LMFDB - Embedded newform 650.2.w.c.357.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(193,650)]

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([9, 7]))

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

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

chi := DirichletCharacter("650.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.w (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:	$1$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			357.1
Root			$0.500000 + 1.56488i$ of defining polynomial
Character	$\chi$	$=$	650.357
Dual form			650.2.w.c.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.849429	−	3.17011i	−0.490418	−	1.83026i	−0.554314	−	0.832308i	$-0.687019\pi$
$3$	−0.849429	−	3.17011i	−0.490418	−	1.83026i	0.0638964	−	0.997957i	$-0.479647\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	3.17011	+	0.849429i	1.29419	+	0.346778i
$7$	0.344430	−	0.198857i	0.130182	−	0.0751609i	−0.433494	−	0.901156i	$-0.642720\pi$
$7$	0.344430	−	0.198857i	0.130182	−	0.0751609i	0.563677	+	0.825995i	$0.309386\pi$
$8$	1.00000			0.353553
$9$	−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
$13$	2.73499	−	2.34943i	0.758551	−	0.651614i
$13$	2.73499	−	2.34943i	0.758551	−	0.651614i
$14$			0.397714i			0.106294i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.10523	−	0.564094i	−0.510593	−	0.136813i	−0.00568097	−	0.999984i	$-0.501808\pi$
$17$	−2.10523	−	0.564094i	−0.510593	−	0.136813i	−0.504912	+	0.863171i	$0.668475\pi$
$18$		−	7.77113i		−	1.83167i
$19$	−0.507152	+	1.89272i	−0.116349	+	0.434219i	−0.999384	−	0.0350870i	$-0.988829\pi$
$19$	−0.507152	+	1.89272i	−0.116349	+	0.434219i	0.883036	+	0.469306i	$0.155496\pi$
$20$		0			0
$21$	−0.922968	−	0.922968i	−0.201408	−	0.201408i
$22$	1.43012	−	5.33728i	0.304903	−	1.13791i
$23$	−5.75159	+	1.54113i	−1.19929	+	0.321349i	−0.802551	−	0.596583i	$-0.796525\pi$
$23$	−5.75159	+	1.54113i	−1.19929	+	0.321349i	−0.396738	+	0.917932i	$0.629858\pi$
$24$	−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
$28$	−0.344430	−	0.198857i	−0.0650912	−	0.0375804i
$29$	3.96205	+	2.28749i	0.735733	+	0.424776i	0.820516	−	0.571624i	$-0.193686\pi$
$29$	3.96205	+	2.28749i	0.735733	+	0.424776i	−0.0847826	+	0.996399i	$0.527020\pi$
$30$		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	$0.147244\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	9.06727	+	15.7050i	1.57841	+	2.73389i
$34$	1.54113	−	1.54113i	0.264302	−	0.264302i
$35$		0			0
$36$	6.72999	+	3.88556i	1.12167	+	0.647594i
$37$	−2.77661	−	1.60307i	−0.456471	−	0.263544i	0.254088	−	0.967181i	$-0.418225\pi$
$37$	−2.77661	−	1.60307i	−0.456471	−	0.263544i	−0.710559	+	0.703637i	$0.751558\pi$
$38$	−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	$0.674213\pi$
$42$	1.26080	−	0.337830i	0.194545	−	0.0521282i
$43$	−1.85658	+	6.92885i	−0.283126	+	1.05664i	0.667072	+	0.744993i	$0.267547\pi$
$43$	−1.85658	+	6.92885i	−0.283126	+	1.05664i	−0.950198	+	0.311647i	$0.899119\pi$
$44$	3.90716	+	3.90716i	0.589026	+	0.589026i
$45$		0			0
$46$	1.54113	−	5.75159i	0.227228	−	0.848026i
$47$		−	11.8102i		−	1.72270i	−0.508016	−	0.861348i	$-0.669621\pi$
$47$		−	11.8102i		−	1.72270i	0.508016	−	0.861348i	$-0.330379\pi$
$48$	3.17011	+	0.849429i	0.457566	+	0.122604i
$49$	−3.42091	+	5.92519i	−0.488702	+	0.846456i
$50$		0			0
$51$			7.15296i			1.00162i
$52$	−3.40216	−	1.19386i	−0.471795	−	0.165558i
$53$	−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
$57$	6.43091			0.851795
$58$	−3.96205	+	2.28749i	−0.520242	+	0.300362i
$59$	−6.38556	−	1.71101i	−0.831330	−	0.222754i	−0.182036	−	0.983292i	$-0.558269\pi$
$59$	−6.38556	−	1.71101i	−0.831330	−	0.222754i	−0.649294	+	0.760538i	$0.724935\pi$
$60$		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	$0.675085\pi$
$62$	0.914311	+	3.41225i	0.116118	+	0.433357i
$63$	−1.54534	+	2.67661i	−0.194695	+	0.337222i
$64$	1.00000			0.125000
$65$		0			0
$66$	−18.1345			−2.23221
$67$	−0.621825	+	1.07703i	−0.0759680	+	0.131580i	−0.901507	−	0.432765i	$-0.857538\pi$
$67$	−0.621825	+	1.07703i	−0.0759680	+	0.131580i	0.825539	+	0.564345i	$0.190871\pi$
$68$	0.564094	+	2.10523i	0.0684065	+	0.255296i
$69$	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	$0.792965\pi$
$72$	−6.72999	+	3.88556i	−0.793137	+	0.457918i
$73$	1.92362			0.225142			0.112571	−	0.993644i	$-0.464091\pi$
$73$	1.92362			0.225142			0.112571	+	0.993644i	$0.464091\pi$
$74$	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
$78$	10.6659	−	5.12477i	1.20768	−	0.580266i
$79$		−	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
$82$	−8.53702	−	2.28749i	−0.942756	−	0.252611i
$83$		−	6.90343i		−	0.757750i	−0.925448	−	0.378875i	$-0.876311\pi$
$83$		−	6.90343i		−	0.757750i	0.925448	−	0.378875i	$-0.123689\pi$
$84$	−0.337830	+	1.26080i	−0.0368602	+	0.137564i
$85$		0			0
$86$	−5.07227	−	5.07227i	−0.546957	−	0.546957i
$87$	3.88612	−	14.5032i	0.416635	−	1.55490i
$88$	−5.33728	+	1.43012i	−0.568956	+	0.152451i
$89$	−1.88556	−	7.03702i	−0.199869	−	0.745923i	−0.990952	−	0.134214i	$-0.957149\pi$
$89$	−1.88556	−	7.03702i	−0.199869	−	0.745923i	0.791083	−	0.611709i	$-0.209518\pi$
$90$		0			0
$91$	0.474815	−	1.35309i	0.0497741	−	0.141842i
$92$	4.21046	+	4.21046i	0.438970	+	0.438970i
$93$	−10.0406	−	5.79693i	−1.04116	−	0.601114i
$94$	10.2279	+	5.90510i	1.05493	+	0.609065i
$95$		0			0
$96$	−2.32068	+	2.32068i	−0.236854	+	0.236854i
$97$	−2.07203	−	3.58887i	−0.210383	−	0.364394i	0.741451	−	0.671007i	$-0.234138\pi$
$97$	−2.07203	−	3.58887i	−0.210383	−	0.364394i	−0.951834	+	0.306612i	$0.900804\pi$
$98$	−3.42091	−	5.92519i	−0.345564	−	0.598535i
$99$	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	$0.510167\pi$
$102$	−6.19465	−	3.57648i	−0.613361	−	0.354124i
$103$	3.97420	+	3.97420i	0.391589	+	0.391589i	0.875254	−	0.483664i	$-0.160694\pi$
$103$	3.97420	+	3.97420i	0.391589	+	0.391589i	−0.483664	+	0.875254i	$0.660694\pi$
$104$	2.73499	−	2.34943i	0.268188	−	0.230380i
$105$		0			0
$106$	−2.14636	−	8.01033i	−0.208473	−	0.778032i
$107$	−10.1890	+	2.73013i	−0.985008	+	0.263932i	−0.715152	−	0.698969i	$-0.753643\pi$
