LMFDB - Embedded newform 65.2.f.b.47.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(18,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("65.18");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.f (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:	$0.519027613138$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.619810816.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{5} + 14x^{4} - 8x^{3} + 2x^{2} + 2x + 1 $ x^8 - 2x^5 + 14x^4 - 8x^3 + 2x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.3
Root			$-1.49094 - 1.49094i$ of defining polynomial
Character	$\chi$	$=$	65.47
Dual form			65.2.f.b.18.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.134632i q^{2} +(-2.15558 + 2.15558i) q^{3} +1.98187 q^{4} +(-1.29021 + 1.82630i) q^{5} +(0.290209 + 0.290209i) q^{6} +1.90970 q^{7} -0.536087i q^{8} -6.29303i q^{9} +O(q^{10})$	\(q-0.134632i q^{2} +(-2.15558 + 2.15558i) q^{3} +1.98187 q^{4} +(-1.29021 + 1.82630i) q^{5} +(0.290209 + 0.290209i) q^{6} +1.90970 q^{7} -0.536087i q^{8} -6.29303i q^{9} +(0.245878 + 0.173703i) q^{10} +(-0.290209 + 0.290209i) q^{11} +(-4.27208 + 4.27208i) q^{12} +(0.173703 - 3.60136i) q^{13} -0.257106i q^{14} +(-1.15558 - 6.71787i) q^{15} +3.89157 q^{16} +(2.53609 - 2.53609i) q^{17} -0.847242 q^{18} +(-3.15558 + 3.15558i) q^{19} +(-2.55703 + 3.61949i) q^{20} +(-4.11651 + 4.11651i) q^{21} +(0.0390714 + 0.0390714i) q^{22} +(2.27208 + 2.27208i) q^{23} +(1.15558 + 1.15558i) q^{24} +(-1.67072 - 4.71261i) q^{25} +(-0.484858 - 0.0233860i) q^{26} +(7.09838 + 7.09838i) q^{27} +3.78478 q^{28} -2.40146i q^{29} +(-0.904440 + 0.155578i) q^{30} +(2.02095 + 2.02095i) q^{31} -1.59610i q^{32} -1.25114i q^{33} +(-0.341438 - 0.341438i) q^{34} +(-2.46391 + 3.48768i) q^{35} -12.4720i q^{36} -5.32928 q^{37} +(0.424841 + 0.424841i) q^{38} +(7.38859 + 8.13745i) q^{39} +(0.979054 + 0.691665i) q^{40} +(-1.51796 - 1.51796i) q^{41} +(0.554213 + 0.554213i) q^{42} +(-0.888754 - 0.888754i) q^{43} +(-0.575159 + 0.575159i) q^{44} +(11.4929 + 8.11933i) q^{45} +(0.305895 - 0.305895i) q^{46} -6.94562 q^{47} +(-8.38859 + 8.38859i) q^{48} -3.35305 q^{49} +(-0.634468 + 0.224932i) q^{50} +10.9335i q^{51} +(0.344258 - 7.13745i) q^{52} +(-1.09030 + 1.09030i) q^{53} +(0.955668 - 0.955668i) q^{54} +(-0.155578 - 0.904440i) q^{55} -1.02377i q^{56} -13.6042i q^{57} -0.323312 q^{58} +(-8.31642 - 8.31642i) q^{59} +(-2.29021 - 13.3140i) q^{60} +7.17300 q^{61} +(0.272084 - 0.272084i) q^{62} -12.0178i q^{63} +7.56826 q^{64} +(6.35305 + 4.96375i) q^{65} -0.168443 q^{66} -0.939983i q^{67} +(5.02621 - 5.02621i) q^{68} -9.79531 q^{69} +(0.469553 + 0.331721i) q^{70} +(-7.37643 - 7.37643i) q^{71} -3.37361 q^{72} +6.63447i q^{73} +0.717491i q^{74} +(13.7598 + 6.55703i) q^{75} +(-6.25396 + 6.25396i) q^{76} +(-0.554213 + 0.554213i) q^{77} +(1.09556 - 0.994740i) q^{78} +4.39982i q^{79} +(-5.02095 + 7.10717i) q^{80} -11.7231 q^{81} +(-0.204366 + 0.204366i) q^{82} +13.4842 q^{83} +(-8.15840 + 8.15840i) q^{84} +(1.35956 + 7.90373i) q^{85} +(-0.119655 + 0.119655i) q^{86} +(5.17652 + 5.17652i) q^{87} +(0.155578 + 0.155578i) q^{88} +(10.0238 + 10.0238i) q^{89} +(1.09312 - 1.54732i) q^{90} +(0.331721 - 6.87753i) q^{91} +(4.50298 + 4.50298i) q^{92} -8.71261 q^{93} +0.935102i q^{94} +(-1.69166 - 9.83438i) q^{95} +(3.44053 + 3.44053i) q^{96} -4.39982i q^{97} +0.451427i q^{98} +(1.82630 + 1.82630i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 6 q^{6}+O(q^{10}) $ 8 * q - 6 * q^3 - 8 * q^4 - 2 * q^5 - 6 * q^6	$ 8 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 6 q^{6} + 6 q^{10} + 6 q^{11} - 2 q^{12} + 14 q^{13} + 2 q^{15} - 8 q^{16} + 16 q^{17} + 20 q^{18} - 14 q^{19} - 2 q^{20} - 12 q^{21} + 10 q^{22} - 14 q^{23} - 2 q^{24} - 12 q^{25} + 6 q^{26} + 12 q^{27} - 8 q^{28} - 14 q^{30} + 2 q^{31} - 24 q^{35} - 44 q^{37} - 2 q^{38} + 6 q^{39} + 22 q^{40} + 16 q^{41} + 24 q^{42} - 6 q^{43} - 10 q^{44} + 22 q^{45} + 2 q^{46} + 16 q^{47} - 14 q^{48} + 24 q^{49} + 44 q^{50} - 38 q^{52} - 24 q^{53} + 20 q^{54} + 10 q^{55} + 24 q^{58} - 22 q^{59} - 10 q^{60} + 20 q^{61} - 30 q^{62} + 48 q^{64} - 36 q^{66} + 4 q^{68} + 4 q^{69} - 68 q^{70} - 10 q^{71} - 16 q^{72} + 30 q^{75} + 6 q^{76} - 24 q^{77} + 2 q^{78} - 26 q^{80} - 20 q^{81} + 20 q^{82} + 48 q^{83} - 16 q^{84} + 32 q^{85} - 46 q^{86} + 16 q^{87} - 10 q^{88} + 28 q^{89} - 14 q^{90} + 20 q^{91} + 50 q^{92} - 40 q^{93} + 2 q^{95} + 30 q^{96} + 2 q^{99}+O(q^{100}) $ 8 * q - 6 * q^3 - 8 * q^4 - 2 * q^5 - 6 * q^6 + 6 * q^10 + 6 * q^11 - 2 * q^12 + 14 * q^13 + 2 * q^15 - 8 * q^16 + 16 * q^17 + 20 * q^18 - 14 * q^19 - 2 * q^20 - 12 * q^21 + 10 * q^22 - 14 * q^23 - 2 * q^24 - 12 * q^25 + 6 * q^26 + 12 * q^27 - 8 * q^28 - 14 * q^30 + 2 * q^31 - 24 * q^35 - 44 * q^37 - 2 * q^38 + 6 * q^39 + 22 * q^40 + 16 * q^41 + 24 * q^42 - 6 * q^43 - 10 * q^44 + 22 * q^45 + 2 * q^46 + 16 * q^47 - 14 * q^48 + 24 * q^49 + 44 * q^50 - 38 * q^52 - 24 * q^53 + 20 * q^54 + 10 * q^55 + 24 * q^58 - 22 * q^59 - 10 * q^60 + 20 * q^61 - 30 * q^62 + 48 * q^64 - 36 * q^66 + 4 * q^68 + 4 * q^69 - 68 * q^70 - 10 * q^71 - 16 * q^72 + 30 * q^75 + 6 * q^76 - 24 * q^77 + 2 * q^78 - 26 * q^80 - 20 * q^81 + 20 * q^82 + 48 * q^83 - 16 * q^84 + 32 * q^85 - 46 * q^86 + 16 * q^87 - 10 * q^88 + 28 * q^89 - 14 * q^90 + 20 * q^91 + 50 * q^92 - 40 * q^93 + 2 * q^95 + 30 * q^96 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		−	0.134632i		−	0.0951991i	−0.998866	−	0.0475996i	$-0.984843\pi$
$2$		−	0.134632i		−	0.0951991i	0.998866	−	0.0475996i	$-0.0151571\pi$
$3$	−2.15558	+	2.15558i	−1.24452	+	1.24452i	−0.286419	+	0.958105i	$0.592465\pi$
$3$	−2.15558	+	2.15558i	−1.24452	+	1.24452i	−0.958105	+	0.286419i	$0.907535\pi$
$4$	1.98187			0.990937
$5$	−1.29021	+	1.82630i	−0.576999	+	0.816745i
$5$	−1.29021	+	1.82630i	−0.576999	+	0.816745i
$6$	0.290209	+	0.290209i	0.118478	+	0.118478i
$7$	1.90970			0.721799			0.360899	−	0.932605i	$-0.382470\pi$
$7$	1.90970			0.721799			0.360899	+	0.932605i	$0.382470\pi$
$8$		−	0.536087i		−	0.189535i
$9$		−	6.29303i		−	2.09768i
$10$	0.245878	+	0.173703i	0.0777534	+	0.0549298i
$11$	−0.290209	+	0.290209i	−0.0875014	+	0.0875014i	−0.749503	−	0.662001i	$-0.769707\pi$
$11$	−0.290209	+	0.290209i	−0.0875014	+	0.0875014i	0.662001	+	0.749503i	$0.269707\pi$
$12$	−4.27208	+	4.27208i	−1.23324	+	1.23324i
$13$	0.173703	−	3.60136i	0.0481766	−	0.998839i
$13$	0.173703	−	3.60136i	0.0481766	−	0.998839i
$14$		−	0.257106i		−	0.0687146i
$15$	−1.15558	−	6.71787i	−0.298369	−	1.73455i
$16$	3.89157			0.972894
$17$	2.53609	−	2.53609i	0.615091	−	0.615091i	−0.329177	−	0.944268i	$-0.606771\pi$
$17$	2.53609	−	2.53609i	0.615091	−	0.615091i	0.944268	+	0.329177i	$0.106771\pi$
$18$	−0.847242			−0.199697
$19$	−3.15558	+	3.15558i	−0.723939	+	0.723939i	−0.969405	−	0.245466i	$-0.921059\pi$
$19$	−3.15558	+	3.15558i	−0.723939	+	0.723939i	0.245466	+	0.969405i	$0.421059\pi$
$20$	−2.55703	+	3.61949i	−0.571770	+	0.809343i
$21$	−4.11651	+	4.11651i	−0.898295	+	0.898295i
$22$	0.0390714	+	0.0390714i	0.00833006	+	0.00833006i
$23$	2.27208	+	2.27208i	0.473762	+	0.473762i	0.903130	−	0.429368i	$-0.141264\pi$
$23$	2.27208	+	2.27208i	0.473762	+	0.473762i	−0.429368	+	0.903130i	$0.641264\pi$
$24$	1.15558	+	1.15558i	0.235881	+	0.235881i
$25$	−1.67072	−	4.71261i	−0.334144	−	0.942522i
$26$	−0.484858	−	0.0233860i	−0.0950886	−	0.00458637i
$27$	7.09838	+	7.09838i	1.36608	+	1.36608i
$28$	3.78478			0.715257
$29$		−	2.40146i		−	0.445939i	−0.974825	−	0.222970i	$-0.928425\pi$
$29$		−	2.40146i		−	0.445939i	0.974825	−	0.222970i	$-0.0715750\pi$
$30$	−0.904440	+	0.155578i	−0.165127	+	0.0284045i
$31$	2.02095	+	2.02095i	0.362973	+	0.362973i	0.864906	−	0.501934i	$-0.167378\pi$
$31$	2.02095	+	2.02095i	0.362973	+	0.362973i	−0.501934	+	0.864906i	$0.667378\pi$
$32$		−	1.59610i		−	0.282154i
$33$		−	1.25114i		−	0.217795i
$34$	−0.341438	−	0.341438i	−0.0585562	−	0.0585562i
$35$	−2.46391	+	3.48768i	−0.416477	+	0.589525i
$36$		−	12.4720i		−	2.07867i
$37$	−5.32928			−0.876128			−0.438064	−	0.898944i	$-0.644336\pi$
$37$	−5.32928			−0.876128			−0.438064	+	0.898944i	$0.644336\pi$
$38$	0.424841	+	0.424841i	0.0689184	+	0.0689184i
$39$	7.38859	+	8.13745i	1.18312	+	1.30304i
$40$	0.979054	+	0.691665i	0.154802	+	0.109362i
$41$	−1.51796	−	1.51796i	−0.237066	−	0.237066i	0.578568	−	0.815634i	$-0.303612\pi$
$41$	−1.51796	−	1.51796i	−0.237066	−	0.237066i	−0.815634	+	0.578568i	$0.803612\pi$
$42$	0.554213	+	0.554213i	0.0855169	+	0.0855169i
$43$	−0.888754	−	0.888754i	−0.135534	−	0.135534i	0.636085	−	0.771619i	$-0.280553\pi$
$43$	−0.888754	−	0.888754i	−0.135534	−	0.135534i	−0.771619	+	0.636085i	$0.780553\pi$
$44$	−0.575159	+	0.575159i	−0.0867084	+	0.0867084i
$45$	11.4929	+	8.11933i	1.71327	+	1.21036i
$46$	0.305895	−	0.305895i	0.0451017	−	0.0451017i
$47$	−6.94562			−1.01312			−0.506562	−	0.862204i	$-0.669084\pi$
$47$	−6.94562			−1.01312			−0.506562	+	0.862204i	$0.669084\pi$
$48$	−8.38859	+	8.38859i	−1.21079	+	1.21079i
$49$	−3.35305			−0.479007
$50$	−0.634468	+	0.224932i	−0.0897273	+	0.0318102i
$51$			10.9335i			1.53099i
