0
$352$	15.4728	+	3.77401i	0.824702	+	0.201156i
$353$	−13.7886	+	13.7886i	−0.733893	+	0.733893i	−0.971389	−	0.237495i	$-0.923674\pi$
$353$	−13.7886	+	13.7886i	−0.733893	+	0.733893i	0.237495	+	0.971389i	$0.423674\pi$
$354$		0			0
$355$	15.0873	−	1.27326i	0.800753	−	0.0675774i
$356$	13.8179	−	10.0393i	0.732345	−	0.532079i
$357$		0			0
$358$	−37.0084	+	18.8567i	−1.95596	+	0.996610i
$359$	13.3648	−	9.71011i	0.705368	−	0.512480i	−0.176308	−	0.984335i	$-0.556415\pi$
$359$	13.3648	−	9.71011i	0.705368	−	0.512480i	0.881676	+	0.471855i	$0.156415\pi$
$360$		0			0
$361$	−5.34436	−	16.4483i	−0.281282	−	0.865697i
$362$	26.6462	−	26.6462i	1.40049	−	1.40049i
$363$		0			0
$364$			18.0588i			0.946537i
$365$	5.04571	+	20.5055i	0.264105	+	1.07331i
$366$		0			0
$367$	−6.36207	−	1.00765i	−0.332097	−	0.0525990i	−0.0118406	−	0.999930i	$-0.503769\pi$
$367$	−6.36207	−	1.00765i	−0.332097	−	0.0525990i	−0.320256	+	0.947331i	$0.603769\pi$
$368$	13.7150	+	26.9172i	0.714943	+	1.40315i
$369$		0			0
$370$	−4.14672	+	17.7129i	−0.215578	+	0.920848i
$371$	−6.76851	+	9.31606i	−0.351404	+	0.483666i
$372$		0			0
$373$	−9.69631	−	9.69631i	−0.502056	−	0.502056i	0.410021	−	0.912076i	$-0.365522\pi$
$373$	−9.69631	−	9.69631i	−0.502056	−	0.502056i	−0.912076	+	0.410021i	$0.865522\pi$
$374$	−24.1720	+	14.6925i	−1.24991	+	0.759730i
$375$		0			0
$376$	−45.2131	+	14.6906i	−2.33169	+	0.757612i
$377$	−1.03625	−	6.54262i	−0.0533696	−	0.336962i
$378$		0			0
$379$	−20.4487	−	6.64419i	−1.05038	−	0.341289i	−0.267563	−	0.963540i	$-0.586218\pi$
$379$	−20.4487	−	6.64419i	−1.05038	−	0.341289i	−0.782818	+	0.622251i	$0.786218\pi$
$380$	−11.9168	+	5.01520i	−0.611317	+	0.257274i
$381$		0			0
$382$	−4.78176	+	0.757356i	−0.244656	+	0.0387497i
$383$	−0.270362	−	0.137756i	−0.0138148	−	0.00703902i	0.447069	−	0.894499i	$-0.352468\pi$
$383$	−0.270362	−	0.137756i	−0.0138148	−	0.00703902i	−0.460884	+	0.887460i	$0.652468\pi$
$384$		0			0
$385$	−9.50058	−	9.46207i	−0.484194	−	0.482232i
$386$	28.8592			1.46889
$387$		0			0
$388$	3.40262	−	0.538921i	0.172742	−	0.0273596i
$389$	2.11680	+	2.91353i	0.107326	+	0.147722i	0.859301	−	0.511470i	$-0.170899\pi$
$389$	2.11680	+	2.91353i	0.107326	+	0.147722i	−0.751975	+	0.659191i	$0.770899\pi$
$390$		0			0
$391$	−14.3199	−	4.65281i	−0.724187	−	0.235303i
$392$	−3.59254	+	22.6824i	−0.181451	+	1.14563i
$393$		0			0
$394$	47.0890	−	15.3001i	2.37231	−	0.770810i
$395$	1.93763	−	1.67393i	0.0974927	−	0.0842244i
$396$		0			0
$397$	22.1781	+	22.1781i	1.11309	+	1.11309i	0.992731	+	0.120357i	$0.0384039\pi$
$397$	22.1781	+	22.1781i	1.11309	+	1.11309i	0.120357	+	0.992731i	$0.461596\pi$
$398$	−25.7259	+	50.4898i	−1.28952	+	2.53083i
$399$		0			0
$400$	−15.6602	−	29.8945i	−0.783010	−	1.49472i
$401$	3.08934	−	9.50802i	0.154274	−	0.474808i	−0.843812	−	0.536639i	$-0.819694\pi$
$401$	3.08934	−	9.50802i	0.154274	−	0.474808i	0.998087	+	0.0618306i	$0.0196939\pi$
$402$		0			0
$403$	8.93502	+	1.41517i	0.445085	+	0.0704945i
$404$	−34.9891	−	25.4211i	−1.74077	−	1.26475i
$405$		0			0
$406$			13.4606i			0.668040i
$407$	−4.03719	−	9.84737i	−0.200116	−	0.488116i
$408$		0			0
$409$	9.39140	+	28.9037i	0.464375	+	1.42920i	0.859767	+	0.510686i	$0.170609\pi$
$409$	9.39140	+	28.9037i	0.464375	+	1.42920i	−0.395393	+	0.918512i	$0.629391\pi$
$410$	−5.64701	−	4.76806i	−0.278886	−	0.235477i
$411$		0			0
$412$	18.4313	−	9.39122i	0.908045	−	0.462672i
$413$	19.9562	−	10.1682i	0.981981	−	0.500344i
$414$		0			0
$415$	17.8791	+	15.0963i	0.877653	+	0.741047i
$416$	−3.34737	−	10.3021i	−0.164118	−	0.505104i
$417$		0			0
$418$	5.77121	−	9.34163i	0.282279	−	0.456914i
$419$			7.48185i			0.365512i	0.983158	+	0.182756i	$0.0585019\pi$
$419$			7.48185i			0.365512i	−0.983158	+	0.182756i	$0.941498\pi$
$420$		0			0
$421$	−16.5226	−	12.0043i	−0.805260	−	0.585056i	0.107192	−	0.994238i	$-0.465814\pi$
$421$	−16.5226	−	12.0043i	−0.805260	−	0.585056i	−0.912453	+	0.409182i	$0.865814\pi$
$422$	−0.942896	−	0.149340i	−0.0458995	−	0.00726976i
$423$		0			0
$424$	12.1141	−	37.2833i	0.588311	−	1.81064i
$425$	16.0547	+	5.01654i	0.778767	+	0.243338i
$426$		0			0
$427$	−7.64189	+	14.9981i	−0.369817	+	0.725807i
$428$	−47.9083	−	47.9083i	−2.31573	−	2.31573i
$429$		0			0
$430$	27.6305	−	23.8702i	1.33246	−	1.15112i
$431$	32.0182	−	10.4034i	1.54226	−	0.501112i	0.590264	−	0.807210i	$-0.299024\pi$
$431$	32.0182	−	10.4034i	1.54226	−	0.501112i	0.952000	+	0.306098i	$0.0990236\pi$
$432$		0			0
$433$	1.81451	−	11.4564i	0.0871997	−	0.550557i	−0.904952	−	0.425514i	$-0.860093\pi$
$433$	1.81451	−	11.4564i	0.0871997	−	0.550557i	0.992151	−	0.125043i	$-0.0399068\pi$
$434$	−17.4830	−	5.68056i	−0.839210	−	0.272676i
$435$		0			0
$436$	−46.5438	−	64.0620i	−2.22904	−	3.06801i
$437$	5.77285	−	0.914330i	0.276153	−	0.0437383i
$438$		0			0
$439$	10.7242			0.511837			0.255918	−	0.966698i	$-0.417622\pi$
$439$	10.7242			0.511837			0.255918	+	0.966698i	$0.417622\pi$
$440$	40.7143	+	20.6409i	1.94098	+	0.984019i
$441$		0			0
$442$	17.1424	+	8.73450i	0.815382	+	0.415458i
$443$	39.8371	−	6.30958i	1.89272	−	0.299777i	0.901580	−	0.432612i	$-0.142408\pi$
