LMFDB - Embedded newform 205.2.y.a.112.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [205,2,Mod(7,205)] 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("205.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(205, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([10, 39])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 205 = 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	205.y (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.63693324144$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$19$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			112.19
Character	$\chi$	$=$	205.112
Dual form			205.2.y.a.108.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.11806 + 1.53886i) q^{2} +(0.102214 + 0.246766i) q^{3} +(1.50004 + 4.61666i) q^{4} +(-1.53067 - 1.63004i) q^{5} +(-0.163243 + 0.679956i) q^{6} +(-0.625128 + 1.02012i) q^{7} +(-2.30916 + 7.10685i) q^{8} +(2.07087 - 2.07087i) q^{9} +(-0.733648 - 5.80801i) q^{10} +(0.564490 - 0.660933i) q^{11} +(-0.985909 + 0.842046i) q^{12} +(-0.501278 + 2.08797i) q^{13} +(-2.89387 + 1.19868i) q^{14} +(0.245783 - 0.544331i) q^{15} +(-7.97302 + 5.79274i) q^{16} +(-3.44696 - 2.94398i) q^{17} +(7.57301 - 1.19945i) q^{18} +(2.84759 - 4.64685i) q^{19} +(5.22928 - 9.51173i) q^{20} +(-0.315627 - 0.0499904i) q^{21} +(2.21270 - 0.531223i) q^{22} +(-1.24990 - 7.89153i) q^{23} +(-1.98975 + 0.156597i) q^{24} +(-0.314078 + 4.99013i) q^{25} +(-4.27483 + 3.65105i) q^{26} +(1.46299 + 0.605990i) q^{27} +(-5.64725 - 1.35579i) q^{28} +(-0.635029 + 8.06881i) q^{29} +(1.35823 - 0.774698i) q^{30} +(0.866563 + 0.281563i) q^{31} -10.8563 q^{32} +(0.220794 + 0.0717404i) q^{33} +(-2.77048 - 11.5399i) q^{34} +(2.61970 - 0.542480i) q^{35} +(12.6669 + 6.45412i) q^{36} +(-0.682139 + 1.33877i) q^{37} +(13.1822 - 5.46025i) q^{38} +(-0.566478 + 0.0897213i) q^{39} +(15.1190 - 7.11424i) q^{40} +(-6.40037 + 0.187746i) q^{41} +(-0.591587 - 0.591587i) q^{42} +(-2.09219 + 2.87965i) q^{43} +(3.89806 + 1.61463i) q^{44} +(-6.54545 - 0.205781i) q^{45} +(9.49659 - 18.6381i) q^{46} +(-8.83625 + 5.41486i) q^{47} +(-2.24440 - 1.37537i) q^{48} +(2.52808 + 4.96164i) q^{49} +(-8.34433 + 10.0860i) q^{50} +(0.374147 - 1.15151i) q^{51} +(-10.3914 + 0.817822i) q^{52} +(4.44471 + 5.20409i) q^{53} +(2.16616 + 3.53486i) q^{54} +(-1.94140 + 0.0915296i) q^{55} +(-5.80630 - 6.79830i) q^{56} +(1.43775 + 0.227717i) q^{57} +(-13.7618 + 16.1130i) q^{58} +(2.60497 - 3.58544i) q^{59} +(2.88167 + 0.318177i) q^{60} +(1.87536 - 11.8406i) q^{61} +(1.40214 + 1.92988i) q^{62} +(0.817972 + 3.40710i) q^{63} +(-7.04828 - 5.12087i) q^{64} +(4.17078 - 2.37890i) q^{65} +(0.357256 + 0.491721i) q^{66} +(-8.05987 - 0.634326i) q^{67} +(8.42076 - 20.3295i) q^{68} +(1.81960 - 1.11505i) q^{69} +(6.38347 + 2.88235i) q^{70} +(0.211223 + 0.180401i) q^{71} +(9.93542 + 19.4994i) q^{72} +6.74336i q^{73} +(-3.50499 + 1.78588i) q^{74} +(-1.26350 + 0.432556i) q^{75} +(25.7244 + 6.17589i) q^{76} +(0.321350 + 0.989014i) q^{77} +(-1.33790 - 0.681695i) q^{78} +(-3.34625 + 8.07856i) q^{79} +(21.6465 + 4.12957i) q^{80} -8.36302i q^{81} +(-13.8453 - 9.45160i) q^{82} +(6.09303 - 6.09303i) q^{83} +(-0.242665 - 1.53213i) q^{84} +(0.477353 + 10.1250i) q^{85} +(-8.86275 + 2.87968i) q^{86} +(-2.05602 + 0.668040i) q^{87} +(3.39366 + 5.53794i) q^{88} +(10.0355 - 2.40931i) q^{89} +(-13.5470 - 10.5084i) q^{90} +(-1.81661 - 1.81661i) q^{91} +(34.5576 - 17.6080i) q^{92} +(0.0190944 + 0.242618i) q^{93} +(-27.0484 - 2.12875i) q^{94} +(-11.9333 + 2.47111i) q^{95} +(-1.10967 - 2.67897i) q^{96} +(-0.685758 + 8.71338i) q^{97} +(-2.28064 + 14.3994i) q^{98} +(-0.199721 - 2.53770i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q - 16 q^{2} - 16 q^{3} - 68 q^{4} - 16 q^{5} - 32 q^{6} - 16 q^{7} - 8 q^{8} - 8 q^{9} - 12 q^{10} - 32 q^{11} + 20 q^{12} - 4 q^{13} - 16 q^{14} + 16 q^{15} - 76 q^{16} - 16 q^{17} + 28 q^{18} - 40 q^{20}+ \cdots - 72 q^{99}+O(q^{100}) $ 304 * q - 16 * q^2 - 16 * q^3 - 68 * q^4 - 16 * q^5 - 32 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^9 - 12 * q^10 - 32 * q^11 + 20 * q^12 - 4 * q^13 - 16 * q^14 + 16 * q^15 - 76 * q^16 - 16 * q^17 + 28 * q^18 - 40 * q^20 - 40 * q^21 - 40 * q^22 - 20 * q^23 + 40 * q^24 - 20 * q^25 - 24 * q^26 - 76 * q^27 - 4 * q^28 + 76 * q^29 - 8 * q^30 - 40 * q^31 + 48 * q^32 - 120 * q^33 + 16 * q^34 - 80 * q^35 - 24 * q^36 + 24 * q^37 - 20 * q^38 - 16 * q^39 + 56 * q^40 - 32 * q^41 + 176 * q^42 + 20 * q^43 + 16 * q^44 - 32 * q^46 + 40 * q^47 + 76 * q^48 - 8 * q^49 - 8 * q^50 - 24 * q^51 - 80 * q^52 - 16 * q^53 + 40 * q^54 + 48 * q^55 + 24 * q^56 + 12 * q^57 + 20 * q^58 - 40 * q^59 + 120 * q^60 + 4 * q^61 - 20 * q^62 + 108 * q^63 - 68 * q^64 - 92 * q^65 - 40 * q^66 + 8 * q^67 + 76 * q^68 + 32 * q^69 + 48 * q^70 - 40 * q^71 - 220 * q^72 + 144 * q^74 + 44 * q^75 - 48 * q^76 + 72 * q^77 - 212 * q^78 + 232 * q^80 - 72 * q^82 - 112 * q^83 - 256 * q^84 + 116 * q^85 - 40 * q^86 - 20 * q^87 + 92 * q^88 - 80 * q^89 + 212 * q^90 - 72 * q^91 + 20 * q^92 + 96 * q^93 - 40 * q^94 - 36 * q^95 - 8 * q^96 - 136 * q^97 - 12 * q^98 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/205\mathbb{Z}\right)^\times$.

$n$	$6$	$42$
$\chi(n)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	2.11806	+	1.53886i	1.49769	+	1.08814i	0.971289	+	0.237901i	$0.0764594\pi$
$2$	2.11806	+	1.53886i	1.49769	+	1.08814i	0.526402	+	0.850236i	$0.323541\pi$
$3$	0.102214	+	0.246766i	0.0590131	+	0.142470i	0.950636	−	0.310309i	$-0.100433\pi$
$3$	0.102214	+	0.246766i	0.0590131	+	0.142470i	−0.891623	+	0.452779i	$0.850433\pi$
$4$	1.50004	+	4.61666i	0.750022	+	2.30833i
$5$	−1.53067	−	1.63004i	−0.684538	−	0.728977i
$5$	−1.53067	−	1.63004i	−0.684538	−	0.728977i
$6$	−0.163243	+	0.679956i	−0.0666437	+	0.277591i
$7$	−0.625128	+	1.02012i	−0.236276	+	0.385568i	−0.948698	−	0.316184i	$-0.897598\pi$
$7$	−0.625128	+	1.02012i	−0.236276	+	0.385568i	0.712422	+	0.701752i	$0.247598\pi$
$8$	−2.30916	+	7.10685i	−0.816410	+	2.51265i
$9$	2.07087	−	2.07087i	0.690292	−	0.690292i
$10$	−0.733648	−	5.80801i	−0.232000	−	1.83665i
$11$	0.564490	−	0.660933i	0.170200	−	0.199279i	−0.668750	−	0.743488i	$-0.733170\pi$
$11$	0.564490	−	0.660933i	0.170200	−	0.199279i	0.838950	+	0.544209i	$0.183170\pi$
$12$	−0.985909	+	0.842046i	−0.284607	+	0.243078i
$13$	−0.501278	+	2.08797i	−0.139030	+	0.579100i	0.858744	+	0.512405i	$0.171245\pi$
$13$	−0.501278	+	2.08797i	−0.139030	+	0.579100i	−0.997773	+	0.0666948i	$0.978755\pi$
$14$	−2.89387	+	1.19868i	−0.773420	+	0.320361i
$15$	0.245783	−	0.544331i	0.0634609	−	0.140546i
$16$	−7.97302	+	5.79274i	−1.99325	+	1.44818i
$17$	−3.44696	−	2.94398i	−0.836010	−	0.714020i	0.124514	−	0.992218i	$-0.460263\pi$
$17$	−3.44696	−	2.94398i	−0.836010	−	0.714020i	−0.960524	+	0.278198i	$0.910263\pi$
$18$	7.57301	−	1.19945i	1.78498	−	0.282712i
$19$	2.84759	−	4.64685i	0.653283	−	1.06606i	−0.338847	−	0.940842i	$-0.610037\pi$
$19$	2.84759	−	4.64685i	0.653283	−	1.06606i	0.992129	−	0.125219i	$-0.0399633\pi$
$20$	5.22928	−	9.51173i	1.16930	−	2.12689i
$21$	−0.315627	−	0.0499904i	−0.0688754	−	0.0109088i
$22$	2.21270	−	0.531223i	0.471750	−	0.113257i
$23$	−1.24990	−	7.89153i	−0.260621	−	1.64550i	−0.676765	−	0.736199i	$-0.736619\pi$
$23$	−1.24990	−	7.89153i	−0.260621	−	1.64550i	0.416144	−	0.909299i	$-0.363381\pi$
$24$	−1.98975	+	0.156597i	−0.406157	+	0.0319653i
$25$	−0.314078	+	4.99013i	−0.0628156	+	0.998025i
$26$	−4.27483	+	3.65105i	−0.838363	+	0.716030i
$27$	1.46299	+	0.605990i	0.281553	+	0.116623i
$28$	−5.64725	−	1.35579i	−1.06723	−	0.256219i
$29$	−0.635029	+	8.06881i	−0.117922	+	1.49834i	0.598753	+	0.800934i	$0.295663\pi$
$29$	−0.635029	+	8.06881i	−0.117922	+	1.49834i	−0.716675	+	0.697407i	$0.754337\pi$
$30$	1.35823	−	0.774698i	0.247978	−	0.141440i
$31$	0.866563	+	0.281563i	0.155639	+	0.0505703i	0.385800	−	0.922582i	$-0.373925\pi$
$31$	0.866563	+	0.281563i	0.155639	+	0.0505703i	−0.230161	+	0.973153i	$0.573925\pi$
$32$	−10.8563			−1.91915
$33$	0.220794	+	0.0717404i	0.0384354	+	0.0124884i
$34$	−2.77048	−	11.5399i	−0.475134	−	1.97907i
$35$	2.61970	−	0.542480i	0.442810	−	0.0916958i
$36$	12.6669	+	6.45412i	2.11115	+	1.07569i
$37$	−0.682139	+	1.33877i	−0.112143	+	0.220093i	−0.940256	−	0.340468i	$-0.889414\pi$
$37$	−0.682139	+	1.33877i	−0.112143	+	0.220093i	0.828113	+	0.560561i	$0.189414\pi$
$38$	13.1822	−	5.46025i	2.13844	−	0.885769i
$39$	−0.566478	+	0.0897213i	−0.0907091	+	0.0143669i
$40$	15.1190	−	7.11424i	2.39053	−	1.12486i
$41$	−6.40037	+	0.187746i	−0.999570	+	0.0293210i
$41$	−6.40037	+	0.187746i	−0.999570	+	0.0293210i
$42$	−0.591587	−	0.591587i	−0.0912838	−	0.0912838i
$43$	−2.09219	+	2.87965i	−0.319056	+	0.439143i	−0.938179	−	0.346151i	$-0.887488\pi$
$43$	−2.09219	+	2.87965i	−0.319056	+	0.439143i	0.619123	+	0.785294i	$0.287488\pi$
$44$	3.89806	+	1.61463i	0.587655	+	0.243415i
$45$	−6.54545	−	0.205781i	−0.975738	−	0.0306761i
$46$	9.49659	−	18.6381i	1.40020	−	2.74804i
$47$	−8.83625	+	5.41486i	−1.28890	+	0.789839i	−0.986566	−	0.163363i	$-0.947766\pi$
$47$	−8.83625	+	5.41486i	−1.28890	+	0.789839i	−0.302334	+	0.953202i	$0.597766\pi$
$48$	−2.24440	−	1.37537i	−0.323951	−	0.198518i
$49$	2.52808	+	4.96164i	0.361154	+	0.708805i
$50$	−8.34433	+	10.0860i	−1.18007	+	1.42638i
$51$	0.374147	−	1.15151i	0.0523911	−	0.161243i
$52$	−10.3914	+	0.817822i	−1.44103	+	0.113411i
$53$	4.44471	+	5.20409i	0.610528	+	0.714837i	0.976434	−	0.215815i	$-0.0692408\pi$
$53$	4.44471	+	5.20409i	0.610528	+	0.714837i	−0.365906	+	0.930652i	$0.619241\pi$
$54$	2.16616	+	3.53486i	0.294777	+	0.481033i
$55$	−1.94140	+	0.0915296i	−0.261778	+	0.0123418i
$56$	−5.80630	−	6.79830i	−0.775899	−	0.908461i
$57$	1.43775	+	0.227717i	0.190434	+	0.0301618i
$58$	−13.7618	+	16.1130i	−1.80701	+	2.11574i
