LMFDB - Embedded newform 207.2.i.d.82.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [207,2,Mod(55,207)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("207.55"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(207, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.i (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 7 x^{19} + 24 x^{18} - 70 x^{17} + 209 x^{16} - 527 x^{15} + 1115 x^{14} - 2187 x^{13} + \cdots + 529 $ x^20 - 7x^19 + 24x^18 - 70x^17 + 209x^16 - 527x^15 + 1115x^14 - 2187x^13 + 4165x^12 - 7040x^11 + 10649x^10 - 13519x^9 + 15111x^8 - 12101x^7 + 8244x^6 - 2837x^5 + 1859x^4 - 1730x^3 + 1957x^2 - 1656*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 69)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			82.1
Root			$1.76796 - 1.13620i$ of defining polynomial
Character	$\chi$	$=$	207.82
Dual form			207.2.i.d.154.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.460828 - 0.531824i) q^{2} +(0.214155 - 1.48948i) q^{4} +(0.700489 - 1.53386i) q^{5} +(-3.11747 - 0.915371i) q^{7} +(-2.07482 + 1.33341i) q^{8} +(-1.13855 + 0.334308i) q^{10} +(1.33800 - 1.54413i) q^{11} +(-0.227131 + 0.0666916i) q^{13} +(0.949800 + 2.07977i) q^{14} +(-1.22242 - 0.358935i) q^{16} +(0.427674 + 2.97454i) q^{17} +(0.682288 - 4.74542i) q^{19} +(-2.13464 - 1.37185i) q^{20} -1.43779 q^{22} +(0.779295 - 4.73209i) q^{23} +(1.41227 + 1.62985i) q^{25} +(0.140136 + 0.0900602i) q^{26} +(-2.03105 + 4.44738i) q^{28} +(-1.01178 - 7.03706i) q^{29} +(5.64145 - 3.62554i) q^{31} +(2.42155 + 5.30245i) q^{32} +(1.38485 - 1.59820i) q^{34} +(-3.58780 + 4.14054i) q^{35} +(4.77286 + 10.4511i) q^{37} +(-2.83815 + 1.82397i) q^{38} +(0.591865 + 4.11651i) q^{40} +(-3.40729 + 7.46093i) q^{41} +(2.42547 + 1.55876i) q^{43} +(-2.01342 - 2.32361i) q^{44} +(-2.87576 + 1.76623i) q^{46} +13.2857 q^{47} +(2.99192 + 1.92279i) q^{49} +(0.215978 - 1.50216i) q^{50} +(0.0506948 + 0.352590i) q^{52} +(0.510122 + 0.149785i) q^{53} +(-1.43123 - 3.13395i) q^{55} +(7.68874 - 2.25762i) q^{56} +(-3.27622 + 3.78096i) q^{58} +(-3.30904 + 0.971623i) q^{59} +(4.08228 - 2.62352i) q^{61} +(-4.52789 - 1.32951i) q^{62} +(0.645553 - 1.41356i) q^{64} +(-0.0568072 + 0.395103i) q^{65} +(-9.77557 - 11.2816i) q^{67} +4.52211 q^{68} +3.85540 q^{70} +(8.80741 + 10.1643i) q^{71} +(-0.632363 + 4.39818i) q^{73} +(3.35868 - 7.35449i) q^{74} +(-6.92211 - 2.03251i) q^{76} +(-5.58462 + 3.58902i) q^{77} +(-2.00690 + 0.589280i) q^{79} +(-1.40685 + 1.62359i) q^{80} +(5.53808 - 1.62613i) q^{82} +(-2.67666 - 5.86108i) q^{83} +(4.86210 + 1.42764i) q^{85} +(-0.288742 - 2.00824i) q^{86} +(-0.717150 + 4.98789i) q^{88} +(-2.11082 - 1.35654i) q^{89} +0.769120 q^{91} +(-6.88149 - 2.17415i) q^{92} +(-6.12245 - 7.06568i) q^{94} +(-6.80086 - 4.37065i) q^{95} +(0.753920 - 1.65086i) q^{97} +(-0.356175 - 2.47725i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 10 q^{8} - 18 q^{10} + 16 q^{11} + 14 q^{13} + 22 q^{14} - 8 q^{16} - 11 q^{17} - 11 q^{19} - 57 q^{20} + 26 q^{22} - 4 q^{25} + 14 q^{26} - 14 q^{28} - 12 q^{29}+ \cdots - 85 q^{98}+O(q^{100}) $ 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 10 * q^8 - 18 * q^10 + 16 * q^11 + 14 * q^13 + 22 * q^14 - 8 * q^16 - 11 * q^17 - 11 * q^19 - 57 * q^20 + 26 * q^22 - 4 * q^25 + 14 * q^26 - 14 * q^28 - 12 * q^29 + 41 * q^31 + 46 * q^32 - 3 * q^34 + 26 * q^35 - 18 * q^37 - 70 * q^38 - 13 * q^40 - 10 * q^43 + 3 * q^44 - 24 * q^46 - 18 * q^47 - 10 * q^49 - 33 * q^50 + 61 * q^52 + 20 * q^53 - 17 * q^55 - 6 * q^56 - 37 * q^58 - 40 * q^59 - 12 * q^61 + 89 * q^62 - 2 * q^64 + 51 * q^65 - 47 * q^67 + 12 * q^68 + 32 * q^70 + 47 * q^71 + 39 * q^73 + 50 * q^74 - 39 * q^76 - 22 * q^77 - 2 * q^79 - 12 * q^80 + 26 * q^82 + 52 * q^83 + 35 * q^85 - 34 * q^86 + 30 * q^88 - 36 * q^89 + 8 * q^91 + 19 * q^92 + 21 * q^94 - 89 * q^95 - 85 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$

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 $

$2$	−0.460828	−	0.531824i	−0.325855	−	0.376056i	0.569058	−	0.822297i	$-0.307308\pi$
$2$	−0.460828	−	0.531824i	−0.325855	−	0.376056i	−0.894913	+	0.446241i	$0.852762\pi$
$3$		0			0
$3$		0			0
$4$	0.214155	−	1.48948i	0.107078	−	0.744742i
$5$	0.700489	−	1.53386i	0.313268	−	0.685962i	−0.685859	−	0.727735i	$-0.740573\pi$
$5$	0.700489	−	1.53386i	0.313268	−	0.685962i	0.999127	+	0.0417726i	$0.0133005\pi$
$6$		0			0
$7$	−3.11747	−	0.915371i	−1.17829	−	0.345978i	−0.366777	−	0.930309i	$-0.619539\pi$
$7$	−3.11747	−	0.915371i	−1.17829	−	0.345978i	−0.811515	+	0.584331i	$0.801357\pi$
$8$	−2.07482	+	1.33341i	−0.733559	+	0.471430i
$9$		0			0
$10$	−1.13855	+	0.334308i	−0.360040	+	0.105717i
$11$	1.33800	−	1.54413i	0.403422	−	0.465573i	−0.517294	−	0.855808i	$-0.673061\pi$
$11$	1.33800	−	1.54413i	0.403422	−	0.465573i	0.920716	+	0.390234i	$0.127606\pi$
$12$		0			0
$13$	−0.227131	+	0.0666916i	−0.0629947	+	0.0184969i	−0.313078	−	0.949727i	$-0.601360\pi$
$13$	−0.227131	+	0.0666916i	−0.0629947	+	0.0184969i	0.250083	+	0.968224i	$0.419542\pi$
$14$	0.949800	+	2.07977i	0.253845	+	0.555843i
$15$		0			0
$16$	−1.22242	−	0.358935i	−0.305605	−	0.0897336i
$17$	0.427674	+	2.97454i	0.103726	+	0.721431i	0.973617	+	0.228187i	$0.0732799\pi$
$17$	0.427674	+	2.97454i	0.103726	+	0.721431i	−0.869891	+	0.493244i	$0.835811\pi$
$18$		0			0
$19$	0.682288	−	4.74542i	0.156528	−	1.08867i	−0.748443	−	0.663199i	$-0.769198\pi$
$19$	0.682288	−	4.74542i	0.156528	−	1.08867i	0.904970	−	0.425474i	$-0.139893\pi$
$20$	−2.13464	−	1.37185i	−0.477321	−	0.306755i
$21$		0			0
$22$	−1.43779			−0.306539
$23$	0.779295	−	4.73209i	0.162494	−	0.986710i
$23$	0.779295	−	4.73209i	0.162494	−	0.986710i
$24$		0			0
$25$	1.41227	+	1.62985i	0.282454	+	0.325969i
$26$	0.140136	+	0.0900602i	0.0274830	+	0.0176623i
$27$		0			0
$28$	−2.03105	+	4.44738i	−0.383833	+	0.840477i
$29$	−1.01178	−	7.03706i	−0.187882	−	1.30675i	−0.837479	−	0.546470i	$-0.815971\pi$
$29$	−1.01178	−	7.03706i	−0.187882	−	1.30675i	0.649597	−	0.760279i	$-0.274938\pi$
$30$		0			0
$31$	5.64145	−	3.62554i	1.01323	−	0.651166i	0.0750062	−	0.997183i	$-0.476102\pi$
$31$	5.64145	−	3.62554i	1.01323	−	0.651166i	0.938228	+	0.346017i	$0.112466\pi$
$32$	2.42155	+	5.30245i	0.428073	+	0.937349i
$33$		0			0
$34$	1.38485	−	1.59820i	0.237499	−	0.274089i
$35$	−3.58780	+	4.14054i	−0.606449	+	0.699880i
$36$		0			0
$37$	4.77286	+	10.4511i	0.784653	+	1.71815i	0.691358	+	0.722513i	$0.257013\pi$
$37$	4.77286	+	10.4511i	0.784653	+	1.71815i	0.0932958	+	0.995638i	$0.470260\pi$
$38$	−2.83815	+	1.82397i	−0.460408	+	0.295886i
$39$		0			0
$40$	0.591865	+	4.11651i	0.0935821	+	0.650878i
$41$	−3.40729	+	7.46093i	−0.532130	+	1.16520i	0.432510	+	0.901629i	$0.357628\pi$
$41$	−3.40729	+	7.46093i	−0.532130	+	1.16520i	−0.964640	+	0.263573i	$0.915099\pi$
$42$		0			0
$43$	2.42547	+	1.55876i	0.369881	+	0.237708i	0.712355	−	0.701819i	$-0.247629\pi$
$43$	2.42547	+	1.55876i	0.369881	+	0.237708i	−0.342474	+	0.939527i	$0.611265\pi$
$44$	−2.01342	−	2.32361i	−0.303535	−	0.350298i
$45$		0			0
$46$	−2.87576	+	1.76623i	−0.424008	+	0.260417i
$47$	13.2857			1.93793			0.968963	−	0.247206i	$-0.0795125\pi$
$47$	13.2857			1.93793			0.968963	+	0.247206i	$0.0795125\pi$
$48$		0			0
$49$	2.99192	+	1.92279i	0.427417	+	0.274684i
$50$	0.215978	−	1.50216i	0.0305439	−	0.212437i
$51$		0			0
$52$	0.0506948	+	0.352590i	0.00703010	+	0.0488954i
$53$	0.510122	+	0.149785i	0.0700706	+	0.0205746i	0.316580	−	0.948566i	$-0.397465\pi$
$53$	0.510122	+	0.149785i	0.0700706	+	0.0205746i	−0.246509	+	0.969140i	$0.579284\pi$
$54$		0			0
$55$	−1.43123	−	3.13395i	−0.192986	−	0.422581i
$56$	7.68874	−	2.25762i	1.02745	−	0.301687i
$57$		0			0
$58$	−3.27622	+	3.78096i	−0.430189	+	0.496465i
$59$	−3.30904	+	0.971623i	−0.430801	+	0.126495i	−0.489942	−	0.871755i	$-0.662982\pi$
$59$	−3.30904	+	0.971623i	−0.430801	+	0.126495i	0.0591410	+	0.998250i	$0.481164\pi$
$60$		0			0