$443$	39.8371	−	6.30958i	1.89272	−	0.299777i	0.991138	+	0.132835i	$0.0424079\pi$
$444$		0			0
$445$	7.95012	−	3.34582i	0.376872	−	0.158607i
$446$	18.3479	+	5.96159i	0.868797	+	0.282289i
$447$		0			0
$448$	−0.374664	−	2.36553i	−0.0177012	−	0.111761i
$449$	3.46337	−	1.12532i	0.163447	−	0.0531070i	−0.226151	−	0.974092i	$-0.572614\pi$
$449$	3.46337	−	1.12532i	0.163447	−	0.0531070i	0.389597	+	0.920985i	$0.372614\pi$
$450$		0			0
$451$	4.30925	+	0.354856i	0.202915	+	0.0167095i
$452$	−23.3865	−	23.3865i	−1.10001	−	1.10001i
$453$		0			0
$454$	−12.2237	+	16.8245i	−0.573688	+	0.789613i
$455$	−2.07883	+	8.87978i	−0.0974569	+	0.416291i
$456$		0			0
$457$	−8.21391	−	16.1207i	−0.384230	−	0.754094i	0.615182	−	0.788385i	$-0.289083\pi$
$457$	−8.21391	−	16.1207i	−0.384230	−	0.754094i	−0.999412	+	0.0342910i	$0.989083\pi$
$458$	−19.0039	−	3.00993i	−0.887996	−	0.140645i
$459$		0			0
$460$	10.5883	+	43.0305i	0.493683	+	2.00631i
$461$		−	35.5884i		−	1.65751i	−0.559608	−	0.828757i	$-0.689048\pi$
$461$		−	35.5884i		−	1.65751i	0.559608	−	0.828757i	$-0.310952\pi$
$462$		0			0
$463$	−4.46802	+	4.46802i	−0.207647	+	0.207647i	−0.803266	−	0.595620i	$-0.796907\pi$
$463$	−4.46802	+	4.46802i	−0.207647	+	0.207647i	0.595620	+	0.803266i	$0.296907\pi$
$464$	−6.12479	−	18.8502i	−0.284336	−	0.875097i
$465$		0			0
$466$	53.7742	−	39.0692i	2.49104	−	1.80985i
$467$	7.70967	−	3.92827i	0.356761	−	0.181779i	−0.266419	−	0.963857i	$-0.585840\pi$
$467$	7.70967	−	3.92827i	0.356761	−	0.181779i	0.623180	+	0.782079i	$0.285840\pi$
$468$		0			0
$469$	−5.09363	+	3.70074i	−0.235202	+	0.170884i
$470$	−43.6310	+	3.68212i	−2.01255	+	0.169844i
$471$		0			0
$472$	−53.9157	+	53.9157i	−2.48167	+	2.48167i
$473$	−5.06198	+	20.7532i	−0.232750	+	0.954233i
$474$		0			0
$475$	−6.43698	+	1.09426i	−0.295349	+	0.0502080i
$476$	−21.7875	−	15.8295i	−0.998628	−	0.725545i
$477$		0			0
$478$	−2.61970	−	5.14145i	−0.119822	−	0.235165i
$479$	4.75378	−	14.6306i	0.217206	−	0.668490i	−0.781784	−	0.623549i	$-0.785690\pi$
$479$	4.75378	−	14.6306i	0.217206	−	0.668490i	0.998990	−	0.0449410i	$-0.0143100\pi$
$480$		0			0
$481$	−4.25480	+	5.85623i	−0.194002	+	0.267021i
$482$	−7.24593	+	14.2209i	−0.330043	+	0.647746i
$483$		0			0
$484$	−48.1597	+	7.27051i	−2.18908	+	0.330478i
$485$	1.73516	+	0.126694i	0.0787894	+	0.00575290i
$486$		0			0
$487$	−0.930218	−	5.87316i	−0.0421522	−	0.266138i	0.957607	−	0.288077i	$-0.0930160\pi$
$487$	−0.930218	−	5.87316i	−0.0421522	−	0.266138i	−0.999759	+	0.0219390i	$0.993016\pi$
$488$	8.96437	−	56.5988i	0.405798	−	2.56211i
$489$		0			0
$490$	−7.98384	+	19.5871i	−0.360673	+	0.884857i
$491$	−24.0702	−	33.1298i	−1.08627	−	1.49513i	−0.852422	−	0.522855i	$-0.824867\pi$
$491$	−24.0702	−	33.1298i	−1.08627	−	1.49513i	−0.233851	−	0.972272i	$-0.575133\pi$
$492$		0			0
$493$	8.80185	+	4.48477i	0.396415	+	0.201984i
$494$	−7.46842			−0.336020
$495$		0			0
$496$	27.0678			1.21538
$497$	−10.9082	−	5.55801i	−0.489300	−	0.249311i
$498$		0			0
$499$	−13.6289	−	18.7585i	−0.610111	−	0.839746i	0.386475	−	0.922300i	$-0.373692\pi$
$499$	−13.6289	−	18.7585i	−0.610111	−	0.839746i	−0.996587	+	0.0825534i	$0.973692\pi$
$500$	−12.3711	−	47.9332i	−0.553253	−	2.14364i
$501$		0			0
$502$	−10.5478	+	66.5959i	−0.470769	+	2.97232i
$503$	−0.523026	−	3.30226i	−0.0233206	−	0.147240i	0.973280	−	0.229619i	$-0.0737482\pi$
$503$	−0.523026	−	3.30226i	−0.0233206	−	0.147240i	−0.996601	+	0.0823791i	$0.973748\pi$
$504$		0			0
$505$	−14.2784	−	16.5277i	−0.635379	−	0.735473i
$506$	−28.5296	−	24.5458i	−1.26829	−	1.09120i
$507$		0			0
$508$	0.414474	−	0.813450i	0.0183893	−	0.0360910i
$509$	−13.0172	+	17.9166i	−0.576977	+	0.794141i	−0.993360	−	0.115049i	$-0.963298\pi$
$509$	−13.0172	+	17.9166i	−0.576977	+	0.794141i	0.416383	+	0.909189i	$0.363298\pi$
$510$		0			0
$511$	5.27640	−	16.2391i	0.233414	−	0.718375i
$512$	23.0072	+	45.1541i	1.01678	+	1.99555i
$513$		0			0
$514$	−40.5589	−	29.4678i	−1.78898	−	1.29977i
$515$	10.1440	−	2.49610i	0.446999	−	0.109991i
$516$		0			0
$517$	19.5390	−	16.5658i	0.859323	−	0.728565i
$518$	10.4011	−	10.4011i	0.456998	−	0.456998i
$519$		0			0
$520$	−2.61086	−	30.9372i	−0.114494	−	1.35669i
$521$	−8.59679	+	6.24594i	−0.376632	+	0.273639i	−0.759956	−	0.649975i	$-0.774779\pi$
$521$	−8.59679	+	6.24594i	−0.376632	+	0.273639i	0.383323	+	0.923614i	$0.374779\pi$
$522$		0			0
$523$	38.5151	−	19.6244i	1.68415	−	0.858116i	0.693694	−	0.720269i	$-0.255982\pi$
$523$	38.5151	−	19.6244i	1.68415	−	0.858116i	0.990454	−	0.137847i	$-0.0440181\pi$
$524$	−1.97629	+	1.43586i	−0.0863348	+	0.0627259i
$525$		0			0
$526$	−6.55638	−	20.1785i	−0.285872	−	0.879823i
$527$	−9.53941	+	9.53941i	−0.415543	+	0.415543i
$528$		0			0
$529$			2.96712i			0.129005i
$530$	18.6913	−	30.8921i	0.811898	−	1.34187i
$531$		0			0
$532$	10.3254	+	1.63538i	0.447663	+	0.0709028i
$533$	−1.33512	−	2.62032i	−0.0578304	−	0.113499i
$534$		0			0
$535$	−18.0423	−	29.0722i	−0.780037	−	1.25690i
$536$	12.5986	−	17.3405i	0.544176	−	0.748994i
$537$		0			0
$538$	−17.4086	−	17.4086i	−0.750538	−	0.750538i
