LMFDB - Embedded newform 336.2.w.b.85.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(85,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("336.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.w (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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			85.3
Character	$\chi$	$=$	336.85
Dual form			336.2.w.b.253.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14710 - 0.827134i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(0.631698 + 1.89762i) q^{4} +(2.39875 + 2.39875i) q^{5} +(1.39600 - 0.226253i) q^{6} -1.00000i q^{7} +(0.844961 - 2.69927i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-1.14710 - 0.827134i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(0.631698 + 1.89762i) q^{4} +(2.39875 + 2.39875i) q^{5} +(1.39600 - 0.226253i) q^{6} -1.00000i q^{7} +(0.844961 - 2.69927i) q^{8} -1.00000i q^{9} +(-0.767531 - 4.73571i) q^{10} +(0.853527 + 0.853527i) q^{11} +(-1.78850 - 0.895141i) q^{12} +(-3.62524 + 3.62524i) q^{13} +(-0.827134 + 1.14710i) q^{14} -3.39235 q^{15} +(-3.20191 + 2.39745i) q^{16} +5.93949 q^{17} +(-0.827134 + 1.14710i) q^{18} +(-4.47354 + 4.47354i) q^{19} +(-3.03663 + 6.06721i) q^{20} +(0.707107 + 0.707107i) q^{21} +(-0.273103 - 1.68507i) q^{22} -2.09274i q^{23} +(1.31119 + 2.50615i) q^{24} +6.50804i q^{25} +(7.15710 - 1.15997i) q^{26} +(0.707107 + 0.707107i) q^{27} +(1.89762 - 0.631698i) q^{28} +(0.577547 - 0.577547i) q^{29} +(3.89138 + 2.80593i) q^{30} +3.23168 q^{31} +(5.65594 - 0.101709i) q^{32} -1.20707 q^{33} +(-6.81321 - 4.91275i) q^{34} +(2.39875 - 2.39875i) q^{35} +(1.89762 - 0.631698i) q^{36} +(6.16154 + 6.16154i) q^{37} +(8.83184 - 1.43140i) q^{38} -5.12687i q^{39} +(8.50173 - 4.44802i) q^{40} +8.30581i q^{41} +(-0.226253 - 1.39600i) q^{42} +(-5.68209 - 5.68209i) q^{43} +(-1.08050 + 2.15884i) q^{44} +(2.39875 - 2.39875i) q^{45} +(-1.73098 + 2.40060i) q^{46} -4.36705 q^{47} +(0.568845 - 3.95935i) q^{48} -1.00000 q^{49} +(5.38302 - 7.46540i) q^{50} +(-4.19985 + 4.19985i) q^{51} +(-9.16939 - 4.58927i) q^{52} +(-1.19135 - 1.19135i) q^{53} +(-0.226253 - 1.39600i) q^{54} +4.09480i q^{55} +(-2.69927 - 0.844961i) q^{56} -6.32654i q^{57} +(-1.14022 + 0.184798i) q^{58} +(7.94499 + 7.94499i) q^{59} +(-2.14294 - 6.43739i) q^{60} +(-5.56516 + 5.56516i) q^{61} +(-3.70708 - 2.67303i) q^{62} -1.00000 q^{63} +(-6.57208 - 4.56155i) q^{64} -17.3921 q^{65} +(1.38463 + 0.998408i) q^{66} +(7.32789 - 7.32789i) q^{67} +(3.75196 + 11.2709i) q^{68} +(1.47979 + 1.47979i) q^{69} +(-4.73571 + 0.767531i) q^{70} +1.22507i q^{71} +(-2.69927 - 0.844961i) q^{72} -16.7458i q^{73} +(-1.97151 - 12.1643i) q^{74} +(-4.60188 - 4.60188i) q^{75} +(-11.3150 - 5.66315i) q^{76} +(0.853527 - 0.853527i) q^{77} +(-4.24061 + 5.88106i) q^{78} -5.39231 q^{79} +(-13.4315 - 1.92972i) q^{80} -1.00000 q^{81} +(6.87002 - 9.52763i) q^{82} +(9.38249 - 9.38249i) q^{83} +(-0.895141 + 1.78850i) q^{84} +(14.2474 + 14.2474i) q^{85} +(1.81810 + 11.2178i) q^{86} +0.816775i q^{87} +(3.02509 - 1.58270i) q^{88} -8.85777i q^{89} +(-4.73571 + 0.767531i) q^{90} +(3.62524 + 3.62524i) q^{91} +(3.97123 - 1.32198i) q^{92} +(-2.28514 + 2.28514i) q^{93} +(5.00946 + 3.61213i) q^{94} -21.4618 q^{95} +(-3.92743 + 4.07127i) q^{96} +14.4012 q^{97} +(1.14710 + 0.827134i) q^{98} +(0.853527 - 0.853527i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q+O(q^{10}) $ 28 * q	$ 28 q - 4 q^{10} - 4 q^{11} - 8 q^{12} + 8 q^{15} + 4 q^{16} + 8 q^{19} - 28 q^{20} - 8 q^{22} - 16 q^{24} - 20 q^{26} + 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{33} + 12 q^{34} + 4 q^{36} + 4 q^{37} + 60 q^{38} - 56 q^{40} - 4 q^{42} + 20 q^{43} + 56 q^{44} - 44 q^{46} + 16 q^{48} - 28 q^{49} + 20 q^{50} - 8 q^{51} - 32 q^{52} + 20 q^{53} - 4 q^{54} - 12 q^{56} - 12 q^{58} - 12 q^{60} - 40 q^{61} - 60 q^{62} - 28 q^{63} + 60 q^{64} + 16 q^{65} + 24 q^{66} + 4 q^{67} - 108 q^{68} - 16 q^{69} - 4 q^{70} - 12 q^{72} + 28 q^{74} - 16 q^{75} - 8 q^{76} - 4 q^{77} + 12 q^{78} + 24 q^{79} - 72 q^{80} - 28 q^{81} + 36 q^{82} + 40 q^{83} + 48 q^{85} + 24 q^{86} + 4 q^{88} - 4 q^{90} + 52 q^{92} - 8 q^{94} + 40 q^{96} + 72 q^{97} - 4 q^{99}+O(q^{100}) $ 28 * q - 4 * q^10 - 4 * q^11 - 8 * q^12 + 8 * q^15 + 4 * q^16 + 8 * q^19 - 28 * q^20 - 8 * q^22 - 16 * q^24 - 20 * q^26 + 4 * q^28 + 4 * q^29 + 8 * q^30 + 24 * q^33 + 12 * q^34 + 4 * q^36 + 4 * q^37 + 60 * q^38 - 56 * q^40 - 4 * q^42 + 20 * q^43 + 56 * q^44 - 44 * q^46 + 16 * q^48 - 28 * q^49 + 20 * q^50 - 8 * q^51 - 32 * q^52 + 20 * q^53 - 4 * q^54 - 12 * q^56 - 12 * q^58 - 12 * q^60 - 40 * q^61 - 60 * q^62 - 28 * q^63 + 60 * q^64 + 16 * q^65 + 24 * q^66 + 4 * q^67 - 108 * q^68 - 16 * q^69 - 4 * q^70 - 12 * q^72 + 28 * q^74 - 16 * q^75 - 8 * q^76 - 4 * q^77 + 12 * q^78 + 24 * q^79 - 72 * q^80 - 28 * q^81 + 36 * q^82 + 40 * q^83 + 48 * q^85 + 24 * q^86 + 4 * q^88 - 4 * q^90 + 52 * q^92 - 8 * q^94 + 40 * q^96 + 72 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$1$

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 $

$2$	−1.14710	−	0.827134i	−0.811126	−	0.584872i
$2$	−1.14710	−	0.827134i	−0.811126	−	0.584872i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	0.631698	+	1.89762i	0.315849	+	0.948809i
$5$	2.39875	+	2.39875i	1.07276	+	1.07276i	0.997137	+	0.0756185i	$0.0240931\pi$
$5$	2.39875	+	2.39875i	1.07276	+	1.07276i	0.0756185	+	0.997137i	$0.475907\pi$
$6$	1.39600	−	0.226253i	0.569914	−	0.0923676i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	0.844961	−	2.69927i	0.298739	−	0.954335i
$9$		−	1.00000i		−	0.333333i
$10$	−0.767531	−	4.73571i	−0.242715	−	1.49756i
$11$	0.853527	+	0.853527i	0.257348	+	0.257348i	0.823975	−	0.566627i	$-0.191752\pi$
$11$	0.853527	+	0.853527i	0.257348	+	0.257348i	−0.566627	+	0.823975i	$0.691752\pi$
$12$	−1.78850	−	0.895141i	−0.516295	−	0.258405i
$13$	−3.62524	+	3.62524i	−1.00546	+	1.00546i	−0.00547668	+	0.999985i	$0.501743\pi$
$13$	−3.62524	+	3.62524i	−1.00546	+	1.00546i	−0.999985	+	0.00547668i	$0.998257\pi$
$14$	−0.827134	+	1.14710i	−0.221061	+	0.306577i
$15$	−3.39235			−0.875901
$16$	−3.20191	+	2.39745i	−0.800479	+	0.599361i
$17$	5.93949			1.44054			0.720269	−	0.693695i	$-0.244019\pi$
$17$	5.93949			1.44054			0.720269	+	0.693695i	$0.244019\pi$
$18$	−0.827134	+	1.14710i	−0.194957	+	0.270375i
$19$	−4.47354	+	4.47354i	−1.02630	+	1.02630i	−0.0266560	+	0.999645i	$0.508486\pi$
$19$	−4.47354	+	4.47354i	−1.02630	+	1.02630i	−0.999645	+	0.0266560i	$0.991514\pi$
$20$	−3.03663	+	6.06721i	−0.679011	+	1.35667i
$21$	0.707107	+	0.707107i	0.154303	+	0.154303i
$22$	−0.273103	−	1.68507i	−0.0582259	−	0.359257i
$23$		−	2.09274i		−	0.436367i	−0.975908	−	0.218184i	$-0.929987\pi$
$23$		−	2.09274i		−	0.436367i	0.975908	−	0.218184i	$-0.0700131\pi$
$24$	1.31119	+	2.50615i	0.267646	+	0.511565i
$25$			6.50804i			1.30161i
$26$	7.15710	−	1.15997i	1.40362	−	0.227489i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	1.89762	−	0.631698i	0.358616	−	0.119380i
$29$	0.577547	−	0.577547i	0.107248	−	0.107248i	−0.651447	−	0.758694i	$-0.725838\pi$
$29$	0.577547	−	0.577547i	0.107248	−	0.107248i	0.758694	+	0.651447i	$0.225838\pi$
$30$	3.89138	+	2.80593i	0.710466	+	0.512290i
$31$	3.23168			0.580427			0.290214	−	0.956962i	$-0.406274\pi$
$31$	3.23168			0.580427			0.290214	+	0.956962i	$0.406274\pi$
$32$	5.65594	−	0.101709i	0.999838	−	0.0179797i
$33$	−1.20707			−0.210124
$34$	−6.81321	−	4.91275i	−1.16846	−	0.842530i
$35$	2.39875	−	2.39875i	0.405463	−	0.405463i
$36$	1.89762	−	0.631698i	0.316270	−	0.105283i
$37$	6.16154	+	6.16154i	1.01295	+	1.01295i	0.999915	+	0.0130355i	$0.00414945\pi$
$37$	6.16154	+	6.16154i	1.01295	+	1.01295i	0.0130355	+	0.999915i	$0.495851\pi$
$38$	8.83184	−	1.43140i	1.43271	−	0.232204i
$39$		−	5.12687i		−	0.820956i
$40$	8.50173	−	4.44802i	1.34424	−	0.703294i
$41$			8.30581i			1.29715i	0.761151	+	0.648575i	$0.224635\pi$
$41$			8.30581i			1.29715i	−0.761151	+	0.648575i	$0.775365\pi$
$42$	−0.226253	−	1.39600i	−0.0349117	−	0.215407i
$43$	−5.68209	−	5.68209i	−0.866511	−	0.866511i	0.125573	−	0.992084i	$-0.459923\pi$
$43$	−5.68209	−	5.68209i	−0.866511	−	0.866511i	−0.992084	+	0.125573i	$0.959923\pi$
$44$	−1.08050	+	2.15884i	−0.162891	+	0.325457i
$45$	2.39875	−	2.39875i	0.357585	−	0.357585i
$46$	−1.73098	+	2.40060i	−0.255219	+	0.353948i
$47$	−4.36705			−0.636999			−0.318500	−	0.947923i	$-0.603179\pi$
$47$	−4.36705			−0.636999			−0.318500	+	0.947923i	$0.603179\pi$
$48$	0.568845	−	3.95935i	0.0821057	−	0.571482i
$49$	−1.00000			−0.142857
$50$	5.38302	−	7.46540i	0.761274	−	1.05577i
$51$	−4.19985	+	4.19985i	−0.588097	+	0.588097i
$52$	−9.16939	−	4.58927i	−1.27157	−	0.636417i
$53$	−1.19135	−	1.19135i	−0.163644	−	0.163644i	0.620535	−	0.784179i	$-0.286916\pi$
$53$	−1.19135	−	1.19135i	−0.163644	−	0.163644i	−0.784179	+	0.620535i	$0.786916\pi$
$54$	−0.226253	−	1.39600i	−0.0307892	−	0.189971i
$55$			4.09480i			0.552143i
$56$	−2.69927	−	0.844961i	−0.360705	−	0.112913i
$57$		−	6.32654i		−	0.837971i
$58$	−1.14022	+	0.184798i	−0.149718	+	0.0242652i
