LMFDB - Embedded newform 2100.2.bo.h.1349.1

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:	$\Z[a_1, \ldots, a_{7}]$
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			1349.1
Root			$1.70278 + 0.317079i$ of defining polynomial
Character	$\chi$	$=$	2100.1349
Dual form			2100.2.bo.h.1949.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70278 - 0.317079i) q^{3} +(1.99797 + 1.73439i) q^{7} +(2.79892 + 1.07983i) q^{9} +O(q^{10})$	\(q+(-1.70278 - 0.317079i) q^{3} +(1.99797 + 1.73439i) q^{7} +(2.79892 + 1.07983i) q^{9} +(-3.38064 + 1.95181i) q^{11} +6.06329 q^{13} +(2.65516 - 1.53296i) q^{17} +(2.94930 + 1.70278i) q^{19} +(-2.85217 - 3.58680i) q^{21} +(-1.43686 + 2.48871i) q^{23} +(-4.42356 - 2.72620i) q^{27} -7.97997i q^{29} +(-5.63161 + 3.25141i) q^{31} +(6.37537 - 2.25158i) q^{33} +(0.113447 + 0.0654987i) q^{37} +(-10.3245 - 1.92254i) q^{39} -12.3654 q^{41} +4.43247i q^{43} +(8.71153 + 5.02960i) q^{47} +(0.983778 + 6.93053i) q^{49} +(-5.00723 + 1.76839i) q^{51} +(2.67959 + 4.64119i) q^{53} +(-4.48210 - 3.83462i) q^{57} +(-1.28860 - 2.23193i) q^{59} +(7.44930 + 4.30086i) q^{61} +(3.71931 + 7.01190i) q^{63} +(13.8544 - 7.99884i) q^{67} +(3.23578 - 3.78214i) q^{69} +3.63245i q^{71} +(-3.88250 - 6.72468i) q^{73} +(-10.1396 - 1.96368i) q^{77} +(1.22311 - 2.11848i) q^{79} +(6.66792 + 6.04473i) q^{81} +7.63648i q^{83} +(-2.53028 + 13.5881i) q^{87} +(-4.11874 + 7.13387i) q^{89} +(12.1143 + 10.5161i) q^{91} +(10.6203 - 3.75077i) q^{93} -5.74985 q^{97} +(-11.5698 + 1.81245i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{9}+O(q^{10}) $ 20 * q + 6 * q^9	$ 20 q + 6 q^{9} - 12 q^{11} - 6 q^{19} + 20 q^{21} + 30 q^{31} - 30 q^{39} - 16 q^{41} + 26 q^{49} - 88 q^{51} + 84 q^{61} + 28 q^{69} - 2 q^{79} + 82 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 + 20 * q^21 + 30 * q^31 - 30 * q^39 - 16 * q^41 + 26 * q^49 - 88 * q^51 + 84 * q^61 + 28 * q^69 - 2 * q^79 + 82 * 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
$3$	−1.70278	−	0.317079i	−0.983101	−	0.183066i
$3$	−1.70278	−	0.317079i	−0.983101	−	0.183066i
$4$		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
$9$	2.79892	+	1.07983i	0.932974	+	0.359944i
$10$		0			0
$11$	−3.38064	+	1.95181i	−1.01930	+	0.588494i	−0.913902	−	0.405936i	$-0.866946\pi$
$11$	−3.38064	+	1.95181i	−1.01930	+	0.588494i	−0.105400	+	0.994430i	$0.533612\pi$
$12$		0			0
$13$	6.06329			1.68166			0.840828	−	0.541303i	$-0.182069\pi$
$13$	6.06329			1.68166			0.840828	+	0.541303i	$0.182069\pi$
$14$		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
$21$	−2.85217	−	3.58680i	−0.622394	−	0.782704i
$22$		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	$-0.734389\pi$
$29$		−	7.97997i		−	1.48184i	0.671591	−	0.740922i	$-0.265611\pi$
$30$		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
$33$	6.37537	−	2.25158i	1.10981	−	0.391950i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.113447	+	0.0654987i	0.0186506	+	0.0107679i	0.509296	−	0.860591i	$-0.329906\pi$
$37$	0.113447	+	0.0654987i	0.0186506	+	0.0107679i	−0.490646	+	0.871359i	$0.663239\pi$
$38$		0			0
$39$	−10.3245	−	1.92254i	−1.65324	−	0.307853i
$40$		0			0
$41$	−12.3654			−1.93116			−0.965579	−	0.260108i	$-0.916242\pi$
$41$	−12.3654			−1.93116			−0.965579	+	0.260108i	$0.916242\pi$
$42$		0			0
$43$			4.43247i			0.675945i	0.941156	+	0.337972i	$0.109741\pi$
$43$			4.43247i			0.675945i	−0.941156	+	0.337972i	$0.890259\pi$
$44$		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
$51$	−5.00723	+	1.76839i	−0.701152	+	0.247625i
$52$		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	0.769871	−	0.638200i	$-0.220321\pi$
$59$	−1.28860	−	2.23193i	−0.167762	−	0.290572i	−0.937633	+	0.347628i	$0.886987\pi$
$60$		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
