LMFDB - Embedded newform 570.2.bi.a.557.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(17,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 9, 20]))

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

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

chi := DirichletCharacter("570.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bi (of order $36$, degree $12$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$40$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			557.23
Character	$\chi$	$=$	570.557
Dual form			570.2.bi.a.263.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0871557 - 0.996195i) q^{2} +(-1.66215 - 0.487090i) q^{3} +(-0.984808 - 0.173648i) q^{4} +(2.04009 - 0.915434i) q^{5} +(-0.630102 + 1.61337i) q^{6} +(-0.956140 + 0.256197i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(2.52549 + 1.61923i) q^{9} +O(q^{10})$	\(q+(0.0871557 - 0.996195i) q^{2} +(-1.66215 - 0.487090i) q^{3} +(-0.984808 - 0.173648i) q^{4} +(2.04009 - 0.915434i) q^{5} +(-0.630102 + 1.61337i) q^{6} +(-0.956140 + 0.256197i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(2.52549 + 1.61923i) q^{9} +(-0.734145 - 2.11212i) q^{10} +(1.68727 - 0.974147i) q^{11} +(1.55232 + 0.768319i) q^{12} +(2.53459 - 5.43545i) q^{13} +(0.171889 + 0.974830i) q^{14} +(-3.83684 + 0.527881i) q^{15} +(0.939693 + 0.342020i) q^{16} +(0.249112 - 2.84737i) q^{17} +(1.83318 - 2.37475i) q^{18} +(-4.19757 + 1.17490i) q^{19} +(-2.16806 + 0.547268i) q^{20} +(1.71404 + 0.0398880i) q^{21} +(-0.823385 - 1.76575i) q^{22} +(-2.28307 + 1.59862i) q^{23} +(0.900689 - 1.47945i) q^{24} +(3.32396 - 3.73514i) q^{25} +(-5.19386 - 2.99868i) q^{26} +(-3.40903 - 3.92155i) q^{27} +(0.986102 - 0.0862727i) q^{28} +(-0.831703 - 0.697882i) q^{29} +(0.191470 + 3.86825i) q^{30} +(0.207050 - 0.358622i) q^{31} +(0.422618 - 0.906308i) q^{32} +(-3.27900 + 0.797326i) q^{33} +(-2.81482 - 0.496329i) q^{34} +(-1.71608 + 1.39795i) q^{35} +(-2.20594 - 2.03318i) q^{36} +(-6.98105 - 6.98105i) q^{37} +(0.804584 + 4.28400i) q^{38} +(-6.86042 + 7.79996i) q^{39} +(0.356226 + 2.20751i) q^{40} +(0.231277 - 0.635428i) q^{41} +(0.189124 - 1.70404i) q^{42} +(-0.540510 - 0.378469i) q^{43} +(-1.83080 + 0.666356i) q^{44} +(6.63453 + 0.991467i) q^{45} +(1.39356 + 2.41371i) q^{46} +(9.29672 - 0.813358i) q^{47} +(-1.39532 - 1.02620i) q^{48} +(-5.21361 + 3.01008i) q^{49} +(-3.43123 - 3.63685i) q^{50} +(-1.80099 + 4.61141i) q^{51} +(-3.43994 + 4.91274i) q^{52} +(-7.05061 + 4.93689i) q^{53} +(-4.20374 + 3.05427i) q^{54} +(2.55043 - 3.53194i) q^{55} -0.989869i q^{56} +(7.54928 + 0.0917376i) q^{57} +(-0.767714 + 0.767714i) q^{58} +(-0.996800 + 0.836415i) q^{59} +(3.87022 + 0.146399i) q^{60} +(1.19209 - 6.76066i) q^{61} +(-0.339211 - 0.237518i) q^{62} +(-2.82956 - 0.901190i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(0.195008 - 13.4091i) q^{65} +(0.508509 + 3.33601i) q^{66} +(-1.15572 - 13.2100i) q^{67} +(-0.739768 + 2.76085i) q^{68} +(4.57347 - 1.54509i) q^{69} +(1.24306 + 1.83139i) q^{70} +(8.83250 - 1.55741i) q^{71} +(-2.21770 + 2.02035i) q^{72} +(5.75154 - 2.68199i) q^{73} +(-7.56293 + 6.34605i) q^{74} +(-7.34427 + 4.58930i) q^{75} +(4.33782 - 0.428147i) q^{76} +(-1.36369 + 1.36369i) q^{77} +(7.17235 + 7.51413i) q^{78} +(-3.54991 + 9.75331i) q^{79} +(2.23016 - 0.162474i) q^{80} +(3.75617 + 8.17870i) q^{81} +(-0.612853 - 0.285778i) q^{82} +(6.81831 - 1.82696i) q^{83} +(-1.68107 - 0.336922i) q^{84} +(-2.09836 - 6.03694i) q^{85} +(-0.424137 + 0.505467i) q^{86} +(1.04249 + 1.56510i) q^{87} +(0.504256 + 1.88191i) q^{88} +(15.9299 - 5.79801i) q^{89} +(1.56593 - 6.52287i) q^{90} +(-1.03088 + 5.84640i) q^{91} +(2.52598 - 1.17788i) q^{92} +(-0.518830 + 0.495231i) q^{93} -9.33223i q^{94} +(-7.48790 + 6.23950i) q^{95} +(-1.14391 + 1.30057i) q^{96} +(-10.1176 - 0.885172i) q^{97} +(2.54423 + 5.45612i) q^{98} +(5.83856 + 0.271889i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q+O(q^{10}) $ 480 * q	$ 480 q - 36 q^{15} - 48 q^{18} + 24 q^{22} - 24 q^{25} + 72 q^{33} + 24 q^{43} - 36 q^{45} + 24 q^{51} - 120 q^{55} + 108 q^{57} - 48 q^{60} - 48 q^{61} - 36 q^{63} - 24 q^{66} + 48 q^{67} - 48 q^{70} - 48 q^{78} - 144 q^{81} - 48 q^{85} - 96 q^{87} - 168 q^{90} - 144 q^{91} - 228 q^{93} + 48 q^{97}+O(q^{100}) $ 480 * q - 36 * q^15 - 48 * q^18 + 24 * q^22 - 24 * q^25 + 72 * q^33 + 24 * q^43 - 36 * q^45 + 24 * q^51 - 120 * q^55 + 108 * q^57 - 48 * q^60 - 48 * q^61 - 36 * q^63 - 24 * q^66 + 48 * q^67 - 48 * q^70 - 48 * q^78 - 144 * q^81 - 48 * q^85 - 96 * q^87 - 168 * q^90 - 144 * q^91 - 228 * q^93 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.0871557	−	0.996195i	0.0616284	−	0.704416i
$2$	0.0871557	−	0.996195i	0.0616284	−	0.704416i
$3$	−1.66215	−	0.487090i	−0.959643	−	0.281221i
$3$	−1.66215	−	0.487090i	−0.959643	−	0.281221i
$4$	−0.984808	−	0.173648i	−0.492404	−	0.0868241i
$5$	2.04009	−	0.915434i	0.912357	−	0.409395i
$5$	2.04009	−	0.915434i	0.912357	−	0.409395i
$6$	−0.630102	+	1.61337i	−0.257238	+	0.658657i
$7$	−0.956140	+	0.256197i	−0.361387	+	0.0968333i	−0.434944	−	0.900458i	$-0.643232\pi$
$7$	−0.956140	+	0.256197i	−0.361387	+	0.0968333i	0.0735567	+	0.997291i	$0.476565\pi$
$8$	−0.258819	+	0.965926i	−0.0915064	+	0.341506i
$9$	2.52549	+	1.61923i	0.841829	+	0.539744i
$10$	−0.734145	−	2.11212i	−0.232157	−	0.667910i
$11$	1.68727	−	0.974147i	0.508732	−	0.293716i	−0.223580	−	0.974685i	$-0.571775\pi$
$11$	1.68727	−	0.974147i	0.508732	−	0.293716i	0.732312	+	0.680969i	$0.238441\pi$
$12$	1.55232	+	0.768319i	0.448115	+	0.221795i
$13$	2.53459	−	5.43545i	0.702969	−	1.50752i	−0.151743	−	0.988420i	$-0.548489\pi$
$13$	2.53459	−	5.43545i	0.702969	−	1.50752i	0.854712	−	0.519102i	$-0.173734\pi$
$14$	0.171889	+	0.974830i	0.0459392	+	0.260534i
$15$	−3.83684	+	0.527881i	−0.990668	+	0.136298i
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	0.249112	−	2.84737i	0.0604186	−	0.690588i	−0.904230	−	0.427047i	$-0.859554\pi$
$17$	0.249112	−	2.84737i	0.0604186	−	0.690588i	0.964648	−	0.263541i	$-0.0848905\pi$
$18$	1.83318	−	2.37475i	0.432085	−	0.559734i
$19$	−4.19757	+	1.17490i	−0.962989	+	0.269540i
$19$	−4.19757	+	1.17490i	−0.962989	+	0.269540i
$20$	−2.16806	+	0.547268i	−0.484794	+	0.122373i
$21$	1.71404	+	0.0398880i	0.374034	+	0.00870427i
$22$	−0.823385	−	1.76575i	−0.175546	−	0.376460i
$23$	−2.28307	+	1.59862i	−0.476053	+	0.333336i	−0.786854	−	0.617139i	$-0.788292\pi$
$23$	−2.28307	+	1.59862i	−0.476053	+	0.333336i	0.310801	+	0.950475i	$0.399403\pi$
$24$	0.900689	−	1.47945i	0.183852	−	0.301991i
$25$	3.32396	−	3.73514i	0.664792	−	0.747028i
$26$	−5.19386	−	2.99868i	−1.01860	−	0.588089i
$27$	−3.40903	−	3.92155i	−0.656068	−	0.754702i
$28$	0.986102	−	0.0862727i	0.186356	−	0.0163040i
$29$	−0.831703	−	0.697882i	−0.154443	−	0.129593i	0.562292	−	0.826939i	$-0.309920\pi$
$29$	−0.831703	−	0.697882i	−0.154443	−	0.129593i	−0.716735	+	0.697346i	$0.754364\pi$
$30$	0.191470	+	3.86825i	0.0349574	+	0.706242i
$31$	0.207050	−	0.358622i	0.0371873	−	0.0644104i	−0.846833	−	0.531859i	$-0.821494\pi$
$31$	0.207050	−	0.358622i	0.0371873	−	0.0644104i	0.884020	+	0.467449i	$0.154827\pi$
$32$	0.422618	−	0.906308i	0.0747091	−	0.160214i
$33$	−3.27900	+	0.797326i	−0.570800	+	0.138797i
$34$	−2.81482	−	0.496329i	−0.482738	−	0.0851197i
$35$	−1.71608	+	1.39795i	−0.290071	+	0.236296i
$36$	−2.20594	−	2.03318i	−0.367657	−	0.338863i
$37$	−6.98105	−	6.98105i	−1.14768	−	1.14768i	−0.987008	−	0.160670i	$-0.948634\pi$
$37$	−6.98105	−	6.98105i	−1.14768	−	1.14768i	−0.160670	−	0.987008i	$-0.551366\pi$
$38$	0.804584	+	4.28400i	0.130521	+	0.694956i
$39$	−6.86042	+	7.79996i	−1.09855	+	1.24899i
$40$	0.356226	+	2.20751i	0.0563243	+	0.349038i
$41$	0.231277	−	0.635428i	0.0361194	−	0.0992372i	−0.920322	−	0.391162i	$-0.872073\pi$
$41$	0.231277	−	0.635428i	0.0361194	−	0.0992372i	0.956441	+	0.291924i	$0.0942956\pi$
$42$	0.189124	−	1.70404i	0.0291825	−	0.262939i
$43$	−0.540510	−	0.378469i	−0.0824270	−	0.0577160i	0.531637	−	0.846973i	$-0.321577\pi$
$43$	−0.540510	−	0.378469i	−0.0824270	−	0.0577160i	−0.614064	+	0.789257i	$0.710466\pi$
$44$	−1.83080	+	0.666356i	−0.276003	+	0.100457i
$45$	6.63453	+	0.991467i	0.989017	+	0.147799i
$46$	1.39356	+	2.41371i	0.205469	+	0.355882i
$47$	9.29672	−	0.813358i	1.35607	−	0.118640i	0.614180	−	0.789166i	$-0.289487\pi$
$47$	9.29672	−	0.813358i	1.35607	−	0.118640i	0.741886	+	0.670526i	$0.233931\pi$
$48$	−1.39532	−	1.02620i	−0.201397	−	0.148120i
$49$	−5.21361	+	3.01008i	−0.744802	+	0.430011i
$50$	−3.43123	−	3.63685i	−0.485249	−	0.514328i
$51$	−1.80099	+	4.61141i	−0.252188	+	0.645727i
$52$	−3.43994	+	4.91274i	−0.477034	+	0.681275i
$53$	−7.05061	+	4.93689i	−0.968476	+	0.678134i	−0.946865	−	0.321632i	$-0.895768\pi$
$53$	−7.05061	+	4.93689i	−0.968476	+	0.678134i	−0.0216112	+	0.999766i	$0.506880\pi$
$54$	−4.20374	+	3.05427i	−0.572057	+	0.415634i
$55$	2.55043	−	3.53194i	0.343899	−	0.476246i
$56$		−	0.989869i		−	0.132277i
$57$	7.54928	+	0.0917376i	0.999926	+	0.0121509i
$58$	−0.767714	+	0.767714i	−0.100806	+	0.100806i
$59$	−0.996800	+	0.836415i	−0.129772	+	0.108892i	−0.705364	−	0.708846i	$-0.749216\pi$
$59$	−0.996800	+	0.836415i	−0.129772	+	0.108892i	0.575591	+	0.817737i	$0.304772\pi$
$60$	3.87022	+	0.146399i	0.499643	+	0.0189000i
$61$	1.19209	−	6.76066i	0.152631	−	0.865613i	−0.808289	−	0.588786i	$-0.799606\pi$
$61$	1.19209	−	6.76066i	0.152631	−	0.865613i	0.960920	−	0.276827i	$-0.0892829\pi$
$62$	−0.339211	−	0.237518i	−0.0430799	−	0.0301649i
$63$	−2.82956	−	0.901190i	−0.356491	−	0.113539i
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	0.195008	−	13.4091i	0.0241877	−	1.66319i
$66$	0.508509	+	3.33601i	0.0625931	+	0.410635i
$67$	−1.15572	−	13.2100i	−0.141194	−	1.61386i	−0.654782	−	0.755818i	$-0.727239\pi$
