LMFDB - Embedded newform 920.2.bn.a.339.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(19,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 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("920.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bn (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:	$7.34623698596$
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			339.1
Character	$\chi$	$=$	920.339
Dual form			920.2.bn.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587486 + 1.28641i) q^{2} +(-1.30972 - 1.51150i) q^{4} +(-1.20891 - 1.88110i) q^{5} +(-0.707757 - 0.101760i) q^{7} +(2.71386 - 0.796860i) q^{8} +(2.52376 + 1.62192i) q^{9} +O(q^{10})$	\(q+(-0.587486 + 1.28641i) q^{2} +(-1.30972 - 1.51150i) q^{4} +(-1.20891 - 1.88110i) q^{5} +(-0.707757 - 0.101760i) q^{7} +(2.71386 - 0.796860i) q^{8} +(2.52376 + 1.62192i) q^{9} +(3.13009 - 0.450039i) q^{10} +(-2.39252 + 1.09263i) q^{11} +(-1.02135 - 7.10362i) q^{13} +(0.546703 - 0.850686i) q^{14} +(-0.569259 + 3.95929i) q^{16} +(-3.56914 + 2.29374i) q^{18} +(-5.86368 + 5.08091i) q^{19} +(-1.25995 + 4.29098i) q^{20} -3.71967i q^{22} +(3.44081 + 3.34078i) q^{23} +(-2.07708 + 4.54816i) q^{25} +(9.73822 + 2.85940i) q^{26} +(0.773155 + 1.20305i) q^{28} +(-4.75885 - 3.05833i) q^{32} +(0.664194 + 1.45438i) q^{35} +(-0.853889 - 5.93893i) q^{36} +(-5.71030 + 8.88540i) q^{37} +(-3.09132 - 10.5281i) q^{38} +(-4.77978 - 4.14170i) q^{40} +(1.38359 - 0.889181i) q^{41} +(4.78504 + 2.18525i) q^{44} -6.70820i q^{45} +(-6.31905 + 2.46365i) q^{46} -13.6824 q^{47} +(-6.22589 - 1.82808i) q^{49} +(-4.63056 - 5.34396i) q^{50} +(-9.39944 + 10.8475i) q^{52} +(-8.14452 - 1.17101i) q^{53} +(4.94768 + 3.17968i) q^{55} +(-2.00184 + 0.287821i) q^{56} +(-0.607367 - 4.22433i) q^{59} +(-1.62116 - 1.40475i) q^{63} +(6.73003 - 4.32513i) q^{64} +(-12.1279 + 10.5089i) q^{65} -2.26114 q^{70} +(8.14157 + 2.39058i) q^{72} +(-8.07559 - 12.5659i) q^{74} +(15.3596 + 2.20837i) q^{76} +(1.80451 - 0.529851i) q^{77} +(8.13600 - 3.71558i) q^{80} +(3.73874 + 8.18669i) q^{81} +(0.331014 + 2.30225i) q^{82} +(-5.62228 + 4.87173i) q^{88} +(4.41127 - 15.0234i) q^{89} +(8.62953 + 3.94097i) q^{90} +5.13157i q^{91} +(0.543085 - 9.57628i) q^{92} +(8.03820 - 17.6012i) q^{94} +(16.6464 + 4.88781i) q^{95} +(6.00929 - 6.93509i) q^{98} +(-7.81030 - 1.12295i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{4} - 12 q^{9}+O(q^{10}) $ 40 * q - 8 * q^4 - 12 * q^9	$ 40 q - 8 q^{4} - 12 q^{9} - 16 q^{16} + 20 q^{25} + 32 q^{26} - 180 q^{35} - 24 q^{36} - 8 q^{41} - 24 q^{46} + 52 q^{49} + 252 q^{59} - 32 q^{64} - 36 q^{81} + 16 q^{94}+O(q^{100}) $ 40 * q - 8 * q^4 - 12 * q^9 - 16 * q^16 + 20 * q^25 + 32 * q^26 - 180 * q^35 - 24 * q^36 - 8 * q^41 - 24 * q^46 + 52 * q^49 + 252 * q^59 - 32 * q^64 - 36 * q^81 + 16 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$-1$	$e\left(\frac{7}{22}\right)$	$-1$	$-1$

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 $

$2$	−0.587486	+	1.28641i	−0.415415	+	0.909632i
$2$	−0.587486	+	1.28641i	−0.415415	+	0.909632i
$3$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$3$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$4$	−1.30972	−	1.51150i	−0.654861	−	0.755750i
$5$	−1.20891	−	1.88110i	−0.540641	−	0.841254i
$5$	−1.20891	−	1.88110i	−0.540641	−	0.841254i
$6$		0			0
$7$	−0.707757	−	0.101760i	−0.267507	−	0.0384617i	0.00725596	−	0.999974i	$-0.497690\pi$
$7$	−0.707757	−	0.101760i	−0.267507	−	0.0384617i	−0.274763	+	0.961512i	$0.588599\pi$
$8$	2.71386	−	0.796860i	0.959493	−	0.281733i
$9$	2.52376	+	1.62192i	0.841254	+	0.540641i
$10$	3.13009	−	0.450039i	0.989821	−	0.142315i
$11$	−2.39252	+	1.09263i	−0.721371	+	0.329439i	−0.742048	−	0.670347i	$-0.766145\pi$
$11$	−2.39252	+	1.09263i	−0.721371	+	0.329439i	0.0206766	+	0.999786i	$0.493418\pi$
$12$		0			0
$13$	−1.02135	−	7.10362i	−0.283271	−	1.97019i	−0.238251	−	0.971203i	$-0.576574\pi$
$13$	−1.02135	−	7.10362i	−0.283271	−	1.97019i	−0.0450190	−	0.998986i	$-0.514335\pi$
$14$	0.546703	−	0.850686i	0.146112	−	0.227355i
$15$		0			0
$16$	−0.569259	+	3.95929i	−0.142315	+	0.989821i
$17$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$17$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$18$	−3.56914	+	2.29374i	−0.841254	+	0.540641i
$19$	−5.86368	+	5.08091i	−1.34522	+	1.16564i	−0.374008	+	0.927425i	$0.622017\pi$
$19$	−5.86368	+	5.08091i	−1.34522	+	1.16564i	−0.971212	+	0.238215i	$0.923438\pi$
$20$	−1.25995	+	4.29098i	−0.281733	+	0.959493i
$21$		0			0
$22$		−	3.71967i		−	0.793036i
$23$	3.44081	+	3.34078i	0.717459	+	0.696601i
$23$	3.44081	+	3.34078i	0.717459	+	0.696601i
$24$		0			0
$25$	−2.07708	+	4.54816i	−0.415415	+	0.909632i
$26$	9.73822	+	2.85940i	1.90982	+	0.560774i
$27$		0			0
$28$	0.773155	+	1.20305i	0.146112	+	0.227355i
$29$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$29$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$30$		0			0
$31$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$31$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$32$	−4.75885	−	3.05833i	−0.841254	−	0.540641i
$33$		0			0
$34$		0			0
$35$	0.664194	+	1.45438i	0.112269	+	0.245835i
$36$	−0.853889	−	5.93893i	−0.142315	−	0.989821i
$37$	−5.71030	+	8.88540i	−0.938768	+	1.46075i	−0.0519407	+	0.998650i	$0.516541\pi$
$37$	−5.71030	+	8.88540i	−0.938768	+	1.46075i	−0.886827	+	0.462101i	$0.847096\pi$
$38$	−3.09132	−	10.5281i	−0.501479	−	1.70788i
$39$		0			0
$40$	−4.77978	−	4.14170i	−0.755750	−	0.654861i
$41$	1.38359	−	0.889181i	0.216081	−	0.138867i	−0.428123	−	0.903720i	$-0.640825\pi$
$41$	1.38359	−	0.889181i	0.216081	−	0.138867i	0.644204	+	0.764854i	$0.277189\pi$
$42$		0			0
$43$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$43$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$44$	4.78504	+	2.18525i	0.721371	+	0.329439i
$45$		−	6.70820i		−	1.00000i
$46$	−6.31905	+	2.46365i	−0.931694	+	0.363245i
$47$	−13.6824			−1.99578			−0.997890	−	0.0649306i	$-0.979317\pi$
$47$	−13.6824			−1.99578			−0.997890	+	0.0649306i	$0.979317\pi$
$48$		0			0
$49$	−6.22589	−	1.82808i	−0.889412	−	0.261155i
$50$	−4.63056	−	5.34396i	−0.654861	−	0.755750i
$51$		0			0
$52$	−9.39944	+	10.8475i	−1.30347	+	1.50428i
$53$	−8.14452	−	1.17101i	−1.11874	−	0.160850i	−0.441957	−	0.897036i	$-0.645716\pi$
