LMFDB - Embedded newform 650.2.t.d.557.2

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			557.2
Root			$0.500000 + 1.56488i$ of defining polynomial
Character	$\chi$	$=$	650.557
Dual form			650.2.t.d.643.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(3.17011 + 0.849429i) q^{3} +(0.500000 - 0.866025i) q^{4} +(3.17011 - 0.849429i) q^{6} +(-0.198857 + 0.344430i) q^{7} -1.00000i q^{8} +(6.72999 + 3.88556i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{12}\right)$

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	$-0.0203527\pi$
$3$	3.17011	+	0.849429i	1.83026	+	0.490418i	0.832308	+	0.554314i	$0.187019\pi$
$4$	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	$-0.857280\pi$
$7$	−0.198857	+	0.344430i	−0.0751609	+	0.130182i	0.825995	+	0.563677i	$0.190614\pi$
$8$		−	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	−0.661431	−	0.750006i	$-0.730051\pi$
$11$	−5.33728	−	1.43012i	−1.60925	−	0.431197i	−0.947819	+	0.318809i	$0.896717\pi$
$12$	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	−0.999984	−	0.00568097i	$-0.998192\pi$
$17$	−0.564094	−	2.10523i	−0.136813	−	0.510593i	0.863171	−	0.504912i	$-0.168475\pi$
$18$	7.77113			1.83167
$19$	0.507152	+	1.89272i	0.116349	+	0.434219i	0.999384	−	0.0350870i	$-0.0111708\pi$
$19$	0.507152	+	1.89272i	0.116349	+	0.434219i	−0.883036	+	0.469306i	$0.844504\pi$
$20$		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	0.596583	+	0.802551i	$0.296525\pi$
$23$	−1.54113	+	5.75159i	−0.321349	+	1.19929i	−0.917932	+	0.396738i	$0.870142\pi$
$24$	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	−0.820516	−	0.571624i	$-0.806314\pi$
$29$	−3.96205	+	2.28749i	−0.735733	+	0.424776i	0.0847826	+	0.996399i	$0.472980\pi$
$30$		0			0
$31$	2.49794	+	2.49794i	0.448644	+	0.448644i	0.894904	−	0.446260i	$-0.147244\pi$
$31$	2.49794	+	2.49794i	0.448644	+	0.448644i	−0.446260	+	0.894904i	$0.647244\pi$
$32$	−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	$-0.251558\pi$
$37$	−1.60307	−	2.77661i	−0.263544	−	0.456471i	−0.967181	+	0.254088i	$0.918225\pi$
$38$	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	−0.520389	−	0.853929i	$-0.674213\pi$
$41$	2.28749	−	8.53702i	0.357246	−	1.33326i	0.877635	−	0.479330i	$-0.159120\pi$
$42$	−0.337830	+	1.26080i	−0.0521282	+	0.194545i
$43$	−6.92885	+	1.85658i	−1.05664	+	0.283126i	−0.744993	−	0.667072i	$-0.767547\pi$
$43$	−6.92885	+	1.85658i	−1.05664	+	0.283126i	−0.311647	+	0.950198i	$0.600881\pi$
$44$	−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	$-0.830379\pi$
$47$	−11.8102			−1.72270			−0.861348	+	0.508016i	$0.830379\pi$
$48$	−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	$-0.942886\pi$
$53$	−5.86397	+	5.86397i	−0.805478	+	0.805478i	0.178468	+	0.983946i	$0.442886\pi$
$54$	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	0.182036	−	0.983292i	$-0.441731\pi$
$59$	6.38556	−	1.71101i	0.831330	−	0.222754i	0.649294	+	0.760538i	$0.275065\pi$
$60$		0			0
$61$	3.72490	−	6.45171i	0.476924	−	0.826057i	−0.522726	−	0.852501i	$-0.675085\pi$
$61$	3.72490	−	6.45171i	0.476924	−	0.826057i	0.999650	+	0.0264434i	$0.00841819\pi$
$62$	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	$-0.642462\pi$
$67$	1.07703	−	0.621825i	0.131580	−	0.0759680i	0.564345	+	0.825539i	$0.309129\pi$
$68$	−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	−0.795829	−	0.605521i	$-0.792965\pi$
$71$	−9.96205	+	2.66932i	−1.18228	+	0.316790i	−0.386448	+	0.922311i	$0.626298\pi$
$72$	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	$-0.824082\pi$