$63$	3.71931	+	7.01190i	0.468589	+	0.883416i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	13.8544	−	7.99884i	1.69258	−	0.977213i	0.740162	−	0.672429i	$-0.234749\pi$
$67$	13.8544	−	7.99884i	1.69258	−	0.977213i	0.952421	−	0.304785i	$-0.0985845\pi$
$68$		0			0
$69$	3.23578	−	3.78214i	0.389542	−	0.455316i
$70$		0			0
$71$			3.63245i			0.431093i	0.976494	+	0.215547i	$0.0691533\pi$
$71$			3.63245i			0.431093i	−0.976494	+	0.215547i	$0.930847\pi$
$72$		0			0
$73$	−3.88250	−	6.72468i	−0.454412	−	0.787064i	0.544242	−	0.838928i	$-0.316817\pi$
$73$	−3.88250	−	6.72468i	−0.454412	−	0.787064i	−0.998654	+	0.0518638i	$0.983484\pi$
$74$		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
$81$	6.66792	+	6.04473i	0.740880	+	0.671637i
$82$		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
$87$	−2.53028	+	13.5881i	−0.271275	+	1.45680i
$88$		0			0
$89$	−4.11874	+	7.13387i	−0.436586	+	0.756189i	−0.997424	−	0.0717367i	$-0.977146\pi$
$89$	−4.11874	+	7.13387i	−0.436586	+	0.756189i	0.560838	+	0.827926i	$0.310479\pi$
$90$		0			0
$91$	12.1143	+	10.5161i	1.26992	+	1.10239i
$92$		0			0
$93$	10.6203	−	3.75077i	1.10128	−	0.388937i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−5.74985			−0.583809			−0.291904	−	0.956447i	$-0.594289\pi$
$97$	−5.74985			−0.583809			−0.291904	+	0.956447i	$0.594289\pi$
$98$		0			0
$99$	−11.5698	+	1.81245i	−1.16281	+	0.182158i
$100$		0			0
$101$	4.54502	+	7.87220i	0.452246	+	0.783313i	0.998525	−	0.0542901i	$-0.0172896\pi$
$101$	4.54502	+	7.87220i	0.452246	+	0.783313i	−0.546279	+	0.837603i	$0.683956\pi$
$102$		0			0
$103$	0.492615	−	0.853234i	0.0485388	−	0.0840717i	−0.840735	−	0.541446i	$-0.817877\pi$
$103$	0.492615	−	0.853234i	0.0485388	−	0.0840717i	0.889274	+	0.457375i	$0.151210\pi$
$104$		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
$117$	16.9707	+	6.54734i	1.56894	+	0.605302i
$118$		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
$123$	21.0556	+	3.92083i	1.89852	+	0.353529i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			0.700855i			0.0621908i	0.999516	+	0.0310954i	$0.00989957\pi$
$127$			0.700855i			0.0621908i	−0.999516	+	0.0310954i	$0.990100\pi$
$128$		0			0
$129$	1.40544	−	7.54752i	0.123742	−	0.664522i
$130$		0			0
$131$	2.66028	−	4.60774i	0.232430	−	0.402580i	−0.726093	−	0.687597i	$-0.758666\pi$
$131$	2.66028	−	4.60774i	0.232430	−	0.402580i	0.958523	+	0.285016i	$0.0919991\pi$
$132$		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
$147$	0.522368	−	12.1131i	0.0430841	−	0.999071i
$148$		0			0
$149$	17.4366	+	10.0670i	1.42846	+	0.824721i	0.996999	−	0.0774116i	$-0.0246655\pi$
$149$	17.4366	+	10.0670i	1.42846	+	0.824721i	0.431459	+	0.902132i	$0.357999\pi$
$150$		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	0.671955	−	0.740592i	$-0.265455\pi$
$157$	−3.82658	−	6.62784i	−0.305395	−	0.528959i	−0.977349	+	0.211633i	$0.932122\pi$
$158$		0			0
$159$	−3.09113	−	8.75257i	−0.245143	−	0.694124i
$160$		0			0
$161$	−7.18721	+	2.48030i	−0.566431	+	0.195475i
$162$		0			0
$163$	7.33954	+	4.23749i	0.574877	+	0.331906i	0.759095	−	0.650980i	$-0.225642\pi$
$163$	7.33954	+	4.23749i	0.574877	+	0.331906i	−0.184218	+	0.982885i	$0.558975\pi$
$164$		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
$171$	6.41615	+	7.95070i	0.490655	+	0.608005i
$172$		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
$177$	1.48651	+	4.20907i	0.111733	+	0.316373i
$178$		0			0
$179$	0.336240	−	0.194128i	0.0251318	−	0.0145098i	−0.487381	−	0.873189i	$-0.662048\pi$
$179$	0.336240	−	0.194128i	0.0251318	−	0.0145098i	0.512513	+	0.858679i	$0.328715\pi$
$180$		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
$189$	−4.10985	−	13.1190i	−0.298947	−	0.954270i
$190$		0			0
$191$	15.2933	+	8.82961i	1.10659	+	0.638888i	0.937943	−	0.346789i	$-0.112728\pi$
