LMFDB - Embedded newform 603.2.z.c.10.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(10,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("603.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.z (of order $33$, degree $20$, 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:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$5$ over $\Q(\zeta_{33})$
Twist minimal:	no (minimal twist has level 67)
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			10.5
Character	$\chi$	$=$	603.10
Dual form			603.2.z.c.181.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.86173 + 1.77515i) q^{2} +(0.219695 + 4.61197i) q^{4} +(-0.754900 + 1.65300i) q^{5} +(-0.561736 + 2.31551i) q^{7} +(-4.40882 + 5.08805i) q^{8} +O(q^{10})$	\(q+(1.86173 + 1.77515i) q^{2} +(0.219695 + 4.61197i) q^{4} +(-0.754900 + 1.65300i) q^{5} +(-0.561736 + 2.31551i) q^{7} +(-4.40882 + 5.08805i) q^{8} +(-4.33974 + 1.73737i) q^{10} +(-0.558411 - 0.784179i) q^{11} +(2.04927 - 5.92099i) q^{13} +(-5.15617 + 3.31367i) q^{14} +(-8.04750 + 0.768443i) q^{16} +(-0.0160394 + 0.336709i) q^{17} +(-0.0302113 - 0.124533i) q^{19} +(-7.78943 - 3.11842i) q^{20} +(0.352428 - 2.45119i) q^{22} +(3.05448 - 2.40207i) q^{23} +(1.11177 + 1.28305i) q^{25} +(14.3258 - 7.38549i) q^{26} +(-10.8024 - 2.08200i) q^{28} +(-3.15521 + 5.46499i) q^{29} +(0.950033 + 2.74494i) q^{31} +(-5.76222 - 4.53146i) q^{32} +(-0.627570 + 0.598387i) q^{34} +(-3.40348 - 2.67652i) q^{35} +(2.91909 + 5.05602i) q^{37} +(0.164820 - 0.285476i) q^{38} +(-5.08232 - 11.1287i) q^{40} +(-5.28177 + 2.72294i) q^{41} +(4.79837 + 3.08373i) q^{43} +(3.49393 - 2.74765i) q^{44} +(9.95066 + 0.950173i) q^{46} +(-5.05247 - 2.02271i) q^{47} +(1.17583 + 0.606182i) q^{49} +(-0.207800 + 4.36225i) q^{50} +(27.7576 + 8.15037i) q^{52} +(11.3238 - 7.27737i) q^{53} +(1.71779 - 0.331077i) q^{55} +(-9.30481 - 13.0668i) q^{56} +(-15.5753 + 4.57333i) q^{58} +(-2.96131 + 3.41753i) q^{59} +(0.219000 - 0.307542i) q^{61} +(-3.10399 + 6.79679i) q^{62} +(-0.382671 - 2.66153i) q^{64} +(8.24039 + 7.85720i) q^{65} +(-2.01453 - 7.93358i) q^{67} -1.55641 q^{68} +(-1.58510 - 11.0246i) q^{70} +(-0.388199 - 8.14929i) q^{71} +(4.48201 - 6.29411i) q^{73} +(-3.54065 + 14.5948i) q^{74} +(0.567704 - 0.166693i) q^{76} +(2.12945 - 0.852503i) q^{77} +(-8.90008 + 1.71535i) q^{79} +(4.80482 - 13.8826i) q^{80} +(-14.6668 - 4.30657i) q^{82} +(7.61233 - 0.726890i) q^{83} +(-0.544471 - 0.280694i) q^{85} +(3.45917 + 14.2589i) q^{86} +(6.45187 + 0.616079i) q^{88} +(1.67719 - 11.6651i) q^{89} +(12.5589 + 8.07113i) q^{91} +(11.7493 + 13.5594i) q^{92} +(-5.81572 - 12.7346i) q^{94} +(0.228659 + 0.0440705i) q^{95} +(2.10502 + 3.64600i) q^{97} +(1.11301 + 3.21582i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8}+O(q^{10}) $ 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8	$ 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8} + 8 q^{10} + 24 q^{11} - 22 q^{13} + 32 q^{14} - 28 q^{16} - 17 q^{17} + 15 q^{20} + 49 q^{22} + 13 q^{23} - 34 q^{25} + 27 q^{26} + 22 q^{28} - 8 q^{29} + 10 q^{31} - 34 q^{32} - 50 q^{34} + q^{35} + 7 q^{37} - 50 q^{38} + 43 q^{40} + 5 q^{41} + 2 q^{43} + 19 q^{44} + 52 q^{46} + 6 q^{47} - 27 q^{49} - 134 q^{50} + 120 q^{52} + 52 q^{53} - 64 q^{55} + 124 q^{56} - 56 q^{58} - 27 q^{59} - 16 q^{61} + 74 q^{62} - 197 q^{64} + 92 q^{65} - 56 q^{67} - 16 q^{68} - 22 q^{70} + 113 q^{71} + q^{73} + 24 q^{74} - 144 q^{76} - 85 q^{77} + 36 q^{79} + 13 q^{80} - 20 q^{82} + 61 q^{83} - 6 q^{85} - 189 q^{86} + 129 q^{88} - 95 q^{89} + 42 q^{91} - 4 q^{92} + 70 q^{94} + 20 q^{95} + 53 q^{97} - q^{98}+O(q^{100}) $ 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8 + 8 * q^10 + 24 * q^11 - 22 * q^13 + 32 * q^14 - 28 * q^16 - 17 * q^17 + 15 * q^20 + 49 * q^22 + 13 * q^23 - 34 * q^25 + 27 * q^26 + 22 * q^28 - 8 * q^29 + 10 * q^31 - 34 * q^32 - 50 * q^34 + q^35 + 7 * q^37 - 50 * q^38 + 43 * q^40 + 5 * q^41 + 2 * q^43 + 19 * q^44 + 52 * q^46 + 6 * q^47 - 27 * q^49 - 134 * q^50 + 120 * q^52 + 52 * q^53 - 64 * q^55 + 124 * q^56 - 56 * q^58 - 27 * q^59 - 16 * q^61 + 74 * q^62 - 197 * q^64 + 92 * q^65 - 56 * q^67 - 16 * q^68 - 22 * q^70 + 113 * q^71 + q^73 + 24 * q^74 - 144 * q^76 - 85 * q^77 + 36 * q^79 + 13 * q^80 - 20 * q^82 + 61 * q^83 - 6 * q^85 - 189 * q^86 + 129 * q^88 - 95 * q^89 + 42 * q^91 - 4 * q^92 + 70 * q^94 + 20 * q^95 + 53 * q^97 - q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{8}{33}\right)$	$1$

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 $

$2$	1.86173	+	1.77515i	1.31644	+	1.25522i	0.945122	+	0.326717i	$0.105942\pi$
$2$	1.86173	+	1.77515i	1.31644	+	1.25522i	0.371317	+	0.928506i	$0.378906\pi$
$3$		0			0
$3$		0			0
$4$	0.219695	+	4.61197i	0.109848	+	2.30598i
$5$	−0.754900	+	1.65300i	−0.337601	+	0.739244i	−0.999950	−	0.00995145i	$-0.996832\pi$
$5$	−0.754900	+	1.65300i	−0.337601	+	0.739244i	0.662349	+	0.749195i	$0.269560\pi$
$6$		0			0
$7$	−0.561736	+	2.31551i	−0.212316	+	0.875179i	0.761559	+	0.648095i	$0.224434\pi$
$7$	−0.561736	+	2.31551i	−0.212316	+	0.875179i	−0.973875	+	0.227083i	$0.927081\pi$
$8$	−4.40882	+	5.08805i	−1.55875	+	1.79890i
$9$		0			0
$10$	−4.33974	+	1.73737i	−1.37235	+	0.549405i
$11$	−0.558411	−	0.784179i	−0.168367	−	0.236439i	0.721768	−	0.692135i	$-0.243330\pi$
$11$	−0.558411	−	0.784179i	−0.168367	−	0.236439i	−0.890135	+	0.455696i	$0.849390\pi$
$12$		0			0
$13$	2.04927	−	5.92099i	0.568366	−	1.64219i	−0.183612	−	0.982999i	$-0.558779\pi$
$13$	2.04927	−	5.92099i	0.568366	−	1.64219i	0.751978	−	0.659188i	$-0.229100\pi$
$14$	−5.15617	+	3.31367i	−1.37805	+	0.885616i
$15$		0			0
$16$	−8.04750	+	0.768443i	−2.01187	+	0.192111i
$17$	−0.0160394	+	0.336709i	−0.00389013	+	0.0816638i	−0.999977	−	0.00671022i	$-0.997864\pi$
$17$	−0.0160394	+	0.336709i	−0.00389013	+	0.0816638i	0.996087	+	0.0883741i	$0.0281671\pi$
$18$		0			0
$19$	−0.0302113	−	0.124533i	−0.00693096	−	0.0285698i	0.968241	−	0.250018i	$-0.0804367\pi$
$19$	−0.0302113	−	0.124533i	−0.00693096	−	0.0285698i	−0.975172	+	0.221449i	$0.928922\pi$
$20$	−7.78943	−	3.11842i	−1.74177	−	0.697299i
$21$		0			0
$22$	0.352428	−	2.45119i	0.0751380	−	0.522596i
$23$	3.05448	−	2.40207i	0.636904	−	0.500867i	−0.246706	−	0.969090i	$-0.579348\pi$
$23$	3.05448	−	2.40207i	0.636904	−	0.500867i	0.883610	+	0.468224i	$0.155106\pi$
$24$		0			0
$25$	1.11177	+	1.28305i	0.222354	+	0.256610i
$26$	14.3258	−	7.38549i	2.80953	−	1.44841i
$27$		0			0
$28$	−10.8024	−	2.08200i	−2.04147	−	0.393461i
$29$	−3.15521	+	5.46499i	−0.585908	+	1.01482i	0.408853	+	0.912600i	$0.365929\pi$
$29$	−3.15521	+	5.46499i	−0.585908	+	1.01482i	−0.994762	+	0.102223i	$0.967405\pi$
$30$		0			0
$31$	0.950033	+	2.74494i	0.170631	+	0.493006i	0.997600	−	0.0692417i	$-0.0220580\pi$
$31$	0.950033	+	2.74494i	0.170631	+	0.493006i	−0.826969	+	0.562248i	$0.809937\pi$
$32$	−5.76222	−	4.53146i	−1.01863	−	0.801057i
$33$		0			0
$34$	−0.627570	+	0.598387i	−0.107627	+	0.102623i
$35$	−3.40348	−	2.67652i	−0.575292	−	0.452415i
$36$		0			0
$37$	2.91909	+	5.05602i	0.479896	+	0.831205i	0.999734	−	0.0230603i	$-0.00734098\pi$
$37$	2.91909	+	5.05602i	0.479896	+	0.831205i	−0.519838	+	0.854265i	$0.674008\pi$
$38$	0.164820	−	0.285476i	0.0267373	−	0.0463103i
$39$		0			0
$40$	−5.08232	−	11.1287i	−0.803586	−	1.75961i
$41$	−5.28177	+	2.72294i	−0.824873	+	0.425252i	−0.818345	−	0.574727i	$-0.805108\pi$
$41$	−5.28177	+	2.72294i	−0.824873	+	0.425252i	−0.00652797	+	0.999979i	$0.502078\pi$
$42$		0			0
$43$	4.79837	+	3.08373i	0.731745	+	0.470264i	0.852704	−	0.522394i	$-0.174961\pi$
$43$	4.79837	+	3.08373i	0.731745	+	0.470264i	−0.120960	+	0.992657i	$0.538597\pi$
$44$	3.49393	−	2.74765i	0.526729	−	0.414225i
$45$		0			0
$46$	9.95066	+	0.950173i	1.46714	+	0.140095i
$47$	−5.05247	−	2.02271i	−0.736979	−	0.295042i	−0.0273583	−	0.999626i	$-0.508709\pi$
$47$	−5.05247	−	2.02271i	−0.736979	−	0.295042i	−0.709621	+	0.704584i	$0.751134\pi$
$48$		0			0
$49$	1.17583	+	0.606182i	0.167976	+	0.0865975i
$50$	−0.207800	+	4.36225i	−0.0293873	+	0.616915i
$51$		0			0
$52$	27.7576	+	8.15037i	3.84929	+	1.13025i
$53$	11.3238	−	7.27737i	1.55544	−	0.999623i	0.571613	−	0.820523i	$-0.306318\pi$