$61$	4.08228	−	2.62352i	0.522683	−	0.335908i	−0.252550	−	0.967584i	$-0.581269\pi$
$61$	4.08228	−	2.62352i	0.522683	−	0.335908i	0.775232	+	0.631676i	$0.217633\pi$
$62$	−4.52789	−	1.32951i	−0.575042	−	0.168848i
$63$		0			0
$64$	0.645553	−	1.41356i	0.0806941	−	0.176696i
$65$	−0.0568072	+	0.395103i	−0.00704607	+	0.0490065i
$66$		0			0
$67$	−9.77557	−	11.2816i	−1.19428	−	1.37827i	−0.907383	−	0.420305i	$-0.861923\pi$
$67$	−9.77557	−	11.2816i	−1.19428	−	1.37827i	−0.286893	−	0.957963i	$-0.592623\pi$
$68$	4.52211			0.548387
$69$		0			0
$70$	3.85540			0.460808
$71$	8.80741	+	10.1643i	1.04525	+	1.20628i	0.978013	+	0.208543i	$0.0668720\pi$
$71$	8.80741	+	10.1643i	1.04525	+	1.20628i	0.0672342	+	0.997737i	$0.478583\pi$
$72$		0			0
$73$	−0.632363	+	4.39818i	−0.0740124	+	0.514768i	0.918766	+	0.394803i	$0.129187\pi$
$73$	−0.632363	+	4.39818i	−0.0740124	+	0.514768i	−0.992778	+	0.119965i	$0.961722\pi$
$74$	3.35868	−	7.35449i	0.390439	−	0.854942i
$75$		0			0
$76$	−6.92211	−	2.03251i	−0.794020	−	0.233145i
$77$	−5.58462	+	3.58902i	−0.636426	+	0.409006i
$78$		0			0
$79$	−2.00690	+	0.589280i	−0.225794	+	0.0662992i	−0.392673	−	0.919678i	$-0.628449\pi$
$79$	−2.00690	+	0.589280i	−0.225794	+	0.0662992i	0.166878	+	0.985977i	$0.446631\pi$
$80$	−1.40685	+	1.62359i	−0.157290	+	0.181523i
$81$		0			0
$82$	5.53808	−	1.62613i	0.611579	−	0.179576i
$83$	−2.67666	−	5.86108i	−0.293802	−	0.643337i	0.703957	−	0.710242i	$-0.251415\pi$
$83$	−2.67666	−	5.86108i	−0.293802	−	0.643337i	−0.997759	+	0.0669055i	$0.978687\pi$
$84$		0			0
$85$	4.86210	+	1.42764i	0.527368	+	0.154849i
$86$	−0.288742	−	2.00824i	−0.0311358	−	0.216555i
$87$		0			0
$88$	−0.717150	+	4.98789i	−0.0764485	+	0.531711i
$89$	−2.11082	−	1.35654i	−0.223746	−	0.143793i	0.423966	−	0.905678i	$-0.360638\pi$
$89$	−2.11082	−	1.35654i	−0.223746	−	0.143793i	−0.647712	+	0.761885i	$0.724274\pi$
$90$		0			0
$91$	0.769120			0.0806257
$92$	−6.88149	−	2.17415i	−0.717444	−	0.226671i
$93$		0			0
$94$	−6.12245	−	7.06568i	−0.631482	−	0.728769i
$95$	−6.80086	−	4.37065i	−0.697754	−	0.448419i
$96$		0			0
$97$	0.753920	−	1.65086i	0.0765490	−	0.167619i	−0.867488	−	0.497458i	$-0.834267\pi$
$97$	0.753920	−	1.65086i	0.0765490	−	0.167619i	0.944037	+	0.329839i	$0.106994\pi$
$98$	−0.356175	−	2.47725i	−0.0359791	−	0.250240i
$99$		0			0
$100$	2.73007	−	1.75451i	0.273007	−	0.175451i
$101$	0.996737	+	2.18255i	0.0991791	+	0.217172i	0.952717	−	0.303859i	$-0.0982751\pi$
$101$	0.996737	+	2.18255i	0.0991791	+	0.217172i	−0.853538	+	0.521030i	$0.825548\pi$
$102$		0			0
$103$	−2.69154	+	3.10620i	−0.265205	+	0.306063i	−0.872696	−	0.488263i	$-0.837631\pi$
$103$	−2.69154	+	3.10620i	−0.265205	+	0.306063i	0.607491	+	0.794326i	$0.292176\pi$
$104$	0.382328	−	0.441230i	0.0374904	−	0.0432662i
$105$		0			0
$106$	−0.155419	−	0.340320i	−0.0150956	−	0.0330548i
$107$	−11.3204	+	7.27515i	−1.09438	+	0.703315i	−0.957835	−	0.287319i	$-0.907236\pi$
$107$	−11.3204	+	7.27515i	−1.09438	+	0.703315i	−0.136545	+	0.990634i	$0.543600\pi$
$108$		0			0
$109$	−2.25241	−	15.6658i	−0.215741	−	1.50051i	−0.753518	−	0.657427i	$-0.771645\pi$
$109$	−2.25241	−	15.6658i	−0.215741	−	1.50051i	0.537777	−	0.843087i	$-0.319264\pi$
$110$	−1.00716	+	2.20537i	−0.0960289	+	0.210274i
$111$		0			0
$112$	3.48229	+	2.23793i	0.329046	+	0.211465i
$113$	−8.47022	−	9.77515i	−0.796811	−	0.919569i	0.201391	−	0.979511i	$-0.435454\pi$
$113$	−8.47022	−	9.77515i	−0.796811	−	0.919569i	−0.998202	+	0.0599420i	$0.980908\pi$
$114$		0			0
$115$	−6.71247	−	4.51011i	−0.625941	−	0.420570i
$116$	−10.6983			−0.993309
$117$		0			0
$118$	2.04163	+	1.31208i	0.187948	+	0.120787i
$119$	1.38955	−	9.66450i	0.127379	−	0.885943i
$120$		0			0
$121$	0.971358	+	6.75594i	0.0883053	+	0.614177i
$122$	−3.27648	−	0.962062i	−0.296639	−	0.0871010i
$123$		0			0
$124$	−4.19204	−	9.17928i	−0.376456	−	0.824324i
$125$	11.5789	−	3.39987i	1.03565	−	0.304094i
$126$		0			0
$127$	−3.48534	+	4.02229i	−0.309274	+	0.356921i	−0.889014	−	0.457881i	$-0.848609\pi$
$127$	−3.48534	+	4.02229i	−0.309274	+	0.356921i	0.579740	+	0.814802i	$0.303154\pi$
$128$	10.1369	−	2.97647i	0.895987	−	0.263086i
$129$		0			0
$130$	0.236304	−	0.151863i	0.0207252	−	0.0133193i
$131$	4.35715	+	1.27937i	0.380686	+	0.111779i	0.466476	−	0.884534i	$-0.345523\pi$
$131$	4.35715	+	1.27937i	0.380686	+	0.111779i	−0.0857904	+	0.996313i	$0.527342\pi$
$132$		0			0
$133$	−6.47083	+	14.1691i	−0.561092	+	1.22862i
$134$	−1.49497	+	10.3978i	−0.129146	+	0.898230i
$135$		0			0
$136$	−4.85361	−	5.60136i	−0.416194	−	0.480313i
$137$	16.4974			1.40947			0.704734	−	0.709471i	$-0.251066\pi$
$137$	16.4974			1.40947			0.704734	+	0.709471i	$0.251066\pi$
$138$		0			0
$139$	3.46582			0.293967			0.146984	−	0.989139i	$-0.453044\pi$
$139$	3.46582			0.293967			0.146984	+	0.989139i	$0.453044\pi$
$140$	5.39893	+	6.23069i	0.456292	+	0.526590i
$141$		0			0
$142$	1.34691	−	9.36799i	0.113030	−	0.786144i
$143$	−0.200920	+	0.439953i	−0.0168018	+	0.0367907i
$144$		0			0
$145$	−11.5026	−	3.37746i	−0.955238	−	0.280483i
$146$	2.63047	−	1.69050i	0.217699	−	0.139907i
$147$		0			0
$148$	16.5889	−	4.87094i	1.36360	−	0.400389i
$149$	2.00991	−	2.31956i	0.164658	−	0.190026i	−0.667424	−	0.744678i	$-0.732603\pi$
$149$	2.00991	−	2.31956i	0.164658	−	0.190026i	0.832082	+	0.554652i	$0.187149\pi$
$150$		0			0
$151$	−1.81890	+	0.534078i	−0.148020	+	0.0434627i	−0.354903	−	0.934903i	$-0.615486\pi$
$151$	−1.81890	+	0.534078i	−0.148020	+	0.0434627i	0.206883	+	0.978366i	$0.433668\pi$
$152$	4.91194	+	10.7557i	0.398411	+	0.872399i
$153$		0			0
$154$	4.48228	+	1.31611i	0.361192	+	0.106056i
$155$	−1.60929	−	11.1928i	−0.129261	−	0.899030i
$156$		0			0
$157$	−0.307090	+	2.13586i	−0.0245085	+	0.170460i	−0.998399	−	0.0565561i	$-0.981988\pi$
$157$	−0.307090	+	2.13586i	−0.0245085	+	0.170460i	0.973891	+	0.227016i	$0.0728971\pi$
$158$	1.23823	+	0.795763i	0.0985084	+	0.0633075i
$159$		0			0
$160$	9.82947			0.777088
$161$	−6.76105	+	14.0388i	−0.532845	+	1.10641i
$162$		0			0
$163$	7.92140	+	9.14179i	0.620452	+	0.716040i	0.975793	−	0.218697i	$-0.0701806\pi$
$163$	7.92140	+	9.14179i	0.620452	+	0.716040i	−0.355341	+	0.934737i	$0.615635\pi$
$164$	10.3832	+	6.67291i	0.810795	+	0.521067i
$165$		0			0
$166$	−1.88358	+	4.12446i	−0.146194	+	0.320120i
$167$	−1.87408	−	13.0345i	−0.145021	−	1.00864i	−0.924219	−	0.381864i	$-0.875282\pi$
$167$	−1.87408	−	13.0345i	−0.145021	−	1.00864i	0.779198	−	0.626778i	$-0.215627\pi$
$168$		0			0
$169$	−10.8892	+	6.99804i	−0.837627	+	0.538310i
$170$	−1.48134	−	3.24368i	−0.113613	−	0.248779i
$171$		0			0
$172$	2.84117	−	3.27889i	0.216637	−	0.250013i
$173$	−11.5528	+	13.3327i	−0.878346	+	1.01367i	0.121432	+	0.992600i	$0.461251\pi$
$173$	−11.5528	+	13.3327i	−0.878346	+	1.01367i	−0.999778	+	0.0210657i	$0.993294\pi$
$174$		0			0
$175$	−2.91079	−	6.37374i	−0.220035	−	0.481809i
$176$	−2.18984	+	1.40732i	−0.165065	+	0.106081i
$177$		0			0
$178$	0.251283	+	1.74771i	0.0188345	+	0.130997i
$179$	−4.47341	+	9.79541i	−0.334359	+	0.732143i	−0.999899	−	0.0142186i	$-0.995474\pi$
$179$	−4.47341	+	9.79541i	−0.334359	+	0.732143i	0.665540	+	0.746362i	$0.268201\pi$
$180$		0			0
$181$	−1.20016	−	0.771298i	−0.0892074	−	0.0573301i	0.495277	−	0.868735i	$-0.335067\pi$
$181$	−1.20016	−	0.771298i	−0.0892074	−	0.0573301i	−0.584484	+	0.811405i	$0.698703\pi$
$182$	−0.354432	−	0.409037i	−0.0262723	−	0.0303198i
$183$		0			0
$184$	4.69290	+	10.8574i	0.345965	+	0.800415i
$185$	19.3738			1.42439
$186$		0			0
$187$	5.16531	+	3.31954i	0.377725	+	0.242749i
$188$	2.84522	−	19.7889i	0.207509	−	1.44325i
$189$		0			0
$190$	0.809613	+	5.63098i	0.0587355	+	0.408514i
$191$	−13.3309	−	3.91430i	−0.964590	−	0.283229i	−0.238741	−	0.971083i	$-0.576735\pi$
$191$	−13.3309	−	3.91430i	−0.964590	−	0.283229i	−0.725849	+	0.687854i	$0.758553\pi$
$192$		0			0
$193$	3.36305	+	7.36404i	0.242077	+	0.530075i	0.991203	−	0.132353i	$-0.0422532\pi$
