LMFDB - Embedded newform 368.2.j.c.93.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [368,2,Mod(93,368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(368, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("368.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.j (of order $4$, degree $2$, 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:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.221124989353984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 2 x^{10} + 2 x^{9} + 12 x^{8} - 8 x^{7} - 14 x^{6} - 16 x^{5} + 48 x^{4} + 16 x^{3} + \cdots + 64 $ x^12 - 2x^11 - 2x^10 + 2x^9 + 12x^8 - 8x^7 - 14x^6 - 16x^5 + 48x^4 + 16x^3 - 32x^2 - 64*x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			93.1
Root			$-1.14441 - 0.830857i$ of defining polynomial
Character	$\chi$	$=$	368.93
Dual form			368.2.j.c.277.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40983 - 0.111202i) q^{2} +(-1.70582 - 1.70582i) q^{3} +(1.97527 + 0.313554i) q^{4} +(-2.61219 + 2.61219i) q^{5} +(2.21524 + 2.59462i) q^{6} +1.66171i q^{7} +(-2.74993 - 0.661714i) q^{8} +2.81967i q^{9} +O(q^{10})$	\(q+(-1.40983 - 0.111202i) q^{2} +(-1.70582 - 1.70582i) q^{3} +(1.97527 + 0.313554i) q^{4} +(-2.61219 + 2.61219i) q^{5} +(2.21524 + 2.59462i) q^{6} +1.66171i q^{7} +(-2.74993 - 0.661714i) q^{8} +2.81967i q^{9} +(3.97323 - 3.39227i) q^{10} +(3.35563 - 3.35563i) q^{11} +(-2.83459 - 3.90433i) q^{12} +(1.50815 + 1.50815i) q^{13} +(0.184787 - 2.34274i) q^{14} +8.91186 q^{15} +(3.80337 + 1.23871i) q^{16} -0.812201 q^{17} +(0.313554 - 3.97527i) q^{18} +(-3.81967 - 3.81967i) q^{19} +(-5.97883 + 4.34071i) q^{20} +(2.83459 - 2.83459i) q^{21} +(-5.10404 + 4.35773i) q^{22} -1.00000i q^{23} +(3.56213 + 5.81967i) q^{24} -8.64704i q^{25} +(-1.95853 - 2.29395i) q^{26} +(-0.307612 + 0.307612i) q^{27} +(-0.521037 + 3.28233i) q^{28} +(-7.12138 - 7.12138i) q^{29} +(-12.5642 - 0.991020i) q^{30} +10.7058 q^{31} +(-5.22437 - 2.16932i) q^{32} -11.4482 q^{33} +(1.14507 + 0.0903187i) q^{34} +(-4.34071 - 4.34071i) q^{35} +(-0.884119 + 5.56960i) q^{36} +(3.80475 - 3.80475i) q^{37} +(4.96035 + 5.80986i) q^{38} -5.14528i q^{39} +(8.91186 - 5.45482i) q^{40} -0.765711i q^{41} +(-4.31152 + 3.68109i) q^{42} +(3.75797 - 3.75797i) q^{43} +(7.68044 - 5.57609i) q^{44} +(-7.36550 - 7.36550i) q^{45} +(-0.111202 + 1.40983i) q^{46} +2.18890 q^{47} +(-4.37486 - 8.60089i) q^{48} +4.23871 q^{49} +(-0.961571 + 12.1909i) q^{50} +(1.38547 + 1.38547i) q^{51} +(2.50612 + 3.45189i) q^{52} +(-1.48798 + 1.48798i) q^{53} +(0.467889 - 0.399475i) q^{54} +17.5311i q^{55} +(1.09958 - 4.56960i) q^{56} +13.0314i q^{57} +(9.24805 + 10.8319i) q^{58} +(9.46671 - 9.46671i) q^{59} +(17.6033 + 2.79435i) q^{60} +(0.442628 + 0.442628i) q^{61} +(-15.0933 - 1.19051i) q^{62} -4.68548 q^{63} +(7.12427 + 3.63934i) q^{64} -7.87914 q^{65} +(16.1401 + 1.27307i) q^{66} +(-7.97172 - 7.97172i) q^{67} +(-1.60431 - 0.254669i) q^{68} +(-1.70582 + 1.70582i) q^{69} +(5.63698 + 6.60238i) q^{70} -2.88774i q^{71} +(1.86581 - 7.75390i) q^{72} -7.28135i q^{73} +(-5.78716 + 4.94097i) q^{74} +(-14.7503 + 14.7503i) q^{75} +(-6.34720 - 8.74254i) q^{76} +(5.57609 + 5.57609i) q^{77} +(-0.572167 + 7.25399i) q^{78} +1.36206 q^{79} +(-13.1708 + 6.69937i) q^{80} +9.50847 q^{81} +(-0.0851489 + 1.07953i) q^{82} +(6.09040 + 6.09040i) q^{83} +(6.48788 - 4.71028i) q^{84} +(2.12162 - 2.12162i) q^{85} +(-5.71602 + 4.88023i) q^{86} +24.2956i q^{87} +(-11.4482 + 7.00729i) q^{88} +4.98060i q^{89} +(9.56508 + 11.2032i) q^{90} +(-2.50612 + 2.50612i) q^{91} +(0.313554 - 1.97527i) q^{92} +(-18.2621 - 18.2621i) q^{93} +(-3.08598 - 0.243411i) q^{94} +19.9554 q^{95} +(5.21139 + 12.6123i) q^{96} -7.46120 q^{97} +(-5.97588 - 0.471354i) q^{98} +(9.46176 + 9.46176i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 2 q^{3} - 4 q^{5} - 4 q^{8}+O(q^{10}) $ 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^5 - 4 * q^8	$ 12 q + 2 q^{2} + 2 q^{3} - 4 q^{5} - 4 q^{8} - 6 q^{10} - 4 q^{11} - 8 q^{12} + 18 q^{13} - 2 q^{14} + 8 q^{16} - 8 q^{17} - 4 q^{18} - 8 q^{19} - 32 q^{20} + 8 q^{21} - 34 q^{22} + 12 q^{24} - 14 q^{26} + 14 q^{27} + 12 q^{28} + 2 q^{29} - 30 q^{30} + 20 q^{31} - 8 q^{32} - 36 q^{33} + 10 q^{34} + 4 q^{35} + 4 q^{36} - 4 q^{37} + 24 q^{38} - 14 q^{42} + 20 q^{43} + 4 q^{44} - 20 q^{45} - 2 q^{46} - 16 q^{47} - 12 q^{48} + 52 q^{49} + 6 q^{50} - 4 q^{51} - 16 q^{53} + 16 q^{54} + 28 q^{56} + 14 q^{58} + 8 q^{59} + 48 q^{60} + 12 q^{61} - 44 q^{62} - 4 q^{63} + 24 q^{64} - 52 q^{65} + 34 q^{66} - 4 q^{67} - 16 q^{68} + 2 q^{69} + 28 q^{70} + 8 q^{72} - 26 q^{74} - 46 q^{75} - 8 q^{76} - 12 q^{77} - 44 q^{78} - 4 q^{79} + 4 q^{80} + 48 q^{81} - 6 q^{82} + 28 q^{83} + 12 q^{84} - 8 q^{85} + 44 q^{86} - 36 q^{88} + 4 q^{90} - 4 q^{92} - 14 q^{93} + 48 q^{95} + 32 q^{96} + 36 q^{97} - 2 q^{98} + 36 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^5 - 4 * q^8 - 6 * q^10 - 4 * q^11 - 8 * q^12 + 18 * q^13 - 2 * q^14 + 8 * q^16 - 8 * q^17 - 4 * q^18 - 8 * q^19 - 32 * q^20 + 8 * q^21 - 34 * q^22 + 12 * q^24 - 14 * q^26 + 14 * q^27 + 12 * q^28 + 2 * q^29 - 30 * q^30 + 20 * q^31 - 8 * q^32 - 36 * q^33 + 10 * q^34 + 4 * q^35 + 4 * q^36 - 4 * q^37 + 24 * q^38 - 14 * q^42 + 20 * q^43 + 4 * q^44 - 20 * q^45 - 2 * q^46 - 16 * q^47 - 12 * q^48 + 52 * q^49 + 6 * q^50 - 4 * q^51 - 16 * q^53 + 16 * q^54 + 28 * q^56 + 14 * q^58 + 8 * q^59 + 48 * q^60 + 12 * q^61 - 44 * q^62 - 4 * q^63 + 24 * q^64 - 52 * q^65 + 34 * q^66 - 4 * q^67 - 16 * q^68 + 2 * q^69 + 28 * q^70 + 8 * q^72 - 26 * q^74 - 46 * q^75 - 8 * q^76 - 12 * q^77 - 44 * q^78 - 4 * q^79 + 4 * q^80 + 48 * q^81 - 6 * q^82 + 28 * q^83 + 12 * q^84 - 8 * q^85 + 44 * q^86 - 36 * q^88 + 4 * q^90 - 4 * q^92 - 14 * q^93 + 48 * q^95 + 32 * q^96 + 36 * q^97 - 2 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.40983	−	0.111202i	−0.996904	−	0.0786320i
$2$	−1.40983	−	0.111202i	−0.996904	−	0.0786320i
$3$	−1.70582	−	1.70582i	−0.984858	−	0.984858i	0.0150292	−	0.999887i	$-0.495216\pi$
$3$	−1.70582	−	1.70582i	−0.984858	−	0.984858i	−0.999887	+	0.0150292i	$0.995216\pi$
$4$	1.97527	+	0.313554i	0.987634	+	0.156777i
$5$	−2.61219	+	2.61219i	−1.16821	+	1.16821i	−0.185575	+	0.982630i	$0.559415\pi$
$5$	−2.61219	+	2.61219i	−1.16821	+	1.16821i	−0.982630	+	0.185575i	$0.940585\pi$
$6$	2.21524	+	2.59462i	0.904367	+	1.05925i
$7$			1.66171i			0.628069i	0.949412	+	0.314034i	$0.101681\pi$
$7$			1.66171i			0.628069i	−0.949412	+	0.314034i	$0.898319\pi$
$8$	−2.74993	−	0.661714i	−0.972248	−	0.233951i
$9$			2.81967i			0.939890i
$10$	3.97323	−	3.39227i	1.25645	−	1.07273i
$11$	3.35563	−	3.35563i	1.01176	−	1.01176i	0.0118300	−	0.999930i	$-0.496234\pi$
$11$	3.35563	−	3.35563i	1.01176	−	1.01176i	0.999930	−	0.0118300i	$-0.00376570\pi$
$12$	−2.83459	−	3.90433i	−0.818276	−	1.12708i
$13$	1.50815	+	1.50815i	0.418286	+	0.418286i	0.884613	−	0.466327i	$-0.154423\pi$
$13$	1.50815	+	1.50815i	0.418286	+	0.418286i	−0.466327	+	0.884613i	$0.654423\pi$
$14$	0.184787	−	2.34274i	0.0493863	−	0.626124i
$15$	8.91186			2.30103
$16$	3.80337	+	1.23871i	0.950842	+	0.309677i
$17$	−0.812201			−0.196988			−0.0984938	−	0.995138i	$-0.531402\pi$
$17$	−0.812201			−0.196988			−0.0984938	+	0.995138i	$0.531402\pi$
$18$	0.313554	−	3.97527i	0.0739054	−	0.936980i
$19$	−3.81967	−	3.81967i	−0.876292	−	0.876292i	0.116857	−	0.993149i	$-0.462718\pi$
