LMFDB - Embedded newform 300.2.n.a.11.14

Newspace parameters

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.n (of order $10$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$56$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			11.14
Character	$\chi$	$=$	300.11
Dual form			300.2.n.a.191.14

$q$-expansion

$f(q)$	$=$	$q+(-1.01770 + 0.981981i) q^{2} +(-1.62298 - 0.604914i) q^{3} +(0.0714277 - 1.99872i) q^{4} +(-0.345709 + 2.20918i) q^{5} +(2.24573 - 0.978119i) q^{6} +0.309856i q^{7} +(1.89002 + 2.10424i) q^{8} +(2.26816 + 1.96353i) q^{9} +O(q^{10})$	\(q+(-1.01770 + 0.981981i) q^{2} +(-1.62298 - 0.604914i) q^{3} +(0.0714277 - 1.99872i) q^{4} +(-0.345709 + 2.20918i) q^{5} +(2.24573 - 0.978119i) q^{6} +0.309856i q^{7} +(1.89002 + 2.10424i) q^{8} +(2.26816 + 1.96353i) q^{9} +(-1.81755 - 2.58776i) q^{10} +(1.53656 - 1.11637i) q^{11} +(-1.32498 + 3.20069i) q^{12} +(-3.79520 - 2.75737i) q^{13} +(-0.304272 - 0.315340i) q^{14} +(1.89744 - 3.37634i) q^{15} +(-3.98980 - 0.285528i) q^{16} +(-4.30413 + 1.39850i) q^{17} +(-4.23646 + 0.229003i) q^{18} +(-5.24788 + 1.70514i) q^{19} +(4.39085 + 0.848774i) q^{20} +(0.187436 - 0.502891i) q^{21} +(-0.467497 + 2.64500i) q^{22} +(-5.20321 + 3.78035i) q^{23} +(-1.79458 - 4.55845i) q^{24} +(-4.76097 - 1.52747i) q^{25} +(6.57006 - 0.920633i) q^{26} +(-2.49342 - 4.55882i) q^{27} +(0.619316 + 0.0221323i) q^{28} +(-6.49757 - 2.11119i) q^{29} +(1.38448 + 5.29936i) q^{30} +(5.73466 - 1.86330i) q^{31} +(4.34080 - 3.62732i) q^{32} +(-3.16912 + 0.882374i) q^{33} +(3.00702 - 5.64982i) q^{34} +(-0.684528 - 0.107120i) q^{35} +(4.08657 - 4.39317i) q^{36} +(3.24583 + 2.35823i) q^{37} +(3.66636 - 6.88864i) q^{38} +(4.49158 + 6.77094i) q^{39} +(-5.30205 + 3.44793i) q^{40} +(-0.902077 + 1.24160i) q^{41} +(0.303076 + 0.695851i) q^{42} -3.75970i q^{43} +(-2.12157 - 3.15090i) q^{44} +(-5.12192 + 4.33197i) q^{45} +(1.58307 - 8.95671i) q^{46} +(-2.19448 + 6.75392i) q^{47} +(6.30266 + 2.87689i) q^{48} +6.90399 q^{49} +(6.34519 - 3.12068i) q^{50} +(7.83151 + 0.333888i) q^{51} +(-5.78231 + 7.38860i) q^{52} +(0.721525 + 0.234438i) q^{53} +(7.01423 + 2.19102i) q^{54} +(1.93507 + 3.78048i) q^{55} +(-0.652012 + 0.585633i) q^{56} +(9.54870 + 0.407098i) q^{57} +(8.68572 - 4.23193i) q^{58} +(-11.0576 - 8.03382i) q^{59} +(-6.61285 - 4.03363i) q^{60} +(-7.66779 + 5.57097i) q^{61} +(-4.00643 + 7.52761i) q^{62} +(-0.608411 + 0.702802i) q^{63} +(-0.855674 + 7.95411i) q^{64} +(7.40358 - 7.43104i) q^{65} +(2.35874 - 4.01001i) q^{66} +(6.37132 - 2.07017i) q^{67} +(2.48778 + 8.70266i) q^{68} +(10.7315 - 2.98796i) q^{69} +(0.801834 - 0.563177i) q^{70} +(-0.750346 + 2.30933i) q^{71} +(0.155113 + 8.48386i) q^{72} +(-7.60274 + 5.52372i) q^{73} +(-5.61902 + 0.787367i) q^{74} +(6.80300 + 5.35903i) q^{75} +(3.03326 + 10.6109i) q^{76} +(0.345915 + 0.476111i) q^{77} +(-11.2200 - 2.48015i) q^{78} +(-1.81171 - 0.588659i) q^{79} +(2.01009 - 8.71548i) q^{80} +(1.28909 + 8.90720i) q^{81} +(-0.301186 - 2.14940i) q^{82} +(0.792743 + 2.43981i) q^{83} +(-0.991753 - 0.410553i) q^{84} +(-1.60156 - 9.99208i) q^{85} +(3.69195 + 3.82625i) q^{86} +(9.26837 + 7.35689i) q^{87} +(5.25324 + 1.12332i) q^{88} +(5.28769 + 7.27788i) q^{89} +(0.958673 - 9.43827i) q^{90} +(0.854388 - 1.17596i) q^{91} +(7.18422 + 10.6698i) q^{92} +(-10.4344 - 0.444859i) q^{93} +(-4.39890 - 9.02841i) q^{94} +(-1.95272 - 12.1830i) q^{95} +(-9.23927 + 3.26128i) q^{96} +(3.88035 - 11.9425i) q^{97} +(-7.02619 + 6.77958i) q^{98} +(5.67719 + 0.484963i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224q - 6q^{4} + q^{6} - 6q^{9} + O(q^{10}) $	$ 224q - 6q^{4} + q^{6} - 6q^{9} - 8q^{10} - 9q^{12} - 12q^{13} - 18q^{16} - 26q^{18} + 12q^{21} - 6q^{22} - 16q^{24} - 12q^{25} + 2q^{28} - 13q^{30} + 6q^{33} - 30q^{34} + 35q^{36} + 12q^{37} - 24q^{40} - 13q^{42} - 6q^{45} - 18q^{46} - 34q^{48} - 168q^{49} - 28q^{52} - 38q^{54} - 44q^{57} - 34q^{58} - 76q^{60} + 4q^{61} + 18q^{64} - 46q^{66} - 18q^{69} + 72q^{70} - 29q^{72} - 20q^{73} + 16q^{76} + 5q^{78} - 30q^{81} - 20q^{82} - 18q^{84} - 76q^{85} + 6q^{88} + 2q^{90} - 52q^{93} + 96q^{94} - 50q^{96} - 72q^{97} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.01770	+	0.981981i	−0.719623	+	0.694365i
$2$	−1.01770	+	0.981981i	−0.719623	+	0.694365i
$3$	−1.62298	−	0.604914i	−0.937031	−	0.349247i
$3$	−1.62298	−	0.604914i	−0.937031	−	0.349247i
$4$	0.0714277	−	1.99872i	0.0357138	−	0.999362i
$5$	−0.345709	+	2.20918i	−0.154606	+	0.987976i
$5$	−0.345709	+	2.20918i	−0.154606	+	0.987976i
$6$	2.24573	−	0.978119i	0.916814	−	0.399315i
$7$			0.309856i			0.117114i	0.998284	+	0.0585572i	$0.0186500\pi$
$7$			0.309856i			0.117114i	−0.998284	+	0.0585572i	$0.981350\pi$
$8$	1.89002	+	2.10424i	0.668222	+	0.743962i
$9$	2.26816	+	1.96353i	0.756053	+	0.654510i
$10$	−1.81755	−	2.58776i	−0.574758	−	0.818323i
$11$	1.53656	−	1.11637i	0.463290	−	0.336600i	−0.331531	−	0.943444i	$-0.607565\pi$
$11$	1.53656	−	1.11637i	0.463290	−	0.336600i	0.794820	+	0.606845i	$0.207565\pi$
$12$	−1.32498	+	3.20069i	−0.382489	+	0.923960i
$13$	−3.79520	−	2.75737i	−1.05260	−	0.764758i	−0.0798941	−	0.996803i	$-0.525458\pi$
$13$	−3.79520	−	2.75737i	−1.05260	−	0.764758i	−0.972705	+	0.232045i	$0.925458\pi$
$14$	−0.304272	−	0.315340i	−0.0813202	−	0.0842783i
$15$	1.89744	−	3.37634i	0.489918	−	0.871768i
$16$	−3.98980	−	0.285528i	−0.997449	−	0.0713821i
$17$	−4.30413	+	1.39850i	−1.04391	+	0.339185i	−0.780274	−	0.625438i	$-0.784920\pi$
$17$	−4.30413	+	1.39850i	−1.04391	+	0.339185i	−0.263631	+	0.964623i	$0.584920\pi$
$18$	−4.23646	+	0.229003i	−0.998542	+	0.0539765i
$19$	−5.24788	+	1.70514i	−1.20395	+	0.391186i	−0.841212	−	0.540706i	$-0.818157\pi$
$19$	−5.24788	+	1.70514i	−1.20395	+	0.391186i	−0.362735	+	0.931892i	$0.618157\pi$
$20$	4.39085	+	0.848774i	0.981824	+	0.189792i
$21$	0.187436	−	0.502891i	0.0409019	−	0.109740i
$22$	−0.467497	+	2.64500i	−0.0996707	+	0.563917i
$23$	−5.20321	+	3.78035i	−1.08494	+	0.788257i	−0.978538	−	0.206065i	$-0.933934\pi$
$23$	−5.20321	+	3.78035i	−1.08494	+	0.788257i	−0.106405	+	0.994323i	$0.533934\pi$
$24$	−1.79458	−	4.55845i	−0.366318	−	0.930490i
$25$	−4.76097	−	1.52747i	−0.952194	−	0.305494i
$26$	6.57006	−	0.920633i	1.28850	−	0.180551i
$27$	−2.49342	−	4.55882i	−0.479859	−	0.877345i
$28$	0.619316	+	0.0221323i	0.117040	+	0.00418261i
$29$	−6.49757	−	2.11119i	−1.20657	−	0.392038i	−0.364395	−	0.931245i	$-0.618724\pi$
$29$	−6.49757	−	2.11119i	−1.20657	−	0.392038i	−0.842173	+	0.539207i	$0.818724\pi$
$30$	1.38448	+	5.29936i	0.252769	+	0.967527i
$31$	5.73466	−	1.86330i	1.02997	−	0.334659i	0.255195	−	0.966890i	$-0.417860\pi$
$31$	5.73466	−	1.86330i	1.02997	−	0.334659i	0.774780	+	0.632231i	$0.217860\pi$
$32$	4.34080	−	3.62732i	0.767352	−	0.641226i
$33$	−3.16912	+	0.882374i	−0.551673	+	0.153602i
$34$	3.00702	−	5.64982i	0.515699	−	0.968937i
$35$	−0.684528	−	0.107120i	−0.115706	−	0.0181066i
$36$	4.08657	−	4.39317i	0.681094	−	0.732196i
$37$	3.24583	+	2.35823i	0.533611	+	0.387691i	0.821707	−	0.569911i	$-0.193022\pi$
$37$	3.24583	+	2.35823i	0.533611	+	0.387691i	−0.288096	+	0.957602i	$0.593022\pi$
$38$	3.66636	−	6.88864i	0.594762	−	1.11749i
$39$	4.49158	+	6.77094i	0.719228	+	1.08422i
$40$	−5.30205	+	3.44793i	−0.838328	+	0.545166i
$41$	−0.902077	+	1.24160i	−0.140881	+	0.193906i	−0.873627	−	0.486596i	$-0.838238\pi$
$41$	−0.902077	+	1.24160i	−0.140881	+	0.193906i	0.732746	+	0.680502i	$0.238238\pi$
$42$	0.303076	+	0.695851i	0.0467656	+	0.107372i
$43$		−	3.75970i		−	0.573349i	−0.958028	−	0.286674i	$-0.907450\pi$