$53$	−8.14452	−	1.17101i	−1.11874	−	0.160850i	−0.676779	+	0.736186i	$0.736625\pi$
$54$		0			0
$55$	4.94768	+	3.17968i	0.667145	+	0.428748i
$56$	−2.00184	+	0.287821i	−0.267507	+	0.0384617i
$57$		0			0
$58$		0			0
$59$	−0.607367	−	4.22433i	−0.0790725	−	0.549961i	−0.990395	−	0.138268i	$-0.955847\pi$
$59$	−0.607367	−	4.22433i	−0.0790725	−	0.549961i	0.911322	−	0.411693i	$-0.135063\pi$
$60$		0			0
$61$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$61$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$62$		0			0
$63$	−1.62116	−	1.40475i	−0.204247	−	0.176981i
$64$	6.73003	−	4.32513i	0.841254	−	0.540641i
$65$	−12.1279	+	10.5089i	−1.50428	+	1.30347i
$66$		0			0
$67$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$67$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$68$		0			0
$69$		0			0
$70$	−2.26114			−0.270258
$71$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$71$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$72$	8.14157	+	2.39058i	0.959493	+	0.281733i
$73$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$73$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$74$	−8.07559	−	12.5659i	−0.938768	−	1.46075i
$75$		0			0
$76$	15.3596	+	2.20837i	1.76186	+	0.253318i
$77$	1.80451	−	0.529851i	0.205643	−	0.0603822i
$78$		0			0
$79$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$79$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$80$	8.13600	−	3.71558i	0.909632	−	0.415415i
$81$	3.73874	+	8.18669i	0.415415	+	0.909632i
$82$	0.331014	+	2.30225i	0.0365544	+	0.254241i
$83$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$83$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−5.62228	+	4.87173i	−0.599337	+	0.519328i
$89$	4.41127	−	15.0234i	0.467594	−	1.59248i	−0.301581	−	0.953440i	$-0.597514\pi$
$89$	4.41127	−	15.0234i	0.467594	−	1.59248i	0.769175	−	0.639038i	$-0.220667\pi$
$90$	8.62953	+	3.94097i	0.909632	+	0.415415i
$91$			5.13157i			0.537935i
$92$	0.543085	−	9.57628i	0.0566205	−	0.998396i
$93$		0			0
$94$	8.03820	−	17.6012i	0.829077	−	1.81542i
$95$	16.6464	+	4.88781i	1.70788	+	0.501479i
$96$		0			0
$97$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$97$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$98$	6.00929	−	6.93509i	0.607030	−	0.700550i
$99$	−7.81030	−	1.12295i	−0.784964	−	0.112861i
$100$	9.59493	−	2.81733i	0.959493	−	0.281733i
$101$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$101$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$102$		0			0
$103$	−13.1590	+	6.00954i	−1.29660	+	0.592137i	−0.939698	−	0.342005i	$-0.888894\pi$
$103$	−13.1590	+	6.00954i	−1.29660	+	0.592137i	−0.356901	+	0.934142i	$0.616167\pi$
$104$	−8.43238	−	18.4643i	−0.826863	−	1.81058i
$105$		0			0
$106$	6.29119	−	9.78928i	0.611054	−	0.950819i
$107$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$107$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$108$		0			0
$109$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$109$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$110$	−6.99707	+	4.49674i	−0.667145	+	0.428748i
$111$		0			0
$112$	0.805795	−	2.74429i	0.0761405	−	0.259311i
$113$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$113$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$114$		0			0
$115$	2.12472	−	10.5112i	0.198131	−	0.980176i
$116$		0			0
$117$	8.94389	−	19.5844i	0.826863	−	1.81058i
$118$	5.79106	+	1.70041i	0.533110	+	0.156535i
$119$		0			0
$120$		0			0
$121$	−2.67316	+	3.08499i	−0.243015	+	0.280454i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.0665	−	1.59113i	0.989821	−	0.142315i
$126$	2.75949	−	1.26022i	0.245835	−	0.112269i
$127$	7.96144	+	17.4331i	0.706463	+	1.54694i	0.831954	+	0.554844i	$0.187222\pi$
$127$	7.96144	+	17.4331i	0.706463	+	1.54694i	−0.125491	+	0.992095i	$0.540051\pi$
$128$	1.61011	+	11.1986i	0.142315	+	0.989821i
$129$		0			0
$130$	−6.39381	−	21.7753i	−0.560774	−	1.90982i
$131$	−3.25768	+	22.6577i	−0.284625	+	1.97961i	−0.136702	+	0.990612i	$0.543650\pi$
$131$	−3.25768	+	22.6577i	−0.284625	+	1.97961i	−0.147923	+	0.988999i	$0.547259\pi$
$132$		0			0
$133$	4.66710	−	2.99936i	0.404689	−	0.260078i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0			−	1.00000i	$-0.5\pi$
$137$		0			0				1.00000i	$0.5\pi$
$138$		0			0
$139$	5.17129			0.438623			0.219312	−	0.975655i	$-0.429619\pi$
$139$	5.17129			0.438623			0.219312	+	0.975655i	$0.429619\pi$
$140$	1.32839	−	2.90876i	0.112269	−	0.245835i
$141$		0			0
$142$		0			0
$143$	10.2052	+	15.8796i	0.853401	+	1.32792i
$144$	−7.85833	+	9.06899i	−0.654861	+	0.755750i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	20.9092	−	3.00629i	1.71872	−	0.247115i
$149$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$149$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$150$		0			0
$151$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$151$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$152$	−11.8644	+	18.4614i	−0.962331	+	1.49742i
$153$		0			0
$154$	−0.378514	+	2.63262i	−0.0305015	+	0.212143i
$155$		0			0
$156$		0			0
$157$	−13.8056	+	11.9627i	−1.10181	+	0.954724i	−0.999200	−	0.0399981i	$-0.987265\pi$
$157$	−13.8056	+	11.9627i	−1.10181	+	0.954724i	−0.102610	+	0.994722i	$0.532719\pi$
$158$		0			0
$159$		0			0
$160$			12.6491i			1.00000i
$161$	−2.09530	−	2.71460i	−0.165133	−	0.213940i
$162$	−12.7279			−1.00000
$163$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$163$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$164$	−3.15612	−	0.926720i	−0.246451	−	0.0723647i
$165$		0			0
$166$		0			0
$167$	9.58895	−	11.0662i	0.742016	−	0.856332i	−0.251753	−	0.967791i	$-0.581007\pi$
$167$	9.58895	−	11.0662i	0.742016	−	0.856332i	0.993769	+	0.111460i	$0.0355526\pi$
$168$		0			0
$169$	−36.9449	+	10.8480i	−2.84191	+	0.834461i
$170$		0			0
$171$	−23.0394	+	3.31256i	−1.76186	+	0.253318i
$172$		0			0
$173$	−10.3676	−	22.7019i	−0.788235	−	1.72599i	−0.681635	−	0.731693i	$-0.738731\pi$
$173$	−10.3676	−	22.7019i	−0.788235	−	1.72599i	−0.106601	−	0.994302i	$-0.533997\pi$
$174$		0			0
$175$	1.93289	−	3.00763i	0.146112	−	0.227355i
$176$	−2.96406	−	10.0946i	−0.223424	−	0.760913i
$177$		0			0
$178$	16.7348	+	14.5008i	1.25432	+	1.08688i
$179$	18.3445	−	11.7893i	1.37113	−	0.881174i	0.372236	−	0.928138i	$-0.378591\pi$
