LMFDB - Embedded newform 403.2.r.a.218.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(218,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0]))

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

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

chi := DirichletCharacter("403.218");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.r (of order $6$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			218.3
Character	$\chi$	$=$	403.218
Dual form			403.2.r.a.342.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.18149 + 1.25949i) q^{2} +(-0.435889 - 0.754983i) q^{3} +(2.17261 - 3.76307i) q^{4} +3.48615i q^{5} +(1.90178 + 1.09799i) q^{6} +(-2.02718 - 1.17039i) q^{7} +5.90753i q^{8} +(1.12000 - 1.93990i) q^{9} +O(q^{10})$	\(q+(-2.18149 + 1.25949i) q^{2} +(-0.435889 - 0.754983i) q^{3} +(2.17261 - 3.76307i) q^{4} +3.48615i q^{5} +(1.90178 + 1.09799i) q^{6} +(-2.02718 - 1.17039i) q^{7} +5.90753i q^{8} +(1.12000 - 1.93990i) q^{9} +(-4.39076 - 7.60502i) q^{10} +(-2.90796 + 1.67891i) q^{11} -3.78807 q^{12} +(3.60052 + 0.190323i) q^{13} +5.89638 q^{14} +(2.63199 - 1.51958i) q^{15} +(-3.09524 - 5.36111i) q^{16} +(-3.20334 + 5.54835i) q^{17} +5.64250i q^{18} +(-2.21181 - 1.27699i) q^{19} +(13.1186 + 7.57404i) q^{20} +2.04065i q^{21} +(4.22913 - 7.32507i) q^{22} +(-0.899656 - 1.55825i) q^{23} +(4.46009 - 2.57503i) q^{24} -7.15326 q^{25} +(-8.09423 + 4.11962i) q^{26} -4.56812 q^{27} +(-8.80854 + 5.08562i) q^{28} +(-4.28958 - 7.42978i) q^{29} +(-3.82777 + 6.62990i) q^{30} -1.00000i q^{31} +(3.27233 + 1.88928i) q^{32} +(2.53510 + 1.46364i) q^{33} -16.1383i q^{34} +(4.08017 - 7.06707i) q^{35} +(-4.86665 - 8.42928i) q^{36} +(-7.27475 + 4.20008i) q^{37} +6.43339 q^{38} +(-1.42574 - 2.80129i) q^{39} -20.5946 q^{40} +(5.15694 - 2.97736i) q^{41} +(-2.57017 - 4.45166i) q^{42} +(1.63471 - 2.83139i) q^{43} +14.5905i q^{44} +(6.76278 + 3.90449i) q^{45} +(3.92519 + 2.26621i) q^{46} -5.36535i q^{47} +(-2.69836 + 4.67370i) q^{48} +(-0.760356 - 1.31697i) q^{49} +(15.6048 - 9.00943i) q^{50} +5.58522 q^{51} +(8.53873 - 13.1355i) q^{52} -9.35639 q^{53} +(9.96533 - 5.75349i) q^{54} +(-5.85294 - 10.1376i) q^{55} +(6.91414 - 11.9756i) q^{56} +2.22650i q^{57} +(18.7154 + 10.8053i) q^{58} +(-11.1821 - 6.45596i) q^{59} -13.2058i q^{60} +(-1.79696 + 3.11243i) q^{61} +(1.25949 + 2.18149i) q^{62} +(-4.54089 + 2.62168i) q^{63} +2.86286 q^{64} +(-0.663494 + 12.5520i) q^{65} -7.37373 q^{66} +(-0.992706 + 0.573139i) q^{67} +(13.9192 + 24.1088i) q^{68} +(-0.784301 + 1.35845i) q^{69} +20.5557i q^{70} +(-8.59612 - 4.96297i) q^{71} +(11.4600 + 6.61644i) q^{72} +5.97373i q^{73} +(10.5799 - 18.3249i) q^{74} +(3.11803 + 5.40059i) q^{75} +(-9.61078 + 5.54879i) q^{76} +7.85995 q^{77} +(6.63843 + 4.31530i) q^{78} +1.26210 q^{79} +(18.6896 - 10.7905i) q^{80} +(-1.36881 - 2.37084i) q^{81} +(-7.49989 + 12.9902i) q^{82} +7.88496i q^{83} +(7.67910 + 4.43353i) q^{84} +(-19.3424 - 11.1673i) q^{85} +8.23555i q^{86} +(-3.73957 + 6.47712i) q^{87} +(-9.91822 - 17.1789i) q^{88} +(8.94186 - 5.16258i) q^{89} -19.6706 q^{90} +(-7.07617 - 4.59985i) q^{91} -7.81840 q^{92} +(-0.754983 + 0.435889i) q^{93} +(6.75759 + 11.7045i) q^{94} +(4.45177 - 7.71069i) q^{95} -3.29407i q^{96} +(-0.0440012 - 0.0254041i) q^{97} +(3.31742 + 1.91531i) q^{98} +7.52153i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 32 q^{4} - 34 q^{9}+O(q^{10}) $ 68 * q + 32 * q^4 - 34 * q^9	$ 68 q + 32 q^{4} - 34 q^{9} + 8 q^{10} - 12 q^{11} - 16 q^{12} + 6 q^{13} - 8 q^{14} - 36 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 48 q^{24} - 72 q^{25} - 12 q^{27} - 6 q^{28} + 32 q^{30} + 6 q^{33} + 30 q^{35} + 40 q^{36} - 42 q^{37} - 36 q^{38} - 14 q^{39} + 8 q^{40} + 18 q^{41} - 16 q^{42} + 12 q^{43} + 60 q^{45} + 30 q^{46} - 46 q^{48} + 22 q^{49} + 56 q^{51} + 20 q^{53} - 114 q^{54} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 6 q^{59} + 6 q^{61} - 8 q^{62} - 30 q^{63} + 24 q^{64} + 24 q^{65} + 8 q^{66} - 48 q^{67} + 58 q^{68} - 28 q^{69} - 30 q^{71} + 72 q^{72} + 8 q^{74} - 4 q^{75} - 12 q^{76} - 20 q^{77} + 26 q^{78} + 16 q^{79} + 42 q^{80} - 58 q^{81} - 42 q^{82} - 72 q^{84} + 30 q^{85} - 20 q^{87} + 64 q^{88} + 18 q^{89} + 52 q^{90} - 22 q^{91} + 48 q^{92} + 8 q^{94} - 32 q^{95} - 168 q^{98}+O(q^{100}) $ 68 * q + 32 * q^4 - 34 * q^9 + 8 * q^10 - 12 * q^11 - 16 * q^12 + 6 * q^13 - 8 * q^14 - 36 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 48 * q^24 - 72 * q^25 - 12 * q^27 - 6 * q^28 + 32 * q^30 + 6 * q^33 + 30 * q^35 + 40 * q^36 - 42 * q^37 - 36 * q^38 - 14 * q^39 + 8 * q^40 + 18 * q^41 - 16 * q^42 + 12 * q^43 + 60 * q^45 + 30 * q^46 - 46 * q^48 + 22 * q^49 + 56 * q^51 + 20 * q^53 - 114 * q^54 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 6 * q^59 + 6 * q^61 - 8 * q^62 - 30 * q^63 + 24 * q^64 + 24 * q^65 + 8 * q^66 - 48 * q^67 + 58 * q^68 - 28 * q^69 - 30 * q^71 + 72 * q^72 + 8 * q^74 - 4 * q^75 - 12 * q^76 - 20 * q^77 + 26 * q^78 + 16 * q^79 + 42 * q^80 - 58 * q^81 - 42 * q^82 - 72 * q^84 + 30 * q^85 - 20 * q^87 + 64 * q^88 + 18 * q^89 + 52 * q^90 - 22 * q^91 + 48 * q^92 + 8 * q^94 - 32 * q^95 - 168 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−2.18149	+	1.25949i	−1.54255	+	0.890591i	−0.543872	+	0.839168i	$0.683042\pi$
$2$	−2.18149	+	1.25949i	−1.54255	+	0.890591i	−0.998677	+	0.0514224i	$0.983625\pi$
$3$	−0.435889	−	0.754983i	−0.251661	−	0.435889i	0.712322	−	0.701852i	$-0.247643\pi$
$3$	−0.435889	−	0.754983i	−0.251661	−	0.435889i	−0.963983	+	0.265963i	$0.914310\pi$
$4$	2.17261	−	3.76307i	1.08630	−	1.88153i
$5$			3.48615i			1.55905i	0.626368	+	0.779527i	$0.284541\pi$
$5$			3.48615i			1.55905i	−0.626368	+	0.779527i	$0.715459\pi$
$6$	1.90178	+	1.09799i	0.776398	+	0.448254i
$7$	−2.02718	−	1.17039i	−0.766203	−	0.442367i	0.0653156	−	0.997865i	$-0.479195\pi$
$7$	−2.02718	−	1.17039i	−0.766203	−	0.442367i	−0.831518	+	0.555497i	$0.812528\pi$
$8$			5.90753i			2.08863i
$9$	1.12000	−	1.93990i	0.373334	−	0.646633i
$10$	−4.39076	−	7.60502i	−1.38848	−	2.40492i
$11$	−2.90796	+	1.67891i	−0.876783	+	0.506211i	−0.869596	−	0.493764i	$-0.835621\pi$
$11$	−2.90796	+	1.67891i	−0.876783	+	0.506211i	−0.00718636	+	0.999974i	$0.502288\pi$
$12$	−3.78807			−1.09352
$13$	3.60052	+	0.190323i	0.998606	+	0.0527860i
$13$	3.60052	+	0.190323i	0.998606	+	0.0527860i
$14$	5.89638			1.57587
$15$	2.63199	−	1.51958i	0.679576	−	0.392353i
$16$	−3.09524	−	5.36111i	−0.773809	−	1.34028i
$17$	−3.20334	+	5.54835i	−0.776925	+	1.34567i	0.156781	+	0.987633i	$0.449888\pi$
$17$	−3.20334	+	5.54835i	−0.776925	+	1.34567i	−0.933706	+	0.358040i	$0.883445\pi$
$18$			5.64250i			1.32995i
$19$	−2.21181	−	1.27699i	−0.507423	−	0.292961i	0.224351	−	0.974508i	$-0.427974\pi$
$19$	−2.21181	−	1.27699i	−0.507423	−	0.292961i	−0.731774	+	0.681548i	$0.761307\pi$
$20$	13.1186	+	7.57404i	2.93341	+	1.69361i
$21$			2.04065i			0.445306i
$22$	4.22913	−	7.32507i	0.901653	−	1.56171i
$23$	−0.899656	−	1.55825i	−0.187591	−	0.324918i	0.756855	−	0.653582i	$-0.226735\pi$
$23$	−0.899656	−	1.55825i	−0.187591	−	0.324918i	−0.944447	+	0.328665i	$0.893401\pi$
$24$	4.46009	−	2.57503i	0.910411	−	0.525626i
$25$	−7.15326			−1.43065
$26$	−8.09423	+	4.11962i	−1.58741	+	0.807924i
$27$	−4.56812			−0.879136
$28$	−8.80854	+	5.08562i	−1.66466	+	0.961091i
$29$	−4.28958	−	7.42978i	−0.796556	−	1.37967i	−0.921847	−	0.387555i	$-0.873320\pi$
$29$	−4.28958	−	7.42978i	−0.796556	−	1.37967i	0.125291	−	0.992120i	$-0.460014\pi$
$30$	−3.82777	+	6.62990i	−0.698852	+	1.21045i
$31$		−	1.00000i		−	0.179605i
$31$		−	1.00000i		−	0.179605i
$32$	3.27233	+	1.88928i	0.578472	+	0.333981i
$33$	2.53510	+	1.46364i	0.441304	+	0.254787i
$34$		−	16.1383i		−	2.76769i
$35$	4.08017	−	7.06707i	0.689675	−	1.19455i
$36$	−4.86665	−	8.42928i	−0.811108	−	1.40488i
$37$	−7.27475	+	4.20008i	−1.19596	+	0.690489i	−0.959653	−	0.281189i	$-0.909271\pi$
$37$	−7.27475	+	4.20008i	−1.19596	+	0.690489i	−0.236310	+	0.971678i	$0.575938\pi$
$38$	6.43339			1.04363
$39$	−1.42574	−	2.80129i	−0.228301	−	0.448566i
$40$	−20.5946			−3.25629
$41$	5.15694	−	2.97736i	0.805379	−	0.464986i	−0.0399692	−	0.999201i	$-0.512726\pi$
$41$	5.15694	−	2.97736i	0.805379	−	0.464986i	0.845349	+	0.534215i	$0.179393\pi$
$42$	−2.57017	−	4.45166i	−0.396586	−	0.686907i
$43$	1.63471	−	2.83139i	0.249290	−	0.431783i	−0.714039	−	0.700106i	$-0.753136\pi$
$43$	1.63471	−	2.83139i	0.249290	−	0.431783i	0.963329	+	0.268323i	$0.0864694\pi$
$44$			14.5905i			2.19960i
$45$	6.76278	+	3.90449i	1.00814	+	0.582048i
$46$	3.92519	+	2.26621i	0.578737	+	0.334134i
$47$		−	5.36535i		−	0.782617i	−0.920259	−	0.391309i	$-0.872022\pi$
$47$		−	5.36535i		−	0.782617i	0.920259	−	0.391309i	$-0.127978\pi$
$48$	−2.69836	+	4.67370i	−0.389475	+	0.674591i
$49$	−0.760356	−	1.31697i	−0.108622	−	0.188139i
$50$	15.6048	−	9.00943i	2.20685	−	1.27413i
$51$	5.58522			0.782087
$52$	8.53873	−	13.1355i	1.18411	−	1.82157i
