LMFDB - Embedded newform 650.2.t.g.643.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(7,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.t (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,8,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{13} - 48 x^{12} + 16 x^{11} + 8 x^{10} + 80 x^{9} + 2208 x^{8} + 760 x^{7} + 192 x^{6} + \cdots + 4096 $ x^16 - 4x^13 - 48x^12 + 16x^11 + 8x^10 + 80x^9 + 2208x^8 + 760x^7 + 192x^6 + 1696x^5 - 2812x^4 - 2080x^3 + 128x^2 - 1024*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			643.4
Root			$2.63533 - 0.706135i$ of defining polynomial
Character	$\chi$	$=$	650.643
Dual form			650.2.t.g.557.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(2.63533 - 0.706135i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.63533 + 0.706135i) q^{6} +(-1.79804 - 3.11430i) q^{7} +1.00000i q^{8} +(3.84827 - 2.22180i) q^{9} +(4.64166 - 1.24373i) q^{11} +(1.92920 + 1.92920i) q^{12} +(-3.33348 + 1.37401i) q^{13} -3.59608i q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.819442 - 3.05820i) q^{17} +4.44360 q^{18} +(-0.782374 + 2.91986i) q^{19} +(-6.93755 - 6.93755i) q^{21} +(4.64166 + 1.24373i) q^{22} +(1.00673 + 3.75715i) q^{23} +(0.706135 + 2.63533i) q^{24} +(-3.57388 - 0.476810i) q^{26} +(2.78499 - 2.78499i) q^{27} +(1.79804 - 3.11430i) q^{28} +(4.52655 + 2.61340i) q^{29} +(-4.00252 + 4.00252i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(11.3541 - 6.55528i) q^{33} +(2.23876 - 2.23876i) q^{34} +(3.84827 + 2.22180i) q^{36} +(-2.55430 + 4.42418i) q^{37} +(-2.13749 + 2.13749i) q^{38} +(-7.81459 + 5.97487i) q^{39} +(-0.124135 - 0.463279i) q^{41} +(-2.53932 - 9.47687i) q^{42} +(-2.77485 - 0.743519i) q^{43} +(3.39793 + 3.39793i) q^{44} +(-1.00673 + 3.75715i) q^{46} -7.17950 q^{47} +(-0.706135 + 2.63533i) q^{48} +(-2.96590 + 5.13709i) q^{49} -8.63801i q^{51} +(-2.85667 - 2.19987i) q^{52} +(2.20166 + 2.20166i) q^{53} +(3.80437 - 1.01938i) q^{54} +(3.11430 - 1.79804i) q^{56} +8.24727i q^{57} +(2.61340 + 4.52655i) q^{58} +(-10.0282 - 2.68705i) q^{59} +(0.826168 + 1.43097i) q^{61} +(-5.46754 + 1.46502i) q^{62} +(-13.8387 - 7.98978i) q^{63} -1.00000 q^{64} +13.1106 q^{66} +(3.02310 + 1.74539i) q^{67} +(3.05820 - 0.819442i) q^{68} +(5.30612 + 9.19046i) q^{69} +(-9.32721 - 2.49922i) q^{71} +(2.22180 + 3.84827i) q^{72} -11.2159i q^{73} +(-4.42418 + 2.55430i) q^{74} +(-2.91986 + 0.782374i) q^{76} +(-12.2192 - 12.2192i) q^{77} +(-9.75507 + 1.26709i) q^{78} -1.21846i q^{79} +(-1.29260 + 2.23886i) q^{81} +(0.124135 - 0.463279i) q^{82} +10.8721 q^{83} +(2.53932 - 9.47687i) q^{84} +(-2.03133 - 2.03133i) q^{86} +(13.7744 + 3.69083i) q^{87} +(1.24373 + 4.64166i) q^{88} +(-2.64966 - 9.88867i) q^{89} +(10.2728 + 7.91092i) q^{91} +(-2.75043 + 2.75043i) q^{92} +(-7.72165 + 13.3743i) q^{93} +(-6.21763 - 3.58975i) q^{94} +(-1.92920 + 1.92920i) q^{96} +(9.00422 - 5.19859i) q^{97} +(-5.13709 + 2.96590i) q^{98} +(15.0991 - 15.0991i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 6 q^{11} - 2 q^{13} - 8 q^{16} + 16 q^{17} + 16 q^{18} + 6 q^{22} + 6 q^{23} - 6 q^{26} + 12 q^{27} - 6 q^{29} + 6 q^{33} - 14 q^{34} + 20 q^{37} - 6 q^{38} - 6 q^{39} - 44 q^{41} - 6 q^{42}+ \cdots - 26 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 6 * q^11 - 2 * q^13 - 8 * q^16 + 16 * q^17 + 16 * q^18 + 6 * q^22 + 6 * q^23 - 6 * q^26 + 12 * q^27 - 6 * q^29 + 6 * q^33 - 14 * q^34 + 20 * q^37 - 6 * q^38 - 6 * q^39 - 44 * q^41 - 6 * q^42 + 6 * q^44 - 6 * q^46 - 52 * q^47 - 2 * q^49 - 10 * q^52 + 24 * q^53 + 6 * q^54 + 6 * q^56 - 8 * q^58 - 46 * q^59 + 6 * q^61 - 12 * q^62 - 90 * q^63 - 16 * q^64 + 52 * q^66 - 12 * q^67 + 2 * q^68 + 58 * q^69 + 6 * q^71 + 8 * q^72 + 24 * q^74 - 6 * q^76 - 58 * q^77 - 38 * q^78 - 24 * q^81 + 44 * q^82 + 64 * q^83 + 6 * q^84 + 44 * q^87 - 24 * q^89 + 38 * q^91 + 26 * q^93 + 6 * q^97 - 26 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	2.63533	−	0.706135i	1.52151	−	0.407687i	0.601271	−	0.799045i	$-0.294661\pi$
$3$	2.63533	−	0.706135i	1.52151	−	0.407687i	0.920239	+	0.391358i	$0.127995\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	2.63533	+	0.706135i	1.07587	+	0.288278i
$7$	−1.79804	−	3.11430i	−0.679595	−	1.17709i	−0.975103	−	0.221753i	$-0.928822\pi$
$7$	−1.79804	−	3.11430i	−0.679595	−	1.17709i	0.295507	−	0.955340i	$-0.404511\pi$
$8$			1.00000i			0.353553i
$9$	3.84827	−	2.22180i	1.28276	−	0.740600i
$10$		0			0
$11$	4.64166	−	1.24373i	1.39951	−	0.374999i	0.521344	−	0.853347i	$-0.325431\pi$
$11$	4.64166	−	1.24373i	1.39951	−	0.374999i	0.878170	+	0.478348i	$0.158764\pi$
$12$	1.92920	+	1.92920i	0.556911	+	0.556911i
$13$	−3.33348	+	1.37401i	−0.924541	+	0.381082i
$13$	−3.33348	+	1.37401i	−0.924541	+	0.381082i
$14$		−	3.59608i		−	0.961093i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.819442	−	3.05820i	0.198744	−	0.741722i	−0.792522	−	0.609843i	$-0.791232\pi$
$17$	0.819442	−	3.05820i	0.198744	−	0.741722i	0.991266	−	0.131879i	$-0.0421010\pi$
$18$	4.44360			1.04737
$19$	−0.782374	+	2.91986i	−0.179489	+	0.669862i	0.816254	+	0.577693i	$0.196047\pi$
$19$	−0.782374	+	2.91986i	−0.179489	+	0.669862i	−0.995743	+	0.0921694i	$0.970620\pi$
$20$		0			0
$21$	−6.93755	−	6.93755i	−1.51390	−	1.51390i
$22$	4.64166	+	1.24373i	0.989606	+	0.265164i
$23$	1.00673	+	3.75715i	0.209917	+	0.783421i	0.987894	+	0.155128i	$0.0495791\pi$
$23$	1.00673	+	3.75715i	0.209917	+	0.783421i	−0.777977	+	0.628292i	$0.783754\pi$
$24$	0.706135	+	2.63533i	0.144139	+	0.537935i
$25$		0			0
$26$	−3.57388	−	0.476810i	−0.700896	−	0.0935102i
$27$	2.78499	−	2.78499i	0.535972	−	0.535972i
$28$	1.79804	−	3.11430i	0.339798	−	0.588547i
$29$	4.52655	+	2.61340i	0.840559	+	0.485297i	0.857454	−	0.514560i	$-0.172045\pi$
$29$	4.52655	+	2.61340i	0.840559	+	0.485297i	−0.0168954	+	0.999857i	$0.505378\pi$
$30$		0			0
$31$	−4.00252	+	4.00252i	−0.718874	+	0.718874i	−0.968375	−	0.249501i	$-0.919733\pi$
$31$	−4.00252	+	4.00252i	−0.718874	+	0.718874i	0.249501	+	0.968375i	$0.419733\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	11.3541	−	6.55528i	1.97649	−	1.14113i
$34$	2.23876	−	2.23876i	0.383944	−	0.383944i
$35$		0			0
$36$	3.84827	+	2.22180i	0.641379	+	0.370300i
$37$	−2.55430	+	4.42418i	−0.419924	+	0.727330i	−0.995931	−	0.0901146i	$-0.971277\pi$
$37$	−2.55430	+	4.42418i	−0.419924	+	0.727330i	0.576007	+	0.817445i	$0.304610\pi$
$38$	−2.13749	+	2.13749i	−0.346746	+	0.346746i
$39$	−7.81459	+	5.97487i	−1.25134	+	0.956744i
$40$		0			0
$41$	−0.124135	−	0.463279i	−0.0193867	−	0.0723521i	0.955555	−	0.294814i	$-0.0952575\pi$
$41$	−0.124135	−	0.463279i	−0.0193867	−	0.0723521i	−0.974941	+	0.222461i	$0.928591\pi$
$42$	−2.53932	−	9.47687i	−0.391825	−	1.46231i
$43$	−2.77485	−	0.743519i	−0.423161	−	0.113386i	0.0409532	−	0.999161i	$-0.486961\pi$
$43$	−2.77485	−	0.743519i	−0.423161	−	0.113386i	−0.464114	+	0.885775i	$0.653627\pi$
$44$	3.39793	+	3.39793i	0.512258	+	0.512258i
$45$		0			0
$46$	−1.00673	+	3.75715i	−0.148434	+	0.553962i
$47$	−7.17950			−1.04724			−0.523619	−	0.851953i	$-0.675418\pi$
$47$	−7.17950			−1.04724			−0.523619	+	0.851953i	$0.675418\pi$
$48$	−0.706135	+	2.63533i	−0.101922	+	0.380377i
$49$	−2.96590	+	5.13709i	−0.423700	+	0.733869i
$50$		0			0
$51$		−	8.63801i		−	1.20956i
$52$	−2.85667	−	2.19987i	−0.396149	−	0.305067i
$53$	2.20166	+	2.20166i	0.302421	+	0.302421i	0.841960	−	0.539539i	$-0.181402\pi$
$53$	2.20166	+	2.20166i	0.302421	+	0.302421i	−0.539539	+	0.841960i	$0.681402\pi$
$54$	3.80437	−	1.01938i	0.517709	−	0.138720i
$55$		0			0
$56$	3.11430	−	1.79804i	0.416165	−	0.240273i
$57$			8.24727i			1.09238i
$58$	2.61340	+	4.52655i	0.343157	+	0.594365i
$59$	−10.0282	−	2.68705i	−1.30556	−	0.349825i	−0.462012	−	0.886874i	$-0.652872\pi$
$59$	−10.0282	−	2.68705i	−1.30556	−	0.349825i	−0.843551	+	0.537049i	$0.819539\pi$
$60$		0			0
$61$	0.826168	+	1.43097i	0.105780	+	0.183216i	0.914057	−	0.405587i	$-0.132933\pi$
$61$	0.826168	+	1.43097i	0.105780	+	0.183216i	−0.808277	+	0.588803i	$0.799599\pi$
$62$	−5.46754	+	1.46502i	−0.694379	+	0.186058i
$63$	−13.8387	−	7.98978i	−1.74351	−	1.00662i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	13.1106			1.61380
$67$	3.02310	+	1.74539i	0.369330	+	0.213233i	0.673166	−	0.739492i	$-0.264934\pi$