$179$	18.3445	−	11.7893i	1.37113	−	0.881174i	0.998897	+	0.0469643i	$0.0149547\pi$
$180$	−10.1394	+	8.78588i	−0.755750	+	0.654861i
$181$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$181$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$182$	−6.60132	−	3.01472i	−0.489323	−	0.223466i
$183$		0			0
$184$	12.0000	+	6.32456i	0.884652	+	0.466252i
$185$	23.6176			1.73640
$186$		0			0
$187$		0			0
$188$	17.9201	+	20.6809i	1.30696	+	1.50831i
$189$		0			0
$190$	−16.0672	+	18.5426i	−1.16564	+	1.34522i
$191$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$191$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$192$		0			0
$193$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$193$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$194$		0			0
$195$		0			0
$196$	5.39103	+	11.8047i	0.385073	+	0.843193i
$197$	−2.80615	−	19.5172i	−0.199930	−	1.39054i	−0.804481	−	0.593978i	$-0.797557\pi$
$197$	−2.80615	−	19.5172i	−0.199930	−	1.39054i	0.604551	−	0.796566i	$-0.293352\pi$
$198$	6.03302	−	9.38756i	0.428748	−	0.667145i
$199$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$199$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$200$	−2.01264	+	13.9982i	−0.142315	+	0.989821i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−3.34528	−	1.52774i	−0.233644	−	0.106702i
$206$		−	20.4585i		−	1.42541i
$207$	3.26529	+	14.0121i	0.226954	+	0.973906i
$208$	28.7067			1.99045
$209$	8.47743	−	18.5630i	0.586396	−	1.28403i
$210$		0			0
$211$	−5.40236	−	6.23466i	−0.371914	−	0.429212i	0.538682	−	0.842509i	$-0.318922\pi$
$211$	−5.40236	−	6.23466i	−0.371914	−	0.429212i	−0.910596	+	0.413297i	$0.864377\pi$
$212$	8.89708	+	13.8441i	0.611054	+	0.950819i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−1.67400	−	11.6429i	−0.112861	−	0.784964i
$221$		0			0
$222$		0			0
$223$	1.80701	−	12.5680i	0.121006	−	0.841617i	−0.835414	−	0.549622i	$-0.814772\pi$
$223$	1.80701	−	12.5680i	0.121006	−	0.841617i	0.956420	−	0.291995i	$-0.0943191\pi$
$224$	3.05689	+	2.64881i	0.204247	+	0.176981i
$225$	−12.6188	+	8.10961i	−0.841254	+	0.540641i
$226$		0			0
$227$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$227$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$228$		0			0
$229$		0			0			−	1.00000i	$-0.5\pi$
$229$		0			0				1.00000i	$0.5\pi$
$230$	12.2735	+	8.90845i	0.809293	+	0.587406i
$231$		0			0
$232$		0			0
$233$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$233$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$234$	19.9392	+	23.0111i	1.30347	+	1.50428i
$235$	16.5408	+	25.7379i	1.07900	+	1.67896i
$236$	−5.58959	+	6.45073i	−0.363852	+	0.419907i
$237$		0			0
$238$		0			0
$239$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$239$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$240$		0			0
$241$	12.9318	−	5.90574i	0.833008	−	0.380422i	0.0471945	−	0.998886i	$-0.484972\pi$
$241$	12.9318	−	5.90574i	0.833008	−	0.380422i	0.785813	+	0.618464i	$0.212245\pi$
$242$	−2.39813	−	5.25118i	−0.154158	−	0.337558i
$243$		0			0
$244$		0			0
$245$	4.08772	+	13.9215i	0.261155	+	0.889412i
$246$		0			0
$247$	42.0817	+	36.4640i	2.67759	+	2.32015i
$248$		0			0
$249$		0			0
$250$	−4.45458	+	15.1709i	−0.281733	+	0.959493i
$251$	25.1823	+	11.5004i	1.58949	+	0.725897i	0.996831	−	0.0795541i	$-0.0253496\pi$
$251$	25.1823	+	11.5004i	1.58949	+	0.725897i	0.592662	+	0.805451i	$0.298077\pi$
$252$			4.29021i			0.270258i
$253$	−11.8824	−	4.23336i	−0.747042	−	0.266149i
$254$	−27.1034			−1.70062
$255$		0			0
$256$	−15.3519	−	4.50772i	−0.959493	−	0.281733i
$257$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$257$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$258$		0			0
$259$	4.94569	−	5.70763i	0.307310	−	0.354655i
$260$	31.7684	+	4.56760i	1.97019	+	0.283271i
$261$		0			0
$262$	−27.2333	−	17.5018i	−1.68248	−	1.08126i
$263$	−30.6081	+	4.40079i	−1.88738	+	0.271364i	−0.986630	−	0.162976i	$-0.947891\pi$
$263$	−30.6081	+	4.40079i	−1.88738	+	0.271364i	−0.900749	+	0.434340i	$0.856981\pi$
$264$		0			0
$265$	7.64321	+	16.7363i	0.469519	+	1.02810i
$266$	1.11657	+	7.76590i	0.0684612	+	0.476158i
$267$		0			0
$268$		0			0
$269$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$269$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$270$		0			0
$271$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$271$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	13.1510i		−	0.793036i
$276$		0			0
$277$	19.6750			1.18216			0.591080	−	0.806613i	$-0.298702\pi$
$277$	19.6750			1.18216			0.591080	+	0.806613i	$0.298702\pi$
$278$	−3.03806	+	6.65242i	−0.182211	+	0.398986i
$279$		0			0
$280$	2.96146	+	3.41771i	0.176981	+	0.204247i
$281$	−9.77227	−	15.2060i	−0.582965	−	0.907111i	0.417034	−	0.908891i	$-0.363070\pi$
$281$	−9.77227	−	15.2060i	−0.582965	−	0.907111i	−0.999998	+	0.00178007i	$0.999433\pi$
$282$		0			0
$283$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$283$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$284$		0			0
$285$		0			0
$286$	−26.4231	+	3.79907i	−1.56243	+	0.224644i
$287$	−1.06973	+	0.488530i	−0.0631443	+	0.0288370i
$288$	−7.04983	−	15.4370i	−0.415415	−	0.909632i
$289$	2.41935	+	16.8270i	0.142315	+	0.989821i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−17.1724	−	14.8800i	−1.00322	−	0.869298i	−0.0117925	−	0.999930i	$-0.503754\pi$
$293$	−17.1724	−	14.8800i	−1.00322	−	0.869298i	−0.991431	+	0.130632i	$0.958299\pi$
$294$		0			0
$295$	−7.21214	+	6.24936i	−0.419907	+	0.363852i
$296$	−8.41652	+	28.6640i	−0.489200	+	1.66606i
$297$		0			0
$298$		0			0
$299$	20.2174	−	27.8543i	1.16920	−	1.61086i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−16.7788	−	26.1083i	−0.962331	−	1.49742i
$305$		0			0
$306$		0			0
$307$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$307$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$308$	−3.16427	−	2.03355i	−0.180301	−	0.115873i
$309$		0			0
$310$		0			0
$311$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$311$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$312$		0			0
$313$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$313$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$314$	−7.27831	−	24.7876i	−0.410739	−	1.39885i
$315$	−0.682628	+	4.74778i	−0.0384617	+	0.267507i
$316$		0			0
$317$	18.0248	−	11.5839i	1.01238	−	0.650614i	0.0743686	−	0.997231i	$-0.476306\pi$
