LMFDB - Embedded newform 503.2.c.a.2.7

Newspace parameters

Level:	$ N $	$=$	$ 503 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	503.c (of order $251$, degree $250$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.01647522167$
Analytic rank:	$0$
Dimension:	$10250$
Relative dimension:	$41$ over $\Q(\zeta_{251})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{251}]$

Embedding invariants

Embedding label			2.7
Character	$\chi$	$=$	503.2
Dual form			503.2.c.a.252.7

$q$-expansion

$f(q)$	$=$	$q+(-1.35722 - 1.67103i) q^{2} +(2.35620 - 2.03931i) q^{3} +(-0.540193 + 2.57841i) q^{4} +(-0.767603 - 2.42424i) q^{5} +(-6.60563 - 1.16949i) q^{6} +(0.954936 - 2.77271i) q^{7} +(1.21411 - 0.625336i) q^{8} +(0.962553 - 6.64105i) q^{9} +O(q^{10})$	\(q+(-1.35722 - 1.67103i) q^{2} +(2.35620 - 2.03931i) q^{3} +(-0.540193 + 2.57841i) q^{4} +(-0.767603 - 2.42424i) q^{5} +(-6.60563 - 1.16949i) q^{6} +(0.954936 - 2.77271i) q^{7} +(1.21411 - 0.625336i) q^{8} +(0.962553 - 6.64105i) q^{9} +(-3.00917 + 4.57291i) q^{10} +(-2.12003 + 0.685909i) q^{11} +(3.98538 + 7.17686i) q^{12} +(4.27581 - 1.44274i) q^{13} +(-5.92934 + 2.16745i) q^{14} +(-6.75239 - 4.14660i) q^{15} +(2.13293 + 0.934753i) q^{16} +(6.07671 + 3.03422i) q^{17} +(-12.4038 + 7.40491i) q^{18} +(1.70491 + 3.82500i) q^{19} +(6.66533 - 0.669642i) q^{20} +(-3.40440 - 8.48046i) q^{21} +(4.02353 + 2.61172i) q^{22} +(-2.42681 + 8.38838i) q^{23} +(1.58544 - 3.94937i) q^{24} +(-1.19894 + 0.843860i) q^{25} +(-8.21408 - 5.18689i) q^{26} +(-6.23447 - 9.73752i) q^{27} +(6.63334 + 3.96002i) q^{28} +(-0.352149 + 2.94763i) q^{29} +(2.23539 + 16.9113i) q^{30} +(-0.670422 - 8.22241i) q^{31} +(-2.05903 - 7.46594i) q^{32} +(-3.59644 + 5.93954i) q^{33} +(-3.17715 - 14.2725i) q^{34} +(-7.45471 - 0.186650i) q^{35} +(16.6034 + 6.06931i) q^{36} +(4.79454 + 6.05647i) q^{37} +(4.07775 - 8.04032i) q^{38} +(7.13245 - 12.1191i) q^{39} +(-2.44792 - 2.46329i) q^{40} +(-1.30716 + 6.65308i) q^{41} +(-9.55060 + 17.1987i) q^{42} +(-0.160747 + 0.875980i) q^{43} +(-0.623327 - 5.83684i) q^{44} +(-16.8383 + 2.76424i) q^{45} +(17.3109 - 7.32960i) q^{46} +(-5.01661 + 0.188457i) q^{47} +(6.93186 - 2.14725i) q^{48} +(-1.26054 - 0.985123i) q^{49} +(3.03734 + 0.858157i) q^{50} +(20.5056 - 5.24307i) q^{51} +(1.41022 + 11.8042i) q^{52} +(2.60771 - 5.85045i) q^{53} +(-7.81016 + 23.6339i) q^{54} +(3.29015 + 4.61296i) q^{55} +(-0.574475 - 3.96354i) q^{56} +(11.8175 + 5.53560i) q^{57} +(5.40353 - 3.41213i) q^{58} +(-1.62800 + 3.91302i) q^{59} +(14.3392 - 15.1705i) q^{60} +(-4.88503 - 8.06766i) q^{61} +(-12.8300 + 12.2799i) q^{62} +(-17.4945 - 9.01066i) q^{63} +(-6.97675 + 9.78177i) q^{64} +(-6.77967 - 9.25811i) q^{65} +(14.8063 - 2.05150i) q^{66} +(-12.4111 + 7.62159i) q^{67} +(-11.1061 + 14.0292i) q^{68} +(11.3885 + 24.7137i) q^{69} +(9.80578 + 12.7104i) q^{70} +(0.991264 + 6.28404i) q^{71} +(-2.98424 - 8.66491i) q^{72} +(1.43252 + 1.37110i) q^{73} +(3.61331 - 16.2318i) q^{74} +(-1.10404 + 4.43330i) q^{75} +(-10.7834 + 2.32973i) q^{76} +(-0.122672 + 6.53324i) q^{77} +(-29.9317 + 4.52972i) q^{78} +(0.383916 + 6.80907i) q^{79} +(0.628817 - 5.88825i) q^{80} +(-15.2445 - 4.51390i) q^{81} +(12.8916 - 6.84539i) q^{82} +(1.05577 + 2.01868i) q^{83} +(23.7051 - 4.19685i) q^{84} +(2.69117 - 17.0604i) q^{85} +(1.68196 - 0.920284i) q^{86} +(5.18140 + 7.66334i) q^{87} +(-2.14504 + 2.15851i) q^{88} +(-1.96657 - 7.49550i) q^{89} +(27.4725 + 24.3857i) q^{90} +(0.0828171 - 13.2333i) q^{91} +(-20.3177 - 10.7886i) q^{92} +(-18.3477 - 18.0064i) q^{93} +(7.12355 + 8.12713i) q^{94} +(7.96400 - 7.06918i) q^{95} +(-20.0769 - 13.3922i) q^{96} +(0.199590 + 0.846508i) q^{97} +(0.0646561 + 3.44343i) q^{98} +(2.51451 + 14.7395i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10250q - 249q^{2} - 249q^{3} - 285q^{4} - 245q^{5} - 237q^{6} - 247q^{7} - 239q^{8} - 280q^{9} + O(q^{10}) $	\( 10250q - 249q^{2} - 249q^{3} - 285q^{4} - 245q^{5} - 237q^{6} - 247q^{7} - 239q^{8} - 280q^{9} - 233q^{10} - 239q^{11} - 239q^{12} - 245q^{13} - 223q^{14} - 231q^{15} - 263q^{16} - 243q^{17} - 217q^{18} - 229q^{19} - 195q^{20} - 215q^{21} - 233q^{22} - 241q^{23} - 181q^{24} - 280q^{25} - 215q^{26} - 237q^{27} - 185q^{28} - 217q^{29} - 159q^{30} - 219q^{31} - 185q^{32} - 209q^{33} - 167q^{34} - 187q^{35} - 203q^{36} - 237q^{37} - 161q^{38} - 197q^{39} - 135q^{40} - 209q^{41} - 117q^{42} - 221q^{43} - 147q^{44} - 167q^{45} - 167q^{46} - 195q^{47} - 141q^{48} - 234q^{49} - 145q^{50} - 177q^{51} - 179q^{52} - 211q^{53} - 83q^{54} - 165q^{55} - 125q^{56} - 177q^{57} - 205q^{58} - 189q^{59} - 27q^{60} - 193q^{61} - 143q^{62} - 159q^{63} - 185q^{64} - 155q^{65} - 97q^{66} - 201q^{67} - 155q^{68} - 113q^{69} - 123q^{70} - 153q^{71} - 21q^{72} - 213q^{73} - 83q^{74} - 161q^{75} - 97q^{76} - 139q^{77} - 43q^{78} - 191q^{79} + 3q^{80} - 188q^{81} - 97q^{82} - 161q^{83} + 67q^{84} - 159q^{85} - 121q^{86} - 121q^{87} - 143q^{88} - 155q^{89} + 115q^{90} - 137q^{91} - 119q^{92} - 123q^{93} - 99q^{94} - 181q^{95} + 67q^{96} - 229q^{97} - 63q^{98} - 85q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/503\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{101}{251}\right)$

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 $

$2$	−1.35722	−	1.67103i	−0.959699	−	1.18160i	−0.983321	−	0.181877i	$-0.941783\pi$
$2$	−1.35722	−	1.67103i	−0.959699	−	1.18160i	0.0236222	−	0.999721i	$-0.492480\pi$
$3$	2.35620	−	2.03931i	1.36035	−	1.17740i	0.394319	−	0.918974i	$-0.370981\pi$
$3$	2.35620	−	2.03931i	1.36035	−	1.17740i	0.966032	−	0.258423i	$-0.0832027\pi$
$4$	−0.540193	+	2.57841i	−0.270096	+	1.28921i
$5$	−0.767603	−	2.42424i	−0.343283	−	1.08415i	−0.955880	−	0.293756i	$-0.905095\pi$
$5$	−0.767603	−	2.42424i	−0.343283	−	1.08415i	0.612598	−	0.790395i	$-0.290125\pi$
$6$	−6.60563	−	1.16949i	−2.69674	−	0.477441i
$7$	0.954936	−	2.77271i	0.360932	−	1.04799i	−0.606550	−	0.795045i	$-0.707447\pi$
$7$	0.954936	−	2.77271i	0.360932	−	1.04799i	0.967482	−	0.252940i	$-0.0813976\pi$
$8$	1.21411	−	0.625336i	0.429254	−	0.221090i
$9$	0.962553	−	6.64105i	0.320851	−	2.21368i
$10$	−3.00917	+	4.57291i	−0.951583	+	1.44608i
$11$	−2.12003	+	0.685909i	−0.639214	+	0.206809i	−0.609546	−	0.792751i	$-0.708648\pi$
$11$	−2.12003	+	0.685909i	−0.639214	+	0.206809i	−0.0296683	+	0.999560i	$0.509445\pi$
$12$	3.98538	+	7.17686i	1.15048	+	2.07178i
$13$	4.27581	−	1.44274i	1.18590	−	0.400145i	0.343577	−	0.939124i	$-0.388361\pi$
$13$	4.27581	−	1.44274i	1.18590	−	0.400145i	0.842319	+	0.538980i	$0.181190\pi$
$14$	−5.92934	+	2.16745i	−1.58468	+	0.579275i
$15$	−6.75239	−	4.14660i	−1.74346	−	1.07065i
$16$	2.13293	+	0.934753i	0.533233	+	0.233688i
$17$	6.07671	+	3.03422i	1.47382	+	0.735907i	0.990237	−	0.139393i	$-0.0445152\pi$
$17$	6.07671	+	3.03422i	1.47382	+	0.735907i	0.483581	+	0.875300i	$0.339336\pi$
$18$	−12.4038	+	7.40491i	−2.92361	+	1.74535i
$19$	1.70491	+	3.82500i	0.391133	+	0.877514i	0.996658	+	0.0816878i	$0.0260310\pi$
$19$	1.70491	+	3.82500i	0.391133	+	0.877514i	−0.605525	+	0.795827i	$0.707037\pi$
$20$	6.66533	−	0.669642i	1.49041	−	0.149737i
$21$	−3.40440	−	8.48046i	−0.742900	−	1.85059i
$22$	4.02353	+	2.61172i	0.857819	+	0.556820i
$23$	−2.42681	+	8.38838i	−0.506024	+	1.74910i	0.144393	+	0.989520i	$0.453877\pi$
$23$	−2.42681	+	8.38838i	−0.506024	+	1.74910i	−0.650417	+	0.759577i	$0.725406\pi$
$24$	1.58544	−	3.94937i	0.323626	−	0.806162i
$25$	−1.19894	+	0.843860i	−0.239787	+	0.168772i
$26$	−8.21408	−	5.18689i	−1.61091	−	1.01723i
$27$	−6.23447	−	9.73752i	−1.19982	−	1.87399i
$28$	6.63334	+	3.96002i	1.25358	+	0.748373i
$29$	−0.352149	+	2.94763i	−0.0653925	+	0.547362i	0.921781	+	0.387711i	$0.126734\pi$
$29$	−0.352149	+	2.94763i	−0.0653925	+	0.547362i	−0.987174	+	0.159651i	$0.948963\pi$
$30$	2.23539	+	16.9113i	0.408124	+	3.08757i
$31$	−0.670422	−	8.22241i	−0.120411	−	1.47679i	−0.729661	−	0.683809i	$-0.760322\pi$