$52$	0.344258	−	7.13745i	0.0477400	−	0.989786i
$53$	−1.09030	+	1.09030i	−0.149764	+	0.149764i	−0.778013	−	0.628248i	$-0.783772\pi$
$53$	−1.09030	+	1.09030i	−0.149764	+	0.149764i	0.628248	+	0.778013i	$0.283772\pi$
$54$	0.955668	−	0.955668i	0.130050	−	0.130050i
$55$	−0.155578	−	0.904440i	−0.0209781	−	0.121955i
$56$		−	1.02377i		−	0.136806i
$57$		−	13.6042i		−	1.80192i
$58$	−0.323312			−0.0424530
$59$	−8.31642	−	8.31642i	−1.08271	−	1.08271i	−0.996256	−	0.0864488i	$-0.972448\pi$
$59$	−8.31642	−	8.31642i	−1.08271	−	1.08271i	−0.0864488	−	0.996256i	$-0.527552\pi$
$60$	−2.29021	−	13.3140i	−0.295665	−	1.71883i
$61$	7.17300			0.918408			0.459204	−	0.888331i	$-0.348135\pi$
$61$	7.17300			0.918408			0.459204	+	0.888331i	$0.348135\pi$
$62$	0.272084	−	0.272084i	0.0345547	−	0.0345547i
$63$		−	12.0178i		−	1.51410i
$64$	7.56826			0.946033
$65$	6.35305	+	4.96375i	0.787998	+	0.615677i
$66$	−0.168443			−0.0207339
$67$		−	0.939983i		−	0.114837i	−0.998350	−	0.0574186i	$-0.981713\pi$
$67$		−	0.939983i		−	0.114837i	0.998350	−	0.0574186i	$-0.0182870\pi$
$68$	5.02621	−	5.02621i	0.609517	−	0.609517i
$69$	−9.79531			−1.17922
$70$	0.469553	+	0.331721i	0.0561223	+	0.0396483i
$71$	−7.37643	−	7.37643i	−0.875421	−	0.875421i	0.117635	−	0.993057i	$-0.462469\pi$
$71$	−7.37643	−	7.37643i	−0.875421	−	0.875421i	−0.993057	+	0.117635i	$0.962469\pi$
$72$	−3.37361			−0.397584
$73$			6.63447i			0.776506i	0.921553	+	0.388253i	$0.126921\pi$
$73$			6.63447i			0.776506i	−0.921553	+	0.388253i	$0.873079\pi$
$74$			0.717491i			0.0834066i
$75$	13.7598	+	6.55703i	1.58884	+	0.757141i
$76$	−6.25396	+	6.25396i	−0.717378	+	0.717378i
$77$	−0.554213	+	0.554213i	−0.0631584	+	0.0631584i
$78$	1.09556	−	0.994740i	0.124048	−	0.112632i
$79$			4.39982i			0.495018i	0.968886	+	0.247509i	$0.0796120\pi$
$79$			4.39982i			0.495018i	−0.968886	+	0.247509i	$0.920388\pi$
$80$	−5.02095	+	7.10717i	−0.561359	+	0.794606i
$81$	−11.7231			−1.30257
$82$	−0.204366	+	0.204366i	−0.0225684	+	0.0225684i
$83$	13.4842			1.48008			0.740039	−	0.672564i	$-0.234807\pi$
$83$	13.4842			1.48008			0.740039	+	0.672564i	$0.234807\pi$
$84$	−8.15840	+	8.15840i	−0.890154	+	0.890154i
$85$	1.35956	+	7.90373i	0.147465	+	0.857280i
$86$	−0.119655	+	0.119655i	−0.0129027	+	0.0129027i
$87$	5.17652	+	5.17652i	0.554982	+	0.554982i
$88$	0.155578	+	0.155578i	0.0165846	+	0.0165846i
$89$	10.0238	+	10.0238i	1.06252	+	1.06252i	0.997911	+	0.0646062i	$0.0205791\pi$
$89$	10.0238	+	10.0238i	1.06252	+	1.06252i	0.0646062	+	0.997911i	$0.479421\pi$
$90$	1.09312	−	1.54732i	0.115225	−	0.163101i
$91$	0.331721	−	6.87753i	0.0347738	−	0.720961i
$92$	4.50298	+	4.50298i	0.469469	+	0.469469i
$93$	−8.71261			−0.903456
$94$			0.935102i			0.0964484i
$95$	−1.69166	−	9.83438i	−0.173561	−	1.00899i
$96$	3.44053	+	3.44053i	0.351147	+	0.351147i
$97$		−	4.39982i		−	0.446734i	−0.974734	−	0.223367i	$-0.928295\pi$
$97$		−	4.39982i		−	0.446734i	0.974734	−	0.223367i	$-0.0717048\pi$
$98$			0.451427i			0.0456010i
$99$	1.82630	+	1.82630i	0.183550	+	0.183550i
$100$	−3.31116	−	9.33980i	−0.331116	−	0.933980i
$101$			3.55014i			0.353252i	0.984278	+	0.176626i	$0.0565183\pi$
$101$			3.55014i			0.353252i	−0.984278	+	0.176626i	$0.943482\pi$
$102$	1.47199			0.145749
$103$	−7.44861	−	7.44861i	−0.733933	−	0.733933i	0.237463	−	0.971396i	$-0.423684\pi$
$103$	−7.44861	−	7.44861i	−0.733933	−	0.733933i	−0.971396	+	0.237463i	$0.923684\pi$
$104$	−1.93065	−	0.0931201i	−0.189315	−	0.00913118i
$105$	−2.20681	−	12.8291i	−0.215362	−	1.25199i
$106$	0.146789	+	0.146789i	0.0142574	+	0.0142574i
$107$	9.56511	+	9.56511i	0.924694	+	0.924694i	0.997357	−	0.0726622i	$-0.0231495\pi$
$107$	9.56511	+	9.56511i	0.924694	+	0.924694i	−0.0726622	+	0.997357i	$0.523150\pi$
$108$	14.0681	+	14.0681i	1.35370	+	1.35370i
$109$	−8.08622	+	8.08622i	−0.774520	+	0.774520i	−0.978893	−	0.204373i	$-0.934484\pi$
$109$	−8.08622	+	8.08622i	−0.774520	+	0.774520i	0.204373	+	0.978893i	$0.434484\pi$
$110$	−0.121766	+	0.0209457i	−0.0116100	+	0.00199709i
$111$	11.4877	−	11.4877i	1.09036	−	1.09036i
$112$	7.43174			0.702233
$113$	4.97943	−	4.97943i	0.468426	−	0.468426i	−0.432979	−	0.901404i	$-0.642537\pi$
$113$	4.97943	−	4.97943i	0.468426	−	0.468426i	0.901404	+	0.432979i	$0.142537\pi$
$114$	−1.83156			−0.171541
$115$	−7.08096	+	1.21804i	−0.660303	+	0.113582i
$116$		−	4.75938i		−	0.441898i
$117$	−22.6635	−	1.09312i	−2.09524	−	0.101059i
$118$	−1.11965	+	1.11965i	−0.103073	+	0.103073i
$119$	4.84317	−	4.84317i	0.443972	−	0.443972i
$120$	−3.60136	+	0.619490i	−0.328758	+	0.0565515i
$121$			10.8316i			0.984687i
$122$		−	0.965714i		−	0.0874316i
$123$	6.54417			0.590068
$124$	4.00526	+	4.00526i	0.359683	+	0.359683i
$125$	10.7622	+	3.02903i	0.962601	+	0.270924i
$126$	−1.61798			−0.144141
$127$	−7.01742	+	7.01742i	−0.622695	+	0.622695i	−0.946220	−	0.323525i	$-0.895132\pi$
$127$	−7.01742	+	7.01742i	−0.622695	+	0.622695i	0.323525	+	0.946220i	$0.395132\pi$
$128$		−	4.21114i		−	0.372216i
$129$	3.83156			0.337350
$130$	0.668279	−	0.855323i	0.0586119	−	0.0750168i
$131$	−11.3052			−0.987739			−0.493869	−	0.869536i	$-0.664418\pi$
$131$	−11.3052			−0.987739			−0.493869	+	0.869536i	$0.664418\pi$
$132$		−	2.47960i		−	0.215821i
$133$	−6.02621	+	6.02621i	−0.522538	+	0.522538i
$134$	−0.126552			−0.0109324
$135$	−22.1221	+	3.80535i	−1.90397	+	0.327512i
$136$	−1.35956	−	1.35956i	−0.116582	−	0.116582i
$137$	1.92186			0.164195			0.0820977	−	0.996624i	$-0.473838\pi$
$137$	1.92186			0.164195			0.0820977	+	0.996624i	$0.473838\pi$
$138$			1.31876i			0.112260i
$139$		−	15.2914i		−	1.29700i	−0.761215	−	0.648499i	$-0.775397\pi$
$139$		−	15.2914i		−	1.29700i	0.761215	−	0.648499i	$-0.224603\pi$
$140$	−4.88317	+	6.91214i	−0.412703	+	0.584182i
$141$	14.9718	−	14.9718i	1.26086	−	1.26086i
$142$	−0.993103	+	0.993103i	−0.0833394	+	0.0833394i
$143$	0.994740	+	1.09556i	0.0831843	+	0.0916154i
$144$		−	24.4898i		−	2.04082i
$145$	4.38577	+	3.09838i	0.364218	+	0.257306i
$146$	0.893211			0.0739227
$147$	7.22775	−	7.22775i	0.596135	−	0.596135i
$148$	−10.5620			−0.868188
$149$	13.8291	−	13.8291i	1.13293	−	1.13293i	0.143237	−	0.989688i	$-0.454249\pi$
$149$	13.8291	−	13.8291i	1.13293	−	1.13293i	0.989688	−	0.143237i	$-0.0457511\pi$
$150$	0.882786	−	1.85250i	0.0720791	−	0.151256i
$151$	−8.55106	+	8.55106i	−0.695876	+	0.695876i	−0.963518	−	0.267643i	$-0.913755\pi$
$151$	−8.55106	+	8.55106i	−0.695876	+	0.695876i	0.267643	+	0.963518i	$0.413755\pi$
$152$	1.69166	+	1.69166i	0.137212	+	0.137212i
$153$	−15.9597	−	15.9597i	−1.29026	−	1.29026i
$154$	0.0746147	+	0.0746147i	0.00601263	+	0.00601263i
$155$	−6.29829	+	1.08340i	−0.505891	+	0.0870210i
$156$	14.6433	+	16.1274i	1.17240	+	1.29123i
$157$	−4.00808	−	4.00808i	−0.319880	−	0.319880i	0.528841	−	0.848721i	$-0.322627\pi$
$157$	−4.00808	−	4.00808i	−0.319880	−	0.319880i	−0.848721	+	0.528841i	$0.822627\pi$
$158$	0.592356			0.0471253
$159$		−	4.70045i		−	0.372770i
$160$	2.91496	+	2.05931i	0.230448	+	0.162803i
$161$	4.33900	+	4.33900i	0.341961	+	0.341961i
$162$			1.57831i			0.124004i
$163$			13.2930i			1.04119i	0.853804	+	0.520595i	$0.174290\pi$
$163$			13.2930i			1.04119i	−0.853804	+	0.520595i	$0.825710\pi$
$164$	−3.00841	−	3.00841i	−0.234917	−	0.234917i
$165$	2.28495	+	1.61423i	0.177883	+	0.125668i
$166$		−	1.81540i		−	0.140902i
$167$	−12.9980			−1.00582			−0.502909	−	0.864339i	$-0.667737\pi$
$167$	−12.9980			−1.00582			−0.502909	+	0.864339i	$0.667737\pi$
$168$	2.20681	+	2.20681i	0.170259	+	0.170259i
$169$	−12.9397	−	1.25114i	−0.995358	−	0.0962414i
$170$	1.06409	−	0.183041i	0.0816123	−	0.0140386i
$171$	19.8581	+	19.8581i	1.51859	+	1.51859i
$172$	−1.76140	−	1.76140i	−0.134305	−	0.134305i
$173$	−10.3052	−	10.3052i	−0.783489	−	0.783489i	0.196929	−	0.980418i	$-0.436903\pi$
$173$	−10.3052	−	10.3052i	−0.783489	−	0.783489i	−0.980418	+	0.196929i	$0.936903\pi$
$174$	0.696925	−	0.696925i	0.0528338	−	0.0528338i
$175$	−3.19057	−	8.99967i	−0.241185	−	0.680311i
$176$	−1.12937	+	1.12937i	−0.0851296	+	0.0851296i
$177$	35.8534			2.69490
$178$	1.34952	−	1.34952i	0.101151	−	0.101151i
$179$	6.59094			0.492630			0.246315	−	0.969190i	$-0.420780\pi$
$179$	6.59094			0.492630			0.246315	+	0.969190i	$0.420780\pi$
$180$	22.7776	+	16.0915i	1.69774	+	1.19939i
$181$		−	15.7953i		−	1.17406i	−0.809567	−	0.587028i	$-0.800298\pi$
$181$		−	15.7953i		−	1.17406i	0.809567	−	0.587028i	$-0.199702\pi$
$182$	−0.925934	−	0.0446602i	−0.0686348	−	0.00331044i
$183$	−15.4619	+	15.4619i	−1.14298	+	1.14298i
$184$	1.21804	−	1.21804i	0.0897947	−	0.0897947i
$185$	6.87589	−	9.73285i	0.505525	−	0.715573i
$186$			1.17300i			0.0860082i
$187$			1.47199i			0.107643i
$188$	−13.7654			−1.00394
$189$	13.5558	+	13.5558i	0.986038	+	0.986038i
$190$	−1.32402	+	0.227752i	−0.0960546	+	0.0165229i
$191$	−13.0116			−0.941487			−0.470743	−	0.882270i	$-0.656014\pi$
$191$	−13.0116			−0.941487			−0.470743	+	0.882270i	$0.656014\pi$
$192$	−16.3140	+	16.3140i	−1.17736	+	1.17736i
$193$			17.4833i			1.25847i	0.777214	+	0.629237i	$0.216632\pi$
$193$			17.4833i			1.25847i	−0.777214	+	0.629237i	$0.783368\pi$
$194$	−0.592356			−0.0425287