$191$	15.2933	+	8.82961i	1.10659	+	0.638888i	0.168644	+	0.985677i	$0.446061\pi$
$192$		0			0
$193$	−18.5161	+	10.6903i	−1.33282	+	0.769505i	−0.985731	−	0.168327i	$-0.946163\pi$
$193$	−18.5161	+	10.6903i	−1.33282	+	0.769505i	−0.347090	+	0.937832i	$0.612830\pi$
$194$		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
$201$	−26.1272	+	9.22732i	−1.84287	+	0.650845i
$202$		0			0
$203$	13.8404	−	15.9438i	0.971405	−	1.11903i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−6.70905	+	5.41415i	−0.466311	+	0.376309i
$208$		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
$213$	1.15178	−	6.18527i	0.0789184	−	0.423808i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−16.8910	−	3.27118i	−1.14664	−	0.222062i
$218$		0			0
$219$	4.47878	+	12.6817i	0.302648	+	0.856951i
$220$		0			0
$221$	16.0990	−	9.29478i	1.08294	−	0.625234i
$222$		0			0
$223$	−1.78864			−0.119776			−0.0598882	−	0.998205i	$-0.519074\pi$
$223$	−1.78864			−0.119776			−0.0598882	+	0.998205i	$0.519074\pi$
$224$		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
$231$	16.6429	+	6.55879i	1.09502	+	0.431537i
$232$		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	$-0.906955\pi$
$239$		−	8.90983i		−	0.576329i	0.957581	−	0.288165i	$-0.0930450\pi$
$240$		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
$243$	−9.43735	−	12.4071i	−0.605406	−	0.795917i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	17.8825	+	10.3245i	1.13784	+	0.656930i
$248$		0			0
$249$	2.42137	−	13.0033i	0.153448	−	0.824048i
$250$		0			0
$251$	−29.8229			−1.88241			−0.941204	−	0.337840i	$-0.890304\pi$
$251$	−29.8229			−1.88241			−0.941204	+	0.337840i	$0.890304\pi$
$252$		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
$261$	8.61703	−	22.3353i	0.533381	−	1.38252i
$262$		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	$-0.926861\pi$
$269$	−11.2201	−	19.4338i	−0.684101	−	1.18490i	0.289617	−	0.957143i	$-0.406472\pi$
$270$		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
$273$	−17.2935	−	21.7478i	−1.04665	−	1.31624i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−5.24547	+	3.02848i	−0.315170	+	0.181963i	−0.649238	−	0.760586i	$-0.724912\pi$
$277$	−5.24547	+	3.02848i	−0.315170	+	0.181963i	0.334068	+	0.942549i	$0.391579\pi$
$278$		0			0
$279$	−19.2734	+	3.01925i	−1.15387	+	0.180758i
$280$		0			0
$281$		−	17.5771i		−	1.04856i	−0.851545	−	0.524282i	$-0.824334\pi$
$281$		−	17.5771i		−	1.04856i	0.851545	−	0.524282i	$-0.175666\pi$
$282$		0			0
$283$	4.10407	+	7.10845i	0.243961	+	0.422554i	0.961839	−	0.273616i	$-0.0882196\pi$
$283$	4.10407	+	7.10845i	0.243961	+	0.422554i	−0.717878	+	0.696169i	$0.754886\pi$
$284$		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
$291$	9.79073	+	1.82316i	0.573943	+	0.106875i
$292$		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
$297$	20.2755	+	0.582334i	1.17650	+	0.0337905i
$298$		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
$303$	−5.24305	−	14.8458i	−0.301206	−	0.852866i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−0.119756			−0.00683482			−0.00341741	−	0.999994i	$-0.501088\pi$
$307$	−0.119756			−0.00683482			−0.00341741	+	0.999994i	$0.501088\pi$
$308$		0			0
$309$	−1.10936	+	1.29667i	−0.0631092	+	0.0737651i
$310$		0			0
$311$	−6.57207	−	11.3832i	−0.372668	−	0.645480i	0.617307	−	0.786722i	$-0.288224\pi$
$311$	−6.57207	−	11.3832i	−0.372668	−	0.645480i	−0.989975	+	0.141243i	$0.954890\pi$
$312$		0			0
$313$	−11.6346	+	20.1517i	−0.657625	+	1.13904i	0.323604	+	0.946192i	$0.395105\pi$
$313$	−11.6346	+	20.1517i	−0.657625	+	1.13904i	−0.981229	+	0.192847i	$0.938228\pi$
$314$		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
$327$	4.25149	+	12.0381i	0.235108	+	0.665711i
$328$		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