$193$	3.36305	+	7.36404i	0.242077	+	0.530075i	−0.749125	+	0.662428i	$0.769526\pi$
$194$	−1.22539	+	0.359808i	−0.0879780	+	0.0258327i
$195$		0			0
$196$	3.50470	−	4.04464i	0.250336	−	0.288903i
$197$	1.70543	−	0.500760i	0.121507	−	0.0356777i	−0.220414	−	0.975406i	$-0.570741\pi$
$197$	1.70543	−	0.500760i	0.121507	−	0.0356777i	0.341921	+	0.939729i	$0.388923\pi$
$198$		0			0
$199$	5.53721	−	3.55855i	0.392522	−	0.252259i	−0.329461	−	0.944169i	$-0.606867\pi$
$199$	5.53721	−	3.55855i	0.392522	−	0.252259i	0.721983	+	0.691910i	$0.243231\pi$
$200$	−5.10345	−	1.49851i	−0.360868	−	0.105960i
$201$		0			0
$202$	0.701408	−	1.53587i	0.0493509	−	0.108063i
$203$	−3.28734	+	22.8639i	−0.230726	+	1.60473i
$204$		0			0
$205$	9.05724	+	10.4526i	0.632585	+	0.730042i
$206$	2.89229			0.201515
$207$		0			0
$208$	0.301587			0.0209113
$209$	−6.41466	−	7.40291i	−0.443711	−	0.512070i
$210$		0			0
$211$	−1.94389	+	13.5201i	−0.133823	+	0.930760i	0.806683	+	0.590984i	$0.201260\pi$
$211$	−1.94389	+	13.5201i	−0.133823	+	0.930760i	−0.940506	+	0.339776i	$0.889649\pi$
$212$	0.332348	−	0.727741i	0.0228258	−	0.0499814i
$213$		0			0
$214$	9.08584	+	2.66784i	0.621095	+	0.182370i
$215$	4.08993	−	2.62844i	0.278931	−	0.179258i
$216$		0			0
$217$	−20.9057	+	6.13848i	−1.41917	+	0.416707i
$218$	−7.29349	+	8.41714i	−0.493978	+	0.570081i
$219$		0			0
$220$	−4.97447	+	1.46064i	−0.335379	+	0.0984761i
$221$	−0.295514	−	0.647086i	−0.0198785	−	0.0435277i
$222$		0			0
$223$	−10.9392	−	3.21204i	−0.732542	−	0.215094i	−0.105874	−	0.994380i	$-0.533764\pi$
$223$	−10.9392	−	3.21204i	−0.732542	−	0.215094i	−0.626669	+	0.779286i	$0.715582\pi$
$224$	−2.69539	−	18.7468i	−0.180093	−	1.25257i
$225$		0			0
$226$	−1.29535	+	9.00933i	−0.0861651	+	0.599292i
$227$	1.33704	+	0.859266i	0.0887427	+	0.0570315i	0.584260	−	0.811567i	$-0.301385\pi$
$227$	1.33704	+	0.859266i	0.0887427	+	0.0570315i	−0.495517	+	0.868598i	$0.665021\pi$
$228$		0			0
$229$	26.2296			1.73330			0.866650	−	0.498916i	$-0.166268\pi$
$229$	26.2296			1.73330			0.866650	+	0.498916i	$0.166268\pi$
$230$	0.694711	+	5.64824i	0.0458079	+	0.372434i
$231$		0			0
$232$	11.4825	+	13.2515i	0.753863	+	0.870005i
$233$	8.36970	+	5.37888i	0.548317	+	0.352382i	0.785284	−	0.619136i	$-0.212517\pi$
$233$	8.36970	+	5.37888i	0.548317	+	0.352382i	−0.236967	+	0.971518i	$0.576153\pi$
$234$		0			0
$235$	9.30653	−	20.3785i	0.607091	−	1.32934i
$236$	0.738567	+	5.13685i	0.0480766	+	0.334380i
$237$		0			0
$238$	−5.78015	+	3.71468i	−0.374672	+	0.240787i
$239$	−4.79659	−	10.5031i	−0.310266	−	0.679387i	0.688691	−	0.725055i	$-0.258186\pi$
$239$	−4.79659	−	10.5031i	−0.310266	−	0.679387i	−0.998957	+	0.0456678i	$0.985458\pi$
$240$		0			0
$241$	3.59998	−	4.15459i	0.231895	−	0.267621i	−0.627862	−	0.778325i	$-0.716070\pi$
$241$	3.59998	−	4.15459i	0.231895	−	0.267621i	0.859757	+	0.510704i	$0.170615\pi$
$242$	3.14534	−	3.62992i	0.202190	−	0.233340i
$243$		0			0
$244$	−3.03345	−	6.64233i	−0.194197	−	0.425232i
$245$	5.04510	−	3.24229i	0.322319	−	0.207142i
$246$		0			0
$247$	0.161511	+	1.12333i	0.0102767	+	0.0714760i
$248$	−6.87068	+	15.0447i	−0.436288	+	0.955338i
$249$		0			0
$250$	−7.14402	−	4.59118i	−0.451828	−	0.290372i
$251$	−13.4416	−	15.5124i	−0.848425	−	0.979135i	0.151532	−	0.988452i	$-0.451579\pi$
$251$	−13.4416	−	15.5124i	−0.848425	−	0.979135i	−0.999957	+	0.00931785i	$0.997034\pi$
$252$		0			0
$253$	−6.26428	−	7.53487i	−0.393832	−	0.473713i
$254$	3.74529			0.235001
$255$		0			0
$256$	−8.86896	−	5.69973i	−0.554310	−	0.356233i
$257$	−2.47969	+	17.2466i	−0.154679	+	1.07581i	0.753566	+	0.657373i	$0.228332\pi$
$257$	−2.47969	+	17.2466i	−0.154679	+	1.07581i	−0.908244	+	0.418441i	$0.862577\pi$
$258$		0			0
$259$	−5.31260	−	36.9499i	−0.330109	−	2.29596i
$260$	0.576334	+	0.169227i	0.0357427	+	0.0104950i
$261$		0			0
$262$	−1.32749	−	2.90681i	−0.0820129	−	0.179583i
$263$	−18.4511	+	5.41773i	−1.13774	+	0.334072i	−0.795747	−	0.605630i	$-0.792921\pi$
$263$	−18.4511	+	5.41773i	−1.13774	+	0.334072i	−0.341997	+	0.939701i	$0.611103\pi$
$264$		0			0
$265$	0.587084	−	0.677531i	0.0360643	−	0.0416204i
$266$	10.5174	−	3.08820i	0.644865	−	0.189349i
$267$		0			0
$268$	−18.8973	+	12.1445i	−1.15433	+	0.741846i
$269$	23.0209	+	6.75956i	1.40361	+	0.412138i	0.893923	−	0.448221i	$-0.147942\pi$
$269$	23.0209	+	6.75956i	1.40361	+	0.412138i	0.509689	+	0.860359i	$0.329760\pi$
$270$		0			0
$271$	−9.38523	+	20.5508i	−0.570112	+	1.24837i	0.376626	+	0.926365i	$0.377084\pi$
$271$	−9.38523	+	20.5508i	−0.570112	+	1.24837i	−0.946738	+	0.322005i	$0.895643\pi$
$272$	0.544868	−	3.78964i	0.0330374	−	0.229780i
$273$		0			0
$274$	−7.60247	−	8.77372i	−0.459282	−	0.530040i
$275$	4.40631			0.265711
$276$		0			0
$277$	2.08852			0.125487			0.0627435	−	0.998030i	$-0.480015\pi$
$277$	2.08852			0.125487			0.0627435	+	0.998030i	$0.480015\pi$
$278$	−1.59715	−	1.84321i	−0.0957907	−	0.110548i
$279$		0			0
$280$	1.92302	−	13.3749i	0.114922	−	0.799302i
$281$	−8.14441	+	17.8338i	−0.485855	+	1.06387i	0.494958	+	0.868917i	$0.335184\pi$
$281$	−8.14441	+	17.8338i	−0.485855	+	1.06387i	−0.980812	+	0.194956i	$0.937544\pi$
$282$		0			0
$283$	−4.82108	−	1.41560i	−0.286583	−	0.0841484i	0.135282	−	0.990807i	$-0.456806\pi$
$283$	−4.82108	−	1.41560i	−0.286583	−	0.0841484i	−0.421865	+	0.906659i	$0.638624\pi$
$284$	17.0257	−	10.9418i	1.01029	−	0.649274i
$285$		0			0
$286$	0.326567	−	0.0958888i	0.0193103	−	0.00567002i
$287$	17.4516	−	20.1403i	1.03014	−	1.18884i
$288$		0			0
$289$	7.64642	−	2.24519i	0.449789	−	0.132070i
$290$	3.50450	+	7.67378i	0.205791	+	0.450620i
$291$		0			0
$292$	6.41559	+	1.88379i	0.375444	+	0.110240i
$293$	0.420981	+	2.92798i	0.0245940	+	0.171055i	0.998416	−	0.0562552i	$-0.0179161\pi$
$293$	0.420981	+	2.92798i	0.0245940	+	0.171055i	−0.973822	+	0.227310i	$0.927007\pi$
$294$		0			0
$295$	−0.827619	+	5.75621i	−0.0481858	+	0.335140i
$296$	−23.8384	−	15.3200i	−1.38558	−	0.890457i
$297$		0			0
$298$	−2.15982			−0.125115
$299$	0.138589	+	1.12678i	0.00801481	+	0.0651631i
$300$		0			0
$301$	−6.13449	−	7.07958i	−0.353586	−	0.408060i
$302$	1.12224	+	0.721218i	0.0645775	+	0.0415014i
$303$		0			0
$304$	−2.53734	+	5.55599i	−0.145526	+	0.318658i
$305$	−1.16452	−	8.09939i	−0.0666800	−	0.463770i
$306$		0			0
$307$	19.9296	−	12.8079i	1.13744	−	0.730988i	0.170340	−	0.985385i	$-0.445513\pi$
$307$	19.9296	−	12.8079i	1.13744	−	0.730988i	0.967100	+	0.254397i	$0.0818770\pi$
$308$	4.14981	+	9.08681i	0.236457	+	0.517769i
$309$		0			0
$310$	−5.21101	+	6.01383i	−0.295966	+	0.341563i
$311$	17.1662	−	19.8109i	0.973409	−	1.12337i	−0.0189294	−	0.999821i	$-0.506026\pi$
$311$	17.1662	−	19.8109i	0.973409	−	1.12337i	0.992338	−	0.123553i	$-0.0394288\pi$
$312$		0			0
$313$	−2.75232	−	6.02675i	−0.155570	−	0.340652i	0.815758	−	0.578393i	$-0.196320\pi$
$313$	−2.75232	−	6.02675i	−0.155570	−	0.340652i	−0.971328	+	0.237742i	$0.923593\pi$
$314$	1.27742	−	0.820947i	0.0720889	−	0.0463287i
$315$		0			0
$316$	0.447934	+	3.11545i	0.0251983	+	0.175258i
$317$	−4.61225	+	10.0994i	−0.259050	+	0.567240i	−0.993811	−	0.111086i	$-0.964567\pi$
$317$	−4.61225	+	10.0994i	−0.259050	+	0.567240i	0.734761	+	0.678326i	$0.237294\pi$
$318$		0			0
$319$	−12.2199	−	7.85326i	−0.684183	−	0.439698i
$320$	−1.71600	−	1.98037i	−0.0959275	−	0.110706i
$321$		0			0
$322$	10.5819	−	2.87379i	0.589703	−	0.160150i
$323$	14.4072			0.801639
$324$		0			0
$325$	−0.429467	−	0.276002i	−0.0238225	−	0.0153098i
$326$	1.21142	−	8.42559i	0.0670942	−	0.466650i
$327$		0			0
$328$	−2.87893	−	20.0234i	−0.158962	−	1.10561i
$329$	−41.4179	−	12.1614i	−2.28344	−	0.670479i
$330$		0			0
$331$	9.32901	+	20.4277i	0.512769	+	1.12281i	0.972105	+	0.234545i	$0.0753599\pi$
$331$	9.32901	+	20.4277i	0.512769	+	1.12281i	−0.459337	+	0.888262i	$0.651913\pi$
$332$	−9.30320	+	2.73167i	−0.510580	+	0.149920i
$333$		0			0
$334$	−6.06844	+	7.00336i	−0.332050	+	0.383207i
