LMFDB - Embedded newform 460.2.o.a.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(19,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 15]))

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

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

chi := DirichletCharacter("460.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.o (of order $22$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{22}]$

Embedding invariants

Embedding label			199.1
Character	$\chi$	$=$	460.199
Dual form			460.2.o.a.319.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.201264 + 1.39982i) q^{2} +(-1.38389 - 3.03031i) q^{3} +(-1.91899 - 0.563465i) q^{4} +(1.68991 - 1.46431i) q^{5} +(4.52041 - 1.32731i) q^{6} +(2.67835 - 4.16759i) q^{7} +(1.17497 - 2.57283i) q^{8} +(-5.30301 + 6.12000i) q^{9} +O(q^{10})$	\(q+(-0.201264 + 1.39982i) q^{2} +(-1.38389 - 3.03031i) q^{3} +(-1.91899 - 0.563465i) q^{4} +(1.68991 - 1.46431i) q^{5} +(4.52041 - 1.32731i) q^{6} +(2.67835 - 4.16759i) q^{7} +(1.17497 - 2.57283i) q^{8} +(-5.30301 + 6.12000i) q^{9} +(1.70966 + 2.66028i) q^{10} +(0.948202 + 6.59489i) q^{12} +(5.29482 + 4.58798i) q^{14} +(-6.77597 - 3.09448i) q^{15} +(3.36501 + 2.16256i) q^{16} +(-7.49959 - 8.65498i) q^{18} +(-4.06800 + 1.85779i) q^{20} +(-16.3356 - 2.34871i) q^{21} +(-4.79577 + 0.0248509i) q^{23} -9.42249 q^{24} +(0.711574 - 4.94911i) q^{25} +(16.2950 + 4.78466i) q^{27} +(-7.48800 + 6.48839i) q^{28} +(2.71581 - 0.797434i) q^{29} +(5.69547 - 8.86232i) q^{30} +(-3.70445 + 4.27517i) q^{32} +(-1.57650 - 10.9648i) q^{35} +(13.6248 - 8.75613i) q^{36} +(-1.78183 - 6.06837i) q^{40} +(5.02751 + 5.80206i) q^{41} +(6.57553 - 22.3942i) q^{42} +(0.501832 - 0.229179i) q^{43} +18.1075i q^{45} +(0.930426 - 6.71821i) q^{46} -13.6525 q^{47} +(1.89640 - 13.1898i) q^{48} +(-7.28735 - 15.9571i) q^{49} +(6.78464 + 1.99215i) q^{50} +(-9.97725 + 21.8471i) q^{54} +(-7.57551 - 11.7877i) q^{56} +(0.569670 + 3.96214i) q^{58} +(11.2594 + 9.75629i) q^{60} +(9.65946 + 4.41133i) q^{61} +(11.3023 + 38.4922i) q^{63} +(-5.23889 - 6.04600i) q^{64} +(2.68147 + 0.385537i) q^{67} +(6.71214 + 14.4983i) q^{69} +15.6660 q^{70} +(9.51482 + 20.8345i) q^{72} +(-15.9821 + 4.69275i) q^{75} +(8.85323 - 1.27290i) q^{80} +(-4.59428 - 31.9539i) q^{81} +(-9.13369 + 5.86986i) q^{82} +(7.71589 + 6.68585i) q^{83} +(30.0244 + 13.7117i) q^{84} +(0.219809 + 0.748599i) q^{86} +(-6.17487 - 7.12618i) q^{87} +(-3.08649 + 1.40955i) q^{89} +(-25.3472 - 3.64438i) q^{90} +(9.21701 + 2.65456i) q^{92} +(2.74774 - 19.1110i) q^{94} +(18.0816 + 5.30925i) q^{96} +(23.8037 - 6.98939i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) $ 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9	$ 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9} - 16 q^{16} - 16 q^{24} + 20 q^{25} + 24 q^{29} + 8 q^{36} + 48 q^{41} - 4 q^{46} + 100 q^{49} - 276 q^{54} - 264 q^{56} - 32 q^{64} - 4 q^{69} - 40 q^{70} + 20 q^{81} + 352 q^{84} + 396 q^{86} - 56 q^{94} - 32 q^{96}+O(q^{100}) $ 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9 - 16 * q^16 - 16 * q^24 + 20 * q^25 + 24 * q^29 + 8 * q^36 + 48 * q^41 - 4 * q^46 + 100 * q^49 - 276 * q^54 - 264 * q^56 - 32 * q^64 - 4 * q^69 - 40 * q^70 + 20 * q^81 + 352 * q^84 + 396 * q^86 - 56 * q^94 - 32 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{17}{22}\right)$

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 $

$2$	−0.201264	+	1.39982i	−0.142315	+	0.989821i
$2$	−0.201264	+	1.39982i	−0.142315	+	0.989821i
$3$	−1.38389	−	3.03031i	−0.798992	−	1.74955i	−0.648897	−	0.760876i	$-0.724769\pi$
$3$	−1.38389	−	3.03031i	−0.798992	−	1.74955i	−0.150095	−	0.988672i	$-0.547958\pi$
$4$	−1.91899	−	0.563465i	−0.959493	−	0.281733i
$5$	1.68991	−	1.46431i	0.755750	−	0.654861i
$5$	1.68991	−	1.46431i	0.755750	−	0.654861i
$6$	4.52041	−	1.32731i	1.84545	−	0.541873i
$7$	2.67835	−	4.16759i	1.01232	−	1.57520i	0.210536	−	0.977586i	$-0.432479\pi$
$7$	2.67835	−	4.16759i	1.01232	−	1.57520i	0.801784	−	0.597614i	$-0.203885\pi$
$8$	1.17497	−	2.57283i	0.415415	−	0.909632i
$9$	−5.30301	+	6.12000i	−1.76767	+	2.04000i
$10$	1.70966	+	2.66028i	0.540641	+	0.841254i
$11$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$11$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$12$	0.948202	+	6.59489i	0.273722	+	1.90378i
$13$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$13$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$14$	5.29482	+	4.58798i	1.41510	+	1.22619i
$15$	−6.77597	−	3.09448i	−1.74955	−	0.798992i
$16$	3.36501	+	2.16256i	0.841254	+	0.540641i
$17$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$17$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$18$	−7.49959	−	8.65498i	−1.76767	−	2.04000i
$19$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$19$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$20$	−4.06800	+	1.85779i	−0.909632	+	0.415415i
$21$	−16.3356	−	2.34871i	−3.56472	−	0.512530i
$22$		0			0
$23$	−4.79577	+	0.0248509i	−0.999987	+	0.00518177i
$23$	−4.79577	+	0.0248509i	−0.999987	+	0.00518177i
$24$	−9.42249			−1.92336
$25$	0.711574	−	4.94911i	0.142315	−	0.989821i
$26$		0			0
$27$	16.2950	+	4.78466i	3.13598	+	0.920807i
$28$	−7.48800	+	6.48839i	−1.41510	+	1.22619i
$29$	2.71581	−	0.797434i	0.504314	−	0.148080i	−0.0196728	−	0.999806i	$-0.506262\pi$
$29$	2.71581	−	0.797434i	0.504314	−	0.148080i	0.523986	+	0.851727i	$0.324444\pi$
$30$	5.69547	−	8.86232i	1.03985	−	1.61803i
$31$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$31$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$32$	−3.70445	+	4.27517i	−0.654861	+	0.755750i
$33$		0			0
$34$		0			0
$35$	−1.57650	−	10.9648i	−0.266477	−	1.85339i
$36$	13.6248	−	8.75613i	2.27080	−	1.45936i
$37$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$37$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$38$		0			0
$39$		0			0
$40$	−1.78183	−	6.06837i	−0.281733	−	0.959493i
$41$	5.02751	+	5.80206i	0.785165	+	0.906129i	0.997471	−	0.0710741i	$-0.0226427\pi$
$41$	5.02751	+	5.80206i	0.785165	+	0.906129i	−0.212306	+	0.977203i	$0.568097\pi$
$42$	6.57553	−	22.3942i	1.01463	−	3.45550i
$43$	0.501832	−	0.229179i	0.0765287	−	0.0349495i	−0.376783	−	0.926302i	$-0.622970\pi$
$43$	0.501832	−	0.229179i	0.0765287	−	0.0349495i	0.453312	+	0.891352i	$0.350242\pi$
$44$		0			0
$45$			18.1075i			2.69931i
$46$	0.930426	−	6.71821i	0.137184	−	0.990546i
$47$	−13.6525			−1.99142			−0.995708	−	0.0925502i	$-0.970498\pi$
$47$	−13.6525			−1.99142			−0.995708	+	0.0925502i	$0.970498\pi$