$107$	−10.1890	+	2.73013i	−0.985008	+	0.263932i	−0.269856	+	0.962901i	$0.586976\pi$
$108$	4.05273	−	15.1250i	0.389974	−	1.45540i
$109$	−4.56067	−	4.56067i	−0.436833	−	0.436833i	0.454112	−	0.890945i	$-0.349957\pi$
$109$	−4.56067	−	4.56067i	−0.436833	−	0.436833i	−0.890945	+	0.454112i	$0.849957\pi$
$110$		0			0
$111$	−2.72339	+	10.1638i	−0.258493	+	0.964709i
$112$			0.397714i			0.0375804i
$113$	−16.9477	−	4.54113i	−1.59431	−	0.427194i	−0.650992	−	0.759085i	$-0.725647\pi$
$113$	−16.9477	−	4.54113i	−1.59431	−	0.427194i	−0.943318	+	0.331891i	$0.892313\pi$
$114$	−3.21545	+	5.56933i	−0.301155	+	0.521616i
$115$		0			0
$116$		−	4.57498i		−	0.424776i
$117$	−9.27763	+	26.4386i	−0.857717	+	2.44425i
$118$	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
$122$	−7.44980			−0.674473
$123$	25.1202	−	14.5032i	2.26502	−	1.30771i
$124$	−3.41225	−	0.914311i	−0.306430	−	0.0821075i
$125$		0			0
$126$	−1.54534	−	2.67661i	−0.137670	−	0.238452i
$127$	−0.323386	−	1.20689i	−0.0286959	−	0.107095i	0.950092	−	0.311968i	$-0.100988\pi$
$127$	−0.323386	−	1.20689i	−0.0286959	−	0.107095i	−0.978788	+	0.204874i	$0.934322\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	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	$0.351552\pi$
$132$	9.06727	−	15.7050i	0.789205	−	1.36694i
$133$	0.201701	+	0.752760i	0.0174897	+	0.0652726i
$134$	−0.621825	−	1.07703i	−0.0537175	−	0.0930414i
$135$		0			0
$136$	−2.10523	−	0.564094i	−0.180522	−	0.0483707i
$137$	−5.35364	+	3.09092i	−0.457392	+	0.264076i	−0.710947	−	0.703245i	$-0.751733\pi$
$137$	−5.35364	+	3.09092i	−0.457392	+	0.264076i	0.253555	+	0.967321i	$0.418400\pi$
$138$	−19.5423			−1.66355
$139$	−17.5740	+	10.1464i	−1.49061	+	0.860603i	−0.999942	−	0.0107445i	$-0.996580\pi$
$139$	−17.5740	+	10.1464i	−1.49061	+	0.860603i	−0.490666	+	0.871348i	$0.663247\pi$
$140$		0			0
$141$	−37.4397	+	10.0319i	−3.15299	+	0.844841i
$142$	7.29272	−	7.29272i	0.611992	−	0.611992i
$143$	−11.2375	+	16.4509i	−0.939723	+	1.37570i
$144$		−	7.77113i		−	0.647594i
$145$		0			0
$146$	−0.961808	+	1.66590i	−0.0795998	+	0.137871i
$147$	21.6893	+	5.81164i	1.78891	+	0.479336i
$148$			3.20615i			0.263544i
$149$	−3.13976	+	11.7177i	−0.257219	+	0.959955i	0.709623	+	0.704581i	$0.248865\pi$
$149$	−3.13976	+	11.7177i	−0.257219	+	0.959955i	−0.966842	+	0.255374i	$0.917801\pi$
$150$		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	$0.983465\pi$
$152$	−0.507152	+	1.89272i	−0.0411354	+	0.153520i
$153$	16.3600	−	4.38365i	1.32263	−	0.354397i
$154$	−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	$0.982114\pi$
$158$	8.08158	+	4.66590i	0.642936	+	0.371199i
$159$	23.5705	+	13.6084i	1.86926	+	1.07922i
$160$		0			0
$161$	−1.67456	+	1.67456i	−0.131974	+	0.131974i
$162$	14.0385	+	24.3154i	1.10297	+	1.91040i
$163$	−4.90281	−	8.49192i	−0.384018	−	0.665138i	0.607615	−	0.794232i	$-0.292127\pi$
$163$	−4.90281	−	8.49192i	−0.384018	−	0.665138i	−0.991632	+	0.129094i	$0.958793\pi$
$164$	6.24953	−	6.24953i	0.488007	−	0.488007i
$165$		0			0
$166$	5.97854	+	3.45171i	0.464025	+	0.267905i
$167$	−1.49354	−	0.862295i	−0.115574	−	0.0667264i	0.441099	−	0.897459i	$-0.354589\pi$
$167$	−1.49354	−	0.862295i	−0.115574	−	0.0667264i	−0.556672	+	0.830732i	$0.687922\pi$
$168$	−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
$172$	6.92885	−	1.85658i	0.528320	−	0.141563i
$173$	1.59092	−	5.93741i	0.120956	−	0.451413i	−0.878708	−	0.477360i	$-0.841594\pi$
$173$	1.59092	−	5.93741i	0.120956	−	0.451413i	0.999663	+	0.0259475i	$0.00826027\pi$
$174$	10.6171	+	10.6171i	0.804878	+	0.804878i
$175$		0			0
$176$	1.43012	−	5.33728i	0.107799	−	0.402313i
$177$			21.6963i			1.63080i
$178$	7.03702	+	1.88556i	0.527447	+	0.141329i
$179$	−4.29272	+	7.43522i	−0.320853	+	0.555734i	−0.980664	−	0.195697i	$-0.937303\pi$
$179$	−4.29272	+	7.43522i	−0.320853	+	0.555734i	0.659811	+	0.751432i	$0.270636\pi$
$180$		0			0
$181$			2.60797i			0.193849i	0.995292	+	0.0969246i	$0.0309006\pi$
$181$			2.60797i			0.193849i	−0.995292	+	0.0969246i	$0.969099\pi$
$182$	0.934401	+	1.08775i	0.0692624	+	0.0806290i
$183$	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
$187$	12.0429			0.880665
$188$	−10.2279	+	5.90510i	−0.745949	+	0.430674i
$189$	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	$0.842474\pi$
$192$	−0.849429	−	3.17011i	−0.0613022	−	0.228783i
$193$	−7.27684	+	12.6039i	−0.523799	+	0.907246i	0.475818	+	0.879544i	$0.342152\pi$
$193$	−7.27684	+	12.6039i	−0.523799	+	0.907246i	−0.999616	+	0.0277019i	$0.991181\pi$
$194$	4.14407			0.297527
$195$		0			0
$196$	6.84182			0.488702
$197$	7.03549	−	12.1858i	0.501258	−	0.868204i	−0.498741	−	0.866751i	$-0.666204\pi$
$197$	7.03549	−	12.1858i	0.501258	−	0.868204i	0.999999	−	0.00145289i	$-0.000462468\pi$
$198$	11.1136	+	41.4767i	0.789812	+	2.94762i
$199$	−8.96205	−	15.5227i	−0.635303	−	1.10038i	−0.986451	−	0.164056i	$-0.947542\pi$
$199$	−8.96205	−	15.5227i	−0.635303	−	1.10038i	0.351148	−	0.936320i	$-0.385791\pi$
$200$		0			0
$201$	3.94251	+	1.05639i	0.278083	+	0.0745121i
$202$	−8.21761	+	4.74444i	−0.578189	+	0.333817i
$203$	1.81953			0.127706
$204$	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
$208$	0.667168	+	3.54329i	0.0462598	+	0.245683i
$209$		−	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	$0.0363046\pi$
$212$	8.01033	+	2.14636i	0.550152	+	0.147413i
$213$			33.8482i			2.31924i
$214$	2.73013	−	10.1890i	0.186628	−	0.696506i
$215$		0			0
$216$	11.0723	+	11.0723i	0.753373	+	0.753373i
$217$	0.363634	−	1.35710i	0.0246851	−	0.0921261i
$218$	6.22999	−	1.66932i	0.421948	−	0.113061i
$219$	−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
$223$	−7.20043	−	4.15717i	−0.482177	−	0.278385i	0.239146	−	0.970984i	$-0.423132\pi$
$223$	−7.20043	−	4.15717i	−0.482177	−	0.278385i	−0.721323	+	0.692599i	$0.756466\pi$
$224$	−0.344430	−	0.198857i	−0.0230132	−	0.0132867i
$225$		0			0
$226$	12.4066	−	12.4066i	0.825275	−	0.825275i
$227$	1.56478	+	2.71029i	0.103858	+	0.179888i	0.913271	−	0.407352i	$-0.133548\pi$
$227$	1.56478	+	2.71029i	0.103858	+	0.179888i	−0.809413	+	0.587240i	$0.800214\pi$
$228$	−3.21545	−	5.56933i	−0.212949	−	0.368838i