$335$	−24.1521	+	7.09169i	−1.31957	+	0.387460i
$336$		0			0
$337$	−29.3824	+	18.8830i	−1.60056	+	1.02862i	−0.633615	+	0.773648i	$0.718430\pi$
$337$	−29.3824	+	18.8830i	−1.60056	+	1.02862i	−0.966949	+	0.254972i	$0.917934\pi$
$338$	8.73975	+	2.56622i	0.475380	+	0.139584i
$339$		0			0
$340$	3.16769	−	6.93628i	0.171792	−	0.376173i
$341$	1.94994	−	13.5621i	0.105595	−	0.734430i
$342$		0			0
$343$	7.32670	+	8.45547i	0.395605	+	0.456552i
$344$	−7.11087			−0.383393
$345$		0			0
$346$	12.4145			0.667409
$347$	−6.72501	−	7.76108i	−0.361018	−	0.416637i	0.545963	−	0.837809i	$-0.316164\pi$
$347$	−6.72501	−	7.76108i	−0.361018	−	0.416637i	−0.906980	+	0.421173i	$0.861619\pi$
$348$		0			0
$349$	4.30303	−	29.9282i	0.230336	−	1.60202i	−0.466319	−	0.884616i	$-0.654420\pi$
$349$	4.30303	−	29.9282i	0.230336	−	1.60202i	0.696655	−	0.717406i	$-0.254671\pi$
$350$	−2.04833	+	4.48523i	−0.109488	+	0.239745i
$351$		0			0
$352$	11.4277	+	3.35548i	0.609099	+	0.178848i
$353$	2.65533	−	1.70648i	0.141329	−	0.0908266i	−0.468066	−	0.883694i	$-0.655049\pi$
$353$	2.65533	−	1.70648i	0.141329	−	0.0908266i	0.609395	+	0.792867i	$0.291413\pi$
$354$		0			0
$355$	21.7601	−	6.38934i	1.15491	−	0.339111i
$356$	−2.47259	+	2.85352i	−0.131047	+	0.151236i
$357$		0			0
$358$	7.27091	−	2.13493i	0.384280	−	0.112835i
$359$	9.08412	+	19.8915i	0.479442	+	1.04983i	0.982617	+	0.185646i	$0.0594378\pi$
$359$	9.08412	+	19.8915i	0.479442	+	1.04983i	−0.503175	+	0.864184i	$0.667835\pi$
$360$		0			0
$361$	−3.82312	−	1.12257i	−0.201217	−	0.0590826i
$362$	0.142874	+	0.993711i	0.00750930	+	0.0522283i
$363$		0			0
$364$	0.164711	−	1.14559i	0.00863322	−	0.0600453i
$365$	6.30322	+	4.05083i	0.329925	+	0.212030i
$366$		0			0
$367$	−8.13884			−0.424844			−0.212422	−	0.977178i	$-0.568135\pi$
$367$	−8.13884			−0.424844			−0.212422	+	0.977178i	$0.568135\pi$
$368$	−2.65114	+	5.50488i	−0.138200	+	0.286962i
$369$		0			0
$370$	−8.92801	−	10.3035i	−0.464145	−	0.535652i
$371$	−1.45318	−	0.933901i	−0.0754453	−	0.0484857i
$372$		0			0
$373$	1.83693	−	4.02231i	0.0951124	−	0.208267i	−0.856096	−	0.516818i	$-0.827117\pi$
$373$	1.83693	−	4.02231i	0.0951124	−	0.208267i	0.951208	+	0.308550i	$0.0998438\pi$
$374$	−0.614907	−	4.27677i	−0.0317961	−	0.221147i
$375$		0			0
$376$	−27.5655	+	17.7153i	−1.42158	+	0.913596i
$377$	0.699118	+	1.53086i	0.0360064	+	0.0788430i
$378$		0			0
$379$	−6.90798	+	7.97223i	−0.354839	+	0.409506i	−0.904904	−	0.425616i	$-0.860057\pi$
$379$	−6.90798	+	7.97223i	−0.354839	+	0.409506i	0.550065	+	0.835122i	$0.314603\pi$
$380$	−7.96645	+	9.19378i	−0.408670	+	0.471631i
$381$		0			0
$382$	4.06153	+	8.89351i	0.207806	+	0.455032i
$383$	4.54448	−	2.92056i	0.232212	−	0.149234i	−0.419361	−	0.907820i	$-0.637746\pi$
$383$	4.54448	−	2.92056i	0.232212	−	0.149234i	0.651573	+	0.758586i	$0.274109\pi$
$384$		0			0
$385$	1.59308	+	11.0801i	0.0811906	+	0.564693i
$386$	2.36659	−	5.18211i	0.120456	−	0.263762i
$387$		0			0
$388$	−2.29747	−	1.47649i	−0.116636	−	0.0749575i
$389$	1.04941	+	1.21108i	0.0532070	+	0.0614042i	0.781729	−	0.623618i	$-0.214338\pi$
$389$	1.04941	+	1.21108i	0.0532070	+	0.0614042i	−0.728522	+	0.685022i	$0.759792\pi$
$390$		0			0
$391$	14.4091	+	0.294249i	0.728698	+	0.0148808i
$392$	−8.77156			−0.443030
$393$		0			0
$394$	−1.05223	−	0.676225i	−0.0530104	−	0.0340677i
$395$	−0.501943	+	3.49109i	−0.0252555	+	0.175656i
$396$		0			0
$397$	0.992549	+	6.90333i	0.0498146	+	0.346468i	0.999452	+	0.0331158i	$0.0105430\pi$
$397$	0.992549	+	6.90333i	0.0498146	+	0.346468i	−0.949637	+	0.313352i	$0.898548\pi$
$398$	−4.44422	−	1.30494i	−0.222769	−	0.0654108i
$399$		0			0
$400$	−1.14138	−	2.49927i	−0.0570688	−	0.124963i
$401$	−0.916430	+	0.269088i	−0.0457643	+	0.0134376i	−0.304535	−	0.952501i	$-0.598501\pi$
$401$	−0.916430	+	0.269088i	−0.0457643	+	0.0134376i	0.258770	+	0.965939i	$0.416683\pi$
$402$		0			0
$403$	−1.03955	+	1.19971i	−0.0517839	+	0.0597618i
$404$	3.46433	−	1.01722i	0.172357	−	0.0506085i
$405$		0			0
$406$	13.6745	−	8.78806i	0.678654	−	0.436144i
$407$	22.5240	+	6.61363i	1.11647	+	0.327826i
$408$		0			0
$409$	6.47056	−	14.1686i	0.319949	−	0.700590i	−0.679504	−	0.733672i	$-0.737805\pi$
$409$	6.47056	−	14.1686i	0.319949	−	0.700590i	0.999453	+	0.0330820i	$0.0105323\pi$
$410$	1.38512	−	9.63371i	0.0684061	−	0.475775i
$411$		0			0
$412$	4.05023	+	4.67421i	0.199540	+	0.230282i
$413$	11.2052			0.551373
$414$		0			0
$415$	−10.8650			−0.533344
$416$	−0.903636	−	1.04285i	−0.0443044	−	0.0511300i
$417$		0			0
$418$	−0.980990	+	6.82294i	−0.0479818	+	0.333721i
$419$	12.6482	−	27.6957i	0.617905	−	1.35302i	−0.299128	−	0.954213i	$-0.596696\pi$
$419$	12.6482	−	27.6957i	0.617905	−	1.35302i	0.917033	−	0.398811i	$-0.130577\pi$
$420$		0			0
$421$	23.2692	+	6.83246i	1.13407	+	0.332993i	0.794307	−	0.607517i	$-0.207834\pi$
$421$	23.2692	+	6.83246i	1.13407	+	0.332993i	0.339765	+	0.940510i	$0.389652\pi$
$422$	8.08610	−	5.19662i	0.393625	−	0.252968i
$423$		0			0
$424$	−1.25813	+	0.369422i	−0.0611004	+	0.0179407i
$425$	−4.24404	+	4.89789i	−0.205866	+	0.237583i
$426$		0			0
$427$	−15.1279	+	4.44194i	−0.732089	+	0.214961i
$428$	8.41190	+	18.4195i	0.406605	+	0.890340i
$429$		0			0
$430$	−3.28262	−	0.963865i	−0.158302	−	0.0464817i
$431$	1.38617	+	9.64102i	0.0667694	+	0.464392i	0.995586	+	0.0938521i	$0.0299181\pi$
$431$	1.38617	+	9.64102i	0.0667694	+	0.464392i	−0.928817	+	0.370539i	$0.879173\pi$
$432$		0			0
$433$	0.888425	−	6.17913i	0.0426950	−	0.296950i	−0.957275	−	0.289180i	$-0.906617\pi$
$433$	0.888425	−	6.17913i	0.0426950	−	0.296950i	0.999970	−	0.00777039i	$-0.00247342\pi$
$434$	12.8986	+	8.28940i	0.619150	+	0.397904i
$435$		0			0
$436$	−23.8164			−1.14060
$437$	−21.9241	−	6.92673i	−1.04877	−	0.331351i
$438$		0			0
$439$	10.9508	+	12.6379i	0.522655	+	0.603176i	0.954294	−	0.298871i	$-0.0966099\pi$
$439$	10.9508	+	12.6379i	0.522655	+	0.603176i	−0.431639	+	0.902047i	$0.642064\pi$
$440$	7.14836	+	4.59397i	0.340785	+	0.219009i
$441$		0			0
$442$	−0.207955	+	0.455357i	−0.00989140	+	0.0216591i
$443$	4.32524	+	30.0827i	0.205498	+	1.42927i	0.787615	+	0.616168i	$0.211316\pi$
$443$	4.32524	+	30.0827i	0.205498	+	1.42927i	−0.582117	+	0.813105i	$0.697775\pi$
$444$		0			0
$445$	−3.55934	+	2.28745i	−0.168729	+	0.108436i
$446$	3.33285	+	7.29792i	0.157815	+	0.345567i
$447$		0			0
$448$	−3.30643	+	3.81582i	−0.156214	+	0.180280i
$449$	11.2761	−	13.0133i	0.532153	−	0.614137i	−0.424478	−	0.905438i	$-0.639543\pi$
$449$	11.2761	−	13.0133i	0.532153	−	0.614137i	0.956632	+	0.291301i	$0.0940880\pi$
$450$		0			0
$451$	6.96171	+	15.2440i	0.327814	+	0.717813i
$452$	−16.3739	+	10.5228i	−0.770162	+	0.494953i
$453$		0			0
$454$	−0.159169	−	1.10705i	−0.00747018	−	0.0519562i
$455$	0.538760	−	1.17972i	0.0252575	−	0.0553062i
$456$		0			0
$457$	−9.70917	−	6.23971i	−0.454176	−	0.291881i	0.293483	−	0.955964i	$-0.405186\pi$
$457$	−9.70917	−	6.23971i	−0.454176	−	0.291881i	−0.747659	+	0.664083i	$0.768822\pi$
$458$	−12.0873	−	13.9495i	−0.564804	−	0.651819i
$459$		0			0
$460$	−8.15524	+	9.03225i	−0.380240	+	0.421131i
$461$	36.3205			1.69162			0.845808	−	0.533488i	$-0.179119\pi$
$461$	36.3205			1.69162			0.845808	+	0.533488i	$0.179119\pi$
$462$		0			0
$463$	−12.4043	−	7.97178i	−0.576478	−	0.370480i	0.219677	−	0.975573i	$-0.429500\pi$
$463$	−12.4043	−	7.97178i	−0.576478	−	0.370480i	−0.796155	+	0.605093i	$0.793136\pi$
$464$	−1.28903	+	8.96539i	−0.0598417	+	0.416208i
$465$		0			0
$466$	−0.996376	−	6.92995i	−0.0461562	−	0.321024i
$467$	−7.78126	−	2.28478i	−0.360074	−	0.105727i	0.0966917	−	0.995314i	$-0.469174\pi$
$467$	−7.78126	−	2.28478i	−0.360074	−	0.105727i	−0.456765	+	0.889587i	$0.650992\pi$
$468$		0			0
$469$	20.1482	+	44.1183i	0.930356	+	2.03719i
$470$	−15.1265	+	4.44153i	−0.697732	+	0.204872i
$471$		0			0
$472$	5.57010	−	6.42824i	0.256385	−	0.295884i
$473$	5.65221	−	1.65964i	0.259889	−	0.0763102i
$474$		0			0
$475$	8.69788	−	5.58979i	0.399086	−	0.256477i
