LMFDB - Embedded newform 2100.2.bo.g.1349.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(1349,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))

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

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

chi := DirichletCharacter("2100.1349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.bo (of order $6$, degree $2$, not 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:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{18} - 16 x^{16} + 87 x^{14} + 91 x^{12} - 1104 x^{10} + 819 x^{8} + 7047 x^{6} + \cdots + 59049 $ x^20 - 3x^18 - 16x^16 + 87x^14 + 91x^12 - 1104x^10 + 819x^8 + 7047x^6 - 11664x^4 - 19683*x^2 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1349.4
Root			$1.70278 + 0.317079i$ of defining polynomial
Character	$\chi$	$=$	2100.1349
Dual form			2100.2.bo.g.1949.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.576792 + 1.63319i) q^{3} +(-1.99797 - 1.73439i) q^{7} +(-2.33462 - 1.88402i) q^{9} +O(q^{10})$	\(q+(-0.576792 + 1.63319i) q^{3} +(-1.99797 - 1.73439i) q^{7} +(-2.33462 - 1.88402i) q^{9} +(3.38064 - 1.95181i) q^{11} -6.06329 q^{13} +(2.65516 - 1.53296i) q^{17} +(2.94930 + 1.70278i) q^{19} +(3.98500 - 2.26269i) q^{21} +(-1.43686 + 2.48871i) q^{23} +(4.42356 - 2.72620i) q^{27} +7.97997i q^{29} +(-5.63161 + 3.25141i) q^{31} +(1.23776 + 6.64702i) q^{33} +(-0.113447 - 0.0654987i) q^{37} +(3.49726 - 9.90252i) q^{39} +12.3654 q^{41} -4.43247i q^{43} +(8.71153 + 5.02960i) q^{47} +(0.983778 + 6.93053i) q^{49} +(0.972138 + 5.22058i) q^{51} +(2.67959 + 4.64119i) q^{53} +(-4.48210 + 3.83462i) q^{57} +(1.28860 + 2.23193i) q^{59} +(7.44930 + 4.30086i) q^{61} +(1.39688 + 7.81337i) q^{63} +(-13.8544 + 7.99884i) q^{67} +(-3.23578 - 3.78214i) q^{69} -3.63245i q^{71} +(3.88250 + 6.72468i) q^{73} +(-10.1396 - 1.96368i) q^{77} +(1.22311 - 2.11848i) q^{79} +(1.90093 + 8.79696i) q^{81} +7.63648i q^{83} +(-13.0328 - 4.60278i) q^{87} +(4.11874 - 7.13387i) q^{89} +(12.1143 + 10.5161i) q^{91} +(-2.06191 - 11.0729i) q^{93} +5.74985 q^{97} +(-11.5698 - 1.81245i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{9}+O(q^{10}) $ 20 * q - 6 * q^9	$ 20 q - 6 q^{9} + 12 q^{11} - 6 q^{19} + 24 q^{21} + 30 q^{31} + 42 q^{39} + 16 q^{41} + 26 q^{49} + 80 q^{51} + 84 q^{61} - 28 q^{69} - 2 q^{79} - 26 q^{81} + 56 q^{89} - 22 q^{91} - 72 q^{99}+O(q^{100}) $ 20 * q - 6 * q^9 + 12 * q^11 - 6 * q^19 + 24 * q^21 + 30 * q^31 + 42 * q^39 + 16 * q^41 + 26 * q^49 + 80 * q^51 + 84 * q^61 - 28 * q^69 - 2 * q^79 - 26 * q^81 + 56 * q^89 - 22 * q^91 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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			0
$2$		0			0
$3$	−0.576792	+	1.63319i	−0.333011	+	0.942923i
$3$	−0.576792	+	1.63319i	−0.333011	+	0.942923i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.99797	−	1.73439i	−0.755162	−	0.655538i
$7$	−1.99797	−	1.73439i	−0.755162	−	0.655538i
$8$		0			0
$9$	−2.33462	−	1.88402i	−0.778208	−	0.628007i
$10$		0			0
$11$	3.38064	−	1.95181i	1.01930	−	0.588494i	0.105400	−	0.994430i	$-0.466388\pi$
$11$	3.38064	−	1.95181i	1.01930	−	0.588494i	0.913902	+	0.405936i	$0.133054\pi$
$12$		0			0
$13$	−6.06329			−1.68166			−0.840828	−	0.541303i	$-0.817931\pi$
$13$	−6.06329			−1.68166			−0.840828	+	0.541303i	$0.817931\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.65516	−	1.53296i	0.643971	−	0.371797i	−0.142171	−	0.989842i	$-0.545408\pi$
$17$	2.65516	−	1.53296i	0.643971	−	0.371797i	0.786143	+	0.618045i	$0.212075\pi$
$18$		0			0
$19$	2.94930	+	1.70278i	0.676616	+	0.390645i	0.798579	−	0.601890i	$-0.205585\pi$
$19$	2.94930	+	1.70278i	0.676616	+	0.390645i	−0.121963	+	0.992535i	$0.538919\pi$
$20$		0			0
$21$	3.98500	−	2.26269i	0.869599	−	0.493759i
$22$		0			0
$23$	−1.43686	+	2.48871i	−0.299606	+	0.518933i	−0.976046	−	0.217565i	$-0.930189\pi$
$23$	−1.43686	+	2.48871i	−0.299606	+	0.518933i	0.676440	+	0.736498i	$0.263522\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	4.42356	−	2.72620i	0.851314	−	0.524657i
$28$		0			0
$29$			7.97997i			1.48184i	0.671591	+	0.740922i	$0.265611\pi$
$29$			7.97997i			1.48184i	−0.671591	+	0.740922i	$0.734389\pi$
$30$		0			0
$31$	−5.63161	+	3.25141i	−1.01147	+	0.583971i	−0.911621	−	0.411032i	$-0.865168\pi$
$31$	−5.63161	+	3.25141i	−1.01147	+	0.583971i	−0.0998461	+	0.995003i	$0.531835\pi$
$32$		0			0
$33$	1.23776	+	6.64702i	0.215466	+	1.15710i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−0.113447	−	0.0654987i	−0.0186506	−	0.0107679i	0.490646	−	0.871359i	$-0.336761\pi$
$37$	−0.113447	−	0.0654987i	−0.0186506	−	0.0107679i	−0.509296	+	0.860591i	$0.670094\pi$
$38$		0			0
$39$	3.49726	−	9.90252i	0.560009	−	1.58567i
$40$		0			0
$41$	12.3654			1.93116			0.965579	−	0.260108i	$-0.0837583\pi$
$41$	12.3654			1.93116			0.965579	+	0.260108i	$0.0837583\pi$
$42$		0			0
$43$		−	4.43247i		−	0.675945i	−0.941156	−	0.337972i	$-0.890259\pi$
$43$		−	4.43247i		−	0.675945i	0.941156	−	0.337972i	$-0.109741\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	8.71153	+	5.02960i	1.27071	+	0.733643i	0.975121	−	0.221674i	$-0.0711519\pi$
$47$	8.71153	+	5.02960i	1.27071	+	0.733643i	0.295586	+	0.955316i	$0.404485\pi$
$48$		0			0
$49$	0.983778	+	6.93053i	0.140540	+	0.990075i
$50$		0			0
$51$	0.972138	+	5.22058i	0.136127	+	0.731028i
$52$		0			0
$53$	2.67959	+	4.64119i	0.368070	+	0.637516i	0.989264	−	0.146141i	$-0.0466853\pi$
$53$	2.67959	+	4.64119i	0.368070	+	0.637516i	−0.621194	+	0.783657i	$0.713352\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−4.48210	+	3.83462i	−0.593668	+	0.507908i
$58$		0			0
$59$	1.28860	+	2.23193i	0.167762	+	0.290572i	0.937633	−	0.347628i	$-0.113013\pi$
$59$	1.28860	+	2.23193i	0.167762	+	0.290572i	−0.769871	+	0.638200i	$0.779679\pi$
$60$		0			0
$61$	7.44930	+	4.30086i	0.953785	+	0.550668i	0.894255	−	0.447558i	$-0.147706\pi$
$61$	7.44930	+	4.30086i	0.953785	+	0.550668i	0.0595306	+	0.998226i	$0.481040\pi$
$62$		0			0
$63$	1.39688	+	7.81337i	0.175990	+	0.984392i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−13.8544	+	7.99884i	−1.69258	+	0.977213i	−0.740162	+	0.672429i	$0.765251\pi$
$67$	−13.8544	+	7.99884i	−1.69258	+	0.977213i	−0.952421	+	0.304785i	$0.901415\pi$
$68$		0			0
$69$	−3.23578	−	3.78214i	−0.389542	−	0.455316i
$70$		0			0
$71$		−	3.63245i		−	0.431093i	−0.976494	−	0.215547i	$-0.930847\pi$
$71$		−	3.63245i		−	0.431093i	0.976494	−	0.215547i	$-0.0691533\pi$