$229$	−8.68998	+	8.68998i	−0.574250	+	0.574250i	−0.933313	−	0.359063i	$-0.883096\pi$
$229$	−8.68998	+	8.68998i	−0.574250	+	0.574250i	0.359063	+	0.933313i	$0.383096\pi$
$230$		0			0
$231$	6.24609	+	3.60618i	0.410963	+	0.237269i
$232$	3.96205	+	2.28749i	0.260121	+	0.150181i
$233$	10.1868	+	10.1868i	0.667360	+	0.667360i	0.957104	−	0.289744i	$-0.0935703\pi$
$233$	10.1868	+	10.1868i	0.667360	+	0.667360i	−0.289744	+	0.957104i	$0.593570\pi$
$234$	−18.2577	−	21.2540i	−1.19354	−	1.38942i
$235$		0			0
$236$	1.71101	+	6.38556i	0.111377	+	0.415665i
$237$	−29.5828	+	7.92670i	−1.92161	+	0.514894i
$238$	0.224348	−	0.837279i	0.0145423	−	0.0542727i
$239$	14.4047	+	14.4047i	0.931764	+	0.931764i	0.997816	−	0.0660522i	$-0.0210404\pi$
$239$	14.4047	+	14.4047i	0.931764	+	0.931764i	−0.0660522	+	0.997816i	$0.521040\pi$
$240$		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	$-0.294126\pi$
$242$			19.5318i			1.25555i
$243$	−43.6323	−	11.6913i	−2.79902	−	0.749994i
$244$	3.72490	−	6.45171i	0.238462	−	0.413029i
$245$		0			0
$246$			29.0064i			1.84938i
$247$	3.05974	+	6.36808i	0.194687	+	0.405191i
$248$	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	$0.588764\pi$
$252$	3.09069			0.194695
$253$	28.4938	−	16.4509i	1.79139	−	1.03426i
$254$	1.20689	+	0.323386i	0.0757273	+	0.0202911i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.05226	−	3.92708i	−0.0656380	−	0.244965i	0.925310	−	0.379212i	$-0.123805\pi$
$257$	−1.05226	−	3.92708i	−0.0656380	−	0.244965i	−0.990948	+	0.134248i	$0.957138\pi$
$258$	−11.7711	+	20.3882i	−0.732838	+	1.26931i
$259$	−1.27513			−0.0792327
$260$		0			0
$261$	−35.5527			−2.20066
$262$	−5.14636	+	8.91376i	−0.317943	+	0.550694i
$263$	−2.38612	−	8.90510i	−0.147134	−	0.549112i	−0.999651	−	0.0264126i	$-0.991592\pi$
$263$	−2.38612	−	8.90510i	−0.147134	−	0.549112i	0.852517	−	0.522700i	$-0.175075\pi$
$264$	9.06727	+	15.7050i	0.558052	+	0.966575i
$265$		0			0
$266$	−0.752760	−	0.201701i	−0.0461547	−	0.0123671i
$267$	−20.7065	+	11.9549i	−1.26722	+	0.731628i
$268$	1.24365			0.0759680
$269$	−5.07512	+	2.93012i	−0.309435	+	0.178653i	−0.646674	−	0.762767i	$-0.723840\pi$
$269$	−5.07512	+	2.93012i	−0.309435	+	0.178653i	0.337238	+	0.941419i	$0.390507\pi$
$270$		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
$273$	−4.69276	−	0.355863i	−0.284019	−	0.0215378i
$274$		−	6.18185i		−	0.373459i
$275$		0			0
$276$	9.77113	−	16.9241i	0.588153	−	1.01871i
$277$	25.4675	+	6.82400i	1.53019	+	0.410014i	0.923083	−	0.384602i	$-0.125661\pi$
$277$	25.4675	+	6.82400i	1.53019	+	0.410014i	0.607112	+	0.794616i	$0.292328\pi$
$278$		−	20.2927i		−	1.21708i
$279$	−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	$0.751877\pi$
$282$	10.0319	−	37.4397i	0.597393	−	2.22950i
$283$	−5.94251	+	1.59229i	−0.353245	+	0.0946518i	−0.431078	−	0.902315i	$-0.641867\pi$
$283$	−5.94251	+	1.59229i	−0.353245	+	0.0946518i	0.0778327	+	0.996966i	$0.475200\pi$
$284$	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
$288$	6.72999	+	3.88556i	0.396569	+	0.228959i
$289$	−10.6086	−	6.12491i	−0.624038	−	0.360289i
$290$		0			0
$291$	−9.61706	+	9.61706i	−0.563762	+	0.563762i
$292$	−0.961808	−	1.66590i	−0.0562856	−	0.0974895i
$293$	−2.50715	−	4.34251i	−0.146469	−	0.253692i	0.783451	−	0.621454i	$-0.213458\pi$
$293$	−2.50715	−	4.34251i	−0.146469	−	0.253692i	−0.929920	+	0.367761i	$0.880124\pi$
$294$	−15.8777	+	15.8777i	−0.926006	+	0.926006i
$295$		0			0
$296$	−2.77661	−	1.60307i	−0.161387	−	0.0931768i
$297$	−74.9305	−	43.2611i	−4.34791	−	2.51027i
$298$	−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
$302$	15.8918	−	4.25819i	0.914469	−	0.245031i
$303$	8.06012	−	30.0808i	0.463042	−	1.72810i
$304$	−1.38556	−	1.38556i	−0.0794676	−	0.0794676i
$305$		0			0
$306$	−4.38365	+	16.3600i	−0.250596	+	0.935239i
$307$			3.05180i			0.174176i	0.996201	+	0.0870878i	$0.0277561\pi$
$307$			3.05180i			0.174176i	−0.996201	+	0.0870878i	$0.972244\pi$
$308$	2.12271	+	0.568779i	0.120953	+	0.0324092i
$309$	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	$0.879715\pi$
$312$	−9.77113	−	6.67456i	−0.553181	−	0.377872i
$313$	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
$317$	−23.0586			−1.29510			−0.647551	−	0.762022i	$-0.724207\pi$
$317$	−23.0586			−1.29510			−0.647551	+	0.762022i	$0.724207\pi$
$318$	−23.5705	+	13.6084i	−1.32177	+	0.763122i
$319$	−24.4179	−	6.54276i	−1.36714	−	0.366324i
$320$		0			0
$321$	17.3097	+	29.9812i	0.966131	+	1.67339i
$322$	−0.612931	−	2.28749i	−0.0341573	−	0.127477i
$323$	2.13534	−	3.69852i	0.118813	−	0.205791i
$324$	−28.0771			−1.55984
$325$		0			0
$326$	9.80562			0.543083
$327$	−10.5839	+	18.3318i	−0.585289	+	1.01375i
$328$	2.28749	+	8.53702i	0.126305	+	0.471378i
$329$	−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	$0.377327\pi$
$332$	−5.97854	+	3.45171i	−0.328115	+	0.189437i
$333$	24.9154			1.36536
$334$	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	−0.949388	−	0.314107i	$-0.898295\pi$
$337$	−11.6622	+	11.6622i	−0.635281	+	0.635281i	0.314107	+	0.949388i	$0.398295\pi$
$338$	10.1494	+	8.12340i	0.552055	+	0.441855i
$339$			57.5836i			3.12751i
$340$		0			0
$341$	−9.75986	+	16.9046i	−0.528526	+	0.915434i
$342$	14.7085	+	3.94114i	0.795347	+	0.213113i
$343$			5.50509i			0.297247i
$344$	−1.85658	+	6.92885i	−0.100100	+	0.373579i
$345$		0			0
$346$	4.34649	+	4.34649i	0.233669	+	0.233669i
$347$	−1.25395	+	4.67982i	−0.0673158	+	0.251226i	−0.991381	−	0.131008i	$-0.958179\pi$
$347$	−1.25395	+	4.67982i	−0.0673158	+	0.251226i	0.924065	+	0.382234i	$0.124845\pi$
$348$	−14.5032	+	3.88612i	−0.777452	+	0.208318i
$349$	−2.97604	−	11.1067i	−0.159304	−	0.594530i	−0.998698	−	0.0510072i	$-0.983757\pi$
$349$	−2.97604	−	11.1067i	−0.159304	−	0.594530i	0.839395	−	0.543523i	$-0.182910\pi$
$350$		0			0
$351$	56.2961	+	4.26907i	3.00486	+	0.227866i
$352$	3.90716	+	3.90716i	0.208252	+	0.208252i
$353$	−2.22407	−	1.28407i	−0.118375	−	0.0683440i	0.439643	−	0.898172i	$-0.355105\pi$
$353$	−2.22407	−	1.28407i	−0.118375	−	0.0683440i	−0.558019	+	0.829828i	$0.688438\pi$
$354$	−18.7896	−	10.8482i	−0.998654	−	0.576573i
$355$		0			0
$356$	−5.15146	+	5.15146i	−0.273027	+	0.273027i
$357$	1.42242	+	2.46370i	0.0752823	+	0.130393i
