LMFDB - Embedded newform 930.2.j.g.497.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(497,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("930.497");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			497.2
Character	$\chi$	$=$	930.497
Dual form			930.2.j.g.683.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.47409 - 0.909430i) q^{3} -1.00000i q^{4} +(2.03224 - 0.932730i) q^{5} +(1.68540 - 0.399274i) q^{6} +(-2.61297 - 2.61297i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.34588 + 2.68116i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.47409 - 0.909430i) q^{3} -1.00000i q^{4} +(2.03224 - 0.932730i) q^{5} +(1.68540 - 0.399274i) q^{6} +(-2.61297 - 2.61297i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.34588 + 2.68116i) q^{9} +(-0.777474 + 2.09655i) q^{10} +2.69413i q^{11} +(-0.909430 + 1.47409i) q^{12} +(-3.30937 + 3.30937i) q^{13} +3.69530 q^{14} +(-3.84396 - 0.473257i) q^{15} -1.00000 q^{16} +(-5.75053 + 5.75053i) q^{17} +(-2.84754 - 0.944189i) q^{18} -5.51611i q^{19} +(-0.932730 - 2.03224i) q^{20} +(1.47544 + 6.22806i) q^{21} +(-1.90504 - 1.90504i) q^{22} +(6.03462 + 6.03462i) q^{23} +(-0.399274 - 1.68540i) q^{24} +(3.26003 - 3.79107i) q^{25} -4.68015i q^{26} +(0.454387 - 5.17625i) q^{27} +(-2.61297 + 2.61297i) q^{28} +5.99409 q^{29} +(3.05273 - 2.38345i) q^{30} +1.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(2.45013 - 3.97139i) q^{33} -8.13247i q^{34} +(-7.74738 - 2.87300i) q^{35} +(2.68116 - 1.34588i) q^{36} +(6.06796 + 6.06796i) q^{37} +(3.90048 + 3.90048i) q^{38} +(7.88794 - 1.86866i) q^{39} +(2.09655 + 0.777474i) q^{40} +2.10704i q^{41} +(-5.44719 - 3.36061i) q^{42} +(-5.90761 + 5.90761i) q^{43} +2.69413 q^{44} +(5.23594 + 4.19343i) q^{45} -8.53424 q^{46} +(5.62807 - 5.62807i) q^{47} +(1.47409 + 0.909430i) q^{48} +6.65521i q^{49} +(0.375500 + 4.98588i) q^{50} +(13.7065 - 3.24709i) q^{51} +(3.30937 + 3.30937i) q^{52} +(-1.97089 - 1.97089i) q^{53} +(3.33886 + 3.98146i) q^{54} +(2.51290 + 5.47514i) q^{55} -3.69530i q^{56} +(-5.01652 + 8.13124i) q^{57} +(-4.23846 + 4.23846i) q^{58} +3.53235 q^{59} +(-0.473257 + 3.84396i) q^{60} +1.96650 q^{61} +(-0.707107 + 0.707107i) q^{62} +(3.48906 - 10.5225i) q^{63} +1.00000i q^{64} +(-3.63870 + 9.81219i) q^{65} +(1.07570 + 4.54070i) q^{66} +(-3.81869 - 3.81869i) q^{67} +(5.75053 + 5.75053i) q^{68} +(-3.40750 - 14.3836i) q^{69} +(7.50974 - 3.44671i) q^{70} +9.25687i q^{71} +(-0.944189 + 2.84754i) q^{72} +(-1.58612 + 1.58612i) q^{73} -8.58139 q^{74} +(-8.25329 + 2.62360i) q^{75} -5.51611 q^{76} +(7.03969 - 7.03969i) q^{77} +(-4.25627 + 6.89896i) q^{78} +5.86965i q^{79} +(-2.03224 + 0.932730i) q^{80} +(-5.37724 + 7.21701i) q^{81} +(-1.48990 - 1.48990i) q^{82} +(2.85071 + 2.85071i) q^{83} +(6.22806 - 1.47544i) q^{84} +(-6.32279 + 17.0502i) q^{85} -8.35462i q^{86} +(-8.83582 - 5.45120i) q^{87} +(-1.90504 + 1.90504i) q^{88} -5.13546 q^{89} +(-6.66758 + 0.737166i) q^{90} +17.2945 q^{91} +(6.03462 - 6.03462i) q^{92} +(-1.47409 - 0.909430i) q^{93} +7.95929i q^{94} +(-5.14504 - 11.2101i) q^{95} +(-1.68540 + 0.399274i) q^{96} +(1.82697 + 1.82697i) q^{97} +(-4.70594 - 4.70594i) q^{98} +(-7.22341 + 3.62597i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} - 8 q^{7}+O(q^{10}) $ 40 * q - 4 * q^3 - 8 * q^7	$ 40 q - 4 q^{3} - 8 q^{7} + 8 q^{10} + 4 q^{12} - 20 q^{13} - 44 q^{15} - 40 q^{16} + 16 q^{18} - 32 q^{21} - 4 q^{22} + 8 q^{25} + 8 q^{27} - 8 q^{28} - 4 q^{30} + 40 q^{31} + 48 q^{33} + 64 q^{37} - 4 q^{40} - 20 q^{42} - 48 q^{43} - 4 q^{45} - 80 q^{46} + 4 q^{48} + 48 q^{51} + 20 q^{52} + 164 q^{55} + 40 q^{57} + 56 q^{58} + 24 q^{60} - 128 q^{61} + 56 q^{63} + 8 q^{66} - 4 q^{67} - 56 q^{70} - 16 q^{72} - 48 q^{73} - 48 q^{75} - 40 q^{76} - 36 q^{78} - 24 q^{81} - 16 q^{82} - 56 q^{85} - 12 q^{87} - 4 q^{88} - 28 q^{90} - 32 q^{91} - 4 q^{93} - 52 q^{97}+O(q^{100}) $ 40 * q - 4 * q^3 - 8 * q^7 + 8 * q^10 + 4 * q^12 - 20 * q^13 - 44 * q^15 - 40 * q^16 + 16 * q^18 - 32 * q^21 - 4 * q^22 + 8 * q^25 + 8 * q^27 - 8 * q^28 - 4 * q^30 + 40 * q^31 + 48 * q^33 + 64 * q^37 - 4 * q^40 - 20 * q^42 - 48 * q^43 - 4 * q^45 - 80 * q^46 + 4 * q^48 + 48 * q^51 + 20 * q^52 + 164 * q^55 + 40 * q^57 + 56 * q^58 + 24 * q^60 - 128 * q^61 + 56 * q^63 + 8 * q^66 - 4 * q^67 - 56 * q^70 - 16 * q^72 - 48 * q^73 - 48 * q^75 - 40 * q^76 - 36 * q^78 - 24 * q^81 - 16 * q^82 - 56 * q^85 - 12 * q^87 - 4 * q^88 - 28 * q^90 - 32 * q^91 - 4 * q^93 - 52 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−1.47409	−	0.909430i	−0.851066	−	0.525059i
$3$	−1.47409	−	0.909430i	−0.851066	−	0.525059i
$4$		−	1.00000i		−	0.500000i
$5$	2.03224	−	0.932730i	0.908847	−	0.417129i
$5$	2.03224	−	0.932730i	0.908847	−	0.417129i
$6$	1.68540	−	0.399274i	0.688063	−	0.163003i
$7$	−2.61297	−	2.61297i	−0.987609	−	0.987609i	0.0123150	−	0.999924i	$-0.496080\pi$
$7$	−2.61297	−	2.61297i	−0.987609	−	0.987609i	−0.999924	+	0.0123150i	$0.996080\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	1.34588	+	2.68116i	0.448625	+	0.893720i
$10$	−0.777474	+	2.09655i	−0.245859	+	0.662988i
$11$			2.69413i			0.812312i	0.913804	+	0.406156i	$0.133131\pi$
$11$			2.69413i			0.812312i	−0.913804	+	0.406156i	$0.866869\pi$
$12$	−0.909430	+	1.47409i	−0.262530	+	0.425533i
$13$	−3.30937	+	3.30937i	−0.917854	+	0.917854i	−0.996873	−	0.0790195i	$-0.974821\pi$
$13$	−3.30937	+	3.30937i	−0.917854	+	0.917854i	0.0790195	+	0.996873i	$0.474821\pi$
$14$	3.69530			0.987609
$15$	−3.84396	−	0.473257i	−0.992506	−	0.122194i
$16$	−1.00000			−0.250000
$17$	−5.75053	+	5.75053i	−1.39471	+	1.39471i	−0.580317	+	0.814391i	$0.697071\pi$
$17$	−5.75053	+	5.75053i	−1.39471	+	1.39471i	−0.814391	+	0.580317i	$0.802929\pi$
$18$	−2.84754	−	0.944189i	−0.671173	−	0.222547i
$19$		−	5.51611i		−	1.26548i	−0.774363	−	0.632742i	$-0.781930\pi$
$19$		−	5.51611i		−	1.26548i	0.774363	−	0.632742i	$-0.218070\pi$
$20$	−0.932730	−	2.03224i	−0.208565	−	0.454424i
$21$	1.47544	+	6.22806i	0.321967	+	1.35907i
$22$	−1.90504	−	1.90504i	−0.406156	−	0.406156i
$23$	6.03462	+	6.03462i	1.25831	+	1.25831i	0.951901	+	0.306404i	$0.0991259\pi$
$23$	6.03462	+	6.03462i	1.25831	+	1.25831i	0.306404	+	0.951901i	$0.400874\pi$
$24$	−0.399274	−	1.68540i	−0.0815015	−	0.344031i
$25$	3.26003	−	3.79107i	0.652006	−	0.758214i
$26$		−	4.68015i		−	0.917854i
$27$	0.454387	−	5.17625i	0.0874468	−	0.996169i
$28$	−2.61297	+	2.61297i	−0.493805	+	0.493805i
$29$	5.99409			1.11307			0.556537	−	0.830823i	$-0.312130\pi$
$29$	5.99409			1.11307			0.556537	+	0.830823i	$0.312130\pi$
$30$	3.05273	−	2.38345i	0.557350	−	0.435156i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	2.45013	−	3.97139i	0.426512	−	0.691331i
$34$		−	8.13247i		−	1.39471i
$35$	−7.74738	−	2.87300i	−1.30955	−	0.485625i
$36$	2.68116	−	1.34588i	0.446860	−	0.224313i
$37$	6.06796	+	6.06796i	0.997567	+	0.997567i	0.999997	−	0.00243044i	$-0.000773635\pi$
$37$	6.06796	+	6.06796i	0.997567	+	0.997567i	−0.00243044	+	0.999997i	$0.500774\pi$
$38$	3.90048	+	3.90048i	0.632742	+	0.632742i
$39$	7.88794	−	1.86866i	1.26308	−	0.299226i
$40$	2.09655	+	0.777474i	0.331494	+	0.122929i
$41$			2.10704i			0.329064i	0.986372	+	0.164532i	$0.0526114\pi$
$41$			2.10704i			0.329064i	−0.986372	+	0.164532i	$0.947389\pi$
$42$	−5.44719	−	3.36061i	−0.840520	−	0.518554i
$43$	−5.90761	+	5.90761i	−0.900902	+	0.900902i	−0.995514	−	0.0946125i	$-0.969839\pi$
$43$	−5.90761	+	5.90761i	−0.900902	+	0.900902i	0.0946125	+	0.995514i	$0.469839\pi$
$44$	2.69413			0.406156
$45$	5.23594	+	4.19343i	0.780528	+	0.625120i
$46$	−8.53424			−1.25831
$47$	5.62807	−	5.62807i	0.820938	−	0.820938i	−0.165304	−	0.986243i	$-0.552861\pi$
$47$	5.62807	−	5.62807i	0.820938	−	0.820938i	0.986243	+	0.165304i	$0.0528606\pi$
$48$	1.47409	+	0.909430i	0.212766	+	0.131265i
$49$			6.65521i			0.950744i
$50$	0.375500	+	4.98588i	0.0531037	+	0.705110i
$51$	13.7065	−	3.24709i	1.91929	−	0.454683i
$52$	3.30937	+	3.30937i	0.458927	+	0.458927i
$53$	−1.97089	−	1.97089i	−0.270723	−	0.270723i	0.558668	−	0.829391i	$-0.311312\pi$
$53$	−1.97089	−	1.97089i	−0.270723	−	0.270723i	−0.829391	+	0.558668i	$0.811312\pi$
$54$	3.33886	+	3.98146i	0.454361	+	0.541808i
$55$	2.51290	+	5.47514i	0.338839	+	0.738268i
$56$		−	3.69530i		−	0.493805i
$57$	−5.01652	+	8.13124i	−0.664454	+	1.07701i
$58$	−4.23846	+	4.23846i	−0.556537	+	0.556537i
$59$	3.53235			0.459873			0.229936	−	0.973206i	$-0.426148\pi$
$59$	3.53235			0.459873			0.229936	+	0.973206i	$0.426148\pi$
$60$	−0.473257	+	3.84396i	−0.0610972	+	0.496253i
$61$	1.96650			0.251784			0.125892	−	0.992044i	$-0.459821\pi$
$61$	1.96650			0.251784			0.125892	+	0.992044i	$0.459821\pi$
$62$	−0.707107	+	0.707107i	−0.0898027	+	0.0898027i
$63$	3.48906	−	10.5225i	0.439580	−	1.32571i
$64$			1.00000i			0.125000i
$65$	−3.63870	+	9.81219i	−0.451325	+	1.21705i
