LMFDB - Embedded newform 73.2.k.a.12.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [73,2,Mod(6,73)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(73, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("73.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	73.k (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.582907934755$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			12.6
Character	$\chi$	$=$	73.12
Dual form			73.2.k.a.67.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.463635 + 2.62940i) q^{2} +(2.23144 - 1.28832i) q^{3} +(-4.81942 + 1.75412i) q^{4} +(-1.23921 - 1.76977i) q^{5} +(4.42210 + 5.27005i) q^{6} +(-1.07446 - 0.287902i) q^{7} +(-4.17678 - 7.23440i) q^{8} +(1.81956 - 3.15157i) q^{9} +O(q^{10})$	\(q+(0.463635 + 2.62940i) q^{2} +(2.23144 - 1.28832i) q^{3} +(-4.81942 + 1.75412i) q^{4} +(-1.23921 - 1.76977i) q^{5} +(4.42210 + 5.27005i) q^{6} +(-1.07446 - 0.287902i) q^{7} +(-4.17678 - 7.23440i) q^{8} +(1.81956 - 3.15157i) q^{9} +(4.07890 - 4.07890i) q^{10} +(-2.53825 + 1.77730i) q^{11} +(-8.49437 + 10.1232i) q^{12} +(-0.697325 - 0.0610080i) q^{13} +(0.258851 - 2.95868i) q^{14} +(-5.04526 - 2.35264i) q^{15} +(9.22800 - 7.74321i) q^{16} +(1.75209 + 6.53890i) q^{17} +(9.13035 + 3.32318i) q^{18} +(5.79509 - 1.02183i) q^{19} +(9.07665 + 6.35554i) q^{20} +(-2.76851 + 0.741821i) q^{21} +(-5.85007 - 5.85007i) q^{22} +(1.46219 + 0.257824i) q^{23} +(-18.6405 - 10.7621i) q^{24} +(0.113645 - 0.312238i) q^{25} +(-0.162889 - 1.86183i) q^{26} -1.64678i q^{27} +(5.68330 - 0.497224i) q^{28} +(-1.67364 + 2.39020i) q^{29} +(3.84689 - 14.3568i) q^{30} +(-1.03139 - 2.21183i) q^{31} +(11.8400 + 9.93497i) q^{32} +(-3.37423 + 7.23605i) q^{33} +(-16.3811 + 7.63862i) q^{34} +(0.821962 + 2.25832i) q^{35} +(-3.24097 + 18.3805i) q^{36} +(1.13454 - 6.43430i) q^{37} +(5.37361 + 14.7639i) q^{38} +(-1.63464 + 0.762245i) q^{39} +(-7.62733 + 16.3569i) q^{40} +(-4.83816 - 4.05970i) q^{41} +(-3.23413 - 6.93560i) q^{42} +(0.124549 - 0.464822i) q^{43} +(9.11529 - 13.0180i) q^{44} +(-7.83237 + 0.685243i) q^{45} +3.96422i q^{46} +(-0.158116 - 1.80728i) q^{47} +(10.6160 - 29.1672i) q^{48} +(-4.99059 - 2.88132i) q^{49} +(0.873690 + 0.154055i) q^{50} +(12.3339 + 12.3339i) q^{51} +(3.46771 - 0.929171i) q^{52} +(-7.69457 - 5.38780i) q^{53} +(4.33006 - 0.763506i) q^{54} +(6.29084 + 2.28968i) q^{55} +(2.40500 + 8.97560i) q^{56} +(11.6150 - 9.74611i) q^{57} +(-7.06076 - 3.29249i) q^{58} +(-0.360607 + 4.12176i) q^{59} +(28.4420 + 2.48836i) q^{60} +(5.15086 - 6.13856i) q^{61} +(5.33759 - 3.73742i) q^{62} +(-2.86239 + 2.86239i) q^{63} +(-8.58729 + 14.8736i) q^{64} +(0.756160 + 1.30971i) q^{65} +(-20.5909 - 5.51731i) q^{66} +(1.64388 + 1.95910i) q^{67} +(-19.9141 - 28.4403i) q^{68} +(3.59495 - 1.30846i) q^{69} +(-5.55695 + 3.20831i) q^{70} +(1.55394 + 8.81283i) q^{71} -30.3996 q^{72} +(-0.0396405 + 8.54391i) q^{73} +17.4444 q^{74} +(-0.148671 - 0.843154i) q^{75} +(-26.1365 + 15.0899i) q^{76} +(3.23895 - 1.17888i) q^{77} +(-2.76212 - 3.94472i) q^{78} +(8.35500 + 9.95711i) q^{79} +(-25.1391 - 6.73600i) q^{80} +(3.33709 + 5.78000i) q^{81} +(8.43144 - 14.6037i) q^{82} +(4.84782 - 4.84782i) q^{83} +(12.0414 - 8.43146i) q^{84} +(9.40115 - 11.2039i) q^{85} +(1.27995 + 0.111981i) q^{86} +(-0.655271 + 7.48979i) q^{87} +(23.4595 + 10.9393i) q^{88} +(-4.65932 + 3.90964i) q^{89} +(-5.43314 - 20.2767i) q^{90} +(0.731685 + 0.266312i) q^{91} +(-7.49916 + 1.32230i) q^{92} +(-5.15104 - 3.60680i) q^{93} +(4.67875 - 1.25367i) q^{94} +(-8.98972 - 8.98972i) q^{95} +(39.2198 + 6.91551i) q^{96} +(-7.29546 - 4.21203i) q^{97} +(5.26234 - 14.4582i) q^{98} +(0.982795 + 11.2334i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 12 q^{2} - 18 q^{3} - 12 q^{4} - 12 q^{5} - 24 q^{6} - 18 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) $ 72 * q - 12 * q^2 - 18 * q^3 - 12 * q^4 - 12 * q^5 - 24 * q^6 - 18 * q^7 - 24 * q^8 + 36 * q^9	\( 72 q - 12 q^{2} - 18 q^{3} - 12 q^{4} - 12 q^{5} - 24 q^{6} - 18 q^{7} - 24 q^{8} + 36 q^{9} - 6 q^{11} + 6 q^{12} - 12 q^{13} - 12 q^{14} - 30 q^{15} + 30 q^{17} - 12 q^{18} - 6 q^{19} + 60 q^{20} - 30 q^{21} - 12 q^{22} - 12 q^{23} - 18 q^{24} + 36 q^{25} + 12 q^{26} + 120 q^{28} - 6 q^{29} - 72 q^{30} - 18 q^{31} - 18 q^{32} - 60 q^{33} - 60 q^{34} - 36 q^{35} + 60 q^{36} - 6 q^{37} + 48 q^{38} + 78 q^{39} - 18 q^{40} + 54 q^{42} - 24 q^{43} + 48 q^{44} + 36 q^{47} + 30 q^{48} - 18 q^{49} + 132 q^{50} - 18 q^{51} - 24 q^{53} - 6 q^{54} + 72 q^{55} + 24 q^{56} - 6 q^{57} - 18 q^{58} - 66 q^{60} - 36 q^{61} - 36 q^{62} + 12 q^{63} - 84 q^{64} + 24 q^{65} + 156 q^{66} - 54 q^{67} - 84 q^{68} - 6 q^{69} - 162 q^{70} + 48 q^{71} - 72 q^{72} - 36 q^{73} + 144 q^{74} + 6 q^{75} - 180 q^{76} - 24 q^{77} - 198 q^{78} - 36 q^{79} - 126 q^{80} - 48 q^{81} + 30 q^{82} - 48 q^{83} - 126 q^{84} - 6 q^{85} - 120 q^{86} + 6 q^{87} + 6 q^{88} + 6 q^{89} + 210 q^{90} + 48 q^{91} + 96 q^{92} + 144 q^{93} - 6 q^{94} - 12 q^{95} + 162 q^{96} - 18 q^{97} + 186 q^{98} + 78 q^{99}+O(q^{100}) \) 72 * q - 12 * q^2 - 18 * q^3 - 12 * q^4 - 12 * q^5 - 24 * q^6 - 18 * q^7 - 24 * q^8 + 36 * q^9 - 6 * q^11 + 6 * q^12 - 12 * q^13 - 12 * q^14 - 30 * q^15 + 30 * q^17 - 12 * q^18 - 6 * q^19 + 60 * q^20 - 30 * q^21 - 12 * q^22 - 12 * q^23 - 18 * q^24 + 36 * q^25 + 12 * q^26 + 120 * q^28 - 6 * q^29 - 72 * q^30 - 18 * q^31 - 18 * q^32 - 60 * q^33 - 60 * q^34 - 36 * q^35 + 60 * q^36 - 6 * q^37 + 48 * q^38 + 78 * q^39 - 18 * q^40 + 54 * q^42 - 24 * q^43 + 48 * q^44 + 36 * q^47 + 30 * q^48 - 18 * q^49 + 132 * q^50 - 18 * q^51 - 24 * q^53 - 6 * q^54 + 72 * q^55 + 24 * q^56 - 6 * q^57 - 18 * q^58 - 66 * q^60 - 36 * q^61 - 36 * q^62 + 12 * q^63 - 84 * q^64 + 24 * q^65 + 156 * q^66 - 54 * q^67 - 84 * q^68 - 6 * q^69 - 162 * q^70 + 48 * q^71 - 72 * q^72 - 36 * q^73 + 144 * q^74 + 6 * q^75 - 180 * q^76 - 24 * q^77 - 198 * q^78 - 36 * q^79 - 126 * q^80 - 48 * q^81 + 30 * q^82 - 48 * q^83 - 126 * q^84 - 6 * q^85 - 120 * q^86 + 6 * q^87 + 6 * q^88 + 6 * q^89 + 210 * q^90 + 48 * q^91 + 96 * q^92 + 144 * q^93 - 6 * q^94 - 12 * q^95 + 162 * q^96 - 18 * q^97 + 186 * q^98 + 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/73\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{11}{36}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.463635	+	2.62940i	0.327839	+	1.85927i	0.488922	+	0.872328i	$0.337390\pi$
$2$	0.463635	+	2.62940i	0.327839	+	1.85927i	−0.161083	+	0.986941i	$0.551499\pi$
$3$	2.23144	−	1.28832i	1.28832	−	0.743814i	0.309969	−	0.950747i	$-0.399681\pi$
$3$	2.23144	−	1.28832i	1.28832	−	0.743814i	0.978355	+	0.206932i	$0.0663480\pi$
$4$	−4.81942	+	1.75412i	−2.40971	+	0.877062i
$5$	−1.23921	−	1.76977i	−0.554190	−	0.791466i	0.440126	−	0.897936i	$-0.354934\pi$
$5$	−1.23921	−	1.76977i	−0.554190	−	0.791466i	−0.994316	+	0.106471i	$0.966045\pi$
$6$	4.42210	+	5.27005i	1.80531	+	2.15149i
$7$	−1.07446	−	0.287902i	−0.406109	−	0.108817i	0.0499812	−	0.998750i	$-0.484084\pi$
$7$	−1.07446	−	0.287902i	−0.406109	−	0.108817i	−0.456090	+	0.889934i	$0.650751\pi$
$8$	−4.17678	−	7.23440i	−1.47672	−	2.55775i
$9$	1.81956	−	3.15157i	0.606520	−	1.05052i
$10$	4.07890	−	4.07890i	1.28986	−	1.28986i
$11$	−2.53825	+	1.77730i	−0.765312	+	0.535878i	−0.889804	−	0.456343i	$-0.849159\pi$
$11$	−2.53825	+	1.77730i	−0.765312	+	0.535878i	0.124491	+	0.992221i	$0.460270\pi$
$12$	−8.49437	+	10.1232i	−2.45211	+	2.92232i
$13$	−0.697325	−	0.0610080i	−0.193403	−	0.0169206i	−0.00995740	−	0.999950i	$-0.503170\pi$
$13$	−0.697325	−	0.0610080i	−0.193403	−	0.0169206i	−0.183446	+	0.983030i	$0.558725\pi$
$14$	0.258851	−	2.95868i	0.0691808	−	0.790740i
$15$	−5.04526	−	2.35264i	−1.30268	−	0.607450i
$16$	9.22800	−	7.74321i	2.30700	−	1.93580i
$17$	1.75209	+	6.53890i	0.424945	+	1.58592i	0.764043	+	0.645166i	$0.223212\pi$
$17$	1.75209	+	6.53890i	0.424945	+	1.58592i	−0.339097	+	0.940751i	$0.610122\pi$
$18$	9.13035	+	3.32318i	2.15205	+	0.783280i
$19$	5.79509	−	1.02183i	1.32948	−	0.234424i	0.536621	−	0.843823i	$-0.319700\pi$
$19$	5.79509	−	1.02183i	1.32948	−	0.234424i	0.792864	+	0.609399i	$0.208589\pi$
$20$	9.07665	+	6.35554i	2.02960	+	1.42114i
$21$	−2.76851	+	0.741821i	−0.604139	+	0.161879i
$22$	−5.85007	−	5.85007i	−1.24724	−	1.24724i
$23$	1.46219	+	0.257824i	0.304888	+	0.0537599i	0.323999	−	0.946057i	$-0.394973\pi$
$23$	1.46219	+	0.257824i	0.304888	+	0.0537599i	−0.0191113	+	0.999817i	$0.506084\pi$
$24$	−18.6405	−	10.7621i	−3.80498	−	2.19680i
$25$	0.113645	−	0.312238i	0.0227291	−	0.0624477i
$26$	−0.162889	−	1.86183i	−0.0319452	−	0.365136i
$27$		−	1.64678i		−	0.316924i
$28$	5.68330	−	0.497224i	1.07404	−	0.0939666i
$29$	−1.67364	+	2.39020i	−0.310787	+	0.443849i	−0.943911	−	0.330201i	$-0.892883\pi$
$29$	−1.67364	+	2.39020i	−0.310787	+	0.443849i	0.633124	+	0.774050i	$0.281772\pi$
$30$	3.84689	−	14.3568i	0.702343	−	2.62118i
$31$	−1.03139	−	2.21183i	−0.185243	−	0.397256i	0.791652	−	0.610972i	$-0.209221\pi$
$31$	−1.03139	−	2.21183i	−0.185243	−	0.397256i	−0.976896	+	0.213716i	$0.931443\pi$
$32$	11.8400	+	9.93497i	2.09304	+	1.75627i
$33$	−3.37423	+	7.23605i	−0.587377	+	1.25963i
$34$	−16.3811	+	7.63862i	−2.80933	+	1.31001i
$35$	0.821962	+	2.25832i	0.138937	+	0.381726i
$36$	−3.24097	+	18.3805i	−0.540162	+	3.06341i
$37$	1.13454	−	6.43430i	0.186517	−	1.05779i	−0.737473	−	0.675376i	$-0.763981\pi$
$37$	1.13454	−	6.43430i	0.186517	−	1.05779i	0.923990	−	0.382416i	$-0.124908\pi$
$38$	5.37361	+	14.7639i	0.871714	+	2.39502i
$39$	−1.63464	+	0.762245i	−0.261752	+	0.122057i
$40$	−7.62733	+	16.3569i	−1.20599	+	2.58625i
$41$	−4.83816	−	4.05970i	−0.755593	−	0.634018i	0.181383	−	0.983413i	$-0.441943\pi$
$41$	−4.83816	−	4.05970i	−0.755593	−	0.634018i	−0.936976	+	0.349395i	$0.886387\pi$
$42$	−3.23413	−	6.93560i	−0.499036	−	1.07019i
$43$	0.124549	−	0.464822i	0.0189935	−	0.0708847i	−0.955779	−	0.294087i	$-0.904984\pi$
$43$	0.124549	−	0.464822i	0.0189935	−	0.0708847i	0.974772	+	0.223202i	$0.0716511\pi$