$79$		−	9.33180i		−	1.04991i	0.851130	−	0.524955i	$-0.175918\pi$
$80$		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	$-0.376311\pi$
$83$	6.90343			0.757750			0.378875	+	0.925448i	$0.376311\pi$
$84$	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	−0.791083	−	0.611709i	$-0.790482\pi$
$89$	1.88556	−	7.03702i	0.199869	−	0.745923i	0.990952	−	0.134214i	$-0.0428509\pi$
$90$		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	$-0.400804\pi$
$97$	−3.58887	−	2.07203i	−0.364394	−	0.210383i	−0.671007	+	0.741451i	$0.734138\pi$
$98$	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	−0.0319341	−	0.999490i	$-0.510167\pi$
$101$	8.21761	−	4.74444i	0.817683	−	0.472089i	0.849617	+	0.527401i	$0.176833\pi$
$102$	−3.57648	−	6.19465i	−0.354124	−	0.613361i
$103$	−3.97420	−	3.97420i	−0.391589	−	0.391589i	0.483664	−	0.875254i	$-0.339306\pi$
$103$	−3.97420	−	3.97420i	−0.391589	−	0.391589i	−0.875254	+	0.483664i	$0.839306\pi$
$104$	−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	−0.698969	−	0.715152i	$-0.746357\pi$
$107$	2.73013	−	10.1890i	0.263932	−	0.985008i	0.962901	−	0.269856i	$-0.0869760\pi$
$108$	15.1250	−	4.05273i	1.45540	−	0.389974i
$109$	4.56067	−	4.56067i	0.436833	−	0.436833i	−0.454112	−	0.890945i	$-0.650043\pi$
$109$	4.56067	−	4.56067i	0.436833	−	0.436833i	0.890945	+	0.454112i	$0.150043\pi$
$110$		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	0.759085	+	0.650992i	$0.225647\pi$
$113$	4.54113	+	16.9477i	0.427194	+	1.59431i	−0.331891	+	0.943318i	$0.607687\pi$
$114$	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	$-0.434322\pi$
$127$	−1.20689	−	0.323386i	−0.107095	−	0.0286959i	−0.311968	+	0.950092i	$0.600988\pi$
$128$	−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	$-0.748267\pi$
$137$	3.09092	−	5.35364i	0.264076	−	0.457392i	0.967321	+	0.253555i	$0.0815999\pi$
$138$			19.5423i			1.66355i
$139$	17.5740	+	10.1464i	1.49061	+	0.860603i	0.999942	−	0.0107445i	$-0.00342014\pi$
$139$	17.5740	+	10.1464i	1.49061	+	0.860603i	0.490666	+	0.871348i	$0.336753\pi$
$140$		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	0.966842	+	0.255374i	$0.0821985\pi$
$149$	3.13976	+	11.7177i	0.257219	+	0.959955i	−0.709623	+	0.704581i	$0.751135\pi$
$150$		0			0
$151$	−11.6336	+	11.6336i	−0.946728	+	0.946728i	−0.998651	−	0.0519227i	$-0.983465\pi$
$151$	−11.6336	+	11.6336i	−0.946728	+	0.946728i	0.0519227	+	0.998651i	$0.483465\pi$
$152$	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	$-0.482114\pi$
$157$	−11.8065	−	11.8065i	−0.942259	−	0.942259i	−0.998422	+	0.0561623i	$0.982114\pi$
$158$	−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	$-0.207873\pi$
$163$	8.49192	+	4.90281i	0.665138	+	0.384018i	−0.129094	+	0.991632i	$0.541207\pi$
$164$	−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	$-0.187922\pi$
$167$	−0.862295	−	1.49354i	−0.0667264	−	0.115574i	−0.897459	+	0.441099i	$0.854589\pi$
$168$	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	$-0.508260\pi$
$173$	5.93741	−	1.59092i	0.451413	−	0.120956i	0.477360	+	0.878708i	$0.341594\pi$
$174$	−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	0.980664	−	0.195697i	$-0.0626970\pi$
$179$	4.29272	+	7.43522i	0.320853	+	0.555734i	−0.659811	+	0.751432i	$0.729364\pi$
$180$		0			0
$181$		−	2.60797i		−	0.193849i	−0.995292	−	0.0969246i	$-0.969099\pi$
$181$		−	2.60797i		−	0.193849i	0.995292	−	0.0969246i	$-0.0309006\pi$
$182$	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	−0.880025	−	0.474927i	$-0.842474\pi$