$66$	1.07570	+	4.54070i	0.132409	+	0.558922i
$67$	−3.81869	−	3.81869i	−0.466527	−	0.466527i	0.434260	−	0.900787i	$-0.357010\pi$
$67$	−3.81869	−	3.81869i	−0.466527	−	0.466527i	−0.900787	+	0.434260i	$0.857010\pi$
$68$	5.75053	+	5.75053i	0.697354	+	0.697354i
$69$	−3.40750	−	14.3836i	−0.410215	−	1.73159i
$70$	7.50974	−	3.44671i	0.897586	−	0.411961i
$71$			9.25687i			1.09859i	0.835629	+	0.549294i	$0.185103\pi$
$71$			9.25687i			1.09859i	−0.835629	+	0.549294i	$0.814897\pi$
$72$	−0.944189	+	2.84754i	−0.111274	+	0.335586i
$73$	−1.58612	+	1.58612i	−0.185641	+	0.185641i	−0.793809	−	0.608167i	$-0.791905\pi$
$73$	−1.58612	+	1.58612i	−0.185641	+	0.185641i	0.608167	+	0.793809i	$0.291905\pi$
$74$	−8.58139			−0.997567
$75$	−8.25329	+	2.62360i	−0.953007	+	0.302947i
$76$	−5.51611			−0.632742
$77$	7.03969	−	7.03969i	0.802247	−	0.802247i
$78$	−4.25627	+	6.89896i	−0.481928	+	0.781154i
$79$			5.86965i			0.660387i	0.943913	+	0.330193i	$0.107114\pi$
$79$			5.86965i			0.660387i	−0.943913	+	0.330193i	$0.892886\pi$
$80$	−2.03224	+	0.932730i	−0.227212	+	0.104282i
$81$	−5.37724	+	7.21701i	−0.597471	+	0.801890i
$82$	−1.48990	−	1.48990i	−0.164532	−	0.164532i
$83$	2.85071	+	2.85071i	0.312906	+	0.312906i	0.846034	−	0.533128i	$-0.178984\pi$
$83$	2.85071	+	2.85071i	0.312906	+	0.312906i	−0.533128	+	0.846034i	$0.678984\pi$
$84$	6.22806	−	1.47544i	0.679537	−	0.160983i
$85$	−6.32279	+	17.0502i	−0.685803	+	1.84935i
$86$		−	8.35462i		−	0.900902i
$87$	−8.83582	−	5.45120i	−0.947299	−	0.584430i
$88$	−1.90504	+	1.90504i	−0.203078	+	0.203078i
$89$	−5.13546			−0.544357			−0.272179	−	0.962247i	$-0.587744\pi$
$89$	−5.13546			−0.544357			−0.272179	+	0.962247i	$0.587744\pi$
$90$	−6.66758	+	0.737166i	−0.702824	+	0.0777041i
$91$	17.2945			1.81296
$92$	6.03462	−	6.03462i	0.629153	−	0.629153i
$93$	−1.47409	−	0.909430i	−0.152856	−	0.0943035i
$94$			7.95929i			0.820938i
$95$	−5.14504	−	11.2101i	−0.527870	−	1.15013i
$96$	−1.68540	+	0.399274i	−0.172016	+	0.0407508i
$97$	1.82697	+	1.82697i	0.185500	+	0.185500i	0.793748	−	0.608247i	$-0.208127\pi$
$97$	1.82697	+	1.82697i	0.185500	+	0.185500i	−0.608247	+	0.793748i	$0.708127\pi$
$98$	−4.70594	−	4.70594i	−0.475372	−	0.475372i
$99$	−7.22341	+	3.62597i	−0.725980	+	0.364424i
$100$	−3.79107	−	3.26003i	−0.379107	−	0.326003i
$101$			13.1616i			1.30962i	0.755792	+	0.654812i	$0.227252\pi$
$101$			13.1616i			1.30962i	−0.755792	+	0.654812i	$0.772748\pi$
$102$	−7.39591	+	11.9880i	−0.732305	+	1.18699i
$103$	3.80259	−	3.80259i	0.374680	−	0.374680i	−0.494498	−	0.869179i	$-0.664648\pi$
$103$	3.80259	−	3.80259i	0.374680	−	0.374680i	0.869179	+	0.494498i	$0.164648\pi$
$104$	−4.68015			−0.458927
$105$	8.80754	+	11.2808i	0.859528	+	1.10089i
$106$	2.78726			0.270723
$107$	4.25578	−	4.25578i	0.411422	−	0.411422i	−0.470812	−	0.882234i	$-0.656039\pi$
$107$	4.25578	−	4.25578i	0.411422	−	0.411422i	0.882234	+	0.470812i	$0.156039\pi$
$108$	−5.17625	−	0.454387i	−0.498085	−	0.0437234i
$109$			18.9374i			1.81387i	0.421270	+	0.906935i	$0.361585\pi$
$109$			18.9374i			1.81387i	−0.421270	+	0.906935i	$0.638415\pi$
$110$	−5.64840	−	2.09462i	−0.538553	−	0.199714i
$111$	−3.42633	−	14.4631i	−0.325213	−	1.37278i
$112$	2.61297	+	2.61297i	0.246902	+	0.246902i
$113$	3.90901	+	3.90901i	0.367729	+	0.367729i	0.866648	−	0.498920i	$-0.166270\pi$
$113$	3.90901	+	3.90901i	0.367729	+	0.367729i	−0.498920	+	0.866648i	$0.666270\pi$
$114$	−2.20244	−	9.29687i	−0.206278	−	0.870731i
$115$	17.8925	+	6.63515i	1.66848	+	0.618731i
$116$		−	5.99409i		−	0.556537i
$117$	−13.3269	−	4.41895i	−1.23208	−	0.408532i
$118$	−2.49775	+	2.49775i	−0.229936	+	0.229936i
$119$	30.0519			2.75485
$120$	−2.38345	−	3.05273i	−0.217578	−	0.278675i
$121$	3.74164			0.340149
$122$	−1.39052	+	1.39052i	−0.125892	+	0.125892i
$123$	1.91621	−	3.10596i	0.172778	−	0.280055i
$124$		−	1.00000i		−	0.0898027i
$125$	3.08914	−	10.7451i	0.276301	−	0.961071i
$126$	4.97341	+	9.90768i	0.443066	+	0.882646i
$127$	−2.51273	−	2.51273i	−0.222968	−	0.222968i	0.586779	−	0.809747i	$-0.300396\pi$
$127$	−2.51273	−	2.51273i	−0.222968	−	0.222968i	−0.809747	+	0.586779i	$0.800396\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	14.0809	−	3.33578i	1.23975	−	0.293699i
$130$	−4.36532	−	9.51121i	−0.382864	−	0.834189i
$131$			6.35172i			0.554953i	0.960732	+	0.277476i	$0.0894980\pi$
$131$			6.35172i			0.554953i	−0.960732	+	0.277476i	$0.910502\pi$
$132$	−3.97139	−	2.45013i	−0.345665	−	0.213256i
$133$	−14.4134	+	14.4134i	−1.24980	+	1.24980i
$134$	5.40044			0.466527
$135$	−3.90461	−	10.9432i	−0.336056	−	0.941842i
$136$	−8.13247			−0.697354
$137$	−2.97942	+	2.97942i	−0.254549	+	0.254549i	−0.822833	−	0.568284i	$-0.807608\pi$
$137$	−2.97942	+	2.97942i	−0.254549	+	0.254549i	0.568284	+	0.822833i	$0.307608\pi$
$138$	12.5802	+	7.76130i	1.07090	+	0.660685i
$139$			1.55086i			0.131542i	0.997835	+	0.0657711i	$0.0209507\pi$
$139$			1.55086i			0.131542i	−0.997835	+	0.0657711i	$0.979049\pi$
$140$	−2.87300	+	7.74738i	−0.242813	+	0.654773i
$141$	−13.4146	+	3.17794i	−1.12971	+	0.267631i
$142$	−6.54560	−	6.54560i	−0.549294	−	0.549294i
$143$	−8.91588	−	8.91588i	−0.745584	−	0.745584i
$144$	−1.34588	−	2.68116i	−0.112156	−	0.223430i
$145$	12.1814	−	5.59086i	1.01161	−	0.464296i
$146$		−	2.24311i		−	0.185641i
$147$	6.05244	−	9.81037i	0.499197	−	0.809145i
$148$	6.06796	−	6.06796i	0.498783	−	0.498783i
$149$	−14.7180			−1.20575			−0.602874	−	0.797837i	$-0.705978\pi$
$149$	−14.7180			−1.20575			−0.602874	+	0.797837i	$0.705978\pi$
$150$	3.98079	−	7.69112i	0.325030	−	0.627977i
$151$	7.23667			0.588912			0.294456	−	0.955665i	$-0.404862\pi$
$151$	7.23667			0.588912			0.294456	+	0.955665i	$0.404862\pi$
$152$	3.90048	−	3.90048i	0.316371	−	0.316371i
$153$	−23.1576	−	7.67859i	−1.87218	−	0.620777i
$154$			9.95562i			0.802247i
$155$	2.03224	−	0.932730i	0.163234	−	0.0749186i
$156$	−1.86866	−	7.88794i	−0.149613	−	0.631541i
$157$	−5.52139	−	5.52139i	−0.440655	−	0.440655i	0.451577	−	0.892232i	$-0.350862\pi$
$157$	−5.52139	−	5.52139i	−0.440655	−	0.440655i	−0.892232	+	0.451577i	$0.850862\pi$
$158$	−4.15047	−	4.15047i	−0.330193	−	0.330193i
$159$	1.11288	+	4.69766i	0.0882573	+	0.372548i
$160$	0.777474	−	2.09655i	0.0614647	−	0.165747i
$161$		−	31.5366i		−	2.48543i
$162$	−1.30092	−	8.90548i	−0.102210	−	0.699681i
$163$	6.13605	−	6.13605i	0.480613	−	0.480613i	−0.424715	−	0.905327i	$-0.639626\pi$
$163$	6.13605	−	6.13605i	0.480613	−	0.480613i	0.905327	+	0.424715i	$0.139626\pi$
$164$	2.10704			0.164532
$165$	1.27502	−	10.3561i	0.0992600	−	0.806225i
$166$	−4.03151			−0.312906
$167$	−13.2634	+	13.2634i	−1.02635	+	1.02635i	−0.0267081	+	0.999643i	$0.508502\pi$
$167$	−13.2634	+	13.2634i	−1.02635	+	1.02635i	−0.999643	+	0.0267081i	$0.991498\pi$
$168$	−3.36061	+	5.44719i	−0.259277	+	0.420260i
$169$		−	8.90383i		−	0.684910i
$170$	−7.58540	−	16.5272i	−0.581774	−	1.26758i
$171$	14.7896	−	7.42400i	1.13099	−	0.567728i
$172$	5.90761	+	5.90761i	0.450451	+	0.450451i
$173$	8.71739	+	8.71739i	0.662771	+	0.662771i	0.956032	−	0.293261i	$-0.0947406\pi$
$173$	8.71739	+	8.71739i	0.662771	+	0.662771i	−0.293261	+	0.956032i	$0.594741\pi$
$174$	10.1024	−	2.39328i	0.765864	−	0.181434i
$175$	−18.4243	+	1.38758i	−1.39275	+	0.104891i
$176$		−	2.69413i		−	0.203078i
$177$	−5.20699	−	3.21242i	−0.391382	−	0.241460i
$178$	3.63132	−	3.63132i	0.272179	−	0.272179i
$179$	−16.8402			−1.25869			−0.629347	−	0.777124i	$-0.716678\pi$
$179$	−16.8402			−1.25869			−0.629347	+	0.777124i	$0.716678\pi$
$180$	4.19343	−	5.23594i	0.312560	−	0.390264i
$181$	−5.61874			−0.417638			−0.208819	−	0.977954i	$-0.566962\pi$
$181$	−5.61874			−0.417638			−0.208819	+	0.977954i	$0.566962\pi$
$182$	−12.2291	+	12.2291i	−0.906481	+	0.906481i
$183$	−2.89879	−	1.78839i	−0.214285	−	0.132202i
$184$			8.53424i			0.629153i
$185$	17.9913	+	6.67181i	1.32275	+	0.490521i
$186$	1.68540	−	0.399274i	0.123580	−	0.0292762i
$187$	−15.4927	−	15.4927i	−1.13294	−	1.13294i
$188$	−5.62807	−	5.62807i	−0.410469	−	0.410469i
$189$	−14.7127	+	12.3381i	−1.07019	+	0.897463i
$190$	11.5648	+	4.28864i	0.839000	+	0.311130i
$191$			13.8073i			0.999063i	0.866296	+	0.499532i	$0.166495\pi$
$191$			13.8073i			0.999063i	−0.866296	+	0.499532i	$0.833505\pi$
$192$	0.909430	−	1.47409i	0.0656324	−	0.106383i
$193$	−2.52903	+	2.52903i	−0.182043	+	0.182043i	−0.792246	−	0.610202i	$-0.791088\pi$
$193$	−2.52903	+	2.52903i	−0.182043	+	0.182043i	0.610202	+	0.792246i	$0.291088\pi$
$194$	−2.58372			−0.185500
$195$	14.2873	−	11.1549i	1.02313	−	0.798819i
$196$	6.65521			0.475372
$197$	13.4212	−	13.4212i	0.956221	−	0.956221i	−0.0428604	−	0.999081i	$-0.513647\pi$
$197$	13.4212	−	13.4212i	0.956221	−	0.956221i	0.999081	+	0.0428604i	$0.0136471\pi$
$198$	2.54377	−	7.67167i	0.180778	−	0.545202i
$199$		−	9.51656i		−	0.674611i	−0.941395	−	0.337306i	$-0.890484\pi$
$199$		−	9.51656i		−	0.674611i	0.941395	−	0.337306i	$-0.109516\pi$