$53$	11.3238	−	7.27737i	1.55544	−	0.999623i	0.983831	−	0.179100i	$-0.0573186\pi$
$54$		0			0
$55$	1.71779	−	0.331077i	0.231627	−	0.0446425i
$56$	−9.30481	−	13.0668i	−1.24341	−	1.74612i
$57$		0			0
$58$	−15.5753	+	4.57333i	−2.04514	+	0.600508i
$59$	−2.96131	+	3.41753i	−0.385530	+	0.444925i	−0.915031	−	0.403384i	$-0.867834\pi$
$59$	−2.96131	+	3.41753i	−0.385530	+	0.444925i	0.529501	+	0.848309i	$0.322379\pi$
$60$		0			0
$61$	0.219000	−	0.307542i	0.0280401	−	0.0393768i	−0.800318	−	0.599576i	$-0.795336\pi$
$61$	0.219000	−	0.307542i	0.0280401	−	0.0393768i	0.828358	+	0.560199i	$0.189275\pi$
$62$	−3.10399	+	6.79679i	−0.394207	+	0.863193i
$63$		0			0
$64$	−0.382671	−	2.66153i	−0.0478338	−	0.332691i
$65$	8.24039	+	7.85720i	1.02210	+	0.974566i
$66$		0			0
$67$	−2.01453	−	7.93358i	−0.246114	−	0.969241i
$67$	−2.01453	−	7.93358i	−0.246114	−	0.969241i
$68$	−1.55641			−0.188743
$69$		0			0
$70$	−1.58510	−	11.0246i	−0.189456	−	1.31770i
$71$	−0.388199	−	8.14929i	−0.0460707	−	0.967143i	−0.897046	−	0.441937i	$-0.854291\pi$
$71$	−0.388199	−	8.14929i	−0.0460707	−	0.967143i	0.850975	−	0.525206i	$-0.176012\pi$
$72$		0			0
$73$	4.48201	−	6.29411i	0.524580	−	0.736670i	−0.464252	−	0.885703i	$-0.653677\pi$
$73$	4.48201	−	6.29411i	0.524580	−	0.736670i	0.988832	+	0.149033i	$0.0476162\pi$
$74$	−3.54065	+	14.5948i	−0.411593	+	1.69661i
$75$		0			0
$76$	0.567704	−	0.166693i	0.0651201	−	0.0191210i
$77$	2.12945	−	0.852503i	0.242673	−	0.0971518i
$78$		0			0
$79$	−8.90008	+	1.71535i	−1.00134	+	0.192992i	−0.663471	−	0.748202i	$-0.730917\pi$
$79$	−8.90008	+	1.71535i	−1.00134	+	0.192992i	−0.337867	+	0.941194i	$0.609705\pi$
$80$	4.80482	−	13.8826i	0.537195	−	1.55212i
$81$		0			0
$82$	−14.6668	−	4.30657i	−1.61968	−	0.475581i
$83$	7.61233	−	0.726890i	0.835562	−	0.0797865i	0.331501	−	0.943455i	$-0.392445\pi$
$83$	7.61233	−	0.726890i	0.835562	−	0.0797865i	0.504061	+	0.863668i	$0.331839\pi$
$84$		0			0
$85$	−0.544471	−	0.280694i	−0.0590562	−	0.0304456i
$86$	3.45917	+	14.2589i	0.373012	+	1.53758i
$87$		0			0
$88$	6.45187	+	0.616079i	0.687772	+	0.0656743i
$89$	1.67719	−	11.6651i	0.177782	−	1.23650i	−0.684098	−	0.729390i	$-0.739804\pi$
$89$	1.67719	−	11.6651i	0.177782	−	1.23650i	0.861880	−	0.507112i	$-0.169287\pi$
$90$		0			0
$91$	12.5589	+	8.07113i	1.31653	+	0.846085i
$92$	11.7493	+	13.5594i	1.22495	+	1.41367i
$93$		0			0
$94$	−5.81572	−	12.7346i	−0.599845	−	1.31348i
$95$	0.228659	+	0.0440705i	0.0234599	+	0.00452153i
$96$		0			0
$97$	2.10502	+	3.64600i	0.213732	+	0.370195i	0.952880	−	0.303349i	$-0.0981047\pi$
$97$	2.10502	+	3.64600i	0.213732	+	0.370195i	−0.739148	+	0.673544i	$0.764771\pi$
$98$	1.11301	+	3.21582i	0.112431	+	0.324847i
$99$		0			0
$100$	−5.67313	+	5.40932i	−0.567313	+	0.540932i
$101$	12.7248	−	12.1331i	1.26616	−	1.20729i	0.298681	−	0.954353i	$-0.403453\pi$
$101$	12.7248	−	12.1331i	1.26616	−	1.20729i	0.967484	−	0.252933i	$-0.0813951\pi$
$102$		0			0
$103$	−4.53246	−	13.0957i	−0.446596	−	1.29035i	−0.913785	−	0.406197i	$-0.866855\pi$
$103$	−4.53246	−	13.0957i	−0.446596	−	1.29035i	0.467189	−	0.884157i	$-0.345267\pi$
$104$	21.0914	+	36.5314i	2.06818	+	3.58219i
$105$		0			0
$106$	34.0003	+	6.55302i	3.30240	+	0.636485i
$107$	0.00817512	+	0.0179010i	0.000790318	+	0.00173056i	0.910027	−	0.414550i	$-0.136061\pi$
$107$	0.00817512	+	0.0179010i	0.000790318	+	0.00173056i	−0.909236	+	0.416280i	$0.863334\pi$
$108$		0			0
$109$	2.03292	+	2.34612i	0.194719	+	0.224717i	0.844710	−	0.535224i	$-0.179773\pi$
$109$	2.03292	+	2.34612i	0.194719	+	0.224717i	−0.649991	+	0.759942i	$0.725227\pi$
$110$	3.78577	+	2.43297i	0.360959	+	0.231974i
$111$		0			0
$112$	2.74123	−	19.0657i	0.259022	−	1.80154i
$113$	−5.64512	−	0.539044i	−0.531049	−	0.0507090i	−0.173912	−	0.984761i	$-0.555641\pi$
$113$	−5.64512	−	0.539044i	−0.531049	−	0.0507090i	−0.357137	+	0.934052i	$0.616247\pi$
$114$		0			0
$115$	1.66480	+	6.86238i	0.155243	+	0.639920i
$116$	−25.8975	−	13.3511i	−2.40453	−	1.23962i
$117$		0			0
$118$	−11.5798	+	1.10574i	−1.06601	+	0.101791i
$119$	−0.770641	−	0.226281i	−0.0706445	−	0.0207431i
$120$		0			0
$121$	3.29463	−	9.51922i	0.299512	−	0.865384i
$122$	0.953653	−	0.183801i	0.0863397	−	0.0166406i
$123$		0			0
$124$	−12.4509	+	4.98457i	−1.11812	+	0.447628i
$125$	−11.6782	+	3.42903i	−1.04453	+	0.306702i
$126$		0			0
$127$	−2.94486	+	12.1389i	−0.261314	+	1.07715i	0.678264	+	0.734819i	$0.262733\pi$
$127$	−2.94486	+	12.1389i	−0.261314	+	1.07715i	−0.939578	+	0.342334i	$0.888782\pi$
$128$	−4.49210	+	6.30828i	−0.397050	+	0.557578i
$129$		0			0
$130$	1.39363	+	29.2559i	0.122230	+	2.56591i
$131$	−1.49233	−	10.3794i	−0.130385	−	0.906849i	−0.945052	−	0.326920i	$-0.893989\pi$
$131$	−1.49233	−	10.3794i	−0.130385	−	0.906849i	0.814667	−	0.579929i	$-0.196920\pi$
$132$		0			0
$133$	0.305327			0.0264752
$134$	10.3328	−	18.3463i	0.892619	−	1.58488i
$135$		0			0
$136$	−1.64247	−	1.56610i	−0.140841	−	0.134292i
$137$	−0.502113	−	3.49228i	−0.0428984	−	0.298365i	−0.999964	−	0.00849346i	$-0.997296\pi$
$137$	−0.502113	−	3.49228i	−0.0428984	−	0.298365i	0.957065	−	0.289872i	$-0.0936127\pi$
$138$		0			0
$139$	3.91046	−	8.56271i	0.331681	−	0.726280i	−0.668162	−	0.744016i	$-0.732919\pi$
$139$	3.91046	−	8.56271i	0.331681	−	0.726280i	0.999843	+	0.0177363i	$0.00564594\pi$
$140$	11.5963	−	16.2847i	0.980067	−	1.37631i
$141$		0			0
$142$	13.7435	−	15.8609i	1.15333	−	1.33101i
$143$	−5.78745	+	1.69935i	−0.483971	+	0.142107i
$144$		0			0
$145$	−6.65176	−	9.34108i	−0.552398	−	0.775735i
$146$	19.5173	−	3.76165i	1.61526	−	0.311316i
$147$		0			0
$148$	−22.6769	+	14.5735i	−1.86403	+	1.19794i
$149$	−9.85168	−	2.89271i	−0.807081	−	0.236980i	−0.147937	−	0.988997i	$-0.547263\pi$
$149$	−9.85168	−	2.89271i	−0.807081	−	0.236980i	−0.659144	+	0.752017i	$0.729081\pi$
$150$		0			0
$151$	−0.235686	+	4.94766i	−0.0191799	+	0.402635i	0.968780	+	0.247923i	$0.0797480\pi$
$151$	−0.235686	+	4.94766i	−0.0191799	+	0.402635i	−0.987960	+	0.154712i	$0.950555\pi$
$152$	0.766825	+	0.395326i	0.0621977	+	0.0320652i
$153$		0			0
$154$	5.47778	+	2.19297i	0.441412	+	0.176715i
$155$	−5.25457	−	0.501750i	−0.422057	−	0.0403016i
$156$		0			0
$157$	−11.4726	+	9.02217i	−0.915615	+	0.720048i	−0.960305	−	0.278953i	$-0.910013\pi$
$157$	−11.4726	+	9.02217i	−0.915615	+	0.720048i	0.0446895	+	0.999001i	$0.485770\pi$
$158$	−19.6145	−	12.6055i	−1.56045	−	1.00284i
$159$		0			0
$160$	11.8404	−	6.10415i	0.936066	−	0.482576i
$161$	3.84620	+	8.42200i	0.303123	+	0.663747i
$162$		0			0
$163$	−4.45606	+	7.71812i	−0.349025	+	0.604530i	−0.986077	−	0.166292i	$-0.946821\pi$
$163$	−4.45606	+	7.71812i	−0.349025	+	0.604530i	0.637051	+	0.770822i	$0.280154\pi$
$164$	−13.7185	−	23.7611i	−1.07123	−	1.85543i
$165$		0			0
$166$	15.4624	+	12.1598i	1.20012	+	0.943782i
$167$	−2.43384	+	2.32066i	−0.188336	+	0.179578i	−0.778381	−	0.627793i	$-0.783959\pi$
$167$	−2.43384	+	2.32066i	−0.188336	+	0.179578i	0.590045	+	0.807371i	$0.299110\pi$
$168$		0			0
$169$	−20.6399	−	16.2314i	−1.58768	−	1.24857i
$170$	−0.515381	−	1.48910i	−0.0395279	−	0.114208i
$171$		0			0
$172$	−13.1679	+	22.8074i	−1.00404	+	1.73905i
$173$	19.4242	+	3.74370i	1.47679	+	0.284628i	0.863147	−	0.504953i	$-0.168490\pi$
$173$	19.4242	+	3.74370i	1.47679	+	0.284628i	0.613646	+	0.789581i	$0.289702\pi$
$174$		0			0
$175$	−3.59543	+	1.85357i	−0.271789	+	0.140117i
$176$	5.09641	+	5.88157i	0.384157	+	0.443340i
$177$		0			0
$178$	23.8299	−	18.7400i	1.78613	−	1.40463i
$179$	−2.34681	+	16.3224i	−0.175408	+	1.21999i	0.691815	+	0.722074i	$0.256811\pi$
$179$	−2.34681	+	16.3224i	−0.175408	+	1.21999i	−0.867224	+	0.497918i	$0.834098\pi$
$180$		0			0
$181$	−18.5810	−	7.43871i	−1.38111	−	0.552915i	−0.442154	−	0.896939i	$-0.645785\pi$
$181$	−18.5810	−	7.43871i	−1.38111	−	0.552915i	−0.938961	+	0.344025i	$0.888210\pi$
$182$	9.05380	+	37.3203i	0.671112	+	2.76636i
$183$		0			0
$184$	−1.24480	+	26.1316i	−0.0917681	+	1.92645i
$185$	−10.5612	+	1.00847i	−0.776477	+	0.0741445i
$186$		0			0
$187$	0.272996	−	0.175444i	0.0199635	−	0.0128298i
$188$	8.21865	−	23.7462i	0.599406	−	1.73187i
$189$		0			0
$190$	0.347469	+	0.487952i	0.0252081	+	0.0353998i
$191$	4.47213	−	1.79037i	0.323592	−	0.129547i	−0.204179	−	0.978934i	$-0.565452\pi$