$67$	−1.15572	−	13.2100i	−0.141194	−	1.61386i	0.513588	−	0.858037i	$-0.328316\pi$
$68$	−0.739768	+	2.76085i	−0.0897100	+	0.334802i
$69$	4.57347	−	1.54509i	0.550582	−	0.186007i
$70$	1.24306	+	1.83139i	0.148574	+	0.218893i
$71$	8.83250	−	1.55741i	1.04822	−	0.184830i	0.377098	−	0.926173i	$-0.376922\pi$
$71$	8.83250	−	1.55741i	1.04822	−	0.184830i	0.671126	+	0.741343i	$0.265811\pi$
$72$	−2.21770	+	2.02035i	−0.261359	+	0.238100i
$73$	5.75154	−	2.68199i	0.673167	−	0.313903i	−0.0558096	−	0.998441i	$-0.517774\pi$
$73$	5.75154	−	2.68199i	0.673167	−	0.313903i	0.728977	+	0.684538i	$0.239996\pi$
$74$	−7.56293	+	6.34605i	−0.879173	+	0.737713i
$75$	−7.34427	+	4.58930i	−0.848043	+	0.529927i
$76$	4.33782	−	0.428147i	0.497582	−	0.0491119i
$77$	−1.36369	+	1.36369i	−0.155407	+	0.155407i
$78$	7.17235	+	7.51413i	0.812109	+	0.850807i
$79$	−3.54991	+	9.75331i	−0.399396	+	1.09733i	0.563183	+	0.826332i	$0.309577\pi$
$79$	−3.54991	+	9.75331i	−0.399396	+	1.09733i	−0.962579	+	0.271000i	$0.912646\pi$
$80$	2.23016	−	0.162474i	0.249339	−	0.0181651i
$81$	3.75617	+	8.17870i	0.417353	+	0.908745i
$82$	−0.612853	−	0.285778i	−0.0676783	−	0.0315589i
$83$	6.81831	−	1.82696i	0.748407	−	0.200535i	0.135596	−	0.990764i	$-0.456705\pi$
$83$	6.81831	−	1.82696i	0.748407	−	0.200535i	0.612811	+	0.790229i	$0.290039\pi$
$84$	−1.68107	−	0.336922i	−0.183420	−	0.0367612i
$85$	−2.09836	−	6.03694i	−0.227600	−	0.654798i
$86$	−0.424137	+	0.505467i	−0.0457359	+	0.0545059i
$87$	1.04249	+	1.56510i	0.111766	+	0.167796i
$88$	0.504256	+	1.88191i	0.0537538	+	0.200612i
$89$	15.9299	−	5.79801i	1.68857	−	0.614588i	0.694123	−	0.719856i	$-0.255792\pi$
$89$	15.9299	−	5.79801i	1.68857	−	0.614588i	0.994444	+	0.105268i	$0.0335700\pi$
$90$	1.56593	−	6.52287i	0.165064	−	0.687571i
$91$	−1.03088	+	5.84640i	−0.108065	+	0.612869i
$92$	2.52598	−	1.17788i	0.263352	−	0.122803i
$93$	−0.518830	+	0.495231i	−0.0538001	+	0.0513531i
$94$		−	9.33223i		−	0.962547i
$95$	−7.48790	+	6.23950i	−0.768242	+	0.640159i
$96$	−1.14391	+	1.30057i	−0.116750	+	0.132739i
$97$	−10.1176	−	0.885172i	−1.02728	−	0.0898756i	−0.438964	−	0.898505i	$-0.644654\pi$
$97$	−10.1176	−	0.885172i	−1.02728	−	0.0898756i	−0.588319	+	0.808629i	$0.700210\pi$
$98$	2.54423	+	5.45612i	0.257006	+	0.551151i
$99$	5.83856	+	0.271889i	0.586797	+	0.0273259i
$100$	−3.92206	+	3.10120i	−0.392206	+	0.310120i
$101$	5.27281	+	14.4869i	0.524664	+	1.44150i	0.865275	+	0.501298i	$0.167144\pi$
$101$	5.27281	+	14.4869i	0.524664	+	1.44150i	−0.340611	+	0.940204i	$0.610634\pi$
$102$	4.43690	+	2.19604i	0.439318	+	0.217441i
$103$	0.0930424	+	0.0249306i	0.00916774	+	0.00245649i	0.263400	−	0.964687i	$-0.415156\pi$
$103$	0.0930424	+	0.0249306i	0.00916774	+	0.00245649i	−0.254232	+	0.967143i	$0.581823\pi$
$104$	4.59424	+	3.85502i	0.450502	+	0.378016i
$105$	3.53331	−	1.48771i	0.344816	−	0.145186i
$106$	4.30360	+	7.45406i	0.418003	+	0.724002i
$107$	−1.51693	−	5.66126i	−0.146647	−	0.547295i	−0.999677	−	0.0254320i	$-0.991904\pi$
$107$	−1.51693	−	5.66126i	−0.146647	−	0.547295i	0.853029	−	0.521863i	$-0.174763\pi$
$108$	2.67627	+	4.45394i	0.257524	+	0.428581i
$109$	10.3517	−	1.82529i	0.991518	−	0.174831i	0.345718	−	0.938338i	$-0.387635\pi$
$109$	10.3517	−	1.82529i	0.991518	−	0.174831i	0.645799	+	0.763507i	$0.276524\pi$
$110$	−3.29621	−	2.84855i	−0.314282	−	0.271598i
$111$	8.20316	+	15.0040i	0.778610	+	1.42411i
$112$	−0.986102	−	0.0862727i	−0.0931779	−	0.00815201i
$113$	9.80637	+	9.80637i	0.922506	+	0.922506i	0.997206	−	0.0747004i	$-0.0238000\pi$
$113$	9.80637	+	9.80637i	0.922506	+	0.922506i	−0.0747004	+	0.997206i	$0.523800\pi$
$114$	0.749351	−	7.51255i	0.0701832	−	0.703615i
$115$	−3.19424	+	5.35134i	−0.297864	+	0.499015i
$116$	0.697882	+	0.831703i	0.0647967	+	0.0772217i
$117$	15.2023	−	9.62307i	1.40546	−	0.889653i
$118$	0.746355	+	1.06591i	0.0687075	+	0.0981245i
$119$	0.491300	+	2.78630i	0.0450374	+	0.255420i
$120$	0.483153	−	3.84273i	0.0441057	−	0.350792i
$121$	−3.60207	+	6.23898i	−0.327461	+	0.567180i
$122$	−6.63103	−	1.77678i	−0.600346	−	0.160862i
$123$	−0.693927	+	0.943524i	−0.0625693	+	0.0850747i
$124$	−0.266179	+	0.317220i	−0.0239036	+	0.0284872i
$125$	3.36191	−	10.6629i	0.300699	−	0.953719i
$126$	−1.14437	+	2.74025i	−0.101949	+	0.244121i
$127$	13.0867	+	6.10243i	1.16126	+	0.541503i	0.905128	−	0.425140i	$-0.139775\pi$
$127$	13.0867	+	6.10243i	1.16126	+	0.541503i	0.256129	+	0.966643i	$0.417553\pi$
$128$	−0.573576	+	0.819152i	−0.0506975	+	0.0724035i
$129$	0.714060	+	0.892349i	0.0628695	+	0.0785670i
$130$	−13.3411	−	1.36294i	−1.17009	−	0.119538i
$131$	1.84166	+	2.19480i	0.160906	+	0.191761i	0.840474	−	0.541853i	$-0.182277\pi$
$131$	1.84166	+	2.19480i	0.160906	+	0.191761i	−0.679567	+	0.733613i	$0.737832\pi$
$132$	3.36764	−	0.215821i	0.293115	−	0.0187848i
$133$	3.71246	−	2.19877i	0.321911	−	0.190658i
$134$	−13.2604			−1.14553
$135$	−10.5447	−	4.87958i	−0.907539	−	0.419967i
$136$	2.68587	+	0.977577i	0.230312	+	0.0838265i
$137$	6.76863	+	9.66661i	0.578283	+	0.825874i	0.996597	−	0.0824285i	$-0.0262676\pi$
$137$	6.76863	+	9.66661i	0.578283	+	0.825874i	−0.418314	+	0.908303i	$0.637379\pi$
$138$	−1.14061	−	4.69073i	−0.0970949	−	0.399302i
$139$	1.70250	+	4.67758i	0.144404	+	0.396747i	0.990717	−	0.135939i	$-0.0434050\pi$
$139$	1.70250	+	4.67758i	0.144404	+	0.396747i	−0.846313	+	0.532686i	$0.821183\pi$
$140$	1.93276	−	1.07872i	0.163348	−	0.0911681i
$141$	−15.8487	−	3.17641i	−1.33470	−	0.267502i
$142$	−0.781678	−	8.93462i	−0.0655970	−	0.749777i
$143$	−1.01838	−	11.6401i	−0.0851613	−	0.973398i
$144$	1.81937	+	2.38535i	0.151614	+	0.198779i
$145$	−2.33562	−	0.662375i	−0.193962	−	0.0550072i
$146$	−2.17050	−	5.96341i	−0.179632	−	0.493535i
$147$	10.1320	−	2.46371i	0.835672	−	0.203203i
$148$	5.66275	+	8.08724i	0.465475	+	0.664767i
$149$	8.46674	+	3.08164i	0.693622	+	0.252458i	0.664685	−	0.747123i	$-0.268566\pi$
$149$	8.46674	+	3.08164i	0.693622	+	0.252458i	0.0289370	+	0.999581i	$0.490788\pi$
$150$	3.93174	+	7.71631i	0.321025	+	0.630034i
$151$	−18.9891			−1.54531			−0.772656	−	0.634824i	$-0.781072\pi$
$151$	−18.9891			−1.54531			−0.772656	+	0.634824i	$0.781072\pi$
$152$	−0.0484520	−	4.35863i	−0.00392998	−	0.353532i
$153$	5.23968	−	6.78762i	0.423603	−	0.548747i
$154$	1.23965	+	1.47736i	0.0998940	+	0.119049i
$155$	0.0941075	−	0.921163i	0.00755889	−	0.0739896i
$156$	8.11064	−	6.49016i	0.649371	−	0.519629i
$157$	−6.89192	+	9.84268i	−0.550035	+	0.785531i	−0.993867	−	0.110579i	$-0.964730\pi$
$157$	−6.89192	+	9.84268i	−0.550035	+	0.785531i	0.443833	+	0.896110i	$0.353619\pi$
$158$	9.40680	+	4.38646i	0.748365	+	0.348968i
$159$	14.1239	−	4.77158i	1.12010	−	0.378411i
$160$	0.0325156	−	2.23583i	0.00257059	−	0.176758i
$161$	1.77337	−	2.11342i	0.139761	−	0.166561i
$162$	8.47495	−	3.02906i	0.665855	−	0.237985i
$163$	4.87656	+	1.30667i	0.381962	+	0.102346i	0.444691	−	0.895684i	$-0.353314\pi$
$163$	4.87656	+	1.30667i	0.381962	+	0.102346i	−0.0627289	+	0.998031i	$0.519980\pi$
$164$	−0.338104	+	0.585614i	−0.0264015	+	0.0457287i
$165$	−5.95956	+	4.62833i	−0.463951	+	0.360315i
$166$	−1.22575	−	6.95160i	−0.0951370	−	0.539549i
$167$	−9.62203	−	13.7417i	−0.744575	−	1.06336i	−0.995445	−	0.0953423i	$-0.969605\pi$
$167$	−9.62203	−	13.7417i	−0.744575	−	1.06336i	0.250870	−	0.968021i	$-0.419283\pi$
$168$	−0.482155	+	1.64531i	−0.0371990	+	0.126938i
$169$	−14.7637	−	17.5947i	−1.13567	−	1.35344i
$170$	−6.19685	+	1.56423i	−0.475277	+	0.119971i
$171$	−12.5033	−	3.82966i	−0.956155	−	0.292861i
$172$	0.466578	+	0.466578i	0.0355762	+	0.0355762i
$173$	14.1724	+	1.23993i	1.07751	+	0.0942698i	0.612065	−	0.790807i	$-0.290339\pi$
$173$	14.1724	+	1.23993i	1.07751	+	0.0942698i	0.465444	+	0.885077i	$0.345895\pi$
$174$	1.65000	−	0.902111i	0.125086	−	0.0683888i
$175$	−2.22124	+	4.42291i	−0.167910	+	0.334340i
$176$	1.91870	−	0.338318i	0.144627	−	0.0255017i
$177$	2.06424	−	0.904716i	0.155158	−	0.0680026i
$178$	−4.38757	−	16.3746i	−0.328862	−	1.22733i
$179$	−11.9567	−	20.7095i	−0.893682	−	1.54790i	−0.835427	−	0.549601i	$-0.814780\pi$
$179$	−11.9567	−	20.7095i	−0.893682	−	1.54790i	−0.0582551	−	0.998302i	$-0.518554\pi$
$180$	−6.36157	−	2.12848i	−0.474163	−	0.158647i
$181$	13.2459	+	11.1147i	0.984563	+	0.826147i	0.984772	−	0.173853i	$-0.0556219\pi$
$181$	13.2459	+	11.1147i	0.984563	+	0.826147i	−0.000208366		1.00000i	$0.500066\pi$
$182$	5.73431	+	1.53650i	0.425055	+	0.113893i
$183$	−5.27447	+	10.6566i	−0.389900	+	0.787757i
$184$	−0.953248	−	2.61903i	−0.0702744	−	0.193077i
$185$	−20.6327	−	7.85131i	−1.51695	−	0.577240i
$186$	0.448128	+	0.560018i	0.0328583	+	0.0410625i
$187$	−2.35343	−	5.04696i	−0.172100	−	0.369070i
$188$	−9.29672	−	0.813358i	−0.678033	−	0.0593202i
$189$	4.26420	+	2.87616i	0.310175	+	0.209210i
$190$	5.56314	+	8.00321i	0.403593	+	0.580614i
$191$			1.77826i			0.128671i	0.997928	+	0.0643354i	$0.0204927\pi$
$191$			1.77826i			0.128671i	−0.997928	+	0.0643354i	$0.979507\pi$
$192$	1.19592	+	1.25291i	0.0863081	+	0.0904208i
$193$	−6.51188	+	3.03654i	−0.468735	+	0.218575i	−0.642611	−	0.766193i	$-0.722149\pi$
$193$	−6.51188	+	3.03654i	−0.468735	+	0.218575i	0.173876	+	0.984768i	$0.444371\pi$
$194$	−1.76361	+	10.0019i	−0.126620	+	0.718096i
$195$	−6.85555	+	22.1929i	−0.490936	+	1.58927i
$196$	5.65710	−	2.05902i	0.404079	−	0.147073i
$197$	−0.610076	−	2.27684i	−0.0434661	−	0.162218i	0.940781	−	0.339014i	$-0.110093\pi$
$197$	−0.610076	−	2.27684i	−0.0434661	−	0.162218i	−0.984248	+	0.176796i	$0.943427\pi$
$198$	0.779718	−	5.79264i	0.0554122	−	0.411665i
$199$	−4.03872	+	4.81316i	−0.286298	+	0.341196i	−0.889956	−	0.456047i	$-0.849265\pi$
$199$	−4.03872	+	4.81316i	−0.286298	+	0.341196i	0.603658	+	0.797243i	$0.293709\pi$
$200$	2.74757	+	4.17743i	0.194282	+	0.295389i
