LMFDB - Embedded newform 418.2.v.b.29.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(13,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([9, 25]))

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

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

chi := DirichletCharacter("418.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.v (of order $90$, degree $24$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$10$ over $\Q(\zeta_{90})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{90}]$

Embedding invariants

Embedding label			29.2
Character	$\chi$	$=$	418.29
Dual form			418.2.v.b.173.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.438371 - 0.898794i) q^{2} +(-2.41147 + 0.974297i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(-2.76916 + 0.794045i) q^{5} +(-0.181426 + 2.59452i) q^{6} +(0.709936 - 3.33998i) q^{7} +(-0.978148 + 0.207912i) q^{8} +(2.70791 - 2.61500i) q^{9} +O(q^{10})$	\(q+(0.438371 - 0.898794i) q^{2} +(-2.41147 + 0.974297i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(-2.76916 + 0.794045i) q^{5} +(-0.181426 + 2.59452i) q^{6} +(0.709936 - 3.33998i) q^{7} +(-0.978148 + 0.207912i) q^{8} +(2.70791 - 2.61500i) q^{9} +(-0.500239 + 2.83699i) q^{10} +(2.68936 + 1.94096i) q^{11} +(2.25240 + 1.30043i) q^{12} +(1.28783 + 5.16520i) q^{13} +(-2.69074 - 2.10224i) q^{14} +(5.90412 - 4.61280i) q^{15} +(-0.241922 + 0.970296i) q^{16} +(2.31565 - 2.39793i) q^{17} +(-1.16327 - 3.58019i) q^{18} +(-1.48948 + 4.09652i) q^{19} +(2.33058 + 1.69327i) q^{20} +(1.54215 + 8.74595i) q^{21} +(2.92347 - 1.56632i) q^{22} +(7.53973 - 2.74424i) q^{23} +(2.15620 - 1.45438i) q^{24} +(2.79752 - 1.74808i) q^{25} +(5.20699 + 1.10678i) q^{26} +(-0.808666 + 1.81629i) q^{27} +(-3.06902 + 1.49686i) q^{28} +(4.59371 - 0.645604i) q^{29} +(-1.55776 - 7.32870i) q^{30} +(3.43535 + 7.71591i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-8.37638 - 2.06034i) q^{33} +(-1.14013 - 3.13248i) q^{34} +(0.686170 + 9.81268i) q^{35} +(-3.72780 - 0.523908i) q^{36} +(-8.90077 + 2.89204i) q^{37} +(3.02898 + 3.13453i) q^{38} +(-8.13799 - 11.2010i) q^{39} +(2.54356 - 1.35243i) q^{40} +(-1.88623 - 4.66858i) q^{41} +(8.53684 + 2.44790i) q^{42} +(0.626209 - 1.72049i) q^{43} +(-0.126235 - 3.31422i) q^{44} +(-5.42222 + 9.39155i) q^{45} +(0.838696 - 7.97966i) q^{46} +(6.17065 + 3.28099i) q^{47} +(-0.361969 - 2.57554i) q^{48} +(-4.25667 - 1.89519i) q^{49} +(-0.344816 - 3.28070i) q^{50} +(-3.24783 + 8.03867i) q^{51} +(3.27736 - 4.19483i) q^{52} +(1.17638 - 4.10251i) q^{53} +(1.27798 + 1.52304i) q^{54} +(-8.98849 - 3.23938i) q^{55} +3.41460i q^{56} +(-0.399393 - 11.3298i) q^{57} +(1.43349 - 4.41181i) q^{58} +(-1.29911 - 2.44327i) q^{59} +(-7.26987 - 1.81258i) q^{60} +(-3.49846 - 2.35974i) q^{61} +(8.44097 + 0.294765i) q^{62} +(-6.81161 - 10.9008i) q^{63} +(0.913545 - 0.406737i) q^{64} +(-7.66760 - 13.2807i) q^{65} +(-5.52379 + 6.62545i) q^{66} +(10.0107 + 1.76515i) q^{67} +(-3.31525 - 0.348447i) q^{68} +(-15.5081 + 13.9636i) q^{69} +(9.12038 + 3.68487i) q^{70} +(2.78128 + 9.69949i) q^{71} +(-2.10505 + 3.12086i) q^{72} +(-6.34348 + 10.1517i) q^{73} +(-1.30250 + 9.26774i) q^{74} +(-5.04298 + 6.94107i) q^{75} +(4.14511 - 1.34834i) q^{76} +(8.39206 - 7.60446i) q^{77} +(-13.6348 + 2.40419i) q^{78} +(1.37398 - 0.0960778i) q^{79} +(-0.100537 - 2.87900i) q^{80} +(-0.213666 + 6.11861i) q^{81} +(-5.02296 - 0.351240i) q^{82} +(7.96687 - 0.837352i) q^{83} +(5.94247 - 6.59978i) q^{84} +(-4.50836 + 8.47899i) q^{85} +(-1.27186 - 1.31705i) q^{86} +(-10.4486 + 6.03249i) q^{87} +(-3.03414 - 1.33940i) q^{88} +(-6.12588 + 7.30054i) q^{89} +(6.06413 + 8.99044i) q^{90} +(18.1659 - 0.634369i) q^{91} +(-6.80441 - 4.25187i) q^{92} +(-15.8018 - 15.2596i) q^{93} +(5.65397 - 4.10785i) q^{94} +(0.871790 - 12.5266i) q^{95} +(-2.47356 - 0.803708i) q^{96} +(13.2150 + 6.44538i) q^{97} +(-3.56939 + 2.99507i) q^{98} +(12.3582 - 1.77671i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9}+O(q^{10}) $ 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9	$ 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9} - 3 q^{11} + 6 q^{13} - 18 q^{14} - 69 q^{15} + 9 q^{17} + 60 q^{18} - 45 q^{19} + 12 q^{20} - 48 q^{21} - 12 q^{22} + 3 q^{24} - 18 q^{25} + 84 q^{26} - 9 q^{27} + 6 q^{28} + 12 q^{29} + 9 q^{31} - 69 q^{33} - 24 q^{34} + 36 q^{35} + 3 q^{36} + 24 q^{38} - 30 q^{41} - 6 q^{42} + 12 q^{43} - 48 q^{44} + 48 q^{45} - 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} + 21 q^{50} + 45 q^{51} - 3 q^{52} + 81 q^{53} - 27 q^{54} - 72 q^{55} - 30 q^{57} - 24 q^{58} + 114 q^{59} + 78 q^{60} - 66 q^{61} - 45 q^{62} + 9 q^{63} + 30 q^{64} - 135 q^{66} - 9 q^{67} - 42 q^{68} - 54 q^{69} + 39 q^{70} - 102 q^{71} - 6 q^{72} + 12 q^{74} + 72 q^{77} + 36 q^{79} - 117 q^{81} + 30 q^{82} - 36 q^{83} - 36 q^{84} - 90 q^{85} + 3 q^{86} - 216 q^{87} - 3 q^{88} + 18 q^{89} - 24 q^{90} + 102 q^{91} + 30 q^{92} + 147 q^{93} + 18 q^{94} - 66 q^{95} - 24 q^{97} + 12 q^{98} - 195 q^{99}+O(q^{100}) $ 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9 - 3 * q^11 + 6 * q^13 - 18 * q^14 - 69 * q^15 + 9 * q^17 + 60 * q^18 - 45 * q^19 + 12 * q^20 - 48 * q^21 - 12 * q^22 + 3 * q^24 - 18 * q^25 + 84 * q^26 - 9 * q^27 + 6 * q^28 + 12 * q^29 + 9 * q^31 - 69 * q^33 - 24 * q^34 + 36 * q^35 + 3 * q^36 + 24 * q^38 - 30 * q^41 - 6 * q^42 + 12 * q^43 - 48 * q^44 + 48 * q^45 - 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 + 21 * q^50 + 45 * q^51 - 3 * q^52 + 81 * q^53 - 27 * q^54 - 72 * q^55 - 30 * q^57 - 24 * q^58 + 114 * q^59 + 78 * q^60 - 66 * q^61 - 45 * q^62 + 9 * q^63 + 30 * q^64 - 135 * q^66 - 9 * q^67 - 42 * q^68 - 54 * q^69 + 39 * q^70 - 102 * q^71 - 6 * q^72 + 12 * q^74 + 72 * q^77 + 36 * q^79 - 117 * q^81 + 30 * q^82 - 36 * q^83 - 36 * q^84 - 90 * q^85 + 3 * q^86 - 216 * q^87 - 3 * q^88 + 18 * q^89 - 24 * q^90 + 102 * q^91 + 30 * q^92 + 147 * q^93 + 18 * q^94 - 66 * q^95 - 24 * q^97 + 12 * q^98 - 195 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.438371	−	0.898794i	0.309975	−	0.635543i
$2$	0.438371	−	0.898794i	0.309975	−	0.635543i
$3$	−2.41147	+	0.974297i	−1.39226	+	0.562510i	−0.943569	−	0.331176i	$-0.892555\pi$
$3$	−2.41147	+	0.974297i	−1.39226	+	0.562510i	−0.448693	+	0.893686i	$0.648110\pi$
$4$	−0.615661	−	0.788011i	−0.307831	−	0.394005i
$5$	−2.76916	+	0.794045i	−1.23841	+	0.355108i	−0.830037	−	0.557708i	$-0.811681\pi$
$5$	−2.76916	+	0.794045i	−1.23841	+	0.355108i	−0.408371	+	0.912816i	$0.633903\pi$
$6$	−0.181426	+	2.59452i	−0.0740670	+	1.05921i
$7$	0.709936	−	3.33998i	0.268330	−	1.26240i	−0.613071	−	0.790028i	$-0.710066\pi$
$7$	0.709936	−	3.33998i	0.268330	−	1.26240i	0.881402	−	0.472368i	$-0.156601\pi$
$8$	−0.978148	+	0.207912i	−0.345827	+	0.0735079i
$9$	2.70791	−	2.61500i	0.902636	−	0.871665i
$10$	−0.500239	+	2.83699i	−0.158189	+	0.897136i
$11$	2.68936	+	1.94096i	0.810873	+	0.585223i
$11$	2.68936	+	1.94096i	0.810873	+	0.585223i
$12$	2.25240	+	1.30043i	0.650213	+	0.375401i
$13$	1.28783	+	5.16520i	0.357179	+	1.43257i	0.833121	+	0.553091i	$0.186552\pi$
$13$	1.28783	+	5.16520i	0.357179	+	1.43257i	−0.475942	+	0.879477i	$0.657893\pi$
$14$	−2.69074	−	2.10224i	−0.719131	−	0.561847i
$15$	5.90412	−	4.61280i	1.52444	−	1.19102i
$16$	−0.241922	+	0.970296i	−0.0604805	+	0.242574i
$17$	2.31565	−	2.39793i	0.561629	−	0.581583i	−0.377129	−	0.926161i	$-0.623089\pi$
$17$	2.31565	−	2.39793i	0.561629	−	0.581583i	0.938758	+	0.344577i	$0.111978\pi$
$18$	−1.16327	−	3.58019i	−0.274186	−	0.843859i
$19$	−1.48948	+	4.09652i	−0.341710	+	0.939806i
$19$	−1.48948	+	4.09652i	−0.341710	+	0.939806i
$20$	2.33058	+	1.69327i	0.521134	+	0.378626i
$21$	1.54215	+	8.74595i	0.336524	+	1.90852i
$22$	2.92347	−	1.56632i	0.623285	−	0.333940i
$23$	7.53973	−	2.74424i	1.57214	−	0.572213i	0.598665	−	0.800999i	$-0.295698\pi$
$23$	7.53973	−	2.74424i	1.57214	−	0.572213i	0.973477	+	0.228786i	$0.0734757\pi$
$24$	2.15620	−	1.45438i	0.440133	−	0.296874i
$25$	2.79752	−	1.74808i	0.559504	−	0.349617i
$26$	5.20699	+	1.10678i	1.02118	+	0.217058i
$27$	−0.808666	+	1.81629i	−0.155628	+	0.349546i
$28$	−3.06902	+	1.49686i	−0.579991	+	0.282880i
$29$	4.59371	−	0.645604i	0.853031	−	0.119886i	0.300913	−	0.953652i	$-0.402709\pi$
$29$	4.59371	−	0.645604i	0.853031	−	0.119886i	0.552118	+	0.833766i	$0.313820\pi$
$30$	−1.55776	−	7.32870i	−0.284407	−	1.33803i
$31$	3.43535	+	7.71591i	0.617006	+	1.38582i	0.903853	+	0.427842i	$0.140726\pi$
$31$	3.43535	+	7.71591i	0.617006	+	1.38582i	−0.286847	+	0.957976i	$0.592607\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	−8.37638	−	2.06034i	−1.45814	−	0.358659i
$34$	−1.14013	−	3.13248i	−0.195531	−	0.537216i
$35$	0.686170	+	9.81268i	0.115984	+	1.65865i
$36$	−3.72780	−	0.523908i	−0.621300	−	0.0873180i
$37$	−8.90077	+	2.89204i	−1.46328	+	0.475448i	−0.929069	−	0.369905i	$-0.879390\pi$
$37$	−8.90077	+	2.89204i	−1.46328	+	0.475448i	−0.534208	+	0.845353i	$0.679390\pi$
$38$	3.02898	+	3.13453i	0.491366	+	0.508488i
$39$	−8.13799	−	11.2010i	−1.30312	−	1.79359i
$40$	2.54356	−	1.35243i	0.402172	−	0.213839i
$41$	−1.88623	−	4.66858i	−0.294579	−	0.729110i	−0.999798	−	0.0201193i	$-0.993595\pi$
$41$	−1.88623	−	4.66858i	−0.294579	−	0.729110i	0.705218	−	0.708990i	$-0.250849\pi$
$42$	8.53684	+	2.44790i	1.31726	+	0.377719i
$43$	0.626209	−	1.72049i	0.0954960	−	0.262373i	−0.882742	−	0.469857i	$-0.844305\pi$
$43$	0.626209	−	1.72049i	0.0954960	−	0.262373i	0.978238	+	0.207484i	$0.0665276\pi$
$44$	−0.126235	−	3.31422i	−0.0190306	−	0.499638i
$45$	−5.42222	+	9.39155i	−0.808296	+	1.40001i
$46$	0.838696	−	7.97966i	0.123659	−	1.17654i
$47$	6.17065	+	3.28099i	0.900082	+	0.478582i	0.853951	−	0.520353i	$-0.174200\pi$
$47$	6.17065	+	3.28099i	0.900082	+	0.478582i	0.0461311	+	0.998935i	$0.485311\pi$
$48$	−0.361969	−	2.57554i	−0.0522457	−	0.371747i
$49$	−4.25667	−	1.89519i	−0.608095	−	0.270741i
$50$	−0.344816	−	3.28070i	−0.0487643	−	0.463962i
$51$	−3.24783	+	8.03867i	−0.454787	+	1.12564i