$59$	2.60497	−	3.58544i	0.339139	−	0.466784i	−0.605051	−	0.796187i	$-0.706847\pi$
$59$	2.60497	−	3.58544i	0.339139	−	0.466784i	0.944190	+	0.329402i	$0.106847\pi$
$60$	2.88167	+	0.318177i	0.372023	+	0.0410764i
$61$	1.87536	−	11.8406i	0.240115	−	1.51603i	−0.513144	−	0.858303i	$-0.671519\pi$
$61$	1.87536	−	11.8406i	0.240115	−	1.51603i	0.753259	−	0.657724i	$-0.228481\pi$
$62$	1.40214	+	1.92988i	0.178072	+	0.245096i
$63$	0.817972	+	3.40710i	0.103055	+	0.429254i
$64$	−7.04828	−	5.12087i	−0.881034	−	0.640109i
$65$	4.17078	−	2.37890i	0.517322	−	0.295066i
$66$	0.357256	+	0.491721i	0.0439752	+	0.0605267i
$67$	−8.05987	−	0.634326i	−0.984670	−	0.0774952i	−0.424111	−	0.905610i	$-0.639413\pi$
$67$	−8.05987	−	0.634326i	−0.984670	−	0.0774952i	−0.560558	+	0.828115i	$0.689413\pi$
$68$	8.42076	−	20.3295i	1.02117	−	2.46532i
$69$	1.81960	−	1.11505i	0.219055	−	0.134237i
$70$	6.38347	+	2.88235i	0.762971	+	0.344506i
$71$	0.211223	+	0.180401i	0.0250676	+	0.0214097i	0.661894	−	0.749598i	$-0.269753\pi$
$71$	0.211223	+	0.180401i	0.0250676	+	0.0214097i	−0.636826	+	0.771008i	$0.719753\pi$
$72$	9.93542	+	19.4994i	1.17090	+	2.29802i
$73$			6.74336i			0.789251i	0.918842	+	0.394626i	$0.129126\pi$
$73$			6.74336i			0.789251i	−0.918842	+	0.394626i	$0.870874\pi$
$74$	−3.50499	+	1.78588i	−0.407447	+	0.207605i
$75$	−1.26350	+	0.432556i	−0.145896	+	0.0499472i
$76$	25.7244	+	6.17589i	2.95080	+	0.708423i
$77$	0.321350	+	0.989014i	0.0366212	+	0.112709i
$78$	−1.33790	−	0.681695i	−0.151487	−	0.0771867i
$79$	−3.34625	+	8.07856i	−0.376483	+	0.908909i	0.616137	+	0.787639i	$0.288697\pi$
$79$	−3.34625	+	8.07856i	−0.376483	+	0.908909i	−0.992620	+	0.121270i	$0.961303\pi$
$80$	21.6465	+	4.12957i	2.42015	+	0.461700i
$81$		−	8.36302i		−	0.929224i
$82$	−13.8453	−	9.45160i	−1.52895	−	1.04376i
$83$	6.09303	−	6.09303i	0.668797	−	0.668797i	−0.288640	−	0.957438i	$-0.593203\pi$
$83$	6.09303	−	6.09303i	0.668797	−	0.668797i	0.957438	+	0.288640i	$0.0932032\pi$
$84$	−0.242665	−	1.53213i	−0.0264770	−	0.167169i
$85$	0.477353	+	10.1250i	0.0517762	+	1.09821i
$86$	−8.86275	+	2.87968i	−0.955695	+	0.310524i
$87$	−2.05602	+	0.668040i	−0.220428	+	0.0716214i
$88$	3.39366	+	5.53794i	0.361765	+	0.590347i
$89$	10.0355	−	2.40931i	1.06376	−	0.255387i	0.336456	−	0.941699i	$-0.390772\pi$
$89$	10.0355	−	2.40931i	1.06376	−	0.255387i	0.727307	+	0.686313i	$0.240772\pi$
$90$	−13.5470	−	10.5084i	−1.42797	−	1.10768i
$91$	−1.81661	−	1.81661i	−0.190433	−	0.190433i
$92$	34.5576	−	17.6080i	3.60288	−	1.83576i
$93$	0.0190944	+	0.242618i	0.00198000	+	0.0251583i
$94$	−27.0484	−	2.12875i	−2.78983	−	0.219564i
$95$	−11.9333	+	2.47111i	−1.22433	+	0.253531i
$96$	−1.10967	−	2.67897i	−0.113255	−	0.273421i
$97$	−0.685758	+	8.71338i	−0.0696282	+	0.884710i	0.858587	+	0.512667i	$0.171343\pi$
$97$	−0.685758	+	8.71338i	−0.0696282	+	0.884710i	−0.928216	+	0.372043i	$0.878657\pi$
$98$	−2.28064	+	14.3994i	−0.230379	+	1.45456i
$99$	−0.199721	−	2.53770i	−0.0200727	−	0.255048i
$100$	−23.5088	+	6.03541i	−2.35088	+	0.603541i
$101$	−13.0107	−	7.97298i	−1.29462	−	0.793341i	−0.307224	−	0.951637i	$-0.599400\pi$
$101$	−13.0107	−	7.97298i	−1.29462	−	0.793341i	−0.987392	+	0.158296i	$0.949400\pi$
$102$	2.56447	−	1.86319i	0.253920	−	0.184484i
$103$	−6.90444	+	5.01637i	−0.680315	+	0.494278i	−0.873462	−	0.486892i	$-0.838131\pi$
$103$	−6.90444	+	5.01637i	−0.680315	+	0.494278i	0.193147	+	0.981170i	$0.438131\pi$
$104$	−13.6814	−	8.38397i	−1.34157	−	0.822116i
$105$	0.401635	+	0.591004i	0.0391956	+	0.0576761i
$106$	1.40580	+	17.8623i	0.136543	+	1.73494i
$107$	2.40820	−	15.2048i	0.232810	−	1.46990i	−0.543424	−	0.839458i	$-0.682872\pi$
$107$	2.40820	−	15.2048i	0.232810	−	1.46990i	0.776234	−	0.630445i	$-0.217128\pi$
$108$	−0.603102	+	7.66314i	−0.0580335	+	0.737386i
$109$	−1.47316	−	3.55652i	−0.141103	−	0.340653i	0.837492	−	0.546450i	$-0.184021\pi$
$109$	−1.47316	−	3.55652i	−0.141103	−	0.340653i	−0.978595	+	0.205797i	$0.934021\pi$
$110$	−4.25284	−	2.79367i	−0.405493	−	0.266366i
$111$	−0.400087	−	0.0314876i	−0.0379746	−	0.00298867i
$112$	−0.925108	−	11.7546i	−0.0874145	−	1.11071i
$113$	0.565539	−	0.288156i	0.0532014	−	0.0271075i	−0.427187	−	0.904163i	$-0.640496\pi$
$113$	0.565539	−	0.288156i	0.0532014	−	0.0271075i	0.480389	+	0.877056i	$0.340496\pi$
$114$	2.69480	+	2.69480i	0.252392	+	0.252392i
$115$	−10.9504	+	14.1167i	−1.02113	+	1.31639i
$116$	−38.2035	+	9.17186i	−3.54711	+	0.851586i
$117$	3.28585	+	5.36202i	0.303777	+	0.495719i
$118$	11.0350	−	3.58548i	1.01585	−	0.330070i
$119$	5.15799	−	1.67593i	0.472832	−	0.153633i
$120$	3.30092	+	3.00369i	0.301332	+	0.274198i
$121$	1.60260	+	10.1184i	0.145691	+	0.919854i
$122$	22.1930	−	22.1930i	2.00926	−	2.00926i
$123$	−0.700535	−	1.56020i	−0.0631651	−	0.140679i
$124$			4.42298i			0.397196i
$125$	8.61487	−	7.12629i	0.770537	−	0.637395i
$126$	−3.51053	+	8.47516i	−0.312743	+	0.755028i
$127$	14.2731	+	7.27251i	1.26653	+	0.645331i	0.952632	−	0.304125i	$-0.0983640\pi$
$127$	14.2731	+	7.27251i	1.26653	+	0.645331i	0.313901	+	0.949456i	$0.398364\pi$
$128$	−0.338767	−	1.04262i	−0.0299431	−	0.0921553i
$129$	−0.924450	−	0.221941i	−0.0813933	−	0.0195408i
$130$	12.4947	+	1.37959i	1.09586	+	0.120998i
$131$	13.1260	−	6.68803i	1.14682	−	0.584336i	0.225927	−	0.974144i	$-0.427459\pi$
$131$	13.1260	−	6.68803i	1.14682	−	0.584336i	0.920896	+	0.389809i	$0.127459\pi$
$132$			1.12695i			0.0980881i
$133$	2.96022	+	5.80976i	0.256683	+	0.503770i
$134$	−16.0951	−	13.7465i	−1.39041	−	1.18752i
$135$	−1.25157	−	3.31231i	−0.107718	−	0.285078i
$136$	28.8820	−	17.6989i	2.47661	−	1.51767i
$137$	−5.12638	+	12.3762i	−0.437976	+	1.05737i	0.538671	+	0.842516i	$0.318927\pi$
$137$	−5.12638	+	12.3762i	−0.437976	+	1.05737i	−0.976647	+	0.214851i	$0.931073\pi$
$138$	5.56993	+	0.438363i	0.474144	+	0.0373160i
$139$	−7.77591	−	10.7026i	−0.659544	−	0.907785i	0.339922	−	0.940454i	$-0.389599\pi$
$139$	−7.77591	−	10.7026i	−0.659544	−	0.907785i	−0.999466	+	0.0326688i	$0.989599\pi$
$140$	6.43411	+	11.2805i	0.543782	+	0.953379i
$141$	−2.23939	−	1.62701i	−0.188591	−	0.137019i
$142$	0.169770	+	0.707142i	0.0142468	+	0.0593421i
$143$	1.09704	+	1.50995i	0.0917395	+	0.126269i
$144$	−4.51509	+	28.5072i	−0.376257	+	2.37560i
$145$	14.1245	−	11.3156i	1.17298	−	0.939709i
$146$	−10.3771	+	14.2828i	−0.858813	+	1.18205i
$147$	−0.965958	+	1.13099i	−0.0796709	+	0.0932826i
$148$	−7.20390	−	1.14099i	−0.592157	−	0.0937884i
$149$	8.36686	+	9.79634i	0.685440	+	0.802547i	0.988628	−	0.150384i	$-0.0480509\pi$
$149$	8.36686	+	9.79634i	0.685440	+	0.802547i	−0.303188	+	0.952931i	$0.598051\pi$
$150$	−3.34180	−	1.02816i	−0.272856	−	0.0839491i
$151$	0.148099	+	0.241675i	0.0120521	+	0.0196672i	0.858610	−	0.512630i	$-0.171329\pi$
$151$	0.148099	+	0.241675i	0.0120521	+	0.0196672i	−0.846557	+	0.532297i	$0.821329\pi$
$152$	26.4489	+	30.9677i	2.14529	+	2.51181i
$153$	−13.2348	+	1.04160i	−1.06997	+	0.0842086i
$154$	−0.841314	+	2.58930i	−0.0677950	+	0.208652i
$155$	−0.867465	−	1.84352i	−0.0696764	−	0.148075i
$156$	−1.26396	−	2.48065i	−0.101197	−	0.198611i
$157$	8.04151	+	4.92784i	0.641782	+	0.393285i	0.804974	−	0.593310i	$-0.202179\pi$
$157$	8.04151	+	4.92784i	0.641782	+	0.393285i	−0.163192	+	0.986594i	$0.552179\pi$
$158$	−19.5193	+	11.9614i	−1.55287	+	0.951601i
$159$	−0.829881	+	1.62873i	−0.0658138	+	0.129167i
$160$	16.6175	+	17.6963i	1.31373	+	1.39901i
$161$	8.83163	+	3.65818i	0.696030	+	0.288305i
$162$	12.8695	−	17.7133i	1.01112	−	1.39169i
$163$	−6.31206	−	6.31206i	−0.494399	−	0.494399i	0.415290	−	0.909689i	$-0.363680\pi$
$163$	−6.31206	−	6.31206i	−0.494399	−	0.494399i	−0.909689	+	0.415290i	$0.863680\pi$
$164$	−10.4676	−	29.2667i	−0.817382	−	2.28535i
$165$	−0.221024	−	0.469715i	−0.0172067	−	0.0365673i
$166$	22.2817	−	3.52907i	1.72939	−	0.273909i
$167$	−9.53862	+	3.95103i	−0.738121	+	0.305740i	−0.719884	−	0.694094i	$-0.755805\pi$
$167$	−9.53862	+	3.95103i	−0.738121	+	0.305740i	−0.0182364	+	0.999834i	$0.505805\pi$
$168$	1.08411	−	2.12768i	0.0836405	−	0.164154i
$169$	7.47473	+	3.80856i	0.574979	+	0.292966i
$170$	−14.5698	+	22.1798i	−1.11745	+	1.70111i
$171$	−3.72603	−	15.5201i	−0.284937	−	1.18685i
$172$	−16.4328	−	5.33932i	−1.25299	−	0.407120i
$173$	14.0496			1.06817			0.534085	−	0.845431i	$-0.320656\pi$
$173$	14.0496			1.06817			0.534085	+	0.845431i	$0.320656\pi$
$174$	−5.38278	−	1.74897i	−0.408067	−	0.132589i
$175$	−4.89417	−	3.43987i	−0.369965	−	0.260029i
$176$	−0.672079	+	8.53957i	−0.0506599	+	0.643695i
$177$	1.15103	+	0.276337i	0.0865166	+	0.0207708i
$178$	24.9634	+	10.3402i	1.87108	+	0.775028i
$179$	10.1249	−	8.64747i	0.756770	−	0.646343i	−0.184947	−	0.982748i	$-0.559211\pi$
$179$	10.1249	−	8.64747i	0.756770	−	0.646343i	0.941717	+	0.336406i	$0.109211\pi$
$180$	−8.86843	−	30.5268i	−0.661014	−	2.27533i
$181$	2.18062	−	0.171619i	0.162084	−	0.0127563i	0.00284271	−	0.999996i	$-0.499095\pi$
$181$	2.18062	−	0.171619i	0.162084	−	0.0127563i	0.159242	+	0.987240i	$0.449095\pi$
$182$	−1.05218	−	6.64320i	−0.0779928	−	0.492427i
$183$	3.11353	−	0.747493i	0.230159	−	0.0552562i
$184$	58.9701	+	9.33995i	4.34734	+	0.688550i
$185$	3.22639	−	0.937309i	0.237209	−	0.0689123i
$186$	−0.332911	+	0.543262i	−0.0244102	+	0.0398339i
$187$	−3.89155	+	0.616360i	−0.284578	+	0.0450727i
$188$	−38.2534	−	32.6714i	−2.78991	−	2.38281i
$189$	−1.53274	+	1.11360i	−0.111490	+	0.0810024i
$190$	−29.0781	−	13.1297i	−2.10955	−	0.952528i
$191$	4.36462	−	1.80789i	0.315813	−	0.130814i	−0.219146	−	0.975692i	$-0.570327\pi$
$191$	4.36462	−	1.80789i	0.315813	−	0.130814i	0.534959	+	0.844878i	$0.320327\pi$
$192$	0.543225	−	2.26270i	0.0392039	−	0.163296i
$193$	17.1505	−	14.6479i	1.23452	−	1.05438i	0.237978	−	0.971271i	$-0.423516\pi$
$193$	17.1505	−	14.6479i	1.23452	−	1.05438i	0.996541	−	0.0831075i	$-0.0264845\pi$