$44$	9.11529	−	13.0180i	1.37418	−	1.96254i
$45$	−7.83237	+	0.685243i	−1.16758	+	0.102150i
$46$			3.96422i			0.584493i
$47$	−0.158116	−	1.80728i	−0.0230636	−	0.263618i	−0.998968	−	0.0454196i	$-0.985538\pi$
$47$	−0.158116	−	1.80728i	−0.0230636	−	0.263618i	0.975904	−	0.218199i	$-0.0700180\pi$
$48$	10.6160	−	29.1672i	1.53229	−	4.20992i
$49$	−4.99059	−	2.88132i	−0.712942	−	0.411617i
$50$	0.873690	+	0.154055i	0.123558	+	0.0217867i
$51$	12.3339	+	12.3339i	1.72710	+	1.72710i
$52$	3.46771	−	0.929171i	0.480885	−	0.128853i
$53$	−7.69457	−	5.38780i	−1.05693	−	0.740071i	−0.0902149	−	0.995922i	$-0.528755\pi$
$53$	−7.69457	−	5.38780i	−1.05693	−	0.740071i	−0.966716	+	0.255851i	$0.917644\pi$
$54$	4.33006	−	0.763506i	0.589246	−	0.103900i
$55$	6.29084	+	2.28968i	0.848257	+	0.308740i
$56$	2.40500	+	8.97560i	0.321382	+	1.19941i
$57$	11.6150	−	9.74611i	1.53844	−	1.29090i
$58$	−7.06076	−	3.29249i	−0.927123	−	0.432325i
$59$	−0.360607	+	4.12176i	−0.0469471	+	0.536607i	0.935910	+	0.352239i	$0.114580\pi$
$59$	−0.360607	+	4.12176i	−0.0469471	+	0.536607i	−0.982857	+	0.184368i	$0.940976\pi$
$60$	28.4420	+	2.48836i	3.67185	+	0.321245i
$61$	5.15086	−	6.13856i	0.659500	−	0.785962i	−0.327814	−	0.944742i	$-0.606312\pi$
$61$	5.15086	−	6.13856i	0.659500	−	0.785962i	0.987314	+	0.158781i	$0.0507563\pi$
$62$	5.33759	−	3.73742i	0.677875	−	0.474653i
$63$	−2.86239	+	2.86239i	−0.360627	+	0.360627i
$64$	−8.58729	+	14.8736i	−1.07341	+	1.85920i
$65$	0.756160	+	1.30971i	0.0937900	+	0.162449i
$66$	−20.5909	−	5.51731i	−2.53456	−	0.679134i
$67$	1.64388	+	1.95910i	0.200831	+	0.239342i	0.857055	−	0.515225i	$-0.172292\pi$
$67$	1.64388	+	1.95910i	0.200831	+	0.239342i	−0.656224	+	0.754567i	$0.727847\pi$
$68$	−19.9141	−	28.4403i	−2.41494	−	3.44889i
$69$	3.59495	−	1.30846i	0.432782	−	0.157520i
$70$	−5.55695	+	3.20831i	−0.664183	+	0.383466i
$71$	1.55394	+	8.81283i	0.184419	+	1.04589i	0.926700	+	0.375802i	$0.122633\pi$
$71$	1.55394	+	8.81283i	0.184419	+	1.04589i	−0.742281	+	0.670089i	$0.766256\pi$
$72$	−30.3996			−3.58263
$73$	−0.0396405	+	8.54391i	−0.00463957	+	0.999989i
$73$	−0.0396405	+	8.54391i	−0.00463957	+	0.999989i
$74$	17.4444			2.02787
$75$	−0.148671	−	0.843154i	−0.0171670	−	0.0973591i
$76$	−26.1365	+	15.0899i	−2.99807	+	1.73093i
$77$	3.23895	−	1.17888i	0.369113	−	0.134346i
$78$	−2.76212	−	3.94472i	−0.312749	−	0.446652i
$79$	8.35500	+	9.95711i	0.940011	+	1.12026i	0.992574	+	0.121644i	$0.0388167\pi$
$79$	8.35500	+	9.95711i	0.940011	+	1.12026i	−0.0525624	+	0.998618i	$0.516739\pi$
$80$	−25.1391	−	6.73600i	−2.81064	−	0.753108i
$81$	3.33709	+	5.78000i	0.370787	+	0.642223i
$82$	8.43144	−	14.6037i	0.931096	−	1.61271i
$83$	4.84782	−	4.84782i	0.532117	−	0.532117i	−0.389085	−	0.921202i	$-0.627209\pi$
$83$	4.84782	−	4.84782i	0.532117	−	0.532117i	0.921202	+	0.389085i	$0.127209\pi$
$84$	12.0414	−	8.43146i	1.31382	−	0.919948i
$85$	9.40115	−	11.2039i	1.01970	−	1.21523i
$86$	1.27995	+	0.111981i	0.138020	+	0.0120752i
$87$	−0.655271	+	7.48979i	−0.0702525	+	0.802989i
$88$	23.4595	+	10.9393i	2.50079	+	1.16614i
$89$	−4.65932	+	3.90964i	−0.493887	+	0.414421i	−0.855417	−	0.517940i	$-0.826699\pi$
$89$	−4.65932	+	3.90964i	−0.493887	+	0.414421i	0.361530	+	0.932361i	$0.382255\pi$
$90$	−5.43314	−	20.2767i	−0.572703	−	2.13736i
$91$	0.731685	+	0.266312i	0.0767015	+	0.0279171i
$92$	−7.49916	+	1.32230i	−0.781841	+	0.137860i
$93$	−5.15104	−	3.60680i	−0.534138	−	0.374008i
$94$	4.67875	−	1.25367i	0.482576	−	0.129306i
$95$	−8.98972	−	8.98972i	−0.922326	−	0.922326i
$96$	39.2198	+	6.91551i	4.00286	+	0.705812i
$97$	−7.29546	−	4.21203i	−0.740742	−	0.427667i	0.0815973	−	0.996665i	$-0.473998\pi$
$97$	−7.29546	−	4.21203i	−0.740742	−	0.427667i	−0.822339	+	0.568998i	$0.807331\pi$
$98$	5.26234	−	14.4582i	0.531577	−	1.46049i
$99$	0.982795	+	11.2334i	0.0987746	+	1.12900i
$100$			1.70416i			0.170416i
$101$	−10.9278	+	0.956058i	−1.08736	+	0.0951313i	−0.616710	−	0.787191i	$-0.711535\pi$
$101$	−10.9278	+	0.956058i	−1.08736	+	0.0951313i	−0.470646	+	0.882322i	$0.655979\pi$
$102$	−26.7124	+	38.1493i	−2.64492	+	3.77734i
$103$	−1.99384	+	7.44112i	−0.196459	+	0.733196i	0.795425	+	0.606052i	$0.207248\pi$
$103$	−1.99384	+	7.44112i	−0.196459	+	0.733196i	−0.991884	+	0.127144i	$0.959419\pi$
$104$	2.47122	+	5.29954i	0.242323	+	0.519663i
$105$	4.74361	+	3.98037i	0.462929	+	0.388444i
$106$	10.5992	−	22.7301i	1.02949	−	2.20774i
$107$	14.9981	−	6.99373i	1.44992	−	0.676109i	0.471337	−	0.881953i	$-0.343772\pi$
$107$	14.9981	−	6.99373i	1.44992	−	0.676109i	0.978585	+	0.205844i	$0.0659939\pi$
$108$	2.88866	+	7.93654i	0.277962	+	0.763694i
$109$	1.27776	−	7.24656i	0.122388	−	0.694095i	−0.860438	−	0.509556i	$-0.829810\pi$
$109$	1.27776	−	7.24656i	0.122388	−	0.694095i	0.982825	−	0.184539i	$-0.0590792\pi$
$110$	−3.10384	+	17.6027i	−0.295939	+	1.67836i
$111$	−5.75780	−	15.8194i	−0.546506	−	1.50151i
$112$	−12.1444	+	5.66304i	−1.14754	+	0.535107i
$113$	−2.10837	+	4.52142i	−0.198339	+	0.425339i	−0.980172	−	0.198149i	$-0.936507\pi$
$113$	−2.10837	+	4.52142i	−0.198339	+	0.425339i	0.781833	+	0.623488i	$0.214285\pi$
$114$	31.0116	+	26.0218i	2.90450	+	2.43716i
$115$	−1.35567	−	2.90724i	−0.126417	−	0.271101i
$116$	3.87324	−	14.4551i	0.359622	−	1.34213i
$117$	−1.46109	+	2.08666i	−0.135078	+	0.192912i
$118$	−11.0050	+	0.962809i	−1.01309	+	0.0886337i
$119$		−	7.53024i		−	0.690296i
$120$	4.05299	+	46.3259i	0.369986	+	4.22896i
$121$	−0.478299	+	1.31412i	−0.0434817	+	0.119465i
$122$	18.5289	+	10.6976i	1.67752	+	0.968519i
$123$	−16.0263	−	2.82586i	−1.44504	−	0.254800i
$124$	8.85052	+	8.85052i	0.794801	+	0.794801i
$125$	−11.1278	+	2.98168i	−0.995300	+	0.266690i
$126$	−8.85348	−	6.19927i	−0.788731	−	0.552275i
$127$	−14.4524	+	2.54834i	−1.28244	+	0.226129i	−0.773016	−	0.634387i	$-0.781253\pi$
$127$	−14.4524	+	2.54834i	−1.28244	+	0.226129i	−0.509424	+	0.860515i	$0.670142\pi$
$128$	−14.0422	−	5.11094i	−1.24117	−	0.451747i
$129$	−0.320918	−	1.19768i	−0.0282553	−	0.105450i
$130$	−3.09316	+	2.59547i	−0.271288	+	0.227638i
$131$	17.5293	+	8.17403i	1.53154	+	0.714168i	0.991816	−	0.127675i	$-0.0407513\pi$
$131$	17.5293	+	8.17403i	1.53154	+	0.714168i	0.539723	+	0.841843i	$0.318529\pi$
$132$	3.56887	−	40.7923i	0.310630	−	3.55052i
$133$	−6.52080	−	0.570496i	−0.565425	−	0.0494683i
$134$	−4.38909	+	5.23072i	−0.379160	+	0.451865i
$135$	−2.91443	+	2.04071i	−0.250834	+	0.175636i
$136$	39.9869	−	39.9869i	3.42885	−	3.42885i
$137$	6.87093	−	11.9008i	0.587023	−	1.01675i	−0.407596	−	0.913162i	$-0.633633\pi$
$137$	6.87093	−	11.9008i	0.587023	−	1.01675i	0.994620	−	0.103592i	$-0.0330337\pi$
$138$	5.10720	+	8.84594i	0.434754	+	0.753016i
$139$	2.67036	+	0.715521i	0.226497	+	0.0606897i	0.370283	−	0.928919i	$-0.379261\pi$
$139$	2.67036	+	0.715521i	0.226497	+	0.0606897i	−0.143785	+	0.989609i	$0.545928\pi$
$140$	−7.92276	−	9.44198i	−0.669595	−	0.797993i
$141$	−2.68118	−	3.82913i	−0.225796	−	0.322471i
$142$	−22.4520	+	8.17187i	−1.88413	+	0.685768i
$143$	1.87842	−	1.08450i	0.157081	−	0.0906909i
$144$	−7.61237	−	43.1719i	−0.634364	−	3.59766i
$145$	6.30409			0.523526
$146$	−22.4838	+	3.85702i	−1.86077	+	0.319209i
$147$	−14.8483			−1.22467
$148$	5.81873	+	32.9997i	0.478297	+	2.71256i
$149$	−11.0360	+	6.37161i	−0.904101	+	0.521983i	−0.878528	−	0.477690i	$-0.841474\pi$
$149$	−11.0360	+	6.37161i	−0.904101	+	0.521983i	−0.0255724	+	0.999673i	$0.508141\pi$
$150$	2.14806	−	0.781831i	0.175389	−	0.0638363i
$151$	−3.77779	−	5.39524i	−0.307432	−	0.439058i	0.635472	−	0.772124i	$-0.280806\pi$
$151$	−3.77779	−	5.39524i	−0.307432	−	0.439058i	−0.942904	+	0.333066i	$0.891917\pi$
$152$	−31.5972	−	37.6560i	−2.56287	−	3.05431i
$153$	23.7958	+	6.37608i	1.92378	+	0.515475i
$154$	4.60144	+	7.96993i	0.370795	+	0.642235i
$155$	−2.63632	+	4.56624i	−0.211754	+	0.366769i
$156$	6.54093	−	6.54093i	0.523694	−	0.523694i
$157$	15.4307	−	10.8047i	1.23151	−	0.862311i	0.237475	−	0.971394i	$-0.423680\pi$
$157$	15.4307	−	10.8047i	1.23151	−	0.862311i	0.994033	+	0.109083i	$0.0347914\pi$
$158$	−22.3076	+	26.5851i	−1.77470	+	2.11500i
$159$	−24.1112	−	2.10946i	−1.91215	−	0.167291i
$160$	2.91037	−	33.2656i	0.230085	−	2.62988i
$161$	−1.49684	−	0.697989i	−0.117968	−	0.0550092i
$162$	−13.6508	+	11.4544i	−1.07251	+	0.899939i
$163$	−1.71211	−	6.38968i	−0.134103	−	0.500478i	−1.00000		0.000256375i	$-0.999918\pi$
$163$	−1.71211	−	6.38968i	−0.134103	−	0.500478i	0.865897	−	0.500222i	$-0.166748\pi$
$164$	30.4383	+	11.0786i	2.37683	+	0.865096i
$165$	16.9875	−	2.99536i	1.32248	−	0.233188i
$166$	14.9945	+	10.4993i	1.16380	+	0.814900i
$167$	2.44586	−	0.655365i	0.189266	−	0.0507137i	−0.162941	−	0.986636i	$-0.552098\pi$
$167$	2.44586	−	0.655365i	0.189266	−	0.0507137i	0.352207	+	0.935922i	$0.385431\pi$
$168$	16.9301	+	16.9301i	1.30619	+	1.30619i
$169$	−12.3200	−	2.17234i	−0.947689	−	0.167103i
$170$	33.8182	+	19.5249i	2.59373	+	1.49749i
$171$	7.32414	−	20.1229i	0.560091	−	1.53884i
$172$	0.215103	+	2.45864i	0.0164015	+	0.187470i
$173$			11.3241i			0.860953i	0.902602	+	0.430477i	$0.141655\pi$
$173$			11.3241i			0.860953i	−0.902602	+	0.430477i	$0.858345\pi$
$174$	−19.9975	+	1.74955i	−1.51600	+	0.132633i
$175$	−0.212002	+	0.302770i	−0.0160258	+	0.0228873i
$176$	−9.66096	+	36.0552i	−0.728222	+	2.71776i
$177$	4.50549	+	9.66205i	0.338653	+	0.726244i
$178$	−12.4402	−	10.4386i	−0.932435	−	0.782406i
$179$	0.252201	−	0.540846i	0.0188504	−	0.0404247i	−0.896657	−	0.442726i	$-0.854012\pi$
$179$	0.252201	−	0.540846i	0.0188504	−	0.0404247i	0.915508	+	0.402301i	$0.131789\pi$
$180$	36.5454	−	17.0414i	2.72394	−	1.27019i
$181$	6.11130	+	16.7907i	0.454249	+	1.24804i	0.929707	+	0.368301i	$0.120060\pi$
$181$	6.11130	+	16.7907i	0.454249	+	1.24804i	−0.475457	+	0.879739i	$0.657717\pi$
$182$	−0.361006	+	2.04737i	−0.0267595	+	0.151761i
$183$	3.58540	−	20.3338i	0.265041	−	1.50312i
$184$	−4.24205	−	11.6549i	−0.312728	−	0.859213i
$185$	−12.7932	+	5.96555i	−0.940572	+	0.438596i
$186$	7.09552	−	15.2164i	0.520269	−	1.11572i