$53$	−9.35639			−1.28520			−0.642599	−	0.766203i	$-0.722144\pi$
$53$	−9.35639			−1.28520			−0.642599	+	0.766203i	$0.722144\pi$
$54$	9.96533	−	5.75349i	1.35611	−	0.782950i
$55$	−5.85294	−	10.1376i	−0.789210	−	1.36695i
$56$	6.91414	−	11.9756i	0.923941	−	1.60031i
$57$			2.22650i			0.294907i
$58$	18.7154	+	10.8053i	2.45745	+	1.41881i
$59$	−11.1821	−	6.45596i	−1.45578	−	0.840495i	−0.456980	−	0.889477i	$-0.651069\pi$
$59$	−11.1821	−	6.45596i	−1.45578	−	0.840495i	−0.998800	+	0.0489826i	$0.984402\pi$
$60$		−	13.2058i		−	1.70486i
$61$	−1.79696	+	3.11243i	−0.230078	+	0.398506i	−0.957831	−	0.287333i	$-0.907231\pi$
$61$	−1.79696	+	3.11243i	−0.230078	+	0.398506i	0.727753	+	0.685839i	$0.240565\pi$
$62$	1.25949	+	2.18149i	0.159955	+	0.277050i
$63$	−4.54089	+	2.62168i	−0.572098	+	0.330301i
$64$	2.86286			0.357858
$65$	−0.663494	+	12.5520i	−0.0822963	+	1.55688i
$66$	−7.37373			−0.907643
$67$	−0.992706	+	0.573139i	−0.121278	+	0.0700201i	−0.559412	−	0.828890i	$-0.688973\pi$
$67$	−0.992706	+	0.573139i	−0.121278	+	0.0700201i	0.438134	+	0.898910i	$0.355640\pi$
$68$	13.9192	+	24.1088i	1.68795	+	2.92362i
$69$	−0.784301	+	1.35845i	−0.0944188	+	0.163538i
$70$			20.5557i			2.45687i
$71$	−8.59612	−	4.96297i	−1.02017	−	0.588997i	−0.106018	−	0.994364i	$-0.533810\pi$
$71$	−8.59612	−	4.96297i	−1.02017	−	0.588997i	−0.914154	+	0.405367i	$0.867144\pi$
$72$	11.4600	+	6.61644i	1.35058	+	0.779755i
$73$			5.97373i			0.699172i	0.936904	+	0.349586i	$0.113678\pi$
$73$			5.97373i			0.699172i	−0.936904	+	0.349586i	$0.886322\pi$
$74$	10.5799	−	18.3249i	1.22989	−	2.13023i
$75$	3.11803	+	5.40059i	0.360039	+	0.623606i
$76$	−9.61078	+	5.54879i	−1.10243	+	0.636489i
$77$	7.85995			0.895724
$78$	6.63843	+	4.31530i	0.751654	+	0.488612i
$79$	1.26210			0.141998			0.0709989	−	0.997476i	$-0.477381\pi$
$79$	1.26210			0.141998			0.0709989	+	0.997476i	$0.477381\pi$
$80$	18.6896	−	10.7905i	2.08957	−	1.20641i
$81$	−1.36881	−	2.37084i	−0.152089	−	0.263427i
$82$	−7.49989	+	12.9902i	−0.828225	+	1.43453i
$83$			7.88496i			0.865486i	0.901517	+	0.432743i	$0.142454\pi$
$83$			7.88496i			0.865486i	−0.901517	+	0.432743i	$0.857546\pi$
$84$	7.67910	+	4.43353i	0.837859	+	0.483738i
$85$	−19.3424	−	11.1673i	−2.09798	−	1.21127i
$86$			8.23555i			0.888062i
$87$	−3.73957	+	6.47712i	−0.400924	+	0.694421i
$88$	−9.91822	−	17.1789i	−1.05729	−	1.83127i
$89$	8.94186	−	5.16258i	0.947835	−	0.547233i	0.0554274	−	0.998463i	$-0.482348\pi$
$89$	8.94186	−	5.16258i	0.947835	−	0.547233i	0.892408	+	0.451230i	$0.149015\pi$
$90$	−19.6706			−2.07346
$91$	−7.07617	−	4.59985i	−0.741784	−	0.482195i
$92$	−7.81840			−0.815125
$93$	−0.754983	+	0.435889i	−0.0782881	+	0.0451996i
$94$	6.75759	+	11.7045i	0.696992	+	1.20723i
$95$	4.45177	−	7.71069i	0.456742	−	0.791101i
$96$		−	3.29407i		−	0.336200i
$97$	−0.0440012	−	0.0254041i	−0.00446764	−	0.00257939i	0.497765	−	0.867312i	$-0.334154\pi$
$97$	−0.0440012	−	0.0254041i	−0.00446764	−	0.00257939i	−0.502232	+	0.864733i	$0.667488\pi$
$98$	3.31742	+	1.91531i	0.335110	+	0.193476i
$99$			7.52153i			0.755942i
$100$	−15.5412	+	26.9182i	−1.55412	+	2.69182i
$101$	5.72933	+	9.92349i	0.570090	+	0.987424i	0.996556	+	0.0829207i	$0.0264248\pi$
$101$	5.72933	+	9.92349i	0.570090	+	0.987424i	−0.426467	+	0.904503i	$0.640242\pi$
$102$	−12.1841	+	7.03450i	−1.20641	+	0.696519i
$103$	−12.2972			−1.21168			−0.605840	−	0.795586i	$-0.707163\pi$
$103$	−12.2972			−1.21168			−0.605840	+	0.795586i	$0.707163\pi$
$104$	−1.12434	+	21.2702i	−0.110250	+	2.08572i
$105$	−7.11402			−0.694257
$106$	20.4109	−	11.7842i	1.98248	−	1.14459i
$107$	6.91166	+	11.9713i	0.668175	+	1.15731i	0.978414	+	0.206654i	$0.0662576\pi$
$107$	6.91166	+	11.9713i	0.668175	+	1.15731i	−0.310239	+	0.950659i	$0.600409\pi$
$108$	−9.92474	+	17.1902i	−0.955009	+	1.65412i
$109$			19.5564i			1.87316i	0.350448	+	0.936582i	$0.386029\pi$
$109$			19.5564i			1.87316i	−0.350448	+	0.936582i	$0.613971\pi$
$110$	25.5363	+	14.7434i	2.43479	+	1.40573i
$111$	6.34198	+	3.66154i	0.601954	+	0.347538i
$112$			14.4906i			1.36923i
$113$	3.23548	−	5.60402i	0.304368	−	0.527182i	−0.672752	−	0.739868i	$-0.734888\pi$
$113$	3.23548	−	5.60402i	0.304368	−	0.527182i	0.977121	+	0.212686i	$0.0682213\pi$
$114$	−2.80425	−	4.85710i	−0.262642	−	0.454909i
$115$	5.43230	−	3.13634i	0.506564	−	0.292465i
$116$	−37.2783			−3.46121
$117$	4.40180	−	6.77149i	0.406946	−	0.626024i
$118$	32.5248			2.99415
$119$	12.9875	−	7.49835i	1.19056	−	0.687372i
$120$	8.97695	+	15.5485i	0.819480	+	1.41938i
$121$	0.137483	−	0.238128i	0.0124985	−	0.0216480i
$122$		−	9.05300i		−	0.819620i
$123$	−4.49572	−	2.59560i	−0.405365	−	0.234038i
$124$	−3.76307	−	2.17261i	−0.337933	−	0.195106i
$125$		−	7.50660i		−	0.671410i
$126$	6.60395	−	11.4384i	0.588326	−	1.01901i
$127$	7.56729	+	13.1069i	0.671488	+	1.16305i	0.977482	+	0.211019i	$0.0676780\pi$
$127$	7.56729	+	13.1069i	0.671488	+	1.16305i	−0.305994	+	0.952034i	$0.598989\pi$
$128$	−12.7900	+	7.38429i	−1.13048	+	0.652686i
$129$	−2.85020			−0.250946
$130$	−14.3616	−	28.2177i	−1.25960	−	2.47486i
$131$	8.07670			0.705664			0.352832	−	0.935687i	$-0.385219\pi$
$131$	8.07670			0.705664			0.352832	+	0.935687i	$0.385219\pi$
$132$	11.0155	−	6.35983i	0.958780	−	0.553552i
$133$	2.98916	+	5.17737i	0.259193	+	0.448935i
$134$	1.44372	−	2.50060i	0.124718	−	0.216019i
$135$		−	15.9252i		−	1.37062i
$136$	−32.7771	−	18.9239i	−2.81061	−	1.62271i
$137$	9.44794	+	5.45477i	0.807192	+	0.466032i	0.845980	−	0.533215i	$-0.179016\pi$
$137$	9.44794	+	5.45477i	0.807192	+	0.466032i	−0.0387880	+	0.999247i	$0.512350\pi$
$138$		−	3.95126i		−	0.336354i
$139$	−2.36106	+	4.08948i	−0.200263	+	0.346865i	−0.948613	−	0.316438i	$-0.897513\pi$
$139$	−2.36106	+	4.08948i	−0.200263	+	0.346865i	0.748350	+	0.663304i	$0.230846\pi$
$140$	−17.7292	−	30.7079i	−1.49839	−	2.59529i
$141$	−4.05075	+	2.33870i	−0.341135	+	0.196954i
$142$	25.0032			2.09822
$143$	−10.7897	+	5.49151i	−0.902281	+	0.459223i
$144$	−13.8667			−1.15556
$145$	25.9013	−	14.9541i	2.15099	−	1.24187i
$146$	−7.52383	−	13.0317i	−0.622676	−	1.07851i
$147$	−0.662862	+	1.14811i	−0.0546719	+	0.0946946i
$148$			36.5005i			3.00032i
$149$	−14.8506	−	8.57399i	−1.21661	−	0.702409i	−0.252417	−	0.967619i	$-0.581225\pi$
$149$	−14.8506	−	8.57399i	−1.21661	−	0.702409i	−0.964191	+	0.265210i	$0.914559\pi$
$150$	−13.6039	−	7.85423i	−1.11076	−	0.641295i
$151$		−	15.4892i		−	1.26049i	−0.776396	−	0.630245i	$-0.782954\pi$
$151$		−	15.4892i		−	1.26049i	0.776396	−	0.630245i	$-0.217046\pi$
$152$	7.54384	−	13.0663i	0.611887	−	1.05982i
$153$	7.17549	+	12.4283i	0.580104	+	1.00477i
$154$	−17.1464	+	9.89949i	−1.38170	+	0.797724i
$155$	3.48615			0.280015
$156$	−13.6390	−	0.720955i	−1.09200	−	0.0577226i
$157$	4.19102			0.334480			0.167240	−	0.985916i	$-0.446515\pi$
$157$	4.19102			0.334480			0.167240	+	0.985916i	$0.446515\pi$
$158$	−2.75327	+	1.58960i	−0.219038	+	0.126462i
$159$	4.07835	+	7.06391i	0.323434	+	0.560204i
$160$	−6.58632	+	11.4078i	−0.520694	+	0.901869i
$161$			4.21181i			0.331937i
$162$	5.97208	+	3.44798i	0.469211	+	0.270899i
$163$	−18.5900	−	10.7329i	−1.45608	−	0.840668i	−0.457265	−	0.889331i	$-0.651171\pi$
$163$	−18.5900	−	10.7329i	−1.45608	−	0.840668i	−0.998815	+	0.0486625i	$0.984504\pi$
$164$		−	25.8746i		−	2.02047i
$165$	−5.10247	+	8.83774i	−0.397227	+	0.688017i
$166$	−9.93099	−	17.2010i	−0.770794	−	1.33506i
$167$	−0.586483	+	0.338606i	−0.0453834	+	0.0262021i	−0.522520	−	0.852627i	$-0.675008\pi$
$167$	−0.586483	+	0.338606i	−0.0453834	+	0.0262021i	0.477137	+	0.878829i	$0.341675\pi$
$168$	−12.0552			−0.930079
$169$	12.9276	+	1.37052i	0.994427	+	0.105425i
$170$	56.2604			4.31498
$171$	−4.95445	+	2.86045i	−0.378876	+	0.218744i
$172$	−7.10315	−	12.3030i	−0.541610	−	0.938096i
$173$	2.62376	−	4.54449i	0.199481	−	0.345511i	−0.748879	−	0.662706i	$-0.769408\pi$
$173$	2.62376	−	4.54449i	0.199481	−	0.345511i	0.948360	+	0.317195i	$0.102741\pi$
$174$		−	18.8397i		−	1.42824i
$175$	14.5010	+	8.37213i	1.09617	+	0.632874i
$176$	18.0016	+	10.3933i	1.35693	+	0.783421i
$177$			11.2563i			0.846079i
$178$	−13.0044	+	22.5243i	−0.974721	+	1.68827i
$179$	−0.164276	−	0.284534i	−0.0122786	−	0.0212671i	0.859821	−	0.510596i	$-0.170575\pi$
$179$	−0.164276	−	0.284534i	−0.0122786	−	0.0212671i	−0.872099	+	0.489329i	$0.837242\pi$
$180$	29.3857	−	16.9659i	2.19028	−	1.26456i
$181$	3.09350			0.229938			0.114969	−	0.993369i	$-0.463323\pi$
$181$	3.09350			0.229938			0.114969	+	0.993369i	$0.463323\pi$
$182$	21.2301	+	1.12221i	1.57368	+	0.0831841i
$183$	3.13311			0.231606
$184$	9.20541	−	5.31475i	0.678632	−	0.391808i
$185$	−14.6421	−	25.3609i	−1.07651	−	1.86457i
$186$	1.09799	−	1.90178i	0.0805088	−	0.139445i
$187$		−	21.5125i		−	1.57315i
$188$	−20.1902	−	11.6568i	−1.47252	−	0.850161i
$189$	9.26042	+	5.34650i	0.673596	+	0.388901i
$190$			22.4278i			1.62708i
$191$	−5.14674	+	8.91441i	−0.372405	+	0.645024i	−0.989935	−	0.141523i	$-0.954800\pi$
