LMFDB - Embedded newform 2100.2.bo.g.1949.7

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			1949.7
Root			$-1.70278 + 0.317079i$ of defining polynomial
Character	$\chi$	$=$	2100.1949
Dual form			2100.2.bo.g.1349.7

$q$-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 $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

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

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	0.913902	−	0.405936i	$-0.133054\pi$
$11$	3.38064	+	1.95181i	1.01930	+	0.588494i	0.105400	+	0.994430i	$0.466388\pi$
$12$		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	$-0.454592\pi$
$17$	−2.65516	−	1.53296i	−0.643971	−	0.371797i	−0.786143	+	0.618045i	$0.787925\pi$
$18$		0			0
$19$	2.94930	−	1.70278i	0.676616	−	0.390645i	−0.121963	−	0.992535i	$-0.538919\pi$
$19$	2.94930	−	1.70278i	0.676616	−	0.390645i	0.798579	+	0.601890i	$0.205585\pi$
$20$		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	$-0.0698114\pi$
$23$	1.43686	+	2.48871i	0.299606	+	0.518933i	−0.676440	+	0.736498i	$0.736478\pi$
$24$		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	−0.0998461	−	0.995003i	$-0.531835\pi$
$31$	−5.63161	−	3.25141i	−1.01147	−	0.583971i	−0.911621	+	0.411032i	$0.865168\pi$
$32$		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	$-0.663239\pi$
$37$	0.113447	−	0.0654987i	0.0186506	−	0.0107679i	0.509296	+	0.860591i	$0.329906\pi$
$38$		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	$-0.928848\pi$
$47$	−8.71153	+	5.02960i	−1.27071	+	0.733643i	−0.295586	+	0.955316i	$0.595515\pi$
$48$		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	$-0.953315\pi$
$53$	−2.67959	+	4.64119i	−0.368070	+	0.637516i	0.621194	+	0.783657i	$0.286648\pi$
$54$		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	$-0.779679\pi$
$59$	1.28860	−	2.23193i	0.167762	−	0.290572i	0.937633	+	0.347628i	$0.113013\pi$
$60$		0			0
$61$	7.44930	−	4.30086i	0.953785	−	0.550668i	0.0595306	−	0.998226i	$-0.481040\pi$
$61$	7.44930	−	4.30086i	0.953785	−	0.550668i	0.894255	+	0.447558i	$0.147706\pi$
$62$		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	0.952421	+	0.304785i	$0.0985845\pi$
$67$	13.8544	+	7.99884i	1.69258	+	0.977213i	0.740162	+	0.672429i	$0.234749\pi$
$68$		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	−0.998654	−	0.0518638i	$-0.983484\pi$
$73$	−3.88250	+	6.72468i	−0.454412	+	0.787064i	0.544242	+	0.838928i	$0.316817\pi$
$74$		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	0.926591	−	0.376069i	$-0.122725\pi$
$79$	1.22311	+	2.11848i	0.137610	+	0.238348i	−0.788981	+	0.614417i	$0.789391\pi$
$80$		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	0.997424	−	0.0717367i	$-0.0228541\pi$
$89$	4.11874	+	7.13387i	0.436586	+	0.756189i	−0.560838	+	0.827926i	$0.689521\pi$
$90$		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	$-0.594289\pi$
$97$	−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	$-0.982710\pi$
$101$	−4.54502	+	7.87220i	−0.452246	+	0.783313i	0.546279	+	0.837603i	$0.316044\pi$
$102$		0			0
$103$	0.492615	+	0.853234i	0.0485388	+	0.0840717i	0.889274	−	0.457375i	$-0.151210\pi$
$103$	0.492615	+	0.853234i	0.0485388	+	0.0840717i	−0.840735	+	0.541446i	$0.817877\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.645758	−	1.11849i	−0.0624278	−	0.108128i	0.833122	−	0.553089i	$-0.186551\pi$
$107$	−0.645758	−	1.11849i	−0.0624278	−	0.108128i	−0.895550	+	0.444961i	$0.853218\pi$
