LMFDB - Embedded newform 930.2.y.b.29.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(29,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("930.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.y (of order $10$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.10
Character	$\chi$	$=$	930.29
Dual form			930.2.y.b.449.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-1.07416 - 1.35874i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.07804 + 0.825684i) q^{5} +(-0.0703609 - 1.73062i) q^{6} +(-1.53398 + 0.498419i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.692375 + 2.91901i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-1.07416 - 1.35874i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.07804 + 0.825684i) q^{5} +(-0.0703609 - 1.73062i) q^{6} +(-1.53398 + 0.498419i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.692375 + 2.91901i) q^{9} +(1.19584 + 1.88943i) q^{10} +(-1.91843 - 5.90433i) q^{11} +(0.960310 - 1.44146i) q^{12} +(3.99946 - 2.90578i) q^{13} +(-1.53398 - 0.498419i) q^{14} +(-1.11025 - 3.71044i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(5.69242 + 1.84958i) q^{17} +(-2.27589 + 1.95456i) q^{18} +(0.0874977 + 0.0635708i) q^{19} +(-0.143123 + 2.23148i) q^{20} +(2.32495 + 1.54890i) q^{21} +(1.91843 - 5.90433i) q^{22} +(3.22177 + 1.04682i) q^{23} +(1.62418 - 0.601709i) q^{24} +(3.63649 + 3.43161i) q^{25} +4.94361 q^{26} +(4.70991 - 2.19471i) q^{27} +(-0.948049 - 1.30488i) q^{28} +(4.58615 + 3.33203i) q^{29} +(1.28273 - 3.65439i) q^{30} +(-2.70260 - 4.86785i) q^{31} -1.00000 q^{32} +(-5.96178 + 8.94884i) q^{33} +(3.51811 + 4.84226i) q^{34} +(-3.59920 - 0.230845i) q^{35} +(-2.99010 + 0.243536i) q^{36} -7.69830 q^{37} +(0.0334212 + 0.102860i) q^{38} +(-8.24426 - 2.31299i) q^{39} +(-1.42742 + 1.72118i) q^{40} +(3.33946 - 4.59637i) q^{41} +(0.970506 + 2.61966i) q^{42} +(7.35446 + 5.34333i) q^{43} +(5.02252 - 3.64908i) q^{44} +(-3.84896 + 5.49413i) q^{45} +(1.99116 + 2.74060i) q^{46} +(9.33830 - 6.78467i) q^{47} +(1.66766 + 0.467874i) q^{48} +(-3.55846 + 2.58537i) q^{49} +(0.924936 + 4.91370i) q^{50} +(-3.60144 - 9.72128i) q^{51} +(3.99946 + 2.90578i) q^{52} +(3.86974 + 1.25735i) q^{53} +(5.10042 + 0.992854i) q^{54} +(0.888532 - 13.8534i) q^{55} -1.61292i q^{56} +(-0.00760975 - 0.187172i) q^{57} +(1.75175 + 5.39134i) q^{58} +(-0.241063 - 0.331795i) q^{59} +(3.18575 - 2.20250i) q^{60} -3.66714i q^{61} +(0.674798 - 5.52672i) q^{62} +(-0.392804 - 4.82278i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(10.7103 - 2.73603i) q^{65} +(-10.0832 + 3.73551i) q^{66} +12.9886i q^{67} +5.98536i q^{68} +(-2.03833 - 5.50201i) q^{69} +(-2.77612 - 2.30231i) q^{70} +(-1.72411 - 0.560197i) q^{71} +(-2.56219 - 1.56051i) q^{72} +(-5.11682 - 15.7479i) q^{73} +(-6.22805 - 4.52495i) q^{74} +(0.756516 - 8.62715i) q^{75} +(-0.0334212 + 0.102860i) q^{76} +(5.88566 + 8.10091i) q^{77} +(-5.31021 - 6.71710i) q^{78} +(-4.75321 - 1.54441i) q^{79} +(-2.16649 + 0.553448i) q^{80} +(-8.04123 - 4.04210i) q^{81} +(5.40335 - 1.75566i) q^{82} +(-6.27926 + 8.64265i) q^{83} +(-0.754642 + 2.68980i) q^{84} +(10.3019 + 8.54363i) q^{85} +(2.80916 + 8.64569i) q^{86} +(-0.398861 - 9.81053i) q^{87} +6.20818 q^{88} +(0.0659604 + 0.203005i) q^{89} +(-6.34325 + 2.18248i) q^{90} +(-4.68678 + 6.45080i) q^{91} +3.38757i q^{92} +(-3.71114 + 8.90098i) q^{93} +11.5428 q^{94} +(0.129334 + 0.204348i) q^{95} +(1.07416 + 1.35874i) q^{96} +(13.8908 - 4.51339i) q^{97} -4.39850 q^{98} +(18.5631 - 1.51192i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9}+O(q^{10}) $ 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9	$ 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9} + 2 q^{10} - 35 q^{15} - 32 q^{16} - 6 q^{18} - 8 q^{19} + 3 q^{20} + 20 q^{23} - 10 q^{25} - 48 q^{31} - 128 q^{32} + 8 q^{33} + 10 q^{34} - 16 q^{35} - 4 q^{36} - 12 q^{38} + 4 q^{39} - 3 q^{40} + 5 q^{45} + 10 q^{46} - 6 q^{47} + 46 q^{49} + 5 q^{50} + 34 q^{51} + 20 q^{53} + 35 q^{60} + 8 q^{62} - 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} - 6 q^{72} + 5 q^{75} + 12 q^{76} - 50 q^{77} - 4 q^{78} - 10 q^{79} - 2 q^{80} - 24 q^{81} + 40 q^{83} - 30 q^{85} + 4 q^{87} - 5 q^{90} + 20 q^{91} + 26 q^{93} - 4 q^{94} + 26 q^{95} + 124 q^{98}+O(q^{100}) $ 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9 + 2 * q^10 - 35 * q^15 - 32 * q^16 - 6 * q^18 - 8 * q^19 + 3 * q^20 + 20 * q^23 - 10 * q^25 - 48 * q^31 - 128 * q^32 + 8 * q^33 + 10 * q^34 - 16 * q^35 - 4 * q^36 - 12 * q^38 + 4 * q^39 - 3 * q^40 + 5 * q^45 + 10 * q^46 - 6 * q^47 + 46 * q^49 + 5 * q^50 + 34 * q^51 + 20 * q^53 + 35 * q^60 + 8 * q^62 - 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 - 6 * q^72 + 5 * q^75 + 12 * q^76 - 50 * q^77 - 4 * q^78 - 10 * q^79 - 2 * q^80 - 24 * q^81 + 40 * q^83 - 30 * q^85 + 4 * q^87 - 5 * q^90 + 20 * q^91 + 26 * q^93 - 4 * q^94 + 26 * q^95 + 124 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−1.07416	−	1.35874i	−0.620165	−	0.784472i
$3$	−1.07416	−	1.35874i	−0.620165	−	0.784472i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	2.07804	+	0.825684i	0.929327	+	0.369257i
$5$	2.07804	+	0.825684i	0.929327	+	0.369257i
$6$	−0.0703609	−	1.73062i	−0.0287247	−	0.706523i
$7$	−1.53398	+	0.498419i	−0.579788	+	0.188385i	−0.584206	−	0.811606i	$-0.698594\pi$
$7$	−1.53398	+	0.498419i	−0.579788	+	0.188385i	0.00441746	+	0.999990i	$0.498594\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−0.692375	+	2.91901i	−0.230792	+	0.973003i
$10$	1.19584	+	1.88943i	0.378159	+	0.597491i
$11$	−1.91843	−	5.90433i	−0.578429	−	1.78022i	−0.624193	−	0.781270i	$-0.714572\pi$
$11$	−1.91843	−	5.90433i	−0.578429	−	1.78022i	0.0457639	−	0.998952i	$-0.485428\pi$
$12$	0.960310	−	1.44146i	0.277218	−	0.416113i
$13$	3.99946	−	2.90578i	1.10925	−	0.805918i	0.126706	−	0.991940i	$-0.459560\pi$
$13$	3.99946	−	2.90578i	1.10925	−	0.805918i	0.982546	+	0.186022i	$0.0595596\pi$
$14$	−1.53398	−	0.498419i	−0.409972	−	0.133208i
$15$	−1.11025	−	3.71044i	−0.286664	−	0.958031i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	5.69242	+	1.84958i	1.38061	+	0.448589i	0.902871	−	0.429911i	$-0.141455\pi$
$17$	5.69242	+	1.84958i	1.38061	+	0.448589i	0.477742	+	0.878500i	$0.341455\pi$
$18$	−2.27589	+	1.95456i	−0.536433	+	0.460694i
$19$	0.0874977	+	0.0635708i	0.0200734	+	0.0145841i	0.597777	−	0.801663i	$-0.296051\pi$
$19$	0.0874977	+	0.0635708i	0.0200734	+	0.0145841i	−0.577703	+	0.816247i	$0.696051\pi$
$20$	−0.143123	+	2.23148i	−0.0320032	+	0.498975i
$21$	2.32495	+	1.54890i	0.507347	+	0.337998i
$22$	1.91843	−	5.90433i	0.409011	−	1.25881i
$23$	3.22177	+	1.04682i	0.671785	+	0.218276i	0.624995	−	0.780628i	$-0.285101\pi$
$23$	3.22177	+	1.04682i	0.671785	+	0.218276i	0.0467899	+	0.998905i	$0.485101\pi$
$24$	1.62418	−	0.601709i	0.331533	−	0.122823i
$25$	3.63649	+	3.43161i	0.727298	+	0.686321i
$26$	4.94361			0.969521
$27$	4.70991	−	2.19471i	0.906422	−	0.422373i
$28$	−0.948049	−	1.30488i	−0.179164	−	0.246599i
$29$	4.58615	+	3.33203i	0.851626	+	0.618743i	0.925594	−	0.378518i	$-0.123566\pi$
$29$	4.58615	+	3.33203i	0.851626	+	0.618743i	−0.0739678	+	0.997261i	$0.523566\pi$
$30$	1.28273	−	3.65439i	0.234194	−	0.667198i
$31$	−2.70260	−	4.86785i	−0.485402	−	0.874291i
$31$	−2.70260	−	4.86785i	−0.485402	−	0.874291i
$32$	−1.00000			−0.176777
$33$	−5.96178	+	8.94884i	−1.03781	+	1.55779i
$34$	3.51811	+	4.84226i	0.603350	+	0.830440i
$35$	−3.59920	−	0.230845i	−0.608375	−	0.0390200i
$36$	−2.99010	+	0.243536i	−0.498350	+	0.0405894i
$37$	−7.69830			−1.26559			−0.632796	−	0.774318i	$-0.718093\pi$
$37$	−7.69830			−1.26559			−0.632796	+	0.774318i	$0.718093\pi$
$38$	0.0334212	+	0.102860i	0.00542163	+	0.0166861i
$39$	−8.24426	−	2.31299i	−1.32014	−	0.370374i
$40$	−1.42742	+	1.72118i	−0.225695	+	0.272143i
$41$	3.33946	−	4.59637i	0.521536	−	0.717832i	−0.464276	−	0.885691i	$-0.653685\pi$
$41$	3.33946	−	4.59637i	0.521536	−	0.717832i	0.985811	+	0.167859i	$0.0536853\pi$
$42$	0.970506	+	2.61966i	0.149752	+	0.404223i
$43$	7.35446	+	5.34333i	1.12155	+	0.814850i	0.984443	−	0.175707i	$-0.0562210\pi$
$43$	7.35446	+	5.34333i	1.12155	+	0.814850i	0.137103	+	0.990557i	$0.456221\pi$
$44$	5.02252	−	3.64908i	0.757174	−	0.550119i
$45$	−3.84896	+	5.49413i	−0.573769	+	0.819017i
$46$	1.99116	+	2.74060i	0.293581	+	0.404079i
$47$	9.33830	−	6.78467i	1.36213	−	0.989647i	0.363825	−	0.931467i	$-0.381470\pi$
$47$	9.33830	−	6.78467i	1.36213	−	0.989647i	0.998306	−	0.0581794i	$-0.0185295\pi$
$48$	1.66766	+	0.467874i	0.240706	+	0.0675318i
$49$	−3.55846	+	2.58537i	−0.508351	+	0.369339i
$50$	0.924936	+	4.91370i	0.130806	+	0.694903i
$51$	−3.60144	−	9.72128i	−0.504303	−	1.36125i
$52$	3.99946	+	2.90578i	0.554626	+	0.402959i
$53$	3.86974	+	1.25735i	0.531549	+	0.172711i	0.562480	−	0.826811i	$-0.309847\pi$
$53$	3.86974	+	1.25735i	0.531549	+	0.172711i	−0.0309309	+	0.999522i	$0.509847\pi$
$54$	5.10042	+	0.992854i	0.694079	+	0.135110i
$55$	0.888532	−	13.8534i	0.119810	−	1.86800i
$56$		−	1.61292i		−	0.215535i
$57$	−0.00760975	−	0.187172i	−0.00100794	−	0.0247915i
$58$	1.75175	+	5.39134i	0.230016	+	0.707917i
$59$	−0.241063	−	0.331795i	−0.0313838	−	0.0431961i	0.793037	−	0.609174i	$-0.208499\pi$
$59$	−0.241063	−	0.331795i	−0.0313838	−	0.0431961i	−0.824421	+	0.565978i	$0.808499\pi$
$60$	3.18575	−	2.20250i	0.411279	−	0.284341i
$61$		−	3.66714i		−	0.469529i	−0.972052	−	0.234765i	$-0.924568\pi$
$61$		−	3.66714i		−	0.469529i	0.972052	−	0.234765i	$-0.0754319\pi$
$62$	0.674798	−	5.52672i	0.0856994	−	0.701894i
