LMFDB - Embedded newform 650.2.t.c.643.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(7,650)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.56070144.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 $ x^8 - 4x^7 + 16x^6 - 34x^5 + 63x^4 - 74x^3 + 70x^2 - 38*x + 13
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			643.1
Root			$0.500000 - 1.56488i$ of defining polynomial
Character	$\chi$	$=$	650.643
Dual form			650.2.t.c.557.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-3.17011 + 0.849429i) q^{3} +(0.500000 + 0.866025i) q^{4} +(3.17011 + 0.849429i) q^{6} +(0.198857 + 0.344430i) q^{7} -1.00000i q^{8} +(6.72999 - 3.88556i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-3.17011 + 0.849429i) q^{3} +(0.500000 + 0.866025i) q^{4} +(3.17011 + 0.849429i) q^{6} +(0.198857 + 0.344430i) q^{7} -1.00000i q^{8} +(6.72999 - 3.88556i) q^{9} +(-5.33728 + 1.43012i) q^{11} +(-2.32068 - 2.32068i) q^{12} +(-2.34943 - 2.73499i) q^{13} -0.397714i q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.564094 - 2.10523i) q^{17} -7.77113 q^{18} +(0.507152 - 1.89272i) q^{19} +(-0.922968 - 0.922968i) q^{21} +(5.33728 + 1.43012i) q^{22} +(1.54113 + 5.75159i) q^{23} +(0.849429 + 3.17011i) q^{24} +(0.667168 + 3.54329i) q^{26} +(-11.0723 + 11.0723i) q^{27} +(-0.198857 + 0.344430i) q^{28} +(-3.96205 - 2.28749i) q^{29} +(2.49794 - 2.49794i) q^{31} +(0.866025 - 0.500000i) q^{32} +(15.7050 - 9.06727i) q^{33} +(-1.54113 + 1.54113i) q^{34} +(6.72999 + 3.88556i) q^{36} +(1.60307 - 2.77661i) q^{37} +(-1.38556 + 1.38556i) q^{38} +(9.77113 + 6.67456i) q^{39} +(2.28749 + 8.53702i) q^{41} +(0.337830 + 1.26080i) q^{42} +(6.92885 + 1.85658i) q^{43} +(-3.90716 - 3.90716i) q^{44} +(1.54113 - 5.75159i) q^{46} +11.8102 q^{47} +(0.849429 - 3.17011i) q^{48} +(3.42091 - 5.92519i) q^{49} +7.15296i q^{51} +(1.19386 - 3.40216i) q^{52} +(5.86397 + 5.86397i) q^{53} +(15.1250 - 4.05273i) q^{54} +(0.344430 - 0.198857i) q^{56} +6.43091i q^{57} +(2.28749 + 3.96205i) q^{58} +(6.38556 + 1.71101i) q^{59} +(3.72490 + 6.45171i) q^{61} +(-3.41225 + 0.914311i) q^{62} +(2.67661 + 1.54534i) q^{63} -1.00000 q^{64} -18.1345 q^{66} +(-1.07703 - 0.621825i) q^{67} +(2.10523 - 0.564094i) q^{68} +(-9.77113 - 16.9241i) q^{69} +(-9.96205 - 2.66932i) q^{71} +(-3.88556 - 6.72999i) q^{72} -1.92362i q^{73} +(-2.77661 + 1.60307i) q^{74} +(1.89272 - 0.507152i) q^{76} +(-1.55393 - 1.55393i) q^{77} +(-5.12477 - 10.6659i) q^{78} +9.33180i q^{79} +(14.0385 - 24.3154i) q^{81} +(2.28749 - 8.53702i) q^{82} -6.90343 q^{83} +(0.337830 - 1.26080i) q^{84} +(-5.07227 - 5.07227i) q^{86} +(14.5032 + 3.88612i) q^{87} +(1.43012 + 5.33728i) q^{88} +(1.88556 + 7.03702i) q^{89} +(0.474815 - 1.35309i) q^{91} +(-4.21046 + 4.21046i) q^{92} +(-5.79693 + 10.0406i) q^{93} +(-10.2279 - 5.90510i) q^{94} +(-2.32068 + 2.32068i) q^{96} +(3.58887 - 2.07203i) q^{97} +(-5.92519 + 3.42091i) q^{98} +(-30.3630 + 30.3630i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{3} + 4 q^{4} + 6 q^{6} + 12 q^{9}+O(q^{10}) $ 8 * q - 6 * q^3 + 4 * q^4 + 6 * q^6 + 12 * q^9	$ 8 q - 6 q^{3} + 4 q^{4} + 6 q^{6} + 12 q^{9} - 18 q^{11} - 18 q^{13} - 4 q^{16} + 6 q^{17} - 8 q^{18} + 14 q^{19} + 8 q^{21} + 18 q^{22} + 6 q^{24} - 36 q^{27} + 24 q^{29} - 8 q^{31} + 42 q^{33} + 12 q^{36} + 6 q^{37} + 16 q^{38} + 24 q^{39} + 12 q^{41} + 22 q^{42} + 12 q^{43} - 12 q^{44} + 6 q^{48} - 16 q^{49} - 6 q^{52} + 12 q^{53} + 36 q^{54} - 12 q^{56} + 12 q^{58} + 24 q^{59} + 6 q^{61} + 10 q^{62} - 8 q^{64} - 12 q^{66} - 24 q^{67} + 6 q^{68} - 24 q^{69} - 24 q^{71} - 4 q^{72} - 30 q^{74} - 2 q^{76} - 36 q^{77} - 10 q^{78} + 28 q^{81} + 12 q^{82} - 60 q^{83} + 22 q^{84} + 12 q^{86} + 48 q^{87} + 6 q^{88} - 12 q^{89} - 2 q^{91} - 12 q^{92} - 24 q^{93} - 12 q^{94} - 30 q^{97} - 24 q^{98} - 84 q^{99}+O(q^{100}) $ 8 * q - 6 * q^3 + 4 * q^4 + 6 * q^6 + 12 * q^9 - 18 * q^11 - 18 * q^13 - 4 * q^16 + 6 * q^17 - 8 * q^18 + 14 * q^19 + 8 * q^21 + 18 * q^22 + 6 * q^24 - 36 * q^27 + 24 * q^29 - 8 * q^31 + 42 * q^33 + 12 * q^36 + 6 * q^37 + 16 * q^38 + 24 * q^39 + 12 * q^41 + 22 * q^42 + 12 * q^43 - 12 * q^44 + 6 * q^48 - 16 * q^49 - 6 * q^52 + 12 * q^53 + 36 * q^54 - 12 * q^56 + 12 * q^58 + 24 * q^59 + 6 * q^61 + 10 * q^62 - 8 * q^64 - 12 * q^66 - 24 * q^67 + 6 * q^68 - 24 * q^69 - 24 * q^71 - 4 * q^72 - 30 * q^74 - 2 * q^76 - 36 * q^77 - 10 * q^78 + 28 * q^81 + 12 * q^82 - 60 * q^83 + 22 * q^84 + 12 * q^86 + 48 * q^87 + 6 * q^88 - 12 * q^89 - 2 * q^91 - 12 * q^92 - 24 * q^93 - 12 * q^94 - 30 * q^97 - 24 * q^98 - 84 * q^99

Display 100 coefficients 10 coefficients

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
$3$	−3.17011	+	0.849429i	−1.83026	+	0.490418i	−0.997957	−	0.0638964i	$-0.979647\pi$
$3$	−3.17011	+	0.849429i	−1.83026	+	0.490418i	−0.832308	+	0.554314i	$0.812981\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	3.17011	+	0.849429i	1.29419	+	0.346778i
$7$	0.198857	+	0.344430i	0.0751609	+	0.130182i	0.901156	−	0.433494i	$-0.142720\pi$
$7$	0.198857	+	0.344430i	0.0751609	+	0.130182i	−0.825995	+	0.563677i	$0.809386\pi$
$8$		−	1.00000i		−	0.353553i
$9$	6.72999	−	3.88556i	2.24333	−	1.29519i
$10$		0			0
$11$	−5.33728	+	1.43012i	−1.60925	+	0.431197i	−0.947819	−	0.318809i	$-0.896717\pi$
$11$	−5.33728	+	1.43012i	−1.60925	+	0.431197i	−0.661431	+	0.750006i	$0.730051\pi$
$12$	−2.32068	−	2.32068i	−0.669923	−	0.669923i
$13$	−2.34943	−	2.73499i	−0.651614	−	0.758551i
$13$	−2.34943	−	2.73499i	−0.651614	−	0.758551i
$14$		−	0.397714i		−	0.106294i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.564094	−	2.10523i	0.136813	−	0.510593i	−0.863171	−	0.504912i	$-0.831525\pi$
$17$	0.564094	−	2.10523i	0.136813	−	0.510593i	0.999984	−	0.00568097i	$-0.00180832\pi$
$18$	−7.77113			−1.83167
$19$	0.507152	−	1.89272i	0.116349	−	0.434219i	−0.883036	−	0.469306i	$-0.844504\pi$
$19$	0.507152	−	1.89272i	0.116349	−	0.434219i	0.999384	+	0.0350870i	$0.0111708\pi$
$20$		0			0
$21$	−0.922968	−	0.922968i	−0.201408	−	0.201408i
$22$	5.33728	+	1.43012i	1.13791	+	0.304903i
$23$	1.54113	+	5.75159i	0.321349	+	1.19929i	0.917932	+	0.396738i	$0.129858\pi$
$23$	1.54113	+	5.75159i	0.321349	+	1.19929i	−0.596583	+	0.802551i	$0.703475\pi$
$24$	0.849429	+	3.17011i	0.173389	+	0.647096i
$25$		0			0
$26$	0.667168	+	3.54329i	0.130842	+	0.694896i
$27$	−11.0723	+	11.0723i	−2.13086	+	2.13086i
$28$	−0.198857	+	0.344430i	−0.0375804	+	0.0650912i
$29$	−3.96205	−	2.28749i	−0.735733	−	0.424776i	0.0847826	−	0.996399i	$-0.472980\pi$
$29$	−3.96205	−	2.28749i	−0.735733	−	0.424776i	−0.820516	+	0.571624i	$0.806314\pi$
$30$		0			0
$31$	2.49794	−	2.49794i	0.448644	−	0.448644i	−0.446260	−	0.894904i	$-0.647244\pi$
$31$	2.49794	−	2.49794i	0.448644	−	0.448644i	0.894904	+	0.446260i	$0.147244\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	15.7050	−	9.06727i	2.73389	−	1.57841i
$34$	−1.54113	+	1.54113i	−0.264302	+	0.264302i
$35$		0			0
$36$	6.72999	+	3.88556i	1.12167	+	0.647594i
$37$	1.60307	−	2.77661i	0.263544	−	0.456471i	−0.703637	−	0.710559i	$-0.748442\pi$
$37$	1.60307	−	2.77661i	0.263544	−	0.456471i	0.967181	+	0.254088i	$0.0817753\pi$
$38$	−1.38556	+	1.38556i	−0.224768	+	0.224768i
$39$	9.77113	+	6.67456i	1.56463	+	1.06878i
$40$		0			0
$41$	2.28749	+	8.53702i	0.357246	+	1.33326i	0.877635	+	0.479330i	$0.159120\pi$
$41$	2.28749	+	8.53702i	0.357246	+	1.33326i	−0.520389	+	0.853929i	$0.674213\pi$
$42$	0.337830	+	1.26080i	0.0521282	+	0.194545i
$43$	6.92885	+	1.85658i	1.05664	+	0.283126i	0.744993	−	0.667072i	$-0.232453\pi$
$43$	6.92885	+	1.85658i	1.05664	+	0.283126i	0.311647	+	0.950198i	$0.399119\pi$
$44$	−3.90716	−	3.90716i	−0.589026	−	0.589026i
$45$		0			0
$46$	1.54113	−	5.75159i	0.227228	−	0.848026i
$47$	11.8102			1.72270			0.861348	−	0.508016i	$-0.169621\pi$
$47$	11.8102			1.72270			0.861348	+	0.508016i	$0.169621\pi$
$48$	0.849429	−	3.17011i	0.122604	−	0.457566i
$49$	3.42091	−	5.92519i	0.488702	−	0.846456i
$50$		0			0
$51$			7.15296i			1.00162i
$52$	1.19386	−	3.40216i	0.165558	−	0.471795i
$53$	5.86397	+	5.86397i	0.805478	+	0.805478i	0.983946	−	0.178468i	$-0.0571140\pi$
$53$	5.86397	+	5.86397i	0.805478	+	0.805478i	−0.178468	+	0.983946i	$0.557114\pi$
$54$	15.1250	−	4.05273i	2.05825	−	0.551507i
$55$		0			0
$56$	0.344430	−	0.198857i	0.0460265	−	0.0265734i
$57$			6.43091i			0.851795i
$58$	2.28749	+	3.96205i	0.300362	+	0.520242i
$59$	6.38556	+	1.71101i	0.831330	+	0.222754i	0.649294	−	0.760538i	$-0.275065\pi$
