LMFDB - Embedded newform 768.2.z.a.421.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(13,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 47, 0]))

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

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

chi := DirichletCharacter("768.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.z (of order $64$, degree $32$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$2048$
Relative dimension:	$64$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			421.31
Character	$\chi$	$=$	768.421
Dual form			768.2.z.a.301.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.120719 - 1.40905i) q^{2} +(0.857729 + 0.514103i) q^{3} +(-1.97085 + 0.340198i) q^{4} +(-0.180480 + 0.0645768i) q^{5} +(0.620853 - 1.27065i) q^{6} +(-2.44714 + 0.742333i) q^{7} +(0.717276 + 2.73597i) q^{8} +(0.471397 + 0.881921i) q^{9} +O(q^{10})$	\(q+(-0.120719 - 1.40905i) q^{2} +(0.857729 + 0.514103i) q^{3} +(-1.97085 + 0.340198i) q^{4} +(-0.180480 + 0.0645768i) q^{5} +(0.620853 - 1.27065i) q^{6} +(-2.44714 + 0.742333i) q^{7} +(0.717276 + 2.73597i) q^{8} +(0.471397 + 0.881921i) q^{9} +(0.112779 + 0.246510i) q^{10} +(0.138343 - 0.186534i) q^{11} +(-1.86535 - 0.721424i) q^{12} +(0.567844 - 0.268570i) q^{13} +(1.34140 + 3.35854i) q^{14} +(-0.188002 - 0.0373959i) q^{15} +(3.76853 - 1.34096i) q^{16} +(-7.12371 + 1.41699i) q^{17} +(1.18577 - 0.770687i) q^{18} +(0.0680985 + 1.38618i) q^{19} +(0.333731 - 0.188670i) q^{20} +(-2.48062 - 0.621363i) q^{21} +(-0.279537 - 0.172414i) q^{22} +(0.435489 + 4.42159i) q^{23} +(-0.791340 + 2.71547i) q^{24} +(-3.83665 + 3.14866i) q^{25} +(-0.446979 - 0.767700i) q^{26} +(-0.0490677 + 0.998795i) q^{27} +(4.57042 - 2.29554i) q^{28} +(-1.14825 + 7.74084i) q^{29} +(-0.0299974 + 0.269419i) q^{30} +(2.74221 + 1.13586i) q^{31} +(-2.34442 - 5.14818i) q^{32} +(0.214559 - 0.0888731i) q^{33} +(2.85658 + 9.86662i) q^{34} +(0.393723 - 0.292005i) q^{35} +(-1.22908 - 1.57777i) q^{36} +(6.30993 + 6.96194i) q^{37} +(1.94497 - 0.263292i) q^{38} +(0.625129 + 0.0615698i) q^{39} +(-0.306134 - 0.447468i) q^{40} +(-7.22305 - 5.92780i) q^{41} +(-0.576076 + 3.57033i) q^{42} +(-1.82217 - 3.04010i) q^{43} +(-0.209196 + 0.414695i) q^{44} +(-0.142029 - 0.128728i) q^{45} +(6.17768 - 1.14739i) q^{46} +(7.20244 + 4.81252i) q^{47} +(3.92177 + 0.787231i) q^{48} +(-0.382829 + 0.255798i) q^{49} +(4.89978 + 5.02594i) q^{50} +(-6.83869 - 2.44692i) q^{51} +(-1.02777 + 0.722492i) q^{52} +(-0.758428 - 5.11290i) q^{53} +(1.41328 - 0.0514344i) q^{54} +(-0.0129224 + 0.0425994i) q^{55} +(-3.78628 - 6.16285i) q^{56} +(-0.654227 + 1.22397i) q^{57} +(11.0459 + 0.683473i) q^{58} +(-3.89154 - 1.84056i) q^{59} +(0.383247 + 0.00974401i) q^{60} +(-6.52987 + 1.63565i) q^{61} +(1.26945 - 4.00103i) q^{62} +(-1.80826 - 1.80826i) q^{63} +(-6.97103 + 3.92488i) q^{64} +(-0.0851411 + 0.0851411i) q^{65} +(-0.151128 - 0.291595i) q^{66} +(1.61543 + 6.44917i) q^{67} +(13.5577 - 5.21616i) q^{68} +(-1.89962 + 4.01641i) q^{69} +(-0.458980 - 0.519526i) q^{70} +(-3.56615 - 1.90615i) q^{71} +(-2.07479 + 1.92231i) q^{72} +(4.81749 + 1.46137i) q^{73} +(9.04800 - 9.73146i) q^{74} +(-4.90954 + 0.728261i) q^{75} +(-0.605786 - 2.70878i) q^{76} +(-0.200075 + 0.559173i) q^{77} +(0.0112903 - 0.888271i) q^{78} +(2.21548 + 3.31569i) q^{79} +(-0.593550 + 0.485376i) q^{80} +(-0.555570 + 0.831470i) q^{81} +(-7.48063 + 10.8932i) q^{82} +(3.70775 - 4.09087i) q^{83} +(5.10033 + 0.380714i) q^{84} +(1.19418 - 0.715766i) q^{85} +(-4.06369 + 2.93452i) q^{86} +(-4.96447 + 6.04923i) q^{87} +(0.609581 + 0.244706i) q^{88} +(1.57509 - 15.9921i) q^{89} +(-0.164239 + 0.215667i) q^{90} +(-1.19023 + 1.07876i) q^{91} +(-2.36250 - 8.56616i) q^{92} +(1.76812 + 2.38404i) q^{93} +(5.91162 - 10.7296i) q^{94} +(-0.101805 - 0.245780i) q^{95} +(0.635819 - 5.62101i) q^{96} +(2.43022 - 5.86708i) q^{97} +(0.406648 + 0.508547i) q^{98} +(0.229723 + 0.0340762i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2048 q+O(q^{10}) $ 2048 * q	$ 2048 q+O(q^{100}) $ 2048 * q

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{57}{64}\right)$

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 $

$2$	−0.120719	−	1.40905i	−0.0853610	−	0.996350i
$2$	−0.120719	−	1.40905i	−0.0853610	−	0.996350i
$3$	0.857729	+	0.514103i	0.495210	+	0.296817i
$3$	0.857729	+	0.514103i	0.495210	+	0.296817i
$4$	−1.97085	+	0.340198i	−0.985427	+	0.170099i
$5$	−0.180480	+	0.0645768i	−0.0807131	+	0.0288796i	−0.376937	−	0.926239i	$-0.623023\pi$
$5$	−0.180480	+	0.0645768i	−0.0807131	+	0.0288796i	0.296224	+	0.955119i	$0.404273\pi$
$6$	0.620853	−	1.27065i	0.253462	−	0.518739i
$7$	−2.44714	+	0.742333i	−0.924934	+	0.280576i	−0.716602	−	0.697483i	$-0.754303\pi$
$7$	−2.44714	+	0.742333i	−0.924934	+	0.280576i	−0.208332	+	0.978058i	$0.566803\pi$
$8$	0.717276	+	2.73597i	0.253595	+	0.967310i
$9$	0.471397	+	0.881921i	0.157132	+	0.293974i
$10$	0.112779	+	0.246510i	0.0356640	+	0.0779534i
$11$	0.138343	−	0.186534i	0.0417120	−	0.0562421i	−0.781859	−	0.623455i	$-0.785728\pi$
$11$	0.138343	−	0.186534i	0.0417120	−	0.0562421i	0.823571	+	0.567213i	$0.191978\pi$
$12$	−1.86535	−	0.721424i	−0.538481	−	0.208257i
$13$	0.567844	−	0.268570i	0.157492	−	0.0744880i	−0.347184	−	0.937797i	$-0.612862\pi$
$13$	0.567844	−	0.268570i	0.157492	−	0.0744880i	0.504676	+	0.863309i	$0.331612\pi$
$14$	1.34140	+	3.35854i	0.358505	+	0.897608i
$15$	−0.188002	−	0.0373959i	−0.0485419	−	0.00965559i
$16$	3.76853	−	1.34096i	0.942133	−	0.335240i
$17$	−7.12371	+	1.41699i	−1.72775	+	0.343672i	−0.956250	−	0.292552i	$-0.905496\pi$
$17$	−7.12371	+	1.41699i	−1.72775	+	0.343672i	−0.771505	+	0.636224i	$0.780496\pi$
$18$	1.18577	−	0.770687i	0.279488	−	0.181653i
$19$	0.0680985	+	1.38618i	0.0156229	+	0.318011i	0.993869	+	0.110563i	$0.0352655\pi$
$19$	0.0680985	+	1.38618i	0.0156229	+	0.318011i	−0.978246	+	0.207447i	$0.933484\pi$
$20$	0.333731	−	0.188670i	0.0746245	−	0.0421880i
$21$	−2.48062	−	0.621363i	−0.541316	−	0.135593i
$22$	−0.279537	−	0.172414i	−0.0595974	−	0.0367589i
$23$	0.435489	+	4.42159i	0.0908057	+	0.921965i	0.927382	+	0.374115i	$0.122054\pi$
$23$	0.435489	+	4.42159i	0.0908057	+	0.921965i	−0.836577	+	0.547850i	$0.815446\pi$
$24$	−0.791340	+	2.71547i	−0.161532	+	0.554293i
$25$	−3.83665	+	3.14866i	−0.767330	+	0.629731i
$26$	−0.446979	−	0.767700i	−0.0876597	−	0.150558i
$27$	−0.0490677	+	0.998795i	−0.00944308	+	0.192218i
$28$	4.57042	−	2.29554i	0.863729	−	0.433817i
$29$	−1.14825	+	7.74084i	−0.213224	+	1.43744i	0.573030	+	0.819535i	$0.305768\pi$
$29$	−1.14825	+	7.74084i	−0.213224	+	1.43744i	−0.786254	+	0.617904i	$0.787982\pi$
$30$	−0.0299974	+	0.269419i	−0.00547676	+	0.0491890i
$31$	2.74221	+	1.13586i	0.492515	+	0.204006i	0.615096	−	0.788452i	$-0.289117\pi$
$31$	2.74221	+	1.13586i	0.492515	+	0.204006i	−0.122581	+	0.992458i	$0.539117\pi$
$32$	−2.34442	−	5.14818i	−0.414438	−	0.910078i
$33$	0.214559	−	0.0888731i	0.0373498	−	0.0154708i
$34$	2.85658	+	9.86662i	0.489900	+	1.69211i
$35$	0.393723	−	0.292005i	0.0665514	−	0.0493579i
$36$	−1.22908	−	1.57777i	−0.204847	−	0.262962i
$37$	6.30993	+	6.96194i	1.03735	+	1.14454i	0.989330	+	0.145689i	$0.0465399\pi$
$37$	6.30993	+	6.96194i	1.03735	+	1.14454i	0.0480160	+	0.998847i	$0.484710\pi$
$38$	1.94497	−	0.263292i	0.315516	−	0.0427115i
$39$	0.625129	+	0.0615698i	0.100101	+	0.00985906i
$40$	−0.306134	−	0.447468i	−0.0484040	−	0.0707509i
$41$	−7.22305	−	5.92780i	−1.12805	−	0.925768i	−0.130213	−	0.991486i	$-0.541566\pi$
$41$	−7.22305	−	5.92780i	−1.12805	−	0.925768i	−0.997838	+	0.0657185i	$0.979066\pi$
$42$	−0.576076	+	3.57033i	−0.0888904	+	0.550915i
$43$	−1.82217	−	3.04010i	−0.277878	−	0.463611i	0.686873	−	0.726778i	$-0.258983\pi$
$43$	−1.82217	−	3.04010i	−0.277878	−	0.463611i	−0.964750	+	0.263167i	$0.915233\pi$
$44$	−0.209196	+	0.414695i	−0.0315374	+	0.0625177i
$45$	−0.142029	−	0.128728i	−0.0211725	−	0.0191896i
$46$	6.17768	−	1.14739i	0.910849	−	0.169174i
$47$	7.20244	+	4.81252i	1.05058	+	0.701978i	0.955949	−	0.293534i	$-0.0948313\pi$
$47$	7.20244	+	4.81252i	1.05058	+	0.701978i	0.0946358	+	0.995512i	$0.469831\pi$
$48$	3.92177	+	0.787231i	0.566058	+	0.113627i
$49$	−0.382829	+	0.255798i	−0.0546899	+	0.0365426i
$50$	4.89978	+	5.02594i	0.692933	+	0.710775i
$51$	−6.83869	−	2.44692i	−0.957609	−	0.342638i
$52$	−1.02777	+	0.722492i	−0.142526	+	0.100192i
$53$	−0.758428	−	5.11290i	−0.104178	−	0.702311i	−0.976838	−	0.213982i	$-0.931357\pi$
$53$	−0.758428	−	5.11290i	−0.104178	−	0.702311i	0.872660	−	0.488329i	$-0.162393\pi$
$54$	1.41328	−	0.0514344i	0.192323	−	0.00699934i
$55$	−0.0129224	+	0.0425994i	−0.00174246	+	0.00574411i
$56$	−3.78628	−	6.16285i	−0.505962	−	0.823545i
$57$	−0.654227	+	1.22397i	−0.0866545	+	0.162119i
$58$	11.0459	+	0.683473i	1.45039	+	0.0897444i
$59$	−3.89154	−	1.84056i	−0.506636	−	0.239621i	0.157107	−	0.987582i	$-0.449783\pi$
$59$	−3.89154	−	1.84056i	−0.506636	−	0.239621i	−0.663743	+	0.747961i	$0.731033\pi$
$60$	0.383247	+	0.00974401i	0.0494769	+	0.00125795i
$61$	−6.52987	+	1.63565i	−0.836065	+	0.209423i	−0.637292	−	0.770622i	$-0.719946\pi$
$61$	−6.52987	+	1.63565i	−0.836065	+	0.209423i	−0.198773	+	0.980046i	$0.563696\pi$
$62$	1.26945	−	4.00103i	0.161220	−	0.508131i
$63$	−1.80826	−	1.80826i	−0.227819	−	0.227819i
$64$	−6.97103	+	3.92488i	−0.871379	+	0.490611i
$65$	−0.0851411	+	0.0851411i	−0.0105605	+	0.0105605i
$66$	−0.151128	−	0.291595i	−0.0186026	−	0.0358929i
$67$	1.61543	+	6.44917i	0.197356	+	0.787891i	0.985114	+	0.171905i	$0.0549923\pi$
$67$	1.61543	+	6.44917i	0.197356	+	0.787891i	−0.787757	+	0.615986i	$0.788758\pi$
$68$	13.5577	−	5.21616i	1.64412	−	0.632553i