$476$	−14.0975	−	4.13941i	−0.646160	−	0.189730i
$477$		0			0
$478$	−3.37538	+	7.39105i	−0.154386	+	0.338059i
$479$	−4.40254	+	30.6204i	−0.201157	+	1.39908i	0.599700	+	0.800225i	$0.295286\pi$
$479$	−4.40254	+	30.6204i	−0.201157	+	1.39908i	−0.800858	+	0.598855i	$0.795623\pi$
$480$		0			0
$481$	−1.78106	−	2.05546i	−0.0812095	−	0.0937208i
$482$	−3.86848			−0.176205
$483$		0			0
$484$	10.2709			0.466859
$485$	−2.00406	−	2.31281i	−0.0909999	−	0.105019i
$486$		0			0
$487$	−2.25517	+	15.6850i	−0.102191	+	0.710757i	0.872729	+	0.488205i	$0.162348\pi$
$487$	−2.25517	+	15.6850i	−0.102191	+	0.710757i	−0.974921	+	0.222553i	$0.928561\pi$
$488$	−4.97178	+	10.8867i	−0.225062	+	0.492816i
$489$		0			0
$490$	−4.04925	−	1.18897i	−0.182926	−	0.0537120i
$491$	−0.632340	+	0.406380i	−0.0285371	+	0.0183397i	−0.554832	−	0.831963i	$-0.687217\pi$
$491$	−0.632340	+	0.406380i	−0.0285371	+	0.0183397i	0.526294	+	0.850302i	$0.323581\pi$
$492$		0			0
$493$	20.4993	−	6.01913i	0.923241	−	0.271088i
$494$	0.522987	−	0.603559i	0.0235303	−	0.0271554i
$495$		0			0
$496$	−8.19755	+	2.40702i	−0.368081	+	0.108078i
$497$	−18.1527	−	39.7489i	−0.814261	−	1.78298i
$498$		0			0
$499$	29.6761	+	8.71370i	1.32849	+	0.390079i	0.867548	−	0.497354i	$-0.165695\pi$
$499$	29.6761	+	8.71370i	1.32849	+	0.390079i	0.460938	+	0.887432i	$0.347513\pi$
$500$	−2.58437	−	17.9747i	−0.115577	−	0.803853i
$501$		0			0
$502$	−2.05561	+	14.2971i	−0.0917465	+	0.638111i
$503$	23.5817	+	15.1550i	1.05145	+	0.675729i	0.947794	−	0.318884i	$-0.103308\pi$
$503$	23.5817	+	15.1550i	1.05145	+	0.675729i	0.103661	+	0.994613i	$0.466944\pi$
$504$		0			0
$505$	4.04593			0.180041
$506$	−1.12047	+	6.80377i	−0.0498108	+	0.302465i
$507$		0			0
$508$	5.24474	+	6.05275i	0.232698	+	0.268547i
$509$	−18.7265	−	12.0348i	−0.830038	−	0.533433i	0.0552522	−	0.998472i	$-0.482404\pi$
$509$	−18.7265	−	12.0348i	−0.830038	−	0.533433i	−0.885290	+	0.465040i	$0.846040\pi$
$510$		0			0
$511$	5.99733	−	13.1323i	0.265306	−	0.580940i
$512$	−1.95127	−	13.5714i	−0.0862348	−	0.599776i
$513$		0			0
$514$	10.3149	−	6.62896i	0.454969	−	0.292391i
$515$	2.87908	+	6.30430i	0.126867	+	0.277801i
$516$		0			0
$517$	17.7763	−	20.5150i	0.781801	−	0.902247i
$518$	−17.2027	+	19.8529i	−0.755841	+	0.872288i
$519$		0			0
$520$	−0.408968	−	0.895514i	−0.0179344	−	0.0392709i
$521$	10.2196	−	6.56776i	0.447730	−	0.287739i	−0.297282	−	0.954790i	$-0.596080\pi$
$521$	10.2196	−	6.56776i	0.447730	−	0.287739i	0.745012	+	0.667051i	$0.232444\pi$
$522$		0			0
$523$	−2.87440	−	19.9919i	−0.125689	−	0.874183i	−0.950931	−	0.309404i	$-0.899870\pi$
$523$	−2.87440	−	19.9919i	−0.125689	−	0.874183i	0.825242	−	0.564779i	$-0.191039\pi$
$524$	2.83871	−	6.21591i	0.124010	−	0.271543i
$525$		0			0
$526$	11.3841	+	7.31609i	0.496369	+	0.318997i
$527$	13.1970	+	15.2302i	0.574870	+	0.663436i
$528$		0			0
$529$	−21.7854	−	7.37539i	−0.947191	−	0.320669i
$530$	−0.630872			−0.0274033
$531$		0			0
$532$	19.7189	+	12.6726i	0.854925	+	0.549427i
$533$	0.276320	−	1.92184i	0.0119687	−	0.0832443i
$534$		0			0
$535$	3.22926	+	22.4600i	0.139613	+	0.971030i
$536$	35.3255	+	10.3725i	1.52583	+	0.448024i
$537$		0			0
$538$	−7.01381	−	15.3581i	−0.302387	−	0.662134i
$539$	6.97223	−	2.04723i	0.300315	−	0.0881805i
$540$		0			0
$541$	12.4594	−	14.3789i	0.535670	−	0.618196i	−0.421814	−	0.906682i	$-0.638606\pi$
$541$	12.4594	−	14.3789i	0.535670	−	0.618196i	0.957484	+	0.288486i	$0.0931519\pi$
$542$	15.2544	−	4.47909i	0.655231	−	0.192393i
$543$		0			0
$544$	−14.7367	+	9.47070i	−0.631830	+	0.406053i
$545$	−25.6069	−	7.51888i	−1.09688	−	0.322073i
$546$		0			0
$547$	−0.147373	+	0.322702i	−0.00630122	+	0.0137977i	−0.912756	−	0.408504i	$-0.866051\pi$
$547$	−0.147373	+	0.322702i	−0.00630122	+	0.0137977i	0.906455	+	0.422302i	$0.138778\pi$
$548$	3.53301	−	24.5726i	0.150923	−	1.04969i
$549$		0			0
$550$	−2.03055	−	2.34338i	−0.0865830	−	0.0999222i
$551$	−34.0841			−1.45203
$552$		0			0
$553$	6.79587			0.288990
$554$	−0.962449	−	1.11073i	−0.0408905	−	0.0471902i
$555$		0			0
$556$	0.742225	−	5.16229i	0.0314774	−	0.218930i
$557$	4.30127	−	9.41847i	0.182251	−	0.399073i	−0.796352	−	0.604834i	$-0.793240\pi$
$557$	4.30127	−	9.41847i	0.182251	−	0.399073i	0.978602	+	0.205760i	$0.0659668\pi$
$558$		0			0
$559$	−0.654855	−	0.192283i	−0.0276974	−	0.00813270i
$560$	5.87198	−	3.77369i	0.248136	−	0.159468i
$561$		0			0
$562$	13.2376	−	3.88691i	0.558394	−	0.163959i
$563$	9.43294	−	10.8862i	0.397551	−	0.458799i	−0.521317	−	0.853363i	$-0.674559\pi$
$563$	9.43294	−	10.8862i	0.397551	−	0.458799i	0.918868	+	0.394565i	$0.129105\pi$
$564$		0			0
$565$	−20.9270	+	6.14472i	−0.880405	+	0.258510i
$566$	1.46884	+	3.21631i	0.0617399	+	0.135192i
$567$		0			0
$568$	−31.8269	−	9.34522i	−1.33543	−	0.392117i
$569$	2.69816	+	18.7661i	0.113113	+	0.786716i	0.964860	+	0.262764i	$0.0846339\pi$
$569$	2.69816	+	18.7661i	0.113113	+	0.786716i	−0.851748	+	0.523952i	$0.824457\pi$
$570$		0			0
$571$	−0.955235	+	6.64381i	−0.0399754	+	0.278035i	−0.999998	−	0.00188690i	$-0.999399\pi$
$571$	−0.955235	+	6.64381i	−0.0399754	+	0.278035i	0.960023	+	0.279922i	$0.0903085\pi$
$572$	0.612275	+	0.393485i	0.0256005	+	0.0164524i
$573$		0			0
$574$	−18.7533			−0.782747
$575$	8.81315	−	5.41286i	0.367534	−	0.225732i
$576$		0			0
$577$	−8.20449	−	9.46849i	−0.341557	−	0.394178i	0.558819	−	0.829289i	$-0.311255\pi$
$577$	−8.20449	−	9.46849i	−0.341557	−	0.394178i	−0.900377	+	0.435111i	$0.856709\pi$
$578$	−4.71773	−	3.03190i	−0.196232	−	0.126110i
$579$		0			0
$580$	−7.49402	+	16.4096i	−0.311172	+	0.681372i
$581$	2.97935	+	20.7219i	0.123604	+	0.859687i
$582$		0			0
$583$	0.913830	−	0.587283i	0.0378470	−	0.0243228i
$584$	−4.55252	−	9.96862i	−0.188384	−	0.412504i
$585$		0			0
$586$	1.36317	−	1.57319i	0.0563122	−	0.0649877i
$587$	−4.51105	+	5.20603i	−0.186191	+	0.214876i	−0.841169	−	0.540772i	$-0.818132\pi$
$587$	−4.51105	+	5.20603i	−0.186191	+	0.214876i	0.654978	+	0.755648i	$0.272678\pi$
$588$		0			0
$589$	−13.3556	−	29.2447i	−0.550308	−	1.20501i
$590$	3.44268	−	2.21248i	0.141733	−	0.0910863i
$591$		0			0
$592$	−2.08317	−	14.4888i	−0.0856178	−	0.595485i
$593$	13.5898	−	29.7575i	0.558067	−	1.22200i	−0.394845	−	0.918748i	$-0.629202\pi$
$593$	13.5898	−	29.7575i	0.558067	−	1.22200i	0.952912	−	0.303248i	$-0.0980710\pi$
$594$		0			0
$595$	−13.8506	−	8.90124i	−0.567819	−	0.364915i
$596$	−3.02451	−	3.49047i	−0.123889	−	0.142975i
$597$		0			0
$598$	0.535381	−	0.592955i	0.0218934	−	0.0242477i
$599$	−26.8624			−1.09757			−0.548784	−	0.835964i	$-0.684909\pi$
$599$	−26.8624			−1.09757			−0.548784	+	0.835964i	$0.684909\pi$
$600$		0			0
$601$	−25.9428	−	16.6724i	−1.05823	−	0.680083i	−0.108800	−	0.994064i	$-0.534701\pi$
$601$	−25.9428	−	16.6724i	−1.05823	−	0.680083i	−0.949429	+	0.313981i	$0.898337\pi$
$602$	−0.938145	+	6.52494i	−0.0382359	+	0.265937i
$603$		0			0
$604$	0.405973	+	2.82360i	0.0165188	+	0.114891i
$605$	11.0431	+	3.24254i	0.448965	+	0.131828i
$606$		0			0
$607$	−14.9460	−	32.7272i	−0.606640	−	1.32836i	−0.924849	−	0.380335i	$-0.875809\pi$
$607$	−14.9460	−	32.7272i	−0.606640	−	1.32836i	0.318209	−	0.948021i	$-0.396919\pi$
$608$	26.8145	−	7.87346i	1.08747	−	0.319311i
$609$		0			0
$610$	−3.77081	+	4.35174i	−0.152676	+	0.176197i
$611$	−3.01760	+	0.886048i	−0.122079	+	0.0358457i
$612$		0			0
$613$	17.5091	−	11.2524i	0.707187	−	0.454481i	−0.136972	−	0.990575i	$-0.543737\pi$
$613$	17.5091	−	11.2524i	0.707187	−	0.454481i	0.844158	+	0.536094i	$0.180101\pi$
$614$	−15.9957	−	4.69675i	−0.645533	−	0.189546i
$615$		0			0
$616$	6.80146	−	14.8931i	0.274039	−	0.600061i
$617$	−2.59278	+	18.0332i	−0.104382	+	0.725990i	0.868668	+	0.495394i	$0.164976\pi$
$617$	−2.59278	+	18.0332i	−0.104382	+	0.725990i	−0.973050	+	0.230595i	$0.925933\pi$
$618$		0			0
$619$	13.8159	+	15.9444i	0.555310	+	0.640862i	0.962112	−	0.272655i	$-0.0879017\pi$