$59$	6.38556	+	1.71101i	0.831330	+	0.222754i	0.182036	+	0.983292i	$0.441731\pi$
$60$		0			0
$61$	3.72490	+	6.45171i	0.476924	+	0.826057i	0.999650	−	0.0264434i	$-0.00841819\pi$
$61$	3.72490	+	6.45171i	0.476924	+	0.826057i	−0.522726	+	0.852501i	$0.675085\pi$
$62$	−3.41225	+	0.914311i	−0.433357	+	0.116118i
$63$	2.67661	+	1.54534i	0.337222	+	0.194695i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−18.1345			−2.23221
$67$	−1.07703	−	0.621825i	−0.131580	−	0.0759680i	0.432765	−	0.901507i	$-0.357538\pi$
$67$	−1.07703	−	0.621825i	−0.131580	−	0.0759680i	−0.564345	+	0.825539i	$0.690871\pi$
$68$	2.10523	−	0.564094i	0.255296	−	0.0684065i
$69$	−9.77113	−	16.9241i	−1.17631	−	2.03742i
$70$		0			0
$71$	−9.96205	−	2.66932i	−1.18228	−	0.316790i	−0.386448	−	0.922311i	$-0.626298\pi$
$71$	−9.96205	−	2.66932i	−1.18228	−	0.316790i	−0.795829	+	0.605521i	$0.792965\pi$
$72$	−3.88556	−	6.72999i	−0.457918	−	0.793137i
$73$		−	1.92362i		−	0.225142i	−0.993644	−	0.112571i	$-0.964091\pi$
$73$		−	1.92362i		−	0.225142i	0.993644	−	0.112571i	$-0.0359086\pi$
$74$	−2.77661	+	1.60307i	−0.322774	+	0.186354i
$75$		0			0
$76$	1.89272	−	0.507152i	0.217109	−	0.0581743i
$77$	−1.55393	−	1.55393i	−0.177087	−	0.177087i
$78$	−5.12477	−	10.6659i	−0.580266	−	1.20768i
$79$			9.33180i			1.04991i	0.851130	+	0.524955i	$0.175918\pi$
$79$			9.33180i			1.04991i	−0.851130	+	0.524955i	$0.824082\pi$
$80$		0			0
$81$	14.0385	−	24.3154i	1.55984	−	2.70172i
$82$	2.28749	−	8.53702i	0.252611	−	0.942756i
$83$	−6.90343			−0.757750			−0.378875	−	0.925448i	$-0.623689\pi$
$83$	−6.90343			−0.757750			−0.378875	+	0.925448i	$0.623689\pi$
$84$	0.337830	−	1.26080i	0.0368602	−	0.137564i
$85$		0			0
$86$	−5.07227	−	5.07227i	−0.546957	−	0.546957i
$87$	14.5032	+	3.88612i	1.55490	+	0.416635i
$88$	1.43012	+	5.33728i	0.152451	+	0.568956i
$89$	1.88556	+	7.03702i	0.199869	+	0.745923i	0.990952	+	0.134214i	$0.0428509\pi$
$89$	1.88556	+	7.03702i	0.199869	+	0.745923i	−0.791083	+	0.611709i	$0.790482\pi$
$90$		0			0
$91$	0.474815	−	1.35309i	0.0497741	−	0.141842i
$92$	−4.21046	+	4.21046i	−0.438970	+	0.438970i
$93$	−5.79693	+	10.0406i	−0.601114	+	1.04116i
$94$	−10.2279	−	5.90510i	−1.05493	−	0.609065i
$95$		0			0
$96$	−2.32068	+	2.32068i	−0.236854	+	0.236854i
$97$	3.58887	−	2.07203i	0.364394	−	0.210383i	−0.306612	−	0.951834i	$-0.599196\pi$
$97$	3.58887	−	2.07203i	0.364394	−	0.210383i	0.671007	+	0.741451i	$0.265862\pi$
$98$	−5.92519	+	3.42091i	−0.598535	+	0.345564i
$99$	−30.3630	+	30.3630i	−3.05160	+	3.05160i
$100$		0			0
$101$	8.21761	+	4.74444i	0.817683	+	0.472089i	0.849617	−	0.527401i	$-0.176833\pi$
$101$	8.21761	+	4.74444i	0.817683	+	0.472089i	−0.0319341	+	0.999490i	$0.510167\pi$
$102$	3.57648	−	6.19465i	0.354124	−	0.613361i
$103$	3.97420	−	3.97420i	0.391589	−	0.391589i	−0.483664	−	0.875254i	$-0.660694\pi$
$103$	3.97420	−	3.97420i	0.391589	−	0.391589i	0.875254	+	0.483664i	$0.160694\pi$
$104$	−2.73499	+	2.34943i	−0.268188	+	0.230380i
$105$		0			0
$106$	−2.14636	−	8.01033i	−0.208473	−	0.778032i
$107$	−2.73013	−	10.1890i	−0.263932	−	0.985008i	−0.962901	−	0.269856i	$-0.913024\pi$
$107$	−2.73013	−	10.1890i	−0.263932	−	0.985008i	0.698969	−	0.715152i	$-0.253643\pi$
$108$	−15.1250	−	4.05273i	−1.45540	−	0.389974i
$109$	4.56067	+	4.56067i	0.436833	+	0.436833i	0.890945	−	0.454112i	$-0.150043\pi$
$109$	4.56067	+	4.56067i	0.436833	+	0.436833i	−0.454112	+	0.890945i	$0.650043\pi$
$110$		0			0
$111$	−2.72339	+	10.1638i	−0.258493	+	0.964709i
$112$	−0.397714			−0.0375804
$113$	−4.54113	+	16.9477i	−0.427194	+	1.59431i	0.331891	+	0.943318i	$0.392313\pi$
$113$	−4.54113	+	16.9477i	−0.427194	+	1.59431i	−0.759085	+	0.650992i	$0.774353\pi$
$114$	3.21545	−	5.56933i	0.301155	−	0.521616i
$115$		0			0
$116$		−	4.57498i		−	0.424776i
$117$	−26.4386	−	9.27763i	−2.44425	−	0.857717i
$118$	−4.67456	−	4.67456i	−0.430328	−	0.430328i
$119$	0.837279	−	0.224348i	0.0767532	−	0.0205660i
$120$		0			0
$121$	16.9150	−	9.76589i	1.53773	−	0.887808i
$122$		−	7.44980i		−	0.674473i
$123$	−14.5032	−	25.1202i	−1.30771	−	2.26502i
$124$	3.41225	+	0.914311i	0.306430	+	0.0821075i
$125$		0			0
$126$	−1.54534	−	2.67661i	−0.137670	−	0.238452i
$127$	1.20689	−	0.323386i	0.107095	−	0.0286959i	−0.204874	−	0.978788i	$-0.565678\pi$
$127$	1.20689	−	0.323386i	0.107095	−	0.0286959i	0.311968	+	0.950092i	$0.399012\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−23.5423			−2.07278
$130$		0			0
$131$	10.2927			0.899279			0.449640	−	0.893210i	$-0.351552\pi$
$131$	10.2927			0.899279			0.449640	+	0.893210i	$0.351552\pi$
$132$	15.7050	+	9.06727i	1.36694	+	0.789205i
$133$	0.752760	−	0.201701i	0.0652726	−	0.0174897i
$134$	0.621825	+	1.07703i	0.0537175	+	0.0930414i
$135$		0			0
$136$	−2.10523	−	0.564094i	−0.180522	−	0.0483707i
$137$	−3.09092	−	5.35364i	−0.264076	−	0.457392i	0.703245	−	0.710947i	$-0.251733\pi$
$137$	−3.09092	−	5.35364i	−0.264076	−	0.457392i	−0.967321	+	0.253555i	$0.918400\pi$
$138$			19.5423i			1.66355i
$139$	17.5740	−	10.1464i	1.49061	−	0.860603i	0.490666	−	0.871348i	$-0.336753\pi$
$139$	17.5740	−	10.1464i	1.49061	−	0.860603i	0.999942	+	0.0107445i	$0.00342014\pi$
$140$		0			0
$141$	−37.4397	+	10.0319i	−3.15299	+	0.844841i
$142$	7.29272	+	7.29272i	0.611992	+	0.611992i
$143$	16.4509	+	11.2375i	1.37570	+	0.939723i
$144$			7.77113i			0.647594i
$145$		0			0
$146$	−0.961808	+	1.66590i	−0.0795998	+	0.137871i
$147$	−5.81164	+	21.6893i	−0.479336	+	1.78891i
$148$	3.20615			0.263544
$149$	3.13976	−	11.7177i	0.257219	−	0.959955i	−0.709623	−	0.704581i	$-0.751135\pi$
$149$	3.13976	−	11.7177i	0.257219	−	0.959955i	0.966842	−	0.255374i	$-0.0821985\pi$
$150$		0			0
$151$	−11.6336	−	11.6336i	−0.946728	−	0.946728i	0.0519227	−	0.998651i	$-0.483465\pi$
$151$	−11.6336	−	11.6336i	−0.946728	−	0.946728i	−0.998651	+	0.0519227i	$0.983465\pi$
$152$	−1.89272	−	0.507152i	−0.153520	−	0.0411354i
$153$	−4.38365	−	16.3600i	−0.354397	−	1.32263i
$154$	0.568779	+	2.12271i	0.0458335	+	0.171053i
$155$		0			0
$156$	−0.894772	+	11.7993i	−0.0716391	+	0.944702i
$157$	11.8065	−	11.8065i	0.942259	−	0.942259i	−0.0561623	−	0.998422i	$-0.517886\pi$
$157$	11.8065	−	11.8065i	0.942259	−	0.942259i	0.998422	+	0.0561623i	$0.0178864\pi$
$158$	4.66590	−	8.08158i	0.371199	−	0.642936i
$159$	−23.5705	−	13.6084i	−1.86926	−	1.07922i
$160$		0			0
$161$	−1.67456	+	1.67456i	−0.131974	+	0.131974i
$162$	−24.3154	+	14.0385i	−1.91040	+	1.10297i
$163$	−8.49192	+	4.90281i	−0.665138	+	0.384018i	−0.794232	−	0.607615i	$-0.792127\pi$
$163$	−8.49192	+	4.90281i	−0.665138	+	0.384018i	0.129094	+	0.991632i	$0.458793\pi$
$164$	−6.24953	+	6.24953i	−0.488007	+	0.488007i
$165$		0			0
$166$	5.97854	+	3.45171i	0.464025	+	0.267905i
$167$	0.862295	−	1.49354i	0.0667264	−	0.115574i	−0.830732	−	0.556672i	$-0.812078\pi$
$167$	0.862295	−	1.49354i	0.0667264	−	0.115574i	0.897459	+	0.441099i	$0.145411\pi$
$168$	−0.922968	+	0.922968i	−0.0712085	+	0.0712085i
$169$	−1.96037	+	12.8513i	−0.150798	+	0.988565i
$170$		0			0
$171$	−3.94114	−	14.7085i	−0.301387	−	1.12479i
$172$	1.85658	+	6.92885i	0.141563	+	0.528320i
$173$	−5.93741	−	1.59092i	−0.451413	−	0.120956i	0.0259475	−	0.999663i	$-0.491740\pi$
$173$	−5.93741	−	1.59092i	−0.451413	−	0.120956i	−0.477360	+	0.878708i	$0.658406\pi$
$174$	−10.6171	−	10.6171i	−0.804878	−	0.804878i
$175$		0			0
$176$	1.43012	−	5.33728i	0.107799	−	0.402313i
$177$	−21.6963			−1.63080
$178$	1.88556	−	7.03702i	0.141329	−	0.527447i
$179$	4.29272	−	7.43522i	0.320853	−	0.555734i	−0.659811	−	0.751432i	$-0.729364\pi$
$179$	4.29272	−	7.43522i	0.320853	−	0.555734i	0.980664	+	0.195697i	$0.0626970\pi$
$180$		0			0
$181$			2.60797i			0.193849i	0.995292	+	0.0969246i	$0.0309006\pi$
$181$			2.60797i			0.193849i	−0.995292	+	0.0969246i	$0.969099\pi$
$182$	−1.08775	+	0.934401i	−0.0806290	+	0.0692624i
$183$	−17.2886	−	17.2886i	−1.27801	−	1.27801i
$184$	5.75159	−	1.54113i	0.424013	−	0.113614i
$185$		0			0
$186$	10.0406	−	5.79693i	0.736211	−	0.425052i
$187$			12.0429i			0.880665i
$188$	5.90510	+	10.2279i	0.430674	+	0.745949i
$189$	−6.01543	−	1.61183i	−0.437558	−	0.117243i
$190$		0			0
$191$	−0.396828	−	0.687326i	−0.0287135	−	0.0497332i	0.851312	−	0.524660i	$-0.175808\pi$
$191$	−0.396828	−	0.687326i	−0.0287135	−	0.0497332i	−0.880025	+	0.474927i	$0.842474\pi$
$192$	3.17011	−	0.849429i	0.228783	−	0.0613022i
$193$	12.6039	+	7.27684i	0.907246	+	0.523799i	0.879544	−	0.475818i	$-0.157848\pi$
$193$	12.6039	+	7.27684i	0.907246	+	0.523799i	0.0277019	+	0.999616i	$0.491181\pi$
$194$	−4.14407			−0.297527
$195$		0			0