$52$	3.27736	−	4.19483i	0.454489	−	0.581719i
$53$	1.17638	−	4.10251i	0.161588	−	0.563524i	−0.838246	−	0.545292i	$-0.816419\pi$
$53$	1.17638	−	4.10251i	0.161588	−	0.563524i	0.999834	−	0.0182314i	$-0.00580355\pi$
$54$	1.27798	+	1.52304i	0.173911	+	0.207259i
$55$	−8.98849	−	3.23938i	−1.21201	−	0.436797i
$56$			3.41460i			0.456295i
$57$	−0.399393	−	11.3298i	−0.0529009	−	1.50067i
$58$	1.43349	−	4.41181i	0.188226	−	0.579299i
$59$	−1.29911	−	2.44327i	−0.169130	−	0.318087i	0.783941	−	0.620836i	$-0.213207\pi$
$59$	−1.29911	−	2.44327i	−0.169130	−	0.318087i	−0.953070	+	0.302749i	$0.902096\pi$
$60$	−7.26987	−	1.81258i	−0.938537	−	0.234003i
$61$	−3.49846	−	2.35974i	−0.447932	−	0.302134i	0.314435	−	0.949279i	$-0.398185\pi$
$61$	−3.49846	−	2.35974i	−0.447932	−	0.302134i	−0.762367	+	0.647145i	$0.775963\pi$
$62$	8.44097	+	0.294765i	1.07200	+	0.0374352i
$63$	−6.81161	−	10.9008i	−0.858182	−	1.37338i
$64$	0.913545	−	0.406737i	0.114193	−	0.0508421i
$65$	−7.66760	−	13.2807i	−0.951049	−	1.64727i
$66$	−5.52379	+	6.62545i	−0.679931	+	0.815536i
$67$	10.0107	+	1.76515i	1.22300	+	0.215647i	0.747615	−	0.664132i	$-0.231199\pi$
$67$	10.0107	+	1.76515i	1.22300	+	0.215647i	0.475382	+	0.879780i	$0.342310\pi$
$68$	−3.31525	−	0.348447i	−0.402034	−	0.0422554i
$69$	−15.5081	+	13.9636i	−1.86696	+	1.68102i
$70$	9.12038	+	3.68487i	1.09009	+	0.440426i
$71$	2.78128	+	9.69949i	0.330078	+	1.15112i	0.934945	+	0.354792i	$0.115448\pi$
$71$	2.78128	+	9.69949i	0.330078	+	1.15112i	−0.604868	+	0.796326i	$0.706774\pi$
$72$	−2.10505	+	3.12086i	−0.248082	+	0.367797i
$73$	−6.34348	+	10.1517i	−0.742448	+	1.18817i	0.233963	+	0.972246i	$0.424831\pi$
$73$	−6.34348	+	10.1517i	−0.742448	+	1.18817i	−0.976411	+	0.215920i	$0.930725\pi$
$74$	−1.30250	+	9.26774i	−0.151412	+	1.07735i
$75$	−5.04298	+	6.94107i	−0.582313	+	0.801485i
$76$	4.14511	−	1.34834i	0.475477	−	0.154666i
$77$	8.39206	−	7.60446i	0.956364	−	0.866609i
$78$	−13.6348	+	2.40419i	−1.54384	+	0.272221i
$79$	1.37398	−	0.0960778i	0.154584	−	0.0108096i	0.00774544	−	0.999970i	$-0.497535\pi$
$79$	1.37398	−	0.0960778i	0.154584	−	0.0108096i	0.146839	+	0.989160i	$0.453090\pi$
$80$	−0.100537	−	2.87900i	−0.0112404	−	0.321883i
$81$	−0.213666	+	6.11861i	−0.0237407	+	0.679845i
$82$	−5.02296	−	0.351240i	−0.554693	−	0.0387879i
$83$	7.96687	−	0.837352i	0.874478	−	0.0919113i	0.343354	−	0.939206i	$-0.388437\pi$
$83$	7.96687	−	0.837352i	0.874478	−	0.0919113i	0.531123	+	0.847295i	$0.321770\pi$
$84$	5.94247	−	6.59978i	0.648376	−	0.720095i
$85$	−4.50836	+	8.47899i	−0.489000	+	0.919676i
$86$	−1.27186	−	1.31705i	−0.137148	−	0.142021i
$87$	−10.4486	+	6.03249i	−1.12021	+	0.646751i
$88$	−3.03414	−	1.33940i	−0.323440	−	0.142781i
$89$	−6.12588	+	7.30054i	−0.649342	+	0.773856i	−0.985815	−	0.167838i	$-0.946322\pi$
$89$	−6.12588	+	7.30054i	−0.649342	+	0.773856i	0.336473	+	0.941693i	$0.390766\pi$
$90$	6.06413	+	8.99044i	0.639215	+	0.947676i
$91$	18.1659	−	0.634369i	1.90431	−	0.0664999i
$92$	−6.80441	−	4.25187i	−0.709409	−	0.443288i
$93$	−15.8018	−	15.2596i	−1.63857	−	1.58235i
$94$	5.65397	−	4.10785i	0.583163	−	0.423693i
$95$	0.871790	−	12.5266i	0.0894438	−	1.28521i
$96$	−2.47356	−	0.803708i	−0.252456	−	0.0820281i
$97$	13.2150	+	6.44538i	1.34178	+	0.654429i	0.962608	−	0.270898i	$-0.0873206\pi$
$97$	13.2150	+	6.44538i	1.34178	+	0.654429i	0.379170	+	0.925327i	$0.376210\pi$
$98$	−3.56939	+	2.99507i	−0.360562	+	0.302548i
$99$	12.3582	−	1.77671i	1.24204	−	0.178566i
$100$	−3.09983	−	1.12825i	−0.309983	−	0.112825i
$101$	−0.954163	+	0.237899i	−0.0949427	+	0.0236719i	−0.289104	−	0.957298i	$-0.593357\pi$
$101$	−0.954163	+	0.237899i	−0.0949427	+	0.0236719i	0.194161	+	0.980970i	$0.437802\pi$
$102$	5.80135	+	6.44305i	0.574419	+	0.637957i
$103$	−1.82488	−	1.64313i	−0.179811	−	0.161902i	0.574310	−	0.818638i	$-0.305270\pi$
$103$	−1.82488	−	1.64313i	−0.179811	−	0.161902i	−0.754121	+	0.656735i	$0.771937\pi$
$104$	−2.33359	−	4.78457i	−0.228827	−	0.469166i
$105$	−11.2151	−	22.9944i	−1.09449	−	2.24403i
$106$	−3.17163	−	2.85574i	−0.308056	−	0.277374i
$107$	−4.05195	−	4.50014i	−0.391717	−	0.435045i	0.514739	−	0.857347i	$-0.327889\pi$
$107$	−4.05195	−	4.50014i	−0.391717	−	0.435045i	−0.906455	+	0.422302i	$0.861222\pi$
$108$	1.92912	−	0.480985i	0.185630	−	0.0462828i
$109$	−5.68629	−	2.06964i	−0.544647	−	0.198235i	0.0550193	−	0.998485i	$-0.482478\pi$
$109$	−5.68629	−	2.06964i	−0.544647	−	0.198235i	−0.599667	+	0.800250i	$0.704700\pi$
$110$	−6.85183	+	6.65875i	−0.653296	+	0.634887i
$111$	18.6462	−	15.6460i	1.76982	−	1.48506i
$112$	3.06902	+	1.49686i	0.289995	+	0.141440i
$113$	11.9697	+	3.88920i	1.12602	+	0.365865i	0.812061	−	0.583572i	$-0.198345\pi$
$113$	11.9697	+	3.88920i	1.12602	+	0.365865i	0.313956	+	0.949437i	$0.398345\pi$
$114$	−10.3583	−	4.60769i	−0.970139	−	0.431550i
$115$	−18.6997	+	13.5861i	−1.74376	+	1.26691i
$116$	−3.33691	−	3.22242i	−0.309825	−	0.299194i
$117$	16.9943	+	10.6192i	1.57112	+	0.981746i
$118$	−2.76549	+	0.0965730i	−0.254584	+	0.00889027i
$119$	−6.36508	−	9.43662i	−0.583486	−	0.865054i
$120$	−4.81604	+	5.73954i	−0.439642	+	0.523945i
$121$	3.46531	+	10.4399i	0.315029	+	0.949082i
$122$	−3.65455	+	2.10995i	−0.330867	+	0.191026i
$123$	9.09716	+	9.42039i	0.820264	+	0.849408i
$124$	3.96521	−	7.45748i	0.356087	−	0.669701i
$125$	3.27929	−	3.64202i	0.293308	−	0.325752i
$126$	−12.7836	+	1.34361i	−1.13886	+	0.119699i
$127$	8.38632	+	0.586428i	0.744165	+	0.0520371i	0.436805	−	0.899556i	$-0.356110\pi$
$127$	8.38632	+	0.586428i	0.744165	+	0.0520371i	0.307360	+	0.951593i	$0.400554\pi$
$128$	0.0348995	−	0.999391i	0.00308471	−	0.0883345i
$129$	0.166189	+	4.75903i	0.0146321	+	0.419009i
$130$	−15.2979	+	1.06973i	−1.34171	+	0.0938215i
$131$	4.85437	−	0.855957i	0.424128	−	0.0747853i	0.0424898	−	0.999097i	$-0.486471\pi$
$131$	4.85437	−	0.855957i	0.424128	−	0.0747853i	0.381639	+	0.924312i	$0.375360\pi$
$132$	3.53345	+	7.86915i	0.307547	+	0.684922i
$133$	12.6249	+	7.88310i	1.09472	+	0.683551i
$134$	5.97489	−	8.22373i	0.516152	−	0.710422i
$135$	0.797110	−	5.67173i	0.0686043	−	0.488145i
$136$	−1.76649	+	2.82698i	−0.151476	+	0.242412i
$137$	1.89082	−	2.80325i	0.161543	−	0.239498i	−0.739572	−	0.673078i	$-0.764972\pi$
$137$	1.89082	−	2.80325i	0.161543	−	0.239498i	0.901115	+	0.433580i	$0.142750\pi$
$138$	5.75206	+	20.0598i	0.489648	+	1.70761i
$139$	13.1582	+	5.31626i	1.11606	+	0.450919i	0.857194	−	0.514993i	$-0.172206\pi$
$139$	13.1582	+	5.31626i	1.11606	+	0.450919i	0.258870	+	0.965912i	$0.416650\pi$
$140$	7.31005	−	6.58200i	0.617812	−	0.556281i
$141$	−18.0770	−	1.89997i	−1.52236	−	0.160006i
$142$	9.93708	+	1.75218i	0.833901	+	0.147039i
$143$	−6.56203	+	16.3907i	−0.548744	+	1.37066i
$144$	1.88222	+	3.26010i	0.156851	+	0.271675i
$145$	−12.2081	+	5.43539i	−1.01383	+	0.451385i
$146$	6.34348	+	10.1517i	0.524990	+	0.840160i
$147$	12.1113	+	0.422936i	0.998923	+	0.0348832i
$148$	7.75882	+	5.23339i	0.637771	+	0.430182i
$149$	−22.7024	−	5.66034i	−1.85985	−	0.463713i	−0.860869	−	0.508826i	$-0.830080\pi$
$149$	−22.7024	−	5.66034i	−1.85985	−	0.463713i	−0.998982	+	0.0451132i	$0.985635\pi$
$150$	4.02789	+	7.57536i	0.328876	+	0.618526i
$151$	−2.48558	+	7.64982i	−0.202273	+	0.622533i	0.797541	+	0.603265i	$0.206134\pi$
$151$	−2.48558	+	7.64982i	−0.202273	+	0.622533i	−0.999814	+	0.0192687i	$0.993866\pi$
$152$	0.605216	−	4.31668i	0.0490895	−	0.350129i
$153$		−	12.5488i		−	1.01451i
$154$	−3.15601	−	10.8763i	−0.254318	−	0.876438i
$155$	−15.6398	−	18.6388i	−1.25622	−	1.49710i
$156$	−3.81625	+	13.3088i	−0.305544	+	1.06556i
$157$	4.86858	−	6.23149i	0.388555	−	0.497327i	−0.553471	−	0.832869i	$-0.686697\pi$
$157$	4.86858	−	6.23149i	0.388555	−	0.497327i	0.942026	+	0.335541i	$0.108919\pi$
$158$	0.515957	−	1.27704i	0.0410474	−	0.101596i
$159$	1.16027	+	11.0392i	0.0920153	+	0.875467i
$160$	−2.63170	−	1.17171i	−0.208055	−	0.0926318i
$161$	−3.81299	−	27.1308i	−0.300505	−	2.13821i
$162$	5.40570	+	2.87426i	0.424712	+	0.225823i
$163$	1.31474	−	12.5090i	0.102979	−	0.979777i	−0.814007	−	0.580856i	$-0.802718\pi$
$163$	1.31474	−	12.5090i	0.102979	−	0.979777i	0.916985	−	0.398921i	$-0.130615\pi$
$164$	−2.51761	+	4.36063i	−0.196593	+	0.340508i
$165$	24.8316	−	0.945804i	1.93314	−	0.0736307i
$166$	2.73984	−	7.52765i	0.212653	−	0.584259i
$167$	−12.0652	−	3.45965i	−0.933636	−	0.267716i	−0.225866	−	0.974158i	$-0.572521\pi$
$167$	−12.0652	−	3.45965i	−0.933636	−	0.267716i	−0.707770	+	0.706443i	$0.750299\pi$
$168$	−3.32683	−	8.23420i	−0.256671	−	0.635283i
$169$	−13.5424	+	7.20063i	−1.04172	+	0.553895i
$170$	5.64453	+	7.76904i	0.432916	+	0.595858i
$171$	6.67901	+	14.9880i	0.510756	+	1.14616i
$172$	−1.74130	+	0.565783i	−0.132773	+	0.0431406i
$173$	7.01824	+	0.986350i	0.533587	+	0.0749908i	0.400821	−	0.916157i	$-0.368725\pi$
$173$	7.01824	+	0.986350i	0.533587	+	0.0749908i	0.132767	+	0.991147i	$0.457614\pi$
$174$	0.841610	+	12.0356i	0.0638023	+	0.912416i
$175$	−3.85252	−	10.5847i	−0.291223	−	0.800128i
$176$	−2.53392	+	2.13991i	−0.191002	+	0.161302i
$177$	5.51323	+	4.62615i	0.414400	+	0.347723i
$178$	3.87627	+	8.70625i	0.290539	+	0.652561i
$179$	4.26755	+	20.0772i	0.318971	+	1.50064i	0.787013	+	0.616936i	$0.211626\pi$
$179$	4.26755	+	20.0772i	0.318971	+	1.50064i	−0.468042	+	0.883706i	$0.655040\pi$
$180$	10.7389	−	1.50925i	0.800430	−	0.112493i
$181$	−12.8243	+	6.25485i	−0.953226	+	0.464919i	−0.848274	−	0.529558i	$-0.822358\pi$
$181$	−12.8243	+	6.25485i	−0.953226	+	0.464919i	−0.104952	+	0.994477i	$0.533469\pi$
$182$	7.39326	−	16.6055i	0.548025	−	1.23088i
$183$	10.7355	+	2.28191i	0.793593	+	0.168683i
$184$	−6.80441	+	4.25187i	−0.501628	+	0.313452i
$185$	22.3513	−	15.0761i	1.64330	−	1.10842i
$186$	−20.6423	+	7.51319i	−1.51357	+	0.550894i
$187$	10.8819	−	1.95430i	0.795765	−	0.142912i
$188$	−1.21357	−	6.88252i	−0.0885090	−	0.501960i
$189$	5.49229	+	3.99038i	0.399506	+	0.290258i
$190$	−10.8767	−	6.27488i	−0.789079	−	0.455227i
$191$	−1.20188	−	3.69900i	−0.0869649	−	0.267651i	0.898112	−	0.439768i	$-0.144939\pi$
