LMFDB - Embedded newform 798.2.cj.b.241.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(241,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.241"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.cj (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [84] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			241.4
Character	$\chi$	$=$	798.241
Dual form			798.2.cj.b.649.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.342020 + 0.939693i) q^{2} +(-0.766044 + 0.642788i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.363191 + 0.432835i) q^{5} +(-0.342020 - 0.939693i) q^{6} +(1.43186 - 2.22481i) q^{7} +(0.866025 - 0.500000i) q^{8} +(0.173648 - 0.984808i) q^{9} +(-0.530950 + 0.193250i) q^{10} -2.91557 q^{11} +1.00000 q^{12} +(-2.97113 + 1.08140i) q^{13} +(1.60091 + 2.10644i) q^{14} +(-0.556442 - 0.0981157i) q^{15} +(0.173648 + 0.984808i) q^{16} +(0.966147 - 0.170358i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-4.32736 + 0.523436i) q^{19} -0.565026i q^{20} +(0.333211 + 2.62468i) q^{21} +(0.997183 - 2.73974i) q^{22} +(-8.63662 + 3.14347i) q^{23} +(-0.342020 + 0.939693i) q^{24} +(0.812803 - 4.60964i) q^{25} -3.16181i q^{26} +(0.500000 + 0.866025i) q^{27} +(-2.52695 + 0.783921i) q^{28} +(-3.99240 + 4.75796i) q^{29} +(0.282513 - 0.489327i) q^{30} +(-2.29000 - 3.96640i) q^{31} +(-0.984808 - 0.173648i) q^{32} +(2.23345 - 1.87409i) q^{33} +(-0.170358 + 0.966147i) q^{34} +(1.48301 - 0.188273i) q^{35} +(-0.766044 + 0.642788i) q^{36} +(-4.95444 + 2.86045i) q^{37} +(0.988174 - 4.24541i) q^{38} +(1.58091 - 2.73821i) q^{39} +(0.530950 + 0.193250i) q^{40} +(3.26924 + 1.18991i) q^{41} +(-2.58036 - 0.584579i) q^{42} +(-0.688830 - 3.90655i) q^{43} +(2.23345 + 1.87409i) q^{44} +(0.489327 - 0.282513i) q^{45} -9.19090i q^{46} +(4.36792 + 0.770182i) q^{47} +(-0.766044 - 0.642788i) q^{48} +(-2.89955 - 6.37123i) q^{49} +(4.05365 + 2.34037i) q^{50} +(-0.630608 + 0.751529i) q^{51} +(2.97113 + 1.08140i) q^{52} +(0.985273 - 1.17420i) q^{53} +(-0.984808 + 0.173648i) q^{54} +(-1.05891 - 1.26196i) q^{55} +(0.127623 - 2.64267i) q^{56} +(2.97849 - 3.18255i) q^{57} +(-3.10554 - 5.37895i) q^{58} +(-1.19940 - 6.80214i) q^{59} +(0.363191 + 0.432835i) q^{60} +(-0.669898 - 1.84053i) q^{61} +(4.51043 - 0.795310i) q^{62} +(-1.94237 - 1.79644i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-1.54716 - 0.893253i) q^{65} +(0.997183 + 2.73974i) q^{66} +(0.319286 + 0.877230i) q^{67} +(-0.849616 - 0.490526i) q^{68} +(4.59545 - 7.95955i) q^{69} +(-0.330302 + 1.45797i) q^{70} +(-0.935428 + 0.164941i) q^{71} +(-0.342020 - 0.939693i) q^{72} +(-6.08842 - 7.25590i) q^{73} +(-0.993423 - 5.63398i) q^{74} +(2.34037 + 4.05365i) q^{75} +(3.65141 + 2.38060i) q^{76} +(-4.17469 + 6.48658i) q^{77} +(2.03237 + 2.42209i) q^{78} +(5.34236 - 0.942002i) q^{79} +(-0.363191 + 0.432835i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(-2.23629 + 2.66511i) q^{82} +(-9.70625 - 5.60391i) q^{83} +(1.43186 - 2.22481i) q^{84} +(0.424633 + 0.356310i) q^{85} +(3.90655 + 0.688830i) q^{86} -6.21108i q^{87} +(-2.52496 + 1.45778i) q^{88} +(3.33791 + 2.80084i) q^{89} +(0.0981157 + 0.556442i) q^{90} +(-1.84833 + 8.15862i) q^{91} +(8.63662 + 3.14347i) q^{92} +(4.30380 + 1.56646i) q^{93} +(-2.21765 + 3.84109i) q^{94} +(-1.79822 - 1.68292i) q^{95} +(0.866025 - 0.500000i) q^{96} +(4.10065 - 3.44086i) q^{97} +(6.97870 - 0.545599i) q^{98} +(-0.506283 + 2.87127i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 12 q^{7} - 12 q^{10} - 12 q^{11} + 84 q^{12} + 24 q^{13} + 6 q^{14} + 6 q^{19} - 6 q^{21} + 12 q^{22} - 42 q^{23} - 30 q^{25} + 42 q^{27} + 6 q^{28} + 6 q^{31} + 12 q^{33} - 30 q^{34} - 42 q^{35}+ \cdots + 6 q^{99}+O(q^{100}) $ 84 * q + 12 * q^7 - 12 * q^10 - 12 * q^11 + 84 * q^12 + 24 * q^13 + 6 * q^14 + 6 * q^19 - 6 * q^21 + 12 * q^22 - 42 * q^23 - 30 * q^25 + 42 * q^27 + 6 * q^28 + 6 * q^31 + 12 * q^33 - 30 * q^34 - 42 * q^35 - 18 * q^37 + 12 * q^38 + 12 * q^40 + 36 * q^41 + 18 * q^42 + 12 * q^43 + 12 * q^44 - 18 * q^45 + 18 * q^47 - 24 * q^49 + 18 * q^51 - 24 * q^52 + 60 * q^53 - 30 * q^55 - 18 * q^56 + 6 * q^57 + 48 * q^59 - 12 * q^62 - 6 * q^63 + 42 * q^64 + 108 * q^65 + 12 * q^66 + 42 * q^67 + 6 * q^69 + 18 * q^70 + 42 * q^71 - 48 * q^73 - 18 * q^74 - 48 * q^75 + 18 * q^76 - 96 * q^77 - 12 * q^78 - 60 * q^79 - 6 * q^82 + 54 * q^83 + 12 * q^84 - 24 * q^85 - 12 * q^86 - 24 * q^89 + 6 * q^90 + 24 * q^91 + 42 * q^92 - 36 * q^93 + 18 * q^94 - 12 * q^95 - 78 * q^97 + 24 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{18}\right)$	$1$

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 $

$2$	−0.342020	+	0.939693i	−0.241845	+	0.664463i
$2$	−0.342020	+	0.939693i	−0.241845	+	0.664463i
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$4$	−0.766044	−	0.642788i	−0.383022	−	0.321394i
$5$	0.363191	+	0.432835i	0.162424	+	0.193570i	0.841118	−	0.540852i	$-0.181898\pi$
$5$	0.363191	+	0.432835i	0.162424	+	0.193570i	−0.678694	+	0.734421i	$0.737454\pi$
$6$	−0.342020	−	0.939693i	−0.139629	−	0.383628i
$7$	1.43186	−	2.22481i	0.541192	−	0.840899i
$7$	1.43186	−	2.22481i	0.541192	−	0.840899i
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$	−0.530950	+	0.193250i	−0.167901	+	0.0611111i
$11$	−2.91557			−0.879077			−0.439538	−	0.898224i	$-0.644858\pi$
$11$	−2.91557			−0.879077			−0.439538	+	0.898224i	$0.644858\pi$
$12$	1.00000			0.288675
$13$	−2.97113	+	1.08140i	−0.824044	+	0.299927i	−0.719412	−	0.694584i	$-0.755589\pi$
$13$	−2.97113	+	1.08140i	−0.824044	+	0.299927i	−0.104632	+	0.994511i	$0.533366\pi$
$14$	1.60091	+	2.10644i	0.427862	+	0.562969i
$15$	−0.556442	−	0.0981157i	−0.143673	−	0.0253334i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	0.966147	−	0.170358i	0.234325	−	0.0413178i	−0.0552523	−	0.998472i	$-0.517596\pi$
$17$	0.966147	−	0.170358i	0.234325	−	0.0413178i	0.289577	+	0.957155i	$0.406485\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	−4.32736	+	0.523436i	−0.992764	+	0.120084i
$19$	−4.32736	+	0.523436i	−0.992764	+	0.120084i
$20$		−	0.565026i		−	0.126344i
$21$	0.333211	+	2.62468i	0.0727127	+	0.572753i
$22$	0.997183	−	2.73974i	0.212600	−	0.584114i
$23$	−8.63662	+	3.14347i	−1.80086	+	0.655460i	−0.802599	+	0.596519i	$0.796550\pi$
$23$	−8.63662	+	3.14347i	−1.80086	+	0.655460i	−0.998262	+	0.0589402i	$0.981228\pi$
$24$	−0.342020	+	0.939693i	−0.0698146	+	0.191814i
$25$	0.812803	−	4.60964i	0.162561	−	0.921927i
$26$		−	3.16181i		−	0.620083i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	−2.52695	+	0.783921i	−0.477548	+	0.148147i
$29$	−3.99240	+	4.75796i	−0.741371	+	0.883531i	−0.996519	−	0.0833706i	$-0.973431\pi$
$29$	−3.99240	+	4.75796i	−0.741371	+	0.883531i	0.255148	+	0.966902i	$0.417876\pi$
$30$	0.282513	−	0.489327i	0.0515795	−	0.0893384i
$31$	−2.29000	−	3.96640i	−0.411297	−	0.712387i	0.583735	−	0.811944i	$-0.301591\pi$
$31$	−2.29000	−	3.96640i	−0.411297	−	0.712387i	−0.995032	+	0.0995572i	$0.968257\pi$
$32$	−0.984808	−	0.173648i	−0.174091	−	0.0306970i
$33$	2.23345	−	1.87409i	0.388795	−	0.326237i
$34$	−0.170358	+	0.966147i	−0.0292161	+	0.165693i
$35$	1.48301	−	0.188273i	0.250675	−	0.0318239i
$36$	−0.766044	+	0.642788i	−0.127674	+	0.107131i
$37$	−4.95444	+	2.86045i	−0.814505	+	0.470255i	−0.848518	−	0.529167i	$-0.822505\pi$
$37$	−4.95444	+	2.86045i	−0.814505	+	0.470255i	0.0340130	+	0.999421i	$0.489171\pi$
$38$	0.988174	−	4.24541i	0.160303	−	0.688697i
$39$	1.58091	−	2.73821i	0.253148	−	0.438465i
$40$	0.530950	+	0.193250i	0.0839506	+	0.0305555i
$41$	3.26924	+	1.18991i	0.510570	+	0.185832i	0.584442	−	0.811435i	$-0.301313\pi$
$41$	3.26924	+	1.18991i	0.510570	+	0.185832i	−0.0738720	+	0.997268i	$0.523536\pi$
$42$	−2.58036	−	0.584579i	−0.398158	−	0.0902025i
$43$	−0.688830	−	3.90655i	−0.105046	−	0.595743i	−0.991202	−	0.132357i	$-0.957745\pi$
$43$	−0.688830	−	3.90655i	−0.105046	−	0.595743i	0.886156	−	0.463386i	$-0.153366\pi$
$44$	2.23345	+	1.87409i	0.336706	+	0.282530i
$45$	0.489327	−	0.282513i	0.0729445	−	0.0421145i
$46$		−	9.19090i		−	1.35512i
$47$	4.36792	+	0.770182i	0.637127	+	0.112343i	0.482876	−	0.875689i	$-0.339592\pi$
$47$	4.36792	+	0.770182i	0.637127	+	0.112343i	0.154251	+	0.988032i	$0.450703\pi$
$48$	−0.766044	−	0.642788i	−0.110569	−	0.0927784i
$49$	−2.89955	−	6.37123i	−0.414222	−	0.910176i
$50$	4.05365	+	2.34037i	0.573272	+	0.330979i
$51$	−0.630608	+	0.751529i	−0.0883028	+	0.105235i
$52$	2.97113	+	1.08140i	0.412022	+	0.149964i
$53$	0.985273	−	1.17420i	0.135338	−	0.161289i	−0.694119	−	0.719860i	$-0.744206\pi$
$53$	0.985273	−	1.17420i	0.135338	−	0.161289i	0.829457	+	0.558571i	$0.188650\pi$
$54$	−0.984808	+	0.173648i	−0.134015	+	0.0236305i
$55$	−1.05891	−	1.26196i	−0.142783	−	0.170163i
$56$	0.127623	−	2.64267i	0.0170543	−	0.353142i
$57$	2.97849	−	3.18255i	0.394511	−	0.421539i
$58$	−3.10554	−	5.37895i	−0.407777	−	0.706291i
$59$	−1.19940	−	6.80214i	−0.156149	−	0.885563i	−0.957728	−	0.287675i	$-0.907118\pi$
$59$	−1.19940	−	6.80214i	−0.156149	−	0.885563i	0.801579	−	0.597888i	$-0.203993\pi$
$60$	0.363191	+	0.432835i	0.0468878	+	0.0558787i
$61$	−0.669898	−	1.84053i	−0.0857716	−	0.235656i	0.889390	−	0.457149i	$-0.151129\pi$
$61$	−0.669898	−	1.84053i	−0.0857716	−	0.235656i	−0.975162	+	0.221493i	$0.928907\pi$
$62$	4.51043	−	0.795310i	0.572825	−	0.101004i
$63$	−1.94237	−	1.79644i	−0.244716	−	0.226330i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−1.54716	−	0.893253i	−0.191901	−	0.110794i
$66$	0.997183	+	2.73974i	0.122745	+	0.337238i