$196$	6.84182			0.488702
$197$	12.1858	+	7.03549i	0.868204	+	0.501258i	0.866751	−	0.498741i	$-0.166204\pi$
$197$	12.1858	+	7.03549i	0.868204	+	0.501258i	0.00145289	+	0.999999i	$0.499538\pi$
$198$	41.4767	−	11.1136i	2.94762	−	0.789812i
$199$	8.96205	+	15.5227i	0.635303	+	1.10038i	0.986451	+	0.164056i	$0.0524579\pi$
$199$	8.96205	+	15.5227i	0.635303	+	1.10038i	−0.351148	+	0.936320i	$0.614209\pi$
$200$		0			0
$201$	3.94251	+	1.05639i	0.278083	+	0.0745121i
$202$	−4.74444	−	8.21761i	−0.333817	−	0.578189i
$203$		−	1.81953i		−	0.127706i
$204$	−6.19465	+	3.57648i	−0.433712	+	0.250404i
$205$		0			0
$206$	−5.42885	+	1.45466i	−0.378246	+	0.101351i
$207$	32.7200	+	32.7200i	2.27420	+	2.27420i
$208$	3.54329	−	0.667168i	0.245683	−	0.0462598i
$209$			10.8272i			0.748936i
$210$		0			0
$211$	5.78407	−	10.0183i	0.398192	−	0.689688i	−0.595311	−	0.803495i	$-0.702971\pi$
$211$	5.78407	−	10.0183i	0.398192	−	0.689688i	0.993503	+	0.113807i	$0.0363046\pi$
$212$	−2.14636	+	8.01033i	−0.147413	+	0.550152i
$213$	33.8482			2.31924
$214$	−2.73013	+	10.1890i	−0.186628	+	0.696506i
$215$		0			0
$216$	11.0723	+	11.0723i	0.753373	+	0.753373i
$217$	1.35710	+	0.363634i	0.0921261	+	0.0246851i
$218$	−1.66932	−	6.22999i	−0.113061	−	0.421948i
$219$	1.63397	+	6.09808i	0.110414	+	0.412070i
$220$		0			0
$221$	−7.08308	+	3.40329i	−0.476460	+	0.228930i
$222$	7.44045	−	7.44045i	0.499370	−	0.499370i
$223$	−4.15717	+	7.20043i	−0.278385	+	0.482177i	−0.970984	−	0.239146i	$-0.923132\pi$
$223$	−4.15717	+	7.20043i	−0.278385	+	0.482177i	0.692599	+	0.721323i	$0.256466\pi$
$224$	0.344430	+	0.198857i	0.0230132	+	0.0132867i
$225$		0			0
$226$	12.4066	−	12.4066i	0.825275	−	0.825275i
$227$	−2.71029	+	1.56478i	−0.179888	+	0.103858i	−0.587240	−	0.809413i	$-0.699786\pi$
$227$	−2.71029	+	1.56478i	−0.179888	+	0.103858i	0.407352	+	0.913271i	$0.366452\pi$
$228$	−5.56933	+	3.21545i	−0.368838	+	0.212949i
$229$	8.68998	−	8.68998i	0.574250	−	0.574250i	−0.359063	−	0.933313i	$-0.616904\pi$
$229$	8.68998	−	8.68998i	0.574250	−	0.574250i	0.933313	+	0.359063i	$0.116904\pi$
$230$		0			0
$231$	6.24609	+	3.60618i	0.410963	+	0.237269i
$232$	−2.28749	+	3.96205i	−0.150181	+	0.260121i
$233$	10.1868	−	10.1868i	0.667360	−	0.667360i	−0.289744	−	0.957104i	$-0.593570\pi$
$233$	10.1868	−	10.1868i	0.667360	−	0.667360i	0.957104	+	0.289744i	$0.0935703\pi$
$234$	18.2577	+	21.2540i	1.19354	+	1.38942i
$235$		0			0
$236$	1.71101	+	6.38556i	0.111377	+	0.415665i
$237$	−7.92670	−	29.5828i	−0.514894	−	1.92161i
$238$	−0.837279	−	0.224348i	−0.0542727	−	0.0145423i
$239$	−14.4047	−	14.4047i	−0.931764	−	0.931764i	0.0660522	−	0.997816i	$-0.478960\pi$
$239$	−14.4047	−	14.4047i	−0.931764	−	0.931764i	−0.997816	+	0.0660522i	$0.978960\pi$
$240$		0			0
$241$	7.44774	−	27.7954i	0.479751	−	1.79046i	−0.122863	−	0.992424i	$-0.539208\pi$
$241$	7.44774	−	27.7954i	0.479751	−	1.79046i	0.602615	−	0.798032i	$-0.294126\pi$
$242$	−19.5318			−1.25555
$243$	−11.6913	+	43.6323i	−0.749994	+	2.79902i
$244$	−3.72490	+	6.45171i	−0.238462	+	0.413029i
$245$		0			0
$246$			29.0064i			1.84938i
$247$	−6.36808	+	3.05974i	−0.405191	+	0.194687i
$248$	−2.49794	−	2.49794i	−0.158620	−	0.158620i
$249$	21.8846	−	5.86397i	1.38688	−	0.371614i
$250$		0			0
$251$	−19.7318	+	11.3922i	−1.24546	+	0.719067i	−0.970201	−	0.242303i	$-0.922097\pi$
$251$	−19.7318	+	11.3922i	−1.24546	+	0.719067i	−0.275260	+	0.961370i	$0.588764\pi$
$252$			3.09069i			0.194695i
$253$	−16.4509	−	28.4938i	−1.03426	−	1.79139i
$254$	−1.20689	−	0.323386i	−0.0757273	−	0.0202911i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.92708	−	1.05226i	0.244965	−	0.0656380i	−0.134248	−	0.990948i	$-0.542862\pi$
$257$	3.92708	−	1.05226i	0.244965	−	0.0656380i	0.379212	+	0.925310i	$0.376195\pi$
$258$	20.3882	+	11.7711i	1.26931	+	0.732838i
$259$	1.27513			0.0792327
$260$		0			0
$261$	−35.5527			−2.20066
$262$	−8.91376	−	5.14636i	−0.550694	−	0.317943i
$263$	−8.90510	+	2.38612i	−0.549112	+	0.147134i	−0.522700	−	0.852517i	$-0.675075\pi$
$263$	−8.90510	+	2.38612i	−0.549112	+	0.147134i	−0.0264126	+	0.999651i	$0.508408\pi$
$264$	−9.06727	−	15.7050i	−0.558052	−	0.966575i
$265$		0			0
$266$	−0.752760	−	0.201701i	−0.0461547	−	0.0123671i
$267$	−11.9549	−	20.7065i	−0.731628	−	1.26722i
$268$		−	1.24365i		−	0.0759680i
$269$	5.07512	−	2.93012i	0.309435	−	0.178653i	−0.337238	−	0.941419i	$-0.609493\pi$
$269$	5.07512	−	2.93012i	0.309435	−	0.178653i	0.646674	+	0.762767i	$0.276160\pi$
$270$		0			0
$271$	12.4457	−	3.33481i	0.756022	−	0.202575i	0.139834	−	0.990175i	$-0.455343\pi$
$271$	12.4457	−	3.33481i	0.756022	−	0.202575i	0.616187	+	0.787600i	$0.288676\pi$
$272$	1.54113	+	1.54113i	0.0934450	+	0.0934450i
$273$	−0.355863	+	4.69276i	−0.0215378	+	0.284019i
$274$			6.18185i			0.373459i
$275$		0			0
$276$	9.77113	−	16.9241i	0.588153	−	1.01871i
$277$	−6.82400	+	25.4675i	−0.410014	+	1.53019i	0.384602	+	0.923083i	$0.374339\pi$
$277$	−6.82400	+	25.4675i	−0.410014	+	1.53019i	−0.794616	+	0.607112i	$0.792328\pi$
$278$	−20.2927			−1.21708
$279$	7.10523	−	26.5171i	0.425379	−	1.58754i
$280$		0			0
$281$	−0.139761	−	0.139761i	−0.00833744	−	0.00833744i	0.702926	−	0.711263i	$-0.251877\pi$
$281$	−0.139761	−	0.139761i	−0.00833744	−	0.00833744i	−0.711263	+	0.702926i	$0.751877\pi$
$282$	37.4397	+	10.0319i	2.22950	+	0.597393i
$283$	1.59229	+	5.94251i	0.0946518	+	0.353245i	0.996966	−	0.0778327i	$-0.0248000\pi$
$283$	1.59229	+	5.94251i	0.0946518	+	0.353245i	−0.902315	+	0.431078i	$0.858133\pi$
$284$	−2.66932	−	9.96205i	−0.158395	−	0.591139i
$285$		0			0
$286$	−8.62819	−	17.9574i	−0.510195	−	1.06184i
$287$	−2.48553	+	2.48553i	−0.146716	+	0.146716i
$288$	3.88556	−	6.72999i	0.228959	−	0.396569i
$289$	10.6086	+	6.12491i	0.624038	+	0.360289i
$290$		0			0
$291$	−9.61706	+	9.61706i	−0.563762	+	0.563762i
$292$	1.66590	−	0.961808i	0.0974895	−	0.0562856i
$293$	−4.34251	+	2.50715i	−0.253692	+	0.146469i	−0.621454	−	0.783451i	$-0.713458\pi$
$293$	−4.34251	+	2.50715i	−0.253692	+	0.146469i	0.367761	+	0.929920i	$0.380124\pi$
$294$	15.8777	−	15.8777i	0.926006	−	0.926006i
$295$		0			0
$296$	−2.77661	−	1.60307i	−0.161387	−	0.0931768i
$297$	43.2611	−	74.9305i	2.51027	−	4.34791i
$298$	−8.57799	+	8.57799i	−0.496909	+	0.496909i
$299$	12.1098	−	17.7279i	0.700326	−	1.02523i
$300$		0			0
$301$	0.738388	+	2.75570i	0.0425600	+	0.158836i
$302$	4.25819	+	15.8918i	0.245031	+	0.914469i
$303$	−30.0808	−	8.06012i	−1.72810	−	0.463042i
$304$	1.38556	+	1.38556i	0.0794676	+	0.0794676i
$305$		0			0
$306$	−4.38365	+	16.3600i	−0.250596	+	0.935239i
$307$	−3.05180			−0.174176			−0.0870878	−	0.996201i	$-0.527756\pi$
$307$	−3.05180			−0.174176			−0.0870878	+	0.996201i	$0.527756\pi$
$308$	0.568779	−	2.12271i	0.0324092	−	0.120953i
$309$	−9.22284	+	15.9744i	−0.524669	+	0.908754i
$310$		0			0
$311$			13.0132i			0.737911i	0.929447	+	0.368955i	$0.120285\pi$
$311$			13.0132i			0.737911i	−0.929447	+	0.368955i	$0.879715\pi$
$312$	6.67456	−	9.77113i	0.377872	−	0.553181i
$313$	−11.3443	−	11.3443i	−0.641220	−	0.641220i	0.309636	−	0.950855i	$-0.399793\pi$
$313$	−11.3443	−	11.3443i	−0.641220	−	0.641220i	−0.950855	+	0.309636i	$0.899793\pi$
$314$	−16.1279	+	4.32147i	−0.910153	+	0.243875i
$315$		0			0
$316$	−8.08158	+	4.66590i	−0.454624	+	0.262477i
$317$		−	23.0586i		−	1.29510i	−0.762022	−	0.647551i	$-0.775793\pi$
$317$		−	23.0586i		−	1.29510i	0.762022	−	0.647551i	$-0.224207\pi$
$318$	13.6084	+	23.5705i	0.763122	+	1.32177i
$319$	24.4179	+	6.54276i	1.36714	+	0.366324i
$320$		0			0
$321$	17.3097	+	29.9812i	0.966131	+	1.67339i
$322$	2.28749	−	0.612931i	0.127477	−	0.0341573i
$323$	−3.69852	−	2.13534i	−0.205791	−	0.118813i
$324$	28.0771			1.55984
$325$		0			0
$326$	9.80562			0.543083
$327$	−18.3318	−	10.5839i	−1.01375	−	0.585289i
$328$	8.53702	−	2.28749i	0.471378	−	0.126305i
$329$	2.34854	+	4.06780i	0.129479	+	0.224265i
$330$		0			0
$331$	21.1917	+	5.67829i	1.16480	+	0.312107i	0.788881	−	0.614546i	$-0.210661\pi$
$331$	21.1917	+	5.67829i	1.16480	+	0.312107i	0.375918	+	0.926653i	$0.377327\pi$
$332$	−3.45171	−	5.97854i	−0.189437	−	0.328115i
$333$		−	24.9154i		−	1.36536i
$334$	−1.49354	+	0.862295i	−0.0817228	+	0.0471827i
$335$		0			0
$336$	1.26080	−	0.337830i	0.0687821	−	0.0184301i
$337$	−11.6622	−	11.6622i	−0.635281	−	0.635281i	0.314107	−	0.949388i	$-0.398295\pi$
$337$	−11.6622	−	11.6622i	−0.635281	−	0.635281i	−0.949388	+	0.314107i	$0.898295\pi$
$338$	8.12340	−	10.1494i	0.441855	−	0.552055i
$339$		−	57.5836i		−	3.12751i
$340$		0			0