$48$	1.89640	−	13.1898i	0.273722	−	1.90378i
$49$	−7.28735	−	15.9571i	−1.04105	−	2.27958i
$50$	6.78464	+	1.99215i	0.959493	+	0.281733i
$51$		0			0
$52$		0			0
$53$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$53$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$54$	−9.97725	+	21.8471i	−1.35773	+	2.97302i
$55$		0			0
$56$	−7.57551	−	11.7877i	−1.01232	−	1.57520i
$57$		0			0
$58$	0.569670	+	3.96214i	0.0748013	+	0.520254i
$59$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$59$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$60$	11.2594	+	9.75629i	1.45358	+	1.25953i
$61$	9.65946	+	4.41133i	1.23677	+	0.564813i	0.923041	−	0.384701i	$-0.125695\pi$
$61$	9.65946	+	4.41133i	1.23677	+	0.564813i	0.313726	+	0.949514i	$0.398423\pi$
$62$		0			0
$63$	11.3023	+	38.4922i	1.42396	+	4.84957i
$64$	−5.23889	−	6.04600i	−0.654861	−	0.755750i
$65$		0			0
$66$		0			0
$67$	2.68147	+	0.385537i	0.327594	+	0.0471009i	0.304150	−	0.952624i	$-0.401628\pi$
$67$	2.68147	+	0.385537i	0.327594	+	0.0471009i	0.0234443	+	0.999725i	$0.492537\pi$
$68$		0			0
$69$	6.71214	+	14.4983i	0.808047	+	1.74538i
$70$	15.6660			1.87244
$71$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$71$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$72$	9.51482	+	20.8345i	1.12133	+	2.45538i
$73$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$73$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$74$		0			0
$75$	−15.9821	+	4.69275i	−1.84545	+	0.541873i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$79$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$80$	8.85323	−	1.27290i	0.989821	−	0.142315i
$81$	−4.59428	−	31.9539i	−0.510476	−	3.55044i
$82$	−9.13369	+	5.86986i	−1.00865	+	0.648218i
$83$	7.71589	+	6.68585i	0.846928	+	0.733868i	0.965868	−	0.259034i	$-0.0834041\pi$
$83$	7.71589	+	6.68585i	0.846928	+	0.733868i	−0.118940	+	0.992901i	$0.537950\pi$
$84$	30.0244	+	13.7117i	3.27593	+	1.49607i
$85$		0			0
$86$	0.219809	+	0.748599i	0.0237026	+	0.0807235i
$87$	−6.17487	−	7.12618i	−0.662015	−	0.764006i
$88$		0			0
$89$	−3.08649	+	1.40955i	−0.327168	+	0.149412i	−0.572226	−	0.820096i	$-0.693920\pi$
$89$	−3.08649	+	1.40955i	−0.327168	+	0.149412i	0.245059	+	0.969508i	$0.421193\pi$
$90$	−25.3472	−	3.64438i	−2.67183	−	0.384151i
$91$		0			0
$92$	9.21701	+	2.65456i	0.960940	+	0.276757i
$93$		0			0
$94$	2.74774	−	19.1110i	0.283408	−	1.97115i
$95$		0			0
$96$	18.0816	+	5.30925i	1.84545	+	0.541873i
$97$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$97$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$98$	23.8037	−	6.98939i	2.40454	−	0.706035i
$99$		0			0
$100$	−4.15415	+	9.09632i	−0.415415	+	0.909632i
$101$	0.431243	−	0.497680i	0.0429102	−	0.0495211i	−0.733889	−	0.679270i	$-0.762297\pi$
$101$	0.431243	−	0.497680i	0.0429102	−	0.0495211i	0.776799	+	0.629749i	$0.216842\pi$
$102$		0			0
$103$	−0.727653	+	0.104621i	−0.0716978	+	0.0103086i	−0.178070	−	0.984018i	$-0.556985\pi$
$103$	−0.727653	+	0.104621i	−0.0716978	+	0.0103086i	0.106373	+	0.994326i	$0.466076\pi$
$104$		0			0
$105$	−31.0449	+	19.9514i	−3.02967	+	1.94705i
$106$		0			0
$107$	18.2898	+	8.35268i	1.76814	+	0.807484i	0.981857	+	0.189623i	$0.0607267\pi$
$107$	18.2898	+	8.35268i	1.76814	+	0.807484i	0.786287	+	0.617861i	$0.212001\pi$
$108$	−28.5740	−	18.3634i	−2.74953	−	1.76702i
$109$	−3.92391	−	13.3636i	−0.375843	−	1.28000i	−0.902782	−	0.430099i	$-0.858479\pi$
$109$	−3.92391	−	13.3636i	−0.375843	−	1.28000i	0.526939	−	0.849903i	$-0.323340\pi$
$110$		0			0
$111$		0			0
$112$	18.0253	−	8.23190i	1.70324	−	0.777841i
$113$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$113$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$114$		0			0
$115$	−8.06801	+	7.06450i	−0.752346	+	0.658768i
$116$	−5.66093			−0.525604
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−15.9231	+	13.7975i	−1.45358	+	1.25953i
$121$	10.5544	−	3.09906i	0.959493	−	0.281733i
$122$	−8.11916	+	12.6337i	−0.735074	+	1.14380i
$123$	10.6245	−	23.2643i	0.957976	−	2.09767i
$124$		0			0
$125$	−6.04455	−	9.40550i	−0.540641	−	0.841254i
$126$	−56.1569	+	8.07414i	−5.00285	+	0.719302i
$127$	−3.11641	−	21.6751i	−0.276537	−	1.92336i	−0.372621	−	0.927983i	$-0.621541\pi$
$127$	−3.11641	−	21.6751i	−0.276537	−	1.92336i	0.0960844	−	0.995373i	$-0.469368\pi$
$128$	9.51770	−	6.11665i	0.841254	−	0.540641i
$129$	−1.38896	−	1.20354i	−0.122292	−	0.105966i
$130$		0			0
$131$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$131$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$132$		0			0
$133$		0			0
$134$	−1.07937	+	3.67598i	−0.0932430	+	0.317556i
$135$	34.5433	−	15.7754i	2.97302	−	1.35773i
$136$		0			0
$137$		0			0			−	1.00000i	$-0.5\pi$
$137$		0			0				1.00000i	$0.5\pi$
$138$	−21.6458	+	6.47781i	−1.84262	+	0.551428i
$139$		0			0		1.00000			$0$
$139$		0			0		−1.00000			$\pi$
$140$	−3.15299	+	21.9296i	−0.266477	+	1.85339i
$141$	18.8936	+	41.3711i	1.59113	+	3.48408i
$142$		0			0
$143$		0			0
$144$	−31.0796	+	9.12579i	−2.58997	+	0.760482i
$145$	3.42178	−	5.32439i	0.284163	−	0.442166i
$146$		0			0
$147$	−38.2699	+	44.1658i	−3.15645	+	3.64273i
$148$		0			0
$149$	20.8522	−	2.99809i	1.70828	−	0.245613i	0.782222	−	0.623000i	$-0.214086\pi$
$149$	20.8522	−	2.99809i	1.70828	−	0.245613i	0.926056	+	0.377387i	$0.123177\pi$
$150$	−3.35240	−	23.3165i	−0.273722	−	1.90378i
$151$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$151$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$157$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$158$		0			0
$159$		0			0
$160$			12.6491i			1.00000i
$161$	−12.7412	+	20.0533i	−1.00414	+	1.58042i
$162$	45.6544			3.58695
$163$	−0.850464	+	5.91511i	−0.0666135	+	0.463307i	0.929025	+	0.370016i	$0.120648\pi$
$163$	−0.850464	+	5.91511i	−0.0666135	+	0.463307i	−0.995639	+	0.0932911i	$0.970261\pi$
$164$	−6.37847	−	13.9669i	−0.498075	−	1.09063i
$165$		0			0
$166$	−10.9119	+	9.45522i	−0.846928	+	0.733868i
$167$	19.5689	−	5.74594i	1.51429	−	0.444634i	0.584087	−	0.811691i	$-0.301453\pi$
$167$	19.5689	−	5.74594i	1.51429	−	0.444634i	0.930199	+	0.367057i	$0.119634\pi$
$168$	−25.2367	+	39.2691i	−1.94705	+	3.02967i
$169$	5.40040	−	11.8252i	0.415415	−	0.909632i
$170$		0			0
$171$		0			0
$172$	−1.09214	+	0.157026i	−0.0832751	+	0.0119732i
$173$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$173$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$174$	11.2181	−	7.20945i	0.850444	−	0.546547i
$175$	−18.7200	−	16.2210i	−1.41510	−	1.22619i
$176$		0			0
$177$		0			0