$72$		0			0
$73$	3.88250	+	6.72468i	0.454412	+	0.787064i	0.998654	−	0.0518638i	$-0.0165162\pi$
$73$	3.88250	+	6.72468i	0.454412	+	0.787064i	−0.544242	+	0.838928i	$0.683183\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−10.1396	−	1.96368i	−1.15552	−	0.223783i
$78$		0			0
$79$	1.22311	−	2.11848i	0.137610	−	0.238348i	−0.788981	−	0.614417i	$-0.789391\pi$
$79$	1.22311	−	2.11848i	0.137610	−	0.238348i	0.926591	+	0.376069i	$0.122725\pi$
$80$		0			0
$81$	1.90093	+	8.79696i	0.211214	+	0.977440i
$82$		0			0
$83$			7.63648i			0.838213i	0.907937	+	0.419106i	$0.137657\pi$
$83$			7.63648i			0.838213i	−0.907937	+	0.419106i	$0.862343\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−13.0328	−	4.60278i	−1.39726	−	0.493470i
$88$		0			0
$89$	4.11874	−	7.13387i	0.436586	−	0.756189i	−0.560838	−	0.827926i	$-0.689521\pi$
$89$	4.11874	−	7.13387i	0.436586	−	0.756189i	0.997424	+	0.0717367i	$0.0228541\pi$
$90$		0			0
$91$	12.1143	+	10.5161i	1.26992	+	1.10239i
$92$		0			0
$93$	−2.06191	−	11.0729i	−0.213810	−	1.14820i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	5.74985			0.583809			0.291904	−	0.956447i	$-0.405711\pi$
$97$	5.74985			0.583809			0.291904	+	0.956447i	$0.405711\pi$
$98$		0			0
$99$	−11.5698	−	1.81245i	−1.16281	−	0.182158i
$100$		0			0
$101$	−4.54502	−	7.87220i	−0.452246	−	0.783313i	0.546279	−	0.837603i	$-0.316044\pi$
$101$	−4.54502	−	7.87220i	−0.452246	−	0.783313i	−0.998525	+	0.0542901i	$0.982710\pi$
$102$		0			0
$103$	−0.492615	+	0.853234i	−0.0485388	+	0.0840717i	−0.889274	−	0.457375i	$-0.848790\pi$
$103$	−0.492615	+	0.853234i	−0.0485388	+	0.0840717i	0.840735	+	0.541446i	$0.182123\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.645758	−	1.11849i	0.0624278	−	0.108128i	−0.833122	−	0.553089i	$-0.813449\pi$
$107$	0.645758	−	1.11849i	0.0624278	−	0.108128i	0.895550	+	0.444961i	$0.146782\pi$
$108$		0			0
$109$	−3.68547	−	6.38342i	−0.353004	−	0.611421i	0.633770	−	0.773521i	$-0.281506\pi$
$109$	−3.68547	−	6.38342i	−0.353004	−	0.611421i	−0.986774	+	0.162101i	$0.948173\pi$
$110$		0			0
$111$	0.172407	−	0.147502i	0.0163642	−	0.0140002i
$112$		0			0
$113$	4.52778			0.425938			0.212969	−	0.977059i	$-0.431687\pi$
$113$	4.52778			0.425938			0.212969	+	0.977059i	$0.431687\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	14.1555	+	11.4234i	1.30868	+	1.05609i
$118$		0			0
$119$	−7.96368	−	1.54228i	−0.730030	−	0.141381i
$120$		0			0
$121$	2.11916	−	3.67050i	0.192651	−	0.333681i
$122$		0			0
$123$	−7.13229	+	20.1951i	−0.643097	+	1.82093i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	0.700855i		−	0.0621908i	−0.999516	−	0.0310954i	$-0.990100\pi$
$127$		−	0.700855i		−	0.0621908i	0.999516	−	0.0310954i	$-0.00989957\pi$
$128$		0			0
$129$	7.23906	+	2.55661i	0.637364	+	0.225097i
$130$		0			0
$131$	−2.66028	+	4.60774i	−0.232430	+	0.402580i	−0.958523	−	0.285016i	$-0.908001\pi$
$131$	−2.66028	+	4.60774i	−0.232430	+	0.402580i	0.726093	+	0.687597i	$0.241334\pi$
$132$		0			0
$133$	−2.93933	−	8.51735i	−0.254873	−	0.738548i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.96252	+	3.39919i	0.167670	+	0.290412i	0.937600	−	0.347715i	$-0.113042\pi$
$137$	1.96252	+	3.39919i	0.167670	+	0.290412i	−0.769930	+	0.638128i	$0.779709\pi$
$138$		0			0
$139$			16.1726i			1.37174i	0.727724	+	0.685870i	$0.240578\pi$
$139$			16.1726i			1.37174i	−0.727724	+	0.685870i	$0.759422\pi$
$140$		0			0
$141$	−13.2390	+	11.3265i	−1.11493	+	0.953868i
$142$		0			0
$143$	−20.4978	+	11.8344i	−1.71411	+	0.989645i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−11.8863	−	2.39077i	−0.980366	−	0.197188i
$148$		0			0
$149$	−17.4366	−	10.0670i	−1.42846	−	0.824721i	−0.431459	−	0.902132i	$-0.642001\pi$
$149$	−17.4366	−	10.0670i	−1.42846	−	0.824721i	−0.996999	+	0.0774116i	$0.975334\pi$
$150$		0			0
$151$	−2.38980	−	4.13926i	−0.194479	−	0.336848i	0.752250	−	0.658877i	$-0.228968\pi$
$151$	−2.38980	−	4.13926i	−0.194479	−	0.336848i	−0.946730	+	0.322029i	$0.895635\pi$
$152$		0			0
$153$	−9.08693	−	1.42350i	−0.734635	−	0.115083i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	3.82658	+	6.62784i	0.305395	+	0.528959i	0.977349	−	0.211633i	$-0.0678783\pi$
$157$	3.82658	+	6.62784i	0.305395	+	0.528959i	−0.671955	+	0.740592i	$0.734545\pi$
$158$		0			0
$159$	−9.12551	+	1.69929i	−0.723700	+	0.134762i
$160$		0			0
$161$	7.18721	−	2.48030i	0.566431	−	0.195475i
$162$		0			0
$163$	−7.33954	−	4.23749i	−0.574877	−	0.331906i	0.184218	−	0.982885i	$-0.441025\pi$
$163$	−7.33954	−	4.23749i	−0.574877	−	0.331906i	−0.759095	+	0.650980i	$0.774358\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			20.5669i			1.59152i	0.605614	+	0.795759i	$0.292928\pi$
$167$			20.5669i			1.59152i	−0.605614	+	0.795759i	$0.707072\pi$
$168$		0			0
$169$	23.7635			1.82796
$170$		0			0
$171$	−3.67743	−	9.53190i	−0.281220	−	0.728922i
$172$		0			0
$173$	14.3819	+	8.30340i	1.09344	+	0.631296i	0.934489	−	0.355991i	$-0.115857\pi$
$173$	14.3819	+	8.30340i	1.09344	+	0.631296i	0.158948	+	0.987287i	$0.449190\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−4.38842	+	0.817179i	−0.329854	+	0.0614229i
$178$		0			0
$179$	−0.336240	+	0.194128i	−0.0251318	+	0.0145098i	−0.512513	−	0.858679i	$-0.671285\pi$
$179$	−0.336240	+	0.194128i	−0.0251318	+	0.0145098i	0.487381	+	0.873189i	$0.337952\pi$
$180$		0			0
$181$			20.6789i			1.53705i	0.639820	+	0.768524i	$0.279009\pi$
$181$			20.6789i			1.53705i	−0.639820	+	0.768524i	$0.720991\pi$
$182$		0			0
$183$	−11.3208	+	9.68543i	−0.836859	+	0.715968i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	5.98410	−	10.3648i	0.437601	−	0.757947i
$188$		0			0
$189$	−13.5664	−	2.22531i	−0.986812	−	0.161868i
$190$		0			0
$191$	−15.2933	−	8.82961i	−1.10659	−	0.638888i	−0.168644	−	0.985677i	$-0.553939\pi$
$191$	−15.2933	−	8.82961i	−1.10659	−	0.638888i	−0.937943	+	0.346789i	$0.887272\pi$
$192$		0			0
$193$	18.5161	−	10.6903i	1.33282	−	0.769505i	0.347090	−	0.937832i	$-0.387170\pi$
$193$	18.5161	−	10.6903i	1.33282	−	0.769505i	0.985731	+	0.168327i	$0.0538365\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	22.5070			1.60356			0.801780	−	0.597619i	$-0.203886\pi$
$197$	22.5070			1.60356			0.801780	+	0.597619i	$0.203886\pi$
$198$		0			0
$199$	8.48532	−	4.89900i	0.601509	−	0.347281i	−0.168126	−	0.985765i	$-0.553772\pi$
$199$	8.48532	−	4.89900i	0.601509	−	0.347281i	0.769635	+	0.638484i	$0.220438\pi$
$200$		0			0
$201$	−5.07253	−	27.2405i	−0.357789	−	1.92140i