$317$	18.0248	−	11.5839i	1.01238	−	0.650614i	0.938007	+	0.346617i	$0.112670\pi$
$318$		0			0
$319$		0			0
$320$	−16.2720	−	7.43117i	−0.909632	−	0.415415i
$321$		0			0
$322$	4.72306	−	1.10064i	0.263206	−	0.0613360i
$323$		0			0
$324$	7.47747	−	16.3734i	0.415415	−	0.909632i
$325$	34.4298	+	10.1095i	1.90982	+	0.560774i
$326$		0			0
$327$		0			0
$328$	3.04632	−	3.51564i	0.168205	−	0.194119i
$329$	9.68380	+	1.39232i	0.533885	+	0.0767611i
$330$		0			0
$331$	−22.0241	−	14.1540i	−1.21055	−	0.777974i	−0.229801	−	0.973238i	$-0.573807\pi$
$331$	−22.0241	−	14.1540i	−1.21055	−	0.777974i	−0.980751	+	0.195264i	$0.937444\pi$
$332$		0			0
$333$	−28.8229	+	13.1630i	−1.57948	+	0.721326i
$334$	8.60240	+	18.8366i	0.470702	+	1.03069i
$335$		0			0
$336$		0			0
$337$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$337$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$338$	7.74957	−	53.8994i	0.421521	−	2.93174i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	9.27397	−	31.5842i	0.501479	−	1.70788i
$343$	8.77332	+	4.00664i	0.473715	+	0.216338i
$344$		0			0
$345$		0			0
$346$	35.2949			1.89746
$347$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$347$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$348$		0			0
$349$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$349$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$350$	2.73351	+	4.25343i	0.146112	+	0.227355i
$351$		0			0
$352$	14.7272	+	2.11746i	0.784964	+	0.112861i
$353$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$353$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$354$		0			0
$355$		0			0
$356$	−28.4854	+	13.0089i	−1.50972	+	0.689468i
$357$		0			0
$358$	4.38879	+	30.5247i	0.231955	+	1.61328i
$359$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$359$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$360$	−5.34550	−	18.2051i	−0.281733	−	0.959493i
$361$	5.86314	−	40.7790i	0.308586	−	2.14627i
$362$		0			0
$363$		0			0
$364$	7.75637	−	6.72093i	0.406544	−	0.352272i
$365$		0			0
$366$		0			0
$367$		−	1.99021i		−	0.103888i	−0.998650	−	0.0519440i	$-0.983458\pi$
$367$		−	1.99021i		−	0.103888i	0.998650	−	0.0519440i	$-0.0165417\pi$
$368$	−15.1858	+	11.7214i	−0.791616	+	0.611019i
$369$	4.93404			0.256856
$370$	−13.8750	+	30.3820i	−0.721326	+	1.57948i
$371$	5.64518	+	1.65758i	0.293083	+	0.0860570i
$372$		0			0
$373$	20.3287	+	31.6320i	1.05258	+	1.63784i	0.718837	+	0.695179i	$0.244675\pi$
$373$	20.3287	+	31.6320i	1.05258	+	1.63784i	0.333741	+	0.942665i	$0.391689\pi$
$374$		0			0
$375$		0			0
$376$	−37.1320	+	10.9029i	−1.91494	+	0.562276i
$377$		0			0
$378$		0			0
$379$	−35.3023	+	16.1220i	−1.81336	+	0.828133i	−0.873231	+	0.487306i	$0.837980\pi$
$379$	−35.3023	+	16.1220i	−1.81336	+	0.828133i	−0.940126	+	0.340827i	$0.889293\pi$
$380$	−14.4142	−	31.5626i	−0.739431	−	1.61913i
$381$		0			0
$382$		0			0
$383$	−5.35368	−	18.2330i	−0.273560	−	0.931660i	−0.975606	−	0.219529i	$-0.929548\pi$
$383$	−5.35368	−	18.2330i	−0.273560	−	0.931660i	0.702046	−	0.712132i	$-0.252270\pi$
$384$		0			0
$385$	−3.17819	−	2.75392i	−0.161976	−	0.140353i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$389$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$390$		0			0
$391$		0			0
$392$	−18.3529			−0.926961
$393$		0			0
$394$	26.7558	+	7.85621i	1.34794	+	0.395790i
$395$		0			0
$396$	8.53197	+	13.2760i	0.428748	+	0.667145i
$397$	−8.10822	+	9.35739i	−0.406940	+	0.469634i	−0.921814	−	0.387632i	$-0.873293\pi$
$397$	−8.10822	+	9.35739i	−0.406940	+	0.469634i	0.514874	+	0.857266i	$0.327839\pi$
$398$		0			0
$399$		0			0
$400$	−16.8251	−	10.8128i	−0.841254	−	0.540641i
$401$	39.4153	−	5.66707i	1.96831	−	0.283000i	0.968946	−	0.247272i	$-0.0795342\pi$
$401$	39.4153	−	5.66707i	1.96831	−	0.283000i	0.999362	−	0.0357278i	$-0.0113749\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	10.8802	−	16.9299i	0.540641	−	0.841254i
$406$		0			0
$407$	3.95357	−	27.4977i	0.195971	−	1.36301i
$408$		0			0
$409$	24.1459	−	15.5176i	1.19394	−	0.767298i	0.216041	−	0.976384i	$-0.430685\pi$
$409$	24.1459	−	15.5176i	1.19394	−	0.767298i	0.977897	+	0.209087i	$0.0670491\pi$
$410$	3.93061	−	3.40589i	0.194119	−	0.168205i
$411$		0			0
$412$	26.3181	+	12.0191i	1.29660	+	0.592137i
$413$			3.05161i			0.150160i
$414$	−19.9436	−	4.03136i	−0.980176	−	0.198131i
$415$		0			0
$416$	−16.8648	+	36.9287i	−0.826863	+	1.81058i
$417$		0			0
$418$	18.8993	+	21.8110i	0.924395	+	1.06681i
$419$	−19.8886	−	30.9472i	−0.971620	−	1.51187i	−0.854958	−	0.518698i	$-0.826417\pi$
$419$	−19.8886	−	30.9472i	−0.971620	−	1.51187i	−0.116662	−	0.993172i	$-0.537219\pi$
$420$		0			0
$421$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$421$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$422$	11.1942	−	3.28690i	0.544924	−	0.160004i
$423$	−34.5310	−	22.1918i	−1.67896	−	1.07900i
$424$	−23.0362	+	3.31210i	−1.11874	+	0.160850i
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$431$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$432$		0			0
$433$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$433$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−37.1500	−	2.10683i	−1.77713	−	0.100783i
$438$		0			0
$439$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$439$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$440$	15.9610	+	4.68658i	0.760913	+	0.223424i
$441$	−12.7476	−	14.7116i	−0.607030	−	0.700550i
$442$		0			0
$443$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$443$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$444$		0			0
$445$	−33.5934	+	9.86390i	−1.59248	+	0.467594i
$446$	15.1061	+	9.70809i	0.715294	+	0.459691i
$447$		0			0
$448$	−5.20335	+	2.37629i	−0.245835	+	0.112269i
$449$	−1.30696	−	2.86183i	−0.0616791	−	0.135058i	0.876282	−	0.481798i	$-0.160016\pi$
$449$	−1.30696	−	2.86183i	−0.0616791	−	0.135058i	−0.937961	+	0.346740i	$0.887289\pi$
$450$	−3.01895	−	20.9973i	−0.142315	−	0.989821i
$451$	−2.33873	+	3.63913i	−0.110126	+	0.171360i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	9.65300	−	6.20361i	0.452540	−	0.290830i
$456$		0			0
$457$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$457$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$458$		0			0
$459$		0			0
$460$	−18.6705	+	10.5553i	−0.870515	+	0.492141i