$358$	−4.29272	−	7.43522i	−0.226877	−	0.392963i
$359$	9.62118	−	9.62118i	0.507786	−	0.507786i	−0.406060	−	0.913846i	$-0.633098\pi$
$359$	9.62118	−	9.62118i	0.507786	−	0.507786i	0.913846	+	0.406060i	$0.133098\pi$
$360$		0			0
$361$	13.1293	+	7.58021i	0.691016	+	0.398959i
$362$	−2.25857	−	1.30399i	−0.118708	−	0.0685361i
$363$	−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
$367$	−16.2901	+	4.36492i	−0.850337	+	0.227847i	−0.657566	−	0.753397i	$-0.728414\pi$
$367$	−16.2901	+	4.36492i	−0.850337	+	0.227847i	−0.192771	+	0.981244i	$0.561747\pi$
$368$	1.54113	−	5.75159i	0.0803372	−	0.299822i
$369$	−48.5659	−	48.5659i	−2.52824	−	2.52824i
$370$		0			0
$371$	−0.853638	+	3.18582i	−0.0443187	+	0.165400i
$372$			11.5939i			0.601114i
$373$	2.52552	+	0.676711i	0.130766	+	0.0350388i	0.323609	−	0.946191i	$-0.395104\pi$
$373$	2.52552	+	0.676711i	0.130766	+	0.0350388i	−0.192842	+	0.981230i	$0.561771\pi$
$374$	−6.02146	+	10.4295i	−0.311362	+	0.539295i
$375$		0			0
$376$		−	11.8102i		−	0.609065i
$377$	16.2105	−	3.05228i	0.834881	−	0.157200i
$378$	−4.40360	+	4.40360i	−0.226497	+	0.226497i
$379$	1.46920	−	0.393670i	0.0754676	−	0.0202215i	−0.220888	−	0.975299i	$-0.570895\pi$
$379$	1.46920	−	0.393670i	0.0754676	−	0.0202215i	0.296355	+	0.955078i	$0.404229\pi$
$380$		0			0
$381$	−3.55130	+	2.05034i	−0.181938	+	0.105042i
$382$	0.793656			0.0406070
$383$	3.25326	−	1.87827i	0.166234	−	0.0959753i	−0.414575	−	0.910015i	$-0.636070\pi$
$383$	3.25326	−	1.87827i	0.166234	−	0.0959753i	0.580809	+	0.814040i	$0.302736\pi$
$384$	3.17011	+	0.849429i	0.161774	+	0.0433472i
$385$		0			0
$386$	−7.27684	−	12.6039i	−0.370382	−	0.641520i
$387$	−14.4277	−	53.8450i	−0.733402	−	2.73710i
$388$	−2.07203	+	3.58887i	−0.105192	+	0.182197i
$389$	14.0639			0.713066			0.356533	−	0.934283i	$-0.383959\pi$
$389$	14.0639			0.713066			0.356533	+	0.934283i	$0.383959\pi$
$390$		0			0
$391$	12.9778			0.656313
$392$	−3.42091	+	5.92519i	−0.172782	+	0.299267i
$393$	−8.74293	−	32.6291i	−0.441023	−	1.64592i
$394$	7.03549	+	12.1858i	0.354443	+	0.613913i
$395$		0			0
$396$	−41.4767	−	11.1136i	−2.08428	−	0.558482i
$397$	14.8529	−	8.57531i	0.745444	−	0.430383i	−0.0786011	−	0.996906i	$-0.525045\pi$
$397$	14.8529	−	8.57531i	0.745444	−	0.430383i	0.824046	+	0.566524i	$0.191712\pi$
$398$	17.9241			0.898454
$399$	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
$403$	0.963118	−	12.7006i	0.0479763	−	0.632662i
$404$		−	9.48888i		−	0.472089i
$405$		0			0
$406$	−0.909766	+	1.57576i	−0.0451509	+	0.0782037i
$407$	17.1121	+	4.58518i	0.848216	+	0.227279i
$408$			7.15296i			0.354124i
$409$	4.81911	−	17.9851i	0.238289	−	0.889308i	−0.738349	−	0.674419i	$-0.764394\pi$
$409$	4.81911	−	17.9851i	0.238289	−	0.889308i	0.976638	−	0.214889i	$-0.0689391\pi$
$410$		0			0
$411$	14.3461	+	14.3461i	0.707641	+	0.707641i
$412$	1.45466	−	5.42885i	0.0716658	−	0.267460i
$413$	−2.53963	+	0.680491i	−0.124967	+	0.0334848i
$414$	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
$418$	9.37667	+	5.41362i	0.458628	+	0.264789i
$419$	−8.19164	−	4.72944i	−0.400188	−	0.231048i	0.286377	−	0.958117i	$-0.407549\pi$
$419$	−8.19164	−	4.72944i	−0.400188	−	0.231048i	−0.686565	+	0.727068i	$0.740882\pi$
$420$		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	$0.952040\pi$
$422$	5.78407	+	10.0183i	0.281564	+	0.487683i
$423$	45.8893	+	79.4826i	2.23121	+	3.86458i
$424$	−5.86397	+	5.86397i	−0.284780	+	0.284780i
$425$		0			0
$426$	−29.3134	−	16.9241i	−1.42024	−	0.819975i
$427$	2.56594	+	1.48144i	0.124174	+	0.0716921i
$428$	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	$-0.335770\pi$
$432$	−15.1250	+	4.05273i	−0.727702	+	0.194987i
$433$	−6.41568	+	23.9436i	−0.308318	+	1.15066i	0.621734	+	0.783229i	$0.286429\pi$
$433$	−6.41568	+	23.9436i	−0.308318	+	1.15066i	−0.930052	+	0.367429i	$0.880238\pi$
$434$	0.993467	+	0.993467i	0.0476880	+	0.0476880i
$435$		0			0
$436$	−1.66932	+	6.22999i	−0.0799460	+	0.298363i
$437$		−	11.6677i		−	0.558142i
$438$	6.09808	+	1.63397i	0.291377	+	0.0780743i
$439$	3.29091	−	5.70002i	0.157067	−	0.272047i	−0.776743	−	0.629818i	$-0.783130\pi$
$439$	3.29091	−	5.70002i	0.157067	−	0.272047i	0.933810	+	0.357770i	$0.116463\pi$
$440$		0			0
$441$		−	53.1687i		−	2.53184i
$442$	0.594206	−	7.83577i	0.0282635	−	0.372710i
$443$	−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
$447$	39.8136			1.88312
$448$	0.344430	−	0.198857i	0.0162728	−	0.00939511i
$449$	−5.40716	−	1.44884i	−0.255180	−	0.0683752i	0.128961	−	0.991650i	$-0.458836\pi$
$449$	−5.40716	−	1.44884i	−0.255180	−	0.0683752i	−0.384141	+	0.923274i	$0.625502\pi$
$450$		0			0
$451$	−24.4179	−	42.2931i	−1.14980	−	1.99150i
$452$	4.54113	+	16.9477i	0.213597	+	0.797155i
$453$	−26.9979	+	46.7617i	−1.26847	+	2.19706i
$454$	−3.12957			−0.146878
$455$		0			0
$456$	6.43091			0.301155
$457$	−10.3741	+	17.9685i	−0.485280	+	0.840530i	−0.999857	−	0.0169144i	$-0.994616\pi$
$457$	−10.3741	+	17.9685i	−0.485280	+	0.840530i	0.514577	+	0.857444i	$0.327949\pi$
$458$	−3.18076	−	11.8707i	−0.148627	−	0.554683i
$459$	−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	$0.383834\pi$
$462$	−6.24609	+	3.60618i	−0.290594	+	0.167775i
$463$	32.2152			1.49717			0.748585	−	0.663039i	$-0.230734\pi$
$463$	32.2152			1.49717			0.748585	+	0.663039i	$0.230734\pi$
$464$	−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	−0.0484344	−	0.998826i	$-0.515423\pi$
$467$	20.5381	−	20.5381i	0.950392	−	0.950392i	0.998826	+	0.0484344i	$0.0154232\pi$
$468$	27.5353	−	5.18465i	1.27282	−	0.239661i
$469$			0.494617i			0.0228393i
$470$		0			0
$471$	−27.3991	+	47.4566i	−1.26248	+	2.18668i
$472$	−6.38556	−	1.71101i	−0.293919	−	0.0787555i
$473$		−	39.6363i		−	1.82248i
$474$	7.92670	−	29.5828i	0.364085	−	1.35878i
$475$		0			0
$476$	0.612931	+	0.612931i	0.0280936	+	0.0280936i
$477$	16.6797	−	62.2493i	0.763709	−	2.85020i
$478$	−19.6772	+	5.27249i	−0.900015	+	0.241158i
$479$	7.18639	+	26.8200i	0.328355	+	1.22544i	0.910896	+	0.412636i	$0.135392\pi$
$479$	7.18639	+	26.8200i	0.328355	+	1.22544i	−0.582542	+	0.812801i	$0.697942\pi$
$480$		0			0
$481$	−11.3603	+	2.13904i	−0.517985	+	0.0975319i
