LMFDB - Embedded newform 370.2.q.d.97.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(97,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("370.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.q (of order $12$, degree $4$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} - 4x^{10} + 6x^{8} + 44x^{7} + 56x^{6} + 32x^{5} + 92x^{4} - 16x^{3} + 36x^{2} - 24x + 4 $ x^12 - 2x^11 - 4x^10 + 6x^8 + 44x^7 + 56x^6 + 32x^5 + 92x^4 - 16x^3 + 36x^2 - 24x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			97.2
Root			$2.78638 + 0.746609i$ of defining polynomial
Character	$\chi$	$=$	370.97
Dual form			370.2.q.d.103.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.434319 - 1.62090i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.34690 + 1.78490i) q^{5} +(1.18658 + 1.18658i) q^{6} +(-0.632846 + 2.36181i) q^{7} +1.00000 q^{8} +(0.159392 + 0.0920251i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.434319 - 1.62090i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.34690 + 1.78490i) q^{5} +(1.18658 + 1.18658i) q^{6} +(-0.632846 + 2.36181i) q^{7} +1.00000 q^{8} +(0.159392 + 0.0920251i) q^{9} +(-2.21922 + 0.274000i) q^{10} +3.49322i q^{11} +(-1.62090 + 0.434319i) q^{12} +(-1.48236 - 2.56752i) q^{13} +(-1.72897 - 1.72897i) q^{14} +(3.47813 - 1.40797i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.91666 + 1.10658i) q^{17} +(-0.159392 + 0.0920251i) q^{18} +(1.37008 + 0.367111i) q^{19} +(0.872317 - 2.05890i) q^{20} +(3.55340 + 2.05156i) q^{21} +(-3.02521 - 1.74661i) q^{22} +2.35663 q^{23} +(0.434319 - 1.62090i) q^{24} +(-1.37172 + 4.80816i) q^{25} +2.96472 q^{26} +(3.77813 - 3.77813i) q^{27} +(2.36181 - 0.632846i) q^{28} +(2.69380 + 2.69380i) q^{29} +(-0.519721 + 3.71613i) q^{30} +(1.18350 - 1.18350i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(5.66216 + 1.51717i) q^{33} +(-1.91666 + 1.10658i) q^{34} +(-5.06797 + 2.05156i) q^{35} -0.184050i q^{36} +(5.95275 + 1.25090i) q^{37} +(-1.00297 + 1.00297i) q^{38} +(-4.80551 + 1.28763i) q^{39} +(1.34690 + 1.78490i) q^{40} +(2.80211 - 1.61780i) q^{41} +(-3.55340 + 2.05156i) q^{42} -9.95193 q^{43} +(3.02521 - 1.74661i) q^{44} +(0.0504298 + 0.408447i) q^{45} +(-1.17832 + 2.04090i) q^{46} +(-7.46221 - 7.46221i) q^{47} +(1.18658 + 1.18658i) q^{48} +(0.884516 + 0.510676i) q^{49} +(-3.47813 - 3.59203i) q^{50} +(2.62610 - 2.62610i) q^{51} +(-1.48236 + 2.56752i) q^{52} +(-2.23615 - 8.34541i) q^{53} +(1.38289 + 5.16103i) q^{54} +(-6.23504 + 4.70501i) q^{55} +(-0.632846 + 2.36181i) q^{56} +(1.19010 - 2.06132i) q^{57} +(-3.67980 + 0.985999i) q^{58} +(0.795776 + 2.96988i) q^{59} +(-2.95840 - 2.30816i) q^{60} +(-3.62907 - 0.972406i) q^{61} +(0.433190 + 1.61669i) q^{62} +(-0.318216 + 0.318216i) q^{63} +1.00000 q^{64} +(2.58617 - 6.10405i) q^{65} +(-4.14499 + 4.14499i) q^{66} +(-7.62035 - 2.04187i) q^{67} -2.21317i q^{68} +(1.02353 - 3.81986i) q^{69} +(0.757284 - 5.41477i) q^{70} +(2.78149 + 4.81768i) q^{71} +(0.159392 + 0.0920251i) q^{72} +(6.28228 + 6.28228i) q^{73} +(-4.05969 + 4.52978i) q^{74} +(7.19778 + 4.31170i) q^{75} +(-0.367111 - 1.37008i) q^{76} +(-8.25032 - 2.21067i) q^{77} +(1.28763 - 4.80551i) q^{78} +(-14.7958 - 3.96452i) q^{79} +(-2.21922 + 0.274000i) q^{80} +(-4.20699 - 7.28672i) q^{81} +3.23559i q^{82} +(-2.69465 - 10.0566i) q^{83} -4.10312i q^{84} +(0.606408 + 4.91150i) q^{85} +(4.97597 - 8.61863i) q^{86} +(5.53635 - 3.19641i) q^{87} +3.49322i q^{88} +(7.87485 - 2.11006i) q^{89} +(-0.378941 - 0.160550i) q^{90} +(7.00210 - 1.87621i) q^{91} +(-1.17832 - 2.04090i) q^{92} +(-1.40431 - 2.43234i) q^{93} +(10.1936 - 2.73136i) q^{94} +(1.19010 + 2.93991i) q^{95} +(-1.62090 + 0.434319i) q^{96} -10.8299i q^{97} +(-0.884516 + 0.510676i) q^{98} +(-0.321464 + 0.556791i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{4} + 2 q^{5} + 6 q^{6} - 4 q^{7} + 12 q^{8} + 18 q^{9}+O(q^{10}) $ 12 * q - 6 * q^2 - 6 * q^4 + 2 * q^5 + 6 * q^6 - 4 * q^7 + 12 * q^8 + 18 * q^9	$ 12 q - 6 q^{2} - 6 q^{4} + 2 q^{5} + 6 q^{6} - 4 q^{7} + 12 q^{8} + 18 q^{9} - 4 q^{10} - 6 q^{12} + 8 q^{14} - 10 q^{15} - 6 q^{16} - 12 q^{17} - 18 q^{18} - 8 q^{19} + 2 q^{20} + 54 q^{21} - 6 q^{22} - 4 q^{23} - 14 q^{25} + 18 q^{27} - 4 q^{28} + 4 q^{29} - 4 q^{30} - 2 q^{31} - 6 q^{32} + 20 q^{33} + 12 q^{34} + 6 q^{35} + 14 q^{37} + 16 q^{38} - 30 q^{39} + 2 q^{40} + 12 q^{41} - 54 q^{42} + 44 q^{43} + 6 q^{44} - 60 q^{45} + 2 q^{46} - 28 q^{47} + 6 q^{48} + 24 q^{49} + 10 q^{50} - 8 q^{51} + 8 q^{53} - 18 q^{54} - 4 q^{56} - 28 q^{57} - 14 q^{58} + 14 q^{60} + 24 q^{61} - 14 q^{62} + 8 q^{63} + 12 q^{64} - 10 q^{65} + 8 q^{66} + 18 q^{67} - 40 q^{69} - 30 q^{70} + 18 q^{72} - 28 q^{73} + 38 q^{74} - 30 q^{75} - 8 q^{76} + 10 q^{77} + 48 q^{78} - 56 q^{79} - 4 q^{80} + 4 q^{81} + 14 q^{83} - 28 q^{85} - 22 q^{86} + 18 q^{87} - 2 q^{89} + 18 q^{90} + 38 q^{91} + 2 q^{92} - 16 q^{94} - 28 q^{95} - 6 q^{96} - 24 q^{98} + 28 q^{99}+O(q^{100}) $ 12 * q - 6 * q^2 - 6 * q^4 + 2 * q^5 + 6 * q^6 - 4 * q^7 + 12 * q^8 + 18 * q^9 - 4 * q^10 - 6 * q^12 + 8 * q^14 - 10 * q^15 - 6 * q^16 - 12 * q^17 - 18 * q^18 - 8 * q^19 + 2 * q^20 + 54 * q^21 - 6 * q^22 - 4 * q^23 - 14 * q^25 + 18 * q^27 - 4 * q^28 + 4 * q^29 - 4 * q^30 - 2 * q^31 - 6 * q^32 + 20 * q^33 + 12 * q^34 + 6 * q^35 + 14 * q^37 + 16 * q^38 - 30 * q^39 + 2 * q^40 + 12 * q^41 - 54 * q^42 + 44 * q^43 + 6 * q^44 - 60 * q^45 + 2 * q^46 - 28 * q^47 + 6 * q^48 + 24 * q^49 + 10 * q^50 - 8 * q^51 + 8 * q^53 - 18 * q^54 - 4 * q^56 - 28 * q^57 - 14 * q^58 + 14 * q^60 + 24 * q^61 - 14 * q^62 + 8 * q^63 + 12 * q^64 - 10 * q^65 + 8 * q^66 + 18 * q^67 - 40 * q^69 - 30 * q^70 + 18 * q^72 - 28 * q^73 + 38 * q^74 - 30 * q^75 - 8 * q^76 + 10 * q^77 + 48 * q^78 - 56 * q^79 - 4 * q^80 + 4 * q^81 + 14 * q^83 - 28 * q^85 - 22 * q^86 + 18 * q^87 - 2 * q^89 + 18 * q^90 + 38 * q^91 + 2 * q^92 - 16 * q^94 - 28 * q^95 - 6 * q^96 - 24 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.434319	−	1.62090i	0.250754	−	0.935827i	−0.719649	−	0.694338i	$-0.755697\pi$
$3$	0.434319	−	1.62090i	0.250754	−	0.935827i	0.970403	−	0.241489i	$-0.0776359\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.34690	+	1.78490i	0.602352	+	0.798231i
$5$	1.34690	+	1.78490i	0.602352	+	0.798231i
$6$	1.18658	+	1.18658i	0.484420	+	0.484420i
$7$	−0.632846	+	2.36181i	−0.239193	+	0.892681i	0.737021	+	0.675870i	$0.236232\pi$
$7$	−0.632846	+	2.36181i	−0.239193	+	0.892681i	−0.976214	+	0.216811i	$0.930435\pi$
$8$	1.00000			0.353553
$9$	0.159392	+	0.0920251i	0.0531307	+	0.0306750i
$10$	−2.21922	+	0.274000i	−0.701778	+	0.0866465i
$11$			3.49322i			1.05324i	0.850099	+	0.526622i	$0.176542\pi$
$11$			3.49322i			1.05324i	−0.850099	+	0.526622i	$0.823458\pi$
$12$	−1.62090	+	0.434319i	−0.467914	+	0.125377i
$13$	−1.48236	−	2.56752i	−0.411132	−	0.712102i	0.583882	−	0.811839i	$-0.301533\pi$
$13$	−1.48236	−	2.56752i	−0.411132	−	0.712102i	−0.995014	+	0.0997371i	$0.968200\pi$
$14$	−1.72897	−	1.72897i	−0.462086	−	0.462086i
$15$	3.47813	−	1.40797i	0.898048	−	0.363538i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.91666	+	1.10658i	0.464858	+	0.268386i	0.714085	−	0.700059i	$-0.246843\pi$
$17$	1.91666	+	1.10658i	0.464858	+	0.268386i	−0.249227	+	0.968445i	$0.580176\pi$
$18$	−0.159392	+	0.0920251i	−0.0375691	+	0.0216905i
$19$	1.37008	+	0.367111i	0.314317	+	0.0842211i	0.412529	−	0.910944i	$-0.364646\pi$
$19$	1.37008	+	0.367111i	0.314317	+	0.0842211i	−0.0982116	+	0.995166i	$0.531312\pi$
$20$	0.872317	−	2.05890i	0.195056	−	0.460384i
$21$	3.55340	+	2.05156i	0.775416	+	0.447687i
$22$	−3.02521	−	1.74661i	−0.644978	−	0.372378i
$23$	2.35663			0.491391			0.245696	−	0.969347i	$-0.420984\pi$
$23$	2.35663			0.491391			0.245696	+	0.969347i	$0.420984\pi$
$24$	0.434319	−	1.62090i	0.0886550	−	0.330865i
$25$	−1.37172	+	4.80816i	−0.274344	+	0.961631i
$26$	2.96472			0.581428
$27$	3.77813	−	3.77813i	0.727102	−	0.727102i
$28$	2.36181	−	0.632846i	0.446340	−	0.119597i
$29$	2.69380	+	2.69380i	0.500226	+	0.500226i	0.911508	−	0.411282i	$-0.134919\pi$
$29$	2.69380	+	2.69380i	0.500226	+	0.500226i	−0.411282	+	0.911508i	$0.634919\pi$
$30$	−0.519721	+	3.71613i	−0.0948876	+	0.678470i
$31$	1.18350	−	1.18350i	0.212562	−	0.212562i	−0.592793	−	0.805355i	$-0.701975\pi$
$31$	1.18350	−	1.18350i	0.212562	−	0.212562i	0.805355	+	0.592793i	$0.201975\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	5.66216	+	1.51717i	0.985655	+	0.264105i
$34$	−1.91666	+	1.10658i	−0.328704	+	0.189777i
$35$	−5.06797	+	2.05156i	−0.856644	+	0.346777i
$36$		−	0.184050i		−	0.0306750i
$37$	5.95275	+	1.25090i	0.978626	+	0.205647i
$37$	5.95275	+	1.25090i	0.978626	+	0.205647i
$38$	−1.00297	+	1.00297i	−0.162703	+	0.162703i
$39$	−4.80551	+	1.28763i	−0.769497	+	0.206186i
$40$	1.34690	+	1.78490i	0.212964	+	0.282217i
$41$	2.80211	−	1.61780i	0.437615	−	0.252657i	−0.264970	−	0.964257i	$-0.585362\pi$
$41$	2.80211	−	1.61780i	0.437615	−	0.252657i	0.702586	+	0.711599i	$0.252029\pi$
$42$	−3.55340	+	2.05156i	−0.548302	+	0.316562i
$43$	−9.95193			−1.51766			−0.758828	−	0.651291i	$-0.774228\pi$
$43$	−9.95193			−1.51766			−0.758828	+	0.651291i	$0.774228\pi$
$44$	3.02521	−	1.74661i	0.456068	−	0.263311i
$45$	0.0504298	+	0.408447i	0.00751763	+	0.0608877i
$46$	−1.17832	+	2.04090i	−0.173733	+	0.300915i
$47$	−7.46221	−	7.46221i	−1.08847	−	1.08847i	−0.995686	−	0.0927889i	$-0.970422\pi$
$47$	−7.46221	−	7.46221i	−1.08847	−	1.08847i	−0.0927889	−	0.995686i	$-0.529578\pi$
$48$	1.18658	+	1.18658i	0.171268	+	0.171268i
$49$	0.884516	+	0.510676i	0.126359	+	0.0729537i
$50$	−3.47813	−	3.59203i	−0.491881	−	0.507989i
$51$	2.62610	−	2.62610i	0.367728	−	0.367728i
$52$	−1.48236	+	2.56752i	−0.205566	+	0.356051i