$341$	−9.75986	+	16.9046i	−0.528526	+	0.915434i
$342$	−3.94114	+	14.7085i	−0.213113	+	0.795347i
$343$	5.50509			0.297247
$344$	1.85658	−	6.92885i	0.100100	−	0.373579i
$345$		0			0
$346$	4.34649	+	4.34649i	0.233669	+	0.233669i
$347$	−4.67982	−	1.25395i	−0.251226	−	0.0673158i	0.131008	−	0.991381i	$-0.458179\pi$
$347$	−4.67982	−	1.25395i	−0.251226	−	0.0673158i	−0.382234	+	0.924065i	$0.624845\pi$
$348$	3.88612	+	14.5032i	0.208318	+	0.777452i
$349$	2.97604	+	11.1067i	0.159304	+	0.594530i	0.998698	+	0.0510072i	$0.0162431\pi$
$349$	2.97604	+	11.1067i	0.159304	+	0.594530i	−0.839395	+	0.543523i	$0.817090\pi$
$350$		0			0
$351$	56.2961	+	4.26907i	3.00486	+	0.227866i
$352$	−3.90716	+	3.90716i	−0.208252	+	0.208252i
$353$	−1.28407	+	2.22407i	−0.0683440	+	0.118375i	−0.898172	−	0.439643i	$-0.855105\pi$
$353$	−1.28407	+	2.22407i	−0.0683440	+	0.118375i	0.829828	+	0.558019i	$0.188438\pi$
$354$	18.7896	+	10.8482i	0.998654	+	0.576573i
$355$		0			0
$356$	−5.15146	+	5.15146i	−0.273027	+	0.273027i
$357$	−2.46370	+	1.42242i	−0.130393	+	0.0752823i
$358$	−7.43522	+	4.29272i	−0.392963	+	0.226877i
$359$	−9.62118	+	9.62118i	−0.507786	+	0.507786i	−0.913846	−	0.406060i	$-0.866902\pi$
$359$	−9.62118	+	9.62118i	−0.507786	+	0.507786i	0.406060	+	0.913846i	$0.366902\pi$
$360$		0			0
$361$	13.1293	+	7.58021i	0.691016	+	0.398959i
$362$	1.30399	−	2.25857i	0.0685361	−	0.118708i
$363$	−45.3271	+	45.3271i	−2.37905	+	2.37905i
$364$	1.40922	−	0.265342i	0.0738629	−	0.0139077i
$365$		0			0
$366$	6.32807	+	23.6167i	0.330774	+	1.23446i
$367$	−4.36492	−	16.2901i	−0.227847	−	0.850337i	−0.981244	−	0.192771i	$-0.938253\pi$
$367$	−4.36492	−	16.2901i	−0.227847	−	0.850337i	0.753397	−	0.657566i	$-0.228414\pi$
$368$	−5.75159	−	1.54113i	−0.299822	−	0.0803372i
$369$	48.5659	+	48.5659i	2.52824	+	2.52824i
$370$		0			0
$371$	−0.853638	+	3.18582i	−0.0443187	+	0.165400i
$372$	−11.5939			−0.601114
$373$	0.676711	−	2.52552i	0.0350388	−	0.130766i	−0.946191	−	0.323609i	$-0.895104\pi$
$373$	0.676711	−	2.52552i	0.0350388	−	0.130766i	0.981230	+	0.192842i	$0.0617705\pi$
$374$	6.02146	−	10.4295i	0.311362	−	0.539295i
$375$		0			0
$376$		−	11.8102i		−	0.609065i
$377$	3.05228	+	16.2105i	0.157200	+	0.834881i
$378$	4.40360	+	4.40360i	0.226497	+	0.226497i
$379$	−1.46920	+	0.393670i	−0.0754676	+	0.0202215i	−0.296355	−	0.955078i	$-0.595771\pi$
$379$	−1.46920	+	0.393670i	−0.0754676	+	0.0202215i	0.220888	+	0.975299i	$0.429105\pi$
$380$		0			0
$381$	−3.55130	+	2.05034i	−0.181938	+	0.105042i
$382$			0.793656i			0.0406070i
$383$	−1.87827	−	3.25326i	−0.0959753	−	0.166234i	0.814040	−	0.580809i	$-0.197264\pi$
$383$	−1.87827	−	3.25326i	−0.0959753	−	0.166234i	−0.910015	+	0.414575i	$0.863930\pi$
$384$	−3.17011	−	0.849429i	−0.161774	−	0.0433472i
$385$		0			0
$386$	−7.27684	−	12.6039i	−0.370382	−	0.641520i
$387$	53.8450	−	14.4277i	2.73710	−	0.733402i
$388$	3.58887	+	2.07203i	0.182197	+	0.105192i
$389$	−14.0639			−0.713066			−0.356533	−	0.934283i	$-0.616041\pi$
$389$	−14.0639			−0.713066			−0.356533	+	0.934283i	$0.616041\pi$
$390$		0			0
$391$	12.9778			0.656313
$392$	−5.92519	−	3.42091i	−0.299267	−	0.172782i
$393$	−32.6291	+	8.74293i	−1.64592	+	0.441023i
$394$	−7.03549	−	12.1858i	−0.354443	−	0.613913i
$395$		0			0
$396$	−41.4767	−	11.1136i	−2.08428	−	0.558482i
$397$	8.57531	+	14.8529i	0.430383	+	0.745444i	0.996906	−	0.0786011i	$-0.0250453\pi$
$397$	8.57531	+	14.8529i	0.430383	+	0.745444i	−0.566524	+	0.824046i	$0.691712\pi$
$398$		−	17.9241i		−	0.898454i
$399$	−2.21500	+	1.27883i	−0.110889	+	0.0640216i
$400$		0			0
$401$	−2.20232	+	0.590110i	−0.109979	+	0.0294687i	−0.313389	−	0.949625i	$-0.601464\pi$
$401$	−2.20232	+	0.590110i	−0.109979	+	0.0294687i	0.203410	+	0.979094i	$0.434798\pi$
$402$	−2.88612	−	2.88612i	−0.143946	−	0.143946i
$403$	−12.7006	−	0.963118i	−0.632662	−	0.0479763i
$404$			9.48888i			0.472089i
$405$		0			0
$406$	−0.909766	+	1.57576i	−0.0451509	+	0.0782037i
$407$	−4.58518	+	17.1121i	−0.227279	+	0.848216i
$408$	7.15296			0.354124
$409$	−4.81911	+	17.9851i	−0.238289	+	0.889308i	0.738349	+	0.674419i	$0.235606\pi$
$409$	−4.81911	+	17.9851i	−0.238289	+	0.889308i	−0.976638	+	0.214889i	$0.931061\pi$
$410$		0			0
$411$	14.3461	+	14.3461i	0.707641	+	0.707641i
$412$	5.42885	+	1.45466i	0.267460	+	0.0716658i
$413$	0.680491	+	2.53963i	0.0334848	+	0.124967i
$414$	−11.9763	−	44.6963i	−0.588605	−	2.19671i
$415$		0			0
$416$	−3.40216	−	1.19386i	−0.166805	−	0.0585338i
$417$	−47.0930	+	47.0930i	−2.30615	+	2.30615i
$418$	5.41362	−	9.37667i	0.264789	−	0.458628i
$419$	8.19164	+	4.72944i	0.400188	+	0.231048i	0.686565	−	0.727068i	$-0.259118\pi$
$419$	8.19164	+	4.72944i	0.400188	+	0.231048i	−0.286377	+	0.958117i	$0.592451\pi$
$420$		0			0
$421$	−23.3656	+	23.3656i	−1.13877	+	1.13877i	−0.150101	+	0.988671i	$0.547960\pi$
$421$	−23.3656	+	23.3656i	−1.13877	+	1.13877i	−0.988671	+	0.150101i	$0.952040\pi$
$422$	−10.0183	+	5.78407i	−0.487683	+	0.281564i
$423$	79.4826	−	45.8893i	3.86458	−	2.23121i
$424$	5.86397	−	5.86397i	0.284780	−	0.284780i
$425$		0			0
$426$	−29.3134	−	16.9241i	−1.42024	−	0.819975i
$427$	−1.48144	+	2.56594i	−0.0716921	+	0.124174i
$428$	7.45887	−	7.45887i	0.360538	−	0.360538i
$429$	−61.6967	−	21.6501i	−2.97874	−	1.04528i
$430$		0			0
$431$	−7.65683	−	28.5757i	−0.368817	−	1.37644i	−0.862172	−	0.506615i	$-0.830897\pi$
$431$	−7.65683	−	28.5757i	−0.368817	−	1.37644i	0.493356	−	0.869828i	$-0.335770\pi$
$432$	−4.05273	−	15.1250i	−0.194987	−	0.727702i
$433$	23.9436	+	6.41568i	1.15066	+	0.308318i	0.783229	−	0.621734i	$-0.213571\pi$
$433$	23.9436	+	6.41568i	1.15066	+	0.308318i	0.367429	+	0.930052i	$0.380238\pi$
$434$	−0.993467	−	0.993467i	−0.0476880	−	0.0476880i
$435$		0			0
$436$	−1.66932	+	6.22999i	−0.0799460	+	0.298363i
$437$	11.6677			0.558142
$438$	1.63397	−	6.09808i	0.0780743	−	0.291377i
$439$	−3.29091	+	5.70002i	−0.157067	+	0.272047i	−0.933810	−	0.357770i	$-0.883537\pi$
$439$	−3.29091	+	5.70002i	−0.157067	+	0.272047i	0.776743	+	0.629818i	$0.216870\pi$
$440$		0			0
$441$		−	53.1687i		−	2.53184i
$442$	7.83577	+	0.594206i	0.372710	+	0.0282635i
$443$	20.1315	+	20.1315i	0.956478	+	0.956478i	0.999092	−	0.0426135i	$-0.0135684\pi$
$443$	20.1315	+	20.1315i	0.956478	+	0.956478i	−0.0426135	+	0.999092i	$0.513568\pi$
$444$	−10.1638	+	2.72339i	−0.482355	+	0.129247i
$445$		0			0
$446$	7.20043	−	4.15717i	0.340950	−	0.196848i
$447$			39.8136i			1.88312i
$448$	−0.198857	−	0.344430i	−0.00939511	−	0.0162728i
$449$	5.40716	+	1.44884i	0.255180	+	0.0683752i	0.384141	−	0.923274i	$-0.374498\pi$
$449$	5.40716	+	1.44884i	0.255180	+	0.0683752i	−0.128961	+	0.991650i	$0.541164\pi$
$450$		0			0
$451$	−24.4179	−	42.2931i	−1.14980	−	1.99150i
$452$	−16.9477	+	4.54113i	−0.797155	+	0.213597i
$453$	46.7617	+	26.9979i	2.19706	+	1.26847i
$454$	3.12957			0.146878
$455$		0			0
$456$	6.43091			0.301155
$457$	−17.9685	−	10.3741i	−0.840530	−	0.485280i	0.0169144	−	0.999857i	$-0.494616\pi$
$457$	−17.9685	−	10.3741i	−0.840530	−	0.485280i	−0.857444	+	0.514577i	$0.827949\pi$
$458$	−11.8707	+	3.18076i	−0.554683	+	0.148627i
$459$	17.0639	+	29.5555i	0.796472	+	1.37953i
$460$		0			0
$461$	24.3277	+	6.51858i	1.13305	+	0.303600i	0.776154	−	0.630543i	$-0.217168\pi$
$461$	24.3277	+	6.51858i	1.13305	+	0.303600i	0.356898	+	0.934143i	$0.383834\pi$
$462$	−3.60618	−	6.24609i	−0.167775	−	0.290594i
$463$		−	32.2152i		−	1.49717i	−0.663039	−	0.748585i	$-0.730734\pi$
$463$		−	32.2152i		−	1.49717i	0.663039	−	0.748585i	$-0.269266\pi$
$464$	3.96205	−	2.28749i	0.183933	−	0.106194i
$465$		0			0
$466$	−13.9154	+	3.72863i	−0.644620	+	0.172725i
$467$	20.5381	+	20.5381i	0.950392	+	0.950392i	0.998826	−	0.0484344i	$-0.0154232\pi$
$467$	20.5381	+	20.5381i	0.950392	+	0.950392i	−0.0484344	+	0.998826i	$0.515423\pi$
$468$	−5.18465	−	27.5353i	−0.239661	−	1.27282i
$469$		−	0.494617i		−	0.0228393i
$470$		0			0
$471$	−27.3991	+	47.4566i	−1.26248	+	2.18668i
$472$	1.71101	−	6.38556i	0.0787555	−	0.293919i
$473$	−39.6363			−1.82248
$474$	−7.92670	+	29.5828i	−0.364085	+	1.35878i
$475$		0			0
$476$	0.612931	+	0.612931i	0.0280936	+	0.0280936i
$477$	62.2493	+	16.6797i	2.85020	+	0.763709i
$478$	5.27249	+	19.6772i	0.241158	+	0.900015i
$479$	−7.18639	−	26.8200i	−0.328355	−	1.22544i	−0.910896	−	0.412636i	$-0.864608\pi$
$479$	−7.18639	−	26.8200i	−0.328355	−	1.22544i	0.582542	−	0.812801i	$-0.302058\pi$
$480$		0			0
$481$	−11.3603	+	2.13904i	−0.517985	+	0.0975319i
$482$	−20.3476	+	20.3476i	−0.926808	+	0.926808i
$483$	3.88612	−	6.73095i	0.176824	−	0.306269i