$178$	−1.35192	−	4.60422i	−0.101331	−	0.345101i
$179$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$179$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$180$	10.2029	−	34.7480i	0.760482	−	2.58997i
$181$	−11.7943	+	5.38628i	−0.876664	+	0.400359i	−0.802334	−	0.596875i	$-0.796409\pi$
$181$	−11.7943	+	5.38628i	−0.876664	+	0.400359i	−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$		−	35.3759i		−	2.61506i
$184$	−5.57095	+	12.3679i	−0.410696	+	0.911772i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	26.1989	+	7.69269i	1.91075	+	0.561047i
$189$	63.5842	−	55.0961i	4.62507	−	4.00765i
$190$		0			0
$191$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$191$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$192$	−11.0712	+	24.2424i	−0.798992	+	1.74955i
$193$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$193$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$194$		0			0
$195$		0			0
$196$	4.99307	+	34.7276i	0.356648	+	2.48054i
$197$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$197$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$198$		0			0
$199$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$199$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$200$	−11.8971	−	7.64582i	−0.841254	−	0.540641i
$201$	−2.54258	−	8.65922i	−0.179340	−	0.610775i
$202$	0.609869	+	0.703827i	0.0429102	+	0.0495211i
$203$	3.95051	−	13.4542i	0.277271	−	0.944299i
$204$		0			0
$205$	16.9921	+	2.44309i	1.18678	+	0.170633i
$206$		−	1.03964i		−	0.0724351i
$207$	25.2799	−	29.4819i	1.75708	−	2.04913i
$208$		0			0
$209$		0			0
$210$	−21.6801	−	47.4728i	−1.49607	−	3.27593i
$211$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$211$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$212$		0			0
$213$		0			0
$214$	−15.3733	+	23.9214i	−1.05090	+	1.63523i
$215$	0.512460	−	1.12213i	0.0349495	−	0.0765287i
$216$	31.4563	−	36.3025i	2.14033	−	2.47007i
$217$		0			0
$218$	19.4964	−	2.80316i	1.32046	−	0.189854i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−23.2224	−	14.9242i	−1.55509	−	0.999396i	−0.983930	−	0.178557i	$-0.942857\pi$
$223$	−23.2224	−	14.9242i	−1.55509	−	0.999396i	−0.571160	−	0.820839i	$-0.693507\pi$
$224$	7.89532	+	26.8890i	0.527529	+	1.79660i
$225$	26.5150	+	30.6000i	1.76767	+	2.04000i
$226$		0			0
$227$	−10.1480	+	4.63442i	−0.673544	+	0.307597i	−0.722668	−	0.691195i	$-0.757084\pi$
$227$	−10.1480	+	4.63442i	−0.673544	+	0.307597i	0.0491237	+	0.998793i	$0.484357\pi$
$228$		0			0
$229$		−	17.6762i		−	1.16808i	−0.811726	−	0.584038i	$-0.801472\pi$
$229$		−	17.6762i		−	1.16808i	0.811726	−	0.584038i	$-0.198528\pi$
$230$	−8.26522	−	12.7156i	−0.544993	−	0.838441i
$231$		0			0
$232$	1.13934	−	7.92428i	0.0748013	−	0.520254i
$233$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$233$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$234$		0			0
$235$	−23.0714	+	19.9915i	−1.50501	+	1.30410i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$239$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$240$	−16.1092	−	25.0664i	−1.03985	−	1.61803i
$241$	3.81214	−	0.548103i	0.245562	−	0.0353064i	−0.0184349	−	0.999830i	$-0.505868\pi$
$241$	3.81214	−	0.548103i	0.245562	−	0.0353064i	0.263997	+	0.964524i	$0.414959\pi$
$242$	2.21390	+	15.3980i	0.142315	+	0.989821i
$243$	−47.6113	+	30.5979i	−3.05426	+	1.96286i
$244$	−16.0507	−	13.9080i	−1.02754	−	0.890372i
$245$	−35.6811	−	16.2950i	−2.27958	−	1.04105i
$246$	30.4275	+	19.5546i	1.93999	+	1.24676i
$247$		0			0
$248$		0			0
$249$	9.58221	−	32.6340i	0.607248	−	2.06810i
$250$	14.3825	−	6.56829i	0.909632	−	0.415415i
$251$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$251$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$252$		−	80.2345i		−	5.05430i
$253$		0			0
$254$	30.9685			1.94313
$255$		0			0
$256$	6.64664	+	14.5541i	0.415415	+	0.909632i
$257$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$257$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$258$	1.96429	−	1.70207i	0.122292	−	0.105966i
$259$		0			0
$260$		0			0
$261$	−9.52168	+	20.8496i	−0.589377	+	1.29056i
$262$		0			0
$263$	17.1331	+	26.6596i	1.05647	+	1.64390i	0.707408	+	0.706806i	$0.249864\pi$
$263$	17.1331	+	26.6596i	1.05647	+	1.64390i	0.349065	+	0.937098i	$0.386499\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	8.54276	+	7.40235i	0.522809	+	0.453016i
$268$	−4.92847	−	2.25076i	−0.301054	−	0.137487i
$269$	25.4984	+	16.3868i	1.55466	+	0.999121i	0.984048	+	0.177902i	$0.0569310\pi$
$269$	25.4984	+	16.3868i	1.55466	+	0.999121i	0.570614	+	0.821219i	$0.306705\pi$
$270$	15.1304	+	51.5294i	0.920807	+	3.13598i
$271$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$271$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−4.71125	−	31.6040i	−0.283584	−	1.90234i
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$		0			0
$279$		0			0
$280$	−30.0628	−	8.82724i	−1.79660	−	0.527529i
$281$	−25.2554	+	21.8839i	−1.50661	+	1.30549i	−0.700678	+	0.713478i	$0.747119\pi$
$281$	−25.2554	+	21.8839i	−1.50661	+	1.30549i	−0.805932	+	0.592008i	$0.798336\pi$
$282$	−61.7147	+	18.1211i	−3.67506	+	1.07909i
$283$	14.6762	−	22.8367i	0.872412	−	1.35750i	−0.0607917	−	0.998150i	$-0.519363\pi$
$283$	14.6762	−	22.8367i	0.872412	−	1.35750i	0.933203	−	0.359349i	$-0.117001\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	37.6460	−	5.41268i	2.22217	−	0.319500i
$288$	−6.51926	−	45.3425i	−0.384151	−	2.67183i
$289$	−14.3013	+	9.19089i	−0.841254	+	0.540641i
$290$	6.76450	+	5.86147i	0.397225	+	0.344198i
$291$		0			0
$292$		0			0
$293$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$293$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$294$	−54.1218	−	62.4599i	−3.15645	−	3.64273i
$295$		0			0
$296$		0			0
$297$		0			0
$298$			29.7927i			1.72584i
$299$		0			0
$300$	33.3135			1.92336
$301$	0.388956	−	2.70525i	0.0224191	−	0.155928i
$302$		0			0
$303$	−2.10492	−	0.618060i	−0.120924	−	0.0355066i
$304$		0			0
$305$	22.7832	−	6.68974i	1.30456	−	0.383053i
$306$		0			0
$307$	−9.29506	+	20.3533i	−0.530497	+	1.16163i	0.434813	+	0.900521i	$0.356814\pi$
$307$	−9.29506	+	20.3533i	−0.530497	+	1.16163i	−0.965310	+	0.261106i	$0.915913\pi$
$308$		0			0
$309$	1.32403	+	2.06023i	0.0753213	+	0.117202i
$310$		0			0
$311$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$311$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$312$		0			0
$313$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$313$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$314$		0			0