$195$	−24.3942	+	2.99474i	−1.74691	+	0.214458i
$196$	−6.64532			−0.474665
$197$			14.2749i			1.01704i	0.861049	+	0.508522i	$0.169808\pi$
$197$			14.2749i			1.01704i	−0.861049	+	0.508522i	$0.830192\pi$
$198$	0.245878	−	0.245878i	0.0174738	−	0.0174738i
$199$	4.76666			0.337900			0.168950	−	0.985625i	$-0.445962\pi$
$199$	4.76666			0.337900			0.168950	+	0.985625i	$0.445962\pi$
$200$	−2.52637	+	0.895651i	−0.178641	+	0.0633321i
$201$	2.02621	+	2.02621i	0.142918	+	0.142918i
$202$	0.477961			0.0336293
$203$		−	4.58606i		−	0.321878i
$204$			21.6688i			1.51712i
$205$	4.73074	−	0.813760i	0.330409	−	0.0568354i
$206$	−1.00282	+	1.00282i	−0.0698698	+	0.0698698i
$207$	14.2983	−	14.2983i	0.993800	−	0.993800i
$208$	0.675979	−	14.0150i	0.0468707	−	0.971764i
$209$		−	1.83156i		−	0.126691i
$210$	−1.72721	+	0.297106i	−0.119189	+	0.0205023i
$211$	11.6025			0.798752			0.399376	−	0.916787i	$-0.369227\pi$
$211$	11.6025			0.798752			0.399376	+	0.916787i	$0.369227\pi$
$212$	−2.16084	+	2.16084i	−0.148407	+	0.148407i
$213$	31.8009			2.17896
$214$	1.28777	−	1.28777i	0.0880301	−	0.0880301i
$215$	2.76981	−	0.476450i	0.188899	−	0.0324936i
$216$	3.80535	−	3.80535i	0.258921	−	0.258921i
$217$	3.85940	+	3.85940i	0.261993	+	0.261993i
$218$	1.08866	+	1.08866i	0.0737336	+	0.0737336i
$219$	−14.3011	−	14.3011i	−0.966379	−	0.966379i
$220$	−0.308335	−	1.79249i	−0.0207880	−	0.120849i
$221$	−8.69285	−	9.57390i	−0.584744	−	0.644010i
$222$	−1.54661	−	1.54661i	−0.103802	−	0.103802i
$223$	15.2511			1.02129			0.510646	−	0.859791i	$-0.329406\pi$
$223$	15.2511			1.02129			0.510646	+	0.859791i	$0.329406\pi$
$224$		−	3.04808i		−	0.203658i
$225$	−29.6566	+	10.5139i	−1.97711	+	0.700926i
$226$	−0.670391	−	0.670391i	−0.0445937	−	0.0445937i
$227$			15.4292i			1.02407i	0.858964	+	0.512037i	$0.171109\pi$
$227$			15.4292i			1.02407i	−0.858964	+	0.512037i	$0.828891\pi$
$228$		−	26.9618i		−	1.78559i
$229$	−4.10191	−	4.10191i	−0.271062	−	0.271062i	0.558466	−	0.829528i	$-0.311390\pi$
$229$	−4.10191	−	4.10191i	−0.271062	−	0.271062i	−0.829528	+	0.558466i	$0.811390\pi$
$230$	0.163986	+	0.953323i	0.0108129	+	0.0628603i
$231$		−	2.38930i		−	0.157204i
$232$	−1.28739			−0.0845213
$233$	18.4776	+	18.4776i	1.21051	+	1.21051i	0.970859	+	0.239651i	$0.0770330\pi$
$233$	18.4776	+	18.4776i	1.21051	+	1.21051i	0.239651	+	0.970859i	$0.422967\pi$
$234$	−0.147169	+	3.05123i	−0.00962073	+	0.199465i
$235$	8.96131	−	12.6848i	0.584571	−	0.827463i
$236$	−16.4821	−	16.4821i	−1.07289	−	1.07289i
$237$	−9.48415	−	9.48415i	−0.616062	−	0.616062i
$238$	−0.652044	−	0.652044i	−0.0422658	−	0.0422658i
$239$	7.82819	−	7.82819i	0.506363	−	0.506363i	−0.407045	−	0.913408i	$-0.633441\pi$
$239$	7.82819	−	7.82819i	0.506363	−	0.506363i	0.913408	+	0.407045i	$0.133441\pi$
$240$	−4.49702	−	26.1431i	−0.290281	−	1.68753i
$241$	−9.29059	+	9.29059i	−0.598459	+	0.598459i	−0.939902	−	0.341443i	$-0.889084\pi$
$241$	−9.29059	+	9.29059i	−0.598459	+	0.598459i	0.341443	+	0.939902i	$0.389084\pi$
$242$	1.45827			0.0937413
$243$	3.97498	−	3.97498i	0.254995	−	0.254995i
$244$	14.2160			0.910085
$245$	4.32613	−	6.12366i	0.276386	−	0.391226i
$246$		−	0.881054i		−	0.0561739i
$247$	10.8163	+	11.9125i	0.688222	+	0.757975i
$248$	1.08340	−	1.08340i	0.0687962	−	0.0687962i
$249$	−29.0661	+	29.0661i	−1.84199	+	1.84199i
$250$	0.407803	−	1.44894i	0.0257918	−	0.0916387i
$251$			13.4477i			0.848810i	0.905472	+	0.424405i	$0.139517\pi$
$251$			13.4477i			0.848810i	−0.905472	+	0.424405i	$0.860483\pi$
$252$		−	23.8178i		−	1.50038i
$253$	−1.31876			−0.0829098
$254$	0.944768	+	0.944768i	0.0592800	+	0.0592800i
$255$	−19.9678	−	14.1065i	−1.25043	−	0.883381i
$256$	14.5696			0.910598
$257$	−2.36553	+	2.36553i	−0.147558	+	0.147558i	−0.777026	−	0.629468i	$-0.783273\pi$
$257$	−2.36553	+	2.36553i	−0.147558	+	0.147558i	0.629468	+	0.777026i	$0.283273\pi$
$258$		−	0.515850i		−	0.0321154i
$259$	−10.1773			−0.632388
$260$	12.5909	+	9.83753i	0.780857	+	0.610097i
$261$	−15.1124			−0.935436
$262$			1.52204i			0.0940319i
$263$	−10.3418	+	10.3418i	−0.637704	+	0.637704i	−0.949989	−	0.312285i	$-0.898906\pi$
$263$	−10.3418	+	10.3418i	−0.637704	+	0.637704i	0.312285	+	0.949989i	$0.398906\pi$
$264$	−0.670719			−0.0412799
$265$	−0.584496	−	3.39793i	−0.0359053	−	0.208733i
$266$	0.811319	+	0.811319i	0.0497452	+	0.0497452i
$267$	−43.2140			−2.64465
$268$		−	1.86293i		−	0.113796i
$269$			31.6138i			1.92753i	0.266754	+	0.963765i	$0.414049\pi$
$269$			31.6138i			1.92753i	−0.266754	+	0.963765i	$0.585951\pi$
$270$	0.512322	+	2.97835i	0.0311789	+	0.181256i
$271$	20.1850	−	20.1850i	1.22615	−	1.22615i	0.260742	−	0.965409i	$-0.416033\pi$
$271$	20.1850	−	20.1850i	1.22615	−	1.22615i	0.965409	−	0.260742i	$-0.0839671\pi$
$272$	9.86937	−	9.86937i	0.598419	−	0.598419i
$273$	14.1100	+	15.5401i	0.853975	+	0.940529i
$274$		−	0.258743i		−	0.0156313i
$275$	1.85250	+	0.882786i	0.111710	+	0.0532340i
$276$	−19.4131			−1.16853
$277$	9.04189	−	9.04189i	0.543275	−	0.543275i	−0.381213	−	0.924487i	$-0.624493\pi$
$277$	9.04189	−	9.04189i	0.543275	−	0.543275i	0.924487	+	0.381213i	$0.124493\pi$
$278$	−2.05871			−0.123473
$279$	12.7179	−	12.7179i	0.761399	−	0.761399i
$280$	1.86970	+	1.32087i	0.111736	+	0.0789372i
$281$	6.06213	−	6.06213i	0.361636	−	0.361636i	−0.502779	−	0.864415i	$-0.667689\pi$
$281$	6.06213	−	6.06213i	0.361636	−	0.361636i	0.864415	+	0.502779i	$0.167689\pi$
$282$	−2.01569	−	2.01569i	−0.120032	−	0.120032i
$283$	−10.6076	−	10.6076i	−0.630554	−	0.630554i	0.317653	−	0.948207i	$-0.397105\pi$
$283$	−10.6076	−	10.6076i	−0.630554	−	0.630554i	−0.948207	+	0.317653i	$0.897105\pi$
$284$	−14.6192	−	14.6192i	−0.867488	−	0.867488i
$285$	24.8453	+	17.5522i	1.47171	+	1.03971i
$286$	0.147497	−	0.133924i	0.00872170	−	0.00791907i
$287$	−2.89885	−	2.89885i	−0.171114	−	0.171114i
$288$	−10.0443			−0.591868
$289$			4.13652i			0.243325i
$290$	0.417141	−	0.590464i	0.0244953	−	0.0346733i
$291$	9.48415	+	9.48415i	0.555971	+	0.555971i
$292$			13.1487i			0.769468i
$293$		−	21.9991i		−	1.28520i	−0.766201	−	0.642601i	$-0.777855\pi$
$293$		−	21.9991i		−	1.28520i	0.766201	−	0.642601i	$-0.222145\pi$
$294$	−0.973086	−	0.973086i	−0.0567515	−	0.0567515i
$295$	25.9182	−	4.45832i	1.50901	−	0.259574i
$296$			2.85696i			0.166057i
$297$	−4.12003			−0.239069
$298$	−1.86184	−	1.86184i	−0.107853	−	0.107853i
$299$	8.57727	−	7.78793i	0.496036	−	0.450388i
$300$	27.2701	+	12.9952i	1.57444	+	0.750279i
$301$	−1.69725	−	1.69725i	−0.0978281	−	0.0978281i
$302$	1.15125	+	1.15125i	0.0662468	+	0.0662468i
$303$	−7.65259	−	7.65259i	−0.439630	−	0.439630i
$304$	−12.2802	+	12.2802i	−0.704316	+	0.704316i
$305$	−9.25467	+	13.1000i	−0.529921	+	0.750105i
$306$	−2.14868	+	2.14868i	−0.122832	+	0.122832i
$307$	9.59930			0.547861			0.273931	−	0.961749i	$-0.411676\pi$
$307$	9.59930			0.547861			0.273931	+	0.961749i	$0.411676\pi$
$308$	−1.09838	+	1.09838i	−0.0625860	+	0.0625860i
$309$	32.1121			1.82679
$310$	0.145861	+	0.847951i	0.00828433	+	0.0481604i
$311$		−	4.28684i		−	0.243084i	−0.992586	−	0.121542i	$-0.961216\pi$
$311$		−	4.28684i		−	0.243084i	0.992586	−	0.121542i	$-0.0387840\pi$
$312$	4.36238	−	3.96093i	0.246971	−	0.224243i
$313$	5.55258	−	5.55258i	0.313850	−	0.313850i	−0.532549	−	0.846399i	$-0.678766\pi$
$313$	5.55258	−	5.55258i	0.313850	−	0.313850i	0.846399	+	0.532549i	$0.178766\pi$
$314$	−0.539615	+	0.539615i	−0.0304523	+	0.0304523i
$315$	21.9481	+	15.5055i	1.23663	+	0.873635i
$316$			8.71989i			0.490532i
$317$		−	18.5306i		−	1.04078i	−0.853928	−	0.520391i	$-0.825786\pi$
$317$		−	18.5306i		−	1.04078i	0.853928	−	0.520391i	$-0.174214\pi$
$318$	−0.632831			−0.0354874
$319$	0.696925	+	0.696925i	0.0390203	+	0.0390203i
$320$	−9.76464	+	13.8219i	−0.545860	+	0.772667i
$321$	−41.2367			−2.30161
$322$	0.584167	−	0.584167i	0.0325544	−	0.0325544i
$323$			16.0056i			0.890578i
$324$	−23.2338			−1.29077
$325$	−17.2620	+	5.19827i	−0.957526	+	0.288348i
$326$	1.78967			0.0991204
$327$		−	34.8610i		−	1.92782i
$328$	−0.813760	+	0.813760i	−0.0449324	+	0.0449324i
$329$	−13.2641			−0.731271
$330$	0.217327	−	0.307627i	0.0119634	−	0.0169343i
$331$	1.66302	+	1.66302i	0.0914078	+	0.0914078i	0.751332	−	0.659924i	$-0.229412\pi$
$331$	1.66302	+	1.66302i	0.0914078	+	0.0914078i	−0.659924	+	0.751332i	$0.729412\pi$
$332$	26.7239			1.46666
$333$			33.5373i			1.83783i
$334$			1.74995i			0.0957530i
$335$	1.71669	+	1.21277i	0.0937927	+	0.0662610i
$336$	−16.0197	+	16.0197i	−0.873946	+	0.873946i
$337$	−7.30111	+	7.30111i	−0.397717	+	0.397717i	−0.877427	−	0.479710i	$-0.840742\pi$
$337$	−7.30111	+	7.30111i	−0.397717	+	0.397717i	0.479710	+	0.877427i	$0.340742\pi$
$338$	−0.168443	+	1.74209i	−0.00916209	+	0.0947572i
$339$			21.4671i			1.16593i
$340$	2.69448	+	15.6642i	0.146129	+	0.849511i
$341$	−1.17300			−0.0635212
$342$	2.67354	−	2.67354i	0.144568	−	0.144568i
$343$	−19.7712			−1.06755
$344$	−0.476450	+	0.476450i	−0.0256884	+	0.0256884i
$345$	12.6380	−	17.8891i	0.680407	−	0.963119i
$346$	−1.38741	+	1.38741i	−0.0745874	+	0.0745874i
$347$	−9.54455	−	9.54455i	−0.512378	−	0.512378i	0.402876	−	0.915254i	$-0.368010\pi$