$539$	−2.84517	−	12.0430i	−0.122550	−	0.518728i
$540$		0			0
$541$	−20.0780	+	6.52373i	−0.863220	+	0.280477i	−0.706973	−	0.707241i	$-0.749940\pi$
$541$	−20.0780	+	6.52373i	−0.863220	+	0.280477i	−0.156247	+	0.987718i	$0.549940\pi$
$542$	1.21024	+	7.64114i	0.0519841	+	0.328215i
$543$		0			0
$544$	15.3634	+	4.99188i	0.658702	+	0.214025i
$545$	−15.5118	−	36.8582i	−0.664454	−	1.57883i
$546$		0			0
$547$	−1.37675	+	0.218056i	−0.0588658	+	0.00932342i	−0.185798	−	0.982588i	$-0.559487\pi$
$547$	−1.37675	+	0.218056i	−0.0588658	+	0.00932342i	0.126932	+	0.991911i	$0.459487\pi$
$548$	61.0571	+	31.1101i	2.60823	+	1.32896i
$549$		0			0
$550$	32.1788	+	27.0585i	1.37211	+	1.15378i
$551$	−3.83469			−0.163363
$552$		0			0
$553$	−2.04490	+	0.323881i	−0.0869581	+	0.0137728i
$554$	−3.54693	−	4.88193i	−0.150695	−	0.207414i
$555$		0			0
$556$	−5.99117	−	1.94665i	−0.254082	−	0.0825563i
$557$	−0.599510	+	3.78516i	−0.0254021	+	0.160382i	−0.997129	−	0.0757269i	$-0.975872\pi$
$557$	−0.599510	+	3.78516i	−0.0254021	+	0.160382i	0.971727	+	0.236109i	$0.0758723\pi$
$558$		0			0
$559$	13.8180	−	4.48973i	0.584438	−	0.189895i
$560$	−1.98715	+	27.2152i	−0.0839722	+	1.15005i
$561$		0			0
$562$	−50.6125	−	50.6125i	−2.13496	−	2.13496i
$563$	1.10871	−	2.17596i	0.0467264	−	0.0917058i	−0.866463	−	0.499242i	$-0.833612\pi$
$563$	1.10871	−	2.17596i	0.0467264	−	0.0917058i	0.913189	+	0.407536i	$0.133612\pi$
$564$		0			0
$565$	−8.80736	−	14.1916i	−0.370529	−	0.597045i
$566$	13.3292	−	41.0231i	0.560269	−	1.72433i
$567$		0			0
$568$	41.1648	+	6.51986i	1.72723	+	0.273567i
$569$	−5.21403	−	3.78822i	−0.218584	−	0.158810i	0.473105	−	0.881006i	$-0.343133\pi$
$569$	−5.21403	−	3.78822i	−0.218584	−	0.158810i	−0.691689	+	0.722196i	$0.743133\pi$
$570$		0			0
$571$			13.2864i			0.556019i	0.960578	+	0.278009i	$0.0896747\pi$
$571$			13.2864i			0.556019i	−0.960578	+	0.278009i	$0.910325\pi$
$572$	21.4228	+	25.2677i	0.895733	+	1.05649i
$573$		0			0
$574$	1.84667	+	5.68346i	0.0770785	+	0.237223i
$575$	0.253012	+	22.3776i	0.0105513	+	0.933211i
$576$		0			0
$577$	16.6874	−	8.50263i	0.694704	−	0.353969i	−0.0707197	−	0.997496i	$-0.522530\pi$
$577$	16.6874	−	8.50263i	0.694704	−	0.353969i	0.765423	+	0.643527i	$0.222530\pi$
$578$	12.8383	−	6.54143i	0.534002	−	0.272088i
$579$		0			0
$580$	−2.44491	−	28.9708i	−0.101520	−	1.20295i
$581$	−5.84679	−	17.9946i	−0.242566	−	0.746540i
$582$		0			0
$583$	1.58105	+	21.0643i	0.0654803	+	0.872395i
$584$			58.1284i			2.40537i
$585$		0			0
$586$	−21.9158	−	15.9228i	−0.905334	−	0.657764i
$587$	8.32531	+	1.31860i	0.343622	+	0.0544244i	0.325861	−	0.945418i	$-0.394346\pi$
$587$	8.32531	+	1.31860i	0.343622	+	0.0544244i	0.0177617	+	0.999842i	$0.494346\pi$
$588$		0			0
$589$	1.61829	−	4.98059i	0.0666805	−	0.205221i
$590$	−59.6706	+	37.0318i	−2.45660	+	1.52457i
$591$		0			0
$592$	−9.83295	+	19.2983i	−0.404132	+	0.793153i
$593$	4.37233	+	4.37233i	0.179550	+	0.179550i	0.791160	−	0.611610i	$-0.209478\pi$
$593$	4.37233	+	4.37233i	0.179550	+	0.179550i	−0.611610	+	0.791160i	$0.709478\pi$
$594$		0			0
$595$	−8.89103	−	10.2917i	−0.364497	−	0.421918i
$596$	−100.244	+	32.5713i	−4.10616	+	1.33417i
$597$		0			0
$598$	−4.00437	+	25.2826i	−0.163751	+	1.03388i
$599$	34.7989	+	11.3068i	1.42184	+	0.461985i	0.916187	−	0.400750i	$-0.131250\pi$
$599$	34.7989	+	11.3068i	1.42184	+	0.461985i	0.505656	+	0.862735i	$0.331250\pi$
$600$		0			0
$601$	6.33088	+	8.71371i	0.258242	+	0.355440i	0.918376	−	0.395708i	$-0.129501\pi$
$601$	6.33088	+	8.71371i	0.258242	+	0.355440i	−0.660134	+	0.751147i	$0.729501\pi$
$602$	−29.1603	+	4.61853i	−1.18848	+	0.188237i
$603$		0			0
$604$	−63.6982			−2.59184
$605$	−24.5178	−	1.96886i	−0.996791	−	0.0800455i
$606$		0			0
$607$	29.4880	+	15.0249i	1.19688	+	0.609842i	0.934790	−	0.355201i	$-0.115588\pi$
$607$	29.4880	+	15.0249i	1.19688	+	0.609842i	0.262092	+	0.965043i	$0.415588\pi$
$608$	−6.19355	+	0.980962i	−0.251182	+	0.0397833i
$609$		0			0
$610$	19.9219	−	48.8753i	0.806614	−	1.97890i
$611$	−16.5702	−	5.38398i	−0.670359	−	0.217813i
$612$		0			0
$613$	3.38501	+	21.3721i	0.136719	+	0.863213i	0.956754	+	0.290898i	$0.0939542\pi$
$613$	3.38501	+	21.3721i	0.136719	+	0.863213i	−0.820034	+	0.572314i	$0.806046\pi$
$614$	78.4030	−	25.4747i	3.16409	−	1.02807i
$615$		0			0
$616$	−19.1710	−	31.5401i	−0.772421	−	1.27079i
$617$	23.2611	+	23.2611i	0.936455	+	0.936455i	0.998098	−	0.0616431i	$-0.0196341\pi$
$617$	23.2611	+	23.2611i	0.936455	+	0.936455i	−0.0616431	+	0.998098i	$0.519634\pi$
$618$		0			0
$619$	−24.3484	+	33.5126i	−0.978643	+	1.34699i	−0.0410856	+	0.999156i	$0.513082\pi$
$619$	−24.3484	+	33.5126i	−0.978643	+	1.34699i	−0.937557	+	0.347831i	$0.886918\pi$
$620$	38.6597	+	9.05055i	1.55261	+	0.363479i
$621$		0			0
$622$	15.9859	+	31.3741i	0.640975	+	1.25798i
$623$	−6.88845	−	1.09102i	−0.275980	−	0.0437109i
$624$		0			0
$625$	−0.565252	−	24.9936i	−0.0226101	−	0.999744i
$626$			44.0839i			1.76195i
$627$		0			0
$628$	−42.2480	+	42.2480i	−1.68588	+	1.68588i
$629$	−3.33583	−	10.2666i	−0.133008	−	0.409357i
$630$		0			0