$53$	−2.23615	−	8.34541i	−0.307158	−	1.14633i	−0.931071	−	0.364837i	$-0.881125\pi$
$53$	−2.23615	−	8.34541i	−0.307158	−	1.14633i	0.623913	−	0.781494i	$-0.285542\pi$
$54$	1.38289	+	5.16103i	0.188188	+	0.702327i
$55$	−6.23504	+	4.70501i	−0.840732	+	0.634424i
$56$	−0.632846	+	2.36181i	−0.0845675	+	0.315610i
$57$	1.19010	−	2.06132i	0.157633	−	0.273028i
$58$	−3.67980	+	0.985999i	−0.483181	+	0.129468i
$59$	0.795776	+	2.96988i	0.103601	+	0.386645i	0.998183	−	0.0602597i	$-0.0191929\pi$
$59$	0.795776	+	2.96988i	0.103601	+	0.386645i	−0.894581	+	0.446905i	$0.852526\pi$
$60$	−2.95840	−	2.30816i	−0.381928	−	0.297982i
$61$	−3.62907	−	0.972406i	−0.464654	−	0.124504i	0.0188938	−	0.999821i	$-0.493986\pi$
$61$	−3.62907	−	0.972406i	−0.464654	−	0.124504i	−0.483548	+	0.875318i	$0.660652\pi$
$62$	0.433190	+	1.61669i	0.0550152	+	0.205319i
$63$	−0.318216	+	0.318216i	−0.0400915	+	0.0400915i
$64$	1.00000			0.125000
$65$	2.58617	−	6.10405i	0.320775	−	0.757114i
$66$	−4.14499	+	4.14499i	−0.510212	+	0.510212i
$67$	−7.62035	−	2.04187i	−0.930974	−	0.249454i	−0.238704	−	0.971092i	$-0.576723\pi$
$67$	−7.62035	−	2.04187i	−0.930974	−	0.249454i	−0.692270	+	0.721639i	$0.743389\pi$
$68$		−	2.21317i		−	0.268386i
$69$	1.02353	−	3.81986i	0.123218	−	0.459857i
$70$	0.757284	−	5.41477i	0.0905128	−	0.647189i
$71$	2.78149	+	4.81768i	0.330102	+	0.571754i	0.982532	−	0.186096i	$-0.0595834\pi$
$71$	2.78149	+	4.81768i	0.330102	+	0.571754i	−0.652429	+	0.757850i	$0.726250\pi$
$72$	0.159392	+	0.0920251i	0.0187845	+	0.0108453i
$73$	6.28228	+	6.28228i	0.735285	+	0.735285i	0.971662	−	0.236376i	$-0.0759598\pi$
$73$	6.28228	+	6.28228i	0.735285	+	0.735285i	−0.236376	+	0.971662i	$0.575960\pi$
$74$	−4.05969	+	4.52978i	−0.471929	+	0.526577i
$75$	7.19778	+	4.31170i	0.831128	+	0.497872i
$76$	−0.367111	−	1.37008i	−0.0421105	−	0.157159i
$77$	−8.25032	−	2.21067i	−0.940211	−	0.251929i
$78$	1.28763	−	4.80551i	0.145796	−	0.544117i
$79$	−14.7958	−	3.96452i	−1.66466	−	0.446043i	−0.700994	−	0.713167i	$-0.747260\pi$
$79$	−14.7958	−	3.96452i	−1.66466	−	0.446043i	−0.963662	+	0.267123i	$0.913927\pi$
$80$	−2.21922	+	0.274000i	−0.248116	+	0.0306342i
$81$	−4.20699	−	7.28672i	−0.467443	−	0.809635i
$82$			3.23559i			0.357312i
$83$	−2.69465	−	10.0566i	−0.295777	−	1.10385i	−0.940599	−	0.339521i	$-0.889735\pi$
$83$	−2.69465	−	10.0566i	−0.295777	−	1.10385i	0.644822	−	0.764333i	$-0.276932\pi$
$84$		−	4.10312i		−	0.447687i
$85$	0.606408	+	4.91150i	0.0657742	+	0.532726i
$86$	4.97597	−	8.61863i	0.536572	−	0.929371i
$87$	5.53635	−	3.19641i	0.593559	−	0.342691i
$88$			3.49322i			0.372378i
$89$	7.87485	−	2.11006i	0.834732	−	0.223666i	0.183955	−	0.982935i	$-0.441110\pi$
$89$	7.87485	−	2.11006i	0.834732	−	0.223666i	0.650777	+	0.759269i	$0.274443\pi$
$90$	−0.378941	−	0.160550i	−0.0399438	−	0.0169235i
$91$	7.00210	−	1.87621i	0.734019	−	0.196680i
$92$	−1.17832	−	2.04090i	−0.122848	−	0.212779i
$93$	−1.40431	−	2.43234i	−0.145621	−	0.252222i
$94$	10.1936	−	2.73136i	1.05139	−	0.281718i
$95$	1.19010	+	2.93991i	0.122102	+	0.301629i
$96$	−1.62090	+	0.434319i	−0.165432	+	0.0443275i
$97$		−	10.8299i		−	1.09961i	−0.835294	−	0.549803i	$-0.814703\pi$
$97$		−	10.8299i		−	1.09961i	0.835294	−	0.549803i	$-0.185297\pi$
$98$	−0.884516	+	0.510676i	−0.0893496	+	0.0515860i
$99$	−0.321464	+	0.556791i	−0.0323083	+	0.0559596i
$100$	4.84985	−	1.21613i	0.484985	−	0.121613i
$101$		−	5.97730i		−	0.594763i	−0.954759	−	0.297382i	$-0.903887\pi$
$101$		−	5.97730i		−	0.594763i	0.954759	−	0.297382i	$-0.0961134\pi$
$102$	0.961220	+	3.58732i	0.0951749	+	0.355198i
$103$		−	4.06301i		−	0.400341i	−0.979761	−	0.200170i	$-0.935850\pi$
$103$		−	4.06301i		−	0.400341i	0.979761	−	0.200170i	$-0.0641495\pi$
$104$	−1.48236	−	2.56752i	−0.145357	−	0.251766i
$105$	1.12426	+	9.10571i	0.109716	+	0.888626i
$106$	8.34541	+	2.23615i	0.810578	+	0.217194i
$107$	5.07945	−	18.9567i	0.491049	−	1.83262i	−0.0600742	−	0.998194i	$-0.519134\pi$
$107$	5.07945	−	18.9567i	0.491049	−	1.83262i	0.551123	−	0.834424i	$-0.314200\pi$
$108$	−5.16103	−	1.38289i	−0.496620	−	0.133069i
$109$	3.99357	+	14.9042i	0.382515	+	1.42756i	0.842047	+	0.539404i	$0.181350\pi$
$109$	3.99357	+	14.9042i	0.382515	+	1.42756i	−0.459533	+	0.888161i	$0.651983\pi$
$110$	−0.957143	−	7.75221i	−0.0912600	−	0.739144i
$111$	4.61298	−	9.10552i	0.437845	−	0.864258i
$112$	−1.72897	−	1.72897i	−0.163372	−	0.163372i
$113$	3.49304	+	2.01671i	0.328598	+	0.189716i	0.655218	−	0.755440i	$-0.272577\pi$
$113$	3.49304	+	2.01671i	0.328598	+	0.189716i	−0.326621	+	0.945156i	$0.605910\pi$
$114$	1.19010	+	2.06132i	0.111463	+	0.193060i
$115$	3.17414	+	4.20634i	0.295991	+	0.392244i
$116$	0.985999	−	3.67980i	0.0915477	−	0.341661i
$117$		−	0.545656i		−	0.0504459i
$118$	−2.96988	−	0.795776i	−0.273399	−	0.0732572i
$119$	−3.82649	+	3.82649i	−0.350774	+	0.350774i
$120$	3.47813	−	1.40797i	0.317508	−	0.128530i
$121$	−1.20257			−0.109324
$122$	2.65666	−	2.65666i	0.240523	−	0.240523i
$123$	−1.40528	−	5.24457i	−0.126710	−	0.472887i
$124$	−1.61669	−	0.433190i	−0.145183	−	0.0389016i
$125$	−10.4296	+	4.02772i	−0.932856	+	0.360250i
$126$	−0.116475	−	0.434692i	−0.0103764	−	0.0387254i
$127$	−17.5535	+	4.70345i	−1.55762	+	0.417363i	−0.931910	−	0.362691i	$-0.881858\pi$
$127$	−17.5535	+	4.70345i	−1.55762	+	0.417363i	−0.625712	+	0.780054i	$0.715191\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−4.32231	+	16.1311i	−0.380558	+	1.42026i
$130$	3.99317	+	5.29171i	0.350225	+	0.464114i
$131$	−0.340371	−	1.27028i	−0.0297384	−	0.110985i	0.949461	−	0.313884i	$-0.101630\pi$
$131$	−0.340371	−	1.27028i	−0.0297384	−	0.110985i	−0.979200	+	0.202899i	$0.934964\pi$
$132$	−1.51717	−	5.66216i	−0.132053	−	0.492827i
$133$	−1.73410	+	3.00354i	−0.150365	+	0.260440i
$134$	5.57848	−	5.57848i	0.481907	−	0.481907i
$135$	11.8324	+	1.65482i	1.01837	+	0.142424i
$136$	1.91666	+	1.10658i	0.164352	+	0.0948887i
$137$	−1.14123	−	1.14123i	−0.0975023	−	0.0975023i	0.656673	−	0.754175i	$-0.271963\pi$
$137$	−1.14123	−	1.14123i	−0.0975023	−	0.0975023i	−0.754175	+	0.656673i	$0.771963\pi$
$138$	2.79633	+	2.79633i	0.238040	+	0.238040i
$139$	−6.46760	+	11.2022i	−0.548574	+	0.950159i	0.449798	+	0.893130i	$0.351496\pi$
$139$	−6.46760	+	11.2022i	−0.548574	+	0.950159i	−0.998373	+	0.0570285i	$0.981837\pi$
$140$	4.31069	+	3.36321i	0.364320	+	0.284243i
$141$	−15.3365	+	8.85451i	−1.29156	+	0.745685i
$142$	−5.56298			−0.466835
$143$	8.96890	−	5.17820i	0.750017	−	0.433023i
$144$	−0.159392	+	0.0920251i	−0.0132827	+	0.00766876i
$145$	−1.17988	+	8.43644i	−0.0979837	+	0.700608i
$146$	−8.58176	+	2.29947i	−0.710231	+	0.190306i
$147$	1.21192	−	1.21192i	0.0999572	−	0.0999572i
$148$	−1.89306	−	5.78068i	−0.155609	−	0.475169i
$149$		−	12.7009i		−	1.04050i	−0.854014	−	0.520250i	$-0.825839\pi$
$149$		−	12.7009i		−	1.04050i	0.854014	−	0.520250i	$-0.174161\pi$
$150$	−7.33293	+	4.07761i	−0.598731	+	0.332935i
$151$	1.78346	−	1.02968i	0.145136	−	0.0837943i	−0.425674	−	0.904877i	$-0.639963\pi$
$151$	1.78346	−	1.02968i	0.145136	−	0.0837943i	0.570810	+	0.821082i	$0.306629\pi$
$152$	1.37008	+	0.367111i	0.111128	+	0.0297767i
$153$	0.203667	+	0.352761i	0.0164655	+	0.0285190i
$154$	6.03965	−	6.03965i	0.486689	−	0.486689i
$155$	3.70647	+	0.518370i	0.297711	+	0.0416364i
$156$	3.51788	+	3.51788i	0.281655	+	0.281655i
$157$	−17.9576	+	4.81173i	−1.43318	+	0.384018i	−0.890138	−	0.455690i	$-0.849392\pi$
$157$	−17.9576	+	4.81173i	−1.43318	+	0.384018i	−0.543037	+	0.839709i	$0.682726\pi$
$158$	10.8313	−	10.8313i	0.861690	−	0.861690i
$159$	−14.4983			−1.14979
$160$	0.872317	−	2.05890i	0.0689627	−	0.162770i
$161$	−1.49138	+	5.56592i	−0.117537	+	0.438656i
$162$	8.41398			0.661064
$163$	19.4762	+	11.2446i	1.52549	+	0.880743i	0.999543	+	0.0302266i	$0.00962290\pi$
$163$	19.4762	+	11.2446i	1.52549	+	0.880743i	0.525949	+	0.850516i	$0.323710\pi$
$164$	−2.80211	−	1.61780i	−0.218808	−	0.126329i
$165$	4.91836	+	12.1498i	0.382894	+	0.945864i
$166$	10.0566	+	2.69465i	0.780542	+	0.209146i
$167$	−0.557240	+	0.321723i	−0.0431206	+	0.0248957i	−0.521405	−	0.853309i	$-0.674592\pi$
$167$	−0.557240	+	0.321723i	−0.0431206	+	0.0248957i	0.478285	+	0.878205i	$0.341259\pi$
$168$	3.55340	+	2.05156i	0.274151	+	0.158281i
$169$	2.10523	−	3.64637i	0.161941	−	0.280490i
$170$	−4.55668	−	1.93058i	−0.349482	−	0.148069i
$171$	0.184596	+	0.184596i	0.0141164	+	0.0141164i
$172$	4.97597	+	8.61863i	0.379414	+	0.657164i
$173$	−2.76867	+	0.741863i	−0.210498	+	0.0564028i	−0.362527	−	0.931973i	$-0.618086\pi$
$173$	−2.76867	+	0.741863i	−0.210498	+	0.0564028i	0.152029	+	0.988376i	$0.451419\pi$
$174$			6.39282i			0.484639i
$175$	−10.4879	−	6.28257i	−0.792809	−	0.474918i
$176$	−3.02521	−	1.74661i	−0.228034	−	0.131656i
$177$	5.15950			0.387811
$178$	−2.11006	+	7.87485i	−0.158156	+	0.590245i
$179$	−0.470627	−	0.470627i	−0.0351763	−	0.0351763i	0.689300	−	0.724476i	$-0.257918\pi$
$179$	−0.470627	−	0.470627i	−0.0351763	−	0.0351763i	−0.724476	+	0.689300i	$0.757918\pi$
$180$	0.328511	−	0.247897i	0.0244857	−	0.0184772i
$181$	−3.15781	−	5.46948i	−0.234718	−	0.406543i	0.724473	−	0.689303i	$-0.242083\pi$
$181$	−3.15781	−	5.46948i	−0.234718	−	0.406543i	−0.959191	+	0.282760i	$0.908750\pi$
$182$	−1.87621	+	7.00210i	−0.139074	+	0.519030i
$183$	−3.15234	+	5.46002i	−0.233028	+	0.403616i
$184$	2.35663			0.173733
$185$	5.78503	+	12.3099i	0.425324	+	0.905041i
$186$	2.80863			0.205939
$187$	−3.86553	+	6.69530i	−0.282676	+	0.489609i
$188$	−2.73136	+	10.1936i	−0.199205	+	0.743442i
$189$	6.53227	+	11.3142i	0.475152	+	0.822988i
$190$	−3.14109	−	0.439298i	−0.227879	−	0.0318700i
$191$	4.70925	+	4.70925i	0.340749	+	0.340749i	0.856649	−	0.515900i	$-0.172542\pi$