$191$	−1.20188	−	3.69900i	−0.0869649	−	0.267651i	−0.985076	+	0.172117i	$0.944939\pi$
$192$	−1.80670	+	1.87090i	−0.130388	+	0.135020i
$193$	2.11781	−	8.49408i	0.152443	−	0.611417i	−0.844656	−	0.535309i	$-0.820195\pi$
$193$	2.11781	−	8.49408i	0.152443	−	0.611417i	0.997100	−	0.0761081i	$-0.0242494\pi$
$194$	11.5861	−	9.05208i	0.831836	−	0.649901i
$195$	31.4295	+	24.5554i	2.25071	+	1.75845i
$196$	1.12724	+	4.52110i	0.0805168	+	0.322935i
$197$	−7.86168	−	4.53894i	−0.560122	−	0.323386i	0.193073	−	0.981184i	$-0.438155\pi$
$197$	−7.86168	−	4.53894i	−0.560122	−	0.323386i	−0.753194	+	0.657798i	$0.771488\pi$
$198$	3.82056	−	11.8863i	0.271515	−	0.844722i
$199$	1.09148	−	6.19010i	0.0773731	−	0.438804i	−0.921370	−	0.388686i	$-0.872929\pi$
$199$	1.09148	−	6.19010i	0.0773731	−	0.438804i	0.998743	−	0.0501183i	$-0.0159598\pi$
$200$	−2.37294	+	2.29152i	−0.167792	+	0.162035i
$201$	−25.8602	+	5.49675i	−1.82404	+	0.387711i
$202$	−0.204455	+	0.961884i	−0.0143854	+	0.0676779i
$203$	1.10493	−	15.8013i	0.0775510	−	1.10903i
$204$	8.33412	−	2.38977i	0.583505	−	0.167317i
$205$	8.93034	+	11.4303i	0.623722	+	0.798328i
$206$	−2.27681	+	0.919891i	−0.158633	+	0.0640918i
$207$	13.2407	−	27.1475i	0.920294	−	1.88688i
$208$	−5.32332			−0.369106
$209$	−11.9569	+	8.12599i	−0.827079	+	0.562086i
$210$	−25.5837			−1.76544
$211$	11.2335	−	23.0321i	0.773346	−	1.58559i	−0.0367699	−	0.999324i	$-0.511707\pi$
$211$	11.2335	−	23.0321i	0.773346	−	1.58559i	0.810116	−	0.586270i	$-0.199404\pi$
$212$	−3.95708	+	1.59876i	−0.271773	+	0.109803i
$213$	−16.1572	−	20.6802i	−1.10707	−	1.41699i
$214$	−5.82096	+	1.66913i	−0.397913	+	0.114100i
$215$	−0.367925	+	5.26157i	−0.0250923	+	0.358836i
$216$	0.413366	−	1.94473i	0.0281260	−	0.132322i
$217$	28.2099	−	5.99620i	1.91501	−	0.407049i
$218$	−4.35288	+	4.20353i	−0.294814	+	0.284699i
$219$	5.40635	−	30.6609i	0.365327	−	2.07187i
$220$	2.98121	+	9.07739i	0.200993	+	0.611997i
$221$	15.3679	+	8.87269i	1.03376	+	0.596841i
$222$	−5.88860	−	23.6179i	−0.395217	−	1.58513i
$223$	−17.7726	−	13.8855i	−1.19014	−	0.929842i	−0.191479	−	0.981497i	$-0.561328\pi$
$223$	−17.7726	−	13.8855i	−1.19014	−	0.929842i	−0.998665	+	0.0516545i	$0.983551\pi$
$224$	2.69074	−	2.10224i	0.179783	−	0.140462i
$225$	3.00419	−	12.0492i	0.200279	−	0.803277i
$226$	8.74278	−	9.05341i	0.581561	−	0.602224i
$227$	1.15009	+	3.53961i	0.0763340	+	0.234932i	0.981941	−	0.189185i	$-0.0605846\pi$
$227$	1.15009	+	3.53961i	0.0763340	+	0.234932i	−0.905607	+	0.424117i	$0.860585\pi$
$228$	−8.68213	+	7.29006i	−0.574988	+	0.482796i
$229$	−3.57028	−	2.59396i	−0.235931	−	0.171414i	0.463538	−	0.886077i	$-0.346580\pi$
$229$	−3.57028	−	2.59396i	−0.235931	−	0.171414i	−0.699468	+	0.714663i	$0.746580\pi$
$230$	4.01372	+	22.7629i	0.264657	+	1.50094i
$231$	−12.8282	+	26.5143i	−0.844033	+	1.74451i
$232$	−4.35910	+	1.58658i	−0.286189	+	0.104164i
$233$	−6.76765	+	4.56484i	−0.443364	+	0.299053i	−0.760513	−	0.649323i	$-0.775052\pi$
$233$	−6.76765	+	4.56484i	−0.443364	+	0.299053i	0.317149	+	0.948376i	$0.397275\pi$
$234$	16.9943	−	10.6192i	1.11095	−	0.694199i
$235$	−19.6928	−	4.18584i	−1.28462	−	0.273054i
$236$	−1.12551	+	2.52794i	−0.0732646	+	0.164555i
$237$	−3.21969	+	1.57035i	−0.209142	+	0.102005i
$238$	−11.2719	+	1.58416i	−0.730646	+	0.102686i
$239$	2.11004	+	9.92696i	0.136487	+	0.642122i	0.992198	+	0.124668i	$0.0397866\pi$
$239$	2.11004	+	9.92696i	0.136487	+	0.642122i	−0.855711	+	0.517454i	$0.826880\pi$
$240$	3.04745	+	6.84468i	0.196712	+	0.441822i
$241$	16.1880	+	13.5834i	1.04276	+	0.874983i	0.992314	−	0.123744i	$-0.0394901\pi$
$241$	16.1880	+	13.5834i	1.04276	+	0.874983i	0.0504496	+	0.998727i	$0.483935\pi$
$242$	10.9024	+	1.46195i	0.700834	+	0.0939776i
$243$	−7.48608	−	20.5678i	−0.480232	−	1.31943i
$244$	0.294366	+	4.20963i	0.0188448	+	0.269494i
$245$	13.2923	+	1.86811i	0.849212	+	0.119349i
$246$	12.4549	−	4.04685i	0.794097	−	0.258018i
$247$	−23.0775	−	2.41784i	−1.46839	−	0.153843i
$248$	−4.96450	−	6.83305i	−0.315246	−	0.433899i
$249$	−18.3960	+	9.78134i	−1.16580	+	0.619867i
$250$	−1.83588	−	4.54396i	−0.116111	−	0.287385i
$251$	−7.44314	−	2.13429i	−0.469807	−	0.134715i	0.0323772	−	0.999476i	$-0.489692\pi$
$251$	−7.44314	−	2.13429i	−0.469807	−	0.134715i	−0.502184	+	0.864761i	$0.667470\pi$
$252$	−4.39634	+	12.0788i	−0.276943	+	0.760896i
$253$	25.6035	+	7.25410i	1.60968	+	0.456062i
$254$	4.20340	−	7.28050i	0.263745	−	0.456819i
$255$	2.61072	−	24.8393i	0.163489	−	1.55550i
$256$	−0.882948	−	0.469472i	−0.0551842	−	0.0293420i
$257$	−0.0444657	−	0.316390i	−0.00277369	−	0.0197358i	0.988832	−	0.149034i	$-0.0476164\pi$
$257$	−0.0444657	−	0.316390i	−0.00277369	−	0.0197358i	−0.991606	+	0.129298i	$0.958728\pi$
$258$	4.35024	+	1.93685i	0.270834	+	0.120583i
$259$	3.34038	+	31.7816i	0.207561	+	1.97481i
$260$	−5.74467	+	14.2186i	−0.356269	+	0.881797i
$261$	10.7511	−	13.7608i	0.665476	−	0.851770i
$262$	1.35869	−	4.73831i	0.0839400	−	0.292734i
$263$	16.0266	+	19.0998i	0.988243	+	1.17774i	0.984076	+	0.177750i	$0.0568820\pi$
$263$	16.0266	+	19.0998i	0.988243	+	1.17774i	0.00416711	+	0.999991i	$0.498674\pi$
$264$	8.62171	+	0.273769i	0.530629	+	0.0168493i
$265$			12.2946i			0.755253i
$266$	12.6197	−	7.89144i	0.773761	−	0.483855i
$267$	7.65948	−	23.5734i	0.468752	−	1.44267i
$268$	−4.77222	−	8.97525i	−0.291510	−	0.548250i
$269$	13.1464	+	3.27777i	0.801550	+	0.199849i	0.621096	−	0.783734i	$-0.286688\pi$
$269$	13.1464	+	3.27777i	0.801550	+	0.199849i	0.180454	+	0.983583i	$0.442243\pi$
$270$	−4.74829	−	3.20276i	−0.288972	−	0.194914i
$271$	−31.2086	−	1.08983i	−1.89579	−	0.0662025i	−0.936837	−	0.349767i	$-0.886261\pi$
$271$	−31.2086	−	1.08983i	−1.89579	−	0.0662025i	−0.958953	+	0.283564i	$0.908483\pi$
$272$	1.76649	+	2.82698i	0.107109	+	0.171411i
$273$	−43.1885	+	19.2288i	−2.61389	+	1.16378i
$274$	−1.69066	−	2.92832i	−0.102137	−	0.176906i
$275$	10.9165	+	0.728658i	0.658290	+	0.0439397i
$276$	20.5512	+	3.62373i	1.23704	+	0.218123i
$277$	4.10906	+	0.431880i	0.246890	+	0.0259492i	0.227165	−	0.973856i	$-0.427054\pi$
$277$	4.10906	+	0.431880i	0.246890	+	0.0259492i	0.0197248	+	0.999805i	$0.493721\pi$
$278$	10.5464	−	9.49602i	0.632531	−	0.569533i
$279$	29.4797	+	11.9106i	1.76490	+	0.713067i
$280$	−2.71135	−	9.45559i	−0.162034	−	0.565080i
$281$	2.76463	−	4.09873i	0.164924	−	0.244510i	−0.737512	−	0.675334i	$-0.763999\pi$
$281$	2.76463	−	4.09873i	0.164924	−	0.244510i	0.902436	+	0.430824i	$0.141777\pi$
$282$	−9.63212	+	15.4146i	−0.573584	+	0.917926i
$283$	1.03417	−	7.35847i	0.0614747	−	0.437415i	−0.935077	−	0.354444i	$-0.884670\pi$
$283$	1.03417	−	7.35847i	0.0614747	−	0.437415i	0.996552	−	0.0829713i	$-0.0264410\pi$
$284$	5.93097	−	8.16329i	0.351939	−	0.484402i
$285$	10.1024	+	31.0570i	0.598413	+	1.83966i
$286$	11.8553	+	13.0831i	0.701016	+	0.773621i
$287$	−16.9321	+	2.98558i	−0.999469	+	0.176233i
$288$	3.75526	−	0.262594i	0.221281	−	0.0154735i
$289$	0.205477	+	5.88409i	0.0120869	+	0.346123i
$290$	−0.466377	+	13.3553i	−0.0273866	+	0.784249i
$291$	−38.1472	−	2.66751i	−2.23623	−	0.156372i
$292$	11.9051	−	1.25127i	0.696692	−	0.0732253i
$293$	2.82295	−	3.13520i	0.164918	−	0.183160i	−0.655021	−	0.755611i	$-0.727340\pi$
$293$	2.82295	−	3.13520i	0.164918	−	0.183160i	0.819940	+	0.572450i	$0.194007\pi$
$294$	5.68937	−	10.7002i	0.331811	−	0.624046i
$295$	5.53752	+	5.73427i	0.322407	+	0.333862i
$296$	8.10498	−	4.67941i	0.471092	−	0.271985i
$297$	−5.70016	+	3.31508i	−0.330757	+	0.192360i
$298$	−15.0395	+	17.9234i	−0.871217	+	1.03828i
$299$	23.8844	+	35.4101i	1.38127	+	2.04782i
$300$	8.57440	−	0.299425i	0.495043	−	0.0172873i
$301$	−5.30186	−	3.31297i	−0.305594	−	0.190956i
$302$	5.78601	+	5.58748i	0.332947	+	0.321523i
$303$	2.06915	−	1.50332i	0.118869	−	0.0863637i
$304$	−3.61450	−	2.43627i	−0.207306	−	0.139730i
$305$	11.5616	+	3.75658i	0.662013	+	0.215101i
$306$	−11.2788	−	5.50103i	−0.644765	−	0.314473i
$307$	−7.01499	+	5.88628i	−0.400367	+	0.335948i	−0.820635	−	0.571452i	$-0.806380\pi$
$307$	−7.01499	+	5.88628i	−0.400367	+	0.335948i	0.420269	+	0.907400i	$0.361936\pi$
$308$	−11.1591	−	1.93126i	−0.635847	−	0.110044i
$309$	6.00154	+	2.18438i	0.341415	+	0.124265i
$310$	−23.6085	+	5.88626i	−1.34087	+	0.334317i
$311$	−7.06987	−	7.85188i	−0.400895	−	0.445239i	0.508569	−	0.861021i	$-0.330175\pi$
$311$	−7.06987	−	7.85188i	−0.400895	−	0.445239i	−0.909464	+	0.415782i	$0.863508\pi$
$312$	10.2890	+	9.26423i	0.582498	+	0.524484i
$313$	−13.0362	−	26.7281i	−0.736849	−	1.51076i	−0.855486	−	0.517826i	$-0.826741\pi$
$313$	−13.0362	−	26.7281i	−0.736849	−	1.51076i	0.118637	−	0.992938i	$-0.462147\pi$
$314$	−3.46659	−	7.10755i	−0.195631	−	0.401102i
$315$	27.5182	+	24.7775i	1.55048	+	1.39605i
$316$	−0.921615	−	1.02356i	−0.0518449	−	0.0575796i
$317$	11.3141	−	2.82093i	0.635465	−	0.158439i	0.0891492	−	0.996018i	$-0.471585\pi$
$317$	11.3141	−	2.82093i	0.635465	−	0.158439i	0.546316	+	0.837579i	$0.316030\pi$
$318$	10.4306	+	3.79643i	0.584920	+	0.212893i
$319$	13.6072	+	7.17997i	0.761859	+	0.402001i
$320$	−2.20679	+	1.85172i	−0.123363	+	0.103514i
$321$	14.1556	+	6.90416i	0.790090	+	0.385352i
$322$	−26.0565	−	8.46627i	−1.45207	−	0.471807i
$323$	6.37405	+	13.0578i	0.354661	+	0.726554i
$324$	4.95307	−	3.59862i	0.275171	−	0.199923i
$325$	12.6319	+	12.1985i	0.700693	+	0.676651i
$326$	−10.6666	−	6.66525i	−0.590770	−	0.369154i
$327$	15.7287	−	0.549260i	0.869801	−	0.0303741i
$328$	2.81566	+	4.17439i	0.155469	+	0.230492i
$329$	15.3392	−	18.2806i	0.845679	−	1.00784i
$330$	10.0354	−	22.7331i	0.552429	−	1.25142i
$331$	−16.0800	+	9.28381i	−0.883838	+	0.510284i	−0.871922	−	0.489645i	$-0.837126\pi$
$331$	−16.0800	+	9.28381i	−0.883838	+	0.510284i	−0.0119162	+	0.999929i	$0.503793\pi$
$332$	−5.56474	−	5.76245i	−0.305405	−	0.316256i
$333$	−16.5398	+	31.1068i	−0.906375	+	1.70464i
$334$	−8.39856	+	9.32755i	−0.459549	+	0.510381i
$335$	−29.1228	+	3.06093i	−1.59115	+	0.167236i
$336$	−8.85924	−	0.619499i	−0.483311	−	0.0337964i
