LMFDB - Embedded newform 300.2.w.a.67.15

Newspace parameters

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, degree $8$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			67.15
Character	$\chi$	$=$	300.67
Dual form			300.2.w.a.103.15

$q$-expansion

$f(q)$	$=$	$q+(-0.194555 - 1.40077i) q^{2} +(-0.987688 - 0.156434i) q^{3} +(-1.92430 + 0.545051i) q^{4} +(1.56105 + 1.60098i) q^{5} +(-0.0269690 + 1.41396i) q^{6} +(1.26539 - 1.26539i) q^{7} +(1.13787 + 2.58945i) q^{8} +(0.951057 + 0.309017i) q^{9} +O(q^{10})$	\(q+(-0.194555 - 1.40077i) q^{2} +(-0.987688 - 0.156434i) q^{3} +(-1.92430 + 0.545051i) q^{4} +(1.56105 + 1.60098i) q^{5} +(-0.0269690 + 1.41396i) q^{6} +(1.26539 - 1.26539i) q^{7} +(1.13787 + 2.58945i) q^{8} +(0.951057 + 0.309017i) q^{9} +(1.93889 - 2.49814i) q^{10} +(2.45369 - 0.797253i) q^{11} +(1.98587 - 0.237314i) q^{12} +(0.719314 + 1.41173i) q^{13} +(-2.01871 - 1.52633i) q^{14} +(-1.29138 - 1.82547i) q^{15} +(3.40584 - 2.09768i) q^{16} +(-0.968521 - 6.11500i) q^{17} +(0.247828 - 1.39233i) q^{18} +(4.18468 + 3.04035i) q^{19} +(-3.87653 - 2.22991i) q^{20} +(-1.44777 + 1.05186i) q^{21} +(-1.59414 - 3.28194i) q^{22} +(2.77576 - 5.44773i) q^{23} +(-0.718783 - 2.73557i) q^{24} +(-0.126271 + 4.99841i) q^{25} +(1.83756 - 1.28225i) q^{26} +(-0.891007 - 0.453990i) q^{27} +(-1.74529 + 3.12470i) q^{28} +(-2.10923 - 2.90311i) q^{29} +(-2.30582 + 2.16407i) q^{30} +(-3.46723 + 4.77223i) q^{31} +(-3.60098 - 4.36267i) q^{32} +(-2.54820 + 0.403595i) q^{33} +(-8.37726 + 2.54637i) q^{34} +(4.00121 + 0.0505318i) q^{35} +(-1.99855 - 0.0762659i) q^{36} +(8.50512 - 4.33357i) q^{37} +(3.44467 - 6.45327i) q^{38} +(-0.489614 - 1.50688i) q^{39} +(-2.36939 + 5.86396i) q^{40} +(-2.24529 + 6.91028i) q^{41} +(1.75509 + 1.82334i) q^{42} +(1.96263 + 1.96263i) q^{43} +(-4.28709 + 2.87154i) q^{44} +(0.989913 + 2.00501i) q^{45} +(-8.17104 - 2.82831i) q^{46} +(0.00589566 - 0.0372238i) q^{47} +(-3.69206 + 1.53906i) q^{48} +3.79756i q^{49} +(7.02617 - 0.795586i) q^{50} +6.19122i q^{51} +(-2.15364 - 2.32453i) q^{52} +(-1.13623 + 7.17385i) q^{53} +(-0.462586 + 1.33642i) q^{54} +(5.10671 + 2.68376i) q^{55} +(4.71653 + 1.83682i) q^{56} +(-3.65754 - 3.65754i) q^{57} +(-3.65622 + 3.51935i) q^{58} +(2.91440 - 8.96960i) q^{59} +(3.47997 + 2.80888i) q^{60} +(-0.911425 - 2.80508i) q^{61} +(7.35935 + 3.92832i) q^{62} +(1.59449 - 0.812433i) q^{63} +(-5.41050 + 5.89292i) q^{64} +(-1.13727 + 3.35539i) q^{65} +(1.06111 + 3.49091i) q^{66} +(-6.72692 + 1.06544i) q^{67} +(5.19671 + 11.2392i) q^{68} +(-3.59380 + 4.94644i) q^{69} +(-0.707670 - 5.61459i) q^{70} +(1.78138 + 2.45186i) q^{71} +(0.281995 + 2.81433i) q^{72} +(6.68488 + 3.40612i) q^{73} +(-7.72504 - 11.0706i) q^{74} +(0.906640 - 4.91711i) q^{75} +(-9.70971 - 3.56967i) q^{76} +(2.09605 - 4.11372i) q^{77} +(-2.01553 + 0.979005i) q^{78} +(-3.75981 + 2.73166i) q^{79} +(8.67501 + 2.17810i) q^{80} +(0.809017 + 0.587785i) q^{81} +(10.1165 + 1.80070i) q^{82} +(-1.32439 - 8.36187i) q^{83} +(2.21261 - 2.81320i) q^{84} +(8.27808 - 11.0964i) q^{85} +(2.36735 - 3.13103i) q^{86} +(1.62912 + 3.19732i) q^{87} +(4.85643 + 5.44654i) q^{88} +(-2.83952 + 0.922614i) q^{89} +(2.61596 - 1.77672i) q^{90} +(2.69661 + 0.876183i) q^{91} +(-2.37209 + 11.9960i) q^{92} +(4.17109 - 4.17109i) q^{93} +(-0.0532888 - 0.00101640i) q^{94} +(1.66494 + 11.4457i) q^{95} +(2.87418 + 4.87228i) q^{96} +(-12.1121 - 1.91837i) q^{97} +(5.31949 - 0.738832i) q^{98} +2.57996 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240q + 12q^{8} + O(q^{10}) $	$ 240q + 12q^{8} + 8q^{10} + 8q^{12} + 4q^{13} + 20q^{17} - 20q^{20} - 12q^{22} + 20q^{25} + 4q^{28} - 8q^{30} - 20q^{32} - 8q^{33} - 4q^{37} - 76q^{38} - 92q^{40} - 20q^{42} - 140q^{44} - 4q^{45} - 16q^{48} - 164q^{50} - 172q^{52} - 4q^{53} - 120q^{58} + 20q^{60} - 44q^{62} - 60q^{64} - 20q^{65} + 16q^{68} - 44q^{70} + 12q^{72} - 44q^{73} - 48q^{77} + 24q^{78} - 4q^{80} + 60q^{81} + 24q^{82} + 80q^{84} - 64q^{85} + 60q^{88} - 260q^{89} + 48q^{90} + 144q^{92} - 64q^{93} + 40q^{94} - 20q^{96} - 180q^{97} + 256q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{20}\right)$

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 $

$2$	−0.194555	−	1.40077i	−0.137571	−	0.990492i
$2$	−0.194555	−	1.40077i	−0.137571	−	0.990492i
$3$	−0.987688	−	0.156434i	−0.570242	−	0.0903175i
$3$	−0.987688	−	0.156434i	−0.570242	−	0.0903175i
$4$	−1.92430	+	0.545051i	−0.962149	+	0.272526i
$5$	1.56105	+	1.60098i	0.698121	+	0.715980i
$5$	1.56105	+	1.60098i	0.698121	+	0.715980i
$6$	−0.0269690	+	1.41396i	−0.0110100	+	0.577245i
$7$	1.26539	−	1.26539i	0.478274	−	0.478274i	−0.426305	−	0.904579i	$-0.640185\pi$
$7$	1.26539	−	1.26539i	0.478274	−	0.478274i	0.904579	+	0.426305i	$0.140185\pi$
$8$	1.13787	+	2.58945i	0.402298	+	0.915509i
$9$	0.951057	+	0.309017i	0.317019	+	0.103006i
$10$	1.93889	−	2.49814i	0.613131	−	0.789981i
$11$	2.45369	−	0.797253i	0.739816	−	0.240381i	0.0852225	−	0.996362i	$-0.472840\pi$
$11$	2.45369	−	0.797253i	0.739816	−	0.240381i	0.654593	+	0.755981i	$0.272840\pi$
$12$	1.98587	−	0.237314i	0.573271	−	0.0685068i
$13$	0.719314	+	1.41173i	0.199502	+	0.391544i	0.968984	−	0.247124i	$-0.0794856\pi$
$13$	0.719314	+	1.41173i	0.199502	+	0.391544i	−0.769482	+	0.638668i	$0.779486\pi$
$14$	−2.01871	−	1.52633i	−0.539523	−	0.407930i
$15$	−1.29138	−	1.82547i	−0.333432	−	0.471334i
$16$	3.40584	−	2.09768i	0.851460	−	0.524420i
$17$	−0.968521	−	6.11500i	−0.234901	−	1.48310i	−0.769852	−	0.638222i	$-0.779670\pi$
$17$	−0.968521	−	6.11500i	−0.234901	−	1.48310i	0.534952	−	0.844883i	$-0.320330\pi$
$18$	0.247828	−	1.39233i	0.0584137	−	0.328175i
$19$	4.18468	+	3.04035i	0.960031	+	0.697503i	0.953158	−	0.302473i	$-0.0978122\pi$
$19$	4.18468	+	3.04035i	0.960031	+	0.697503i	0.00687313	+	0.999976i	$0.497812\pi$
$20$	−3.87653	−	2.22991i	−0.866819	−	0.498623i
$21$	−1.44777	+	1.05186i	−0.315928	+	0.229535i
$22$	−1.59414	−	3.28194i	−0.339872	−	0.699712i
$23$	2.77576	−	5.44773i	0.578786	−	1.13593i	−0.397126	−	0.917764i	$-0.629992\pi$
$23$	2.77576	−	5.44773i	0.578786	−	1.13593i	0.975912	−	0.218167i	$-0.0700077\pi$
$24$	−0.718783	−	2.73557i	−0.146721	−	0.558396i
$25$	−0.126271	+	4.99841i	−0.0252543	+	0.999681i
$26$	1.83756	−	1.28225i	0.360376	−	0.251470i
$27$	−0.891007	−	0.453990i	−0.171474	−	0.0873705i
$28$	−1.74529	+	3.12470i	−0.329829	+	0.590512i
$29$	−2.10923	−	2.90311i	−0.391674	−	0.539093i	0.566956	−	0.823748i	$-0.308121\pi$
$29$	−2.10923	−	2.90311i	−0.391674	−	0.539093i	−0.958630	+	0.284655i	$0.908121\pi$
$30$	−2.30582	+	2.16407i	−0.420982	+	0.395104i
$31$	−3.46723	+	4.77223i	−0.622733	+	0.857119i	−0.997548	−	0.0699809i	$-0.977706\pi$
$31$	−3.46723	+	4.77223i	−0.622733	+	0.857119i	0.374815	+	0.927100i	$0.377706\pi$
$32$	−3.60098	−	4.36267i	−0.636570	−	0.771219i
$33$	−2.54820	+	0.403595i	−0.443585	+	0.0702569i
$34$	−8.37726	+	2.54637i	−1.43669	+	0.436699i
$35$	4.00121	+	0.0505318i	0.676328	+	0.00854144i
$36$	−1.99855	−	0.0762659i	−0.333091	−	0.0127110i
$37$	8.50512	−	4.33357i	1.39823	−	0.712435i	0.417662	−	0.908602i	$-0.362850\pi$
$37$	8.50512	−	4.33357i	1.39823	−	0.712435i	0.980570	+	0.196167i	$0.0628495\pi$
$38$	3.44467	−	6.45327i	0.558799	−	1.04686i
$39$	−0.489614	−	1.50688i	−0.0784010	−	0.241293i
$40$	−2.36939	+	5.86396i	−0.374633	+	0.927173i
$41$	−2.24529	+	6.91028i	−0.350655	+	1.07920i	0.607831	+	0.794066i	$0.292040\pi$
$41$	−2.24529	+	6.91028i	−0.350655	+	1.07920i	−0.958486	+	0.285139i	$0.907960\pi$
$42$	1.75509	+	1.82334i	0.270816	+	0.281347i
$43$	1.96263	+	1.96263i	0.299299	+	0.299299i	0.840739	−	0.541440i	$-0.182121\pi$