$43$		−	3.75970i		−	0.573349i	0.958028	−	0.286674i	$-0.0925498\pi$
$44$	−2.12157	−	3.15090i	−0.319839	−	0.475015i
$45$	−5.12192	+	4.33197i	−0.763531	+	0.645771i
$46$	1.58307	−	8.95671i	0.233411	−	1.32059i
$47$	−2.19448	+	6.75392i	−0.320098	+	0.985161i	0.653507	+	0.756921i	$0.273297\pi$
$47$	−2.19448	+	6.75392i	−0.320098	+	0.985161i	−0.973605	+	0.228240i	$0.926703\pi$
$48$	6.30266	+	2.87689i	0.909710	+	0.415243i
$49$	6.90399			0.986284
$50$	6.34519	−	3.12068i	0.897345	−	0.441330i
$51$	7.83151	+	0.333888i	1.09663	+	0.0467536i
$52$	−5.78231	+	7.38860i	−0.801862	+	1.02462i
$53$	0.721525	+	0.234438i	0.0991091	+	0.0322025i	0.358152	−	0.933663i	$-0.383407\pi$
$53$	0.721525	+	0.234438i	0.0991091	+	0.0322025i	−0.259043	+	0.965866i	$0.583407\pi$
$54$	7.01423	+	2.19102i	0.954516	+	0.298160i
$55$	1.93507	+	3.78048i	0.260925	+	0.509759i
$56$	−0.652012	+	0.585633i	−0.0871287	+	0.0782585i
$57$	9.54870	+	0.407098i	1.26476	+	0.0539215i
$58$	8.68572	−	4.23193i	1.14049	−	0.555680i
$59$	−11.0576	−	8.03382i	−1.43958	−	1.04591i	−0.988131	−	0.153617i	$-0.950908\pi$
$59$	−11.0576	−	8.03382i	−1.43958	−	1.04591i	−0.451447	−	0.892298i	$-0.649092\pi$
$60$	−6.61285	−	4.03363i	−0.853715	−	0.520740i
$61$	−7.66779	+	5.57097i	−0.981760	+	0.713290i	−0.958101	−	0.286430i	$-0.907531\pi$
$61$	−7.66779	+	5.57097i	−0.981760	+	0.713290i	−0.0236585	+	0.999720i	$0.507531\pi$
$62$	−4.00643	+	7.52761i	−0.508818	+	0.956007i
$63$	−0.608411	+	0.702802i	−0.0766526	+	0.0885448i
$64$	−0.855674	+	7.95411i	−0.106959	+	0.994263i
$65$	7.40358	−	7.43104i	0.918301	−	0.921707i
$66$	2.35874	−	4.01001i	0.290341	−	0.493598i
$67$	6.37132	−	2.07017i	0.778380	−	0.252911i	0.107232	−	0.994234i	$-0.465801\pi$
$67$	6.37132	−	2.07017i	0.778380	−	0.252911i	0.671149	+	0.741323i	$0.265801\pi$
$68$	2.48778	+	8.70266i	0.301687	+	1.05535i
$69$	10.7315	−	2.98796i	1.29192	−	0.359708i
$70$	0.801834	−	0.563177i	0.0958375	−	0.0673125i
$71$	−0.750346	+	2.30933i	−0.0890497	+	0.274067i	−0.985657	−	0.168759i	$-0.946024\pi$
$71$	−0.750346	+	2.30933i	−0.0890497	+	0.274067i	0.896608	+	0.442826i	$0.146024\pi$
$72$	0.155113	+	8.48386i	0.0182803	+	0.999833i
$73$	−7.60274	+	5.52372i	−0.889834	+	0.646502i	−0.935835	−	0.352439i	$-0.885352\pi$
$73$	−7.60274	+	5.52372i	−0.889834	+	0.646502i	0.0460010	+	0.998941i	$0.485352\pi$
$74$	−5.61902	+	0.787367i	−0.653198	+	0.0915296i
$75$	6.80300	+	5.35903i	0.785542	+	0.618808i
$76$	3.03326	+	10.6109i	0.347939	+	1.21715i
$77$	0.345915	+	0.476111i	0.0394207	+	0.0542579i
$78$	−11.2200	−	2.48015i	−1.27042	−	0.280821i
$79$	−1.81171	−	0.588659i	−0.203833	−	0.0662293i	0.205321	−	0.978695i	$-0.434176\pi$
$79$	−1.81171	−	0.588659i	−0.203833	−	0.0662293i	−0.409154	+	0.912465i	$0.634176\pi$
$80$	2.01009	−	8.71548i	0.224735	−	0.974420i
$81$	1.28909	+	8.90720i	0.143233	+	0.989689i
$82$	−0.301186	−	2.14940i	−0.0332604	−	0.237362i
$83$	0.792743	+	2.43981i	0.0870149	+	0.267804i	0.985091	−	0.172037i	$-0.0550348\pi$
$83$	0.792743	+	2.43981i	0.0870149	+	0.267804i	−0.898076	+	0.439841i	$0.855035\pi$
$84$	−0.991753	−	0.410553i	−0.108209	−	0.0447950i
$85$	−1.60156	−	9.99208i	−0.173713	−	1.08379i
$86$	3.69195	+	3.82625i	0.398114	+	0.412595i
$87$	9.26837	+	7.35689i	0.993673	+	0.788741i
$88$	5.25324	+	1.12332i	0.559998	+	0.119747i
$89$	5.28769	+	7.27788i	0.560494	+	0.771454i	0.991389	−	0.130948i	$-0.0418021\pi$
$89$	5.28769	+	7.27788i	0.560494	+	0.771454i	−0.430895	+	0.902402i	$0.641802\pi$
$90$	0.958673	−	9.43827i	0.101053	−	0.994881i
$91$	0.854388	−	1.17596i	0.0895642	−	0.123275i
$92$	7.18422	+	10.6698i	0.749007	+	1.11240i
$93$	−10.4344	−	0.444859i	−1.08200	−	0.0461297i
$94$	−4.39890	−	9.02841i	−0.453711	−	0.931209i
$95$	−1.95272	−	12.1830i	−0.200345	−	1.24995i
$96$	−9.23927	+	3.26128i	−0.942979	+	0.332853i
$97$	3.88035	−	11.9425i	0.393990	−	1.21258i	−0.535755	−	0.844374i	$-0.679973\pi$
$97$	3.88035	−	11.9425i	0.393990	−	1.21258i	0.929745	−	0.368204i	$-0.120027\pi$
$98$	−7.02619	+	6.77958i	−0.709753	+	0.684841i
$99$	5.67719	+	0.484963i	0.570579	+	0.0487406i
$100$	−3.39305	+	9.40676i	−0.339305	+	0.940676i
$101$			8.75109i			0.870766i	0.900245	+	0.435383i	$0.143387\pi$
$101$			8.75109i			0.870766i	−0.900245	+	0.435383i	$0.856613\pi$
$102$	−8.29800	+	7.35059i	−0.821625	+	0.727817i
$103$	−4.44126	−	1.44305i	−0.437610	−	0.142188i	0.0819226	−	0.996639i	$-0.473894\pi$
$103$	−4.44126	−	1.44305i	−0.437610	−	0.142188i	−0.519533	+	0.854451i	$0.673894\pi$
$104$	−1.37081	−	13.1975i	−0.134419	−	1.29412i
$105$	1.04618	+	0.587934i	0.102097	+	0.0573765i
$106$	−0.964509	+	0.469936i	−0.0936814	+	0.0456442i
$107$	0.307528			0.0297299			0.0148649	−	0.999890i	$-0.495268\pi$
$107$	0.307528			0.0297299			0.0148649	+	0.999890i	$0.495268\pi$
$108$	−9.28992	+	4.65804i	−0.893923	+	0.448220i
$109$	7.14020	+	5.18766i	0.683908	+	0.496888i	0.874652	−	0.484752i	$-0.161090\pi$
$109$	7.14020	+	5.18766i	0.683908	+	0.496888i	−0.190744	+	0.981640i	$0.561090\pi$
$110$	−5.68168	−	1.94719i	−0.541727	−	0.185657i
$111$	−3.84140	−	5.79082i	−0.364610	−	0.549640i
$112$	0.0884726	−	1.23626i	0.00835988	−	0.116816i
$113$	5.33456	−	7.34239i	0.501833	−	0.690714i	−0.480682	−	0.876895i	$-0.659611\pi$
$113$	5.33456	−	7.34239i	0.501833	−	0.690714i	0.982516	+	0.186181i	$0.0596109\pi$
$114$	−10.1175	+	8.96233i	−0.947588	+	0.839399i
$115$	−6.55269	−	12.8017i	−0.611041	−	1.19377i
$116$	−4.68379	+	12.8360i	−0.434879	+	1.19180i
$117$	−3.19393	−	13.7062i	−0.295279	−	1.26713i
$118$	19.1424	−	2.68233i	1.76220	−	0.246929i
$119$	−0.433332	−	1.33366i	−0.0397235	−	0.122256i
$120$	10.6909	−	2.38866i	0.975937	−	0.218054i
$121$	−2.28447	+	7.03087i	−0.207679	+	0.639170i
$122$	2.33292	−	13.1992i	0.211213	−	1.19500i
$123$	2.21512	−	1.46942i	0.199731	−	0.132493i
$124$	−3.31462	−	11.5951i	−0.297661	−	1.04127i
$125$	5.02037	−	9.98979i	0.449035	−	0.893514i
$126$	−0.0709579	−	1.31269i	−0.00632143	−	0.116944i
$127$	8.06366	+	11.0987i	0.715534	+	0.984848i	0.999660	+	0.0260609i	$0.00829639\pi$
$127$	8.06366	+	11.0987i	0.715534	+	0.984848i	−0.284127	+	0.958787i	$0.591704\pi$
$128$	−6.93996	−	8.93515i	−0.613412	−	0.789763i
$129$	−2.27429	+	6.10194i	−0.200240	+	0.537246i
$130$	−0.237486	+	14.8327i	−0.0208289	+	1.30092i
$131$	−0.458670	−	1.41164i	−0.0400742	−	0.123336i	0.929018	−	0.370035i	$-0.120654\pi$
$131$	−0.458670	−	1.41164i	−0.0400742	−	0.123336i	−0.969092	+	0.246699i	$0.920654\pi$
$132$	1.53726	+	6.39722i	0.133801	+	0.556807i
$133$	−0.528348	−	1.62609i	−0.0458136	−	0.141000i
$134$	−4.45123	+	8.36332i	−0.384528	+	0.722481i
$135$	10.9333	−	3.93240i	0.940986	−	0.338447i
$136$	−11.0777	−	6.41375i	−0.949901	−	0.549975i
$137$	10.6892	−	14.7124i	0.913236	−	1.25696i	−0.0528136	−	0.998604i	$-0.516819\pi$
$137$	10.6892	−	14.7124i	0.913236	−	1.25696i	0.966050	−	0.258357i	$-0.0831811\pi$
$138$	−7.98734	+	13.5790i	−0.679927	+	1.15592i
$139$	−6.52821	−	8.98531i	−0.553715	−	0.762124i	0.436795	−	0.899561i	$-0.356113\pi$
$139$	−6.52821	−	8.98531i	−0.553715	−	0.762124i	−0.990510	+	0.137437i	$0.956113\pi$
$140$	−0.262998	+	1.36053i	−0.0222274	+	0.114986i
$141$	7.64715	−	9.63404i	0.644006	−	0.811332i
$142$	−1.50409	−	3.08703i	−0.126220	−	0.259058i
$143$	−8.90981			−0.745075
$144$	−8.48885	−	8.48171i	−0.707404	−	0.706809i
$145$	6.91027	−	13.6245i	0.573866	−	1.13145i
$146$	2.31313	−	13.0872i	0.191436	−	1.08311i
$147$	−11.2051	−	4.17632i	−0.924179	−	0.344457i
$148$	4.94530	−	6.31907i	0.406501	−	0.519425i
$149$		−	10.3539i		−	0.848222i	−0.905610	−	0.424111i	$-0.860587\pi$
$149$		−	10.3539i		−	0.848222i	0.905610	−	0.424111i	$-0.139413\pi$
$150$	−12.1859	+	1.22652i	−0.994973	+	0.100145i