$484$	16.9150	+	9.76589i	0.768865	+	0.443904i
$485$		0			0
$486$	31.9411	−	31.9411i	1.44888	−	1.44888i
$487$	−34.6529	+	20.0068i	−1.57027	+	0.906596i	−0.574136	+	0.818760i	$0.694662\pi$
$487$	−34.6529	+	20.0068i	−1.57027	+	0.906596i	−0.996135	+	0.0878365i	$0.972005\pi$
$488$	6.45171	−	3.72490i	0.292055	−	0.168618i
$489$	22.7557	−	22.7557i	1.02905	−	1.02905i
$490$		0			0
$491$	15.8394	+	9.14486i	0.714820	+	0.412702i	0.812843	−	0.582483i	$-0.197919\pi$
$491$	15.8394	+	9.14486i	0.714820	+	0.412702i	−0.0980231	+	0.995184i	$0.531252\pi$
$492$	14.5032	−	25.1202i	0.653854	−	1.13251i
$493$	−7.05065	+	7.05065i	−0.317545	+	0.317545i
$494$	7.04479	+	0.534224i	0.316960	+	0.0240359i
$495$		0			0
$496$	0.914311	+	3.41225i	0.0410538	+	0.153215i
$497$	−1.06163	−	3.96205i	−0.0476205	−	0.177722i
$498$	−21.8846	−	5.86397i	−0.980674	−	0.262771i
$499$	−17.4889	−	17.4889i	−0.782910	−	0.782910i	0.197411	−	0.980321i	$-0.436747\pi$
$499$	−17.4889	−	17.4889i	−0.782910	−	0.782910i	−0.980321	+	0.197411i	$0.936747\pi$
$500$		0			0
$501$	−1.46492	+	5.46714i	−0.0654476	+	0.244254i
$502$	22.7843			1.01691
$503$	3.10609	−	11.5921i	0.138494	−	0.516865i	−0.861465	−	0.507816i	$-0.830453\pi$
$503$	3.10609	−	11.5921i	0.138494	−	0.516865i	0.999959	−	0.00904899i	$-0.00288042\pi$
$504$	1.54534	−	2.67661i	0.0688351	−	0.119226i
$505$		0			0
$506$			32.9018i			1.46267i
$507$	−4.70170	−	42.4054i	−0.208810	−	1.88329i
$508$	0.883508	+	0.883508i	0.0391993	+	0.0391993i
$509$	−17.3871	+	4.65885i	−0.770668	+	0.206500i	−0.622667	−	0.782487i	$-0.713951\pi$
$509$	−17.3871	+	4.65885i	−0.770668	+	0.206500i	−0.148002	+	0.988987i	$0.547284\pi$
$510$		0			0
$511$	0.662552	−	0.382525i	0.0293096	−	0.0169219i
$512$			1.00000i			0.0441942i
$513$	15.3413	+	26.5720i	0.677337	+	1.17318i
$514$	−3.92708	−	1.05226i	−0.173216	−	0.0464131i
$515$		0			0
$516$	−11.7711	−	20.3882i	−0.518195	−	0.897540i
$517$	−63.0344	+	16.8900i	−2.77225	+	0.742822i
$518$	−1.10430	−	0.637565i	−0.0485199	−	0.0280130i
$519$	20.1736			0.885524
$520$		0			0
$521$	21.4787			0.940998			0.470499	−	0.882400i	$-0.344074\pi$
$521$	21.4787			0.940998			0.470499	+	0.882400i	$0.344074\pi$
$522$	30.7896	+	17.7764i	1.34762	+	0.778050i
$523$	10.9477	−	2.93344i	0.478711	−	0.128270i	−0.0113912	−	0.999935i	$-0.503626\pi$
$523$	10.9477	−	2.93344i	0.478711	−	0.128270i	0.490103	+	0.871665i	$0.336959\pi$
$524$	5.14636	+	8.91376i	0.224820	+	0.389399i
$525$		0			0
$526$	8.90510	+	2.38612i	0.388281	+	0.104040i
$527$	−3.84967	−	6.66782i	−0.167694	−	0.290455i
$528$			18.1345i			0.789205i
$529$	−10.7871	+	6.22794i	−0.469005	+	0.270780i
$530$		0			0
$531$	49.6230	−	13.2965i	2.15346	−	0.577017i
$532$	0.551058	+	0.551058i	0.0238914	+	0.0238914i
$533$	17.9744	−	26.3134i	0.778558	−	1.13976i
$534$			23.9098i			1.03468i
$535$		0			0
$536$	−0.621825	+	1.07703i	−0.0268587	+	0.0465207i
$537$	−7.29272	+	27.2168i	−0.314704	+	1.17449i
$538$	−5.86024			−0.252653
$539$	−9.78463	+	36.5167i	−0.421454	+	1.57289i
$540$		0			0
$541$	8.33292	+	8.33292i	0.358260	+	0.358260i	0.863171	−	0.504911i	$-0.168475\pi$
$541$	8.33292	+	8.33292i	0.358260	+	0.358260i	−0.504911	+	0.863171i	$0.668475\pi$
$542$	−12.4457	−	3.33481i	−0.534588	−	0.143242i
$543$	−2.21529	−	8.26757i	−0.0950671	−	0.354795i
$544$	−0.564094	−	2.10523i	−0.0241853	−	0.0902609i
$545$		0			0
$546$	2.65457	−	3.88612i	0.113605	−	0.166310i
$547$	−0.364520	+	0.364520i	−0.0155858	+	0.0155858i	−0.714857	−	0.699271i	$-0.753508\pi$
$547$	−0.364520	+	0.364520i	−0.0155858	+	0.0155858i	0.699271	+	0.714857i	$0.253508\pi$
$548$	3.09092	−	5.35364i	0.132038	−	0.228696i
$549$	50.1371	+	28.9467i	2.13980	+	1.23541i
$550$		0			0
$551$	−6.33892	+	6.33892i	−0.270047	+	0.270047i
$552$	−16.9241	+	9.77113i	−0.720337	+	0.415887i
$553$	−3.21416	+	1.85569i	−0.136680	+	0.0789121i
$554$	18.6435	−	18.6435i	0.792087	−	0.792087i
$555$		0			0
$556$	17.5740	+	10.1464i	0.745304	+	0.430302i
$557$	1.92806	−	3.33950i	0.0816947	−	0.141499i	−0.822283	−	0.569078i	$-0.807300\pi$
$557$	1.92806	−	3.33950i	0.0816947	−	0.141499i	0.903978	+	0.427579i	$0.140633\pi$
$558$	−19.4118	+	19.4118i	−0.821769	+	0.821769i
$559$	−11.2011	−	23.3123i	−0.473756	−	0.986004i
$560$		0			0
$561$	−10.2296	−	38.1774i	−0.431894	−	1.61185i
$562$	0.0511561	+	0.190917i	0.00215789	+	0.00805335i
$563$	21.0699	+	5.64567i	0.887992	+	0.237937i	0.673852	−	0.738866i	$-0.264639\pi$
$563$	21.0699	+	5.64567i	0.887992	+	0.237937i	0.214140	+	0.976803i	$0.431305\pi$
$564$	−27.4077	−	27.4077i	−1.15407	−	1.15407i
$565$		0			0
$566$	1.59229	−	5.94251i	0.0669289	−	0.249782i
$567$	11.1666			0.468955
$568$	−2.66932	+	9.96205i	−0.112002	+	0.417998i
$569$	−18.5740	+	32.1712i	−0.778664	+	1.34869i	0.154047	+	0.988063i	$0.450769\pi$
$569$	−18.5740	+	32.1712i	−0.778664	+	1.34869i	−0.932712	+	0.360623i	$0.882564\pi$
$570$		0			0
$571$			12.6031i			0.527423i	0.964602	+	0.263712i	$0.0849467\pi$
$571$			12.6031i			0.527423i	−0.964602	+	0.263712i	$0.915053\pi$
$572$	−1.50646	+	19.8656i	−0.0629883	+	0.830624i
$573$	1.84182	+	1.84182i	0.0769433	+	0.0769433i
$574$	3.39529	−	0.909766i	0.141717	−	0.0379729i
$575$		0			0
$576$	−6.72999	+	3.88556i	−0.280416	+	0.161899i
$577$		−	2.81590i		−	0.117227i	−0.998281	−	0.0586136i	$-0.981332\pi$
$577$		−	2.81590i		−	0.117227i	0.998281	−	0.0586136i	$-0.0186680\pi$
$578$	−6.12491	−	10.6086i	−0.254763	−	0.441262i
$579$	−46.1368	−	12.3623i	−1.91738	−	0.513760i
$580$		0			0
$581$	−1.37280	−	2.37775i	−0.0569531	−	0.0986457i
$582$	13.1372	−	3.52009i	0.544553	−	0.145912i
$583$	−39.6838	−	22.9115i	−1.64354	−	0.948896i
$584$	−1.92362			−0.0795998
$585$		0			0
$586$	5.01430			0.207139
$587$	17.6850	+	10.2105i	0.729939	+	0.421431i	0.818400	−	0.574649i	$-0.194861\pi$
$587$	17.6850	+	10.2105i	0.729939	+	0.421431i	−0.0884607	+	0.996080i	$0.528195\pi$
$588$	−21.6893	+	5.81164i	−0.894453	+	0.239668i
$589$	−3.46106	−	5.99474i	−0.142611	−	0.247009i
$590$		0			0
$591$	−44.6065	−	11.9523i	−1.83487	−	0.491651i
$592$	1.60307	+	2.77661i	0.0658859	+	0.114118i
$593$		−	24.9304i		−	1.02377i	−0.859054	−	0.511885i	$-0.828947\pi$
$593$		−	24.9304i		−	1.02377i	0.859054	−	0.511885i	$-0.171053\pi$
$594$	−74.9305	+	43.2611i	−3.07443	+	1.77503i
$595$		0			0
$596$	11.7177	−	3.13976i	0.479978	−	0.128610i
$597$	−41.5961	−	41.5961i	−1.70242	−	1.70242i
$598$	−19.3513	+	9.29796i	−0.791335	+	0.380222i
$599$		−	25.0801i		−	1.02474i	−0.858764	−	0.512372i	$-0.828767\pi$
$599$		−	25.0801i		−	1.02474i	0.858764	−	0.512372i	$-0.171233\pi$
$600$		0			0
$601$	−7.69465	+	13.3275i	−0.313871	+	0.543641i	−0.979197	−	0.202912i	$-0.934959\pi$
$601$	−7.69465	+	13.3275i	−0.313871	+	0.543641i	0.665326	+	0.746553i	$0.268293\pi$
$602$	0.738388	−	2.75570i	0.0300945	−	0.112314i
$603$	−9.66456			−0.393571
$604$	4.25819	−	15.8918i	0.173263	−	0.646627i
$605$		0			0
$606$	22.0207	+	22.0207i	0.894528	+	0.894528i
$607$	17.6439	+	4.72767i	0.716144	+	0.191890i	0.598450	−	0.801160i	$-0.295783\pi$
$607$	17.6439	+	4.72767i	0.716144	+	0.191890i	0.117693	+	0.993050i	$0.462450\pi$
$608$	−0.507152	−	1.89272i	−0.0205677	−	0.0767598i
$609$	1.54556	+	5.76812i	0.0626294	+	0.233736i
$610$		0			0
$611$	−27.7472	−	32.3008i	−1.12253	−	1.30675i
$612$	11.9763	−	11.9763i	0.484115	−	0.484115i
$613$	−19.3521	+	33.5187i	−0.781622	+	1.35381i	0.149374	+	0.988781i	$0.452274\pi$
$613$	−19.3521	+	33.5187i	−0.781622	+	1.35381i	−0.930996	+	0.365029i	$0.881059\pi$
$614$	2.64294	+	1.52590i	0.106660	+	0.0615804i
$615$		0			0
$616$	−1.55393	+	1.55393i	−0.0626097	+	0.0626097i
$617$	24.9068	−	14.3799i	1.00271	−	0.578915i	0.0936610	−	0.995604i	$-0.470143\pi$
$617$	24.9068	−	14.3799i	1.00271	−	0.578915i	0.909049	+	0.416689i	$0.136810\pi$
$618$	15.9744	−	9.22284i	0.642586	−	0.370997i
$619$	21.8733	−	21.8733i	0.879164	−	0.879164i	−0.114284	−	0.993448i	$-0.536458\pi$
$619$	21.8733	−	21.8733i	0.879164	−	0.879164i	0.993448	+	0.114284i	$0.0364575\pi$
$620$		0			0
$621$	−80.7470	−	46.6193i	−3.24027	−	1.87077i
$622$	6.50660	−	11.2698i	0.260891	−	0.451876i
$623$	−2.04881	+	2.04881i	−0.0820837	+	0.0820837i
$624$	−10.6659	+	5.12477i	−0.426978	+	0.205155i
$625$		0			0
$626$	4.15231	+	15.4966i	0.165960	+	0.619371i
$627$	−9.19697	−	34.3235i	−0.367291	−	1.37075i
$628$	16.1279	+	4.32147i	0.643575	+	0.172445i
$629$	−4.94110	−	4.94110i	−0.197015	−	0.197015i
$630$		0			0
$631$	6.51748	−	24.3236i	0.259457	−	0.968306i	−0.706100	−	0.708113i	$-0.749547\pi$