$194$	−14.8611	+	17.4001i	−1.06697	+	1.24926i
$195$	1.01334	+	0.786050i	0.0725670	+	0.0562902i
$196$	−19.1140	+	19.1140i	−1.36528	+	1.36528i
$197$	−0.505006	+	1.55425i	−0.0359802	+	0.110736i	−0.967434	−	0.253125i	$-0.918542\pi$
$197$	−0.505006	+	1.55425i	−0.0359802	+	0.110736i	0.931453	+	0.363861i	$0.118542\pi$
$198$	3.48214	−	5.68233i	0.247465	−	0.403825i
$199$	−4.24594	+	17.6856i	−0.300987	+	1.25370i	0.592852	+	0.805311i	$0.298002\pi$
$199$	−4.24594	+	17.6856i	−0.300987	+	1.25370i	−0.893839	+	0.448388i	$0.851998\pi$
$200$	−34.7388	−	13.7551i	−2.45641	−	0.972631i
$201$	−0.667300	−	2.05374i	−0.0470677	−	0.144859i
$202$	−15.2882	−	36.9089i	−1.07567	−	2.59690i
$203$	−7.83416	−	5.69185i	−0.549850	−	0.399490i
$204$	5.87735			0.411497
$205$	10.1029	+	10.1455i	0.705618	+	0.708593i
$206$	−22.3435			−1.55674
$207$	−18.9307	−	13.7540i	−1.31578	−	0.955969i
$208$	−8.09839	−	19.5512i	−0.561522	−	1.35563i
$209$	−1.46382	−	4.50517i	−0.101254	−	0.311629i
$210$	−0.0587856	+	1.86984i	−0.00405659	+	0.129031i
$211$	6.66238	−	27.7508i	0.458657	−	1.91045i	0.0475251	−	0.998870i	$-0.484867\pi$
$211$	6.66238	−	27.7508i	0.458657	−	1.91045i	0.411132	−	0.911576i	$-0.365133\pi$
$212$	−17.3583	+	28.3261i	−1.19217	+	1.94544i
$213$	−0.0229270	+	0.0705621i	−0.00157093	+	0.00483484i
$214$	28.4987	−	28.4987i	1.94813	−	1.94813i
$215$	7.89641	−	0.997448i	0.538531	−	0.0680254i
$216$	−7.68495	+	8.99793i	−0.522895	+	0.612231i
$217$	−0.828941	+	0.707982i	−0.0562722	+	0.0480610i
$218$	2.35275	−	9.79990i	0.159348	−	0.663733i
$219$	−1.66403	+	0.689264i	−0.112445	+	0.0465762i
$220$	−3.33474	−	8.82548i	−0.224828	−	0.595014i
$221$	7.87484	−	5.72140i	0.529719	−	0.384863i
$222$	−0.798953	−	0.682370i	−0.0536222	−	0.0457977i
$223$	3.17996	−	0.503656i	0.212946	−	0.0337273i	−0.0490499	−	0.998796i	$-0.515619\pi$
$223$	3.17996	−	0.503656i	0.212946	−	0.0337273i	0.261996	+	0.965069i	$0.415619\pi$
$224$	6.78660	−	11.0747i	0.453449	−	0.739961i
$225$	9.68351	+	10.9843i	0.645567	+	0.732289i
$226$	1.64127	+	0.259952i	0.109176	+	0.0172918i
$227$	5.06934	−	1.21704i	0.336464	−	0.0807778i	−0.0616930	−	0.998095i	$-0.519650\pi$
$227$	5.06934	−	1.21704i	0.336464	−	0.0807778i	0.398157	+	0.917317i	$0.369650\pi$
$228$	1.10539	+	6.97917i	0.0732064	+	0.462207i
$229$	−9.31680	+	0.733248i	−0.615672	+	0.0484544i	−0.382461	−	0.923972i	$-0.624923\pi$
$229$	−9.31680	+	0.733248i	−0.615672	+	0.0484544i	−0.233211	+	0.972426i	$0.574923\pi$
$230$	−44.9171	+	13.0490i	−2.96175	+	0.860426i
$231$	−0.211208	+	0.180389i	−0.0138965	+	0.0118687i
$232$	−55.8775	−	23.1452i	−3.66854	−	1.51956i
$233$	−15.4948	−	3.71998i	−1.01510	−	0.243704i	−0.308430	−	0.951247i	$-0.599804\pi$
$233$	−15.4948	−	3.71998i	−1.01510	−	0.243704i	−0.706670	+	0.707543i	$0.749804\pi$
$234$	−1.29177	+	16.4135i	−0.0844457	+	1.07298i
$235$	22.3519	+	6.11508i	1.45808	+	0.398904i
$236$	20.4603	+	6.64796i	1.33185	+	0.432746i
$237$	−2.33555			−0.151710
$238$	13.5039	+	4.38770i	0.875330	+	0.284412i
$239$	−4.40752	−	18.3587i	−0.285099	−	1.18752i	−0.912582	−	0.408893i	$-0.865915\pi$
$239$	−4.40752	−	18.3587i	−0.285099	−	1.18752i	0.627483	−	0.778630i	$-0.284085\pi$
$240$	1.19353	+	5.76371i	0.0770422	+	0.372046i
$241$	2.00432	+	1.02125i	0.129109	+	0.0657845i	0.517352	−	0.855773i	$-0.326918\pi$
$241$	2.00432	+	1.02125i	0.129109	+	0.0657845i	−0.388243	+	0.921557i	$0.626918\pi$
$242$	−12.1764	+	23.8975i	−0.782727	+	1.53619i
$243$	6.45268	−	2.67279i	0.413940	−	0.171459i
$244$	57.4769	−	9.10345i	3.67958	−	0.582789i
$245$	4.21802	−	11.7155i	0.269479	−	0.748477i
$246$	0.917157	−	4.38262i	0.0584758	−	0.279426i
$247$	8.27507	+	8.27507i	0.526530	+	0.526530i
$248$	−4.00206	+	5.50836i	−0.254131	+	0.349781i
$249$	2.12634	+	0.880760i	0.134752	+	0.0558159i
$250$	29.2131	−	1.83683i	1.84760	−	0.116171i
$251$	−0.961088	+	1.88624i	−0.0606634	+	0.119059i	−0.919347	−	0.393447i	$-0.871283\pi$
$251$	−0.961088	+	1.88624i	−0.0606634	+	0.119059i	0.858684	+	0.512505i	$0.171283\pi$
$252$	−14.5024	+	8.88709i	−0.913566	+	0.559834i
$253$	−5.92133	−	3.62859i	−0.372271	−	0.228128i
$254$	19.0399	+	37.3679i	1.19467	+	2.34467i
$255$	−2.44970	+	1.15270i	−0.153406	+	0.0721851i
$256$	−4.49749	+	13.8419i	−0.281093	+	0.865116i
$257$	−8.13784	+	0.640462i	−0.507625	+	0.0399509i	−0.329686	−	0.944091i	$-0.606943\pi$
$257$	−8.13784	+	0.640462i	−0.507625	+	0.0399509i	−0.177939	+	0.984042i	$0.556943\pi$
$258$	−1.61650	−	1.89268i	−0.100639	−	0.117833i
$259$	−0.939281	−	1.53277i	−0.0583641	−	0.0952415i
$260$	17.2389	+	15.6866i	1.06911	+	0.972843i
$261$	15.3944	+	18.0246i	0.952892	+	1.11569i
$262$	38.0935	+	6.03342i	2.35342	+	0.372746i
$263$	12.4103	−	14.5306i	0.765252	−	0.895995i	−0.231797	−	0.972764i	$-0.574460\pi$
$263$	12.4103	−	14.5306i	0.765252	−	0.895995i	0.997049	+	0.0767689i	$0.0244604\pi$
$264$	−1.01970	+	1.40349i	−0.0627580	+	0.0863790i
$265$	1.67949	−	15.2108i	0.103170	−	0.934394i
$266$	−2.67048	+	16.8607i	−0.163738	+	1.03380i
$267$	1.62030	+	2.23016i	0.0991610	+	0.136483i
$268$	−9.16169	−	38.1612i	−0.559639	−	2.33107i
$269$	−4.89286	−	3.55487i	−0.298323	−	0.216744i	0.428547	−	0.903520i	$-0.359026\pi$
$269$	−4.89286	−	3.55487i	−0.298323	−	0.216744i	−0.726870	+	0.686775i	$0.759026\pi$
$270$	2.44628	−	8.94165i	0.148876	−	0.544171i
$271$	9.76464	+	13.4399i	0.593160	+	0.816415i	0.995061	−	0.0992687i	$-0.0316503\pi$
$271$	9.76464	+	13.4399i	0.593160	+	0.816415i	−0.401901	+	0.915683i	$0.631650\pi$
$272$	44.5363	+	3.50509i	2.70041	+	0.212527i
$273$	0.262595	−	0.633961i	0.0158930	−	0.0383691i
$274$	−29.9031	+	18.3247i	−1.80651	+	1.10703i
$275$	3.12084	+	3.02446i	0.188194	+	0.182382i
$276$	7.87731	+	6.72786i	0.474158	+	0.404970i
$277$	5.70261	+	11.1920i	0.342637	+	0.672462i	0.996449	−	0.0841943i	$-0.0268316\pi$
$277$	5.70261	+	11.1920i	0.342637	+	0.672462i	−0.653813	+	0.756656i	$0.726832\pi$
$278$		−	34.6348i		−	2.07726i
$279$	2.37763	−	1.21146i	0.142345	−	0.0725283i
$280$	−2.19398	+	19.8705i	−0.131115	+	1.18749i
$281$	−29.5021	−	7.08282i	−1.75995	−	0.422526i	−0.780652	−	0.624966i	$-0.785113\pi$
$281$	−29.5021	−	7.08282i	−1.75995	−	0.422526i	−0.979295	+	0.202440i	$0.935113\pi$
$282$	−2.23941	−	6.89220i	−0.133355	−	0.410425i
$283$	−25.0704	−	12.7740i	−1.49028	−	0.759337i	−0.496226	−	0.868193i	$-0.665281\pi$
$283$	−25.0704	−	12.7740i	−1.49028	−	0.759337i	−0.994058	+	0.108856i	$0.965281\pi$
$284$	−0.516009	+	1.24575i	−0.0306195	+	0.0739219i
$285$	−1.82953	−	2.69215i	−0.108372	−	0.159469i
$286$			4.88636i			0.288936i
$287$	3.80953	−	6.64649i	0.224870	−	0.392330i
$288$	−22.4821	+	22.4821i	−1.32477	+	1.32477i
$289$	0.555110	+	3.50483i	0.0326535	+	0.206166i
$290$	47.3296	−	2.23141i	2.77929	−	0.131033i
$291$	−2.22026	+	0.721406i	−0.130154	+	0.0422896i
$292$	−31.1318	+	10.1153i	−1.82185	+	0.591956i
$293$	−1.89923	−	3.09927i	−0.110954	−	0.181061i	0.792343	−	0.610076i	$-0.208861\pi$
$293$	−1.89923	−	3.09927i	−0.110954	−	0.181061i	−0.903298	+	0.429014i	$0.858861\pi$
$294$	−3.78639	+	0.909031i	−0.220827	+	0.0530158i
$295$	−9.83178	+	1.24192i	−0.572429	+	0.0723072i
$296$	−7.93930	−	7.93930i	−0.461462	−	0.461462i
$297$	1.22636	−	0.624863i	0.0711608	−	0.0362582i
$298$	2.64631	+	33.6246i	0.153297	+	1.94782i
$299$	17.1039	+	1.34610i	0.989142	+	0.0778472i
$300$	−3.89226	−	5.18428i	−0.224720	−	0.299314i
$301$	−1.62969	−	3.93443i	−0.0939340	−	0.226777i
$302$	−0.0582223	+	0.739784i	−0.00335032	+	0.0425698i
$303$	0.637584	−	4.02555i	0.0366283	−	0.231262i
$304$	4.21407	+	53.5448i	0.241693	+	3.07100i
$305$	−22.1712	+	15.0671i	−1.26952	+	0.862740i
$306$	−29.6350	−	18.1603i	−1.69412	−	1.03816i
$307$	−6.44946	+	4.68581i	−0.368090	+	0.267433i	−0.756419	−	0.654088i	$-0.773053\pi$
$307$	−6.44946	+	4.68581i	−0.368090	+	0.267433i	0.388328	+	0.921521i	$0.373053\pi$
$308$	−4.08390	+	2.96713i	−0.232702	+	0.169068i
$309$	−1.94360	−	1.19104i	−0.110567	−	0.0677558i
$310$	0.999571	−	5.23958i	0.0567718	−	0.297588i
$311$	2.52935	+	32.1384i	0.143426	+	1.82240i	0.476133	+	0.879373i	$0.342038\pi$
$311$	2.52935	+	32.1384i	0.143426	+	1.82240i	−0.332707	+	0.943030i	$0.607962\pi$
$312$	0.670450	−	4.23306i	0.0379568	−	0.239650i
$313$	−1.77891	+	22.6032i	−0.100550	+	1.27761i	0.715084	+	0.699039i	$0.246388\pi$
$313$	−1.77891	+	22.6032i	−0.100550	+	1.27761i	−0.815634	+	0.578569i	$0.803612\pi$
$314$	9.44912	+	22.8122i	0.533245	+	1.28737i
$315$	4.30167	−	6.54848i	0.242371	−	0.368965i
$316$	−42.3155	−	3.33030i	−2.38043	−	0.187344i
$317$	−0.870812	−	11.0647i	−0.0489097	−	0.621456i	−0.971710	−	0.236178i	$-0.924105\pi$
$317$	−0.870812	−	11.0647i	−0.0489097	−	0.621456i	0.922800	−	0.385279i	$-0.125895\pi$
$318$	−4.26412	+	2.17268i	−0.239120	+	0.121838i
$319$	4.97448	+	4.97448i	0.278517	+	0.278517i
$320$	2.44137	+	19.3274i	0.136477	+	1.08043i
$321$	3.99818	−	0.959877i	0.223156	−	0.0535751i
$322$	13.0765	+	21.3389i	0.728723	+	1.18917i
$323$	−23.4958	+	7.63423i	−1.30734	+	0.424780i
$324$	38.6092	−	12.5449i	2.14496	−	0.696939i
$325$	−10.2618	−	3.15723i	−0.569223	−	0.175132i
$326$	−3.65594	−	23.0827i	−0.202484	−	1.27843i
$327$	0.727051	−	0.727051i	0.0402060	−	0.0402060i
$328$	13.4452	−	45.9200i	0.742385	−	2.53551i
$329$		−	12.3990i		−	0.683579i
$330$	0.254684	−	1.33501i	0.0140199	−	0.0734898i
$331$	−1.15957	+	2.79946i	−0.0637360	+	0.153872i	−0.952539	−	0.304418i	$-0.901538\pi$
$331$	−1.15957	+	2.79946i	−0.0637360	+	0.153872i	0.888803	+	0.458290i	$0.151538\pi$
$332$	37.2693	+	18.9896i	2.04542	+	1.04219i
$333$	1.35981	+	4.18506i	0.0745170	+	0.229340i
$334$	−26.2834	−	6.31009i	−1.43816	−	0.345273i
$335$	11.3031	+	14.1089i	0.617552	+	0.770850i
$336$	2.80608	−	1.42977i	0.153084	−	0.0780003i
$337$		−	10.2487i		−	0.558285i	−0.960250	−	0.279142i	$-0.909950\pi$
$337$		−	10.2487i		−	0.558285i	0.960250	−	0.279142i	$-0.0900501\pi$