$63$	−0.392804	−	4.82278i	−0.0494886	−	0.607613i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	10.7103	−	2.73603i	1.32845	−	0.339363i
$66$	−10.0832	+	3.73551i	−1.24115	+	0.459810i
$67$			12.9886i			1.58681i	0.608691	+	0.793407i	$0.291695\pi$
$67$			12.9886i			1.58681i	−0.608691	+	0.793407i	$0.708305\pi$
$68$			5.98536i			0.725831i
$69$	−2.03833	−	5.50201i	−0.245386	−	0.662364i
$70$	−2.77612	−	2.30231i	−0.331810	−	0.275179i
$71$	−1.72411	−	0.560197i	−0.204614	−	0.0664832i	0.204917	−	0.978779i	$-0.434308\pi$
$71$	−1.72411	−	0.560197i	−0.204614	−	0.0664832i	−0.409531	+	0.912296i	$0.634308\pi$
$72$	−2.56219	−	1.56051i	−0.301957	−	0.183908i
$73$	−5.11682	−	15.7479i	−0.598878	−	1.84316i	−0.534388	−	0.845239i	$-0.679458\pi$
$73$	−5.11682	−	15.7479i	−0.598878	−	1.84316i	−0.0644904	−	0.997918i	$-0.520542\pi$
$74$	−6.22805	−	4.52495i	−0.723997	−	0.526014i
$75$	0.756516	−	8.62715i	0.0873549	−	0.996177i
$76$	−0.0334212	+	0.102860i	−0.00383367	+	0.0117988i
$77$	5.88566	+	8.10091i	0.670733	+	0.923185i
$78$	−5.31021	−	6.71710i	−0.601263	−	0.760562i
$79$	−4.75321	−	1.54441i	−0.534778	−	0.173760i	0.0291637	−	0.999575i	$-0.490716\pi$
$79$	−4.75321	−	1.54441i	−0.534778	−	0.173760i	−0.563941	+	0.825815i	$0.690716\pi$
$80$	−2.16649	+	0.553448i	−0.242221	+	0.0618774i
$81$	−8.04123	−	4.04210i	−0.893471	−	0.449122i
$82$	5.40335	−	1.75566i	0.596701	−	0.193880i
$83$	−6.27926	+	8.64265i	−0.689238	+	0.948655i	−0.999998	−	0.00183366i	$-0.999416\pi$
$83$	−6.27926	+	8.64265i	−0.689238	+	0.948655i	0.310760	+	0.950488i	$0.399416\pi$
$84$	−0.754642	+	2.68980i	−0.0823382	+	0.293481i
$85$	10.3019	+	8.54363i	1.11740	+	0.926687i
$86$	2.80916	+	8.64569i	0.302919	+	0.932289i
$87$	−0.398861	−	9.81053i	−0.0427624	−	1.05180i
$88$	6.20818			0.661794
$89$	0.0659604	+	0.203005i	0.00699179	+	0.0215185i	0.954492	−	0.298238i	$-0.0963989\pi$
$89$	0.0659604	+	0.203005i	0.00699179	+	0.0215185i	−0.947500	+	0.319756i	$0.896399\pi$
$90$	−6.34325	+	2.18248i	−0.668637	+	0.230054i
$91$	−4.68678	+	6.45080i	−0.491308	+	0.676228i
$92$			3.38757i			0.353178i
$93$	−3.71114	+	8.90098i	−0.384828	+	0.922988i
$94$	11.5428			1.19055
$95$	0.129334	+	0.204348i	0.0132694	+	0.0209657i
$96$	1.07416	+	1.35874i	0.109631	+	0.138676i
$97$	13.8908	−	4.51339i	1.41040	−	0.458266i	0.497859	−	0.867258i	$-0.334120\pi$
$97$	13.8908	−	4.51339i	1.41040	−	0.458266i	0.912538	+	0.408992i	$0.134120\pi$
$98$	−4.39850			−0.444315
$99$	18.5631	−	1.51192i	1.86566	−	0.151953i
$100$	−2.13991	+	4.51893i	−0.213991	+	0.451893i
$101$	−3.01823	−	0.980681i	−0.300325	−	0.0975814i	0.154979	−	0.987918i	$-0.450469\pi$
$101$	−3.01823	−	0.980681i	−0.300325	−	0.0975814i	−0.455303	+	0.890336i	$0.650469\pi$
$102$	2.80039	−	9.98155i	0.277280	−	0.988321i
$103$	−5.93202	+	8.16473i	−0.584500	+	0.804495i	−0.994180	−	0.107735i	$-0.965640\pi$
$103$	−5.93202	+	8.16473i	−0.584500	+	0.804495i	0.409680	+	0.912229i	$0.365640\pi$
$104$	1.52766	+	4.70165i	0.149799	+	0.461035i
$105$	3.55244	+	5.13835i	0.346683	+	0.501452i
$106$	2.39163	+	3.29180i	0.232296	+	0.319727i
$107$	1.82739	−	5.62413i	0.176661	−	0.543705i	−0.823045	−	0.567976i	$-0.807726\pi$
$107$	1.82739	−	5.62413i	0.176661	−	0.543705i	0.999705	+	0.0242711i	$0.00772649\pi$
$108$	3.54274	+	3.80118i	0.340900	+	0.365769i
$109$	−4.48963	+	3.26191i	−0.430029	+	0.312434i	−0.781660	−	0.623704i	$-0.785627\pi$
$109$	−4.48963	+	3.26191i	−0.430029	+	0.312434i	0.351632	+	0.936138i	$0.385627\pi$
$110$	8.86169	−	10.6854i	0.844929	−	1.01881i
$111$	8.26918	+	10.4600i	0.784876	+	0.992821i
$112$	0.948049	−	1.30488i	0.0895822	−	0.123299i
$113$	−3.73185	−	11.4854i	−0.351062	−	1.08046i	−0.958258	−	0.285906i	$-0.907705\pi$
$113$	−3.73185	−	11.4854i	−0.351062	−	1.08046i	0.607195	−	0.794553i	$-0.292295\pi$
$114$	0.103861	−	0.155898i	0.00972743	−	0.0146012i
$115$	5.83062	+	4.83549i	0.543708	+	0.450912i
$116$	−1.75175	+	5.39134i	−0.162646	+	0.500573i
$117$	5.71287	+	13.6864i	0.528155	+	1.26530i
$118$		−	0.410121i		−	0.0377547i
$119$	−9.65389			−0.884971
$120$	3.87192	+	0.0906821i	0.353456	+	0.00827811i
$121$	−22.2815	+	16.1885i	−2.02559	+	1.47168i
$122$	2.15549	−	2.96678i	0.195149	−	0.268600i
$123$	−9.83239	+	0.399750i	−0.886557	+	0.0360443i
$124$	3.79445	−	4.07458i	0.340752	−	0.365908i
$125$	4.72335	+	10.1336i	0.422469	+	0.906377i
$126$	2.51698	−	4.13260i	0.224230	−	0.368161i
$127$	−9.60902	+	6.98136i	−0.852663	+	0.619496i	−0.925879	−	0.377820i	$-0.876674\pi$
$127$	−9.60902	+	6.98136i	−0.852663	+	0.619496i	0.0732161	+	0.997316i	$0.476674\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−0.639624	−	15.7324i	−0.0563158	−	1.38516i
$130$	10.2730	+	4.08186i	0.901003	+	0.358003i
$131$	−19.5994	+	6.36822i	−1.71240	+	0.556394i	−0.990731	−	0.135839i	$-0.956627\pi$
$131$	−19.5994	+	6.36822i	−1.71240	+	0.556394i	−0.721674	+	0.692233i	$0.756627\pi$
$132$	−10.3531	−	2.90465i	−0.901125	−	0.252817i
$133$	−0.165904	−	0.0539056i	−0.0143857	−	0.00467420i
$134$	−7.63453	+	10.5080i	−0.659523	+	0.907755i
$135$	11.5995	−	0.671804i	0.998327	−	0.0578197i
$136$	−3.51811	+	4.84226i	−0.301675	+	0.415220i
$137$	−5.54543	−	7.63263i	−0.473778	−	0.652099i	0.503516	−	0.863986i	$-0.332039\pi$
$137$	−5.54543	−	7.63263i	−0.473778	−	0.652099i	−0.977294	+	0.211886i	$0.932039\pi$
$138$	1.58496	−	5.64932i	0.134920	−	0.480902i
$139$	−0.847249	−	1.16614i	−0.0718627	−	0.0989106i	0.771573	−	0.636141i	$-0.219470\pi$
$139$	−0.847249	−	1.16614i	−0.0718627	−	0.0989106i	−0.843435	+	0.537231i	$0.819470\pi$
$140$	−0.892666	−	3.49438i	−0.0754441	−	0.295329i
$141$	−19.2494	−	5.40057i	−1.62110	−	0.454810i
$142$	−1.06556	−	1.46662i	−0.0894197	−	0.123076i
$143$	−24.8294	−	18.0396i	−2.07634	−	1.50855i
$144$	−1.15561	−	2.76850i	−0.0963007	−	0.230708i
$145$	6.77899	+	10.7108i	0.562964	+	0.889483i
$146$	5.11682	−	15.7479i	0.423471	−	1.30331i
$147$	7.33520	+	2.05794i	0.604997	+	0.169736i
$148$	−2.37891	−	7.32152i	−0.195545	−	0.601825i
$149$		−	1.46137i		−	0.119720i	−0.998207	−	0.0598599i	$-0.980935\pi$
$149$		−	1.46137i		−	0.119720i	0.998207	−	0.0598599i	$-0.0190654\pi$
$150$	5.68294	−	6.53484i	0.464010	−	0.533568i
$151$	2.39413	−	0.777901i	0.194832	−	0.0633047i	−0.209976	−	0.977707i	$-0.567339\pi$
$151$	2.39413	−	0.777901i	0.194832	−	0.0633047i	0.404808	+	0.914402i	$0.367339\pi$
$152$	−0.0874977	+	0.0635708i	−0.00709700	+	0.00515627i
$153$	−9.34022	+	15.3356i	−0.755112	+	1.23981i
$154$			10.0133i			0.806893i
$155$	−1.59681	−	12.3471i	−0.128259	−	0.991741i
$156$	−0.347837	−	8.55551i	−0.0278492	−	0.684989i
$157$	0.813338	−	1.11946i	0.0649115	−	0.0893430i	−0.775327	−	0.631560i	$-0.782415\pi$
$157$	0.813338	−	1.11946i	0.0649115	−	0.0893430i	0.840238	+	0.542217i	$0.182415\pi$
$158$	−2.93764	−	4.04332i	−0.233706	−	0.321669i
$159$	−2.44828	−	6.60858i	−0.194161	−	0.524095i
$160$	−2.07804	−	0.825684i	−0.164283	−	0.0652760i
$161$	−5.46387			−0.430613
$162$	−4.12961	−	7.99664i	−0.324453	−	0.628276i
$163$	20.5098	+	6.66403i	1.60645	+	0.521967i	0.968691	−	0.248269i	$-0.0798618\pi$
$163$	20.5098	+	6.66403i	1.60645	+	0.521967i	0.637758	+	0.770236i	$0.279862\pi$
$164$	5.40335	+	1.75566i	0.421931	+	0.137094i
$165$	−19.7777	+	13.6735i	−1.53969	+	1.06448i
$166$	−10.1601	+	3.30120i	−0.788573	+	0.256223i
$167$	0.411093	−	0.565821i	0.0318113	−	0.0437845i	−0.792815	−	0.609462i	$-0.791385\pi$
$167$	0.411093	−	0.565821i	0.0318113	−	0.0437845i	0.824626	+	0.565678i	$0.191385\pi$
$168$	−2.19154	+	1.73253i	−0.169081	+	0.133667i
$169$	3.53493	−	10.8794i	0.271917	−	0.836876i
$170$	3.31259	+	12.9672i	0.254064	+	0.994542i
$171$	−0.246145	+	0.211392i	−0.0188232	+	0.0161655i
$172$	−2.80916	+	8.64569i	−0.214196	+	0.659228i
$173$	−8.79848	+	6.39247i	−0.668936	+	0.486010i	−0.869669	−	0.493636i	$-0.835668\pi$
$173$	−8.79848	+	6.39247i	−0.668936	+	0.486010i	0.200733	+	0.979646i	$0.435668\pi$
$174$	5.44380	−	8.17133i	0.412693	−	0.619467i
$175$	−7.28867	−	3.45151i	−0.550971	−	0.260909i
$176$	5.02252	+	3.64908i	0.378587	+	0.275059i
$177$	−0.191885	+	0.683943i	−0.0144230	+	0.0514083i
$178$	−0.0659604	+	0.203005i	−0.00494394	+	0.0152159i
$179$	2.46376	+	7.58268i	0.184150	+	0.566756i	0.999933	−	0.0116028i	$-0.00369335\pi$
$179$	2.46376	+	7.58268i	0.184150	+	0.566756i	−0.815782	+	0.578359i	$0.803693\pi$
$180$	−6.41463	−	1.96280i	−0.478118	−	0.146298i
$181$			7.87271i			0.585174i	0.956239	+	0.292587i	$0.0945160\pi$
$181$			7.87271i			0.585174i	−0.956239	+	0.292587i	$0.905484\pi$
$182$	−7.58337	+	2.46399i	−0.562117	+	0.182643i
$183$	−4.98271	+	3.93908i	−0.368332	+	0.291185i
$184$	−1.99116	+	2.74060i	−0.146790	+	0.202040i
$185$	−15.9974	−	6.35636i	−1.17615	−	0.467329i
$186$	−8.23424	+	5.01969i	−0.603764	+	0.368061i
$187$		−	37.1582i		−	2.71728i
$188$	9.33830	+	6.78467i	0.681066	+	0.494823i
$189$	−6.13100	+	5.71414i	−0.445964	+	0.415643i
$190$	−0.0154792	+	0.241342i	−0.00112298	+	0.0175088i
$191$			9.55241i			0.691188i	0.938384	+	0.345594i	$0.112323\pi$
$191$			9.55241i			0.691188i	−0.938384	+	0.345594i	$0.887677\pi$
$192$	0.0703609	+	1.73062i	0.00507786	+	0.124897i
$193$	−12.3482	+	4.01216i	−0.888840	+	0.288802i	−0.717623	−	0.696432i	$-0.754770\pi$
$193$	−12.3482	+	4.01216i	−0.888840	+	0.288802i	−0.171217	+	0.985233i	$0.554770\pi$
$194$	13.8908	+	4.51339i	0.997301	+	0.324043i
$195$	−15.2221	−	11.6136i	−1.09008	−	0.831669i
$196$	−3.55846	−	2.58537i	−0.254176	−	0.184669i
$197$	−19.8631	+	6.45390i	−1.41519	+	0.459822i	−0.914069	−	0.405558i	$-0.867077\pi$
$197$	−19.8631	+	6.45390i	−1.41519	+	0.459822i	−0.501116	+	0.865380i	$0.667077\pi$