$333$	0.246802	+	0.305829i	0.0135247	+	0.0167593i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	26.5502i		−	1.44628i	−0.690702	−	0.723140i	$-0.742698\pi$
$337$		−	26.5502i		−	1.44628i	0.690702	−	0.723140i	$-0.257302\pi$
$338$		0			0
$339$	−7.70982	−	1.43567i	−0.418740	−	0.0779747i
$340$		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
$357$	−13.0714	−	5.15128i	−0.691811	−	0.272635i
$358$		0			0
$359$	−19.1592	−	11.0615i	−1.01118	−	0.583806i	−0.0996440	−	0.995023i	$-0.531770\pi$
$359$	−19.1592	−	11.0615i	−1.01118	−	0.583806i	−0.911537	+	0.411217i	$0.865104\pi$
$360$		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	0.984888	−	0.173194i	$-0.0554087\pi$
$367$	6.56047	+	11.3631i	0.342454	+	0.593147i	−0.642434	+	0.766341i	$0.722075\pi$
$368$		0			0
$369$	−34.6099	−	13.3526i	−1.80172	−	0.695109i
$370$		0			0
$371$	−2.69589	+	13.9204i	−0.139964	+	0.722712i
$372$		0			0
$373$	−12.7826	−	7.38003i	−0.661857	−	0.382123i	0.131127	−	0.991366i	$-0.458140\pi$
$373$	−12.7826	−	7.38003i	−0.661857	−	0.382123i	−0.792984	+	0.609242i	$0.791474\pi$
$374$		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
$381$	0.222226	−	1.19340i	0.0113850	−	0.0611398i
$382$		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
$387$	−4.78632	+	12.4061i	−0.243302	+	0.630639i
$388$		0			0
$389$	7.53666	−	4.35129i	0.382124	−	0.220619i	−0.296618	−	0.954996i	$-0.595859\pi$
$389$	7.53666	−	4.35129i	0.382124	−	0.220619i	0.678742	+	0.734377i	$0.262525\pi$
$390$		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	$-0.596281\pi$
$397$	13.5044	−	23.3904i	0.677768	−	1.17393i	0.975651	−	0.219327i	$-0.0703861\pi$
$398$		0			0
$399$	−2.30437	−	15.4352i	−0.115363	−	0.772725i
$400$		0			0
$401$	4.30215	+	2.48385i	0.214839	+	0.124037i	0.603558	−	0.797319i	$-0.293749\pi$
$401$	4.30215	+	2.48385i	0.214839	+	0.124037i	−0.388719	+	0.921356i	$0.627082\pi$
$402$		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
$411$	−2.26393	−	6.41035i	−0.111672	−	0.316199i
$412$		0			0
$413$	1.29644	−	6.69427i	0.0637937	−	0.329403i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	5.12799	−	27.5383i	0.251119	−	1.34856i
$418$		0			0
$419$	7.60294			0.371428			0.185714	−	0.982604i	$-0.440540\pi$
$419$	7.60294			0.371428			0.185714	+	0.982604i	$0.440540\pi$
$420$		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
$423$	18.9517	+	23.4844i	0.921466	+	1.14185i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	7.42413	+	21.5130i	0.359279	+	1.04109i
$428$		0			0
$429$	38.6558	−	13.6520i	1.86632	−	0.659125i
$430$		0			0
$431$	4.24065	−	2.44834i	0.204265	−	0.117932i	−0.394378	−	0.918948i	$-0.629040\pi$
$431$	4.24065	−	2.44834i	0.204265	−	0.117932i	0.598643	+	0.801016i	$0.295707\pi$
$432$		0			0
$433$	−18.6390			−0.895732			−0.447866	−	0.894101i	$-0.647816\pi$
$433$	−18.6390			−0.895732			−0.447866	+	0.894101i	$0.647816\pi$
$434$		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
$441$	−4.73029	+	20.4603i	−0.225252	+	0.974301i
$442$		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	$0.0389962\pi$
$449$			5.17892i			0.244408i	−0.992505	+	0.122204i	$0.961004\pi$
$450$		0			0
$451$	41.8032	−	24.1351i	1.96843	−	1.13648i
$452$		0			0
$453$	2.75684	+	7.80601i	0.129528	+	0.366758i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	10.4250	+	6.01889i	0.487662	+	0.281552i	0.723604	−	0.690215i	$-0.242484\pi$
$457$	10.4250	+	6.01889i	0.487662	+	0.281552i	−0.235942	+	0.971767i	$0.575817\pi$
$458$		0			0
$459$	−15.9244	−	0.457366i	−0.743287	−	0.0213480i
$460$		0			0
$461$	23.0451			1.07332			0.536658	−	0.843800i	$-0.319686\pi$
$461$	23.0451			1.07332			0.536658	+	0.843800i	$0.319686\pi$
$462$		0			0
$463$			27.8549i			1.29453i	0.762267	+	0.647263i	$0.224086\pi$
$463$			27.8549i			1.29453i	−0.762267	+	0.647263i	$0.775914\pi$