$191$	−0.396828	+	0.687326i	−0.0287135	+	0.0497332i	0.851312	+	0.524660i	$0.175808\pi$
$192$	−3.17011	−	0.849429i	−0.228783	−	0.0613022i
$193$	−12.6039	+	7.27684i	−0.907246	+	0.523799i	−0.879544	−	0.475818i	$-0.842152\pi$
$193$	−12.6039	+	7.27684i	−0.907246	+	0.523799i	−0.0277019	+	0.999616i	$0.508819\pi$
$194$	−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	$-0.833796\pi$
$197$	−12.1858	+	7.03549i	−0.868204	+	0.501258i	−0.00145289	+	0.999999i	$0.500462\pi$
$198$	−41.4767	−	11.1136i	−2.94762	−	0.789812i
$199$	8.96205	−	15.5227i	0.635303	−	1.10038i	−0.351148	−	0.936320i	$-0.614209\pi$
$199$	8.96205	−	15.5227i	0.635303	−	1.10038i	0.986451	−	0.164056i	$-0.0524579\pi$
$200$		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	0.993503	−	0.113807i	$-0.0363046\pi$
$211$	5.78407	+	10.0183i	0.398192	+	0.689688i	−0.595311	+	0.803495i	$0.702971\pi$
$212$	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	$-0.0768676\pi$
$223$	4.15717	+	7.20043i	0.278385	+	0.482177i	−0.692599	+	0.721323i	$0.743534\pi$
$224$	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	$-0.300214\pi$
$227$	2.71029	+	1.56478i	0.179888	+	0.103858i	−0.407352	+	0.913271i	$0.633548\pi$
$228$	5.56933	+	3.21545i	0.368838	+	0.212949i
$229$	8.68998	+	8.68998i	0.574250	+	0.574250i	0.933313	−	0.359063i	$-0.116904\pi$
$229$	8.68998	+	8.68998i	0.574250	+	0.574250i	−0.359063	+	0.933313i	$0.616904\pi$
$230$		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	$-0.406430\pi$
$233$	−10.1868	−	10.1868i	−0.667360	−	0.667360i	−0.957104	+	0.289744i	$0.906430\pi$
$234$	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	−0.997816	−	0.0660522i	$-0.978960\pi$
$239$	−14.4047	+	14.4047i	−0.931764	+	0.931764i	0.0660522	+	0.997816i	$0.478960\pi$
$240$		0			0
$241$	7.44774	+	27.7954i	0.479751	+	1.79046i	0.602615	+	0.798032i	$0.294126\pi$
$241$	7.44774	+	27.7954i	0.479751	+	1.79046i	−0.122863	+	0.992424i	$0.539208\pi$
$242$	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	−0.275260	−	0.961370i	$-0.588764\pi$
$251$	−19.7318	−	11.3922i	−1.24546	−	0.719067i	−0.970201	+	0.242303i	$0.922097\pi$
$252$			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	$-0.457138\pi$
$257$	−3.92708	−	1.05226i	−0.244965	−	0.0656380i	−0.379212	+	0.925310i	$0.623805\pi$
$258$	−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	$-0.324925\pi$
$263$	8.90510	+	2.38612i	0.549112	+	0.147134i	0.0264126	+	0.999651i	$0.491592\pi$
$264$	−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	0.646674	−	0.762767i	$-0.276160\pi$
$269$	5.07512	+	2.93012i	0.309435	+	0.178653i	−0.337238	+	0.941419i	$0.609493\pi$
$270$		0			0
$271$	12.4457	+	3.33481i	0.756022	+	0.202575i	0.616187	−	0.787600i	$-0.288676\pi$
$271$	12.4457	+	3.33481i	0.756022	+	0.202575i	0.139834	+	0.990175i	$0.455343\pi$
$272$	−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	0.794616	+	0.607112i	$0.207672\pi$
$277$	6.82400	+	25.4675i	0.410014	+	1.53019i	−0.384602	+	0.923083i	$0.625661\pi$
$278$	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	−0.711263	−	0.702926i	$-0.751877\pi$
$281$	−0.139761	+	0.139761i	−0.00833744	+	0.00833744i	0.702926	+	0.711263i	$0.251877\pi$
$282$	−37.4397	+	10.0319i	−2.22950	+	0.597393i
$283$	−1.59229	+	5.94251i	−0.0946518	+	0.353245i	−0.996966	−	0.0778327i	$-0.975200\pi$
$283$	−1.59229	+	5.94251i	−0.0946518	+	0.353245i	0.902315	+	0.431078i	$0.141867\pi$
$284$	−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	$-0.286542\pi$
$293$	4.34251	+	2.50715i	0.253692	+	0.146469i	−0.367761	+	0.929920i	$0.619876\pi$