$108$		0			0
$109$	−3.68547	+	6.38342i	−0.353004	+	0.611421i	−0.986774	−	0.162101i	$-0.948173\pi$
$109$	−3.68547	+	6.38342i	−0.353004	+	0.611421i	0.633770	+	0.773521i	$0.281506\pi$
$110$		0			0
$111$	0.172407	+	0.147502i	0.0163642	+	0.0140002i
$112$		0			0
$113$	−4.52778			−0.425938			−0.212969	−	0.977059i	$-0.568313\pi$
$113$	−4.52778			−0.425938			−0.212969	+	0.977059i	$0.568313\pi$
$114$		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	0.726093	−	0.687597i	$-0.241334\pi$
$131$	−2.66028	−	4.60774i	−0.232430	−	0.402580i	−0.958523	+	0.285016i	$0.908001\pi$
$132$		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	$-0.886958\pi$
$137$	−1.96252	+	3.39919i	−0.167670	+	0.290412i	0.769930	+	0.638128i	$0.220291\pi$
$138$		0			0
$139$		−	16.1726i		−	1.37174i	−0.727724	−	0.685870i	$-0.759422\pi$
$139$		−	16.1726i		−	1.37174i	0.727724	−	0.685870i	$-0.240578\pi$
$140$		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	−0.996999	−	0.0774116i	$-0.975334\pi$
$149$	−17.4366	+	10.0670i	−1.42846	+	0.824721i	−0.431459	+	0.902132i	$0.642001\pi$
$150$		0			0
$151$	−2.38980	+	4.13926i	−0.194479	+	0.336848i	−0.946730	−	0.322029i	$-0.895635\pi$
$151$	−2.38980	+	4.13926i	−0.194479	+	0.336848i	0.752250	+	0.658877i	$0.228968\pi$
$152$		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	$-0.932122\pi$
$157$	−3.82658	+	6.62784i	−0.305395	+	0.528959i	0.671955	+	0.740592i	$0.265455\pi$
$158$		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	$-0.558975\pi$
$163$	7.33954	−	4.23749i	0.574877	−	0.331906i	0.759095	+	0.650980i	$0.225642\pi$
$164$		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	$-0.884143\pi$
$173$	−14.3819	+	8.30340i	−1.09344	+	0.631296i	−0.158948	+	0.987287i	$0.550810\pi$
$174$		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	0.487381	−	0.873189i	$-0.337952\pi$
$179$	−0.336240	−	0.194128i	−0.0251318	−	0.0145098i	−0.512513	+	0.858679i	$0.671285\pi$
$180$		0			0
$181$		−	20.6789i		−	1.53705i	−0.639820	−	0.768524i	$-0.720991\pi$
$181$		−	20.6789i		−	1.53705i	0.639820	−	0.768524i	$-0.279009\pi$
$182$		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	−0.937943	−	0.346789i	$-0.887272\pi$
$191$	−15.2933	+	8.82961i	−1.10659	+	0.638888i	−0.168644	+	0.985677i	$0.553939\pi$
$192$		0			0
$193$	−18.5161	−	10.6903i	−1.33282	−	0.769505i	−0.347090	−	0.937832i	$-0.612830\pi$
$193$	−18.5161	−	10.6903i	−1.33282	−	0.769505i	−0.985731	+	0.168327i	$0.946163\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−22.5070			−1.60356			−0.801780	−	0.597619i	$-0.796114\pi$
$197$	−22.5070			−1.60356			−0.801780	+	0.597619i	$0.796114\pi$
$198$		0			0
$199$	8.48532	+	4.89900i	0.601509	+	0.347281i	0.769635	−	0.638484i	$-0.220438\pi$
$199$	8.48532	+	4.89900i	0.601509	+	0.347281i	−0.168126	+	0.985765i	$0.553772\pi$
$200$		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	$-0.519074\pi$
$223$	−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	0.993920	+	0.110106i	$0.0351191\pi$
$227$	23.8990	+	13.7981i	1.58623	+	0.915813i	0.592315	+	0.805707i	$0.298214\pi$
$228$		0			0
$229$	8.37613	−	4.83596i	0.553510	−	0.319569i	−0.197026	−	0.980398i	$-0.563128\pi$
$229$	8.37613	−	4.83596i	0.553510	−	0.319569i	0.750537	+	0.660829i	$0.229795\pi$
$230$		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	$-0.160445\pi$
$233$	0.298355	+	0.516767i	0.0195459	+	0.0338545i	−0.856087	+	0.516832i	$0.827111\pi$