$631$	6.51748	−	24.3236i	0.259457	−	0.968306i	0.965556	−	0.260194i	$-0.0837864\pi$
$632$	9.33180			0.371199
$633$	−9.82630	+	36.6723i	−0.390560	+	1.45759i
$634$	−11.5293	+	19.9694i	−0.457888	+	0.793085i
$635$		0			0
$636$		−	27.2168i		−	1.07922i
$637$	−24.2425	+	4.56465i	−0.960525	+	0.180858i
$638$	−17.8752	−	17.8752i	−0.707684	−	0.707684i
$639$	−77.4163	+	20.7436i	−3.06254	+	0.820606i
$640$		0			0
$641$	−16.3685	+	9.45035i	−0.646516	+	0.373266i	−0.787120	−	0.616800i	$-0.788429\pi$
$641$	−16.3685	+	9.45035i	−0.646516	+	0.373266i	0.140604	+	0.990066i	$0.455096\pi$
$642$		−	34.6193i		−	1.36632i
$643$	−0.0117386	−	0.0203318i	−0.000462925	−	0.000801809i	0.865794	−	0.500401i	$-0.166814\pi$
$643$	−0.0117386	−	0.0203318i	−0.000462925	−	0.000801809i	−0.866257	+	0.499599i	$0.833481\pi$
$644$	−2.28749	−	0.612931i	−0.0901397	−	0.0241528i
$645$		0			0
$646$	2.13534	+	3.69852i	0.0840138	+	0.145516i
$647$	14.3260	−	3.83864i	0.563214	−	0.150913i	0.0340314	−	0.999421i	$-0.489165\pi$
$647$	14.3260	−	3.83864i	0.563214	−	0.150913i	0.529182	+	0.848508i	$0.322499\pi$
$648$	−24.3154	−	14.0385i	−0.955201	−	0.551485i
$649$	−36.5285			−1.43387
$650$		0			0
$651$	−4.61104			−0.180721
$652$	−8.49192	−	4.90281i	−0.332569	−	0.192009i
$653$	2.01033	−	0.538667i	0.0786703	−	0.0210797i	−0.219269	−	0.975664i	$-0.570367\pi$
$653$	2.01033	−	0.538667i	0.0786703	−	0.0210797i	0.297940	+	0.954585i	$0.403701\pi$
$654$	10.5839	+	18.3318i	0.413862	+	0.716830i
$655$		0			0
$656$	−8.53702	−	2.28749i	−0.333315	−	0.0893114i
$657$	−7.47434	−	12.9459i	−0.291602	−	0.505069i
$658$		−	4.69709i		−	0.183111i
$659$	1.41305	−	0.815824i	0.0550445	−	0.0317800i	−0.472225	−	0.881478i	$-0.656549\pi$
$659$	1.41305	−	0.815824i	0.0550445	−	0.0317800i	0.527270	+	0.849698i	$0.323216\pi$
$660$		0			0
$661$	9.86055	−	2.64213i	0.383531	−	0.102767i	−0.0619018	−	0.998082i	$-0.519717\pi$
$661$	9.86055	−	2.64213i	0.383531	−	0.102767i	0.445433	+	0.895315i	$0.353050\pi$
$662$	−15.5134	−	15.5134i	−0.602944	−	0.602944i
$663$	19.5633	−	16.8054i	0.759776	−	0.652667i
$664$			6.90343i			0.267905i
$665$		0			0
$666$	−12.4577	+	21.5774i	−0.482726	+	0.836106i
$667$	7.05065	−	26.3134i	0.273002	−	1.01886i
$668$	1.72459			0.0667264
$669$	7.06244	−	26.3574i	0.273050	−	1.01904i
$670$		0			0
$671$	−29.1075	−	29.1075i	−1.12368	−	1.12368i
$672$	−1.26080	−	0.337830i	−0.0486363	−	0.0130321i
$673$	5.77572	+	21.5553i	0.222637	+	0.830894i	0.983337	+	0.181791i	$0.0581893\pi$
$673$	5.77572	+	21.5553i	0.222637	+	0.830894i	−0.760700	+	0.649104i	$0.775144\pi$
$674$	4.26866	+	15.9309i	0.164423	+	0.613634i
$675$		0			0
$676$	−12.1098	+	4.72794i	−0.465760	+	0.181844i
$677$	23.5555	−	23.5555i	0.905310	−	0.905310i	−0.0905794	−	0.995889i	$-0.528872\pi$
$677$	23.5555	−	23.5555i	0.905310	−	0.905310i	0.995889	+	0.0905794i	$0.0288719\pi$
$678$	−28.7918	+	49.8688i	−1.10574	+	1.91520i
$679$	1.42734	+	0.824077i	0.0547764	+	0.0316252i
$680$		0			0
$681$	7.26274	−	7.26274i	0.278309	−	0.278309i
$682$	16.9046	−	9.75986i	0.647310	−	0.373725i
$683$	−15.5475	+	8.97635i	−0.594908	+	0.343470i	−0.767036	−	0.641604i	$-0.778269\pi$
$683$	−15.5475	+	8.97635i	−0.594908	+	0.343470i	0.172128	+	0.985075i	$0.444936\pi$
$684$	10.7674	−	10.7674i	0.411702	−	0.411702i
$685$		0			0
$686$	−4.76755	−	2.75254i	−0.182026	−	0.105093i
$687$	−20.1667	+	34.9297i	−0.769407	+	1.33265i
$688$	−5.07227	+	5.07227i	−0.193379	+	0.193379i
$689$	2.26094	−	29.8149i	0.0861348	−	1.13586i
$690$		0			0
$691$	−2.72708	−	10.1776i	−0.103743	−	0.387174i	0.894457	−	0.447155i	$-0.147563\pi$
$691$	−2.72708	−	10.1776i	−0.103743	−	0.387174i	−0.998200	+	0.0599808i	$0.980896\pi$
$692$	−1.59092	−	5.93741i	−0.0604779	−	0.225706i
$693$	−16.4959	−	4.42005i	−0.626626	−	0.167904i
$694$	3.42587	+	3.42587i	0.130044	+	0.130044i
$695$		0			0
$696$	3.88612	−	14.5032i	0.147303	−	0.549742i
$697$	19.2627			0.729628
$698$	2.97604	−	11.1067i	0.112645	−	0.420396i
$699$	−23.6403	+	40.9463i	−0.894160	+	1.54873i
$700$		0			0
$701$			36.5789i			1.38156i	0.723063	+	0.690782i	$0.242734\pi$
$701$			36.5789i			1.38156i	−0.723063	+	0.690782i	$0.757266\pi$
$702$	−46.6193	−	31.8452i	−1.75953	−	1.20192i
$703$	−4.44232	−	4.44232i	−0.167545	−	0.167545i
$704$	5.33728	−	1.43012i	0.201156	−	0.0538997i
$705$		0			0
$706$	2.22407	−	1.28407i	0.0837039	−	0.0483265i
$707$			3.77386i			0.141931i
$708$	−10.8482	−	18.7896i	−0.407699	−	0.706155i
$709$	−0.801931	−	0.214877i	−0.0301172	−	0.00806987i	0.243729	−	0.969843i	$-0.421629\pi$
$709$	−0.801931	−	0.214877i	−0.0301172	−	0.00806987i	−0.273846	+	0.961774i	$0.588296\pi$
$710$		0			0
$711$	36.2593	+	62.8030i	1.35983	+	2.35530i
$712$	7.03702	−	1.88556i	0.263724	−	0.0706645i
$713$	18.2168	+	10.5175i	0.682225	+	0.393883i
$714$	2.84483			0.106465
$715$		0			0
$716$	8.58545			0.320853
$717$	57.9003	+	33.4288i	2.16233	+	1.24842i
$718$	13.1428	−	3.52159i	0.490484	−	0.131425i
$719$	20.6441	+	35.7566i	0.769894	+	1.33349i	0.937620	+	0.347661i	$0.113024\pi$
$719$	20.6441	+	35.7566i	0.769894	+	1.33349i	−0.167726	+	0.985834i	$0.553643\pi$
$720$		0			0
$721$	2.15913	+	0.578537i	0.0804102	+	0.0215459i
$722$	−7.58021	−	13.1293i	−0.282106	−	0.488622i
$723$			94.4407i			3.51229i
$724$	−2.25857	+	1.30399i	−0.0839392	+	0.0484623i
$725$		0			0
$726$	61.9179	−	16.5909i	2.29799	−	0.615744i
$727$	33.1540	+	33.1540i	1.22961	+	1.22961i	0.964110	+	0.265503i	$0.0855381\pi$
$727$	33.1540	+	33.1540i	1.22961	+	1.22961i	0.265503	+	0.964110i	$0.414462\pi$
$728$	−1.35309	−	0.474815i	−0.0501488	−	0.0175978i
$729$		−	64.0191i		−	2.37108i
$730$		0			0
$731$	7.81705	−	13.5395i	0.289124	−	0.500777i
$732$	6.32807	−	23.6167i	0.233892	−	0.872898i
$733$	24.3075			0.897818			0.448909	−	0.893577i	$-0.351813\pi$
$733$	24.3075			0.897818			0.448909	+	0.893577i	$0.351813\pi$
$734$	−4.36492	+	16.2901i	−0.161112	+	0.601279i
$735$		0			0
$736$	4.21046	+	4.21046i	0.155199	+	0.155199i
$737$	6.63770	+	1.77857i	0.244503	+	0.0655144i
$738$	−17.7764	−	66.3423i	−0.654357	−	2.44209i
$739$	4.44320	+	16.5822i	0.163446	+	0.609987i	0.998233	+	0.0594155i	$0.0189237\pi$
$739$	4.44320	+	16.5822i	0.163446	+	0.609987i	−0.834788	+	0.550572i	$0.814410\pi$
$740$		0			0
$741$	17.5885	−	15.1090i	0.646129	−	0.555041i
$742$	2.33218	−	2.33218i	0.0856171	−	0.0856171i
$743$	6.57760	−	11.3927i	0.241309	−	0.417959i	−0.719778	−	0.694204i	$-0.755757\pi$
$743$	6.57760	−	11.3927i	0.241309	−	0.417959i	0.961087	+	0.276245i	$0.0890900\pi$
$744$	10.0406	+	5.79693i	0.368106	+	0.212526i
$745$		0			0
$746$	−1.84881	+	1.84881i	−0.0676897	+	0.0676897i
$747$	−46.4600	+	26.8237i	−1.69988	+	0.981428i
$748$	−10.4295	+	6.02146i	−0.381339	+	0.220166i
$749$	2.96650	−	2.96650i	0.108393	−	0.108393i
$750$		0			0
$751$	−35.8322	−	20.6878i	−1.30754	−	0.754907i	−0.325853	−	0.945421i	$-0.605651\pi$
$751$	−35.8322	−	20.6878i	−1.30754	−	0.754907i	−0.981685	+	0.190513i	$0.938985\pi$
$752$	−5.90510	+	10.2279i	−0.215337	+	0.372975i
$753$	52.8752	−	52.8752i	1.92688	−	1.92688i
$754$	5.46188	−	15.5648i	0.198910	−	0.566837i
$755$		0			0
$756$	−1.61183	−	6.01543i	−0.0586216	−	0.218779i
$757$	12.2598	+	45.7542i	0.445590	+	1.66296i	0.714375	+	0.699763i	$0.246711\pi$
$757$	12.2598	+	45.7542i	0.445590	+	1.66296i	−0.268785	+	0.963200i	$0.586622\pi$
$758$	1.46920	+	0.393670i	0.0533636	+	0.0142987i
$759$	76.3547	+	76.3547i	2.77150	+	2.77150i
$760$		0			0
$761$	1.40042	−	5.22643i	0.0507651	−	0.189458i	−0.935887	−	0.352300i	$-0.885400\pi$
$761$	1.40042	−	5.22643i	0.0507651	−	0.189458i	0.986652	+	0.162842i	$0.0520662\pi$
$762$	4.10068			0.148552
$763$	−0.663913	+	2.47776i	−0.0240353	+	0.0897008i
$764$	0.396828	−	0.687326i	0.0143567	−	0.0248666i
$765$		0			0
$766$			3.75655i			0.135730i
$767$	−10.3228	−	21.4844i	−0.372736	−	0.775755i
$768$	2.32068	+	2.32068i	0.0837404	+	0.0837404i
$769$	−36.2611	+	9.71614i	−1.30761	+	0.350373i	−0.844323	−	0.535835i	$-0.819997\pi$
$769$	−36.2611	+	9.71614i	−1.30761	+	0.350373i	−0.463287	+	0.886208i	$0.653330\pi$
$770$		0			0
$771$	−11.5555	+	6.67155i	−0.416160	+	0.240270i
$772$			14.5537i			0.523799i
$773$	−7.26671	−	12.5863i	−0.261365	−	0.452698i	0.705240	−	0.708969i	$-0.250839\pi$
$773$	−7.26671	−	12.5863i	−0.261365	−	0.452698i	−0.966605	+	0.256271i	$0.917506\pi$
$774$	−53.8450	−	14.4277i	−1.93542	−	0.518594i
$775$		0			0
$776$	−2.07203	−	3.58887i	−0.0743817	−	0.128833i
$777$	−4.04230	+	1.08313i	−0.145017	+	0.0388571i
$778$	12.1797	+	7.03193i	0.436662	+	0.252107i
$779$	17.3183			0.620491
$780$		0			0
$781$	56.9877			2.03918