$31$	−0.670422	−	8.22241i	−0.120411	−	1.47679i	0.609250	−	0.792978i	$-0.291471\pi$
$32$	−2.05903	−	7.46594i	−0.363989	−	1.31980i
$33$	−3.59644	+	5.93954i	−0.626059	+	1.03394i
$34$	−3.17715	−	14.2725i	−0.544876	−	2.44771i
$35$	−7.45471	−	0.186650i	−1.26008	−	0.0315496i
$36$	16.6034	+	6.06931i	2.76723	+	1.01155i
$37$	4.79454	+	6.05647i	0.788218	+	0.995678i	0.999832	+	0.0183244i	$0.00583316\pi$
$37$	4.79454	+	6.05647i	0.788218	+	0.995678i	−0.211614	+	0.977353i	$0.567872\pi$
$38$	4.07775	−	8.04032i	0.661499	−	1.30431i
$39$	7.13245	−	12.1191i	1.14211	−	1.94061i
$40$	−2.44792	−	2.46329i	−0.387050	−	0.389480i
$41$	−1.30716	+	6.65308i	−0.204144	+	1.03904i	0.730354	+	0.683069i	$0.239355\pi$
$41$	−1.30716	+	6.65308i	−0.204144	+	1.03904i	−0.934498	+	0.355969i	$0.884151\pi$
$42$	−9.55060	+	17.1987i	−1.47369	+	2.65382i
$43$	−0.160747	+	0.875980i	−0.0245137	+	0.133586i	−0.993563	−	0.113282i	$-0.963864\pi$
$43$	−0.160747	+	0.875980i	−0.0245137	+	0.133586i	0.969049	+	0.246868i	$0.0794014\pi$
$44$	−0.623327	−	5.83684i	−0.0939701	−	0.879937i
$45$	−16.8383	+	2.76424i	−2.51011	+	0.412068i
$46$	17.3109	−	7.32960i	2.55236	−	1.08069i
$47$	−5.01661	+	0.188457i	−0.731747	+	0.0274892i	−0.400807	−	0.916162i	$-0.631270\pi$
$47$	−5.01661	+	0.188457i	−0.731747	+	0.0274892i	−0.330940	+	0.943652i	$0.607366\pi$
$48$	6.93186	−	2.14725i	1.00053	−	0.309928i
$49$	−1.26054	−	0.985123i	−0.180077	−	0.140732i
$50$	3.03734	+	0.858157i	0.429544	+	0.121362i
$51$	20.5056	−	5.24307i	2.87136	−	0.734177i
$52$	1.41022	+	11.8042i	0.195563	+	1.63694i
$53$	2.60771	−	5.85045i	0.358197	−	0.803621i	−0.641148	−	0.767418i	$-0.721541\pi$
$53$	2.60771	−	5.85045i	0.358197	−	0.803621i	0.999344	−	0.0362033i	$-0.0115264\pi$
$54$	−7.81016	+	23.6339i	−1.06283	+	3.21617i
$55$	3.29015	+	4.61296i	0.443644	+	0.622011i
$56$	−0.574475	−	3.96354i	−0.0767674	−	0.529650i
$57$	11.8175	+	5.53560i	1.56526	+	0.733208i
$58$	5.40353	−	3.41213i	0.709518	−	0.448035i
$59$	−1.62800	+	3.91302i	−0.211948	+	0.509432i	−0.993423	−	0.114505i	$-0.963472\pi$
$59$	−1.62800	+	3.91302i	−0.211948	+	0.509432i	0.781475	+	0.623937i	$0.214468\pi$
$60$	14.3392	−	15.1705i	1.85119	−	1.95850i
$61$	−4.88503	−	8.06766i	−0.625464	−	1.03296i	−0.994620	−	0.103591i	$-0.966967\pi$
$61$	−4.88503	−	8.06766i	−0.625464	−	1.03296i	0.369156	−	0.929367i	$-0.379647\pi$
$62$	−12.8300	+	12.2799i	−1.62941	+	1.55955i
$63$	−17.4945	−	9.01066i	−2.20410	−	1.13524i
$64$	−6.97675	+	9.78177i	−0.872094	+	1.22272i
$65$	−6.77967	−	9.25811i	−0.840915	−	1.14833i
$66$	14.8063	−	2.05150i	1.82253	−	0.252523i
$67$	−12.4111	+	7.62159i	−1.51626	+	0.931125i	−0.519189	+	0.854659i	$0.673766\pi$
$67$	−12.4111	+	7.62159i	−1.51626	+	0.931125i	−0.997072	+	0.0764661i	$0.975636\pi$
$68$	−11.1061	+	14.0292i	−1.34681	+	1.70129i
$69$	11.3885	+	24.7137i	1.37101	+	2.97518i
$70$	9.80578	+	12.7104i	1.17202	+	1.51918i
$71$	0.991264	+	6.28404i	0.117641	+	0.745779i	0.973520	+	0.228602i	$0.0734154\pi$
$71$	0.991264	+	6.28404i	0.117641	+	0.745779i	−0.855879	+	0.517177i	$0.826983\pi$
$72$	−2.98424	−	8.66491i	−0.351696	−	1.02117i
$73$	1.43252	+	1.37110i	0.167664	+	0.160476i	0.770611	−	0.637306i	$-0.219951\pi$
$73$	1.43252	+	1.37110i	0.167664	+	0.160476i	−0.602947	+	0.797781i	$0.706007\pi$
$74$	3.61331	−	16.2318i	0.420038	−	1.88691i
$75$	−1.10404	+	4.43330i	−0.127483	+	0.511914i
$76$	−10.7834	+	2.32973i	−1.23694	+	0.267238i
$77$	−0.122672	+	6.53324i	−0.0139798	+	0.744532i
$78$	−29.9317	+	4.52972i	−3.38909	+	0.512890i
$79$	0.383916	+	6.80907i	0.0431939	+	0.766081i	0.943612	+	0.331054i	$0.107404\pi$
$79$	0.383916	+	6.80907i	0.0431939	+	0.766081i	−0.900418	+	0.435026i	$0.856739\pi$
$80$	0.628817	−	5.88825i	0.0703038	−	0.658326i
$81$	−15.2445	−	4.51390i	−1.69384	−	0.501545i
$82$	12.8916	−	6.84539i	1.42364	−	0.755947i
$83$	1.05577	+	2.01868i	0.115886	+	0.221579i	0.937116	−	0.349018i	$-0.113485\pi$
$83$	1.05577	+	2.01868i	0.115886	+	0.221579i	−0.821230	+	0.570597i	$0.806712\pi$
$84$	23.7051	−	4.19685i	2.58644	−	0.457914i
$85$	2.69117	−	17.0604i	0.291898	−	1.85047i
$86$	1.68196	−	0.920284i	0.181370	−	0.0992368i
$87$	5.18140	+	7.66334i	0.555505	+	0.821597i
$88$	−2.14504	+	2.15851i	−0.228662	+	0.230097i
$89$	−1.96657	−	7.49550i	−0.208456	−	0.794521i	−0.986147	−	0.165874i	$-0.946956\pi$
$89$	−1.96657	−	7.49550i	−0.208456	−	0.794521i	0.777691	−	0.628647i	$-0.216391\pi$
$90$	27.4725	+	24.3857i	2.89585	+	2.57048i
$91$	0.0828171	−	13.2333i	0.00868159	−	1.38723i
$92$	−20.3177	−	10.7886i	−2.11827	−	1.12479i
$93$	−18.3477	−	18.0064i	−1.90257	−	1.86718i
$94$	7.12355	+	8.12713i	0.734738	+	0.838249i
$95$	7.96400	−	7.06918i	0.817089	−	0.725283i
$96$	−20.0769	−	13.3922i	−2.04909	−	1.36684i
$97$	0.199590	+	0.846508i	0.0202653	+	0.0859499i	0.982495	−	0.186289i	$-0.0596462\pi$
$97$	0.199590	+	0.846508i	0.0202653	+	0.0859499i	−0.962230	+	0.272239i	$0.912236\pi$
$98$	0.0646561	+	3.44343i	0.00653125	+	0.347839i
$99$	2.51451	+	14.7395i	0.252718	+	1.48137i
$100$	−1.52816	−	3.54720i	−0.152816	−	0.354720i
$101$	3.42527	−	1.35021i	0.340827	−	0.134351i	−0.190109	−	0.981763i	$-0.560884\pi$
$101$	3.42527	−	1.35021i	0.340827	−	0.134351i	0.530936	+	0.847412i	$0.321840\pi$
$102$	−36.5920	−	27.1496i	−3.62315	−	2.68821i
$103$	13.7523	−	2.79146i	1.35505	−	0.275051i	0.533797	−	0.845612i	$-0.320765\pi$
$103$	13.7523	−	2.79146i	1.35505	−	0.275051i	0.821255	+	0.570562i	$0.193274\pi$
$104$	4.28912	−	4.42547i	0.420583	−	0.433953i
$105$	−17.9454	+	14.7627i	−1.75129	+	1.44069i
$106$	−13.3155	+	3.58277i	−1.29332	+	0.347990i
$107$	−2.18758	−	0.0821797i	−0.211481	−	0.00794462i	−0.0684112	−	0.997657i	$-0.521793\pi$
$107$	−2.18758	−	0.0821797i	−0.211481	−	0.00794462i	−0.143070	+	0.989713i	$0.545697\pi$
$108$	28.4751	−	10.8149i	2.74002	−	1.04066i
$109$	−7.52889	−	7.96535i	−0.721137	−	0.762942i	0.258000	−	0.966145i	$-0.416937\pi$
$109$	−7.52889	−	7.96535i	−0.721137	−	0.762942i	−0.979137	+	0.203203i	$0.934865\pi$
$110$	3.24294	−	11.7587i	0.309203	−	1.12115i
$111$	23.6479	+	4.49268i	2.24456	+	0.426426i
$112$	4.62861	−	5.02137i	0.437363	−	0.474475i
$113$	−1.10682	−	2.25181i	−0.104121	−	0.211832i	0.839116	−	0.543952i	$-0.183073\pi$
$113$	−1.10682	−	2.25181i	−0.104121	−	0.211832i	−0.943237	+	0.332120i	$0.892236\pi$
$114$	−6.78872	−	27.2604i	−0.635822	−	2.55317i
$115$	22.1982	−	0.555796i	2.07000	−	0.0518282i
$116$	−7.40998	−	2.50028i	−0.688000	−	0.232145i
$117$	−5.46564	−	29.7846i	−0.505299	−	2.75359i
$118$	8.74833	−	2.59038i	0.805349	−	0.238464i
$119$	14.2159	−	13.9515i	1.30317	−	1.27893i
$120$	−10.7912	−	0.811922i	−0.985096	−	0.0741180i
$121$	−4.89127	+	3.53504i	−0.444661	+	0.321367i
$122$	−6.85126	+	19.1126i	−0.620284	+	1.73038i
$123$	10.4878	+	18.3417i	0.945652	+	1.65381i
$124$	21.5629	+	2.71306i	1.93641	+	0.243640i
$125$	−7.14909	−	5.44434i	−0.639434	−	0.486957i
$126$	8.68683	+	41.4634i	0.773884	+	3.69385i
$127$	−4.65737	+	2.62455i	−0.413275	+	0.232891i	−0.683568	−	0.729887i	$-0.739573\pi$
$127$	−4.65737	+	2.62455i	−0.413275	+	0.232891i	0.270293	+	0.962778i	$0.412879\pi$
$128$	10.3556	−	0.648917i	0.915315	−	0.0573567i
$129$	1.40764	+	2.39180i	0.123936	+	0.210586i
$130$	−6.26910	+	23.8943i	−0.549836	+	2.09567i
$131$	2.48012	−	1.65436i	0.216689	−	0.144542i	−0.441849	−	0.897089i	$-0.645677\pi$
$131$	2.48012	−	1.65436i	0.216689	−	0.144542i	0.658538	+	0.752548i	$0.271175\pi$
$132$	−13.3718	−	12.4816i	−1.16387	−	1.08638i
$133$	12.2337	−	1.07459i	1.06079	−	0.0931792i
$134$	29.5806	+	10.3952i	2.55537	+	0.898011i
$135$	−18.8204	+	22.5884i	−1.61981	+	1.94410i
$136$	9.27522	−	0.116098i	0.795344	−	0.00995528i
$137$	−1.76026	−	4.54872i	−0.150389	−	0.388624i	0.836943	−	0.547290i	$-0.184340\pi$
$137$	−1.76026	−	4.54872i	−0.150389	−	0.388624i	−0.987332	+	0.158666i	$0.949281\pi$
$138$	25.8407	−	52.5724i	2.19970	−	4.47526i
$139$	8.37289	+	1.80894i	0.710179	+	0.153432i	0.551837	−	0.833952i	$-0.313927\pi$
$139$	8.37289	+	1.80894i	0.710179	+	0.153432i	0.158342	+	0.987384i	$0.449385\pi$