$202$		0			0
$203$	13.8404	−	15.9438i	0.971405	−	1.11903i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	8.04332	−	3.10314i	0.559049	−	0.215683i
$208$		0			0
$209$	13.2940			0.919568
$210$		0			0
$211$	−1.96291			−0.135132			−0.0675660	−	0.997715i	$-0.521523\pi$
$211$	−1.96291			−0.135132			−0.0675660	+	0.997715i	$0.521523\pi$
$212$		0			0
$213$	5.93249	+	2.09517i	0.406488	+	0.143559i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	16.8910	+	3.27118i	1.14664	+	0.222062i
$218$		0			0
$219$	−13.2221	+	2.46212i	−0.893465	+	0.166374i
$220$		0			0
$221$	−16.0990	+	9.29478i	−1.08294	+	0.625234i
$222$		0			0
$223$	1.78864			0.119776			0.0598882	−	0.998205i	$-0.480926\pi$
$223$	1.78864			0.119776			0.0598882	+	0.998205i	$0.480926\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−23.8990	+	13.7981i	−1.58623	+	0.915813i	−0.592315	+	0.805707i	$0.701786\pi$
$227$	−23.8990	+	13.7981i	−1.58623	+	0.915813i	−0.993920	+	0.110106i	$0.964881\pi$
$228$		0			0
$229$	8.37613	+	4.83596i	0.553510	+	0.319569i	0.750537	−	0.660829i	$-0.229795\pi$
$229$	8.37613	+	4.83596i	0.553510	+	0.319569i	−0.197026	+	0.980398i	$0.563128\pi$
$230$		0			0
$231$	9.05553	−	15.4273i	0.595810	−	1.01504i
$232$		0			0
$233$	−0.298355	+	0.516767i	−0.0195459	+	0.0338545i	−0.875633	−	0.482977i	$-0.839555\pi$
$233$	−0.298355	+	0.516767i	−0.0195459	+	0.0338545i	0.856087	+	0.516832i	$0.172889\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	2.75441	+	3.21949i	0.178918	+	0.209128i
$238$		0			0
$239$			8.90983i			0.576329i	0.957581	+	0.288165i	$0.0930450\pi$
$239$			8.90983i			0.576329i	−0.957581	+	0.288165i	$0.906955\pi$
$240$		0			0
$241$	1.82543	−	1.05391i	0.117586	−	0.0678886i	−0.440053	−	0.897972i	$-0.645040\pi$
$241$	1.82543	−	1.05391i	0.117586	−	0.0678886i	0.557640	+	0.830083i	$0.311707\pi$
$242$		0			0
$243$	−15.4635	−	1.96943i	−0.991987	−	0.126339i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−17.8825	−	10.3245i	−1.13784	−	0.656930i
$248$		0			0
$249$	−12.4718	−	4.40466i	−0.790370	−	0.279134i
$250$		0			0
$251$	29.8229			1.88241			0.941204	−	0.337840i	$-0.109696\pi$
$251$	29.8229			1.88241			0.941204	+	0.337840i	$0.109696\pi$
$252$		0			0
$253$			11.2179i			0.705266i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−11.7518	−	6.78489i	−0.733055	−	0.423230i	0.0864836	−	0.996253i	$-0.472437\pi$
$257$	−11.7518	−	6.78489i	−0.733055	−	0.423230i	−0.819539	+	0.573024i	$0.805770\pi$
$258$		0			0
$259$	0.113064	+	0.327626i	0.00702543	+	0.0203577i
$260$		0			0
$261$	15.0344	−	18.6302i	0.930608	−	1.15318i
$262$		0			0
$263$	−6.07897	−	10.5291i	−0.374846	−	0.649252i	0.615458	−	0.788169i	$-0.288971\pi$
$263$	−6.07897	−	10.5291i	−0.374846	−	0.649252i	−0.990304	+	0.138918i	$0.955638\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	9.27532	+	10.8415i	0.567640	+	0.663486i
$268$		0			0
$269$	11.2201	+	19.4338i	0.684101	+	1.18490i	0.973718	+	0.227756i	$0.0731388\pi$
$269$	11.2201	+	19.4338i	0.684101	+	1.18490i	−0.289617	+	0.957143i	$0.593528\pi$
$270$		0			0
$271$	−7.19179	−	4.15218i	−0.436870	−	0.252227i	0.265399	−	0.964139i	$-0.414496\pi$
$271$	−7.19179	−	4.15218i	−0.436870	−	0.252227i	−0.702269	+	0.711912i	$0.747830\pi$
$272$		0			0
$273$	−24.1622	+	13.7193i	−1.46237	+	0.830332i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	5.24547	−	3.02848i	0.315170	−	0.181963i	−0.334068	−	0.942549i	$-0.608421\pi$
$277$	5.24547	−	3.02848i	0.315170	−	0.181963i	0.649238	+	0.760586i	$0.275088\pi$
$278$		0			0
$279$	19.2734	+	3.01925i	1.15387	+	0.180758i
$280$		0			0
$281$			17.5771i			1.04856i	0.851545	+	0.524282i	$0.175666\pi$
$281$			17.5771i			1.04856i	−0.851545	+	0.524282i	$0.824334\pi$
$282$		0			0
$283$	−4.10407	−	7.10845i	−0.243961	−	0.422554i	0.717878	−	0.696169i	$-0.245114\pi$
$283$	−4.10407	−	7.10845i	−0.243961	−	0.422554i	−0.961839	+	0.273616i	$0.911780\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−24.7058	−	21.4465i	−1.45834	−	1.26595i
$288$		0			0
$289$	−3.80008	+	6.58193i	−0.223534	+	0.387172i
$290$		0			0
$291$	−3.31647	+	9.39060i	−0.194415	+	0.550487i
$292$		0			0
$293$		−	3.88610i		−	0.227028i	−0.993536	−	0.113514i	$-0.963789\pi$
$293$		−	3.88610i		−	0.227028i	0.993536	−	0.113514i	$-0.0362107\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	9.63343	−	17.8503i	0.558988	−	1.03578i
$298$		0			0
$299$	8.71210	−	15.0898i	0.503834	−	0.872666i
$300$		0			0
$301$	−7.68763	+	8.85594i	−0.443108	+	0.510448i
$302$		0			0
$303$	15.4783	−	2.88226i	0.889207	−	0.165581i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	0.119756			0.00683482			0.00341741	−	0.999994i	$-0.498912\pi$
$307$	0.119756			0.00683482			0.00341741	+	0.999994i	$0.498912\pi$
$308$		0			0
$309$	−1.10936	−	1.29667i	−0.0631092	−	0.0737651i
$310$		0			0
$311$	6.57207	+	11.3832i	0.372668	+	0.645480i	0.989975	−	0.141243i	$-0.0451097\pi$
$311$	6.57207	+	11.3832i	0.372668	+	0.645480i	−0.617307	+	0.786722i	$0.711776\pi$
$312$		0			0
$313$	11.6346	−	20.1517i	0.657625	−	1.13904i	−0.323604	−	0.946192i	$-0.604895\pi$
$313$	11.6346	−	20.1517i	0.657625	−	1.13904i	0.981229	−	0.192847i	$-0.0617720\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	17.3744	−	30.0933i	0.975841	−	1.69021i	0.298709	−	0.954344i	$-0.403444\pi$
$317$	17.3744	−	30.0933i	0.975841	−	1.69021i	0.677132	−	0.735861i	$-0.263223\pi$
$318$		0			0
$319$	15.5754	+	26.9774i	0.872056	+	1.51045i
$320$		0			0
$321$	1.45423	+	1.69978i	0.0811674	+	0.0948725i
$322$		0			0
$323$	10.4412			0.580962
$324$		0			0
$325$		0			0
$326$		0			0
$327$	12.5511	−	2.33717i	0.694077	−	0.129246i
$328$		0			0
$329$	−8.68208	−	25.1582i	−0.478659	−	1.38702i
$330$		0			0
$331$	12.8024	−	22.1744i	0.703684	−	1.21882i	−0.263481	−	0.964665i	$-0.584871\pi$
$331$	12.8024	−	22.1744i	0.703684	−	1.21882i	0.967165	−	0.254151i	$-0.0817961\pi$
$332$		0			0
$333$	0.141455	+	0.366651i	0.00775169	+	0.0200924i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			26.5502i			1.44628i	0.690702	+	0.723140i	$0.257302\pi$
$337$			26.5502i			1.44628i	−0.690702	+	0.723140i	$0.742698\pi$
$338$		0			0
$339$	−2.61159	+	7.39473i	−0.141842	+	0.401627i
$340$		0			0
$341$	−12.6923	+	21.9837i	−0.687327	+	1.19048i
$342$		0			0
$343$	10.0547	−	15.5532i	0.542902	−	0.839796i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	9.61397	+	16.6519i	0.516105	+	0.893920i	0.999825	+	0.0186975i	$0.00595193\pi$
$347$	9.61397	+	16.6519i	0.516105	+	0.893920i	−0.483720	+	0.875223i	$0.660715\pi$