$347$	−9.54455	−	9.54455i	−0.512378	−	0.512378i	−0.915254	+	0.402876i	$0.868010\pi$
$348$	10.2592	+	10.2592i	0.549952	+	0.549952i
$349$	18.1608	+	18.1608i	0.972127	+	0.972127i	0.999622	−	0.0274946i	$-0.00875290\pi$
$349$	18.1608	+	18.1608i	0.972127	+	0.972127i	−0.0274946	+	0.999622i	$0.508753\pi$
$350$	−1.21164	+	0.429553i	−0.0647650	+	0.0229606i
$351$	26.7969	−	24.3308i	1.43031	−	1.29868i
$352$	0.463205	+	0.463205i	0.0246889	+	0.0246889i
$353$	4.19276			0.223158			0.111579	−	0.993756i	$-0.464409\pi$
$353$	4.19276			0.223158			0.111579	+	0.993756i	$0.464409\pi$
$354$		−	4.82700i		−	0.256552i
$355$	22.9887	−	3.95441i	1.22011	−	0.209878i
$356$	19.8658	+	19.8658i	1.05289	+	1.05289i
$357$			20.8796i			1.10507i
$358$		−	0.887351i		−	0.0468979i
$359$	−6.13909	−	6.13909i	−0.324009	−	0.324009i	0.526294	−	0.850303i	$-0.323581\pi$
$359$	−6.13909	−	6.13909i	−0.324009	−	0.324009i	−0.850303	+	0.526294i	$0.823581\pi$
$360$	4.35267	−	6.16122i	0.229406	−	0.324725i
$361$		−	0.915340i		−	0.0481758i
$362$	−2.12655			−0.111769
$363$	−23.3483	−	23.3483i	−1.22547	−	1.22547i
$364$	0.657430	−	13.6304i	0.0344587	−	0.714427i
$365$	−12.1165	−	8.55985i	−0.634207	−	0.448043i
$366$	2.08167	+	2.08167i	0.108811	+	0.108811i
$367$	−4.59729	−	4.59729i	−0.239976	−	0.239976i	0.576864	−	0.816840i	$-0.304276\pi$
$367$	−4.59729	−	4.59729i	−0.239976	−	0.239976i	−0.816840	+	0.576864i	$0.804276\pi$
$368$	8.84198	+	8.84198i	0.460920	+	0.460920i
$369$	−9.55258	+	9.55258i	−0.497287	+	0.497287i
$370$	−1.31035	−	0.925714i	−0.0681219	−	0.0481256i
$371$	−2.08215	+	2.08215i	−0.108100	+	0.108100i
$372$	−17.2673			−0.895268
$373$	13.6188	−	13.6188i	0.705154	−	0.705154i	−0.260358	−	0.965512i	$-0.583841\pi$
$373$	13.6188	−	13.6188i	0.705154	−	0.705154i	0.965512	+	0.260358i	$0.0838407\pi$
$374$	0.198177			0.0102475
$375$	−29.7281	+	16.6695i	−1.53515	+	0.860807i
$376$			3.72346i			0.192023i
$377$	−8.64852	−	0.417141i	−0.445421	−	0.0214838i
$378$	1.82504	−	1.82504i	0.0938699	−	0.0938699i
$379$	19.3439	−	19.3439i	0.993631	−	0.993631i	−0.00634892	−	0.999980i	$-0.502021\pi$
$379$	19.3439	−	19.3439i	0.993631	−	0.993631i	0.999980	+	0.00634892i	$0.00202094\pi$
$380$	−3.35267	−	19.4905i	−0.171988	−	0.999841i
$381$		−	30.2532i		−	1.54992i
$382$			1.75178i			0.0896287i
$383$	−7.13110			−0.364382			−0.182191	−	0.983263i	$-0.558319\pi$
$383$	−7.13110			−0.364382			−0.182191	+	0.983263i	$0.558319\pi$
$384$	9.07743	+	9.07743i	0.463231	+	0.463231i
$385$	−0.297106	−	1.72721i	−0.0151419	−	0.0880267i
$386$	2.35381			0.119806
$387$	−5.59296	+	5.59296i	−0.284306	+	0.284306i
$388$		−	8.71989i		−	0.442685i
$389$	−25.6987			−1.30298			−0.651488	−	0.758659i	$-0.725855\pi$
$389$	−25.6987			−1.30298			−0.651488	+	0.758659i	$0.725855\pi$
$390$	0.403187	+	3.28424i	0.0204162	+	0.166304i
$391$	11.5244			0.582814
$392$			1.79753i			0.0907887i
$393$	24.3692	−	24.3692i	1.22926	−	1.22926i
$394$	1.92186			0.0968218
$395$	−8.03537	−	5.67669i	−0.404304	−	0.285625i
$396$	3.61949	+	3.61949i	0.181886	+	0.181886i
$397$	−14.8794			−0.746777			−0.373388	−	0.927675i	$-0.621804\pi$
$397$	−14.8794			−0.746777			−0.373388	+	0.927675i	$0.621804\pi$
$398$		−	0.641744i		−	0.0321677i
$399$		−	25.9799i		−	1.30062i
$400$	−6.50173	−	18.3395i	−0.325086	−	0.916974i
$401$	9.52637	−	9.52637i	0.475724	−	0.475724i	−0.428037	−	0.903761i	$-0.640795\pi$
$401$	9.52637	−	9.52637i	0.475724	−	0.475724i	0.903761	+	0.428037i	$0.140795\pi$
$402$	0.272792	−	0.272792i	0.0136056	−	0.0136056i
$403$	7.62921	−	6.92712i	0.380038	−	0.345064i
$404$			7.03592i			0.350050i
$405$	15.1253	−	21.4099i	0.751582	−	1.06387i
$406$	−0.617430			−0.0306425
$407$	1.54661	−	1.54661i	0.0766625	−	0.0766625i
$408$	5.86129			0.290177
$409$	8.19410	−	8.19410i	0.405172	−	0.405172i	−0.474879	−	0.880051i	$-0.657508\pi$
$409$	8.19410	−	8.19410i	0.405172	−	0.405172i	0.880051	+	0.474879i	$0.157508\pi$
$410$	−0.109558	−	0.636908i	−0.00541068	−	0.0314546i
$411$	−4.14271	+	4.14271i	−0.204345	+	0.204345i
$412$	−14.7622	−	14.7622i	−0.727282	−	0.727282i
$413$	−15.8819	−	15.8819i	−0.781495	−	0.781495i
$414$	−1.92501	−	1.92501i	−0.0946089	−	0.0946089i
$415$	−17.3974	+	24.6261i	−0.854004	+	1.20885i
$416$	−5.74815	−	0.277249i	−0.281826	−	0.0135932i
$417$	32.9618	+	32.9618i	1.61415	+	1.61415i
$418$	−0.246586			−0.0120609
$419$			26.7652i			1.30757i	0.756681	+	0.653784i	$0.226819\pi$
$419$			26.7652i			1.30757i	−0.756681	+	0.653784i	$0.773181\pi$
$420$	−4.37361	−	25.4257i	−0.213410	−	1.24065i
$421$	−25.6977	−	25.6977i	−1.25243	−	1.25243i	−0.954628	−	0.297800i	$-0.903747\pi$
$421$	−25.6977	−	25.6977i	−1.25243	−	1.25243i	−0.297800	−	0.954628i	$-0.596253\pi$
$422$		−	1.56207i		−	0.0760405i
$423$			43.7090i			2.12520i
$424$	0.584496	+	0.584496i	0.0283856	+	0.0283856i
$425$	−16.1887	−	7.71450i	−0.785266	−	0.374208i
$426$		−	4.28142i		−	0.207436i
$427$	13.6983			0.662906
$428$	18.9569	+	18.9569i	0.916314	+	0.916314i
$429$	−4.50580	−	0.217327i	−0.217542	−	0.0104926i
$430$	−0.0641453	−	0.372904i	−0.00309336	−	0.0179830i
$431$	−13.6422	−	13.6422i	−0.657120	−	0.657120i	0.297578	−	0.954698i	$-0.403821\pi$
$431$	−13.6422	−	13.6422i	−0.657120	−	0.657120i	−0.954698	+	0.297578i	$0.903821\pi$
$432$	27.6239	+	27.6239i	1.32905	+	1.32905i
$433$	25.0267	+	25.0267i	1.20271	+	1.20271i	0.973340	+	0.229365i	$0.0736650\pi$
$433$	25.0267	+	25.0267i	1.20271	+	1.20271i	0.229365	+	0.973340i	$0.426335\pi$
$434$	0.519598	−	0.519598i	0.0249415	−	0.0249415i
$435$	−16.1327	+	2.77507i	−0.773502	+	0.133054i
$436$	−16.0259	+	16.0259i	−0.767500	+	0.767500i
$437$	−14.3395			−0.685950
$438$	−1.92539	+	1.92539i	−0.0919985	+	0.0919985i
$439$	−32.0588			−1.53008			−0.765042	−	0.643981i	$-0.777282\pi$
$439$	−32.0588			−1.53008			−0.765042	+	0.643981i	$0.777282\pi$
$440$	−0.484858	+	0.0834032i	−0.0231147	+	0.00397609i
$441$			21.1008i			1.00480i
$442$	−1.28895	+	1.17033i	−0.0613092	+	0.0556671i
$443$	3.91063	−	3.91063i	0.185800	−	0.185800i	−0.608078	−	0.793877i	$-0.708059\pi$
$443$	3.91063	−	3.91063i	0.185800	−	0.185800i	0.793877	+	0.608078i	$0.208059\pi$
$444$	22.7671	−	22.7671i	1.08048	−	1.08048i
$445$	−31.2391	+	5.37361i	−1.48088	+	0.254734i
$446$		−	2.05329i		−	0.0972261i
$447$			59.6195i			2.81990i
$448$	14.4531			0.682845
$449$	2.54173	+	2.54173i	0.119952	+	0.119952i	0.764534	−	0.644583i	$-0.222969\pi$
$449$	2.54173	+	2.54173i	0.119952	+	0.119952i	−0.644583	+	0.764534i	$0.722969\pi$
$450$	1.41550	+	3.99272i	0.0667275	+	0.188219i
$451$	0.881054			0.0414872
$452$	9.86861	−	9.86861i	0.464180	−	0.464180i
$453$		−	36.8650i		−	1.73207i
$454$	2.07727			0.0974909
$455$	12.1324	+	9.47927i	0.568776	+	0.444395i
$456$	−7.29303			−0.341527
$457$		−	23.2189i		−	1.08613i	−0.839689	−	0.543067i	$-0.817263\pi$
$457$		−	23.2189i		−	1.08613i	0.839689	−	0.543067i	$-0.182737\pi$
$458$	−0.552248	+	0.552248i	−0.0258048	+	0.0258048i
$459$	36.0042			1.68053
$460$	−14.0336	+	2.41399i	−0.654319	+	0.112553i
$461$	28.8356	+	28.8356i	1.34301	+	1.34301i	0.893052	+	0.449954i	$0.148560\pi$
$461$	28.8356	+	28.8356i	1.34301	+	1.34301i	0.449954	+	0.893052i	$0.351440\pi$
$462$	−0.321676			−0.0149657
$463$		−	5.03192i		−	0.233853i	−0.993141	−	0.116927i	$-0.962696\pi$
$463$		−	5.03192i		−	0.233853i	0.993141	−	0.116927i	$-0.0373042\pi$
$464$		−	9.34544i		−	0.433851i
$465$	11.2411	−	15.9118i	0.521293	−	0.737893i
$466$	2.48768	−	2.48768i	0.115239	−	0.115239i
$467$	−4.64570	+	4.64570i	−0.214977	+	0.214977i	−0.806378	−	0.591401i	$-0.798575\pi$
$467$	−4.64570	+	4.64570i	−0.214977	+	0.214977i	0.591401	+	0.806378i	$0.298575\pi$
$468$	−44.9162	−	2.16643i	−2.07625	−	0.100143i
$469$		−	1.79509i		−	0.0828893i
$470$	−1.70777	−	1.20648i	−0.0787737	−	0.0556507i
$471$	17.2795			0.796195
$472$	−4.45832	+	4.45832i	−0.205211	+	0.205211i
$473$	0.515850			0.0237188
$474$	−1.27687	+	1.27687i	−0.0586485	+	0.0586485i
$475$	20.1431	+	9.59892i	0.924228	+	0.440429i
$476$	9.59854	−	9.59854i	0.439949	−	0.439949i
$477$	6.86129	+	6.86129i	0.314157	+	0.314157i
$478$	−1.05392	−	1.05392i	−0.0482053	−	0.0482053i
$479$	6.05279	+	6.05279i	0.276559	+	0.276559i	0.831734	−	0.555175i	$-0.187349\pi$
$479$	6.05279	+	6.05279i	0.276559	+	0.276559i	−0.555175	+	0.831734i	$0.687349\pi$
$480$	−10.7224	+	1.84442i	−0.489409	+	0.0841860i
$481$	−0.925714	+	19.1927i	−0.0422089	+	0.875111i
$482$	1.25081	+	1.25081i	0.0569728	+	0.0569728i
$483$	−18.7061			−0.851157
$484$			21.4668i			0.975763i
$485$	8.03537	+	5.67669i	0.364868	+	0.257765i
$486$	−0.535159	−	0.535159i	−0.0242753	−	0.0242753i
$487$		−	8.30574i		−	0.376369i	−0.982134	−	0.188184i	$-0.939740\pi$
$487$		−	8.30574i		−	0.376369i	0.982134	−	0.188184i	$-0.0602603\pi$
$488$		−	3.84535i		−	0.174071i
$489$	−28.6542	−	28.6542i	−1.29579	−	1.29579i
$490$	−0.824440	−	0.582435i	−0.0372444	−	0.0263117i
$491$			4.54905i			0.205296i	0.994718	+	0.102648i	$0.0327315\pi$
$491$			4.54905i			0.205296i	−0.994718	+	0.102648i	$0.967269\pi$
$492$	12.9697			0.584720
$493$	−6.09030	−	6.09030i	−0.274293	−	0.274293i
$494$	1.60380	−	1.45621i	0.0721586	−	0.0655181i
$495$	−5.69166	+	0.979054i	−0.255821	+	0.0440052i
