LMFDB - Embedded newform 570.2.bi.a.263.23

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			263.23
Character	$\chi$	$=$	570.263
Dual form			570.2.bi.a.557.23

$q$-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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{3}{4}\right)$

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	0.0735567	−	0.997291i	$-0.476565\pi$
$7$	−0.956140	−	0.256197i	−0.361387	−	0.0968333i	−0.434944	+	0.900458i	$0.643232\pi$
$8$	−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	0.732312	−	0.680969i	$-0.238441\pi$
$11$	1.68727	+	0.974147i	0.508732	+	0.293716i	−0.223580	+	0.974685i	$0.571775\pi$
$12$	1.55232	−	0.768319i	0.448115	−	0.221795i
$13$	2.53459	+	5.43545i	0.702969	+	1.50752i	0.854712	+	0.519102i	$0.173734\pi$
$13$	2.53459	+	5.43545i	0.702969	+	1.50752i	−0.151743	+	0.988420i	$0.548489\pi$
$14$	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	0.964648	+	0.263541i	$0.0848905\pi$
$17$	0.249112	+	2.84737i	0.0604186	+	0.690588i	−0.904230	+	0.427047i	$0.859554\pi$
$18$	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	0.310801	−	0.950475i	$-0.399403\pi$
$23$	−2.28307	−	1.59862i	−0.476053	−	0.333336i	−0.786854	+	0.617139i	$0.788292\pi$
$24$	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	−0.716735	−	0.697346i	$-0.754364\pi$
$29$	−0.831703	+	0.697882i	−0.154443	+	0.129593i	0.562292	+	0.826939i	$0.309920\pi$
$30$	0.191470	−	3.86825i	0.0349574	−	0.706242i
$31$	0.207050	+	0.358622i	0.0371873	+	0.0644104i	0.884020	−	0.467449i	$-0.154827\pi$
$31$	0.207050	+	0.358622i	0.0371873	+	0.0644104i	−0.846833	+	0.531859i	$0.821494\pi$
$32$	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	−0.160670	+	0.987008i	$0.551366\pi$
$37$	−6.98105	+	6.98105i	−1.14768	+	1.14768i	−0.987008	+	0.160670i	$0.948634\pi$
$38$	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	0.956441	−	0.291924i	$-0.0942956\pi$
$41$	0.231277	+	0.635428i	0.0361194	+	0.0992372i	−0.920322	+	0.391162i	$0.872073\pi$
$42$	0.189124	+	1.70404i	0.0291825	+	0.262939i
$43$	−0.540510	+	0.378469i	−0.0824270	+	0.0577160i	−0.614064	−	0.789257i	$-0.710466\pi$
$43$	−0.540510	+	0.378469i	−0.0824270	+	0.0577160i	0.531637	+	0.846973i	$0.321577\pi$
$44$	−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	0.741886	−	0.670526i	$-0.233931\pi$
$47$	9.29672	+	0.813358i	1.35607	+	0.118640i	0.614180	+	0.789166i	$0.289487\pi$
$48$	−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	−0.0216112	−	0.999766i	$-0.506880\pi$
$53$	−7.05061	−	4.93689i	−0.968476	−	0.678134i	−0.946865	+	0.321632i	$0.895768\pi$
$54$	−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	0.575591	−	0.817737i	$-0.304772\pi$
$59$	−0.996800	−	0.836415i	−0.129772	−	0.108892i	−0.705364	+	0.708846i	$0.749216\pi$
$60$	3.87022	−	0.146399i	0.499643	−	0.0189000i
$61$	1.19209	+	6.76066i	0.152631	+	0.865613i	0.960920	+	0.276827i	$0.0892829\pi$
$61$	1.19209	+	6.76066i	0.152631	+	0.865613i	−0.808289	+	0.588786i	$0.799606\pi$
$62$	−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	0.513588	+	0.858037i	$0.328316\pi$
$67$	−1.15572	+	13.2100i	−0.141194	+	1.61386i	−0.654782	+	0.755818i	$0.727239\pi$
$68$	−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	0.671126	−	0.741343i	$-0.265811\pi$
$71$	8.83250	+	1.55741i	1.04822	+	0.184830i	0.377098	+	0.926173i	$0.376922\pi$
$72$	−2.21770	−	2.02035i	−0.261359	−	0.238100i
$73$	5.75154	+	2.68199i	0.673167	+	0.313903i	0.728977	−	0.684538i	$-0.239996\pi$
$73$	5.75154	+	2.68199i	0.673167	+	0.313903i	−0.0558096	+	0.998441i	$0.517774\pi$
$74$	−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	−0.962579	−	0.271000i	$-0.912646\pi$
$79$	−3.54991	−	9.75331i	−0.399396	−	1.09733i	0.563183	−	0.826332i	$-0.309577\pi$
$80$	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	0.612811	−	0.790229i	$-0.290039\pi$
$83$	6.81831	+	1.82696i	0.748407	+	0.200535i	0.135596	+	0.990764i	$0.456705\pi$
