LMFDB - Embedded newform 930.2.j.g.497.4

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			497.4
Character	$\chi$	$=$	930.497
Dual form			930.2.j.g.683.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.731811 + 1.56986i) q^{3} -1.00000i q^{4} +(-1.45516 + 1.69779i) q^{5} +(-0.592589 - 1.62753i) q^{6} +(1.76311 + 1.76311i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.92891 - 2.29768i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.731811 + 1.56986i) q^{3} -1.00000i q^{4} +(-1.45516 + 1.69779i) q^{5} +(-0.592589 - 1.62753i) q^{6} +(1.76311 + 1.76311i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.92891 - 2.29768i) q^{9} +(-0.171568 - 2.22948i) q^{10} -5.31589i q^{11} +(1.56986 + 0.731811i) q^{12} +(3.35958 - 3.35958i) q^{13} -2.49342 q^{14} +(-1.60039 - 3.52686i) q^{15} -1.00000 q^{16} +(2.77112 - 2.77112i) q^{17} +(2.98865 + 0.260761i) q^{18} -1.86557i q^{19} +(1.69779 + 1.45516i) q^{20} +(-4.05810 + 1.47757i) q^{21} +(3.75890 + 3.75890i) q^{22} +(-3.75550 - 3.75550i) q^{23} +(-1.62753 + 0.592589i) q^{24} +(-0.765014 - 4.94113i) q^{25} +4.75116i q^{26} +(5.01862 - 1.34664i) q^{27} +(1.76311 - 1.76311i) q^{28} -3.62239 q^{29} +(3.62552 + 1.36222i) q^{30} +1.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(8.34519 + 3.89023i) q^{33} +3.91895i q^{34} +(-5.55901 + 0.427791i) q^{35} +(-2.29768 + 1.92891i) q^{36} +(1.42681 + 1.42681i) q^{37} +(1.31916 + 1.31916i) q^{38} +(2.81548 + 7.73263i) q^{39} +(-2.22948 + 0.171568i) q^{40} +6.12646i q^{41} +(1.82471 - 3.91431i) q^{42} +(6.90667 - 6.90667i) q^{43} -5.31589 q^{44} +(6.70785 + 0.0686037i) q^{45} +5.31107 q^{46} +(-5.33412 + 5.33412i) q^{47} +(0.731811 - 1.56986i) q^{48} -0.782871i q^{49} +(4.03485 + 2.95296i) q^{50} +(2.32233 + 6.37819i) q^{51} +(-3.35958 - 3.35958i) q^{52} +(-7.93890 - 7.93890i) q^{53} +(-2.59648 + 4.50092i) q^{54} +(9.02529 + 7.73548i) q^{55} +2.49342i q^{56} +(2.92869 + 1.36525i) q^{57} +(2.56141 - 2.56141i) q^{58} +8.98420 q^{59} +(-3.52686 + 1.60039i) q^{60} -3.54388 q^{61} +(-0.707107 + 0.707107i) q^{62} +(0.650185 - 7.45194i) q^{63} +1.00000i q^{64} +(0.815147 + 10.5926i) q^{65} +(-8.65175 + 3.15014i) q^{66} +(3.66547 + 3.66547i) q^{67} +(-2.77112 - 2.77112i) q^{68} +(8.64390 - 3.14728i) q^{69} +(3.62832 - 4.23331i) q^{70} -8.57648i q^{71} +(0.260761 - 2.98865i) q^{72} +(0.0629195 - 0.0629195i) q^{73} -2.01781 q^{74} +(8.31671 + 2.41501i) q^{75} -1.86557 q^{76} +(9.37251 - 9.37251i) q^{77} +(-7.45864 - 3.47695i) q^{78} -13.3800i q^{79} +(1.45516 - 1.69779i) q^{80} +(-1.55864 + 8.86401i) q^{81} +(-4.33206 - 4.33206i) q^{82} +(4.31021 + 4.31021i) q^{83} +(1.47757 + 4.05810i) q^{84} +(0.672367 + 8.73721i) q^{85} +9.76750i q^{86} +(2.65090 - 5.68663i) q^{87} +(3.75890 - 3.75890i) q^{88} -5.00586 q^{89} +(-4.79168 + 4.69466i) q^{90} +11.8466 q^{91} +(-3.75550 + 3.75550i) q^{92} +(-0.731811 + 1.56986i) q^{93} -7.54358i q^{94} +(3.16736 + 2.71471i) q^{95} +(0.592589 + 1.62753i) q^{96} +(7.70070 + 7.70070i) q^{97} +(0.553574 + 0.553574i) q^{98} +(-12.2142 + 10.2539i) 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
$3$	−0.731811	+	1.56986i	−0.422511	+	0.906358i
$3$	−0.731811	+	1.56986i	−0.422511	+	0.906358i
$4$		−	1.00000i		−	0.500000i
$5$	−1.45516	+	1.69779i	−0.650768	+	0.759277i
$5$	−1.45516	+	1.69779i	−0.650768	+	0.759277i
$6$	−0.592589	−	1.62753i	−0.241923	−	0.664434i
$7$	1.76311	+	1.76311i	0.666394	+	0.666394i	0.956879	−	0.290486i	$-0.0938168\pi$
$7$	1.76311	+	1.76311i	0.666394	+	0.666394i	−0.290486	+	0.956879i	$0.593817\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.92891	−	2.29768i	−0.642969	−	0.765892i
$10$	−0.171568	−	2.22948i	−0.0542546	−	0.705022i
$11$		−	5.31589i		−	1.60280i	−0.598128	−	0.801401i	$-0.704088\pi$
$11$		−	5.31589i		−	1.60280i	0.598128	−	0.801401i	$-0.295912\pi$
$12$	1.56986	+	0.731811i	0.453179	+	0.211256i
$13$	3.35958	−	3.35958i	0.931779	−	0.931779i	−0.0660382	−	0.997817i	$-0.521036\pi$
$13$	3.35958	−	3.35958i	0.931779	−	0.931779i	0.997817	+	0.0660382i	$0.0210359\pi$
$14$	−2.49342			−0.666394
$15$	−1.60039	−	3.52686i	−0.413220	−	0.910631i
$16$	−1.00000			−0.250000
$17$	2.77112	−	2.77112i	0.672095	−	0.672095i	−0.286104	−	0.958199i	$-0.592360\pi$
$17$	2.77112	−	2.77112i	0.672095	−	0.672095i	0.958199	+	0.286104i	$0.0923603\pi$
$18$	2.98865	+	0.260761i	0.704431	+	0.0614619i
$19$		−	1.86557i		−	0.427992i	−0.976835	−	0.213996i	$-0.931352\pi$
$19$		−	1.86557i		−	0.427992i	0.976835	−	0.213996i	$-0.0686480\pi$
$20$	1.69779	+	1.45516i	0.379638	+	0.325384i
$21$	−4.05810	+	1.47757i	−0.885550	+	0.322432i
$22$	3.75890	+	3.75890i	0.801401	+	0.801401i
$23$	−3.75550	−	3.75550i	−0.783075	−	0.783075i	0.197274	−	0.980348i	$-0.436791\pi$
$23$	−3.75550	−	3.75550i	−0.783075	−	0.783075i	−0.980348	+	0.197274i	$0.936791\pi$
$24$	−1.62753	+	0.592589i	−0.332217	+	0.120962i
$25$	−0.765014	−	4.94113i	−0.153003	−	0.988226i
$26$			4.75116i			0.931779i
$27$	5.01862	−	1.34664i	0.965834	−	0.259162i
$28$	1.76311	−	1.76311i	0.333197	−	0.333197i
$29$	−3.62239			−0.672660			−0.336330	−	0.941744i	$-0.609186\pi$
$29$	−3.62239			−0.672660			−0.336330	+	0.941744i	$0.609186\pi$
$30$	3.62552	+	1.36222i	0.661926	+	0.248706i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	8.34519	+	3.89023i	1.45271	+	0.677201i
$34$			3.91895i			0.672095i
$35$	−5.55901	+	0.427791i	−0.939645	+	0.0723098i
$36$	−2.29768	+	1.92891i	−0.382946	+	0.321484i
$37$	1.42681	+	1.42681i	0.234566	+	0.234566i	0.814596	−	0.580029i	$-0.196959\pi$
$37$	1.42681	+	1.42681i	0.234566	+	0.234566i	−0.580029	+	0.814596i	$0.696959\pi$
$38$	1.31916	+	1.31916i	0.213996	+	0.213996i
$39$	2.81548	+	7.73263i	0.450838	+	1.23821i
$40$	−2.22948	+	0.171568i	−0.352511	+	0.0271273i
$41$			6.12646i			0.956792i	0.878144	+	0.478396i	$0.158782\pi$
$41$			6.12646i			0.956792i	−0.878144	+	0.478396i	$0.841218\pi$
$42$	1.82471	−	3.91431i	0.281559	−	0.603991i
$43$	6.90667	−	6.90667i	1.05326	−	1.05326i	0.0547572	−	0.998500i	$-0.482562\pi$
$43$	6.90667	−	6.90667i	1.05326	−	1.05326i	0.998500	−	0.0547572i	$-0.0174385\pi$
$44$	−5.31589			−0.801401
$45$	6.70785	+	0.0686037i	0.999948	+	0.0102268i
$46$	5.31107			0.783075
$47$	−5.33412	+	5.33412i	−0.778061	+	0.778061i	−0.979501	−	0.201440i	$-0.935438\pi$
$47$	−5.33412	+	5.33412i	−0.778061	+	0.778061i	0.201440	+	0.979501i	$0.435438\pi$
$48$	0.731811	−	1.56986i	0.105628	−	0.226589i
$49$		−	0.782871i		−	0.111839i
$50$	4.03485	+	2.95296i	0.570614	+	0.417612i
$51$	2.32233	+	6.37819i	0.325191	+	0.893126i
$52$	−3.35958	−	3.35958i	−0.465889	−	0.465889i
$53$	−7.93890	−	7.93890i	−1.09049	−	1.09049i	−0.995476	−	0.0950167i	$-0.969710\pi$
$53$	−7.93890	−	7.93890i	−1.09049	−	1.09049i	−0.0950167	−	0.995476i	$-0.530290\pi$
$54$	−2.59648	+	4.50092i	−0.353336	+	0.612498i
$55$	9.02529	+	7.73548i	1.21697	+	1.04305i
$56$			2.49342i			0.333197i
$57$	2.92869	+	1.36525i	0.387914	+	0.180831i
$58$	2.56141	−	2.56141i	0.336330	−	0.336330i
$59$	8.98420			1.16964			0.584821	−	0.811162i	$-0.301165\pi$
$59$	8.98420			1.16964			0.584821	+	0.811162i	$0.301165\pi$
$60$	−3.52686	+	1.60039i	−0.455316	+	0.206610i
$61$	−3.54388			−0.453748			−0.226874	−	0.973924i	$-0.572850\pi$
$61$	−3.54388			−0.453748			−0.226874	+	0.973924i	$0.572850\pi$
$62$	−0.707107	+	0.707107i	−0.0898027	+	0.0898027i
$63$	0.650185	−	7.45194i	0.0819156	−	0.938856i
$64$			1.00000i			0.125000i
$65$	0.815147	+	10.5926i	0.101107	+	1.31385i
$66$	−8.65175	+	3.15014i	−1.06496	+	0.387755i
$67$	3.66547	+	3.66547i	0.447809	+	0.447809i	0.894625	−	0.446817i	$-0.147442\pi$
$67$	3.66547	+	3.66547i	0.447809	+	0.447809i	−0.446817	+	0.894625i	$0.647442\pi$
$68$	−2.77112	−	2.77112i	−0.336047	−	0.336047i
$69$	8.64390	−	3.14728i	1.04060	−	0.378888i
$70$	3.62832	−	4.23331i	0.433668	−	0.505977i
$71$		−	8.57648i		−	1.01784i	−0.860814	−	0.508920i	$-0.830045\pi$
$71$		−	8.57648i		−	1.01784i	0.860814	−	0.508920i	$-0.169955\pi$
$72$	0.260761	−	2.98865i	0.0307309	−	0.352215i
$73$	0.0629195	−	0.0629195i	0.00736417	−	0.00736417i	−0.703415	−	0.710779i	$-0.748342\pi$
$73$	0.0629195	−	0.0629195i	0.00736417	−	0.00736417i	0.710779	+	0.703415i	$0.248342\pi$
$74$	−2.01781			−0.234566
$75$	8.31671	+	2.41501i	0.960331	+	0.278861i
$76$	−1.86557			−0.213996
$77$	9.37251	−	9.37251i	1.06810	−	1.06810i
$78$	−7.45864	−	3.47695i	−0.844525	−	0.393687i
$79$		−	13.3800i		−	1.50536i	−0.658385	−	0.752682i	$-0.728760\pi$
$79$		−	13.3800i		−	1.50536i	0.658385	−	0.752682i	$-0.271240\pi$
$80$	1.45516	−	1.69779i	0.162692	−	0.189819i
