LMFDB - Embedded newform 2100.2.bi.n.1601.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(101,2100)]

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, 0, 1]))

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

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

chi := DirichletCharacter("2100.101");

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.bi (of order $6$, degree $2$, 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1601.11
Character	$\chi$	$=$	2100.1601
Dual form			2100.2.bi.n.101.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.884700 - 1.48906i) q^{3} +(-2.64396 - 0.0973684i) q^{7} +(-1.43461 - 2.63475i) q^{9} +O(q^{10})$	\(q+(0.884700 - 1.48906i) q^{3} +(-2.64396 - 0.0973684i) q^{7} +(-1.43461 - 2.63475i) q^{9} +(-2.62913 + 1.51793i) q^{11} +2.31738i q^{13} +(2.59625 + 4.49684i) q^{17} +(5.58515 + 3.22459i) q^{19} +(-2.48410 + 3.85088i) q^{21} +(-4.21654 - 2.43442i) q^{23} +(-5.19250 - 0.194737i) q^{27} +3.48622i q^{29} +(1.16615 - 0.673279i) q^{31} +(-0.0657018 + 5.25784i) q^{33} +(-1.40630 + 2.43579i) q^{37} +(3.45072 + 2.05018i) q^{39} +1.06401 q^{41} +2.42063 q^{43} +(-1.90660 + 3.30233i) q^{47} +(6.98104 + 0.514876i) q^{49} +(8.99298 + 0.112376i) q^{51} +(-6.11386 + 3.52984i) q^{53} +(9.74279 - 5.46384i) q^{57} +(6.18029 + 10.7046i) q^{59} +(11.4447 + 6.60758i) q^{61} +(3.53651 + 7.10585i) q^{63} +(2.14821 + 3.72081i) q^{67} +(-7.35538 + 4.12496i) q^{69} -7.08288i q^{71} +(0.132196 - 0.0763237i) q^{73} +(7.09910 - 3.75734i) q^{77} +(3.04462 - 5.27344i) q^{79} +(-4.88378 + 7.55967i) q^{81} +10.2758 q^{83} +(5.19119 + 3.08426i) q^{87} +(-7.10913 + 12.3134i) q^{89} +(0.225639 - 6.12705i) q^{91} +(0.0291421 - 2.33212i) q^{93} -8.63266i q^{97} +(7.77113 + 4.74945i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 12 q^{19} - 8 q^{21} - 12 q^{31} - 24 q^{39} + 44 q^{49} - 10 q^{51} - 24 q^{61} + 28 q^{79} - 20 q^{81} + 16 q^{91} + 28 q^{99}+O(q^{100}) $ 32 * q - 12 * q^19 - 8 * q^21 - 12 * q^31 - 24 * q^39 + 44 * q^49 - 10 * q^51 - 24 * q^61 + 28 * q^79 - 20 * q^81 + 16 * q^91 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.884700	−	1.48906i	0.510782	−	0.859710i
$3$	0.884700	−	1.48906i	0.510782	−	0.859710i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.64396	−	0.0973684i	−0.999323	−	0.0368018i
$7$	−2.64396	−	0.0973684i	−0.999323	−	0.0368018i
$8$		0			0
$9$	−1.43461	−	2.63475i	−0.478204	−	0.878249i
$10$		0			0
$11$	−2.62913	+	1.51793i	−0.792712	+	0.457672i	−0.840916	−	0.541165i	$-0.817983\pi$
$11$	−2.62913	+	1.51793i	−0.792712	+	0.457672i	0.0482045	+	0.998837i	$0.484650\pi$
$12$		0			0
$13$			2.31738i			0.642724i	0.946956	+	0.321362i	$0.104141\pi$
$13$			2.31738i			0.642724i	−0.946956	+	0.321362i	$0.895859\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.59625	+	4.49684i	0.629683	+	1.09064i	0.987615	+	0.156896i	$0.0501487\pi$
$17$	2.59625	+	4.49684i	0.629683	+	1.09064i	−0.357932	+	0.933748i	$0.616518\pi$
$18$		0			0
$19$	5.58515	+	3.22459i	1.28132	+	0.739771i	0.977090	−	0.212827i	$-0.0682671\pi$
$19$	5.58515	+	3.22459i	1.28132	+	0.739771i	0.304231	+	0.952598i	$0.401600\pi$
$20$		0			0
$21$	−2.48410	+	3.85088i	−0.542075	+	0.840330i
$22$		0			0
$23$	−4.21654	−	2.43442i	−0.879209	−	0.507612i	−0.00881178	−	0.999961i	$-0.502805\pi$
$23$	−4.21654	−	2.43442i	−0.879209	−	0.507612i	−0.870398	+	0.492349i	$0.836138\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−5.19250	−	0.194737i	−0.999297	−	0.0374771i
$28$		0			0
$29$			3.48622i			0.647374i	0.946164	+	0.323687i	$0.104923\pi$
$29$			3.48622i			0.647374i	−0.946164	+	0.323687i	$0.895077\pi$
$30$		0			0
$31$	1.16615	−	0.673279i	0.209447	−	0.120924i	−0.391607	−	0.920132i	$-0.628081\pi$
$31$	1.16615	−	0.673279i	0.209447	−	0.120924i	0.601054	+	0.799208i	$0.294747\pi$
$32$		0			0
$33$	−0.0657018	+	5.25784i	−0.0114372	+	0.915273i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.40630	+	2.43579i	−0.231195	+	0.400441i	−0.958160	−	0.286233i	$-0.907597\pi$
$37$	−1.40630	+	2.43579i	−0.231195	+	0.400441i	0.726965	+	0.686674i	$0.240930\pi$
$38$		0			0
$39$	3.45072	+	2.05018i	0.552557	+	0.328292i
$40$		0			0
$41$	1.06401			0.166171			0.0830853	−	0.996542i	$-0.473523\pi$
$41$	1.06401			0.166171			0.0830853	+	0.996542i	$0.473523\pi$
$42$		0			0
$43$	2.42063			0.369142			0.184571	−	0.982819i	$-0.440910\pi$
$43$	2.42063			0.369142			0.184571	+	0.982819i	$0.440910\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.90660	+	3.30233i	−0.278106	+	0.481695i	−0.970914	−	0.239428i	$-0.923040\pi$
$47$	−1.90660	+	3.30233i	−0.278106	+	0.481695i	0.692808	+	0.721122i	$0.256373\pi$
$48$		0			0
$49$	6.98104	+	0.514876i	0.997291	+	0.0735537i
$50$		0			0
$51$	8.99298	+	0.112376i	1.25927	+	0.0157358i
$52$		0			0
$53$	−6.11386	+	3.52984i	−0.839803	+	0.484861i	−0.857197	−	0.514988i	$-0.827796\pi$
$53$	−6.11386	+	3.52984i	−0.839803	+	0.484861i	0.0173942	+	0.999849i	$0.494463\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	9.74279	−	5.46384i	1.29046	−	0.723703i
$58$		0			0
$59$	6.18029	+	10.7046i	0.804605	+	1.39362i	0.916558	+	0.399903i	$0.130956\pi$
$59$	6.18029	+	10.7046i	0.804605	+	1.39362i	−0.111953	+	0.993714i	$0.535711\pi$
$60$		0			0
$61$	11.4447	+	6.60758i	1.46534	+	0.846014i	0.999250	−	0.0387246i	$-0.0123295\pi$
$61$	11.4447	+	6.60758i	1.46534	+	0.846014i	0.466088	+	0.884738i	$0.345663\pi$
$62$		0			0
$63$	3.53651	+	7.10585i	0.445559	+	0.895253i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.14821	+	3.72081i	0.262446	+	0.454569i	0.966891	−	0.255189i	$-0.0821376\pi$
$67$	2.14821	+	3.72081i	0.262446	+	0.454569i	−0.704446	+	0.709758i	$0.748804\pi$
$68$		0			0
$69$	−7.35538	+	4.12496i	−0.885483	+	0.496586i
$70$		0			0
$71$		−	7.08288i		−	0.840583i	−0.907389	−	0.420292i	$-0.861928\pi$
$71$		−	7.08288i		−	0.840583i	0.907389	−	0.420292i	$-0.138072\pi$
$72$		0			0
$73$	0.132196	−	0.0763237i	0.0154724	−	0.00893301i	−0.492244	−	0.870457i	$-0.663823\pi$
$73$	0.132196	−	0.0763237i	0.0154724	−	0.00893301i	0.507716	+	0.861524i	$0.330490\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	7.09910	−	3.75734i	0.809018	−	0.428189i
$78$		0			0
$79$	3.04462	−	5.27344i	0.342547	−	0.593309i	−0.642358	−	0.766405i	$-0.722044\pi$
$79$	3.04462	−	5.27344i	0.342547	−	0.593309i	0.984905	+	0.173096i	$0.0553771\pi$
$80$		0			0
$81$	−4.88378	+	7.55967i	−0.542643	+	0.839964i
$82$		0			0