$464$		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
$471$	4.41428	+	12.4991i	0.203399	+	0.575927i
$472$		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	0.935377	−	0.353653i	$-0.115061\pi$
$479$	3.53276	+	6.11892i	0.161416	+	0.279581i	−0.773961	+	0.633234i	$0.781727\pi$
$480$		0			0
$481$	0.687863	+	0.397138i	0.0313638	+	0.0181079i
$482$		0			0
$483$	13.0247	−	1.94450i	0.592644	−	0.0884777i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−8.00270	+	4.62036i	−0.362637	+	0.209368i	−0.670237	−	0.742147i	$-0.733807\pi$
$487$	−8.00270	+	4.62036i	−0.362637	+	0.209368i	0.307600	+	0.951516i	$0.400474\pi$
$488$		0			0
$489$	−11.1540	−	9.54273i	−0.504402	−	0.431537i
$490$		0			0
$491$		−	14.0713i		−	0.635031i	−0.948253	−	0.317515i	$-0.897152\pi$
$491$		−	14.0713i		−	0.635031i	0.948253	−	0.317515i	$-0.102848\pi$
$492$		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
$501$	6.52135	−	35.0210i	0.291352	−	1.56462i
$502$		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
$507$	−40.4641	−	7.53492i	−1.79707	−	0.334638i
$508$		0			0
$509$	−9.86251	+	17.0824i	−0.437148	+	0.757163i	−0.997468	−	0.0711133i	$-0.977345\pi$
$509$	−9.86251	+	17.0824i	−0.437148	+	0.757163i	0.560320	+	0.828276i	$0.310678\pi$
$510$		0			0
$511$	3.90611	−	20.1695i	0.172796	−	0.892245i
$512$		0			0
$513$	−8.40429	−	15.5727i	−0.371058	−	0.687553i
$514$		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	$0.122640\pi$
$521$	18.0051	+	31.1857i	0.788818	+	1.36627i	−0.137874	+	0.990450i	$0.544027\pi$
$522$		0			0
$523$	10.7033	−	18.5387i	0.468023	−	0.810640i	−0.531309	−	0.847178i	$-0.678300\pi$
$523$	10.7033	−	18.5387i	0.468023	−	0.810640i	0.999332	+	0.0365378i	$0.0116329\pi$
$524$		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
$537$	−0.634097	+	0.223943i	−0.0273633	+	0.00966387i
$538$		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
$543$	6.55684	−	35.2116i	0.281381	−	1.51107i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	7.34057i		−	0.313860i	−0.987610	−	0.156930i	$-0.949840\pi$
$547$		−	7.34057i		−	0.313860i	0.987610	−	0.156930i	$-0.0501597\pi$
$548$		0			0
$549$	16.2058	+	20.0818i	0.691647	+	0.857069i
$550$		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
$567$	2.83839	+	23.6420i	0.119201	+	0.992870i
$568$		0			0
$569$	16.0347	+	9.25765i	0.672211	+	0.388101i	0.796914	−	0.604093i	$-0.206465\pi$
$569$	16.0347	+	9.25765i	0.672211	+	0.388101i	−0.124703	+	0.992194i	$0.539798\pi$
$570$		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	0.634177	−	0.773188i	$-0.281339\pi$
$577$	−8.46761	−	14.6663i	−0.352511	−	0.610568i	−0.986689	+	0.162620i	$0.948006\pi$
$578$		0			0
$579$	34.9186	−	12.3321i	1.45117	−	0.512507i
$580$		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
$591$	−38.3246	−	7.13651i	−1.57646	−	0.293557i
$592$		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
$597$	−16.0020	+	5.65141i	−0.654919	+	0.231297i
$598$		0			0
$599$	19.2300	−	11.1024i	0.785716	−	0.453634i	−0.0527360	−	0.998608i	$-0.516794\pi$
$599$	19.2300	−	11.1024i	0.785716	−	0.453634i	0.838452	+	0.544975i	$0.183461\pi$
$600$		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	−0.609649	−	0.792671i	$-0.708690\pi$
$607$	9.40283	−	16.2862i	0.381649	−	0.661035i	0.991298	+	0.131636i	$0.0420230\pi$
$608$		0			0
$609$	−28.6226	+	22.7602i	−1.15985	+	0.922290i
$610$		0			0
$611$	52.8205	+	30.4960i	2.13689	+	1.23373i
$612$		0			0
$613$	13.4196	−	7.74783i	0.542014	−	0.312932i	−0.203881	−	0.978996i	$-0.565355\pi$
$613$	13.4196	−	7.74783i	0.542014	−	0.312932i	0.745895	+	0.666064i	$0.232022\pi$
$614$		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
$621$	13.1408	−	7.09180i	0.527320	−	0.284584i
$622$		0			0
$623$	−20.6021	+	7.10976i	−0.825404	+	0.284847i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	22.6368	+	4.21527i	0.904028	+	0.168341i