$294$	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	$-0.472244\pi$
$307$	3.05180			0.174176			0.0870878	+	0.996201i	$0.472244\pi$
$308$	−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	$-0.879715\pi$
$311$		−	13.0132i		−	0.737911i	0.929447	−	0.368955i	$-0.120285\pi$
$312$	−6.67456	−	9.77113i	−0.377872	−	0.553181i
$313$	11.3443	−	11.3443i	0.641220	−	0.641220i	−0.309636	−	0.950855i	$-0.600207\pi$
$313$	11.3443	−	11.3443i	0.641220	−	0.641220i	0.950855	+	0.309636i	$0.100207\pi$
$314$	−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	0.375918	−	0.926653i	$-0.377327\pi$
$331$	21.1917	−	5.67829i	1.16480	−	0.312107i	0.788881	+	0.614546i	$0.210661\pi$
$332$	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	$-0.601705\pi$
$337$	11.6622	−	11.6622i	0.635281	−	0.635281i	0.949388	+	0.314107i	$0.101705\pi$
$338$	−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	$-0.541821\pi$
$347$	4.67982	−	1.25395i	0.251226	−	0.0673158i	0.382234	+	0.924065i	$0.375155\pi$
$348$	−3.88612	+	14.5032i	−0.208318	+	0.777452i
$349$	2.97604	−	11.1067i	0.159304	−	0.594530i	−0.839395	−	0.543523i	$-0.817090\pi$
$349$	2.97604	−	11.1067i	0.159304	−	0.594530i	0.998698	−	0.0510072i	$-0.0162431\pi$
$350$		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	$-0.144895\pi$
$353$	1.28407	+	2.22407i	0.0683440	+	0.118375i	−0.829828	+	0.558019i	$0.811562\pi$
$354$	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	0.406060	−	0.913846i	$-0.366902\pi$
$359$	−9.62118	−	9.62118i	−0.507786	−	0.507786i	−0.913846	+	0.406060i	$0.866902\pi$
$360$		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	−0.753397	−	0.657566i	$-0.771586\pi$
$367$	4.36492	−	16.2901i	0.227847	−	0.850337i	0.981244	−	0.192771i	$-0.0617474\pi$
$368$	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	$-0.104896\pi$
$373$	−0.676711	−	2.52552i	−0.0350388	−	0.130766i	−0.981230	+	0.192842i	$0.938229\pi$
$374$	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	0.220888	−	0.975299i	$-0.429105\pi$
$379$	−1.46920	−	0.393670i	−0.0754676	−	0.0202215i	−0.296355	+	0.955078i	$0.595771\pi$
$380$		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	$-0.802736\pi$
$383$	1.87827	−	3.25326i	0.0959753	−	0.166234i	0.910015	+	0.414575i	$0.136070\pi$
$384$	−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	$-0.974955\pi$
$397$	−8.57531	+	14.8529i	−0.430383	+	0.745444i	0.566524	+	0.824046i	$0.308288\pi$
$398$		−	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	0.203410	−	0.979094i	$-0.434798\pi$
$401$	−2.20232	−	0.590110i	−0.109979	−	0.0294687i	−0.313389	+	0.949625i	$0.601464\pi$
$402$	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	−0.976638	−	0.214889i	$-0.931061\pi$
$409$	−4.81911	−	17.9851i	−0.238289	−	0.889308i	0.738349	−	0.674419i	$-0.235606\pi$
$410$		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	−0.286377	−	0.958117i	$-0.592451\pi$
$419$	8.19164	−	4.72944i	0.400188	−	0.231048i	0.686565	+	0.727068i	$0.259118\pi$
$420$		0			0
$421$	−23.3656	−	23.3656i	−1.13877	−	1.13877i	−0.988671	−	0.150101i	$-0.952040\pi$
$421$	−23.3656	−	23.3656i	−1.13877	−	1.13877i	−0.150101	−	0.988671i	$-0.547960\pi$
$422$	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	0.493356	+	0.869828i	$0.335770\pi$
$431$	−7.65683	+	28.5757i	−0.368817	+	1.37644i	−0.862172	+	0.506615i	$0.830897\pi$
$432$	4.05273	−	15.1250i	0.194987	−	0.727702i
$433$	−23.9436	+	6.41568i	−1.15066	+	0.308318i	−0.783229	−	0.621734i	$-0.786429\pi$
$433$	−23.9436	+	6.41568i	−1.15066	+	0.308318i	−0.367429	+	0.930052i	$0.619762\pi$