$191$	4.70925	+	4.70925i	0.340749	+	0.340749i	−0.515900	+	0.856649i	$0.672542\pi$
$192$	0.434319	−	1.62090i	0.0313443	−	0.116978i
$193$	15.2352			1.09665			0.548326	−	0.836264i	$-0.315265\pi$
$193$	15.2352			1.09665			0.548326	+	0.836264i	$0.315265\pi$
$194$	9.37894	+	5.41493i	0.673369	+	0.388770i
$195$	−8.77083	−	6.84303i	−0.628092	−	0.490040i
$196$		−	1.02135i		−	0.0729537i
$197$	−17.7146	+	4.74662i	−1.26212	+	0.338183i	−0.827005	−	0.562194i	$-0.809957\pi$
$197$	−17.7146	+	4.74662i	−1.26212	+	0.338183i	−0.435110	+	0.900377i	$0.643291\pi$
$198$	−0.321464	−	0.556791i	−0.0228454	−	0.0395694i
$199$	1.80868	+	1.80868i	0.128214	+	0.128214i	0.768302	−	0.640088i	$-0.221102\pi$
$199$	1.80868	+	1.80868i	0.128214	+	0.128214i	−0.640088	+	0.768302i	$0.721102\pi$
$200$	−1.37172	+	4.80816i	−0.0969954	+	0.339988i
$201$	−6.61932	+	11.4650i	−0.466891	+	0.808679i
$202$	5.17649	+	2.98865i	0.364217	+	0.210281i
$203$	−8.06701	+	4.65749i	−0.566193	+	0.326892i
$204$	−3.58732	−	0.961220i	−0.251163	−	0.0672988i
$205$	6.66176	+	2.82246i	0.465277	+	0.197129i
$206$	3.51867	+	2.03151i	0.245158	+	0.141542i
$207$	0.375628	+	0.216869i	0.0261080	+	0.0150734i
$208$	2.96472			0.205566
$209$	−1.28240	+	4.78598i	−0.0887054	+	0.331053i
$210$	−8.44790	−	3.57922i	−0.582961	−	0.246990i
$211$	−0.988606			−0.0680585			−0.0340292	−	0.999421i	$-0.510834\pi$
$211$	−0.988606			−0.0680585			−0.0340292	+	0.999421i	$0.510834\pi$
$212$	−6.10927	+	6.10927i	−0.419586	+	0.419586i
$213$	9.01704	−	2.41611i	0.617837	−	0.165549i
$214$	13.8773	+	13.8773i	0.948633	+	0.948633i
$215$	−13.4043	−	17.7632i	−0.914163	−	1.21144i
$216$	3.77813	−	3.77813i	0.257069	−	0.257069i
$217$	2.04623	+	3.54417i	0.138907	+	0.240594i
$218$	−14.9042	−	3.99357i	−1.00944	−	0.270479i
$219$	12.9115	−	7.45444i	0.872476	−	0.503724i
$220$	7.19218	+	3.04719i	0.484897	+	0.205442i
$221$		−	6.56141i		−	0.441368i
$222$	5.57913	+	8.54772i	0.374446	+	0.573685i
$223$	9.31830	−	9.31830i	0.624000	−	0.624000i	−0.322552	−	0.946552i	$-0.604541\pi$
$223$	9.31830	−	9.31830i	0.624000	−	0.624000i	0.946552	+	0.322552i	$0.104541\pi$
$224$	2.36181	−	0.632846i	0.157805	−	0.0422838i
$225$	−0.661113	+	0.640149i	−0.0440742	+	0.0426766i
$226$	−3.49304	+	2.01671i	−0.232354	+	0.134149i
$227$	14.2263	−	8.21358i	0.944235	−	0.545154i	0.0529497	−	0.998597i	$-0.483138\pi$
$227$	14.2263	−	8.21358i	0.944235	−	0.545154i	0.891285	+	0.453443i	$0.149804\pi$
$228$	−2.38020			−0.157633
$229$	7.10267	−	4.10073i	0.469357	−	0.270984i	−0.246613	−	0.969114i	$-0.579318\pi$
$229$	7.10267	−	4.10073i	0.469357	−	0.270984i	0.715971	+	0.698130i	$0.245984\pi$
$230$	−5.22987	+	0.645718i	−0.344848	+	0.0425774i
$231$	−7.16654	+	12.4128i	−0.471524	+	0.816703i
$232$	2.69380	+	2.69380i	0.176857	+	0.176857i
$233$	20.0962	+	20.0962i	1.31654	+	1.31654i	0.916493	+	0.400052i	$0.131008\pi$
$233$	20.0962	+	20.0962i	1.31654	+	1.31654i	0.400052	+	0.916493i	$0.368992\pi$
$234$	0.472552	+	0.272828i	0.0308917	+	0.0178353i
$235$	3.26843	−	23.3701i	0.213209	−	1.52450i
$236$	2.17410	−	2.17410i	0.141522	−	0.141522i
$237$	−12.8522	+	22.2606i	−0.834839	+	1.44598i
$238$	−1.40059	−	5.22708i	−0.0907869	−	0.338821i
$239$	−2.33098	−	8.69934i	−0.150779	−	0.562714i	−0.999430	−	0.0337608i	$-0.989252\pi$
$239$	−2.33098	−	8.69934i	−0.150779	−	0.562714i	0.848651	−	0.528953i	$-0.177415\pi$
$240$	−0.519721	+	3.71613i	−0.0335478	+	0.239875i
$241$	6.50247	−	24.2676i	0.418861	−	1.56321i	−0.358113	−	0.933678i	$-0.616580\pi$
$241$	6.50247	−	24.2676i	0.418861	−	1.56321i	0.776974	−	0.629532i	$-0.216753\pi$
$242$	0.601283	−	1.04145i	0.0386520	−	0.0669472i
$243$	1.84487	−	0.494331i	0.118348	−	0.0317113i
$244$	0.972406	+	3.62907i	0.0622519	+	0.232327i
$245$	0.279851	+	2.26660i	0.0178790	+	0.144808i
$246$	5.24457	+	1.40528i	0.334382	+	0.0895973i
$247$	−1.08838	−	4.06189i	−0.0692520	−	0.258452i
$248$	1.18350	−	1.18350i	0.0751521	−	0.0751521i
$249$	−17.4711			−1.10718
$250$	1.72671	−	11.0462i	0.109207	−	0.698623i
$251$	14.1633	−	14.1633i	0.893979	−	0.893979i	−0.100916	−	0.994895i	$-0.532177\pi$
$251$	14.1633	−	14.1633i	0.893979	−	0.893979i	0.994895	+	0.100916i	$0.0321772\pi$
$252$	0.434692	+	0.116475i	0.0273830	+	0.00733726i
$253$			8.23222i			0.517555i
$254$	4.70345	−	17.5535i	0.295121	−	1.10140i
$255$	8.22442	+	1.15023i	0.515033	+	0.0720301i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	21.3340	+	12.3172i	1.33078	+	0.768327i	0.985419	−	0.170143i	$-0.0544229\pi$
$257$	21.3340	+	12.3172i	1.33078	+	0.768327i	0.345362	+	0.938470i	$0.387756\pi$
$258$	−11.8088	−	11.8088i	−0.735182	−	0.735182i
$259$	−6.72157	+	13.2677i	−0.417658	+	0.824412i
$260$	−6.57935	+	0.812333i	−0.408034	+	0.0503788i
$261$	0.181473	+	0.677267i	0.0112329	+	0.0419218i
$262$	1.27028	+	0.340371i	0.0784784	+	0.0210282i
$263$	−3.27692	+	12.2296i	−0.202064	+	0.754112i	0.788261	+	0.615341i	$0.210982\pi$
$263$	−3.27692	+	12.2296i	−0.202064	+	0.754112i	−0.990325	+	0.138771i	$0.955685\pi$
$264$	5.66216	+	1.51717i	0.348482	+	0.0933754i
$265$	11.8838	−	15.2317i	0.730019	−	0.935678i
$266$	−1.73410	−	3.00354i	−0.106324	−	0.184159i
$267$		−	13.6808i		−	0.837250i
$268$	2.04187	+	7.62035i	0.124727	+	0.465487i
$269$		−	30.2272i		−	1.84299i	−0.388394	−	0.921493i	$-0.626970\pi$
$269$		−	30.2272i		−	1.84299i	0.388394	−	0.921493i	$-0.373030\pi$
$270$	−7.34929	+	9.41971i	−0.447263	+	0.573265i
$271$	7.93046	−	13.7360i	0.481741	−	0.834400i	−0.518039	−	0.855357i	$-0.673338\pi$
$271$	7.93046	−	13.7360i	0.481741	−	0.834400i	0.999780	+	0.0209568i	$0.00667123\pi$
$272$	−1.91666	+	1.10658i	−0.116214	+	0.0670964i
$273$		−	12.1646i		−	0.736234i
$274$	1.55896	−	0.417721i	0.0941800	−	0.0252354i
$275$	−16.7959	−	4.79172i	−1.01283	−	0.288952i
$276$	−3.81986	+	1.02353i	−0.229929	+	0.0616092i
$277$	−2.11778	−	3.66810i	−0.127245	−	0.220395i	0.795363	−	0.606133i	$-0.207280\pi$
$277$	−2.11778	−	3.66810i	−0.127245	−	0.220395i	−0.922608	+	0.385738i	$0.873947\pi$
$278$	−6.46760	−	11.2022i	−0.387901	−	0.671864i
$279$	0.297551	−	0.0797286i	0.0178139	−	0.00477323i
$280$	−5.06797	+	2.05156i	−0.302869	+	0.122604i
$281$	−15.6022	+	4.18061i	−0.930751	+	0.249394i	−0.692175	−	0.721730i	$-0.743347\pi$
$281$	−15.6022	+	4.18061i	−0.930751	+	0.249394i	−0.238576	+	0.971124i	$0.576681\pi$
$282$		−	17.7090i		−	1.05456i
$283$	−14.2912	+	8.25105i	−0.849526	+	0.490474i	−0.860491	−	0.509466i	$-0.829843\pi$
$283$	−14.2912	+	8.25105i	−0.849526	+	0.490474i	0.0109650	+	0.999940i	$0.496510\pi$
$284$	2.78149	−	4.81768i	0.165051	−	0.285877i
$285$	5.28219	−	0.652176i	0.312890	−	0.0386316i
$286$			10.3564i			0.612386i
$287$	2.04763	+	7.64186i	0.120868	+	0.451085i
$288$		−	0.184050i		−	0.0108453i
$289$	−6.05095	−	10.4806i	−0.355938	−	0.616503i
$290$	−6.71623	−	5.24002i	−0.394390	−	0.307705i
$291$	−17.5541	−	4.70362i	−1.02904	−	0.275731i
$292$	2.29947	−	8.58176i	0.134567	−	0.502209i
$293$	−13.2858	−	3.55993i	−0.776167	−	0.207973i	−0.151073	−	0.988523i	$-0.548273\pi$
$293$	−13.2858	−	3.55993i	−0.776167	−	0.207973i	−0.625094	+	0.780549i	$0.714939\pi$
$294$	0.443592	+	1.65551i	0.0258708	+	0.0965512i
$295$	−4.22910	+	5.42051i	−0.246228	+	0.315594i
$296$	5.95275	+	1.25090i	0.345997	+	0.0727072i
$297$	13.1978	+	13.1978i	0.765817	+	0.765817i
$298$	10.9993	+	6.35046i	0.637174	+	0.367872i
$299$	−3.49337	−	6.05069i	−0.202027	−	0.349921i
$300$	0.135151	−	8.38931i	0.00780296	−	0.484357i
$301$	6.29804	−	23.5046i	0.363013	−	1.35478i
$302$			2.05936i			0.118503i
$303$	−9.68860	−	2.59605i	−0.556596	−	0.149139i
$304$	−1.00297	+	1.00297i	−0.0575241	+	0.0575241i
$305$	−3.15234	−	7.78725i	−0.180503	−	0.445897i
$306$	−0.407333			−0.0232857
$307$	5.60560	−	5.60560i	0.319928	−	0.319928i	−0.528811	−	0.848740i	$-0.677362\pi$
$307$	5.60560	−	5.60560i	0.319928	−	0.319928i	0.848740	+	0.528811i	$0.177362\pi$
$308$	2.21067	+	8.25032i	0.125964	+	0.470106i
$309$	−6.58574	−	1.76464i	−0.374650	−	0.100387i
$310$	−2.30216	+	2.95071i	−0.130754	+	0.167589i
$311$	6.86912	+	25.6359i	0.389512	+	1.45368i	0.830930	+	0.556377i	$0.187809\pi$
$311$	6.86912	+	25.6359i	0.389512	+	1.45368i	−0.441417	+	0.897302i	$0.645524\pi$
$312$	−4.80551	+	1.28763i	−0.272058	+	0.0728978i
$313$	−11.0739	+	19.1806i	−0.625934	+	1.08415i	0.362425	+	0.932013i	$0.381949\pi$
$313$	−11.0739	+	19.1806i	−0.625934	+	1.08415i	−0.988359	+	0.152137i	$0.951385\pi$
$314$	4.81173	−	17.9576i	0.271542	−	1.01341i
$315$	−0.996590	−	0.139378i	−0.0561515	−	0.00785308i
$316$	3.96452	+	14.7958i	0.223022	+	0.832328i
$317$	1.33273	+	4.97383i	0.0748537	+	0.279358i	0.993200	−	0.116420i	$-0.0371418\pi$
$317$	1.33273	+	4.97383i	0.0748537	+	0.279358i	−0.918346	+	0.395778i	$0.870475\pi$
$318$	7.24914	−	12.5559i	0.406512	−	0.704099i
$319$	−9.41003	+	9.41003i	−0.526860	+	0.526860i
$320$	1.34690	+	1.78490i	0.0752940	+	0.0997788i
$321$	−28.5209	−	16.4665i	−1.59188	−	0.919073i
$322$	−4.07453	−	4.07453i	−0.227065	−	0.227065i
$323$	2.21973	+	2.21973i	0.123509	+	0.123509i
$324$	−4.20699	+	7.28672i	−0.233722	+	0.404818i
$325$	14.3784	−	3.60549i	0.797571	−	0.199996i
$326$	−19.4762	+	11.2446i	−1.07869	+	0.622779i
$327$	25.8927			1.43187
$328$	2.80211	−	1.61780i	0.154720	−	0.0893279i
$329$	22.3468	−	12.9019i	1.23202	−	0.711305i
$330$	−12.9813	−	1.81550i	−0.714595	−	0.0999398i
$331$	11.0330	−	2.95628i	0.606428	−	0.162492i	0.0574777	−	0.998347i	$-0.481694\pi$
$331$	11.0330	−	2.95628i	0.606428	−	0.162492i	0.548951	+	0.835855i	$0.315028\pi$
$332$	−7.36193	+	7.36193i	−0.404038	+	0.404038i
$333$	0.833707	+	0.747186i	0.0456869	+	0.0409455i
$334$		−	0.643446i		−	0.0352078i
$335$	−6.61932	−	16.3517i	−0.361652	−	0.893391i
$336$	−3.55340	+	2.05156i	−0.193854	+	0.111922i
$337$	24.0026	+	6.43147i	1.30750	+	0.350344i	0.844283	−	0.535898i	$-0.180027\pi$