$187$	−16.0689	−	13.4834i	−1.17507	−	0.986004i
$188$	3.93221	+	8.43266i	0.286786	+	0.615015i
$189$	−0.474112	+	1.76941i	−0.0344865	+	0.128706i
$190$	19.4697	−	27.8055i	1.41248	−	2.01723i
$191$	3.22921	−	0.282519i	0.233657	−	0.0204424i	0.0302744	−	0.999542i	$-0.490362\pi$
$191$	3.22921	−	0.282519i	0.233657	−	0.0204424i	0.203383	+	0.979099i	$0.434806\pi$
$192$			44.2528i			3.19367i
$193$	−1.12391	−	12.8464i	−0.0809011	−	0.924704i	−0.922853	−	0.385152i	$-0.874149\pi$
$193$	−1.12391	−	12.8464i	−0.0809011	−	0.924704i	0.841952	−	0.539552i	$-0.181406\pi$
$194$	7.69271	−	21.1355i	0.552304	−	1.51744i
$195$	3.37465	+	1.94836i	0.241664	+	0.139525i
$196$	29.1059	+	5.13216i	2.07900	+	0.366583i
$197$	−7.24166	−	7.24166i	−0.515947	−	0.515947i	0.400395	−	0.916342i	$-0.368873\pi$
$197$	−7.24166	−	7.24166i	−0.515947	−	0.515947i	−0.916342	+	0.400395i	$0.868873\pi$
$198$	−29.0815	+	7.79235i	−2.06673	+	0.553779i
$199$	9.42647	+	6.60048i	0.668224	+	0.467896i	0.857809	−	0.513969i	$-0.171825\pi$
$199$	9.42647	+	6.60048i	0.668224	+	0.467896i	−0.189585	+	0.981864i	$0.560714\pi$
$200$	−2.73353	+	0.481995i	−0.193290	+	0.0340822i
$201$	6.19217	+	2.25376i	0.436762	+	0.158968i
$202$	−7.58036	−	28.2903i	−0.533352	−	1.99050i
$203$	2.48640	−	2.08634i	0.174511	−	0.146432i
$204$	−81.0776	−	37.8071i	−5.67657	−	2.64703i
$205$	−1.18925	+	13.5932i	−0.0830611	+	0.949392i
$206$	−20.4901	−	1.79265i	−1.42761	−	0.124900i
$207$	3.47309	−	4.13907i	0.241396	−	0.287685i
$208$	−6.90731	+	4.83655i	−0.478936	+	0.335354i
$209$	−12.8933	+	12.8933i	−0.891849	+	0.891849i
$210$	−8.26668	+	14.3183i	−0.570455	+	0.988057i
$211$	8.48541	+	14.6972i	0.584160	+	1.01179i	0.994980	+	0.100078i	$0.0319093\pi$
$211$	8.48541	+	14.6972i	0.584160	+	1.01179i	−0.410820	+	0.911717i	$0.634757\pi$
$212$	46.5342	+	12.4688i	3.19598	+	0.856361i
$213$	14.8213	+	17.6634i	1.01554	+	1.21027i
$214$	25.3430	+	36.1935i	1.73241	+	2.47414i
$215$	−0.976970	+	0.355588i	−0.0666288	+	0.0242509i
$216$	−11.9135	+	6.87826i	−0.810610	+	0.468006i
$217$	0.471404	+	2.67347i	0.0320010	+	0.181487i
$218$	19.6465			1.33063
$219$	10.9189	+	19.1163i	0.737829	+	1.29176i
$220$	−34.3346			−2.31484
$221$	−0.822853	−	4.66663i	−0.0553511	−	0.313912i
$222$	38.9261	−	22.4740i	2.61255	−	1.50836i
$223$	1.70950	−	0.622208i	0.114477	−	0.0416661i	−0.284147	−	0.958781i	$-0.591710\pi$
$223$	1.70950	−	0.622208i	0.114477	−	0.0416661i	0.398623	+	0.917115i	$0.369488\pi$
$224$	−9.86139	−	14.0835i	−0.658892	−	0.940995i
$225$	−0.777256	−	0.926298i	−0.0518171	−	0.0617532i
$226$	−12.8661	−	3.44747i	−0.855843	−	0.229322i
$227$	−11.1338	−	19.2843i	−0.738977	−	1.27995i	−0.952956	−	0.303107i	$-0.901976\pi$
$227$	−11.1338	−	19.2843i	−0.738977	−	1.27995i	0.213979	−	0.976838i	$-0.431357\pi$
$228$	−38.8815	+	67.3447i	−2.57499	+	4.46001i
$229$	−9.59783	+	9.59783i	−0.634242	+	0.634242i	−0.949129	−	0.314887i	$-0.898033\pi$
$229$	−9.59783	+	9.59783i	−0.634242	+	0.634242i	0.314887	+	0.949129i	$0.398033\pi$
$230$	7.01576	−	4.91249i	0.462606	−	0.323920i
$231$	5.70875	−	6.80342i	0.375608	−	0.447632i
$232$	24.2821	+	2.12441i	1.59420	+	0.139474i
$233$	1.90637	−	21.7899i	0.124890	−	1.42750i	−0.632511	−	0.774551i	$-0.717976\pi$
$233$	1.90637	−	21.7899i	0.124890	−	1.42750i	0.757401	−	0.652950i	$-0.226469\pi$
$234$	−6.16408	−	2.87436i	−0.402959	−	0.187903i
$235$	−3.00252	+	2.51942i	−0.195863	+	0.164349i
$236$	−5.49216	−	20.4970i	−0.357509	−	1.33424i
$237$	31.4717	+	11.4548i	2.04431	+	0.744067i
$238$	19.8000	−	3.49128i	1.28345	−	0.226306i
$239$	−17.3523	−	12.1502i	−1.12243	−	0.785934i	−0.143403	−	0.989664i	$-0.545805\pi$
$239$	−17.3523	−	12.1502i	−1.12243	−	0.785934i	−0.979027	+	0.203730i	$0.934693\pi$
$240$	−64.7746	+	17.3563i	−4.18118	+	1.12035i
$241$	2.32329	+	2.32329i	0.149656	+	0.149656i	0.777964	−	0.628308i	$-0.216252\pi$
$241$	2.32329	+	2.32329i	0.149656	+	0.149656i	−0.628308	+	0.777964i	$0.716252\pi$
$242$	−3.67709	−	0.648371i	−0.236373	−	0.0416789i
$243$	19.1715	+	11.0687i	1.22985	+	0.710056i
$244$	−14.0564	+	38.6195i	−0.899866	+	2.47236i
$245$	1.08510	+	12.4028i	0.0693246	+	0.792383i
$246$		−	43.4497i		−	2.77025i
$247$	−4.10340	+	0.359001i	−0.261093	+	0.0228427i
$248$	−11.6933	+	16.6998i	−0.742528	+	1.06044i
$249$	4.57207	−	17.0632i	0.289743	−	1.08134i
$250$	−12.9993	−	27.8770i	−0.822146	−	1.76310i
$251$	11.1163	+	9.32767i	0.701654	+	0.588758i	0.922244	−	0.386609i	$-0.126354\pi$
$251$	11.1163	+	9.32767i	0.701654	+	0.588758i	−0.220590	+	0.975367i	$0.570798\pi$
$252$	8.77406	−	18.8160i	0.552714	−	1.18530i
$253$	−4.16964	+	1.94434i	−0.262143	+	0.122239i
$254$	−13.4012	−	36.8196i	−0.840869	−	2.31027i
$255$	6.54394	−	37.1125i	0.409797	−	2.32408i
$256$	0.963603	−	5.46487i	0.0602252	−	0.341554i
$257$	−3.28010	−	9.01199i	−0.204607	−	0.562152i	0.794367	−	0.607438i	$-0.207803\pi$
$257$	−3.28010	−	9.01199i	−0.204607	−	0.562152i	−0.998974	+	0.0452853i	$0.985580\pi$
$258$	3.00040	−	1.39911i	0.186797	−	0.0871048i
$259$	−3.07147	+	6.58678i	−0.190852	+	0.409283i
$260$	−5.94164	−	4.98562i	−0.368485	−	0.309195i
$261$	4.48760	+	9.62370i	0.277776	+	0.595692i
$262$	−13.3656	+	49.8813i	−0.825732	+	3.08167i
$263$	16.1488	−	23.0629i	0.995778	−	1.42212i	0.0911890	−	0.995834i	$-0.470933\pi$
$263$	16.1488	−	23.0629i	0.995778	−	1.42212i	0.904589	−	0.426285i	$-0.140178\pi$
$264$	66.4419	−	5.81291i	4.08921	−	0.357760i
$265$			20.2942i			1.24666i
$266$	−1.52320	−	17.4103i	−0.0933936	−	1.06749i
$267$	−5.36013	+	14.7268i	−0.328035	+	0.901268i
$268$	−11.3590	−	6.55813i	−0.693863	−	0.400602i
$269$	7.52591	+	1.32702i	0.458863	+	0.0809099i	0.398301	−	0.917255i	$-0.369600\pi$
$269$	7.52591	+	1.32702i	0.458863	+	0.0809099i	0.0605613	+	0.998164i	$0.480711\pi$
$270$	−6.71707	−	6.71707i	−0.408788	−	0.408788i
$271$	−9.71044	+	2.60190i	−0.589867	+	0.158054i	−0.541392	−	0.840770i	$-0.682103\pi$
$271$	−9.71044	+	2.60190i	−0.589867	+	0.158054i	−0.0484746	+	0.998824i	$0.515436\pi$
$272$	66.8004	+	46.7742i	4.05037	+	2.83610i
$273$	1.97581	−	0.348389i	0.119581	−	0.0210854i
$274$	34.4776	+	12.5488i	2.08287	+	0.758102i
$275$	0.266482	+	0.994523i	0.0160694	+	0.0599720i
$276$	−15.0304	+	12.6120i	−0.904723	+	0.759153i
$277$	29.7370	+	13.8666i	1.78672	+	0.833163i	0.964538	+	0.263945i	$0.0850239\pi$
$277$	29.7370	+	13.8666i	1.78672	+	0.833163i	0.822187	+	0.569218i	$0.192754\pi$
$278$	−0.643321	+	7.35320i	−0.0385838	+	0.441015i
$279$	−8.84740	−	0.774047i	−0.529680	−	0.0463410i
$280$	12.9045	−	15.3789i	0.771188	−	0.919067i
$281$	−5.06668	+	3.54772i	−0.302253	+	0.211639i	−0.714857	−	0.699271i	$-0.753508\pi$
$281$	−5.06668	+	3.54772i	−0.302253	+	0.211639i	0.412604	+	0.910910i	$0.364619\pi$
$282$	8.82523	−	8.82523i	0.525535	−	0.525535i
$283$	−2.28208	+	3.95268i	−0.135656	+	0.234963i	−0.925848	−	0.377897i	$-0.876647\pi$
$283$	−2.28208	+	3.95268i	−0.135656	+	0.234963i	0.790192	+	0.612859i	$0.209981\pi$
$284$	−22.9479	−	39.7469i	−1.36171	−	2.35855i
$285$	−31.6417	−	8.47838i	−1.87429	−	0.502216i
$286$	3.72250	+	4.43630i	0.220116	+	0.262324i
$287$	4.02963	+	5.75491i	0.237861	+	0.339701i
$288$	52.8544	−	19.2374i	3.11447	−	1.13358i
$289$	−24.9650	+	14.4135i	−1.46853	+	0.847856i
$290$	2.92280	+	16.5760i	0.171632	+	0.973376i
$291$	−21.7059			−1.27242
$292$	−14.7960	−	41.2462i	−0.865873	−	2.41375i
$293$	22.4269			1.31020			0.655098	−	0.755544i	$-0.272627\pi$
$293$	22.4269			1.31020			0.655098	+	0.755544i	$0.272627\pi$
$294$	−6.88419	−	39.0422i	−0.401494	−	2.27699i
$295$	7.74144	−	4.46952i	0.450724	−	0.260226i
$296$	−51.2870	+	18.6669i	−2.98100	+	1.08499i
$297$	2.92684	+	4.17996i	0.169832	+	0.242546i
$298$	−21.8702	−	26.0639i	−1.26691	−	1.50984i
$299$	−1.00389	−	0.268992i	−0.0580566	−	0.0155562i
$300$	2.19550	+	3.80273i	0.126758	+	0.219550i
$301$	−0.267646	+	0.463576i	−0.0154269	+	0.0267201i
$302$	12.4347	−	12.4347i	0.715539	−	0.715539i
$303$	−23.1530	+	16.2119i	−1.33011	+	0.931351i
$304$	45.5648	−	54.3020i	2.61332	−	3.11444i
$305$	−17.2468	−	1.50890i	−0.987550	−	0.0863994i
$306$	−5.73270	+	65.5250i	−0.327716	+	3.74582i
$307$	−30.7291	−	14.3292i	−1.75380	−	0.817811i	−0.983683	−	0.179911i	$-0.942419\pi$
$307$	−30.7291	−	14.3292i	−1.75380	−	0.817811i	−0.770119	−	0.637900i	$-0.779803\pi$
$308$	−13.5419	+	11.3630i	−0.771624	+	0.647469i
$309$	5.13743	+	19.1732i	0.292258	+	1.09072i
$310$	−13.2288	−	4.81488i	−0.751343	−	0.273467i
$311$	−32.8894	+	5.79929i	−1.86499	+	0.328847i	−0.988337	−	0.152282i	$-0.951338\pi$
$311$	−32.8894	+	5.79929i	−1.86499	+	0.328847i	−0.876650	+	0.481129i	$0.840227\pi$
$312$	12.3419	+	8.64190i	0.698723	+	0.489251i
$313$	2.60898	−	0.699074i	0.147468	−	0.0395140i	−0.184330	−	0.982864i	$-0.559011\pi$
$313$	2.60898	−	0.699074i	0.147468	−	0.0395140i	0.331798	+	0.943350i	$0.392345\pi$
$314$	35.5642	+	35.5642i	2.00700	+	2.00700i
$315$	8.61287	+	1.51868i	0.485280	+	0.0855680i
$316$	−57.7322	−	33.3317i	−3.24769	−	1.87506i
$317$	4.20834	−	11.5623i	0.236364	−	0.649404i	−0.763629	−	0.645655i	$-0.776584\pi$
$317$	4.20834	−	11.5623i	0.236364	−	0.649404i	0.999993	−	0.00374893i	$-0.00119332\pi$
$318$	−5.63219	−	64.3762i	−0.315837	−	3.61004i
$319$		−	9.04150i		−	0.506227i
$320$	36.9643	−	3.23396i	2.06637	−	0.180784i
$321$	24.4572	−	34.9285i	1.36507	−	1.94952i
$322$	1.14131	−	4.25941i	0.0636025	−	0.237368i
$323$	16.8352	+	36.1032i	0.936735	+	2.00884i
$324$	−26.2217	−	22.0026i	−1.45676	−	1.22237i
$325$	−0.0982969	+	0.210798i	−0.00545253	+	0.0116930i
$326$	16.0072	−	7.46430i	0.886560	−	0.413410i
$327$	−6.48466	−	17.8165i	−0.358603	−	0.985253i
$328$	−9.16153	+	51.9576i	−0.505861	+	2.86888i
$329$	−0.350427	+	1.98737i	−0.0193197	+	0.109567i
$330$	15.7520	+	43.2783i	0.867119	+	2.38239i
$331$	17.4938	−	8.15748i	0.961545	−	0.448376i	0.122518	−	0.992466i	$-0.460903\pi$
$331$	17.4938	−	8.15748i	0.961545	−	0.448376i	0.839026	+	0.544091i	$0.183125\pi$
$332$	−14.8600	+	31.8673i	−0.815548	+	1.74895i
$333$	−18.2138	−	15.2832i	−0.998108	−	0.837512i
$334$	2.85720	+	6.12729i	0.156339	+	0.335270i