$315$	75.4646	+	48.4981i	4.25195	+	2.73256i
$316$		0			0
$317$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$317$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$318$		0			0
$319$		0			0
$320$	−17.7065	−	2.54581i	−0.989821	−	0.142315i
$321$		−	66.9830i		−	3.73863i
$322$	−25.5067	−	21.8713i	−1.42143	−	1.21884i
$323$		0			0
$324$	−9.18856	+	63.9079i	−0.510476	+	3.55044i
$325$		0			0
$326$	−8.10891	−	2.38099i	−0.449111	−	0.131871i
$327$	−35.0656	+	30.3845i	−1.93913	+	1.68027i
$328$	20.8349	−	6.11767i	1.15041	−	0.337792i
$329$	−36.5660	+	56.8978i	−2.01595	+	3.13688i
$330$		0			0
$331$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$331$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$332$	−11.0394	−	17.1777i	−0.605868	−	0.942748i
$333$		0			0
$334$	4.10478	+	28.5493i	0.224603	+	1.56215i
$335$	5.09599	−	3.27499i	0.278424	−	0.178932i
$336$	−49.8904	−	43.2302i	−2.72174	−	2.35840i
$337$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$337$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$338$	15.4663	+	9.93956i	0.841254	+	0.540641i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−51.6954	−	7.43267i	−2.79129	−	0.401326i
$344$		−	1.56041i		−	0.0841315i
$345$	32.5729	+	14.6720i	1.75366	+	0.789915i
$346$		0			0
$347$	5.10566	−	35.5107i	0.274086	−	1.90631i	−0.129864	−	0.991532i	$-0.541454\pi$
$347$	5.10566	−	35.5107i	0.274086	−	1.90631i	0.403950	−	0.914781i	$-0.367637\pi$
$348$	7.83413	+	17.1544i	0.419953	+	0.919570i
$349$	7.06731	+	2.07515i	0.378305	+	0.111080i	0.465356	−	0.885124i	$-0.345926\pi$
$349$	7.06731	+	2.07515i	0.378305	+	0.111080i	−0.0870514	+	0.996204i	$0.527744\pi$
$350$	26.4741	−	22.9399i	1.41510	−	1.22619i
$351$		0			0
$352$		0			0
$353$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$353$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$354$		0			0
$355$		0			0
$356$	6.71717	−	0.965784i	0.356009	−	0.0511864i
$357$		0			0
$358$		0			0
$359$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$359$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$360$	46.5875	+	21.2758i	2.45538	+	1.12133i
$361$	−15.9838	−	10.2722i	−0.841254	−	0.540641i
$362$	−5.16605	−	17.5940i	−0.271522	−	0.924718i
$363$	−23.9973	−	27.6944i	−1.25953	−	1.45358i
$364$		0			0
$365$		0			0
$366$	49.5199	+	7.11989i	2.58845	+	0.372163i
$367$			36.0468i			1.88163i	0.338921	+	0.940815i	$0.389938\pi$
$367$			36.0468i			1.88163i	−0.338921	+	0.940815i	$0.610062\pi$
$368$	−16.1916	−	10.2875i	−0.844044	−	0.536274i
$369$	−62.1695			−3.23642
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$373$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$374$		0			0
$375$	−20.1365	+	31.3330i	−1.03985	+	1.61803i
$376$	−16.0412	+	35.1254i	−0.827264	+	1.81146i
$377$		0			0
$378$	64.3273	+	100.095i	3.30864	+	5.14834i
$379$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$379$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$380$		0			0
$381$	−61.3695	+	39.4398i	−3.14405	+	2.02056i
$382$		0			0
$383$	−8.56459	−	3.91132i	−0.437630	−	0.199859i	0.184402	−	0.982851i	$-0.440965\pi$
$383$	−8.56459	−	3.91132i	−0.437630	−	0.199859i	−0.622032	+	0.782992i	$0.713693\pi$
$384$	−31.7068	−	20.3767i	−1.61803	−	1.03985i
$385$		0			0
$386$		0			0
$387$	−1.25864	+	4.28655i	−0.0639805	+	0.217898i
$388$		0			0
$389$	−27.9237	−	4.01483i	−1.41579	−	0.203560i	−0.608424	−	0.793612i	$-0.708198\pi$
$389$	−27.9237	−	4.01483i	−1.41579	−	0.203560i	−0.807365	+	0.590052i	$0.799107\pi$
$390$		0			0
$391$		0			0
$392$	−49.6172			−2.50605
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$397$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$398$		0			0
$399$		0			0
$400$	13.0972	−	15.1150i	0.654861	−	0.755750i
$401$	16.8873	+	26.2772i	0.843312	+	1.31222i	0.948180	+	0.317732i	$0.102921\pi$
$401$	16.8873	+	26.2772i	0.843312	+	1.31222i	−0.104869	+	0.994486i	$0.533442\pi$
$402$	12.6331	−	1.81636i	0.630080	−	0.0905919i
$403$		0			0
$404$	−1.10797	+	0.712052i	−0.0551238	+	0.0354259i
$405$	−54.5545	−	47.2717i	−2.71083	−	2.34895i
$406$	18.0383	+	8.23783i	0.895228	+	0.408837i
$407$		0			0
$408$		0			0
$409$	18.2044	+	21.0090i	0.900150	+	1.03883i	0.999043	+	0.0437302i	$0.0139242\pi$
$409$	18.2044	+	21.0090i	0.900150	+	1.03883i	−0.0988936	+	0.995098i	$0.531530\pi$
$410$	−6.83977	+	23.2941i	−0.337792	+	1.15041i
$411$		0			0
$412$	1.45531	+	0.209241i	0.0716978	+	0.0103086i
$413$		0			0
$414$	36.1814	+	41.3209i	1.77822	+	2.03081i
$415$	22.8293			1.12065
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$419$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$420$	70.8167	−	20.7936i	3.45550	−	1.01463i
$421$	20.6443	−	32.1232i	1.00614	−	1.56559i	0.194948	−	0.980814i	$-0.437546\pi$
$421$	20.6443	−	32.1232i	1.00614	−	1.56559i	0.811195	−	0.584776i	$-0.198817\pi$
$422$		0			0
$423$	72.3991	−	83.5530i	3.52017	−	4.06249i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	44.2560	−	28.4416i	2.14170	−	1.37639i
$428$	−30.3915	−	26.3344i	−1.46903	−	1.27292i
$429$		0			0
$430$	1.46764	+	0.943195i	0.0707759	+	0.0454849i
$431$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$431$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$432$	44.4859	+	51.3395i	2.14033	+	2.47007i
$433$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$433$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$434$		0			0
$435$	−20.8699	−	3.00064i	−1.00064	−	0.143870i
$436$			27.8556i			1.33404i
$437$		0			0
$438$		0			0
$439$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$439$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$440$		0			0
$441$	136.302	+	40.0219i	6.49058	+	1.90581i
$442$		0			0
$443$	−40.3214	+	11.8394i	−1.91573	+	0.562508i	−0.941454	+	0.337142i	$0.890540\pi$
$443$	−40.3214	+	11.8394i	−1.91573	+	0.562508i	−0.974274	+	0.225367i	$0.927642\pi$
$444$		0			0
$445$	−3.15186	+	6.90161i	−0.149412	+	0.327168i
$446$	25.5650	−	29.5035i	1.21054	−	1.39703i
$447$	−37.9424	−	59.0395i	−1.79461	−	2.79247i
$448$	−39.2288	+	5.64025i	−1.85339	+	0.266477i
$449$	−2.42074	−	16.8366i	−0.114242	−	0.794569i	−0.963714	−	0.266936i	$-0.913989\pi$
$449$	−2.42074	−	16.8366i	−0.114242	−	0.794569i	0.849473	−	0.527633i	$-0.176920\pi$
$450$	−48.1710	+	30.9576i	−2.27080	+	1.45936i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−4.44493	−	15.1381i	−0.208611	−	0.710464i
$455$		0			0
$456$		0			0
$457$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$457$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$458$	24.7435	+	3.55758i	1.15619	+	0.166235i