$67$	0.319286	+	0.877230i	0.0390070	+	0.107171i	0.957667	−	0.287878i	$-0.0929498\pi$
$67$	0.319286	+	0.877230i	0.0390070	+	0.107171i	−0.918660	+	0.395049i	$0.870728\pi$
$68$	−0.849616	−	0.490526i	−0.103031	−	0.0594850i
$69$	4.59545	−	7.95955i	0.553227	−	0.958218i
$70$	−0.330302	+	1.45797i	−0.0394786	+	0.174261i
$71$	−0.935428	+	0.164941i	−0.111015	+	0.0195749i	−0.228880	−	0.973455i	$-0.573506\pi$
$71$	−0.935428	+	0.164941i	−0.111015	+	0.0195749i	0.117865	+	0.993030i	$0.462395\pi$
$72$	−0.342020	−	0.939693i	−0.0403075	−	0.110744i
$73$	−6.08842	−	7.25590i	−0.712596	−	0.849239i	0.281293	−	0.959622i	$-0.409237\pi$
$73$	−6.08842	−	7.25590i	−0.712596	−	0.849239i	−0.993889	+	0.110383i	$0.964792\pi$
$74$	−0.993423	−	5.63398i	−0.115483	−	0.654937i
$75$	2.34037	+	4.05365i	0.270243	+	0.468075i
$76$	3.65141	+	2.38060i	0.418845	+	0.273073i
$77$	−4.17469	+	6.48658i	−0.475750	+	0.739215i
$78$	2.03237	+	2.42209i	0.230121	+	0.274248i
$79$	5.34236	−	0.942002i	0.601062	−	0.105983i	0.135166	−	0.990823i	$-0.456843\pi$
$79$	5.34236	−	0.942002i	0.601062	−	0.105983i	0.465896	+	0.884840i	$0.345732\pi$
$80$	−0.363191	+	0.432835i	−0.0406060	+	0.0483924i
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$	−2.23629	+	2.66511i	−0.246957	+	0.294312i
$83$	−9.70625	−	5.60391i	−1.06540	−	0.615109i	−0.138479	−	0.990365i	$-0.544221\pi$
$83$	−9.70625	−	5.60391i	−1.06540	−	0.615109i	−0.926921	+	0.375257i	$0.877555\pi$
$84$	1.43186	−	2.22481i	0.156229	−	0.242747i
$85$	0.424633	+	0.356310i	0.0460579	+	0.0386472i
$86$	3.90655	+	0.688830i	0.421254	+	0.0742785i
$87$		−	6.21108i		−	0.665898i
$88$	−2.52496	+	1.45778i	−0.269161	+	0.155400i
$89$	3.33791	+	2.80084i	0.353818	+	0.296888i	0.802321	−	0.596893i	$-0.203598\pi$
$89$	3.33791	+	2.80084i	0.353818	+	0.296888i	−0.448503	+	0.893781i	$0.648043\pi$
$90$	0.0981157	+	0.556442i	0.0103423	+	0.0586541i
$91$	−1.84833	+	8.15862i	−0.193758	+	0.855256i
$92$	8.63662	+	3.14347i	0.900430	+	0.327730i
$93$	4.30380	+	1.56646i	0.446283	+	0.162434i
$94$	−2.21765	+	3.84109i	−0.228733	+	0.396178i
$95$	−1.79822	−	1.68292i	−0.184493	−	0.172664i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	4.10065	−	3.44086i	0.416358	−	0.349366i	−0.410417	−	0.911898i	$-0.634617\pi$
$97$	4.10065	−	3.44086i	0.416358	−	0.349366i	0.826776	+	0.562532i	$0.190173\pi$
$98$	6.97870	−	0.545599i	0.704956	−	0.0551138i
$99$	−0.506283	+	2.87127i	−0.0508834	+	0.288574i
$100$	−3.58566	+	3.00873i	−0.358566	+	0.300873i
$101$	6.47111	+	1.14103i	0.643899	+	0.113537i	0.486056	−	0.873927i	$-0.338435\pi$
$101$	6.47111	+	1.14103i	0.643899	+	0.113537i	0.157843	+	0.987464i	$0.449546\pi$
$102$	−0.490526	−	0.849616i	−0.0485693	−	0.0841245i
$103$	−3.26432	+	5.65396i	−0.321643	+	0.557101i	−0.980827	−	0.194880i	$-0.937568\pi$
$103$	−3.26432	+	5.65396i	−0.321643	+	0.557101i	0.659185	+	0.751981i	$0.270902\pi$
$104$	−2.03237	+	2.42209i	−0.199291	+	0.237505i
$105$	−1.01504	+	1.09749i	−0.0990573	+	0.107104i
$106$	0.766406	+	1.32745i	0.0744400	+	0.128934i
$107$			10.7872i			1.04283i	0.853302	+	0.521417i	$0.174596\pi$
$107$			10.7872i			1.04283i	−0.853302	+	0.521417i	$0.825404\pi$
$108$	0.173648	−	0.984808i	0.0167093	−	0.0947632i
$109$	−5.73774	+	15.7643i	−0.549576	+	1.50995i	0.284709	+	0.958614i	$0.408103\pi$
$109$	−5.73774	+	15.7643i	−0.549576	+	1.50995i	−0.834285	+	0.551333i	$0.814119\pi$
$110$	1.54802	−	0.563434i	0.147598	−	0.0537213i
$111$	1.95666	−	5.37588i	0.185718	−	0.510256i
$112$	2.43965	+	1.02377i	0.230525	+	0.0967375i
$113$			2.63663i			0.248033i	0.992280	+	0.124017i	$0.0395776\pi$
$113$			2.63663i			0.248033i	−0.992280	+	0.124017i	$0.960422\pi$
$114$	1.97191	+	3.88736i	0.184686	+	0.364085i
$115$	−4.49735	−	2.59655i	−0.419380	−	0.242129i
$116$	6.11672	−	1.07854i	0.567923	−	0.100140i
$117$	0.549043	+	3.11378i	0.0507590	+	0.287869i
$118$	6.80214	+	1.19940i	0.626188	+	0.110414i
$119$	1.00437	−	2.39342i	0.0920708	−	0.219405i
$120$	−0.530950	+	0.193250i	−0.0484689	+	0.0176412i
$121$	−2.49946			−0.227224
$122$	1.95865			0.177328
$123$	−3.26924	+	1.18991i	−0.294778	+	0.107290i
$124$	−0.795310	+	4.51043i	−0.0714210	+	0.405048i
$125$	4.73705	−	2.73493i	0.423694	−	0.244620i
$126$	2.35243	−	1.21081i	0.209571	−	0.107868i
$127$	−5.39653	−	14.8268i	−0.478865	−	1.31567i	−0.910458	−	0.413601i	$-0.864271\pi$
$127$	−5.39653	−	14.8268i	−0.478865	−	1.31567i	0.431593	−	0.902068i	$-0.357952\pi$
$128$	0.642788	+	0.766044i	0.0568149	+	0.0677094i
$129$	3.03876	+	2.54982i	0.267548	+	0.224499i
$130$	1.36854	−	1.14834i	0.120029	−	0.100716i
$131$	−5.74551	+	15.7857i	−0.501988	+	1.37920i	0.387343	+	0.921936i	$0.373393\pi$
$131$	−5.74551	+	15.7857i	−0.501988	+	1.37920i	−0.889331	+	0.457265i	$0.848829\pi$
$132$	−2.91557			−0.253768
$133$	−5.03162	+	10.3770i	−0.436297	+	0.899803i
$134$	−0.933529			−0.0806446
$135$	−0.193250	+	0.530950i	−0.0166323	+	0.0456969i
$136$	0.751529	−	0.630608i	0.0644431	−	0.0540742i
$137$	15.0309	+	12.6124i	1.28418	+	1.07755i	0.992654	+	0.120989i	$0.0386065\pi$
$137$	15.0309	+	12.6124i	1.28418	+	1.07755i	0.291523	+	0.956564i	$0.405838\pi$
$138$	5.90780	+	7.04064i	0.502905	+	0.599339i
$139$	−6.98443	−	19.1896i	−0.592412	−	1.62764i	−0.766016	−	0.642822i	$-0.777764\pi$
$139$	−6.98443	−	19.1896i	−0.592412	−	1.62764i	0.173604	−	0.984815i	$-0.444459\pi$
$140$	−1.25707	−	0.809038i	−0.106242	−	0.0683762i
$141$	−3.84109	+	2.21765i	−0.323478	+	0.186760i
$142$	0.164941	−	0.935428i	0.0138416	−	0.0784994i
$143$	8.66254	−	3.15291i	0.724398	−	0.263659i
$144$	1.00000			0.0833333
$145$	−3.50942			−0.291441
$146$	8.90068	−	3.23958i	0.736626	−	0.268110i
$147$	6.31654	+	3.01685i	0.520979	+	0.248826i
$148$	5.63398	+	0.993423i	0.463110	+	0.0816588i
$149$	−1.03129	−	5.84872i	−0.0844863	−	0.479146i	−0.997466	−	0.0711412i	$-0.977336\pi$
$149$	−1.03129	−	5.84872i	−0.0844863	−	0.479146i	0.912980	−	0.408004i	$-0.133775\pi$
$150$	−4.60964	+	0.812803i	−0.376375	+	0.0663651i
$151$	−9.29318	−	5.36542i	−0.756268	−	0.436632i	0.0716861	−	0.997427i	$-0.477162\pi$
$151$	−9.29318	−	5.36542i	−0.756268	−	0.436632i	−0.827954	+	0.560796i	$0.810495\pi$
$152$	−3.48588	+	2.61699i	−0.282742	+	0.212266i
$153$		−	0.981052i		−	0.0793133i
$154$	−4.66757	−	6.14146i	−0.376123	−	0.494893i
$155$	0.885087	−	2.43176i	0.0710919	−	0.195323i
$156$	−2.97113	+	1.08140i	−0.237881	+	0.0865816i
$157$	2.93135	−	8.05381i	0.233947	−	0.642764i	−0.766053	−	0.642777i	$-0.777782\pi$
$157$	2.93135	−	8.05381i	0.233947	−	0.642764i	1.00000		1.32861e-5i	$4.22909e-6\pi$
$158$	−0.942002	+	5.34236i	−0.0749416	+	0.425015i
$159$			1.53281i			0.121560i
$160$	−0.282513	−	0.489327i	−0.0223346	−	0.0386847i
$161$	−5.37281	+	23.7159i	−0.423437	+	1.86907i
$162$	0.642788	−	0.766044i	0.0505022	−	0.0601861i
$163$	−8.35830	+	14.4770i	−0.654672	+	1.13393i	0.327303	+	0.944919i	$0.393860\pi$
$163$	−8.35830	+	14.4770i	−0.654672	+	1.13393i	−0.981976	+	0.189007i	$0.939473\pi$
$164$	−1.73953	−	3.01295i	−0.135834	−	0.235272i
$165$	1.62234	+	0.286063i	0.126299	+	0.0222700i
$166$	8.58568	−	7.20424i	0.666378	−	0.559158i
$167$	0.872290	−	4.94700i	0.0674998	−	0.382810i	−0.932278	−	0.361742i	$-0.882182\pi$
$167$	0.872290	−	4.94700i	0.0674998	−	0.382810i	0.999778	−	0.0210684i	$-0.00670678\pi$
$168$	1.60091	+	2.10644i	0.123513	+	0.162515i
$169$	−2.30038	+	1.93025i	−0.176953	+	0.148481i
$170$	−0.480055	+	0.277160i	−0.0368185	+	0.0212572i
$171$	−0.235954	+	4.35251i	−0.0180438	+	0.332845i
$172$	−1.98341	+	3.43536i	−0.151233	+	0.261944i
$173$	14.2830	+	5.19859i	1.08592	+	0.395241i	0.822107	−	0.569333i	$-0.192799\pi$
$173$	14.2830	+	5.19859i	1.08592	+	0.395241i	0.263810	+	0.964575i	$0.415021\pi$
$174$	5.83651	+	2.12431i	0.442464	+	0.161044i
$175$	−9.09174	−	8.40868i	−0.687271	−	0.635637i
$176$	−0.506283	−	2.87127i	−0.0381625	−	0.216430i
$177$	5.29113	+	4.43978i	0.397705	+	0.333715i
$178$	−3.77356	+	2.17867i	−0.282840	+	0.163298i
$179$		−	11.7060i		−	0.874951i	−0.899230	−	0.437475i	$-0.855873\pi$
$179$		−	11.7060i		−	0.874951i	0.899230	−	0.437475i	$-0.144127\pi$
$180$	−0.556442	−	0.0981157i	−0.0414747	−	0.00731311i
$181$	13.1026	+	10.9944i	0.973905	+	0.817204i	0.983159	−	0.182754i	$-0.0585010\pi$
$181$	13.1026	+	10.9944i	0.973905	+	0.817204i	−0.00925339	+	0.999957i	$0.502945\pi$
$182$	−7.03443	−	4.52727i	−0.521427	−	0.335584i
$183$	1.69624	+	0.979325i	0.125390	+	0.0723938i
$184$	−5.90780	+	7.04064i	−0.435529	+	0.519043i
$185$	−3.03751	−	1.10556i	−0.223322	−	0.0812826i
$186$	−2.94397	+	3.50849i	−0.215863	+	0.257255i
$187$	−2.81687	+	0.496690i	−0.205990	+	0.0363216i
$188$	−2.85096	−	3.39764i	−0.207928	−	0.247798i
$189$	2.64267	+	0.127623i	0.192226	+	0.00928318i
$190$	2.19646	−	1.11418i	0.159348	−	0.0808312i
$191$	−6.67511	−	11.5616i	−0.482994	−	0.836570i	0.516815	−	0.856097i	$-0.327117\pi$
$191$	−6.67511	−	11.5616i	−0.482994	−	0.836570i	−0.999809	+	0.0195268i	$0.993784\pi$
$192$	0.173648	+	0.984808i	0.0125320	+	0.0710724i
$193$	16.0915	+	19.1771i	1.15829	+	1.38040i	0.911484	+	0.411335i	$0.134937\pi$
$193$	16.0915	+	19.1771i	1.15829	+	1.38040i	0.246808	+	0.969064i	$0.420618\pi$
$194$	1.83084	+	5.03020i	0.131447	+	0.361147i
$195$	1.75936	−	0.310223i	0.125991	−	0.0222156i
$196$	−1.87416	+	6.74444i	−0.133869	+	0.481746i
$197$	−7.10437	+	12.3051i	−0.506165	+	0.876704i	0.493809	+	0.869570i	$0.335604\pi$
$197$	−7.10437	+	12.3051i	−0.506165	+	0.876704i	−0.999975	+	0.00713354i	$0.997729\pi$
$198$	−2.52496	−	1.45778i	−0.179441	−	0.103600i
$199$	−0.405063	−	1.11290i	−0.0287141	−	0.0788915i	0.924507	−	0.381164i	$-0.124477\pi$