$482$	20.3476	+	20.3476i	0.926808	+	0.926808i
$483$	6.73095	+	3.88612i	0.306269	+	0.176824i
$484$	−16.9150	−	9.76589i	−0.768865	−	0.443904i
$485$		0			0
$486$	31.9411	−	31.9411i	1.44888	−	1.44888i
$487$	20.0068	+	34.6529i	0.906596	+	1.57027i	0.818760	+	0.574136i	$0.194662\pi$
$487$	20.0068	+	34.6529i	0.906596	+	1.57027i	0.0878365	+	0.996135i	$0.472005\pi$
$488$	3.72490	+	6.45171i	0.168618	+	0.292055i
$489$	−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	$0.531252\pi$
$492$	−25.1202	−	14.5032i	−1.13251	−	0.653854i
$493$	−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
$497$	−3.96205	+	1.06163i	−0.177722	+	0.0476205i
$498$	5.86397	−	21.8846i	0.262771	−	0.980674i
$499$	17.4889	+	17.4889i	0.782910	+	0.782910i	0.980321	−	0.197411i	$-0.0632534\pi$
$499$	17.4889	+	17.4889i	0.782910	+	0.782910i	−0.197411	+	0.980321i	$0.563253\pi$
$500$		0			0
$501$	−1.46492	+	5.46714i	−0.0654476	+	0.244254i
$502$		−	22.7843i		−	1.01691i
$503$	11.5921	+	3.10609i	0.516865	+	0.138494i	0.507816	−	0.861465i	$-0.330453\pi$
$503$	11.5921	+	3.10609i	0.516865	+	0.138494i	0.00904899	+	0.999959i	$0.497120\pi$
$504$	−1.54534	+	2.67661i	−0.0688351	+	0.119226i
$505$		0			0
$506$			32.9018i			1.46267i
$507$	−42.4054	+	4.70170i	−1.88329	+	0.208810i
$508$	−0.883508	+	0.883508i	−0.0391993	+	0.0391993i
$509$	17.3871	−	4.65885i	0.770668	−	0.206500i	0.148002	−	0.988987i	$-0.452716\pi$
$509$	17.3871	−	4.65885i	0.770668	−	0.206500i	0.622667	+	0.782487i	$0.286049\pi$
$510$		0			0
$511$	0.662552	−	0.382525i	0.0293096	−	0.0169219i
$512$	1.00000			0.0441942
$513$	−26.5720	+	15.3413i	−1.17318	+	0.677337i
$514$	3.92708	+	1.05226i	0.173216	+	0.0464131i
$515$		0			0
$516$	−11.7711	−	20.3882i	−0.518195	−	0.897540i
$517$	16.8900	+	63.0344i	0.742822	+	2.77225i
$518$	0.637565	−	1.10430i	0.0280130	−	0.0485199i
$519$	−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	$0.344074\pi$
$522$	17.7764	−	30.7896i	0.778050	−	1.34762i
$523$	2.93344	+	10.9477i	0.128270	+	0.478711i	0.999935	−	0.0113912i	$-0.00362600\pi$
$523$	2.93344	+	10.9477i	0.128270	+	0.478711i	−0.871665	+	0.490103i	$0.836959\pi$
$524$	−5.14636	−	8.91376i	−0.224820	−	0.389399i
$525$		0			0
$526$	8.90510	+	2.38612i	0.388281	+	0.104040i
$527$	−6.66782	+	3.84967i	−0.290455	+	0.167694i
$528$	−18.1345			−0.789205
$529$	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
$533$	26.3134	+	17.9744i	1.13976	+	0.778558i
$534$		−	23.9098i		−	1.03468i
$535$		0			0
$536$	−0.621825	+	1.07703i	−0.0268587	+	0.0465207i
$537$	27.2168	+	7.29272i	1.17449	+	0.314704i
$538$		−	5.86024i		−	0.252653i
$539$	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	$0.668475\pi$
$542$	−3.33481	+	12.4457i	−0.143242	+	0.534588i
$543$	8.26757	−	2.21529i	0.354795	−	0.0950671i
$544$	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	$0.746492\pi$
$548$	5.35364	+	3.09092i	0.228696	+	0.132038i
$549$	−50.1371	−	28.9467i	−2.13980	−	1.23541i
$550$		0			0
$551$	−6.33892	+	6.33892i	−0.270047	+	0.270047i
$552$	9.77113	+	16.9241i	0.415887	+	0.720337i
$553$	−1.85569	−	3.21416i	−0.0789121	−	0.136680i
$554$	−18.6435	+	18.6435i	−0.792087	+	0.792087i
$555$		0			0
$556$	17.5740	+	10.1464i	0.745304	+	0.430302i
$557$	−3.33950	−	1.92806i	−0.141499	−	0.0816947i	0.427579	−	0.903978i	$-0.359367\pi$
$557$	−3.33950	−	1.92806i	−0.141499	−	0.0816947i	−0.569078	+	0.822283i	$0.692700\pi$
$558$	−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
$562$	0.190917	−	0.0511561i	0.00805335	−	0.00215789i
$563$	−5.64567	+	21.0699i	−0.237937	+	0.887992i	0.738866	+	0.673852i	$0.235361\pi$
$563$	−5.64567	+	21.0699i	−0.237937	+	0.887992i	−0.976803	+	0.214140i	$0.931305\pi$
$564$	27.4077	+	27.4077i	1.15407	+	1.15407i
$565$		0			0
$566$	1.59229	−	5.94251i	0.0669289	−	0.249782i
$567$		−	11.1666i		−	0.468955i
$568$	−9.96205	−	2.66932i	−0.417998	−	0.112002i
$569$	18.5740	−	32.1712i	0.778664	−	1.34869i	−0.154047	−	0.988063i	$-0.549231\pi$
$569$	18.5740	−	32.1712i	0.778664	−	1.34869i	0.932712	−	0.360623i	$-0.117436\pi$
$570$		0			0
$571$			12.6031i			0.527423i	0.964602	+	0.263712i	$0.0849467\pi$
$571$			12.6031i			0.527423i	−0.964602	+	0.263712i	$0.915053\pi$
$572$	19.8656	+	1.50646i	0.830624	+	0.0629883i
$573$	−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
$577$	−2.81590			−0.117227			−0.0586136	−	0.998281i	$-0.518668\pi$
$577$	−2.81590			−0.117227			−0.0586136	+	0.998281i	$0.518668\pi$
$578$	10.6086	−	6.12491i	0.441262	−	0.254763i
$579$	46.1368	+	12.3623i	1.91738	+	0.513760i
$580$		0			0
$581$	−1.37280	−	2.37775i	−0.0569531	−	0.0986457i
$582$	−3.52009	−	13.1372i	−0.145912	−	0.544553i
$583$	22.9115	−	39.6838i	0.948896	−	1.64354i
$584$	1.92362			0.0795998
$585$		0			0
$586$	5.01430			0.207139
$587$	10.2105	−	17.6850i	0.421431	−	0.729939i	−0.574649	−	0.818400i	$-0.694861\pi$
$587$	10.2105	−	17.6850i	0.421431	−	0.729939i	0.996080	+	0.0884607i	$0.0281948\pi$
$588$	−5.81164	−	21.6893i	−0.239668	−	0.894453i
$589$	3.46106	+	5.99474i	0.142611	+	0.247009i
$590$		0			0
$591$	−44.6065	−	11.9523i	−1.83487	−	0.491651i
$592$	2.77661	−	1.60307i	0.114118	−	0.0658859i
$593$	24.9304			1.02377			0.511885	−	0.859054i	$-0.328947\pi$
$593$	24.9304			1.02377			0.511885	+	0.859054i	$0.328947\pi$
$594$	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
$598$	−9.29796	−	19.3513i	−0.380222	−	0.791335i
$599$			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	−0.979197	−	0.202912i	$-0.934959\pi$
$601$	−7.69465	+	13.3275i	−0.313871	+	0.543641i	0.665326	+	0.746553i	$0.268293\pi$
$602$	−2.75570	−	0.738388i	−0.112314	−	0.0300945i
$603$		−	9.66456i		−	0.393571i
$604$	−4.25819	+	15.8918i	−0.173263	+	0.646627i
$605$		0			0
$606$	22.0207	+	22.0207i	0.894528	+	0.894528i
$607$	4.72767	−	17.6439i	0.191890	−	0.716144i	−0.801160	−	0.598450i	$-0.795783\pi$
$607$	4.72767	−	17.6439i	0.191890	−	0.716144i	0.993050	−	0.117693i	$-0.0375500\pi$
$608$	1.89272	−	0.507152i	0.0767598	−	0.0205677i
$609$	−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
$613$	−33.5187	−	19.3521i	−1.35381	−	0.781622i	−0.365029	−	0.930996i	$-0.618941\pi$
$613$	−33.5187	−	19.3521i	−1.35381	−	0.781622i	−0.988781	+	0.149374i	$0.952274\pi$