$84$	−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	0.994444	−	0.105268i	$-0.0335700\pi$
$89$	15.9299	+	5.79801i	1.68857	+	0.614588i	0.694123	+	0.719856i	$0.255792\pi$
$90$	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	−0.588319	−	0.808629i	$-0.700210\pi$
$97$	−10.1176	+	0.885172i	−1.02728	+	0.0898756i	−0.438964	+	0.898505i	$0.644654\pi$
$98$	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	−0.340611	−	0.940204i	$-0.610634\pi$
$101$	5.27281	−	14.4869i	0.524664	−	1.44150i	0.865275	−	0.501298i	$-0.167144\pi$
$102$	4.43690	−	2.19604i	0.439318	−	0.217441i
$103$	0.0930424	−	0.0249306i	0.00916774	−	0.00245649i	−0.254232	−	0.967143i	$-0.581823\pi$
$103$	0.0930424	−	0.0249306i	0.00916774	−	0.00245649i	0.263400	+	0.964687i	$0.415156\pi$
$104$	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	0.853029	+	0.521863i	$0.174763\pi$
$107$	−1.51693	+	5.66126i	−0.146647	+	0.547295i	−0.999677	+	0.0254320i	$0.991904\pi$
$108$	2.67627	−	4.45394i	0.257524	−	0.428581i
$109$	10.3517	+	1.82529i	0.991518	+	0.174831i	0.645799	−	0.763507i	$-0.276524\pi$
$109$	10.3517	+	1.82529i	0.991518	+	0.174831i	0.345718	+	0.938338i	$0.387635\pi$
$110$	−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	−0.0747004	−	0.997206i	$-0.523800\pi$
$113$	9.80637	−	9.80637i	0.922506	−	0.922506i	0.997206	+	0.0747004i	$0.0238000\pi$
$114$	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	0.256129	−	0.966643i	$-0.417553\pi$
$127$	13.0867	−	6.10243i	1.16126	−	0.541503i	0.905128	+	0.425140i	$0.139775\pi$
$128$	−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	−0.679567	−	0.733613i	$-0.737832\pi$
$131$	1.84166	−	2.19480i	0.160906	−	0.191761i	0.840474	+	0.541853i	$0.182277\pi$
$132$	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	−0.418314	−	0.908303i	$-0.637379\pi$
$137$	6.76863	−	9.66661i	0.578283	−	0.825874i	0.996597	+	0.0824285i	$0.0262676\pi$
$138$	−1.14061	+	4.69073i	−0.0970949	+	0.399302i
$139$	1.70250	−	4.67758i	0.144404	−	0.396747i	−0.846313	−	0.532686i	$-0.821183\pi$
$139$	1.70250	−	4.67758i	0.144404	−	0.396747i	0.990717	+	0.135939i	$0.0434050\pi$
$140$	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	0.0289370	−	0.999581i	$-0.490788\pi$
$149$	8.46674	−	3.08164i	0.693622	−	0.252458i	0.664685	+	0.747123i	$0.268566\pi$
$150$	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	0.443833	−	0.896110i	$-0.353619\pi$
$157$	−6.89192	−	9.84268i	−0.550035	−	0.785531i	−0.993867	+	0.110579i	$0.964730\pi$
$158$	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	−0.0627289	−	0.998031i	$-0.519980\pi$
$163$	4.87656	−	1.30667i	0.381962	−	0.102346i	0.444691	+	0.895684i	$0.353314\pi$
$164$	−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	0.250870	+	0.968021i	$0.419283\pi$
$167$	−9.62203	+	13.7417i	−0.744575	+	1.06336i	−0.995445	+	0.0953423i	$0.969605\pi$
$168$	−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	0.465444	−	0.885077i	$-0.345895\pi$
$173$	14.1724	−	1.23993i	1.07751	−	0.0942698i	0.612065	+	0.790807i	$0.290339\pi$
$174$	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	−0.0582551	+	0.998302i	$0.518554\pi$
$179$	−11.9567	+	20.7095i	−0.893682	+	1.54790i	−0.835427	+	0.549601i	$0.814780\pi$
$180$	−6.36157	+	2.12848i	−0.474163	+	0.158647i
$181$	13.2459	−	11.1147i	0.984563	−	0.826147i	−0.000208366	−	1.00000i	$-0.500066\pi$
$181$	13.2459	−	11.1147i	0.984563	−	0.826147i	0.984772	+	0.173853i	$0.0556219\pi$
$182$	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	$-0.979507\pi$
$191$		−	1.77826i		−	0.128671i	0.997928	−	0.0643354i	$-0.0204927\pi$
$192$	1.19592	−	1.25291i	0.0863081	−	0.0904208i
$193$	−6.51188	−	3.03654i	−0.468735	−	0.218575i	0.173876	−	0.984768i	$-0.444371\pi$
$193$	−6.51188	−	3.03654i	−0.468735	−	0.218575i	−0.642611	+	0.766193i	$0.722149\pi$
$194$	−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	−0.984248	−	0.176796i	$-0.943427\pi$