$200$	4.98588	−	0.375500i	0.352555	−	0.0265518i
$201$	2.15626	+	9.10191i	0.152091	+	0.641999i
$202$	−9.30662	−	9.30662i	−0.654812	−	0.654812i
$203$	−15.6624	−	15.6624i	−1.09928	−	1.09928i
$204$	−3.24709	−	13.7065i	−0.227342	−	0.959646i
$205$	1.96530	+	4.28202i	0.137262	+	0.299069i
$206$			5.37768i			0.374680i
$207$	−8.05794	+	24.3016i	−0.560066	+	1.68908i
$208$	3.30937	−	3.30937i	0.229463	−	0.229463i
$209$	14.8612			1.02797
$210$	−14.2046	−	1.74882i	−0.980208	−	0.120680i
$211$	−17.0364			−1.17283			−0.586417	−	0.810009i	$-0.699462\pi$
$211$	−17.0364			−1.17283			−0.586417	+	0.810009i	$0.699462\pi$
$212$	−1.97089	+	1.97089i	−0.135361	+	0.135361i
$213$	8.41847	−	13.6454i	0.576824	−	0.934971i
$214$			6.01858i			0.411422i
$215$	−6.49550	+	17.5159i	−0.442989	+	1.19457i
$216$	3.98146	−	3.33886i	0.270904	−	0.227181i
$217$	−2.61297	−	2.61297i	−0.177380	−	0.177380i
$218$	−13.3907	−	13.3907i	−0.906935	−	0.906935i
$219$	3.78055	−	0.895618i	0.255466	−	0.0605203i
$220$	5.47514	−	2.51290i	0.369134	−	0.169420i
$221$		−	38.0612i		−	2.56027i
$222$	12.6497	+	7.80417i	0.848995	+	0.523782i
$223$	−5.56677	+	5.56677i	−0.372779	+	0.372779i	−0.868488	−	0.495710i	$-0.834908\pi$
$223$	−5.56677	+	5.56677i	−0.372779	+	0.372779i	0.495710	+	0.868488i	$0.334908\pi$
$224$	−3.69530			−0.246902
$225$	14.5521	+	3.63836i	0.970137	+	0.242557i
$226$	−5.52818			−0.367729
$227$	12.2488	−	12.2488i	0.812981	−	0.812981i	−0.172099	−	0.985080i	$-0.555055\pi$
$227$	12.2488	−	12.2488i	0.812981	−	0.812981i	0.985080	+	0.172099i	$0.0550549\pi$
$228$	8.13124	+	5.01652i	0.538505	+	0.332227i
$229$		−	23.5554i		−	1.55658i	−0.627903	−	0.778292i	$-0.716086\pi$
$229$		−	23.5554i		−	1.55658i	0.627903	−	0.778292i	$-0.283914\pi$
$230$	−17.3437	+	7.96014i	−1.14361	+	0.524876i
$231$	−16.7792	+	3.97502i	−1.10399	+	0.261537i
$232$	4.23846	+	4.23846i	0.278268	+	0.278268i
$233$	8.55243	+	8.55243i	0.560288	+	0.560288i	0.929389	−	0.369101i	$-0.120334\pi$
$233$	8.55243	+	8.55243i	0.560288	+	0.560288i	−0.369101	+	0.929389i	$0.620334\pi$
$234$	12.5482	−	6.29890i	0.820304	−	0.411772i
$235$	6.18815	−	16.6871i	0.403670	−	1.08855i
$236$		−	3.53235i		−	0.229936i
$237$	5.33803	−	8.65238i	0.346742	−	0.562032i
$238$	−21.2499	+	21.2499i	−1.37743	+	1.37743i
$239$	−17.8938			−1.15745			−0.578727	−	0.815522i	$-0.696450\pi$
$239$	−17.8938			−1.15745			−0.578727	+	0.815522i	$0.696450\pi$
$240$	3.84396	+	0.473257i	0.248127	+	0.0305486i
$241$	17.7279			1.14196			0.570978	−	0.820965i	$-0.306564\pi$
$241$	17.7279			1.14196			0.570978	+	0.820965i	$0.306564\pi$
$242$	−2.64574	+	2.64574i	−0.170074	+	0.170074i
$243$	14.4899	−	5.74830i	0.929527	−	0.368754i
$244$		−	1.96650i		−	0.125892i
$245$	6.20751	+	13.5250i	0.396583	+	0.864081i
$246$	0.841287	+	3.55121i	0.0536385	+	0.226417i
$247$	18.2548	+	18.2548i	1.16153	+	1.16153i
$248$	0.707107	+	0.707107i	0.0449013	+	0.0449013i
$249$	−1.60968	−	6.79472i	−0.102009	−	0.430598i
$250$	5.41358	+	9.78229i	0.342385	+	0.618686i
$251$			18.0154i			1.13712i	0.822641	+	0.568561i	$0.192500\pi$
$251$			18.0154i			1.13712i	−0.822641	+	0.568561i	$0.807500\pi$
$252$	−10.5225	−	3.48906i	−0.662856	−	0.219790i
$253$	−16.2581	+	16.2581i	−1.02214	+	1.02214i
$254$	3.55353			0.222968
$255$	24.8263	−	19.3833i	1.55468	−	1.21383i
$256$	1.00000			0.0625000
$257$	2.84184	−	2.84184i	0.177269	−	0.177269i	−0.612895	−	0.790164i	$-0.709995\pi$
$257$	2.84184	−	2.84184i	0.177269	−	0.177269i	0.790164	+	0.612895i	$0.209995\pi$
$258$	−7.59794	+	12.3154i	−0.473027	+	0.766726i
$259$		−	31.7108i		−	1.97041i
$260$	9.81219	+	3.63870i	0.608526	+	0.225662i
$261$	8.06729	+	16.0711i	0.499353	+	0.994776i
$262$	−4.49135	−	4.49135i	−0.277476	−	0.277476i
$263$	−4.13665	−	4.13665i	−0.255077	−	0.255077i	0.567972	−	0.823048i	$-0.307728\pi$
$263$	−4.13665	−	4.13665i	−0.255077	−	0.255077i	−0.823048	+	0.567972i	$0.807728\pi$
$264$	4.54070	−	1.07570i	0.279461	−	0.0662047i
$265$	−5.84364	−	2.16702i	−0.358972	−	0.133119i
$266$		−	20.3837i		−	1.24980i
$267$	7.57012	+	4.67034i	0.463284	+	0.285820i
$268$	−3.81869	+	3.81869i	−0.233263	+	0.233263i
$269$	−15.1503			−0.923729			−0.461865	−	0.886950i	$-0.652819\pi$
$269$	−15.1503			−0.923729			−0.461865	+	0.886950i	$0.652819\pi$
$270$	10.4990	+	4.97704i	0.638949	+	0.302893i
$271$	−12.4573			−0.756728			−0.378364	−	0.925657i	$-0.623513\pi$
$271$	−12.4573			−0.756728			−0.378364	+	0.925657i	$0.623513\pi$
$272$	5.75053	−	5.75053i	0.348677	−	0.348677i
$273$	−25.4937	−	15.7282i	−1.54295	−	0.951912i
$274$		−	4.21354i		−	0.254549i
$275$	10.2136	+	8.78296i	0.615906	+	0.529633i
$276$	−14.3836	+	3.40750i	−0.865793	+	0.205108i
$277$	16.2191	+	16.2191i	0.974510	+	0.974510i	0.999683	−	0.0251729i	$-0.00801364\pi$
$277$	16.2191	+	16.2191i	0.974510	+	0.974510i	−0.0251729	+	0.999683i	$0.508014\pi$
$278$	−1.09662	−	1.09662i	−0.0657711	−	0.0657711i
$279$	1.34588	+	2.68116i	0.0805754	+	0.160517i
$280$	−3.44671	−	7.50974i	−0.205980	−	0.448793i
$281$			22.4136i			1.33708i	0.743676	+	0.668540i	$0.233081\pi$
$281$			22.4136i			1.33708i	−0.743676	+	0.668540i	$0.766919\pi$
$282$	7.23842	−	11.7327i	0.431042	−	0.698672i
$283$	−6.80866	+	6.80866i	−0.404733	+	0.404733i	−0.879897	−	0.475164i	$-0.842389\pi$
$283$	−6.80866	+	6.80866i	−0.404733	+	0.404733i	0.475164	+	0.879897i	$0.342389\pi$
$284$	9.25687			0.549294
$285$	−2.61054	+	21.2037i	−0.154635	+	1.25600i
$286$	12.6090			0.745584
$287$	5.50563	−	5.50563i	0.324987	−	0.324987i
$288$	2.84754	+	0.944189i	0.167793	+	0.0556369i
$289$		−	49.1371i		−	2.89042i
$290$	−4.66025	+	12.5669i	−0.273659	+	0.737955i
$291$	−1.03161	−	4.35461i	−0.0604743	−	0.255272i
$292$	1.58612	+	1.58612i	0.0928207	+	0.0928207i
$293$	−4.38747	−	4.38747i	−0.256318	−	0.256318i	0.567236	−	0.823555i	$-0.308013\pi$
$293$	−4.38747	−	4.38747i	−0.256318	−	0.256318i	−0.823555	+	0.567236i	$0.808013\pi$
$294$	2.65725	+	11.2167i	0.154974	+	0.654171i
$295$	7.17859	−	3.29473i	0.417954	−	0.191826i
$296$			8.58139i			0.498783i
$297$	13.9455	+	1.22418i	0.809200	+	0.0710341i
$298$	10.4072	−	10.4072i	0.602874	−	0.602874i
$299$	−39.9416			−2.30988
$300$	2.62360	+	8.25329i	0.151474	+	0.476504i
$301$	30.8728			1.77948
$302$	−5.11710	+	5.11710i	−0.294456	+	0.294456i
$303$	11.9695	−	19.4013i	0.687630	−	1.11458i
$304$			5.51611i			0.316371i
$305$	3.99640	−	1.83421i	0.228833	−	0.105027i
$306$	21.8045	−	10.9453i	1.24648	−	0.625701i
$307$	20.2987	+	20.2987i	1.15851	+	1.15851i	0.984797	+	0.173709i	$0.0555752\pi$
$307$	20.2987	+	20.2987i	1.15851	+	1.15851i	0.173709	+	0.984797i	$0.444425\pi$
$308$	−7.03969	−	7.03969i	−0.401124	−	0.401124i
$309$	−9.06355	+	2.14717i	−0.515607	+	0.122148i
$310$	−0.777474	+	2.09655i	−0.0441576	+	0.119076i
$311$			15.1195i			0.857348i	0.903459	+	0.428674i	$0.141019\pi$
$311$			15.1195i			0.857348i	−0.903459	+	0.428674i	$0.858981\pi$
$312$	6.89896	+	4.25627i	0.390577	+	0.240964i
$313$	−9.11114	+	9.11114i	−0.514992	+	0.514992i	−0.916052	−	0.401060i	$-0.868642\pi$
$313$	−9.11114	+	9.11114i	−0.514992	+	0.514992i	0.401060	+	0.916052i	$0.368642\pi$
$314$	7.80842			0.440655
$315$	−2.72405	−	24.6387i	−0.153483	−	1.38823i
$316$	5.86965			0.330193
$317$	−6.25420	+	6.25420i	−0.351271	+	0.351271i	−0.860582	−	0.509311i	$-0.829900\pi$
$317$	−6.25420	+	6.25420i	−0.351271	+	0.351271i	0.509311	+	0.860582i	$0.329900\pi$
$318$	−4.10867	−	2.53482i	−0.230403	−	0.142146i
$319$			16.1489i			0.904163i
$320$	0.932730	+	2.03224i	0.0521412	+	0.113606i
$321$	−10.1437	+	2.40307i	−0.566168	+	0.134126i
$322$	22.2997	+	22.2997i	1.24271	+	1.24271i
$323$	31.7206	+	31.7206i	1.76498	+	1.76498i
$324$	7.21701	+	5.37724i	0.400945	+	0.298736i
$325$	1.75740	+	23.3347i	0.0974828	+	1.29438i
$326$			8.67769i			0.480613i
$327$	17.2222	−	27.9154i	0.952390	−	1.54372i
$328$	−1.48990	+	1.48990i	−0.0822661	+	0.0822661i
$329$	−29.4119			−1.62153
$330$	6.42133	+	8.22448i	0.353482	+	0.452742i
$331$	−8.87423			−0.487772			−0.243886	−	0.969804i	$-0.578422\pi$
$331$	−8.87423			−0.487772			−0.243886	+	0.969804i	$0.578422\pi$
$332$	2.85071	−	2.85071i	0.156453	−	0.156453i
$333$	−8.10246	+	24.4359i	−0.444012	+	1.33908i
$334$		−	18.7573i		−	1.02635i
$335$	−11.3223	−	4.19870i	−0.618604	−	0.229400i
$336$	−1.47544	−	6.22806i	−0.0804916	−	0.339768i
$337$	12.0405	+	12.0405i	0.655887	+	0.655887i	0.954404	−	0.298517i	$-0.0964921\pi$
$337$	12.0405	+	12.0405i	0.655887	+	0.655887i	−0.298517	+	0.954404i	$0.596492\pi$
$338$	6.29596	+	6.29596i	0.342455	+	0.342455i
$339$	−2.20726	−	9.31720i	−0.119882	−	0.506041i
$340$	17.0502	+	6.32279i	0.924675	+	0.342901i
$341$			2.69413i			0.145896i
$342$	−5.20825	+	15.7074i	−0.281630	+	0.849358i
$343$	−0.900934	+	0.900934i	−0.0486459	+	0.0486459i
$344$	−8.35462			−0.450451
$345$	−20.3409	−	26.0528i	−1.09512	−	1.40263i
$346$	−12.3283			−0.662771