$151$			19.3082i			1.57128i	0.618685	+	0.785639i	$0.287666\pi$
$151$			19.3082i			1.57128i	−0.618685	+	0.785639i	$0.712334\pi$
$152$	−13.5066	−	7.82007i	−1.09553	−	0.634292i
$153$	−12.5084	−	5.27928i	−1.01125	−	0.426805i
$154$	−0.819570	−	0.144857i	−0.0660428	−	0.0116729i
$155$	2.13385	+	13.3131i	0.171395	+	1.06933i
$156$	13.8541	−	8.49379i	1.10921	−	0.680048i
$157$	5.03933			0.402182			0.201091	−	0.979573i	$-0.435551\pi$
$157$	5.03933			0.402182			0.201091	+	0.979573i	$0.435551\pi$
$158$	2.42182	−	1.17998i	0.192670	−	0.0938743i
$159$	−1.02921	−	0.816949i	−0.0816216	−	0.0647883i
$160$	6.51276	+	10.8436i	0.514879	+	0.857263i
$161$	−1.17136	−	1.61224i	−0.0923164	−	0.127063i
$162$	−10.0586	−	7.79900i	−0.790279	−	0.612747i
$163$	−6.18477	+	8.51261i	−0.484429	+	0.666759i	−0.979348	−	0.202180i	$-0.935197\pi$
$163$	−6.18477	+	8.51261i	−0.484429	+	0.666759i	0.494920	+	0.868939i	$0.335197\pi$
$164$	2.41719	+	1.89169i	0.188751	+	0.147716i
$165$	−0.853732	−	7.30621i	−0.0664629	−	0.568788i
$166$	−3.20262	−	1.70454i	−0.248572	−	0.132298i
$167$	−1.55001	−	4.77044i	−0.119943	−	0.369148i	0.873003	−	0.487716i	$-0.162170\pi$
$167$	−1.55001	−	4.77044i	−0.119943	−	0.369148i	−0.992946	+	0.118568i	$0.962170\pi$
$168$	1.41246	−	0.556062i	0.108974	−	0.0429011i
$169$	2.78321	+	8.56584i	0.214093	+	0.658911i
$170$	11.4419	+	8.59625i	0.877557	+	0.659302i
$171$	−15.2511	−	6.43685i	−1.16628	−	0.492238i
$172$	−7.51460	−	0.268547i	−0.572983	−	0.0204765i
$173$	7.28298	+	10.0242i	0.553715	+	0.762123i	0.990510	−	0.137438i	$-0.0438868\pi$
$173$	7.28298	+	10.0242i	0.553715	+	0.762123i	−0.436796	+	0.899561i	$0.643887\pi$
$174$	−16.6567	+	1.61425i	−1.26274	+	0.122376i
$175$	0.473295	−	1.47521i	0.0357778	−	0.111516i
$176$	−6.44931	+	4.01538i	−0.486135	+	0.302670i
$177$	13.0866	+	19.7277i	0.983646	+	1.48282i
$178$	−12.5280	−	2.21429i	−0.939015	−	0.165968i
$179$	−6.67793	+	20.5526i	−0.499132	+	1.53617i	0.311285	+	0.950317i	$0.399241\pi$
$179$	−6.67793	+	20.5526i	−0.499132	+	1.53617i	−0.810417	+	0.585854i	$0.800759\pi$
$180$	8.29256	+	10.5467i	0.618091	+	0.786107i
$181$	6.78493	+	20.8819i	0.504320	+	1.55214i	0.801911	+	0.597443i	$0.203817\pi$
$181$	6.78493	+	20.8819i	0.504320	+	1.55214i	−0.297592	+	0.954693i	$0.596183\pi$
$182$	0.285263	+	2.03577i	0.0211451	+	0.150902i
$183$	15.8147	−	4.40326i	1.16905	−	0.325498i
$184$	−17.7889	−	3.80388i	−1.31142	−	0.280426i
$185$	−6.33188	+	6.35536i	−0.465529	+	0.467256i
$186$	11.0559	−	9.79365i	0.810660	−	0.718105i
$187$	−5.05230	+	6.95389i	−0.369461	+	0.508519i
$188$	13.3425	+	4.86858i	0.973100	+	0.355078i
$189$	1.41258	−	0.772601i	0.102750	−	0.0561985i
$190$	13.9508	+	10.4811i	1.01210	+	0.760380i
$191$	4.26831	+	3.10111i	0.308844	+	0.224389i	0.731400	−	0.681948i	$-0.238867\pi$
$191$	4.26831	+	3.10111i	0.308844	+	0.224389i	−0.422556	+	0.906337i	$0.638867\pi$
$192$	6.20029	−	12.3918i	0.447468	−	0.894300i
$193$	2.61953			0.188558			0.0942788	−	0.995546i	$-0.469945\pi$
$193$	2.61953			0.188558			0.0942788	+	0.995546i	$0.469945\pi$
$194$	7.77827	+	15.9643i	0.558447	+	1.14617i
$195$	−16.5110	+	7.58194i	−1.18238	+	0.542954i
$196$	0.493136	−	13.7992i	0.0352240	−	0.985655i
$197$	−21.8387	−	7.09582i	−1.55594	−	0.505556i	−0.600222	−	0.799834i	$-0.704921\pi$
$197$	−21.8387	−	7.09582i	−1.55594	−	0.505556i	−0.955720	+	0.294277i	$0.904921\pi$
$198$	−6.25391	+	5.08135i	−0.444446	+	0.361116i
$199$		−	6.62396i		−	0.469560i	−0.972049	−	0.234780i	$-0.924563\pi$
$199$		−	6.62396i		−	0.469560i	0.972049	−	0.234780i	$-0.0754370\pi$
$200$	−5.78415	−	12.9052i	−0.409001	−	0.912534i
$201$	−11.5928	−	0.494247i	−0.817695	−	0.0348615i
$202$	−8.59340	−	8.90599i	−0.604630	−	0.626623i
$203$	0.654164	−	2.01331i	0.0459133	−	0.141307i
$204$	1.22674	−	15.6292i	0.0858887	−	1.09426i
$205$	−2.43107	−	2.42209i	−0.169793	−	0.169166i
$206$	5.93692	−	2.89264i	0.413645	−	0.201539i
$207$	−19.2245	−	1.64222i	−1.33620	−	0.114142i
$208$	14.3548	+	12.0850i	0.995324	+	0.837944i
$209$	−6.16010	+	8.47865i	−0.426103	+	0.586480i
$210$	−1.64204	+	0.428988i	−0.113311	+	0.0296030i
$211$	−9.71127	−	13.3664i	−0.668551	−	0.920182i	0.331175	−	0.943569i	$-0.392555\pi$
$211$	−9.71127	−	13.3664i	−0.668551	−	0.920182i	−0.999726	+	0.0233873i	$0.992555\pi$
$212$	0.520113	−	1.42538i	0.0357215	−	0.0978958i
$213$	2.61474	−	3.29411i	0.179159	−	0.225709i
$214$	−0.312971	+	0.301987i	−0.0213943	+	0.0206434i
$215$	8.30586	+	1.29976i	0.566455	+	0.0886431i
$216$	4.88026	−	13.8630i	0.332059	−	0.943258i
$217$	0.577355	+	1.77692i	0.0391934	+	0.120625i
$218$	−12.3608	+	1.73206i	−0.837177	+	0.117310i
$219$	15.6805	−	4.36590i	1.05959	−	0.295020i
$220$	7.69435	−	3.59765i	0.518753	−	0.242553i
$221$	20.1912	+	6.56052i	1.35821	+	0.441309i
$222$	9.59587	+	2.12114i	0.644033	+	0.142361i
$223$	12.0612	+	16.6009i	0.807679	+	1.11168i	0.991677	+	0.128749i	$0.0410960\pi$
$223$	12.0612	+	16.6009i	0.807679	+	1.11168i	−0.183998	+	0.982927i	$0.558904\pi$
$224$	1.12395	+	1.34502i	0.0750968	+	0.0898681i
$225$	−7.79941	−	12.8129i	−0.519960	−	0.854190i
$226$	1.78110	+	12.7108i	0.118477	+	0.845509i
$227$	9.87438	−	7.17416i	0.655386	−	0.476166i	−0.209716	−	0.977762i	$-0.567254\pi$
$227$	9.87438	−	7.17416i	0.655386	−	0.476166i	0.865102	+	0.501597i	$0.167254\pi$
$228$	1.49572	−	19.0561i	0.0990563	−	1.26202i
$229$	0.971101	−	2.98874i	0.0641721	−	0.197502i	−0.913830	−	0.406097i	$-0.866889\pi$
$229$	0.971101	−	2.98874i	0.0641721	−	0.197502i	0.978002	+	0.208596i	$0.0668893\pi$
$230$	19.2397	+	6.59371i	1.26863	+	0.434777i
$231$	−0.273409	−	0.981970i	−0.0179890	−	0.0646089i
$232$	−7.83806	−	17.6626i	−0.514594	−	1.15961i
$233$	8.86597	−	2.88073i	0.580829	−	0.188723i	−0.00384306	−	0.999993i	$-0.501223\pi$
$233$	8.86597	−	2.88073i	0.580829	−	0.188723i	0.584672	+	0.811270i	$0.301223\pi$
$234$	16.7096	+	10.8124i	1.09234	+	0.706828i
$235$	−14.1620	−	7.18290i	−0.923826	−	0.468561i
$236$	−16.8472	+	21.5273i	−1.09666	+	1.40131i
$237$	2.58428	+	2.05131i	0.167867	+	0.133247i
$238$	1.75063	+	0.931742i	0.113477	+	0.0603959i
$239$	18.5823	−	13.5009i	1.20199	−	0.873298i	0.207512	−	0.978232i	$-0.433463\pi$
$239$	18.5823	−	13.5009i	1.20199	−	0.873298i	0.994479	+	0.104935i	$0.0334634\pi$
$240$	−8.53446	+	12.9292i	−0.550897	+	0.834573i
$241$	−6.49962	−	4.72225i	−0.418677	−	0.304187i	0.358428	−	0.933557i	$-0.383313\pi$
$241$	−6.49962	−	4.72225i	−0.418677	−	0.304187i	−0.777105	+	0.629371i	$0.783313\pi$
$242$	−4.57928	−	9.39863i	−0.294367	−	0.604167i
$243$	3.29591	−	15.2360i	0.211433	−	0.977393i
$244$	10.5871	+	15.7237i	0.677773	+	1.00661i
$245$	−2.38677	+	15.2522i	−0.152485	+	0.974425i
$246$	−0.811382	+	3.67064i	−0.0517318	+	0.234031i
$247$	24.6185	+	7.99903i	1.56644	+	0.508966i
$248$	14.7594	+	8.54544i	0.937225	+	0.542636i
$249$	0.189265	−	4.43932i	0.0119942	−	0.281330i
$250$	4.70055	+	15.0965i	0.297289	+	0.954788i
$251$	−26.8547			−1.69505			−0.847527	−	0.530752i	$-0.821909\pi$
$251$	−26.8547			−1.69505			−0.847527	+	0.530752i	$0.821909\pi$
$252$	1.36125	+	1.26625i	0.0857507	+	0.0797660i
$253$	−3.77474	+	11.6175i	−0.237316	+	0.730383i
$254$	−19.1051	−	3.37676i	−1.19876	−	0.211877i
$255$	−3.44504	+	17.1858i	−0.215737	+	1.07622i
$256$	15.8369	+	2.27840i	0.989809	+	0.142400i
$257$		−	3.87994i		−	0.242024i	−0.992651	−	0.121012i	$-0.961386\pi$
$257$		−	3.87994i		−	0.242024i	0.992651	−	0.121012i	$-0.0386140\pi$
$258$	−3.67744	−	8.44326i	−0.228947	−	0.525654i
$259$	−0.730712	+	1.00574i	−0.0454042	+	0.0624936i
$260$	−14.3238	−	15.3285i	−0.888323	−	0.950633i
$261$	−10.5921	−	17.5467i	−0.655637	−	1.08611i