$83$	10.2758			1.12791			0.563957	−	0.825804i	$-0.309278\pi$
$83$	10.2758			1.12791			0.563957	+	0.825804i	$0.309278\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	5.19119	+	3.08426i	0.556555	+	0.330667i
$88$		0			0
$89$	−7.10913	+	12.3134i	−0.753567	+	1.30522i	0.192517	+	0.981294i	$0.438335\pi$
$89$	−7.10913	+	12.3134i	−0.753567	+	1.30522i	−0.946084	+	0.323922i	$0.894998\pi$
$90$		0			0
$91$	0.225639	−	6.12705i	0.0236534	−	0.642289i
$92$		0			0
$93$	0.0291421	−	2.33212i	0.00302189	−	0.241830i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	8.63266i		−	0.876514i	−0.898850	−	0.438257i	$-0.855596\pi$
$97$		−	8.63266i		−	0.876514i	0.898850	−	0.438257i	$-0.144404\pi$
$98$		0			0
$99$	7.77113	+	4.74945i	0.781028	+	0.477338i
$100$		0			0
$101$	−8.23108	−	14.2566i	−0.819023	−	1.41859i	−0.906403	−	0.422414i	$-0.861183\pi$
$101$	−8.23108	−	14.2566i	−0.819023	−	1.41859i	0.0873801	−	0.996175i	$-0.472151\pi$
$102$		0			0
$103$	−5.71987	−	3.30237i	−0.563596	−	0.325392i	0.190992	−	0.981592i	$-0.438830\pi$
$103$	−5.71987	−	3.30237i	−0.563596	−	0.325392i	−0.754588	+	0.656199i	$0.772163\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−16.0502	−	9.26659i	−1.55163	−	0.895835i	−0.998009	−	0.0630674i	$-0.979912\pi$
$107$	−16.0502	−	9.26659i	−1.55163	−	0.895835i	−0.553623	−	0.832768i	$-0.686755\pi$
$108$		0			0
$109$	9.25130	+	16.0237i	0.886114	+	1.53479i	0.844432	+	0.535664i	$0.179938\pi$
$109$	9.25130	+	16.0237i	0.886114	+	1.53479i	0.0416824	+	0.999131i	$0.486728\pi$
$110$		0			0
$111$	2.38288	+	4.24901i	0.226173	+	0.403299i
$112$		0			0
$113$			5.86968i			0.552173i	0.961133	+	0.276087i	$0.0890376\pi$
$113$			5.86968i			0.552173i	−0.961133	+	0.276087i	$0.910962\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	6.10570	−	3.32453i	0.564472	−	0.307353i
$118$		0			0
$119$	−6.42653	−	12.1423i	−0.589119	−	1.11308i
$120$		0			0
$121$	−0.891792	+	1.54463i	−0.0810720	+	0.140421i
$122$		0			0
$123$	0.941331	−	1.58438i	0.0848769	−	0.142859i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−14.5896			−1.29462			−0.647311	−	0.762226i	$-0.724106\pi$
$127$	−14.5896			−1.29462			−0.647311	+	0.762226i	$0.724106\pi$
$128$		0			0
$129$	2.14153	−	3.60446i	0.188551	−	0.317355i
$130$		0			0
$131$	−10.0356	+	17.3822i	−0.876817	+	1.51869i	−0.0220016	+	0.999758i	$0.507004\pi$
$131$	−10.0356	+	17.3822i	−0.876817	+	1.51869i	−0.854815	+	0.518933i	$0.826329\pi$
$132$		0			0
$133$	−14.4529	−	9.06949i	−1.25323	−	0.786425i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.04491	−	2.33533i	0.345580	−	0.199521i	−0.317157	−	0.948373i	$-0.602728\pi$
$137$	4.04491	−	2.33533i	0.345580	−	0.199521i	0.662737	+	0.748852i	$0.269395\pi$
$138$		0			0
$139$		−	5.51296i		−	0.467603i	−0.972284	−	0.233801i	$-0.924883\pi$
$139$		−	5.51296i		−	0.467603i	0.972284	−	0.233801i	$-0.0751166\pi$
$140$		0			0
$141$	3.23060	+	5.76062i	0.272066	+	0.485132i
$142$		0			0
$143$	−3.51761	−	6.09268i	−0.294157	−	0.509495i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	6.94281	−	9.93969i	0.572633	−	0.819812i
$148$		0			0
$149$	12.6579	+	7.30806i	1.03698	+	0.598700i	0.918976	−	0.394313i	$-0.129018\pi$
$149$	12.6579	+	7.30806i	1.03698	+	0.598700i	0.118003	+	0.993013i	$0.462351\pi$
$150$		0			0
$151$	−4.48104	−	7.76139i	−0.364662	−	0.631613i	0.624060	−	0.781376i	$-0.285482\pi$
$151$	−4.48104	−	7.76139i	−0.364662	−	0.631613i	−0.988722	+	0.149764i	$0.952149\pi$
$152$		0			0
$153$	8.12342	−	13.2917i	0.656740	−	1.07457i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−17.7886	+	10.2703i	−1.41969	+	0.819657i	−0.996271	−	0.0862784i	$-0.972503\pi$
$157$	−17.7886	+	10.2703i	−1.41969	+	0.819657i	−0.423416	+	0.905935i	$0.639169\pi$
$158$		0			0
$159$	−0.152785	+	12.2268i	−0.0121166	+	0.969645i
$160$		0			0
$161$	10.9113	+	6.84707i	0.859933	+	0.539624i
$162$		0			0
$163$	−10.0254	+	17.3645i	−0.785250	+	1.36009i	0.143600	+	0.989636i	$0.454132\pi$
$163$	−10.0254	+	17.3645i	−0.785250	+	1.36009i	−0.928850	+	0.370457i	$0.879201\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	12.2463			0.947646			0.473823	−	0.880620i	$-0.342874\pi$
$167$	12.2463			0.947646			0.473823	+	0.880620i	$0.342874\pi$
$168$		0			0
$169$	7.62977			0.586906
$170$		0			0
$171$	0.483456	−	19.3415i	0.0369708	−	1.47908i
$172$		0			0
$173$	10.9123	−	18.9007i	0.829647	−	1.43699i	−0.0686676	−	0.997640i	$-0.521875\pi$
$173$	10.9123	−	18.9007i	0.829647	−	1.43699i	0.898315	−	0.439352i	$-0.144792\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	21.4075	+	0.267507i	1.60908	+	0.0201070i
$178$		0			0
$179$	1.11034	−	0.641056i	0.0829909	−	0.0479148i	−0.457930	−	0.888988i	$-0.651409\pi$
$179$	1.11034	−	0.641056i	0.0829909	−	0.0479148i	0.540921	+	0.841073i	$0.318076\pi$
$180$		0			0
$181$			14.5617i			1.08236i	0.840906	+	0.541182i	$0.182023\pi$
$181$			14.5617i			1.08236i	−0.840906	+	0.541182i	$0.817977\pi$
$182$		0			0
$183$	19.9642	−	11.1961i	1.47579	−	0.827638i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−13.6518	−	7.88184i	−0.998315	−	0.576377i
$188$		0			0
$189$	13.7098	+	1.02046i	0.997241	+	0.0742277i
$190$		0			0
$191$	20.7027	+	11.9527i	1.49800	+	0.864869i	0.999997	−	0.00230818i	$-0.000734719\pi$
$191$	20.7027	+	11.9527i	1.49800	+	0.864869i	0.498000	+	0.867177i	$0.334068\pi$
$192$		0			0
$193$	4.21891	+	7.30736i	0.303684	+	0.525996i	0.976967	−	0.213389i	$-0.0684500\pi$
$193$	4.21891	+	7.30736i	0.303684	+	0.525996i	−0.673284	+	0.739384i	$0.735117\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			8.25869i			0.588408i	0.955743	+	0.294204i	$0.0950544\pi$
$197$			8.25869i			0.588408i	−0.955743	+	0.294204i	$0.904946\pi$
$198$		0			0
$199$	−8.94051	+	5.16181i	−0.633776	+	0.365911i	−0.782213	−	0.623011i	$-0.785909\pi$
$199$	−8.94051	+	5.16181i	−0.633776	+	0.365911i	0.148437	+	0.988922i	$0.452576\pi$
$200$		0			0
$201$	7.44104	+	0.0929828i	0.524850	+	0.00655850i
$202$		0			0
$203$	0.339448	−	9.21742i	0.0238245	−	0.646936i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.364988	+	14.6020i	−0.0253684	+	1.01491i
$208$		0			0
$209$	−19.5788			−1.35429
$210$		0			0
$211$	−5.75694			−0.396324			−0.198162	−	0.980169i	$-0.563497\pi$
$211$	−5.75694			−0.396324			−0.198162	+	0.980169i	$0.563497\pi$
$212$		0			0
$213$	−10.5468	−	6.26623i	−0.722658	−	0.429355i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−3.14882	+	1.66657i	−0.213756	+	0.113134i