$59$	7.94499	+	7.94499i	1.03435	+	1.03435i	0.999389	+	0.0349608i	$0.0111306\pi$
$59$	7.94499	+	7.94499i	1.03435	+	1.03435i	0.0349608	+	0.999389i	$0.488869\pi$
$60$	−2.14294	−	6.43739i	−0.276653	−	0.831063i
$61$	−5.56516	+	5.56516i	−0.712546	+	0.712546i	−0.967067	−	0.254521i	$-0.918082\pi$
$61$	−5.56516	+	5.56516i	−0.712546	+	0.712546i	0.254521	+	0.967067i	$0.418082\pi$
$62$	−3.70708	−	2.67303i	−0.470799	−	0.339476i
$63$	−1.00000			−0.125988
$64$	−6.57208	−	4.56155i	−0.821510	−	0.570194i
$65$	−17.3921			−2.15723
$66$	1.38463	+	0.998408i	0.170437	+	0.122896i
$67$	7.32789	−	7.32789i	0.895244	−	0.895244i	−0.0997668	−	0.995011i	$-0.531810\pi$
$67$	7.32789	−	7.32789i	0.895244	−	0.895244i	0.995011	+	0.0997668i	$0.0318097\pi$
$68$	3.75196	+	11.2709i	0.454993	+	1.36680i
$69$	1.47979	+	1.47979i	0.178146	+	0.178146i
$70$	−4.73571	+	0.767531i	−0.566026	+	0.0917375i
$71$			1.22507i			0.145389i	0.997354	+	0.0726944i	$0.0231598\pi$
$71$			1.22507i			0.145389i	−0.997354	+	0.0726944i	$0.976840\pi$
$72$	−2.69927	−	0.844961i	−0.318112	−	0.0995796i
$73$		−	16.7458i		−	1.95994i	−0.199139	−	0.979971i	$-0.563815\pi$
$73$		−	16.7458i		−	1.95994i	0.199139	−	0.979971i	$-0.436185\pi$
$74$	−1.97151	−	12.1643i	−0.229184	−	1.41408i
$75$	−4.60188	−	4.60188i	−0.531379	−	0.531379i
$76$	−11.3150	−	5.66315i	−1.29792	−	0.649607i
$77$	0.853527	−	0.853527i	0.0972684	−	0.0972684i
$78$	−4.24061	+	5.88106i	−0.480154	+	0.665898i
$79$	−5.39231			−0.606682			−0.303341	−	0.952882i	$-0.598102\pi$
$79$	−5.39231			−0.606682			−0.303341	+	0.952882i	$0.598102\pi$
$80$	−13.4315	−	1.92972i	−1.50169	−	0.215750i
$81$	−1.00000			−0.111111
$82$	6.87002	−	9.52763i	0.758666	−	1.05215i
$83$	9.38249	−	9.38249i	1.02986	−	1.02986i	0.0303221	−	0.999540i	$-0.490347\pi$
$83$	9.38249	−	9.38249i	1.02986	−	1.02986i	0.999540	−	0.0303221i	$-0.00965329\pi$
$84$	−0.895141	+	1.78850i	−0.0976679	+	0.195141i
$85$	14.2474	+	14.2474i	1.54534	+	1.54534i
$86$	1.81810	+	11.2178i	0.196051	+	1.20965i
$87$			0.816775i			0.0875675i
$88$	3.02509	−	1.58270i	0.322476	−	0.168716i
$89$		−	8.85777i		−	0.938921i	−0.882953	−	0.469461i	$-0.844448\pi$
$89$		−	8.85777i		−	0.938921i	0.882953	−	0.469461i	$-0.155552\pi$
$90$	−4.73571	+	0.767531i	−0.499188	+	0.0809048i
$91$	3.62524	+	3.62524i	0.380029	+	0.380029i
$92$	3.97123	−	1.32198i	0.414029	−	0.137826i
$93$	−2.28514	+	2.28514i	−0.236958	+	0.236958i
$94$	5.00946	+	3.61213i	0.516686	+	0.372563i
$95$	−21.4618			−2.20194
$96$	−3.92743	+	4.07127i	−0.400842	+	0.415522i
$97$	14.4012			1.46222			0.731112	−	0.682258i	$-0.239002\pi$
$97$	14.4012			1.46222			0.731112	+	0.682258i	$0.239002\pi$
$98$	1.14710	+	0.827134i	0.115875	+	0.0835532i
$99$	0.853527	−	0.853527i	0.0857827	−	0.0857827i
$100$	−12.3498	+	4.11112i	−1.23498	+	0.411112i
$101$	−5.40546	−	5.40546i	−0.537863	−	0.537863i	0.385038	−	0.922901i	$-0.374188\pi$
$101$	−5.40546	−	5.40546i	−0.537863	−	0.537863i	−0.922901	+	0.385038i	$0.874188\pi$
$102$	8.29151	−	1.34383i	0.820982	−	0.133059i
$103$		−	0.651718i		−	0.0642157i	−0.999484	−	0.0321079i	$-0.989778\pi$
$103$		−	0.651718i		−	0.0642157i	0.999484	−	0.0321079i	$-0.0102220\pi$
$104$	6.72231	+	12.8487i	0.659177	+	1.25992i
$105$			3.39235i			0.331059i
$106$	0.381196	+	2.35200i	0.0370250	+	0.228447i
$107$	−3.08596	−	3.08596i	−0.298331	−	0.298331i	0.542029	−	0.840360i	$-0.317656\pi$
$107$	−3.08596	−	3.08596i	−0.298331	−	0.298331i	−0.840360	+	0.542029i	$0.817656\pi$
$108$	−0.895141	+	1.78850i	−0.0861350	+	0.172098i
$109$	2.62063	−	2.62063i	0.251011	−	0.251011i	−0.570374	−	0.821385i	$-0.693202\pi$
$109$	2.62063	−	2.62063i	0.251011	−	0.251011i	0.821385	+	0.570374i	$0.193202\pi$
$110$	3.38695	−	4.69717i	0.322933	−	0.447857i
$111$	−8.71373			−0.827071
$112$	2.39745	+	3.20191i	0.226537	+	0.302552i
$113$	−0.711732			−0.0669541			−0.0334771	−	0.999439i	$-0.510658\pi$
$113$	−0.711732			−0.0669541			−0.0334771	+	0.999439i	$0.510658\pi$
$114$	−5.23290	+	7.25721i	−0.490106	+	0.679700i
$115$	5.01998	−	5.01998i	0.468115	−	0.468115i
$116$	1.46080	+	0.731129i	0.135632	+	0.0678836i
$117$	3.62524	+	3.62524i	0.335154	+	0.335154i
$118$	−2.54216	−	15.6853i	−0.234025	−	1.44395i
$119$		−	5.93949i		−	0.544472i
$120$	−2.86640	+	9.15686i	−0.261666	+	0.835903i
$121$		−	9.54298i		−	0.867544i
$122$	10.9870	−	1.78069i	0.994712	−	0.161216i
$123$	−5.87309	−	5.87309i	−0.529559	−	0.529559i
$124$	2.04145	+	6.13250i	0.183327	+	0.550715i
$125$	−3.61742	+	3.61742i	−0.323552	+	0.323552i
$126$	1.14710	+	0.827134i	0.102192	+	0.0736870i
$127$	−4.50611			−0.399853			−0.199926	−	0.979811i	$-0.564070\pi$
$127$	−4.50611			−0.399853			−0.199926	+	0.979811i	$0.564070\pi$
$128$	3.76585	+	10.6686i	0.332857	+	0.942977i
$129$	8.03569			0.707503
$130$	19.9506	+	14.3856i	1.74978	+	1.26170i
$131$	12.1840	−	12.1840i	1.06452	−	1.06452i	0.0667551	−	0.997769i	$-0.478735\pi$
$131$	12.1840	−	12.1840i	1.06452	−	1.06452i	0.997769	−	0.0667551i	$-0.0212646\pi$
$132$	−0.762504	−	2.29056i	−0.0663674	−	0.199367i
$133$	4.47354	+	4.47354i	0.387905	+	0.387905i
$134$	−14.4670	+	2.34471i	−1.24976	+	0.202552i
$135$			3.39235i			0.291967i
$136$	5.01863	−	16.0323i	0.430344	−	1.37475i
$137$		−	13.2021i		−	1.12793i	−0.825798	−	0.563966i	$-0.809275\pi$
$137$		−	13.2021i		−	1.12793i	0.825798	−	0.563966i	$-0.190725\pi$
$138$	−0.473490	−	2.92146i	−0.0403062	−	0.248692i
$139$	−4.64113	−	4.64113i	−0.393655	−	0.393655i	0.482333	−	0.875988i	$-0.339790\pi$
$139$	−4.64113	−	4.64113i	−0.393655	−	0.393655i	−0.875988	+	0.482333i	$0.839790\pi$
$140$	6.06721	+	3.03663i	0.512773	+	0.256642i
$141$	3.08797	−	3.08797i	0.260054	−	0.260054i
$142$	1.01329	−	1.40528i	0.0850338	−	0.117928i
$143$	−6.18848			−0.517507
$144$	2.39745	+	3.20191i	0.199787	+	0.266826i
$145$	2.77079			0.230101
$146$	−13.8510	+	19.2091i	−1.14632	+	1.58976i
$147$	0.707107	−	0.707107i	0.0583212	−	0.0583212i
$148$	−7.80002	+	15.5845i	−0.641157	+	1.28104i
$149$	−3.52400	−	3.52400i	−0.288697	−	0.288697i	0.547868	−	0.836565i	$-0.315440\pi$
$149$	−3.52400	−	3.52400i	−0.288697	−	0.288697i	−0.836565	+	0.547868i	$0.815440\pi$
$150$	1.47247	+	9.08521i	0.120226	+	0.741804i
$151$			13.7247i			1.11690i	0.829538	+	0.558450i	$0.188604\pi$
$151$			13.7247i			1.11690i	−0.829538	+	0.558450i	$0.811396\pi$
$152$	8.29531	+	15.8552i	0.672839	+	1.28603i
$153$		−	5.93949i		−	0.480179i
$154$	−1.68507	+	0.273103i	−0.135786	+	0.0220073i
$155$	7.75201	+	7.75201i	0.622656	+	0.622656i
$156$	9.72884	−	3.23863i	0.778931	−	0.259298i
$157$	11.6938	−	11.6938i	0.933270	−	0.933270i	−0.0646385	−	0.997909i	$-0.520589\pi$
$157$	11.6938	−	11.6938i	0.933270	−	0.933270i	0.997909	+	0.0646385i	$0.0205894\pi$
$158$	6.18554	+	4.46016i	0.492095	+	0.354831i
$159$	1.68482			0.133615
$160$	13.8112	+	13.3232i	1.09187	+	1.05329i
$161$	−2.09274			−0.164931
$162$	1.14710	+	0.827134i	0.0901251	+	0.0649858i
$163$	−11.4247	+	11.4247i	−0.894853	+	0.894853i	−0.994975	−	0.100122i	$-0.968077\pi$
$163$	−11.4247	+	11.4247i	−0.894853	+	0.894853i	0.100122	+	0.994975i	$0.468077\pi$
$164$	−15.7613	+	5.24677i	−1.23075	+	0.409704i
$165$	−2.89546	−	2.89546i	−0.225411	−	0.225411i
$166$	−18.5233	+	3.00212i	−1.43769	+	0.233010i
$167$			10.7449i			0.831467i	0.909487	+	0.415733i	$0.136475\pi$
$167$			10.7449i			0.831467i	−0.909487	+	0.415733i	$0.863525\pi$
$168$	2.50615	−	1.31119i	0.193353	−	0.101161i
$169$		−	13.2848i		−	1.02191i
$170$	−4.55874	−	28.1277i	−0.349639	−	2.15730i
$171$	4.47354	+	4.47354i	0.342100	+	0.342100i
$172$	7.19308	−	14.3718i	0.548467	−	1.09584i
$173$	6.57192	−	6.57192i	0.499654	−	0.499654i	−0.411676	−	0.911330i	$-0.635057\pi$
$173$	6.57192	−	6.57192i	0.499654	−	0.499654i	0.911330	+	0.411676i	$0.135057\pi$
$174$	0.675582	−	0.936926i	0.0512158	−	0.0710282i
$175$	6.50804			0.491962
$176$	−4.77920	−	0.686635i	−0.360246	−	0.0517571i
$177$	−11.2359			−0.844543
$178$	−7.32656	+	10.1608i	−0.549149	+	0.761583i
$179$	6.90771	−	6.90771i	0.516307	−	0.516307i	−0.400145	−	0.916452i	$-0.631040\pi$
$179$	6.90771	−	6.90771i	0.516307	−	0.516307i	0.916452	+	0.400145i	$0.131040\pi$
$180$	6.06721	+	3.03663i	0.452223	+	0.226337i
$181$	11.5423	+	11.5423i	0.857930	+	0.857930i	0.991094	−	0.133164i	$-0.0425137\pi$
$181$	11.5423	+	11.5423i	0.857930	+	0.857930i	−0.133164	+	0.991094i	$0.542514\pi$
$182$	−1.15997	−	7.15710i	−0.0859828	−	0.530519i
$183$		−	7.87032i		−	0.581791i
$184$	−5.64887	−	1.76829i	−0.416440	−	0.130360i
$185$			29.5600i			2.17330i
$186$	4.51142	−	0.731179i	0.330793	−	0.0536126i
$187$	5.06951	+	5.06951i	0.370719	+	0.370719i
$188$	−2.75866	−	8.28699i	−0.201196	−	0.604391i
$189$	0.707107	−	0.707107i	0.0514344	−	0.0514344i
$190$	24.6190	+	17.7518i	1.78605	+	1.28785i
$191$	23.0461			1.66756			0.833779	−	0.552098i	$-0.186172\pi$
$191$	23.0461			1.66756			0.833779	+	0.552098i	$0.186172\pi$
$192$	7.87267	−	1.42166i	0.568161	−	0.102600i
$193$	−3.92688			−0.282663			−0.141332	−	0.989962i	$-0.545138\pi$
$193$	−3.92688			−0.282663			−0.141332	+	0.989962i	$0.545138\pi$
$194$	−16.5197	−	11.9117i	−1.18605	−	0.855214i