$496$	7.86466	+	7.86466i	0.353134	+	0.353134i
$497$	−14.0868	−	14.0868i	−0.631878	−	0.631878i
$498$	3.91323	+	3.91323i	0.175356	+	0.175356i
$499$	10.9444	−	10.9444i	0.489937	−	0.489937i	−0.418349	−	0.908286i	$-0.637391\pi$
$499$	10.9444	−	10.9444i	0.489937	−	0.489937i	0.908286	+	0.418349i	$0.137391\pi$
$500$	21.3293	+	6.00315i	0.953877	+	0.268469i
$501$	28.0183	−	28.0183i	1.25176	−	1.25176i
$502$	1.81049			0.0808060
$503$	−9.60700	+	9.60700i	−0.428355	+	0.428355i	−0.888068	−	0.459713i	$-0.847952\pi$
$503$	−9.60700	+	9.60700i	−0.428355	+	0.428355i	0.459713	+	0.888068i	$0.347952\pi$
$504$	−6.44259			−0.286976
$505$	−6.48360	−	4.58042i	−0.288516	−	0.203826i
$506$			0.177547i			0.00789294i
$507$	30.5894	−	25.1955i	1.35852	−	1.11897i
$508$	−13.9076	+	13.9076i	−0.617052	+	0.617052i
$509$	−1.01052	+	1.01052i	−0.0447905	+	0.0447905i	−0.729147	−	0.684357i	$-0.760083\pi$
$509$	−1.01052	+	1.01052i	−0.0447905	+	0.0447905i	0.684357	+	0.729147i	$0.260083\pi$
$510$	−1.89918	+	2.68830i	−0.0840971	+	0.119040i
$511$			12.6698i			0.560481i
$512$		−	10.3838i		−	0.458904i
$513$	−44.7990			−1.97792
$514$	0.318476	+	0.318476i	0.0140474	+	0.0140474i
$515$	23.2136	−	3.99310i	1.02291	−	0.175957i
$516$	7.59366			0.334292
$517$	2.01569	−	2.01569i	0.0886497	−	0.0886497i
$518$			1.37019i			0.0602028i
$519$	44.4273			1.95014
$520$	2.66100	−	3.40579i	0.116693	−	0.149354i
$521$	39.4816			1.72972			0.864861	−	0.502012i	$-0.167406\pi$
$521$	39.4816			1.72972			0.864861	+	0.502012i	$0.167406\pi$
$522$			2.03461i			0.0890527i
$523$	−15.7663	+	15.7663i	−0.689411	+	0.689411i	−0.962102	−	0.272691i	$-0.912086\pi$
$523$	−15.7663	+	15.7663i	−0.689411	+	0.689411i	0.272691	+	0.962102i	$0.412086\pi$
$524$	−22.4055			−0.978787
$525$	26.2770	+	12.5220i	1.14682	+	0.546503i
$526$	1.39234	+	1.39234i	0.0607088	+	0.0607088i
$527$	10.2506			0.446523
$528$		−	4.86890i		−	0.211892i
$529$		−	12.6753i		−	0.551099i
$530$	−0.457469	+	0.0786918i	−0.0198712	+	0.00341815i
$531$	−52.3354	+	52.3354i	−2.27116	+	2.27116i
$532$	−11.9432	+	11.9432i	−0.517803	+	0.517803i
$533$	−5.73041	+	5.20306i	−0.248212	+	0.225369i
$534$			5.81798i			0.251769i
$535$	−29.8097	+	5.12773i	−1.28879	+	0.221691i
$536$	−0.503913			−0.0217657
$537$	−14.2073	+	14.2073i	−0.613089	+	0.613089i
$538$	4.25623			0.183499
$539$	0.973086	−	0.973086i	0.0419138	−	0.0419138i
$540$	−43.8433	+	7.54173i	−1.88672	+	0.324544i
$541$	−22.2954	+	22.2954i	−0.958554	+	0.958554i	−0.999175	−	0.0406207i	$-0.987066\pi$
$541$	−22.2954	+	22.2954i	−0.958554	+	0.958554i	0.0406207	+	0.999175i	$0.487066\pi$
$542$	−2.71754	−	2.71754i	−0.116728	−	0.116728i
$543$	34.0480	+	34.0480i	1.46114	+	1.46114i
$544$	−4.04786	−	4.04786i	−0.173551	−	0.173551i
$545$	−4.33492	−	25.2008i	−0.185688	−	1.07948i
$546$	2.09219	−	1.89965i	0.0895375	−	0.0812977i
$547$	3.38779	+	3.38779i	0.144851	+	0.144851i	0.775814	−	0.630962i	$-0.217340\pi$
$547$	3.38779	+	3.38779i	0.144851	+	0.144851i	−0.630962	+	0.775814i	$0.717340\pi$
$548$	3.80888			0.162707
$549$		−	45.1399i		−	1.92652i
$550$	0.118851	−	0.249406i	0.00506783	−	0.0106347i
$551$	7.57798	+	7.57798i	0.322833	+	0.322833i
$552$			5.25114i			0.223503i
$553$			8.40233i			0.357304i
$554$	−1.21733	−	1.21733i	−0.0517193	−	0.0517193i
$555$	6.15840	+	35.8014i	0.261409	+	1.51969i
$556$		−	30.3056i		−	1.28524i
$557$	−5.28065			−0.223748			−0.111874	−	0.993722i	$-0.535685\pi$
$557$	−5.28065			−0.223748			−0.111874	+	0.993722i	$0.535685\pi$
$558$	−1.71223	−	1.71223i	−0.0724845	−	0.0724845i
$559$	−3.35511	+	3.04635i	−0.141906	+	0.128847i
$560$	−9.58850	+	13.5726i	−0.405188	+	0.573545i
$561$	−3.17300	−	3.17300i	−0.133964	−	0.133964i
$562$	−0.816156	−	0.816156i	−0.0344275	−	0.0344275i
$563$	−29.6592	−	29.6592i	−1.24999	−	1.24999i	−0.955725	−	0.294261i	$-0.904927\pi$
$563$	−29.6592	−	29.6592i	−1.24999	−	1.24999i	−0.294261	−	0.955725i	$-0.595073\pi$
$564$	29.6723	−	29.6723i	1.24943	−	1.24943i
$565$	2.66941	+	15.5184i	0.112303	+	0.652866i
$566$	−1.42811	+	1.42811i	−0.0600281	+	0.0600281i
$567$	−22.3877			−0.940193
$568$	−3.95441	+	3.95441i	−0.165923	+	0.165923i
$569$	22.3322			0.936216			0.468108	−	0.883671i	$-0.344936\pi$
$569$	22.3322			0.936216			0.468108	+	0.883671i	$0.344936\pi$
$570$	2.36309	−	3.34497i	0.0989790	−	0.140105i
$571$		−	11.9099i		−	0.498415i	−0.968450	−	0.249207i	$-0.919830\pi$
$571$		−	11.9099i		−	0.498415i	0.968450	−	0.249207i	$-0.0801701\pi$
$572$	1.97145	+	2.17126i	0.0824304	+	0.0907851i
$573$	28.0475	−	28.0475i	1.17170	−	1.17170i
$574$	−0.390278	+	0.390278i	−0.0162899	+	0.0162899i
$575$	6.91143	−	14.5035i	0.288227	−	0.604836i
$576$		−	47.6273i		−	1.98447i
$577$		−	31.5179i		−	1.31211i	−0.754714	−	0.656053i	$-0.772225\pi$
$577$		−	31.5179i		−	1.31211i	0.754714	−	0.656053i	$-0.227775\pi$
$578$	0.556908			0.0231643
$579$	−37.6866	−	37.6866i	−1.56620	−	1.56620i
$580$	8.69204	+	6.14060i	0.360918	+	0.254975i
$581$	25.7507			1.06832
$582$	1.27687	−	1.27687i	0.0529279	−	0.0529279i
$583$		−	0.632831i		−	0.0262092i
$584$	3.55665			0.147175
$585$	31.2370	−	39.9799i	1.29149	−	1.65297i
$586$	−2.96178			−0.122350
$587$			33.0231i			1.36301i	0.731814	+	0.681505i	$0.238674\pi$
$587$			33.0231i			1.36301i	−0.731814	+	0.681505i	$0.761326\pi$
$588$	14.3245	−	14.3245i	0.590732	−	0.590732i
$589$	−12.7545			−0.525540
$590$	−0.600233	−	3.48941i	−0.0247112	−	0.143657i
$591$	−30.7707	−	30.7707i	−1.26574	−	1.26574i
$592$	−20.7393			−0.852380
$593$		−	20.1991i		−	0.829479i	−0.909940	−	0.414739i	$-0.863873\pi$
$593$		−	20.1991i		−	0.829479i	0.909940	−	0.414739i	$-0.136127\pi$
$594$			0.554688i			0.0227591i
$595$	2.59636	+	15.0938i	0.106440	+	0.618784i
$596$	27.4076	−	27.4076i	1.12266	−	1.12266i
$597$	−10.2749	+	10.2749i	−0.420524	+	0.420524i
$598$	−1.04850	−	1.15477i	−0.0428765	−	0.0472222i
$599$			10.8205i			0.442113i	0.975261	+	0.221057i	$0.0709505\pi$
$599$			10.8205i			0.442113i	−0.975261	+	0.221057i	$0.929049\pi$
$600$	3.51514	−	7.37643i	0.143505	−	0.301142i
$601$	−5.12131			−0.208903			−0.104451	−	0.994530i	$-0.533309\pi$
$601$	−5.12131			−0.208903			−0.104451	+	0.994530i	$0.533309\pi$
$602$	−0.228504	+	0.228504i	−0.00931315	+	0.00931315i
$603$	−5.91534			−0.240891
$604$	−16.9471	+	16.9471i	−0.689569	+	0.689569i
$605$	−19.7816	−	13.9750i	−0.804238	−	0.568164i
$606$	−1.03028	+	1.03028i	−0.0418524	+	0.0418524i
$607$	11.3669	+	11.3669i	0.461370	+	0.461370i	0.899104	−	0.437735i	$-0.144219\pi$
$607$	11.3669	+	11.3669i	0.461370	+	0.461370i	−0.437735	+	0.899104i	$0.644219\pi$
$608$	5.03663	+	5.03663i	0.204262	+	0.204262i
$609$	9.88561	+	9.88561i	0.400585	+	0.400585i
$610$	1.76368	+	1.24597i	0.0714093	+	0.0504480i
$611$	−1.20648	+	25.0137i	−0.0488089	+	1.01195i
$612$	−31.6301	−	31.6301i	−1.27857	−	1.27857i
$613$	31.0334			1.25343			0.626714	−	0.779250i	$-0.284400\pi$
$613$	31.0334			1.25343			0.626714	+	0.779250i	$0.284400\pi$
$614$		−	1.29237i		−	0.0521559i
$615$	−8.44335	+	11.9516i	−0.340469	+	0.481935i
$616$	0.297106	+	0.297106i	0.0119708	+	0.0119708i
$617$		−	39.2697i		−	1.58094i	−0.612502	−	0.790469i	$-0.709837\pi$
$617$		−	39.2697i		−	1.58094i	0.612502	−	0.790469i	$-0.290163\pi$
$618$		−	4.32331i		−	0.173909i
$619$	20.7839	+	20.7839i	0.835374	+	0.835374i	0.988246	−	0.152872i	$-0.0488523\pi$
$619$	20.7839	+	20.7839i	0.835374	+	0.835374i	−0.152872	+	0.988246i	$0.548852\pi$
$620$	−12.4824	+	2.14717i	−0.501306	+	0.0862324i
$621$			32.2562i			1.29440i
$622$	−0.577145			−0.0231414
$623$	19.1424	+	19.1424i	0.766923	+	0.766923i
$624$	28.7532	+	31.6675i	1.15105	+	1.26771i
$625$	−19.4174	+	15.7469i	−0.776696	+	0.629876i
$626$	−0.747554	−	0.747554i	−0.0298783	−	0.0298783i
$627$	3.94806	+	3.94806i	0.157670	+	0.157670i
$628$	−7.94351	−	7.94351i	−0.316981	−	0.316981i
$629$	−13.5155	+	13.5155i	−0.538899	+	0.538899i
$630$	2.08753	−	2.95491i	0.0831692	−	0.117726i
$631$	13.0898	−	13.0898i	0.521099	−	0.521099i	−0.396805	−	0.917903i	$-0.629881\pi$
$631$	13.0898	−	13.0898i	0.521099	−	0.521099i	0.917903	+	0.396805i	$0.129881\pi$
$632$	2.35869			0.0938235
$633$	−25.0102	+	25.0102i	−0.994066	+	0.994066i
$634$	−2.49481			−0.0990815
$635$	−3.76195	−	21.8698i	−0.149288	−	0.867878i
$636$		−	9.31571i		−	0.369392i
$637$	−0.582435	+	12.0755i	−0.0230769	+	0.478450i
$638$	0.0938283	−	0.0938283i	0.00371470	−	0.00371470i
$639$	−46.4201	+	46.4201i	−1.83635	+	1.83635i
$640$	7.69079	+	5.43325i	0.304005	+	0.214768i
$641$			41.7149i			1.64764i	0.566853	+	0.823819i	$0.308161\pi$
$641$			41.7149i			1.64764i	−0.566853	+	0.823819i	$0.691839\pi$
$642$			5.55177i			0.219111i
$643$	38.6757			1.52522			0.762610	−	0.646858i	$-0.223917\pi$
$643$	38.6757			1.52522			0.762610	+	0.646858i	$0.223917\pi$
$644$	8.59935	+	8.59935i	0.338862	+	0.338862i
$645$	−4.94351	+	6.99756i	−0.194651	+	0.275529i
$646$	2.15487			0.0847822
$647$	21.8936	−	21.8936i	0.860726	−	0.860726i	−0.130697	−	0.991422i	$-0.541721\pi$
$647$	21.8936	−	21.8936i	0.860726	−	0.860726i	0.991422	+	0.130697i	$0.0417214\pi$
$648$			6.28462i			0.246883i
$649$	4.82700			0.189477
$650$	0.699853	+	2.32402i	0.0274505	+	0.0911556i
$651$	−16.6385			−0.652113