$43$	1.96263	+	1.96263i	0.299299	+	0.299299i	−0.541440	+	0.840739i	$0.682121\pi$
$44$	−4.28709	+	2.87154i	−0.646303	+	0.432901i
$45$	0.989913	+	2.00501i	0.147568	+	0.298890i
$46$	−8.17104	−	2.82831i	−1.20475	−	0.417012i
$47$	0.00589566	−	0.0372238i	0.000859971	−	0.00542964i	−0.987255	−	0.159149i	$-0.949125\pi$
$47$	0.00589566	−	0.0372238i	0.000859971	−	0.00542964i	0.988115	+	0.153719i	$0.0491251\pi$
$48$	−3.69206	+	1.53906i	−0.532902	+	0.222145i
$49$			3.79756i			0.542508i
$50$	7.02617	−	0.795586i	0.993650	−	0.112513i
$51$			6.19122i			0.866944i
$52$	−2.15364	−	2.32453i	−0.298656	−	0.322354i
$53$	−1.13623	+	7.17385i	−0.156073	+	0.985404i	0.777985	+	0.628283i	$0.216242\pi$
$53$	−1.13623	+	7.17385i	−0.156073	+	0.985404i	−0.934058	+	0.357122i	$0.883758\pi$
$54$	−0.462586	+	1.33642i	−0.0629499	+	0.181864i
$55$	5.10671	+	2.68376i	0.688589	+	0.361878i
$56$	4.71653	+	1.83682i	0.630273	+	0.245455i
$57$	−3.65754	−	3.65754i	−0.484453	−	0.484453i
$58$	−3.65622	+	3.51935i	−0.480085	+	0.462114i
$59$	2.91440	−	8.96960i	0.379422	−	1.16774i	−0.561024	−	0.827800i	$-0.689592\pi$
$59$	2.91440	−	8.96960i	0.379422	−	1.16774i	0.940446	−	0.339942i	$-0.110408\pi$
$60$	3.47997	+	2.80888i	0.449262	+	0.362625i
$61$	−0.911425	−	2.80508i	−0.116696	−	0.359153i	0.875601	−	0.483035i	$-0.160466\pi$
$61$	−0.911425	−	2.80508i	−0.116696	−	0.359153i	−0.992297	+	0.123882i	$0.960466\pi$
$62$	7.35935	+	3.92832i	0.934639	+	0.498898i
$63$	1.59449	−	0.812433i	0.200887	−	0.102357i
$64$	−5.41050	+	5.89292i	−0.676313	+	0.736615i
$65$	−1.13727	+	3.35539i	−0.141061	+	0.416184i
$66$	1.06111	+	3.49091i	0.130613	+	0.429702i
$67$	−6.72692	+	1.06544i	−0.821825	+	0.130164i	−0.553166	−	0.833071i	$-0.686580\pi$
$67$	−6.72692	+	1.06544i	−0.821825	+	0.130164i	−0.268659	+	0.963235i	$0.586580\pi$
$68$	5.19671	+	11.2392i	0.630194	+	1.36295i
$69$	−3.59380	+	4.94644i	−0.432642	+	0.595481i
$70$	−0.707670	−	5.61459i	−0.0845827	−	0.671072i
$71$	1.78138	+	2.45186i	0.211411	+	0.290982i	0.901533	−	0.432711i	$-0.142443\pi$
$71$	1.78138	+	2.45186i	0.211411	+	0.290982i	−0.690122	+	0.723693i	$0.742443\pi$
$72$	0.281995	+	2.81433i	0.0332335	+	0.331672i
$73$	6.68488	+	3.40612i	0.782406	+	0.398656i	0.799095	−	0.601205i	$-0.205312\pi$
$73$	6.68488	+	3.40612i	0.782406	+	0.398656i	−0.0166887	+	0.999861i	$0.505312\pi$
$74$	−7.72504	−	11.0706i	−0.898017	−	1.28693i
$75$	0.906640	−	4.91711i	0.104690	−	0.567779i
$76$	−9.70971	−	3.56967i	−1.11378	−	0.409469i
$77$	2.09605	−	4.11372i	0.238867	−	0.468802i
$78$	−2.01553	+	0.979005i	−0.228214	+	0.110851i
$79$	−3.75981	+	2.73166i	−0.423012	+	0.307336i	−0.778848	−	0.627212i	$-0.784196\pi$
$79$	−3.75981	+	2.73166i	−0.423012	+	0.307336i	0.355837	+	0.934548i	$0.384196\pi$
$80$	8.67501	+	2.17810i	0.969896	+	0.243519i
$81$	0.809017	+	0.587785i	0.0898908	+	0.0653095i
$82$	10.1165	+	1.80070i	1.11718	+	0.198854i
$83$	−1.32439	−	8.36187i	−0.145371	−	0.917835i	−0.947284	−	0.320395i	$-0.896185\pi$
$83$	−1.32439	−	8.36187i	−0.145371	−	0.917835i	0.801913	−	0.597440i	$-0.203815\pi$
$84$	2.21261	−	2.81320i	0.241416	−	0.306946i
$85$	8.27808	−	11.0964i	0.897884	−	1.20357i
$86$	2.36735	−	3.13103i	0.255278	−	0.337628i
$87$	1.62912	+	3.19732i	0.174660	+	0.342789i
$88$	4.85643	+	5.44654i	0.517697	+	0.580603i
$89$	−2.83952	+	0.922614i	−0.300988	+	0.0977969i	−0.455618	−	0.890176i	$-0.650582\pi$
$89$	−2.83952	+	0.922614i	−0.300988	+	0.0977969i	0.154630	+	0.987973i	$0.450582\pi$
$90$	2.61596	−	1.77672i	0.275747	−	0.187283i
$91$	2.69661	+	0.876183i	0.282682	+	0.0918489i
$92$	−2.37209	+	11.9960i	−0.247307	+	1.25067i
$93$	4.17109	−	4.17109i	0.432521	−	0.432521i
$94$	−0.0532888	−	0.00101640i	−0.00549632	−	0.000104834i
$95$	1.66494	+	11.4457i	0.170819	+	1.17430i
$96$	2.87418	+	4.87228i	0.293345	+	0.497275i
$97$	−12.1121	−	1.91837i	−1.22980	−	0.194781i	−0.492479	−	0.870324i	$-0.663909\pi$
$97$	−12.1121	−	1.91837i	−1.22980	−	0.194781i	−0.737320	+	0.675543i	$0.763909\pi$
$98$	5.31949	−	0.738832i	0.537350	−	0.0746333i
$99$	2.57996			0.259296
$100$	−2.48140	−	9.68724i	−0.248140	−	0.968724i
$101$	−18.4944			−1.84026			−0.920129	−	0.391616i	$-0.871916\pi$
$101$	−18.4944			−1.84026			−0.920129	+	0.391616i	$0.871916\pi$
$102$	8.67246	−	1.20453i	0.858702	−	0.119266i
$103$	−19.8981	−	3.15155i	−1.96062	−	0.310532i	−0.999396	−	0.0347649i	$-0.988932\pi$
$103$	−19.8981	−	3.15155i	−1.96062	−	0.310532i	−0.961225	−	0.275767i	$-0.911068\pi$
$104$	−2.83712	+	3.46900i	−0.278203	+	0.340163i
$105$	−3.94404	−	0.675836i	−0.384899	−	0.0659549i
$106$	10.2700	+	0.195883i	0.997506	+	0.0190258i
$107$	−9.72003	+	9.72003i	−0.939671	+	0.939671i	−0.998281	−	0.0586099i	$-0.981333\pi$
$107$	−9.72003	+	9.72003i	−0.939671	+	0.939671i	0.0586099	+	0.998281i	$0.481333\pi$
$108$	1.96201	+	0.387968i	0.188794	+	0.0373323i
$109$	9.37929	+	3.04752i	0.898373	+	0.291899i	0.721565	−	0.692346i	$-0.243423\pi$
$109$	9.37929	+	3.04752i	0.898373	+	0.291899i	0.176808	+	0.984245i	$0.443423\pi$
$110$	2.76579	−	7.67545i	0.263708	−	0.731825i
$111$	−9.07833	+	2.94973i	−0.861677	+	0.279976i
$112$	1.65533	−	6.96412i	0.156414	−	0.658047i
$113$	−2.97994	−	5.84847i	−0.280330	−	0.550178i	0.707313	−	0.706900i	$-0.249907\pi$
$113$	−2.97994	−	5.84847i	−0.280330	−	0.550178i	−0.987643	+	0.156723i	$0.949907\pi$
$114$	−4.41177	+	5.83496i	−0.413201	+	0.546494i
$115$	13.0548	−	4.06023i	1.21737	−	0.378618i
$116$	5.64113	+	4.43680i	0.523766	+	0.411947i
$117$	0.247859	+	1.56492i	0.0229145	+	0.144677i
$118$	−13.1313	−	2.33732i	−1.20884	−	0.215168i
$119$	−8.96344	−	6.51232i	−0.821677	−	0.596983i
$120$	3.25754	−	5.42111i	0.297372	−	0.494877i
$121$	−3.51420	+	2.55321i	−0.319473	+	0.232110i
$122$	−3.75194	+	1.82243i	−0.339684	+	0.164995i
$123$	3.29865	−	6.47397i	0.297429	−	0.583738i
$124$	4.07087	−	11.0730i	0.365575	−	0.994386i
$125$	−8.19946	+	7.60058i	−0.733382	+	0.679817i
$126$	−1.44824	−	2.07545i	−0.129020	−	0.184895i
$127$	−15.0362	−	7.66131i	−1.33424	−	0.679831i	−0.366182	−	0.930543i	$-0.619335\pi$
$127$	−15.0362	−	7.66131i	−1.33424	−	0.679831i	−0.968062	+	0.250712i	$0.919335\pi$
$128$	9.30724	+	6.43236i	0.822652	+	0.568545i
$129$	−1.63145	−	2.24550i	−0.143641	−	0.197705i
$130$	4.92138	+	0.940250i	0.431633	+	0.0824653i
$131$	−2.64378	+	3.63885i	−0.230988	+	0.317928i	−0.908740	−	0.417363i	$-0.862954\pi$
$131$	−2.64378	+	3.63885i	−0.230988	+	0.317928i	0.677752	+	0.735291i	$0.262954\pi$
$132$	4.68351	−	2.16554i	0.407648	−	0.188486i
$133$	9.14250	−	1.44803i	0.792756	−	0.125560i
$134$	2.80119	+	9.21557i	0.241986	+	0.796104i
$135$	−0.664073	−	2.13518i	−0.0571543	−	0.183767i
$136$	14.7324	−	9.46601i	1.26330	−	0.811704i
$137$	15.3805	−	7.83674i	1.31404	−	0.669538i	0.350367	−	0.936613i	$-0.386057\pi$
$137$	15.3805	−	7.83674i	1.31404	−	0.669538i	0.963676	+	0.267074i	$0.0860569\pi$
$138$	7.62800	+	4.07172i	0.649338	+	0.346608i
$139$	4.36271	+	13.4270i	0.370040	+	1.13887i	0.946764	+	0.321928i	$0.104331\pi$
$139$	4.36271	+	13.4270i	0.370040	+	1.13887i	−0.576724	+	0.816939i	$0.695669\pi$
$140$	−7.72705	+	2.08363i	−0.653055	+	0.176098i
$141$	−0.0116462	+	0.0358432i	−0.000980783	+	0.00301854i
$142$	3.08791	−	2.97232i	0.259131	−	0.249431i
$143$	2.89048	+	2.89048i	0.241714	+	0.241714i
$144$	3.88736	−	0.942552i	0.323947	−	0.0785460i
$145$	1.35521	−	7.90872i	0.112544	−	0.656783i
$146$	3.47060	−	10.0266i	0.287229	−	0.829811i
$147$	0.594069	−	3.75080i	0.0489980	−	0.309361i
$148$	−14.0044	+	12.9748i	−1.15115	+	1.06652i
$149$		−	17.2353i		−	1.41197i	−0.708227	−	0.705985i	$-0.750505\pi$
$149$		−	17.2353i		−	1.41197i	0.708227	−	0.705985i	$-0.249495\pi$
$150$	−7.06412	−	0.313344i	−0.576783	−	0.0255844i
$151$			9.16179i			0.745576i	0.927917	+	0.372788i	$0.121598\pi$