$628$		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
$633$	3.34240	+	0.622396i	0.132848	+	0.0247380i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	5.96493	+	42.0218i	0.236339	+	1.66496i
$638$		0			0
$639$	−3.92244	+	10.1670i	−0.155169	+	0.402199i
$640$		0			0
$641$	−23.3007	+	13.4527i	−0.920324	+	0.531349i	−0.883738	−	0.467981i	$-0.844981\pi$
$641$	−23.3007	+	13.4527i	−0.920324	+	0.531349i	−0.0365856	+	0.999331i	$0.511648\pi$
$642$		0			0
$643$	13.9638			0.550679			0.275339	−	0.961347i	$-0.411210\pi$
$643$	13.9638			0.550679			0.275339	+	0.961347i	$0.411210\pi$
$644$		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
$651$	27.7245	+	10.9259i	1.08661	+	0.428220i
$652$		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	$-0.742670\pi$
$659$		−	37.1306i		−	1.44640i	0.690638	−	0.723201i	$-0.257330\pi$
$660$		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
$663$	−30.3603	+	10.7223i	−1.17910	+	0.416420i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	19.8599	+	11.4661i	0.768977	+	0.443969i
$668$		0			0
$669$	3.04567	+	0.567142i	0.117752	+	0.0219270i
$670$		0			0
$671$	−33.5779			−1.29626
$672$		0			0
$673$			29.0339i			1.11918i	0.828771	+	0.559588i	$0.189040\pi$
$673$			29.0339i			1.11918i	−0.828771	+	0.559588i	$0.810960\pi$
$674$		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
$681$	45.0699	−	15.9173i	1.72708	−	0.609951i
$682$		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
$693$	−26.2596	−	16.4453i	−0.997519	−	0.624706i
$694$		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	$-0.855678\pi$
$701$		−	23.1947i		−	0.876052i	0.898962	−	0.438026i	$-0.144322\pi$
$702$		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
$711$	5.71098	−	4.60871i	0.214178	−	0.172840i
$712$		0			0
$713$		−	18.6873i		−	0.699844i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−2.82512	+	15.1715i	−0.105506	+	0.566590i
$718$		0			0
$719$	9.35171	−	16.1976i	0.348760	−	0.604070i	−0.637270	−	0.770641i	$-0.719936\pi$
$719$	9.35171	−	16.1976i	0.348760	−	0.604070i	0.986029	+	0.166571i	$0.0532696\pi$
$720$		0			0
$721$	2.46407	−	0.850351i	0.0917668	−	0.0316687i
$722$		0			0
$723$	−3.44249	+	1.21578i	−0.128027	+	0.0452153i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	23.0483			0.854815			0.427407	−	0.904059i	$-0.359427\pi$
$727$	23.0483			0.854815			0.427407	+	0.904059i	$0.359427\pi$
$728$		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	−0.982241	−	0.187622i	$-0.939922\pi$
$733$	−8.89746	+	15.4109i	−0.328635	+	0.569213i	0.653606	+	0.756835i	$0.273255\pi$
$734$		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
$747$	−8.24612	+	21.3739i	−0.301710	+	0.782031i
$748$		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
$753$	50.7819	+	9.45623i	1.85060	+	0.344604i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	25.7901i		−	0.937357i	−0.883369	−	0.468679i	$-0.844730\pi$
$757$		−	25.7901i		−	0.937357i	0.883369	−	0.468679i	$-0.155270\pi$
$758$		0			0
$759$	−3.55697	+	19.1017i	−0.129110	+	0.693347i
$760$		0			0
$761$	−9.03119	+	15.6425i	−0.327380	+	0.567039i	−0.981991	−	0.188927i	$-0.939499\pi$
$761$	−9.03119	+	15.6425i	−0.327380	+	0.567039i	0.654611	+	0.755966i	$0.272832\pi$
$762$		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
$777$	−0.0886391	−	0.593725i	−0.00317991	−	0.0212998i
$778$		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	0.743354	−	0.668898i	$-0.233234\pi$
$787$	−5.82407	−	10.0876i	−0.207606	−	0.359584i	−0.950960	+	0.309314i	$0.899900\pi$
$788$		0			0
$789$	7.01260	+	19.8562i	0.249655	+	0.706901i
$790$		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
$801$	−19.2314	+	15.5196i	−0.679509	+	0.548358i
$802$		0			0
