LMFDB - Embedded newform 802.2.e.b.45.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [802,2,Mod(45,802)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(802, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("802.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 802 = 2 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	802.e (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.40400224211$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			45.14
Character	$\chi$	$=$	802.45
Dual form			802.2.e.b.303.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(2.08581 + 0.863972i) q^{3} +1.00000i q^{4} +0.323043 q^{5} +(0.863972 + 2.08581i) q^{6} +(3.25849 - 3.25849i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.48285 + 1.48285i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(2.08581 + 0.863972i) q^{3} +1.00000i q^{4} +0.323043 q^{5} +(0.863972 + 2.08581i) q^{6} +(3.25849 - 3.25849i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.48285 + 1.48285i) q^{9} +(0.228426 + 0.228426i) q^{10} +(-0.394144 - 0.394144i) q^{11} +(-0.863972 + 2.08581i) q^{12} +(-1.62022 + 0.671118i) q^{13} +4.60820 q^{14} +(0.673807 + 0.279100i) q^{15} -1.00000 q^{16} +(1.09934 - 0.455363i) q^{17} +2.09706i q^{18} +(2.55543 + 6.16936i) q^{19} +0.323043i q^{20} +(9.61185 - 3.98136i) q^{21} -0.557403i q^{22} +(0.504209 + 1.21727i) q^{23} +(-2.08581 + 0.863972i) q^{24} -4.89564 q^{25} +(-1.62022 - 0.671118i) q^{26} +(-0.780112 - 1.88336i) q^{27} +(3.25849 + 3.25849i) q^{28} +4.02659 q^{29} +(0.279100 + 0.673807i) q^{30} +(-3.32988 - 8.03905i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.481581 - 1.16264i) q^{33} +(1.09934 + 0.455363i) q^{34} +(1.05263 - 1.05263i) q^{35} +(-1.48285 + 1.48285i) q^{36} +(8.88064 + 3.67848i) q^{37} +(-2.55543 + 6.16936i) q^{38} -3.95931 q^{39} +(-0.228426 + 0.228426i) q^{40} -7.62871 q^{41} +(9.61185 + 3.98136i) q^{42} +(-8.69784 + 8.69784i) q^{43} +(0.394144 - 0.394144i) q^{44} +(0.479023 + 0.479023i) q^{45} +(-0.504209 + 1.21727i) q^{46} +(-8.73364 - 8.73364i) q^{47} +(-2.08581 - 0.863972i) q^{48} -14.2355i q^{49} +(-3.46174 - 3.46174i) q^{50} +2.68645 q^{51} +(-0.671118 - 1.62022i) q^{52} +(-4.80063 + 11.5897i) q^{53} +(0.780112 - 1.88336i) q^{54} +(-0.127325 - 0.127325i) q^{55} +4.60820i q^{56} +15.0760i q^{57} +(2.84723 + 2.84723i) q^{58} +(1.25797 - 0.521066i) q^{59} +(-0.279100 + 0.673807i) q^{60} +(3.20513 + 7.73786i) q^{61} +(3.32988 - 8.03905i) q^{62} +9.66369 q^{63} -1.00000i q^{64} +(-0.523401 + 0.216800i) q^{65} +(0.481581 - 1.16264i) q^{66} +(5.66041 - 13.6654i) q^{67} +(0.455363 + 1.09934i) q^{68} +2.97461i q^{69} +1.48865 q^{70} +(-5.17609 + 12.4962i) q^{71} -2.09706 q^{72} +(0.675230 - 0.675230i) q^{73} +(3.67848 + 8.88064i) q^{74} +(-10.2114 - 4.22970i) q^{75} +(-6.16936 + 2.55543i) q^{76} -2.56863 q^{77} +(-2.79965 - 2.79965i) q^{78} +(-3.24560 - 7.83557i) q^{79} -0.323043 q^{80} -10.8935i q^{81} +(-5.39431 - 5.39431i) q^{82} -5.37325 q^{83} +(3.98136 + 9.61185i) q^{84} +(0.355135 - 0.147102i) q^{85} -12.3006 q^{86} +(8.39872 + 3.47886i) q^{87} +0.557403 q^{88} +(-6.71987 + 6.71987i) q^{89} +0.677441i q^{90} +(-3.09265 + 7.46631i) q^{91} +(-1.21727 + 0.504209i) q^{92} -19.6449i q^{93} -12.3512i q^{94} +(0.825514 + 1.99297i) q^{95} +(-0.863972 - 2.08581i) q^{96} +(2.79481 + 6.74728i) q^{97} +(10.0660 - 10.0660i) q^{98} -1.16891i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{6} + 20 q^{9}+O(q^{10}) $ 68 * q + 4 * q^6 + 20 * q^9	$ 68 q + 4 q^{6} + 20 q^{9} - 4 q^{10} + 12 q^{11} - 4 q^{12} - 8 q^{13} + 8 q^{14} - 4 q^{15} - 68 q^{16} + 4 q^{17} + 20 q^{19} - 40 q^{21} - 16 q^{23} + 20 q^{25} - 8 q^{26} - 12 q^{27} + 16 q^{29} - 4 q^{30} - 8 q^{31} + 8 q^{33} + 4 q^{34} + 16 q^{35} - 20 q^{36} + 12 q^{37} - 20 q^{38} + 40 q^{39} + 4 q^{40} + 24 q^{41} - 40 q^{42} + 40 q^{43} - 12 q^{44} + 28 q^{45} + 16 q^{46} + 4 q^{47} - 8 q^{50} + 24 q^{51} + 4 q^{52} + 12 q^{53} + 12 q^{54} - 24 q^{55} - 4 q^{58} + 4 q^{59} + 4 q^{60} - 20 q^{61} + 8 q^{62} - 16 q^{63} + 36 q^{65} - 8 q^{66} + 48 q^{67} + 8 q^{68} - 16 q^{71} - 68 q^{72} + 40 q^{73} - 8 q^{74} - 96 q^{75} - 16 q^{77} + 32 q^{78} + 28 q^{79} - 16 q^{82} + 16 q^{83} - 4 q^{84} + 16 q^{85} - 32 q^{86} + 8 q^{87} + 8 q^{88} - 20 q^{89} - 4 q^{91} + 8 q^{92} - 24 q^{95} - 4 q^{96} + 24 q^{97} + 24 q^{98}+O(q^{100}) $ 68 * q + 4 * q^6 + 20 * q^9 - 4 * q^10 + 12 * q^11 - 4 * q^12 - 8 * q^13 + 8 * q^14 - 4 * q^15 - 68 * q^16 + 4 * q^17 + 20 * q^19 - 40 * q^21 - 16 * q^23 + 20 * q^25 - 8 * q^26 - 12 * q^27 + 16 * q^29 - 4 * q^30 - 8 * q^31 + 8 * q^33 + 4 * q^34 + 16 * q^35 - 20 * q^36 + 12 * q^37 - 20 * q^38 + 40 * q^39 + 4 * q^40 + 24 * q^41 - 40 * q^42 + 40 * q^43 - 12 * q^44 + 28 * q^45 + 16 * q^46 + 4 * q^47 - 8 * q^50 + 24 * q^51 + 4 * q^52 + 12 * q^53 + 12 * q^54 - 24 * q^55 - 4 * q^58 + 4 * q^59 + 4 * q^60 - 20 * q^61 + 8 * q^62 - 16 * q^63 + 36 * q^65 - 8 * q^66 + 48 * q^67 + 8 * q^68 - 16 * q^71 - 68 * q^72 + 40 * q^73 - 8 * q^74 - 96 * q^75 - 16 * q^77 + 32 * q^78 + 28 * q^79 - 16 * q^82 + 16 * q^83 - 4 * q^84 + 16 * q^85 - 32 * q^86 + 8 * q^87 + 8 * q^88 - 20 * q^89 - 4 * q^91 + 8 * q^92 - 24 * q^95 - 4 * q^96 + 24 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/802\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	2.08581	+	0.863972i	1.20424	+	0.498814i	0.892368	−	0.451308i	$-0.149042\pi$
$3$	2.08581	+	0.863972i	1.20424	+	0.498814i	0.311876	+	0.950123i	$0.399042\pi$
$4$			1.00000i			0.500000i
$5$	0.323043			0.144469			0.0722345	−	0.997388i	$-0.476987\pi$
$5$	0.323043			0.144469			0.0722345	+	0.997388i	$0.476987\pi$
$6$	0.863972	+	2.08581i	0.352715	+	0.851530i
$7$	3.25849	−	3.25849i	1.23159	−	1.23159i	0.268242	−	0.963352i	$-0.413557\pi$
$7$	3.25849	−	3.25849i	1.23159	−	1.23159i	0.963352	−	0.268242i	$-0.0864427\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	1.48285	+	1.48285i	0.494282	+	0.494282i
$10$	0.228426	+	0.228426i	0.0722345	+	0.0722345i
$11$	−0.394144	−	0.394144i	−0.118839	−	0.118839i	0.645186	−	0.764025i	$-0.276780\pi$
$11$	−0.394144	−	0.394144i	−0.118839	−	0.118839i	−0.764025	+	0.645186i	$0.776780\pi$
$12$	−0.863972	+	2.08581i	−0.249407	+	0.602122i
$13$	−1.62022	+	0.671118i	−0.449369	+	0.186135i	−0.595879	−	0.803075i	$-0.703196\pi$
$13$	−1.62022	+	0.671118i	−0.449369	+	0.186135i	0.146510	+	0.989209i	$0.453196\pi$
$14$	4.60820			1.23159
$15$	0.673807	+	0.279100i	0.173976	+	0.0720633i
$16$	−1.00000			−0.250000
$17$	1.09934	−	0.455363i	0.266630	−	0.110442i	−0.245363	−	0.969431i	$-0.578907\pi$
$17$	1.09934	−	0.455363i	0.266630	−	0.110442i	0.511993	+	0.858989i	$0.328907\pi$
$18$			2.09706i			0.494282i
$19$	2.55543	+	6.16936i	0.586256	+	1.41535i	0.887056	+	0.461661i	$0.152746\pi$
$19$	2.55543	+	6.16936i	0.586256	+	1.41535i	−0.300800	+	0.953687i	$0.597254\pi$
$20$			0.323043i			0.0722345i
$21$	9.61185	−	3.98136i	2.09748	−	0.868803i
$22$		−	0.557403i		−	0.118839i
$23$	0.504209	+	1.21727i	0.105135	+	0.253818i	0.967689	−	0.252147i	$-0.0811366\pi$
$23$	0.504209	+	1.21727i	0.105135	+	0.253818i	−0.862554	+	0.505965i	$0.831137\pi$
$24$	−2.08581	+	0.863972i	−0.425765	+	0.176358i
$25$	−4.89564			−0.979129
$26$	−1.62022	−	0.671118i	−0.317752	−	0.131617i
$27$	−0.780112	−	1.88336i	−0.150133	−	0.362452i
$28$	3.25849	+	3.25849i	0.615797	+	0.615797i
$29$	4.02659			0.747719			0.373860	−	0.927485i	$-0.378034\pi$
$29$	4.02659			0.747719			0.373860	+	0.927485i	$0.378034\pi$
$30$	0.279100	+	0.673807i	0.0509564	+	0.123020i
$31$	−3.32988	−	8.03905i	−0.598065	−	1.44386i	−0.875550	−	0.483127i	$-0.839501\pi$
$31$	−3.32988	−	8.03905i	−0.598065	−	1.44386i	0.277485	−	0.960730i	$-0.410499\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−0.481581	−	1.16264i	−0.0838324	−	0.202389i
$34$	1.09934	+	0.455363i	0.188536	+	0.0780941i
$35$	1.05263	−	1.05263i	0.177927	−	0.177927i
$36$	−1.48285	+	1.48285i	−0.247141	+	0.247141i
$37$	8.88064	+	3.67848i	1.45997	+	0.604739i	0.964546	−	0.263913i	$-0.0850132\pi$
$37$	8.88064	+	3.67848i	1.45997	+	0.604739i	0.495423	+	0.868652i	$0.335013\pi$
$38$	−2.55543	+	6.16936i	−0.414546	+	1.00080i
$39$	−3.95931			−0.633997
$40$	−0.228426	+	0.228426i	−0.0361173	+	0.0361173i
$41$	−7.62871			−1.19140			−0.595702	−	0.803206i	$-0.703126\pi$
$41$	−7.62871			−1.19140			−0.595702	+	0.803206i	$0.703126\pi$
$42$	9.61185	+	3.98136i	1.48314	+	0.614337i
$43$	−8.69784	+	8.69784i	−1.32641	+	1.32641i	−0.417929	+	0.908480i	$0.637244\pi$
$43$	−8.69784	+	8.69784i	−1.32641	+	1.32641i	−0.908480	+	0.417929i	$0.862756\pi$
$44$	0.394144	−	0.394144i	0.0594194	−	0.0594194i
$45$	0.479023	+	0.479023i	0.0714085	+	0.0714085i
$46$	−0.504209	+	1.21727i	−0.0743415	+	0.179476i
$47$	−8.73364	−	8.73364i	−1.27393	−	1.27393i	−0.944007	−	0.329925i	$-0.892977\pi$
$47$	−8.73364	−	8.73364i	−1.27393	−	1.27393i	−0.329925	−	0.944007i	$-0.607023\pi$
$48$	−2.08581	−	0.863972i	−0.301061	−	0.124704i
$49$		−	14.2355i		−	2.03365i
$50$	−3.46174	−	3.46174i	−0.489564	−	0.489564i
$51$	2.68645			0.376178
$52$	−0.671118	−	1.62022i	−0.0930673	−	0.224684i
$53$	−4.80063	+	11.5897i	−0.659417	+	1.59197i	0.139290	+	0.990252i	$0.455518\pi$