$151$			9.16179i			0.745576i	−0.927917	+	0.372788i	$0.878402\pi$
$152$	−3.11120	+	14.2955i	−0.252352	+	1.15952i
$153$	0.968521	−	6.11500i	0.0783002	−	0.494368i
$154$	−6.17017	−	2.13573i	−0.497206	−	0.172102i
$155$	−13.0528	+	1.89871i	−1.04842	+	0.152508i
$156$	1.76349	+	2.63281i	0.141192	+	0.210794i
$157$	−3.35617	−	3.35617i	−0.267851	−	0.267851i	0.560383	−	0.828234i	$-0.310654\pi$
$157$	−3.35617	−	3.35617i	−0.267851	−	0.267851i	−0.828234	+	0.560383i	$0.810654\pi$
$158$	4.55791	+	4.73516i	0.362608	+	0.376709i
$159$	2.24447	−	6.90778i	0.177998	−	0.547823i
$160$	1.36325	−	12.5754i	0.107774	−	0.994175i
$161$	−3.38110	−	10.4060i	−0.266468	−	0.820104i
$162$	0.665952	−	1.24760i	0.0523222	−	0.0980208i
$163$	4.84163	−	2.46694i	0.379226	−	0.193225i	−0.253978	−	0.967210i	$-0.581739\pi$
$163$	4.84163	−	2.46694i	0.379226	−	0.193225i	0.633204	+	0.773985i	$0.281739\pi$
$164$	0.554140	−	14.5212i	0.0432711	−	1.13392i
$165$	−4.62400	−	3.44959i	−0.359978	−	0.268550i
$166$	−11.4554	+	3.48200i	−0.889109	+	0.270256i
$167$	−16.3746	+	2.59348i	−1.26710	+	0.200690i	−0.753563	−	0.657375i	$-0.771667\pi$
$167$	−16.3746	+	2.59348i	−1.26710	+	0.200690i	−0.513541	+	0.858065i	$0.671667\pi$
$168$	−4.37112	−	2.55203i	−0.337239	−	0.196894i
$169$	6.16563	−	8.48626i	0.474279	−	0.652789i
$170$	−17.1540	−	9.43681i	−1.31565	−	0.723771i
$171$	3.04035	+	4.18468i	0.232501	+	0.320010i
$172$	−4.84643	−	2.70696i	−0.369537	−	0.206403i
$173$	17.8380	+	9.08892i	1.35620	+	0.691018i	0.972601	−	0.232483i	$-0.0746849\pi$
$173$	17.8380	+	9.08892i	1.35620	+	0.691018i	0.383598	+	0.923500i	$0.374685\pi$
$174$	4.16175	−	2.90407i	0.315501	−	0.220157i
$175$	6.16517	+	6.48473i	0.466043	+	0.490200i
$176$	6.68449	−	7.86238i	0.503863	−	0.592649i
$177$	−4.28167	+	8.40325i	−0.321830	+	0.631627i
$178$	1.84481	+	3.79800i	0.138274	+	0.284672i
$179$	16.1069	−	11.7023i	1.20389	−	0.874674i	0.209224	−	0.977868i	$-0.432906\pi$
$179$	16.1069	−	11.7023i	1.20389	−	0.874674i	0.994661	+	0.103194i	$0.0329062\pi$
$180$	−2.99772	−	3.31868i	−0.223437	−	0.247360i
$181$	−8.23772	−	5.98505i	−0.612305	−	0.444866i	0.237920	−	0.971285i	$-0.423534\pi$
$181$	−8.23772	−	5.98505i	−0.612305	−	0.444866i	−0.850225	+	0.526419i	$0.823534\pi$
$182$	0.702690	−	3.94779i	0.0520868	−	0.292630i
$183$	0.461393	+	2.91312i	0.0341071	+	0.215344i
$184$	17.2651	+	0.988871i	1.27280	+	0.0729006i
$185$	20.2148	+	6.85161i	1.48622	+	0.503741i
$186$	−6.65422	−	5.03122i	−0.487911	−	0.368907i
$187$	−7.25165	−	14.2322i	−0.530293	−	1.04076i
$188$	0.00894385	+	0.0748430i	0.000652297	+	0.00545849i
$189$	−1.70195	+	0.552997i	−0.123799	+	0.0402246i
$190$	15.7088	−	4.55901i	1.13964	−	0.330745i
$191$	−12.1738	−	3.95551i	−0.880866	−	0.286211i	−0.166549	−	0.986033i	$-0.553262\pi$
$191$	−12.1738	−	3.95551i	−0.880866	−	0.286211i	−0.714317	+	0.699823i	$0.753262\pi$
$192$	6.26574	−	4.97398i	0.452191	−	0.358966i
$193$	3.19755	−	3.19755i	0.230165	−	0.230165i	−0.582597	−	0.812761i	$-0.697963\pi$
$193$	3.19755	−	3.19755i	0.230165	−	0.230165i	0.812761	+	0.582597i	$0.197963\pi$
$194$	−0.330723	+	17.3395i	−0.0237445	+	1.24490i
$195$	1.64817	−	3.13617i	0.118028	−	0.224586i
$196$	−2.06986	−	7.30763i	−0.147847	−	0.521973i
$197$	−11.4480	−	1.81319i	−0.815639	−	0.129184i	−0.265343	−	0.964154i	$-0.585485\pi$
$197$	−11.4480	−	1.81319i	−0.815639	−	0.129184i	−0.550296	+	0.834970i	$0.685485\pi$
$198$	−0.501944	−	3.61393i	−0.0356716	−	0.256831i
$199$	8.34981			0.591902			0.295951	−	0.955203i	$-0.404363\pi$
$199$	8.34981			0.591902			0.295951	+	0.955203i	$0.404363\pi$
$200$	−13.0868	+	5.36057i	−0.925376	+	0.379049i
$201$	6.81078			0.480395
$202$	3.59816	+	25.9063i	0.253166	+	1.82276i
$203$	−6.34258	−	1.00457i	−0.445162	−	0.0705067i
$204$	−3.37453	−	11.9138i	−0.236265	−	0.834129i
$205$	−14.5682	+	7.19261i	−1.01749	+	0.502354i
$206$	−0.543321	+	28.4858i	−0.0378550	+	1.98470i
$207$	4.32335	−	4.32335i	0.300493	−	0.300493i
$208$	5.41123	+	3.29924i	0.375201	+	0.228761i
$209$	12.6918	+	4.12383i	0.877912	+	0.285251i
$210$	−0.179358	+	5.65617i	−0.0123769	+	0.390313i
$211$	14.6855	−	4.77161i	1.01099	−	0.328491i	0.243743	−	0.969840i	$-0.421625\pi$
$211$	14.6855	−	4.77161i	1.01099	−	0.328491i	0.767250	+	0.641348i	$0.221625\pi$
$212$	−1.72368	−	14.4239i	−0.118383	−	0.990639i
$213$	−1.37589	−	2.70034i	−0.0942745	−	0.185024i
$214$	15.5066	+	11.7244i	1.06001	+	0.801465i
$215$	−0.0783752	+	6.20590i	−0.00534515	+	0.423239i
$216$	0.161735	−	2.82380i	0.0110047	−	0.192135i
$217$	1.65134	+	10.4262i	0.112100	+	0.707775i
$218$	2.44408	−	13.7311i	0.165534	−	0.929988i
$219$	−6.06975	−	4.40993i	−0.410155	−	0.297995i
$220$	−11.2896	−	2.38094i	−0.761146	−	0.160523i
$221$	7.93607	−	5.76589i	0.533838	−	0.387856i
$222$	5.89811	+	12.1427i	0.395855	+	0.814967i
$223$	−3.75855	+	7.37657i	−0.251691	+	0.493972i	−0.981936	−	0.189214i	$-0.939406\pi$
$223$	−3.75855	+	7.37657i	−0.251691	+	0.493972i	0.730245	+	0.683186i	$0.239406\pi$
$224$	−10.0772	−	0.963835i	−0.673309	−	0.0643990i
$225$	−1.66468	+	4.71475i	−0.110979	+	0.314316i
$226$	−7.61258	+	5.31205i	−0.506381	+	0.353353i
$227$	24.4631	+	12.4646i	1.62367	+	0.827303i	0.998919	+	0.0464825i	$0.0148012\pi$
$227$	24.4631	+	12.4646i	1.62367	+	0.827303i	0.624755	+	0.780821i	$0.285199\pi$
$228$	9.03175	+	5.04465i	0.598142	+	0.334090i
$229$	10.4537	+	14.3883i	0.690803	+	0.950808i	1.00000		0.000189558i	$-6.03382e-5\pi$
$229$	10.4537	+	14.3883i	0.690803	+	0.950808i	−0.309197	+	0.950998i	$0.600060\pi$
$230$	−8.22731	−	17.4968i	−0.542492	−	1.15370i
$231$	−2.71377	+	3.73518i	−0.178553	+	0.245757i
$232$	5.11742	−	8.76511i	0.335975	−	0.575457i
$233$	−5.32769	+	0.843823i	−0.349029	+	0.0552807i	−0.328488	−	0.944508i	$-0.606539\pi$
$233$	−5.32769	+	0.843823i	−0.349029	+	0.0552807i	−0.0205411	+	0.999789i	$0.506539\pi$
$234$	2.14386	−	0.651654i	0.140149	−	0.0426000i
$235$	0.0687979	−	0.0486692i	0.00448788	−	0.00317483i
$236$	−0.719278	+	18.8487i	−0.0468210	+	1.22694i
$237$	4.14085	−	2.10987i	0.268977	−	0.137051i
$238$	−7.37837	+	13.8227i	−0.478268	+	0.895992i
$239$	3.11661	+	9.59193i	0.201596	+	0.620450i	0.999836	+	0.0181100i	$0.00576491\pi$
$239$	3.11661	+	9.59193i	0.201596	+	0.620450i	−0.798240	+	0.602340i	$0.794235\pi$
$240$	−8.22748	−	3.50836i	−0.531082	−	0.226463i
$241$	−1.59822	+	4.91881i	−0.102950	+	0.316848i	−0.989244	−	0.146275i	$-0.953271\pi$
$241$	−1.59822	+	4.91881i	−0.102950	+	0.316848i	0.886294	+	0.463124i	$0.153271\pi$
$242$	4.26016	+	4.42583i	0.273854	+	0.284503i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	3.28276	+	4.90103i	0.210157	+	0.313756i
$245$	−6.07981	+	5.92816i	−0.388425	+	0.378736i
$246$	−9.71028	−	3.36110i	−0.619105	−	0.214296i
$247$	−1.28206	+	8.09461i	−0.0815756	+	0.515048i
$248$	−16.3027	−	3.54804i	−1.03522	−	0.225300i
$249$			8.46610i			0.536518i
$250$	12.2419	+	10.0068i	0.774245	+	0.632886i
$251$		−	13.6267i		−	0.860111i	−0.902803	−	0.430055i	$-0.858494\pi$
$251$		−	13.6267i		−	0.860111i	0.902803	−	0.430055i	$-0.141506\pi$
$252$	−2.62545	+	2.43244i	−0.165388	+	0.153229i
$253$	2.46764	−	15.5800i	0.155139	−	0.979508i
$254$	−7.80635	+	22.5527i	−0.489814	+	1.41508i
$255$	−9.91202	+	9.66478i	−0.620715	+	0.605232i
$256$	7.19947	−	14.2887i	0.449967	−	0.893045i
$257$	10.7300	+	10.7300i	0.669319	+	0.669319i	0.957558	−	0.288239i	$-0.0930698\pi$
$257$	10.7300	+	10.7300i	0.669319	+	0.669319i	−0.288239	+	0.957558i	$0.593070\pi$
$258$	−2.82801	+	2.72215i	−0.176064	+	0.169474i
$259$	5.27865	−	16.2460i	0.327999	−	1.00948i
$260$	0.359594	−	7.07663i	0.0223011	−	0.438874i
$261$	−1.10889	−	3.41281i	−0.0686384	−	0.211247i
$262$	5.61154	+	2.99536i	0.346682	+	0.185054i