$201$	−4.51346	+	22.5199i	−0.318355	+	1.58843i
$202$	14.8914	−	3.99013i	1.04775	−	0.280744i
$203$	0.974020	+	0.454193i	0.0683628	+	0.0318781i
$204$	2.57439	−	4.22862i	0.180243	−	0.296062i
$205$	−0.109866	−	1.50805i	−0.00767338	−	0.105327i
$206$	0.0329449	−	0.0905155i	0.00229538	−	0.00630651i
$207$	−8.35440	+	0.340482i	−0.580671	+	0.0236651i
$208$	4.24077	−	4.24077i	0.294044	−	0.294044i
$209$	−5.93793	+	6.07143i	−0.410735	+	0.419969i
$210$	−1.17410	−	3.64953i	−0.0810209	−	0.251842i
$211$	11.3522	−	9.52562i	0.781517	−	0.655770i	−0.162113	−	0.986772i	$-0.551831\pi$
$211$	11.3522	−	9.52562i	0.781517	−	0.655770i	0.943630	+	0.331002i	$0.107387\pi$
$212$	7.80078	−	3.63756i	0.535760	−	0.249829i
$213$	−15.4395	−	1.71357i	−1.05790	−	0.117412i
$214$	−5.77193	+	1.01775i	−0.394561	+	0.0695717i
$215$	−1.44915	−	0.277311i	−0.0988315	−	0.0189125i
$216$	4.67024	−	2.27790i	0.317770	−	0.154991i
$217$	−0.106091	+	0.395938i	−0.00720195	+	0.0268780i
$218$	−0.916132	−	10.4714i	−0.0620483	−	0.709216i
$219$	−10.8663	+	1.65635i	−0.734276	+	0.111926i
$220$	−3.12499	+	3.03540i	−0.210687	+	0.204647i
$221$	−14.8453	−	8.57095i	−0.998604	−	0.576544i
$222$	15.6618	−	6.86427i	1.05115	−	0.460699i
$223$	14.0901	+	9.86602i	0.943546	+	0.660678i	0.940672	−	0.339318i	$-0.110196\pi$
$223$	14.0901	+	9.86602i	0.943546	+	0.660678i	0.00287403	+	0.999996i	$0.499085\pi$
$224$	−0.171889	+	0.974830i	−0.0114848	+	0.0651336i
$225$	14.4427	−	4.05079i	0.962846	−	0.270053i
$226$	10.6237	−	8.91437i	0.706680	−	0.592975i
$227$	−17.2331	+	17.2331i	−1.14380	+	1.14380i	−0.156051	+	0.987749i	$0.549876\pi$
$227$	−17.2331	+	17.2331i	−1.14380	+	1.14380i	−0.987749	+	0.156051i	$0.950124\pi$
$228$	−7.41866	−	1.40126i	−0.491313	−	0.0928008i
$229$		−	8.52084i		−	0.563073i	−0.959551	−	0.281536i	$-0.909156\pi$
$229$		−	8.52084i		−	0.563073i	0.959551	−	0.281536i	$-0.0908440\pi$
$230$	5.05258	+	3.64848i	0.333157	+	0.240574i
$231$	2.93091	−	1.60242i	0.192840	−	0.105432i
$232$	0.889363	−	0.622739i	0.0583895	−	0.0408848i
$233$	−11.4867	+	16.4047i	−0.752518	+	1.07471i	0.242013	+	0.970273i	$0.422192\pi$
$233$	−11.4867	+	16.4047i	−0.752518	+	1.07471i	−0.994532	+	0.104435i	$0.966697\pi$
$234$	−8.26148	−	15.9832i	−0.540070	−	1.04485i
$235$	18.2216	−	10.1699i	1.18865	−	0.663409i
$236$	1.12690	−	0.650615i	0.0733548	−	0.0423514i
$237$	10.6512	−	14.4823i	0.691871	−	0.940729i
$238$	2.81852	−	0.246589i	0.182698	−	0.0159840i
$239$	8.58302	+	14.8662i	0.555190	+	0.961617i	0.997889	+	0.0649463i	$0.0206876\pi$
$239$	8.58302	+	14.8662i	0.555190	+	0.961617i	−0.442699	+	0.896670i	$0.645979\pi$
$240$	−3.78600	−	0.816231i	−0.244385	−	0.0526875i
$241$	−3.85394	+	1.40272i	−0.248254	+	0.0903571i	−0.463150	−	0.886280i	$-0.653281\pi$
$241$	−3.85394	+	1.40272i	−0.248254	+	0.0903571i	0.214896	+	0.976637i	$0.431059\pi$
$242$	5.90129	+	4.13213i	0.379350	+	0.265623i
$243$	−2.25957	−	15.4238i	−0.144951	−	0.989439i
$244$	−2.34795	+	6.45094i	−0.150312	+	0.412979i
$245$	−7.88072	+	10.9136i	−0.503481	+	0.697242i
$246$	0.879454	+	0.773520i	0.0560719	+	0.0493178i
$247$	−4.25304	+	25.7936i	−0.270614	+	1.64121i
$248$	0.292813	+	0.292813i	0.0185937	+	0.0185937i
$249$	−12.2230	−	0.284444i	−0.774598	−	0.0180259i
$250$	−10.3293	−	4.27845i	−0.653283	−	0.270593i
$251$	11.9820	+	2.11275i	0.756297	+	0.133356i	0.538485	−	0.842635i	$-0.318997\pi$
$251$	11.9820	+	2.11275i	0.756297	+	0.133356i	0.217812	+	0.975991i	$0.430108\pi$
$252$	2.63008	+	1.37885i	0.165680	+	0.0868592i
$253$	−2.29487	+	4.92135i	−0.144277	+	0.309403i
$254$	7.21978	−	12.5050i	0.453010	−	0.784636i
$255$	0.547267	+	11.0564i	0.0342712	+	0.692378i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−6.04376	+	0.528760i	−0.376999	+	0.0329832i	−0.274081	−	0.961707i	$-0.588374\pi$
$257$	−6.04376	+	0.528760i	−0.376999	+	0.0329832i	−0.102918	+	0.994690i	$0.532818\pi$
$258$	0.951188	−	0.633570i	0.0592184	−	0.0394443i
$259$	8.46339	+	4.88634i	0.525889	+	0.303622i
$260$	−2.52051	+	13.1715i	−0.156315	+	0.816861i
$261$	−0.970424	−	3.10921i	−0.0600677	−	0.192455i
$262$	2.34696	−	1.64336i	0.144996	−	0.101527i
$263$	−5.44933	−	11.6861i	−0.336020	−	0.720598i	0.663602	−	0.748086i	$-0.269027\pi$
$263$	−5.44933	−	11.6861i	−0.336020	−	0.720598i	−0.999622	+	0.0274880i	$0.991249\pi$
$264$	0.0785089	−	3.37363i	0.00483189	−	0.207633i
$265$	−9.86450	+	16.5261i	−0.605972	+	1.01519i
$266$	−1.86684	−	3.88997i	−0.114463	−	0.238509i
$267$	−29.3021	+	1.87788i	−1.79326	+	0.114924i
$268$	−1.15572	+	13.2100i	−0.0705970	+	0.806928i
$269$	−3.57049	−	1.29955i	−0.217697	−	0.0792351i	0.230869	−	0.972985i	$-0.425843\pi$
$269$	−3.57049	−	1.29955i	−0.217697	−	0.0792351i	−0.448566	+	0.893750i	$0.648065\pi$
$270$	−5.78004	+	10.0792i	−0.351762	+	0.613403i
$271$	0.469395	+	2.66207i	0.0285137	+	0.161709i	0.995740	−	0.0922072i	$-0.0293922\pi$
$271$	0.469395	+	2.66207i	0.0285137	+	0.161709i	−0.967226	+	0.253917i	$0.918281\pi$
$272$	1.20795	−	2.59045i	0.0732425	−	0.157069i
$273$	4.56120	−	9.21547i	0.276056	−	0.557746i
$274$	10.2198	−	5.90038i	0.617398	−	0.356455i
$275$	1.96985	−	9.54023i	0.118786	−	0.575297i
$276$	−4.77230	+	0.727442i	−0.287258	+	0.0437869i
$277$	2.13084	−	7.95241i	0.128030	−	0.477814i	−0.871900	−	0.489685i	$-0.837112\pi$
$277$	2.13084	−	7.95241i	0.128030	−	0.477814i	0.999930	+	0.0118706i	$0.00377863\pi$
$278$	4.80816	−	1.28834i	0.288374	−	0.0772697i
$279$	1.10360	−	0.570432i	0.0660705	−	0.0341509i
$280$	−0.906160	−	2.01942i	−0.0541534	−	0.120684i
$281$	5.75773	+	1.01524i	0.343477	+	0.0605643i	0.342726	−	0.939435i	$-0.388650\pi$
$281$	5.75773	+	1.01524i	0.343477	+	0.0605643i	0.000751340		1.00000i	$0.499761\pi$
$282$	−4.54563	+	15.5116i	−0.270689	+	0.923701i
$283$	−1.30076	+	14.8678i	−0.0773224	+	0.883799i	0.854160	+	0.520011i	$0.174072\pi$
$283$	−1.30076	+	14.8678i	−0.0773224	+	0.883799i	−0.931482	+	0.363788i	$0.881483\pi$
$284$	−8.96875			−0.532198
$285$	15.4852	−	6.72371i	0.917265	−	0.398278i
$286$	−11.6846			−0.690925
$287$	−0.0583383	+	0.666810i	−0.00344360	+	0.0393606i
$288$	2.53484	−	1.60455i	0.149367	−	0.0945491i
$289$	8.69629	+	1.53339i	0.511546	+	0.0901994i
$290$	−0.863417	+	2.26900i	−0.0507016	+	0.133240i
$291$	16.3858	+	6.39945i	0.960550	+	0.375142i
$292$	−6.12989	+	1.64250i	−0.358724	+	0.0961199i
$293$	−4.10815	+	15.3318i	−0.240001	+	0.895695i	0.735830	+	0.677166i	$0.236792\pi$
$293$	−4.10815	+	15.3318i	−0.240001	+	0.895695i	−0.975831	+	0.218528i	$0.929874\pi$
$294$	−1.57127	−	10.3082i	−0.0916386	−	0.601184i
$295$	−1.26788	+	2.61887i	−0.0738190	+	0.152476i
$296$	8.55001	−	4.93635i	0.496959	−	0.286920i
$297$	−9.57212	−	3.29582i	−0.555431	−	0.191243i
$298$	3.80784	−	8.16594i	0.220582	−	0.473040i
$299$	2.90258	+	16.4614i	0.167861	+	0.951985i
$300$	8.02962	−	3.24426i	0.463590	−	0.187307i
$301$	0.613765	+	0.223392i	0.0353769	+	0.0128761i
$302$	−1.65501	+	18.9169i	−0.0952352	+	1.08854i
$303$	−1.70777	−	26.6478i	−0.0981089	−	1.53087i
$304$	−4.34627	−	0.331612i	−0.249275	−	0.0190192i
$305$	−3.75697	−	14.8836i	−0.215123	−	0.852235i
$306$	−6.30512	−	5.81132i	−0.360440	−	0.332211i
$307$	12.6496	+	27.1272i	0.721952	+	1.54823i	0.832293	+	0.554337i	$0.187028\pi$
$307$	12.6496	+	27.1272i	0.721952	+	1.54823i	−0.110341	+	0.993894i	$0.535194\pi$
$308$	1.57978	−	1.10617i	0.0900163	−	0.0630301i
$309$	−0.142507	−	0.0867584i	−0.00810694	−	0.00493551i
$310$	−0.909455	−	0.174034i	−0.0516536	−	0.00988447i
$311$	−20.0600	−	11.5817i	−1.13750	−	0.656735i	−0.191689	−	0.981456i	$-0.561396\pi$
$311$	−20.0600	−	11.5817i	−1.13750	−	0.656735i	−0.945810	+	0.324721i	$0.894730\pi$
$312$	−5.75857	−	8.64544i	−0.326015	−	0.489451i
$313$	−6.29186	+	0.550466i	−0.355637	+	0.0311142i	−0.263575	−	0.964639i	$-0.584901\pi$
$313$	−6.29186	+	0.550466i	−0.355637	+	0.0311142i	−0.0920624	+	0.995753i	$0.529346\pi$
$314$	9.20455	+	7.72354i	0.519443	+	0.435864i
$315$	−6.59755	+	0.751765i	−0.371730	+	0.0423571i
$316$	5.18963	−	8.98870i	0.291939	−	0.505654i
$317$	1.05257	−	2.25724i	0.0591181	−	0.126779i	−0.874529	−	0.484973i	$-0.838829\pi$
$317$	1.05257	−	2.25724i	0.0591181	−	0.126779i	0.933647	+	0.358194i	$0.116607\pi$
$318$	−3.52244	−	14.4860i	−0.197529	−	0.812335i
$319$	−2.08315	−	0.367316i	−0.116634	−	0.0205657i
$320$	−2.22449	−	0.227257i	−0.124353	−	0.0127041i
$321$	−0.236175	+	10.1488i	−0.0131820	+	0.566448i
$322$	−1.95082	−	1.95082i	−0.108715	−	0.108715i
$323$	2.29970	+	12.2447i	0.127959	+	0.681314i
$324$	−2.27889	−	8.70670i	−0.126605	−	0.483706i
$325$	−11.8773	−	27.5343i	−0.658833	−	1.52733i
$326$	1.72672	−	4.74412i	0.0956341	−	0.262752i
$327$	−18.0952	−	2.00832i	−1.00067	−	0.111060i
$328$	0.553917	+	0.387857i	0.0305850	+	0.0214158i
$329$	−8.68059	+	3.15948i	−0.478576	+	0.174188i
$330$	4.09130	+	6.34027i	0.225219	+	0.349020i
$331$	−15.9880	−	27.6920i	−0.878779	−	1.52209i	−0.852682	−	0.522430i	$-0.825026\pi$
$331$	−15.9880	−	27.6920i	−0.878779	−	1.52209i	−0.0260966	−	0.999659i	$-0.508308\pi$
$332$	−7.03197	+	0.615218i	−0.385930	+	0.0337645i
$333$	−6.32662	−	28.9345i	−0.346697	−	1.58560i
$334$	−14.5280	+	8.38775i	−0.794937	+	0.458957i
$335$	−14.4506	−	25.8916i	−0.789523	−	1.41461i
$336$	1.59703	+	0.623718i	0.0871250	+	0.0340266i
$337$	4.22875	−	6.03928i	0.230354	−	0.328980i	−0.687290	−	0.726383i	$-0.741200\pi$
$337$	4.22875	−	6.03928i	0.230354	−	0.328980i	0.917644	+	0.397403i	$0.130089\pi$
$338$	−18.8145	+	13.1740i	−1.02337	+	0.716574i
$339$	−11.5231	−	21.0762i	−0.625848	−	1.14470i
$340$	1.01818	+	6.30960i	0.0552187	+	0.342186i
$341$		−	0.806790i		−	0.0436901i
$342$	−4.90482	+	12.1220i	−0.265222	+	0.655482i
$343$	9.11337	−	9.11337i	0.492076	−	0.492076i
$344$	0.505467	−	0.424137i	0.0272530	−	0.0228680i
$345$	7.91589	−	7.33884i	0.426177	−	0.395110i