$335$	1.43005	−	5.33701i	0.0781318	−	0.291592i
$336$	−19.8038	+	28.2827i	−1.08038	+	1.54295i
$337$	−3.56852	+	0.312205i	−0.194390	+	0.0170069i	−0.183935	−	0.982938i	$-0.558884\pi$
$337$	−3.56852	+	0.312205i	−0.194390	+	0.0170069i	−0.0104550	+	0.999945i	$0.503328\pi$
$338$		−	33.4013i		−	1.81679i
$339$	1.12034	+	12.8055i	0.0608485	+	0.695502i
$340$	−25.6551	+	70.4869i	−1.39134	+	3.82269i
$341$	6.54902	+	3.78108i	0.354650	+	0.204757i
$342$	56.3069	+	9.92843i	3.04473	+	0.536868i
$343$	10.0386	+	10.0386i	0.542034	+	0.542034i
$344$	−3.88292	+	1.04043i	−0.209353	+	0.0560960i
$345$	−6.77056	−	4.74080i	−0.364515	−	0.255236i
$346$	−29.7755	+	5.25023i	−1.60074	+	0.282254i
$347$	−14.1540	−	5.15164i	−0.759827	−	0.276555i	−0.0670924	−	0.997747i	$-0.521372\pi$
$347$	−14.1540	−	5.15164i	−0.759827	−	0.276555i	−0.692735	+	0.721192i	$0.743594\pi$
$348$	−9.97999	−	37.2458i	−0.534984	−	1.99659i
$349$	5.30175	−	4.44870i	0.283796	−	0.238133i	−0.489766	−	0.871854i	$-0.662918\pi$
$349$	5.30175	−	4.44870i	0.283796	−	0.238133i	0.773562	+	0.633721i	$0.218473\pi$
$350$	−0.894395	−	0.417063i	−0.0478074	−	0.0222930i
$351$	−0.100467	+	1.14834i	−0.00536253	+	0.0612940i
$352$	−47.7105	−	4.17413i	−2.54298	−	0.222482i
$353$	−4.48636	+	5.34664i	−0.238785	+	0.284573i	−0.872107	−	0.489316i	$-0.837247\pi$
$353$	−4.48636	+	5.34664i	−0.238785	+	0.284573i	0.633322	+	0.773889i	$0.281691\pi$
$354$	−23.3165	+	16.3264i	−1.23926	+	0.867739i
$355$	13.6710	−	13.6710i	0.725584	−	0.725584i
$356$	15.5972	−	27.0152i	0.826651	−	1.43180i
$357$	−9.70139	−	16.8033i	−0.513452	−	0.889325i
$358$	1.53903	+	0.412382i	0.0813403	+	0.0217951i
$359$	19.0721	+	22.7292i	1.00658	+	1.19960i	0.979804	+	0.199960i	$0.0640812\pi$
$359$	19.0721	+	22.7292i	1.00658	+	1.19960i	0.0267808	+	0.999641i	$0.491474\pi$
$360$	37.6714	+	53.8003i	1.98546	+	2.83553i
$361$	14.6848	−	5.34482i	0.772882	−	0.281306i
$362$	−41.3160	+	23.8538i	−2.17152	+	1.25373i
$363$	0.625710	+	3.54858i	0.0328413	+	0.186252i
$364$	−3.99344			−0.209313
$365$	15.1699	−	10.5175i	0.794028	−	0.550512i
$366$	55.1281			2.88159
$367$	2.02588	+	11.4893i	0.105750	+	0.599739i	0.990918	+	0.134467i	$0.0429322\pi$
$367$	2.02588	+	11.4893i	0.105750	+	0.599739i	−0.885168	+	0.465272i	$0.845957\pi$
$368$	15.4895	−	8.94285i	0.807444	−	0.466178i
$369$	−21.5977	+	7.86093i	−1.12433	+	0.409224i
$370$	−21.6172	−	30.8725i	−1.12382	−	1.60499i
$371$	6.71638	+	8.00427i	0.348697	+	0.415561i
$372$	31.1518	+	8.34710i	1.61515	+	0.432777i
$373$	2.15242	+	3.72809i	0.111448	+	0.193033i	0.916354	−	0.400368i	$-0.131118\pi$
$373$	2.15242	+	3.72809i	0.111448	+	0.193033i	−0.804906	+	0.593402i	$0.797785\pi$
$374$	28.0032	−	48.5029i	1.44801	−	2.50803i
$375$	−20.9897	+	20.9897i	−1.08390	+	1.08390i
$376$	−12.4141	+	8.69247i	−0.640210	+	0.448280i
$377$	1.31289	−	1.56464i	0.0676173	−	0.0805831i
$378$	−4.87230	−	0.426271i	−0.250604	−	0.0219250i
$379$	−1.26971	+	14.5129i	−0.0652207	+	0.745476i	0.891224	+	0.453563i	$0.149847\pi$
$379$	−1.26971	+	14.5129i	−0.0652207	+	0.745476i	−0.956445	+	0.291913i	$0.905708\pi$
$380$	59.0943	+	27.5561i	3.03147	+	1.41360i
$381$	−28.9666	+	24.3058i	−1.48400	+	1.24523i
$382$	2.24003	+	8.35991i	0.114610	+	0.427730i
$383$	−6.60046	−	2.40237i	−0.337268	−	0.122755i	0.167834	−	0.985815i	$-0.446323\pi$
$383$	−6.60046	−	2.40237i	−0.337268	−	0.122755i	−0.505102	+	0.863060i	$0.668545\pi$
$384$	−37.9189	+	6.68612i	−1.93504	+	0.341200i
$385$	−6.10008	−	4.27132i	−0.310889	−	0.217687i
$386$	33.2573	−	8.91126i	1.69275	−	0.453571i
$387$	−1.23829	−	1.23829i	−0.0629461	−	0.0629461i
$388$	42.5483	+	7.50241i	2.16006	+	0.380877i
$389$	−10.0437	−	5.79874i	−0.509236	−	0.294008i	0.223283	−	0.974754i	$-0.428323\pi$
$389$	−10.0437	−	5.79874i	−0.509236	−	0.294008i	−0.732520	+	0.680746i	$0.761656\pi$
$390$	−3.55841	+	9.77665i	−0.180187	+	0.495060i
$391$	0.876011	+	10.0128i	0.0443018	+	0.506372i
$392$			48.1386i			2.43137i
$393$	49.6464	−	4.34349i	2.50433	−	0.219100i
$394$	15.6838	−	22.3987i	0.790137	−	1.12843i
$395$	7.26822	−	27.1254i	0.365704	−	1.36482i
$396$	−24.4413	−	52.4145i	−1.22822	−	2.63393i
$397$	1.97729	+	1.65914i	0.0992371	+	0.0832698i	0.691056	−	0.722801i	$-0.257146\pi$
$397$	1.97729	+	1.65914i	0.0992371	+	0.0832698i	−0.591819	+	0.806071i	$0.701590\pi$
$398$	−12.9849	+	27.8462i	−0.650874	+	1.39580i
$399$	−15.2858	+	7.12787i	−0.765246	+	0.356840i
$400$	−1.36901	−	3.76132i	−0.0684503	−	0.188066i
$401$	2.99655	−	16.9943i	0.149641	−	0.848654i	−0.813883	−	0.581029i	$-0.802650\pi$
$401$	2.99655	−	16.9943i	0.149641	−	0.848654i	0.963523	−	0.267625i	$-0.0862388\pi$
$402$	−3.05515	+	17.3266i	−0.152377	+	0.864173i
$403$	0.584276	+	1.60528i	0.0291049	+	0.0799649i
$404$	50.9885	−	23.7763i	2.53677	−	1.18292i
$405$	6.09394	−	13.0685i	0.302810	−	0.649379i
$406$	6.63861	+	5.57046i	0.329469	+	0.276457i
$407$	8.55596	+	18.3483i	0.424103	+	0.909492i
$408$	37.7124	−	140.745i	1.86704	−	6.96790i
$409$	−2.30549	+	3.29259i	−0.113999	+	0.162808i	−0.872097	−	0.489333i	$-0.837240\pi$
$409$	−2.30549	+	3.29259i	−0.113999	+	0.162808i	0.758098	+	0.652141i	$0.226129\pi$
$410$	−36.2935	+	3.17527i	−1.79241	+	0.156815i
$411$		−	35.4080i		−	1.74655i
$412$	−3.44349	−	39.3593i	−0.169649	−	1.93909i
$413$	1.57412	−	4.32486i	0.0774574	−	0.212812i
$414$	12.4935	+	7.21314i	0.614023	+	0.354506i
$415$	−14.5870	−	2.57208i	−0.716047	−	0.126258i
$416$	−7.65024	−	7.65024i	−0.375084	−	0.375084i
$417$	6.88058	−	1.84365i	0.336944	−	0.0902838i
$418$	−39.8795	−	27.9239i	−1.95057	−	1.36580i
$419$	22.0112	−	3.88117i	1.07532	−	0.189608i	0.392174	−	0.919891i	$-0.371723\pi$
$419$	22.0112	−	3.88117i	1.07532	−	0.189608i	0.683145	+	0.730283i	$0.260612\pi$
$420$	−29.8435	−	10.8621i	−1.45621	−	0.530019i
$421$	−1.36835	−	5.10675i	−0.0666893	−	0.248888i	0.924531	−	0.381106i	$-0.124457\pi$
$421$	−1.36835	−	5.10675i	−0.0666893	−	0.248888i	−0.991221	+	0.132218i	$0.957790\pi$
$422$	−34.7106	+	29.1257i	−1.68969	+	1.41782i
$423$	−5.98345	−	2.79013i	−0.290926	−	0.135661i
$424$	−6.83893	+	78.1693i	−0.332128	+	3.79624i
$425$	2.24081	+	0.196046i	0.108695	+	0.00950962i
$426$	−39.5724	+	47.1606i	−1.91729	+	2.28494i
$427$	−7.30171	+	5.11271i	−0.353355	+	0.247422i
$428$	−60.0142	+	60.0142i	−2.90090	+	2.90090i
$429$	2.79439	−	4.84002i	0.134914	−	0.233678i
$430$	−1.38794	−	2.40398i	−0.0669325	−	0.115930i
$431$	17.1986	+	4.60836i	0.828429	+	0.221977i	0.648028	−	0.761616i	$-0.275594\pi$
$431$	17.1986	+	4.60836i	0.828429	+	0.221977i	0.180401	+	0.983593i	$0.442260\pi$
$432$	−12.7514	−	15.1965i	−0.613502	−	0.731143i
$433$	−22.8388	−	32.6172i	−1.09756	−	1.56748i	−0.787023	−	0.616924i	$-0.788379\pi$
$433$	−22.8388	−	32.6172i	−1.09756	−	1.56748i	−0.310541	−	0.950560i	$-0.600510\pi$
$434$	−6.81106	+	2.47902i	−0.326941	+	0.118997i
$435$	14.0672	−	8.12171i	0.674472	−	0.389406i
$436$	6.55329	+	37.1656i	0.313846	+	1.77991i
$437$	8.73697			0.417946
$438$	−45.2021	+	37.5731i	−2.15984	+	1.79531i
$439$	−17.2603			−0.823789			−0.411895	−	0.911231i	$-0.635133\pi$
$439$	−17.2603			−0.823789			−0.411895	+	0.911231i	$0.635133\pi$
$440$	−9.71103	−	55.0740i	−0.462955	−	2.62555i
$441$	−18.1614	+	10.4855i	−0.864827	+	0.499308i
$442$	11.8890	−	4.32722i	0.565500	−	0.205825i
$443$	−3.51627	−	5.02175i	−0.167063	−	0.238591i	0.726887	−	0.686757i	$-0.240966\pi$
$443$	−3.51627	−	5.02175i	−0.167063	−	0.238591i	−0.893950	+	0.448166i	$0.852077\pi$
$444$	55.4985	+	66.1405i	2.63384	+	3.13889i
$445$	12.6930	+	3.40109i	0.601707	+	0.161227i
$446$	2.42862	+	4.20649i	0.114998	+	0.199183i
$447$	−16.4174	+	28.4358i	−0.776517	+	1.34497i
$448$	13.5089	−	13.5089i	0.638234	−	0.638234i
$449$	11.6317	−	8.14463i	0.548936	−	0.384369i	−0.265953	−	0.963986i	$-0.585687\pi$
$449$	11.6317	−	8.14463i	0.548936	−	0.384369i	0.814889	+	0.579617i	$0.196798\pi$
$450$	2.07525	−	2.47318i	0.0978281	−	0.116587i
$451$	19.4958	+	1.70566i	0.918021	+	0.0803164i
$452$	2.22999	−	25.4889i	0.104890	−	1.19890i
$453$	−15.3807	−	7.17215i	−0.722650	−	0.336977i
$454$	45.5442	−	38.2162i	2.13750	−	1.79357i
$455$	−0.435399	−	1.62493i	−0.0204118	−	0.0761779i
$456$	−119.020	−	43.3199i	−5.57364	−	2.02864i
$457$	29.5405	−	5.20879i	1.38185	−	0.243657i	0.567184	−	0.823591i	$-0.308033\pi$
$457$	29.5405	−	5.20879i	1.38185	−	0.243657i	0.814663	+	0.579934i	$0.196922\pi$
$458$	−29.6864	−	20.7867i	−1.38716	−	0.971297i
$459$	10.7682	−	2.88532i	0.502615	−	0.134675i
$460$	11.6332	+	11.6332i	0.542400	+	0.542400i
$461$	−3.04171	−	0.536336i	−0.141667	−	0.0249797i	0.102365	−	0.994747i	$-0.467359\pi$
$461$	−3.04171	−	0.536336i	−0.141667	−	0.0249797i	−0.244032	+	0.969767i	$0.578470\pi$
$462$	20.5357	+	11.8563i	0.955408	+	0.551605i
$463$	0.936136	−	2.57201i	0.0435059	−	0.119532i	−0.916037	−	0.401093i	$-0.868630\pi$
$463$	0.936136	−	2.57201i	0.0435059	−	0.119532i	0.959543	+	0.281562i	$0.0908525\pi$
$464$	3.06351	+	35.0161i	0.142220	+	1.62558i
$465$			13.5857i			0.630023i
$466$	58.1782	−	5.08993i	2.69505	−	0.235786i
$467$	10.2048	−	14.5739i	0.472220	−	0.674400i	−0.510419	−	0.859926i	$-0.670510\pi$
$467$	10.2048	−	14.5739i	0.472220	−	0.674400i	0.982639	+	0.185525i	$0.0593987\pi$
$468$	3.38136	−	12.6194i	0.156304	−	0.583333i
$469$	−1.20226	−	2.57825i	−0.0555151	−	0.119053i
$470$	−8.01664	−	6.72676i	−0.369780	−	0.310282i
$471$	20.5128	−	43.9899i	0.945182	−	2.02695i
$472$	31.3246	−	14.6069i	1.44183	−	0.672338i
$473$	0.509994	+	1.40120i	0.0234496	+	0.0644271i
$474$	−15.5278	+	88.0626i	−0.713216	+	4.04485i
$475$	0.339531	−	1.92558i	0.0155787	−	0.0883515i
$476$	13.2090	+	36.2914i	0.605433	+	1.66341i
$477$	−30.9808	+	14.4466i	−1.41851	+	0.661463i
$478$	23.9027	−	51.2596i	1.09329	−	2.34456i
$479$	−5.88864	−	4.94115i	−0.269059	−	0.225767i	0.498269	−	0.867023i	$-0.333969\pi$
$479$	−5.88864	−	4.94115i	−0.269059	−	0.225767i	−0.767327	+	0.641256i	$0.778414\pi$
$480$	−36.3626	−	77.9798i	−1.65972	−	3.55928i
$481$	−1.18369	+	4.41758i	−0.0539715	+	0.201424i
$482$	−5.03170	+	7.18601i	−0.229188	+	0.327314i