$53$	−4.80063	+	11.5897i	−0.659417	+	1.59197i	−0.798706	+	0.601721i	$0.794482\pi$
$54$	0.780112	−	1.88336i	0.106160	−	0.256293i
$55$	−0.127325	−	0.127325i	−0.0171685	−	0.0171685i
$56$			4.60820i			0.615797i
$57$			15.0760i			1.99686i
$58$	2.84723	+	2.84723i	0.373860	+	0.373860i
$59$	1.25797	−	0.521066i	0.163773	−	0.0678371i	−0.299291	−	0.954162i	$-0.596750\pi$
$59$	1.25797	−	0.521066i	0.163773	−	0.0678371i	0.463064	+	0.886325i	$0.346750\pi$
$60$	−0.279100	+	0.673807i	−0.0360316	+	0.0869881i
$61$	3.20513	+	7.73786i	0.410374	+	0.990731i	0.985037	+	0.172341i	$0.0551332\pi$
$61$	3.20513	+	7.73786i	0.410374	+	0.990731i	−0.574663	+	0.818390i	$0.694867\pi$
$62$	3.32988	−	8.03905i	0.422896	−	1.02096i
$63$	9.66369			1.21751
$64$		−	1.00000i		−	0.125000i
$65$	−0.523401	+	0.216800i	−0.0649199	+	0.0268907i
$66$	0.481581	−	1.16264i	0.0592785	−	0.143111i
$67$	5.66041	−	13.6654i	0.691529	−	1.66950i	−0.0501474	−	0.998742i	$-0.515969\pi$
$67$	5.66041	−	13.6654i	0.691529	−	1.66950i	0.741677	−	0.670758i	$-0.234031\pi$
$68$	0.455363	+	1.09934i	0.0552209	+	0.133315i
$69$			2.97461i			0.358101i
$70$	1.48865			0.177927
$71$	−5.17609	+	12.4962i	−0.614288	+	1.48302i	0.243958	+	0.969786i	$0.421554\pi$
$71$	−5.17609	+	12.4962i	−0.614288	+	1.48302i	−0.858247	+	0.513238i	$0.828446\pi$
$72$	−2.09706			−0.247141
$73$	0.675230	−	0.675230i	0.0790297	−	0.0790297i	−0.666487	−	0.745517i	$-0.732203\pi$
$73$	0.675230	−	0.675230i	0.0790297	−	0.0790297i	0.745517	+	0.666487i	$0.232203\pi$
$74$	3.67848	+	8.88064i	0.427615	+	1.03235i
$75$	−10.2114	−	4.22970i	−1.17911	−	0.488404i
$76$	−6.16936	+	2.55543i	−0.707674	+	0.293128i
$77$	−2.56863			−0.292722
$78$	−2.79965	−	2.79965i	−0.316998	−	0.316998i
$79$	−3.24560	−	7.83557i	−0.365159	−	0.881571i	−0.994529	−	0.104465i	$-0.966687\pi$
$79$	−3.24560	−	7.83557i	−0.365159	−	0.881571i	0.629370	−	0.777106i	$-0.283313\pi$
$80$	−0.323043			−0.0361173
$81$		−	10.8935i		−	1.21039i
$82$	−5.39431	−	5.39431i	−0.595702	−	0.595702i
$83$	−5.37325			−0.589790			−0.294895	−	0.955530i	$-0.595285\pi$
$83$	−5.37325			−0.589790			−0.294895	+	0.955530i	$0.595285\pi$
$84$	3.98136	+	9.61185i	0.434402	+	1.04874i
$85$	0.355135	−	0.147102i	0.0385198	−	0.0159554i
$86$	−12.3006			−1.32641
$87$	8.39872	+	3.47886i	0.900437	+	0.372973i
$88$	0.557403			0.0594194
$89$	−6.71987	+	6.71987i	−0.712304	+	0.712304i	−0.967017	−	0.254712i	$-0.918019\pi$
$89$	−6.71987	+	6.71987i	−0.712304	+	0.712304i	0.254712	+	0.967017i	$0.418019\pi$
$90$			0.677441i			0.0714085i
$91$	−3.09265	+	7.46631i	−0.324198	+	0.782682i
$92$	−1.21727	+	0.504209i	−0.126909	+	0.0525674i
$93$		−	19.6449i		−	2.03708i
$94$		−	12.3512i		−	1.27393i
$95$	0.825514	+	1.99297i	0.0846959	+	0.204474i
$96$	−0.863972	−	2.08581i	−0.0881788	−	0.212882i
$97$	2.79481	+	6.74728i	0.283770	+	0.685082i	0.999917	−	0.0128674i	$-0.00409592\pi$
$97$	2.79481	+	6.74728i	0.283770	+	0.685082i	−0.716147	+	0.697950i	$0.754096\pi$
$98$	10.0660	−	10.0660i	1.01682	−	1.01682i
$99$		−	1.16891i		−	0.117480i
$100$		−	4.89564i		−	0.489564i
$101$	4.35739	−	10.5197i	0.433577	−	1.04675i	−0.544548	−	0.838729i	$-0.683299\pi$
$101$	4.35739	−	10.5197i	0.433577	−	1.04675i	0.978125	−	0.208017i	$-0.0667011\pi$
$102$	1.89960	+	1.89960i	0.188089	+	0.188089i
$103$	9.86748	−	9.86748i	0.972272	−	0.972272i	−0.0273542	−	0.999626i	$-0.508708\pi$
$103$	9.86748	−	9.86748i	0.972272	−	0.972272i	0.999626	+	0.0273542i	$0.00870821\pi$
$104$	0.671118	−	1.62022i	0.0658086	−	0.158876i
$105$	3.10504	−	1.28615i	0.303021	−	0.125515i
$106$	−11.5897	+	4.80063i	−1.12569	+	0.466278i
$107$	2.74516	−	1.13708i	0.265384	−	0.109926i	−0.246024	−	0.969264i	$-0.579124\pi$
$107$	2.74516	−	1.13708i	0.265384	−	0.109926i	0.511408	+	0.859338i	$0.329124\pi$
$108$	1.88336	−	0.780112i	0.181226	−	0.0750664i
$109$	−5.23332	−	5.23332i	−0.501261	−	0.501261i	0.410568	−	0.911830i	$-0.365330\pi$
$109$	−5.23332	−	5.23332i	−0.501261	−	0.501261i	−0.911830	+	0.410568i	$0.865330\pi$
$110$		−	0.180065i		−	0.0171685i
$111$	15.3453	+	15.3453i	1.45651	+	1.45651i
$112$	−3.25849	+	3.25849i	−0.307898	+	0.307898i
$113$		−	9.62673i		−	0.905607i	−0.891610	−	0.452803i	$-0.850424\pi$
$113$		−	9.62673i		−	0.905607i	0.891610	−	0.452803i	$-0.149576\pi$
$114$	−10.6603	+	10.6603i	−0.998429	+	0.998429i
$115$	0.162881	+	0.393229i	0.0151887	+	0.0366688i
$116$			4.02659i			0.373860i
$117$	−3.39771	−	1.40738i	−0.314118	−	0.130112i
$118$	1.25797	+	0.521066i	0.115805	+	0.0479680i
$119$	2.09840	−	5.06600i	0.192360	−	0.464399i
$120$	−0.673807	+	0.279100i	−0.0615098	+	0.0254782i
$121$		−	10.6893i		−	0.971755i
$122$	−3.20513	+	7.73786i	−0.290179	+	0.700553i
$123$	−15.9121	−	6.59099i	−1.43474	−	0.594289i
$124$	8.03905	−	3.32988i	0.721928	−	0.299032i
$125$	−3.19672			−0.285923
$126$	6.83326	+	6.83326i	0.608755	+	0.608755i
$127$	−0.528234	−	1.27527i	−0.0468731	−	0.113162i	0.898709	−	0.438546i	$-0.144506\pi$
$127$	−0.528234	−	1.27527i	−0.0468731	−	0.113162i	−0.945582	+	0.325384i	$0.894506\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−25.6568	+	10.6274i	−2.25895	+	0.935689i
$130$	−0.523401	−	0.216800i	−0.0459053	−	0.0190146i
$131$	−3.82756	+	9.24054i	−0.334415	+	0.807350i	0.663816	+	0.747896i	$0.268936\pi$
$131$	−3.82756	+	9.24054i	−0.334415	+	0.807350i	−0.998231	+	0.0594539i	$0.981064\pi$
$132$	1.16264	−	0.481581i	0.101195	−	0.0419162i
$133$	28.4297	+	11.7759i	2.46516	+	1.02110i
$134$	13.6654	−	5.66041i	1.18051	−	0.488985i
$135$	−0.252010	−	0.608405i	−0.0216895	−	0.0523632i
$136$	−0.455363	+	1.09934i	−0.0390471	+	0.0942679i
$137$	3.65870	+	1.51548i	0.312584	+	0.129477i	0.533460	−	0.845825i	$-0.320892\pi$
$137$	3.65870	+	1.51548i	0.312584	+	0.129477i	−0.220876	+	0.975302i	$0.570892\pi$
$138$	−2.10337	+	2.10337i	−0.179051	+	0.179051i
$139$	10.4592	−	4.33233i	0.887135	−	0.367463i	0.107875	−	0.994164i	$-0.465595\pi$
$139$	10.4592	−	4.33233i	0.887135	−	0.367463i	0.779260	+	0.626701i	$0.215595\pi$
$140$	1.05263	+	1.05263i	0.0889636	+	0.0889636i
$141$	−10.6711	−	25.7624i	−0.898670	−	2.16958i
$142$	−12.4962	+	5.17609i	−1.04866	+	0.434368i
$143$	0.903117	+	0.374083i	0.0755225	+	0.0312824i
$144$	−1.48285	−	1.48285i	−0.123571	−	0.123571i
$145$	1.30076			0.108022
$146$	0.954920			0.0790297
$147$	12.2991	−	29.6926i	1.01441	−	2.44901i
$148$	−3.67848	+	8.88064i	−0.302369	+	0.729984i
$149$			10.6002i			0.868401i	0.900816	+	0.434200i	$0.142969\pi$
$149$			10.6002i			0.868401i	−0.900816	+	0.434200i	$0.857031\pi$
$150$	−4.22970	−	10.2114i	−0.345353	−	0.833757i
$151$	9.45544	+	9.45544i	0.769473	+	0.769473i	0.978014	−	0.208541i	$-0.0668714\pi$
$151$	9.45544	+	9.45544i	0.769473	+	0.769473i	−0.208541	+	0.978014i	$0.566871\pi$
$152$	−6.16936	−	2.55543i	−0.500401	−	0.207273i
$153$	2.30539	+	0.954925i	0.186380	+	0.0772011i
$154$	−1.81629	−	1.81629i	−0.146361	−	0.146361i
$155$	−1.07569	−	2.59696i	−0.0864019	−	0.208593i
$156$		−	3.95931i		−	0.316998i
$157$	17.1574	−	7.10682i	1.36931	−	0.567186i	0.427707	−	0.903917i	$-0.359321\pi$
$157$	17.1574	−	7.10682i	1.36931	−	0.567186i	0.941601	+	0.336731i	$0.109321\pi$
$158$	3.24560	−	7.83557i	0.258206	−	0.623365i
$159$	−20.0264	+	20.0264i	−1.58820	+	1.58820i
$160$	−0.228426	−	0.228426i	−0.0180586	−	0.0180586i
$161$	5.60941	+	2.32349i	0.442084	+	0.183117i
$162$	7.70288	−	7.70288i	0.605195	−	0.605195i
$163$	1.92910	−	0.799061i	0.151099	−	0.0625873i	−0.305852	−	0.952079i	$-0.598941\pi$
$163$	1.92910	−	0.799061i	0.151099	−	0.0625873i	0.456951	+	0.889492i	$0.348941\pi$
$164$		−	7.62871i		−	0.595702i
$165$	−0.155571	−	0.375582i	−0.0121112	−	0.0292390i
$166$	−3.79946	−	3.79946i	−0.294895	−	0.294895i
$167$	7.01331	+	16.9316i	0.542707	+	1.31021i	0.922806	+	0.385264i	$0.125890\pi$
$167$	7.01331	+	16.9316i	0.542707	+	1.31021i	−0.380100	+	0.924945i	$0.624110\pi$
$168$	−3.98136	+	9.61185i	−0.307168	+	0.741570i
$169$	−7.01767	+	7.01767i	−0.539820	+	0.539820i
$170$	0.355135	+	0.147102i	0.0272376	+	0.0112822i
$171$	−5.35890	+	12.9375i	−0.409806	+	0.989358i
$172$	−8.69784	−	8.69784i	−0.663204	−	0.663204i
$173$	−18.3734			−1.39690			−0.698452	−	0.715657i	$-0.746127\pi$
$173$	−18.3734			−1.39690			−0.698452	+	0.715657i	$0.746127\pi$
$174$	3.47886	+	8.39872i	0.263732	+	0.636705i
$175$	−15.9524	+	15.9524i	−1.20589	+	1.20589i
$176$	0.394144	+	0.394144i	0.0297097	+	0.0297097i
$177$	3.07407			0.231061
$178$	−9.50333			−0.712304
$179$			1.80017i			0.134551i	0.997734	+	0.0672755i	$0.0214306\pi$
$179$			1.80017i			0.134551i	−0.997734	+	0.0672755i	$0.978569\pi$
$180$	−0.479023	+	0.479023i	−0.0357043	+	0.0357043i
$181$	−4.01498	+	4.01498i	−0.298431	+	0.298431i	−0.840399	−	0.541968i	$-0.817679\pi$
$181$	−4.01498	+	4.01498i	−0.298431	+	0.298431i	0.541968	+	0.840399i	$0.317679\pi$
$182$	−7.46631	+	3.09265i	−0.553440	+	0.229242i
$183$			18.9089i			1.39778i
$184$	−1.21727	−	0.504209i	−0.0897381	−	0.0371707i
$185$	2.86883	+	1.18831i	0.210920	+	0.0873661i
$186$	13.8910	−	13.8910i	1.01854	−	1.01854i
$187$	−0.612778	−	0.253821i	−0.0448107	−	0.0185612i
$188$	8.73364	−	8.73364i	0.636966	−	0.636966i
$189$	−8.67889	−	3.59492i	−0.631297	−	0.261492i
$190$	−0.825514	+	1.99297i	−0.0598891	+	0.144585i
$191$	13.0117	+	5.38963i	0.941495	+	0.389980i	0.800028	−	0.599963i	$-0.204818\pi$