$346$	2.47042	−	14.0104i	0.132810	−	0.753205i
$347$	21.9095	+	15.3412i	1.17616	+	0.823558i	0.987366	−	0.158458i	$-0.0506521\pi$
$347$	21.9095	+	15.3412i	1.17616	+	0.823558i	0.188798	+	0.982016i	$0.439541\pi$
$348$	−0.754871	−	1.72235i	−0.0404653	−	0.0923275i
$349$	21.7920	+	12.5816i	1.16650	+	0.673480i	0.952853	−	0.303431i	$-0.0981322\pi$
$349$	21.7920	+	12.5816i	1.16650	+	0.673480i	0.213648	+	0.976911i	$0.431466\pi$
$350$	4.21248	+	2.59827i	0.225167	+	0.138883i
$351$	−29.9559	+	8.59008i	−1.59893	+	0.458505i
$352$	−0.169805	−	1.94088i	−0.00905064	−	0.103449i
$353$	−1.58505	+	5.91549i	−0.0843638	+	0.314850i	−0.995193	−	0.0979336i	$-0.968777\pi$
$353$	−1.58505	+	5.91549i	−0.0843638	+	0.314850i	0.910829	+	0.412784i	$0.135443\pi$
$354$	−0.721363	−	2.13524i	−0.0383400	−	0.113487i
$355$	16.5934	−	11.2628i	0.880687	−	0.597769i
$356$	−16.6947	+	2.94373i	−0.884818	+	0.156017i
$357$	0.540564	−	4.87056i	0.0286097	−	0.257777i
$358$	−21.6728	+	10.1062i	−1.14544	+	0.534129i
$359$	8.35473	−	7.01045i	0.440946	−	0.369998i	−0.395117	−	0.918631i	$-0.629296\pi$
$359$	8.35473	−	7.01045i	0.440946	−	0.369998i	0.836063	+	0.548633i	$0.184852\pi$
$360$	−2.67483	+	6.15185i	−0.140976	+	0.324231i
$361$	16.2392	−	9.86343i	0.854696	−	0.519128i
$362$	12.2268	−	12.2268i	0.642628	−	0.642628i
$363$	9.02613	−	8.61558i	0.473749	−	0.452201i
$364$	2.03043	−	5.57857i	0.106424	−	0.292397i
$365$	9.27850	−	10.7367i	0.485659	−	0.561983i
$366$	10.1563	+	6.18318i	0.530880	+	0.323200i
$367$	−24.0552	−	11.2171i	−1.25567	−	0.585529i	−0.323048	−	0.946383i	$-0.604707\pi$
$367$	−24.0552	−	11.2171i	−1.25567	−	0.585529i	−0.932622	+	0.360854i	$0.882485\pi$
$368$	−2.69214	+	0.721358i	−0.140338	+	0.0376034i
$369$	1.61299	−	1.23027i	0.0839690	−	0.0640455i
$370$	−9.61969	+	19.8699i	−0.500104	+	1.03299i
$371$	5.47655	−	6.52670i	0.284328	−	0.338849i
$372$	0.596944	−	0.397614i	0.0309501	−	0.0206153i
$373$	4.92284	+	18.3723i	0.254895	+	0.951281i	0.968149	+	0.250375i	$0.0805540\pi$
$373$	4.92284	+	18.3723i	0.254895	+	0.951281i	−0.713254	+	0.700906i	$0.752779\pi$
$374$	−5.23287	+	1.90461i	−0.270585	+	0.0984849i
$375$	−10.7818	+	16.0858i	−0.556770	+	0.830667i
$376$	−1.62053	+	9.19046i	−0.0835722	+	0.473962i
$377$	−5.90133	+	2.75183i	−0.303934	+	0.141727i
$378$	3.23687	−	3.99730i	0.166487	−	0.205599i
$379$		−	30.1362i		−	1.54799i	−0.633191	−	0.773995i	$-0.718255\pi$
$379$		−	30.1362i		−	1.54799i	0.633191	−	0.773995i	$-0.281745\pi$
$380$	8.45762	−	4.84445i	0.433867	−	0.248515i
$381$	−18.7796	−	16.5175i	−0.962109	−	0.846219i
$382$	1.77150	+	0.154986i	0.0906377	+	0.00792977i
$383$	−1.72926	−	3.70840i	−0.0883609	−	0.189491i	0.857161	−	0.515048i	$-0.172226\pi$
$383$	−1.72926	−	3.70840i	−0.0883609	−	0.189491i	−0.945522	+	0.325557i	$0.894448\pi$
$384$	1.35237	−	1.08217i	0.0690129	−	0.0552243i
$385$	−1.53369	+	4.03044i	−0.0781642	+	0.205410i
$386$	2.45744	+	6.75175i	0.125080	+	0.343655i
$387$	−0.752222	−	1.83103i	−0.0382376	−	0.0930765i
$388$	9.81015	+	2.62862i	0.498035	+	0.133448i
$389$	6.57884	+	5.52031i	0.333561	+	0.279891i	0.794149	−	0.607723i	$-0.207917\pi$
$389$	6.57884	+	5.52031i	0.333561	+	0.279891i	−0.460588	+	0.887614i	$0.652361\pi$
$390$	21.5110	+	8.76370i	1.08925	+	0.443767i
$391$	3.98312	+	6.89897i	0.201435	+	0.348896i
$392$	−1.55813	−	5.81503i	−0.0786976	−	0.293703i
$393$	−1.99205	−	4.54514i	−0.100485	−	0.229272i
$394$	−2.32134	+	0.409315i	−0.116948	+	0.0206210i
$395$	1.68636	+	23.1474i	0.0848497	+	1.16467i
$396$	−5.70264	−	1.28161i	−0.286569	−	0.0644035i
$397$	30.0571	+	2.62965i	1.50852	+	0.131978i	0.811195	−	0.584776i	$-0.198818\pi$
$397$	30.0571	+	2.62965i	1.50852	+	0.131978i	0.697326	+	0.716754i	$0.254373\pi$
$398$	4.44285	+	4.44285i	0.222700	+	0.222700i
$399$	−7.24167	+	1.84639i	−0.362537	+	0.0924350i
$400$	4.40100	−	2.37302i	0.220050	−	0.118651i
$401$	14.1302	+	16.8397i	0.705630	+	0.840937i	0.993151	−	0.116837i	$-0.0372756\pi$
$401$	14.1302	+	16.8397i	0.705630	+	0.840937i	−0.287521	+	0.957774i	$0.592831\pi$
$402$	22.0408	+	6.45902i	1.09930	+	0.322147i
$403$	−1.42448	−	2.03437i	−0.0709585	−	0.101339i
$404$	−2.67708	−	15.1824i	−0.133189	−	0.755355i
$405$	15.1500	+	13.2468i	0.752810	+	0.658238i
$406$	0.537356	−	0.930728i	0.0266685	−	0.0461912i
$407$	−18.5795	−	4.97837i	−0.920952	−	0.246768i
$408$	−3.98815	−	2.93314i	−0.197443	−	0.145212i
$409$	−21.9670	+	26.1793i	−1.08620	+	1.29448i	−0.133340	+	0.991070i	$0.542570\pi$
$409$	−21.9670	+	26.1793i	−1.08620	+	1.29448i	−0.952860	+	0.303412i	$0.901874\pi$
$410$	−1.51189	−	0.0219873i	−0.0746668	−	0.00108588i
$411$	−6.54198	−	19.3643i	−0.322692	−	0.955170i
$412$	−0.0872997	−	0.0407085i	−0.00430095	−	0.00200556i
$413$	0.738793	−	1.05511i	0.0363536	−	0.0519184i
$414$	−0.388948	+	8.35228i	−0.0191158	+	0.410492i
$415$	12.2375	−	9.96889i	0.600717	−	0.489353i
$416$	−3.85502	−	4.59424i	−0.189008	−	0.225251i
$417$	−0.551410	−	8.60411i	−0.0270027	−	0.421345i
$418$	5.53080	+	6.44449i	0.270520	+	0.315210i
$419$	39.1047			1.91039			0.955194	−	0.295979i	$-0.0956460\pi$
$419$	39.1047			1.91039			0.955194	+	0.295979i	$0.0956460\pi$
$420$	−3.73797	+	0.851559i	−0.182394	+	0.0415518i
$421$	−18.0729	−	6.57799i	−0.880818	−	0.320592i	−0.138278	−	0.990393i	$-0.544157\pi$
$421$	−18.0729	−	6.57799i	−0.880818	−	0.320592i	−0.742540	+	0.669802i	$0.766379\pi$
$422$	−8.49996	−	12.1392i	−0.413772	−	0.590927i
$423$	24.7958	+	12.9994i	1.20561	+	0.632054i
$424$	−2.94384	−	8.08813i	−0.142965	−	0.392794i
$425$	−9.80728	−	10.3950i	−0.475723	−	0.504232i
$426$	−3.05269	+	15.2314i	−0.147904	+	0.737965i
$427$	0.592258	+	6.76954i	0.0286614	+	0.327601i
$428$	0.510817	+	5.83867i	0.0246913	+	0.282223i
$429$	−3.97709	+	19.8437i	−0.192016	+	0.958064i
$430$	−0.402558	+	1.41947i	−0.0194131	+	0.0684529i
$431$	−4.32017	−	11.8696i	−0.208095	−	0.571737i	0.791107	−	0.611678i	$-0.209505\pi$
$431$	−4.32017	−	11.8696i	−0.208095	−	0.571737i	−0.999202	+	0.0399412i	$0.987283\pi$
$432$	−1.86219	−	4.85100i	−0.0895947	−	0.233394i
$433$	6.76713	+	9.66447i	0.325208	+	0.464445i	0.948150	−	0.317823i	$-0.102952\pi$
$433$	6.76713	+	9.66447i	0.325208	+	0.464445i	−0.622942	+	0.782268i	$0.714063\pi$
$434$	0.385185	+	0.140196i	0.0184895	+	0.00672962i
$435$	3.55951	+	2.23862i	0.170666	+	0.107334i
$436$	−10.5114			−0.503407
$437$	7.70513	−	9.39270i	0.368586	−	0.449314i
$438$	0.702989	+	10.9693i	0.0335901	+	0.524134i
$439$	20.9543	+	24.9724i	1.00010	+	1.19187i	0.981386	+	0.192044i	$0.0615115\pi$
$439$	20.9543	+	24.9724i	1.00010	+	1.19187i	0.0187100	+	0.999825i	$0.494044\pi$
$440$	2.75149	+	3.37765i	0.131172	+	0.161023i
$441$	−18.0409	−	0.840128i	−0.859092	−	0.0400061i
$442$	−9.83219	+	14.0418i	−0.467670	+	0.667901i
$443$	−4.56049	−	2.12659i	−0.216675	−	0.101037i	0.311250	−	0.950328i	$-0.399252\pi$
$443$	−4.56049	−	2.12659i	−0.216675	−	0.101037i	−0.527926	+	0.849291i	$0.677030\pi$
$444$	−5.47313	−	16.2005i	−0.259743	−	0.768841i
$445$	27.1908	−	26.4113i	1.28897	−	1.25201i
$446$	11.0565	−	13.1766i	0.523541	−	0.623932i
$447$	−12.5720	−	9.24621i	−0.594633	−	0.437331i
$448$	0.956140	+	0.256197i	0.0451734	+	0.0121042i
$449$	15.2377	−	26.3924i	0.719110	−	1.24554i	−0.242242	−	0.970216i	$-0.577883\pi$
$449$	15.2377	−	26.3924i	0.719110	−	1.24554i	0.961353	−	0.275320i	$-0.0887838\pi$
$450$	−2.77661	−	14.7408i	−0.130891	−	0.694887i
$451$	−0.228773	−	1.29744i	−0.0107725	−	0.0610940i
$452$	−7.95453	−	11.3602i	−0.374150	−	0.534341i
$453$	31.5628	+	9.24940i	1.48295	+	0.434575i
$454$	15.6655	+	18.6695i	0.735220	+	0.876202i
$455$	3.24891	+	12.8709i	0.152311	+	0.603397i
$456$	−2.04251	+	7.26830i	−0.0956492	+	0.340369i
$457$	−2.25517	−	2.25517i	−0.105492	−	0.105492i	0.652391	−	0.757883i	$-0.273766\pi$
$457$	−2.25517	−	2.25517i	−0.105492	−	0.105492i	−0.757883	+	0.652391i	$0.773766\pi$
$458$	−8.48841	−	0.742640i	−0.396638	−	0.0347013i
$459$	−12.0153	+	8.72985i	−0.560827	+	0.407475i
$460$	4.07496	−	4.71536i	0.189996	−	0.219855i
$461$	22.0568	−	3.88920i	1.02729	−	0.181138i	0.365484	−	0.930817i	$-0.380903\pi$
$461$	22.0568	−	3.88920i	1.02729	−	0.181138i	0.661801	+	0.749679i	$0.269792\pi$
$462$	−1.34088	−	3.05941i	−0.0623834	−	0.142337i
$463$	−3.58939	−	13.3958i	−0.166813	−	0.622556i	−0.997802	−	0.0662664i	$-0.978891\pi$
$463$	−3.58939	−	13.3958i	−0.166813	−	0.622556i	0.830989	−	0.556289i	$-0.187775\pi$
$464$	−0.542856	−	0.940254i	−0.0252014	−	0.0436502i
$465$	−0.605110	+	1.48527i	−0.0280613	+	0.0688779i
$466$	15.3411	+	12.8727i	0.710665	+	0.596318i
$467$	17.6671	+	4.73387i	0.817534	+	0.219057i	0.643268	−	0.765641i	$-0.277578\pi$
$467$	17.6671	+	4.73387i	0.817534	+	0.219057i	0.174266	+	0.984699i	$0.444245\pi$
$468$	−16.6424	+	6.83701i	−0.769295	+	0.316041i
$469$	4.48939	+	12.3345i	0.207301	+	0.569554i
$470$	−8.54305	−	19.0386i	−0.394061	−	0.878186i
$471$	16.2497	−	13.0030i	0.748745	−	0.599148i
$472$	−0.549924	−	1.17931i	−0.0253123	−	0.0542824i
$473$	−1.28067	−	0.112044i	−0.0588853	−	0.00515180i
$474$	−13.4989	−	11.8729i	−0.620025	−	0.545341i
$475$	−9.56416	+	19.5838i	−0.438834	+	0.898568i
$476$		−	2.82929i		−	0.129680i
$477$	−25.8002	+	1.05148i	−1.18131	+	0.0481440i
$478$	15.5577	−	7.25468i	0.711594	−	0.331822i
$479$	−0.0425891	+	0.241535i	−0.00194594	+	0.0110360i	−0.985765	−	0.168127i	$-0.946228\pi$
$479$	−0.0425891	+	0.241535i	−0.00194594	+	0.0110360i	0.983819	+	0.179163i	$0.0573391\pi$
$480$	−1.14310	+	3.70045i	−0.0521750	+	0.168902i
$481$	−55.6393	+	20.2510i	−2.53693	+	0.923368i
$482$	1.06149	+	3.96153i	0.0483495	+	0.180443i
$483$	−3.97703	+	2.64903i	−0.180961	+	0.120535i
$484$	4.63074	−	5.51870i	0.210488	−	0.250850i
$485$	−21.4511	+	7.45613i	−0.974044	+	0.338565i
$486$	−15.5621	+	0.906694i	−0.705910	+	0.0411285i
$487$	−3.73107	+	0.999737i	−0.169071	+	0.0453024i	−0.342361	−	0.939568i	$-0.611227\pi$