$234$		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	0.557640	−	0.830083i	$-0.311707\pi$
$241$	1.82543	+	1.05391i	0.117586	+	0.0678886i	−0.440053	+	0.897972i	$0.645040\pi$
$242$		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	$-0.527563\pi$
$257$	11.7518	−	6.78489i	0.733055	−	0.423230i	0.819539	+	0.573024i	$0.194230\pi$
$258$		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	$-0.711029\pi$
$263$	6.07897	−	10.5291i	0.374846	−	0.649252i	0.990304	+	0.138918i	$0.0443624\pi$
$264$		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	−0.289617	−	0.957143i	$-0.593528\pi$
$269$	11.2201	−	19.4338i	0.684101	−	1.18490i	0.973718	−	0.227756i	$-0.0731388\pi$
$270$		0			0
$271$	−7.19179	+	4.15218i	−0.436870	+	0.252227i	−0.702269	−	0.711912i	$-0.747830\pi$
$271$	−7.19179	+	4.15218i	−0.436870	+	0.252227i	0.265399	+	0.964139i	$0.414496\pi$
$272$		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	$-0.391579\pi$
$277$	−5.24547	−	3.02848i	−0.315170	−	0.181963i	−0.649238	+	0.760586i	$0.724912\pi$
$278$		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	−0.717878	−	0.696169i	$-0.754886\pi$
$283$	4.10407	−	7.10845i	0.243961	−	0.422554i	0.961839	+	0.273616i	$0.0882196\pi$
$284$		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	$-0.501088\pi$
$307$	−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	$-0.711776\pi$
$311$	6.57207	−	11.3832i	0.372668	−	0.645480i	0.989975	+	0.141243i	$0.0451097\pi$
$312$		0			0
$313$	−11.6346	−	20.1517i	−0.657625	−	1.13904i	−0.981229	−	0.192847i	$-0.938228\pi$
$313$	−11.6346	−	20.1517i	−0.657625	−	1.13904i	0.323604	−	0.946192i	$-0.395105\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−17.3744	−	30.0933i	−0.975841	−	1.69021i	−0.677132	−	0.735861i	$-0.736777\pi$
$317$	−17.3744	−	30.0933i	−0.975841	−	1.69021i	−0.298709	−	0.954344i	$-0.596556\pi$
$318$		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	0.967165	+	0.254151i	$0.0817961\pi$
$331$	12.8024	+	22.1744i	0.703684	+	1.21882i	−0.263481	+	0.964665i	$0.584871\pi$
$332$		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	0.483720	+	0.875223i	$0.339285\pi$
$347$	−9.61397	+	16.6519i	−0.516105	+	0.893920i	−0.999825	+	0.0186975i	$0.994048\pi$
$348$		0			0
$349$		−	1.40475i		−	0.0751943i	−0.999293	−	0.0375972i	$-0.988030\pi$
$349$		−	1.40475i		−	0.0751943i	0.999293	−	0.0375972i	$-0.0119704\pi$
$350$		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	$-0.500840\pi$
$353$	−16.3454	−	9.43705i	−0.869980	−	0.502283i	−0.867342	+	0.497713i	$0.834173\pi$
$354$		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	0.0996440	−	0.995023i	$-0.468230\pi$
$359$	19.1592	−	11.0615i	1.01118	−	0.583806i	0.911537	+	0.411217i	$0.134896\pi$
$360$		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	$-0.722075\pi$
$367$	6.56047	−	11.3631i	0.342454	−	0.593147i	0.984888	+	0.173194i	$0.0554087\pi$
$368$		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	$-0.791474\pi$
$373$	−12.7826	+	7.38003i	−0.661857	+	0.382123i	0.131127	+	0.991366i	$0.458140\pi$
$374$		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	$-0.537584\pi$
$383$	13.3723	−	7.72052i	0.683294	−	0.394500i	0.801095	+	0.598537i	$0.204251\pi$
$384$		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	0.296618	−	0.954996i	$-0.404141\pi$
$389$	−7.53666	−	4.35129i	−0.382124	−	0.220619i	−0.678742	+	0.734377i	$0.737475\pi$