$337$	24.0026	+	6.43147i	1.30750	+	0.350344i	0.463221	+	0.886243i	$0.346694\pi$
$338$	2.10523	+	3.64637i	0.114510	+	0.198336i
$339$	4.78598	−	4.78598i	0.259939	−	0.259939i
$340$	3.95028	−	2.98091i	0.214234	−	0.161663i
$341$	4.13421	+	4.13421i	0.223880	+	0.223880i
$342$	−0.252163	+	0.0675669i	−0.0136354	+	0.00365360i
$343$	−13.8686	+	13.8686i	−0.748836	+	0.748836i
$344$	−9.95193			−0.536572
$345$	8.19666	−	3.31808i	0.441293	−	0.178639i
$346$	0.741863	−	2.76867i	0.0398828	−	0.148845i
$347$	22.1398			1.18853			0.594264	−	0.804270i	$-0.297443\pi$
$347$	22.1398			1.18853			0.594264	+	0.804270i	$0.297443\pi$
$348$	−5.53635	−	3.19641i	−0.296779	−	0.171346i
$349$	−8.85764	−	5.11396i	−0.474139	−	0.273744i	0.243832	−	0.969818i	$-0.421595\pi$
$349$	−8.85764	−	5.11396i	−0.474139	−	0.273744i	−0.717971	+	0.696073i	$0.754929\pi$
$350$	10.6848	−	5.94148i	0.571127	−	0.317585i
$351$	−15.3010	−	4.09988i	−0.816706	−	0.218836i
$352$	3.02521	−	1.74661i	0.161244	−	0.0930946i
$353$	−10.2385	−	5.91121i	−0.544941	−	0.314622i	0.202138	−	0.979357i	$-0.435211\pi$
$353$	−10.2385	−	5.91121i	−0.544941	−	0.314622i	−0.747079	+	0.664735i	$0.768544\pi$
$354$	−2.57975	+	4.46825i	−0.137112	+	0.237485i
$355$	−4.85269	+	11.4536i	−0.257554	+	0.607895i
$356$	−5.76479	−	5.76479i	−0.305533	−	0.305533i
$357$	4.54044	+	7.86427i	0.240306	+	0.416221i
$358$	0.642888	−	0.172261i	0.0339777	−	0.00910430i
$359$			10.0299i			0.529357i	0.964337	+	0.264678i	$0.0852658\pi$
$359$			10.0299i			0.529357i	−0.964337	+	0.264678i	$0.914734\pi$
$360$	0.0504298	+	0.408447i	0.00265788	+	0.0215271i
$361$	−14.7121	−	8.49406i	−0.774323	−	0.447056i
$362$	6.31561			0.331941
$363$	−0.522297	+	1.94924i	−0.0274135	+	0.102309i
$364$	−5.12589	−	5.12589i	−0.268670	−	0.268670i
$365$	−2.75163	+	19.6748i	−0.144027	+	1.02983i
$366$	−3.15234	−	5.46002i	−0.164776	−	0.285400i
$367$	−0.343035	+	1.28022i	−0.0179063	+	0.0668271i	−0.974301	−	0.225251i	$-0.927680\pi$
$367$	−0.343035	+	1.28022i	−0.0179063	+	0.0668271i	0.956395	+	0.292078i	$0.0943466\pi$
$368$	−1.17832	+	2.04090i	−0.0614239	+	0.106389i
$369$	0.595511			0.0310011
$370$	−13.5532	−	1.14497i	−0.704597	−	0.0595240i
$371$	21.1254			1.09678
$372$	−1.40431	+	2.43234i	−0.0728103	+	0.126111i
$373$	2.80135	−	10.4548i	0.145049	−	0.541329i	−0.854705	−	0.519115i	$-0.826262\pi$
$373$	2.80135	−	10.4548i	0.145049	−	0.541329i	0.999753	−	0.0222142i	$-0.00707159\pi$
$374$	−3.86553	−	6.69530i	−0.199882	−	0.346206i
$375$	1.99874	+	18.6547i	0.103215	+	0.963326i
$376$	−7.46221	−	7.46221i	−0.384834	−	0.384834i
$377$	2.92321	−	10.9096i	0.150553	−	0.561871i
$378$	−13.0645			−0.671967
$379$	−23.6555	−	13.6575i	−1.21510	−	0.701540i	−0.251237	−	0.967926i	$-0.580837\pi$
$379$	−23.6555	−	13.6575i	−1.21510	−	0.701540i	−0.963867	+	0.266386i	$0.914171\pi$
$380$	1.95099	−	2.50061i	0.100084	−	0.128279i
$381$			30.4953i			1.56232i
$382$	−6.43295	+	1.72370i	−0.329138	+	0.0881923i
$383$	10.9382	+	18.9456i	0.558918	+	0.968075i	0.997587	+	0.0694263i	$0.0221169\pi$
$383$	10.9382	+	18.9456i	0.558918	+	0.968075i	−0.438669	+	0.898649i	$0.644550\pi$
$384$	1.18658	+	1.18658i	0.0605525	+	0.0605525i
$385$	−7.16654	−	17.7035i	−0.365241	−	0.902255i
$386$	−7.61759	+	13.1941i	−0.387725	+	0.671560i
$387$	−1.58626	−	0.915827i	−0.0806341	−	0.0465541i
$388$	−9.37894	+	5.41493i	−0.476144	+	0.274902i
$389$	15.2282	+	4.08038i	0.772100	+	0.206884i	0.623299	−	0.781984i	$-0.285792\pi$
$389$	15.2282	+	4.08038i	0.772100	+	0.206884i	0.148801	+	0.988867i	$0.452459\pi$
$390$	10.3117	−	4.17424i	0.522151	−	0.211371i
$391$	4.51685	+	2.60781i	0.228427	+	0.131882i
$392$	0.884516	+	0.510676i	0.0446748	+	0.0257930i
$393$	−2.20683			−0.111320
$394$	4.74662	−	17.7146i	0.239131	−	0.892450i
$395$	−12.8522	−	31.7488i	−0.646663	−	1.59746i
$396$	0.642927			0.0323083
$397$	20.1070	−	20.1070i	1.00914	−	1.00914i	0.00918282	−	0.999958i	$-0.497077\pi$
$397$	20.1070	−	20.1070i	1.00914	−	1.00914i	0.999958	−	0.00918282i	$-0.00292302\pi$
$398$	−2.47071	+	0.662025i	−0.123845	+	0.0331843i
$399$	4.11529	+	4.11529i	0.206022	+	0.206022i
$400$	−3.47813	−	3.59203i	−0.173906	−	0.179601i
$401$	−12.4652	+	12.4652i	−0.622484	+	0.622484i	−0.946166	−	0.323682i	$-0.895079\pi$
$401$	−12.4652	+	12.4652i	−0.622484	+	0.622484i	0.323682	+	0.946166i	$0.395079\pi$
$402$	−6.61932	−	11.4650i	−0.330142	−	0.571822i
$403$	−4.79301	−	1.28428i	−0.238757	−	0.0639748i
$404$	−5.17649	+	2.98865i	−0.257540	+	0.148691i
$405$	7.33966	−	17.3235i	0.364710	−	0.860813i
$406$		−	9.31498i		−	0.462295i
$407$	−4.36967	+	20.7943i	−0.216597	+	1.03073i
$408$	2.62610	−	2.62610i	0.130011	−	0.130011i
$409$	−34.1278	+	9.14453i	−1.68751	+	0.452168i	−0.969746	−	0.244116i	$-0.921502\pi$
$409$	−34.1278	+	9.14453i	−1.68751	+	0.452168i	−0.717767	+	0.696283i	$0.754836\pi$
$410$	−5.77520	+	4.35802i	−0.285217	+	0.215227i
$411$	−2.34549	+	1.35417i	−0.115694	+	0.0667962i
$412$	−3.51867	+	2.03151i	−0.173353	+	0.100085i
$413$	−7.51790			−0.369932
$414$	−0.375628	+	0.216869i	−0.0184611	+	0.0106585i
$415$	14.3206	−	18.3549i	0.702968	−	0.901006i
$416$	−1.48236	+	2.56752i	−0.0726786	+	0.125883i
$417$	15.3487	+	15.3487i	0.751627	+	0.751627i
$418$	−3.50358	−	3.50358i	−0.171366	−	0.171366i
$419$	20.5291	+	11.8525i	1.00291	+	0.579032i	0.909109	−	0.416559i	$-0.136764\pi$
$419$	20.5291	+	11.8525i	1.00291	+	0.579032i	0.0938034	+	0.995591i	$0.470097\pi$
$420$	7.32365	−	5.52649i	0.357357	−	0.269665i
$421$	−7.38381	+	7.38381i	−0.359865	+	0.359865i	−0.863763	−	0.503898i	$-0.831899\pi$
$421$	−7.38381	+	7.38381i	−0.359865	+	0.359865i	0.503898	+	0.863763i	$0.331899\pi$
$422$	0.494303	−	0.856158i	0.0240623	−	0.0416771i
$423$	−0.502707	−	1.87613i	−0.0244424	−	0.0912204i
$424$	−2.23615	−	8.34541i	−0.108597	−	0.405289i
$425$	−7.94975	+	7.69767i	−0.385619	+	0.373392i
$426$	−2.41611	+	9.01704i	−0.117061	+	0.436877i
$427$	4.59328	−	7.95579i	0.222284	−	0.385008i
$428$	−18.9567	+	5.07945i	−0.916309	+	0.245524i
$429$	−4.49798	−	16.7867i	−0.217164	−	0.810469i
$430$	22.0855	−	2.72683i	1.06506	−	0.131500i
$431$	6.79675	+	1.82118i	0.327388	+	0.0877234i	0.418769	−	0.908093i	$-0.362462\pi$
$431$	6.79675	+	1.82118i	0.327388	+	0.0877234i	−0.0913813	+	0.995816i	$0.529128\pi$
$432$	1.38289	+	5.16103i	0.0665345	+	0.248310i
$433$	−13.5027	+	13.5027i	−0.648898	+	0.648898i	−0.952727	−	0.303829i	$-0.901735\pi$
$433$	−13.5027	+	13.5027i	−0.648898	+	0.648898i	0.303829	+	0.952727i	$0.401735\pi$
$434$	−4.09245			−0.196444
$435$	13.1622	+	5.57657i	0.631078	+	0.267376i
$436$	10.9106	−	10.9106i	0.522525	−	0.522525i
$437$	3.22877	+	0.865146i	0.154453	+	0.0413855i
$438$			14.9089i			0.712374i
$439$	−8.08839	+	30.1863i	−0.386038	+	1.44071i	0.450487	+	0.892783i	$0.351250\pi$
$439$	−8.08839	+	30.1863i	−0.386038	+	1.44071i	−0.836525	+	0.547929i	$0.815416\pi$
$440$	−6.23504	+	4.70501i	−0.297244	+	0.224303i
$441$	0.0939899	+	0.162795i	0.00447571	+	0.00775216i
$442$	5.68234	+	3.28070i	0.270282	+	0.156047i
$443$	−19.8158	−	19.8158i	−0.941475	−	0.941475i	0.0569049	−	0.998380i	$-0.481877\pi$
$443$	−19.8158	−	19.8158i	−0.941475	−	0.941475i	−0.998380	+	0.0569049i	$0.981877\pi$
$444$	−10.1921	+	0.557805i	−0.483696	+	0.0264723i
$445$	14.3729	+	11.2138i	0.681340	+	0.531584i
$446$	3.41073	+	12.7290i	0.161503	+	0.602737i
$447$	−20.5869	−	5.51625i	−0.973728	−	0.260910i
$448$	−0.632846	+	2.36181i	−0.0298991	+	0.111585i
$449$	18.4205	+	4.93575i	0.869315	+	0.232932i	0.665791	−	0.746138i	$-0.268094\pi$
$449$	18.4205	+	4.93575i	0.869315	+	0.232932i	0.203523	+	0.979070i	$0.434761\pi$
$450$	−0.223829	−	0.892615i	−0.0105514	−	0.0420783i
$451$	5.65132	+	9.78837i	0.266110	+	0.460916i
$452$		−	4.03342i		−	0.189716i
$453$	−0.894421	−	3.33802i	−0.0420236	−	0.156834i
$454$			16.4272i			0.770965i
$455$	12.7800	+	9.97097i	0.599134	+	0.467446i
$456$	1.19010	−	2.06132i	0.0557316	−	0.0965300i
$457$	−28.4891	+	16.4482i	−1.33266	+	0.769414i	−0.985707	−	0.168468i	$-0.946118\pi$
$457$	−28.4891	+	16.4482i	−1.33266	+	0.769414i	−0.346956	+	0.937881i	$0.612785\pi$
$458$			8.20145i			0.383229i
$459$	11.4222	−	3.06057i	0.533143	−	0.142855i
$460$	2.05573	−	4.85206i	0.0958489	−	0.226229i
$461$	35.0617	−	9.39475i	1.63299	−	0.437557i	0.678206	−	0.734872i	$-0.262758\pi$
$461$	35.0617	−	9.39475i	1.63299	−	0.437557i	0.954780	+	0.297314i	$0.0960909\pi$
$462$	−7.16654	−	12.4128i	−0.333418	−	0.577496i
$463$	−11.9672	−	20.7278i	−0.556163	−	0.963303i	−0.997812	−	0.0661149i	$-0.978940\pi$
$463$	−11.9672	−	20.7278i	−0.556163	−	0.963303i	0.441649	−	0.897188i	$-0.354394\pi$
$464$	−3.67980	+	0.985999i	−0.170830	+	0.0457739i
$465$	2.45002	−	5.78268i	0.113617	−	0.268166i
$466$	−27.4519	+	7.35571i	−1.27168	+	0.340747i
$467$		−	27.3563i		−	1.26590i	−0.774194	−	0.632948i	$-0.781845\pi$
$467$		−	27.3563i		−	1.26590i	0.774194	−	0.632948i	$-0.218155\pi$
$468$	−0.472552	+	0.272828i	−0.0218437	+	0.0126115i
$469$	9.64501	−	16.7056i	0.445365	−	0.771395i
$470$	18.6049	+	14.5156i	0.858180	+	0.669555i
$471$			31.1974i			1.43750i
$472$	0.795776	+	2.96988i	0.0366286	+	0.136700i
$473$		−	34.7643i		−	1.59846i
$474$	−12.8522	−	22.2606i	−0.590320	−	1.02246i
$475$	−3.64449	+	6.08398i	−0.167221	+	0.279152i
$476$	5.22708	+	1.40059i	0.239583	+	0.0641960i
$477$	0.411563	−	1.53597i	0.0188442	−	0.0703274i
$478$	8.69934	+	2.33098i	0.397899	+	0.106617i
$479$	5.57077	+	20.7904i	0.254535	+	0.949938i	0.968349	+	0.249602i	$0.0802997\pi$
$479$	5.57077	+	20.7904i	0.254535	+	0.949938i	−0.713814	+	0.700336i	$0.753034\pi$
$480$	−2.95840	−	2.30816i	−0.135032	−	0.105352i
$481$	−5.61239	−	17.1381i	−0.255903	−	0.781429i
$482$	17.7651	+	17.7651i	0.809177	+	0.809177i
$483$	8.37406	+	4.83477i	0.381033	+	0.219989i