$191$	13.0117	+	5.38963i	0.941495	+	0.389980i	0.141467	+	0.989943i	$0.454818\pi$
$192$	0.863972	−	2.08581i	0.0623518	−	0.150531i
$193$	0.00770943	−	0.00319335i	0.000554937	−	0.000229862i	−0.382406	−	0.923994i	$-0.624904\pi$
$193$	0.00770943	−	0.00319335i	0.000554937	−	0.000229862i	0.382961	+	0.923765i	$0.374904\pi$
$194$	−2.79481	+	6.74728i	−0.200656	+	0.484426i
$195$	−1.27903			−0.0915929
$196$	14.2355			1.01682
$197$		−	26.5350i		−	1.89054i	−0.326287	−	0.945271i	$-0.605798\pi$
$197$		−	26.5350i		−	1.89054i	0.326287	−	0.945271i	$-0.394202\pi$
$198$	0.826544	−	0.826544i	0.0587399	−	0.0587399i
$199$	−3.68628	+	1.52691i	−0.261314	+	0.108240i	−0.509494	−	0.860474i	$-0.670167\pi$
$199$	−3.68628	+	1.52691i	−0.261314	+	0.108240i	0.248180	+	0.968714i	$0.420167\pi$
$200$	3.46174	−	3.46174i	0.244782	−	0.244782i
$201$	23.6131	−	23.6131i	1.66554	−	1.66554i
$202$	10.5197	−	4.35739i	0.740162	−	0.306585i
$203$	13.1206	−	13.1206i	0.920886	−	0.920886i
$204$			2.68645i			0.188089i
$205$	−2.46440			−0.172121
$206$	13.9547			0.972272
$207$	−1.05736	+	2.55269i	−0.0734914	+	0.177424i
$208$	1.62022	−	0.671118i	0.112342	−	0.0465337i
$209$	1.42441	−	3.43882i	0.0985282	−	0.237868i
$210$	3.10504	+	1.28615i	0.214268	+	0.0887527i
$211$	4.27229	−	10.3142i	0.294117	−	0.710060i	−0.705882	−	0.708330i	$-0.749449\pi$
$211$	4.27229	−	10.3142i	0.294117	−	0.710060i	0.999999	−	0.00173077i	$-0.000550921\pi$
$212$	−11.5897	−	4.80063i	−0.795986	−	0.329708i
$213$	−21.5927	+	21.5927i	−1.47951	+	1.47951i
$214$	2.74516	+	1.13708i	0.187655	+	0.0777293i
$215$	−2.80977	+	2.80977i	−0.191625	+	0.191625i
$216$	1.88336	+	0.780112i	0.128146	+	0.0530799i
$217$	−37.0456	−	15.3448i	−2.51482	−	1.04167i
$218$		−	7.40104i		−	0.501261i
$219$	1.99178	−	0.825024i	0.134592	−	0.0557499i
$220$	0.127325	−	0.127325i	0.00858426	−	0.00858426i
$221$	−1.47558	+	1.47558i	−0.0992582	+	0.0992582i
$222$			21.7015i			1.45651i
$223$	−2.47933			−0.166028			−0.0830140	−	0.996548i	$-0.526455\pi$
$223$	−2.47933			−0.166028			−0.0830140	+	0.996548i	$0.526455\pi$
$224$	−4.60820			−0.307898
$225$	−7.25949	−	7.25949i	−0.483966	−	0.483966i
$226$	6.80713	−	6.80713i	0.452803	−	0.452803i
$227$	5.93913	+	14.3383i	0.394194	+	0.951668i	0.989016	+	0.147810i	$0.0472226\pi$
$227$	5.93913	+	14.3383i	0.394194	+	0.951668i	−0.594822	+	0.803857i	$0.702777\pi$
$228$	−15.0760			−0.998429
$229$	2.40575	+	2.40575i	0.158977	+	0.158977i	0.782113	−	0.623136i	$-0.214142\pi$
$229$	2.40575	+	2.40575i	0.158977	+	0.158977i	−0.623136	+	0.782113i	$0.714142\pi$
$230$	−0.162881	+	0.393229i	−0.0107400	+	0.0259288i
$231$	−5.35767	−	2.21922i	−0.352509	−	0.146014i
$232$	−2.84723	+	2.84723i	−0.186930	+	0.186930i
$233$	5.96559	−	14.4022i	0.390819	−	0.943520i	−0.598943	−	0.800791i	$-0.704413\pi$
$233$	5.96559	−	14.4022i	0.390819	−	0.943520i	0.989762	−	0.142728i	$-0.0455875\pi$
$234$	−1.40738	−	3.39771i	−0.0920031	−	0.222115i
$235$	−2.82134	−	2.82134i	−0.184044	−	0.184044i
$236$	0.521066	+	1.25797i	0.0339185	+	0.0818866i
$237$		−	19.1477i		−	1.24377i
$238$	5.06600	−	2.09840i	0.328380	−	0.136019i
$239$	4.27246	−	4.27246i	0.276363	−	0.276363i	−0.555293	−	0.831655i	$-0.687394\pi$
$239$	4.27246	−	4.27246i	0.276363	−	0.276363i	0.831655	+	0.555293i	$0.187394\pi$
$240$	−0.673807	−	0.279100i	−0.0434940	−	0.0180158i
$241$	−6.87772	−	6.87772i	−0.443033	−	0.443033i	0.449997	−	0.893030i	$-0.351425\pi$
$241$	−6.87772	−	6.87772i	−0.443033	−	0.443033i	−0.893030	+	0.449997i	$0.851425\pi$
$242$	7.55848	−	7.55848i	0.485877	−	0.485877i
$243$	7.07136	−	17.0718i	0.453628	−	1.09515i
$244$	−7.73786	+	3.20513i	−0.495366	+	0.205187i
$245$		−	4.59868i		−	0.293799i
$246$	−6.59099	−	15.9121i	−0.420226	−	1.01452i
$247$	−8.28074	−	8.28074i	−0.526891	−	0.526891i
$248$	8.03905	+	3.32988i	0.510480	+	0.211448i
$249$	−11.2076	−	4.64233i	−0.710252	−	0.294196i
$250$	−2.26042	−	2.26042i	−0.142961	−	0.142961i
$251$	−1.89611	−	4.57761i	−0.119681	−	0.288936i	0.852674	−	0.522444i	$-0.174980\pi$
$251$	−1.89611	−	4.57761i	−0.119681	−	0.288936i	−0.972355	+	0.233508i	$0.924980\pi$
$252$			9.66369i			0.608755i
$253$	0.281047	−	0.678509i	0.0176693	−	0.0426575i
$254$	0.528234	−	1.27527i	0.0331443	−	0.0800175i
$255$	0.867837			0.0543460
$256$	1.00000			0.0625000
$257$	2.80069	+	2.80069i	0.174702	+	0.174702i	0.789042	−	0.614340i	$-0.210577\pi$
$257$	2.80069	+	2.80069i	0.174702	+	0.174702i	−0.614340	+	0.789042i	$0.710577\pi$
$258$	−25.6568	−	10.6274i	−1.59732	−	0.661632i
$259$	40.9238	−	16.9512i	2.54288	−	1.05330i
$260$	−0.216800	−	0.523401i	−0.0134454	−	0.0324600i
$261$	5.97082	+	5.97082i	0.369585	+	0.369585i
$262$	−9.24054	+	3.82756i	−0.570883	+	0.236467i
$263$	−3.48324	+	3.48324i	−0.214786	+	0.214786i	−0.806297	−	0.591511i	$-0.798532\pi$
$263$	−3.48324	+	3.48324i	−0.214786	+	0.214786i	0.591511	+	0.806297i	$0.298532\pi$
$264$	1.16264	+	0.481581i	0.0715555	+	0.0296392i
$265$	−1.55081	+	3.74398i	−0.0952653	+	0.229991i
$266$	11.7759	+	28.4297i	0.722030	+	1.74313i
$267$	−19.8222	+	8.21061i	−1.21310	+	0.502481i
$268$	13.6654	+	5.66041i	0.834750	+	0.345765i
$269$	−25.9788	+	10.7608i	−1.58396	+	0.656096i	−0.989034	−	0.147687i	$-0.952817\pi$
$269$	−25.9788	+	10.7608i	−1.58396	+	0.656096i	−0.594922	+	0.803783i	$0.702817\pi$
$270$	0.252010	−	0.608405i	0.0153368	−	0.0370264i
$271$	6.80766	+	2.81983i	0.413536	+	0.171292i	0.579744	−	0.814798i	$-0.303152\pi$
$271$	6.80766	+	2.81983i	0.413536	+	0.171292i	−0.166208	+	0.986091i	$0.553152\pi$
$272$	−1.09934	+	0.455363i	−0.0666575	+	0.0276104i
$273$	−12.9014	+	12.9014i	−0.780826	+	0.780826i
$274$	1.51548	+	3.65870i	0.0915538	+	0.221030i
$275$	1.92959	+	1.92959i	0.116358	+	0.116358i
$276$	−2.97461			−0.179051
$277$	−11.8059	+	4.89014i	−0.709345	+	0.293820i	−0.708033	−	0.706179i	$-0.750417\pi$
$277$	−11.8059	+	4.89014i	−0.709345	+	0.293820i	−0.00131139	+	0.999999i	$0.500417\pi$
$278$	10.4592	+	4.33233i	0.627299	+	0.259836i
$279$	6.98298	−	16.8584i	0.418060	−	1.00929i
$280$			1.48865i			0.0889636i
$281$	7.36653	−	3.05132i	0.439450	−	0.182026i	−0.151978	−	0.988384i	$-0.548564\pi$
$281$	7.36653	−	3.05132i	0.439450	−	0.182026i	0.591428	+	0.806358i	$0.298564\pi$
$282$	10.6711	−	25.7624i	0.635456	−	1.53413i
$283$	3.47605	+	1.43983i	0.206630	+	0.0855888i	0.483598	−	0.875290i	$-0.339330\pi$
$283$	3.47605	+	1.43983i	0.206630	+	0.0855888i	−0.276968	+	0.960879i	$0.589330\pi$
$284$	−12.4962	−	5.17609i	−0.741512	−	0.307144i
$285$			4.87018i			0.288484i
$286$	0.374083	+	0.903117i	0.0221200	+	0.0534024i
$287$	−24.8581	+	24.8581i	−1.46733	+	1.46733i
$288$		−	2.09706i		−	0.123571i
$289$	−11.0196	+	11.0196i	−0.648213	+	0.648213i
$290$	0.919777	+	0.919777i	0.0540112	+	0.0540112i
$291$			16.4882i			0.966555i
$292$	0.675230	+	0.675230i	0.0395149	+	0.0395149i
$293$	8.88804	−	3.68155i	0.519245	−	0.215078i	−0.107640	−	0.994190i	$-0.534329\pi$
$293$	8.88804	−	3.68155i	0.519245	−	0.215078i	0.626885	+	0.779112i	$0.284329\pi$
$294$	29.6926	−	12.2991i	1.73171	−	0.717297i
$295$	0.406377	−	0.168327i	0.0236602	−	0.00980036i
$296$	−8.88064	+	3.67848i	−0.516177	+	0.213808i
$297$	−0.434837	+	1.04979i	−0.0252318	+	0.0609150i
$298$	−7.49546	+	7.49546i	−0.434200	+	0.434200i
$299$	−1.63386	−	1.63386i	−0.0944886	−	0.0944886i
$300$	4.22970	−	10.2114i	0.244202	−	0.589555i
$301$			56.6837i			3.26719i
$302$			13.3720i			0.769473i
$303$	18.1774	−	18.1774i	1.04426	−	1.04426i
$304$	−2.55543	−	6.16936i	−0.146564	−	0.353837i
$305$	1.03539	+	2.49966i	0.0592864	+	0.143130i
$306$	0.954925	+	2.30539i	0.0545894	+	0.131791i
$307$		−	24.3356i		−	1.38891i	−0.719537	−	0.694454i	$-0.755646\pi$
$307$		−	24.3356i		−	1.38891i	0.719537	−	0.694454i	$-0.244354\pi$
$308$		−	2.56863i		−	0.146361i
$309$	29.1069	−	12.0565i	1.65584	−	0.685870i
$310$	1.07569	−	2.59696i	0.0610954	−	0.147497i
$311$		−	16.6339i		−	0.943220i	−0.881807	−	0.471610i	$-0.843673\pi$
$311$		−	16.6339i		−	0.943220i	0.881807	−	0.471610i	$-0.156327\pi$
$312$	2.79965	−	2.79965i	0.158499	−	0.158499i
$313$	−1.29499			−0.0731971			−0.0365985	−	0.999330i	$-0.511652\pi$
$313$	−1.29499			−0.0731971			−0.0365985	+	0.999330i	$0.511652\pi$
$314$	17.1574	+	7.10682i	0.968247	+	0.401061i
$315$	3.12178			0.175893
$316$	7.83557	−	3.24560i	0.440786	−	0.182579i
$317$	−0.483945	−	1.16835i	−0.0271811	−	0.0656209i	0.909706	−	0.415252i	$-0.136307\pi$
$317$	−0.483945	−	1.16835i	−0.0271811	−	0.0656209i	−0.936887	+	0.349632i	$0.886307\pi$
$318$	−28.3216			−1.58820
$319$	−1.58706	−	1.58706i	−0.0888581	−	0.0888581i
$320$		−	0.323043i		−	0.0180586i
$321$	6.70829			0.374420
$322$	2.32349	+	5.60941i	0.129483	+	0.312600i
$323$	5.61860	+	5.61860i	0.312627	+	0.312627i
$324$	10.8935			0.605195
$325$	7.93203	−	3.28556i	0.439990	−	0.182250i
$326$	1.92910	+	0.799061i	0.106843	+	0.0442559i
$327$	−6.39429	−	15.4372i	−0.353605	−	0.853678i
$328$	5.39431	−	5.39431i	0.297851	−	0.297851i
$329$	−56.9170			−3.13793
$330$	0.155571	−	0.375582i	0.00856391	−	0.0206751i
$331$	8.73734			0.480247			0.240124	−	0.970742i	$-0.422812\pi$
$331$	8.73734			0.480247			0.240124	+	0.970742i	$0.422812\pi$
$332$		−	5.37325i		−	0.294895i
$333$	7.71401	+	18.6233i	0.422725	+	1.02055i
