LMFDB - Embedded newform 2100.2.bo.i.1949.2

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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1949.2
Character	$\chi$	$=$	2100.1949
Dual form			2100.2.bo.i.1349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68089 + 0.417865i) q^{3} +(2.33003 + 1.25338i) q^{7} +(2.65078 - 1.40477i) q^{9} +O(q^{10})$	\(q+(-1.68089 + 0.417865i) q^{3} +(2.33003 + 1.25338i) q^{7} +(2.65078 - 1.40477i) q^{9} +(4.63831 + 2.67793i) q^{11} +4.13670 q^{13} +(0.134025 + 0.0773793i) q^{17} +(3.40485 - 1.96579i) q^{19} +(-4.44027 - 1.13315i) q^{21} +(-2.99803 - 5.19273i) q^{23} +(-3.86866 + 3.46893i) q^{27} -10.3150i q^{29} +(6.70071 + 3.86866i) q^{31} +(-8.91550 - 2.56312i) q^{33} +(-9.07719 + 5.24072i) q^{37} +(-6.95334 + 1.72858i) q^{39} -2.33876 q^{41} +1.78236i q^{43} +(3.11974 - 1.80118i) q^{47} +(3.85809 + 5.84082i) q^{49} +(-0.257615 - 0.0740617i) q^{51} +(-2.47955 + 4.29470i) q^{53} +(-4.90174 + 4.72705i) q^{57} +(5.27011 - 9.12810i) q^{59} +(-3.25602 + 1.87987i) q^{61} +(7.93710 + 0.0492651i) q^{63} +(-0.770225 - 0.444690i) q^{67} +(7.20921 + 7.47564i) q^{69} -11.6200i q^{71} +(6.12550 - 10.6097i) q^{73} +(7.45095 + 12.0532i) q^{77} +(-3.61147 - 6.25525i) q^{79} +(5.05324 - 7.44747i) q^{81} -5.14180i q^{83} +(4.31026 + 17.3383i) q^{87} +(8.58428 + 14.8684i) q^{89} +(9.63865 + 5.18485i) q^{91} +(-12.8797 - 3.70279i) q^{93} +4.28309 q^{97} +(16.0570 + 0.582836i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 18 q^{9}+O(q^{10}) $ 32 * q + 18 * q^9	$ 32 q + 18 q^{9} + 36 q^{19} - 22 q^{21} - 36 q^{31} - 24 q^{39} + 36 q^{49} - 2 q^{51} + 72 q^{61} + 14 q^{81} + 40 q^{91} + 60 q^{99}+O(q^{100}) $ 32 * q + 18 * q^9 + 36 * q^19 - 22 * q^21 - 36 * q^31 - 24 * q^39 + 36 * q^49 - 2 * q^51 + 72 * q^61 + 14 * q^81 + 40 * q^91 + 60 * 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
$3$	−1.68089	+	0.417865i	−0.970462	+	0.241255i
$3$	−1.68089	+	0.417865i	−0.970462	+	0.241255i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.33003	+	1.25338i	0.880669	+	0.473732i
$7$	2.33003	+	1.25338i	0.880669	+	0.473732i
$8$		0			0
$9$	2.65078	−	1.40477i	0.883592	−	0.468257i
$10$		0			0
$11$	4.63831	+	2.67793i	1.39850	+	0.807426i	0.994236	−	0.107214i	$-0.0341931\pi$
$11$	4.63831	+	2.67793i	1.39850	+	0.807426i	0.404268	+	0.914641i	$0.367526\pi$
$12$		0			0
$13$	4.13670			1.14732			0.573658	−	0.819095i	$-0.305524\pi$
$13$	4.13670			1.14732			0.573658	+	0.819095i	$0.305524\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.134025	+	0.0773793i	0.0325058	+	0.0187672i	0.516165	−	0.856489i	$-0.327359\pi$
$17$	0.134025	+	0.0773793i	0.0325058	+	0.0187672i	−0.483659	+	0.875257i	$0.660693\pi$
$18$		0			0
$19$	3.40485	−	1.96579i	0.781126	−	0.450983i	−0.0557031	−	0.998447i	$-0.517740\pi$