$191$	4.47213	−	1.79037i	0.323592	−	0.129547i	0.527771	+	0.849387i	$0.323028\pi$
$192$		0			0
$193$	9.16810	−	10.5805i	0.659934	−	0.761604i	−0.322832	−	0.946456i	$-0.604635\pi$
$193$	9.16810	−	10.5805i	0.659934	−	0.761604i	0.982766	+	0.184852i	$0.0591805\pi$
$194$	−2.55323	+	10.5246i	−0.183312	+	0.755621i
$195$		0			0
$196$	−2.53737	+	5.55606i	−0.181241	+	0.396862i
$197$	0.0796281	+	1.67160i	0.00567327	+	0.119097i	0.999927	+	0.0120510i	$0.00383605\pi$
$197$	0.0796281	+	1.67160i	0.00567327	+	0.119097i	−0.994254	+	0.107046i	$0.965861\pi$
$198$		0			0
$199$	2.98225	+	2.84357i	0.211406	+	0.201575i	0.788382	−	0.615186i	$-0.210919\pi$
$199$	2.98225	+	2.84357i	0.211406	+	0.201575i	−0.576976	+	0.816761i	$0.695767\pi$
$200$	−11.4298			−0.808210
$201$		0			0
$202$	45.2282			3.18224
$203$	−10.8818	−	10.3758i	−0.763754	−	0.728238i
$204$		0			0
$205$	−0.513815	−	10.7863i	−0.0358864	−	0.753348i
$206$	14.8086	−	32.4264i	1.03177	−	2.25925i
$207$		0			0
$208$	−11.9416	+	49.2239i	−0.828000	+	3.41306i
$209$	−0.0807857	+	0.0932317i	−0.00558806	+	0.00644897i
$210$		0			0
$211$	−3.73973	+	1.49716i	−0.257454	+	0.103069i	−0.496799	−	0.867866i	$-0.665491\pi$
$211$	−3.73973	+	1.49716i	−0.257454	+	0.103069i	0.239345	+	0.970934i	$0.423067\pi$
$212$	36.0508	+	50.6262i	2.47598	+	3.47702i
$213$		0			0
$214$	−0.0165572	+	0.0478389i	−0.00113183	+	0.00327020i
$215$	−8.71969	+	5.60380i	−0.594678	+	0.382176i
$216$		0			0
$217$	−6.88959	+	0.657876i	−0.467696	+	0.0446596i
$218$	−0.379971	+	7.97658i	−0.0257349	+	0.540242i
$219$		0			0
$220$	1.90431	+	7.84966i	0.128388	+	0.529224i
$221$	1.96078	+	0.784977i	0.131896	+	0.0528033i
$222$		0			0
$223$	−2.23472	+	15.5428i	−0.149648	+	1.04082i	0.767149	+	0.641469i	$0.221675\pi$
$223$	−2.23472	+	15.5428i	−0.149648	+	1.04082i	−0.916797	+	0.399354i	$0.869235\pi$
$224$	13.7295	−	10.7970i	0.917339	−	0.721403i
$225$		0			0
$226$	−9.55280	−	11.0245i	−0.635443	−	0.733340i
$227$	4.81226	−	2.48089i	0.319401	−	0.164663i	−0.291069	−	0.956702i	$-0.594011\pi$
$227$	4.81226	−	2.48089i	0.319401	−	0.164663i	0.610470	+	0.792039i	$0.290981\pi$
$228$		0			0
$229$	21.3254	+	4.11014i	1.40922	+	0.271606i	0.836421	−	0.548087i	$-0.184644\pi$
$229$	21.3254	+	4.11014i	1.40922	+	0.271606i	0.572803	+	0.819693i	$0.305856\pi$
$230$	−9.08238	+	15.7311i	−0.598875	+	1.03728i
$231$		0			0
$232$	−13.8954	−	40.1480i	−0.912275	−	2.63585i
$233$	8.14345	+	6.40408i	0.533495	+	0.419545i	0.848225	−	0.529636i	$-0.177672\pi$
$233$	8.14345	+	6.40408i	0.533495	+	0.419545i	−0.314730	+	0.949181i	$0.601914\pi$
$234$		0			0
$235$	7.15764	−	6.82480i	0.466913	−	0.445201i
$236$	−16.4121	−	12.9066i	−1.06834	−	0.840151i
$237$		0			0
$238$	−1.03304	−	1.78928i	−0.0669620	−	0.115982i
$239$	−10.5498	+	18.2728i	−0.682410	+	1.18197i	0.291833	+	0.956469i	$0.405735\pi$
$239$	−10.5498	+	18.2728i	−0.682410	+	1.18197i	−0.974243	+	0.225500i	$0.927599\pi$
$240$		0			0
$241$	−4.05164	−	8.87186i	−0.260989	−	0.571487i	0.733092	−	0.680130i	$-0.238077\pi$
$241$	−4.05164	−	8.87186i	−0.260989	−	0.571487i	−0.994081	+	0.108643i	$0.965349\pi$
$242$	23.0318	−	11.8737i	1.48054	−	0.763271i
$243$		0			0
$244$	1.46649	+	0.942455i	0.0938823	+	0.0603345i
$245$	−1.88965	+	1.48604i	−0.120726	+	0.0949396i
$246$		0			0
$247$	−0.799269	−	0.0763209i	−0.0508563	−	0.00485618i
$248$	−18.1549	−	7.26813i	−1.15284	−	0.461527i
$249$		0			0
$250$	−27.8287	−	14.3467i	−1.76004	−	0.907363i
$251$	−0.216942	+	4.55417i	−0.0136932	+	0.287456i	0.981626	+	0.190815i	$0.0611130\pi$
$251$	−0.216942	+	4.55417i	−0.0136932	+	0.287456i	−0.995319	+	0.0966415i	$0.969190\pi$
$252$		0			0
$253$	−3.58931	−	1.05392i	−0.225658	−	0.0662592i
$254$	−27.0309	+	17.3717i	−1.69607	+	1.09000i
$255$		0			0
$256$	−24.8419	+	4.78787i	−1.55262	+	0.299242i
$257$	−12.4172	−	17.4375i	−0.774564	−	1.08772i	−0.993705	−	0.112030i	$-0.964265\pi$
$257$	−12.4172	−	17.4375i	−0.774564	−	1.08772i	0.219141	−	0.975693i	$-0.429675\pi$
$258$		0			0
$259$	−13.3470	+	3.91903i	−0.829342	+	0.243517i
$260$	−34.4268	+	39.7306i	−2.13506	+	2.46399i
$261$		0			0
$262$	15.6467	−	21.9727i	0.966654	−	1.35748i
$263$	−0.367451	+	0.804604i	−0.0226580	+	0.0496140i	−0.920623	−	0.390453i	$-0.872318\pi$
$263$	−0.367451	+	0.804604i	−0.0226580	+	0.0496140i	0.897965	+	0.440068i	$0.145045\pi$
$264$		0			0
$265$	3.48115	+	24.2119i	0.213845	+	1.48733i
$266$	0.568436	+	0.542003i	0.0348530	+	0.0332323i
$267$		0			0
$268$	36.1468	−	11.0339i	2.20802	−	0.674004i
$269$	17.7676			1.08331			0.541654	−	0.840601i	$-0.317798\pi$
$269$	17.7676			1.08331			0.541654	+	0.840601i	$0.317798\pi$
$270$		0			0
$271$	−2.36892	−	16.4762i	−0.143902	−	1.00086i	−0.925951	−	0.377643i	$-0.876735\pi$
$271$	−2.36892	−	16.4762i	−0.143902	−	1.00086i	0.782049	−	0.623217i	$-0.214175\pi$
$272$	−0.129664	−	2.72199i	−0.00786205	−	0.165045i
$273$		0			0
$274$	5.26453	−	7.39299i	0.318042	−	0.446627i
$275$	0.385317	−	1.58830i	0.0232355	−	0.0957779i
$276$		0			0
$277$	4.60723	−	1.35281i	0.276822	−	0.0812822i	−0.140375	−	0.990098i	$-0.544831\pi$
$277$	4.60723	−	1.35281i	0.276822	−	0.0812822i	0.417197	+	0.908816i	$0.363013\pi$
$278$	22.4803	−	8.99977i	1.34828	−	0.539770i
$279$		0			0
$280$	28.6236	−	5.51674i	1.71059	−	0.329688i
$281$	6.03628	−	17.4407i	0.360094	−	1.04042i	−0.608880	−	0.793262i	$-0.708381\pi$
$281$	6.03628	−	17.4407i	0.360094	−	1.04042i	0.968974	−	0.247162i	$-0.0794979\pi$
$282$		0			0
$283$	−28.4468	−	8.35274i	−1.69099	−	0.496519i	−0.712301	−	0.701874i	$-0.752347\pi$
$283$	−28.4468	−	8.35274i	−1.69099	−	0.496519i	−0.978688	+	0.205355i	$0.934165\pi$
$284$	37.4990	−	3.58072i	2.22515	−	0.212476i
$285$		0			0
$286$	−13.7913	−	7.10989i	−0.815494	−	0.420417i
$287$	−3.33803	−	13.7595i	−0.197037	−	0.812199i
$288$		0			0
$289$	16.8099	+	1.60515i	0.988818	+	0.0944207i
$290$	4.19810	−	29.1984i	0.246521	−	1.71459i
$291$		0			0
$292$	30.0129	+	19.2881i	1.75637	+	1.12875i
$293$	1.30365	+	1.50449i	0.0761600	+	0.0878933i	0.792551	−	0.609806i	$-0.208753\pi$
$293$	1.30365	+	1.50449i	0.0761600	+	0.0878933i	−0.716391	+	0.697699i	$0.754207\pi$
$294$		0			0
$295$	−3.41369	−	7.47494i	−0.198753	−	0.435208i
$296$	−38.5950	−	7.43858i	−2.24329	−	0.432359i
$297$		0			0
$298$	−13.2061	−	22.8737i	−0.765010	−	1.32504i
$299$	−7.96317	−	23.0081i	−0.460522	−	1.33059i
$300$		0			0
$301$	−9.83580	+	9.37842i	−0.566926	+	0.540563i
$302$	−9.22164	+	8.79282i	−0.530646	+	0.505970i
$303$		0			0
$304$	0.338822	+	0.978962i	0.0194328	+	0.0561473i
$305$	0.343044	+	0.594170i	0.0196427	+	0.0340221i
$306$		0			0
$307$	19.2516	+	3.71044i	1.09875	+	0.211766i	0.706233	−	0.707980i	$-0.250393\pi$
$307$	19.2516	+	3.71044i	1.09875	+	0.211766i	0.392514	+	0.919746i	$0.371605\pi$
$308$	4.39955	+	9.63366i	0.250687	+	0.548929i
$309$		0			0
$310$	−8.89188	−	10.2618i	−0.505025	−	0.582830i
$311$	−5.62301	−	3.61369i	−0.318852	−	0.204913i	0.371418	−	0.928466i	$-0.378872\pi$
$311$	−5.62301	−	3.61369i	−0.318852	−	0.204913i	−0.690270	+	0.723552i	$0.742508\pi$
$312$		0			0
$313$	−1.37797	+	9.58402i	−0.0778877	+	0.541721i	0.913097	+	0.407743i	$0.133684\pi$
$313$	−1.37797	+	9.58402i	−0.0778877	+	0.541721i	−0.990984	+	0.133978i	$0.957225\pi$
$314$	−37.3746	−	3.56884i	−2.10917	−	0.201402i
$315$		0			0
$316$	−9.86644	−	40.6700i	−0.555031	−	2.28787i
$317$	−1.49970	−	0.773149i	−0.0842315	−	0.0434243i	0.415596	−	0.909549i	$-0.363573\pi$
$317$	−1.49970	−	0.773149i	−0.0842315	−	0.0434243i	−0.499828	+	0.866125i	$0.666603\pi$
$318$		0			0
$319$	6.04744	−	0.577460i	0.338591	−	0.0323316i
$320$	4.68839	+	1.37664i	0.262089	+	0.0769562i
$321$		0			0
$322$	−7.78977	+	22.5071i	−0.434107	+	1.25427i
$323$	0.0424159	−	0.00817499i	0.00236008	−	0.000454868i
$324$		0			0
$325$	9.87525	−	3.95345i	0.547780	−	0.219298i
$326$	−21.9968	+	6.45885i	−1.21829	+	0.357722i
$327$		0			0
$328$	9.43190	−	38.8788i	0.520789	−	2.14672i
$329$	7.52174	−	10.5628i	0.414687	−	0.582346i
$330$		0			0
$331$	−1.64894	−	34.6156i	−0.0906342	−	1.90265i	−0.349817	−	0.936818i	$-0.613756\pi$
$331$	−1.64894	−	34.6156i	−0.0906342	−	1.90265i	0.259183	−	0.965828i	$-0.416547\pi$
$332$	5.02478	+	34.9481i	0.275771	+	1.91803i
$333$		0			0
$334$	−8.65066			−0.473343
$335$	14.6350	+	2.65904i	0.799594	+	0.145279i
$336$		0			0