$337$	−0.200186	+	5.73257i	−0.0109048	+	0.312273i	0.981666	+	0.190607i	$0.0610457\pi$
$337$	−0.200186	+	5.73257i	−0.0109048	+	0.312273i	−0.992571	+	0.121665i	$0.961176\pi$
$338$	0.535280	+	15.3284i	0.0291154	+	0.833755i
$339$	−32.6539	+	2.28338i	−1.77351	+	0.124016i
$340$	9.45716	−	1.66755i	0.512887	−	0.0904358i
$341$	−5.73743	+	27.4187i	−0.310699	+	1.48481i
$342$	16.3990	+	0.567242i	0.886755	+	0.0306729i
$343$	4.69750	−	6.46556i	0.253641	−	0.349107i
$344$	−0.254814	+	1.81309i	−0.0137386	+	0.0977555i
$345$	31.8568	−	50.9816i	1.71511	−	2.74475i
$346$	3.96312	−	5.87557i	0.213059	−	0.315872i
$347$	−4.47364	−	15.6014i	−0.240158	−	0.837529i	−0.985330	−	0.170658i	$-0.945411\pi$
$347$	−4.47364	−	15.6014i	−0.240158	−	0.837529i	0.745173	−	0.666871i	$-0.232367\pi$
$348$	11.1865	+	4.51962i	0.599657	+	0.242277i
$349$	−0.456175	+	0.410742i	−0.0244185	+	0.0219865i	−0.681250	−	0.732051i	$-0.738563\pi$
$349$	−0.456175	+	0.410742i	−0.0244185	+	0.0219865i	0.656831	+	0.754038i	$0.271896\pi$
$350$	−11.2023	−	1.17741i	−0.598788	−	0.0629352i
$351$	−10.4229	−	1.83785i	−0.556335	−	0.0980969i
$352$	0.812541	+	3.21555i	0.0433086	+	0.171390i
$353$	0.0623427	+	0.107981i	0.00331816	+	0.00574723i	0.867680	−	0.497124i	$-0.165610\pi$
$353$	0.0623427	+	0.107981i	0.00331816	+	0.00574723i	−0.864362	+	0.502871i	$0.832277\pi$
$354$	6.57480	−	2.92729i	0.349447	−	0.155584i
$355$	−15.4037	−	24.6510i	−0.817542	−	1.30834i
$356$	9.52437	+	0.332598i	0.504791	+	0.0176277i
$357$	24.5433	+	16.5546i	1.29897	+	0.876165i
$358$	19.9161	+	4.96563i	1.05260	+	0.262442i
$359$	−8.60922	−	16.1916i	−0.454377	−	0.854559i	−0.999865	−	0.0164403i	$-0.994767\pi$
$359$	−8.60922	−	16.1916i	−0.454377	−	0.854559i	0.545488	−	0.838119i	$-0.316344\pi$
$360$	3.35111	−	10.3137i	0.176619	−	0.543578i
$361$	−14.5629	−	12.2033i	−0.766469	−	0.642281i
$362$			14.2684i			0.749930i
$363$	−18.5281	−	21.7993i	−0.972471	−	1.14416i
$364$	−11.6840	−	13.9244i	−0.612406	−	0.729837i
$365$	9.50524	−	33.1487i	0.497527	−	1.73508i
$366$	6.75711	−	8.64870i	0.353200	−	0.452075i
$367$	3.73207	−	9.23720i	0.194813	−	0.482178i	−0.797885	−	0.602810i	$-0.794048\pi$
$367$	3.73207	−	9.23720i	0.194813	−	0.482178i	0.992697	+	0.120632i	$0.0384921\pi$
$368$	0.838696	+	7.97966i	0.0437200	+	0.415968i
$369$	−17.3161	−	7.70960i	−0.901438	−	0.401346i
$370$	−3.75218	−	26.6981i	−0.195066	−	1.38797i
$371$	−12.8672	−	6.84160i	−0.668031	−	0.355198i
$372$	−2.29619	+	21.8468i	−0.119052	+	1.13270i
$373$	−11.1077	+	19.2392i	−0.575137	+	0.996167i	0.420889	+	0.907112i	$0.361718\pi$
$373$	−11.1077	+	19.2392i	−0.575137	+	0.996167i	−0.996027	+	0.0890552i	$0.971615\pi$
$374$	3.01381	−	10.6373i	0.155841	−	0.550043i
$375$	−4.35949	+	11.9776i	−0.225123	+	0.618521i
$376$	−6.71797	−	1.92635i	−0.346453	−	0.0993437i
$377$	9.25058	+	22.8960i	0.476429	+	1.17920i
$378$	5.99420	−	3.18717i	0.308308	−	0.163930i
$379$	8.12788	+	11.1871i	0.417501	+	0.574641i	0.965028	−	0.262147i	$-0.0844306\pi$
$379$	8.12788	+	11.1871i	0.417501	+	0.574641i	−0.547527	+	0.836788i	$0.684431\pi$
$380$	−10.4079	+	7.02519i	−0.533912	+	0.360385i
$381$	−20.7947	+	6.75661i	−1.06534	+	0.346151i
$382$	−3.85151	−	0.541295i	−0.197060	−	0.0276950i
$383$	−0.692871	−	9.90852i	−0.0354041	−	0.506302i	−0.982611	−	0.185678i	$-0.940552\pi$
$383$	−0.692871	−	9.90852i	−0.0354041	−	0.506302i	0.947207	−	0.320624i	$-0.103893\pi$
$384$	0.889544	+	2.44400i	0.0453944	+	0.124720i
$385$	−17.2007	+	27.7217i	−0.876629	+	1.41283i
$386$	−6.70604	−	5.62704i	−0.341329	−	0.286409i
$387$	−2.80337	−	6.29648i	−0.142503	−	0.320068i
$388$	−3.05693	−	14.3817i	−0.155192	−	0.730121i
$389$	10.9568	−	1.53988i	0.555531	−	0.0780748i	0.144179	−	0.989552i	$-0.453946\pi$
$389$	10.9568	−	1.53988i	0.555531	−	0.0780748i	0.411352	+	0.911477i	$0.365057\pi$
$390$	35.8481	−	17.4843i	1.81524	−	0.885350i
$391$	10.8789	−	24.4344i	0.550170	−	1.23570i
$392$	4.55768	+	0.968765i	0.230198	+	0.0489300i
$393$	−10.8722	+	6.79371i	−0.548430	+	0.342697i
$394$	−7.52591	+	5.07629i	−0.379150	+	0.255740i
$395$	−3.72848	+	1.35705i	−0.187600	+	0.0682808i
$396$	−9.00851	−	8.64450i	−0.452695	−	0.434403i
$397$	3.25914	+	18.4835i	0.163572	+	0.927660i	0.950525	+	0.310648i	$0.100546\pi$
$397$	3.25914	+	18.4835i	0.163572	+	0.927660i	−0.786954	+	0.617012i	$0.788343\pi$
$398$	−5.08515	−	3.69458i	−0.254896	−	0.185192i
$399$	−38.1249	−	6.70947i	−1.90863	−	0.335894i
$400$	1.01938	+	3.13732i	0.0509689	+	0.156866i
$401$	10.4256	−	10.7960i	0.520631	−	0.539129i	−0.406607	−	0.913603i	$-0.633288\pi$
$401$	10.4256	−	10.7960i	0.520631	−	0.539129i	0.927237	+	0.374475i	$0.122177\pi$
$402$	−6.39591	+	25.6526i	−0.318999	+	1.27944i
$403$	−35.4301	+	27.6810i	−1.76490	+	1.37889i
$404$	0.774909	+	0.605425i	0.0385531	+	0.0301210i
$405$	−4.26677	−	17.1131i	−0.212018	−	0.850356i
$406$	−13.7177	−	7.91992i	−0.680798	−	0.393059i
$407$	−29.5507	−	9.49835i	−1.46477	−	0.470816i
$408$	1.50553	−	8.53827i	0.0745347	−	0.422707i
$409$	−4.56061	+	4.40413i	−0.225508	+	0.217770i	−0.798825	−	0.601563i	$-0.794545\pi$
$409$	−4.56061	+	4.40413i	−0.225508	+	0.217770i	0.573318	+	0.819333i	$0.305656\pi$
$410$	14.1883	−	3.01582i	0.700710	−	0.148941i
$411$	−1.82845	+	8.60216i	−0.0901906	+	0.424313i
$412$	−0.171295	+	2.44964i	−0.00843911	+	0.120685i
$413$	−9.08277	+	2.60444i	−0.446934	+	0.128156i
$414$	−18.5957	−	23.8014i	−0.913927	−	1.16977i
$415$	−21.3967	+	8.64482i	−1.05032	+	0.424357i
$416$	−2.33359	+	4.78457i	−0.114414	+	0.234583i
$417$	−36.9102			−1.80750
$418$	2.06201	+	14.3090i	0.100856	+	0.699877i
$419$	23.3767			1.14203			0.571014	−	0.820940i	$-0.306550\pi$
$419$	23.3767			1.14203			0.571014	+	0.820940i	$0.306550\pi$
$420$	−11.2151	+	22.9944i	−0.547243	+	1.12201i
$421$	−23.7190	+	9.58311i	−1.15599	+	0.467052i	−0.870906	−	0.491449i	$-0.836467\pi$
$421$	−23.7190	+	9.58311i	−1.15599	+	0.467052i	−0.285088	+	0.958501i	$0.592023\pi$
$422$	−15.7767	−	20.1932i	−0.767996	−	0.982990i
$423$	25.2893	−	7.25160i	1.22961	−	0.352585i
$424$	−0.297710	+	4.25745i	−0.0144581	+	0.206760i
$425$	2.28630	−	10.7562i	0.110902	−	0.521753i
$426$	−25.6701	+	5.45635i	−1.24372	+	0.264361i
$427$	−10.3652	+	10.0095i	−0.501606	+	0.484396i
$428$	−1.05153	+	5.96354i	−0.0508278	+	0.288259i
$429$	−0.145278	−	45.9190i	−0.00701407	−	2.21699i
$430$	4.56778	+	2.63721i	0.220278	+	0.127178i
$431$	−8.58966	−	34.4513i	−0.413750	−	1.65946i	−0.709888	−	0.704314i	$-0.751255\pi$
$431$	−8.58966	−	34.4513i	−0.413750	−	1.65946i	0.296139	−	0.955145i	$-0.404301\pi$
$432$	−1.56671	−	1.22405i	−0.0753783	−	0.0588920i
$433$	−8.48886	+	6.63222i	−0.407949	+	0.318724i	−0.798653	−	0.601792i	$-0.794454\pi$
$433$	−8.48886	+	6.63222i	−0.407949	+	0.318724i	0.390704	+	0.920516i	$0.372231\pi$
$434$	6.97706	−	27.9834i	0.334909	−	1.34325i
$435$	24.1438	−	25.0016i	1.15760	−	1.19873i
$436$	1.86993	+	5.75505i	0.0895534	+	0.275617i
$437$	0.0115525	+	34.9741i	0.000552629	+	1.67304i
$438$	−25.1879	−	18.3001i	−1.20352	−	0.874411i
$439$	1.31675	+	7.46766i	0.0628451	+	0.356412i	0.999972	+	0.00742453i	$0.00236332\pi$
$439$	1.31675	+	7.46766i	0.0628451	+	0.356412i	−0.937127	+	0.348987i	$0.886526\pi$
$440$	9.46558	+	1.29977i	0.451254	+	0.0619643i
$441$	−16.4826	+	5.99917i	−0.784885	+	0.285675i
$442$	14.7116	−	9.92309i	0.699758	−	0.471993i
$443$	0.767930	−	0.479856i	0.0364855	−	0.0227987i	−0.511554	−	0.859251i	$-0.670930\pi$
$443$	0.767930	−	0.479856i	0.0364855	−	0.0227987i	0.548039	+	0.836453i	$0.315374\pi$
$444$	−23.8090	−	5.06076i	−1.12993	−	0.240173i
$445$	11.1666	−	25.0806i	0.529348	−	1.18894i
$446$	−20.2712	+	9.88694i	−0.959870	+	0.468160i
$447$	60.2609	−	8.46912i	2.85024	−	0.400576i
$448$	−0.709936	−	3.33998i	−0.0335413	−	0.157799i
$449$	5.98875	+	13.4510i	0.282627	+	0.634790i	0.997950	−	0.0640041i	$-0.0203871\pi$
$449$	5.98875	+	13.4510i	0.282627	+	0.634790i	−0.715323	+	0.698794i	$0.753720\pi$
$450$	−9.51276	−	7.98215i	−0.448436	−	0.376282i
$451$	3.98880	−	16.2166i	0.187825	−	0.763610i
$452$	−4.30457	−	11.8267i	−0.202470	−	0.556282i
$453$	−1.45930	−	20.8690i	−0.0685640	−	0.980511i
$454$	3.68554	+	0.517969i	0.172971	+	0.0243095i
$455$	−49.8008	+	16.1812i	−2.33470	+	0.758589i
$456$	2.74627	+	10.9992i	0.128606	+	0.515084i
$457$	−14.2437	−	19.6048i	−0.666293	−	0.917074i	0.333376	−	0.942794i	$-0.391812\pi$
$457$	−14.2437	−	19.6048i	−0.666293	−	0.917074i	−0.999669	+	0.0257199i	$0.991812\pi$
$458$	−3.89654	+	2.07183i	−0.182074	+	0.0968102i
$459$	2.48276	+	6.14503i	0.115885	+	0.286826i
$460$	22.2187	+	6.37111i	1.03595	+	0.297054i
$461$	1.79762	−	4.93891i	0.0837234	−	0.230028i	−0.890766	−	0.454463i	$-0.849831\pi$
$461$	1.79762	−	4.93891i	0.0837234	−	0.230028i	0.974489	+	0.224435i	$0.0720535\pi$
$462$	18.2074	+	23.1530i	0.847083	+	1.07717i
$463$	−2.62046	+	4.53877i	−0.121783	+	0.210935i	−0.920471	−	0.390811i	$-0.872195\pi$
$463$	−2.62046	+	4.53877i	−0.121783	+	0.210935i	0.798688	+	0.601746i	$0.205528\pi$
$464$	−0.484892	+	4.61344i	−0.0225106	+	0.214174i
$465$	55.8746	+	29.7091i	2.59112	+	1.37773i
$466$	1.13611	+	8.08382i	0.0526291	+	0.374476i
$467$	7.56633	+	3.36875i	0.350128	+	0.155887i	0.574263	−	0.818671i	$-0.305289\pi$
$467$	7.56633	+	3.36875i	0.350128	+	0.155887i	−0.224135	+	0.974558i	$0.571955\pi$
$468$	−2.09468	−	19.9295i	−0.0968265	−	0.921242i
$469$	13.0025	−	32.1823i	0.600400	−	1.48604i
$470$	−12.3950	+	15.8648i	−0.571737	+	0.731790i
$471$	−5.66910	+	19.7705i	−0.261218	+	0.910976i
$472$	1.77871	+	2.11978i	0.0818716	+	0.0975707i
$473$	5.02352	−	3.41158i	0.230982	−	0.156865i
$474$			3.58224i			0.164538i
$475$	2.99421	+	14.0638i	0.137384	+	0.645292i
$476$	−3.51742	+	10.8255i	−0.161221	+	0.496187i
$477$	−7.54254	−	14.1855i	−0.345349	−	0.649507i
$478$	9.84728	+	2.45520i	0.450404	+	0.112298i
$479$	20.6141	+	13.9044i	0.941881	+	0.635307i	0.931150	−	0.364635i	$-0.118806\pi$
$479$	20.6141	+	13.9044i	0.941881	+	0.635307i	0.0107309	+	0.999942i	$0.496584\pi$
$480$	7.48787	+	0.261482i	0.341773	+	0.0119350i
$481$	−26.4006	−	42.2498i	−1.20376	−	1.92642i
$482$	19.3050	−	8.59516i	0.879320	−	0.391499i