$67$	3.02310	+	1.74539i	0.369330	+	0.213233i	−0.303836	+	0.952724i	$0.598267\pi$
$68$	3.05820	−	0.819442i	0.370861	−	0.0993719i
$69$	5.30612	+	9.19046i	0.638781	+	1.10640i
$70$		0			0
$71$	−9.32721	−	2.49922i	−1.10694	−	0.296603i	−0.341350	−	0.939936i	$-0.610884\pi$
$71$	−9.32721	−	2.49922i	−1.10694	−	0.296603i	−0.765586	+	0.643334i	$0.777551\pi$
$72$	2.22180	+	3.84827i	0.261842	+	0.453523i
$73$		−	11.2159i		−	1.31272i	−0.754446	−	0.656362i	$-0.772095\pi$
$73$		−	11.2159i		−	1.31272i	0.754446	−	0.656362i	$-0.227905\pi$
$74$	−4.42418	+	2.55430i	−0.514300	+	0.296931i
$75$		0			0
$76$	−2.91986	+	0.782374i	−0.334931	+	0.0897445i
$77$	−12.2192	−	12.2192i	−1.39251	−	1.39251i
$78$	−9.75507	+	1.26709i	−1.10454	+	0.143470i
$79$		−	1.21846i		−	0.137087i	−0.997648	−	0.0685435i	$-0.978165\pi$
$79$		−	1.21846i		−	0.137087i	0.997648	−	0.0685435i	$-0.0218352\pi$
$80$		0			0
$81$	−1.29260	+	2.23886i	−0.143623	+	0.248762i
$82$	0.124135	−	0.463279i	0.0137085	−	0.0511606i
$83$	10.8721			1.19337			0.596685	−	0.802475i	$-0.296484\pi$
$83$	10.8721			1.19337			0.596685	+	0.802475i	$0.296484\pi$
$84$	2.53932	−	9.47687i	0.277062	−	1.03401i
$85$		0			0
$86$	−2.03133	−	2.03133i	−0.219044	−	0.219044i
$87$	13.7744	+	3.69083i	1.47677	+	0.395699i
$88$	1.24373	+	4.64166i	0.132582	+	0.494803i
$89$	−2.64966	−	9.88867i	−0.280863	−	1.04820i	−0.951809	−	0.306690i	$-0.900778\pi$
$89$	−2.64966	−	9.88867i	−0.280863	−	1.04820i	0.670946	−	0.741506i	$-0.265888\pi$
$90$		0			0
$91$	10.2728	+	7.91092i	1.07688	+	0.829290i
$92$	−2.75043	+	2.75043i	−0.286752	+	0.286752i
$93$	−7.72165	+	13.3743i	−0.800697	+	1.38685i
$94$	−6.21763	−	3.58975i	−0.641300	−	0.370254i
$95$		0			0
$96$	−1.92920	+	1.92920i	−0.196898	+	0.196898i
$97$	9.00422	−	5.19859i	0.914240	−	0.527837i	0.0324473	−	0.999473i	$-0.489670\pi$
$97$	9.00422	−	5.19859i	0.914240	−	0.527837i	0.881793	+	0.471637i	$0.156337\pi$
$98$	−5.13709	+	2.96590i	−0.518924	+	0.299601i
$99$	15.0991	−	15.0991i	1.51751	−	1.51751i
$100$		0			0
$101$	8.55490	+	4.93918i	0.851245	+	0.491466i	0.861071	−	0.508485i	$-0.169794\pi$
$101$	8.55490	+	4.93918i	0.851245	+	0.491466i	−0.00982597	+	0.999952i	$0.503128\pi$
$102$	4.31900	−	7.48073i	0.427645	−	0.740703i
$103$	0.742128	−	0.742128i	0.0731241	−	0.0731241i	−0.669599	−	0.742723i	$-0.733534\pi$
$103$	0.742128	−	0.742128i	0.0731241	−	0.0731241i	0.742723	+	0.669599i	$0.233534\pi$
$104$	−1.37401	−	3.33348i	−0.134733	−	0.326875i
$105$		0			0
$106$	0.805862	+	3.00752i	0.0782723	+	0.292116i
$107$	1.88954	+	7.05186i	0.182669	+	0.681729i	0.995118	+	0.0986963i	$0.0314672\pi$
$107$	1.88954	+	7.05186i	0.182669	+	0.681729i	−0.812449	+	0.583032i	$0.801866\pi$
$108$	3.80437	+	1.01938i	0.366076	+	0.0980897i
$109$	−0.0493096	−	0.0493096i	−0.00472300	−	0.00472300i	0.704741	−	0.709464i	$-0.251063\pi$
$109$	−0.0493096	−	0.0493096i	−0.00472300	−	0.00472300i	−0.709464	+	0.704741i	$0.751063\pi$
$110$		0			0
$111$	−3.60736	+	13.4629i	−0.342395	+	1.27784i
$112$	3.59608			0.339798
$113$	−1.24405	+	4.64287i	−0.117031	+	0.436764i	−0.999431	−	0.0337354i	$-0.989260\pi$
$113$	−1.24405	+	4.64287i	−0.117031	+	0.436764i	0.882400	+	0.470500i	$0.155926\pi$
$114$	−4.12363	+	7.14234i	−0.386214	+	0.668942i
$115$		0			0
$116$			5.22681i			0.485297i
$117$	−9.77536	+	12.6939i	−0.903732	+	1.17355i
$118$	−7.34117	−	7.34117i	−0.675809	−	0.675809i
$119$	−10.9975	+	2.94678i	−1.00814	+	0.270131i
$120$		0			0
$121$	10.4719	−	6.04595i	0.951989	−	0.549631i
$122$			1.65234i			0.149595i
$123$	−0.654276	−	1.13324i	−0.0589940	−	0.102181i
$124$	−5.46754	−	1.46502i	−0.491000	−	0.131563i
$125$		0			0
$126$	−7.98978	−	13.8387i	−0.711786	−	1.23285i
$127$	10.5899	−	2.83754i	0.939698	−	0.251791i	0.243713	−	0.969847i	$-0.421635\pi$
$127$	10.5899	−	2.83754i	0.939698	−	0.251791i	0.695985	+	0.718056i	$0.254968\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−7.83768			−0.690069
$130$		0			0
$131$	−15.6797			−1.36994			−0.684970	−	0.728571i	$-0.740185\pi$
$131$	−15.6797			−1.36994			−0.684970	+	0.728571i	$0.740185\pi$
$132$	11.3541	+	6.55528i	0.988246	+	0.570564i
$133$	10.5001	−	2.81348i	0.910470	−	0.243960i
$134$	1.74539	+	3.02310i	0.150778	+	0.261156i
$135$		0			0
$136$	3.05820	+	0.819442i	0.262238	+	0.0702666i
$137$	−1.42075	−	2.46082i	−0.121383	−	0.210242i	0.798930	−	0.601424i	$-0.205400\pi$
$137$	−1.42075	−	2.46082i	−0.121383	−	0.210242i	−0.920313	+	0.391182i	$0.872066\pi$
$138$			10.6122i			0.903373i
$139$	13.8773	−	8.01209i	1.17706	−	0.679577i	0.221728	−	0.975108i	$-0.428830\pi$
$139$	13.8773	−	8.01209i	1.17706	−	0.679577i	0.955333	+	0.295532i	$0.0954968\pi$
$140$		0			0
$141$	−18.9204	+	5.06970i	−1.59338	+	0.426946i
$142$	−6.82799	−	6.82799i	−0.572992	−	0.572992i
$143$	−13.7640	+	10.5236i	−1.15100	+	0.880032i
$144$			4.44360i			0.370300i
$145$		0			0
$146$	5.60796	−	9.71326i	0.464118	−	0.803875i
$147$	−4.18865	+	15.6323i	−0.345474	+	1.28933i
$148$	−5.10860			−0.419924
$149$	−2.86654	+	10.6981i	−0.234836	+	0.876420i	0.743387	+	0.668862i	$0.233218\pi$
$149$	−2.86654	+	10.6981i	−0.234836	+	0.876420i	−0.978223	+	0.207558i	$0.933448\pi$
$150$		0			0
$151$	−0.609536	−	0.609536i	−0.0496034	−	0.0496034i	0.681870	−	0.731473i	$-0.261167\pi$
$151$	−0.609536	−	0.609536i	−0.0496034	−	0.0496034i	−0.731473	+	0.681870i	$0.761167\pi$
$152$	−2.91986	−	0.782374i	−0.236832	−	0.0634589i
$153$	−3.64127	−	13.5894i	−0.294380	−	1.09864i
$154$	−4.47255	−	16.6918i	−0.360409	−	1.34506i
$155$		0			0
$156$	−9.08168	−	3.78020i	−0.727116	−	0.302658i
$157$	−9.16772	+	9.16772i	−0.731664	+	0.731664i	−0.970949	−	0.239285i	$-0.923087\pi$
$157$	−9.16772	+	9.16772i	−0.731664	+	0.731664i	0.239285	+	0.970949i	$0.423087\pi$
$158$	0.609228	−	1.05521i	0.0484676	−	0.0839483i
$159$	7.35677	+	4.24743i	0.583429	+	0.336843i
$160$		0			0
$161$	9.89076	−	9.89076i	0.779501	−	0.779501i
$162$	−2.23886	+	1.29260i	−0.175901	+	0.101557i
$163$	−15.5425	+	8.97349i	−1.21739	+	0.702858i	−0.964358	−	0.264602i	$-0.914760\pi$
$163$	−15.5425	+	8.97349i	−1.21739	+	0.702858i	−0.253027	+	0.967459i	$0.581426\pi$
$164$	0.339144	−	0.339144i	0.0264827	−	0.0264827i
$165$		0			0
$166$	9.41554	+	5.43606i	0.730787	+	0.421920i
$167$	9.77996	−	16.9394i	0.756796	−	1.31081i	−0.187680	−	0.982230i	$-0.560097\pi$
$167$	9.77996	−	16.9394i	0.756796	−	1.31081i	0.944476	−	0.328579i	$-0.106570\pi$
$168$	6.93755	−	6.93755i	0.535243	−	0.535243i
$169$	9.22418	−	9.16049i	0.709552	−	0.704653i
$170$		0			0
$171$	3.47656	+	12.9747i	0.265859	+	0.992200i
$172$	−0.743519	−	2.77485i	−0.0566928	−	0.211580i
$173$	14.4420	+	3.86971i	1.09800	+	0.294209i	0.761951	−	0.647635i	$-0.224242\pi$
$173$	14.4420	+	3.86971i	1.09800	+	0.294209i	0.336051	+	0.941844i	$0.390908\pi$
$174$	10.0835	+	10.0835i	0.764431	+	0.764431i
$175$		0			0
$176$	−1.24373	+	4.64166i	−0.0937496	+	0.349878i
$177$	−28.3251			−2.12905
$178$	2.64966	−	9.88867i	0.198600	−	0.741187i
$179$	0.973054	−	1.68538i	0.0727295	−	0.125971i	−0.827367	−	0.561661i	$-0.810162\pi$
$179$	0.973054	−	1.68538i	0.0727295	−	0.125971i	0.900097	+	0.435690i	$0.143496\pi$
$180$		0			0
$181$		−	23.5819i		−	1.75283i	−0.481556	−	0.876415i	$-0.659928\pi$
$181$		−	23.5819i		−	1.75283i	0.481556	−	0.876415i	$-0.340072\pi$
$182$	4.94106	+	11.9875i	0.366256	+	0.888570i
$183$	3.18768	+	3.18768i	0.235640	+	0.235640i
$184$	−3.75715	+	1.00673i	−0.276981	+	0.0742168i
$185$		0			0
$186$	−13.3743	+	7.72165i	−0.980650	+	0.566179i
$187$		−	15.2143i		−	1.11258i
$188$	−3.58975	−	6.21763i	−0.261809	−	0.453467i
$189$	−13.6808	−	3.66577i	−0.995133	−	0.266645i
$190$		0			0
$191$	0.306187	+	0.530332i	0.0221549	+	0.0383734i	0.876890	−	0.480691i	$-0.159614\pi$
$191$	0.306187	+	0.530332i	0.0221549	+	0.0383734i	−0.854735	+	0.519064i	$0.826281\pi$
$192$	−2.63533	+	0.706135i	−0.190189	+	0.0509609i
$193$	−19.5230	−	11.2716i	−1.40529	−	0.811347i	−0.410365	−	0.911921i	$-0.634599\pi$
$193$	−19.5230	−	11.2716i	−1.40529	−	0.811347i	−0.994930	+	0.100574i	$0.967932\pi$
$194$	10.3972			0.746474
$195$		0			0
$196$	−5.93180			−0.423700
$197$	10.7381	+	6.19964i	0.765057	+	0.441706i	0.831109	−	0.556110i	$-0.187707\pi$
$197$	10.7381	+	6.19964i	0.765057	+	0.441706i	−0.0660512	+	0.997816i	$0.521040\pi$
$198$	20.6257	−	5.52664i	1.46580	−	0.392761i
$199$	−2.59326	−	4.49166i	−0.183831	−	0.318405i	0.759351	−	0.650681i	$-0.225517\pi$