$140$	4.50824	−	19.1205i	0.381016	−	1.61598i
$141$	−11.4358	+	10.6745i	−0.963067	+	0.898951i
$142$	9.15547	−	10.1853i	0.768310	−	0.854728i
$143$	−8.07527	+	5.99148i	−0.675288	+	0.501033i
$144$	8.26080	−	13.2652i	0.688400	−	1.10543i
$145$	7.41607	−	1.40892i	0.615871	−	0.117004i
$146$	0.346910	−	4.25468i	0.0287104	−	0.352120i
$147$	−4.97905	+	0.249486i	−0.410665	+	0.0205772i
$148$	−18.2061	+	9.09064i	−1.49653	+	0.747246i
$149$	11.4837	−	17.9362i	0.940780	−	1.46939i	0.0587092	−	0.998275i	$-0.481302\pi$
$149$	11.4837	−	17.9362i	0.940780	−	1.46939i	0.882071	−	0.471116i	$-0.156149\pi$
$150$	8.90661	−	4.17209i	0.727222	−	0.340649i
$151$	−10.4012	−	15.8063i	−0.846439	−	1.28630i	−0.956310	−	0.292353i	$-0.905562\pi$
$151$	−10.4012	−	15.8063i	−0.846439	−	1.28630i	0.109871	−	0.993946i	$-0.464956\pi$
$152$	4.46186	+	3.57784i	0.361905	+	0.290201i
$153$	25.9996	−	37.4351i	2.10194	−	3.02645i
$154$	11.0837	−	8.66205i	0.893153	−	0.698008i
$155$	−19.4184	+	7.93680i	−1.55973	+	0.637499i
$156$	27.3951	+	24.9370i	2.19336	+	1.99656i
$157$	−10.1540	+	21.3283i	−0.810373	+	1.70218i	−0.103736	+	0.994605i	$0.533080\pi$
$157$	−10.1540	+	21.3283i	−0.810373	+	1.70218i	−0.706638	+	0.707576i	$0.749789\pi$
$158$	10.8571	−	9.88295i	0.863746	−	0.786245i
$159$	−5.78660	−	19.1027i	−0.458907	−	1.51495i
$160$	−16.5187	+	10.7225i	−1.30592	+	0.847685i
$161$	20.9411	+	14.7392i	1.65039	+	1.16161i
$162$	13.1473	+	31.6004i	1.03295	+	2.48276i
$163$	−4.74667	−	1.80279i	−0.371788	−	0.141205i	0.162071	−	0.986779i	$-0.448183\pi$
$163$	−4.74667	−	1.80279i	−0.371788	−	0.141205i	−0.533858	+	0.845574i	$0.679258\pi$
$164$	−16.4483	−	6.96434i	−1.28439	−	0.543823i
$165$	17.1595	+	4.15940i	1.33586	+	0.323809i
$166$	1.94037	−	4.50402i	0.150602	−	0.349580i
$167$	−0.0893946	+	2.85597i	−0.00691756	+	0.221001i	0.989925	+	0.141595i	$0.0452229\pi$
$167$	−0.0893946	+	2.85597i	−0.00691756	+	0.221001i	−0.996842	+	0.0794068i	$0.974697\pi$
$168$	−9.43646	−	8.16735i	−0.728039	−	0.630125i
$169$	5.85862	−	4.46159i	0.450663	−	0.343199i
$170$	−32.1610	+	18.6578i	−2.46664	+	1.43098i
$171$	27.0431	−	7.64064i	2.06804	−	0.584294i
$172$	−2.17180	−	0.887671i	−0.165598	−	0.0676843i
$173$	−6.79222	−	14.2670i	−0.516403	−	1.08470i	−0.980063	−	0.198686i	$-0.936333\pi$
$173$	−6.79222	−	14.2670i	−0.516403	−	1.08470i	0.463660	−	0.886013i	$-0.346536\pi$
$174$	5.77338	−	19.0591i	0.437679	−	1.44487i
$175$	1.19487	+	4.13013i	0.0903238	+	0.312209i
$176$	−5.16304	−	0.518712i	−0.389179	−	0.0390994i
$177$	4.14396	+	12.5398i	0.311479	+	0.942552i
$178$	−9.85614	+	13.4592i	−0.738749	+	1.00881i
$179$	−1.82365	+	3.38310i	−0.136306	+	0.252865i	−0.939282	−	0.343146i	$-0.888507\pi$
$179$	−1.82365	+	3.38310i	−0.136306	+	0.252865i	0.802976	+	0.596011i	$0.203248\pi$
$180$	1.96861	−	44.9094i	0.146731	−	3.34735i
$181$	1.71632	+	24.8927i	0.127573	+	1.85026i	0.437152	+	0.899388i	$0.355987\pi$
$181$	1.71632	+	24.8927i	0.127573	+	1.85026i	−0.309579	+	0.950874i	$0.600188\pi$
$182$	−22.2257	+	17.8221i	−1.64748	+	1.32106i
$183$	−27.9626	−	9.04691i	−2.06705	−	0.668767i
$184$	2.29914	+	11.7020i	0.169495	+	0.862684i
$185$	11.0020	−	16.2721i	0.808884	−	1.19635i
$186$	−5.18744	+	55.0982i	−0.380362	+	4.04000i
$187$	−14.9640	−	2.26459i	−1.09428	−	0.165603i
$188$	2.22402	−	13.0367i	0.162203	−	0.950797i
$189$	−32.9528	+	7.98765i	−2.39697	+	0.581016i
$190$	−22.6217	−	3.71366i	−1.64115	−	0.269417i
$191$	0.920762	−	16.3305i	0.0666240	−	1.18163i	−0.771528	−	0.636196i	$-0.780507\pi$
$191$	0.920762	−	16.3305i	0.0666240	−	1.18163i	0.838152	−	0.545437i	$-0.183636\pi$
$192$	3.50945	+	37.2755i	0.253273	+	2.69013i
$193$	−21.5616	−	11.7974i	−1.55203	−	0.849195i	−0.999881	−	0.0154531i	$-0.995081\pi$
$193$	−21.5616	−	11.7974i	−1.55203	−	0.849195i	−0.552154	−	0.833742i	$-0.686194\pi$
$194$	1.14365	−	1.48242i	0.0821096	−	0.106431i
$195$	−34.8544	−	7.98808i	−2.49598	−	0.572038i
$196$	3.22099	−	2.71803i	0.230071	−	0.194145i
$197$	0.462524	−	0.0348000i	0.0329534	−	0.00247939i	−0.0585403	−	0.998285i	$-0.518645\pi$
$197$	0.462524	−	0.0348000i	0.0329534	−	0.00247939i	0.0914937	+	0.995806i	$0.470836\pi$
$198$	21.2174	−	24.2065i	1.50786	−	1.72028i
$199$	0.0825688	+	13.1936i	0.00585314	+	0.935271i	0.886826	+	0.462104i	$0.152905\pi$
$199$	0.0825688	+	13.1936i	0.00585314	+	0.935271i	−0.880973	+	0.473167i	$0.843111\pi$
$200$	−0.927948	+	1.77428i	−0.0656159	+	0.125461i
$201$	−13.7003	+	43.2681i	−0.966344	+	3.05190i
$202$	−6.90509	−	3.89120i	−0.485840	−	0.273784i
$203$	7.83665	+	3.79121i	0.550025	+	0.266091i
$204$	2.44180	+	55.7042i	0.170960	+	3.90008i
$205$	17.1320	−	1.93807i	1.19655	−	0.135361i
$206$	−23.3295	−	19.1919i	−1.62544	−	1.33716i
$207$	53.3717	+	24.1908i	3.70959	+	1.68138i
$208$	10.4686	+	0.919553i	0.725868	+	0.0637595i
$209$	−6.23807	−	6.93971i	−0.431496	−	0.480030i
$210$	49.0248	+	9.95113i	3.38303	+	0.686693i
$211$	−4.38204	+	3.00296i	−0.301672	+	0.206732i	−0.706594	−	0.707620i	$-0.749769\pi$
$211$	−4.38204	+	3.00296i	−0.301672	+	0.206732i	0.404921	+	0.914352i	$0.367299\pi$
$212$	13.6762	+	9.88413i	0.939285	+	0.678845i
$213$	15.1507	+	12.7849i	1.03811	+	0.876010i
$214$	2.83170	+	3.76704i	0.193571	+	0.257510i
$215$	2.24697	−	0.282716i	0.153242	−	0.0192811i
$216$	−13.6586	−	7.92382i	−0.929348	−	0.539147i
$217$	−23.4386	−	5.99299i	−1.59111	−	0.406830i
$218$	−3.09199	+	23.3917i	−0.209416	+	1.58429i
$219$	6.17141	+	0.309232i	0.417026	+	0.0208959i
$220$	−13.6714	+	5.99147i	−0.921727	+	0.403945i
$221$	30.3604	+	4.20662i	2.04226	+	0.282968i
$222$	−24.5880	−	45.6139i	−1.65024	−	3.06141i
$223$	−2.06097	+	0.997055i	−0.138013	+	0.0667677i	−0.503219	−	0.864159i	$-0.667851\pi$
$223$	−2.06097	+	0.997055i	−0.138013	+	0.0667677i	0.365206	+	0.930927i	$0.380998\pi$
$224$	−22.6671	−	1.42040i	−1.51451	−	0.0949044i
$225$	4.45008	+	8.77446i	0.296672	+	0.584964i
$226$	−2.26064	+	4.90573i	−0.150376	+	0.326325i
$227$	2.48282	−	0.569024i	0.164791	−	0.0377674i	−0.140198	−	0.990124i	$-0.544774\pi$
$227$	2.48282	−	0.569024i	0.164791	−	0.0377674i	0.304988	+	0.952356i	$0.401347\pi$
$228$	−20.6568	+	27.4800i	−1.36803	+	1.81991i
$229$	−2.83841	+	4.96398i	−0.187567	+	0.328029i	−0.946253	−	0.323428i	$-0.895165\pi$
$229$	−2.83841	+	4.96398i	−0.187567	+	0.328029i	0.758686	+	0.651457i	$0.225842\pi$
$230$	−31.0566	−	36.3396i	−2.04781	−	2.39616i
$231$	13.0343	+	15.6438i	0.857591	+	1.02928i
$232$	1.41571	+	3.79897i	0.0929461	+	0.249415i
$233$	3.32302	+	0.0415941i	0.217698	+	0.00272492i	0.121291	−	0.992617i	$-0.461297\pi$
$233$	3.32302	+	0.0415941i	0.217698	+	0.00272492i	0.0964075	+	0.995342i	$0.469265\pi$
$234$	−42.3529	+	49.5575i	−2.76870	+	3.23967i
$235$	4.30763	+	12.0168i	0.280999	+	0.783888i
$236$	−9.20994	−	6.31144i	−0.599516	−	0.410840i
$237$	14.7904	+	15.2606i	0.960740	+	0.991282i
$238$	−42.6074	−	4.81999i	−2.76183	−	0.312433i
$239$	−0.371795	+	5.39235i	−0.0240494	+	0.348802i	0.970245	+	0.242127i	$0.0778451\pi$
$239$	−0.371795	+	5.39235i	−0.0240494	+	0.348802i	−0.994294	+	0.106675i	$0.965980\pi$
$240$	−10.5263	−	15.1562i	−0.679473	−	0.978330i
$241$	−0.922015	−	0.285608i	−0.0593922	−	0.0183976i	0.266055	−	0.963958i	$-0.414280\pi$
$241$	−0.922015	−	0.285608i	−0.0593922	−	0.0183976i	−0.325447	+	0.945560i	$0.605515\pi$
$242$	12.5457	+	3.37564i	0.806467	+	0.216994i
$243$	−13.5310	+	6.13296i	−0.868017	+	0.393430i
$244$	23.4406	−	8.23752i	1.50063	−	0.527353i
$245$	−1.42058	+	3.81203i	−0.0907574	+	0.243542i
$246$	16.4153	−	42.4191i	1.04660	−	2.70454i
$247$	12.8084	+	13.8952i	0.814976	+	0.884131i
$248$	−5.95574	−	9.56369i	−0.378190	−	0.607295i
$249$	6.60432	+	2.60337i	0.418532	+	0.164982i
$250$	0.605221	+	19.3355i	0.0382775	+	1.22289i
$251$	−6.97325	+	8.58558i	−0.440147	+	0.541917i	−0.947472	−	0.319838i	$-0.896371\pi$
$251$	−6.97325	+	8.58558i	−0.440147	+	0.541917i	0.507325	+	0.861755i	$0.330634\pi$
$252$	32.6836	−	40.2406i	2.05887	−	2.53492i
$253$	−0.608748	−	19.4482i	−0.0382717	−	1.22270i