$390$		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	0.975651	+	0.219327i	$0.0703861\pi$
$397$	13.5044	+	23.3904i	0.677768	+	1.17393i	−0.297883	+	0.954602i	$0.596281\pi$
$398$		0			0
$399$	15.6058	−	0.112241i	0.781269	−	0.00561909i
$400$		0			0
$401$	−4.30215	+	2.48385i	−0.214839	+	0.124037i	−0.603558	−	0.797319i	$-0.706251\pi$
$401$	−4.30215	+	2.48385i	−0.214839	+	0.124037i	0.388719	+	0.921356i	$0.372918\pi$
$402$		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	0.663063	−	0.748564i	$-0.269256\pi$
$409$	7.00387	+	4.04369i	0.346319	+	0.199947i	−0.316744	+	0.948511i	$0.602590\pi$
$410$		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	0.394378	−	0.918948i	$-0.370960\pi$
$431$	−4.24065	−	2.44834i	−0.204265	−	0.117932i	−0.598643	+	0.801016i	$0.704293\pi$
$432$		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	−0.429936	−	0.902860i	$-0.641464\pi$
$439$	2.87038	−	1.65722i	0.136996	−	0.0790946i	0.566932	+	0.823765i	$0.308130\pi$
$440$		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	$-0.172846\pi$
$443$	−0.408581	−	0.707683i	−0.0194123	−	0.0336231i	−0.875568	+	0.483094i	$0.839513\pi$
$444$		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
$453$	−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	$-0.575817\pi$
$457$	10.4250	−	6.01889i	0.487662	−	0.281552i	0.723604	+	0.690215i	$0.242484\pi$
$458$		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	$-0.682998\pi$
$467$	−1.91950	+	1.10822i	−0.0888240	+	0.0512825i	0.454930	+	0.890527i	$0.349664\pi$
$468$		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	−0.935377	−	0.353653i	$-0.884939\pi$
$479$	−3.53276	+	6.11892i	−0.161416	+	0.279581i	0.773961	+	0.633234i	$0.218273\pi$
$480$		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	$-0.400474\pi$
$487$	−8.00270	−	4.62036i	−0.362637	−	0.209368i	−0.670237	+	0.742147i	$0.733807\pi$
$488$		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	0.974069	−	0.226252i	$-0.0726474\pi$
$499$	6.50255	+	11.2627i	0.291094	+	0.504190i	−0.682975	+	0.730442i	$0.739314\pi$
$500$		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	0.997468	−	0.0711133i	$-0.0226552\pi$
$509$	9.86251	+	17.0824i	0.437148	+	0.757163i	−0.560320	+	0.828276i	$0.689322\pi$
$510$		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	0.137874	+	0.990450i	$0.455973\pi$
$521$	−18.0051	+	31.1857i	−0.788818	+	1.36627i	−0.926692	+	0.375822i	$0.877360\pi$
$522$		0			0
$523$	10.7033	+	18.5387i	0.468023	+	0.810640i	0.999332	−	0.0365378i	$-0.0116329\pi$
$523$	10.7033	+	18.5387i	0.468023	+	0.810640i	−0.531309	+	0.847178i	$0.678300\pi$
$524$		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	0.811643	−	0.584154i	$-0.198574\pi$
$541$	−2.32759	−	4.03151i	−0.100071	−	0.173328i	−0.911714	+	0.410826i	$0.865240\pi$
$542$		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	0.291196	+	0.956663i	$0.405947\pi$
$557$	−16.1169	+	27.9154i	−0.682897	+	1.18281i	−0.974093	+	0.226149i	$0.927386\pi$
$558$		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	$-0.494132\pi$
$563$	−19.8892	−	11.4830i	−0.838230	−	0.483952i	−0.856662	+	0.515878i	$0.827466\pi$
$564$		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	−0.796914	−	0.604093i	$-0.793535\pi$
$569$	−16.0347	+	9.25765i	−0.672211	+	0.388101i	0.124703	+	0.992194i	$0.460202\pi$
$570$		0			0
$571$	−21.9408	+	38.0025i	−0.918193	+	1.59036i	−0.116035	+	0.993245i	$0.537019\pi$