$631$	25.4513	−	18.4915i	1.01320	−	0.736134i	0.0483238	−	0.998832i	$-0.484612\pi$
$631$	25.4513	−	18.4915i	1.01320	−	0.736134i	0.964878	+	0.262697i	$0.0846121\pi$
$632$	6.28010	−	3.19987i	0.249809	−	0.127284i
$633$		0			0
$634$	33.1397	−	24.0774i	1.31615	−	0.956236i
$635$	0.297443	−	0.352274i	0.0118037	−	0.0139796i
$636$		0			0
$637$	−5.95137	+	5.95137i	−0.235802	+	0.235802i
$638$	15.9681	+	18.8340i	0.632184	+	0.745645i
$639$		0			0
$640$	6.92558	+	28.1453i	0.273758	+	1.11254i
$641$	16.6022	+	12.0622i	0.655749	+	0.476430i	0.865225	−	0.501384i	$-0.167176\pi$
$641$	16.6022	+	12.0622i	0.655749	+	0.476430i	−0.209476	+	0.977814i	$0.567176\pi$
$642$		0			0
$643$	−8.00058	−	15.7020i	−0.315512	−	0.619228i	0.677727	−	0.735314i	$-0.262965\pi$
$643$	−8.00058	−	15.7020i	−0.315512	−	0.619228i	−0.993239	+	0.116086i	$0.962965\pi$
$644$	11.0724	−	34.0774i	0.436314	−	1.34284i
$645$		0			0
$646$	6.54649	−	9.01047i	0.257568	−	0.354512i
$647$	2.61567	−	5.13354i	0.102833	−	0.201820i	−0.833857	−	0.551980i	$-0.813873\pi$
$647$	2.61567	−	5.13354i	0.102833	−	0.201820i	0.936690	+	0.350159i	$0.113873\pi$
$648$		0			0
$649$	15.8602	−	37.9010i	0.622566	−	1.48774i
$650$	4.15374	−	28.2924i	0.162923	−	1.10972i
$651$		0			0
$652$	0.743366	+	4.69343i	0.0291125	+	0.183809i
$653$	−0.912669	+	5.76236i	−0.0357155	+	0.225499i	−0.999090	−	0.0426625i	$-0.986416\pi$
$653$	−0.912669	+	5.76236i	−0.0357155	+	0.225499i	0.963374	+	0.268161i	$0.0864160\pi$
$654$		0			0
$655$	−1.13706	+	0.478535i	−0.0444287	+	0.0186979i
$656$	−5.17212	−	7.11881i	−0.201937	−	0.277943i
$657$		0			0
$658$	31.5454	+	16.0732i	1.22977	+	0.626598i
$659$	−5.21347			−0.203088			−0.101544	−	0.994831i	$-0.532378\pi$
$659$	−5.21347			−0.203088			−0.101544	+	0.994831i	$0.532378\pi$
$660$		0			0
$661$	4.56016			0.177369			0.0886847	−	0.996060i	$-0.471734\pi$
$661$	4.56016			0.177369			0.0886847	+	0.996060i	$0.471734\pi$
$662$	33.1701	+	16.9010i	1.28919	+	0.656877i
$663$		0			0
$664$	37.8606	+	52.1106i	1.46927	+	2.02228i
$665$	4.88890	+	1.99275i	0.189584	+	0.0772754i
$666$		0			0
$667$	−2.05606	+	12.9815i	−0.0796110	+	0.502644i
$668$	1.31039	+	8.27346i	0.0507004	+	0.320110i
$669$		0			0
$670$	14.9389	−	12.9058i	0.577139	−	0.498593i
$671$	7.09949	+	30.0506i	0.274073	+	1.16009i
$672$		0			0
$673$	−0.253956	+	0.498417i	−0.00978930	+	0.0192126i	−0.895849	−	0.444358i	$-0.853432\pi$
$673$	−0.253956	+	0.498417i	−0.00978930	+	0.0192126i	0.886060	+	0.463570i	$0.153432\pi$
$674$	20.1046	−	27.6716i	0.774401	−	1.06587i
$675$		0			0
$676$	−10.8248	+	33.3153i	−0.416338	+	1.28136i
$677$	13.2166	+	25.9390i	0.507955	+	0.996918i	0.992511	+	0.122157i	$0.0389813\pi$
$677$	13.2166	+	25.9390i	0.507955	+	0.996918i	−0.484556	+	0.874760i	$0.661019\pi$
$678$		0			0
$679$	−1.13807	−	0.826858i	−0.0436752	−	0.0317319i
$680$	39.6135	+	23.9682i	1.51911	+	0.919140i
$681$		0			0
$682$	−31.2008	+	12.7916i	−1.19474	+	0.489815i
$683$	−5.43554	+	5.43554i	−0.207985	+	0.207985i	−0.803411	−	0.595425i	$-0.796984\pi$
$683$	−5.43554	+	5.43554i	−0.207985	+	0.207985i	0.595425	+	0.803411i	$0.296984\pi$
$684$		0			0
$685$	26.4415	+	22.3259i	1.01028	+	0.853029i
$686$	39.7955	−	28.9131i	1.51940	−	1.10391i
$687$		0			0
$688$	38.7343	−	19.7361i	1.47673	−	0.752432i
$689$	11.6233	−	8.44481i	0.442812	−	0.321722i
$690$		0			0
$691$	−2.91716	−	8.97809i	−0.110974	−	0.341542i	0.880112	−	0.474766i	$-0.157467\pi$
$691$	−2.91716	−	8.97809i	−0.110974	−	0.341542i	−0.991086	+	0.133223i	$0.957467\pi$
$692$	−59.3222	+	59.3222i	−2.25509	+	2.25509i
$693$		0			0
$694$		−	31.0215i		−	1.17756i
$695$	−2.72186	−	1.64687i	−0.103246	−	0.0624693i
$696$		0			0
$697$	4.33166	+	0.686067i	0.164073	+	0.0259866i
$698$	23.4474	+	46.0182i	0.887499	+	1.74181i
$699$		0			0
$700$	−11.9380	+	38.2058i	−0.451214	+	1.44404i
$701$	11.5843	−	15.9445i	0.437535	−	0.602215i	−0.532127	−	0.846664i	$-0.678607\pi$
$701$	11.5843	−	15.9445i	0.437535	−	0.602215i	0.969662	+	0.244449i	$0.0786072\pi$
$702$		0			0
$703$	2.96308	+	2.96308i	0.111755	+	0.111755i
$704$	−3.33042	−	2.86537i	−0.125520	−	0.107993i
$705$		0			0
$706$	−47.0188	+	15.2773i	−1.76958	+	0.574970i
$707$	2.76266	+	17.4427i	0.103900	+	0.656001i
$708$		0			0
$709$	42.2836	+	13.7388i	1.58799	+	0.515970i	0.964100	−	0.265540i	$-0.0855503\pi$
$709$	42.2836	+	13.7388i	1.58799	+	0.515970i	0.623893	+	0.781510i	$0.285550\pi$
$710$	35.5474	+	14.4893i	1.33407	+	0.543775i
$711$		0			0
$712$	23.4507	−	3.71422i	0.878850	−	0.139196i
$713$	−15.9929	−	8.14881i	−0.598940	−	0.305175i
$714$		0			0
$715$	7.62526	+	14.8906i	0.285169	+	0.556876i
$716$	−72.5395			−2.71093
$717$		0			0
$718$	41.3671	−	6.55191i	1.54381	−	0.244515i
$719$	−14.1002	−	19.4073i	−0.525850	−	0.723770i	0.460641	−	0.887587i	$-0.347620\pi$
$719$	−14.1002	−	19.4073i	−0.525850	−	0.723770i	−0.986491	+	0.163816i	$0.947620\pi$
$720$		0			0
$721$	−8.03342	−	2.61022i	−0.299180	−	0.0972095i
$722$	6.85924	−	43.3075i	0.255274	−	1.61174i
$723$		0			0
$724$	62.5908	−	20.3370i	2.32617	−	0.755819i
$725$	2.13276	−	14.5268i	0.0792087	−	0.539513i
$726$		0			0