$19$	−3.81967	−	3.81967i	−0.876292	−	0.876292i	−0.993149	+	0.116857i	$0.962718\pi$
$20$	−5.97883	+	4.34071i	−1.33691	+	0.970612i
$21$	2.83459	−	2.83459i	0.618559	−	0.618559i
$22$	−5.10404	+	4.35773i	−1.08818	+	0.929071i
$23$		−	1.00000i		−	0.208514i
$23$		−	1.00000i		−	0.208514i
$24$	3.56213	+	5.81967i	0.727118	+	1.18794i
$25$		−	8.64704i		−	1.72941i
$26$	−1.95853	−	2.29395i	−0.384100	−	0.449881i
$27$	−0.307612	+	0.307612i	−0.0592000	+	0.0592000i
$28$	−0.521037	+	3.28233i	−0.0984668	+	0.620302i
$29$	−7.12138	−	7.12138i	−1.32241	−	1.32241i	−0.911823	−	0.410584i	$-0.865325\pi$
$29$	−7.12138	−	7.12138i	−1.32241	−	1.32241i	−0.410584	−	0.911823i	$-0.634675\pi$
$30$	−12.5642	−	0.991020i	−2.29391	−	0.180935i
$31$	10.7058			1.92281			0.961405	−	0.275136i	$-0.0887229\pi$
$31$	10.7058			1.92281			0.961405	+	0.275136i	$0.0887229\pi$
$32$	−5.22437	−	2.16932i	−0.923547	−	0.383484i
$33$	−11.4482			−1.99288
$34$	1.14507	+	0.0903187i	0.196378	+	0.0154895i
$35$	−4.34071	−	4.34071i	−0.733713	−	0.733713i
$36$	−0.884119	+	5.56960i	−0.147353	+	0.928267i
$37$	3.80475	−	3.80475i	0.625497	−	0.625497i	−0.321435	−	0.946932i	$-0.604165\pi$
$37$	3.80475	−	3.80475i	0.625497	−	0.625497i	0.946932	+	0.321435i	$0.104165\pi$
$38$	4.96035	+	5.80986i	0.804674	+	0.942484i
$39$		−	5.14528i		−	0.823904i
$40$	8.91186	−	5.45482i	1.40909	−	0.862483i
$41$		−	0.765711i		−	0.119584i	−0.998211	−	0.0597920i	$-0.980956\pi$
$41$		−	0.765711i		−	0.119584i	0.998211	−	0.0597920i	$-0.0190437\pi$
$42$	−4.31152	+	3.68109i	−0.665282	+	0.568005i
$43$	3.75797	−	3.75797i	0.573086	−	0.573086i	−0.359904	−	0.932989i	$-0.617190\pi$
$43$	3.75797	−	3.75797i	0.573086	−	0.573086i	0.932989	+	0.359904i	$0.117190\pi$
$44$	7.68044	−	5.57609i	1.15787	−	0.840628i
$45$	−7.36550	−	7.36550i	−1.09798	−	1.09798i
$46$	−0.111202	+	1.40983i	−0.0163959	+	0.207869i
$47$	2.18890			0.319284			0.159642	−	0.987175i	$-0.448966\pi$
$47$	2.18890			0.319284			0.159642	+	0.987175i	$0.448966\pi$
$48$	−4.37486	−	8.60089i	−0.631457	−	1.24143i
$49$	4.23871			0.605530
$50$	−0.961571	+	12.1909i	−0.135987	+	1.72405i
$51$	1.38547	+	1.38547i	0.194005	+	0.194005i
$52$	2.50612	+	3.45189i	0.347536	+	0.478691i
$53$	−1.48798	+	1.48798i	−0.204390	+	0.204390i	−0.801878	−	0.597488i	$-0.796166\pi$
$53$	−1.48798	+	1.48798i	−0.204390	+	0.204390i	0.597488	+	0.801878i	$0.296166\pi$
$54$	0.467889	−	0.399475i	0.0636717	−	0.0543617i
$55$			17.5311i			2.36389i
$56$	1.09958	−	4.56960i	0.146937	−	0.610639i
$57$			13.0314i			1.72605i
$58$	9.24805	+	10.8319i	1.21433	+	1.42230i
$59$	9.46671	−	9.46671i	1.23246	−	1.23246i	0.269444	−	0.963016i	$-0.413160\pi$
$59$	9.46671	−	9.46671i	1.23246	−	1.23246i	0.963016	−	0.269444i	$-0.0868399\pi$
$60$	17.6033	+	2.79435i	2.27258	+	0.360749i
$61$	0.442628	+	0.442628i	0.0566727	+	0.0566727i	0.734875	−	0.678202i	$-0.237241\pi$
$61$	0.442628	+	0.442628i	0.0566727	+	0.0566727i	−0.678202	+	0.734875i	$0.737241\pi$
$62$	−15.0933	−	1.19051i	−1.91686	−	0.151194i
$63$	−4.68548			−0.590316
$64$	7.12427	+	3.63934i	0.890534	+	0.454917i
$65$	−7.87914			−0.977287
$66$	16.1401	+	1.27307i	1.98671	+	0.156704i
$67$	−7.97172	−	7.97172i	−0.973901	−	0.973901i	0.0257672	−	0.999668i	$-0.491797\pi$
$67$	−7.97172	−	7.97172i	−0.973901	−	0.973901i	−0.999668	+	0.0257672i	$0.991797\pi$
$68$	−1.60431	−	0.254669i	−0.194552	−	0.0308831i
$69$	−1.70582	+	1.70582i	−0.205357	+	0.205357i
$70$	5.63698	+	6.60238i	0.673748	+	0.789135i
$71$		−	2.88774i		−	0.342712i	−0.985209	−	0.171356i	$-0.945185\pi$
$71$		−	2.88774i		−	0.342712i	0.985209	−	0.171356i	$-0.0548149\pi$
$72$	1.86581	−	7.75390i	0.219888	−	0.913806i
$73$		−	7.28135i		−	0.852218i	−0.904672	−	0.426109i	$-0.859884\pi$
$73$		−	7.28135i		−	0.852218i	0.904672	−	0.426109i	$-0.140116\pi$
$74$	−5.78716	+	4.94097i	−0.672744	+	0.574376i
$75$	−14.7503	+	14.7503i	−1.70322	+	1.70322i
$76$	−6.34720	−	8.74254i	−0.728074	−	1.00284i
$77$	5.57609	+	5.57609i	0.635455	+	0.635455i
$78$	−0.572167	+	7.25399i	−0.0647852	+	0.821353i
$79$	1.36206			0.153243			0.0766217	−	0.997060i	$-0.475587\pi$
$79$	1.36206			0.153243			0.0766217	+	0.997060i	$0.475587\pi$
$80$	−13.1708	+	6.69937i	−1.47254	+	0.749013i
$81$	9.50847			1.05650
$82$	−0.0851489	+	1.07953i	−0.00940313	+	0.119214i
$83$	6.09040	+	6.09040i	0.668508	+	0.668508i	0.957371	−	0.288863i	$-0.0932771\pi$
$83$	6.09040	+	6.09040i	0.668508	+	0.668508i	−0.288863	+	0.957371i	$0.593277\pi$
$84$	6.48788	−	4.71028i	0.707885	−	0.513934i
$85$	2.12162	−	2.12162i	0.230122	−	0.230122i
$86$	−5.71602	+	4.88023i	−0.616374	+	0.526248i
$87$			24.2956i			2.60477i
$88$	−11.4482	+	7.00729i	−1.22038	+	0.746980i
$89$			4.98060i			0.527942i	0.964531	+	0.263971i	$0.0850324\pi$
$89$			4.98060i			0.527942i	−0.964531	+	0.263971i	$0.914968\pi$
$90$	9.56508	+	11.2032i	1.00825	+	1.18092i
$91$	−2.50612	+	2.50612i	−0.262712	+	0.262712i
$92$	0.313554	−	1.97527i	0.0326903	−	0.205936i
$93$	−18.2621	−	18.2621i	−1.89370	−	1.89370i
$94$	−3.08598	−	0.243411i	−0.318295	−	0.0251059i
$95$	19.9554			2.04738
$96$	5.21139	+	12.6123i	0.531885	+	1.28724i
$97$	−7.46120			−0.757571			−0.378785	−	0.925485i	$-0.623658\pi$
$97$	−7.46120			−0.757571			−0.378785	+	0.925485i	$0.623658\pi$
$98$	−5.97588	−	0.471354i	−0.603655	−	0.0476140i
$99$	9.46176	+	9.46176i	0.950943	+	0.950943i
$100$	2.71131	−	17.0802i	0.271131	−	1.70802i
$101$	−4.78167	+	4.78167i	−0.475794	+	0.475794i	−0.903784	−	0.427989i	$-0.859222\pi$
$101$	−4.78167	+	4.78167i	−0.475794	+	0.475794i	0.427989	+	0.903784i	$0.359222\pi$
$102$	−1.79922	−	2.10735i	−0.178149	−	0.208659i
$103$		−	2.63340i		−	0.259477i	−0.991548	−	0.129738i	$-0.958586\pi$
$103$		−	2.63340i		−	0.259477i	0.991548	−	0.129738i	$-0.0414137\pi$
$104$	−3.14935	−	5.14528i	−0.308819	−	0.504536i
$105$			14.8090i			1.44521i
$106$	2.26327	−	1.93234i	0.219829	−	0.187685i
$107$	2.82518	−	2.82518i	0.273121	−	0.273121i	−0.557234	−	0.830355i	$-0.688138\pi$
$107$	2.82518	−	2.82518i	0.273121	−	0.273121i	0.830355	+	0.557234i	$0.188138\pi$
$108$	−0.704069	+	0.511163i	−0.0677491	+	0.0491867i
$109$	3.66953	+	3.66953i	0.351477	+	0.351477i	0.860659	−	0.509182i	$-0.170052\pi$
$109$	3.66953	+	3.66953i	0.351477	+	0.351477i	−0.509182	+	0.860659i	$0.670052\pi$
$110$	1.94950	−	24.7159i	0.185877	−	2.35657i
$111$	−12.9805			−1.23205
$112$	−2.05838	+	6.32011i	−0.194498	+	0.597194i
$113$	12.9321			1.21655			0.608273	−	0.793728i	$-0.291863\pi$
$113$	12.9321			1.21655			0.608273	+	0.793728i	$0.291863\pi$
$114$	1.44912	−	18.3721i	0.135722	−	1.72070i
$115$	2.61219	+	2.61219i	0.243588	+	0.243588i
$116$	−11.8337	−	16.2996i	−1.09873	−	1.51338i
$117$	−4.25249	+	4.25249i	−0.393143	+	0.393143i
$118$	−14.3992	+	12.2938i	−1.32555	+	1.13173i
$119$		−	1.34965i		−	0.123722i
$120$	−24.5070	−	5.89710i	−2.23717	−	0.538329i
$121$		−	11.5205i		−	1.04732i
$122$	−0.574811	−	0.673253i	−0.0520409	−	0.0609535i
$123$	−1.30617	+	1.30617i	−0.117773	+	0.117773i
$124$	21.1467	+	3.35683i	1.89903	+	0.301453i
$125$	9.52674	+	9.52674i	0.852097	+	0.852097i
$126$	6.60576	+	0.521037i	0.588488	+	0.0464177i
$127$	−16.2134			−1.43870			−0.719352	−	0.694646i	$-0.755561\pi$
$127$	−16.2134			−1.43870			−0.719352	+	0.694646i	$0.755561\pi$
$128$	−9.63934	−	5.92310i	−0.852005	−	0.523533i
$129$	−12.8209			−1.12882
$130$	11.1083	+	0.876180i	0.974261	+	0.0768460i
$131$	4.32736	+	4.32736i	0.378083	+	0.378083i	0.870410	−	0.492327i	$-0.163854\pi$