$484$	0.601283	+	1.04145i	0.0273311	+	0.0473388i
$485$	19.3302	−	14.5867i	0.877740	−	0.662350i
$486$	−0.494331	+	1.84487i	−0.0224233	+	0.0836849i
$487$			18.4473i			0.835928i	0.908464	+	0.417964i	$0.137256\pi$
$487$			18.4473i			0.835928i	−0.908464	+	0.417964i	$0.862744\pi$
$488$	−3.62907	−	0.972406i	−0.164280	−	0.0440187i
$489$	26.6852	−	26.6852i	1.20675	−	1.20675i
$490$	−2.10286	−	0.890942i	−0.0949975	−	0.0402487i
$491$	−11.6850			−0.527338			−0.263669	−	0.964613i	$-0.584933\pi$
$491$	−11.6850			−0.527338			−0.263669	+	0.964613i	$0.584933\pi$
$492$	−3.83929	+	3.83929i	−0.173089	+	0.173089i
$493$	2.18218	+	8.14400i	0.0982804	+	0.366787i
$494$	4.06189	+	1.08838i	0.182753	+	0.0489685i
$495$	−1.42679	+	0.176162i	−0.0641297	+	0.00791790i
$496$	0.433190	+	1.61669i	0.0194508	+	0.0725914i
$497$	−13.1387	+	3.52051i	−0.589352	+	0.157916i
$498$	8.73553	−	15.1304i	0.391448	−	0.678009i
$499$	9.24703	−	34.5104i	0.413954	−	1.54490i	−0.372968	−	0.927844i	$-0.621660\pi$
$499$	9.24703	−	34.5104i	0.413954	−	1.54490i	0.786922	−	0.617053i	$-0.211673\pi$
$500$	8.70293	+	7.01848i	0.389207	+	0.313876i
$501$	0.279461	+	1.04296i	0.0124854	+	0.0465961i
$502$	5.18413	+	19.3474i	0.231379	+	0.863518i
$503$	−4.74122	+	8.21204i	−0.211401	+	0.366157i	−0.952153	−	0.305621i	$-0.901136\pi$
$503$	−4.74122	+	8.21204i	−0.211401	+	0.366157i	0.740752	+	0.671778i	$0.234469\pi$
$504$	−0.318216	+	0.318216i	−0.0141745	+	0.0141745i
$505$	10.6689	−	8.05082i	0.474758	−	0.358257i
$506$	−7.12931	−	4.11611i	−0.316937	−	0.182983i
$507$	−4.99606	−	4.99606i	−0.221883	−	0.221883i
$508$	12.8501	+	12.8501i	0.570129	+	0.570129i
$509$	−6.92535	+	11.9951i	−0.306961	+	0.531672i	−0.977696	−	0.210025i	$-0.932645\pi$
$509$	−6.92535	+	11.9951i	−0.306961	+	0.531672i	0.670735	+	0.741697i	$0.265979\pi$
$510$	−5.10834	+	6.54744i	−0.226201	+	0.289926i
$511$	−18.8133	+	10.8619i	−0.832251	+	0.480500i
$512$	1.00000			0.0441942
$513$	6.56333	−	3.78934i	0.289778	−	0.167304i
$514$	−21.3340	+	12.3172i	−0.941004	+	0.543289i
$515$	7.25206	−	5.47247i	0.319564	−	0.241146i
$516$	16.1311	−	4.32231i	0.710132	−	0.190279i
$517$	26.0671	−	26.0671i	1.14643	−	1.14643i
$518$	−8.12934	−	12.4549i	−0.357183	−	0.547236i
$519$			4.80994i			0.211133i
$520$	2.58617	−	6.10405i	0.113411	−	0.267680i
$521$	1.49191	−	0.861352i	0.0653615	−	0.0377365i	−0.466963	−	0.884277i	$-0.654652\pi$
$521$	1.49191	−	0.861352i	0.0653615	−	0.0377365i	0.532325	+	0.846540i	$0.321319\pi$
$522$	−0.677267	−	0.181473i	−0.0296432	−	0.00794287i
$523$	16.7690	+	29.0447i	0.733256	+	1.27004i	0.955484	+	0.295042i	$0.0953337\pi$
$523$	16.7690	+	29.0447i	0.733256	+	1.27004i	−0.222228	+	0.974995i	$0.571333\pi$
$524$	−0.929912	+	0.929912i	−0.0406234	+	0.0406234i
$525$	−14.7385	+	14.2712i	−0.643241	+	0.622844i
$526$	−8.95272	−	8.95272i	−0.390357	−	0.390357i
$527$	3.57800	−	0.958721i	0.155860	−	0.0417625i
$528$	−4.14499	+	4.14499i	−0.180387	+	0.180387i
$529$	−17.4463			−0.758534
$530$	7.24914	+	17.9076i	0.314883	+	0.777855i
$531$	−0.146463	+	0.546606i	−0.00635594	+	0.0237207i
$532$	3.46819			0.150365
$533$	−8.30745	−	4.79631i	−0.359835	−	0.207751i
$534$	11.8479	+	6.84039i	0.512709	+	0.296013i
$535$	40.6774	−	16.4665i	1.75864	−	0.711911i
$536$	−7.62035	−	2.04187i	−0.329149	−	0.0881952i
$537$	−0.967241	+	0.558437i	−0.0417395	+	0.0240983i
$538$	26.1775	+	15.1136i	1.12859	+	0.651594i
$539$	−1.78390	+	3.08981i	−0.0768381	+	0.133087i
$540$	−4.48306	−	11.0745i	−0.192920	−	0.476572i
$541$	−31.7923	−	31.7923i	−1.36686	−	1.36686i	−0.864881	−	0.501976i	$-0.832606\pi$
$541$	−31.7923	−	31.7923i	−1.36686	−	1.36686i	−0.501976	−	0.864881i	$-0.667394\pi$
$542$	7.93046	+	13.7360i	0.340642	+	0.590010i
$543$	−10.2370	+	2.74299i	−0.439311	+	0.117713i
$544$		−	2.21317i		−	0.0948887i
$545$	−21.2236	+	27.2026i	−0.909117	+	1.16523i
$546$	10.5348	+	6.08229i	0.450849	+	0.260298i
$547$	−16.9250			−0.723662			−0.361831	−	0.932244i	$-0.617848\pi$
$547$	−16.9250			−0.723662			−0.361831	+	0.932244i	$0.617848\pi$
$548$	−0.417721	+	1.55896i	−0.0178442	+	0.0665953i
$549$	−0.488959	−	0.488959i	−0.0208683	−	0.0208683i
$550$	12.5477	−	12.1498i	0.535037	−	0.518071i
$551$	2.70179	+	4.67964i	0.115100	+	0.199359i
$552$	1.02353	−	3.81986i	0.0435643	−	0.162584i
$553$	18.7269	−	32.4359i	0.796349	−	1.37932i
$554$	4.23555			0.179951
$555$	22.4657	−	4.03053i	0.953614	−	0.171087i
$556$	12.9352			0.548574
$557$	−8.05558	+	13.9527i	−0.341326	+	0.591194i	−0.984679	−	0.174376i	$-0.944209\pi$
$557$	−8.05558	+	13.9527i	−0.341326	+	0.591194i	0.643353	+	0.765569i	$0.277543\pi$
$558$	−0.0797286	+	0.297551i	−0.00337518	+	0.0125964i
$559$	14.7523	+	25.5518i	0.623957	+	1.08073i
$560$	0.757284	−	5.41477i	0.0320011	−	0.228816i
$561$	9.17354	+	9.17354i	0.387307	+	0.387307i
$562$	4.18061	−	15.6022i	0.176348	−	0.658141i
$563$	9.61453			0.405204			0.202602	−	0.979261i	$-0.435060\pi$
$563$	9.61453			0.405204			0.202602	+	0.979261i	$0.435060\pi$
$564$	15.3365	+	8.85451i	0.645782	+	0.372842i
$565$	1.10516	+	8.95103i	0.0464943	+	0.376572i
$566$		−	16.5021i		−	0.693635i
$567$	19.8722	−	5.32475i	0.834555	−	0.223618i
$568$	2.78149	+	4.81768i	0.116709	+	0.202146i
$569$	−11.8059	−	11.8059i	−0.494930	−	0.494930i	0.414926	−	0.909855i	$-0.363808\pi$
$569$	−11.8059	−	11.8059i	−0.494930	−	0.494930i	−0.909855	+	0.414926i	$0.863808\pi$
$570$	−2.07629	+	4.90060i	−0.0869663	+	0.205263i
$571$	−2.04047	+	3.53420i	−0.0853911	+	0.147902i	−0.905558	−	0.424223i	$-0.860547\pi$
$571$	−2.04047	+	3.53420i	−0.0853911	+	0.147902i	0.820167	+	0.572125i	$0.193881\pi$
$572$	−8.96890	−	5.17820i	−0.375009	−	0.216511i
$573$	9.67853	−	5.58790i	0.404326	−	0.233438i
$574$	−7.64186	−	2.04763i	−0.318965	−	0.0854665i
$575$	−3.23264	+	11.3310i	−0.134811	+	0.472537i
$576$	0.159392	+	0.0920251i	0.00664134	+	0.00383438i
$577$	−31.3189	−	18.0820i	−1.30382	−	0.752762i	−0.322764	−	0.946479i	$-0.604612\pi$
$577$	−31.3189	−	18.0820i	−1.30382	−	0.752762i	−0.981057	+	0.193718i	$0.937945\pi$
$578$	12.1019			0.503373
$579$	6.61693	−	24.6947i	0.274990	−	1.02628i
$580$	7.89611	−	3.19641i	0.327868	−	0.132724i
$581$	25.4571			1.05614
$582$	12.8505	−	12.8505i	0.532671	−	0.532671i
$583$	29.1523	−	7.81135i	1.20737	−	0.323513i
$584$	6.28228	+	6.28228i	0.259963	+	0.259963i
$585$	0.973941	−	0.734944i	0.0402675	−	0.0303862i
$586$	9.72590	−	9.72590i	0.401773	−	0.401773i
$587$	17.5629	+	30.4198i	0.724897	+	1.25556i	0.959017	+	0.283350i	$0.0914459\pi$
$587$	17.5629	+	30.4198i	0.724897	+	1.25556i	−0.234120	+	0.972208i	$0.575221\pi$
$588$	−1.65551	−	0.443592i	−0.0682720	−	0.0182934i
$589$	2.05596	−	1.18701i	0.0847142	−	0.0489098i
$590$	−2.57975	−	6.37276i	−0.106207	−	0.262362i
$591$			30.7752i			1.26592i
$592$	−4.05969	+	4.52978i	−0.166852	+	0.186173i
$593$	−6.62602	+	6.62602i	−0.272098	+	0.272098i	−0.829944	−	0.557846i	$-0.811628\pi$
$593$	−6.62602	+	6.62602i	−0.272098	+	0.272098i	0.557846	+	0.829944i	$0.311628\pi$
$594$	−18.0286	+	4.83075i	−0.739722	+	0.198208i
$595$	−11.9838	−	1.67600i	−0.491287	−	0.0687091i
$596$	−10.9993	+	6.35046i	−0.450550	+	0.260125i
$597$	3.71724	−	2.14615i	0.152137	−	0.0878361i
$598$	6.98674			0.285709
$599$	−35.4303	+	20.4557i	−1.44764	+	0.835797i	−0.998341	−	0.0575829i	$-0.981661\pi$
$599$	−35.4303	+	20.4557i	−1.44764	+	0.835797i	−0.449302	+	0.893380i	$0.648327\pi$
$600$	7.19778	+	4.31170i	0.293848	+	0.176024i
$601$	−13.4363	+	23.2723i	−0.548078	+	0.949299i	0.450328	+	0.892863i	$0.351307\pi$
$601$	−13.4363	+	23.2723i	−0.548078	+	0.949299i	−0.998406	+	0.0564357i	$0.982026\pi$
$602$	17.2066	+	17.2066i	0.701287	+	0.701287i
$603$	−1.02672	−	1.02672i	−0.0418113	−	0.0418113i
$604$	−1.78346	−	1.02968i	−0.0725680	−	0.0418972i
$605$	−1.61974	−	2.14646i	−0.0658517	−	0.0872660i
$606$	7.09255	−	7.09255i	0.288115	−	0.288115i
$607$	−19.4079	+	33.6155i	−0.787743	+	1.36441i	0.139604	+	0.990207i	$0.455417\pi$
$607$	−19.4079	+	33.6155i	−0.787743	+	1.36441i	−0.927347	+	0.374203i	$0.877916\pi$
$608$	−0.367111	−	1.37008i	−0.0148883	−	0.0555640i
$609$	4.04567	+	15.0986i	0.163939	+	0.611828i
$610$	8.32013	+	1.16361i	0.336872	+	0.0471133i
$611$	−8.09770	+	30.2210i	−0.327598	+	1.22261i
$612$	0.203667	−	0.352761i	0.00823274	−	0.0142595i
$613$	−2.98045	+	0.798609i	−0.120379	+	0.0322555i	−0.318506	−	0.947921i	$-0.603181\pi$
$613$	−2.98045	+	0.798609i	−0.120379	+	0.0322555i	0.198126	+	0.980176i	$0.436514\pi$
$614$	2.05179	+	7.65739i	0.0828036	+	0.309027i
$615$	7.46826	−	9.57220i	0.301149	−	0.385988i
$616$	−8.25032	−	2.21067i	−0.332415	−	0.0890703i
$617$	0.869197	+	3.24389i	0.0349926	+	0.130594i	0.981213	−	0.192930i	$-0.0617990\pi$
$617$	0.869197	+	3.24389i	0.0349926	+	0.130594i	−0.946220	+	0.323524i	$0.895132\pi$
$618$	4.82110	−	4.82110i	0.193933	−	0.193933i
$619$	−12.8047			−0.514665			−0.257332	−	0.966323i	$-0.582844\pi$
$619$	−12.8047			−0.514665			−0.257332	+	0.966323i	$0.582844\pi$
$620$	−1.40431	−	3.46908i	−0.0563986	−	0.139322i
$621$	8.90367	−	8.90367i	0.357292	−	0.357292i
$622$	−25.6359	−	6.86912i	−1.02791	−	0.275427i
$623$			19.9343i			0.798649i
$624$	1.28763	−	4.80551i	0.0515465	−	0.192374i
$625$	−21.2368	−	13.1909i	−0.849470	−	0.527637i
$626$	−11.0739	−	19.1806i	−0.442602	−	0.766610i
$627$	7.20062	+	4.15728i	0.287565	+	0.166026i
$628$	13.1459	+	13.1459i	0.524579	+	0.524579i
$629$	10.0252	+	8.98476i	0.399729	+	0.358246i
$630$	0.619000	−	0.793383i	0.0246615	−	0.0316091i
$631$	12.1780	+	45.4491i	0.484800	+	1.80930i	0.580959	+	0.813933i	$0.302678\pi$
$631$	12.1780	+	45.4491i	0.484800	+	1.80930i	−0.0961584	+	0.995366i	$0.530656\pi$
$632$	−14.7958	−	3.96452i	−0.588545	−	0.157700i
$633$	−0.429370	+	1.60243i	−0.0170659	+	0.0636909i