$198$	15.9065	+	9.68793i	1.13043	+	0.688491i
$199$	5.02054	+	6.91018i	0.355896	+	0.489849i	0.949000	−	0.315277i	$-0.102097\pi$
$199$	5.02054	+	6.91018i	0.355896	+	0.489849i	−0.593103	+	0.805126i	$0.702097\pi$
$200$	−4.38739	+	2.39808i	−0.310235	+	0.169570i
$201$	17.6482	−	13.9518i	1.24481	−	0.984086i
$202$	−1.86537	−	2.56746i	−0.131247	−	0.180646i
$203$	−8.69578	−	2.82543i	−0.610324	−	0.198306i
$204$	8.13258	−	6.42921i	0.569394	−	0.450135i
$205$	10.7347	−	6.79410i	0.749742	−	0.474520i
$206$	−9.59822	+	3.11865i	−0.668739	+	0.217287i
$207$	−5.28634	+	8.67959i	−0.367426	+	0.603273i
$208$	−1.52766	+	4.70165i	−0.105924	+	0.326001i
$209$	0.207485	−	0.638572i	0.0143520	−	0.0441709i
$210$	−0.146263	+	6.24509i	−0.0100931	+	0.430952i
$211$	−16.8087			−1.15716			−0.578579	−	0.815626i	$-0.696393\pi$
$211$	−16.8087			−1.15716			−0.578579	+	0.815626i	$0.696393\pi$
$212$			4.06888i			0.279452i
$213$	1.09080	+	2.94437i	0.0747403	+	0.201745i
$214$	4.78417	−	3.47590i	0.327039	−	0.237608i
$215$	10.8710	+	17.1761i	0.741393	+	1.17140i
$216$	0.631855	+	5.15759i	0.0429923	+	0.350930i
$217$	6.57195	+	6.12013i	0.446133	+	0.415462i
$218$	−5.54949			−0.375859
$219$	−15.9012	+	23.8682i	−1.07450	+	1.61286i
$220$	13.4500	−	3.43591i	0.906798	−	0.231649i
$221$	28.1411	−	9.14359i	1.89297	−	0.615064i
$222$	0.541659	+	13.3228i	0.0363538	+	0.894170i
$223$	−8.14672			−0.545545			−0.272772	−	0.962079i	$-0.587941\pi$
$223$	−8.14672			−0.545545			−0.272772	+	0.962079i	$0.587941\pi$
$224$	1.53398	−	0.498419i	0.102493	−	0.0333020i
$225$	−12.5347	+	8.23900i	−0.835647	+	0.549266i
$226$	3.73185	−	11.4854i	0.248239	−	0.764000i
$227$	2.34033	+	1.70035i	0.155333	+	0.112856i	0.662737	−	0.748852i	$-0.269395\pi$
$227$	2.34033	+	1.70035i	0.155333	+	0.112856i	−0.507404	+	0.861708i	$0.669395\pi$
$228$	0.175660	−	0.0650767i	0.0116333	−	0.00430981i
$229$	−10.5629	+	14.5386i	−0.698016	+	0.960737i	0.301956	+	0.953322i	$0.402360\pi$
$229$	−10.5629	+	14.5386i	−0.698016	+	0.960737i	−0.999973	+	0.00741539i	$0.997640\pi$
$230$	1.87484	+	7.33915i	0.123624	+	0.483929i
$231$	4.68495	−	16.6988i	0.308247	−	1.09870i
$232$	−4.58615	+	3.33203i	−0.301095	+	0.218759i
$233$	14.4296	−	10.4837i	0.945313	−	0.686810i	−0.00438080	−	0.999990i	$-0.501394\pi$
$233$	14.4296	−	10.4837i	0.945313	−	0.686810i	0.949694	+	0.313180i	$0.101394\pi$
$234$	−3.42283	+	14.4304i	−0.223757	+	0.943347i
$235$	25.0074	−	6.38833i	1.63130	−	0.416729i
$236$	0.241063	−	0.331795i	0.0156919	−	0.0215980i
$237$	3.00723	+	8.11734i	0.195341	+	0.527278i
$238$	−7.81016	−	5.67441i	−0.506258	−	0.367818i
$239$	0.968746	−	2.98149i	0.0626630	−	0.192857i	−0.914824	−	0.403853i	$-0.867671\pi$
$239$	0.968746	−	2.98149i	0.0626630	−	0.192857i	0.977487	+	0.210996i	$0.0676707\pi$
$240$	3.07915	+	2.34922i	0.198758	+	0.151642i
$241$	5.37755	−	1.74727i	0.346398	−	0.112552i	−0.130650	−	0.991428i	$-0.541707\pi$
$241$	5.37755	−	1.74727i	0.346398	−	0.112552i	0.477049	+	0.878877i	$0.341707\pi$
$242$	−27.5415			−1.77043
$243$	3.14537	+	15.2678i	0.201775	+	0.979432i
$244$	3.48766	−	1.13321i	0.223274	−	0.0725463i
$245$	−9.52932	+	2.43434i	−0.608806	+	0.155524i
$246$	−8.18954	−	5.45593i	−0.522146	−	0.347857i
$247$	0.534667			0.0340200
$248$	5.46475	−	1.06608i	0.347012	−	0.0676961i
$249$	18.4881	−	0.751659i	1.17163	−	0.0476345i
$250$	−2.13511	+	10.9746i	−0.135037	+	0.694093i
$251$	13.5355	−	9.83412i	0.854354	−	0.620724i	−0.0719893	−	0.997405i	$-0.522935\pi$
$251$	13.5355	−	9.83412i	0.854354	−	0.620724i	0.926343	+	0.376681i	$0.122935\pi$
$252$	4.46536	−	1.86390i	0.281291	−	0.117415i
$253$		−	21.0306i		−	1.32218i
$254$	−11.8774			−0.745255
$255$	0.542765	−	23.1748i	0.0339893	−	1.45126i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−4.16295	+	12.8123i	−0.259678	+	0.799207i	0.733194	+	0.680020i	$0.238029\pi$
$257$	−4.16295	+	12.8123i	−0.259678	+	0.799207i	−0.992872	+	0.119187i	$0.961971\pi$
$258$	8.72981	−	13.1038i	0.543495	−	0.815804i
$259$	11.8090	−	3.83698i	0.733776	−	0.238418i
$260$	5.91178	+	9.34062i	0.366633	+	0.579280i
$261$	−12.9016	+	11.0800i	−0.798587	+	0.685834i
$262$	−19.5994	−	6.36822i	−1.21085	−	0.393430i
$263$	−10.4819	−	14.4271i	−0.646344	−	0.889616i	0.352590	−	0.935778i	$-0.385301\pi$
$263$	−10.4819	−	14.4271i	−0.646344	−	0.889616i	−0.998934	+	0.0461621i	$0.985301\pi$
$264$	−6.66856	−	8.43533i	−0.410421	−	0.519159i
$265$	7.00329	+	5.80801i	0.430209	+	0.356783i
$266$	−0.102534	−	0.141127i	−0.00628679	−	0.00865303i
$267$	0.204981	−	0.307683i	0.0125446	−	0.0188299i
$268$	−12.3529	+	4.01371i	−0.754575	+	0.245176i
$269$	−4.08784	−	2.96999i	−0.249240	−	0.181084i	0.456150	−	0.889903i	$-0.349228\pi$
$269$	−4.08784	−	2.96999i	−0.249240	−	0.181084i	−0.705390	+	0.708819i	$0.749228\pi$
$270$	9.77908	+	6.27452i	0.595136	+	0.381855i
$271$	24.5372	+	7.97262i	1.49053	+	0.484302i	0.937239	−	0.348687i	$-0.113372\pi$
$271$	24.5372	+	7.97262i	1.49053	+	0.484302i	0.553289	+	0.832989i	$0.313372\pi$
$272$	−5.69242	+	1.84958i	−0.345153	+	0.112147i
$273$	13.7993	−	0.561032i	0.835174	−	0.0339552i
$274$		−	9.43445i		−	0.569956i
$275$	13.2850	−	28.0544i	0.801114	−	1.69174i
$276$	4.60284	−	3.63878i	0.277058	−	0.219029i
$277$	12.6389	+	9.18272i	0.759400	+	0.551736i	0.898726	−	0.438510i	$-0.144494\pi$
$277$	12.6389	+	9.18272i	0.759400	+	0.551736i	−0.139326	+	0.990247i	$0.544494\pi$
$278$		−	1.44143i		−	0.0864510i
$279$	16.0805	−	4.51855i	0.962715	−	0.270518i
$280$	1.33176	−	3.35171i	0.0795879	−	0.200303i
$281$	−2.89412	+	3.98342i	−0.172649	+	0.237631i	−0.886569	−	0.462596i	$-0.846918\pi$
$281$	−2.89412	+	3.98342i	−0.172649	+	0.237631i	0.713920	+	0.700227i	$0.246918\pi$
$282$	−12.3988	−	15.6837i	−0.738335	−	0.933950i
$283$	−3.61804	+	1.17557i	−0.215070	+	0.0698805i	−0.414570	−	0.910017i	$-0.636068\pi$
$283$	−3.61804	+	1.17557i	−0.215070	+	0.0698805i	0.199500	+	0.979898i	$0.436068\pi$
$284$		−	1.81284i		−	0.107572i
$285$	0.138732	−	0.395234i	0.00821775	−	0.0234116i
$286$	−9.48398	−	29.1887i	−0.560800	−	1.72596i
$287$	−2.83173	+	8.71516i	−0.167152	+	0.514440i
$288$	0.692375	−	2.91901i	0.0407986	−	0.172004i
$289$	15.2294	+	11.0648i	0.895845	+	0.650869i
$290$	−0.811333	+	12.6498i	−0.0476431	+	0.742822i
$291$	−21.0534	−	14.0260i	−1.23417	−	0.822216i
$292$	13.3960	−	9.73277i	0.783942	−	0.569567i
$293$	7.43862	−	22.8937i	0.434569	−	1.33747i	−0.458959	−	0.888458i	$-0.651777\pi$
$293$	7.43862	−	22.8937i	0.434569	−	1.33747i	0.893528	−	0.449008i	$-0.148223\pi$
$294$	4.72468	+	5.97644i	0.275549	+	0.348553i
$295$	−0.226981	−	0.888525i	−0.0132153	−	0.0517319i
$296$	2.37891	−	7.32152i	0.138271	−	0.425555i
$297$	−21.9940	−	23.5984i	−1.27622	−	1.36932i
$298$	0.858969	−	1.18227i	0.0497587	−	0.0684870i
$299$	15.9272	−	5.17505i	0.921092	−	0.299281i
$300$	8.43868	−	1.94645i	0.487208	−	0.112378i
$301$	−13.9448	−	4.53094i	−0.803764	−	0.261159i
$302$	2.39413	+	0.777901i	0.137767	+	0.0447632i
$303$	1.90955	+	5.15440i	0.109701	+	0.296113i
$304$	−0.108153			−0.00620301
$305$	3.02790	−	7.62046i	0.173377	−	0.436346i
$306$	−16.5704	+	6.91673i	−0.947269	+	0.395403i
$307$	4.57041	+	6.29063i	0.260847	+	0.359025i	0.919273	−	0.393620i	$-0.128777\pi$
$307$	4.57041	+	6.29063i	0.260847	+	0.359025i	−0.658426	+	0.752645i	$0.728777\pi$
$308$	−5.88566	+	8.10091i	−0.335367	+	0.461592i
$309$	17.4657	−	0.710094i	0.993589	−	0.0403958i
$310$	5.96558	−	10.9276i	0.338822	−	0.620644i
$311$			18.4582i			1.04667i	0.852127	+	0.523335i	$0.175312\pi$
$311$			18.4582i			1.04667i	−0.852127	+	0.523335i	$0.824688\pi$
$312$	4.74740	−	7.12601i	0.268768	−	0.403431i
$313$	−4.34007	+	3.15325i	−0.245315	+	0.178232i	−0.703648	−	0.710549i	$-0.748447\pi$
$313$	−4.34007	+	3.15325i	−0.245315	+	0.178232i	0.458333	+	0.888781i	$0.348447\pi$
$314$	1.31601	−	0.427597i	0.0742667	−	0.0241307i
$315$	3.16583	−	10.3463i	0.178374	−	0.582946i
$316$		−	4.99782i		−	0.281149i
$317$	0.125138	+	0.385136i	0.00702847	+	0.0216314i	0.954509	−	0.298181i	$-0.0963800\pi$
$317$	0.125138	+	0.385136i	0.00702847	+	0.0216314i	−0.947481	+	0.319813i	$0.896380\pi$
$318$	1.90373	−	6.78552i	0.106756	−	0.380513i
$319$	10.8752	−	33.4704i	0.608894	−	1.87398i
$320$	−1.19584	−	1.88943i	−0.0668497	−	0.105623i
$321$	−9.60466	+	3.55824i	−0.536080	+	0.198602i
$322$	−4.42036	−	3.21158i	−0.246337	−	0.178974i
$323$	0.380494	+	0.523705i	0.0211713	+	0.0291397i
$324$	1.35938	−	8.89675i	0.0755213	−	0.494264i
$325$	24.5155	+	3.15774i	1.35988	+	0.175160i
$326$	12.6757	+	17.4467i	0.702044	+	0.966281i
$327$	9.25467	+	2.59646i	0.511784	+	0.143585i
$328$	3.33946	+	4.59637i	0.184391	+	0.253792i
$329$	−10.9431	+	15.0619i	−0.603314	+	0.830390i
$330$	−24.0376	−	0.562971i	−1.32323	−	0.0309905i
$331$	−6.65630	+	9.16161i	−0.365863	+	0.503568i	−0.951771	−	0.306810i	$-0.900738\pi$
$331$	−6.65630	+	9.16161i	−0.365863	+	0.503568i	0.585907	+	0.810378i	$0.300738\pi$
$332$	−10.1601	−	3.30120i	−0.557605	−	0.181177i
$333$	5.33011	−	22.4714i	0.292088	−	1.23143i
$334$	0.665162	−	0.216124i	0.0363961	−	0.0118258i
$335$	−10.7245	+	26.9909i	−0.585942	+	1.47467i
$336$	−2.79135	+	0.113486i	−0.152281	+	0.00619119i
$337$	0.930657	+	2.86427i	0.0506961	+	0.156027i	0.973200	−	0.229962i	$-0.0738603\pi$
$337$	0.930657	+	2.86427i	0.0506961	+	0.156027i	−0.922503	+	0.385989i	$0.873860\pi$
$338$	9.25456	−	6.72383i	0.503381	−	0.365728i
$339$	−11.5972	+	17.4078i	−0.629873	+	0.945461i
$340$	−4.94202	+	12.4378i	−0.268018	+	0.674535i
$341$	−23.5566	+	25.2957i	−1.27566	+	1.36984i
$342$	−0.323388	+	0.0263392i	−0.0174868	+	0.00142426i
$343$	10.8063	−	14.8736i	0.583487	−	0.803101i