$487$	−3.73107	+	0.999737i	−0.169071	+	0.0453024i	0.173290	+	0.984871i	$0.444560\pi$
$488$	6.22176	+	2.90125i	0.281646	+	0.131334i
$489$	−7.46911	−	4.54720i	−0.337765	−	0.205632i
$490$	10.1852	+	8.80191i	0.460120	+	0.397630i
$491$	0.935546	−	2.57039i	0.0422206	−	0.116000i	−0.916791	−	0.399368i	$-0.869230\pi$
$491$	0.935546	−	2.57039i	0.0422206	−	0.116000i	0.959011	+	0.283368i	$0.0914518\pi$
$492$	0.847226	−	0.808691i	0.0381959	−	0.0364586i
$493$	−2.19431	+	2.19431i	−0.0988269	+	0.0988269i
$494$	25.3247	+	6.48491i	1.13941	+	0.291770i
$495$	12.1601	−	4.79013i	0.546556	−	0.215301i
$496$	0.317220	−	0.266179i	0.0142436	−	0.0119518i
$497$	−8.04610	+	3.75196i	−0.360917	+	0.168298i
$498$	−1.34866	+	12.1517i	−0.0604350	+	0.544528i
$499$	11.3962	−	2.00945i	0.510162	−	0.0899553i	0.0873588	−	0.996177i	$-0.472157\pi$
$499$	11.3962	−	2.00945i	0.510162	−	0.0899553i	0.422803	+	0.906222i	$0.361046\pi$
$500$	−5.16243	+	9.91712i	−0.230871	+	0.443507i
$501$	9.29983	+	27.5275i	0.415486	+	1.22984i
$502$	3.14901	−	11.7523i	0.140547	−	0.524529i
$503$	−1.17659	−	13.4484i	−0.0524614	−	0.599637i	−0.976237	−	0.216704i	$-0.930470\pi$
$503$	−1.17659	−	13.4484i	−0.0524614	−	0.599637i	0.923776	−	0.382933i	$-0.125086\pi$
$504$	1.60283	−	2.49990i	0.0713956	−	0.111354i
$505$	24.0188	+	24.7278i	1.06882	+	1.10037i
$506$	4.70262	+	2.71506i	0.209057	+	0.120699i
$507$	15.9693	+	36.4363i	0.709222	+	1.61819i
$508$	−11.8282	−	8.28220i	−0.524792	−	0.367463i
$509$	3.19818	−	18.1378i	0.141757	−	0.803944i	−0.828157	−	0.560496i	$-0.810610\pi$
$509$	3.19818	−	18.1378i	0.141757	−	0.803944i	0.969914	−	0.243448i	$-0.0782784\pi$
$510$	11.0620	+	0.418444i	0.489834	+	0.0185290i
$511$	−4.81216	+	4.03788i	−0.212878	+	0.178625i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	18.9171	+	12.4557i	0.835209	+	0.549933i
$514$			6.06684i			0.267597i
$515$	0.212637	−	0.0343134i	0.00936993	−	0.00151203i
$516$	−0.548257	−	1.00279i	−0.0241357	−	0.0441453i
$517$	14.8938	−	10.4287i	0.655027	−	0.458655i
$518$	5.60538	−	8.00531i	0.246286	−	0.351733i
$519$	−22.9527	−	8.96418i	−1.00751	−	0.393484i
$520$	12.9017	+	3.65889i	0.565777	+	0.160453i
$521$	28.1545	−	16.2550i	1.23347	−	0.712144i	0.265718	−	0.964051i	$-0.414391\pi$
$521$	28.1545	−	16.2550i	1.23347	−	0.712144i	0.967752	+	0.251907i	$0.0810576\pi$
$522$	−3.18196	+	0.695745i	−0.139271	+	0.0304519i
$523$	−43.2478	+	3.78369i	−1.89109	+	0.165449i	−0.972983	−	0.230876i	$-0.925841\pi$
$523$	−43.2478	+	3.78369i	−1.89109	+	0.165449i	−0.918110	+	0.396325i	$0.870285\pi$
$524$	−1.43255	−	2.48126i	−0.0625814	−	0.108394i
$525$	5.84639	−	6.26959i	0.255157	−	0.273627i
$526$	−12.1166	+	4.41008i	−0.528309	+	0.192289i
$527$	−0.969549	−	0.678886i	−0.0422342	−	0.0295727i
$528$	−3.35395	−	0.372241i	−0.145962	−	0.0161997i
$529$	−5.20965	+	14.3134i	−0.226507	+	0.622322i
$530$	15.6035	+	11.2673i	0.677771	+	0.489421i
$531$	−3.87176	+	0.498304i	−0.168020	+	0.0216245i
$532$	−4.03787	+	1.52070i	−0.175064	+	0.0659309i
$533$	−2.86764	−	2.86764i	−0.124211	−	0.124211i
$534$	−0.683112	+	29.3542i	−0.0295611	+	1.27028i
$535$	−8.27719	−	10.1609i	−0.357854	−	0.439292i
$536$	13.0590	+	2.30265i	0.564062	+	0.0994593i
$537$	9.78636	+	40.2463i	0.422313	+	1.73676i
$538$	−1.60580	+	3.44364i	−0.0692308	+	0.148466i
$539$	−5.86452	+	10.1576i	−0.252603	+	0.437521i
$540$	9.53713	+	6.63651i	0.410413	+	0.285590i
$541$	6.27431	+	5.26477i	0.269754	+	0.226350i	0.767623	−	0.640902i	$-0.221439\pi$
$541$	6.27431	+	5.26477i	0.269754	+	0.226350i	−0.497869	+	0.867252i	$0.665884\pi$
$542$	2.69285	−	0.235594i	0.115668	−	0.0101196i
$543$	−16.6029	−	24.9262i	−0.712499	−	1.06969i
$544$	−2.47531	−	1.42912i	−0.106128	−	0.0612731i
$545$	19.4476	−	13.2001i	0.833044	−	0.565431i
$546$	−8.78287	−	5.34702i	−0.375872	−	0.228831i
$547$	−12.4039	+	8.68530i	−0.530352	+	0.371357i	−0.807867	−	0.589365i	$-0.799378\pi$
$547$	−12.4039	+	8.68530i	−0.530352	+	0.371357i	0.277515	+	0.960721i	$0.410489\pi$
$548$	−4.98721	−	10.6951i	−0.213043	−	0.456873i
$549$	13.9577	−	15.1437i	0.595699	−	0.646317i
$550$	−9.33224	−	2.79384i	−0.397928	−	0.119130i
$551$	4.31107	+	1.95224i	0.183658	+	0.0831684i
$552$	0.308741	+	4.81754i	0.0131409	+	0.205048i
$553$	0.895446	−	10.2350i	0.0380783	−	0.435236i
$554$	−7.73643	−	2.81583i	−0.328689	−	0.119633i
$555$	30.4704	+	23.1000i	1.29339	+	0.980541i
$556$	−0.864381	−	4.90215i	−0.0366579	−	0.207897i
$557$	−16.6924	+	35.7970i	−0.707280	+	1.51677i	0.142595	+	0.989781i	$0.454455\pi$
$557$	−16.6924	+	35.7970i	−0.707280	+	1.51677i	−0.849874	+	0.526985i	$0.823322\pi$
$558$	−0.472077	−	1.14911i	−0.0199846	−	0.0486458i
$559$	−3.42712	+	1.97865i	−0.144952	+	0.0836879i
$560$	−2.09072	+	0.726707i	−0.0883489	+	0.0307090i
$561$	1.45344	+	9.53513i	0.0613644	+	0.402574i
$562$	1.51320	−	5.64734i	0.0638305	−	0.238219i
$563$	37.0977	−	9.94029i	1.56348	−	0.418933i	0.629717	−	0.776824i	$-0.283171\pi$
$563$	37.0977	−	9.94029i	1.56348	−	0.418933i	0.933763	+	0.357891i	$0.116504\pi$
$564$	15.0564	+	5.88026i	0.633988	+	0.247604i
$565$	28.9830	+	11.0288i	1.21932	+	0.463986i
$566$	14.6979	+	2.59163i	0.617797	+	0.108934i
$567$	−5.68679	−	6.85766i	−0.238823	−	0.287995i
$568$	−0.781678	+	8.93462i	−0.0327985	+	0.374888i
$569$	−34.6147			−1.45112			−0.725561	−	0.688158i	$-0.758420\pi$
$569$	−34.6147			−1.45112			−0.725561	+	0.688158i	$0.758420\pi$
$570$	−5.34850	−	16.0123i	−0.224024	−	0.670681i
$571$	−17.4318			−0.729498			−0.364749	−	0.931106i	$-0.618845\pi$
$571$	−17.4318			−0.729498			−0.364749	+	0.931106i	$0.618845\pi$
$572$	−1.01838	+	11.6401i	−0.0425806	+	0.486699i
$573$	0.866174	−	2.95574i	0.0361849	−	0.123478i
$574$	0.659188	+	0.116233i	0.0275140	+	0.00485146i
$575$	−1.61775	+	13.8413i	−0.0674649	+	0.577224i
$576$	−1.37752	−	2.66504i	−0.0573967	−	0.111043i
$577$	35.4567	−	9.50061i	1.47608	−	0.395515i	0.571071	−	0.820901i	$-0.306528\pi$
$577$	35.4567	−	9.50061i	1.47608	−	0.395515i	0.905012	+	0.425385i	$0.139861\pi$
$578$	2.28549	−	8.52955i	0.0950637	−	0.354783i
$579$	12.3028	−	1.87532i	0.511286	−	0.0779355i
$580$	2.18511	+	1.05789i	0.0907319	+	0.0439264i
$581$	−6.05120	+	3.49366i	−0.251046	+	0.144941i
$582$	7.80321	−	15.7657i	0.323453	−	0.653507i
$583$	−7.08704	+	15.1982i	−0.293515	+	0.629446i
$584$	1.10199	+	6.24971i	0.0456008	+	0.258615i
$585$	22.2049	−	33.5487i	0.918059	−	1.38707i
$586$	14.9154	+	5.42877i	0.616151	+	0.224261i
$587$	1.58604	−	18.1285i	0.0654629	−	0.748245i	−0.890543	−	0.454899i	$-0.849676\pi$
$587$	1.58604	−	18.1285i	0.0654629	−	0.748245i	0.956006	−	0.293346i	$-0.0947689\pi$
$588$	−10.4059	+	0.666880i	−0.429131	+	0.0275017i
$589$	−0.447765	+	1.74860i	−0.0184498	+	0.0720500i
$590$	2.49840	+	1.49131i	0.102857	+	0.0613962i
$591$	−0.0949843	+	4.08160i	−0.00390713	+	0.167895i
$592$	−4.17238	−	8.94771i	−0.171484	−	0.367748i
$593$	21.2939	−	14.9102i	0.874436	−	0.612287i	−0.0478241	−	0.998856i	$-0.515229\pi$
$593$	21.2939	−	14.9102i	0.874436	−	0.612287i	0.922261	+	0.386569i	$0.126340\pi$
$594$	−4.11754	+	9.24845i	−0.168945	+	0.379468i
$595$	3.55298	+	5.23456i	0.145658	+	0.214596i
$596$	−7.80299	−	4.50506i	−0.319623	−	0.184534i
$597$	9.05741	−	6.03298i	0.370695	−	0.246914i
$598$	16.6517	−	1.45683i	0.680938	−	0.0595744i
$599$	20.3376	+	17.0653i	0.830973	+	0.697270i	0.955514	−	0.294945i	$-0.0953013\pi$
$599$	20.3376	+	17.0653i	0.830973	+	0.697270i	−0.124541	+	0.992214i	$0.539746\pi$
$600$	−2.53209	−	8.28182i	−0.103372	−	0.338104i
$601$	10.2267	−	17.7131i	0.417155	−	0.722534i	−0.578497	−	0.815685i	$-0.696360\pi$
$601$	10.2267	−	17.7131i	0.417155	−	0.722534i	0.995652	+	0.0931506i	$0.0296938\pi$
$602$	0.276035	−	0.591960i	0.0112504	−	0.0241265i
$603$	18.4713	−	35.2330i	0.752207	−	1.43480i
$604$	18.7006	+	3.29743i	0.760918	+	0.134170i
$605$	−1.63720	+	16.0256i	−0.0665615	+	0.651531i
$606$	−26.6952	−	0.621233i	−1.08442	−	0.0252359i
$607$	−7.03076	−	7.03076i	−0.285370	−	0.285370i	0.549876	−	0.835246i	$-0.314675\pi$
$607$	−7.03076	−	7.03076i	−0.285370	−	0.285370i	−0.835246	+	0.549876i	$0.814675\pi$
$608$	−0.709152	+	4.30083i	−0.0287599	+	0.174422i
$609$	−1.39773	−	1.22937i	−0.0566391	−	0.0498167i
$610$	−15.1545	+	2.44548i	−0.613586	+	0.0990145i
$611$	19.1424	−	52.5934i	0.774420	−	2.12770i
$612$	−6.33873	+	5.77464i	−0.256228	+	0.233426i
$613$	−23.7076	−	16.6002i	−0.957540	−	0.670476i	−0.0133611	−	0.999911i	$-0.504253\pi$
$613$	−23.7076	−	16.6002i	−0.957540	−	0.670476i	−0.944179	+	0.329434i	$0.893142\pi$
$614$	28.1264	−	10.2372i	1.13509	−	0.413139i
$615$	−0.551942	+	2.56012i	−0.0222564	+	0.103234i
$616$	−0.964278	−	1.67018i	−0.0388519	−	0.0672934i
$617$	−47.2470	+	4.13357i	−1.90209	+	0.166411i	−0.976987	−	0.213301i	$-0.931579\pi$
$617$	−47.2470	+	4.13357i	−1.90209	+	0.166411i	−0.925105	+	0.379712i	$0.876023\pi$
$618$	−0.0988486	+	0.134403i	−0.00397627	+	0.00540649i
$619$	−0.691678	+	0.399341i	−0.0278009	+	0.0160509i	−0.513836	−	0.857888i	$-0.671776\pi$
$619$	−0.691678	+	0.399341i	−0.0278009	+	0.0160509i	0.486035	+	0.873939i	$0.338443\pi$
$620$	−0.252636	+	0.890827i	−0.0101461	+	0.0357765i
$621$	14.0521	+	3.50341i	0.563892	+	0.140587i
$622$	−13.2859	+	18.9743i	−0.532717	+	0.760799i
$623$	−13.7458	+	9.62490i	−0.550713	+	0.385614i
$624$	−9.11443	+	4.98316i	−0.364869	+	0.199486i
$625$	−2.90257	−	24.8309i	−0.116103	−	0.993237i
$626$			6.31589i			0.252434i
$627$	12.8271	−	7.19932i	0.512263	−	0.287513i
$628$	8.49638	−	8.49638i	0.339042	−	0.339042i
$629$	−21.6167	+	18.1386i	−0.861914	+	0.723232i
$630$	0.173890	+	6.63796i	0.00692794	+	0.264463i
$631$	0.491998	−	2.79026i	0.0195861	−	0.111078i	−0.973447	−	0.228911i	$-0.926484\pi$
$631$	0.491998	−	2.79026i	0.0195861	−	0.111078i	0.993033	+	0.117833i	$0.0375946\pi$