$254$	10.7068	+	4.22052i	0.671803	+	0.264819i
$255$	−28.4506	−	45.6859i	−1.78165	−	2.86096i
$256$	1.14741	+	1.24477i	0.0717129	+	0.0777980i
$257$	−2.14476	+	5.54233i	−0.133787	+	0.345721i	−0.983338	−	0.181784i	$-0.941813\pi$
$257$	−2.14476	+	5.54233i	−0.133787	+	0.345721i	0.849552	+	0.527505i	$0.176873\pi$
$258$	2.08628	−	5.59841i	0.129886	−	0.348542i
$259$	21.3713	−	7.51033i	1.32795	−	0.466669i
$260$	27.5336	−	12.4796i	1.70756	−	0.773953i
$261$	19.2364	+	5.17590i	1.19070	+	0.320380i
$262$	−6.13054	−	1.89903i	−0.378746	−	0.117322i
$263$	−14.8651	−	21.4033i	−0.916621	−	1.31979i	−0.947331	−	0.320257i	$-0.896231\pi$
$263$	−14.8651	−	21.4033i	−0.916621	−	1.31979i	0.0307093	−	0.999528i	$-0.490223\pi$
$264$	−0.652272	+	9.46026i	−0.0401446	+	0.582239i
$265$	−16.1846	−	1.83089i	−0.994209	−	0.112471i
$266$	−18.3995	−	18.9844i	−1.12814	−	1.16401i
$267$	−19.9193	−	13.6504i	−1.21904	−	0.835391i
$268$	−12.9472	−	36.1181i	−0.790875	−	2.20627i
$269$	3.85464	−	4.51034i	0.235022	−	0.275001i	−0.630153	−	0.776471i	$-0.717008\pi$
$269$	3.85464	−	4.51034i	0.235022	−	0.275001i	0.865175	+	0.501470i	$0.167207\pi$
$270$	63.2893	+	0.792190i	3.85167	+	0.0482112i
$271$	4.82843	+	12.9568i	0.293306	+	0.787069i	0.997060	+	0.0766244i	$0.0244142\pi$
$271$	4.82843	+	12.9568i	0.293306	+	0.787069i	−0.703754	+	0.710444i	$0.748494\pi$
$272$	10.1250	+	12.1520i	0.613915	+	0.736823i
$273$	−26.7917	−	31.3492i	−1.62151	−	1.89734i
$274$	−5.21200	+	9.11506i	−0.314868	+	0.550661i
$275$	1.96298	−	2.61137i	0.118372	−	0.157472i
$276$	−69.8740	+	16.0140i	−4.20592	+	0.963931i
$277$	−1.47986	+	3.21139i	−0.0889164	+	0.192954i	−0.947528	−	0.319673i	$-0.896427\pi$
$277$	−1.47986	+	3.21139i	−0.0889164	+	0.192954i	0.858612	+	0.512627i	$0.171327\pi$
$278$	−8.34105	−	16.4465i	−0.500263	−	0.986395i
$279$	−55.2508	−	3.46220i	−3.30778	−	0.207276i
$280$	−9.16759	+	4.43509i	−0.547868	+	0.265047i
$281$	6.71649	+	12.4600i	0.400672	+	0.743299i	0.998288	−	0.0584829i	$-0.0186263\pi$
$281$	6.71649	+	12.4600i	0.400672	+	0.743299i	−0.597616	+	0.801782i	$0.703885\pi$
$282$	33.3582	+	4.62198i	1.98645	+	0.275235i
$283$	13.1445	−	5.76057i	0.781362	−	0.342430i	0.0276351	−	0.999618i	$-0.491202\pi$
$283$	13.1445	−	5.76057i	0.781362	−	0.342430i	0.753727	+	0.657188i	$0.228254\pi$
$284$	−16.7383	−	0.838708i	−0.993236	−	0.0497682i
$285$	4.34849	−	32.8974i	0.257582	−	1.94868i
$286$	20.9719	+	5.36228i	1.24009	+	0.317078i
$287$	17.1988	+	9.97764i	1.01521	+	0.588961i
$288$	−51.5637	+	6.48778i	−3.03842	+	0.382296i
$289$	17.5051	+	23.2873i	1.02971	+	1.36984i
$290$	−12.4196	−	10.4803i	−0.729303	−	0.615423i
$291$	2.19657	+	1.58751i	0.128765	+	0.0930617i
$292$	−4.30911	+	2.95297i	−0.252172	+	0.172810i
$293$	17.1420	+	3.47951i	1.00145	+	0.203275i	0.671723	−	0.740802i	$-0.265554\pi$
$293$	17.1420	+	3.47951i	1.00145	+	0.203275i	0.329724	+	0.944077i	$0.393044\pi$
$294$	7.17456	+	7.98154i	0.418429	+	0.465493i
$295$	10.7357	+	0.943017i	0.625059	+	0.0549046i
$296$	9.60845	+	4.35504i	0.558480	+	0.253132i
$297$	19.8963	+	16.3676i	1.15450	+	0.949745i
$298$	−45.5578	+	5.15376i	−2.63910	+	0.298549i
$299$	1.72572	+	39.3683i	0.0998007	+	2.27673i
$300$	−10.8345	−	5.24150i	−0.625529	−	0.302618i
$301$	2.27534	+	1.28221i	0.131148	+	0.0739054i
$302$	−12.2961	+	38.8334i	−0.707561	+	2.23461i
$303$	5.31711	−	10.1666i	0.305460	−	0.584053i
$304$	0.0610311	+	9.75212i	0.00350037	+	0.559323i
$305$	−15.8081	+	18.0352i	−0.905172	+	1.03269i
$306$	−97.8424	+	7.36160i	−5.59328	+	0.420835i
$307$	−24.3522	+	20.5496i	−1.38985	+	1.17283i	−0.426535	+	0.904471i	$0.640266\pi$
$307$	−24.3522	+	20.5496i	−1.38985	+	1.17283i	−0.963319	+	0.268358i	$0.913519\pi$
$308$	−16.7791	−	3.84551i	−0.956079	−	0.219118i
$309$	26.7104	−	34.6224i	1.51950	−	1.96960i
$310$	39.6177	+	21.6768i	2.25014	+	1.23116i
$311$	−0.730941	−	7.76367i	−0.0414479	−	0.440237i	−0.991683	−	0.128704i	$-0.958918\pi$
$311$	−0.730941	−	7.76367i	−0.0414479	−	0.440237i	0.950235	−	0.311533i	$-0.100843\pi$
$312$	1.08109	−	19.1741i	0.0612049	−	1.08552i
$313$	−15.2485	−	2.50324i	−0.861895	−	0.141491i	−0.285217	−	0.958463i	$-0.592066\pi$
$313$	−15.2485	−	2.50324i	−0.861895	−	0.141491i	−0.576678	+	0.816972i	$0.695651\pi$
$314$	49.4213	−	11.9796i	2.78901	−	0.676046i
$315$	−8.41511	+	49.3275i	−0.474138	+	2.77929i
$316$	−17.7640	−	2.68832i	−0.999302	−	0.151230i
$317$	−1.38283	+	14.6877i	−0.0776676	+	0.824944i	0.867301	+	0.497784i	$0.165853\pi$
$317$	−1.38283	+	14.6877i	−0.0776676	+	0.824944i	−0.944969	+	0.327160i	$0.893908\pi$
$318$	−24.0676	+	35.5962i	−1.34964	+	1.99614i
$319$	−1.27524	−	6.49063i	−0.0713996	−	0.363405i
$320$	29.0687	+	9.40478i	1.62499	+	0.525743i
$321$	−5.32195	+	4.26751i	−0.297042	+	0.238189i
$322$	−3.79200	−	54.9975i	−0.211320	−	3.06489i
$323$	−1.24564	+	28.4165i	−0.0693092	+	1.58113i
$324$	19.8737	−	36.8683i	1.10409	−	2.04824i
$325$	−3.90895	+	5.33794i	−0.216829	+	0.296096i
$326$	3.42976	+	10.3786i	0.189957	+	0.574818i
$327$	−33.9833	−	3.41419i	−1.87928	−	0.188805i
$328$	2.57338	+	8.89501i	0.142091	+	0.491145i
$329$	−4.26800	+	14.0896i	−0.235303	+	0.776782i
$330$	−16.3387	−	34.3193i	−0.899416	−	1.88921i
$331$	−5.00805	−	2.04692i	−0.275267	−	0.112509i	0.236504	−	0.971631i	$-0.423998\pi$
$331$	−5.00805	−	2.04692i	−0.275267	−	0.112509i	−0.511771	+	0.859122i	$0.671010\pi$
$332$	−5.77531	+	1.63173i	−0.316961	+	0.0895529i
$333$	44.8364	−	26.0111i	2.45702	−	1.42540i
$334$	4.89374	−	3.72679i	0.267774	−	0.203921i
$335$	28.0034	+	24.2372i	1.52999	+	1.32422i
$336$	0.665788	−	21.2705i	0.0363217	−	1.16040i
$337$	3.86460	−	8.97057i	0.210518	−	0.488658i	−0.780044	−	0.625725i	$-0.784803\pi$
$337$	3.86460	−	8.97057i	0.210518	−	0.488658i	0.990562	+	0.137067i	$0.0437675\pi$
$338$	−15.4069	−	3.73458i	−0.838024	−	0.203134i
$339$	−7.20003	−	3.04855i	−0.391052	−	0.165575i
$340$	42.5351	+	16.1549i	2.30679	+	0.876121i
$341$	7.06114	+	16.9719i	0.382382	+	0.919082i
$342$	−49.4711	−	34.8198i	−2.67509	−	1.88284i
$343$	13.2832	−	8.62228i	0.717226	−	0.465559i
$344$	0.352617	+	1.16406i	0.0190118	+	0.0627620i
$345$	51.1699	−	46.5786i	2.75490	−	2.50771i
$346$	−14.6220	+	30.7135i	−0.786086	+	1.65117i
$347$	−2.39254	−	2.17787i	−0.128438	−	0.116914i	0.606389	−	0.795168i	$-0.292617\pi$
$347$	−2.39254	−	2.17787i	−0.128438	−	0.116914i	−0.734828	+	0.678254i	$0.762737\pi$
$348$	−22.5582	+	9.22011i	−1.20925	+	0.494250i
$349$	0.514534	−	0.402113i	0.0275424	−	0.0215246i	−0.601906	−	0.798567i	$-0.705592\pi$
$349$	0.514534	−	0.402113i	0.0275424	−	0.0215246i	0.629448	+	0.777042i	$0.283281\pi$
$350$	5.27988	−	7.60217i	0.282222	−	0.406353i
$351$	−40.7061	−	32.6410i	−2.17273	−	1.74225i
$352$	9.48618	+	14.4158i	0.505615	+	0.768362i
$353$	16.6256	−	7.78787i	0.884893	−	0.414507i	0.0723305	−	0.997381i	$-0.476956\pi$
$353$	16.6256	−	7.78787i	0.884893	−	0.414507i	0.812562	+	0.582874i	$0.198072\pi$
$354$	15.3302	−	23.9440i	0.814791	−	1.27261i
$355$	14.4731	−	7.22671i	0.768153	−	0.383554i
$356$	20.3888	−	1.02162i	1.08060	−	0.0541459i
$357$	5.04406	−	61.8630i	0.266960	−	3.27414i
$358$	8.12836	−	1.54424i	0.429597	−	0.0816157i
$359$	5.88139	−	9.44432i	0.310408	−	0.498452i	−0.656243	−	0.754550i	$-0.727855\pi$
$359$	5.88139	−	9.44432i	0.310408	−	0.498452i	0.966651	+	0.256098i	$0.0824369\pi$
$360$	−18.7151	+	13.8857i	−0.986371	+	0.731842i
$361$	0.977819	−	1.08780i	0.0514642	−	0.0572528i
$362$	39.2671	−	36.6529i	2.06383	−	1.92643i
$363$	−4.31574	+	18.3041i	−0.226518	+	0.960714i
$364$	34.0762	+	7.36207i	1.78608	+	0.385877i
$365$	2.22427	−	4.52524i	0.116424	−	0.236862i
$366$	22.8337	+	59.0049i	1.19353	+	3.08424i
$367$	22.0484	−	0.275979i	1.15092	−	0.0144060i	0.565223	−	0.824938i	$-0.308790\pi$
$367$	22.0484	−	0.275979i	1.15092	−	0.0144060i	0.585694	+	0.810533i	$0.300822\pi$
$368$	−13.0173	+	15.6234i	−0.678572	+	0.814424i
$369$	42.9253	+	15.0848i	2.23460	+	0.785286i
$370$	−42.1233	+	3.70007i	−2.18988	+	0.192357i
$371$	−13.7314	−	12.8172i	−0.712899	−	0.665438i