$199$	−2.59326	−	4.49166i	−0.183831	−	0.318405i	−0.943182	+	0.332276i	$0.892183\pi$
$200$		0			0
$201$	9.19935	+	2.46496i	0.648872	+	0.173865i
$202$	4.93918	+	8.55490i	0.347519	+	0.601921i
$203$		−	18.7960i		−	1.31922i
$204$	7.48073	−	4.31900i	0.523756	−	0.302391i
$205$		0			0
$206$	1.01377	−	0.271638i	0.0706324	−	0.0189259i
$207$	12.2218	+	12.2218i	0.849474	+	0.849474i
$208$	0.476810	−	3.57388i	0.0330609	−	0.247804i
$209$			14.5261i			1.00479i
$210$		0			0
$211$	0.875261	−	1.51600i	0.0602555	−	0.104366i	−0.834324	−	0.551274i	$-0.814142\pi$
$211$	0.875261	−	1.51600i	0.0602555	−	0.104366i	0.894580	+	0.446909i	$0.147475\pi$
$212$	−0.805862	+	3.00752i	−0.0553469	+	0.206557i
$213$	−26.3451			−1.80513
$214$	−1.88954	+	7.05186i	−0.129166	+	0.482055i
$215$		0			0
$216$	2.78499	+	2.78499i	0.189495	+	0.189495i
$217$	19.6617	+	5.26834i	1.33472	+	0.357638i
$218$	−0.0180486	−	0.0673581i	−0.00122240	−	0.00456207i
$219$	−7.91995	−	29.5577i	−0.535181	−	1.99732i
$220$		0			0
$221$	1.47041	+	11.3204i	0.0989105	+	0.761490i
$222$	−9.85549	+	9.85549i	−0.661457	+	0.661457i
$223$	8.93366	−	15.4736i	0.598242	−	1.03619i	−0.394838	−	0.918751i	$-0.629199\pi$
$223$	8.93366	−	15.4736i	0.598242	−	1.03619i	0.993081	−	0.117435i	$-0.0374672\pi$
$224$	3.11430	+	1.79804i	0.208083	+	0.120137i
$225$		0			0
$226$	−3.39882	+	3.39882i	−0.226086	+	0.226086i
$227$	−14.2956	+	8.25357i	−0.948833	+	0.547809i	−0.892718	−	0.450615i	$-0.851205\pi$
$227$	−14.2956	+	8.25357i	−0.948833	+	0.547809i	−0.0561147	+	0.998424i	$0.517871\pi$
$228$	−7.14234	+	4.12363i	−0.473013	+	0.273094i
$229$	−20.6370	+	20.6370i	−1.36373	+	1.36373i	−0.494626	+	0.869106i	$0.664695\pi$
$229$	−20.6370	+	20.6370i	−1.36373	+	1.36373i	−0.869106	+	0.494626i	$0.835305\pi$
$230$		0			0
$231$	−40.8302	−	23.5733i	−2.68643	−	1.55101i
$232$	−2.61340	+	4.52655i	−0.171578	+	0.297182i
$233$	−5.24071	+	5.24071i	−0.343330	+	0.343330i	−0.857618	−	0.514288i	$-0.828056\pi$
$233$	−5.24071	+	5.24071i	−0.343330	+	0.343330i	0.514288	+	0.857618i	$0.328056\pi$
$234$	−14.8127	+	6.10556i	−0.968334	+	0.399133i
$235$		0			0
$236$	−2.68705	−	10.0282i	−0.174912	−	0.652782i
$237$	−0.860395	−	3.21104i	−0.0558886	−	0.208579i
$238$	−10.9975	−	2.94678i	−0.712864	−	0.191011i
$239$	−12.8912	−	12.8912i	−0.833859	−	0.833859i	0.154183	−	0.988042i	$-0.450725\pi$
$239$	−12.8912	−	12.8912i	−0.833859	−	0.833859i	−0.988042	+	0.154183i	$0.950725\pi$
$240$		0			0
$241$	−3.59785	+	13.4274i	−0.231758	+	0.864933i	0.747826	+	0.663895i	$0.231098\pi$
$241$	−3.59785	+	13.4274i	−0.231758	+	0.864933i	−0.979584	+	0.201037i	$0.935569\pi$
$242$	12.0919			0.777296
$243$	−4.88364	+	18.2260i	−0.313286	+	1.16920i
$244$	−0.826168	+	1.43097i	−0.0528900	+	0.0916081i
$245$		0			0
$246$		−	1.30855i		−	0.0834302i
$247$	−1.40390	−	10.8083i	−0.0893278	−	0.687715i
$248$	−4.00252	−	4.00252i	−0.254160	−	0.254160i
$249$	28.6517	−	7.67719i	1.81573	−	0.486522i
$250$		0			0
$251$	4.88932	−	2.82285i	0.308611	−	0.178177i	−0.337694	−	0.941256i	$-0.609647\pi$
$251$	4.88932	−	2.82285i	0.308611	−	0.178177i	0.646305	+	0.763079i	$0.276313\pi$
$252$		−	15.9796i		−	1.00662i
$253$	9.34576	+	16.1873i	0.587563	+	1.01769i
$254$	10.5899	+	2.83754i	0.664467	+	0.178043i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.522706	−	0.140059i	0.0326055	−	0.00873661i	−0.242479	−	0.970157i	$-0.577961\pi$
$257$	0.522706	−	0.140059i	0.0326055	−	0.00873661i	0.275085	+	0.961420i	$0.411294\pi$
$258$	−6.78763	−	3.91884i	−0.422579	−	0.243976i
$259$	18.3709			1.14151
$260$		0			0
$261$	23.2258			1.43764
$262$	−13.5790	−	7.83984i	−0.838914	−	0.484347i
$263$	−0.812458	+	0.217697i	−0.0500983	+	0.0134238i	−0.283781	−	0.958889i	$-0.591589\pi$
$263$	−0.812458	+	0.217697i	−0.0500983	+	0.0134238i	0.233683	+	0.972313i	$0.424922\pi$
$264$	6.55528	+	11.3541i	0.403450	+	0.698795i
$265$		0			0
$266$	10.5001	+	2.81348i	0.643800	+	0.172506i
$267$	−13.9655	−	24.1889i	−0.854673	−	1.48034i
$268$			3.49077i			0.213233i
$269$	−16.9355	+	9.77771i	−1.03258	+	0.596158i	−0.917721	−	0.397225i	$-0.869973\pi$
$269$	−16.9355	+	9.77771i	−1.03258	+	0.596158i	−0.114854	+	0.993382i	$0.536640\pi$
$270$		0			0
$271$	15.9289	−	4.26814i	0.967613	−	0.259271i	0.259793	−	0.965664i	$-0.416346\pi$
$271$	15.9289	−	4.26814i	0.967613	−	0.259271i	0.707820	+	0.706393i	$0.249679\pi$
$272$	2.23876	+	2.23876i	0.135745	+	0.135745i
$273$	32.6585	+	13.5939i	1.97658	+	0.822740i
$274$		−	2.84151i		−	0.171662i
$275$		0			0
$276$	−5.30612	+	9.19046i	−0.319391	+	0.553201i
$277$	4.14104	−	15.4546i	0.248811	−	0.928575i	−0.722619	−	0.691247i	$-0.757062\pi$
$277$	4.14104	−	15.4546i	0.248811	−	0.928575i	0.971430	−	0.237328i	$-0.0762716\pi$
$278$	16.0242			0.961067
$279$	−6.50998	+	24.2956i	−0.389742	+	1.45454i
$280$		0			0
$281$	11.8817	+	11.8817i	0.708805	+	0.708805i	0.966284	−	0.257479i	$-0.0828917\pi$
$281$	11.8817	+	11.8817i	0.708805	+	0.708805i	−0.257479	+	0.966284i	$0.582892\pi$
$282$	−18.9204	−	5.06970i	−1.12669	−	0.301896i
$283$	6.19613	+	23.1243i	0.368322	+	1.37460i	0.862862	+	0.505440i	$0.168670\pi$
$283$	6.19613	+	23.1243i	0.368322	+	1.37460i	−0.494540	+	0.869155i	$0.664663\pi$
$284$	−2.49922	−	9.32721i	−0.148301	−	0.553468i
$285$		0			0
$286$	−17.1818	+	2.23175i	−1.01598	+	0.131966i
$287$	−1.21959	+	1.21959i	−0.0719901	+	0.0719901i
$288$	−2.22180	+	3.84827i	−0.130921	+	0.226762i
$289$	6.04134	+	3.48797i	0.355373	+	0.205175i
$290$		0			0
$291$	20.0582	−	20.0582i	1.17583	−	1.17583i
$292$	9.71326	−	5.60796i	0.568426	−	0.328181i
$293$	15.1081	−	8.72268i	0.882626	−	0.509584i	0.0111027	−	0.999938i	$-0.496466\pi$
$293$	15.1081	−	8.72268i	0.882626	−	0.509584i	0.871523	+	0.490354i	$0.163133\pi$
$294$	−11.4436	+	11.4436i	−0.667404	+	0.667404i
$295$		0			0
$296$	−4.42418	−	2.55430i	−0.257150	−	0.148466i
$297$	9.46322	−	16.3908i	0.549111	−	0.951089i
$298$	−7.83153	+	7.83153i	−0.453668	+	0.453668i
$299$	−8.51828	−	11.1411i	−0.492625	−	0.644309i
$300$		0			0
$301$	2.67375	+	9.97859i	0.154113	+	0.575156i
$302$	−0.223106	−	0.832642i	−0.0128383	−	0.0479132i
$303$	26.0327	+	6.97545i	1.49554	+	0.400729i
$304$	−2.13749	−	2.13749i	−0.122593	−	0.122593i
$305$		0			0
$306$	3.64127	−	13.5894i	0.208158	−	0.776855i
$307$	17.4109			0.993691			0.496845	−	0.867839i	$-0.334492\pi$
$307$	17.4109			0.993691			0.496845	+	0.867839i	$0.334492\pi$
$308$	4.47255	−	16.6918i	0.254847	−	0.951103i
$309$	1.43171	−	2.47980i	0.0814472	−	0.141071i
$310$		0			0
$311$		−	7.12206i		−	0.403855i	−0.979400	−	0.201928i	$-0.935279\pi$
$311$		−	7.12206i		−	0.403855i	0.979400	−	0.201928i	$-0.0647206\pi$
$312$	−5.97487	−	7.81459i	−0.338260	−	0.442414i
$313$	4.01387	+	4.01387i	0.226878	+	0.226878i	0.811387	−	0.584509i	$-0.198713\pi$
$313$	4.01387	+	4.01387i	0.226878	+	0.226878i	−0.584509	+	0.811387i	$0.698713\pi$
$314$	−12.5233	+	3.35562i	−0.706733	+	0.189369i
$315$		0			0
$316$	1.05521	−	0.609228i	0.0593604	−	0.0342718i
$317$		−	3.84438i		−	0.215922i	−0.994155	−	0.107961i	$-0.965568\pi$
$317$		−	3.84438i		−	0.215922i	0.994155	−	0.107961i	$-0.0344322\pi$
$318$	4.24743	+	7.35677i	0.238184	+	0.412547i
$319$	24.2611	+	6.50073i	1.35836	+	0.363971i
$320$		0			0
$321$	9.95913	+	17.2497i	0.555864	+	0.962785i
$322$	13.5110	−	3.62027i	0.752940	−	0.201750i
$323$	8.28841	+	4.78531i	0.461179	+	0.266262i
$324$	−2.58521			−0.143623
$325$		0			0
$326$	−17.9470			−0.993991
$327$	−0.164766	−	0.0951279i	−0.00911160	−	0.00526058i
$328$	0.463279	−	0.124135i	0.0255803	−	0.00685423i
$329$	12.9090	+	22.3591i	0.711698	+	1.23270i
$330$		0			0
$331$	13.5816	+	3.63918i	0.746513	+	0.200028i	0.611971	−	0.790880i	$-0.290377\pi$
$331$	13.5816	+	3.63918i	0.746513	+	0.200028i	0.134542	+	0.990908i	$0.457044\pi$
$332$	5.43606	+	9.41554i	0.298343	+	0.516745i
$333$			22.7006i			1.24398i
$334$	16.9394	−	9.77996i	0.926882	−	0.535136i
$335$		0			0
$336$	9.47687	−	2.53932i	0.517005	−	0.138531i
$337$	21.2997	+	21.2997i	1.16027	+	1.16027i	0.984417	+	0.175850i	$0.0562673\pi$
$337$	21.2997	+	21.2997i	1.16027	+	1.16027i	0.175850	+	0.984417i	$0.443733\pi$
$338$	12.5686	−	3.32112i	0.683643	−	0.180645i
$339$			13.1140i			0.712253i
$340$		0			0
$341$	−13.6003	+	23.5564i	−0.736497	+	1.27565i
$342$	−3.47656	+	12.9747i	−0.187991	+	0.701591i
$343$	−3.84135			−0.207413