$262$	1.85299	+	0.986223i	0.114478	+	0.0609290i
$263$	11.2726	+	8.19005i	0.695101	+	0.505020i	0.878333	−	0.478049i	$-0.158656\pi$
$263$	11.2726	+	8.19005i	0.695101	+	0.505020i	−0.183232	+	0.983070i	$0.558656\pi$
$264$	−7.84642	−	5.00090i	−0.482914	−	0.307784i
$265$	−0.767353	+	1.51293i	−0.0471381	+	0.0929387i
$266$	2.13449	+	1.13604i	0.130874	+	0.0696552i
$267$	−4.17935	−	15.0105i	−0.255772	−	0.918627i
$268$	−3.68260	−	12.8824i	−0.224951	−	0.786916i
$269$	−13.6533	+	4.43622i	−0.832456	+	0.270481i	−0.694079	−	0.719899i	$-0.744188\pi$
$269$	−13.6533	+	4.43622i	−0.832456	+	0.270481i	−0.138376	+	0.990380i	$0.544188\pi$
$270$	−7.26525	+	14.7383i	−0.442149	+	0.896942i
$271$	−1.44312	−	0.468897i	−0.0876630	−	0.0284834i	0.264857	−	0.964288i	$-0.414675\pi$
$271$	−1.44312	−	0.468897i	−0.0876630	−	0.0284834i	−0.352520	+	0.935804i	$0.614675\pi$
$272$	17.5719	−	4.35077i	1.06545	−	0.263804i
$273$	−2.09802	+	1.39174i	−0.126978	+	0.0842321i
$274$	3.56890	+	25.4693i	0.215605	+	1.53866i
$275$	−9.02073	+	2.96798i	−0.543971	+	0.178976i
$276$	−5.20558	−	21.6627i	−0.313339	−	1.30394i
$277$	10.4349	−	7.58142i	0.626974	−	0.455523i	−0.228377	−	0.973573i	$-0.573342\pi$
$277$	10.4349	−	7.58142i	0.626974	−	0.455523i	0.855350	+	0.518050i	$0.173342\pi$
$278$	15.4672	+	2.73378i	0.927659	+	0.163961i
$279$	16.6658	+	7.03391i	0.997754	+	0.421109i
$280$	−1.06836	−	1.64287i	−0.0638469	−	0.0981803i
$281$	−24.2794	+	7.88884i	−1.44838	+	0.470609i	−0.924501	−	0.381181i	$-0.875518\pi$
$281$	−24.2794	+	7.88884i	−1.44838	+	0.470609i	−0.523884	+	0.851789i	$0.675518\pi$
$282$	1.67794	+	17.3139i	0.0999196	+	1.03103i
$283$	2.52345	−	0.819917i	0.150003	−	0.0487390i	−0.233053	−	0.972464i	$-0.574872\pi$
$283$	2.52345	−	0.819917i	0.150003	−	0.0487390i	0.383056	+	0.923725i	$0.374872\pi$
$284$	4.56211	+	1.66468i	0.270712	+	0.0987808i
$285$	−4.20043	+	20.9541i	−0.248812	+	1.24121i
$286$	9.06751	−	8.74926i	0.536173	−	0.517354i
$287$	−0.384718	−	0.279514i	−0.0227092	−	0.0164992i
$288$	16.9680	+	0.295954i	0.999848	+	0.0174392i
$289$	2.81646	−	2.04628i	0.165674	−	0.120369i
$290$	6.34637	+	20.6514i	0.372672	+	1.21269i
$291$	−13.5219	+	17.0352i	−0.792670	+	0.998622i
$292$	10.4973	+	15.5903i	0.614310	+	0.912355i
$293$			25.7575i			1.50477i	0.658726	+	0.752383i	$0.271096\pi$
$293$			25.7575i			1.50477i	−0.658726	+	0.752383i	$0.728904\pi$
$294$	15.5045	−	6.75292i	0.904239	−	0.393839i
$295$	21.5709	−	21.6509i	1.25591	−	1.26056i
$296$	1.17238	+	11.2871i	0.0681430	+	0.656050i
$297$	−8.92064	−	4.22130i	−0.517628	−	0.244945i
$298$	10.1673	+	10.5371i	0.588976	+	0.610400i
$299$	30.1710			1.74484
$300$	11.1972	−	13.2145i	0.646468	−	0.762941i
$301$	1.16497			0.0671475
$302$	−18.9603	−	19.6500i	−1.09104	−	1.13073i
$303$	5.29365	−	14.2029i	0.304112	−	0.815935i
$304$	21.4248	−	5.30474i	1.22880	−	0.304248i
$305$	−9.65647	−	18.8655i	−0.552928	−	1.08023i
$306$	17.9140	−	6.91033i	1.02408	−	0.395037i
$307$			12.4595i			0.711099i	0.934657	+	0.355550i	$0.115706\pi$
$307$			12.4595i			0.711099i	−0.934657	+	0.355550i	$0.884294\pi$
$308$	0.976323	−	0.657381i	0.0556312	−	0.0374578i
$309$	6.33517	+	5.02863i	0.360395	+	0.286069i
$310$	−15.2448	−	11.4533i	−0.865846	−	0.650504i
$311$	6.46908	−	4.70006i	0.366828	−	0.266516i	−0.389067	−	0.921210i	$-0.627202\pi$
$311$	6.46908	−	4.70006i	0.366828	−	0.266516i	0.755894	+	0.654694i	$0.227202\pi$
$312$	−5.75855	+	22.2486i	−0.326014	+	1.25958i
$313$	−18.1139	−	13.1605i	−1.02386	−	0.743875i	−0.0567864	−	0.998386i	$-0.518085\pi$
$313$	−18.1139	−	13.1605i	−1.02386	−	0.743875i	−0.967070	+	0.254511i	$0.918085\pi$
$314$	−5.12853	+	4.94852i	−0.289419	+	0.279261i
$315$	−1.34228	−	1.58706i	−0.0756292	−	0.0894205i
$316$	−1.30597	+	3.57905i	−0.0734667	+	0.201337i
$317$	−16.3147	+	5.30095i	−0.916323	+	0.297731i	−0.728957	−	0.684559i	$-0.759995\pi$
$317$	−16.3147	+	5.30095i	−0.916323	+	0.297731i	−0.187365	+	0.982290i	$0.559995\pi$
$318$	1.84965	−	0.179255i	0.103723	−	0.0100521i
$319$	−12.3408	+	4.00976i	−0.690950	+	0.224503i
$320$	−17.2763	−	4.64015i	−0.965772	−	0.259392i
$321$	−0.499113	−	0.186028i	−0.0278578	−	0.0103831i
$322$	2.77529	+	0.490524i	0.154661	+	0.0273358i
$323$	20.2029	−	14.6783i	1.12412	−	0.816722i
$324$	17.8951	−	1.94032i	0.994173	−	0.107796i
$325$	13.8570	+	18.9248i	0.768650	+	1.04976i
$326$	−2.06497	−	14.7366i	−0.114368	−	0.816185i
$327$	−8.45036	−	12.7387i	−0.467306	−	0.704452i
$328$	−4.31757	+	0.448460i	−0.238398	+	0.0247621i
$329$	−2.09274	−	0.679973i	−0.115377	−	0.0374881i
$330$	8.04340	+	6.59718i	0.442775	+	0.363163i
$331$	33.9964	−	11.0461i	1.86861	−	0.607149i	0.876566	−	0.481282i	$-0.159829\pi$
$331$	33.9964	−	11.0461i	1.86861	−	0.607149i	0.992047	−	0.125867i	$-0.0401713\pi$
$332$	4.93314	−	1.41020i	0.270741	−	0.0773950i
$333$	2.73159	+	11.7221i	0.149690	+	0.642369i
$334$	6.26192	+	3.33280i	0.342637	+	0.182363i
$335$	2.37075	+	14.7911i	0.129528	+	0.808123i
$336$	−0.891421	+	1.95292i	−0.0486310	+	0.106540i
$337$	−3.49101	−	2.53637i	−0.190167	−	0.138165i	0.488628	−	0.872492i	$-0.337498\pi$
$337$	−3.49101	−	2.53637i	−0.190167	−	0.138165i	−0.678795	+	0.734328i	$0.737498\pi$
$338$	−11.2440	−	5.98440i	−0.611591	−	0.325508i
$339$	−13.0994	+	8.68964i	−0.711463	+	0.471957i
$340$	−20.0858	+	2.48736i	−1.08931	+	0.134896i
$341$	6.73149	−	9.26510i	0.364531	−	0.501733i
$342$	21.8419	−	8.42553i	1.18108	−	0.455601i
$343$			4.30823i			0.232623i
$344$	7.91132	−	7.10590i	0.426550	−	0.383124i
$345$	2.89097	+	24.7408i	0.155645	+	1.33200i
$346$	−17.2554	−	3.04985i	−0.927657	−	0.163961i
$347$	4.70767	−	14.4887i	0.252721	−	0.777795i	−0.741549	−	0.670898i	$-0.765909\pi$
$347$	4.70767	−	14.4887i	0.252721	−	0.777795i	0.994270	−	0.106896i	$-0.0340913\pi$
$348$	15.3664	−	17.9994i	0.823726	−	0.964870i
$349$	6.71463			0.359426			0.179713	−	0.983719i	$-0.442483\pi$
$349$	6.71463			0.359426			0.179713	+	0.983719i	$0.442483\pi$
$350$	0.966959	+	1.96609i	0.0516862	+	0.105092i
$351$	−3.10734	+	24.1769i	−0.165858	+	1.29047i
$352$	2.62044	−	10.4195i	0.139670	−	0.555364i
$353$	−12.7469	−	4.14173i	−0.678451	−	0.220442i	−0.0505337	−	0.998722i	$-0.516092\pi$
$353$	−12.7469	−	4.14173i	−0.678451	−	0.220442i	−0.627917	+	0.778280i	$0.716092\pi$
$354$	−32.6904	−	7.22610i	−1.73747	−	0.384063i
$355$	−4.84232	−	2.45601i	−0.257004	−	0.130351i
$356$	14.9242	−	10.0488i	0.790979	−	0.532585i
$357$	−0.103457	+	2.42664i	−0.00547553	+	0.128431i
$358$	−13.3861	−	27.4739i	−0.707477	−	1.45204i
$359$	−19.8499	−	14.4218i	−1.04764	−	0.761153i	−0.0758753	−	0.997117i	$-0.524175\pi$
$359$	−19.8499	−	14.4218i	−1.04764	−	0.761153i	−0.971762	+	0.235965i	$0.924175\pi$
$360$	−18.7960	−	2.59028i	−0.990637	−	0.136520i
$361$	9.26145	−	6.72883i	0.487445	−	0.354149i
$362$	−27.4106	−	14.5888i	−1.44067	−	0.766770i
$363$	7.96073	−	10.0291i	0.417830	−	0.526391i
$364$	−2.28940	−	1.79168i	−0.119997	−	0.0939097i
$365$	−9.57455	−	18.7054i	−0.501155	−	0.979087i
$366$	−11.7707	+	20.0109i	−0.615263	+	1.04599i
$367$	−29.8410	+	9.69594i	−1.55769	+	0.506124i	−0.956190	−	0.292748i	$-0.905430\pi$
$367$	−29.8410	+	9.69594i	−1.55769	+	0.506124i	−0.601500	+	0.798872i	$0.705430\pi$
$368$	21.8391	−	13.5972i	1.13844	−	0.708801i
$369$	−4.48398	+	1.04490i	−0.233427	+	0.0543951i
$370$	0.203109	−	12.6856i	0.0105591	−	0.659495i
$371$	−0.0726419	+	0.223569i	−0.00377138	+	0.0116071i
$372$	−1.63446	+	20.8237i	−0.0847426	+	1.07966i
$373$	2.56104	−	1.86070i	0.132606	−	0.0963436i	−0.519505	−	0.854467i	$-0.673884\pi$
$373$	2.56104	−	1.86070i	0.132606	−	0.0963436i	0.652111	+	0.758124i	$0.273884\pi$
$374$	−1.68686	−	12.0382i	−0.0872256	−	0.622483i