$195$	12.2981	−	12.2981i	0.880685	−	0.880685i
$196$	−0.631698	−	1.89762i	−0.0451213	−	0.135544i
$197$	1.86086	+	1.86086i	0.132581	+	0.132581i	0.770283	−	0.637702i	$-0.220115\pi$
$197$	1.86086	+	1.86086i	0.132581	+	0.132581i	−0.637702	+	0.770283i	$0.720115\pi$
$198$	−1.68507	+	0.273103i	−0.119752	+	0.0194086i
$199$			19.5860i			1.38841i	0.719775	+	0.694207i	$0.244245\pi$
$199$			19.5860i			1.38841i	−0.719775	+	0.694207i	$0.755755\pi$
$200$	17.5669	+	5.49904i	1.24217	+	0.388841i
$201$			10.3632i			0.730964i
$202$	1.72959	+	10.6717i	0.121693	+	0.750856i
$203$	−0.577547	−	0.577547i	−0.0405359	−	0.0405359i
$204$	−10.6228	−	5.31668i	−0.743742	−	0.372242i
$205$	−19.9236	+	19.9236i	−1.39152	+	1.39152i
$206$	−0.539059	+	0.747589i	−0.0375580	+	0.0520870i
$207$	−2.09274			−0.145456
$208$	2.91639	−	20.2990i	0.202216	−	1.40749i
$209$	−7.63657			−0.528233
$210$	2.80593	−	3.89138i	0.193627	−	0.268531i
$211$	−11.5602	+	11.5602i	−0.795839	+	0.795839i	−0.982436	−	0.186597i	$-0.940254\pi$
$211$	−11.5602	+	11.5602i	−0.795839	+	0.795839i	0.186597	+	0.982436i	$0.440254\pi$
$212$	1.50815	−	3.01330i	0.103580	−	0.206954i
$213$	−0.866253	−	0.866253i	−0.0593547	−	0.0593547i
$214$	0.987417	+	6.09242i	0.0674984	+	0.416469i
$215$		−	27.2599i		−	1.85911i
$216$	2.50615	−	1.31119i	0.170522	−	0.0892153i
$217$		−	3.23168i		−	0.219381i
$218$	−5.17375	+	0.838524i	−0.350410	+	0.0567920i
$219$	11.8410	+	11.8410i	0.800143	+	0.800143i
$220$	−7.77037	+	2.58668i	−0.523878	+	0.174394i
$221$	−21.5321	+	21.5321i	−1.44840	+	1.44840i
$222$	9.99556	+	7.20742i	0.670858	+	0.483731i
$223$	2.81057			0.188210			0.0941050	−	0.995562i	$-0.470001\pi$
$223$	2.81057			0.188210			0.0941050	+	0.995562i	$0.470001\pi$
$224$	−0.101709	−	5.65594i	−0.00679570	−	0.377903i
$225$	6.50804			0.433869
$226$	0.816431	+	0.588698i	0.0543082	+	0.0391596i
$227$	3.83261	−	3.83261i	0.254379	−	0.254379i	−0.568384	−	0.822763i	$-0.692431\pi$
$227$	3.83261	−	3.83261i	0.254379	−	0.254379i	0.822763	+	0.568384i	$0.192431\pi$
$228$	12.0054	−	3.99647i	0.795075	−	0.264672i
$229$	−15.1988	−	15.1988i	−1.00436	−	1.00436i	−0.999990	−	0.00437398i	$-0.998608\pi$
$229$	−15.1988	−	15.1988i	−1.00436	−	1.00436i	−0.00437398	−	0.999990i	$-0.501392\pi$
$230$	−9.91063	+	1.60624i	−0.653488	+	0.105913i
$231$			1.20707i			0.0794193i
$232$	−1.07095	−	2.04696i	−0.0703112	−	0.134389i
$233$		−	11.6958i		−	0.766218i	−0.923703	−	0.383109i	$-0.874853\pi$
$233$		−	11.6958i		−	0.766218i	0.923703	−	0.383109i	$-0.125147\pi$
$234$	−1.15997	−	7.15710i	−0.0758297	−	0.467874i
$235$	−10.4755	−	10.4755i	−0.683344	−	0.683344i
$236$	−10.0577	+	20.0954i	−0.654702	+	1.30810i
$237$	3.81294	−	3.81294i	0.247677	−	0.247677i
$238$	−4.91275	+	6.81321i	−0.318446	+	0.441635i
$239$	7.55216			0.488509			0.244254	−	0.969711i	$-0.421457\pi$
$239$	7.55216			0.488509			0.244254	+	0.969711i	$0.421457\pi$
$240$	10.8620	−	8.13298i	0.701140	−	0.524981i
$241$	12.4497			0.801954			0.400977	−	0.916088i	$-0.368671\pi$
$241$	12.4497			0.801954			0.400977	+	0.916088i	$0.368671\pi$
$242$	−7.89333	+	10.9468i	−0.507402	+	0.703687i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−14.0761	−	7.04505i	−0.901127	−	0.451013i
$245$	−2.39875	−	2.39875i	−0.153251	−	0.153251i
$246$	1.87922	+	11.5949i	0.119815	+	0.739263i
$247$		−	32.4354i		−	2.06381i
$248$	2.73065	−	8.72317i	0.173396	−	0.553922i
$249$			13.2688i			0.840879i
$250$	7.14165	−	1.15747i	0.451677	−	0.0732047i
$251$	4.65128	+	4.65128i	0.293586	+	0.293586i	0.838495	−	0.544909i	$-0.183436\pi$
$251$	4.65128	+	4.65128i	0.293586	+	0.293586i	−0.544909	+	0.838495i	$0.683436\pi$
$252$	−0.631698	−	1.89762i	−0.0397933	−	0.119539i
$253$	1.78621	−	1.78621i	0.112298	−	0.112298i
$254$	5.16898	+	3.72716i	0.324331	+	0.233863i
$255$	−20.1488			−1.26177
$256$	4.50451	−	15.3528i	0.281532	−	0.959552i
$257$	−17.3066			−1.07955			−0.539777	−	0.841808i	$-0.681491\pi$
$257$	−17.3066			−1.07955			−0.539777	+	0.841808i	$0.681491\pi$
$258$	−9.21778	−	6.64660i	−0.573874	−	0.413799i
$259$	6.16154	−	6.16154i	0.382859	−	0.382859i
$260$	−10.9866	−	33.0036i	−0.681359	−	2.04680i
$261$	−0.577547	−	0.577547i	−0.0357493	−	0.0357493i
$262$	−24.0542	+	3.89853i	−1.48607	+	0.240852i
$263$			29.7288i			1.83316i	0.399855	+	0.916578i	$0.369060\pi$
$263$			29.7288i			1.83316i	−0.399855	+	0.916578i	$0.630940\pi$
$264$	−1.01993	+	3.25820i	−0.0627721	+	0.200528i
$265$		−	5.71550i		−	0.351100i
$266$	−1.43140	−	8.83184i	−0.0877649	−	0.541515i
$267$	6.26339	+	6.26339i	0.383313	+	0.383313i
$268$	18.5346	+	9.27652i	1.13218	+	0.566654i
$269$	−7.58274	+	7.58274i	−0.462328	+	0.462328i	−0.899418	−	0.437090i	$-0.856009\pi$
$269$	−7.58274	+	7.58274i	−0.462328	+	0.462328i	0.437090	+	0.899418i	$0.356009\pi$
$270$	2.80593	−	3.89138i	0.170763	−	0.236822i
$271$	−6.97285			−0.423570			−0.211785	−	0.977316i	$-0.567928\pi$
$271$	−6.97285			−0.423570			−0.211785	+	0.977316i	$0.567928\pi$
$272$	−19.0177	+	14.2396i	−1.15312	+	0.863402i
$273$	−5.12687			−0.310292
$274$	−10.9199	+	15.1442i	−0.659696	+	0.914895i
$275$	−5.55479	+	5.55479i	−0.334966	+	0.334966i
$276$	−1.87330	+	3.74287i	−0.112759	+	0.225294i
$277$	−19.5642	−	19.5642i	−1.17550	−	1.17550i	−0.980879	−	0.194617i	$-0.937654\pi$
$277$	−19.5642	−	19.5642i	−1.17550	−	1.17550i	−0.194617	−	0.980879i	$-0.562346\pi$
$278$	1.48502	+	9.16269i	0.0890658	+	0.549542i
$279$		−	3.23168i		−	0.193476i
$280$	−4.44802	−	8.50173i	−0.265820	−	0.508076i
$281$		−	26.2137i		−	1.56378i	−0.623419	−	0.781888i	$-0.714257\pi$
$281$		−	26.2137i		−	1.56378i	0.623419	−	0.781888i	$-0.285743\pi$
$282$	−6.09639	+	0.988059i	−0.363035	+	0.0588381i
$283$	3.87349	+	3.87349i	0.230255	+	0.230255i	0.812799	−	0.582544i	$-0.197943\pi$
$283$	3.87349	+	3.87349i	0.230255	+	0.230255i	−0.582544	+	0.812799i	$0.697943\pi$
$284$	−2.32471	+	0.773873i	−0.137946	+	0.0459209i
$285$	15.1758	−	15.1758i	0.898938	−	0.898938i
$286$	7.09884	+	5.11871i	0.419763	+	0.302675i
$287$	8.30581			0.490276
$288$	−0.101709	−	5.65594i	−0.00599324	−	0.333279i
$289$	18.2775			1.07515
$290$	−3.17838	−	2.29181i	−0.186641	−	0.134580i
$291$	−10.1832	+	10.1832i	−0.596950	+	0.596950i
$292$	31.7771	−	10.5783i	1.85961	−	0.619046i
$293$	−16.0156	−	16.0156i	−0.935639	−	0.935639i	0.0624114	−	0.998051i	$-0.480121\pi$
$293$	−16.0156	−	16.0156i	−0.935639	−	0.935639i	−0.998051	+	0.0624114i	$0.980121\pi$
$294$	−1.39600	+	0.226253i	−0.0814162	+	0.0131954i
$295$			38.1161i			2.21921i
$296$	21.8379	−	11.4254i	1.26930	−	0.664086i
$297$			1.20707i			0.0700412i
$298$	1.12758	+	6.95721i	0.0653187	+	0.403020i
$299$	7.58670	+	7.58670i	0.438750	+	0.438750i
$300$	5.82561	−	11.6396i	0.336342	−	0.672013i
$301$	−5.68209	+	5.68209i	−0.327510	+	0.327510i
$302$	11.3522	−	15.7437i	0.653244	−	0.905947i
$303$	7.64447			0.439163
$304$	3.59882	−	25.0490i	0.206407	−	1.43666i
$305$	−26.6989			−1.52877
$306$	−4.91275	+	6.81321i	−0.280843	+	0.389485i
$307$	18.0941	−	18.0941i	1.03269	−	1.03269i	0.0332401	−	0.999447i	$-0.489417\pi$
$307$	18.0941	−	18.0941i	1.03269	−	1.03269i	0.999447	−	0.0332401i	$-0.0105826\pi$
$308$	2.15884	+	1.08050i	0.123011	+	0.0615670i
$309$	0.460835	+	0.460835i	0.0262160	+	0.0262160i
$310$	−2.48042	−	15.3043i	−0.140878	−	0.869227i
$311$		−	14.7667i		−	0.837341i	−0.908138	−	0.418671i	$-0.862496\pi$
$311$		−	14.7667i		−	0.837341i	0.908138	−	0.418671i	$-0.137504\pi$
$312$	−13.8388	−	4.33200i	−0.783467	−	0.245251i
$313$			17.5260i			0.990629i	0.868714	+	0.495314i	$0.164947\pi$
$313$			17.5260i			0.990629i	−0.868714	+	0.495314i	$0.835053\pi$
$314$	−23.0864	+	3.74169i	−1.30284	+	0.211156i
$315$	−2.39875	−	2.39875i	−0.135154	−	0.135154i
$316$	−3.40631	−	10.2325i	−0.191620	−	0.575625i
$317$	−9.97053	+	9.97053i	−0.560001	+	0.560001i	−0.929308	−	0.369307i	$-0.879595\pi$
$317$	−9.97053	+	9.97053i	−0.560001	+	0.560001i	0.369307	+	0.929308i	$0.379595\pi$
$318$	−1.93266	−	1.39357i	−0.108378	−	0.0781476i
$319$	0.985904			0.0552000
$320$	−4.82277	−	26.7068i	−0.269601	−	1.49296i
$321$	4.36421			0.243586
$322$	2.40060	+	1.73098i	0.133780	+	0.0964637i
$323$	−26.5705	+	26.5705i	−1.47842	+	1.47842i
$324$	−0.631698	−	1.89762i	−0.0350944	−	0.105423i
$325$	−23.5932	−	23.5932i	−1.30872	−	1.30872i
$326$	22.5551	−	3.65558i	1.24921	−	0.202464i
$327$			3.70613i			0.204949i
$328$	22.4196	+	7.01808i	1.23791	+	0.387509i
$329$			4.36705i			0.240763i
$330$	0.926463	+	5.71633i	0.0510001	+	0.314674i
$331$	−19.6341	−	19.6341i	−1.07919	−	1.07919i	−0.996582	−	0.0826082i	$-0.973675\pi$
$331$	−19.6341	−	19.6341i	−1.07919	−	1.07919i	−0.0826082	−	0.996582i	$-0.526325\pi$
$332$	23.7313	+	11.8775i	1.30242	+	0.651862i
$333$	6.16154	−	6.16154i	0.337650	−	0.337650i
$334$	8.88749	−	12.3255i	0.486302	−	0.674424i
$335$	35.1556			1.92076
$336$	−3.95935	−	0.568845i	−0.216000	−	0.0310331i
$337$	1.88595			0.102734			0.0513670	−	0.998680i	$-0.483642\pi$
$337$	1.88595			0.102734			0.0513670	+	0.998680i	$0.483642\pi$
$338$	−10.9883	+	15.2390i	−0.597685	+	0.828894i
$339$	0.503270	−	0.503270i	0.0273339	−	0.0273339i
$340$	−18.0360	+	36.0361i	−0.978141	+	1.95433i