$634$	−4.97383	−	1.33273i	−0.197536	−	0.0529296i
$635$	−32.0380	−	24.9961i	−1.27139	−	0.991942i
$636$	7.24914	+	12.5559i	0.287447	+	0.497873i
$637$		−	3.02802i		−	0.119974i
$638$	−3.44431	−	12.8543i	−0.136361	−	0.508908i
$639$			1.02387i			0.0405036i
$640$	−2.21922	+	0.274000i	−0.0877223	+	0.0108308i
$641$	3.89777	−	6.75113i	0.153953	−	0.266654i	−0.778725	−	0.627366i	$-0.784133\pi$
$641$	3.89777	−	6.75113i	0.153953	−	0.266654i	0.932677	+	0.360712i	$0.117466\pi$
$642$	28.5209	−	16.4665i	1.12563	−	0.649883i
$643$		−	11.1150i		−	0.438333i	−0.975687	−	0.219167i	$-0.929666\pi$
$643$		−	11.1150i		−	0.438333i	0.975687	−	0.219167i	$-0.0703339\pi$
$644$	5.56592	−	1.49138i	0.219328	−	0.0587687i
$645$	−34.6141	+	14.0121i	−1.36293	+	0.551725i
$646$	−3.03221	+	0.812478i	−0.119301	+	0.0319665i
$647$	−18.8220	−	32.6007i	−0.739970	−	1.28167i	−0.952508	−	0.304513i	$-0.901506\pi$
$647$	−18.8220	−	32.6007i	−0.739970	−	1.28167i	0.212538	−	0.977153i	$-0.431827\pi$
$648$	−4.20699	−	7.28672i	−0.165266	−	0.286249i
$649$	−10.3744	+	2.77982i	−0.407232	+	0.109117i
$650$	−4.06677	+	14.2548i	−0.159512	+	0.559120i
$651$	6.63345	−	1.77743i	0.259986	−	0.0696629i
$652$		−	22.4891i		−	0.880743i
$653$	−19.4806	+	11.2471i	−0.762335	+	0.440135i	−0.830134	−	0.557564i	$-0.811736\pi$
$653$	−19.4806	+	11.2471i	−0.762335	+	0.440135i	0.0677982	+	0.997699i	$0.478403\pi$
$654$	−12.9464	+	22.4238i	−0.506243	+	0.876838i
$655$	1.80888	−	2.31847i	0.0706788	−	0.0905902i
$656$			3.23559i			0.126329i
$657$	0.423219	+	1.57947i	0.0165113	+	0.0616211i
$658$			25.8038i			1.00594i
$659$	−5.01498	−	8.68620i	−0.195356	−	0.338366i	0.751661	−	0.659549i	$-0.229253\pi$
$659$	−5.01498	−	8.68620i	−0.195356	−	0.338366i	−0.947017	+	0.321183i	$0.895920\pi$
$660$	8.06290	−	10.3344i	0.313848	−	0.402264i
$661$	−2.00913	−	0.538344i	−0.0781459	−	0.0209391i	0.219534	−	0.975605i	$-0.429546\pi$
$661$	−2.00913	−	0.538344i	−0.0781459	−	0.0209391i	−0.297680	+	0.954666i	$0.596213\pi$
$662$	−2.95628	+	11.0330i	−0.114899	+	0.428810i
$663$	−10.6354	−	2.84974i	−0.413044	−	0.110675i
$664$	−2.69465	−	10.0566i	−0.104573	−	0.390271i
$665$	−7.69667	+	0.950285i	−0.298464	+	0.0368505i
$666$	−1.06394	+	0.348418i	−0.0412267	+	0.0135009i
$667$	6.34829	+	6.34829i	0.245807	+	0.245807i
$668$	0.557240	+	0.321723i	0.0215603	+	0.0124478i
$669$	−11.0569	−	19.1511i	−0.427485	−	0.740426i
$670$	17.4707	+	2.44337i	0.674951	+	0.0943955i
$671$	3.39682	−	12.6771i	0.131133	−	0.489395i
$672$		−	4.10312i		−	0.158281i
$673$	39.6590	+	10.6266i	1.52874	+	0.409625i	0.922609	−	0.385738i	$-0.126053\pi$
$673$	39.6590	+	10.6266i	1.52874	+	0.409625i	0.606134	+	0.795363i	$0.292720\pi$
$674$	−17.5711	+	17.5711i	−0.676814	+	0.676814i
$675$	12.9833	+	23.3484i	0.499728	+	0.898681i
$676$	−4.21046			−0.161941
$677$	−31.0400	+	31.0400i	−1.19296	+	1.19296i	−0.216732	+	0.976231i	$0.569540\pi$
$677$	−31.0400	+	31.0400i	−1.19296	+	1.19296i	−0.976231	+	0.216732i	$0.930460\pi$
$678$	1.75179	+	6.53776i	0.0672770	+	0.251081i
$679$	25.5781	+	6.85363i	0.981598	+	0.263018i
$680$	0.606408	+	4.91150i	0.0232547	+	0.188347i
$681$	−7.13462	−	26.6268i	−0.273399	−	1.02034i
$682$	−5.64744	+	1.51323i	−0.216252	+	0.0579444i
$683$	−3.59677	+	6.22979i	−0.137627	+	0.238376i	−0.926598	−	0.376054i	$-0.877281\pi$
$683$	−3.59677	+	6.22979i	−0.137627	+	0.238376i	0.788971	+	0.614430i	$0.210614\pi$
$684$	0.0675669	−	0.252163i	0.00258348	−	0.00964169i
$685$	0.499859	−	3.57412i	0.0190986	−	0.136560i
$686$	−5.07628	−	18.9449i	−0.193813	−	0.723321i
$687$	−3.56205	−	13.2937i	−0.135901	−	0.507188i
$688$	4.97597	−	8.61863i	0.189707	−	0.328582i
$689$	−18.1122	+	18.1122i	−0.690021	+	0.690021i
$690$	−1.22479	+	8.75755i	−0.0466269	+	0.333394i
$691$	−6.86509	−	3.96356i	−0.261160	−	0.150781i	0.363703	−	0.931515i	$-0.381512\pi$
$691$	−6.86509	−	3.96356i	−0.261160	−	0.150781i	−0.624864	+	0.780734i	$0.714846\pi$
$692$	2.02681	+	2.02681i	0.0770476	+	0.0770476i
$693$	−1.11160	−	1.11160i	−0.0422262	−	0.0422262i
$694$	−11.0699	+	19.1736i	−0.420208	+	0.727822i
$695$	−28.7060	+	3.54425i	−1.08888	+	0.134441i
$696$	5.53635	−	3.19641i	0.209855	−	0.121160i
$697$	7.16091			0.271239
$698$	8.85764	−	5.11396i	0.335267	−	0.193566i
$699$	41.3020	−	23.8457i	1.56219	−	0.901929i
$700$	−0.196929	+	12.2241i	−0.00744321	+	0.462026i
$701$	−34.5973	+	9.27031i	−1.30672	+	0.350135i	−0.843987	−	0.536363i	$-0.819798\pi$
$701$	−34.5973	+	9.27031i	−1.30672	+	0.350135i	−0.462733	+	0.886498i	$0.653131\pi$
$702$	11.2011	−	11.2011i	0.422758	−	0.422758i
$703$	7.69651	+	3.89915i	0.290279	+	0.147059i
$704$			3.49322i			0.131656i
$705$	−36.4611	−	15.4479i	−1.37320	−	0.581801i
$706$	10.2385	−	5.91121i	0.385332	−	0.222471i
$707$	14.1173	+	3.78271i	0.530934	+	0.142263i
$708$	−2.57975	−	4.46825i	−0.0969529	−	0.167927i
$709$	3.06214	−	3.06214i	0.115001	−	0.115001i	−0.647264	−	0.762266i	$-0.724087\pi$
$709$	3.06214	−	3.06214i	0.115001	−	0.115001i	0.762266	+	0.647264i	$0.224087\pi$
$710$	−7.49278	−	9.92936i	−0.281199	−	0.372642i
$711$	−1.99350	−	1.99350i	−0.0747620	−	0.0747620i
$712$	7.87485	−	2.11006i	0.295122	−	0.0790778i
$713$	2.78906	−	2.78906i	0.104451	−	0.104451i
$714$	−9.08088			−0.339843
$715$	21.3228	+	9.03406i	0.797426	+	0.337855i
$716$	−0.172261	+	0.642888i	−0.00643771	+	0.0240259i
$717$	−15.1132			−0.564411
$718$	−8.68613	−	5.01494i	−0.324163	−	0.187156i
$719$	23.9560	+	13.8310i	0.893409	+	0.515810i	0.875056	−	0.484022i	$-0.160825\pi$
$719$	23.9560	+	13.8310i	0.893409	+	0.515810i	0.0183527	+	0.999832i	$0.494158\pi$
$720$	−0.378941	−	0.160550i	−0.0141223	−	0.00598335i
$721$	9.59607	+	2.57126i	0.357376	+	0.0957587i
$722$	14.7121	−	8.49406i	0.547529	−	0.316116i
$723$	−36.5111	−	21.0797i	−1.35786	−	0.783963i
$724$	−3.15781	+	5.46948i	−0.117359	+	0.203272i
$725$	−16.6474	+	9.25707i	−0.618267	+	0.343799i
$726$	−1.42694	−	1.42694i	−0.0529588	−	0.0529588i
$727$	−11.3377	−	19.6374i	−0.420491	−	0.728312i	0.575496	−	0.817804i	$-0.304809\pi$
$727$	−11.3377	−	19.6374i	−0.420491	−	0.728312i	−0.995988	+	0.0894923i	$0.971476\pi$
$728$	7.00210	−	1.87621i	0.259515	−	0.0695369i
$729$		−	28.4470i		−	1.05359i
$730$	−15.6631	−	12.2204i	−0.579717	−	0.452297i
$731$	−19.0745	−	11.0126i	−0.705494	−	0.407317i
$732$	6.30469			0.233028
$733$	−3.56873	+	13.3187i	−0.131814	+	0.491937i	−0.999991	−	0.00431824i	$-0.998625\pi$
$733$	−3.56873	+	13.3187i	−0.131814	+	0.491937i	0.868176	+	0.496256i	$0.165292\pi$
$734$	−0.937188	−	0.937188i	−0.0345922	−	0.0345922i
$735$	3.79548	+	0.530817i	0.139998	+	0.0195795i
$736$	−1.17832	−	2.04090i	−0.0434333	−	0.0752286i
$737$	7.13268	−	26.6195i	0.262736	−	0.980543i
$738$	−0.297756	+	0.515728i	−0.0109605	+	0.0189842i
$739$	0.943189			0.0346958			0.0173479	−	0.999850i	$-0.494478\pi$
$739$	0.943189			0.0346958			0.0173479	+	0.999850i	$0.494478\pi$
$740$	7.76817	−	11.1649i	0.285563	−	0.410431i
$741$	−7.05662			−0.259232
$742$	−10.5627	+	18.2952i	−0.387769	+	0.671636i
$743$	1.36337	−	5.08817i	0.0500172	−	0.186667i	−0.936397	−	0.350941i	$-0.885862\pi$
$743$	1.36337	−	5.08817i	0.0500172	−	0.186667i	0.986415	+	0.164275i	$0.0525283\pi$
$744$	−1.40431	−	2.43234i	−0.0514847	−	0.0891741i
$745$	22.6699	−	17.1069i	0.830559	−	0.626747i
$746$	7.65344	+	7.65344i	0.280212	+	0.280212i
$747$	0.495951	−	1.85092i	0.0181459	−	0.0677215i
$748$	7.73107			0.282676
$749$	41.5578	+	23.9934i	1.51849	+	0.876699i
$750$	−17.1548	−	7.59640i	−0.626406	−	0.277381i
$751$		−	31.9929i		−	1.16744i	−0.811956	−	0.583718i	$-0.801597\pi$
$751$		−	31.9929i		−	1.16744i	0.811956	−	0.583718i	$-0.198403\pi$
$752$	10.1936	−	2.73136i	0.371721	−	0.0996024i
$753$	−16.8059	−	29.1087i	−0.612441	−	1.06078i
$754$	7.98635	+	7.98635i	0.290846	+	0.290846i
$755$	4.24002	+	1.79642i	0.154310	+	0.0653784i
$756$	6.53227	−	11.3142i	0.237576	−	0.411494i
$757$	30.5668	+	17.6478i	1.11097	+	0.641419i	0.939081	−	0.343697i	$-0.111679\pi$
$757$	30.5668	+	17.6478i	1.11097	+	0.641419i	0.171890	+	0.985116i	$0.445013\pi$
$758$	23.6555	−	13.6575i	0.859208	−	0.496064i
$759$	13.3436	+	3.57541i	0.484342	+	0.129779i
$760$	1.19010	+	2.93991i	0.0431695	+	0.106642i
$761$	37.6582	+	21.7420i	1.36511	+	0.788147i	0.990299	−	0.138954i	$-0.0443741\pi$
$761$	37.6582	+	21.7420i	1.36511	+	0.788147i	0.374811	+	0.927101i	$0.377707\pi$
$762$	−26.4097	−	15.2476i	−0.956722	−	0.552364i
$763$	−37.7283			−1.36585
$764$	1.72370	−	6.43295i	0.0623614	−	0.232736i
$765$	−0.355324	+	0.838658i	−0.0128468	+	0.0303218i
$766$	−21.8765			−0.790430
$767$	6.44559	−	6.44559i	0.232737	−	0.232737i
$768$	−1.62090	+	0.434319i	−0.0584892	+	0.0156721i
$769$	−33.4001	−	33.4001i	−1.20444	−	1.20444i	−0.972803	−	0.231635i	$-0.925593\pi$
$769$	−33.4001	−	33.4001i	−1.20444	−	1.20444i	−0.231635	−	0.972803i	$-0.574407\pi$
$770$	18.9150	+	2.64536i	0.681648	+	0.0953321i
$771$	29.2308	−	29.2308i	1.05272	−	1.05272i
$772$	−7.61759	−	13.1941i	−0.274163	−	0.474865i
$773$	−18.3598	−	4.91951i	−0.660358	−	0.176942i	−0.0869502	−	0.996213i	$-0.527712\pi$
$773$	−18.3598	−	4.91951i	−0.660358	−	0.176942i	−0.573407	+	0.819270i	$0.694379\pi$
$774$	1.58626	−	0.915827i	0.0570169	−	0.0329187i
$775$	4.06701	+	7.31387i	0.146091	+	0.262722i
$776$		−	10.8299i		−	0.388770i
$777$	18.5862	+	16.6574i	0.666777	+	0.597580i
$778$	−11.1478	+	11.1478i	−0.399668	+	0.399668i
$779$	4.43302	−	1.18782i	0.158829	−	0.0425582i
$780$	−1.54082	+	11.0173i	−0.0551703	+	0.394482i
$781$	−16.8292	+	9.71635i	−0.602197	+	0.347678i
$782$	−4.51685	+	2.60781i	−0.161522	+	0.0932550i
$783$	20.3551			0.727431
$784$	−0.884516	+	0.510676i	−0.0315899	+	0.0182384i
$785$	−32.7756	−	25.5716i	−1.16981	−	0.912691i
$786$	1.10342	−	1.91117i	0.0393575	−	0.0681693i