$338$	9.97105	+	19.5693i	0.542354	+	1.06443i
$339$	0.128913	+	0.110102i	0.00700159	+	0.00597992i
$340$	−46.0274	+	17.3917i	−2.49619	+	0.943195i
$341$	0.675261	−	0.413800i	0.0365674	−	0.0224085i
$342$	15.9912	−	38.6062i	0.864705	−	2.08758i
$343$	−14.9910	−	1.17981i	−0.809436	−	0.0637040i
$344$	−15.6341	−	21.5184i	−0.842932	−	1.16020i
$345$	−4.60280	−	1.25925i	−0.247807	−	0.0677956i
$346$	29.7578	+	21.6203i	1.59979	+	1.16232i
$347$	0.999708	+	4.16408i	0.0536671	+	0.223540i	0.992758	−	0.120128i	$-0.0383305\pi$
$347$	0.999708	+	4.16408i	0.0536671	+	0.223540i	−0.939091	+	0.343668i	$0.888331\pi$
$348$	−6.16823	−	8.48984i	−0.330652	−	0.455103i
$349$	−2.20092	+	13.8961i	−0.117813	+	0.743841i	0.856082	+	0.516840i	$0.172892\pi$
$349$	−2.20092	+	13.8961i	−0.117813	+	0.743841i	−0.973895	+	0.227000i	$0.927108\pi$
$350$	−5.07267	−	14.8173i	−0.271145	−	0.792016i
$351$	−1.99866	+	2.75092i	−0.106680	+	0.146833i
$352$	−6.12829	+	7.17531i	−0.326639	+	0.382445i
$353$	29.9714	+	4.74700i	1.59521	+	0.252657i	0.889872	−	0.456209i	$-0.150793\pi$
$353$	29.9714	+	4.74700i	1.59521	+	0.252657i	0.705343	+	0.708867i	$0.250793\pi$
$354$	2.01270	+	2.35657i	0.106974	+	0.125250i
$355$	−0.0292513	−	0.620438i	−0.00155250	−	0.0329294i
$356$	26.1767	+	42.7165i	1.38736	+	2.26397i
$357$	0.940781	+	1.10151i	0.0497914	+	0.0582982i
$358$	34.7523	−	2.73507i	1.83672	−	0.144553i
$359$	3.08569	−	9.49677i	0.162856	−	0.501220i	−0.836016	−	0.548706i	$-0.815121\pi$
$359$	3.08569	−	9.49677i	0.162856	−	0.501220i	0.998872	+	0.0474854i	$0.0151208\pi$
$360$	16.5769	−	46.0423i	0.873680	−	2.42664i
$361$	−4.85861	−	9.53555i	−0.255716	−	0.501871i
$362$	4.88277	+	2.99217i	0.256633	+	0.157265i
$363$	−2.33307	+	1.42970i	−0.122454	+	0.0750400i
$364$	5.66169	−	11.1117i	0.296753	−	0.582411i
$365$	10.9920	−	10.3219i	0.575346	−	0.540272i
$366$	7.74492	+	3.20805i	0.404833	+	0.167687i
$367$	1.79300	−	2.46785i	0.0935937	−	0.128821i	−0.759652	−	0.650330i	$-0.774631\pi$
$367$	1.79300	−	2.46785i	0.0935937	−	0.128821i	0.853246	+	0.521509i	$0.174631\pi$
$368$	55.6790	+	55.6790i	2.90247	+	2.90247i
$369$	−12.8656	+	13.6432i	−0.669755	+	0.710235i
$370$	8.27606	+	2.97968i	0.430252	+	0.154906i
$371$	−8.08730	+	1.28090i	−0.419872	+	0.0665011i
$372$	−1.09144	+	0.452090i	−0.0565886	+	0.0234398i
$373$	−7.73711	+	15.1849i	−0.400612	+	0.786246i	−0.999898	−	0.0142892i	$-0.995451\pi$
$373$	−7.73711	+	15.1849i	−0.400612	+	0.786246i	0.599285	+	0.800535i	$0.295451\pi$
$374$	−9.19100	−	4.68305i	−0.475255	−	0.242155i
$375$	2.63908	+	1.39745i	0.136282	+	0.0721640i
$376$	−18.0783	−	75.3017i	−0.932319	−	3.88339i
$377$	−16.5292	−	5.37065i	−0.851295	−	0.276602i
$378$	−4.96010			−0.255120
$379$	6.29312	+	2.04476i	0.323256	+	0.105032i	0.466150	−	0.884706i	$-0.345641\pi$
$379$	6.29312	+	2.04476i	0.323256	+	0.105032i	−0.142894	+	0.989738i	$0.545641\pi$
$380$	−29.3087	−	51.3852i	−1.50351	−	2.63601i
$381$	−0.335699	+	4.26546i	−0.0171984	+	0.218526i
$382$	12.0266	+	2.88733i	0.615334	+	0.147729i
$383$	8.61013	+	3.56643i	0.439957	+	0.182236i	0.591656	−	0.806191i	$-0.298474\pi$
$383$	8.61013	+	3.56643i	0.439957	+	0.182236i	−0.151699	+	0.988427i	$0.548474\pi$
$384$	0.222656	−	0.190166i	0.0113624	−	0.00970437i
$385$	1.12025	−	2.03767i	0.0570934	−	0.103849i
$386$	58.8667	−	4.63291i	2.99624	−	0.235809i
$387$	1.63074	+	10.2961i	0.0828950	+	0.523378i
$388$	−41.2554	+	9.90454i	−2.09443	+	0.502827i
$389$	−13.3039	−	2.10714i	−0.674536	−	0.106836i	−0.190237	−	0.981738i	$-0.560925\pi$
$389$	−13.3039	−	2.10714i	−0.674536	−	0.106836i	−0.484299	+	0.874902i	$0.660925\pi$
$390$	0.936698	+	3.22429i	0.0474315	+	0.163268i
$391$	−18.9242	+	30.8814i	−0.957036	+	1.56174i
$392$	−41.0993	+	6.50950i	−2.07583	+	0.328779i
$393$	2.99203	+	2.55544i	0.150928	+	0.128905i
$394$	−3.46140	+	2.51485i	−0.174383	+	0.126696i
$395$	18.2904	−	6.91111i	0.920291	−	0.347736i
$396$	11.4161	−	4.72870i	0.573680	−	0.237626i
$397$	−1.21813	+	5.07386i	−0.0611360	+	0.254650i	−0.994566	−	0.104110i	$-0.966800\pi$
$397$	−1.21813	+	5.07386i	−0.0611360	+	0.254650i	0.933430	+	0.358760i	$0.116800\pi$
$398$	−36.2088	+	30.9252i	−1.81498	+	1.55014i
$399$	−1.13107	+	1.32432i	−0.0566245	+	0.0662988i
$400$	−26.4023	−	41.6057i	−1.32012	−	2.08029i
$401$	−4.33637	+	4.33637i	−0.216548	+	0.216548i	−0.807042	−	0.590494i	$-0.798933\pi$
$401$	−4.33637	+	4.33637i	−0.216548	+	0.216548i	0.590494	+	0.807042i	$0.298933\pi$
$402$	1.74703	−	5.37681i	0.0871340	−	0.268171i
$403$	−1.02229	+	1.66822i	−0.0509237	+	0.0831000i
$404$	17.2919	−	72.0259i	0.860304	−	3.58342i
$405$	−13.6321	+	12.8011i	−0.677384	+	0.636089i
$406$	−7.83424	−	24.1113i	−0.388807	−	1.19662i
$407$	0.499779	+	1.20657i	0.0247731	+	0.0598076i
$408$	7.31962	+	5.31801i	0.362375	+	0.263281i
$409$	−0.142363			−0.00703940			−0.00351970	−	0.999994i	$-0.501120\pi$
$409$	−0.142363			−0.00703940			−0.00351970	+	0.999994i	$0.501120\pi$
$410$	5.78605	+	37.0357i	0.285753	+	1.82906i
$411$	−3.57800			−0.176490
$412$	−33.5159	−	24.3507i	−1.65121	−	1.19967i
$413$	2.02912	+	4.89874i	0.0998467	+	0.241051i
$414$	−18.9309	−	58.2635i	−0.930405	−	2.86349i
$415$	−19.2583	−	0.605460i	−0.945355	−	0.0297209i
$416$	5.44204	−	22.6677i	0.266818	−	1.11138i
$417$	1.84624	−	3.01278i	0.0904106	−	0.147537i
$418$	3.83237	−	11.7948i	0.187447	−	0.576903i
$419$	−20.1474	+	20.1474i	−0.984266	+	0.984266i	−0.999878	−	0.0156125i	$-0.995030\pi$
$419$	−20.1474	+	20.1474i	−0.984266	+	0.984266i	0.0156125	+	0.999878i	$0.495030\pi$
$420$	−2.12599	+	2.74074i	−0.103738	+	0.133735i
$421$	−1.91629	+	2.24369i	−0.0933944	+	0.109351i	−0.805135	−	0.593092i	$-0.797907\pi$
$421$	−1.91629	+	2.24369i	−0.0933944	+	0.109351i	0.711741	+	0.702442i	$0.247907\pi$
$422$	56.8159	−	48.5253i	2.76575	−	2.36218i
$423$	−7.08527	+	29.5123i	−0.344498	+	1.43494i
$424$	−47.2482	+	19.5709i	−2.29458	+	0.950445i
$425$	15.7734	−	16.2761i	0.765124	−	0.789507i
$426$	−0.157146	+	0.114173i	−0.00761374	+	0.00553170i
$427$	10.9064	+	9.31495i	0.527798	+	0.450782i
$428$	73.8078	−	11.6900i	3.56763	−	0.565058i
$429$	−0.260472	+	0.425051i	−0.0125757	+	0.0205217i
$430$	18.2600	+	10.0388i	0.880574	+	0.484114i
$431$	−30.0469	−	4.75897i	−1.44731	−	0.229231i	−0.617189	−	0.786815i	$-0.711729\pi$
$431$	−30.0469	−	4.75897i	−1.44731	−	0.229231i	−0.830121	+	0.557583i	$0.811729\pi$
$432$	−15.1748	+	3.64315i	−0.730098	+	0.175281i
$433$	−1.24631	−	7.86889i	−0.0598938	−	0.378155i	−0.999368	−	0.0355361i	$-0.988686\pi$
$433$	−1.24631	−	7.86889i	−0.0598938	−	0.378155i	0.939475	−	0.342619i	$-0.111314\pi$
$434$	−2.84523	+	0.223924i	−0.136575	+	0.0107487i
$435$	4.23602	+	2.32884i	0.203102	+	0.111659i
$436$	14.2095	−	12.1360i	0.680509	−	0.581210i
$437$	−40.2300	−	16.6638i	−1.92446	−	0.797137i
$438$	−4.58519	−	1.10081i	−0.219089	−	0.0525986i
$439$	0.571762	−	7.26493i	0.0272887	−	0.346736i	−0.968083	−	0.250632i	$-0.919362\pi$
$439$	0.571762	−	7.26493i	0.0272887	−	0.346736i	0.995371	−	0.0961045i	$-0.0306383\pi$
$440$	3.83251	−	14.0086i	0.182708	−	0.667833i
$441$	15.5103	+	5.03959i	0.738584	+	0.239981i
$442$	25.4838			1.21214
$443$	−23.4237	−	7.61081i	−1.11289	−	0.361600i	−0.305841	−	0.952083i	$-0.598938\pi$
$443$	−23.4237	−	7.61081i	−1.11289	−	0.361600i	−0.807051	+	0.590482i	$0.798938\pi$
$444$	−0.454781	−	1.89430i	−0.0215830	−	0.0898995i
$445$	−19.2884	−	12.6704i	−0.914357	−	0.600637i
$446$	7.51039	+	3.82674i	0.355627	+	0.181201i
$447$	−1.56219	+	3.06598i	−0.0738892	+	0.145016i
$448$	9.62997	−	3.98886i	0.454973	−	0.188456i
$449$	−32.9014	+	5.21107i	−1.55271	+	0.245925i	−0.873061	−	0.487610i	$-0.837869\pi$
$449$	−32.9014	+	5.21107i	−1.55271	+	0.245925i	−0.679651	+	0.733536i	$0.737869\pi$
$450$	3.60687	+	38.1670i	0.170030	+	1.79921i
$451$	−3.48886	+	4.33620i	−0.164284	+	0.204184i
$452$	2.17865	+	2.17865i	0.102475	+	0.102475i
$453$	−0.0444994	+	0.0612482i	−0.00209077	+	0.00287769i
$454$	12.6100	+	5.22323i	0.591816	+	0.245138i
$455$	−0.180516	+	5.74180i	−0.00846271	+	0.269180i
$456$	−4.93833	+	9.69202i	−0.231258	+	0.453870i
$457$	19.8411	−	12.1587i	0.928128	−	0.568758i	0.0257340	−	0.999669i	$-0.491808\pi$
$457$	19.8411	−	12.1587i	0.928128	−	0.568758i	0.902394	+	0.430911i	$0.141808\pi$
$458$	−20.8619	−	12.7842i	−0.974811	−	0.597365i
$459$	−3.25884	−	6.39583i	−0.152110	−	0.298532i
$460$	−81.5982	−	29.3783i	−3.80454	−	1.36977i
$461$	−5.04659	+	15.5318i	−0.235043	+	0.723389i	0.762072	+	0.647492i	$0.224182\pi$
$461$	−5.04659	+	15.5318i	−0.235043	+	0.723389i	−0.997116	+	0.0758969i	$0.975818\pi$
$462$	−0.724944	+	0.0570544i	−0.0337275	+	0.00265441i
$463$	−12.6212	−	14.7776i	−0.586558	−	0.686771i	0.385178	−	0.922842i	$-0.374140\pi$
$463$	−12.6212	−	14.7776i	−0.586558	−	0.686771i	−0.971736	+	0.236071i	$0.924140\pi$
$464$	−41.6774	−	68.0114i	−1.93483	−	3.15735i
$465$	0.366250	−	0.402493i	0.0169844	−	0.0186652i
$466$	−27.0944	−	31.7235i	−1.25512	−	1.46956i
$467$	27.5121	+	4.35749i	1.27311	+	0.201640i	0.756166	−	0.654380i	$-0.227070\pi$
$467$	27.5121	+	4.35749i	1.27311	+	0.201640i	0.516942	+	0.856021i	$0.327070\pi$
$468$	−19.8257	+	23.2129i	−0.916443	+	1.07302i
$469$	5.68554	−	7.82547i	0.262534	−	0.361347i
$470$	37.9323	+	47.3484i	1.74969	+	2.18402i
$471$	−0.394071	+	2.48806i	−0.0181578	+	0.114644i
$472$	19.4659	+	26.7925i	0.895990	+	1.23322i
$473$	0.722237	+	3.00833i	0.0332085	+	0.138323i
$474$	−4.94682	−	3.59407i	−0.227215	−	0.165081i
$475$	22.2940	+	15.6693i	1.02292	+	0.718958i
$476$	15.4744	+	21.2987i	0.709269	+	0.976225i
$477$	19.9815	+	1.57258i	0.914888	+	0.0720033i
$478$	18.9160	−	45.6672i	0.865197	−	2.08877i
$479$	15.3845	−	9.42761i	0.702934	−	0.430758i	−0.124576	−	0.992210i	$-0.539757\pi$
$479$	15.3845	−	9.42761i	0.702934	−	0.430758i	0.827509	+	0.561452i	$0.189757\pi$
$480$	−2.66830	+	5.90943i	−0.121791	+	0.269727i