$344$	0.743519	−	2.77485i	0.0400879	−	0.149610i
$345$		0			0
$346$	10.5723	+	10.5723i	0.568368	+	0.568368i
$347$	4.59560	+	1.23139i	0.246705	+	0.0661043i	0.380052	−	0.924965i	$-0.375906\pi$
$347$	4.59560	+	1.23139i	0.246705	+	0.0661043i	−0.133348	+	0.991069i	$0.542573\pi$
$348$	3.69083	+	13.7744i	0.197849	+	0.738384i
$349$	−4.94358	−	18.4497i	−0.264624	−	0.987589i	−0.962480	−	0.271351i	$-0.912529\pi$
$349$	−4.94358	−	18.4497i	−0.264624	−	0.987589i	0.697857	−	0.716237i	$-0.254137\pi$
$350$		0			0
$351$	−5.45710	+	13.1103i	−0.291279	+	0.699778i
$352$	−3.39793	+	3.39793i	−0.181110	+	0.181110i
$353$	2.01134	−	3.48374i	0.107053	−	0.185421i	−0.807522	−	0.589837i	$-0.799192\pi$
$353$	2.01134	−	3.48374i	0.107053	−	0.185421i	0.914575	+	0.404416i	$0.132525\pi$
$354$	−24.5303	−	14.1626i	−1.30377	−	0.752731i
$355$		0			0
$356$	7.23901	−	7.23901i	0.383667	−	0.383667i
$357$	−26.9013	+	15.5315i	−1.42377	+	0.822013i
$358$	1.68538	−	0.973054i	0.0890751	−	0.0514275i
$359$	13.3497	−	13.3497i	0.704572	−	0.704572i	−0.260816	−	0.965388i	$-0.583992\pi$
$359$	13.3497	−	13.3497i	0.704572	−	0.704572i	0.965388	+	0.260816i	$0.0839918\pi$
$360$		0			0
$361$	8.54100	+	4.93115i	0.449526	+	0.259534i
$362$	11.7910	−	20.4225i	0.619719	−	1.07338i
$363$	23.3276	−	23.3276i	1.22438	−	1.22438i
$364$	−1.71465	+	12.8520i	−0.0898720	+	0.673627i
$365$		0			0
$366$	1.16677	+	4.35445i	0.0609882	+	0.227611i
$367$	−9.44083	−	35.2337i	−0.492807	−	1.83918i	−0.541979	−	0.840392i	$-0.682325\pi$
$367$	−9.44083	−	35.2337i	−0.492807	−	1.83918i	0.0491716	−	0.998790i	$-0.484342\pi$
$368$	−3.75715	−	1.00673i	−0.195855	−	0.0524792i
$369$	−1.50702	−	1.50702i	−0.0784524	−	0.0784524i
$370$		0			0
$371$	2.89795	−	10.8153i	0.150454	−	0.561502i
$372$	−15.4433			−0.800697
$373$	4.67650	−	17.4530i	0.242140	−	0.903680i	−0.732659	−	0.680596i	$-0.761721\pi$
$373$	4.67650	−	17.4530i	0.242140	−	0.903680i	0.974799	−	0.223084i	$-0.0716123\pi$
$374$	7.60715	−	13.1760i	0.393356	−	0.681313i
$375$		0			0
$376$		−	7.17950i		−	0.370254i
$377$	−18.6800	−	2.49220i	−0.962069	−	0.128355i
$378$	−10.0151	−	10.0151i	−0.515119	−	0.515119i
$379$	13.1989	−	3.53663i	0.677982	−	0.181665i	0.0966343	−	0.995320i	$-0.469192\pi$
$379$	13.1989	−	3.53663i	0.677982	−	0.181665i	0.581348	+	0.813655i	$0.302526\pi$
$380$		0			0
$381$	25.9041	−	14.9557i	1.32711	−	0.766206i
$382$			0.612374i			0.0313318i
$383$	−18.7783	−	32.5250i	−0.959527	−	1.66195i	−0.723650	−	0.690168i	$-0.757537\pi$
$383$	−18.7783	−	32.5250i	−0.959527	−	1.66195i	−0.235878	−	0.971783i	$-0.575797\pi$
$384$	−2.63533	−	0.706135i	−0.134484	−	0.0360348i
$385$		0			0
$386$	−11.2716	−	19.5230i	−0.573709	−	0.993693i
$387$	−12.3303	+	3.30390i	−0.626786	+	0.167947i
$388$	9.00422	+	5.19859i	0.457120	+	0.263918i
$389$	18.5691			0.941492			0.470746	−	0.882269i	$-0.343985\pi$
$389$	18.5691			0.941492			0.470746	+	0.882269i	$0.343985\pi$
$390$		0			0
$391$	12.3151			0.622800
$392$	−5.13709	−	2.96590i	−0.259462	−	0.149800i
$393$	−41.3212	+	11.0720i	−2.08438	+	0.558507i
$394$	6.19964	+	10.7381i	0.312333	+	0.540977i
$395$		0			0
$396$	20.6257	+	5.52664i	1.03648	+	0.277724i
$397$	15.9502	+	27.6266i	0.800517	+	1.38654i	0.919276	+	0.393614i	$0.128775\pi$
$397$	15.9502	+	27.6266i	0.800517	+	1.38654i	−0.118759	+	0.992923i	$0.537891\pi$
$398$		−	5.18652i		−	0.259977i
$399$	25.6844	−	14.8289i	1.28583	−	0.742374i
$400$		0			0
$401$	−23.9250	+	6.41067i	−1.19476	+	0.320134i	−0.800764	−	0.598980i	$-0.795573\pi$
$401$	−23.9250	+	6.41067i	−1.19476	+	0.320134i	−0.393992	+	0.919114i	$0.628906\pi$
$402$	6.73439	+	6.73439i	0.335881	+	0.335881i
$403$	7.84281	−	18.8418i	0.390678	−	0.938578i
$404$			9.87835i			0.491466i
$405$		0			0
$406$	9.39801	−	16.2778i	0.466415	−	0.807855i
$407$	−6.35371	+	23.7124i	−0.314942	+	1.17538i
$408$	8.63801			0.427645
$409$	−0.0418829	+	0.156309i	−0.00207098	+	0.00772899i	−0.966954	−	0.254952i	$-0.917940\pi$
$409$	−0.0418829	+	0.156309i	−0.00207098	+	0.00772899i	0.964883	+	0.262681i	$0.0846068\pi$
$410$		0			0
$411$	−5.48183	−	5.48183i	−0.270399	−	0.270399i
$412$	1.01377	+	0.271638i	0.0499447	+	0.0133826i
$413$	9.66286	+	36.0623i	0.475478	+	1.77451i
$414$	4.47349	+	16.6953i	0.219860	+	0.820529i
$415$		0			0
$416$	2.19987	−	2.85667i	0.107858	−	0.140060i
$417$	30.9138	−	30.9138i	1.51386	−	1.51386i
$418$	−7.26304	+	12.5799i	−0.355247	+	0.615305i
$419$	−30.7441	−	17.7501i	−1.50195	−	0.867150i	−0.999997	−	0.00225390i	$-0.999283\pi$
$419$	−30.7441	−	17.7501i	−1.50195	−	0.867150i	−0.501951	−	0.864896i	$-0.667384\pi$
$420$		0			0
$421$	−9.73738	+	9.73738i	−0.474571	+	0.474571i	−0.903390	−	0.428819i	$-0.858930\pi$
$421$	−9.73738	+	9.73738i	−0.474571	+	0.474571i	0.428819	+	0.903390i	$0.358930\pi$
$422$	1.51600	−	0.875261i	0.0737976	−	0.0426070i
$423$	−27.6287	+	15.9514i	−1.34335	+	0.775585i
$424$	−2.20166	+	2.20166i	−0.106922	+	0.106922i
$425$		0			0
$426$	−22.8155	−	13.1725i	−1.10541	−	0.638211i
$427$	2.97097	−	5.14587i	0.143775	−	0.249026i
$428$	−5.16232	+	5.16232i	−0.249530	+	0.249530i
$429$	−28.8416	+	37.4525i	−1.39248	+	1.80823i
$430$		0			0
$431$	−5.14321	−	19.1947i	−0.247740	−	0.924577i	−0.971987	−	0.235036i	$-0.924479\pi$
$431$	−5.14321	−	19.1947i	−0.247740	−	0.924577i	0.724247	−	0.689541i	$-0.242188\pi$
$432$	1.01938	+	3.80437i	0.0490448	+	0.183038i
$433$	13.0872	+	3.50671i	0.628931	+	0.168522i	0.559185	−	0.829043i	$-0.311114\pi$
$433$	13.0872	+	3.50671i	0.628931	+	0.168522i	0.0697465	+	0.997565i	$0.477781\pi$
$434$	14.3934	+	14.3934i	0.690904	+	0.690904i
$435$		0			0
$436$	0.0180486	−	0.0673581i	0.000864369	−	0.00322587i
$437$	−11.7580			−0.562462
$438$	7.91995	−	29.5577i	0.378430	−	1.41232i
$439$	6.26431	−	10.8501i	0.298979	−	0.517848i	−0.676923	−	0.736054i	$-0.736687\pi$
$439$	6.26431	−	10.8501i	0.298979	−	0.517848i	0.975903	+	0.218206i	$0.0700205\pi$
$440$		0			0
$441$			26.3585i			1.25517i
$442$	−4.38677	+	10.5389i	−0.208657	+	0.501286i
$443$	18.7098	+	18.7098i	0.888931	+	0.888931i	0.994420	−	0.105489i	$-0.0336408\pi$
$443$	18.7098	+	18.7098i	0.888931	+	0.888931i	−0.105489	+	0.994420i	$0.533641\pi$
$444$	−13.4629	+	3.60736i	−0.638919	+	0.171198i
$445$		0			0
$446$	15.4736	−	8.93366i	0.732694	−	0.423021i
$447$			30.2171i			1.42922i
$448$	1.79804	+	3.11430i	0.0849494	+	0.147137i
$449$	−8.84055	−	2.36882i	−0.417212	−	0.111791i	0.0441055	−	0.999027i	$-0.485956\pi$
$449$	−8.84055	−	2.36882i	−0.417212	−	0.111791i	−0.461317	+	0.887235i	$0.652623\pi$
$450$		0			0
$451$	−1.15239	−	1.99600i	−0.0542639	−	0.0939878i
$452$	−4.64287	+	1.24405i	−0.218382	+	0.0585153i
$453$	−2.03675	−	1.17592i	−0.0956946	−	0.0552493i
$454$	−16.5071			−0.774719
$455$		0			0
$456$	−8.24727			−0.386214
$457$	13.6510	+	7.88142i	0.638568	+	0.368677i	0.784063	−	0.620682i	$-0.213144\pi$
$457$	13.6510	+	7.88142i	0.638568	+	0.368677i	−0.145495	+	0.989359i	$0.546477\pi$
$458$	−28.1907	+	7.55367i	−1.31726	+	0.352960i
$459$	−6.23492	−	10.7992i	−0.291021	−	0.504064i
$460$		0			0
$461$	−20.0961	−	5.38473i	−0.935968	−	0.250792i	−0.241570	−	0.970383i	$-0.577662\pi$
$461$	−20.0961	−	5.38473i	−0.935968	−	0.250792i	−0.694398	+	0.719592i	$0.744329\pi$
$462$	−23.5733	−	40.8302i	−1.09673	−	1.89959i
$463$		−	27.9249i		−	1.29778i	−0.760883	−	0.648889i	$-0.775234\pi$
$463$		−	27.9249i		−	1.29778i	0.760883	−	0.648889i	$-0.224766\pi$
$464$	−4.52655	+	2.61340i	−0.210140	+	0.121324i
$465$		0			0
$466$	−7.15894	+	1.91823i	−0.331632	+	0.0888604i
$467$	−23.6492	−	23.6492i	−1.09435	−	1.09435i	−0.995058	−	0.0992957i	$-0.968341\pi$
$467$	−23.6492	−	23.6492i	−1.09435	−	1.09435i	−0.0992957	−	0.995058i	$-0.531659\pi$
$468$	−15.8809	−	2.11876i	−0.734096	−	0.0979395i
$469$		−	12.5531i		−	0.579648i
$470$		0			0
$471$	−17.6863	+	30.6336i	−0.814944	+	1.41152i
$472$	2.68705	−	10.0282i	0.123682	−	0.461586i
$473$	−13.8047			−0.634739
$474$	0.860395	−	3.21104i	0.0395192	−	0.147488i
$475$		0			0
$476$	−8.05075	−	8.05075i	−0.369006	−	0.369006i
$477$	13.3642	+	3.58093i	0.611906	+	0.163960i
$478$	−4.71849	−	17.6096i	−0.215819	−	0.805446i
$479$	6.87884	+	25.6722i	0.314302	+	1.17299i	0.924638	+	0.380848i	$0.124368\pi$
$479$	6.87884	+	25.6722i	0.314302	+	1.17299i	−0.610335	+	0.792143i	$0.708965\pi$
$480$		0			0
$481$	2.43583	−	18.2575i	0.111064	−	0.832472i
$482$	−9.82951	+	9.82951i	−0.447722	+	0.447722i