$131$	4.32736	+	4.32736i	0.378083	+	0.378083i	−0.492327	+	0.870410i	$0.663854\pi$
$132$	−22.6133	−	3.58964i	−1.96824	−	0.312438i
$133$	6.34720	−	6.34720i	0.550372	−	0.550372i
$134$	10.3523	+	12.1253i	0.894306	+	1.04747i
$135$		−	1.60708i		−	0.138315i
$136$	2.23350	+	0.537445i	0.191521	+	0.0460855i
$137$			11.7584i			1.00459i	0.864698	+	0.502293i	$0.167510\pi$
$137$			11.7584i			1.00459i	−0.864698	+	0.502293i	$0.832490\pi$
$138$	2.59462	−	2.21524i	0.220869	−	0.188574i
$139$	−7.86498	+	7.86498i	−0.667099	+	0.667099i	−0.957044	−	0.289944i	$-0.906363\pi$
$139$	−7.86498	+	7.86498i	−0.667099	+	0.667099i	0.289944	+	0.957044i	$0.406363\pi$
$140$	−7.21301	−	9.93511i	−0.609611	−	0.839670i
$141$	−3.73387	−	3.73387i	−0.314449	−	0.314449i
$142$	−0.321124	+	4.07124i	−0.0269481	+	0.341651i
$143$	10.1216			0.846410
$144$	−3.49274	+	10.7242i	−0.291062	+	0.893687i
$145$	37.2047			3.08968
$146$	−0.809704	+	10.2655i	−0.0670116	+	0.849579i
$147$	−7.23049	−	7.23049i	−0.596360	−	0.596360i
$148$	8.70839	−	6.32240i	0.715825	−	0.519698i
$149$	−0.992711	+	0.992711i	−0.0813261	+	0.0813261i	−0.746600	−	0.665274i	$-0.768315\pi$
$149$	−0.992711	+	0.992711i	−0.0813261	+	0.0813261i	0.665274	+	0.746600i	$0.268315\pi$
$150$	22.4358	−	19.1552i	1.83187	−	1.56402i
$151$		−	20.4191i		−	1.66168i	−0.556508	−	0.830842i	$-0.687859\pi$
$151$		−	20.4191i		−	1.66168i	0.556508	−	0.830842i	$-0.312141\pi$
$152$	7.97631	+	13.0314i	0.646964	+	1.05698i
$153$		−	2.29014i		−	0.185147i
$154$	−7.24130	−	8.48145i	−0.583520	−	0.683454i
$155$	−27.9654	+	27.9654i	−2.24624	+	2.24624i
$156$	1.61332	−	10.1633i	0.129169	−	0.813716i
$157$	12.4153	+	12.4153i	0.990847	+	0.990847i	0.999958	−	0.00911182i	$-0.00290042\pi$
$157$	12.4153	+	12.4153i	0.990847	+	0.990847i	−0.00911182	+	0.999958i	$0.502900\pi$
$158$	−1.92027	−	0.151464i	−0.152769	−	0.0120498i
$159$	5.07647			0.402590
$160$	19.3137	−	7.98038i	1.52688	−	0.630904i
$161$	1.66171			0.130961
$162$	−13.4054	−	1.05737i	−1.05323	−	0.0830744i
$163$	−5.10777	−	5.10777i	−0.400072	−	0.400072i	0.478187	−	0.878258i	$-0.341294\pi$
$163$	−5.10777	−	5.10777i	−0.400072	−	0.400072i	−0.878258	+	0.478187i	$0.841294\pi$
$164$	0.240092	−	1.51248i	0.0187480	−	0.118105i
$165$	29.9049	−	29.9049i	2.32809	−	2.32809i
$166$	−7.90919	−	9.26372i	−0.613872	−	0.719004i
$167$		−	21.0732i		−	1.63069i	−0.578972	−	0.815347i	$-0.696546\pi$
$167$		−	21.0732i		−	1.63069i	0.578972	−	0.815347i	$-0.303454\pi$
$168$	−9.67063	+	5.91925i	−0.746105	+	0.456680i
$169$		−	8.45096i		−	0.650074i
$170$	−3.22706	+	2.75520i	−0.247504	+	0.211315i
$171$	10.7702	−	10.7702i	0.823618	−	0.823618i
$172$	8.60134	−	6.24468i	0.655846	−	0.476152i
$173$	0.742883	+	0.742883i	0.0564804	+	0.0564804i	0.734783	−	0.678302i	$-0.237284\pi$
$173$	0.742883	+	0.742883i	0.0564804	+	0.0564804i	−0.678302	+	0.734783i	$0.737284\pi$
$174$	2.70173	−	34.2528i	0.204818	−	2.59670i
$175$	14.3689			1.08619
$176$	16.9193	−	8.60605i	1.27534	−	0.648705i
$177$	−32.2971			−2.42760
$178$	0.553855	−	7.02182i	0.0415132	−	0.526308i
$179$	−5.87835	−	5.87835i	−0.439369	−	0.439369i	0.452431	−	0.891799i	$-0.350557\pi$
$179$	−5.87835	−	5.87835i	−0.439369	−	0.439369i	−0.891799	+	0.452431i	$0.850557\pi$
$180$	−12.2394	−	16.8583i	−0.912268	−	1.25655i
$181$	−12.5257	+	12.5257i	−0.931028	+	0.931028i	−0.997770	−	0.0667421i	$-0.978740\pi$
$181$	−12.5257	+	12.5257i	−0.931028	+	0.931028i	0.0667421	+	0.997770i	$0.478740\pi$
$182$	3.81189	−	3.25452i	0.282556	−	0.241241i
$183$		−	1.51009i		−	0.111629i
$184$	−0.661714	+	2.74993i	−0.0487822	+	0.202728i
$185$			19.8774i			1.46142i
$186$	23.7158	+	27.7774i	1.73893	+	2.03674i
$187$	−2.72544	+	2.72544i	−0.199304	+	0.199304i
$188$	4.32366	+	0.686338i	0.315335	+	0.0500563i
$189$	−0.511163	−	0.511163i	−0.0371817	−	0.0371817i
$190$	−28.1338	−	2.21909i	−2.04104	−	0.160989i
$191$	1.64397			0.118954			0.0594768	−	0.998230i	$-0.481057\pi$
$191$	1.64397			0.118954			0.0594768	+	0.998230i	$0.481057\pi$
$192$	−5.94468	−	18.3608i	−0.429020	−	1.32508i
$193$	−19.0438			−1.37080			−0.685401	−	0.728166i	$-0.740373\pi$
$193$	−19.0438			−1.37080			−0.685401	+	0.728166i	$0.740373\pi$
$194$	10.5191	+	0.829704i	0.755225	+	0.0595693i
$195$	13.4404	+	13.4404i	0.962489	+	0.962489i
$196$	8.37258	+	1.32906i	0.598042	+	0.0949331i
$197$	12.5735	−	12.5735i	0.895824	−	0.895824i	−0.0992395	−	0.995064i	$-0.531641\pi$
$197$	12.5735	−	12.5735i	0.895824	−	0.895824i	0.995064	+	0.0992395i	$0.0316410\pi$
$198$	−12.2874	−	14.3917i	−0.873224	−	1.02277i
$199$		−	15.8114i		−	1.12084i	−0.828209	−	0.560419i	$-0.810640\pi$
$199$		−	15.8114i		−	1.12084i	0.828209	−	0.560419i	$-0.189360\pi$
$200$	−5.72186	+	23.7788i	−0.404597	+	1.68141i
$201$			27.1967i			1.91831i
$202$	7.27310	−	6.20964i	0.511734	−	0.436908i
$203$	11.8337	−	11.8337i	0.830562	−	0.830562i
$204$	2.30226	+	3.17110i	0.161190	+	0.222021i
$205$	2.00018	+	2.00018i	0.139699	+	0.139699i
$206$	−0.292841	+	3.71266i	−0.0204032	+	0.258673i
$207$	2.81967			0.195981
$208$	3.86790	+	7.60421i	0.268190	+	0.527257i
$209$	−25.6348			−1.77320
$210$	1.64679	−	20.8782i	0.113639	−	1.44073i
$211$	8.18793	+	8.18793i	0.563680	+	0.563680i	0.930351	−	0.366671i	$-0.119502\pi$
$211$	8.18793	+	8.18793i	0.563680	+	0.563680i	−0.366671	+	0.930351i	$0.619502\pi$
$212$	−3.40572	+	2.47260i	−0.233906	+	0.169819i
$213$	−4.92598	+	4.92598i	−0.337523	+	0.337523i
$214$	−4.29721	+	3.66888i	−0.293751	+	0.250799i
$215$			19.6331i			1.33896i
$216$	1.04946	−	0.642362i	0.0714070	−	0.0437072i
$217$			17.7899i			1.20766i
$218$	−4.76537	−	5.58149i	−0.322751	−	0.378026i
$219$	−12.4207	+	12.4207i	−0.839314	+	0.839314i
$220$	−5.49693	+	34.6285i	−0.370603	+	2.33466i
$221$	−1.22492	−	1.22492i	−0.0823972	−	0.0823972i
$222$	18.3003	+	1.44346i	1.22824	+	0.0968786i
$223$	−13.6729			−0.915607			−0.457804	−	0.889053i	$-0.651364\pi$
$223$	−13.6729			−0.915607			−0.457804	+	0.889053i	$0.651364\pi$
$224$	3.60478	−	8.68141i	0.240855	−	0.580051i
$225$	24.3818			1.62545
$226$	−18.2321	−	1.43808i	−1.21278	−	0.0956594i
$227$	−10.5639	−	10.5639i	−0.701148	−	0.701148i	0.263509	−	0.964657i	$-0.415120\pi$
$227$	−10.5639	−	10.5639i	−0.701148	−	0.701148i	−0.964657	+	0.263509i	$0.915120\pi$
$228$	−4.08604	+	25.7404i	−0.270604	+	1.70470i
$229$	−18.5926	+	18.5926i	−1.22863	+	1.22863i	−0.264155	+	0.964480i	$0.585093\pi$
$229$	−18.5926	+	18.5926i	−1.22863	+	1.22863i	−0.964480	+	0.264155i	$0.914907\pi$
$230$	−3.39227	−	3.97323i	−0.223680	−	0.261987i
$231$		−	19.0237i		−	1.25167i
$232$	14.8710	+	24.2956i	0.976329	+	1.59509i
$233$		−	15.7207i		−	1.02990i	−0.857220	−	0.514950i	$-0.827811\pi$
$233$		−	15.7207i		−	1.02990i	0.857220	−	0.514950i	$-0.172189\pi$
$234$	6.46819	−	5.52242i	0.422839	−	0.361012i
$235$	−5.71781	+	5.71781i	−0.372989	+	0.372989i
$236$	21.6676	−	15.7310i	1.41044	−	1.02400i
$237$	−2.32343	−	2.32343i	−0.150923	−	0.150923i
$238$	−0.150084	+	1.90278i	−0.00972849	+	0.123339i
$239$	−3.11445			−0.201457			−0.100729	−	0.994914i	$-0.532117\pi$
$239$	−3.11445			−0.201457			−0.100729	+	0.994914i	$0.532117\pi$
$240$	33.8951	+	11.0392i	2.18792	+	0.712576i
$241$	−11.6111			−0.747938			−0.373969	−	0.927441i	$-0.622003\pi$
$241$	−11.6111			−0.747938			−0.373969	+	0.927441i	$0.622003\pi$
$242$	−1.28111	+	16.2420i	−0.0823526	+	1.04407i
$243$	−15.2969	−	15.2969i	−0.981299	−	0.981299i
$244$	0.735521	+	1.01310i	0.0470869	+	0.0648568i