$344$	−7.35446	+	5.34333i	−0.396526	+	0.288093i
$345$	0.307192	−	13.1164i	0.0165387	−	0.706163i
$346$	−10.8755			−0.584671
$347$			8.76948i			0.470770i	0.971902	+	0.235385i	$0.0756352\pi$
$347$			8.76948i			0.470770i	−0.971902	+	0.235385i	$0.924365\pi$
$348$	9.20711	−	3.41096i	0.493553	−	0.182847i
$349$	−7.02070	+	21.6075i	−0.375809	+	1.15662i	0.567122	+	0.823634i	$0.308057\pi$
$349$	−7.02070	+	21.6075i	−0.375809	+	1.15662i	−0.942931	+	0.332988i	$0.891943\pi$
$350$	−3.86791	−	7.07650i	−0.206749	−	0.378255i
$351$	12.4597	−	22.4636i	0.665052	−	1.19902i
$352$	1.91843	+	5.90433i	0.102253	+	0.314702i
$353$	15.5865	−	21.4529i	0.829584	−	1.14182i	−0.158416	−	0.987372i	$-0.550639\pi$
$353$	15.5865	−	21.4529i	0.829584	−	1.14182i	0.988000	−	0.154452i	$-0.0493613\pi$
$354$	−0.557250	+	0.440535i	−0.0296175	+	0.0234142i
$355$	−3.12022	−	2.58768i	−0.165604	−	0.137340i
$356$	−0.172687	+	0.125464i	−0.00915237	+	0.00664959i
$357$	10.3698	+	13.1172i	0.548828	+	0.694234i
$358$	−2.46376	+	7.58268i	−0.130214	+	0.400757i
$359$	−15.2144	−	20.9409i	−0.802987	−	1.10522i	−0.992368	−	0.123313i	$-0.960648\pi$
$359$	−15.2144	−	20.9409i	−0.802987	−	1.10522i	0.189381	−	0.981904i	$-0.439352\pi$
$360$	−4.03584	−	5.35836i	−0.212707	−	0.282410i
$361$	−5.86771	−	18.0589i	−0.308827	−	0.950471i
$362$	−4.62746	+	6.36915i	−0.243214	+	0.334755i
$363$	45.9299	+	12.8860i	2.41069	+	0.676337i
$364$	−7.58337	−	2.46399i	−0.397477	−	0.129148i
$365$	2.36988	−	36.9497i	0.124045	−	1.93404i
$366$	−6.34643	+	0.258023i	−0.331733	+	0.0134871i
$367$	−5.74182			−0.299721			−0.149860	−	0.988707i	$-0.547882\pi$
$367$	−5.74182			−0.299721			−0.149860	+	0.988707i	$0.547882\pi$
$368$	−3.22177	+	1.04682i	−0.167946	+	0.0545691i
$369$	11.1047	+	12.9303i	0.578087	+	0.673125i
$370$	−9.20596	−	14.5454i	−0.478595	−	0.756180i
$371$	−6.56277			−0.340722
$372$	−9.61214	−	0.778954i	−0.498366	−	0.0403869i
$373$			24.6210i			1.27483i	0.770521	+	0.637414i	$0.219996\pi$
$373$			24.6210i			1.27483i	−0.770521	+	0.637414i	$0.780004\pi$
$374$	21.8410	−	30.0616i	1.12937	−	1.55445i
$375$	8.69537	−	17.3029i	0.449027	−	0.893518i
$376$	3.56691	+	10.9778i	0.183950	+	0.566139i
$377$	28.0243			1.44332
$378$	−8.31877	+	1.01913i	−0.427871	+	0.0524184i
$379$	−8.33039	−	25.6383i	−0.427903	−	1.31695i	−0.900187	−	0.435505i	$-0.856570\pi$
$379$	−8.33039	−	25.6383i	−0.427903	−	1.31695i	0.472283	−	0.881447i	$-0.343430\pi$
$380$	−0.154380	+	0.186151i	−0.00791953	+	0.00954936i
$381$	19.8075	+	5.55713i	1.01477	+	0.284700i
$382$	−5.61477	+	7.72806i	−0.287277	+	0.395402i
$383$	−13.2125	+	4.29301i	−0.675128	+	0.219362i	−0.626461	−	0.779453i	$-0.715497\pi$
$383$	−13.2125	+	4.29301i	−0.675128	+	0.219362i	−0.0486670	+	0.998815i	$0.515497\pi$
$384$	−0.960310	+	1.44146i	−0.0490056	+	0.0735591i
$385$	5.54183	+	21.6937i	0.282438	+	1.10561i
$386$	−12.3482	−	4.01216i	−0.628505	−	0.204214i
$387$	−20.6893	+	17.7682i	−1.05170	+	0.903207i
$388$	8.58499	+	11.8162i	0.435837	+	0.599878i
$389$	7.33966	−	22.5891i	0.372135	−	1.14532i	−0.573256	−	0.819377i	$-0.694320\pi$
$389$	7.33966	−	22.5891i	0.372135	−	1.14532i	0.945391	−	0.325939i	$-0.105680\pi$
$390$	−5.48862	−	18.3430i	−0.277927	−	0.928832i
$391$	16.4035	+	11.9178i	0.829560	+	0.602710i
$392$	−1.35921	−	4.18322i	−0.0686505	−	0.211285i
$393$	29.7056	+	19.7901i	1.49845	+	0.998277i
$394$	−19.8631	−	6.45390i	−1.00069	−	0.325143i
$395$	−8.60216	−	7.13399i	−0.432821	−	0.358950i
$396$	7.17422	+	17.1873i	0.360518	+	0.863695i
$397$			34.3949i			1.72623i	0.505006	+	0.863116i	$0.331490\pi$
$397$			34.3949i			1.72623i	−0.505006	+	0.863116i	$0.668510\pi$
$398$			8.54145i			0.428144i
$399$	0.104963	+	0.283325i	0.00525474	+	0.0141840i
$400$	−4.95903	−	0.638752i	−0.247952	−	0.0319376i
$401$	−25.3796	−	18.4393i	−1.26740	−	0.920817i	−0.268300	−	0.963335i	$-0.586462\pi$
$401$	−25.3796	−	18.4393i	−1.26740	−	0.920817i	−0.999096	+	0.0425186i	$0.986462\pi$
$402$	22.4784	−	0.913892i	1.12112	−	0.0455808i
$403$	−24.9539	−	11.6156i	−1.24304	−	0.578615i
$404$		−	3.17355i		−	0.157890i
$405$	−13.3725	−	15.0392i	−0.664485	−	0.747302i
$406$	−5.37429	−	7.39708i	−0.266722	−	0.367111i
$407$	14.7687	+	45.4533i	0.732056	+	2.25304i
$408$	10.3584	−	0.421135i	0.512817	−	0.0208493i
$409$			22.2425i			1.09982i	0.835223	+	0.549911i	$0.185338\pi$
$409$			22.2425i			1.09982i	−0.835223	+	0.549911i	$0.814662\pi$
$410$	12.6780	+	0.813141i	0.626122	+	0.0401582i
$411$	−4.41413	+	15.7335i	−0.217733	+	0.776074i
$412$	−9.59822	−	3.11865i	−0.472870	−	0.153645i
$413$	0.535158	+	0.388815i	0.0263334	+	0.0191323i
$414$	−9.37847	+	3.91470i	−0.460927	+	0.192397i
$415$	−20.1846	+	12.7751i	−0.990825	+	0.627105i
$416$	−3.99946	+	2.90578i	−0.196090	+	0.142468i
$417$	−0.674406	+	2.40381i	−0.0330258	+	0.117715i
$418$	0.543201	−	0.394659i	0.0265689	−	0.0193034i
$419$	−0.968397	−	1.33288i	−0.0473093	−	0.0651157i	0.784707	−	0.619867i	$-0.212813\pi$
$419$	−0.968397	−	1.33288i	−0.0473093	−	0.0651157i	−0.832016	+	0.554751i	$0.812813\pi$
$420$	−3.78910	+	4.96641i	−0.184889	+	0.242336i
$421$	22.9013	−	16.6387i	1.11614	−	0.810923i	0.132520	−	0.991180i	$-0.457693\pi$
$421$	22.9013	−	16.6387i	1.11614	−	0.810923i	0.983619	+	0.180257i	$0.0576931\pi$
$422$	−13.5985	−	9.87991i	−0.661966	−	0.480946i
$423$	13.3389	+	31.9561i	0.648561	+	1.55376i
$424$	−2.39163	+	3.29180i	−0.116148	+	0.159864i
$425$	14.3534	+	26.2601i	0.696242	+	1.27380i
$426$	−0.848179	+	3.02320i	−0.0410944	+	0.146474i
$427$	1.82777	+	5.62530i	0.0884521	+	0.272228i
$428$	5.91356			0.285843
$429$	2.15943	+	53.1142i	0.104258	+	2.56438i
$430$	−1.30107	+	20.2856i	−0.0627434	+	0.978256i
$431$	7.37850	+	10.1556i	0.355410	+	0.489180i	0.948863	−	0.315689i	$-0.102236\pi$
$431$	7.37850	+	10.1556i	0.355410	+	0.489180i	−0.593453	+	0.804869i	$0.702236\pi$
$432$	−2.52038	+	4.54397i	−0.121262	+	0.218622i
$433$	5.08767			0.244498			0.122249	−	0.992499i	$-0.460989\pi$
$433$	5.08767			0.244498			0.122249	+	0.992499i	$0.460989\pi$
$434$	1.71950	+	8.81419i	0.0825386	+	0.423095i
$435$	7.27155	−	20.7160i	0.348644	−	0.993256i
$436$	−4.48963	−	3.26191i	−0.215014	−	0.156217i
$437$	0.215350	+	0.296404i	0.0103016	+	0.0141789i
$438$	−26.8937	+	9.96331i	−1.28503	+	0.476066i
$439$	−22.9375			−1.09474			−0.547372	−	0.836889i	$-0.684372\pi$
$439$	−22.9375			−1.09474			−0.547372	+	0.836889i	$0.684372\pi$
$440$	12.9008	+	5.12599i	0.615023	+	0.244372i
$441$	−5.08294	−	12.1772i	−0.242045	−	0.579868i
$442$	28.1411	+	9.14359i	1.33853	+	0.434916i
$443$	−1.40859	+	4.33519i	−0.0669240	+	0.205971i	−0.978926	−	0.204214i	$-0.934536\pi$
$443$	−1.40859	+	4.33519i	−0.0669240	+	0.205971i	0.912002	+	0.410185i	$0.134536\pi$
$444$	−7.39276	+	11.0968i	−0.350845	+	0.526630i
$445$	−0.0305499	+	0.476315i	−0.00144820	+	0.0225795i
$446$	−6.59083	−	4.78852i	−0.312085	−	0.226743i
$447$	−1.98562	+	1.56974i	−0.0939167	+	0.0742459i
$448$	1.53398	+	0.498419i	0.0724735	+	0.0235481i
$449$	−12.4616	+	9.05385i	−0.588097	+	0.427278i	−0.841634	−	0.540048i	$-0.818406\pi$
$449$	−12.4616	+	9.05385i	−0.588097	+	0.427278i	0.253537	+	0.967326i	$0.418406\pi$
$450$	−14.9836	−	0.702228i	−0.706331	−	0.0331033i
$451$	−33.5450	−	10.8994i	−1.57957	−	0.513234i
$452$	9.77010	−	7.09839i	0.459547	−	0.333880i
$453$	−3.62864	−	2.41743i	−0.170489	−	0.113581i
$454$	0.893927	+	2.75122i	0.0419541	+	0.129121i
$455$	−15.0656	+	9.53522i	−0.706288	+	0.447018i
$456$	0.180363	+	0.0506020i	0.00844626	+	0.00236966i
$457$	11.0395	−	33.9762i	0.516407	−	1.58934i	−0.264299	−	0.964441i	$-0.585141\pi$
$457$	11.0395	−	33.9762i	0.516407	−	1.58934i	0.780707	−	0.624898i	$-0.214859\pi$
$458$	−17.0911	+	5.55325i	−0.798617	+	0.259486i
$459$	30.8700	−	3.78188i	1.44089	−	0.176523i
$460$	−2.79706	+	7.03950i	−0.130414	+	0.328218i
$461$	2.58997	+	7.97110i	0.120627	+	0.371251i	0.993079	−	0.117448i	$-0.0374714\pi$
$461$	2.58997	+	7.97110i	0.120627	+	0.371251i	−0.872452	+	0.488700i	$0.837471\pi$
$462$	13.6055	−	10.7558i	0.632985	−	0.500407i
$463$	9.22851	+	6.70490i	0.428885	+	0.311603i	0.781203	−	0.624277i	$-0.214606\pi$
$463$	9.22851	+	6.70490i	0.428885	+	0.311603i	−0.352318	+	0.935880i	$0.614606\pi$
$464$	−5.66879			−0.263167
$465$	−15.0613	+	15.4323i	−0.698451	+	0.715658i
$466$	17.8359			0.826234
$467$	17.7873	+	12.9233i	0.823100	+	0.598017i	0.917599	−	0.397508i	$-0.130125\pi$
$467$	17.7873	+	12.9233i	0.823100	+	0.598017i	−0.0944986	+	0.995525i	$0.530125\pi$
$468$	−11.2511	+	9.66258i	−0.520084	+	0.446653i
$469$	−6.47378	−	19.9242i	−0.298931	−	0.920016i
$470$	23.9863	+	9.53069i	1.10641	+	0.439618i
$471$	−2.39472	+	0.0973608i	−0.110343	+	0.00448615i
$472$	0.390049	−	0.126734i	0.0179534	−	0.00583343i
$473$	17.4397	−	53.6740i	0.801880	−	2.46793i
$474$	−2.33835	+	8.33467i	−0.107404	+	0.382824i
$475$	0.100035	+	0.531432i	0.00458991	+	0.0243838i
$476$	−2.98322	−	9.18140i	−0.136735	−	0.420829i
$477$	−6.34954	+	10.4252i	−0.290725	+	0.477339i
$478$	2.53621	−	1.84267i	0.116004	−	0.0842815i
$479$	6.04683	+	1.96474i	0.276287	+	0.0897710i	0.443883	−	0.896085i	$-0.353601\pi$
$479$	6.04683	+	1.96474i	0.276287	+	0.0897710i	−0.167596	+	0.985856i	$0.553601\pi$
$480$	1.11025	+	3.71044i	0.0506756	+	0.169358i
$481$	−30.7891	+	22.3696i	−1.40386	+	1.01996i
$482$	5.37755	+	1.74727i	0.244940	+	0.0795860i
$483$	5.86905	+	7.42400i	0.267051	+	0.337804i
$484$	−22.2815	−	16.1885i	−1.01280	−	0.735840i
$485$	32.5923	+	2.09040i	1.47994	+	0.0949202i
$486$	−6.42955	+	14.2007i	−0.291650	+	0.644158i
$487$	1.68879	−	5.19757i	0.0765265	−	0.235524i	−0.905474	−	0.424401i	$-0.860485\pi$