$69$	−1.89962	+	4.01641i	−0.228687	+	0.483519i
$70$	−0.458980	−	0.519526i	−0.0548586	−	0.0620952i
$71$	−3.56615	−	1.90615i	−0.423224	−	0.226218i	0.246013	−	0.969266i	$-0.420879\pi$
$71$	−3.56615	−	1.90615i	−0.423224	−	0.226218i	−0.669238	+	0.743048i	$0.733379\pi$
$72$	−2.07479	+	1.92231i	−0.244516	+	0.226546i
$73$	4.81749	+	1.46137i	0.563845	+	0.171040i	0.559324	−	0.828949i	$-0.311061\pi$
$73$	4.81749	+	1.46137i	0.563845	+	0.171040i	0.00452097	+	0.999990i	$0.498561\pi$
$74$	9.04800	−	9.73146i	1.05181	−	1.13126i
$75$	−4.90954	+	0.728261i	−0.566905	+	0.0840923i
$76$	−0.605786	−	2.70878i	−0.0694884	−	0.310719i
$77$	−0.200075	+	0.559173i	−0.0228007	+	0.0637236i
$78$	0.0112903	−	0.888271i	0.00127837	−	0.100577i
$79$	2.21548	+	3.31569i	0.249261	+	0.373045i	0.934909	−	0.354888i	$-0.115481\pi$
$79$	2.21548	+	3.31569i	0.249261	+	0.373045i	−0.685648	+	0.727933i	$0.740481\pi$
$80$	−0.593550	+	0.485376i	−0.0663609	+	0.0542667i
$81$	−0.555570	+	0.831470i	−0.0617300	+	0.0923855i
$82$	−7.48063	+	10.8932i	−0.826097	+	1.20296i
$83$	3.70775	−	4.09087i	0.406978	−	0.449031i	−0.502628	−	0.864503i	$-0.667633\pi$
$83$	3.70775	−	4.09087i	0.406978	−	0.449031i	0.909606	+	0.415472i	$0.136383\pi$
$84$	5.10033	+	0.380714i	0.556492	+	0.0415393i
$85$	1.19418	−	0.715766i	0.129527	−	0.0776357i
$86$	−4.06369	+	2.93452i	−0.438199	+	0.316438i
$87$	−4.96447	+	6.04923i	−0.532247	+	0.648545i
$88$	0.609581	+	0.244706i	0.0649816	+	0.0260857i
$89$	1.57509	−	15.9921i	0.166959	−	1.69516i	−0.438056	−	0.898948i	$-0.644333\pi$
$89$	1.57509	−	15.9921i	0.166959	−	1.69516i	0.605015	−	0.796214i	$-0.293167\pi$
$90$	−0.164239	+	0.215667i	−0.0173123	+	0.0227333i
$91$	−1.19023	+	1.07876i	−0.124770	+	0.113085i
$92$	−2.36250	−	8.56616i	−0.246308	−	0.893083i
$93$	1.76812	+	2.38404i	0.183346	+	0.247213i
$94$	5.91162	−	10.7296i	0.609737	−	1.10667i
$95$	−0.101805	−	0.245780i	−0.0104450	−	0.0252164i
$96$	0.635819	−	5.62101i	0.0648930	−	0.573692i
$97$	2.43022	−	5.86708i	0.246752	−	0.595712i	−0.751173	−	0.660106i	$-0.770511\pi$
$97$	2.43022	−	5.86708i	0.246752	−	0.595712i	0.997925	+	0.0643940i	$0.0205114\pi$
$98$	0.406648	+	0.508547i	0.0410776	+	0.0513710i
$99$	0.229723	+	0.0340762i	0.0230880	+	0.00342478i
$100$	6.49031	−	7.51076i	0.649031	−	0.751076i
$101$	−14.8717	−	0.730601i	−1.47979	−	0.0726975i	−0.706935	−	0.707278i	$-0.749923\pi$
$101$	−14.8717	−	0.730601i	−1.47979	−	0.0726975i	−0.772857	+	0.634581i	$0.781173\pi$
$102$	−2.62228	+	9.93146i	−0.259645	+	0.983361i
$103$	8.11521	+	9.88841i	0.799615	+	0.974334i	0.999985	−	0.00538608i	$-0.00171445\pi$
$103$	8.11521	+	9.88841i	0.799615	+	0.974334i	−0.200370	+	0.979720i	$0.564214\pi$
$104$	1.14210	+	1.36096i	0.111992	+	0.133453i
$105$	0.487828	−	0.0480469i	0.0476072	−	0.00468890i
$106$	−7.11279	+	1.68589i	−0.690855	+	0.163748i
$107$	4.49568	−	17.9477i	0.434613	−	1.73507i	−0.216675	−	0.976244i	$-0.569521\pi$
$107$	4.49568	−	17.9477i	0.434613	−	1.73507i	0.651289	−	0.758830i	$-0.274229\pi$
$108$	−0.243083	−	1.98517i	−0.0233907	−	0.191023i
$109$	6.26946	−	0.307999i	0.600505	−	0.0295009i	0.253454	−	0.967347i	$-0.418433\pi$
$109$	6.26946	−	0.307999i	0.600505	−	0.0295009i	0.347051	+	0.937846i	$0.387183\pi$
$110$	0.0615848	+	0.0130658i	0.00587188	+	0.00124577i
$111$	1.83306	+	9.21541i	0.173986	+	0.874688i
$112$	−8.22670	+	6.07903i	−0.777350	+	0.574414i
$113$	−0.904508	+	4.54727i	−0.0850890	+	0.427771i	0.914635	+	0.404280i	$0.132478\pi$
$113$	−0.904508	+	4.54727i	−0.0850890	+	0.427771i	−0.999724	+	0.0234907i	$0.992522\pi$
$114$	1.80362	+	0.774083i	0.168924	+	0.0724995i
$115$	−0.364129	−	0.769886i	−0.0339552	−	0.0717923i
$116$	−0.370395	−	15.6467i	−0.0343903	−	1.45276i
$117$	0.504538	+	0.374191i	0.0466445	+	0.0345939i
$118$	−2.12367	+	5.70558i	−0.195499	+	0.525241i
$119$	16.3809	−	8.75576i	1.50163	−	0.802639i
$120$	−0.0325352	−	0.541191i	−0.00297005	−	0.0494037i
$121$	3.17748	+	10.4747i	0.288861	+	0.952248i
$122$	3.09299	+	9.00348i	0.280026	+	0.815137i
$123$	−3.14792	−	8.79784i	−0.283838	−	0.793274i
$124$	−5.79091	−	1.30572i	−0.520039	−	0.117257i
$125$	0.981838	−	1.63810i	0.0878183	−	0.146516i
$126$	−2.32964	+	2.76622i	−0.207540	+	0.246434i
$127$		−	20.4816i		−	1.81745i	−0.417396	−	0.908725i	$-0.637057\pi$
$127$		−	20.4816i		−	1.81745i	0.417396	−	0.908725i	$-0.362943\pi$
$128$	6.37190	+	9.34874i	0.563202	+	0.826319i
$129$		−	3.54436i		−	0.312064i
$130$	0.130246	+	0.109690i	0.0114234	+	0.00962046i
$131$	−1.94703	+	3.24843i	−0.170113	+	0.283817i	−0.930965	−	0.365109i	$-0.881032\pi$
$131$	−1.94703	+	3.24843i	−0.170113	+	0.283817i	0.760851	+	0.648926i	$0.224782\pi$
$132$	−0.392629	+	0.248148i	−0.0341740	+	0.0215985i
$133$	−1.19565	−	3.34162i	−0.103676	−	0.289755i
$134$	8.89220	−	3.05476i	0.768169	−	0.263891i
$135$	−0.0556433	−	0.183431i	−0.00478901	−	0.0157873i
$136$	−8.98652	−	18.4739i	−0.770587	−	1.58412i
$137$	−8.35054	+	4.46346i	−0.713435	+	0.381339i	−0.787832	−	0.615890i	$-0.788797\pi$
$137$	−8.35054	+	4.46346i	−0.713435	+	0.381339i	0.0743974	+	0.997229i	$0.476297\pi$
$138$	5.88865	+	2.19181i	0.501275	+	0.186579i
$139$	−6.06611	−	4.49893i	−0.514521	−	0.381594i	0.307057	−	0.951691i	$-0.400656\pi$
$139$	−6.06611	−	4.49893i	−0.514521	−	0.381594i	−0.821578	+	0.570097i	$0.806906\pi$
$140$	−0.676632	+	0.709443i	−0.0571858	+	0.0599589i
$141$	3.70361	+	7.83063i	0.311901	+	0.659458i
$142$	−2.25536	+	5.25500i	−0.189266	+	0.440990i
$143$	0.0284598	−	0.143077i	0.00237993	−	0.0119647i
$144$	2.95910	+	2.69142i	0.246591	+	0.224285i
$145$	−0.292643	−	1.47122i	−0.0243027	−	0.122178i
$146$	1.47758	−	6.96451i	0.122286	−	0.576387i
$147$	−0.459870	+	0.0225920i	−0.0379295	+	0.00186335i
$148$	−14.8044	−	11.5743i	−1.21691	−	0.951405i
$149$	−3.06129	+	12.2214i	−0.250791	+	1.00121i	0.705480	+	0.708730i	$0.250731\pi$
$149$	−3.06129	+	12.2214i	−0.250791	+	1.00121i	−0.956271	+	0.292483i	$0.905519\pi$
$150$	1.61883	+	6.82988i	0.132177	+	0.557657i
$151$	20.6913	−	2.03792i	1.68384	−	0.165844i	0.789656	−	0.613549i	$-0.210259\pi$
$151$	20.6913	−	2.03792i	1.68384	−	0.165844i	0.894181	+	0.447706i	$0.147759\pi$
$152$	−3.74369	+	1.18059i	−0.303653	+	0.0957581i
$153$	−4.60777	−	5.61459i	−0.372516	−	0.453913i
$154$	0.812056	+	0.214414i	0.0654373	+	0.0172779i
$155$	−0.568264	−	0.0279170i	−0.0456441	−	0.00224235i
$156$	−1.25298	+	0.0913224i	−0.100319	+	0.00731164i
$157$	7.44620	+	1.10454i	0.594272	+	0.0881519i	0.437090	−	0.899418i	$-0.356009\pi$
$157$	7.44620	+	1.10454i	0.594272	+	0.0881519i	0.157182	+	0.987570i	$0.449759\pi$
$158$	4.40454	−	3.52199i	0.350406	−	0.280194i
$159$	1.97803	−	4.77539i	0.156868	−	0.378713i
$160$	0.755573	+	0.777748i	0.0597333	+	0.0614864i
$161$	−4.34800	−	10.4970i	−0.342670	−	0.827279i
$162$	1.23865	+	0.682453i	0.0973177	+	0.0536186i
$163$	7.12411	+	9.60575i	0.558003	+	0.752380i	0.988666	−	0.150133i	$-0.0479701\pi$
$163$	7.12411	+	9.60575i	0.558003	+	0.752380i	−0.430663	+	0.902513i	$0.641720\pi$
$164$	16.2522	+	9.22557i	1.26908	+	0.720396i
$165$	−0.0329844	+	0.0298953i	−0.00256783	+	0.00232735i
$166$	−6.21184	−	4.73056i	−0.482132	−	0.367163i
$167$	1.39268	−	14.1402i	0.107769	−	1.09420i	−0.777425	−	0.628976i	$-0.783474\pi$
$167$	1.39268	−	14.1402i	0.107769	−	1.09420i	0.885194	−	0.465222i	$-0.154026\pi$
$168$	−0.0792595	−	7.23259i	−0.00611500	−	0.558006i
$169$	−7.99680	+	9.74412i	−0.615138	+	0.749548i
$170$	−1.15271	−	1.59626i	−0.0884090	−	0.122428i
$171$	−1.19040	+	0.713496i	−0.0910319	+	0.0545624i
$172$	4.62546	+	5.37170i	0.352688	+	0.409588i
$173$	−6.73176	+	7.42735i	−0.511806	+	0.564691i	−0.940950	−	0.338545i	$-0.890065\pi$
$173$	−6.73176	+	7.42735i	−0.511806	+	0.564691i	0.429144	+	0.903236i	$0.358815\pi$
$174$	9.12298	+	6.26494i	0.691611	+	0.474944i
$175$	7.05148	−	10.5533i	0.533042	−	0.797754i
$176$	0.271215	−	0.888472i	0.0204436	−	0.0669711i
$177$	−2.39165	−	3.57936i	−0.179767	−	0.269041i
$178$	−22.7239	−	0.288830i	−1.70323	−	0.0216487i
$179$	−1.74673	+	4.88178i	−0.130557	+	0.364882i	−0.988978	−	0.148064i	$-0.952696\pi$
$179$	−1.74673	+	4.88178i	−0.130557	+	0.364882i	0.858421	+	0.512946i	$0.171446\pi$
$180$	0.323712	+	0.205386i	0.0241281	+	0.0153086i
$181$	−20.7853	+	3.08320i	−1.54496	+	0.229173i	−0.864129	−	0.503270i	$-0.832130\pi$
$181$	−20.7853	+	3.08320i	−1.54496	+	0.229173i	−0.680828	+	0.732443i	$0.738380\pi$
$182$	1.66371	+	1.54687i	0.123322	+	0.114661i
$183$	−6.44175	−	1.95408i	−0.476188	−	0.144450i
$184$	−11.7850	+	4.36298i	−0.868799	+	0.321643i
$185$	−1.58840	−	0.849016i	−0.116781	−	0.0624209i
$186$	3.14578	−	2.77917i	0.230660	−	0.203779i
$187$	−0.721199	+	1.52485i	−0.0527393	+	0.111508i
$188$	−15.8322	−	7.03452i	−1.15468	−	0.513045i
$189$	−0.621363	−	2.48062i	−0.0451975	−	0.180439i
$190$	−0.334026	+	0.173119i	−0.0242328	+	0.0125594i
$191$	−13.7415	+	13.7415i	−0.994298	+	0.994298i	−0.999984	−	0.00568620i	$-0.998190\pi$
$191$	−13.7415	+	13.7415i	−0.994298	+	0.994298i	0.00568620	+	0.999984i	$0.498190\pi$
$192$	−7.99705	−	0.217341i	−0.577137	−	0.0156852i
$193$	3.29045	+	3.29045i	0.236852	+	0.236852i	0.815545	−	0.578694i	$-0.196437\pi$
$193$	3.29045	+	3.29045i	0.236852	+	0.236852i	−0.578694	+	0.815545i	$0.696437\pi$
$194$	−8.56039	−	2.71605i	−0.614601	−	0.195001i
$195$	−0.116799	+	0.0292567i	−0.00836417	+	0.00209512i
$196$	0.667478	−	0.634379i	0.0476770	−	0.0453128i
$197$	−20.1300	−	9.52077i	−1.43420	−	0.678327i	−0.456771	−	0.889584i	$-0.650994\pi$
$197$	−20.1300	−	9.52077i	−1.43420	−	0.678327i	−0.977430	+	0.211258i	$0.932244\pi$
$198$	0.0202832	−	0.327805i	0.00144147	−	0.0232961i
$199$	2.06217	−	3.85805i	0.146183	−	0.273490i	−0.798164	−	0.602440i	$-0.794195\pi$
$199$	2.06217	−	3.85805i	0.146183	−	0.273490i	0.944347	+	0.328951i	$0.106695\pi$