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$	−18.0801	−	5.30880i	−0.840255	−	0.246721i	−0.166838	−	0.985984i	$-0.553356\pi$
$463$	−18.0801	−	5.30880i	−0.840255	−	0.246721i	−0.673417	+	0.739263i	$0.735174\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$467$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$468$	−41.3158	+	12.1314i	−1.90982	+	0.560774i
$469$		0			0
$470$	−42.8271	+	6.15760i	−1.97547	+	0.284029i
$471$		0			0
$472$	−5.01451	−	10.9802i	−0.230812	−	0.505407i
$473$		0			0
$474$		0			0
$475$	−10.9295	−	37.2224i	−0.501479	−	1.70788i
$476$		0			0
$477$	−18.6555	−	16.1651i	−0.854179	−	0.740150i
$478$		0			0
$479$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$479$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$480$		0			0
$481$	68.9507	+	31.4887i	3.14388	+	1.43576i
$482$			20.1051i			0.915764i
$483$		0			0
$484$	8.16406			0.371093
$485$		0			0
$486$		0			0
$487$	−28.8356	−	33.2781i	−1.30667	−	1.50797i	−0.704925	−	0.709281i	$-0.749020\pi$
$487$	−28.8356	−	33.2781i	−1.30667	−	1.50797i	−0.601741	−	0.798692i	$-0.705526\pi$
$488$		0			0
$489$		0			0
$490$	−20.3103	−	2.92018i	−0.917526	−	0.131920i
$491$	30.8465	−	9.05735i	1.39208	−	0.408752i	0.502125	−	0.864795i	$-0.332552\pi$
$491$	30.8465	−	9.05735i	1.39208	−	0.408752i	0.889958	+	0.456043i	$0.150734\pi$
$492$		0			0
$493$		0			0
$494$	−71.6302	+	32.7124i	−3.22279	+	1.47180i
$495$	7.32956	+	16.0495i	0.329439	+	0.721371i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	6.11489	−	42.5300i	0.273740	−	1.90391i	−0.134298	−	0.990941i	$-0.542878\pi$
$499$	6.11489	−	42.5300i	0.273740	−	1.90391i	0.408039	−	0.912965i	$-0.366213\pi$
$500$	−16.8991	−	14.6431i	−0.755750	−	0.654861i
$501$		0			0
$502$	−29.5885	+	25.6386i	−1.32060	+	1.14430i
$503$	−11.6414	+	39.6469i	−0.519064	+	1.76777i	0.113797	+	0.993504i	$0.463699\pi$
$503$	−11.6414	+	39.6469i	−0.519064	+	1.76777i	−0.632861	+	0.774265i	$0.718120\pi$
$504$	−5.51899	−	2.52044i	−0.245835	−	0.112269i
$505$		0			0
$506$	12.4266	−	12.7987i	0.552430	−	0.568971i
$507$		0			0
$508$	15.9229	−	34.8662i	0.706463	−	1.54694i
$509$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$509$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$510$		0			0
$511$		0			0
$512$	14.8178	−	17.1007i	0.654861	−	0.755750i
$513$		0			0
$514$		0			0
$515$	27.2126	+	17.4885i	1.19913	+	0.770635i
$516$		0			0
$517$	32.7353	−	14.9497i	1.43970	−	0.657488i
$518$	4.43685	+	9.71535i	0.194944	+	0.426868i
$519$		0			0
$520$	−24.5393	+	38.1839i	−1.07612	+	1.67447i
$521$	−12.7583	−	43.4509i	−0.558953	−	1.90362i	−0.400658	−	0.916228i	$-0.631218\pi$
$521$	−12.7583	−	43.4509i	−0.558953	−	1.90362i	−0.158295	−	0.987392i	$-0.550600\pi$
$522$		0			0
$523$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$523$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$524$	38.5137	−	24.7513i	1.68248	−	1.08126i
$525$		0			0
$526$	12.3206	−	41.9601i	0.537204	−	1.82955i
$527$		0			0
$528$		0			0
$529$	0.678358	+	22.9900i	0.0294938	+	0.999565i
$530$	−26.0201			−1.13024
$531$	5.31869	−	11.6463i	0.230812	−	0.505407i
$532$	−10.6461	−	3.12599i	−0.461568	−	0.135529i
$533$	−7.72953	−	8.92036i	−0.334803	−	0.386384i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	16.8930	−	2.42884i	0.727631	−	0.104618i
$540$		0			0
$541$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$541$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$547$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$548$		0			0
$549$		0			0
$550$	16.9177	+	7.72603i	0.721371	+	0.329439i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−11.5588	+	25.3103i	−0.491087	+	1.07533i
$555$		0			0
$556$	−6.77295	−	7.81640i	−0.287237	−	0.331489i
$557$	13.8527	+	21.5552i	0.586957	+	0.913323i	0.999997	+	0.00260984i	$0.000830740\pi$
$557$	13.8527	+	21.5552i	0.586957	+	0.913323i	−0.413040	+	0.910713i	$0.635533\pi$
$558$		0			0
$559$		0			0
$560$	−6.13641	+	1.80181i	−0.259311	+	0.0761405i
$561$		0			0
$562$	25.3022	−	3.63791i	1.06731	−	0.153456i
$563$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$563$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.81304	−	6.17464i	−0.0761405	−	0.259311i
$568$		0			0
$569$	−9.55956	−	8.28341i	−0.400758	−	0.347258i	0.431045	−	0.902331i	$-0.358145\pi$
$569$	−9.55956	−	8.28341i	−0.400758	−	0.347258i	−0.831802	+	0.555072i	$0.812691\pi$
$570$		0			0
$571$	−26.2733	+	22.7660i	−1.09950	+	0.952726i	−0.999108	−	0.0422218i	$-0.986556\pi$
$571$	−26.2733	+	22.7660i	−1.09950	+	0.952726i	−0.100396	+	0.994948i	$0.532011\pi$
$572$	10.6360	−	36.2230i	0.444714	−	1.51456i
$573$		0			0
$574$		−	1.66312i		−	0.0694174i
$575$	−22.3412	+	8.71030i	−0.931694	+	0.363245i
$576$	24.0000			1.00000
$577$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$577$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$578$	−23.0678	−	6.77331i	−0.959493	−	0.281733i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	20.7654	−	6.09727i	0.860014	−	0.252523i
$584$		0			0
$585$	−47.6525	+	6.85140i	−1.97019	+	0.283271i
$586$	29.2304	−	13.3491i	1.20750	−	0.551445i
$587$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$587$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$588$		0			0
$589$		0			0
$590$	−3.80223	−	12.9492i	−0.156535	−	0.533110i
$591$		0			0
$592$	−31.9292	−	27.6668i	−1.31228	−	1.13710i
$593$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$593$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	23.9547	+	42.3719i	0.979582	+	1.73272i
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$		0			0
$601$	−45.5049	−	13.3615i	−1.85619	−	0.545025i	−0.999578	−	0.0290573i	$-0.990749\pi$
$601$	−45.5049	−	13.3615i	−1.85619	−	0.545025i	−0.856608	−	0.515968i	$-0.827432\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	9.03479	+	1.29901i	0.367316	+	0.0528121i
$606$		0			0
$607$	−20.3723	−	13.0925i	−0.826886	−	0.531407i	0.0574012	−	0.998351i	$-0.481719\pi$
$607$	−20.3723	−	13.0925i	−0.826886	−	0.531407i	−0.884287	+	0.466944i	$0.845355\pi$
$608$	43.4434	−	6.24622i	1.76186	−	0.253318i
$609$		0			0
$610$		0			0
$611$	13.9744	+	97.1944i	0.565345	+	3.93206i
$612$		0			0
$613$	−3.54990	−	12.0898i	−0.143379	−	0.488304i	0.856220	−	0.516611i	$-0.172807\pi$
$613$	−3.54990	−	12.0898i	−0.143379	−	0.488304i	−0.999599	+	0.0283068i	$0.990988\pi$