$619$	13.8159	+	15.9444i	0.555310	+	0.640862i	−0.406802	+	0.913516i	$0.633356\pi$
$620$	−17.0162			−0.683386
$621$		0			0
$622$	−18.4466			−0.739642
$623$	5.33866	+	6.16114i	0.213889	+	0.246841i
$624$		0			0
$625$	1.36140	−	9.46875i	0.0544561	−	0.378750i
$626$	−1.93682	+	4.24105i	−0.0774109	+	0.169506i
$627$		0			0
$628$	3.11557	+	0.914812i	0.124325	+	0.0365050i
$629$	−29.0460	+	18.6667i	−1.15814	+	0.744291i
$630$		0			0
$631$	−28.2607	+	8.29809i	−1.12504	+	0.330342i	−0.790757	−	0.612131i	$-0.790313\pi$
$631$	−28.2607	+	8.29809i	−1.12504	+	0.330342i	−0.334284	+	0.942472i	$0.608494\pi$
$632$	3.37821	−	3.89867i	0.134378	−	0.155081i
$633$		0			0
$634$	7.49657	−	2.20119i	0.297727	−	0.0874205i
$635$	3.72818	+	8.16358i	0.147948	+	0.323962i
$636$		0			0
$637$	−0.807791	−	0.237189i	−0.0320059	−	0.00939777i
$638$	1.45473	+	10.1178i	0.0575931	+	0.400569i
$639$		0			0
$640$	2.53533	−	17.6336i	0.100218	−	0.697030i
$641$	−33.4698	−	21.5097i	−1.32198	−	0.849584i	−0.326558	−	0.945177i	$-0.605889\pi$
$641$	−33.4698	−	21.5097i	−1.32198	−	0.849584i	−0.995420	+	0.0955936i	$0.969525\pi$
$642$		0			0
$643$	−33.1070			−1.30561			−0.652806	−	0.757525i	$-0.726408\pi$
$643$	−33.1070			−1.30561			−0.652806	+	0.757525i	$0.726408\pi$
$644$	19.4626	+	13.0770i	0.766936	+	0.515304i
$645$		0			0
$646$	−6.63925	−	7.66211i	−0.261218	−	0.301462i
$647$	−26.5632	−	17.0711i	−1.04431	−	0.671134i	−0.0982575	−	0.995161i	$-0.531327\pi$
$647$	−26.5632	−	17.0711i	−1.04431	−	0.671134i	−0.946048	+	0.324027i	$0.894963\pi$
$648$		0			0
$649$	−2.92718	+	6.40963i	−0.114902	+	0.251600i
$650$	0.0511261	+	0.355590i	0.00200533	+	0.0139474i
$651$		0			0
$652$	15.3130	−	9.84104i	0.599702	−	0.385405i
$653$	−5.87583	−	12.8663i	−0.229939	−	0.503496i	0.759132	−	0.650937i	$-0.225624\pi$
$653$	−5.87583	−	12.8663i	−0.229939	−	0.503496i	−0.989071	+	0.147441i	$0.952896\pi$
$654$		0			0
$655$	5.01451	−	5.78706i	0.195933	−	0.226119i
$656$	6.84313	−	7.89739i	0.267179	−	0.308341i
$657$		0			0
$658$	12.6188	+	27.6313i	0.491932	+	1.07718i
$659$	4.37949	−	2.81453i	0.170601	−	0.109638i	−0.452554	−	0.891737i	$-0.649487\pi$
$659$	4.37949	−	2.81453i	0.170601	−	0.109638i	0.623155	+	0.782099i	$0.285851\pi$
$660$		0			0
$661$	1.49548	+	10.4013i	0.0581673	+	0.404563i	0.998015	+	0.0629700i	$0.0200572\pi$
$661$	1.49548	+	10.4013i	0.0581673	+	0.404563i	−0.939848	+	0.341593i	$0.889034\pi$
$662$	6.56486	−	14.3750i	0.255151	−	0.558702i
$663$		0			0
$664$	13.3688	+	8.59160i	0.518810	+	0.333419i
$665$	17.2007	+	19.8507i	0.667015	+	0.769776i
$666$		0			0
$667$	−34.0885	−	0.696124i	−1.31991	−	0.0269540i
$668$	−19.8161			−0.766706
$669$		0			0
$670$	14.9015	+	9.57660i	0.575695	+	0.369976i
$671$	1.41102	−	9.81385i	0.0544718	−	0.378860i
$672$		0			0
$673$	3.94517	+	27.4393i	0.152075	+	1.05771i	0.912734	+	0.408554i	$0.133967\pi$
$673$	3.94517	+	27.4393i	0.152075	+	1.05771i	−0.760659	+	0.649152i	$0.775124\pi$
$674$	23.5827	+	6.92450i	0.908370	+	0.266722i
$675$		0			0
$676$	8.09149	+	17.7179i	0.311211	+	0.681457i
$677$	26.6582	−	7.82754i	1.02456	−	0.300837i	0.274061	−	0.961712i	$-0.411633\pi$
$677$	26.6582	−	7.82754i	1.02456	−	0.300837i	0.750496	+	0.660876i	$0.229815\pi$
$678$		0			0
$679$	−3.86147	+	4.45637i	−0.148189	+	0.171020i
$680$	−11.9916	+	3.52105i	−0.459857	+	0.135026i
$681$		0			0
$682$	−8.11124	+	5.21278i	−0.310596	+	0.199608i
$683$	−10.3732	−	3.04585i	−0.396921	−	0.116546i	0.0771798	−	0.997017i	$-0.475408\pi$
$683$	−10.3732	−	3.04585i	−0.396921	−	0.116546i	−0.474100	+	0.880471i	$0.657227\pi$
$684$		0			0
$685$	11.5563	−	25.3047i	0.441542	−	0.966842i
$686$	1.12047	−	7.79303i	0.0427797	−	0.297539i
$687$		0			0
$688$	−2.40545	−	2.77604i	−0.0917070	−	0.105836i
$689$	−0.125854			−0.00479464
$690$		0			0
$691$	6.10633			0.232296			0.116148	−	0.993232i	$-0.462945\pi$
$691$	6.10633			0.232296			0.116148	+	0.993232i	$0.462945\pi$
$692$	17.3847	+	20.0630i	0.660868	+	0.762682i
$693$		0			0
$694$	−1.02845	+	7.15305i	−0.0390395	+	0.271526i
$695$	2.42777	−	5.31608i	0.0920907	−	0.201650i
$696$		0			0
$697$	−23.6500	−	6.94427i	−0.895809	−	0.263033i
$698$	−17.8995	+	11.5033i	−0.677507	+	0.435407i
$699$		0			0
$700$	−10.1169	+	2.97060i	−0.382385	+	0.112278i
$701$	−12.3067	+	14.2027i	−0.464819	+	0.536430i	−0.938963	−	0.344017i	$-0.888212\pi$
$701$	−12.3067	+	14.2027i	−0.464819	+	0.536430i	0.474144	+	0.880447i	$0.342758\pi$
$702$		0			0
$703$	52.8513	−	15.5186i	1.99333	−	0.585293i
$704$	−1.31898	−	2.88817i	−0.0497110	−	0.108852i
$705$		0			0
$706$	−2.13120	−	0.625776i	−0.0802086	−	0.0235514i
$707$	−1.10945	−	7.71641i	−0.0417253	−	0.290206i
$708$		0			0
$709$	−2.12480	+	14.7783i	−0.0797985	+	0.555011i	0.910226	+	0.414113i	$0.135908\pi$
$709$	−2.12480	+	14.7783i	−0.0797985	+	0.555011i	−0.990024	+	0.140898i	$0.955001\pi$
$710$	−13.4257	−	8.62815i	−0.503856	−	0.323809i
$711$		0			0
$712$	6.18838			0.231919
$713$	−12.7600	−	29.5212i	−0.477867	−	1.10558i
$714$		0			0
$715$	0.534083	+	0.616365i	0.0199736	+	0.0230507i
$716$	13.6321	+	8.76082i	0.509455	+	0.327407i
$717$		0			0
$718$	6.39253	−	13.9977i	0.238567	−	0.522389i
$719$	2.17016	+	15.0938i	0.0809333	+	0.562904i	0.989430	+	0.145012i	$0.0463219\pi$
$719$	2.17016	+	15.0938i	0.0809333	+	0.562904i	−0.908497	+	0.417892i	$0.862769\pi$
$720$		0			0
$721$	11.2341	−	7.21972i	0.418380	−	0.268876i
$722$	1.16479	+	2.55054i	0.0433491	+	0.0949213i
$723$		0			0
$724$	−1.40586	+	1.62245i	−0.0522483	+	0.0602977i
$725$	10.0404	−	11.5873i	0.372892	−	0.430340i
$726$		0			0
$727$	−9.70715	−	21.2557i	−0.360018	−	0.788330i	−0.999804	−	0.0197768i	$-0.993704\pi$
$727$	−9.70715	−	21.2557i	−0.360018	−	0.788330i	0.639786	−	0.768553i	$-0.279023\pi$
$728$	−1.59579	+	1.02555i	−0.0591437	+	0.0380094i
$729$		0			0
$730$	−0.750370	−	5.21894i	−0.0277724	−	0.193162i
$731$	−3.59927	+	7.88130i	−0.133124	+	0.291500i
$732$		0			0
$733$	45.1623	+	29.0240i	1.66811	+	1.07203i	0.904637	+	0.426182i	$0.140142\pi$
$733$	45.1623	+	29.0240i	1.66811	+	1.07203i	0.763469	+	0.645845i	$0.223495\pi$
$734$	3.75061	+	4.32843i	0.138437	+	0.159765i
$735$		0			0
$736$	26.9788	−	7.32681i	0.994451	−	0.270070i
$737$	−30.5000			−1.12348
$738$		0			0
$739$	−7.10502	−	4.56612i	−0.261362	−	0.167967i	0.403397	−	0.915025i	$-0.367829\pi$
$739$	−7.10502	−	4.56612i	−0.261362	−	0.167967i	−0.664759	+	0.747058i	$0.731466\pi$
$740$	4.14902	−	28.8570i	0.152521	−	1.06081i
$741$		0			0
$742$	0.172994	+	1.20320i	0.00635083	+	0.0441710i
$743$	10.3844	+	3.04914i	0.380968	+	0.111862i	0.466609	−	0.884464i	$-0.345476\pi$
$743$	10.3844	+	3.04914i	0.380968	+	0.111862i	−0.0856409	+	0.996326i	$0.527294\pi$
$744$		0			0
$745$	−2.14995	−	4.70774i	−0.0787682	−	0.172478i
$746$	−2.98567	+	0.876671i	−0.109313	+	0.0320972i
$747$		0			0
$748$	6.05058	−	6.98274i	0.221231	−	0.255314i
$749$	41.9503	−	12.3177i	1.53283	−	0.450080i
$750$		0			0
$751$	12.6562	−	8.13365i	0.461832	−	0.296801i	−0.288959	−	0.957342i	$-0.593309\pi$
$751$	12.6562	−	8.13365i	0.461832	−	0.296801i	0.750791	+	0.660540i	$0.229673\pi$
$752$	−16.2408	−	4.76871i	−0.592239	−	0.173897i
$753$		0			0
$754$	0.491972	−	1.07727i	0.0179166	−	0.0392318i
$755$	−0.454922	+	3.16405i	−0.0165563	+	0.115152i
$756$		0			0
$757$	−2.37325	−	2.73887i	−0.0862572	−	0.0995461i	0.710980	−	0.703212i	$-0.248252\pi$
$757$	−2.37325	−	2.73887i	−0.0862572	−	0.0995461i	−0.797237	+	0.603666i	$0.793706\pi$
$758$	7.42321			0.269623
$759$		0			0
$760$	19.9384			0.723242
$761$	−0.554520	−	0.639950i	−0.0201013	−	0.0231982i	0.745610	−	0.666383i	$-0.232158\pi$
$761$	−0.554520	−	0.639950i	−0.0201013	−	0.0231982i	−0.765711	+	0.643185i	$0.777613\pi$
$762$		0			0
$763$	−7.31824	+	50.8995i	−0.264938	+	1.84269i
$764$	−8.68518	+	19.0179i	−0.314219	+	0.688043i
$765$		0			0
$766$	−3.64745	−	1.07099i	−0.131788	−	0.0386963i
$767$	0.686786	−	0.441371i	0.0247984	−	0.0159370i
$768$		0			0