$347$	6.62671	−	6.62671i	0.355740	−	0.355740i	−0.506500	−	0.862240i	$-0.669061\pi$
$347$	6.62671	−	6.62671i	0.355740	−	0.355740i	0.862240	+	0.506500i	$0.169061\pi$
$348$	−5.45120	+	8.83582i	−0.292215	+	0.473649i
$349$			4.28535i			0.229390i	0.993401	+	0.114695i	$0.0365890\pi$
$349$			4.28535i			0.229390i	−0.993401	+	0.114695i	$0.963411\pi$
$350$	12.0468	−	14.0091i	0.643927	−	0.748819i
$351$	15.6264	+	18.6338i	0.834074	+	0.994601i
$352$	1.90504	+	1.90504i	0.101539	+	0.101539i
$353$	−6.65467	−	6.65467i	−0.354193	−	0.354193i	0.507474	−	0.861667i	$-0.330579\pi$
$353$	−6.65467	−	6.65467i	−0.354193	−	0.354193i	−0.861667	+	0.507474i	$0.830579\pi$
$354$	5.95343	−	1.41038i	0.316421	−	0.0749606i
$355$	8.63416	+	18.8122i	0.458253	+	0.998449i
$356$			5.13546i			0.272179i
$357$	−44.2992	−	27.3301i	−2.34456	−	1.44646i
$358$	11.9078	−	11.9078i	0.629347	−	0.629347i
$359$	−25.7032			−1.35656			−0.678280	−	0.734803i	$-0.737274\pi$
$359$	−25.7032			−1.35656			−0.678280	+	0.734803i	$0.737274\pi$
$360$	0.737166	+	6.66758i	0.0388521	+	0.351412i
$361$	−11.4275			−0.601448
$362$	3.97305	−	3.97305i	0.208819	−	0.208819i
$363$	−5.51551	−	3.40276i	−0.289489	−	0.178598i
$364$		−	17.2945i		−	0.906481i
$365$	−1.74396	+	4.70281i	−0.0912832	+	0.246156i
$366$	3.31434	−	0.785172i	0.173243	−	0.0410416i
$367$	−25.0598	−	25.0598i	−1.30811	−	1.30811i	−0.922777	−	0.385334i	$-0.874086\pi$
$367$	−25.0598	−	25.0598i	−1.30811	−	1.30811i	−0.385334	−	0.922777i	$-0.625914\pi$
$368$	−6.03462	−	6.03462i	−0.314576	−	0.314576i
$369$	−5.64931	+	2.83581i	−0.294091	+	0.147627i
$370$	−17.4395	+	8.00412i	−0.906636	+	0.416114i
$371$			10.2998i			0.534737i
$372$	−0.909430	+	1.47409i	−0.0471517	+	0.0764279i
$373$	−5.43211	+	5.43211i	−0.281264	+	0.281264i	−0.833613	−	0.552349i	$-0.813732\pi$
$373$	−5.43211	+	5.43211i	−0.281264	+	0.281264i	0.552349	+	0.833613i	$0.313732\pi$
$374$	21.9100			1.13294
$375$	−14.3256	+	13.0299i	−0.739770	+	0.672860i
$376$	7.95929			0.410469
$377$	−19.8366	+	19.8366i	−1.02164	+	1.02164i
$378$	1.67909	−	19.1278i	0.0863633	−	0.983826i
$379$		−	20.4718i		−	1.05156i	−0.850619	−	0.525782i	$-0.823773\pi$
$379$		−	20.4718i		−	1.05156i	0.850619	−	0.525782i	$-0.176227\pi$
$380$	−11.2101	+	5.14504i	−0.575065	+	0.263935i
$381$	1.41883	+	5.98913i	0.0726890	+	0.306832i
$382$	−9.76325	−	9.76325i	−0.499532	−	0.499532i
$383$	−20.2694	−	20.2694i	−1.03572	−	1.03572i	−0.999338	−	0.0363777i	$-0.988418\pi$
$383$	−20.2694	−	20.2694i	−1.03572	−	1.03572i	−0.0363777	−	0.999338i	$-0.511582\pi$
$384$	0.399274	+	1.68540i	0.0203754	+	0.0860078i
$385$	7.74024	−	20.8725i	0.394479	−	1.06376i
$386$		−	3.57659i		−	0.182043i
$387$	−23.7901	−	7.88834i	−1.20932	−	0.400987i
$388$	1.82697	−	1.82697i	0.0927502	−	0.0927502i
$389$	25.9658			1.31652			0.658258	−	0.752792i	$-0.271294\pi$
$389$	25.9658			1.31652			0.658258	+	0.752792i	$0.271294\pi$
$390$	−2.21491	+	17.9903i	−0.112157	+	0.910975i
$391$	−69.4045			−3.50994
$392$	−4.70594	+	4.70594i	−0.237686	+	0.237686i
$393$	5.77645	−	9.36300i	0.291383	−	0.472301i
$394$			18.9804i			0.956221i
$395$	5.47479	+	11.9286i	0.275467	+	0.600191i
$396$	3.62597	+	7.22341i	0.182212	+	0.362990i
$397$	−13.4195	−	13.4195i	−0.673508	−	0.673508i	0.285015	−	0.958523i	$-0.408001\pi$
$397$	−13.4195	−	13.4195i	−0.673508	−	0.673508i	−0.958523	+	0.285015i	$0.908001\pi$
$398$	6.72923	+	6.72923i	0.337306	+	0.337306i
$399$	34.3547	−	8.13867i	1.71988	−	0.407443i
$400$	−3.26003	+	3.79107i	−0.163002	+	0.189553i
$401$		−	1.11383i		−	0.0556218i	−0.999613	−	0.0278109i	$-0.991146\pi$
$401$		−	1.11383i		−	0.0556218i	0.999613	−	0.0278109i	$-0.00885362\pi$
$402$	−7.96073	−	4.91132i	−0.397045	−	0.244954i
$403$	−3.30937	+	3.30937i	−0.164851	+	0.164851i
$404$	13.1616			0.654812
$405$	−4.19634	+	19.6822i	−0.208518	+	0.978019i
$406$	22.1499			1.09928
$407$	−16.3479	+	16.3479i	−0.810336	+	0.810336i
$408$	11.9880	+	7.39591i	0.593494	+	0.366152i
$409$		−	30.5041i		−	1.50833i	−0.656685	−	0.754165i	$-0.728042\pi$
$409$		−	30.5041i		−	1.50833i	0.656685	−	0.754165i	$-0.271958\pi$
$410$	−4.41752	−	1.63817i	−0.218166	−	0.0809034i
$411$	7.10151	−	1.68236i	0.350292	−	0.0829846i
$412$	−3.80259	−	3.80259i	−0.187340	−	0.187340i
$413$	−9.22991	−	9.22991i	−0.454174	−	0.454174i
$414$	−11.4860	−	22.8817i	−0.564508	−	1.12457i
$415$	8.45228	+	3.13440i	0.414906	+	0.153861i
$416$			4.68015i			0.229463i
$417$	1.41040	−	2.28610i	0.0690674	−	0.111951i
$418$	−10.5084	+	10.5084i	−0.513984	+	0.513984i
$419$	16.5766			0.809820			0.404910	−	0.914357i	$-0.367303\pi$
$419$	16.5766			0.809820			0.404910	+	0.914357i	$0.367303\pi$
$420$	11.2808	−	8.80754i	0.550444	−	0.429764i
$421$	24.3905			1.18872			0.594359	−	0.804200i	$-0.297406\pi$
$421$	24.3905			1.18872			0.594359	+	0.804200i	$0.297406\pi$
$422$	12.0466	−	12.0466i	0.586417	−	0.586417i
$423$	22.6644	+	7.51508i	1.10198	+	0.365396i
$424$		−	2.78726i		−	0.135361i
$425$	3.05374	+	40.5475i	0.148128	+	1.96684i
$426$	3.69603	+	15.6015i	0.179073	+	0.755897i
$427$	−5.13840	−	5.13840i	−0.248664	−	0.248664i
$428$	−4.25578	−	4.25578i	−0.205711	−	0.205711i
$429$	5.03443	+	21.2512i	0.243065	+	1.02602i
$430$	−7.79260	−	16.9786i	−0.375793	−	0.818782i
$431$		−	17.0392i		−	0.820752i	−0.911916	−	0.410376i	$-0.865398\pi$
$431$		−	17.0392i		−	0.820752i	0.911916	−	0.410376i	$-0.134602\pi$
$432$	−0.454387	+	5.17625i	−0.0218617	+	0.249042i
$433$	−12.1100	+	12.1100i	−0.581968	+	0.581968i	−0.935444	−	0.353476i	$-0.885000\pi$
$433$	−12.1100	+	12.1100i	−0.581968	+	0.581968i	0.353476	+	0.935444i	$0.385000\pi$
$434$	3.69530			0.177380
$435$	−23.0410	−	2.83674i	−1.10473	−	0.136011i
$436$	18.9374			0.906935
$437$	33.2877	−	33.2877i	1.59236	−	1.59236i
$438$	−2.03996	+	3.30655i	−0.0974728	+	0.157993i
$439$			8.49304i			0.405351i	0.979246	+	0.202675i	$0.0649636\pi$
$439$			8.49304i			0.405351i	−0.979246	+	0.202675i	$0.935036\pi$
$440$	−2.09462	+	5.64840i	−0.0998571	+	0.269277i
$441$	−17.8437	+	8.95708i	−0.849699	+	0.426528i
$442$	26.9133	+	26.9133i	1.28014	+	1.28014i
$443$	14.3518	+	14.3518i	0.681874	+	0.681874i	0.960422	−	0.278548i	$-0.0898531\pi$
$443$	14.3518	+	14.3518i	0.681874	+	0.681874i	−0.278548	+	0.960422i	$0.589853\pi$
$444$	−14.4631	+	3.42633i	−0.686388	+	0.162606i
$445$	−10.4365	+	4.78999i	−0.494737	+	0.227067i
$446$		−	7.87261i		−	0.372779i
$447$	21.6957	+	13.3850i	1.02617	+	0.633089i
$448$	2.61297	−	2.61297i	0.123451	−	0.123451i
$449$	−22.4866			−1.06121			−0.530603	−	0.847620i	$-0.678035\pi$
$449$	−22.4866			−1.06121			−0.530603	+	0.847620i	$0.678035\pi$
$450$	−12.8626	+	7.71715i	−0.606347	+	0.363790i
$451$	−5.67665			−0.267303
$452$	3.90901	−	3.90901i	0.183864	−	0.183864i
$453$	−10.6675	−	6.58124i	−0.501203	−	0.309214i
$454$			17.3224i			0.812981i
$455$	35.1467	−	16.1311i	1.64770	−	0.756239i
$456$	−9.29687	+	2.20244i	−0.435366	+	0.103139i
$457$	−5.69044	−	5.69044i	−0.266188	−	0.266188i	0.561374	−	0.827562i	$-0.310273\pi$
$457$	−5.69044	−	5.69044i	−0.266188	−	0.266188i	−0.827562	+	0.561374i	$0.810273\pi$
$458$	16.6562	+	16.6562i	0.778292	+	0.778292i
$459$	27.1532	+	32.3791i	1.26740	+	1.51133i
$460$	6.63515	−	17.8925i	0.309366	−	0.834242i
$461$		−	12.6400i		−	0.588706i	−0.955697	−	0.294353i	$-0.904896\pi$
$461$		−	12.6400i		−	0.588706i	0.955697	−	0.294353i	$-0.0951041\pi$
$462$	9.05394	−	14.6755i	0.421227	−	0.682765i
$463$	20.0642	−	20.0642i	0.932463	−	0.932463i	−0.0653961	−	0.997859i	$-0.520831\pi$
$463$	20.0642	−	20.0642i	0.932463	−	0.932463i	0.997859	+	0.0653961i	$0.0208311\pi$
$464$	−5.99409			−0.278268
$465$	−3.84396	−	0.473257i	−0.178259	−	0.0219468i
$466$	−12.0950			−0.560288
$467$	−3.68786	+	3.68786i	−0.170654	+	0.170654i	−0.787267	−	0.616613i	$-0.788504\pi$
$467$	−3.68786	+	3.68786i	−0.170654	+	0.170654i	0.616613	+	0.787267i	$0.288504\pi$
$468$	−4.41895	+	13.3269i	−0.204266	+	0.616038i
$469$			19.9562i			0.921492i
$470$	7.42387	+	16.1752i	0.342438	+	0.746108i
$471$	3.11770	+	13.1603i	0.143656	+	0.606396i
$472$	2.49775	+	2.49775i	0.114968	+	0.114968i
$473$	−15.9159	−	15.9159i	−0.731813	−	0.731813i
$474$	2.34360	+	9.89271i	0.107645	+	0.454387i
$475$	−20.9120	−	17.9827i	−0.959507	−	0.825103i
$476$		−	30.0519i		−	1.37743i
$477$	2.63170	−	7.93685i	0.120497	−	0.363403i
$478$	12.6528	−	12.6528i	0.578727	−	0.578727i
$479$	14.0648			0.642636			0.321318	−	0.946971i	$-0.395874\pi$
$479$	14.0648			0.642636			0.321318	+	0.946971i	$0.395874\pi$
$480$	−3.05273	+	2.38345i	−0.139338	+	0.108789i
$481$	−40.1622			−1.83124
$482$	−12.5355	+	12.5355i	−0.570978	+	0.570978i
$483$	−28.6803	+	46.4877i	−1.30500	+	2.11526i
$484$		−	3.74164i		−	0.170074i
$485$	5.41691	+	2.00878i	0.245969	+	0.0912139i
$486$	−6.18124	+	14.3106i	−0.280387	+	0.649140i
$487$	−19.3373	−	19.3373i	−0.876254	−	0.876254i	0.116890	−	0.993145i	$-0.462707\pi$