$81$	−1.55864	+	8.86401i	−0.173182	+	0.984890i
$82$	−4.33206	−	4.33206i	−0.478396	−	0.478396i
$83$	4.31021	+	4.31021i	0.473107	+	0.473107i	0.902919	−	0.429812i	$-0.141420\pi$
$83$	4.31021	+	4.31021i	0.473107	+	0.473107i	−0.429812	+	0.902919i	$0.641420\pi$
$84$	1.47757	+	4.05810i	0.161216	+	0.442775i
$85$	0.672367	+	8.73721i	0.0729284	+	0.947683i
$86$			9.76750i			1.05326i
$87$	2.65090	−	5.68663i	0.284207	−	0.609671i
$88$	3.75890	−	3.75890i	0.400700	−	0.400700i
$89$	−5.00586			−0.530620			−0.265310	−	0.964163i	$-0.585474\pi$
$89$	−5.00586			−0.530620			−0.265310	+	0.964163i	$0.585474\pi$
$90$	−4.79168	+	4.69466i	−0.505087	+	0.494860i
$91$	11.8466			1.24186
$92$	−3.75550	+	3.75550i	−0.391537	+	0.391537i
$93$	−0.731811	+	1.56986i	−0.0758852	+	0.162787i
$94$		−	7.54358i		−	0.778061i
$95$	3.16736	+	2.71471i	0.324965	+	0.278523i
$96$	0.592589	+	1.62753i	0.0604808	+	0.166109i
$97$	7.70070	+	7.70070i	0.781888	+	0.781888i	0.980149	−	0.198261i	$-0.0635294\pi$
$97$	7.70070	+	7.70070i	0.781888	+	0.781888i	−0.198261	+	0.980149i	$0.563529\pi$
$98$	0.553574	+	0.553574i	0.0559194	+	0.0559194i
$99$	−12.2142	+	10.2539i	−1.22757	+	1.03055i
$100$	−4.94113	+	0.765014i	−0.494113	+	0.0765014i
$101$			6.10793i			0.607762i	0.952710	+	0.303881i	$0.0982825\pi$
$101$			6.10793i			0.607762i	−0.952710	+	0.303881i	$0.901717\pi$
$102$	−6.15220	−	2.86793i	−0.609158	−	0.283967i
$103$	−7.86523	+	7.86523i	−0.774984	+	0.774984i	−0.978973	−	0.203989i	$-0.934609\pi$
$103$	−7.86523	+	7.86523i	−0.774984	+	0.774984i	0.203989	+	0.978973i	$0.434609\pi$
$104$	4.75116			0.465889
$105$	3.39658	−	9.03992i	0.331472	−	0.882206i
$106$	11.2273			1.09049
$107$	2.79803	−	2.79803i	0.270496	−	0.270496i	−0.558804	−	0.829300i	$-0.688740\pi$
$107$	2.79803	−	2.79803i	0.270496	−	0.270496i	0.829300	+	0.558804i	$0.188740\pi$
$108$	−1.34664	−	5.01862i	−0.129581	−	0.482917i
$109$			5.73010i			0.548844i	0.961609	+	0.274422i	$0.0884865\pi$
$109$			5.73010i			0.548844i	−0.961609	+	0.274422i	$0.911513\pi$
$110$	−11.8517	+	0.912037i	−1.13001	+	0.0869593i
$111$	−3.28404	+	1.19573i	−0.311708	+	0.113494i
$112$	−1.76311	−	1.76311i	−0.166598	−	0.166598i
$113$	−0.541653	−	0.541653i	−0.0509544	−	0.0509544i	0.681170	−	0.732125i	$-0.261471\pi$
$113$	−0.541653	−	0.541653i	−0.0509544	−	0.0509544i	−0.732125	+	0.681170i	$0.761471\pi$
$114$	−3.03627	+	1.10552i	−0.284373	+	0.103541i
$115$	11.8409	−	0.911210i	1.10417	−	0.0849708i
$116$			3.62239i			0.336330i
$117$	−14.1995	−	1.23892i	−1.31275	−	0.114538i
$118$	−6.35279	+	6.35279i	−0.584821	+	0.584821i
$119$	9.77158			0.895759
$120$	1.36222	−	3.62552i	0.124353	−	0.330963i
$121$	−17.2587			−1.56897
$122$	2.50590	−	2.50590i	0.226874	−	0.226874i
$123$	−9.61767	−	4.48341i	−0.867196	−	0.404255i
$124$		−	1.00000i		−	0.0898027i
$125$	9.50224	+	5.89130i	0.849906	+	0.526934i
$126$	4.80957	+	5.72907i	0.428470	+	0.510386i
$127$	−13.3408	−	13.3408i	−1.18380	−	1.18380i	−0.978751	−	0.205051i	$-0.934264\pi$
$127$	−13.3408	−	13.3408i	−1.18380	−	1.18380i	−0.205051	−	0.978751i	$-0.565736\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	5.78811	+	15.8969i	0.509615	+	1.39964i
$130$	−8.06649	−	6.91370i	−0.707478	−	0.606372i
$131$		−	0.255148i		−	0.0222924i	−0.999938	−	0.0111462i	$-0.996452\pi$
$131$		−	0.255148i		−	0.0222924i	0.999938	−	0.0111462i	$-0.00354801\pi$
$132$	3.89023	−	8.34519i	0.338601	−	0.726356i
$133$	3.28922	−	3.28922i	0.285211	−	0.285211i
$134$	−5.18376			−0.447809
$135$	−5.01658	+	10.4802i	−0.431758	+	0.901989i
$136$	3.91895			0.336047
$137$	7.91747	−	7.91747i	0.676435	−	0.676435i	−0.282756	−	0.959192i	$-0.591249\pi$
$137$	7.91747	−	7.91747i	0.676435	−	0.676435i	0.959192	+	0.282756i	$0.0912488\pi$
$138$	−3.88670	+	8.33763i	−0.330858	+	0.709746i
$139$			1.09893i			0.0932096i	0.998913	+	0.0466048i	$0.0148401\pi$
$139$			1.09893i			0.0932096i	−0.998913	+	0.0466048i	$0.985160\pi$
$140$	0.427791	+	5.55901i	0.0361549	+	0.469822i
$141$	−4.47024	−	12.2774i	−0.376462	−	1.03394i
$142$	6.06448	+	6.06448i	0.508920	+	0.508920i
$143$	−17.8591	−	17.8591i	−1.49346	−	1.49346i
$144$	1.92891	+	2.29768i	0.160742	+	0.191473i
$145$	5.27116	−	6.15007i	0.437746	−	0.510736i
$146$			0.0889817i			0.00736417i
$147$	1.22900	+	0.572914i	0.101366	+	0.0472531i
$148$	1.42681	−	1.42681i	0.117283	−	0.117283i
$149$	16.7070			1.36869			0.684347	−	0.729156i	$-0.260087\pi$
$149$	16.7070			1.36869			0.684347	+	0.729156i	$0.260087\pi$
$150$	−7.58847	+	4.17314i	−0.619596	+	0.340735i
$151$	−22.2992			−1.81469			−0.907343	−	0.420391i	$-0.861893\pi$
$151$	−22.2992			−1.81469			−0.907343	+	0.420391i	$0.861893\pi$
$152$	1.31916	−	1.31916i	0.106998	−	0.106998i
$153$	−11.7124	−	1.02191i	−0.946888	−	0.0826164i
$154$			13.2547i			1.06810i
$155$	−1.45516	+	1.69779i	−0.116881	+	0.136370i
$156$	7.73263	−	2.81548i	0.619106	−	0.225419i
$157$	13.3935	+	13.3935i	1.06892	+	1.06892i	0.997442	+	0.0714780i	$0.0227716\pi$
$157$	13.3935	+	13.3935i	1.06892	+	1.06892i	0.0714780	+	0.997442i	$0.477228\pi$
$158$	9.46106	+	9.46106i	0.752682	+	0.752682i
$159$	18.2727	−	6.65317i	1.44912	−	0.527631i
$160$	0.171568	+	2.22948i	0.0135636	+	0.176256i
$161$		−	13.2427i		−	1.04367i
$162$	−5.16567	−	7.36993i	−0.405854	−	0.579036i
$163$	−2.50082	+	2.50082i	−0.195880	+	0.195880i	−0.798231	−	0.602351i	$-0.794231\pi$
$163$	−2.50082	+	2.50082i	−0.195880	+	0.195880i	0.602351	+	0.798231i	$0.294231\pi$
$164$	6.12646			0.478396
$165$	−18.7484	+	8.50752i	−1.45956	+	0.662309i
$166$	−6.09556			−0.473107
$167$	5.03410	−	5.03410i	0.389551	−	0.389551i	−0.484977	−	0.874527i	$-0.661172\pi$
$167$	5.03410	−	5.03410i	0.389551	−	0.389551i	0.874527	+	0.484977i	$0.161172\pi$
$168$	−3.91431	−	1.82471i	−0.301996	−	0.140779i
$169$		−	9.57351i		−	0.736424i
$170$	−6.65357	−	5.70270i	−0.510306	−	0.437378i
$171$	−4.28649	+	3.59852i	−0.327796	+	0.275186i
$172$	−6.90667	−	6.90667i	−0.526628	−	0.526628i
$173$	−3.30244	−	3.30244i	−0.251080	−	0.251080i	0.570334	−	0.821413i	$-0.306814\pi$
$173$	−3.30244	−	3.30244i	−0.251080	−	0.251080i	−0.821413	+	0.570334i	$0.806814\pi$
$174$	2.14659	+	5.89553i	0.162732	+	0.446939i
$175$	7.36296	−	10.0606i	0.556587	−	0.760508i
$176$			5.31589i			0.400700i
$177$	−6.57473	+	14.1039i	−0.494187	+	1.06011i
$178$	3.53968	−	3.53968i	0.265310	−	0.265310i
$179$	9.97200			0.745342			0.372671	−	0.927963i	$-0.378442\pi$
$179$	9.97200			0.745342			0.372671	+	0.927963i	$0.378442\pi$
$180$	0.0686037	−	6.70785i	0.00511342	−	0.499974i
$181$	−16.2713			−1.20944			−0.604718	−	0.796439i	$-0.706714\pi$
$181$	−16.2713			−1.20944			−0.604718	+	0.796439i	$0.706714\pi$
$182$	−8.37683	+	8.37683i	−0.620932	+	0.620932i
$183$	2.59345	−	5.56339i	0.191713	−	0.411258i
$184$		−	5.31107i		−	0.391537i
$185$	−4.49867	+	0.346192i	−0.330749	+	0.0254526i
$186$	−0.592589	−	1.62753i	−0.0434507	−	0.119336i
$187$	−14.7310	−	14.7310i	−1.07723	−	1.07723i
$188$	5.33412	+	5.33412i	0.389031	+	0.389031i
$189$	11.2227	+	6.47411i	0.816329	+	0.470922i
$190$	−4.15925	+	0.320073i	−0.301744	+	0.0232205i
$191$		−	14.4761i		−	1.04745i	−0.851886	−	0.523727i	$-0.824541\pi$
$191$		−	14.4761i		−	1.04745i	0.851886	−	0.523727i	$-0.175459\pi$
$192$	−1.56986	−	0.731811i	−0.113295	−	0.0528139i
$193$	6.75153	−	6.75153i	0.485985	−	0.485985i	−0.421051	−	0.907037i	$-0.638339\pi$
$193$	6.75153	−	6.75153i	0.485985	−	0.485985i	0.907037	+	0.421051i	$0.138339\pi$
$194$	−10.8904			−0.781888
$195$	−17.2254	−	6.47211i	−1.23354	−	0.463477i
$196$	−0.782871			−0.0559194
$197$	14.0237	−	14.0237i	0.999150	−	0.999150i	−0.000850008	−	1.00000i	$-0.500271\pi$
$197$	14.0237	−	14.0237i	0.999150	−	0.999150i	1.00000		0.000850008i	$0.000270566\pi$
$198$	1.38618	−	15.8873i	0.0985112	−	1.12906i
$199$		−	11.1677i		−	0.791660i	−0.918324	−	0.395830i	$-0.870457\pi$
$199$		−	11.1677i		−	0.791660i	0.918324	−	0.395830i	$-0.129543\pi$
$200$	2.95296	−	4.03485i	0.208806	−	0.285307i
$201$	−8.43670	+	3.07184i	−0.595079	+	0.216671i
$202$	−4.31896	−	4.31896i	−0.303881	−	0.303881i
$203$	−6.38668	−	6.38668i	−0.448257	−	0.448257i
$204$	6.37819	−	2.32233i	0.446563	−	0.162595i
$205$	−10.4015	−	8.91498i	−0.726470	−	0.622650i
$206$		−	11.1231i		−	0.774984i
$207$	−1.38492	+	15.8729i	−0.0962585	+	1.10324i
$208$	−3.35958	+	3.35958i	−0.232945	+	0.232945i
$209$	−9.91719			−0.685986
$210$	3.99045	+	8.79393i	0.275367	+	0.606839i
$211$	−4.26926			−0.293908			−0.146954	−	0.989143i	$-0.546947\pi$
$211$	−4.26926			−0.293908			−0.146954	+	0.989143i	$0.546947\pi$
$212$	−7.93890	+	7.93890i	−0.545246	+	0.545246i