$375$	−14.1909	+	13.1764i	−0.732817	+	0.680426i
$376$	−18.3595	+	8.14730i	−0.946819	+	0.420165i
$377$	18.8382	+	25.9286i	0.970218	+	1.33539i
$378$	−0.678901	+	2.17340i	−0.0349189	+	0.111788i
$379$	−16.6493	−	5.40969i	−0.855217	−	0.277877i	−0.151588	−	0.988444i	$-0.548439\pi$
$379$	−16.6493	−	5.40969i	−0.855217	−	0.277877i	−0.703630	+	0.710567i	$0.748439\pi$
$380$	−24.4900	+	3.03275i	−1.25631	+	0.155577i
$381$	−6.37346	−	22.8908i	−0.326522	−	1.17273i
$382$	−7.38910	+	1.03540i	−0.378059	+	0.0529757i
$383$	−6.59223	−	20.2888i	−0.336847	−	1.03671i	−0.965805	−	0.259270i	$-0.916518\pi$
$383$	−6.59223	−	20.2888i	−0.336847	−	1.03671i	0.628958	−	0.777439i	$-0.283482\pi$
$384$	5.85846	+	18.6997i	0.298963	+	0.954265i
$385$	−1.17140	+	0.599593i	−0.0597002	+	0.0305581i
$386$	−2.66589	+	2.57232i	−0.135690	+	0.130928i
$387$	7.38229	−	8.52760i	0.375263	−	0.433482i
$388$	−23.5926	−	8.60878i	−1.19773	−	0.437045i
$389$	−4.43623	−	6.10594i	−0.224926	−	0.309583i	0.681608	−	0.731718i	$-0.261281\pi$
$389$	−4.43623	−	6.10594i	−0.224926	−	0.309583i	−0.906533	+	0.422134i	$0.861281\pi$
$390$	9.35796	−	23.9297i	0.473859	−	1.21173i
$391$	17.1085	−	23.5478i	0.865213	−	1.19086i
$392$	13.0487	+	14.5277i	0.659057	+	0.733758i
$393$	−0.109506	+	2.56853i	−0.00552387	+	0.129565i
$394$	29.1932	−	14.2238i	1.47073	−	0.716582i
$395$	1.92678	−	3.79888i	0.0969467	−	0.191142i
$396$	1.37482	−	11.3125i	0.0690871	−	0.568475i
$397$	−8.37440	+	25.7738i	−0.420299	+	1.29355i	0.487125	+	0.873332i	$0.338046\pi$
$397$	−8.37440	+	25.7738i	−0.420299	+	1.29355i	−0.907424	+	0.420216i	$0.861954\pi$
$398$	6.50460	+	6.74121i	0.326046	+	0.337906i
$399$	−0.126142	+	2.95872i	−0.00631498	+	0.148121i
$400$	18.5592	+	7.45368i	0.927958	+	0.372684i
$401$			15.4298i			0.770526i	0.922807	+	0.385263i	$0.125889\pi$
$401$			15.4298i			0.770526i	−0.922807	+	0.385263i	$0.874111\pi$
$402$	12.2834	−	10.8809i	0.612638	−	0.542692i
$403$	−26.9020	−	8.74099i	−1.34008	−	0.435420i
$404$	17.4910	+	0.625070i	0.870211	+	0.0310984i
$405$	−20.1233	−	0.231460i	−0.999934	−	0.0115013i
$406$	1.31129	+	2.69132i	0.0650781	+	0.133568i
$407$	7.62007			0.377713
$408$	14.0991	+	17.1105i	0.698010	+	0.847094i
$409$	−23.6000	−	17.1464i	−1.16694	−	0.847834i	−0.176303	−	0.984336i	$-0.556414\pi$
$409$	−23.6000	−	17.1464i	−1.16694	−	0.847834i	−0.990640	+	0.136502i	$0.956414\pi$
$410$	4.85254	+	0.0776938i	0.239650	+	0.00383703i
$411$	−26.2480	+	17.4119i	−1.29472	+	0.858867i
$412$	−3.20149	+	8.77378i	−0.157726	+	0.432253i
$413$	2.48933	−	3.42626i	0.122492	−	0.168595i
$414$	21.1774	−	17.2068i	1.04081	−	0.845670i
$415$	−5.66405	+	0.907848i	−0.278037	+	0.0445645i
$416$	−26.4761	+	1.79720i	−1.29810	+	0.0881148i
$417$	5.15985	+	18.5320i	0.252679	+	0.907517i
$418$	−2.05674	−	14.6778i	−0.100598	−	0.717916i
$419$	8.89913	+	27.3887i	0.434751	+	1.33803i	0.893342	+	0.449378i	$0.148354\pi$
$419$	8.89913	+	27.3887i	0.434751	+	1.33803i	−0.458591	+	0.888648i	$0.651646\pi$
$420$	1.24984	−	2.04903i	0.0609862	−	0.0999824i
$421$	7.02569	−	21.6229i	0.342411	−	1.05383i	−0.620544	−	0.784172i	$-0.713088\pi$
$421$	7.02569	−	21.6229i	0.342411	−	1.05383i	0.962955	−	0.269662i	$-0.0869119\pi$
$422$	23.0087	+	4.06673i	1.12005	+	0.197965i
$423$	−18.2390	+	11.0100i	−0.886809	+	0.535326i
$424$	0.870380	+	1.96135i	0.0422694	+	0.0952518i
$425$	22.6280	−	0.0837748i	1.09762	−	0.00406367i
$426$	0.573726	+	5.92004i	0.0277971	+	0.286827i
$427$	−1.72620	−	2.37591i	−0.0835366	−	0.114978i
$428$	0.0219660	−	0.614664i	0.00106177	−	0.0297109i
$429$	14.4605	+	5.38966i	0.698159	+	0.260215i
$430$	−9.72922	+	6.83343i	−0.469185	+	0.329537i
$431$	4.98781	+	15.3509i	0.240255	+	0.739428i	0.996381	+	0.0850017i	$0.0270896\pi$
$431$	4.98781	+	15.3509i	0.240255	+	0.739428i	−0.756126	+	0.654426i	$0.772910\pi$
$432$	8.64657	+	18.9007i	0.416008	+	0.909361i
$433$	−3.93756	−	12.1186i	−0.189227	−	0.582380i	0.810769	−	0.585367i	$-0.199049\pi$
$433$	−3.93756	−	12.1186i	−0.189227	−	0.582380i	−0.999996	+	0.00298628i	$0.999049\pi$
$434$	−2.33247	−	1.24142i	−0.111962	−	0.0595899i
$435$	−19.4569	+	17.9322i	−0.932886	+	0.859781i
$436$	10.8787	−	13.9008i	0.520996	−	0.665725i
$437$	20.8598	−	28.7110i	0.997859	−	1.37343i
$438$	−11.6708	+	19.8411i	−0.557653	+	0.948046i
$439$	0.00992669	+	0.0136629i	0.000473775	+	0.000652095i	0.809254	−	0.587459i	$-0.199872\pi$
$439$	0.00992669	+	0.0136629i	0.000473775	+	0.000652095i	−0.808780	+	0.588111i	$0.799872\pi$
$440$	−4.29772	+	11.2170i	−0.204886	+	0.534751i
$441$	15.6593	+	13.5562i	0.745683	+	0.645533i
$442$	−26.9909	+	13.1507i	−1.28383	+	0.625517i
$443$	13.3387			0.633739			0.316870	−	0.948469i	$-0.397368\pi$
$443$	13.3387			0.633739			0.316870	+	0.948469i	$0.397368\pi$
$444$	−11.8486	+	7.26428i	−0.562311	+	0.344747i
$445$	−17.9062	+	9.16544i	−0.848834	+	0.434484i
$446$	−28.5764	−	5.05080i	−1.35313	−	0.239162i
$447$	−6.26319	+	16.8042i	−0.296239	+	0.794810i
$448$	−2.46463	−	0.265136i	−0.116443	−	0.0125265i
$449$			34.1036i			1.60945i	0.593649	+	0.804724i	$0.297687\pi$
$449$			34.1036i			1.60945i	−0.593649	+	0.804724i	$0.702313\pi$
$450$	20.5194	+	5.38078i	0.967295	+	0.253652i
$451$			2.91485i			0.137255i
$452$	−14.2944	−	11.1868i	−0.672351	−	0.526181i
$453$	11.6798	−	31.3369i	0.548764	−	1.47234i
$454$	−3.00428	+	16.9976i	−0.140998	+	0.797737i
$455$	2.30255	+	2.29404i	0.107945	+	0.107546i
$456$	17.1906	+	20.8622i	0.805022	+	0.976962i
$457$	−31.6417			−1.48014			−0.740069	−	0.672531i	$-0.765207\pi$
$457$	−31.6417			−1.48014			−0.740069	+	0.672531i	$0.765207\pi$
$458$	1.94660	+	3.99524i	0.0909585	+	0.186686i
$459$	17.1075	+	16.1347i	0.798510	+	0.753104i
$460$	−26.0552	+	12.1826i	−1.21483	+	0.568017i
$461$	−7.09986	−	9.77212i	−0.330673	−	0.455133i	0.611015	−	0.791619i	$-0.290762\pi$
$461$	−7.09986	−	9.77212i	−0.330673	−	0.455133i	−0.941688	+	0.336486i	$0.890762\pi$
$462$	1.24252	+	0.730869i	0.0578075	+	0.0340031i
$463$	−20.5543	+	28.2905i	−0.955238	+	1.31477i	−0.00607669	+	0.999982i	$0.501934\pi$
$463$	−20.5543	+	28.2905i	−0.955238	+	1.31477i	−0.949161	+	0.314791i	$0.898066\pi$
$464$	25.3212	+	10.2784i	1.17551	+	0.477165i
$465$	4.59004	−	22.8977i	0.212858	−	1.06186i
$466$	−6.19408	+	11.6379i	−0.286935	+	0.539116i
$467$	−3.83021	−	11.7882i	−0.177241	−	0.545492i	0.822488	−	0.568783i	$-0.192586\pi$
$467$	−3.83021	−	11.7882i	−0.177241	−	0.545492i	−0.999729	+	0.0232909i	$0.992586\pi$
$468$	−27.6230	+	5.40478i	−1.27687	+	0.249836i
$469$	0.641453	+	1.97419i	0.0296196	+	0.0911596i
$470$	21.4661	−	6.59676i	0.990159	−	0.304286i
$471$	−8.17875	−	3.04836i	−0.376857	−	0.140461i
$472$	−3.99395	−	38.4519i	−0.183836	−	1.76989i
$473$	−4.19723	−	5.77700i	−0.192989	−	0.265627i
$474$	−4.64437	+	0.450098i	−0.213323	+	0.0206737i
$475$	27.5896	−	0.102144i	1.26590	−	0.00468668i
$476$	−2.69657	+	0.770852i	−0.123597	+	0.0353319i
$477$	1.17621	+	1.94848i	0.0538549	+	0.0892147i
$478$	−5.65366	+	31.9873i	−0.258593	+	1.46307i
$479$	−0.322045	+	0.991153i	−0.0147146	+	0.0452869i	−0.958144	−	0.286286i	$-0.907579\pi$
$479$	−0.322045	+	0.991153i	−0.0147146	+	0.0452869i	0.943430	+	0.331573i	$0.107579\pi$
$480$	−4.01066	−	21.5387i	−0.183061	−	0.983102i
$481$	−5.81604	−	17.8999i	−0.265189	−	0.816166i
$482$	11.2518	−	1.57667i	0.512506	−	0.0718151i
$483$	0.925837	+	3.32522i	0.0421271	+	0.151303i
$484$	13.8896	+	5.06822i	0.631346	+	0.230374i
$485$	25.0417	+	12.7010i	1.13708	+	0.576725i
$486$	11.6073	+	18.7422i	0.526516	+	0.850165i
$487$	15.6093	−	21.4843i	0.707323	−	0.973547i	−0.292527	−	0.956257i	$-0.594496\pi$