$614$		0			0
$615$		0			0
$616$	4.47496	−	2.87588i	0.180301	−	0.115873i
$617$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$617$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$618$		0			0
$619$	17.2591	+	7.88195i	0.693700	+	0.316802i	0.730880	−	0.682506i	$-0.239110\pi$
$619$	17.2591	+	7.88195i	0.693700	+	0.316802i	−0.0371796	+	0.999309i	$0.511837\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−4.65089	+	10.1840i	−0.186334	+	0.408015i
$624$		0			0
$625$	−16.3715	−	18.8937i	−0.654861	−	0.755750i
$626$		0			0
$627$		0			0
$628$	36.1631	+	5.19947i	1.44306	+	0.207481i
$629$		0			0
$630$	−5.70658	−	3.66739i	−0.227355	−	0.146112i
$631$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$631$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$632$		0			0
$633$		0			0
$634$	4.31231	+	29.9927i	0.171264	+	1.19116i
$635$	23.1688	−	36.0513i	0.919425	−	1.43065i
$636$		0			0
$637$	−6.62723	+	46.0934i	−0.262581	+	1.82629i
$638$		0			0
$639$		0			0
$640$	19.1191	−	16.5668i	0.755750	−	0.654861i
$641$	−13.8360	+	47.1211i	−0.546489	+	1.86117i	−0.0394976	+	0.999220i	$0.512576\pi$
$641$	−13.8360	+	47.1211i	−0.546489	+	1.86117i	−0.506991	+	0.861951i	$0.669242\pi$
$642$		0			0
$643$		0			0			−	1.00000i	$-0.5\pi$
$643$		0			0				1.00000i	$0.5\pi$
$644$	−1.35886	+	6.72242i	−0.0535464	+	0.264900i
$645$		0			0
$646$		0			0
$647$	22.7278	+	6.67348i	0.893522	+	0.262362i	0.696090	−	0.717955i	$-0.254922\pi$
$647$	22.7278	+	6.67348i	0.893522	+	0.262362i	0.197432	+	0.980317i	$0.436740\pi$
$648$	16.6700	+	19.2382i	0.654861	+	0.755750i
$649$	6.06875	+	9.44317i	0.238219	+	0.370677i
$650$	−33.2320	+	38.3518i	−1.30347	+	1.50428i
$651$		0			0
$652$		0			0
$653$	−30.8907	−	19.8523i	−1.20885	−	0.776879i	−0.228382	−	0.973572i	$-0.573344\pi$
$653$	−30.8907	−	19.8523i	−1.20885	−	0.776879i	−0.980465	+	0.196692i	$0.936980\pi$
$654$		0			0
$655$	46.5596	−	21.2631i	1.81923	−	0.830817i
$656$	2.73290	+	5.98422i	0.106702	+	0.233644i
$657$		0			0
$658$	−7.48019	+	11.6394i	−0.291608	+	0.453751i
$659$	9.02556	+	30.7382i	0.351586	+	1.19739i	0.925586	+	0.378536i	$0.123573\pi$
$659$	9.02556	+	30.7382i	0.351586	+	1.19739i	−0.574001	+	0.818855i	$0.694609\pi$
$660$		0			0
$661$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$661$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$662$	31.1467	−	20.0168i	1.21055	−	0.777974i
$663$		0			0
$664$		0			0
$665$	−11.2842	−	5.15332i	−0.437582	−	0.199837i
$666$		−	44.8112i		−	1.73640i
$667$		0			0
$668$	−29.2855			−1.13309
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$673$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$674$		0			0
$675$		0			0
$676$	64.7842	+	41.6343i	2.49170	+	1.60132i
$677$	44.5819	−	6.40991i	1.71342	−	0.246353i	0.785430	−	0.618950i	$-0.212442\pi$
$677$	44.5819	−	6.40991i	1.71342	−	0.246353i	0.927993	+	0.372597i	$0.121533\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$683$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$684$	35.1821	+	30.4855i	1.34522	+	1.16564i
$685$		0			0
$686$	−10.3084	+	8.93228i	−0.393577	+	0.341036i
$687$		0			0
$688$		0			0
$689$			59.0516i			2.24969i
$690$		0			0
$691$	−46.2125			−1.75801			−0.879004	−	0.476815i	$-0.841791\pi$
$691$	−46.2125			−1.75801			−0.879004	+	0.476815i	$0.841791\pi$
$692$	−20.7352	+	45.4038i	−0.788235	+	1.72599i
$693$	5.41352	+	1.58955i	0.205643	+	0.0603822i
$694$		0			0
$695$	−6.25162	−	9.72771i	−0.237138	−	0.368993i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−7.07757	+	1.01760i	−0.267507	+	0.0384617i
$701$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$701$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$702$		0			0
$703$	−11.6625	−	81.1147i	−0.439861	−	3.05930i
$704$	−11.3760	+	17.7013i	−0.428748	+	0.667145i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$709$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$710$		0			0
$711$		0			0
$712$		−	44.2865i		−	1.65971i
$713$		0			0
$714$		0			0
$715$	17.5339	−	38.3940i	0.655732	−	1.43585i
$716$	−41.8457	−	12.2870i	−1.56385	−	0.459187i
$717$		0			0
$718$		0			0
$719$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$719$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$720$	26.5597	+	3.81871i	0.989821	+	0.142315i
$721$	9.92494	−	2.91423i	0.369624	−	0.108531i
$722$	49.0142	+	31.4995i	1.82412	+	1.17229i
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$	29.1025	−	45.2843i	1.07935	−	1.67950i	0.489421	−	0.872048i	$-0.337208\pi$
$727$	29.1025	−	45.2843i	1.07935	−	1.67950i	0.589930	−	0.807455i	$-0.299155\pi$
$728$	4.08914	+	13.9263i	0.151554	+	0.516145i
$729$	−3.84250	+	26.7252i	−0.142315	+	0.989821i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−15.1058	+	51.4456i	−0.557945	+	1.90019i	−0.145000	+	0.989432i	$0.546318\pi$
$733$	−15.1058	+	51.4456i	−0.557945	+	1.90019i	−0.412946	+	0.910756i	$0.635500\pi$
$734$	2.56023	+	1.16922i	0.0944998	+	0.0431566i
$735$		0			0
$736$	−6.15710	−	26.4214i	−0.226954	−	0.973906i
$737$		0			0
$738$	−2.89868	+	6.34722i	−0.106702	+	0.233644i
$739$	46.8684	+	13.7618i	1.72408	+	0.506236i	0.985752	−	0.168206i	$-0.0537973\pi$
$739$	46.8684	+	13.7618i	1.72408	+	0.506236i	0.738328	+	0.674441i	$0.235615\pi$
$740$	−30.9324	−	35.6979i	−1.13710	−	1.31228i
$741$		0			0
$742$	−5.44879	+	6.28824i	−0.200031	+	0.230849i
$743$	−30.3551	−	4.36440i	−1.11362	−	0.160114i	−0.439148	−	0.898415i	$-0.644720\pi$
$743$	−30.3551	−	4.36440i	−1.11362	−	0.160114i	−0.674472	+	0.738300i	$0.735629\pi$
$744$		0			0
$745$		0			0
$746$	−52.6347	+	7.56772i	−1.92709	+	0.277074i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$751$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$752$	7.78882	−	54.1724i	0.284029	−	1.97547i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	49.2746	+	22.5029i	1.79091	+	0.817883i	0.968507	+	0.248985i	$0.0800968\pi$
$757$	49.2746	+	22.5029i	1.79091	+	0.817883i	0.822407	+	0.568899i	$0.192630\pi$
$758$		−	54.8848i		−	1.99351i
$759$		0			0
$760$	49.0707			1.77998
$761$	9.89988	−	21.6777i	0.358870	−	0.785817i	−0.640963	−	0.767572i	$-0.721465\pi$
$761$	9.89988	−	21.6777i	0.358870	−	0.785817i	0.999834	−	0.0182449i	$-0.00580787\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	26.6003	+	3.82455i	0.961109	+	0.138187i