$571$	−21.9408	+	38.0025i	−0.918193	+	1.59036i	−0.802158	+	0.597112i	$0.796315\pi$
$572$		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	$-0.948006\pi$
$577$	−8.46761	+	14.6663i	−0.352511	+	0.610568i	0.634177	+	0.773188i	$0.281339\pi$
$578$		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	$-0.697761\pi$
$593$	−4.11363	+	2.37500i	−0.168926	+	0.0975297i	0.413153	+	0.910662i	$0.364427\pi$
$594$		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	0.0527360	−	0.998608i	$-0.483206\pi$
$599$	−19.2300	−	11.1024i	−0.785716	−	0.453634i	−0.838452	+	0.544975i	$0.816539\pi$
$600$		0			0
$601$		−	42.5924i		−	1.73738i	−0.495357	−	0.868689i	$-0.664963\pi$
$601$		−	42.5924i		−	1.73738i	0.495357	−	0.868689i	$-0.335037\pi$
$602$		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	$-0.0420230\pi$
$607$	9.40283	+	16.2862i	0.381649	+	0.661035i	−0.609649	+	0.792671i	$0.708690\pi$
$608$		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	$-0.232022\pi$
$613$	13.4196	+	7.74783i	0.542014	+	0.312932i	−0.203881	+	0.978996i	$0.565355\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−17.7219			−0.713459			−0.356729	−	0.934208i	$-0.616108\pi$
$617$	−17.7219			−0.713459			−0.356729	+	0.934208i	$0.616108\pi$
$618$		0			0
$619$	−5.96204	−	3.44219i	−0.239635	−	0.138353i	0.375374	−	0.926873i	$-0.377514\pi$
$619$	−5.96204	−	3.44219i	−0.239635	−	0.138353i	−0.615009	+	0.788520i	$0.710848\pi$
$620$		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	0.883738	−	0.467981i	$-0.155019\pi$
$641$	23.3007	+	13.4527i	0.920324	+	0.531349i	0.0365856	+	0.999331i	$0.488352\pi$
$642$		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	$-0.539356\pi$
$647$	−26.5656	−	15.3377i	−1.04440	−	0.602985i	−0.921077	+	0.389381i	$0.872689\pi$
$648$		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	$-0.249290\pi$
$653$	−6.55879	−	11.3602i	−0.256665	−	0.444557i	−0.965347	+	0.260971i	$0.915957\pi$
$654$		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	0.583361	−	0.812213i	$-0.301737\pi$
$661$	4.41297	+	2.54783i	0.171645	+	0.0990992i	−0.411716	+	0.911312i	$0.635071\pi$
$662$		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	$-0.825878\pi$
$677$	−21.6131	+	12.4783i	−0.830658	+	0.479581i	0.0234197	+	0.999726i	$0.492545\pi$
$678$		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	−0.336189	−	0.941795i	$-0.609138\pi$
$683$	16.9226	−	29.3107i	0.647524	−	1.12154i	0.983712	−	0.179749i	$-0.0575287\pi$
$684$		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	−0.301339	−	0.953517i	$-0.597434\pi$
$691$	9.82503	−	5.67249i	0.373762	−	0.215792i	0.675101	+	0.737726i	$0.264100\pi$
$692$		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	$-0.855678\pi$
$701$		−	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	0.695908	−	0.718131i	$-0.255002\pi$
$709$	−7.29490	−	12.6351i	−0.273966	−	0.474522i	−0.969874	+	0.243609i	$0.921669\pi$
$710$		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	0.637270	−	0.770641i	$-0.280064\pi$
$719$	−9.35171	−	16.1976i	−0.348760	−	0.604070i	−0.986029	+	0.166571i	$0.946730\pi$
$720$		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	$-0.359427\pi$
$727$	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	0.653606	−	0.756835i	$-0.273255\pi$
$733$	−8.89746	−	15.4109i	−0.328635	−	0.569213i	−0.982241	+	0.187622i	$0.939922\pi$
$734$		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	−0.965299	−	0.261146i	$-0.915900\pi$