$19$	3.40485	−	1.96579i	0.781126	−	0.450983i	0.836829	+	0.547464i	$0.184407\pi$
$20$		0			0
$21$	−4.44027	−	1.13315i	−0.968946	−	0.247273i
$22$		0			0
$23$	−2.99803	−	5.19273i	−0.625132	−	1.08276i	−0.988515	−	0.151120i	$-0.951712\pi$
$23$	−2.99803	−	5.19273i	−0.625132	−	1.08276i	0.363384	−	0.931640i	$-0.381621\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.86866	+	3.46893i	−0.744524	+	0.667596i
$28$		0			0
$29$		−	10.3150i		−	1.91544i	−0.287703	−	0.957720i	$-0.592892\pi$
$29$		−	10.3150i		−	1.91544i	0.287703	−	0.957720i	$-0.407108\pi$
$30$		0			0
$31$	6.70071	+	3.86866i	1.20348	+	0.694832i	0.961328	−	0.275406i	$-0.0888122\pi$
$31$	6.70071	+	3.86866i	1.20348	+	0.694832i	0.242156	+	0.970237i	$0.422146\pi$
$32$		0			0
$33$	−8.91550	−	2.56312i	−1.55199	−	0.446181i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−9.07719	+	5.24072i	−1.49228	+	0.861569i	−0.999961	−	0.00884571i	$-0.997184\pi$
$37$	−9.07719	+	5.24072i	−1.49228	+	0.861569i	−0.492320	+	0.870414i	$0.663851\pi$
$38$		0			0
$39$	−6.95334	+	1.72858i	−1.11343	+	0.276795i
$40$		0			0
$41$	−2.33876			−0.365253			−0.182627	−	0.983182i	$-0.558460\pi$
$41$	−2.33876			−0.365253			−0.182627	+	0.983182i	$0.558460\pi$
$42$		0			0
$43$			1.78236i			0.271807i	0.990722	+	0.135903i	$0.0433937\pi$
$43$			1.78236i			0.271807i	−0.990722	+	0.135903i	$0.956606\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.11974	−	1.80118i	0.455061	−	0.262729i	−0.254905	−	0.966966i	$-0.582044\pi$
$47$	3.11974	−	1.80118i	0.455061	−	0.262729i	0.709965	+	0.704237i	$0.248711\pi$
$48$		0			0
$49$	3.85809	+	5.84082i	0.551156	+	0.834402i
$50$		0			0
$51$	−0.257615	−	0.0740617i	−0.0360733	−	0.0103707i
$52$		0			0
$53$	−2.47955	+	4.29470i	−0.340592	+	0.589923i	−0.984543	−	0.175144i	$-0.943961\pi$
$53$	−2.47955	+	4.29470i	−0.340592	+	0.589923i	0.643951	+	0.765067i	$0.277294\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−4.90174	+	4.72705i	−0.649251	+	0.626112i
$58$		0			0
$59$	5.27011	−	9.12810i	0.686110	−	1.18838i	−0.286976	−	0.957938i	$-0.592650\pi$
$59$	5.27011	−	9.12810i	0.686110	−	1.18838i	0.973087	−	0.230440i	$-0.0740165\pi$
$60$		0			0
$61$	−3.25602	+	1.87987i	−0.416891	+	0.240692i	−0.693746	−	0.720219i	$-0.744041\pi$
$61$	−3.25602	+	1.87987i	−0.416891	+	0.240692i	0.276855	+	0.960912i	$0.410708\pi$
$62$		0			0
$63$	7.93710	+	0.0492651i	0.999981	+	0.00620682i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−0.770225	−	0.444690i	−0.0940980	−	0.0543275i	0.452213	−	0.891910i	$-0.350635\pi$
$67$	−0.770225	−	0.444690i	−0.0940980	−	0.0543275i	−0.546311	+	0.837583i	$0.683968\pi$
$68$		0			0
$69$	7.20921	+	7.47564i	0.867887	+	0.899961i
$70$		0			0
$71$		−	11.6200i		−	1.37904i	−0.724269	−	0.689518i	$-0.757822\pi$
$71$		−	11.6200i		−	1.37904i	0.724269	−	0.689518i	$-0.242178\pi$