$632$	−8.50218	−	5.95329i	−0.338199	−	0.236809i
$633$	−23.5089	+	10.3035i	−0.934394	+	0.409526i
$634$	−2.15691	−	1.24529i	−0.0856619	−	0.0494569i
$635$	32.2844	+	0.469512i	1.28117	+	0.0186320i
$636$	−14.7379	+	2.24650i	−0.584395	+	0.0890795i
$637$	3.14676	+	35.9676i	0.124679	+	1.42509i
$638$	−0.547476	+	2.04321i	−0.0216748	+	0.0808914i
$639$	24.8282	+	10.3686i	0.982187	+	0.410177i
$640$	−0.420270	+	2.19622i	−0.0166126	+	0.0868131i
$641$	7.30973	−	1.28890i	0.288717	−	0.0509086i	−0.0274140	−	0.999624i	$-0.508727\pi$
$641$	7.30973	−	1.28890i	0.288717	−	0.0509086i	0.316131	+	0.948716i	$0.397616\pi$
$642$	10.0895	+	1.11980i	0.398203	+	0.0441949i
$643$	11.1232	−	5.18684i	0.438657	−	0.204549i	−0.190728	−	0.981643i	$-0.561085\pi$
$643$	11.1232	−	5.18684i	0.438657	−	0.204549i	0.629385	+	0.777094i	$0.283307\pi$
$644$	−2.11342	+	1.77337i	−0.0832804	+	0.0698806i
$645$	2.27364	+	1.16680i	0.0895243	+	0.0459427i
$646$	12.3985	−	1.22375i	0.487814	−	0.0481478i
$647$	−31.8896	+	31.8896i	−1.25371	+	1.25371i	−0.299666	+	0.954044i	$0.596875\pi$
$647$	−31.8896	+	31.8896i	−1.25371	+	1.25371i	−0.954044	+	0.299666i	$0.903125\pi$
$648$	−8.87219	+	1.51138i	−0.348532	+	0.0593727i
$649$	−0.867082	+	2.38229i	−0.0340360	+	0.0935130i
$650$	−28.4647	+	9.43232i	−1.11648	+	0.369966i
$651$	0.369197	−	0.606433i	0.0144700	−	0.0237680i
$652$	−4.57557	−	2.13362i	−0.179193	−	0.0835592i
$653$	−34.4800	+	9.23889i	−1.34931	+	0.361546i	−0.859879	−	0.510498i	$-0.829461\pi$
$653$	−34.4800	+	9.23889i	−1.34931	+	0.361546i	−0.489428	+	0.872044i	$0.662794\pi$
$654$	−3.57778	+	17.8513i	−0.139902	+	0.698043i
$655$	5.76635	+	2.79168i	0.225310	+	0.109080i
$656$	0.434658	−	0.518006i	0.0169706	−	0.0202247i
$657$	18.8682	+	2.53975i	0.736119	+	0.0990853i
$658$	2.39089	+	8.92292i	0.0932066	+	0.347852i
$659$	−1.90152	+	0.692096i	−0.0740726	+	0.0269602i	−0.378791	−	0.925482i	$-0.623660\pi$
$659$	−1.90152	+	0.692096i	−0.0740726	+	0.0269602i	0.304718	+	0.952443i	$0.401438\pi$
$660$	6.67272	−	3.52314i	0.259735	−	0.137138i
$661$	−6.69202	+	37.9523i	−0.260289	+	1.47617i	0.521832	+	0.853048i	$0.325249\pi$
$661$	−6.69202	+	37.9523i	−0.260289	+	1.47617i	−0.782122	+	0.623126i	$0.785862\pi$
$662$	−28.9801	+	13.5136i	−1.12634	+	0.525222i
$663$	20.5003	+	21.4772i	0.796167	+	0.834106i
$664$			7.05884i			0.273936i
$665$	5.56094	−	7.88421i	0.215644	−	0.305737i
$666$	−29.3758	+	3.78073i	−1.13829	+	0.146500i
$667$	3.01448	+	0.263733i	0.116721	+	0.0102118i
$668$	7.08963	+	15.2038i	0.274306	+	0.588251i
$669$	−18.6143	−	23.2620i	−0.719670	−	0.899360i
$670$	−27.0525	+	12.1391i	−1.04513	+	0.468973i
$671$	−4.57450	−	12.5683i	−0.176597	−	0.485195i
$672$	0.760535	−	1.53659i	0.0293383	−	0.0592752i
$673$	−19.9158	−	5.33641i	−0.767696	−	0.205704i	−0.146343	−	0.989234i	$-0.546750\pi$
$673$	−19.9158	−	5.33641i	−0.767696	−	0.205704i	−0.621353	+	0.783530i	$0.713417\pi$
$674$	−5.64773	−	4.73901i	−0.217543	−	0.182540i
$675$	−25.9790	−	0.301858i	−0.999933	−	0.0116185i
$676$	11.4841	+	19.8911i	0.441697	+	0.765042i
$677$	−0.515270	−	1.92301i	−0.0198034	−	0.0739074i	0.955317	−	0.295583i	$-0.0955140\pi$
$677$	−0.515270	−	1.92301i	−0.0198034	−	0.0739074i	−0.975120	+	0.221676i	$0.928847\pi$
$678$	−22.0003	+	9.64232i	−0.844918	+	0.370311i
$679$	9.90058	−	1.74574i	0.379950	−	0.0669954i
$680$	6.37433	−	0.464389i	0.244445	−	0.0178085i
$681$	37.0380	−	20.2499i	1.41930	−	0.775979i
$682$	−0.803720	−	0.0703164i	−0.0307760	−	0.00269255i
$683$	25.4468	+	25.4468i	0.973695	+	0.973695i	0.999663	−	0.0259681i	$-0.00826683\pi$
$683$	25.4468	+	25.4468i	0.973695	+	0.973695i	−0.0259681	+	0.999663i	$0.508267\pi$
$684$	11.6484	+	5.94266i	0.445387	+	0.227223i
$685$	22.6578	+	13.5245i	0.865710	+	0.516746i
$686$	−8.28441	−	9.87297i	−0.316300	−	0.376952i
$687$	−4.15041	+	14.1629i	−0.158348	+	0.540349i
$688$	−0.378469	−	0.540510i	−0.0144290	−	0.0206067i
$689$	8.96380	+	50.8362i	0.341493	+	1.93671i
$690$	−6.62100	−	8.52539i	−0.252057	−	0.324556i
$691$	0.00818857	−	0.0141830i	0.000311508	−	0.000539548i	−0.865870	−	0.500270i	$-0.833234\pi$
$691$	0.00818857	−	0.0141830i	0.000311508	−	0.000539548i	0.866181	+	0.499730i	$0.166568\pi$
$692$	−13.7418	−	3.68210i	−0.522385	−	0.139973i
$693$	−5.65213	+	1.23586i	−0.214707	+	0.0469463i
$694$	17.1924	−	20.4891i	0.652613	−	0.777754i
$695$	7.75527	+	7.98417i	0.294174	+	0.302857i
$696$	−1.78158	+	0.601886i	−0.0675308	+	0.0228144i
$697$	−1.75168	−	0.816823i	−0.0663497	−	0.0309394i
$698$	14.4331	−	20.6126i	0.546300	−	0.780197i
$699$	27.0832	−	21.6720i	1.02438	−	0.819711i
$700$	2.95552	−	3.97000i	0.111708	−	0.150052i
$701$	−6.87555	−	8.19396i	−0.259686	−	0.309482i	0.620410	−	0.784278i	$-0.286966\pi$
$701$	−6.87555	−	8.19396i	−0.259686	−	0.309482i	−0.880096	+	0.474796i	$0.842522\pi$
$702$	5.94657	+	30.5905i	0.224439	+	1.15457i
$703$	37.5055	+	21.1015i	1.41455	+	0.795857i
$704$	−1.94829			−0.0734291
$705$	−35.2407	+	8.02829i	−1.32724	+	0.302363i
$706$	5.75484	+	2.09459i	0.216586	+	0.0788309i
$707$	−8.75305	−	12.5006i	−0.329192	−	0.470135i
$708$	−2.18998	+	0.532520i	−0.0823046	+	0.0200133i
$709$	−14.5263	−	39.9106i	−0.545545	−	1.49887i	−0.839665	−	0.543104i	$-0.817249\pi$
$709$	−14.5263	−	39.9106i	−0.545545	−	1.49887i	0.294121	−	0.955768i	$-0.404973\pi$
$710$	−9.77376	−	17.5119i	−0.366803	−	0.657210i
$711$	−24.7581	+	18.8837i	−0.928502	+	0.708195i
$712$	1.47749	+	16.8877i	0.0553711	+	0.632895i
$713$	0.100590	+	1.14975i	0.00376714	+	0.0430586i
$714$	−4.80491	−	0.963004i	−0.179819	−	0.0360395i
$715$	−12.7334	−	22.8147i	−0.476201	−	0.853222i
$716$	8.17883	+	22.4712i	0.305657	+	0.839787i
$717$	−7.02509	−	28.8906i	−0.262357	−	1.07894i
$718$	−6.25561	−	8.93394i	−0.233457	−	0.333412i
$719$	42.2585	+	15.3808i	1.57598	+	0.573608i	0.974324	−	0.225150i	$-0.0722871\pi$
$719$	42.2585	+	15.3808i	1.57598	+	0.573608i	0.601652	+	0.798758i	$0.294509\pi$
$720$	5.89532	+	3.20082i	0.219706	+	0.119287i
$721$	−0.0953487			−0.00355097
$722$	−8.41056	−	17.0371i	−0.313009	−	0.634055i
$723$	7.08908	−	0.454317i	0.263646	−	0.0168962i
$724$	−11.1147	−	13.2459i	−0.413073	−	0.492282i
$725$	−5.37124	+	0.786798i	−0.199483	+	0.0292209i
$726$	−7.79612	−	9.74268i	−0.289341	−	0.361585i
$727$	−6.08564	+	8.69119i	−0.225704	+	0.322339i	−0.915992	−	0.401196i	$-0.868595\pi$
$727$	−6.08564	+	8.69119i	−0.225704	+	0.322339i	0.690288	+	0.723534i	$0.257484\pi$
$728$	−5.38038	−	2.50891i	−0.199410	−	0.0929865i
$729$	−3.75704	+	26.7373i	−0.139150	+	0.990271i
$730$	−9.88713	−	10.1790i	−0.365939	−	0.376740i
$731$	−1.21229	+	1.44475i	−0.0448381	+	0.0534360i
$732$	7.04484	−	9.57878i	0.260385	−	0.354042i
$733$	−51.1849	−	13.7149i	−1.89056	−	0.506573i	−0.998506	−	0.0546376i	$-0.982600\pi$
$733$	−51.1849	−	13.7149i	−1.89056	−	0.506573i	−0.892051	−	0.451936i	$-0.850734\pi$
$734$	−13.2710	+	22.9860i	−0.489841	+	0.848429i
$735$	18.4148	−	14.3014i	0.679241	−	0.527514i
$736$	0.483977	+	2.74477i	0.0178396	+	0.101174i
$737$	−14.8185	−	21.1630i	−0.545846	−	0.779548i
$738$	−1.08501	−	1.71408i	−0.0399398	−	0.0630961i
$739$	−30.1451	−	35.9256i	−1.10891	−	1.32154i	−0.942016	−	0.335567i	$-0.891072\pi$
$739$	−30.1451	−	35.9256i	−1.10891	−	1.32154i	−0.166890	−	0.985976i	$-0.553372\pi$
$740$	18.9559	+	11.3149i	0.696832	+	0.415942i
$741$	19.6330	−	40.8012i	0.721235	−	1.49887i
$742$	−6.02455	−	6.02455i	−0.221168	−	0.221168i
$743$	−28.8612	−	2.52503i	−1.05881	−	0.0926342i	−0.455577	−	0.890196i	$-0.650567\pi$
$743$	−28.8612	−	2.52503i	−1.05881	−	0.0926342i	−0.603237	+	0.797562i	$0.706123\pi$
$744$	−0.344074	−	0.629326i	−0.0126144	−	0.0230722i
$745$	20.0940	−	1.46391i	0.736187	−	0.0536334i
$746$	18.7314	−	3.30286i	0.685806	−	0.120926i
$747$	20.1778	+	6.42646i	0.738268	+	0.235132i
$748$	1.44129	+	5.37895i	0.0526986	+	0.196674i
$749$	2.90080	+	5.02433i	0.105993	+	0.183585i
$750$	15.0849	+	12.1427i	0.550822	+	0.443390i
$751$	−6.27400	−	5.26451i	−0.228942	−	0.192105i	0.521100	−	0.853496i	$-0.325522\pi$
$751$	−6.27400	−	5.26451i	−0.228942	−	0.192105i	−0.750041	+	0.661391i	$0.769966\pi$
$752$	9.01425	+	2.41536i	0.328716	+	0.0880791i
$753$	−18.8868	−	9.34802i	−0.688273	−	0.340661i
$754$	2.22703	+	6.11871i	0.0811036	+	0.222830i
$755$	−38.7396	+	17.3833i	−1.40988	+	0.632643i
$756$	−3.69997	−	3.57294i	−0.134567	−	0.129946i
$757$	0.483510	+	1.03689i	0.0175735	+	0.0376864i	0.914899	−	0.403684i	$-0.132270\pi$
$757$	0.483510	+	1.03689i	0.0175735	+	0.0376864i	−0.897325	+	0.441370i	$0.854493\pi$
$758$	−30.0215	−	2.62654i	−1.09043	−	0.0954002i
$759$	6.21155	−	7.06223i	0.225465	−	0.256343i
$760$	−4.08888	−	8.84766i	−0.148319	−	0.320938i
$761$		−	2.12300i		−	0.0769588i	−0.999259	−	0.0384794i	$-0.987749\pi$
$761$		−	2.12300i		−	0.0769588i	0.999259	−	0.0384794i	$-0.0122514\pi$
$762$	−18.0914	+	17.2686i	−0.655384	+	0.625574i
$763$	−9.43008	+	4.39732i	−0.341392	+	0.159194i
$764$	0.308792	−	1.75125i	0.0111717	−	0.0633580i
$765$	4.47581	−	18.6440i	0.161823	−	0.674074i
$766$	−3.84501	+	1.39947i	−0.138926	+	0.0505648i
$767$	2.01981	+	7.53802i	0.0729310	+	0.272182i
$768$	−0.960186	−	1.44154i	−0.0346477	−	0.0520172i
$769$	17.0304	−	20.2961i	0.614133	−	0.731895i	−0.365917	−	0.930648i	$-0.619244\pi$
$769$	17.0304	−	20.2961i	0.614133	−	0.731895i	0.980050	+	0.198752i	$0.0636889\pi$
$770$	3.88143	+	1.87913i	0.139877	+	0.0677192i
$771$	10.3032	+	2.06497i	0.371060	+	0.0743682i
$772$	6.94024	−	1.85963i	0.249785	−	0.0669296i
$773$	−45.2698	−	21.1096i	−1.62824	−	0.759261i	−0.628414	−	0.777879i	$-0.716296\pi$
$773$	−45.2698	−	21.1096i	−1.62824	−	0.759261i	−0.999827	+	0.0186177i	$0.994073\pi$
$774$	−1.88962	+	0.589774i	−0.0679211	+	0.0211990i
$775$	−0.651276	−	1.96541i	−0.0233945	−	0.0705995i
$776$	3.47363	−	9.54372i	0.124696	−	0.342600i
$777$	−11.6873	−	12.2443i	−0.419281	−	0.439260i