$245$	−11.0723	+	11.0723i	−0.707383	+	0.707383i
$246$	1.98673	−	1.69623i	0.126669	−	0.108148i
$247$		−	11.5213i		−	0.733081i
$248$	−29.4401	−	7.08415i	−1.86945	−	0.449844i
$249$		−	20.7783i		−	1.31677i
$250$	−12.3717	−	14.4905i	−0.782457	−	0.916461i
$251$	14.1075	−	14.1075i	0.890454	−	0.890454i	−0.104111	−	0.994566i	$-0.533200\pi$
$251$	14.1075	−	14.1075i	0.890454	−	0.890454i	0.994566	+	0.104111i	$0.0331998\pi$
$252$	−9.25509	−	1.46915i	−0.583016	−	0.0925479i
$253$	−3.35563	−	3.35563i	−0.210967	−	0.210967i
$254$	22.8582	+	1.80296i	1.43425	+	0.113128i
$255$	−7.23822			−0.453275
$256$	12.9312	+	9.42251i	0.808201	+	0.588907i
$257$	8.50878			0.530763			0.265382	−	0.964143i	$-0.414502\pi$
$257$	8.50878			0.530763			0.265382	+	0.964143i	$0.414502\pi$
$258$	18.0753	+	1.42571i	1.12532	+	0.0887610i
$259$	6.32240	+	6.32240i	0.392855	+	0.392855i
$260$	−15.5634	−	2.47054i	−0.965202	−	0.153216i
$261$	20.0799	−	20.0799i	1.24292	−	1.24292i
$262$	−5.61965	−	6.58208i	−0.347183	−	0.406642i
$263$			5.49050i			0.338559i	0.985568	+	0.169279i	$0.0541440\pi$
$263$			5.49050i			0.338559i	−0.985568	+	0.169279i	$0.945856\pi$
$264$	31.4818	+	7.57545i	1.93757	+	0.466237i
$265$		−	7.77377i		−	0.477539i
$266$	−9.65432	+	8.24268i	−0.591945	+	0.505391i
$267$	8.49602	−	8.49602i	0.519948	−	0.519948i
$268$	−13.2467	−	18.2459i	−0.809172	−	1.11454i
$269$	−1.16630	−	1.16630i	−0.0711108	−	0.0711108i	0.670657	−	0.741768i	$-0.266012\pi$
$269$	−1.16630	−	1.16630i	−0.0711108	−	0.0711108i	−0.741768	+	0.670657i	$0.766012\pi$
$270$	−0.178711	+	2.26572i	−0.0108760	+	0.137887i
$271$	−0.427919			−0.0259942			−0.0129971	−	0.999916i	$-0.504137\pi$
$271$	−0.427919			−0.0259942			−0.0129971	+	0.999916i	$0.504137\pi$
$272$	−3.08910	−	1.00608i	−0.187304	−	0.0610025i
$273$	8.54998			0.517468
$274$	1.30756	−	16.5774i	0.0789926	−	1.00148i
$275$	−29.0162	−	29.0162i	−1.74974	−	1.74974i
$276$	−3.90433	+	2.83459i	−0.235013	+	0.170622i
$277$	14.2225	−	14.2225i	0.854549	−	0.854549i	−0.136141	−	0.990690i	$-0.543470\pi$
$277$	14.2225	−	14.2225i	0.854549	−	0.854549i	0.990690	+	0.136141i	$0.0434699\pi$
$278$	11.9629	−	10.2137i	0.717489	−	0.612578i
$279$			30.1867i			1.80723i
$280$	9.06435	+	14.8090i	0.541698	+	0.885005i
$281$			25.6942i			1.53279i	0.642370	+	0.766395i	$0.277951\pi$
$281$			25.6942i			1.53279i	−0.642370	+	0.766395i	$0.722049\pi$
$282$	4.84893	+	5.67936i	0.288750	+	0.338201i
$283$	4.50559	−	4.50559i	0.267830	−	0.267830i	−0.560396	−	0.828225i	$-0.689351\pi$
$283$	4.50559	−	4.50559i	0.267830	−	0.267830i	0.828225	+	0.560396i	$0.189351\pi$
$284$	0.905464	−	5.70407i	0.0537294	−	0.338474i
$285$	−34.0404	−	34.0404i	−2.01638	−	2.01638i
$286$	−14.2698	−	1.12555i	−0.843789	−	0.0665549i
$287$	1.27239			0.0751070
$288$	6.11675	−	14.7310i	0.360433	−	0.868033i
$289$	−16.3403			−0.961196
$290$	−52.4525	−	4.13726i	−3.08012	−	0.242948i
$291$	12.7275	+	12.7275i	0.746099	+	0.746099i
$292$	2.28310	−	14.3826i	0.133608	−	0.841679i
$293$	14.1998	−	14.1998i	0.829559	−	0.829559i	−0.157897	−	0.987456i	$-0.550471\pi$
$293$	14.1998	−	14.1998i	0.829559	−	0.829559i	0.987456	+	0.157897i	$0.0504713\pi$
$294$	9.38974	+	10.9978i	0.547621	+	0.641407i
$295$			49.4576i			2.87953i
$296$	−12.9805	+	7.94515i	−0.754474	+	0.461802i
$297$			2.06446i			0.119792i
$298$	1.50995	−	1.28917i	0.0874691	−	0.0746794i
$299$	1.50815	−	1.50815i	0.0872186	−	0.0872186i
$300$	−33.7609	+	24.5108i	−1.94918	+	1.41513i
$301$	6.24468	+	6.24468i	0.359937	+	0.359937i
$302$	−2.27066	+	28.7876i	−0.130662	+	1.65654i
$303$	16.3134			0.937179
$304$	−9.79616	−	19.2591i	−0.561848	−	1.10458i
$305$	−2.31245			−0.132411
$306$	−0.254669	+	3.22872i	−0.0145585	+	0.184573i
$307$	8.90060	+	8.90060i	0.507984	+	0.507984i	0.913907	−	0.405923i	$-0.133050\pi$
$307$	8.90060	+	8.90060i	0.507984	+	0.507984i	−0.405923	+	0.913907i	$0.633050\pi$
$308$	9.26587	+	12.7627i	0.527972	+	0.727222i
$309$	−4.49212	+	4.49212i	−0.255548	+	0.255548i
$310$	42.5365	−	36.3168i	2.41591	−	2.06266i
$311$		−	4.52341i		−	0.256499i	−0.991742	−	0.128249i	$-0.959064\pi$
$311$		−	4.52341i		−	0.256499i	0.991742	−	0.128249i	$-0.0409358\pi$
$312$	−3.40470	+	14.1492i	−0.192753	+	0.801039i
$313$			10.0966i			0.570694i	0.958424	+	0.285347i	$0.0921089\pi$
$313$			10.0966i			0.570694i	−0.958424	+	0.285347i	$0.907891\pi$
$314$	−16.1229	−	18.8841i	−0.909866	−	1.06569i
$315$	12.2394	−	12.2394i	0.689610	−	0.689610i
$316$	2.69043	+	0.427078i	0.151348	+	0.0240250i
$317$	13.8631	+	13.8631i	0.778627	+	0.778627i	0.979597	−	0.200970i	$-0.0644094\pi$
$317$	13.8631	+	13.8631i	0.778627	+	0.778627i	−0.200970	+	0.979597i	$0.564409\pi$
$318$	−7.15698	−	0.564515i	−0.401343	−	0.0316564i
$319$	−47.7934			−2.67592
$320$	−28.1166	+	9.10329i	−1.57176	+	0.508889i
$321$	−9.63853			−0.537970
$322$	−2.34274	−	0.184787i	−0.130556	−	0.0102978i
$323$	3.10234	+	3.10234i	0.172619	+	0.172619i
$324$	18.7818	+	2.98142i	1.04343	+	0.165634i
$325$	13.0410	−	13.0410i	0.723386	−	0.723386i
$326$	6.63312	+	7.76911i	0.367374	+	0.430291i
$327$		−	12.5191i		−	0.692310i
$328$	−0.506682	+	2.10565i	−0.0279768	+	0.116265i
$329$			3.63732i			0.200532i
$330$	−45.4864	+	38.8355i	−2.50395	+	2.13782i
$331$	7.42842	−	7.42842i	0.408303	−	0.408303i	−0.472843	−	0.881146i	$-0.656772\pi$
$331$	7.42842	−	7.42842i	0.408303	−	0.408303i	0.881146	+	0.472843i	$0.156772\pi$
$332$	10.1205	+	13.9398i	0.555434	+	0.765048i
$333$	10.7281	+	10.7281i	0.587898	+	0.587898i
$334$	−2.34339	+	29.7098i	−0.128225	+	1.62565i
$335$	41.6472			2.27543
$336$	14.2922	−	7.26977i	0.779705	−	0.396598i
$337$	27.7241			1.51023			0.755113	−	0.655595i	$-0.227582\pi$
$337$	27.7241			1.51023			0.755113	+	0.655595i	$0.227582\pi$
$338$	−0.939767	+	11.9145i	−0.0511166	+	0.648061i
$339$	−22.0598	−	22.0598i	−1.19812	−	1.19812i
$340$	4.85601	−	3.52553i	0.263354	−	0.191199i
$341$	35.9245	−	35.9245i	1.94542	−	1.94542i
$342$	−16.3819	+	13.9865i	−0.885831	+	0.756305i
$343$			18.6755i			1.00838i
$344$	−12.8209	+	7.84748i	−0.691256	+	0.423108i
$345$		−	8.91186i		−	0.479798i
$346$	−0.964733	−	1.12995i	−0.0518643	−	0.0607467i
$347$	−7.58296	+	7.58296i	−0.407075	+	0.407075i	−0.880717	−	0.473643i	$-0.842939\pi$
$347$	−7.58296	+	7.58296i	−0.407075	+	0.407075i	0.473643	+	0.880717i	$0.342939\pi$
$348$	−7.61799	+	47.9904i	−0.408367	+	2.57255i
$349$	23.1963	+	23.1963i	1.24167	+	1.24167i	0.959307	+	0.282364i	$0.0911184\pi$
$349$	23.1963	+	23.1963i	1.24167	+	1.24167i	0.282364	+	0.959307i	$0.408882\pi$
$350$	−20.2578	−	1.59786i	−1.08282	−	0.0854090i
$351$	−0.927851			−0.0495250
$352$	−24.8105	+	10.2516i	−1.32240	+	0.546414i
$353$	−14.5140			−0.772500			−0.386250	−	0.922394i	$-0.626230\pi$
$353$	−14.5140			−0.772500			−0.386250	+	0.922394i	$0.626230\pi$
$354$	45.5335	+	3.59151i	2.42008	+	0.190887i
$355$	7.54333	+	7.54333i	0.400358	+	0.400358i
$356$	−1.56169	+	9.83802i	−0.0827692	+	0.521414i
$357$	−2.30226	+	2.30226i	−0.121848	+	0.121848i
$358$	7.63382	+	8.94119i	0.403460	+	0.472557i
$359$			5.94898i			0.313975i	0.987601	+	0.156988i	$0.0501783\pi$
$359$			5.94898i			0.313975i	−0.987601	+	0.156988i	$0.949822\pi$
$360$	15.3808	+	25.1285i	0.810639	+	1.32439i
$361$			10.1798i			0.535776i
$362$	19.0521	−	16.2663i	1.00135	−	0.854937i
$363$	−19.6519	+	19.6519i	−1.03146	+	1.03146i
$364$	−5.73605	+	4.16445i	−0.300651	+	0.218276i
$365$	19.0203	+	19.0203i	0.995566	+	0.995566i