$72$		0			0
$73$	6.12550	−	10.6097i	0.716935	−	1.24177i	−0.245273	−	0.969454i	$-0.578878\pi$
$73$	6.12550	−	10.6097i	0.716935	−	1.24177i	0.962208	−	0.272314i	$-0.0877890\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	7.45095	+	12.0532i	0.849115	+	1.37359i
$78$		0			0
$79$	−3.61147	−	6.25525i	−0.406322	−	0.703770i	0.588152	−	0.808750i	$-0.299856\pi$
$79$	−3.61147	−	6.25525i	−0.406322	−	0.703770i	−0.994474	+	0.104980i	$0.966522\pi$
$80$		0			0
$81$	5.05324	−	7.44747i	0.561471	−	0.827496i
$82$		0			0
$83$		−	5.14180i		−	0.564386i	−0.959358	−	0.282193i	$-0.908938\pi$
$83$		−	5.14180i		−	0.564386i	0.959358	−	0.282193i	$-0.0910618\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	4.31026	+	17.3383i	0.462108	+	1.85886i
$88$		0			0
$89$	8.58428	+	14.8684i	0.909932	+	1.57605i	0.814156	+	0.580646i	$0.197200\pi$
$89$	8.58428	+	14.8684i	0.909932	+	1.57605i	0.0957761	+	0.995403i	$0.469467\pi$
$90$		0			0
$91$	9.63865	+	5.18485i	1.01041	+	0.543520i
$92$		0			0
$93$	−12.8797	−	3.70279i	−1.33557	−	0.383962i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	4.28309			0.434882			0.217441	−	0.976073i	$-0.430229\pi$
$97$	4.28309			0.434882			0.217441	+	0.976073i	$0.430229\pi$
$98$		0			0
$99$	16.0570	+	0.582836i	1.61379	+	0.0585772i
$100$		0			0
$101$	3.04794	−	5.27919i	0.303282	−	0.525299i	−0.673596	−	0.739100i	$-0.735251\pi$
$101$	3.04794	−	5.27919i	0.303282	−	0.525299i	0.976877	+	0.213801i	$0.0685844\pi$
$102$		0			0
$103$	2.15428	+	3.73132i	0.212267	+	0.367658i	0.952424	−	0.304777i	$-0.0985820\pi$
$103$	2.15428	+	3.73132i	0.212267	+	0.367658i	−0.740157	+	0.672435i	$0.765249\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.28953	+	14.3579i	0.801379	+	1.38803i	0.918709	+	0.394936i	$0.129233\pi$
$107$	8.28953	+	14.3579i	0.801379	+	1.38803i	−0.117330	+	0.993093i	$0.537433\pi$
$108$		0			0
$109$	1.92426	−	3.33292i	0.184311	−	0.319236i	−0.759033	−	0.651052i	$-0.774328\pi$
$109$	1.92426	−	3.33292i	0.184311	−	0.319236i	0.943344	+	0.331816i	$0.107661\pi$
$110$		0			0
$111$	13.0678	−	12.6021i	1.24034	−	1.19614i
$112$		0			0
$113$	−9.94281			−0.935341			−0.467671	−	0.883903i	$-0.654907\pi$
$113$	−9.94281			−0.935341			−0.467671	+	0.883903i	$0.654907\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	10.9655	−	5.81112i	1.01376	−	0.537238i
$118$		0			0
$119$	0.215297	+	0.348280i	0.0197362	+	0.0319268i
$120$		0			0
$121$	8.84262	+	15.3159i	0.803875	+	1.39235i
$122$		0			0
$123$	3.93120	−	0.977287i	0.354464	−	0.0881190i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			4.64472i			0.412152i	0.978536	+	0.206076i	$0.0660694\pi$
$127$			4.64472i			0.412152i	−0.978536	+	0.206076i	$0.933931\pi$
$128$		0			0
$129$	−0.744784	−	2.99594i	−0.0655746	−	0.263778i
$130$		0			0
$131$	3.31417	+	5.74031i	0.289561	+	0.501534i	0.973705	−	0.227813i	$-0.0731575\pi$