$200$	−11.3666	−	8.23849i	−0.803737	−	0.582549i
$201$	−1.92993	+	6.36213i	−0.136127	+	0.448750i
$202$	0.765841	+	21.0432i	0.0538844	+	1.48060i
$203$	−2.93636	−	19.7953i	−0.206092	−	1.38936i
$204$	14.3105	+	2.49602i	1.00194	+	0.174756i
$205$	1.68642	+	0.603409i	0.117784	+	0.0421439i
$206$	12.9536	−	12.6285i	0.902522	−	0.879867i
$207$	−3.69421	+	2.46839i	−0.256765	+	0.171565i
$208$	1.77980	−	1.77357i	0.123407	−	0.122975i
$209$	0.267990	+	0.179065i	0.0185373	+	0.0123862i
$210$	−0.126591	−	0.681575i	−0.00873558	−	0.0470332i
$211$	3.03209	+	2.74813i	0.208738	+	0.189189i	0.769232	−	0.638969i	$-0.220639\pi$
$211$	3.03209	+	2.74813i	0.208738	+	0.189189i	−0.560494	+	0.828158i	$0.689389\pi$
$212$	3.23415	+	9.81877i	0.222122	+	0.674356i
$213$	−2.07883	−	3.46833i	−0.142439	−	0.237646i
$214$	−25.8320	−	4.16801i	−1.76584	−	0.284919i
$215$	0.525185	+	0.431008i	0.0358173	+	0.0293945i
$216$	−2.76787	+	0.582164i	−0.188329	+	0.0396112i
$217$	−7.55376	−	0.743981i	−0.512783	−	0.0505047i
$218$	−1.19083	−	8.79681i	−0.0806530	−	0.595795i
$219$	3.38081	+	3.73014i	0.228454	+	0.252060i
$220$	0.0109759	−	0.0883535i	0.000739996	−	0.00595679i
$221$	−3.66460	+	2.71785i	−0.246507	+	0.182822i
$222$	12.7637	−	3.69535i	0.856643	−	0.248015i
$223$	−6.94102	+	2.87507i	−0.464805	+	0.192529i	−0.602781	−	0.797907i	$-0.705941\pi$
$223$	−6.94102	+	2.87507i	−0.464805	+	0.192529i	0.137975	+	0.990436i	$0.455941\pi$
$224$	9.55879	+	10.8580i	0.638673	+	0.725480i
$225$	−4.58545	−	1.89936i	−0.305697	−	0.126624i
$226$	6.51653	+	0.725558i	0.433473	+	0.0482634i
$227$	−1.80260	+	12.1521i	−0.119643	+	0.806566i	0.843413	+	0.537265i	$0.180543\pi$
$227$	−1.80260	+	12.1521i	−0.119643	+	0.806566i	−0.963056	+	0.269301i	$0.913207\pi$
$228$	0.872993	−	2.63484i	0.0578154	−	0.174496i
$229$	0.105824	−	2.15409i	0.00699302	−	0.142346i	−0.992760	−	0.120116i	$-0.961673\pi$
$229$	0.105824	−	2.15409i	0.00699302	−	0.142346i	0.999753	−	0.0222301i	$-0.00707666\pi$
$230$	−1.04085	+	0.606017i	−0.0686318	+	0.0399596i
$231$	−0.459082	+	0.376759i	−0.0302054	+	0.0247889i
$232$	−22.0023	+	2.41076i	−1.44452	+	0.158274i
$233$	0.494441	+	5.02015i	0.0323919	+	0.328881i	0.997701	+	0.0677706i	$0.0215886\pi$
$233$	0.494441	+	5.02015i	0.0323919	+	0.328881i	−0.965309	+	0.261110i	$0.915911\pi$
$234$	0.466347	−	0.756091i	0.0304860	−	0.0494272i
$235$	−1.61067	−	0.403453i	−0.105069	−	0.0263184i
$236$	8.29582	+	2.30359i	0.540012	+	0.149951i
$237$	0.195670	+	3.98295i	0.0127101	+	0.258720i
$238$	−14.3148	−	22.0245i	−0.927891	−	1.42764i
$239$	19.3083	−	3.84067i	1.24895	−	0.248432i	0.474041	−	0.880503i	$-0.342795\pi$
$239$	19.3083	−	3.84067i	1.24895	−	0.248432i	0.774911	+	0.632071i	$0.217795\pi$
$240$	−0.758638	+	0.111176i	−0.0489699	+	0.00717636i
$241$	−8.71420	−	1.73336i	−0.561331	−	0.111656i	−0.0937336	−	0.995597i	$-0.529880\pi$
$241$	−8.71420	−	1.73336i	−0.561331	−	0.111656i	−0.467597	+	0.883942i	$0.654880\pi$
$242$	14.3759	−	5.74172i	0.924115	−	0.369092i
$243$	−0.903989	+	0.427555i	−0.0579909	+	0.0274277i
$244$	12.3130	−	5.44507i	0.788258	−	0.348585i
$245$	0.0525744	−	0.0708884i	0.00335886	−	0.00452889i
$246$	−12.0166	+	5.49764i	−0.766150	+	0.350517i
$247$	0.410955	+	0.768842i	0.0261484	+	0.0489203i
$248$	−1.14076	+	8.31731i	−0.0724381	+	0.528150i
$249$	5.28337	−	1.60269i	0.334820	−	0.101566i
$250$	−2.42669	−	1.18571i	−0.153477	−	0.0749910i
$251$	7.92099	−	2.83418i	0.499969	−	0.178892i	−0.0748145	−	0.997197i	$-0.523836\pi$
$251$	7.92099	−	2.83418i	0.499969	−	0.178892i	0.574783	+	0.818306i	$0.305086\pi$
$252$	4.17897	+	2.94864i	0.263250	+	0.185747i
$253$	0.885024	+	0.530463i	0.0556410	+	0.0333499i
$254$	−28.8597	+	2.47252i	−1.81082	+	0.155139i
$255$	1.39226			0.0871869
$256$	12.4036	−	10.1069i	0.775228	−	0.631682i
$257$	21.0149			1.31087			0.655436	−	0.755251i	$-0.272485\pi$
$257$	21.0149			1.31087			0.655436	+	0.755251i	$0.272485\pi$
$258$	−4.99419	+	0.427871i	−0.310925	+	0.0266381i
$259$	−20.6094	−	12.3528i	−1.28061	−	0.767565i
$260$	0.138836	−	0.196766i	0.00861024	−	0.0122029i
$261$	−7.36809	+	2.63635i	−0.456074	+	0.163186i
$262$	4.81225	+	2.35132i	0.297302	+	0.145265i
$263$	18.6135	−	5.64635i	1.14776	−	0.348169i	0.341587	−	0.939850i	$-0.389036\pi$
$263$	18.6135	−	5.64635i	1.14776	−	0.348169i	0.806172	+	0.591681i	$0.201536\pi$
$264$	0.397051	+	0.523279i	0.0244368	+	0.0322056i
$265$	0.467056	+	0.873800i	0.0286910	+	0.0536771i
$266$	−4.56418	+	2.08813i	−0.279848	+	0.128032i
$267$	9.57259	−	12.9071i	0.585833	−	0.789904i
$268$	−5.37778	−	12.1608i	−0.328500	−	0.742839i
$269$	10.3676	−	4.90351i	0.632123	−	0.298972i	−0.0845094	−	0.996423i	$-0.526932\pi$
$269$	10.3676	−	4.90351i	0.632123	−	0.298972i	0.716633	+	0.697451i	$0.245682\pi$
$270$	−0.251747	+	0.100548i	−0.0153208	+	0.00611915i
$271$	9.62542	+	1.91461i	0.584702	+	0.116305i	0.478573	−	0.878048i	$-0.341154\pi$
$271$	9.62542	+	1.91461i	0.584702	+	0.116305i	0.106129	+	0.994352i	$0.466154\pi$
$272$	−24.9458	+	14.8926i	−1.51256	+	0.902997i
$273$	−1.57549	+	0.313384i	−0.0953527	+	0.0189668i
$274$	7.29731	+	11.2275i	0.440847	+	0.678279i
$275$	0.0565578	+	1.15126i	0.00341056	+	0.0694236i
$276$	2.37750	−	8.56200i	0.143109	−	0.515372i
$277$	4.79224	+	1.20039i	0.287938	+	0.0721247i	0.384258	−	0.923226i	$-0.374457\pi$
$277$	4.79224	+	1.20039i	0.287938	+	0.0721247i	−0.0963203	+	0.995350i	$0.530707\pi$
$278$	−5.60694	+	9.09057i	−0.336282	+	0.545216i
$279$	0.290929	+	2.95385i	0.0174175	+	0.176842i
$280$	1.08132	+	0.867766i	0.0646215	+	0.0518589i
$281$	−11.6118	+	9.52959i	−0.692704	+	0.568487i	−0.913503	−	0.406832i	$-0.866633\pi$
$281$	−11.6118	+	9.52959i	−0.692704	+	0.568487i	0.220799	+	0.975319i	$0.429133\pi$
$282$	10.5867	−	6.16389i	0.630427	−	0.367054i
$283$	0.173497	−	3.53161i	0.0103133	−	0.209932i	−0.988108	−	0.153762i	$-0.950861\pi$
$283$	0.173497	−	3.53161i	0.0103133	−	0.209932i	0.998421	−	0.0561702i	$-0.0178889\pi$
$284$	7.67683	+	2.54354i	0.455536	+	0.150931i
$285$	0.0390347	−	0.263150i	0.00231222	−	0.0155877i
$286$	−0.205039	−	0.0228293i	−0.0121242	−	0.00134992i
$287$	22.0763	+	9.14428i	1.30312	+	0.539770i
$288$	3.43514	−	4.49442i	0.202417	−	0.264836i
$289$	33.0335	−	13.6829i	1.94315	−	0.804877i
$290$	−2.03769	+	0.589953i	−0.119658	+	0.0346433i
$291$	5.10076	−	3.78298i	0.299012	−	0.221762i
$292$	−9.99172	−	1.24125i	−0.584721	−	0.0726384i
$293$	7.97315	+	8.79701i	0.465796	+	0.513927i	0.927865	−	0.372917i	$-0.121643\pi$
$293$	7.97315	+	8.79701i	0.465796	+	0.513927i	−0.462068	+	0.886844i	$0.652893\pi$
$294$	0.0873482	+	0.645254i	0.00509425	+	0.0376320i
$295$	0.821204	+	0.0808815i	0.0478123	+	0.00470910i
$296$	−14.5217	+	22.2574i	−0.844055	+	1.29368i
$297$	0.179521	+	0.147329i	0.0104169	+	0.00854891i
$298$	17.5901	+	2.83817i	1.01897	+	0.164411i
$299$	1.43480	+	2.39381i	0.0829764	+	0.138438i
$300$	9.42823	−	3.10551i	0.544339	−	0.179297i
$301$	6.71587	+	6.08691i	0.387096	+	0.350844i
$302$	−5.36937	−	28.9092i	−0.308972	−	1.66353i
$303$	−12.3803	−	8.27225i	−0.711230	−	0.475228i
$304$	2.11544	+	5.13253i	0.121329	+	0.294371i
$305$	1.07289	−	0.716880i	0.0614333	−	0.0410485i
$306$	−7.35500	+	7.17038i	−0.420457	+	0.409903i
$307$	4.48216	+	1.60374i	0.255810	+	0.0915304i	0.461672	−	0.887051i	$-0.347250\pi$
$307$	4.48216	+	1.60374i	0.255810	+	0.0915304i	−0.205862	+	0.978581i	$0.566000\pi$
$308$	0.204090	−	1.17011i	0.0116291	−	0.0666734i
$309$	1.87699	+	12.6536i	0.106778	+	0.719840i
$310$	0.0292636	+	0.804083i	0.00166206	+	0.0456689i
$311$	0.883163	−	2.91140i	0.0500796	−	0.165090i	−0.928334	−	0.371748i	$-0.878759\pi$
$311$	0.883163	−	2.91140i	0.0500796	−	0.165090i	0.978413	+	0.206658i	$0.0662586\pi$
$312$	0.279937	+	1.75449i	0.0158483	+	0.0993287i
$313$	11.7919	−	22.0611i	0.666517	−	1.24696i	−0.290484	−	0.956880i	$-0.593816\pi$
$313$	11.7919	−	22.0611i	0.666517	−	1.24696i	0.957001	−	0.290085i	$-0.0936836\pi$
$314$	0.657458	−	10.6254i	0.0371025	−	0.599628i
$315$	0.443125	+	0.209583i	0.0249673	+	0.0118086i
$316$	−5.49437	−	5.78105i	−0.309083	−	0.325209i
$317$	−13.2110	+	3.30918i	−0.742002	+	0.185862i	−0.595508	−	0.803350i	$-0.703049\pi$
$317$	−13.2110	+	3.30918i	−0.742002	+	0.185862i	−0.146494	+	0.989211i	$0.546799\pi$
$318$	−6.96756	−	2.21067i	−0.390722	−	0.123968i
$319$	1.28508	+	1.28508i	0.0719506	+	0.0719506i
$320$	1.00468	−	1.15853i	0.0561631	−	0.0647638i
$321$	13.0831	−	13.0831i	0.730225	−	0.730225i
$322$	−14.2659	+	7.39374i	−0.795009	+	0.412037i
$323$	−2.44932	−	9.77822i	−0.136284	−	0.544075i
$324$	0.812084	−	1.82771i	0.0451158	−	0.101539i
$325$	−1.33298	+	2.81836i	−0.0739406	+	0.156334i
$326$	12.6750	−	11.1978i	0.702003	−	0.620191i
$327$	5.53584	+	2.95897i	0.306132	+	0.163631i
$328$	11.0374	−	24.0139i	0.609436	−	1.32595i
$329$	−21.1979	−	6.43032i	−1.16868	−	0.354515i
$330$	0.0461059	+	0.0428678i	0.00253805	+	0.00235980i
$331$	−25.3720	+	3.76358i	−1.39457	+	0.206865i	−0.801359	−	0.598183i	$-0.795890\pi$
$331$	−25.3720	+	3.76358i	−1.39457	+	0.206865i	−0.593210	+	0.805048i	$0.702140\pi$
$332$	−5.91572	+	9.32387i	−0.324667	+	0.511714i
$333$	−3.16540	+	8.84670i	−0.173463	+	0.484796i
$334$	−20.0923	−	0.255382i	−1.09940	−	0.0139739i
$335$	−0.708020	−	1.05963i	−0.0386833	−	0.0578936i
$336$	−10.1815	+	0.984790i	−0.555448	+	0.0537247i
$337$	12.4513	−	18.6347i	0.678265	−	1.01510i	−0.319455	−	0.947602i	$-0.603500\pi$
$337$	12.4513	−	18.6347i	0.678265	−	1.01510i	0.997720	−	0.0674936i	$-0.0215002\pi$
$338$	14.6953	+	10.0916i	0.799321	+	0.548911i
$339$	−3.11359	+	3.43531i	−0.169107	+	0.186581i
$340$	−2.11006	+	1.81693i	−0.114434	+	0.0985368i
$341$	0.591242	−	0.354377i	0.0320175	−	0.0191906i