$197$	−0.610076	+	2.27684i	−0.0434661	+	0.162218i	0.940781	+	0.339014i	$0.110093\pi$
$198$	0.779718	+	5.79264i	0.0554122	+	0.411665i
$199$	−4.03872	−	4.81316i	−0.286298	−	0.341196i	0.603658	−	0.797243i	$-0.293709\pi$
$199$	−4.03872	−	4.81316i	−0.286298	−	0.341196i	−0.889956	+	0.456047i	$0.849265\pi$
$200$	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	0.943630	−	0.331002i	$-0.107387\pi$
$211$	11.3522	+	9.52562i	0.781517	+	0.655770i	−0.162113	+	0.986772i	$0.551831\pi$
$212$	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	0.00287403	−	0.999996i	$-0.499085\pi$
$223$	14.0901	−	9.86602i	0.943546	−	0.660678i	0.940672	+	0.339318i	$0.110196\pi$
$224$	−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	−0.987749	−	0.156051i	$-0.950124\pi$
$227$	−17.2331	−	17.2331i	−1.14380	−	1.14380i	−0.156051	−	0.987749i	$-0.549876\pi$
$228$	−7.41866	+	1.40126i	−0.491313	+	0.0928008i
$229$			8.52084i			0.563073i	0.959551	+	0.281536i	$0.0908440\pi$
$229$			8.52084i			0.563073i	−0.959551	+	0.281536i	$0.909156\pi$
$230$	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	−0.994532	−	0.104435i	$-0.966697\pi$
$233$	−11.4867	−	16.4047i	−0.752518	−	1.07471i	0.242013	−	0.970273i	$-0.422192\pi$
$234$	−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	−0.442699	−	0.896670i	$-0.645979\pi$
$239$	8.58302	−	14.8662i	0.555190	−	0.961617i	0.997889	−	0.0649463i	$-0.0206876\pi$
$240$	−3.78600	+	0.816231i	−0.244385	+	0.0526875i
$241$	−3.85394	−	1.40272i	−0.248254	−	0.0903571i	0.214896	−	0.976637i	$-0.431059\pi$
$241$	−3.85394	−	1.40272i	−0.248254	−	0.0903571i	−0.463150	+	0.886280i	$0.653281\pi$
$242$	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	0.217812	−	0.975991i	$-0.430108\pi$
$251$	11.9820	−	2.11275i	0.756297	−	0.133356i	0.538485	+	0.842635i	$0.318997\pi$
$252$	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	−0.102918	−	0.994690i	$-0.532818\pi$
$257$	−6.04376	−	0.528760i	−0.376999	−	0.0329832i	−0.274081	+	0.961707i	$0.588374\pi$
$258$	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	−0.999622	−	0.0274880i	$-0.991249\pi$
$263$	−5.44933	+	11.6861i	−0.336020	+	0.720598i	0.663602	+	0.748086i	$0.269027\pi$
$264$	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	−0.448566	−	0.893750i	$-0.648065\pi$
$269$	−3.57049	+	1.29955i	−0.217697	+	0.0792351i	0.230869	+	0.972985i	$0.425843\pi$
$270$	−5.78004	−	10.0792i	−0.351762	−	0.613403i
$271$	0.469395	−	2.66207i	0.0285137	−	0.161709i	−0.967226	−	0.253917i	$-0.918281\pi$
$271$	0.469395	−	2.66207i	0.0285137	−	0.161709i	0.995740	+	0.0922072i	$0.0293922\pi$
$272$	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	0.999930	−	0.0118706i	$-0.00377863\pi$
$277$	2.13084	+	7.95241i	0.128030	+	0.477814i	−0.871900	+	0.489685i	$0.837112\pi$
$278$	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	0.000751340	−	1.00000i	$-0.499761\pi$
$281$	5.75773	−	1.01524i	0.343477	−	0.0605643i	0.342726	+	0.939435i	$0.388650\pi$
$282$	−4.54563	−	15.5116i	−0.270689	−	0.923701i
$283$	−1.30076	−	14.8678i	−0.0773224	−	0.883799i	−0.931482	−	0.363788i	$-0.881483\pi$
$283$	−1.30076	−	14.8678i	−0.0773224	−	0.883799i	0.854160	−	0.520011i	$-0.174072\pi$
$284$	−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	−0.975831	−	0.218528i	$-0.929874\pi$
$293$	−4.10815	−	15.3318i	−0.240001	−	0.895695i	0.735830	−	0.677166i	$-0.236792\pi$
$294$	−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	−0.110341	−	0.993894i	$-0.535194\pi$
$307$	12.6496	−	27.1272i	0.721952	−	1.54823i	0.832293	−	0.554337i	$-0.187028\pi$
$308$	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	−0.945810	−	0.324721i	$-0.894730\pi$
$311$	−20.0600	+	11.5817i	−1.13750	+	0.656735i	−0.191689	+	0.981456i	$0.561396\pi$
$312$	−5.75857	+	8.64544i	−0.326015	+	0.489451i
$313$	−6.29186	−	0.550466i	−0.355637	−	0.0311142i	−0.0920624	−	0.995753i	$-0.529346\pi$
$313$	−6.29186	−	0.550466i	−0.355637	−	0.0311142i	−0.263575	+	0.964639i	$0.584901\pi$