$767$	−29.3877	+	8.62901i	−1.06113	+	0.311576i
$768$		0			0
$769$	−43.4190	+	6.24271i	−1.56573	+	0.225118i	−0.869951	−	0.493138i	$-0.835850\pi$
$769$	−43.4190	+	6.24271i	−1.56573	+	0.225118i	−0.695779	+	0.718256i	$0.744941\pi$
$770$	5.40982	−	2.47058i	0.194956	−	0.0890336i
$771$		0			0
$772$		0			0
$773$	−30.0596	+	46.7736i	−1.08117	+	1.68233i	−0.528337	+	0.849035i	$0.677184\pi$
$773$	−30.0596	+	46.7736i	−1.08117	+	1.68233i	−0.552830	+	0.833294i	$0.686452\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−3.59510	+	12.2438i	−0.128808	+	0.438679i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	10.7821	−	23.6094i	0.385073	−	0.843193i
$785$	39.1927	+	11.5080i	1.39885	+	0.410739i
$786$		0			0
$787$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$787$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$788$	−25.8250	+	29.8036i	−0.919977	+	1.06171i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−22.0909	+	3.17619i	−0.784964	+	0.112861i
$793$		0			0
$794$	−7.27401	−	15.9279i	−0.258145	−	0.565259i
$795$		0			0
$796$		0			0
$797$	14.8585	+	50.6034i	0.526315	+	1.79246i	0.605787	+	0.795627i	$0.292858\pi$
$797$	14.8585	+	50.6034i	0.526315	+	1.79246i	−0.0794719	+	0.996837i	$0.525323\pi$
$798$		0			0
$799$		0			0
$800$	23.7942	−	15.2916i	0.841254	−	0.540641i
$801$	35.4998	−	30.7608i	1.25432	−	1.08688i
$802$	−15.8657	+	54.0337i	−0.560239	+	1.90800i
$803$		0			0
$804$		0			0
$805$	−2.57341	+	7.22318i	−0.0907006	+	0.254584i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−35.2195	−	40.6454i	−1.23825	−	1.42902i	−0.865366	−	0.501140i	$-0.832914\pi$
$809$	−35.2195	−	40.6454i	−1.23825	−	1.42902i	−0.372885	−	0.927878i	$-0.621631\pi$
$810$	15.3869	+	23.9425i	0.540641	+	0.841254i
$811$	−34.4509	+	39.7585i	−1.20973	+	1.39611i	−0.315251	+	0.949008i	$0.602089\pi$
$811$	−34.4509	+	39.7585i	−1.20973	+	1.39611i	−0.894484	+	0.447100i	$0.852457\pi$
$812$		0			0
$813$		0			0
$814$	33.0508	+	21.2404i	1.15843	+	0.744477i
$815$		0			0
$816$		0			0
$817$		0			0
$818$	5.77673	+	40.1780i	0.201979	+	1.40479i
$819$	−8.32301	+	12.9509i	−0.290830	+	0.452540i
$820$	2.07221	+	7.05730i	0.0723647	+	0.246451i
$821$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$821$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$822$		0			0
$823$	40.7591	−	26.1943i	1.42077	−	0.913076i	0.420792	−	0.907157i	$-0.361752\pi$
$823$	40.7591	−	26.1943i	1.42077	−	0.913076i	0.999982	−	0.00591934i	$-0.00188419\pi$
$824$	−30.9230	+	26.7949i	−1.07725	+	0.933446i
$825$		0			0
$826$	−3.92563	−	1.79278i	−0.136590	−	0.0623787i
$827$		0			0			−	1.00000i	$-0.5\pi$
$827$		0			0				1.00000i	$0.5\pi$
$828$	16.9026	−	23.2874i	0.587406	−	0.809293i
$829$		0			0		1.00000			$0$
$829$		0			0		−1.00000			$\pi$
$830$		0			0
$831$		0			0
$832$	−37.5977	−	43.3901i	−1.30347	−	1.50428i
$833$		0			0
$834$		0			0
$835$	−32.4089	−	4.65969i	−1.12156	−	0.161255i
$836$	−39.1610	+	11.4987i	−1.35441	+	0.397691i
$837$		0			0
$838$	51.4951	−	7.40388i	1.77887	−	0.255763i
$839$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$839$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$840$		0			0
$841$	−4.12713	−	28.7048i	−0.142315	−	0.989821i
$842$		0			0
$843$		0			0
$844$	−2.34809	+	16.3313i	−0.0808247	+	0.562148i
$845$	65.0691	+	56.3827i	2.23845	+	1.93963i
$846$	48.8343	−	31.3839i	1.67896	−	1.07900i
$847$	2.20588	−	1.91140i	0.0757949	−	0.0656766i
$848$	9.27269	−	31.5799i	0.318426	−	1.08446i
$849$		0			0
$850$		0			0
$851$	−49.3323	+	11.4961i	−1.69109	+	0.394082i
$852$		0			0
$853$	−22.9450	+	50.2425i	−0.785622	+	1.72027i	−0.0968435	+	0.995300i	$0.530875\pi$
$853$	−22.9450	+	50.2425i	−0.785622	+	1.72027i	−0.688778	+	0.724972i	$0.741853\pi$
$854$		0			0
$855$	34.0838	+	39.3348i	1.16564	+	1.34522i
$856$		0			0
$857$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$857$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$858$		0			0
$859$	−28.2757	+	8.30249i	−0.964754	+	0.283277i	−0.725917	−	0.687782i	$-0.758584\pi$
$859$	−28.2757	+	8.30249i	−0.964754	+	0.283277i	−0.238837	+	0.971060i	$0.576766\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	16.0225	+	35.0844i	0.545413	+	1.19429i	0.958891	+	0.283774i	$0.0915866\pi$
$863$	16.0225	+	35.0844i	0.545413	+	1.19429i	−0.413478	+	0.910514i	$0.635686\pi$
$864$		0			0
$865$	−30.1711	+	46.9471i	−1.02585	+	1.59625i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	24.5354	−	46.5526i	0.829921	−	1.57466i
$875$	−7.99434			−0.270258
$876$		0			0
$877$	49.2666	+	14.4660i	1.66361	+	0.488481i	0.972234	−	0.234009i	$-0.0751846\pi$
$877$	49.2666	+	14.4660i	1.66361	+	0.488481i	0.691381	+	0.722491i	$0.257003\pi$
$878$		0			0
$879$		0			0
$880$	−15.4058	+	17.7792i	−0.519328	+	0.599337i
$881$	28.1874	+	4.05273i	0.949656	+	0.136540i	0.599699	−	0.800226i	$-0.295287\pi$
$881$	28.1874	+	4.05273i	0.949656	+	0.136540i	0.349957	+	0.936766i	$0.386196\pi$
$882$	26.4142	−	7.75591i	0.889412	−	0.261155i
$883$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$883$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	6.76708	+	47.0661i	0.227216	+	1.58032i	0.709754	+	0.704450i	$0.248806\pi$
$887$	6.76708	+	47.0661i	0.227216	+	1.58032i	−0.482538	+	0.875875i	$0.660285\pi$
$888$		0			0
$889$	−3.86077	−	13.1486i	−0.129486	−	0.440989i
$890$	7.04656	−	49.0099i	0.236201	−	1.64281i
$891$	−17.8900	−	15.5018i	−0.599337	−	0.519328i
$892$	−21.3632	+	13.7293i	−0.715294	+	0.459691i
$893$	80.2291	−	69.5189i	2.68476	−	2.32636i
$894$		0			0
$895$	−44.3537	−	20.2557i	−1.48258	−	0.677072i
$896$		−	8.08970i		−	0.270258i
$897$		0			0
$898$	4.44932			0.148476
$899$		0			0
$900$	28.7848	+	8.45198i	0.959493	+	0.281733i
$901$		0			0
$902$	−3.30746	−	5.14651i	−0.110126	−	0.171360i
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$907$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$908$		0			0
$909$		0			0
$910$	2.30941	+	16.0623i	0.0765561	+	0.532459i
$911$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$911$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$	4.61130	−	15.7046i	0.152278	−	0.518613i
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$	−2.60979	−	30.2190i	−0.0860424	−	0.996291i
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−28.5515	−	44.4270i	−0.938768	−	1.46075i
$926$	17.4511	−	20.1397i	0.573480	−	0.661831i