$787$	20.7014	+	20.7014i	0.737927	+	0.737927i	0.972176	−	0.234250i	$-0.0752634\pi$
$787$	20.7014	+	20.7014i	0.737927	+	0.737927i	−0.234250	+	0.972176i	$0.575263\pi$
$788$	12.9680	+	12.9680i	0.461966	+	0.461966i
$789$	18.3998	+	10.6231i	0.655050	+	0.378194i
$790$	33.9214	+	4.74408i	1.20687	+	0.168787i
$791$	−6.97364	+	6.97364i	−0.247954	+	0.247954i
$792$	−0.321464	+	0.556791i	−0.0114227	+	0.0197847i
$793$	2.88291	+	10.7592i	0.102375	+	0.382069i
$794$	7.35967	+	27.4667i	0.261185	+	0.974755i
$795$	−19.5277	−	25.8780i	−0.692577	−	0.917796i
$796$	0.662025	−	2.47071i	0.0234648	−	0.0875720i
$797$	18.7732	−	32.5161i	0.664980	−	1.15178i	−0.314310	−	0.949320i	$-0.601773\pi$
$797$	18.7732	−	32.5161i	0.664980	−	1.15178i	0.979291	−	0.202459i	$-0.0648934\pi$
$798$	−5.62159	+	1.50630i	−0.199002	+	0.0533225i
$799$	−6.04495	−	22.5600i	−0.213855	−	0.798117i
$800$	4.84985	−	1.21613i	0.171468	−	0.0429968i
$801$	1.44937	+	0.388357i	0.0512109	+	0.0137219i
$802$	−4.56259	−	17.0278i	−0.161111	−	0.601273i
$803$	−21.9454	+	21.9454i	−0.774435	+	0.774435i
$804$	13.2386			0.466891
$805$	−11.9433	+	4.83477i	−0.420947	+	0.170403i
$806$	3.50873	−	3.50873i	0.123590	−	0.123590i
$807$	−48.9953	−	13.1283i	−1.72472	−	0.462136i
$808$		−	5.97730i		−	0.210281i
$809$	−11.3061	+	42.1949i	−0.397501	+	1.48350i	0.419976	+	0.907535i	$0.362038\pi$
$809$	−11.3061	+	42.1949i	−0.397501	+	1.48350i	−0.817478	+	0.575960i	$0.804628\pi$
$810$	11.3328	+	15.0181i	0.398193	+	0.527682i
$811$	7.61395	+	13.1877i	0.267362	+	0.463084i	0.968180	−	0.250256i	$-0.0805148\pi$
$811$	7.61395	+	13.1877i	0.267362	+	0.463084i	−0.700818	+	0.713340i	$0.747181\pi$
$812$	8.06701	+	4.65749i	0.283096	+	0.163446i
$813$	−18.8203	−	18.8203i	−0.660056	−	0.660056i
$814$	−15.8235	−	14.1814i	−0.554614	−	0.497057i
$815$	6.16203	+	49.9083i	0.215847	+	1.74821i
$816$	0.961220	+	3.58732i	0.0336494	+	0.125581i
$817$	−13.6349	−	3.65347i	−0.477026	−	0.127819i
$818$	9.14453	−	34.1278i	0.319731	−	1.19325i
$819$	1.28874	+	0.345316i	0.0450321	+	0.0120663i
$820$	−0.886554	−	7.18048i	−0.0309598	−	0.250753i
$821$	−24.1313	−	41.7967i	−0.842189	−	1.45871i	−0.888040	−	0.459766i	$-0.847933\pi$
$821$	−24.1313	−	41.7967i	−0.842189	−	1.45871i	0.0458512	−	0.998948i	$-0.485400\pi$
$822$		−	2.70834i		−	0.0944640i
$823$	−10.2115	−	38.1099i	−0.355951	−	1.32843i	−0.879284	−	0.476298i	$-0.841978\pi$
$823$	−10.2115	−	38.1099i	−0.355951	−	1.32843i	0.523333	−	0.852128i	$-0.324688\pi$
$824$		−	4.06301i		−	0.141542i
$825$	−15.0617	+	25.1434i	−0.524381	+	0.875381i
$826$	3.75895	−	6.51069i	0.130791	−	0.226536i
$827$	15.7414	−	9.08828i	0.547381	−	0.316030i	−0.200684	−	0.979656i	$-0.564317\pi$
$827$	15.7414	−	9.08828i	0.547381	−	0.316030i	0.748065	+	0.663626i	$0.230983\pi$
$828$		−	0.433738i		−	0.0150734i
$829$	−7.66475	+	2.05376i	−0.266208	+	0.0713302i	−0.389454	−	0.921046i	$-0.627336\pi$
$829$	−7.66475	+	2.05376i	−0.266208	+	0.0713302i	0.123246	+	0.992376i	$0.460670\pi$
$830$	8.73553	+	21.5794i	0.303215	+	0.749032i
$831$	−6.86541	+	1.83958i	−0.238158	+	0.0638144i
$832$	−1.48236	−	2.56752i	−0.0513915	−	0.0890127i
$833$	1.13021	+	1.95758i	0.0391595	+	0.0678262i
$834$	−20.9667	+	5.61800i	−0.726016	+	0.194535i
$835$	−1.32479	−	0.561289i	−0.0458462	−	0.0194242i
$836$	4.78598	−	1.28240i	0.165527	−	0.0443527i
$837$		−	8.94282i		−	0.309109i
$838$	−20.5291	+	11.8525i	−0.709166	+	0.409437i
$839$	13.3280	−	23.0848i	0.460135	−	0.796977i	−0.538832	−	0.842413i	$-0.681134\pi$
$839$	13.3280	−	23.0848i	0.460135	−	0.796977i	0.998967	+	0.0454359i	$0.0144677\pi$
$840$	1.12426	+	9.10571i	0.0387905	+	0.314177i
$841$		−	14.4869i		−	0.499548i
$842$	−2.70266	−	10.0865i	−0.0931398	−	0.347603i
$843$			27.1054i			0.933559i
$844$	0.494303	+	0.856158i	0.0170146	+	0.0294702i
$845$	9.34393	−	1.15367i	0.321441	−	0.0396874i
$846$	1.87613	+	0.502707i	0.0645026	+	0.0172834i
$847$	0.761039	−	2.84024i	0.0261496	−	0.0975917i
$848$	8.34541	+	2.23615i	0.286583	+	0.0767896i
$849$	7.16717	+	26.7483i	0.245977	+	0.917998i
$850$	−2.69150	−	10.7335i	−0.0923178	−	0.368157i
$851$	14.0284	+	2.94791i	0.480889	+	0.101053i
$852$	−6.60093	−	6.60093i	−0.226144	−	0.226144i
$853$	41.1535	+	23.7600i	1.40907	+	0.813526i	0.995298	−	0.0968561i	$-0.0308787\pi$
$853$	41.1535	+	23.7600i	1.40907	+	0.813526i	0.413769	+	0.910382i	$0.364212\pi$
$854$	4.59328	+	7.95579i	0.157179	+	0.272242i
$855$	−0.0808528	+	0.578118i	−0.00276511	+	0.0197712i
$856$	5.07945	−	18.9567i	0.173612	−	0.647928i
$857$			50.7542i			1.73373i	0.498543	+	0.866865i	$0.333869\pi$
$857$			50.7542i			1.73373i	−0.498543	+	0.866865i	$0.666131\pi$
$858$	16.7867	+	4.49798i	0.573088	+	0.153558i
$859$	−0.540804	+	0.540804i	−0.0184520	+	0.0184520i	−0.716273	−	0.697821i	$-0.754153\pi$
$859$	−0.540804	+	0.540804i	−0.0184520	+	0.0184520i	0.697821	+	0.716273i	$0.254153\pi$
$860$	−8.68124	+	20.4900i	−0.296028	+	0.698704i
$861$	13.2760			0.452446
$862$	−4.97557	+	4.97557i	−0.169469	+	0.169469i
$863$	−3.38764	−	12.6429i	−0.115317	−	0.430368i	0.883994	−	0.467499i	$-0.154845\pi$
$863$	−3.38764	−	12.6429i	−0.115317	−	0.430368i	−0.999310	+	0.0371310i	$0.988178\pi$
$864$	−5.16103	−	1.38289i	−0.175582	−	0.0470470i
$865$	−5.05327	−	3.94258i	−0.171816	−	0.134052i
$866$	−4.94233	−	18.4450i	−0.167947	−	0.626787i
$867$	−19.6160	+	5.25608i	−0.666193	+	0.178506i
$868$	2.04623	−	3.54417i	0.0694534	−	0.120297i
$869$	13.8489	−	51.6849i	0.469793	−	1.75329i
$870$	−11.4105	+	8.61049i	−0.386853	+	0.291923i
$871$	6.05355	+	22.5922i	0.205117	+	0.765506i
$872$	3.99357	+	14.9042i	0.135239	+	0.504720i
$873$	0.996619	−	1.72620i	0.0337305	−	0.0584229i
$874$	−2.36362	+	2.36362i	−0.0799507	+	0.0799507i
$875$	−2.91237	−	27.1818i	−0.0984560	−	0.918912i
$876$	−12.9115	−	7.45444i	−0.436238	−	0.251862i
$877$	−35.1143	−	35.1143i	−1.18573	−	1.18573i	−0.978238	−	0.207488i	$-0.933471\pi$
$877$	−35.1143	−	35.1143i	−1.18573	−	1.18573i	−0.207488	−	0.978238i	$-0.566529\pi$
$878$	−22.0979	−	22.0979i	−0.745768	−	0.745768i
$879$	−11.5406	+	19.9889i	−0.389254	+	0.674208i
$880$	−0.957143	−	7.75221i	−0.0322653	−	0.261327i
$881$	17.6111	−	10.1678i	0.593333	−	0.342561i	−0.173081	−	0.984908i	$-0.555372\pi$
$881$	17.6111	−	10.1678i	0.593333	−	0.342561i	0.766414	+	0.642346i	$0.222039\pi$
$882$	−0.187980			−0.00632961
$883$	−4.07596	+	2.35326i	−0.137167	+	0.0791935i	−0.567013	−	0.823709i	$-0.691901\pi$
$883$	−4.07596	+	2.35326i	−0.137167	+	0.0791935i	0.429846	+	0.902902i	$0.358568\pi$
$884$	−5.68234	+	3.28070i	−0.191118	+	0.110342i
$885$	6.94932	+	9.20917i	0.233599	+	0.309563i
$886$	27.0688	−	7.25307i	0.909395	−	0.243672i
$887$	−30.0936	+	30.0936i	−1.01044	+	1.01044i	−0.0104992	+	0.999945i	$0.503342\pi$
$887$	−30.0936	+	30.0936i	−1.01044	+	1.01044i	−0.999945	+	0.0104992i	$0.996658\pi$
$888$	4.61298	−	9.10552i	0.154801	−	0.305561i
$889$		−	44.4346i		−	1.49029i
$890$	−16.8978	+	6.84039i	−0.566417	+	0.229290i
$891$	25.4541	−	14.6959i	0.852744	−	0.492332i
$892$	−12.7290	−	3.41073i	−0.426200	−	0.114200i
$893$	−7.48434	−	12.9633i	−0.250454	−	0.433799i
$894$	15.0707	−	15.0707i	0.504039	−	0.504039i
$895$	0.206134	−	1.47391i	0.00689029	−	0.0492673i
$896$	−1.72897	−	1.72897i	−0.0577607	−	0.0577607i
$897$	−11.3248	+	3.03447i	−0.378124	+	0.101318i
$898$	−13.4847	+	13.4847i	−0.449990	+	0.449990i
$899$	6.37621			0.212658
$900$	0.884942	+	0.252466i	0.0294981	+	0.00841552i
$901$	4.94896	−	18.4698i	0.164874	−	0.615318i
$902$	−11.3026			−0.376336
$903$	−35.3632	−	20.4170i	−1.17682	−	0.679435i
$904$	3.49304	+	2.01671i	0.116177	+	0.0670747i
$905$	5.50922	−	13.0032i	0.183133	−	0.432241i
$906$	3.33802	+	0.894421i	0.110898	+	0.0297151i
$907$	−37.2384	+	21.4996i	−1.23648	+	0.713883i	−0.968373	−	0.249506i	$-0.919732\pi$
$907$	−37.2384	+	21.4996i	−1.23648	+	0.713883i	−0.268108	+	0.963389i	$0.586398\pi$
$908$	−14.2263	−	8.21358i	−0.472118	−	0.272577i
$909$	0.550061	−	0.952734i	0.0182444	−	0.0316002i
$910$	−15.0251	+	6.08229i	−0.498077	+	0.201626i
$911$	8.75535	+	8.75535i	0.290078	+	0.290078i	0.837111	−	0.547033i	$-0.184243\pi$
$911$	8.75535	+	8.75535i	0.290078	+	0.290078i	−0.547033	+	0.837111i	$0.684243\pi$
$912$	1.19010	+	2.06132i	0.0394082	+	0.0682570i
$913$	35.1298	−	9.41301i	1.16263	−	0.311525i
$914$		−	32.8964i		−	1.08812i
$915$	−13.9915	+	1.72749i	−0.462544	+	0.0571090i
$916$	−7.10267	−	4.10073i	−0.234679	−	0.135492i
$917$	3.21557			0.106188
$918$	−3.06057	+	11.4222i	−0.101014	+	0.376989i
$919$	−23.4173	−	23.4173i	−0.772465	−	0.772465i	0.206072	−	0.978537i	$-0.433932\pi$
$919$	−23.4173	−	23.4173i	−0.772465	−	0.772465i	−0.978537	+	0.206072i	$0.933932\pi$
$920$	3.17414	+	4.20634i	0.104648	+	0.138679i
$921$	−6.65150	−	11.5207i	−0.219174	−	0.379621i
$922$	−9.39475	+	35.0617i	−0.309400	+	1.15470i
$923$	8.24633	−	14.2831i	0.271431	−	0.470133i
$924$	14.3331			0.471524
$925$	−14.1801	+	26.9059i	−0.466237	+	0.884660i
$926$	23.9344			0.786533
$927$	0.373899	−	0.647612i	0.0122805	−	0.0212704i
$928$	0.985999	−	3.67980i	0.0323670	−	0.120795i
$929$	21.0299	+	36.4248i	0.689967	+	1.19506i	0.971848	+	0.235609i	$0.0757085\pi$
$929$	21.0299	+	36.4248i	0.689967	+	1.19506i	−0.281881	+	0.959449i	$0.590958\pi$
$930$	3.78294	+	5.01312i	0.124048	+	0.164387i
$931$	1.02438	+	1.02438i	0.0335727	+	0.0335727i
$932$	7.35571	−	27.4519i	0.240944	−	0.899216i
$933$	44.5366			1.45806
$934$	23.6912	+	13.6781i	0.775200	+	0.447562i
$935$	−17.1569	+	2.11832i	−0.561091	+	0.0692763i
$936$		−	0.545656i		−	0.0178353i
$937$	−46.8805	+	12.5616i	−1.53152	+	0.410370i	−0.923515	−	0.383563i	$-0.874697\pi$
$937$	−46.8805	+	12.5616i	−1.53152	+	0.410370i	−0.608005	+	0.793933i	$0.708030\pi$
$938$	9.64501	+	16.7056i	0.314921	+	0.545459i
$939$	26.2802	+	26.2802i	0.857621	+	0.857621i