$483$	35.6283	+	61.7101i	1.62115	+	2.80791i
$484$	6.09330	−	9.15815i	0.276968	−	0.416280i
$485$	−41.7124	−	7.35502i	−1.89406	−	0.333974i
$486$	−21.7679	−	2.28790i	−0.987414	−	0.103781i
$487$	7.28771	−	6.56189i	0.330238	−	0.297347i	−0.487286	−	0.873243i	$-0.662013\pi$
$487$	7.28771	−	6.56189i	0.330238	−	0.297347i	0.817524	+	0.575895i	$0.195346\pi$
$488$	3.91263	+	1.58081i	0.177116	+	0.0715597i
$489$	9.01696	+	31.4459i	0.407761	+	1.42203i
$490$	7.50599	−	11.1281i	0.339086	−	0.502716i
$491$	−4.49640	+	7.19574i	−0.202920	+	0.324739i	−0.933819	−	0.357746i	$-0.883545\pi$
$491$	−4.49640	+	7.19574i	−0.202920	+	0.324739i	0.730899	+	0.682485i	$0.239101\pi$
$492$	1.82259	−	12.9684i	0.0821689	−	0.584662i
$493$	9.08933	−	12.5104i	0.409363	−	0.563440i
$494$	−12.2896	+	19.6820i	−0.552937	+	0.885536i
$495$	−32.8110	+	14.7329i	−1.47474	+	0.662196i
$496$	−8.31780	+	1.46665i	−0.373480	+	0.0658547i
$497$	34.3707	−	2.40343i	1.54174	−	0.107809i
$498$	0.727124	+	20.8221i	0.0325832	+	0.933061i
$499$	−0.227708	+	6.52071i	−0.0101936	+	0.291907i	0.983579	+	0.180479i	$0.0577648\pi$
$499$	−0.227708	+	6.52071i	−0.0101936	+	0.291907i	−0.993772	+	0.111428i	$0.964457\pi$
$500$	−4.88888	−	0.341864i	−0.218637	−	0.0152886i
$501$	32.4657	−	3.41228i	1.45046	−	0.152449i
$502$	−5.18114	+	5.75424i	−0.231246	+	0.256824i
$503$	−12.3057	+	23.1437i	−0.548686	+	1.03193i	0.442161	+	0.896936i	$0.354212\pi$
$503$	−12.3057	+	23.1437i	−0.548686	+	1.03193i	−0.990847	+	0.134992i	$0.956899\pi$
$504$	8.92917	+	9.24642i	0.397737	+	0.411868i
$505$	2.45333	−	1.41643i	0.109172	−	0.0630303i
$506$	17.7438	−	19.8323i	0.788807	−	0.881653i
$507$	25.6416	−	30.5584i	1.13878	−	1.35715i
$508$	−4.70102	−	6.96955i	−0.208574	−	0.309224i
$509$	−42.4339	+	1.48182i	−1.88085	+	0.0656807i	−0.952235	−	0.305366i	$-0.901221\pi$
$509$	−42.4339	+	1.48182i	−1.88085	+	0.0656807i	−0.928614	+	0.371047i	$0.878999\pi$
$510$	−21.1810	−	13.2353i	−0.937909	−	0.586070i
$511$	29.4030	+	28.3942i	1.30071	+	1.25608i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−6.23599	−	6.01805i	−0.275326	−	0.265703i
$514$	−0.303862	−	0.0987306i	−0.0134028	−	0.00435482i
$515$	6.35811	+	3.10106i	0.280172	+	0.136649i
$516$	3.64785	−	3.06091i	0.160588	−	0.134749i
$517$	10.2268	+	20.8008i	0.449775	+	0.914818i
$518$	30.0294	+	10.9298i	1.31942	+	0.480229i
$519$	−17.8853	+	4.45930i	−0.785076	+	0.195741i
$520$	10.2613	+	11.3963i	0.449986	+	0.499760i
$521$	22.6854	+	20.4260i	0.993866	+	0.894881i	0.994460	−	0.105119i	$-0.0335224\pi$
$521$	22.6854	+	20.4260i	0.993866	+	0.894881i	−0.000593943		1.00000i	$0.500189\pi$
$522$	−7.65513	−	15.6953i	−0.335056	−	0.686966i
$523$	−7.32890	−	15.0265i	−0.320471	−	0.657062i	0.676364	−	0.736568i	$-0.263555\pi$
$523$	−7.32890	−	15.0265i	−0.320471	−	0.657062i	−0.996834	+	0.0795057i	$0.974666\pi$
$524$	−3.66315	−	3.29832i	−0.160026	−	0.144088i
$525$	19.6029	+	21.7712i	0.855539	+	0.950172i
$526$	24.1924	−	6.03183i	1.05484	−	0.263000i
$527$	26.4573	+	9.62967i	1.15250	+	0.419475i
$528$	4.02557	−	7.62913i	0.175190	−	0.332015i
$529$	31.6976	−	26.5975i	1.37816	−	1.15641i
$530$	11.0503	+	5.38961i	0.479996	+	0.234110i
$531$	−9.90701	−	3.21898i	−0.429928	−	0.139692i
$532$	−1.56068	−	14.8019i	−0.0676641	−	0.641742i
$533$	21.6850	−	15.7551i	0.939281	−	0.682428i
$534$	−17.8300	−	17.2182i	−0.771579	−	0.745105i
$535$	14.7938	+	9.24421i	0.639593	+	0.399662i
$536$	−10.1589	+	0.354757i	−0.438798	+	0.0153232i
$537$	−29.8522	−	44.2577i	−1.28822	−	1.90986i
$538$	8.70904	−	10.3790i	0.375473	−	0.447472i
$539$	−7.76921	−	13.3589i	−0.334644	−	0.575408i
$540$	−4.96014	+	2.86374i	−0.213450	+	0.123236i
$541$	4.10291	+	4.24869i	0.176398	+	0.182665i	0.801717	−	0.597704i	$-0.203920\pi$
$541$	4.10291	+	4.24869i	0.176398	+	0.182665i	−0.625319	+	0.780369i	$0.715031\pi$
$542$	−14.6605	+	27.5724i	−0.629722	+	1.18434i
$543$	24.8314	−	27.5781i	1.06562	−	1.18349i
$544$	3.31525	−	0.348447i	0.142140	−	0.0149396i
$545$	17.3896	+	1.21600i	0.744890	+	0.0520878i
$546$	−1.64990	+	47.2469i	−0.0706092	+	2.02198i
$547$	0.910163	+	26.0637i	0.0389158	+	1.11440i	0.849102	+	0.528229i	$0.177144\pi$
$547$	0.910163	+	26.0637i	0.0389158	+	1.11440i	−0.810186	+	0.586173i	$0.800634\pi$
$548$	−3.37309	+	0.235870i	−0.144091	+	0.0100758i
$549$	−15.6442	+	2.75850i	−0.667679	+	0.117730i
$550$	5.44040	−	9.49227i	0.231979	−	0.404752i
$551$	−4.19750	+	19.7798i	−0.178820	+	0.842649i
$552$	12.2660	−	16.8828i	0.522077	−	0.718578i
$553$	0.654536	−	4.65727i	0.0278337	−	0.198047i
$554$	2.18947	−	3.50388i	0.0930215	−	0.148866i
$555$	−39.2108	+	58.1324i	−1.66441	+	2.46758i
$556$	−3.91173	−	13.6418i	−0.165894	−	0.578542i
$557$	−36.7047	−	14.8297i	−1.55523	−	0.628354i	−0.573598	−	0.819137i	$-0.694453\pi$
$557$	−36.7047	−	14.8297i	−1.55523	−	0.628354i	−0.981632	+	0.190784i	$0.938897\pi$
$558$	23.6282	−	21.2749i	1.00026	−	0.900639i
$559$	9.69314	+	1.01879i	0.409976	+	0.0430902i
$560$	−9.68720	−	1.70812i	−0.409359	−	0.0721811i
$561$	−24.3374	+	15.3149i	−1.02752	+	0.646597i
$562$	−2.47198	−	4.28160i	−0.104274	−	0.180608i
$563$	19.0996	−	8.50371i	0.804954	−	0.358389i	0.0373412	−	0.999303i	$-0.488111\pi$
$563$	19.0996	−	8.50371i	0.804954	−	0.358389i	0.767613	+	0.640914i	$0.221444\pi$
$564$	9.63212	+	15.4146i	0.405585	+	0.649072i
$565$	−36.2344	−	1.26533i	−1.52439	−	0.0532329i
$566$	−6.16040	−	4.15524i	−0.258941	−	0.174658i
$567$	20.2844	+	5.05746i	0.851863	+	0.212393i
$568$	−4.73714	−	8.90927i	−0.198766	−	0.373825i
$569$	5.36534	−	16.5128i	0.224927	−	0.692253i	−0.773372	−	0.633952i	$-0.781432\pi$
$569$	5.36534	−	16.5128i	0.224927	−	0.692253i	0.998299	−	0.0583011i	$-0.0185683\pi$
$570$	32.3424	+	4.53454i	1.35467	+	0.189931i
$571$		−	24.6752i		−	1.03262i	−0.856401	−	0.516312i	$-0.827304\pi$
$571$		−	24.6752i		−	1.03262i	0.856401	−	0.516312i	$-0.172696\pi$
$572$	16.9560	−	4.92017i	0.708967	−	0.205723i
$573$	6.50222	+	7.74904i	0.271634	+	0.323721i
$574$	−4.73911	+	16.5272i	−0.197807	+	0.689834i
$575$	16.2954	−	20.8571i	0.679564	−	0.869803i
$576$	1.41018	−	3.49032i	0.0587576	−	0.145430i
$577$	−1.66382	−	15.8302i	−0.0692656	−	0.659018i	−0.972981	−	0.230885i	$-0.925838\pi$
$577$	−1.66382	−	15.8302i	−0.0692656	−	0.659018i	0.903716	−	0.428133i	$-0.140829\pi$
$578$	5.37866	+	2.39473i	0.223723	+	0.0996078i
$579$	3.16872	+	22.5466i	0.131687	+	0.937004i
$580$	11.7992	+	6.27375i	0.489935	+	0.260503i
$581$	2.85922	−	27.2037i	0.118621	−	1.12860i
$582$	−19.1202	+	33.1171i	−0.792557	+	1.37275i
$583$	11.1265	−	8.74983i	0.460814	−	0.362381i
$584$	4.09421	−	11.2487i	0.169419	−	0.465476i
$585$	−55.4921	−	15.9121i	−2.29432	−	0.657884i
$586$	−1.58040	−	3.91163i	−0.0652858	−	0.161588i
$587$	7.80904	−	4.15214i	0.322314	−	0.171377i	−0.300429	−	0.953804i	$-0.597130\pi$
$587$	7.80904	−	4.15214i	0.322314	−	0.171377i	0.622742	+	0.782427i	$0.286019\pi$
$588$	−7.12318	−	9.80422i	−0.293755	−	0.404319i
$589$	−36.7252	+	2.58027i	−1.51324	+	0.106318i
$590$	7.58141	−	2.46335i	0.312122	−	0.101414i
$591$	23.3805	+	3.28591i	0.961744	+	0.135164i
$592$	−0.652838	−	9.33603i	−0.0268315	−	0.383708i
$593$	−4.57520	−	12.5703i	−0.187881	−	0.516199i	0.809612	−	0.586965i	$-0.199678\pi$
$593$	−4.57520	−	12.5703i	−0.187881	−	0.516199i	−0.997493	+	0.0707669i	$0.977455\pi$
$594$	0.480787	+	6.57650i	0.0197269	+	0.269837i
$595$	25.1191	+	21.0774i	1.02978	+	0.864089i
$596$	9.51657	+	21.3746i	0.389814	+	0.875536i
$597$	3.39892	+	15.9907i	0.139108	+	0.654454i
$598$	42.2966	−	5.94440i	1.72964	−	0.243084i
$599$	−11.4913	+	5.60470i	−0.469523	+	0.229002i	−0.657915	−	0.753092i	$-0.728561\pi$
$599$	−11.4913	+	5.60470i	−0.469523	+	0.229002i	0.188392	+	0.982094i	$0.439673\pi$
$600$	3.48965	−	7.83788i	0.142464	−	0.319980i
$601$	32.3593	+	6.87818i	1.31996	+	0.280567i	0.813434	−	0.581657i	$-0.197595\pi$
$601$	32.3593	+	6.87818i	1.31996	+	0.280567i	0.506528	+	0.862224i	$0.330929\pi$
$602$	−5.30186	+	3.31297i	−0.216088	+	0.135027i
$603$	31.7238	−	21.3980i	1.29189	−	0.871393i
$604$	7.55841	−	2.75104i	0.307547	−	0.111938i
$605$	−17.8858	−	26.1582i	−0.727160	−	1.06348i
$606$	−0.444124	−	2.51875i	−0.0180413	−	0.102317i
$607$	−2.37283	−	1.72396i	−0.0963101	−	0.0699734i	0.538588	−	0.842569i	$-0.318958\pi$
$607$	−2.37283	−	1.72396i	−0.0963101	−	0.0699734i	−0.634898	+	0.772596i	$0.718958\pi$
$608$	−3.77420	+	2.18070i	−0.153064	+	0.0884389i
$609$	12.7306	+	39.1808i	0.515870	+	1.58768i
$610$	8.44464	−	8.74468i	0.341914	−	0.354062i
$611$	−9.00024	+	36.0980i	−0.364111	+	1.46037i
$612$	−9.88859	+	7.72581i	−0.399723	+	0.312297i
$613$	18.7947	+	14.6840i	0.759112	+	0.593083i	0.919095	−	0.394037i	$-0.128922\pi$
$613$	18.7947	+	14.6840i	0.759112	+	0.593083i	−0.159983	+	0.987120i	$0.551144\pi$
$614$	2.21538	+	8.88541i	0.0894055	+	0.358586i
$615$	−32.6717	−	18.8630i	−1.31745	−	0.760631i
$616$	−6.62762	+	9.18309i	−0.267034	+	0.369997i
$617$	−5.14221	+	29.1629i	−0.207018	+	1.17406i	0.687216	+	0.726454i	$0.258833\pi$
$617$	−5.14221	+	29.1629i	−0.207018	+	1.17406i	−0.894233	+	0.447601i	$0.852278\pi$
$618$	4.59421	−	4.43658i	0.184806	−	0.178465i
$619$	36.5899	−	7.77742i	1.47067	−	0.312601i	0.598233	−	0.801322i	$-0.295870\pi$
$619$	36.5899	−	7.77742i	1.47067	−	0.312601i	0.872440	+	0.488721i	$0.162537\pi$
$620$	−5.05875	+	23.7995i	−0.203164	+	0.955812i
$621$	−1.11278	+	15.9135i	−0.0446544	+	0.638588i
$622$	−10.1565	+	2.91232i	−0.407237	+	0.116773i
$623$	20.0347	+	25.6433i	0.802674	+	1.02738i
$624$	12.8370	−	5.18649i	0.513892	−	0.207626i
$625$	−13.4194	+	27.5138i	−0.536776	+	1.10055i
$626$	−29.7378			−1.18856
$627$	20.9167	−	31.2452i	0.835331	−	1.24781i
$628$	−7.90788			−0.315559
$629$	−13.6762	+	28.0404i	−0.545306	+	1.11804i
$630$	34.3331	−	13.8715i	1.36786	−	0.552652i
$631$	28.4302	+	36.3890i	1.13179	+	1.44862i	0.876272	+	0.481817i	$0.160023\pi$
$631$	28.4302	+	36.3890i	1.13179	+	1.44862i	0.255516	+	0.966805i	$0.417755\pi$
$632$	−1.32398	+	0.379644i	−0.0526649	+	0.0151014i
$633$	−4.64915	+	66.4859i	−0.184787	+	2.64258i