$366$	−0.167926	+	2.12898i	−0.00877762	+	0.111283i
$367$	22.5189			1.17548			0.587738	−	0.809052i	$-0.300019\pi$
$367$	22.5189			1.17548			0.587738	+	0.809052i	$0.300019\pi$
$368$	1.23871	−	3.80337i	0.0645720	−	0.198264i
$369$	2.15905			0.112396
$370$	2.21042	−	28.0239i	0.114914	−	1.45689i
$371$	−2.47260	−	2.47260i	−0.128371	−	0.128371i
$372$	−30.3464	−	41.7988i	−1.57339	−	2.16717i
$373$	−3.70962	+	3.70962i	−0.192077	+	0.192077i	−0.796593	−	0.604516i	$-0.793366\pi$
$373$	−3.70962	+	3.70962i	−0.192077	+	0.192077i	0.604516	+	0.796593i	$0.293366\pi$
$374$	4.14550	−	3.53935i	0.214359	−	0.183015i
$375$		−	32.5019i		−	1.67839i
$376$	−6.01932	−	1.44842i	−0.310423	−	0.0746968i
$377$		−	21.4802i		−	1.10629i
$378$	0.663813	+	0.777498i	0.0341429	+	0.0399902i
$379$	−5.06716	+	5.06716i	−0.260282	+	0.260282i	−0.825169	−	0.564886i	$-0.808920\pi$
$379$	−5.06716	+	5.06716i	−0.260282	+	0.260282i	0.564886	+	0.825169i	$0.308920\pi$
$380$	39.4172	+	6.25709i	2.02206	+	0.320982i
$381$	27.6571	+	27.6571i	1.41692	+	1.41692i
$382$	−2.31773	−	0.182814i	−0.118585	−	0.00935355i
$383$	−15.1644			−0.774864			−0.387432	−	0.921898i	$-0.626638\pi$
$383$	−15.1644			−0.774864			−0.387432	+	0.921898i	$0.626638\pi$
$384$	6.33924	+	26.5468i	0.323498	+	1.35471i
$385$	−29.1316			−1.48468
$386$	26.8486	+	2.11771i	1.36656	+	0.107789i
$387$	10.5962	+	10.5962i	0.538637	+	0.538637i
$388$	−14.7379	−	2.33949i	−0.748202	−	0.118770i
$389$	−24.4010	+	24.4010i	−1.23718	+	1.23718i	−0.276029	+	0.961149i	$0.589018\pi$
$389$	−24.4010	+	24.4010i	−1.23718	+	1.23718i	−0.961149	+	0.276029i	$0.910982\pi$
$390$	−17.4542	−	20.4434i	−0.883827	−	1.03519i
$391$			0.812201i			0.0410748i
$392$	−11.6562	−	2.80481i	−0.588725	−	0.141664i
$393$		−	14.7634i		−	0.744716i
$394$	−19.1247	+	16.3283i	−0.963491	+	0.822610i
$395$	−3.55794	+	3.55794i	−0.179020	+	0.179020i
$396$	15.7227	+	21.6563i	0.790098	+	1.08827i
$397$	−15.6879	−	15.6879i	−0.787352	−	0.787352i	0.193707	−	0.981059i	$-0.437949\pi$
$397$	−15.6879	−	15.6879i	−0.787352	−	0.787352i	−0.981059	+	0.193707i	$0.937949\pi$
$398$	−1.75826	+	22.2914i	−0.0881337	+	1.11737i
$399$	−21.6544			−1.08408
$400$	10.7111	−	32.8879i	0.535557	−	1.64439i
$401$	22.7601			1.13659			0.568293	−	0.822826i	$-0.307604\pi$
$401$	22.7601			1.13659			0.568293	+	0.822826i	$0.307604\pi$
$402$	3.02434	−	38.3429i	0.150840	−	1.91237i
$403$	16.1459	+	16.1459i	0.804284	+	0.804284i
$404$	−10.9444	+	7.94577i	−0.544504	+	0.395317i
$405$	−24.8379	+	24.8379i	−1.23421	+	1.23421i
$406$	−17.9995	+	15.3676i	−0.893300	+	0.762682i
$407$		−	25.5346i		−	1.26571i
$408$	−2.89317	−	4.72674i	−0.143233	−	0.234009i
$409$		−	19.7572i		−	0.976929i	−0.872584	−	0.488465i	$-0.837557\pi$
$409$		−	19.7572i		−	0.976929i	0.872584	−	0.488465i	$-0.162443\pi$
$410$	−2.59750	−	3.04235i	−0.128281	−	0.150251i
$411$	20.0577	−	20.0577i	0.989374	−	0.989374i
$412$	0.825714	−	5.20167i	0.0406800	−	0.256268i
$413$	15.7310	+	15.7310i	0.774070	+	0.774070i
$414$	−3.97527	−	0.313554i	−0.195374	−	0.0154103i
$415$	−31.8185			−1.56191
$416$	−4.60749	−	11.1508i	−0.225901	−	0.546713i
$417$	26.8326			1.31400
$418$	36.1408	+	2.85065i	1.76770	+	0.139430i
$419$	13.2965	+	13.2965i	0.649578	+	0.649578i	0.952891	−	0.303313i	$-0.0980928\pi$
$419$	13.2965	+	13.2965i	0.649578	+	0.649578i	−0.303313	+	0.952891i	$0.598093\pi$
$420$	−4.64341	+	29.2517i	−0.226575	+	1.42734i
$421$	10.7611	−	10.7611i	0.524465	−	0.524465i	−0.394451	−	0.918917i	$-0.629065\pi$
$421$	10.7611	−	10.7611i	0.524465	−	0.524465i	0.918917	+	0.394451i	$0.129065\pi$
$422$	−10.6331	−	12.4541i	−0.517611	−	0.606258i
$423$			6.17197i			0.300091i
$424$	5.07647	−	3.10723i	0.246535	−	0.150900i
$425$			7.02313i			0.340672i
$426$	7.49260	−	6.39704i	0.363018	−	0.309938i
$427$	−0.735521	+	0.735521i	−0.0355943	+	0.0355943i
$428$	6.46634	−	4.69465i	0.312563	−	0.226924i
$429$	−17.2656	−	17.2656i	−0.833593	−	0.833593i
$430$	2.18324	−	27.6794i	0.105285	−	1.33482i
$431$	−30.6031			−1.47410			−0.737050	−	0.675838i	$-0.763782\pi$
$431$	−30.6031			−1.47410			−0.737050	+	0.675838i	$0.763782\pi$
$432$	−1.55100	+	0.788921i	−0.0746227	+	0.0379570i
$433$	−18.9640			−0.911352			−0.455676	−	0.890146i	$-0.650602\pi$
$433$	−18.9640			−0.911352			−0.455676	+	0.890146i	$0.650602\pi$
$434$	1.97828	−	25.0808i	0.0949605	−	1.20392i
$435$	−63.4647	−	63.4647i	−3.04290	−	3.04290i
$436$	6.09770	+	8.39889i	0.292027	+	0.402234i
$437$	−3.81967	+	3.81967i	−0.182720	+	0.182720i
$438$	18.8924	−	16.1299i	0.902712	−	0.770718i
$439$			9.69923i			0.462919i	0.972845	+	0.231460i	$0.0743501\pi$
$439$			9.69923i			0.462919i	−0.972845	+	0.231460i	$0.925650\pi$
$440$	11.6005	−	48.2092i	0.553034	−	2.29828i
$441$			11.9518i			0.569131i
$442$	1.59072	+	1.86315i	0.0756630	+	0.0886211i
$443$	−7.91936	+	7.91936i	−0.376260	+	0.376260i	−0.869751	−	0.493491i	$-0.835721\pi$
$443$	−7.91936	+	7.91936i	−0.376260	+	0.376260i	0.493491	+	0.869751i	$0.335721\pi$
$444$	−25.6399	−	4.07008i	−1.21682	−	0.193157i
$445$	−13.0103	−	13.0103i	−0.616745	−	0.616745i
$446$	19.2766	+	1.52046i	0.912772	+	0.0719960i
$447$	3.38678			0.160189
$448$	−6.04754	+	11.8385i	−0.285719	+	0.559316i
$449$	34.5114			1.62869			0.814346	−	0.580380i	$-0.197096\pi$
$449$	34.5114			1.62869			0.814346	+	0.580380i	$0.197096\pi$
$450$	−34.3743	−	2.71131i	−1.62042	−	0.127813i
$451$	−2.56944	−	2.56944i	−0.120990	−	0.120990i
$452$	25.5443	+	4.05490i	1.20150	+	0.190726i
$453$	−34.8314	+	34.8314i	−1.63652	+	1.63652i
$454$	13.7186	+	16.0680i	0.643845	+	0.754110i
$455$		−	13.0929i		−	0.613804i
$456$	8.62304	−	35.8354i	0.403811	−	1.67815i
$457$		−	33.1088i		−	1.54877i	−0.632717	−	0.774383i	$-0.718061\pi$
$457$		−	33.1088i		−	1.54877i	0.632717	−	0.774383i	$-0.281939\pi$
$458$	28.2801	−	24.1450i	1.32144	−	1.12822i
$459$	0.249843	−	0.249843i	0.0116617	−	0.0116617i
$460$	4.34071	+	5.97883i	0.202386	+	0.278764i
$461$	9.64848	+	9.64848i	0.449374	+	0.449374i	0.895147	−	0.445772i	$-0.147071\pi$
$461$	9.64848	+	9.64848i	0.449374	+	0.449374i	−0.445772	+	0.895147i	$0.647071\pi$
$462$	−2.11548	+	26.8202i	−0.0984209	+	1.24779i
$463$	26.3833			1.22613			0.613067	−	0.790031i	$-0.289935\pi$
$463$	26.3833			1.22613			0.613067	+	0.790031i	$0.289935\pi$
$464$	−18.2639	−	35.9065i	−0.847881	−	1.66692i
$465$	95.4082			4.42445
$466$	−1.74818	+	22.1636i	−0.0809830	+	1.02671i
$467$	−9.91627	−	9.91627i	−0.458870	−	0.458870i	0.439414	−	0.898285i	$-0.355186\pi$
$467$	−9.91627	−	9.91627i	−0.458870	−	0.458870i	−0.898285	+	0.439414i	$0.855186\pi$
$468$	−9.73319	+	7.06642i	−0.449917	+	0.326645i
$469$	13.2467	−	13.2467i	0.611677	−	0.611677i
$470$	8.69700	−	7.42533i	0.401163	−	0.342505i
$471$		−	42.3565i		−	1.95169i
$472$	−32.2971	+	19.7686i	−1.48659	+	0.909922i
$473$		−	25.2207i		−	1.15965i
$474$	3.01728	+	3.53402i	0.138588	+	0.162323i
$475$	−33.0288	+	33.0288i	−1.51547	+	1.51547i
$476$	0.423187	−	2.66591i	0.0193967	−	0.122192i
$477$	−4.19561	−	4.19561i	−0.192104	−	0.192104i
$478$	4.39087	+	0.346335i	0.200834	+	0.0158410i
$479$	−6.32910			−0.289184			−0.144592	−	0.989491i	$-0.546187\pi$
$479$	−6.32910			−0.289184			−0.144592	+	0.989491i	$0.546187\pi$
$480$	−46.5589	−	19.3326i	−2.12511	−	0.882410i
$481$	11.4763			0.523273
$482$	16.3698	+	1.29118i	0.745622	+	0.0588118i
$483$	−2.83459	−	2.83459i	−0.128978	−	0.128978i
$484$	3.61229	−	22.7560i	0.164195	−	1.03437i
$485$	19.4901	−	19.4901i	0.884998	−	0.884998i