$263$	−16.1259	+	8.21657i	−0.994367	+	0.506655i	−0.873923	−	0.486065i	$-0.838432\pi$
$263$	−16.1259	+	8.21657i	−0.994367	+	0.506655i	−0.120444	+	0.992720i	$0.538432\pi$
$264$	−3.94461	−	6.13920i	−0.242774	−	0.377841i
$265$	−13.2589	+	9.37963i	−0.814487	+	0.576186i
$266$	−3.80707	−	12.5248i	−0.233426	−	0.767945i
$267$	2.94888	−	0.467057i	0.180469	−	0.0285835i
$268$	12.3639	−	5.71674i	0.755244	−	0.349206i
$269$	−9.43653	+	12.9883i	−0.575355	+	0.791908i	−0.993177	−	0.116621i	$-0.962794\pi$
$269$	−9.43653	+	12.9883i	−0.575355	+	0.791908i	0.417821	+	0.908529i	$0.362794\pi$
$270$	−2.86170	+	1.34562i	−0.174157	+	0.0818919i
$271$	1.76045	+	2.42305i	0.106940	+	0.147190i	0.859132	−	0.511753i	$-0.171004\pi$
$271$	1.76045	+	2.42305i	0.106940	+	0.147190i	−0.752193	+	0.658943i	$0.771004\pi$
$272$	−16.1259	−	18.7950i	−0.977779	−	1.13962i
$273$	−2.52635	−	1.28724i	−0.152902	−	0.0779072i
$274$	−13.9698	−	20.0198i	−0.843946	−	1.20944i
$275$	3.67516	+	12.3652i	0.221621	+	0.745650i
$276$	4.21947	−	11.4772i	0.253982	−	0.690847i
$277$	−7.87265	+	15.4509i	−0.473022	+	0.928357i	0.524036	+	0.851696i	$0.324426\pi$
$277$	−7.87265	+	15.4509i	−0.473022	+	0.928357i	−0.997057	+	0.0766608i	$0.975574\pi$
$278$	17.9594	−	8.72344i	1.07713	−	0.523197i
$279$	−4.77223	+	3.46723i	−0.285706	+	0.207578i
$280$	4.42201	+	10.4184i	0.264266	+	0.622620i
$281$	−8.05625	−	5.85321i	−0.480595	−	0.349173i	0.320961	−	0.947092i	$-0.395994\pi$
$281$	−8.05625	−	5.85321i	−0.480595	−	0.349173i	−0.801556	+	0.597920i	$0.795994\pi$
$282$	0.0524738	+	0.00934010i	0.00312477	+	0.000556195i
$283$	−1.77033	−	11.1775i	−0.105235	−	0.664431i	−0.982758	−	0.184896i	$-0.940805\pi$
$283$	−1.77033	−	11.1775i	−0.105235	−	0.664431i	0.877523	−	0.479535i	$-0.159195\pi$
$284$	−4.76429	−	3.74716i	−0.282709	−	0.222353i
$285$	0.146059	−	11.5652i	0.00865180	−	0.685066i
$286$	3.48653	−	4.61125i	0.206163	−	0.272669i
$287$	5.90306	+	11.5854i	0.348446	+	0.683865i
$288$	−2.07660	−	5.26191i	−0.122365	−	0.310061i
$289$	−20.2872	+	6.59171i	−1.19337	+	0.387748i
$290$	−11.3419	−	0.359655i	−0.666021	−	0.0211197i
$291$	11.6629	+	3.78951i	0.683691	+	0.222145i
$292$	−14.7202	−	2.91078i	−0.861435	−	0.170340i
$293$	−19.4066	+	19.4066i	−1.13375	+	1.13375i	−0.144199	+	0.989549i	$0.546060\pi$
$293$	−19.4066	+	19.4066i	−1.13375	+	1.13375i	−0.989549	+	0.144199i	$0.953940\pi$
$294$	−5.36958	−	0.102416i	−0.313160	−	0.00597303i
$295$	18.9097	−	9.33606i	1.10096	−	0.543566i
$296$	20.8993	+	17.0925i	1.21475	+	0.993483i
$297$	−2.54820	−	0.403595i	−0.147862	−	0.0234190i
$298$	−24.1426	+	3.35320i	−1.39854	+	0.194246i
$299$	9.68738			0.560236
$300$	0.935435	+	9.95615i	0.0540074	+	0.574819i
$301$	4.96701			0.286294
$302$	12.8335	−	1.78247i	0.738487	−	0.102570i
$303$	18.2667	+	2.89315i	1.04939	+	0.166207i
$304$	20.6300	+	1.57681i	1.18321	+	0.0904361i
$305$	3.06809	−	5.83803i	0.175679	−	0.334284i
$306$	−8.75412	−	0.166971i	−0.500440	−	0.00954509i
$307$	3.83564	−	3.83564i	0.218912	−	0.218912i	−0.589128	−	0.808040i	$-0.700529\pi$
$307$	3.83564	−	3.83564i	0.218912	−	0.218912i	0.808040	+	0.589128i	$0.200529\pi$
$308$	−1.79123	+	9.05848i	−0.102065	+	0.516155i
$309$	19.1601	+	6.22550i	1.08998	+	0.354157i
$310$	5.19913	+	17.9145i	0.295290	+	1.01747i
$311$	−7.89005	+	2.56363i	−0.447404	+	0.145370i	−0.524049	−	0.851688i	$-0.675579\pi$
$311$	−7.89005	+	2.56363i	−0.447404	+	0.145370i	0.0766452	+	0.997058i	$0.475579\pi$
$312$	3.34487	−	2.98246i	0.189366	−	0.168849i
$313$	−8.49876	−	16.6797i	−0.480378	−	0.942795i	−0.996282	−	0.0861488i	$-0.972544\pi$
$313$	−8.49876	−	16.6797i	−0.480378	−	0.942795i	0.515904	−	0.856646i	$-0.327456\pi$
$314$	−4.04825	+	5.35417i	−0.228456	+	0.302153i
$315$	3.78976	+	1.28450i	0.213529	+	0.0723734i
$316$	5.74609	−	7.30582i	0.323243	−	0.410984i
$317$	−0.165705	−	1.04622i	−0.00930692	−	0.0587616i	0.982598	−	0.185746i	$-0.0594702\pi$
$317$	−0.165705	−	1.04622i	−0.00930692	−	0.0587616i	−0.991905	+	0.126984i	$0.959470\pi$
$318$	−10.1129	−	1.80005i	−0.567101	−	0.100942i
$319$	−7.48991	−	5.44174i	−0.419354	−	0.304679i
$320$	−17.8805	+	0.537016i	−0.999549	+	0.0300201i
$321$	11.1209	−	8.07981i	0.620709	−	0.450971i
$322$	−13.9185	+	6.76066i	−0.775648	+	0.376757i
$323$	14.5388	−	28.5339i	0.808959	−	1.58767i
$324$	−1.87716	−	0.690118i	−0.104287	−	0.0383399i
$325$	−7.14724	+	3.41716i	−0.396458	+	0.189550i
$326$	−4.39756	−	6.30205i	−0.243559	−	0.349038i
$327$	−8.78708	−	4.47724i	−0.485927	−	0.247592i
$328$	−20.4487	+	2.04895i	−1.12909	+	0.113134i
$329$	−0.0396424	−	0.0545630i	−0.00218555	−	0.00300816i
$330$	−3.93244	+	7.14829i	−0.216474	+	0.393500i
$331$	18.5262	−	25.4991i	1.01829	−	1.40156i	0.104899	−	0.994483i	$-0.466548\pi$
$331$	18.5262	−	25.4991i	1.01829	−	1.40156i	0.913394	−	0.407077i	$-0.133452\pi$
$332$	7.10617	+	15.3689i	0.390002	+	0.843476i
$333$	9.42800	−	1.49325i	0.516651	−	0.0818295i
$334$	6.81862	+	22.4324i	0.373098	+	1.22745i
$335$	−12.2068	−	9.10647i	−0.666928	−	0.497539i
$336$	−2.72438	+	6.61943i	−0.148627	+	0.361119i
$337$	−18.0272	+	9.18532i	−0.982004	+	0.500356i	−0.869840	−	0.493333i	$-0.835778\pi$
$337$	−18.0272	+	9.18532i	−0.982004	+	0.500356i	−0.112164	+	0.993690i	$0.535778\pi$
$338$	−13.0868	−	6.98557i	−0.711830	−	0.379965i
$339$	2.02835	+	6.24263i	0.110165	+	0.339053i
$340$	−9.88139	+	25.8647i	−0.535894	+	1.40271i
$341$	−4.70284	+	14.4738i	−0.254673	+	0.783803i
$342$	5.27025	−	5.07297i	0.284982	−	0.274315i
$343$	13.6632	+	13.6632i	0.737741	+	0.737741i
$344$	−2.84892	+	7.31537i	−0.153603	+	0.394418i
$345$	−13.5292	+	1.96802i	−0.728389	+	0.105955i
$346$	9.26099	−	26.7552i	0.497874	−	1.43837i
$347$	0.0503563	−	0.317937i	0.00270327	−	0.0170678i	−0.986300	−	0.164963i	$-0.947250\pi$
$347$	0.0503563	−	0.317937i	0.00270327	−	0.0170678i	0.989003	+	0.147895i	$0.0472497\pi$
$348$	−4.87761	−	5.26464i	−0.261467	−	0.282214i
$349$			1.90739i			0.102100i	0.998696	+	0.0510501i	$0.0162568\pi$
$349$			1.90739i			0.102100i	−0.998696	+	0.0510501i	$0.983743\pi$
$350$	7.88414	−	9.89760i	0.421425	−	0.529049i
$351$		−	1.58442i		−	0.0845703i
$352$	−12.3139	−	7.83376i	−0.656331	−	0.417541i
$353$	1.39657	−	8.81760i	0.0743319	−	0.469313i	−0.922242	−	0.386612i	$-0.873645\pi$
$353$	1.39657	−	8.81760i	0.0743319	−	0.469313i	0.996574	−	0.0827014i	$-0.0263548\pi$
$354$	12.6040	+	4.36273i	0.669896	+	0.231877i
$355$	−1.14456	+	6.67941i	−0.0607469	+	0.354506i
$356$	4.96120	−	3.32307i	0.262943	−	0.176122i
$357$	7.83433	+	7.83433i	0.414637	+	0.414637i
$358$	−19.5259	−	20.2853i	−1.03198	−	1.07211i
$359$	6.39407	−	19.6789i	0.337466	−	1.03861i	−0.628028	−	0.778191i	$-0.716138\pi$
$359$	6.39407	−	19.6789i	0.337466	−	1.03861i	0.965494	−	0.260424i	$-0.0838623\pi$
$360$	−4.06548	+	4.84477i	−0.214270	+	0.255342i
$361$	2.39650	+	7.37568i	0.126132	+	0.388193i
$362$	−6.78098	+	12.7035i	−0.356400	+	0.667684i
$363$	3.87034	−	1.97204i	0.203140	−	0.103505i
$364$	−5.66665	−	0.216243i	−0.297013	−	0.0113342i
$365$	4.98228	+	16.0195i	0.260785	+	0.838497i
$366$	3.99084	−	1.21306i	0.208604	−	0.0634079i
$367$	15.3559	−	2.43213i	0.801569	−	0.126956i	0.257808	−	0.966196i	$-0.417000\pi$
$367$	15.3559	−	2.43213i	0.801569	−	0.126956i	0.543761	+	0.839240i	$0.317000\pi$
$368$	−1.97382	−	24.3768i	−0.102893	−	1.27073i
$369$	−4.27079	+	5.87824i	−0.222328	+	0.306009i
$370$	5.66462	−	29.6493i	0.294490	−	1.54139i
$371$	7.63997	+	10.5155i	0.396648	+	0.545939i
$372$	−5.75295	+	10.2999i	−0.298277	+	0.534023i
$373$	−6.75054	−	3.43957i	−0.349530	−	0.178094i	0.270407	−	0.962746i	$-0.412842\pi$
$373$	−6.75054	−	3.43957i	−0.349530	−	0.178094i	−0.619937	+	0.784652i	$0.712842\pi$
$374$	−18.5251	+	12.9268i	−0.957910	+	0.668429i