$131$	3.31417	+	5.74031i	0.289561	+	0.501534i	−0.684144	+	0.729347i	$0.739824\pi$
$132$		0			0
$133$	10.3973	−	0.312794i	0.901559	−	0.0271227i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.35783	+	4.08389i	−0.201443	+	0.348910i	−0.948994	−	0.315295i	$-0.897897\pi$
$137$	−2.35783	+	4.08389i	−0.201443	+	0.348910i	0.747550	+	0.664205i	$0.231230\pi$
$138$		0			0
$139$			9.56273i			0.811100i	0.914073	+	0.405550i	$0.132920\pi$
$139$			9.56273i			0.811100i	−0.914073	+	0.405550i	$0.867080\pi$
$140$		0			0
$141$	−4.49128	+	4.33122i	−0.378234	+	0.364754i
$142$		0			0
$143$	19.1873	+	11.0778i	1.60452	+	0.926373i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−8.92570	−	8.20560i	−0.736179	−	0.676787i
$148$		0			0
$149$	−17.6339	+	10.1809i	−1.44462	+	0.834054i	−0.998153	−	0.0607437i	$-0.980653\pi$
$149$	−17.6339	+	10.1809i	−1.44462	+	0.834054i	−0.446471	+	0.894798i	$0.647319\pi$
$150$		0			0
$151$	−5.69396	+	9.86223i	−0.463368	+	0.802577i	−0.999126	−	0.0417947i	$-0.986692\pi$
$151$	−5.69396	+	9.86223i	−0.463368	+	0.802577i	0.535758	+	0.844371i	$0.320026\pi$
$152$		0			0
$153$	0.463970	+	0.0168412i	0.0375098	+	0.00136153i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	3.40612	−	5.89957i	0.271838	−	0.470837i	−0.697495	−	0.716590i	$-0.745702\pi$
$157$	3.40612	−	5.89957i	0.271838	−	0.470837i	0.969332	+	0.245753i	$0.0790353\pi$
$158$		0			0
$159$	2.37324	−	8.25504i	0.188210	−	0.654667i
$160$		0			0
$161$	−0.477042	−	15.8569i	−0.0375962	−	1.24970i
$162$		0			0
$163$	6.85180	−	3.95589i	0.536674	−	0.309849i	−0.207056	−	0.978329i	$-0.566388\pi$
$163$	6.85180	−	3.95589i	0.536674	−	0.309849i	0.743730	+	0.668480i	$0.233055\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	19.2507i		−	1.48966i	−0.667252	−	0.744832i	$-0.732530\pi$
$167$		−	19.2507i		−	1.48966i	0.667252	−	0.744832i	$-0.267470\pi$
$168$		0			0
$169$	4.11232			0.316332
$170$		0			0
$171$	6.26402	−	9.99391i	0.479021	−	0.764253i
$172$		0			0
$173$	−12.2478	+	7.07129i	−0.931186	+	0.537621i	−0.887186	−	0.461411i	$-0.847343\pi$
$173$	−12.2478	+	7.07129i	−0.931186	+	0.537621i	−0.0439995	+	0.999032i	$0.514010\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−5.04416	+	17.5455i	−0.379142	+	1.31880i
$178$		0			0
$179$	1.79606	+	1.03696i	0.134244	+	0.0775058i	0.565618	−	0.824667i	$-0.308638\pi$
$179$	1.79606	+	1.03696i	0.134244	+	0.0775058i	−0.431374	+	0.902173i	$0.641971\pi$
$180$		0			0
$181$			21.7401i			1.61593i	0.589231	+	0.807965i	$0.299431\pi$
$181$			21.7401i			1.61593i	−0.589231	+	0.807965i	$0.700569\pi$
$182$		0			0
$183$	4.68749	−	4.52043i	0.346509	−	0.334160i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.414433	+	0.717819i	0.0303063	+	0.0524921i
$188$		0			0
$189$	−13.3620	+	3.23383i	−0.971941	+	0.235226i