$372$	56.3392	−	37.5809i	2.92105	−	1.94848i
$373$	6.84196	−	26.0778i	0.354263	−	1.35026i	−0.515544	−	0.856863i	$-0.672410\pi$
$373$	6.84196	−	26.0778i	0.354263	−	1.35026i	0.869807	−	0.493393i	$-0.164243\pi$
$374$	16.5253	+	28.0789i	0.854502	+	1.45193i
$375$	−27.9474	+	1.75128i	−1.44320	+	0.0904355i
$376$	−5.97288	+	3.36587i	−0.308028	+	0.173582i
$377$	2.74695	+	13.1116i	0.141475	+	0.675280i
$378$	58.0718	+	44.2242i	2.98689	+	2.27465i
$379$	−9.33161	−	1.17411i	−0.479333	−	0.0603100i	−0.118527	−	0.992951i	$-0.537817\pi$
$379$	−9.33161	−	1.17411i	−0.479333	−	0.0603100i	−0.360806	+	0.932641i	$0.617498\pi$
$380$	13.9252	+	24.3532i	0.714346	+	1.24929i
$381$	−5.62141	+	15.6818i	−0.287993	+	0.803401i
$382$	−28.5384	+	20.6254i	−1.46015	+	1.05529i
$383$	28.8906	+	2.17371i	1.47624	+	0.111071i	0.788568	−	0.614948i	$-0.210823\pi$
$383$	28.8906	+	2.17371i	1.47624	+	0.111071i	0.687674	+	0.726019i	$0.258632\pi$
$384$	23.0765	−	22.6473i	1.17762	−	1.15571i
$385$	15.9323	−	4.71755i	0.811984	−	0.240428i
$386$	9.54994	+	52.0417i	0.486079	+	2.64885i
$387$	5.66271	+	1.91071i	0.287852	+	0.0971268i
$388$	−2.29046	+	0.0573483i	−0.116281	+	0.00291142i
$389$	−1.60768	−	6.45569i	−0.0815124	−	0.327316i	0.915706	−	0.401848i	$-0.131632\pi$
$389$	−1.60768	−	6.45569i	−0.0815124	−	0.327316i	−0.997219	+	0.0745322i	$0.976254\pi$
$390$	33.9567	+	69.0844i	1.71947	+	3.49822i
$391$	−40.1992	+	43.6103i	−2.03296	+	2.20547i
$392$	−2.14647	−	0.407791i	−0.108413	−	0.0205965i
$393$	2.46990	−	8.95571i	0.124590	−	0.451756i
$394$	−0.685898	−	0.725660i	−0.0345550	−	0.0365582i
$395$	16.2121	−	6.15737i	0.815720	−	0.309811i
$396$	−39.3628	−	1.47872i	−1.97805	−	0.0743087i
$397$	0.871499	−	0.234492i	0.0437393	−	0.0117688i	−0.237890	−	0.971292i	$-0.576456\pi$
$397$	0.871499	−	0.234492i	0.0437393	−	0.0117688i	0.281629	+	0.959523i	$0.409125\pi$
$398$	21.9349	−	18.0446i	1.09950	−	0.904495i
$399$	26.6335	−	27.4802i	1.33334	−	1.37573i
$400$	−3.34605	+	0.679187i	−0.167302	+	0.0339593i
$401$	−4.35319	−	3.22986i	−0.217388	−	0.161292i	0.481680	−	0.876347i	$-0.340027\pi$
$401$	−4.35319	−	3.22986i	−0.217388	−	0.161292i	−0.699068	+	0.715056i	$0.746401\pi$
$402$	90.8967	−	35.8307i	4.53351	−	1.78707i
$403$	−14.7294	−	34.1902i	−0.733724	−	1.70313i
$404$	1.63110	+	9.56113i	0.0811501	+	0.475684i
$405$	0.758975	+	40.4212i	0.0377138	+	2.00855i
$406$	−4.30083	−	18.2408i	−0.213446	−	0.905275i
$407$	−14.3188	−	9.55131i	−0.709756	−	0.473441i
$408$	21.6175	−	19.1886i	1.07022	−	0.949977i
$409$	−5.86118	−	6.68691i	−0.289817	−	0.330646i	0.588706	−	0.808347i	$-0.299638\pi$
$409$	−5.86118	−	6.68691i	−0.289817	−	0.330646i	−0.878523	+	0.477701i	$0.841470\pi$
$410$	−26.4905	−	25.9978i	−1.30827	−	1.28394i
$411$	−13.4238	−	7.12797i	−0.662146	−	0.351597i
$412$	−0.231348	+	36.9670i	−0.0113977	+	1.82123i
$413$	9.29503	+	8.25066i	0.457378	+	0.405988i
$414$	−32.0136	−	122.018i	−1.57338	−	5.99686i
$415$	4.08335	−	4.10898i	0.200444	−	0.201702i
$416$	−19.5755	−	28.9523i	−0.959766	−	1.41950i
$417$	23.4172	−	12.8127i	1.14674	−	0.627440i
$418$	−3.13005	+	19.8427i	−0.153096	+	0.970539i
$419$	−38.1102	+	6.74718i	−1.86180	+	0.329621i	−0.987730	−	0.156172i	$-0.950085\pi$
$419$	−38.1102	+	6.74718i	−1.86180	+	0.329621i	−0.874074	+	0.485793i	$0.838531\pi$
$420$	−28.3703	−	54.2453i	−1.38433	−	2.64690i
$421$	28.1354	−	14.9398i	1.37124	−	0.728122i	0.389980	−	0.920823i	$-0.372482\pi$
$421$	28.1354	−	14.9398i	1.37124	−	0.728122i	0.981257	+	0.192701i	$0.0617249\pi$
$422$	10.9654	+	3.24686i	0.533789	+	0.158055i
$423$	−3.57720	+	33.4970i	−0.173929	+	1.62868i
$424$	−0.492438	−	8.73381i	−0.0239149	−	0.424151i
$425$	−9.84604	+	1.49005i	−0.477603	+	0.0722783i
$426$	0.801187	−	42.6693i	0.0388176	−	2.06733i
$427$	−27.0342	+	5.84067i	−1.30828	+	0.282650i
$428$	1.39361	−	5.59608i	0.0673625	−	0.270497i
$429$	−6.80845	+	30.5851i	−0.328715	+	1.47666i
$430$	−3.52206	−	3.37106i	−0.169849	−	0.162567i
$431$	5.10643	+	14.8268i	0.245968	+	0.714182i	0.998455	+	0.0555743i	$0.0176990\pi$
$431$	5.10643	+	14.8268i	0.245968	+	0.714182i	−0.752486	+	0.658608i	$0.771146\pi$
$432$	−4.19551	−	26.5971i	−0.201857	−	1.27966i
$433$	23.7135	+	30.7377i	1.13960	+	1.47716i	0.855086	+	0.518486i	$0.173504\pi$
$433$	23.7135	+	30.7377i	1.13960	+	1.47716i	0.284510	+	0.958673i	$0.408169\pi$
$434$	21.7968	+	47.3004i	1.04628	+	2.27049i
$435$	14.6005	−	18.4434i	0.700040	−	0.884291i
$436$	24.6050	−	15.1097i	1.17837	−	0.723626i
$437$	−36.2230	+	5.01891i	−1.73278	+	0.240087i
$438$	−7.85923	−	10.7323i	−0.375528	−	0.512810i
$439$	−10.8411	+	15.1997i	−0.517416	+	0.725443i	−0.987577	−	0.157137i	$-0.949773\pi$
$439$	−10.8411	+	15.1997i	−0.517416	+	0.725443i	0.470161	+	0.882581i	$0.344196\pi$
$440$	6.87926	+	3.54321i	0.327956	+	0.168916i
$441$	−7.75559	+	7.42307i	−0.369314	+	0.353480i
$442$	−34.1764	−	56.4426i	−1.62560	−	2.68470i
$443$	−12.0717	+	12.7716i	−0.573546	+	0.606795i	−0.947149	−	0.320793i	$-0.896050\pi$
$443$	−12.0717	+	12.7716i	−0.573546	+	0.606795i	0.373603	+	0.927589i	$0.378122\pi$
$444$	−24.3584	+	58.5471i	−1.15600	+	2.77852i
$445$	−16.6613	+	10.5210i	−0.789821	+	0.498743i
$446$	4.46330	+	2.09072i	0.211343	+	0.0989987i
$447$	−9.51965	−	65.6800i	−0.450264	−	3.10656i
$448$	20.4596	+	28.6855i	0.966627	+	1.35526i
$449$	−0.884458	+	2.67641i	−0.0417402	+	0.126308i	−0.968265	−	0.249926i	$-0.919594\pi$
$449$	−0.884458	+	2.67641i	−0.0417402	+	0.126308i	0.926525	+	0.376234i	$0.122781\pi$
$450$	8.62266	−	19.3451i	0.406476	−	0.911937i
$451$	−1.79219	−	15.0014i	−0.0843909	−	0.706386i
$452$	6.40399	−	1.63743i	0.301218	−	0.0770183i
$453$	−56.7413	−	16.0315i	−2.66594	−	0.753223i
$454$	−4.32059	−	3.37658i	−0.202775	−	0.158471i
$455$	−32.1442	+	9.95716i	−1.50694	+	0.466799i
$456$	17.8093	−	0.669036i	0.833999	−	0.0313305i
$457$	−10.9591	+	4.64019i	−0.512646	+	0.217059i	−0.630813	−	0.775935i	$-0.717278\pi$
$457$	−10.9591	+	4.64019i	−0.512646	+	0.217059i	0.118166	+	0.992994i	$0.462298\pi$
$458$	12.1473	−	1.99414i	0.567606	−	0.0931801i
$459$	−8.33924	−	78.0888i	−0.389243	−	3.64487i
$460$	−10.5583	+	57.5364i	−0.492281	+	2.68265i
$461$	3.83705	−	6.90975i	0.178709	−	0.321819i	−0.769958	−	0.638094i	$-0.779723\pi$
$461$	3.83705	−	6.90975i	0.178709	−	0.321819i	0.948668	+	0.316275i	$0.102432\pi$
$462$	8.45087	−	43.0127i	0.393170	−	2.00113i
$463$	15.2260	+	15.3216i	0.707613	+	0.712055i	0.967299	−	0.253638i	$-0.0816271\pi$
$463$	15.2260	+	15.3216i	0.707613	+	0.712055i	−0.259686	+	0.965693i	$0.583619\pi$
$464$	−3.50642	+	5.95793i	−0.162781	+	0.276590i
$465$	−29.5680	+	58.3009i	−1.37118	+	2.70364i
$466$	−4.44056	−	5.60932i	−0.205705	−	0.259847i
$467$	−6.36806	−	2.32782i	−0.294679	−	0.107719i	0.191736	−	0.981446i	$-0.438588\pi$
$467$	−6.36806	−	2.32782i	−0.294679	−	0.107719i	−0.486415	+	0.873728i	$0.661696\pi$
$468$	79.7494	+	1.99675i	3.68642	+	0.0923000i
$469$	9.28061	+	41.6906i	0.428539	+	1.92509i
$470$	14.2340	−	23.5076i	0.656566	−	1.08432i
$471$	19.5702	+	70.9606i	0.901749	+	3.26969i
$472$	0.470373	+	5.76890i	0.0216507	+	0.265535i
$473$	−0.260053	−	1.96737i	−0.0119572	−	0.0904596i
$474$	5.42712	−	45.4272i	0.249276	−	2.08654i
$475$	−5.27184	−	3.14722i	−0.241889	−	0.144404i
$476$	28.2933	+	44.1909i	1.29682	+	2.02548i
$477$	−36.3431	−	22.9493i	−1.66404	−	1.05078i
$478$	9.51540	−	6.69732i	0.435224	−	0.306328i
$479$	8.49380	−	21.1583i	0.388092	−	0.966749i	−0.598142	−	0.801390i	$-0.704094\pi$
$479$	8.49380	−	21.1583i	0.388092	−	0.966749i	0.986234	−	0.165358i	$-0.0528780\pi$
$480$	−17.0548	+	58.9510i	−0.778444	+	2.69073i
$481$	29.2385	+	18.9790i	1.33316	+	0.865369i
$482$	0.774117	+	1.92835i	0.0352601	+	0.0878339i
$483$	79.3991	−	7.97694i	3.61278	−	0.362964i
$484$	−6.47256	−	14.5213i	−0.294207	−	0.660059i
$485$	1.89893	−	1.13364i	0.0862259	−	0.0514758i
$486$	28.6130	+	14.2870i	1.29791	+	0.648072i
$487$	7.53115	+	3.30051i	0.341269	+	0.149561i	0.565001	−	0.825090i	$-0.308876\pi$