$487$	−19.3373	−	19.3373i	−0.876254	−	0.876254i	−0.993145	+	0.116890i	$0.962707\pi$
$488$	1.39052	+	1.39052i	0.0629461	+	0.0629461i
$489$	−14.6254	+	3.46478i	−0.661383	+	0.156683i
$490$	−13.9530	−	5.17425i	−0.630332	−	0.233749i
$491$			25.6618i			1.15810i	0.815291	+	0.579051i	$0.196577\pi$
$491$			25.6618i			1.15810i	−0.815291	+	0.579051i	$0.803423\pi$
$492$	−3.10596	−	1.91621i	−0.140028	−	0.0863892i
$493$	−34.4692	+	34.4692i	−1.55241	+	1.55241i
$494$	−25.8163			−1.16153
$495$	−11.2977	+	14.1063i	−0.507793	+	0.634033i
$496$	−1.00000			−0.0449013
$497$	24.1879	−	24.1879i	1.08498	−	1.08498i
$498$	5.94280	+	3.66638i	0.266303	+	0.164294i
$499$			11.3978i			0.510233i	0.966910	+	0.255117i	$0.0821139\pi$
$499$			11.3978i			0.510233i	−0.966910	+	0.255117i	$0.917886\pi$
$500$	−10.7451	−	3.08914i	−0.480536	−	0.138150i
$501$	31.6135	−	7.48929i	1.41239	−	0.334597i
$502$	−12.7388	−	12.7388i	−0.568561	−	0.568561i
$503$	22.1741	+	22.1741i	0.988694	+	0.988694i	0.999937	−	0.0112432i	$-0.00357891\pi$
$503$	22.1741	+	22.1741i	0.988694	+	0.988694i	−0.0112432	+	0.999937i	$0.503579\pi$
$504$	9.90768	−	4.97341i	0.441323	−	0.221533i
$505$	12.2762	+	26.7475i	0.546282	+	1.19025i
$506$		−	22.9924i		−	1.02214i
$507$	−8.09741	+	13.1250i	−0.359619	+	0.582903i
$508$	−2.51273	+	2.51273i	−0.111484	+	0.111484i
$509$	36.1261			1.60126			0.800630	−	0.599159i	$-0.204498\pi$
$509$	36.1261			1.60126			0.800630	+	0.599159i	$0.204498\pi$
$510$	−3.84875	+	31.2609i	−0.170425	+	1.38426i
$511$	8.28897			0.366682
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−28.5528	−	2.50645i	−1.26064	−	0.110662i
$514$			4.01897i			0.177269i
$515$	4.18100	−	11.2746i	0.184237	−	0.496817i
$516$	−3.33578	−	14.0809i	−0.146850	−	0.619877i
$517$	15.1628	+	15.1628i	0.666858	+	0.666858i
$518$	22.4229	+	22.4229i	0.985206	+	0.985206i
$519$	−4.92235	−	20.7781i	−0.216067	−	0.912056i
$520$	−9.51121	+	4.36532i	−0.417094	+	0.191432i
$521$			21.7545i			0.953084i	0.879152	+	0.476542i	$0.158110\pi$
$521$			21.7545i			0.953084i	−0.879152	+	0.476542i	$0.841890\pi$
$522$	−17.0684	−	5.65955i	−0.747065	−	0.247712i
$523$	0.981245	−	0.981245i	0.0429069	−	0.0429069i	−0.685328	−	0.728235i	$-0.740341\pi$
$523$	0.981245	−	0.981245i	0.0429069	−	0.0429069i	0.728235	+	0.685328i	$0.240341\pi$
$524$	6.35172			0.277476
$525$	28.4210	+	14.7102i	1.24039	+	0.642005i
$526$	5.85010			0.255077
$527$	−5.75053	+	5.75053i	−0.250497	+	0.250497i
$528$	−2.45013	+	3.97139i	−0.106628	+	0.172833i
$529$			49.8333i			2.16667i
$530$	5.66440	−	2.59976i	0.246046	−	0.112926i
$531$	4.75410	+	9.47079i	0.206310	+	0.410997i
$532$	14.4134	+	14.4134i	0.624901	+	0.624901i
$533$	−6.97297	−	6.97297i	−0.302033	−	0.302033i
$534$	−8.65531	+	2.05046i	−0.374552	+	0.0887319i
$535$	4.67929	−	12.6183i	0.202304	−	0.545536i
$536$		−	5.40044i		−	0.233263i
$537$	24.8239	+	15.3150i	1.07123	+	0.660890i
$538$	10.7129	−	10.7129i	0.461865	−	0.461865i
$539$	−17.9300			−0.772301
$540$	−10.9432	+	3.90461i	−0.470921	+	0.168028i
$541$	10.0879			0.433713			0.216857	−	0.976203i	$-0.430420\pi$
$541$	10.0879			0.433713			0.216857	+	0.976203i	$0.430420\pi$
$542$	8.80866	−	8.80866i	0.378364	−	0.378364i
$543$	8.28253	+	5.10985i	0.355437	+	0.219285i
$544$			8.13247i			0.348677i
$545$	17.6634	+	38.4854i	0.756619	+	1.64853i
$546$	29.1483	−	6.90527i	1.24743	−	0.295518i
$547$	17.6589	+	17.6589i	0.755040	+	0.755040i	0.975415	−	0.220375i	$-0.0707282\pi$
$547$	17.6589	+	17.6589i	0.755040	+	0.755040i	−0.220375	+	0.975415i	$0.570728\pi$
$548$	2.97942	+	2.97942i	0.127275	+	0.127275i
$549$	2.64666	+	5.27250i	0.112957	+	0.225025i
$550$	−13.4326	+	1.01165i	−0.572769	+	0.0431368i
$551$		−	33.0641i		−	1.40858i
$552$	7.76130	−	12.5802i	0.330343	−	0.535450i
$553$	15.3372	−	15.3372i	0.652204	−	0.652204i
$554$	−22.9372			−0.974510
$555$	−20.4533	−	26.1967i	−0.868194	−	1.11199i
$556$	1.55086			0.0657711
$557$	19.3094	−	19.3094i	0.818168	−	0.818168i	−0.167675	−	0.985842i	$-0.553626\pi$
$557$	19.3094	−	19.3094i	0.818168	−	0.818168i	0.985842	+	0.167675i	$0.0536258\pi$
$558$	−2.84754	−	0.944189i	−0.120546	−	0.0399707i
$559$		−	39.1009i		−	1.65379i
$560$	7.74738	+	2.87300i	0.327387	+	0.121406i
$561$	8.74809	+	36.9271i	0.369345	+	1.55906i
$562$	−15.8488	−	15.8488i	−0.668540	−	0.668540i
$563$	−17.4104	−	17.4104i	−0.733761	−	0.733761i	0.237602	−	0.971363i	$-0.423639\pi$
$563$	−17.4104	−	17.4104i	−0.733761	−	0.733761i	−0.971363	+	0.237602i	$0.923639\pi$
$564$	3.17794	+	13.4146i	0.133815	+	0.564857i
$565$	11.5901	+	4.29801i	0.487600	+	0.180819i
$566$		−	9.62890i		−	0.404733i
$567$	32.9084	−	4.80727i	1.38202	−	0.201887i
$568$	−6.54560	+	6.54560i	−0.274647	+	0.274647i
$569$	37.3834			1.56719			0.783596	−	0.621271i	$-0.213383\pi$
$569$	37.3834			1.56719			0.783596	+	0.621271i	$0.213383\pi$
$570$	−13.1474	−	16.8392i	−0.550682	−	0.705317i
$571$	6.84518			0.286462			0.143231	−	0.989689i	$-0.454251\pi$
$571$	6.84518			0.286462			0.143231	+	0.989689i	$0.454251\pi$
$572$	−8.91588	+	8.91588i	−0.372792	+	0.372792i
$573$	12.5568	−	20.3532i	0.524568	−	0.850268i
$574$			7.78614i			0.324987i
$575$	42.5507	−	3.20461i	1.77449	−	0.133641i
$576$	−2.68116	+	1.34588i	−0.111715	+	0.0560781i
$577$	−9.55409	−	9.55409i	−0.397742	−	0.397742i	0.479694	−	0.877436i	$-0.340748\pi$
$577$	−9.55409	−	9.55409i	−0.397742	−	0.397742i	−0.877436	+	0.479694i	$0.840748\pi$
$578$	34.7452	+	34.7452i	1.44521	+	1.44521i
$579$	6.02798	−	1.42804i	0.250514	−	0.0593473i
$580$	−5.59086	−	12.1814i	−0.232148	−	0.505807i
$581$		−	14.8976i		−	0.618058i
$582$	3.80864	+	2.34971i	0.157873	+	0.0973987i
$583$	5.30985	−	5.30985i	0.219911	−	0.219911i
$584$	−2.24311			−0.0928207
$585$	−31.2053	+	3.45005i	−1.29018	+	0.142642i
$586$	6.20481			0.256318
$587$	−3.87370	+	3.87370i	−0.159885	+	0.159885i	−0.782516	−	0.622631i	$-0.786064\pi$
$587$	−3.87370	+	3.87370i	−0.159885	+	0.159885i	0.622631	+	0.782516i	$0.286064\pi$
$588$	−9.81037	−	6.05244i	−0.404573	−	0.249599i
$589$		−	5.51611i		−	0.227287i
$590$	−2.74631	+	7.40575i	−0.113064	+	0.304890i
$591$	−31.9897	+	7.57840i	−1.31588	+	0.311734i
$592$	−6.06796	−	6.06796i	−0.249392	−	0.249392i
$593$	−11.6391	−	11.6391i	−0.477962	−	0.477962i	0.426518	−	0.904479i	$-0.359740\pi$
$593$	−11.6391	−	11.6391i	−0.477962	−	0.477962i	−0.904479	+	0.426518i	$0.859740\pi$
$594$	−10.7266	+	8.99534i	−0.440117	+	0.369083i
$595$	61.0728	−	28.0303i	2.50374	−	1.14913i
$596$			14.7180i			0.602874i
$597$	−8.65464	+	14.0283i	−0.354211	+	0.574138i
$598$	28.2430	−	28.2430i	1.15494	−	1.15494i
$599$	−15.8904			−0.649264			−0.324632	−	0.945840i	$-0.605240\pi$
$599$	−15.8904			−0.649264			−0.324632	+	0.945840i	$0.605240\pi$
$600$	−7.69112	−	3.98079i	−0.313989	−	0.162515i
$601$	−26.8883			−1.09680			−0.548399	−	0.836217i	$-0.684763\pi$
$601$	−26.8883			−1.09680			−0.548399	+	0.836217i	$0.684763\pi$
$602$	−21.8304	+	21.8304i	−0.889739	+	0.889739i
$603$	5.09903	−	15.3780i	0.207649	−	0.626240i
$604$		−	7.23667i		−	0.294456i
$605$	7.60392	−	3.48994i	0.309143	−	0.141886i
$606$	5.25507	+	22.1825i	0.213473	+	0.901103i
$607$	−24.2573	−	24.2573i	−0.984573	−	0.984573i	0.0153094	−	0.999883i	$-0.495127\pi$
$607$	−24.2573	−	24.2573i	−0.984573	−	0.984573i	−0.999883	+	0.0153094i	$0.995127\pi$
$608$	−3.90048	−	3.90048i	−0.158185	−	0.158185i
$609$	8.84389	+	37.3315i	0.358373	+	1.51275i
$610$	−1.52890	+	4.12287i	−0.0619034	+	0.166930i
$611$			37.2507i			1.50700i
$612$	−7.67859	+	23.1576i	−0.310389	+	0.936090i
$613$	27.8750	−	27.8750i	1.12586	−	1.12586i	0.135019	−	0.990843i	$-0.456891\pi$
$613$	27.8750	−	27.8750i	1.12586	−	1.12586i	0.990843	−	0.135019i	$-0.0431094\pi$
$614$	−28.7066			−1.15851
$615$	0.997171	−	8.09938i	0.0402098	−	0.326598i
$616$	9.95562			0.401124
$617$	−0.724584	+	0.724584i	−0.0291707	+	0.0291707i	−0.721542	−	0.692371i	$-0.756566\pi$
$617$	−0.724584	+	0.724584i	−0.0291707	+	0.0291707i	0.692371	+	0.721542i	$0.256566\pi$
$618$	4.89062	−	7.92717i	0.196730	−	0.318878i
$619$		−	19.6580i		−	0.790123i	−0.918655	−	0.395062i	$-0.870723\pi$
$619$		−	19.6580i		−	0.790123i	0.918655	−	0.395062i	$-0.129277\pi$
$620$	−0.932730	−	2.03224i	−0.0374593	−	0.0816169i
$621$	33.9787	−	28.4946i	1.36352	−	1.14345i
$622$	−10.6911	−	10.6911i	−0.428674	−	0.428674i
$623$	13.4188	+	13.4188i	0.537612	+	0.537612i
$624$	−7.88794	+	1.86866i	−0.315770	+	0.0748065i
$625$	−3.74439	−	24.7180i	−0.149776	−	0.988720i
$626$		−	12.8851i		−	0.514992i
$627$	−21.9067	−	13.5152i	−0.874868	−	0.539744i
$628$	−5.52139	+	5.52139i	−0.220327	+	0.220327i
$629$	−69.7879			−2.78263
$630$	19.3484	+	15.4960i	0.770857	+	0.617374i
$631$	−19.9190			−0.792961			−0.396480	−	0.918043i	$-0.629769\pi$
$631$	−19.9190			−0.792961			−0.396480	+	0.918043i	$0.629769\pi$
$632$	−4.15047	+	4.15047i	−0.165097	+	0.165097i
$633$	25.1132	+	15.4934i	0.998159	+	0.615808i
$634$		−	8.84477i		−	0.351271i