$348$		0			0
$349$			1.40475i			0.0751943i	0.999293	+	0.0375972i	$0.0119704\pi$
$349$			1.40475i			0.0751943i	−0.999293	+	0.0375972i	$0.988030\pi$
$350$		0			0
$351$	−26.8213	+	16.5297i	−1.43162	+	0.882292i
$352$		0			0
$353$	16.3454	−	9.43705i	0.869980	−	0.502283i	0.00263867	−	0.999997i	$-0.499160\pi$
$353$	16.3454	−	9.43705i	0.869980	−	0.502283i	0.867342	+	0.497713i	$0.165827\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	7.11222	−	12.1166i	0.376419	−	0.641281i
$358$		0			0
$359$	19.1592	+	11.0615i	1.01118	+	0.583806i	0.911537	−	0.411217i	$-0.134896\pi$
$359$	19.1592	+	11.0615i	1.01118	+	0.583806i	0.0996440	+	0.995023i	$0.468230\pi$
$360$		0			0
$361$	−3.70108	−	6.41046i	−0.194794	−	0.337392i
$362$		0			0
$363$	4.77230	+	5.57811i	0.250481	+	0.292775i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−6.56047	−	11.3631i	−0.342454	−	0.593147i	0.642434	−	0.766341i	$-0.277925\pi$
$367$	−6.56047	−	11.3631i	−0.342454	−	0.593147i	−0.984888	+	0.173194i	$0.944591\pi$
$368$		0			0
$369$	−28.8687	−	23.2968i	−1.50284	−	1.21278i
$370$		0			0
$371$	2.69589	−	13.9204i	0.139964	−	0.722712i
$372$		0			0
$373$	12.7826	+	7.38003i	0.661857	+	0.382123i	0.792984	−	0.609242i	$-0.208526\pi$
$373$	12.7826	+	7.38003i	0.661857	+	0.382123i	−0.131127	+	0.991366i	$0.541860\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	48.3849i		−	2.49195i
$378$		0			0
$379$	−29.9980			−1.54089			−0.770447	−	0.637505i	$-0.779967\pi$
$379$	−29.9980			−1.54089			−0.770447	+	0.637505i	$0.779967\pi$
$380$		0			0
$381$	1.14463	+	0.404247i	0.0586411	+	0.0207102i
$382$		0			0
$383$	−13.3723	−	7.72052i	−0.683294	−	0.394500i	0.117801	−	0.993037i	$-0.462416\pi$
$383$	−13.3723	−	7.72052i	−0.683294	−	0.394500i	−0.801095	+	0.598537i	$0.795749\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−8.35086	+	10.3481i	−0.424498	+	0.526025i
$388$		0			0
$389$	−7.53666	+	4.35129i	−0.382124	+	0.220619i	−0.678742	−	0.734377i	$-0.737475\pi$
$389$	−7.53666	+	4.35129i	−0.382124	+	0.220619i	0.296618	+	0.954996i	$0.404141\pi$
$390$		0			0
$391$			8.81059i			0.445570i
$392$		0			0
$393$	−5.99089	−	7.00245i	−0.302201	−	0.353227i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−13.5044	+	23.3904i	−0.677768	+	1.17393i	0.297883	+	0.954602i	$0.403719\pi$
$397$	−13.5044	+	23.3904i	−0.677768	+	1.17393i	−0.975651	+	0.219327i	$0.929614\pi$
$398$		0			0
$399$	15.6058	+	0.112241i	0.781269	+	0.00561909i
$400$		0			0
$401$	−4.30215	−	2.48385i	−0.214839	−	0.124037i	0.388719	−	0.921356i	$-0.372918\pi$
$401$	−4.30215	−	2.48385i	−0.214839	−	0.124037i	−0.603558	+	0.797319i	$0.706251\pi$
$402$		0			0
$403$	34.1461	−	19.7143i	1.70094	−	0.982037i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.511365			−0.0253474
$408$		0			0
$409$	7.00387	−	4.04369i	0.346319	−	0.199947i	−0.316744	−	0.948511i	$-0.602590\pi$
$409$	7.00387	−	4.04369i	0.346319	−	0.199947i	0.663063	+	0.748564i	$0.269256\pi$
$410$		0			0
$411$	−6.68349	+	1.24455i	−0.329672	+	0.0613891i
$412$		0			0
$413$	1.29644	−	6.69427i	0.0637937	−	0.329403i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−26.4129	−	9.32820i	−1.29345	−	0.456804i
$418$		0			0
$419$	−7.60294			−0.371428			−0.185714	−	0.982604i	$-0.559460\pi$
$419$	−7.60294			−0.371428			−0.185714	+	0.982604i	$0.559460\pi$
$420$		0			0
$421$	−4.43892			−0.216340			−0.108170	−	0.994132i	$-0.534499\pi$
$421$	−4.43892			−0.216340			−0.108170	+	0.994132i	$0.534499\pi$
$422$		0			0
$423$	−10.8623	−	28.1549i	−0.528141	−	1.36894i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−7.42413	−	21.5130i	−0.359279	−	1.04109i
$428$		0			0
$429$	−7.50490	−	40.3029i	−0.362340	−	1.94584i
$430$		0			0
$431$	−4.24065	+	2.44834i	−0.204265	+	0.117932i	−0.598643	−	0.801016i	$-0.704293\pi$
$431$	−4.24065	+	2.44834i	−0.204265	+	0.117932i	0.394378	+	0.918948i	$0.370960\pi$
$432$		0			0
$433$	18.6390			0.895732			0.447866	−	0.894101i	$-0.352184\pi$
$433$	18.6390			0.895732			0.447866	+	0.894101i	$0.352184\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−8.47547	+	4.89331i	−0.405437	+	0.234079i
$438$		0			0
$439$	2.87038	+	1.65722i	0.136996	+	0.0790946i	0.566932	−	0.823765i	$-0.308130\pi$
$439$	2.87038	+	1.65722i	0.136996	+	0.0790946i	−0.429936	+	0.902860i	$0.641464\pi$
$440$		0			0
$441$	10.7605	−	18.0336i	0.512405	−	0.858744i
$442$		0			0
$443$	0.408581	−	0.707683i	0.0194123	−	0.0336231i	−0.856156	−	0.516717i	$-0.827154\pi$
$443$	0.408581	−	0.707683i	0.0194123	−	0.0336231i	0.875568	+	0.483094i	$0.160487\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	26.4986	−	22.6707i	1.25334	−	1.07229i
$448$		0			0
$449$		−	5.17892i		−	0.244408i	−0.992505	−	0.122204i	$-0.961004\pi$
$449$		−	5.17892i		−	0.244408i	0.992505	−	0.122204i	$-0.0389962\pi$
$450$		0			0
$451$	41.8032	−	24.1351i	1.96843	−	1.13648i
$452$		0			0
$453$	8.13862	−	1.51551i	0.382386	−	0.0712051i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−10.4250	−	6.01889i	−0.487662	−	0.281552i	0.235942	−	0.971767i	$-0.424183\pi$
$457$	−10.4250	−	6.01889i	−0.487662	−	0.281552i	−0.723604	+	0.690215i	$0.757516\pi$
$458$		0			0
$459$	7.56611	−	14.0196i	0.353156	−	0.654380i
$460$		0			0
$461$	−23.0451			−1.07332			−0.536658	−	0.843800i	$-0.680314\pi$
$461$	−23.0451			−1.07332			−0.536658	+	0.843800i	$0.680314\pi$
$462$		0			0
$463$		−	27.8549i		−	1.29453i	−0.762267	−	0.647263i	$-0.775914\pi$
$463$		−	27.8549i		−	1.29453i	0.762267	−	0.647263i	$-0.224086\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.91950	+	1.10822i	0.0888240	+	0.0512825i	0.543754	−	0.839245i	$-0.317002\pi$
$467$	1.91950	+	1.10822i	0.0888240	+	0.0512825i	−0.454930	+	0.890527i	$0.650336\pi$
$468$		0			0
$469$	41.5538	+	8.04748i	1.91878	+	0.371598i
$470$		0			0
$471$	−13.0317	+	2.42666i	−0.600467	+	0.111815i
$472$		0			0
$473$	−8.65135	−	14.9846i	−0.397790	−	0.688992i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	2.48826	−	15.8838i	0.113930	−	0.727271i
$478$		0			0
$479$	−3.53276	−	6.11892i	−0.161416	−	0.279581i	0.773961	−	0.633234i	$-0.218273\pi$
$479$	−3.53276	−	6.11892i	−0.161416	−	0.279581i	−0.935377	+	0.353653i	$0.884939\pi$
$480$		0			0
$481$	0.687863	+	0.397138i	0.0313638	+	0.0181079i
$482$		0			0
$483$	−0.0947128	+	13.1687i	−0.00430958	+	0.599197i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	8.00270	−	4.62036i	0.362637	−	0.209368i	−0.307600	−	0.951516i	$-0.599526\pi$