$199$	−0.405063	−	1.11290i	−0.0287141	−	0.0788915i	−0.953221	+	0.302273i	$0.902255\pi$
$200$	−1.60091	−	4.39846i	−0.113201	−	0.311018i
$201$	−0.808460	−	0.466764i	−0.0570244	−	0.0329230i
$202$	−3.28547	+	5.69060i	−0.231165	+	0.400389i
$203$	4.86899	+	15.6951i	0.341736	+	1.10158i
$204$	0.966147	−	0.170358i	0.0676438	−	0.0119274i
$205$	0.672328	+	1.84721i	0.0469574	+	0.129015i
$206$	−4.19652	−	5.00122i	−0.292386	−	0.348452i
$207$	1.59598	+	9.05127i	0.110929	+	0.629107i
$208$	−1.58091	−	2.73821i	−0.109616	−	0.189861i
$209$	12.6167	−	1.52611i	0.872716	−	0.105563i
$210$	−0.684139	−	1.32918i	−0.0472101	−	0.0917224i
$211$	7.71785	+	9.19777i	0.531319	+	0.633201i	0.963218	−	0.268721i	$-0.0866009\pi$
$211$	7.71785	+	9.19777i	0.531319	+	0.633201i	−0.431899	+	0.901922i	$0.642156\pi$
$212$	−1.50953	+	0.266170i	−0.103675	+	0.0182806i
$213$	0.610557	−	0.727634i	0.0418347	−	0.0498566i
$214$	−10.1366	−	3.68942i	−0.692924	−	0.252204i
$215$	1.44071	−	1.71698i	0.0982559	−	0.117097i
$216$	0.866025	+	0.500000i	0.0589256	+	0.0340207i
$217$	−12.1035	−	0.584513i	−0.821636	−	0.0396793i
$218$	−12.8512	−	10.7834i	−0.870392	−	0.730346i
$219$	9.32801	+	1.64478i	0.630328	+	0.111144i
$220$			1.64737i			0.111066i
$221$	−2.68633	+	1.55095i	−0.180702	+	0.104328i
$222$	4.38246	+	3.67732i	0.294131	+	0.246806i
$223$	2.48045	+	14.0673i	0.166103	+	0.942016i	0.947920	+	0.318509i	$0.103182\pi$
$223$	2.48045	+	14.0673i	0.166103	+	0.942016i	−0.781817	+	0.623508i	$0.785707\pi$
$224$	−1.79644	+	1.94237i	−0.120030	+	0.129780i
$225$	−4.39846	−	1.60091i	−0.293231	−	0.106727i
$226$	−2.47762	−	0.901781i	−0.164809	−	0.0599856i
$227$	4.22736	−	7.32200i	0.280580	−	0.485978i	−0.690948	−	0.722905i	$-0.742807\pi$
$227$	4.22736	−	7.32200i	0.280580	−	0.485978i	0.971528	+	0.236926i	$0.0761399\pi$
$228$	−4.32736	+	0.523436i	−0.286586	+	0.0346654i
$229$	12.3489	−	7.12963i	0.816037	−	0.471139i	−0.0330108	−	0.999455i	$-0.510510\pi$
$229$	12.3489	−	7.12963i	0.816037	−	0.471139i	0.849048	+	0.528316i	$0.177176\pi$
$230$	3.97814	−	3.33806i	0.262311	−	0.220105i
$231$	−0.971500	−	7.65245i	−0.0639200	−	0.503494i
$232$	−1.07854	+	6.11672i	−0.0708098	+	0.401582i
$233$	−11.1021	+	9.31576i	−0.727322	+	0.610295i	−0.929400	−	0.369074i	$-0.879675\pi$
$233$	−11.1021	+	9.31576i	−0.727322	+	0.610295i	0.202078	+	0.979369i	$0.435230\pi$
$234$	−3.11378	−	0.549043i	−0.203554	−	0.0358921i
$235$	1.25303	+	2.17031i	0.0817387	+	0.141576i
$236$	−3.45354	+	5.98170i	−0.224806	+	0.389376i
$237$	−3.48698	+	4.15562i	−0.226503	+	0.269936i
$238$	1.90556	+	1.76240i	0.123519	+	0.114240i
$239$	5.44103	+	9.42414i	0.351951	+	0.609597i	0.986591	−	0.163211i	$-0.0521851\pi$
$239$	5.44103	+	9.42414i	0.351951	+	0.609597i	−0.634640	+	0.772808i	$0.718852\pi$
$240$		−	0.565026i		−	0.0364722i
$241$	3.83106	−	21.7270i	0.246781	−	1.39956i	−0.569540	−	0.821963i	$-0.692879\pi$
$241$	3.83106	−	21.7270i	0.246781	−	1.39956i	0.816321	−	0.577599i	$-0.196010\pi$
$242$	0.854866	−	2.34873i	0.0549529	−	0.150982i
$243$	0.939693	−	0.342020i	0.0602813	−	0.0219406i
$244$	−0.669898	+	1.84053i	−0.0428858	+	0.117828i
$245$	1.70460	−	3.56900i	0.108903	−	0.228015i
$246$		−	3.47906i		−	0.221817i
$247$	12.2911	−	6.23482i	0.782064	−	0.396712i
$248$	−3.96640	−	2.29000i	−0.251867	−	0.145415i
$249$	11.0375	−	1.94622i	0.699476	−	0.123336i
$250$	0.949833	+	5.38677i	0.0600727	+	0.340689i
$251$	−29.8704	−	5.26696i	−1.88540	−	0.332447i	−0.892468	−	0.451110i	$-0.851028\pi$
$251$	−29.8704	−	5.26696i	−1.88540	−	0.332447i	−0.992935	+	0.118663i	$0.962139\pi$
$252$	0.333211	+	2.62468i	0.0209903	+	0.165340i
$253$	25.1807	−	9.16501i	1.58309	−	0.576199i
$254$	15.7784			0.990025
$255$	−0.554319			−0.0347128
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−1.60930	+	9.12680i	−0.100385	+	0.569314i	0.892578	+	0.450893i	$0.148894\pi$
$257$	−1.60930	+	9.12680i	−0.100385	+	0.569314i	−0.992963	+	0.118421i	$0.962217\pi$
$258$	−3.43536	+	1.98341i	−0.213876	+	0.123482i
$259$	−0.730116	+	15.1184i	−0.0453672	+	0.939414i
$260$	0.611021	+	1.67877i	0.0378939	+	0.104113i
$261$	3.99240	+	4.75796i	0.247124	+	0.294510i
$262$	−12.8686	−	10.7980i	−0.795024	−	0.667105i
$263$	−0.327737	+	0.275004i	−0.0202091	+	0.0169575i	−0.652836	−	0.757499i	$-0.726421\pi$
$263$	−0.327737	+	0.275004i	−0.0202091	+	0.0169575i	0.632627	+	0.774457i	$0.281977\pi$
$264$	0.997183	−	2.73974i	0.0613724	−	0.168619i
$265$	0.866079			0.0532028
$266$	−8.03030	−	8.27733i	−0.492369	−	0.507516i
$267$	−4.35733			−0.266664
$268$	0.319286	−	0.877230i	0.0195035	−	0.0535854i
$269$	−4.59831	+	3.85844i	−0.280364	+	0.235254i	−0.772116	−	0.635482i	$-0.780801\pi$
$269$	−4.59831	+	3.85844i	−0.280364	+	0.235254i	0.491751	+	0.870736i	$0.336357\pi$
$270$	−0.432835	−	0.363191i	−0.0263415	−	0.0221031i
$271$	−11.9788	−	14.2758i	−0.727660	−	0.867191i	0.267691	−	0.963505i	$-0.413739\pi$
$271$	−11.9788	−	14.2758i	−0.727660	−	0.867191i	−0.995351	+	0.0963138i	$0.969295\pi$
$272$	0.335539	+	0.921887i	0.0203451	+	0.0558976i
$273$	−3.82836	−	7.43795i	−0.231703	−	0.450165i
$274$	−16.9927	+	9.81073i	−1.02657	+	0.592688i
$275$	−2.36978	+	13.4397i	−0.142903	+	0.810445i
$276$	−8.63662	+	3.14347i	−0.519864	+	0.189215i
$277$	13.4896			0.810509			0.405255	−	0.914204i	$-0.367183\pi$
$277$	13.4896			0.810509			0.405255	+	0.914204i	$0.367183\pi$
$278$	20.4211			1.22478
$279$	−4.30380	+	1.56646i	−0.257662	+	0.0937812i
$280$	1.19019	−	0.904556i	0.0711275	−	0.0540576i
$281$	−22.6238	−	3.98918i	−1.34962	−	0.237974i	−0.548336	−	0.836258i	$-0.684738\pi$
$281$	−22.6238	−	3.98918i	−1.34962	−	0.237974i	−0.801284	+	0.598284i	$0.795850\pi$
$282$	−0.770182	−	4.36792i	−0.0458637	−	0.260106i
$283$	7.80916	−	1.37697i	0.464206	−	0.0818521i	0.0633467	−	0.997992i	$-0.479823\pi$
$283$	7.80916	−	1.37697i	0.464206	−	0.0818521i	0.400860	+	0.916139i	$0.368711\pi$
$284$	0.822602	+	0.474929i	0.0488124	+	0.0281819i
$285$	2.45928	+	0.133320i	0.145675	+	0.00789719i
$286$			9.21848i			0.545100i
$287$	7.32842	−	5.56966i	0.432583	−	0.328767i
$288$	−0.342020	+	0.939693i	−0.0201537	+	0.0553719i
$289$	−15.0704	+	5.48516i	−0.886492	+	0.322657i
$290$	1.20029	−	3.29777i	0.0704836	−	0.193652i
$291$	−0.929543	+	5.27170i	−0.0544908	+	0.309032i
$292$			9.47191i			0.554301i
$293$	−11.7621	−	20.3726i	−0.687149	−	1.19018i	−0.972756	−	0.231831i	$-0.925528\pi$
$293$	−11.7621	−	20.3726i	−0.687149	−	1.19018i	0.285607	−	0.958347i	$-0.407805\pi$
$294$	−4.99529	+	4.90378i	−0.291331	+	0.285994i
$295$	2.50859	−	2.98962i	0.146056	−	0.174063i
$296$	−2.86045	+	4.95444i	−0.166260	+	0.287971i
$297$	−1.45778	−	2.52496i	−0.0845892	−	0.146513i
$298$	5.84872	+	1.03129i	0.338807	+	0.0597408i
$299$	22.2612	−	18.6794i	1.28740	−	1.08025i
$300$	0.812803	−	4.60964i	0.0469272	−	0.266137i
$301$	−9.67764	−	4.06112i	−0.557810	−	0.234079i
$302$	8.22030	−	6.89765i	0.473025	−	0.396915i
$303$	−5.69060	+	3.28547i	−0.326916	+	0.188745i
$304$	−1.26692	−	4.17072i	−0.0726629	−	0.239207i
$305$	0.553344	−	0.958419i	0.0316844	−	0.0548789i
$306$	0.921887	+	0.335539i	0.0527008	+	0.0191815i
$307$	16.0453	+	5.84001i	0.915753	+	0.333307i	0.756548	−	0.653938i	$-0.226885\pi$
$307$	16.0453	+	5.84001i	0.915753	+	0.333307i	0.159206	+	0.987245i	$0.449107\pi$
$308$	7.36749	−	2.28557i	0.419802	−	0.130233i
$309$	−1.13368	−	6.42945i	−0.0644931	−	0.365758i
$310$	1.98239	+	1.66342i	0.112592	+	0.0944759i
$311$	11.0730	−	6.39302i	0.627894	−	0.362515i	−0.152042	−	0.988374i	$-0.548585\pi$
$311$	11.0730	−	6.39302i	0.627894	−	0.362515i	0.779936	+	0.625859i	$0.215252\pi$
$312$		−	3.16181i		−	0.179002i
$313$	24.2944	+	4.28376i	1.37320	+	0.242132i	0.811086	−	0.584927i	$-0.198877\pi$
$313$	24.2944	+	4.28376i	1.37320	+	0.242132i	0.562114	+	0.827060i	$0.309988\pi$
$314$	6.56553	+	5.50913i	0.370514	+	0.310898i
$315$	0.0721101	−	1.49318i	0.00406294	−	0.0841310i
$316$	−4.69799	−	2.71239i	−0.264283	−	0.152584i
$317$	−0.811991	+	0.967693i	−0.0456059	+	0.0543510i	−0.788365	−	0.615207i	$-0.789072\pi$
$317$	−0.811991	+	0.967693i	−0.0456059	+	0.0543510i	0.742759	+	0.669559i	$0.233517\pi$
$318$	−1.44037	−	0.524253i	−0.0807721	−	0.0293986i
$319$	11.6401	−	13.8722i	0.651722	−	0.776692i
$320$	0.556442	−	0.0981157i	0.0311060	−	0.00548483i
$321$	−6.93385	−	8.26344i	−0.387010	−	0.461220i
$322$	−20.4480	−	13.1601i	−1.13952	−	0.733383i
$323$	−4.09169	+	1.24292i	−0.227668	+	0.0691576i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	2.56993	+	14.5748i	0.142554	+	0.808465i
$326$	−10.7452	−	12.8057i	−0.595123	−	0.709240i
$327$	−5.73774	−	15.7643i	−0.317298	−	0.871768i
$328$	3.42620	−	0.604132i	0.189180	−	0.0333576i
$329$	7.96776	−	8.61500i	0.439277	−	0.474960i
$330$	−0.823685	+	1.42666i	−0.0453424	+	0.0785353i
$331$	−22.0043	−	12.7042i	−1.20947	−	0.698285i	−0.246823	−	0.969061i	$-0.579387\pi$
$331$	−22.0043	−	12.7042i	−1.20947	−	0.698285i	−0.962642	+	0.270776i	$0.912720\pi$
$332$	3.83330	+	10.5319i	0.210380	+	0.578013i
$333$	1.95666	+	5.37588i	0.107224	+	0.294596i
$334$	4.35032	+	2.51166i	0.238039	+	0.137432i
$335$	−0.263734	+	0.456800i	−0.0144093	+	0.0249577i
$336$	−2.52695	+	0.783921i	−0.137856	+	0.0427664i
$337$	31.6542	−	5.58150i	1.72432	−	0.304044i	0.778235	−	0.627973i	$-0.216115\pi$
$337$	31.6542	−	5.58150i	1.72432	−	0.304044i	0.946081	+	0.323929i	$0.105004\pi$
$338$	−1.02707	−	2.82184i	−0.0558650	−	0.153488i
$339$	−1.69479	−	2.01978i	−0.0920486	−	0.109699i
$340$	−0.0962565	−	0.545898i	−0.00522024	−	0.0296055i
$341$	6.67666	+	11.5643i	0.361562	+	0.626243i
$342$	−4.00932	−	1.71037i	−0.216799	−	0.0924862i