$635$	−7.45017	−	2.76278i	−0.295651	−	0.109638i
$636$	4.69766	−	1.11288i	0.186274	−	0.0441286i
$637$	−22.0245	−	22.0245i	−0.872644	−	0.872644i
$638$	−11.4190	−	11.4190i	−0.452082	−	0.452082i
$639$	−24.8191	+	12.4586i	−0.981830	+	0.492854i
$640$	−2.09655	−	0.777474i	−0.0828735	−	0.0307324i
$641$		−	23.9682i		−	0.946689i	−0.880877	−	0.473344i	$-0.843047\pi$
$641$		−	23.9682i		−	0.946689i	0.880877	−	0.473344i	$-0.156953\pi$
$642$	5.47348	−	8.87193i	0.216021	−	0.350147i
$643$	4.67953	−	4.67953i	0.184543	−	0.184543i	−0.608789	−	0.793332i	$-0.708344\pi$
$643$	4.67953	−	4.67953i	0.184543	−	0.184543i	0.793332	+	0.608789i	$0.208344\pi$
$644$	−31.5366			−1.24271
$645$	25.5044	−	19.9128i	1.00424	−	0.784065i
$646$	−44.8596			−1.76498
$647$	−5.89363	+	5.89363i	−0.231703	+	0.231703i	−0.813403	−	0.581700i	$-0.802388\pi$
$647$	−5.89363	+	5.89363i	−0.231703	+	0.231703i	0.581700	+	0.813403i	$0.302388\pi$
$648$	−8.90548	+	1.30092i	−0.349840	+	0.0511049i
$649$			9.51662i			0.373560i
$650$	−17.7428	−	15.2574i	−0.695929	−	0.598446i
$651$	1.47544	+	6.22806i	0.0578269	+	0.244097i
$652$	−6.13605	−	6.13605i	−0.240306	−	0.240306i
$653$	22.3644	+	22.3644i	0.875187	+	0.875187i	0.993032	−	0.117845i	$-0.0375985\pi$
$653$	22.3644	+	22.3644i	0.875187	+	0.875187i	−0.117845	+	0.993032i	$0.537598\pi$
$654$	7.56120	+	31.9171i	0.295666	+	1.24806i
$655$	5.92444	+	12.9083i	0.231487	+	0.504367i
$656$		−	2.10704i		−	0.0822661i
$657$	−6.38737	−	2.11792i	−0.249195	−	0.0826281i
$658$	20.7974	−	20.7974i	0.810766	−	0.810766i
$659$	−5.57611			−0.217214			−0.108607	−	0.994085i	$-0.534639\pi$
$659$	−5.57611			−0.217214			−0.108607	+	0.994085i	$0.534639\pi$
$660$	−10.3561	−	1.27502i	−0.403112	−	0.0496300i
$661$	41.7727			1.62477			0.812385	−	0.583121i	$-0.198169\pi$
$661$	41.7727			1.62477			0.812385	+	0.583121i	$0.198169\pi$
$662$	6.27503	−	6.27503i	0.243886	−	0.243886i
$663$	−34.6140	+	56.1056i	−1.34430	+	2.17896i
$664$			4.03151i			0.156453i
$665$	−15.8478	+	42.7354i	−0.614550	+	1.65721i
$666$	−11.5495	−	23.0081i	−0.447533	−	0.891545i
$667$	36.1720	+	36.1720i	1.40059	+	1.40059i
$668$	13.2634	+	13.2634i	0.513176	+	0.513176i
$669$	13.2685	−	3.14333i	0.512990	−	0.121528i
$670$	10.9750	−	5.03715i	0.424002	−	0.194602i
$671$			5.29801i			0.204527i
$672$	5.44719	+	3.36061i	0.210130	+	0.129638i
$673$	4.24247	−	4.24247i	0.163535	−	0.163535i	−0.620596	−	0.784131i	$-0.713109\pi$
$673$	4.24247	−	4.24247i	0.163535	−	0.163535i	0.784131	+	0.620596i	$0.213109\pi$
$674$	−17.0278			−0.655887
$675$	−18.1422	−	18.5973i	−0.698293	−	0.715812i
$676$	−8.90383			−0.342455
$677$	−7.30064	+	7.30064i	−0.280586	+	0.280586i	−0.833343	−	0.552757i	$-0.813576\pi$
$677$	−7.30064	+	7.30064i	−0.280586	+	0.280586i	0.552757	+	0.833343i	$0.313576\pi$
$678$	8.14902	+	5.02749i	0.312961	+	0.193079i
$679$		−	9.54761i		−	0.366404i
$680$	−16.5272	+	7.58540i	−0.633788	+	0.290887i
$681$	−29.1952	+	6.91639i	−1.11876	+	0.265037i
$682$	−1.90504	−	1.90504i	−0.0729478	−	0.0729478i
$683$	12.5023	+	12.5023i	0.478389	+	0.478389i	0.904616	−	0.426227i	$-0.140158\pi$
$683$	12.5023	+	12.5023i	0.478389	+	0.478389i	−0.426227	+	0.904616i	$0.640158\pi$
$684$	−7.42400	−	14.7896i	−0.283864	−	0.565494i
$685$	−3.27592	+	8.83391i	−0.125166	+	0.337526i
$686$		−	1.27411i		−	0.0486459i
$687$	−21.4220	+	34.7227i	−0.817299	+	1.32475i
$688$	5.90761	−	5.90761i	0.225225	−	0.225225i
$689$	13.0448			0.496968
$690$	32.8053	+	4.03889i	1.24888	+	0.153758i
$691$	38.4636			1.46322			0.731612	−	0.681721i	$-0.238768\pi$
$691$	38.4636			1.46322			0.731612	+	0.681721i	$0.238768\pi$
$692$	8.71739	−	8.71739i	0.331385	−	0.331385i
$693$	28.3491	+	9.39999i	1.07689	+	0.357076i
$694$			9.37158i			0.355740i
$695$	1.44653	+	3.15172i	0.0548701	+	0.119552i
$696$	−2.39328	−	10.1024i	−0.0907172	−	0.382932i
$697$	−12.1166	−	12.1166i	−0.458949	−	0.458949i
$698$	−3.03020	−	3.03020i	−0.114695	−	0.114695i
$699$	−4.82920	−	20.3849i	−0.182657	−	0.771026i
$700$	1.38758	+	18.4243i	0.0524457	+	0.696373i
$701$		−	21.9493i		−	0.829014i	−0.910046	−	0.414507i	$-0.863954\pi$
$701$		−	21.9493i		−	0.829014i	0.910046	−	0.414507i	$-0.136046\pi$
$702$	−24.2256	−	2.12660i	−0.914337	−	0.0802634i
$703$	33.4716	−	33.4716i	1.26240	−	1.26240i
$704$	−2.69413			−0.101539
$705$	−24.2976	+	18.9706i	−0.915101	+	0.714472i
$706$	9.41113			0.354193
$707$	34.3907	−	34.3907i	1.29340	−	1.29340i
$708$	−3.21242	+	5.20699i	−0.120730	+	0.195691i
$709$		−	12.4594i		−	0.467924i	−0.972246	−	0.233962i	$-0.924831\pi$
$709$		−	12.4594i		−	0.467924i	0.972246	−	0.233962i	$-0.0751691\pi$
$710$	−19.4075	−	7.19698i	−0.728351	−	0.270098i
$711$	−15.7375	+	7.89981i	−0.590201	+	0.296266i
$712$	−3.63132	−	3.63132i	−0.136089	−	0.136089i
$713$	6.03462	+	6.03462i	0.225998	+	0.225998i
$714$	50.6495	−	11.9989i	1.89551	−	0.449049i
$715$	−26.4354	−	9.80314i	−0.988626	−	0.366617i
$716$			16.8402i			0.629347i
$717$	26.3770	+	16.2731i	0.985068	+	0.607732i
$718$	18.1749	−	18.1749i	0.678280	−	0.678280i
$719$	−22.5218			−0.839921			−0.419961	−	0.907542i	$-0.637956\pi$
$719$	−22.5218			−0.839921			−0.419961	+	0.907542i	$0.637956\pi$
$720$	−5.23594	−	4.19343i	−0.195132	−	0.156280i
$721$	−19.8721			−0.740076
$722$	8.08047	−	8.08047i	0.300724	−	0.300724i
$723$	−26.1326	−	16.1223i	−0.971880	−	0.599595i
$724$			5.61874i			0.208819i
$725$	19.5409	−	22.7240i	0.725731	−	0.843948i
$726$	6.30616	−	1.49394i	0.234044	−	0.0554453i
$727$	−6.86639	−	6.86639i	−0.254660	−	0.254660i	0.568218	−	0.822878i	$-0.307633\pi$
$727$	−6.86639	−	6.86639i	−0.254660	−	0.254660i	−0.822878	+	0.568218i	$0.807633\pi$
$728$	12.2291	+	12.2291i	0.453240	+	0.453240i
$729$	−26.5871	−	4.70404i	−0.984706	−	0.174224i
$730$	−2.09222	−	4.55856i	−0.0774365	−	0.168720i
$731$		−	67.9437i		−	2.51299i
$732$	−1.78839	+	2.89879i	−0.0661008	+	0.107142i
$733$	15.1413	−	15.1413i	0.559258	−	0.559258i	−0.369839	−	0.929096i	$-0.620587\pi$
$733$	15.1413	−	15.1413i	0.559258	−	0.559258i	0.929096	+	0.369839i	$0.120587\pi$
$734$	35.4399			1.30811
$735$	3.14962	−	25.5823i	0.116176	−	0.943619i
$736$	8.53424			0.314576
$737$	10.2881	−	10.2881i	0.378965	−	0.378965i
$738$	1.98944	−	5.99989i	0.0732325	−	0.220859i
$739$			50.9758i			1.87518i	0.347749	+	0.937588i	$0.386946\pi$
$739$			50.9758i			1.87518i	−0.347749	+	0.937588i	$0.613054\pi$
$740$	6.67181	−	17.9913i	0.245261	−	0.661375i
$741$	−10.3078	−	43.5108i	−0.378665	−	1.59841i
$742$	−7.28303	−	7.28303i	−0.267368	−	0.267368i
$743$	−15.5577	−	15.5577i	−0.570758	−	0.570758i	0.361582	−	0.932340i	$-0.382237\pi$
$743$	−15.5577	−	15.5577i	−0.570758	−	0.570758i	−0.932340	+	0.361582i	$0.882237\pi$
$744$	−0.399274	−	1.68540i	−0.0146381	−	0.0617898i
$745$	−29.9106	+	13.7279i	−1.09584	+	0.502953i
$746$		−	7.68216i		−	0.281264i
$747$	−3.80651	+	11.4799i	−0.139273	+	0.420028i
$748$	−15.4927	+	15.4927i	−0.566469	+	0.566469i
$749$	−22.2404			−0.812648
$750$	0.916196	−	19.3432i	0.0334548	−	0.706315i
$751$	−7.13242			−0.260266			−0.130133	−	0.991497i	$-0.541540\pi$
$751$	−7.13242			−0.260266			−0.130133	+	0.991497i	$0.541540\pi$
$752$	−5.62807	+	5.62807i	−0.205235	+	0.205235i
$753$	16.3837	−	26.5563i	0.597057	−	0.967765i
$754$		−	28.0532i		−	1.02164i
$755$	14.7067	−	6.74985i	0.535231	−	0.245652i
$756$	12.3381	+	14.7127i	0.448731	+	0.535095i
$757$	19.7733	+	19.7733i	0.718672	+	0.718672i	0.968333	−	0.249661i	$-0.0803193\pi$
$757$	19.7733	+	19.7733i	0.718672	+	0.718672i	−0.249661	+	0.968333i	$0.580319\pi$
$758$	14.4757	+	14.4757i	0.525782	+	0.525782i
$759$	38.7514	−	9.18028i	1.40659	−	0.333223i
$760$	4.28864	−	11.5648i	0.155565	−	0.419500i
$761$			2.49810i			0.0905559i	0.998974	+	0.0452780i	$0.0144174\pi$
$761$			2.49810i			0.0905559i	−0.998974	+	0.0452780i	$0.985583\pi$
$762$	−5.23822	−	3.23169i	−0.189761	−	0.117072i
$763$	49.4827	−	49.4827i	1.79140	−	1.79140i
$764$	13.8073			0.499532
$765$	−54.2239	+	5.99498i	−1.96047	+	0.216749i
$766$	28.6652			1.03572
$767$	−11.6898	+	11.6898i	−0.422096	+	0.422096i
$768$	−1.47409	−	0.909430i	−0.0531916	−	0.0328162i
$769$		−	10.6055i		−	0.382443i	−0.981547	−	0.191222i	$-0.938755\pi$
$769$		−	10.6055i		−	0.382443i	0.981547	−	0.191222i	$-0.0612449\pi$
$770$	9.28590	+	20.2323i	0.334641	+	0.729120i
$771$	−6.77358	+	1.60467i	−0.243944	+	0.0577908i
$772$	2.52903	+	2.52903i	0.0910217	+	0.0910217i
$773$	32.2882	+	32.2882i	1.16132	+	1.16132i	0.984186	+	0.177138i	$0.0566840\pi$
$773$	32.2882	+	32.2882i	1.16132	+	1.16132i	0.177138	+	0.984186i	$0.443316\pi$
$774$	22.4001	−	11.2443i	0.805154	−	0.404167i
$775$	3.26003	−	3.79107i	0.117104	−	0.136179i
$776$			2.58372i			0.0927502i
$777$	−28.8387	+	46.7445i	−1.03458	+	1.67695i
$778$	−18.3606	+	18.3606i	−0.658258	+	0.658258i
$779$	11.6227			0.416425
$780$	−11.1549	−	14.2873i	−0.399409	−	0.511566i
$781$	−24.9393			−0.892397
$782$	49.0764	−	49.0764i	1.75497	−	1.75497i