$213$	13.4638	+	6.27636i	0.922527	+	0.430049i
$214$			3.95701i			0.270496i
$215$	1.67579	+	21.7764i	0.114288	+	1.48514i
$216$	4.50092	+	2.59648i	0.306249	+	0.176668i
$217$	1.76311	+	1.76311i	0.119688	+	0.119688i
$218$	−4.05179	−	4.05179i	−0.274422	−	0.274422i
$219$	0.0527295	+	0.144820i	0.00356313	+	0.00978602i
$220$	7.73548	−	9.02529i	0.521526	−	0.608485i
$221$		−	18.6196i		−	1.25249i
$222$	1.47666	−	3.16768i	0.0991068	−	0.212601i
$223$	18.4359	−	18.4359i	1.23456	−	1.23456i	0.272365	−	0.962194i	$-0.412194\pi$
$223$	18.4359	−	18.4359i	1.23456	−	1.23456i	0.962194	−	0.272365i	$-0.0878057\pi$
$224$	2.49342			0.166598
$225$	−9.87748	+	11.2887i	−0.658499	+	0.752582i
$226$	0.766013			0.0509544
$227$	6.34333	−	6.34333i	0.421021	−	0.421021i	−0.464534	−	0.885555i	$-0.653778\pi$
$227$	6.34333	−	6.34333i	0.421021	−	0.421021i	0.885555	+	0.464534i	$0.153778\pi$
$228$	1.36525	−	2.92869i	0.0904157	−	0.193957i
$229$			11.9922i			0.792465i	0.918150	+	0.396232i	$0.129683\pi$
$229$			11.9922i			0.792465i	−0.918150	+	0.396232i	$0.870317\pi$
$230$	−7.72846	+	9.01711i	−0.509600	+	0.594571i
$231$	7.85461	+	21.5724i	0.516795	+	1.41936i
$232$	−2.56141	−	2.56141i	−0.168165	−	0.168165i
$233$	13.0981	+	13.0981i	0.858087	+	0.858087i	0.991113	−	0.133026i	$-0.0424694\pi$
$233$	13.0981	+	13.0981i	0.858087	+	0.858087i	−0.133026	+	0.991113i	$0.542469\pi$
$234$	10.9166	−	9.16454i	0.713642	−	0.599105i
$235$	−1.29424	−	16.8182i	−0.0844267	−	1.09710i
$236$		−	8.98420i		−	0.584821i
$237$	21.0046	+	9.79160i	1.36440	+	0.636033i
$238$	−6.90955	+	6.90955i	−0.447880	+	0.447880i
$239$	−13.8215			−0.894036			−0.447018	−	0.894525i	$-0.647514\pi$
$239$	−13.8215			−0.894036			−0.447018	+	0.894525i	$0.647514\pi$
$240$	1.60039	+	3.52686i	0.103305	+	0.227658i
$241$	−20.8975			−1.34613			−0.673063	−	0.739585i	$-0.735022\pi$
$241$	−20.8975			−1.34613			−0.673063	+	0.739585i	$0.735022\pi$
$242$	12.2037	−	12.2037i	0.784486	−	0.784486i
$243$	−12.7746	−	8.93362i	−0.819491	−	0.573092i
$244$			3.54388i			0.226874i
$245$	1.32915	+	1.13920i	0.0849166	+	0.0727811i
$246$	9.97097	−	3.63047i	0.635726	−	0.231470i
$247$	−6.26754	−	6.26754i	−0.398794	−	0.398794i
$248$	0.707107	+	0.707107i	0.0449013	+	0.0449013i
$249$	−9.92068	+	3.61216i	−0.628697	+	0.228911i
$250$	−10.8849	+	2.55332i	−0.688420	+	0.161486i
$251$		−	8.88807i		−	0.561010i	−0.959853	−	0.280505i	$-0.909498\pi$
$251$		−	8.88807i		−	0.561010i	0.959853	−	0.280505i	$-0.0905019\pi$
$252$	−7.45194	−	0.650185i	−0.469428	−	0.0409578i
$253$	−19.9638	+	19.9638i	−1.25511	+	1.25511i
$254$	18.8667			1.18380
$255$	−14.2082	−	5.33846i	−0.889753	−	0.334308i
$256$	1.00000			0.0625000
$257$	−11.3584	+	11.3584i	−0.708519	+	0.708519i	−0.966224	−	0.257704i	$-0.917034\pi$
$257$	−11.3584	+	11.3584i	−0.708519	+	0.708519i	0.257704	+	0.966224i	$0.417034\pi$
$258$	−15.3336	−	7.14796i	−0.954628	−	0.445013i
$259$			5.03125i			0.312627i
$260$	10.5926	−	0.815147i	0.656925	−	0.0505533i
$261$	6.98725	+	8.32308i	0.432500	+	0.515186i
$262$	0.180417	+	0.180417i	0.0111462	+	0.0111462i
$263$	−22.8829	−	22.8829i	−1.41102	−	1.41102i	−0.752996	−	0.658025i	$-0.771392\pi$
$263$	−22.8829	−	22.8829i	−1.41102	−	1.41102i	−0.658025	−	0.752996i	$-0.728608\pi$
$264$	3.15014	+	8.65175i	0.193878	+	0.532478i
$265$	25.0310	−	1.92625i	1.53764	−	0.118328i
$266$			4.65165i			0.285211i
$267$	3.66334	−	7.85849i	0.224193	−	0.480932i
$268$	3.66547	−	3.66547i	0.223904	−	0.223904i
$269$	0.122472			0.00746727			0.00373364	−	0.999993i	$-0.498812\pi$
$269$	0.122472			0.00746727			0.00373364	+	0.999993i	$0.498812\pi$
$270$	−3.86334	−	10.9579i	−0.235116	−	0.666874i
$271$	−18.0601			−1.09707			−0.548535	−	0.836127i	$-0.684814\pi$
$271$	−18.0601			−1.09707			−0.548535	+	0.836127i	$0.684814\pi$
$272$	−2.77112	+	2.77112i	−0.168024	+	0.168024i
$273$	−8.66948	+	18.5975i	−0.524701	+	1.12557i
$274$			11.1970i			0.676435i
$275$	−26.2665	+	4.06673i	−1.58393	+	0.245233i
$276$	−3.14728	−	8.64390i	−0.189444	−	0.520302i
$277$	18.5836	+	18.5836i	1.11658	+	1.11658i	0.992240	+	0.124338i	$0.0396808\pi$
$277$	18.5836	+	18.5836i	1.11658	+	1.11658i	0.124338	+	0.992240i	$0.460319\pi$
$278$	−0.777057	−	0.777057i	−0.0466048	−	0.0466048i
$279$	−1.92891	−	2.29768i	−0.115481	−	0.137558i
$280$	−4.23331	−	3.62832i	−0.252989	−	0.216834i
$281$			26.1152i			1.55790i	0.627083	+	0.778952i	$0.284249\pi$
$281$			26.1152i			1.55790i	−0.627083	+	0.778952i	$0.715751\pi$
$282$	11.8423	+	5.52047i	0.705202	+	0.328739i
$283$	0.365636	−	0.365636i	0.0217348	−	0.0217348i	−0.696156	−	0.717891i	$-0.745108\pi$
$283$	0.365636	−	0.365636i	0.0217348	−	0.0217348i	0.717891	+	0.696156i	$0.245108\pi$
$284$	−8.57648			−0.508920
$285$	−6.57962	+	2.98565i	−0.389743	+	0.176855i
$286$	25.2566			1.49346
$287$	−10.8016	+	10.8016i	−0.637600	+	0.637600i
$288$	−2.98865	−	0.260761i	−0.176108	−	0.0153655i
$289$			1.64182i			0.0965776i
$290$	0.621486	+	8.07603i	0.0364949	+	0.474241i
$291$	−17.7245	+	6.45355i	−1.03903	+	0.378314i
$292$	−0.0629195	−	0.0629195i	−0.00368209	−	0.00368209i
$293$	5.81410	+	5.81410i	0.339663	+	0.339663i	0.856241	−	0.516577i	$-0.172794\pi$
$293$	5.81410	+	5.81410i	0.339663	+	0.339663i	−0.516577	+	0.856241i	$0.672794\pi$
$294$	−1.27414	+	0.463921i	−0.0743095	+	0.0270564i
$295$	−13.0735	+	15.2533i	−0.761166	+	0.888083i
$296$			2.01781i			0.117283i
$297$	−7.15861	−	26.6784i	−0.415385	−	1.54804i
$298$	−11.8137	+	11.8137i	−0.684347	+	0.684347i
$299$	−25.2337			−1.45931
$300$	2.41501	−	8.31671i	0.139431	−	0.480166i
$301$	24.3545			1.40377
$302$	15.7679	−	15.7679i	0.907343	−	0.907343i
$303$	−9.58859	−	4.46985i	−0.550850	−	0.256786i
$304$			1.86557i			0.106998i
$305$	5.15692	−	6.01678i	0.295284	−	0.344520i
$306$	9.00449	−	7.55929i	0.514752	−	0.432136i
$307$	0.562256	+	0.562256i	0.0320896	+	0.0320896i	0.722970	−	0.690880i	$-0.242777\pi$
$307$	0.562256	+	0.562256i	0.0320896	+	0.0320896i	−0.690880	+	0.722970i	$0.742777\pi$
$308$	−9.37251	−	9.37251i	−0.534048	−	0.534048i
$309$	−6.59143	−	18.1031i	−0.374973	−	1.02985i
$310$	−0.171568	−	2.22948i	−0.00974441	−	0.126626i
$311$		−	15.0371i		−	0.852674i	−0.904564	−	0.426337i	$-0.859804\pi$
$311$		−	15.0371i		−	0.852674i	0.904564	−	0.426337i	$-0.140196\pi$
$312$	−3.47695	+	7.45864i	−0.196843	+	0.422263i
$313$	23.4317	−	23.4317i	1.32444	−	1.32444i	0.414291	−	0.910144i	$-0.364029\pi$
$313$	23.4317	−	23.4317i	1.32444	−	1.32444i	0.910144	−	0.414291i	$-0.135971\pi$
$314$	−18.9413			−1.06892
$315$	11.7057	+	11.9477i	0.659544	+	0.673174i
$316$	−13.3800			−0.752682
$317$	−13.0369	+	13.0369i	−0.732227	+	0.732227i	−0.971061	−	0.238833i	$-0.923235\pi$
$317$	−13.0369	+	13.0369i	−0.732227	+	0.732227i	0.238833	+	0.971061i	$0.423235\pi$
$318$	−8.21626	+	17.6253i	−0.460745	+	0.988376i
$319$			19.2562i			1.07814i
$320$	−1.69779	−	1.45516i	−0.0949096	−	0.0813460i
$321$	2.34488	+	6.44014i	0.130878	+	0.359453i
$322$	9.36402	+	9.36402i	0.521836	+	0.521836i
$323$	−5.16973	−	5.16973i	−0.287651	−	0.287651i
$324$	8.86401	+	1.55864i	0.492445	+	0.0865912i
$325$	−19.1702	−	14.0300i	−1.06337	−	0.778243i
$326$		−	3.53670i		−	0.195880i
$327$	−8.99544	−	4.19335i	−0.497449	−	0.231893i
$328$	−4.33206	+	4.33206i	−0.239198	+	0.239198i
$329$	−18.8093			−1.03699
$330$	7.24140	−	19.2728i	0.398626	−	1.06094i
$331$	22.3579			1.22890			0.614450	−	0.788956i	$-0.289378\pi$
$331$	22.3579			1.22890			0.614450	+	0.788956i	$0.289378\pi$
$332$	4.31021	−	4.31021i	0.236554	−	0.236554i
$333$	0.526166	−	6.03053i	0.0288337	−	0.330471i
$334$			7.11930i			0.389551i
$335$	−11.5571	+	0.889367i	−0.631430	+	0.0485913i
$336$	4.05810	−	1.47757i	0.221387	−	0.0806081i
$337$	14.4378	+	14.4378i	0.786479	+	0.786479i	0.980915	−	0.194436i	$-0.0622877\pi$
$337$	14.4378	+	14.4378i	0.786479	+	0.786479i	−0.194436	+	0.980915i	$0.562288\pi$
$338$	6.76949	+	6.76949i	0.368212	+	0.368212i
$339$	1.24671	−	0.453931i	0.0677117	−	0.0246541i
$340$	8.73721	−	0.672367i	0.473842	−	0.0364642i
$341$		−	5.31589i		−	0.287872i
$342$	0.486468	−	5.57554i	0.0263052	−	0.301491i
$343$	13.7221	−	13.7221i	0.740922	−	0.740922i
$344$	9.76750			0.526628
$345$	−7.23483	+	19.2554i	−0.389510	+	1.03667i
$346$	4.67035			0.251080
$347$	15.0026	−	15.0026i	0.805384	−	0.805384i	−0.178548	−	0.983931i	$-0.557140\pi$
$347$	15.0026	−	15.0026i	0.805384	−	0.805384i	0.983931	+	0.178548i	$0.0571398\pi$
$348$	−5.68663	−	2.65090i	−0.304836	−	0.142103i
$349$		−	4.46110i		−	0.238797i	−0.992846	−	0.119398i	$-0.961903\pi$