$190$		0			0
$191$	−2.00687	+	1.15867i	−0.145212	+	0.0838383i	−0.570846	−	0.821057i	$-0.693385\pi$
$191$	−2.00687	+	1.15867i	−0.145212	+	0.0838383i	0.425634	+	0.904896i	$0.360051\pi$
$192$		0			0
$193$	−15.4707	−	8.93203i	−1.11361	−	0.642942i	−0.173846	−	0.984773i	$-0.555620\pi$
$193$	−15.4707	−	8.93203i	−1.11361	−	0.642942i	−0.939761	+	0.341831i	$0.888953\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	18.3849			1.30987			0.654936	−	0.755685i	$-0.272696\pi$
$197$	18.3849			1.30987			0.654936	+	0.755685i	$0.272696\pi$
$198$		0			0
$199$	1.70763	+	0.985902i	0.121051	+	0.0698887i	0.559303	−	0.828963i	$-0.311069\pi$
$199$	1.70763	+	0.985902i	0.121051	+	0.0698887i	−0.438252	+	0.898852i	$0.644402\pi$
$200$		0			0
$201$	1.48048	+	0.425624i	0.104425	+	0.0300212i
$202$		0			0
$203$	12.9285	−	24.0342i	0.907405	−	1.68687i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−15.2417	−	9.55324i	−1.05937	−	0.663996i
$208$		0			0
$209$	21.0570			1.45654
$210$		0			0
$211$	1.07968			0.0743282			0.0371641	−	0.999309i	$-0.488168\pi$
$211$	1.07968			0.0743282			0.0371641	+	0.999309i	$0.488168\pi$
$212$		0			0
$213$	4.85558	+	19.5319i	0.332699	+	1.33830i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	10.7640	+	17.4126i	0.730707	+	1.18205i
$218$		0			0
$219$	−5.86287	+	20.3933i	−0.396176	+	1.37805i
$220$		0			0
$221$	0.554421	+	0.320095i	0.0372944	+	0.0215319i
$222$		0			0
$223$	15.3841			1.03020			0.515099	−	0.857131i	$-0.327755\pi$
$223$	15.3841			1.03020			0.515099	+	0.857131i	$0.327755\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.68946	−	0.975410i	−0.112133	−	0.0647402i	0.442884	−	0.896579i	$-0.353955\pi$
$227$	−1.68946	−	0.975410i	−0.112133	−	0.0647402i	−0.555018	+	0.831838i	$0.687289\pi$
$228$		0			0
$229$	−2.44750	+	1.41307i	−0.161735	+	0.0933780i	−0.578683	−	0.815553i	$-0.696433\pi$
$229$	−2.44750	+	1.41307i	−0.161735	+	0.0933780i	0.416948	+	0.908930i	$0.363100\pi$
$230$		0			0
$231$	−17.5608	−	17.1466i	−1.15542	−	1.12817i
$232$		0			0
$233$	−2.19563	−	3.80293i	−0.143840	−	0.249139i	0.785099	−	0.619370i	$-0.212612\pi$
$233$	−2.19563	−	3.80293i	−0.143840	−	0.249139i	−0.928940	+	0.370231i	$0.879278\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	8.68433	+	9.00527i	0.564108	+	0.584955i
$238$		0			0
$239$		−	17.6724i		−	1.14313i	−0.820556	−	0.571566i	$-0.806336\pi$
$239$		−	17.6724i		−	1.14313i	0.820556	−	0.571566i	$-0.193664\pi$
$240$		0			0
$241$	−3.69148	−	2.13128i	−0.237789	−	0.137288i	0.376371	−	0.926469i	$-0.377172\pi$
$241$	−3.69148	−	2.13128i	−0.237789	−	0.137288i	−0.614160	+	0.789181i	$0.710505\pi$
$242$		0			0
$243$	−5.38190	+	14.6299i	−0.345249	+	0.938511i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	14.0849	−	8.13190i	0.896198	−	0.517420i
$248$		0			0
$249$	2.14858	+	8.64280i	0.136161	+	0.547715i