$487$	1.68879	−	5.19757i	0.0765265	−	0.235524i	0.982001	+	0.188877i	$0.0604847\pi$
$488$	3.48766	+	1.13321i	0.157879	+	0.0512979i
$489$	−12.9760	−	35.0258i	−0.586795	−	1.58392i
$490$	−9.14025	−	3.63177i	−0.412914	−	0.164067i
$491$	38.3482			1.73063			0.865316	−	0.501226i	$-0.167118\pi$
$491$	38.3482			1.73063			0.865316	+	0.501226i	$0.167118\pi$
$492$	−3.41856	−	9.22763i	−0.154121	−	0.416014i
$493$	19.9434	+	27.4497i	0.898206	+	1.23627i
$494$	0.432554	+	0.314269i	0.0194615	+	0.0141396i
$495$	39.8231	+	12.1854i	1.78992	+	0.547693i
$496$	5.04770	+	2.34962i	0.226648	+	0.105501i
$497$	2.92396			0.131157
$498$	15.3990	+	10.2589i	0.690045	+	0.459713i
$499$	−18.3397	−	25.2425i	−0.821000	−	1.13001i	−0.989532	−	0.144313i	$-0.953903\pi$
$499$	−18.3397	−	25.2425i	−0.821000	−	1.13001i	0.168532	−	0.985696i	$-0.446097\pi$
$500$	−8.17804	+	7.62363i	−0.365733	+	0.340939i
$501$	−1.21038	+	0.0492099i	−0.0540760	+	0.00219854i
$502$	16.7308			0.746732
$503$	−0.440888	−	1.35691i	−0.0196582	−	0.0605018i	0.940746	−	0.339112i	$-0.110126\pi$
$503$	−0.440888	−	1.35691i	−0.0196582	−	0.0605018i	−0.960404	+	0.278610i	$0.910126\pi$
$504$	4.70812	+	1.11674i	0.209716	+	0.0497437i
$505$	−5.46226	−	4.52999i	−0.243067	−	0.201582i
$506$	12.3615	−	17.0141i	0.549535	−	0.756371i
$507$	−18.5794	+	6.88310i	−0.825139	+	0.305689i
$508$	−9.60902	−	6.98136i	−0.426331	−	0.309748i
$509$	1.01734	−	0.739141i	0.0450928	−	0.0327618i	−0.565011	−	0.825084i	$-0.691128\pi$
$509$	1.01734	−	0.739141i	0.0450928	−	0.0327618i	0.610103	+	0.792322i	$0.291128\pi$
$510$	14.0609	−	18.4298i	0.622629	−	0.816086i
$511$	15.6981	+	21.6066i	0.694445	+	0.955822i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	0.551626	+	0.107380i	0.0243549	+	0.00474095i
$514$	−10.8988	+	7.91841i	−0.480724	+	0.349266i
$515$	−19.0685	+	12.0687i	−0.840257	+	0.531808i
$516$	14.7648	−	5.46990i	0.649982	−	0.240799i
$517$	−57.9739	−	42.1205i	−2.54969	−	1.85246i
$518$	11.8090	+	3.83698i	0.518858	+	0.168587i
$519$	18.1367	+	5.08837i	0.796112	+	0.223355i
$520$	−0.707543	+	11.0316i	−0.0310278	+	0.483767i
$521$		−	22.6175i		−	0.990891i	−0.868639	−	0.495445i	$-0.835005\pi$
$521$		−	22.6175i		−	0.990891i	0.868639	−	0.495445i	$-0.164995\pi$
$522$	−16.9502	+	1.38056i	−0.741892	+	0.0604253i
$523$	−3.21176	−	9.88478i	−0.140440	−	0.432231i	0.855956	−	0.517049i	$-0.172969\pi$
$523$	−3.21176	−	9.88478i	−0.140440	−	0.432231i	−0.996397	+	0.0848173i	$0.972969\pi$
$524$	−12.1131	−	16.6722i	−0.529162	−	0.728329i
$525$	3.13946	+	13.6109i	0.137017	+	0.594028i
$526$		−	17.8329i		−	0.777553i
$527$	−6.38087	−	32.7085i	−0.277955	−	1.42480i
$528$	−0.436813	−	10.7440i	−0.0190099	−	0.467573i
$529$	−9.32342	−	6.77386i	−0.405366	−	0.294516i
$530$	2.25192	+	8.81521i	0.0978170	+	0.382908i
$531$	1.13542	−	0.473940i	0.0492730	−	0.0205672i
$532$		−	0.174442i		−	0.00756302i
$533$		−	28.0867i		−	1.21657i
$534$	0.346684	−	0.128436i	0.0150025	−	0.00555797i
$535$	8.44114	−	10.1783i	0.364942	−	0.440047i
$536$	−12.3529	−	4.01371i	−0.533565	−	0.173366i
$537$	7.65646	−	11.4926i	0.330401	−	0.495943i
$538$	−1.56142	−	4.80555i	−0.0673175	−	0.207182i
$539$	22.0916	+	16.0505i	0.951551	+	0.691342i
$540$	4.22337	+	10.8242i	0.181745	+	0.465799i
$541$	−6.28533	+	19.3443i	−0.270227	+	0.831675i	0.720215	+	0.693751i	$0.244043\pi$
$541$	−6.28533	+	19.3443i	−0.270227	+	0.831675i	−0.990443	+	0.137924i	$0.955957\pi$
$542$	15.1648	+	20.8726i	0.651385	+	0.896554i
$543$	10.6970	−	8.45652i	0.459052	−	0.362904i
$544$	−5.69242	−	1.84958i	−0.244060	−	0.0793000i
$545$	−12.0229	+	3.07136i	−0.515006	+	0.131562i
$546$	11.4937	+	7.65716i	0.491883	+	0.327696i
$547$	−1.33777	+	0.434668i	−0.0571989	+	0.0185851i	−0.337477	−	0.941334i	$-0.609573\pi$
$547$	−1.33777	+	0.434668i	−0.0571989	+	0.0185851i	0.280278	+	0.959919i	$0.409573\pi$
$548$	5.54543	−	7.63263i	0.236889	−	0.326050i
$549$	10.7044	+	2.53904i	0.456853	+	0.108363i
$550$	27.2377	−	14.8877i	1.16142	−	0.634815i
$551$	0.189457	+	0.583090i	0.00807116	+	0.0248405i
$552$	5.86260	−	0.238352i	0.249529	−	0.0101450i
$553$	8.06107			0.342791
$554$	4.82764	+	14.8580i	0.205107	+	0.631254i
$555$	8.54700	+	28.5641i	0.362800	+	1.21248i
$556$	0.847249	−	1.16614i	0.0359314	−	0.0494553i
$557$			11.1319i			0.471673i	0.971793	+	0.235836i	$0.0757829\pi$
$557$			11.1319i			0.471673i	−0.971793	+	0.235836i	$0.924217\pi$
$558$	15.6653	+	5.79630i	0.663167	+	0.245377i
$559$	44.9405			1.90078
$560$	3.04750	−	1.92880i	0.128780	−	0.0815066i
$561$	−50.4885	+	39.9137i	−2.13163	+	1.68516i
$562$	−4.68279	+	1.52153i	−0.197532	+	0.0641819i
$563$	19.8469			0.836447			0.418223	−	0.908344i	$-0.362653\pi$
$563$	19.8469			0.836447			0.418223	+	0.908344i	$0.362653\pi$
$564$	−0.812160	−	19.9762i	−0.0341981	−	0.841149i
$565$	1.72842	−	26.9485i	0.0727153	−	1.13373i
$566$	−3.61804	−	1.17557i	−0.152077	−	0.0494129i
$567$	14.3497	+	2.19257i	0.602631	+	0.0920795i
$568$	1.06556	−	1.46662i	0.0447098	−	0.0615378i
$569$	11.6723	+	35.9237i	0.489329	+	1.50600i	0.825612	+	0.564238i	$0.190830\pi$
$569$	11.6723	+	35.9237i	0.489329	+	1.50600i	−0.336284	+	0.941761i	$0.609170\pi$
$570$	0.344549	−	0.238207i	0.0144316	−	0.00997738i
$571$	−2.19559	−	3.02197i	−0.0918827	−	0.126466i	0.760601	−	0.649220i	$-0.224905\pi$
$571$	−2.19559	−	3.02197i	−0.0918827	−	0.126466i	−0.852483	+	0.522754i	$0.824905\pi$
$572$	9.48398	−	29.1887i	0.396545	−	1.22044i
$573$	12.9793	−	10.2608i	0.542218	−	0.428651i
$574$	−7.41356	+	5.38627i	−0.309436	+	0.224818i
$575$	8.12367	+	14.8626i	0.338781	+	0.619813i
$576$	2.27589	−	1.95456i	0.0948289	−	0.0814400i
$577$	−10.2328	+	14.0842i	−0.425997	+	0.586335i	−0.967029	−	0.254668i	$-0.918034\pi$
$577$	−10.2328	+	14.0842i	−0.425997	+	0.586335i	0.541031	+	0.841002i	$0.318034\pi$
$578$	5.81710	+	17.9032i	0.241959	+	0.744675i
$579$	18.7154	+	12.4683i	0.777784	+	0.518165i
$580$	−8.09175	+	9.75702i	−0.335992	+	0.405138i
$581$	5.32456	−	16.3873i	0.220900	−	0.679861i
$582$	−8.78835	−	23.7221i	−0.364289	−	0.983315i
$583$		−	25.2604i		−	1.04618i
$584$	16.5584			0.685190
$585$	0.570965	+	33.1578i	0.0236065	+	1.37091i
$586$	19.4746	−	14.1491i	0.804487	−	0.584494i
$587$	9.77540	−	13.4547i	0.403474	−	0.555334i	−0.558138	−	0.829748i	$-0.688484\pi$
$587$	9.77540	−	13.4547i	0.403474	−	0.555334i	0.961612	+	0.274414i	$0.0884840\pi$
$588$	0.309482	+	7.61213i	0.0127628	+	0.313919i
$589$	0.0729815	−	0.597732i	0.00300715	−	0.0246291i
$590$	0.338631	−	0.852248i	0.0139412	−	0.0350865i
$591$	30.1053	+	20.0563i	1.23836	+	0.825008i
$592$	6.22805	−	4.52495i	0.255971	−	0.185974i
$593$	−3.93199	−	12.1014i	−0.161468	−	0.496946i	0.837291	−	0.546757i	$-0.184138\pi$
$593$	−3.93199	−	12.1014i	−0.161468	−	0.496946i	−0.998759	+	0.0498114i	$0.984138\pi$
$594$	−3.92267	−	32.0193i	−0.160949	−	1.31377i
$595$	−20.0612	−	7.97106i	−0.822427	−	0.326782i
$596$	1.38984	−	0.451587i	0.0569301	−	0.0184977i
$597$	3.99632	−	14.2442i	0.163559	−	0.582978i
$598$	15.9272	+	5.17505i	0.651310	+	0.211623i
$599$	−1.28721	+	1.77169i	−0.0525939	+	0.0723892i	−0.834504	−	0.551002i	$-0.814246\pi$
$599$	−1.28721	+	1.77169i	−0.0525939	+	0.0723892i	0.781910	+	0.623391i	$0.214246\pi$
$600$	7.97113	+	3.38542i	0.325420	+	0.138209i
$601$	16.9431	−	23.3202i	0.691125	−	0.951252i	−0.308875	−	0.951103i	$-0.599952\pi$
$601$	16.9431	−	23.3202i	0.691125	−	0.951252i	1.00000		0.000149436i	$-4.75670e-5\pi$
$602$	−8.61835	−	11.8621i	−0.351258	−	0.483465i
$603$	−37.9139	−	8.99300i	−1.54398	−	0.366223i
$604$	1.47966	+	2.03657i	0.0602064	+	0.0828669i
$605$	−59.6685	+	15.2428i	−2.42587	+	0.619708i
$606$	−1.48482	+	5.29241i	−0.0603168	+	0.214989i
$607$	−2.64877	−	3.64572i	−0.107510	−	0.147975i	0.751871	−	0.659310i	$-0.229151\pi$
$607$	−2.64877	−	3.64572i	−0.107510	−	0.147975i	−0.859382	+	0.511334i	$0.829151\pi$
$608$	−0.0874977	−	0.0635708i	−0.00354850	−	0.00257814i
$609$	5.50159	+	14.8503i	0.222936	+	0.601765i
$610$	6.92882	−	4.38533i	0.280540	−	0.177557i
$611$	17.6334	−	54.2701i	0.713372	−	2.19553i
$612$	−17.4713	−	4.14411i	−0.706236	−	0.167516i
$613$	−2.83064	−	8.71181i	−0.114328	−	0.351867i	0.877478	−	0.479617i	$-0.159224\pi$
$613$	−2.83064	−	8.71181i	−0.114328	−	0.351867i	−0.991806	+	0.127750i	$0.959224\pi$
$614$			7.77565i			0.313800i
$615$	−20.7622	−	7.28775i	−0.837211	−	0.293870i
$616$	−9.52320	+	3.09427i	−0.383700	+	0.124672i
$617$	−32.0624	+	23.2947i	−1.29078	+	0.937810i	−0.999821	−	0.0189242i	$-0.993976\pi$
$617$	−32.0624	+	23.2947i	−1.29078	+	0.937810i	−0.290964	+	0.956734i	$0.593976\pi$
$618$	14.5474	+	9.69161i	0.585184	+	0.389854i
$619$		−	8.47970i		−	0.340828i	−0.985373	−	0.170414i	$-0.945489\pi$
$619$		−	8.47970i		−	0.340828i	0.985373	−	0.170414i	$-0.0545105\pi$
$620$	11.2493	−	5.33411i	0.451784	−	0.214223i
$621$	17.4717	−	2.14045i	0.701115	−	0.0858934i
$622$	−10.8495	+	14.9330i	−0.435025	+	0.598760i
$623$	−0.202363	−	0.278529i	−0.00810751	−	0.0111590i
$624$	8.02929	−	2.97461i	0.321429	−	0.119080i
$625$	1.44815	+	24.9580i	0.0579259	+	0.998321i
$626$	−5.36462			−0.214414
$627$	−1.09053	+	0.404008i	−0.0435514	+	0.0161345i
$628$	1.31601	+	0.427597i	0.0525145	+	0.0170630i
$629$	−43.8219	−	14.2386i	−1.74729	−	0.567730i
$630$	8.64259	−	6.50947i	0.344329	−	0.259344i
$631$	30.5132	−	9.91433i	1.21471	−	0.394683i	0.369557	−	0.929208i	$-0.379509\pi$
$631$	30.5132	−	9.91433i	1.21471	−	0.394683i	0.845153	+	0.534525i	$0.179509\pi$
$632$	2.93764	−	4.04332i	0.116853	−	0.160835i
$633$	18.0552	+	22.8387i	0.717629	+	0.907758i
$634$	−0.125138	+	0.385136i	−0.00496988	+	0.0152957i