$342$	1.14906	+	1.59120i	0.0621338	+	0.0860421i
$343$	12.1031	−	14.7477i	0.653506	−	0.796300i
$344$	7.01062	−	7.16598i	0.377987	−	0.386364i
$345$	0.0834767	−	0.847553i	0.00449424	−	0.0456307i
$346$	11.2782	+	8.58878i	0.606318	+	0.461735i
$347$	−2.54687	+	2.30834i	−0.136723	+	0.123918i	−0.737056	−	0.675832i	$-0.763785\pi$
$347$	−2.54687	+	2.30834i	−0.136723	+	0.123918i	0.600333	+	0.799750i	$0.295035\pi$
$348$	7.72632	−	13.6110i	0.414174	−	0.729629i
$349$	9.94792	+	13.4132i	0.532500	+	0.717993i	0.984765	−	0.173891i	$-0.0556340\pi$
$349$	9.94792	+	13.4132i	0.532500	+	0.717993i	−0.452265	+	0.891883i	$0.649384\pi$
$350$	−15.7214	−	8.66193i	−0.840343	−	0.462999i
$351$	0.240384	+	0.580338i	0.0128307	+	0.0309762i
$352$	−1.28464	−	0.274901i	−0.0684718	−	0.0146523i
$353$	−5.97481	+	14.4245i	−0.318007	+	0.767737i	0.681353	+	0.731955i	$0.261392\pi$
$353$	−5.97481	+	14.4245i	−0.318007	+	0.767737i	−0.999360	+	0.0357817i	$0.988608\pi$
$354$	−4.75478	+	3.80205i	−0.252714	+	0.202077i
$355$	0.766712	+	0.113731i	0.0406929	+	0.00603622i
$356$	2.33622	+	32.0540i	0.123819	+	1.69886i
$357$	18.5517	+	0.911387i	0.981860	+	0.0482357i
$358$	7.08955	+	1.87191i	0.374694	+	0.0989336i
$359$	11.0228	+	13.4313i	0.581760	+	0.708876i	0.977843	−	0.209338i	$-0.0671310\pi$
$359$	11.0228	+	13.4313i	0.581760	+	0.708876i	−0.396084	+	0.918214i	$0.629631\pi$
$360$	0.250321	−	0.480921i	0.0131931	−	0.0253468i
$361$	16.9917	−	1.67353i	0.894298	−	0.0880807i
$362$	6.85357	+	28.9153i	0.360215	+	1.51976i
$363$	−2.65968	+	10.6180i	−0.139597	+	0.557302i
$364$	1.97877	−	2.53099i	0.103716	−	0.132660i
$365$	−0.963832	+	0.0473500i	−0.0504493	+	0.00247841i
$366$	−1.97577	+	9.31266i	−0.103275	+	0.486780i
$367$	4.08067	+	20.5149i	0.213009	+	1.07087i	0.928240	+	0.371982i	$0.121322\pi$
$367$	4.08067	+	20.5149i	0.213009	+	1.07087i	−0.715231	+	0.698888i	$0.753678\pi$
$368$	7.57033	+	16.0789i	0.394631	+	0.838172i
$369$	1.82293	−	9.16451i	0.0948982	−	0.477085i
$370$	−1.00456	+	2.34063i	−0.0522245	+	0.121683i
$371$	5.65146	+	11.9490i	0.293409	+	0.620362i
$372$	−4.29575	−	4.09707i	−0.222724	−	0.212423i
$373$	−8.27093	−	6.13414i	−0.428253	−	0.317614i	0.360015	−	0.932947i	$-0.382772\pi$
$373$	−8.27093	−	6.13414i	−0.428253	−	0.317614i	−0.788267	+	0.615333i	$0.789022\pi$
$374$	2.23565	+	0.832129i	0.115603	+	0.0430284i
$375$	1.68430	−	0.900278i	0.0869769	−	0.0464901i
$376$	−8.00076	+	23.1576i	−0.412608	+	1.19426i
$377$	1.42694	+	4.70398i	0.0734909	+	0.242267i
$378$	−3.42031	+	1.17499i	−0.175922	+	0.0604350i
$379$	7.03198	+	19.6531i	0.361209	+	1.00951i	0.975417	+	0.220367i	$0.0707253\pi$
$379$	7.03198	+	19.6531i	0.361209	+	1.00951i	−0.614209	+	0.789144i	$0.710525\pi$
$380$	0.284257	+	0.449762i	0.0145821	+	0.0230723i
$381$	10.5297	−	17.5677i	0.539451	−	0.900019i
$382$	21.0213	+	17.7036i	1.07554	+	0.905794i
$383$		−	3.37647i		−	0.172529i	−0.996272	−	0.0862647i	$-0.972507\pi$
$383$		−	3.37647i		−	0.172529i	0.996272	−	0.0862647i	$-0.0274931\pi$
$384$	0.659149	+	11.2945i	0.0336371	+	0.576370i
$385$		−	0.113840i		−	0.00580181i
$386$	4.23919	−	5.03363i	0.215769	−	0.256205i
$387$	1.82217	−	3.04010i	0.0926259	−	0.154537i
$388$	−2.79365	+	12.3899i	−0.141826	+	0.629003i
$389$	10.8952	+	30.4499i	0.552406	+	1.54387i	0.815295	+	0.579046i	$0.196575\pi$
$389$	10.8952	+	30.4499i	0.552406	+	1.54387i	−0.262889	+	0.964826i	$0.584675\pi$
$390$	0.0553241	+	0.161044i	0.00280144	+	0.00815480i
$391$	−9.36767	−	30.8811i	−0.473743	−	1.56172i
$392$	−0.974450	−	0.863930i	−0.0492171	−	0.0436351i
$393$	−3.34005	+	1.78530i	−0.168483	+	0.0900562i
$394$	−10.9852	+	29.5135i	−0.553426	+	1.48687i
$395$	−0.613966	−	0.455348i	−0.0308920	−	0.0229111i
$396$	−0.464343	+	0.0109921i	−0.0233341	+	0.000552374i
$397$	4.96387	+	10.4952i	0.249130	+	0.526740i	0.989338	−	0.145637i	$-0.0465232\pi$
$397$	4.96387	+	10.4952i	0.249130	+	0.526740i	−0.740208	+	0.672377i	$0.765273\pi$
$398$	−5.68513	−	2.43996i	−0.284970	−	0.122304i
$399$	0.692392	−	3.48089i	0.0346630	−	0.174263i
$400$	−10.2363	+	17.0106i	−0.511815	+	0.850530i
$401$	−3.61718	−	18.1848i	−0.180633	−	0.908105i	−0.959670	−	0.281127i	$-0.909292\pi$
$401$	−3.61718	−	18.1848i	−0.180633	−	0.908105i	0.779037	−	0.626978i	$-0.215708\pi$
$402$	9.19756	+	1.95135i	0.458732	+	0.0973243i
$403$	1.86220	−	0.0914842i	0.0927630	−	0.00455715i
$404$	29.5585	−	3.61942i	1.47059	−	0.180073i
$405$	0.0465757	−	0.185941i	0.00231437	−	0.00923947i
$406$	−27.5382	+	6.52716i	−1.36670	+	0.323937i
$407$	2.17157	−	0.213881i	0.107641	−	0.0106017i
$408$	1.78948	−	20.4656i	0.0885922	−	1.01320i
$409$	7.56082	+	9.21288i	0.373858	+	0.455548i	0.925620	−	0.378454i	$-0.123544\pi$
$409$	7.56082	+	9.21288i	0.373858	+	0.455548i	−0.551762	+	0.834002i	$0.686044\pi$
$410$	0.646653	−	2.44909i	0.0319359	−	0.120952i
$411$	−9.45717	−	0.464601i	−0.466488	−	0.0229171i
$412$	−19.3579	−	16.7278i	−0.953696	−	0.824121i
$413$	10.8895	+	1.61530i	0.535836	+	0.0794838i
$414$	3.92405	+	4.90735i	0.192856	+	0.241183i
$415$	−0.404999	+	0.977754i	−0.0198806	+	0.0479961i
$416$	−2.71391	−	2.29372i	−0.133060	−	0.112459i
$417$	−2.89016	−	6.97747i	−0.141532	−	0.341688i
$418$	0.219961	−	0.399228i	0.0107586	−	0.0195269i
$419$	22.9249	+	30.9107i	1.11996	+	1.51008i	0.833936	+	0.551861i	$0.186082\pi$
$419$	22.9249	+	30.9107i	1.11996	+	1.51008i	0.286019	+	0.958224i	$0.407668\pi$
$420$	−0.945093	+	0.260652i	−0.0461158	+	0.0127185i
$421$	−12.8706	+	11.6652i	−0.627273	+	0.568527i	−0.922065	−	0.387034i	$-0.873500\pi$
$421$	−12.8706	+	11.6652i	−0.627273	+	0.568527i	0.294792	+	0.955561i	$0.404750\pi$
$422$	3.50622	−	4.60412i	0.170680	−	0.224125i
$423$	−0.849055	+	8.62060i	−0.0412824	+	0.419148i
$424$	13.4447	−	5.74239i	0.652934	−	0.278875i
$425$	22.8696	−	27.8666i	1.10934	−	1.35173i
$426$	−4.63610	+	3.34788i	−0.224620	+	0.162205i
$427$	14.7654	−	8.85001i	0.714545	−	0.428282i
$428$	−2.75453	+	36.9018i	−0.133145	+	1.78372i
$429$	0.0979671	−	0.108090i	0.00472990	−	0.00521864i
$430$	0.543913	−	0.792043i	0.0262298	−	0.0381957i
$431$	−15.5709	+	23.3035i	−0.750025	+	1.12249i	0.238458	+	0.971153i	$0.423358\pi$
$431$	−15.5709	+	23.3035i	−0.750025	+	1.12249i	−0.988482	+	0.151338i	$0.951642\pi$
$432$	1.15443	+	3.82979i	0.0555427	+	0.184261i
$433$	20.1386	+	30.1395i	0.967799	+	1.44841i	0.892392	+	0.451260i	$0.149025\pi$
$433$	20.1386	+	30.1395i	0.967799	+	1.44841i	0.0754061	+	0.997153i	$0.475975\pi$
$434$	−0.136427	+	10.7335i	−0.00654868	+	0.515222i
$435$	0.505349	−	1.41235i	0.0242296	−	0.0677172i
$436$	−12.2514	+	2.73988i	−0.586736	+	0.131216i
$437$	−6.09944	+	0.904767i	−0.291776	+	0.0432809i
$438$	4.84784	−	5.21403i	0.231639	−	0.249136i
$439$	27.0733	+	8.21260i	1.29214	+	0.391966i	0.860209	−	0.509941i	$-0.170333\pi$
$439$	27.0733	+	8.21260i	1.29214	+	0.391966i	0.431929	+	0.901907i	$0.357833\pi$
$440$	−0.125820	−	0.00479972i	−0.00599821	−	0.000228818i
$441$	−0.406058	−	0.217043i	−0.0193361	−	0.0103354i
$442$	4.27198	+	4.83551i	0.203197	+	0.230002i
$443$	1.49852	−	3.16836i	0.0711970	−	0.150533i	−0.865252	−	0.501337i	$-0.832842\pi$
$443$	1.49852	−	3.16836i	0.0711970	−	0.150533i	0.936449	+	0.350804i	$0.114092\pi$
$444$	−6.74775	−	17.5386i	−0.320234	−	0.832346i
$445$	0.748448	+	2.98797i	0.0354799	+	0.141644i
$446$	4.88903	+	9.43319i	0.231502	+	0.446674i
$447$	−8.90879	+	8.90879i	−0.421371	+	0.421371i
$448$	14.1456	−	14.7796i	0.668314	−	0.698270i
$449$	−20.7173	−	20.7173i	−0.977712	−	0.977712i	0.0220449	−	0.999757i	$-0.492982\pi$
$449$	−20.7173	−	20.7173i	−0.977712	−	0.977712i	−0.999757	+	0.0220449i	$0.992982\pi$
$450$	−2.12274	+	6.69043i	−0.100067	+	0.315390i
$451$	−2.10500	+	0.527274i	−0.0991204	+	0.0248284i
$452$	0.235682	−	9.26971i	0.0110855	−	0.436011i
$453$	18.7953	+	8.88949i	0.883078	+	0.417665i
$454$	17.3406	+	1.07297i	0.813835	+	0.0503568i
$455$	0.145150	−	0.271556i	0.00680472	−	0.0127307i
$456$	−3.81801	−	0.912018i	−0.178795	−	0.0427091i
$457$	1.30416	−	4.29925i	0.0610062	−	0.201111i	−0.921139	−	0.389233i	$-0.872740\pi$
$457$	1.30416	−	4.29925i	0.0610062	−	0.201111i	0.982146	+	0.188122i	$0.0602401\pi$
$458$	−3.04800	+	0.110928i	−0.142424	+	0.00518332i
$459$	−1.06574	−	7.18466i	−0.0497447	−	0.335351i
$460$	0.979559	+	1.39346i	0.0456722	+	0.0649703i
$461$	20.4772	+	7.32687i	0.953720	+	0.341246i	0.767347	−	0.641233i	$-0.221577\pi$
$461$	20.4772	+	7.32687i	0.953720	+	0.341246i	0.186373	+	0.982479i	$0.440327\pi$
$462$	0.586293	+	0.601389i	0.0272768	+	0.0279791i
$463$	3.67014	−	2.45231i	0.170566	−	0.113969i	−0.467357	−	0.884069i	$-0.654794\pi$
$463$	3.67014	−	2.45231i	0.170566	−	0.113969i	0.637923	+	0.770100i	$0.279794\pi$
$464$	6.05297	+	30.7114i	0.281002	+	1.42574i
$465$	−0.473064	−	0.316091i	−0.0219378	−	0.0146584i
$466$	7.01396	−	1.30272i	0.324915	−	0.0603473i
$467$	−8.71768	−	7.90125i	−0.403406	−	0.365626i	0.444494	−	0.895782i	$-0.353383\pi$
$467$	−8.71768	−	7.90125i	−0.403406	−	0.365626i	−0.847900	+	0.530156i	$0.822133\pi$
$468$	−1.12167	−	0.565832i	−0.0518492	−	0.0261556i
$469$	−8.74063	−	14.5829i	−0.403605	−	0.673374i
$470$	−0.374048	+	2.31823i	−0.0172535	+	0.106932i
$471$	5.81898	+	4.77551i	0.268124	+	0.220044i
$472$	2.24441	−	11.9673i	0.103307	−	0.550841i
$473$	−0.819167	−	0.0806809i	−0.0376653	−	0.00370971i
$474$	5.58856	−	0.756525i	0.256691	−	0.0347484i
$475$	−4.62586	−	5.10385i	−0.212249	−	0.234181i
$476$	−29.3056	+	22.8291i	−1.34322	+	1.04637i
$477$	4.15166	−	3.07908i	0.190091	−	0.140981i
$478$	−7.74258	−	26.7428i	−0.354137	−	1.22319i
$479$	−15.9369	+	6.60127i	−0.728175	+	0.301620i	−0.715802	−	0.698304i	$-0.753939\pi$
$479$	−15.9369	+	6.60127i	−0.728175	+	0.301620i	−0.0123730	+	0.999923i	$0.503939\pi$
$480$	0.248234	+	1.05554i	0.0113303	+	0.0481786i