$487$	7.53115	+	3.30051i	0.341269	+	0.149561i	−0.223732	+	0.974651i	$0.571824\pi$
$488$	−10.9760	−	6.74027i	−0.496859	−	0.305118i
$489$	−14.8605	+	5.43221i	−0.672017	+	0.245653i
$490$	8.29805	−	2.79993i	0.374868	−	0.126488i
$491$	−14.9306	−	26.8869i	−0.673807	−	1.21339i	−0.966373	−	0.257144i	$-0.917218\pi$
$491$	−14.9306	−	26.8869i	−0.673807	−	1.21339i	0.292566	−	0.956245i	$-0.405491\pi$
$492$	−52.9578	+	17.1338i	−2.38752	+	0.772450i
$493$	−11.0837	+	16.8434i	−0.499184	+	0.758589i
$494$	5.83557	−	40.2620i	0.262555	−	1.81147i
$495$	33.8019	−	17.4098i	1.51928	−	0.782514i
$496$	6.25595	−	18.1645i	0.280901	−	0.815610i
$497$	18.3704	+	3.25237i	0.824026	+	0.145889i
$498$	−4.61320	−	14.5694i	−0.206722	−	0.652869i
$499$	1.83910	−	8.77825i	0.0823293	−	0.392969i	−0.917661	−	0.397364i	$-0.869925\pi$
$499$	1.83910	−	8.77825i	0.0823293	−	0.392969i	0.999990	+	0.00439548i	$0.00139913\pi$
$500$	17.8996	−	15.4923i	0.800497	−	0.692837i
$501$	5.61357	+	6.91153i	0.250796	+	0.308784i
$502$	23.8110			1.06274
$503$	−16.1435	−	15.5688i	−0.719804	−	0.694177i
$503$	−16.1435	−	15.5688i	−0.719804	−	0.694177i
$504$	−26.8750			−1.19711
$505$	−5.90248	−	7.26723i	−0.262657	−	0.323388i
$506$	−31.6724	+	27.4127i	−1.40801	+	1.21864i
$507$	4.70549	−	22.4599i	0.208978	−	0.997480i
$508$	−4.25129	−	13.4264i	−0.188620	−	0.595699i
$509$	−40.6319	−	7.19363i	−1.80098	−	0.318852i	−0.829953	−	0.557834i	$-0.811633\pi$
$509$	−40.6319	−	7.19363i	−1.80098	−	0.318852i	−0.971024	+	0.238982i	$0.923186\pi$
$510$	−37.7288	+	109.548i	−1.67066	+	4.85085i
$511$	5.16964	−	2.66265i	0.228692	−	0.117789i
$512$	3.49943	−	24.1440i	0.154654	−	1.06702i
$513$	26.6168	−	40.4484i	1.17516	−	1.78584i
$514$	12.1723	−	3.93819i	0.536898	−	0.173706i
$515$	−17.3234	−	31.1960i	−0.763362	−	1.37466i
$516$	−6.92743	+	2.33745i	−0.304963	+	0.102901i
$517$	10.5061	−	3.84047i	0.462058	−	0.168904i
$518$	−41.5556	−	25.5190i	−1.82585	−	1.12124i
$519$	−45.0986	−	19.7644i	−1.97961	−	0.867560i
$520$	−14.0207	−	7.00083i	−0.614850	−	0.307007i
$521$	−0.0802623	+	0.0479156i	−0.00351636	+	0.00209922i	−0.514349	−	0.857581i	$-0.671967\pi$
$521$	−0.0802623	+	0.0479156i	−0.00351636	+	0.00209922i	0.510833	+	0.859680i	$0.329337\pi$
$522$	−17.4590	−	39.1695i	−0.764158	−	1.71440i
$523$	−44.8759	+	4.50853i	−1.96229	+	0.197144i	−0.997763	−	0.0668485i	$-0.978706\pi$
$523$	−44.8759	+	4.50853i	−1.96229	+	0.197144i	−0.964525	+	0.263993i	$0.914961\pi$
$524$	2.92587	+	7.28843i	0.127817	+	0.318397i
$525$	11.2380	+	7.29470i	0.490466	+	0.318367i
$526$	−15.5904	+	53.8891i	−0.679774	+	2.34967i
$527$	20.8746	−	51.9994i	0.909313	−	2.26513i
$528$	−13.2230	+	9.30686i	−0.575455	+	0.405029i
$529$	−45.0282	−	28.4337i	−1.95775	−	1.23625i
$530$	18.9065	+	29.5298i	0.821247	+	1.28269i
$531$	24.4195	+	14.5781i	1.05972	+	0.632638i
$532$	−3.83780	+	32.1240i	−0.166390	+	1.39275i
$533$	4.00954	+	30.3332i	0.173672	+	1.31388i
$534$	4.22457	+	51.8123i	0.182815	+	2.24214i
$535$	1.47997	+	5.36628i	0.0639846	+	0.232005i
$536$	−10.3025	+	17.0146i	−0.444999	+	0.734919i
$537$	2.60232	+	11.6902i	0.112299	+	0.504471i
$538$	−12.7685	−	0.319696i	−0.550490	−	0.0137831i
$539$	3.34809	+	1.22388i	0.144212	+	0.0527163i
$540$	−48.0754	−	60.7289i	−2.06884	−	2.61336i
$541$	16.1901	−	31.9229i	0.696068	−	1.37247i	−0.221605	−	0.975137i	$-0.571129\pi$
$541$	16.1901	−	31.9229i	0.696068	−	1.37247i	0.917673	−	0.397338i	$-0.130066\pi$
$542$	15.0979	−	25.6537i	0.648512	−	1.10192i
$543$	54.8080	+	55.1520i	2.35203	+	2.36680i
$544$	10.1412	−	51.6159i	0.434799	−	2.21301i
$545$	−13.5307	+	24.3660i	−0.579591	+	1.04373i
$546$	−16.0232	+	87.3174i	−0.685731	+	3.73684i
$547$	2.87242	+	26.8974i	0.122816	+	1.15005i	0.872624	+	0.488393i	$0.162417\pi$
$547$	2.87242	+	26.8974i	0.122816	+	1.15005i	−0.749808	+	0.661655i	$0.769854\pi$
$548$	12.6794	−	2.08148i	0.541635	−	0.0889166i
$549$	−58.2799	+	24.6762i	−2.48732	+	1.05315i
$550$	−7.02788	+	0.264013i	−0.299670	+	0.0112576i
$551$	−11.8751	+	3.67848i	−0.505895	+	0.156709i
$552$	29.2813	+	22.8836i	1.24629	+	0.973990i
$553$	19.2462	+	5.43774i	0.818432	+	0.231236i
$554$	7.37484	−	1.88567i	0.313327	−	0.0801144i
$555$	−7.26090	−	60.7767i	−0.308208	−	2.57983i
$556$	−9.18717	+	20.6116i	−0.389623	+	0.874125i
$557$	−4.18155	+	12.6536i	−0.177178	+	0.536149i	−0.999458	−	0.0329344i	$-0.989515\pi$
$557$	−4.18155	+	12.6536i	−0.177178	+	0.536149i	0.822280	+	0.569084i	$0.192702\pi$
$558$	69.2020	+	97.0247i	2.92955	+	4.10738i
$559$	0.576490	+	3.97744i	0.0243829	+	0.168228i
$560$	−15.7259	−	7.36643i	−0.664541	−	0.311288i
$561$	−39.8764	+	25.1805i	−1.68358	+	1.06312i
$562$	11.7052	−	28.1344i	0.493756	−	1.18678i
$563$	−4.57371	+	4.83886i	−0.192759	+	0.203933i	−0.815928	−	0.578154i	$-0.803773\pi$
$563$	−4.57371	+	4.83886i	−0.192759	+	0.203933i	0.623169	+	0.782087i	$0.285845\pi$
$564$	−21.3456	−	35.2524i	−0.898812	−	1.48440i
$565$	−4.60932	+	4.41169i	−0.193915	+	0.185601i
$566$	−27.4661	−	14.1466i	−1.15449	−	0.594625i
$567$	−27.0733	+	37.9581i	−1.13697	+	1.59409i
$568$	5.13315	+	7.00967i	0.215382	+	0.294119i
$569$	45.8128	−	6.34763i	1.92057	−	0.266107i	0.926626	−	0.375983i	$-0.122695\pi$
$569$	45.8128	−	6.34763i	1.92057	−	0.266107i	0.993945	+	0.109877i	$0.0350456\pi$
$570$	−60.8745	+	37.3826i	−2.54975	+	1.56578i
$571$	20.5729	−	25.9878i	0.860951	−	1.08755i	−0.134370	−	0.990931i	$-0.542901\pi$
$571$	20.5729	−	25.9878i	0.860951	−	1.08755i	0.995321	−	0.0966229i	$-0.0308041\pi$
$572$	−11.0863	−	24.0579i	−0.463541	−	1.00591i
$573$	−31.1334	−	40.3556i	−1.30062	−	1.68588i
$574$	−6.66963	−	42.2816i	−0.278385	−	1.76480i
$575$	−4.16903	−	12.1050i	−0.173861	−	0.504814i
$576$	58.2458	+	55.7485i	2.42691	+	2.32285i
$577$	0.659657	−	2.96333i	0.0274619	−	0.123365i	−0.960426	−	0.278536i	$-0.910151\pi$
$577$	0.659657	−	2.96333i	0.0274619	−	0.123365i	0.987888	+	0.155171i	$0.0495930\pi$
$578$	15.1555	−	60.8575i	0.630385	−	2.53134i
$579$	−74.8618	+	16.1737i	−3.11115	+	0.672156i
$580$	−0.373332	+	19.8828i	−0.0155018	+	0.825587i
$581$	6.60541	−	0.999632i	0.274038	−	0.0414717i
$582$	−0.328439	−	5.82514i	−0.0136142	−	0.241460i
$583$	−1.51557	+	14.1918i	−0.0627684	+	0.587765i
$584$	2.59665	+	0.768867i	0.107450	+	0.0318160i
$585$	−68.0094	+	36.1127i	−2.81184	+	1.49308i
$586$	−17.4511	−	33.3673i	−0.720898	−	1.37839i
$587$	−32.4925	+	5.75260i	−1.34111	+	0.237435i	−0.798219	−	0.602368i	$-0.794224\pi$
$587$	−32.4925	+	5.75260i	−1.34111	+	0.237435i	−0.542891	+	0.839803i	$0.682670\pi$
$588$	2.04637	−	12.9728i	0.0843909	−	0.534990i
$589$	30.3077	−	16.5828i	1.24881	−	0.683283i
$590$	−12.9949	−	19.2196i	−0.534993	−	0.791260i
$591$	1.01883	−	1.02522i	0.0419090	−	0.0421721i
$592$	4.56513	+	17.3997i	0.187626	+	0.715125i
$593$	16.5737	+	14.7115i	0.680599	+	0.604129i	0.931438	−	0.363900i	$-0.118555\pi$
$593$	16.5737	+	14.7115i	0.680599	+	0.604129i	−0.250839	+	0.968029i	$0.580706\pi$
$594$	0.347093	−	55.4618i	0.0142414	−	2.27563i
$595$	−44.7338	−	23.7535i	−1.83391	−	0.973797i
$596$	40.0435	+	39.2987i	1.64025	+	1.60974i
$597$	27.1004	+	30.9184i	1.10915	+	1.26540i
$598$	63.4436	−	56.3152i	2.59440	−	2.30290i
$599$	11.2846	+	7.52739i	0.461077	+	0.307561i	0.763725	−	0.645542i	$-0.223368\pi$
$599$	11.2846	+	7.52739i	0.461077	+	0.307561i	−0.302647	+	0.953103i	$0.597870\pi$
$600$	1.43188	+	6.07293i	0.0584562	+	0.247926i
$601$	−0.177324	−	9.44383i	−0.00723318	−	0.385222i	−0.984712	−	0.174189i	$-0.944270\pi$
$601$	−0.177324	−	9.44383i	−0.00723318	−	0.385222i	0.977479	−	0.211033i	$-0.0676826\pi$
$602$	−0.945516	−	5.54240i	−0.0385363	−	0.225891i
$603$	38.6690	+	89.7592i	1.57472	+	3.65528i
$604$	46.3738	−	18.2802i	1.88692	−	0.743810i
$605$	12.3243	+	9.14408i	0.501055	+	0.371760i
$606$	−24.2051	+	4.91319i	−0.983265	+	0.199585i
$607$	16.0840	−	16.5953i	0.652830	−	0.673584i	−0.307789	−	0.951455i	$-0.599589\pi$
$607$	16.0840	−	16.5953i	0.652830	−	0.673584i	0.960618	+	0.277871i	$0.0896288\pi$
$608$	25.0467	−	20.6046i	1.01578	−	0.835625i