$487$	8.00270	−	4.62036i	0.362637	−	0.209368i	0.670237	+	0.742147i	$0.266193\pi$
$488$		0			0
$489$	11.1540	−	9.54273i	0.504402	−	0.431537i
$490$		0			0
$491$			14.0713i			0.635031i	0.948253	+	0.317515i	$0.102848\pi$
$491$			14.0713i			0.635031i	−0.948253	+	0.317515i	$0.897152\pi$
$492$		0			0
$493$	12.2330	+	21.1881i	0.550945	+	0.954265i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.30010	+	7.25754i	−0.282598	+	0.325545i
$498$		0			0
$499$	6.50255	−	11.2627i	0.291094	−	0.504190i	−0.682975	−	0.730442i	$-0.739314\pi$
$499$	6.50255	−	11.2627i	0.291094	−	0.504190i	0.974069	+	0.226252i	$0.0726474\pi$
$500$		0			0
$501$	−33.5897	−	11.8628i	−1.50068	−	0.529993i
$502$		0			0
$503$		−	0.580122i		−	0.0258664i	−0.999916	−	0.0129332i	$-0.995883\pi$
$503$		−	0.580122i		−	0.0258664i	0.999916	−	0.0129332i	$-0.00411687\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−13.7066	+	38.8104i	−0.608732	+	1.72363i
$508$		0			0
$509$	9.86251	−	17.0824i	0.437148	−	0.757163i	−0.560320	−	0.828276i	$-0.689322\pi$
$509$	9.86251	−	17.0824i	0.437148	−	0.757163i	0.997468	+	0.0711133i	$0.0226552\pi$
$510$		0			0
$511$	3.90611	−	20.1695i	0.172796	−	0.892245i
$512$		0			0
$513$	17.6885	−	0.508034i	0.780967	−	0.0224302i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	39.2674			1.72698
$518$		0			0
$519$	−21.8564	+	18.6991i	−0.959390	+	0.820799i
$520$		0			0
$521$	−18.0051	−	31.1857i	−0.788818	−	1.36627i	−0.926692	−	0.375822i	$-0.877360\pi$
$521$	−18.0051	−	31.1857i	−0.788818	−	1.36627i	0.137874	−	0.990450i	$-0.455973\pi$
$522$		0			0
$523$	−10.7033	+	18.5387i	−0.468023	+	0.810640i	−0.999332	−	0.0365378i	$-0.988367\pi$
$523$	−10.7033	+	18.5387i	−0.468023	+	0.810640i	0.531309	+	0.847178i	$0.321700\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−9.96855	+	17.2660i	−0.434237	+	0.752121i
$528$		0			0
$529$	7.37087	+	12.7667i	0.320472	+	0.555075i
$530$		0			0
$531$	1.19659	−	7.63846i	0.0519277	−	0.331481i
$532$		0			0
$533$	−74.9754			−3.24754
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−0.123108	−	0.661116i	−0.00531251	−	0.0285293i
$538$		0			0
$539$	16.8529	+	21.5095i	0.725906	+	0.926479i
$540$		0			0
$541$	−2.32759	+	4.03151i	−0.100071	+	0.173328i	−0.911714	−	0.410826i	$-0.865240\pi$
$541$	−2.32759	+	4.03151i	−0.100071	+	0.173328i	0.811643	+	0.584154i	$0.198574\pi$
$542$		0			0
$543$	−33.7725	−	11.9274i	−1.44932	−	0.511854i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			7.34057i			0.313860i	0.987610	+	0.156930i	$0.0501597\pi$
$547$			7.34057i			0.313860i	−0.987610	+	0.156930i	$0.949840\pi$
$548$		0			0
$549$	−9.28841	−	24.0755i	−0.396420	−	1.02752i
$550$		0			0
$551$	−13.5881	+	23.5353i	−0.578874	+	1.00264i
$552$		0			0
$553$	−6.11800	+	2.11132i	−0.260164	+	0.0897825i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	16.1169	+	27.9154i	0.682897	+	1.18281i	0.974093	+	0.226149i	$0.0726135\pi$
$557$	16.1169	+	27.9154i	0.682897	+	1.18281i	−0.291196	+	0.956663i	$0.594053\pi$
$558$		0			0
$559$			26.8753i			1.13671i
$560$		0			0
$561$	13.4761	+	15.7515i	0.568960	+	0.665028i
$562$		0			0
$563$	19.8892	−	11.4830i	0.838230	−	0.483952i	−0.0184324	−	0.999830i	$-0.505868\pi$
$563$	19.8892	−	11.4830i	0.838230	−	0.483952i	0.856662	+	0.515878i	$0.172534\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	11.4594	−	20.8730i	0.481248	−	0.876585i
$568$		0			0
$569$	−16.0347	−	9.25765i	−0.672211	−	0.388101i	0.124703	−	0.992194i	$-0.460202\pi$
$569$	−16.0347	−	9.25765i	−0.672211	−	0.388101i	−0.796914	+	0.604093i	$0.793535\pi$
$570$		0			0
$571$	−21.9408	−	38.0025i	−0.918193	−	1.59036i	−0.802158	−	0.597112i	$-0.796315\pi$
$571$	−21.9408	−	38.0025i	−0.918193	−	1.59036i	−0.116035	−	0.993245i	$-0.537019\pi$
$572$		0			0
$573$	23.2415	−	19.8841i	0.970928	−	0.830670i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	8.46761	+	14.6663i	0.352511	+	0.610568i	0.986689	−	0.162620i	$-0.0519944\pi$
$577$	8.46761	+	14.6663i	0.352511	+	0.610568i	−0.634177	+	0.773188i	$0.718661\pi$
$578$		0			0
$579$	6.77934	+	36.4065i	0.281740	+	1.51300i
$580$		0			0
$581$	13.2446	−	15.2575i	0.549480	−	0.632987i
$582$		0			0
$583$	18.1175	+	10.4601i	0.750349	+	0.433214i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	15.3959i		−	0.635456i	−0.948182	−	0.317728i	$-0.897080\pi$
$587$		−	15.3959i		−	0.635456i	0.948182	−	0.317728i	$-0.102920\pi$
$588$		0			0
$589$	−22.1458			−0.912500
$590$		0			0
$591$	−12.9819	+	36.7583i	−0.534003	+	1.51203i
$592$		0			0
$593$	4.11363	+	2.37500i	0.168926	+	0.0975297i	0.582079	−	0.813132i	$-0.302239\pi$
$593$	4.11363	+	2.37500i	0.168926	+	0.0975297i	−0.413153	+	0.910662i	$0.635573\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	3.10674	+	16.6839i	0.127151	+	0.682825i
$598$		0			0
$599$	−19.2300	+	11.1024i	−0.785716	+	0.453634i	−0.838452	−	0.544975i	$-0.816539\pi$
$599$	−19.2300	+	11.1024i	−0.785716	+	0.453634i	0.0527360	+	0.998608i	$0.483206\pi$
$600$		0			0
$601$			42.5924i			1.73738i	0.495357	+	0.868689i	$0.335037\pi$
$601$			42.5924i			1.73738i	−0.495357	+	0.868689i	$0.664963\pi$
$602$		0			0
$603$	47.4148	+	7.42770i	1.93088	+	0.302479i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−9.40283	+	16.2862i	−0.381649	+	0.661035i	−0.991298	−	0.131636i	$-0.957977\pi$
$607$	−9.40283	+	16.2862i	−0.381649	+	0.661035i	0.609649	+	0.792671i	$0.291310\pi$
$608$		0			0
$609$	18.0562	+	31.8002i	0.731673	+	1.28861i
$610$		0			0
$611$	−52.8205	−	30.4960i	−2.13689	−	1.23373i
$612$		0			0
$613$	−13.4196	+	7.74783i	−0.542014	+	0.312932i	−0.745895	−	0.666064i	$-0.767978\pi$
$613$	−13.4196	+	7.74783i	−0.542014	+	0.312932i	0.203881	+	0.978996i	$0.434645\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	17.7219			0.713459			0.356729	−	0.934208i	$-0.383892\pi$
$617$	17.7219			0.713459			0.356729	+	0.934208i	$0.383892\pi$
$618$		0			0
$619$	−5.96204	+	3.44219i	−0.239635	+	0.138353i	−0.615009	−	0.788520i	$-0.710848\pi$
$619$	−5.96204	+	3.44219i	−0.239635	+	0.138353i	0.375374	+	0.926873i	$0.377514\pi$
$620$		0			0
$621$	0.428695	+	14.9261i	0.0172029	+	0.598965i
$622$		0			0
$623$	−20.6021	+	7.10976i	−0.825404	+	0.284847i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−7.66789	+	21.7117i	−0.306226	+	0.867082i
$628$		0			0
$629$	−0.401627			−0.0160139
$630$		0			0
$631$	−49.6754			−1.97755			−0.988774	−	0.149421i	$-0.952259\pi$
$631$	−49.6754			−1.97755			−0.988774	+	0.149421i	$0.952259\pi$
$632$		0			0