$341$	2.75833	+	2.75833i	0.149372	+	0.149372i
$342$	−1.43140	−	8.83184i	−0.0774013	−	0.477571i
$343$			1.00000i			0.0539949i
$344$	−20.1386	+	10.5363i	−1.08580	+	0.568081i
$345$			7.09932i			0.382214i
$346$	−12.9745	+	2.10282i	−0.697516	+	0.113048i
$347$	20.0890	+	20.0890i	1.07843	+	1.07843i	0.996650	+	0.0817846i	$0.0260620\pi$
$347$	20.0890	+	20.0890i	1.07843	+	1.07843i	0.0817846	+	0.996650i	$0.473938\pi$
$348$	−1.54993	+	0.515955i	−0.0830848	+	0.0276581i
$349$	−14.2013	+	14.2013i	−0.760180	+	0.760180i	−0.976355	−	0.216175i	$-0.930642\pi$
$349$	−14.2013	+	14.2013i	−0.760180	+	0.760180i	0.216175	+	0.976355i	$0.430642\pi$
$350$	−7.46540	−	5.38302i	−0.399043	−	0.287735i
$351$	−5.12687			−0.273652
$352$	4.91431	+	4.74068i	0.261933	+	0.252679i
$353$	16.6971			0.888696			0.444348	−	0.895854i	$-0.353435\pi$
$353$	16.6971			0.888696			0.444348	+	0.895854i	$0.353435\pi$
$354$	12.8888	+	9.29361i	0.685030	+	0.493950i
$355$	−2.93863	+	2.93863i	−0.155967	+	0.155967i
$356$	16.8087	−	5.59544i	0.890857	−	0.296558i
$357$	4.19985	+	4.19985i	0.222280	+	0.222280i
$358$	−13.6375	+	2.21027i	−0.720763	+	0.116816i
$359$		−	14.0866i		−	0.743463i	−0.928340	−	0.371732i	$-0.878764\pi$
$359$		−	14.0866i		−	0.743463i	0.928340	−	0.371732i	$-0.121236\pi$
$360$	−4.44802	−	8.50173i	−0.234431	−	0.448081i
$361$		−	21.0251i		−	1.10659i
$362$	−3.69319	−	22.7872i	−0.194110	−	1.19767i
$363$	6.74791	+	6.74791i	0.354173	+	0.354173i
$364$	−4.58927	+	9.16939i	−0.240543	+	0.480607i
$365$	40.1689	−	40.1689i	2.10254	−	2.10254i
$366$	−6.50981	+	9.02809i	−0.340273	+	0.471906i
$367$	14.4302			0.753253			0.376626	−	0.926365i	$-0.377084\pi$
$367$	14.4302			0.753253			0.376626	+	0.926365i	$0.377084\pi$
$368$	5.01724	+	6.70078i	0.261542	+	0.349302i
$369$	8.30581			0.432383
$370$	24.4501	−	33.9084i	1.27110	−	1.76282i
$371$	−1.19135	+	1.19135i	−0.0618517	+	0.0618517i
$372$	−5.77985	−	2.89281i	−0.299672	−	0.149985i
$373$	17.5493	+	17.5493i	0.908670	+	0.908670i	0.996165	−	0.0874952i	$-0.0278862\pi$
$373$	17.5493	+	17.5493i	0.908670	+	0.908670i	−0.0874952	+	0.996165i	$0.527886\pi$
$374$	−1.62209	−	10.0084i	−0.0838765	−	0.517523i
$375$		−	5.11580i		−	0.264179i
$376$	−3.68998	+	11.7878i	−0.190296	+	0.607911i
$377$			4.18750i			0.215667i
$378$	−1.39600	+	0.226253i	−0.0718024	+	0.0116372i
$379$	6.24414	+	6.24414i	0.320740	+	0.320740i	0.849051	−	0.528311i	$-0.177174\pi$
$379$	6.24414	+	6.24414i	0.320740	+	0.320740i	−0.528311	+	0.849051i	$0.677174\pi$
$380$	−13.5574	−	40.7264i	−0.695481	−	2.08922i
$381$	3.18630	−	3.18630i	0.163239	−	0.163239i
$382$	−26.4363	−	19.0622i	−1.35260	−	0.975309i
$383$	−12.7944			−0.653765			−0.326882	−	0.945065i	$-0.605998\pi$
$383$	−12.7944			−0.653765			−0.326882	+	0.945065i	$0.605998\pi$
$384$	−10.2067	−	4.88096i	−0.520857	−	0.249080i
$385$	4.09480			0.208690
$386$	4.50454	+	3.24806i	0.229275	+	0.165322i
$387$	−5.68209	+	5.68209i	−0.288837	+	0.288837i
$388$	9.09723	+	27.3280i	0.461842	+	1.38737i
$389$	8.04290	+	8.04290i	0.407791	+	0.407791i	0.880968	−	0.473176i	$-0.156893\pi$
$389$	8.04290	+	8.04290i	0.407791	+	0.407791i	−0.473176	+	0.880968i	$0.656893\pi$
$390$	−24.2794	+	3.93503i	−1.22943	+	0.199258i
$391$		−	12.4298i		−	0.628603i
$392$	−0.844961	+	2.69927i	−0.0426770	+	0.136334i
$393$			17.2308i			0.869181i
$394$	−0.595419	−	3.67378i	−0.0299968	−	0.185082i
$395$	−12.9348	−	12.9348i	−0.650821	−	0.650821i
$396$	2.15884	+	1.08050i	0.108486	+	0.0542970i
$397$	−26.8588	+	26.8588i	−1.34800	+	1.34800i	−0.460174	+	0.887829i	$0.652213\pi$
$397$	−26.8588	+	26.8588i	−1.34800	+	1.34800i	−0.887829	+	0.460174i	$0.847787\pi$
$398$	16.2003	−	22.4672i	0.812045	−	1.12618i
$399$	−6.32654			−0.316723
$400$	−15.6027	−	20.8382i	−0.780134	−	1.04191i
$401$	−2.20842			−0.110283			−0.0551417	−	0.998479i	$-0.517561\pi$
$401$	−2.20842			−0.110283			−0.0551417	+	0.998479i	$0.517561\pi$
$402$	8.57176	−	11.8877i	0.427520	−	0.592903i
$403$	−11.7156	+	11.7156i	−0.583597	+	0.583597i
$404$	6.84288	−	13.6721i	0.340446	−	0.680213i
$405$	−2.39875	−	2.39875i	−0.119195	−	0.119195i
$406$	0.184798	+	1.14022i	0.00917138	+	0.0565880i
$407$			10.5181i			0.521362i
$408$	7.78781	+	14.8852i	0.385554	+	0.736929i
$409$			14.0078i			0.692639i	0.938117	+	0.346320i	$0.112569\pi$
$409$			14.0078i			0.692639i	−0.938117	+	0.346320i	$0.887431\pi$
$410$	39.3339	−	6.37496i	1.94256	−	0.314837i
$411$	9.33530	+	9.33530i	0.460476	+	0.460476i
$412$	1.23671	−	0.411690i	0.0609285	−	0.0202825i
$413$	7.94499	−	7.94499i	0.390947	−	0.390947i
$414$	2.40060	+	1.73098i	0.117983	+	0.0850730i
$415$	45.0126			2.20958
$416$	−20.1354	+	20.8729i	−0.987221	+	1.02338i
$417$	6.56354			0.321418
$418$	8.75995	+	6.31647i	0.428463	+	0.308949i
$419$	−27.8858	+	27.8858i	−1.36231	+	1.36231i	−0.491346	+	0.870964i	$0.663495\pi$
$419$	−27.8858	+	27.8858i	−1.36231	+	1.36231i	−0.870964	+	0.491346i	$0.836505\pi$
$420$	−6.43739	+	2.14294i	−0.314112	+	0.104565i
$421$	11.4796	+	11.4796i	0.559479	+	0.559479i	0.929159	−	0.369680i	$-0.120533\pi$
$421$	11.4796	+	11.4796i	0.559479	+	0.559479i	−0.369680	+	0.929159i	$0.620533\pi$
$422$	22.8227	−	3.69893i	1.11099	−	0.180061i
$423$			4.36705i			0.212333i
$424$	−4.22241	+	2.20912i	−0.205058	+	0.107284i
$425$			38.6544i			1.87501i
$426$	0.277176	+	1.71019i	0.0134292	+	0.0828590i
$427$	5.56516	+	5.56516i	0.269317	+	0.269317i
$428$	3.90658	−	7.80537i	0.188832	−	0.377287i
$429$	4.37592	−	4.37592i	0.211271	−	0.211271i
$430$	−22.5476	+	31.2699i	−1.08734	+	1.50797i
$431$	−28.2701			−1.36173			−0.680863	−	0.732411i	$-0.738395\pi$
$431$	−28.2701			−1.36173			−0.680863	+	0.732411i	$0.738395\pi$
$432$	−3.95935	−	0.568845i	−0.190494	−	0.0273686i
$433$	−23.2939			−1.11943			−0.559717	−	0.828684i	$-0.689090\pi$
$433$	−23.2939			−1.11943			−0.559717	+	0.828684i	$0.689090\pi$
$434$	−2.67303	+	3.70708i	−0.128310	+	0.177945i
$435$	−1.95924	+	1.95924i	−0.0939385	+	0.0939385i
$436$	6.62840	+	3.31751i	0.317443	+	0.158880i
$437$	9.36197	+	9.36197i	0.447844	+	0.447844i
$438$	−3.78878	−	23.3770i	−0.181035	−	1.11700i
$439$			15.2907i			0.729783i	0.931050	+	0.364892i	$0.118894\pi$
$439$			15.2907i			0.729783i	−0.931050	+	0.364892i	$0.881106\pi$
$440$	11.0530	+	3.45995i	0.526929	+	0.164946i
$441$			1.00000i			0.0476190i
$442$	42.5095	−	6.88964i	2.02197	−	0.327707i
$443$	−0.931426	−	0.931426i	−0.0442534	−	0.0442534i	0.684634	−	0.728887i	$-0.259962\pi$
$443$	−0.931426	−	0.931426i	−0.0442534	−	0.0442534i	−0.728887	+	0.684634i	$0.759962\pi$
$444$	−5.50445	−	16.5353i	−0.261230	−	0.784732i
$445$	21.2476	−	21.2476i	1.00723	−	1.00723i
$446$	−3.22402	−	2.32472i	−0.152662	−	0.110079i
$447$	4.98368			0.235720
$448$	−4.56155	+	6.57208i	−0.215513	+	0.310502i
$449$	2.44155			0.115224			0.0576118	−	0.998339i	$-0.481651\pi$
$449$	2.44155			0.115224			0.0576118	+	0.998339i	$0.481651\pi$
$450$	−7.46540	−	5.38302i	−0.351923	−	0.253758i
$451$	−7.08923	+	7.08923i	−0.333819	+	0.333819i
$452$	−0.449600	−	1.35060i	−0.0211474	−	0.0635267i
$453$	−9.70483	−	9.70483i	−0.455973	−	0.455973i
$454$	−7.56649	+	1.22632i	−0.355113	+	0.0575542i
$455$			17.3921i			0.815356i
$456$	−17.0770	−	5.34568i	−0.799705	−	0.250334i
$457$		−	18.6600i		−	0.872876i	−0.899734	−	0.436438i	$-0.856240\pi$
$457$		−	18.6600i		−	0.872876i	0.899734	−	0.436438i	$-0.143760\pi$
$458$	4.86317	+	30.0060i	0.227241	+	1.40209i
$459$	4.19985	+	4.19985i	0.196032	+	0.196032i
$460$	12.6971	+	6.35489i	0.592006	+	0.296298i
$461$	5.79479	−	5.79479i	0.269890	−	0.269890i	−0.559166	−	0.829056i	$-0.688878\pi$
$461$	5.79479	−	5.79479i	0.269890	−	0.269890i	0.829056	+	0.559166i	$0.188878\pi$
$462$	0.998408	−	1.38463i	0.0464501	−	0.0644190i
$463$	−16.7406			−0.778004			−0.389002	−	0.921237i	$-0.627180\pi$
$463$	−16.7406			−0.778004			−0.389002	+	0.921237i	$0.627180\pi$
$464$	−0.464619	+	3.23389i	−0.0215694	+	0.150130i
$465$	−10.9630			−0.508397
$466$	−9.67400	+	13.4163i	−0.448139	+	0.621499i
$467$	20.5045	−	20.5045i	0.948835	−	0.948835i	−0.0499181	−	0.998753i	$-0.515896\pi$
$467$	20.5045	−	20.5045i	0.948835	−	0.948835i	0.998753	+	0.0499181i	$0.0158960\pi$
$468$	−4.58927	+	9.16939i	−0.212139	+	0.423855i
$469$	−7.32789	−	7.32789i	−0.338370	−	0.338370i
$470$	3.35184	+	20.6811i	0.154609	+	0.953947i
$471$			16.5376i			0.762012i
$472$	28.1589	−	14.7324i	1.29612	−	0.678115i
$473$		−	9.69964i		−	0.445990i
$474$	−7.52765	+	1.22003i	−0.345756	+	0.0560377i
$475$	−29.1140	−	29.1140i	−1.33584	−	1.33584i
$476$	11.2709	−	3.75196i	0.516600	−	0.171971i
$477$	−1.19135	+	1.19135i	−0.0545481	+	0.0545481i
$478$	−8.66312	−	6.24665i	−0.396242	−	0.285715i
$479$	10.8033			0.493615			0.246808	−	0.969064i	$-0.420618\pi$
$479$	10.8033			0.493615			0.246808	+	0.969064i	$0.420618\pi$
$480$	−19.1869	+	0.345032i	−0.875760	+	0.0157485i
$481$	−44.6742			−2.03697
$482$	−14.2811	−	10.2975i	−0.650485	−	0.469040i
$483$	1.47979	−	1.47979i	0.0673329	−	0.0673329i
$484$	18.1089	−	6.02829i	0.823134	−	0.274013i
$485$	34.5450	+	34.5450i	1.56861	+	1.56861i
$486$	−1.39600	+	0.226253i	−0.0633237	+	0.0102631i