$487$	15.6093	−	21.4843i	0.707323	−	0.973547i	0.999851	−	0.0172900i	$-0.00550384\pi$
$488$	−26.2149	−	5.60565i	−1.18669	−	0.253756i
$489$	15.1872	−	10.0746i	0.686788	−	0.455588i
$490$	−12.5483	−	17.8659i	−0.566875	−	0.807099i
$491$	−25.8833	−	18.8053i	−1.16810	−	0.848671i	−0.177316	−	0.984154i	$-0.556741\pi$
$491$	−25.8833	−	18.8053i	−1.16810	−	0.848671i	−0.990780	+	0.135483i	$0.956741\pi$
$492$	−2.77875	−	4.53237i	−0.125276	−	0.204335i
$493$	30.9189			1.39252
$494$	−32.9091	+	16.0343i	−1.48065	+	0.721415i
$495$	−3.03403	+	12.3743i	−0.136370	+	0.556183i
$496$	−23.4121	+	5.79679i	−1.05124	+	0.260284i
$497$	−0.715558	−	0.232499i	−0.0320972	−	0.0104290i
$498$	4.16671	+	4.70375i	0.186715	+	0.210780i
$499$			22.0312i			0.986252i	0.869958	+	0.493126i	$0.164146\pi$
$499$			22.0312i			0.986252i	−0.869958	+	0.493126i	$0.835854\pi$
$500$	−19.6082	−	10.7479i	−0.876907	−	0.480660i
$501$	−0.370061	+	8.67997i	−0.0165331	+	0.387792i
$502$	27.3300	−	26.3708i	1.21980	−	1.17699i
$503$	−5.57845	+	17.1687i	−0.248731	+	0.765514i	0.746270	+	0.665644i	$0.231843\pi$
$503$	−5.57845	+	17.1687i	−0.248731	+	0.765514i	−0.995000	+	0.0998705i	$0.968157\pi$
$504$	−2.62877	+	0.0480628i	−0.117095	+	0.00214089i
$505$	−19.3328	−	3.02533i	−0.860296	−	0.134626i
$506$	−7.56656	−	15.5298i	−0.336375	−	0.690384i
$507$	0.664484	−	15.5858i	0.0295108	−	0.692191i
$508$	22.7591	−	15.3243i	1.00977	−	0.679905i
$509$	17.7421	−	24.4200i	0.786406	−	1.08240i	−0.208140	−	0.978099i	$-0.566741\pi$
$509$	17.7421	−	24.4200i	0.786406	−	1.08240i	0.994546	−	0.104296i	$-0.0332590\pi$
$510$	−13.3701	−	20.8730i	−0.592038	−	0.924270i
$511$	−1.71156	−	2.35575i	−0.0757147	−	0.104212i
$512$	−18.3546	+	13.2328i	−0.811167	+	0.584815i
$513$	20.8586	+	19.6725i	0.920930	+	0.868563i
$514$	3.81003	+	3.94862i	0.168053	+	0.174166i
$515$	4.72335	−	9.31267i	0.208136	−	0.410365i
$516$	12.0336	+	4.98153i	0.529752	+	0.219300i
$517$	4.16796	+	12.8277i	0.183307	+	0.564160i
$518$	−0.243970	−	1.74109i	−0.0107194	−	0.0764989i
$519$	−5.75641	−	20.6746i	−0.252679	−	0.907516i
$520$	29.6296	+	1.53414i	1.29934	+	0.0672764i
$521$	2.15432	+	0.699982i	0.0943826	+	0.0306668i	0.355828	−	0.934552i	$-0.384199\pi$
$521$	2.15432	+	0.699982i	0.0943826	+	0.0306668i	−0.261445	+	0.965218i	$0.584199\pi$
$522$	28.0101	+	7.45599i	1.22597	+	0.326340i
$523$	−2.94584	−	4.05459i	−0.128812	−	0.177295i	0.739739	−	0.672893i	$-0.234949\pi$
$523$	−2.94584	−	4.05459i	−0.128812	−	0.177295i	−0.868552	+	0.495598i	$0.834949\pi$
$524$	−2.85424	+	0.815925i	−0.124688	+	0.0356438i
$525$	−1.66053	+	2.10795i	−0.0724714	+	0.0919984i
$526$	−19.5146	+	2.73450i	−0.850879	+	0.119230i
$527$	−22.0769	+	16.0398i	−0.961685	+	0.698705i
$528$	12.8961	−	2.61562i	0.561230	−	0.113830i
$529$	5.67491	−	17.4656i	0.246735	−	0.759373i
$530$	−0.704735	−	2.29324i	−0.0306117	−	0.0996119i
$531$	−9.30576	−	39.9339i	−0.403835	−	1.73299i
$532$	−3.28784	+	0.939874i	−0.142546	+	0.0407487i
$533$	6.84712	−	2.22477i	0.296582	−	0.0963653i
$534$	18.9933	+	11.1721i	0.821922	+	0.483466i
$535$	−0.106315	+	0.679386i	−0.00459641	+	0.0293724i
$536$	16.3980	+	9.49415i	0.708287	+	0.410085i
$537$	23.2707	−	29.3169i	1.00421	−	1.26512i
$538$	9.53867	−	17.9220i	0.411241	−	0.772673i
$539$	10.6084	−	7.70744i	0.456935	−	0.331983i
$540$	−7.07884	−	22.1335i	−0.304625	−	0.952472i
$541$	2.54633	+	1.85001i	0.109475	+	0.0795383i	0.641176	−	0.767394i	$-0.278447\pi$
$541$	2.54633	+	1.85001i	0.109475	+	0.0795383i	−0.531701	+	0.846932i	$0.678447\pi$
$542$	1.92911	−	0.939915i	0.0828622	−	0.0403728i
$543$	1.61988	−	37.9952i	0.0695159	−	1.63053i
$544$	−13.6106	+	21.6831i	−0.583549	+	0.929654i
$545$	−13.9289	+	13.9806i	−0.596650	+	0.598863i
$546$	0.768488	−	3.47659i	0.0328883	−	0.148784i
$547$	−19.1348	−	6.21729i	−0.818147	−	0.265832i	−0.130103	−	0.991501i	$-0.541531\pi$
$547$	−19.1348	−	6.21729i	−0.818147	−	0.265832i	−0.688045	+	0.725668i	$0.741531\pi$
$548$	−28.6424	−	22.4155i	−1.22354	−	0.957544i
$549$	−28.3305	−	2.42008i	−1.20912	−	0.103287i
$550$	6.26590	−	11.8787i	0.267179	−	0.506510i
$551$	37.6983			1.60600
$552$	26.5701	+	16.9344i	1.13090	+	0.720776i
$553$	0.182399	−	0.561367i	0.00775641	−	0.0238718i
$554$	−3.17482	+	17.9625i	−0.134885	+	0.763154i
$555$	14.1210	−	6.48442i	0.599402	−	0.275248i
$556$	−18.4254	+	12.4063i	−0.781413	+	0.526144i
$557$			2.68419i			0.113733i	0.998382	+	0.0568664i	$0.0181109\pi$
$557$			2.68419i			0.113733i	−0.998382	+	0.0568664i	$0.981889\pi$
$558$	−23.8679	+	9.20706i	−1.01041	+	0.389766i
$559$	−10.3669	+	14.2688i	−0.438473	+	0.603507i
$560$	2.70054	+	0.622839i	0.114119	+	0.0263198i
$561$	12.4063	−	8.22986i	0.523795	−	0.347465i
$562$	16.9624	−	31.8703i	0.715516	−	1.34437i
$563$	5.37175	+	3.90280i	0.226392	+	0.164483i	0.695199	−	0.718817i	$-0.255316\pi$
$563$	5.37175	+	3.90280i	0.226392	+	0.164483i	−0.468807	+	0.883301i	$0.655316\pi$
$564$	−18.7096	−	15.9727i	−0.787815	−	0.672571i
$565$	14.3765	+	14.3233i	0.604823	+	0.602588i
$566$	−1.76297	+	3.31241i	−0.0741031	+	0.139231i
$567$	−2.75995	+	0.399433i	−0.115907	+	0.0167746i
$568$	−6.27755	+	2.78576i	−0.263400	+	0.116888i
$569$	16.1239	−	5.23898i	0.675950	−	0.219629i	0.0491284	−	0.998792i	$-0.484356\pi$
$569$	16.1239	−	5.23898i	0.675950	−	0.219629i	0.626821	+	0.779163i	$0.284356\pi$
$570$	−16.3017	−	25.4497i	−0.682804	−	1.06597i
$571$	10.2552	+	3.33210i	0.429165	+	0.139444i	0.515631	−	0.856811i	$-0.327557\pi$
$571$	10.2552	+	3.33210i	0.429165	+	0.139444i	−0.0864661	+	0.996255i	$0.527557\pi$
$572$	−0.636407	+	17.8082i	−0.0266095	+	0.744600i
$573$	−5.05150	−	7.61502i	−0.211030	−	0.318122i
$574$	0.666004	−	0.0933241i	0.0277985	−	0.00389527i
$575$	30.5467	−	10.0504i	1.27388	−	0.419131i
$576$	−17.5589	+	16.3610i	−0.731623	+	0.681710i
$577$	−0.900509	+	0.654258i	−0.0374887	+	0.0272371i	−0.606372	−	0.795181i	$-0.707376\pi$
$577$	−0.900509	+	0.654258i	−0.0374887	+	0.0272371i	0.568883	+	0.822418i	$0.307376\pi$
$578$	−0.856908	+	4.84821i	−0.0356427	+	0.201659i
$579$	−4.25145	−	1.58459i	−0.176684	−	0.0658532i
$580$	−26.7379	−	14.7849i	−1.11023	−	0.613909i
$581$	−0.755990	+	0.245636i	−0.0313638	+	0.0101907i
$582$	−2.96698	−	30.6150i	−0.122985	−	1.26903i
$583$	1.37038	−	0.445265i	0.0567555	−	0.0184410i
$584$	−25.9925	−	5.55810i	−1.07558	−	0.229996i
$585$	31.3836	−	2.31763i	1.29755	−	0.0958220i
$586$	−25.2933	−	26.2134i	−1.04486	−	1.08286i
$587$	6.04530	+	4.39217i	0.249516	+	0.181284i	0.705512	−	0.708698i	$-0.250717\pi$
$587$	6.04530	+	4.39217i	0.249516	+	0.181284i	−0.455996	+	0.889982i	$0.650717\pi$
$588$	−9.14766	+	22.0975i	−0.377243	+	0.911287i
$589$	−26.9176	+	19.5568i	−1.10912	+	0.805824i
$590$	−0.691935	+	43.2163i	−0.0284865	+	1.77919i
$591$	31.1515	+	24.7269i	1.28140	+	1.01713i
$592$	−12.2769	−	10.3356i	−0.504575	−	0.424792i
$593$		−	41.8958i		−	1.72045i	−0.509912	−	0.860226i	$-0.670322\pi$
$593$		−	41.8958i		−	1.72045i	0.509912	−	0.860226i	$-0.329678\pi$
$594$	13.2238	−	4.46388i	0.542578	−	0.183155i
$595$	3.09611	−	0.496252i	0.126928	−	0.0203443i
$596$	−20.6945	−	0.739552i	−0.847681	−	0.0302932i
$597$	−4.00692	+	10.7506i	−0.163992	+	0.439992i
$598$	−30.7051	+	29.6274i	−1.25562	+	1.21155i
$599$	−30.2844			−1.23739			−0.618693	−	0.785633i	$-0.712338\pi$
$599$	−30.2844			−1.23739			−0.618693	+	0.785633i	$0.712338\pi$
$600$	1.58107	+	24.4438i	0.0645467	+	0.997915i
$601$	−5.91631			−0.241331			−0.120666	−	0.992693i	$-0.538503\pi$
$601$	−5.91631			−0.241331			−0.120666	+	0.992693i	$0.538503\pi$
$602$	−1.18559	+	1.14397i	−0.0483208	+	0.0466249i
$603$	18.5160	+	7.81481i	0.754030	+	0.318244i
$604$	38.5917	+	1.37914i	1.57028	+	0.0561164i