$633$	1.13219	−	3.20580i	0.0450004	−	0.127419i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−5.96493	−	42.0218i	−0.236339	−	1.66496i
$638$		0			0
$639$	−6.84362	+	8.48041i	−0.270729	+	0.335480i
$640$		0			0
$641$	23.3007	−	13.4527i	0.920324	−	0.531349i	0.0365856	−	0.999331i	$-0.488352\pi$
$641$	23.3007	−	13.4527i	0.920324	−	0.531349i	0.883738	+	0.467981i	$0.155019\pi$
$642$		0			0
$643$	−13.9638			−0.550679			−0.275339	−	0.961347i	$-0.588790\pi$
$643$	−13.9638			−0.550679			−0.275339	+	0.961347i	$0.588790\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	26.5656	−	15.3377i	1.04440	−	0.602985i	0.123324	−	0.992366i	$-0.460644\pi$
$647$	26.5656	−	15.3377i	1.04440	−	0.602985i	0.921077	+	0.389381i	$0.127311\pi$
$648$		0			0
$649$	8.71262	+	5.03023i	0.342000	+	0.197454i
$650$		0			0
$651$	−15.0851	+	25.6994i	−0.591230	+	1.00724i
$652$		0			0
$653$	6.55879	−	11.3602i	0.256665	−	0.444557i	−0.708681	−	0.705529i	$-0.750710\pi$
$653$	6.55879	−	11.3602i	0.256665	−	0.444557i	0.965347	+	0.260971i	$0.0840429\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	3.60527	−	23.0143i	0.140655	−	0.897873i
$658$		0			0
$659$			37.1306i			1.44640i	0.690638	+	0.723201i	$0.257330\pi$
$659$			37.1306i			1.44640i	−0.690638	+	0.723201i	$0.742670\pi$
$660$		0			0
$661$	4.41297	−	2.54783i	0.171645	−	0.0990992i	−0.411716	−	0.911312i	$-0.635071\pi$
$661$	4.41297	−	2.54783i	0.171645	−	0.0990992i	0.583361	+	0.812213i	$0.301737\pi$
$662$		0			0
$663$	−5.89436	−	31.6539i	−0.228918	−	1.22934i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−19.8599	−	11.4661i	−0.768977	−	0.443969i
$668$		0			0
$669$	−1.03168	+	2.92120i	−0.0398869	+	0.112940i
$670$		0			0
$671$	33.5779			1.29626
$672$		0			0
$673$		−	29.0339i		−	1.11918i	−0.828771	−	0.559588i	$-0.810960\pi$
$673$		−	29.0339i		−	1.11918i	0.828771	−	0.559588i	$-0.189040\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	21.6131	+	12.4783i	0.830658	+	0.479581i	0.854078	−	0.520145i	$-0.174122\pi$
$677$	21.6131	+	12.4783i	0.830658	+	0.479581i	−0.0234197	+	0.999726i	$0.507455\pi$
$678$		0			0
$679$	−11.4880	−	9.97249i	−0.440870	−	0.382709i
$680$		0			0
$681$	−8.75019	−	46.9903i	−0.335308	−	1.80067i
$682$		0			0
$683$	−16.9226	−	29.3107i	−0.647524	−	1.12154i	−0.983712	−	0.179749i	$-0.942471\pi$
$683$	−16.9226	−	29.3107i	−0.647524	−	1.12154i	0.336189	−	0.941795i	$-0.390862\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−12.7293	+	10.8905i	−0.485654	+	0.415498i
$688$		0			0
$689$	−16.2472	−	28.1409i	−0.618967	−	1.07208i
$690$		0			0
$691$	9.82503	+	5.67249i	0.373762	+	0.215792i	0.675101	−	0.737726i	$-0.264100\pi$
$691$	9.82503	+	5.67249i	0.373762	+	0.215792i	−0.301339	+	0.953517i	$0.597434\pi$
$692$		0			0
$693$	19.9726	+	23.6878i	0.758696	+	0.899823i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	32.8323	−	18.9557i	1.24361	−	0.717999i
$698$		0			0
$699$	−0.671890	−	0.785338i	−0.0254132	−	0.0297042i
$700$		0			0
$701$			23.1947i			0.876052i	0.898962	+	0.438026i	$0.144322\pi$
$701$			23.1947i			0.876052i	−0.898962	+	0.438026i	$0.855678\pi$
$702$		0			0
$703$	−0.223060	−	0.386351i	−0.00841285	−	0.0145715i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.57266	+	23.6113i	−0.171972	+	0.887993i
$708$		0			0
$709$	−7.29490	+	12.6351i	−0.273966	+	0.474522i	−0.969874	−	0.243609i	$-0.921669\pi$
$709$	−7.29490	+	12.6351i	−0.273966	+	0.474522i	0.695908	+	0.718131i	$0.255002\pi$
$710$		0			0
$711$	−6.84675	+	2.64150i	−0.256773	+	0.0990639i
$712$		0			0
$713$		−	18.6873i		−	0.699844i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−14.5515	−	5.13912i	−0.543434	−	0.191924i
$718$		0			0
$719$	−9.35171	+	16.1976i	−0.348760	+	0.604070i	−0.986029	−	0.166571i	$-0.946730\pi$
$719$	−9.35171	+	16.1976i	−0.348760	+	0.604070i	0.637270	+	0.770641i	$0.280064\pi$
$720$		0			0
$721$	2.46407	−	0.850351i	0.0917668	−	0.0316687i
$722$		0			0
$723$	0.668348	+	3.58917i	0.0248561	+	0.133483i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−23.0483			−0.854815			−0.427407	−	0.904059i	$-0.640573\pi$
$727$	−23.0483			−0.854815			−0.427407	+	0.904059i	$0.640573\pi$
$728$		0			0
$729$	12.1357	−	24.1190i	0.449470	−	0.893295i
$730$		0			0
$731$	−6.79479	−	11.7689i	−0.251314	−	0.435289i
$732$		0			0
$733$	8.89746	−	15.4109i	0.328635	−	0.569213i	−0.653606	−	0.756835i	$-0.726745\pi$
$733$	8.89746	−	15.4109i	0.328635	−	0.569213i	0.982241	+	0.187622i	$0.0600780\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−31.2245	+	54.0824i	−1.15017	+	1.99215i
$738$		0			0
$739$	−6.97258	−	12.0769i	−0.256491	−	0.444255i	0.708809	−	0.705401i	$-0.249233\pi$
$739$	−6.97258	−	12.0769i	−0.256491	−	0.444255i	−0.965299	+	0.261146i	$0.915900\pi$
$740$		0			0
$741$	27.1763	−	23.2504i	0.998345	−	0.854127i
$742$		0			0
$743$	30.8975			1.13352			0.566760	−	0.823883i	$-0.308197\pi$
$743$	30.8975			1.13352			0.566760	+	0.823883i	$0.308197\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	14.3873	−	17.8283i	0.526404	−	0.652304i
$748$		0			0
$749$	−3.23010	+	1.11471i	−0.118025	+	0.0407305i
$750$		0			0
$751$	−11.7085	+	20.2797i	−0.427249	+	0.740017i	−0.996628	−	0.0820583i	$-0.973851\pi$
$751$	−11.7085	+	20.2797i	−0.427249	+	0.740017i	0.569378	+	0.822076i	$0.307184\pi$
$752$		0			0
$753$	−17.2016	+	48.7065i	−0.626862	+	1.77497i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			25.7901i			0.937357i	0.883369	+	0.468679i	$0.155270\pi$
$757$			25.7901i			0.937357i	−0.883369	+	0.468679i	$0.844730\pi$
$758$		0			0
$759$	−18.3210	−	6.47041i	−0.665011	−	0.234861i
$760$		0			0
$761$	9.03119	−	15.6425i	0.327380	−	0.567039i	−0.654611	−	0.755966i	$-0.727168\pi$
$761$	9.03119	−	15.6425i	0.327380	−	0.567039i	0.981991	+	0.188927i	$0.0605008\pi$
$762$		0			0
$763$	−3.70788	+	19.1459i	−0.134234	+	0.693129i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−7.81318	−	13.5328i	−0.282118	−	0.488642i
$768$		0			0
$769$		−	46.2208i		−	1.66677i	−0.552696	−	0.833383i	$-0.686401\pi$
$769$		−	46.2208i		−	1.66677i	0.552696	−	0.833383i	$-0.313599\pi$
$770$		0			0
$771$	17.8593	−	15.2794i	0.643188	−	0.550275i
$772$		0			0
$773$	−3.52734	+	2.03651i	−0.126870	+	0.0732482i	−0.562092	−	0.827075i	$-0.690003\pi$
$773$	−3.52734	+	2.03651i	−0.126870	+	0.0732482i	0.435222	+	0.900323i	$0.356670\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−0.600290	−	0.00431744i	−0.0215353	−	0.000154887i
$778$		0			0
$779$	36.4694	+	21.0556i	1.30665	+	0.754397i