$191$	−5.14674	+	8.91441i	−0.372405	+	0.645024i	0.617530	+	0.786547i	$0.288133\pi$
$192$	−1.24789	−	2.16141i	−0.0900588	−	0.155986i
$193$	3.87859	−	2.23930i	0.279187	−	0.161189i	−0.353868	−	0.935295i	$-0.615134\pi$
$193$	3.87859	−	2.23930i	0.279187	−	0.161189i	0.633055	+	0.774107i	$0.281801\pi$
$194$	0.127984			0.00918874
$195$	9.76574	−	4.97035i	0.699339	−	0.355934i
$196$	−6.60782			−0.471987
$197$	−1.82162	+	1.05171i	−0.129785	+	0.0749314i	−0.563487	−	0.826125i	$-0.690540\pi$
$197$	−1.82162	+	1.05171i	−0.129785	+	0.0749314i	0.433702	+	0.901056i	$0.357207\pi$
$198$	−9.47325	−	16.4082i	−0.673235	−	1.16608i
$199$	6.11364	−	10.5891i	0.433384	−	0.750644i	−0.563778	−	0.825926i	$-0.690653\pi$
$199$	6.11364	−	10.5891i	0.433384	−	0.750644i	0.997162	+	0.0752828i	$0.0239859\pi$
$200$		−	42.2581i		−	2.98810i
$201$	0.865420	+	0.499650i	0.0610420	+	0.0352426i
$202$	−24.9970	−	14.4320i	−1.75878	−	1.01543i
$203$			20.0820i			1.40948i
$204$	12.1345	−	21.0175i	0.849584	−	1.47152i
$205$	10.3795	+	17.9779i	0.724939	+	1.25563i
$206$	26.8263	−	15.4882i	1.86908	−	1.07911i
$207$	−4.03046			−0.280136
$208$	−10.1241	−	19.8919i	−0.701983	−	1.37925i
$209$	8.57579			0.593200
$210$	15.5192	−	8.96000i	1.07093	−	0.618299i
$211$	7.99721	+	13.8516i	0.550551	+	0.953582i	0.998235	+	0.0593904i	$0.0189157\pi$
$211$	7.99721	+	13.8516i	0.550551	+	0.953582i	−0.447684	+	0.894192i	$0.647751\pi$
$212$	−20.3278	+	35.2087i	−1.39612	+	2.41814i
$213$			8.65323i			0.592910i
$214$	−30.1555	−	17.4103i	−2.06138	−	1.19014i
$215$	9.87067	+	5.69883i	0.673174	+	0.388657i
$216$		−	26.9863i		−	1.83619i
$217$	−1.17039	+	2.02718i	−0.0794515	+	0.137614i
$218$	−24.6310	−	42.6622i	−1.66822	−	2.88945i
$219$	4.51006	−	2.60389i	0.304762	−	0.175954i
$220$	−50.8646			−3.42929
$221$	−12.5897	+	19.3673i	−0.846875	+	1.30279i
$222$	−18.4466			−1.23806
$223$	3.98907	−	2.30309i	0.267128	−	0.154226i	−0.360454	−	0.932777i	$-0.617378\pi$
$223$	3.98907	−	2.30309i	0.267128	−	0.154226i	0.627582	+	0.778551i	$0.284045\pi$
$224$	−4.42241	−	7.65983i	−0.295484	−	0.511794i
$225$	−8.01166	+	13.8766i	−0.534110	+	0.925107i
$226$			16.3002i			1.08427i
$227$	−14.2938	−	8.25252i	−0.948712	−	0.547739i	−0.0560313	−	0.998429i	$-0.517845\pi$
$227$	−14.2938	−	8.25252i	−0.948712	−	0.547739i	−0.892681	+	0.450690i	$0.851178\pi$
$228$	8.37847	+	4.83731i	0.554878	+	0.320359i
$229$			6.82480i			0.450995i	0.974244	+	0.225498i	$0.0724008\pi$
$229$			6.82480i			0.450995i	−0.974244	+	0.225498i	$0.927599\pi$
$230$	−7.90035	+	13.6838i	−0.520933	+	0.902283i
$231$	−3.42607	−	5.93413i	−0.225419	−	0.390437i
$232$	43.8917	−	25.3409i	2.88163	−	1.66371i
$233$	−25.5049			−1.67088			−0.835441	−	0.549580i	$-0.814788\pi$
$233$	−25.5049			−1.67088			−0.835441	+	0.549580i	$0.814788\pi$
$234$	−1.07390	+	20.3160i	−0.0702028	+	1.32810i
$235$	18.7044			1.22014
$236$	−48.5884	+	28.0526i	−3.16284	+	1.82607i
$237$	−0.550138	−	0.952866i	−0.0357353	−	0.0618953i
$238$	−18.8881	+	32.7152i	−1.22434	+	2.12061i
$239$			21.7195i			1.40491i	0.711726	+	0.702457i	$0.247914\pi$
$239$			21.7195i			1.40491i	−0.711726	+	0.702457i	$0.752086\pi$
$240$	−16.2932	−	9.40691i	−1.05172	−	0.607213i
$241$	−5.94352	−	3.43149i	−0.382856	−	0.221042i	0.296204	−	0.955125i	$-0.404279\pi$
$241$	−5.94352	−	3.43149i	−0.382856	−	0.221042i	−0.679060	+	0.734083i	$0.737612\pi$
$242$			0.692632i			0.0445240i
$243$	−8.04548	+	13.9352i	−0.516118	+	0.893942i
$244$	7.80820	+	13.5242i	0.499869	+	0.865798i
$245$	4.59118	−	2.65072i	0.293319	−	0.169348i
$246$	13.0765			0.833727
$247$	−7.72062	−	5.01878i	−0.491251	−	0.319337i
$248$	5.90753			0.375129
$249$	5.95301	−	3.43697i	0.377256	−	0.217809i
$250$	9.45445	+	16.3756i	0.597952	+	1.03568i
$251$	5.17485	−	8.96311i	0.326634	−	0.565746i	−0.655208	−	0.755449i	$-0.727419\pi$
$251$	5.17485	−	8.96311i	0.326634	−	0.565746i	0.981842	+	0.189702i	$0.0607523\pi$
$252$			22.7836i			1.43523i
$253$	5.23233	+	3.02088i	0.328953	+	0.189921i
$254$	−33.0160	−	19.0618i	−2.07161	−	1.19604i
$255$			19.4709i			1.21932i
$256$	15.7380	−	27.2590i	0.983623	−	1.70368i
$257$	−4.80560	−	8.32354i	−0.299765	−	0.519208i	0.676317	−	0.736611i	$-0.263575\pi$
$257$	−4.80560	−	8.32354i	−0.299765	−	0.519208i	−0.976082	+	0.217402i	$0.930242\pi$
$258$	6.21770	−	3.58979i	0.387097	−	0.223491i
$259$	19.6630			1.22180
$260$	45.7924	+	29.7673i	2.83993	+	1.84609i
$261$	−19.2173			−1.18952
$262$	−17.6193	+	10.1725i	−1.08852	+	0.628458i
$263$	5.12892	+	8.88356i	0.316263	+	0.547784i	0.979705	−	0.200444i	$-0.0642385\pi$
$263$	5.12892	+	8.88356i	0.316263	+	0.547784i	−0.663442	+	0.748228i	$0.730905\pi$
$264$	−8.64650	+	14.9762i	−0.532155	+	0.921720i
$265$		−	32.6178i		−	2.00369i
$266$	−13.0416	−	7.52960i	−0.799635	−	0.461669i
$267$	−7.79532	−	4.50063i	−0.477066	−	0.275434i
$268$			4.98082i			0.304252i
$269$	−10.3125	+	17.8618i	−0.628766	+	1.08905i	0.359033	+	0.933325i	$0.383106\pi$
$269$	−10.3125	+	17.8618i	−0.628766	+	1.08905i	−0.987800	+	0.155730i	$0.950227\pi$
$270$	20.0575	+	34.7407i	1.22066	+	2.11425i
$271$	14.9081	−	8.60720i	0.905603	−	0.522850i	0.0265894	−	0.999646i	$-0.491535\pi$
$271$	14.9081	−	8.60720i	0.905603	−	0.522850i	0.879014	+	0.476796i	$0.158202\pi$
$272$	39.6604			2.40477
$273$	−0.388382	+	7.34741i	−0.0235059	+	0.444685i
$274$	−27.4808			−1.66018
$275$	20.8014	−	12.0097i	1.25437	−	0.724211i
$276$	3.40796	+	5.90276i	0.205135	+	0.355304i
$277$	−6.48412	+	11.2308i	−0.389593	+	0.674795i	−0.992395	−	0.123096i	$-0.960718\pi$
$277$	−6.48412	+	11.2308i	−0.389593	+	0.674795i	0.602802	+	0.797891i	$0.294051\pi$
$278$		−	11.8949i		−	0.713409i
$279$	−1.93990	−	1.12000i	−0.116139	−	0.0670527i
$280$	41.7489	+	24.1038i	2.49498	+	1.44047i
$281$		−	16.9956i		−	1.01387i	−0.861983	−	0.506937i	$-0.830778\pi$
$281$		−	16.9956i		−	1.01387i	0.861983	−	0.506937i	$-0.169222\pi$
$282$	5.89112	−	10.2037i	0.350811	−	0.607623i
$283$	−15.7183	−	27.2248i	−0.934354	−	1.61835i	−0.775783	−	0.631000i	$-0.782645\pi$
$283$	−15.7183	−	27.2248i	−0.934354	−	1.61835i	−0.158571	−	0.987348i	$-0.550689\pi$
$284$	−37.3520	+	21.5652i	−2.21643	+	1.27966i
$285$	−7.76192			−0.459777
$286$	16.6212	−	25.5692i	0.982833	−	1.51194i
$287$	−13.9388			−0.822779
$288$	7.33003	−	4.23199i	0.431926	−	0.249373i
$289$	−12.0228	−	20.8241i	−0.707225	−	1.22495i
$290$	−37.6691	+	65.2447i	−2.21200	+	3.83130i
$291$			0.0442935i			0.00259653i
$292$	22.4796	+	12.9786i	1.31552	+	0.759514i
$293$	23.0328	+	13.2980i	1.34559	+	0.776877i	0.987621	−	0.156856i	$-0.0501359\pi$
$293$	23.0328	+	13.2980i	1.34559	+	0.776877i	0.357969	+	0.933733i	$0.383469\pi$
$294$		−	3.33946i		−	0.194761i
$295$	22.5065	−	38.9823i	1.31038	−	2.26964i
$296$	−24.8121	−	42.9759i	−1.44218	−	2.49792i
$297$	13.2839	−	7.66947i	0.770811	−	0.445028i
$298$	43.1953			2.50223
$299$	−2.94266	−	5.78174i	−0.170179	−	0.334367i
$300$	27.0970			1.56445
$301$	−6.62769	+	3.82650i	−0.382014	+	0.220556i
$302$	19.5084	+	33.7895i	1.12258	+	1.94437i
$303$	4.99471	−	8.65109i	0.286938	−	0.496992i
$304$			15.8103i			0.906784i
$305$	−10.8504	−	6.26449i	−0.621293	−	0.358704i
$306$	−31.3066	−	18.0749i	−1.78968	−	1.03327i
$307$		−	0.727175i		−	0.0415021i	−0.999785	−	0.0207510i	$-0.993394\pi$
$307$		−	0.727175i		−	0.0415021i	0.999785	−	0.0207510i	$-0.00660573\pi$
$308$	17.0766	−	29.5775i	0.973029	−	1.68534i
$309$	5.36023	+	9.28419i	0.304933	+	0.528159i
$310$	−7.60502	+	4.39076i	−0.431936	+	0.249378i
$311$	10.1605			0.576151			0.288075	−	0.957608i	$-0.406985\pi$
$311$	10.1605			0.576151			0.288075	+	0.957608i	$0.406985\pi$
$312$	16.5487	−	8.42261i	0.936888	−	0.476836i
$313$	28.7974			1.62772			0.813862	−	0.581059i	$-0.197361\pi$
$313$	28.7974			1.62772			0.813862	+	0.581059i	$0.197361\pi$
$314$	−9.14269	+	5.27853i	−0.515952	+	0.297885i
$315$	−9.13959	−	15.8302i	−0.514958	−	0.891933i
$316$	2.74206	−	4.74938i	0.154253	−	0.267174i
$317$		−	20.3636i		−	1.14373i	−0.820346	−	0.571867i	$-0.806219\pi$
$317$		−	20.3636i		−	1.14373i	0.820346	−	0.571867i	$-0.193781\pi$
$318$	−17.7938	−	10.2732i	−0.997826	−	0.576095i
$319$	24.9479	+	14.4037i	1.39681	+	0.806450i
$320$			9.98037i			0.557920i
$321$	6.02544	−	10.4364i	0.336307	−	0.582501i
$322$	−5.30471	−	9.18803i	−0.295620	−	0.512029i
$323$	14.1704	−	8.18126i	0.788459	−	0.455217i
$324$	−11.8955			−0.660862
$325$	−25.7555	−	1.36143i	−1.42866	−	0.0755184i
$326$	54.0719			2.99477
$327$	14.7648	−	8.52443i	0.816493	−	0.471402i
$328$	17.5889	+	30.4648i	0.971183	+	1.68214i
$329$	−6.27958	+	10.8765i	−0.346204	+	0.599644i
$330$		−	25.7060i		−	1.41507i
$331$	28.8308	+	16.6455i	1.58468	+	0.914918i	0.994162	+	0.107896i	$0.0344115\pi$
$331$	28.8308	+	16.6455i	1.58468	+	0.914918i	0.590522	+	0.807022i	$0.298922\pi$
$332$	29.6716	+	17.1309i	1.62844	+	0.940182i
$333$			18.8164i			1.03113i
$334$	0.852939	−	1.47733i	0.0466707	−	0.0808361i
$335$	−1.99805	−	3.46072i	−0.109165	−	0.189080i
$336$	10.9401	−	6.31630i	0.596834	−	0.344582i
$337$	−13.2095			−0.719566			−0.359783	−	0.933036i	$-0.617149\pi$