$314$	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	0.933647	−	0.358194i	$-0.116607\pi$
$317$	1.05257	+	2.25724i	0.0591181	+	0.126779i	−0.874529	+	0.484973i	$0.838829\pi$
$318$	−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	−0.0260966	+	0.999659i	$0.508308\pi$
$331$	−15.9880	+	27.6920i	−0.878779	+	1.52209i	−0.852682	+	0.522430i	$0.825026\pi$
$332$	−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	0.917644	−	0.397403i	$-0.130089\pi$
$337$	4.22875	+	6.03928i	0.230354	+	0.328980i	−0.687290	+	0.726383i	$0.741200\pi$
$338$	−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	0.188798	−	0.982016i	$-0.439541\pi$
$347$	21.9095	−	15.3412i	1.17616	−	0.823558i	0.987366	+	0.158458i	$0.0506521\pi$
$348$	−0.754871	+	1.72235i	−0.0404653	+	0.0923275i
$349$	21.7920	−	12.5816i	1.16650	−	0.673480i	0.213648	−	0.976911i	$-0.431466\pi$
$349$	21.7920	−	12.5816i	1.16650	−	0.673480i	0.952853	+	0.303431i	$0.0981322\pi$
$350$	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	0.910829	−	0.412784i	$-0.135443\pi$
$353$	−1.58505	−	5.91549i	−0.0843638	−	0.314850i	−0.995193	+	0.0979336i	$0.968777\pi$
$354$	−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	0.836063	−	0.548633i	$-0.184852\pi$
$359$	8.35473	+	7.01045i	0.440946	+	0.369998i	−0.395117	+	0.918631i	$0.629296\pi$
$360$	−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	−0.932622	−	0.360854i	$-0.882485\pi$
$367$	−24.0552	+	11.2171i	−1.25567	+	0.585529i	−0.323048	+	0.946383i	$0.604707\pi$
$368$	−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	−0.713254	−	0.700906i	$-0.752779\pi$
$373$	4.92284	−	18.3723i	0.254895	−	0.951281i	0.968149	−	0.250375i	$-0.0805540\pi$
$374$	−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	$0.281745\pi$
$379$			30.1362i			1.54799i	−0.633191	+	0.773995i	$0.718255\pi$
$380$	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	−0.945522	−	0.325557i	$-0.894448\pi$
$383$	−1.72926	+	3.70840i	−0.0883609	+	0.189491i	0.857161	+	0.515048i	$0.172226\pi$
$384$	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	−0.460588	−	0.887614i	$-0.652361\pi$
$389$	6.57884	−	5.52031i	0.333561	−	0.279891i	0.794149	+	0.607723i	$0.207917\pi$
$390$	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	0.697326	−	0.716754i	$-0.254373\pi$
$397$	30.0571	−	2.62965i	1.50852	−	0.131978i	0.811195	+	0.584776i	$0.198818\pi$
$398$	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	−0.287521	−	0.957774i	$-0.592831\pi$
$401$	14.1302	−	16.8397i	0.705630	−	0.840937i	0.993151	+	0.116837i	$0.0372756\pi$
$402$	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	−0.952860	−	0.303412i	$-0.901874\pi$
$409$	−21.9670	−	26.1793i	−1.08620	−	1.29448i	−0.133340	−	0.991070i	$-0.542570\pi$
$410$	−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	−0.742540	−	0.669802i	$-0.766379\pi$
$421$	−18.0729	+	6.57799i	−0.880818	+	0.320592i	−0.138278	+	0.990393i	$0.544157\pi$
$422$	−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	−0.999202	−	0.0399412i	$-0.987283\pi$
$431$	−4.32017	+	11.8696i	−0.208095	+	0.571737i	0.791107	+	0.611678i	$0.209505\pi$
$432$	−1.86219	+	4.85100i	−0.0895947	+	0.233394i
$433$	6.76713	−	9.66447i	0.325208	−	0.464445i	−0.622942	−	0.782268i	$-0.714063\pi$
$433$	6.76713	−	9.66447i	0.325208	−	0.464445i	0.948150	+	0.317823i	$0.102952\pi$
$434$	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	0.0187100	−	0.999825i	$-0.494044\pi$
$439$	20.9543	−	24.9724i	1.00010	−	1.19187i	0.981386	−	0.192044i	$-0.0615115\pi$
$440$	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	−0.527926	−	0.849291i	$-0.677030\pi$
$443$	−4.56049	+	2.12659i	−0.216675	+	0.101037i	0.311250	+	0.950328i	$0.399252\pi$
$444$	−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	0.961353	+	0.275320i	$0.0887838\pi$
$449$	15.2377	+	26.3924i	0.719110	+	1.24554i	−0.242242	+	0.970216i	$0.577883\pi$