$375$	9.28750	−	6.22433i	0.479605	−	0.321423i
$376$	0.103098	−	0.0270893i	0.00531685	−	0.00139702i
$377$	2.58121	−	5.06591i	0.132939	−	0.260908i
$378$	1.10574	+	2.27645i	0.0568733	+	0.117088i
$379$	−28.3717	+	20.6132i	−1.45735	+	1.05883i	−0.473312	+	0.880895i	$0.656942\pi$
$379$	−28.3717	+	20.6132i	−1.45735	+	1.05883i	−0.984042	+	0.177935i	$0.943058\pi$
$380$	−9.44234	−	21.1175i	−0.484382	−	1.08330i
$381$	13.6525	+	9.91916i	0.699441	+	0.508174i
$382$	−3.17228	+	17.8222i	−0.162308	+	0.911864i
$383$	1.80034	+	11.3669i	0.0919932	+	0.580822i	0.990025	+	0.140892i	$0.0449970\pi$
$383$	1.80034	+	11.3669i	0.0919932	+	0.580822i	−0.898032	+	0.439931i	$0.855003\pi$
$384$	−8.18641	−	7.80914i	−0.417761	−	0.398508i
$385$	9.85801	−	3.06598i	0.502411	−	0.156257i
$386$	−5.10113	−	3.85693i	−0.259640	−	0.196313i
$387$	1.26009	+	2.47306i	0.0640539	+	0.125713i
$388$	24.3529	−	2.91021i	1.23633	−	0.147744i
$389$	−9.99966	+	3.24909i	−0.507003	+	0.164735i	−0.551339	−	0.834282i	$-0.685883\pi$
$389$	−9.99966	+	3.24909i	−0.507003	+	0.164735i	0.0443360	+	0.999017i	$0.485883\pi$
$390$	−4.71370	−	1.69855i	−0.238687	−	0.0860092i
$391$	−36.0013	−	11.6975i	−1.82066	−	0.591569i
$392$	−9.83358	+	4.32113i	−0.496671	+	0.218250i
$393$	3.18047	−	3.18047i	0.160434	−	0.160434i
$394$	−0.312590	+	16.3888i	−0.0157481	+	0.825656i
$395$	−10.2426	−	1.75513i	−0.515360	−	0.0883101i
$396$	−4.96462	+	1.40621i	−0.249481	+	0.0706648i
$397$	−6.35706	−	1.00686i	−0.319052	−	0.0505328i	−0.00514536	−	0.999987i	$-0.501638\pi$
$397$	−6.35706	−	1.00686i	−0.319052	−	0.0505328i	−0.313906	+	0.949454i	$0.601638\pi$
$398$	−1.62449	−	11.6961i	−0.0814285	−	0.586274i
$399$	−9.25647			−0.463403
$400$	10.0550	+	17.2886i	0.502750	+	0.864432i
$401$	21.4858			1.07295			0.536476	−	0.843916i	$-0.319755\pi$
$401$	21.4858			1.07295			0.536476	+	0.843916i	$0.319755\pi$
$402$	−1.32507	−	9.54031i	−0.0660884	−	0.475827i
$403$	−9.23115	−	1.46207i	−0.459836	−	0.0728309i
$404$	35.5886	−	10.0804i	1.77060	−	0.501517i
$405$	0.321880	+	2.21278i	0.0159944	+	0.109954i
$406$	−0.173185	+	9.07992i	−0.00859503	+	0.450629i
$407$	17.4140	−	17.4140i	0.863179	−	0.863179i
$408$	−16.0319	+	7.04481i	−0.793695	+	0.348770i
$409$	25.1912	+	8.18512i	1.24563	+	0.404728i	0.856351	−	0.516394i	$-0.172726\pi$
$409$	25.1912	+	8.18512i	1.24563	+	0.404728i	0.389274	+	0.921122i	$0.372726\pi$
$410$	12.9095	+	19.0073i	0.637554	+	0.938705i
$411$	−16.4171	+	5.33422i	−0.809794	+	0.263118i
$412$	40.0077	−	4.78097i	1.97104	−	0.235542i
$413$	−7.66221	−	15.0379i	−0.377033	−	0.739968i
$414$	−6.89713	−	5.21487i	−0.338975	−	0.256297i
$415$	11.3198	−	15.1736i	0.555665	−	0.744842i
$416$	3.56869	−	8.22176i	0.174969	−	0.403105i
$417$	−2.20855	−	13.9442i	−0.108153	−	0.682851i
$418$	3.30727	−	18.5806i	0.161764	−	0.908807i
$419$	24.4346	+	17.7528i	1.19371	+	0.867280i	0.993651	−	0.112504i	$-0.0358871\pi$
$419$	24.4346	+	17.7528i	1.19371	+	0.867280i	0.200058	+	0.979784i	$0.435887\pi$
$420$	7.95787	−	0.849195i	0.388304	−	0.0414365i
$421$	30.7065	−	22.3096i	1.49655	−	1.08730i	0.524814	−	0.851217i	$-0.324135\pi$
$421$	30.7065	−	22.3096i	1.49655	−	1.08730i	0.971732	−	0.236087i	$-0.0758650\pi$
$422$	−9.54105	−	19.6426i	−0.464451	−	0.956189i
$423$	0.0171099	−	0.0335800i	0.000831911	−	0.00163272i
$424$	−19.8692	+	5.22071i	−0.964934	+	0.253540i
$425$	30.6875	−	4.06891i	1.48856	−	0.197371i
$426$	−3.51486	+	2.45267i	−0.170296	+	0.118832i
$427$	−4.70284	−	2.39622i	−0.227586	−	0.115961i
$428$	13.4063	−	24.0021i	0.648019	−	1.16019i
$429$	−2.40272	−	3.30707i	−0.116005	−	0.159667i
$430$	8.70827	−	1.09760i	0.419950	−	0.0529310i
$431$	2.67391	−	3.68032i	0.128798	−	0.177275i	−0.739748	−	0.672884i	$-0.765055\pi$
$431$	2.67391	−	3.68032i	0.128798	−	0.177275i	0.868545	+	0.495609i	$0.165055\pi$
$432$	−3.98695	+	0.322830i	−0.191822	+	0.0155321i
$433$	−12.1409	+	1.92293i	−0.583456	+	0.0924104i	−0.441183	−	0.897417i	$-0.645441\pi$
$433$	−12.1409	+	1.92293i	−0.583456	+	0.0924104i	−0.142273	+	0.989827i	$0.545441\pi$
$434$	14.2834	−	4.34161i	0.685623	−	0.208404i
$435$	−2.57572	+	7.59935i	−0.123496	+	0.364361i
$436$	−19.7096	−	0.752132i	−0.943919	−	0.0360206i
$437$	28.1787	−	14.3577i	1.34797	−	0.686824i
$438$	−4.99639	+	9.36027i	−0.238737	+	0.447251i
$439$	−4.19717	−	12.9175i	−0.200320	−	0.616521i	−0.999873	−	0.0159259i	$-0.994930\pi$
$439$	−4.19717	−	12.9175i	−0.200320	−	0.616521i	0.799553	−	0.600595i	$-0.205070\pi$
$440$	−1.13869	+	16.2773i	−0.0542849	+	0.775992i
$441$	−1.17351	+	3.61169i	−0.0558814	+	0.171985i
$442$	−9.62067	−	9.99481i	−0.457609	−	0.475405i
$443$	10.9593	+	10.9593i	0.520692	+	0.520692i	0.917780	−	0.397088i	$-0.129979\pi$
$443$	10.9593	+	10.9593i	0.520692	+	0.520692i	−0.397088	+	0.917780i	$0.629979\pi$
$444$	15.8616	−	10.6243i	0.752760	−	0.504207i
$445$	−5.90970	−	3.10576i	−0.280147	−	0.147227i
$446$	11.0641	+	3.82971i	0.523900	+	0.181342i
$447$	−2.69619	+	17.0231i	−0.127526	+	0.805164i
$448$	0.610449	+	14.3033i	0.0288410	+	0.675766i
$449$		−	30.6804i		−	1.44790i	−0.689853	−	0.723950i	$-0.742325\pi$
$449$		−	30.6804i		−	1.44790i	0.689853	−	0.723950i	$-0.257675\pi$
$450$	6.92813	+	1.41456i	0.326595	+	0.0666829i
$451$			18.7458i			0.882703i
$452$	8.92201	+	9.62997i	0.419656	+	0.452956i
$453$	1.43322	−	9.04900i	0.0673386	−	0.425159i
$454$	12.7006	−	36.6922i	0.596067	−	1.72205i
$455$	2.80679	+	5.68498i	0.131584	+	0.266516i
$456$	5.30921	−	13.6328i	0.248627	−	0.638416i
$457$	−4.67954	−	4.67954i	−0.218900	−	0.218900i	0.589135	−	0.808035i	$-0.299469\pi$
$457$	−4.67954	−	4.67954i	−0.218900	−	0.218900i	−0.808035	+	0.589135i	$0.799469\pi$
$458$	18.1209	−	17.4426i	0.846734	−	0.815038i
$459$	−1.91319	+	5.88820i	−0.0893002	+	0.274838i
$460$	−22.9083	+	14.9286i	−1.06810	+	0.696051i
$461$	−2.33115	−	7.17453i	−0.108572	−	0.334151i	0.881980	−	0.471287i	$-0.156210\pi$
$461$	−2.33115	−	7.17453i	−0.108572	−	0.334151i	−0.990552	+	0.137136i	$0.956210\pi$
$462$	5.76010	+	3.07466i	0.267984	+	0.143046i
$463$	−15.1118	+	7.69983i	−0.702303	+	0.357841i	−0.768398	−	0.639972i	$-0.778946\pi$
$463$	−15.1118	+	7.69983i	−0.702303	+	0.357841i	0.0660950	+	0.997813i	$0.478946\pi$
$464$	−13.2735	−	5.46302i	−0.616206	−	0.253614i
$465$	13.1891	+	0.166567i	0.611629	+	0.00772435i
$466$	2.21853	+	7.29869i	0.102771	+	0.338105i
$467$	6.42804	−	1.01810i	0.297454	−	0.0471121i	−0.00592362	−	0.999982i	$-0.501886\pi$
$467$	6.42804	−	1.01810i	0.297454	−	0.0471121i	0.303378	+	0.952870i	$0.401886\pi$
$468$	−1.32991	−	2.87627i	−0.0614753	−	0.132956i
$469$	−7.16401	+	9.86041i	−0.330803	+	0.455311i
$470$	−0.0815591	−	0.0869010i	−0.00376204	−	0.00400844i
$471$	2.78983	+	3.83987i	0.128549	+	0.176932i
$472$	26.5425	−	2.65955i	1.22172	−	0.122416i
$473$	6.38042	+	3.25098i	0.293372	+	0.149480i
$474$	−3.76105	−	5.38988i	−0.172751	−	0.247565i
$475$	−15.7253	+	20.5328i	−0.721526	+	0.942110i
$476$	20.7979	+	7.64610i	0.953269	+	0.350459i
$477$	−3.29746	+	6.47162i	−0.150980	+	0.296315i
$478$	12.8297	−	6.23179i	0.586817	−	0.285036i
$479$	−5.30790	+	3.85642i	−0.242524	+	0.176204i	−0.702407	−	0.711775i	$-0.747891\pi$
$479$	−5.30790	+	3.85642i	−0.242524	+	0.176204i	0.459883	+	0.887980i	$0.347891\pi$
$480$	−3.31370	+	12.2074i	−0.151249	+	0.557187i
$481$	12.2357	+	8.88975i	0.557900	+	0.405338i
$482$	7.20104	+	1.28175i	0.327999	+	0.0583823i
$483$	1.71162	+	10.8068i	0.0778815	+	0.491725i
$484$	5.37073	−	6.82856i	0.244124	−	0.310389i
$485$	−15.8363	−	22.3859i	−0.719089	−	1.01649i
$486$	−0.852921	+	1.12806i	−0.0386893	+	0.0511700i
$487$	−12.8302	−	25.1807i	−0.581391	−	1.14104i	−0.975091	−	0.221806i	$-0.928805\pi$