$483$	−4.23935	+	0.370895i	−0.192897	+	0.0168763i
$484$		−	7.17226i		−	0.326012i
$485$	1.58625	+	18.1309i	0.0720277	+	0.823281i
$486$	−20.2154	+	55.5414i	−0.916990	+	2.51941i
$487$	4.47547	+	2.58391i	0.202803	+	0.117088i	0.597962	−	0.801524i	$-0.295977\pi$
$487$	4.47547	+	2.58391i	0.202803	+	0.117088i	−0.395159	+	0.918613i	$0.629311\pi$
$488$	−65.9228	−	11.6240i	−2.98418	−	0.526192i
$489$	−12.0525	−	12.0525i	−0.545031	−	0.545031i
$490$	−32.1088	+	8.60352i	−1.45053	+	0.388667i
$491$	−11.9998	−	8.40233i	−0.541542	−	0.379192i	0.270564	−	0.962702i	$-0.412790\pi$
$491$	−11.9998	−	8.40233i	−0.541542	−	0.379192i	−0.812106	+	0.583510i	$0.801679\pi$
$492$	82.1942	−	14.4931i	3.70560	−	0.653397i
$493$	−18.5617	−	6.75589i	−0.835975	−	0.304270i
$494$	−2.84644	−	10.6230i	−0.128067	−	0.477953i
$495$	18.6626	−	15.6598i	0.838824	−	0.703857i
$496$	−26.6443	−	12.4244i	−1.19637	−	0.557874i
$497$	0.867577	−	9.91645i	0.0389161	−	0.444813i
$498$	46.9858	+	4.11072i	2.10548	+	0.184206i
$499$	17.6662	−	21.0537i	0.790846	−	0.942493i	−0.208523	−	0.978017i	$-0.566866\pi$
$499$	17.6662	−	21.0537i	0.790846	−	0.942493i	0.999369	+	0.0355242i	$0.0113101\pi$
$500$	48.3992	−	33.8895i	2.16448	−	1.51558i
$501$	4.61346	−	4.61346i	0.206114	−	0.206114i
$502$	−19.3723	+	33.5538i	−0.864629	+	1.49758i
$503$	12.0283	+	20.8336i	0.536316	+	0.928927i	0.999098	+	0.0424546i	$0.0135178\pi$
$503$	12.0283	+	20.8336i	0.536316	+	0.928927i	−0.462782	+	0.886472i	$0.653149\pi$
$504$	32.6633	+	8.75209i	1.45494	+	0.389849i
$505$	15.2338	+	18.1549i	0.677895	+	0.807884i
$506$	−7.04563	−	10.0622i	−0.313216	−	0.447320i
$507$	−30.2900	+	11.0246i	−1.34522	+	0.489622i
$508$	65.1819	−	37.6328i	2.89198	−	1.66968i
$509$	−2.45147	−	13.9030i	−0.108660	−	0.616239i	−0.989695	−	0.143189i	$-0.954264\pi$
$509$	−2.45147	−	13.9030i	−0.108660	−	0.616239i	0.881036	−	0.473050i	$-0.156847\pi$
$510$	100.618			4.45543
$511$	2.50240	−	9.16871i	0.110700	−	0.405600i
$512$	−15.0707			−0.666036
$513$	−1.68273	−	9.54326i	−0.0742945	−	0.421345i
$514$	22.1754	−	12.8030i	0.978114	−	0.564714i
$515$	15.6399	−	5.69245i	0.689175	−	0.250839i
$516$	3.64752	+	5.20920i	0.160573	+	0.229322i
$517$	3.61342	+	4.30630i	0.158918	+	0.189391i
$518$	−18.7433	−	5.02226i	−0.823535	−	0.220665i
$519$	14.5891	+	25.2690i	0.640389	+	1.10919i
$520$	6.31663	−	10.9407i	0.277002	−	0.479782i
$521$	−22.8018	+	22.8018i	−0.998963	+	0.998963i	−0.999999	−	0.00103599i	$-0.999670\pi$
$521$	−22.8018	+	22.8018i	−0.998963	+	0.998963i	0.00103599	+	0.999999i	$0.499670\pi$
$522$	−23.2240	+	16.2616i	−1.01649	+	0.711751i
$523$	−6.91498	+	8.24096i	−0.302371	+	0.360352i	−0.895740	−	0.444579i	$-0.853353\pi$
$523$	−6.91498	+	8.24096i	−0.302371	+	0.360352i	0.593368	+	0.804931i	$0.297798\pi$
$524$	−98.8191	−	8.64555i	−4.31693	−	0.377683i
$525$	−0.0830041	+	0.948741i	−0.00362260	+	0.0414065i
$526$	68.1288	+	31.7690i	2.97055	+	1.38519i
$527$	12.6558	−	10.6195i	0.551296	−	0.462593i
$528$	24.8929	+	92.9016i	1.08332	+	4.04302i
$529$	−19.5414	−	7.11249i	−0.849626	−	0.309239i
$530$	−53.3617	+	9.40911i	−2.31788	+	0.408706i
$531$	12.3339	+	8.63626i	0.535244	+	0.374782i
$532$	32.4272	−	8.68883i	1.40590	−	0.376709i
$533$	3.12609	+	3.12609i	0.135406	+	0.135406i
$534$	−41.2080	−	7.26608i	−1.78324	−	0.314434i
$535$	−30.9631	−	17.8765i	−1.33865	−	0.772870i
$536$	7.30676	−	20.0752i	0.315604	−	0.867115i
$537$	−0.134014	−	1.53178i	−0.00578312	−	0.0661013i
$538$			20.4039i			0.879674i
$539$	17.7884	−	1.55628i	0.766200	−	0.0670338i
$540$	10.4662	−	14.9473i	0.450394	−	0.643229i
$541$	−5.62632	+	20.9977i	−0.241894	+	0.902762i	0.733025	+	0.680202i	$0.238108\pi$
$541$	−5.62632	+	20.9977i	−0.241894	+	0.902762i	−0.974919	+	0.222560i	$0.928559\pi$
$542$	−11.3435	−	24.3263i	−0.487247	−	1.04490i
$543$	35.2688	+	29.5941i	1.51353	+	1.27000i
$544$	−44.2189	+	94.8278i	−1.89587	+	4.06571i
$545$	−14.4082	+	6.71864i	−0.617178	+	0.287795i
$546$	1.83211	+	5.03368i	0.0784070	+	0.215421i
$547$	−2.66931	+	15.1384i	−0.114131	+	0.647271i	0.873045	+	0.487639i	$0.162142\pi$
$547$	−2.66931	+	15.1384i	−0.114131	+	0.647271i	−0.987177	+	0.159632i	$0.948969\pi$
$548$	−12.2384	+	69.4074i	−0.522799	+	2.96494i
$549$	−9.97379	−	27.4028i	−0.425671	−	1.16952i
$550$	−2.49145	+	1.16178i	−0.106236	+	0.0495386i
$551$	−7.25650	+	15.5616i	−0.309137	+	0.662947i
$552$	−24.4812	−	20.5422i	−1.04199	−	0.874334i
$553$	−6.11048	−	13.1040i	−0.259844	−	0.557237i
$554$	−22.6738	+	84.6196i	−0.963316	+	3.59514i
$555$	−20.8617	+	29.7935i	−0.885528	+	1.26466i
$556$	−14.1247	+	1.23575i	−0.599021	+	0.0524075i
$557$			27.5524i			1.16743i	0.811958	+	0.583716i	$0.198402\pi$
$557$			27.5524i			1.16743i	−0.811958	+	0.583716i	$0.801598\pi$
$558$	−2.06668	−	23.6223i	−0.0874895	−	1.00001i
$559$	−0.115209	+	0.316533i	−0.00487281	+	0.0133879i
$560$	25.0717	+	14.4752i	1.05947	+	0.611688i
$561$	−53.2278	−	9.38550i	−2.24728	−	0.396256i
$562$	−11.6775	−	11.6775i	−0.492585	−	0.492585i
$563$	23.3400	−	6.25394i	0.983665	−	0.263572i	0.269078	−	0.963118i	$-0.413281\pi$
$563$	23.3400	−	6.25394i	0.983665	−	0.263572i	0.714587	+	0.699546i	$0.246614\pi$
$564$	19.6385	+	13.7510i	0.826930	+	0.579023i
$565$	10.6146	−	1.87164i	0.446559	−	0.0787403i
$566$	−11.4512	−	4.16791i	−0.481332	−	0.175190i
$567$	−1.92150	−	7.17115i	−0.0806956	−	0.301160i
$568$	57.2651	−	48.0511i	2.40279	−	2.01618i
$569$	−3.70238	−	1.72645i	−0.155212	−	0.0723764i	0.343460	−	0.939167i	$-0.388401\pi$
$569$	−3.70238	−	1.72645i	−0.155212	−	0.0723764i	−0.498672	+	0.866791i	$0.666179\pi$
$570$	7.62286	−	87.1297i	0.319287	−	3.64946i
$571$	−22.7431	−	1.98977i	−0.951770	−	0.0832691i	−0.399317	−	0.916813i	$-0.630753\pi$
$571$	−22.7431	−	1.98977i	−0.951770	−	0.0832691i	−0.552453	+	0.833544i	$0.686308\pi$
$572$	−7.15052	+	8.52166i	−0.298978	+	0.356308i
$573$	6.84182	−	4.79069i	0.285821	−	0.200134i
$574$	−13.2637	+	13.2637i	−0.553616	+	0.553616i
$575$	0.246674	−	0.427251i	0.0102870	−	0.0178176i
$576$	31.2501	+	54.1268i	1.30209	+	2.25529i
$577$	−12.7502	−	3.41640i	−0.530798	−	0.142227i	−0.0165410	−	0.999863i	$-0.505265\pi$
$577$	−12.7502	−	3.41640i	−0.530798	−	0.142227i	−0.514257	+	0.857636i	$0.671932\pi$
$578$	−49.4737	−	58.9604i	−2.05783	−	2.45243i
$579$	−19.0583	−	27.2180i	−0.792035	−	1.13114i
$580$	−30.3820	+	11.0582i	−1.26155	+	0.459165i
$581$	−6.60450	+	3.81311i	−0.274001	+	0.158194i
$582$	−10.0636	−	57.0735i	−0.417149	−	2.36577i
$583$	29.1065			1.20547
$584$	61.9756	−	35.3993i	2.56457	−	1.46483i
$585$	5.50351			0.227542
$586$	10.3979	+	58.9694i	0.429533	+	2.43601i
$587$	−7.43148	+	4.29057i	−0.306730	+	0.177091i	−0.645462	−	0.763792i	$-0.723335\pi$
$587$	−7.43148	+	4.29057i	−0.306730	+	0.177091i	0.338732	+	0.940883i	$0.390002\pi$
$588$	71.5602	−	26.0458i	2.95109	−	1.07411i
$589$	−8.23712	−	11.7638i	−0.339405	−	0.484720i
$590$	15.3414	+	18.2831i	0.631594	+	0.752704i
$591$	−25.4890	−	6.82975i	−1.04848	−	0.280938i
$592$	−39.3526	−	68.1607i	−1.61738	−	2.80139i
$593$	−12.2078	+	21.1446i	−0.501316	+	0.868305i	0.498683	+	0.866785i	$0.333817\pi$
$593$	−12.2078	+	21.1446i	−0.501316	+	0.868305i	−0.999999	+	0.00152020i	$0.999516\pi$
$594$	−9.63380	+	9.63380i	−0.395280	+	0.395280i
$595$	−13.3268	+	9.33153i	−0.546346	+	0.382555i
$596$	42.0103	−	50.0659i	1.72081	−	2.05078i
$597$	29.5382	+	2.58426i	1.20892	+	0.105767i
$598$	0.241849	−	2.76435i	0.00988995	−	0.113043i
$599$	−33.5286	−	15.6346i	−1.36994	−	0.638814i	−0.408230	−	0.912879i	$-0.633854\pi$
$599$	−33.5286	−	15.6346i	−1.36994	−	0.638814i	−0.961711	+	0.274065i	$0.911631\pi$
$600$	−5.47875	+	4.59722i	−0.223669	+	0.187681i
$601$	4.12563	+	15.3971i	0.168288	+	0.628060i	0.997598	+	0.0692706i	$0.0220672\pi$
$601$	4.12563	+	15.3971i	0.168288	+	0.628060i	−0.829310	+	0.558789i	$0.811266\pi$
$602$	−1.34302	−	0.488819i	−0.0547373	−	0.0199228i
$603$	9.16535	−	1.61610i	0.373242	−	0.0658126i
$604$	27.6706	+	19.3752i	1.12590	+	0.788365i
$605$	2.91839	−	0.781981i	0.118650	−	0.0317921i
$606$	−53.3622	−	53.3622i	−2.16769	−	2.16769i
$607$	−8.06292	−	1.42171i	−0.327264	−	0.0577054i	0.00760255	−	0.999971i	$-0.497580\pi$
$607$	−8.06292	−	1.42171i	−0.327264	−	0.0577054i	−0.334866	+	0.942266i	$0.608691\pi$
$608$	78.7659	+	45.4755i	3.19438	+	1.84428i
$609$	2.86039	−	7.85885i	0.115909	−	0.318456i
$610$	−4.02871	−	46.0484i	−0.163118	−	1.86445i
$611$			1.26990i			0.0513748i
$612$	−125.867	+	11.0119i	−5.08785	+	0.445129i
$613$	−8.58598	+	12.2620i	−0.346784	+	0.495259i	−0.954218	−	0.299111i	$-0.903310\pi$
$613$	−8.58598	+	12.2620i	−0.346784	+	0.495259i	0.607434	+	0.794370i	$0.292199\pi$
$614$	23.4302	−	87.4427i	0.945566	−	3.52890i
$615$	14.8587	+	31.8647i	0.599162	+	1.28491i
$616$	−22.0569	−	18.5079i	−0.888697	−	0.745705i
$617$	−7.44905	+	15.9745i	−0.299887	+	0.643110i	−0.997290	−	0.0735690i	$-0.976561\pi$
$617$	−7.44905	+	15.9745i	−0.299887	+	0.643110i	0.697403	+	0.716679i	$0.254339\pi$
$618$	−48.0321	+	22.3977i	−1.93213	+	0.900968i
$619$	−9.68575	−	26.6114i	−0.389303	−	1.06960i	−0.967316	−	0.253574i	$-0.918394\pi$
$619$	−9.68575	−	26.6114i	−0.389303	−	1.06960i	0.578013	−	0.816028i	$-0.303828\pi$
$620$	4.69577	−	26.6310i	0.188587	−	1.06953i
$621$	0.424580	−	2.40791i	0.0170378	−	0.0966261i
$622$	−30.4973	−	83.7907i	−1.22283	−	3.35970i
$623$	6.13186	−	2.85933i	0.245668	−	0.114557i
$624$	−9.18222	+	19.6913i	−0.367583	+	0.788285i
$625$	17.7938	+	14.9308i	0.711754	+	0.597232i
$626$	3.04776	+	6.53595i	0.121813	+	0.261229i
$627$	−12.1599	+	45.3814i	−0.485620	+	1.81236i
$628$	−55.4144	+	79.1399i	−2.21127	+	3.15803i
$629$	44.0611	−	3.85484i	1.75683	−	0.153703i
$630$			23.3508i			0.930319i
$631$	2.16327	+	24.7263i	0.0861184	+	0.984338i	0.909185	+	0.416393i	$0.136706\pi$
$631$	2.16327	+	24.7263i	0.0861184	+	0.984338i	−0.823066	+	0.567945i	$0.807739\pi$
$632$	37.1366	−	102.032i	1.47722	−	4.05862i
$633$	37.8694	+	21.8639i	1.50518	+	0.869013i
$634$	32.3531	+	5.70472i	1.28491	+	0.226563i
$635$	22.4195	+	22.4195i	0.889689	+	0.889689i