$780$		0			0
$781$	−7.08988	−	12.2800i	−0.253696	−	0.439414i
$782$		0			0
$783$	21.7550	+	35.2998i	0.777459	+	1.26151i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	5.82407	+	10.0876i	0.207606	+	0.359584i	0.950960	−	0.309314i	$-0.100100\pi$
$787$	5.82407	+	10.0876i	0.207606	+	0.359584i	−0.743354	+	0.668898i	$0.766766\pi$
$788$		0			0
$789$	20.7023	−	3.85503i	0.737022	−	0.137243i
$790$		0			0
$791$	−9.04638	−	7.85295i	−0.321652	−	0.279219i
$792$		0			0
$793$	−45.1673	−	26.0774i	−1.60394	−	0.926034i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	36.7250i		−	1.30087i	−0.759564	−	0.650433i	$-0.774588\pi$
$797$		−	36.7250i		−	1.30087i	0.759564	−	0.650433i	$-0.225412\pi$
$798$		0			0
$799$	30.8407			1.09106
$800$		0			0
$801$	−23.0561	+	8.89511i	−0.814647	+	0.314293i
$802$		0			0
$803$	26.2507	+	15.1558i	0.926366	+	0.534837i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−38.2107	+	7.11532i	−1.34508	+	0.250471i
$808$		0			0
$809$	−34.1224	+	19.7006i	−1.19968	+	0.692635i	−0.960484	−	0.278336i	$-0.910217\pi$
$809$	−34.1224	+	19.7006i	−1.19968	+	0.692635i	−0.239196	+	0.970971i	$0.576884\pi$
$810$		0			0
$811$			50.4733i			1.77236i	0.463345	+	0.886178i	$0.346649\pi$
$811$			50.4733i			1.77236i	−0.463345	+	0.886178i	$0.653351\pi$
$812$		0			0
$813$	10.9295	−	9.35062i	0.383313	−	0.327941i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	7.54752	−	13.0727i	0.264054	−	0.457355i
$818$		0			0
$819$	−8.46970	−	47.3748i	−0.295955	−	1.65541i
$820$		0			0
$821$	−23.6817	−	13.6726i	−0.826498	−	0.477179i	0.0261543	−	0.999658i	$-0.491674\pi$
$821$	−23.6817	−	13.6726i	−0.826498	−	0.477179i	−0.852652	+	0.522479i	$0.825007\pi$
$822$		0			0
$823$	20.8603	−	12.0437i	0.727144	−	0.419817i	−0.0902322	−	0.995921i	$-0.528761\pi$
$823$	20.8603	−	12.0437i	0.727144	−	0.419817i	0.817377	+	0.576104i	$0.195428\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	21.4026			0.744242			0.372121	−	0.928184i	$-0.378631\pi$
$827$	21.4026			0.744242			0.372121	+	0.928184i	$0.378631\pi$
$828$		0			0
$829$	−27.3957	+	15.8169i	−0.951494	+	0.549345i	−0.893545	−	0.448974i	$-0.851789\pi$
$829$	−27.3957	+	15.8169i	−0.951494	+	0.549345i	−0.0579490	+	0.998320i	$0.518456\pi$
$830$		0			0
$831$	1.92053	+	10.3137i	0.0666225	+	0.357777i
$832$		0			0
$833$	13.2363	+	16.8936i	0.458610	+	0.585328i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−16.0478	+	29.7357i	−0.554691	+	1.02782i
$838$		0			0
$839$	40.4562			1.39670			0.698351	−	0.715755i	$-0.253917\pi$
$839$	40.4562			1.39670			0.698351	+	0.715755i	$0.253917\pi$
$840$		0			0
$841$	−34.6799			−1.19586
$842$		0			0
$843$	−28.7068	−	10.1383i	−0.988716	−	0.349183i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−10.6001	+	3.65809i	−0.364224	+	0.125693i
$848$		0			0
$849$	13.9766	−	2.60263i	0.479677	−	0.0893220i
$850$		0			0
$851$	0.326015	−	0.188225i	0.0111756	−	0.00645226i
$852$		0			0
$853$	−45.7681			−1.56707			−0.783536	−	0.621347i	$-0.786586\pi$
$853$	−45.7681			−1.56707			−0.783536	+	0.621347i	$0.786586\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−5.12566	+	2.95930i	−0.175089	+	0.101088i	−0.584983	−	0.811045i	$-0.698899\pi$
$857$	−5.12566	+	2.95930i	−0.175089	+	0.101088i	0.409894	+	0.912133i	$0.365566\pi$
$858$		0			0
$859$	−18.8859	−	10.9038i	−0.644377	−	0.372031i	0.141921	−	0.989878i	$-0.454672\pi$
$859$	−18.8859	−	10.9038i	−0.644377	−	0.372031i	−0.786299	+	0.617847i	$0.788005\pi$
$860$		0			0
$861$	49.2764	−	27.9791i	1.67933	−	0.953526i
$862$		0			0
$863$	−18.9429	+	32.8100i	−0.644823	+	1.11687i	0.339519	+	0.940599i	$0.389736\pi$
$863$	−18.9429	+	32.8100i	−0.644823	+	1.11687i	−0.984342	+	0.176267i	$0.943598\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−8.55769	−	10.0027i	−0.290634	−	0.339708i
$868$		0			0
$869$		−	9.54910i		−	0.323931i
$870$		0			0
$871$	84.0032	−	48.4993i	2.84634	−	1.64334i
$872$		0			0
$873$	−13.4237	−	10.8328i	−0.454325	−	0.366636i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	46.4929	+	26.8427i	1.56995	+	0.906412i	0.996173	+	0.0874025i	$0.0278566\pi$
$877$	46.4929	+	26.8427i	1.56995	+	0.906412i	0.573779	+	0.819010i	$0.305477\pi$
$878$		0			0
$879$	6.34674	+	2.24147i	0.214070	+	0.0756029i
$880$		0			0
$881$	−1.12570			−0.0379259			−0.0189630	−	0.999820i	$-0.506036\pi$
$881$	−1.12570			−0.0379259			−0.0189630	+	0.999820i	$0.506036\pi$
$882$		0			0
$883$			48.0889i			1.61832i	0.587587	+	0.809161i	$0.300078\pi$
$883$			48.0889i			1.61832i	−0.587587	+	0.809161i	$0.699922\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−44.9352	−	25.9434i	−1.50878	−	0.871093i	−0.999948	−	0.0102253i	$-0.996745\pi$
$887$	−44.9352	−	25.9434i	−1.50878	−	0.871093i	−0.508829	−	0.860867i	$-0.669922\pi$
$888$		0			0
$889$	−1.21556	+	1.40029i	−0.0407684	+	0.0469641i
$890$		0			0
$891$	23.5964	+	26.0291i	0.790509	+	0.872008i
$892$		0			0
$893$	17.1286	+	29.6676i	0.573187	+	0.992789i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	19.6195	+	22.9322i	0.655075	+	0.765684i
$898$		0			0
$899$	−25.9462	−	44.9401i	−0.865353	−	1.49884i
$900$		0			0
$901$	14.2295	+	8.21540i	0.474053	+	0.273695i
$902$		0			0
$903$	−10.0293	−	17.6634i	−0.333754	−	0.587801i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−6.18747	+	3.57234i	−0.205452	+	0.118618i	−0.599196	−	0.800602i	$-0.704513\pi$
$907$	−6.18747	+	3.57234i	−0.205452	+	0.118618i	0.393744	+	0.919220i	$0.371180\pi$
$908$		0			0
$909$	−4.22049	+	26.9415i	−0.139985	+	0.893594i
$910$		0			0
$911$			38.4884i			1.27518i	0.770377	+	0.637589i	$0.220068\pi$
$911$			38.4884i			1.27518i	−0.770377	+	0.637589i	$0.779932\pi$
$912$		0			0
$913$	14.9050	+	25.8162i	0.493283	+	0.854392i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	13.3068	−	4.59217i	0.439429	−	0.151647i
$918$		0			0
$919$	27.0403	−	46.8351i	0.891976	−	1.54495i	0.0544730	−	0.998515i	$-0.482652\pi$
$919$	27.0403	−	46.8351i	0.891976	−	1.54495i	0.837503	−	0.546433i	$-0.184015\pi$
$920$		0			0
$921$	−0.0690741	+	0.195584i	−0.00227607	+	0.00644471i
$922$		0			0
$923$			22.0246i			0.724950i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	2.75758	−	1.06388i	0.0905709	−	0.0349425i
$928$		0			0
$929$	−18.8140	+	32.5869i	−0.617269	+	1.06914i	0.372713	+	0.927947i	$0.378427\pi$
$929$	−18.8140	+	32.5869i	−0.617269	+	1.06914i	−0.989982	+	0.141194i	$0.954906\pi$
$930$		0			0
$931$	−8.89970	+	22.1154i	−0.291676	+	0.724802i
$932$		0			0