$487$	−12.8302	−	25.1807i	−0.581391	−	1.14104i	0.393700	−	0.919239i	$-0.371195\pi$
$488$	6.22652	−	5.55190i	0.281861	−	0.251323i
$489$	−5.16794	+	1.67917i	−0.233702	+	0.0759345i
$490$	9.48683	+	7.36305i	0.428571	+	0.332629i
$491$	9.75331	+	3.16904i	0.440161	+	0.143017i	0.520710	−	0.853734i	$-0.325667\pi$
$491$	9.75331	+	3.16904i	0.440161	+	0.143017i	−0.0805490	+	0.996751i	$0.525667\pi$
$492$	−2.81894	+	14.2558i	−0.127088	+	0.642700i
$493$	−15.7097	+	15.7097i	−0.707527	+	0.707527i
$494$	11.5881	+	0.221024i	0.521373	+	0.00994436i
$495$	4.02744	+	4.13047i	0.181020	+	0.185651i
$496$	−1.79820	+	23.5266i	−0.0807416	+	1.05638i
$497$	5.35671	+	0.848420i	0.240281	+	0.0380568i
$498$	11.8590	−	1.64712i	0.531416	−	0.0738092i
$499$	−12.4397			−0.556877			−0.278438	−	0.960454i	$-0.589817\pi$
$499$	−12.4397			−0.556877			−0.278438	+	0.960454i	$0.589817\pi$
$500$	11.6355	−	19.0949i	0.520355	−	0.853950i
$501$	16.5787			0.740682
$502$	−19.0879	+	2.65114i	−0.851933	+	0.118326i
$503$	−37.7591	−	5.98046i	−1.68360	−	0.266655i	−0.759972	−	0.649956i	$-0.774787\pi$
$503$	−37.7591	−	5.98046i	−1.68360	−	0.266655i	−0.923624	+	0.383300i	$0.874787\pi$
$504$	3.91808	+	3.20441i	0.174525	+	0.142736i
$505$	−28.8705	−	29.6091i	−1.28472	−	1.31759i
$506$	−22.3041	−	0.425415i	−0.991538	−	0.0189120i
$507$	−7.41727	+	7.41727i	−0.329412	+	0.329412i
$508$	33.1098	+	6.54715i	1.46901	+	0.290483i
$509$	8.26830	+	2.68653i	0.366486	+	0.119078i	0.486470	−	0.873697i	$-0.338284\pi$
$509$	8.26830	+	2.68653i	0.366486	+	0.119078i	−0.119984	+	0.992776i	$0.538284\pi$
$510$	15.4665	+	12.0041i	0.684870	+	0.531551i
$511$	12.7691	−	4.14893i	0.564871	−	0.183538i
$512$	−21.4159	−	7.30484i	−0.946457	−	0.322831i
$513$	−2.34829	−	4.60877i	−0.103679	−	0.203482i
$514$	12.9427	−	17.1178i	0.570876	−	0.755034i
$515$	−26.0163	−	36.7762i	−1.14642	−	1.62055i
$516$	4.36330	+	3.43178i	0.192084	+	0.151076i
$517$	−0.0152106	−	0.0960359i	−0.000668961	−	0.00422366i
$518$	−23.7839	−	4.23342i	−1.04500	−	0.186006i
$519$	−16.1966	−	11.7675i	−0.710950	−	0.516536i
$520$	−9.98267	+	0.873083i	−0.437769	+	0.0382872i
$521$	−16.2717	+	11.8221i	−0.712877	+	0.517935i	−0.884100	−	0.467297i	$-0.845228\pi$
$521$	−16.2717	+	11.8221i	−0.712877	+	0.517935i	0.171224	+	0.985232i	$0.445228\pi$
$522$	−4.56481	+	2.21727i	−0.199796	+	0.0970473i
$523$	12.0208	−	23.5921i	0.525632	−	1.03161i	−0.463708	−	0.885988i	$-0.653481\pi$
$523$	12.0208	−	23.5921i	0.525632	−	1.03161i	0.989340	−	0.145623i	$-0.0465186\pi$
$524$	3.10406	−	8.44322i	0.135601	−	0.368844i
$525$	−5.07483	−	7.36934i	−0.221484	−	0.321624i
$526$	14.6469	+	20.9901i	0.638634	+	0.915212i
$527$	32.5403	+	16.5801i	1.41748	+	0.722241i
$528$	−7.83214	+	6.71989i	−0.340850	+	0.292446i
$529$	−8.45390	−	11.6358i	−0.367561	−	0.505904i
$530$	15.7183	+	16.7478i	0.682758	+	0.727476i
$531$	5.54352	−	7.62999i	0.240568	−	0.331114i
$532$	−16.8036	+	7.76957i	−0.728530	+	0.336854i
$533$	−11.3705	+	1.80092i	−0.492513	+	0.0780063i
$534$	−1.22796	−	4.03983i	−0.0531389	−	0.174821i
$535$	−30.7350	−	0.388157i	−1.32879	−	0.0167815i
$536$	−10.4133	−	16.2067i	−0.449785	−	0.700023i
$537$	−17.7392	+	9.03859i	−0.765505	+	0.390044i
$538$	20.0295	+	10.6914i	0.863531	+	0.460941i
$539$	3.02761	+	9.31803i	0.130408	+	0.401356i
$540$	2.44166	+	3.74677i	0.105072	+	0.161235i
$541$	5.50745	−	16.9502i	0.236784	−	0.728746i	−0.760096	−	0.649811i	$-0.774848\pi$
$541$	5.50745	−	16.9502i	0.236784	−	0.728746i	0.996880	−	0.0789350i	$-0.0251520\pi$
$542$	3.05162	−	2.93739i	0.131078	−	0.126172i
$543$	7.20003	+	7.20003i	0.308983	+	0.308983i
$544$	−23.1901	+	26.2453i	−0.994268	+	1.12526i
$545$	9.76249	+	19.7734i	0.418179	+	0.846998i
$546$	−1.31161	+	3.78926i	−0.0561317	+	0.162166i
$547$	−3.96056	+	25.0060i	−0.169341	+	1.06918i	0.745837	+	0.666129i	$0.232050\pi$
$547$	−3.96056	+	25.0060i	−0.169341	+	1.06918i	−0.915178	+	0.403050i	$0.867950\pi$
$548$	−25.3252	+	23.4634i	−1.08184	+	1.00231i
$549$		−	2.94943i		−	0.125879i
$550$	16.6058	−	7.55375i	0.708072	−	0.322093i
$551$		−	18.5614i		−	0.790740i
$552$	−16.8978	−	3.67755i	−0.719219	−	0.156527i
$553$	−1.30101	+	8.21427i	−0.0553247	+	0.349306i
$554$	23.1748	+	8.02169i	0.984604	+	0.340809i
$555$	−18.8941	−	9.92956i	−0.802011	−	0.421486i
$556$	−15.7136	−	23.4597i	−0.666404	−	0.994914i
$557$	10.1259	+	10.1259i	0.429048	+	0.429048i	0.888304	−	0.459256i	$-0.151884\pi$
$557$	10.1259	+	10.1259i	0.429048	+	0.429048i	−0.459256	+	0.888304i	$0.651884\pi$
$558$	5.78524	+	6.01022i	0.244909	+	0.254433i
$559$	−1.35897	+	4.18247i	−0.0574781	+	0.176899i
$560$	13.7335	−	8.22116i	0.580345	−	0.347407i
$561$	4.93597	+	15.1913i	0.208397	+	0.641379i
$562$	−6.63160	+	12.4237i	−0.279737	+	0.524062i
$563$	−38.7259	+	19.7318i	−1.63210	+	0.831597i	−0.633789	+	0.773506i	$0.718501\pi$
$563$	−38.7259	+	19.7318i	−1.63210	+	0.831597i	−0.998311	+	0.0580911i	$0.981499\pi$
$564$	0.00287429	−	0.0753207i	0.000121029	−	0.00317157i
$565$	4.71145	−	13.9006i	0.198212	−	0.584801i
$566$	−15.3126	+	4.65445i	−0.643636	+	0.195641i
$567$	1.76751	−	0.279945i	0.0742282	−	0.0117566i
$568$	−4.32198	+	7.40269i	−0.181346	+	0.310610i
$569$	19.2119	−	26.4429i	0.805405	−	1.10855i	−0.186611	−	0.982434i	$-0.559750\pi$
$569$	19.2119	−	26.4429i	0.805405	−	1.10855i	0.992016	−	0.126111i	$-0.0402497\pi$
$570$	−16.2286	+	2.04548i	−0.679743	+	0.0856756i
$571$	−22.6330	−	31.1516i	−0.947160	−	1.30365i	−0.952777	−	0.303670i	$-0.901788\pi$
$571$	−22.6330	−	31.1516i	−0.947160	−	1.30365i	0.00561699	−	0.999984i	$-0.498212\pi$
$572$	−7.13761	−	3.98668i	−0.298438	−	0.166692i
$573$	11.4051	+	5.81121i	0.476457	+	0.242767i
$574$	15.0800	−	10.5228i	0.629426	−	0.439213i
$575$	26.8795	+	14.5623i	1.12095	+	0.607288i
$576$	−6.96670	+	3.93256i	−0.290279	+	0.163857i
$577$	0.778351	−	1.52760i	0.0324032	−	0.0635948i	−0.874237	−	0.485499i	$-0.838638\pi$
$577$	0.778351	−	1.52760i	0.0324032	−	0.0635948i	0.906641	+	0.421904i	$0.138638\pi$
$578$	13.1804	+	27.1352i	0.548233	+	1.12868i
$579$	−3.65839	+	2.65798i	−0.152038	+	0.110462i
$580$	1.70283	+	15.9574i	0.0707063	+	0.662594i
$581$	−12.2569	−	8.90519i	−0.508503	−	0.369449i
$582$	3.03914	−	17.0743i	0.125977	−	0.707751i
$583$	2.93142	+	18.5083i	0.121407	+	0.766534i
$584$	−1.21344	+	21.1859i	−0.0502124	+	0.876678i
$585$	−2.11848	+	2.83973i	−0.0875885	+	0.117408i
$586$	30.9598	+	23.4085i	1.27894	+	0.966997i
$587$	10.0460	+	19.7163i	0.414642	+	0.813780i	0.999995	+	0.00300205i	$0.000955585\pi$
$587$	10.0460	+	19.7163i	0.414642	+	0.813780i	−0.585354	+	0.810778i	$0.699044\pi$
$588$	0.901215	+	7.54146i	0.0371655	+	0.311004i
$589$	−29.0185	+	9.42868i	−1.19569	+	0.388502i
$590$	−16.7566	−	24.6716i	−0.689859	−	1.01572i
$591$	11.0234	+	3.58173i	0.453444	+	0.147333i
$592$	19.8766	−	32.6005i	0.816923	−	1.33987i
$593$	−24.7989	+	24.7989i	−1.01837	+	1.01837i	−0.0185411	+	0.999828i	$0.505902\pi$
$593$	−24.7989	+	24.7989i	−1.01837	+	1.01837i	−0.999828	+	0.0185411i	$0.994098\pi$
$594$	−0.0695789	+	3.64796i	−0.00285486	+	0.149677i
$595$	−3.56625	−	24.5163i	−0.146202	−	1.00507i
$596$	9.39411	+	33.1658i	0.384798	+	1.35852i
$597$	−8.24701	−	1.30620i	−0.337528	−	0.0534591i
$598$	−1.88473	−	13.5698i	−0.0770721	−	0.554909i
$599$	5.41697			0.221331			0.110666	−	0.993858i	$-0.464702\pi$
$599$	5.41697			0.221331			0.110666	+	0.993858i	$0.464702\pi$
$600$	13.7643	−	3.24734i	0.561923	−	0.132572i
$601$	−13.7486			−0.560819			−0.280409	−	0.959881i	$-0.590470\pi$
$601$	−13.7486			−0.560819			−0.280409	+	0.959881i	$0.590470\pi$
$602$	−0.966355	−	6.95763i	−0.0393857	−	0.283572i
$603$	−6.72692	−	1.06544i	−0.273942	−	0.0433881i
$604$	−4.99365	−	17.6300i	−0.203189	−	0.717355i
$605$	−9.57347	−	1.64047i	−0.389217	−	0.0666948i