$343$	−18.3265	−	2.67176i	−0.989540	−	0.144262i
$344$	−2.54982	−	3.03876i	−0.137477	−	0.163839i
$345$	5.11420	−	0.901771i	0.275339	−	0.0485497i
$346$	−9.77015	+	11.6436i	−0.525246	+	0.625964i
$347$	−13.5708	−	4.93937i	−0.728519	−	0.265159i	−0.0489810	−	0.998800i	$-0.515597\pi$
$347$	−13.5708	−	4.93937i	−0.728519	−	0.265159i	−0.679538	+	0.733641i	$0.737820\pi$
$348$	−3.99240	+	4.75796i	−0.214015	+	0.255054i
$349$	8.91157	+	5.14510i	0.477025	+	0.275411i	0.719176	−	0.694828i	$-0.244519\pi$
$349$	8.91157	+	5.14510i	0.477025	+	0.275411i	−0.242151	+	0.970239i	$0.577853\pi$
$350$	11.0111	−	5.66750i	0.588570	−	0.302941i
$351$	−2.42209	−	2.03237i	−0.129282	−	0.108480i
$352$	2.87127	+	0.506283i	0.153039	+	0.0269850i
$353$		−	34.9916i		−	1.86242i	−0.364487	−	0.931208i	$-0.618756\pi$
$353$		−	34.9916i		−	1.86242i	0.364487	−	0.931208i	$-0.381244\pi$
$354$	−5.98170	+	3.45354i	−0.317924	+	0.183553i
$355$	−0.411132	−	0.344980i	−0.0218206	−	0.0183097i
$356$	−0.756643	−	4.29114i	−0.0401020	−	0.227430i
$357$	0.769067	+	2.47907i	0.0407033	+	0.131206i
$358$	11.0001	+	4.00370i	0.581372	+	0.211602i
$359$	17.8889	+	6.51101i	0.944138	+	0.343638i	0.767799	−	0.640691i	$-0.221352\pi$
$359$	17.8889	+	6.51101i	0.944138	+	0.343638i	0.176340	+	0.984329i	$0.443574\pi$
$360$	0.282513	−	0.489327i	0.0148897	−	0.0257898i
$361$	18.4520	−	4.53019i	0.971159	−	0.238431i
$362$	−14.8126	+	8.55209i	−0.778536	+	0.449488i
$363$	1.91470	−	1.60662i	0.100496	−	0.0843259i
$364$	6.66016	−	5.06178i	0.349087	−	0.265310i
$365$	0.929342	−	5.27056i	0.0486440	−	0.275874i
$366$	−1.50041	+	1.25900i	−0.0784278	+	0.0658088i
$367$	18.2022	+	3.20954i	0.950146	+	0.167536i	0.627180	−	0.778874i	$-0.284209\pi$
$367$	18.2022	+	3.20954i	0.950146	+	0.167536i	0.322966	+	0.946411i	$0.395320\pi$
$368$	−4.59545	−	7.95955i	−0.239554	−	0.414920i
$369$	1.73953	−	3.01295i	0.0905562	−	0.156848i
$370$	2.07778	−	2.47620i	0.108019	−	0.128732i
$371$	−1.20160	−	3.87334i	−0.0623842	−	0.201094i
$372$	−2.29000	−	3.96640i	−0.118731	−	0.205648i
$373$			27.1408i			1.40530i	0.711537	+	0.702648i	$0.247999\pi$
$373$			27.1408i			1.40530i	−0.711537	+	0.702648i	$0.752001\pi$
$374$	0.496690	−	2.81687i	0.0256832	−	0.145657i
$375$	−1.87081	+	5.14000i	−0.0966080	+	0.265428i
$376$	4.16782	−	1.51696i	0.214939	−	0.0782314i
$377$	6.71668	−	18.4539i	0.345927	−	0.950426i
$378$	−1.02377	+	2.43965i	−0.0526572	+	0.125482i
$379$		−	18.6693i		−	0.958977i	−0.877548	−	0.479488i	$-0.840822\pi$
$379$		−	18.6693i		−	0.958977i	0.877548	−	0.479488i	$-0.159178\pi$
$380$	0.295755	+	2.44507i	0.0151719	+	0.125429i
$381$	13.6645	+	7.88920i	0.700053	+	0.404176i
$382$	13.1474	−	2.31824i	0.672679	−	0.118612i
$383$	2.76023	+	15.6541i	0.141041	+	0.799885i	0.970461	+	0.241259i	$0.0775603\pi$
$383$	2.76023	+	15.6541i	0.141041	+	0.799885i	−0.829419	+	0.558626i	$0.811329\pi$
$384$	−0.984808	−	0.173648i	−0.0502558	−	0.00886145i
$385$	−4.32383	+	0.548923i	−0.220363	+	0.0279757i
$386$	−23.5242	+	8.56211i	−1.19735	+	0.435800i
$387$	−3.96682			−0.201645
$388$	−5.35302			−0.271759
$389$	−30.3706	+	11.0540i	−1.53985	+	0.560459i	−0.966009	−	0.258508i	$-0.916769\pi$
$389$	−30.3706	+	11.0540i	−1.53985	+	0.560459i	−0.573840	+	0.818968i	$0.694547\pi$
$390$	−0.310223	+	1.75936i	−0.0157088	+	0.0890889i
$391$	−7.80873	+	4.50837i	−0.394905	+	0.227998i
$392$	−5.69670	−	4.06787i	−0.287727	−	0.205459i
$393$	−5.74551	−	15.7857i	−0.289823	−	0.796282i
$394$	−9.13320	−	10.8845i	−0.460124	−	0.548354i
$395$	2.34803	+	1.97023i	0.118142	+	0.0991330i
$396$	2.23345	−	1.87409i	0.112235	−	0.0941766i
$397$	3.15893	−	8.67909i	0.158542	−	0.435591i	−0.834834	−	0.550502i	$-0.814436\pi$
$397$	3.15893	−	8.67909i	0.158542	−	0.435591i	0.993376	+	0.114911i	$0.0366584\pi$
$398$	1.18432			0.0593648
$399$	−2.81578	−	11.1835i	−0.140965	−	0.559877i
$400$	4.68075			0.234037
$401$	−9.78387	+	26.8810i	−0.488583	+	1.34237i	0.413380	+	0.910559i	$0.364348\pi$
$401$	−9.78387	+	26.8810i	−0.488583	+	1.34237i	−0.901963	+	0.431813i	$0.857874\pi$
$402$	0.715125	−	0.600061i	0.0356672	−	0.0299283i
$403$	11.0932	+	9.30829i	0.552591	+	0.463679i
$404$	−4.22372	−	5.03363i	−0.210138	−	0.250432i
$405$	−0.193250	−	0.530950i	−0.00960268	−	0.0263831i
$406$	−16.4138	−	0.792674i	−0.814605	−	0.0393398i
$407$	14.4450	−	8.33983i	0.716012	−	0.413390i
$408$	−0.170358	+	0.966147i	−0.00843397	+	0.0478314i
$409$	−20.0757	+	7.30696i	−0.992680	+	0.361306i	−0.786757	−	0.617262i	$-0.788242\pi$
$409$	−20.0757	+	7.30696i	−0.992680	+	0.361306i	−0.205922	+	0.978568i	$0.566019\pi$
$410$	−1.96576			−0.0970818
$411$	−19.6215			−0.967855
$412$	6.13491	−	2.23292i	0.302245	−	0.110008i
$413$	−16.8508	−	7.07128i	−0.829176	−	0.347955i
$414$	−9.05127	−	1.59598i	−0.444846	−	0.0784383i
$415$	−1.09966	−	6.23649i	−0.0539803	−	0.306137i
$416$	3.11378	−	0.549043i	0.152666	−	0.0269191i
$417$	17.6852	+	10.2106i	0.866048	+	0.500013i
$418$	−2.88109	+	12.3778i	−0.140919	+	0.605417i
$419$		−	22.2828i		−	1.08859i	−0.838895	−	0.544294i	$-0.816798\pi$
$419$		−	22.2828i		−	1.08859i	0.838895	−	0.544294i	$-0.183202\pi$
$420$	1.48301	−	0.188273i	0.0723637	−	0.00918678i
$421$	7.37134	−	20.2526i	0.359257	−	0.987051i	−0.620030	−	0.784578i	$-0.712880\pi$
$421$	7.37134	−	20.2526i	0.359257	−	0.987051i	0.979288	−	0.202474i	$-0.0648980\pi$
$422$	−11.2827	+	4.10658i	−0.549235	+	0.199905i
$423$	1.51696	−	4.16782i	0.0737573	−	0.202646i
$424$	0.266170	−	1.50953i	0.0129264	−	0.0733091i
$425$		−	4.59205i		−	0.222747i
$426$	0.474929	+	0.822602i	0.0230104	+	0.0398552i
$427$	−5.05402	−	1.14499i	−0.244581	−	0.0554097i
$428$	6.93385	−	8.26344i	0.335160	−	0.399428i
$429$	−4.60924	+	7.98344i	−0.222536	+	0.385444i
$430$	1.12068	+	1.94107i	0.0540438	+	0.0936066i
$431$	−2.89922	−	0.511212i	−0.139651	−	0.0246242i	0.103386	−	0.994641i	$-0.467032\pi$
$431$	−2.89922	−	0.511212i	−0.139651	−	0.0246242i	−0.243037	+	0.970017i	$0.578143\pi$
$432$	−0.766044	+	0.642788i	−0.0368563	+	0.0309261i
$433$	0.553421	−	3.13861i	0.0265957	−	0.150832i	−0.968618	−	0.248554i	$-0.920045\pi$
$433$	0.553421	−	3.13861i	0.0265957	−	0.150832i	0.995214	+	0.0977224i	$0.0311557\pi$
$434$	4.68889	−	11.1736i	0.225074	−	0.536351i
$435$	2.68837	−	2.25581i	0.128898	−	0.108158i
$436$	14.5285	−	8.38802i	0.695787	−	0.401713i
$437$	35.7283	−	18.1236i	1.70912	−	0.866972i
$438$	−4.73595	+	8.20291i	−0.226293	+	0.391950i
$439$	5.31973	+	1.93622i	0.253897	+	0.0924108i	0.465833	−	0.884873i	$-0.345755\pi$
$439$	5.31973	+	1.93622i	0.253897	+	0.0924108i	−0.211936	+	0.977283i	$0.567977\pi$
$440$	−1.54802	−	0.563434i	−0.0737991	−	0.0268607i
$441$	−6.77794	+	1.74915i	−0.322759	+	0.0832928i
$442$	−0.538640	−	3.05478i	−0.0256205	−	0.145301i
$443$	−4.08664	−	3.42910i	−0.194162	−	0.162921i	0.540524	−	0.841329i	$-0.318226\pi$
$443$	−4.08664	−	3.42910i	−0.194162	−	0.162921i	−0.734686	+	0.678407i	$0.762671\pi$
$444$	−4.95444	+	2.86045i	−0.235127	+	0.135751i
$445$			2.46200i			0.116710i
$446$	−14.0673	−	2.48045i	−0.666106	−	0.117452i
$447$	4.54949	+	3.81748i	0.215184	+	0.180561i
$448$	−1.21081	−	2.35243i	−0.0572055	−	0.111142i
$449$	−20.7444	−	11.9768i	−0.978990	−	0.565220i	−0.0770247	−	0.997029i	$-0.524542\pi$
$449$	−20.7444	−	11.9768i	−0.978990	−	0.565220i	−0.901965	+	0.431809i	$0.857875\pi$
$450$	3.00873	−	3.58566i	0.141833	−	0.169030i
$451$	−9.53170	−	3.46926i	−0.448830	−	0.163361i
$452$	1.69479	−	2.01978i	0.0797164	−	0.0950023i
$453$	10.5678	−	1.86339i	0.496519	−	0.0875497i
$454$	5.43459	+	6.47669i	0.255058	+	0.303966i
$455$	−4.20263	+	2.16312i	−0.197022	+	0.101409i
$456$	0.988174	−	4.24541i	0.0462755	−	0.198810i
$457$	4.96099	+	8.59268i	0.232065	+	0.401949i	0.958416	−	0.285376i	$-0.0921184\pi$
$457$	4.96099	+	8.59268i	0.232065	+	0.401949i	−0.726351	+	0.687324i	$0.758785\pi$
$458$	2.47610	+	14.0426i	0.115700	+	0.656169i
$459$	0.630608	+	0.751529i	0.0294343	+	0.0350784i
$460$	1.77614	+	4.87991i	0.0828131	+	0.227527i
$461$	−30.0012	+	5.29002i	−1.39729	+	0.246381i	−0.821031	−	0.570883i	$-0.806601\pi$
$461$	−30.0012	+	5.29002i	−1.39729	+	0.246381i	−0.576263	+	0.817264i	$0.695490\pi$
$462$	7.52322	+	1.70438i	0.350012	+	0.0792949i
$463$	−2.33824	+	4.04995i	−0.108667	+	0.188217i	−0.915231	−	0.402930i	$-0.867992\pi$
$463$	−2.33824	+	4.04995i	−0.108667	+	0.188217i	0.806563	+	0.591148i	$0.201325\pi$
$464$	−5.37895	−	3.10554i	−0.249712	−	0.144171i
$465$	0.885087	+	2.43176i	0.0410449	+	0.112770i
$466$	−4.95681	−	13.6187i	−0.229620	−	0.630875i
$467$	−15.0209	−	8.67234i	−0.695086	−	0.401308i	0.110428	−	0.993884i	$-0.464778\pi$
$467$	−15.0209	−	8.67234i	−0.695086	−	0.401308i	−0.805515	+	0.592576i	$0.798111\pi$
$468$	1.58091	−	2.73821i	0.0730774	−	0.126574i
$469$	2.40884	+	0.545721i	0.111230	+	0.0251991i
$470$	−2.46799	+	0.435173i	−0.113840	+	0.0200730i
$471$	2.93135	+	8.05381i	0.135069	+	0.371100i
$472$	−4.43978	−	5.29113i	−0.204358	−	0.243544i
$473$	2.00833	+	11.3898i	0.0923432	+	0.523704i
$474$	−2.71239	−	4.69799i	−0.124584	−	0.215786i
$475$	−1.10444	+	20.3730i	−0.0506752	+	0.934777i
$476$	−2.30786	+	1.18787i	−0.105780	+	0.0544459i
$477$	−0.985273	−	1.17420i	−0.0451126	−	0.0537631i
$478$	−10.7167	+	1.88965i	−0.490172	+	0.0864306i
$479$	11.0310	−	13.1463i	0.504021	−	0.600669i	−0.452704	−	0.891661i	$-0.649541\pi$
$479$	11.0310	−	13.1463i	0.504021	−	0.600669i	0.956726	+	0.290992i	$0.0939852\pi$
$480$	0.530950	+	0.193250i	0.0242345	+	0.00882062i
$481$	11.6270	−	13.8565i	0.530145	−	0.631803i
$482$	19.1064	+	11.0311i	0.870275	+	0.502453i
$483$	−11.1284	−	21.6210i	−0.506362	−	0.983788i