$782$	−11.2391	−	6.48888i	−0.401908	−	0.232042i
$783$	69.1965	−	18.5412i	2.47288	−	0.662607i
$784$	3.42091	+	5.92519i	0.122175	+	0.211614i
$785$		0			0
$786$	32.6291	+	8.74293i	1.16384	+	0.311850i
$787$	−22.2737	−	38.5792i	−0.793971	−	1.37520i	−0.923490	−	0.383622i	$-0.874677\pi$
$787$	−22.2737	−	38.5792i	−0.793971	−	1.37520i	0.129519	−	0.991577i	$-0.458657\pi$
$788$			14.0710i			0.501258i
$789$	26.2033	−	15.1285i	0.932863	−	0.538589i
$790$		0			0
$791$	−6.74036	+	1.80607i	−0.239659	+	0.0642166i
$792$	30.3630	+	30.3630i	1.07890	+	1.07890i
$793$	8.89401	−	25.3454i	0.315836	−	0.900042i
$794$		−	17.1506i		−	0.608653i
$795$		0			0
$796$	−8.96205	+	15.5227i	−0.317651	+	0.550188i
$797$	5.01270	−	18.7076i	0.177559	−	0.662658i	−0.818543	−	0.574445i	$-0.805218\pi$
$797$	5.01270	−	18.7076i	0.177559	−	0.662658i	0.996102	−	0.0882130i	$-0.0281156\pi$
$798$	2.55766			0.0905403
$799$	6.66207	−	24.8632i	0.235687	−	0.879596i
$800$		0			0
$801$	40.0326	+	40.0326i	1.41448	+	1.41448i
$802$	2.20232	+	0.590110i	0.0777666	+	0.0208375i
$803$	2.75100	+	10.2669i	0.0970807	+	0.362310i
$804$	1.05639	+	3.94251i	0.0372561	+	0.139041i
$805$		0			0
$806$	10.5175	+	7.18438i	0.370463	+	0.253059i
$807$	−13.5998	+	13.5998i	−0.478734	+	0.478734i
$808$	4.74444	−	8.21761i	0.166909	−	0.289094i
$809$	−16.2434	−	9.37810i	−0.571086	−	0.329717i	0.186497	−	0.982456i	$-0.440287\pi$
$809$	−16.2434	−	9.37810i	−0.571086	−	0.329717i	−0.757583	+	0.652739i	$0.773620\pi$
$810$		0			0
$811$	−20.8918	+	20.8918i	−0.733609	+	0.733609i	−0.971333	−	0.237724i	$-0.923599\pi$
$811$	−20.8918	+	20.8918i	−0.733609	+	0.733609i	0.237724	+	0.971333i	$0.423599\pi$
$812$	1.57576	−	0.909766i	0.0552984	−	0.0319265i
$813$	−36.6215	+	21.1434i	−1.28437	+	0.741533i
$814$	12.5269	−	12.5269i	0.439069	−	0.439069i
$815$		0			0
$816$	−6.19465	−	3.57648i	−0.216856	−	0.125202i
$817$	7.02796	−	12.1728i	0.245877	−	0.425872i
$818$	13.1660	−	13.1660i	0.460340	−	0.460340i
$819$	−2.06201	−	10.9512i	−0.0720524	−	0.382666i
$820$		0			0
$821$	3.52604	+	13.1594i	0.123060	+	0.459265i	0.999763	−	0.0217666i	$-0.00692907\pi$
$821$	3.52604	+	13.1594i	0.123060	+	0.459265i	−0.876704	+	0.481031i	$0.840262\pi$
$822$	−5.25104	−	19.5971i	−0.183151	−	0.683529i
$823$	18.8654	+	5.05496i	0.657606	+	0.176205i	0.572165	−	0.820138i	$-0.306104\pi$
$823$	18.8654	+	5.05496i	0.657606	+	0.176205i	0.0854405	+	0.996343i	$0.472770\pi$
$824$	−3.97420	−	3.97420i	−0.138448	−	0.138448i
$825$		0			0
$826$	0.680491	−	2.53963i	0.0236773	−	0.0883650i
$827$	6.90343			0.240056			0.120028	−	0.992771i	$-0.461702\pi$
$827$	6.90343			0.240056			0.120028	+	0.992771i	$0.461702\pi$
$828$	−11.9763	+	44.6963i	−0.416207	+	1.55331i
$829$	9.06163	−	15.6952i	0.314723	−	0.545117i	−0.664655	−	0.747150i	$-0.731422\pi$
$829$	9.06163	−	15.6952i	0.314723	−	0.545117i	0.979379	+	0.202033i	$0.0647549\pi$
$830$		0			0
$831$		−	86.5313i		−	3.00174i
$832$	2.34943	+	2.73499i	0.0814518	+	0.0948188i
$833$	−10.5442	−	10.5442i	−0.365334	−	0.365334i
$834$	64.3302	−	17.2372i	2.22757	−	0.596876i
$835$		0			0
$836$	−9.37667	+	5.41362i	−0.324299	+	0.187234i
$837$			55.3158i			1.91199i
$838$	−4.72944	−	8.19164i	−0.163376	−	0.282975i
$839$	13.8579	+	3.71322i	0.478429	+	0.128195i	0.489971	−	0.871739i	$-0.337007\pi$
$839$	13.8579	+	3.71322i	0.478429	+	0.128195i	−0.0115419	+	0.999933i	$0.503674\pi$
$840$		0			0
$841$	−4.03480	−	6.98847i	−0.139131	−	0.240982i
$842$	31.9181	−	8.55242i	1.09997	−	0.294736i
$843$	0.561775	+	0.324341i	0.0193485	+	0.0111709i
$844$	11.5681			0.398192
$845$		0			0
$846$	−91.7786			−3.15541
$847$	6.72734	+	3.88403i	0.231154	+	0.133457i
$848$	−8.01033	+	2.14636i	−0.275076	+	0.0737064i
$849$	−10.0955	−	17.4859i	−0.346476	−	0.600113i
$850$		0			0
$851$	18.4405	+	4.94110i	0.632131	+	0.169379i
$852$	16.9241	+	29.3134i	0.579810	+	1.00426i
$853$			21.5765i			0.738764i	0.929278	+	0.369382i	$0.120431\pi$
$853$			21.5765i			0.738764i	−0.929278	+	0.369382i	$0.879569\pi$
$854$	2.56594	−	1.48144i	0.0878046	−	0.0506940i
$855$		0			0
$856$	−10.1890	+	2.73013i	−0.348253	+	0.0933141i
$857$	5.36230	+	5.36230i	0.183173	+	0.183173i	0.792737	−	0.609564i	$-0.208656\pi$
$857$	5.36230	+	5.36230i	0.183173	+	0.183173i	−0.609564	+	0.792737i	$0.708656\pi$
$858$	42.6058	+	49.5979i	1.45454	+	1.69324i
$859$			28.8595i			0.984673i	0.870405	+	0.492336i	$0.163857\pi$
$859$			28.8595i			0.984673i	−0.870405	+	0.492336i	$0.836143\pi$
$860$		0			0
$861$	5.76812	−	9.99067i	0.196577	−	0.340481i
$862$	−7.65683	+	28.5757i	−0.260793	+	0.973292i
$863$	56.4179			1.92049			0.960245	−	0.279160i	$-0.0900560\pi$
$863$	56.4179			1.92049			0.960245	+	0.279160i	$0.0900560\pi$
$864$	−4.05273	+	15.1250i	−0.137877	+	0.514563i
$865$		0			0
$866$	−17.5280	−	17.5280i	−0.595624	−	0.595624i
$867$	−38.8333	−	10.4053i	−1.31885	−	0.353384i
$868$	0.363634	+	1.35710i	0.0123426	+	0.0460630i
$869$	−13.3456	−	49.8064i	−0.452718	−	1.68957i
$870$		0			0
$871$	0.829724	+	4.40661i	0.0281141	+	0.149312i
$872$	4.56067	−	4.56067i	0.154444	−	0.154444i
$873$	16.1020	−	27.8896i	0.544972	−	0.943919i
$874$	−10.1045	−	5.83386i	−0.341791	−	0.197333i
$875$		0			0
$876$	−4.46410	+	4.46410i	−0.150828	+	0.150828i
$877$	12.2322	−	7.06228i	0.413053	−	0.238476i	−0.279048	−	0.960277i	$-0.590019\pi$
$877$	12.2322	−	7.06228i	0.413053	−	0.238476i	0.692101	+	0.721801i	$0.256685\pi$
$878$	5.70002	−	3.29091i	0.192366	−	0.111063i
$879$	11.6366	−	11.6366i	0.392493	−	0.392493i
$880$		0			0
$881$	−13.6470	−	7.87910i	−0.459779	−	0.265454i	0.252172	−	0.967682i	$-0.418855\pi$
$881$	−13.6470	−	7.87910i	−0.459779	−	0.265454i	−0.711951	+	0.702229i	$0.752188\pi$
$882$	−26.5843	+	46.0454i	−0.895141	+	1.55043i
$883$	5.11749	−	5.11749i	0.172217	−	0.172217i	−0.615736	−	0.787953i	$-0.711141\pi$
$883$	5.11749	−	5.11749i	0.172217	−	0.172217i	0.787953	+	0.615736i	$0.211141\pi$
$884$	−6.48888	−	4.43248i	−0.218245	−	0.149081i
$885$		0			0
$886$	−7.36865	−	27.5002i	−0.247555	−	0.923887i
$887$	−5.68034	−	21.1993i	−0.190727	−	0.711804i	−0.993332	−	0.115292i	$-0.963220\pi$
$887$	−5.68034	−	21.1993i	−0.190727	−	0.711804i	0.802604	−	0.596512i	$-0.203447\pi$
$888$	10.1638	+	2.72339i	0.341076	+	0.0913911i
$889$	0.351384	+	0.351384i	0.0117850	+	0.0117850i
$890$		0			0
$891$	−40.1535	+	149.855i	−1.34519	+	5.02033i
$892$	−8.31434			−0.278385
$893$	5.98957	−	22.3534i	0.200433	−	0.748027i
$894$	19.9068	−	34.4795i	0.665782	−	1.15317i
$895$		0			0
$896$			0.397714i			0.0132867i
$897$	−23.3307	+	66.4859i	−0.778989	+	2.21990i
$898$	−3.95832	−	3.95832i	−0.132091	−	0.132091i
$899$	−15.6110	+	4.18295i	−0.520655	+	0.139509i
$900$		0			0
$901$	15.6528	−	9.03716i	0.521471	−	0.301072i
$902$			48.8358i			1.62606i
$903$	−4.68154	−	8.10867i	−0.155792	−	0.269840i
$904$	16.9477	+	4.54113i	0.563674	+	0.151036i
$905$		0			0
$906$	−26.9979	−	46.7617i	−0.896944	−	1.55355i
$907$	−18.9169	+	5.06878i	−0.628127	+	0.168306i	−0.558819	−	0.829289i	$-0.688746\pi$
$907$	−18.9169	+	5.06878i	−0.628127	+	0.168306i	−0.0693072	+	0.997595i	$0.522079\pi$
$908$	−2.71029	−	1.56478i	−0.0899440	−	0.0519292i
$909$	73.7393			2.44578
$910$		0			0
$911$	51.2386			1.69761			0.848806	−	0.528705i	$-0.177322\pi$
$911$	51.2386			1.69761			0.848806	+	0.528705i	$0.177322\pi$
$912$	−5.56933	−	3.21545i	−0.184419	−	0.106474i
$913$	36.8455	−	9.87273i	1.21941	−	0.326740i
$914$	10.3741	+	17.9685i	0.343145	+	0.594344i
$915$		0			0
$916$	11.8707	+	3.18076i	0.392220	+	0.105095i
$917$	2.04678	+	3.54513i	0.0675906	+	0.117070i
$918$		−	34.1277i		−	1.12638i
$919$	−0.175850	+	0.101527i	−0.00580076	+	0.00334907i	−0.502898	−	0.864346i	$-0.667733\pi$
$919$	−0.175850	+	0.101527i	−0.00580076	+	0.00334907i	0.497097	+	0.867695i	$0.334399\pi$
$920$		0			0
$921$	9.67456	−	2.59229i	0.318788	−	0.0854189i
$922$	−17.8091	−	17.8091i	−0.586511	−	0.586511i
$923$	16.1045	+	33.5175i	0.530087	+	1.10324i
$924$			7.21236i			0.237269i
$925$		0			0
$926$	−16.1076	+	27.8992i	−0.529329	+	0.916825i
$927$	11.3043	−	42.1883i	0.371283	−	1.38565i
$928$	−4.57498			−0.150181
$929$	−9.43399	+	35.2081i	−0.309519	+	1.15514i	0.619466	+	0.785024i	$0.287349\pi$
$929$	−9.43399	+	35.2081i	−0.309519	+	1.15514i	−0.928985	+	0.370118i	$0.879317\pi$
$930$		0			0
$931$	−9.47979	−	9.47979i	−0.310687	−	0.310687i
$932$	13.9154	+	3.72863i	0.455815	+	0.122135i
$933$	−11.0538	−	41.2533i	−0.361885	−	1.35057i
$934$	−7.51748	−	28.0556i	−0.245980	−	0.918008i
$935$		0			0
$936$	−9.27763	+	26.4386i	−0.303249	+	0.864174i