$218$		0			0
$219$	0.00330358	−	0.264372i	0.000223236	−	0.0178646i
$220$		0			0
$221$	−10.4209	+	6.01649i	−0.700983	+	0.404713i
$222$		0			0
$223$		−	27.0927i		−	1.81426i	−0.420852	−	0.907129i	$-0.638269\pi$
$223$		−	27.0927i		−	1.81426i	0.420852	−	0.907129i	$-0.361731\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.58150	−	6.20333i	−0.237712	−	0.411730i	0.722345	−	0.691533i	$-0.243064\pi$
$227$	−3.58150	−	6.20333i	−0.237712	−	0.411730i	−0.960057	+	0.279803i	$0.909731\pi$
$228$		0			0
$229$	−4.16615	−	2.40533i	−0.275307	−	0.158949i	0.355990	−	0.934490i	$-0.384144\pi$
$229$	−4.16615	−	2.40533i	−0.275307	−	0.158949i	−0.631297	+	0.775541i	$0.717477\pi$
$230$		0			0
$231$	0.685661	−	13.8951i	0.0451132	−	0.914232i
$232$		0			0
$233$	15.4259	+	8.90616i	1.01059	+	0.583462i	0.911363	−	0.411604i	$-0.135031\pi$
$233$	15.4259	+	8.90616i	1.01059	+	0.583462i	0.0992223	+	0.995065i	$0.468365\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−5.15890	−	9.19905i	−0.335107	−	0.597542i
$238$		0			0
$239$		−	13.7867i		−	0.891789i	−0.895086	−	0.445894i	$-0.852886\pi$
$239$		−	13.7867i		−	0.891789i	0.895086	−	0.445894i	$-0.147114\pi$
$240$		0			0
$241$	−11.7785	+	6.80032i	−0.758720	+	0.438047i	−0.828836	−	0.559492i	$-0.810996\pi$
$241$	−11.7785	+	6.80032i	−0.758720	+	0.438047i	0.0701158	+	0.997539i	$0.477663\pi$
$242$		0			0
$243$	6.93614	+	13.9603i	0.444953	+	0.895554i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−7.47258	+	12.9429i	−0.475469	+	0.823536i
$248$		0			0
$249$	9.09100	−	15.3013i	0.576119	−	0.969680i
$250$		0			0
$251$	7.89600			0.498391			0.249196	−	0.968453i	$-0.419834\pi$
$251$	7.89600			0.498391			0.249196	+	0.968453i	$0.419834\pi$
$252$		0			0
$253$	14.7811			0.929280
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.23741	+	15.9997i	−0.576214	+	0.998032i	0.419695	+	0.907665i	$0.362137\pi$
$257$	−9.23741	+	15.9997i	−0.576214	+	0.998032i	−0.995909	+	0.0903666i	$0.971196\pi$
$258$		0			0
$259$	3.95538	−	6.30320i	0.245775	−	0.391661i
$260$		0			0
$261$	9.18530	−	5.00137i	0.568556	−	0.309577i
$262$		0			0
$263$	−18.6705	+	10.7794i	−1.15127	+	0.664687i	−0.949197	−	0.314683i	$-0.898102\pi$
$263$	−18.6705	+	10.7794i	−1.15127	+	0.664687i	−0.202075	+	0.979370i	$0.564769\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	12.0459	+	21.4796i	0.737199	+	1.31453i
$268$		0			0
$269$	−7.98483	−	13.8301i	−0.486844	−	0.843238i	0.513042	−	0.858364i	$-0.328519\pi$
$269$	−7.98483	−	13.8301i	−0.486844	−	0.843238i	−0.999886	+	0.0151253i	$0.995185\pi$
$270$		0			0
$271$	−4.72410	−	2.72746i	−0.286968	−	0.165681i	0.349605	−	0.936897i	$-0.386316\pi$
$271$	−4.72410	−	2.72746i	−0.286968	−	0.165681i	−0.636574	+	0.771216i	$0.719649\pi$
$272$		0			0
$273$	−8.92393	−	5.75659i	−0.540101	−	0.348405i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−3.88162	−	6.72315i	−0.233224	−	0.403955i	0.725531	−	0.688189i	$-0.241594\pi$
$277$	−3.88162	−	6.72315i	−0.233224	−	0.403955i	−0.958755	+	0.284234i	$0.908261\pi$
$278$		0			0
$279$	−3.44689	−	2.10662i	−0.206360	−	0.126120i
$280$		0			0
$281$		−	0.742571i		−	0.0442981i	−0.999755	−	0.0221490i	$-0.992949\pi$
$281$		−	0.742571i		−	0.0442981i	0.999755	−	0.0221490i	$-0.00705084\pi$
$282$		0			0
$283$	−8.30562	+	4.79525i	−0.493718	+	0.285048i	−0.726116	−	0.687573i	$-0.758676\pi$
$283$	−8.30562	+	4.79525i	−0.493718	+	0.285048i	0.232398	+	0.972621i	$0.425343\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.81320	−	0.103601i	−0.166058	−	0.00611538i
$288$		0			0
$289$	−4.98104	+	8.62741i	−0.293002	+	0.507495i
$290$		0			0
$291$	−12.8546	−	7.63732i	−0.753548	−	0.447707i
$292$		0			0
$293$	0.569685			0.0332814			0.0166407	−	0.999862i	$-0.494703\pi$
$293$	0.569685			0.0332814			0.0166407	+	0.999862i	$0.494703\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	13.9473	−	7.36985i	0.809307	−	0.427642i
$298$		0			0
$299$	5.64147	−	9.77131i	0.326254	−	0.565089i
$300$		0			0
$301$	−6.40003	−	0.235692i	−0.368892	−	0.0135851i
$302$		0			0
$303$	−28.5111	−	0.356273i	−1.63792	−	0.0204673i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			9.46424i			0.540153i	0.962839	+	0.270076i	$0.0870489\pi$
$307$			9.46424i			0.540153i	−0.962839	+	0.270076i	$0.912951\pi$
$308$		0			0
$309$	−9.97781	+	5.59564i	−0.567618	+	0.318325i
$310$		0			0
$311$	−3.25858	−	5.64403i	−0.184777	−	0.320044i	0.758724	−	0.651412i	$-0.225823\pi$
$311$	−3.25858	−	5.64403i	−0.184777	−	0.320044i	−0.943501	+	0.331368i	$0.892490\pi$
$312$		0			0
$313$	19.1711	+	11.0684i	1.08362	+	0.625626i	0.931869	−	0.362794i	$-0.118177\pi$
$313$	19.1711	+	11.0684i	1.08362	+	0.625626i	0.151746	+	0.988420i	$0.451510\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.65086	−	2.10782i	−0.205053	−	0.118387i	0.393957	−	0.919129i	$-0.371106\pi$
$317$	−3.65086	−	2.10782i	−0.205053	−	0.118387i	−0.599010	+	0.800741i	$0.704439\pi$
$318$		0			0
$319$	−5.29183	−	9.16571i	−0.296285	−	0.513181i
$320$		0			0
$321$	−27.9981	+	15.7016i	−1.56270	+	0.876378i
$322$		0			0
$323$			33.4874i			1.86329i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	32.0449	+	0.400432i	1.77209	+	0.0221439i
$328$		0			0
$329$	5.36252	−	8.54559i	0.295645	−	0.471133i
$330$		0			0
$331$	12.0041	−	20.7918i	0.659807	−	1.14282i	−0.320858	−	0.947127i	$-0.603971\pi$
$331$	12.0041	−	20.7918i	0.659807	−	1.14282i	0.980665	−	0.195693i	$-0.0626955\pi$
$332$		0			0
$333$	8.43518	+	0.210844i	0.462245	+	0.0115542i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	9.42028			0.513155			0.256578	−	0.966524i	$-0.417405\pi$
$337$	9.42028			0.513155			0.256578	+	0.966524i	$0.417405\pi$
$338$		0			0
$339$	8.74032	+	5.19291i	0.474709	+	0.282040i
$340$		0			0
$341$	−2.04398	+	3.54027i	−0.110688	+	0.191716i
$342$		0			0
$343$	−18.4074	−	2.04104i	−0.993909	−	0.110206i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	19.3922	−	11.1961i	1.04103	−	0.601037i	0.120903	−	0.992664i	$-0.461421\pi$
$347$	19.3922	−	11.1961i	1.04103	−	0.601037i	0.920124	+	0.391627i	$0.128088\pi$
$348$		0			0
$349$		−	12.0663i		−	0.645895i	−0.946417	−	0.322948i	$-0.895326\pi$
$349$		−	12.0663i		−	0.645895i	0.946417	−	0.322948i	$-0.104674\pi$
$350$		0			0
$351$	0.451278	−	12.0330i	0.0240875	−	0.642273i
$352$		0			0
$353$	4.15412	+	7.19515i	0.221102	+	0.382959i	0.955143	−	0.296146i	$-0.0957014\pi$