$940$	−21.8733	+	8.85451i	−0.713430	+	0.288802i
$941$	−5.95047	+	10.3065i	−0.193980	+	0.335983i	−0.946566	−	0.322512i	$-0.895473\pi$
$941$	−5.95047	+	10.3065i	−0.193980	+	0.335983i	0.752586	+	0.658494i	$0.228806\pi$
$942$	−27.0177	−	15.5987i	−0.880284	−	0.508232i
$943$	6.60353	−	3.81255i	0.215040	−	0.124154i
$944$	−2.96988	−	0.795776i	−0.0966613	−	0.0259003i
$945$	−11.3964	+	26.8985i	−0.370725	+	0.875010i
$946$	30.1067	+	17.3821i	0.978855	+	0.565142i
$947$	4.52858	+	2.61458i	0.147159	+	0.0849623i	0.571772	−	0.820413i	$-0.306256\pi$
$947$	4.52858	+	2.61458i	0.147159	+	0.0849623i	−0.424613	+	0.905375i	$0.639590\pi$
$948$	25.7044			0.834839
$949$	6.81729	−	25.4425i	0.221299	−	0.825897i
$950$	−3.44663	−	6.19821i	−0.111823	−	0.201097i
$951$	8.64091			0.280201
$952$	−3.82649	+	3.82649i	−0.124017	+	0.124017i
$953$	28.2640	−	7.57331i	0.915560	−	0.245324i	0.229874	−	0.973220i	$-0.426169\pi$
$953$	28.2640	−	7.57331i	0.915560	−	0.245324i	0.685687	+	0.727897i	$0.259502\pi$
$954$	1.12441	+	1.12441i	0.0364042	+	0.0364042i
$955$	−2.06264	+	14.7484i	−0.0667455	+	0.477247i
$956$	−6.36836	+	6.36836i	−0.205967	+	0.205967i
$957$	11.1658	+	19.3397i	0.360938	+	0.625163i
$958$	−20.7904	−	5.57077i	−0.671707	−	0.179983i
$959$	3.41761	−	1.97316i	0.110360	−	0.0637165i
$960$	3.47813	−	1.40797i	0.112256	−	0.0454422i
$961$			28.1987i			0.909635i
$962$	17.6482	+	3.70857i	0.569001	+	0.119569i
$963$	2.55412	−	2.55412i	0.0823054	−	0.0823054i
$964$	−24.2676	+	6.50247i	−0.781605	+	0.209430i
$965$	20.5203	+	27.1933i	0.660571	+	0.875382i
$966$	−8.37406	+	4.83477i	−0.269431	+	0.155556i
$967$	0.973490	−	0.562044i	0.0313053	−	0.0180741i	−0.484266	−	0.874921i	$-0.660913\pi$
$967$	0.973490	−	0.562044i	0.0313053	−	0.0180741i	0.515571	+	0.856847i	$0.327580\pi$
$968$	−1.20257			−0.0386520
$969$	4.56203	−	2.63389i	0.146554	−	0.0846128i
$970$	2.96739	+	24.0338i	0.0952771	+	0.771680i
$971$	18.2601	−	31.6274i	0.585994	−	1.01497i	−0.408757	−	0.912643i	$-0.634038\pi$
$971$	18.2601	−	31.6274i	0.585994	−	1.01497i	0.994751	−	0.102328i	$-0.0326291\pi$
$972$	−1.35054	−	1.35054i	−0.0433185	−	0.0433185i
$973$	−22.3645	−	22.3645i	−0.716973	−	0.716973i
$974$	−15.9758	−	9.22366i	−0.511899	−	0.295545i
$975$	0.400685	−	24.8719i	0.0128322	−	0.796539i
$976$	2.65666	−	2.65666i	0.0850377	−	0.0850377i
$977$	0.173185	−	0.299965i	0.00554067	−	0.00959672i	−0.863242	−	0.504791i	$-0.831570\pi$
$977$	0.173185	−	0.299965i	0.00554067	−	0.00959672i	0.868782	+	0.495194i	$0.164903\pi$
$978$	9.76746	+	36.4527i	0.312329	+	1.16563i
$979$	7.37090	+	27.5086i	0.235575	+	0.879177i
$980$	1.82301	−	1.37566i	0.0582339	−	0.0439438i
$981$	−0.735017	+	2.74312i	−0.0234673	+	0.0875812i
$982$	5.84251	−	10.1195i	0.186442	−	0.322927i
$983$	−23.7215	+	6.35616i	−0.756599	+	0.202730i	−0.616443	−	0.787399i	$-0.711427\pi$
$983$	−23.7215	+	6.35616i	−0.756599	+	0.202730i	−0.140156	+	0.990129i	$0.544760\pi$
$984$	−1.40528	−	5.24457i	−0.0447987	−	0.167191i
$985$	−32.3321	−	25.2256i	−1.03019	−	0.803754i
$986$	−8.14400	−	2.18218i	−0.259358	−	0.0694947i
$987$	−11.2071	−	41.8254i	−0.356725	−	1.33132i
$988$	−2.97351	+	2.97351i	−0.0946000	+	0.0946000i
$989$	−23.4530			−0.745763
$990$	0.560836	−	1.32372i	0.0178246	−	0.0420706i
$991$	13.9031	−	13.9031i	0.441647	−	0.441647i	−0.450918	−	0.892565i	$-0.648903\pi$
$991$	13.9031	−	13.9031i	0.441647	−	0.441647i	0.892565	+	0.450918i	$0.148903\pi$
$992$	−1.61669	−	0.433190i	−0.0513298	−	0.0137538i
$993$		−	19.1674i		−	0.608258i
$994$	3.52051	−	13.1387i	0.111664	−	0.416735i
$995$	−0.792201	+	5.66443i	−0.0251145	+	0.179575i
$996$	8.73553	+	15.1304i	0.276796	+	0.479424i
$997$	−20.9480	−	12.0943i	−0.663429	−	0.383031i	0.130153	−	0.991494i	$-0.458453\pi$
$997$	−20.9480	−	12.0943i	−0.663429	−	0.383031i	−0.793582	+	0.608463i	$0.791786\pi$
$998$	25.2634	+	25.2634i	0.799697	+	0.799697i
$999$	27.2164	−	17.7642i	0.861088	−	0.562035i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.q.d.97.2	✓	12
5.3	odd	4		370.2.r.d.23.2	yes	12
37.29	odd	12		370.2.r.d.177.2	yes	12
185.103	even	12	inner	370.2.q.d.103.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.q.d.97.2	✓	12	1.1	even	1	trivial
370.2.q.d.103.2	yes	12	185.103	even	12	inner
370.2.r.d.23.2	yes	12	5.3	odd	4
370.2.r.d.177.2	yes	12	37.29	odd	12

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.q (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.434319 - 1.62090i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.34690 + 1.78490i) q^{5} +(1.18658 + 1.18658i) q^{6} +(-0.632846 + 2.36181i) q^{7} +1.00000 q^{8} +(0.159392 + 0.0920251i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.434319 - 1.62090i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.34690 + 1.78490i) q^{5} +(1.18658 + 1.18658i) q^{6} +(-0.632846 + 2.36181i) q^{7} +1.00000 q^{8} +(0.159392 + 0.0920251i) q^{9} +(-2.21922 + 0.274000i) q^{10} +3.49322i q^{11} +(-1.62090 + 0.434319i) q^{12} +(-1.48236 - 2.56752i) q^{13} +(-1.72897 - 1.72897i) q^{14} +(3.47813 - 1.40797i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.91666 + 1.10658i) q^{17} +(-0.159392 + 0.0920251i) q^{18} +(1.37008 + 0.367111i) q^{19} +(0.872317 - 2.05890i) q^{20} +(3.55340 + 2.05156i) q^{21} +(-3.02521 - 1.74661i) q^{22} +2.35663 q^{23} +(0.434319 - 1.62090i) q^{24} +(-1.37172 + 4.80816i) q^{25} +2.96472 q^{26} +(3.77813 - 3.77813i) q^{27} +(2.36181 - 0.632846i) q^{28} +(2.69380 + 2.69380i) q^{29} +(-0.519721 + 3.71613i) q^{30} +(1.18350 - 1.18350i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(5.66216 + 1.51717i) q^{33} +(-1.91666 + 1.10658i) q^{34} +(-5.06797 + 2.05156i) q^{35} -0.184050i q^{36} +(5.95275 + 1.25090i) q^{37} +(-1.00297 + 1.00297i) q^{38} +(-4.80551 + 1.28763i) q^{39} +(1.34690 + 1.78490i) q^{40} +(2.80211 - 1.61780i) q^{41} +(-3.55340 + 2.05156i) q^{42} -9.95193 q^{43} +(3.02521 - 1.74661i) q^{44} +(0.0504298 + 0.408447i) q^{45} +(-1.17832 + 2.04090i) q^{46} +(-7.46221 - 7.46221i) q^{47} +(1.18658 + 1.18658i) q^{48} +(0.884516 + 0.510676i) q^{49} +(-3.47813 - 3.59203i) q^{50} +(2.62610 - 2.62610i) q^{51} +(-1.48236 + 2.56752i) q^{52} +(-2.23615 - 8.34541i) q^{53} +(1.38289 + 5.16103i) q^{54} +(-6.23504 + 4.70501i) q^{55} +(-0.632846 + 2.36181i) q^{56} +(1.19010 - 2.06132i) q^{57} +(-3.67980 + 0.985999i) q^{58} +(0.795776 + 2.96988i) q^{59} +(-2.95840 - 2.30816i) q^{60} +(-3.62907 - 0.972406i) q^{61} +(0.433190 + 1.61669i) q^{62} +(-0.318216 + 0.318216i) q^{63} +1.00000 q^{64} +(2.58617 - 6.10405i) q^{65} +(-4.14499 + 4.14499i) q^{66} +(-7.62035 - 2.04187i) q^{67} -2.21317i q^{68} +(1.02353 - 3.81986i) q^{69} +(0.757284 - 5.41477i) q^{70} +(2.78149 + 4.81768i) q^{71} +(0.159392 + 0.0920251i) q^{72} +(6.28228 + 6.28228i) q^{73} +(-4.05969 + 4.52978i) q^{74} +(7.19778 + 4.31170i) q^{75} +(-0.367111 - 1.37008i) q^{76} +(-8.25032 - 2.21067i) q^{77} +(1.28763 - 4.80551i) q^{78} +(-14.7958 - 3.96452i) q^{79} +(-2.21922 + 0.274000i) q^{80} +(-4.20699 - 7.28672i) q^{81} +3.23559i q^{82} +(-2.69465 - 10.0566i) q^{83} -4.10312i q^{84} +(0.606408 + 4.91150i) q^{85} +(4.97597 - 8.61863i) q^{86} +(5.53635 - 3.19641i) q^{87} +3.49322i q^{88} +(7.87485 - 2.11006i) q^{89} +(-0.378941 - 0.160550i) q^{90} +(7.00210 - 1.87621i) q^{91} +(-1.17832 - 2.04090i) q^{92} +(-1.40431 - 2.43234i) q^{93} +(10.1936 - 2.73136i) q^{94} +(1.19010 + 2.93991i) q^{95} +(-1.62090 + 0.434319i) q^{96} -10.8299i q^{97} +(-0.884516 + 0.510676i) q^{98} +(-0.321464 + 0.556791i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{4} + 2 q^{5} + 6 q^{6} - 4 q^{7} + 12 q^{8} + 18 q^{9}+O(q^{10}) \) 12 * q - 6 * q^2 - 6 * q^4 + 2 * q^5 + 6 * q^6 - 4 * q^7 + 12 * q^8 + 18 * q^9	\( 12 q - 6 q^{2} - 6 q^{4} + 2 q^{5} + 6 q^{6} - 4 q^{7} + 12 q^{8} + 18 q^{9} - 4 q^{10} - 6 q^{12} + 8 q^{14} - 10 q^{15} - 6 q^{16} - 12 q^{17} - 18 q^{18} - 8 q^{19} + 2 q^{20} + 54 q^{21} - 6 q^{22} - 4 q^{23} - 14 q^{25} + 18 q^{27} - 4 q^{28} + 4 q^{29} - 4 q^{30} - 2 q^{31} - 6 q^{32} + 20 q^{33} + 12 q^{34} + 6 q^{35} + 14 q^{37} + 16 q^{38} - 30 q^{39} + 2 q^{40} + 12 q^{41} - 54 q^{42} + 44 q^{43} + 6 q^{44} - 60 q^{45} + 2 q^{46} - 28 q^{47} + 6 q^{48} + 24 q^{49} + 10 q^{50} - 8 q^{51} + 8 q^{53} - 18 q^{54} - 4 q^{56} - 28 q^{57} - 14 q^{58} + 14 q^{60} + 24 q^{61} - 14 q^{62} + 8 q^{63} + 12 q^{64} - 10 q^{65} + 8 q^{66} + 18 q^{67} - 40 q^{69} - 30 q^{70} + 18 q^{72} - 28 q^{73} + 38 q^{74} - 30 q^{75} - 8 q^{76} + 10 q^{77} + 48 q^{78} - 56 q^{79} - 4 q^{80} + 4 q^{81} + 14 q^{83} - 28 q^{85} - 22 q^{86} + 18 q^{87} - 2 q^{89} + 18 q^{90} + 38 q^{91} + 2 q^{92} - 16 q^{94} - 28 q^{95} - 6 q^{96} - 24 q^{98} + 28 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^4 + 2 * q^5 + 6 * q^6 - 4 * q^7 + 12 * q^8 + 18 * q^9 - 4 * q^10 - 6 * q^12 + 8 * q^14 - 10 * q^15 - 6 * q^16 - 12 * q^17 - 18 * q^18 - 8 * q^19 + 2 * q^20 + 54 * q^21 - 6 * q^22 - 4 * q^23 - 14 * q^25 + 18 * q^27 - 4 * q^28 + 4 * q^29 - 4 * q^30 - 2 * q^31 - 6 * q^32 + 20 * q^33 + 12 * q^34 + 6 * q^35 + 14 * q^37 + 16 * q^38 - 30 * q^39 + 2 * q^40 + 12 * q^41 - 54 * q^42 + 44 * q^43 + 6 * q^44 - 60 * q^45 + 2 * q^46 - 28 * q^47 + 6 * q^48 + 24 * q^49 + 10 * q^50 - 8 * q^51 + 8 * q^53 - 18 * q^54 - 4 * q^56 - 28 * q^57 - 14 * q^58 + 14 * q^60 + 24 * q^61 - 14 * q^62 + 8 * q^63 + 12 * q^64 - 10 * q^65 + 8 * q^66 + 18 * q^67 - 40 * q^69 - 30 * q^70 + 18 * q^72 - 28 * q^73 + 38 * q^74 - 30 * q^75 - 8 * q^76 + 10 * q^77 + 48 * q^78 - 56 * q^79 - 4 * q^80 + 4 * q^81 + 14 * q^83 - 28 * q^85 - 22 * q^86 + 18 * q^87 - 2 * q^89 + 18 * q^90 + 38 * q^91 + 2 * q^92 - 16 * q^94 - 28 * q^95 - 6 * q^96 - 24 * q^98 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more