$250$		0			0
$251$	−3.87820			−0.244790			−0.122395	−	0.992481i	$-0.539057\pi$
$251$	−3.87820			−0.244790			−0.122395	+	0.992481i	$0.539057\pi$
$252$		0			0
$253$		−	32.1140i		−	2.01899i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−15.3384	+	8.85563i	−0.956784	+	0.552399i	−0.895182	−	0.445702i	$-0.852954\pi$
$257$	−15.3384	+	8.85563i	−0.956784	+	0.552399i	−0.0616020	+	0.998101i	$0.519621\pi$
$258$		0			0
$259$	−27.7187	+	0.833896i	−1.72236	+	0.0518158i
$260$		0			0
$261$	−14.4901	−	27.3427i	−0.896917	−	1.69247i
$262$		0			0
$263$	2.79964	−	4.84912i	0.172633	−	0.299010i	−0.766706	−	0.641998i	$-0.778106\pi$
$263$	2.79964	−	4.84912i	0.172633	−	0.299010i	0.939340	+	0.342988i	$0.111439\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−20.6422	−	21.4051i	−1.26328	−	1.30997i
$268$		0			0
$269$	−8.53335	+	14.7802i	−0.520288	+	0.901165i	0.479434	+	0.877578i	$0.340842\pi$
$269$	−8.53335	+	14.7802i	−0.520288	+	0.901165i	−0.999722	+	0.0235867i	$0.992491\pi$
$270$		0			0
$271$	14.7661	−	8.52521i	0.896977	−	0.517870i	0.0207586	−	0.999785i	$-0.493392\pi$
$271$	14.7661	−	8.52521i	0.896977	−	0.517870i	0.876218	+	0.481915i	$0.160059\pi$
$272$		0			0
$273$	−18.3681	−	4.68750i	−1.11169	−	0.283701i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	9.12563	+	5.26868i	0.548306	+	0.316565i	0.748438	−	0.663204i	$-0.230804\pi$
$277$	9.12563	+	5.26868i	0.548306	+	0.316565i	−0.200133	+	0.979769i	$0.564137\pi$
$278$		0			0
$279$	23.1967	+	0.841992i	1.38875	+	0.0504087i
$280$		0			0
$281$			19.2208i			1.14662i	0.819339	+	0.573309i	$0.194340\pi$
$281$			19.2208i			1.14662i	−0.819339	+	0.573309i	$0.805660\pi$
$282$		0			0
$283$	−8.99126	+	15.5733i	−0.534475	+	0.925738i	0.464713	+	0.885461i	$0.346157\pi$
$283$	−8.99126	+	15.5733i	−0.534475	+	0.925738i	−0.999189	+	0.0402770i	$0.987176\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−5.44939	−	2.93135i	−0.321667	−	0.173032i
$288$		0			0
$289$	−8.48802	−	14.7017i	−0.499296	−	0.864805i
$290$		0			0
$291$	−7.19940	+	1.78975i	−0.422036	+	0.104917i
$292$		0			0
$293$			25.2153i			1.47309i	0.676388	+	0.736546i	$0.263544\pi$
$293$			25.2153i			1.47309i	−0.676388	+	0.736546i	$0.736456\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−27.2336	+	5.72998i	−1.58025	+	0.332487i
$298$		0			0
$299$	−12.4019	−	21.4808i	−0.717223	−	1.24227i
$300$		0			0
$301$	−2.23396	+	4.15294i	−0.128764	+	0.239372i
$302$		0			0
$303$	−2.91726	+	10.1474i	−0.167592	+	0.582951i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	8.28693			0.472960			0.236480	−	0.971636i	$-0.424006\pi$
$307$	8.28693			0.472960			0.236480	+	0.971636i	$0.424006\pi$
$308$		0			0
$309$	−5.18029	−	5.37173i	−0.294696	−	0.305587i
$310$		0			0
$311$	4.28958	−	7.42977i	0.243240	−	0.421304i	−0.718395	−	0.695635i	$-0.755123\pi$