$769$	−38.4180	+	11.2806i	−1.38539	+	0.406787i	−0.887642	−	0.460535i	$-0.847658\pi$
$769$	−38.4180	+	11.2806i	−1.38539	+	0.406787i	−0.497748	+	0.867322i	$0.665840\pi$
$770$	5.15852	−	5.95325i	0.185900	−	0.214540i
$771$		0			0
$772$	11.6888	−	3.43215i	0.420690	−	0.123526i
$773$	−16.2066	−	35.4876i	−0.582913	−	1.27640i	−0.939631	−	0.342189i	$-0.888832\pi$
$773$	−16.2066	−	35.4876i	−0.582913	−	1.27640i	0.356719	−	0.934212i	$-0.383896\pi$
$774$		0			0
$775$	13.8763	+	4.07445i	0.498452	+	0.146359i
$776$	0.637011	+	4.43051i	0.0228674	+	0.159046i
$777$		0			0
$778$	0.160485	−	1.11620i	0.00575367	−	0.0400177i
$779$	33.0805	+	21.2595i	1.18523	+	0.761702i
$780$		0			0
$781$	27.4793			0.983287
$782$	−6.48362	−	7.79869i	−0.231854	−	0.278880i
$783$		0			0
$784$	−2.96722	−	3.42436i	−0.105972	−	0.122299i
$785$	3.06099	+	1.96718i	0.109252	+	0.0702117i
$786$		0			0
$787$	−16.1795	+	35.4281i	−0.576735	+	1.26287i	0.366398	+	0.930458i	$0.380591\pi$
$787$	−16.1795	+	35.4281i	−0.576735	+	1.26287i	−0.943133	+	0.332416i	$0.892136\pi$
$788$	−0.380646	−	2.64745i	−0.0135600	−	0.0943116i
$789$		0			0
$790$	2.08795	−	1.34185i	0.0742861	−	0.0477408i
$791$	17.4577	+	38.2271i	0.620726	+	1.35920i
$792$		0			0
$793$	−0.752245	+	0.868136i	−0.0267130	+	0.0308284i
$794$	3.21396	−	3.70911i	0.114059	−	0.131631i
$795$		0			0
$796$	−4.11458	−	9.00966i	−0.145837	−	0.319339i
$797$	−18.7123	+	12.0257i	−0.662823	+	0.425971i	−0.828332	−	0.560238i	$-0.810710\pi$
$797$	−18.7123	+	12.0257i	−0.662823	+	0.425971i	0.165508	+	0.986208i	$0.447073\pi$
$798$		0			0
$799$	5.68197	+	39.5189i	0.201014	+	1.39808i
$800$	−5.22229	+	11.4352i	−0.184636	+	0.404296i
$801$		0			0
$802$	0.565424	+	0.363376i	0.0199658	+	0.0128313i
$803$	5.94527	+	6.86121i	0.209804	+	0.242127i
$804$		0			0
$805$	16.7975	+	20.2045i	0.592033	+	0.712115i
$806$	1.11709			0.0393478
$807$		0			0
$808$	−4.97827	−	3.19934i	−0.175135	−	0.112552i
$809$	−7.67660	+	53.3919i	−0.269895	+	1.87716i	0.179401	+	0.983776i	$0.442584\pi$
$809$	−7.67660	+	53.3919i	−0.269895	+	1.87716i	−0.449296	+	0.893383i	$0.648325\pi$
$810$		0			0
$811$	7.03044	+	48.8978i	0.246872	+	1.71703i	0.616078	+	0.787685i	$0.288720\pi$
$811$	7.03044	+	48.8978i	0.246872	+	1.71703i	−0.369206	+	0.929347i	$0.620370\pi$
$812$	33.3515	+	9.79288i	1.17041	+	0.343663i
$813$		0			0
$814$	−6.86239	−	15.0265i	−0.240527	−	0.526680i
$815$	19.5711	−	5.74658i	0.685544	−	0.201294i
$816$		0			0
$817$	9.05183	−	10.4464i	0.316683	−	0.365472i
$818$	−10.5170	+	3.08807i	−0.367718	+	0.107972i
$819$		0			0
$820$	17.5086	−	11.2521i	0.611428	−	0.392941i
$821$	16.8019	+	4.93349i	0.586391	+	0.172180i	0.561453	−	0.827509i	$-0.310243\pi$
$821$	16.8019	+	4.93349i	0.586391	+	0.172180i	0.0249388	+	0.999689i	$0.492061\pi$
$822$		0			0
$823$	−5.65453	+	12.3817i	−0.197105	+	0.431599i	−0.982216	−	0.187756i	$-0.939879\pi$
$823$	−5.65453	+	12.3817i	−0.197105	+	0.431599i	0.785111	+	0.619355i	$0.212606\pi$
$824$	1.44263	−	10.0337i	0.0502564	−	0.349541i
$825$		0			0
$826$	−5.16369	−	5.95921i	−0.179668	−	0.207347i
$827$	22.5564			0.784365			0.392182	−	0.919888i	$-0.371720\pi$
$827$	22.5564			0.784365			0.392182	+	0.919888i	$0.371720\pi$
$828$		0			0
$829$	−49.2936			−1.71204			−0.856019	−	0.516944i	$-0.827070\pi$
$829$	−49.2936			−1.71204			−0.856019	+	0.516944i	$0.827070\pi$
$830$	5.00691	+	5.77829i	0.173793	+	0.200567i
$831$		0			0
$832$	−0.0523521	+	0.364117i	−0.00181498	+	0.0126235i
$833$	−4.43985	+	9.72191i	−0.153832	+	0.336844i
$834$		0			0
$835$	−21.3059	−	6.25597i	−0.737320	−	0.216497i
$836$	−12.4002	+	7.96915i	−0.428871	+	0.275619i
$837$		0			0
$838$	−20.5579	+	6.03634i	−0.710161	+	0.208522i
$839$	−3.73033	+	4.30503i	−0.128785	+	0.148626i	−0.816480	−	0.577374i	$-0.804077\pi$
$839$	−3.73033	+	4.30503i	−0.128785	+	0.148626i	0.687694	+	0.726000i	$0.258623\pi$
$840$		0			0
$841$	−20.6712	+	6.06961i	−0.712800	+	0.209297i
$842$	−7.08944	−	15.5237i	−0.244318	−	0.534982i
$843$		0			0
$844$	19.7216	+	5.79079i	0.678847	+	0.199327i
$845$	3.10625	+	21.6045i	0.106858	+	0.743216i
$846$		0			0
$847$	3.15602	−	21.9506i	0.108442	−	0.754231i
$848$	−0.569819	−	0.366201i	−0.0195677	−	0.0125754i
$849$		0			0
$850$	4.56059			0.156427
$851$	53.1751	−	14.4411i	1.82282	−	0.495035i
$852$		0			0
$853$	−23.2854	−	26.8727i	−0.797275	−	0.920105i	0.200953	−	0.979601i	$-0.435596\pi$
$853$	−23.2854	−	26.8727i	−0.797275	−	0.920105i	−0.998229	+	0.0594960i	$0.981051\pi$
$854$	9.33368	+	5.99839i	0.319392	+	0.205261i
$855$		0			0
$856$	13.7870	−	30.1892i	0.471229	−	1.03185i
$857$	−3.63010	−	25.2479i	−0.124002	−	0.862451i	−0.952950	−	0.303126i	$-0.901970\pi$
$857$	−3.63010	−	25.2479i	−0.124002	−	0.862451i	0.828949	−	0.559325i	$-0.188940\pi$
$858$		0			0
$859$	−28.7873	+	18.5005i	−0.982209	+	0.631227i	−0.930058	−	0.367412i	$-0.880244\pi$
$859$	−28.7873	+	18.5005i	−0.982209	+	0.631227i	−0.0521507	+	0.998639i	$0.516608\pi$
$860$	−3.03914	−	6.65478i	−0.103634	−	0.226926i
$861$		0			0
$862$	4.48854	−	5.18005i	0.152880	−	0.176433i
$863$	−18.4346	+	21.2747i	−0.627522	+	0.724199i	−0.977117	−	0.212702i	$-0.931774\pi$
$863$	−18.4346	+	21.2747i	−0.627522	+	0.724199i	0.349595	+	0.936901i	$0.386319\pi$
$864$		0			0
$865$	12.3578	+	27.0598i	0.420178	+	0.920061i
$866$	−3.69562	+	2.37503i	−0.125582	+	0.0807069i
$867$		0			0
$868$	4.66609	+	32.4534i	0.158377	+	1.10154i
$869$	−1.77531	+	3.88738i	−0.0602232	+	0.131870i
$870$		0			0
$871$	2.97272	+	1.91045i	0.100727	+	0.0647332i
$872$	25.5622	+	29.5004i	0.865647	+	0.999009i
$873$		0			0
$874$	6.41942	+	14.8518i	0.217140	+	0.502369i
$875$	−39.2090			−1.32551
$876$		0			0
$877$	−12.5229	−	8.04799i	−0.422869	−	0.271761i	0.311852	−	0.950131i	$-0.399051\pi$
$877$	−12.5229	−	8.04799i	−0.422869	−	0.271761i	−0.734721	+	0.678369i	$0.762687\pi$
$878$	1.67471	−	11.6478i	0.0565186	−	0.393095i
$879$		0			0
$880$	0.624675	+	4.34471i	0.0210578	+	0.146460i
$881$	25.0561	+	7.35715i	0.844163	+	0.247869i	0.675090	−	0.737735i	$-0.264105\pi$
$881$	25.0561	+	7.35715i	0.844163	+	0.247869i	0.169073	+	0.985604i	$0.445923\pi$
$882$		0			0
$883$	−14.3890	−	31.5074i	−0.484227	−	1.06031i	−0.981279	−	0.192589i	$-0.938311\pi$
$883$	−14.3890	−	31.5074i	−0.484227	−	1.06031i	0.497052	−	0.867721i	$-0.334416\pi$
$884$	−1.02711	+	0.301587i	−0.0345455	+	0.0101435i
$885$		0			0
$886$	14.0055	−	16.1632i	0.470525	−	0.543014i
$887$	−52.5394	+	15.4270i	−1.76410	+	0.517987i	−0.992936	−	0.118650i	$-0.962143\pi$
$887$	−52.5394	+	15.4270i	−1.76410	+	0.517987i	−0.771164	+	0.636636i	$0.780325\pi$
$888$		0			0
$889$	14.5473	−	9.34899i	0.487901	−	0.313555i
$890$	2.85677	+	0.838822i	0.0957590	+	0.0281174i
$891$		0			0
$892$	−7.12696	+	15.6059i	−0.238628	+	0.522523i
$893$	9.06471	−	63.0465i	0.303339	−	2.10977i
$894$		0			0
$895$	11.8912	+	13.7232i	0.397479	+	0.458715i
$896$	−34.3261			−1.14676
$897$		0			0
$898$	−12.1172			−0.404355
$899$	−31.2210	−	36.0310i	−1.04128	−	1.20170i
$900$		0			0
$901$	−0.227376	+	1.58143i	−0.00757499	+	0.0526852i
$902$	4.89899	−	10.7273i	0.163118	−	0.357179i
$903$		0			0
$904$	30.6084	+	8.98744i	1.01802	+	0.298918i
$905$	−2.02376	+	1.30059i	−0.0672722	+	0.0432332i
$906$		0			0
$907$	9.75887	−	2.86546i	0.324038	−	0.0951461i	−0.115668	−	0.993288i	$-0.536901\pi$
$907$	9.75887	−	2.86546i	0.324038	−	0.0951461i	0.439706	+	0.898142i	$0.355083\pi$
$908$	1.56620	−	1.80749i	0.0519761	−	0.0599836i
$909$		0			0
$910$	−0.875680	+	0.257123i	−0.0290285	+	0.00852354i
$911$	−12.8358	−	28.1066i	−0.425271	−	0.931213i	−0.994071	−	0.108737i	$-0.965319\pi$
$911$	−12.8358	−	28.1066i	−0.425271	−	0.931213i	0.568800	−	0.822476i	$-0.307408\pi$
$912$		0			0
$913$	−12.6317	−	3.70899i	−0.418047	−	0.122750i
$914$	1.15583	+	8.03900i	0.0382316	+	0.265907i
$915$		0			0
$916$	5.61721	−	39.0686i	0.185598	−	1.29086i
$917$	−12.4122	−	7.97681i	−0.409886	−	0.263417i
$918$		0			0
$919$	1.12747			0.0371917			0.0185959	−	0.999827i	$-0.494080\pi$