$609$	26.1961	−	7.04853i	1.06152	−	0.285621i
$610$	51.5926	+	1.93816i	2.08892	+	0.0784736i
$611$	−21.1782	+	8.04348i	−0.856776	+	0.325404i
$612$	82.4784	+	87.2598i	3.33399	+	3.52727i
$613$	0.0988250	−	0.358334i	0.00399150	−	0.0144730i	−0.961988	−	0.273093i	$-0.911953\pi$
$613$	0.0988250	−	0.358334i	0.00399150	−	0.0144730i	0.965979	+	0.258621i	$0.0832679\pi$
$614$	67.3904	+	12.8030i	2.71965	+	0.516685i
$615$	36.4141	−	39.5040i	1.46836	−	1.59295i
$616$	3.93653	+	8.00881i	0.158607	+	0.322684i
$617$	10.9810	+	44.0945i	0.442078	+	1.77518i	0.613198	+	0.789929i	$0.289883\pi$
$617$	10.9810	+	44.0945i	0.442078	+	1.77518i	−0.171121	+	0.985250i	$0.554739\pi$
$618$	−94.1070	+	2.35624i	−3.78554	+	0.0947817i
$619$	42.4987	+	14.3399i	1.70817	+	0.576370i	0.992519	−	0.122091i	$-0.0389598\pi$
$619$	42.4987	+	14.3399i	1.70817	+	0.576370i	0.715649	+	0.698460i	$0.246131\pi$
$620$	−9.97465	−	54.3561i	−0.400592	−	2.18299i
$621$	96.8118	−	28.6660i	3.88492	−	1.15033i
$622$	−11.9813	+	11.7584i	−0.480406	+	0.471470i
$623$	−22.6608	−	1.70498i	−0.907885	−	0.0683087i
$624$	26.5414	−	19.1821i	1.06250	−	0.767899i
$625$	−10.1844	+	28.4109i	−0.407375	+	1.13644i
$626$	16.5125	+	28.8781i	0.659974	+	1.15420i
$627$	−28.8503	−	3.62997i	−1.15217	−	0.144967i
$628$	−49.5079	−	37.7024i	−1.97558	−	1.50449i
$629$	10.7584	+	51.3511i	0.428964	+	2.04750i
$630$	93.8489	−	52.8863i	3.73903	−	2.10704i
$631$	−33.1429	+	2.07685i	−1.31940	+	0.0826780i	−0.706630	−	0.707583i	$-0.749785\pi$
$631$	−33.1429	+	2.07685i	−1.31940	+	0.0826780i	−0.612770	+	0.790261i	$0.709945\pi$
$632$	4.72408	+	8.02691i	0.187914	+	0.319293i
$633$	−4.20100	+	16.0119i	−0.166975	+	0.636416i
$634$	26.4204	−	17.6237i	1.04929	−	0.699926i
$635$	9.93753	+	9.27595i	0.394359	+	0.368105i
$636$	52.3806	−	4.60106i	2.07703	−	0.182444i
$637$	−6.81110	−	2.39357i	−0.269866	−	0.0948365i
$638$	−9.11526	+	10.9402i	−0.360877	+	0.433125i
$639$	42.6868	−	0.534309i	1.68866	−	0.0211369i
$640$	−9.52212	−	24.6063i	−0.376395	−	0.972650i
$641$	−2.42520	+	4.93403i	−0.0957897	+	0.194882i	−0.940038	−	0.341070i	$-0.889211\pi$
$641$	−2.42520	+	4.93403i	−0.0957897	+	0.194882i	0.844248	+	0.535952i	$0.180047\pi$
$642$	14.3542	+	3.10119i	0.566515	+	0.122394i
$643$	0.562190	−	2.38438i	0.0221706	−	0.0940307i	−0.961090	−	0.276235i	$-0.910913\pi$
$643$	0.562190	−	2.38438i	0.0221706	−	0.0940307i	0.983261	+	0.182205i	$0.0583234\pi$
$644$	−49.3159	+	46.0327i	−1.94332	+	1.81394i
$645$	4.71777	−	5.24841i	0.185762	−	0.206656i
$646$	49.1754	−	36.4859i	1.93478	−	1.43552i
$647$	−10.7864	+	17.3208i	−0.424058	+	0.680950i	−0.989612	−	0.143761i	$-0.954080\pi$
$647$	−10.7864	+	17.3208i	−0.424058	+	0.680950i	0.565555	+	0.824711i	$0.308662\pi$
$648$	−21.3313	+	4.05256i	−0.837972	+	0.159200i
$649$	0.767449	−	9.41240i	0.0301250	−	0.369469i
$650$	14.2252	−	0.712782i	0.557957	−	0.0279576i
$651$	−67.4474	+	33.6778i	−2.64347	+	1.31994i
$652$	7.21245	−	11.2650i	0.282461	−	0.441172i
$653$	−25.3085	+	11.8551i	−0.990397	+	0.463928i	−0.850350	−	0.526217i	$-0.823610\pi$
$653$	−25.3085	+	11.8551i	−0.990397	+	0.463928i	−0.140047	+	0.990145i	$0.544725\pi$
$654$	40.4177	+	61.4210i	1.58046	+	2.40175i
$655$	−5.91429	−	4.74250i	−0.231091	−	0.185305i
$656$	−9.00706	+	12.9687i	−0.351667	+	0.506343i
$657$	10.4845	−	8.19371i	0.409038	−	0.319667i
$658$	29.3367	−	11.9907i	1.14366	−	0.467444i
$659$	2.40741	+	2.19140i	0.0937794	+	0.0853649i	0.718687	−	0.695334i	$-0.244744\pi$
$659$	2.40741	+	2.19140i	0.0937794	+	0.0853649i	−0.624907	+	0.780699i	$0.714863\pi$
$660$	−19.9941	+	41.9973i	−0.778269	+	1.63474i
$661$	23.8419	−	21.7027i	0.927344	−	0.844136i	−0.0607240	−	0.998155i	$-0.519341\pi$
$661$	23.8419	−	21.7027i	0.927344	−	0.844136i	0.988068	+	0.154018i	$0.0492214\pi$
$662$	3.37656	+	11.1467i	0.131234	+	0.433230i
$663$	80.1138	−	52.0027i	3.11136	−	2.01962i
$664$	2.54418	+	1.79070i	0.0987333	+	0.0694925i
$665$	−11.9957	−	28.8325i	−0.465173	−	1.11808i
$666$	−104.318	−	39.6201i	−4.04225	−	1.53525i
$667$	−23.8713	−	10.1073i	−0.924299	−	0.391356i
$668$	−7.31557	−	1.77327i	−0.283048	−	0.0686098i
$669$	−2.82275	+	6.55221i	−0.109134	+	0.253323i
$670$	2.49436	−	79.6896i	0.0963657	−	3.07868i
$671$	15.8901	+	13.7530i	0.613431	+	0.530930i
$672$	−56.3049	+	42.8786i	−2.17201	+	1.65408i
$673$	−2.09394	+	1.21477i	−0.0807155	+	0.0468259i	−0.541617	−	0.840626i	$-0.682188\pi$
$673$	−2.09394	+	1.21477i	−0.0807155	+	0.0468259i	0.460901	+	0.887451i	$0.347526\pi$
$674$	−20.2352	+	5.71717i	−0.779431	+	0.220217i
$675$	15.6918	+	6.41365i	0.603979	+	0.246861i
$676$	8.33903	+	17.5160i	0.320732	+	0.673694i
$677$	3.53341	−	11.6645i	0.135800	−	0.448304i	−0.862534	−	0.505999i	$-0.831124\pi$
$677$	3.53341	−	11.6645i	0.135800	−	0.448304i	0.998334	+	0.0576950i	$0.0183751\pi$
$678$	4.67779	+	16.1690i	0.179650	+	0.620968i
$679$	2.53772	+	0.254955i	0.0973887	+	0.00978429i
$680$	−7.40114	−	22.3962i	−0.283821	−	0.858855i
$681$	4.68960	−	6.40397i	0.179706	−	0.245401i
$682$	18.7771	−	34.8340i	0.719013	−	1.33386i
$683$	−0.864534	+	19.7224i	−0.0330805	+	0.754657i	0.908503	+	0.417878i	$0.137226\pi$
$683$	−0.864534	+	19.7224i	−0.0330805	+	0.754657i	−0.941584	+	0.336779i	$0.890662\pi$
$684$	5.09224	+	73.8556i	0.194707	+	2.82394i
$685$	−9.67599	+	7.75889i	−0.369701	+	0.296452i
$686$	−32.4363	−	10.4943i	−1.23842	−	0.400676i
$687$	3.43525	+	17.4845i	0.131063	+	0.667075i
$688$	−1.16169	+	1.71815i	−0.0442889	+	0.0655037i
$689$	2.70939	−	28.7777i	0.103219	−	1.09634i
$690$	−147.283	−	22.2892i	−5.60698	−	0.848534i
$691$	3.56990	−	20.9259i	0.135805	−	0.796060i	−0.833924	−	0.551879i	$-0.813911\pi$
$691$	3.56990	−	20.9259i	0.135805	−	0.796060i	0.969730	−	0.244181i	$-0.0785192\pi$
$692$	40.4553	−	9.80622i	1.53788	−	0.372777i
$693$	43.2695	+	7.10327i	1.64367	+	0.269831i
$694$	−0.392080	+	6.95386i	−0.0148831	+	0.263965i
$695$	−2.04175	−	21.6864i	−0.0774481	−	0.822612i
$696$	11.0830	+	6.06405i	0.420099	+	0.229857i
$697$	−28.1301	+	36.4626i	−1.06550	+	1.38112i
$698$	−1.37028	−	0.314046i	−0.0518658	−	0.0118868i
$699$	7.91451	−	6.67866i	0.299354	−	0.252610i
$700$	−11.2946	+	0.849802i	−0.426898	+	0.0321195i
$701$	−13.7443	+	15.6806i	−0.519115	+	0.592249i	−0.950812	−	0.309770i	$-0.899748\pi$
$701$	−13.7443	+	15.6806i	−0.519115	+	0.592249i	0.431696	+	0.902019i	$0.357915\pi$
$702$	0.702939	+	112.322i	0.0265307	+	4.23933i
$703$	−14.9917	+	28.6648i	−0.565423	+	1.08112i
$704$	8.08156	−	25.5231i	0.304585	−	0.961938i
$705$	34.6555	+	19.5293i	1.30520	+	0.735516i
$706$	−35.5784	−	17.2121i	−1.33901	−	0.647786i
$707$	−0.472834	−	10.7866i	−0.0177827	−	0.405673i
$708$	−34.5714	+	3.91091i	−1.29927	+	0.146981i
$709$	−7.84862	−	6.45662i	−0.294761	−	0.242484i	0.476243	−	0.879314i	$-0.341998\pi$
$709$	−7.84862	−	6.45662i	−0.294761	−	0.242484i	−0.771004	+	0.636830i	$0.780245\pi$
$710$	−31.7192	−	14.3768i	−1.19040	−	0.539551i
$711$	45.5890	+	4.00449i	1.70972	+	0.150180i
$712$	−7.07485	−	7.87061i	−0.265141	−	0.294964i
$713$	70.5996	+	14.3304i	2.64398	+	0.536679i
$714$	−110.221	+	75.5328i	−4.12491	+	2.82675i
$715$	20.7234	+	14.9773i	0.775010	+	0.560119i
$716$	−7.73791	−	6.52964i	−0.289179	−	0.244024i
$717$	10.1207	+	13.4636i	0.377963	+	0.502809i
$718$	−23.7641	+	2.99002i	−0.886868	+	0.111586i
$719$	4.16289	+	2.41504i	0.155250	+	0.0900657i	0.577405	−	0.816458i	$-0.304065\pi$
$719$	4.16289	+	2.41504i	0.155250	+	0.0900657i	−0.422156	+	0.906523i	$0.638727\pi$
$720$	−38.4989	−	9.84376i	−1.43477	−	0.366855i
$721$	5.39264	−	40.7967i	0.200832	−	1.51935i
$722$	−3.14487	−	0.157580i	−0.117040	−	0.00586453i
$723$	−2.75489	+	1.20733i	−0.102456	+	0.0449009i
$724$	−65.1108	−	9.02149i	−2.41982	−	0.335281i
$725$	−2.06519	−	3.83119i	−0.0766991	−	0.142287i
$726$	36.4441	−	17.6309i	1.35257	−	0.654344i
$727$	−18.5635	−	1.16325i	−0.688481	−	0.0431425i	−0.285537	−	0.958368i	$-0.592172\pi$
$727$	−18.5635	−	1.16325i	−0.688481	−	0.0431425i	−0.402943	+	0.915225i	$0.632013\pi$