$450$	−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	−0.757883	−	0.652391i	$-0.773766\pi$
$457$	−2.25517	+	2.25517i	−0.105492	+	0.105492i	0.652391	+	0.757883i	$0.273766\pi$
$458$	−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	0.661801	−	0.749679i	$-0.269792\pi$
$461$	22.0568	+	3.88920i	1.02729	+	0.181138i	0.365484	+	0.930817i	$0.380903\pi$
$462$	−1.34088	+	3.05941i	−0.0623834	+	0.142337i
$463$	−3.58939	+	13.3958i	−0.166813	+	0.622556i	0.830989	+	0.556289i	$0.187775\pi$
$463$	−3.58939	+	13.3958i	−0.166813	+	0.622556i	−0.997802	+	0.0662664i	$0.978891\pi$
$464$	−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	0.174266	−	0.984699i	$-0.444245\pi$
$467$	17.6671	−	4.73387i	0.817534	−	0.219057i	0.643268	+	0.765641i	$0.277578\pi$
$468$	−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	0.983819	−	0.179163i	$-0.0573391\pi$
$479$	−0.0425891	−	0.241535i	−0.00194594	−	0.0110360i	−0.985765	+	0.168127i	$0.946228\pi$
$480$	−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	0.173290	−	0.984871i	$-0.444560\pi$
$487$	−3.73107	−	0.999737i	−0.169071	−	0.0453024i	−0.342361	+	0.939568i	$0.611227\pi$
$488$	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	0.959011	−	0.283368i	$-0.0914518\pi$
$491$	0.935546	+	2.57039i	0.0422206	+	0.116000i	−0.916791	+	0.399368i	$0.869230\pi$
$492$	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	0.422803	−	0.906222i	$-0.361046\pi$
$499$	11.3962	+	2.00945i	0.510162	+	0.0899553i	0.0873588	+	0.996177i	$0.472157\pi$
$500$	−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	0.923776	+	0.382933i	$0.125086\pi$
$503$	−1.17659	+	13.4484i	−0.0524614	+	0.599637i	−0.976237	+	0.216704i	$0.930470\pi$
$504$	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	0.969914	+	0.243448i	$0.0782784\pi$
$509$	3.19818	+	18.1378i	0.141757	+	0.803944i	−0.828157	+	0.560496i	$0.810610\pi$
$510$	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	0.967752	−	0.251907i	$-0.0810576\pi$
$521$	28.1545	+	16.2550i	1.23347	+	0.712144i	0.265718	+	0.964051i	$0.414391\pi$
$522$	−3.18196	−	0.695745i	−0.139271	−	0.0304519i
$523$	−43.2478	−	3.78369i	−1.89109	−	0.165449i	−0.918110	−	0.396325i	$-0.870285\pi$
$523$	−43.2478	−	3.78369i	−1.89109	−	0.165449i	−0.972983	+	0.230876i	$0.925841\pi$
$524$	−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	−0.497869	−	0.867252i	$-0.665884\pi$
$541$	6.27431	−	5.26477i	0.269754	−	0.226350i	0.767623	+	0.640902i	$0.221439\pi$
$542$	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	0.277515	−	0.960721i	$-0.410489\pi$
$547$	−12.4039	−	8.68530i	−0.530352	−	0.371357i	−0.807867	+	0.589365i	$0.799378\pi$
$548$	−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	−0.849874	−	0.526985i	$-0.823322\pi$
$557$	−16.6924	−	35.7970i	−0.707280	−	1.51677i	0.142595	−	0.989781i	$-0.454455\pi$
$558$	−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	0.933763	−	0.357891i	$-0.116504\pi$
$563$	37.0977	+	9.94029i	1.56348	+	0.418933i	0.629717	+	0.776824i	$0.283171\pi$
$564$	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	0.905012	−	0.425385i	$-0.139861\pi$
$577$	35.4567	+	9.50061i	1.47608	+	0.395515i	0.571071	+	0.820901i	$0.306528\pi$
$578$	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	0.956006	+	0.293346i	$0.0947689\pi$
$587$	1.58604	+	18.1285i	0.0654629	+	0.748245i	−0.890543	+	0.454899i	$0.849676\pi$
$588$	−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	0.922261	−	0.386569i	$-0.126340\pi$
$593$	21.2939	+	14.9102i	0.874436	+	0.612287i	−0.0478241	+	0.998856i	$0.515229\pi$
$594$	−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	−0.124541	−	0.992214i	$-0.539746\pi$
$599$	20.3376	−	17.0653i	0.830973	−	0.697270i	0.955514	+	0.294945i	$0.0953013\pi$
$600$	−2.53209	+	8.28182i	−0.103372	+	0.338104i
$601$	10.2267	+	17.7131i	0.417155	+	0.722534i	0.995652	−	0.0931506i	$-0.0296938\pi$
$601$	10.2267	+	17.7131i	0.417155	+	0.722534i	−0.578497	+	0.815685i	$0.696360\pi$