$481$	−2.45338	−	2.09539i	−0.111865	−	0.0955414i
$482$	2.67369	+	5.24742i	0.121783	+	0.239013i
$483$			2.55326i			0.116177i
$484$	−44.3092	+	22.5767i	−2.01405	+	1.02621i
$485$	15.2529	−	12.2195i	0.692597	−	0.554860i
$486$	17.7802	+	4.26864i	0.806525	+	0.193630i
$487$	−11.0636	−	34.0502i	−0.501339	−	1.54296i	−0.806839	−	0.590772i	$-0.798823\pi$
$487$	−11.0636	−	34.0502i	−0.501339	−	1.54296i	0.305499	−	0.952192i	$-0.401177\pi$
$488$	79.8185	+	40.6696i	3.61321	+	1.84102i
$489$	0.912422	−	2.20278i	0.0412611	−	0.0996132i
$490$	26.9625	−	18.3232i	1.21804	−	0.827758i
$491$			10.8408i			0.489238i	0.969619	+	0.244619i	$0.0786629\pi$
$491$			10.8408i			0.489238i	−0.969619	+	0.244619i	$0.921337\pi$
$492$	6.15209	−	5.57450i	0.277358	−	0.251318i
$493$	25.9433	−	25.9433i	1.16843	−	1.16843i
$494$	4.79290	+	30.2612i	0.215643	+	1.36152i
$495$	−3.83085	+	4.20994i	−0.172184	+	0.189223i
$496$	−8.54015	+	2.77486i	−0.383464	+	0.124595i
$497$	−0.316072	+	0.102698i	−0.0141778	+	0.00460664i
$498$	3.14835	+	5.13764i	0.141081	+	0.230223i
$499$	14.3641	−	3.44851i	0.643025	−	0.154377i	0.101198	−	0.994866i	$-0.467733\pi$
$499$	14.3641	−	3.44851i	0.643025	−	0.154377i	0.541828	+	0.840490i	$0.317733\pi$
$500$	45.8223	+	29.0822i	2.04924	+	1.30059i
$501$	−1.94996	−	1.94996i	−0.0871176	−	0.0871176i
$502$	−4.93830	+	2.51619i	−0.220407	+	0.112303i
$503$	−2.16073	−	27.4546i	−0.0963420	−	1.22414i	−0.835072	−	0.550140i	$-0.814574\pi$
$503$	−2.16073	−	27.4546i	−0.0963420	−	1.22414i	0.738730	−	0.674001i	$-0.235426\pi$
$504$	−26.1025	−	2.05432i	−1.16270	−	0.0915065i
$505$	6.91887	+	33.4121i	0.307886	+	1.48682i
$506$	−6.95781	−	16.7976i	−0.309312	−	0.746746i
$507$	−0.175803	+	2.23379i	−0.00780771	+	0.0992063i
$508$	−12.1644	+	76.8031i	−0.539709	+	3.40759i
$509$	1.03005	+	13.0880i	0.0456561	+	0.580115i	0.976616	+	0.214993i	$0.0689729\pi$
$509$	1.03005	+	13.0880i	0.0456561	+	0.580115i	−0.930960	+	0.365122i	$0.881027\pi$
$510$	−6.96245	−	1.32825i	−0.308302	−	0.0588159i
$511$	−6.87902	−	4.21547i	−0.304310	−	0.186481i
$512$	−32.6004	+	23.6856i	−1.44075	+	1.04676i
$513$	6.98195	−	5.07268i	0.308261	−	0.223964i
$514$	−18.2220	−	11.1664i	−0.803737	−	0.492531i
$515$	18.7454	+	3.57611i	0.826019	+	0.157582i
$516$	−0.362090	−	4.60079i	−0.0159401	−	0.202539i
$517$	−1.40912	+	8.89681i	−0.0619729	+	0.391281i
$518$	0.369261	−	4.69191i	0.0162244	−	0.206151i
$519$	1.43606	+	3.46696i	0.0630361	+	0.152183i
$520$	7.27552	+	35.1344i	0.319052	+	1.54074i
$521$	−4.70974	−	0.370664i	−0.206337	−	0.0162391i	−0.0251309	−	0.999684i	$-0.508000\pi$
$521$	−4.70974	−	0.370664i	−0.206337	−	0.0162391i	−0.181207	+	0.983445i	$0.558000\pi$
$522$	4.86903	+	61.8669i	0.213112	+	2.70784i
$523$	4.47705	−	2.28117i	0.195768	−	0.0997486i	−0.353359	−	0.935488i	$-0.614961\pi$
$523$	4.47705	−	2.28117i	0.195768	−	0.0997486i	0.549126	+	0.835739i	$0.314961\pi$
$524$	50.5659	+	50.5659i	2.20898	+	2.20898i
$525$	0.348590	−	1.55932i	0.0152137	−	0.0680541i
$526$	48.6463	−	11.6789i	2.12108	−	0.509226i
$527$	−2.15809	−	3.52168i	−0.0940078	−	0.153407i
$528$	−2.17597	+	0.707016i	−0.0946970	+	0.0307689i
$529$	−38.8397	+	12.6198i	−1.68868	+	0.548687i
$530$	26.9646	−	29.6329i	1.17127	−	1.28717i
$531$	−2.03042	−	12.8196i	−0.0881127	−	0.556322i
$532$	−22.3812	+	22.3812i	−0.970349	+	0.970349i
$533$	2.81636	−	13.4579i	0.121990	−	0.582927i
$534$			7.21701i			0.312311i
$535$	−28.4706	+	19.3481i	−1.23089	+	0.836492i
$536$	23.1195	−	55.8155i	0.998612	−	2.41086i
$537$	3.16880	+	1.61459i	0.136744	+	0.0696745i
$538$	−4.89291	−	15.0588i	−0.210948	−	0.649232i
$539$	4.70639	+	1.12990i	0.202718	+	0.0486684i
$540$	13.4144	−	10.7467i	0.577264	−	0.462464i
$541$	−4.60711	+	2.34744i	−0.198075	+	0.100924i	−0.550215	−	0.835023i	$-0.685454\pi$
$541$	−4.60711	+	2.34744i	−0.198075	+	0.100924i	0.352140	+	0.935947i	$0.385454\pi$
$542$			43.4928i			1.86818i
$543$	0.265239	+	0.520561i	0.0113825	+	0.0223394i
$544$	37.4213	+	31.9608i	1.60442	+	1.37031i
$545$	−3.54236	+	7.84519i	−0.151738	+	0.336051i
$546$	1.53177	−	0.938669i	0.0655536	−	0.0401713i
$547$	11.1279	−	26.8652i	0.475795	−	1.14867i	−0.485768	−	0.874088i	$-0.661460\pi$
$547$	11.1279	−	26.8652i	0.475795	−	1.14867i	0.961563	−	0.274583i	$-0.0885399\pi$
$548$	−64.8264	−	5.10194i	−2.76924	−	0.217944i
$549$	−20.6367	−	28.4039i	−0.880751	−	1.21225i
$550$	1.95591	+	11.2085i	0.0834002	+	0.477933i
$551$	35.6863	+	25.9276i	1.52029	+	1.10455i
$552$	3.72278	+	15.5065i	0.158452	+	0.660000i
$553$	−6.14924	−	8.46371i	−0.261492	−	0.359913i
$554$	−5.14445	+	32.4808i	−0.218567	+	1.37998i
$555$	0.561077	+	0.700357i	0.0238164	+	0.0297285i
$556$	37.7462	−	51.9531i	1.60079	−	2.20330i
$557$	−0.184290	+	0.215775i	−0.00780860	+	0.00914269i	−0.764297	−	0.644865i	$-0.776914\pi$
$557$	−0.184290	+	0.215775i	−0.00780860	+	0.00914269i	0.756488	+	0.654008i	$0.226914\pi$
$558$	6.90021	+	1.09289i	0.292109	+	0.0462656i
$559$	−4.96387	−	5.81195i	−0.209949	−	0.245819i
$560$	−17.7445	+	19.5004i	−0.749841	+	0.824044i
$561$	−0.549866	−	0.897300i	−0.0232154	−	0.0378840i
$562$	−51.5876	−	60.4013i	−2.17609	−	2.54788i
$563$	18.5899	−	1.46305i	0.783469	−	0.0616604i	0.319587	−	0.947557i	$-0.396456\pi$
$563$	18.5899	−	1.46305i	0.783469	−	0.0616604i	0.463883	+	0.885897i	$0.346456\pi$
$564$	4.15218	−	12.7791i	0.174838	−	0.538097i
$565$	−1.33536	−	0.480779i	−0.0561791	−	0.0202265i
$566$	−33.4432	−	65.6360i	−1.40572	−	2.75889i
$567$	8.53126	+	5.22796i	0.358279	+	0.219554i
$568$	−1.76983	+	1.08455i	−0.0742605	+	0.0455069i
$569$	8.78743	−	17.2463i	0.368388	−	0.723003i	−0.630182	−	0.776447i	$-0.717020\pi$
$569$	8.78743	−	17.2463i	0.368388	−	0.723003i	0.998571	+	0.0534441i	$0.0170199\pi$
$570$	0.267781	−	8.51751i	0.0112161	−	0.356759i
$571$	32.7069	+	13.5476i	1.36874	+	0.566951i	0.941447	−	0.337161i	$-0.109467\pi$
$571$	32.7069	+	13.5476i	1.36874	+	0.566951i	0.427295	+	0.904112i	$0.359467\pi$
$572$	−5.32532	+	7.32968i	−0.222663	+	0.306469i
$573$	0.892249	+	0.892249i	0.0372742	+	0.0372742i
$574$	18.2968	−	8.21532i	0.763694	−	0.342901i
$575$	39.7723	−	3.75858i	1.65862	−	0.156744i
$576$	−25.2008	+	3.99141i	−1.05003	+	0.166309i
$577$	−22.7511	+	9.42383i	−0.947142	+	0.392319i	−0.802156	−	0.597115i	$-0.796314\pi$
$577$	−22.7511	+	9.42383i	−0.947142	+	0.392319i	−0.144986	+	0.989434i	$0.546314\pi$
$578$	−4.21767	+	8.27765i	−0.175432	+	0.344305i
$579$	5.36761	+	2.73494i	0.223070	+	0.113660i
$580$	73.4277	+	48.2343i	3.04892	+	2.00282i
$581$	2.40668	+	10.0245i	0.0998458	+	0.415888i
$582$	−5.81277	−	1.88868i	−0.240947	−	0.0782885i
$583$	5.94855			0.246364
$584$	−47.9241	−	15.5715i	−1.98311	−	0.644352i
$585$	3.71076	−	13.5636i	0.153421	−	0.560785i
$586$	0.746649	−	9.48707i	0.0308438	−	0.391907i
$587$	0.0932905	+	0.0223971i	0.00385051	+	0.000924426i	0.235370	−	0.971906i	$-0.424370\pi$
$587$	0.0932905	+	0.0223971i	0.00385051	+	0.000924426i	−0.231520	+	0.972830i	$0.574370\pi$
$588$	−6.67038	−	2.76296i	−0.275082	−	0.113943i
$589$	3.77600	−	3.22501i	0.155587	−	0.132884i
$590$	−22.7354	−	12.4993i	−0.936002	−	0.514587i
$591$	−0.435154	+	0.0342474i	−0.0178998	+	0.00140875i
$592$	−2.31645	−	14.6255i	−0.0952057	−	0.601105i
$593$	−17.9287	+	4.30431i	−0.736245	+	0.176757i	−0.584192	−	0.811616i	$-0.698588\pi$
$593$	−17.9287	+	4.30431i	−0.736245	+	0.176757i	−0.152053	+	0.988372i	$0.548588\pi$
$594$	3.55908	+	0.563703i	0.146031	+	0.0231290i
$595$	−10.6270	−	5.84244i	−0.435666	−	0.239517i
$596$	−32.6757	+	53.3219i	−1.33845	+	2.18415i
$597$	−4.79820	+	0.759959i	−0.196377	+	0.0311031i
$598$	34.1555	+	29.1715i	1.39672	+	1.19291i
$599$	−7.97350	+	5.79308i	−0.325788	+	0.236699i	−0.738641	−	0.674099i	$-0.764532\pi$
$599$	−7.97350	+	5.79308i	−0.325788	+	0.236699i	0.412853	+	0.910798i	$0.364532\pi$
$600$	−0.156501	−	9.97831i	−0.00638911	−	0.407363i
$601$	15.1486	−	6.27475i	0.617923	−	0.255952i	−0.0516887	−	0.998663i	$-0.516460\pi$
$601$	15.1486	−	6.27475i	0.617923	−	0.255952i	0.669612	+	0.742711i	$0.266460\pi$
$602$	2.60274	−	10.8412i	0.106080	−	0.441855i
$603$	−18.0046	+	15.3774i	−0.733204	+	0.626215i
$604$	−0.893578	+	1.04624i	−0.0363592	+	0.0425711i
$605$	14.0404	−	18.1003i	0.570822	−	0.735880i
$606$	7.54519	−	7.54519i	0.306502	−	0.306502i
$607$	2.83682	−	8.73084i	0.115143	−	0.354374i	−0.876834	−	0.480794i	$-0.840349\pi$
$607$	2.83682	−	8.73084i	0.115143	−	0.354374i	0.991977	+	0.126420i	$0.0403486\pi$
$608$	−30.9144	+	50.4477i	−1.25374	+	2.04593i
$609$	0.603795	−	2.51499i	0.0244670	−	0.101912i
$610$	−70.1459	−	2.20531i	−2.84012	−	0.0892903i
$611$	−6.87667	−	21.1642i	−0.278200	−	0.856213i
$612$	−24.6615	−	59.5382i	−0.996884	−	2.40669i
$613$	−1.98374	−	1.44127i	−0.0801224	−	0.0582123i	0.547003	−	0.837131i	$-0.315769\pi$
$613$	−1.98374	−	1.44127i	−0.0801224	−	0.0582123i	−0.627125	+	0.778918i	$0.715769\pi$
$614$	−20.8711			−0.842290
$615$	−1.47091	+	3.53006i	−0.0593127	+	0.142346i
$616$	−7.77082			−0.313095
$617$	20.1185	+	14.6169i	0.809939	+	0.588455i	0.913813	−	0.406135i	$-0.133124\pi$
$617$	20.1185	+	14.6169i	0.809939	+	0.588455i	−0.103874	+	0.994591i	$0.533124\pi$
$618$	−2.28381	−	5.51361i	−0.0918684	−	0.221790i
$619$	−0.0137850	−	0.0424259i	−0.000554067	−	0.00170524i	0.950779	−	0.309869i	$-0.100285\pi$
$619$	−0.0137850	−	0.0424259i	−0.000554067	−	0.00170524i	−0.951333	+	0.308164i	$0.900285\pi$
$620$	7.20965	−	6.77015i	0.289547	−	0.271896i
$621$	2.95361	−	12.3027i	0.118524	−	0.493689i
$622$	−44.0992	+	71.9633i	−1.76822	+	2.88547i
$623$	−3.81570	+	11.7435i	−0.152873	+	0.470495i
$624$	3.99681	−	3.99681i	0.160000	−	0.160000i
$625$	−24.8027	−	3.13458i	−0.992108	−	0.125383i
$626$	−38.5509	+	45.1373i	−1.54080	+	1.80405i
$627$	0.962099	−	0.821710i	0.0384225	−	0.0328160i
$628$	−10.6876	+	44.5169i	−0.426480	+	1.77642i
$629$	6.29262	−	2.60649i	0.250903	−	0.103928i