$636$	119.902	−	32.1277i	4.75444	−	1.27395i
$637$	3.30428	+	2.31368i	0.130920	+	0.0916714i
$638$	23.7738	−	4.19195i	0.941212	−	0.165961i
$639$	30.6017	+	11.1381i	1.21059	+	0.440617i
$640$	8.35598	+	31.1850i	0.330299	+	1.23269i
$641$	−0.448984	+	0.376743i	−0.0177338	+	0.0148804i	−0.651611	−	0.758553i	$-0.725907\pi$
$641$	−0.448984	+	0.376743i	−0.0177338	+	0.0148804i	0.633878	+	0.773433i	$0.281462\pi$
$642$	103.180	+	48.1138i	4.07221	+	1.89890i
$643$	−1.16334	+	13.2970i	−0.0458776	+	0.524384i	0.938133	+	0.346275i	$0.112554\pi$
$643$	−1.16334	+	13.2970i	−0.0458776	+	0.524384i	−0.984011	+	0.178109i	$0.943002\pi$
$644$	8.43826	+	0.738252i	0.332514	+	0.0290912i
$645$	−1.72194	+	2.05213i	−0.0678013	+	0.0808025i
$646$	−87.1244	+	61.0052i	−3.42787	+	2.40022i
$647$	3.03821	−	3.03821i	0.119444	−	0.119444i	−0.644858	−	0.764302i	$-0.723084\pi$
$647$	3.03821	−	3.03821i	0.119444	−	0.119444i	0.764302	+	0.644858i	$0.223084\pi$
$648$	27.8766	−	48.2836i	1.09509	−	1.89676i
$649$	−6.41031	−	11.1030i	−0.251627	−	0.435830i
$650$	−0.599847	−	0.160729i	−0.0235280	−	0.00630430i
$651$	4.49620	+	5.35836i	0.176220	+	0.210011i
$652$	19.4597	+	27.7913i	0.762099	+	1.08839i
$653$	−38.7264	+	14.0953i	−1.51548	+	0.551590i	−0.960015	−	0.279949i	$-0.909682\pi$
$653$	−38.7264	+	14.0953i	−1.51548	+	0.551590i	−0.555466	+	0.831539i	$0.687460\pi$
$654$	43.8402	−	25.3111i	1.71429	−	0.989743i
$655$	−7.25622	−	41.1521i	−0.283524	−	1.60795i
$656$	−76.0816			−2.97049
$657$	26.8546	+	15.6711i	1.04770	+	0.611387i
$658$	−5.38807			−0.210049
$659$	−5.44964	−	30.9064i	−0.212288	−	1.20394i	−0.885551	−	0.464541i	$-0.846219\pi$
$659$	−5.44964	−	30.9064i	−0.212288	−	1.20394i	0.673264	−	0.739402i	$-0.264892\pi$
$660$	−76.6157	+	44.2341i	−2.98226	+	1.72181i
$661$	9.77351	−	3.55727i	0.380145	−	0.138362i	−0.144878	−	0.989450i	$-0.546279\pi$
$661$	9.77351	−	3.55727i	0.380145	−	0.138362i	0.525023	+	0.851088i	$0.324057\pi$
$662$	29.5600	+	42.2161i	1.14888	+	1.64077i
$663$	−7.84828	−	9.35322i	−0.304802	−	0.363249i
$664$	−55.3193	−	14.8228i	−2.14681	−	0.575235i
$665$	7.07097	+	12.2473i	0.274200	+	0.474929i
$666$	31.7411	−	54.9771i	1.22994	−	2.13032i
$667$	−3.06343	+	3.06343i	−0.118616	+	0.118616i
$668$	−10.6380	+	7.44881i	−0.411597	+	0.288203i
$669$	3.01305	−	3.59081i	0.116491	−	0.138829i
$670$	14.6962	+	1.28575i	0.567762	+	0.0496728i
$671$	−2.16411	+	24.7359i	−0.0835445	+	0.954918i
$672$	−40.1493	−	18.7219i	−1.54879	−	0.722213i
$673$	21.3374	−	17.9042i	0.822495	−	0.690156i	−0.131060	−	0.991374i	$-0.541838\pi$
$673$	21.3374	−	17.9042i	0.822495	−	0.690156i	0.953555	+	0.301219i	$0.0973935\pi$
$674$	−2.47540	−	9.23833i	−0.0953490	−	0.355847i
$675$	−0.514189	−	0.187150i	−0.0197911	−	0.00720339i
$676$	63.1856	−	11.1413i	2.43021	−	0.428512i
$677$	27.8768	+	19.5196i	1.07139	+	0.750198i	0.969622	−	0.244610i	$-0.0786599\pi$
$677$	27.8768	+	19.5196i	1.07139	+	0.750198i	0.101772	+	0.994808i	$0.467549\pi$
$678$	−33.1515	+	8.88292i	−1.27318	+	0.341147i
$679$	6.62605	+	6.62605i	0.254284	+	0.254284i
$680$	−120.320	−	21.2156i	−4.61405	−	0.813582i
$681$	−49.6889	−	28.6879i	−1.90408	−	1.09932i
$682$	−6.90563	+	18.9731i	−0.264430	+	0.726516i
$683$	1.99766	+	22.8333i	0.0764382	+	0.873693i	0.933523	+	0.358517i	$0.116718\pi$
$683$	1.99766	+	22.8333i	0.0764382	+	0.873693i	−0.857085	+	0.515175i	$0.827727\pi$
$684$			109.828i			4.19938i
$685$	−29.5762	+	2.58758i	−1.13005	+	0.0988665i
$686$	−21.7413	+	31.0498i	−0.830086	+	1.18549i
$687$	−9.05189	+	33.7821i	−0.345351	+	1.28887i
$688$	−2.44988	−	5.25378i	−0.0934007	−	0.200299i
$689$	5.03692	+	4.22648i	0.191891	+	0.161016i
$690$	9.32640	−	20.0005i	0.355050	−	0.761407i
$691$	13.4037	−	6.25027i	0.509902	−	0.237771i	−0.150601	−	0.988595i	$-0.548121\pi$
$691$	13.4037	−	6.25027i	0.509902	−	0.237771i	0.660503	+	0.750823i	$0.270343\pi$
$692$	−19.8638	−	54.5754i	−0.755110	−	2.07465i
$693$	2.17813	−	12.3528i	0.0827405	−	0.469245i
$694$	6.98345	−	39.6051i	0.265088	−	1.50339i
$695$	−2.04282	−	5.61261i	−0.0774886	−	0.212898i
$696$	56.9210	−	26.5427i	2.15759	−	1.00610i
$697$	18.0691	−	38.7492i	0.684414	−	1.46773i
$698$	14.1555	+	11.8779i	0.535794	+	0.449584i
$699$	−23.8185	−	51.0788i	−0.900897	−	1.93198i
$700$	0.490629	−	1.83105i	0.0185440	−	0.0692073i
$701$	20.1555	−	28.7851i	0.761264	−	1.08720i	−0.232157	−	0.972678i	$-0.574578\pi$
$701$	20.1555	−	28.7851i	0.761264	−	1.08720i	0.993421	−	0.114519i	$-0.0365327\pi$
$702$	−3.06604	+	0.268243i	−0.115720	+	0.0101242i
$703$		−	38.4466i		−	1.45004i
$704$	−4.63823	−	53.0152i	−0.174810	−	1.99809i
$705$	−3.45414	+	9.49016i	−0.130090	+	0.357420i
$706$	−16.1385	−	9.31756i	−0.607380	−	0.350671i
$707$	12.0168	+	2.11888i	0.451937	+	0.0796886i
$708$	−38.6623	−	38.6623i	−1.45302	−	1.45302i
$709$	49.9180	−	13.3755i	1.87471	−	0.502327i	0.874871	−	0.484357i	$-0.160946\pi$
$709$	49.9180	−	13.3755i	1.87471	−	0.502327i	0.999839	−	0.0179701i	$-0.00572037\pi$
$710$	42.2850	+	29.6083i	1.58693	+	1.11118i
$711$	46.5829	−	8.21383i	1.74700	−	0.308043i
$712$	47.7448	+	17.3777i	1.78931	+	0.651257i
$713$	−0.937830	−	3.50003i	−0.0351220	−	0.131077i
$714$	39.6848	−	33.2995i	1.48516	−	1.24620i
$715$	−4.24707	−	1.98044i	−0.158832	−	0.0740644i
$716$	−0.266749	+	3.04895i	−0.00996888	+	0.113945i
$717$	−54.3742	−	4.75713i	−2.03064	−	0.177658i
$718$	−50.9217	+	60.6862i	−1.90038	+	2.26479i
$719$	7.76213	−	5.43510i	0.289479	−	0.202695i	−0.419812	−	0.907611i	$-0.637904\pi$
$719$	7.76213	−	5.43510i	0.289479	−	0.202695i	0.709291	+	0.704916i	$0.249015\pi$
$720$	−66.9711	+	66.9711i	−2.49586	+	2.49586i
$721$	4.28462	−	7.42118i	0.159568	−	0.276379i
$722$	20.8620	+	36.1341i	0.776405	+	1.34477i
$723$	8.17743	+	2.19114i	0.304122	+	0.0814892i
$724$	−58.9058	−	70.2012i	−2.18922	−	2.60901i
$725$	0.556111	+	0.794209i	0.0206535	+	0.0294962i
$726$	−9.04054	+	3.29049i	−0.335526	+	0.122121i
$727$	1.06824	−	0.616749i	0.0396189	−	0.0228740i	−0.480060	−	0.877236i	$-0.659385\pi$
$727$	1.06824	−	0.616749i	0.0396189	−	0.0228740i	0.519679	+	0.854362i	$0.326052\pi$
$728$	−1.12949	−	6.40563i	−0.0418615	−	0.237408i
$729$	37.0177			1.37102
$730$	34.6881	+	35.0115i	1.28386	+	1.29583i
$731$	3.25765			0.120488
$732$	18.3885	+	104.286i	0.679659	+	3.85454i
$733$	−9.48329	+	5.47518i	−0.350273	+	0.202230i	−0.664806	−	0.747016i	$-0.731486\pi$
$733$	−9.48329	+	5.47518i	−0.350273	+	0.202230i	0.314532	+	0.949247i	$0.398152\pi$
$734$	−29.2708	+	10.6537i	−1.08041	+	0.393236i
$735$	18.4001	+	26.2781i	0.678699	+	0.969282i
$736$	14.7509	+	17.5794i	0.543726	+	0.647987i
$737$	−7.65448	−	2.05101i	−0.281957	−	0.0755500i
$738$	−30.6830	−	53.1445i	−1.12946	−	1.95628i
$739$	−15.6013	+	27.0223i	−0.573904	+	0.994030i	0.422256	+	0.906477i	$0.361238\pi$
$739$	−15.6013	+	27.0223i	−0.573904	+	0.994030i	−0.996160	+	0.0875539i	$0.972095\pi$
$740$	51.1913	−	51.1913i	1.88183	−	1.88183i
$741$	−8.69399	+	6.08760i	−0.319382	+	0.223634i
$742$	−17.9325	+	21.3711i	−0.658323	+	0.784559i
$743$	26.1486	+	2.28770i	0.959297	+	0.0839276i	0.556037	−	0.831158i	$-0.312321\pi$
$743$	26.1486	+	2.28770i	0.959297	+	0.0839276i	0.403260	+	0.915085i	$0.367877\pi$
$744$	−4.57824	+	52.3295i	−0.167846	+	1.91849i
$745$	24.9521	+	11.6354i	0.914175	+	0.426287i
$746$	−8.80472	+	7.38804i	−0.322364	+	0.270495i
$747$	−6.45734	−	24.0991i	−0.236262	−	0.881741i
$748$	101.094	+	36.7953i	3.69637	+	1.34537i
$749$	−18.1284	+	3.19653i	−0.662398	+	0.116799i
$750$	−64.9218	−	45.4587i	−2.37061	−	1.65992i
$751$	−5.98394	+	1.60339i	−0.218357	+	0.0585086i	−0.366339	−	0.930481i	$-0.619389\pi$
$751$	−5.98394	+	1.60339i	−0.218357	+	0.0585086i	0.147982	+	0.988990i	$0.452722\pi$
$752$	−15.4532	−	15.4532i	−0.563520	−	0.563520i
$753$	36.8224	+	6.49279i	1.34188	+	0.236610i
$754$	4.72277	+	2.72669i	0.171993	+	0.0993004i
$755$	−4.86688	+	13.3716i	−0.177124	+	0.486644i
$756$	−0.818821	−	9.35917i	−0.0297802	−	0.340390i
$757$		−	40.0237i		−	1.45469i	−0.686274	−	0.727343i	$-0.740755\pi$
$757$		−	40.0237i		−	1.45469i	0.686274	−	0.727343i	$-0.259245\pi$
$758$	−38.7488	+	3.39009i	−1.40742	+	0.123133i
$759$	−6.79938	+	9.71052i	−0.246802	+	0.352470i
$760$	−27.4871	+	102.583i	−0.997063	+	3.72109i
$761$	7.59512	+	16.2878i	0.275323	+	0.590432i	0.994540	−	0.104353i	$-0.0332772\pi$
$761$	7.59512	+	16.2878i	0.275323	+	0.590432i	−0.719217	+	0.694785i	$0.755499\pi$
$762$	−77.3397	−	64.8957i	−2.80172	−	2.35092i
$763$	−3.45921	+	7.41829i	−0.125232	+	0.268560i
$764$	−15.0673	+	7.02601i	−0.545117	+	0.254192i
$765$	−18.2038	−	50.0145i	−0.658159	−	1.80828i
$766$	3.25660	−	18.4691i	0.117666	−	0.667315i
$767$	0.502921	−	2.85220i	0.0181594	−	0.102987i
$768$	−4.89029	−	13.4360i	−0.176463	−	0.484829i
$769$	−46.4827	+	21.6752i	−1.67621	+	0.781629i	−0.677261	+	0.735742i	$0.736833\pi$
$769$	−46.4827	+	21.6752i	−1.67621	+	0.781629i	−0.998947	+	0.0458863i	$0.985389\pi$
$770$	8.40281	−	18.0199i	0.302816	−	0.649392i
$771$	−18.9297	−	15.8839i	−0.681737	−	0.572045i
$772$	27.9508	+	59.9407i	1.00597	+	2.15731i
$773$	−4.07008	+	15.1898i	−0.146391	+	0.546337i	0.853299	+	0.521422i	$0.174598\pi$
$773$	−4.07008	+	15.1898i	−0.146391	+	0.546337i	−0.999690	+	0.0249153i	$0.992068\pi$
$774$	2.68186	−	3.83009i	0.0963974	−	0.137670i
$775$	−0.807830	+	0.0706760i	−0.0290181	+	0.00253876i
$776$			70.3710i			2.52617i
$777$	1.63211	+	18.6551i	0.0585515	+	0.669247i
$778$	10.5906	−	29.0975i	0.379692	−	1.04319i
$779$	−32.1859	−	18.5825i	−1.15318	−	0.665788i
$780$	−19.6815	−	3.47038i	−0.704712	−	0.124260i
$781$	−19.6074	−	19.6074i	−0.701607	−	0.701607i
$782$	−25.9217	+	6.94569i	−0.926957	+	0.248377i
$783$	3.93614	+	2.75612i	0.140666	+	0.0984956i
$784$	−68.3639	+	12.0544i	−2.44157	+	0.430514i
$785$	−38.2438	−	13.9196i	−1.36498	−	0.496812i
$786$	34.4386	+	128.526i	1.22838	+	4.58439i
$787$	0.864725	−	0.725590i	0.0308241	−	0.0258645i	−0.627245	−	0.778822i	$-0.715818\pi$
$787$	0.864725	−	0.725590i	0.0308241	−	0.0258645i	0.658070	+	0.752957i	$0.271373\pi$