$727$	−17.6187	−	17.6187i	−0.653441	−	0.653441i	0.300379	−	0.953820i	$-0.402887\pi$
$727$	−17.6187	−	17.6187i	−0.653441	−	0.653441i	−0.953820	+	0.300379i	$0.902887\pi$
$728$	−11.3969	+	22.3677i	−0.422398	+	0.829002i
$729$		0			0
$730$	−12.2038	+	52.1291i	−0.451684	+	1.92938i
$731$	−6.69547	+	20.6065i	−0.247641	+	0.762161i
$732$		0			0
$733$	0.0534353	+	0.00846331i	0.00197368	+	0.000312600i	0.157421	−	0.987532i	$-0.449682\pi$
$733$	0.0534353	+	0.00846331i	0.00197368	+	0.000312600i	−0.155448	+	0.987844i	$0.549682\pi$
$734$	−13.2119	−	9.59902i	−0.487661	−	0.354306i
$735$		0			0
$736$			21.4928i			0.792235i
$737$	−2.73683	+	11.2205i	−0.100813	+	0.413313i
$738$		0			0
$739$	5.95011	+	18.3126i	0.218878	+	0.673638i	0.998855	+	0.0478303i	$0.0152307\pi$
$739$	5.95011	+	18.3126i	0.218878	+	0.673638i	−0.779977	+	0.625808i	$0.784769\pi$
$740$	−20.4967	+	24.2751i	−0.753473	+	0.892369i
$741$		0			0
$742$	−26.0127	+	13.2541i	−0.954957	+	0.486575i
$743$	6.63666	−	3.38155i	0.243475	−	0.124057i	−0.327995	−	0.944679i	$-0.606373\pi$
$743$	6.63666	−	3.38155i	0.243475	−	0.124057i	0.571471	+	0.820622i	$0.306373\pi$
$744$		0			0
$745$	−53.0411	+	4.47626i	−1.94327	+	0.163997i
$746$	−10.7432	−	33.0642i	−0.393337	−	1.21057i
$747$		0			0
$748$	−49.2632	+	3.69760i	−1.80124	+	0.135198i
$749$			27.6659i			1.01089i
$750$		0			0
$751$	24.3907	+	17.7209i	0.890031	+	0.646645i	0.935886	−	0.352303i	$-0.114601\pi$
$751$	24.3907	+	17.7209i	0.890031	+	0.646645i	−0.0458552	+	0.998948i	$0.514601\pi$
$752$	−51.4894	−	8.15512i	−1.87763	−	0.297387i
$753$		0			0
$754$	5.18973	−	15.9723i	0.188999	−	0.581678i
$755$	−31.3214	−	7.33259i	−1.13990	−	0.266860i
$756$		0			0
$757$	−20.2037	+	39.6521i	−0.734318	+	1.44118i	0.156905	+	0.987614i	$0.449848\pi$
$757$	−20.2037	+	39.6521i	−0.734318	+	1.44118i	−0.891223	+	0.453566i	$0.850152\pi$
$758$	−38.5456	−	38.5456i	−1.40004	−	1.40004i
$759$		0			0
$760$	−17.9253	−	1.30883i	−0.650218	−	0.0474764i
$761$	−44.8060	+	14.5584i	−1.62422	+	0.527740i	−0.972932	−	0.231093i	$-0.925770\pi$
$761$	−44.8060	+	14.5584i	−1.62422	+	0.527740i	−0.651285	+	0.758833i	$0.725770\pi$
$762$		0			0
$763$	−5.05818	+	31.9361i	−0.183118	+	1.15616i
$764$	−8.04134	−	2.61279i	−0.290926	−	0.0945274i
$765$		0			0
$766$	−0.452182	−	0.622375i	−0.0163380	−	0.0224873i
$767$	−27.6003	+	4.37145i	−0.996588	+	0.157844i
$768$		0			0
$769$	−29.7849			−1.07407			−0.537036	−	0.843559i	$-0.680456\pi$
$769$	−29.7849			−1.07407			−0.537036	+	0.843559i	$0.680456\pi$
$770$	−10.5707	−	32.3098i	−0.380940	−	1.16436i
$771$		0			0
$772$	44.9076	+	22.8815i	1.61626	+	0.823525i
$773$	7.03566	−	1.11434i	0.253055	−	0.0400800i	−0.0286180	−	0.999590i	$-0.509111\pi$
$773$	7.03566	−	1.11434i	0.253055	−	0.0400800i	0.281673	+	0.959510i	$0.409111\pi$
$774$		0			0
$775$	17.9677	+	8.90059i	0.645420	+	0.319719i
$776$	4.55461	+	1.47988i	0.163501	+	0.0531247i
$777$		0			0
$778$	1.42832	+	9.01803i	0.0512076	+	0.323312i
$779$	−1.61912	+	0.526083i	−0.0580108	+	0.0188489i
$780$		0			0
$781$	−21.8560	+	5.16351i	−0.782070	+	0.184765i
$782$	−26.9928	−	26.9928i	−0.965260	−	0.965260i
$783$		0			0
$784$	−14.8022	+	20.3735i	−0.528651	+	0.727626i
$785$	−25.6374	+	15.9106i	−0.915037	+	0.567875i
$786$		0			0
$787$	−13.1008	−	25.7117i	−0.466992	−	0.916524i	−0.997622	−	0.0689202i	$-0.978045\pi$
$787$	−13.1008	−	25.7117i	−0.466992	−	0.916524i	0.530630	−	0.847604i	$-0.321955\pi$
$788$	85.4058	+	13.5270i	3.04246	+	0.481878i
$789$		0			0
$790$	6.30375	−	1.55114i	0.224277	−	0.0551869i
$791$			13.5051i			0.480187i
$792$		0			0
$793$	14.8503	−	14.8503i	0.527350	−	0.527350i
$794$	24.5726	+	75.6268i	0.872051	+	2.68390i
$795$		0			0
$796$	−80.0636	+	58.1696i	−2.83778	+	2.06177i
$797$	27.5666	−	14.0459i	0.976460	−	0.497531i	0.108463	−	0.994100i	$-0.465407\pi$
$797$	27.5666	−	14.0459i	0.976460	−	0.497531i	0.867997	+	0.496569i	$0.165407\pi$
$798$		0			0
$799$	21.0204	−	15.2722i	0.743647	−	0.540291i
$800$	−0.271451	−	24.0084i	−0.00959724	−	0.848825i
$801$		0			0
$802$	17.9225	−	17.9225i	0.632866	−	0.632866i
$803$	−11.8815	−	28.9809i	−0.419288	−	1.02271i
$804$		0			0
$805$	9.36728	−	15.4818i	0.330153	−	0.545661i
$806$	18.5551	+	13.4811i	0.653575	+	0.474850i
$807$		0			0
$808$	−27.2945	−	53.5684i	−0.960215	−	1.88453i
$809$	6.07857	−	18.7079i	0.213711	−	0.657735i	−0.785531	−	0.618822i	$-0.787610\pi$
$809$	6.07857	−	18.7079i	0.213711	−	0.657735i	0.999243	−	0.0389136i	$-0.0123897\pi$
$810$		0			0
$811$	24.8398	−	34.1891i	0.872243	−	1.20054i	−0.106266	−	0.994338i	$-0.533890\pi$
$811$	24.8398	−	34.1891i	0.872243	−	1.20054i	0.978509	−	0.206202i	$-0.0661105\pi$
$812$	−10.6725	+	20.9460i	−0.374532	+	0.735061i
$813$		0			0
$814$	2.21447	−	26.8918i	0.0776170	−	0.942556i
$815$	−0.174757	+	2.39340i	−0.00612147	+	0.0838373i
$816$		0			0
$817$	−1.31574	−	8.30723i	−0.0460318	−	0.290633i
$818$	−12.0534	+	76.1023i	−0.421438	+	2.66085i
$819$		0			0
$820$	−5.00682	−	11.8969i	−0.174846	−	0.415457i
$821$	31.2544	+	43.0180i	1.09079	+	1.50134i	0.847061	+	0.531496i	$0.178370\pi$
$821$	31.2544	+	43.0180i	1.09079	+	1.50134i	0.243726	+	0.969844i	$0.421630\pi$