$652$			26.3451i			1.03175i
$653$	−21.0962	+	21.0962i	−0.825558	+	0.825558i	−0.986899	−	0.161341i	$-0.948418\pi$
$653$	−21.0962	+	21.0962i	−0.825558	+	0.825558i	0.161341	+	0.986899i	$0.448418\pi$
$654$	−4.69340			−0.183526
$655$	14.5861	−	20.6466i	0.569924	−	0.806730i
$656$	−5.90726	−	5.90726i	−0.230640	−	0.230640i
$657$	41.7509			1.62886
$658$			1.78576i			0.0696164i
$659$			26.6328i			1.03747i	0.854936	+	0.518734i	$0.173596\pi$
$659$			26.6328i			1.03747i	−0.854936	+	0.518734i	$0.826404\pi$
$660$	4.52848	+	3.19920i	0.176271	+	0.124529i
$661$	−6.53609	+	6.53609i	−0.254224	+	0.254224i	−0.822700	−	0.568476i	$-0.807533\pi$
$661$	−6.53609	+	6.53609i	−0.254224	+	0.254224i	0.568476	+	0.822700i	$0.307533\pi$
$662$	0.223895	−	0.223895i	0.00870194	−	0.00870194i
$663$	39.3754	+	1.89918i	1.52921	+	0.0737580i
$664$		−	7.22868i		−	0.280527i
$665$	−3.23057	−	18.7807i	−0.125276	−	0.728285i
$666$	4.51519			0.174960
$667$	5.45631	−	5.45631i	0.211269	−	0.211269i
$668$	−25.7605			−0.996703
$669$	−32.8750	+	32.8750i	−1.27102	+	1.27102i
$670$	0.163278	−	0.231121i	0.00630799	−	0.00892898i
$671$	−2.08167	+	2.08167i	−0.0803620	+	0.0803620i
$672$	6.57037	+	6.57037i	0.253458	+	0.253458i
$673$	5.50580	+	5.50580i	0.212233	+	0.212233i	0.805215	−	0.592982i	$-0.202050\pi$
$673$	5.50580	+	5.50580i	0.212233	+	0.212233i	−0.592982	+	0.805215i	$0.702050\pi$
$674$	0.982962	+	0.982962i	0.0378623	+	0.0378623i
$675$	21.5925	−	45.3113i	0.831096	−	1.74403i
$676$	−25.6448	−	2.47960i	−0.986337	−	0.0953692i
$677$	1.67072	+	1.67072i	0.0642110	+	0.0642110i	0.738483	−	0.674272i	$-0.235542\pi$
$677$	1.67072	+	1.67072i	0.0642110	+	0.0642110i	−0.674272	+	0.738483i	$0.735542\pi$
$678$	2.89016			0.110996
$679$		−	8.40233i		−	0.322452i
$680$	4.23709	−	0.728845i	0.162485	−	0.0279499i
$681$	−33.2589	−	33.2589i	−1.27448	−	1.27448i
$682$			0.157923i			0.00604717i
$683$		−	42.2726i		−	1.61752i	−0.588141	−	0.808758i	$-0.700140\pi$
$683$		−	42.2726i		−	1.61752i	0.588141	−	0.808758i	$-0.299860\pi$
$684$	39.3563	+	39.3563i	1.50483	+	1.50483i
$685$	−2.47960	+	3.50988i	−0.0947406	+	0.134106i
$686$			2.66184i			0.101629i
$687$	17.6840			0.674685
$688$	−3.45865	−	3.45865i	−0.131860	−	0.131860i
$689$	3.73718	+	4.11596i	0.142375	+	0.156805i
$690$	−2.40845	−	1.70148i	−0.0916880	−	0.0647741i
$691$	−19.9284	−	19.9284i	−0.758110	−	0.758110i	0.217868	−	0.975978i	$-0.430090\pi$
$691$	−19.9284	−	19.9284i	−0.758110	−	0.758110i	−0.975978	+	0.217868i	$0.930090\pi$
$692$	−20.4236	−	20.4236i	−0.776388	−	0.776388i
$693$	3.48768	+	3.48768i	0.132486	+	0.132486i
$694$	−1.28500	+	1.28500i	−0.0487779	+	0.0487779i
$695$	27.9266	+	19.7291i	1.05932	+	0.748367i
$696$	2.77507	−	2.77507i	0.105189	−	0.105189i
$697$	−7.69937			−0.291634
$698$	2.44503	−	2.44503i	0.0925457	−	0.0925457i
$699$	−79.6599			−3.01302
$700$	−6.32331	−	17.8362i	−0.238999	−	0.674146i
$701$			13.2327i			0.499792i	0.968273	+	0.249896i	$0.0803964\pi$
$701$			13.2327i			0.499792i	−0.968273	+	0.249896i	$0.919604\pi$
$702$	−3.27571	−	3.60771i	−0.123634	−	0.136164i
$703$	16.8170	−	16.8170i	0.634264	−	0.634264i
$704$	−2.19638	+	2.19638i	−0.0827792	+	0.0827792i
$705$	8.02621	+	46.6598i	0.302284	+	1.75731i
$706$		−	0.564479i		−	0.0212444i
$707$			6.77969i			0.254977i
$708$	71.0568			2.67048
$709$	−5.07651	−	5.07651i	−0.190652	−	0.190652i	0.605326	−	0.795978i	$-0.293043\pi$
$709$	−5.07651	−	5.07651i	−0.190652	−	0.190652i	−0.795978	+	0.605326i	$0.793043\pi$
$710$	−0.532390	−	3.09501i	−0.0199802	−	0.116154i
$711$	27.6882			1.03839
$712$	5.37361	−	5.37361i	0.201385	−	0.201385i
$713$			9.18352i			0.343925i
$714$	2.81106			0.105201
$715$	−3.28424	+	0.403187i	−0.122824	+	0.0150784i
$716$	13.0624			0.488165
$717$			33.7485i			1.26036i
$718$	−0.826517	+	0.826517i	−0.0308453	+	0.0308453i
$719$	21.0560			0.785257			0.392628	−	0.919697i	$-0.371566\pi$
$719$	21.0560			0.785257			0.392628	+	0.919697i	$0.371566\pi$
$720$	44.7256	+	31.5970i	1.66683	+	1.17755i
$721$	−14.2246	−	14.2246i	−0.529752	−	0.529752i
$722$	−0.123234			−0.00458629
$723$		−	40.0532i		−	1.48959i
$724$		−	31.3043i		−	1.16342i
$725$	−11.3171	+	4.01216i	−0.420307	+	0.149008i
$726$	−3.14342	+	3.14342i	−0.116663	+	0.116663i
$727$	12.7325	−	12.7325i	0.472221	−	0.472221i	−0.430412	−	0.902633i	$-0.641632\pi$
$727$	12.7325	−	12.7325i	0.472221	−	0.472221i	0.902633	+	0.430412i	$0.141632\pi$
$728$	−3.68695	−	0.177831i	−0.136648	−	0.00659087i
$729$		−	18.0326i		−	0.667876i
$730$	−1.15243	+	1.63127i	−0.0426533	+	0.0603759i
$731$	−4.50792			−0.166731
$732$	−30.6436	+	30.6436i	−1.13262	+	1.13262i
$733$	−21.9710			−0.811517			−0.405759	−	0.913980i	$-0.632993\pi$
$733$	−21.9710			−0.811517			−0.405759	+	0.913980i	$0.632993\pi$
$734$	−0.618941	+	0.618941i	−0.0228455	+	0.0228455i
$735$	3.87471	+	22.5253i	0.142921	+	0.830859i
$736$	3.62648	−	3.62648i	0.133674	−	0.133674i
$737$	0.272792	+	0.272792i	0.0100484	+	0.0100484i
$738$	1.28608	+	1.28608i	0.0473413	+	0.0473413i
$739$	2.55220	+	2.55220i	0.0938841	+	0.0938841i	0.752489	−	0.658605i	$-0.228853\pi$
$739$	2.55220	+	2.55220i	0.0938841	+	0.0938841i	−0.658605	+	0.752489i	$0.728853\pi$
$740$	13.6271	−	19.2893i	0.500944	−	0.709088i
$741$	−48.9936	−	2.36309i	−1.79983	−	0.0868104i
$742$	0.280323	+	0.280323i	0.0102910	+	0.0102910i
$743$	9.53234			0.349708			0.174854	−	0.984594i	$-0.444055\pi$
$743$	9.53234			0.349708			0.174854	+	0.984594i	$0.444055\pi$
$744$			4.67072i			0.171237i
$745$	7.41361	+	43.0985i	0.271614	+	1.57901i
$746$	−1.83352	−	1.83352i	−0.0671300	−	0.0671300i
$747$		−	84.8562i		−	3.10472i
$748$			2.91731i			0.106667i
$749$	18.2665	+	18.2665i	0.667443	+	0.667443i
$750$	2.24424	+	4.00234i	0.0819481	+	0.146145i
$751$			3.05948i			0.111642i	0.998441	+	0.0558210i	$0.0177776\pi$
$751$			3.05948i			0.111642i	−0.998441	+	0.0558210i	$0.982222\pi$
$752$	−27.0294			−0.985661
$753$	−28.9875	−	28.9875i	−1.05636	−	1.05636i
$754$	−0.0561604	+	1.16437i	−0.00204524	+	0.0424037i
$755$	−4.58412	−	26.6494i	−0.166833	−	0.969873i
$756$	26.8658	+	26.8658i	0.977101	+	0.977101i
$757$	−12.1746	−	12.1746i	−0.442495	−	0.442495i	0.450355	−	0.892850i	$-0.351297\pi$
$757$	−12.1746	−	12.1746i	−0.442495	−	0.442495i	−0.892850	+	0.450355i	$0.851297\pi$
$758$	−2.60431	−	2.60431i	−0.0945928	−	0.0945928i
$759$	2.84269	−	2.84269i	0.103183	−	0.103183i
$760$	−5.27208	+	0.906880i	−0.191239	+	0.0328960i
$761$	−32.0020	+	32.0020i	−1.16007	+	1.16007i	−0.175614	+	0.984459i	$0.556191\pi$
$761$	−32.0020	+	32.0020i	−1.16007	+	1.16007i	−0.984459	+	0.175614i	$0.943809\pi$
$762$	−4.07304			−0.147551
$763$	−15.4423	+	15.4423i	−0.559047	+	0.559047i
$764$	−25.7874			−0.932954
$765$	49.7384	−	8.55578i	1.79830	−	0.309335i
$766$			0.960074i			0.0346889i
$767$	−31.3950	+	28.5059i	−1.13361	+	1.02929i
$768$	−31.4058	+	31.4058i	−1.13326	+	1.13326i
$769$	32.4213	−	32.4213i	1.16914	−	1.16914i	0.186730	−	0.982411i	$-0.440211\pi$
$769$	32.4213	−	32.4213i	1.16914	−	1.16914i	0.982411	−	0.186730i	$-0.0597891\pi$
$770$	−0.232537	+	0.0400000i	−0.00838006	+	0.00144150i
$771$		−	10.1982i		−	0.367278i
$772$			34.6496i			1.24707i
$773$	−41.2156			−1.48242			−0.741212	−	0.671271i	$-0.765749\pi$
$773$	−41.2156			−1.48242			−0.741212	+	0.671271i	$0.765749\pi$
$774$	0.752990	+	0.752990i	0.0270657	+	0.0270657i
$775$	6.14750	−	12.9004i	0.220825	−	0.463395i
$776$	−2.35869			−0.0846719
$777$	21.9380	−	21.9380i	0.787022	−	0.787022i
$778$			3.45987i			0.124042i
$779$	9.58009			0.343242
$780$	−48.3463	+	5.93520i	−1.73108	+	0.212514i
$781$	4.28142			0.153201
$782$		−	1.55155i		−	0.0554834i
$783$	17.0464	−	17.0464i	0.609190	−	0.609190i
$784$	−13.0486			−0.466022
$785$	12.4912	−	2.14868i	0.445830	−	0.0766897i
$786$	−3.28087	−	3.28087i	−0.117025	−	0.117025i
$787$	46.0209			1.64047			0.820234	−	0.572028i	$-0.193843\pi$
$787$	46.0209			1.64047			0.820234	+	0.572028i	$0.193843\pi$
$788$			28.2911i			1.00783i
$789$		−	44.5852i		−	1.58727i
$790$	−0.764263	+	1.08182i	−0.0271913	+	0.0384893i
$791$	9.50922	−	9.50922i	0.338109	−	0.338109i
$792$	0.979054	−	0.979054i	0.0347892	−	0.0347892i
$793$	1.24597	−	25.8326i	0.0442458	−	0.917341i
$794$			2.00324i			0.0710925i
$795$	8.58442	+	6.06457i	0.304458	+	0.215088i
$796$	9.44692			0.334837
$797$	31.8556	−	31.8556i	1.12838	−	1.12838i	0.137942	−	0.990440i	$-0.455951\pi$
$797$	31.8556	−	31.8556i	1.12838	−	1.12838i	0.990440	−	0.137942i	$-0.0440488\pi$
$798$	−3.49772			−0.123818
$799$	−17.6147	+	17.6147i	−0.623163	+	0.623163i
$800$	−7.52182	+	2.66664i	−0.265936	+	0.0942800i
$801$	63.0799	−	63.0799i	2.22882	−	2.22882i
$802$	−1.28255	−	1.28255i	−0.0452885	−	0.0452885i
$803$	−1.92539	−	1.92539i	−0.0679454	−	0.0679454i
$804$	4.01569	+	4.01569i	0.141622	+	0.141622i
$805$	−13.5225	+	2.32608i	−0.476606	+	0.0819836i
$806$	−0.932611	−	1.02713i	−0.0328498	−	0.0361793i
$807$	−68.1461	−	68.1461i	−2.39885	−	2.39885i
$808$	1.90318			0.0669537
$809$		−	16.8940i		−	0.593960i	−0.954884	−	0.296980i	$-0.904020\pi$
$809$		−	16.8940i		−	0.593960i	0.954884	−	0.296980i	$-0.0959795\pi$
$810$	−2.88246	−	2.03635i	−0.101279	−	0.0715499i