$337$	−18.9656	−	18.0837i	−1.03312	−	0.985082i	−0.0332279	−	0.999448i	$-0.510579\pi$
$337$	−18.9656	−	18.0837i	−1.03312	−	0.985082i	−0.999897	+	0.0143654i	$0.995427\pi$
$338$	−9.61264	−	66.8574i	−0.522859	−	3.63656i
$339$		0			0
$340$	1.17494	−	2.57275i	0.0637198	−	0.139527i
$341$	1.62202	−	2.27780i	0.0878371	−	0.123350i
$342$		0			0
$343$	−12.9863	+	14.9870i	−0.701196	+	0.809224i
$344$	−36.8453	+	10.8188i	−1.98656	+	0.583308i
$345$		0			0
$346$	29.5169	+	41.4506i	1.58684	+	2.22840i
$347$	−10.7395	+	2.06988i	−0.576528	+	0.111117i	−0.469177	−	0.883104i	$-0.655449\pi$
$347$	−10.7395	+	2.06988i	−0.576528	+	0.111117i	−0.107352	+	0.994221i	$0.534237\pi$
$348$		0			0
$349$	23.7459	−	15.2606i	1.27109	−	0.816879i	0.281328	−	0.959612i	$-0.409225\pi$
$349$	23.7459	−	15.2606i	1.27109	−	0.816879i	0.989761	+	0.142733i	$0.0455889\pi$
$350$	−9.98409	−	2.93159i	−0.533672	−	0.156700i
$351$		0			0
$352$	−0.335787	+	7.04904i	−0.0178975	+	0.375715i
$353$	−7.69078	−	3.96487i	−0.409339	−	0.211029i	0.241243	−	0.970465i	$-0.422445\pi$
$353$	−7.69078	−	3.96487i	−0.409339	−	0.211029i	−0.650582	+	0.759436i	$0.725475\pi$
$354$		0			0
$355$	13.7638	+	5.51020i	0.730508	+	0.292451i
$356$	54.1677	+	5.17239i	2.87088	+	0.274136i
$357$		0			0
$358$	−33.3439	+	26.2219i	−1.76228	+	1.38587i
$359$	−13.1177	−	8.43023i	−0.692326	−	0.444931i	0.146586	−	0.989198i	$-0.453171\pi$
$359$	−13.1177	−	8.43023i	−0.692326	−	0.444931i	−0.838912	+	0.544267i	$0.816808\pi$
$360$		0			0
$361$	16.8733	−	8.69878i	0.888067	−	0.457830i
$362$	−21.3879	−	46.8329i	−1.12412	−	2.46148i
$363$		0			0
$364$	−34.4647	+	59.6945i	−1.80644	+	3.12884i
$365$	7.02069	+	12.1602i	0.367480	+	0.636493i
$366$		0			0
$367$	−22.1509	−	17.4197i	−1.15627	−	0.909298i	−0.159308	−	0.987229i	$-0.550926\pi$
$367$	−22.1509	−	17.4197i	−1.15627	−	0.909298i	−0.996959	+	0.0779305i	$0.975169\pi$
$368$	−22.7351	+	21.6779i	−1.18515	+	1.13004i
$369$		0			0
$370$	−21.4523	−	16.8703i	−1.11525	−	0.877044i
$371$	10.4898	+	30.3083i	0.544603	+	1.57353i
$372$		0			0
$373$	−11.1644	+	19.3373i	−0.578071	+	1.00125i	0.417629	+	0.908618i	$0.362861\pi$
$373$	−11.1644	+	19.3373i	−0.578071	+	1.00125i	−0.995700	+	0.0926315i	$0.970472\pi$
$374$	0.819685	+	0.157981i	0.0423849	+	0.00816902i
$375$		0			0
$376$	32.5671	−	16.7895i	1.67952	−	0.865852i
$377$	25.8922	+	29.8812i	1.33352	+	1.53896i
$378$		0			0
$379$	−24.4813	+	19.2523i	−1.25752	+	0.988926i	−0.257780	+	0.966204i	$0.582991\pi$
$379$	−24.4813	+	19.2523i	−1.25752	+	0.988926i	−0.999742	+	0.0227224i	$0.992767\pi$
$380$	−0.153016	+	1.06425i	−0.00784956	+	0.0545949i
$381$		0			0
$382$	11.5041	+	4.60554i	0.588600	+	0.235640i
$383$	1.05848	+	4.36310i	0.0540857	+	0.222944i	0.992440	−	0.122731i	$-0.0391652\pi$
$383$	1.05848	+	4.36310i	0.0540857	+	0.222944i	−0.938354	+	0.345675i	$0.887650\pi$
$384$		0			0
$385$	−0.198334	+	4.16354i	−0.0101080	+	0.212193i
$386$	35.8506	−	3.42332i	1.82475	−	0.174242i
$387$		0			0
$388$	−16.3527	+	10.5093i	−0.830185	+	0.533528i
$389$	1.28670	−	3.71767i	0.0652382	−	0.188493i	−0.907670	−	0.419684i	$-0.862141\pi$
$389$	1.28670	−	3.71767i	0.0652382	−	0.188493i	0.972908	+	0.231191i	$0.0742621\pi$
$390$		0			0
$391$	0.759806	+	1.06700i	0.0384251	+	0.0539604i
$392$	−8.26830	+	3.31013i	−0.417612	+	0.167187i
$393$		0			0
$394$	−2.81910	+	3.25342i	−0.142024	+	0.163905i
$395$	3.88320	−	16.0068i	0.195385	−	0.805387i
$396$		0			0
$397$	−11.6540	+	25.5187i	−0.584898	+	1.28075i	0.353578	+	0.935405i	$0.384965\pi$
$397$	−11.6540	+	25.5187i	−0.584898	+	1.28075i	−0.938476	+	0.345343i	$0.887763\pi$
$398$	0.504364	+	10.5879i	0.0252815	+	0.530724i
$399$		0			0
$400$	−9.93291	−	9.47102i	−0.496646	−	0.473551i
$401$	15.1771			0.757909			0.378954	−	0.925415i	$-0.376284\pi$
$401$	15.1771			0.757909			0.378954	+	0.925415i	$0.376284\pi$
$402$		0			0
$403$	18.1996			0.906589
$404$	58.7529	+	56.0208i	2.92307	+	2.78714i
$405$		0			0
$406$	−1.84035	−	38.6338i	−0.0913352	−	1.91736i
$407$	2.33477	−	5.11243i	0.115730	−	0.253414i
$408$		0			0
$409$	1.93659	−	7.98271i	0.0957580	−	0.394720i	−0.903681	−	0.428206i	$-0.859146\pi$
$409$	1.93659	−	7.98271i	0.0957580	−	0.394720i	0.999439	+	0.0334861i	$0.0106609\pi$
$410$	18.1908	−	20.9932i	0.898377	−	1.03678i
$411$		0			0
$412$	59.4010	−	23.7806i	2.92648	−	1.17159i
$413$	−6.24984	−	8.77668i	−0.307535	−	0.431872i
$414$		0			0
$415$	−4.54500	+	13.1319i	−0.223105	+	0.644620i
$416$	−38.6391	+	24.8318i	−1.89444	+	1.21748i
$417$		0			0
$418$	−0.315901	+	0.0301649i	−0.0154512	+	0.00147541i
$419$	−0.176707	+	3.70954i	−0.00863271	+	0.181223i	0.990433	+	0.137997i	$0.0440665\pi$
$419$	−0.176707	+	3.70954i	−0.00863271	+	0.181223i	−0.999065	+	0.0432257i	$0.986237\pi$
$420$		0			0
$421$	2.63777	+	10.8730i	0.128557	+	0.529919i	0.999273	+	0.0381325i	$0.0121409\pi$
$421$	2.63777	+	10.8730i	0.128557	+	0.529919i	−0.870716	+	0.491787i	$0.836344\pi$
$422$	−9.62005	−	3.85129i	−0.468297	−	0.187478i
$423$		0			0
$424$	−12.8970	+	89.7006i	−0.626334	+	4.35625i
$425$	−0.449846	+	0.353763i	−0.0218207	+	0.0171600i
$426$		0			0
$427$	0.589096	+	0.679853i	0.0285083	+	0.0329004i
$428$	−0.0807628	+	0.0416361i	−0.00390382	+	0.00201256i
$429$		0			0
$430$	−26.1813	−	5.04603i	−1.26257	−	0.243341i
$431$	−18.9031	+	32.7412i	−0.910531	+	1.57709i	−0.0972161	+	0.995263i	$0.530994\pi$
$431$	−18.9031	+	32.7412i	−0.910531	+	1.57709i	−0.813315	+	0.581823i	$0.802340\pi$
$432$		0			0
$433$	−3.46691	−	10.0170i	−0.166609	−	0.481385i	0.830530	−	0.556974i	$-0.188038\pi$
$433$	−3.46691	−	10.0170i	−0.166609	−	0.481385i	−0.997139	+	0.0755886i	$0.975916\pi$
$434$	−13.9944	−	11.0053i	−0.671751	−	0.528271i
$435$		0			0
$436$	−10.3736	+	9.89120i	−0.496805	+	0.473702i
$437$	−0.391417	−	0.307814i	−0.0187240	−	0.0147247i
$438$		0			0
$439$	4.03018	+	6.98047i	0.192350	+	0.333160i	0.946029	−	0.324083i	$-0.105056\pi$
$439$	4.03018	+	6.98047i	0.192350	+	0.333160i	−0.753679	+	0.657243i	$0.771722\pi$
$440$	−5.88890	+	10.1999i	−0.280742	+	0.486260i
$441$		0			0
$442$	2.25698	+	4.94210i	0.107354	+	0.235072i
$443$	−33.3704	+	17.2036i	−1.58547	+	0.817368i	−0.585496	+	0.810675i	$0.699100\pi$
$443$	−33.3704	+	17.2036i	−1.58547	+	0.817368i	−0.999978	+	0.00669294i	$0.997870\pi$
$444$		0			0
$445$	18.0164	+	11.5784i	0.854058	+	0.548870i
$446$	−31.7513	+	24.9695i	−1.50347	+	1.18234i
$447$		0			0
$448$	6.37775	+	0.609001i	0.301320	+	0.0287726i
$449$	−2.46030	−	0.984957i	−0.116109	−	0.0464830i	0.312881	−	0.949792i	$-0.398706\pi$
$449$	−2.46030	−	0.984957i	−0.116109	−	0.0464830i	−0.428990	+	0.903309i	$0.641130\pi$
$450$		0			0
$451$	5.08467	+	2.62133i	0.239428	+	0.123434i
$452$	1.24585	−	26.1535i	0.0585997	−	1.23016i
$453$		0			0
$454$	13.3631	+	3.92376i	0.627161	+	0.184151i
$455$	−22.8223	+	14.6670i	−1.06993	+	0.687600i
$456$		0			0
$457$	3.15211	−	0.607520i	0.147450	−	0.0284186i	−0.114992	−	0.993366i	$-0.536684\pi$
$457$	3.15211	−	0.607520i	0.147450	−	0.0284186i	0.262442	+	0.964948i	$0.415472\pi$
$458$	32.4060	+	45.5079i	1.51423	+	2.12644i
$459$		0			0
$460$	−31.2833	+	9.18561i	−1.45859	+	0.428281i
$461$	−8.33932	+	9.62409i	−0.388401	+	0.448238i	−0.915954	−	0.401284i	$-0.868564\pi$
$461$	−8.33932	+	9.62409i	−0.388401	+	0.448238i	0.527553	+	0.849522i	$0.323110\pi$
$462$		0			0
$463$	−14.5682	+	20.4582i	−0.677042	+	0.950773i	0.322948	+	0.946417i	$0.395326\pi$
$463$	−14.5682	+	20.4582i	−0.677042	+	0.950773i	−0.999991	+	0.00435596i	$0.998613\pi$
$464$	21.1920	−	46.4041i	0.983816	−	2.15426i
$465$		0			0
$466$	3.79266	+	26.3785i	0.175691	+	1.22196i
$467$	−3.55683	−	3.39143i	−0.164590	−	0.156937i	0.603308	−	0.797508i	$-0.293849\pi$
$467$	−3.55683	−	3.39143i	−0.164590	−	0.156937i	−0.767898	+	0.640572i	$0.778697\pi$
$468$		0			0
$469$	19.5019	−	0.208084i	0.900513	−	0.00960841i
$470$	25.4406			1.17349
$471$		0			0
$472$	−4.33270	−	30.1346i	−0.199429	−	1.38706i
$473$	−0.261272	−	5.48477i	−0.0120133	−	0.252190i
$474$		0			0
$475$	0.126194	−	0.177214i	0.00579017	−	0.00813116i
$476$	0.874292	−	3.60388i	0.0400731	−	0.165184i
$477$		0			0
$478$	−52.0779	+	15.2914i	−2.38199	+	0.699414i
$479$	14.3077	−	5.72796i	0.653737	−	0.261717i	−0.0209948	−	0.999780i	$-0.506683\pi$