$484$	1.91470	+	1.60662i	0.0870318	+	0.0730283i
$485$	2.97865	+	0.525216i	0.135253	+	0.0238488i
$486$			1.00000i			0.0453609i
$487$	−12.1759	+	7.02974i	−0.551741	+	0.318548i	−0.749824	−	0.661637i	$-0.769862\pi$
$487$	−12.1759	+	7.02974i	−0.551741	+	0.318548i	0.198083	+	0.980185i	$0.436529\pi$
$488$	−1.50041	−	1.25900i	−0.0679205	−	0.0569921i
$489$	−2.90281	−	16.4626i	−0.131269	−	0.744466i
$490$	2.77076	+	2.82247i	0.125170	+	0.127506i
$491$	−3.56981	−	1.29930i	−0.161103	−	0.0586368i	0.260210	−	0.965552i	$-0.416208\pi$
$491$	−3.56981	−	1.29930i	−0.161103	−	0.0586368i	−0.421313	+	0.906915i	$0.638431\pi$
$492$	3.26924	+	1.18991i	0.147389	+	0.0536452i
$493$	−3.04669	+	5.27703i	−0.137216	+	0.237665i
$494$	1.65501	+	13.6823i	0.0744623	+	0.615595i
$495$	−1.42666	+	0.823685i	−0.0641238	+	0.0370219i
$496$	3.50849	−	2.94397i	0.157536	−	0.132188i
$497$	−0.972439	+	2.31732i	−0.0436199	+	0.103946i
$498$	−1.94622	+	11.0375i	−0.0872121	+	0.494604i
$499$	−16.3767	+	13.7417i	−0.733122	+	0.615162i	−0.930981	−	0.365068i	$-0.881046\pi$
$499$	−16.3767	+	13.7417i	−0.733122	+	0.615162i	0.197859	+	0.980230i	$0.436601\pi$
$500$	−5.38677	−	0.949833i	−0.240904	−	0.0424778i
$501$	2.51166	+	4.35032i	0.112213	+	0.194358i
$502$	15.1656	−	26.2676i	0.676874	−	1.17238i
$503$	−14.9853	+	17.8588i	−0.668160	+	0.796282i	−0.988532	−	0.151009i	$-0.951748\pi$
$503$	−14.9853	+	17.8588i	−0.668160	+	0.796282i	0.320372	+	0.947292i	$0.396192\pi$
$504$	−2.58036	−	0.584579i	−0.114938	−	0.0260392i
$505$	1.85637	+	3.21533i	0.0826075	+	0.143080i
$506$			26.7967i			1.19126i
$507$	0.521455	−	2.95732i	0.0231586	−	0.131339i
$508$	−5.39653	+	14.8268i	−0.239432	+	0.657835i
$509$	22.5920	−	8.22280i	1.00137	−	0.364469i	0.211258	−	0.977430i	$-0.432244\pi$
$509$	22.5920	−	8.22280i	1.00137	−	0.364469i	0.790113	+	0.612961i	$0.210022\pi$
$510$	0.189588	−	0.520890i	0.00839511	−	0.0230654i
$511$	−24.8608	+	3.15615i	−1.09978	+	0.139620i
$512$		−	1.00000i		−	0.0441942i
$513$	−2.61699	−	3.48588i	−0.115543	−	0.153905i
$514$	−8.02597	−	4.63380i	−0.354010	−	0.204388i
$515$	−3.63280	+	0.640561i	−0.160080	+	0.0282265i
$516$	−0.688830	−	3.90655i	−0.0303241	−	0.171976i
$517$	−12.7350	−	2.24552i	−0.560084	−	0.0987578i
$518$	−13.9570	−	5.85690i	−0.613234	−	0.257337i
$519$	−14.2830	+	5.19859i	−0.626954	+	0.228193i
$520$	−1.78651			−0.0783434
$521$	−38.8694			−1.70290			−0.851449	−	0.524437i	$-0.824276\pi$
$521$	−38.8694			−1.70290			−0.851449	+	0.524437i	$0.824276\pi$
$522$	−5.83651	+	2.12431i	−0.255457	+	0.0929787i
$523$	6.94816	−	39.4050i	0.303822	−	1.72306i	−0.325178	−	0.945653i	$-0.605424\pi$
$523$	6.94816	−	39.4050i	0.303822	−	1.72306i	0.629000	−	0.777406i	$-0.283465\pi$
$524$	14.5482	−	8.39938i	0.635539	−	0.366929i
$525$	12.3697	+	0.597369i	0.539857	+	0.0260713i
$526$	−0.146327	−	0.402029i	−0.00638014	−	0.0175293i
$527$	−2.88819	−	3.44201i	−0.125811	−	0.149936i
$528$	2.23345	+	1.87409i	0.0971986	+	0.0815593i
$529$	47.0908	−	39.5139i	2.04743	−	1.71799i
$530$	−0.296216	+	0.813848i	−0.0128668	+	0.0353513i
$531$	−6.90708			−0.299742
$532$	10.5247	−	4.71500i	0.456303	−	0.204421i
$533$	−11.0001			−0.476468
$534$	1.49030	−	4.09455i	0.0644914	−	0.177189i
$535$	−4.66906	+	3.91780i	−0.201861	+	0.169381i
$536$	0.715125	+	0.600061i	0.0308887	+	0.0259187i
$537$	7.52450	+	8.96735i	0.324706	+	0.386970i
$538$	−2.05304	−	5.64067i	−0.0885126	−	0.243186i
$539$	8.45384	+	18.5758i	0.364133	+	0.800115i
$540$	0.489327	−	0.282513i	0.0210573	−	0.0121574i
$541$	1.08771	−	6.16868i	0.0467641	−	0.265212i	−0.952457	−	0.304673i	$-0.901453\pi$
$541$	1.08771	−	6.16868i	0.0467641	−	0.265212i	0.999221	+	0.0394605i	$0.0125639\pi$
$542$	17.5118	−	6.37378i	0.752197	−	0.273777i
$543$	−17.1042			−0.734010
$544$	−0.981052			−0.0420622
$545$	−8.90724	+	3.24197i	−0.381544	+	0.138871i
$546$	8.29876	−	1.05355i	0.355154	−	0.0450879i
$547$	19.8843	+	3.50615i	0.850193	+	0.149912i	0.581734	−	0.813379i	$-0.302375\pi$
$547$	19.8843	+	3.50615i	0.850193	+	0.149912i	0.268459	+	0.963291i	$0.413486\pi$
$548$	−3.40723	−	19.3234i	−0.145550	−	0.825453i
$549$	−1.92889	+	0.340116i	−0.0823232	+	0.0145158i
$550$	−11.8187	−	6.82352i	−0.503950	−	0.290956i
$551$	14.7861	−	22.6792i	0.629908	−	0.966165i
$552$		−	9.19090i		−	0.391191i
$553$	5.55373	−	13.2345i	0.236169	−	0.562790i
$554$	−4.61370	+	12.6760i	−0.196017	+	0.538554i
$555$	3.03751	−	1.10556i	0.128935	−	0.0469286i
$556$	−6.98443	+	19.1896i	−0.296206	+	0.813819i
$557$	1.21666	−	6.90005i	0.0515517	−	0.292364i	−0.948122	−	0.317907i	$-0.897020\pi$
$557$	1.21666	−	6.90005i	0.0515517	−	0.292364i	0.999674	+	0.0255423i	$0.00813124\pi$
$558$		−	4.58001i		−	0.193887i
$559$	6.27117	+	10.8620i	0.265242	+	0.459413i
$560$	0.442935	+	1.42779i	0.0187174	+	0.0603352i
$561$	1.83858	−	2.19113i	0.0776249	−	0.0925098i
$562$	11.4864	−	19.8950i	0.484524	−	0.839220i
$563$	19.0380	+	32.9748i	0.802356	+	1.38972i	0.918061	+	0.396438i	$0.129754\pi$
$563$	19.0380	+	32.9748i	0.802356	+	1.38972i	−0.115705	+	0.993284i	$0.536913\pi$
$564$	4.36792	+	0.770182i	0.183923	+	0.0324305i
$565$	−1.14123	+	0.957602i	−0.0480117	+	0.0402866i
$566$	−1.37697	+	7.80916i	−0.0578782	+	0.328243i
$567$	−2.10644	+	1.60091i	−0.0884621	+	0.0672320i
$568$	−0.727634	+	0.610557i	−0.0305308	+	0.0256184i
$569$	23.4235	−	13.5236i	0.981964	−	0.566937i	0.0791017	−	0.996867i	$-0.474795\pi$
$569$	23.4235	−	13.5236i	0.981964	−	0.566937i	0.902863	+	0.429929i	$0.141461\pi$
$570$	−0.966403	+	2.26537i	−0.0404781	+	0.0948858i
$571$	12.0865	−	20.9344i	0.505803	−	0.876077i	−0.494174	−	0.869363i	$-0.664529\pi$
$571$	12.0865	−	20.9344i	0.505803	−	0.876077i	0.999977	−	0.00671409i	$-0.00213718\pi$
$572$	−8.66254	−	3.15291i	−0.362199	−	0.131830i
$573$	12.5451	+	4.56604i	0.524079	+	0.190749i
$574$	2.72731	+	8.79140i	0.113836	+	0.366946i
$575$	7.47039	+	42.3667i	0.311537	+	1.76681i
$576$	−0.766044	−	0.642788i	−0.0319185	−	0.0267828i
$577$	−7.54115	+	4.35388i	−0.313942	+	0.181255i	−0.648689	−	0.761053i	$-0.724682\pi$
$577$	−7.54115	+	4.35388i	−0.313942	+	0.181255i	0.334747	+	0.942308i	$0.391349\pi$
$578$		−	16.0375i		−	0.667074i
$579$	−24.6536	−	4.34710i	−1.02457	−	0.180659i
$580$	2.68837	+	2.25581i	0.111629	+	0.0936674i
$581$	−26.3656	+	13.5705i	−1.09383	+	0.563001i
$582$	−4.63585	−	2.67651i	−0.192162	−	0.110945i
$583$	−2.87263	+	3.42347i	−0.118972	+	0.141786i
$584$	−8.90068	−	3.23958i	−0.368313	−	0.134055i
$585$	−1.14834	+	1.36854i	−0.0474782	+	0.0565823i
$586$	23.1668	−	4.08493i	0.957012	−	0.168747i
$587$	21.8680	+	26.0612i	0.902588	+	1.07566i	0.996786	+	0.0801090i	$0.0255268\pi$
$587$	21.8680	+	26.0612i	0.902588	+	1.07566i	−0.0941982	+	0.995553i	$0.530029\pi$
$588$	−2.89955	−	6.37123i	−0.119576	−	0.262745i
$589$	11.9858	+	15.9654i	0.493867	+	0.657842i
$590$	1.95134	+	3.37982i	0.0803353	+	0.139145i
$591$	−2.46732	−	13.9929i	−0.101492	−	0.575590i
$592$	−3.67732	−	4.38246i	−0.151137	−	0.180118i
$593$	−1.43791	−	3.95064i	−0.0590480	−	0.162233i	0.906661	−	0.421860i	$-0.138623\pi$
$593$	−1.43791	−	3.95064i	−0.0590480	−	0.162233i	−0.965709	+	0.259627i	$0.916400\pi$
$594$	2.87127	−	0.506283i	0.117810	−	0.0207730i
$595$	1.40074	−	0.434542i	0.0574246	−	0.0178145i
$596$	−2.96947	+	5.14328i	−0.121634	+	0.210677i
$597$	1.02565	+	0.592162i	0.0419773	+	0.0242356i
$598$	9.93908	+	27.3074i	0.406439	+	1.11668i
$599$	9.47612	+	26.0354i	0.387184	+	1.06378i	0.968263	+	0.249932i	$0.0804083\pi$
$599$	9.47612	+	26.0354i	0.387184	+	1.06378i	−0.581079	+	0.813847i	$0.697369\pi$
$600$	4.05365	+	2.34037i	0.165489	+	0.0955453i
$601$	−2.93215	+	5.07863i	−0.119605	+	0.207162i	−0.919611	−	0.392830i	$-0.871496\pi$
$601$	−2.93215	+	5.07863i	−0.119605	+	0.207162i	0.800006	+	0.599992i	$0.204829\pi$
$602$	7.12615	−	7.70502i	0.290440	−	0.314033i
$603$	0.919346	−	0.162106i	0.0374387	−	0.00660145i
$604$	3.67016	+	10.0837i	0.149337	+	0.410300i
$605$	−0.907783	−	1.08185i	−0.0369066	−	0.0439836i
$606$	−1.14103	−	6.47111i	−0.0463512	−	0.262871i
$607$	21.1122	+	36.5674i	0.856919	+	1.48423i	0.874854	+	0.484387i	$0.160957\pi$
$607$	21.1122	+	36.5674i	0.856919	+	1.48423i	−0.0179352	+	0.999839i	$0.505709\pi$
$608$	4.35251	+	0.235954i	0.176518	+	0.00956919i
$609$	−13.8185	−	8.89340i	−0.559953	−	0.360379i
$610$	0.711365	+	0.847771i	0.0288023	+	0.0343253i
$611$	−13.8106	+	2.43517i	−0.558715	+	0.0985166i
$612$	−0.630608	+	0.751529i	−0.0254908	+	0.0303788i
$613$	−13.0658	−	4.75558i	−0.527724	−	0.192076i	0.0643976	−	0.997924i	$-0.479487\pi$
$613$	−13.0658	−	4.75558i	−0.527724	−	0.192076i	−0.592122	+	0.805848i	$0.701710\pi$
$614$	−10.9756	+	13.0802i	−0.442940	+	0.527876i
$615$	−1.70239	−	0.982878i	−0.0686472	−	0.0396335i
$616$	−0.372093	+	7.70489i	−0.0149920	+	0.310439i
$617$	−22.5331	−	18.9075i	−0.907150	−	0.761189i	0.0644247	−	0.997923i	$-0.479479\pi$
$617$	−22.5331	−	18.9075i	−0.907150	−	0.761189i	−0.971575	+	0.236733i	$0.923923\pi$
$618$	6.42945	+	1.13368i	0.258630	+	0.0456035i
$619$		−	3.31673i		−	0.133311i	−0.997776	−	0.0666554i	$-0.978767\pi$
$619$		−	3.31673i		−	0.133311i	0.997776	−	0.0666554i	$-0.0212328\pi$
$620$	−2.24112	+	1.29391i	−0.0900055	+	0.0519647i
$621$	−7.04064	−	5.90780i	−0.282531	−	0.237072i
$622$	2.22027	+	12.5918i	0.0890248	+	0.504885i
$623$	11.0108	−	3.41580i	0.441137	−	0.136851i
$624$	2.97113	+	1.08140i	0.118940	+	0.0432908i
$625$	−19.0881	−	6.94749i	−0.763523	−	0.277900i
$626$	−12.3346	+	21.3641i	−0.492989	+	0.853882i
$627$	−8.68399	+	9.27893i	−0.346805	+	0.370565i
$628$	−7.42243	+	4.28534i	−0.296187	+	0.171004i