$486$	19.8651	+	23.2672i	0.901099	+	1.05542i
$487$		−	43.0783i		−	1.95207i	−0.217623	−	0.976033i	$-0.569830\pi$
$487$		−	43.0783i		−	1.95207i	0.217623	−	0.976033i	$-0.430170\pi$
$488$	−0.924304	−	1.51009i	−0.0418413	−	0.0683586i
$489$			17.4259i			0.788027i
$490$	16.8414	−	14.3788i	0.760815	−	0.649570i
$491$	4.44148	−	4.44148i	0.200441	−	0.200441i	−0.599748	−	0.800189i	$-0.704732\pi$
$491$	4.44148	−	4.44148i	0.200441	−	0.200441i	0.800189	+	0.599748i	$0.204732\pi$
$492$	−2.98959	+	2.17048i	−0.134781	+	0.0978527i
$493$	5.78399	+	5.78399i	0.260498	+	0.260498i
$494$	−1.28119	+	16.2431i	−0.0576436	+	0.730811i
$495$	−49.4318			−2.22179
$496$	40.7179	+	13.2613i	1.82829	+	0.595450i
$497$	4.79861			0.215247
$498$	−2.31060	+	29.2940i	−0.103540	+	1.31269i
$499$	−7.83750	−	7.83750i	−0.350855	−	0.350855i	0.509573	−	0.860428i	$-0.329803\pi$
$499$	−7.83750	−	7.83750i	−0.350855	−	0.350855i	−0.860428	+	0.509573i	$0.829803\pi$
$500$	15.8307	+	21.8050i	0.707971	+	0.975149i
$501$	−35.9472	+	35.9472i	−1.60600	+	1.60600i
$502$	−21.4580	+	18.3204i	−0.957716	+	0.817679i
$503$			2.51611i			0.112188i	0.998425	+	0.0560939i	$0.0178646\pi$
$503$			2.51611i			0.112188i	−0.998425	+	0.0560939i	$0.982135\pi$
$504$	12.8848	+	3.10045i	0.573933	+	0.138105i
$505$		−	24.9812i		−	1.11165i
$506$	4.35773	+	5.10404i	0.193725	+	0.226902i
$507$	−14.4159	+	14.4159i	−0.640230	+	0.640230i
$508$	−32.0257	−	5.08376i	−1.42091	−	0.225556i
$509$	−18.5730	−	18.5730i	−0.823235	−	0.823235i	0.163336	−	0.986571i	$-0.447775\pi$
$509$	−18.5730	−	18.5730i	−0.823235	−	0.823235i	−0.986571	+	0.163336i	$0.947775\pi$
$510$	10.2047	+	0.804908i	0.451872	+	0.0356419i
$511$	12.0995			0.535252
$512$	−17.1831	−	14.7222i	−0.759391	−	0.650634i
$513$	2.34995			0.103753
$514$	−11.9960	−	0.946197i	−0.529120	−	0.0417350i
$515$	6.87893	+	6.87893i	0.303122	+	0.303122i
$516$	−25.3247	−	4.02004i	−1.11486	−	0.176972i
$517$	7.34513	−	7.34513i	0.323038	−	0.323038i
$518$	−8.21048	−	9.61661i	−0.360748	−	0.422530i
$519$		−	2.53446i		−	0.111250i
$520$	21.6671	+	5.21374i	0.950166	+	0.228638i
$521$		−	26.4008i		−	1.15664i	−0.815810	−	0.578320i	$-0.803708\pi$
$521$		−	26.4008i		−	1.15664i	0.815810	−	0.578320i	$-0.196292\pi$
$522$	−30.5423	+	26.0764i	−1.33680	+	1.14134i
$523$	29.1181	−	29.1181i	1.27324	−	1.27324i	0.328869	−	0.944376i	$-0.393333\pi$
$523$	29.1181	−	29.1181i	1.27324	−	1.27324i	0.944376	−	0.328869i	$-0.106667\pi$
$524$	7.19083	+	9.90456i	0.314133	+	0.432683i
$525$	−24.5108	−	24.5108i	−1.06974	−	1.06974i
$526$	0.610557	−	7.74070i	0.0266215	−	0.337510i
$527$	−8.69523			−0.378770
$528$	−43.5418	−	14.1810i	−1.89491	−	0.617148i
$529$	−1.00000			−0.0434783
$530$	−0.864462	+	10.9597i	−0.0375498	+	0.476060i
$531$	26.6930	+	26.6930i	1.15838	+	1.15838i
$532$	14.5276	−	10.5472i	0.629852	−	0.457280i
$533$	1.15481	−	1.15481i	0.0500203	−	0.0500203i
$534$	−12.9228	+	11.0332i	−0.559223	+	0.477454i
$535$			14.7598i			0.638122i
$536$	16.6467	+	27.1967i	0.719028	+	1.17472i
$537$			20.0549i			0.865431i
$538$	1.51460	+	1.77399i	0.0652990	+	0.0764822i
$539$	14.2235	−	14.2235i	0.612651	−	0.612651i
$540$	0.503906	−	3.17441i	0.0216847	−	0.136605i
$541$	−16.9801	−	16.9801i	−0.730031	−	0.730031i	0.240595	−	0.970626i	$-0.422658\pi$
$541$	−16.9801	−	16.9801i	−0.730031	−	0.730031i	−0.970626	+	0.240595i	$0.922658\pi$
$542$	0.603295	+	0.0475856i	0.0259137	+	0.00204398i
$543$	42.7333			1.83386
$544$	4.24324	+	1.76192i	0.181927	+	0.0755417i
$545$	−19.1710			−0.821194
$546$	−12.0541	−	0.950779i	−0.515866	−	0.0406896i
$547$	−1.44323	−	1.44323i	−0.0617081	−	0.0617081i	0.675579	−	0.737287i	$-0.263894\pi$
$547$	−1.44323	−	1.44323i	−0.0617081	−	0.0617081i	−0.737287	+	0.675579i	$0.763894\pi$
$548$	−3.68689	+	23.2259i	−0.157496	+	0.992163i
$549$	−1.24806	+	1.24806i	−0.0532661	+	0.0532661i
$550$	37.6814	+	44.1348i	1.60674	+	1.88191i
$551$			54.4026i			2.31763i
$552$	5.81967	−	3.56213i	0.247702	−	0.151615i
$553$			2.26335i			0.0962473i
$554$	−21.6330	+	18.4698i	−0.919098	+	0.784708i
$555$	33.9074	−	33.9074i	1.43929	−	1.43929i
$556$	−18.0015	+	13.0694i	−0.763436	+	0.554264i
$557$	5.09710	+	5.09710i	0.215971	+	0.215971i	0.806798	−	0.590827i	$-0.201198\pi$
$557$	5.09710	+	5.09710i	0.215971	+	0.215971i	−0.590827	+	0.806798i	$0.701198\pi$
$558$	3.35683	−	42.5583i	0.142106	−	1.80163i
$559$	11.3352			0.479427
$560$	−11.1324	−	21.8862i	−0.470432	−	0.924859i
$561$	9.29826			0.392573
$562$	2.85726	−	36.2246i	0.120526	−	1.52804i
$563$	6.95433	+	6.95433i	0.293090	+	0.293090i	0.838300	−	0.545210i	$-0.183550\pi$
$563$	6.95433	+	6.95433i	0.293090	+	0.293090i	−0.545210	+	0.838300i	$0.683550\pi$
$564$	−6.20463	−	8.54617i	−0.261262	−	0.359859i
$565$	−33.7809	+	33.7809i	−1.42117	+	1.42117i
$566$	−6.85317	+	5.85111i	−0.288060	+	0.245940i
$567$			15.8004i			0.663553i
$568$	−1.91086	+	7.94111i	−0.0801779	+	0.333201i
$569$		−	0.100497i		−	0.00421306i	−0.999998	−	0.00210653i	$-0.999329\pi$
$569$		−	0.100497i		−	0.00421306i	0.999998	−	0.00210653i	$-0.000670529\pi$
$570$	44.2059	+	51.7766i	1.85158	+	2.16869i
$571$	−29.6374	+	29.6374i	−1.24029	+	1.24029i	−0.280406	+	0.959881i	$0.590469\pi$
$571$	−29.6374	+	29.6374i	−1.24029	+	1.24029i	−0.959881	+	0.280406i	$0.909531\pi$
$572$	19.9928	+	3.17366i	0.835943	+	0.132698i
$573$	−2.80432	−	2.80432i	−0.117152	−	0.117152i
$574$	−1.79386	−	0.141493i	−0.0748744	−	0.00590581i
$575$	−8.64704			−0.360606
$576$	−10.2617	+	20.0881i	−0.427572	+	0.837004i
$577$	11.2586			0.468702			0.234351	−	0.972152i	$-0.424703\pi$
$577$	11.2586			0.468702			0.234351	+	0.972152i	$0.424703\pi$
$578$	23.0372	+	1.81708i	0.958220	+	0.0755807i
$579$	32.4853	+	32.4853i	1.35004	+	1.35004i
$580$	73.4893	+	11.6657i	3.05148	+	0.484392i
$581$	−10.1205	+	10.1205i	−0.419869	+	0.419869i
$582$	−16.5283	−	19.3590i	−0.685122	−	0.802456i
$583$			9.98622i			0.413587i
$584$	−4.81817	+	20.0232i	−0.199377	+	0.828568i
$585$		−	22.2166i		−	0.918542i
$586$	−21.5984	+	18.4403i	−0.892220	+	0.761761i
$587$	2.71169	−	2.71169i	0.111923	−	0.111923i	−0.648927	−	0.760850i	$-0.724782\pi$
$587$	2.71169	−	2.71169i	0.111923	−	0.111923i	0.760850	+	0.648927i	$0.224782\pi$
$588$	−12.0150	−	16.5493i	−0.495490	−	0.682482i
$589$	−40.8925	−	40.8925i	−1.68494	−	1.68494i
$590$	5.49980	−	69.7270i	0.226423	−	2.87062i
$591$	−42.8963			−1.76452
$592$	19.1838	−	9.75789i	0.788450	−	0.401047i
$593$	−11.6754			−0.479451			−0.239726	−	0.970841i	$-0.577058\pi$
$593$	−11.6754			−0.479451			−0.239726	+	0.970841i	$0.577058\pi$
$594$	0.229573	−	2.91055i	0.00941951	−	0.119421i
$595$	3.52553	+	3.52553i	0.144532	+	0.144532i
$596$	−2.27214	+	1.64960i	−0.0930704	+	0.0675703i
$597$	−26.9714	+	26.9714i	−1.10387	+	1.10387i
$598$	−2.29395	+	1.95853i	−0.0938067	+	0.0800904i
$599$			29.4312i			1.20253i	0.799051	+	0.601263i	$0.205336\pi$
$599$			29.4312i			1.20253i	−0.799051	+	0.601263i	$0.794664\pi$
$600$	50.3229	−	30.8019i	2.05442	−	1.25748i
$601$			7.06623i			0.288237i	0.989560	+	0.144119i	$0.0460347\pi$
$601$			7.06623i			0.288237i	−0.989560	+	0.144119i	$0.953965\pi$
$602$	−8.10954	−	9.49839i	−0.330520	−	0.387125i
$603$	22.4776	−	22.4776i	0.915359	−	0.915359i
$604$	6.40250	−	40.3332i	0.260514	−	1.64114i
$605$	30.0937	+	30.0937i	1.22348	+	1.22348i
$606$	−22.9992	−	1.81409i	−0.934278	−	0.0736923i
$607$	0.575135			0.0233440			0.0116720	−	0.999932i	$-0.496285\pi$