$479$	14.3077	−	5.72796i	0.653737	−	0.261717i	0.674732	+	0.738063i	$0.264259\pi$
$480$		0			0
$481$	35.9187	−	6.92275i	1.63775	−	0.315650i
$482$	8.20586	−	23.7093i	0.373767	−	1.07993i
$483$		0			0
$484$	44.6261	+	13.1034i	2.02846	+	0.595610i
$485$	−7.61591	+	0.727231i	−0.345820	+	0.0330219i
$486$		0			0
$487$	−15.1136	−	7.79162i	−0.684864	−	0.353072i	0.0804232	−	0.996761i	$-0.474373\pi$
$487$	−15.1136	−	7.79162i	−0.684864	−	0.353072i	−0.765287	+	0.643689i	$0.777403\pi$
$488$	0.599259	+	2.47018i	0.0271272	+	0.111820i
$489$		0			0
$490$	−6.15597	−	0.587823i	−0.278098	−	0.0265552i
$491$	−2.78316	+	19.3573i	−0.125602	+	0.873583i	0.825433	+	0.564500i	$0.190931\pi$
$491$	−2.78316	+	19.3573i	−0.125602	+	0.873583i	−0.951035	+	0.309083i	$0.899978\pi$
$492$		0			0
$493$	−1.78950	−	1.15004i	−0.0805951	−	0.0517953i
$494$	−1.35254	−	1.56091i	−0.0608536	−	0.0702288i
$495$		0			0
$496$	−9.75472	−	21.3599i	−0.438000	−	0.959086i
$497$	19.0878	+	3.67887i	0.856204	+	0.165020i
$498$		0			0
$499$	−12.5377	−	21.7159i	−0.561264	−	0.972138i	−0.997386	−	0.0722510i	$-0.976982\pi$
$499$	−12.5377	−	21.7159i	−0.561264	−	0.972138i	0.436122	−	0.899888i	$-0.356352\pi$
$500$	−18.3802	−	53.1061i	−0.821988	−	2.37498i
$501$		0			0
$502$	−8.48823	+	8.09351i	−0.378848	+	0.361231i
$503$	15.1693	−	14.4639i	0.676367	−	0.644914i	−0.271924	−	0.962319i	$-0.587660\pi$
$503$	15.1693	−	14.4639i	0.676367	−	0.644914i	0.948290	+	0.317405i	$0.102811\pi$
$504$		0			0
$505$	10.4500	+	30.1933i	0.465020	+	1.34359i
$506$	−4.81146	−	8.33369i	−0.213895	−	0.370477i
$507$		0			0
$508$	−56.6311	−	10.9148i	−2.51260	−	0.484264i
$509$	−4.79230	−	10.4937i	−0.212415	−	0.465124i	0.773193	−	0.634171i	$-0.218658\pi$
$509$	−4.79230	−	10.4937i	−0.212415	−	0.465124i	−0.985608	+	0.169047i	$0.945931\pi$
$510$		0			0
$511$	12.0563	+	13.9138i	0.533341	+	0.615508i
$512$	−41.7182	−	26.8107i	−1.84370	−	1.18487i
$513$		0			0
$514$	7.83683	−	54.5063i	0.345668	−	2.40417i
$515$	25.0687	+	2.39377i	1.10466	+	0.105482i
$516$		0			0
$517$	1.23520	+	5.09155i	0.0543239	+	0.223926i
$518$	−31.8054	−	16.3968i	−1.39745	−	0.720434i
$519$		0			0
$520$	−76.3082	+	7.28655i	−3.34634	+	0.319536i
$521$	14.1004	+	4.14024i	0.617749	+	0.181387i	0.575610	−	0.817724i	$-0.304765\pi$
$521$	14.1004	+	4.14024i	0.617749	+	0.181387i	0.0421387	+	0.999112i	$0.486583\pi$
$522$		0			0
$523$	5.81531	−	16.8022i	0.254286	−	0.734710i	−0.743533	−	0.668699i	$-0.766851\pi$
$523$	5.81531	−	16.8022i	0.254286	−	0.734710i	0.997819	−	0.0660113i	$-0.0210273\pi$
$524$	47.5414	−	9.16286i	2.07686	−	0.400281i
$525$		0			0
$526$	−2.11239	+	0.845673i	−0.0921045	+	0.0368731i
$527$	−0.939483	+	0.275857i	−0.0409245	+	0.0120165i
$528$		0			0
$529$	−1.86254	+	7.67749i	−0.0809800	+	0.333804i
$530$	−36.4989	+	51.2556i	−1.58541	+	2.22640i
$531$		0			0
$532$	0.0670789	+	1.40816i	0.00290824	+	0.0610514i
$533$	5.29871	+	36.8533i	0.229512	+	1.59629i
$534$		0			0
$535$	−0.0357617			−0.00154612
$536$	49.2481	+	24.7277i	2.12719	+	1.06807i
$537$		0			0
$538$	33.0784	+	31.5402i	1.42611	+	1.35979i
$539$	−0.181241	−	1.26056i	−0.00780661	−	0.0542962i
$540$		0			0
$541$	−6.66153	+	14.5867i	−0.286402	+	0.627132i	−0.997078	−	0.0763867i	$-0.975662\pi$
$541$	−6.66153	+	14.5867i	−0.286402	+	0.627132i	0.710677	+	0.703519i	$0.248389\pi$
$542$	24.8375	−	34.8795i	1.06686	−	1.49820i
$543$		0			0
$544$	1.61821	−	1.86751i	0.0693800	−	0.0800688i
$545$	−5.41278	+	1.58934i	−0.231858	+	0.0680797i
$546$		0			0
$547$	14.5148	+	20.3832i	0.620609	+	0.871523i	0.998524	−	0.0543173i	$-0.0172982\pi$
$547$	14.5148	+	20.3832i	0.620609	+	0.871523i	−0.377915	+	0.925840i	$0.623359\pi$
$548$	15.9959	−	3.08297i	0.683313	−	0.131698i
$549$		0			0
$550$	3.53682	−	2.27298i	0.150811	−	0.0969201i
$551$	0.775894	+	0.227823i	0.0330542	+	0.00970559i
$552$		0			0
$553$	1.02759	−	21.5718i	0.0436976	−	0.917325i
$554$	10.9789	+	5.65999i	0.466447	+	0.240470i
$555$		0			0
$556$	40.3500	+	16.1537i	1.71122	+	0.685070i
$557$	4.34030	+	0.414449i	0.183905	+	0.0175608i	0.186602	−	0.982436i	$-0.440253\pi$
$557$	4.34030	+	0.414449i	0.183905	+	0.0175608i	−0.00269735	+	0.999996i	$0.500859\pi$
$558$		0			0
$559$	28.0919	−	22.0917i	1.18816	−	0.934379i
$560$	29.4462	+	18.9239i	1.24433	+	0.799682i
$561$		0			0
$562$	42.1978	−	21.7545i	1.78001	−	0.917657i
$563$	−17.6602	−	38.6706i	−0.744291	−	1.62977i	−0.776365	−	0.630284i	$-0.782938\pi$
$563$	−17.6602	−	38.6706i	−0.744291	−	1.62977i	0.0320740	−	0.999485i	$-0.489789\pi$
$564$		0			0
$565$	5.15254	−	8.92447i	0.216769	−	0.375455i
$566$	−38.1328	−	66.0480i	−1.60284	−	2.77620i
$567$		0			0
$568$	43.1755	+	33.9536i	1.81160	+	1.42466i
$569$	19.3184	−	18.4201i	0.809870	−	0.772209i	−0.167020	−	0.985954i	$-0.553414\pi$
$569$	19.3184	−	18.4201i	0.809870	−	0.772209i	0.976890	+	0.213744i	$0.0685659\pi$
$570$		0			0
$571$	1.67093	+	1.31403i	0.0699260	+	0.0549904i	0.652510	−	0.757780i	$-0.273716\pi$
$571$	1.67093	+	1.31403i	0.0699260	+	0.0549904i	−0.582584	+	0.812770i	$0.697958\pi$
$572$	−9.10882	−	26.3182i	−0.380859	−	1.10042i
$573$		0			0
$574$	18.2108	−	31.5420i	0.760103	−	1.31654i
$575$	6.47786	+	1.24851i	0.270145	+	0.0520663i
$576$		0			0
$577$	7.81772	−	4.03031i	0.325456	−	0.167784i	−0.287754	−	0.957704i	$-0.592908\pi$
$577$	7.81772	−	4.03031i	0.325456	−	0.167784i	0.613209	+	0.789920i	$0.289878\pi$
$578$	28.4461	+	32.8285i	1.18320	+	1.36549i
$579$		0			0
$580$	41.6194	−	32.7299i	1.72815	−	1.35903i
$581$	−2.59300	+	18.0347i	−0.107576	+	0.748206i
$582$		0			0
$583$	−12.0301	−	4.81613i	−0.498236	−	0.199464i
$584$	12.2643	+	50.5543i	0.507502	+	2.09195i
$585$		0			0
$586$	−0.243664	+	5.11513i	−0.0100656	+	0.211304i
$587$	−19.5772	+	1.86940i	−0.808038	+	0.0771583i	−0.490894	−	0.871219i	$-0.663330\pi$
$587$	−19.5772	+	1.86940i	−0.808038	+	0.0771583i	−0.317144	+	0.948377i	$0.602724\pi$
$588$		0			0
$589$	0.313134	−	0.201239i	0.0129024	−	0.00829190i
$590$	6.91380	−	19.9761i	0.284637	−	0.822404i
$591$		0			0
$592$	−27.3767	−	38.4452i	−1.12517	−	1.58009i
$593$	−7.60516	+	3.04465i	−0.312307	+	0.125029i	−0.522521	−	0.852627i	$-0.675008\pi$
$593$	−7.60516	+	3.04465i	−0.312307	+	0.125029i	0.210214	+	0.977655i	$0.432584\pi$
$594$		0			0
$595$	0.955798	−	1.10305i	0.0391839	−	0.0452206i
$596$	11.1767	−	46.0711i	0.457817	−	1.88715i
$597$		0			0
$598$	26.0176	−	56.9706i	1.06394	−	2.32970i
$599$	1.34303	+	28.1936i	0.0548745	+	1.15196i	0.843516	+	0.537104i	$0.180482\pi$
$599$	1.34303	+	28.1936i	0.0548745	+	1.15196i	−0.788641	+	0.614854i	$0.789215\pi$
$600$		0			0
$601$	16.5617	+	15.7915i	0.675565	+	0.644150i	0.948091	−	0.317998i	$-0.103011\pi$
$601$	16.5617	+	15.7915i	0.675565	+	0.644150i	−0.272526	+	0.962148i	$0.587859\pi$
$602$	−34.9597			−1.42485
$603$		0			0
$604$	−22.8702			−0.930577
$605$	13.2481	+	12.6321i	0.538614	+	0.513567i
$606$		0			0
$607$	−0.468844	−	9.84224i	−0.0190298	−	0.399484i	−0.988207	−	0.153121i	$-0.951068\pi$
$607$	−0.468844	−	9.84224i	−0.0190298	−	0.399484i	0.969178	−	0.246363i	$-0.0792355\pi$
$608$	−0.390231	+	0.854488i	−0.0158260	+	0.0346540i
$609$		0			0
$610$	−0.416088	+	1.71514i	−0.0168469	+	0.0694440i
$611$	−22.3303	+	25.7706i	−0.903388	+	1.04257i
$612$		0			0
$613$	−8.06586	+	3.22908i	−0.325777	+	0.130421i	−0.528785	−	0.848756i	$-0.677352\pi$
$613$	−8.06586	+	3.22908i	−0.325777	+	0.130421i	0.203008	+	0.979177i	$0.434928\pi$
$614$	29.2546	+	41.0824i	1.18062	+	1.65795i
$615$		0			0
$616$	−5.05078	+	14.5933i	−0.203502	+	0.587980i
$617$	−2.20007	+	1.41390i	−0.0885715	+	0.0569215i	−0.584177	−	0.811626i	$-0.698583\pi$
$617$	−2.20007	+	1.41390i	−0.0885715	+	0.0569215i	0.495605	+	0.868548i	$0.334946\pi$
$618$		0			0
$619$	26.0850	−	2.49081i	1.04844	−	0.100114i	0.443413	−	0.896317i	$-0.353767\pi$
$619$	26.0850	−	2.49081i	1.04844	−	0.100114i	0.605029	+	0.796203i	$0.293161\pi$
$620$	1.15965	−	24.3441i	0.0465728	−	0.977683i
$621$		0			0
$622$	−4.05366	−	16.7094i	−0.162537	−	0.669986i
$623$	26.0686	+	10.4363i	1.04442	+	0.418121i
$624$		0			0
$625$	1.93963	−	13.4904i	0.0775852	−	0.539617i
$626$	−19.5785	+	15.3967i	−0.782515	+	0.615377i
$627$		0			0
$628$	−44.1304	−	50.9292i	−1.76100	−	2.03230i
$629$	−1.74923	+	0.901789i	−0.0697462	+	0.0359567i
$630$		0			0