$349$		−	4.46110i		−	0.238797i	0.992846	−	0.119398i	$-0.0380966\pi$
$350$	1.90750	+	12.3203i	0.101960	+	0.658547i
$351$	12.3363	−	21.3846i	0.658462	−	1.14143i
$352$	−3.75890	−	3.75890i	−0.200350	−	0.200350i
$353$	21.4307	+	21.4307i	1.14064	+	1.14064i	0.988333	+	0.152310i	$0.0486712\pi$
$353$	21.4307	+	21.4307i	1.14064	+	1.14064i	0.152310	+	0.988333i	$0.451329\pi$
$354$	−5.32393	−	14.6220i	−0.282964	−	0.777151i
$355$	14.5611	+	12.4802i	0.772823	+	0.662378i
$356$			5.00586i			0.265310i
$357$	−7.15095	+	15.3400i	−0.378468	+	0.811878i
$358$	−7.05127	+	7.05127i	−0.372671	+	0.372671i
$359$	4.46782			0.235803			0.117901	−	0.993025i	$-0.462383\pi$
$359$	4.46782			0.235803			0.117901	+	0.993025i	$0.462383\pi$
$360$	4.69466	+	4.79168i	0.247430	+	0.252544i
$361$	15.5196			0.816823
$362$	11.5056	−	11.5056i	0.604718	−	0.604718i
$363$	12.6301	−	27.0937i	0.662909	−	1.42205i
$364$		−	11.8466i		−	0.620932i
$365$	0.0152664	+	0.198383i	0.000799080	+	0.0103838i
$366$	2.10006	+	5.76776i	0.109772	+	0.301486i
$367$	19.9206	+	19.9206i	1.03985	+	1.03985i	0.999172	+	0.0406769i	$0.0129514\pi$
$367$	19.9206	+	19.9206i	1.03985	+	1.03985i	0.0406769	+	0.999172i	$0.487049\pi$
$368$	3.75550	+	3.75550i	0.195769	+	0.195769i
$369$	14.0766	−	11.8174i	0.732800	−	0.615187i
$370$	2.93624	−	3.42583i	0.152648	−	0.178101i
$371$		−	27.9944i		−	1.45339i
$372$	1.56986	+	0.731811i	0.0813933	+	0.0379426i
$373$	0.326405	−	0.326405i	0.0169006	−	0.0169006i	−0.698606	−	0.715507i	$-0.746196\pi$
$373$	0.326405	−	0.326405i	0.0169006	−	0.0169006i	0.715507	+	0.698606i	$0.246196\pi$
$374$	20.8327			1.07723
$375$	−16.2023	+	10.6058i	−0.836686	+	0.547684i
$376$	−7.54358			−0.389031
$377$	−12.1697	+	12.1697i	−0.626771	+	0.626771i
$378$	−12.5135	+	3.35774i	−0.643626	+	0.172704i
$379$			6.15747i			0.316288i	0.987416	+	0.158144i	$0.0505510\pi$
$379$			6.15747i			0.316288i	−0.987416	+	0.158144i	$0.949449\pi$
$380$	2.71471	−	3.16736i	0.139262	−	0.162482i
$381$	30.7060	−	11.1802i	1.57312	−	0.572779i
$382$	10.2361	+	10.2361i	0.523727	+	0.523727i
$383$	24.9090	+	24.9090i	1.27279	+	1.27279i	0.944618	+	0.328171i	$0.106432\pi$
$383$	24.9090	+	24.9090i	1.27279	+	1.27279i	0.328171	+	0.944618i	$0.393568\pi$
$384$	1.62753	−	0.592589i	0.0830543	−	0.0302404i
$385$	2.27409	+	29.5511i	0.115898	+	1.50606i
$386$			9.54810i			0.485985i
$387$	−29.1916	−	2.54698i	−1.48389	−	0.129470i
$388$	7.70070	−	7.70070i	0.390944	−	0.390944i
$389$	22.1377			1.12243			0.561214	−	0.827671i	$-0.310335\pi$
$389$	22.1377			1.12243			0.561214	+	0.827671i	$0.310335\pi$
$390$	16.7567	−	7.60372i	0.848507	−	0.385030i
$391$	−20.8138			−1.05260
$392$	0.553574	−	0.553574i	0.0279597	−	0.0279597i
$393$	0.400546	+	0.186720i	0.0202049	+	0.00941877i
$394$			19.8326i			0.999150i
$395$	22.7164	+	19.4700i	1.14299	+	0.979642i
$396$	10.2539	+	12.2142i	0.515276	+	0.613787i
$397$	−24.1567	−	24.1567i	−1.21239	−	1.21239i	−0.970238	−	0.242154i	$-0.922146\pi$
$397$	−24.1567	−	24.1567i	−1.21239	−	1.21239i	−0.242154	−	0.970238i	$-0.577854\pi$
$398$	7.89679	+	7.89679i	0.395830	+	0.395830i
$399$	2.75652	+	7.57069i	0.137999	+	0.379008i
$400$	0.765014	+	4.94113i	0.0382507	+	0.247056i
$401$			31.1190i			1.55401i	0.629495	+	0.777004i	$0.283262\pi$
$401$			31.1190i			1.55401i	−0.629495	+	0.777004i	$0.716738\pi$
$402$	3.79353	−	8.13776i	0.189204	−	0.405875i
$403$	3.35958	−	3.35958i	0.167352	−	0.167352i
$404$	6.10793			0.303881
$405$	−12.7812	−	15.5448i	−0.635102	−	0.772428i
$406$	9.03212			0.448257
$407$	7.58477	−	7.58477i	0.375963	−	0.375963i
$408$	−2.86793	+	6.15220i	−0.141984	+	0.304579i
$409$		−	22.2078i		−	1.09811i	−0.835788	−	0.549053i	$-0.814989\pi$
$409$		−	22.2078i		−	1.09811i	0.835788	−	0.549053i	$-0.185011\pi$
$410$	13.6588	−	1.05110i	0.674560	−	0.0519103i
$411$	6.63522	+	18.2234i	0.327291	+	0.898894i
$412$	7.86523	+	7.86523i	0.387492	+	0.387492i
$413$	15.8401	+	15.8401i	0.779443	+	0.779443i
$414$	−10.2446	−	12.2031i	−0.503493	−	0.599751i
$415$	−13.5899	+	1.04580i	−0.667102	+	0.0513364i
$416$		−	4.75116i		−	0.232945i
$417$	−1.72516	−	0.804205i	−0.0844813	−	0.0393821i
$418$	7.01251	−	7.01251i	0.342993	−	0.342993i
$419$	24.1596			1.18027			0.590136	−	0.807304i	$-0.299074\pi$
$419$	24.1596			1.18027			0.590136	+	0.807304i	$0.299074\pi$
$420$	−9.03992	−	3.39658i	−0.441103	−	0.165736i
$421$	−33.4804			−1.63173			−0.815867	−	0.578239i	$-0.803740\pi$
$421$	−33.4804			−1.63173			−0.815867	+	0.578239i	$0.803740\pi$
$422$	3.01882	−	3.01882i	0.146954	−	0.146954i
$423$	22.5451	+	1.96707i	1.09618	+	0.0956422i
$424$		−	11.2273i		−	0.545246i
$425$	−15.8124	−	11.5725i	−0.767014	−	0.561349i
$426$	−13.9584	+	5.08232i	−0.676288	+	0.246239i
$427$	−6.24826	−	6.24826i	−0.302375	−	0.302375i
$428$	−2.79803	−	2.79803i	−0.135248	−	0.135248i
$429$	41.1058	−	14.9668i	1.98461	−	0.722604i
$430$	−16.5832	−	14.2133i	−0.799714	−	0.685426i
$431$			11.1430i			0.536739i	0.963316	+	0.268370i	$0.0864848\pi$
$431$			11.1430i			0.536739i	−0.963316	+	0.268370i	$0.913515\pi$
$432$	−5.01862	+	1.34664i	−0.241458	+	0.0647904i
$433$	−27.0728	+	27.0728i	−1.30104	+	1.30104i	−0.373346	+	0.927692i	$0.621790\pi$
$433$	−27.0728	+	27.0728i	−1.30104	+	1.30104i	−0.927692	+	0.373346i	$0.878210\pi$
$434$	−2.49342			−0.119688
$435$	5.79725	+	12.7757i	0.277957	+	0.612546i
$436$	5.73010			0.274422
$437$	−7.00616	+	7.00616i	−0.335150	+	0.335150i
$438$	−0.139689	−	0.0651177i	−0.00667458	−	0.00311145i
$439$		−	31.9187i		−	1.52340i	−0.647933	−	0.761698i	$-0.724366\pi$
$439$		−	31.9187i		−	1.52340i	0.647933	−	0.761698i	$-0.275634\pi$
$440$	0.912037	+	11.8517i	0.0434797	+	0.565005i
$441$	−1.79879	+	1.51009i	−0.0856565	+	0.0719088i
$442$	13.1660	+	13.1660i	0.626244	+	0.626244i
$443$	21.4595	+	21.4595i	1.01957	+	1.01957i	0.999805	+	0.0197682i	$0.00629283\pi$
$443$	21.4595	+	21.4595i	1.01957	+	1.01957i	0.0197682	+	0.999805i	$0.493707\pi$
$444$	1.19573	+	3.28404i	0.0567470	+	0.155854i
$445$	7.28433	−	8.49893i	0.345311	−	0.402888i
$446$			26.0723i			1.23456i
$447$	−12.2264	+	26.2277i	−0.578289	+	1.24053i
$448$	−1.76311	+	1.76311i	−0.0832992	+	0.0832992i
$449$	9.97274			0.470643			0.235321	−	0.971918i	$-0.424386\pi$
$449$	9.97274			0.470643			0.235321	+	0.971918i	$0.424386\pi$
$450$	−0.997903	−	14.9668i	−0.0470416	−	0.705540i
$451$	32.5676			1.53355
$452$	−0.541653	+	0.541653i	−0.0254772	+	0.0254772i
$453$	16.3188	−	35.0066i	0.766725	−	1.64475i
$454$			8.97082i			0.421021i
$455$	−17.2387	+	20.1131i	−0.808165	+	0.942918i
$456$	1.10552	+	3.03627i	0.0517706	+	0.142186i
$457$	−15.4251	−	15.4251i	−0.721554	−	0.721554i	0.247367	−	0.968922i	$-0.420435\pi$
$457$	−15.4251	−	15.4251i	−0.721554	−	0.721554i	−0.968922	+	0.247367i	$0.920435\pi$
$458$	−8.47974	−	8.47974i	−0.396232	−	0.396232i
$459$	10.1755	−	17.6389i	0.474951	−	0.823313i
$460$	−0.911210	−	11.8409i	−0.0424854	−	0.552085i
$461$		−	26.3536i		−	1.22741i	−0.789535	−	0.613705i	$-0.789678\pi$
$461$		−	26.3536i		−	1.22741i	0.789535	−	0.613705i	$-0.210322\pi$
$462$	−20.8080	−	9.69996i	−0.968078	−	0.451283i
$463$	−21.2390	+	21.2390i	−0.987060	+	0.987060i	−0.999917	−	0.0128574i	$-0.995907\pi$
$463$	−21.2390	+	21.2390i	−0.987060	+	0.987060i	0.0128574	+	0.999917i	$0.495907\pi$
$464$	3.62239			0.168165
$465$	−1.60039	−	3.52686i	−0.0742165	−	0.163554i
$466$	−18.5235			−0.858087
$467$	12.0325	−	12.0325i	0.556798	−	0.556798i	−0.371596	−	0.928394i	$-0.621190\pi$
$467$	12.0325	−	12.0325i	0.556798	−	0.556798i	0.928394	+	0.371596i	$0.121190\pi$
$468$	−1.23892	+	14.1995i	−0.0572689	+	0.656374i
$469$			12.9253i			0.596834i
$470$	12.8075	+	10.9771i	0.590764	+	0.506337i
$471$	−30.8275	+	11.2244i	−1.42045	+	0.517193i
$472$	6.35279	+	6.35279i	0.292411	+	0.292411i
$473$	−36.7151	−	36.7151i	−1.68816	−	1.68816i
$474$	−21.7762	+	7.92881i	−1.00022	+	0.364182i
$475$	−9.21804	+	1.42719i	−0.422953	+	0.0654840i
$476$		−	9.77158i		−	0.447880i
$477$	−2.92764	+	33.5544i	−0.134047	+	1.53635i
$478$	9.77324	−	9.77324i	0.447018	−	0.447018i
$479$	−9.47779			−0.433051			−0.216526	−	0.976277i	$-0.569472\pi$
$479$	−9.47779			−0.433051			−0.216526	+	0.976277i	$0.569472\pi$
$480$	−3.62552	−	1.36222i	−0.165481	−	0.0621764i
$481$	9.58695			0.437128
$482$	14.7768	−	14.7768i	0.673063	−	0.673063i
$483$	20.7892	+	9.69116i	0.945941	+	0.440963i
$484$			17.2587i			0.784486i
$485$	−24.2800	+	1.86845i	−1.10250	+	0.0848420i
$486$	15.3500	−	2.71598i	0.696292	−	0.123199i
$487$	13.2910	+	13.2910i	0.602271	+	0.602271i	0.940915	−	0.338644i	$-0.109968\pi$
$487$	13.2910	+	13.2910i	0.602271	+	0.602271i	−0.338644	+	0.940915i	$0.609968\pi$