$602$	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	−0.835246	−	0.549876i	$-0.814675\pi$
$607$	−7.03076	+	7.03076i	−0.285370	+	0.285370i	0.549876	+	0.835246i	$0.314675\pi$
$608$	−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	−0.944179	−	0.329434i	$-0.893142\pi$
$613$	−23.7076	+	16.6002i	−0.957540	+	0.670476i	−0.0133611	+	0.999911i	$0.504253\pi$
$614$	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	−0.925105	−	0.379712i	$-0.876023\pi$
$617$	−47.2470	−	4.13357i	−1.90209	−	0.166411i	−0.976987	+	0.213301i	$0.931579\pi$
$618$	−0.0988486	−	0.134403i	−0.00397627	−	0.00540649i
$619$	−0.691678	−	0.399341i	−0.0278009	−	0.0160509i	0.486035	−	0.873939i	$-0.338443\pi$
$619$	−0.691678	−	0.399341i	−0.0278009	−	0.0160509i	−0.513836	+	0.857888i	$0.671776\pi$
$620$	−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	0.993033	−	0.117833i	$-0.0375946\pi$
$631$	0.491998	+	2.79026i	0.0195861	+	0.111078i	−0.973447	+	0.228911i	$0.926484\pi$
$632$	−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	0.316131	−	0.948716i	$-0.397616\pi$
$641$	7.30973	+	1.28890i	0.288717	+	0.0509086i	−0.0274140	+	0.999624i	$0.508727\pi$
$642$	10.0895	−	1.11980i	0.398203	−	0.0441949i
$643$	11.1232	+	5.18684i	0.438657	+	0.204549i	0.629385	−	0.777094i	$-0.283307\pi$
$643$	11.1232	+	5.18684i	0.438657	+	0.204549i	−0.190728	+	0.981643i	$0.561085\pi$
$644$	−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	−0.954044	−	0.299666i	$-0.903125\pi$
$647$	−31.8896	−	31.8896i	−1.25371	−	1.25371i	−0.299666	−	0.954044i	$-0.596875\pi$
$648$	−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	−0.489428	−	0.872044i	$-0.662794\pi$
$653$	−34.4800	−	9.23889i	−1.34931	−	0.361546i	−0.859879	+	0.510498i	$0.829461\pi$
$654$	−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	0.304718	−	0.952443i	$-0.401438\pi$
$659$	−1.90152	−	0.692096i	−0.0740726	−	0.0269602i	−0.378791	+	0.925482i	$0.623660\pi$
$660$	6.67272	+	3.52314i	0.259735	+	0.137138i
$661$	−6.69202	−	37.9523i	−0.260289	−	1.47617i	−0.782122	−	0.623126i	$-0.785862\pi$
$661$	−6.69202	−	37.9523i	−0.260289	−	1.47617i	0.521832	−	0.853048i	$-0.325249\pi$
$662$	−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	−0.621353	−	0.783530i	$-0.713417\pi$
$673$	−19.9158	+	5.33641i	−0.767696	+	0.205704i	−0.146343	+	0.989234i	$0.546750\pi$
$674$	−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	−0.975120	−	0.221676i	$-0.928847\pi$
$677$	−0.515270	+	1.92301i	−0.0198034	+	0.0739074i	0.955317	+	0.295583i	$0.0955140\pi$
$678$	−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	−0.0259681	−	0.999663i	$-0.508267\pi$
$683$	25.4468	−	25.4468i	0.973695	−	0.973695i	0.999663	+	0.0259681i	$0.00826683\pi$
$684$	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	0.866181	−	0.499730i	$-0.166568\pi$
$691$	0.00818857	+	0.0141830i	0.000311508	+	0.000539548i	−0.865870	+	0.500270i	$0.833234\pi$
$692$	−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	−0.880096	−	0.474796i	$-0.842522\pi$
$701$	−6.87555	+	8.19396i	−0.259686	+	0.309482i	0.620410	+	0.784278i	$0.286966\pi$
$702$	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	0.294121	+	0.955768i	$0.404973\pi$
$709$	−14.5263	+	39.9106i	−0.545545	+	1.49887i	−0.839665	+	0.543104i	$0.817249\pi$
$710$	−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	0.601652	−	0.798758i	$-0.294509\pi$
$719$	42.2585	−	15.3808i	1.57598	−	0.573608i	0.974324	+	0.225150i	$0.0722871\pi$
$720$	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	0.690288	−	0.723534i	$-0.257484\pi$
$727$	−6.08564	−	8.69119i	−0.225704	−	0.322339i	−0.915992	+	0.401196i	$0.868595\pi$
$728$	−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	−0.892051	+	0.451936i	$0.850734\pi$
$733$	−51.1849	+	13.7149i	−1.89056	+	0.506573i	−0.998506	+	0.0546376i	$0.982600\pi$
$734$	−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	−0.166890	+	0.985976i	$0.553372\pi$