$605$	−14.7427	−	7.47745i	−0.599377	−	0.304001i
$606$	8.55961	+	19.6525i	0.347710	+	0.798330i
$607$		−	6.47572i		−	0.262842i	−0.991327	−	0.131421i	$-0.958046\pi$
$607$		−	6.47572i		−	0.262842i	0.991327	−	0.131421i	$-0.0419539\pi$
$608$	−16.5949	+	26.4374i	−0.673013	+	1.07218i
$609$	−2.27958	+	2.87186i	−0.0923731	+	0.116374i
$610$	28.3529	+	9.71693i	1.14798	+	0.393427i
$611$	26.9516	−	19.5815i	1.09034	−	0.792182i
$612$	−11.4453	+	24.6238i	−0.462648	+	0.995360i
$613$	14.2311	+	10.3395i	0.574787	+	0.417607i	0.836841	−	0.547446i	$-0.184400\pi$
$613$	14.2311	+	10.3395i	0.574787	+	0.417607i	−0.262054	+	0.965053i	$0.584400\pi$
$614$	−12.2350	−	12.6800i	−0.493763	−	0.511723i
$615$	2.48044	+	5.40159i	0.100021	+	0.217813i
$616$	−0.348068	+	1.62775i	−0.0140241	+	0.0655838i
$617$	−20.9543	+	6.80846i	−0.843587	+	0.274098i	−0.698758	−	0.715358i	$-0.746263\pi$
$617$	−20.9543	+	6.80846i	−0.843587	+	0.274098i	−0.144830	+	0.989457i	$0.546263\pi$
$618$	−11.3853	+	1.10338i	−0.457985	+	0.0443845i
$619$	19.7409	−	6.41419i	0.793452	−	0.257808i	0.115879	−	0.993263i	$-0.463032\pi$
$619$	19.7409	−	6.41419i	0.793452	−	0.257808i	0.677573	+	0.735455i	$0.263032\pi$
$620$	26.7616	−	3.31406i	1.07477	−	0.133096i
$621$	30.2077	+	14.2945i	1.21219	+	0.573618i
$622$	−1.96821	+	11.1358i	−0.0789182	+	0.446503i
$623$	−2.25509	+	1.63842i	−0.0903484	+	0.0656420i
$624$	−15.9872	−	28.2972i	−0.640000	−	1.13279i
$625$	20.3337	+	14.5445i	0.813347	+	0.581779i
$626$	31.3578	−	4.39403i	1.25331	−	0.175621i
$627$	15.1266	−	10.0344i	0.604098	−	0.400735i
$628$	0.359947	−	10.0722i	0.0143635	−	0.401926i
$629$	−17.2685	−	5.61086i	−0.688538	−	0.223720i
$630$	2.92450	+	0.297050i	0.116515	+	0.0118348i
$631$	30.4448	−	9.89211i	1.21199	−	0.393799i	0.367830	−	0.929893i	$-0.380101\pi$
$631$	30.4448	−	9.89211i	1.21199	−	0.393799i	0.844158	+	0.536094i	$0.180101\pi$
$632$	−2.18547	−	4.92484i	−0.0869334	−	0.195900i
$633$	7.67572	+	27.5680i	0.305082	+	1.09573i
$634$	11.3980	−	21.4155i	0.452672	−	0.850517i
$635$	−27.3067	+	13.9772i	−1.08363	+	0.554667i
$636$	−1.70637	+	1.99875i	−0.0676619	+	0.0792557i
$637$	−26.2020	−	19.0369i	−1.03816	−	0.754269i
$638$	8.62169	−	16.1991i	0.341336	−	0.641329i
$639$	−6.23634	+	3.76459i	−0.246706	+	0.148925i
$640$	22.1386	−	12.2427i	0.875104	−	0.483934i
$641$	27.9458	−	38.4641i	1.10379	−	1.51924i	0.273535	−	0.961862i	$-0.411807\pi$
$641$	27.9458	−	38.4641i	1.10379	−	1.51924i	0.830258	−	0.557379i	$-0.188193\pi$
$642$	0.690624	−	0.300799i	0.0272567	−	0.0118716i
$643$			39.1531i			1.54405i	0.635594	+	0.772024i	$0.280755\pi$
$643$			39.1531i			1.54405i	−0.635594	+	0.772024i	$0.719245\pi$
$644$	−3.30610	+	2.22607i	−0.130279	+	0.0877196i
$645$	−12.6940	−	7.13382i	−0.499828	−	0.280894i
$646$	−6.14674	+	34.7770i	−0.241840	+	1.36828i
$647$	2.07945	−	6.39988i	0.0817515	−	0.251605i	−0.901824	−	0.432104i	$-0.857771\pi$
$647$	2.07945	−	6.39988i	0.0817515	−	0.251605i	0.983575	+	0.180499i	$0.0577713\pi$
$648$	−16.3065	+	19.5473i	−0.640580	+	0.767891i
$649$	−25.9594			−1.01900
$650$	−32.6861	−	5.65247i	−1.28206	−	0.221708i
$651$	0.137842	−	3.23316i	0.00540246	−	0.126718i
$652$	16.5726	+	12.9697i	0.649033	+	0.507932i
$653$	26.7002	+	8.67542i	1.04486	+	0.339495i	0.780649	−	0.624970i	$-0.214889\pi$
$653$	26.7002	+	8.67542i	1.04486	+	0.339495i	0.264210	+	0.964465i	$0.414889\pi$
$654$	21.1091	+	4.66609i	0.825431	+	0.182459i
$655$	3.27714	−	0.525268i	0.128048	−	0.0205239i
$656$	3.95362	−	4.69617i	0.154363	−	0.183355i
$657$	−28.0902	−	2.39955i	−1.09590	−	0.0936154i
$658$	2.79750	−	1.36302i	0.109058	−	0.0531362i
$659$	10.1120	+	7.34678i	0.393906	+	0.286190i	0.767054	−	0.641582i	$-0.221722\pi$
$659$	10.1120	+	7.34678i	0.393906	+	0.286190i	−0.373148	+	0.927772i	$0.621722\pi$
$660$	−14.6641	+	1.18451i	−0.570798	+	0.0461069i
$661$	18.2915	−	13.2896i	0.711457	−	0.516904i	−0.172186	−	0.985064i	$-0.555083\pi$
$661$	18.2915	−	13.2896i	0.711457	−	0.516904i	0.883644	+	0.468160i	$0.155083\pi$
$662$	−23.7511	+	44.6255i	−0.923113	+	1.73442i
$663$	−28.8015	−	22.8616i	−1.11856	−	0.887870i
$664$	−3.63566	+	6.27941i	−0.141091	+	0.243688i
$665$	3.77498	−	0.605063i	0.146387	−	0.0234633i
$666$	−14.2908	−	9.24724i	−0.553759	−	0.358323i
$667$	41.7892	−	13.5781i	1.61808	−	0.525747i
$668$	−9.64550	+	2.75730i	−0.373196	+	0.106683i
$669$	−9.53310	−	34.2389i	−0.368571	−	1.32375i
$670$	−16.9373	−	12.7249i	−0.654344	−	0.491604i
$671$	−5.56271	+	17.1202i	−0.214746	+	0.660920i
$672$	−1.01053	−	2.86284i	−0.0389819	−	0.110436i
$673$	12.8972	−	9.37034i	0.497149	−	0.361200i	−0.310778	−	0.950483i	$-0.600590\pi$
$673$	12.8972	−	9.37034i	0.497149	−	0.361200i	0.807927	+	0.589283i	$0.200590\pi$
$674$	6.04346	−	0.846843i	0.232786	−	0.0326192i
$675$	4.90765	+	25.5130i	0.188895	+	0.981997i
$676$	17.3195	−	4.95103i	0.666136	−	0.190424i
$677$	23.1821	+	31.9074i	0.890960	+	1.22630i	0.973263	+	0.229694i	$0.0737724\pi$
$677$	23.1821	+	31.9074i	0.890960	+	1.22630i	−0.0823033	+	0.996607i	$0.526228\pi$
$678$	4.79822	−	21.7068i	0.184275	−	0.833646i
$679$	3.70045	+	1.20235i	0.142010	+	0.0461420i
$680$	17.9988	−	22.2553i	0.690222	−	0.853451i
$681$	−20.3657	+	5.67040i	−0.780416	+	0.217290i
$682$	2.24751	+	16.0393i	0.0860617	+	0.614176i
$683$	7.28659	+	22.4258i	0.278814	+	0.858100i	0.988185	+	0.153265i	$0.0489789\pi$
$683$	7.28659	+	22.4258i	0.278814	+	0.858100i	−0.709371	+	0.704835i	$0.751021\pi$
$684$	−13.9548	+	30.0230i	−0.533577	+	1.14796i
$685$	28.8069	+	28.7005i	1.10066	+	1.09659i
$686$	−4.23060	−	4.38449i	−0.161525	−	0.167401i
$687$	−3.38401	+	4.26325i	−0.129108	+	0.162653i
$688$	−1.07350	+	15.0004i	−0.0409269	+	0.571886i
$689$	−2.09190	−	2.87925i	−0.0796950	−	0.109691i
$690$	−27.2372	−	22.3399i	−1.03690	−	0.850464i
$691$	−10.9643	+	15.0910i	−0.417100	+	0.574089i	−0.964932	−	0.262500i	$-0.915453\pi$
$691$	−10.9643	+	15.0910i	−0.417100	+	0.574089i	0.547832	+	0.836588i	$0.315453\pi$
$692$	20.5557	−	13.8407i	0.781412	−	0.526143i
$693$	−0.150269	+	1.75911i	−0.00570823	+	0.0668231i
$694$	9.43664	+	19.3680i	0.358210	+	0.735200i
$695$	22.1070	−	11.3157i	0.838568	−	0.429229i
$696$	2.03668	+	33.4075i	0.0772002	+	1.26631i
$697$	2.14628	−	6.60557i	0.0812962	−	0.250204i
$698$	−6.83348	+	6.59364i	−0.258651	+	0.249573i
$699$	−16.1319	−	0.687766i	−0.610165	−	0.0260137i
$700$	−2.91474	−	1.05136i	−0.110167	−	0.0397376i
$701$			22.0139i			0.831452i	0.909490	+	0.415726i	$0.136472\pi$
$701$			22.0139i			0.831452i	−0.909490	+	0.415726i	$0.863528\pi$
$702$	−20.5789	−	27.6562i	−0.776702	−	1.04382i
$703$	−21.0548	−	6.84113i	−0.794098	−	0.258018i
$704$	7.56497	+	13.1772i	0.285116	+	0.496634i
$705$	18.6397	+	20.2245i	0.702010	+	0.761699i
$706$	17.0397	−	8.30220i	0.641296	−	0.312457i
$707$	−2.71158			−0.101979
$708$	40.3649	−	24.7473i	1.51701	−	0.930061i
$709$	−26.2223	−	19.0516i	−0.984798	−	0.715498i	−0.0260224	−	0.999661i	$-0.508284\pi$
$709$	−26.2223	−	19.0516i	−0.984798	−	0.715498i	−0.958776	+	0.284164i	$0.908284\pi$
$710$	7.33978	−	2.25559i	0.275457	−	0.0846507i
$711$	−2.95339	−	4.89251i	−0.110761	−	0.183483i
$712$	−5.32061	+	24.8819i	−0.199398	+	0.932489i
$713$	−22.7947	+	31.3742i	−0.853667	+	1.17497i
$714$	−2.27762	−	2.57118i	−0.0852379	−	0.0962241i
$715$	3.08020	−	19.6834i	0.115193	−	0.736117i
$716$	40.6019	+	14.8154i	1.51736	+	0.553676i
$717$	−38.3257	+	10.6710i	−1.43130	+	0.398515i
$718$	34.3632	−	4.81515i	1.28242	−	0.179700i
$719$	−11.1789	−	34.4052i	−0.416903	−	1.28310i	−0.910538	−	0.413426i	$-0.864332\pi$
$719$	−11.1789	−	34.4052i	−0.416903	−	1.28310i	0.493634	−	0.869669i	$-0.335668\pi$