$337$	−13.2095			−0.719566			−0.359783	+	0.933036i	$0.617149\pi$
$338$	−29.9275	+	13.2923i	−1.62784	+	0.723005i
$339$	−5.64125			−0.306391
$340$	−84.0470	+	48.5245i	−4.55809	+	2.63161i
$341$	1.67891	+	2.90796i	0.0909181	+	0.157475i
$342$	7.20540	−	12.4801i	0.389623	−	0.674847i
$343$			19.9452i			1.07694i
$344$	16.7265	+	9.65708i	0.901835	+	0.520675i
$345$	−4.73576	−	2.73419i	−0.254965	−	0.147204i
$346$			13.2184i			0.710624i
$347$	3.76641	−	6.52362i	0.202192	−	0.350206i	−0.747043	−	0.664776i	$-0.768527\pi$
$347$	3.76641	−	6.52362i	0.202192	−	0.350206i	0.949234	+	0.314570i	$0.101860\pi$
$348$	16.2492	+	28.1445i	0.871051	+	1.50870i
$349$	−27.0545	+	15.6199i	−1.44819	+	0.836116i	−0.998374	−	0.0570031i	$-0.981846\pi$
$349$	−27.0545	+	15.6199i	−1.44819	+	0.836116i	−0.449821	+	0.893119i	$0.648512\pi$
$350$	−42.1783			−2.25453
$351$	−16.4476	−	0.869417i	−0.877910	−	0.0464061i
$352$	−12.6877			−0.676259
$353$	−1.48092	+	0.855010i	−0.0788215	+	0.0455076i	−0.538893	−	0.842374i	$-0.681157\pi$
$353$	−1.48092	+	0.855010i	−0.0788215	+	0.0455076i	0.460071	+	0.887882i	$0.347824\pi$
$354$	−14.1772	−	24.5556i	−0.753510	−	1.30512i
$355$	17.3017	−	29.9674i	0.918278	−	1.59050i
$356$		−	44.8651i		−	2.37785i
$357$	−11.3222	−	6.53690i	−0.599237	−	0.345970i
$358$	0.716734	+	0.413806i	0.0378806	+	0.0218704i
$359$			20.8527i			1.10056i	0.834980	+	0.550281i	$0.185479\pi$
$359$			20.8527i			1.10056i	−0.834980	+	0.550281i	$0.814521\pi$
$360$	−23.0659	+	39.9514i	−1.21568	+	2.10562i
$361$	−6.23861	−	10.8056i	−0.328348	−	0.568715i
$362$	−6.74844	+	3.89622i	−0.354690	+	0.204781i
$363$	−0.239710			−0.0125815
$364$	−32.6833	+	16.6344i	−1.71307	+	0.871880i
$365$	−20.8253			−1.09005
$366$	−6.83486	+	3.94611i	−0.357264	+	0.206266i
$367$	13.1543	+	22.7839i	0.686648	+	1.18931i	0.972916	+	0.231160i	$0.0742520\pi$
$367$	13.1543	+	22.7839i	0.686648	+	1.18931i	−0.286268	+	0.958150i	$0.592415\pi$
$368$	−5.56930	+	9.64631i	−0.290320	+	0.502849i
$369$		−	13.3386i		−	0.694380i
$370$	63.8834	+	36.8831i	3.32114	+	1.91746i
$371$	18.9671	+	10.9507i	0.984723	+	0.568530i
$372$			3.78807i			0.196402i
$373$	3.23862	−	5.60946i	0.167689	−	0.290447i	−0.769918	−	0.638143i	$-0.779703\pi$
$373$	3.23862	−	5.60946i	0.167689	−	0.290447i	0.937607	+	0.347697i	$0.113036\pi$
$374$	27.0947	+	46.9294i	1.40103	+	2.42666i
$375$	−5.66735	+	3.27205i	−0.292661	+	0.168968i
$376$	31.6960			1.63460
$377$	−14.0307	−	27.5675i	−0.722618	−	1.41980i
$378$	−26.9354			−1.38541
$379$	−3.21845	+	1.85817i	−0.165321	+	0.0954479i	−0.580378	−	0.814348i	$-0.697095\pi$
$379$	−3.21845	+	1.85817i	−0.165321	+	0.0954479i	0.415057	+	0.909795i	$0.363762\pi$
$380$	−19.3439	−	33.5046i	−0.992322	−	1.71875i
$381$	6.59700	−	11.4263i	0.337975	−	0.585390i
$382$		−	25.9290i		−	1.32664i
$383$	−3.26178	−	1.88319i	−0.166669	−	0.0962266i	0.414345	−	0.910120i	$-0.364011\pi$
$383$	−3.26178	−	1.88319i	−0.166669	−	0.0962266i	−0.581014	+	0.813893i	$0.697344\pi$
$384$	11.1500	+	6.43747i	0.568998	+	0.328511i
$385$			27.4010i			1.39648i
$386$	−5.64074	+	9.77005i	−0.287106	+	0.497283i
$387$	−3.66174	−	6.34232i	−0.186137	−	0.322398i
$388$	−0.191195	+	0.110386i	−0.00970643	+	0.00560401i
$389$	−6.72119			−0.340778			−0.170389	−	0.985377i	$-0.554502\pi$
$389$	−6.72119			−0.340778			−0.170389	+	0.985377i	$0.554502\pi$
$390$	−15.0438	+	23.1426i	−0.761773	+	1.17187i
$391$	11.5276			0.582977
$392$	7.78007	−	4.49183i	0.392953	−	0.226872i
$393$	−3.52055	−	6.09777i	−0.177588	−	0.307592i
$394$	2.64923	−	4.58861i	0.133466	−	0.231171i
$395$			4.39989i			0.221382i
$396$	28.3040	+	16.3413i	1.42233	+	0.821183i
$397$	−13.0665	−	7.54394i	−0.655789	−	0.378620i	0.134882	−	0.990862i	$-0.456934\pi$
$397$	−13.0665	−	7.54394i	−0.655789	−	0.378620i	−0.790670	+	0.612242i	$0.790268\pi$
$398$			30.8002i			1.54387i
$399$	2.60588	−	4.51352i	0.130457	−	0.225959i
$400$	22.1410	+	38.3494i	1.10705	+	1.91747i
$401$	−17.1317	+	9.89099i	−0.855516	+	0.493933i	−0.862508	−	0.506043i	$-0.831108\pi$
$401$	−17.1317	+	9.89099i	−0.855516	+	0.493933i	0.00699203	+	0.999976i	$0.497774\pi$
$402$	−2.51721			−0.125547
$403$	0.190323	−	3.60052i	0.00948065	−	0.179355i
$404$	49.7903			2.47716
$405$	8.26511	−	4.77186i	0.410697	−	0.237116i
$406$	−25.2930	−	43.8088i	−1.25527	−	2.17419i
$407$	14.1031	−	24.4273i	0.699066	−	1.21082i
$408$			32.9948i			1.63349i
$409$	−9.88926	−	5.70957i	−0.488993	−	0.282320i	0.235164	−	0.971956i	$-0.424437\pi$
$409$	−9.88926	−	5.70957i	−0.488993	−	0.282320i	−0.724156	+	0.689636i	$0.757771\pi$
$410$	−45.2858	−	26.1458i	−2.23651	−	1.29125i
$411$		−	9.51071i		−	0.469128i
$412$	−26.7170	+	46.2753i	−1.31625	+	2.27982i
$413$	15.1120	+	26.1748i	0.743615	+	1.28798i
$414$	8.79242	−	5.07631i	0.432124	−	0.249487i
$415$	−27.4882			−1.34934
$416$	11.4225	+	7.42520i	0.560036	+	0.364050i
$417$	4.11665			0.201593
$418$	−18.7080	+	10.8011i	−0.915039	+	0.528298i
$419$	13.2698	+	22.9840i	0.648274	+	1.12284i	0.983535	+	0.180718i	$0.0578422\pi$
$419$	13.2698	+	22.9840i	0.648274	+	1.12284i	−0.335261	+	0.942125i	$0.608824\pi$
$420$	−15.4560	+	26.7705i	−0.754174	+	1.30627i
$421$			7.03468i			0.342849i	0.985197	+	0.171425i	$0.0548370\pi$
$421$			7.03468i			0.342849i	−0.985197	+	0.171425i	$0.945163\pi$
$422$	−34.8917	−	20.1448i	−1.69850	−	0.980631i
$423$	−10.4082	−	6.00920i	−0.506066	−	0.292177i
$424$		−	55.2732i		−	2.68430i
$425$	22.9144	−	39.6888i	1.11151	−	1.92519i
$426$	−10.8986	−	18.8770i	−0.528040	−	0.914592i
$427$	7.28555	−	4.20631i	0.352572	−	0.203558i
$428$	60.0653			2.90337
$429$	8.84912	+	5.75236i	0.427239	+	0.277726i
$430$	−28.7104			−1.38454
$431$	5.93828	−	3.42847i	0.286037	−	0.165143i	−0.350116	−	0.936706i	$-0.613858\pi$
$431$	5.93828	−	3.42847i	0.286037	−	0.165143i	0.636153	+	0.771563i	$0.280525\pi$
$432$	14.1394	+	24.4902i	0.680283	+	1.17829i
$433$	7.12533	−	12.3414i	0.342422	−	0.593092i	−0.642460	−	0.766319i	$-0.722086\pi$
$433$	7.12533	−	12.3414i	0.342422	−	0.593092i	0.984882	+	0.173227i	$0.0554195\pi$
$434$		−	5.89638i		−	0.283035i
$435$	−22.5802	−	13.0367i	−1.08264	−	0.625062i
$436$	73.5921	+	42.4884i	3.52442	+	2.03483i
$437$			4.59540i			0.219828i
$438$	−6.55911	+	11.3607i	−0.313407	+	0.542836i
$439$	1.62933	+	2.82208i	0.0777637	+	0.134691i	0.902285	−	0.431141i	$-0.141889\pi$
$439$	1.62933	+	2.82208i	0.0777637	+	0.134691i	−0.824521	+	0.565831i	$0.808555\pi$
$440$	59.8881	−	34.5764i	2.85506	−	1.64837i
$441$	−3.40640			−0.162209
$442$	3.07148	−	58.1062i	0.146095	−	2.76383i
$443$	23.8133			1.13140			0.565702	−	0.824610i	$-0.308605\pi$
$443$	23.8133			1.13140			0.565702	+	0.824610i	$0.308605\pi$
$444$	27.5573	−	15.9102i	1.30781	−	0.755065i
$445$	17.9976	+	31.1727i	0.853166	+	1.47773i
$446$	−5.80141	+	10.0483i	−0.274705	+	0.475803i
$447$			14.9492i			0.707075i
$448$	−5.80354	−	3.35068i	−0.274191	−	0.158305i
$449$	3.59124	+	2.07340i	0.169481	+	0.0978500i	0.582341	−	0.812944i	$-0.302137\pi$
$449$	3.59124	+	2.07340i	0.169481	+	0.0978500i	−0.412860	+	0.910795i	$0.635470\pi$
$450$		−	40.3623i		−	1.90270i
$451$	−9.99746	+	17.3161i	−0.470762	+	0.815383i
$452$	−14.0589	−	24.3507i	−0.661274	−	1.14536i
$453$	−11.6940	+	6.75156i	−0.549434	+	0.317216i
$454$	41.5757			1.95125
$455$	16.0358	−	24.6686i	0.751769	−	1.15648i
$456$	−13.1531			−0.615952
$457$	−19.5928	+	11.3119i	−0.916513	+	0.529149i	−0.882521	−	0.470273i	$-0.844155\pi$
$457$	−19.5928	+	11.3119i	−0.916513	+	0.529149i	−0.0339920	+	0.999422i	$0.510822\pi$
$458$	−8.59573	−	14.8882i	−0.401652	−	0.695682i
$459$	14.6333	−	25.3456i	0.683022	−	1.18303i
$460$		−	27.2561i		−	1.27082i
$461$	3.60786	+	2.08300i	0.168035	+	0.0970149i	0.581659	−	0.813433i	$-0.302404\pi$
$461$	3.60786	+	2.08300i	0.168035	+	0.0970149i	−0.413624	+	0.910448i	$0.635737\pi$
$462$	14.9479	+	8.63017i	0.695439	+	0.401512i
$463$		−	12.6288i		−	0.586909i	−0.955973	−	0.293454i	$-0.905195\pi$
$463$		−	12.6288i		−	0.586909i	0.955973	−	0.293454i	$-0.0948049\pi$
$464$	−26.5546	+	45.9938i	−1.23276	+	2.13521i
$465$	−1.51958	−	2.63199i	−0.0704687	−	0.122055i
$466$	55.6388	−	32.1231i	2.57742	−	1.48807i
$467$	−24.1669			−1.11831			−0.559155	−	0.829063i	$-0.688874\pi$
$467$	−24.1669			−1.11831			−0.559155	+	0.829063i	$0.688874\pi$
$468$	−15.9182	−	31.2761i	−0.735819	−	1.44574i
$469$	2.68319			0.123898
$470$	−40.8036	+	23.5580i	−1.88213	+	1.08665i
$471$	−1.82682	−	3.16415i	−0.0841755	−	0.145796i
$472$	38.1388	−	66.0584i	1.75548	−	3.04058i
$473$			10.9781i			0.504774i
$474$	2.40024	+	1.38578i	0.110247	+	0.0636510i
$475$	15.8216	+	9.13462i	0.725946	+	0.419125i
$476$		−	65.1639i		−	2.98678i
$477$	−10.4792	+	18.1504i	−0.479808	+	0.831051i
$478$	−27.3553	−	47.3808i	−1.25120	−	2.16715i
$479$	−28.8341	+	16.6474i	−1.31746	+	0.760637i	−0.983320	−	0.181886i	$-0.941780\pi$
$479$	−28.8341	+	16.6474i	−1.31746	+	0.760637i	−0.334142	+	0.942523i	$0.608447\pi$
$480$	11.4836			0.524154
$481$	−26.9923	+	13.7379i	−1.23074	+	0.626396i