$353$	4.15412	+	7.19515i	0.221102	+	0.382959i	−0.734041	+	0.679105i	$0.762368\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−23.7661	−	1.17275i	−1.25784	−	0.0620684i
$358$		0			0
$359$	−6.27295	−	3.62169i	−0.331074	−	0.191145i	0.325244	−	0.945630i	$-0.394554\pi$
$359$	−6.27295	−	3.62169i	−0.331074	−	0.191145i	−0.656318	+	0.754485i	$0.727887\pi$
$360$		0			0
$361$	11.2959	+	19.5651i	0.594522	+	1.02974i
$362$		0			0
$363$	1.51108	+	2.69447i	0.0793111	+	0.141423i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	1.08164	−	0.624486i	0.0564612	−	0.0325979i	−0.471504	−	0.881864i	$-0.656289\pi$
$367$	1.08164	−	0.624486i	0.0564612	−	0.0325979i	0.527965	+	0.849266i	$0.322955\pi$
$368$		0			0
$369$	−1.52644	−	2.80340i	−0.0794634	−	0.145939i
$370$		0			0
$371$	16.5085	−	8.73745i	0.857078	−	0.453626i
$372$		0			0
$373$	−15.4444	+	26.7505i	−0.799682	+	1.38509i	0.120141	+	0.992757i	$0.461665\pi$
$373$	−15.4444	+	26.7505i	−0.799682	+	1.38509i	−0.919823	+	0.392334i	$0.871668\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−8.07888			−0.416083
$378$		0			0
$379$	−29.6463			−1.52283			−0.761413	−	0.648267i	$-0.775494\pi$
$379$	−29.6463			−1.52283			−0.761413	+	0.648267i	$0.775494\pi$
$380$		0			0
$381$	−12.9075	+	21.7249i	−0.661269	+	1.11300i
$382$		0			0
$383$	−10.4927	+	18.1740i	−0.536154	+	0.928646i	0.462952	+	0.886383i	$0.346790\pi$
$383$	−10.4927	+	18.1740i	−0.536154	+	0.928646i	−0.999107	+	0.0422631i	$0.986543\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.47266	−	6.37774i	−0.176525	−	0.324199i
$388$		0			0
$389$	−14.2540	+	8.22952i	−0.722704	+	0.417253i	−0.815747	−	0.578409i	$-0.803674\pi$
$389$	−14.2540	+	8.22952i	−0.722704	+	0.417253i	0.0930430	+	0.995662i	$0.470341\pi$
$390$		0			0
$391$		−	25.2815i		−	1.27854i
$392$		0			0
$393$	17.0047	+	30.3217i	0.857772	+	1.52953i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−3.54432	−	2.04631i	−0.177884	−	0.102702i	0.408414	−	0.912797i	$-0.366082\pi$
$397$	−3.54432	−	2.04631i	−0.177884	−	0.102702i	−0.586298	+	0.810095i	$0.699415\pi$
$398$		0			0
$399$	−26.2916	+	13.4975i	−1.31622	+	0.675722i
$400$		0			0
$401$	−22.5314	−	13.0085i	−1.12516	−	0.649613i	−0.182449	−	0.983215i	$-0.558402\pi$
$401$	−22.5314	−	13.0085i	−1.12516	−	0.649613i	−0.942714	+	0.333602i	$0.891736\pi$
$402$		0			0
$403$	1.56024	+	2.70241i	0.0777210	+	0.134617i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	8.53866i		−	0.423246i
$408$		0			0
$409$	−30.5083	+	17.6140i	−1.50854	+	0.870955i	−0.508587	+	0.861010i	$0.669832\pi$
$409$	−30.5083	+	17.6140i	−1.50854	+	0.870955i	−0.999951	+	0.00994431i	$0.996835\pi$
$410$		0			0
$411$	0.101082	−	8.08919i	0.00498601	−	0.399010i
$412$		0			0
$413$	−15.2981	−	28.9042i	−0.752772	−	1.42228i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−8.20913	−	4.87731i	−0.402003	−	0.238843i
$418$		0			0
$419$	40.3278			1.97014			0.985072	−	0.172146i	$-0.0550700\pi$
$419$	40.3278			1.97014			0.985072	+	0.172146i	$0.0550700\pi$
$420$		0			0
$421$	0.216416			0.0105475			0.00527375	−	0.999986i	$-0.498321\pi$
$421$	0.216416			0.0105475			0.00527375	+	0.999986i	$0.498321\pi$
$422$		0			0
$423$	11.4360	+	0.285853i	0.556039	+	0.0138986i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−29.6158	−	18.5845i	−1.43321	−	0.899367i
$428$		0			0
$429$	−12.1844	−	0.152256i	−0.588268	−	0.00735097i
$430$		0			0
$431$	25.3179	−	14.6173i	1.21952	−	0.704090i	0.254705	−	0.967019i	$-0.418022\pi$
$431$	25.3179	−	14.6173i	1.21952	−	0.704090i	0.964815	+	0.262928i	$0.0846883\pi$
$432$		0			0
$433$		−	19.8669i		−	0.954743i	−0.878702	−	0.477371i	$-0.841590\pi$
$433$		−	19.8669i		−	0.954743i	0.878702	−	0.477371i	$-0.158410\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−15.7000	−	27.1932i	−0.751033	−	1.30083i
$438$		0			0
$439$	−19.0134	−	10.9774i	−0.907459	−	0.523921i	−0.0278460	−	0.999612i	$-0.508865\pi$
$439$	−19.0134	−	10.9774i	−0.907459	−	0.523921i	−0.879613	+	0.475691i	$0.842198\pi$
$440$		0			0
$441$	−8.65851	−	19.1319i	−0.412310	−	0.911044i
$442$		0			0
$443$	7.55852	+	4.36391i	0.359116	+	0.207336i	0.668693	−	0.743539i	$-0.266854\pi$
$443$	7.55852	+	4.36391i	0.359116	+	0.207336i	−0.309577	+	0.950874i	$0.600187\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	22.0806	−	12.3830i	1.04438	−	0.585696i
$448$		0			0
$449$			1.03244i			0.0487238i	0.999703	+	0.0243619i	$0.00775540\pi$
$449$			1.03244i			0.0487238i	−0.999703	+	0.0243619i	$0.992245\pi$
$450$		0			0
$451$	−2.79742	+	1.61509i	−0.131725	+	0.0760517i
$452$		0			0
$453$	−15.5216	−	0.193957i	−0.729267	−	0.00911288i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−15.7088	+	27.2085i	−0.734828	+	1.27276i	0.219971	+	0.975506i	$0.429404\pi$
$457$	−15.7088	+	27.2085i	−0.734828	+	1.27276i	−0.954799	+	0.297253i	$0.903930\pi$
$458$		0			0
$459$	−12.6053	−	23.8554i	−0.588367	−	1.11348i
$460$		0			0
$461$	−3.22290			−0.150105			−0.0750526	−	0.997180i	$-0.523912\pi$
$461$	−3.22290			−0.150105			−0.0750526	+	0.997180i	$0.523912\pi$
$462$		0			0
$463$	5.06917			0.235584			0.117792	−	0.993038i	$-0.462418\pi$
$463$	5.06917			0.235584			0.117792	+	0.993038i	$0.462418\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4.51214	+	7.81525i	−0.208797	+	0.361647i	−0.951336	−	0.308156i	$-0.900288\pi$
$467$	−4.51214	+	7.81525i	−0.208797	+	0.361647i	0.742539	+	0.669803i	$0.233621\pi$
$468$		0			0
$469$	−5.31749	−	10.0468i	−0.245539	−	0.463920i
$470$		0			0
$471$	−0.444537	+	35.5745i	−0.0204832	+	1.63919i
$472$		0			0
$473$	−6.36413	+	3.67433i	−0.292623	+	0.168946i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	18.0712	+	11.0445i	0.827425	+	0.505694i
$478$		0			0
$479$	−1.26094	−	2.18401i	−0.0576137	−	0.0997899i	0.835780	−	0.549064i	$-0.185016\pi$
$479$	−1.26094	−	2.18401i	−0.0576137	−	0.0997899i	−0.893394	+	0.449275i	$0.851683\pi$
$480$		0			0
$481$	−5.64464	−	3.25893i	−0.257373	−	0.148594i
$482$		0			0
$483$	19.8490	−	10.1900i	0.903159	−	0.463663i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−1.22855	−	2.12791i	−0.0556709	−	0.0964247i	0.836847	−	0.547437i	$-0.184396\pi$
$487$	−1.22855	−	2.12791i	−0.0556709	−	0.0964247i	−0.892518	+	0.451012i	$0.851063\pi$
$488$		0			0
$489$	16.9873	+	30.2908i	0.768194	+	1.36980i
$490$		0			0
$491$		−	14.3239i		−	0.646429i	−0.946326	−	0.323215i	$-0.895236\pi$
$491$		−	14.3239i		−	0.646429i	0.946326	−	0.323215i	$-0.104764\pi$
$492$		0			0
$493$	−15.6770	+	9.05110i	−0.706055	+	0.407641i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.689649	+	18.7268i	−0.0309350	+	0.840014i