$488$	−2.50590	−	2.50590i	−0.113437	−	0.113437i
$489$	−2.09581	−	5.75607i	−0.0947757	−	0.260298i
$490$	−1.74539	+	0.134316i	−0.0788488	+	0.00606776i
$491$		−	6.99037i		−	0.315471i	−0.987481	−	0.157736i	$-0.949581\pi$
$491$		−	6.99037i		−	0.315471i	0.987481	−	0.157736i	$-0.0504194\pi$
$492$	−4.48341	+	9.61767i	−0.202128	+	0.433598i
$493$	−10.0381	+	10.0381i	−0.452091	+	0.452091i
$494$	8.86364			0.398794
$495$	0.364690	−	35.6582i	0.0163916	−	1.60272i
$496$	−1.00000			−0.0449013
$497$	15.1213	−	15.1213i	0.678282	−	0.678282i
$498$	4.46080	−	9.56916i	0.199893	−	0.428804i
$499$			37.1388i			1.66256i	0.555855	+	0.831280i	$0.312391\pi$
$499$			37.1388i			1.66256i	−0.555855	+	0.831280i	$0.687609\pi$
$500$	5.89130	−	9.50224i	0.263467	−	0.424953i
$501$	4.21881	+	11.5868i	0.188483	+	0.517662i
$502$	6.28481	+	6.28481i	0.280505	+	0.280505i
$503$	−9.45292	−	9.45292i	−0.421485	−	0.421485i	0.464230	−	0.885715i	$-0.346331\pi$
$503$	−9.45292	−	9.45292i	−0.421485	−	0.421485i	−0.885715	+	0.464230i	$0.846331\pi$
$504$	5.72907	−	4.80957i	0.255193	−	0.214235i
$505$	−10.3700	−	8.88803i	−0.461460	−	0.395512i
$506$		−	28.2331i		−	1.25511i
$507$	15.0290	+	7.00600i	0.667463	+	0.311147i
$508$	−13.3408	+	13.3408i	−0.591901	+	0.591901i
$509$	−1.81871			−0.0806127			−0.0403064	−	0.999187i	$-0.512833\pi$
$509$	−1.81871			−0.0806127			−0.0403064	+	0.999187i	$0.512833\pi$
$510$	13.8216	−	6.27186i	0.612030	−	0.277723i
$511$	0.221868			0.00981488
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−2.51226	−	9.36261i	−0.110919	−	0.413369i
$514$		−	16.0632i		−	0.708519i
$515$	−1.90837	−	24.7987i	−0.0840928	−	1.09276i
$516$	15.8969	−	5.78811i	0.699820	−	0.254807i
$517$	28.3556	+	28.3556i	1.24708	+	1.24708i
$518$	−3.55763	−	3.55763i	−0.156313	−	0.156313i
$519$	7.60111	−	2.76760i	0.333652	−	0.121484i
$520$	−6.91370	+	8.06649i	−0.303186	+	0.353739i
$521$			1.54036i			0.0674844i	0.999431	+	0.0337422i	$0.0107425\pi$
$521$			1.54036i			0.0674844i	−0.999431	+	0.0337422i	$0.989257\pi$
$522$	−10.8260	−	0.944576i	−0.473843	−	0.0413430i
$523$	−13.0285	+	13.0285i	−0.569695	+	0.569695i	−0.932043	−	0.362348i	$-0.881975\pi$
$523$	−13.0285	+	13.0285i	−0.569695	+	0.569695i	0.362348	+	0.932043i	$0.381975\pi$
$524$	−0.255148			−0.0111462
$525$	10.4054	+	18.9212i	0.454128	+	0.825790i
$526$	32.3613			1.41102
$527$	2.77112	−	2.77112i	0.120712	−	0.120712i
$528$	−8.34519	−	3.89023i	−0.363178	−	0.169300i
$529$			5.20749i			0.226412i
$530$	−16.3375	+	19.0617i	−0.709657	+	0.827986i
$531$	−17.3297	−	20.6428i	−0.752044	−	0.895821i
$532$	−3.28922	−	3.28922i	−0.142606	−	0.142606i
$533$	20.5823	+	20.5823i	0.891519	+	0.891519i
$534$	2.96642	+	8.14717i	0.128369	+	0.352562i
$535$	0.678896	+	8.82206i	0.0293513	+	0.381411i
$536$			5.18376i			0.223904i
$537$	−7.29762	+	15.6546i	−0.314915	+	0.675547i
$538$	−0.0866010	+	0.0866010i	−0.00373364	+	0.00373364i
$539$	−4.16166			−0.179255
$540$	10.4802	+	5.01658i	0.450995	+	0.215879i
$541$	41.2666			1.77419			0.887095	−	0.461587i	$-0.152720\pi$
$541$	41.2666			1.77419			0.887095	+	0.461587i	$0.152720\pi$
$542$	12.7704	−	12.7704i	0.548535	−	0.548535i
$543$	11.9075	−	25.5436i	0.511001	−	1.09618i
$544$		−	3.91895i		−	0.168024i
$545$	−9.72853	−	8.33822i	−0.416725	−	0.357170i
$546$	−7.02017	−	19.2807i	−0.300436	−	0.825137i
$547$	−26.3308	−	26.3308i	−1.12582	−	1.12582i	−0.990849	−	0.134972i	$-0.956905\pi$
$547$	−26.3308	−	26.3308i	−1.12582	−	1.12582i	−0.134972	−	0.990849i	$-0.543095\pi$
$548$	−7.91747	−	7.91747i	−0.338218	−	0.338218i
$549$	6.83582	+	8.14270i	0.291745	+	0.347522i
$550$	15.6976	−	21.4488i	0.669348	−	0.914581i
$551$			6.75783i			0.287893i
$552$	8.33763	+	3.88670i	0.354873	+	0.165429i
$553$	23.5904	−	23.5904i	1.00316	−	1.00316i
$554$	−26.2811			−1.11658
$555$	2.74870	−	7.31562i	0.116676	−	0.310531i
$556$	1.09893			0.0466048
$557$	−14.8040	+	14.8040i	−0.627268	+	0.627268i	−0.947380	−	0.320112i	$-0.896279\pi$
$557$	−14.8040	+	14.8040i	−0.627268	+	0.627268i	0.320112	+	0.947380i	$0.396279\pi$
$558$	2.98865	+	0.260761i	0.126519	+	0.0110389i
$559$		−	46.4070i		−	1.96281i
$560$	5.55901	−	0.427791i	0.234911	−	0.0180775i
$561$	33.9058	−	12.3452i	1.43150	−	0.521216i
$562$	−18.4663	−	18.4663i	−0.778952	−	0.778952i
$563$	29.7240	+	29.7240i	1.25272	+	1.25272i	0.954497	+	0.298219i	$0.0963927\pi$
$563$	29.7240	+	29.7240i	1.25272	+	1.25272i	0.298219	+	0.954497i	$0.403607\pi$
$564$	−12.2774	+	4.47024i	−0.516971	+	0.188231i
$565$	1.70781	−	0.131423i	0.0718480	−	0.00552902i
$566$			0.517087i			0.0217348i
$567$	−18.3763	+	12.8802i	−0.771732	+	0.540917i
$568$	6.06448	−	6.06448i	0.254460	−	0.254460i
$569$	−36.1254			−1.51446			−0.757228	−	0.653150i	$-0.773447\pi$
$569$	−36.1254			−1.51446			−0.757228	+	0.653150i	$0.773447\pi$
$570$	2.54132	−	6.76367i	0.106444	−	0.283299i
$571$	24.6288			1.03068			0.515341	−	0.856985i	$-0.327665\pi$
$571$	24.6288			1.03068			0.515341	+	0.856985i	$0.327665\pi$
$572$	−17.8591	+	17.8591i	−0.746728	+	0.746728i
$573$	22.7254	+	10.5938i	0.949368	+	0.442561i
$574$		−	15.2758i		−	0.637600i
$575$	−15.6834	+	21.4294i	−0.654042	+	0.893667i
$576$	2.29768	−	1.92891i	0.0957366	−	0.0803711i
$577$	−11.7196	−	11.7196i	−0.487893	−	0.487893i	0.419748	−	0.907641i	$-0.362119\pi$
$577$	−11.7196	−	11.7196i	−0.487893	−	0.487893i	−0.907641	+	0.419748i	$0.862119\pi$
$578$	−1.16094	−	1.16094i	−0.0482888	−	0.0482888i
$579$	5.65810	+	15.5398i	0.235142	+	0.645811i
$580$	−6.15007	−	5.27116i	−0.255368	−	0.218873i
$581$			15.1988i			0.630551i
$582$	7.96974	−	17.0964i	0.330356	−	0.708670i
$583$	−42.2024	+	42.2024i	−1.74784	+	1.74784i
$584$	0.0889817			0.00368209
$585$	22.7660	−	22.3051i	0.941259	−	0.922201i
$586$	−8.22238			−0.339663
$587$	10.6912	−	10.6912i	0.441275	−	0.441275i	−0.451166	−	0.892440i	$-0.648992\pi$
$587$	10.6912	−	10.6912i	0.441275	−	0.441275i	0.892440	+	0.451166i	$0.148992\pi$
$588$	0.572914	−	1.22900i	0.0236266	−	0.0506830i
$589$		−	1.86557i		−	0.0768697i
$590$	−1.54140	−	20.0301i	−0.0634585	−	0.824624i
$591$	11.7525	+	32.2780i	0.483435	+	1.32774i
$592$	−1.42681	−	1.42681i	−0.0586415	−	0.0586415i
$593$	−23.5587	−	23.5587i	−0.967441	−	0.967441i	0.0320459	−	0.999486i	$-0.489798\pi$
$593$	−23.5587	−	23.5587i	−0.967441	−	0.967441i	−0.999486	+	0.0320459i	$0.989798\pi$
$594$	23.9264	+	13.8026i	0.981712	+	0.566328i
$595$	−14.2192	+	16.5901i	−0.582931	+	0.680129i
$596$		−	16.7070i		−	0.684347i
$597$	17.5318	+	8.17267i	0.717527	+	0.334485i
$598$	17.8430	−	17.8430i	0.729653	−	0.729653i
$599$	0.0185367			0.000757390			0.000378695	−	1.00000i	$-0.499879\pi$
$599$	0.0185367			0.000757390			0.000378695		1.00000i	$0.499879\pi$
$600$	4.17314	+	7.58847i	0.170368	+	0.309798i
$601$	−8.10421			−0.330578			−0.165289	−	0.986245i	$-0.552856\pi$
$601$	−8.10421			−0.330578			−0.165289	+	0.986245i	$0.552856\pi$
$602$	−17.2212	+	17.2212i	−0.701884	+	0.701884i
$603$	1.35172	−	15.4924i	0.0550463	−	0.630900i
$604$			22.2992i			0.907343i
$605$	25.1142	−	29.3017i	1.02104	−	1.19128i
$606$	9.94082	−	3.61949i	0.403818	−	0.147032i
$607$	5.34558	+	5.34558i	0.216970	+	0.216970i	0.807220	−	0.590250i	$-0.200971\pi$
$607$	5.34558	+	5.34558i	0.216970	+	0.216970i	−0.590250	+	0.807220i	$0.700971\pi$
$608$	−1.31916	−	1.31916i	−0.0534990	−	0.0534990i
$609$	14.7000	−	5.35233i	0.595674	−	0.216888i
$610$	0.608017	+	7.90100i	0.0246179	+	0.319902i
$611$			35.8408i			1.44996i
$612$	−1.02191	+	11.7124i	−0.0413082	+	0.473444i
$613$	−30.9751	+	30.9751i	−1.25107	+	1.25107i	−0.295833	+	0.955240i	$0.595597\pi$
$613$	−30.9751	+	30.9751i	−1.25107	+	1.25107i	−0.955240	+	0.295833i	$0.904403\pi$
$614$	−0.795149			−0.0320896
$615$	21.6072	−	9.80475i	0.871285	−	0.395366i
$616$	13.2547			0.534048
$617$	20.6041	−	20.6041i	0.829491	−	0.829491i	−0.157956	−	0.987446i	$-0.550490\pi$
$617$	20.6041	−	20.6041i	0.829491	−	0.829491i	0.987446	+	0.157956i	$0.0504903\pi$
$618$	17.4617	+	8.14001i	0.702413	+	0.327439i
$619$		−	29.7973i		−	1.19765i	−0.800879	−	0.598827i	$-0.795634\pi$
$619$		−	29.7973i		−	1.19765i	0.800879	−	0.598827i	$-0.204366\pi$
$620$	1.69779	+	1.45516i	0.0681851	+	0.0584407i
$621$	−23.9047	−	13.7901i	−0.959263	−	0.553377i
$622$	10.6328	+	10.6328i	0.426337	+	0.426337i
$623$	−8.82590	−	8.82590i	−0.353602	−	0.353602i
$624$	−2.81548	−	7.73263i	−0.112710	−	0.309553i
$625$	−23.8295	+	7.56006i	−0.953180	+	0.302402i
$626$			33.1374i			1.32444i
$627$	7.25751	−	15.5686i	0.289837	−	0.621749i
$628$	13.3935	−	13.3935i	0.534460	−	0.534460i