$630$	19.1883	−	7.25040i	0.764482	−	0.288863i
$631$	−3.66974	+	2.66622i	−0.146090	+	0.106140i	−0.658429	−	0.752642i	$-0.728779\pi$
$631$	−3.66974	+	2.66622i	−0.146090	+	0.106140i	0.512340	+	0.858783i	$0.328779\pi$
$632$	−49.6861	−	42.4360i	−1.97641	−	1.68801i
$633$	7.52894	−	1.19247i	0.299249	−	0.0473963i
$634$	15.1826	−	24.7757i	0.602978	−	0.983970i
$635$	−9.99296	−	34.3976i	−0.396558	−	1.36503i
$636$	−8.76416	−	1.38811i	−0.347522	−	0.0550420i
$637$	−11.6270	+	2.79141i	−0.460680	+	0.110600i
$638$	2.88121	+	18.1912i	0.114068	+	0.720198i
$639$	0.811005	−	0.0638275i	0.0320829	−	0.00252498i
$640$	−1.18097	+	2.14811i	−0.0466820	+	0.0849116i
$641$	5.68516	−	4.85559i	0.224550	−	0.191784i	−0.530055	−	0.847964i	$-0.677829\pi$
$641$	5.68516	−	4.85559i	0.224550	−	0.191784i	0.754605	+	0.656179i	$0.227829\pi$
$642$	9.94547	+	4.11955i	0.392517	+	0.162586i
$643$	−24.9387	−	5.98725i	−0.983485	−	0.236114i	−0.290349	−	0.956921i	$-0.593772\pi$
$643$	−24.9387	−	5.98725i	−0.983485	−	0.236114i	−0.693136	+	0.720807i	$0.743772\pi$
$644$	−3.64075	+	46.2601i	−0.143465	+	1.82290i
$645$	1.05326	+	1.84661i	0.0414720	+	0.0727103i
$646$	−61.5133	−	19.9869i	−2.42021	−	0.786374i
$647$	−45.8817			−1.80380			−0.901898	−	0.431949i	$-0.857826\pi$
$647$	−45.8817			−1.80380			−0.901898	+	0.431949i	$0.857826\pi$
$648$	59.4347	+	19.3115i	2.33482	+	0.758628i
$649$	−0.899253	−	3.74566i	−0.0352988	−	0.147030i
$650$	−16.8766	−	22.4787i	−0.661954	−	0.881686i
$651$	−0.259435	−	0.132189i	−0.0101681	−	0.00518089i
$652$	19.6723	−	38.6090i	0.770426	−	1.51205i
$653$	12.4880	−	5.17271i	0.488694	−	0.202424i	−0.124710	−	0.992193i	$-0.539800\pi$
$653$	12.4880	−	5.17271i	0.488694	−	0.202424i	0.613404	+	0.789770i	$0.289800\pi$
$654$	2.65876	−	0.421107i	0.103966	−	0.0164666i
$655$	−30.9934	−	11.1587i	−1.21101	−	0.436008i
$656$	49.9427	−	38.5726i	1.94994	−	1.50601i
$657$	13.9647	+	13.9647i	0.544813	+	0.544813i
$658$	19.0803	−	26.2618i	0.743827	−	1.02379i
$659$	44.4081	+	18.3945i	1.72990	+	0.716546i	0.999436	+	0.0335902i	$0.0106941\pi$
$659$	44.4081	+	18.3945i	1.72990	+	0.716546i	0.730460	+	0.682956i	$0.239306\pi$
$660$	1.83697	−	1.72499i	0.0715040	−	0.0671450i
$661$	−3.41915	+	6.71046i	−0.132990	+	0.261007i	−0.947892	−	0.318591i	$-0.896790\pi$
$661$	−3.41915	+	6.71046i	−0.132990	+	0.261007i	0.814903	+	0.579598i	$0.196790\pi$
$662$	−6.76402	+	4.14500i	−0.262891	+	0.161100i
$663$	2.21676	+	1.35843i	0.0860919	+	0.0527572i
$664$	29.2325	+	57.3720i	1.13444	+	2.22647i
$665$	4.93902	−	13.7181i	0.191527	−	0.531966i
$666$	−3.56006	+	10.9567i	−0.137949	+	0.424565i
$667$	64.4690	−	5.07382i	2.49625	−	0.196459i
$668$	−32.5489	−	38.1099i	−1.25935	−	1.47451i
$669$	0.449321	+	0.733225i	0.0173718	+	0.0283481i
$670$	2.22894	+	47.2772i	0.0861114	+	1.82648i
$671$	−6.76719	−	7.92336i	−0.261244	−	0.305878i
$672$	3.42655	+	0.542712i	0.132182	+	0.0209356i
$673$	31.2527	−	36.5922i	1.20470	−	1.41052i	0.318058	−	0.948071i	$-0.396969\pi$
$673$	31.2527	−	36.5922i	1.20470	−	1.41052i	0.886644	−	0.462453i	$-0.153031\pi$
$674$	15.7714	−	21.7074i	0.607490	−	0.836138i
$675$	−3.48346	+	7.11018i	−0.134079	+	0.273671i
$676$	−6.37043	+	40.2213i	−0.245016	+	1.54697i
$677$	−3.73483	−	5.14056i	−0.143541	−	0.197568i	0.731193	−	0.682171i	$-0.238964\pi$
$677$	−3.73483	−	5.14056i	−0.143541	−	0.197568i	−0.874734	+	0.484603i	$0.838964\pi$
$678$	0.103613	+	0.431581i	0.00397925	+	0.0165748i
$679$	−8.45998	−	6.14654i	−0.324664	−	0.235882i
$680$	−73.0588	−	19.9876i	−2.80168	−	0.766490i
$681$	0.818480	+	1.12654i	0.0313642	+	0.0431692i
$682$	2.06702	+	0.162678i	0.0791503	+	0.00622926i
$683$	0.480695	−	1.16050i	0.0183933	−	0.0444053i	−0.914416	−	0.404776i	$-0.867350\pi$
$683$	0.480695	−	1.16050i	0.0183933	−	0.0444053i	0.932809	+	0.360370i	$0.117350\pi$
$684$	66.0616	−	40.4826i	2.52593	−	1.54789i
$685$	28.0205	−	10.5877i	1.07061	−	0.404534i
$686$	−29.9361	−	25.5679i	−1.14297	−	0.976186i
$687$	−1.13325	−	2.22412i	−0.0432360	−	0.0848555i
$688$		−	35.0790i		−	1.33738i
$689$	−13.0940	+	6.67175i	−0.498843	+	0.254173i
$690$	−7.81120	−	9.75022i	−0.297367	−	0.371184i
$691$	2.64691	+	0.635466i	0.100693	+	0.0241743i	0.283479	−	0.958979i	$-0.408511\pi$
$691$	2.64691	+	0.635466i	0.100693	+	0.0241743i	−0.182786	+	0.983153i	$0.558511\pi$
$692$	21.0750	+	64.8622i	0.801151	+	2.46569i
$693$	2.71360	+	1.38265i	0.103081	+	0.0525225i
$694$	−4.29050	+	10.3582i	−0.162865	+	0.393191i
$695$	−5.54335	+	29.0573i	−0.210271	+	1.10221i
$696$		−	16.1544i		−	0.612331i
$697$	22.6145	+	18.1954i	0.856586	+	0.689200i
$698$	−26.0458	+	26.0458i	−0.985848	+	0.985848i
$699$	−0.665821	−	4.20383i	−0.0251837	−	0.159003i
$700$	8.53922	−	27.7547i	0.322752	−	1.04903i
$701$	19.8349	−	6.44475i	0.749154	−	0.243415i	0.0905366	−	0.995893i	$-0.471142\pi$
$701$	19.8349	−	6.44475i	0.749154	−	0.243415i	0.658617	+	0.752478i	$0.271142\pi$
$702$	−8.46654	+	2.75094i	−0.319549	+	0.103828i
$703$	4.27862	+	6.98208i	0.161371	+	0.263334i
$704$	−7.36324	+	1.76776i	−0.277512	+	0.0666248i
$705$	0.775675	+	6.14072i	0.0292136	+	0.231273i
$706$	56.1761	+	56.1761i	2.11421	+	2.11421i
$707$	16.2667	−	8.28832i	0.611774	−	0.311714i
$708$	0.450837	+	5.72842i	0.0169435	+	0.215287i
$709$	−22.7107	−	1.78737i	−0.852916	−	0.0671260i	−0.355540	−	0.934661i	$-0.615703\pi$
$709$	−22.7107	−	1.78737i	−0.852916	−	0.0671260i	−0.497376	+	0.867535i	$0.665703\pi$
$710$	0.892810	−	1.35914i	0.0335066	−	0.0510075i
$711$	9.80003	+	23.6594i	0.367530	+	0.887295i
$712$	−6.05093	+	76.8844i	−0.226768	+	2.88136i
$713$	1.13885	−	7.19044i	0.0426504	−	0.269284i
$714$	0.297555	+	3.78079i	0.0111357	+	0.141493i
$715$	0.782070	−	4.09947i	0.0292478	−	0.153312i
$716$	55.1102	+	33.7716i	2.05957	+	1.26210i
$717$	4.07978	−	2.96413i	0.152362	−	0.110698i
$718$	21.1498	−	15.3663i	0.789305	−	0.573464i
$719$	16.9246	+	10.3714i	0.631181	+	0.386788i	0.800980	−	0.598690i	$-0.204312\pi$
$719$	16.9246	+	10.3714i	0.631181	+	0.386788i	−0.169800	+	0.985479i	$0.554312\pi$
$720$	53.3790	−	36.2754i	1.98932	−	1.35190i
$721$	−0.801122	−	10.1792i	−0.0298353	−	0.379094i
$722$	4.38306	−	27.6735i	0.163120	−	1.02990i
$723$	−0.0471409	+	0.598982i	−0.00175319	+	0.0222764i
$724$	4.06333	+	9.80975i	0.151013	+	0.364576i
$725$	−40.0650	−	5.70312i	−1.48797	−	0.211808i
$726$	−7.14168	−	0.562062i	−0.265052	−	0.0208601i
$727$	−2.79870	−	35.5609i	−0.103798	−	1.31888i	−0.799551	−	0.600599i	$-0.794929\pi$
$727$	−2.79870	−	35.5609i	−0.103798	−	1.31888i	0.695753	−	0.718282i	$-0.255071\pi$
$728$	17.1053	−	8.71556i	0.633963	−	0.323020i
$729$	−16.4215	−	16.4215i	−0.608205	−	0.608205i
$730$	39.1655	−	4.94726i	1.44958	−	0.183106i
$731$	15.6893	−	3.76667i	0.580290	−	0.139315i
$732$	8.12135	+	13.2528i	0.300174	+	0.489839i
$733$	4.28390	−	1.39192i	0.158230	−	0.0514119i	−0.228831	−	0.973466i	$-0.573490\pi$
$733$	4.28390	−	1.39192i	0.158230	−	0.0514119i	0.387061	+	0.922054i	$0.373490\pi$
$734$	7.59534	−	2.46787i	0.280349	−	0.0910909i
$735$	3.32213	−	0.156626i	0.122539	−	0.00577723i
$736$	13.5693	+	85.6731i	0.500170	+	3.15795i
$737$	−4.96896	+	4.96896i	−0.183034	+	0.183034i
$738$	−48.2449	+	9.09871i	−1.77592	+	0.334928i
$739$		−	7.06443i		−	0.259869i	−0.991523	−	0.129935i	$-0.958523\pi$
$739$		−	7.06443i		−	0.259869i	0.991523	−	0.129935i	$-0.0414767\pi$
$740$	9.16696	+	13.4891i	0.336984	+	0.495871i
$741$	−1.19618	+	2.88783i	−0.0439427	+	0.106087i
$742$	−19.1005	−	9.73218i	−0.701201	−	0.357280i
$743$	0.946386	+	2.91268i	0.0347195	+	0.106856i	0.966914	−	0.255101i	$-0.0821088\pi$
$743$	0.946386	+	2.91268i	0.0347195	+	0.106856i	−0.932195	+	0.361957i	$0.882109\pi$
$744$	−1.76834	−	0.424541i	−0.0648305	−	0.0155644i
$745$	3.16151	−	28.6333i	0.115829	−	1.04904i
$746$	−39.7551	+	20.2562i	−1.45554	+	0.741633i
$747$		−	25.2358i		−	0.923330i
$748$	−8.68301	−	17.0414i	−0.317482	−	0.623094i
$749$	14.0052	+	11.9616i	0.511740	+	0.437067i
$750$	3.43925	+	7.02105i	0.125584	+	0.256373i
$751$	−35.2832	+	21.6216i	−1.28750	+	0.788982i	−0.986361	−	0.164597i	$-0.947368\pi$
$751$	−35.2832	+	21.6216i	−1.28750	+	0.788982i	−0.301141	+	0.953580i	$0.597368\pi$
$752$	39.0847	−	94.3589i	1.42527	−	3.44092i
$753$	−0.563696	−	0.0443639i	−0.0205422	−	0.00161671i
$754$	−26.7450	−	36.8113i	−0.973996	−	1.34059i
$755$	0.167250	−	0.611333i	0.00608685	−	0.0222487i
$756$	−7.44028	−	5.40568i	−0.270600	−	0.196603i
$757$	4.73645	+	19.7287i	0.172149	+	0.717052i	0.989934	+	0.141529i	$0.0452018\pi$
$757$	4.73645	+	19.7287i	0.172149	+	0.717052i	−0.817785	+	0.575524i	$0.804798\pi$
$758$	10.1826	+	14.0151i	0.369848	+	0.509052i
$759$	0.290172	−	1.83207i	0.0105326	−	0.0665000i
$760$	9.99403	−	90.5143i	0.362522	−	3.28330i
$761$	−20.6850	+	28.4705i	−0.749831	+	1.03205i	0.248161	+	0.968719i	$0.420174\pi$
$761$	−20.6850	+	28.4705i	−0.749831	+	1.03205i	−0.997992	+	0.0633350i	$0.979826\pi$
$762$	−7.27497	+	8.51790i	−0.263544	+	0.308571i
$763$	4.54898	+	0.720488i	0.164684	+	0.0260834i
$764$	14.8935	+	17.4381i	0.538829	+	0.630887i
$765$	21.9560	+	19.9790i	0.793823	+	0.722341i
$766$	12.7485	+	20.8037i	0.460622	+	0.751667i
$767$	6.18049	+	7.23642i	0.223165	+	0.261292i
$768$	−3.87540	+	0.305001i	−0.139841	+	0.0110058i
$769$	8.11071	−	24.9622i	0.292480	−	0.900160i	−0.691577	−	0.722303i	$-0.743084\pi$
$769$	8.11071	−	24.9622i	0.292480	−	0.900160i	0.984056	−	0.177857i	$-0.0569164\pi$
$770$	5.50845	−	2.59199i	0.198511	−	0.0934089i
$771$	−0.989843	−	1.94268i	−0.0356483	−	0.0699638i
$772$	93.3508	+	57.2054i	3.35977	+	2.05887i
$773$	−45.8295	+	28.0843i	−1.64837	+	1.01012i	−0.690330	+	0.723494i	$0.742535\pi$
$773$	−45.8295	+	28.0843i	−1.64837	+	1.01012i	−0.958042	+	0.286629i	$0.907465\pi$
$774$	−12.3902	+	24.3171i	−0.445356	+	0.874060i
$775$	−1.67721	+	4.23583i	−0.0602470	+	0.152155i
$776$	−60.3412	−	24.9941i	−2.16612	−	0.897237i