$720$	21.6723	−	15.8212i	0.807680	−	0.589622i
$721$	0.447138	−	1.37615i	0.0166523	−	0.0512505i
$722$	−2.81779	+	15.9425i	−0.104867	+	0.593318i
$723$	7.69223	+	11.5958i	0.286077	+	0.431254i
$724$	42.2217	−	12.0697i	1.56916	−	0.448565i
$725$	27.7099	+	19.9761i	1.02912	+	0.741895i
$726$	1.74674	+	18.0239i	0.0648277	+	0.668929i
$727$	9.73296	+	13.3963i	0.360976	+	0.496840i	0.950420	−	0.310969i	$-0.100653\pi$
$727$	9.73296	+	13.3963i	0.360976	+	0.496840i	−0.589445	+	0.807809i	$0.700653\pi$
$728$	4.08932	−	0.424752i	0.151560	−	0.0157424i
$729$	−14.5657	+	22.7341i	−0.539470	+	0.842005i
$730$	28.1124	+	9.63450i	1.04049	+	0.356589i
$731$	5.25793	+	16.1822i	0.194472	+	0.598522i
$732$	−7.67129	−	31.9237i	−0.283539	−	1.17993i
$733$	−2.17150	−	6.68320i	−0.0802063	−	0.246850i	0.902911	−	0.429829i	$-0.141426\pi$
$733$	−2.17150	−	6.68320i	−0.0802063	−	0.246850i	−0.983117	+	0.182979i	$0.941426\pi$
$734$	20.8480	−	39.1709i	0.769514	−	1.44582i
$735$	13.0999	−	23.3102i	0.483199	−	0.859811i
$736$	−8.87353	+	35.2834i	−0.327083	+	1.30056i
$737$	7.47882	−	10.2937i	0.275486	−	0.379174i
$738$	3.53728	−	5.46657i	0.130209	−	0.201227i
$739$	−13.1867	−	18.1499i	−0.485081	−	0.667656i	0.494391	−	0.869240i	$-0.335391\pi$
$739$	−13.1867	−	18.1499i	−0.485081	−	0.667656i	−0.979471	+	0.201584i	$0.935391\pi$
$740$	12.2503	+	13.1096i	0.450332	+	0.481919i
$741$	−35.1167	−	27.8743i	−1.29004	−	1.02399i
$742$	−0.145612	−	0.298859i	−0.00534560	−	0.0109715i
$743$	−45.8197			−1.68096			−0.840480	−	0.541842i	$-0.817727\pi$
$743$	−45.8197			−1.68096			−0.840480	+	0.541842i	$0.817727\pi$
$744$	−18.7851	−	22.7973i	−0.688695	−	0.835790i
$745$	22.8736	+	3.57943i	0.838023	+	0.131140i
$746$	−0.779195	+	4.40853i	−0.0285283	+	0.161408i
$747$	−2.99258	+	7.09046i	−0.109493	+	0.259426i
$748$	13.5380	+	10.5949i	0.495000	+	0.387386i
$749$			0.0952894i			0.00348180i
$750$	1.50317	−	27.3448i	0.0548878	−	0.998493i
$751$		−	12.7397i		−	0.464880i	−0.972611	−	0.232440i	$-0.925329\pi$
$751$		−	12.7397i		−	0.464880i	0.972611	−	0.232440i	$-0.0746709\pi$
$752$	10.6840	−	26.3202i	0.389604	−	0.959798i
$753$	43.5848	+	16.2448i	1.58832	+	0.591992i
$754$	−44.6331	−	7.88876i	−1.62544	−	0.287292i
$755$	−42.6553	−	6.67502i	−1.55239	−	0.242929i
$756$	−1.44332	−	2.87854i	−0.0524930	−	0.104691i
$757$	8.77358			0.318881			0.159441	−	0.987208i	$-0.449031\pi$
$757$	8.77358			0.318881			0.159441	+	0.987208i	$0.449031\pi$
$758$	22.2562	−	10.8439i	0.808382	−	0.393867i
$759$	13.1539	−	16.5716i	0.477456	−	0.601509i
$760$	21.9453	−	27.1351i	0.796041	−	0.984293i
$761$	−19.8575	−	27.3316i	−0.719836	−	0.990769i	−0.999529	−	0.0306793i	$-0.990233\pi$
$761$	−19.8575	−	27.3316i	−0.719836	−	0.990769i	0.279694	−	0.960089i	$-0.409767\pi$
$762$	28.9646	+	17.0373i	1.04928	+	0.617198i
$763$	−1.60743	+	2.21243i	−0.0581928	+	0.0800955i
$764$	6.50314	−	8.30968i	0.235275	−	0.300634i
$765$	15.9872	−	25.8083i	0.578018	−	0.933103i
$766$	26.6321	+	14.1745i	0.962258	+	0.512145i
$767$	19.8136	+	60.9799i	0.715427	+	2.20186i
$768$	−24.3249	−	13.2778i	−0.877749	−	0.479121i
$769$	−5.09067	−	15.6675i	−0.183574	−	0.564984i	0.816346	−	0.577563i	$-0.195996\pi$
$769$	−5.09067	−	15.6675i	−0.183574	−	0.564984i	−0.999921	+	0.0125785i	$0.995996\pi$
$770$	0.603348	−	1.76050i	0.0217431	−	0.0634441i
$771$	−2.34703	+	6.29709i	−0.0845262	+	0.226784i
$772$	0.187107	−	5.23571i	0.00673412	−	0.188437i
$773$	−8.59165	−	11.8254i	−0.309020	−	0.425330i	0.626055	−	0.779779i	$-0.284668\pi$
$773$	−8.59165	−	11.8254i	−0.309020	−	0.425330i	−0.935075	+	0.354449i	$0.884668\pi$
$774$	0.860982

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.01770 + 0.981981i) q^{2} +(-1.62298 - 0.604914i) q^{3} +(0.0714277 - 1.99872i) q^{4} +(-0.345709 + 2.20918i) q^{5} +(2.24573 - 0.978119i) q^{6} +0.309856i q^{7} +(1.89002 + 2.10424i) q^{8} +(2.26816 + 1.96353i) q^{9} +O(q^{10})\)	\(q+(-1.01770 + 0.981981i) q^{2} +(-1.62298 - 0.604914i) q^{3} +(0.0714277 - 1.99872i) q^{4} +(-0.345709 + 2.20918i) q^{5} +(2.24573 - 0.978119i) q^{6} +0.309856i q^{7} +(1.89002 + 2.10424i) q^{8} +(2.26816 + 1.96353i) q^{9} +(-1.81755 - 2.58776i) q^{10} +(1.53656 - 1.11637i) q^{11} +(-1.32498 + 3.20069i) q^{12} +(-3.79520 - 2.75737i) q^{13} +(-0.304272 - 0.315340i) q^{14} +(1.89744 - 3.37634i) q^{15} +(-3.98980 - 0.285528i) q^{16} +(-4.30413 + 1.39850i) q^{17} +(-4.23646 + 0.229003i) q^{18} +(-5.24788 + 1.70514i) q^{19} +(4.39085 + 0.848774i) q^{20} +(0.187436 - 0.502891i) q^{21} +(-0.467497 + 2.64500i) q^{22} +(-5.20321 + 3.78035i) q^{23} +(-1.79458 - 4.55845i) q^{24} +(-4.76097 - 1.52747i) q^{25} +(6.57006 - 0.920633i) q^{26} +(-2.49342 - 4.55882i) q^{27} +(0.619316 + 0.0221323i) q^{28} +(-6.49757 - 2.11119i) q^{29} +(1.38448 + 5.29936i) q^{30} +(5.73466 - 1.86330i) q^{31} +(4.34080 - 3.62732i) q^{32} +(-3.16912 + 0.882374i) q^{33} +(3.00702 - 5.64982i) q^{34} +(-0.684528 - 0.107120i) q^{35} +(4.08657 - 4.39317i) q^{36} +(3.24583 + 2.35823i) q^{37} +(3.66636 - 6.88864i) q^{38} +(4.49158 + 6.77094i) q^{39} +(-5.30205 + 3.44793i) q^{40} +(-0.902077 + 1.24160i) q^{41} +(0.303076 + 0.695851i) q^{42} -3.75970i q^{43} +(-2.12157 - 3.15090i) q^{44} +(-5.12192 + 4.33197i) q^{45} +(1.58307 - 8.95671i) q^{46} +(-2.19448 + 6.75392i) q^{47} +(6.30266 + 2.87689i) q^{48} +6.90399 q^{49} +(6.34519 - 3.12068i) q^{50} +(7.83151 + 0.333888i) q^{51} +(-5.78231 + 7.38860i) q^{52} +(0.721525 + 0.234438i) q^{53} +(7.01423 + 2.19102i) q^{54} +(1.93507 + 3.78048i) q^{55} +(-0.652012 + 0.585633i) q^{56} +(9.54870 + 0.407098i) q^{57} +(8.68572 - 4.23193i) q^{58} +(-11.0576 - 8.03382i) q^{59} +(-6.61285 - 4.03363i) q^{60} +(-7.66779 + 5.57097i) q^{61} +(-4.00643 + 7.52761i) q^{62} +(-0.608411 + 0.702802i) q^{63} +(-0.855674 + 7.95411i) q^{64} +(7.40358 - 7.43104i) q^{65} +(2.35874 - 4.01001i) q^{66} +(6.37132 - 2.07017i) q^{67} +(2.48778 + 8.70266i) q^{68} +(10.7315 - 2.98796i) q^{69} +(0.801834 - 0.563177i) q^{70} +(-0.750346 + 2.30933i) q^{71} +(0.155113 + 8.48386i) q^{72} +(-7.60274 + 5.52372i) q^{73} +(-5.61902 + 0.787367i) q^{74} +(6.80300 + 5.35903i) q^{75} +(3.03326 + 10.6109i) q^{76} +(0.345915 + 0.476111i) q^{77} +(-11.2200 - 2.48015i) q^{78} +(-1.81171 - 0.588659i) q^{79} +(2.01009 - 8.71548i) q^{80} +(1.28909 + 8.90720i) q^{81} +(-0.301186 - 2.14940i) q^{82} +(0.792743 + 2.43981i) q^{83} +(-0.991753 - 0.410553i) q^{84} +(-1.60156 - 9.99208i) q^{85} +(3.69195 + 3.82625i) q^{86} +(9.26837 + 7.35689i) q^{87} +(5.25324 + 1.12332i) q^{88} +(5.28769 + 7.27788i) q^{89} +(0.958673 - 9.43827i) q^{90} +(0.854388 - 1.17596i) q^{91} +(7.18422 + 10.6698i) q^{92} +(-10.4344 - 0.444859i) q^{93} +(-4.39890 - 9.02841i) q^{94} +(-1.95272 - 12.1830i) q^{95} +(-9.23927 + 3.26128i) q^{96} +(3.88035 - 11.9425i) q^{97} +(-7.02619 + 6.77958i) q^{98} +(5.67719 + 0.484963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224q - 6q^{4} + q^{6} - 6q^{9} + O(q^{10}) \)	\( 224q - 6q^{4} + q^{6} - 6q^{9} - 8q^{10} - 9q^{12} - 12q^{13} - 18q^{16} - 26q^{18} + 12q^{21} - 6q^{22} - 16q^{24} - 12q^{25} + 2q^{28} - 13q^{30} + 6q^{33} - 30q^{34} + 35q^{36} + 12q^{37} - 24q^{40} - 13q^{42} - 6q^{45} - 18q^{46} - 34q^{48} - 168q^{49} - 28q^{52} - 38q^{54} - 44q^{57} - 34q^{58} - 76q^{60} + 4q^{61} + 18q^{64} - 46q^{66} - 18q^{69} + 72q^{70} - 29q^{72} - 20q^{73} + 16q^{76} + 5q^{78} - 30q^{81} - 20q^{82} - 18q^{84} - 76q^{85} + 6q^{88} + 2q^{90} - 52q^{93} + 96q^{94} - 50q^{96} - 72q^{97} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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