$607$	0.575135			0.0233440			0.0116720	+	0.999932i	$0.496285\pi$
$608$	11.6693	+	28.2414i	0.473253	+	1.14534i
$609$	−40.3724			−1.63597
$610$	3.26018	+	0.257150i	0.132001	+	0.0104117i
$611$	3.30119	+	3.30119i	0.133552	+	0.133552i
$612$	0.718082	−	4.52364i	0.0290268	−	0.182857i
$613$	−26.7943	+	26.7943i	−1.08221	+	1.08221i	−0.0859064	+	0.996303i	$0.527379\pi$
$613$	−26.7943	+	26.7943i	−1.08221	+	1.08221i	−0.996303	+	0.0859064i	$0.972621\pi$
$614$	−11.5586	−	13.5381i	−0.466467	−	0.546355i
$615$		−	6.82391i		−	0.275167i
$616$	−11.6441	−	19.0237i	−0.469155	−	0.766485i
$617$		−	39.6599i		−	1.59665i	−0.602229	−	0.798323i	$-0.705721\pi$
$617$		−	39.6599i		−	1.59665i	0.602229	−	0.798323i	$-0.294279\pi$
$618$	6.83268	−	5.83361i	0.274851	−	0.234662i
$619$	−14.8037	+	14.8037i	−0.595011	+	0.595011i	−0.938981	−	0.343970i	$-0.888228\pi$
$619$	−14.8037	+	14.8037i	−0.595011	+	0.595011i	0.343970	+	0.938981i	$0.388228\pi$
$620$	−64.0079	+	46.4705i	−2.57062	+	1.86630i
$621$	0.307612	+	0.307612i	0.0123440	+	0.0123440i
$622$	−0.503014	+	6.37726i	−0.0201690	+	0.255705i
$623$	−8.27633			−0.331584
$624$	6.37349	−	19.5694i	0.255144	−	0.783403i
$625$	−6.53605			−0.261442
$626$	1.12277	−	14.2346i	0.0448748	−	0.568927i
$627$	43.7284	+	43.7284i	1.74634	+	1.74634i
$628$	20.6306	+	28.4164i	0.823252	+	1.13394i
$629$	−3.09022	+	3.09022i	−0.123215	+	0.123215i
$630$	−18.6165	+	15.8944i	−0.741700	+	0.633249i
$631$		−	14.6400i		−	0.582807i	−0.956600	−	0.291404i	$-0.905878\pi$
$631$		−	14.6400i		−	0.582807i	0.956600	−	0.291404i	$-0.0941223\pi$
$632$	−3.74556	−	0.901292i	−0.148991	−	0.0358515i
$633$		−	27.9343i		−	1.11029i
$634$	−18.0030	−	21.0862i	−0.714991	−	0.837441i
$635$	42.3523	−	42.3523i	1.68070	−	1.68070i
$636$	10.0274	+	1.59175i	0.397612	+	0.0631169i
$637$	6.39261	+	6.39261i	0.253284	+	0.253284i
$638$	67.3808	+	5.31474i	2.66763	+	0.210413i
$639$	8.14248			0.322112
$640$	40.6520	−	9.70750i	1.60691	−	0.383723i
$641$	43.2014			1.70635			0.853176	−	0.521622i	$-0.174673\pi$
$641$	43.2014			1.70635			0.853176	+	0.521622i	$0.174673\pi$
$642$	13.5887	+	1.07183i	0.536305	+	0.0423017i
$643$	−10.5494	−	10.5494i	−0.416029	−	0.416029i	0.467803	−	0.883833i	$-0.345046\pi$
$643$	−10.5494	−	10.5494i	−0.416029	−	0.416029i	−0.883833	+	0.467803i	$0.845046\pi$
$644$	3.28233	+	0.521037i	0.129342	+	0.0205317i
$645$	33.4905	−	33.4905i	1.31869	−	1.31869i
$646$	−4.02880	−	4.71877i	−0.158511	−	0.185658i
$647$			28.3175i			1.11328i	0.830755	+	0.556638i	$0.187909\pi$
$647$			28.3175i			1.11328i	−0.830755	+	0.556638i	$0.812091\pi$
$648$	−26.1477	−	6.29189i	−1.02718	−	0.247169i
$649$		−	63.5335i		−	2.49391i
$650$	−19.8359	+	16.9355i	−0.778028	+	0.664265i
$651$	30.3464	−	30.3464i	1.18937	−	1.18937i
$652$	−8.48766	−	11.6908i	−0.332402	−	0.457846i
$653$	10.8329	+	10.8329i	0.423926	+	0.423926i	0.886553	−	0.462627i	$-0.153093\pi$
$653$	10.8329	+	10.8329i	0.423926	+	0.423926i	−0.462627	+	0.886553i	$0.653093\pi$
$654$	−1.39216	+	17.6499i	−0.0544377	+	0.690166i
$655$	−22.6077			−0.883358
$656$	0.948491	−	2.91228i	0.0370324	−	0.113705i
$657$	20.5310			0.800991
$658$	0.404479	−	5.12802i	0.0157682	−	0.199911i
$659$	21.1434	+	21.1434i	0.823630	+	0.823630i	0.986627	−	0.162997i	$-0.0521160\pi$
$659$	21.1434	+	21.1434i	0.823630	+	0.823630i	−0.162997	+	0.986627i	$0.552116\pi$
$660$	68.4470	−	49.6934i	2.66429	−	1.93431i
$661$	3.71648	−	3.71648i	0.144554	−	0.144554i	−0.631126	−	0.775680i	$-0.717407\pi$
$661$	3.71648	−	3.71648i	0.144554	−	0.144554i	0.775680	+	0.631126i	$0.217407\pi$
$662$	−11.2989	+	9.64679i	−0.439144	+	0.374933i
$663$			4.17900i			0.162299i
$664$	−12.7181	−	20.7783i	−0.493557	−	0.806354i
$665$			33.1601i			1.28589i
$666$	−13.9319	−	16.3179i	−0.539850	−	0.632305i
$667$	−7.12138	+	7.12138i	−0.275741	+	0.275741i
$668$	6.60759	−	41.6253i	0.255655	−	1.61053i
$669$	23.3236	+	23.3236i	0.901743	+	0.901743i
$670$	−58.7157	−	4.63127i	−2.26839	−	0.178922i
$671$	2.97059			0.114678
$672$	−20.9581	+	8.65984i	−0.808476	+	0.334061i
$673$	−18.1480			−0.699552			−0.349776	−	0.936833i	$-0.613742\pi$
$673$	−18.1480			−0.699552			−0.349776	+	0.936833i	$0.613742\pi$
$674$	−39.0863	−	3.08298i	−1.50555	−	0.118752i
$675$	2.65993	+	2.65993i	0.102381	+	0.102381i
$676$	2.64983	−	16.6929i	0.101917	−	0.642035i
$677$	−8.16589	+	8.16589i	−0.313841	+	0.313841i	−0.846396	−	0.532555i	$-0.821232\pi$
$677$	−8.16589	+	8.16589i	−0.313841	+	0.313841i	0.532555	+	0.846396i	$0.321232\pi$
$678$	28.6476	+	33.5538i	1.10020	+	1.28863i
$679$		−	12.3984i		−	0.475806i
$680$	−7.23822	+	4.43041i	−0.277573	+	0.169898i
$681$			36.0402i			1.38106i
$682$	−54.6426	+	46.6528i	−2.09237	+	1.78643i
$683$	4.85358	−	4.85358i	0.185717	−	0.185717i	−0.608125	−	0.793842i	$-0.708078\pi$
$683$	4.85358	−	4.85358i	0.185717	−	0.185717i	0.793842	+	0.608125i	$0.208078\pi$
$684$	24.6511	−	17.8970i	0.942558	−	0.684309i
$685$	−30.7151	−	30.7151i	−1.17356	−	1.17356i
$686$	2.07676	−	26.3294i	0.0792912	−	1.00526i
$687$	63.4315			2.42006
$688$	18.9480	−	9.63793i	0.722385	−	0.367443i
$689$	−4.48820			−0.170987
$690$	−0.991020	+	12.5642i	−0.0377275	+	0.478313i
$691$	10.8867	+	10.8867i	0.414149	+	0.414149i	0.883181	−	0.469032i	$-0.155397\pi$
$691$	10.8867	+	10.8867i	0.414149	+	0.414149i	−0.469032	+	0.883181i	$0.655397\pi$
$692$	1.23446	+	1.70033i	0.0469271	+	0.0646368i
$693$	−15.7227	+	15.7227i	−0.597258	+	0.597258i
$694$	11.5340	−	9.84748i	0.437823	−	0.373805i
$695$		−	41.0896i		−	1.55862i
$696$	16.0768	−	66.8114i	0.609388	−	2.53248i
$697$			0.621911i			0.0235566i
$698$	−30.1235	−	35.2825i	−1.14019	−	1.33546i
$699$	−26.8168	+	26.8168i	−1.01430	+	1.01430i
$700$	28.3824	+	4.50543i	1.07275	+	0.170289i
$701$	−4.48997	−	4.48997i	−0.169584	−	0.169584i	0.617212	−	0.786797i	$-0.288262\pi$
$701$	−4.48997	−	4.48997i	−0.169584	−	0.169584i	−0.786797	+	0.617212i	$0.788262\pi$
$702$	1.30812	+	0.103179i	0.0493717	+	0.00389425i
$703$	−29.0658			−1.09624
$704$	36.1187	−	11.6941i	1.36127	−	0.440739i
$705$	19.5072			0.734682
$706$	20.4623	+	1.61399i	0.770108	+	0.0607432i
$707$	−7.94577	−	7.94577i	−0.298832	−	0.298832i
$708$	−63.7954	−	10.1269i	−2.39758	−	0.380591i
$709$	8.56006	−	8.56006i	0.321480	−	0.321480i	−0.527855	−	0.849335i	$-0.677003\pi$
$709$	8.56006	−	8.56006i	0.321480	−	0.321480i	0.849335	+	0.527855i	$0.177003\pi$
$710$	−9.79601	−	11.4737i	−0.367638	−	0.430600i
$711$			3.84055i			0.144032i
$712$	3.29573	−	13.6963i	0.123513	−	0.513291i
$713$		−	10.7058i		−	0.400934i
$714$	3.50182	−	2.98979i	0.131052	−	0.111890i
$715$	−26.4395	+	26.4395i	−0.988780	+	0.988780i
$716$	−9.76814	−	13.4545i	−0.365053	−	0.502818i
$717$	5.31271	+	5.31271i	0.198407	+	0.198407i
$718$	0.661541	−	8.38708i	0.0246885	−	0.313003i
$719$	−17.5883			−0.655932			−0.327966	−	0.944689i	$-0.606363\pi$
$719$	−17.5883			−0.655932			−0.327966	+	0.944689i	$0.606363\pi$
$720$	−18.8900	−	37.1374i	−0.703989	−	1.38403i
$721$	4.37596			0.162969
$722$	1.13201	−	14.3518i	0.0421292	−	0.534117i
$723$	19.8065	+	19.8065i	0.736612	+	0.736612i
$724$	−28.6691	+	20.8141i	−1.06548	+	0.773551i
$725$	−61.5788	+	61.5788i	−2.28698	+	2.28698i
$726$	29.8913	−	25.5206i	1.10937	−	0.947159i
$727$			41.4212i			1.53623i	0.640315	+	0.768113i	$0.278804\pi$
$727$			41.4212i			1.53623i	−0.640315	+	0.768113i	$0.721196\pi$
$728$	8.54998	−	5.23332i	0.316883	−	0.193960i
$729$			23.6624i			0.876384i
$730$	−24.7003	−	28.9305i	−0.914200	−	1.07077i