$483$	19.0812	−	33.0496i	0.868225	−	1.50381i
$484$	10.4719	+	6.04595i	0.475995	+	0.274816i
$485$		0			0
$486$	−13.3424	+	13.3424i	−0.605221	+	0.605221i
$487$	14.9953	−	8.65752i	0.679500	−	0.392310i	−0.120166	−	0.992754i	$-0.538343\pi$
$487$	14.9953	−	8.65752i	0.679500	−	0.392310i	0.799667	+	0.600444i	$0.205009\pi$
$488$	−1.43097	+	0.826168i	−0.0647767	+	0.0373989i
$489$	−34.6232	+	34.6232i	−1.56572	+	1.56572i
$490$		0			0
$491$	3.48033	+	2.00937i	0.157065	+	0.0906815i	0.576472	−	0.817117i	$-0.304429\pi$
$491$	3.48033	+	2.00937i	0.157065	+	0.0906815i	−0.419407	+	0.907798i	$0.637762\pi$
$492$	0.654276	−	1.13324i	0.0294970	−	0.0510903i
$493$	11.7016	−	11.7016i	0.527011	−	0.527011i
$494$	4.18834	−	10.0622i	0.188442	−	0.452720i
$495$		0			0
$496$	−1.46502	−	5.46754i	−0.0657815	−	0.245500i
$497$	8.98739	+	33.5414i	0.403139	+	1.50454i
$498$	28.6517	+	7.67719i	1.28391	+	0.344023i
$499$	−7.93374	−	7.93374i	−0.355163	−	0.355163i	0.506864	−	0.862026i	$-0.330805\pi$
$499$	−7.93374	−	7.93374i	−0.355163	−	0.355163i	−0.862026	+	0.506864i	$0.830805\pi$
$500$		0			0
$501$	13.8119	−	51.5469i	0.617072	−	2.30295i
$502$	5.64570			0.251980
$503$	−0.784369	+	2.92730i	−0.0349733	+	0.130522i	−0.981205	−	0.192967i	$-0.938189\pi$
$503$	−0.784369	+	2.92730i	−0.0349733	+	0.130522i	0.946232	+	0.323489i	$0.104856\pi$
$504$	7.98978	−	13.8387i	0.355893	−	0.616425i
$505$		0			0
$506$			18.6915i			0.830940i
$507$	17.8402	−	30.6544i	0.792313	−	1.36141i
$508$	7.75232	+	7.75232i	0.343953	+	0.343953i
$509$	39.0675	−	10.4681i	1.73164	−	0.463991i	0.751078	−	0.660214i	$-0.229534\pi$
$509$	39.0675	−	10.4681i	1.73164	−	0.463991i	0.980559	+	0.196223i	$0.0628676\pi$
$510$		0			0
$511$	−34.9297	+	20.1667i	−1.54520	+	0.892121i
$512$		−	1.00000i		−	0.0441942i
$513$	5.95288	+	10.3107i	0.262826	+	0.455228i
$514$	0.522706	+	0.140059i	0.0230556	+	0.00617772i
$515$		0			0
$516$	−3.91884	−	6.78763i	−0.172517	−	0.298809i
$517$	−33.3248	+	8.92936i	−1.46562	+	0.392713i
$518$	15.9097	+	9.18547i	0.699032	+	0.403586i
$519$	40.7919			1.79057
$520$		0			0
$521$	17.0630			0.747546			0.373773	−	0.927520i	$-0.378064\pi$
$521$	17.0630			0.747546			0.373773	+	0.927520i	$0.378064\pi$
$522$	20.1142	+	11.6129i	0.880374	+	0.508284i
$523$	−31.0973	+	8.33249i	−1.35979	+	0.364354i	−0.863739	−	0.503939i	$-0.831884\pi$
$523$	−31.0973	+	8.33249i	−1.35979	+	0.364354i	−0.496050	+	0.868294i	$0.665217\pi$
$524$	−7.83984	−	13.5790i	−0.342485	−	0.593202i
$525$		0			0
$526$	−0.812458	−	0.217697i	−0.0354249	−	0.00949206i
$527$	8.96067	+	15.5203i	0.390333	+	0.676076i
$528$			13.1106i			0.570564i
$529$	6.81588	−	3.93515i	0.296343	−	0.171094i
$530$		0			0
$531$	−44.5614	+	11.9402i	−1.93380	+	0.518160i
$532$	7.68657	+	7.68657i	0.333255	+	0.333255i
$533$	1.05035	+	1.37377i	0.0454959	+	0.0595045i
$534$		−	27.9309i		−	1.20869i
$535$		0			0
$536$	−1.74539	+	3.02310i	−0.0753892	+	0.130578i
$537$	1.37422	−	5.12864i	0.0593018	−	0.221317i
$538$	−19.5554			−0.843094
$539$	−7.37755	+	27.5334i	−0.317774	+	1.18595i
$540$		0			0
$541$	−6.85528	−	6.85528i	−0.294732	−	0.294732i	0.544215	−	0.838946i	$-0.316828\pi$
$541$	−6.85528	−	6.85528i	−0.294732	−	0.294732i	−0.838946	+	0.544215i	$0.816828\pi$
$542$	15.9289	+	4.26814i	0.684206	+	0.183332i
$543$	−16.6520	−	62.1462i	−0.714607	−	2.66695i
$544$	0.819442	+	3.05820i	0.0351333	+	0.131119i
$545$		0			0
$546$	21.4861	+	28.1019i	0.919520	+	1.20265i
$547$	−2.06001	+	2.06001i	−0.0880795	+	0.0880795i	−0.749774	−	0.661694i	$-0.769838\pi$
$547$	−2.06001	+	2.06001i	−0.0880795	+	0.0880795i	0.661694	+	0.749774i	$0.269838\pi$
$548$	1.42075	−	2.46082i	0.0606916	−	0.105121i
$549$	6.35864	+	3.67116i	0.271380	+	0.156681i
$550$		0			0
$551$	−11.1722	+	11.1722i	−0.475953	+	0.475953i
$552$	−9.19046	+	5.30612i	−0.391172	+	0.225843i
$553$	−3.79463	+	2.19083i	−0.161364	+	0.0931637i
$554$	11.3135	−	11.3135i	0.480666	−	0.480666i
$555$		0			0
$556$	13.8773	+	8.01209i	0.588531	+	0.339788i
$557$	13.4218	−	23.2473i	0.568701	−	0.985019i	−0.427994	−	0.903782i	$-0.640779\pi$
$557$	13.4218	−	23.2473i	0.568701	−	0.985019i	0.996695	−	0.0812375i	$-0.0258872\pi$
$558$	−17.7856	+	17.7856i	−0.752924	+	0.752924i
$559$	10.2715	−	1.33417i	0.434439	−	0.0564295i
$560$		0			0
$561$	−10.7433	−	40.0947i	−0.453584	−	1.69280i
$562$	4.34902	+	16.2308i	0.183452	+	0.684653i
$563$	−29.0211	−	7.77619i	−1.22309	−	0.327727i	−0.411208	−	0.911542i	$-0.634893\pi$
$563$	−29.0211	−	7.77619i	−1.22309	−	0.327727i	−0.811887	+	0.583815i	$0.801560\pi$
$564$	−13.8507	−	13.8507i	−0.583218	−	0.583218i
$565$		0			0
$566$	−6.19613	+	23.1243i	−0.260443	+	0.971986i
$567$	9.29662			0.390421
$568$	2.49922	−	9.32721i	0.104865	−	0.391361i
$569$	10.0733	−	17.4475i	0.422296	−	0.731438i	−0.573868	−	0.818948i	$-0.694558\pi$
$569$	10.0733	−	17.4475i	0.422296	−	0.731438i	0.996164	+	0.0875099i	$0.0278909\pi$
$570$		0			0
$571$		−	13.4281i		−	0.561947i	−0.959716	−	0.280973i	$-0.909343\pi$
$571$		−	13.4281i		−	0.561947i	0.959716	−	0.280973i	$-0.0906573\pi$
$572$	−15.9957	−	6.65814i	−0.668816	−	0.278391i
$573$	1.18139	+	1.18139i	0.0493533	+	0.0493533i
$574$	−1.66599	+	0.446401i	−0.0695371	+	0.0186324i
$575$		0			0
$576$	−3.84827	+	2.22180i	−0.160345	+	0.0925750i
$577$			42.6338i			1.77487i	0.460935	+	0.887434i	$0.347514\pi$
$577$			42.6338i			1.77487i	−0.460935	+	0.887434i	$0.652486\pi$
$578$	3.48797	+	6.04134i	0.145080	+	0.251286i
$579$	−59.4088	−	15.9185i	−2.46895	−	0.661552i
$580$		0			0
$581$	−19.5485	−	33.8590i	−0.811009	−	1.40471i
$582$	27.4000	−	7.34181i	1.13577	−	0.304328i
$583$	12.9576	+	7.48108i	0.536650	+	0.309835i
$584$	11.2159			0.464118
$585$		0			0
$586$	17.4454			0.720661
$587$	−9.58635	−	5.53468i	−0.395671	−	0.228441i	0.288943	−	0.957346i	$-0.406696\pi$
$587$	−9.58635	−	5.53468i	−0.395671	−	0.228441i	−0.684614	+	0.728905i	$0.740029\pi$
$588$	−15.6323	+	4.18865i	−0.644663	+	0.172737i
$589$	−8.55533	−	14.8183i	−0.352516	−	0.610576i
$590$		0			0
$591$	32.6762	+	8.75557i	1.34412	+	0.360156i
$592$	−2.55430	−	4.42418i	−0.104981	−	0.181833i
$593$			14.9703i			0.614758i	0.951587	+	0.307379i	$0.0994519\pi$
$593$			14.9703i			0.614758i	−0.951587	+	0.307379i	$0.900548\pi$
$594$	16.3908	−	9.46322i	0.672521	−	0.388280i
$595$		0			0
$596$	−10.6981	+	2.86654i	−0.438210	+	0.117418i
$597$	−10.0058	−	10.0058i	−0.409511	−	0.409511i
$598$	−1.80647	−	13.9076i	−0.0738722	−	0.568726i
$599$			31.8600i			1.30176i	0.759179	+	0.650882i	$0.225601\pi$
$599$			31.8600i			1.30176i	−0.759179	+	0.650882i	$0.774399\pi$
$600$		0			0
$601$	12.5762	−	21.7825i	0.512992	−	0.888528i	−0.486895	−	0.873461i	$-0.661870\pi$
$601$	12.5762	−	21.7825i	0.512992	−	0.888528i	0.999886	−	0.0150673i	$-0.00479624\pi$
$602$	−2.67375	+	9.97859i	−0.108974	+	0.406697i
$603$	15.5116			0.631681
$604$	0.223106	−	0.832642i	0.00907804	−	0.0338797i
$605$		0			0
$606$	19.0573	+	19.0573i	0.774149	+	0.774149i
$607$	−13.0370	−	3.49326i	−0.529156	−	0.141787i	−0.0156574	−	0.999877i	$-0.504984\pi$
$607$	−13.0370	−	3.49326i	−0.529156	−	0.141787i	−0.513498	+	0.858091i	$0.671651\pi$
$608$	−0.782374	−	2.91986i	−0.0317295	−	0.118416i
$609$	−13.2725	−	49.5337i	−0.537830	−	2.00721i
$610$		0			0
$611$	23.9327	−	9.86472i	0.968214	−	0.399084i
$612$	9.94814	−	9.94814i	0.402130	−	0.402130i
$613$	−0.774696	+	1.34181i	−0.0312897	+	0.0541953i	−0.881246	−	0.472658i	$-0.843295\pi$
$613$	−0.774696	+	1.34181i	−0.0312897	+	0.0541953i	0.849957	+	0.526853i	$0.176628\pi$
$614$	15.0783	+	8.70544i	0.608509	+	0.351323i
$615$		0			0
$616$	12.2192	−	12.2192i	0.492327	−	0.492327i
$617$	−0.323594	+	0.186827i	−0.0130274	+	0.00752138i	−0.506500	−	0.862240i	$-0.669061\pi$
$617$	−0.323594	+	0.186827i	−0.0130274	+	0.00752138i	0.493472	+	0.869762i	$0.335727\pi$
$618$	2.47980	−	1.43171i	0.0997521	−	0.0575919i
$619$	−10.9674	+	10.9674i	−0.440817	+	0.440817i	−0.892287	−	0.451469i	$-0.850900\pi$
$619$	−10.9674	+	10.9674i	−0.440817	+	0.440817i	0.451469	+	0.892287i	$0.350900\pi$
$620$		0			0
$621$	13.2674	+	7.65992i	0.532401	+	0.307382i
$622$	3.56103	−	6.16789i	0.142784	−	0.247310i
$623$	−26.0321	+	26.0321i	−1.04295	+	1.04295i
$624$	−1.26709	−	9.75507i	−0.0507243	−	0.390515i
$625$		0			0
$626$	1.46918	+	5.48305i	0.0587202	+	0.219147i
$627$	10.2574	+	38.2810i	0.409640	+	1.52880i