$459$		0			0
$460$	19.4630	−	9.01063i	0.907467	−	0.420123i
$461$	−2.87601			−0.133949			−0.0669745	−	0.997755i	$-0.521335\pi$
$461$	−2.87601			−0.133949			−0.0669745	+	0.997755i	$0.521335\pi$
$462$		0			0
$463$	4.78480	+	10.4773i	0.222369	+	0.486919i	0.987630	−	0.156800i	$-0.0501178\pi$
$463$	4.78480	+	10.4773i	0.222369	+	0.486919i	−0.765262	+	0.643719i	$0.777390\pi$
$464$	10.8632	+	3.18974i	0.504314	+	0.148080i
$465$		0			0
$466$		0			0
$467$	−15.3869	+	23.9425i	−0.712021	+	1.10793i	0.277103	+	0.960840i	$0.410626\pi$
$467$	−15.3869	+	23.9425i	−0.712021	+	1.10793i	−0.989124	+	0.147086i	$0.953011\pi$
$468$		0			0
$469$	8.78867	−	10.1427i	0.405823	−	0.468345i
$470$	−23.3410	−	36.3193i	−1.07664	−	1.67529i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$479$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$480$	38.3307	−	17.5050i	1.74955	−	0.798992i
$481$		0			0
$482$			5.44662i			0.248087i
$483$	78.4002	+	10.8579i	3.56733	+	0.494051i
$484$	−22.0000			−1.00000
$485$		0			0
$486$	−33.2491	−	72.8054i	−1.50821	−	3.30252i
$487$	42.3039	+	12.4215i	1.91697	+	0.562874i	0.971391	+	0.237485i	$0.0763230\pi$
$487$	42.3039	+	12.4215i	1.91697	+	0.562874i	0.945580	+	0.325389i	$0.105495\pi$
$488$	22.6992	−	19.6690i	1.02754	−	0.890372i
$489$	19.1015	−	5.60872i	0.863802	−	0.253635i
$490$	29.9914	−	46.6675i	1.35487	−	2.10822i
$491$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$491$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$492$	−33.4968	+	38.6574i	−1.51015	+	1.74281i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	43.7532	+	19.9814i	1.96063	+	0.895388i
$499$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$499$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$500$	6.29973	+	21.4549i	0.281733	+	0.959493i
$501$	−44.4932	−	51.3479i	−1.98781	−	2.29406i
$502$		0			0
$503$	−38.2448	+	17.4658i	−1.70525	+	0.778762i	−0.707878	+	0.706334i	$0.750347\pi$
$503$	−38.2448	+	17.4658i	−1.70525	+	0.778762i	−0.997374	+	0.0724280i	$0.976925\pi$
$504$	112.314	+	16.1483i	5.00285	+	0.719302i
$505$		−	1.47251i		−	0.0655258i
$506$		0			0
$507$	−43.3076			−1.92336
$508$	−6.23283	+	43.3503i	−0.276537	+	1.92336i
$509$	−2.84248	−	6.22416i	−0.125991	−	0.275881i	0.836117	−	0.548551i	$-0.184820\pi$
$509$	−2.84248	−	6.22416i	−0.125991	−	0.275881i	−0.962108	+	0.272670i	$0.912093\pi$
$510$		0			0
$511$		0			0
$512$	−21.7108	+	6.37488i	−0.959493	+	0.281733i
$513$		0			0
$514$		0			0
$515$	−1.07647	+	1.24231i	−0.0474349	+	0.0547428i
$516$	1.98725	+	3.09222i	0.0874837	+	0.136127i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−18.2172	−	8.31951i	−0.798109	−	0.364484i	−0.0257485	−	0.999668i	$-0.508197\pi$
$521$	−18.2172	−	8.31951i	−0.798109	−	0.364484i	−0.772361	+	0.635184i	$0.780924\pi$
$522$	−27.2692	−	17.5249i	−1.19354	−	0.767043i
$523$	11.6820	+	39.7853i	0.510819	+	1.73969i	0.660374	+	0.750937i	$0.270398\pi$
$523$	11.6820	+	39.7853i	0.510819	+	1.73969i	−0.149555	+	0.988753i	$0.547784\pi$
$524$		0			0
$525$	−23.2480	+	79.1754i	−1.01463	+	3.45550i
$526$	−40.7669	+	18.6176i	−1.77752	+	0.811768i
$527$		0			0
$528$		0			0
$529$	22.9988	−	0.238358i	0.999946	−	0.0103634i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−12.0813	+	10.4685i	−0.522809	+	0.453016i
$535$	43.1391	−	12.6668i	1.86506	−	0.547632i
$536$	4.14257	−	6.44597i	0.178932	−	0.278424i
$537$		0			0
$538$	−28.0704	+	32.3950i	−1.21020	+	1.39665i
$539$		0			0
$540$	−75.1771	+	10.8088i	−3.23511	+	0.465138i
$541$	5.72017	+	39.7846i	0.245929	+	1.71048i	0.621277	+	0.783591i	$0.286614\pi$
$541$	5.72017	+	39.7846i	0.245929	+	1.71048i	−0.375347	+	0.926884i	$0.622477\pi$
$542$		0			0
$543$	32.6441	+	28.2863i	1.40089	+	1.21388i
$544$		0			0
$545$	−26.1996	−	16.8374i	−1.12227	−	0.721237i
$546$		0			0
$547$	21.5787	+	24.9032i	0.922639	+	1.06478i	0.997712	+	0.0676046i	$0.0215356\pi$
$547$	21.5787	+	24.9032i	0.922639	+	1.06478i	−0.0750728	+	0.997178i	$0.523919\pi$
$548$		0			0
$549$	−78.2215	+	35.7226i	−3.33841	+	1.52460i
$550$		0			0
$551$		0			0
$552$	45.1881	−	0.234157i	1.92333	−	0.00996640i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$557$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$558$		0			0
$559$		0			0
$560$	18.4071	−	40.3059i	0.777841	−	1.70324i
$561$		0			0
$562$	−25.5505	−	39.7574i	−1.07778	−	1.67707i
$563$	38.7412	−	5.57014i	1.63275	−	0.234754i	0.735898	−	0.677092i	$-0.236760\pi$
$563$	38.7412	−	5.57014i	1.63275	−	0.234754i	0.896848	+	0.442338i	$0.145851\pi$
$564$	−12.9453	−	90.0365i	−0.545095	−	3.79122i
$565$		0			0
$566$	29.0134	+	25.1403i	1.21952	+	1.05672i
$567$	−145.476	−	66.4366i	−6.10941	−	2.79008i
$568$		0			0
$569$	−5.56202	−	18.9425i	−0.233172	−	0.794111i	−0.990070	−	0.140578i	$-0.955104\pi$
$569$	−5.56202	−	18.9425i	−0.233172	−	0.794111i	0.756898	−	0.653534i	$-0.226714\pi$
$570$		0			0
$571$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$571$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$572$		0			0
$573$		0			0
$574$			53.7870i			2.24502i
$575$	−3.28955	+	23.7524i	−0.137184	+	0.990546i
$576$	64.7833			2.69931
$577$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$577$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$578$	−9.98725	−	21.8690i	−0.415415	−	0.909632i
$579$		0			0
$580$	−9.56645	+	8.28937i	−0.397225	+	0.344198i
$581$	48.5297	−	14.2496i	2.01335	−	0.591173i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	3.25364	+	22.6295i	0.134292	+	0.934021i	0.939870	+	0.341532i	$0.110946\pi$
$587$	3.25364	+	22.6295i	0.134292	+	0.934021i	−0.805578	+	0.592489i	$0.798145\pi$
$588$	98.3252	−	63.1898i	4.05486	−	2.60590i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$593$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$594$		0			0
$595$		0			0
$596$	−41.7044	−	5.99618i	−1.70828	−	0.245613i
$597$		0			0
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	−6.70480	+	46.6329i	−0.273722	+	1.90378i
$601$	−14.8946	−	32.6146i	−0.607563	−	1.33038i	−0.924228	−	0.381840i	$-0.875290\pi$
$601$	−14.8946	−	32.6146i	−0.607563	−	1.33038i	0.316665	−	0.948537i	$-0.397437\pi$
$602$	3.70858	+	1.08894i	0.151150	+	0.0443817i
$603$	−16.5794	+	14.3661i	−0.675164	+	0.585033i
$604$		0			0
$605$	13.2980	−	20.6921i	0.540641	−	0.841254i
$606$	1.28882	−	2.82211i	0.0523545	−	0.114640i
$607$	32.2409	−	37.2080i	1.30862	−	1.51023i	0.623285	−	0.781995i	$-0.285798\pi$
$607$	32.2409	−	37.2080i	1.30862	−	1.51023i	0.685332	−	0.728231i	$-0.259657\pi$
$608$		0			0
$609$	−46.2374	+	6.64793i	−1.87363	+	0.269388i