$606$	0.498774	−	26.1502i	0.0202613	−	1.06228i
$607$	25.1868	−	25.1868i	1.02230	−	1.02230i	0.0225567	−	0.999746i	$-0.492819\pi$
$607$	25.1868	−	25.1868i	1.02230	−	1.02230i	0.999746	−	0.0225567i	$-0.00718063\pi$
$608$	−1.80492	−	29.2046i	−0.0731993	−	1.18440i
$609$	6.10734	+	1.98440i	0.247482	+	0.0804118i
$610$	−8.77463	−	3.16187i	−0.355274	−	0.128020i
$611$	0.0567908	−	0.0184525i	0.00229751	−	0.000746506i
$612$	1.46927	+	12.2950i	0.0593916	+	0.496995i
$613$	9.17652	+	18.0099i	0.370636	+	0.727415i	0.998712	−	0.0507375i	$-0.0161572\pi$
$613$	9.17652	+	18.0099i	0.370636	+	0.727415i	−0.628076	+	0.778152i	$0.716157\pi$
$614$	−6.11908	−	4.62660i	−0.246946	−	0.186714i
$615$	15.5140	−	4.82509i	0.625586	−	0.194566i
$616$	13.0373	+	0.746722i	0.525288	+	0.0300863i
$617$	−2.43800	−	15.3930i	−0.0981503	−	0.619697i	−0.986904	−	0.161311i	$-0.948428\pi$
$617$	−2.43800	−	15.3930i	−0.0981503	−	0.619697i	0.888753	−	0.458386i	$-0.151572\pi$
$618$	4.99279	−	28.0501i	0.200839	−	1.12834i
$619$	11.5048	+	8.35870i	0.462415	+	0.335964i	0.794478	−	0.607293i	$-0.207745\pi$
$619$	11.5048	+	8.35870i	0.462415	+	0.335964i	−0.332063	+	0.943257i	$0.607745\pi$
$620$	24.0825	−	10.7681i	0.967176	−	0.432458i
$621$	−4.94644	+	3.59380i	−0.198494	+	0.144214i
$622$	5.12610	+	10.5534i	0.205538	+	0.423151i
$623$	−2.42563	+	4.76058i	−0.0971810	+	0.190728i
$624$	−4.82850	−	4.10513i	−0.193295	−	0.164337i
$625$	−24.9681	−	1.26231i	−0.998724	−	0.0504924i
$626$	−21.7110	+	15.1499i	−0.867745	+	0.605512i
$627$	−11.8905	−	6.05850i	−0.474860	−	0.241953i
$628$	8.28755	+	4.62898i	0.330709	+	0.184716i
$629$	−34.7372	−	47.8116i	−1.38506	−	1.90637i
$630$	1.06197	−	5.55848i	0.0423099	−	0.221455i
$631$	−12.7859	+	17.5983i	−0.508999	+	0.700577i	−0.983750	−	0.179543i	$-0.942538\pi$
$631$	−12.7859	+	17.5983i	−0.508999	+	0.700577i	0.474751	+	0.880120i	$0.342538\pi$
$632$	−11.3517	−	6.62756i	−0.451545	−	0.263630i
$633$	−15.2512	+	2.41555i	−0.606179	+	0.0960093i
$634$	−1.43327	+	0.435661i	−0.0569225	+	0.0173023i
$635$	−11.2065	−	36.0322i	−0.444718	−	1.42990i
$636$	−0.553940	+	14.5160i	−0.0219651	+	0.575596i
$637$	−5.36114	+	2.73163i	−0.212416	+	0.108231i
$638$	−6.16541	+	11.5503i	−0.244091	+	0.457282i
$639$	0.936526	+	2.88233i	0.0370484	+	0.114023i
$640$	4.23096	+	24.9419i	0.167244	+	0.985916i
$641$	3.91015	−	12.0342i	0.154442	−	0.475322i	−0.843662	−	0.536874i	$-0.819605\pi$
$641$	3.91015	−	12.0342i	0.154442	−	0.475322i	0.998104	+	0.0615520i	$0.0196050\pi$
$642$	−13.4816	−	14.0058i	−0.532075	−	0.552766i
$643$	31.0681	+	31.0681i	1.22521	+	1.22521i	0.965756	+	0.259450i	$0.0835414\pi$
$643$	31.0681	+	31.0681i	1.22521	+	1.22521i	0.259450	+	0.965756i	$0.416459\pi$
$644$	12.1780	+	18.1813i	0.479881	+	0.716443i
$645$	1.04823	−	6.11724i	0.0412739	−	0.240866i
$646$	−42.7980	−	14.8140i	−1.68386	−	0.582850i
$647$	7.56645	−	47.7727i	0.297468	−	1.87814i	−0.157336	−	0.987545i	$-0.550290\pi$
$647$	7.56645	−	47.7727i	0.297468	−	1.87814i	0.454803	−	0.890592i	$-0.349710\pi$
$648$	−0.601484	+	2.76373i	−0.0236285	+	0.108570i
$649$		−	24.3321i		−	0.955120i
$650$	6.17717	+	9.34680i	0.242289	+	0.366612i
$651$		−	10.5561i		−	0.413727i
$652$	−7.97214	+	7.38606i	−0.312213	+	0.289260i
$653$	−0.865641	+	5.46544i	−0.0338752	+	0.213879i	−0.998820	−	0.0485752i	$-0.984532\pi$
$653$	−0.865641	+	5.46544i	−0.0338752	+	0.213879i	0.964944	+	0.262454i	$0.0845320\pi$
$654$	−4.56201	+	13.1797i	−0.178389	+	0.515368i
$655$	−9.95278	+	1.44777i	−0.388887	+	0.0565692i
$656$	6.84849	+	28.2452i	0.267388	+	1.10279i
$657$	5.30515	+	5.30515i	0.206974	+	0.206974i
$658$	−0.0687175	+	0.0661452i	−0.00267889	+	0.00257861i
$659$	−14.2601	+	43.8880i	−0.555494	+	1.70963i	0.139141	+	0.990273i	$0.455566\pi$
$659$	−14.2601	+	43.8880i	−0.555494	+	1.70963i	−0.694635	+	0.719362i	$0.744434\pi$
$660$	10.7782	+	4.11771i	0.419539	+	0.160282i
$661$	10.7448	+	33.0690i	0.417923	+	1.28624i	0.909610	+	0.415463i	$0.136381\pi$
$661$	10.7448	+	33.0690i	0.417923	+	1.28624i	−0.491687	+	0.870772i	$0.663619\pi$
$662$	−39.3227	−	20.9899i	−1.52832	−	0.815797i
$663$	−8.74035	+	4.45343i	−0.339447	+	0.172957i
$664$	20.1457	−	12.9442i	0.781803	−	0.502331i
$665$	16.5901	+	12.3765i	0.643338	+	0.479941i
$666$	−3.92595	−	12.9159i	−0.152128	−	0.500481i
$667$	−21.6701	+	3.43220i	−0.839068	+	0.132895i
$668$	30.0960	−	13.9156i	1.16445	−	0.538412i
$669$	4.86623	−	6.69779i	0.188139	−	0.258951i
$670$	−10.3812	+	18.8706i	−0.401059	+	0.729034i
$671$	−4.47271	−	6.15616i	−0.172667	−	0.237656i
$672$	9.80232	+	2.52838i	0.378133	+	0.0975346i
$673$	22.2414	+	11.3325i	0.857342	+	0.436838i	0.826667	−	0.562692i	$-0.190234\pi$
$673$	22.2414	+	11.3325i	0.857342	+	0.436838i	0.0306753	+	0.999529i	$0.490234\pi$
$674$	16.3738	+	23.4649i	0.630694	+	0.903833i
$675$	2.38174	−	4.39629i	0.0916731	−	0.169213i
$676$	−7.23906	+	19.6907i	−0.278425	+	0.757334i
$677$	−8.19739	+	16.0883i	−0.315051	+	0.618323i	−0.993176	−	0.116624i	$-0.962793\pi$
$677$	−8.19739	+	16.0883i	−0.315051	+	0.618323i	0.678125	+	0.734947i	$0.262793\pi$
$678$	8.34985	−	4.05578i	0.320674	−	0.155761i
$679$	−17.7541	+	12.8991i	−0.681340	+	0.495022i
$680$	38.1529	+	8.80944i	1.46310	+	0.337826i
$681$	−22.2120	−	16.1380i	−0.851167	−	0.618409i
$682$	21.1895	+	3.77163i	0.811386	+	0.144423i
$683$	−3.32035	−	20.9639i	−0.127050	−	0.802161i	−0.966112	−	0.258125i	$-0.916895\pi$
$683$	−3.32035	−	20.9639i	−0.127050	−	0.802161i	0.839062	−	0.544036i	$-0.183105\pi$
$684$	−8.13140	−	6.39542i	−0.310912	−	0.244535i
$685$	36.5561	+	12.3903i	1.39674	+	0.473409i
$686$	16.4807	−	21.7971i	0.629235	−	0.832219i
$687$	−8.07421	−	15.8465i	−0.308050	−	0.604583i
$688$	10.8014	+	2.56743i	0.411800	+	0.0978825i
$689$	−10.9449	+	3.55620i	−0.416966	+	0.135480i
$690$	5.38891	+	18.5684i	0.205152	+	0.706887i
$691$	27.8609	+	9.05257i	1.05988	+	0.344376i	0.786539	−	0.617541i	$-0.211871\pi$
$691$	27.8609	+	9.05257i	1.05988	+	0.344376i	0.273342	+	0.961917i	$0.411871\pi$
$692$	−39.2795	−	7.76715i	−1.49318	−	0.295263i
$693$	3.26467	−	3.26467i	0.124015	−	0.124015i
$694$	−0.455153	−	0.00868131i	−0.0172774	−	0.000329538i
$695$	−14.6860	+	27.9449i	−0.557073	+	1.06001i
$696$	−6.42558	+	7.85665i	−0.243561	+	0.297806i
$697$	44.4310	+	7.03717i	1.68294	+	0.266552i
$698$	2.67181	−	0.371092i	0.101130	−	0.0140460i
$699$	5.39410			0.204024
$700$	−15.3981	−	9.11822i	−0.581995	−	0.344636i
$701$	−26.3853			−0.996559			−0.498279	−	0.867016i	$-0.666035\pi$
$701$	−26.3853			−0.996559			−0.498279	+	0.867016i	$0.666035\pi$
$702$	−2.21941	+	0.308257i	−0.0837662	+	0.0116344i
$703$	48.7668	+	7.72390i	1.83927	+	0.291312i
$704$	−8.57755	+	18.7729i	−0.323279	+	0.707532i
$705$	−0.0755644	+	0.0373076i	−0.00284592	+	0.00140509i
$706$	−12.6231	−	0.240766i	−0.475077	−	0.00906134i
$707$	−23.4026	+	23.4026i	−0.880147	+	0.880147i
$708$	3.65900	−	18.5041i	0.137514	−	0.695426i
$709$	−12.9991	−	4.22365i	−0.488190	−	0.158623i	0.0545707	−	0.998510i	$-0.482621\pi$
$709$	−12.9991	−	4.22365i	−0.488190	−	0.158623i	−0.542761	+	0.839887i	$0.682621\pi$
$710$	9.57898	+	0.303751i	0.359493	+	0.0113996i
$711$	−4.41992	+	1.43612i	−0.165760	+	0.0538587i
$712$	−5.62007	−	6.30297i	−0.210621	−	0.236214i
$713$	16.3737	+	32.1351i	0.613198	+	1.20347i
$714$	9.44987	−	12.4983i	0.353653	−	0.467737i
$715$	−0.115428	+	9.13978i	−0.00431674	+	0.341808i
$716$	−24.6161	+	31.2979i	−0.919945	+	1.16966i
$717$	−1.57773	−	9.96138i	−0.0589213	−	0.372015i
$718$	−28.8096	−	5.12798i	−1.07516	−	0.191375i
$719$	−28.1664	−	20.4641i	−1.05043	−	0.763183i	−0.0781367	−	0.996943i	$-0.524897\pi$
$719$	−28.1664	−	20.4641i	−1.05043	−	0.763183i	−0.972294	+	0.233760i	$0.924897\pi$