$822$		0			0
$823$	−1.24781	−	0.635792i	−0.0434960	−	0.0221623i	0.432107	−	0.901822i	$-0.357770\pi$
$823$	−1.24781	−	0.635792i	−0.0434960	−	0.0221623i	−0.475603	+	0.879660i	$0.657770\pi$
$824$	28.7559			1.00176
$825$		0			0
$826$	56.7841			1.97577
$827$	15.4022	+	7.84783i	0.535588	+	0.272896i	0.700794	−	0.713363i	$-0.252829\pi$
$827$	15.4022	+	7.84783i	0.535588	+	0.272896i	−0.165206	+	0.986259i	$0.552829\pi$
$828$		0			0
$829$	−21.0969	−	29.0374i	−0.732727	−	1.00851i	−0.999004	−	0.0446158i	$-0.985794\pi$
$829$	−21.0969	−	29.0374i	−0.732727	−	1.00851i	0.266277	−	0.963897i	$-0.414206\pi$
$830$	23.0126	+	54.6810i	0.798780	+	1.89801i
$831$		0			0
$832$	−0.467453	+	2.95138i	−0.0162060	+	0.102321i
$833$	−1.96348	−	12.3969i	−0.0680304	−	0.429527i
$834$		0			0
$835$	−0.308058	+	4.21903i	−0.0106608	+	0.146006i
$836$	16.3872	−	9.96064i	0.566764	−	0.344496i
$837$		0			0
$838$	−8.61164	+	16.9013i	−0.297484	+	0.583845i
$839$	2.91587	−	4.01335i	0.100667	−	0.138556i	−0.755712	−	0.654904i	$-0.772709\pi$
$839$	2.91587	−	4.01335i	0.100667	−	0.138556i	0.856379	+	0.516348i	$0.172709\pi$
$840$		0			0
$841$	−6.29681	+	19.3796i	−0.217131	+	0.668261i
$842$	−23.5070	−	46.1350i	−0.810103	−	1.58992i
$843$		0			0
$844$	−1.34883	−	0.979980i	−0.0464285	−	0.0337323i
$845$	−9.15778	+	15.1355i	−0.315037	+	0.520678i
$846$		0			0
$847$	16.0048	+	11.8063i	0.549932	+	0.405668i
$848$	30.3971	−	30.3971i	1.04384	−	1.04384i
$849$		0			0
$850$	30.4931	+	29.8112i	1.04590	+	1.02252i
$851$	11.6196	−	8.44211i	0.398313	−	0.289392i
$852$		0			0
$853$	−23.6804	+	12.0658i	−0.810803	+	0.413125i	−0.809678	−	0.586875i	$-0.800358\pi$
$853$	−23.6804	+	12.0658i	−0.810803	+	0.413125i	−0.00112492	+	0.999999i	$0.500358\pi$
$854$	−34.5257	+	25.0844i	−1.18144	+	0.858369i
$855$		0			0
$856$	−29.1045	−	89.5744i	−0.994771	−	3.06159i
$857$	−1.04396	+	1.04396i	−0.0356609	+	0.0356609i	−0.724712	−	0.689051i	$-0.758027\pi$
$857$	−1.04396	+	1.04396i	−0.0356609	+	0.0356609i	0.689051	+	0.724712i	$0.258027\pi$
$858$		0			0
$859$			13.9402i			0.475633i	0.971310	+	0.237816i	$0.0764316\pi$
$859$			13.9402i			0.475633i	−0.971310	+	0.237816i	$0.923568\pi$
$860$	61.9216	−	15.2368i	2.11151	−	0.519570i
$861$		0			0
$862$	84.3026	+	13.3522i	2.87136	+	0.454778i
$863$	−23.2938	−	45.7166i	−0.792929	−	1.55621i	−0.830567	−	0.556919i	$-0.811983\pi$
$863$	−23.2938	−	45.7166i	−0.792929	−	1.55621i	0.0376382	−	0.999291i	$-0.488017\pi$
$864$		0			0
$865$	−35.9985	+	22.3408i	−1.22399	+	0.759610i
$866$	17.2852	−	23.7911i	0.587376	−	0.808454i
$867$		0			0
$868$	−22.7012	−	22.7012i	−0.770529	−	0.770529i
$869$	−2.47699	+	2.87900i	−0.0840262	+	0.0976635i
$870$		0			0
$871$	7.47089	−	2.42744i	0.253141	−	0.0822507i
$872$	−17.2198	−	108.721i	−0.583135	−	3.68177i
$873$		0			0
$874$	14.0931	+	4.57913i	0.476706	+	0.154891i
$875$	−10.2681	+	17.4122i	−0.347126	+	0.588638i
$876$		0			0
$877$	−6.59105	+	1.04392i	−0.222564	+	0.0352507i	−0.266720	−	0.963774i	$-0.585940\pi$
$877$	−6.59105	+	1.04392i	−0.222564	+	0.0352507i	0.0441563	+	0.999025i	$0.485940\pi$
$878$	24.2256	+	12.3436i	0.817574	+	0.416575i
$879$		0			0
$880$	29.5045	+	40.4365i	0.994596	+	1.36311i
$881$	14.4573			0.487080			0.243540	−	0.969891i	$-0.421691\pi$
$881$	14.4573			0.487080			0.243540	+	0.969891i	$0.421691\pi$
$882$		0			0
$883$	−10.3324	+	1.63650i	−0.347714	+	0.0550725i	−0.327849	−	0.944730i	$-0.606324\pi$
$883$	−10.3324	+	1.63650i	−0.347714	+	0.0550725i	−0.0198651	+	0.999803i	$0.506324\pi$
$884$	19.7499	+	27.1834i	0.664260	+	0.914276i
$885$		0			0
$886$	97.2533	+	31.5995i	3.26729	+	1.06161i
$887$	1.54605	−	9.76140i	0.0519114	−	0.327756i	−0.948042	−	0.318144i	$-0.896940\pi$
$887$	1.54605	−	9.76140i	0.0519114	−	0.327756i	0.999954	−	0.00961170i	$-0.00305955\pi$
$888$		0			0
$889$	−0.354548	+	0.115200i	−0.0118912	+	0.00386368i
$890$	21.8101	+	1.59249i	0.731078	+	0.0533805i
$891$		0			0
$892$	23.8243	+	23.8243i	0.797695	+	0.797695i
$893$	−4.57896	+	8.98671i	−0.153229	+	0.300729i
$894$		0			0
$895$	−35.6688	−	8.35035i	−1.19228	−	0.279121i
$896$	7.24221	−	22.2892i	0.241945	−	0.744631i
$897$		0			0
$898$	9.11891	+	1.44429i	0.304302	+	0.0481967i
$899$	9.52719	+	6.92191i	0.317750	+	0.230859i
$900$		0			0
$901$			21.4256i			0.713789i
$902$	9.32604	+	5.76157i	0.310523	+	0.191839i
$903$		0			0
$904$	−14.2074	−	43.7258i	−0.472530	−	1.45430i
$905$	33.1180	−	2.79490i	1.10088	−	0.0929057i
$906$		0			0
$907$	−10.3100	+	5.25319i	−0.342337	+	0.174429i	−0.616703	−	0.787196i	$-0.711532\pi$
$907$	−10.3100	+	5.25319i	−0.342337	+	0.174429i	0.274366	+	0.961625i	$0.411532\pi$
$908$	−32.3609	+	16.4887i	−1.07393	+	0.547196i
$909$		0			0
$910$	−14.9167	+	17.6664i	−0.494483	+	0.585637i
$911$	2.69510	+	8.29465i	0.0892925	+	0.274814i	0.985724	−	0.168368i	$-0.0538496\pi$
$911$	2.69510	+	8.29465i	0.0892925	+	0.274814i	−0.896432	+	0.443182i	$0.853850\pi$
$912$		0			0
$913$	−29.5274	−	18.2419i	−0.977215	−	0.603718i
$914$		−	45.8704i		−	1.51726i
$915$		0			0
$916$	−27.1854	−	19.7514i	−0.898231	−	0.652603i
$917$	0.985219	+	0.156043i	0.0325348	+	0.00515301i