$334$	−7.01331	+	16.9316i	−0.383752	+	0.926458i
$335$	1.82855	−	4.41452i	0.0999046	−	0.241191i
$336$	−9.61185	+	3.98136i	−0.524369	+	0.217201i
$337$			4.31588i			0.235101i	0.993067	+	0.117550i	$0.0375042\pi$
$337$			4.31588i			0.235101i	−0.993067	+	0.117550i	$0.962496\pi$
$338$	−9.92448			−0.539820
$339$	8.31723	−	20.0796i	0.451730	−	1.09057i
$340$	0.147102	+	0.355135i	0.00797771	+	0.0192599i
$341$	−1.85609	+	4.48099i	−0.100513	+	0.242659i
$342$	−12.9375	+	5.35890i	−0.699582	+	0.289776i
$343$	−23.5769	−	23.5769i	−1.27303	−	1.27303i
$344$		−	12.3006i		−	0.663204i
$345$			0.960927i			0.0517346i
$346$	−12.9920	−	12.9920i	−0.698452	−	0.698452i
$347$	−2.51433	+	6.07013i	−0.134976	+	0.325862i	−0.976887	−	0.213755i	$-0.931431\pi$
$347$	−2.51433	+	6.07013i	−0.134976	+	0.325862i	0.841911	+	0.539616i	$0.181431\pi$
$348$	−3.47886	+	8.39872i	−0.186487	+	0.450219i
$349$	11.8561	+	28.6232i	0.634643	+	1.53216i	0.833724	+	0.552181i	$0.186204\pi$
$349$	11.8561	+	28.6232i	0.634643	+	1.53216i	−0.199081	+	0.979983i	$0.563796\pi$
$350$	−22.5601			−1.20589
$351$	2.52791	+	2.52791i	0.134930	+	0.134930i
$352$			0.557403i			0.0297097i
$353$	25.2799	+	10.4713i	1.34551	+	0.557330i	0.935040	−	0.354542i	$-0.115363\pi$
$353$	25.2799	+	10.4713i	1.34551	+	0.557330i	0.410474	+	0.911872i	$0.365363\pi$
$354$	2.17369	+	2.17369i	0.115531	+	0.115531i
$355$	−1.67210	+	4.03680i	−0.0887457	+	0.214251i
$356$	−6.71987	−	6.71987i	−0.356152	−	0.356152i
$357$	8.75376	−	8.75376i	0.463298	−	0.463298i
$358$	−1.27291	+	1.27291i	−0.0672755	+	0.0672755i
$359$	23.5230	+	9.74357i	1.24150	+	0.514246i	0.904183	−	0.427146i	$-0.140481\pi$
$359$	23.5230	+	9.74357i	1.24150	+	0.514246i	0.337316	+	0.941391i	$0.390481\pi$
$360$	−0.677441			−0.0357043
$361$	−18.0957	+	18.0957i	−0.952407	+	0.952407i
$362$	−5.67804			−0.298431
$363$	9.23526	−	22.2959i	0.484725	−	1.17023i
$364$	−7.46631	−	3.09265i	−0.391341	−	0.162099i
$365$	0.218128	−	0.218128i	0.0114174	−	0.0114174i
$366$	−13.3706	+	13.3706i	−0.698892	+	0.698892i
$367$	23.0808	+	9.56038i	1.20481	+	0.499048i	0.892550	−	0.450949i	$-0.148915\pi$
$367$	23.0808	+	9.56038i	1.20481	+	0.499048i	0.312258	+	0.949997i	$0.398915\pi$
$368$	−0.504209	−	1.21727i	−0.0262837	−	0.0634544i
$369$	−11.3122	−	11.3122i	−0.588890	−	0.588890i
$370$	1.18831	+	2.86883i	0.0617771	+	0.149143i
$371$	22.1222	+	53.4078i	1.14853	+	2.77280i
$372$	19.6449			1.01854
$373$	4.74225	+	4.74225i	0.245544	+	0.245544i	0.819139	−	0.573595i	$-0.194452\pi$
$373$	4.74225	+	4.74225i	0.245544	+	0.245544i	−0.573595	+	0.819139i	$0.694452\pi$
$374$	−0.253821	−	0.612778i	−0.0131248	−	0.0316860i
$375$	−6.66775	−	2.76187i	−0.344321	−	0.142622i
$376$	12.3512			0.636966
$377$	−6.52398	+	2.70232i	−0.336002	+	0.139177i
$378$	−3.59492	−	8.67889i	−0.184902	−	0.446394i
$379$			5.10758i			0.262359i	0.991359	+	0.131179i	$0.0418764\pi$
$379$			5.10758i			0.262359i	−0.991359	+	0.131179i	$0.958124\pi$
$380$	−1.99297	+	0.825514i	−0.102237	+	0.0423480i
$381$		−	3.11635i		−	0.159655i
$382$	5.38963	+	13.0117i	0.275757	+	0.665737i
$383$			31.4900i			1.60907i	0.593908	+	0.804533i	$0.297584\pi$
$383$			31.4900i			1.60907i	−0.593908	+	0.804533i	$0.702416\pi$
$384$	2.08581	−	0.863972i	0.106441	−	0.0440894i
$385$	−0.829776			−0.0422893
$386$	0.00770943	+	0.00319335i	0.000392399	+	0.000162537i
$387$	−25.7951			−1.31124
$388$	−6.74728	+	2.79481i	−0.342541	+	0.141885i
$389$	−10.7451	+	25.9409i	−0.544797	+	1.31526i	0.376508	+	0.926414i	$0.377125\pi$
$389$	−10.7451	+	25.9409i	−0.544797	+	1.31526i	−0.921304	+	0.388842i	$0.872875\pi$
$390$	−0.904408	−	0.904408i	−0.0457965	−	0.0457965i
$391$	1.10860	+	1.10860i	0.0560642	+	0.0560642i
$392$	10.0660	+	10.0660i	0.508411	+	0.508411i
$393$	−15.9671	+	15.9671i	−0.805436	+	0.805436i
$394$	18.7631	−	18.7631i	0.945271	−	0.945271i
$395$	−1.04847	−	2.53122i	−0.0527541	−	0.127360i
$396$	1.16891			0.0587399
$397$		−	25.8459i		−	1.29717i	−0.761143	−	0.648585i	$-0.775361\pi$
$397$		−	25.8459i		−	1.29717i	0.761143	−	0.648585i	$-0.224639\pi$
$398$	−3.68628	−	1.52691i	−0.184777	−	0.0765370i
$399$	49.1248	+	49.1248i	2.45932	+	2.45932i
$400$	4.89564			0.244782
$401$	−3.60065	+	19.6986i	−0.179808	+	0.983702i
$401$	−3.60065	+	19.6986i	−0.179808	+	0.983702i
$402$	33.3940			1.66554
$403$	10.7903	+	10.7903i	0.537504	+	0.537504i
$404$	10.5197	+	4.35739i	0.523373	+	0.216788i
$405$		−	3.51907i		−	0.174864i
$406$	18.5553			0.920886
$407$	−2.05040	−	4.95010i	−0.101634	−	0.245367i
$408$	−1.89960	+	1.89960i	−0.0940444	+	0.0940444i
$409$	13.7125	−	13.7125i	0.678039	−	0.678039i	−0.281517	−	0.959556i	$-0.590838\pi$
$409$	13.7125	−	13.7125i	0.678039	−	0.678039i	0.959556	+	0.281517i	$0.0908375\pi$
$410$	−1.74259	−	1.74259i	−0.0860605	−	0.0860605i
$411$	6.32203	+	6.32203i	0.311843	+	0.311843i
$412$	9.86748	+	9.86748i	0.486136	+	0.486136i
$413$	2.40118	−	5.79696i	0.118154	−	0.285250i
$414$	−2.55269	+	1.05736i	−0.125458	+	0.0519663i
$415$	−1.73579			−0.0852065
$416$	1.62022	+	0.671118i	0.0794380	+	0.0329043i
$417$	25.5589			1.25162
$418$	3.43882	−	1.42441i	0.168198	−	0.0696700i
$419$		−	7.85024i		−	0.383509i	−0.981443	−	0.191755i	$-0.938582\pi$
$419$		−	7.85024i		−	0.383509i	0.981443	−	0.191755i	$-0.0614178\pi$
$420$	1.28615	+	3.10504i	0.0627576	+	0.151510i
$421$			28.8485i			1.40599i	0.711195	+	0.702994i	$0.248154\pi$
$421$			28.8485i			1.40599i	−0.711195	+	0.702994i	$0.751846\pi$
$422$	10.3142	−	4.27229i	0.502088	−	0.207972i
$423$		−	25.9013i		−	1.25936i
$424$	−4.80063	−	11.5897i	−0.233139	−	0.562847i
$425$	−5.38199	+	2.22930i	−0.261065	+	0.108137i
$426$	−30.5367			−1.47951
$427$	35.6576	+	14.7699i	1.72559	+	0.714764i
$428$	1.13708	+	2.74516i	0.0549629	+	0.132692i
$429$	1.56054	+	1.56054i	0.0753434	+	0.0753434i
$430$	−3.97362			−0.191625
$431$	11.3031	+	27.2881i	0.544450	+	1.31442i	0.921555	+	0.388249i	$0.126920\pi$
$431$	11.3031	+	27.2881i	0.544450	+	1.31442i	−0.377104	+	0.926171i	$0.623080\pi$
$432$	0.780112	+	1.88336i	0.0375332	+	0.0906131i
$433$	−15.5926	−	15.5926i	−0.749331	−	0.749331i	0.225022	−	0.974354i	$-0.427754\pi$
$433$	−15.5926	−	15.5926i	−0.749331	−	0.749331i	−0.974354	+	0.225022i	$0.927754\pi$
$434$	−15.3448	−	37.0456i	−0.736573	−	1.77824i
$435$	2.71314	+	1.12382i	0.130085	+	0.0538831i
$436$	5.23332	−	5.23332i	0.250631	−	0.250631i
$437$	−6.22129	+	6.22129i	−0.297605	+	0.297605i
$438$	1.99178	+	0.825024i	0.0951711	+	0.0394212i
$439$	14.9565	−	36.1082i	0.713836	−	1.72335i	0.0236487	−	0.999720i	$-0.492472\pi$
$439$	14.9565	−	36.1082i	0.713836	−	1.72335i	0.690187	−	0.723631i	$-0.257528\pi$
$440$	0.180065			0.00858426
$441$	21.1091	−	21.1091i	1.00520	−	1.00520i
$442$	−2.08678			−0.0992582
$443$	−25.8541	−	10.7091i	−1.22837	−	0.508806i	−0.328305	−	0.944572i	$-0.606478\pi$
$443$	−25.8541	−	10.7091i	−1.22837	−	0.508806i	−0.900060	+	0.435766i	$0.856478\pi$
$444$	−15.3453	+	15.3453i	−0.728254	+	0.728254i
$445$	−2.17080	+	2.17080i	−0.102906	+	0.102906i
$446$	−1.75315	−	1.75315i	−0.0830140	−	0.0830140i
$447$	−9.15826	+	22.1100i	−0.433171	+	1.04577i
$448$	−3.25849	−	3.25849i	−0.153949	−	0.153949i
$449$	−13.8694	−	5.74491i	−0.654540	−	0.271119i	0.0305992	−	0.999532i	$-0.490258\pi$
$449$	−13.8694	−	5.74491i	−0.654540	−	0.271119i	−0.685139	+	0.728413i	$0.740258\pi$
$450$		−	10.2665i		−	0.483966i
$451$	3.00681	+	3.00681i	0.141585	+	0.141585i
$452$	9.62673			0.452803
$453$	11.5530	+	27.8915i	0.542809	+	1.31046i
$454$	−5.93913	+	14.3383i	−0.278737	+	0.672931i
$455$	−0.999057	+	2.41194i	−0.0468365	+	0.113073i
$456$	−10.6603	−	10.6603i	−0.499215	−	0.499215i
$457$		−	19.2216i		−	0.899147i	−0.893243	−	0.449574i	$-0.851576\pi$
$457$		−	19.2216i		−	0.899147i	0.893243	−	0.449574i	$-0.148424\pi$
$458$			3.40225i			0.158977i
$459$	−1.71522	−	1.71522i	−0.0800598	−	0.0800598i
$460$	−0.393229	+	0.162881i	−0.0183344	+	0.00759436i
$461$	−3.64703	+	8.80471i	−0.169859	+	0.410076i	−0.985770	−	0.168102i	$-0.946236\pi$
$461$	−3.64703	+	8.80471i	−0.169859	+	0.410076i	0.815910	+	0.578178i	$0.196236\pi$
$462$	−2.21922	−	5.35767i	−0.103248	−	0.249262i
$463$	−9.66384	+	23.3306i	−0.449117	+	1.08426i	0.523537	+	0.852003i	$0.324612\pi$
$463$	−9.66384	+	23.3306i	−0.449117	+	1.08426i	−0.972654	+	0.232260i	$0.925388\pi$
$464$	−4.02659			−0.186930
$465$		−	6.34614i		−	0.294295i
$466$	14.4022	−	5.96559i	0.667169	−	0.276350i
$467$	−11.8057	+	28.5015i	−0.546303	+	1.31889i	0.373906	+	0.927466i	$0.378018\pi$
$467$	−11.8057	+	28.5015i	−0.546303	+	1.31889i	−0.920210	+	0.391426i	$0.871982\pi$
$468$	1.40738	−	3.39771i	0.0650560	−	0.157059i
$469$	−26.0843	−	62.9731i	−1.20446	−	2.90783i
$470$		−	3.98997i		−	0.184044i
$471$	41.9272			1.93190
$472$	−0.521066	+	1.25797i	−0.0239840	+	0.0579026i
$473$	6.85640			0.315258
$474$	13.5394	−	13.5394i	0.621887	−	0.621887i
$475$	−12.5105	−	30.2030i	−0.574021	−	1.38581i
$476$	5.06600	+	2.09840i	0.232200	+	0.0961802i
$477$	−24.3044	+	10.0672i	−1.11282	+	0.460946i
$478$	6.04217			0.276363
$479$	−23.7708	−	23.7708i	−1.08612	−	1.08612i	−0.995924	−	0.0901917i	$-0.971252\pi$
$479$	−23.7708	−	23.7708i	−1.08612	−	1.08612i	−0.0901917	−	0.995924i	$-0.528748\pi$
$480$	−0.279100	−	0.673807i	−0.0127391	−	0.0307549i