$311$	4.28958	−	7.42977i	0.243240	−	0.421304i	0.961635	+	0.274331i	$0.0884564\pi$
$312$		0			0
$313$	0.466406	+	0.807839i	0.0263628	+	0.0456617i	0.878906	−	0.476995i	$-0.158274\pi$
$313$	0.466406	+	0.807839i	0.0263628	+	0.0456617i	−0.852543	+	0.522657i	$0.824941\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.49108	−	2.58262i	−0.0837472	−	0.145054i	0.821109	−	0.570771i	$-0.193355\pi$
$317$	−1.49108	−	2.58262i	−0.0837472	−	0.145054i	−0.904857	+	0.425716i	$0.860022\pi$
$318$		0			0
$319$	27.6227	−	47.8440i	1.54658	−	2.67875i
$320$		0			0
$321$	−19.9334	−	20.6701i	−1.11258	−	1.15369i
$322$		0			0
$323$	0.608446			0.0338549
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−1.84176	+	6.40636i	−0.101850	+	0.354272i
$328$		0			0
$329$	9.52665	−	0.286602i	0.525221	−	0.0158009i
$330$		0			0
$331$	10.9541	+	18.9730i	0.602091	+	1.04285i	0.992504	+	0.122213i	$0.0389990\pi$
$331$	10.9541	+	18.9730i	0.602091	+	1.04285i	−0.390413	+	0.920640i	$0.627668\pi$
$332$		0			0
$333$	−16.6996	+	26.6433i	−0.915133	+	1.46005i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	36.4696i		−	1.98663i	−0.115448	−	0.993314i	$-0.536830\pi$
$337$		−	36.4696i		−	1.98663i	0.115448	−	0.993314i	$-0.463170\pi$
$338$		0			0
$339$	16.7128	−	4.15476i	0.907713	−	0.225655i
$340$		0			0
$341$	20.7200	+	35.8881i	1.12205	+	1.94345i
$342$		0			0
$343$	1.66873	+	18.4449i	0.0901031	+	0.995932i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.09509	+	3.62881i	−0.112471	+	0.194805i	−0.916766	−	0.399425i	$-0.869210\pi$
$347$	−2.09509	+	3.62881i	−0.112471	+	0.194805i	0.804295	+	0.594230i	$0.202543\pi$
$348$		0			0
$349$			22.2897i			1.19314i	0.802560	+	0.596571i	$0.203470\pi$
$349$			22.2897i			1.19314i	−0.802560	+	0.596571i	$0.796530\pi$
$350$		0			0
$351$	−16.0035	+	14.3499i	−0.854203	+	0.765943i
$352$		0			0
$353$	−15.1073	−	8.72220i	−0.804080	−	0.464236i	0.0408157	−	0.999167i	$-0.487004\pi$
$353$	−15.1073	−	8.72220i	−0.804080	−	0.464236i	−0.844896	+	0.534931i	$0.820338\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.507424	−	0.495455i	−0.0268557	−	0.0262223i
$358$		0			0
$359$	−25.2564	+	14.5818i	−1.33298	+	0.769599i	−0.985756	−	0.168182i	$-0.946210\pi$
$359$	−25.2564	+	14.5818i	−1.33298	+	0.769599i	−0.347228	+	0.937781i	$0.612877\pi$
$360$		0			0
$361$	−1.77133	+	3.06803i	−0.0932279	+	0.161476i
$362$		0			0
$363$	−21.2634	−	22.0493i	−1.11604	−	1.15729i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	13.3734	−	23.1633i	0.698084	−	1.20912i	−0.271046	−	0.962566i	$-0.587370\pi$
$367$	13.3734	−	23.1633i	0.698084	−	1.20912i	0.969130	−	0.246550i	$-0.0792971\pi$
$368$		0			0
$369$	−6.19954	+	3.28542i	−0.322735	+	0.171032i
$370$		0			0
$371$	−11.1603	+	6.89898i	−0.579414	+	0.358177i
$372$		0			0