$434$	−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	0.776743	−	0.629818i	$-0.216870\pi$
$439$	−3.29091	−	5.70002i	−0.157067	−	0.272047i	−0.933810	+	0.357770i	$0.883537\pi$
$440$		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	$-0.986432\pi$
$443$	−20.1315	+	20.1315i	−0.956478	+	0.956478i	0.0426135	+	0.999092i	$0.486432\pi$
$444$	−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	−0.128961	−	0.991650i	$-0.541164\pi$
$449$	5.40716	−	1.44884i	0.255180	−	0.0683752i	0.384141	+	0.923274i	$0.374498\pi$
$450$		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	$-0.505384\pi$
$457$	17.9685	−	10.3741i	0.840530	−	0.485280i	0.857444	+	0.514577i	$0.172051\pi$
$458$	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	0.356898	−	0.934143i	$-0.383834\pi$
$461$	24.3277	−	6.51858i	1.13305	−	0.303600i	0.776154	+	0.630543i	$0.217168\pi$
$462$	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	$-0.984577\pi$
$467$	−20.5381	+	20.5381i	−0.950392	+	0.950392i	0.0484344	+	0.998826i	$0.484577\pi$
$468$	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	0.582542	+	0.812801i	$0.302058\pi$
$479$	−7.18639	+	26.8200i	−0.328355	+	1.22544i	−0.910896	+	0.412636i	$0.864608\pi$
$480$		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	0.996135	+	0.0878365i	$0.0279953\pi$
$487$	34.6529	+	20.0068i	1.57027	+	0.906596i	0.574136	+	0.818760i	$0.305338\pi$
$488$	−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	−0.0980231	−	0.995184i	$-0.531252\pi$
$491$	15.8394	−	9.14486i	0.714820	−	0.412702i	0.812843	+	0.582483i	$0.197919\pi$
$492$	−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	−0.980321	−	0.197411i	$-0.936747\pi$
$499$	−17.4889	+	17.4889i	−0.782910	+	0.782910i	0.197411	+	0.980321i	$0.436747\pi$
$500$		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	−0.999959	−	0.00904899i	$-0.997120\pi$
$503$	−3.10609	−	11.5921i	−0.138494	−	0.516865i	0.861465	−	0.507816i	$-0.169547\pi$
$504$	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	−0.148002	−	0.988987i	$-0.547284\pi$
$509$	−17.3871	−	4.65885i	−0.770668	−	0.206500i	−0.622667	+	0.782487i	$0.713951\pi$
$510$		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	$-0.496374\pi$
$523$	−10.9477	−	2.93344i	−0.478711	−	0.128270i	−0.490103	+	0.871665i	$0.663041\pi$
$524$	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	−0.504911	−	0.863171i	$-0.668475\pi$
$541$	8.33292	−	8.33292i	0.358260	−	0.358260i	0.863171	+	0.504911i	$0.168475\pi$
$542$	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	$-0.246492\pi$
$547$	0.364520	+	0.364520i	0.0155858	+	0.0155858i	−0.699271	+	0.714857i	$0.746492\pi$
$548$	−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	$-0.192700\pi$
$557$	−1.92806	−	3.33950i	−0.0816947	−	0.141499i	−0.903978	+	0.427579i	$0.859367\pi$
$558$	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	$-0.735361\pi$
$563$	−21.0699	+	5.64567i	−0.887992	+	0.237937i	−0.214140	+	0.976803i	$0.568695\pi$
$564$	−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	−0.932712	−	0.360623i	$-0.882564\pi$
$569$	−18.5740	−	32.1712i	−0.778664	−	1.34869i	0.154047	−	0.988063i	$-0.450769\pi$
$570$		0			0
$571$		−	12.6031i		−	0.527423i	−0.964602	−	0.263712i	$-0.915053\pi$
$571$		−	12.6031i		−	0.527423i	0.964602	−	0.263712i	$-0.0849467\pi$
$572$	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	$-0.805139\pi$
$587$	−17.6850	+	10.2105i	−0.729939	+	0.421431i	0.0884607	+	0.996080i	$0.471805\pi$
$588$	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	$0.171233\pi$