$937$	25.1436	−	25.1436i	0.821405	−	0.821405i	−0.164904	−	0.986310i	$-0.552732\pi$
$937$	25.1436	−	25.1436i	0.821405	−	0.821405i	0.986310	+	0.164904i	$0.0527316\pi$
$938$	−0.247308	+	0.428351i	−0.00807491	+	0.0139862i
$939$	45.5990	+	26.3266i	1.48807	+	0.859136i
$940$		0			0
$941$	32.5125	−	32.5125i	1.05988	−	1.05988i	0.0617896	−	0.998089i	$-0.480319\pi$
$941$	32.5125	−	32.5125i	1.05988	−	1.05988i	0.998089	−	0.0617896i	$-0.0196808\pi$
$942$	47.4566	−	27.3991i	1.54622	−	0.892710i
$943$	−45.5761	+	26.3134i	−1.48416	+	0.856882i
$944$	−4.67456	+	4.67456i	−0.152144	+	0.152144i
$945$		0			0
$946$	34.3261	+	19.8182i	1.11604	+	0.644344i
$947$	−17.2526	+	29.8823i	−0.560633	+	0.971045i	0.436808	+	0.899555i	$0.356109\pi$
$947$	−17.2526	+	29.8823i	−0.560633	+	0.971045i	−0.997441	+	0.0714906i	$0.977224\pi$
$948$	21.6561	−	21.6561i	0.703359	−	0.703359i
$949$	−5.26108	+	4.51940i	−0.170782	+	0.146706i
$950$		0			0
$951$	19.5867	+	73.0984i	0.635141	+	2.37038i
$952$	−0.224348	−	0.837279i	−0.00727117	−	0.0271364i
$953$	−46.7133	−	12.5168i	−1.51319	−	0.405459i	−0.595698	−	0.803208i	$-0.703125\pi$
$953$	−46.7133	−	12.5168i	−1.51319	−	0.405459i	−0.917494	+	0.397750i	$0.869791\pi$
$954$	−45.5697	−	45.5697i	−1.47537	−	1.47537i
$955$		0			0
$956$	5.27249	−	19.6772i	0.170525	−	0.636407i
$957$	−82.9651			−2.68188
$958$	−7.18639	+	26.8200i	−0.232182	+	0.866514i
$959$	1.22930	−	2.12922i	0.0396963	−	0.0687560i
$960$		0			0
$961$			18.5206i			0.597437i
$962$	10.9078	+	3.82769i	0.351683	+	0.123410i
$963$	−57.9638	−	57.9638i	−1.86786	−	1.86786i
$964$	27.7954	−	7.44774i	0.895228	−	0.239876i
$965$		0			0
$966$	−6.73095	+	3.88612i	−0.216565	+	0.125034i
$967$		−	59.9161i		−	1.92677i	−0.268121	−	0.963385i	$-0.586403\pi$
$967$		−	59.9161i		−	1.92677i	0.268121	−	0.963385i	$-0.413597\pi$
$968$	−9.76589	−	16.9150i	−0.313888	−	0.543669i
$969$	13.5385	+	3.62764i	0.434920	+	0.116537i
$970$		0			0
$971$	−22.8825	−	39.6337i	−0.734336	−	1.27191i	−0.955014	−	0.296560i	$-0.904160\pi$
$971$	−22.8825	−	39.6337i	−0.734336	−	1.27191i	0.220678	−	0.975347i	$-0.429173\pi$
$972$	−43.6323	+	11.6913i	−1.39951	+	0.374997i
$973$	6.98943	+	4.03535i	0.224071	+	0.129367i
$974$	40.0137			1.28212
$975$		0			0
$976$	−7.44980			−0.238462
$977$	45.2364	+	26.1173i	1.44724	+	0.835565i	0.998316	−	0.0580046i	$-0.0184738\pi$
$977$	45.2364	+	26.1173i	1.44724	+	0.835565i	0.448925	+	0.893570i	$0.351807\pi$
$978$	−31.0849	+	8.32917i	−0.993985	+	0.266338i
$979$	−20.1276	−	34.8620i	−0.643280	−	1.11419i
$980$		0			0
$981$	48.4141	+	12.9725i	1.54574	+	0.414181i
$982$	−9.14486	−	15.8394i	−0.291824	−	0.505454i
$983$			52.3414i			1.66943i	0.550680	+	0.834716i	$0.314368\pi$
$983$			52.3414i			1.66943i	−0.550680	+	0.834716i	$0.685632\pi$
$984$	−25.1202	+	14.5032i	−0.800804	+	0.462344i
$985$		0			0
$986$	9.63137	−	2.58072i	0.306725	−	0.0821868i
$987$	−10.9004	−	10.9004i	−0.346965	−	0.346965i
$988$	−5.83386	−	3.98505i	−0.185600	−	0.126781i
$989$			42.7132i			1.35820i
$990$		0			0
$991$	−21.4130	+	37.0883i	−0.680205	+	1.17815i	0.294713	+	0.955586i	$0.404776\pi$
$991$	−21.4130	+	37.0883i	−0.680205	+	1.17815i	−0.974918	+	0.222564i	$0.928557\pi$
$992$	0.914311	−	3.41225i	0.0290294	−	0.108339i
$993$	−72.0032			−2.28495
$994$	−1.06163	+	3.96205i	−0.0336728	+	0.125668i
$995$		0			0
$996$	16.0207	+	16.0207i	0.507634	+	0.507634i
$997$	−20.5326	−	5.50169i	−0.650274	−	0.174240i	−0.0814210	−	0.996680i	$-0.525946\pi$
$997$	−20.5326	−	5.50169i	−0.650274	−	0.174240i	−0.568853	+	0.822440i	$0.692612\pi$
$998$	6.40137	+	23.8902i	0.202632	+	0.756233i
$999$	12.9937	+	48.4930i	0.411101	+	1.53425i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.t.c.643.1	yes	8
5.2	odd	4		650.2.w.d.357.2	yes	8
5.3	odd	4		650.2.w.c.357.1	yes	8
5.4	even	2		650.2.t.d.643.2	yes	8
13.11	odd	12		650.2.w.d.193.2	yes	8
65.24	odd	12		650.2.w.c.193.1	yes	8
65.37	even	12	inner	650.2.t.c.557.1	✓	8
65.63	even	12		650.2.t.d.557.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.t.c.557.1	✓	8	65.37	even	12	inner
650.2.t.c.643.1	yes	8	1.1	even	1	trivial
650.2.t.d.557.2	yes	8	65.63	even	12
650.2.t.d.643.2	yes	8	5.4	even	2
650.2.w.c.193.1	yes	8	65.24	odd	12
650.2.w.c.357.1	yes	8	5.3	odd	4
650.2.w.d.193.2	yes	8	13.11	odd	12
650.2.w.d.357.2	yes	8	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-3.17011 + 0.849429i) q^{3} +(0.500000 + 0.866025i) q^{4} +(3.17011 + 0.849429i) q^{6} +(0.198857 + 0.344430i) q^{7} -1.00000i q^{8} +(6.72999 - 3.88556i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-3.17011 + 0.849429i) q^{3} +(0.500000 + 0.866025i) q^{4} +(3.17011 + 0.849429i) q^{6} +(0.198857 + 0.344430i) q^{7} -1.00000i q^{8} +(6.72999 - 3.88556i) q^{9} +(-5.33728 + 1.43012i) q^{11} +(-2.32068 - 2.32068i) q^{12} +(-2.34943 - 2.73499i) q^{13} -0.397714i q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.564094 - 2.10523i) q^{17} -7.77113 q^{18} +(0.507152 - 1.89272i) q^{19} +(-0.922968 - 0.922968i) q^{21} +(5.33728 + 1.43012i) q^{22} +(1.54113 + 5.75159i) q^{23} +(0.849429 + 3.17011i) q^{24} +(0.667168 + 3.54329i) q^{26} +(-11.0723 + 11.0723i) q^{27} +(-0.198857 + 0.344430i) q^{28} +(-3.96205 - 2.28749i) q^{29} +(2.49794 - 2.49794i) q^{31} +(0.866025 - 0.500000i) q^{32} +(15.7050 - 9.06727i) q^{33} +(-1.54113 + 1.54113i) q^{34} +(6.72999 + 3.88556i) q^{36} +(1.60307 - 2.77661i) q^{37} +(-1.38556 + 1.38556i) q^{38} +(9.77113 + 6.67456i) q^{39} +(2.28749 + 8.53702i) q^{41} +(0.337830 + 1.26080i) q^{42} +(6.92885 + 1.85658i) q^{43} +(-3.90716 - 3.90716i) q^{44} +(1.54113 - 5.75159i) q^{46} +11.8102 q^{47} +(0.849429 - 3.17011i) q^{48} +(3.42091 - 5.92519i) q^{49} +7.15296i q^{51} +(1.19386 - 3.40216i) q^{52} +(5.86397 + 5.86397i) q^{53} +(15.1250 - 4.05273i) q^{54} +(0.344430 - 0.198857i) q^{56} +6.43091i q^{57} +(2.28749 + 3.96205i) q^{58} +(6.38556 + 1.71101i) q^{59} +(3.72490 + 6.45171i) q^{61} +(-3.41225 + 0.914311i) q^{62} +(2.67661 + 1.54534i) q^{63} -1.00000 q^{64} -18.1345 q^{66} +(-1.07703 - 0.621825i) q^{67} +(2.10523 - 0.564094i) q^{68} +(-9.77113 - 16.9241i) q^{69} +(-9.96205 - 2.66932i) q^{71} +(-3.88556 - 6.72999i) q^{72} -1.92362i q^{73} +(-2.77661 + 1.60307i) q^{74} +(1.89272 - 0.507152i) q^{76} +(-1.55393 - 1.55393i) q^{77} +(-5.12477 - 10.6659i) q^{78} +9.33180i q^{79} +(14.0385 - 24.3154i) q^{81} +(2.28749 - 8.53702i) q^{82} -6.90343 q^{83} +(0.337830 - 1.26080i) q^{84} +(-5.07227 - 5.07227i) q^{86} +(14.5032 + 3.88612i) q^{87} +(1.43012 + 5.33728i) q^{88} +(1.88556 + 7.03702i) q^{89} +(0.474815 - 1.35309i) q^{91} +(-4.21046 + 4.21046i) q^{92} +(-5.79693 + 10.0406i) q^{93} +(-10.2279 - 5.90510i) q^{94} +(-2.32068 + 2.32068i) q^{96} +(3.58887 - 2.07203i) q^{97} +(-5.92519 + 3.42091i) q^{98} +(-30.3630 + 30.3630i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{3} + 4 q^{4} + 6 q^{6} + 12 q^{9}+O(q^{10}) \) 8 * q - 6 * q^3 + 4 * q^4 + 6 * q^6 + 12 * q^9	\( 8 q - 6 q^{3} + 4 q^{4} + 6 q^{6} + 12 q^{9} - 18 q^{11} - 18 q^{13} - 4 q^{16} + 6 q^{17} - 8 q^{18} + 14 q^{19} + 8 q^{21} + 18 q^{22} + 6 q^{24} - 36 q^{27} + 24 q^{29} - 8 q^{31} + 42 q^{33} + 12 q^{36} + 6 q^{37} + 16 q^{38} + 24 q^{39} + 12 q^{41} + 22 q^{42} + 12 q^{43} - 12 q^{44} + 6 q^{48} - 16 q^{49} - 6 q^{52} + 12 q^{53} + 36 q^{54} - 12 q^{56} + 12 q^{58} + 24 q^{59} + 6 q^{61} + 10 q^{62} - 8 q^{64} - 12 q^{66} - 24 q^{67} + 6 q^{68} - 24 q^{69} - 24 q^{71} - 4 q^{72} - 30 q^{74} - 2 q^{76} - 36 q^{77} - 10 q^{78} + 28 q^{81} + 12 q^{82} - 60 q^{83} + 22 q^{84} + 12 q^{86} + 48 q^{87} + 6 q^{88} - 12 q^{89} - 2 q^{91} - 12 q^{92} - 24 q^{93} - 12 q^{94} - 30 q^{97} - 24 q^{98} - 84 q^{99}+O(q^{100}) \) 8 * q - 6 * q^3 + 4 * q^4 + 6 * q^6 + 12 * q^9 - 18 * q^11 - 18 * q^13 - 4 * q^16 + 6 * q^17 - 8 * q^18 + 14 * q^19 + 8 * q^21 + 18 * q^22 + 6 * q^24 - 36 * q^27 + 24 * q^29 - 8 * q^31 + 42 * q^33 + 12 * q^36 + 6 * q^37 + 16 * q^38 + 24 * q^39 + 12 * q^41 + 22 * q^42 + 12 * q^43 - 12 * q^44 + 6 * q^48 - 16 * q^49 - 6 * q^52 + 12 * q^53 + 36 * q^54 - 12 * q^56 + 12 * q^58 + 24 * q^59 + 6 * q^61 + 10 * q^62 - 8 * q^64 - 12 * q^66 - 24 * q^67 + 6 * q^68 - 24 * q^69 - 24 * q^71 - 4 * q^72 - 30 * q^74 - 2 * q^76 - 36 * q^77 - 10 * q^78 + 28 * q^81 + 12 * q^82 - 60 * q^83 + 22 * q^84 + 12 * q^86 + 48 * q^87 + 6 * q^88 - 12 * q^89 - 2 * q^91 - 12 * q^92 - 24 * q^93 - 12 * q^94 - 30 * q^97 - 24 * q^98 - 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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