$629$	7.90772			0.315301
$630$	−16.7255	−	0.171058i	−0.666359	−	0.00681510i
$631$	−14.0062			−0.557577			−0.278789	−	0.960352i	$-0.589933\pi$
$631$	−14.0062			−0.557577			−0.278789	+	0.960352i	$0.589933\pi$
$632$	9.46106	−	9.46106i	0.376341	−	0.376341i
$633$	3.12429	−	6.70213i	0.124179	−	0.266386i
$634$		−	18.4370i		−	0.732227i
$635$	42.0629	−	3.23692i	1.66921	−	0.128453i
$636$	−6.65317	−	18.2727i	−0.263816	−	0.724561i
$637$	−2.63012	−	2.63012i	−0.104209	−	0.104209i
$638$	−13.6162	−	13.6162i	−0.539071	−	0.539071i
$639$	−19.7060	+	16.5432i	−0.779556	+	0.654439i
$640$	2.22948	−	0.171568i	0.0881278	−	0.00678182i
$641$		−	11.0951i		−	0.438231i	−0.975699	−	0.219116i	$-0.929683\pi$
$641$		−	11.0951i		−	0.438231i	0.975699	−	0.219116i	$-0.0703172\pi$
$642$	−6.21194	−	2.89578i	−0.245166	−	0.114287i
$643$	5.70015	−	5.70015i	0.224792	−	0.224792i	−0.585721	−	0.810513i	$-0.699188\pi$
$643$	5.70015	−	5.70015i	0.224792	−	0.224792i	0.810513	+	0.585721i	$0.199188\pi$
$644$	−13.2427			−0.521836
$645$	−35.4122	−	13.3055i	−1.39436	−	0.523902i
$646$	7.31110			0.287651
$647$	7.49872	−	7.49872i	0.294805	−	0.294805i	−0.544170	−	0.838975i	$-0.683155\pi$
$647$	7.49872	−	7.49872i	0.294805	−	0.294805i	0.838975	+	0.544170i	$0.183155\pi$
$648$	−7.36993	+	5.16567i	−0.289518	+	0.202927i
$649$		−	47.7590i		−	1.87471i
$650$	23.4761	−	3.63470i	0.920808	−	0.142565i
$651$	−4.05810	+	1.47757i	−0.159049	+	0.0579106i
$652$	2.50082	+	2.50082i	0.0979398	+	0.0979398i
$653$	16.8945	+	16.8945i	0.661133	+	0.661133i	0.955647	−	0.294514i	$-0.0951577\pi$
$653$	16.8945	+	16.8945i	0.661133	+	0.661133i	−0.294514	+	0.955647i	$0.595158\pi$
$654$	9.32588	−	3.39559i	0.364671	−	0.132778i
$655$	0.433189	+	0.371281i	0.0169261	+	0.0145072i
$656$		−	6.12646i		−	0.239198i
$657$	−0.265935	−	0.0232029i	−0.0103751	−	0.000905232i
$658$	13.3002	−	13.3002i	0.518495	−	0.518495i
$659$	−45.2653			−1.76329			−0.881643	−	0.471917i	$-0.843562\pi$
$659$	−45.2653			−1.76329			−0.881643	+	0.471917i	$0.843562\pi$
$660$	8.50752	+	18.7484i	0.331155	+	0.729781i
$661$	−6.67439			−0.259604			−0.129802	−	0.991540i	$-0.541434\pi$
$661$	−6.67439			−0.259604			−0.129802	+	0.991540i	$0.541434\pi$
$662$	−15.8094	+	15.8094i	−0.614450	+	0.614450i
$663$	29.2301	+	13.6260i	1.13520	+	0.529190i
$664$			6.09556i			0.236554i
$665$	0.798075	+	10.3708i	0.0309480	+	0.402161i
$666$	3.89217	+	4.63629i	0.150819	+	0.179652i
$667$	13.6039	+	13.6039i	0.526743	+	0.526743i
$668$	−5.03410	−	5.03410i	−0.194775	−	0.194775i
$669$	15.4501	+	42.4333i	0.597337	+	1.64057i
$670$	7.54320	−	8.80096i	0.291419	−	0.340011i
$671$			18.8389i			0.727267i
$672$	−1.82471	+	3.91431i	−0.0703897	+	0.150998i
$673$	13.5402	−	13.5402i	0.521935	−	0.521935i	−0.396220	−	0.918155i	$-0.629678\pi$
$673$	13.5402	−	13.5402i	0.521935	−	0.521935i	0.918155	+	0.396220i	$0.129678\pi$
$674$	−20.4182			−0.786479
$675$	−10.4932	−	23.7675i	−0.403885	−	0.914810i
$676$	−9.57351			−0.368212
$677$	−16.0012	+	16.0012i	−0.614976	+	0.614976i	−0.944238	−	0.329262i	$-0.893200\pi$
$677$	−16.0012	+	16.0012i	−0.614976	+	0.614976i	0.329262	+	0.944238i	$0.393200\pi$
$678$	−0.560576	+	1.20253i	−0.0215288	+	0.0461829i
$679$			27.1544i			1.04209i
$680$	−5.70270	+	6.65357i	−0.218689	+	0.255153i
$681$	5.31600	+	14.6002i	0.203710	+	0.559482i
$682$	3.75890	+	3.75890i	0.143936	+	0.143936i
$683$	3.42852	+	3.42852i	0.131189	+	0.131189i	0.769652	−	0.638463i	$-0.220430\pi$
$683$	3.42852	+	3.42852i	0.131189	+	0.131189i	−0.638463	+	0.769652i	$0.720430\pi$
$684$	3.59852	+	4.28649i	0.137593	+	0.163898i
$685$	1.92105	+	24.9634i	0.0733994	+	0.953804i
$686$			19.4059i			0.740922i
$687$	−18.8260	−	8.77600i	−0.718257	−	0.334825i
$688$	−6.90667	+	6.90667i	−0.263314	+	0.263314i
$689$	−53.3427			−2.03220
$690$	−8.49981	−	18.7314i	−0.323582	−	0.713092i
$691$	−13.9403			−0.530316			−0.265158	−	0.964205i	$-0.585424\pi$
$691$	−13.9403			−0.530316			−0.265158	+	0.964205i	$0.585424\pi$
$692$	−3.30244	+	3.30244i	−0.125540	+	0.125540i
$693$	−39.6137	−	3.45631i	−1.50480	−	0.131294i
$694$			21.2169i			0.805384i
$695$	−1.86575	−	1.59911i	−0.0707719	−	0.0606578i
$696$	5.89553	−	2.14659i	0.223469	−	0.0813661i
$697$	16.9771	+	16.9771i	0.643055	+	0.643055i
$698$	3.15447	+	3.15447i	0.119398	+	0.119398i
$699$	−30.1475	+	10.9768i	−1.14028	+	0.415182i
$700$	−10.0606	−	7.36296i	−0.380254	−	0.278294i
$701$			17.0635i			0.644480i	0.946658	+	0.322240i	$0.104436\pi$
$701$			17.0635i			0.644480i	−0.946658	+	0.322240i	$0.895564\pi$
$702$	6.39812	+	23.8443i	0.241481	+	0.899944i
$703$	2.66182	−	2.66182i	0.100392	−	0.100392i
$704$	5.31589			0.200350
$705$	27.3494	+	10.2760i	1.03004	+	0.387016i
$706$	−30.3076			−1.14064
$707$	−10.7690	+	10.7690i	−0.405009	+	0.405009i
$708$	14.1039	+	6.57473i	0.530057	+	0.247094i
$709$			21.8486i			0.820541i	0.911964	+	0.410270i	$0.134566\pi$
$709$			21.8486i			0.820541i	−0.911964	+	0.410270i	$0.865434\pi$
$710$	−19.1210	+	1.47145i	−0.717600	+	0.0552225i
$711$	−30.7428	+	25.8087i	−1.15295	+	0.967901i
$712$	−3.53968	−	3.53968i	−0.132655	−	0.132655i
$713$	−3.75550	−	3.75550i	−0.140644	−	0.140644i
$714$	−5.79053	−	15.9035i	−0.216705	−	0.595173i
$715$	56.3091	−	4.33323i	2.10584	−	0.162054i
$716$		−	9.97200i		−	0.372671i
$717$	10.1147	−	21.6977i	0.377740	−	0.810316i
$718$	−3.15923	+	3.15923i	−0.117901	+	0.117901i
$719$	−6.72001			−0.250614			−0.125307	−	0.992118i	$-0.539992\pi$
$719$	−6.72001			−0.250614			−0.125307	+	0.992118i	$0.539992\pi$
$720$	−6.70785	−	0.0686037i	−0.249987	−	0.00255671i
$721$	−27.7346			−1.03289
$722$	−10.9740	+	10.9740i	−0.408411	+	0.408411i
$723$	15.2930	−	32.8061i	0.568754	−	1.22007i
$724$			16.2713i			0.604718i
$725$	2.77118	+	17.8987i	0.102919	+	0.664740i
$726$	10.2273	+	28.0890i	0.379571	+	1.04248i
$727$	−2.57592	−	2.57592i	−0.0955356	−	0.0955356i	0.657724	−	0.753259i	$-0.271519\pi$
$727$	−2.57592	−	2.57592i	−0.0955356	−	0.0955356i	−0.753259	+	0.657724i	$0.771519\pi$
$728$	8.37683	+	8.37683i	0.310466	+	0.310466i
$729$	23.3731	−	13.5166i	0.865671	−	0.500614i
$730$	−0.151073	−	0.129483i	−0.00559145	−	0.00479237i
$731$		−	38.2784i		−	1.41578i
$732$	−5.56339	−	2.59345i	−0.205629	−	0.0958567i
$733$	12.8296	−	12.8296i	0.473870	−	0.473870i	−0.429294	−	0.903165i	$-0.641238\pi$
$733$	12.8296	−	12.8296i	0.473870	−	0.473870i	0.903165	+	0.429294i	$0.141238\pi$
$734$	−28.1720			−1.03985
$735$	−2.76108	+	1.25290i	−0.101844	+	0.0462140i
$736$	−5.31107			−0.195769
$737$	19.4852	−	19.4852i	0.717748	−	0.717748i
$738$	−1.59754	+	18.3098i	−0.0588062	+	0.673994i
$739$			5.13226i			0.188793i	0.995535	+	0.0943966i	$0.0300922\pi$
$739$			5.13226i			0.188793i	−0.995535	+	0.0943966i	$0.969908\pi$
$740$	0.346192	+	4.49867i	0.0127263	+	0.165374i
$741$	14.4258	−	5.25249i	0.529945	−	0.192955i
$742$	19.7950	+	19.7950i	0.726697	+	0.726697i
$743$	11.8016	+	11.8016i	0.432961	+	0.432961i	0.889634	−	0.456674i	$-0.150959\pi$
$743$	11.8016	+	11.8016i	0.432961	+	0.432961i	−0.456674	+	0.889634i	$0.650959\pi$
$744$	−1.62753	+	0.592589i	−0.0596680	+	0.0217254i
$745$	−24.3114	+	28.3651i	−0.890702	+	1.03922i
$746$			0.461607i			0.0169006i
$747$	1.58948	−	18.2175i	0.0581561	−	0.666542i
$748$	−14.7310	+	14.7310i	−0.538617	+	0.538617i
$749$	9.86648			0.360513
$750$	3.95732	−	18.9563i	0.144501	−	0.692185i
$751$	11.9892			0.437493			0.218747	−	0.975782i	$-0.429803\pi$
$751$	11.9892			0.437493			0.218747	+	0.975782i	$0.429803\pi$
$752$	5.33412	−	5.33412i	0.194515	−	0.194515i
$753$	13.9530	+	6.50438i	0.508476	+	0.237033i
$754$		−	17.2105i		−	0.626771i
$755$	32.4490	−	37.8595i	1.18094	−	1.37785i
$756$	6.47411	−	11.2227i	0.235461	−	0.408165i
$757$	29.9624	+	29.9624i	1.08900	+	1.08900i	0.995631	+	0.0933711i	$0.0297643\pi$
$757$	29.9624	+	29.9624i	1.08900	+	1.08900i	0.0933711	+	0.995631i	$0.470236\pi$
$758$	−4.35399	−	4.35399i	−0.158144	−	0.158144i
$759$	−16.7306	−	45.9501i	−0.607282	−	1.66788i
$760$	0.320073	+	4.15925i	0.0116103	+	0.150872i
$761$			23.2384i			0.842393i	0.906969	+	0.421196i	$0.138390\pi$
$761$			23.2384i			0.842393i	−0.906969	+	0.421196i	$0.861610\pi$
$762$	−13.8069	+	29.6180i	−0.500170	+	1.07295i
$763$	−10.1028	+	10.1028i	−0.365746	+	0.365746i
$764$	−14.4761			−0.523727
$765$	18.7784	−	18.3981i	0.678933	−	0.665186i
$766$	−35.2266			−1.27279
$767$	30.1831	−	30.1831i	1.08985	−	1.08985i
$768$	−0.731811	+	1.56986i	−0.0264069	+	0.0566474i
$769$		−	33.2909i		−	1.20050i	−0.799812	−	0.600251i	$-0.795067\pi$
$769$		−	33.2909i		−	1.20050i	0.799812	−	0.600251i	$-0.204933\pi$