$635$	−25.7323	+	6.57353i	−1.02116	+	0.260863i
$636$	5.52857	−	4.37062i	0.219222	−	0.173306i
$637$	−6.71940	+	20.6802i	−0.266232	+	0.819379i
$638$	28.4716	−	20.6858i	1.12720	−	0.818960i
$639$	2.82895	−	4.64483i	0.111912	−	0.183747i
$640$	0.143123	−	2.23148i	0.00565742	−	0.0882071i
$641$	0.303848	+	0.220758i	0.0120013	+	0.00871944i	0.593770	−	0.804635i	$-0.297639\pi$
$641$	0.303848	+	0.220758i	0.0120013	+	0.00871944i	−0.581768	+	0.813354i	$0.697639\pi$
$642$	−9.86182	−	2.76680i	−0.389215	−	0.109197i
$643$	−0.732474	+	2.25432i	−0.0288860	+	0.0889018i	−0.964460	−	0.264228i	$-0.914883\pi$
$643$	−0.732474	+	2.25432i	−0.0288860	+	0.0889018i	0.935574	+	0.353130i	$0.114883\pi$
$644$	−1.68843	−	5.19645i	−0.0665334	−	0.204769i
$645$	11.6608	−	33.2207i	0.459145	−	1.30806i
$646$			0.647335i			0.0254691i
$647$	10.2514	−	3.33089i	0.403025	−	0.130951i	−0.100488	−	0.994938i	$-0.532041\pi$
$647$	10.2514	−	3.33089i	0.403025	−	0.130951i	0.503513	+	0.863988i	$0.332041\pi$
$648$	6.32914	−	6.39859i	0.248632	−	0.251360i
$649$	−1.49656	+	2.05984i	−0.0587453	+	0.0808559i
$650$	17.9774	+	16.9645i	0.705131	+	0.665403i
$651$	1.25639	−	15.5036i	0.0492418	−	0.607633i
$652$			21.5653i			0.844560i
$653$	16.8974	+	12.2767i	0.661245	+	0.480423i	0.867083	−	0.498163i	$-0.165992\pi$
$653$	16.8974	+	12.2767i	0.661245	+	0.480423i	−0.205838	+	0.978586i	$0.565992\pi$
$654$	5.96102	+	7.54034i	0.233094	+	0.294851i
$655$	−45.9864	−	2.94947i	−1.79684	−	0.115245i
$656$			5.68142i			0.221822i
$657$	49.5112	−	4.03256i	1.93161	−	0.157325i
$658$	−17.7063	+	5.75314i	−0.690265	+	0.224281i
$659$	−35.5052	−	11.5363i	−1.38308	−	0.449391i	−0.479403	−	0.877595i	$-0.659147\pi$
$659$	−35.5052	−	11.5363i	−1.38308	−	0.449391i	−0.903682	+	0.428204i	$0.859147\pi$
$660$	−19.1159	−	14.5844i	−0.744086	−	0.567697i
$661$	−7.93185	−	5.76282i	−0.308513	−	0.224148i	0.422745	−	0.906249i	$-0.361067\pi$
$661$	−7.93185	−	5.76282i	−0.308513	−	0.224148i	−0.731258	+	0.682101i	$0.761067\pi$
$662$	−10.7701	+	3.49942i	−0.418593	+	0.136009i
$663$	−42.6517	−	28.4149i	−1.65646	−	1.10354i
$664$	−6.27926	−	8.64265i	−0.243682	−	0.335400i
$665$	−0.300247	−	0.249002i	−0.0116431	−	0.00965590i
$666$	17.5205	−	15.0468i	0.678906	−	0.583051i
$667$	11.2875	+	15.5359i	0.437053	+	0.601552i
$668$	0.665162	+	0.216124i	0.0257359	+	0.00836210i
$669$	8.75085	+	11.0693i	0.338328	+	0.427964i
$670$	−24.5412	+	15.5324i	−0.948107	+	0.600068i
$671$	−21.6520	+	7.03516i	−0.835866	+	0.271589i
$672$	−2.32495	−	1.54890i	−0.0896871	−	0.0597502i
$673$	−7.42011	+	22.8368i	−0.286024	+	0.880293i	0.700065	+	0.714079i	$0.253154\pi$
$673$	−7.42011	+	22.8368i	−0.286024	+	0.880293i	−0.986090	+	0.166214i	$0.946846\pi$
$674$	−0.930657	+	2.86427i	−0.0358476	+	0.110328i
$675$	24.6589	+	8.18150i	0.949123	+	0.314906i
$676$	11.4393			0.439972
$677$			24.9767i			0.959933i	0.877287	+	0.479967i	$0.159351\pi$
$677$			24.9767i			0.959933i	−0.877287	+	0.479967i	$0.840649\pi$
$678$	−19.6144	+	7.26654i	−0.753285	+	0.279070i
$679$	−19.0586	+	13.8469i	−0.731401	+	0.531394i
$680$	−11.3089	+	7.15756i	−0.433678	+	0.274480i
$681$	−0.203541	−	5.00635i	−0.00779969	−	0.191844i
$682$	−33.9261	+	6.61842i	−1.29910	+	0.253432i
$683$	4.30319			0.164657			0.0823285	−	0.996605i	$-0.473764\pi$
$683$	4.30319			0.164657			0.0823285	+	0.996605i	$0.473764\pi$
$684$	−0.277109	−	0.168774i	−0.0105955	−	0.00645324i
$685$	−5.22148	−	20.4397i	−0.199502	−	0.780960i
$686$	17.4850	−	5.68123i	0.667581	−	0.216910i
$687$	31.1005	−	1.26443i	1.18656	−	0.0482412i
$688$	−9.09062			−0.346577
$689$	19.1305	−	6.21587i	0.728813	−	0.236806i
$690$	7.95815	−	10.4308i	0.302962	−	0.397095i
$691$	−1.98710	+	6.11567i	−0.0755929	+	0.232651i	−0.981712	−	0.190371i	$-0.939031\pi$
$691$	−1.98710	+	6.11567i	−0.0755929	+	0.232651i	0.906119	+	0.423022i	$0.139031\pi$
$692$	−8.79848	−	6.39247i	−0.334468	−	0.243005i
$693$	−27.7217	+	11.5714i	−1.05306	+	0.439562i
$694$	−5.15457	+	7.09466i	−0.195665	+	0.269310i
$695$	−0.797755	−	3.12284i	−0.0302606	−	0.118456i
$696$	9.45362	+	2.65228i	0.358339	+	0.100534i
$697$	27.5109	−	19.9878i	1.04205	−	0.757094i
$698$	−18.3804	+	13.3542i	−0.695709	+	0.505462i
$699$	−29.7443	−	8.34497i	−1.12503	−	0.315636i
$700$	1.03025	−	7.99851i	0.0389399	−	0.302315i
$701$	10.1350	−	13.9497i	0.382794	−	0.526871i	−0.573528	−	0.819186i	$-0.694426\pi$
$701$	10.1350	−	13.9497i	0.382794	−	0.526871i	0.956322	+	0.292315i	$0.0944255\pi$
$702$	23.2839	−	10.8498i	0.878796	−	0.409499i
$703$	−0.673583	−	0.489387i	−0.0254047	−	0.0184576i
$704$	−1.91843	+	5.90433i	−0.0723037	+	0.222528i
$705$	−35.5419	−	27.1165i	−1.33859	−	1.02127i
$706$	25.2194	−	8.19429i	0.949146	−	0.308396i
$707$	5.11867			0.192508
$708$	−0.709765	+	0.0288565i	−0.0266746	+	0.00108449i
$709$	10.8762	−	3.53390i	0.408465	−	0.132718i	−0.0975753	−	0.995228i	$-0.531109\pi$
$709$	10.8762	−	3.53390i	0.408465	−	0.132718i	0.506040	+	0.862510i	$0.331109\pi$
$710$	−1.00331	−	3.92750i	−0.0376536	−	0.147396i
$711$	7.79915	−	12.8053i	0.292491	−	0.480238i
$712$	−0.213452			−0.00799947
$713$	−3.61142	−	18.5122i	−0.135249	−	0.693288i
$714$	0.679257	+	16.7072i	0.0254205	+	0.625252i
$715$	−36.7014	−	57.9882i	−1.37256	−	2.16864i
$716$	−6.45021	+	4.68635i	−0.241056	+	0.175137i
$717$	−5.09168	+	1.88631i	−0.190152	+	0.0704457i
$718$		−	25.8843i		−	0.965995i
$719$	−9.95560			−0.371281			−0.185641	−	0.982618i	$-0.559436\pi$
$719$	−9.95560			−0.371281			−0.185641	+	0.982618i	$0.559436\pi$
$720$	−0.115496	−	6.70721i	−0.00430427	−	0.249963i
$721$	5.03012	−	15.4811i	0.187332	−	0.576547i
$722$	5.86771	−	18.0589i	0.218373	−	0.672084i
$723$	−8.15042	−	5.42987i	−0.303117	−	0.201939i
$724$	−7.48739	+	2.43280i	−0.278267	+	0.0904143i
$725$	5.24327	+	27.8548i	0.194730	+	1.03450i
$726$	29.5839	+	37.4219i	1.09796	+	1.38886i
$727$	5.97017	+	1.93983i	0.221421	+	0.0719442i	0.417627	−	0.908619i	$-0.362862\pi$
$727$	5.97017	+	1.93983i	0.221421	+	0.0719442i	−0.196205	+	0.980563i	$0.562862\pi$
$728$	−4.68678	−	6.45080i	−0.173704	−	0.239083i
$729$	17.3665	−	20.6738i	0.643202	−	0.765696i
$730$	23.6358	−	28.5000i	0.874799	−	1.05483i
$731$	31.9818	+	44.0191i	1.18289	+	1.62811i
$732$	−5.28603	−	3.52159i	−0.195377	−	0.130162i
$733$	−16.8992	+	5.49088i	−0.624186	+	0.202810i	−0.603998	−	0.796986i	$-0.706426\pi$
$733$	−16.8992	+	5.49088i	−0.624186	+	0.202810i	−0.0201878	+	0.999796i	$0.506426\pi$
$734$	−4.64523	−	3.37496i	−0.171459	−	0.124572i
$735$	13.5436	+	10.3330i	0.499564	+	0.381140i
$736$	−3.22177	−	1.04682i	−0.118756	−	0.0385862i
$737$	76.6892	−	24.9178i	2.82488	−	0.917860i
$738$	1.38363	+	16.9880i	0.0509322	+	0.625338i
$739$			4.45916i			0.164033i	0.996631	+	0.0820164i	$0.0261360\pi$
$739$			4.45916i			0.164033i	−0.996631	+	0.0820164i	$0.973864\pi$
$740$	1.10180	−	17.1786i	0.0405030	−	0.631499i
$741$	−0.574316	−	0.726475i	−0.0210980	−	0.0266877i
$742$	−5.30939	−	3.85750i	−0.194914	−	0.141613i
$743$		−	32.4959i		−	1.19216i	−0.802925	−	0.596080i	$-0.796724\pi$
$743$		−	32.4959i		−	1.19216i	0.802925	−	0.596080i	$-0.203276\pi$
$744$	−7.31853	−	6.28006i	−0.268310	−	0.230238i
$745$	1.20663	−	3.03677i	0.0442074	−	0.111259i
$746$	−14.4719	+	19.9188i	−0.529853	+	0.729280i
$747$	−20.8804	−	24.3132i	−0.763974	−	0.889572i
$748$	35.3395	−	11.4825i	1.29214	−	0.419842i
$749$			9.53809i			0.348514i
$750$	17.2051	−	8.88734i	0.628241	−	0.324520i
$751$	−5.21993	−	16.0653i	−0.190478	−	0.586231i	0.809522	−	0.587090i	$-0.199727\pi$
$751$	−5.21993	−	16.0653i	−0.190478	−	0.586231i	−1.00000		0.000859215i	$0.999727\pi$
$752$	−3.56691	+	10.9778i	−0.130072	+	0.400320i
$753$	−27.9013	−	7.82791i	−1.01678	−	0.285265i
$754$	22.6721	+	16.4723i	0.825670	+	0.599884i
$755$	5.61740	+	0.360289i	0.204438	+	0.0131123i
$756$	−7.32906	−	4.06516i	−0.266555	−	0.147848i
$757$	−19.1547	+	13.9167i	−0.696191	+	0.505812i	−0.878689	−	0.477394i	$-0.841581\pi$
$757$	−19.1547	+	13.9167i	−0.696191	+	0.505812i	0.182499	+	0.983206i	$0.441581\pi$
$758$	8.33039	−	25.6383i	0.302573	−	0.931225i
$759$	−28.5753	+	22.5902i	−1.03722	+	0.819972i
$760$	−0.234313	+	0.0598572i	−0.00849943	+	0.00217125i
$761$	−1.84626	+	5.68221i	−0.0669269	+	0.205980i	−0.978927	−	0.204210i	$-0.934538\pi$
$761$	−1.84626	+	5.68221i	−0.0669269	+	0.205980i	0.912000	+	0.410190i	$0.134538\pi$
$762$	12.7582	+	16.1384i	0.462181	+	0.584631i
$763$	5.26119	−	7.24140i	0.190468	−	0.262156i
$764$	−9.08489	+	2.95186i	−0.328680	+	0.106794i
$765$	−32.0717	+	24.1559i	−1.15956	+	0.873360i
$766$	−13.2125	−	4.29301i	−0.477388	−	0.155113i
$767$	−1.92825	−	0.626526i	−0.0696250	−	0.0226225i
$768$	−1.62418	+	0.601709i	−0.0586074	+	0.0217123i
$769$	8.59837			0.310065			0.155033	−	0.987909i	$-0.450452\pi$
$769$	8.59837			0.310065			0.155033	+	0.987909i	$0.450452\pi$
$770$	−8.26780	+	20.8080i	−0.297951	+	0.749868i
$771$	21.8803	−	8.10598i	0.787998	−	0.291930i
$772$	−7.63158	−	10.5040i	−0.274667	−	0.378046i
$773$	−17.1954	+	23.6675i	−0.618476	+	0.851260i	−0.997241	−	0.0742334i	$-0.976349\pi$
$773$	−17.1954	+	23.6675i	−0.618476	+	0.851260i	0.378765	+	0.925493i	$0.376349\pi$
$774$	−27.1818	+	2.21389i	−0.977031	+	0.0795768i
$775$	6.87655	−	26.9762i	0.247013	−	0.969012i
$776$			14.6057i			0.524312i
$777$	−17.8982	−	11.9239i	−0.642094	−	0.427768i
$778$	19.2155	−	13.9609i	0.688908	−	0.500521i
$779$	0.584390	−	0.189880i	0.0209379	−	0.00680315i
$780$	6.34133	−	18.0659i	0.227056	−	0.646863i
$781$			11.2544i			0.402715i
$782$	6.26557	+	19.2834i	0.224056	+	0.689575i
$783$	28.9132	+	5.62828i	1.03327	+	0.201138i
$784$	1.35921	−	4.18322i	0.0485432	−	0.149401i