$788$	47.6034	+	22.1978i	1.69580	+	0.790764i
$789$	6.32267	−	72.2684i	0.225093	−	2.57282i
$790$	74.6933	+	6.53482i	2.65747	+	0.232498i
$791$	3.56709	−	4.25109i	0.126831	−	0.151151i
$792$	77.1619	−	54.0294i	2.74183	−	1.91985i
$793$	−3.96632	+	3.96632i	−0.140848	+	0.140848i
$794$	−3.44581	+	5.96831i	−0.122287	+	0.211808i
$795$	26.1456	+	45.2854i	0.927287	+	1.60611i
$796$	−57.0081	−	15.2753i	−2.02060	−	0.541418i
$797$	−18.1773	−	21.6628i	−0.643872	−	0.767337i	0.341105	−	0.940025i	$-0.389199\pi$
$797$	−18.1773	−	21.6628i	−0.643872	−	0.767337i	−0.984976	+	0.172689i	$0.944755\pi$
$798$	−25.8291	−	36.8877i	−0.914339	−	1.30581i
$799$	11.5406	−	4.20042i	0.408276	−	0.148600i
$800$	4.44764	−	2.56785i	0.157248	−	0.0907872i
$801$	3.84357	+	21.7980i	0.135806	+	0.770194i
$802$	46.0741			1.62693
$803$	−15.0845	−	21.7571i	−0.532321	−	0.767790i
$804$	−33.7960			−1.19189
$805$	0.619616	+	3.51402i	0.0218386	+	0.123853i
$806$	−3.95005	+	2.28056i	−0.139135	+	0.0803294i
$807$	18.5033	−	6.73464i	0.651346	−	0.237071i
$808$	52.5595	+	75.0627i	1.84904	+	2.64070i
$809$	−9.23266	−	11.0031i	−0.324603	−	0.386847i	0.578921	−	0.815383i	$-0.303474\pi$
$809$	−9.23266	−	11.0031i	−0.324603	−	0.386847i	−0.903524	+	0.428537i	$0.859029\pi$
$810$	37.1877	+	9.96442i	1.30664	+	0.350114i
$811$	22.7025	+	39.3219i	0.797193	+	1.38078i	0.921437	+	0.388527i	$0.127016\pi$
$811$	22.7025	+	39.3219i	0.797193	+	1.38078i	−0.124244	+	0.992252i	$0.539651\pi$
$812$	−8.32332	+	14.4164i	−0.292091	+	0.505917i
$813$	−18.3162	+	18.3162i	−0.642377	+	0.642377i
$814$	−44.2783	+	31.0040i	−1.55195	+	1.08669i
$815$	−9.18661	+	10.9482i	−0.321793	+	0.383498i
$816$	209.322	+	18.3133i	7.32772	+	0.641093i
$817$	0.246801	−	2.82095i	0.00863449	−	0.0986926i
$818$	−9.72644	−	4.53552i	−0.340077	−	0.158581i
$819$	2.17064	−	1.82139i	0.0758485	−	0.0636444i
$820$	−18.1127	−	67.5975i	−0.632523	−	2.36061i
$821$	10.0529	+	3.65897i	0.350850	+	0.127699i	0.511433	−	0.859323i	$-0.329115\pi$
$821$	10.0529	+	3.65897i	0.350850	+	0.127699i	−0.160582	+	0.987022i	$0.551337\pi$
$822$	93.1018	−	16.4164i	3.24730	−	0.572586i
$823$	−34.1223	−	23.8927i	−1.18943	−	0.832848i	−0.200278	−	0.979739i	$-0.564184\pi$
$823$	−34.1223	−	23.8927i	−1.18943	−	0.832848i	−0.989153	+	0.146891i	$0.953073\pi$
$824$	62.1599	−	16.6557i	2.16544	−	0.580229i
$825$	1.87591	+	1.87591i	0.0653107	+	0.0653107i
$826$	12.1016	+	2.13384i	0.421069	+	0.0742458i
$827$	15.1111	+	8.72442i	0.525466	+	0.303378i	0.739168	−	0.673521i	$-0.235219\pi$
$827$	15.1111	+	8.72442i	0.525466	+	0.303378i	−0.213702	+	0.976899i	$0.568552\pi$
$828$	−9.47783	+	26.0401i	−0.329377	+	0.904957i
$829$	1.19560	+	13.6657i	0.0415248	+	0.474631i	0.988277	+	0.152669i	$0.0487868\pi$
$829$	1.19560	+	13.6657i	0.0415248	+	0.474631i	−0.946753	+	0.321962i	$0.895658\pi$
$830$		−	39.5476i		−	1.37272i
$831$	84.2212	−	7.36840i	2.92160	−	0.255607i
$832$	6.89554	−	9.84785i	0.239060	−	0.341413i
$833$	10.0967	−	37.6814i	0.349830	−	1.30558i
$834$	8.03777	+	17.2370i	0.278325	+	0.596870i
$835$	−4.19077	−	3.51647i	−0.145027	−	0.121692i
$836$	39.5218	−	84.7547i	1.36689	−	2.93130i
$837$	−3.64240	+	1.69848i	−0.125900	+	0.0587080i
$838$	20.4103	+	56.0769i	0.705063	+	1.93715i
$839$	−3.09680	+	17.5628i	−0.106913	+	0.606335i	0.883526	+	0.468383i	$0.155163\pi$
$839$	−3.09680	+	17.5628i	−0.106913	+	0.606335i	−0.990439	+	0.137952i	$0.955948\pi$
$840$	8.98251	−	50.9423i	0.309926	−	1.75768i
$841$	7.00658	+	19.2504i	0.241606	+	0.663808i
$842$	12.7933	−	5.96561i	0.440886	−	0.205589i
$843$	−6.73538	+	14.4441i	−0.231979	+	0.497480i
$844$	−66.6754	−	55.9473i	−2.29506	−	1.92579i
$845$	11.4224	+	24.4955i	0.392944	+	0.842670i
$846$	4.56224	−	17.0265i	0.156853	−	0.585384i
$847$	0.892250	−	1.27427i	0.0306581	−	0.0437843i
$848$	−112.724	+	9.86210i	−3.87097	+	0.338666i
$849$			11.7602i			0.403611i
$850$	0.523436	+	5.98290i	0.0179537	+	0.205212i
$851$	3.31783	−	9.11565i	0.113734	−	0.312481i
$852$	−102.414	−	59.1286i	−3.50864	−	2.02571i
$853$	−27.5459	−	4.85708i	−0.943153	−	0.166303i	−0.319131	−	0.947711i	$-0.603391\pi$
$853$	−27.5459	−	4.85708i	−0.943153	−	0.166303i	−0.624021	+	0.781407i	$0.714502\pi$
$854$	−16.8287	−	16.8287i	−0.575866	−	0.575866i
$855$	−44.6891	+	11.9744i	−1.52833	+	0.409516i
$856$	−113.239	−	79.2910i	−3.87044	−	2.71011i
$857$	−2.50878	+	0.442366i	−0.0856983	+	0.0151109i	−0.216333	−	0.976320i	$-0.569410\pi$
$857$	−2.50878	+	0.442366i	−0.0856983	+	0.0151109i	0.130635	+	0.991431i	$0.458299\pi$
$858$	14.0219	+	5.10357i	0.478701	+	0.174233i
$859$	−0.0399527	−	0.149105i	−0.00136317	−	0.00508741i	0.965241	−	0.261362i	$-0.0841716\pi$
$859$	−0.0399527	−	0.149105i	−0.00136317	−	0.00508741i	−0.966604	+	0.256274i	$0.917505\pi$
$860$	4.08468	−	3.42745i	0.139286	−	0.116875i
$861$	16.4061	+	7.65028i	0.559117	+	0.260721i
$862$	−4.14335	+	47.3587i	−0.141123	+	1.61305i
$863$	−5.62032	−	0.491714i	−0.191318	−	0.0167381i	−0.00890589	−	0.999960i	$-0.502835\pi$
$863$	−5.62032	−	0.491714i	−0.191318	−	0.0167381i	−0.182412	+	0.983222i	$0.558390\pi$
$864$	16.3607	−	19.4980i	0.556604	−	0.663334i
$865$	20.0410	−	14.0329i	0.681415	−	0.477132i
$866$	75.1750	−	75.1750i	2.55455	−	2.55455i
$867$	−37.1386	+	64.3260i	−1.26129	+	2.18463i
$868$	−6.96148	−	12.0576i	−0.236288	−	0.409263i
$869$	−38.9039	−	10.4243i	−1.31973	−	0.353619i
$870$	27.8773	+	33.2229i	0.945129	+	1.12636i
$871$	−1.02679	−	1.46642i	−0.0347916	−	0.0496876i
$872$	−57.7615	+	21.0235i	−1.95605	+	0.711944i
$873$	−26.5490	+	15.3281i	−0.898549	+	0.518777i
$874$	4.05076	+	22.9730i	0.137019	+	0.777074i
$875$	12.8148			0.433220
$876$	−86.1550	−	72.9765i	−2.91091	−	2.46565i
$877$	29.9129			1.01009			0.505044	−	0.863094i	$-0.331476\pi$
$877$	29.9129			1.01009			0.505044	+	0.863094i	$0.331476\pi$
$878$	−8.00247	−	45.3843i	−0.270070	−	1.53165i
$879$	50.0444	−	28.8932i	1.68796	−	0.974542i
$880$	75.7814	−	27.5822i	2.55459	−	0.929795i
$881$	20.5375	+	29.3306i	0.691926	+	0.988173i	0.999330	+	0.0365940i	$0.0116508\pi$
$881$	20.5375	+	29.3306i	0.691926	+	0.988173i	−0.307404	+	0.951579i	$0.599460\pi$
$882$	−35.9908	−	42.8921i	−1.21187	−	1.44425i
$883$	−34.4616	−	9.23396i	−1.15973	−	0.310748i	−0.372869	−	0.927884i	$-0.621626\pi$
$883$	−34.4616	−	9.23396i	−1.15973	−	0.310748i	−0.786856	+	0.617136i	$0.788293\pi$
$884$	12.1515	+	21.0471i	0.408700	+	0.707889i
$885$	11.5164	−	19.9470i	0.387119	−	0.670510i
$886$	11.5739	−	11.5739i	0.388834	−	0.388834i
$887$	−25.3649	+	17.7607i	−0.851670	+	0.596346i	−0.915817	−	0.401595i	$-0.868456\pi$
$887$	−25.3649	+	17.7607i	−0.851670	+	0.596346i	0.0641476	+	0.997940i	$0.479567\pi$
$888$	−90.3950	+	107.729i	−3.03346	+	3.61513i
$889$	16.2622	+	1.42276i	0.545417	+	0.0477178i
$890$	−3.05790	+	34.9519i	−0.102501	+	1.17159i
$891$	−18.7432	−	8.74010i	−0.627921	−	0.292804i
$892$	−7.14737	+	5.99736i	−0.239312	+	0.200806i
$893$	−2.76303	−	10.3118i	−0.0924612	−	0.345070i
$894$	−82.3808	−	29.9842i	−2.75523	−	1.00282i
$895$	−1.26970	+	0.223883i	−0.0424415	+	0.00748358i
$896$	13.6164	+	9.53428i	0.454891	+	0.318518i
$897$	−2.58668	+	0.693098i	−0.0863666	+	0.0231419i
$898$	26.8084	+	26.8084i	0.894608	+	0.894608i
$899$	7.01289	+	1.23656i	0.233893	+	0.0412416i
$900$	5.37076	+	3.10081i	0.179025	+	0.103360i
$901$	21.7487	−	59.7540i	0.724554	−	1.99069i
$902$	4.55405	+	52.0531i	0.151633	+	1.73318i
$903$			1.37926i			0.0458989i
$904$	41.5159	−	3.63217i	1.38080	−	0.120804i
$905$	22.1425	−	31.6227i	0.736040	−	1.05117i
$906$	11.7274	−	43.7674i	0.389618	−	1.45407i
$907$	−16.8212	−	36.0731i	−0.558538	−	1.19779i	−0.959504	−	0.281696i	$-0.909103\pi$
$907$	−16.8212	−	36.0731i	−0.558538	−	1.19779i	0.400966	−	0.916093i	$-0.368675\pi$
$908$	87.4856	+	73.4091i	2.90331	+	2.43617i
$909$	−16.8707	+	36.1793i	−0.559565	+	1.19999i
$910$	4.07073	−	1.89821i	0.134943	−	0.0629252i
$911$	4.23693	+	11.6409i	0.140376	+	0.385679i	0.989881	−	0.141901i	$-0.0453216\pi$
$911$	4.23693	+	11.6409i	0.140376	+	0.385679i	−0.849505	+	0.527580i	$0.823099\pi$
$912$	31.7167	−	179.874i	1.05024	−	5.95623i
$913$	−3.68895	+	20.9211i	−0.122086	+	0.692386i
$914$	27.3920	+	75.2590i	0.906048	+	2.48935i
$915$	−40.4293	+	18.8525i	−1.33655	+	0.623244i
$916$	29.4201	−	63.0917i	0.972069	−	2.08461i
$917$	−16.4812	−	13.8294i	−0.544258	−	0.456687i
$918$	12.5792	+	26.9761i	0.415174	+	0.890344i
$919$	6.80849	−	25.4096i	0.224591	−	0.838187i	−0.757976	−	0.652282i	$-0.773812\pi$
$919$	6.80849	−	25.4096i	0.224591	−	0.838187i	0.982568	−	0.185905i	$-0.0595215\pi$
$920$	−15.3698	+	21.9503i	−0.506727	+	0.723681i
$921$	−87.0309	+	7.61422i	−2.86777	+	0.250897i
$922$		−	8.24655i		−	0.271586i
$923$	−0.545948	−	6.24021i	−0.0179701	−	0.205399i
$924$	−15.5788	+	42.8024i	−0.512505	+	1.40810i
$925$	−1.88010	−	1.08548i	−0.0618173	−	0.0356902i
$926$	7.19688	+	1.26900i	0.236504	+	0.0417021i
$927$	19.8233	+	19.8233i	0.651082	+	0.651082i
$928$	−43.5625	+	11.6725i	−1.43001	+	0.383170i
$929$	22.4434	+	15.7150i	0.736343	+	0.515593i	0.880549	−	0.473955i	$-0.157174\pi$
$929$	22.4434	+	15.7150i	0.736343	+	0.515593i	−0.144206	+	0.989548i	$0.546063\pi$
$930$	−35.7224	+	6.29882i	−1.17138	+	0.206546i
$931$	−31.8652	−	11.5980i	−1.04434	−	0.380108i
$932$	29.0345	+	108.358i	0.951058	+	3.54940i
$933$	−65.9195	+	55.3130i	−2.15811	+	1.81087i
$934$	43.0520	+	20.0755i	1.40870	+	0.656889i
$935$	−3.94985	+	45.1470i	−0.129174	+	1.47646i
$936$	21.1984	+	1.85462i	0.692891	+	0.0606201i
$937$	8.27409	−	9.86068i	0.270303	−	0.322134i	−0.613769	−	0.789486i	$-0.710347\pi$
$937$	8.27409	−	9.86068i	0.270303	−	0.322134i	0.884072	+	0.467352i	$0.154792\pi$
$938$	6.22185	−	4.35659i	0.203151	−	0.142248i
$939$	4.92116	−	4.92116i	0.160596	−	0.160596i
$940$	10.0510	−	17.4089i	0.327829	−	0.567816i
$941$	−6.30119	−	10.9140i	−0.205413	−	0.355786i	0.744851	−	0.667231i	$-0.232520\pi$
$941$	−6.30119	−	10.9140i	−0.205413	−	0.355786i	−0.950264	+	0.311445i	$0.899187\pi$
$942$	125.178	+	33.5413i	4.07851	+	1.09283i
$943$	−6.02762	−	7.18344i	−0.196286	−	0.233925i