$482$	17.2877			0.787432
$483$	3.17984	−	1.83588i	0.144688	−	0.0835356i
$484$	−0.597394	−	1.03472i	−0.0271543	−	0.0470325i
$485$	0.0885625	−	0.153395i	0.00402142	−	0.00696530i
$486$		−	40.5327i		−	1.83860i
$487$	−29.3757	−	16.9601i	−1.33114	−	0.768535i	−0.345667	−	0.938357i	$-0.612347\pi$
$487$	−29.3757	−	16.9601i	−1.33114	−	0.768535i	−0.985475	+	0.169822i	$0.945681\pi$
$488$	−18.3868	−	10.6156i	−0.832332	−	0.480547i
$489$			18.7135i			0.846253i
$490$	−6.67708	+	11.5650i	−0.301640	+	0.522455i
$491$	−10.4136	−	18.0369i	−0.469961	−	0.813996i	0.529449	−	0.848342i	$-0.322399\pi$
$491$	−10.4136	−	18.0369i	−0.469961	−	0.813996i	−0.999410	+	0.0343458i	$0.989065\pi$
$492$	−19.5349	+	11.2785i	−0.880700	+	0.508472i
$493$	54.9640			2.47546
$494$	23.1636	+	1.22442i	1.04218	+	0.0550892i
$495$	−26.2212			−1.17855
$496$	−5.36111	+	3.09524i	−0.240721	+	0.138980i
$497$	11.6173	+	20.1217i	0.521106	+	0.902582i
$498$	−8.65763	+	14.9955i	−0.387958	+	0.671962i
$499$			29.3616i			1.31441i	0.753713	+	0.657203i	$0.228261\pi$
$499$			29.3616i			1.31441i	−0.753713	+	0.657203i	$0.771739\pi$
$500$	−28.2478	−	16.3089i	−1.26328	−	0.729356i
$501$	0.511283	+	0.295190i	0.0228425	+	0.0131881i
$502$			26.0706i			1.16359i
$503$	−20.7934	+	36.0153i	−0.927133	+	1.60584i	−0.139039	+	0.990287i	$0.544401\pi$
$503$	−20.7934	+	36.0153i	−0.927133	+	1.60584i	−0.788094	+	0.615555i	$0.788932\pi$
$504$	−15.4877	−	26.8255i	−0.689876	−	1.19490i
$505$	−34.5948	+	19.9733i	−1.53945	+	0.888801i
$506$	−15.2190			−0.676569
$507$	−4.60026	−	10.3575i	−0.204305	−	0.459992i
$508$	65.7630			2.91776
$509$	18.0105	−	10.3984i	0.798301	−	0.460899i	−0.0445756	−	0.999006i	$-0.514194\pi$
$509$	18.0105	−	10.3984i	0.798301	−	0.460899i	0.842877	+	0.538107i	$0.180860\pi$
$510$	−24.5233	−	42.4757i	−1.08591	−	1.88085i
$511$	6.99162	−	12.1098i	0.309291	−	0.535708i
$512$			49.7498i			2.19865i
$513$	10.1038	+	5.83343i	0.446094	+	0.257552i
$514$	20.9668	+	12.1052i	0.924804	+	0.533936i
$515$		−	42.8700i		−	1.88908i
$516$	−6.19238	+	10.7255i	−0.272604	+	0.472164i
$517$	9.00795	+	15.6022i	0.396169	+	0.686185i
$518$	−42.8947	+	24.7653i	−1.88469	+	1.08812i
$519$	−4.57468			−0.200806
$520$	−74.1512	−	3.91961i	−3.25175	−	0.171886i
$521$	11.5948			0.507977			0.253988	−	0.967207i	$-0.418258\pi$
$521$	11.5948			0.507977			0.253988	+	0.967207i	$0.418258\pi$
$522$	41.9225	−	24.2040i	1.83490	−	1.05938i
$523$	−8.48180	−	14.6909i	−0.370883	−	0.642389i	0.618818	−	0.785534i	$-0.287612\pi$
$523$	−8.48180	−	14.6909i	−0.370883	−	0.642389i	−0.989702	+	0.143145i	$0.954278\pi$
$524$	17.5475	−	30.3932i	0.766566	−	1.32773i
$525$		−	14.5973i		−	0.637078i
$526$	−22.3774	−	12.9196i	−0.975702	−	0.563322i
$527$	5.54835	+	3.20334i	0.241690	+	0.139540i
$528$		−	18.1212i		−	0.788626i
$529$	9.88124	−	17.1148i	0.429619	−	0.744122i
$530$	41.0816	+	71.1555i	1.78447	+	3.09080i
$531$	−25.0478	+	14.4614i	−1.08698	+	0.627570i
$532$	25.9771			1.12625
$533$	19.1344	−	9.73859i	0.828801	−	0.421825i
$534$	22.6739			0.981197
$535$	−41.7339	+	24.0951i	−1.80431	+	1.04172i
$536$	−3.38584	−	5.86444i	−0.146246	−	0.253305i
$537$	−0.143212	+	0.248051i	−0.00618007	+	0.0107042i
$538$		−	51.9539i		−	2.23989i
$539$	4.42217	+	2.55314i	0.190476	+	0.109971i
$540$	−59.9275	−	34.5992i	−2.57887	−	1.48891i
$541$		−	3.21511i		−	0.138229i	−0.997609	−	0.0691143i	$-0.977983\pi$
$541$		−	3.21511i		−	0.138229i	0.997609	−	0.0691143i	$-0.0220173\pi$
$542$	−21.6813	+	37.5531i	−0.931291	+	1.61304i
$543$	−1.34842	−	2.33554i	−0.0578664	−	0.100228i
$544$	−20.9648	+	12.1040i	−0.898858	+	0.518956i
$545$	−68.1766			−2.92037
$546$	−8.40670	−	16.5175i	−0.359774	−	0.706883i
$547$	−14.0441			−0.600482			−0.300241	−	0.953863i	$-0.597067\pi$
$547$	−14.0441			−0.600482			−0.300241	+	0.953863i	$0.597067\pi$
$548$	41.0533	−	23.7022i	1.75371	−	1.01251i
$549$	4.02520	+	6.97186i	0.171791	+	0.297552i
$550$	−30.2521	+	52.3981i	−1.28995	+	2.23426i
$551$			21.9110i			0.933439i
$552$	−8.02509	−	4.63329i	−0.341570	−	0.197206i
$553$	−2.55851	−	1.47716i	−0.108799	−	0.0628152i
$554$		−	32.6666i		−	1.38787i
$555$	−12.7647	+	22.1091i	−0.541831	+	0.938479i
$556$	10.2593	+	17.7697i	0.435093	+	0.753603i
$557$	35.1818	−	20.3122i	1.49070	−	0.860656i	0.490756	−	0.871297i	$-0.336721\pi$
$557$	35.1818	−	20.3122i	1.49070	−	0.860656i	0.999943	+	0.0106414i	$0.00338734\pi$
$558$	5.64250			0.238866
$559$	6.42468	−	9.88338i	0.271735	−	0.418022i
$560$	−50.5164			−2.13471
$561$	−16.2416	+	9.37708i	−0.685720	+	0.395901i
$562$	21.4057	+	37.0758i	0.902946	+	1.56395i
$563$	−1.17660	+	2.03793i	−0.0495878	+	0.0858886i	−0.889754	−	0.456441i	$-0.849124\pi$
$563$	−1.17660	+	2.03793i	−0.0495878	+	0.0858886i	0.840166	+	0.542329i	$0.182457\pi$
$564$			20.3243i			0.855809i
$565$	19.5365	+	11.2794i	0.821905	+	0.474527i
$566$	68.5785	+	39.5938i	2.88257	+	1.66425i
$567$			6.40817i			0.269118i
$568$	29.3189	−	50.7819i	1.23020	−	2.13076i
$569$	2.33265	+	4.04027i	0.0977899	+	0.169377i	0.910770	−	0.412915i	$-0.135489\pi$
$569$	2.33265	+	4.04027i	0.0977899	+	0.169377i	−0.812980	+	0.582292i	$0.802156\pi$
$570$	16.9326	−	9.77603i	0.709228	−	0.409473i
$571$	5.12289			0.214386			0.107193	−	0.994238i	$-0.465814\pi$
$571$	5.12289			0.214386			0.107193	+	0.994238i	$0.465814\pi$
$572$	−2.77690	+	52.5333i	−0.116108	+	2.19653i
$573$	8.97364			0.374879
$574$	30.4073	−	17.5557i	1.26918	−	0.732759i
$575$	6.43547	+	11.1466i	0.268378	+	0.464844i
$576$	3.20641	−	5.55366i	0.133600	−	0.231402i
$577$		−	17.6334i		−	0.734087i	−0.930204	−	0.367043i	$-0.880370\pi$
$577$		−	17.6334i		−	0.734087i	0.930204	−	0.367043i	$-0.119630\pi$
$578$	52.4554	+	30.2851i	2.18186	+	1.25970i
$579$	−3.38127	−	1.95218i	−0.140521	−	0.0811297i
$580$		−	129.958i		−	5.39621i
$581$	9.22851	−	15.9842i	0.382863	−	0.663138i
$582$	−0.0557870	−	0.0966259i	−0.00231245	−	0.00400527i
$583$	27.2080	−	15.7085i	1.12684	−	0.650581i
$584$	−35.2900			−1.46031
$585$	23.6064	+	15.3453i	0.976006	+	0.634452i
$586$	−66.9945			−2.76752
$587$	5.89271	−	3.40216i	0.243218	−	0.140422i	−0.373437	−	0.927656i	$-0.621821\pi$
$587$	5.89271	−	3.40216i	0.243218	−	0.140422i	0.616655	+	0.787234i	$0.288487\pi$
$588$	2.88028	+	4.98879i	0.118781	+	0.205734i
$589$	−1.27699	+	2.21181i	−0.0526173	+	0.0911359i
$590$			113.386i			4.66804i
$591$	1.58805	+	0.916861i	0.0653236	+	0.0377146i
$592$	45.0342	+	26.0005i	1.85089	+	1.06861i
$593$		−	8.04442i		−	0.330345i	−0.986265	−	0.165172i	$-0.947182\pi$
$593$		−	8.04442i		−	0.330345i	0.986265	−	0.165172i	$-0.0528181\pi$
$594$	−19.3192	+	33.4618i	−0.792676	+	1.37295i
$595$	26.1404	+	45.2765i	1.07165	+	1.85615i
$596$	−64.5290	+	37.2558i	−2.64321	+	1.52606i
$597$	−10.6595			−0.436264
$598$	13.7014	+	8.90659i	0.560293	+	0.364218i
$599$	−7.11258			−0.290612			−0.145306	−	0.989387i	$-0.546417\pi$
$599$	−7.11258			−0.290612			−0.145306	+	0.989387i	$0.546417\pi$
$600$	−31.9042	+	18.4199i	−1.30248	+	0.751988i
$601$	14.9383	+	25.8739i	0.609346	+	1.05542i	0.991348	+	0.131256i	$0.0419011\pi$
$601$	14.9383	+	25.8739i	0.609346	+	1.05542i	−0.382003	+	0.924161i	$0.624766\pi$
$602$	9.63884	−	16.6950i	0.392850	−	0.680436i
$603$			2.56766i			0.104563i
$604$	−58.2868	−	33.6519i	−2.37165	−	1.36928i
$605$	0.830149	+	0.479287i	0.0337504	+	0.0194858i
$606$			25.1631i			1.02218i
$607$	18.1562	−	31.4474i	0.736936	−	1.27641i	−0.216933	−	0.976187i	$-0.569605\pi$
$607$	18.1562	−	31.4474i	0.736936	−	1.27641i	0.953869	−	0.300224i	$-0.0970614\pi$
$608$	−4.82517	−	8.35745i	−0.195687	−	0.338939i
$609$	15.1616	−	8.75354i	0.614378	−	0.354711i
$610$	31.5602			1.27783
$611$	1.02115	−	19.3181i	0.0413113	−	0.781526i
$612$	62.3582			2.52068
$613$	2.51547	−	1.45231i	0.101599	−	0.0586582i	−0.448340	−	0.893863i	$-0.647984\pi$
$613$	2.51547	−	1.45231i	0.101599	−	0.0586582i	0.549939	+	0.835205i	$0.314651\pi$
$614$	0.915867	+	1.58633i	0.0369614	+	0.0640190i
$615$	9.04867	−	15.6728i	0.364878	−	0.631986i
$616$			46.4329i			1.87084i
$617$	8.70864	+	5.02793i	0.350597	+	0.202417i	0.664948	−	0.746890i	$-0.268454\pi$
$617$	8.70864	+	5.02793i	0.350597	+	0.202417i	−0.314351	+	0.949307i	$0.601787\pi$
$618$	−23.3866	−	13.5023i	−0.940747	−	0.543140i
$619$			22.3512i			0.898371i	0.893439	+	0.449185i	$0.148286\pi$
$619$			22.3512i			0.898371i	−0.893439	+	0.449185i	$0.851714\pi$
$620$	7.57404	−	13.1186i	0.304181	−	0.526857i
$621$	4.10974	+	7.11828i	0.164918	+	0.285647i
$622$	−22.1651	+	12.7970i	−0.888741	+	0.513115i
$623$	−24.1690			−0.968312
$624$	−10.6050	+	16.3142i	−0.424541	+	0.653091i
$625$	−9.59716			−0.383886
$626$	−62.8213	+	36.2699i	−2.51084	+	1.44964i
$627$	−3.73810	−	6.47457i	−0.149285	−	0.258570i
$628$	9.10545	−	15.7711i	0.363347	−	0.629336i
$629$		−	53.8172i		−	2.14583i
$630$	39.8759	+	23.0224i	1.58869	+	0.917233i
$631$	−41.1418	−	23.7532i	−1.63783	−	0.945602i	−0.981578	−	0.191060i	$-0.938807\pi$
$631$	−41.1418	−	23.7532i	−1.63783	−	0.945602i	−0.656252	−	0.754542i	$-0.727859\pi$