$498$		0			0
$499$	19.8770	−	34.4279i	0.889816	−	1.54121i	0.0497229	−	0.998763i	$-0.484166\pi$
$499$	19.8770	−	34.4279i	0.889816	−	1.54121i	0.840093	−	0.542443i	$-0.182500\pi$
$500$		0			0
$501$	10.8343	−	18.2355i	0.484040	−	0.814701i
$502$		0			0
$503$	10.6486			0.474796			0.237398	−	0.971412i	$-0.423705\pi$
$503$	10.6486			0.474796			0.237398	+	0.971412i	$0.423705\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	6.75006	−	11.3612i	0.299781	−	0.504569i
$508$		0			0
$509$	18.5593	−	32.1456i	0.822626	−	1.42483i	−0.0810950	−	0.996706i	$-0.525842\pi$
$509$	18.5593	−	32.1456i	0.822626	−	1.42483i	0.903721	−	0.428123i	$-0.140825\pi$
$510$		0			0
$511$	−0.356954	+	0.188925i	−0.0157907	+	0.00835755i
$512$		0			0
$513$	−28.3730	−	17.8313i	−1.25270	−	0.787272i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	11.5763i		−	0.509127i
$518$		0			0
$519$	−18.4901	−	32.9705i	−0.811627	−	1.44725i
$520$		0			0
$521$	8.12000	+	14.0642i	0.355744	+	0.616166i	0.987245	−	0.159209i	$-0.0508943\pi$
$521$	8.12000	+	14.0642i	0.355744	+	0.616166i	−0.631501	+	0.775375i	$0.717561\pi$
$522$		0			0
$523$	−15.3715	−	8.87476i	−0.672150	−	0.388066i	0.124741	−	0.992189i	$-0.460190\pi$
$523$	−15.3715	−	8.87476i	−0.672150	−	0.388066i	−0.796891	+	0.604123i	$0.793523\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.05525	+	3.49600i	0.263771	+	0.152288i
$528$		0			0
$529$	0.352809	+	0.611082i	0.0153395	+	0.0265688i
$530$		0			0
$531$	19.3375	−	31.6404i	0.839177	−	1.37308i
$532$		0			0
$533$			2.46571i			0.106802i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.0277474	−	2.22051i	0.00119739	−	0.0958221i
$538$		0			0
$539$	−19.1356	+	9.24304i	−0.824228	+	0.398126i
$540$		0			0
$541$	−0.167695	+	0.290456i	−0.00720976	+	0.0124877i	−0.869608	−	0.493743i	$-0.835628\pi$
$541$	−0.167695	+	0.290456i	−0.00720976	+	0.0124877i	0.862398	+	0.506231i	$0.168962\pi$
$542$		0			0
$543$	21.6833	+	12.8827i	0.930519	+	0.552852i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	11.7041			0.500433			0.250216	−	0.968190i	$-0.419498\pi$
$547$	11.7041			0.500433			0.250216	+	0.968190i	$0.419498\pi$
$548$		0			0
$549$	0.990661	−	39.6331i	0.0422804	−	1.69150i
$550$		0			0
$551$	−11.2416	+	19.4710i	−0.478909	+	0.829495i
$552$		0			0
$553$	−8.56333	+	13.6463i	−0.364150	+	0.580300i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.43115	+	2.55833i	−0.187754	+	0.108400i	−0.590931	−	0.806722i	$-0.701239\pi$
$557$	−4.43115	+	2.55833i	−0.187754	+	0.108400i	0.403177	+	0.915122i	$0.367906\pi$
$558$		0			0
$559$			5.60950i			0.237256i
$560$		0			0
$561$	−23.8143	+	13.3552i	−1.00544	+	0.563858i
$562$		0			0
$563$	−9.70464	−	16.8089i	−0.409002	−	0.708412i	0.585776	−	0.810473i	$-0.300790\pi$
$563$	−9.70464	−	16.8089i	−0.409002	−	0.708412i	−0.994778	+	0.102061i	$0.967456\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	13.6486	−	19.5119i	0.573187	−	0.819424i
$568$		0			0
$569$	20.1553	+	11.6367i	0.844954	+	0.487834i	0.858945	−	0.512068i	$-0.171120\pi$
$569$	20.1553	+	11.6367i	0.844954	+	0.487834i	−0.0139912	+	0.999902i	$0.504454\pi$
$570$		0			0
$571$	7.04462	+	12.2016i	0.294808	+	0.510623i	0.974940	−	0.222467i	$-0.0714109\pi$
$571$	7.04462	+	12.2016i	0.294808	+	0.510623i	−0.680132	+	0.733090i	$0.738078\pi$
$572$		0			0
$573$	36.1141	−	20.2531i	1.50869	−	0.846084i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−19.1938	+	11.0816i	−0.799050	+	0.461332i	−0.843139	−	0.537696i	$-0.819295\pi$
$577$	−19.1938	+	11.0816i	−0.799050	+	0.461332i	0.0440886	+	0.999028i	$0.485962\pi$
$578$		0			0
$579$	14.6136	+	0.182611i	0.607320	+	0.00758904i
$580$		0			0
$581$	−27.1688	−	1.00054i	−1.12715	−	0.0415093i
$582$		0			0
$583$	10.7161	−	18.5608i	0.443815	−	0.768709i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	11.5459			0.476550			0.238275	−	0.971198i	$-0.423418\pi$
$587$	11.5459			0.476550			0.238275	+	0.971198i	$0.423418\pi$
$588$		0			0
$589$	8.68418			0.357825
$590$		0			0
$591$	12.2977	+	7.30647i	0.505860	+	0.300548i
$592$		0			0
$593$	10.7259	−	18.5778i	0.440461	−	0.762901i	−0.557263	−	0.830336i	$-0.688148\pi$
$593$	10.7259	−	18.5778i	0.440461	−	0.762901i	0.997724	+	0.0674357i	$0.0214817\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.223423	+	17.8796i	−0.00914409	+	0.731765i
$598$		0			0
$599$	−3.19001	+	1.84175i	−0.130340	+	0.0752519i	−0.563752	−	0.825944i	$-0.690643\pi$
$599$	−3.19001	+	1.84175i	−0.130340	+	0.0752519i	0.433412	+	0.901196i	$0.357309\pi$
$600$		0			0
$601$		−	8.20607i		−	0.334733i	−0.985895	−	0.167366i	$-0.946474\pi$
$601$		−	8.20607i		−	0.334733i	0.985895	−	0.167366i	$-0.0535263\pi$
$602$		0			0
$603$	6.72154	−	10.9979i	0.273722	−	0.447869i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	6.10733	+	3.52607i	0.247889	+	0.143119i	0.618797	−	0.785551i	$-0.287620\pi$
$607$	6.10733	+	3.52607i	0.247889	+	0.143119i	−0.370908	+	0.928670i	$0.620954\pi$
$608$		0			0
$609$	−13.4250	−	8.66011i	−0.544008	−	0.350925i
$610$		0			0
$611$	−7.65274	−	4.41831i	−0.309597	−	0.178746i
$612$		0			0
$613$	9.86586	+	17.0882i	0.398478	+	0.690185i	0.993538	−	0.113496i	$-0.0362051\pi$
$613$	9.86586	+	17.0882i	0.398478	+	0.690185i	−0.595060	+	0.803681i	$0.702872\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	7.15802i		−	0.288171i	−0.989565	−	0.144086i	$-0.953976\pi$
$617$		−	7.15802i		−	0.288171i	0.989565	−	0.144086i	$-0.0460240\pi$
$618$		0			0
$619$	8.50675	−	4.91137i	0.341915	−	0.197405i	−0.319204	−	0.947686i	$-0.603415\pi$
$619$	8.50675	−	4.91137i	0.341915	−	0.197405i	0.661119	+	0.750281i	$0.270082\pi$
$620$		0			0
$621$	21.4203	+	13.4619i	0.859568	+	0.540205i
$622$		0			0
$623$	19.9952	−	31.8639i	0.801090	−	1.27660i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−17.3213	+	29.1540i	−0.691747	+	1.16430i
$628$		0			0
$629$	−14.6045			−0.582318
$630$		0			0
$631$	−13.2595			−0.527854			−0.263927	−	0.964543i	$-0.585018\pi$
$631$	−13.2595			−0.527854			−0.263927	+	0.964543i	$0.585018\pi$
$632$		0			0
$633$	−5.09317	+	8.57244i	−0.202435	+	0.340724i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−1.19316	+	16.1777i	−0.0472748	+	0.640983i
$638$		0			0
$639$	−18.6616	+	10.1612i	−0.738242	+	0.401970i
$640$		0			0
$641$	24.8302	−	14.3357i	0.980734	−	0.566227i	0.0782423	−	0.996934i	$-0.475069\pi$