$778$	6.07268	−	6.07268i	0.217716	−	0.217716i
$779$	−0.224239	+	2.93898i	−0.00803419	+	0.105300i
$780$	10.6052	−	20.6653i	0.379726	−	0.739936i
$781$	13.3857	−	11.2319i	0.478977	−	0.401910i
$782$	7.21987	−	3.36668i	0.258182	−	0.120392i
$783$	0.0985247	+	5.64066i	0.00352099	+	0.201581i
$784$	−5.92870	+	1.04539i	−0.211739	+	0.0373354i
$785$	−5.04983	+	26.3891i	−0.180236	+	0.941867i
$786$	−4.70146	+	1.58833i	−0.167696	+	0.0566539i
$787$	2.89392	−	10.8003i	0.103157	−	0.384988i	−0.894972	−	0.446121i	$-0.852805\pi$
$787$	2.89392	−	10.8003i	0.103157	−	0.384988i	0.998130	+	0.0611338i	$0.0194716\pi$
$788$	0.205439	+	2.34818i	0.00731848	+	0.0836506i
$789$	3.36542	+	22.0784i	0.119812	+	0.786013i
$790$	23.2063	+	0.337488i	0.825642	+	0.0120073i
$791$	−11.8886	−	6.86390i	−0.422711	−	0.244052i
$792$	−1.77375	+	5.56924i	−0.0630276	+	0.197894i
$793$	−33.7258	−	23.6150i	−1.19764	−	0.838594i
$794$	5.23929	−	29.7135i	0.185935	−	1.05449i
$795$	24.4460	−	22.6639i	0.867009	−	0.803807i
$796$	4.81316	−	4.03872i	0.170598	−	0.143149i
$797$	10.2625	−	10.2625i	0.363515	−	0.363515i	−0.501590	−	0.865105i	$-0.667252\pi$
$797$	10.2625	−	10.2625i	0.363515	−	0.363515i	0.865105	+	0.501590i	$0.167252\pi$
$798$	1.20821	+	7.37503i	0.0427701	+	0.261073i
$799$		−	26.6738i		−	0.943651i
$800$	−1.98042	−	4.59107i	−0.0700185	−	0.162319i
$801$	49.6191	+	11.1514i	1.75321	+	0.394016i
$802$	18.0072	−	12.6088i	0.635856	−	0.445231i
$803$	7.09177	−	10.1281i	0.250263	−	0.357413i
$804$	8.35543	−	21.3940i	0.294673	−	0.754509i
$805$	1.68314	−	5.93498i	0.0593230	−	0.209181i
$806$	−2.15078	+	1.24175i	−0.0757580	+	0.0437389i
$807$	5.30170	+	3.89920i	0.186629	+	0.137258i
$808$	−15.3580	+	1.34365i	−0.540292	+	0.0472695i
$809$	−11.6162	−	20.1198i	−0.408402	−	0.707374i	0.586308	−	0.810088i	$-0.300581\pi$
$809$	−11.6162	−	20.1198i	−0.408402	−	0.707374i	−0.994711	+	0.102714i	$0.967247\pi$
$810$	14.5168	−	13.9378i	0.510068	−	0.489725i
$811$	18.6817	−	6.79958i	0.656003	−	0.238766i	0.00749342	−	0.999972i	$-0.497615\pi$
$811$	18.6817	−	6.79958i	0.656003	−	0.238766i	0.648510	+	0.761206i	$0.275393\pi$
$812$	−0.880352	−	0.616429i	−0.0308943	−	0.0216324i
$813$	0.516462	−	4.65340i	0.0181131	−	0.163202i
$814$	−6.57873	+	18.0749i	−0.230584	+	0.633526i
$815$	11.1448	−	1.79844i	0.390386	−	0.0629966i
$816$	−3.26957	+	3.71734i	−0.114458	+	0.130133i
$817$	2.71349	+	0.953608i	0.0949330	+	0.0333625i
$818$	24.1651	+	24.1651i	0.844913	+	0.844913i
$819$	−12.0702	+	13.0958i	−0.421765	+	0.457604i
$820$	−0.153673	+	1.50422i	−0.00536651	+	0.0525296i
$821$	−16.5219	−	2.91326i	−0.576619	−	0.101673i	−0.122269	−	0.992497i	$-0.539017\pi$
$821$	−16.5219	−	2.91326i	−0.576619	−	0.101673i	−0.454350	+	0.890824i	$0.650128\pi$
$822$	−19.8608	+	4.82938i	−0.692724	+	0.168444i
$823$	−11.1077	+	23.8204i	−0.387188	+	0.830328i	0.612031	+	0.790833i	$0.290353\pi$
$823$	−11.1077	+	23.8204i	−0.387188	+	0.830328i	−0.999220	+	0.0394947i	$0.987425\pi$
$824$	−0.0481623	+	0.0834195i	−0.00167781	+	0.00290606i
$825$	−7.92113	+	14.8978i	−0.275778	+	0.518675i
$826$	−0.986701	−	0.827941i	−0.0343317	−	0.0288077i
$827$	21.6162	−	1.89117i	0.751668	−	0.0657624i	0.295119	−	0.955461i	$-0.404641\pi$
$827$	21.6162	−	1.89117i	0.751668	−	0.0657624i	0.456549	+	0.889698i	$0.349085\pi$
$828$	8.28660	+	1.11542i	0.287979	+	0.0387634i
$829$	0.950996	+	0.549058i	0.0330295	+	0.0190696i	0.516424	−	0.856333i	$-0.327263\pi$
$829$	0.950996	+	0.549058i	0.0330295	+	0.0190696i	−0.483394	+	0.875403i	$0.660596\pi$
$830$	−8.86438	−	13.0598i	−0.307687	−	0.453313i
$831$	−7.41531	+	12.1802i	−0.257234	+	0.422526i
$832$	−4.91274	+	3.43994i	−0.170319	+	0.119258i
$833$	7.27203	+	15.5949i	0.251961	+	0.540332i
$834$	−8.61942	−	0.200585i	−0.298466	−	0.00694570i
$835$	−32.2094	−	19.2260i	−1.11465	−	0.665342i
$836$	6.90201	−	4.94808i	0.238711	−	0.171133i
$837$	−2.11219	+	0.410594i	−0.0730080	+	0.0141922i
$838$	3.40820	−	38.9559i	0.117734	−	1.34571i
$839$	−28.5912	−	10.4063i	−0.987078	−	0.359267i	−0.202490	−	0.979284i	$-0.564903\pi$
$839$	−28.5912	−	10.4063i	−0.987078	−	0.359267i	−0.784588	+	0.620017i	$0.787126\pi$
$840$	0.522533	+	3.79797i	0.0180291	+	0.131042i
$841$	−4.83111	−	27.3986i	−0.166590	−	0.944778i
$842$	−8.12811	+	17.4308i	−0.280113	+	0.600705i
$843$	−9.07570	−	4.49202i	−0.312584	−	0.154713i
$844$	−12.8338	+	7.40961i	−0.441759	+	0.255049i
$845$	−46.2261	−	22.3796i	−1.59023	−	0.769883i
$846$	15.1111	−	23.5684i	0.519529	−	0.810300i
$847$	1.84568	−	6.88817i	0.0634183	−	0.236680i
$848$	−8.31392	+	2.22771i	−0.285501	+	0.0764998i
$849$	9.40401	−	24.0789i	0.322745	−	0.826387i
$850$	−11.2102	+	8.86398i	−0.384507	+	0.304032i
$851$	27.0983	+	4.77816i	0.928917	+	0.163793i
$852$	14.9074	+	4.36859i	0.510720	+	0.149665i
$853$	4.23609	−	48.4187i	0.145041	−	1.65782i	−0.480027	−	0.877254i	$-0.659373\pi$
$853$	4.23609	−	48.4187i	0.145041	−	1.65782i	0.625068	−	0.780570i	$-0.285071\pi$
$854$	6.79540			0.232534
$855$	−29.0138	+	3.63314i	−0.992251	+	0.124251i
$856$	5.86097			0.200324
$857$	−2.29778	+	26.2638i	−0.0784907	+	0.897153i	0.850239	+	0.526396i	$0.176457\pi$
$857$	−2.29778	+	26.2638i	−0.0784907	+	0.897153i	−0.928730	+	0.370757i	$0.879098\pi$
$858$	19.4216	+	5.69145i	0.663042	+	0.194303i
$859$	−15.7329	−	2.77414i	−0.536800	−	0.0946524i	−0.101325	−	0.994853i	$-0.532308\pi$
$859$	−15.7329	−	2.77414i	−0.536800	−	0.0946524i	−0.435475	+	0.900201i	$0.643419\pi$
$860$	1.37898	+	0.524741i	0.0470229	+	0.0178935i
$861$	0.421763	−	1.07992i	0.0143737	−	0.0368037i
$862$	−12.2009	+	3.26923i	−0.415565	+	0.111350i
$863$	−11.4475	+	42.7227i	−0.389678	+	1.45430i	0.440981	+	0.897517i	$0.354631\pi$
$863$	−11.4475	+	42.7227i	−0.389678	+	1.45430i	−0.830659	+	0.556782i	$0.812036\pi$
$864$	−4.99485	+	1.43231i	−0.169928	+	0.0487283i
$865$	30.0481	−	10.4444i	1.02167	−	0.355119i
$866$	10.2175	−	5.89907i	0.347204	−	0.200458i
$867$	−13.7076	−	6.78460i	−0.465536	−	0.230417i
$868$	0.173233	−	0.371500i	0.00587993	−	0.0126095i
$869$	3.51149	+	19.9146i	0.119119	+	0.675557i
$870$	2.54033	−	3.35086i	0.0861254	−	0.113605i
$871$	−74.7314	−	27.2000i	−2.53218	−	0.921637i
$872$	−0.916132	+	10.4714i	−0.0310242	+	0.354608i
$873$	−24.1185	−	18.6182i	−0.816287	−	0.630130i
$874$	−8.68541	−	8.49444i	−0.293788	−	0.287329i
$875$	−0.482657	+	11.0565i	−0.0163168	+	0.373779i
$876$	10.9888	+	0.255725i	0.371278	+	0.00864014i
$877$	20.8875	+	44.7934i	0.705320	+	1.51256i	0.852091	+	0.523394i	$0.175334\pi$
$877$	20.8875	+	44.7934i	0.705320	+	1.51256i	−0.146771	+	0.989171i	$0.546888\pi$
$878$	26.7037	−	18.6981i	0.901206	−	0.631031i
$879$	14.2963	−	23.4828i	0.482203	−	0.792054i
$880$	3.60461	−	2.44664i	0.121511	−	0.0824762i
$881$	−6.46178	−	3.73071i	−0.217703	−	0.125691i	0.387183	−	0.922003i	$-0.373448\pi$
$881$	−6.46178	−	3.73071i	−0.217703	−	0.125691i	−0.604886	+	0.796312i	$0.706781\pi$
$882$	−2.40930	+	17.8991i	−0.0811254	+	0.602693i
$883$	43.7282	−	3.82572i	1.47157	−	0.128746i	0.677030	−	0.735956i	$-0.263267\pi$
$883$	43.7282	−	3.82572i	1.47157	−	0.128746i	0.794542	+	0.607210i	$0.207711\pi$
$884$	13.1315	+	11.0186i	0.441659	+	0.370596i
$885$	3.38303	−	3.73538i	0.113719	−	0.125563i
$886$	−2.51597	+	4.35779i	−0.0845257	+	0.146403i
$887$	5.83964	−	12.5232i	0.196076	−	0.420486i	−0.783547	−	0.621333i	$-0.786591\pi$
$887$	5.83964	−	12.5232i	0.196076	−	0.420486i	0.979623	+	0.200847i	$0.0643693\pi$
$888$	−16.6158	+	4.04034i	−0.557591	+	0.135585i
$889$	−14.0761	−	2.48200i	−0.472098	−	0.0832437i
$890$	−23.9409	−	29.3892i	−0.802502	−	0.985129i
$891$	14.3049	+	10.1406i	0.479234	+	0.339724i
$892$	−12.1629	−	12.1629i	−0.407243	−	0.407243i
$893$	−38.0681	+	14.3368i	−1.27390	+	0.479764i
$894$	−10.3067	+	11.7183i	−0.344709	+	0.391917i
$895$	−43.3509	−	31.3038i	−1.44906	−	1.04637i
$896$	0.338555	−	0.930172i	0.0113103	−	0.0310749i
$897$	3.19363	−	28.7751i	0.106632	−	0.960771i
$898$	−24.9639	−	17.4799i	−0.833058	−	0.583313i
$899$	−0.422480	+	0.153770i	−0.0140905	+	0.00512852i
$900$	−14.9267	+	1.48130i	−0.497556	+	0.0493768i
$901$	12.3007	+	21.3055i	0.409797	+	0.709790i
$902$	−1.31244	+	0.114824i	−0.0436995	+	0.00382321i
$903$	−0.911358	−	0.670270i	−0.0303281	−	0.0223052i
$904$	−12.0103	+	6.93415i	−0.399457	+	0.230626i
$905$	37.1977	+	10.5492i	1.23649	+	0.350666i
$906$	11.9651	−	30.6365i	0.397513	−	1.01783i
$907$	14.7228	−	21.0263i	0.488862	−	0.698167i	−0.496616	−	0.867970i	$-0.665424\pi$
$907$	14.7228	−	21.0263i	0.488862	−	0.698167i	0.985478	+	0.169803i	$0.0543132\pi$
$908$	19.9638	−	13.9788i	0.662521	−	0.463902i
$909$	−10.1413	+	45.1244i	−0.336365	+	1.49668i
$910$	13.1051	−	2.11477i	0.434430	−	0.0701040i
$911$			26.0118i			0.861809i	0.902398	+	0.430904i	$0.141805\pi$
$911$			26.0118i			0.861809i	−0.902398	+	0.430904i	$0.858195\pi$
$912$	7.06262	+	2.66821i	0.233867	+	0.0883533i
$913$	9.72462	−	9.72462i	0.321838	−	0.321838i
$914$	−2.44313	+	2.05003i	−0.0808117	+	0.0678091i
$915$	−1.00502	+	26.5688i	−0.0332250	+	0.878339i
$916$	−1.47963	+	8.39139i	−0.0488883	+	0.277259i
$917$	−2.32318	−	1.62671i	−0.0767182	−	0.0537187i
$918$	7.64943	+	12.7304i	0.252469	+	0.420167i
$919$	−13.5876	−	7.84479i	−0.448213	−	0.258776i	0.258862	−	0.965914i	$-0.416652\pi$
$919$	−13.5876	−	7.84479i	−0.448213	−	0.258776i	−0.707075	+	0.707138i	$0.749986\pi$
$920$	−4.34226	−	4.47043i	−0.143160	−	0.147386i
$921$	−7.81219	−	51.2510i	−0.257421	−	1.68878i
$922$	−1.95203	−	22.3118i	−0.0642866	−	0.734800i
$923$	13.9216	−	51.9560i	0.458234	−	1.71015i
$924$	−3.16464	+	1.06913i	−0.104109	+	0.0351719i
$925$	−49.2800	+	2.87048i	−1.62032	+	0.0943807i
$926$	−13.6577	+	2.40821i	−0.448819	+	0.0791388i
$927$	0.194609	+	0.213619i	0.00639180	+	0.00701618i
$928$	−0.983989	+	0.458842i	−0.0323010	+	0.0150622i