$599$			25.0801i			1.02474i	−0.858764	+	0.512372i	$0.828767\pi$
$600$		0			0
$601$	−7.69465	−	13.3275i	−0.313871	−	0.543641i	0.665326	−	0.746553i	$-0.268293\pi$
$601$	−7.69465	−	13.3275i	−0.313871	−	0.543641i	−0.979197	+	0.202912i	$0.934959\pi$
$602$	−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	$-0.704217\pi$
$607$	−17.6439	+	4.72767i	−0.716144	+	0.191890i	−0.117693	+	0.993050i	$0.537550\pi$
$608$	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	0.930996	+	0.365029i	$0.118941\pi$
$613$	19.3521	+	33.5187i	0.781622	+	1.35381i	−0.149374	+	0.988781i	$0.547726\pi$
$614$	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	$-0.529857\pi$
$617$	−24.9068	−	14.3799i	−1.00271	−	0.578915i	−0.909049	+	0.416689i	$0.863190\pi$
$618$	−15.9744	−	9.22284i	−0.642586	−	0.370997i
$619$	21.8733	+	21.8733i	0.879164	+	0.879164i	0.993448	−	0.114284i	$-0.0364575\pi$
$619$	21.8733	+	21.8733i	0.879164	+	0.879164i	−0.114284	+	0.993448i	$0.536458\pi$
$620$		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	0.965556	+	0.260194i	$0.0837864\pi$
$631$	6.51748	+	24.3236i	0.259457	+	0.968306i	−0.706100	+	0.708113i	$0.749547\pi$
$632$	−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	0.140604	−	0.990066i	$-0.455096\pi$
$641$	−16.3685	−	9.45035i	−0.646516	−	0.373266i	−0.787120	+	0.616800i	$0.788429\pi$
$642$		−	34.6193i		−	1.36632i
$643$	0.0117386	−	0.0203318i	0.000462925	−	0.000801809i	−0.865794	−	0.500401i	$-0.833186\pi$
$643$	0.0117386	−	0.0203318i	0.000462925	−	0.000801809i	0.866257	+	0.499599i	$0.166519\pi$
$644$	−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	$-0.510835\pi$
$647$	−14.3260	−	3.83864i	−0.563214	−	0.150913i	−0.529182	+	0.848508i	$0.677501\pi$
$648$	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	$-0.429633\pi$
$653$	−2.01033	−	0.538667i	−0.0786703	−	0.0210797i	−0.297940	+	0.954585i	$0.596299\pi$
$654$	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	0.527270	−	0.849698i	$-0.323216\pi$
$659$	1.41305	+	0.815824i	0.0550445	+	0.0317800i	−0.472225	+	0.881478i	$0.656549\pi$
$660$		0			0
$661$	9.86055	+	2.64213i	0.383531	+	0.102767i	0.445433	−	0.895315i	$-0.353050\pi$
$661$	9.86055	+	2.64213i	0.383531	+	0.102767i	−0.0619018	+	0.998082i	$0.519717\pi$
$662$	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	0.760700	+	0.649104i	$0.224856\pi$
$673$	−5.77572	+	21.5553i	−0.222637	+	0.830894i	−0.983337	+	0.181791i	$0.941811\pi$
$674$	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	$-0.471128\pi$
$677$	−23.5555	−	23.5555i	−0.905310	−	0.905310i	−0.995889	+	0.0905794i	$0.971128\pi$
$678$	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	$-0.221731\pi$
$683$	15.5475	+	8.97635i	0.594908	+	0.343470i	−0.172128	+	0.985075i	$0.555064\pi$
$684$	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	−0.998200	−	0.0599808i	$-0.980896\pi$
$691$	−2.72708	+	10.1776i	−0.103743	+	0.387174i	0.894457	+	0.447155i	$0.147563\pi$
$692$	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	$-0.757266\pi$
$701$		−	36.5789i		−	1.38156i	0.723063	−	0.690782i	$-0.242734\pi$
$702$	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	−0.273846	−	0.961774i	$-0.588296\pi$
$709$	−0.801931	+	0.214877i	−0.0301172	+	0.00806987i	0.243729	+	0.969843i	$0.421629\pi$
$710$		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	−0.167726	−	0.985834i	$-0.553643\pi$
$719$	20.6441	−	35.7566i	0.769894	−	1.33349i	0.937620	−	0.347661i	$-0.113024\pi$
$720$		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	−0.265503	+	0.964110i	$0.585538\pi$