$610$	4.77900	+	33.2387i	0.193496	+	1.34580i
$611$		0			0
$612$		0			0
$613$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$613$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$614$	−26.6202	−	17.1078i	−1.07431	−	0.690414i
$615$	−16.1119	−	54.8721i	−0.649695	−	2.21266i
$616$		0			0
$617$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$617$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$618$	−3.15042	+	1.43875i	−0.126729	+	0.0578750i
$619$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$619$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$620$		0			0
$621$	−78.2661	−	22.5411i	−3.14071	−	0.904545i
$622$		0			0
$623$	−2.39226	+	16.6385i	−0.0958437	+	0.666608i
$624$		0			0
$625$	−23.9873	−	7.04331i	−0.959493	−	0.281733i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−83.0769	+	95.8758i	−3.30986	+	3.81979i
$631$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$631$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−37.0056	−	32.0656i	−1.46852	−	1.27248i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	7.12733	−	24.2735i	0.281733	−	0.959493i
$641$	21.0542	−	9.61515i	0.831593	−	0.379776i	0.0463207	−	0.998927i	$-0.485250\pi$
$641$	21.0542	−	9.61515i	0.831593	−	0.379776i	0.785272	+	0.619151i	$0.212523\pi$
$642$	93.7641	+	13.4812i	3.70057	+	0.532062i
$643$			47.8114i			1.88550i	0.333503	+	0.942749i	$0.391769\pi$
$643$			47.8114i			1.88550i	−0.333503	+	0.942749i	$0.608231\pi$
$644$	35.7495	−	31.3029i	1.40873	−	1.23351i
$645$	−4.10959			−0.161815
$646$		0			0
$647$	21.0968	+	46.1956i	0.829402	+	1.81614i	0.468012	+	0.883722i	$0.344970\pi$
$647$	21.0968	+	46.1956i	0.829402	+	1.81614i	0.361390	+	0.932415i	$0.382302\pi$
$648$	−87.6101	−	25.7247i	−3.44165	−	1.01056i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	4.96499	−	10.8718i	0.194444	−	0.425773i
$653$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$653$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$654$	−35.4754	−	55.2007i	−1.38720	−	2.15852i
$655$		0			0
$656$	4.37033	+	30.3963i	0.170633	+	1.18678i
$657$		0			0
$658$	−72.2873	−	62.6373i	−2.81805	−	2.44185i
$659$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$659$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$660$		0			0
$661$	−14.2392	−	48.4943i	−0.553841	−	1.88621i	−0.453496	−	0.891258i	$-0.649823\pi$
$661$	−14.2392	−	48.4943i	−0.553841	−	1.88621i	−0.100345	−	0.994953i	$-0.531995\pi$
$662$		0			0
$663$		0			0
$664$	26.2675	−	11.9960i	1.01938	−	0.465534i
$665$		0			0
$666$		0			0
$667$	−13.0046	+	3.89180i	−0.503539	+	0.150691i
$668$	−40.7901			−1.57821
$669$	−13.0874	+	91.0246i	−0.505986	+	3.51921i
$670$	3.55876	+	7.79260i	0.137487	+	0.301054i
$671$		0			0
$672$	70.5556	−	61.1368i	2.72174	−	2.35840i
$673$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$673$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$674$		0			0
$675$	35.2749	−	77.2413i	1.35773	−	2.97302i
$676$	−17.0264	+	19.6495i	−0.654861	+	0.755750i
$677$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$677$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	28.0874	+	24.3379i	1.07631	+	0.932630i
$682$		0			0
$683$	−18.0820	−	11.6206i	−0.691890	−	0.444651i	0.146867	−	0.989156i	$-0.453081\pi$
$683$	−18.0820	−	11.6206i	−0.691890	−	0.444651i	−0.838757	+	0.544505i	$0.816717\pi$
$684$		0			0
$685$		0			0
$686$	20.8088	−	70.8682i	0.794483	−	2.70576i
$687$	−53.5643	+	24.4620i	−2.04361	+	0.933284i
$688$	2.18429	+	0.314053i	0.0832751	+	0.0119732i
$689$		0			0
$690$	−27.0939	+	42.6432i	−1.03145	+	1.62340i
$691$		0			0		1.00000			$0$
$691$		0			0		−1.00000			$\pi$
$692$		0			0
$693$		0			0
$694$	48.6809	+	14.2940i	1.84790	+	0.542593i
$695$		0			0
$696$	−25.5897	+	7.51382i	−0.969975	+	0.284811i
$697$		0			0
$698$	−4.32723	+	9.47531i	−0.163788	+	0.358646i
$699$		0			0
$700$	26.7835	+	41.6759i	1.01232	+	1.57520i
$701$	−34.6221	+	4.97790i	−1.30766	+	0.188013i	−0.760676	−	0.649132i	$-0.775132\pi$
$701$	−34.6221	+	4.97790i	−1.30766	+	0.188013i	−0.546981	+	0.837145i	$0.684223\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	92.5087	+	42.2473i	3.48408	+	1.59113i
$706$		0			0
$707$	−0.919110	−	3.13020i	−0.0345667	−	0.117723i
$708$		0			0
$709$	7.55968	−	25.7459i	0.283910	−	0.966908i	−0.686839	−	0.726810i	$-0.741002\pi$
$709$	7.55968	−	25.7459i	0.283910	−	0.966908i	0.970749	−	0.240098i	$-0.0771796\pi$
$710$		0			0
$711$		0			0
$712$			9.59720i			0.359670i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$719$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$720$	−39.1586	+	60.9320i	−1.45936	+	2.27080i
$721$	−1.51289	+	3.31277i	−0.0563430	+	0.123374i
$722$	17.5961	−	20.3070i	0.654861	−	0.755750i
$723$	−6.93652	−	10.7934i	−0.257972	−	0.401412i
$724$	25.6681	−	3.69051i	0.953947	−	0.137157i
$725$	−2.01409	−	14.0083i	−0.0748013	−	0.520254i
$726$	43.5969	−	28.0180i	1.61803	−	1.03985i
$727$	24.1826	+	20.9543i	0.896881	+	0.777152i	0.975557	−	0.219748i	$-0.0705236\pi$
$727$	24.1826	+	20.9543i	0.896881	+	0.777152i	−0.0786754	+	0.996900i	$0.525069\pi$
$728$		0			0
$729$	77.1366	+	49.5727i	2.85691	+	1.83602i
$730$		0			0
$731$		0			0
$732$	−19.9331	+	67.8859i	−0.736749	+	2.50914i
$733$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$733$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$734$	−50.4590	−	7.25491i	−1.86248	−	0.267784i
$735$			130.675i			4.82003i
$736$	17.6594	−	20.5948i	0.650936	−	0.759133i
$737$		0			0
$738$	12.5125	−	87.0261i	0.460590	−	3.20347i
$739$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$739$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	27.7726	−	43.2150i	1.01888	−	1.58541i	0.227784	−	0.973712i	$-0.426852\pi$
$743$	27.7726	−	43.2150i	1.01888	−	1.58541i	0.791094	−	0.611694i	$-0.209512\pi$
$744$		0			0
$745$	30.8481	−	35.6006i	1.13019	−	1.30431i
$746$		0			0
$747$	−81.8348	+	11.7661i	−2.99418	+	0.430498i
$748$		0			0
$749$	83.7970	−	53.8531i	3.06188	−	1.96775i
$750$	−39.8078	−	34.4937i	−1.45358	−	1.25953i
$751$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$751$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$752$	−45.9407	−	29.5243i	−1.67529	−	1.07664i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−153.062	+	69.9011i	−5.56681	+	2.54228i
$757$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$757$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−7.78109	+	54.1187i	−0.282064	+	1.96180i	−0.00843957	+	0.999964i	$0.502686\pi$
$761$	−7.78109	+	54.1187i	−0.282064	+	1.96180i	−0.273625	+	0.961837i	$0.588223\pi$