$929$	−10.7533	+	9.02305i	−0.352803	+	0.296037i	−0.801914	−	0.597439i	$-0.796185\pi$
$929$	−10.7533	+	9.02305i	−0.352803	+	0.296037i	0.449112	+	0.893476i	$0.351741\pi$
$930$	1.42688	+	0.732257i	0.0467893	+	0.0240117i
$931$	18.3480	−	18.7605i	0.601331	−	0.614850i
$932$	14.1608	−	14.1608i	0.463853	−	0.463853i
$933$	27.7014	+	29.0215i	0.906905	+	0.950120i
$934$	6.25564	−	17.1872i	0.204691	−	0.562384i
$935$	−9.42138	−	8.14185i	−0.308112	−	0.266267i
$936$	5.36051	+	17.1750i	0.175214	+	0.561381i
$937$	−6.81373	−	3.17729i	−0.222595	−	0.103798i	0.308122	−	0.951347i	$-0.400299\pi$
$937$	−6.81373	−	3.17729i	−0.222595	−	0.103798i	−0.530717	+	0.847549i	$0.678077\pi$
$938$	12.6788	−	3.39728i	0.413978	−	0.110925i
$939$	10.7261	+	2.14974i	0.350034	+	0.0701542i
$940$	−19.7108	+	6.85121i	−0.642894	+	0.223462i
$941$	−17.9668	+	21.4119i	−0.585699	+	0.698009i	−0.974773	−	0.223197i	$-0.928351\pi$
$941$	−17.9668	+	21.4119i	−0.585699	+	0.698009i	0.389074	+	0.921207i	$0.372795\pi$
$942$	−11.5373	−	17.3211i	−0.375905	−	0.564353i
$943$	0.487788	+	1.82045i	0.0158846	+	0.0592820i
$944$	−1.22276	+	0.445047i	−0.0397973	+	0.0144850i
$945$	11.3323	+	1.96405i	0.368640	+	0.0638906i
$946$	−0.223236	+	1.26603i	−0.00725802	+	0.0411623i
$947$	28.5984	−	13.3356i	0.929323	−	0.433350i	0.101814	−	0.994803i	$-0.467535\pi$
$947$	28.5984	−	13.3356i	0.929323	−	0.433350i	0.827509	+	0.561453i	$0.189758\pi$
$948$	−13.0042	+	12.4128i	−0.422358	+	0.403147i
$949$		−	38.0600i		−	1.23548i
$950$	18.6757	+	11.2346i	0.605921	+	0.364499i
$951$	−2.84900	+	3.23918i	−0.0923853	+	0.105037i
$952$	−2.81852	−	0.246589i	−0.0913488	−	0.00799198i
$953$	16.0928	+	34.5112i	0.521298	+	1.11793i	0.974059	+	0.226295i	$0.0726615\pi$
$953$	16.0928	+	34.5112i	0.521298	+	1.11793i	−0.452761	+	0.891632i	$0.649561\pi$
$954$	−1.20116	+	25.7937i	−0.0388889	+	0.835101i
$955$	1.62788	+	3.62783i	0.0526771	+	0.117394i
$956$	−5.87113	−	16.1308i	−0.189886	−	0.521708i
$957$	3.28359	+	1.62521i	0.106143	+	0.0525357i
$958$	0.236904	+	0.0634781i	0.00765401	+	0.00205088i
$959$	−8.94831	−	7.50853i	−0.288956	−	0.242463i
$960$	3.58674	+	1.46126i	0.115762	+	0.0471620i
$961$	15.4143	+	26.6983i	0.497234	+	0.861235i
$962$	15.3247	+	57.1925i	0.494088	+	1.84396i
$963$	5.33591	−	16.7537i	0.171947	−	0.539881i
$964$	4.03897	−	0.712179i	0.130086	−	0.0229377i
$965$	−10.5051	+	12.1560i	−0.338171	+	0.391316i
$966$	2.29233	+	4.19278i	0.0737545	+	0.134900i
$967$	3.91548	+	0.342560i	0.125913	+	0.0110160i	0.149938	−	0.988695i	$-0.452093\pi$
$967$	3.91548	+	0.342560i	0.125913	+	0.0110160i	−0.0240249	+	0.999711i	$0.507648\pi$
$968$	−5.09410	−	5.09410i	−0.163731	−	0.163731i
$969$	2.14183	−	21.4727i	0.0688055	−	0.689803i
$970$	5.55817	+	22.0193i	0.178462	+	0.706997i
$971$	−9.14300	−	10.8962i	−0.293413	−	0.349676i	0.599119	−	0.800660i	$-0.295518\pi$
$971$	−9.14300	−	10.8962i	−0.293413	−	0.349676i	−0.892532	+	0.450984i	$0.851073\pi$
$972$	−0.453080	+	15.5819i	−0.0145325	+	0.499789i
$973$	−2.82621	−	4.03624i	−0.0906040	−	0.129396i
$974$	0.670749	+	3.80401i	0.0214922	+	0.121888i
$975$	6.33018	+	51.5514i	0.202728	+	1.65097i
$976$	3.43248	−	5.94522i	0.109871	−	0.190302i
$977$	−15.8016	−	4.23403i	−0.505538	−	0.135459i	−0.00296924	−	0.999996i	$-0.500945\pi$
$977$	−15.8016	−	4.23403i	−0.505538	−	0.135459i	−0.502569	+	0.864537i	$0.667612\pi$
$978$	−5.18088	+	7.04437i	−0.165666	+	0.225254i
$979$	21.2300	−	25.3009i	0.678513	−	0.808620i
$980$	9.65612	−	9.37929i	0.308453	−	0.299610i
$981$	29.0988	+	12.1521i	0.929053	+	0.387988i
$982$	−2.47907	−	1.15601i	−0.0791104	−	0.0368898i
$983$	−11.6787	+	16.6789i	−0.372493	+	0.531975i	−0.961011	−	0.276509i	$-0.910823\pi$
$983$	−11.6787	+	16.6789i	−0.372493	+	0.531975i	0.588518	+	0.808484i	$0.299711\pi$
$984$	−0.731773	−	0.914484i	−0.0233281	−	0.0291527i
$985$	−3.32891	−	4.08647i	−0.106068	−	0.130206i
$986$	1.99472	+	2.37721i	0.0635247	+	0.0757058i
$987$	15.9674	−	1.02330i	0.508248	−	0.0325720i
$988$	8.66743	−	24.6632i	0.275748	−	0.784640i
$989$	1.83905			0.0584784
$990$	−3.71208	−	12.5313i	−0.117978	−	0.398271i
$991$	48.2996	+	17.5796i	1.53429	+	0.558435i	0.964667	−	0.263472i	$-0.0848677\pi$
$991$	48.2996	+	17.5796i	1.53429	+	0.558435i	0.569621	+	0.821907i	$0.307090\pi$
$992$	−0.237518	−	0.339211i	−0.00754122	−	0.0107700i
$993$	13.0859	+	53.8158i	0.415270	+	1.70779i
$994$	3.03642	+	8.34249i	0.0963093	+	0.264608i
$995$	−3.83324	+	13.5165i	−0.121522	+	0.428502i
$996$	11.9879	+	2.40262i	0.379850	+	0.0761298i
$997$	−0.360517	−	4.12073i	−0.0114177	−	0.130505i	0.988346	−	0.152221i	$-0.0486426\pi$
$997$	−0.360517	−	4.12073i	−0.0114177	−	0.130505i	−0.999764	+	0.0217161i	$0.993087\pi$
$998$	−1.00856	−	11.5279i	−0.0319255	−	0.364910i
$999$	−3.57791	+	51.1751i	−0.113200	+	1.61911i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bi.a.557.23	yes	480
3.2	odd	2	inner	570.2.bi.a.557.9	yes	480
5.3	odd	4	inner	570.2.bi.a.443.13	yes	480
15.8	even	4	inner	570.2.bi.a.443.23	yes	480
19.16	even	9	inner	570.2.bi.a.377.23	yes	480
57.35	odd	18	inner	570.2.bi.a.377.13	yes	480
95.73	odd	36	inner	570.2.bi.a.263.9	✓	480
285.263	even	36	inner	570.2.bi.a.263.23	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bi.a.263.9	✓	480	95.73	odd	36	inner
570.2.bi.a.263.23	yes	480	285.263	even	36	inner
570.2.bi.a.377.13	yes	480	57.35	odd	18	inner
570.2.bi.a.377.23	yes	480	19.16	even	9	inner
570.2.bi.a.443.13	yes	480	5.3	odd	4	inner
570.2.bi.a.443.23	yes	480	15.8	even	4	inner
570.2.bi.a.557.9	yes	480	3.2	odd	2	inner
570.2.bi.a.557.23	yes	480	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bi (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0871557 - 0.996195i) q^{2} +(-1.66215 - 0.487090i) q^{3} +(-0.984808 - 0.173648i) q^{4} +(2.04009 - 0.915434i) q^{5} +(-0.630102 + 1.61337i) q^{6} +(-0.956140 + 0.256197i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(2.52549 + 1.61923i) q^{9} +O(q^{10})\)	\(q+(0.0871557 - 0.996195i) q^{2} +(-1.66215 - 0.487090i) q^{3} +(-0.984808 - 0.173648i) q^{4} +(2.04009 - 0.915434i) q^{5} +(-0.630102 + 1.61337i) q^{6} +(-0.956140 + 0.256197i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(2.52549 + 1.61923i) q^{9} +(-0.734145 - 2.11212i) q^{10} +(1.68727 - 0.974147i) q^{11} +(1.55232 + 0.768319i) q^{12} +(2.53459 - 5.43545i) q^{13} +(0.171889 + 0.974830i) q^{14} +(-3.83684 + 0.527881i) q^{15} +(0.939693 + 0.342020i) q^{16} +(0.249112 - 2.84737i) q^{17} +(1.83318 - 2.37475i) q^{18} +(-4.19757 + 1.17490i) q^{19} +(-2.16806 + 0.547268i) q^{20} +(1.71404 + 0.0398880i) q^{21} +(-0.823385 - 1.76575i) q^{22} +(-2.28307 + 1.59862i) q^{23} +(0.900689 - 1.47945i) q^{24} +(3.32396 - 3.73514i) q^{25} +(-5.19386 - 2.99868i) q^{26} +(-3.40903 - 3.92155i) q^{27} +(0.986102 - 0.0862727i) q^{28} +(-0.831703 - 0.697882i) q^{29} +(0.191470 + 3.86825i) q^{30} +(0.207050 - 0.358622i) q^{31} +(0.422618 - 0.906308i) q^{32} +(-3.27900 + 0.797326i) q^{33} +(-2.81482 - 0.496329i) q^{34} +(-1.71608 + 1.39795i) q^{35} +(-2.20594 - 2.03318i) q^{36} +(-6.98105 - 6.98105i) q^{37} +(0.804584 + 4.28400i) q^{38} +(-6.86042 + 7.79996i) q^{39} +(0.356226 + 2.20751i) q^{40} +(0.231277 - 0.635428i) q^{41} +(0.189124 - 1.70404i) q^{42} +(-0.540510 - 0.378469i) q^{43} +(-1.83080 + 0.666356i) q^{44} +(6.63453 + 0.991467i) q^{45} +(1.39356 + 2.41371i) q^{46} +(9.29672 - 0.813358i) q^{47} +(-1.39532 - 1.02620i) q^{48} +(-5.21361 + 3.01008i) q^{49} +(-3.43123 - 3.63685i) q^{50} +(-1.80099 + 4.61141i) q^{51} +(-3.43994 + 4.91274i) q^{52} +(-7.05061 + 4.93689i) q^{53} +(-4.20374 + 3.05427i) q^{54} +(2.55043 - 3.53194i) q^{55} -0.989869i q^{56} +(7.54928 + 0.0917376i) q^{57} +(-0.767714 + 0.767714i) q^{58} +(-0.996800 + 0.836415i) q^{59} +(3.87022 + 0.146399i) q^{60} +(1.19209 - 6.76066i) q^{61} +(-0.339211 - 0.237518i) q^{62} +(-2.82956 - 0.901190i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(0.195008 - 13.4091i) q^{65} +(0.508509 + 3.33601i) q^{66} +(-1.15572 - 13.2100i) q^{67} +(-0.739768 + 2.76085i) q^{68} +(4.57347 - 1.54509i) q^{69} +(1.24306 + 1.83139i) q^{70} +(8.83250 - 1.55741i) q^{71} +(-2.21770 + 2.02035i) q^{72} +(5.75154 - 2.68199i) q^{73} +(-7.56293 + 6.34605i) q^{74} +(-7.34427 + 4.58930i) q^{75} +(4.33782 - 0.428147i) q^{76} +(-1.36369 + 1.36369i) q^{77} +(7.17235 + 7.51413i) q^{78} +(-3.54991 + 9.75331i) q^{79} +(2.23016 - 0.162474i) q^{80} +(3.75617 + 8.17870i) q^{81} +(-0.612853 - 0.285778i) q^{82} +(6.81831 - 1.82696i) q^{83} +(-1.68107 - 0.336922i) q^{84} +(-2.09836 - 6.03694i) q^{85} +(-0.424137 + 0.505467i) q^{86} +(1.04249 + 1.56510i) q^{87} +(0.504256 + 1.88191i) q^{88} +(15.9299 - 5.79801i) q^{89} +(1.56593 - 6.52287i) q^{90} +(-1.03088 + 5.84640i) q^{91} +(2.52598 - 1.17788i) q^{92} +(-0.518830 + 0.495231i) q^{93} -9.33223i q^{94} +(-7.48790 + 6.23950i) q^{95} +(-1.14391 + 1.30057i) q^{96} +(-10.1176 - 0.885172i) q^{97} +(2.54423 + 5.45612i) q^{98} +(5.83856 + 0.271889i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q+O(q^{10}) \) 480 * q	\( 480 q - 36 q^{15} - 48 q^{18} + 24 q^{22} - 24 q^{25} + 72 q^{33} + 24 q^{43} - 36 q^{45} + 24 q^{51} - 120 q^{55} + 108 q^{57} - 48 q^{60} - 48 q^{61} - 36 q^{63} - 24 q^{66} + 48 q^{67} - 48 q^{70} - 48 q^{78} - 144 q^{81} - 48 q^{85} - 96 q^{87} - 168 q^{90} - 144 q^{91} - 228 q^{93} + 48 q^{97}+O(q^{100}) \) 480 * q - 36 * q^15 - 48 * q^18 + 24 * q^22 - 24 * q^25 + 72 * q^33 + 24 * q^43 - 36 * q^45 + 24 * q^51 - 120 * q^55 + 108 * q^57 - 48 * q^60 - 48 * q^61 - 36 * q^63 - 24 * q^66 + 48 * q^67 - 48 * q^70 - 48 * q^78 - 144 * q^81 - 48 * q^85 - 96 * q^87 - 168 * q^90 - 144 * q^91 - 228 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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