$614$	−2.64294	−	1.52590i	−0.106660	−	0.0615804i
$615$		0			0
$616$	−1.55393	+	1.55393i	−0.0626097	+	0.0626097i
$617$	−14.3799	−	24.9068i	−0.578915	−	1.00271i	−0.995604	−	0.0936610i	$-0.970143\pi$
$617$	−14.3799	−	24.9068i	−0.578915	−	1.00271i	0.416689	−	0.909049i	$-0.363190\pi$
$618$	9.22284	+	15.9744i	0.370997	+	0.642586i
$619$	−21.8733	+	21.8733i	−0.879164	+	0.879164i	−0.993448	−	0.114284i	$-0.963542\pi$
$619$	−21.8733	+	21.8733i	−0.879164	+	0.879164i	0.114284	+	0.993448i	$0.463542\pi$
$620$		0			0
$621$	−80.7470	−	46.6193i	−3.24027	−	1.87077i
$622$	−11.2698	−	6.50660i	−0.451876	−	0.260891i
$623$	−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
$627$	−34.3235	+	9.19697i	−1.37075	+	0.367291i
$628$	−4.32147	+	16.1279i	−0.172445	+	0.643575i
$629$	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	$-0.0837864\pi$
$632$		−	9.33180i		−	0.371199i
$633$	−36.6723	−	9.82630i	−1.45759	−	0.390560i
$634$	11.5293	−	19.9694i	0.457888	−	0.793085i
$635$		0			0
$636$		−	27.2168i		−	1.07922i
$637$	4.56465	+	24.2425i	0.180858	+	0.960525i
$638$	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	$0.455096\pi$
$642$	−34.6193			−1.36632
$643$	0.0203318	−	0.0117386i	0.000801809	−	0.000462925i	−0.499599	−	0.866257i	$-0.666519\pi$
$643$	0.0203318	−	0.0117386i	0.000801809	−	0.000462925i	0.500401	+	0.865794i	$0.333186\pi$
$644$	2.28749	+	0.612931i	0.0901397	+	0.0241528i
$645$		0			0
$646$	2.13534	+	3.69852i	0.0840138	+	0.145516i
$647$	−3.83864	−	14.3260i	−0.150913	−	0.563214i	−0.999421	−	0.0340314i	$-0.989165\pi$
$647$	−3.83864	−	14.3260i	−0.150913	−	0.563214i	0.848508	−	0.529182i	$-0.177501\pi$
$648$	14.0385	−	24.3154i	0.551485	−	0.955201i
$649$	36.5285			1.43387
$650$		0			0
$651$	−4.61104			−0.180721
$652$	−4.90281	+	8.49192i	−0.192009	+	0.332569i
$653$	0.538667	+	2.01033i	0.0210797	+	0.0786703i	0.975664	−	0.219269i	$-0.0703673\pi$
$653$	0.538667	+	2.01033i	0.0210797	+	0.0786703i	−0.954585	+	0.297940i	$0.903701\pi$
$654$	−10.5839	−	18.3318i	−0.413862	−	0.716830i
$655$		0			0
$656$	−8.53702	−	2.28749i	−0.333315	−	0.0893114i
$657$	−12.9459	+	7.47434i	−0.505069	+	0.291602i
$658$	4.69709			0.183111
$659$	−1.41305	+	0.815824i	−0.0550445	+	0.0317800i	−0.527270	−	0.849698i	$-0.676784\pi$
$659$	−1.41305	+	0.815824i	−0.0550445	+	0.0317800i	0.472225	+	0.881478i	$0.343451\pi$
$660$		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
$663$	16.8054	+	19.5633i	0.652667	+	0.759776i
$664$		−	6.90343i		−	0.267905i
$665$		0			0
$666$	−12.4577	+	21.5774i	−0.482726	+	0.836106i
$667$	−26.3134	−	7.05065i	−1.01886	−	0.273002i
$668$			1.72459i			0.0667264i
$669$	−7.06244	+	26.3574i	−0.273050	+	1.01904i
$670$		0			0
$671$	−29.1075	−	29.1075i	−1.12368	−	1.12368i
$672$	−0.337830	+	1.26080i	−0.0130321	+	0.0486363i
$673$	−21.5553	+	5.77572i	−0.830894	+	0.222637i	−0.649104	−	0.760700i	$-0.724856\pi$
$673$	−21.5553	+	5.77572i	−0.830894	+	0.222637i	−0.181791	+	0.983337i	$0.558189\pi$
$674$	−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	$0.971128\pi$
$678$	−49.8688	−	28.7918i	−1.91520	−	1.10574i
$679$	−1.42734	−	0.824077i	−0.0547764	−	0.0316252i
$680$		0			0
$681$	7.26274	−	7.26274i	0.278309	−	0.278309i
$682$	−9.75986	−	16.9046i	−0.373725	−	0.647310i
$683$	−8.97635	−	15.5475i	−0.343470	−	0.594908i	0.641604	−	0.767036i	$-0.278269\pi$
$683$	−8.97635	−	15.5475i	−0.343470	−	0.594908i	−0.985075	+	0.172128i	$0.944936\pi$
$684$	−10.7674	+	10.7674i	−0.411702	+	0.411702i
$685$		0			0
$686$	−4.76755	−	2.75254i	−0.182026	−	0.105093i
$687$	34.9297	+	20.1667i	1.33265	+	0.769407i
$688$	−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	$0.980896\pi$
$692$	−5.93741	+	1.59092i	−0.225706	+	0.0604779i
$693$	4.42005	−	16.4959i	0.167904	−	0.626626i
$694$	−3.42587	−	3.42587i	−0.130044	−	0.130044i
$695$		0			0
$696$	3.88612	−	14.5032i	0.147303	−	0.549742i
$697$		−	19.2627i		−	0.729628i
$698$	11.1067	+	2.97604i	0.420396	+	0.112645i
$699$	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	$0.757266\pi$
$702$	−31.8452	+	46.6193i	−1.20192	+	1.75953i
$703$	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
$707$	3.77386			0.141931
$708$	18.7896	−	10.8482i	0.706155	−	0.407699i
$709$	0.801931	+	0.214877i	0.0301172	+	0.00806987i	0.273846	−	0.961774i	$-0.411704\pi$
$709$	0.801931	+	0.214877i	0.0301172	+	0.00806987i	−0.243729	+	0.969843i	$0.578371\pi$
$710$		0			0
$711$	36.2593	+	62.8030i	1.35983	+	2.35530i
$712$	−1.88556	−	7.03702i	−0.0706645	−	0.263724i
$713$	−10.5175	+	18.2168i	−0.393883	+	0.682225i
$714$	−2.84483			−0.106465
$715$		0			0
$716$	8.58545			0.320853
$717$	33.4288	−	57.9003i	1.24842	−	2.16233i
$718$	3.52159	+	13.1428i	0.131425	+	0.490484i
$719$	−20.6441	−	35.7566i	−0.769894	−	1.33349i	−0.937620	−	0.347661i	$-0.886976\pi$
$719$	−20.6441	−	35.7566i	−0.769894	−	1.33349i	0.167726	−	0.985834i	$-0.446357\pi$
$720$		0			0
$721$	2.15913	+	0.578537i	0.0804102	+	0.0215459i
$722$	−13.1293	+	7.58021i	−0.488622	+	0.282106i
$723$	−94.4407			−3.51229
$724$	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	$-0.414462\pi$
$727$	33.1540	−	33.1540i	1.22961	−	1.22961i	0.964110	−	0.265503i	$-0.0855381\pi$
$728$	0.474815	−	1.35309i	0.0175978	−	0.0501488i
$729$			64.0191i			2.37108i
$730$		0			0
$731$	7.81705	−	13.5395i	0.289124	−	0.500777i
$732$	−23.6167	−	6.32807i	−0.872898	−	0.233892i
$733$			24.3075i			0.897818i	0.893577	+	0.448909i	$0.148187\pi$
$733$			24.3075i			0.897818i	−0.893577	+	0.448909i	$0.851813\pi$
$734$	4.36492	−	16.2901i	0.161112	−	0.601279i
$735$		0			0
$736$	4.21046	+	4.21046i	0.155199	+	0.155199i
$737$	1.77857	−	6.63770i	0.0655144	−	0.244503i
$738$	66.3423	−	17.7764i	2.44209	−	0.654357i
$739$	−4.44320	−	16.5822i	−0.163446	−	0.609987i	−0.998233	−	0.0594155i	$-0.981076\pi$
$739$	−4.44320	−	16.5822i	−0.163446	−	0.609987i	0.834788	−	0.550572i	$-0.185590\pi$
$740$		0			0
$741$	17.5885	−	15.1090i	0.646129	−	0.555041i
$742$	−2.33218	−	2.33218i	−0.0856171	−	0.0856171i
$743$	11.3927	+	6.57760i	0.417959	+	0.241309i	0.694204	−	0.719778i	$-0.255757\pi$
$743$	11.3927	+	6.57760i	0.417959	+	0.241309i	−0.276245	+	0.961087i	$0.589090\pi$