$628$	−12.5233	−	3.35562i	−0.499736	−	0.133904i
$629$	11.4369	+	11.4369i	0.456019	+	0.456019i
$630$		0			0
$631$	−5.85911	+	21.8665i	−0.233247	+	0.870491i	0.745684	+	0.666300i	$0.232123\pi$
$631$	−5.85911	+	21.8665i	−0.233247	+	0.870491i	−0.978931	+	0.204191i	$0.934544\pi$
$632$	1.21846			0.0484676
$633$	1.23611	−	4.61321i	0.0491308	−	0.183359i
$634$	1.92219	−	3.32933i	0.0763400	−	0.132225i
$635$		0			0
$636$			8.49486i			0.336843i
$637$	2.82834	−	21.1996i	0.112063	−	0.839957i
$638$	17.7603	+	17.7603i	0.703138	+	0.703138i
$639$	−41.4464	+	11.1055i	−1.63959	+	0.439328i
$640$		0			0
$641$	−7.24531	+	4.18308i	−0.286173	+	0.165222i	−0.636215	−	0.771512i	$-0.719501\pi$
$641$	−7.24531	+	4.18308i	−0.286173	+	0.165222i	0.350042	+	0.936734i	$0.386167\pi$
$642$			19.9183i			0.786111i
$643$	12.3583	+	21.4051i	0.487362	+	0.844136i	0.999894	−	0.0145319i	$-0.00462582\pi$
$643$	12.3583	+	21.4051i	0.487362	+	0.844136i	−0.512532	+	0.858668i	$0.671292\pi$
$644$	13.5110	+	3.62027i	0.532409	+	0.142659i
$645$		0			0
$646$	4.78531	+	8.28841i	0.188276	+	0.326103i
$647$	−32.3337	+	8.66380i	−1.27117	+	0.340609i	−0.830479	−	0.557049i	$-0.811933\pi$
$647$	−32.3337	+	8.66380i	−1.27117	+	0.340609i	−0.440691	+	0.897659i	$0.645267\pi$
$648$	−2.23886	−	1.29260i	−0.0879506	−	0.0507783i
$649$	−49.8896			−1.95834
$650$		0			0
$651$	55.5353			2.17660
$652$	−15.5425	−	8.97349i	−0.608693	−	0.351429i
$653$	−16.2850	+	4.36355i	−0.637281	+	0.170759i	−0.562972	−	0.826476i	$-0.690342\pi$
$653$	−16.2850	+	4.36355i	−0.637281	+	0.170759i	−0.0743095	+	0.997235i	$0.523675\pi$
$654$	−0.0951279	−	0.164766i	−0.00371979	−	0.00644287i
$655$		0			0
$656$	0.463279	+	0.124135i	0.0180880	+	0.00484667i
$657$	−24.9195	−	43.1619i	−0.972203	−	1.68391i
$658$			25.8181i			1.00649i
$659$	15.3740	−	8.87621i	0.598888	−	0.345768i	−0.169716	−	0.985493i	$-0.554285\pi$
$659$	15.3740	−	8.87621i	0.598888	−	0.345768i	0.768604	+	0.639725i	$0.220952\pi$
$660$		0			0
$661$	−3.40284	+	0.911788i	−0.132355	+	0.0354645i	−0.324388	−	0.945924i	$-0.605158\pi$
$661$	−3.40284	+	0.911788i	−0.132355	+	0.0354645i	0.192033	+	0.981388i	$0.438492\pi$
$662$	9.94243	+	9.94243i	0.386423	+	0.386423i
$663$	11.8687	+	28.7946i	0.460943	+	1.11829i
$664$			10.8721i			0.421920i
$665$		0			0
$666$	−11.3503	+	19.6593i	−0.439815	+	0.761781i
$667$	−5.26196	+	19.6379i	−0.203744	+	0.760383i
$668$	19.5599			0.756796
$669$	12.6167	−	47.0863i	0.487791	−	1.82046i
$670$		0			0
$671$	5.61453	+	5.61453i	0.216746	+	0.216746i
$672$	9.47687	+	2.53932i	0.365578	+	0.0979563i
$673$	−6.12305	−	22.8515i	−0.236026	−	0.880861i	−0.977684	−	0.210083i	$-0.932627\pi$
$673$	−6.12305	−	22.8515i	−0.236026	−	0.880861i	0.741657	−	0.670779i	$-0.234040\pi$
$674$	7.79622	+	29.0959i	0.300299	+	1.12073i
$675$		0			0
$676$	12.5453	+	3.40813i	0.482512	+	0.131082i
$677$	−12.1351	+	12.1351i	−0.466389	+	0.466389i	−0.900742	−	0.434354i	$-0.856977\pi$
$677$	−12.1351	+	12.1351i	−0.466389	+	0.466389i	0.434354	+	0.900742i	$0.356977\pi$
$678$	−6.55699	+	11.3570i	−0.251819	+	0.436164i
$679$	−32.3799	−	18.6946i	−1.24263	−	0.717431i
$680$		0			0
$681$	−31.8455	+	31.8455i	−1.22032	+	1.22032i
$682$	−23.5564	+	13.6003i	−0.902021	+	0.520782i
$683$	−14.7605	+	8.52200i	−0.564796	+	0.326085i	−0.755068	−	0.655646i	$-0.772396\pi$
$683$	−14.7605	+	8.52200i	−0.564796	+	0.326085i	0.190272	+	0.981731i	$0.439063\pi$
$684$	−9.49814	+	9.49814i	−0.363170	+	0.363170i
$685$		0			0
$686$	−3.32671	−	1.92067i	−0.127014	−	0.0733317i
$687$	−39.8128	+	68.9579i	−1.51895	+	2.63091i
$688$	2.03133	−	2.03133i	0.0774438	−	0.0774438i
$689$	−10.3643	−	4.31408i	−0.394848	−	0.164353i
$690$		0			0
$691$	3.39371	+	12.6655i	0.129103	+	0.481818i	0.999953	−	0.00973090i	$-0.00309749\pi$
$691$	3.39371	+	12.6655i	0.129103	+	0.481818i	−0.870850	+	0.491549i	$0.836431\pi$
$692$	3.86971	+	14.4420i	0.147104	+	0.549001i
$693$	−74.1717	−	19.8742i	−2.81755	−	0.754960i
$694$	3.36421	+	3.36421i	0.127704	+	0.127704i
$695$		0			0
$696$	−3.69083	+	13.7744i	−0.139901	+	0.522116i
$697$	−1.51852			−0.0575181
$698$	4.94358	−	18.4497i	0.187117	−	0.698331i
$699$	−10.1104	+	17.5117i	−0.382409	+	0.662352i
$700$		0			0
$701$			46.8894i			1.77099i	0.464649	+	0.885495i	$0.346180\pi$
$701$			46.8894i			1.77099i	−0.464649	+	0.885495i	$0.653820\pi$
$702$	−11.2812	+	8.62533i	−0.425780	+	0.325542i
$703$	−10.9196	−	10.9196i	−0.411839	−	0.411839i
$704$	−4.64166	+	1.24373i	−0.174939	+	0.0468748i
$705$		0			0
$706$	3.48374	−	2.01134i	0.131112	−	0.0756978i
$707$		−	35.5233i		−	1.33599i
$708$	−14.1626	−	24.5303i	−0.532262	−	0.921904i
$709$	5.34513	+	1.43222i	0.200741	+	0.0537883i	0.357788	−	0.933803i	$-0.383531\pi$
$709$	5.34513	+	1.43222i	0.200741	+	0.0537883i	−0.157048	+	0.987591i	$0.550198\pi$
$710$		0			0
$711$	−2.70717	−	4.68895i	−0.101527	−	0.175849i
$712$	9.88867	−	2.64966i	0.370594	−	0.0993002i
$713$	−19.0675	−	11.0086i	−0.714084	−	0.412277i
$714$	−31.0630			−1.16250
$715$		0			0
$716$	1.94611			0.0727295
$717$	−43.0754	−	24.8696i	−1.60868	−	0.928771i
$718$	18.2361	−	4.88634i	0.680564	−	0.182357i
$719$	−16.6164	−	28.7804i	−0.619686	−	1.07333i	−0.989543	−	0.144239i	$-0.953927\pi$
$719$	−16.6164	−	28.7804i	−0.619686	−	1.07333i	0.369857	−	0.929089i	$-0.379407\pi$
$720$		0			0
$721$	−3.64558	−	0.976831i	−0.135769	−	0.0363791i
$722$	4.93115	+	8.54100i	0.183518	+	0.317863i
$723$			37.9261i			1.41049i
$724$	20.4225	−	11.7910i	0.758998	−	0.438208i
$725$		0			0
$726$	31.8661	−	8.53851i	1.18266	−	0.316894i
$727$	16.7584	+	16.7584i	0.621535	+	0.621535i	0.945924	−	0.324389i	$-0.105159\pi$
$727$	16.7584	+	16.7584i	0.621535	+	0.621535i	−0.324389	+	0.945924i	$0.605159\pi$
$728$	−7.91092	+	10.2728i	−0.293198	+	0.380736i
$729$			43.7244i			1.61942i
$730$		0			0
$731$	−4.54766	+	7.87677i	−0.168201	+	0.291333i
$732$	−1.16677	+	4.35445i	−0.0431252	+	0.160945i
$733$	17.6137			0.650578			0.325289	−	0.945615i	$-0.394538\pi$
$733$	17.6137			0.650578			0.325289	+	0.945615i	$0.394538\pi$
$734$	9.44083	−	35.2337i	0.348467	−	1.30050i
$735$		0			0
$736$	−2.75043	−	2.75043i	−0.101382	−	0.101382i
$737$	16.2030	+	4.34158i	0.596845	+	0.159924i
$738$	−0.551608	−	2.05863i	−0.0203050	−	0.0757792i
$739$	8.08488	+	30.1732i	0.297407	+	1.10994i	0.939287	+	0.343133i	$0.111488\pi$
$739$	8.08488	+	30.1732i	0.297407	+	1.10994i	−0.641879	+	0.766806i	$0.721845\pi$
$740$		0			0
$741$	−11.3318	−	27.4921i	−0.416286	−	1.00995i
$742$	7.91734	−	7.91734i	0.290655	−	0.290655i
$743$	−7.20098	+	12.4725i	−0.264178	+	0.457570i	−0.967348	−	0.253452i	$-0.918434\pi$
$743$	−7.20098	+	12.4725i	−0.264178	+	0.457570i	0.703170	+	0.711022i	$0.251767\pi$
$744$	−13.3743	−	7.72165i	−0.490325	−	0.283089i
$745$		0			0
$746$	12.7764	−	12.7764i	0.467779	−	0.467779i
$747$	41.8389	−	24.1557i	1.53081	−	0.883811i
$748$	13.1760	−	7.60715i	0.481761	−	0.278145i
$749$	18.5641	−	18.5641i	0.678318	−	0.678318i
$750$		0			0
$751$	−22.8244	−	13.1777i	−0.832875	−	0.480861i	0.0219611	−	0.999759i	$-0.493009\pi$
$751$	−22.8244	−	13.1777i	−0.832875	−	0.480861i	−0.854836	+	0.518898i	$0.826342\pi$
$752$	3.58975	−	6.21763i	0.130905	−	0.226734i
$753$	10.8917	−	10.8917i	0.396915	−	0.396915i
$754$	−14.9313	−	11.4983i	−0.543764	−	0.418744i
$755$		0			0
$756$	−3.66577	−	13.6808i	−0.133323	−	0.497567i
$757$	−12.8291	−	47.8787i	−0.466280	−	1.74018i	−0.652610	−	0.757694i	$-0.726326\pi$
$757$	−12.8291	−	47.8787i	−0.466280	−	1.74018i	0.186330	−	0.982487i	$-0.440341\pi$
$758$	13.1989	+	3.53663i	0.479406	+	0.128456i
$759$	36.0596	+	36.0596i	1.30888	+	1.30888i
$760$		0			0
$761$	−9.10073	+	33.9644i	−0.329901	+	1.23121i	0.579391	+	0.815050i	$0.303290\pi$
$761$	−9.10073	+	33.9644i	−0.329901	+	1.23121i	−0.909292	+	0.416158i	$0.863376\pi$
$762$	29.9115			1.08358
$763$	−0.0649040	+	0.242225i	−0.00234968	+	0.00876914i
$764$	−0.306187	+	0.530332i	−0.0110775	+	0.0191867i
$765$		0			0
$766$		−	37.5566i		−	1.35698i
$767$	37.1209	−	4.82166i	1.34036	−	0.174100i
$768$	−1.92920	−	1.92920i	−0.0696139	−	0.0696139i
$769$	36.6444	−	9.81885i	1.32143	−	0.354077i	0.471918	−	0.881642i	$-0.343562\pi$
$769$	36.6444	−	9.81885i	1.32143	−	0.354077i	0.849514	+	0.527566i	$0.176895\pi$
$770$		0			0
$771$	1.27860	−	0.738202i	0.0460478	−	0.0265857i
$772$		−	22.5432i		−	0.811347i