$641$	24.8302	−	14.3357i	0.980734	−	0.566227i	0.902492	+	0.430707i	$0.141736\pi$
$642$		0			0
$643$		−	38.1006i		−	1.50254i	−0.659994	−	0.751271i	$-0.729441\pi$
$643$		−	38.1006i		−	1.50254i	0.659994	−	0.751271i	$-0.270559\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	19.2908	+	33.4126i	0.758399	+	1.31359i	0.943667	+	0.330897i	$0.107351\pi$
$647$	19.2908	+	33.4126i	0.758399	+	1.31359i	−0.185268	+	0.982688i	$0.559315\pi$
$648$		0			0
$649$	−32.4975	−	18.7625i	−1.27564	−	0.736491i
$650$		0			0
$651$	−0.304126	+	6.16320i	−0.0119196	+	0.241555i
$652$		0			0
$653$	−36.8826	−	21.2942i	−1.44333	−	0.833306i	−0.445259	−	0.895402i	$-0.646888\pi$
$653$	−36.8826	−	21.2942i	−1.44333	−	0.833306i	−0.998070	+	0.0620956i	$0.980222\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−0.390744	−	0.238810i	−0.0152444	−	0.00931685i
$658$		0			0
$659$			13.0441i			0.508128i	0.967187	+	0.254064i	$0.0817674\pi$
$659$			13.0441i			0.508128i	−0.967187	+	0.254064i	$0.918233\pi$
$660$		0			0
$661$	−12.9159	+	7.45701i	−0.502371	+	0.290044i	−0.729692	−	0.683776i	$-0.760337\pi$
$661$	−12.9159	+	7.45701i	−0.502371	+	0.290044i	0.227321	+	0.973820i	$0.427003\pi$
$662$		0			0
$663$	−0.260417	+	20.8401i	−0.0101138	+	0.809362i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	8.48692	−	14.6998i	0.328615	−	0.569178i
$668$		0			0
$669$	−40.3426	−	23.9689i	−1.55974	−	0.926690i
$670$		0			0
$671$	−40.1193			−1.54879
$672$		0			0
$673$	51.0490			1.96780			0.983898	−	0.178732i	$-0.0571994\pi$
$673$	51.0490			1.96780			0.983898	+	0.178732i	$0.0571994\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	0.162345	−	0.281190i	0.00623942	−	0.0108070i	−0.862889	−	0.505394i	$-0.831347\pi$
$677$	0.162345	−	0.281190i	0.00623942	−	0.0108070i	0.869128	+	0.494587i	$0.164681\pi$
$678$		0			0
$679$	−0.840548	+	22.8244i	−0.0322573	+	0.875920i
$680$		0			0
$681$	−12.4057	−	0.155021i	−0.475387	−	0.00594042i
$682$		0			0
$683$	25.7563	−	14.8704i	0.985538	−	0.569001i	0.0816004	−	0.996665i	$-0.473997\pi$
$683$	25.7563	−	14.8704i	0.985538	−	0.569001i	0.903938	+	0.427665i	$0.140664\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−7.26748	+	4.07566i	−0.277272	+	0.155496i
$688$		0			0
$689$	−8.17996	−	14.1681i	−0.311632	−	0.539762i
$690$		0			0
$691$	−25.2719	−	14.5907i	−0.961388	−	0.555058i	−0.0647879	−	0.997899i	$-0.520637\pi$
$691$	−25.2719	−	14.5907i	−0.961388	−	0.555058i	−0.896600	+	0.442842i	$0.853970\pi$
$692$		0			0
$693$	−20.0841	−	13.3140i	−0.762932	−	0.505758i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	2.76244	+	4.78468i	0.104635	+	0.181233i
$698$		0			0
$699$	26.9091	−	15.0909i	1.01780	−	0.570789i
$700$		0			0
$701$			4.22879i			0.159719i	0.996806	+	0.0798596i	$0.0254472\pi$
$701$			4.22879i			0.159719i	−0.996806	+	0.0798596i	$0.974553\pi$
$702$		0			0
$703$	−15.7088	+	9.06949i	−0.592470	+	0.342062i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	20.3745	+	38.4954i	0.766261	+	1.44777i
$708$		0			0
$709$	−13.9852	+	24.2230i	−0.525225	+	0.909716i	0.474344	+	0.880340i	$0.342685\pi$
$709$	−13.9852	+	24.2230i	−0.525225	+	0.909716i	−0.999568	+	0.0293760i	$0.990648\pi$
$710$		0			0
$711$	−18.2620	−	0.456474i	−0.684880	−	0.0171191i
$712$		0			0
$713$	−6.55617			−0.245531
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−20.5293	−	12.1971i	−0.766680	−	0.455510i
$718$		0			0
$719$	2.81744	−	4.87995i	0.105073	−	0.181991i	−0.808695	−	0.588228i	$-0.799826\pi$
$719$	2.81744	−	4.87995i	0.105073	−	0.181991i	0.913768	+	0.406237i	$0.133159\pi$
$720$		0			0
$721$	14.8016	+	9.28827i	0.551239	+	0.345913i
$722$		0			0
$723$	−0.294344	+	23.5552i	−0.0109468	+	0.876026i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	36.1095i		−	1.33923i	−0.742710	−	0.669613i	$-0.766460\pi$
$727$		−	36.1095i		−	1.33923i	0.742710	−	0.669613i	$-0.233540\pi$
$728$		0			0
$729$	26.9242	+	2.02234i	0.997191	+	0.0749016i
$730$		0			0
$731$	6.28455	+	10.8852i	0.232443	+	0.402602i
$732$		0			0
$733$	5.18062	+	2.99103i	0.191351	+	0.110476i	0.592615	−	0.805486i	$-0.298096\pi$
$733$	5.18062	+	2.99103i	0.191351	+	0.110476i	−0.401264	+	0.915962i	$0.631429\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−11.2958	−	6.52165i	−0.416087	−	0.240228i
$738$		0			0
$739$	19.1257	+	33.1266i	0.703549	+	1.21858i	0.967213	+	0.253968i	$0.0817359\pi$
$739$	19.1257	+	33.1266i	0.703549	+	1.21858i	−0.263663	+	0.964615i	$0.584931\pi$
$740$		0			0
$741$	12.6618	+	22.5777i	0.465142	+	0.829413i
$742$		0			0
$743$		−	3.60215i		−	0.132150i	−0.997815	−	0.0660750i	$-0.978952\pi$
$743$		−	3.60215i		−	0.132150i	0.997815	−	0.0660750i	$-0.0210477\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−14.7418	−	27.0741i	−0.539373	−	0.990590i
$748$		0			0
$749$	41.5338	+	26.0633i	1.51761	+	0.952331i
$750$		0			0
$751$	2.07691	−	3.59731i	0.0757874	−	0.131268i	−0.825641	−	0.564196i	$-0.809186\pi$
$751$	2.07691	−	3.59731i	0.0757874	−	0.131268i	0.901428	+	0.432928i	$0.142520\pi$
$752$		0			0
$753$	6.98559	−	11.7576i	0.254569	−	0.428472i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	15.4535			0.561668			0.280834	−	0.959756i	$-0.409389\pi$
$757$	15.4535			0.561668			0.280834	+	0.959756i	$0.409389\pi$
$758$		0			0
$759$	13.0768	−	22.0100i	0.474659	−	0.798911i
$760$		0			0
$761$	14.2676	−	24.7122i	0.517199	−	0.895816i	−0.482601	−	0.875840i	$-0.660308\pi$
$761$	14.2676	−	24.7122i	0.517199	−	0.895816i	0.999800	−	0.0199755i	$-0.00635881\pi$
$762$		0			0
$763$	−22.8999	−	43.2669i	−0.829031	−	1.56637i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−24.8065	+	14.3220i	−0.895711	+	0.517139i
$768$		0			0
$769$		−	19.5067i		−	0.703431i	−0.936107	−	0.351716i	$-0.885598\pi$
$769$		−	19.5067i		−	0.703431i	0.936107	−	0.351716i	$-0.114402\pi$
$770$		0			0
$771$	15.6522	+	27.9100i	0.563699	+	1.00515i
$772$		0			0
$773$	10.5473	+	18.2685i	0.379362	+	0.657074i	0.990970	−	0.134087i	$-0.0428102\pi$
$773$	10.5473	+	18.2685i	0.379362	+	0.657074i	−0.611608	+	0.791161i	$0.709477\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−5.88653	−	11.4662i	−0.211178	−	0.411349i
$778$		0			0
$779$	5.94266	+	3.43100i	0.212918	+	0.122928i
$780$		0			0
$781$	10.7513	+	18.6218i	0.384712	+	0.666340i
$782$		0			0
$783$	0.678895	−	18.1022i	0.0242617	−	0.646920i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	4.51062	−	2.60421i	0.160786	−	0.0928301i	−0.417448	−	0.908701i	$-0.637075\pi$