$744$	−10.0406	−	5.79693i	−0.368106	−	0.212526i
$745$		0			0
$746$	−1.84881	+	1.84881i	−0.0676897	+	0.0676897i
$747$	26.8237	+	46.4600i	0.981428	+	1.69988i
$748$	−6.02146	−	10.4295i	−0.220166	−	0.381339i
$749$	−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	$0.938985\pi$
$752$	10.2279	+	5.90510i	0.372975	+	0.215337i
$753$	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
$757$	45.7542	−	12.2598i	1.66296	−	0.445590i	0.699763	−	0.714375i	$-0.253289\pi$
$757$	45.7542	−	12.2598i	1.66296	−	0.445590i	0.963200	+	0.268785i	$0.0866221\pi$
$758$	−0.393670	+	1.46920i	−0.0142987	+	0.0533636i
$759$	−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	$0.0520662\pi$
$762$		−	4.10068i		−	0.148552i
$763$	−2.47776	−	0.663913i	−0.0897008	−	0.0240353i
$764$	−0.396828	+	0.687326i	−0.0143567	+	0.0248666i
$765$		0			0
$766$			3.75655i			0.135730i
$767$	−21.4844	+	10.3228i	−0.775755	+	0.372736i
$768$	−2.32068	+	2.32068i	−0.0837404	+	0.0837404i
$769$	36.2611	−	9.71614i	1.30761	−	0.350373i	0.463287	−	0.886208i	$-0.346670\pi$
$769$	36.2611	−	9.71614i	1.30761	−	0.350373i	0.844323	+	0.535835i	$0.180003\pi$
$770$		0			0
$771$	−11.5555	+	6.67155i	−0.416160	+	0.240270i
$772$	14.5537			0.523799
$773$	12.5863	−	7.26671i	0.452698	−	0.261365i	−0.256271	−	0.966605i	$-0.582494\pi$
$773$	12.5863	−	7.26671i	0.452698	−	0.261365i	0.708969	+	0.705240i	$0.249161\pi$
$774$	53.8450	+	14.4277i	1.93542	+	0.518594i
$775$		0			0
$776$	−2.07203	−	3.58887i	−0.0743817	−	0.128833i
$777$	1.08313	+	4.04230i	0.0388571	+	0.145017i
$778$	−7.03193	+	12.1797i	−0.252107	+	0.436662i
$779$	−17.3183			−0.620491
$780$		0			0
$781$	56.9877			2.03918
$782$	−6.48888	+	11.2391i	−0.232042	+	0.401908i
$783$	18.5412	+	69.1965i	0.662607	+	2.47288i
$784$	−3.42091	−	5.92519i	−0.122175	−	0.211614i
$785$		0			0
$786$	32.6291	+	8.74293i	1.16384	+	0.311850i
$787$	−38.5792	+	22.2737i	−1.37520	+	0.793971i	−0.991577	−	0.129519i	$-0.958657\pi$
$787$	−38.5792	+	22.2737i	−1.37520	+	0.793971i	−0.383622	+	0.923490i	$0.625323\pi$
$788$	−14.0710			−0.501258
$789$	−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
$793$	25.3454	+	8.89401i	0.900042	+	0.315836i
$794$			17.1506i			0.608653i
$795$		0			0
$796$	−8.96205	+	15.5227i	−0.317651	+	0.550188i
$797$	−18.7076	−	5.01270i	−0.662658	−	0.177559i	−0.0882130	−	0.996102i	$-0.528116\pi$
$797$	−18.7076	−	5.01270i	−0.662658	−	0.177559i	−0.574445	+	0.818543i	$0.694782\pi$
$798$			2.55766i			0.0905403i
$799$	−6.66207	+	24.8632i	−0.235687	+	0.879596i
$800$		0			0
$801$	40.0326	+	40.0326i	1.41448	+	1.41448i
$802$	0.590110	−	2.20232i	0.0208375	−	0.0777666i
$803$	−10.2669	+	2.75100i	−0.362310	+	0.0970807i
$804$	−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
$808$	8.21761	+	4.74444i	0.289094	+	0.166909i
$809$	16.2434	+	9.37810i	0.571086	+	0.329717i	0.757583	−	0.652739i	$-0.226380\pi$
$809$	16.2434	+	9.37810i	0.571086	+	0.329717i	−0.186497	+	0.982456i	$0.559713\pi$
$810$		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	$0.423599\pi$
$812$	−0.909766	−	1.57576i	−0.0319265	−	0.0552984i
$813$	−21.1434	−	36.6215i	−0.741533	−	1.28437i
$814$	−12.5269	+	12.5269i	−0.439069	+	0.439069i
$815$		0			0
$816$	−6.19465	−	3.57648i	−0.216856	−	0.125202i
$817$	−12.1728	−	7.02796i	−0.425872	−	0.245877i
$818$	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	$0.840262\pi$
$822$	−19.5971	+	5.25104i	−0.683529	+	0.183151i
$823$	−5.05496	+	18.8654i	−0.176205	+	0.657606i	0.820138	+	0.572165i	$0.193896\pi$
$823$	−5.05496	+	18.8654i	−0.176205	+	0.657606i	−0.996343	+	0.0854405i	$0.972770\pi$
$824$	3.97420	+	3.97420i	0.138448	+	0.138448i
$825$		0			0
$826$	0.680491	−	2.53963i	0.0236773	−	0.0883650i
$827$		−	6.90343i		−	0.240056i	−0.992771	−	0.120028i	$-0.961702\pi$
$827$		−	6.90343i		−	0.240056i	0.992771	−	0.120028i	$-0.0382984\pi$
$828$	−44.6963	−	11.9763i	−1.55331	−	0.416207i
$829$	−9.06163	+	15.6952i	−0.314723	+	0.545117i	−0.979379	−	0.202033i	$-0.935245\pi$
$829$	−9.06163	+	15.6952i	−0.314723	+	0.545117i	0.664655	+	0.747150i	$0.268578\pi$
$830$		0			0
$831$		−	86.5313i		−	3.00174i
$832$	2.73499	−	2.34943i	0.0948188	−	0.0814518i
$833$	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
$837$	55.3158			1.91199
$838$	8.19164	−	4.72944i	0.282975	−	0.163376i
$839$	−13.8579	−	3.71322i	−0.478429	−	0.128195i	0.0115419	−	0.999933i	$-0.496326\pi$
$839$	−13.8579	−	3.71322i	−0.478429	−	0.128195i	−0.489971	+	0.871739i	$0.662993\pi$
$840$		0			0
$841$	−4.03480	−	6.98847i	−0.139131	−	0.240982i
$842$	−8.55242	−	31.9181i	−0.294736	−	1.09997i
$843$	−0.324341	+	0.561775i	−0.0111709	+	0.0193485i
$844$	−11.5681			−0.398192
$845$		0			0
$846$	−91.7786			−3.15541
$847$	3.88403	−	6.72734i	0.133457	−	0.231154i
$848$	−2.14636	−	8.01033i	−0.0737064	−	0.275076i
$849$	10.0955	+	17.4859i	0.346476	+	0.600113i
$850$		0			0
$851$	18.4405	+	4.94110i	0.632131	+	0.169379i
$852$	29.3134	−	16.9241i	1.00426	−	0.579810i
$853$	−21.5765			−0.738764			−0.369382	−	0.929278i	$-0.620431\pi$
$853$	−21.5765			−0.738764			−0.369382	+	0.929278i	$0.620431\pi$
$854$	−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	−0.609564	−	0.792737i	$-0.708656\pi$
$857$	5.36230	−	5.36230i	0.183173	−	0.183173i	0.792737	+	0.609564i	$0.208656\pi$
$858$	−49.5979	+	42.6058i	−1.69324	+	1.45454i
$859$		−	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
$862$	28.5757	+	7.65683i	0.973292	+	0.260793i
$863$			56.4179i			1.92049i	0.279160	+	0.960245i	$0.409944\pi$
$863$			56.4179i			1.92049i	−0.279160	+	0.960245i	$0.590056\pi$
$864$	4.05273	−	15.1250i	0.137877	−	0.514563i
$865$		0			0
$866$	−17.5280	−	17.5280i	−0.595624	−	0.595624i
$867$	−10.4053	+	38.8333i	−0.353384	+	1.31885i
$868$	−1.35710	+	0.363634i	−0.0460630	+	0.0123426i
$869$	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
$873$	27.8896	+	16.1020i	0.943919	+	0.544972i
$874$	10.1045	+	5.83386i	0.341791	+	0.197333i
$875$		0			0
$876$	−4.46410	+	4.46410i	−0.150828	+	0.150828i
$877$	−7.06228	−	12.2322i	−0.238476	−	0.413053i	0.721801	−	0.692101i	$-0.243315\pi$
$877$	−7.06228	−	12.2322i	−0.238476	−	0.413053i	−0.960277	+	0.279048i	$0.909981\pi$