$933$	−22.3816	+	4.16773i	−0.732740	+	0.136445i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−3.05652			−0.0998522			−0.0499261	−	0.998753i	$-0.515899\pi$
$937$	−3.05652			−0.0998522			−0.0499261	+	0.998753i	$0.515899\pi$
$938$		0			0
$939$	26.2008	+	30.6248i	0.855030	+	0.999402i
$940$		0			0
$941$	27.3577	+	47.3849i	0.891835	+	1.54470i	0.837674	+	0.546171i	$0.183915\pi$
$941$	27.3577	+	47.3849i	0.891835	+	1.54470i	0.0541612	+	0.998532i	$0.482752\pi$
$942$		0			0
$943$	−17.7674	+	30.7741i	−0.578587	+	1.00214i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3.58341	−	6.20664i	0.116445	−	0.201689i	−0.801911	−	0.597443i	$-0.796183\pi$
$947$	3.58341	−	6.20664i	0.116445	−	0.201689i	0.918356	+	0.395754i	$0.129517\pi$
$948$		0			0
$949$	−23.5407	−	40.7737i	−0.764164	−	1.32357i
$950$		0			0
$951$	39.1266	+	45.7332i	1.26877	+	1.48300i
$952$		0			0
$953$	−0.140553			−0.00455295			−0.00227648	−	0.999997i	$-0.500725\pi$
$953$	−0.140553			−0.00455295			−0.00227648	+	0.999997i	$0.500725\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−53.0431	+	9.87729i	−1.71464	+	0.319287i
$958$		0			0
$959$	1.97446	−	10.1953i	0.0637586	−	0.329222i
$960$		0			0
$961$	5.64335	−	9.77457i	0.182043	−	0.315309i
$962$		0			0
$963$	−3.61485	+	1.39462i	−0.116487	+	0.0449410i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			21.4958i			0.691258i	0.938371	+	0.345629i	$0.112334\pi$
$967$			21.4958i			0.691258i	−0.938371	+	0.345629i	$0.887666\pi$
$968$		0			0
$969$	−6.02238	+	17.0524i	−0.193467	+	0.547802i
$970$		0			0
$971$	7.37642	−	12.7763i	0.236721	−	0.410012i	−0.723051	−	0.690795i	$-0.757261\pi$
$971$	7.37642	−	12.7763i	0.236721	−	0.410012i	0.959771	+	0.280783i	$0.0905940\pi$
$972$		0			0
$973$	28.0496	−	32.3123i	0.899228	−	1.03589i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.621141	−	1.07585i	−0.0198720	−	0.0344194i	0.855918	−	0.517111i	$-0.172993\pi$
$977$	−0.621141	−	1.07585i	−0.0198720	−	0.0344194i	−0.875790	+	0.482692i	$0.839659\pi$
$978$		0			0
$979$		−	32.1561i		−	1.02771i
$980$		0			0
$981$	−3.42232	+	21.8464i	−0.109266	+	0.697501i
$982$		0			0
$983$	−10.4680	+	6.04373i	−0.333879	+	0.192765i	−0.657562	−	0.753401i	$-0.728412\pi$
$983$	−10.4680	+	6.04373i	−0.333879	+	0.192765i	0.323683	+	0.946166i	$0.395079\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	46.0959	+	0.331534i	1.46725	+	0.0105528i
$988$		0			0
$989$	11.0311	+	6.36883i	0.350770	+	0.202517i
$990$		0			0
$991$	−4.50767	−	7.80752i	−0.143191	−	0.248014i	0.785506	−	0.618854i	$-0.212403\pi$
$991$	−4.50767	−	7.80752i	−0.143191	−	0.248014i	−0.928697	+	0.370841i	$0.879070\pi$
$992$		0			0
$993$	28.8307	+	33.6988i	0.914915	+	1.06940i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−21.5205	−	37.2746i	−0.681562	−	1.18050i	−0.974504	−	0.224370i	$-0.927968\pi$
$997$	−21.5205	−	37.2746i	−0.681562	−	1.18050i	0.292942	−	0.956130i	$-0.405366\pi$
$998$		0			0
$999$	−0.680401	+	0.0195419i	−0.0215270	+	0.000618278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bo.g.1349.4		20
3.2	odd	2		2100.2.bo.h.1349.10		20
5.2	odd	4		2100.2.bi.j.1601.5		10
5.3	odd	4		420.2.bh.b.341.1	yes	10
5.4	even	2	inner	2100.2.bo.g.1349.7		20
7.3	odd	6		2100.2.bo.h.1949.1		20
15.2	even	4		2100.2.bi.k.1601.3		10
15.8	even	4		420.2.bh.a.341.3	yes	10
15.14	odd	2		2100.2.bo.h.1349.1		20
21.17	even	6	inner	2100.2.bo.g.1949.7		20
35.3	even	12		420.2.bh.a.101.3	✓	10
35.17	even	12		2100.2.bi.k.101.3		10
35.23	odd	12		2940.2.d.a.881.9		10
35.24	odd	6		2100.2.bo.h.1949.10		20
35.33	even	12		2940.2.d.b.881.2		10
105.17	odd	12		2100.2.bi.j.101.5		10
105.23	even	12		2940.2.d.b.881.1		10
105.38	odd	12		420.2.bh.b.101.1	yes	10
105.59	even	6	inner	2100.2.bo.g.1949.4		20
105.68	odd	12		2940.2.d.a.881.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bh.a.101.3	✓	10	35.3	even	12
420.2.bh.a.341.3	yes	10	15.8	even	4
420.2.bh.b.101.1	yes	10	105.38	odd	12
420.2.bh.b.341.1	yes	10	5.3	odd	4
2100.2.bi.j.101.5		10	105.17	odd	12
2100.2.bi.j.1601.5		10	5.2	odd	4
2100.2.bi.k.101.3		10	35.17	even	12
2100.2.bi.k.1601.3		10	15.2	even	4
2100.2.bo.g.1349.4		20	1.1	even	1	trivial
2100.2.bo.g.1349.7		20	5.4	even	2	inner
2100.2.bo.g.1949.4		20	105.59	even	6	inner
2100.2.bo.g.1949.7		20	21.17	even	6	inner
2100.2.bo.h.1349.1		20	15.14	odd	2
2100.2.bo.h.1349.10		20	3.2	odd	2
2100.2.bo.h.1949.1		20	7.3	odd	6
2100.2.bo.h.1949.10		20	35.24	odd	6
2940.2.d.a.881.9		10	35.23	odd	12
2940.2.d.a.881.10		10	105.68	odd	12
2940.2.d.b.881.1		10	105.23	even	12
2940.2.d.b.881.2		10	35.33	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.bo (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.576792 + 1.63319i) q^{3} +(-1.99797 - 1.73439i) q^{7} +(-2.33462 - 1.88402i) q^{9} +O(q^{10})\)	\(q+(-0.576792 + 1.63319i) q^{3} +(-1.99797 - 1.73439i) q^{7} +(-2.33462 - 1.88402i) q^{9} +(3.38064 - 1.95181i) q^{11} -6.06329 q^{13} +(2.65516 - 1.53296i) q^{17} +(2.94930 + 1.70278i) q^{19} +(3.98500 - 2.26269i) q^{21} +(-1.43686 + 2.48871i) q^{23} +(4.42356 - 2.72620i) q^{27} +7.97997i q^{29} +(-5.63161 + 3.25141i) q^{31} +(1.23776 + 6.64702i) q^{33} +(-0.113447 - 0.0654987i) q^{37} +(3.49726 - 9.90252i) q^{39} +12.3654 q^{41} -4.43247i q^{43} +(8.71153 + 5.02960i) q^{47} +(0.983778 + 6.93053i) q^{49} +(0.972138 + 5.22058i) q^{51} +(2.67959 + 4.64119i) q^{53} +(-4.48210 + 3.83462i) q^{57} +(1.28860 + 2.23193i) q^{59} +(7.44930 + 4.30086i) q^{61} +(1.39688 + 7.81337i) q^{63} +(-13.8544 + 7.99884i) q^{67} +(-3.23578 - 3.78214i) q^{69} -3.63245i q^{71} +(3.88250 + 6.72468i) q^{73} +(-10.1396 - 1.96368i) q^{77} +(1.22311 - 2.11848i) q^{79} +(1.90093 + 8.79696i) q^{81} +7.63648i q^{83} +(-13.0328 - 4.60278i) q^{87} +(4.11874 - 7.13387i) q^{89} +(12.1143 + 10.5161i) q^{91} +(-2.06191 - 11.0729i) q^{93} +5.74985 q^{97} +(-11.5698 - 1.81245i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{9}+O(q^{10}) \) 20 * q - 6 * q^9	\( 20 q - 6 q^{9} + 12 q^{11} - 6 q^{19} + 24 q^{21} + 30 q^{31} + 42 q^{39} + 16 q^{41} + 26 q^{49} + 80 q^{51} + 84 q^{61} - 28 q^{69} - 2 q^{79} - 26 q^{81} + 56 q^{89} - 22 q^{91} - 72 q^{99}+O(q^{100}) \) 20 * q - 6 * q^9 + 12 * q^11 - 6 * q^19 + 24 * q^21 + 30 * q^31 + 42 * q^39 + 16 * q^41 + 26 * q^49 + 80 * q^51 + 84 * q^61 - 28 * q^69 - 2 * q^79 - 26 * q^81 + 56 * q^89 - 22 * q^91 - 72 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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