$739$	−6.97258	+	12.0769i	−0.256491	+	0.444255i	0.708809	+	0.705401i	$0.249233\pi$
$740$		0			0
$741$	27.1763	+	23.2504i	0.998345	+	0.854127i
$742$		0			0
$743$	−30.8975			−1.13352			−0.566760	−	0.823883i	$-0.691803\pi$
$743$	−30.8975			−1.13352			−0.566760	+	0.823883i	$0.691803\pi$
$744$		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	0.569378	−	0.822076i	$-0.307184\pi$
$751$	−11.7085	−	20.2797i	−0.427249	−	0.740017i	−0.996628	+	0.0820583i	$0.973851\pi$
$752$		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	0.981991	−	0.188927i	$-0.0605008\pi$
$761$	9.03119	+	15.6425i	0.327380	+	0.567039i	−0.654611	+	0.755966i	$0.727168\pi$
$762$		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	$0.313599\pi$
$769$			46.2208i			1.66677i	−0.552696	+	0.833383i	$0.686401\pi$
$770$		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	$-0.309997\pi$
$773$	3.52734	+	2.03651i	0.126870	+	0.0732482i	−0.435222	+	0.900323i	$0.643330\pi$
$774$		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	$-0.899900\pi$
$787$	−5.82407	+	10.0876i	−0.207606	+	0.359584i	0.743354	+	0.668898i	$0.233234\pi$
$788$		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	−0.239196	−	0.970971i	$-0.576884\pi$
$809$	−34.1224	−	19.7006i	−1.19968	−	0.692635i	−0.960484	+	0.278336i	$0.910217\pi$
$810$		0			0
$811$		−	50.4733i		−	1.77236i	−0.463345	−	0.886178i	$-0.653351\pi$
$811$		−	50.4733i		−	1.77236i	0.463345	−	0.886178i	$-0.346649\pi$
$812$		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	−0.852652	−	0.522479i	$-0.825007\pi$
$821$	−23.6817	+	13.6726i	−0.826498	+	0.477179i	0.0261543	+	0.999658i	$0.491674\pi$
$822$		0			0
$823$	−20.8603	−	12.0437i	−0.727144	−	0.419817i	0.0902322	−	0.995921i	$-0.471239\pi$
$823$	−20.8603	−	12.0437i	−0.727144	−	0.419817i	−0.817377	+	0.576104i	$0.804572\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−21.4026			−0.744242			−0.372121	−	0.928184i	$-0.621369\pi$
$827$	−21.4026			−0.744242			−0.372121	+	0.928184i	$0.621369\pi$
$828$		0			0
$829$	−27.3957	−	15.8169i	−0.951494	−	0.549345i	−0.0579490	−	0.998320i	$-0.518456\pi$
$829$	−27.3957	−	15.8169i	−0.951494	−	0.549345i	−0.893545	+	0.448974i	$0.851789\pi$
$830$		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	$-0.213414\pi$
$853$	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	$-0.301101\pi$
$857$	5.12566	+	2.95930i	0.175089	+	0.101088i	−0.409894	+	0.912133i	$0.634434\pi$
$858$		0			0
$859$	−18.8859	+	10.9038i	−0.644377	+	0.372031i	−0.786299	−	0.617847i	$-0.788005\pi$
$859$	−18.8859	+	10.9038i	−0.644377	+	0.372031i	0.141921	+	0.989878i	$0.454672\pi$
$860$		0			0
$861$	49.2764	+	27.9791i	1.67933	+	0.953526i
$862$		0			0
$863$	18.9429	+	32.8100i	0.644823	+	1.11687i	0.984342	+	0.176267i	$0.0564023\pi$
$863$	18.9429	+	32.8100i	0.644823	+	1.11687i	−0.339519	+	0.940599i	$0.610264\pi$
$864$		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	−0.573779	+	0.819010i	$0.694523\pi$
$877$	−46.4929	+	26.8427i	−1.56995	+	0.906412i	−0.996173	+	0.0874025i	$0.972143\pi$
$878$		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	0.508829	−	0.860867i	$-0.330078\pi$
$887$	44.9352	−	25.9434i	1.50878	−	0.871093i	0.999948	−	0.0102253i	$-0.00325487\pi$
$888$		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	$-0.295487\pi$
$907$	6.18747	+	3.57234i	0.205452	+	0.118618i	−0.393744	+	0.919220i	$0.628820\pi$
$908$		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	0.837503	+	0.546433i	$0.184015\pi$