$927$	−42.9573	−	6.17633i	−1.41090	−	0.202857i
$928$		0			0
$929$	26.8360	+	17.2465i	0.880461	+	0.565838i	0.900936	−	0.433952i	$-0.142881\pi$
$929$	26.8360	+	17.2465i	0.880461	+	0.565838i	−0.0204747	+	0.999790i	$0.506518\pi$
$930$		0			0
$931$	45.7949	−	20.9138i	1.50087	−	0.685424i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	8.66641	−	60.2762i	0.283271	−	1.97019i
$937$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$937$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$938$		0			0
$939$		0			0
$940$	17.2391	−	58.7108i	0.562276	−	1.91494i
$941$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$941$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$942$		0			0
$943$	7.73124	+	1.56278i	0.251764	+	0.0508910i
$944$	17.0711			0.555617
$945$		0			0
$946$		0			0
$947$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$947$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$948$		0			0
$949$		0			0
$950$	54.3043	+	7.80778i	1.76186	+	0.253318i
$951$		0			0
$952$		0			0
$953$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$953$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$954$	31.7549	−	14.5020i	1.02810	−	0.469519i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	26.0789	−	16.7599i	0.841254	−	0.540641i
$962$	−81.0151	+	70.2000i	−2.61203	+	2.26334i
$963$		0			0
$964$	−25.8635	−	11.8115i	−0.833008	−	0.380422i
$965$		0			0
$966$		0			0
$967$	−42.7436			−1.37454			−0.687271	−	0.726401i	$-0.741192\pi$
$967$	−42.7436			−1.37454			−0.687271	+	0.726401i	$0.741192\pi$
$968$	−4.79626	+	10.5024i	−0.154158	+	0.337558i
$969$		0			0
$970$		0			0
$971$	−32.6919	−	50.8696i	−1.04913	−	1.63248i	−0.728175	−	0.685391i	$-0.759631\pi$
$971$	−32.6919	−	50.8696i	−1.04913	−	1.63248i	−0.320959	−	0.947093i	$-0.604005\pi$
$972$		0			0
$973$	−3.66002	−	0.526231i	−0.117335	−	0.0168702i
$974$	59.7499	−	17.5441i	1.91451	−	0.562151i
$975$		0			0
$976$		0			0
$977$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$977$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$978$		0			0
$979$	5.86093	+	40.7636i	0.187316	+	1.30281i
$980$	15.6886	−	24.4119i	0.501153	−	0.779809i
$981$		0			0
$982$	−6.47037	+	45.0024i	−0.206478	+	1.43608i
$983$	−45.2358	−	39.1971i	−1.44280	−	1.25019i	−0.916585	−	0.399840i	$-0.869066\pi$
$983$	−45.2358	−	39.1971i	−1.44280	−	1.25019i	−0.526214	−	0.850352i	$-0.676389\pi$
$984$		0			0
$985$	−33.3215	+	28.8732i	−1.06171	+	0.919977i
$986$		0			0
$987$		0			0
$988$		−	111.364i		−	3.54296i
$989$		0			0
$990$	−24.9523			−0.793036
$991$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$991$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−60.5528	+	17.7799i	−1.91773	+	0.563095i	−0.948652	+	0.316322i	$0.897552\pi$
$997$	−60.5528	+	17.7799i	−1.91773	+	0.563095i	−0.969073	+	0.246773i	$0.920630\pi$
$998$	51.1188	+	32.8521i	1.61814	+	1.03991i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bn.a.339.1	yes	40
5.4	even	2	inner	920.2.bn.a.339.4	yes	40
8.3	odd	2	inner	920.2.bn.a.339.4	yes	40
23.19	odd	22	inner	920.2.bn.a.19.1	✓	40
40.19	odd	2	CM	920.2.bn.a.339.1	yes	40
115.19	odd	22	inner	920.2.bn.a.19.4	yes	40
184.19	even	22	inner	920.2.bn.a.19.4	yes	40
920.19	even	22	inner	920.2.bn.a.19.1	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bn.a.19.1	✓	40	23.19	odd	22	inner
920.2.bn.a.19.1	✓	40	920.19	even	22	inner
920.2.bn.a.19.4	yes	40	115.19	odd	22	inner
920.2.bn.a.19.4	yes	40	184.19	even	22	inner
920.2.bn.a.339.1	yes	40	1.1	even	1	trivial
920.2.bn.a.339.1	yes	40	40.19	odd	2	CM
920.2.bn.a.339.4	yes	40	5.4	even	2	inner
920.2.bn.a.339.4	yes	40	8.3	odd	2	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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bn (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587486 + 1.28641i) q^{2} +(-1.30972 - 1.51150i) q^{4} +(-1.20891 - 1.88110i) q^{5} +(-0.707757 - 0.101760i) q^{7} +(2.71386 - 0.796860i) q^{8} +(2.52376 + 1.62192i) q^{9} +O(q^{10})\)	\(q+(-0.587486 + 1.28641i) q^{2} +(-1.30972 - 1.51150i) q^{4} +(-1.20891 - 1.88110i) q^{5} +(-0.707757 - 0.101760i) q^{7} +(2.71386 - 0.796860i) q^{8} +(2.52376 + 1.62192i) q^{9} +(3.13009 - 0.450039i) q^{10} +(-2.39252 + 1.09263i) q^{11} +(-1.02135 - 7.10362i) q^{13} +(0.546703 - 0.850686i) q^{14} +(-0.569259 + 3.95929i) q^{16} +(-3.56914 + 2.29374i) q^{18} +(-5.86368 + 5.08091i) q^{19} +(-1.25995 + 4.29098i) q^{20} -3.71967i q^{22} +(3.44081 + 3.34078i) q^{23} +(-2.07708 + 4.54816i) q^{25} +(9.73822 + 2.85940i) q^{26} +(0.773155 + 1.20305i) q^{28} +(-4.75885 - 3.05833i) q^{32} +(0.664194 + 1.45438i) q^{35} +(-0.853889 - 5.93893i) q^{36} +(-5.71030 + 8.88540i) q^{37} +(-3.09132 - 10.5281i) q^{38} +(-4.77978 - 4.14170i) q^{40} +(1.38359 - 0.889181i) q^{41} +(4.78504 + 2.18525i) q^{44} -6.70820i q^{45} +(-6.31905 + 2.46365i) q^{46} -13.6824 q^{47} +(-6.22589 - 1.82808i) q^{49} +(-4.63056 - 5.34396i) q^{50} +(-9.39944 + 10.8475i) q^{52} +(-8.14452 - 1.17101i) q^{53} +(4.94768 + 3.17968i) q^{55} +(-2.00184 + 0.287821i) q^{56} +(-0.607367 - 4.22433i) q^{59} +(-1.62116 - 1.40475i) q^{63} +(6.73003 - 4.32513i) q^{64} +(-12.1279 + 10.5089i) q^{65} -2.26114 q^{70} +(8.14157 + 2.39058i) q^{72} +(-8.07559 - 12.5659i) q^{74} +(15.3596 + 2.20837i) q^{76} +(1.80451 - 0.529851i) q^{77} +(8.13600 - 3.71558i) q^{80} +(3.73874 + 8.18669i) q^{81} +(0.331014 + 2.30225i) q^{82} +(-5.62228 + 4.87173i) q^{88} +(4.41127 - 15.0234i) q^{89} +(8.62953 + 3.94097i) q^{90} +5.13157i q^{91} +(0.543085 - 9.57628i) q^{92} +(8.03820 - 17.6012i) q^{94} +(16.6464 + 4.88781i) q^{95} +(6.00929 - 6.93509i) q^{98} +(-7.81030 - 1.12295i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{4} - 12 q^{9}+O(q^{10}) \) 40 * q - 8 * q^4 - 12 * q^9	\( 40 q - 8 q^{4} - 12 q^{9} - 16 q^{16} + 20 q^{25} + 32 q^{26} - 180 q^{35} - 24 q^{36} - 8 q^{41} - 24 q^{46} + 52 q^{49} + 252 q^{59} - 32 q^{64} - 36 q^{81} + 16 q^{94}+O(q^{100}) \) 40 * q - 8 * q^4 - 12 * q^9 - 16 * q^16 + 20 * q^25 + 32 * q^26 - 180 * q^35 - 24 * q^36 - 8 * q^41 - 24 * q^46 + 52 * q^49 + 252 * q^59 - 32 * q^64 - 36 * q^81 + 16 * q^94

Introduction

L-functions

Modular forms

Varieties

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Database

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