$783$	2.72363	−	31.0269i	0.0973348	−	1.10881i
$784$		−	6.65521i		−	0.237686i
$785$	−16.3708	−	6.07085i	−0.584298	−	0.216678i
$786$	2.53608	+	10.7052i	0.0904590	+	0.381842i
$787$	21.9600	+	21.9600i	0.782791	+	0.782791i	0.980301	−	0.197510i	$-0.0632856\pi$
$787$	21.9600	+	21.9600i	0.782791	+	0.782791i	−0.197510	+	0.980301i	$0.563286\pi$
$788$	−13.4212	−	13.4212i	−0.478110	−	0.478110i
$789$	2.33580	+	9.85978i	0.0831565	+	0.351017i
$790$	−12.3060	−	4.56350i	−0.437829	−	0.162362i
$791$		−	20.4282i		−	0.726345i
$792$	−7.67167	−	2.54377i	−0.272601	−	0.0903890i
$793$	−6.50786	+	6.50786i	−0.231101	+	0.231101i
$794$	18.9781			0.673508
$795$	6.64329	+	8.50877i	0.235613	+	0.301775i
$796$	−9.51656			−0.337306
$797$	−23.6560	+	23.6560i	−0.837940	+	0.837940i	−0.988588	−	0.150647i	$-0.951864\pi$
$797$	−23.6560	+	23.6560i	−0.837940	+	0.837940i	0.150647	+	0.988588i	$0.451864\pi$
$798$	−18.5375	+	30.0473i	−0.656221	+	1.06366i
$799$			64.7287i			2.28994i
$800$	−0.375500	−	4.98588i	−0.0132759	−	0.176277i
$801$	−6.91168	−	13.7690i	−0.244212	−	0.486503i
$802$	0.787593	+	0.787593i	0.0278109	+	0.0278109i
$803$	−4.27323	−	4.27323i	−0.150799	−	0.150799i
$804$	9.10191	−	2.15626i	0.321000	−	0.0760453i
$805$	−29.4151	−	64.0900i	−1.03675	−	2.25887i
$806$		−	4.68015i		−	0.164851i
$807$	22.3329	+	13.7781i	0.786154	+	0.485013i
$808$	−9.30662	+	9.30662i	−0.327406	+	0.327406i
$809$	0.735637			0.0258636			0.0129318	−	0.999916i	$-0.495884\pi$
$809$	0.735637			0.0258636			0.0129318	+	0.999916i	$0.495884\pi$
$810$	−10.9502	−	16.8847i	−0.384750	−	0.593268i
$811$	5.50096			0.193165			0.0965823	−	0.995325i	$-0.469209\pi$
$811$	5.50096			0.193165			0.0965823	+	0.995325i	$0.469209\pi$
$812$	−15.6624	+	15.6624i	−0.549641	+	0.549641i
$813$	18.3632	+	11.3291i	0.644025	+	0.397327i
$814$		−	23.1194i		−	0.810336i
$815$	6.74668	−	18.1932i	0.236326	−	0.637281i
$816$	−13.7065	+	3.24709i	−0.479823	+	0.113671i
$817$	32.5870	+	32.5870i	1.14008	+	1.14008i
$818$	21.5696	+	21.5696i	0.754165	+	0.754165i
$819$	23.2763	+	46.3695i	0.813340	+	1.62028i
$820$	4.28202	−	1.96530i	0.149535	−	0.0686312i
$821$		−	39.6824i		−	1.38492i	−0.721454	−	0.692462i	$-0.756526\pi$
$821$		−	39.6824i		−	1.38492i	0.721454	−	0.692462i	$-0.243474\pi$
$822$	−3.83192	+	6.21113i	−0.133653	+	0.216638i
$823$	−1.69421	+	1.69421i	−0.0590564	+	0.0590564i	−0.736018	−	0.676962i	$-0.763296\pi$
$823$	−1.69421	+	1.69421i	−0.0590564	+	0.0590564i	0.676962	+	0.736018i	$0.263296\pi$
$824$	5.37768			0.187340
$825$	−7.06834	−	22.2355i	−0.246088	−	0.774139i
$826$	13.0531			0.454174
$827$	−3.58990	+	3.58990i	−0.124833	+	0.124833i	−0.766763	−	0.641930i	$-0.778134\pi$
$827$	−3.58990	+	3.58990i	−0.124833	+	0.124833i	0.641930	+	0.766763i	$0.278134\pi$
$828$	24.3016	+	8.05794i	0.844540	+	0.280033i
$829$		−	9.63165i		−	0.334521i	−0.985913	−	0.167260i	$-0.946508\pi$
$829$		−	9.63165i		−	0.334521i	0.985913	−	0.167260i	$-0.0534921\pi$
$830$	−8.19301	+	3.76031i	−0.284384	+	0.130522i
$831$	−9.15825	−	38.6585i	−0.317696	−	1.34105i
$832$	−3.30937	−	3.30937i	−0.114732	−	0.114732i
$833$	−38.2709	−	38.2709i	−1.32601	−	1.32601i
$834$	0.619218	+	2.61382i	0.0214418	+	0.0905092i
$835$	−14.5833	+	39.3256i	−0.504675	+	1.36092i
$836$		−	14.8612i		−	0.513984i
$837$	0.454387	−	5.17625i	0.0157059	−	0.178917i
$838$	−11.7214	+	11.7214i	−0.404910	+	0.404910i
$839$	41.8454			1.44466			0.722332	−	0.691546i	$-0.243070\pi$
$839$	41.8454			1.44466			0.722332	+	0.691546i	$0.243070\pi$
$840$	−1.74882	+	14.2046i	−0.0603402	+	0.490104i
$841$	6.92907			0.238933
$842$	−17.2467	+	17.2467i	−0.594359	+	0.594359i
$843$	20.3836	−	33.0396i	0.702047	−	1.13794i
$844$			17.0364i			0.586417i
$845$	−8.30487	−	18.0948i	−0.285696	−	0.622479i
$846$	−21.3401	+	10.7122i	−0.733689	+	0.368294i
$847$	−9.77678	−	9.77678i	−0.335934	−	0.335934i
$848$	1.97089	+	1.97089i	0.0676807	+	0.0676807i
$849$	16.2286	−	3.84457i	0.556963	−	0.131945i
$850$	−30.8308	−	26.5121i	−1.05749	−	0.909358i
$851$			73.2357i			2.51049i
$852$	−13.6454	−	8.41847i	−0.467485	−	0.288412i
$853$	−14.2236	+	14.2236i	−0.487008	+	0.487008i	−0.907361	−	0.420353i	$-0.861906\pi$
$853$	−14.2236	+	14.2236i	−0.487008	+	0.487008i	0.420353	+	0.907361i	$0.361906\pi$
$854$	7.26679			0.248664
$855$	23.1315	−	28.8821i	0.791079	−	0.987746i
$856$	6.01858			0.205711
$857$	27.8455	−	27.8455i	0.951183	−	0.951183i	−0.0476794	−	0.998863i	$-0.515183\pi$
$857$	27.8455	−	27.8455i	0.951183	−	0.951183i	0.998863	+	0.0476794i	$0.0151826\pi$
$858$	−18.5867	−	11.4670i	−0.634541	−	0.391476i
$859$		−	43.0375i		−	1.46842i	−0.678922	−	0.734211i	$-0.737552\pi$
$859$		−	43.0375i		−	1.46842i	0.678922	−	0.734211i	$-0.262448\pi$
$860$	17.5159	+	6.49550i	0.597287	+	0.221495i
$861$	−13.1228	+	3.10880i	−0.447223	+	0.105948i
$862$	12.0486	+	12.0486i	0.410376	+	0.410376i
$863$	−18.9466	−	18.9466i	−0.644951	−	0.644951i	0.306817	−	0.951768i	$-0.400736\pi$
$863$	−18.9466	−	18.9466i	−0.644951	−	0.644951i	−0.951768	+	0.306817i	$0.900736\pi$
$864$	−3.33886	−	3.98146i	−0.113590	−	0.135452i
$865$	25.8468	+	9.58490i	0.878819	+	0.325896i
$866$		−	17.1261i		−	0.581968i
$867$	−44.6868	+	72.4325i	−1.51764	+	2.45994i
$868$	−2.61297	+	2.61297i	−0.0886899	+	0.0886899i
$869$	−15.8136			−0.536440
$870$	18.2983	−	14.2866i	0.620372	−	0.484361i
$871$	25.2749			0.856407
$872$	−13.3907	+	13.3907i	−0.453468	+	0.453468i
$873$	−2.43952	+	7.35726i	−0.0825653	+	0.249006i
$874$			47.0759i			1.59236i
$875$	−36.1484	+	20.0048i	−1.22204	+	0.676285i
$876$	−0.895618	−	3.78055i	−0.0302601	−	0.127733i
$877$	−35.0040	−	35.0040i	−1.18200	−	1.18200i	−0.979225	−	0.202777i	$-0.935003\pi$
$877$	−35.0040	−	35.0040i	−1.18200	−	1.18200i	−0.202777	−	0.979225i	$-0.564997\pi$
$878$	−6.00549	−	6.00549i	−0.202675	−	0.202675i
$879$	2.47742	+	10.4576i	0.0835614	+	0.352726i
$880$	−2.51290	−	5.47514i	−0.0847098	−	0.184567i
$881$		−	19.9154i		−	0.670966i	−0.942046	−	0.335483i	$-0.891101\pi$
$881$		−	19.9154i		−	0.670966i	0.942046	−	0.335483i	$-0.108899\pi$
$882$	6.28377	−	18.9510i	0.211586	−	0.638113i
$883$	−1.11091	+	1.11091i	−0.0373851	+	0.0373851i	−0.725552	−	0.688167i	$-0.758416\pi$
$883$	−1.11091	+	1.11091i	−0.0373851	+	0.0373851i	0.688167	+	0.725552i	$0.258416\pi$
$884$	−38.0612			−1.28014
$885$	−13.5782	−	1.67171i	−0.456426	−	0.0561938i
$886$	−20.2965			−0.681874
$887$	−4.60625	+	4.60625i	−0.154663	+	0.154663i	−0.780197	−	0.625534i	$-0.784881\pi$
$887$	−4.60625	+	4.60625i	−0.154663	+	0.154663i	0.625534	+	0.780197i	$0.284881\pi$
$888$	7.80417	−	12.6497i	0.261891	−	0.424497i
$889$			13.1313i			0.440411i
$890$	3.99268	−	10.7668i	0.133835	−	0.360902i
$891$	−19.4436	−	14.4870i	−0.651385	−	0.485333i
$892$	5.56677	+	5.56677i	0.186389	+	0.186389i
$893$	−31.0451	−	31.0451i	−1.03888	−	1.03888i
$894$	−24.8058	+	5.87653i	−0.829630	+	0.196541i
$895$	−34.2234	+	15.7073i	−1.14396	+	0.525039i
$896$			3.69530i			0.123451i
$897$	58.8774	+	36.3241i	1.96586	+	1.21282i
$898$	15.9004	−	15.9004i	0.530603	−	0.530603i
$899$	5.99409			0.199914
$900$	3.63836	−	14.5521i	0.121279	−	0.485069i
$901$	22.6673			0.755158
$902$	4.01400	−	4.01400i	0.133652	−	0.133652i
$903$	−45.5092	−	28.0766i	−1.51445	−	0.934332i
$904$			5.52818i			0.183864i
$905$	−11.4187	+	5.24077i	−0.379569	+	0.174209i
$906$	12.1967	−	2.88942i	0.405208	−	0.0959944i
$907$	6.86880	+	6.86880i	0.228075	+	0.228075i	0.811888	−	0.583813i	$-0.198440\pi$
$907$	6.86880	+	6.86880i	0.228075	+	0.228075i	−0.583813	+	0.811888i	$0.698440\pi$
$908$	−12.2488	−	12.2488i	−0.406490	−	0.406490i
$909$	−35.2882	+	17.7138i	−1.17044	+	0.587530i
$910$	−13.4461	+	36.2589i	−0.445733	+	1.20197i
$911$			53.1468i			1.76083i	0.474202	+	0.880416i	$0.342737\pi$
$911$			53.1468i			1.76083i	−0.474202	+	0.880416i	$0.657263\pi$
$912$	5.01652	−	8.13124i	0.166113	−	0.269252i
$913$	−7.68019	+	7.68019i	−0.254177	+	0.254177i
$914$	8.04750			0.266188
$915$	−7.55914	−	0.930659i	−0.249897	−	0.0307666i
$916$	−23.5554			−0.778292
$917$	16.5969	−	16.5969i	0.548076	−	0.548076i
$918$	−42.0957	−	3.69529i	−1.38936	−	0.121963i
$919$			11.6847i			0.385442i	0.981254	+	0.192721i	$0.0617312\pi$
$919$			11.6847i			0.385442i	−0.981254	+	0.192721i	$0.938269\pi$
$920$	7.96014	+	17.3437i	0.262438	+	0.571804i
$921$	−11.4618	−	48.3822i	−0.377680	−	1.59425i
$922$	8.93786	+	8.93786i	0.294353	+	0.294353i
$923$	−30.6344	−	30.6344i	−1.00834	−	1.00834i
$924$	3.97502	+	16.7792i	0.130769	+	0.551996i
$925$	42.7858	−	3.22231i	1.40679	−	0.105949i
$926$			28.3751i			0.932463i
$927$	15.3132	+	5.07754i	0.502951	+	0.166768i
$928$	4.23846	−	4.23846i	0.139134	−	0.139134i
$929$	−10.6857			−0.350587			−0.175294	−	0.984516i	$-0.556087\pi$
$929$	−10.6857			−0.350587			−0.175294	+	0.984516i	$0.556087\pi$
$930$	3.05273	−	2.38345i	0.100103	−	0.0781563i
$931$	36.7109			1.20315
$932$	8.55243	−	8.55243i	0.280144	−	0.280144i