$944$	28.5880	+	40.8278i	0.930459	+	1.32883i
$945$	3.71897	−	1.35359i	0.120978	−	0.0440324i
$946$	−3.44786	+	1.99062i	−0.112100	+	0.0647207i
$947$	−8.52430	−	48.3437i	−0.277003	−	1.57096i	−0.732528	−	0.680737i	$-0.761660\pi$
$947$	−8.52430	−	48.3437i	−0.277003	−	1.57096i	0.455526	−	0.890223i	$-0.349451\pi$
$948$	−171.768			−5.57877
$949$	0.548889	−	5.95546i	0.0178177	−	0.193323i
$950$	5.22053			0.169376
$951$	−5.50534	−	31.2223i	−0.178523	−	1.01245i
$952$	−54.4768	+	31.4522i	−1.76560	+	1.01937i
$953$	3.98434	−	1.45018i	0.129065	−	0.0469760i	−0.276680	−	0.960962i	$-0.589234\pi$
$953$	3.98434	−	1.45018i	0.129065	−	0.0469760i	0.405745	+	0.913986i	$0.367012\pi$
$954$	−52.3496	−	74.7630i	−1.69488	−	2.42054i
$955$	−4.50165	−	5.36486i	−0.145670	−	0.173603i
$956$	104.941	+	28.1189i	3.39404	+	0.909431i
$957$	−11.6484	−	20.1756i	−0.376539	−	0.652185i
$958$	10.2621	−	17.7745i	0.331554	−	0.574268i
$959$	−10.8088	+	10.8088i	−0.349035	+	0.349035i
$960$	78.3174	−	54.8384i	2.52768	−	1.76990i
$961$	16.0980	−	19.1849i	0.519291	−	0.618866i
$962$	−12.1644	−	1.06425i	−0.392196	−	0.0343127i
$963$	5.24871	−	59.9931i	0.169137	−	1.93325i
$964$	−15.2722	−	7.12155i	−0.491885	−	0.229370i
$965$	−21.3424	+	17.9084i	−0.687037	+	0.576492i
$966$	−2.94074	−	10.9750i	−0.0946169	−	0.353115i
$967$	41.1301	+	14.9701i	1.32265	+	0.481407i	0.904308	−	0.426881i	$-0.140388\pi$
$967$	41.1301	+	14.9701i	1.32265	+	0.481407i	0.418346	+	0.908288i	$0.362610\pi$
$968$	11.5046	−	2.02857i	0.369771	−	0.0652007i
$969$	84.0794	+	58.8730i	2.70102	+	1.89127i
$970$	−46.9379	+	12.5770i	−1.50709	+	0.403822i
$971$	6.04453	+	6.04453i	0.193978	+	0.193978i	0.797413	−	0.603434i	$-0.206201\pi$
$971$	6.04453	+	6.04453i	0.193978	+	0.193978i	−0.603434	+	0.797413i	$0.706201\pi$
$972$	−111.811	−	19.7153i	−3.58635	−	0.632370i
$973$	−2.66320	−	1.53760i	−0.0853784	−	0.0492933i
$974$	−4.71917	+	12.9658i	−0.151212	+	0.415451i
$975$	0.0522327	+	0.597023i	0.00167279	+	0.0191200i
$976$		−	96.5308i		−	3.08988i
$977$	−37.3936	+	3.27152i	−1.19633	+	0.104665i	−0.667860	−	0.744287i	$-0.732789\pi$
$977$	−37.3936	+	3.27152i	−1.19633	+	0.104665i	−0.528469	+	0.848953i	$0.677234\pi$
$978$	26.1028	−	37.2787i	0.834676	−	1.19204i
$979$	4.87793	−	18.2047i	0.155899	−	0.581824i
$980$	−26.9855	−	57.8707i	−0.862021	−	1.84861i
$981$	−20.5131	−	17.2125i	−0.654932	−	0.549553i
$982$	16.5296	−	35.4479i	0.527481	−	1.13119i
$983$	21.4945	−	10.0230i	0.685568	−	0.319686i	−0.0484403	−	0.998826i	$-0.515425\pi$
$983$	21.4945	−	10.0230i	0.685568	−	0.319686i	0.734008	+	0.679140i	$0.237647\pi$
$984$	46.4948	+	127.743i	1.48220	+	4.07231i
$985$	−3.84217	+	21.7900i	−0.122422	+	0.694287i
$986$	9.15813	−	51.9384i	0.291654	−	1.65405i
$987$	1.77842	+	4.88617i	0.0566078	+	0.155529i
$988$	19.1463	−	8.92805i	0.609124	−	0.284039i
$989$	0.301956	−	0.647546i	0.00960164	−	0.0205908i
$990$	49.8286	+	41.8112i	1.58366	+	1.32885i
$991$	14.9344	+	32.0269i	0.474406	+	1.01737i	0.987293	+	0.158911i	$0.0507984\pi$
$991$	14.9344	+	32.0269i	0.474406	+	1.01737i	−0.512886	+	0.858456i	$0.671424\pi$
$992$	9.76271	−	36.4349i	0.309966	−	1.15681i
$993$	28.5269	−	40.7406i	0.905273	−	1.29286i
$994$	26.4766	−	2.31640i	0.839786	−	0.0734717i
$995$		−	24.8620i		−	0.788180i
$996$	7.89626	+	90.2546i	0.250202	+	2.85983i
$997$	−14.0844	+	38.6967i	−0.446058	+	1.22554i	0.489388	+	0.872066i	$0.337220\pi$
$997$	−14.0844	+	38.6967i	−0.446058	+	1.22554i	−0.935446	+	0.353469i	$0.885002\pi$
$998$	63.5493	+	36.6902i	2.01162	+	1.16141i
$999$	−10.5959	−	1.86834i	−0.335239	−	0.0591117i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	73.2.k.a.12.6	✓	72
3.2	odd	2		657.2.cc.d.523.1		72
73.33	odd	72		5329.2.a.o.1.67		72
73.40	odd	72		5329.2.a.o.1.68		72
73.67	even	36	inner	73.2.k.a.67.6	yes	72
219.140	odd	36		657.2.cc.d.505.1		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
73.2.k.a.12.6	✓	72	1.1	even	1	trivial
73.2.k.a.67.6	yes	72	73.67	even	36	inner
657.2.cc.d.505.1		72	219.140	odd	36
657.2.cc.d.523.1		72	3.2	odd	2
5329.2.a.o.1.67		72	73.33	odd	72
5329.2.a.o.1.68		72	73.40	odd	72

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	73.k (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.463635 + 2.62940i) q^{2} +(2.23144 - 1.28832i) q^{3} +(-4.81942 + 1.75412i) q^{4} +(-1.23921 - 1.76977i) q^{5} +(4.42210 + 5.27005i) q^{6} +(-1.07446 - 0.287902i) q^{7} +(-4.17678 - 7.23440i) q^{8} +(1.81956 - 3.15157i) q^{9} +O(q^{10})\)	\(q+(0.463635 + 2.62940i) q^{2} +(2.23144 - 1.28832i) q^{3} +(-4.81942 + 1.75412i) q^{4} +(-1.23921 - 1.76977i) q^{5} +(4.42210 + 5.27005i) q^{6} +(-1.07446 - 0.287902i) q^{7} +(-4.17678 - 7.23440i) q^{8} +(1.81956 - 3.15157i) q^{9} +(4.07890 - 4.07890i) q^{10} +(-2.53825 + 1.77730i) q^{11} +(-8.49437 + 10.1232i) q^{12} +(-0.697325 - 0.0610080i) q^{13} +(0.258851 - 2.95868i) q^{14} +(-5.04526 - 2.35264i) q^{15} +(9.22800 - 7.74321i) q^{16} +(1.75209 + 6.53890i) q^{17} +(9.13035 + 3.32318i) q^{18} +(5.79509 - 1.02183i) q^{19} +(9.07665 + 6.35554i) q^{20} +(-2.76851 + 0.741821i) q^{21} +(-5.85007 - 5.85007i) q^{22} +(1.46219 + 0.257824i) q^{23} +(-18.6405 - 10.7621i) q^{24} +(0.113645 - 0.312238i) q^{25} +(-0.162889 - 1.86183i) q^{26} -1.64678i q^{27} +(5.68330 - 0.497224i) q^{28} +(-1.67364 + 2.39020i) q^{29} +(3.84689 - 14.3568i) q^{30} +(-1.03139 - 2.21183i) q^{31} +(11.8400 + 9.93497i) q^{32} +(-3.37423 + 7.23605i) q^{33} +(-16.3811 + 7.63862i) q^{34} +(0.821962 + 2.25832i) q^{35} +(-3.24097 + 18.3805i) q^{36} +(1.13454 - 6.43430i) q^{37} +(5.37361 + 14.7639i) q^{38} +(-1.63464 + 0.762245i) q^{39} +(-7.62733 + 16.3569i) q^{40} +(-4.83816 - 4.05970i) q^{41} +(-3.23413 - 6.93560i) q^{42} +(0.124549 - 0.464822i) q^{43} +(9.11529 - 13.0180i) q^{44} +(-7.83237 + 0.685243i) q^{45} +3.96422i q^{46} +(-0.158116 - 1.80728i) q^{47} +(10.6160 - 29.1672i) q^{48} +(-4.99059 - 2.88132i) q^{49} +(0.873690 + 0.154055i) q^{50} +(12.3339 + 12.3339i) q^{51} +(3.46771 - 0.929171i) q^{52} +(-7.69457 - 5.38780i) q^{53} +(4.33006 - 0.763506i) q^{54} +(6.29084 + 2.28968i) q^{55} +(2.40500 + 8.97560i) q^{56} +(11.6150 - 9.74611i) q^{57} +(-7.06076 - 3.29249i) q^{58} +(-0.360607 + 4.12176i) q^{59} +(28.4420 + 2.48836i) q^{60} +(5.15086 - 6.13856i) q^{61} +(5.33759 - 3.73742i) q^{62} +(-2.86239 + 2.86239i) q^{63} +(-8.58729 + 14.8736i) q^{64} +(0.756160 + 1.30971i) q^{65} +(-20.5909 - 5.51731i) q^{66} +(1.64388 + 1.95910i) q^{67} +(-19.9141 - 28.4403i) q^{68} +(3.59495 - 1.30846i) q^{69} +(-5.55695 + 3.20831i) q^{70} +(1.55394 + 8.81283i) q^{71} -30.3996 q^{72} +(-0.0396405 + 8.54391i) q^{73} +17.4444 q^{74} +(-0.148671 - 0.843154i) q^{75} +(-26.1365 + 15.0899i) q^{76} +(3.23895 - 1.17888i) q^{77} +(-2.76212 - 3.94472i) q^{78} +(8.35500 + 9.95711i) q^{79} +(-25.1391 - 6.73600i) q^{80} +(3.33709 + 5.78000i) q^{81} +(8.43144 - 14.6037i) q^{82} +(4.84782 - 4.84782i) q^{83} +(12.0414 - 8.43146i) q^{84} +(9.40115 - 11.2039i) q^{85} +(1.27995 + 0.111981i) q^{86} +(-0.655271 + 7.48979i) q^{87} +(23.4595 + 10.9393i) q^{88} +(-4.65932 + 3.90964i) q^{89} +(-5.43314 - 20.2767i) q^{90} +(0.731685 + 0.266312i) q^{91} +(-7.49916 + 1.32230i) q^{92} +(-5.15104 - 3.60680i) q^{93} +(4.67875 - 1.25367i) q^{94} +(-8.98972 - 8.98972i) q^{95} +(39.2198 + 6.91551i) q^{96} +(-7.29546 - 4.21203i) q^{97} +(5.26234 - 14.4582i) q^{98} +(0.982795 + 11.2334i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 12 q^{2} - 18 q^{3} - 12 q^{4} - 12 q^{5} - 24 q^{6} - 18 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) \) 72 * q - 12 * q^2 - 18 * q^3 - 12 * q^4 - 12 * q^5 - 24 * q^6 - 18 * q^7 - 24 * q^8 + 36 * q^9	\( 72 q - 12 q^{2} - 18 q^{3} - 12 q^{4} - 12 q^{5} - 24 q^{6} - 18 q^{7} - 24 q^{8} + 36 q^{9} - 6 q^{11} + 6 q^{12} - 12 q^{13} - 12 q^{14} - 30 q^{15} + 30 q^{17} - 12 q^{18} - 6 q^{19} + 60 q^{20} - 30 q^{21} - 12 q^{22} - 12 q^{23} - 18 q^{24} + 36 q^{25} + 12 q^{26} + 120 q^{28} - 6 q^{29} - 72 q^{30} - 18 q^{31} - 18 q^{32} - 60 q^{33} - 60 q^{34} - 36 q^{35} + 60 q^{36} - 6 q^{37} + 48 q^{38} + 78 q^{39} - 18 q^{40} + 54 q^{42} - 24 q^{43} + 48 q^{44} + 36 q^{47} + 30 q^{48} - 18 q^{49} + 132 q^{50} - 18 q^{51} - 24 q^{53} - 6 q^{54} + 72 q^{55} + 24 q^{56} - 6 q^{57} - 18 q^{58} - 66 q^{60} - 36 q^{61} - 36 q^{62} + 12 q^{63} - 84 q^{64} + 24 q^{65} + 156 q^{66} - 54 q^{67} - 84 q^{68} - 6 q^{69} - 162 q^{70} + 48 q^{71} - 72 q^{72} - 36 q^{73} + 144 q^{74} + 6 q^{75} - 180 q^{76} - 24 q^{77} - 198 q^{78} - 36 q^{79} - 126 q^{80} - 48 q^{81} + 30 q^{82} - 48 q^{83} - 126 q^{84} - 6 q^{85} - 120 q^{86} + 6 q^{87} + 6 q^{88} + 6 q^{89} + 210 q^{90} + 48 q^{91} + 96 q^{92} + 144 q^{93} - 6 q^{94} - 12 q^{95} + 162 q^{96} - 18 q^{97} + 186 q^{98} + 78 q^{99}+O(q^{100}) \) 72 * q - 12 * q^2 - 18 * q^3 - 12 * q^4 - 12 * q^5 - 24 * q^6 - 18 * q^7 - 24 * q^8 + 36 * q^9 - 6 * q^11 + 6 * q^12 - 12 * q^13 - 12 * q^14 - 30 * q^15 + 30 * q^17 - 12 * q^18 - 6 * q^19 + 60 * q^20 - 30 * q^21 - 12 * q^22 - 12 * q^23 - 18 * q^24 + 36 * q^25 + 12 * q^26 + 120 * q^28 - 6 * q^29 - 72 * q^30 - 18 * q^31 - 18 * q^32 - 60 * q^33 - 60 * q^34 - 36 * q^35 + 60 * q^36 - 6 * q^37 + 48 * q^38 + 78 * q^39 - 18 * q^40 + 54 * q^42 - 24 * q^43 + 48 * q^44 + 36 * q^47 + 30 * q^48 - 18 * q^49 + 132 * q^50 - 18 * q^51 - 24 * q^53 - 6 * q^54 + 72 * q^55 + 24 * q^56 - 6 * q^57 - 18 * q^58 - 66 * q^60 - 36 * q^61 - 36 * q^62 + 12 * q^63 - 84 * q^64 + 24 * q^65 + 156 * q^66 - 54 * q^67 - 84 * q^68 - 6 * q^69 - 162 * q^70 + 48 * q^71 - 72 * q^72 - 36 * q^73 + 144 * q^74 + 6 * q^75 - 180 * q^76 - 24 * q^77 - 198 * q^78 - 36 * q^79 - 126 * q^80 - 48 * q^81 + 30 * q^82 - 48 * q^83 - 126 * q^84 - 6 * q^85 - 120 * q^86 + 6 * q^87 + 6 * q^88 + 6 * q^89 + 210 * q^90 + 48 * q^91 + 96 * q^92 + 144 * q^93 - 6 * q^94 - 12 * q^95 + 162 * q^96 - 18 * q^97 + 186 * q^98 + 78 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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