$727$	−33.1540	+	33.1540i	−1.22961	+	1.22961i	−0.964110	+	0.265503i	$0.914462\pi$
$728$	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	$-0.648187\pi$
$733$	−24.3075			−0.897818			−0.448909	+	0.893577i	$0.648187\pi$
$734$	−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	−0.834788	−	0.550572i	$-0.814410\pi$
$739$	4.44320	−	16.5822i	0.163446	−	0.609987i	0.998233	−	0.0594155i	$-0.0189237\pi$
$740$		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	$-0.244243\pi$
$743$	−6.57760	−	11.3927i	−0.241309	−	0.417959i	−0.961087	+	0.276245i	$0.910910\pi$
$744$	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	−0.981685	−	0.190513i	$-0.938985\pi$
$751$	−35.8322	+	20.6878i	−1.30754	+	0.754907i	−0.325853	+	0.945421i	$0.605651\pi$
$752$	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	0.268785	+	0.963200i	$0.413378\pi$
$757$	−12.2598	+	45.7542i	−0.445590	+	1.66296i	−0.714375	+	0.699763i	$0.753289\pi$
$758$	−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	0.986652	−	0.162842i	$-0.0520662\pi$
$761$	1.40042	+	5.22643i	0.0507651	+	0.189458i	−0.935887	+	0.352300i	$0.885400\pi$
$762$	−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	−0.463287	−	0.886208i	$-0.653330\pi$
$769$	−36.2611	−	9.71614i	−1.30761	−	0.350373i	−0.844323	+	0.535835i	$0.819997\pi$
$770$		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	$-0.749161\pi$
$773$	7.26671	−	12.5863i	0.261365	−	0.452698i	0.966605	+	0.256271i	$0.0824939\pi$
$774$	−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	−0.129519	−	0.991577i	$-0.541343\pi$
$787$	22.2737	−	38.5792i	0.793971	−	1.37520i	0.923490	−	0.383622i	$-0.125323\pi$
$788$			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	−0.996102	−	0.0882130i	$-0.971884\pi$
$797$	−5.01270	−	18.7076i	−0.177559	−	0.662658i	0.818543	−	0.574445i	$-0.194782\pi$
$798$	−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	−0.757583	−	0.652739i	$-0.773620\pi$
$809$	−16.2434	+	9.37810i	−0.571086	+	0.329717i	0.186497	+	0.982456i	$0.440287\pi$
$810$		0			0
$811$	−20.8918	−	20.8918i	−0.733609	−	0.733609i	0.237724	−	0.971333i	$-0.423599\pi$
$811$	−20.8918	−	20.8918i	−0.733609	−	0.733609i	−0.971333	+	0.237724i	$0.923599\pi$
$812$	−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	−0.876704	−	0.481031i	$-0.840262\pi$
$821$	3.52604	−	13.1594i	0.123060	−	0.459265i	0.999763	+	0.0217666i	$0.00692907\pi$
$822$	5.25104	−	19.5971i	0.183151	−	0.683529i
$823$	−18.8654	+	5.05496i	−0.657606	+	0.176205i	−0.572165	−	0.820138i	$-0.693896\pi$
$823$	−18.8654	+	5.05496i	−0.657606	+	0.176205i	−0.0854405	+	0.996343i	$0.527230\pi$
$824$	−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	$-0.538298\pi$
$827$	−6.90343			−0.240056			−0.120028	+	0.992771i	$0.538298\pi$
$828$	11.9763	+	44.6963i	0.416207	+	1.55331i
$829$	9.06163	+	15.6952i	0.314723	+	0.545117i	0.979379	−	0.202033i	$-0.0647549\pi$
$829$	9.06163	+	15.6952i	0.314723	+	0.545117i	−0.664655	+	0.747150i	$0.731422\pi$
$830$		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	−0.0115419	−	0.999933i	$-0.503674\pi$
$839$	13.8579	−	3.71322i	0.478429	−	0.128195i	0.489971	+	0.871739i	$0.337007\pi$
$840$		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	$-0.791344\pi$
$857$	−5.36230	+	5.36230i	−0.183173	+	0.183173i	0.609564	+	0.792737i	$0.291344\pi$
$858$	−42.6058	+	49.5979i	−1.45454	+	1.69324i
$859$		−	28.8595i		−	0.984673i	−0.870405	−	0.492336i	$-0.836143\pi$
$859$		−	28.8595i		−	0.984673i	0.870405	−	0.492336i	$-0.163857\pi$