$481$	−16.8573			−0.768628
$482$		−	9.72656i		−	0.443033i
$483$	9.69275	+	9.69275i	0.441035	+	0.441035i
$484$	10.6893			0.485877
$485$	0.902844	+	2.17966i	0.0409960	+	0.0989732i
$486$	17.0718	−	7.07136i	0.774391	−	0.320763i
$487$	39.1675			1.77485			0.887425	−	0.460953i	$-0.152492\pi$
$487$	39.1675			1.77485			0.887425	+	0.460953i	$0.152492\pi$
$488$	−7.73786	−	3.20513i	−0.350276	−	0.145089i
$489$	4.71412			0.213180
$490$	3.25176	−	3.25176i	0.146899	−	0.146899i
$491$			3.82528i			0.172632i	0.996268	+	0.0863162i	$0.0275095\pi$
$491$			3.82528i			0.172632i	−0.996268	+	0.0863162i	$0.972490\pi$
$492$	6.59099	−	15.9121i	0.297145	−	0.717371i
$493$	4.42661	−	1.83356i	0.199364	−	0.0825795i
$494$		−	11.7107i		−	0.526891i
$495$		−	0.377608i		−	0.0169722i
$496$	3.32988	+	8.03905i	0.149516	+	0.360964i
$497$	23.8524	+	57.5849i	1.06993	+	2.58304i
$498$	−4.64233	−	11.2076i	−0.208028	−	0.502224i
$499$	−4.09409	+	4.09409i	−0.183277	+	0.183277i	−0.792782	−	0.609505i	$-0.791368\pi$
$499$	−4.09409	+	4.09409i	−0.183277	+	0.183277i	0.609505	+	0.792782i	$0.291368\pi$
$500$		−	3.19672i		−	0.142961i
$501$			41.3755i			1.84852i
$502$	1.89611	−	4.57761i	0.0846274	−	0.204309i
$503$	20.5874	+	20.5874i	0.917949	+	0.917949i	0.996880	−	0.0789314i	$-0.0251508\pi$
$503$	20.5874	+	20.5874i	0.917949	+	0.917949i	−0.0789314	+	0.996880i	$0.525151\pi$
$504$	−6.83326	+	6.83326i	−0.304378	+	0.304378i
$505$	1.40762	−	3.39830i	0.0626384	−	0.151223i
$506$	0.678509	−	0.281047i	0.0301634	−	0.0124941i
$507$	−20.7006	+	8.57447i	−0.919346	+	0.380806i
$508$	1.27527	−	0.528234i	0.0565809	−	0.0234366i
$509$	−31.4767	+	13.0381i	−1.39518	+	0.577903i	−0.948496	−	0.316788i	$-0.897396\pi$
$509$	−31.4767	+	13.0381i	−1.39518	+	0.577903i	−0.446686	+	0.894691i	$0.647396\pi$
$510$	0.613653	+	0.613653i	0.0271730	+	0.0271730i
$511$		−	4.40046i		−	0.194665i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	9.62559	−	9.62559i	0.424980	−	0.424980i
$514$			3.96077i			0.174702i
$515$	3.18762	−	3.18762i	0.140463	−	0.140463i
$516$	−10.6274	−	25.6568i	−0.467844	−	1.12948i
$517$			6.88461i			0.302785i
$518$	40.9238	+	16.9512i	1.79809	+	0.744793i
$519$	−38.3235	−	15.8741i	−1.68221	−	0.696795i
$520$	0.216800	−	0.523401i	0.00950730	−	0.0229527i
$521$	15.7716	−	6.53282i	0.690968	−	0.286208i	−0.00943553	−	0.999955i	$-0.503003\pi$
$521$	15.7716	−	6.53282i	0.690968	−	0.286208i	0.700403	+	0.713747i	$0.253003\pi$
$522$			8.44402i			0.369585i
$523$	−8.39030	+	20.2560i	−0.366882	+	0.885732i	0.627375	+	0.778717i	$0.284129\pi$
$523$	−8.39030	+	20.2560i	−0.366882	+	0.885732i	−0.994257	+	0.107015i	$0.965871\pi$
$524$	−9.24054	−	3.82756i	−0.403675	−	0.167208i
$525$	−47.0562	+	19.4913i	−2.05370	+	0.850670i
$526$	−4.92605			−0.214786
$527$	−7.32138	−	7.32138i	−0.318924	−	0.318924i
$528$	0.481581	+	1.16264i	0.0209581	+	0.0505974i
$529$	15.0359	−	15.0359i	0.653737	−	0.653737i
$530$	−3.74398	+	1.55081i	−0.162628	+	0.0673627i
$531$	2.63803	+	1.09271i	0.114481	+	0.0474195i
$532$	−11.7759	+	28.4297i	−0.510552	+	1.23258i
$533$	12.3602	−	5.11976i	0.535380	−	0.221762i
$534$	−19.8222	−	8.21061i	−0.857789	−	0.355308i
$535$	0.886803	−	0.367326i	0.0383398	−	0.0158809i
$536$	5.66041	+	13.6654i	0.244493	+	0.590257i
$537$	−1.55530	+	3.75481i	−0.0671159	+	0.162032i
$538$	−25.9788	−	10.7608i	−1.12003	−	0.463930i
$539$	−5.61084	+	5.61084i	−0.241676	+	0.241676i
$540$	0.608405	−	0.252010i	0.0261816	−	0.0108448i
$541$	−7.26843	−	7.26843i	−0.312494	−	0.312494i	0.533381	−	0.845875i	$-0.320921\pi$
$541$	−7.26843	−	7.26843i	−0.312494	−	0.312494i	−0.845875	+	0.533381i	$0.820921\pi$
$542$	2.81983	+	6.80766i	0.121122	+	0.292414i
$543$	−11.8433	+	4.90567i	−0.508246	+	0.210522i
$544$	−1.09934	−	0.455363i	−0.0471340	−	0.0195235i
$545$	−1.69059	−	1.69059i	−0.0724168	−	0.0724168i
$546$	−18.2453			−0.780826
$547$	−9.50040			−0.406208			−0.203104	−	0.979157i	$-0.565103\pi$
$547$	−9.50040			−0.406208			−0.203104	+	0.979157i	$0.565103\pi$
$548$	−1.51548	+	3.65870i	−0.0647383	+	0.156292i
$549$	−6.72135	+	16.2268i	−0.286860	+	0.692542i
$550$			2.72885i			0.116358i
$551$	10.2897	+	24.8415i	0.438355	+	1.05828i
$552$	−2.10337	−	2.10337i	−0.0895253	−	0.0895253i
$553$	−36.1079	−	14.9564i	−1.53546	−	0.636010i
$554$	−11.8059	−	4.89014i	−0.501583	−	0.207762i
$555$	4.95717	+	4.95717i	0.210420	+	0.210420i
$556$	4.33233	+	10.4592i	0.183732	+	0.443568i
$557$			19.1094i			0.809691i	0.914385	+	0.404845i	$0.132675\pi$
$557$			19.1094i			0.809691i	−0.914385	+	0.404845i	$0.867325\pi$
$558$	16.8584	−	6.98298i	0.713673	−	0.295613i
$559$	8.25516	−	19.9297i	0.349156	−	0.842938i
$560$	−1.05263	+	1.05263i	−0.0444818	+	0.0444818i
$561$	−1.05885	−	1.05885i	−0.0447045	−	0.0447045i
$562$	7.36653	+	3.05132i	0.310738	+	0.128712i
$563$	14.8870	−	14.8870i	0.627412	−	0.627412i	−0.320004	−	0.947416i	$-0.603684\pi$
$563$	14.8870	−	14.8870i	0.627412	−	0.627412i	0.947416	+	0.320004i	$0.103684\pi$
$564$	25.7624	−	10.6711i	1.08479	−	0.449335i
$565$		−	3.10985i		−	0.130832i
$566$	1.43983	+	3.47605i	0.0605204	+	0.146109i
$567$	−35.4964	−	35.4964i	−1.49071	−	1.49071i
$568$	−5.17609	−	12.4962i	−0.217184	−	0.524328i
$569$	1.53825	−	3.71367i	0.0644870	−	0.155685i	−0.888351	−	0.459165i	$-0.848149\pi$
$569$	1.53825	−	3.71367i	0.0644870	−	0.155685i	0.952838	+	0.303480i	$0.0981486\pi$
$570$	−3.44373	+	3.44373i	−0.144242	+	0.144242i
$571$	13.5330	+	5.60556i	0.566339	+	0.234585i	0.647435	−	0.762121i	$-0.275842\pi$
$571$	13.5330	+	5.60556i	0.566339	+	0.234585i	−0.0810954	+	0.996706i	$0.525842\pi$
$572$	−0.374083	+	0.903117i	−0.0156412	+	0.0377612i
$573$	22.4835	+	22.4835i	0.939262	+	0.939262i
$574$	−35.1546			−1.46733
$575$	−2.46843	−	5.95931i	−0.102940	−	0.248520i
$576$	1.48285	−	1.48285i	0.0617853	−	0.0617853i
$577$	−0.451884	−	0.451884i	−0.0188122	−	0.0188122i	0.697638	−	0.716450i	$-0.254234\pi$
$577$	−0.451884	−	0.451884i	−0.0188122	−	0.0188122i	−0.716450	+	0.697638i	$0.754234\pi$
$578$	−15.5841			−0.648213
$579$	0.0188394			0.000782938
$580$			1.30076i			0.0540112i
$581$	−17.5087	+	17.5087i	−0.726382	+	0.726382i
$582$	−11.6589	+	11.6589i	−0.483278	+	0.483278i
$583$	6.46016	−	2.67588i	0.267552	−	0.110824i
$584$			0.954920i			0.0395149i
$585$	−1.09760	−	0.454643i	−0.0453804	−	0.0187972i
$586$	8.88804	+	3.68155i	0.367162	+	0.152083i
$587$	2.49992	−	2.49992i	0.103183	−	0.103183i	−0.653631	−	0.756814i	$-0.726755\pi$
$587$	2.49992	−	2.49992i	0.103183	−	0.103183i	0.756814	+	0.653631i	$0.226755\pi$
$588$	29.6926	+	12.2991i	1.22450	+	0.507206i
$589$	41.0865	−	41.0865i	1.69294	−	1.69294i
$590$	0.406377	+	0.168327i	0.0167303	+	0.00692990i
$591$	22.9255	−	55.3471i	0.943029	−	2.27667i
$592$	−8.88064	−	3.67848i	−0.364992	−	0.151185i
$593$	−11.7419	+	28.3475i	−0.482184	+	1.16409i	0.476386	+	0.879236i	$0.341946\pi$
$593$	−11.7419	+	28.3475i	−0.482184	+	1.16409i	−0.958570	+	0.284858i	$0.908054\pi$
$594$	−1.04979	+	0.434837i	−0.0430734	+	0.0178416i
$595$	0.677874	−	1.63653i	0.0277901	−	0.0670913i
$596$	−10.6002			−0.434200
$597$	−9.00810			−0.368677
$598$		−	2.31063i		−	0.0944886i
$599$	−2.80499	+	2.80499i	−0.114609	+	0.114609i	−0.762085	−	0.647477i	$-0.775824\pi$
$599$	−2.80499	+	2.80499i	−0.114609	+	0.114609i	0.647477	+	0.762085i	$0.275824\pi$
$600$	10.2114	−	4.22970i	0.416878	−	0.172677i
$601$	20.9775	−	20.9775i	0.855689	−	0.855689i	−0.135138	−	0.990827i	$-0.543148\pi$
$601$	20.9775	−	20.9775i	0.855689	−	0.855689i	0.990827	+	0.135138i	$0.0431476\pi$
$602$	−40.0814	+	40.0814i	−1.63360	+	1.63360i
$603$	28.6573	−	11.8702i	1.16701	−	0.483393i
$604$	−9.45544	+	9.45544i	−0.384736	+	0.384736i
$605$		−	3.45310i		−	0.140389i
$606$	25.7067			1.04426
$607$	−6.10318			−0.247720			−0.123860	−	0.992300i	$-0.539527\pi$
$607$	−6.10318			−0.247720			−0.123860	+	0.992300i	$0.539527\pi$
$608$	2.55543	−	6.16936i	0.103636	−	0.250201i
$609$	38.7030	−	16.0313i	1.56832	−	0.649621i
$610$	−1.03539	+	2.49966i	−0.0419218	+	0.101208i
$611$	20.0117	+	8.28913i	0.809588	+	0.335342i
$612$	−0.954925	+	2.30539i	−0.0386006	+	0.0931900i
$613$	−33.6854	−	13.9530i	−1.36054	−	0.563554i	−0.421334	−	0.906906i	$-0.638438\pi$
$613$	−33.6854	−	13.9530i	−1.36054	−	0.563554i	−0.939207	+	0.343351i	$0.888438\pi$
$614$	17.2079	−	17.2079i	0.694454	−	0.694454i
$615$	−5.14027	−	2.12917i	−0.207276	−	0.0858564i
$616$	1.81629	−	1.81629i	0.0731805	−	0.0731805i
$617$	−18.3126	−	7.58532i	−0.737237	−	0.305374i	−0.0177149	−	0.999843i	$-0.505639\pi$
$617$	−18.3126	−	7.58532i	−0.737237	−	0.305374i	−0.719522	+	0.694470i	$0.755639\pi$
$618$	29.1069	+	12.0565i	1.17085	+	0.484983i
$619$		−	7.53186i		−	0.302731i	−0.988478	−	0.151365i	$-0.951633\pi$
$619$		−	7.53186i		−	0.302731i	0.988478	−	0.151365i	$-0.0483670\pi$
$620$	2.59696	−	1.07569i	0.104296	−	0.0432009i
$621$	1.89921	−	1.89921i	0.0762127	−	0.0762127i
$622$	11.7619	−	11.7619i	0.471610	−	0.471610i
$623$			43.7932i			1.75454i
$624$	3.95931			0.158499
$625$	23.4455			0.937822
$626$	−0.915695	−	0.915695i	−0.0365985	−	0.0365985i
$627$	5.94209	−	5.94209i	0.237304	−	0.237304i
$628$	7.10682	+	17.1574i	0.283593	+	0.684654i
$629$	11.4379			0.456060
$630$	2.20743	+	2.20743i	0.0879463	+	0.0879463i