$785$	2.61447	−	1.65473i	0.0933145	−	0.0590598i
$786$	12.4000	+	33.4710i	0.442294	+	1.19387i
$787$	29.1477	+	21.1770i	1.03900	+	0.754880i	0.970091	−	0.242743i	$-0.0780472\pi$
$787$	29.1477	+	21.1770i	1.03900	+	0.754880i	0.0689120	+	0.997623i	$0.478047\pi$
$788$	−12.2761	−	16.8965i	−0.437316	−	0.601914i
$789$	−8.34357	+	29.7393i	−0.297039	+	1.05875i
$790$	−2.76603	−	10.8277i	−0.0984111	−	0.385234i
$791$	11.4491	+	15.7584i	0.407084	+	0.560303i
$792$	−4.29839	+	18.1217i	−0.152736	+	0.643928i
$793$	−10.6559	−	14.6666i	−0.378402	−	0.520826i
$794$	−20.2168	+	27.8261i	−0.717468	+	0.987510i
$795$	0.368975	−	15.7544i	0.0130862	−	0.558751i
$796$	−5.02054	+	6.91018i	−0.177948	+	0.244925i
$797$	17.9934	+	5.84643i	0.637361	+	0.207091i	0.609833	−	0.792530i	$-0.291237\pi$
$797$	17.9934	+	5.84643i	0.637361	+	0.207091i	0.0275277	+	0.999621i	$0.491237\pi$
$798$	−0.0816169	+	0.290910i	−0.00288921	+	0.0102981i
$799$	65.7063	−	21.3493i	2.32452	−	0.755283i
$800$	−3.63649	−	3.43161i	−0.128569	−	0.121326i
$801$	−0.638244	+	0.0519834i	−0.0225512	+	0.00183674i
$802$	−9.69414	−	29.8355i	−0.342312	−	1.05353i
$803$	−83.1648	+	60.4228i	−2.93482	+	2.13227i
$804$	18.7226	+	12.4731i	0.660295	+	0.439893i
$805$	−11.3541	−	4.51143i	−0.400180	−	0.159007i
$806$	−13.3606	−	24.0647i	−0.470607	−	0.847644i
$807$	0.355523	+	8.74457i	0.0125150	+	0.307824i
$808$	1.86537	−	2.56746i	0.0656234	−	0.0903228i
$809$	30.8900	−	22.4429i	1.08604	−	0.789051i	0.107310	−	0.994226i	$-0.465776\pi$
$809$	30.8900	−	22.4429i	1.08604	−	0.789051i	0.978725	+	0.205174i	$0.0657762\pi$
$810$	−1.97879	−	20.0271i	−0.0695276	−	0.703680i
$811$	−3.81914			−0.134108			−0.0670540	−	0.997749i	$-0.521360\pi$
$811$	−3.81914			−0.134108			−0.0670540	+	0.997749i	$0.521360\pi$
$812$		−	9.14329i		−	0.320867i
$813$	−15.5240	−	41.9036i	−0.544452	−	1.46962i
$814$	−14.7687	+	45.4533i	−0.517642	+	1.59314i
$815$	37.1177	+	30.7827i	1.30018	+	1.07827i
$816$	8.62765	+	5.74780i	0.302028	+	0.201213i
$817$	0.303819	+	0.935058i	0.0106293	+	0.0327136i
$818$	−13.0738	+	17.9946i	−0.457116	+	0.629166i
$819$	−15.5849	−	18.1471i	−0.544582	−	0.634112i
$820$	9.77876	+	8.10979i	0.341489	+	0.283206i
$821$	20.5392	−	14.9226i	0.716823	−	0.520802i	−0.168545	−	0.985694i	$-0.553907\pi$
$821$	20.5392	−	14.9226i	0.716823	−	0.520802i	0.885367	+	0.464892i	$0.153907\pi$
$822$	−12.8190	+	10.1341i	−0.447114	+	0.353466i
$823$	−7.65322	+	23.5542i	−0.266774	+	0.821047i	0.724505	+	0.689270i	$0.242068\pi$
$823$	−7.65322	+	23.5542i	−0.266774	+	0.821047i	−0.991279	+	0.131777i	$0.957932\pi$
$824$	−5.93202	−	8.16473i	−0.206652	−	0.284432i
$825$	−52.3888	+	12.0839i	−1.82395	+	0.420707i
$826$	0.204412	+	0.629116i	0.00711241	+	0.0218898i
$827$	−16.6620	+	22.9332i	−0.579394	+	0.797467i	−0.993629	−	0.112703i	$-0.964049\pi$
$827$	−16.6620	+	22.9332i	−0.579394	+	0.797467i	0.414235	+	0.910170i	$0.364049\pi$
$828$	−9.88834	−	2.34547i	−0.343644	−	0.0815106i
$829$	−36.4990	−	11.8592i	−1.26766	−	0.411888i	−0.403443	−	0.915005i	$-0.632187\pi$
$829$	−36.4990	−	11.8592i	−1.26766	−	0.411888i	−0.864218	+	0.503117i	$0.832187\pi$
$830$	−23.8387	−	1.52897i	−0.827454	−	0.0530712i
$831$	−1.09922	−	27.0368i	−0.0381315	−	0.937895i
$832$	−4.94361			−0.171389
$833$	−25.0381	+	8.13536i	−0.867518	+	0.281874i
$834$	−1.95853	+	1.54832i	−0.0678184	+	0.0536139i
$835$	1.32146	−	0.836365i	0.0457309	−	0.0289436i
$836$	0.671434			0.0232220
$837$	−23.4125	−	16.9957i	−0.809256	−	0.587457i
$838$		−	1.64754i		−	0.0569132i
$839$	30.6783	−	42.2251i	1.05913	−	1.45777i	0.178521	−	0.983936i	$-0.442869\pi$
$839$	30.6783	−	42.2251i	1.05913	−	1.45777i	0.880613	−	0.473837i	$-0.157131\pi$
$840$	−5.98463	+	1.79073i	−0.206489	+	0.0617862i
$841$	0.968821	+	2.98172i	0.0334076	+	0.102818i
$842$	28.3075			0.975542
$843$	8.52120	−	0.346442i	0.293486	−	0.0119321i
$844$	−5.19417	−	15.9860i	−0.178791	−	0.550262i
$845$	16.3286	−	19.6891i	0.561723	−	0.677324i
$846$	−7.99193	+	33.6935i	−0.274768	+	1.15841i
$847$	26.1107	−	35.9383i	0.897174	−	1.23485i
$848$	−3.86974	+	1.25735i	−0.132887	+	0.0431777i
$849$	5.48364	+	3.65324i	0.188198	+	0.125379i
$850$	−3.82316	+	29.6816i	−0.131133	+	1.01807i
$851$	−24.8021	−	8.05870i	−0.850206	−	0.276249i
$852$	−2.46318	+	1.94727i	−0.0843872	+	0.0667124i
$853$	3.28529	+	4.52182i	0.112486	+	0.154824i	0.861548	−	0.507676i	$-0.169495\pi$
$853$	3.28529	+	4.52182i	0.112486	+	0.154824i	−0.749062	+	0.662500i	$0.769495\pi$
$854$	−1.82777	+	5.62530i	−0.0625451	+	0.192494i
$855$	−0.686042	+	0.236043i	−0.0234621	+	0.00807248i
$856$	4.78417	+	3.47590i	0.163520	+	0.118804i
$857$	12.8159	+	39.4432i	0.437782	+	1.34735i	0.890209	+	0.455553i	$0.150559\pi$
$857$	12.8159	+	39.4432i	0.437782	+	1.34735i	−0.452426	+	0.891802i	$0.649441\pi$
$858$	−29.4727	+	44.2395i	−1.00618	+	1.51031i
$859$	−32.3293	−	10.5044i	−1.10306	−	0.358406i	−0.299781	−	0.954008i	$-0.596914\pi$
$859$	−32.3293	−	10.5044i	−1.10306	−	0.358406i	−0.803280	+	0.595602i	$0.796914\pi$
$860$	−12.9761	+	15.6466i	−0.442483	+	0.533545i
$861$	14.8834	−	5.51386i	0.507225	−	0.187912i
$862$			12.5531i			0.427559i
$863$			27.2377i			0.927180i	0.886050	+	0.463590i	$0.153439\pi$
$863$			27.2377i			0.927180i	−0.886050	+	0.463590i	$0.846561\pi$
$864$	−4.70991	+	2.19471i	−0.160234	+	0.0746657i
$865$	−23.5617	+	6.01903i	−0.801123	+	0.204653i
$866$	4.11602	+	2.99046i	0.139868	+	0.101620i
$867$	−1.32451	−	32.5781i	−0.0449828	−	1.10641i
$868$	−3.78975	+	8.14152i	−0.128632	+	0.276341i
$869$			31.0274i			1.05253i
$870$	18.0594	−	12.4855i	0.612270	−	0.423297i
$871$	37.7421	+	51.9476i	1.27884	+	1.76018i
$872$	−1.71489	−	5.27788i	−0.0580734	−	0.178731i
$873$	3.55700	+	43.6723i	0.120386	+	1.47808i
$874$			0.366376i			0.0123929i
$875$	−12.2963	−	13.1905i	−0.415690	−	0.445920i
$876$	−27.6138	−	7.74723i	−0.932982	−	0.261755i
$877$	35.8893	+	11.6611i	1.21190	+	0.393769i	0.844125	−	0.536147i	$-0.180121\pi$
$877$	35.8893	+	11.6611i	1.21190	+	0.393769i	0.367772	+	0.929916i	$0.380121\pi$
$878$	−18.5568	−	13.4823i	−0.626261	−	0.455005i
$879$	−39.0970	+	14.4843i	−1.31871	+	0.488542i
$880$	7.42401	+	11.7299i	0.250263	+	0.395416i
$881$	−46.6520	+	33.8947i	−1.57175	+	1.14194i	−0.646286	+	0.763096i	$0.723679\pi$
$881$	−46.6520	+	33.8947i	−1.57175	+	1.14194i	−0.925460	+	0.378845i	$0.876321\pi$
$882$	3.04541	−	12.8393i	0.102544	−	0.432320i
$883$	−38.2340	+	27.7786i	−1.28668	+	0.934826i	−0.999733	−	0.0231217i	$-0.992639\pi$
$883$	−38.2340	+	27.7786i	−1.28668	+	0.934826i	−0.286944	+	0.957947i	$0.592639\pi$
$884$	17.3921	+	23.9382i	0.584961	+	0.805130i
$885$	−0.963466	+	1.26282i	−0.0323866	+	0.0424494i
$886$	−3.68773	+	2.67929i	−0.123892	+	0.0900126i
$887$	−7.42695	−	5.39600i	−0.249373	−	0.181180i	0.456076	−	0.889941i	$-0.349254\pi$
$887$	−7.42695	−	5.39600i	−0.249373	−	0.181180i	−0.705449	+	0.708761i	$0.749254\pi$
$888$	−12.5034	+	4.63213i	−0.419586	+	0.155444i
$889$	11.2604	−	15.4986i	0.377660	−	0.519805i
$890$	−0.304686	+	0.367390i	−0.0102131	+	0.0123150i
$891$	−8.43930	+	55.2326i	−0.282727	+	1.85036i
$892$	−2.51747	−	7.74799i	−0.0842913	−	0.259422i
$893$	1.24839			0.0417757
$894$	−2.52907	+	0.102823i	−0.0845848	+	0.00343892i
$895$	−1.14110	+	17.7914i	−0.0381429	+	0.594701i
$896$	0.948049	+	1.30488i	0.0316721	+	0.0435929i
$897$	−24.1398	−	16.0821i	−0.806006	−	0.536967i
$898$	−15.4033			−0.514016
$899$	3.82529	−	31.3298i	0.127580	−	1.04491i
$900$	−11.7092	−	9.37523i	−0.390306	−	0.312508i
$901$	19.7026	+	14.3148i	0.656388	+	0.476894i
$902$	−20.7319	−	28.5351i	−0.690298	−	0.950114i
$903$	8.82250	+	23.8143i	0.293594	+	0.792492i
$904$	12.0765			0.401659
$905$	−6.50037	+	16.3598i	−0.216079	+	0.543818i
$906$	−1.51471	−	4.08860i	−0.0503227	−	0.135835i
$907$	−33.2716	−	10.8106i	−1.10477	−	0.358960i	−0.300831	−	0.953677i	$-0.597264\pi$
$907$	−33.2716	−	10.8106i	−1.10477	−	0.358960i	−0.803935	+	0.594717i	$0.797264\pi$
$908$	−0.893927	+	2.75122i	−0.0296660	+	0.0913026i
$909$	4.95236	−	8.13123i	0.164259	−	0.269696i
$910$	−17.7930	−	1.14121i	−0.589833	−	0.0378307i
$911$	−5.68972	−	4.13382i	−0.188509	−	0.136960i	0.489528	−	0.871988i	$-0.337169\pi$
$911$	−5.68972	−	4.13382i	−0.188509	−	0.136960i	−0.678037	+	0.735028i	$0.737169\pi$
$912$	0.116173	+	0.146952i	0.00384689	+	0.00486608i
$913$	63.0754	+	20.4944i	2.08749	+	0.678267i
$914$	28.9019	−	20.9984i	0.955989	−	0.694566i
$915$	−13.6067	+	4.07143i	−0.449824	+	0.134597i
$916$	−17.0911	−	5.55325i	−0.564707	−	0.183484i
$917$	26.8909	−	19.5374i	0.888016	−	0.645182i
$918$	27.1973	+	15.0854i	0.897645	+	0.497891i
$919$	12.0051	+	36.9480i	0.396013	+	1.21880i	0.928170	+	0.372157i	$0.121382\pi$
$919$	12.0051	+	36.9480i	0.396013	+	1.21880i	−0.532157	+	0.846646i	$0.678618\pi$
$920$	−6.40058	+	4.05100i	−0.211021	+	0.133558i
$921$	3.63802	−	12.9671i	0.119877	−	0.427282i
$922$	−2.58997	+	7.97110i	−0.0852961	+	0.262514i
$923$	−8.52332	+	2.76940i	−0.280549	+	0.0911558i
$924$	17.3292	−	0.704544i	0.570089	−	0.0231778i
$925$	−27.9948	−	26.4175i	−0.920463	−	0.868603i
$926$	3.52498	+	10.8488i	0.115838	+	0.356512i
$927$	−19.7257	−	22.9687i	−0.647878	−	0.754391i
$928$	−4.58615	−	3.33203i	−0.150548	−	0.109379i
$929$	−3.75817			−0.123301			−0.0616507	−	0.998098i	$-0.519636\pi$
$929$	−3.75817			−0.123301			−0.0616507	+	0.998098i	$0.519636\pi$
$930$	−21.2558	+	3.63222i	−0.697004	+	0.119105i
$931$	−0.475711			−0.0155908
$932$	14.4296	+	10.4837i	0.472656	+	0.343405i
$933$	25.0800	−	19.8270i	0.821083	−	0.649108i
$934$	6.79416	+	20.9103i	0.222312	+	0.684205i
$935$	30.6809	−	77.2162i	1.00337	−	2.52524i