$918$		0			0
$919$	−1.78507	+	5.49388i	−0.0588840	+	0.181226i	−0.976172	−	0.216998i	$-0.930373\pi$
$919$	−1.78507	+	5.49388i	−0.0588840	+	0.181226i	0.917288	+	0.398224i	$0.130373\pi$
$920$	−14.0418	+	59.9801i	−0.462945	+	1.97749i
$921$		0			0
$922$	40.9623	−	80.3931i	1.34902	−	2.64761i
$923$	10.8007	+	10.8007i	0.355511	+	0.355511i
$924$		0			0
$925$	−12.8729	+	9.57696i	−0.423260	+	0.314889i
$926$	−15.2359	+	4.95043i	−0.500681	+	0.162681i
$927$		0			0
$928$	2.20590	−	13.9275i	0.0724121	−	0.457192i
$929$	−17.2514	−	5.60532i	−0.566000	−	0.183905i	0.0120191	−	0.999928i	$-0.496174\pi$
$929$	−17.2514	−	5.60532i	−0.566000	−	0.183905i	−0.578019	+	0.816023i	$0.696174\pi$
$930$		0			0
$931$	2.86384	+	3.94174i	0.0938587	+	0.129185i
$932$	114.654	−	18.1595i	3.75563	−	0.594833i
$933$		0			0
$934$	21.9374			0.717813
$935$	−24.6491	−	3.85274i	−0.806112	−	0.125998i
$936$		0			0
$937$	−28.6359	−	14.5907i	−0.935496	−	0.476659i	−0.0813459	−	0.996686i	$-0.525922\pi$
$937$	−28.6359	−	14.5907i	−0.935496	−	0.476659i	−0.854150	+	0.520027i	$0.825922\pi$
$938$	−15.7659	+	2.49708i	−0.514776	+	0.0815325i
$939$		0			0
$940$	−70.8134	−	28.8640i	−2.30968	−	0.941438i
$941$	4.95612	+	1.61034i	0.161565	+	0.0524956i	0.388683	−	0.921372i	$-0.372930\pi$
$941$	4.95612	+	1.61034i	0.161565	+	0.0524956i	−0.227118	+	0.973867i	$0.572930\pi$
$942$		0			0
$943$	0.912803	+	5.76321i	0.0297250	+	0.187676i
$944$	−79.5200	+	25.8376i	−2.58816	+	0.840943i
$945$		0			0
$946$	−35.3219	+	41.0545i	−1.14841	+	1.33480i
$947$	0.545091	+	0.545091i	0.0177131	+	0.0177131i	0.715908	−	0.698195i	$-0.246013\pi$
$947$	0.545091	+	0.545091i	0.0177131	+	0.0177131i	−0.698195	+	0.715908i	$0.746013\pi$
$948$		0			0
$949$	−12.5219	+	17.2349i	−0.406478	+	0.559469i
$950$	−15.8005	−	4.93710i	−0.512635	−	0.160181i
$951$		0			0
$952$	−16.9961	−	33.3567i	−0.550846	−	1.08110i
$953$	13.4139	+	2.12456i	0.434519	+	0.0688211i	0.369863	−	0.929086i	$-0.379405\pi$
$953$	13.4139	+	2.12456i	0.434519	+	0.0688211i	0.0646568	+	0.997908i	$0.479405\pi$
$954$		0			0
$955$	−3.65328	−	2.21042i	−0.118217	−	0.0715277i
$956$		−	10.0777i		−	0.325935i
$957$		0			0
$958$	27.5786	−	27.5786i	0.891023	−	0.891023i
$959$	−8.64682	−	26.6122i	−0.279221	−	0.859352i
$960$		0			0
$961$	12.0686	−	8.76834i	0.389309	−	0.282850i
$962$	−16.3520	+	8.33177i	−0.527210	+	0.268627i
$963$		0			0
$964$	−22.5507	+	16.3840i	−0.726309	+	0.527694i
$965$	19.4477	+	16.4207i	0.626045	+	0.528602i
$966$		0			0
$967$	−28.7882	+	28.7882i	−0.925767	+	0.925767i	−0.997429	−	0.0716619i	$-0.977170\pi$
$967$	−28.7882	+	28.7882i	−0.925767	+	0.925767i	0.0716619	+	0.997429i	$0.477170\pi$
$968$	−64.2393	−	21.3884i	−2.06473	−	0.687448i
$969$		0			0
$970$	3.77385	+	2.28337i	0.121171	+	0.0733147i
$971$	−23.7651	−	17.2663i	−0.762657	−	0.554103i	0.137067	−	0.990562i	$-0.456232\pi$
$971$	−23.7651	−	17.2663i	−0.762657	−	0.554103i	−0.899724	+	0.436459i	$0.856232\pi$
$972$		0			0
$973$	1.16781	+	2.29195i	0.0374382	+	0.0734765i
$974$	4.65870	−	14.3380i	0.149274	−	0.459419i
$975$		0			0
$976$	36.9357	−	50.8376i	1.18228	−	1.62727i
$977$	−10.6212	+	20.8453i	−0.339803	+	0.666901i	−0.996160	−	0.0875496i	$-0.972096\pi$
$977$	−10.6212	+	20.8453i	−0.339803	+	0.666901i	0.656357	+	0.754450i	$0.272096\pi$
$978$		0			0
$979$	−10.9325	+	6.64511i	−0.349405	+	0.212379i
$980$	−27.9536	+	24.1493i	−0.892946	+	0.771420i
$981$		0			0
$982$	−16.2414	−	102.544i	−0.518284	−	3.27232i
$983$	3.26285	−	20.6008i	0.104069	−	0.657064i	−0.879413	−	0.476059i	$-0.842065\pi$
$983$	3.26285	−	20.6008i	0.104069	−	0.657064i	0.983482	−	0.181005i	$-0.0579351\pi$
$984$		0			0
$985$	40.4382	+	16.4829i	1.28847	+	0.525188i
$986$	14.7212	+	20.2619i	0.468817	+	0.645271i
$987$		0			0
$988$	−11.6216	−	5.92148i	−0.369731	−	0.188387i
$989$	−28.8277			−0.916666
$990$		0			0
$991$	−6.50787			−0.206729			−0.103365	−	0.994644i	$-0.532961\pi$
$991$	−6.50787			−0.206729			−0.103365	+	0.994644i	$0.532961\pi$
$992$	17.1584	+	8.74265i	0.544780	+	0.277579i
$993$		0			0
$994$	−18.2440	−	25.1108i	−0.578666	−	0.796465i
$995$	−46.0647	+	19.3864i	−1.46035	+	0.614591i
$996$		0			0
$997$	−4.13075	+	26.0805i	−0.130822	+	0.825978i	0.831789	+	0.555092i	$0.187317\pi$
$997$	−4.13075	+	26.0805i	−0.130822	+	0.825978i	−0.962611	+	0.270886i	$0.912683\pi$
$998$	−9.19609	−	58.0618i	−0.291097	−	1.83792i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.bj.a.127.4		32
3.2	odd	2		55.2.l.a.17.1	yes	32
5.3	odd	4	inner	495.2.bj.a.28.4		32
11.2	odd	10	inner	495.2.bj.a.442.4		32
12.11	even	2		880.2.cm.a.17.1		32
15.2	even	4		275.2.bm.b.193.4		32
15.8	even	4		55.2.l.a.28.1	yes	32
15.14	odd	2		275.2.bm.b.182.4		32
33.2	even	10		55.2.l.a.2.1	✓	32
33.5	odd	10		605.2.m.c.282.4		32
33.8	even	10		605.2.e.b.362.16		32
33.14	odd	10		605.2.e.b.362.1		32
33.17	even	10		605.2.m.d.282.1		32
33.20	odd	10		605.2.m.e.112.4		32
33.26	odd	10		605.2.m.d.602.4		32
33.29	even	10		605.2.m.c.602.1		32
33.32	even	2		605.2.m.e.457.4		32
55.13	even	20	inner	495.2.bj.a.343.4		32
60.23	odd	4		880.2.cm.a.193.1		32
132.35	odd	10		880.2.cm.a.497.1		32