$632$			7.45592i			0.296581i
$633$	6.97180	−	12.0755i	0.277104	−	0.479959i
$634$	25.6477	+	44.4231i	1.01860	+	1.76427i
$635$	−45.6928	+	26.3807i	−1.81326	+	1.04689i
$636$	35.4426			1.40539
$637$	−2.48703	−	4.88651i	−0.0985397	−	0.193611i
$638$	−72.5648			−2.87287
$639$	−19.2553	+	11.1171i	−0.761729	+	0.439785i
$640$	−25.7428	−	44.5878i	−1.01757	−	1.76249i
$641$	6.60585	−	11.4417i	0.260916	−	0.451919i	−0.705570	−	0.708640i	$-0.749309\pi$
$641$	6.60585	−	11.4417i	0.260916	−	0.451919i	0.966485	+	0.256721i	$0.0826423\pi$
$642$			30.3558i			1.19805i
$643$	−12.4035	−	7.16117i	−0.489146	−	0.282409i	0.235074	−	0.971978i	$-0.424467\pi$
$643$	−12.4035	−	7.16117i	−0.489146	−	0.282409i	−0.724220	+	0.689569i	$0.757800\pi$
$644$	15.8493	+	9.15061i	0.624551	+	0.360585i
$645$		−	9.93625i		−	0.391239i
$646$	−20.6083	+	35.6947i	−0.810825	+	1.40439i
$647$	−9.27006	−	16.0562i	−0.364444	−	0.631235i	0.624243	−	0.781230i	$-0.285407\pi$
$647$	−9.27006	−	16.0562i	−0.364444	−	0.631235i	−0.988687	+	0.149995i	$0.952074\pi$
$648$	14.0058	−	8.08626i	0.550201	−	0.317658i
$649$	43.3559			1.70187
$650$	57.9001	−	29.4687i	2.27103	−	1.15586i
$651$	2.04065			0.0799794
$652$	−80.7775	+	46.6369i	−3.16349	+	1.82644i
$653$	−17.5697	−	30.4316i	−0.687554	−	1.19088i	−0.972627	−	0.232373i	$-0.925351\pi$
$653$	−17.5697	−	30.4316i	−0.687554	−	1.19088i	0.285072	−	0.958506i	$-0.407982\pi$
$654$	−21.4728	+	37.1920i	−0.839653	+	1.45432i
$655$			28.1566i			1.10017i
$656$	−31.9239	−	18.4313i	−1.24642	−	0.719621i
$657$	11.5884	+	6.69058i	0.452108	+	0.261024i
$658$		−	31.6362i		−	1.23331i
$659$	9.99841	−	17.3177i	0.389483	−	0.674604i	−0.602897	−	0.797819i	$-0.705987\pi$
$659$	9.99841	−	17.3177i	0.389483	−	0.674604i	0.992380	+	0.123215i	$0.0393205\pi$
$660$	22.1713	+	38.4019i	0.863018	+	1.49479i
$661$	−25.6051	+	14.7831i	−0.995922	+	0.574996i	−0.907039	−	0.421046i	$-0.861663\pi$
$661$	−25.6051	+	14.7831i	−0.995922	+	0.574996i	−0.0888828	+	0.996042i	$0.528330\pi$
$662$	−83.8589			−3.25927
$663$	20.1097	+	1.06299i	0.780996	+	0.0412832i
$664$	−46.5807			−1.80768
$665$	−18.0491	+	10.4207i	−0.699914	+	0.404096i
$666$	−23.6990	−	41.0478i	−0.918316	−	1.59057i
$667$	−7.71830	+	13.3685i	−0.298854	+	0.517630i
$668$			2.94263i			0.113854i
$669$	−3.47758	−	2.00778i	−0.134451	−	0.0776254i
$670$	8.71746	+	5.03303i	0.336785	+	0.194443i
$671$		−	12.0678i		−	0.465871i
$672$	−3.85536	+	6.67768i	−0.148724	+	0.257597i
$673$	14.2163	+	24.6234i	0.547999	+	0.949163i	0.998412	+	0.0563420i	$0.0179437\pi$
$673$	14.2163	+	24.6234i	0.547999	+	0.949163i	−0.450412	+	0.892821i	$0.648723\pi$
$674$	28.8164	−	16.6371i	1.10997	−	0.640839i
$675$	32.6770			1.25774
$676$	33.2439	−	45.6697i	1.27861	−	1.75653i
$677$	−9.50286			−0.365224			−0.182612	−	0.983185i	$-0.558455\pi$
$677$	−9.50286			−0.365224			−0.182612	+	0.983185i	$0.558455\pi$
$678$	12.3063	−	7.10507i	0.472622	−	0.272869i
$679$	0.0594656	+	0.102997i	0.00228208	+	0.00395268i
$680$	65.9715	−	114.266i	2.52989	−	4.38190i
$681$			14.3887i			0.551378i
$682$	−7.32507	−	4.22913i	−0.280491	−	0.161942i
$683$	20.1116	+	11.6115i	0.769551	+	0.444300i	0.832714	−	0.553703i	$-0.186786\pi$
$683$	20.1116	+	11.6115i	0.769551	+	0.444300i	−0.0631635	+	0.998003i	$0.520119\pi$
$684$			24.8586i			0.950491i
$685$	−19.0162	+	32.9369i	−0.726570	+	1.25846i
$686$	−25.1207	−	43.5103i	−0.959112	−	1.66123i
$687$	5.15260	−	2.97486i	0.196584	−	0.113498i
$688$	−20.2392			−0.771613
$689$	−33.6879	−	1.78073i	−1.28341	−	0.0678405i
$690$	13.7747			0.524394
$691$	10.1433	−	5.85622i	0.385868	−	0.222781i	−0.294500	−	0.955651i	$-0.595153\pi$
$691$	10.1433	−	5.85622i	0.385868	−	0.222781i	0.680368	+	0.732870i	$0.261820\pi$
$692$	−11.4008	−	19.7468i	−0.433394	−	0.750660i
$693$	8.80315	−	15.2475i	0.334404	−	0.579205i
$694$			18.9750i			0.720280i
$695$	−14.2566	−	8.23103i	−0.540782	−	0.312221i
$696$	−38.2638	−	22.0916i	−1.45039	−	0.837381i
$697$			38.1501i			1.44504i
$698$	39.3462	−	68.1495i	1.48927	−	2.57950i
$699$	11.1173	+	19.2558i	0.420496	+	0.728320i
$700$	63.0098	−	36.3787i	2.38155	−	1.37499i
$701$	15.6200			0.589960			0.294980	−	0.955503i	$-0.404687\pi$
$701$	15.6200			0.589960			0.294980	+	0.955503i	$0.404687\pi$
$702$	36.9754	−	18.8189i	1.39555	−	0.710275i
$703$	21.4538			0.809145
$704$	−8.32508	+	4.80649i	−0.313763	+	0.181151i
$705$	−8.15307	−	14.1215i	−0.307062	−	0.531848i
$706$	2.15375	−	3.73040i	0.0810573	−	0.140395i
$707$		−	26.8223i		−	1.00876i
$708$	42.3584	+	24.4556i	1.59193	+	0.919099i
$709$	10.1283	+	5.84760i	0.380378	+	0.219611i	0.677983	−	0.735078i	$-0.262854\pi$
$709$	10.1283	+	5.84760i	0.380378	+	0.219611i	−0.297605	+	0.954689i	$0.596188\pi$
$710$			87.1649i			3.27124i
$711$	1.41356	−	2.44835i	0.0530125	−	0.0918204i
$712$	30.4981	+	52.8243i	1.14297	+	1.97968i
$713$	−1.55825	+	0.899656i	−0.0583569	+	0.0336924i
$714$	32.9325			1.23247
$715$	−19.1442	−	37.6146i	−0.715954	−	1.40671i
$716$	−1.42763			−0.0533530
$717$	16.3978	−	9.46728i	0.612387	−	0.353562i
$718$	−26.2636	−	45.4900i	−0.980150	−	1.69767i
$719$	−17.5310	+	30.3646i	−0.653797	+	1.13241i	0.328397	+	0.944540i	$0.393492\pi$
$719$	−17.5310	+	30.3646i	−0.653797	+	1.13241i	−0.982194	+	0.187870i	$0.939842\pi$
$720$		−	48.3413i		−	1.80158i
$721$	24.9287	+	14.3926i	0.928393	+	0.536008i
$722$	27.2190	+	15.7149i	1.01298	+	0.584847i
$723$			5.98301i			0.222510i
$724$	6.72096	−	11.6410i	0.249782	−	0.432636i
$725$	30.6845	+	53.1471i	1.13959	+	1.97384i
$726$	0.522925	−	0.301911i	0.0194076	−	0.0112050i
$727$	−22.2228			−0.824197			−0.412098	−	0.911139i	$-0.635204\pi$
$727$	−22.2228			−0.824197			−0.412098	+	0.911139i	$0.635204\pi$
$728$	27.1738	−	41.8027i	1.00713	−	1.54931i
$729$	5.81493			0.215368
$730$	45.4303	−	26.2292i	1.68145	−	0.970787i
$731$	10.4730	+	18.1398i	0.387360	+	0.670927i
$732$	6.80702	−	11.7901i	0.251595	−	0.435775i
$733$		−	51.8952i		−	1.91679i	−0.285440	−	0.958397i	$-0.592140\pi$
$733$		−	51.8952i		−	1.91679i	0.285440	−	0.958397i	$-0.407860\pi$
$734$	−57.3920	−	33.1353i	−2.11838	−	1.22305i
$735$	−4.00249	−	2.31084i	−0.147634	−	0.0852366i
$736$		−	6.79881i		−	0.250608i
$737$	1.92450	−	3.33333i	0.0708898	−	0.122785i
$738$	16.7998	+	29.0981i	0.618408	+	1.07111i
$739$	−0.522228	+	0.301508i	−0.0192105	+	0.0110912i	−0.509574	−	0.860427i	$-0.670197\pi$
$739$	−0.522228	+	0.301508i	−0.0192105	+	0.0110912i	0.490364	+	0.871518i	$0.336864\pi$
$740$	−127.246			−4.67767
$741$	−0.423754	+	8.01657i	−0.0155670	+	0.294496i
$742$	−55.1688			−2.02531
$743$	44.2930	−	25.5726i	1.62495	−	0.938166i	0.639384	−	0.768888i	$-0.279190\pi$
$743$	44.2930	−	25.5726i	1.62495	−	0.938166i	0.985568	−	0.169278i	$-0.0541437\pi$
$744$	−2.57503	−	4.46009i	−0.0944053	−	0.163515i
$745$	29.8902	−	51.7714i	1.09509	−	1.89676i
$746$			16.3160i			0.597371i
$747$	15.2960	+	8.83116i	0.559652	+	0.323115i
$748$	−80.9531	−	46.7383i	−2.95994	−	1.70892i
$749$		−	32.3574i		−	1.18232i
$750$	8.24219	−	14.2759i	0.300962	−	0.521282i
$751$	−3.85546	−	6.67785i	−0.140688	−	0.243678i	0.787068	−	0.616866i	$-0.211598\pi$
$751$	−3.85546	−	6.67785i	−0.140688	−	0.243678i	−0.927756	+	0.373188i	$0.878265\pi$
$752$	−28.7642	+	16.6070i	−1.04892	+	0.605597i
$753$	−9.02265			−0.328804
$754$	65.3287	+	42.4669i	2.37913	+	1.54655i
$755$	53.9976			1.96517
$756$	40.2385	−	23.2317i	1.46346	−	0.844929i
$757$	−7.73358	−	13.3950i	−0.281082	−	0.486848i	0.690570	−	0.723266i	$-0.257360\pi$
$757$	−7.73358	−	13.3950i	−0.281082	−	0.486848i	−0.971651	+	0.236418i	$0.924027\pi$
$758$	4.68068	−	8.10718i	0.170010	−	0.294466i
$759$		−	5.26709i		−	0.191183i
$760$	45.5512	+	26.2990i	1.65232	+	0.953965i
$761$	−2.97180	−	1.71577i	−0.107728	−	0.0621966i	0.445168	−	0.895447i	$-0.353144\pi$
$761$	−2.97180	−	1.71577i	−0.107728	−	0.0621966i	−0.552896	+	0.833250i	$0.686477\pi$
$762$			33.2353i			1.20399i
$763$	22.8887	−	39.6444i	0.828627	−	1.43522i
$764$	22.3637	+	38.7350i	0.809090	+	1.40138i
$765$	−43.3270	+	25.0149i	−1.56649	+	0.904414i
$766$	9.48741			0.342794
$767$	−39.0325	−	25.3730i	−1.40938	−	0.916168i
$768$	−27.4401			−0.990158
$769$	−10.6766	+	6.16415i	−0.385009	+	0.222285i	−0.679995	−	0.733217i	$-0.738018\pi$
$769$	−10.6766	+	6.16415i	−0.385009	+	0.222285i	0.294987	+	0.955501i	$0.404685\pi$
$770$	−34.5111	−	59.7751i	−1.24370	−	2.15414i
$771$	−4.18942	+	7.25629i	−0.150878	+	0.261329i
$772$		−	19.4605i		−	0.700399i
$773$	15.2625	+	8.81183i	0.548955	+	0.316939i	0.748700	−	0.662908i	$-0.230678\pi$
$773$	15.2625	+	8.81183i	0.548955	+	0.316939i	−0.199745	+	0.979848i	$0.564011\pi$
$774$	15.9761	+	9.22382i	0.574250	+	0.331544i
$775$			7.15326i			0.256953i
$776$	0.150075	−	0.259938i	0.00538739	−	0.00933124i
$777$	−8.57090	−	14.8452i	−0.307479	−	0.532570i
$778$	14.6622	−	8.46525i	0.525667	−	0.303494i
$779$	−15.2082			−0.544891
$780$	2.51336	−	47.5478i	0.0899928	−	1.70248i
$781$	33.3296			1.19263
$782$	−25.1474	+	14.5189i	−0.899271	+	0.519194i