$720$	7.57736	+	4.75222i	0.282392	+	0.177105i
$721$	−29.1669	+	21.1910i	−1.08623	+	0.789194i
$722$	9.86535	−	4.79191i	0.367150	−	0.178337i
$723$	2.34801	−	4.60823i	0.0873235	−	0.171382i
$724$	19.1140	+	7.02704i	0.710366	+	0.261158i
$725$	14.7772	−	10.1762i	0.548813	−	0.377935i
$726$	−3.51536	−	5.03778i	−0.130467	−	0.186970i
$727$	31.4045	+	16.0014i	1.16473	+	0.593458i	0.925961	−	0.377619i	$-0.123257\pi$
$727$	31.4045	+	16.0014i	1.16473	+	0.593458i	0.238766	+	0.971077i	$0.423257\pi$
$728$	0.799566	+	7.97973i	0.0296339	+	0.295748i
$729$	0.587785	+	0.809017i	0.0217698	+	0.0299636i
$730$	21.4702	−	10.0957i	0.794648	−	0.373658i
$731$	10.1007	−	13.9024i	0.373586	−	0.514197i
$732$	−2.47566	−	5.35422i	−0.0915029	−	0.197898i
$733$	−21.4328	+	3.39462i	−0.791637	+	0.125383i	−0.539142	−	0.842215i	$-0.681251\pi$
$733$	−21.4328	+	3.39462i	−0.791637	+	0.125383i	−0.252495	+	0.967598i	$0.581251\pi$
$734$	−6.39440	−	21.0368i	−0.236022	−	0.776482i
$735$	6.93233	−	4.90408i	0.255703	−	0.180890i
$736$	−33.7621	+	7.50748i	−1.24449	+	0.276729i
$737$	−15.6564	+	7.97732i	−0.576710	+	0.293848i
$738$	9.06494	+	4.83874i	0.333685	+	0.178117i
$739$	7.04674	+	21.6876i	0.259219	+	0.797793i	0.992969	+	0.118374i	$0.0377681\pi$
$739$	7.04674	+	21.6876i	0.259219	+	0.797793i	−0.733751	+	0.679419i	$0.762232\pi$
$740$	−42.6338	−	2.16641i	−1.56725	−	0.0796388i
$741$	2.53255	−	7.79439i	0.0930356	−	0.286334i
$742$	13.2434	−	12.7477i	0.486181	−	0.467981i
$743$	12.9863	+	12.9863i	0.476422	+	0.476422i	0.903985	−	0.427563i	$-0.140628\pi$
$743$	12.9863	+	12.9863i	0.476422	+	0.476422i	−0.427563	+	0.903985i	$0.640628\pi$
$744$	15.5470	+	6.05466i	0.569980	+	0.221975i
$745$	27.5933	−	26.9051i	1.01094	−	0.985725i
$746$	−3.50469	+	10.1251i	−0.128316	+	0.370707i
$747$	1.32439	−	8.36187i	0.0484569	−	0.305945i
$748$	21.7116	+	23.4344i	0.793854	+	0.856846i
$749$			24.5993i			0.898840i
$750$	−10.5258	−	11.7987i	−0.384346	−	0.430826i
$751$			17.3842i			0.634360i	0.948365	+	0.317180i	$0.102736\pi$
$751$			17.3842i			0.634360i	−0.948365	+	0.317180i	$0.897264\pi$
$752$	−0.0580039	−	0.139145i	−0.00211518	−	0.00507411i
$753$	−2.13169	+	13.4589i	−0.0776830	+	0.490471i
$754$	−7.59835	−	2.63008i	−0.276716	−	0.0957819i
$755$	−14.6678	+	14.3020i	−0.533817	+	0.520502i
$756$	2.97365	−	1.99178i	0.108151	−	0.0724404i
$757$	−0.770220	−	0.770220i	−0.0279941	−	0.0279941i	0.692971	−	0.720965i	$-0.256301\pi$
$757$	−0.770220	−	0.770220i	−0.0279941	−	0.0279941i	−0.720965	+	0.692971i	$0.756301\pi$
$758$	34.3942	+	35.7317i	1.24925	+	1.29783i
$759$	−4.87451	+	15.0022i	−0.176933	+	0.544545i
$760$	−27.7436	+	17.3350i	−1.00637	+	0.628807i
$761$	5.86337	+	18.0456i	0.212547	+	0.654152i	0.999319	+	0.0369083i	$0.0117509\pi$
$761$	5.86337	+	18.0456i	0.212547	+	0.654152i	−0.786772	+	0.617244i	$0.788249\pi$
$762$	11.2383	−	21.0539i	0.407119	−	0.762701i
$763$	15.7248	−	8.01219i	0.569276	−	0.290061i
$764$	25.5820	+	0.976226i	0.925523	+	0.0353186i
$765$	11.3019	−	7.99521i	0.408621	−	0.289067i
$766$	15.5721	−	4.73335i	0.562644	−	0.171023i
$767$	14.7590	−	2.33760i	0.532918	−	0.0844059i
$768$	−9.34608	+	12.9866i	−0.337248	+	0.468612i
$769$	23.8890	−	32.8804i	0.861459	−	1.18570i	−0.119761	−	0.992803i	$-0.538213\pi$
$769$	23.8890	−	32.8804i	0.861459	−	1.18570i	0.981220	−	0.192894i	$-0.0617872\pi$
$770$	−6.21265	−	13.2123i	−0.223888	−	0.476138i
$771$	−8.91936	−	12.2764i	−0.321223	−	0.442125i
$772$	−4.41021	+	7.89587i	−0.158727	+	0.284179i
$773$	8.89205	+	4.53072i	0.319825	+	0.162959i	0.606531	−	0.795060i	$-0.292560\pi$
$773$	8.89205	+	4.53072i	0.319825	+	0.162959i

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.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.194555 - 1.40077i) q^{2} +(-0.987688 - 0.156434i) q^{3} +(-1.92430 + 0.545051i) q^{4} +(1.56105 + 1.60098i) q^{5} +(-0.0269690 + 1.41396i) q^{6} +(1.26539 - 1.26539i) q^{7} +(1.13787 + 2.58945i) q^{8} +(0.951057 + 0.309017i) q^{9} +O(q^{10})\)	\(q+(-0.194555 - 1.40077i) q^{2} +(-0.987688 - 0.156434i) q^{3} +(-1.92430 + 0.545051i) q^{4} +(1.56105 + 1.60098i) q^{5} +(-0.0269690 + 1.41396i) q^{6} +(1.26539 - 1.26539i) q^{7} +(1.13787 + 2.58945i) q^{8} +(0.951057 + 0.309017i) q^{9} +(1.93889 - 2.49814i) q^{10} +(2.45369 - 0.797253i) q^{11} +(1.98587 - 0.237314i) q^{12} +(0.719314 + 1.41173i) q^{13} +(-2.01871 - 1.52633i) q^{14} +(-1.29138 - 1.82547i) q^{15} +(3.40584 - 2.09768i) q^{16} +(-0.968521 - 6.11500i) q^{17} +(0.247828 - 1.39233i) q^{18} +(4.18468 + 3.04035i) q^{19} +(-3.87653 - 2.22991i) q^{20} +(-1.44777 + 1.05186i) q^{21} +(-1.59414 - 3.28194i) q^{22} +(2.77576 - 5.44773i) q^{23} +(-0.718783 - 2.73557i) q^{24} +(-0.126271 + 4.99841i) q^{25} +(1.83756 - 1.28225i) q^{26} +(-0.891007 - 0.453990i) q^{27} +(-1.74529 + 3.12470i) q^{28} +(-2.10923 - 2.90311i) q^{29} +(-2.30582 + 2.16407i) q^{30} +(-3.46723 + 4.77223i) q^{31} +(-3.60098 - 4.36267i) q^{32} +(-2.54820 + 0.403595i) q^{33} +(-8.37726 + 2.54637i) q^{34} +(4.00121 + 0.0505318i) q^{35} +(-1.99855 - 0.0762659i) q^{36} +(8.50512 - 4.33357i) q^{37} +(3.44467 - 6.45327i) q^{38} +(-0.489614 - 1.50688i) q^{39} +(-2.36939 + 5.86396i) q^{40} +(-2.24529 + 6.91028i) q^{41} +(1.75509 + 1.82334i) q^{42} +(1.96263 + 1.96263i) q^{43} +(-4.28709 + 2.87154i) q^{44} +(0.989913 + 2.00501i) q^{45} +(-8.17104 - 2.82831i) q^{46} +(0.00589566 - 0.0372238i) q^{47} +(-3.69206 + 1.53906i) q^{48} +3.79756i q^{49} +(7.02617 - 0.795586i) q^{50} +6.19122i q^{51} +(-2.15364 - 2.32453i) q^{52} +(-1.13623 + 7.17385i) q^{53} +(-0.462586 + 1.33642i) q^{54} +(5.10671 + 2.68376i) q^{55} +(4.71653 + 1.83682i) q^{56} +(-3.65754 - 3.65754i) q^{57} +(-3.65622 + 3.51935i) q^{58} +(2.91440 - 8.96960i) q^{59} +(3.47997 + 2.80888i) q^{60} +(-0.911425 - 2.80508i) q^{61} +(7.35935 + 3.92832i) q^{62} +(1.59449 - 0.812433i) q^{63} +(-5.41050 + 5.89292i) q^{64} +(-1.13727 + 3.35539i) q^{65} +(1.06111 + 3.49091i) q^{66} +(-6.72692 + 1.06544i) q^{67} +(5.19671 + 11.2392i) q^{68} +(-3.59380 + 4.94644i) q^{69} +(-0.707670 - 5.61459i) q^{70} +(1.78138 + 2.45186i) q^{71} +(0.281995 + 2.81433i) q^{72} +(6.68488 + 3.40612i) q^{73} +(-7.72504 - 11.0706i) q^{74} +(0.906640 - 4.91711i) q^{75} +(-9.70971 - 3.56967i) q^{76} +(2.09605 - 4.11372i) q^{77} +(-2.01553 + 0.979005i) q^{78} +(-3.75981 + 2.73166i) q^{79} +(8.67501 + 2.17810i) q^{80} +(0.809017 + 0.587785i) q^{81} +(10.1165 + 1.80070i) q^{82} +(-1.32439 - 8.36187i) q^{83} +(2.21261 - 2.81320i) q^{84} +(8.27808 - 11.0964i) q^{85} +(2.36735 - 3.13103i) q^{86} +(1.62912 + 3.19732i) q^{87} +(4.85643 + 5.44654i) q^{88} +(-2.83952 + 0.922614i) q^{89} +(2.61596 - 1.77672i) q^{90} +(2.69661 + 0.876183i) q^{91} +(-2.37209 + 11.9960i) q^{92} +(4.17109 - 4.17109i) q^{93} +(-0.0532888 - 0.00101640i) q^{94} +(1.66494 + 11.4457i) q^{95} +(2.87418 + 4.87228i) q^{96} +(-12.1121 - 1.91837i) q^{97} +(5.31949 - 0.738832i) q^{98} +2.57996 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240q + 12q^{8} + O(q^{10}) \)	\( 240q + 12q^{8} + 8q^{10} + 8q^{12} + 4q^{13} + 20q^{17} - 20q^{20} - 12q^{22} + 20q^{25} + 4q^{28} - 8q^{30} - 20q^{32} - 8q^{33} - 4q^{37} - 76q^{38} - 92q^{40} - 20q^{42} - 140q^{44} - 4q^{45} - 16q^{48} - 164q^{50} - 172q^{52} - 4q^{53} - 120q^{58} + 20q^{60} - 44q^{62} - 60q^{64} - 20q^{65} + 16q^{68} - 44q^{70} + 12q^{72} - 44q^{73} - 48q^{77} + 24q^{78} - 4q^{80} + 60q^{81} + 24q^{82} + 80q^{84} - 64q^{85} + 60q^{88} - 260q^{89} + 48q^{90} + 144q^{92} - 64q^{93} + 40q^{94} - 20q^{96} - 180q^{97} + 256q^{98} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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