$487$		−	20.7316i		−	0.939440i	−0.882815	−	0.469720i	$-0.844355\pi$
$487$		−	20.7316i		−	0.939440i	0.882815	−	0.469720i	$-0.155645\pi$
$488$	10.3195	+	19.7242i	0.467142	+	0.892872i
$489$		−	16.1570i		−	0.730645i
$490$	0.767531	+	4.73571i	0.0346735	+	0.213938i
$491$	−5.14822	−	5.14822i	−0.232336	−	0.232336i	0.581331	−	0.813667i	$-0.302532\pi$
$491$	−5.14822	−	5.14822i	−0.232336	−	0.232336i	−0.813667	+	0.581331i	$0.802532\pi$
$492$	7.43487	−	14.8549i	0.335190	−	0.669711i
$493$	3.43033	−	3.43033i	0.154494	−	0.154494i
$494$	−26.8284	+	37.2067i	−1.20707	+	1.67401i
$495$	4.09480			0.184048
$496$	−10.3476	+	7.74778i	−0.464620	+	0.347886i
$497$	1.22507			0.0549518
$498$	10.9751	−	15.2208i	0.491807	−	0.682058i
$499$	4.51117	−	4.51117i	0.201948	−	0.201948i	−0.598886	−	0.800834i	$-0.704390\pi$
$499$	4.51117	−	4.51117i	0.201948	−	0.201948i	0.800834	+	0.598886i	$0.204390\pi$
$500$	−9.14960	−	4.57936i	−0.409183	−	0.204795i
$501$	−7.59780	−	7.59780i	−0.339445	−	0.339445i
$502$	−1.48827	−	9.18274i	−0.0664249	−	0.409846i
$503$			1.60307i			0.0714773i	0.999361	+	0.0357386i	$0.0113784\pi$
$503$			1.60307i			0.0714773i	−0.999361	+	0.0357386i	$0.988622\pi$
$504$	−0.844961	+	2.69927i	−0.0376376	+	0.120235i
$505$		−	25.9327i		−	1.15399i
$506$	−3.52641	+	0.571535i	−0.156768	+	0.0254078i
$507$	9.39376	+	9.39376i	0.417192	+	0.417192i
$508$	−2.84651	−	8.55089i	−0.126293	−	0.379384i
$509$	−19.9091	+	19.9091i	−0.882457	+	0.882457i	−0.993784	−	0.111327i	$-0.964490\pi$
$509$	−19.9091	+	19.9091i	−0.882457	+	0.882457i	0.111327	+	0.993784i	$0.464490\pi$
$510$	23.1128	+	16.6658i	1.02345	+	0.737973i
$511$	−16.7458			−0.740789
$512$	−17.8660	+	13.8855i	−0.789573	+	0.613657i
$513$	−6.32654			−0.279324
$514$	19.8524	+	14.3148i	0.875654	+	0.631401i
$515$	1.56331	−	1.56331i	0.0688878	−	0.0688878i
$516$	5.07614	+	15.2487i	0.223464	+	0.671286i
$517$	−3.72739	−	3.72739i	−0.163930	−	0.163930i
$518$	−12.1643	+	1.97151i	−0.534471	+	0.0866232i
$519$			9.29410i			0.407966i
$520$	−14.6957	+	46.9460i	−0.644448	+	2.05872i
$521$			31.5251i			1.38114i	0.723266	+	0.690570i	$0.242640\pi$
$521$			31.5251i			1.38114i	−0.723266	+	0.690570i	$0.757360\pi$
$522$	0.184798	+	1.14022i	0.00808839	+	0.0499059i
$523$	−11.4795	−	11.4795i	−0.501963	−	0.501963i	0.410085	−	0.912047i	$-0.365499\pi$
$523$	−11.4795	−	11.4795i	−0.501963	−	0.501963i	−0.912047	+	0.410085i	$0.865499\pi$
$524$	30.8173	+	15.4240i	1.34626	+	0.673802i
$525$	−4.60188	+	4.60188i	−0.200842	+	0.200842i
$526$	24.5897	−	34.1020i	1.07216	−	1.48692i
$527$	19.1945			0.836127
$528$	3.86493	−	2.89388i	0.168200	−	0.125940i
$529$	18.6204			0.809584
$530$	−4.72748	+	6.55628i	−0.205349	+	0.284786i
$531$	7.94499	−	7.94499i	0.344783	−	0.344783i
$532$	−5.66315	+	11.3150i	−0.245529	+	0.490568i
$533$	−30.1106	−	30.1106i	−1.30423	−	1.30423i
$534$	−2.00410	−	12.3654i	−0.0867259	−	0.535104i
$535$		−	14.8049i		−	0.640072i
$536$	−13.5881	−	25.9717i	−0.586919	−	1.12181i
$537$			9.76898i			0.421563i
$538$	14.9701	−	2.42625i	0.645408	−	0.104603i
$539$	−0.853527	−	0.853527i	−0.0367640	−	0.0367640i
$540$	−6.43739	+	2.14294i	−0.277021	+	0.0922176i
$541$	12.9271	−	12.9271i	0.555777	−	0.555777i	−0.372325	−	0.928102i	$-0.621439\pi$
$541$	12.9271	−	12.9271i	0.555777	−	0.555777i	0.928102	+	0.372325i	$0.121439\pi$
$542$	7.99859	+	5.76748i	0.343569	+	0.247735i
$543$	−16.3232			−0.700497
$544$	33.5934	−	0.604097i	1.44030	−	0.0259005i
$545$	12.5725			0.538546
$546$	5.88106	+	4.24061i	0.251686	+	0.181481i
$547$	−5.39276	+	5.39276i	−0.230578	+	0.230578i	−0.812934	−	0.582356i	$-0.802131\pi$
$547$	−5.39276	+	5.39276i	−0.230578	+	0.230578i	0.582356	+	0.812934i	$0.302131\pi$
$548$	25.0526	−	8.33975i	1.07019	−	0.356257i
$549$	5.56516	+	5.56516i	0.237515	+	0.237515i
$550$	10.9665	−	1.77737i	0.467612	−	0.0757872i
$551$			5.16736i			0.220137i
$552$	5.24472	−	2.74399i	0.223230	−	0.116792i
$553$			5.39231i			0.229304i
$554$	6.25996	+	38.6243i	0.265960	+	1.64099i
$555$	−20.9021	−	20.9021i	−0.887244	−	0.887244i
$556$	5.87530	−	11.7389i	0.249168	−	0.497839i
$557$	23.8530	−	23.8530i	1.01068	−	1.01068i	0.0107409	−	0.999942i	$-0.496581\pi$
$557$	23.8530	−	23.8530i	1.01068	−	1.01068i	0.999942	−	0.0107409i	$-0.00341900\pi$
$558$	−2.67303	+	3.70708i	−0.113159	+	0.156933i
$559$	41.1980			1.74249
$560$	−1.92972	+	13.4315i	−0.0815457	+	0.567584i
$561$	−7.16937			−0.302691
$562$	−21.6822	+	30.0698i	−0.914609	+	1.26842i
$563$	−18.4196	+	18.4196i	−0.776295	+	0.776295i	−0.979199	−	0.202904i	$-0.934962\pi$
$563$	−18.4196	+	18.4196i	−0.776295	+	0.776295i	0.202904	+	0.979199i	$0.434962\pi$
$564$	7.81045	+	3.90912i	0.328879	+	0.164604i
$565$	−1.70727	−	1.70727i	−0.0718254	−	0.0718254i
$566$	−1.23940	−	7.64719i	−0.0520960	−	0.321436i
$567$			1.00000i			0.0419961i
$568$	3.30678	+	1.03513i	0.138750	+	0.0434333i
$569$		−	11.6801i		−	0.489654i	−0.969567	−	0.244827i	$-0.921269\pi$
$569$		−	11.6801i		−	0.489654i	0.969567	−	0.244827i	$-0.0787312\pi$
$570$	−29.9607	+	4.85582i	−1.25492	+	0.203388i
$571$	−21.6469	−	21.6469i	−0.905895	−	0.905895i	0.0900427	−	0.995938i	$-0.471300\pi$
$571$	−21.6469	−	21.6469i	−0.905895	−	0.905895i	−0.995938	+	0.0900427i	$0.971300\pi$
$572$	−3.90926	−	11.7434i	−0.163454	−	0.491016i
$573$	−16.2961	+	16.2961i	−0.680778	+	0.680778i
$574$	−9.52763	−	6.87002i	−0.397676	−	0.286749i
$575$	13.6197			0.567979
$576$	−4.56155	+	6.57208i	−0.190065	+	0.273837i
$577$	2.98173			0.124131			0.0620655	−	0.998072i	$-0.480231\pi$
$577$	2.98173			0.124131			0.0620655	+	0.998072i	$0.480231\pi$
$578$	−20.9662	−	15.1179i	−0.872080	−	0.628824i
$579$	2.77672	−	2.77672i	0.115397	−	0.115397i
$580$	1.75030	+	5.25790i	0.0726773	+	0.218322i
$581$	−9.38249	−	9.38249i	−0.389251	−	0.389251i
$582$	20.1041	−	3.25833i	0.833341	−	0.135062i
$583$		−	2.03369i		−	0.0842270i
$584$	−45.2013	−	14.1495i	−1.87044	−	0.585511i
$585$			17.3921i			0.719076i
$586$	5.12451	+	31.6185i	0.211692	+	1.30615i
$587$	15.3183	+	15.3183i	0.632253	+	0.632253i	0.948633	−	0.316380i	$-0.102467\pi$
$587$	15.3183	+	15.3183i	0.632253	+	0.632253i	−0.316380	+	0.948633i	$0.602467\pi$
$588$	1.78850	+	0.895141i	0.0737564	+	0.0369150i
$589$	−14.4571	+	14.4571i	−0.595693	+	0.595693i
$590$	31.5272	−	43.7232i	1.29795	−	1.80006i
$591$	−2.63165			−0.108252
$592$	−34.5007	−	4.95676i	−1.41797	−	0.203722i
$593$	14.9357			0.613338			0.306669	−	0.951816i	$-0.400786\pi$
$593$	14.9357			0.613338			0.306669	+	0.951816i	$0.400786\pi$
$594$	0.998408	−	1.38463i	0.0409652	−	0.0568122i
$595$	14.2474	−	14.2474i	0.584085	−	0.584085i
$596$	4.46110	−	8.91331i	0.182734	−	0.365103i
$597$	−13.8494	−	13.8494i	−0.566818	−	0.566818i
$598$	−2.42752	−	14.9780i	−0.0992688	−	0.612494i
$599$		−	7.78712i		−	0.318173i	−0.987265	−	0.159087i	$-0.949145\pi$
$599$		−	7.78712i		−	0.318173i	0.987265	−	0.159087i	$-0.0508549\pi$
$600$	−16.3101	+	8.53329i	−0.665857	+	0.348370i
$601$			20.9038i			0.852682i	0.904562	+	0.426341i	$0.140198\pi$
$601$			20.9038i			0.852682i	−0.904562	+	0.426341i	$0.859802\pi$
$602$	11.2178	−	1.81810i	0.457204	−	0.0741004i
$603$	−7.32789	−	7.32789i	−0.298415	−	0.298415i
$604$	−26.0443	+	8.66988i	−1.05973	+	0.352772i
$605$	22.8913	−	22.8913i	0.930663	−	0.930663i
$606$	−8.76901	−	6.32300i	−0.356217	−	0.256854i
$607$	−13.7472			−0.557982			−0.278991	−	0.960294i	$-0.590000\pi$
$607$	−13.7472			−0.557982			−0.278991	+	0.960294i	$0.590000\pi$
$608$	−24.8471	+	25.7571i	−1.00768	+	1.04459i
$609$	0.816775			0.0330974
$610$	30.6264	+	22.0836i	1.24003	+	0.894138i
$611$	15.8316	−	15.8316i	0.640478	−	0.640478i
$612$	11.2709	−	3.75196i	0.455598	−	0.151664i
$613$	−5.83991	−	5.83991i	−0.235872	−	0.235872i	0.579266	−	0.815138i	$-0.303339\pi$
$613$	−5.83991	−	5.83991i	−0.235872	−	0.235872i	−0.815138	+	0.579266i	$0.803339\pi$
$614$	−35.7222	+	5.78960i	−1.44163	+	0.233649i
$615$		−	28.1762i		−	1.13617i
$616$	−1.58270	−	3.02509i	−0.0637688	−	0.121884i
$617$		−	9.41702i		−	0.379115i	−0.981870	−	0.189558i	$-0.939295\pi$
$617$		−	9.41702i		−	0.379115i	0.981870	−	0.189558i	$-0.0607054\pi$
$618$	−0.147454	−	0.909797i	−0.00593145	−	0.0365974i
$619$	1.68975	+	1.68975i	0.0679167	+	0.0679167i	0.740249	−	0.672333i	$-0.234707\pi$
$619$	1.68975	+	1.68975i	0.0679167	+	0.0679167i	−0.672333	+	0.740249i	$0.734707\pi$
$620$	−9.81343	+	19.6073i	−0.394117	+	0.787448i
$621$	1.47979	−	1.47979i	0.0593820	−	0.0593820i
$622$	−12.2140	+	16.9389i	−0.489738	+	0.679189i
$623$	−8.85777			−0.354879
$624$	12.2914	+	16.4158i	0.492049	+	0.657158i
$625$	15.1856			0.607424
$626$	14.4964	−	20.1042i	0.579391	−	0.803524i
$627$	5.39987	−	5.39987i	0.215650	−	0.215650i
$628$	29.5774	+	14.8035i	1.18027	+	0.590723i
$629$	36.5964	+	36.5964i	1.45919	+	1.45919i
$630$	0.767531	+	4.73571i	0.0305792	+	0.188675i
$631$		−	20.6808i		−	0.823291i	−0.911344	−	0.411645i	$-0.864954\pi$
$631$		−	20.6808i		−	0.823291i	0.911344	−	0.411645i	$-0.135046\pi$
$632$	−4.55629	+	14.5553i	−0.181239	+	0.578978i
$633$		−	16.3486i		−	0.649800i
$634$	19.6842	−	3.19028i	0.781760	−	0.126702i
$635$	−10.8091	−	10.8091i	−0.428944	−	0.428944i