$783$	19.5953	+	33.9401i	0.700281	+	1.21292i
$784$	−4.70696	+	8.15270i	−0.168106	+	0.291168i
$785$			14.6105i			0.521473i
$786$	15.3601	+	8.86816i	0.547877	+	0.316317i
$787$	−0.0148418	−	0.00856892i	−0.000529053	−	0.000305449i	0.499735	−	0.866178i	$-0.333431\pi$
$787$	−0.0148418	−	0.00856892i	−0.000529053	−	0.000305449i	−0.500265	+	0.865873i	$0.666764\pi$
$788$			9.13983i			0.325593i
$789$	4.47129	−	7.74450i	0.159182	−	0.275711i
$790$	−5.54159	−	9.59832i	−0.197161	−	0.341493i
$791$	−13.1178	+	7.57358i	−0.466416	+	0.269285i
$792$	−44.4337			−1.57888
$793$	−7.06238	+	10.8644i	−0.250793	+	0.385806i
$794$	38.0060			1.34878
$795$	−24.6259	+	14.2178i	−0.873390	+	0.504252i
$796$	−26.5651	−	46.0121i	−0.941574	−	1.63085i
$797$	−2.19977	+	3.81011i	−0.0779198	+	0.134961i	−0.902352	−	0.430999i	$-0.858161\pi$
$797$	−2.19977	+	3.81011i	−0.0779198	+	0.134961i	0.824432	+	0.565960i	$0.191494\pi$
$798$			13.1283i			0.464736i
$799$	29.7689	+	17.1871i	1.05315	+	0.608035i
$800$	−23.4078	−	13.5145i	−0.827592	−	0.477810i
$801$		−	23.1284i		−	0.817202i
$802$	24.9151	−	43.1543i	0.879784	−	1.52383i
$803$	−10.0294	−	17.3714i	−0.353928	−	0.613022i
$804$	3.76044	−	2.17109i	0.132620	−	0.0765684i
$805$	−14.6830			−0.517508
$806$	4.11962	+	8.09423i	0.145107	+	0.285107i
$807$	17.9805			0.632943
$808$	−58.6233	+	33.8462i	−2.06236	+	1.19071i
$809$	−18.6316	−	32.2709i	−0.655052	−	1.13458i	−0.981881	−	0.189499i	$-0.939314\pi$
$809$	−18.6316	−	32.2709i	−0.655052	−	1.13458i	0.326829	−	0.945083i	$-0.394020\pi$
$810$	−12.0202	+	20.8196i	−0.422346	+	0.731525i
$811$			2.11791i			0.0743697i	0.999308	+	0.0371849i	$0.0118390\pi$
$811$			2.11791i			0.0743697i	−0.999308	+	0.0371849i	$0.988161\pi$
$812$	75.5700	+	43.6303i	2.65199	+	1.53113i
$813$	−12.9966	−	7.50358i	−0.455810	−	0.263162i
$814$			71.0507i			2.49033i
$815$	37.4166	−	64.8075i	1.31065	−	2.27011i
$816$	−17.2876	−	29.9429i	−0.605186	−	1.04821i
$817$	−7.23130	+	4.17499i	−0.252991	+	0.146065i
$818$	28.7645			1.00573
$819$	−16.8486	+	8.57520i	−0.588736	+	0.299642i
$820$	90.2027			3.15002
$821$	32.7122	−	18.8864i	1.14167	−	0.659141i	0.194823	−	0.980838i	$-0.437587\pi$
$821$	32.7122	−	18.8864i	1.14167	−	0.659141i	0.946842	+	0.321698i	$0.104254\pi$
$822$	11.9786	+	20.7475i	0.417802	+	0.723654i
$823$	−26.0929	+	45.1942i	−0.909540	+	1.57537i	−0.0948354	+	0.995493i	$0.530232\pi$
$823$	−26.0929	+	45.1942i	−0.909540	+	1.57537i	−0.814705	+	0.579876i	$0.803101\pi$
$824$		−	72.6462i		−	2.53075i
$825$	−18.1342	−	10.4698i	−0.631352	−	0.364511i
$826$	−65.9336	−	38.0668i	−2.29412	−	1.32451i
$827$			50.3438i			1.75062i	0.483559	+	0.875312i	$0.339344\pi$
$827$			50.3438i			1.75062i	−0.483559	+	0.875312i	$0.660656\pi$
$828$	−8.75661	+	15.1669i	−0.304313	+	0.527086i
$829$	13.6448	+	23.6334i	0.473902	+	0.820823i	0.999554	−	0.0298771i	$-0.00951160\pi$
$829$	13.6448	+	23.6334i	0.473902	+	0.820823i	−0.525651	+	0.850700i	$0.676178\pi$
$830$	59.9652	−	34.6210i	2.08142	−	1.20171i
$831$	11.3054			0.392181
$832$	10.3078	+	0.544867i	0.357359	+	0.0188899i
$833$	9.74272			0.337565
$834$	−8.98045	+	5.18486i	−0.310967	+	0.179537i
$835$	−1.18043	−	2.04457i	−0.0408505	−	0.0707552i
$836$	18.6318	−	32.2713i	0.644395	−	1.11613i
$837$			4.56812i			0.157897i
$838$	−57.8961	−	33.4263i	−1.99999	−	1.15469i
$839$	−27.7033	−	15.9945i	−0.956425	−	0.552192i	−0.0613540	−	0.998116i	$-0.519542\pi$
$839$	−27.7033	−	15.9945i	−0.956425	−	0.552192i	−0.895071	+	0.445924i	$0.852875\pi$
$840$		−	42.0263i		−	1.45004i
$841$	−22.3011	+	38.6266i	−0.769002	+	1.33195i
$842$	−8.86007	−	15.3461i	−0.305338	−	0.528862i
$843$	−12.8314	+	7.40821i	−0.441937	+	0.255152i
$844$	69.4993			2.39226
$845$	−4.77785	+	45.0674i	−0.164363	+	1.55037i
$846$	30.2740			1.04084
$847$	−0.557406	+	0.321819i	−0.0191527	+	0.0110578i
$848$	28.9602	+	50.1606i	0.994499	+	1.72252i
$849$	−13.7028	+	23.7340i	−0.470281	+	0.814550i
$850$			115.441i			3.95960i
$851$	13.0896	+	7.55726i	0.448704	+	0.259059i
$852$	32.5627	+	18.8001i	1.11558	+	0.644080i
$853$			30.4079i			1.04115i	0.853817	+	0.520573i	$0.174281\pi$
$853$			30.4079i			1.04115i	−0.853817	+	0.520573i	$0.825719\pi$
$854$	−10.5956	+	18.3521i	−0.362573	+	0.627995i
$855$	−9.97197	−	17.2720i	−0.341034	−	0.590689i
$856$	−70.7211	+	40.8308i	−2.41720	+	1.39557i
$857$	4.47970			0.153024			0.0765119	−	0.997069i	$-0.475622\pi$
$857$	4.47970			0.153024			0.0765119	+	0.997069i	$0.475622\pi$
$858$	−26.5493	−	1.40339i	−0.906378	−	0.0479109i
$859$	−3.16887			−0.108120			−0.0540602	−	0.998538i	$-0.517216\pi$
$859$	−3.16887			−0.108120			−0.0540602	+	0.998538i	$0.517216\pi$
$860$	42.8902	−	24.7627i	1.46254	−	0.844400i
$861$	6.07576	+	10.5235i	0.207061	+	0.358641i
$862$	−8.63621	+	14.9584i	−0.294150	+	0.509484i
$863$			14.2213i			0.484098i	0.970264	+	0.242049i	$0.0778195\pi$
$863$			14.2213i			0.484098i	−0.970264	+	0.242049i	$0.922180\pi$
$864$	−14.9484	−	8.63047i	−0.508555	−	0.293614i
$865$	15.8428	+	9.14683i	0.538671	+	0.311002i
$866$			35.8970i			1.21983i
$867$	−10.4812	+	18.1540i	−0.355962	+	0.616544i
$868$	5.08562	+	8.80854i	0.172617	+	0.298981i
$869$	−3.67014	+	2.11896i	−0.124501	+	0.0718808i
$870$	65.6782			2.22670
$871$	−3.68334	+	1.87467i	−0.124805	+	0.0635206i
$872$	−115.530			−3.91235
$873$	−0.0985626	+	0.0569052i	−0.00333584	+	0.00192595i
$874$	−5.78784	−	10.0248i	−0.195776	−	0.339095i
$875$	−8.78568	+	15.2172i	−0.297010	+	0.514437i
$876$		−	22.6289i		−	0.764560i
$877$	16.5909	+	9.57875i	0.560234	+	0.323452i	0.753240	−	0.657746i	$-0.228490\pi$
$877$	16.5909	+	9.57875i	0.560234	+	0.323452i	−0.193005	+	0.981198i	$0.561823\pi$
$878$	−7.10874	−	4.10424i	−0.239909	−	0.138511i
$879$		−	23.1858i		−	0.782038i
$880$	−36.2325	+	62.7565i	−1.22140	+	2.11552i
$881$	−22.2218	−	38.4893i	−0.748671	−	1.29674i	−0.948460	−	0.316898i	$-0.897359\pi$
$881$	−22.2218	−	38.4893i	−0.748671	−	1.29674i	0.199788	−	0.979839i	$-0.435975\pi$
$882$	7.43103	−	4.29031i	0.250216	−	0.144462i
$883$	−0.0651954			−0.00219400			−0.00109700	−	0.999999i	$-0.500349\pi$
$883$	−0.0651954			−0.00219400			−0.00109700	+	0.999999i	$0.500349\pi$
$884$	45.5280	+	89.4535i	1.53127	+	3.00865i
$885$	−39.2413			−1.31908
$886$	−51.9485	+	29.9925i	−1.74524	+	1.00762i
$887$	−24.7592	−	42.8841i	−0.831331	−	1.43991i	−0.896983	−	0.442065i	$-0.854246\pi$
$887$	−24.7592	−	42.8841i	−0.831331	−	1.43991i	0.0656517	−	0.997843i	$-0.479087\pi$
$888$	−21.6307	+	37.4655i	−0.725878	+	1.25726i
$889$		−	35.4268i		−	1.18818i
$890$	−78.5231	−	45.3353i	−2.63210	−	1.51964i
$891$	7.96086	+	4.59620i	0.266699	+	0.153979i
$892$		−	20.0148i		−	0.670146i
$893$	−6.85149	+	11.8671i	−0.229276	+	0.397118i
$894$	−18.8284	−	32.6117i	−0.629715	−	1.09070i
$895$	0.991930	−	0.572691i	0.0331566	−	0.0191430i
$896$	34.5701			1.15491
$897$	−3.08244	+	4.74186i	−0.102920	+	0.158326i
$898$	−10.4457			−0.348577
$899$	−7.42978	+	4.28958i	−0.247797	+	0.143066i
$900$	34.8124	+	60.2968i	1.16041	+	2.00989i
$901$	29.9717	−	51.9125i	0.998503	−	1.72946i
$902$		−	50.3666i		−	1.67702i
$903$	5.77788	+	3.33586i	0.192276	+	0.111011i
$904$	33.1059	+	19.1137i	1.10109	+	0.635713i
$905$			10.7844i			0.358486i
$906$	17.0070	−	29.4570i	0.565019	−	0.978642i
$907$	−4.64020	−	8.03707i	−0.154075	−	0.266866i	0.778647	−	0.627463i	$-0.215907\pi$
$907$	−4.64020	−	8.03707i	−0.154075	−	0.266866i	−0.932722	+	0.360596i	$0.882573\pi$
$908$	−62.1096	+	35.8590i	−2.06118	+	1.19002i
$909$	25.6674			0.851334
$910$	−3.91221	+	74.0112i	−0.129689	+	2.45345i
$911$	−13.3510			−0.442338			−0.221169	−	0.975235i	$-0.570987\pi$
$911$	−13.3510			−0.442338			−0.221169	+	0.975235i	$0.570987\pi$
$912$	11.9365	−	6.89155i	0.395257	−	0.228202i
$913$	−13.2381	−	22.9291i	−0.438118	−	0.758843i
$914$	28.4944	−	49.3537i	0.942510	−	1.63248i
$915$			10.9225i			0.361087i
$916$	25.6822	+	14.8276i	0.848563	+	0.489918i
$917$	−16.3729	−	9.45292i	−0.540682	−	0.312163i
$918$			73.7216i			2.43317i
$919$	−20.2046	+	34.9954i	−0.666488	+	1.15439i	0.312392	+	0.949953i	$0.398870\pi$
$919$	−20.2046	+	34.9954i	−0.666488	+	1.15439i	−0.978880	+	0.204437i	$0.934464\pi$
$920$	18.5280	+	32.0915i	0.610851	+	1.05802i
$921$	−0.549005	+	0.316968i	−0.0180903	+	0.0104444i
$922$	−10.4940			−0.345602
$923$	−30.0060	−	19.5054i	−0.987659	−	0.642026i
$924$	−29.7740			−0.979494
$925$	52.0382	−	30.0443i	1.71101	−	0.987850i
$926$	15.9058	+	27.5496i	0.522695	+	0.905335i
$927$	−13.7729	+	23.8553i	−0.452361	+	0.783512i
$928$		−	32.4169i		−	1.06414i
$929$	−3.13149	−	1.80797i	−0.102741	−	0.0593174i	0.447749	−	0.894159i	$-0.352226\pi$
$929$	−3.13149	−	1.80797i	−0.102741	−	0.0593174i	−0.550490	+	0.834842i	$0.685559\pi$
$930$	6.62990	+	3.82777i	0.217403	+	0.125518i
$931$			3.88386i			0.127288i
$932$	−55.4122	+	95.9767i	−1.81509	+	3.14382i
$933$	−4.42887	−	7.67103i	−0.144995	−	0.251138i
$934$	52.7199	−	30.4378i	1.72505	−	0.995957i
$935$	74.9959			2.45263
$936$	40.0028	+	26.0038i	1.30753	+	0.849960i