$631$	−7.42468	+	17.9248i	−0.295572	+	0.713573i	0.704421	+	0.709782i	$0.251207\pi$
$631$	−7.42468	+	17.9248i	−0.295572	+	0.713573i	−0.999993	+	0.00379099i	$0.998793\pi$
$632$	7.83557	+	3.24560i	0.311682	+	0.129103i
$633$	17.8224	−	17.8224i	0.708377	−	0.708377i
$634$	0.483945	−	1.16835i	0.0192199	−	0.0464010i
$635$	−0.170642	−	0.411966i	−0.00677172	−	0.0163484i
$636$	−20.0264	−	20.0264i	−0.794099	−	0.794099i
$637$	9.55372	+	23.0647i	0.378532	+	0.913857i
$638$		−	2.24444i		−	0.0888581i
$639$	−26.2053	+	10.8546i	−1.03666	+	0.429400i
$640$	0.228426	−	0.228426i	0.00902932	−	0.00902932i
$641$	−24.3535	−	10.0876i	−0.961906	−	0.398435i	−0.154213	−	0.988038i	$-0.549284\pi$
$641$	−24.3535	−	10.0876i	−0.961906	−	0.398435i	−0.807693	+	0.589603i	$0.799284\pi$
$642$	4.74348	+	4.74348i	0.187210	+	0.187210i
$643$	4.47949	−	4.47949i	0.176654	−	0.176654i	−0.613241	−	0.789895i	$-0.710135\pi$
$643$	4.47949	−	4.47949i	0.176654	−	0.176654i	0.789895	+	0.613241i	$0.210135\pi$
$644$	−2.32349	+	5.60941i	−0.0915585	+	0.221042i
$645$	−8.28823	+	3.43310i	−0.326349	+	0.135178i
$646$			7.94590i			0.312627i
$647$	−16.9489	−	40.9182i	−0.666328	−	1.60866i	−0.787705	−	0.616053i	$-0.788731\pi$
$647$	−16.9489	−	40.9182i	−0.666328	−	1.60866i	0.121377	−	0.992607i	$-0.461269\pi$
$648$	7.70288	+	7.70288i	0.302598	+	0.302598i
$649$	−0.701194	−	0.290444i	−0.0275243	−	0.0114009i
$650$	7.93203	+	3.28556i	0.311120	+	0.128870i
$651$	−64.0127	−	64.0127i	−2.50885	−	2.50885i
$652$	0.799061	+	1.92910i	0.0312937	+	0.0755496i
$653$		−	20.7830i		−	0.813302i	−0.913584	−	0.406651i	$-0.866697\pi$
$653$		−	20.7830i		−	0.813302i	0.913584	−	0.406651i	$-0.133303\pi$
$654$	6.39429	−	15.4372i	0.250036	−	0.603641i
$655$	−1.23646	+	2.98509i	−0.0483127	+	0.116637i
$656$	7.62871			0.297851
$657$	2.00253			0.0781260
$658$	−40.2464	−	40.2464i	−1.56897	−	1.56897i
$659$	33.2608	+	13.7771i	1.29566	+	0.536678i	0.920666	−	0.390351i	$-0.127646\pi$
$659$	33.2608	+	13.7771i	1.29566	+	0.536678i	0.374990	+	0.927029i	$0.377646\pi$
$660$	0.375582	−	0.155571i	0.0146195	−	0.00605560i
$661$	2.40019	+	5.79458i	0.0933567	+	0.225383i	0.963659	−	0.267134i	$-0.0860768\pi$
$661$	2.40019	+	5.79458i	0.0933567	+	0.225383i	−0.870303	+	0.492517i	$0.836077\pi$
$662$	6.17823	+	6.17823i	0.240124	+	0.240124i
$663$	−4.35264	+	1.80292i	−0.169043	+	0.0700197i
$664$	3.79946	−	3.79946i	0.147448	−	0.147448i
$665$	9.18399	+	3.80413i	0.356140	+	0.147518i
$666$	−7.71401	+	18.6233i	−0.298912	+	0.721637i
$667$	2.03024	+	4.90144i	0.0786113	+	0.189784i
$668$	−16.9316	+	7.01331i	−0.655105	+	0.271353i
$669$	−5.17141	−	2.14207i	−0.199938	−	0.0828172i
$670$	4.41452	−	1.82855i	0.170548	−	0.0706432i
$671$	1.78655	−	4.31311i	0.0689689	−	0.166506i
$672$	−9.61185	−	3.98136i	−0.370785	−	0.153584i
$673$	−14.1069	+	5.84326i	−0.543781	+	0.225241i	−0.637627	−	0.770345i	$-0.720084\pi$
$673$	−14.1069	+	5.84326i	−0.543781	+	0.225241i	0.0938462	+	0.995587i	$0.470084\pi$
$674$	−3.05178	+	3.05178i	−0.117550	+	0.117550i
$675$	3.81915	+	9.22025i	0.146999	+	0.354888i
$676$	−7.01767	−	7.01767i	−0.269910	−	0.269910i
$677$	4.34766			0.167094			0.0835471	−	0.996504i	$-0.473375\pi$
$677$	4.34766			0.167094			0.0835471	+	0.996504i	$0.473375\pi$
$678$	20.0796	−	8.31723i	0.771151	−	0.319421i
$679$	31.0928	+	12.8791i	1.19323	+	0.494253i
$680$	−0.147102	+	0.355135i	−0.00564109	+	0.0136188i
$681$			35.0383i			1.34267i
$682$	−4.48099	+	1.85609i	−0.171586	+	0.0710733i
$683$	9.84825	−	23.7758i	0.376833	−	0.909755i	−0.615723	−	0.787963i	$-0.711136\pi$
$683$	9.84825	−	23.7758i	0.376833	−	0.909755i	0.992556	−	0.121792i	$-0.0388641\pi$
$684$	−12.9375	−	5.35890i	−0.494679	−	0.204903i
$685$	1.18192	+	0.489566i	0.0451587	+	0.0187054i
$686$		−	33.3427i		−	1.27303i
$687$	2.93945	+	7.09645i	0.112147	+	0.270747i
$688$	8.69784	−	8.69784i	0.331602	−	0.331602i
$689$		−	21.9997i		−	0.838123i
$690$	−0.679478	+	0.679478i	−0.0258673	+	0.0258673i
$691$	−18.5373	−	18.5373i	−0.705194	−	0.705194i	0.260327	−	0.965521i	$-0.416170\pi$
$691$	−18.5373	−	18.5373i	−0.705194	−	0.705194i	−0.965521	+	0.260327i	$0.916170\pi$
$692$		−	18.3734i		−	0.698452i
$693$	−3.80888	−	3.80888i	−0.144687	−	0.144687i
$694$	−6.07013	+	2.51433i	−0.230419	+	0.0954427i
$695$	3.37876	−	1.39953i	0.128164	−	0.0530871i
$696$	−8.39872	+	3.47886i	−0.318353	+	0.131866i
$697$	−8.38657	+	3.47383i	−0.317664	+	0.131581i
$698$	−11.8561	+	28.6232i	−0.448761	+	1.08340i
$699$	24.8862	−	24.8862i	0.941282	−	0.941282i
$700$	−15.9524	−	15.9524i	−0.602944	−	0.602944i
$701$	12.7645	−	30.8162i	0.482108	−	1.16391i	−0.476498	−	0.879175i	$-0.658094\pi$
$701$	12.7645	−	30.8162i	0.482108	−	1.16391i	0.958606	−	0.284736i	$-0.0919059\pi$
$702$			3.57501i			0.134930i
$703$			64.1880i			2.42090i
$704$	−0.394144	+	0.394144i	−0.0148548	+	0.0148548i
$705$	−3.44723	−	8.32234i	−0.129830	−	0.313437i
$706$	10.4713	+	25.2799i	0.394092	+	0.951422i
$707$	−20.0797	−	48.4768i	−0.755176	−	1.82316i
$708$			3.07407i			0.115531i
$709$		−	19.4424i		−	0.730174i	−0.930973	−	0.365087i	$-0.881039\pi$
$709$		−	19.4424i		−	0.730174i	0.930973	−	0.365087i	$-0.118961\pi$
$710$	−4.03680	+	1.67210i	−0.151498	+	0.0627527i
$711$	6.80623	−	16.4317i	0.255254	−	0.616237i
$712$		−	9.50333i		−	0.356152i
$713$	8.10672	−	8.10672i	0.303599	−	0.303599i
$714$	12.3797			0.463298
$715$	0.291745	+	0.120845i	0.0109107	+	0.00451934i
$716$	−1.80017			−0.0672755
$717$	12.6028	−	5.22027i	0.470662	−	0.194954i
$718$	9.74357	+	23.5230i	0.363627	+	0.877872i
$719$	−17.4558			−0.650991			−0.325495	−	0.945544i	$-0.605531\pi$
$719$	−17.4558			−0.650991			−0.325495	+	0.945544i	$0.605531\pi$
$720$	−0.479023	−	0.479023i	−0.0178521	−	0.0178521i
$721$		−	64.3062i		−	2.39489i
$722$	−25.5912			−0.952407
$723$	−8.40347	−	20.2878i	−0.312529	−	0.754511i
$724$	−4.01498	−	4.01498i	−0.149216	−	0.149216i
$725$	−19.7128			−0.732114
$726$	22.2959	−	9.23526i	0.827478	−	0.342753i
$727$	25.0827	+	10.3896i	0.930264	+	0.385328i	0.795779	−	0.605587i	$-0.207062\pi$
$727$	25.0827	+	10.3896i	0.930264	+	0.385328i	0.134486	+	0.990916i	$0.457062\pi$
$728$	−3.09265	−	7.46631i	−0.114621	−	0.276720i
$729$	6.39041	−	6.39041i	0.236682	−	0.236682i
$730$	0.308480			0.0114174
$731$	−5.60124	+	13.5226i	−0.207169	+	0.500151i
$732$	−18.9089			−0.698892
$733$			13.9250i			0.514333i	0.966367	+	0.257167i	$0.0827889\pi$
$733$			13.9250i			0.514333i	−0.966367	+	0.257167i	$0.917211\pi$
$734$	9.56038	+	23.0808i	0.352880	+	0.851928i
$735$	3.97313	−	9.59199i	0.146551	−	0.353806i
$736$	0.504209	−	1.21727i	0.0185854	−	0.0448691i
$737$	−7.61716	+	3.15513i	−0.280582	+	0.116221i
$738$		−	15.9979i		−	0.588890i
$739$	17.7947			0.654588			0.327294	−	0.944922i	$-0.393863\pi$
$739$	17.7947			0.654588			0.327294	+	0.944922i	$0.393863\pi$
$740$	−1.18831	+	2.86883i	−0.0436830	+	0.105460i
$741$	−10.1177	−	24.4264i	−0.371685	−	0.897326i
$742$	−22.1222	+	53.4078i	−0.812133	+	1.96066i
$743$	9.10065	−	3.76961i	0.333870	−	0.138294i	−0.209449	−	0.977819i	$-0.567167\pi$
$743$	9.10065	−	3.76961i	0.333870	−	0.138294i	0.543320	+	0.839526i	$0.317167\pi$
$744$	13.8910	+	13.8910i	0.509270	+	0.509270i
$745$			3.42431i			0.125457i
$746$			6.70655i			0.245544i
$747$	−7.96770	−	7.96770i	−0.291523	−	0.291523i
$748$	0.253821	−	0.612778i	0.00928061	−	0.0224054i
$749$	5.23990	−	12.6502i	0.191462	−	0.462230i
$750$	−2.76187	−	6.66775i	−0.100849	−	0.243472i
$751$	9.47977			0.345922			0.172961	−	0.984929i	$-0.444667\pi$
$751$	9.47977			0.345922			0.172961	+	0.984929i	$0.444667\pi$
$752$	8.73364	+	8.73364i	0.318483	+	0.318483i
$753$		−	11.1862i		−	0.407648i
$754$	−6.52398	−	2.70232i	−0.237589	−	0.0984127i
$755$	3.05451	+	3.05451i	0.111165	+	0.111165i
$756$	3.59492	−	8.67889i	0.130746	−	0.315648i
$757$	22.3678	+	22.3678i	0.812970	+	0.812970i	0.985078	−	0.172108i	$-0.0550579\pi$
$757$	22.3678	+	22.3678i	0.812970	+	0.812970i	−0.172108	+	0.985078i	$0.555058\pi$
$758$	−3.61161	+	3.61161i	−0.131179	+	0.131179i
$759$	1.17242	−	1.17242i	0.0425563	−	0.0425563i
$760$	−1.99297	−	0.825514i	−0.0722925	−	0.0299445i
$761$	12.2013			0.442297			0.221148	−	0.975240i	$-0.429019\pi$
$761$	12.2013			0.442297			0.221148	+	0.975240i	$0.429019\pi$
$762$	2.20359	−	2.20359i	0.0798277	−	0.0798277i
$763$	−34.1055			−1.23470
$764$	−5.38963	+	13.0117i	−0.194990	+	0.470747i
$765$	0.744740	+	0.308481i	0.0269261	+	0.0111532i
$766$	−22.2668	+	22.2668i	−0.804533	+	0.804533i
$767$	−1.68849	+	1.68849i	−0.0609677	+	0.0609677i
$768$	2.08581	+	0.863972i	0.0752653	+	0.0311759i
$769$	−16.2487	−	39.2279i	−0.585945	−	1.41460i	−0.887349	−	0.461099i	$-0.847455\pi$
$769$	−16.2487	−	39.2279i	−0.585945	−	1.41460i	0.301404	−	0.953497i	$-0.402545\pi$
$770$	−0.586740	−	0.586740i	−0.0211446	−	0.0211446i
$771$	3.42200	+	8.26143i	0.123240	+	0.297528i
$772$	0.00319335	+	0.00770943i	0.000114931	+	0.000277468i
$773$	−1.05311			−0.0378779			−0.0189389	−	0.999821i	$-0.506029\pi$
$773$	−1.05311			−0.0378779			−0.0189389	+	0.999821i	$0.506029\pi$
$774$	−18.2399	−	18.2399i	−0.655621	−	0.655621i
$775$	16.3019	+	39.3563i	0.585583	+	1.41372i
$776$	−6.74728	−	2.79481i	−0.242213	−	0.100328i
$777$	100.005			3.58765
$778$	−25.9409	+	10.7451i	−0.930026	+	0.385229i