$762$	−42.8571	−	93.8440i	−1.55255	−	3.39961i
$763$	−66.2036	−	19.4391i	−2.39673	−	0.703744i
$764$		0			0
$765$		0			0
$766$	7.19888	−	11.2017i	0.260106	−	0.404733i
$767$		0			0
$768$	34.9052	−	40.2827i	1.25953	−	1.45358i
$769$	29.9710	+	46.6358i	1.08078	+	1.68173i	0.565971	+	0.824425i	$0.308501\pi$
$769$	29.9710	+	46.6358i	1.08078	+	1.68173i	0.514810	+	0.857304i	$0.327862\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$773$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$774$	−5.74707	−	2.62460i	−0.206574	−	0.0943393i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	11.2401	−	38.2801i	0.402976	−	1.37241i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	48.0697			1.71787
$784$	9.98614	−	69.4551i	0.356648	−	2.48054i
$785$		0			0
$786$		0			0
$787$	24.1421	−	20.9193i	0.860574	−	0.745691i	−0.108071	−	0.994143i	$-0.534467\pi$
$787$	24.1421	−	20.9193i	0.860574	−	0.745691i	0.968644	+	0.248452i	$0.0799218\pi$
$788$		0			0
$789$	57.0765	−	88.8127i	2.03198	−	3.16182i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$797$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$798$		0			0
$799$		0			0
$800$	18.5223	+	21.3758i	0.654861	+	0.755750i
$801$	7.74123	−	26.3642i	0.273523	−	0.931534i
$802$	−40.1821	+	18.3505i	−1.41888	+	0.647980i
$803$		0			0
$804$			18.0496i			0.636560i
$805$	7.83300	+	52.5453i	0.276077	+	1.85198i
$806$		0			0
$807$	14.3700	−	99.9454i	0.505847	−	3.51824i
$808$	−0.773749	−	1.69427i	−0.0272204	−	0.0596043i
$809$	24.3629	+	7.15360i	0.856555	+	0.251507i	0.680387	−	0.732853i	$-0.261812\pi$
$809$	24.3629	+	7.15360i	0.856555	+	0.251507i	0.176168	+	0.984360i	$0.443630\pi$
$810$	77.1517	−	66.8523i	2.71083	−	2.34895i
$811$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$811$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$812$	−15.1619	+	23.5924i	−0.532080	+	0.827932i
$813$		0			0
$814$		0			0
$815$	7.22437	+	11.2413i	0.253059	+	0.393767i
$816$		0			0
$817$		0			0
$818$	−33.0727	+	21.2545i	−1.15636	+	0.743147i
$819$		0			0
$820$	−31.2309	−	14.2627i	−1.09063	−	0.498075i
$821$	46.3464	+	29.7850i	1.61750	+	1.03950i	0.957580	+	0.288166i	$0.0930456\pi$
$821$	46.3464	+	29.7850i	1.61750	+	1.03950i	0.659919	+	0.751337i	$0.270591\pi$
$822$		0			0
$823$	35.9827	+	41.5262i	1.25428	+	1.44751i	0.844702	+	0.535236i	$0.179777\pi$
$823$	35.9827	+	41.5262i	1.25428	+	1.44751i	0.409575	+	0.912277i	$0.365677\pi$
$824$	−0.585800	+	1.99505i	−0.0204073	+	0.0695009i
$825$		0			0
$826$		0			0
$827$		−	47.4342i		−	1.64945i	−0.565536	−	0.824724i	$-0.691331\pi$
$827$		−	47.4342i		−	1.64945i	0.565536	−	0.824724i	$-0.308669\pi$
$828$	−65.1238	+	42.3310i	−2.26321	+	1.47110i
$829$	54.3637			1.88813			0.944064	−	0.329763i	$-0.106969\pi$
$829$	54.3637			1.88813			0.944064	+	0.329763i	$0.106969\pi$
$830$	−4.59471	+	31.9569i	−0.159485	+	1.10924i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	24.6557	−	38.3651i	0.853247	−	1.32768i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$839$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$840$	14.8545	+	103.316i	0.512530	+	3.56472i
$841$	−17.6566	+	11.3472i	−0.608849	+	0.391284i
$842$	40.8117	+	35.3636i	1.40646	+	1.21871i
$843$	101.266	+	46.2465i	3.48778	+	1.59282i
$844$		0			0
$845$	−8.18965	−	27.8914i	−0.281733	−	0.959493i
$846$	102.388	+	118.162i	3.52017	+	4.06249i
$847$	15.3528	−	52.2868i	0.527529	−	1.79660i
$848$		0			0
$849$	−89.5125	−	12.8699i	−3.07206	−	0.441695i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$853$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$854$	30.9060	+	67.6746i	1.05758	+	2.31578i
$855$		0			0
$856$	42.9800	−	37.2424i	1.46903	−	1.27292i
$857$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$857$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$858$		0			0
$859$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$859$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$860$	−1.61568	+	1.86460i	−0.0550944	+	0.0635823i
$861$	−68.5002	−	106.588i	−2.33448	−	3.63252i
$862$		0			0
$863$	6.21193	+	43.2049i	0.211457	+	1.47071i	0.768297	+	0.640094i	$0.221104\pi$
$863$	6.21193	+	43.2049i	0.211457	+	1.47071i	−0.556840	+	0.830620i	$0.687986\pi$
$864$	−80.8194	+	51.9395i	−2.74953	+	1.76702i
$865$		0			0
$866$		0			0
$867$	47.6427	+	30.6181i	1.61803	+	1.03985i
$868$		0			0
$869$		0			0
$870$	8.40070	−	28.6102i	0.284811	−	0.969975i
$871$		0			0
$872$	−38.9928	−	5.60631i	−1.32046	−	0.189854i
$873$		0			0
$874$		0			0
$875$	−55.3876			−1.87244
$876$		0			0
$877$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$877$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−18.9586	+	29.5001i	−0.638731	+	0.993885i	0.359424	+	0.933174i	$0.382973\pi$
$881$	−18.9586	+	29.5001i	−0.638731	+	0.993885i	−0.998155	+	0.0607108i	$0.980663\pi$
$882$	−83.4561	+	182.743i	−2.81011	+	6.15329i
$883$	−9.20823	+	10.6269i	−0.309882	+	0.357622i	−0.889232	−	0.457456i	$-0.848761\pi$
$883$	−9.20823	+	10.6269i	−0.309882	+	0.357622i	0.579351	+	0.815078i	$0.303306\pi$
$884$		0			0
$885$		0			0
$886$	−8.45783	−	58.8255i	−0.284146	−	1.97628i
$887$	−17.4342	+	11.2043i	−0.585383	+	0.376203i	−0.799555	−	0.600593i	$-0.794931\pi$
$887$	−17.4342	+	11.2043i	−0.585383	+	0.376203i	0.214172	+	0.976796i	$0.431295\pi$
$888$		0			0
$889$	−98.6799	−	45.0656i	−3.30962	−	1.51145i
$890$	−9.02665	−	5.80108i	−0.302574	−	0.194452i
$891$		0			0
$892$	36.1543	+	41.7243i	1.21054	+	1.39703i
$893$		0			0
$894$	90.2810	−	41.2299i	3.01945	−	1.37894i
$895$		0			0
$896$		−	56.0484i		−	1.87244i
$897$		0			0
$898$	24.0554			0.802740
$899$		0			0
$900$	−33.6400	−	73.6613i	−1.12133	−	2.45538i
$901$		0			0
$902$		0			0
$903$	−8.73601	+	2.56512i	−0.290716	+	0.0853620i
$904$		0			0
$905$	−12.0441	+	26.3729i	−0.400359	+	0.876664i
$906$		0			0
$907$	6.89328	+	10.7261i	0.228888	+	0.356156i	0.936633	−	0.350311i	$-0.113924\pi$
$907$	6.89328	+	10.7261i	0.228888	+	0.356156i	−0.707746	+	0.706467i	$0.750288\pi$
$908$	22.0851	−	3.17536i	0.732921	−	0.105378i
$909$	0.758920	+	5.27841i	0.0251718	+	0.175074i
$910$		0			0
$911$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$911$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−51.8015	−	59.7821i	−1.71250	−	1.97633i
$916$	−9.95993	+	33.9204i	−0.329085	+	1.12076i
$917$		0			0
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$	8.69606	+	29.0582i	0.286701	+	0.958020i
$921$	74.5402			2.45618