$636$	1.06430	+	3.19715i	0.0422022	+	0.126775i
$637$	3.62524	−	3.62524i	0.143637	−	0.143637i
$638$	−1.13093	−	0.815475i	−0.0447741	−	0.0322849i
$639$	1.22507			0.0484629
$640$	−16.5579	+	34.6246i	−0.654509	+	1.36866i
$641$	31.7448			1.25384			0.626922	−	0.779082i	$-0.284314\pi$
$641$	31.7448			1.25384			0.626922	+	0.779082i	$0.284314\pi$
$642$	−5.00620	−	3.60978i	−0.197579	−	0.142467i
$643$	−27.6574	+	27.6574i	−1.09070	+	1.09070i	−0.0952464	+	0.995454i	$0.530364\pi$
$643$	−27.6574	+	27.6574i	−1.09070	+	1.09070i	−0.995454	+	0.0952464i	$0.969636\pi$
$644$	−1.32198	−	3.97123i	−0.0520934	−	0.156488i
$645$	19.2757	+	19.2757i	0.758978	+	0.758978i
$646$	52.4566	−	8.50179i	2.06388	−	0.334499i
$647$		−	25.3768i		−	0.997663i	−0.866699	−	0.498832i	$-0.833763\pi$
$647$		−	25.3768i		−	0.997663i	0.866699	−	0.498832i	$-0.166237\pi$
$648$	−0.844961	+	2.69927i	−0.0331932	+	0.106037i
$649$			13.5625i			0.532375i
$650$	7.54914	+	46.5787i	0.296102	+	1.82697i
$651$	2.28514	+	2.28514i	0.0895619	+	0.0895619i
$652$	−28.8967	−	14.4628i	−1.13168	−	0.566406i
$653$	−17.1123	+	17.1123i	−0.669656	+	0.669656i	−0.957636	−	0.287980i	$-0.907016\pi$
$653$	−17.1123	+	17.1123i	−0.669656	+	0.669656i	0.287980	+	0.957636i	$0.407016\pi$
$654$	3.06547	−	4.25132i	0.119869	−	0.166240i
$655$	58.4530			2.28395
$656$	−19.9127	−	26.5945i	−0.777461	−	1.03834i
$657$	−16.7458			−0.653314
$658$	3.61213	−	5.00946i	0.140816	−	0.195289i
$659$	19.8733	−	19.8733i	0.774154	−	0.774154i	−0.204676	−	0.978830i	$-0.565614\pi$
$659$	19.8733	−	19.8733i	0.774154	−	0.774154i	0.978830	+	0.204676i	$0.0656141\pi$
$660$	3.66542	−	7.32354i	0.142676	−	0.285068i
$661$	2.81718	+	2.81718i	0.109576	+	0.109576i	0.759769	−	0.650193i	$-0.225312\pi$
$661$	2.81718	+	2.81718i	0.109576	+	0.109576i	−0.650193	+	0.759769i	$0.725312\pi$
$662$	6.28235	+	38.7625i	0.244170	+	1.50655i
$663$		−	30.4510i		−	1.18262i
$664$	−17.3980	−	33.2537i	−0.675174	−	1.29049i
$665$			21.4618i			0.832255i
$666$	−12.1643	+	1.97151i	−0.471359	+	0.0763945i
$667$	−1.20866	−	1.20866i	−0.0467994	−	0.0467994i
$668$	−20.3898	+	6.78755i	−0.788903	+	0.262618i
$669$	−1.98738	+	1.98738i	−0.0768364	+	0.0768364i
$670$	−40.3272	−	29.0784i	−1.55797	−	1.12340i
$671$	−9.50002			−0.366744
$672$	4.07127	+	3.92743i	0.157053	+	0.151504i
$673$	3.42787			0.132135			0.0660674	−	0.997815i	$-0.478955\pi$
$673$	3.42787			0.132135			0.0660674	+	0.997815i	$0.478955\pi$
$674$	−2.16338	−	1.55993i	−0.0833302	−	0.0600863i
$675$	−4.60188	+	4.60188i	−0.177126	+	0.177126i
$676$	25.2095	−	8.39198i	0.969594	−	0.322768i
$677$	−17.5257	−	17.5257i	−0.673569	−	0.673569i	0.284968	−	0.958537i	$-0.408017\pi$
$677$	−17.5257	−	17.5257i	−0.673569	−	0.673569i	−0.958537	+	0.284968i	$0.908017\pi$
$678$	−0.993576	+	0.161032i	−0.0381581	+	0.00618439i
$679$		−	14.4012i		−	0.552668i
$680$	50.4959	−	26.4190i	1.93643	−	1.01312i
$681$			5.42013i			0.207700i
$682$	−0.882584	−	5.44560i	−0.0337959	−	0.208523i
$683$	11.1841	+	11.1841i	0.427946	+	0.427946i	0.887928	−	0.459982i	$-0.152144\pi$
$683$	11.1841	+	11.1841i	0.427946	+	0.427946i	−0.459982	+	0.887928i	$0.652144\pi$
$684$	−5.66315	+	11.3150i	−0.216536	+	0.432640i
$685$	31.6686	−	31.6686i	1.21000	−	1.21000i
$686$	0.827134	−	1.14710i	0.0315801	−	0.0437967i
$687$	21.4943			0.820060
$688$	31.8161	+	4.57107i	1.21298	+	0.174270i
$689$	8.63785			0.329076
$690$	5.87209	−	8.14366i	0.223547	−	0.310024i
$691$	−2.39896	+	2.39896i	−0.0912609	+	0.0912609i	−0.751263	−	0.660002i	$-0.770555\pi$
$691$	−2.39896	+	2.39896i	−0.0912609	+	0.0912609i	0.660002	+	0.751263i	$0.270555\pi$
$692$	16.6225	+	8.31953i	0.631892	+	0.316261i
$693$	−0.853527	−	0.853527i	−0.0324228	−	0.0324228i
$694$	−6.42789	−	39.6605i	−0.244000	−	1.50549i
$695$		−	22.2658i		−	0.844591i
$696$	2.20469	+	0.690143i	0.0835687	+	0.0261598i
$697$			49.3322i			1.86859i
$698$	28.0368	−	4.54401i	1.06121	−	0.171993i
$699$	8.27018	+	8.27018i	0.312807	+	0.312807i
$700$	4.11112	+	12.3498i	0.155386	+	0.466778i
$701$	21.4447	−	21.4447i	0.809955	−	0.809955i	−0.174672	−	0.984627i	$-0.555886\pi$
$701$	21.4447	−	21.4447i	0.809955	−	0.809955i	0.984627	+	0.174672i	$0.0558864\pi$
$702$	5.88106	+	4.24061i	0.221966	+	0.160051i
$703$	−55.1278			−2.07918
$704$	−1.71604	−	9.50285i	−0.0646758	−	0.358152i
$705$	14.8146			0.557948
$706$	−19.1533	−	13.8107i	−0.720844	−	0.519774i
$707$	−5.40546	+	5.40546i	−0.203293	+	0.203293i
$708$	−7.09771	−	21.3215i	−0.266748	−	0.801310i
$709$	−0.515890	−	0.515890i	−0.0193747	−	0.0193747i	0.697353	−	0.716728i	$-0.254361\pi$
$709$	−0.515890	−	0.515890i	−0.0193747	−	0.0193747i	−0.716728	+	0.697353i	$0.754361\pi$
$710$	5.80157	−	0.940277i	0.217729	−	0.0352880i
$711$			5.39231i			0.202227i
$712$	−23.9095	−	7.48447i	−0.896045	−	0.280492i
$713$		−	6.76308i		−	0.253279i
$714$	−1.34383	−	8.29151i	−0.0502915	−	0.310302i
$715$	−14.8447	−	14.8447i	−0.555158	−	0.555158i
$716$	17.4718	+	8.74461i	0.652952	+	0.326802i
$717$	−5.34018	+	5.34018i	−0.199433	+	0.199433i
$718$	−11.6515	+	16.1588i	−0.434831	+	0.603042i
$719$	28.7028			1.07043			0.535216	−	0.844715i	$-0.320230\pi$
$719$	28.7028			1.07043			0.535216	+	0.844715i	$0.320230\pi$
$720$	−1.92972	+	13.4315i	−0.0719165	+	0.500562i
$721$	−0.651718			−0.0242713
$722$	−17.3906	+	24.1180i	−0.647211	+	0.897580i
$723$	−8.80325	+	8.80325i	−0.327396	+	0.327396i
$724$	−14.6116	+	29.1941i	−0.543036	+	1.08499i
$725$	3.75870	+	3.75870i	0.139595	+	0.139595i
$726$	−2.15913	−	13.3220i	−0.0801329	−	0.494425i
$727$		−	6.78646i		−	0.251696i	−0.992050	−	0.125848i	$-0.959835\pi$
$727$		−	6.78646i		−	0.251696i	0.992050	−	0.125848i	$-0.0401652\pi$
$728$	12.8487	−	6.72231i	0.476204	−	0.249145i
$729$			1.00000i			0.0370370i
$730$	−79.3031	+	12.8529i	−2.93514	+	0.475707i
$731$	−33.7487	−	33.7487i	−1.24824	−	1.24824i
$732$	14.9349	−	4.97167i	0.552009	−	0.183758i
$733$	−11.4999	+	11.4999i	−0.424758	+	0.424758i	−0.886838	−	0.462080i	$-0.847103\pi$
$733$	−11.4999	+	11.4999i	−0.424758	+	0.424758i	0.462080	+	0.886838i	$0.347103\pi$
$734$	−16.5530	−	11.9357i	−0.610982	−	0.440556i
$735$	3.39235			0.125129
$736$	−0.212850	−	11.8364i	−0.00784576	−	0.436297i
$737$	12.5091			0.460778
$738$	−9.52763	−	6.87002i	−0.350717	−	0.252889i
$739$	−11.6478	+	11.6478i	−0.428472	+	0.428472i	−0.888108	−	0.459636i	$-0.847980\pi$
$739$	−11.6478	+	11.6478i	−0.428472	+	0.428472i	0.459636	+	0.888108i	$0.347980\pi$
$740$	−56.0937	+	18.6730i	−2.06204	+	0.686434i
$741$	22.9353	+	22.9353i	0.842548	+	0.842548i
$742$	2.35200	−	0.381196i	0.0863448	−	0.0139942i
$743$		−	1.28228i		−	0.0470423i	−0.999723	−	0.0235212i	$-0.992512\pi$
$743$		−	1.28228i		−	0.0470423i	0.999723	−	0.0235212i	$-0.00748771\pi$
$744$	4.23736	+	8.09907i	0.155349	+	0.296926i
$745$		−	16.9064i		−	0.619403i
$746$	−5.61527	−	34.6466i	−0.205590	−	1.26850i
$747$	−9.38249	−	9.38249i	−0.343287	−	0.343287i
$748$	−6.41760	+	12.8224i	−0.234651	+	0.468833i
$749$	−3.08596	+	3.08596i	−0.112759	+	0.112759i
$750$	−4.23145	+	5.86836i	−0.154511	+	0.214282i
$751$	35.6166			1.29967			0.649835	−	0.760076i	$-0.274838\pi$
$751$	35.6166			1.29967			0.649835	+	0.760076i	$0.274838\pi$
$752$	13.9829	−	10.4698i	0.509904	−	0.381793i
$753$	−6.57791			−0.239712
$754$	3.46362	−	4.80350i	0.126138	−	0.174933i
$755$	−32.9222	+	32.9222i	−1.19816	+	1.19816i
$756$	1.78850	+	0.895141i	0.0650470	+	0.0325560i
$757$	−31.5023	−	31.5023i	−1.14497	−	1.14497i	−0.987528	−	0.157444i	$-0.949675\pi$
$757$	−31.5023	−	31.5023i	−1.14497	−	1.14497i	−0.157444	−	0.987528i	$-0.550325\pi$
$758$	−1.99794	−	12.3274i	−0.0725685	−	0.447752i
$759$			2.52609i			0.0916911i
$760$	−18.1344	+	57.9313i	−0.657805	+	2.10139i
$761$			9.70700i			0.351878i	0.984401	+	0.175939i	$0.0562962\pi$
$761$			9.70700i			0.351878i	−0.984401	+	0.175939i	$0.943704\pi$
$762$	−6.29052	+	1.01952i	−0.227882	+	0.0369334i
$763$	−2.62063	−	2.62063i	−0.0948731	−	0.0948731i
$764$	14.5582	+	43.7328i	0.526697	+	1.58220i
$765$	14.2474	−	14.2474i	0.515115	−	0.515115i
$766$	14.6766	+	10.5827i	0.530285	+	0.382369i
$767$	−57.6050			−2.08000
$768$	7.67092	+	14.0413i	0.276801	+	0.506670i
$769$	−28.1661			−1.01569			−0.507847	−	0.861447i	$-0.669558\pi$
$769$	−28.1661			−1.01569			−0.507847	+	0.861447i	$0.669558\pi$
$770$	−4.69717	−	3.38695i	−0.169274	−	0.122057i
$771$	12.2376	−	12.2376i	0.440726	−	0.440726i
$772$	−2.48061	−	7.45173i	−0.0892789	−	0.268193i
$773$	−32.4984	−	32.4984i	−1.16889	−	1.16889i	−0.982471	−	0.186414i	$-0.940313\pi$
$773$	−32.4984	−	32.4984i	−1.16889	−	1.16889i	−0.186414	−	0.982471i	$-0.559687\pi$
$774$	11.2178	−	1.81810i	0.403216	−	0.0653504i
$775$			21.0319i			0.755489i
$776$	12.1685	−	38.8728i	0.436823	−	1.39545i
$777$			8.71373i			0.312603i
$778$	−2.57349	−	15.8786i	−0.0922642	−	0.569276i
$779$	−37.1564	−	37.1564i	−1.33127	−	1.33127i
$780$	31.1058	+	15.5684i	1.11377	+	0.557439i
$781$	−1.04563	+	1.04563i	−0.0374155	+	0.0374155i
$782$	−10.2811	+	14.2583i	−0.367652	+	0.509876i
$783$	0.816775			0.0291892
$784$	3.20191	−	2.39745i	0.114354	−	0.0856231i
$785$	56.1013			2.00234