$770$	−22.5038	−	19.2878i	−0.810981	−	0.695083i
$771$	−9.51890	−	26.1433i	−0.342815	−	0.941529i
$772$	−6.75153	−	6.75153i	−0.242993	−	0.242993i
$773$	−4.90985	−	4.90985i	−0.176595	−	0.176595i	0.613275	−	0.789870i	$-0.289852\pi$
$773$	−4.90985	−	4.90985i	−0.176595	−	0.176595i	−0.789870	+	0.613275i	$0.789852\pi$
$774$	22.4426	−	18.8406i	0.806682	−	0.677211i
$775$	−0.765014	−	4.94113i	−0.0274801	−	0.177491i
$776$			10.8904i			0.390944i
$777$	−7.89835	−	3.68192i	−0.283352	−	0.132088i
$778$	−15.6537	+	15.6537i	−0.561214	+	0.561214i
$779$	11.4294			0.409500
$780$	−6.47211	+	17.2254i	−0.231739	+	0.616768i
$781$	−45.5916			−1.63140
$782$	14.7176	−	14.7176i	0.526300	−	0.526300i
$783$	−18.1794	+	4.87806i	−0.649678	+	0.174328i
$784$			0.782871i			0.0279597i
$785$	−42.2292	+	3.24972i	−1.50723	+	0.115988i
$786$	−0.415260	+	0.151198i	−0.0148118	+	0.00539304i
$787$	29.7522	+	29.7522i	1.06055	+	1.06055i	0.998045	+	0.0625074i	$0.0199097\pi$
$787$	29.7522	+	29.7522i	1.06055	+	1.06055i	0.0625074	+	0.998045i	$0.480090\pi$
$788$	−14.0237	−	14.0237i	−0.499575	−	0.499575i
$789$	52.6689	−	19.1770i	1.87506	−	0.682718i
$790$	−29.8303	+	2.29557i	−1.06131	+	0.0816728i
$791$		−	1.90999i		−	0.0679114i
$792$	−15.8873	−	1.38618i	−0.564531	−	0.0492556i
$793$	−11.9059	+	11.9059i	−0.422792	+	0.422792i
$794$	34.1628			1.21239
$795$	−15.2940	+	40.7048i	−0.542423	+	1.44365i
$796$	−11.1677			−0.395830
$797$	−25.8025	+	25.8025i	−0.913971	+	0.913971i	−0.996582	−	0.0826107i	$-0.973674\pi$
$797$	−25.8025	+	25.8025i	−0.913971	+	0.913971i	0.0826107	+	0.996582i	$0.473674\pi$
$798$	−7.30244	−	3.40413i	−0.258503	−	0.120505i
$799$			29.5629i			1.04586i
$800$	−4.03485	−	2.95296i	−0.142654	−	0.104403i
$801$	9.65584	+	11.5019i	0.341172	+	0.406398i
$802$	−22.0044	−	22.0044i	−0.777004	−	0.777004i
$803$	−0.334473	−	0.334473i	−0.0118033	−	0.0118033i
$804$	3.07184	+	8.43670i	0.108335	+	0.297539i
$805$	22.4834	+	19.2703i	0.792436	+	0.679188i
$806$			4.75116i			0.167352i
$807$	−0.0896266	+	0.192264i	−0.00315501	+	0.00676802i
$808$	−4.31896	+	4.31896i	−0.151941	+	0.151941i
$809$	30.9649			1.08867			0.544334	−	0.838869i	$-0.316782\pi$
$809$	30.9649			1.08867			0.544334	+	0.838869i	$0.316782\pi$
$810$	20.0295	+	1.95418i	0.703765	+	0.0686627i
$811$	28.5123			1.00120			0.500602	−	0.865678i	$-0.333112\pi$
$811$	28.5123			1.00120			0.500602	+	0.865678i	$0.333112\pi$
$812$	−6.38668	+	6.38668i	−0.224128	+	0.224128i
$813$	13.2165	−	28.3517i	0.463525	−	0.994339i
$814$			10.7265i			0.375963i
$815$	−0.606784	−	7.88499i	−0.0212547	−	0.276199i
$816$	−2.32233	−	6.37819i	−0.0812977	−	0.223281i
$817$	−12.8849	−	12.8849i	−0.450786	−	0.450786i
$818$	15.7033	+	15.7033i	0.549053	+	0.549053i
$819$	−22.8510	−	27.2197i	−0.798479	−	0.951134i
$820$	−8.91498	+	10.4015i	−0.311325	+	0.363235i
$821$		−	17.0697i		−	0.595736i	−0.954607	−	0.297868i	$-0.903724\pi$
$821$		−	17.0697i		−	0.595736i	0.954607	−	0.297868i	$-0.0962755\pi$
$822$	−17.5777	−	8.19408i	−0.613093	−	0.285802i
$823$	−38.0364	+	38.0364i	−1.32586	+	1.32586i	−0.416922	+	0.908942i	$0.636891\pi$
$823$	−38.0364	+	38.0364i	−1.32586	+	1.32586i	−0.908942	+	0.416922i	$0.863109\pi$
$824$	−11.1231			−0.387492
$825$	12.8379	−	44.2107i	0.446959	−	1.53922i
$826$	−22.4014			−0.779443
$827$	12.7698	−	12.7698i	0.444048	−	0.444048i	−0.449322	−	0.893370i	$-0.648334\pi$
$827$	12.7698	−	12.7698i	0.444048	−	0.444048i	0.893370	+	0.449322i	$0.148334\pi$
$828$	15.8729	+	1.38492i	0.551622	+	0.0481292i
$829$		−	32.6869i		−	1.13526i	−0.823283	−	0.567631i	$-0.807860\pi$
$829$		−	32.6869i		−	1.13526i	0.823283	−	0.567631i	$-0.192140\pi$
$830$	8.87002	−	10.3490i	0.307883	−	0.359219i
$831$	−42.7732	+	15.5739i	−1.48379	+	0.540253i
$832$	3.35958	+	3.35958i	0.116472	+	0.116472i
$833$	−2.16943	−	2.16943i	−0.0751662	−	0.0751662i
$834$	1.78853	−	0.651211i	0.0619317	−	0.0225496i
$835$	1.22144	+	15.8723i	0.0422698	+	0.549284i
$836$			9.91719i			0.342993i
$837$	5.01862	−	1.34664i	0.173469	−	0.0465468i
$838$	−17.0834	+	17.0834i	−0.590136	+	0.590136i
$839$	−49.2199			−1.69926			−0.849630	−	0.527379i	$-0.823175\pi$
$839$	−49.2199			−1.69926			−0.849630	+	0.527379i	$0.823175\pi$
$840$	8.79393	−	3.99045i	0.303419	−	0.137684i
$841$	−15.8783			−0.547528
$842$	23.6742	−	23.6742i	0.815867	−	0.815867i
$843$	−40.9972	−	19.1114i	−1.41202	−	0.658232i
$844$			4.26926i			0.146954i
$845$	16.2539	+	13.9310i	0.559150	+	0.479241i
$846$	−17.3327	+	14.5509i	−0.595911	+	0.500269i
$847$	−30.4290	−	30.4290i	−1.04555	−	1.04555i
$848$	7.93890	+	7.93890i	0.272623	+	0.272623i
$849$	0.306420	+	0.841573i	0.0105163	+	0.0288827i
$850$	19.3640	−	2.99805i	0.664181	−	0.102832i
$851$		−	10.7168i		−	0.367366i
$852$	6.27636	−	13.4638i	0.215024	−	0.461264i
$853$	−3.00535	+	3.00535i	−0.102901	+	0.102901i	−0.756683	−	0.653782i	$-0.773181\pi$
$853$	−3.00535	+	3.00535i	−0.102901	+	0.102901i	0.653782	+	0.756683i	$0.273181\pi$
$854$	8.83638			0.302375
$855$	0.127985	−	12.5140i	0.00437700	−	0.427970i
$856$	3.95701			0.135248
$857$	−4.52371	+	4.52371i	−0.154527	+	0.154527i	−0.780136	−	0.625609i	$-0.784850\pi$
$857$	−4.52371	+	4.52371i	−0.154527	+	0.154527i	0.625609	+	0.780136i	$0.284850\pi$
$858$	−18.4831	+	39.6493i	−0.631002	+	1.35361i
$859$		−	13.8864i		−	0.473799i	−0.971534	−	0.236899i	$-0.923869\pi$
$859$		−	13.8864i		−	0.473799i	0.971534	−	0.236899i	$-0.0761312\pi$
$860$	21.7764	−	1.67579i	0.742570	−	0.0571440i
$861$	−9.05228	−	24.8618i	−0.308501	−	0.847287i
$862$	−7.87929	−	7.87929i	−0.268370	−	0.268370i
$863$	−19.1746	−	19.1746i	−0.652712	−	0.652712i	0.300933	−	0.953645i	$-0.402702\pi$
$863$	−19.1746	−	19.1746i	−0.652712	−	0.652712i	−0.953645	+	0.300933i	$0.902702\pi$
$864$	2.59648	−	4.50092i	0.0883340	−	0.153124i
$865$	10.4124	−	0.801283i	0.354033	−	0.0272444i
$866$		−	38.2868i		−	1.30104i
$867$	−2.57742	−	1.20150i	−0.0875339	−	0.0408051i
$868$	1.76311	−	1.76311i	0.0598439	−	0.0598439i
$869$	−71.1264			−2.41280
$870$	−13.1330	−	4.93448i	−0.445251	−	0.167295i
$871$	24.6289			0.834517
$872$	−4.05179	+	4.05179i	−0.137211	+	0.137211i
$873$	2.83980	−	32.5477i	0.0961126	−	1.10157i
$874$		−	9.90820i		−	0.335150i
$875$	6.36649	+	27.1405i	0.215227	+	0.917518i
$876$	0.144820	−	0.0527295i	0.00489301	−	0.00178157i
$877$	−9.57875	−	9.57875i	−0.323452	−	0.323452i	0.526638	−	0.850090i	$-0.323452\pi$
$877$	−9.57875	−	9.57875i	−0.323452	−	0.323452i	−0.850090	+	0.526638i	$0.823452\pi$
$878$	22.5699	+	22.5699i	0.761698	+	0.761698i
$879$	−13.3821	+	4.87249i	−0.451368	+	0.164345i
$880$	−9.02529	−	7.73548i	−0.304243	−	0.260763i
$881$			34.9896i			1.17883i	0.807831	+	0.589414i	$0.200641\pi$
$881$			34.9896i			1.17883i	−0.807831	+	0.589414i	$0.799359\pi$
$882$	0.204142	−	2.33972i	0.00687382	−	0.0787826i
$883$	−24.3320	+	24.3320i	−0.818836	+	0.818836i	−0.985939	−	0.167103i	$-0.946559\pi$
$883$	−24.3320	+	24.3320i	−0.818836	+	0.818836i	0.167103	+	0.985939i	$0.446559\pi$
$884$	−18.6196			−0.626244
$885$	−14.3783	−	31.6860i	−0.483320	−	1.06511i
$886$	−30.3484			−1.01957
$887$	−34.5491	+	34.5491i	−1.16005	+	1.16005i	−0.175582	+	0.984465i	$0.556181\pi$
$887$	−34.5491	+	34.5491i	−1.16005	+	1.16005i	−0.984465	+	0.175582i	$0.943819\pi$
$888$	−3.16768	−	1.47666i	−0.106300	−	0.0495534i
$889$		−	47.0426i		−	1.57776i
$890$	0.858846	+	11.1605i	0.0287886	+	0.374099i
$891$	47.1201	+	8.28557i	1.57858	+	0.277577i
$892$	−18.4359	−	18.4359i	−0.617279	−	0.617279i
$893$	9.95119	+	9.95119i	0.333004	+	0.333004i
$894$	−9.90041	−	27.1911i	−0.331119	−	0.909408i
$895$	−14.5109	+	16.9304i	−0.485045	+	0.565921i
$896$		−	2.49342i		−	0.0832992i
$897$	18.4663	−	39.6134i	0.616573	−	1.32265i
$898$	−7.05179	+	7.05179i	−0.235321	+	0.235321i
$899$	−3.62239			−0.120813
$900$	11.2887	+	9.87748i	0.376291	+	0.329249i
$901$	−43.9993			−1.46583
$902$	−23.0288	+	23.0288i	−0.766774	+	0.766774i
$903$	−17.8229	+	38.2330i	−0.593107	+	1.27232i
$904$		−	0.766013i		−	0.0254772i
$905$	23.6774	−	27.6253i	0.787063	−	0.918297i
$906$	13.2143	+	36.2926i	0.439015	+	1.20574i
$907$	−25.5536	−	25.5536i	−0.848493	−	0.848493i	0.141452	−	0.989945i	$-0.454823\pi$
$907$	−25.5536	−	25.5536i	−0.848493	−	0.848493i	−0.989945	+	0.141452i	$0.954823\pi$
$908$	−6.34333	−	6.34333i	−0.210511	−	0.210511i
$909$	14.0341	−	11.7816i	0.465480	−	0.390772i
$910$	−2.03250	−	26.4118i	−0.0673768	−	0.875541i
$911$			2.98577i			0.0989231i	0.998776	+	0.0494615i	$0.0157505\pi$
$911$			2.98577i			0.0989231i	−0.998776	+	0.0494615i	$0.984249\pi$
$912$	−2.92869	−	1.36525i	−0.0969785	−	0.0452079i