$773$	−0.546174	−	0.946002i	−0.0196445	−	0.0340253i	0.856036	−	0.516916i	$-0.172920\pi$
$773$	−0.546174	−	0.946002i	−0.0196445	−	0.0340253i	−0.875681	+	0.482891i	$0.839587\pi$
$774$	−12.3303	−	3.30390i	−0.443205	−	0.118756i
$775$		0			0
$776$	5.19859	+	9.00422i	0.186619	+	0.323233i
$777$	48.4135	−	12.9724i	1.73682	−	0.465381i
$778$	16.0813	+	9.28456i	0.576544	+	0.332868i
$779$	1.44983			0.0519456
$780$		0			0
$781$	−46.4021			−1.66040
$782$	10.6652	+	6.15754i	0.381386	+	0.220193i
$783$	19.8847	−	5.32809i	0.710622	−	0.190410i
$784$	−2.96590	−	5.13709i	−0.105925	−	0.183467i
$785$		0			0
$786$	−41.3212	−	11.0720i	−1.47388	−	0.394924i
$787$	−8.13003	−	14.0816i	−0.289804	−	0.501956i	0.683958	−	0.729521i	$-0.260257\pi$
$787$	−8.13003	−	14.0816i	−0.289804	−	0.501956i	−0.973763	+	0.227565i	$0.926924\pi$
$788$			12.3993i			0.441706i
$789$	−1.98737	+	1.14741i	−0.0707524	+	0.0408489i
$790$		0			0
$791$	16.6961	−	4.47371i	0.593646	−	0.159067i
$792$	15.0991	+	15.0991i	0.536522	+	0.536522i
$793$	−4.72018	−	3.63493i	−0.167618	−	0.129080i
$794$			31.9004i			1.13210i
$795$		0			0
$796$	2.59326	−	4.49166i	0.0919156	−	0.159203i
$797$	−1.64815	+	6.15098i	−0.0583805	+	0.217879i	−0.988953	−	0.148228i	$-0.952643\pi$
$797$	−1.64815	+	6.15098i	−0.0583805	+	0.217879i	0.930573	+	0.366107i	$0.119310\pi$
$798$	29.6578			1.04988
$799$	−5.88318	+	21.9563i	−0.208132	+	0.776760i
$800$		0			0
$801$	−32.1673	−	32.1673i	−1.13657	−	1.13657i
$802$	−23.9250	−	6.41067i	−0.844820	−	0.226369i
$803$	−13.9496	−	52.0605i	−0.492269	−	1.83717i
$804$	2.46496	+	9.19935i	0.0869323	+	0.324436i
$805$		0			0
$806$	16.2130	−	12.3961i	0.571078	−	0.436634i
$807$	−37.7263	+	37.7263i	−1.32803	+	1.32803i
$808$	−4.93918	+	8.55490i	−0.173760	+	0.300960i
$809$	−42.1143	−	24.3147i	−1.48066	−	0.854859i	−0.480900	−	0.876776i	$-0.659690\pi$
$809$	−42.1143	−	24.3147i	−1.48066	−	0.854859i	−0.999760	+	0.0219163i	$0.993023\pi$
$810$		0			0
$811$	30.3677	−	30.3677i	1.06635	−	1.06635i	0.0687168	−	0.997636i	$-0.478110\pi$
$811$	30.3677	−	30.3677i	1.06635	−	1.06635i	0.997636	−	0.0687168i	$-0.0218905\pi$
$812$	16.2778	−	9.39801i	0.571240	−	0.329805i
$813$	38.9641	−	22.4959i	1.36653	−	0.788967i
$814$	−17.3587	+	17.3587i	−0.608421	+	0.608421i
$815$		0			0
$816$	7.48073	+	4.31900i	0.261878	+	0.151195i
$817$	4.34194	−	7.52047i	0.151905	−	0.263108i
$818$	−0.114426	+	0.114426i	−0.00400082	+	0.00400082i
$819$	57.1091	+	7.61922i	1.99555	+	0.266237i
$820$		0			0
$821$	2.22871	+	8.31766i	0.0777826	+	0.290288i	0.993850	−	0.110736i	$-0.0353209\pi$
$821$	2.22871	+	8.31766i	0.0777826	+	0.290288i	−0.916067	+	0.401025i	$0.868654\pi$
$822$	−2.00649	−	7.48832i	−0.0699844	−	0.261185i
$823$	19.5380	+	5.23518i	0.681050	+	0.182487i	0.582727	−	0.812668i	$-0.301986\pi$
$823$	19.5380	+	5.23518i	0.681050	+	0.182487i	0.0983229	+	0.995155i	$0.468652\pi$
$824$	0.742128	+	0.742128i	0.0258533	+	0.0258533i
$825$		0			0
$826$	−9.66286	+	36.0623i	−0.336214	+	1.25477i
$827$	27.1385			0.943698			0.471849	−	0.881679i	$-0.343587\pi$
$827$	27.1385			0.943698			0.471849	+	0.881679i	$0.343587\pi$
$828$	−4.47349	+	16.6953i	−0.155465	+	0.580202i
$829$	−6.63461	+	11.4915i	−0.230430	+	0.399116i	−0.957935	−	0.286987i	$-0.907346\pi$
$829$	−6.63461	+	11.4915i	−0.230430	+	0.399116i	0.727505	+	0.686102i	$0.240680\pi$
$830$		0			0
$831$		−	43.6520i		−	1.51427i
$832$	3.33348	−	1.37401i	0.115568	−	0.0476353i
$833$	13.2798	+	13.2798i	0.460119	+	0.460119i
$834$	42.2290	−	11.3152i	1.46227	−	0.391815i
$835$		0			0
$836$	−12.5799	+	7.26304i	−0.435087	+	0.251197i
$837$			22.2940i			0.770592i
$838$	−17.7501	−	30.7441i	−0.613168	−	1.06204i
$839$	−20.8525	−	5.58740i	−0.719907	−	0.192899i	−0.119777	−	0.992801i	$-0.538218\pi$
$839$	−20.8525	−	5.58740i	−0.719907	−	0.192899i	−0.600130	+	0.799902i	$0.704885\pi$
$840$		0			0
$841$	−0.840245	−	1.45535i	−0.0289740	−	0.0501844i
$842$	−13.3015	+	3.56413i	−0.458400	+	0.122828i
$843$	39.7024	+	22.9222i	1.36742	+	0.789483i
$844$	1.75052			0.0602555
$845$		0			0
$846$	−31.9028			−1.09684
$847$	−37.6577	−	21.7417i	−1.29394	−	0.747054i
$848$	−3.00752	+	0.805862i	−0.103279	+	0.0276734i
$849$	32.6577	+	56.5648i	1.12081	+	1.94130i
$850$		0			0
$851$	−19.1938	−	5.14296i	−0.657954	−	0.176298i
$852$	−13.1725	−	22.8155i	−0.451284	−	0.781646i
$853$			8.54409i			0.292544i	0.989244	+	0.146272i	$0.0467275\pi$
$853$			8.54409i			0.292544i	−0.989244	+	0.146272i	$0.953273\pi$
$854$	5.14587	−	2.97097i	0.176088	−	0.101664i
$855$		0			0
$856$	−7.05186	+	1.88954i	−0.241027	+	0.0645831i
$857$	−25.0597	−	25.0597i	−0.856023	−	0.856023i	0.134844	−	0.990867i	$-0.456947\pi$
$857$	−25.0597	−	25.0597i	−0.856023	−	0.856023i	−0.990867	+	0.134844i	$0.956947\pi$
$858$	−43.7038	+	18.0141i	−1.49202	+	0.614990i
$859$			20.1553i			0.687691i	0.939026	+	0.343845i	$0.111730\pi$
$859$			20.1553i			0.687691i	−0.939026	+	0.343845i	$0.888270\pi$
$860$		0			0
$861$	−2.35283	+	4.07522i	−0.0801842	+	0.138883i
$862$	5.14321	−	19.1947i	0.175178	−	0.653775i
$863$	−50.9511			−1.73440			−0.867198	−	0.497964i	$-0.834081\pi$
$863$	−50.9511			−1.73440			−0.867198	+	0.497964i	$0.834081\pi$
$864$	−1.01938	+	3.80437i	−0.0346799	+	0.129427i
$865$		0			0
$866$	9.58050	+	9.58050i	0.325559	+	0.325559i
$867$	18.3839	+	4.92595i	0.624350	+	0.167294i
$868$	5.26834	+	19.6617i	0.178819	+	0.667362i
$869$	−1.51543	−	5.65566i	−0.0514074	−	0.191855i
$870$		0			0
$871$	−12.4756	−	1.66444i	−0.422720	−	0.0563973i
$872$	0.0493096	−	0.0493096i	0.00166983	−	0.00166983i
$873$	23.1005	−	40.0112i	0.781832	−	1.35417i
$874$	−10.1827	−	5.87900i	−0.344436	−	0.198860i
$875$		0			0
$876$	21.6377	−	21.6377i	0.731070	−	0.731070i
$877$	−36.5646	+	21.1106i	−1.23470	+	0.712854i	−0.968006	−	0.250928i	$-0.919264\pi$
$877$	−36.5646	+	21.1106i	−1.23470	+	0.712854i	−0.266693	+	0.963781i	$0.585931\pi$
$878$	10.8501	−	6.26431i	0.366174	−	0.211410i
$879$	33.6555	−	33.6555i	1.13517	−	1.13517i
$880$		0			0
$881$	4.93061	+	2.84669i	0.166116	+	0.0959074i	0.580753	−	0.814080i	$-0.302758\pi$
$881$	4.93061	+	2.84669i	0.166116	+	0.0959074i	−0.414637	+	0.909987i	$0.636091\pi$
$882$	−13.1793	+	22.8272i	−0.443769	+	0.768631i
$883$	6.32029	−	6.32029i	0.212695	−	0.212695i	−0.592717	−	0.805411i	$-0.701945\pi$
$883$	6.32029	−	6.32029i	0.212695	−	0.212695i	0.805411	+	0.592717i	$0.201945\pi$
$884$	−9.06852	+	6.93360i	−0.305007	+	0.233202i
$885$		0			0
$886$	6.84828	+	25.5581i	0.230072	+	0.858642i
$887$	−12.3916	−	46.2462i	−0.416070	−	1.55279i	−0.782683	−	0.622421i	$-0.786149\pi$
$887$	−12.3916	−	46.2462i	−0.416070	−	1.55279i	0.366613	−	0.930374i	$-0.380517\pi$
$888$	−13.4629	−	3.60736i	−0.451784	−	0.121055i
$889$	−27.8780	−	27.8780i	−0.934996	−	0.934996i
$890$		0			0
$891$	−3.21530	+	11.9997i	−0.107717	+	0.402004i
$892$	17.8673			0.598242
$893$	5.61706	−	20.9631i	0.187968	−	0.701505i
$894$	−15.1086	+	26.1688i	−0.505306	+	0.875215i
$895$		0			0
$896$			3.59608i			0.120137i
$897$	−30.3156	−	23.3456i	−1.01221	−	0.779485i
$898$	−6.47173	−	6.47173i	−0.215965	−	0.215965i
$899$	−28.5778	+	7.65739i	−0.953122	+	0.255388i
$900$		0			0
$901$	8.53724	−	4.92898i	0.284417	−	0.164208i
$902$		−	2.30478i		−	0.0767407i
$903$	14.0925	+	24.4089i	0.468968	+	0.812276i
$904$	−4.64287	−	1.24405i	−0.154420	−	0.0413766i
$905$		0			0
$906$	−1.17592	−	2.03675i	−0.0390672	−	0.0676663i
$907$	20.9354	−	5.60963i	0.695149	−	0.186265i	0.106092	−	0.994356i	$-0.466166\pi$
$907$	20.9354	−	5.60963i	0.695149	−	0.186265i	0.589057	+	0.808092i	$0.299499\pi$
$908$	−14.2956	−	8.25357i	−0.474416	−	0.273904i
$909$	43.8955			1.45592
$910$		0			0
$911$	−10.5156			−0.348398			−0.174199	−	0.984710i	$-0.555734\pi$
$911$	−10.5156			−0.348398			−0.174199	+	0.984710i	$0.555734\pi$
$912$	−7.14234	−	4.12363i	−0.236507	−	0.136547i
$913$	50.4647	−	13.5220i	1.67014	−	0.447512i
$914$	7.88142	+	13.6510i	0.260694	+	0.451536i
$915$		0			0
$916$	−28.1907	−	7.55367i	−0.931446	−	0.249580i
$917$	28.1927	+	48.8312i	0.931005	+	1.61255i
$918$		−	12.4698i		−	0.411566i
$919$	−30.4569	+	17.5843i	−1.00468	+	0.580052i	−0.909630	−	0.415420i	$-0.863635\pi$
$919$	−30.4569	+	17.5843i	−1.00468	+	0.580052i	−0.0950505	+	0.995472i	$0.530301\pi$
$920$		0			0
$921$	45.8834	−	12.2944i	1.51191	−	0.405115i
$922$	−14.7114	−	14.7114i	−0.484493	−	0.484493i