$919$	1.12747			0.0371917			0.0185959	+	0.999827i	$0.494080\pi$
$920$	19.9410	+	0.407216i	0.657434	+	0.0134255i
$921$		0			0
$922$	−16.7375	−	19.3161i	−0.551221	−	0.636143i
$923$	−2.67831	−	1.72124i	−0.0881575	−	0.0566554i
$924$		0			0
$925$	−10.2931	+	22.5388i	−0.338436	+	0.741071i
$926$	1.47668	+	10.2705i	0.0485268	+	0.337511i
$927$		0			0
$928$	34.8636	−	22.4055i	1.14445	−	0.735495i
$929$	−4.61059	−	10.0958i	−0.151269	−	0.331232i	0.818794	−	0.574088i	$-0.194643\pi$
$929$	−4.61059	−	10.0958i	−0.151269	−	0.331232i	−0.970062	+	0.242856i	$0.921916\pi$
$930$		0			0
$931$	11.1658	−	12.8860i	0.365944	−	0.422322i
$932$	9.80417	−	11.3146i	0.321146	−	0.370623i
$933$		0			0
$934$	2.37072	+	5.19115i	0.0775723	+	0.169860i
$935$	8.70994	−	5.59754i	0.284846	−	0.183059i
$936$		0			0
$937$	−5.05507	−	35.1588i	−0.165142	−	1.14859i	−0.888755	−	0.458382i	$-0.848429\pi$
$937$	−5.05507	−	35.1588i	−0.165142	−	1.14859i	0.723613	−	0.690206i	$-0.242480\pi$
$938$	14.1783	−	31.0462i	0.462939	−	1.01370i
$939$		0			0
$940$	−28.3603	−	18.2261i	−0.925012	−	0.594469i
$941$	37.5077	+	43.2862i	1.22272	+	1.41109i	0.882217	+	0.470844i	$0.156050\pi$
$941$	37.5077	+	43.2862i	1.22272	+	1.41109i	0.340499	+	0.940245i	$0.389404\pi$
$942$		0			0
$943$	32.6505	+	21.9379i	1.06325	+	0.714396i
$944$	4.39379			0.143006
$945$		0			0
$946$	−3.48733	−	2.24117i	−0.113383	−	0.0728668i
$947$	−3.46314	+	24.0867i	−0.112537	+	0.782712i	0.852900	+	0.522075i	$0.174842\pi$
$947$	−3.46314	+	24.0867i	−0.112537	+	0.782712i	−0.965437	+	0.260637i	$0.916067\pi$
$948$		0			0
$949$	−0.149693	−	1.04113i	−0.00485923	−	0.0337967i
$950$	−6.98101	−	2.04981i	−0.226494	−	0.0665046i
$951$		0			0
$952$	10.0036	+	21.9049i	0.324220	+	0.709942i
$953$	−47.7219	+	14.0124i	−1.54586	+	0.453906i	−0.939861	−	0.341557i	$-0.889046\pi$
$953$	−47.7219	+	14.0124i	−1.54586	+	0.453906i	−0.606002	+	0.795463i	$0.707228\pi$
$954$		0			0
$955$	−15.3421	+	17.7058i	−0.496460	+	0.572945i
$956$	−16.6714	+	4.89516i	−0.539191	+	0.158321i
$957$		0			0
$958$	18.3135	−	11.7693i	0.591681	−	0.380250i
$959$	−51.4301	−	15.1012i	−1.66077	−	0.487645i
$960$		0			0
$961$	5.80356	−	12.7080i	0.187212	−	0.409936i
$962$	−0.272377	+	1.89443i	−0.00878180	+	0.0610787i
$963$		0			0
$964$	−5.41725	−	6.25183i	−0.174478	−	0.201358i
$965$	13.6512			0.439447
$966$		0			0
$967$	46.0629			1.48128			0.740641	−	0.671901i	$-0.234522\pi$
$967$	46.0629			1.48128			0.740641	+	0.671901i	$0.234522\pi$
$968$	−11.0238	−	12.7221i	−0.354318	−	0.408905i
$969$		0			0
$970$	−0.306481	+	2.13162i	−0.00984050	+	0.0684422i
$971$	10.3764	−	22.7210i	0.332993	−	0.729153i	−0.666879	−	0.745166i	$-0.732370\pi$
$971$	10.3764	−	22.7210i	0.332993	−	0.729153i	0.999872	+	0.0160132i	$0.00509738\pi$
$972$		0			0
$973$	−10.8046	−	3.17251i	−0.346379	−	0.101706i
$974$	9.38093	−	6.02876i	0.300584	−	0.193174i
$975$		0			0
$976$	−5.93193	+	1.74177i	−0.189876	+	0.0557528i
$977$	−15.7122	+	18.1328i	−0.502678	+	0.580121i	−0.949209	−	0.314647i	$-0.898114\pi$
$977$	−15.7122	+	18.1328i	−0.502678	+	0.580121i	0.446531	+	0.894768i	$0.352659\pi$
$978$		0			0
$979$	−4.91894	+	1.44433i	−0.157210	+	0.0461611i
$980$	−3.74890	−	8.20894i	−0.119754	−	0.262225i
$981$		0			0
$982$	0.507523	+	0.149022i	0.0161957	+	0.00475549i
$983$	0.868902	+	6.04334i	0.0277137	+	0.192753i	0.998975	−	0.0452623i	$-0.0144123\pi$
$983$	0.868902	+	6.04334i	0.0277137	+	0.192753i	−0.971261	+	0.238015i	$0.923503\pi$
$984$		0			0
$985$	0.426542	−	2.96667i	0.0135908	−	0.0945258i
$986$	−12.6478	−	8.12822i	−0.402787	−	0.258855i
$987$		0			0
$988$	1.70778			0.0543316
$989$	9.26634	−	10.2628i	0.294652	−	0.326339i
$990$		0			0
$991$	10.5406	+	12.1645i	0.334833	+	0.386418i	0.898052	−	0.439890i	$-0.144983\pi$
$991$	10.5406	+	12.1645i	0.334833	+	0.386418i	−0.563219	+	0.826308i	$0.690437\pi$
$992$	32.8853	+	21.1341i	1.04411	+	0.671008i
$993$		0			0
$994$	−12.7741	+	27.9715i	−0.405171	+	0.887201i
$995$	−1.57955	−	10.9860i	−0.0500751	−	0.348280i
$996$		0			0
$997$	14.2420	−	9.15281i	0.451050	−	0.289872i	−0.295326	−	0.955397i	$-0.595428\pi$
$997$	14.2420	−	9.15281i	0.451050	−	0.289872i	0.746376	+	0.665524i	$0.231792\pi$
$998$	−9.04144	−	19.7980i	−0.286202	−	0.626694i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.i.d.82.1		20
3.2	odd	2		69.2.e.c.13.2	✓	20
23.4	even	11		4761.2.a.bt.1.6		10
23.16	even	11	inner	207.2.i.d.154.1		20
23.19	odd	22		4761.2.a.bu.1.6		10
69.50	odd	22		1587.2.a.u.1.5		10
69.62	odd	22		69.2.e.c.16.2	yes	20
69.65	even	22		1587.2.a.t.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.c.13.2	✓	20	3.2	odd	2
69.2.e.c.16.2	yes	20	69.62	odd	22
207.2.i.d.82.1		20	1.1	even	1	trivial
207.2.i.d.154.1		20	23.16	even	11	inner
1587.2.a.t.1.5		10	69.65	even	22
1587.2.a.u.1.5		10	69.50	odd	22
4761.2.a.bt.1.6		10	23.4	even	11
4761.2.a.bu.1.6		10	23.19	odd	22

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.460828 - 0.531824i) q^{2} +(0.214155 - 1.48948i) q^{4} +(0.700489 - 1.53386i) q^{5} +(-3.11747 - 0.915371i) q^{7} +(-2.07482 + 1.33341i) q^{8} +(-1.13855 + 0.334308i) q^{10} +(1.33800 - 1.54413i) q^{11} +(-0.227131 + 0.0666916i) q^{13} +(0.949800 + 2.07977i) q^{14} +(-1.22242 - 0.358935i) q^{16} +(0.427674 + 2.97454i) q^{17} +(0.682288 - 4.74542i) q^{19} +(-2.13464 - 1.37185i) q^{20} -1.43779 q^{22} +(0.779295 - 4.73209i) q^{23} +(1.41227 + 1.62985i) q^{25} +(0.140136 + 0.0900602i) q^{26} +(-2.03105 + 4.44738i) q^{28} +(-1.01178 - 7.03706i) q^{29} +(5.64145 - 3.62554i) q^{31} +(2.42155 + 5.30245i) q^{32} +(1.38485 - 1.59820i) q^{34} +(-3.58780 + 4.14054i) q^{35} +(4.77286 + 10.4511i) q^{37} +(-2.83815 + 1.82397i) q^{38} +(0.591865 + 4.11651i) q^{40} +(-3.40729 + 7.46093i) q^{41} +(2.42547 + 1.55876i) q^{43} +(-2.01342 - 2.32361i) q^{44} +(-2.87576 + 1.76623i) q^{46} +13.2857 q^{47} +(2.99192 + 1.92279i) q^{49} +(0.215978 - 1.50216i) q^{50} +(0.0506948 + 0.352590i) q^{52} +(0.510122 + 0.149785i) q^{53} +(-1.43123 - 3.13395i) q^{55} +(7.68874 - 2.25762i) q^{56} +(-3.27622 + 3.78096i) q^{58} +(-3.30904 + 0.971623i) q^{59} +(4.08228 - 2.62352i) q^{61} +(-4.52789 - 1.32951i) q^{62} +(0.645553 - 1.41356i) q^{64} +(-0.0568072 + 0.395103i) q^{65} +(-9.77557 - 11.2816i) q^{67} +4.52211 q^{68} +3.85540 q^{70} +(8.80741 + 10.1643i) q^{71} +(-0.632363 + 4.39818i) q^{73} +(3.35868 - 7.35449i) q^{74} +(-6.92211 - 2.03251i) q^{76} +(-5.58462 + 3.58902i) q^{77} +(-2.00690 + 0.589280i) q^{79} +(-1.40685 + 1.62359i) q^{80} +(5.53808 - 1.62613i) q^{82} +(-2.67666 - 5.86108i) q^{83} +(4.86210 + 1.42764i) q^{85} +(-0.288742 - 2.00824i) q^{86} +(-0.717150 + 4.98789i) q^{88} +(-2.11082 - 1.35654i) q^{89} +0.769120 q^{91} +(-6.88149 - 2.17415i) q^{92} +(-6.12245 - 7.06568i) q^{94} +(-6.80086 - 4.37065i) q^{95} +(0.753920 - 1.65086i) q^{97} +(-0.356175 - 2.47725i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 10 q^{8} - 18 q^{10} + 16 q^{11} + 14 q^{13} + 22 q^{14} - 8 q^{16} - 11 q^{17} - 11 q^{19} - 57 q^{20} + 26 q^{22} - 4 q^{25} + 14 q^{26} - 14 q^{28} - 12 q^{29}+ \cdots - 85 q^{98}+O(q^{100}) \) 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 10 * q^8 - 18 * q^10 + 16 * q^11 + 14 * q^13 + 22 * q^14 - 8 * q^16 - 11 * q^17 - 11 * q^19 - 57 * q^20 + 26 * q^22 - 4 * q^25 + 14 * q^26 - 14 * q^28 - 12 * q^29 + 41 * q^31 + 46 * q^32 - 3 * q^34 + 26 * q^35 - 18 * q^37 - 70 * q^38 - 13 * q^40 - 10 * q^43 + 3 * q^44 - 24 * q^46 - 18 * q^47 - 10 * q^49 - 33 * q^50 + 61 * q^52 + 20 * q^53 - 17 * q^55 - 6 * q^56 - 37 * q^58 - 40 * q^59 - 12 * q^61 + 89 * q^62 - 2 * q^64 + 51 * q^65 - 47 * q^67 + 12 * q^68 + 32 * q^70 + 47 * q^71 + 39 * q^73 + 50 * q^74 - 39 * q^76 - 22 * q^77 - 2 * q^79 - 12 * q^80 + 26 * q^82 + 52 * q^83 + 35 * q^85 - 34 * q^86 + 30 * q^88 - 36 * q^89 + 8 * q^91 + 19 * q^92 + 21 * q^94 - 89 * q^95 - 85 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more