$913$	22.9126	−	22.9126i	0.758297	−	0.758297i
$914$	21.8143			0.721554
$915$	5.67161	+	12.4988i	0.187498	+	0.413197i
$916$	11.9922			0.396232
$917$	0.449854	−	0.449854i	0.0148555	−	0.0148555i
$918$	5.27743	+	19.6677i	0.174181	+	0.649132i
$919$		−	15.7119i		−	0.518289i	−0.965839	−	0.259144i	$-0.916559\pi$
$919$		−	15.7119i		−	0.518289i	0.965839	−	0.259144i	$-0.0834406\pi$
$920$	9.01711	+	7.72846i	0.297285	+	0.254800i
$921$	−1.29413	+	0.471197i	−0.0426429	+	0.0155265i
$922$	18.6348	+	18.6348i	0.613705	+	0.613705i
$923$	−28.8133	−	28.8133i	−0.948402	−	0.948402i
$924$	21.5724	−	7.85461i	0.709680	−	0.258398i
$925$	5.95852	−	8.14158i	0.195915	−	0.267694i
$926$		−	30.0365i		−	0.987060i
$927$	33.2430	+	2.90047i	1.09184	+	0.0952639i
$928$	−2.56141	+	2.56141i	−0.0840826	+	0.0840826i
$929$	27.0438			0.887278			0.443639	−	0.896206i	$-0.353687\pi$
$929$	27.0438			0.887278			0.443639	+	0.896206i	$0.353687\pi$
$930$	3.62552	+	1.36222i	0.118885	+	0.0446689i
$931$	−1.46050			−0.0478661
$932$	13.0981	−	13.0981i	0.429043	−	0.429043i
$933$	23.6061	+	11.0043i	0.772828	+	0.360264i
$934$			17.0165i			0.556798i
$935$	46.4461	−	3.57423i	1.51895	−	0.116890i
$936$	−9.16454	−	10.9166i	−0.299552	−	0.356821i
$937$	−4.59656	−	4.59656i	−0.150163	−	0.150163i	0.628028	−	0.778191i	$-0.283862\pi$
$937$	−4.59656	−	4.59656i	−0.150163	−	0.150163i	−0.778191	+	0.628028i	$0.783862\pi$
$938$	−9.13955	−	9.13955i	−0.298417	−	0.298417i
$939$	19.6368	+	53.9319i	0.640824	+	1.76000i
$940$	−16.8182	+	1.29424i	−0.548550	+	0.0422134i
$941$		−	26.6136i		−	0.867580i	−0.901014	−	0.433790i	$-0.857176\pi$
$941$		−	26.6136i		−	0.867580i	0.901014	−	0.433790i	$-0.142824\pi$
$942$	13.8615	−	29.7352i	0.451631	−	0.968824i
$943$	23.0079	−	23.0079i	0.749240	−	0.749240i
$944$	−8.98420			−0.292411
$945$	−27.3225	+	9.63293i	−0.888801	+	0.313359i
$946$	51.9230			1.68816
$947$	11.3623	−	11.3623i	0.369225	−	0.369225i	−0.497970	−	0.867194i	$-0.665921\pi$
$947$	11.3623	−	11.3623i	0.369225	−	0.369225i	0.867194	+	0.497970i	$0.165921\pi$
$948$	9.79160	−	21.0046i	0.318016	−	0.682199i
$949$		−	0.422766i		−	0.0137236i
$950$	5.50897	−	7.52732i	0.178734	−	0.244218i
$951$	−10.9256	−	30.0067i	−0.354286	−	0.973034i
$952$	6.90955	+	6.90955i	0.223940	+	0.223940i
$953$	1.11734	+	1.11734i	0.0361943	+	0.0361943i	0.724972	−	0.688778i	$-0.241853\pi$
$953$	1.11734	+	1.11734i	0.0361943	+	0.0361943i	−0.688778	+	0.724972i	$0.741853\pi$
$954$	−21.6564	−	25.7967i	−0.701152	−	0.835200i
$955$	24.5774	+	21.0651i	0.795307	+	0.681649i
$956$			13.8215i			0.447018i
$957$	−30.2295	−	14.0919i	−0.977182	−	0.455527i
$958$	6.70181	−	6.70181i	0.216526	−	0.216526i
$959$	27.9188			0.901545
$960$	3.52686	−	1.60039i	0.113829	−	0.0516525i
$961$	1.00000			0.0322581
$962$	−6.77900	+	6.77900i	−0.218564	+	0.218564i
$963$	−11.8261	−	1.03183i	−0.381091	−	0.0332503i
$964$			20.8975i			0.673063i
$965$	1.63815	+	21.2873i	0.0527339	+	0.685261i
$966$	−21.5529	+	7.84748i	−0.693452	+	0.252489i
$967$	−25.4252	−	25.4252i	−0.817618	−	0.817618i	0.168144	−	0.985762i	$-0.446223\pi$
$967$	−25.4252	−	25.4252i	−0.817618	−	0.817618i	−0.985762	+	0.168144i	$0.946223\pi$
$968$	−12.2037	−	12.2037i	−0.392243	−	0.392243i
$969$	11.8990	−	4.33247i	0.382251	−	0.139179i
$970$	15.8473	−	18.4897i	0.508827	−	0.593669i
$971$		−	61.8055i		−	1.98343i	−0.128452	−	0.991716i	$-0.541001\pi$
$971$		−	61.8055i		−	1.98343i	0.128452	−	0.991716i	$-0.458999\pi$
$972$	−8.93362	+	12.7746i	−0.286546	+	0.409745i
$973$	−1.93753	+	1.93753i	−0.0621143	+	0.0621143i
$974$	−18.7962			−0.602271
$975$	36.0540	−	19.8272i	1.15465	−	0.634980i
$976$	3.54388			0.113437
$977$	−5.25621	+	5.25621i	−0.168161	+	0.168161i	−0.786171	−	0.618010i	$-0.787939\pi$
$977$	−5.25621	+	5.25621i	−0.168161	+	0.168161i	0.618010	+	0.786171i	$0.287939\pi$
$978$	5.55212	+	2.58819i	0.177537	+	0.0827613i
$979$			26.6106i			0.850479i
$980$	1.13920	−	1.32915i	0.0363905	−	0.0424583i
$981$	13.1659	−	11.0528i	0.420355	−	0.352890i
$982$	4.94294	+	4.94294i	0.157736	+	0.157736i
$983$	17.7765	+	17.7765i	0.566983	+	0.566983i	0.931282	−	0.364299i	$-0.118691\pi$
$983$	17.7765	+	17.7765i	0.566983	+	0.566983i	−0.364299	+	0.931282i	$0.618691\pi$
$984$	−3.63047	−	9.97097i	−0.115735	−	0.317863i
$985$	3.40263	+	44.2162i	0.108417	+	1.40885i
$986$		−	14.1960i		−	0.452091i
$987$	13.7648	−	29.5279i	0.438140	−	0.939884i
$988$	−6.26754	+	6.26754i	−0.199397	+	0.199397i
$989$	−51.8759			−1.64956
$990$	24.9563	+	25.4720i	0.793163	+	0.809555i
$991$	−28.3639			−0.901008			−0.450504	−	0.892774i	$-0.648756\pi$
$991$	−28.3639			−0.901008			−0.450504	+	0.892774i	$0.648756\pi$
$992$	0.707107	−	0.707107i	0.0224507	−	0.0224507i
$993$	−16.3617	+	35.0987i	−0.519224	+	1.11382i
$994$			21.3847i			0.678282i
$995$	18.9605	+	16.2509i	0.601089	+	0.515187i
$996$	3.61216	+	9.92068i	0.114456	+	0.314349i
$997$	−7.52405	−	7.52405i	−0.238289	−	0.238289i	0.577852	−	0.816141i	$-0.303891\pi$
$997$	−7.52405	−	7.52405i	−0.238289	−	0.238289i	−0.816141	+	0.577852i	$0.803891\pi$
$998$	−26.2611	−	26.2611i	−0.831280	−	0.831280i
$999$	9.08202	+	5.23921i	0.287342	+	0.165761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.g.497.4	✓	40
3.2	odd	2	inner	930.2.j.g.497.11	yes	40
5.3	odd	4	inner	930.2.j.g.683.11	yes	40
15.8	even	4	inner	930.2.j.g.683.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.g.497.4	✓	40	1.1	even	1	trivial
930.2.j.g.497.11	yes	40	3.2	odd	2	inner
930.2.j.g.683.4	yes	40	15.8	even	4	inner
930.2.j.g.683.11	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.731811 + 1.56986i) q^{3} -1.00000i q^{4} +(-1.45516 + 1.69779i) q^{5} +(-0.592589 - 1.62753i) q^{6} +(1.76311 + 1.76311i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.92891 - 2.29768i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.731811 + 1.56986i) q^{3} -1.00000i q^{4} +(-1.45516 + 1.69779i) q^{5} +(-0.592589 - 1.62753i) q^{6} +(1.76311 + 1.76311i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.92891 - 2.29768i) q^{9} +(-0.171568 - 2.22948i) q^{10} -5.31589i q^{11} +(1.56986 + 0.731811i) q^{12} +(3.35958 - 3.35958i) q^{13} -2.49342 q^{14} +(-1.60039 - 3.52686i) q^{15} -1.00000 q^{16} +(2.77112 - 2.77112i) q^{17} +(2.98865 + 0.260761i) q^{18} -1.86557i q^{19} +(1.69779 + 1.45516i) q^{20} +(-4.05810 + 1.47757i) q^{21} +(3.75890 + 3.75890i) q^{22} +(-3.75550 - 3.75550i) q^{23} +(-1.62753 + 0.592589i) q^{24} +(-0.765014 - 4.94113i) q^{25} +4.75116i q^{26} +(5.01862 - 1.34664i) q^{27} +(1.76311 - 1.76311i) q^{28} -3.62239 q^{29} +(3.62552 + 1.36222i) q^{30} +1.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(8.34519 + 3.89023i) q^{33} +3.91895i q^{34} +(-5.55901 + 0.427791i) q^{35} +(-2.29768 + 1.92891i) q^{36} +(1.42681 + 1.42681i) q^{37} +(1.31916 + 1.31916i) q^{38} +(2.81548 + 7.73263i) q^{39} +(-2.22948 + 0.171568i) q^{40} +6.12646i q^{41} +(1.82471 - 3.91431i) q^{42} +(6.90667 - 6.90667i) q^{43} -5.31589 q^{44} +(6.70785 + 0.0686037i) q^{45} +5.31107 q^{46} +(-5.33412 + 5.33412i) q^{47} +(0.731811 - 1.56986i) q^{48} -0.782871i q^{49} +(4.03485 + 2.95296i) q^{50} +(2.32233 + 6.37819i) q^{51} +(-3.35958 - 3.35958i) q^{52} +(-7.93890 - 7.93890i) q^{53} +(-2.59648 + 4.50092i) q^{54} +(9.02529 + 7.73548i) q^{55} +2.49342i q^{56} +(2.92869 + 1.36525i) q^{57} +(2.56141 - 2.56141i) q^{58} +8.98420 q^{59} +(-3.52686 + 1.60039i) q^{60} -3.54388 q^{61} +(-0.707107 + 0.707107i) q^{62} +(0.650185 - 7.45194i) q^{63} +1.00000i q^{64} +(0.815147 + 10.5926i) q^{65} +(-8.65175 + 3.15014i) q^{66} +(3.66547 + 3.66547i) q^{67} +(-2.77112 - 2.77112i) q^{68} +(8.64390 - 3.14728i) q^{69} +(3.62832 - 4.23331i) q^{70} -8.57648i q^{71} +(0.260761 - 2.98865i) q^{72} +(0.0629195 - 0.0629195i) q^{73} -2.01781 q^{74} +(8.31671 + 2.41501i) q^{75} -1.86557 q^{76} +(9.37251 - 9.37251i) q^{77} +(-7.45864 - 3.47695i) q^{78} -13.3800i q^{79} +(1.45516 - 1.69779i) q^{80} +(-1.55864 + 8.86401i) q^{81} +(-4.33206 - 4.33206i) q^{82} +(4.31021 + 4.31021i) q^{83} +(1.47757 + 4.05810i) q^{84} +(0.672367 + 8.73721i) q^{85} +9.76750i q^{86} +(2.65090 - 5.68663i) q^{87} +(3.75890 - 3.75890i) q^{88} -5.00586 q^{89} +(-4.79168 + 4.69466i) q^{90} +11.8466 q^{91} +(-3.75550 + 3.75550i) q^{92} +(-0.731811 + 1.56986i) q^{93} -7.54358i q^{94} +(3.16736 + 2.71471i) q^{95} +(0.592589 + 1.62753i) q^{96} +(7.70070 + 7.70070i) q^{97} +(0.553574 + 0.553574i) q^{98} +(-12.2142 + 10.2539i) 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

Related objects

Downloads

Learn more