$936$	−14.7819	+	1.20395i	−0.483161	+	0.0393522i
$937$	−36.5383	+	11.8720i	−1.19365	+	0.387842i	−0.837423	−	0.546556i	$-0.815939\pi$
$937$	−36.5383	+	11.8720i	−1.19365	+	0.387842i	−0.356232	+	0.934398i	$0.615939\pi$
$938$	6.47378	−	19.9242i	0.211376	−	0.650550i
$939$	8.94638	+	2.50997i	0.291954	+	0.0819097i
$940$	13.8034	+	21.8093i	0.450216	+	0.711341i
$941$	5.70299	+	17.5520i	0.185912	+	0.572179i	0.999963	−	0.00861474i	$-0.00274219\pi$
$941$	5.70299	+	17.5520i	0.185912	+	0.572179i	−0.814051	+	0.580794i	$0.802742\pi$
$942$	−1.99460	−	1.32881i	−0.0649874	−	0.0432951i
$943$	15.5705	−	11.3126i	0.507046	−	0.368390i
$944$	0.390049	+	0.126734i	0.0126950	+	0.00412486i
$945$	−17.4585	+	6.81195i	−0.567926	+	0.221593i
$946$	45.6578	−	33.1724i	1.48446	−	1.07853i
$947$	−4.83016	−	1.56941i	−0.156959	−	0.0509991i	0.229484	−	0.973313i	$-0.426296\pi$
$947$	−4.83016	−	1.56941i	−0.156959	−	0.0509991i	−0.386443	+	0.922313i	$0.626296\pi$
$948$	−6.79076	+	5.36844i	−0.220554	+	0.174359i
$949$	−66.2246	−	48.1150i	−2.14974	−	1.56188i
$950$	−0.231438	+	0.488737i	−0.00750885	+	0.0158567i
$951$	0.388884	−	0.583728i	0.0126104	−	0.0189287i
$952$	2.98322	−	9.18140i	0.0966866	−	0.297571i
$953$	−17.6265	−	5.72720i	−0.570979	−	0.185522i	0.00927631	−	0.999957i	$-0.497047\pi$
$953$	−17.6265	−	5.72720i	−0.570979	−	0.185522i	−0.580255	+	0.814435i	$0.697047\pi$
$954$	−11.2647	+	4.70203i	−0.364708	+	0.152234i
$955$	−7.88727	+	19.8503i	−0.255226	+	0.642340i
$956$	3.13493			0.101391
$957$	−57.1594	+	21.1758i	−1.84770	+	0.684518i
$958$	3.73715	+	5.14374i	0.120742	+	0.166187i
$959$	12.3108	+	8.94432i	0.397536	+	0.288827i
$960$	−1.28273	+	3.65439i	−0.0414000	+	0.117945i
$961$	−16.3919	+	26.3117i	−0.528770	+	0.848765i
$962$	−38.0574			−1.22702
$963$	15.1517	+	9.22818i	0.488255	+	0.297374i
$964$	3.32351	+	4.57441i	0.107043	+	0.147332i
$965$	−28.9727	−	1.85825i	−0.932665	−	0.0598193i
$966$	0.384443	+	9.45588i	0.0123692	+	0.304238i
$967$	11.9867			0.385466			0.192733	−	0.981251i	$-0.438265\pi$
$967$	11.9867			0.385466			0.192733	+	0.981251i	$0.438265\pi$
$968$	−8.51079	−	26.1935i	−0.273547	−	0.841891i
$969$	0.302871	−	1.07954i	0.00972963	−	0.0346797i
$970$	25.1390	+	20.8484i	0.807164	+	0.669402i
$971$	−21.4511	+	29.5249i	−0.688398	+	0.947498i	−0.999996	−	0.00271558i	$-0.999136\pi$
$971$	−21.4511	+	29.5249i	−0.688398	+	0.947498i	0.311599	+	0.950214i	$0.399136\pi$
$972$	−13.5486	+	7.70944i	−0.434571	+	0.247280i
$973$	1.88088	+	1.36654i	0.0602984	+	0.0438093i
$974$	4.42131	−	3.21227i	0.141668	−	0.102928i
$975$	−22.0429	−	36.7022i	−0.705939	−	1.17541i
$976$	2.15549	+	2.96678i	0.0689956	+	0.0949643i
$977$	1.74397	−	1.26706i	0.0557944	−	0.0405370i	−0.559538	−	0.828804i	$-0.689022\pi$
$977$	1.74397	−	1.26706i	0.0557944	−	0.0405370i	0.615333	+	0.788267i	$0.289022\pi$
$978$	10.0898	−	35.9635i	0.322637	−	1.14999i
$979$	1.07207	−	0.778904i	0.0342635	−	0.0248939i
$980$	−5.25992	−	8.31067i	−0.168022	−	0.265475i
$981$	−6.41303	−	15.3637i	−0.204752	−	0.490526i
$982$	31.0244	+	22.5405i	0.990028	+	0.719297i
$983$	−5.82985	−	1.89423i	−0.185943	−	0.0604166i	0.214565	−	0.976710i	$-0.431167\pi$
$983$	−5.82985	−	1.89423i	−0.185943	−	0.0604166i	−0.400509	+	0.916293i	$0.631167\pi$
$984$	2.65819	−	9.47469i	0.0847400	−	0.302042i
$985$	−46.6051	−	2.98916i	−1.48496	−	0.0952425i
$986$			33.9297i			1.08054i
$987$	32.2199	−	1.30995i	1.02557	−	0.0416961i
$988$	0.165221	+	0.508498i	0.00525638	+	0.0161775i
$989$	18.1009	+	24.9137i	0.575575	+	0.792211i
$990$	25.0552	+	33.2657i	0.796306	+	1.05725i
$991$			0.188097i			0.00597509i	0.999996	+	0.00298755i	$0.000950967\pi$
$991$			0.188097i			0.00597509i	−0.999996	+	0.00298755i	$0.999049\pi$
$992$	2.70260	+	4.86785i	0.0858077	+	0.154554i
$993$	19.5982	−	0.796793i	0.621930	−	0.0252855i
$994$	2.36553	+	1.71866i	0.0750301	+	0.0545125i
$995$	4.72725	+	18.5050i	0.149864	+	0.586648i
$996$	6.42800	+	17.3509i	0.203679	+	0.549785i
$997$		−	16.7853i		−	0.531595i	−0.964029	−	0.265797i	$-0.914365\pi$
$997$		−	16.7853i		−	0.531595i	0.964029	−	0.265797i	$-0.0856352\pi$
$998$		−	31.2014i		−	0.987664i
$999$	−36.2583	+	16.8956i	−1.14716	+	0.534552i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.y.b.29.10	yes	128
3.2	odd	2		930.2.y.a.29.22	✓	128
5.4	even	2		930.2.y.a.29.23	yes	128
15.14	odd	2	inner	930.2.y.b.29.11	yes	128
31.15	odd	10	inner	930.2.y.b.449.11	yes	128
93.77	even	10		930.2.y.a.449.23	yes	128
155.139	odd	10		930.2.y.a.449.22	yes	128
465.449	even	10	inner	930.2.y.b.449.10	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.y.a.29.22	✓	128	3.2	odd	2
930.2.y.a.29.23	yes	128	5.4	even	2
930.2.y.a.449.22	yes	128	155.139	odd	10
930.2.y.a.449.23	yes	128	93.77	even	10
930.2.y.b.29.10	yes	128	1.1	even	1	trivial
930.2.y.b.29.11	yes	128	15.14	odd	2	inner
930.2.y.b.449.10	yes	128	465.449	even	10	inner
930.2.y.b.449.11	yes	128	31.15	odd	10	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-1.07416 - 1.35874i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.07804 + 0.825684i) q^{5} +(-0.0703609 - 1.73062i) q^{6} +(-1.53398 + 0.498419i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.692375 + 2.91901i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-1.07416 - 1.35874i) q^{3} +(0.309017 + 0.951057i) q^{4} +(2.07804 + 0.825684i) q^{5} +(-0.0703609 - 1.73062i) q^{6} +(-1.53398 + 0.498419i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.692375 + 2.91901i) q^{9} +(1.19584 + 1.88943i) q^{10} +(-1.91843 - 5.90433i) q^{11} +(0.960310 - 1.44146i) q^{12} +(3.99946 - 2.90578i) q^{13} +(-1.53398 - 0.498419i) q^{14} +(-1.11025 - 3.71044i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(5.69242 + 1.84958i) q^{17} +(-2.27589 + 1.95456i) q^{18} +(0.0874977 + 0.0635708i) q^{19} +(-0.143123 + 2.23148i) q^{20} +(2.32495 + 1.54890i) q^{21} +(1.91843 - 5.90433i) q^{22} +(3.22177 + 1.04682i) q^{23} +(1.62418 - 0.601709i) q^{24} +(3.63649 + 3.43161i) q^{25} +4.94361 q^{26} +(4.70991 - 2.19471i) q^{27} +(-0.948049 - 1.30488i) q^{28} +(4.58615 + 3.33203i) q^{29} +(1.28273 - 3.65439i) q^{30} +(-2.70260 - 4.86785i) q^{31} -1.00000 q^{32} +(-5.96178 + 8.94884i) q^{33} +(3.51811 + 4.84226i) q^{34} +(-3.59920 - 0.230845i) q^{35} +(-2.99010 + 0.243536i) q^{36} -7.69830 q^{37} +(0.0334212 + 0.102860i) q^{38} +(-8.24426 - 2.31299i) q^{39} +(-1.42742 + 1.72118i) q^{40} +(3.33946 - 4.59637i) q^{41} +(0.970506 + 2.61966i) q^{42} +(7.35446 + 5.34333i) q^{43} +(5.02252 - 3.64908i) q^{44} +(-3.84896 + 5.49413i) q^{45} +(1.99116 + 2.74060i) q^{46} +(9.33830 - 6.78467i) q^{47} +(1.66766 + 0.467874i) q^{48} +(-3.55846 + 2.58537i) q^{49} +(0.924936 + 4.91370i) q^{50} +(-3.60144 - 9.72128i) q^{51} +(3.99946 + 2.90578i) q^{52} +(3.86974 + 1.25735i) q^{53} +(5.10042 + 0.992854i) q^{54} +(0.888532 - 13.8534i) q^{55} -1.61292i q^{56} +(-0.00760975 - 0.187172i) q^{57} +(1.75175 + 5.39134i) q^{58} +(-0.241063 - 0.331795i) q^{59} +(3.18575 - 2.20250i) q^{60} -3.66714i q^{61} +(0.674798 - 5.52672i) q^{62} +(-0.392804 - 4.82278i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(10.7103 - 2.73603i) q^{65} +(-10.0832 + 3.73551i) q^{66} +12.9886i q^{67} +5.98536i q^{68} +(-2.03833 - 5.50201i) q^{69} +(-2.77612 - 2.30231i) q^{70} +(-1.72411 - 0.560197i) q^{71} +(-2.56219 - 1.56051i) q^{72} +(-5.11682 - 15.7479i) q^{73} +(-6.22805 - 4.52495i) q^{74} +(0.756516 - 8.62715i) q^{75} +(-0.0334212 + 0.102860i) q^{76} +(5.88566 + 8.10091i) q^{77} +(-5.31021 - 6.71710i) q^{78} +(-4.75321 - 1.54441i) q^{79} +(-2.16649 + 0.553448i) q^{80} +(-8.04123 - 4.04210i) q^{81} +(5.40335 - 1.75566i) q^{82} +(-6.27926 + 8.64265i) q^{83} +(-0.754642 + 2.68980i) q^{84} +(10.3019 + 8.54363i) q^{85} +(2.80916 + 8.64569i) q^{86} +(-0.398861 - 9.81053i) q^{87} +6.20818 q^{88} +(0.0659604 + 0.203005i) q^{89} +(-6.34325 + 2.18248i) q^{90} +(-4.68678 + 6.45080i) q^{91} +3.38757i q^{92} +(-3.71114 + 8.90098i) q^{93} +11.5428 q^{94} +(0.129334 + 0.204348i) q^{95} +(1.07416 + 1.35874i) q^{96} +(13.8908 - 4.51339i) q^{97} -4.39850 q^{98} +(18.5631 - 1.51192i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9}+O(q^{10}) \) 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9	\( 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9} + 2 q^{10} - 35 q^{15} - 32 q^{16} - 6 q^{18} - 8 q^{19} + 3 q^{20} + 20 q^{23} - 10 q^{25} - 48 q^{31} - 128 q^{32} + 8 q^{33} + 10 q^{34} - 16 q^{35} - 4 q^{36} - 12 q^{38} + 4 q^{39} - 3 q^{40} + 5 q^{45} + 10 q^{46} - 6 q^{47} + 46 q^{49} + 5 q^{50} + 34 q^{51} + 20 q^{53} + 35 q^{60} + 8 q^{62} - 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} - 6 q^{72} + 5 q^{75} + 12 q^{76} - 50 q^{77} - 4 q^{78} - 10 q^{79} - 2 q^{80} - 24 q^{81} + 40 q^{83} - 30 q^{85} + 4 q^{87} - 5 q^{90} + 20 q^{91} + 26 q^{93} - 4 q^{94} + 26 q^{95} + 124 q^{98}+O(q^{100}) \) 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9 + 2 * q^10 - 35 * q^15 - 32 * q^16 - 6 * q^18 - 8 * q^19 + 3 * q^20 + 20 * q^23 - 10 * q^25 - 48 * q^31 - 128 * q^32 + 8 * q^33 + 10 * q^34 - 16 * q^35 - 4 * q^36 - 12 * q^38 + 4 * q^39 - 3 * q^40 + 5 * q^45 + 10 * q^46 - 6 * q^47 + 46 * q^49 + 5 * q^50 + 34 * q^51 + 20 * q^53 + 35 * q^60 + 8 * q^62 - 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 - 6 * q^72 + 5 * q^75 + 12 * q^76 - 50 * q^77 - 4 * q^78 - 10 * q^79 - 2 * q^80 - 24 * q^81 + 40 * q^83 - 30 * q^85 + 4 * q^87 - 5 * q^90 + 20 * q^91 + 26 * q^93 - 4 * q^94 + 26 * q^95 + 124 * q^98

Introduction

L-functions

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