$481$	5.45283	+	2.25863i	0.248627	+	0.102985i
$482$	−1.39043	+	12.4880i	−0.0633323	+	0.568813i
$483$	1.66713	−	11.2389i	0.0758571	−	0.511387i
$484$	−9.82582	−	19.5632i	−0.446628	−	0.889236i
$485$	−0.0597298	+	1.21583i	−0.00271219	+	0.0552079i
$486$	0.711576	+	1.22215i	0.0322777	+	0.0554380i
$487$	−7.79865	+	6.40019i	−0.353391	+	0.290020i	−0.794293	−	0.607535i	$-0.792158\pi$
$487$	−7.79865	+	6.40019i	−0.353391	+	0.290020i	0.440902	+	0.897555i	$0.354658\pi$
$488$	−9.15880	−	16.6923i	−0.414599	−	0.755625i
$489$	1.17221	+	11.9017i	0.0530092	+	0.538211i
$490$	−0.106232	−	0.0655225i	−0.00479908	−	0.00296001i
$491$	−21.9360	−	5.49469i	−0.989960	−	0.247972i	−0.286014	−	0.958226i	$-0.592330\pi$
$491$	−21.9360	−	5.49469i	−0.989960	−	0.247972i	−0.703946	+	0.710253i	$0.748580\pi$
$492$	9.19709	+	16.2683i	0.414637	+	0.733433i
$493$	−2.78896	−	56.7706i	−0.125608	−	2.55682i
$494$	1.03373	−	0.671870i	0.0465097	−	0.0302289i
$495$	−0.0436609	+	0.00868470i	−0.00196241	+	0.000390348i
$496$	11.8572	+	0.603328i	0.532406	+	0.0270902i
$497$	10.1419	+	2.01735i	0.454926	+	0.0904904i
$498$	−2.89608	−	7.25106i	−0.129776	−	0.324928i
$499$	−17.4819	+	8.26834i	−0.782599	+	0.370142i	−0.776724	−	0.629841i	$-0.783120\pi$
$499$	−17.4819	+	8.26834i	−0.782599	+	0.370142i	−0.00587486	+	0.999983i	$0.501870\pi$
$500$	−1.37778	+	3.56247i	−0.0616163	+	0.159319i
$501$	8.46404	−	11.4124i	0.378145	−	0.509870i
$502$	−4.94971	−	10.8189i	−0.220917	−	0.482873i
$503$	3.60164	+	6.73819i	0.160589	+	0.300441i	0.949328	−	0.314287i	$-0.101766\pi$
$503$	3.60164	+	6.73819i	0.160589	+	0.300441i	−0.788739	+	0.614729i	$0.789266\pi$
$504$	3.65031	−	6.24434i	0.162598	−	0.278145i
$505$	2.73123	−	0.828510i	0.121538	−	0.0368682i
$506$	0.640611	−	1.31108i	0.0284786	−	0.0582847i
$507$	−11.8686	+	4.24664i	−0.527101	+	0.188600i
$508$	6.96780	+	40.3663i	0.309146	+	1.79096i
$509$	3.55388	+	2.13012i	0.157523	+	0.0944157i	0.590692	−	0.806897i	$-0.298855\pi$
$509$	3.55388	+	2.13012i	0.157523	+	0.0944157i	−0.433169	+	0.901313i	$0.642605\pi$
$510$	−0.168072	−	1.96177i	−0.00744236	−	0.0868686i
$511$	−12.8739			−0.569509
$512$	−15.7385	−	16.2573i	−0.695550	−	0.718477i
$513$	−1.38785			−0.0612750
$514$	−2.53689	−	29.6110i	−0.111897	−	1.30609i
$515$	−2.10320	−	1.26061i	−0.0926779	−	0.0555490i
$516$	1.20578	+	6.98542i	0.0530817	+	0.307516i
$517$	1.89411	−	0.677723i	0.0833028	−	0.0298062i
$518$	−14.9178	+	30.5309i	−0.655450	+	1.34145i
$519$	−9.59244	+	2.90984i	−0.421061	+	0.127728i
$520$	−0.294013	−	0.171874i	−0.0128933	−	0.00753716i
$521$	−1.61285	−	3.01742i	−0.0706600	−	0.132196i	0.844111	−	0.536169i	$-0.180129\pi$
$521$	−1.61285	−	3.01742i	−0.0706600	−	0.132196i	−0.914771	+	0.403973i	$0.867629\pi$
$522$	4.60422	+	10.0638i	0.201521	+	0.440479i
$523$	7.13852	−	9.62518i	0.312146	−	0.420880i	−0.619077	−	0.785330i	$-0.712493\pi$
$523$	7.13852	−	9.62518i	0.312146	−	0.420880i	0.931223	+	0.364451i	$0.118743\pi$
$524$	2.73221	−	7.06456i	0.119357	−	0.308617i
$525$	11.4737	−	5.42667i	0.500755	−	0.236839i
$526$	−10.2030	−	25.5458i	−0.444872	−	1.11385i
$527$	−21.1442	−	4.20584i	−0.921056	−	0.183209i
$528$	0.689395	−	0.622635i	0.0300021	−	0.0270967i
$529$	3.19725	−	0.635973i	0.139011	−	0.0276510i
$530$	1.17485	−	0.763590i	0.0510321	−	0.0331682i
$531$	−0.211229	−	4.29967i	−0.00916657	−	0.186590i
$532$	3.49327	+	6.17909i	0.151452	+	0.267897i
$533$	−5.69360	−	1.42617i	−0.246617	−	0.0617744i
$534$	−19.3424	−	11.9301i	−0.837029	−	0.516268i
$535$	0.347628	+	3.52953i	0.0150293	+	0.152595i
$536$	−16.4860	+	9.04560i	−0.712087	+	0.390710i
$537$	−4.00796	+	3.28925i	−0.172956	+	0.141942i
$538$	−8.16086	−	14.0165i	−0.351840	−	0.604296i
$539$	−0.00524668	+	0.106799i	−0.000225991	+	0.00460014i
$540$	0.172068	+	0.342587i	0.00740462	+	0.0147426i
$541$	−0.898697	+	6.05852i	−0.0386380	+	0.260476i	−0.999884	−	0.0152150i	$-0.995157\pi$
$541$	−0.898697	+	6.05852i	−0.0386380	+	0.260476i	0.961246	+	0.275691i	$0.0889067\pi$
$542$	1.53582	−	13.7938i	0.0659692	−	0.592496i
$543$	−19.4132	−	8.04121i	−0.833101	−	0.345082i
$544$	23.9959	+	33.3521i	1.02882	+	1.42996i
$545$	−1.11162	+	0.460449i	−0.0476167	+	0.0197235i
$546$	0.631764	+	2.18211i	0.0270370	+	0.0933857i
$547$	−34.8986	+	25.8826i	−1.49216	+	1.10666i	−0.525435	+	0.850834i	$0.676098\pi$
$547$	−34.8986	+	25.8826i	−1.49216	+	1.10666i	−0.966723	+	0.255826i	$0.917652\pi$
$548$	14.9392	−	11.6377i	0.638173	−	0.497136i
$549$	−4.52067	−	4.98780i	−0.192938	−	0.212874i
$550$	1.61536	−	0.218672i	0.0688791	−	0.00932419i
$551$	−10.8084	−	1.06453i	−0.460452	−	0.0453505i
$552$	−12.3513	−	2.31643i	−0.525707	−	0.0985937i
$553$	−7.88294	−	6.46936i	−0.335217	−	0.275105i
$554$	1.11290	−	6.89742i	0.0472827	−	0.293043i
$555$	−0.925932	−	1.54482i	−0.0393036	−	0.0655741i
$556$	13.4859	+	6.80306i	0.571931	+	0.288514i
$557$	14.2214	+	12.8895i	0.602578	+	0.546145i	0.914822	−	0.403857i	$-0.132331\pi$
$557$	14.2214	+	12.8895i	0.602578	+	0.546145i	−0.312244	+	0.950002i	$0.601081\pi$
$558$	4.12701	−	0.766519i	0.174710	−	0.0324493i
$559$	−1.85119	−	1.23692i	−0.0782969	−	0.0523163i
$560$	1.09219	−	1.62840i	0.0461535	−	0.0688124i
$561$	−1.40252	+	0.937134i	−0.0592145	+	0.0395658i
$562$	14.8294	+	15.2113i	0.625542	+	0.641649i
$563$	7.41983	+	2.65486i	0.312709	+	0.111889i	0.488567	−	0.872527i	$-0.337520\pi$
$563$	7.41983	+	2.65486i	0.312709	+	0.111889i	−0.175858	+	0.984416i	$0.556270\pi$
$564$	−9.96325	−	14.1731i	−0.419528	−	0.596794i
$565$	−0.130402	−	0.879102i	−0.00548607	−	0.0369841i
$566$	−4.99716	+	0.181865i	−0.210046	+	0.00764437i
$567$	0.742333	−	2.44714i	0.0311751	−	0.102770i
$568$	2.65724	−	11.1241i	0.111495	−	0.466757i
$569$	8.21980	−	15.3782i	0.344592	−	0.644686i	−0.648606	−	0.761124i	$-0.724648\pi$
$569$	8.21980	−	15.3782i	0.344592	−	0.644686i	0.993198	+	0.116438i	$0.0371477\pi$
$570$	−0.375505	−	0.0232347i	−0.0157282	−	0.000973194i
$571$	−10.5314	−	4.98098i	−0.440726	−	0.208448i	0.194295	−	0.980943i	$-0.437758\pi$
$571$	−10.5314	−	4.98098i	−0.440726	−	0.208448i	−0.635020	+	0.772496i	$0.719008\pi$
$572$	−0.00741558	+	0.291666i	−0.000310061	+	0.0121952i
$573$	−18.8510	+	4.72192i	−0.787511	+	0.197261i
$574$	10.2198	−	32.2105i	0.426564	−	1.34444i
$575$	−15.5929	−	15.5929i	−0.650268	−	0.650268i
$576$	−6.74756	−	4.29772i	−0.281148	−	0.179072i
$577$	32.3479	−	32.3479i	1.34666	−	1.34666i	0.457397	−	0.889263i	$-0.348782\pi$
$577$	32.3479	−	32.3479i	1.34666	−	1.34666i	0.889263	−	0.457397i	$-0.151218\pi$
$578$	−23.2677	−	44.8941i	−0.967808	−	1.86735i
$579$	1.13068	+	4.51394i	0.0469896	+	0.187593i
$580$	1.07726	+	2.80000i	0.0447309	+	0.116264i
$581$	−6.03660	+	12.7633i	−0.250441	+	0.529512i
$582$	−5.94617	−	6.73055i	−0.246477	−	0.278990i
$583$	−1.05865	−	0.565862i	−0.0438450	−	0.0234356i
$584$	−0.542791	+	14.2287i	−0.0224609	+	0.588788i
$585$	−0.115223	−	0.0349525i	−0.00476389	−	0.00144511i
$586$	11.4329	−	12.2965i	0.472290	−	0.507965i
$587$	25.4923	−	3.78143i	1.05218	−	0.156076i	0.401833	−	0.915713i	$-0.368373\pi$
$587$	25.4923	−	3.78143i	1.05218	−	0.156076i	0.650347	+	0.759637i	$0.274623\pi$
$588$	0.898651	−	0.200972i	0.0370598	−	0.00828796i
$589$	−1.38776	+	3.87853i	−0.0571817	+	0.159812i
$590$	0.0148315	−	1.16688i	0.000610605	−	0.0480398i
$591$	−12.3714	−	18.5151i	−0.508891	−	0.761610i
$592$	33.1149	+	17.7749i	1.36101	+	0.730544i
$593$	−19.5431	+	29.2483i	−0.802539	+	1.20109i	0.173787	+	0.984783i	$0.444400\pi$
$593$	−19.5431	+	29.2483i	−0.802539	+	1.20109i	−0.976327	+	0.216302i	$0.930600\pi$
$594$	0.185923	−	0.270740i	0.00762851	−	0.0111086i
$595$	−2.39100	+	2.63806i	−0.0980216	+	0.108150i
$596$	1.87568	−	25.1280i	0.0768307	−	1.02928i
$597$	3.75221	−	2.24899i	0.153568	−	0.0920450i
$598$	3.19980	−	2.31068i	0.130850	−	0.0944908i
$599$	4.78537	−	5.83099i	0.195525	−	0.238248i	−0.666014	−	0.745939i	$-0.732001\pi$
$599$	4.78537	−	5.83099i	0.195525	−	0.238248i	0.861539	+	0.507691i	$0.169501\pi$
$600$	−5.51399	−	12.9100i	−0.225108	−	0.527047i
$601$	−4.26161	+	43.2689i	−0.173835	+	1.76498i	0.373092	+	0.927794i	$0.378298\pi$
$601$	−4.26161	+	43.2689i	−0.173835	+	1.76498i	−0.546927	+	0.837181i	$0.684202\pi$
$602$	7.76604	−	10.1978i	0.316520	−	0.415632i
$603$	−4.92615	+	4.46480i	−0.200608	+	0.181821i
$604$	−40.0863	+	11.0556i	−1.63109	+	0.449846i
$605$	−1.24990	−	1.68529i	−0.0508155	−	0.0685168i
$606$	−10.1615	+	18.4431i	−0.412783	+	0.749200i
$607$	−1.48057	−	3.57441i	−0.0600944	−	0.145081i	0.890980	−	0.454042i	$-0.150019\pi$
$607$	−1.48057	−	3.57441i	−0.0600944	−	0.145081i	−0.951075	+	0.308962i	$0.900019\pi$
$608$	6.97663	−	3.60036i	0.282940	−	0.146014i
$609$	7.65824	−	18.4886i	0.310328	−	0.749197i
$610$	−1.13964	−	1.42521i	−0.0461426	−	0.0577052i
$611$	5.38236	+	0.798398i	0.217747	+	0.0322997i
$612$	10.9913	+	9.49798i	0.444298	+	0.383933i
$613$	−8.17727	−	0.401723i	−0.330277	−	0.0162255i	−0.116746	−	0.993162i	$-0.537246\pi$
$613$	−8.17727	−	0.401723i	−0.330277	−	0.0162255i	−0.213531	+	0.976936i	$0.568496\pi$
$614$	1.71868	−	6.50920i	0.0693601	−	0.262690i
$615$	1.13627	+	1.38455i	0.0458189	+	0.0558305i
$616$	−1.67339	−	0.146318i	−0.0674227	−	0.00589533i
$617$	−40.7625	+	4.01476i	−1.64104	+	0.161628i	−0.875984	−	0.482340i	$-0.839787\pi$
$617$	−40.7625	+	4.01476i	−1.64104	+	0.161628i	−0.765052	+	0.643968i	$0.777287\pi$
$618$	17.6030	−	4.17230i	0.708098	−	0.167835i
$619$	−4.03124	+	16.0936i	−0.162029	+	0.646858i	0.833509	+	0.552505i	$0.186328\pi$
$619$	−4.03124	+	16.0936i	−0.162029	+	0.646858i	−0.995539	+	0.0943524i	$0.969922\pi$
$620$	1.12946	−	0.138302i	0.0453603	−	0.00555434i
$621$	−4.43763	+	0.218007i	−0.178076	+	0.00874832i
$622$	−4.20892	−	0.892962i	−0.168762	−	0.0358045i