$629$	−4.29942	+	3.60764i	−0.171429	+	0.143846i
$630$	1.37846	+	0.578458i	0.0549193	+	0.0230463i
$631$	−4.39430	+	24.9213i	−0.174934	+	0.992101i	0.763286	+	0.646061i	$0.223585\pi$
$631$	−4.39430	+	24.9213i	−0.174934	+	0.992101i	−0.938220	+	0.346040i	$0.887526\pi$
$632$	4.15562	−	3.48698i	0.165301	−	0.138704i
$633$	−11.8244	−	2.08497i	−0.469979	−	0.0828700i
$634$	−0.631617	−	1.09399i	−0.0250847	−	0.0434480i
$635$	4.45760	−	7.72079i	0.176894	−	0.306390i
$636$	0.985273	−	1.17420i	0.0390686	−	0.0465602i
$637$	15.5048	+	15.7942i	0.614324	+	0.625788i
$638$	9.05441	+	15.6827i	0.358468	+	0.620884i
$639$			0.949858i			0.0375758i
$640$	−0.0981157	+	0.556442i	−0.00387836	+	0.0219953i
$641$	2.36806	−	6.50619i	0.0935328	−	0.256979i	−0.884100	−	0.467297i	$-0.845228\pi$
$641$	2.36806	−	6.50619i	0.0935328	−	0.256979i	0.977633	+	0.210318i	$0.0674500\pi$
$642$	10.1366	−	3.68942i	0.400060	−	0.145610i
$643$	−9.21261	+	25.3114i	−0.363310	+	0.998186i	0.614541	+	0.788885i	$0.289341\pi$
$643$	−9.21261	+	25.3114i	−0.363310	+	0.998186i	−0.977851	+	0.209301i	$0.932881\pi$
$644$	19.3601	−	14.7138i	0.762893	−	0.579806i
$645$			2.24135i			0.0882532i
$646$	0.231483	−	4.27003i	0.00910757	−	0.168002i
$647$	8.64227	+	4.98961i	0.339763	+	0.196162i	0.660167	−	0.751119i	$-0.270485\pi$
$647$	8.64227	+	4.98961i	0.339763	+	0.196162i	−0.320404	+	0.947281i	$0.603819\pi$
$648$	−0.984808	+	0.173648i	−0.0386869	+	0.00682154i
$649$	3.49694	+	19.8321i	0.137267	+	0.778478i
$650$	−14.5748	−	2.56993i	−0.571671	−	0.100801i
$651$	9.64750	−	7.33219i	0.378115	−	0.287371i
$652$	15.7085	−	5.71741i	0.615191	−	0.223911i
$653$	36.0845			1.41210			0.706048	−	0.708164i	$-0.250476\pi$
$653$	36.0845			1.41210			0.706048	+	0.708164i	$0.250476\pi$
$654$	16.7760			0.655995
$655$	−8.91931	+	3.24636i	−0.348506	+	0.126846i
$656$	−0.604132	+	3.42620i	−0.0235874	+	0.133771i
$657$	−8.20291	+	4.73595i	−0.320026	+	0.184767i
$658$	5.37032	+	10.4338i	0.209357	+	0.406750i
$659$	−13.2928	−	36.5217i	−0.517815	−	1.42269i	−0.872922	−	0.487860i	$-0.837778\pi$
$659$	−13.2928	−	36.5217i	−0.517815	−	1.42269i	0.355107	−	0.934826i	$-0.384444\pi$
$660$	−1.05891	−	1.26196i	−0.0412180	−	0.0491217i
$661$	−1.79140	−	1.50316i	−0.0696772	−	0.0584661i	0.607284	−	0.794485i	$-0.292259\pi$
$661$	−1.79140	−	1.50316i	−0.0696772	−	0.0584661i	−0.676961	+	0.736019i	$0.736703\pi$
$662$	19.4639	−	16.3322i	0.756487	−	0.634768i
$663$	1.06091	−	2.91483i	0.0412024	−	0.113203i
$664$	−11.2078			−0.434948
$665$	−6.31898	+	1.59099i	−0.245040	+	0.0616958i
$666$	−5.72089			−0.221680
$667$	19.5244	−	53.6427i	0.755986	−	2.07706i
$668$	−3.84808	+	3.22893i	−0.148887	+	0.124931i
$669$	−10.9424	−	9.18178i	−0.423058	−	0.354988i
$670$	−0.339050	−	0.404064i	−0.0130986	−	0.0156103i
$671$	1.95313	+	5.36619i	0.0753998	+	0.207159i
$672$	0.127623	−	2.64267i	0.00492315	−	0.101943i
$673$	−0.0138190	+	0.00797841i	−0.000532683	+	0.000307545i	−0.500266	−	0.865872i	$-0.666765\pi$
$673$	−0.0138190	+	0.00797841i	−0.000532683	+	0.000307545i	0.499734	+	0.866179i	$0.333431\pi$
$674$	−5.58150	+	31.6542i	−0.214991	+	1.21928i
$675$	4.39846	−	1.60091i	0.169297	−	0.0616190i
$676$	3.00294			0.115498
$677$	−28.9658			−1.11325			−0.556624	−	0.830765i	$-0.687903\pi$
$677$	−28.9658			−1.11325			−0.556624	+	0.830765i	$0.687903\pi$
$678$	2.47762	−	0.901781i	0.0951525	−	0.0346327i
$679$	−1.78369	−	14.0500i	−0.0684517	−	0.539190i
$680$	0.545898	+	0.0962565i	0.0209342	+	0.00369127i
$681$	1.46815	+	8.32628i	0.0562595	+	0.319064i
$682$	−13.1505	+	2.31878i	−0.503557	+	0.0887907i
$683$	3.82913	+	2.21075i	0.146517	+	0.0845919i	0.571467	−	0.820625i	$-0.306375\pi$
$683$	3.82913	+	2.21075i	0.146517	+	0.0845919i	−0.424949	+	0.905217i	$0.639708\pi$
$684$	2.97849	−	3.18255i	0.113885	−	0.121688i
$685$			11.0866i			0.423598i
$686$	8.77868	−	16.3075i	0.335171	−	0.622624i
$687$	−4.87696	+	13.3993i	−0.186067	+	0.511216i
$688$	3.72759	−	1.35673i	0.142113	−	0.0517249i
$689$	−1.65759	+	4.55419i	−0.0631491	+	0.173501i
$690$	−0.901771	+	5.11420i	−0.0343299	+	0.194694i
$691$			35.6702i			1.35696i	0.734620	+	0.678479i	$0.237361\pi$
$691$			35.6702i			1.35696i	−0.734620	+	0.678479i	$0.762639\pi$
$692$	−7.59983	−	13.1633i	−0.288902	−	0.500393i
$693$	5.66311	+	5.23765i	0.215124	+	0.198962i
$694$	9.28297	−	11.0630i	0.352377	−	0.419946i
$695$	5.76922	−	9.99259i	0.218839	−	0.379040i
$696$	−3.10554	−	5.37895i	−0.117715	−	0.203889i
$697$	3.36128	+	0.592685i	0.127318	+	0.0224495i
$698$	−7.88275	+	6.61441i	−0.298366	+	0.250359i
$699$	2.51664	−	14.2726i	0.0951880	−	0.539838i
$700$	1.55968	+	12.2855i	0.0589503	+	0.464348i
$701$	−9.12772	+	7.65907i	−0.344749	+	0.289279i	−0.798678	−	0.601759i	$-0.794467\pi$
$701$	−9.12772	+	7.65907i	−0.344749	+	0.289279i	0.453928	+	0.891038i	$0.350022\pi$
$702$	2.73821	−	1.58091i	0.103347	−	0.0596675i
$703$	19.9424	−	14.9715i	0.752141	−	0.564661i
$704$	−1.45778	+	2.52496i	−0.0549423	+	0.0951629i
$705$	−2.35493	−	0.857123i	−0.0886917	−	0.0322811i
$706$	32.8814	+	11.9678i	1.23751	+	0.450416i
$707$	11.8043	−	12.7632i	0.443946	−	0.480009i
$708$	−1.19940	−	6.80214i	−0.0450763	−	0.255640i
$709$	−33.3609	−	27.9931i	−1.25289	−	1.05130i	−0.996402	−	0.0847567i	$-0.972989\pi$
$709$	−33.3609	−	27.9931i	−1.25289	−	1.05130i	−0.256492	−	0.966546i	$-0.582567\pi$
$710$	0.464791	−	0.268347i	0.0174433	−	0.0100709i
$711$		−	5.42477i		−	0.203445i
$712$	4.29114	+	0.756643i	0.160817	+	0.0283564i
$713$	32.2462	+	27.0578i	1.20763	+	1.01332i
$714$	−2.59260	−	0.125204i	−0.0970255	−	0.00468566i
$715$	4.51085	+	2.60434i	0.168696	+	0.0973968i
$716$	−7.52450	+	8.96735i	−0.281204	+	0.335126i
$717$	−10.2258	−	3.72188i	−0.381889	−	0.138996i
$718$	−12.2367	+	14.5831i	−0.456670	+	0.544238i
$719$	4.75106	−	0.837741i	0.177185	−	0.0312425i	−0.0843517	−	0.996436i	$-0.526882\pi$
$719$	4.75106	−	0.837741i	0.177185	−	0.0312425i	0.261537	+	0.965194i	$0.415771\pi$
$720$	0.363191	+	0.432835i	0.0135353	+	0.0161308i
$721$	7.90494	+	15.3582i	0.294395	+	0.571968i
$722$	−2.05398	+	18.8887i	−0.0764413	+	0.702963i
$723$	11.0311	+	19.1064i	0.410251	+	0.710576i
$724$	−2.97011	−	16.8443i	−0.110383	−	0.626014i
$725$	18.6874	+	22.2708i	0.694034	+	0.827117i
$726$	0.854866	+	2.34873i	0.0317271	+	0.0871694i
$727$	−19.8277	+	3.49615i	−0.735368	+	0.129665i	−0.528775	−	0.848762i	$-0.677349\pi$
$727$	−19.8277	+	3.49615i	−0.735368	+	0.129665i	−0.206593	+	0.978427i	$0.566237\pi$
$728$	2.47861	+	7.98974i	0.0918634	+	0.296119i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	4.63485	+	2.67593i	0.171544	+	0.0990408i
$731$	−1.33102	−	3.65696i	−0.0492297	−	0.135257i
$732$	−0.669898	−	1.84053i	−0.0247601	−	0.0680279i
$733$	9.03820	+	5.21821i	0.333834	+	0.192739i	0.657542	−	0.753418i	$-0.271596\pi$
$733$	9.03820	+	5.21821i	0.333834	+	0.192739i	−0.323708	+	0.946157i	$0.604930\pi$
$734$	−9.24149	+	16.0067i	−0.341110	+	0.590819i
$735$	0.988314	+	3.82971i	0.0364545	+	0.141261i
$736$	9.05127	−	1.59598i	0.333634	−	0.0588287i
$737$	−0.930899	−	2.55762i	−0.0342901	−	0.0942113i
$738$	2.23629	+	2.66511i	0.0823191	+	0.0981041i
$739$	8.46533	+	48.0093i	0.311402	+	1.76605i	0.591721	+	0.806143i	$0.298449\pi$
$739$	8.46533	+	48.0093i	0.311402	+	1.76605i	−0.280318	+	0.959907i	$0.590440\pi$
$740$	1.61623	+	2.79939i	0.0594136	+	0.102907i
$741$	−5.40787	+	12.6767i	−0.198663	+	0.465691i
$742$	4.05072	+	0.195622i	0.148707	+	0.00718150i
$743$	−11.9629	−	14.2568i	−0.438876	−	0.523032i	0.500585	−	0.865687i	$-0.333118\pi$
$743$	−11.9629	−	14.2568i	−0.438876	−	0.523032i	−0.939461	+	0.342655i	$0.888674\pi$
$744$	4.51043	−	0.795310i	0.165360	−	0.0291575i
$745$	2.15697	−	2.57058i	0.0790254	−	0.0941788i
$746$	−25.5040	−	9.28270i	−0.933768	−	0.339864i
$747$	−7.20424	+	8.58568i	−0.263590	+	0.314134i
$748$	2.47711	+	1.43016i	0.0905722	+	0.0522919i
$749$	23.9994	+	15.4457i	0.876918	+	0.564374i
$750$	−4.19016	−	3.51596i	−0.153003	−	0.128385i
$751$	−38.3989	−	6.77076i	−1.40119	−	0.247068i	−0.578561	−	0.815639i	$-0.696385\pi$
$751$	−38.3989	−	6.77076i	−1.40119	−	0.247068i	−0.822634	+	0.568571i	$0.807496\pi$
$752$			4.43530i			0.161739i
$753$	26.2676	−	15.1656i	0.957244	−	0.552665i
$754$	15.0438	+	12.6232i	0.547862	+	0.459711i
$755$	−1.05286	−	5.97109i	−0.0383176	−	0.217310i
$756$	−1.94237	−	1.79644i	−0.0706433	−	0.0653359i
$757$	−17.5666	−	6.39373i	−0.638470	−	0.232384i	0.00244358	−	0.999997i	$-0.499222\pi$
$757$	−17.5666	−	6.39373i	−0.638470	−	0.232384i	−0.640914	+	0.767613i	$0.721444\pi$
$758$	17.5434	+	6.38527i	0.637205	+	0.231924i
$759$	−13.3984	+	23.2066i	−0.486329	+	0.842347i
$760$	−2.39877	−	0.558344i	−0.0870124	−	0.0202533i
$761$	−40.1251	+	23.1662i	−1.45453	+	0.839776i	−0.998734	−	0.0503066i	$-0.983980\pi$
$761$	−40.1251	+	23.1662i	−1.45453	+	0.839776i	−0.455800	+	0.890082i	$0.650647\pi$
$762$	−12.0870	+	10.1422i	−0.437864	+	0.367412i
$763$	26.8569	+	35.3377i	0.972287	+	1.27931i
$764$	−2.31824	+	13.1474i	−0.0838710	+	0.475656i
$765$	0.424633	−	0.356310i	0.0153526	−	0.0128824i
$766$	−15.6541	−	2.76023i	−0.565604	−	0.0997313i
$767$	10.9194	+	18.9130i	0.394278	+	0.682910i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	3.65134	−	4.35150i	0.131671	−	0.156919i	−0.696180	−	0.717867i	$-0.745119\pi$
$769$	3.65134	−	4.35150i	0.131671	−	0.156919i	0.827851	+	0.560948i	$0.189563\pi$
$770$	0.963018	−	4.25081i	0.0347048	−	0.153189i
$771$	−4.63380	−	8.02597i	−0.166882	−	0.289048i
$772$		−	25.0339i		−	0.900992i
$773$	−3.83186	+	21.7316i	−0.137823	+	0.781631i	0.835030	+	0.550205i	$0.185450\pi$