$634$	2.42436	−	11.4057i	0.0962835	−	0.452978i
$635$	−23.6887	+	5.03520i	−0.940059	+	0.199816i
$636$	7.98469	−	7.71073i	0.316614	−	0.305750i
$637$	4.30717	−	24.4272i	0.170656	−	0.967841i
$638$	12.4183	−	9.08261i	0.491646	−	0.359584i
$639$	32.8956	+	18.9923i	1.30133	+	0.751323i
$640$	0.696919	+	2.79519i	0.0275481	+	0.110490i
$641$	−2.48788	−	1.94374i	−0.0982652	−	0.0767732i	0.565331	−	0.824864i	$-0.308748\pi$
$641$	−2.48788	−	1.94374i	−0.0982652	−	0.0767732i	−0.663596	+	0.748091i	$0.730971\pi$
$642$	12.4108	−	9.69640i	0.489816	−	0.382687i
$643$	−3.95301	+	15.8547i	−0.155892	+	0.625247i	0.840608	+	0.541645i	$0.182198\pi$
$643$	−3.95301	+	15.8547i	−0.155892	+	0.625247i	−0.996499	+	0.0836025i	$0.973357\pi$
$644$	−19.0319	+	19.7081i	−0.749960	+	0.776606i
$645$	−4.23909	−	13.0466i	−0.166914	−	0.513709i
$646$	14.5305	−	0.00479963i	0.571693	−	0.000188839i
$647$	−32.1960	−	23.3917i	−1.26575	−	0.919624i	−0.266729	−	0.963772i	$-0.585943\pi$
$647$	−32.1960	−	23.3917i	−1.26575	−	0.919624i	−0.999025	+	0.0441478i	$0.985943\pi$
$648$	−1.06313	−	6.02932i	−0.0417638	−	0.236854i
$649$	1.24853	−	9.09236i	0.0490090	−	0.356906i
$650$	16.5014	−	6.00602i	0.647239	−	0.235576i
$651$	−62.1852	+	41.9445i	−2.43723	+	1.64393i
$652$	−10.6666	+	6.66525i	−0.417737	+	0.261031i
$653$	22.3655	+	4.75394i	0.875231	+	0.186036i	0.623559	−	0.781776i	$-0.285686\pi$
$653$	22.3655	+	4.75394i	0.875231	+	0.186036i	0.251672	+	0.967812i	$0.419019\pi$
$654$	6.40135	−	14.3777i	0.250313	−	0.562212i
$655$	−12.7629	+	6.22487i	−0.498687	+	0.243226i
$656$	4.98622	−	0.700768i	0.194679	−	0.0273604i
$657$	9.36907	+	44.0780i	0.365522	+	1.71965i
$658$	−9.70621	−	21.8005i	−0.378387	−	0.849872i
$659$	−13.0208	−	10.9258i	−0.507219	−	0.425608i	0.352930	−	0.935650i	$-0.385185\pi$
$659$	−13.0208	−	10.9258i	−0.507219	−	0.425608i	−0.860149	+	0.510042i	$0.829630\pi$
$660$	−16.0331	−	18.9853i	−0.624089	−	0.739000i
$661$	−10.6432	−	29.2419i	−0.413972	−	1.13738i	−0.955060	−	0.296412i	$-0.904210\pi$
$661$	−10.6432	−	29.2419i	−0.413972	−	1.13738i	0.541088	−	0.840966i	$-0.318012\pi$
$662$	1.29521	+	18.5224i	0.0503398	+	0.719893i
$663$	−45.7039	−	6.42327i	−1.77499	−	0.249459i
$664$	−7.61868	+	2.47546i	−0.295662	+	0.0960665i
$665$	−41.2199	−	11.8049i	−1.59844	−	0.457773i
$666$	20.7081	+	28.5022i	0.802421	+	1.10444i
$667$	32.8636	−	17.4739i	1.27248	−	0.676592i
$668$	4.70186	+	11.6375i	0.181920	+	0.450269i
$669$	56.3868	+	16.1686i	2.18004	+	0.625116i
$670$	−10.0154	+	27.5172i	−0.386930	+	1.06308i
$671$	−4.82845	−	13.1366i	−0.186400	−	0.507132i
$672$	−4.44044	+	7.69106i	−0.171294	+	0.296689i
$673$	−0.0664632	+	0.632355i	−0.00256197	+	0.0243755i	−0.995728	−	0.0923329i	$-0.970568\pi$
$673$	−0.0664632	+	0.632355i	−0.00256197	+	0.0243755i	0.993166	+	0.116708i	$0.0372343\pi$
$674$	5.06464	+	2.69292i	0.195083	+	0.103727i
$675$	0.912776	+	6.49474i	0.0351328	+	0.249983i
$676$	14.0117	+	6.23842i	0.538913	+	0.239939i
$677$	−1.58964	−	15.1244i	−0.0610947	−	0.581277i	−0.981654	−	0.190673i	$-0.938933\pi$
$677$	−1.58964	−	15.1244i	−0.0610947	−	0.581277i	0.920559	−	0.390604i	$-0.127734\pi$
$678$	−12.2622	+	30.3501i	−0.470928	+	1.16559i
$679$	30.9092	−	39.5620i	1.18619	−	1.51825i
$680$	2.64696	−	9.23105i	0.101506	−	0.353995i
$681$	−6.22203	−	7.41513i	−0.238429	−	0.284148i
$682$	22.1287	+	17.1764i	0.847351	+	0.657717i
$683$		−	38.8403i		−	1.48618i	−0.669190	−	0.743092i	$-0.733359\pi$
$683$		−	38.8403i		−	1.48618i	0.669190	−	0.743092i	$-0.266641\pi$
$684$	7.69867	−	14.4906i	0.294366	−	0.554064i
$685$	−3.01007	+	9.26405i	−0.115009	+	0.353961i
$686$	−3.75195	−	7.05640i	−0.143250	−	0.269415i
$687$	11.1369	+	2.77674i	0.424899	+	0.105939i
$688$	1.51790	+	1.02383i	0.0578692	+	0.0390333i
$689$	22.7053	+	0.792885i	0.865001	+	0.0302065i
$690$	−31.8568	−	50.9816i	−1.21277	−	1.94083i
$691$	−11.7458	+	5.22955i	−0.446830	+	0.198941i	−0.617801	−	0.786335i	$-0.711976\pi$
$691$	−11.7458	+	5.22955i	−0.446830	+	0.198941i	0.170971	+	0.985276i	$0.445309\pi$
$692$	−3.54361	−	6.13771i	−0.134708	−	0.233321i
$693$	2.83930	−	42.5374i	0.107856	−	1.61586i
$694$	−15.9836	−	2.81834i	−0.606729	−	0.106983i
$695$	−40.6586	−	4.27339i	−1.54227	−	0.162099i
$696$	8.96603	−	8.07305i	0.339856	−	0.306008i
$697$	−15.5628	−	6.28777i	−0.589482	−	0.238166i
$698$	0.169198	+	0.590065i	0.00640425	+	0.0223343i
$699$	11.8725	−	17.6017i	0.449058	−	0.665756i
$700$	−5.96901	+	9.55242i	−0.225607	+	0.361047i
$701$	4.85664	−	34.5568i	0.183433	−	1.30519i	−0.653099	−	0.757272i	$-0.726532\pi$
$701$	4.85664	−	34.5568i	0.183433	−	1.30519i	0.836532	−	0.547918i	$-0.184580\pi$
$702$	−6.22096	+	8.56242i	−0.234795	+	0.323168i
$703$	1.41023	−	40.7698i	0.0531878	−	1.53766i
$704$	3.24631	+	0.679298i	0.122350	+	0.0256020i
$705$	51.5668	−	9.09262i	1.94212	−	0.342448i
$706$	0.124382	−	0.00869761i	0.00468116	−	0.000327339i
$707$	0.117186	+	3.35578i	0.00440725	+	0.126207i
$708$	0.251172	−	7.19263i	0.00943963	−	0.270316i
$709$	−9.73719	−	0.680891i	−0.365688	−	0.0255714i	−0.114269	−	0.993450i	$-0.536453\pi$
$709$	−9.73719	−	0.680891i	−0.365688	−	0.0255714i	−0.251419	+	0.967878i	$0.580897\pi$
$710$	−28.9087	+	3.03843i	−1.08492	+	0.114030i
$711$	3.46936	−	3.85311i	0.130111	−	0.144503i
$712$	4.47415	−	8.41465i	0.167676	−	0.315352i
$713$	47.0759	+	48.7485i	1.76300	+	1.82564i
$714$	25.6383	−	14.8023i	0.959488	−	0.553961i
$715$	5.15638	−	50.5991i	0.192838	−	1.89230i
$716$	13.1937	−	15.7236i	0.493072	−	0.587620i
$717$	−14.7601	−	21.8828i	−0.551226	−	0.817226i
$718$	−18.3269	+	0.639991i	−0.683955	+	0.0238842i
$719$	−13.5287	−	8.45365i	−0.504534	−	0.315268i	0.253664	−	0.967293i	$-0.418364\pi$
$719$	−13.5287	−	8.45365i	−0.504534	−	0.315268i	−0.758198	+	0.652024i	$0.773920\pi$
$720$	−7.80083	−	7.53317i	−0.290720	−	0.280745i
$721$	−6.78357	+	4.92855i	−0.252633	+	0.183549i
$722$	−17.3523	+	7.73946i	−0.645784	+	0.288033i
$723$	−52.2712	−	16.9839i	−1.94399	−	0.631640i
$724$	12.8243	+	6.25485i	0.476613	+	0.232460i
$725$	11.7224	−	9.83628i	0.435360	−	0.365310i
$726$	−27.7152	+	7.09675i	−1.02861	+	0.263385i
$727$	−45.4602	−	16.5461i	−1.68602	−	0.613663i	−0.691909	−	0.721985i	$-0.743230\pi$
$727$	−45.4602	−	16.5461i	−1.68602	−	0.613663i	−0.994116	+	0.108322i	$0.965452\pi$
$728$	−17.6371	+	4.39742i	−0.653674	+	0.162979i
$729$	25.8017	+	28.6557i	0.955619	+	1.06132i
$730$	−25.6270	−	23.0747i	−0.948499	−	0.854033i
$731$	−2.67554	−	5.48568i	−0.0989585	−	0.202895i
$732$	−4.81128	−	9.86459i	−0.177830	−	0.364606i
$733$	−4.92563	−	4.43505i	−0.181932	−	0.163812i	0.573133	−	0.819463i	$-0.305728\pi$
$733$	−4.92563	−	4.43505i	−0.181932	−	0.163812i	−0.755065	+	0.655650i	$0.772395\pi$
$734$	−6.66631	−	7.40369i	−0.246058	−	0.273275i
$735$	−33.8740	+	8.44573i	−1.24946	+	0.311526i
$736$	7.53973	+	2.74424i	0.277918	+	0.101154i
$737$	23.4962	+	24.1775i	0.865493	+	0.890588i
$738$	−14.5202	+	12.1839i	−0.534496	+	0.448495i
$739$	40.3535	+	19.6817i	1.48443	+	0.724003i	0.989446	−	0.144901i	$-0.0462862\pi$
$739$	40.3535	+	19.6817i	1.48443	+	0.724003i	0.494981	+	0.868904i	$0.335175\pi$
$740$	−25.6410	−	8.33126i	−0.942581	−	0.306263i
$741$	58.0064	−	16.6538i	2.13092	−	0.611792i
$742$	−11.7898	+	8.56578i	−0.432817	+	0.314460i
$743$	8.41207	+	8.12344i	0.308609	+	0.298020i	0.832793	−	0.553585i	$-0.186741\pi$
$743$	8.41207	+	8.12344i	0.308609	+	0.298020i	−0.524184	+	0.851605i	$0.675630\pi$
$744$	18.6292	+	11.6408i	0.682978	+	0.426772i
$745$	67.3612	−	2.35230i	2.46792	−	0.0861817i
$746$	12.4227	+	18.4175i	0.454829	+	0.674312i
$747$	19.3839	−	23.1008i	0.709219	−	0.845214i
$748$	−8.23959	−	7.37189i	−0.301269	−	0.269543i
$749$	−17.9070	+	10.3386i	−0.654309	+	0.377765i
$750$	8.85433	+	9.16893i	0.323314	+	0.334802i
$751$	11.8866	−	22.3554i	0.433746	−	0.815758i	−0.566217	−	0.824256i	$-0.691594\pi$
$751$	11.8866	−	22.3554i	0.433746	−	0.815758i	0.999964	+	0.00849748i	$0.00270486\pi$
$752$	−4.67635	+	5.19361i	−0.170529	+	0.189392i
$753$	20.0283	−	2.10506i	0.729873	−	0.0767127i
$754$	24.6340	+	1.72257i	0.897116	+	0.0627325i
$755$	0.808669	−	23.1573i	0.0294305	−	0.842779i
$756$	−0.236927	−	6.78471i	−0.00861696	−	0.246758i
$757$	−41.1800	+	2.87958i	−1.49671	+	0.104660i	−0.794481	−	0.607289i	$-0.792257\pi$
$757$	−41.1800	+	2.87958i	−1.49671	+	0.104660i	−0.702231	+	0.711949i	$0.747812\pi$
$758$	13.6179	−	2.40120i	0.494624	−	0.0872156i
$759$	−68.8097	+	7.45237i	−2.49763	+	0.270504i
$760$	1.75170	+	12.4342i	0.0635407	+	0.451034i
$761$	6.39780	−	8.80582i	0.231920	−	0.319211i	−0.677157	−	0.735839i	$-0.736788\pi$
$761$	6.39780	−	8.80582i	0.231920	−	0.319211i	0.909077	+	0.416628i	$0.136788\pi$
$762$	−3.04300	+	21.6520i	−0.110236	+	0.784371i
$763$	−10.9495	+	17.5228i	−0.396397	+	0.634368i
$764$	−2.17490	+	3.22443i	−0.0786853	+	0.116656i
$765$	9.96431	+	34.7497i	0.360260	+	1.25638i
$766$	−9.20945	−	3.72086i	−0.332751	−	0.134440i
$767$	10.9469	−	9.85667i	0.395271	−	0.355904i
$768$	2.58660	+	0.271863i	0.0933361	+	0.00981002i
$769$	−9.50366	−	1.67575i	−0.342711	−	0.0604291i	−0.000355992	−	1.00000i	$-0.500113\pi$
$769$	−9.50366	−	1.67575i	−0.342711	−	0.0604291i	−0.342355	+	0.939571i	$0.611224\pi$
$770$	17.3758	+	27.6123i	0.626180	+	0.995077i
$771$	0.415485	+	0.719641i	0.0149633	+	0.0259172i
$772$	−7.99728	+	3.56062i	−0.287829	+	0.128150i
$773$	−1.57384	−	2.51868i	−0.0566072	−	0.0905905i	0.818534	−	0.574458i	$-0.194787\pi$
$773$	−1.57384	−	2.51868i	−0.0566072	−	0.0905905i	−0.875141	+	0.483868i	$0.839232\pi$
$774$	−6.88815	−	0.240540i	−0.247589	−	0.00864602i
$775$	23.0985	+	15.5801i	0.829723	+	0.559655i
$776$	−14.2663	−	3.55698i	−0.512129	−	0.127688i
$777$	−39.0199	−	73.3858i	−1.39983	−	2.63270i
$778$	3.41911	−	10.5229i	0.122581	−	0.377265i
$779$	21.9344	−	0.773221i	0.785882	−	0.0277035i
$780$		−	39.8846i		−	1.42810i
$781$	−11.3465	+	31.4838i	−0.406009	+	1.12658i
$782$	−17.1925	−	20.4893i	−0.614804	−	0.732694i
$783$	−2.54217	+	8.86561i	−0.0908498	+	0.316831i
$784$	2.86868	−	3.67174i	0.102453	−	0.131133i