$623$	8.01702	+	40.3043i	0.321195	+	1.61476i
$624$	2.43838	−	0.606245i	0.0976133	−	0.0242692i
$625$	4.77000	−	23.9804i	0.190800	−	0.959216i
$626$	−32.5087	−	13.9522i	−1.29931	−	0.557642i
$627$	0.137805	+	0.291364i	0.00550339	+	0.0116359i
$628$	−15.0511	+	0.356296i	−0.600606	+	0.0142178i
$629$	−54.8152	−	40.6537i	−2.18562	−	1.62097i
$630$	0.241819	−	0.649687i	0.00963431	−	0.0258842i
$631$	23.0555	−	12.3234i	0.917824	−	0.490587i	0.0563626	−	0.998410i	$-0.482050\pi$
$631$	23.0555	−	12.3234i	0.917824	−	0.490587i	0.861461	+	0.507823i	$0.169550\pi$
$632$	−7.48252	+	8.43974i	−0.297639	+	0.335715i
$633$	1.18789	+	3.91595i	0.0472145	+	0.155645i
$634$	6.25761	+	18.2155i	0.248522	+	0.723428i
$635$	1.32264	+	3.69652i	0.0524873	+	0.146692i
$636$	−2.27383	+	10.0845i	−0.0901634	+	0.399877i
$637$	−0.148687	+	0.248070i	−0.00589121	+	0.00982889i
$638$	1.65561	−	1.96588i	0.0655462	−	0.0778298i
$639$		−	4.04362i		−	0.159963i
$640$	−1.75371	−	1.27578i	−0.0693216	−	0.0504298i
$641$		−	47.4201i		−	1.87298i	−0.350693	−	0.936491i	$-0.614054\pi$
$641$		−	47.4201i		−	1.87298i	0.350693	−	0.936491i	$-0.385946\pi$
$642$	−20.0141	−	16.8553i	−0.789892	−	0.665227i
$643$	6.73920	−	11.2437i	0.265768	−	0.443407i	−0.695697	−	0.718336i	$-0.744904\pi$
$643$	6.73920	−	11.2437i	0.265768	−	0.443407i	0.961465	+	0.274929i	$0.0886542\pi$
$644$	12.1403	+	19.2089i	0.478396	+	0.756935i
$645$	0.228884	+	0.639687i	0.00901228	+	0.0251876i
$646$	−13.4823	+	4.63163i	−0.530456	+	0.182229i
$647$	−1.08187	−	3.56644i	−0.0425326	−	0.140211i	0.933103	−	0.359610i	$-0.117090\pi$
$647$	−1.08187	−	3.56644i	−0.0425326	−	0.140211i	−0.975635	+	0.219399i	$0.929590\pi$
$648$	−2.67337	−	0.923629i	−0.105020	−	0.0362836i
$649$	−0.881696	+	0.471276i	−0.0346096	+	0.0184992i
$650$	4.13213	+	1.53801i	0.162075	+	0.0603259i
$651$	−6.09660	−	4.52154i	−0.238944	−	0.177213i
$652$	−17.3084	−	16.5079i	−0.677851	−	0.646500i
$653$	16.5466	+	34.9847i	0.647517	+	1.36906i	0.914195	+	0.405274i	$0.132824\pi$
$653$	16.5466	+	34.9847i	0.647517	+	1.36906i	−0.266679	+	0.963785i	$0.585926\pi$
$654$	3.50106	−	8.15748i	0.136902	−	0.318983i
$655$	0.141628	−	0.712010i	0.00553385	−	0.0278205i
$656$	−35.1692	−	12.6533i	−1.37313	−	0.494028i
$657$	0.982136	+	4.93753i	0.0383168	+	0.192631i
$658$	−6.50166	+	30.6452i	−0.253461	+	1.19468i
$659$	−31.3212	+	1.53871i	−1.22010	+	0.0599398i	−0.648903	−	0.760871i	$-0.724772\pi$
$659$	−31.3212	+	1.53871i	−1.22010	+	0.0599398i	−0.571200	+	0.820811i	$0.693522\pi$
$660$	0.0548371	−	0.0701405i	0.00213453	−	0.00273022i
$661$	8.95676	−	35.7574i	0.348377	−	1.39080i	−0.502109	−	0.864804i	$-0.667442\pi$
$661$	8.95676	−	35.7574i	0.348377	−	1.39080i	0.850487	−	0.525997i	$-0.176308\pi$
$662$	8.36594	+	35.2961i	0.325152	+	1.37182i
$663$	−4.54048	+	0.447198i	−0.176338	+	0.0173677i
$664$	13.8520	+	7.20999i	0.537560	+	0.279802i
$665$	0.431582	+	0.525885i	0.0167360	+	0.0203929i
$666$	12.8476	+	3.39225i	0.497834	+	0.131447i
$667$	−34.7269	−	1.70602i	−1.34463	−	0.0660575i
$668$	2.06568	+	28.3420i	0.0799234	+	1.09658i
$669$	−7.43159	−	1.10237i	−0.287322	−	0.0426202i
$670$	−1.40760	+	1.12555i	−0.0543802	+	0.0434839i
$671$	−0.598259	+	1.44432i	−0.0230955	+	0.0557575i
$672$	2.61672	+	14.2274i	0.100942	+	0.548834i
$673$	9.11156	+	21.9973i	0.351225	+	0.847932i	0.996469	+	0.0839560i	$0.0267555\pi$
$673$	9.11156	+	21.9973i	0.351225	+	0.847932i	−0.645244	+	0.763976i	$0.723244\pi$
$674$	−27.7603	−	15.2950i	−1.06929	−	0.589140i
$675$	−2.95661	−	3.98653i	−0.113800	−	0.153441i
$676$	12.4456	−	21.9247i	0.478676	−	0.843259i
$677$	21.8976	−	19.8468i	0.841591	−	0.762774i	−0.131957	−	0.991255i	$-0.542126\pi$
$677$	21.8976	−	19.8468i	0.841591	−	0.762774i	0.973548	+	0.228482i	$0.0733761\pi$
$678$	5.21640	+	3.97250i	0.200335	+	0.152563i
$679$	−1.59178	+	16.1616i	−0.0610870	+	0.620227i
$680$	2.81487	+	2.75385i	0.107945	+	0.105605i
$681$	−7.79359	+	9.49652i	−0.298651	+	0.363907i
$682$	−0.570709	−	0.790311i	−0.0218536	−	0.0302626i
$683$	34.1582	−	20.4737i	1.30703	−	0.783403i	0.320541	−	0.947235i	$-0.396135\pi$
$683$	34.1582	−	20.4737i	1.30703	−	0.783403i	0.986488	+	0.163832i	$0.0523854\pi$
$684$	2.10337	−	1.81117i	0.0804243	−	0.0692517i
$685$	1.21887	−	1.34482i	0.0465706	−	0.0513828i
$686$	−22.2413	−	15.2736i	−0.849177	−	0.583148i
$687$	1.19819	−	1.79322i	0.0457138	−	0.0684156i
$688$	−10.9435	−	9.01326i	−0.417219	−	0.343627i
$689$	−1.80384	−	2.69964i	−0.0687209	−	0.102848i
$690$	−1.20432	−	0.0153074i	−0.0458478	−	0.000582744i
$691$	−12.3474	+	34.5086i	−0.469716	+	1.31277i	0.440171	+	0.897914i	$0.354918\pi$
$691$	−12.3474	+	34.5086i	−0.469716	+	1.31277i	−0.909887	+	0.414855i	$0.863832\pi$
$692$	10.7405	−	16.9284i	0.408294	−	0.643519i
$693$	−0.587461	+	0.0871416i	−0.0223158	+	0.00331024i
$694$	3.56003	+	3.31001i	0.135137	+	0.125646i
$695$	1.38534	+	0.420238i	0.0525489	+	0.0159405i
$696$	−20.1114	−	9.24367i	−0.762320	−	0.350380i
$697$	59.8546	+	31.9930i	2.26716	+	1.21182i
$698$	17.6990	−	15.6364i	0.669917	−	0.591845i
$699$	−2.15678	+	4.56012i	−0.0815767	+	0.172479i
$700$	−10.3072	+	23.1979i	−0.389577	+	0.876798i
$701$	2.57683	+	10.2873i	0.0973255	+	0.388545i	0.999041	−	0.0437847i	$-0.0139416\pi$
$701$	2.57683	+	10.2873i	0.0973255	+	0.388545i	−0.901715	+	0.432330i	$0.857692\pi$
$702$	0.788708	−	0.408771i	0.0297679	−	0.0154281i
$703$	−9.22077	+	9.22077i	−0.347768	+	0.347768i
$704$	−0.232269	+	1.84332i	−0.00875398	+	0.0694726i
$705$	−1.17411	−	1.17411i	−0.0442194	−	0.0442194i
$706$	21.0461	+	6.67751i	0.792080	+	0.251312i
$707$	36.9356	−	9.25189i	1.38911	−	0.347953i
$708$	5.93128	+	6.24076i	0.222911	+	0.234542i
$709$	−21.9989	−	10.4047i	−0.826185	−	0.390756i	−0.0327890	−	0.999462i	$-0.510439\pi$
$709$	−21.9989	−	10.4047i	−0.826185	−	0.390756i	−0.793396	+	0.608706i	$0.791689\pi$
$710$	0.0676964	−	1.09407i	0.00254060	−	0.0410596i
$711$	−1.87981	+	3.51688i	−0.0704985	+	0.131893i
$712$	44.8837	−	7.16137i	1.68209	−	0.268384i
$713$	−3.82810	+	12.6196i	−0.143364	+	0.472607i
$714$	−0.955347	−	26.2503i	−0.0357530	−	0.982394i
$715$	0.00410303	+	0.0276604i	0.000153445	+	0.00103444i
$716$	1.78178	−	10.2155i	0.0665882	−	0.381772i
$717$	18.5358	+	6.63222i	0.692232	+	0.247685i
$718$	17.5947	−	17.1531i	0.656629	−	0.640147i
$719$	1.35925	−	0.908222i	0.0506915	−	0.0338710i	−0.529966	−	0.848019i	$-0.677795\pi$
$719$	1.35925	−	0.908222i	0.0506915	−	0.0338710i	0.580658	+	0.814148i	$0.302795\pi$
$720$	−0.707861	−	0.294659i	−0.0263804	−	0.0109813i
$721$	−27.1996	−	18.1742i	−1.01297	−	0.676842i
$722$	−4.40931	−	23.7401i	−0.164097	−	0.883515i
$723$	−6.58329	−	5.96675i	−0.244835	−	0.221906i
$724$	39.9158	−	13.1477i	1.48346	−	0.488629i
$725$	−19.9678	−	33.3143i	−0.741587	−	1.23726i
$726$	15.2824	+	2.46583i	0.567184	+	0.0915155i
$727$	21.2471	+	17.4371i	0.788012	+	0.646705i	0.939807	−	0.341707i	$-0.111005\pi$
$727$	21.2471	+	17.4371i	0.788012	+	0.646705i	−0.151794	+	0.988412i	$0.548505\pi$
$728$	−3.80517	−	2.48266i	−0.141029	−	0.0920134i
$729$	−0.995185	−	0.0980171i	−0.0368587	−	0.00363026i
$730$	0.183071	+	1.35237i	0.00677577	+	0.0500536i
$731$	17.2884	+	19.0748i	0.639435	+	0.705507i
$732$	13.3605	+	1.65974i	0.493819	+	0.0613459i
$733$	−16.4465	+	12.1976i	−0.607467	+	0.450528i	−0.855198	−	0.518301i	$-0.826565\pi$
$733$	−16.4465	+	12.1976i	−0.607467	+	0.450528i	0.247732	+	0.968829i	$0.420315\pi$
$734$	28.4140	−	8.22641i	1.04878	−	0.303642i
$735$	0.0815385	−	0.0337743i	0.00300759	−	0.00124579i
$736$	21.7422	−	12.6080i	0.801427	−	0.464738i
$737$	1.42647	+	0.590865i	0.0525448	+	0.0217648i
$738$	−13.1333	−	1.46228i	−0.483445	−	0.0538273i
$739$	−2.27026	+	15.3048i	−0.0835128	+	0.562998i	0.906520	+	0.422162i	$0.138729\pi$
$739$	−2.27026	+	15.3048i	−0.0835128	+	0.562998i	−0.990033	+	0.140835i	$0.955021\pi$
$740$	3.41933	+	1.13292i	0.125697	+	0.0416468i
$741$	−0.0427763	+	0.870731i	−0.00157143	+	0.0319871i
$742$	16.1545	−	9.40567i	0.593052	−	0.345293i
$743$	−28.1134	+	23.0721i	−1.03138	+	0.846432i	−0.988282	−	0.152639i	$-0.951223\pi$
$743$	−28.1134	+	23.0721i	−1.03138	+	0.846432i	−0.0430981	+	0.999071i	$0.513723\pi$
$744$	−5.25441	+	6.54753i	−0.192636	+	0.240044i
$745$	−0.236714	−	2.40340i	−0.00867254	−	0.0880538i
$746$	−7.64487	+	12.3947i	−0.279899	+	0.453801i
$747$	5.35564	+	1.34152i	0.195953	+	0.0490836i
$748$	0.902628	−	3.25060i	0.0330033	−	0.118854i
$749$	2.32164	+	47.2580i	0.0848308	+	1.72677i
$750$	−1.47186	−	2.26459i	−0.0537449	−	0.0826910i
$751$	−3.49298	+	0.694797i	−0.127461	+	0.0253535i	−0.258408	−	0.966036i	$-0.583198\pi$
$751$	−3.49298	+	0.694797i	−0.127461	+	0.0253535i	0.130948	+	0.991389i	$0.458198\pi$
$752$	33.5960	+	8.47793i	1.22512	+	0.309158i
$753$	8.25112	+	1.64125i	0.300687	+	0.0598105i
$754$	6.45589	−	2.57848i	0.235110	−	0.0939029i
$755$	−3.60277	+	1.70398i	−0.131118	+	0.0620143i
$756$	2.06852	+	4.67756i	0.0752313	+	0.170121i
$757$	3.07529	−	4.14655i	0.111773	−	0.150709i	−0.743778	−	0.668426i	$-0.766968\pi$
$757$	3.07529	−	4.14655i	0.111773	−	0.150709i	0.855552	+	0.517717i	$0.173218\pi$
$758$	26.8433	−	12.2809i	0.974992	−	0.446063i
$759$	0.486398	+	0.909987i	0.0176551	+	0.0330304i
$760$	0.599422	−	0.454827i	0.0217433	−	0.0164983i
$761$	−18.2095	+	5.52378i	−0.660092	+	0.200237i	−0.602519	−	0.798104i	$-0.705836\pi$
$761$	−18.2095	+	5.52378i	−0.660092	+	0.200237i	−0.0575732	+	0.998341i	$0.518336\pi$
$762$	−26.0249	−	12.7161i	−0.942782	−	0.460655i
$763$	−15.1136	+	5.40774i	−0.547150	+	0.195773i
$764$	22.4076	−	31.7572i	0.810679	−	1.14894i
$765$	1.19418	+	0.715766i	0.0431758	+	0.0258786i
$766$	−4.75762	+	0.407603i	−0.171900	+	0.0147273i
$767$	−2.70411			−0.0976398