$933$	13.7501	−	22.2875i	0.450159	−	0.729659i
$934$		−	5.21543i		−	0.170654i
$935$	−45.9354	−	17.0344i	−1.50225	−	0.557086i
$936$	−6.29890	−	12.5482i	−0.205886	−	0.410152i
$937$	−0.437803	−	0.437803i	−0.0143024	−	0.0143024i	0.699919	−	0.714222i	$-0.253219\pi$
$937$	−0.437803	−	0.437803i	−0.0143024	−	0.0143024i	−0.714222	+	0.699919i	$0.753219\pi$
$938$	−14.1112	−	14.1112i	−0.460746	−	0.460746i
$939$	21.7166	−	5.14469i	0.708693	−	0.167891i
$940$	−16.6871	−	6.18815i	−0.544273	−	0.201835i
$941$			54.2650i			1.76899i	0.466552	+	0.884494i	$0.345496\pi$
$941$			54.2650i			1.76899i	−0.466552	+	0.884494i	$0.654504\pi$
$942$	−11.5103	−	7.10121i	−0.375026	−	0.231370i
$943$	−12.7152	+	12.7152i	−0.414064	+	0.414064i
$944$	−3.53235			−0.114968
$945$	−18.3916	+	38.7969i	−0.598280	+	1.26206i
$946$	22.5085			0.731813
$947$	7.38802	−	7.38802i	0.240078	−	0.240078i	−0.576804	−	0.816883i	$-0.695700\pi$
$947$	7.38802	−	7.38802i	0.240078	−	0.240078i	0.816883	+	0.576804i	$0.195700\pi$
$948$	−8.65238	−	5.33803i	−0.281016	−	0.173371i
$949$		−	10.4981i		−	0.340783i
$950$	27.5027	−	2.07130i	0.892305	−	0.0672018i
$951$	14.9070	−	3.53149i	0.483393	−	0.114516i
$952$	21.2499	+	21.2499i	0.688713	+	0.688713i
$953$	−9.66224	−	9.66224i	−0.312991	−	0.312991i	0.533076	−	0.846067i	$-0.321036\pi$
$953$	−9.66224	−	9.66224i	−0.312991	−	0.312991i	−0.846067	+	0.533076i	$0.821036\pi$
$954$	3.75131	+	7.47310i	0.121453	+	0.241950i
$955$	12.8785	+	28.0599i	0.416739	+	0.907996i
$956$			17.8938i			0.578727i
$957$	14.6863	−	23.8049i	0.474740	−	0.769502i
$958$	−9.94530	+	9.94530i	−0.321318	+	0.321318i
$959$	15.5703			0.502790
$960$	0.473257	−	3.84396i	0.0152743	−	0.124063i
$961$	1.00000			0.0322581
$962$	28.3990	−	28.3990i	0.915620	−	0.915620i
$963$	17.1382	+	5.68268i	0.552270	+	0.183122i
$964$		−	17.7279i		−	0.570978i
$965$	−2.78070	+	7.49850i	−0.0895140	+	0.241385i
$966$	−12.5917	−	53.1518i	−0.405132	−	1.71013i
$967$	9.57359	+	9.57359i	0.307866	+	0.307866i	0.844081	−	0.536215i	$-0.180147\pi$
$967$	9.57359	+	9.57359i	0.307866	+	0.307866i	−0.536215	+	0.844081i	$0.680147\pi$
$968$	2.64574	+	2.64574i	0.0850372	+	0.0850372i
$969$	−17.9113	−	75.6065i	−0.575394	−	2.42883i
$970$	−5.25075	+	2.40991i	−0.168592	+	0.0773777i
$971$		−	38.4908i		−	1.23523i	−0.786481	−	0.617614i	$-0.788099\pi$
$971$		−	38.4908i		−	1.23523i	0.786481	−	0.617614i	$-0.211901\pi$
$972$	−5.74830	−	14.4899i	−0.184377	−	0.464764i
$973$	4.05234	−	4.05234i	0.129912	−	0.129912i
$974$	27.3470			0.876254
$975$	18.6307	−	35.9956i	0.596660	−	1.15278i
$976$	−1.96650			−0.0629461
$977$	15.7232	−	15.7232i	0.503031	−	0.503031i	−0.409348	−	0.912379i	$-0.634244\pi$
$977$	15.7232	−	15.7232i	0.503031	−	0.503031i	0.912379	+	0.409348i	$0.134244\pi$
$978$	7.89175	−	12.7917i	0.252350	−	0.409033i
$979$		−	13.8356i		−	0.442188i
$980$	13.5250	−	6.20751i	0.432040	−	0.198292i
$981$	−50.7741	+	25.4873i	−1.62109	+	0.813748i
$982$	−18.1457	−	18.1457i	−0.579051	−	0.579051i
$983$	−2.73046	−	2.73046i	−0.0870880	−	0.0870880i	0.662221	−	0.749309i	$-0.269614\pi$
$983$	−2.73046	−	2.73046i	−0.0870880	−	0.0870880i	−0.749309	+	0.662221i	$0.769614\pi$
$984$	3.55121	−	0.841287i	0.113208	−	0.0268193i
$985$	14.7568	−	39.7935i	0.470191	−	1.26793i
$986$		−	48.7467i		−	1.55241i
$987$	43.3558	+	26.7481i	1.38003	+	0.851401i
$988$	18.2548	−	18.2548i	0.580764	−	0.580764i
$989$	−71.3004			−2.26722
$990$	−1.98603	−	17.9634i	−0.0631200	−	0.570913i
$991$	−14.4796			−0.459959			−0.229979	−	0.973196i	$-0.573866\pi$
$991$	−14.4796			−0.459959			−0.229979	+	0.973196i	$0.573866\pi$
$992$	0.707107	−	0.707107i	0.0224507	−	0.0224507i
$993$	13.0814	+	8.07049i	0.415126	+	0.256109i
$994$			34.2069i			1.08498i
$995$	−8.87638	−	19.3400i	−0.281400	−	0.613118i
$996$	−6.79472	+	1.60968i	−0.215299	+	0.0510046i
$997$	−10.6784	−	10.6784i	−0.338187	−	0.338187i	0.517497	−	0.855685i	$-0.326864\pi$
$997$	−10.6784	−	10.6784i	−0.338187	−	0.338187i	−0.855685	+	0.517497i	$0.826864\pi$
$998$	−8.05943	−	8.05943i	−0.255117	−	0.255117i
$999$	34.1665	−	28.6521i	1.08098	−	0.906511i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.g.497.2	✓	40
3.2	odd	2	inner	930.2.j.g.497.17	yes	40
5.3	odd	4	inner	930.2.j.g.683.17	yes	40
15.8	even	4	inner	930.2.j.g.683.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.g.497.2	✓	40	1.1	even	1	trivial
930.2.j.g.497.17	yes	40	3.2	odd	2	inner
930.2.j.g.683.2	yes	40	15.8	even	4	inner
930.2.j.g.683.17	yes	40	5.3	odd	4	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.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.47409 - 0.909430i) q^{3} -1.00000i q^{4} +(2.03224 - 0.932730i) q^{5} +(1.68540 - 0.399274i) q^{6} +(-2.61297 - 2.61297i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.34588 + 2.68116i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.47409 - 0.909430i) q^{3} -1.00000i q^{4} +(2.03224 - 0.932730i) q^{5} +(1.68540 - 0.399274i) q^{6} +(-2.61297 - 2.61297i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.34588 + 2.68116i) q^{9} +(-0.777474 + 2.09655i) q^{10} +2.69413i q^{11} +(-0.909430 + 1.47409i) q^{12} +(-3.30937 + 3.30937i) q^{13} +3.69530 q^{14} +(-3.84396 - 0.473257i) q^{15} -1.00000 q^{16} +(-5.75053 + 5.75053i) q^{17} +(-2.84754 - 0.944189i) q^{18} -5.51611i q^{19} +(-0.932730 - 2.03224i) q^{20} +(1.47544 + 6.22806i) q^{21} +(-1.90504 - 1.90504i) q^{22} +(6.03462 + 6.03462i) q^{23} +(-0.399274 - 1.68540i) q^{24} +(3.26003 - 3.79107i) q^{25} -4.68015i q^{26} +(0.454387 - 5.17625i) q^{27} +(-2.61297 + 2.61297i) q^{28} +5.99409 q^{29} +(3.05273 - 2.38345i) q^{30} +1.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(2.45013 - 3.97139i) q^{33} -8.13247i q^{34} +(-7.74738 - 2.87300i) q^{35} +(2.68116 - 1.34588i) q^{36} +(6.06796 + 6.06796i) q^{37} +(3.90048 + 3.90048i) q^{38} +(7.88794 - 1.86866i) q^{39} +(2.09655 + 0.777474i) q^{40} +2.10704i q^{41} +(-5.44719 - 3.36061i) q^{42} +(-5.90761 + 5.90761i) q^{43} +2.69413 q^{44} +(5.23594 + 4.19343i) q^{45} -8.53424 q^{46} +(5.62807 - 5.62807i) q^{47} +(1.47409 + 0.909430i) q^{48} +6.65521i q^{49} +(0.375500 + 4.98588i) q^{50} +(13.7065 - 3.24709i) q^{51} +(3.30937 + 3.30937i) q^{52} +(-1.97089 - 1.97089i) q^{53} +(3.33886 + 3.98146i) q^{54} +(2.51290 + 5.47514i) q^{55} -3.69530i q^{56} +(-5.01652 + 8.13124i) q^{57} +(-4.23846 + 4.23846i) q^{58} +3.53235 q^{59} +(-0.473257 + 3.84396i) q^{60} +1.96650 q^{61} +(-0.707107 + 0.707107i) q^{62} +(3.48906 - 10.5225i) q^{63} +1.00000i q^{64} +(-3.63870 + 9.81219i) q^{65} +(1.07570 + 4.54070i) q^{66} +(-3.81869 - 3.81869i) q^{67} +(5.75053 + 5.75053i) q^{68} +(-3.40750 - 14.3836i) q^{69} +(7.50974 - 3.44671i) q^{70} +9.25687i q^{71} +(-0.944189 + 2.84754i) q^{72} +(-1.58612 + 1.58612i) q^{73} -8.58139 q^{74} +(-8.25329 + 2.62360i) q^{75} -5.51611 q^{76} +(7.03969 - 7.03969i) q^{77} +(-4.25627 + 6.89896i) q^{78} +5.86965i q^{79} +(-2.03224 + 0.932730i) q^{80} +(-5.37724 + 7.21701i) q^{81} +(-1.48990 - 1.48990i) q^{82} +(2.85071 + 2.85071i) q^{83} +(6.22806 - 1.47544i) q^{84} +(-6.32279 + 17.0502i) q^{85} -8.35462i q^{86} +(-8.83582 - 5.45120i) q^{87} +(-1.90504 + 1.90504i) q^{88} -5.13546 q^{89} +(-6.66758 + 0.737166i) q^{90} +17.2945 q^{91} +(6.03462 - 6.03462i) q^{92} +(-1.47409 - 0.909430i) q^{93} +7.95929i q^{94} +(-5.14504 - 11.2101i) q^{95} +(-1.68540 + 0.399274i) q^{96} +(1.82697 + 1.82697i) q^{97} +(-4.70594 - 4.70594i) q^{98} +(-7.22341 + 3.62597i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} - 8 q^{7}+O(q^{10}) \) 40 * q - 4 * q^3 - 8 * q^7	\( 40 q - 4 q^{3} - 8 q^{7} + 8 q^{10} + 4 q^{12} - 20 q^{13} - 44 q^{15} - 40 q^{16} + 16 q^{18} - 32 q^{21} - 4 q^{22} + 8 q^{25} + 8 q^{27} - 8 q^{28} - 4 q^{30} + 40 q^{31} + 48 q^{33} + 64 q^{37} - 4 q^{40} - 20 q^{42} - 48 q^{43} - 4 q^{45} - 80 q^{46} + 4 q^{48} + 48 q^{51} + 20 q^{52} + 164 q^{55} + 40 q^{57} + 56 q^{58} + 24 q^{60} - 128 q^{61} + 56 q^{63} + 8 q^{66} - 4 q^{67} - 56 q^{70} - 16 q^{72} - 48 q^{73} - 48 q^{75} - 40 q^{76} - 36 q^{78} - 24 q^{81} - 16 q^{82} - 56 q^{85} - 12 q^{87} - 4 q^{88} - 28 q^{90} - 32 q^{91} - 4 q^{93} - 52 q^{97}+O(q^{100}) \) 40 * q - 4 * q^3 - 8 * q^7 + 8 * q^10 + 4 * q^12 - 20 * q^13 - 44 * q^15 - 40 * q^16 + 16 * q^18 - 32 * q^21 - 4 * q^22 + 8 * q^25 + 8 * q^27 - 8 * q^28 - 4 * q^30 + 40 * q^31 + 48 * q^33 + 64 * q^37 - 4 * q^40 - 20 * q^42 - 48 * q^43 - 4 * q^45 - 80 * q^46 + 4 * q^48 + 48 * q^51 + 20 * q^52 + 164 * q^55 + 40 * q^57 + 56 * q^58 + 24 * q^60 - 128 * q^61 + 56 * q^63 + 8 * q^66 - 4 * q^67 - 56 * q^70 - 16 * q^72 - 48 * q^73 - 48 * q^75 - 40 * q^76 - 36 * q^78 - 24 * q^81 - 16 * q^82 - 56 * q^85 - 12 * q^87 - 4 * q^88 - 28 * q^90 - 32 * q^91 - 4 * q^93 - 52 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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