$728$	−8.17471	−	16.1185i	−0.302975	−	0.597392i
$729$	0.586962	−	1.27374i	0.0217393	−	0.0471757i
$730$	−10.5806	+	2.42492i	−0.391607	+	0.0897502i
$731$	−3.63473	+	4.83533i	−0.134435	+	0.178841i
$732$	38.4318	−	67.2119i	1.42048	−	2.48422i
$733$	−15.0991	−	17.6676i	−0.557700	−	0.652569i	0.407770	−	0.913085i	$-0.366307\pi$
$733$	−15.0991	−	17.6676i	−0.557700	−	0.652569i	−0.965470	+	0.260516i	$0.916107\pi$
$734$	−30.3857	−	36.4690i	−1.12156	−	1.34609i
$735$	4.42675	+	11.8789i	0.163283	+	0.438159i
$736$	67.6240	+	0.846447i	2.49265	+	0.0312005i
$737$	21.0843	−	24.6709i	0.776651	−	0.908766i
$738$	−33.0518	−	92.2029i	−1.21665	−	3.39404i
$739$	−8.31824	−	5.70038i	−0.305991	−	0.209692i	0.402484	−	0.915427i	$-0.368147\pi$
$739$	−8.31824	−	5.70038i	−0.305991	−	0.209692i	−0.708476	+	0.705735i	$0.750617\pi$
$740$	36.0129	+	37.1578i	1.32386	+	1.36595i
$741$	58.5156	+	6.61962i	2.14963	+	0.243178i
$742$	−2.78148	+	40.3414i	−0.102111	+	1.48098i
$743$	−5.77030	−	8.30829i	−0.211692	−	0.304802i	0.701231	−	0.712934i	$-0.252634\pi$
$743$	−5.77030	−	8.30829i	−0.211692	−	0.304802i	−0.912923	+	0.408133i	$0.866180\pi$
$744$	−33.5362	−	10.3884i	−1.22950	−	0.380855i
$745$	−52.2965	−	14.0713i	−1.91600	−	0.515532i
$746$	−52.8628	+	23.9601i	−1.93545	+	0.877243i
$747$	14.4224	−	5.06834i	0.527688	−	0.185441i
$748$	13.9225	−	37.3601i	0.509057	−	1.36602i
$749$	−2.31686	+	5.98704i	−0.0846561	+	0.218762i
$750$	40.8572	+	44.3241i	1.49189	+	1.61849i
$751$	6.83240	+	10.9714i	0.249318	+	0.400354i	0.949576	−	0.313536i	$-0.101514\pi$
$751$	6.83240	+	10.9714i	0.249318	+	0.400354i	−0.700258	+	0.713889i	$0.746932\pi$
$752$	−10.8762	−	4.28732i	−0.396616	−	0.156343i
$753$	1.07832	+	34.4499i	0.0392960	+	1.25542i
$754$	18.1816	−	22.3855i	0.662136	−	0.815233i
$755$	−30.3342	+	37.3480i	−1.10397	+	1.35923i
$756$	−2.79458	−	89.2808i	−0.101638	−	3.24711i
$757$	−16.9872	−	6.69623i	−0.617412	−	0.243379i	0.0372433	−	0.999306i	$-0.488142\pi$
$757$	−16.9872	−	6.69623i	−0.617412	−	0.243379i	−0.654655	+	0.755928i	$0.727186\pi$
$758$	10.7031	+	17.1869i	0.388753	+	0.624258i
$759$	−41.0953	−	44.5824i	−1.49166	−	1.61824i
$760$	5.24858	−	13.5630i	0.190386	−	0.491981i
$761$	−8.47967	+	22.7547i	−0.307388	+	0.824855i	0.687712	+	0.725983i	$0.258615\pi$
$761$	−8.47967	+	22.7547i	−0.307388	+	0.824855i	−0.995100	+	0.0988720i	$0.968477\pi$
$762$	33.8342	−	11.8901i	1.22568	−	0.430731i
$763$	−29.2752	+	13.2690i	−1.05983	+	0.480371i
$764$	41.6093	+	11.1957i	1.50537	+	0.405047i
$765$	−110.709	−	34.2938i	−4.00269	−	1.23989i
$766$	−35.5786	−	51.2274i	−1.28551	−	1.85092i
$767$	−1.31555	+	19.0801i	−0.0475017	+	0.688943i
$768$	5.24198	+	0.593003i	0.189154	+	0.0213981i
$769$	30.7551	+	31.7329i	1.10906	+	1.14432i	0.988439	+	0.151618i	$0.0484482\pi$
$769$	30.7551	+	31.7329i	1.10906	+	1.14432i	0.120619	+	0.992699i	$0.461512\pi$
$770$	−29.5068	−	20.2206i	−1.06335	−	0.728699i
$771$	6.24905	+	17.4327i	0.225054	+	0.627822i
$772$	42.0659	−	49.2217i	1.51399	−	1.77153i
$773$	−4.09303	−	0.0512323i	−0.147216	−	0.00184270i	−0.0611260

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:	\( N \)	\(=\)	\( 503 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	503.c (of order \(251\), degree \(250\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35722 - 1.67103i) q^{2} +(2.35620 - 2.03931i) q^{3} +(-0.540193 + 2.57841i) q^{4} +(-0.767603 - 2.42424i) q^{5} +(-6.60563 - 1.16949i) q^{6} +(0.954936 - 2.77271i) q^{7} +(1.21411 - 0.625336i) q^{8} +(0.962553 - 6.64105i) q^{9} +O(q^{10})\)	\(q+(-1.35722 - 1.67103i) q^{2} +(2.35620 - 2.03931i) q^{3} +(-0.540193 + 2.57841i) q^{4} +(-0.767603 - 2.42424i) q^{5} +(-6.60563 - 1.16949i) q^{6} +(0.954936 - 2.77271i) q^{7} +(1.21411 - 0.625336i) q^{8} +(0.962553 - 6.64105i) q^{9} +(-3.00917 + 4.57291i) q^{10} +(-2.12003 + 0.685909i) q^{11} +(3.98538 + 7.17686i) q^{12} +(4.27581 - 1.44274i) q^{13} +(-5.92934 + 2.16745i) q^{14} +(-6.75239 - 4.14660i) q^{15} +(2.13293 + 0.934753i) q^{16} +(6.07671 + 3.03422i) q^{17} +(-12.4038 + 7.40491i) q^{18} +(1.70491 + 3.82500i) q^{19} +(6.66533 - 0.669642i) q^{20} +(-3.40440 - 8.48046i) q^{21} +(4.02353 + 2.61172i) q^{22} +(-2.42681 + 8.38838i) q^{23} +(1.58544 - 3.94937i) q^{24} +(-1.19894 + 0.843860i) q^{25} +(-8.21408 - 5.18689i) q^{26} +(-6.23447 - 9.73752i) q^{27} +(6.63334 + 3.96002i) q^{28} +(-0.352149 + 2.94763i) q^{29} +(2.23539 + 16.9113i) q^{30} +(-0.670422 - 8.22241i) q^{31} +(-2.05903 - 7.46594i) q^{32} +(-3.59644 + 5.93954i) q^{33} +(-3.17715 - 14.2725i) q^{34} +(-7.45471 - 0.186650i) q^{35} +(16.6034 + 6.06931i) q^{36} +(4.79454 + 6.05647i) q^{37} +(4.07775 - 8.04032i) q^{38} +(7.13245 - 12.1191i) q^{39} +(-2.44792 - 2.46329i) q^{40} +(-1.30716 + 6.65308i) q^{41} +(-9.55060 + 17.1987i) q^{42} +(-0.160747 + 0.875980i) q^{43} +(-0.623327 - 5.83684i) q^{44} +(-16.8383 + 2.76424i) q^{45} +(17.3109 - 7.32960i) q^{46} +(-5.01661 + 0.188457i) q^{47} +(6.93186 - 2.14725i) q^{48} +(-1.26054 - 0.985123i) q^{49} +(3.03734 + 0.858157i) q^{50} +(20.5056 - 5.24307i) q^{51} +(1.41022 + 11.8042i) q^{52} +(2.60771 - 5.85045i) q^{53} +(-7.81016 + 23.6339i) q^{54} +(3.29015 + 4.61296i) q^{55} +(-0.574475 - 3.96354i) q^{56} +(11.8175 + 5.53560i) q^{57} +(5.40353 - 3.41213i) q^{58} +(-1.62800 + 3.91302i) q^{59} +(14.3392 - 15.1705i) q^{60} +(-4.88503 - 8.06766i) q^{61} +(-12.8300 + 12.2799i) q^{62} +(-17.4945 - 9.01066i) q^{63} +(-6.97675 + 9.78177i) q^{64} +(-6.77967 - 9.25811i) q^{65} +(14.8063 - 2.05150i) q^{66} +(-12.4111 + 7.62159i) q^{67} +(-11.1061 + 14.0292i) q^{68} +(11.3885 + 24.7137i) q^{69} +(9.80578 + 12.7104i) q^{70} +(0.991264 + 6.28404i) q^{71} +(-2.98424 - 8.66491i) q^{72} +(1.43252 + 1.37110i) q^{73} +(3.61331 - 16.2318i) q^{74} +(-1.10404 + 4.43330i) q^{75} +(-10.7834 + 2.32973i) q^{76} +(-0.122672 + 6.53324i) q^{77} +(-29.9317 + 4.52972i) q^{78} +(0.383916 + 6.80907i) q^{79} +(0.628817 - 5.88825i) q^{80} +(-15.2445 - 4.51390i) q^{81} +(12.8916 - 6.84539i) q^{82} +(1.05577 + 2.01868i) q^{83} +(23.7051 - 4.19685i) q^{84} +(2.69117 - 17.0604i) q^{85} +(1.68196 - 0.920284i) q^{86} +(5.18140 + 7.66334i) q^{87} +(-2.14504 + 2.15851i) q^{88} +(-1.96657 - 7.49550i) q^{89} +(27.4725 + 24.3857i) q^{90} +(0.0828171 - 13.2333i) q^{91} +(-20.3177 - 10.7886i) q^{92} +(-18.3477 - 18.0064i) q^{93} +(7.12355 + 8.12713i) q^{94} +(7.96400 - 7.06918i) q^{95} +(-20.0769 - 13.3922i) q^{96} +(0.199590 + 0.846508i) q^{97} +(0.0646561 + 3.44343i) q^{98} +(2.51451 + 14.7395i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10250q - 249q^{2} - 249q^{3} - 285q^{4} - 245q^{5} - 237q^{6} - 247q^{7} - 239q^{8} - 280q^{9} + O(q^{10}) \)	\( 10250q - 249q^{2} - 249q^{3} - 285q^{4} - 245q^{5} - 237q^{6} - 247q^{7} - 239q^{8} - 280q^{9} - 233q^{10} - 239q^{11} - 239q^{12} - 245q^{13} - 223q^{14} - 231q^{15} - 263q^{16} - 243q^{17} - 217q^{18} - 229q^{19} - 195q^{20} - 215q^{21} - 233q^{22} - 241q^{23} - 181q^{24} - 280q^{25} - 215q^{26} - 237q^{27} - 185q^{28} - 217q^{29} - 159q^{30} - 219q^{31} - 185q^{32} - 209q^{33} - 167q^{34} - 187q^{35} - 203q^{36} - 237q^{37} - 161q^{38} - 197q^{39} - 135q^{40} - 209q^{41} - 117q^{42} - 221q^{43} - 147q^{44} - 167q^{45} - 167q^{46} - 195q^{47} - 141q^{48} - 234q^{49} - 145q^{50} - 177q^{51} - 179q^{52} - 211q^{53} - 83q^{54} - 165q^{55} - 125q^{56} - 177q^{57} - 205q^{58} - 189q^{59} - 27q^{60} - 193q^{61} - 143q^{62} - 159q^{63} - 185q^{64} - 155q^{65} - 97q^{66} - 201q^{67} - 155q^{68} - 113q^{69} - 123q^{70} - 153q^{71} - 21q^{72} - 213q^{73} - 83q^{74} - 161q^{75} - 97q^{76} - 139q^{77} - 43q^{78} - 191q^{79} + 3q^{80} - 188q^{81} - 97q^{82} - 161q^{83} + 67q^{84} - 159q^{85} - 121q^{86} - 121q^{87} - 143q^{88} - 155q^{89} + 115q^{90} - 137q^{91} - 119q^{92} - 123q^{93} - 99q^{94} - 181q^{95} + 67q^{96} - 229q^{97} - 63q^{98} - 85q^{99} + O(q^{100}) \)

Introduction

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