$811$	13.2761	+	13.2761i	0.466186	+	0.466186i	0.900677	−	0.434490i	$-0.143071\pi$
$811$	13.2761	+	13.2761i	0.466186	+	0.466186i	−0.434490	+	0.900677i	$0.643071\pi$
$812$		−	9.08899i		−	0.318961i
$813$			87.0206i			3.05195i
$814$	−0.208223	−	0.208223i	−0.00729820	−	0.00729820i
$815$	−24.2770	−	17.1508i	−0.850387	−	0.600766i
$816$			42.5484i			1.48949i
$817$	5.60907			0.196236
$818$	−1.10319	−	1.10319i	−0.0385720	−	0.0385720i
$819$	−43.2805	−	2.08753i	−1.51234	−	0.0729442i
$820$	9.37572	−	1.61277i	0.327414	−	0.0563204i
$821$	3.78395	+	3.78395i	0.132061	+	0.132061i	0.770047	−	0.637987i	$-0.220233\pi$
$821$	3.78395	+	3.78395i	0.132061	+	0.132061i	−0.637987	+	0.770047i	$0.720233\pi$
$822$	0.557741	+	0.557741i	0.0194535	+	0.0194535i
$823$	−17.1423	−	17.1423i	−0.597544	−	0.597544i	0.342114	−	0.939658i	$-0.388857\pi$
$823$	−17.1423	−	17.1423i	−0.597544	−	0.597544i	−0.939658	+	0.342114i	$0.888857\pi$
$824$	−3.99310	+	3.99310i	−0.139106	+	0.139106i
$825$	−5.89613	+	2.09030i	−0.205277	+	0.0727749i
$826$	−2.13820	+	2.13820i	−0.0743976	+	0.0743976i
$827$	−43.2856			−1.50519			−0.752594	−	0.658484i	$-0.771198\pi$
$827$	−43.2856			−1.50519			−0.752594	+	0.658484i	$0.771198\pi$
$828$	28.3374	−	28.3374i	0.984793	−	0.984793i
$829$	−1.24389			−0.0432021			−0.0216011	−	0.999767i	$-0.506876\pi$
$829$	−1.24389			−0.0432021			−0.0216011	+	0.999767i	$0.506876\pi$
$830$	3.31545	+	2.34224i	0.115081	+	0.0813004i
$831$			38.9810i			1.35224i
$832$	1.31463	−	27.2561i	0.0455767	−	0.944934i
$833$	−8.50362	+	8.50362i	−0.294633	+	0.294633i
$834$	4.43771	−	4.43771i	0.153665	−	0.153665i
$835$	16.7702	−	23.7383i	0.580356	−	0.821497i
$836$		−	3.62992i		−	0.125543i
$837$			28.6909i			0.991702i
$838$	3.60345			0.124479
$839$	0.836014	+	0.836014i	0.0288624	+	0.0288624i	0.721391	−	0.692528i	$-0.243503\pi$
$839$	0.836014	+	0.836014i	0.0288624	+	0.0288624i	−0.692528	+	0.721391i	$0.743503\pi$
$840$	−6.87753	+	1.18304i	−0.237297	+	0.0408188i
$841$	23.2330			0.801138
$842$	−3.45973	+	3.45973i	−0.119230	+	0.119230i
$843$			26.1348i			0.900130i
$844$	22.9948			0.791513
$845$	18.9798	−	22.0174i	0.652925	−	0.757422i
$846$	5.88463			0.202318
$847$			20.6850i			0.710746i
$848$	−4.24298	+	4.24298i	−0.145705	+	0.145705i
$849$	45.7308			1.56948
$850$	−1.03862	+	2.17951i	−0.0356243	+	0.0747567i
$851$	−12.1086	−	12.1086i	−0.415077	−	0.415077i
$852$	63.0255			2.15922
$853$		−	29.9196i		−	1.02443i	−0.858858	−	0.512213i	$-0.828826\pi$
$853$		−	29.9196i		−	1.02443i	0.858858	−	0.512213i	$-0.171174\pi$
$854$		−	1.84422i		−	0.0631080i
$855$	−61.8880	+	10.6457i	−2.11653	+	0.364075i
$856$	5.12773	−	5.12773i	0.175262	−	0.175262i
$857$	−25.1427	+	25.1427i	−0.858859	+	0.858859i	−0.991204	−	0.132345i	$-0.957749\pi$
$857$	−25.1427	+	25.1427i	−0.858859	+	0.858859i	0.132345	+	0.991204i	$0.457749\pi$
$858$	−0.0292591	+	0.606625i	−0.000998890	+	0.0207098i
$859$		−	27.3069i		−	0.931699i	−0.884864	−	0.465850i	$-0.845749\pi$
$859$		−	27.3069i		−	0.931699i	0.884864	−	0.465850i	$-0.154251\pi$
$860$	5.48941	−	0.944263i	0.187187	−	0.0321991i
$861$	12.4974			0.425910
$862$	−1.83667	+	1.83667i	−0.0625573	+	0.0625573i
$863$	1.25980			0.0428841			0.0214421	−	0.999770i	$-0.493174\pi$
$863$	1.25980			0.0428841			0.0214421	+	0.999770i	$0.493174\pi$
$864$	11.3298	−	11.3298i	0.385446	−	0.385446i
$865$	32.1162	−	5.52448i	1.09198	−	0.187838i
$866$	3.36939	−	3.36939i	0.114497	−	0.114497i
$867$	−8.91660	−	8.91660i	−0.302824	−	0.302824i
$868$	7.64884	+	7.64884i	0.259619	+	0.259619i
$869$	−1.27687	−	1.27687i	−0.0433148	−	0.0433148i
$870$	0.373613	+	2.17197i	0.0126667	+	0.0736367i
$871$	−3.38522	−	0.163278i	−0.114704	−	0.00553247i
$872$	4.33492	+	4.33492i	0.146799	+	0.146799i
$873$	−27.6882			−0.937103
$874$			1.93055i			0.0653018i
$875$	20.5526	+	5.78453i	0.694804	+	0.195553i
$876$	−28.3430	−	28.3430i	−0.957621	−	0.957621i
$877$			30.9560i			1.04531i	0.852544	+	0.522655i	$0.175059\pi$
$877$			30.9560i			1.04531i	−0.852544	+	0.522655i	$0.824941\pi$
$878$			4.31614i			0.145663i
$879$	47.4208	+	47.4208i	1.59946	+	1.59946i
$880$	−0.605442	−	3.51969i	−0.0204094	−	0.118649i
$881$		−	20.3144i		−	0.684409i	−0.939625	−	0.342205i	$-0.888826\pi$
$881$		−	20.3144i		−	0.684409i	0.939625	−	0.342205i	$-0.111174\pi$
$882$	2.84084			0.0956562
$883$	3.19427	+	3.19427i	0.107496	+	0.107496i	0.758809	−	0.651313i	$-0.225782\pi$
$883$	3.19427	+	3.19427i	0.107496	+	0.107496i	−0.651313	+	0.758809i	$0.725782\pi$
$884$	−17.2281	−	18.9743i	−0.579445	−	0.638174i
$885$	−46.2583	+	65.4789i	−1.55496	+	2.20105i
$886$	−0.526495	−	0.526495i	−0.0176880	−	0.0176880i
$887$	36.4242	+	36.4242i	1.22300	+	1.22300i	0.966559	+	0.256446i	$0.0825515\pi$
$887$	36.4242	+	36.4242i	1.22300	+	1.22300i	0.256446	+	0.966559i	$0.417448\pi$
$888$	−6.15840	−	6.15840i	−0.206662	−	0.206662i
$889$	−13.4012	+	13.4012i	−0.449461	+	0.449461i
$890$	0.723460	+	4.20578i	0.0242504	+	0.140978i
$891$	3.40216	−	3.40216i	0.113977	−	0.113977i
$892$	30.2258			1.01204
$893$	21.9175	−	21.9175i	0.733440	−	0.733440i
$894$	8.02668			0.268452
$895$	−8.50369	+	12.0370i	−0.284247	+	0.402353i
$896$		−	8.04201i		−	0.268665i
$897$	−1.70148	+	35.2765i	−0.0568107	+	1.17785i
$898$	0.342198	−	0.342198i	0.0114193	−	0.0114193i
$899$	4.85321	−	4.85321i	0.161864	−	0.161864i
$900$	−58.7756	+	20.8372i	−1.95919	+	0.694573i
$901$			5.53019i			0.184237i
$902$		−	0.118618i		−	0.00394954i
$903$	7.31712			0.243499
$904$	−2.66941	−	2.66941i	−0.0887833	−	0.0887833i
$905$	28.8469	+	20.3793i	0.958904	+	0.677429i
$906$	−4.96320			−0.164891
$907$	−9.20854	+	9.20854i	−0.305764	+	0.305764i	−0.843264	−	0.537500i	$-0.819369\pi$
$907$	−9.20854	+	9.20854i	−0.305764	+	0.305764i	0.537500	+	0.843264i	$0.319369\pi$
$908$			30.5788i			1.01479i
$909$	22.3411			0.741008
$910$	1.27621	−	1.63341i	0.0423060	−	0.0541470i
$911$	−34.8310			−1.15400			−0.577001	−	0.816743i	$-0.695777\pi$
$911$	−34.8310			−1.15400			−0.577001	+	0.816743i	$0.695777\pi$
$912$		−	52.9417i		−	1.75307i
$913$	−3.91323	+	3.91323i	−0.129509	+	0.129509i
$914$	−3.12600			−0.103399
$915$	−8.28895	−	48.1873i	−0.274024	−	1.59302i
$916$	−8.12947	−	8.12947i	−0.268605	−	0.268605i
$917$	−21.5895			−0.712949
$918$		−	4.84732i		−	0.159985i
$919$			31.7568i			1.04756i	0.851854	+	0.523779i	$0.175478\pi$
$919$			31.7568i			1.04756i	−0.851854	+	0.523779i	$0.824522\pi$
$920$	0.652973	+	3.79601i	0.0215279	+	0.125151i
$921$	−20.6920	+	20.6920i	−0.681826	+	0.681826i
$922$	3.88219	−	3.88219i	0.127853	−	0.127853i
$923$	−27.8465	+	25.2839i	−0.916580	+	0.832230i
$924$		−	4.73529i		−	0.155780i
$925$	8.90373	+	25.1148i	0.292753	+	0.825770i
$926$	−0.677457			−0.0222626
$927$	−46.8743	+	46.8743i	−1.53955	+	1.53955i
$928$	−3.83297			−0.125824
$929$	7.17522	−	7.17522i	0.235411	−	0.235411i	−0.579536	−	0.814947i	$-0.696766\pi$
$929$	7.17522	−	7.17522i	0.235411	−	0.235411i	0.814947	+	0.579536i	$0.196766\pi$
$930$	−2.14224	−	1.51341i	−0.0702467	−	0.0496266i
$931$	10.5808	−	10.5808i	0.346772	−	0.346772i
$932$	36.6203	+	36.6203i	1.19954	+	1.19954i
$933$	9.24062	+	9.24062i	0.302524	+	0.302524i
$934$	0.625459	+	0.625459i	0.0204656	+	0.0204656i
$935$	−2.68830	−	1.89918i	−0.0879167	−	0.0621098i
$936$	−0.586008	+	12.1496i	−0.0191543	+	0.397122i
$937$	7.87778	+	7.87778i	0.257356	+	0.257356i	0.823978	−	0.566622i	$-0.191750\pi$
$937$	7.87778	+	7.87778i	0.257356	+	0.257356i	−0.566622	+	0.823978i	$0.691750\pi$
$938$	−0.241676			−0.00789099
$939$			23.9380i			0.781188i
$940$	17.7602	−	25.1396i	0.579273	−	0.819964i
$941$	4.01889	+	4.01889i	0.131012	+	0.131012i	0.769572	−	0.638560i	$-0.220470\pi$
$941$	4.01889	+	4.01889i	0.131012	+	0.131012i	−0.638560	+	0.769572i	$0.720470\pi$
$942$		−	2.32637i		−	0.0757971i
$943$		−	6.89787i		−	0.224626i
$944$	−32.3639	−	32.3639i	−1.05336	−	1.05336i
$945$	−42.2467	+	7.26708i	−1.37428	+	0.236398i
$946$		−	0.0694498i		−	0.00225801i
$947$	46.1032			1.49815			0.749076	−	0.662484i	$-0.230498\pi$
$947$	46.1032			1.49815			0.749076	+	0.662484i	$0.230498\pi$
$948$	−18.7964	−	18.7964i	−0.610478	−	0.610478i
$949$	23.8931	+	1.15243i	0.775604	+	0.0374094i
$950$	1.29232	−	2.71190i	0.0419284	−	0.0879857i
$951$	39.9441	+	39.9441i	1.29528	+	1.29528i
$952$	−2.59636	−	2.59636i	−0.0841485	−	0.0841485i
$953$	24.8080	+	24.8080i	0.803610	+	0.803610i	0.983658	−	0.180048i	$-0.0576253\pi$
$953$	24.8080	+	24.8080i	0.803610	+	0.803610i	−0.180048	+	0.983658i	$0.557625\pi$
$954$	0.923749	−	0.923749i	0.0299075	−	0.0299075i
$955$	16.7877	−	23.7631i	0.543237	−	0.768954i
$956$	15.5145	−	15.5145i	0.501774	−	0.501774i
$957$	−3.00455			−0.0971234
$958$	0.814899	−	0.814899i	0.0263282	−	0.0263282i
$959$	3.67017			0.118516
$960$	−8.74571	−	50.8426i	−0.282267	−	1.64094i
$961$		−	22.8316i		−	0.736502i
$962$	2.58395	+	0.124631i	0.0833098	+	0.00401825i
$963$	60.1935	−	60.1935i	1.93971	−	1.93971i
$964$	−18.4128	+	18.4128i	−0.593036	+	0.593036i
$965$	−31.9296	−	22.5571i	−1.02785	−	0.726138i
$966$			2.51844i			0.0810294i
$967$			58.4700i			1.88027i	0.340803	+	0.940135i	$0.389301\pi$
$967$			58.4700i			1.88027i	−0.340803	+	0.940135i	$0.610699\pi$