$739$	−30.1451	+	35.9256i	−1.10891	+	1.32154i	−0.942016	+	0.335567i	$0.891072\pi$
$740$	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	−0.603237	−	0.797562i	$-0.706123\pi$
$743$	−28.8612	+	2.52503i	−1.05881	+	0.0926342i	−0.455577	+	0.890196i	$0.650567\pi$
$744$	−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	−0.750041	−	0.661391i	$-0.769966\pi$
$751$	−6.27400	+	5.26451i	−0.228942	+	0.192105i	0.521100	+	0.853496i	$0.325522\pi$
$752$	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	−0.897325	−	0.441370i	$-0.854493\pi$
$757$	0.483510	−	1.03689i	0.0175735	−	0.0376864i	0.914899	+	0.403684i	$0.132270\pi$
$758$	−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	$0.0122514\pi$
$761$			2.12300i			0.0769588i	−0.999259	+	0.0384794i	$0.987749\pi$
$762$	−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	0.980050	−	0.198752i	$-0.0636889\pi$
$769$	17.0304	+	20.2961i	0.614133	+	0.731895i	−0.365917	+	0.930648i	$0.619244\pi$
$770$	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	−0.999827	−	0.0186177i	$-0.994073\pi$
$773$	−45.2698	+	21.1096i	−1.62824	+	0.759261i	−0.628414	+	0.777879i	$0.716296\pi$
$774$	−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	0.998130	−	0.0611338i	$-0.0194716\pi$
$787$	2.89392	+	10.8003i	0.103157	+	0.384988i	−0.894972	+	0.446121i	$0.852805\pi$
$788$	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	0.865105	−	0.501590i	$-0.167252\pi$
$797$	10.2625	+	10.2625i	0.363515	+	0.363515i	−0.501590	+	0.865105i	$0.667252\pi$
$798$	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	−0.994711	−	0.102714i	$-0.967247\pi$
$809$	−11.6162	+	20.1198i	−0.408402	+	0.707374i	0.586308	+	0.810088i	$0.300581\pi$
$810$	14.5168	+	13.9378i	0.510068	+	0.489725i
$811$	18.6817	+	6.79958i	0.656003	+	0.238766i	0.648510	−	0.761206i	$-0.275393\pi$
$811$	18.6817	+	6.79958i	0.656003	+	0.238766i	0.00749342	+	0.999972i	$0.497615\pi$
$812$	−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	−0.454350	−	0.890824i	$-0.650128\pi$
$821$	−16.5219	+	2.91326i	−0.576619	+	0.101673i	−0.122269	+	0.992497i	$0.539017\pi$
$822$	−19.8608	−	4.82938i	−0.692724	−	0.168444i
$823$	−11.1077	−	23.8204i	−0.387188	−	0.830328i	−0.999220	−	0.0394947i	$-0.987425\pi$
$823$	−11.1077	−	23.8204i	−0.387188	−	0.830328i	0.612031	−	0.790833i	$-0.290353\pi$
$824$	−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	0.456549	−	0.889698i	$-0.349085\pi$
$827$	21.6162	+	1.89117i	0.751668	+	0.0657624i	0.295119	+	0.955461i	$0.404641\pi$
$828$	8.28660	−	1.11542i	0.287979	−	0.0387634i
$829$	0.950996	−	0.549058i	0.0330295	−	0.0190696i	−0.483394	−	0.875403i	$-0.660596\pi$
$829$	0.950996	−	0.549058i	0.0330295	−	0.0190696i	0.516424	+	0.856333i	$0.327263\pi$
$830$	−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	−0.784588	−	0.620017i	$-0.787126\pi$
$839$	−28.5912	+	10.4063i	−0.987078	+	0.359267i	−0.202490	+	0.979284i	$0.564903\pi$
$840$	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	0.625068	+	0.780570i	$0.285071\pi$
$853$	4.23609	+	48.4187i	0.145041	+	1.65782i	−0.480027	+	0.877254i	$0.659373\pi$
$854$	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	−0.928730	−	0.370757i	$-0.879098\pi$
$857$	−2.29778	−	26.2638i	−0.0784907	−	0.897153i	0.850239	−	0.526396i	$-0.176457\pi$
$858$	19.4216	−	5.69145i	0.663042	−	0.194303i
$859$	−15.7329	+	2.77414i	−0.536800	+	0.0946524i	−0.435475	−	0.900201i	$-0.643419\pi$
$859$	−15.7329	+	2.77414i	−0.536800	+	0.0946524i	−0.101325	+	0.994853i	$0.532308\pi$
$860$	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	−0.830659	−	0.556782i	$-0.812036\pi$
$863$	−11.4475	−	42.7227i	−0.389678	−	1.45430i	0.440981	−	0.897517i	$-0.354631\pi$
$864$	−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	−0.146771	−	0.989171i	$-0.546888\pi$
$877$	20.8875	−	44.7934i	0.705320	−	1.51256i	0.852091	−	0.523394i	$-0.175334\pi$
$878$	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	−0.604886	−	0.796312i	$-0.706781\pi$