$773$	−3.83186	+	21.7316i	−0.137823	+	0.781631i	−0.972852	+	0.231426i	$0.925661\pi$
$774$	1.35673	−	3.72759i	0.0487667	−	0.133985i
$775$	−20.1450	+	7.33218i	−0.723630	+	0.263380i
$776$	1.83084	−	5.03020i	0.0657234	−	0.180574i
$777$	−9.15865	−	12.0507i	−0.328565	−	0.432317i
$778$		−	32.3197i		−	1.15872i
$779$	−14.7700	−	3.43791i	−0.529191	−	0.123176i
$780$	−1.54716	−	0.893253i	−0.0553972	−	0.0319836i
$781$	2.72730	−	0.480897i	0.0975906	−	0.0172079i
$782$	−1.56574	−	8.87976i	−0.0559908	−	0.317540i
$783$	−6.11672	−	1.07854i	−0.218594	−	0.0385440i
$784$	5.77094	−	3.96185i	0.206105	−	0.141495i
$785$	4.55061	−	1.65629i	0.162418	−	0.0591154i
$786$	16.7988			0.599192
$787$	−6.18366			−0.220424			−0.110212	−	0.993908i	$-0.535153\pi$
$787$	−6.18366			−0.220424			−0.110212	+	0.993908i	$0.535153\pi$
$788$	13.3518	−	4.85967i	0.475640	−	0.173119i
$789$	0.0742920	−	0.421331i	0.00264486	−	0.0149998i
$790$	−2.65448	+	1.53257i	−0.0944423	+	0.0545263i
$791$	5.86600	+	3.77529i	0.208571	+	0.134234i
$792$	0.997183	+	2.73974i	0.0354334	+	0.0973523i
$793$	3.98071	+	4.74402i	0.141359	+	0.168465i
$794$	7.07526	+	5.93685i	0.251091	+	0.210691i
$795$	−0.663455	+	0.556705i	−0.0235303	+	0.0197443i
$796$	−0.405063	+	1.11290i	−0.0143571	+	0.0394457i
$797$	23.2661			0.824126			0.412063	−	0.911155i	$-0.364808\pi$
$797$	23.2661			0.824126			0.412063	+	0.911155i	$0.364808\pi$
$798$	11.4721	+	1.17903i	0.406109	+	0.0417371i
$799$	4.35126			0.153937
$800$	−1.60091	+	4.39846i	−0.0566007	+	0.155509i
$801$	3.33791	−	2.80084i	0.117939	−	0.0989628i
$802$	−21.9136	−	18.3877i	−0.773795	−	0.649291i
$803$	17.7512	+	21.1551i	0.626427	+	0.746546i
$804$	0.319286	+	0.877230i	0.0112603	+	0.0309375i
$805$	−12.2164	+	6.28786i	−0.430572	+	0.221618i
$806$	−12.5410	+	7.24057i	−0.441739	+	0.255038i
$807$	1.04235	−	5.91148i	0.0366926	−	0.208094i
$808$	6.17466	−	2.24739i	0.217224	−	0.0790630i
$809$	−40.4049			−1.42056			−0.710281	−	0.703918i	$-0.751432\pi$
$809$	−40.4049			−1.42056			−0.710281	+	0.703918i	$0.751432\pi$
$810$	0.565026			0.0198530
$811$	−20.3330	+	7.40060i	−0.713987	+	0.259870i	−0.673371	−	0.739305i	$-0.735154\pi$
$811$	−20.3330	+	7.40060i	−0.713987	+	0.259870i	−0.0406164	+	0.999175i	$0.512932\pi$
$812$	6.35873	−	15.1529i	0.223148	−	0.531761i
$813$	18.3526	+	3.23605i	0.643653	+	0.113493i
$814$	2.89639	+	16.4263i	0.101518	+	0.575740i
$815$	−9.30181	+	1.64016i	−0.325828	+	0.0574523i
$816$	−0.849616	−	0.490526i	−0.0297425	−	0.0171718i
$817$	5.02564	+	16.5445i	0.175825	+	0.578818i
$818$		−	21.3641i		−	0.746979i
$819$	7.71372	+	3.23698i	0.269539	+	0.113109i
$820$	0.672328	−	1.84721i	0.0234787	−	0.0645073i
$821$	24.4008	−	8.88116i	0.851593	−	0.309955i	0.120903	−	0.992664i	$-0.461421\pi$
$821$	24.4008	−	8.88116i	0.851593	−	0.309955i	0.730690	+	0.682710i	$0.239199\pi$
$822$	6.71093	−	18.4381i	0.234071	−	0.643104i
$823$	8.00978	−	45.4257i	0.279203	−	1.58344i	−0.446082	−	0.894992i	$-0.647181\pi$
$823$	8.00978	−	45.4257i	0.279203	−	1.58344i	0.725285	−	0.688449i	$-0.241708\pi$
$824$			6.52863i			0.227436i
$825$	−6.82352	−	11.8187i	−0.237564	−	0.411474i
$826$	12.4082	−	13.4161i	0.431735	−	0.466806i
$827$	−28.4863	+	33.9486i	−0.990566	+	1.18051i	−0.00699691	+	0.999976i	$0.502227\pi$
$827$	−28.4863	+	33.9486i	−0.990566	+	1.18051i	−0.983569	+	0.180535i	$0.942217\pi$
$828$	4.59545	−	7.95955i	0.159703	−	0.276614i
$829$	6.60774	+	11.4449i	0.229496	+	0.397499i	0.957659	−	0.287905i	$-0.0929588\pi$
$829$	6.60774	+	11.4449i	0.229496	+	0.397499i	−0.728163	+	0.685404i	$0.759625\pi$
$830$	6.23649	+	1.09966i	0.216472	+	0.0381698i
$831$	−10.3336	+	8.67093i	−0.358469	+	0.300791i
$832$	−0.549043	+	3.11378i	−0.0190346	+	0.107951i
$833$	−3.88678	−	5.66159i	−0.134669	−	0.196162i
$834$	−15.6435	+	13.1264i	−0.541689	+	0.454531i
$835$	2.45804	−	1.41915i	0.0850641	−	0.0491118i
$836$	−10.6459	−	6.94079i	−0.368197	−	0.240052i
$837$	2.29000	−	3.96640i	0.0791541	−	0.137099i
$838$	20.9390	+	7.62118i	0.723326	+	0.263269i
$839$	18.7782	+	6.83471i	0.648296	+	0.235960i	0.645175	−	0.764035i	$-0.276784\pi$
$839$	18.7782	+	6.83471i	0.648296	+	0.235960i	0.00312057	+	0.999995i	$0.499007\pi$
$840$	−0.330302	+	1.45797i	−0.0113965	+	0.0503048i
$841$	−1.66312	−	9.43200i	−0.0573488	−	0.325241i
$842$	16.5101	+	13.8536i	0.568975	+	0.477426i
$843$	19.8950	−	11.4864i	0.685220	−	0.395612i
$844$		−	12.0068i		−	0.413293i
$845$	−1.67096	−	0.294635i	−0.0574828	−	0.0101358i
$846$	3.39764	+	2.85096i	0.116813	+	0.0980180i
$847$	−3.57888	+	5.56083i	−0.122972	+	0.191072i
$848$	1.32745	+	0.766406i	0.0455850	+	0.0263185i
$849$	−5.09707	+	6.07445i	−0.174931	+	0.208475i
$850$	4.31512	+	1.57057i	0.148007	+	0.0538703i
$851$	33.7979	−	40.2787i	1.15858	−	1.38074i
$852$	−0.935428	+	0.164941i	−0.0320472	+	0.00565079i
$853$	31.3222	+	37.3283i	1.07245	+	1.27810i	0.958648	+	0.284594i	$0.0918588\pi$
$853$	31.3222	+	37.3283i	1.07245	+	1.27810i	0.113803	+	0.993503i	$0.463697\pi$
$854$	2.80451	−	4.35762i	0.0959684	−	0.149115i
$855$	−1.96961	+	1.47866i	−0.0673593	+	0.0505693i
$856$	5.39358	+	9.34195i	0.184349	+	0.319301i
$857$	−5.43305	−	30.8123i	−0.185589	−	1.05253i	−0.925196	−	0.379490i	$-0.876099\pi$
$857$	−5.43305	−	30.8123i	−0.185589	−	1.05253i	0.739606	−	0.673040i	$-0.235012\pi$
$858$	−5.92553	−	7.06177i	−0.202294	−	0.241085i
$859$	−17.0600	−	46.8719i	−0.582078	−	1.59925i	−0.784622	−	0.619974i	$-0.787143\pi$
$859$	−17.0600	−	46.8719i	−0.582078	−	1.59925i	0.202544	−	0.979273i	$-0.435079\pi$
$860$	−2.20730	+	0.389207i	−0.0752684	+	0.0132718i
$861$	−2.03378	+	8.97723i	−0.0693111	+	0.305943i
$862$	1.47197	−	2.54954i	0.0501357	−	0.0868375i
$863$	−39.9040	−	23.0386i	−1.35835	−	0.784243i	−0.368947	−	0.929450i	$-0.620282\pi$
$863$	−39.9040	−	23.0386i	−1.35835	−	0.784243i	−0.989401	+	0.145207i	$0.953615\pi$
$864$	−0.342020	−	0.939693i	−0.0116358	−	0.0319690i
$865$	2.93734	+	8.07026i	0.0998724	+	0.274397i
$866$	2.76004	+	1.59351i	0.0937901	+	0.0541497i
$867$	8.01877	−	13.8889i	0.272332	−	0.471692i
$868$	8.89607	+	8.22772i	0.301952	+	0.279267i
$869$	−15.5760	+	2.74647i	−0.528380	+	0.0931676i
$870$	1.20029	+	3.29777i	0.0406937	+	0.111805i
$871$	−1.89728	−	2.26109i	−0.0642869	−	0.0766141i
$872$	2.91313	+	16.5212i	0.0986509	+	0.559477i
$873$	−2.67651	−	4.63585i	−0.0905862	−	0.156900i
$874$	4.81085	+	39.7723i	0.162729	+	1.34532i
$875$	0.698079	−	14.4551i	0.0235994	−	0.488670i
$876$	−6.08842	−	7.25590i	−0.205709	−	0.245154i
$877$	36.8558	−	6.49866i	1.24453	−	0.219444i	0.487674	−	0.873026i	$-0.337845\pi$
$877$	36.8558	−	6.49866i	1.24453	−	0.219444i	0.756856	+	0.653581i	$0.226734\pi$
$878$	−3.63891	+	4.33668i	−0.122807	+	0.146356i
$879$	22.1055	+	8.04575i	0.745601	+	0.271376i
$880$	1.05891	−	1.26196i	0.0356958	−	0.0425406i
$881$	−23.2703	−	13.4351i	−0.783995	−	0.452640i	0.0538494	−	0.998549i	$-0.482851\pi$
$881$	−23.2703	−	13.4351i	−0.783995	−	0.452640i	−0.837844	+	0.545910i	$0.816184\pi$
$882$	0.674530	−	6.96742i	0.0227126	−	0.234605i
$883$	−0.937138	−	0.786352i	−0.0315372	−	0.0264629i	0.626883	−	0.779114i	$-0.284330\pi$
$883$	−0.937138	−	0.786352i	−0.0315372	−	0.0264629i	−0.658420	+	0.752651i	$0.728775\pi$
$884$	3.05478	+	0.538640i	0.102743	+	0.0181164i
$885$			3.90267i			0.131187i
$886$	4.62001	−	2.66737i	0.155212	−	0.0896119i
$887$	−38.3603	−	32.1881i	−1.28801	−	1.08077i	−0.992086	−	0.125558i	$-0.959928\pi$
$887$	−38.3603	−	32.1881i	−1.28801	−	1.08077i	−0.295925	−	0.955211i	$-0.595628\pi$
$888$	−0.993423	−	5.63398i	−0.0333371	−	0.189064i
$889$	−40.7140	−	9.22372i	−1.36550	−	0.309354i
$890$	−2.31353	−	0.842055i	−0.0775496	−	0.0282258i
$891$	2.73974	+	0.997183i	0.0917847	+	0.0334069i
$892$	7.14216	−	12.3706i	0.239137	−	0.414198i
$893$	−19.3047	−	1.04653i	−0.646007	−	0.0350207i
$894$	−5.14328	+	2.96947i	−0.172017	+	0.0993140i
$895$	5.06678	−	4.25154i	0.169364	−	0.142113i
$896$	2.62468	−	0.333211i	0.0876846	−	0.0111318i
$897$	−5.04620	+	28.6184i	−0.168488	+	0.955541i
$898$	18.3495	−	15.3971i	0.612331	−	0.513807i
$899$	28.0146	+	4.93973i	0.934340	+	0.164749i
$900$	2.34037	+	4.05365i	0.0780124	+	0.135122i
$901$	0.751884	−	1.30230i	0.0250489	−	0.0433860i
$902$	6.52007	−	7.77032i	0.217095	−	0.258723i
$903$	10.0239	−	3.10967i	0.333576	−	0.103483i
$904$	1.31832	+	2.28339i	0.0438465	+	0.0759444i
$905$			9.66430i			0.321252i
$906$	−1.86339	+	10.5678i	−0.0619070	+	0.351092i
$907$	−9.09920	+	24.9998i	−0.302134	+	0.830106i	0.691995	+	0.721902i	$0.256732\pi$
$907$	−9.09920	+	24.9998i	−0.302134	+	0.830106i	−0.994129	+	0.108204i	$0.965490\pi$
$908$	−7.94484	+	2.89169i	−0.263659	+	0.0959639i
$909$	2.24739	−	6.17466i	0.0745413	−	0.204801i
$910$	−0.595284	−	4.68901i	−0.0197335	−	0.155439i
$911$		−	2.86345i		−	0.0948702i	−0.998874	−	0.0474351i	$-0.984895\pi$
$911$		−	2.86345i		−	0.0948702i	0.998874	−	0.0474351i	$-0.0151047\pi$
$912$	3.65141	+	2.38060i	0.120910	+	0.0788294i
$913$	28.2992	+	16.3386i	0.936568	+	0.540728i
$914$	−9.77124	+	1.72293i	−0.323204	+	0.0569896i
$915$	0.192174	+	1.08987i	0.00635308	+	0.0360301i
$916$	−14.0426	−	2.47610i	−0.463982	−	0.0818125i
$917$	26.8933	+	35.3855i	0.888096	+	1.16853i
$918$	−0.921887	+	0.335539i	−0.0304268	+	0.0110745i
$919$	42.5421			1.40334			0.701668	−	0.712504i	$-0.252439\pi$
$919$	42.5421			1.40334			0.701668	+	0.712504i	$0.252439\pi$
$920$	−5.19309			−0.171211
$921$	−16.0453	+	5.84001i	−0.528710	+	0.192435i
$922$	5.29002	−	30.0012i	0.174217	−	0.988036i
$923$	2.60091	−	1.50164i	0.0856101	−	0.0494270i
$924$	−4.17469	+	6.48658i	−0.137337	+	0.213393i