$919$	27.0403	+	46.8351i	0.891976	+	1.54495i	0.0544730	+	0.998515i	$0.482652\pi$
$920$		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	−0.989982	−	0.141194i	$-0.954906\pi$
$929$	−18.8140	−	32.5869i	−0.617269	−	1.06914i	0.372713	−	0.927947i	$-0.378427\pi$
$930$		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	$-0.484101\pi$
$937$	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	0.0541612	−	0.998532i	$-0.482752\pi$
$941$	27.3577	−	47.3849i	0.891835	−	1.54470i	0.837674	−	0.546171i	$-0.183915\pi$
$942$		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	$-0.203817\pi$
$947$	−3.58341	−	6.20664i	−0.116445	−	0.201689i	−0.918356	+	0.395754i	$0.870483\pi$
$948$		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	$-0.499275\pi$
$953$	0.140553			0.00455295			0.00227648	+	0.999997i	$0.499275\pi$
$954$		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	0.959771	−	0.280783i	$-0.0905940\pi$
$971$	7.37642	+	12.7763i	0.236721	+	0.410012i	−0.723051	+	0.690795i	$0.757261\pi$
$972$		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	$-0.827007\pi$
$977$	0.621141	−	1.07585i	0.0198720	−	0.0344194i	0.875790	+	0.482692i	$0.160341\pi$
$978$		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	$-0.271588\pi$
$983$	10.4680	+	6.04373i	0.333879	+	0.192765i	−0.323683	+	0.946166i	$0.604921\pi$
$984$		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	−0.928697	−	0.370841i	$-0.879070\pi$
$991$	−4.50767	+	7.80752i	−0.143191	+	0.248014i	0.785506	+	0.618854i	$0.212403\pi$
$992$		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	−0.292942	−	0.956130i	$-0.594634\pi$
$997$	21.5205	−	37.2746i	0.681562	−	1.18050i	0.974504	−	0.224370i	$-0.0720323\pi$
$998$		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.1949.7		20
3.2	odd	2		2100.2.bo.h.1949.1		20
5.2	odd	4		2100.2.bi.j.101.5		10
5.3	odd	4		420.2.bh.b.101.1	yes	10
5.4	even	2	inner	2100.2.bo.g.1949.4		20
7.5	odd	6		2100.2.bo.h.1349.10		20
15.2	even	4		2100.2.bi.k.101.3		10
15.8	even	4		420.2.bh.a.101.3	✓	10
15.14	odd	2		2100.2.bo.h.1949.10		20
21.5	even	6	inner	2100.2.bo.g.1349.4		20
35.3	even	12		2940.2.d.b.881.1		10
35.12	even	12		2100.2.bi.k.1601.3		10
35.18	odd	12		2940.2.d.a.881.10		10
35.19	odd	6		2100.2.bo.h.1349.1		20
35.33	even	12		420.2.bh.a.341.3	yes	10
105.38	odd	12		2940.2.d.a.881.9		10
105.47	odd	12		2100.2.bi.j.1601.5		10
105.53	even	12		2940.2.d.b.881.2		10
105.68	odd	12		420.2.bh.b.341.1	yes	10
105.89	even	6	inner	2100.2.bo.g.1349.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bh.a.101.3	✓	10	15.8	even	4
420.2.bh.a.341.3	yes	10	35.33	even	12
420.2.bh.b.101.1	yes	10	5.3	odd	4
420.2.bh.b.341.1	yes	10	105.68	odd	12
2100.2.bi.j.101.5		10	5.2	odd	4
2100.2.bi.j.1601.5		10	105.47	odd	12
2100.2.bi.k.101.3		10	15.2	even	4
2100.2.bi.k.1601.3		10	35.12	even	12
2100.2.bo.g.1349.4		20	21.5	even	6	inner
2100.2.bo.g.1349.7		20	105.89	even	6	inner
2100.2.bo.g.1949.4		20	5.4	even	2	inner
2100.2.bo.g.1949.7		20	1.1	even	1	trivial
2100.2.bo.h.1349.1		20	35.19	odd	6
2100.2.bo.h.1349.10		20	7.5	odd	6
2100.2.bo.h.1949.1		20	3.2	odd	2
2100.2.bo.h.1949.10		20	15.14	odd	2
2940.2.d.a.881.9		10	105.38	odd	12
2940.2.d.a.881.10		10	35.18	odd	12
2940.2.d.b.881.1		10	35.3	even	12
2940.2.d.b.881.2		10	105.53	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

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