$786$	14.2522	−	19.7656i	0.508360	−	0.705015i
$787$	3.32141	−	3.32141i	0.118396	−	0.118396i	−0.645427	−	0.763822i	$-0.723320\pi$
$787$	3.32141	−	3.32141i	0.118396	−	0.118396i	0.763822	+	0.645427i	$0.223320\pi$
$788$	−2.35570	+	4.70670i	−0.0839182	+	0.167669i
$789$	−21.0214	−	21.0214i	−0.748383	−	0.748383i
$790$	4.13876	+	25.5364i	0.147251	+	0.908545i
$791$			0.711732i			0.0253063i
$792$	−1.58270	−	3.02509i	−0.0562388	−	0.107492i
$793$		−	40.3501i		−	1.43287i
$794$	53.0256	−	8.59402i	1.88181	−	0.304990i
$795$	4.04147	+	4.04147i	0.143336	+	0.143336i
$796$	−37.1668	+	12.3724i	−1.31734	+	0.438530i
$797$	−29.9715	+	29.9715i	−1.06165	+	1.06165i	−0.0636754	+	0.997971i	$0.520282\pi$
$797$	−29.9715	+	29.9715i	−1.06165	+	1.06165i	−0.997971	+	0.0636754i	$0.979718\pi$
$798$	7.25721	+	5.23290i	0.256902	+	0.185243i
$799$	−25.9380			−0.917621
$800$	0.661924	+	36.8091i	0.0234026	+	1.30140i
$801$	−8.85777			−0.312974
$802$	2.53329	+	1.82666i	0.0894537	+	0.0645017i
$803$	14.2929	−	14.2929i	0.504387	−	0.504387i
$804$	−19.6654	+	6.54642i	−0.693545	+	0.230874i
$805$	−5.01998	−	5.01998i	−0.176931	−	0.176931i
$806$	23.1295	−	3.74866i	0.814701	−	0.132041i
$807$		−	10.7236i		−	0.377489i
$808$	−19.1582	+	10.0234i	−0.673982	+	0.352621i
$809$			11.1522i			0.392091i	0.980595	+	0.196046i	$0.0628101\pi$
$809$			11.1522i			0.392091i	−0.980595	+	0.196046i	$0.937190\pi$
$810$	0.767531	+	4.73571i	0.0269683	+	0.166396i
$811$	−30.6743	−	30.6743i	−1.07712	−	1.07712i	−0.996766	−	0.0803529i	$-0.974395\pi$
$811$	−30.6743	−	30.6743i	−1.07712	−	1.07712i	−0.0803529	−	0.996766i	$-0.525605\pi$
$812$	0.731129	−	1.46080i	0.0256576	−	0.0512640i
$813$	4.93055	−	4.93055i	0.172922	−	0.172922i
$814$	8.69986	−	12.0653i	0.304930	−	0.422890i
$815$	−54.8102			−1.91992
$816$	3.37865	−	23.5165i	0.118276	−	0.823241i
$817$	50.8382			1.77860
$818$	11.5863	−	16.0684i	0.405105	−	0.561817i
$819$	3.62524	−	3.62524i	0.126676	−	0.126676i
$820$	−50.3931	−	25.2217i	−1.75980	−	0.880779i
$821$	−8.99851	−	8.99851i	−0.314050	−	0.314050i	0.532426	−	0.846476i	$-0.321280\pi$
$821$	−8.99851	−	8.99851i	−0.314050	−	0.314050i	−0.846476	+	0.532426i	$0.821280\pi$
$822$	−2.98702	−	18.4301i	−0.104184	−	0.642824i
$823$		−	5.89932i		−	0.205637i	−0.994700	−	0.102819i	$-0.967214\pi$
$823$		−	5.89932i		−	0.205637i	0.994700	−	0.102819i	$-0.0327861\pi$
$824$	−1.75916	−	0.550677i	−0.0612833	−	0.0191837i
$825$		−	7.85565i		−	0.273499i
$826$	−15.6853	+	2.54216i	−0.545762	+	0.0884532i
$827$	−11.1880	−	11.1880i	−0.389045	−	0.389045i	0.485301	−	0.874347i	$-0.338710\pi$
$827$	−11.1880	−	11.1880i	−0.389045	−	0.389045i	−0.874347	+	0.485301i	$0.838710\pi$
$828$	−1.32198	−	3.97123i	−0.0459421	−	0.138010i
$829$	3.97683	−	3.97683i	0.138121	−	0.138121i	−0.634666	−	0.772787i	$-0.718862\pi$
$829$	3.97683	−	3.97683i	0.138121	−	0.138121i	0.772787	+	0.634666i	$0.218862\pi$
$830$	−51.6341	−	37.2314i	−1.79225	−	1.29232i
$831$	27.6679			0.959789
$832$	40.3621	−	7.28867i	1.39931	−	0.252689i
$833$	−5.93949			−0.205791
$834$	−7.52907	−	5.42893i	−0.260710	−	0.187988i
$835$	−25.7744	+	25.7744i	−0.891960	+	0.891960i
$836$	−4.82401	−	14.4913i	−0.166842	−	0.501192i
$837$	2.28514	+	2.28514i	0.0789861	+	0.0789861i
$838$	55.0532	−	8.92264i	1.90178	−	0.308227i
$839$		−	51.0715i		−	1.76318i	−0.472013	−	0.881591i	$-0.656473\pi$
$839$		−	51.0715i		−	1.76318i	0.472013	−	0.881591i	$-0.343527\pi$
$840$	9.15686	+	2.86640i	0.315942	+	0.0989003i
$841$			28.3329i			0.976996i
$842$	−3.67312	−	22.6634i	−0.126584	−	0.781031i
$843$	18.5359	+	18.5359i	0.638409	+	0.638409i
$844$	−29.2395	−	14.6343i	−1.00646	−	0.503734i
$845$	31.8669	−	31.8669i	1.09626	−	1.09626i
$846$	3.61213	−	5.00946i	0.124188	−	0.172229i
$847$	−9.54298			−0.327901
$848$	6.67078	+	0.958402i	0.229076	+	0.0329117i
$849$	−5.47794			−0.188003
$850$	31.9724	−	44.3407i	1.09664	−	1.52087i
$851$	12.8945	−	12.8945i	0.442018	−	0.442018i
$852$	1.09661	−	2.19103i	0.0375692	−	0.0750634i
$853$	17.7024	+	17.7024i	0.606119	+	0.606119i	0.941929	−	0.335811i	$-0.109010\pi$
$853$	17.7024	+	17.7024i	0.606119	+	0.606119i	−0.335811	+	0.941929i	$0.609010\pi$
$854$	−1.78069	−	10.9870i	−0.0609339	−	0.375966i
$855$			21.4618i			0.733980i
$856$	−10.9373	+	5.72231i	−0.373831	+	0.195585i
$857$			53.6777i			1.83360i	0.399352	+	0.916798i	$0.369235\pi$
$857$			53.6777i			1.83360i	−0.399352	+	0.916798i	$0.630765\pi$
$858$	−8.63911	+	1.40017i	−0.294934	+	0.0478009i
$859$	19.5744	+	19.5744i	0.667870	+	0.667870i	0.957223	−	0.289352i	$-0.0934399\pi$
$859$	19.5744	+	19.5744i	0.667870	+	0.667870i	−0.289352	+	0.957223i	$0.593440\pi$
$860$	51.7289	−	17.2200i	1.76394	−	0.587198i
$861$	−5.87309	+	5.87309i	−0.200154	+	0.200154i
$862$	32.4288	+	23.3832i	1.10453	+	0.796435i
$863$	−45.0596			−1.53385			−0.766923	−	0.641739i	$-0.778213\pi$
$863$	−45.0596			−1.53385			−0.766923	+	0.641739i	$0.778213\pi$
$864$	4.07127	+	3.92743i	0.138507	+	0.133614i
$865$	31.5288			1.07201
$866$	26.7206	+	19.2672i	0.908001	+	0.654726i
$867$	−12.9241	+	12.9241i	−0.438927	+	0.438927i
$868$	6.13250	−	2.04145i	0.208151	−	0.0692913i
$869$	−4.60248	−	4.60248i	−0.156128	−	0.156128i
$870$	3.86801	−	0.626900i	0.131138	−	0.0212539i
$871$			53.1308i			1.80027i
$872$	−4.85945	−	9.28811i	−0.164562	−	0.314535i
$873$		−	14.4012i		−	0.487408i
$874$	−2.99556	−	18.4828i	−0.101326	−	0.625189i
$875$	3.61742	+	3.61742i	0.122291	+	0.122291i
$876$	−14.9898	+	29.9497i	−0.506459	+	1.01191i
$877$	−12.8551	+	12.8551i	−0.434086	+	0.434086i	−0.890016	−	0.455930i	$-0.849307\pi$
$877$	−12.8551	+	12.8551i	−0.434086	+	0.434086i	0.455930	+	0.890016i	$0.349307\pi$
$878$	12.6474	−	17.5400i	0.426830	−	0.591946i
$879$	22.6494			0.763946
$880$	−9.81706	−	13.1112i	−0.330933	−	0.441978i
$881$	−25.0649			−0.844457			−0.422229	−	0.906489i	$-0.638752\pi$
$881$	−25.0649			−0.844457			−0.422229	+	0.906489i	$0.638752\pi$
$882$	0.827134	−	1.14710i	0.0278511	−	0.0386250i
$883$	−1.66652	+	1.66652i	−0.0560830	+	0.0560830i	−0.734592	−	0.678509i	$-0.762626\pi$
$883$	−1.66652	+	1.66652i	−0.0560830	+	0.0560830i	0.678509	+	0.734592i	$0.262626\pi$
$884$	−54.4615	−	27.2579i	−1.83174	−	0.916783i
$885$	−26.9522	−	26.9522i	−0.905988	−	0.905988i
$886$	0.298029	+	1.83886i	0.0100125	+	0.0617776i
$887$			18.4374i			0.619066i	0.950889	+	0.309533i	$0.100173\pi$
$887$			18.4374i			0.619066i	−0.950889	+	0.309533i	$0.899827\pi$
$888$	−7.36276	+	23.5207i	−0.247078	+	0.789302i
$889$			4.50611i			0.151130i
$890$	−41.9478	+	6.79861i	−1.40609	+	0.227890i
$891$	−0.853527	−	0.853527i	−0.0285942	−	0.0285942i
$892$	1.77543	+	5.33340i	0.0594459	+	0.178575i
$893$	19.5362	−	19.5362i	0.653753	−	0.653753i
$894$	−5.71681	−	4.12217i	−0.191199	−	0.137866i
$895$	33.1398			1.10774
$896$	10.6686	−	3.76585i	0.356412	−	0.125808i
$897$	−10.7292			−0.358238
$898$	−2.80071	−	2.01949i	−0.0934608	−	0.0673911i
$899$	1.86645	−	1.86645i	0.0622496	−	0.0622496i
$900$	4.11112	+	12.3498i	0.137037	+	0.411659i
$901$	−7.07599	−	7.07599i	−0.235736	−	0.235736i
$902$	13.9958	−	2.26834i	0.466010	−	0.0755276i
$903$		−	8.03569i		−	0.267411i
$904$	−0.601386	+	1.92115i	−0.0200018	+	0.0638966i
$905$			55.3741i			1.84070i
$906$	3.10526	+	19.1597i	0.103165	+	0.636537i
$907$	12.8896	+	12.8896i	0.427992	+	0.427992i	0.887944	−	0.459952i	$-0.152133\pi$
$907$	12.8896	+	12.8896i	0.427992	+	0.427992i	−0.459952	+	0.887944i	$0.652133\pi$
$908$	9.69389	+	4.85178i	0.321703	+	0.161012i
$909$	−5.40546	+	5.40546i	−0.179288	+	0.179288i
$910$	14.3856	−	19.9506i	0.476879	−	0.661356i
$911$	−4.17946			−0.138472			−0.0692358	−	0.997600i	$-0.522056\pi$
$911$	−4.17946			−0.138472			−0.0692358	+	0.997600i	$0.522056\pi$
$912$	15.1675	+	20.2570i	0.502247	+	0.670778i
$913$	16.0164			0.530066
$914$	−15.4343	+	21.4049i	−0.510521	+	0.708012i
$915$	18.8790	−	18.8790i	0.624120	−	0.624120i
$916$	19.2405	−	38.4426i	0.635723	−	1.27018i
$917$	−12.1840	−	12.1840i	−0.402352	−	0.402352i
$918$	−1.34383	−	8.29151i	−0.0443530	−	0.273661i
$919$			50.5990i			1.66911i	0.550928	+	0.834553i	$0.314274\pi$
$919$			50.5990i			1.66911i	−0.550928	+	0.834553i	$0.685726\pi$
$920$	−9.30857	−	17.7919i	−0.306894	−	0.586583i
$921$			25.5890i			0.843186i
$922$	−11.4403	+	1.85416i	−0.376766	+	0.0610636i
$923$	−4.44117	−	4.44117i	−0.146183	−	0.146183i
$924$	−2.29056	+	0.762504i	−0.0753538	+	0.0250845i
$925$	−40.0995	+	40.0995i	−1.31846	+	1.31846i
$926$	19.2033	+	13.8468i	0.631059	+	0.455033i
$927$	−0.651718			−0.0214052
$928$	3.20783	−	3.32531i	0.105302	−	0.109159i
$929$	36.2558			1.18952			0.594758	−	0.803905i	$-0.297248\pi$
$929$	36.2558			1.18952			0.594758	+	0.803905i	$0.297248\pi$
$930$	12.5757	+	9.06787i	0.412374	+	0.297347i
$931$	4.47354	−	4.47354i	0.146614	−	0.146614i
$932$	22.1942	−	7.38822i	0.726994	−	0.242009i
$933$	10.4416	+	10.4416i	0.341843	+	0.341843i
$934$	−40.4808	+	6.56084i	−1.32457	+	0.214677i
$935$			24.3210i			0.795382i
$936$	12.8487	−	6.72231i	0.419973	−	0.219726i
$937$		−	23.3485i		−	0.762763i	−0.924418	−	0.381381i	$-0.875449\pi$
$937$		−	23.3485i		−	0.762763i	0.924418	−	0.381381i	$-0.124551\pi$