$631$	−22.4077	−	4.31874i	−0.892038	−	0.171926i	−0.277418	−	0.960749i	$-0.589479\pi$
$631$	−22.4077	−	4.31874i	−0.892038	−	0.171926i	−0.614620	+	0.788823i	$0.710691\pi$
$632$	30.5111	−	52.8467i	1.21366	−	2.10213i
$633$		0			0
$634$	−1.41957	−	4.10159i	−0.0563784	−	0.162895i
$635$	−17.8425	−	14.0315i	−0.708059	−	0.556823i
$636$		0			0
$637$	5.99880	−	5.71984i	0.237681	−	0.226628i
$638$	12.2838	+	9.66005i	0.486319	+	0.382445i
$639$		0			0
$640$	−7.03649	−	12.1876i	−0.278142	−	0.481756i
$641$	22.0580	−	38.2055i	0.871238	−	1.50903i	0.0105203	−	0.999945i	$-0.496651\pi$
$641$	22.0580	−	38.2055i	0.871238	−	1.50903i	0.860717	−	0.509083i	$-0.170015\pi$
$642$		0			0
$643$	4.83053	+	10.5774i	0.190497	+	0.417131i	0.980647	−	0.195782i	$-0.0627246\pi$
$643$	4.83053	+	10.5774i	0.190497	+	0.417131i	−0.790150	+	0.612914i	$0.789997\pi$
$644$	−37.9970	+	19.5888i	−1.49729	+	0.771907i
$645$		0			0
$646$	0.0934786	+	0.0600751i	0.00367787	+	0.00236362i
$647$	9.74961	−	7.66717i	0.383297	−	0.301428i	−0.407856	−	0.913046i	$-0.633724\pi$
$647$	9.74961	−	7.66717i	0.383297	−	0.301428i	0.791153	+	0.611618i	$0.209481\pi$
$648$		0			0
$649$	4.33359	+	0.413808i	0.170108	+	0.0162434i
$650$	25.4030	+	10.1698i	0.996387	+	0.398893i
$651$		0			0
$652$	−36.5747	−	18.8556i	−1.43237	−	0.738441i
$653$	0.483285	−	10.1454i	0.0189124	−	0.397020i	−0.969487	−	0.245143i	$-0.921165\pi$
$653$	0.483285	−	10.1454i	0.0189124	−	0.397020i	0.988399	−	0.151877i	$-0.0485319\pi$
$654$		0			0
$655$	18.2836	+	5.36856i	0.714401	+	0.209767i
$656$	40.4126	−	25.9716i	1.57785	−	1.01402i
$657$		0			0
$658$	32.7540	−	6.31282i	1.27688	−	0.246099i
$659$	13.6208	+	19.1278i	0.530593	+	0.745113i	0.989683	−	0.143277i	$-0.0457639\pi$
$659$	13.6208	+	19.1278i	0.530593	+	0.745113i	−0.459090	+	0.888390i	$0.651824\pi$
$660$		0			0
$661$	−47.5626	+	13.9656i	−1.84997	+	0.543200i	−0.850107	+	0.526610i	$0.823463\pi$
$661$	−47.5626	+	13.9656i	−1.84997	+	0.543200i	−0.999862	+	0.0165904i	$0.994719\pi$
$662$	58.3781	−	67.3720i	2.26893	−	2.61849i
$663$		0			0
$664$	−29.8629	+	41.9366i	−1.15891	+	1.62746i
$665$	−0.230491	+	0.504706i	−0.00893807	+	0.0195717i
$666$		0			0
$667$	3.48975	+	24.2718i	0.135124	+	0.939806i
$668$	−11.2375	−	10.7149i	−0.434792	−	0.414573i
$669$		0			0
$670$	22.5261	+	30.9297i	0.870260	+	1.19492i
$671$	−0.363460			−0.0140312
$672$		0			0
$673$	2.91867	+	20.2998i	0.112506	+	0.782499i	0.965467	+	0.260524i	$0.0838954\pi$
$673$	2.91867	+	20.2998i	0.112506	+	0.782499i	−0.852961	+	0.521975i	$0.825196\pi$
$674$	−3.20751	−	67.3339i	−0.123549	−	2.59360i
$675$		0			0
$676$	70.3241	−	98.7564i	2.70477	−	3.79832i
$677$	−10.5425	+	43.4567i	−0.405180	+	1.67018i	0.294447	+	0.955668i	$0.404865\pi$
$677$	−10.5425	+	43.4567i	−0.405180	+	1.67018i	−0.699627	+	0.714508i	$0.746651\pi$
$678$		0			0
$679$	−9.62479	+	2.82609i	−0.369365	+	0.108455i
$680$	3.82866	−	1.53276i	0.146822	−	0.0587788i
$681$		0			0
$682$	7.06320	−	1.36132i	0.270464	−	0.0521276i
$683$	−8.04470	+	23.2436i	−0.307822	+	0.889393i	0.679919	+	0.733288i	$0.262015\pi$
$683$	−8.04470	+	23.2436i	−0.307822	+	0.889393i	−0.987740	+	0.156105i	$0.950106\pi$
$684$		0			0
$685$	6.15178	+	1.80632i	0.235047	+	0.0690161i
$686$	−50.7813	+	4.84903i	−1.93884	+	0.185137i
$687$		0			0
$688$	−40.9846	−	21.1290i	−1.56252	−	0.805536i
$689$	−19.8836	−	81.9614i	−0.757506	−	3.12248i
$690$		0			0
$691$	−11.1149	−	1.06134i	−0.422830	−	0.0403754i	−0.118528	−	0.992951i	$-0.537817\pi$
$691$	−11.1149	−	1.06134i	−0.422830	−	0.0403754i	−0.304303	+	0.952575i	$0.598423\pi$
$692$	−12.9984	+	90.4061i	−0.494126	+	3.43672i
$693$		0			0
$694$	−23.6684	−	15.2108i	−0.898441	−	0.577393i
$695$	11.2022	+	12.9280i	0.424922	+	0.490386i
$696$		0			0
$697$	−0.832121	−	1.82209i	−0.0315188	−	0.0690166i
$698$	71.2982	+	13.7416i	2.69868	+	0.520127i
$699$		0			0
$700$	−9.33851	−	16.1748i	−0.352963	−	0.611349i
$701$	1.48693	+	4.29620i	0.0561606	+	0.162265i	0.969592	−	0.244728i	$-0.0786986\pi$
$701$	1.48693	+	4.29620i	0.0561606	+	0.162265i	−0.913431	+	0.406993i	$0.866577\pi$
$702$		0			0
$703$	0.541451	−	0.516272i	0.0204212	−	0.0194716i
$704$	−1.87343	+	1.78631i	−0.0706076	+	0.0673242i
$705$		0			0
$706$	−7.27988	−	21.0338i	−0.273982	−	0.791618i
$707$	20.9462	+	36.2799i	0.787764	+	1.36445i
$708$		0			0
$709$	0.832177	+	0.160389i	0.0312531	+	0.00602353i	0.204854	−	0.978793i	$-0.434328\pi$
$709$	0.832177	+	0.160389i	0.0312531	+	0.00602353i	−0.173601	+	0.984816i	$0.555540\pi$
$710$	15.8430	+	34.6914i	0.594578	+	1.30194i
$711$		0			0
$712$	51.9584	+	59.9631i	1.94722	+	2.24721i
$713$	9.49541	+	6.10233i	0.355606	+	0.228534i
$714$		0			0
$715$	1.55992	−	10.8495i	0.0583378	−	0.405748i
$716$	−75.7939	−	7.23744i	−2.83255	−	0.270476i
$717$		0			0
$718$	−9.45662	−	38.9807i	−0.352918	−	1.45475i
$719$	29.8517	+	15.3896i	1.11328	+	0.573935i	0.913881	−	0.405983i	$-0.133071\pi$
$719$	29.8517	+	15.3896i	1.11328	+	0.573935i	0.199399	+	0.979918i	$0.436101\pi$
$720$		0			0
$721$	32.8691	−	3.13862i	1.22411	−	0.116888i
$722$	46.8551	+	13.7579i	1.74377	+	0.512016i
$723$		0			0
$724$	30.2249	−	87.3291i	1.12330	−	3.24556i
$725$	−10.5197	+	2.02751i	−0.390693	+	0.0752999i
$726$		0			0
$727$	−29.7846	+	11.9239i	−1.10465	+	0.442235i	−0.851055	−	0.525076i	$-0.824037\pi$
$727$	−29.7846	+	11.9239i	−1.10465	+	0.442235i	−0.253594	+	0.967311i	$0.581613\pi$
$728$	−96.4363	+	28.3163i	−3.57417	+	1.04947i
$729$		0			0
$730$	−8.51559	+	35.1017i	−0.315176	+	1.29917i
$731$	−1.11528	+	1.56619i	−0.0412501	+	0.0579277i
$732$		0			0
$733$	1.61322	+	33.8656i	0.0595855	+	1.25085i	0.808624	+	0.588326i	$0.200213\pi$
$733$	1.61322	+	33.8656i	0.0595855	+	1.25085i	−0.749038	+	0.662527i	$0.769484\pi$
$734$	−10.3164	−	71.7519i	−0.380784	−	2.64841i
$735$		0			0
$736$	−28.4855			−1.04999
$737$	−5.09641	+	6.00995i	−0.187729	+	0.221380i
$738$		0			0
$739$	4.10687	+	3.91589i	0.151074	+	0.144049i	0.761847	−	0.647757i	$-0.224293\pi$
$739$	4.10687	+	3.91589i	0.151074	+	0.144049i	−0.610773	+	0.791806i	$0.709141\pi$
$740$	−6.97130	−	48.4864i	−0.256270	−	1.78240i
$741$		0			0
$742$	−34.2727	+	75.0467i	−1.25819	+	2.75505i
$743$	15.5015	−	21.7688i	0.568695	−	0.798620i	−0.425642	−	0.904891i	$-0.639952\pi$
$743$	15.5015	−	21.7688i	0.568695	−	0.798620i	0.994337	+	0.106271i	$0.0338912\pi$
$744$		0			0
$745$	12.2187	−	14.1011i	0.447658	−	0.516625i
$746$	−55.1118	+	16.1823i	−2.01779	+	0.592476i
$747$		0			0
$748$	0.869119	+	1.22051i	0.0317781	+	0.0446261i
$749$	−0.0460421	+	0.00887389i	−0.00168234	+	0.000324245i
$750$		0			0
$751$	−6.19304	+	3.98002i	−0.225987	+	0.145233i	−0.648735	−	0.761014i	$-0.724702\pi$
$751$	−6.19304	+	3.98002i	−0.225987	+	0.145233i	0.422748	+	0.906247i	$0.361065\pi$
$752$	42.2141	+	12.3952i	1.53939	+	0.452006i
$753$		0			0
$754$	−4.83949	+	101.593i	−0.176244	+	3.69981i
$755$	−8.00057	−	4.12458i	−0.291170	−	0.150109i
$756$		0			0
$757$	36.3216	+	14.5410i	1.32013	+	0.528500i	0.921417	−	0.388576i	$-0.127033\pi$
$757$	36.3216	+	14.5410i	1.32013	+	0.528500i	0.398713	+	0.917076i	$0.369457\pi$
$758$	−79.7534	−	7.61553i	−2.89677	−	0.276608i
$759$		0			0
$760$	−1.23235	+	0.969130i	−0.0447020	+	0.0351541i
$761$	−4.31518	−	2.77320i	−0.156425	−	0.100528i	0.460087	−	0.887874i	$-0.347818\pi$
$761$	−4.31518	−	2.77320i	−0.156425	−	0.100528i	−0.616512	+	0.787346i	$0.711455\pi$
$762$		0			0
$763$	−6.57441	+	3.38934i	−0.238010	+	0.122703i
$764$	9.23964	+	20.2320i	0.334278	+	0.731967i
$765$		0			0
$766$	−5.77458	+	10.0019i	−0.208644	+	0.361382i
$767$	14.1666	+	24.5373i	0.511528	+	0.885992i
$768$		0			0
$769$	−18.6900	−	14.6980i	−0.673978	−	0.530023i	0.221482	−	0.975165i	$-0.428911\pi$
$769$	−18.6900	−	14.6980i	−0.673978	−	0.530023i	−0.895460	+	0.445142i	$0.853153\pi$
$770$	−7.76016	+	7.39929i	−0.279657	+	0.266652i
$771$		0			0
$772$	50.8113	+	39.9585i	1.82874	+	1.43814i
$773$	4.69643	+	13.5695i	0.168919	+	0.488059i	0.997409	−	0.0719450i	$-0.0229206\pi$
$773$	4.69643	+	13.5695i	0.168919	+	0.488059i	−0.828490	+	0.560004i	$0.810799\pi$
$774$		0			0
$775$	−2.46568	+	4.27068i	−0.0885698	+	0.153407i
$776$	−27.8316	−	5.36411i	−0.999097	−	0.192560i
$777$		0			0
$778$	8.99492	−	4.63720i	0.322483	−	0.166252i
$779$	0.498665	+	0.575490i	0.0178665	+	0.0206191i