165.2	odd	20		275.2.bm.b.68.4		32
165.8	odd	20		605.2.e.b.483.1		32
165.38	even	20		605.2.m.c.403.1		32
165.53	even	20		605.2.m.e.233.4		32
165.68	odd	20		55.2.l.a.13.1	yes	32
165.83	odd	20		605.2.m.d.403.4		32
165.98	odd	4		605.2.m.e.578.4		32
165.113	even	20		605.2.e.b.483.16		32
165.128	odd	20		605.2.m.c.118.4		32
165.134	even	10		275.2.bm.b.57.4		32
165.158	even	20		605.2.m.d.118.1		32
660.563	even	20		880.2.cm.a.673.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.2.1	✓	32	33.2	even	10
55.2.l.a.13.1	yes	32	165.68	odd	20
55.2.l.a.17.1	yes	32	3.2	odd	2
55.2.l.a.28.1	yes	32	15.8	even	4
275.2.bm.b.57.4		32	165.134	even	10
275.2.bm.b.68.4		32	165.2	odd	20
275.2.bm.b.182.4		32	15.14	odd	2
275.2.bm.b.193.4		32	15.2	even	4
495.2.bj.a.28.4		32	5.3	odd	4	inner
495.2.bj.a.127.4		32	1.1	even	1	trivial
495.2.bj.a.343.4		32	55.13	even	20	inner
495.2.bj.a.442.4		32	11.2	odd	10	inner
605.2.e.b.362.1		32	33.14	odd	10
605.2.e.b.362.16		32	33.8	even	10
605.2.e.b.483.1		32	165.8	odd	20
605.2.e.b.483.16		32	165.113	even	20
605.2.m.c.118.4		32	165.128	odd	20
605.2.m.c.282.4		32	33.5	odd	10
605.2.m.c.403.1		32	165.38	even	20
605.2.m.c.602.1		32	33.29	even	10
605.2.m.d.118.1		32	165.158	even	20
605.2.m.d.282.1		32	33.17	even	10
605.2.m.d.403.4		32	165.83	odd	20
605.2.m.d.602.4		32	33.26	odd	10
605.2.m.e.112.4		32	33.20	odd	10
605.2.m.e.233.4		32	165.53	even	20
605.2.m.e.457.4		32	33.32	even	2
605.2.m.e.578.4		32	165.98	odd	4
880.2.cm.a.17.1		32	12.11	even	2
880.2.cm.a.193.1		32	60.23	odd	4
880.2.cm.a.497.1		32	132.35	odd	10
880.2.cm.a.673.1		32	660.563	even	20

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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.25897 + 1.15100i) q^{2} +(2.60258 + 3.58214i) q^{4} +(0.867371 + 2.06099i) q^{5} +(0.282837 - 1.78576i) q^{7} +(0.962874 + 6.07934i) q^{8} +O(q^{10})\)	\(q+(2.25897 + 1.15100i) q^{2} +(2.60258 + 3.58214i) q^{4} +(0.867371 + 2.06099i) q^{5} +(0.282837 - 1.78576i) q^{7} +(0.962874 + 6.07934i) q^{8} +(-0.412838 + 5.65406i) q^{10} +(-1.72268 - 2.83415i) q^{11} +(-1.02411 + 2.00993i) q^{13} +(2.69434 - 3.70844i) q^{14} +(-2.08573 + 6.41923i) q^{16} +(-1.52724 - 2.99738i) q^{17} +(1.05647 + 0.767569i) q^{19} +(-5.12534 + 8.47092i) q^{20} +(-0.629367 - 8.38507i) q^{22} +(3.16488 - 3.16488i) q^{23} +(-3.49534 + 3.57528i) q^{25} +(-4.62687 + 3.36162i) q^{26} +(7.13295 - 3.63442i) q^{28} +(-2.37569 + 1.72604i) q^{29} +(-1.23925 - 3.81401i) q^{31} +(-3.39552 + 3.39552i) q^{32} -8.52886i q^{34} +(3.92576 - 0.965994i) q^{35} +(3.16942 + 0.501987i) q^{37} +(1.50306 + 2.94992i) q^{38} +(-11.6943 + 7.25752i) q^{40} +(-0.766287 + 1.05470i) q^{41} +(-4.55431 - 4.55431i) q^{43} +(5.66890 - 13.5469i) q^{44} +(10.7922 - 3.50658i) q^{46} +(1.20824 + 7.62854i) q^{47} +(3.54845 + 1.15296i) q^{49} +(-12.0110 + 4.05331i) q^{50} +(-9.86517 + 1.56249i) q^{52} +(-5.67482 - 2.89146i) q^{53} +(4.34694 - 6.00867i) q^{55} +11.1286 q^{56} +(-7.35329 + 1.16465i) q^{58} +(7.28135 + 10.0219i) q^{59} +(-8.85435 - 2.87695i) q^{61} +(1.59052 - 10.0421i) q^{62} +(1.25983 - 0.409344i) q^{64} +(-5.03072 - 0.367324i) q^{65} +(-2.46236 - 2.46236i) q^{67} +(6.76227 - 13.2717i) q^{68} +(9.98004 + 2.33641i) q^{70} +(2.09243 - 6.43984i) q^{71} +(9.32763 + 1.47735i) q^{73} +(6.58185 + 4.78199i) q^{74} +5.78207i q^{76} +(-5.54835 + 2.27469i) q^{77} +(-0.353860 - 1.08907i) q^{79} +(-15.0391 + 1.26918i) q^{80} +(-2.94499 + 1.50055i) q^{82} +(9.32422 - 4.75092i) q^{83} +(4.85288 - 5.74747i) q^{85} +(-5.04603 - 15.5301i) q^{86} +(15.5710 - 13.2017i) q^{88} -3.85743i q^{89} +(3.29960 + 2.39730i) q^{91} +(19.5739 + 3.10019i) q^{92} +(-6.05109 + 18.6233i) q^{94} +(-0.665600 + 2.84313i) q^{95} +(0.353228 - 0.693249i) q^{97} +(6.68878 + 6.68878i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{2} + 2 q^{5} + 10 q^{8}+O(q^{10}) \) 32 * q + 10 * q^2 + 2 * q^5 + 10 * q^8	\( 32 q + 10 q^{2} + 2 q^{5} + 10 q^{8} + 24 q^{11} - 10 q^{13} - 8 q^{16} - 16 q^{20} + 10 q^{22} + 24 q^{23} + 16 q^{25} - 20 q^{26} + 50 q^{28} - 28 q^{31} + 10 q^{35} - 8 q^{37} - 10 q^{38} - 50 q^{40} - 40 q^{41} + 60 q^{46} + 28 q^{47} + 50 q^{50} - 50 q^{52} + 24 q^{53} - 64 q^{55} + 80 q^{56} - 50 q^{58} - 60 q^{61} - 100 q^{62} - 8 q^{67} + 30 q^{68} + 30 q^{70} - 24 q^{71} + 50 q^{73} - 70 q^{77} - 98 q^{80} - 10 q^{82} - 90 q^{83} + 30 q^{85} - 100 q^{86} + 170 q^{88} + 20 q^{91} + 68 q^{92} + 40 q^{95} - 8 q^{97}+O(q^{100}) \) 32 * q + 10 * q^2 + 2 * q^5 + 10 * q^8 + 24 * q^11 - 10 * q^13 - 8 * q^16 - 16 * q^20 + 10 * q^22 + 24 * q^23 + 16 * q^25 - 20 * q^26 + 50 * q^28 - 28 * q^31 + 10 * q^35 - 8 * q^37 - 10 * q^38 - 50 * q^40 - 40 * q^41 + 60 * q^46 + 28 * q^47 + 50 * q^50 - 50 * q^52 + 24 * q^53 - 64 * q^55 + 80 * q^56 - 50 * q^58 - 60 * q^61 - 100 * q^62 - 8 * q^67 + 30 * q^68 + 30 * q^70 - 24 * q^71 + 50 * q^73 - 70 * q^77 - 98 * q^80 - 10 * q^82 - 90 * q^83 + 30 * q^85 - 100 * q^86 + 170 * q^88 + 20 * q^91 + 68 * q^92 + 40 * q^95 - 8 * q^97

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