$938$	2.34471	+	14.4670i	0.0765575	+	0.472364i
$939$	−12.3928	−	12.3928i	−0.404422	−	0.404422i
$940$	13.2611	−	26.4958i	0.432530	−	0.864197i
$941$	12.7609	−	12.7609i	0.415995	−	0.415995i	−0.467826	−	0.883821i	$-0.654963\pi$
$941$	12.7609	−	12.7609i	0.415995	−	0.415995i	0.883821	+	0.467826i	$0.154963\pi$
$942$	13.6788	−	18.9703i	0.445680	−	0.618087i
$943$	17.3819			0.566033
$944$	−44.4869	−	6.39149i	−1.44792	−	0.208025i
$945$	3.39235			0.110353
$946$	−8.02290	+	11.1265i	−0.260847	+	0.361754i
$947$	−22.6296	+	22.6296i	−0.735364	+	0.735364i	−0.971677	−	0.236313i	$-0.924061\pi$
$947$	−22.6296	+	22.6296i	−0.735364	+	0.735364i	0.236313	+	0.971677i	$0.424061\pi$
$948$	9.64413	+	4.82687i	0.313227	+	0.156770i
$949$	60.7074	+	60.7074i	1.97065	+	1.97065i
$950$	9.31562	+	57.4780i	0.302239	+	1.86483i
$951$		−	14.1005i		−	0.457239i
$952$	−16.0323	−	5.01863i	−0.519609	−	0.162655i
$953$		−	12.6868i		−	0.410966i	−0.978661	−	0.205483i	$-0.934124\pi$
$953$		−	12.6868i		−	0.410966i	0.978661	−	0.205483i	$-0.0658765\pi$
$954$	2.35200	−	0.381196i	0.0761490	−	0.0123417i
$955$	55.2820	+	55.2820i	1.78888	+	1.78888i
$956$	4.77069	+	14.3311i	0.154295	+	0.463502i
$957$	−0.697139	+	0.697139i	−0.0225353	+	0.0225353i
$958$	−12.3925	−	8.93578i	−0.400384	−	0.288702i
$959$	−13.2021			−0.426318
$960$	22.2948	+	15.4744i	0.719562	+	0.499433i
$961$	−20.5562			−0.663104
$962$	51.2459	+	36.9515i	1.65224	+	1.19136i
$963$	−3.08596	+	3.08596i	−0.0994437	+	0.0994437i
$964$	7.86444	+	23.6247i	0.253296	+	0.760901i
$965$	−9.41962	−	9.41962i	−0.303228	−	0.303228i
$966$	−2.92146	+	0.473490i	−0.0939966	+	0.0152343i
$967$		−	38.7411i		−	1.24583i	−0.782289	−	0.622915i	$-0.785948\pi$
$967$		−	38.7411i		−	1.24583i	0.782289	−	0.622915i	$-0.214052\pi$
$968$	−25.7591	−	8.06345i	−0.827928	−	0.259169i
$969$		−	37.5764i		−	1.20713i
$970$	−11.0534	−	68.2001i	−0.354903	−	2.18977i
$971$	13.0553	+	13.0553i	0.418965	+	0.418965i	0.884847	−	0.465882i	$-0.154263\pi$
$971$	13.0553	+	13.0553i	0.418965	+	0.418965i	−0.465882	+	0.884847i	$0.654263\pi$
$972$	1.78850	+	0.895141i	0.0573661	+	0.0287117i
$973$	−4.64113	+	4.64113i	−0.148788	+	0.148788i
$974$	−17.1478	+	23.7814i	−0.549452	+	0.762004i
$975$	33.3659			1.06856
$976$	4.47700	−	31.1613i	0.143305	−	0.997450i
$977$	−23.8979			−0.764563			−0.382281	−	0.924046i	$-0.624862\pi$
$977$	−23.8979			−0.764563			−0.382281	+	0.924046i	$0.624862\pi$
$978$	−13.3640	+	18.5338i	−0.427334	+	0.592644i
$979$	7.56034	−	7.56034i	0.241629	−	0.241629i
$980$	3.03663	−	6.06721i	0.0970016	−	0.193810i
$981$	−2.62063	−	2.62063i	−0.0836702	−	0.0836702i
$982$	1.64728	+	10.1638i	0.0525667	+	0.324340i
$983$			4.59652i			0.146606i	0.997310	+	0.0733031i	$0.0233540\pi$
$983$			4.59652i			0.146606i	−0.997310	+	0.0733031i	$0.976646\pi$
$984$	−20.8156	+	10.8905i	−0.663576	+	0.347177i
$985$			8.92747i			0.284453i
$986$	−6.77230	+	1.09761i	−0.215674	+	0.0349549i
$987$	−3.08797	−	3.08797i	−0.0982911	−	0.0982911i
$988$	61.5499	−	20.4894i	1.95816	−	0.651853i
$989$	−11.8912	+	11.8912i	−0.378117	+	0.378117i
$990$	−4.69717	−	3.38695i	−0.149286	−	0.107644i
$991$	22.0752			0.701243			0.350621	−	0.936517i	$-0.385970\pi$
$991$	22.0752			0.701243			0.350621	+	0.936517i	$0.385970\pi$
$992$	18.2782	−	0.328690i	0.580333	−	0.0104359i
$993$	27.7669			0.881155
$994$	−1.40528	−	1.01329i	−0.0445728	−	0.0321398i
$995$	−46.9820	+	46.9820i	−1.48943	+	1.48943i
$996$	−25.1792	+	8.38191i	−0.797834	+	0.265591i
$997$	10.7932	+	10.7932i	0.341825	+	0.341825i	0.857053	−	0.515228i	$-0.172293\pi$
$997$	10.7932	+	10.7932i	0.341825	+	0.341825i	−0.515228	+	0.857053i	$0.672293\pi$
$998$	−8.90612	+	1.44344i	−0.281918	+	0.0456913i
$999$			8.71373i			0.275690i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.w.b.85.3	✓	28
4.3	odd	2		1344.2.w.b.1009.12		28
8.3	odd	2		2688.2.w.c.2017.3		28
8.5	even	2		2688.2.w.d.2017.12		28
16.3	odd	4		1344.2.w.b.337.12		28
16.5	even	4		2688.2.w.d.673.12		28
16.11	odd	4		2688.2.w.c.673.3		28
16.13	even	4	inner	336.2.w.b.253.3	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.w.b.85.3	✓	28	1.1	even	1	trivial
336.2.w.b.253.3	yes	28	16.13	even	4	inner
1344.2.w.b.337.12		28	16.3	odd	4
1344.2.w.b.1009.12		28	4.3	odd	2
2688.2.w.c.673.3		28	16.11	odd	4
2688.2.w.c.2017.3		28	8.3	odd	2
2688.2.w.d.673.12		28	16.5	even	4
2688.2.w.d.2017.12		28	8.5	even	2

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14710 - 0.827134i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(0.631698 + 1.89762i) q^{4} +(2.39875 + 2.39875i) q^{5} +(1.39600 - 0.226253i) q^{6} -1.00000i q^{7} +(0.844961 - 2.69927i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-1.14710 - 0.827134i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(0.631698 + 1.89762i) q^{4} +(2.39875 + 2.39875i) q^{5} +(1.39600 - 0.226253i) q^{6} -1.00000i q^{7} +(0.844961 - 2.69927i) q^{8} -1.00000i q^{9} +(-0.767531 - 4.73571i) q^{10} +(0.853527 + 0.853527i) q^{11} +(-1.78850 - 0.895141i) q^{12} +(-3.62524 + 3.62524i) q^{13} +(-0.827134 + 1.14710i) q^{14} -3.39235 q^{15} +(-3.20191 + 2.39745i) q^{16} +5.93949 q^{17} +(-0.827134 + 1.14710i) q^{18} +(-4.47354 + 4.47354i) q^{19} +(-3.03663 + 6.06721i) q^{20} +(0.707107 + 0.707107i) q^{21} +(-0.273103 - 1.68507i) q^{22} -2.09274i q^{23} +(1.31119 + 2.50615i) q^{24} +6.50804i q^{25} +(7.15710 - 1.15997i) q^{26} +(0.707107 + 0.707107i) q^{27} +(1.89762 - 0.631698i) q^{28} +(0.577547 - 0.577547i) q^{29} +(3.89138 + 2.80593i) q^{30} +3.23168 q^{31} +(5.65594 - 0.101709i) q^{32} -1.20707 q^{33} +(-6.81321 - 4.91275i) q^{34} +(2.39875 - 2.39875i) q^{35} +(1.89762 - 0.631698i) q^{36} +(6.16154 + 6.16154i) q^{37} +(8.83184 - 1.43140i) q^{38} -5.12687i q^{39} +(8.50173 - 4.44802i) q^{40} +8.30581i q^{41} +(-0.226253 - 1.39600i) q^{42} +(-5.68209 - 5.68209i) q^{43} +(-1.08050 + 2.15884i) q^{44} +(2.39875 - 2.39875i) q^{45} +(-1.73098 + 2.40060i) q^{46} -4.36705 q^{47} +(0.568845 - 3.95935i) q^{48} -1.00000 q^{49} +(5.38302 - 7.46540i) q^{50} +(-4.19985 + 4.19985i) q^{51} +(-9.16939 - 4.58927i) q^{52} +(-1.19135 - 1.19135i) q^{53} +(-0.226253 - 1.39600i) q^{54} +4.09480i q^{55} +(-2.69927 - 0.844961i) q^{56} -6.32654i q^{57} +(-1.14022 + 0.184798i) q^{58} +(7.94499 + 7.94499i) q^{59} +(-2.14294 - 6.43739i) q^{60} +(-5.56516 + 5.56516i) q^{61} +(-3.70708 - 2.67303i) q^{62} -1.00000 q^{63} +(-6.57208 - 4.56155i) q^{64} -17.3921 q^{65} +(1.38463 + 0.998408i) q^{66} +(7.32789 - 7.32789i) q^{67} +(3.75196 + 11.2709i) q^{68} +(1.47979 + 1.47979i) q^{69} +(-4.73571 + 0.767531i) q^{70} +1.22507i q^{71} +(-2.69927 - 0.844961i) q^{72} -16.7458i q^{73} +(-1.97151 - 12.1643i) q^{74} +(-4.60188 - 4.60188i) q^{75} +(-11.3150 - 5.66315i) q^{76} +(0.853527 - 0.853527i) q^{77} +(-4.24061 + 5.88106i) q^{78} -5.39231 q^{79} +(-13.4315 - 1.92972i) q^{80} -1.00000 q^{81} +(6.87002 - 9.52763i) q^{82} +(9.38249 - 9.38249i) q^{83} +(-0.895141 + 1.78850i) q^{84} +(14.2474 + 14.2474i) q^{85} +(1.81810 + 11.2178i) q^{86} +0.816775i q^{87} +(3.02509 - 1.58270i) q^{88} -8.85777i q^{89} +(-4.73571 + 0.767531i) q^{90} +(3.62524 + 3.62524i) q^{91} +(3.97123 - 1.32198i) q^{92} +(-2.28514 + 2.28514i) q^{93} +(5.00946 + 3.61213i) q^{94} -21.4618 q^{95} +(-3.92743 + 4.07127i) q^{96} +14.4012 q^{97} +(1.14710 + 0.827134i) q^{98} +(0.853527 - 0.853527i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q+O(q^{10}) \) 28 * q	\( 28 q - 4 q^{10} - 4 q^{11} - 8 q^{12} + 8 q^{15} + 4 q^{16} + 8 q^{19} - 28 q^{20} - 8 q^{22} - 16 q^{24} - 20 q^{26} + 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{33} + 12 q^{34} + 4 q^{36} + 4 q^{37} + 60 q^{38} - 56 q^{40} - 4 q^{42} + 20 q^{43} + 56 q^{44} - 44 q^{46} + 16 q^{48} - 28 q^{49} + 20 q^{50} - 8 q^{51} - 32 q^{52} + 20 q^{53} - 4 q^{54} - 12 q^{56} - 12 q^{58} - 12 q^{60} - 40 q^{61} - 60 q^{62} - 28 q^{63} + 60 q^{64} + 16 q^{65} + 24 q^{66} + 4 q^{67} - 108 q^{68} - 16 q^{69} - 4 q^{70} - 12 q^{72} + 28 q^{74} - 16 q^{75} - 8 q^{76} - 4 q^{77} + 12 q^{78} + 24 q^{79} - 72 q^{80} - 28 q^{81} + 36 q^{82} + 40 q^{83} + 48 q^{85} + 24 q^{86} + 4 q^{88} - 4 q^{90} + 52 q^{92} - 8 q^{94} + 40 q^{96} + 72 q^{97} - 4 q^{99}+O(q^{100}) \) 28 * q - 4 * q^10 - 4 * q^11 - 8 * q^12 + 8 * q^15 + 4 * q^16 + 8 * q^19 - 28 * q^20 - 8 * q^22 - 16 * q^24 - 20 * q^26 + 4 * q^28 + 4 * q^29 + 8 * q^30 + 24 * q^33 + 12 * q^34 + 4 * q^36 + 4 * q^37 + 60 * q^38 - 56 * q^40 - 4 * q^42 + 20 * q^43 + 56 * q^44 - 44 * q^46 + 16 * q^48 - 28 * q^49 + 20 * q^50 - 8 * q^51 - 32 * q^52 + 20 * q^53 - 4 * q^54 - 12 * q^56 - 12 * q^58 - 12 * q^60 - 40 * q^61 - 60 * q^62 - 28 * q^63 + 60 * q^64 + 16 * q^65 + 24 * q^66 + 4 * q^67 - 108 * q^68 - 16 * q^69 - 4 * q^70 - 12 * q^72 + 28 * q^74 - 16 * q^75 - 8 * q^76 - 4 * q^77 + 12 * q^78 + 24 * q^79 - 72 * q^80 - 28 * q^81 + 36 * q^82 + 40 * q^83 + 48 * q^85 + 24 * q^86 + 4 * q^88 - 4 * q^90 + 52 * q^92 - 8 * q^94 + 40 * q^96 + 72 * q^97 - 4 * q^99

Introduction

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