$923$	34.5260	−	4.48461i	1.13644	−	0.147613i
$924$		−	47.1466i		−	1.55101i
$925$		0			0
$926$	13.9624	−	24.1836i	0.458834	−	0.794723i
$927$	1.20705	−	4.50477i	0.0396447	−	0.147956i
$928$	−5.22681			−0.171578
$929$	−2.03384	+	7.59039i	−0.0667281	+	0.249033i	−0.991231	−	0.132143i	$-0.957814\pi$
$929$	−2.03384	+	7.59039i	−0.0667281	+	0.249033i	0.924503	+	0.381176i	$0.124481\pi$
$930$		0			0
$931$	−12.6791	−	12.6791i	−0.415542	−	0.415542i
$932$	−7.15894	−	1.91823i	−0.234499	−	0.0628338i
$933$	−5.02914	−	18.7690i	−0.164647	−	0.614469i
$934$	−8.65620	−	32.3054i	−0.283240	−	1.05706i
$935$		0			0
$936$	−12.6939	−	9.77536i	−0.414913	−	0.319518i
$937$	−30.8186	+	30.8186i	−1.00680	+	1.00680i	−0.00682291	+	0.999977i	$0.502172\pi$
$937$	−30.8186	+	30.8186i	−1.00680	+	1.00680i	−0.999977	+	0.00682291i	$0.997828\pi$
$938$	6.27655	−	10.8713i	0.204937	−	0.354961i
$939$	13.4122	+	7.74355i	0.437691	+	0.252701i
$940$		0			0
$941$	−18.5705	+	18.5705i	−0.605382	+	0.605382i	−0.941736	−	0.336354i	$-0.890806\pi$
$941$	−18.5705	+	18.5705i	−0.605382	+	0.605382i	0.336354	+	0.941736i	$0.390806\pi$
$942$	−30.6336	+	17.6863i	−0.998098	+	0.576252i
$943$	1.61564	−	0.932791i	0.0526125	−	0.0303758i
$944$	7.34117	−	7.34117i	0.238935	−	0.238935i
$945$		0			0
$946$	−11.9552	−	6.90233i	−0.388697	−	0.224414i
$947$	−4.48242	+	7.76379i	−0.145659	+	0.252289i	−0.929619	−	0.368523i	$-0.879864\pi$
$947$	−4.48242	+	7.76379i	−0.145659	+	0.252289i	0.783959	+	0.620812i	$0.213197\pi$
$948$	2.35064	−	2.35064i	0.0763453	−	0.0763453i
$949$	15.4108	+	37.3880i	0.500256	+	1.21367i
$950$		0			0
$951$	−2.71465	−	10.1312i	−0.0880287	−	0.328528i
$952$	−2.94678	−	10.9975i	−0.0955057	−	0.356432i
$953$	−36.7363	−	9.84347i	−1.19001	−	0.318861i	−0.391118	−	0.920341i	$-0.627912\pi$
$953$	−36.7363	−	9.84347i	−1.19001	−	0.318861i	−0.798888	+	0.601479i	$0.794578\pi$
$954$	9.78329	+	9.78329i	0.316746	+	0.316746i
$955$		0			0
$956$	4.71849	−	17.6096i	0.152607	−	0.569536i
$957$	68.5264			2.21514
$958$	−6.87884	+	25.6722i	−0.222245	+	0.829430i
$959$	−5.10915	+	8.84931i	−0.164983	+	0.285759i
$960$		0			0
$961$		−	1.04031i		−	0.0335583i
$962$	11.2383	−	14.5936i	0.362336	−	0.470516i
$963$	22.9393	+	22.9393i	0.739208	+	0.739208i
$964$	−13.4274	+	3.59785i	−0.432466	+	0.115879i
$965$		0			0
$966$	33.0496	−	19.0812i	1.06335	−	0.613928i
$967$			33.0128i			1.06162i	0.847491	+	0.530810i	$0.178112\pi$
$967$			33.0128i			1.06162i	−0.847491	+	0.530810i	$0.821888\pi$
$968$	6.04595	+	10.4719i	0.194324	+	0.336579i
$969$	25.2218	+	6.75816i	0.810240	+	0.217103i
$970$		0			0
$971$	17.4084	+	30.1522i	0.558662	+	0.967631i	0.997608	+	0.0691180i	$0.0220185\pi$
$971$	17.4084	+	30.1522i	0.558662	+	0.967631i	−0.438946	+	0.898513i	$0.644648\pi$
$972$	−18.2260	+	4.88364i	−0.584599	+	0.156643i
$973$	−49.9041	−	28.8121i	−1.59985	−	0.923674i
$974$	17.3150			0.554810
$975$		0			0
$976$	−1.65234			−0.0528900
$977$	19.7509	+	11.4032i	0.631888	+	0.364821i	0.781483	−	0.623927i	$-0.214464\pi$
$977$	19.7509	+	11.4032i	0.631888	+	0.364821i	−0.149595	+	0.988747i	$0.547797\pi$
$978$	−47.2962	+	12.6730i	−1.51237	+	0.405237i
$979$	−24.5977	−	42.6044i	−0.786145	−	1.36164i
$980$		0			0
$981$	−0.299313	−	0.0802006i	−0.00955632	−	0.00256061i
$982$	2.00937	+	3.48033i	0.0641215	+	0.111062i
$983$		−	5.82429i		−	0.185766i	−0.995677	−	0.0928831i	$-0.970392\pi$
$983$		−	5.82429i		−	0.185766i	0.995677	−	0.0928831i	$-0.0296083\pi$
$984$	1.13324	−	0.654276i	0.0361263	−	0.0208575i
$985$		0			0
$986$	15.9846	−	4.28306i	0.509054	−	0.136401i
$987$	49.8081	+	49.8081i	1.58541	+	1.58541i
$988$	8.65831	−	6.61996i	0.275457	−	0.210609i
$989$		−	11.1741i		−	0.355314i
$990$		0			0
$991$	8.25583	−	14.2995i	0.262255	−	0.454239i	−0.704586	−	0.709619i	$-0.748867\pi$
$991$	8.25583	−	14.2995i	0.262255	−	0.454239i	0.966841	+	0.255380i	$0.0822005\pi$
$992$	1.46502	−	5.46754i	0.0465145	−	0.173595i
$993$	38.3618			1.21738
$994$	−8.98739	+	33.5414i	−0.285063	+	1.06387i
$995$		0			0
$996$	20.9745	+	20.9745i	0.664601	+	0.664601i
$997$	30.2008	+	8.09228i	0.956469	+	0.256285i	0.703105	−	0.711086i	$-0.251796\pi$
$997$	30.2008	+	8.09228i	0.956469	+	0.256285i	0.253364	+	0.967371i	$0.418463\pi$
$998$	−2.90395	−	10.8377i	−0.0919229	−	0.343061i
$999$	5.20759	+	19.4350i	0.164761	+	0.614896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.t.g.643.4		16
5.2	odd	4		650.2.w.g.357.1		16
5.3	odd	4		130.2.s.b.97.4	yes	16
5.4	even	2		130.2.p.b.123.1	yes	16
13.11	odd	12		650.2.w.g.193.1		16
65.24	odd	12		130.2.s.b.63.4	yes	16
65.37	even	12	inner	650.2.t.g.557.4		16
65.63	even	12		130.2.p.b.37.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.p.b.37.1	✓	16	65.63	even	12
130.2.p.b.123.1	yes	16	5.4	even	2
130.2.s.b.63.4	yes	16	65.24	odd	12
130.2.s.b.97.4	yes	16	5.3	odd	4
650.2.t.g.557.4		16	65.37	even	12	inner
650.2.t.g.643.4		16	1.1	even	1	trivial
650.2.w.g.193.1		16	13.11	odd	12
650.2.w.g.357.1		16	5.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.t (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(2.63533 - 0.706135i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.63533 + 0.706135i) q^{6} +(-1.79804 - 3.11430i) q^{7} +1.00000i q^{8} +(3.84827 - 2.22180i) q^{9} +(4.64166 - 1.24373i) q^{11} +(1.92920 + 1.92920i) q^{12} +(-3.33348 + 1.37401i) q^{13} -3.59608i q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.819442 - 3.05820i) q^{17} +4.44360 q^{18} +(-0.782374 + 2.91986i) q^{19} +(-6.93755 - 6.93755i) q^{21} +(4.64166 + 1.24373i) q^{22} +(1.00673 + 3.75715i) q^{23} +(0.706135 + 2.63533i) q^{24} +(-3.57388 - 0.476810i) q^{26} +(2.78499 - 2.78499i) q^{27} +(1.79804 - 3.11430i) q^{28} +(4.52655 + 2.61340i) q^{29} +(-4.00252 + 4.00252i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(11.3541 - 6.55528i) q^{33} +(2.23876 - 2.23876i) q^{34} +(3.84827 + 2.22180i) q^{36} +(-2.55430 + 4.42418i) q^{37} +(-2.13749 + 2.13749i) q^{38} +(-7.81459 + 5.97487i) q^{39} +(-0.124135 - 0.463279i) q^{41} +(-2.53932 - 9.47687i) q^{42} +(-2.77485 - 0.743519i) q^{43} +(3.39793 + 3.39793i) q^{44} +(-1.00673 + 3.75715i) q^{46} -7.17950 q^{47} +(-0.706135 + 2.63533i) q^{48} +(-2.96590 + 5.13709i) q^{49} -8.63801i q^{51} +(-2.85667 - 2.19987i) q^{52} +(2.20166 + 2.20166i) q^{53} +(3.80437 - 1.01938i) q^{54} +(3.11430 - 1.79804i) q^{56} +8.24727i q^{57} +(2.61340 + 4.52655i) q^{58} +(-10.0282 - 2.68705i) q^{59} +(0.826168 + 1.43097i) q^{61} +(-5.46754 + 1.46502i) q^{62} +(-13.8387 - 7.98978i) q^{63} -1.00000 q^{64} +13.1106 q^{66} +(3.02310 + 1.74539i) q^{67} +(3.05820 - 0.819442i) q^{68} +(5.30612 + 9.19046i) q^{69} +(-9.32721 - 2.49922i) q^{71} +(2.22180 + 3.84827i) q^{72} -11.2159i q^{73} +(-4.42418 + 2.55430i) q^{74} +(-2.91986 + 0.782374i) q^{76} +(-12.2192 - 12.2192i) q^{77} +(-9.75507 + 1.26709i) q^{78} -1.21846i q^{79} +(-1.29260 + 2.23886i) q^{81} +(0.124135 - 0.463279i) q^{82} +10.8721 q^{83} +(2.53932 - 9.47687i) q^{84} +(-2.03133 - 2.03133i) q^{86} +(13.7744 + 3.69083i) q^{87} +(1.24373 + 4.64166i) q^{88} +(-2.64966 - 9.88867i) q^{89} +(10.2728 + 7.91092i) q^{91} +(-2.75043 + 2.75043i) q^{92} +(-7.72165 + 13.3743i) q^{93} +(-6.21763 - 3.58975i) q^{94} +(-1.92920 + 1.92920i) q^{96} +(9.00422 - 5.19859i) q^{97} +(-5.13709 + 2.96590i) q^{98} +(15.0991 - 15.0991i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 6 q^{11} - 2 q^{13} - 8 q^{16} + 16 q^{17} + 16 q^{18} + 6 q^{22} + 6 q^{23} - 6 q^{26} + 12 q^{27} - 6 q^{29} + 6 q^{33} - 14 q^{34} + 20 q^{37} - 6 q^{38} - 6 q^{39} - 44 q^{41} - 6 q^{42}+ \cdots - 26 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 6 * q^11 - 2 * q^13 - 8 * q^16 + 16 * q^17 + 16 * q^18 + 6 * q^22 + 6 * q^23 - 6 * q^26 + 12 * q^27 - 6 * q^29 + 6 * q^33 - 14 * q^34 + 20 * q^37 - 6 * q^38 - 6 * q^39 - 44 * q^41 - 6 * q^42 + 6 * q^44 - 6 * q^46 - 52 * q^47 - 2 * q^49 - 10 * q^52 + 24 * q^53 + 6 * q^54 + 6 * q^56 - 8 * q^58 - 46 * q^59 + 6 * q^61 - 12 * q^62 - 90 * q^63 - 16 * q^64 + 52 * q^66 - 12 * q^67 + 2 * q^68 + 58 * q^69 + 6 * q^71 + 8 * q^72 + 24 * q^74 - 6 * q^76 - 58 * q^77 - 38 * q^78 - 24 * q^81 + 44 * q^82 + 64 * q^83 + 6 * q^84 + 44 * q^87 - 24 * q^89 + 38 * q^91 + 26 * q^93 + 6 * q^97 - 26 * q^99

Introduction

L-functions

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