$779$	−19.4946	−	47.0642i	−0.698468	−	1.68625i
$780$		−	1.27903i		−	0.0457965i
$781$	6.96541	−	2.88517i	0.249242	−	0.103239i
$782$			1.56779i			0.0560642i
$783$	−3.14120	−	7.58352i	−0.112257	−	0.271013i
$784$			14.2355i			0.508411i
$785$	5.54257	−	2.29581i	0.197823	−	0.0819408i
$786$	−22.5809			−0.805436
$787$	−28.9850	−	12.0060i	−1.03320	−	0.427967i	−0.199335	−	0.979931i	$-0.563878\pi$
$787$	−28.9850	−	12.0060i	−1.03320	−	0.427967i	−0.833868	+	0.551965i	$0.813878\pi$
$788$	26.5350			0.945271
$789$	−10.2748	+	4.25597i	−0.365793	+	0.151517i
$790$	1.04847	−	2.53122i	0.0373028	−	0.0900569i
$791$	−31.3686	−	31.3686i	−1.11534	−	1.11534i
$792$	0.826544	+	0.826544i	0.0293700	+	0.0293700i
$793$	−10.3860	−	10.3860i	−0.368819	−	0.368819i
$794$	18.2758	−	18.2758i	0.648585	−	0.648585i
$795$	−6.46939	+	6.46939i	−0.229445	+	0.229445i
$796$	−1.52691	−	3.68628i	−0.0541198	−	0.130657i
$797$	43.4173			1.53792			0.768960	−	0.639297i	$-0.220775\pi$
$797$	43.4173			1.53792			0.768960	+	0.639297i	$0.220775\pi$
$798$			69.4730i			2.45932i
$799$	−13.5782	−	5.62429i	−0.480364	−	0.198973i
$800$	3.46174	+	3.46174i	0.122391	+	0.122391i
$801$	−19.9291			−0.704159
$802$	−16.4751	+	11.3830i	−0.581755	+	0.401947i
$803$	−0.532275			−0.0187836
$804$	23.6131	+	23.6131i	0.832770	+	0.832770i
$805$	1.81208	+	0.750588i	0.0638674	+	0.0264547i
$806$			15.2598i			0.537504i
$807$	−63.4840			−2.23474
$808$	4.35739	+	10.5197i	0.153293	+	0.370081i
$809$	−24.1225	+	24.1225i	−0.848102	+	0.848102i	−0.989896	−	0.141794i	$-0.954713\pi$
$809$	−24.1225	+	24.1225i	−0.848102	+	0.848102i	0.141794	+	0.989896i	$0.454713\pi$
$810$	2.48836	−	2.48836i	0.0874320	−	0.0874320i
$811$	23.8513	+	23.8513i	0.837531	+	0.837531i	0.988533	−	0.151002i	$-0.0482501\pi$
$811$	23.8513	+	23.8513i	0.837531	+	0.837531i	−0.151002	+	0.988533i	$0.548250\pi$
$812$	13.1206	+	13.1206i	0.460443	+	0.460443i
$813$	11.7633	+	11.7633i	0.412556	+	0.412556i
$814$	2.05040	−	4.95010i	0.0718664	−	0.173501i
$815$	0.623183	−	0.258131i	0.0218292	−	0.00904193i
$816$	−2.68645			−0.0940444
$817$	−75.8869	−	31.4334i	−2.65495	−	1.09971i
$818$	19.3924			0.678039
$819$	−15.6573	+	6.48548i	−0.547111	+	0.226621i
$820$		−	2.46440i		−	0.0860605i
$821$	0.340771	+	0.822694i	0.0118930	+	0.0287122i	0.929714	−	0.368281i	$-0.120054\pi$
$821$	0.340771	+	0.822694i	0.0118930	+	0.0287122i	−0.917821	+	0.396993i	$0.870054\pi$
$822$			8.94071i			0.311843i
$823$	2.07693	−	0.860294i	0.0723973	−	0.0299880i	−0.346191	−	0.938164i	$-0.612525\pi$
$823$	2.07693	−	0.860294i	0.0723973	−	0.0299880i	0.418588	+	0.908176i	$0.362525\pi$
$824$			13.9547i			0.486136i
$825$	2.35765	+	5.69186i	0.0820828	+	0.198165i
$826$	5.79696	−	2.40118i	0.201702	−	0.0835477i
$827$	9.54326			0.331852			0.165926	−	0.986138i	$-0.446939\pi$
$827$	9.54326			0.331852			0.165926	+	0.986138i	$0.446939\pi$
$828$	−2.55269	−	1.05736i	−0.0887120	−	0.0367457i
$829$	17.7811	+	42.9274i	0.617564	+	1.49093i	0.854524	+	0.519412i	$0.173849\pi$
$829$	17.7811	+	42.9274i	0.617564	+	1.49093i	−0.236960	+	0.971519i	$0.576151\pi$
$830$	−1.22739	−	1.22739i	−0.0426032	−	0.0426032i
$831$	−28.8497			−1.00079
$832$	0.671118	+	1.62022i	0.0232668	+	0.0561711i
$833$	−6.48233	−	15.6497i	−0.224599	−	0.542231i
$834$	18.0729	+	18.0729i	0.625812	+	0.625812i
$835$	2.26560	+	5.46964i	0.0784043	+	0.189285i
$836$	3.43882	+	1.42441i	0.118934	+	0.0492641i
$837$	−12.5427	+	12.5427i	−0.433540	+	0.433540i
$838$	5.55096	−	5.55096i	0.191755	−	0.191755i
$839$	16.8756	+	6.99010i	0.582610	+	0.241325i	0.654468	−	0.756090i	$-0.272893\pi$
$839$	16.8756	+	6.99010i	0.582610	+	0.241325i	−0.0718578	+	0.997415i	$0.522893\pi$
$840$	−1.28615	+	3.10504i	−0.0443763	+	0.107134i
$841$	−12.7866			−0.440916
$842$	−20.3990	+	20.3990i	−0.702994	+	0.702994i
$843$	18.0015			0.620003
$844$	10.3142	+	4.27229i	0.355030	+	0.147058i
$845$	−2.26701	+	2.26701i	−0.0779874	+	0.0779874i
$846$	18.3150	−	18.3150i	0.629682	−	0.629682i
$847$	−34.8310	−	34.8310i	−1.19681	−	1.19681i
$848$	4.80063	−	11.5897i	0.164854	−	0.397993i
$849$	6.00642	+	6.00642i	0.206140	+	0.206140i
$850$	−5.38199	−	2.22930i	−0.184601	−	0.0764642i
$851$			12.6648i			0.434145i
$852$	−21.5927	−	21.5927i	−0.739754	−	0.739754i
$853$	−13.7175			−0.469678			−0.234839	−	0.972034i	$-0.575456\pi$
$853$	−13.7175			−0.469678			−0.234839	+	0.972034i	$0.575456\pi$
$854$	14.7699	+	35.6576i	0.505414	+	1.22018i
$855$	−1.73115	+	4.17938i	−0.0592042	+	0.142932i
$856$	−1.13708	+	2.74516i	−0.0388646	+	0.0938275i
$857$	−16.1185	−	16.1185i	−0.550596	−	0.550596i	0.376017	−	0.926613i	$-0.377294\pi$
$857$	−16.1185	−	16.1185i	−0.550596	−	0.550596i	−0.926613	+	0.376017i	$0.877294\pi$
$858$			2.20693i			0.0753434i
$859$			7.73345i			0.263862i	0.991259	+	0.131931i	$0.0421177\pi$
$859$			7.73345i			0.263862i	−0.991259	+	0.131931i	$0.957882\pi$
$860$	−2.80977	−	2.80977i	−0.0958125	−	0.0958125i
$861$	−73.3259	+	30.3726i	−2.49894	+	1.03510i
$862$	−11.3031	+	27.2881i	−0.384985	+	0.929435i
$863$	8.72998	+	21.0760i	0.297172	+	0.717436i	0.999982	+	0.00605848i	$0.00192848\pi$
$863$	8.72998	+	21.0760i	0.297172	+	0.717436i	−0.702810	+	0.711378i	$0.748072\pi$
$864$	−0.780112	+	1.88336i	−0.0265400	+	0.0640731i
$865$	−5.93539			−0.201809
$866$		−	22.0512i		−	0.749331i
$867$	−32.5055	+	13.4642i	−1.10394	+	0.457269i
$868$	15.3448	−	37.0456i	0.520836	−	1.25741i
$869$	−1.80911	+	4.36757i	−0.0613698	+	0.148160i
$870$	1.12382	+	2.71314i	0.0381011	+	0.0919842i
$871$			25.9399i			0.878939i
$872$	7.40104			0.250631
$873$	−5.86090	+	14.1495i	−0.198361	+	0.478887i
$874$	−8.79823			−0.297605
$875$	−10.4165	+	10.4165i	−0.352141	+	0.352141i
$876$	0.825024	+	1.99178i	0.0278750	+	0.0672961i
$877$	−44.5213	−	18.4413i	−1.50338	−	0.622719i	−0.529199	−	0.848498i	$-0.677507\pi$
$877$	−44.5213	−	18.4413i	−1.50338	−	0.622719i	−0.974179	+	0.225779i	$0.927507\pi$
$878$	36.1082	−	14.9565i	1.21859	−	0.504758i
$879$	21.7195			0.732582
$880$	0.127325	+	0.127325i	0.00429213	+	0.00429213i
$881$	1.58584	+	3.82855i	0.0534282	+	0.128987i	0.948340	−	0.317256i	$-0.102762\pi$
$881$	1.58584	+	3.82855i	0.0534282	+	0.128987i	−0.894912	+	0.446243i	$0.852762\pi$
$882$	29.8528			1.00520
$883$			8.13229i			0.273673i	0.990594	+	0.136837i	$0.0436935\pi$
$883$			8.13229i			0.273673i	−0.990594	+	0.136837i	$0.956306\pi$
$884$	−1.47558	−	1.47558i	−0.0496291	−	0.0496291i
$885$	0.993055			0.0333812
$886$	−10.7091	−	25.8541i	−0.359780	−	0.868585i
$887$	50.0549	−	20.7334i	1.68068	−	0.696160i	0.681322	−	0.731984i	$-0.261405\pi$
$887$	50.0549	−	20.7334i	1.68068	−	0.696160i	0.999358	+	0.0358237i	$0.0114055\pi$
$888$	−21.7015			−0.728254
$889$	−5.87669	−	2.43421i	−0.197098	−	0.0816407i
$890$	−3.06998			−0.102906
$891$	−4.29361	+	4.29361i	−0.143841	+	0.143841i
$892$		−	2.47933i		−	0.0830140i
$893$	31.5627	−	76.1992i	1.05621	−	2.54991i
$894$	−22.1100	+	9.15826i	−0.739469	+	0.306298i
$895$			0.581531i			0.0194384i
$896$		−	4.60820i		−	0.153949i
$897$	−1.99632	−	4.81954i	−0.0666551	−	0.160920i
$898$	−5.74491	−	13.8694i	−0.191710	−	0.462829i
$899$	−13.4081	−	32.3700i	−0.447185	−	1.07960i
$900$	7.25949	−	7.25949i	0.241983	−	0.241983i
$901$			14.9271i			0.497295i
$902$			4.25227i			0.141585i
$903$	−48.9731	+	118.232i	−1.62972	+	3.93450i
$904$	6.80713	+	6.80713i	0.226402	+	0.226402i
$905$	−1.29701	+	1.29701i	−0.0431141	+	0.0431141i
$906$	−11.5530	+	27.8915i	−0.383824	+	0.926634i
$907$	30.2743	−	12.5400i	1.00524	−	0.416385i	0.181525	−	0.983386i	$-0.441897\pi$
$907$	30.2743	−	12.5400i	1.00524	−	0.416385i	0.823717	+	0.567001i	$0.191897\pi$
$908$	−14.3383	+	5.93913i	−0.475834	+	0.197097i
$909$	22.0604	−	9.13772i	0.731698	−	0.303079i
$910$	−2.41194	+	0.999057i	−0.0799549	+	0.0331184i
$911$	−22.5841	−	22.5841i	−0.748245	−	0.748245i	0.225905	−	0.974149i	$-0.427466\pi$
$911$	−22.5841	−	22.5841i	−0.748245	−	0.748245i	−0.974149	+	0.225905i	$0.927466\pi$
$912$		−	15.0760i		−	0.499215i
$913$	2.11783	+	2.11783i	0.0700899	+	0.0700899i
$914$	13.5917	−	13.5917i	0.449574	−	0.449574i
$915$			6.10837i			0.201937i
$916$	−2.40575	+	2.40575i	−0.0794883	+	0.0794883i
$917$	17.6382	+	42.5823i	0.582463	+	1.40619i
$918$		−	2.42569i		−	0.0800598i
$919$	−24.9844	−	10.3489i	−0.824158	−	0.341377i	−0.0695705	−	0.997577i	$-0.522163\pi$
$919$	−24.9844	−	10.3489i	−0.824158	−	0.341377i	−0.754587	+	0.656200i	$0.772163\pi$
$920$	−0.393229	−	0.162881i	−0.0129644	−	0.00537002i
$921$	21.0253	−	50.7596i	0.692807	−	1.67258i
$922$	−8.80471	+	3.64703i	−0.289968	+	0.120109i
$923$		−	23.7204i		−	0.780765i
$924$	2.21922	−	5.35767i	0.0730070	−	0.176255i
$925$	−43.4765	−	18.0085i	−1.42950	−	0.592117i
$926$	−23.3306	+	9.66384i	−0.766690	+	0.317573i
$927$	29.2639			0.961153
$928$	−2.84723	−	2.84723i	−0.0934649	−	0.0934649i
$929$	−18.2176	−	43.9812i	−0.597700	−	1.44298i	−0.875919	−	0.482459i	$-0.839744\pi$
$929$	−18.2176	−	43.9812i	−0.597700	−	1.44298i	0.278218	−	0.960518i	$-0.410256\pi$
$930$	4.48740	−	4.48740i	0.147148	−	0.147148i
$931$	87.8240	−	36.3779i	2.87832	−	1.19224i
$932$	14.4022	+	5.96559i	0.471760	+	0.195409i
$933$	14.3712	−	34.6951i	0.470492	−	1.13587i
$934$	−28.5015	+	11.8057i	−0.932598	+	0.386295i
$935$	−0.197953	−	0.0819950i	−0.00647377	−	0.00268152i