$803$	26.2507	+	15.1558i	0.926366	+	0.534837i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	12.9433	+	36.6491i	0.455626	+	1.29011i
$808$		0			0
$809$	34.1224	−	19.7006i	1.19968	−	0.692635i	0.239196	−	0.970971i	$-0.423116\pi$
$809$	34.1224	−	19.7006i	1.19968	−	0.692635i	0.960484	+	0.278336i	$0.0897829\pi$
$810$		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
$819$	22.5513	+	42.5152i	0.788006	+	1.48560i
$820$		0			0
$821$	23.6817	+	13.6726i	0.826498	+	0.477179i	0.852652	−	0.522479i	$-0.174993\pi$
$821$	23.6817	+	13.6726i	0.826498	+	0.477179i	−0.0261543	+	0.999658i	$0.508326\pi$
$822$		0			0
$823$	−20.8603	+	12.0437i	−0.727144	+	0.419817i	−0.817377	−	0.576104i	$-0.804572\pi$
$823$	−20.8603	+	12.0437i	−0.727144	+	0.419817i	0.0902322	+	0.995921i	$0.471239\pi$
$824$		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
$831$	9.89216	−	3.49360i	0.343155	−	0.121192i
$832$		0			0
$833$	13.2363	+	16.8936i	0.458610	+	0.585328i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	33.7757	+	0.970076i	1.16746	+	0.0335307i
$838$		0			0
$839$	−40.4562			−1.39670			−0.698351	−	0.715755i	$-0.746083\pi$
$839$	−40.4562			−1.39670			−0.698351	+	0.715755i	$0.746083\pi$
$840$		0			0
$841$	−34.6799			−1.19586
$842$		0			0
$843$	−5.57335	+	29.9300i	−0.191956	+	1.03084i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	10.6001	−	3.65809i	0.364224	−	0.125693i
$848$		0			0
$849$	−4.73438	−	13.4054i	−0.162484	−	0.460074i
$850$		0			0
$851$	−0.326015	+	0.188225i	−0.0111756	+	0.00645226i
$852$		0			0
$853$	45.7681			1.56707			0.783536	−	0.621347i	$-0.213414\pi$
$853$	45.7681			1.56707			0.783536	+	0.621347i	$0.213414\pi$
$854$		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
$861$	35.2683	+	44.3524i	1.20194	+	1.51153i
$862$		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
$873$	−16.0934	−	6.20888i	−0.544678	−	0.210139i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−46.4929	−	26.8427i	−1.56995	−	0.906412i	−0.996173	−	0.0874025i	$-0.972143\pi$
$877$	−46.4929	−	26.8427i	−1.56995	−	0.906412i	−0.573779	−	0.819010i	$-0.694523\pi$
$878$		0			0
$879$	−1.23220	+	6.61717i	−0.0415611	+	0.223192i
$880$		0			0
$881$	1.12570			0.0379259			0.0189630	−	0.999820i	$-0.493964\pi$
$881$	1.12570			0.0379259			0.0189630	+	0.999820i	$0.493964\pi$
$882$		0			0
$883$		−	48.0889i		−	1.61832i	−0.587587	−	0.809161i	$-0.699922\pi$
$883$		−	48.0889i		−	1.61832i	0.587587	−	0.809161i	$-0.300078\pi$
$884$		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
$891$	−34.3401	−	7.42052i	−1.15044	−	0.248597i
$892$		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
$903$	15.8984	−	12.6421i	0.529065	−	0.420704i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	6.18747	−	3.57234i	0.205452	−	0.118618i	−0.393744	−	0.919220i	$-0.628820\pi$
$907$	6.18747	−	3.57234i	0.205452	−	0.118618i	0.599196	+	0.800602i	$0.295487\pi$
$908$		0			0
$909$	4.22049	+	26.9415i	0.139985	+	0.893594i
$910$		0			0
$911$		−	38.4884i		−	1.27518i	−0.770377	−	0.637589i	$-0.779932\pi$
$911$		−	38.4884i		−	1.27518i	0.770377	−	0.637589i	$-0.220068\pi$
$912$		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
$921$	0.203918	+	0.0379721i	0.00671932	+	0.00125122i
$922$		0			0
$923$			22.0246i			0.724950i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	2.30014	−	1.85619i	0.0755465	−	0.0609654i
$928$		0			0
$929$	18.8140	−	32.5869i	0.617269	−	1.06914i	−0.372713	−	0.927947i	$-0.621573\pi$
$929$	18.8140	−	32.5869i	0.617269	−	1.06914i	0.989982	−	0.141194i	$-0.0450942\pi$
$930$		0			0
$931$	−8.89970	+	22.1154i	−0.291676	+	0.724802i
$932$		0			0
$933$	7.58143	+	21.4669i	0.248205	+	0.702794i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	3.05652			0.0998522			0.0499261	−	0.998753i	$-0.484101\pi$
$937$	3.05652			0.0998522			0.0499261	+	0.998753i	$0.484101\pi$