$937$	−40.1351			−1.31116			−0.655578	−	0.755127i	$-0.727575\pi$
$937$	−40.1351			−1.31116			−0.655578	+	0.755127i	$0.727575\pi$
$938$	−5.85337	+	3.37944i	−0.191119	+	0.110343i
$939$	−12.5525	−	21.7415i	−0.409634	−	0.709508i
$940$	40.6374	−	70.3861i	1.32545	−	2.29574i
$941$			40.3391i			1.31502i	0.753447	+	0.657509i	$0.228390\pi$
$941$			40.3391i			1.31502i	−0.753447	+	0.657509i	$0.771610\pi$
$942$	7.97040	+	4.60171i	0.259690	+	0.149932i
$943$	−9.27895	−	5.35721i	−0.302164	−	0.174455i
$944$			79.9309i			2.60153i
$945$	−18.6387	+	32.2832i	−0.606318	+	1.05017i
$946$	−13.8268	−	23.9486i	−0.449547	−	0.778638i
$947$	−45.8147	+	26.4511i	−1.48878	+	0.859546i	−0.999918	−	0.0128160i	$-0.995920\pi$
$947$	−45.8147	+	26.4511i	−1.48878	+	0.859546i	−0.488860	+	0.872362i	$0.662587\pi$
$948$	−4.78093			−0.155278
$949$	−1.13694	+	21.5086i	−0.0369065	+	0.698197i
$950$	−46.0197			−1.49308
$951$	−15.3742	+	8.87629i	−0.498542	+	0.287833i
$952$	44.2967	+	76.7242i	1.43567	+	2.48665i
$953$	10.9473	−	18.9612i	0.354616	−	0.614213i	−0.632436	−	0.774613i	$-0.717945\pi$
$953$	10.9473	−	18.9612i	0.354616	−	0.614213i	0.987052	+	0.160399i	$0.0512782\pi$
$954$		−	52.7934i		−	1.70925i
$955$	−31.0770	−	17.9423i	−1.00563	−	0.580600i
$956$	81.7318	+	47.1879i	2.64339	+	1.52616i
$957$		−	25.1136i		−	0.811808i
$958$	41.9342	−	72.6322i	1.35483	−	2.34664i
$959$	−12.7685	−	22.1156i	−0.412315	−	0.714151i
$960$	7.53501	−	4.35034i	0.243191	−	0.140407i
$961$	−1.00000			−0.0322581
$962$	41.5808	−	63.9657i	1.34062	−	2.06234i
$963$	30.9642			0.997809
$964$	−25.8259	+	14.9106i	−0.831796	+	0.480237i
$965$	7.80655	+	13.5213i	0.251302	+	0.435268i
$966$	−4.62454	+	8.00993i	−0.148792	+	0.257715i
$967$			39.3531i			1.26551i	0.774352	+	0.632755i	$0.218076\pi$
$967$			39.3531i			1.26551i	−0.774352	+	0.632755i	$0.781924\pi$
$968$	1.40675	+	0.812186i	0.0452146	+	0.0261046i
$969$	−12.3534	−	7.13225i	−0.396849	−	0.229121i
$970$			0.446173i			0.0143257i
$971$	1.40969	−	2.44166i	0.0452392	−	0.0783566i	−0.842519	−	0.538666i	$-0.818928\pi$
$971$	1.40969	−	2.44166i	0.0452392	−	0.0783566i	0.887758	+	0.460310i	$0.152262\pi$
$972$	34.9594	+	60.5514i	1.12132	+	1.94219i
$973$	9.57261	−	5.52675i	0.306884	−	0.177179i
$974$	85.4440			2.73780
$975$	10.1987	+	20.0384i	0.326620	+	0.641742i
$976$	22.2481			0.712145
$977$	27.8383	−	16.0724i	0.890625	−	0.514203i	0.0164783	−	0.999864i	$-0.494755\pi$
$977$	27.8383	−	16.0724i	0.890625	−	0.514203i	0.874147	+	0.485661i	$0.161421\pi$
$978$	−23.5694	−	40.8234i	−0.753665	−	1.30539i
$979$	−17.3350	+	30.0252i	−0.554030	+	0.959608i
$980$		−	23.0359i		−	0.735854i
$981$	37.9374	+	21.9032i	1.21125	+	0.699315i
$982$	45.4345	+	26.2316i	1.44987	+	0.837085i
$983$		−	40.0679i		−	1.27797i	−0.769221	−	0.638983i	$-0.779355\pi$
$983$		−	40.0679i		−	1.27797i	0.769221	−	0.638983i	$-0.220645\pi$
$984$	15.3336	−	26.5586i	0.488818	−	0.846657i
$985$	−3.66643	−	6.35044i	−0.116822	−	0.202342i
$986$	−119.904	+	69.2264i	−3.81851	+	2.20462i
$987$	10.9488			0.348504
$988$	−35.6599	+	18.1494i	−1.13449	+	0.577409i
$989$	−5.88269			−0.187059
$990$	57.2013	−	33.0252i	1.81798	−	1.04961i
$991$	21.4622	+	37.1736i	0.681770	+	1.18086i	0.974440	+	0.224646i	$0.0721226\pi$
$991$	21.4622	+	37.1736i	0.681770	+	1.18086i	−0.292671	+	0.956213i	$0.594544\pi$
$992$	1.88928	−	3.27233i	0.0599847	−	0.103897i
$993$		−	29.0223i		−	0.920996i
$994$	−50.6860	−	29.2636i	−1.60766	−	0.928184i
$995$	36.9153	+	21.3131i	1.17029	+	0.675670i
$996$		−	29.8688i		−	0.946428i
$997$	−18.7367	+	32.4530i	−0.593398	+	1.02780i	0.400373	+	0.916352i	$0.368881\pi$
$997$	−18.7367	+	32.4530i	−0.593398	+	1.02780i	−0.993771	+	0.111443i	$0.964453\pi$
$998$	−36.9805	−	64.0522i	−1.17060	−	2.02754i
$999$	33.2320	−	19.1865i	1.05141	−	0.607034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.r.a.218.3	✓	68
13.2	odd	12		5239.2.a.r.1.1		34
13.4	even	6	inner	403.2.r.a.342.3	yes	68
13.11	odd	12		5239.2.a.q.1.34		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.r.a.218.3	✓	68	1.1	even	1	trivial
403.2.r.a.342.3	yes	68	13.4	even	6	inner
5239.2.a.q.1.34		34	13.11	odd	12
5239.2.a.r.1.1		34	13.2	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.18149 + 1.25949i) q^{2} +(-0.435889 - 0.754983i) q^{3} +(2.17261 - 3.76307i) q^{4} +3.48615i q^{5} +(1.90178 + 1.09799i) q^{6} +(-2.02718 - 1.17039i) q^{7} +5.90753i q^{8} +(1.12000 - 1.93990i) q^{9} +O(q^{10})\)	\(q+(-2.18149 + 1.25949i) q^{2} +(-0.435889 - 0.754983i) q^{3} +(2.17261 - 3.76307i) q^{4} +3.48615i q^{5} +(1.90178 + 1.09799i) q^{6} +(-2.02718 - 1.17039i) q^{7} +5.90753i q^{8} +(1.12000 - 1.93990i) q^{9} +(-4.39076 - 7.60502i) q^{10} +(-2.90796 + 1.67891i) q^{11} -3.78807 q^{12} +(3.60052 + 0.190323i) q^{13} +5.89638 q^{14} +(2.63199 - 1.51958i) q^{15} +(-3.09524 - 5.36111i) q^{16} +(-3.20334 + 5.54835i) q^{17} +5.64250i q^{18} +(-2.21181 - 1.27699i) q^{19} +(13.1186 + 7.57404i) q^{20} +2.04065i q^{21} +(4.22913 - 7.32507i) q^{22} +(-0.899656 - 1.55825i) q^{23} +(4.46009 - 2.57503i) q^{24} -7.15326 q^{25} +(-8.09423 + 4.11962i) q^{26} -4.56812 q^{27} +(-8.80854 + 5.08562i) q^{28} +(-4.28958 - 7.42978i) q^{29} +(-3.82777 + 6.62990i) q^{30} -1.00000i q^{31} +(3.27233 + 1.88928i) q^{32} +(2.53510 + 1.46364i) q^{33} -16.1383i q^{34} +(4.08017 - 7.06707i) q^{35} +(-4.86665 - 8.42928i) q^{36} +(-7.27475 + 4.20008i) q^{37} +6.43339 q^{38} +(-1.42574 - 2.80129i) q^{39} -20.5946 q^{40} +(5.15694 - 2.97736i) q^{41} +(-2.57017 - 4.45166i) q^{42} +(1.63471 - 2.83139i) q^{43} +14.5905i q^{44} +(6.76278 + 3.90449i) q^{45} +(3.92519 + 2.26621i) q^{46} -5.36535i q^{47} +(-2.69836 + 4.67370i) q^{48} +(-0.760356 - 1.31697i) q^{49} +(15.6048 - 9.00943i) q^{50} +5.58522 q^{51} +(8.53873 - 13.1355i) q^{52} -9.35639 q^{53} +(9.96533 - 5.75349i) q^{54} +(-5.85294 - 10.1376i) q^{55} +(6.91414 - 11.9756i) q^{56} +2.22650i q^{57} +(18.7154 + 10.8053i) q^{58} +(-11.1821 - 6.45596i) q^{59} -13.2058i q^{60} +(-1.79696 + 3.11243i) q^{61} +(1.25949 + 2.18149i) q^{62} +(-4.54089 + 2.62168i) q^{63} +2.86286 q^{64} +(-0.663494 + 12.5520i) q^{65} -7.37373 q^{66} +(-0.992706 + 0.573139i) q^{67} +(13.9192 + 24.1088i) q^{68} +(-0.784301 + 1.35845i) q^{69} +20.5557i q^{70} +(-8.59612 - 4.96297i) q^{71} +(11.4600 + 6.61644i) q^{72} +5.97373i q^{73} +(10.5799 - 18.3249i) q^{74} +(3.11803 + 5.40059i) q^{75} +(-9.61078 + 5.54879i) q^{76} +7.85995 q^{77} +(6.63843 + 4.31530i) q^{78} +1.26210 q^{79} +(18.6896 - 10.7905i) q^{80} +(-1.36881 - 2.37084i) q^{81} +(-7.49989 + 12.9902i) q^{82} +7.88496i q^{83} +(7.67910 + 4.43353i) q^{84} +(-19.3424 - 11.1673i) q^{85} +8.23555i q^{86} +(-3.73957 + 6.47712i) q^{87} +(-9.91822 - 17.1789i) q^{88} +(8.94186 - 5.16258i) q^{89} -19.6706 q^{90} +(-7.07617 - 4.59985i) q^{91} -7.81840 q^{92} +(-0.754983 + 0.435889i) q^{93} +(6.75759 + 11.7045i) q^{94} +(4.45177 - 7.71069i) q^{95} -3.29407i q^{96} +(-0.0440012 - 0.0254041i) q^{97} +(3.31742 + 1.91531i) q^{98} +7.52153i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 32 q^{4} - 34 q^{9}+O(q^{10}) \) 68 * q + 32 * q^4 - 34 * q^9	\( 68 q + 32 q^{4} - 34 q^{9} + 8 q^{10} - 12 q^{11} - 16 q^{12} + 6 q^{13} - 8 q^{14} - 36 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 48 q^{24} - 72 q^{25} - 12 q^{27} - 6 q^{28} + 32 q^{30} + 6 q^{33} + 30 q^{35} + 40 q^{36} - 42 q^{37} - 36 q^{38} - 14 q^{39} + 8 q^{40} + 18 q^{41} - 16 q^{42} + 12 q^{43} + 60 q^{45} + 30 q^{46} - 46 q^{48} + 22 q^{49} + 56 q^{51} + 20 q^{53} - 114 q^{54} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 6 q^{59} + 6 q^{61} - 8 q^{62} - 30 q^{63} + 24 q^{64} + 24 q^{65} + 8 q^{66} - 48 q^{67} + 58 q^{68} - 28 q^{69} - 30 q^{71} + 72 q^{72} + 8 q^{74} - 4 q^{75} - 12 q^{76} - 20 q^{77} + 26 q^{78} + 16 q^{79} + 42 q^{80} - 58 q^{81} - 42 q^{82} - 72 q^{84} + 30 q^{85} - 20 q^{87} + 64 q^{88} + 18 q^{89} + 52 q^{90} - 22 q^{91} + 48 q^{92} + 8 q^{94} - 32 q^{95} - 168 q^{98}+O(q^{100}) \) 68 * q + 32 * q^4 - 34 * q^9 + 8 * q^10 - 12 * q^11 - 16 * q^12 + 6 * q^13 - 8 * q^14 - 36 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 48 * q^24 - 72 * q^25 - 12 * q^27 - 6 * q^28 + 32 * q^30 + 6 * q^33 + 30 * q^35 + 40 * q^36 - 42 * q^37 - 36 * q^38 - 14 * q^39 + 8 * q^40 + 18 * q^41 - 16 * q^42 + 12 * q^43 + 60 * q^45 + 30 * q^46 - 46 * q^48 + 22 * q^49 + 56 * q^51 + 20 * q^53 - 114 * q^54 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 6 * q^59 + 6 * q^61 - 8 * q^62 - 30 * q^63 + 24 * q^64 + 24 * q^65 + 8 * q^66 - 48 * q^67 + 58 * q^68 - 28 * q^69 - 30 * q^71 + 72 * q^72 + 8 * q^74 - 4 * q^75 - 12 * q^76 - 20 * q^77 + 26 * q^78 + 16 * q^79 + 42 * q^80 - 58 * q^81 - 42 * q^82 - 72 * q^84 + 30 * q^85 - 20 * q^87 + 64 * q^88 + 18 * q^89 + 52 * q^90 - 22 * q^91 + 48 * q^92 + 8 * q^94 - 32 * q^95 - 168 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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