$768$	15.8350	−	2.29223i	0.571395	−	0.0827138i
$769$	−8.17053			−0.294637			−0.147318	−	0.989089i	$-0.547064\pi$
$769$	−8.17053			−0.294637			−0.147318	+	0.989089i	$0.547064\pi$
$770$	−0.160406	+	0.0137426i	−0.00578063	+	0.000495249i
$771$	18.0250	+	10.8038i	0.649156	+	0.389089i
$772$	−7.60439	−	5.36559i	−0.273688	−	0.193112i
$773$	−13.7409	+	4.91656i	−0.494225	+	0.176836i	−0.572192	−	0.820120i	$-0.693907\pi$
$773$	−13.7409	+	4.91656i	−0.494225	+	0.176836i	0.0779677	+	0.996956i	$0.475157\pi$
$774$	−4.50363	−	2.20053i	−0.161880	−	0.0790964i
$775$	−14.0973	+	4.27637i	−0.506391	+	0.153612i
$776$	17.7953	+	2.44070i	0.638813	+	0.0876160i
$777$	−11.3267	−	21.1907i	−0.406342	−	0.760212i
$778$	41.5903	−	19.0277i	1.49108	−	0.682177i
$779$	7.72510	−	10.4161i	0.276780	−	0.373195i
$780$	0.220241	−	0.0973955i	0.00788590	−	0.00348732i
$781$	−0.848914	+	0.401506i	−0.0303765	+	0.0143670i
$782$	−42.3822	+	16.9274i	−1.51558	+	0.605324i
$783$	−7.67518	−	1.52669i	−0.274288	−	0.0545594i
$784$	−1.09969	+	1.47734i	−0.0392746	+	0.0527622i
$785$	−1.41522	+	0.281505i	−0.0505113	+	0.0100473i
$786$	2.91878	+	4.49079i	0.104109	+	0.160181i
$787$	−0.186138	−	3.78892i	−0.00663509	−	0.135060i	−0.999827	−	0.0185748i	$-0.994087\pi$
$787$	−0.186138	−	3.78892i	−0.00663509	−	0.135060i	0.993192	−	0.116486i	$-0.0371629\pi$
$788$	42.9122	+	11.9159i	1.52868	+	0.424485i
$789$	18.8682	+	4.72623i	0.671724	+	0.168258i
$790$	−0.567492	+	0.920079i	−0.0201905	+	0.0327350i
$791$	−1.16213	−	11.7993i	−0.0413205	−	0.419534i
$792$	0.0715433	+	0.652956i	0.00254218	+	0.0232018i
$793$	−3.26866	+	2.68252i	−0.116074	+	0.0952592i
$794$	14.1891	−	8.26132i	0.503552	−	0.293183i
$795$	−0.0486159	+	0.989599i	−0.00172423	+	0.0350974i
$796$	−2.75173	+	8.30519i	−0.0975326	+	0.294370i
$797$	6.93338	−	46.7411i	0.245593	−	1.65565i	−0.418658	−	0.908144i	$-0.637499\pi$
$797$	6.93338	−	46.7411i	0.245593	−	1.65565i	0.664251	−	0.747510i	$-0.268751\pi$
$798$	−4.98834	−	0.555408i	−0.176585	−	0.0196612i
$799$	−58.1275	−	24.0772i	−2.05640	−	0.851790i
$800$	25.2045	+	12.3700i	0.891115	+	0.437345i
$801$	14.8463	−	6.14953i	0.524568	−	0.217283i
$802$	−25.1866	+	7.29204i	−0.889371	+	0.257491i
$803$	0.939062	−	0.696456i	0.0331388	−	0.0245774i
$804$	1.63923	−	13.1954i	0.0578112	−	0.465366i
$805$	1.46259	+	1.61372i	0.0515495	+	0.0568761i
$806$	−0.353709	−	2.61290i	−0.0124589	−	0.0920354i
$807$	11.4135	+	1.12413i	0.401774	+	0.0395713i
$808$	−8.66823	−	41.2126i	−0.304947	−	1.44985i
$809$	7.89463	+	6.47896i	0.277560	+	0.227788i	0.762866	−	0.646557i	$-0.223792\pi$
$809$	7.89463	+	6.47896i	0.277560	+	0.227788i	−0.485306	+	0.874345i	$0.661292\pi$
$810$	−0.267623	−	0.0431811i	−0.00940330	−	0.00151723i
$811$	−23.8034	−	39.7136i	−0.835850	−	1.39453i	−0.917444	−	0.397866i	$-0.869751\pi$
$811$	−23.8034	−	39.7136i	−0.835850	−	1.39453i	0.0815937	−	0.996666i	$-0.473999\pi$
$812$	12.5215	+	38.0148i	0.439418	+	1.33406i
$813$	7.27169	+	6.59067i	0.255029	+	0.231145i
$814$	−0.563520	−	3.03404i	−0.0197514	−	0.106343i
$815$	−1.90607	−	1.27359i	−0.0667667	−	0.0446121i
$816$	−29.0531	−	0.0508862i	−1.01706	−	0.00178137i
$817$	4.09003	−	2.73287i	0.143092	−	0.0956110i
$818$	12.0687	−	11.7657i	0.421972	−	0.411380i
$819$	−1.51245	−	0.541163i	−0.0528493	−	0.0189098i
$820$	−3.52896	−	0.615516i	−0.123237	−	0.0214948i
$821$	−0.484401	−	3.26556i	−0.0169057	−	0.113969i	0.979081	−	0.203471i	$-0.0652224\pi$
$821$	−0.484401	−	3.26556i	−0.0169057	−	0.113969i	−0.995987	+	0.0895023i	$0.971472\pi$
$822$	0.487011	+	13.3817i	0.0169865	+	0.466742i
$823$	12.3213	−	40.6180i	0.429495	−	1.41586i	−0.429126	−	0.903245i	$-0.641178\pi$
$823$	12.3213	−	40.6180i	0.429495	−	1.41586i	0.858621	−	0.512611i	$-0.171322\pi$
$824$	−21.2335	+	29.2957i	−0.739705	+	1.02056i
$825$	−0.543355	+	1.01655i	−0.0189172	+	0.0353916i
$826$	0.961480	−	15.5388i	0.0334542	−	0.540665i
$827$	−16.6027	−	7.85250i	−0.577333	−	0.273058i	0.116504	−	0.993190i	$-0.462831\pi$
$827$	−16.6027	−	7.85250i	−0.577333	−	0.273058i	−0.693837	+	0.720132i	$0.744081\pi$
$828$	6.44100	−	6.12160i	0.223840	−	0.212740i
$829$	−10.5075	+	2.63199i	−0.364941	+	0.0914128i	−0.421113	−	0.907008i	$-0.638360\pi$
$829$	−10.5075	+	2.63199i	−0.364941	+	0.0914128i	0.0561723	+	0.998421i	$0.482110\pi$
$830$	1.42660	+	0.452631i	0.0495179	+	0.0157111i
$831$	3.49332	+	3.49332i	0.121182	+	0.121182i
$832$	−2.90435	+	4.10093i	−0.100690	+	0.142174i
$833$	2.36470	−	2.36470i	0.0819320	−	0.0819320i
$834$	−9.48271	+	4.91470i	−0.328360	+	0.170182i
$835$	0.661774	+	2.64195i	0.0229016	+	0.0914285i
$836$	−0.589087	−	0.261742i	−0.0203740	−	0.00905253i
$837$	−1.26904	+	2.68317i	−0.0438646	+	0.0927439i
$838$	40.7873	−	36.0339i	1.40897	−	1.24477i
$839$	−13.1033	−	7.00385i	−0.452376	−	0.241800i	0.229442	−	0.973322i	$-0.426310\pi$
$839$	−13.1033	−	7.00385i	−0.452376	−	0.241800i	−0.681817	+	0.731523i	$0.738810\pi$
$840$	0.481362	+	1.30022i	0.0166086	+	0.0448618i
$841$	−30.8509	−	9.35852i	−1.06382	−	0.322708i
$842$	17.9906	+	16.7271i	0.619997	+	0.576454i
$843$	−14.8590	+	2.20412i	−0.511771	+	0.0759140i
$844$	−6.91072	−	4.38465i	−0.237877	−	0.150926i
$845$	0.814018	−	2.27503i	0.0280031	−	0.0782633i
$846$	12.2494	+	0.155694i	0.421142	+	0.00535288i
$847$	−15.5515	−	23.2744i	−0.534355	−	0.799719i
$848$	−9.71436	−	18.2511i	−0.333593	−	0.626746i
$849$	1.96442	−	2.93996i	0.0674188	−	0.100899i
$850$	−42.0263	−	28.8604i	−1.44149	−	0.989903i
$851$	−28.0349	+	30.9318i	−0.961025	+	1.06033i
$852$	5.27700	+	6.12835i	0.180787	+	0.209954i
$853$	25.7377	−	15.4266i	0.881242	−	0.528196i	−0.000461416	−	1.00000i	$-0.500147\pi$
$853$	25.7377	−	15.4266i	0.881242	−	0.528196i	0.881704	+	0.471804i	$0.156397\pi$
$854$	−14.2526	−	19.7368i	−0.487713	−	0.675379i
$855$	0.168768	−	0.205644i	0.00577173	−	0.00703287i
$856$	52.3291	−	0.573457i	1.78857	−	0.0196004i
$857$	1.47561	−	14.9822i	0.0504060	−	0.511781i	−0.936521	−	0.350612i	$-0.885974\pi$
$857$	1.47561	−	14.9822i	0.0504060	−	0.511781i	0.986927	−	0.161169i	$-0.0515263\pi$
$858$	−0.164131	−	0.124992i	−0.00560334	−	0.00426716i
$859$	−35.3868	+	32.0727i	−1.20738	+	1.09431i	−0.214315	+	0.976765i	$0.568752\pi$
$859$	−35.3868	+	32.0727i	−1.20738	+	1.09431i	−0.993068	+	0.117543i	$0.962498\pi$
$860$	−1.18169	−	0.670787i	−0.0402953	−	0.0228736i
$861$	14.2343	+	19.1928i	0.485105	+	0.654088i
$862$	34.7156	+	19.1271i	1.18242	+	0.651470i
$863$	7.33168	+	17.7003i	0.249573	+	0.602524i	0.998168	−	0.0605046i	$-0.0192710\pi$
$863$	7.33168	+	17.7003i	0.249573	+	0.602524i	−0.748594	+	0.663028i	$0.769271\pi$
$864$	5.25701	−	2.08898i	0.178847	−	0.0710686i
$865$	0.735314	−	1.77520i	0.0250014	−	0.0603588i
$866$	40.0370	−	32.0147i	1.36051	−	1.08790i
$867$	35.3682	+	5.24637i	1.20117	+	0.178176i
$868$	15.1405	−	1.10350i	0.513901	−	0.0374551i
$869$	0.924986	+	0.0454416i	0.0313780	+	0.00154150i
$870$	−2.05109	−	0.541565i	−0.0695383	−	0.0183608i
$871$	2.64937	+	3.22826i	0.0897704	+	0.109386i
$872$	5.33960	+	16.9321i	0.180822	+	0.573394i
$873$	6.31990	−	0.622456i	0.213896	−	0.0210669i
$874$	2.01118	+	8.48521i	0.0680292	+	0.287017i
$875$	−1.18669	+	4.73751i	−0.0401173	+	0.160157i
$876$	−7.93206	−	6.20143i	−0.267999	−	0.209527i
$877$	−11.6898	+	0.574285i	−0.394738	+	0.0193922i	−0.245469	−	0.969404i	$-0.578942\pi$
$877$	−11.6898	+	0.574285i	−0.394738	+	0.0193922i	−0.149269	+	0.988797i	$0.547692\pi$
$878$	8.30372	−	39.1391i	0.280237	−	1.32088i
$879$	2.31623	+	11.6445i	0.0781244	+	0.392758i
$880$	0.00842573	+	0.177866i	0.000284031	+	0.00599585i
$881$	−6.37461	+	32.0473i	−0.214766	+	1.07970i	0.711458	+	0.702728i	$0.248035\pi$
$881$	−6.37461	+	32.0473i	−0.214766	+	1.07970i	−0.926224	+	0.376973i	$0.876965\pi$
$882$	−0.256806	+	0.598358i	−0.00864709	+	0.0201478i
$883$	−10.8671	−	22.9765i	−0.365705	−	0.773219i	−1.00000		0.000127678i	$-0.999959\pi$
$883$	−10.8671	−	22.9765i	−0.365705	−	0.773219i	0.634295	−	0.773091i	$-0.281291\pi$
$884$	6.29778	−	6.60317i	0.211817	−	0.222089i
$885$	0.662789	+	0.491557i	0.0222794	+	0.0165235i
$886$	−4.64528	−	1.72902i	−0.156061	−	0.0580874i
$887$	21.2715	−	11.3699i	0.714227	−	0.381762i	−0.0739075	−	0.997265i	$-0.523547\pi$
$887$	21.2715	−	11.3699i	0.714227	−	0.381762i	0.788135	+	0.615503i	$0.211047\pi$
$888$	−23.8982	+	11.6252i	−0.801972	+	0.390115i
$889$	15.2042	+	50.1215i	0.509932	+	1.68102i
$890$	4.11986	−	1.41531i	0.138098	−	0.0474412i
$891$	0.0782381	+	0.218661i	0.00262108	+	0.00732541i
$892$	12.7017	−	8.02766i	0.425283	−	0.268786i
$893$	−6.18052	+	10.3116i	−0.206823	+	0.345064i
$894$	13.6284	+	11.4775i	0.455802	+	0.383865i
$895$		−	0.993863i		−	0.0332212i
$896$	−22.5328	−	18.1476i	−0.752769	−	0.606270i
$897$			2.79088i			0.0931846i
$898$	−26.6908	+	31.6928i	−0.890685	+	1.05760i
$899$	−11.9412	+	19.9227i	−0.398263	+	0.664461i
$900$	9.68341	+	2.18339i	0.322780	+	0.0727797i
$901$	12.6478	+	35.3482i	0.421359	+	1.17762i
$902$	0.997069	+	2.90240i	0.0331988	+	0.0966393i
$903$	2.63110	+	8.67357i	0.0875575	+	0.288638i
$904$	−13.0900	+	0.786941i	−0.435366	+	0.0261733i
$905$	3.55222	−	1.89870i	0.118080	−	0.0631150i
$906$	10.2568	−	27.5566i	0.340760	−	0.915507i
$907$	−37.1959	−	27.5864i	−1.23507	−	0.915990i	−0.236618	−	0.971603i	$-0.576039\pi$
$907$	−37.1959	−	27.5864i	−1.23507	−	0.915990i	−0.998452	+	0.0556124i	$0.982289\pi$
$908$	−0.581472	−	24.5633i	−0.0192968	−	0.815163i
$909$	−6.36615	−	13.4601i	−0.211152	−	0.446443i
$910$	−0.400158	−	0.171741i	−0.0132651	−	0.00569317i
$911$	−7.74846	+	38.9542i	−0.256718	+	1.29061i	0.610236	+	0.792220i	$0.291075\pi$
$911$	−7.74846	+	38.9542i	−0.256718	+	1.29061i	−0.866954	+	0.498389i	$0.833925\pi$
$912$	−0.824175	+	5.48987i	−0.0272912	+	0.181788i