$938$		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	$-0.816085\pi$
$941$	−27.3577	−	47.3849i	−0.891835	−	1.54470i	−0.0541612	−	0.998532i	$-0.517248\pi$
$942$		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
$957$	−17.9675	−	50.8753i	−0.580808	−	1.64456i
$958$		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
$963$	3.01520	−	2.43324i	0.0971636	−	0.0784102i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	21.4958i		−	0.691258i	−0.938371	−	0.345629i	$-0.887666\pi$
$967$		−	21.4958i		−	0.691258i	0.938371	−	0.345629i	$-0.112334\pi$
$968$		0			0
$969$	−17.7790	−	3.31068i	−0.571144	−	0.106354i
$970$		0			0
$971$	−7.37642	+	12.7763i	−0.236721	+	0.410012i	−0.959771	−	0.280783i	$-0.909406\pi$
$971$	−7.37642	+	12.7763i	−0.236721	+	0.410012i	0.723051	+	0.690795i	$0.242739\pi$
$972$		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
$987$	−6.80654	−	45.5918i	−0.216655	−	1.45120i
$988$		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	$0.0720323\pi$
$997$	21.5205	+	37.2746i	0.681562	+	1.18050i	−0.292942	+	0.956130i	$0.594634\pi$
$998$		0			0
$999$	−0.323277	−	0.599016i	−0.0102280	−	0.0189520i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bh.a.101.3	✓	10	105.17	odd	12
420.2.bh.a.341.3	yes	10	5.2	odd	4
420.2.bh.b.101.1	yes	10	35.17	even	12
420.2.bh.b.341.1	yes	10	15.2	even	4
2100.2.bi.j.101.5		10	35.3	even	12
2100.2.bi.j.1601.5		10	15.8	even	4
2100.2.bi.k.101.3		10	105.38	odd	12
2100.2.bi.k.1601.3		10	5.3	odd	4
2100.2.bo.g.1349.4		20	15.14	odd	2
2100.2.bo.g.1349.7		20	3.2	odd	2
2100.2.bo.g.1949.4		20	7.3	odd	6
2100.2.bo.g.1949.7		20	35.24	odd	6
2100.2.bo.h.1349.1		20	1.1	even	1	trivial
2100.2.bo.h.1349.10		20	5.4	even	2	inner
2100.2.bo.h.1949.1		20	105.59	even	6	inner
2100.2.bo.h.1949.10		20	21.17	even	6	inner
2940.2.d.a.881.9		10	105.2	even	12
2940.2.d.a.881.10		10	35.12	even	12
2940.2.d.b.881.1		10	35.2	odd	12
2940.2.d.b.881.2		10	105.47	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.70278 - 0.317079i) q^{3} +(1.99797 + 1.73439i) q^{7} +(2.79892 + 1.07983i) q^{9} +O(q^{10})\)	\(q+(-1.70278 - 0.317079i) q^{3} +(1.99797 + 1.73439i) q^{7} +(2.79892 + 1.07983i) q^{9} +(-3.38064 + 1.95181i) q^{11} +6.06329 q^{13} +(2.65516 - 1.53296i) q^{17} +(2.94930 + 1.70278i) q^{19} +(-2.85217 - 3.58680i) q^{21} +(-1.43686 + 2.48871i) q^{23} +(-4.42356 - 2.72620i) q^{27} -7.97997i q^{29} +(-5.63161 + 3.25141i) q^{31} +(6.37537 - 2.25158i) q^{33} +(0.113447 + 0.0654987i) q^{37} +(-10.3245 - 1.92254i) q^{39} -12.3654 q^{41} +4.43247i q^{43} +(8.71153 + 5.02960i) q^{47} +(0.983778 + 6.93053i) q^{49} +(-5.00723 + 1.76839i) q^{51} +(2.67959 + 4.64119i) q^{53} +(-4.48210 - 3.83462i) q^{57} +(-1.28860 - 2.23193i) q^{59} +(7.44930 + 4.30086i) q^{61} +(3.71931 + 7.01190i) q^{63} +(13.8544 - 7.99884i) q^{67} +(3.23578 - 3.78214i) q^{69} +3.63245i q^{71} +(-3.88250 - 6.72468i) q^{73} +(-10.1396 - 1.96368i) q^{77} +(1.22311 - 2.11848i) q^{79} +(6.66792 + 6.04473i) q^{81} +7.63648i q^{83} +(-2.53028 + 13.5881i) q^{87} +(-4.11874 + 7.13387i) q^{89} +(12.1143 + 10.5161i) q^{91} +(10.6203 - 3.75077i) q^{93} -5.74985 q^{97} +(-11.5698 + 1.81245i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{9}+O(q^{10}) \) 20 * q + 6 * q^9	\( 20 q + 6 q^{9} - 12 q^{11} - 6 q^{19} + 20 q^{21} + 30 q^{31} - 30 q^{39} - 16 q^{41} + 26 q^{49} - 88 q^{51} + 84 q^{61} + 28 q^{69} - 2 q^{79} + 82 q^{81} - 56 q^{89} - 22 q^{91} - 72 q^{99}+O(q^{100}) \) 20 * q + 6 * q^9 - 12 * q^11 - 6 * q^19 + 20 * q^21 + 30 * q^31 - 30 * q^39 - 16 * q^41 + 26 * q^49 - 88 * q^51 + 84 * q^61 + 28 * q^69 - 2 * q^79 + 82 * q^81 - 56 * q^89 - 22 * q^91 - 72 * q^99

Introduction

L-functions

Modular forms

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Database

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