$878$	3.29091	+	5.70002i	0.111063	+	0.192366i
$879$	−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	$0.752188\pi$
$882$	46.0454	+	26.5843i	1.55043	+	0.895141i
$883$	5.11749	+	5.11749i	0.172217	+	0.172217i	0.787953	−	0.615736i	$-0.211141\pi$
$883$	5.11749	+	5.11749i	0.172217	+	0.172217i	−0.615736	+	0.787953i	$0.711141\pi$
$884$	6.48888	+	4.43248i	0.218245	+	0.149081i
$885$		0			0
$886$	−7.36865	−	27.5002i	−0.247555	−	0.923887i
$887$	−21.1993	+	5.68034i	−0.711804	+	0.190727i	−0.596512	−	0.802604i	$-0.703447\pi$
$887$	−21.1993	+	5.68034i	−0.711804	+	0.190727i	−0.115292	+	0.993332i	$0.536780\pi$
$888$	−2.72339	+	10.1638i	−0.0913911	+	0.341076i
$889$	−0.351384	−	0.351384i	−0.0117850	−	0.0117850i
$890$		0			0
$891$	−40.1535	+	149.855i	−1.34519	+	5.02033i
$892$			8.31434i			0.278385i
$893$	22.3534	+	5.98957i	0.748027	+	0.200433i
$894$	−19.9068	+	34.4795i	−0.665782	+	1.15317i
$895$		0			0
$896$			0.397714i			0.0132867i
$897$	66.4859	+	23.3307i	2.21990	+	0.778989i
$898$	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
$902$	48.8358			1.62606
$903$	8.10867	−	4.68154i	0.269840	−	0.155792i
$904$	−16.9477	−	4.54113i	−0.563674	−	0.151036i
$905$		0			0
$906$	−26.9979	−	46.7617i	−0.896944	−	1.55355i
$907$	5.06878	+	18.9169i	0.168306	+	0.628127i	0.997595	+	0.0693072i	$0.0220789\pi$
$907$	5.06878	+	18.9169i	0.168306	+	0.628127i	−0.829289	+	0.558819i	$0.811254\pi$
$908$	1.56478	−	2.71029i	0.0519292	−	0.0899440i
$909$	−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	$0.177322\pi$
$912$	−3.21545	+	5.56933i	−0.106474	+	0.184419i
$913$	9.87273	+	36.8455i	0.326740	+	1.21941i
$914$	−10.3741	−	17.9685i	−0.343145	−	0.594344i
$915$		0			0
$916$	11.8707	+	3.18076i	0.392220	+	0.105095i
$917$	3.54513	−	2.04678i	0.117070	−	0.0675906i
$918$	34.1277			1.12638
$919$	0.175850	−	0.101527i	0.00580076	−	0.00334907i	−0.497097	−	0.867695i	$-0.665601\pi$
$919$	0.175850	−	0.101527i	0.00580076	−	0.00334907i	0.502898	+	0.864346i	$0.332267\pi$
$920$		0			0
$921$	9.67456	−	2.59229i	0.318788	−	0.0854189i
$922$	−17.8091	+	17.8091i	−0.586511	+	0.586511i
$923$	−33.5175	+	16.1045i	−1.10324	+	0.530087i
$924$		−	7.21236i		−	0.237269i
$925$		0			0
$926$	−16.1076	+	27.8992i	−0.529329	+	0.916825i
$927$	−42.1883	−	11.3043i	−1.38565	−	0.371283i
$928$		−	4.57498i		−	0.150181i
$929$	9.43399	−	35.2081i	0.309519	−	1.15514i	−0.619466	−	0.785024i	$-0.712651\pi$
$929$	9.43399	−	35.2081i	0.309519	−	1.15514i	0.928985	−	0.370118i	$-0.120683\pi$
$930$		0			0
$931$	−9.47979	−	9.47979i	−0.310687	−	0.310687i
$932$	3.72863	−	13.9154i	0.122135	−	0.455815i
$933$	41.2533	−	11.0538i	1.35057	−	0.361885i
$934$	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	$0.947268\pi$
$938$	−0.428351	−	0.247308i	−0.0139862	−	0.00807491i
$939$	−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	$-0.0196808\pi$
$942$	−27.3991	−	47.4566i	−0.892710	−	1.54622i
$943$	−26.3134	−	45.5761i	−0.856882	−	1.48416i
$944$	4.67456	−	4.67456i	0.152144	−	0.152144i
$945$		0			0
$946$	34.3261	+	19.8182i	1.11604	+	0.644344i
$947$	29.8823	+	17.2526i	0.971045	+	0.560633i	0.899555	−	0.436808i	$-0.143891\pi$
$947$	29.8823	+	17.2526i	0.971045	+	0.560633i	0.0714906	+	0.997441i	$0.477224\pi$
$948$	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
$952$	−0.837279	+	0.224348i	−0.0271364	+	0.00727117i
$953$	12.5168	−	46.7133i	0.405459	−	1.51319i	−0.397750	−	0.917494i	$-0.630209\pi$
$953$	12.5168	−	46.7133i	0.405459	−	1.51319i	0.803208	−	0.595698i	$-0.203125\pi$
$954$	45.5697	+	45.5697i	1.47537	+	1.47537i
$955$		0			0
$956$	5.27249	−	19.6772i	0.170525	−	0.636407i
$957$			82.9651i			2.68188i
$958$	−26.8200	−	7.18639i	−0.866514	−	0.232182i
$959$	−1.22930	+	2.12922i	−0.0396963	+	0.0687560i
$960$		0			0
$961$			18.5206i			0.597437i
$962$	3.82769	−	10.9078i	0.123410	−	0.351683i
$963$	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
$967$	−59.9161			−1.92677			−0.963385	−	0.268121i	$-0.913597\pi$
$967$	−59.9161			−1.92677			−0.963385	+	0.268121i	$0.913597\pi$
$968$	16.9150	−	9.76589i	0.543669	−	0.313888i
$969$	−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	$-0.429173\pi$
$972$	11.6913	+	43.6323i	0.374997	+	1.39951i
$973$	−4.03535	+	6.98943i	−0.129367	+	0.224071i
$974$	−40.0137			−1.28212
$975$		0			0
$976$	−7.44980			−0.238462
$977$	26.1173	−	45.2364i	0.835565	−	1.44724i	−0.0580046	−	0.998316i	$-0.518474\pi$
$977$	26.1173	−	45.2364i	0.835565	−	1.44724i	0.893570	−	0.448925i	$-0.148193\pi$
$978$	−8.32917	−	31.0849i	−0.266338	−	0.993985i
$979$	20.1276	+	34.8620i	0.643280	+	1.11419i
$980$		0			0
$981$	48.4141	+	12.9725i	1.54574	+	0.414181i
$982$	−15.8394	+	9.14486i	−0.505454	+	0.291824i
$983$	−52.3414			−1.66943			−0.834716	−	0.550680i	$-0.814368\pi$
$983$	−52.3414			−1.66943			−0.834716	+	0.550680i	$0.814368\pi$
$984$	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
$988$	3.98505	−	5.83386i	0.126781	−	0.185600i
$989$		−	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	$0.928557\pi$
$992$	−3.41225	−	0.914311i	−0.108339	−	0.0290294i
$993$		−	72.0032i		−	2.28495i
$994$	1.06163	−	3.96205i	0.0336728	−	0.125668i
$995$		0			0
$996$	16.0207	+	16.0207i	0.507634	+	0.507634i
$997$	−5.50169	+	20.5326i	−0.174240	+	0.650274i	0.822440	+	0.568853i	$0.192612\pi$
$997$	−5.50169	+	20.5326i	−0.174240	+	0.650274i	−0.996680	+	0.0814210i	$0.974054\pi$
$998$	−23.8902	+	6.40137i	−0.756233	+	0.202632i
$999$	−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.w.c.357.1	yes	8
5.2	odd	4		650.2.t.c.643.1	yes	8
5.3	odd	4		650.2.t.d.643.2	yes	8
5.4	even	2		650.2.w.d.357.2	yes	8
13.11	odd	12		650.2.t.d.557.2	yes	8
65.24	odd	12		650.2.t.c.557.1	✓	8
65.37	even	12		650.2.w.d.193.2	yes	8
65.63	even	12	inner	650.2.w.c.193.1	yes	8

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

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.w (of order \(12\), degree \(4\), minimal)

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

Introduction

L-functions

Modular forms

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Database

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