$780$		0			0
$781$	−6.17373	+	4.85507i	−0.220913	+	0.173728i
$782$	−0.479534	+	3.33523i	−0.0171481	+	0.119268i
$783$		0			0
$784$	−9.92831	−	3.97469i	−0.354582	−	0.141953i
$785$	−6.25297	−	25.7751i	−0.223178	−	0.919952i
$786$		0			0
$787$	0.735570	−	15.4415i	0.0262202	−	0.550431i	−0.947094	−	0.320956i	$-0.895996\pi$
$787$	0.735570	−	15.4415i	0.0262202	−	0.550431i	0.973315	−	0.229475i	$-0.0737010\pi$
$788$	−7.69187	+	0.734485i	−0.274012	+	0.0261649i
$789$		0			0
$790$	35.6439	−	22.9069i	1.26815	−	0.814992i
$791$	4.41923	−	12.7685i	0.157130	−	0.453996i
$792$		0			0
$793$	−1.37216	−	1.92693i	−0.0487270	−	0.0684274i
$794$	−66.9962	+	26.8212i	−2.37761	+	0.951850i
$795$		0			0
$796$	−12.4593	+	14.3788i	−0.441607	+	0.509642i
$797$	−7.35039	+	30.2987i	−0.260364	+	1.07324i	0.680040	+	0.733175i	$0.261963\pi$
$797$	−7.35039	+	30.2987i	−0.260364	+	1.07324i	−0.940404	+	0.340060i	$0.889553\pi$
$798$		0			0
$799$	0.762101	−	1.66877i	0.0269612	−	0.0590368i
$800$	−0.592169	−	12.4312i	−0.0209363	−	0.439508i
$801$		0			0
$802$	28.2556	+	26.9417i	0.997741	+	0.951344i
$803$	−7.43852			−0.262500
$804$		0			0
$805$	−16.8251			−0.593005
$806$	33.8828	+	32.3072i	1.19347	+	1.13797i
$807$		0			0
$808$	5.63232	+	118.237i	0.198144	+	4.15956i
$809$	16.9855	−	37.1931i	0.597179	−	1.30764i	−0.333826	−	0.942635i	$-0.608340\pi$
$809$	16.9855	−	37.1931i	0.597179	−	1.30764i	0.931005	−	0.365005i	$-0.118933\pi$
$810$		0			0
$811$	5.48211	−	22.5975i	0.192503	−	0.793507i	−0.790881	−	0.611970i	$-0.790377\pi$
$811$	5.48211	−	22.5975i	0.192503	−	0.793507i	0.983384	−	0.181538i	$-0.0581074\pi$
$812$	45.4621	−	52.4661i	1.59541	−	1.84120i
$813$		0			0
$814$	13.4221	−	5.37338i	0.470443	−	0.188337i
$815$	−9.39417	−	13.1923i	−0.329063	−	0.462105i
$816$		0			0
$817$	0.239060	−	0.690718i	0.00836365	−	0.0241652i
$818$	17.7759	−	11.4239i	0.621521	−	0.399427i
$819$		0			0
$820$	49.6332	−	4.73939i	1.73327	−	0.165507i
$821$	−0.126429	+	2.65407i	−0.00441240	+	0.0926276i	−0.999999	−	0.00121692i	$-0.999613\pi$
$821$	−0.126429	+	2.65407i	−0.00441240	+	0.0926276i	0.995587	+	0.0938446i	$0.0299157\pi$
$822$		0			0
$823$	−5.65060	−	23.2921i	−0.196968	−	0.811911i	−0.981443	−	0.191752i	$-0.938583\pi$
$823$	−5.65060	−	23.2921i	−0.196968	−	0.811911i	0.784476	−	0.620159i	$-0.212932\pi$
$824$	86.6141	+	34.6751i	3.01735	+	1.20796i
$825$		0			0
$826$	3.94444	−	27.4342i	0.137245	−	0.954558i
$827$	7.44496	−	5.85478i	0.258886	−	0.203591i	−0.480277	−	0.877117i	$-0.659464\pi$
$827$	7.44496	−	5.85478i	0.258886	−	0.203591i	0.739163	+	0.673527i	$0.235221\pi$
$828$		0			0
$829$	15.1612	+	17.4970i	0.526570	+	0.607694i	0.955264	−	0.295756i	$-0.0955714\pi$
$829$	15.1612	+	17.4970i	0.526570	+	0.607694i	−0.428694	+	0.903450i	$0.641026\pi$
$830$	−31.7727	+	16.3800i	−1.10285	+	0.568557i
$831$		0			0
$832$	−16.5431	−	3.18842i	−0.573529	−	0.110539i
$833$	−0.222967	+	0.386189i	−0.00772533	+	0.0133807i
$834$		0			0
$835$	−1.99874	−	5.77499i	−0.0691694	−	0.199852i
$836$	−0.447730	−	0.352098i	−0.0154850	−	0.0121776i
$837$		0			0
$838$	−6.91398	+	6.59247i	−0.238840	+	0.227733i
$839$	−17.4117	−	13.6927i	−0.601117	−	0.472724i	0.270628	−	0.962684i	$-0.412769\pi$
$839$	−17.4117	−	13.6927i	−0.601117	−	0.472724i	−0.871745	+	0.489960i	$0.837011\pi$
$840$		0			0
$841$	−5.41074	−	9.37167i	−0.186577	−	0.323161i
$842$	−14.3905	+	24.9251i	−0.495929	+	0.858975i
$843$		0			0
$844$	−7.72646	−	16.9186i	−0.265956	−	0.582362i
$845$	42.4115	−	21.8647i	1.45900	−	0.752167i
$846$		0			0
$847$	20.1911	+	12.9760i	0.693774	+	0.445862i
$848$	−85.5361	+	67.2663i	−2.93732	+	2.30993i
$849$		0			0
$850$	−1.46547	−	0.139936i	−0.0502654	−	0.00479976i
$851$	21.0612	+	8.43165i	0.721970	+	0.289033i
$852$		0			0
$853$	−13.6749	−	7.04992i	−0.468221	−	0.241385i	0.207936	−	0.978142i	$-0.433325\pi$
$853$	−13.6749	−	7.04992i	−0.468221	−	0.241385i	−0.676157	+	0.736758i	$0.736356\pi$
$854$	−0.110107	+	2.31144i	−0.00376779	+	0.0790957i
$855$		0			0
$856$	−0.127124	−	0.0373269i	−0.00434500	−	0.00127581i
$857$	−3.47764	+	2.23495i	−0.118794	+	0.0763443i	−0.598689	−	0.800982i	$-0.704311\pi$
$857$	−3.47764	+	2.23495i	−0.118794	+	0.0763443i	0.479895	+	0.877326i	$0.340675\pi$
$858$		0			0
$859$	54.0320	−	10.4138i	1.84355	−	0.355315i	0.856553	−	0.516059i	$-0.172602\pi$
$859$	54.0320	−	10.4138i	1.84355	−	0.355315i	0.986996	+	0.160745i	$0.0513895\pi$
$860$	−27.7602	−	38.9838i	−0.946615	−	1.32934i
$861$		0			0
$862$	−93.3130	+	27.3992i	−3.17825	+	0.933220i
$863$	−15.1180	+	17.4471i	−0.514622	+	0.593906i	−0.952276	−	0.305238i	$-0.901264\pi$
$863$	−15.1180	+	17.4471i	−0.514622	+	0.593906i	0.437654	+	0.899143i	$0.355809\pi$
$864$		0			0
$865$	−20.8516	+	29.2820i	−0.708977	+	0.995619i
$866$	11.3272	−	24.8032i	0.384915	−	0.842846i
$867$		0			0
$868$	−4.54771	−	31.6300i	−0.154359	−	1.07359i
$869$	6.31505	+	6.02139i	0.214223	+	0.204262i
$870$		0			0
$871$	−51.1029	−	4.33006i	−1.73156	−	0.146719i
$872$	−20.8999			−0.707761
$873$		0			0
$874$	−0.182295	−	1.26789i	−0.00616622	−	0.0428870i
$875$	−1.37987	−	28.9671i	−0.0466483	−	0.979268i
$876$		0			0
$877$	−12.5965	+	17.6893i	−0.425352	+	0.597324i	−0.970525	−	0.241000i	$-0.922525\pi$
$877$	−12.5965	+	17.6893i	−0.425352	+	0.597324i	0.545173	+	0.838324i	$0.316464\pi$
$878$	−4.88832	+	20.1499i	−0.164973	+	0.680027i
$879$		0			0
$880$	−13.5695	+	3.98437i	−0.457428	+	0.134313i
$881$	1.58809	−	0.635774i	0.0535040	−	0.0214198i	−0.344756	−	0.938692i	$-0.612038\pi$
$881$	1.58809	−	0.635774i	0.0535040	−	0.0214198i	0.398260	+	0.917273i	$0.369614\pi$
$882$		0			0
$883$	−9.19614	+	1.77241i	−0.309475	+	0.0596464i	−0.341624	−	0.939837i	$-0.610977\pi$
$883$	−9.19614	+	1.77241i	−0.309475	+	0.0596464i	0.0321492	+	0.999483i	$0.489765\pi$
$884$	−3.18952	+	9.21550i	−0.107275	+	0.309951i
$885$		0			0
$886$	−92.6655	−	27.2091i	−3.11316	−	0.914106i
$887$	−0.503877	+	0.0481144i	−0.0169185	+	0.00161552i	−0.103512	−	0.994628i	$-0.533008\pi$
$887$	−0.503877	+	0.0481144i	−0.0169185	+	0.00161552i	0.0865933	+	0.996244i	$0.472402\pi$
$888$		0			0
$889$	−26.4534	−	13.6377i	−0.887220	−	0.457394i
$890$	12.9881	+	53.5377i	0.435362	+	1.79459i
$891$		0			0
$892$	−72.1738	−	6.89176i	−2.41656	−	0.230753i
$893$	−0.0992513	+	0.690308i	−0.00332132	+	0.0231003i
$894$		0			0
$895$	−25.2093	−	16.2010i	−0.842654	−	0.541541i
$896$	−12.0835	−	13.9451i	−0.403681	−	0.465872i
$897$		0			0
$898$	−2.83197	−	6.20114i	−0.0945039	−	0.206935i
$899$	−17.9986	−	3.46895i	−0.600288	−	0.115696i
$900$		0			0
$901$	2.26873	+	3.92955i	0.0755822	+	0.130912i
$902$	4.81301	+	13.9063i	0.160256	+	0.463028i
$903$		0			0
$904$	27.6310	−	26.3461i	0.918994	−	0.876259i
$905$	26.3230	−	25.0989i	0.875005	−	0.834315i
$906$		0			0
$907$	19.0353	+	54.9990i	0.632058	+	1.82621i	0.559472	+	0.828849i	$0.311004\pi$
$907$	19.0353	+	54.9990i	0.632058	+	1.82621i	0.0725860	+	0.997362i	$0.476875\pi$
$908$	12.4990	+	21.6490i	0.414795	+	0.718446i
$909$		0			0
$910$	−68.5251	−	13.2071i	−2.27158	−	0.437812i
$911$	−11.4554	−	25.0839i	−0.379536	−	0.831068i	−0.998942	−	0.0459967i	$-0.985354\pi$
$911$	−11.4554	−	25.0839i	−0.379536	−	0.831068i	0.619406	−	0.785071i	$-0.287374\pi$
$912$		0			0
$913$	−4.82083	−	5.56353i	−0.159546	−	0.184126i
$914$	6.94682	+	4.46445i	0.229780	+	0.147671i
$915$		0			0
$916$	−14.2707	+	99.2551i	−0.471518	+	3.27948i
$917$	24.8718	+	2.37497i	0.821338	+	0.0784283i
$918$		0			0
$919$	−10.4593	−	43.1137i	−0.345019	−	1.42219i	−0.834901	−	0.550400i	$-0.814475\pi$
$919$	−10.4593	−	43.1137i	−0.345019	−	1.42219i	0.489882	−	0.871789i	$-0.337040\pi$
$920$	−42.2559	−	21.7844i	−1.39314	−	0.718211i
$921$		0			0
$922$	−32.6098	+	3.11385i	−1.07395	+	0.102549i
$923$	−49.0474	−	14.4016i	−1.61441	−	0.474035i
$924$		0			0
$925$	−3.24177	+	9.36647i	−0.106589	+	0.307968i
$926$	−63.4384	+	12.2268i	−2.08472	+	0.401796i
$927$		0			0
$928$	42.9454	−	17.1928i	1.40975	−	0.564380i
$929$	0.174077	−	0.0511136i	0.00571128	−	0.00167698i	−0.278876	−	0.960327i	$-0.589962\pi$
$929$	0.174077	−	0.0511136i	0.00571128	−	0.00167698i	0.284587	+	0.958650i	$0.408144\pi$
$930$		0			0
$931$	0.0399662	−	0.164743i	0.00130984	−	0.00539924i
$932$	−27.7463	+	38.9642i	−0.908861	+	1.27632i