$913$	−0.250145	−	1.25756i	−0.00827859	−	0.0416193i
$914$	−6.21531	−	1.31863i	−0.205584	−	0.0436166i
$915$	1.28880	−	0.0633145i	0.0426063	−	0.00209311i
$916$	0.524254	+	4.28139i	0.0173218	+	0.141461i
$917$	2.35326	−	9.39472i	0.0777113	−	0.310241i
$918$	−9.99490	+	2.36901i	−0.329881	+	0.0781890i
$919$	−7.36118	+	0.725013i	−0.242823	+	0.0239160i	−0.218696	−	0.975793i	$-0.570180\pi$
$919$	−7.36118	+	0.725013i	−0.242823	+	0.0239160i	−0.0241265	+	0.999709i	$0.507680\pi$
$920$	1.84520	−	1.54847i	0.0608345	−	0.0510514i
$921$	3.01999	+	3.67987i	0.0995120	+	0.121256i
$922$	7.85195	−	29.7380i	0.258590	−	0.979368i
$923$	−2.53695	−	0.124632i	−0.0835048	−	0.00410233i
$924$	0.776612	−	0.898716i	0.0255486	−	0.0295656i
$925$	−46.1297	−	6.84270i	−1.51674	−	0.224987i
$926$	−3.89849	−	4.87538i	−0.128112	−	0.160215i
$927$	−4.89532	+	11.8183i	−0.160783	+	0.388165i
$928$	42.5432	−	12.2364i	1.39655	−	0.401679i
$929$	10.0602	+	24.2875i	0.330064	+	0.796846i	0.998586	+	0.0531536i	$0.0169273\pi$
$929$	10.0602	+	24.2875i	0.330064	+	0.796846i	−0.668522	+	0.743692i	$0.733073\pi$
$930$	−0.388281	+	0.704730i	−0.0127322	+	0.0231090i
$931$	−0.380651	−	0.513249i	−0.0124753	−	0.0168211i
$932$	−2.68232	−	9.72577i	−0.0878622	−	0.318578i
$933$	2.25427	−	2.04315i	0.0738015	−	0.0668898i
$934$	−10.0809	+	13.2375i	−0.329856	+	0.433144i
$935$	0.0316923	−	0.321777i	0.00103645	−	0.0105232i
$936$	−0.661881	+	1.64880i	−0.0216342	+	0.0538926i
$937$	0.821531	−	1.00104i	0.0268382	−	0.0327025i	−0.759418	−	0.650603i	$-0.774516\pi$
$937$	0.821531	−	1.00104i	0.0268382	−	0.0327025i	0.786257	+	0.617900i	$0.212016\pi$
$938$	−19.4928	+	14.0764i	−0.636464	+	0.459611i
$939$	21.4559	−	12.8602i	0.700186	−	0.419676i
$940$	3.31166	+	0.247199i	0.108014	+	0.00806274i
$941$	21.3992	−	23.6104i	0.697595	−	0.769677i	−0.284376	−	0.958713i	$-0.591786\pi$
$941$	21.3992	−	23.6104i	0.697595	−	0.769677i	0.981970	+	0.189036i	$0.0605363\pi$
$942$	6.02648	−	8.77573i	0.196353	−	0.285929i
$943$	23.0648	−	34.5189i	0.751092	−	1.12409i
$944$	−17.1335	−	1.71781i	−0.557649	−	0.0559100i
$945$	0.272334	+	0.407577i	0.00885904	+	0.0132585i
$946$	−0.0147948	+	1.16399i	−0.000481019	+	0.0378445i
$947$	−16.9173	+	47.2806i	−0.549738	+	1.53641i	0.269524	+	0.962994i	$0.413134\pi$
$947$	−16.9173	+	47.2806i	−0.549738	+	1.53641i	−0.819262	+	0.573420i	$0.805616\pi$
$948$	−1.74063	−	7.78324i	−0.0565329	−	0.252788i
$949$	3.12806	−	0.464004i	0.101541	−	0.0150622i
$950$	−6.63316	+	7.13421i	−0.215208	+	0.231464i
$951$	−13.0327	−	3.95342i	−0.422614	−	0.128198i
$952$	35.7051	+	38.5372i	1.15721	+	1.24900i
$953$	38.6967	+	20.6838i	1.25351	+	0.670015i	0.958395	−	0.285446i	$-0.0921418\pi$
$953$	38.6967	+	20.6838i	1.25351	+	0.670015i	0.295116	+	0.955462i	$0.404642\pi$
$954$	−4.83977	−	5.47820i	−0.156693	−	0.177363i
$955$	1.59268	−	3.36744i	0.0515379	−	0.108968i
$956$	−36.7473	+	14.1380i	−1.18849	+	0.457257i
$957$	0.441586	+	1.76291i	0.0142745	+	0.0569869i
$958$	11.2254	+	21.6590i	0.362677	+	0.699770i
$959$	17.1216	−	17.1216i	0.552886	−	0.552886i
$960$	1.45734	−	0.477198i	0.0470355	−	0.0154015i
$961$	−15.6908	−	15.6908i	−0.506154	−	0.506154i
$962$	2.52427	−	7.95597i	0.0813859	−	0.256511i
$963$	17.9477	−	4.49568i	0.578358	−	0.144871i
$964$	17.7641	+	0.451651i	0.572143	+	0.0145467i
$965$	−0.806347	−	0.381374i	−0.0259572	−	0.0122768i
$966$	−16.0374	−	0.992330i	−0.515996	−	0.0319277i
$967$	−16.0867	+	30.0961i	−0.517314	+	0.967826i	0.478645	+	0.878009i	$0.341128\pi$
$967$	−16.0867	+	30.0961i	−0.517314	+	0.967826i	−0.995958	+	0.0898171i	$0.971372\pi$
$968$	−26.3794	+	16.2067i	−0.847866	+	0.520904i
$969$	2.92616	−	9.64626i	0.0940019	−	0.309883i
$970$	1.72037	−	0.0626108i	0.0552379	−	0.00201031i
$971$	−2.10845	−	14.2140i	−0.0676632	−	0.456148i	−0.996356	−	0.0852973i	$-0.972816\pi$
$971$	−2.10845	−	14.2140i	−0.0676632	−	0.456148i	0.928692	−	0.370851i	$-0.120934\pi$
$972$	1.63618	−	1.15018i	0.0524804	−	0.0368922i
$973$	18.1843	+	6.50646i	0.582963	+	0.208588i
$974$	9.95964	+	10.2161i	0.319127	+	0.327344i
$975$	−2.59226	+	1.73209i	−0.0830188	+	0.0554714i
$976$	−22.4147	+	14.9203i	−0.717477	+	0.477587i
$977$	−27.5429	−	18.4036i	−0.881175	−	0.588782i	0.0305729	−	0.999533i	$-0.490267\pi$
$977$	−27.5429	−	18.4036i	−0.881175	−	0.588782i	−0.911748	+	0.410750i	$0.865267\pi$
$978$	16.6285	−	3.08846i	0.531722	−	0.0987580i
$979$	−2.76517	−	2.50621i	−0.0883753	−	0.0800987i
$980$	−0.0795004	+	0.157596i	−0.00253955	+	0.00503423i
$981$	3.22703	+	5.38398i	0.103031	+	0.171897i
$982$	−5.09422	+	31.5723i	−0.162563	+	1.00751i
$983$	−26.4800	−	21.7316i	−0.844581	−	0.693130i	0.109073	−	0.994034i	$-0.465212\pi$
$983$	−26.4800	−	21.7316i	−0.844581	−	0.693130i	−0.953655	+	0.300904i	$0.902712\pi$
$984$	21.8127	−	14.9231i	0.695363	−	0.475730i
$985$	4.24788	+	0.418380i	0.135349	+	0.0133307i
$986$	−79.6561	+	10.7831i	−2.53677	+	0.343403i
$987$	−14.8762	−	16.4134i	−0.473515	−	0.522443i
$988$	−1.07149	−	1.37547i	−0.0340887	−	0.0437595i
$989$	12.6485	−	9.38080i	0.402200	−	0.298292i
$990$	0.0175079	+	0.0604721i	0.000556437	+	0.00192193i
$991$	−14.1227	+	5.84981i	−0.448622	+	0.185825i	−0.595544	−	0.803323i	$-0.703063\pi$
$991$	−14.1227	+	5.84981i	−0.448622	+	0.185825i	0.146922	+	0.989148i	$0.453063\pi$
$992$	−0.581270	−	16.7803i	−0.0184553	−	0.532775i
$993$	−23.6971	−	9.81567i	−0.752006	−	0.311491i
$994$	1.61823	−	14.5340i	0.0513271	−	0.460990i
$995$	−0.123040	+	0.829468i	−0.00390063	+	0.0262959i
$996$	−9.86751	+	4.95606i	−0.312664	+	0.157039i
$997$	1.56496	−	31.8554i	0.0495627	−	1.00887i	−0.837272	−	0.546786i	$-0.815851\pi$
$997$	1.56496	−	31.8554i	0.0495627	−	1.00887i	0.886835	−	0.462086i	$-0.152899\pi$
$998$	13.7609	+	23.6348i	0.435594	+	0.748147i
$999$	−7.26317	+	5.96073i	−0.229796	+	0.188589i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.z.a.421.31	yes	2048
256.45	even	64	inner	768.2.z.a.301.31	✓	2048

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
768.2.z.a.301.31	✓	2048	256.45	even	64	inner
768.2.z.a.421.31	yes	2048	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.z (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.120719 - 1.40905i) q^{2} +(0.857729 + 0.514103i) q^{3} +(-1.97085 + 0.340198i) q^{4} +(-0.180480 + 0.0645768i) q^{5} +(0.620853 - 1.27065i) q^{6} +(-2.44714 + 0.742333i) q^{7} +(0.717276 + 2.73597i) q^{8} +(0.471397 + 0.881921i) q^{9} +O(q^{10})\)	\(q+(-0.120719 - 1.40905i) q^{2} +(0.857729 + 0.514103i) q^{3} +(-1.97085 + 0.340198i) q^{4} +(-0.180480 + 0.0645768i) q^{5} +(0.620853 - 1.27065i) q^{6} +(-2.44714 + 0.742333i) q^{7} +(0.717276 + 2.73597i) q^{8} +(0.471397 + 0.881921i) q^{9} +(0.112779 + 0.246510i) q^{10} +(0.138343 - 0.186534i) q^{11} +(-1.86535 - 0.721424i) q^{12} +(0.567844 - 0.268570i) q^{13} +(1.34140 + 3.35854i) q^{14} +(-0.188002 - 0.0373959i) q^{15} +(3.76853 - 1.34096i) q^{16} +(-7.12371 + 1.41699i) q^{17} +(1.18577 - 0.770687i) q^{18} +(0.0680985 + 1.38618i) q^{19} +(0.333731 - 0.188670i) q^{20} +(-2.48062 - 0.621363i) q^{21} +(-0.279537 - 0.172414i) q^{22} +(0.435489 + 4.42159i) q^{23} +(-0.791340 + 2.71547i) q^{24} +(-3.83665 + 3.14866i) q^{25} +(-0.446979 - 0.767700i) q^{26} +(-0.0490677 + 0.998795i) q^{27} +(4.57042 - 2.29554i) q^{28} +(-1.14825 + 7.74084i) q^{29} +(-0.0299974 + 0.269419i) q^{30} +(2.74221 + 1.13586i) q^{31} +(-2.34442 - 5.14818i) q^{32} +(0.214559 - 0.0888731i) q^{33} +(2.85658 + 9.86662i) q^{34} +(0.393723 - 0.292005i) q^{35} +(-1.22908 - 1.57777i) q^{36} +(6.30993 + 6.96194i) q^{37} +(1.94497 - 0.263292i) q^{38} +(0.625129 + 0.0615698i) q^{39} +(-0.306134 - 0.447468i) q^{40} +(-7.22305 - 5.92780i) q^{41} +(-0.576076 + 3.57033i) q^{42} +(-1.82217 - 3.04010i) q^{43} +(-0.209196 + 0.414695i) q^{44} +(-0.142029 - 0.128728i) q^{45} +(6.17768 - 1.14739i) q^{46} +(7.20244 + 4.81252i) q^{47} +(3.92177 + 0.787231i) q^{48} +(-0.382829 + 0.255798i) q^{49} +(4.89978 + 5.02594i) q^{50} +(-6.83869 - 2.44692i) q^{51} +(-1.02777 + 0.722492i) q^{52} +(-0.758428 - 5.11290i) q^{53} +(1.41328 - 0.0514344i) q^{54} +(-0.0129224 + 0.0425994i) q^{55} +(-3.78628 - 6.16285i) q^{56} +(-0.654227 + 1.22397i) q^{57} +(11.0459 + 0.683473i) q^{58} +(-3.89154 - 1.84056i) q^{59} +(0.383247 + 0.00974401i) q^{60} +(-6.52987 + 1.63565i) q^{61} +(1.26945 - 4.00103i) q^{62} +(-1.80826 - 1.80826i) q^{63} +(-6.97103 + 3.92488i) q^{64} +(-0.0851411 + 0.0851411i) q^{65} +(-0.151128 - 0.291595i) q^{66} +(1.61543 + 6.44917i) q^{67} +(13.5577 - 5.21616i) q^{68} +(-1.89962 + 4.01641i) q^{69} +(-0.458980 - 0.519526i) q^{70} +(-3.56615 - 1.90615i) q^{71} +(-2.07479 + 1.92231i) q^{72} +(4.81749 + 1.46137i) q^{73} +(9.04800 - 9.73146i) q^{74} +(-4.90954 + 0.728261i) q^{75} +(-0.605786 - 2.70878i) q^{76} +(-0.200075 + 0.559173i) q^{77} +(0.0112903 - 0.888271i) q^{78} +(2.21548 + 3.31569i) q^{79} +(-0.593550 + 0.485376i) q^{80} +(-0.555570 + 0.831470i) q^{81} +(-7.48063 + 10.8932i) q^{82} +(3.70775 - 4.09087i) q^{83} +(5.10033 + 0.380714i) q^{84} +(1.19418 - 0.715766i) q^{85} +(-4.06369 + 2.93452i) q^{86} +(-4.96447 + 6.04923i) q^{87} +(0.609581 + 0.244706i) q^{88} +(1.57509 - 15.9921i) q^{89} +(-0.164239 + 0.215667i) q^{90} +(-1.19023 + 1.07876i) q^{91} +(-2.36250 - 8.56616i) q^{92} +(1.76812 + 2.38404i) q^{93} +(5.91162 - 10.7296i) q^{94} +(-0.101805 - 0.245780i) q^{95} +(0.635819 - 5.62101i) q^{96} +(2.43022 - 5.86708i) q^{97} +(0.406648 + 0.508547i) q^{98} +(0.229723 + 0.0340762i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2048 q+O(q^{10}) \) 2048 * q	\( 2048 q+O(q^{100}) \) 2048 * q

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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