$936$	3.39771	−	1.40738i	0.111058	−	0.0460016i
$937$	5.45119	+	13.1603i	0.178083	+	0.429930i	0.987564	−	0.157216i	$-0.0502518\pi$
$937$	5.45119	+	13.1603i	0.178083	+	0.429930i	−0.809482	+	0.587145i	$0.800252\pi$
$938$	26.0843	−	62.9731i	0.851683	−	2.05614i
$939$	−2.70110	−	1.11883i	−0.0881472	−	0.0365118i
$940$	2.82134	−	2.82134i	0.0920219	−	0.0920219i
$941$	22.8093	−	9.44794i	0.743563	−	0.307994i	0.0214511	−	0.999770i	$-0.493171\pi$
$941$	22.8093	−	9.44794i	0.743563	−	0.307994i	0.722112	+	0.691776i	$0.243171\pi$
$942$	29.6470	+	29.6470i	0.965951	+	0.965951i
$943$	−3.84646	−	9.28617i	−0.125258	−	0.302399i
$944$	−1.25797	+	0.521066i	−0.0409433	+	0.0169593i
$945$	−2.80365	−	1.16131i	−0.0912028	−	0.0377775i
$946$	4.84821	+	4.84821i	0.157629	+	0.157629i
$947$	4.39640			0.142864			0.0714319	−	0.997445i	$-0.477243\pi$
$947$	4.39640			0.142864			0.0714319	+	0.997445i	$0.477243\pi$
$948$	19.1477			0.621887
$949$	−0.640864	+	1.54718i	−0.0208033	+	0.0502237i
$950$	12.5105	−	30.2030i	0.405894	−	0.979914i
$951$		−	2.85507i		−	0.0925819i
$952$	2.09840	+	5.06600i	0.0680097	+	0.164190i
$953$	28.2571	+	28.2571i	0.915336	+	0.915336i	0.996686	−	0.0813493i	$-0.0259229\pi$
$953$	28.2571	+	28.2571i	0.915336	+	0.915336i	−0.0813493	+	0.996686i	$0.525923\pi$
$954$	−24.3044	−	10.0672i	−0.786884	−	0.325938i
$955$	4.20334	+	1.74108i	0.136017	+	0.0563400i
$956$	4.27246	+	4.27246i	0.138181	+	0.138181i
$957$	−1.93913	−	4.68147i	−0.0626831	−	0.151331i
$958$		−	33.6170i		−	1.08612i
$959$	16.8600	−	6.98366i	0.544439	−	0.225514i
$960$	0.279100	−	0.673807i	0.00900791	−	0.0217470i
$961$	−31.6179	+	31.6179i	−1.01993	+	1.01993i
$962$	−11.9199	−	11.9199i	−0.384314	−	0.384314i
$963$	5.75677	+	2.38453i	0.185509	+	0.0768404i
$964$	6.87772	−	6.87772i	0.221516	−	0.221516i
$965$	0.00249047	−	0.00103159i	8.01712e−5	−	3.32080e-5i
$966$			13.7076i			0.441035i
$967$	3.29354	+	7.95131i	0.105913	+	0.255697i	0.967947	−	0.251153i	$-0.0808098\pi$
$967$	3.29354	+	7.95131i	0.105913	+	0.255697i	−0.862034	+	0.506850i	$0.830810\pi$
$968$	7.55848	+	7.55848i	0.242939	+	0.242939i
$969$	6.86503	+	16.5737i	0.220537	+	0.532422i
$970$	−0.902844	+	2.17966i	−0.0289886	+	0.0699846i
$971$	7.01680	−	7.01680i	0.225180	−	0.225180i	−0.585496	−	0.810676i	$-0.699100\pi$
$971$	7.01680	−	7.01680i	0.225180	−	0.225180i	0.810676	+	0.585496i	$0.199100\pi$
$972$	17.0718	+	7.07136i	0.547577	+	0.226814i
$973$	19.9643	−	48.1980i	0.640024	−	1.54516i
$974$	27.6956	+	27.6956i	0.887425	+	0.887425i
$975$	19.3834			0.620764
$976$	−3.20513	−	7.73786i	−0.102594	−	0.247683i
$977$	14.6232	−	14.6232i	0.467836	−	0.467836i	−0.433376	−	0.901213i	$-0.642678\pi$
$977$	14.6232	−	14.6232i	0.467836	−	0.467836i	0.901213	+	0.433376i	$0.142678\pi$
$978$	3.33338	+	3.33338i	0.106590	+	0.106590i
$979$	5.29718			0.169299
$980$	4.59868			0.146899
$981$		−	15.5204i		−	0.495529i
$982$	−2.70488	+	2.70488i	−0.0863162	+	0.0863162i
$983$	−34.3837	+	34.3837i	−1.09667	+	1.09667i	−0.101872	+	0.994798i	$0.532483\pi$
$983$	−34.3837	+	34.3837i	−1.09667	+	1.09667i	−0.994798	+	0.101872i	$0.967517\pi$
$984$	15.9121	−	6.59099i	0.507258	−	0.210113i
$985$		−	8.57194i		−	0.273125i
$986$	4.42661	+	1.83356i	0.140972	+	0.0583925i
$987$	−118.718	−	49.1746i	−3.77884	−	1.56525i
$988$	8.28074	−	8.28074i	0.263445	−	0.263445i
$989$	−14.9731	−	6.20207i	−0.476118	−	0.197214i
$990$	0.267009	−	0.267009i	0.00848610	−	0.00848610i
$991$	12.3255	+	5.10540i	0.391534	+	0.162178i	0.569760	−	0.821811i	$-0.307036\pi$
$991$	12.3255	+	5.10540i	0.391534	+	0.162178i	−0.178227	+	0.983989i	$0.557036\pi$
$992$	−3.32988	+	8.03905i	−0.105724	+	0.255240i
$993$	18.2244	+	7.54881i	0.578335	+	0.239554i
$994$	−23.8524	+	57.5849i	−0.756554	+	1.82648i
$995$	−1.19083	+	0.493256i	−0.0377517	+	0.0156373i
$996$	4.64233	−	11.2076i	0.147098	−	0.355126i
$997$	25.2029			0.798183			0.399091	−	0.916911i	$-0.369326\pi$
$997$	25.2029			0.798183			0.399091	+	0.916911i	$0.369326\pi$
$998$	−5.78992			−0.183277
$999$		−	19.5951i		−	0.619960i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	802.2.e.b.45.14	✓	68
401.303	even	8	inner	802.2.e.b.303.14	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
802.2.e.b.45.14	✓	68	1.1	even	1	trivial
802.2.e.b.303.14	yes	68	401.303	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 802 = 2 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	802.e (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(2.08581 + 0.863972i) q^{3} +1.00000i q^{4} +0.323043 q^{5} +(0.863972 + 2.08581i) q^{6} +(3.25849 - 3.25849i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.48285 + 1.48285i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(2.08581 + 0.863972i) q^{3} +1.00000i q^{4} +0.323043 q^{5} +(0.863972 + 2.08581i) q^{6} +(3.25849 - 3.25849i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.48285 + 1.48285i) q^{9} +(0.228426 + 0.228426i) q^{10} +(-0.394144 - 0.394144i) q^{11} +(-0.863972 + 2.08581i) q^{12} +(-1.62022 + 0.671118i) q^{13} +4.60820 q^{14} +(0.673807 + 0.279100i) q^{15} -1.00000 q^{16} +(1.09934 - 0.455363i) q^{17} +2.09706i q^{18} +(2.55543 + 6.16936i) q^{19} +0.323043i q^{20} +(9.61185 - 3.98136i) q^{21} -0.557403i q^{22} +(0.504209 + 1.21727i) q^{23} +(-2.08581 + 0.863972i) q^{24} -4.89564 q^{25} +(-1.62022 - 0.671118i) q^{26} +(-0.780112 - 1.88336i) q^{27} +(3.25849 + 3.25849i) q^{28} +4.02659 q^{29} +(0.279100 + 0.673807i) q^{30} +(-3.32988 - 8.03905i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.481581 - 1.16264i) q^{33} +(1.09934 + 0.455363i) q^{34} +(1.05263 - 1.05263i) q^{35} +(-1.48285 + 1.48285i) q^{36} +(8.88064 + 3.67848i) q^{37} +(-2.55543 + 6.16936i) q^{38} -3.95931 q^{39} +(-0.228426 + 0.228426i) q^{40} -7.62871 q^{41} +(9.61185 + 3.98136i) q^{42} +(-8.69784 + 8.69784i) q^{43} +(0.394144 - 0.394144i) q^{44} +(0.479023 + 0.479023i) q^{45} +(-0.504209 + 1.21727i) q^{46} +(-8.73364 - 8.73364i) q^{47} +(-2.08581 - 0.863972i) q^{48} -14.2355i q^{49} +(-3.46174 - 3.46174i) q^{50} +2.68645 q^{51} +(-0.671118 - 1.62022i) q^{52} +(-4.80063 + 11.5897i) q^{53} +(0.780112 - 1.88336i) q^{54} +(-0.127325 - 0.127325i) q^{55} +4.60820i q^{56} +15.0760i q^{57} +(2.84723 + 2.84723i) q^{58} +(1.25797 - 0.521066i) q^{59} +(-0.279100 + 0.673807i) q^{60} +(3.20513 + 7.73786i) q^{61} +(3.32988 - 8.03905i) q^{62} +9.66369 q^{63} -1.00000i q^{64} +(-0.523401 + 0.216800i) q^{65} +(0.481581 - 1.16264i) q^{66} +(5.66041 - 13.6654i) q^{67} +(0.455363 + 1.09934i) q^{68} +2.97461i q^{69} +1.48865 q^{70} +(-5.17609 + 12.4962i) q^{71} -2.09706 q^{72} +(0.675230 - 0.675230i) q^{73} +(3.67848 + 8.88064i) q^{74} +(-10.2114 - 4.22970i) q^{75} +(-6.16936 + 2.55543i) q^{76} -2.56863 q^{77} +(-2.79965 - 2.79965i) q^{78} +(-3.24560 - 7.83557i) q^{79} -0.323043 q^{80} -10.8935i q^{81} +(-5.39431 - 5.39431i) q^{82} -5.37325 q^{83} +(3.98136 + 9.61185i) q^{84} +(0.355135 - 0.147102i) q^{85} -12.3006 q^{86} +(8.39872 + 3.47886i) q^{87} +0.557403 q^{88} +(-6.71987 + 6.71987i) q^{89} +0.677441i q^{90} +(-3.09265 + 7.46631i) q^{91} +(-1.21727 + 0.504209i) q^{92} -19.6449i q^{93} -12.3512i q^{94} +(0.825514 + 1.99297i) q^{95} +(-0.863972 - 2.08581i) q^{96} +(2.79481 + 6.74728i) q^{97} +(10.0660 - 10.0660i) q^{98} -1.16891i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{6} + 20 q^{9}+O(q^{10}) \) 68 * q + 4 * q^6 + 20 * q^9	\( 68 q + 4 q^{6} + 20 q^{9} - 4 q^{10} + 12 q^{11} - 4 q^{12} - 8 q^{13} + 8 q^{14} - 4 q^{15} - 68 q^{16} + 4 q^{17} + 20 q^{19} - 40 q^{21} - 16 q^{23} + 20 q^{25} - 8 q^{26} - 12 q^{27} + 16 q^{29} - 4 q^{30} - 8 q^{31} + 8 q^{33} + 4 q^{34} + 16 q^{35} - 20 q^{36} + 12 q^{37} - 20 q^{38} + 40 q^{39} + 4 q^{40} + 24 q^{41} - 40 q^{42} + 40 q^{43} - 12 q^{44} + 28 q^{45} + 16 q^{46} + 4 q^{47} - 8 q^{50} + 24 q^{51} + 4 q^{52} + 12 q^{53} + 12 q^{54} - 24 q^{55} - 4 q^{58} + 4 q^{59} + 4 q^{60} - 20 q^{61} + 8 q^{62} - 16 q^{63} + 36 q^{65} - 8 q^{66} + 48 q^{67} + 8 q^{68} - 16 q^{71} - 68 q^{72} + 40 q^{73} - 8 q^{74} - 96 q^{75} - 16 q^{77} + 32 q^{78} + 28 q^{79} - 16 q^{82} + 16 q^{83} - 4 q^{84} + 16 q^{85} - 32 q^{86} + 8 q^{87} + 8 q^{88} - 20 q^{89} - 4 q^{91} + 8 q^{92} - 24 q^{95} - 4 q^{96} + 24 q^{97} + 24 q^{98}+O(q^{100}) \) 68 * q + 4 * q^6 + 20 * q^9 - 4 * q^10 + 12 * q^11 - 4 * q^12 - 8 * q^13 + 8 * q^14 - 4 * q^15 - 68 * q^16 + 4 * q^17 + 20 * q^19 - 40 * q^21 - 16 * q^23 + 20 * q^25 - 8 * q^26 - 12 * q^27 + 16 * q^29 - 4 * q^30 - 8 * q^31 + 8 * q^33 + 4 * q^34 + 16 * q^35 - 20 * q^36 + 12 * q^37 - 20 * q^38 + 40 * q^39 + 4 * q^40 + 24 * q^41 - 40 * q^42 + 40 * q^43 - 12 * q^44 + 28 * q^45 + 16 * q^46 + 4 * q^47 - 8 * q^50 + 24 * q^51 + 4 * q^52 + 12 * q^53 + 12 * q^54 - 24 * q^55 - 4 * q^58 + 4 * q^59 + 4 * q^60 - 20 * q^61 + 8 * q^62 - 16 * q^63 + 36 * q^65 - 8 * q^66 + 48 * q^67 + 8 * q^68 - 16 * q^71 - 68 * q^72 + 40 * q^73 - 8 * q^74 - 96 * q^75 - 16 * q^77 + 32 * q^78 + 28 * q^79 - 16 * q^82 + 16 * q^83 - 4 * q^84 + 16 * q^85 - 32 * q^86 + 8 * q^87 + 8 * q^88 - 20 * q^89 - 4 * q^91 + 8 * q^92 - 24 * q^95 - 4 * q^96 + 24 * q^97 + 24 * q^98

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