$933$		0			0
$934$	−0.601537	−	12.6278i	−0.0196829	−	0.413195i
$935$	0.0839242	+	0.583706i	0.00274462	+	0.0190892i
$936$		0			0
$937$	−10.3454			−0.337969			−0.168985	−	0.985619i	$-0.554049\pi$
$937$	−10.3454			−0.337969			−0.168985	+	0.985619i	$0.554049\pi$
$938$	36.6765	+	34.2314i	1.19753	+	1.11770i
$939$		0			0
$940$	33.0482	+	31.5114i	1.07791	+	1.02779i
$941$	1.47752	+	10.2764i	0.0481659	+	0.335001i	0.999629	+	0.0272382i	$0.00867127\pi$
$941$	1.47752	+	10.2764i	0.0481659	+	0.335001i	−0.951463	+	0.307763i	$0.900420\pi$
$942$		0			0
$943$	−9.59236	+	21.0043i	−0.312370	+	0.683996i
$944$	21.2050	−	29.7782i	0.690163	−	0.969198i
$945$		0			0
$946$	9.24989	−	10.6749i	0.300740	−	0.347072i
$947$	24.6452	−	7.23648i	0.800861	−	0.235154i	0.144405	−	0.989519i	$-0.453873\pi$
$947$	24.6452	−	7.23648i	0.800861	−	0.235154i	0.656456	+	0.754365i	$0.272055\pi$
$948$		0			0
$949$	−28.0825	−	39.4363i	−0.911595	−	1.28016i
$950$	0.549521	−	0.105912i	0.0178288	−	0.00343622i
$951$		0			0
$952$	4.54894	−	2.92343i	0.147432	−	0.0947488i
$953$	−43.9766	−	12.9127i	−1.42454	−	0.418283i	−0.523503	−	0.852024i	$-0.675375\pi$
$953$	−43.9766	−	12.9127i	−1.42454	−	0.418283i	−0.901038	+	0.433741i	$0.857193\pi$
$954$		0			0
$955$	−0.416527	+	8.74398i	−0.0134785	+	0.282949i
$956$	−86.5912	−	44.6409i	−2.80056	−	1.44379i
$957$		0			0
$958$	36.8051	+	14.7345i	1.18912	+	0.476051i
$959$	8.36844	+	0.799089i	0.270231	+	0.0258039i
$960$		0			0
$961$	17.7355	−	13.9474i	0.572113	−	0.449915i
$962$	79.1597	+	50.8728i	2.55221	+	1.64021i
$963$		0			0
$964$	40.0266	−	20.6351i	1.28917	−	0.664613i
$965$	10.5686	+	23.1421i	0.340217	+	0.744971i
$966$		0			0
$967$	3.84346	−	6.65707i	0.123597	−	0.214077i	−0.797586	−	0.603205i	$-0.793890\pi$
$967$	3.84346	−	6.65707i	0.123597	−	0.214077i	0.921184	+	0.389128i	$0.127224\pi$
$968$	33.9088	+	58.7318i	1.08987	+	1.88771i
$969$		0			0
$970$	−15.4697	−	12.1655i	−0.496702	−	0.390610i
$971$	−20.7830	+	19.8166i	−0.666958	+	0.635944i	−0.945936	−	0.324354i	$-0.894853\pi$
$971$	−20.7830	+	19.8166i	−0.666958	+	0.635944i	0.278977	+	0.960298i	$0.410005\pi$
$972$		0			0
$973$	17.6304	+	13.8647i	0.565203	+	0.444481i
$974$	−14.3061	−	41.3349i	−0.458398	−	1.32446i
$975$		0			0
$976$	−1.52607	+	2.64324i	−0.0488484	+	0.0846079i
$977$	−10.5375	−	2.03093i	−0.337123	−	0.0649752i	0.0178803	−	0.999840i	$-0.494308\pi$
$977$	−10.5375	−	2.03093i	−0.337123	−	0.0649752i	−0.355004	+	0.934865i	$0.615520\pi$
$978$		0			0
$979$	−10.0841	+	5.19873i	−0.322290	+	0.166152i
$980$	−7.26871	−	8.38854i	−0.232190	−	0.267962i
$981$		0			0
$982$	−39.5437	+	31.0975i	−1.26189	+	0.992360i
$983$	−1.39203	+	9.68176i	−0.0443988	+	0.308800i	0.955506	+	0.294973i	$0.0953106\pi$
$983$	−1.39203	+	9.68176i	−0.0443988	+	0.308800i	−0.999904	+	0.0138273i	$0.995598\pi$
$984$		0			0
$985$	−2.82327	−	1.13027i	−0.0899567	−	0.0360132i
$986$	−1.29006	−	5.31770i	−0.0410839	−	0.169350i
$987$		0			0
$988$	0.176394	−	3.70297i	0.00561184	−	0.117807i
$989$	22.0639	−	2.10684i	0.701590	−	0.0669937i
$990$		0			0
$991$	−6.08662	+	3.91163i	−0.193348	+	0.124257i	−0.633733	−	0.773552i	$-0.718478\pi$
$991$	−6.08662	+	3.91163i	−0.193348	+	0.124257i	0.440385	+	0.897809i	$0.354842\pi$
$992$	6.96429	−	20.1220i	0.221117	−	0.638874i
$993$		0			0
$994$	29.0057	+	40.7328i	0.920005	+	1.29197i
$995$	−6.95172	+	2.78305i	−0.220384	+	0.0882286i
$996$		0			0
$997$	28.7626	−	33.1938i	0.910920	−	1.05126i	−0.0875609	−	0.996159i	$-0.527907\pi$
$997$	28.7626	−	33.1938i	0.910920	−	1.05126i	0.998481	−	0.0550986i	$-0.0175473\pi$
$998$	15.2073	−	62.6855i	0.481380	−	1.98427i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.z.c.10.5		100
3.2	odd	2		67.2.g.a.10.1	✓	100
67.47	even	33	inner	603.2.z.c.181.5		100
201.47	odd	66		67.2.g.a.47.1	yes	100
201.95	even	66		4489.2.a.q.1.45		50
201.173	odd	66		4489.2.a.p.1.6		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.g.a.10.1	✓	100	3.2	odd	2
67.2.g.a.47.1	yes	100	201.47	odd	66
603.2.z.c.10.5		100	1.1	even	1	trivial
603.2.z.c.181.5		100	67.47	even	33	inner
4489.2.a.p.1.6		50	201.173	odd	66
4489.2.a.q.1.45		50	201.95	even	66

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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.z (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.86173 + 1.77515i) q^{2} +(0.219695 + 4.61197i) q^{4} +(-0.754900 + 1.65300i) q^{5} +(-0.561736 + 2.31551i) q^{7} +(-4.40882 + 5.08805i) q^{8} +O(q^{10})\)	\(q+(1.86173 + 1.77515i) q^{2} +(0.219695 + 4.61197i) q^{4} +(-0.754900 + 1.65300i) q^{5} +(-0.561736 + 2.31551i) q^{7} +(-4.40882 + 5.08805i) q^{8} +(-4.33974 + 1.73737i) q^{10} +(-0.558411 - 0.784179i) q^{11} +(2.04927 - 5.92099i) q^{13} +(-5.15617 + 3.31367i) q^{14} +(-8.04750 + 0.768443i) q^{16} +(-0.0160394 + 0.336709i) q^{17} +(-0.0302113 - 0.124533i) q^{19} +(-7.78943 - 3.11842i) q^{20} +(0.352428 - 2.45119i) q^{22} +(3.05448 - 2.40207i) q^{23} +(1.11177 + 1.28305i) q^{25} +(14.3258 - 7.38549i) q^{26} +(-10.8024 - 2.08200i) q^{28} +(-3.15521 + 5.46499i) q^{29} +(0.950033 + 2.74494i) q^{31} +(-5.76222 - 4.53146i) q^{32} +(-0.627570 + 0.598387i) q^{34} +(-3.40348 - 2.67652i) q^{35} +(2.91909 + 5.05602i) q^{37} +(0.164820 - 0.285476i) q^{38} +(-5.08232 - 11.1287i) q^{40} +(-5.28177 + 2.72294i) q^{41} +(4.79837 + 3.08373i) q^{43} +(3.49393 - 2.74765i) q^{44} +(9.95066 + 0.950173i) q^{46} +(-5.05247 - 2.02271i) q^{47} +(1.17583 + 0.606182i) q^{49} +(-0.207800 + 4.36225i) q^{50} +(27.7576 + 8.15037i) q^{52} +(11.3238 - 7.27737i) q^{53} +(1.71779 - 0.331077i) q^{55} +(-9.30481 - 13.0668i) q^{56} +(-15.5753 + 4.57333i) q^{58} +(-2.96131 + 3.41753i) q^{59} +(0.219000 - 0.307542i) q^{61} +(-3.10399 + 6.79679i) q^{62} +(-0.382671 - 2.66153i) q^{64} +(8.24039 + 7.85720i) q^{65} +(-2.01453 - 7.93358i) q^{67} -1.55641 q^{68} +(-1.58510 - 11.0246i) q^{70} +(-0.388199 - 8.14929i) q^{71} +(4.48201 - 6.29411i) q^{73} +(-3.54065 + 14.5948i) q^{74} +(0.567704 - 0.166693i) q^{76} +(2.12945 - 0.852503i) q^{77} +(-8.90008 + 1.71535i) q^{79} +(4.80482 - 13.8826i) q^{80} +(-14.6668 - 4.30657i) q^{82} +(7.61233 - 0.726890i) q^{83} +(-0.544471 - 0.280694i) q^{85} +(3.45917 + 14.2589i) q^{86} +(6.45187 + 0.616079i) q^{88} +(1.67719 - 11.6651i) q^{89} +(12.5589 + 8.07113i) q^{91} +(11.7493 + 13.5594i) q^{92} +(-5.81572 - 12.7346i) q^{94} +(0.228659 + 0.0440705i) q^{95} +(2.10502 + 3.64600i) q^{97} +(1.11301 + 3.21582i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8}+O(q^{10}) \) 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8	\( 100 q + 24 q^{2} - 18 q^{4} + 16 q^{5} - 24 q^{7} - 23 q^{8} + 8 q^{10} + 24 q^{11} - 22 q^{13} + 32 q^{14} - 28 q^{16} - 17 q^{17} + 15 q^{20} + 49 q^{22} + 13 q^{23} - 34 q^{25} + 27 q^{26} + 22 q^{28} - 8 q^{29} + 10 q^{31} - 34 q^{32} - 50 q^{34} + q^{35} + 7 q^{37} - 50 q^{38} + 43 q^{40} + 5 q^{41} + 2 q^{43} + 19 q^{44} + 52 q^{46} + 6 q^{47} - 27 q^{49} - 134 q^{50} + 120 q^{52} + 52 q^{53} - 64 q^{55} + 124 q^{56} - 56 q^{58} - 27 q^{59} - 16 q^{61} + 74 q^{62} - 197 q^{64} + 92 q^{65} - 56 q^{67} - 16 q^{68} - 22 q^{70} + 113 q^{71} + q^{73} + 24 q^{74} - 144 q^{76} - 85 q^{77} + 36 q^{79} + 13 q^{80} - 20 q^{82} + 61 q^{83} - 6 q^{85} - 189 q^{86} + 129 q^{88} - 95 q^{89} + 42 q^{91} - 4 q^{92} + 70 q^{94} + 20 q^{95} + 53 q^{97} - q^{98}+O(q^{100}) \) 100 * q + 24 * q^2 - 18 * q^4 + 16 * q^5 - 24 * q^7 - 23 * q^8 + 8 * q^10 + 24 * q^11 - 22 * q^13 + 32 * q^14 - 28 * q^16 - 17 * q^17 + 15 * q^20 + 49 * q^22 + 13 * q^23 - 34 * q^25 + 27 * q^26 + 22 * q^28 - 8 * q^29 + 10 * q^31 - 34 * q^32 - 50 * q^34 + q^35 + 7 * q^37 - 50 * q^38 + 43 * q^40 + 5 * q^41 + 2 * q^43 + 19 * q^44 + 52 * q^46 + 6 * q^47 - 27 * q^49 - 134 * q^50 + 120 * q^52 + 52 * q^53 - 64 * q^55 + 124 * q^56 - 56 * q^58 - 27 * q^59 - 16 * q^61 + 74 * q^62 - 197 * q^64 + 92 * q^65 - 56 * q^67 - 16 * q^68 - 22 * q^70 + 113 * q^71 + q^73 + 24 * q^74 - 144 * q^76 - 85 * q^77 + 36 * q^79 + 13 * q^80 - 20 * q^82 + 61 * q^83 - 6 * q^85 - 189 * q^86 + 129 * q^88 - 95 * q^89 + 42 * q^91 - 4 * q^92 + 70 * q^94 + 20 * q^95 + 53 * q^97 - q^98

Introduction

L-functions

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