$968$	5.80666			0.186633
$969$	−34.5014	−	34.5014i	−1.10834	−	1.10834i
$970$	0.764263	−	1.08182i	0.0245390	−	0.0347351i
$971$	−20.3886			−0.654303			−0.327151	−	0.944972i	$-0.606089\pi$
$971$	−20.3886			−0.654303			−0.327151	+	0.944972i	$0.606089\pi$
$972$	7.87791	−	7.87791i	0.252684	−	0.252684i
$973$		−	29.2020i		−	0.936172i
$974$	−1.11822			−0.0358300
$975$	26.0044	−	48.4149i	0.832807	−	1.55052i
$976$	27.9142			0.893513
$977$			14.0603i			0.449830i	0.974378	+	0.224915i	$0.0722105\pi$
$977$			14.0603i			0.449830i	−0.974378	+	0.224915i	$0.927790\pi$
$978$	−3.85776	+	3.85776i	−0.123358	+	0.123358i
$979$	−5.81798			−0.185944
$980$	8.57385	−	12.1363i	0.273882	−	0.387681i
$981$	50.8868	+	50.8868i	1.62469	+	1.62469i
$982$	0.612447			0.0195440
$983$			1.48069i			0.0472266i	0.999721	+	0.0236133i	$0.00751704\pi$
$983$			1.48069i			0.0472266i	−0.999721	+	0.0236133i	$0.992483\pi$
$984$		−	3.50824i		−	0.111839i
$985$	−26.0702	−	18.4176i	−0.830666	−	0.586834i
$986$	−0.819949	+	0.819949i	−0.0261125	+	0.0261125i
$987$	28.5917	−	28.5917i	0.910084	−	0.910084i
$988$	21.4364	+	23.6091i	0.681984	+	0.751106i
$989$		−	4.03865i		−	0.128422i
$990$	0.131812	+	0.766280i	0.00418926	+	0.0243540i
$991$	8.59028			0.272879			0.136440	−	0.990648i	$-0.456434\pi$
$991$	8.59028			0.272879			0.136440	+	0.990648i	$0.456434\pi$
$992$	3.22564	−	3.22564i	0.102414	−	0.102414i
$993$	−7.16953			−0.227518
$994$	−1.89653	+	1.89653i	−0.0601542	+	0.0601542i
$995$	−6.14999	+	8.70533i	−0.194968	+	0.275978i
$996$	−57.6054	+	57.6054i	−1.82530	+	1.82530i
$997$	−8.77426	−	8.77426i	−0.277884	−	0.277884i	0.554380	−	0.832264i	$-0.312955\pi$
$997$	−8.77426	−	8.77426i	−0.277884	−	0.277884i	−0.832264	+	0.554380i	$0.812955\pi$
$998$	−1.47346	−	1.47346i	−0.0466416	−	0.0466416i
$999$	−37.8293	−	37.8293i	−1.19686	−	1.19686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.f.b.47.3	yes	8
3.2	odd	2		585.2.n.e.307.2		8
4.3	odd	2		1040.2.cd.n.177.4		8
5.2	odd	4		325.2.k.b.268.2		8
5.3	odd	4		65.2.k.b.8.3	yes	8
5.4	even	2		325.2.f.b.307.2		8
13.2	odd	12		845.2.o.d.357.2		16
13.3	even	3		845.2.t.c.657.2		16
13.4	even	6		845.2.t.d.427.2		16
13.5	odd	4		65.2.k.b.57.3	yes	8
13.6	odd	12		845.2.o.d.587.2		16
13.7	odd	12		845.2.o.c.587.3		16
13.8	odd	4		845.2.k.b.577.2		8
13.9	even	3		845.2.t.c.427.3		16
13.10	even	6		845.2.t.d.657.3		16
13.11	odd	12		845.2.o.c.357.3		16
13.12	even	2		845.2.f.b.437.2		8
15.8	even	4		585.2.w.e.73.2		8
20.3	even	4		1040.2.bg.n.593.4		8
39.5	even	4		585.2.w.e.577.2		8
52.31	even	4		1040.2.bg.n.577.4		8
65.3	odd	12		845.2.o.d.488.2		16
65.8	even	4		845.2.f.b.408.3		8
65.18	even	4	inner	65.2.f.b.18.2	✓	8
65.23	odd	12		845.2.o.c.488.3		16
65.28	even	12		845.2.t.c.188.3		16
65.33	even	12		845.2.t.d.418.3		16
65.38	odd	4		845.2.k.b.268.2		8
65.43	odd	12		845.2.o.c.258.3		16
65.44	odd	4		325.2.k.b.57.2		8
65.48	odd	12		845.2.o.d.258.2		16
65.57	even	4		325.2.f.b.18.3		8
65.58	even	12		845.2.t.c.418.2		16
65.63	even	12		845.2.t.d.188.2		16
195.83	odd	4		585.2.n.e.343.3		8
260.83	odd	4		1040.2.cd.n.993.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.f.b.18.2	✓	8	65.18	even	4	inner
65.2.f.b.47.3	yes	8	1.1	even	1	trivial
65.2.k.b.8.3	yes	8	5.3	odd	4
65.2.k.b.57.3	yes	8	13.5	odd	4
325.2.f.b.18.3		8	65.57	even	4
325.2.f.b.307.2		8	5.4	even	2
325.2.k.b.57.2		8	65.44	odd	4
325.2.k.b.268.2		8	5.2	odd	4
585.2.n.e.307.2		8	3.2	odd	2
585.2.n.e.343.3		8	195.83	odd	4
585.2.w.e.73.2		8	15.8	even	4
585.2.w.e.577.2		8	39.5	even	4
845.2.f.b.408.3		8	65.8	even	4
845.2.f.b.437.2		8	13.12	even	2
845.2.k.b.268.2		8	65.38	odd	4
845.2.k.b.577.2		8	13.8	odd	4
845.2.o.c.258.3		16	65.43	odd	12
845.2.o.c.357.3		16	13.11	odd	12
845.2.o.c.488.3		16	65.23	odd	12
845.2.o.c.587.3		16	13.7	odd	12
845.2.o.d.258.2		16	65.48	odd	12
845.2.o.d.357.2		16	13.2	odd	12
845.2.o.d.488.2		16	65.3	odd	12
845.2.o.d.587.2		16	13.6	odd	12
845.2.t.c.188.3		16	65.28	even	12
845.2.t.c.418.2		16	65.58	even	12
845.2.t.c.427.3		16	13.9	even	3
845.2.t.c.657.2		16	13.3	even	3
845.2.t.d.188.2		16	65.63	even	12
845.2.t.d.418.3		16	65.33	even	12
845.2.t.d.427.2		16	13.4	even	6
845.2.t.d.657.3		16	13.10	even	6
1040.2.bg.n.577.4		8	52.31	even	4
1040.2.bg.n.593.4		8	20.3	even	4
1040.2.cd.n.177.4		8	4.3	odd	2
1040.2.cd.n.993.4		8	260.83	odd	4

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.134632i q^{2} +(-2.15558 + 2.15558i) q^{3} +1.98187 q^{4} +(-1.29021 + 1.82630i) q^{5} +(0.290209 + 0.290209i) q^{6} +1.90970 q^{7} -0.536087i q^{8} -6.29303i q^{9} +O(q^{10})\)	\(q-0.134632i q^{2} +(-2.15558 + 2.15558i) q^{3} +1.98187 q^{4} +(-1.29021 + 1.82630i) q^{5} +(0.290209 + 0.290209i) q^{6} +1.90970 q^{7} -0.536087i q^{8} -6.29303i q^{9} +(0.245878 + 0.173703i) q^{10} +(-0.290209 + 0.290209i) q^{11} +(-4.27208 + 4.27208i) q^{12} +(0.173703 - 3.60136i) q^{13} -0.257106i q^{14} +(-1.15558 - 6.71787i) q^{15} +3.89157 q^{16} +(2.53609 - 2.53609i) q^{17} -0.847242 q^{18} +(-3.15558 + 3.15558i) q^{19} +(-2.55703 + 3.61949i) q^{20} +(-4.11651 + 4.11651i) q^{21} +(0.0390714 + 0.0390714i) q^{22} +(2.27208 + 2.27208i) q^{23} +(1.15558 + 1.15558i) q^{24} +(-1.67072 - 4.71261i) q^{25} +(-0.484858 - 0.0233860i) q^{26} +(7.09838 + 7.09838i) q^{27} +3.78478 q^{28} -2.40146i q^{29} +(-0.904440 + 0.155578i) q^{30} +(2.02095 + 2.02095i) q^{31} -1.59610i q^{32} -1.25114i q^{33} +(-0.341438 - 0.341438i) q^{34} +(-2.46391 + 3.48768i) q^{35} -12.4720i q^{36} -5.32928 q^{37} +(0.424841 + 0.424841i) q^{38} +(7.38859 + 8.13745i) q^{39} +(0.979054 + 0.691665i) q^{40} +(-1.51796 - 1.51796i) q^{41} +(0.554213 + 0.554213i) q^{42} +(-0.888754 - 0.888754i) q^{43} +(-0.575159 + 0.575159i) q^{44} +(11.4929 + 8.11933i) q^{45} +(0.305895 - 0.305895i) q^{46} -6.94562 q^{47} +(-8.38859 + 8.38859i) q^{48} -3.35305 q^{49} +(-0.634468 + 0.224932i) q^{50} +10.9335i q^{51} +(0.344258 - 7.13745i) q^{52} +(-1.09030 + 1.09030i) q^{53} +(0.955668 - 0.955668i) q^{54} +(-0.155578 - 0.904440i) q^{55} -1.02377i q^{56} -13.6042i q^{57} -0.323312 q^{58} +(-8.31642 - 8.31642i) q^{59} +(-2.29021 - 13.3140i) q^{60} +7.17300 q^{61} +(0.272084 - 0.272084i) q^{62} -12.0178i q^{63} +7.56826 q^{64} +(6.35305 + 4.96375i) q^{65} -0.168443 q^{66} -0.939983i q^{67} +(5.02621 - 5.02621i) q^{68} -9.79531 q^{69} +(0.469553 + 0.331721i) q^{70} +(-7.37643 - 7.37643i) q^{71} -3.37361 q^{72} +6.63447i q^{73} +0.717491i q^{74} +(13.7598 + 6.55703i) q^{75} +(-6.25396 + 6.25396i) q^{76} +(-0.554213 + 0.554213i) q^{77} +(1.09556 - 0.994740i) q^{78} +4.39982i q^{79} +(-5.02095 + 7.10717i) q^{80} -11.7231 q^{81} +(-0.204366 + 0.204366i) q^{82} +13.4842 q^{83} +(-8.15840 + 8.15840i) q^{84} +(1.35956 + 7.90373i) q^{85} +(-0.119655 + 0.119655i) q^{86} +(5.17652 + 5.17652i) q^{87} +(0.155578 + 0.155578i) q^{88} +(10.0238 + 10.0238i) q^{89} +(1.09312 - 1.54732i) q^{90} +(0.331721 - 6.87753i) q^{91} +(4.50298 + 4.50298i) q^{92} -8.71261 q^{93} +0.935102i q^{94} +(-1.69166 - 9.83438i) q^{95} +(3.44053 + 3.44053i) q^{96} -4.39982i q^{97} +0.451427i q^{98} +(1.82630 + 1.82630i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 6 q^{6}+O(q^{10}) \) 8 * q - 6 * q^3 - 8 * q^4 - 2 * q^5 - 6 * q^6	\( 8 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 6 q^{6} + 6 q^{10} + 6 q^{11} - 2 q^{12} + 14 q^{13} + 2 q^{15} - 8 q^{16} + 16 q^{17} + 20 q^{18} - 14 q^{19} - 2 q^{20} - 12 q^{21} + 10 q^{22} - 14 q^{23} - 2 q^{24} - 12 q^{25} + 6 q^{26} + 12 q^{27} - 8 q^{28} - 14 q^{30} + 2 q^{31} - 24 q^{35} - 44 q^{37} - 2 q^{38} + 6 q^{39} + 22 q^{40} + 16 q^{41} + 24 q^{42} - 6 q^{43} - 10 q^{44} + 22 q^{45} + 2 q^{46} + 16 q^{47} - 14 q^{48} + 24 q^{49} + 44 q^{50} - 38 q^{52} - 24 q^{53} + 20 q^{54} + 10 q^{55} + 24 q^{58} - 22 q^{59} - 10 q^{60} + 20 q^{61} - 30 q^{62} + 48 q^{64} - 36 q^{66} + 4 q^{68} + 4 q^{69} - 68 q^{70} - 10 q^{71} - 16 q^{72} + 30 q^{75} + 6 q^{76} - 24 q^{77} + 2 q^{78} - 26 q^{80} - 20 q^{81} + 20 q^{82} + 48 q^{83} - 16 q^{84} + 32 q^{85} - 46 q^{86} + 16 q^{87} - 10 q^{88} + 28 q^{89} - 14 q^{90} + 20 q^{91} + 50 q^{92} - 40 q^{93} + 2 q^{95} + 30 q^{96} + 2 q^{99}+O(q^{100}) \) 8 * q - 6 * q^3 - 8 * q^4 - 2 * q^5 - 6 * q^6 + 6 * q^10 + 6 * q^11 - 2 * q^12 + 14 * q^13 + 2 * q^15 - 8 * q^16 + 16 * q^17 + 20 * q^18 - 14 * q^19 - 2 * q^20 - 12 * q^21 + 10 * q^22 - 14 * q^23 - 2 * q^24 - 12 * q^25 + 6 * q^26 + 12 * q^27 - 8 * q^28 - 14 * q^30 + 2 * q^31 - 24 * q^35 - 44 * q^37 - 2 * q^38 + 6 * q^39 + 22 * q^40 + 16 * q^41 + 24 * q^42 - 6 * q^43 - 10 * q^44 + 22 * q^45 + 2 * q^46 + 16 * q^47 - 14 * q^48 + 24 * q^49 + 44 * q^50 - 38 * q^52 - 24 * q^53 + 20 * q^54 + 10 * q^55 + 24 * q^58 - 22 * q^59 - 10 * q^60 + 20 * q^61 - 30 * q^62 + 48 * q^64 - 36 * q^66 + 4 * q^68 + 4 * q^69 - 68 * q^70 - 10 * q^71 - 16 * q^72 + 30 * q^75 + 6 * q^76 - 24 * q^77 + 2 * q^78 - 26 * q^80 - 20 * q^81 + 20 * q^82 + 48 * q^83 - 16 * q^84 + 32 * q^85 - 46 * q^86 + 16 * q^87 - 10 * q^88 + 28 * q^89 - 14 * q^90 + 20 * q^91 + 50 * q^92 - 40 * q^93 + 2 * q^95 + 30 * q^96 + 2 * q^99

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