$922$	0.578836	−	4.02589i	0.0190629	−	0.132586i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−15.6293	+	4.58917i	−0.513609	+	0.150809i
$927$	3.21847	−	5.00804i	0.105708	−	0.164486i
$928$	−6.65143	+	14.5646i	−0.218344	+	0.478106i
$929$	−39.7847	+	45.9140i	−1.30529	+	1.50639i	−0.590561	+	0.806993i	$0.701093\pi$
$929$	−39.7847	+	45.9140i	−1.30529	+	1.50639i	−0.714734	+	0.699397i	$0.753452\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−30.4183	−	26.3576i	−0.995318	−	0.862448i
$935$		0			0
$936$		0			0
$937$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$937$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$938$	12.4291	+	14.3439i	0.405823	+	0.468345i
$939$		0			0
$940$	55.5382	−	25.3634i	1.81146	−	0.827264i
$941$	30.7607	+	4.42273i	1.00277	+	0.144177i	0.624092	−	0.781351i	$-0.285469\pi$
$941$	30.7607	+	4.42273i	1.00277	+	0.144177i	0.378680	+	0.925528i	$0.376378\pi$
$942$		0			0
$943$	−24.2550	−	27.7004i	−0.789850	−	0.902049i
$944$		0			0
$945$	26.7736	−	186.214i	0.870945	−	6.05756i
$946$		0			0
$947$	0.706126	+	0.207337i	0.0229460	+	0.00673756i	0.293185	−	0.956056i	$-0.405285\pi$
$947$	0.706126	+	0.207337i	0.0229460	+	0.00673756i	−0.270239	+	0.962793i	$0.587103\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$953$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	16.7893	+	57.1791i	0.541873	+	1.84545i
$961$	−20.3007	−	23.4282i	−0.654861	−	0.755750i
$962$		0			0
$963$	−148.110	+	67.6393i	−4.77276	+	2.17965i
$964$	−7.62428	−	1.09621i	−0.245562	−	0.0353064i
$965$		0			0
$966$	−30.9782	+	107.561i	−0.996707	+	3.46071i
$967$	−34.0495			−1.09496			−0.547479	−	0.836820i	$-0.684412\pi$
$967$	−34.0495			−1.09496			−0.547479	+	0.836820i	$0.684412\pi$
$968$	4.42780	−	30.7960i	0.142315	−	0.989821i
$969$		0			0
$970$		0			0
$971$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$971$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$972$	108.606	−	31.8896i	3.48354	−	1.02286i
$973$		0			0
$974$	−25.9021	+	56.7178i	−0.829958	+	1.81735i
$975$		0			0
$976$	22.9645	+	35.7334i	0.735074	+	1.14380i
$977$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$977$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$978$	4.00675	+	27.8675i	0.128122	+	0.891105i
$979$		0			0
$980$	59.2898	+	51.3749i	1.89394	+	1.64111i
$981$	102.594	+	46.8530i	3.27557	+	1.49590i
$982$		0			0
$983$	−13.3387	−	45.4275i	−0.425439	−	1.44891i	−0.841838	−	0.539731i	$-0.818526\pi$
$983$	−13.3387	−	45.4275i	−0.425439	−	1.44891i	0.416399	−	0.909182i	$-0.363292\pi$
$984$	−47.3717	−	54.6698i	−1.51015	−	1.74281i
$985$		0			0
$986$		0			0
$987$	223.021	+	32.0656i	7.09885	+	1.02066i
$988$		0			0
$989$	−2.40097	+	1.11156i	−0.0763465	+	0.0353456i
$990$		0			0
$991$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$991$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−36.7763	+	57.2250i	−1.16530	+	1.81324i
$997$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$997$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.o.a.199.1	✓	40
4.3	odd	2	inner	460.2.o.a.199.4	yes	40
5.4	even	2	inner	460.2.o.a.199.4	yes	40
20.19	odd	2	CM	460.2.o.a.199.1	✓	40
23.20	odd	22	inner	460.2.o.a.319.1	yes	40
92.43	even	22	inner	460.2.o.a.319.4	yes	40
115.89	odd	22	inner	460.2.o.a.319.4	yes	40
460.319	even	22	inner	460.2.o.a.319.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.o.a.199.1	✓	40	1.1	even	1	trivial
460.2.o.a.199.1	✓	40	20.19	odd	2	CM
460.2.o.a.199.4	yes	40	4.3	odd	2	inner
460.2.o.a.199.4	yes	40	5.4	even	2	inner
460.2.o.a.319.1	yes	40	23.20	odd	22	inner
460.2.o.a.319.1	yes	40	460.319	even	22	inner
460.2.o.a.319.4	yes	40	92.43	even	22	inner
460.2.o.a.319.4	yes	40	115.89	odd	22	inner

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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.201264 + 1.39982i) q^{2} +(-1.38389 - 3.03031i) q^{3} +(-1.91899 - 0.563465i) q^{4} +(1.68991 - 1.46431i) q^{5} +(4.52041 - 1.32731i) q^{6} +(2.67835 - 4.16759i) q^{7} +(1.17497 - 2.57283i) q^{8} +(-5.30301 + 6.12000i) q^{9} +O(q^{10})\)	\(q+(-0.201264 + 1.39982i) q^{2} +(-1.38389 - 3.03031i) q^{3} +(-1.91899 - 0.563465i) q^{4} +(1.68991 - 1.46431i) q^{5} +(4.52041 - 1.32731i) q^{6} +(2.67835 - 4.16759i) q^{7} +(1.17497 - 2.57283i) q^{8} +(-5.30301 + 6.12000i) q^{9} +(1.70966 + 2.66028i) q^{10} +(0.948202 + 6.59489i) q^{12} +(5.29482 + 4.58798i) q^{14} +(-6.77597 - 3.09448i) q^{15} +(3.36501 + 2.16256i) q^{16} +(-7.49959 - 8.65498i) q^{18} +(-4.06800 + 1.85779i) q^{20} +(-16.3356 - 2.34871i) q^{21} +(-4.79577 + 0.0248509i) q^{23} -9.42249 q^{24} +(0.711574 - 4.94911i) q^{25} +(16.2950 + 4.78466i) q^{27} +(-7.48800 + 6.48839i) q^{28} +(2.71581 - 0.797434i) q^{29} +(5.69547 - 8.86232i) q^{30} +(-3.70445 + 4.27517i) q^{32} +(-1.57650 - 10.9648i) q^{35} +(13.6248 - 8.75613i) q^{36} +(-1.78183 - 6.06837i) q^{40} +(5.02751 + 5.80206i) q^{41} +(6.57553 - 22.3942i) q^{42} +(0.501832 - 0.229179i) q^{43} +18.1075i q^{45} +(0.930426 - 6.71821i) q^{46} -13.6525 q^{47} +(1.89640 - 13.1898i) q^{48} +(-7.28735 - 15.9571i) q^{49} +(6.78464 + 1.99215i) q^{50} +(-9.97725 + 21.8471i) q^{54} +(-7.57551 - 11.7877i) q^{56} +(0.569670 + 3.96214i) q^{58} +(11.2594 + 9.75629i) q^{60} +(9.65946 + 4.41133i) q^{61} +(11.3023 + 38.4922i) q^{63} +(-5.23889 - 6.04600i) q^{64} +(2.68147 + 0.385537i) q^{67} +(6.71214 + 14.4983i) q^{69} +15.6660 q^{70} +(9.51482 + 20.8345i) q^{72} +(-15.9821 + 4.69275i) q^{75} +(8.85323 - 1.27290i) q^{80} +(-4.59428 - 31.9539i) q^{81} +(-9.13369 + 5.86986i) q^{82} +(7.71589 + 6.68585i) q^{83} +(30.0244 + 13.7117i) q^{84} +(0.219809 + 0.748599i) q^{86} +(-6.17487 - 7.12618i) q^{87} +(-3.08649 + 1.40955i) q^{89} +(-25.3472 - 3.64438i) q^{90} +(9.21701 + 2.65456i) q^{92} +(2.74774 - 19.1110i) q^{94} +(18.0816 + 5.30925i) q^{96} +(23.8037 - 6.98939i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) \) 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9	\( 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9} - 16 q^{16} - 16 q^{24} + 20 q^{25} + 24 q^{29} + 8 q^{36} + 48 q^{41} - 4 q^{46} + 100 q^{49} - 276 q^{54} - 264 q^{56} - 32 q^{64} - 4 q^{69} - 40 q^{70} + 20 q^{81} + 352 q^{84} + 396 q^{86} - 56 q^{94} - 32 q^{96}+O(q^{100}) \) 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9 - 16 * q^16 - 16 * q^24 + 20 * q^25 + 24 * q^29 + 8 * q^36 + 48 * q^41 - 4 * q^46 + 100 * q^49 - 276 * q^54 - 264 * q^56 - 32 * q^64 - 4 * q^69 - 40 * q^70 + 20 * q^81 + 352 * q^84 + 396 * q^86 - 56 * q^94 - 32 * q^96

Introduction

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