$925$	9.15863	+	25.1631i	0.301134	+	0.827359i
$926$	−3.00598	−	3.58239i	−0.0987828	−	0.117725i
$927$	5.00122	+	4.19652i	0.164262	+	0.137832i
$928$	4.75796	−	3.99240i	0.156188	−	0.131057i
$929$	15.0157	−	41.2553i	0.492649	−	1.35354i	−0.405598	−	0.914052i	$-0.632937\pi$
$929$	15.0157	−	41.2553i	0.492649	−	1.35354i	0.898247	−	0.439491i	$-0.144841\pi$
$930$	−2.58782			−0.0848580
$931$	15.8823	+	26.0529i	0.520522	+	0.853848i
$932$	14.4927			0.474726
$933$	−4.37308	+	12.0149i	−0.143168	+	0.393352i
$934$	13.2868	−	11.1490i	0.434757	−	0.364805i
$935$	−1.23805	−	1.03884i	−0.0404885	−	0.0339739i
$936$	2.03237	+	2.42209i	0.0664302	+	0.0791685i
$937$	0.824297	+	2.26474i	0.0269286	+	0.0739857i	0.952428	−	0.304762i	$-0.0985770\pi$
$937$	0.824297	+	2.26474i	0.0269286	+	0.0739857i	−0.925500	+	0.378748i	$0.876355\pi$
$938$	−1.33668	+	2.07692i	−0.0436442	+	0.0678140i
$939$	−21.3641	+	12.3346i	−0.697192	+	0.402524i
$940$	0.435173	−	2.46799i	0.0141938	−	0.0804969i
$941$	−20.1755	+	7.34328i	−0.657703	+	0.239384i	−0.649244	−	0.760580i	$-0.724915\pi$
$941$	−20.1755	+	7.34328i	−0.657703	+	0.239384i	−0.00845841	+	0.999964i	$0.502692\pi$
$942$	−8.57069			−0.279248
$943$	−31.9757			−1.04127
$944$	6.49053	−	2.36236i	0.211249	−	0.0768882i
$945$	0.904556	+	1.19019i	0.0294252	+	0.0387169i
$946$	−11.3898	−	2.00833i	−0.370315	−	0.0652965i
$947$	−8.60358	−	48.7933i	−0.279579	−	1.58557i	−0.724031	−	0.689767i	$-0.757713\pi$
$947$	−8.60358	−	48.7933i	−0.279579	−	1.58557i	0.444452	−	0.895802i	$-0.353398\pi$
$948$	5.34236	−	0.942002i	0.173512	−	0.0305948i
$949$	25.9361	+	14.9742i	0.841920	+	0.486083i
$950$	−18.7666	−	8.00581i	−0.608869	−	0.259743i
$951$		−	1.26323i		−	0.0409631i
$952$	−0.326897	−	2.57495i	−0.0105948	−	0.0834546i
$953$	−1.34779	+	3.70301i	−0.0436590	+	0.119952i	−0.959606	−	0.281347i	$-0.909219\pi$
$953$	−1.34779	+	3.70301i	−0.0436590	+	0.119952i	0.915947	+	0.401299i	$0.131441\pi$
$954$	1.44037	−	0.524253i	0.0466338	−	0.0169733i
$955$	2.57993	−	7.08830i	0.0834846	−	0.229372i
$956$	1.88965	−	10.7167i	0.0611156	−	0.346604i
$957$			18.1088i			0.585375i
$958$	8.58063	+	14.8621i	0.277227	+	0.480172i
$959$	49.5824	−	15.3817i	1.60110	−	0.496700i
$960$	−0.363191	+	0.432835i	−0.0117220	+	0.0139697i
$961$	5.01176	−	8.68063i	0.161670	−	0.280020i
$962$	9.04420	+	15.6650i	0.291597	+	0.505060i
$963$	10.6233	+	1.87317i	0.342330	+	0.0603621i
$964$	−16.9006	+	14.1813i	−0.544333	+	0.456750i
$965$	−2.45622	+	13.9299i	−0.0790686	+	0.448420i
$966$	24.1232	−	3.06251i	0.776152	−	0.0985347i
$967$	13.1227	−	11.0112i	0.421997	−	0.354097i	−0.406925	−	0.913461i	$-0.633399\pi$
$967$	13.1227	−	11.0112i	0.421997	−	0.354097i	0.828922	+	0.559364i	$0.188955\pi$
$968$	−2.16460	+	1.24973i	−0.0695728	+	0.0401679i
$969$	2.33549	−	3.58222i	0.0750267	−	0.115077i
$970$	−1.51230	+	2.61938i	−0.0485570	+	0.0841031i
$971$	57.0335	+	20.7585i	1.83029	+	0.666171i	0.992809	+	0.119705i	$0.0381950\pi$
$971$	57.0335	+	20.7585i	1.83029	+	0.666171i	0.837481	+	0.546466i	$0.184027\pi$
$972$	−0.939693	−	0.342020i	−0.0301407	−	0.0109703i
$973$	−52.6938	−	11.9377i	−1.68929	−	0.382707i
$974$	−2.44140	−	13.8459i	−0.0782276	−	0.443651i
$975$	−11.3372	−	9.51303i	−0.363080	−	0.304661i
$976$	1.69624	−	0.979325i	0.0542953	−	0.0313474i
$977$		−	14.7206i		−	0.470952i	−0.971880	−	0.235476i	$-0.924335\pi$
$977$		−	14.7206i		−	0.470952i	0.971880	−	0.235476i	$-0.0756649\pi$
$978$	16.4626	+	2.90281i	0.526417	+	0.0928215i
$979$	−9.73191	−	8.16604i	−0.311033	−	0.260988i
$980$	−3.59991	+	1.63832i	−0.114995	+	0.0523343i
$981$	14.5285	+	8.38802i	0.463858	+	0.267809i
$982$	2.44189	−	2.91013i	0.0779239	−	0.0928661i
$983$	6.16675	+	2.24451i	0.196689	+	0.0715889i	0.438486	−	0.898738i	$-0.355515\pi$
$983$	6.16675	+	2.24451i	0.196689	+	0.0715889i	−0.241798	+	0.970327i	$0.577737\pi$
$984$	−2.23629	+	2.66511i	−0.0712905	+	0.0849607i
$985$	−7.90633	+	1.39410i	−0.251917	+	0.0444197i
$986$	−3.91675	−	4.66781i	−0.124735	−	0.148653i
$987$	−0.566045	+	11.7211i	−0.0180174	+	0.373085i
$988$	−13.4232	−	3.12442i	−0.427049	−	0.0994011i
$989$	18.2293	+	31.5741i	0.579658	+	1.00400i
$990$	−0.286063	−	1.62234i	−0.00909168	−	0.0515615i
$991$	−16.8959	−	20.1357i	−0.536715	−	0.639633i	0.427733	−	0.903905i	$-0.359313\pi$
$991$	−16.8959	−	20.1357i	−0.536715	−	0.639633i	−0.964448	+	0.264273i	$0.914868\pi$
$992$	1.56646	+	4.30380i	0.0497350	+	0.136646i
$993$	25.0224	−	4.41212i	0.794060	−	0.140014i
$994$	−1.84498	−	1.70636i	−0.0585191	−	0.0541226i
$995$	0.334587	−	0.579521i	0.0106071	−	0.0183721i
$996$	−9.70625	−	5.60391i	−0.307554	−	0.177567i
$997$	5.06455	+	13.9147i	0.160396	+	0.440684i	0.993692	−	0.112142i	$-0.0357713\pi$
$997$	5.06455	+	13.9147i	0.160396	+	0.440684i	−0.833296	+	0.552827i	$0.813549\pi$
$998$	−7.31180	−	20.0890i	−0.231451	−	0.635906i
$999$	−4.95444	−	2.86045i	−0.156752	−	0.0905005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.cj.b.241.4	yes	84
7.5	odd	6		798.2.ca.b.355.11	✓	84
19.3	odd	18		798.2.ca.b.535.11	yes	84
133.117	even	18	inner	798.2.cj.b.649.4	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.ca.b.355.11	✓	84	7.5	odd	6
798.2.ca.b.535.11	yes	84	19.3	odd	18
798.2.cj.b.241.4	yes	84	1.1	even	1	trivial
798.2.cj.b.649.4	yes	84	133.117	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.cj (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.342020 + 0.939693i) q^{2} +(-0.766044 + 0.642788i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.363191 + 0.432835i) q^{5} +(-0.342020 - 0.939693i) q^{6} +(1.43186 - 2.22481i) q^{7} +(0.866025 - 0.500000i) q^{8} +(0.173648 - 0.984808i) q^{9} +(-0.530950 + 0.193250i) q^{10} -2.91557 q^{11} +1.00000 q^{12} +(-2.97113 + 1.08140i) q^{13} +(1.60091 + 2.10644i) q^{14} +(-0.556442 - 0.0981157i) q^{15} +(0.173648 + 0.984808i) q^{16} +(0.966147 - 0.170358i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-4.32736 + 0.523436i) q^{19} -0.565026i q^{20} +(0.333211 + 2.62468i) q^{21} +(0.997183 - 2.73974i) q^{22} +(-8.63662 + 3.14347i) q^{23} +(-0.342020 + 0.939693i) q^{24} +(0.812803 - 4.60964i) q^{25} -3.16181i q^{26} +(0.500000 + 0.866025i) q^{27} +(-2.52695 + 0.783921i) q^{28} +(-3.99240 + 4.75796i) q^{29} +(0.282513 - 0.489327i) q^{30} +(-2.29000 - 3.96640i) q^{31} +(-0.984808 - 0.173648i) q^{32} +(2.23345 - 1.87409i) q^{33} +(-0.170358 + 0.966147i) q^{34} +(1.48301 - 0.188273i) q^{35} +(-0.766044 + 0.642788i) q^{36} +(-4.95444 + 2.86045i) q^{37} +(0.988174 - 4.24541i) q^{38} +(1.58091 - 2.73821i) q^{39} +(0.530950 + 0.193250i) q^{40} +(3.26924 + 1.18991i) q^{41} +(-2.58036 - 0.584579i) q^{42} +(-0.688830 - 3.90655i) q^{43} +(2.23345 + 1.87409i) q^{44} +(0.489327 - 0.282513i) q^{45} -9.19090i q^{46} +(4.36792 + 0.770182i) q^{47} +(-0.766044 - 0.642788i) q^{48} +(-2.89955 - 6.37123i) q^{49} +(4.05365 + 2.34037i) q^{50} +(-0.630608 + 0.751529i) q^{51} +(2.97113 + 1.08140i) q^{52} +(0.985273 - 1.17420i) q^{53} +(-0.984808 + 0.173648i) q^{54} +(-1.05891 - 1.26196i) q^{55} +(0.127623 - 2.64267i) q^{56} +(2.97849 - 3.18255i) q^{57} +(-3.10554 - 5.37895i) q^{58} +(-1.19940 - 6.80214i) q^{59} +(0.363191 + 0.432835i) q^{60} +(-0.669898 - 1.84053i) q^{61} +(4.51043 - 0.795310i) q^{62} +(-1.94237 - 1.79644i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-1.54716 - 0.893253i) q^{65} +(0.997183 + 2.73974i) q^{66} +(0.319286 + 0.877230i) q^{67} +(-0.849616 - 0.490526i) q^{68} +(4.59545 - 7.95955i) q^{69} +(-0.330302 + 1.45797i) q^{70} +(-0.935428 + 0.164941i) q^{71} +(-0.342020 - 0.939693i) q^{72} +(-6.08842 - 7.25590i) q^{73} +(-0.993423 - 5.63398i) q^{74} +(2.34037 + 4.05365i) q^{75} +(3.65141 + 2.38060i) q^{76} +(-4.17469 + 6.48658i) q^{77} +(2.03237 + 2.42209i) q^{78} +(5.34236 - 0.942002i) q^{79} +(-0.363191 + 0.432835i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(-2.23629 + 2.66511i) q^{82} +(-9.70625 - 5.60391i) q^{83} +(1.43186 - 2.22481i) q^{84} +(0.424633 + 0.356310i) q^{85} +(3.90655 + 0.688830i) q^{86} -6.21108i q^{87} +(-2.52496 + 1.45778i) q^{88} +(3.33791 + 2.80084i) q^{89} +(0.0981157 + 0.556442i) q^{90} +(-1.84833 + 8.15862i) q^{91} +(8.63662 + 3.14347i) q^{92} +(4.30380 + 1.56646i) q^{93} +(-2.21765 + 3.84109i) q^{94} +(-1.79822 - 1.68292i) q^{95} +(0.866025 - 0.500000i) q^{96} +(4.10065 - 3.44086i) q^{97} +(6.97870 - 0.545599i) q^{98} +(-0.506283 + 2.87127i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 12 q^{7} - 12 q^{10} - 12 q^{11} + 84 q^{12} + 24 q^{13} + 6 q^{14} + 6 q^{19} - 6 q^{21} + 12 q^{22} - 42 q^{23} - 30 q^{25} + 42 q^{27} + 6 q^{28} + 6 q^{31} + 12 q^{33} - 30 q^{34} - 42 q^{35}+ \cdots + 6 q^{99}+O(q^{100}) \) 84 * q + 12 * q^7 - 12 * q^10 - 12 * q^11 + 84 * q^12 + 24 * q^13 + 6 * q^14 + 6 * q^19 - 6 * q^21 + 12 * q^22 - 42 * q^23 - 30 * q^25 + 42 * q^27 + 6 * q^28 + 6 * q^31 + 12 * q^33 - 30 * q^34 - 42 * q^35 - 18 * q^37 + 12 * q^38 + 12 * q^40 + 36 * q^41 + 18 * q^42 + 12 * q^43 + 12 * q^44 - 18 * q^45 + 18 * q^47 - 24 * q^49 + 18 * q^51 - 24 * q^52 + 60 * q^53 - 30 * q^55 - 18 * q^56 + 6 * q^57 + 48 * q^59 - 12 * q^62 - 6 * q^63 + 42 * q^64 + 108 * q^65 + 12 * q^66 + 42 * q^67 + 6 * q^69 + 18 * q^70 + 42 * q^71 - 48 * q^73 - 18 * q^74 - 48 * q^75 + 18 * q^76 - 96 * q^77 - 12 * q^78 - 60 * q^79 - 6 * q^82 + 54 * q^83 + 12 * q^84 - 24 * q^85 - 12 * q^86 - 24 * q^89 + 6 * q^90 + 24 * q^91 + 42 * q^92 - 36 * q^93 + 18 * q^94 - 12 * q^95 - 78 * q^97 + 24 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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