$785$	−8.53380	+	21.1219i	−0.304584	+	0.753873i
$786$	1.34008	+	12.7500i	0.0477992	+	0.454779i
$787$	5.28032	+	2.35095i	0.188223	+	0.0838024i	0.498684	−	0.866784i	$-0.333817\pi$
$787$	5.28032	+	2.35095i	0.188223	+	0.0838024i	−0.310461	+	0.950586i	$0.600483\pi$
$788$	1.26340	+	8.98954i	0.0450067	+	0.320239i
$789$	−57.2565	−	30.4438i	−2.03838	−	1.08383i
$790$	−0.414744	+	3.94603i	−0.0147559	+	0.140393i
$791$	21.4876	−	37.2176i	0.764012	−	1.32331i
$792$	−11.7187	+	4.30729i	−0.416406	+	0.153053i
$793$	7.68311	−	21.1092i	0.272835	−	0.749609i
$794$	18.0416	+	5.17334i	0.640271	+	0.183595i
$795$	−11.9786	−	29.6481i	−0.424838	−	1.05151i
$796$	−5.54985	+	2.95091i	−0.196709	+	0.104592i
$797$	14.3683	+	19.7763i	0.508952	+	0.700513i	0.983742	−	0.179586i	$-0.0574760\pi$
$797$	14.3683	+	19.7763i	0.508952	+	0.700513i	−0.474790	+	0.880099i	$0.657476\pi$
$798$	−22.7433	+	31.3252i	−0.805105	+	1.10890i
$799$	22.1567	−	7.19915i	0.783848	−	0.254688i
$800$	3.26667	+	0.459101i	0.115494	+	0.0162317i
$801$	2.50256	+	35.7883i	0.0884238	+	1.26452i
$802$	−5.13313	−	14.1032i	−0.181257	−	0.498000i
$803$	−36.7640	+	14.9891i	−1.29737	+	0.528953i
$804$	20.2526	+	16.9940i	0.714255	+	0.599331i
$805$	32.1019	+	72.1020i	1.13144	+	2.54126i
$806$	9.34800	+	43.9789i	0.329269	+	1.54909i
$807$	−34.8957	+	4.90427i	−1.22839	+	0.172638i
$808$	0.883850	−	0.431082i	0.0310937	−	0.0151654i
$809$	−14.2976	+	32.1129i	−0.502676	+	1.12903i	0.466916	+	0.884302i	$0.345365\pi$
$809$	−14.2976	+	32.1129i	−0.502676	+	1.12903i	−0.969592	+	0.244727i	$0.921302\pi$
$810$	−17.2516	−	3.66693i	−0.606158	−	0.128843i
$811$	3.73393	−	2.33322i	0.131116	−	0.0819303i	−0.462776	−	0.886475i	$-0.653146\pi$
$811$	3.73393	−	2.33322i	0.131116	−	0.0819303i	0.593891	+	0.804545i	$0.297591\pi$
$812$	−13.1318	+	8.85753i	−0.460837	+	0.310838i
$813$	76.3205	−	27.7784i	2.67668	−	0.974230i
$814$	−21.4912	+	22.3962i	−0.753268	+	0.784986i
$815$	6.29193	+	35.6833i	0.220397	+	1.24993i
$816$	−7.01416	−	5.09609i	−0.245545	−	0.178399i
$817$	6.11531	+	5.12792i	0.213948	+	0.179403i
$818$	1.95917	+	6.02969i	0.0685006	+	0.210823i
$819$	47.5328	−	49.2217i	1.66093	−	1.71994i
$820$	3.50914	−	14.0744i	0.122545	−	0.491500i
$821$	29.3542	−	22.9340i	1.02447	−	0.800403i	0.0443908	−	0.999014i	$-0.485865\pi$
$821$	29.3542	−	22.9340i	1.02447	−	0.800403i	0.980078	+	0.198611i	$0.0636431\pi$
$822$	6.93003	+	5.41434i	0.241713	+	0.188847i
$823$	3.84161	+	15.4078i	0.133910	+	0.537084i	0.999349	+	0.0360698i	$0.0114839\pi$
$823$	3.84161	+	15.4078i	0.133910	+	0.537084i	−0.865439	+	0.501014i	$0.832961\pi$
$824$	2.12663	+	1.22781i	0.0740846	+	0.0427728i
$825$	−27.0347	+	8.87878i	−0.941229	+	0.309119i
$826$	−1.64077	+	9.30525i	−0.0570896	+	0.323771i
$827$	7.23686	−	6.98855i	0.251650	−	0.243016i	−0.558124	−	0.829758i	$-0.688479\pi$
$827$	7.23686	−	6.98855i	0.251650	−	0.243016i	0.809774	+	0.586742i	$0.199590\pi$
$828$	−29.5443	+	6.27984i	−1.02674	+	0.218239i
$829$	−1.79728	+	8.45554i	−0.0624221	+	0.293673i	−0.998275	−	0.0587191i	$-0.981298\pi$
$829$	−1.79728	+	8.45554i	−0.0624221	+	0.293673i	0.935852	+	0.352392i	$0.114632\pi$
$830$	−1.60977	+	23.0208i	−0.0558761	+	0.799065i
$831$	−10.3297	+	2.96198i	−0.358332	+	0.102750i
$832$	3.27736	+	4.19483i	0.113622	+	0.145430i
$833$	−14.4015	+	5.81858i	−0.498983	+	0.201602i
$834$	−16.1804	+	33.1747i	−0.560280	+	1.14874i
$835$	36.1577			1.25129
$836$	13.7648	+	4.41934i	0.476065	+	0.152846i
$837$	−16.7924			−0.580431
$838$	10.2477	−	21.0109i	0.354001	−	0.725809i
$839$	−15.6969	+	6.34197i	−0.541918	+	0.218949i	−0.629212	−	0.777233i	$-0.716622\pi$
$839$	−15.6969	+	6.34197i	−0.541918	+	0.218949i	0.0872942	+	0.996183i	$0.472178\pi$
$840$	15.7509	+	20.1602i	0.543457	+	0.695593i
$841$	−7.19122	+	2.06205i	−0.247973	+	0.0711052i
$842$	−1.78450	+	25.5195i	−0.0614978	+	0.879459i
$843$	−2.67344	+	12.5775i	−0.0920780	+	0.433193i
$844$	−25.0656	+	5.32785i	−0.862792	+	0.183392i
$845$	31.7836	−	30.6930i	1.09339	−	1.05587i
$846$	4.56842	−	25.9088i	0.157066	−	0.890763i
$847$	37.3293	−	4.16244i	1.28265	−	0.143023i
$848$	3.69606	+	2.13392i	0.126923	+	0.0732792i
$849$	4.67547	+	18.7523i	0.160462	+	0.643577i
$850$	−8.66537	−	6.77013i	−0.297220	−	0.232214i
$851$	−59.1729	+	46.2310i	−2.02842	+	1.58478i
$852$	−6.34890	+	25.4640i	−0.217510	+	0.872383i
$853$	18.9606	−	19.6343i	0.649199	−	0.672266i	−0.311375	−	0.950287i	$-0.600790\pi$
$853$	18.9606	−	19.6343i	0.649199	−	0.672266i	0.960575	+	0.278021i	$0.0896786\pi$
$854$	4.45272	+	13.7041i	0.152369	+	0.468943i
$855$	−30.3964	−	36.2007i	−1.03953	−	1.23804i
$856$	4.89904	+	3.55936i	0.167446	+	0.121656i
$857$	−6.01468	−	34.1109i	−0.205457	−	1.16521i	−0.896718	−	0.442602i	$-0.854056\pi$
$857$	−6.01468	−	34.1109i	−0.205457	−	1.16521i	0.691261	−	0.722605i	$-0.257056\pi$
$858$	−41.3354	−	19.9990i	−1.41117	−	0.682754i
$859$	−30.0900	+	10.9519i	−1.02666	+	0.373673i	−0.799807	−	0.600257i	$-0.795065\pi$
$859$	−30.0900	+	10.9519i	−1.02666	+	0.373673i	−0.226851	+	0.973930i	$0.572843\pi$
$860$	4.37269	−	2.94942i	0.149108	−	0.100574i
$861$	37.9223	−	23.6965i	1.29239	−	0.807575i
$862$	−34.7301	−	7.38210i	−1.18291	−	0.251435i
$863$	17.7913	−	39.9599i	0.605622	−	1.36025i	−0.307103	−	0.951676i	$-0.599360\pi$
$863$	17.7913	−	39.9599i	0.605622	−	1.36025i	0.912725	−	0.408573i	$-0.133974\pi$
$864$	−1.78697	+	0.871561i	−0.0607938	+	0.0296511i
$865$	−20.2179	+	2.84144i	−0.687428	+	0.0966117i
$866$	2.23973	+	10.5371i	0.0761092	+	0.358066i
$867$	−6.22835	−	13.9891i	−0.211526	−	0.475095i
$868$	−22.0928	−	18.5381i	−0.749879	−	0.629223i
$869$	3.88160	+	2.40845i	0.131674	+	0.0817011i
$870$	−11.8874	−	32.6602i	−0.403019	−	1.10729i
$871$	3.77467	+	53.9802i	0.127900	+	1.82905i
$872$	5.99233	+	0.842167i	0.202926	+	0.0285194i
$873$	52.6396	−	17.1036i	1.78158	−	0.578870i
$874$	31.4396	+	15.3213i	1.06346	+	0.518249i
$875$	−9.83620	−	13.5384i	−0.332524	−	0.457680i
$876$	−27.4896	+	14.6165i	−0.928788	+	0.493845i
$877$	4.05866	+	10.0455i	0.137051	+	0.339214i	0.980065	−	0.198679i	$-0.0636651\pi$
$877$	4.05866	+	10.0455i	0.137051	+	0.339214i	−0.843013	+	0.537892i	$0.819221\pi$
$878$	7.28911	+	2.09012i	0.245996	+	0.0705381i
$879$	−3.75284	+	10.3108i	−0.126580	+	0.347776i
$880$	5.31767	−	7.93782i	0.179258	−	0.267584i
$881$	−2.88865	+	5.00329i	−0.0973211	+	0.168565i	−0.910575	−	0.413344i	$-0.864361\pi$
$881$	−2.88865	+	5.00329i	−0.0973211	+	0.168565i	0.813254	+	0.581909i	$0.197694\pi$
$882$	−1.83347	+	17.4443i	−0.0617361	+	0.587380i
$883$	12.3076	+	6.54408i	0.414184	+	0.220226i	0.663468	−	0.748205i	$-0.269084\pi$
$883$	12.3076	+	6.54408i	0.414184	+	0.220226i	−0.249283	+	0.968431i	$0.580195\pi$
$884$	−2.46968	−	17.5727i	−0.0830643	−	0.591033i
$885$	−18.9404	−	8.43282i	−0.636675	−	0.283466i
$886$	−0.0946533	−	0.900566i	−0.00317994	−	0.0302551i
$887$	19.9821	−	49.4573i	0.670932	−	1.66061i	−0.0771596	−	0.997019i	$-0.524585\pi$
$887$	19.9821	−	49.4573i	0.670932	−	1.66061i	0.748091	−	0.663596i	$-0.230970\pi$
$888$	−14.9858	+	19.1809i	−0.502889	+	0.643669i
$889$	7.91241	−	27.5938i	0.265374	−	0.925468i
$890$	−17.6472	−	21.0311i	−0.591535	−	0.704964i
$891$	−12.4506	+	16.0404i	−0.417112	+	0.537374i
$892$			22.5538i			0.755157i
$893$	−22.6317	+	20.3912i	−0.757341	+	0.682366i
$894$	18.8047	−	57.8748i	0.628922	−	1.93562i
$895$	−27.7597	−	52.2085i	−0.927906	−	1.74514i
$896$	−3.31317	−	0.826067i	−0.110685	−	0.0275970i
$897$	−92.0964	−	62.1198i	−3.07501	−	2.07412i
$898$	14.7149	+	0.513857i	0.491044	+	0.0171476i
$899$	20.7624	+	33.2268i	0.692465	+	1.10818i
$900$	−11.3444	+	5.05087i	−0.378148	+	0.168362i
$901$	−7.11346	−	12.3209i	−0.236984	−	0.410468i
$902$	−12.8268	−	10.6940i	−0.427086	−	0.356071i
$903$	16.0131	+	2.82354i	0.532882	+	0.0939614i
$904$	−12.5168	−	1.31557i	−0.416302	−	0.0437551i
$905$	30.5461	−	27.5038i	1.01539	−	0.914257i
$906$	−19.3966	−	7.83675i	−0.644410	−	0.260359i
$907$	−1.14766	−	4.00238i	−0.0381076	−	0.132897i	0.939909	−	0.341426i	$-0.110910\pi$
$907$	−1.14766	−	4.00238i	−0.0381076	−	0.132897i	−0.978016	+	0.208530i	$0.933132\pi$
$908$	2.08118	−	3.08548i	0.0690665	−	0.102395i
$909$	−1.96168	+	3.13934i	−0.0650648	+	0.104125i
$910$	−7.28761	+	51.8540i	−0.241582	+	1.71894i
$911$	−3.02854	+	4.16842i	−0.100340	+	0.138106i	−0.856235	−	0.516587i	$-0.827202\pi$
$911$	−3.02854	+	4.16842i	−0.100340	+	0.138106i	0.755895	+	0.654693i	$0.227202\pi$
$912$	11.0899	+	2.35340i	0.367223	+	0.0779289i
$913$	23.0511	+	13.2115i	0.762879	+	0.437236i
$914$	−23.8647	+	4.20799i	−0.789375	+	0.139188i
$915$	−31.5404	+	2.20552i	−1.04269	+	0.0729121i
$916$	0.154015	+	4.41042i	0.00508881	+	0.145724i
$917$	0.587409	−	16.8212i	0.0193980	−	0.555485i
$918$	6.61149	+	0.462320i	0.218212	+	0.0152588i
$919$	53.4817	−	5.62116i	1.76420	−	0.185425i	0.833824	−	0.552031i	$-0.186147\pi$
$919$	53.4817	−	5.62116i	1.76420	−	0.185425i	0.930376	+	0.366606i	$0.119480\pi$
$920$	15.4663	−	17.1771i	0.509910	−	0.566313i
$921$	11.1815	−	21.0293i	0.368441	−	0.692937i
$922$	−3.65104	−	3.78076i	−0.120241	−	0.124513i
$923$	−46.5180	+	26.8572i	−1.53116	+	0.884014i
$924$	28.7914	−	6.21506i	0.947166	−	0.204461i
$925$	−19.8446	+	23.6498i	−0.652485	+	0.777601i
$926$	2.93069	+	4.34492i	0.0963084	+	0.142783i
$927$	−9.23838	+	0.322611i	−0.303428	+	0.0105960i
$928$	3.93397	+	2.45822i	0.129139	+	0.0806950i
$929$	18.3707	+	17.7404i	0.602724	+	0.582044i	0.932121	−	0.362148i	$-0.117957\pi$
$929$	18.3707	+	17.7404i	0.602724	+	0.582044i	−0.329397	+	0.944192i	$0.606845\pi$
$930$	51.1962	−	37.1962i	1.67879	−	1.21971i
$931$	14.1039	−	14.6147i	0.462236	−	0.478976i
$932$	7.76373	+	2.52259i	0.254309	+	0.0826301i
$933$	24.6988	+	12.0464i	0.808603	+	0.394382i
$934$	6.34467	−	5.32381i	0.207604	−	0.174200i
$935$	−28.5820	+	14.0525i	−0.934732	+	0.459566i
$936$	−18.8308	−	6.85384i	−0.615503	−	0.224025i
$937$	40.2336	−	10.0314i	1.31438	−	0.327711i	0.479206	−	0.877703i	$-0.340925\pi$
$937$	40.2336	−	10.0314i	1.31438	−	0.327711i	0.835170	+	0.549992i	$0.185369\pi$