$777$	0.282227	−	0.388452i	0.0101248	−	0.0139356i
$778$	−24.9359	−	24.9359i	−0.893995	−	0.893995i
$779$	−17.3532	+	30.2762i	−0.621744	+	1.08476i
$780$	−2.10887	+	5.85737i	−0.0755095	+	0.209727i
$781$	0.238467	−	0.0377694i	0.00853301	−	0.00135150i
$782$	−87.6045	+	36.2870i	−3.13273	+	1.29762i
$783$	−5.81867	+	11.4198i	−0.207942	+	0.408109i
$784$	−48.8979	−	24.9147i	−1.74635	−	0.889811i
$785$	−4.27633	−	20.6509i	−0.152629	−	0.737063i
$786$	2.40484	+	10.0169i	0.0857777	+	0.357290i
$787$	6.04213	+	1.96321i	0.215379	+	0.0699808i	0.414719	−	0.909950i	$-0.363880\pi$
$787$	6.04213	+	1.96321i	0.215379	+	0.0699808i	−0.199340	+	0.979930i	$0.563880\pi$
$788$	−7.93297			−0.282600
$789$	4.85416	+	1.57721i	0.172813	+	0.0561502i
$790$	49.3753	+	13.5082i	1.75670	+	0.480601i
$791$	−0.0595811	+	0.757050i	−0.00211846	+	0.0269176i
$792$	18.4962	+	4.44055i	0.657235	+	0.157788i
$793$	23.7827	+	9.85111i	0.844548	+	0.349823i
$794$	−10.3880	+	8.87220i	−0.368657	+	0.314863i
$795$	3.92518	−	1.14032i	0.139212	−	0.0404429i
$796$	−88.0175	+	6.92713i	−3.11970	+	0.245526i
$797$	−6.66765	−	42.0979i	−0.236180	−	1.49118i	−0.765872	−	0.642993i	$-0.777693\pi$
$797$	−6.66765	−	42.0979i	−0.236180	−	1.49118i	0.529692	−	0.848190i	$-0.322307\pi$
$798$	−4.43361	+	1.06442i	−0.156948	+	0.0376799i
$799$	46.3994	+	7.34895i	1.64149	+	0.259987i
$800$	3.40974	−	54.1745i	0.120552	−	1.91536i
$801$	15.7929	−	25.7717i	0.558015	−	0.910597i
$802$	−15.8577	+	2.51162i	−0.559956	+	0.0886883i
$803$	4.45691	+	3.80656i	0.157281	+	0.134331i
$804$	8.48043	−	6.16139i	0.299082	−	0.217296i
$805$	−7.55535	−	19.9954i	−0.266291	−	0.704746i
$806$	−4.73241	+	1.96023i	−0.166692	+	0.0690462i
$807$	0.377103	−	1.57075i	0.0132747	−	0.0552929i
$808$	86.7066	−	74.0544i	3.05033	−	2.60522i
$809$	−7.11134	+	8.32630i	−0.250021	+	0.292737i	−0.871197	−	0.490934i	$-0.836655\pi$
$809$	−7.11134	+	8.32630i	−0.250021	+	0.292737i	0.621175	+	0.783672i	$0.286655\pi$
$810$	−48.5725	+	6.13551i	−1.70666	+	0.215580i
$811$	−7.19374	+	7.19374i	−0.252606	+	0.252606i	−0.822038	−	0.569432i	$-0.807163\pi$
$811$	−7.19374	+	7.19374i	−0.252606	+	0.252606i	0.569432	+	0.822038i	$0.307163\pi$
$812$	14.5258	−	44.7057i	0.509754	−	1.56886i
$813$	−2.31842	+	3.78332i	−0.0813106	+	0.132687i
$814$	−0.798184	+	3.32468i	−0.0279763	+	0.116530i
$815$	−0.627225	+	19.9506i	−0.0219707	+	0.698840i
$816$	3.68729	+	11.3483i	0.129081	+	0.397270i
$817$	7.42361	+	17.9222i	0.259719	+	0.627017i
$818$	−0.301533	−	0.219076i	−0.0105428	−	0.00765983i
$819$	−7.52396			−0.262909
$820$	−31.6835	+	61.8604i	−1.10644	+	2.16026i
$821$	23.0787			0.805452			0.402726	−	0.915321i	$-0.368063\pi$
$821$	23.0787			0.805452			0.402726	+	0.915321i	$0.368063\pi$
$822$	−7.57841	−	5.50604i	−0.264327	−	0.192045i
$823$	13.8498	+	33.4364i	0.482775	+	1.16552i	0.958286	+	0.285811i	$0.0922631\pi$
$823$	13.8498	+	33.4364i	0.482775	+	1.16552i	−0.475511	+	0.879710i	$0.657737\pi$
$824$	−19.7072	−	60.6524i	−0.686532	−	2.11293i
$825$	−0.427340	+	1.07926i	−0.0148781	+	0.0375750i
$826$	−3.24066	+	13.4983i	−0.112757	+	0.469667i
$827$	−9.37852	+	15.3044i	−0.326123	+	0.532184i	−0.973117	−	0.230311i	$-0.926026\pi$
$827$	−9.37852	+	15.3044i	−0.326123	+	0.532184i	0.646994	+	0.762495i	$0.276026\pi$
$828$	35.1006	−	108.028i	1.21983	−	3.75425i
$829$	15.7295	−	15.7295i	0.546307	−	0.546307i	−0.379064	−	0.925371i	$-0.623754\pi$
$829$	15.7295	−	15.7295i	0.546307	−	0.546307i	0.925371	+	0.379064i	$0.123754\pi$
$830$	−39.8585	−	30.9182i	−1.38351	−	1.07319i
$831$	−2.17892	+	2.55118i	−0.0755858	+	0.0884996i
$832$	14.2254	−	12.1496i	0.493177	−	0.421213i
$833$	5.89277	−	24.5452i	0.204172	−	0.850439i
$834$	8.54668	−	3.54015i	0.295947	−	0.122585i
$835$	21.0409	+	9.50063i	0.728149	+	0.328783i
$836$	18.6030	−	13.5159i	0.643400	−	0.467457i
$837$	1.09715	+	0.937054i	0.0379230	+	0.0323893i
$838$	−73.6774	+	11.6693i	−2.54514	+	0.403111i
$839$	−17.6675	+	28.8307i	−0.609949	+	0.995346i	0.387353	+	0.921932i	$0.373390\pi$
$839$	−17.6675	+	28.8307i	−0.609949	+	0.995346i	−0.997302	+	0.0734143i	$0.976610\pi$
$840$	−5.12761	+	1.48964i	−0.176919	+	0.0513974i
$841$	−36.0595	−	5.71127i	−1.24343	−	0.196940i
$842$	−7.51154	+	1.80336i	−0.258865	+	0.0621479i
$843$	−1.26772	−	8.00407i	−0.0436626	−	0.275675i
$844$	138.110	−	10.8695i	4.75394	−	0.374143i
$845$	−5.23324	−	18.0138i	−0.180029	−	0.619693i
$846$	−60.4222	+	51.6054i	−2.07736	+	1.77423i
$847$	−11.3238	−	4.69046i	−0.389089	−	0.161166i
$848$	−65.5837	−	15.7453i	−2.25215	−	0.540694i
$849$	0.589650	−	7.49221i	0.0202367	−	0.257132i
$850$	58.4556	−	10.2006i	2.00501	−	0.349878i
$851$	11.4176	+	3.70979i	0.391389	+	0.127170i
$852$	−0.360153			−0.0123386
$853$	0.674895	+	0.219287i	0.0231080	+	0.00750823i	0.320548	−	0.947232i	$-0.396133\pi$
$853$	0.674895	+	0.219287i	0.0231080	+	0.00750823i	−0.297440	+	0.954740i	$0.596133\pi$
$854$	8.76599	+	36.5130i	0.299966	+	1.24945i
$855$	−19.5950	+	29.8297i	−0.670135	+	1.02016i
$856$	102.497	+	52.2250i	3.50329	+	1.78501i
$857$	−4.81078	+	9.44168i	−0.164333	+	0.322522i	−0.958458	−	0.285232i	$-0.907929\pi$
$857$	−4.81078	+	9.44168i	−0.164333	+	0.322522i	0.794125	+	0.607754i	$0.207929\pi$
$858$	−1.20579	+	0.499453i	−0.0411649	+	0.0170510i
$859$	27.3478	−	4.33147i	0.933095	−	0.147788i	0.328666	−	0.944446i	$-0.393401\pi$
$859$	27.3478	−	4.33147i	0.933095	−	0.147788i	0.604430	+	0.796659i	$0.293401\pi$
$860$	16.4498	+	34.9588i	0.560935	+	1.19209i
$861$	2.02951	+	0.260699i	0.0691656	+	0.00888461i
$862$	−56.3177	−	56.3177i	−1.91819	−	1.91819i
$863$	20.9855	−	28.8841i	0.714354	−	0.983225i	−0.285338	−	0.958427i	$-0.592106\pi$
$863$	20.9855	−	28.8841i	0.714354	−	0.983225i	0.999692	−	0.0247976i	$-0.00789414\pi$
$864$	−15.8827	−	6.57883i	−0.540341	−	0.223816i
$865$	−21.5053	−	22.9014i	−0.731203	−	0.778672i
$866$	9.46935	−	18.5846i	0.321782	−	0.631532i
$867$	−0.808131	+	0.495223i	−0.0274456	+	0.0168187i
$868$	−4.51196	−	2.76493i	−0.153146	−	0.0938480i
$869$	3.45046	+	6.77192i	0.117049	+	0.229722i
$870$	5.38838	+	11.4513i	0.182683	+	0.388234i
$871$	5.36469	−	16.5108i	0.181776	−	0.559448i
$872$	28.6774	−	2.25696i	0.971140	−	0.0764304i
$873$	16.6242	+	19.4644i	0.562644	+	0.658772i
$874$	−59.5661	−	97.2030i	−2.01485	−	3.28794i
$875$	1.88425	+	13.2430i	0.0636993	+	0.447696i
$876$	−5.67822	−	6.64834i	−0.191849	−	0.224627i
$877$	14.4549	+	2.28943i	0.488108	+	0.0773087i	0.395638	−	0.918407i	$-0.370524\pi$
$877$	14.4549	+	2.28943i	0.488108	+	0.0773087i	0.0924703	+	0.995715i	$0.470524\pi$
$878$	12.3907	−	14.5077i	0.418166	−	0.489610i
$879$	0.570666	−	0.785454i	0.0192481	−	0.0264927i
$880$	14.9486	−	11.9758i	0.503917	−	0.403704i
$881$	−2.88652	+	18.2248i	−0.0972495	+	0.614009i	0.890139	+	0.455690i	$0.150607\pi$
$881$	−2.88652	+	18.2248i	−0.0972495	+	0.614009i	−0.987388	+	0.158319i	$0.949393\pi$
$882$	25.0964	+	34.5422i	0.845040	+	1.16310i
$883$	4.80839	+	20.0284i	0.161815	+	0.674009i	0.993010	+	0.118028i	$0.0376573\pi$
$883$	4.80839	+	20.0284i	0.161815	+	0.674009i	−0.831195	+	0.555981i	$0.812343\pi$
$884$	38.2264	+	27.7731i	1.28569	+	0.934110i
$885$	−1.31141	−	2.29921i	−0.0440824	−	0.0772870i
$886$	−37.9007	−	52.1658i	−1.27330	−	1.75254i
$887$	12.1870	+	0.959141i	0.409201	+	0.0322048i	0.281389	−	0.959594i	$-0.409205\pi$
$887$	12.1870	+	0.959141i	0.409201	+	0.0322048i	0.127811	+	0.991798i	$0.459205\pi$
$888$	1.14764	−	2.77065i	0.0385123	−	0.0929770i
$889$	−16.3413	+	10.0140i	−0.548071	+	0.335858i
$890$	−21.3559	−	56.5188i	−0.715850	−	1.89451i
$891$	−5.52740	−	4.72084i	−0.185175	−	0.158154i
$892$	7.09529	+	13.9253i	0.237568	+	0.466253i
$893$			56.4801i			1.89003i
$894$	−8.02691	+	4.08992i	−0.268460	+	0.136787i
$895$	−29.5937	−	3.26755i	−0.989207	−	0.109222i
$896$	1.27537	+	0.306188i	0.0426070	+	0.0102290i
$897$	1.41608	+	4.35824i	0.0472815	+	0.145517i
$898$	−77.7061	−	39.5932i	−2.59309	−	1.32124i
$899$	−2.82218	+	6.81334i	−0.0941249	+	0.227237i
$900$	−36.1853	+	61.1825i	−1.20618	+	2.03942i
$901$		−	31.0234i		−	1.03354i
$902$	−14.0624	+	3.81545i	−0.468226	+	0.127041i
$903$	0.804306	−	0.804306i	0.0267656	−	0.0267656i
$904$	0.741967	+	4.68460i	0.0246775	+	0.155807i
$905$	−3.61756	−	3.29181i	−0.120252	−	0.109424i
$906$	−0.188505	+	0.0612489i	−0.00626265	+	0.00203486i
$907$	10.0335	−	3.26008i	0.333157	−	0.108249i	−0.137662	−	0.990479i	$-0.543959\pi$
$907$	10.0335	−	3.26008i	0.333157	−	0.108249i	0.470818	+	0.882230i	$0.343959\pi$
$908$	13.2229	+	21.5778i	0.438817	+	0.716084i
$909$	−43.4546	+	10.4325i	−1.44130	+	0.346025i
$910$	−9.21816	+	11.8837i	−0.305579	+	0.393940i
$911$	35.3573	+	35.3573i	1.17144	+	1.17144i	0.981866	+	0.189575i	$0.0607110\pi$
$911$	35.3573	+	35.3573i	1.17144	+	1.17144i	0.189575	+	0.981866i	$0.439289\pi$
$912$	−12.7823	+	6.51290i	−0.423264	+	0.215664i
$913$	−0.587630	−	7.46654i	−0.0194477	−	0.247106i
$914$	60.7350	+	4.77995i	2.00894	+	0.158107i
$915$	−5.98424	−	3.93102i	−0.197833	−	0.129956i
$916$	−17.3608	−	41.9126i	−0.573616	−	1.38483i
$917$	−1.38286	+	17.5709i	−0.0456661	+	0.580243i
$918$	2.93987	−	18.5616i	0.0970303	−	0.612625i
$919$	0.175606	+	2.23128i	0.00579269	+	0.0736031i	0.999134	−	0.0416041i	$-0.0132468\pi$
$919$	0.175606	+	2.23128i	0.00579269	+	0.0736031i	−0.993341	+	0.115207i	$0.963247\pi$
$920$	−75.0395	−	110.420i	−2.47398	−	3.64045i
$921$	−1.81552	−	1.11255i	−0.0598235	−	0.0366599i
$922$	−34.5902	+	25.1313i	−1.13917	+	0.827654i
$923$	−0.482555	+	0.350597i	−0.0158835	+	0.0115400i
$924$	−1.14962	−	0.704486i	−0.0378196	−	0.0231759i
$925$	−6.46640	−	3.82444i	−0.212614	−	0.125747i
$926$	−3.99191	−	50.7220i	−0.131182	−	1.66683i
$927$	−3.90996	+	24.6865i	−0.128420	+	0.810812i
$928$	6.89409	−	87.5977i	0.226310	−	2.87554i
$929$	16.0770	+	38.8134i	0.527471	+	1.27343i	0.933175	+	0.359423i	$0.117026\pi$