$787$	4.51062	−	2.60421i	0.160786	−	0.0928301i	0.578234	+	0.815871i	$0.303742\pi$
$788$		0			0
$789$	−0.466575	+	37.3381i	−0.0166105	+	1.32927i
$790$		0			0
$791$	0.571521	−	15.5192i	0.0203210	−	0.551799i
$792$		0			0
$793$	−15.3122	+	26.5216i	−0.543753	+	0.941808i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	41.1247			1.45671			0.728356	−	0.685199i	$-0.240285\pi$
$797$	41.1247			1.45671			0.728356	+	0.685199i	$0.240285\pi$
$798$		0			0
$799$	−19.8001			−0.700476
$800$		0			0
$801$	42.6415	+	1.06586i	1.50666	+	0.0376602i
$802$		0			0
$803$	−0.231708	+	0.401329i	−0.00817679	+	0.0141626i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−27.6581	−	0.345614i	−0.973612	−	0.0121662i
$808$		0			0
$809$	−8.18379	+	4.72491i	−0.287727	+	0.166119i	−0.636916	−	0.770933i	$-0.719790\pi$
$809$	−8.18379	+	4.72491i	−0.287727	+	0.166119i	0.349190	+	0.937052i	$0.386457\pi$
$810$		0			0
$811$		−	13.1110i		−	0.460388i	−0.973145	−	0.230194i	$-0.926064\pi$
$811$		−	13.1110i		−	0.460388i	0.973145	−	0.230194i	$-0.0739361\pi$
$812$		0			0
$813$	−8.24076	+	4.62149i	−0.289016	+	0.162083i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	13.5196	+	7.80552i	0.472989	+	0.273081i
$818$		0			0
$819$	−16.4669	+	8.19542i	−0.575401	+	0.286371i
$820$		0			0
$821$	−24.7530	−	14.2911i	−0.863885	−	0.498764i	0.00142663	−	0.999999i	$-0.499546\pi$
$821$	−24.7530	−	14.2911i	−0.863885	−	0.498764i	−0.865311	+	0.501235i	$0.832879\pi$
$822$		0			0
$823$	12.3787	+	21.4406i	0.431495	+	0.747371i	0.997002	−	0.0773725i	$-0.0246531\pi$
$823$	12.3787	+	21.4406i	0.431495	+	0.747371i	−0.565508	+	0.824743i	$0.691320\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	35.9582i		−	1.25039i	−0.780470	−	0.625194i	$-0.785020\pi$
$827$		−	35.9582i		−	1.25039i	0.780470	−	0.625194i	$-0.214980\pi$
$828$		0			0
$829$	12.8068	−	7.39399i	0.444798	−	0.256804i	−0.260833	−	0.965384i	$-0.583997\pi$
$829$	12.8068	−	7.39399i	0.444798	−	0.256804i	0.705631	+	0.708580i	$0.250664\pi$
$830$		0			0
$831$	−13.4453	−	0.168011i	−0.466411	−	0.00582825i
$832$		0			0
$833$	15.8092	+	32.7294i	0.547757	+	1.13400i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−6.18636	+	3.26891i	−0.213832	+	0.112990i
$838$		0			0
$839$	−0.979006			−0.0337991			−0.0168995	−	0.999857i	$-0.505380\pi$
$839$	−0.979006			−0.0337991			−0.0168995	+	0.999857i	$0.505380\pi$
$840$		0			0
$841$	16.8463			0.580906
$842$		0			0
$843$	−1.10573	−	0.656953i	−0.0380835	−	0.0226267i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	2.50826	−	3.99710i	0.0861848	−	0.137342i
$848$		0			0
$849$	−0.207557	+	16.6099i	−0.00712334	+	0.570052i
$850$		0			0
$851$	11.8595	−	6.84707i	0.406537	−	0.234714i
$852$		0			0
$853$		−	31.6889i		−	1.08501i	−0.840053	−	0.542504i	$-0.817476\pi$
$853$		−	31.6889i		−	1.08501i	0.840053	−	0.542504i	$-0.182524\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−16.1820	−	28.0280i	−0.552766	−	0.957419i	−0.998074	−	0.0620413i	$-0.980239\pi$
$857$	−16.1820	−	28.0280i	−0.552766	−	0.957419i	0.445307	−	0.895378i	$-0.353094\pi$
$858$		0			0
$859$	41.2350	+	23.8070i	1.40692	+	0.812285i	0.995090	−	0.0989753i	$-0.0315565\pi$
$859$	41.2350	+	23.8070i	1.40692	+	0.812285i	0.411830	+	0.911261i	$0.364890\pi$
$860$		0			0
$861$	−2.64311	+	4.09737i	−0.0900769	+	0.139638i
$862$		0			0
$863$	−5.16975	−	2.98476i	−0.175980	−	0.101602i	0.409422	−	0.912345i	$-0.365730\pi$
$863$	−5.16975	−	2.98476i	−0.175980	−	0.101602i	−0.585403	+	0.810743i	$0.699064\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	8.44002	+	15.0497i	0.286638	+	0.511116i
$868$		0			0
$869$			18.4861i			0.627097i
$870$		0			0
$871$	−8.62251	+	4.97821i	−0.292163	+	0.168680i
$872$		0			0
$873$	−22.7449	+	12.3845i	−0.769797	+	0.419152i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	8.54159	−	14.7945i	0.288429	−	0.499574i	−0.685006	−	0.728537i	$-0.740200\pi$
$877$	8.54159	−	14.7945i	0.288429	−	0.499574i	0.973435	+	0.228964i	$0.0735338\pi$
$878$		0			0
$879$	0.504001	−	0.848296i	0.0169995	−	0.0286123i
$880$		0			0
$881$	13.7490			0.463215			0.231607	−	0.972809i	$-0.425601\pi$
$881$	13.7490			0.463215			0.231607	+	0.972809i	$0.425601\pi$
$882$		0			0
$883$	29.4325			0.990482			0.495241	−	0.868756i	$-0.335080\pi$
$883$	29.4325			0.990482			0.495241	+	0.868756i	$0.335080\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	8.42380	−	14.5904i	0.282843	−	0.489899i	−0.689240	−	0.724533i	$-0.742056\pi$
$887$	8.42380	−	14.5904i	0.282843	−	0.489899i	0.972084	+	0.234633i	$0.0753890\pi$
$888$		0			0
$889$	38.5744	+	1.42057i	1.29374	+	0.0476444i
$890$		0			0
$891$	1.36505	−	27.2886i	0.0457310	−	0.914202i
$892$		0			0
$893$	−21.2973	+	12.2960i	−0.712687	+	0.411470i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−9.55907	−	17.0452i	−0.319168	−	0.569122i
$898$		0			0
$899$	2.34720	+	4.06546i	0.0782834	+	0.135591i
$900$		0			0
$901$	−31.7462	−	18.3287i	−1.05762	−	0.610617i
$902$		0			0
$903$	−6.01307	+	9.32153i	−0.200103	+	0.310201i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	8.08581	+	14.0050i	0.268485	+	0.465030i	0.968471	−	0.249127i	$-0.0801437\pi$
$907$	8.08581	+	14.0050i	0.268485	+	0.465030i	−0.699986	+	0.714157i	$0.746810\pi$
$908$		0			0
$909$	−25.7543	+	42.1395i	−0.854215	+	1.39768i
$910$		0			0
$911$			13.3127i			0.441071i	0.975379	+	0.220535i	$0.0707805\pi$
$911$			13.3127i			0.441071i	−0.975379	+	0.220535i	$0.929220\pi$
$912$		0			0
$913$	−27.0164	+	15.5979i	−0.894111	+	0.516216i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	28.2263	−	44.9807i	0.932113	−	1.48539i
$918$		0			0
$919$	−6.00415	+	10.3995i	−0.198058	+	0.343047i	−0.947899	−	0.318571i	$-0.896797\pi$
$919$	−6.00415	+	10.3995i	−0.198058	+	0.343047i	0.749840	+	0.661619i	$0.230130\pi$
$920$		0			0
$921$	14.0928	+	8.37301i	0.464375	+	0.275900i
$922$		0			0
$923$	16.4137			0.540263
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−0.495118	+	19.8080i	−0.0162618	+	0.650581i
$928$		0			0
$929$	−3.50004	+	6.06225i	−0.114833	+	0.198896i	−0.917713	−	0.397244i	$-0.869966\pi$
$929$	−3.50004	+	6.06225i	−0.114833	+	0.198896i	0.802880	+	0.596140i	$0.203300\pi$
$930$		0			0
$931$	37.3299	+	25.3866i	1.22344	+	0.832013i
$932$		0			0
$933$	−11.2872	−	0.141044i	−0.369526	−	0.00461758i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			20.7984i			0.679456i	0.940524	+	0.339728i	$0.110335\pi$
$937$			20.7984i			0.679456i	−0.940524	+	0.339728i	$0.889665\pi$