$860$		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	$-0.909944\pi$
$863$	−56.4179			−1.92049			−0.960245	+	0.279160i	$0.909944\pi$
$864$	−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	$-0.409981\pi$
$877$	−12.2322	−	7.06228i	−0.413053	−	0.238476i	−0.692101	+	0.721801i	$0.743315\pi$
$878$	−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	−0.711951	−	0.702229i	$-0.752188\pi$
$881$	−13.6470	+	7.87910i	−0.459779	+	0.265454i	0.252172	+	0.967682i	$0.418855\pi$
$882$	26.5843	+	46.0454i	0.895141	+	1.55043i
$883$	−5.11749	−	5.11749i	−0.172217	−	0.172217i	0.615736	−	0.787953i	$-0.288859\pi$
$883$	−5.11749	−	5.11749i	−0.172217	−	0.172217i	−0.787953	+	0.615736i	$0.788859\pi$
$884$	−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	−0.802604	−	0.596512i	$-0.796553\pi$
$887$	5.68034	−	21.1993i	0.190727	−	0.711804i	0.993332	−	0.115292i	$-0.0367804\pi$
$888$	−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	$-0.311254\pi$
$907$	18.9169	+	5.06878i	0.628127	+	0.168306i	0.0693072	+	0.997595i	$0.477921\pi$
$908$	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	0.497097	−	0.867695i	$-0.334399\pi$
$919$	−0.175850	−	0.101527i	−0.00580076	−	0.00334907i	−0.502898	+	0.864346i	$0.667733\pi$
$920$		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	−0.928985	−	0.370118i	$-0.879317\pi$
$929$	−9.43399	−	35.2081i	−0.309519	−	1.15514i	0.619466	−	0.785024i	$-0.287349\pi$
$930$		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	$-0.447268\pi$
$937$	−25.1436	−	25.1436i	−0.821405	−	0.821405i	−0.986310	+	0.164904i	$0.947268\pi$
$938$	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	0.998089	+	0.0617896i	$0.0196808\pi$
$941$	32.5125	+	32.5125i	1.05988	+	1.05988i	0.0617896	+	0.998089i	$0.480319\pi$
$942$	−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	0.997441	+	0.0714906i	$0.0227756\pi$
$947$	17.2526	+	29.8823i	0.560633	+	0.971045i	−0.436808	+	0.899555i	$0.643891\pi$
$948$	−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	$-0.296875\pi$
$953$	46.7133	−	12.5168i	1.51319	−	0.405459i	0.917494	+	0.397750i	$0.130209\pi$
$954$	−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	0.220678	+	0.975347i	$0.429173\pi$
$971$	−22.8825	+	39.6337i	−0.734336	+	1.27191i	−0.955014	+	0.296560i	$0.904160\pi$
$972$	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	$-0.981526\pi$
$977$	−45.2364	+	26.1173i	−1.44724	+	0.835565i	−0.448925	+	0.893570i	$0.648193\pi$
$978$	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	−0.974918	−	0.222564i	$-0.928557\pi$
$991$	−21.4130	−	37.0883i	−0.680205	−	1.17815i	0.294713	−	0.955586i	$-0.404776\pi$
$992$	−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	$-0.474054\pi$
$997$	20.5326	−	5.50169i	0.650274	−	0.174240i	0.568853	+	0.822440i	$0.307388\pi$
$998$	−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.d.557.2	yes	8
5.2	odd	4		650.2.w.d.193.2	yes	8
5.3	odd	4		650.2.w.c.193.1	yes	8
5.4	even	2		650.2.t.c.557.1	✓	8
13.6	odd	12		650.2.w.c.357.1	yes	8
65.19	odd	12		650.2.w.d.357.2	yes	8
65.32	even	12		650.2.t.c.643.1	yes	8
65.58	even	12	inner	650.2.t.d.643.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.t.c.557.1	✓	8	5.4	even	2
650.2.t.c.643.1	yes	8	65.32	even	12
650.2.t.d.557.2	yes	8	1.1	even	1	trivial
650.2.t.d.643.2	yes	8	65.58	even	12	inner
650.2.w.c.193.1	yes	8	5.3	odd	4
650.2.w.c.357.1	yes	8	13.6	odd	12
650.2.w.d.193.2	yes	8	5.2	odd	4
650.2.w.d.357.2	yes	8	65.19	odd	12

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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