$929$	16.0770	+	38.8134i	0.527471	+	1.27343i	−0.405704	+	0.914005i	$0.632974\pi$
$930$	1.39512	−	0.288897i	0.0457477	−	0.00947330i
$931$	30.2549	+	2.38111i	0.991565	+	0.0780379i
$932$	−6.06904	−	77.1145i	−0.198798	−	2.52597i
$933$	−7.67213	+	3.90915i	−0.251174	+	0.127980i
$934$	51.5666	+	51.5666i	1.68731	+	1.68731i
$935$	6.96138	+	5.39994i	0.227661	+	0.176597i
$936$	−45.6946	+	10.9703i	−1.49357	+	0.358575i
$937$	−19.3953	−	31.6502i	−0.633615	−	1.03397i	−0.994837	−	0.101486i	$-0.967640\pi$
$937$	−19.3953	−	31.6502i	−0.633615	−	1.03397i	0.361222	−	0.932480i	$-0.382360\pi$
$938$	24.0846	−	7.82556i	0.786390	−	0.255513i
$939$	−5.75952	+	1.87138i	−0.187955	+	0.0610702i
$940$	5.29753	+	112.364i	0.172786	+	3.66491i
$941$	−6.56064	−	41.4222i	−0.213871	−	1.35033i	−0.827826	−	0.560986i	$-0.810422\pi$
$941$	−6.56064	−	41.4222i	−0.213871	−	1.35033i	0.613955	−	0.789341i	$-0.289578\pi$
$942$	−4.66344	+	4.66344i	−0.151943	+	0.151943i
$943$	9.48140	+	50.2741i	0.308757	+	1.63715i
$944$			43.6767i			1.42156i
$945$	4.16134	+	0.793872i	0.135368	+	0.0258246i
$946$	−3.09966	+	7.48324i	−0.100779	+	0.243301i
$947$	−27.3559	−	13.9386i	−0.888949	−	0.452942i	−0.0510049	−	0.998698i	$-0.516242\pi$
$947$	−27.3559	−	13.9386i	−0.888949	−	0.452942i	−0.837944	+	0.545756i	$0.816242\pi$
$948$	−3.50342	−	10.7824i	−0.113786	−	0.350197i
$949$	−14.0800	−	3.38030i	−0.457055	−	0.109729i
$950$	23.1071	+	67.4958i	0.749692	+	2.18985i
$951$	2.64138	−	1.34585i	0.0856527	−	0.0436423i
$952$			40.5271i			1.31349i
$953$	25.3470	+	49.7463i	0.821070	+	1.61144i	0.790940	+	0.611894i	$0.209592\pi$
$953$	25.3470	+	49.7463i	0.821070	+	1.61144i	0.0301303	+	0.999546i	$0.490408\pi$
$954$	39.9019	+	34.0794i	1.29187	+	1.10336i
$955$	−9.62775	−	4.34724i	−0.311547	−	0.140673i
$956$	78.1442	−	47.8868i	2.52736	−	1.54877i
$957$	−0.719071	+	1.73599i	−0.0232443	+	0.0561166i
$958$	47.0929	+	3.70629i	1.52150	+	0.119745i
$959$	−9.42050	−	12.9662i	−0.304204	−	0.418700i
$960$	−4.51979	+	2.57797i	−0.145876	+	0.0832036i
$961$	−24.4079	−	17.7334i	−0.787351	−	0.572044i
$962$	−1.97190	−	8.21355i	−0.0635766	−	0.264816i
$963$	−26.5001	−	36.4743i	−0.853955	−	1.17537i
$964$	−1.70820	+	10.7852i	−0.0550175	+	0.347367i
$965$	−50.1285	−	5.53487i	−1.61369	−	0.178174i
$966$	−3.92910	+	5.40795i	−0.126417	+	0.173998i
$967$	21.4786	−	25.1482i	0.690706	−	0.808713i	−0.298629	−	0.954369i	$-0.596529\pi$
$967$	21.4786	−	25.1482i	0.690706	−	0.808713i	0.989335	+	0.145656i	$0.0465294\pi$
$968$	−75.6105	−	11.9755i	−2.43021	−	0.384908i
$969$	−4.28546	−	5.01762i	−0.137669	−	0.161189i
$970$	51.1105	−	2.40967i	1.64106	−	0.0773697i
$971$	−25.7447	−	42.0115i	−0.826186	−	1.34821i	−0.935181	−	0.354171i	$-0.884763\pi$
$971$	−25.7447	−	42.0115i	−0.826186	−	1.34821i	0.108995	−	0.994042i	$-0.465237\pi$
$972$	22.0186	+	25.7805i	0.706248	+	0.826911i
$973$	15.7789	−	1.24182i	0.505847	−	0.0398111i
$974$	28.9652	−	89.1456i	0.928104	−	2.85641i
$975$	−0.269802	−	2.85498i	−0.00864059	−	0.0914324i
$976$	53.6369	+	105.268i	1.71688	+	3.36956i
$977$	−42.3476	−	25.9507i	−1.35482	−	0.830235i	−0.360106	−	0.932911i	$-0.617260\pi$
$977$	−42.3476	−	25.9507i	−1.35482	−	0.830235i	−0.994715	+	0.102676i	$0.967260\pi$
$978$	5.32233	−	3.26153i	0.170189	−	0.104292i
$979$	4.07255	−	7.99284i	0.130159	−	0.255452i
$980$	60.4138	+	1.89934i	1.92985	+	0.0606722i
$981$	−10.4158	−	4.31438i	−0.332552	−	0.137748i
$982$	−16.6824	+	22.9614i	−0.532358	+	0.732727i
$983$	−1.39998	−	1.39998i	−0.0446524	−	0.0446524i	0.684428	−	0.729080i	$-0.260052\pi$
$983$	−1.39998	−	1.39998i	−0.0446524	−	0.0446524i	−0.729080	+	0.684428i	$0.760052\pi$
$984$	12.7058	−	1.37585i	0.405045	−	0.0438604i
$985$	3.30649	−	1.55587i	0.105354	−	0.0495740i
$986$	94.8725	−	15.0263i	3.02136	−	0.478536i
$987$	3.05965	−	1.26735i	0.0973897	−	0.0403401i
$988$	−25.7902	+	50.6161i	−0.820496	+	1.61031i
$989$	25.3399	+	12.9113i	0.805761	+	0.410556i
$990$	−14.5924	+	3.02176i	−0.463778	+	0.0960378i
$991$	5.21570	+	21.7249i	0.165682	+	0.690115i	0.991928	+	0.126805i	$0.0404723\pi$
$991$	5.21570	+	21.7249i	0.165682	+	0.690115i	−0.826246	+	0.563310i	$0.809528\pi$
$992$	−9.40770	−	3.05675i	−0.298695	−	0.0970518i
$993$	−0.809336			−0.0256835
$994$	−0.827496	−	0.268870i	−0.0262466	−	0.00852803i
$995$	35.3274	−	20.1498i	1.11995	−	0.638792i
$996$	−0.876563	+	11.1378i	−0.0277749	+	0.352914i
$997$	−11.0913	−	2.66278i	−0.351264	−	0.0843309i	0.0539739	−	0.998542i	$-0.482811\pi$
$997$	−11.0913	−	2.66278i	−0.351264	−	0.0843309i	−0.405238	+	0.914211i	$0.632811\pi$
$998$	35.7307	+	14.8002i	1.13104	+	0.468491i
$999$	−1.80925	+	1.54524i	−0.0572420	+	0.0488893i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	205.2.y.a.112.19	yes	304
5.3	odd	4		205.2.bb.a.153.19	yes	304
41.26	odd	40		205.2.bb.a.67.19	yes	304
205.108	even	40	inner	205.2.y.a.108.19	✓	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
205.2.y.a.108.19	✓	304	205.108	even	40	inner
205.2.y.a.112.19	yes	304	1.1	even	1	trivial
205.2.bb.a.67.19	yes	304	41.26	odd	40
205.2.bb.a.153.19	yes	304	5.3	odd	4

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:	\( N \)	\(=\)	\( 205 = 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	205.y (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(2.11806 + 1.53886i) q^{2} +(0.102214 + 0.246766i) q^{3} +(1.50004 + 4.61666i) q^{4} +(-1.53067 - 1.63004i) q^{5} +(-0.163243 + 0.679956i) q^{6} +(-0.625128 + 1.02012i) q^{7} +(-2.30916 + 7.10685i) q^{8} +(2.07087 - 2.07087i) q^{9} +(-0.733648 - 5.80801i) q^{10} +(0.564490 - 0.660933i) q^{11} +(-0.985909 + 0.842046i) q^{12} +(-0.501278 + 2.08797i) q^{13} +(-2.89387 + 1.19868i) q^{14} +(0.245783 - 0.544331i) q^{15} +(-7.97302 + 5.79274i) q^{16} +(-3.44696 - 2.94398i) q^{17} +(7.57301 - 1.19945i) q^{18} +(2.84759 - 4.64685i) q^{19} +(5.22928 - 9.51173i) q^{20} +(-0.315627 - 0.0499904i) q^{21} +(2.21270 - 0.531223i) q^{22} +(-1.24990 - 7.89153i) q^{23} +(-1.98975 + 0.156597i) q^{24} +(-0.314078 + 4.99013i) q^{25} +(-4.27483 + 3.65105i) q^{26} +(1.46299 + 0.605990i) q^{27} +(-5.64725 - 1.35579i) q^{28} +(-0.635029 + 8.06881i) q^{29} +(1.35823 - 0.774698i) q^{30} +(0.866563 + 0.281563i) q^{31} -10.8563 q^{32} +(0.220794 + 0.0717404i) q^{33} +(-2.77048 - 11.5399i) q^{34} +(2.61970 - 0.542480i) q^{35} +(12.6669 + 6.45412i) q^{36} +(-0.682139 + 1.33877i) q^{37} +(13.1822 - 5.46025i) q^{38} +(-0.566478 + 0.0897213i) q^{39} +(15.1190 - 7.11424i) q^{40} +(-6.40037 + 0.187746i) q^{41} +(-0.591587 - 0.591587i) q^{42} +(-2.09219 + 2.87965i) q^{43} +(3.89806 + 1.61463i) q^{44} +(-6.54545 - 0.205781i) q^{45} +(9.49659 - 18.6381i) q^{46} +(-8.83625 + 5.41486i) q^{47} +(-2.24440 - 1.37537i) q^{48} +(2.52808 + 4.96164i) q^{49} +(-8.34433 + 10.0860i) q^{50} +(0.374147 - 1.15151i) q^{51} +(-10.3914 + 0.817822i) q^{52} +(4.44471 + 5.20409i) q^{53} +(2.16616 + 3.53486i) q^{54} +(-1.94140 + 0.0915296i) q^{55} +(-5.80630 - 6.79830i) q^{56} +(1.43775 + 0.227717i) q^{57} +(-13.7618 + 16.1130i) q^{58} +(2.60497 - 3.58544i) q^{59} +(2.88167 + 0.318177i) q^{60} +(1.87536 - 11.8406i) q^{61} +(1.40214 + 1.92988i) q^{62} +(0.817972 + 3.40710i) q^{63} +(-7.04828 - 5.12087i) q^{64} +(4.17078 - 2.37890i) q^{65} +(0.357256 + 0.491721i) q^{66} +(-8.05987 - 0.634326i) q^{67} +(8.42076 - 20.3295i) q^{68} +(1.81960 - 1.11505i) q^{69} +(6.38347 + 2.88235i) q^{70} +(0.211223 + 0.180401i) q^{71} +(9.93542 + 19.4994i) q^{72} +6.74336i q^{73} +(-3.50499 + 1.78588i) q^{74} +(-1.26350 + 0.432556i) q^{75} +(25.7244 + 6.17589i) q^{76} +(0.321350 + 0.989014i) q^{77} +(-1.33790 - 0.681695i) q^{78} +(-3.34625 + 8.07856i) q^{79} +(21.6465 + 4.12957i) q^{80} -8.36302i q^{81} +(-13.8453 - 9.45160i) q^{82} +(6.09303 - 6.09303i) q^{83} +(-0.242665 - 1.53213i) q^{84} +(0.477353 + 10.1250i) q^{85} +(-8.86275 + 2.87968i) q^{86} +(-2.05602 + 0.668040i) q^{87} +(3.39366 + 5.53794i) q^{88} +(10.0355 - 2.40931i) q^{89} +(-13.5470 - 10.5084i) q^{90} +(-1.81661 - 1.81661i) q^{91} +(34.5576 - 17.6080i) q^{92} +(0.0190944 + 0.242618i) q^{93} +(-27.0484 - 2.12875i) q^{94} +(-11.9333 + 2.47111i) q^{95} +(-1.10967 - 2.67897i) q^{96} +(-0.685758 + 8.71338i) q^{97} +(-2.28064 + 14.3994i) q^{98} +(-0.199721 - 2.53770i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q - 16 q^{2} - 16 q^{3} - 68 q^{4} - 16 q^{5} - 32 q^{6} - 16 q^{7} - 8 q^{8} - 8 q^{9} - 12 q^{10} - 32 q^{11} + 20 q^{12} - 4 q^{13} - 16 q^{14} + 16 q^{15} - 76 q^{16} - 16 q^{17} + 28 q^{18} - 40 q^{20}+ \cdots - 72 q^{99}+O(q^{100}) \) 304 * q - 16 * q^2 - 16 * q^3 - 68 * q^4 - 16 * q^5 - 32 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^9 - 12 * q^10 - 32 * q^11 + 20 * q^12 - 4 * q^13 - 16 * q^14 + 16 * q^15 - 76 * q^16 - 16 * q^17 + 28 * q^18 - 40 * q^20 - 40 * q^21 - 40 * q^22 - 20 * q^23 + 40 * q^24 - 20 * q^25 - 24 * q^26 - 76 * q^27 - 4 * q^28 + 76 * q^29 - 8 * q^30 - 40 * q^31 + 48 * q^32 - 120 * q^33 + 16 * q^34 - 80 * q^35 - 24 * q^36 + 24 * q^37 - 20 * q^38 - 16 * q^39 + 56 * q^40 - 32 * q^41 + 176 * q^42 + 20 * q^43 + 16 * q^44 - 32 * q^46 + 40 * q^47 + 76 * q^48 - 8 * q^49 - 8 * q^50 - 24 * q^51 - 80 * q^52 - 16 * q^53 + 40 * q^54 + 48 * q^55 + 24 * q^56 + 12 * q^57 + 20 * q^58 - 40 * q^59 + 120 * q^60 + 4 * q^61 - 20 * q^62 + 108 * q^63 - 68 * q^64 - 92 * q^65 - 40 * q^66 + 8 * q^67 + 76 * q^68 + 32 * q^69 + 48 * q^70 - 40 * q^71 - 220 * q^72 + 144 * q^74 + 44 * q^75 - 48 * q^76 + 72 * q^77 - 212 * q^78 + 232 * q^80 - 72 * q^82 - 112 * q^83 - 256 * q^84 + 116 * q^85 - 40 * q^86 - 20 * q^87 + 92 * q^88 - 80 * q^89 + 212 * q^90 - 72 * q^91 + 20 * q^92 + 96 * q^93 - 40 * q^94 - 36 * q^95 - 8 * q^96 - 136 * q^97 - 12 * q^98 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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