$938$	−23.2254	−	25.7944i	−0.758335	−	0.842216i
$939$	57.4775	+	51.7530i	1.87571	+	1.68889i
$940$	8.82562	+	18.0952i	0.287860	+	0.590200i
$941$	−12.6421	−	25.9201i	−0.412119	−	0.844970i	−0.999367	−	0.0355628i	$-0.988678\pi$
$941$	−12.6421	−	25.9201i	−0.412119	−	0.844970i	0.587248	−	0.809407i	$-0.300211\pi$
$942$	15.2844	+	13.7622i	0.497994	+	0.448395i
$943$	−27.0333	−	30.0236i	−0.880327	−	0.977702i
$944$	2.68498	−	0.669440i	0.0873886	−	0.0217884i
$945$	−18.3776	−	6.68890i	−0.597823	−	0.217590i
$946$	−0.864142	−	6.01065i	−0.0280957	−	0.195423i
$947$	34.6304	−	29.0583i	1.12534	−	0.944269i	0.126474	−	0.991970i	$-0.459634\pi$
$947$	34.6304	−	29.0583i	1.12534	−	0.944269i	0.998862	+	0.0477007i	$0.0151894\pi$
$948$	3.21969	+	1.57035i	0.104571	+	0.0510026i
$949$	−60.6048	−	19.6917i	−1.96731	−	0.639219i
$950$	13.9531	+	3.47399i	0.452697	+	0.112711i
$951$	−24.5353	+	17.8259i	−0.795611	+	0.578045i
$952$	8.18798	+	7.90704i	0.265374	+	0.256269i
$953$	1.95003	+	1.21851i	0.0631676	+	0.0394715i	0.561135	−	0.827724i	$-0.310365\pi$
$953$	1.95003	+	1.21851i	0.0631676	+	0.0394715i	−0.497968	+	0.867196i	$0.665920\pi$
$954$	−16.0562	+	0.560696i	−0.519840	+	0.0181532i
$955$	6.26538	+	9.28880i	0.202743	+	0.300579i
$956$	6.52348	−	7.77438i	0.210984	−	0.251442i
$957$	−39.8088	−	4.05678i	−1.28684	−	0.131137i
$958$	21.5338	−	12.4325i	0.695725	−	0.401677i
$959$	−8.02045	−	8.30542i	−0.258994	−	0.268196i
$960$	3.51748	−	6.61542i	0.113526	−	0.213512i
$961$	−26.9907	+	29.9762i	−0.870666	+	0.966973i
$962$	−49.5471	+	5.20761i	−1.59746	+	0.167900i
$963$	−22.7402	−	1.59015i	−0.732791	−	0.0512418i
$964$	0.737496	−	21.1191i	0.0237531	−	0.680201i
$965$	0.880113	+	25.2031i	0.0283318	+	0.811318i
$966$	71.0831	−	4.97061i	2.28706	−	0.159927i
$967$	−33.3317	+	5.87728i	−1.07188	+	0.189000i	−0.681620	−	0.731706i	$-0.738724\pi$
$967$	−33.3317	+	5.87728i	−1.07188	+	0.189000i	−0.390255	+	0.920707i	$0.627613\pi$
$968$	−5.56017	−	9.49129i	−0.178711	−	0.305062i
$969$	−28.0930	−	25.2782i	−0.902476	−	0.812053i
$970$	−24.8961	+	34.2666i	−0.799367	+	1.10023i
$971$	−5.98699	+	42.5997i	−0.192132	+	1.36709i	0.620452	+	0.784244i	$0.286949\pi$
$971$	−5.98699	+	42.5997i	−0.192132	+	1.36709i	−0.812584	+	0.582844i	$0.801940\pi$
$972$	−11.5988	+	18.5619i	−0.372031	+	0.595375i
$973$	27.0977	−	40.1740i	0.868712	−	1.28792i
$974$	−2.70306	−	9.42669i	−0.0866117	−	0.302051i
$975$	−42.3464	−	17.1091i	−1.35617	−	0.547929i
$976$	3.13600	−	2.82367i	0.100381	−	0.0903835i
$977$	−28.0449	−	2.94764i	−0.897237	−	0.0943034i	−0.355329	−	0.934741i	$-0.615631\pi$
$977$	−28.0449	−	2.94764i	−0.897237	−	0.0943034i	−0.541908	+	0.840438i	$0.682298\pi$
$978$	32.2162	+	5.68058i	1.03016	+	0.181645i
$979$	−30.6448	+	7.74366i	−0.979412	+	0.247489i
$980$	−6.71145	−	11.6246i	−0.214389	−	0.371333i
$981$	−20.8100	+	9.26522i	−0.664413	+	0.295816i
$982$	4.49640	+	7.19574i	0.143486	+	0.229625i
$983$	−54.1117	−	1.88962i	−1.72589	−	0.0602696i	−0.845344	−	0.534222i	$-0.820605\pi$
$983$	−54.1117	−	1.88962i	−1.72589	−	0.0602696i	−0.880551	+	0.473952i	$0.842827\pi$
$984$	−10.8570	−	7.32312i	−0.346108	−	0.233453i
$985$	25.3744	+	6.32655i	0.808496	+	0.201581i
$986$	−7.25976	−	13.6536i	−0.231198	−	0.434820i
$987$	−19.1794	+	59.0280i	−0.610486	+	1.87888i
$988$	12.3026	+	19.6739i	0.391399	+	0.625910i
$989$		−	14.6905i		−	0.467132i
$990$	−1.14150	+	35.9488i	−0.0362792	+	1.14253i
$991$	−15.0705	−	17.9603i	−0.478729	−	0.570528i	0.471584	−	0.881821i	$-0.343682\pi$
$991$	−15.0705	−	17.9603i	−0.478729	−	0.570528i	−0.950314	+	0.311293i	$0.899238\pi$
$992$	−2.32807	+	8.11893i	−0.0739162	+	0.257776i
$993$	29.7313	−	38.0543i	0.943494	−	1.20762i
$994$	12.9069	−	31.9458i	0.409383	−	1.01326i
$995$	1.89273	+	18.0081i	0.0600034	+	0.570895i
$996$	19.0335	+	8.47427i	0.603101	+	0.268518i
$997$	0.589623	+	4.19539i	0.0186736	+	0.132869i	0.997374	−	0.0724249i	$-0.0230738\pi$
$997$	0.589623	+	4.19539i	0.0186736	+	0.132869i	−0.978700	+	0.205294i	$0.934185\pi$
$998$	5.76096	+	3.06316i	0.182360	+	0.0969625i
$999$	1.94497	−	18.5051i	0.0615360	−	0.585476i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.v.b.29.2	yes	240
11.8	odd	10		418.2.v.a.371.9	yes	240
19.2	odd	18		418.2.v.a.249.9	✓	240
209.173	even	90	inner	418.2.v.b.173.2	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.v.a.249.9	✓	240	19.2	odd	18
418.2.v.a.371.9	yes	240	11.8	odd	10
418.2.v.b.29.2	yes	240	1.1	even	1	trivial
418.2.v.b.173.2	yes	240	209.173	even	90	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.v (of order \(90\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.438371 - 0.898794i) q^{2} +(-2.41147 + 0.974297i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(-2.76916 + 0.794045i) q^{5} +(-0.181426 + 2.59452i) q^{6} +(0.709936 - 3.33998i) q^{7} +(-0.978148 + 0.207912i) q^{8} +(2.70791 - 2.61500i) q^{9} +O(q^{10})\)	\(q+(0.438371 - 0.898794i) q^{2} +(-2.41147 + 0.974297i) q^{3} +(-0.615661 - 0.788011i) q^{4} +(-2.76916 + 0.794045i) q^{5} +(-0.181426 + 2.59452i) q^{6} +(0.709936 - 3.33998i) q^{7} +(-0.978148 + 0.207912i) q^{8} +(2.70791 - 2.61500i) q^{9} +(-0.500239 + 2.83699i) q^{10} +(2.68936 + 1.94096i) q^{11} +(2.25240 + 1.30043i) q^{12} +(1.28783 + 5.16520i) q^{13} +(-2.69074 - 2.10224i) q^{14} +(5.90412 - 4.61280i) q^{15} +(-0.241922 + 0.970296i) q^{16} +(2.31565 - 2.39793i) q^{17} +(-1.16327 - 3.58019i) q^{18} +(-1.48948 + 4.09652i) q^{19} +(2.33058 + 1.69327i) q^{20} +(1.54215 + 8.74595i) q^{21} +(2.92347 - 1.56632i) q^{22} +(7.53973 - 2.74424i) q^{23} +(2.15620 - 1.45438i) q^{24} +(2.79752 - 1.74808i) q^{25} +(5.20699 + 1.10678i) q^{26} +(-0.808666 + 1.81629i) q^{27} +(-3.06902 + 1.49686i) q^{28} +(4.59371 - 0.645604i) q^{29} +(-1.55776 - 7.32870i) q^{30} +(3.43535 + 7.71591i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-8.37638 - 2.06034i) q^{33} +(-1.14013 - 3.13248i) q^{34} +(0.686170 + 9.81268i) q^{35} +(-3.72780 - 0.523908i) q^{36} +(-8.90077 + 2.89204i) q^{37} +(3.02898 + 3.13453i) q^{38} +(-8.13799 - 11.2010i) q^{39} +(2.54356 - 1.35243i) q^{40} +(-1.88623 - 4.66858i) q^{41} +(8.53684 + 2.44790i) q^{42} +(0.626209 - 1.72049i) q^{43} +(-0.126235 - 3.31422i) q^{44} +(-5.42222 + 9.39155i) q^{45} +(0.838696 - 7.97966i) q^{46} +(6.17065 + 3.28099i) q^{47} +(-0.361969 - 2.57554i) q^{48} +(-4.25667 - 1.89519i) q^{49} +(-0.344816 - 3.28070i) q^{50} +(-3.24783 + 8.03867i) q^{51} +(3.27736 - 4.19483i) q^{52} +(1.17638 - 4.10251i) q^{53} +(1.27798 + 1.52304i) q^{54} +(-8.98849 - 3.23938i) q^{55} +3.41460i q^{56} +(-0.399393 - 11.3298i) q^{57} +(1.43349 - 4.41181i) q^{58} +(-1.29911 - 2.44327i) q^{59} +(-7.26987 - 1.81258i) q^{60} +(-3.49846 - 2.35974i) q^{61} +(8.44097 + 0.294765i) q^{62} +(-6.81161 - 10.9008i) q^{63} +(0.913545 - 0.406737i) q^{64} +(-7.66760 - 13.2807i) q^{65} +(-5.52379 + 6.62545i) q^{66} +(10.0107 + 1.76515i) q^{67} +(-3.31525 - 0.348447i) q^{68} +(-15.5081 + 13.9636i) q^{69} +(9.12038 + 3.68487i) q^{70} +(2.78128 + 9.69949i) q^{71} +(-2.10505 + 3.12086i) q^{72} +(-6.34348 + 10.1517i) q^{73} +(-1.30250 + 9.26774i) q^{74} +(-5.04298 + 6.94107i) q^{75} +(4.14511 - 1.34834i) q^{76} +(8.39206 - 7.60446i) q^{77} +(-13.6348 + 2.40419i) q^{78} +(1.37398 - 0.0960778i) q^{79} +(-0.100537 - 2.87900i) q^{80} +(-0.213666 + 6.11861i) q^{81} +(-5.02296 - 0.351240i) q^{82} +(7.96687 - 0.837352i) q^{83} +(5.94247 - 6.59978i) q^{84} +(-4.50836 + 8.47899i) q^{85} +(-1.27186 - 1.31705i) q^{86} +(-10.4486 + 6.03249i) q^{87} +(-3.03414 - 1.33940i) q^{88} +(-6.12588 + 7.30054i) q^{89} +(6.06413 + 8.99044i) q^{90} +(18.1659 - 0.634369i) q^{91} +(-6.80441 - 4.25187i) q^{92} +(-15.8018 - 15.2596i) q^{93} +(5.65397 - 4.10785i) q^{94} +(0.871790 - 12.5266i) q^{95} +(-2.47356 - 0.803708i) q^{96} +(13.2150 + 6.44538i) q^{97} +(-3.56939 + 2.99507i) q^{98} +(12.3582 - 1.77671i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9}+O(q^{10}) \) 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9	\( 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9} - 3 q^{11} + 6 q^{13} - 18 q^{14} - 69 q^{15} + 9 q^{17} + 60 q^{18} - 45 q^{19} + 12 q^{20} - 48 q^{21} - 12 q^{22} + 3 q^{24} - 18 q^{25} + 84 q^{26} - 9 q^{27} + 6 q^{28} + 12 q^{29} + 9 q^{31} - 69 q^{33} - 24 q^{34} + 36 q^{35} + 3 q^{36} + 24 q^{38} - 30 q^{41} - 6 q^{42} + 12 q^{43} - 48 q^{44} + 48 q^{45} - 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} + 21 q^{50} + 45 q^{51} - 3 q^{52} + 81 q^{53} - 27 q^{54} - 72 q^{55} - 30 q^{57} - 24 q^{58} + 114 q^{59} + 78 q^{60} - 66 q^{61} - 45 q^{62} + 9 q^{63} + 30 q^{64} - 135 q^{66} - 9 q^{67} - 42 q^{68} - 54 q^{69} + 39 q^{70} - 102 q^{71} - 6 q^{72} + 12 q^{74} + 72 q^{77} + 36 q^{79} - 117 q^{81} + 30 q^{82} - 36 q^{83} - 36 q^{84} - 90 q^{85} + 3 q^{86} - 216 q^{87} - 3 q^{88} + 18 q^{89} - 24 q^{90} + 102 q^{91} + 30 q^{92} + 147 q^{93} + 18 q^{94} - 66 q^{95} - 24 q^{97} + 12 q^{98} - 195 q^{99}+O(q^{100}) \) 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9 - 3 * q^11 + 6 * q^13 - 18 * q^14 - 69 * q^15 + 9 * q^17 + 60 * q^18 - 45 * q^19 + 12 * q^20 - 48 * q^21 - 12 * q^22 + 3 * q^24 - 18 * q^25 + 84 * q^26 - 9 * q^27 + 6 * q^28 + 12 * q^29 + 9 * q^31 - 69 * q^33 - 24 * q^34 + 36 * q^35 + 3 * q^36 + 24 * q^38 - 30 * q^41 - 6 * q^42 + 12 * q^43 - 48 * q^44 + 48 * q^45 - 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 + 21 * q^50 + 45 * q^51 - 3 * q^52 + 81 * q^53 - 27 * q^54 - 72 * q^55 - 30 * q^57 - 24 * q^58 + 114 * q^59 + 78 * q^60 - 66 * q^61 - 45 * q^62 + 9 * q^63 + 30 * q^64 - 135 * q^66 - 9 * q^67 - 42 * q^68 - 54 * q^69 + 39 * q^70 - 102 * q^71 - 6 * q^72 + 12 * q^74 + 72 * q^77 + 36 * q^79 - 117 * q^81 + 30 * q^82 - 36 * q^83 - 36 * q^84 - 90 * q^85 + 3 * q^86 - 216 * q^87 - 3 * q^88 + 18 * q^89 - 24 * q^90 + 102 * q^91 + 30 * q^92 + 147 * q^93 + 18 * q^94 - 66 * q^95 - 24 * q^97 + 12 * q^98 - 195 * q^99

Introduction

L-functions

Modular forms

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