$731$	−3.05223	+	3.05223i	−0.112891	+	0.112891i
$732$	0.473495	−	2.98283i	0.0175009	−	0.110249i
$733$	24.4478	+	24.4478i	0.902998	+	0.902998i	0.995694	−	0.0926961i	$-0.0295485\pi$
$733$	24.4478	+	24.4478i	0.902998	+	0.902998i	−0.0926961	+	0.995694i	$0.529549\pi$
$734$	−31.7479	−	2.50415i	−1.17184	−	0.0924300i
$735$	37.7748			1.39334
$736$	−2.16932	+	5.22437i	−0.0799620	+	0.192573i
$737$	−53.5003			−1.97071
$738$	−3.04391	−	0.240092i	−0.112048	−	0.00883790i
$739$	−28.9582	−	28.9582i	−1.06525	−	1.06525i	−0.997717	−	0.0675288i	$-0.978489\pi$
$739$	−28.9582	−	28.9582i	−1.06525	−	1.06525i	−0.0675288	−	0.997717i	$-0.521511\pi$
$740$	−6.23265	+	39.2632i	−0.229117	+	1.44335i
$741$	−19.6533	+	19.6533i	−0.721981	+	0.721981i
$742$	3.21100	+	3.76091i	0.117879	+	0.138068i
$743$			27.0393i			0.991975i	0.868330	+	0.495987i	$0.165194\pi$
$743$			27.0393i			0.991975i	−0.868330	+	0.495987i	$0.834806\pi$
$744$	38.1353	+	62.3040i	1.39811	+	2.28417i
$745$		−	5.18629i		−	0.190011i
$746$	5.64247	−	4.81743i	0.206585	−	0.176379i
$747$	−17.1729	+	17.1729i	−0.628324	+	0.628324i
$748$	−6.23806	+	4.52891i	−0.228086	+	0.165593i
$749$	4.69465	+	4.69465i	0.171539	+	0.171539i
$750$	−3.61429	+	45.8223i	−0.131975	+	1.67319i
$751$	8.86802			0.323598			0.161799	−	0.986824i	$-0.448270\pi$
$751$	8.86802			0.323598			0.161799	+	0.986824i	$0.448270\pi$
$752$	8.32518	+	2.71140i	0.303588	+	0.0988747i
$753$	−48.1297			−1.75394
$754$	−2.38865	+	30.2836i	−0.0869896	+	1.10286i
$755$	53.3385	+	53.3385i	1.94119	+	1.94119i
$756$	−0.849407	−	1.16996i	−0.0308926	−	0.0425511i
$757$	−4.85766	+	4.85766i	−0.176555	+	0.176555i	−0.789852	−	0.613297i	$-0.789843\pi$
$757$	−4.85766	+	4.85766i	−0.176555	+	0.176555i	0.613297	+	0.789852i	$0.289843\pi$
$758$	7.70733	−	6.58037i	0.279943	−	0.239010i
$759$			11.4482i			0.415544i
$760$	−54.8760	−	13.2048i	−1.99056	−	0.478987i
$761$			16.9685i			0.615109i	0.951530	+	0.307554i	$0.0995106\pi$
$761$			16.9685i			0.615109i	−0.951530	+	0.307554i	$0.900489\pi$
$762$	−35.9164	−	42.0675i	−1.30112	−	1.52395i
$763$	−6.09770	+	6.09770i	−0.220752	+	0.220752i
$764$	3.24728	+	0.515474i	0.117483	+	0.0186492i
$765$	5.98227	+	5.98227i	0.216289	+	0.216289i
$766$	21.3793	+	1.68632i	0.772465	+	0.0609291i
$767$	28.5544			1.03104
$768$	−5.98522	−	38.1315i	−0.215973	−	1.37595i
$769$	−31.9813

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:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40983 - 0.111202i) q^{2} +(-1.70582 - 1.70582i) q^{3} +(1.97527 + 0.313554i) q^{4} +(-2.61219 + 2.61219i) q^{5} +(2.21524 + 2.59462i) q^{6} +1.66171i q^{7} +(-2.74993 - 0.661714i) q^{8} +2.81967i q^{9} +O(q^{10})\)	\(q+(-1.40983 - 0.111202i) q^{2} +(-1.70582 - 1.70582i) q^{3} +(1.97527 + 0.313554i) q^{4} +(-2.61219 + 2.61219i) q^{5} +(2.21524 + 2.59462i) q^{6} +1.66171i q^{7} +(-2.74993 - 0.661714i) q^{8} +2.81967i q^{9} +(3.97323 - 3.39227i) q^{10} +(3.35563 - 3.35563i) q^{11} +(-2.83459 - 3.90433i) q^{12} +(1.50815 + 1.50815i) q^{13} +(0.184787 - 2.34274i) q^{14} +8.91186 q^{15} +(3.80337 + 1.23871i) q^{16} -0.812201 q^{17} +(0.313554 - 3.97527i) q^{18} +(-3.81967 - 3.81967i) q^{19} +(-5.97883 + 4.34071i) q^{20} +(2.83459 - 2.83459i) q^{21} +(-5.10404 + 4.35773i) q^{22} -1.00000i q^{23} +(3.56213 + 5.81967i) q^{24} -8.64704i q^{25} +(-1.95853 - 2.29395i) q^{26} +(-0.307612 + 0.307612i) q^{27} +(-0.521037 + 3.28233i) q^{28} +(-7.12138 - 7.12138i) q^{29} +(-12.5642 - 0.991020i) q^{30} +10.7058 q^{31} +(-5.22437 - 2.16932i) q^{32} -11.4482 q^{33} +(1.14507 + 0.0903187i) q^{34} +(-4.34071 - 4.34071i) q^{35} +(-0.884119 + 5.56960i) q^{36} +(3.80475 - 3.80475i) q^{37} +(4.96035 + 5.80986i) q^{38} -5.14528i q^{39} +(8.91186 - 5.45482i) q^{40} -0.765711i q^{41} +(-4.31152 + 3.68109i) q^{42} +(3.75797 - 3.75797i) q^{43} +(7.68044 - 5.57609i) q^{44} +(-7.36550 - 7.36550i) q^{45} +(-0.111202 + 1.40983i) q^{46} +2.18890 q^{47} +(-4.37486 - 8.60089i) q^{48} +4.23871 q^{49} +(-0.961571 + 12.1909i) q^{50} +(1.38547 + 1.38547i) q^{51} +(2.50612 + 3.45189i) q^{52} +(-1.48798 + 1.48798i) q^{53} +(0.467889 - 0.399475i) q^{54} +17.5311i q^{55} +(1.09958 - 4.56960i) q^{56} +13.0314i q^{57} +(9.24805 + 10.8319i) q^{58} +(9.46671 - 9.46671i) q^{59} +(17.6033 + 2.79435i) q^{60} +(0.442628 + 0.442628i) q^{61} +(-15.0933 - 1.19051i) q^{62} -4.68548 q^{63} +(7.12427 + 3.63934i) q^{64} -7.87914 q^{65} +(16.1401 + 1.27307i) q^{66} +(-7.97172 - 7.97172i) q^{67} +(-1.60431 - 0.254669i) q^{68} +(-1.70582 + 1.70582i) q^{69} +(5.63698 + 6.60238i) q^{70} -2.88774i q^{71} +(1.86581 - 7.75390i) q^{72} -7.28135i q^{73} +(-5.78716 + 4.94097i) q^{74} +(-14.7503 + 14.7503i) q^{75} +(-6.34720 - 8.74254i) q^{76} +(5.57609 + 5.57609i) q^{77} +(-0.572167 + 7.25399i) q^{78} +1.36206 q^{79} +(-13.1708 + 6.69937i) q^{80} +9.50847 q^{81} +(-0.0851489 + 1.07953i) q^{82} +(6.09040 + 6.09040i) q^{83} +(6.48788 - 4.71028i) q^{84} +(2.12162 - 2.12162i) q^{85} +(-5.71602 + 4.88023i) q^{86} +24.2956i q^{87} +(-11.4482 + 7.00729i) q^{88} +4.98060i q^{89} +(9.56508 + 11.2032i) q^{90} +(-2.50612 + 2.50612i) q^{91} +(0.313554 - 1.97527i) q^{92} +(-18.2621 - 18.2621i) q^{93} +(-3.08598 - 0.243411i) q^{94} +19.9554 q^{95} +(5.21139 + 12.6123i) q^{96} -7.46120 q^{97} +(-5.97588 - 0.471354i) q^{98} +(9.46176 + 9.46176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 2 q^{3} - 4 q^{5} - 4 q^{8}+O(q^{10}) \) 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^5 - 4 * q^8	\( 12 q + 2 q^{2} + 2 q^{3} - 4 q^{5} - 4 q^{8} - 6 q^{10} - 4 q^{11} - 8 q^{12} + 18 q^{13} - 2 q^{14} + 8 q^{16} - 8 q^{17} - 4 q^{18} - 8 q^{19} - 32 q^{20} + 8 q^{21} - 34 q^{22} + 12 q^{24} - 14 q^{26} + 14 q^{27} + 12 q^{28} + 2 q^{29} - 30 q^{30} + 20 q^{31} - 8 q^{32} - 36 q^{33} + 10 q^{34} + 4 q^{35} + 4 q^{36} - 4 q^{37} + 24 q^{38} - 14 q^{42} + 20 q^{43} + 4 q^{44} - 20 q^{45} - 2 q^{46} - 16 q^{47} - 12 q^{48} + 52 q^{49} + 6 q^{50} - 4 q^{51} - 16 q^{53} + 16 q^{54} + 28 q^{56} + 14 q^{58} + 8 q^{59} + 48 q^{60} + 12 q^{61} - 44 q^{62} - 4 q^{63} + 24 q^{64} - 52 q^{65} + 34 q^{66} - 4 q^{67} - 16 q^{68} + 2 q^{69} + 28 q^{70} + 8 q^{72} - 26 q^{74} - 46 q^{75} - 8 q^{76} - 12 q^{77} - 44 q^{78} - 4 q^{79} + 4 q^{80} + 48 q^{81} - 6 q^{82} + 28 q^{83} + 12 q^{84} - 8 q^{85} + 44 q^{86} - 36 q^{88} + 4 q^{90} - 4 q^{92} - 14 q^{93} + 48 q^{95} + 32 q^{96} + 36 q^{97} - 2 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^5 - 4 * q^8 - 6 * q^10 - 4 * q^11 - 8 * q^12 + 18 * q^13 - 2 * q^14 + 8 * q^16 - 8 * q^17 - 4 * q^18 - 8 * q^19 - 32 * q^20 + 8 * q^21 - 34 * q^22 + 12 * q^24 - 14 * q^26 + 14 * q^27 + 12 * q^28 + 2 * q^29 - 30 * q^30 + 20 * q^31 - 8 * q^32 - 36 * q^33 + 10 * q^34 + 4 * q^35 + 4 * q^36 - 4 * q^37 + 24 * q^38 - 14 * q^42 + 20 * q^43 + 4 * q^44 - 20 * q^45 - 2 * q^46 - 16 * q^47 - 12 * q^48 + 52 * q^49 + 6 * q^50 - 4 * q^51 - 16 * q^53 + 16 * q^54 + 28 * q^56 + 14 * q^58 + 8 * q^59 + 48 * q^60 + 12 * q^61 - 44 * q^62 - 4 * q^63 + 24 * q^64 - 52 * q^65 + 34 * q^66 - 4 * q^67 - 16 * q^68 + 2 * q^69 + 28 * q^70 + 8 * q^72 - 26 * q^74 - 46 * q^75 - 8 * q^76 - 12 * q^77 - 44 * q^78 - 4 * q^79 + 4 * q^80 + 48 * q^81 - 6 * q^82 + 28 * q^83 + 12 * q^84 - 8 * q^85 + 44 * q^86 - 36 * q^88 + 4 * q^90 - 4 * q^92 - 14 * q^93 + 48 * q^95 + 32 * q^96 + 36 * q^97 - 2 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more