$881$	−6.46178	+	3.73071i	−0.217703	+	0.125691i	0.387183	+	0.922003i	$0.373448\pi$
$882$	−2.40930	−	17.8991i	−0.0811254	−	0.602693i
$883$	43.7282	+	3.82572i	1.47157	+	0.128746i	0.794542	−	0.607210i	$-0.207711\pi$
$883$	43.7282	+	3.82572i	1.47157	+	0.128746i	0.677030	+	0.735956i	$0.263267\pi$
$884$	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	0.979623	−	0.200847i	$-0.0643693\pi$
$887$	5.83964	+	12.5232i	0.196076	+	0.420486i	−0.783547	+	0.621333i	$0.786591\pi$
$888$	−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	0.985478	−	0.169803i	$-0.0543132\pi$
$907$	14.7228	+	21.0263i	0.488862	+	0.698167i	−0.496616	+	0.867970i	$0.665424\pi$
$908$	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	$-0.858195\pi$
$911$		−	26.0118i		−	0.861809i	0.902398	−	0.430904i	$-0.141805\pi$
$912$	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	−0.707075	−	0.707138i	$-0.749986\pi$
$919$	−13.5876	+	7.84479i	−0.448213	+	0.258776i	0.258862	+	0.965914i	$0.416652\pi$
$920$	−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	0.449112	−	0.893476i	$-0.351741\pi$
$929$	−10.7533	−	9.02305i	−0.352803	−	0.296037i	−0.801914	+	0.597439i	$0.796185\pi$
$930$	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	−0.530717	−	0.847549i	$-0.678077\pi$
$937$	−6.81373	+	3.17729i	−0.222595	+	0.103798i	0.308122	+	0.951347i	$0.400299\pi$
$938$	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	0.389074	−	0.921207i	$-0.372795\pi$
$941$	−17.9668	−	21.4119i	−0.585699	−	0.698009i	−0.974773	+	0.223197i	$0.928351\pi$
$942$	−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	0.827509	−	0.561453i	$-0.189758\pi$
$947$	28.5984	+	13.3356i	0.929323	+	0.433350i	0.101814	+	0.994803i	$0.467535\pi$
$948$	−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	−0.452761	−	0.891632i	$-0.649561\pi$
$953$	16.0928	−	34.5112i	0.521298	−	1.11793i	0.974059	−	0.226295i	$-0.0726615\pi$
$954$	−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	−0.0240249	−	0.999711i	$-0.507648\pi$
$967$	3.91548	−	0.342560i	0.125913	−	0.0110160i	0.149938	+	0.988695i	$0.452093\pi$
$968$	−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	−0.892532	−	0.450984i	$-0.851073\pi$
$971$	−9.14300	+	10.8962i	−0.293413	+	0.349676i	0.599119	+	0.800660i	$0.295518\pi$
$972$	−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	−0.502569	−	0.864537i	$-0.667612\pi$
$977$	−15.8016	+	4.23403i	−0.505538	+	0.135459i	−0.00296924	+	0.999996i	$0.500945\pi$
$978$	−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	0.588518	−	0.808484i	$-0.299711\pi$
$983$	−11.6787	−	16.6789i	−0.372493	−	0.531975i	−0.961011	+	0.276509i	$0.910823\pi$
$984$	−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	0.569621	−	0.821907i	$-0.307090\pi$
$991$	48.2996	−	17.5796i	1.53429	−	0.558435i	0.964667	+	0.263472i	$0.0848677\pi$
$992$	−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	−0.999764	−	0.0217161i	$-0.993087\pi$
$997$	−0.360517	+	4.12073i	−0.0114177	+	0.130505i	0.988346	+	0.152221i	$0.0486426\pi$
$998$	−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.263.23	yes	480
3.2	odd	2	inner	570.2.bi.a.263.9	✓	480
5.2	odd	4	inner	570.2.bi.a.377.13	yes	480
15.2	even	4	inner	570.2.bi.a.377.23	yes	480
19.6	even	9	inner	570.2.bi.a.443.23	yes	480
57.44	odd	18	inner	570.2.bi.a.443.13	yes	480
95.82	odd	36	inner	570.2.bi.a.557.9	yes	480
285.272	even	36	inner	570.2.bi.a.557.23	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bi.a.263.9	✓	480	3.2	odd	2	inner
570.2.bi.a.263.23	yes	480	1.1	even	1	trivial
570.2.bi.a.377.13	yes	480	5.2	odd	4	inner
570.2.bi.a.377.23	yes	480	15.2	even	4	inner
570.2.bi.a.443.13	yes	480	57.44	odd	18	inner
570.2.bi.a.443.23	yes	480	19.6	even	9	inner
570.2.bi.a.557.9	yes	480	95.82	odd	36	inner
570.2.bi.a.557.23	yes	480	285.272	even	36	inner

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

Related objects

Downloads

Learn more