$938$		0			0
$939$	33.4423	−	18.7547i	1.09135	−	0.612037i
$940$		0			0
$941$	14.5688	+	25.2339i	0.474929	+	0.822600i	0.999588	−	0.0287120i	$-0.00914058\pi$
$941$	14.5688	+	25.2339i	0.474929	+	0.822600i	−0.524659	+	0.851312i	$0.675807\pi$
$942$		0			0
$943$	−4.48644	−	2.59025i	−0.146099	−	0.0843501i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−13.8318	−	7.98578i	−0.449472	−	0.259503i	0.258135	−	0.966109i	$-0.416892\pi$
$947$	−13.8318	−	7.98578i	−0.449472	−	0.259503i	−0.707607	+	0.706606i	$0.750225\pi$
$948$		0			0
$949$	0.176871	+	0.306349i	0.00574146	+	0.00994451i
$950$		0			0
$951$	−6.36860	+	3.57156i	−0.206516	+	0.115816i
$952$		0			0
$953$			24.9487i			0.808167i	0.914722	+	0.404084i	$0.132410\pi$
$953$			24.9487i			0.808167i	−0.914722	+	0.404084i	$0.867590\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−18.3300	−	0.229051i	−0.592525	−	0.00740416i
$958$		0			0
$959$	−10.9220	+	5.78067i	−0.352689	+	0.186668i
$960$		0			0
$961$	−14.5934	+	25.2765i	−0.470755	+	0.815371i
$962$		0			0
$963$	−1.38932	+	55.5822i	−0.0447703	+	1.79111i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−7.93647			−0.255220			−0.127610	−	0.991824i	$-0.540731\pi$
$967$	−7.93647			−0.255220			−0.127610	+	0.991824i	$0.540731\pi$
$968$		0			0
$969$	49.8647	+	29.6263i	1.60189	+	0.951733i
$970$		0			0
$971$	17.5378	−	30.3763i	0.562814	−	0.974822i	−0.434436	−	0.900703i	$-0.643052\pi$
$971$	17.5378	−	30.3763i	0.562814	−	0.974822i	0.997249	−	0.0741192i	$-0.0236145\pi$
$972$		0			0
$973$	−0.536788	+	14.5760i	−0.0172086	+	0.467286i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2.70546	+	1.56200i	−0.0865554	+	0.0499728i	−0.542653	−	0.839957i	$-0.682580\pi$
$977$	−2.70546	+	1.56200i	−0.0865554	+	0.0499728i	0.456098	+	0.889930i	$0.349247\pi$
$978$		0			0
$979$		−	43.1646i		−	1.37955i
$980$		0			0
$981$	28.9464	−	47.3626i	0.924189	−	1.51217i
$982$		0			0
$983$	11.4489	+	19.8301i	0.365163	+	0.632481i	0.988802	−	0.149231i	$-0.0476799\pi$
$983$	11.4489	+	19.8301i	0.365163	+	0.632481i	−0.623639	+	0.781712i	$0.714347\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−7.98068	−	15.5454i	−0.254028	−	0.494816i
$988$		0			0
$989$	−10.2067	−	5.89282i	−0.324553	−	0.187381i
$990$		0			0
$991$	−5.34209	−	9.25277i	−0.169697	−	0.293924i	0.768616	−	0.639710i	$-0.220946\pi$
$991$	−5.34209	−	9.25277i	−0.169697	−	0.293924i	−0.938313	+	0.345786i	$0.887612\pi$
$992$		0			0
$993$	−20.3402	−	36.2694i	−0.645476	−	1.15098i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	43.6367	−	25.1937i	1.38199	−	0.797892i	0.389595	−	0.920986i	$-0.372615\pi$
$997$	43.6367	−	25.1937i	1.38199	−	0.797892i	0.992395	+	0.123094i	$0.0392818\pi$
$998$		0			0
$999$	7.77657	−	12.3740i	0.246040	−	0.391495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bi.n.1601.11		32
3.2	odd	2	inner	2100.2.bi.n.1601.16		32
5.2	odd	4		420.2.bn.a.89.3	✓	32
5.3	odd	4		420.2.bn.a.89.14	yes	32
5.4	even	2	inner	2100.2.bi.n.1601.6		32
7.3	odd	6	inner	2100.2.bi.n.101.16		32
15.2	even	4		420.2.bn.a.89.8	yes	32
15.8	even	4		420.2.bn.a.89.9	yes	32
15.14	odd	2	inner	2100.2.bi.n.1601.1		32
21.17	even	6	inner	2100.2.bi.n.101.11		32
35.2	odd	12		2940.2.f.a.1469.25		32
35.3	even	12		420.2.bn.a.269.8	yes	32
35.12	even	12		2940.2.f.a.1469.8		32
35.17	even	12		420.2.bn.a.269.9	yes	32
35.23	odd	12		2940.2.f.a.1469.7		32
35.24	odd	6	inner	2100.2.bi.n.101.1		32
35.33	even	12		2940.2.f.a.1469.26		32
105.2	even	12		2940.2.f.a.1469.28		32
105.17	odd	12		420.2.bn.a.269.14	yes	32
105.23	even	12		2940.2.f.a.1469.6		32
105.38	odd	12		420.2.bn.a.269.3	yes	32
105.47	odd	12		2940.2.f.a.1469.5		32
105.59	even	6	inner	2100.2.bi.n.101.6		32
105.68	odd	12		2940.2.f.a.1469.27		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bn.a.89.3	✓	32	5.2	odd	4
420.2.bn.a.89.8	yes	32	15.2	even	4
420.2.bn.a.89.9	yes	32	15.8	even	4
420.2.bn.a.89.14	yes	32	5.3	odd	4
420.2.bn.a.269.3	yes	32	105.38	odd	12
420.2.bn.a.269.8	yes	32	35.3	even	12
420.2.bn.a.269.9	yes	32	35.17	even	12
420.2.bn.a.269.14	yes	32	105.17	odd	12
2100.2.bi.n.101.1		32	35.24	odd	6	inner
2100.2.bi.n.101.6		32	105.59	even	6	inner
2100.2.bi.n.101.11		32	21.17	even	6	inner
2100.2.bi.n.101.16		32	7.3	odd	6	inner
2100.2.bi.n.1601.1		32	15.14	odd	2	inner
2100.2.bi.n.1601.6		32	5.4	even	2	inner
2100.2.bi.n.1601.11		32	1.1	even	1	trivial
2100.2.bi.n.1601.16		32	3.2	odd	2	inner
2940.2.f.a.1469.5		32	105.47	odd	12
2940.2.f.a.1469.6		32	105.23	even	12
2940.2.f.a.1469.7		32	35.23	odd	12
2940.2.f.a.1469.8		32	35.12	even	12
2940.2.f.a.1469.25		32	35.2	odd	12
2940.2.f.a.1469.26		32	35.33	even	12
2940.2.f.a.1469.27		32	105.68	odd	12
2940.2.f.a.1469.28		32	105.2	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.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.884700 - 1.48906i) q^{3} +(-2.64396 - 0.0973684i) q^{7} +(-1.43461 - 2.63475i) q^{9} +O(q^{10})\)	\(q+(0.884700 - 1.48906i) q^{3} +(-2.64396 - 0.0973684i) q^{7} +(-1.43461 - 2.63475i) q^{9} +(-2.62913 + 1.51793i) q^{11} +2.31738i q^{13} +(2.59625 + 4.49684i) q^{17} +(5.58515 + 3.22459i) q^{19} +(-2.48410 + 3.85088i) q^{21} +(-4.21654 - 2.43442i) q^{23} +(-5.19250 - 0.194737i) q^{27} +3.48622i q^{29} +(1.16615 - 0.673279i) q^{31} +(-0.0657018 + 5.25784i) q^{33} +(-1.40630 + 2.43579i) q^{37} +(3.45072 + 2.05018i) q^{39} +1.06401 q^{41} +2.42063 q^{43} +(-1.90660 + 3.30233i) q^{47} +(6.98104 + 0.514876i) q^{49} +(8.99298 + 0.112376i) q^{51} +(-6.11386 + 3.52984i) q^{53} +(9.74279 - 5.46384i) q^{57} +(6.18029 + 10.7046i) q^{59} +(11.4447 + 6.60758i) q^{61} +(3.53651 + 7.10585i) q^{63} +(2.14821 + 3.72081i) q^{67} +(-7.35538 + 4.12496i) q^{69} -7.08288i q^{71} +(0.132196 - 0.0763237i) q^{73} +(7.09910 - 3.75734i) q^{77} +(3.04462 - 5.27344i) q^{79} +(-4.88378 + 7.55967i) q^{81} +10.2758 q^{83} +(5.19119 + 3.08426i) q^{87} +(-7.10913 + 12.3134i) q^{89} +(0.225639 - 6.12705i) q^{91} +(0.0291421 - 2.33212i) q^{93} -8.63266i q^{97} +(7.77113 + 4.74945i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 12 q^{19} - 8 q^{21} - 12 q^{31} - 24 q^{39} + 44 q^{49} - 10 q^{51} - 24 q^{61} + 28 q^{79} - 20 q^{81} + 16 q^{91} + 28 q^{99}+O(q^{100}) \) 32 * q - 12 * q^19 - 8 * q^21 - 12 * q^31 - 24 * q^39 + 44 * q^49 - 10 * q^51 - 24 * q^61 + 28 * q^79 - 20 * q^81 + 16 * q^91 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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