$373$	−4.44649	+	2.56718i	−0.230231	+	0.132924i	−0.610678	−	0.791879i	$-0.709103\pi$
$373$	−4.44649	+	2.56718i	−0.230231	+	0.132924i	0.380448	+	0.924802i	$0.375770\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	42.6699i		−	2.19761i
$378$		0			0
$379$	17.3320			0.890284			0.445142	−	0.895460i	$-0.353153\pi$
$379$	17.3320			0.890284			0.445142	+	0.895460i	$0.353153\pi$
$380$		0			0
$381$	−1.94087	−	7.80726i	−0.0994336	−	0.399978i
$382$		0			0
$383$	−18.7852	+	10.8457i	−0.959881	+	0.554188i	−0.896136	−	0.443779i	$-0.853638\pi$
$383$	−18.7852	+	10.8457i	−0.959881	+	0.554188i	−0.0637447	+	0.997966i	$0.520304\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.50380	+	4.72463i	0.127275	+	0.240166i
$388$		0			0
$389$	−11.6759	−	6.74110i	−0.591993	−	0.341787i	0.173892	−	0.984765i	$-0.444366\pi$
$389$	−11.6759	−	6.74110i	−0.591993	−	0.341787i	−0.765885	+	0.642977i	$0.777699\pi$
$390$		0			0
$391$		−	0.927941i		−	0.0469280i
$392$		0			0
$393$	−7.96943	−	8.26396i	−0.402005	−	0.416861i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−6.85891	−	11.8800i	−0.344239	−	0.596240i	0.640976	−	0.767561i	$-0.278530\pi$
$397$	−6.85891	−	11.8800i	−0.344239	−	0.596240i	−0.985215	+	0.171321i	$0.945196\pi$
$398$		0			0
$399$	−17.3460	+	4.87044i	−0.868385	+	0.243827i
$400$		0			0
$401$	−16.4976	+	9.52487i	−0.823849	+	0.475649i	−0.851742	−	0.523962i	$-0.824453\pi$
$401$	−16.4976	+	9.52487i	−0.823849	+	0.475649i	0.0278932	+	0.999611i	$0.491120\pi$
$402$		0			0
$403$	27.7189	+	16.0035i	1.38078	+	0.797191i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−56.1371			−2.78261
$408$		0			0
$409$	−30.1428	−	17.4030i	−1.49047	−	0.860521i	−0.490526	−	0.871427i	$-0.663195\pi$
$409$	−30.1428	−	17.4030i	−1.49047	−	0.860521i	−0.999941	+	0.0109054i	$0.996529\pi$
$410$		0			0
$411$	2.25674	−	7.84982i	0.111317	−	0.387203i
$412$		0			0
$413$	23.7205	−	14.6633i	1.16721	−	0.721535i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−3.99593	−	16.0739i	−0.195682	−	0.787142i
$418$		0			0
$419$	19.7934			0.966971			0.483486	−	0.875352i	$-0.339371\pi$
$419$	19.7934			0.966971			0.483486	+	0.875352i	$0.339371\pi$
$420$		0			0
$421$	−12.2279			−0.595951			−0.297975	−	0.954574i	$-0.596311\pi$
$421$	−12.2279			−0.595951			−0.297975	+	0.954574i	$0.596311\pi$
$422$		0			0
$423$	5.73949	−	9.15705i	0.279063	−	0.445231i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−9.94282	+	0.299122i	−0.481167	+	0.0144755i
$428$		0			0
$429$	−36.8808	−	10.6029i	−1.78062	−	0.511910i
$430$		0			0
$431$	−9.22781	−	5.32768i	−0.444488	−	0.256625i	0.261012	−	0.965336i	$-0.415944\pi$
$431$	−9.22781	−	5.32768i	−0.444488	−	0.256625i	−0.705499	+	0.708711i	$0.749277\pi$
$432$		0			0
$433$	25.5027			1.22558			0.612791	−	0.790245i	$-0.290047\pi$
$433$	25.5027			1.22558			0.612791	+	0.790245i	$0.290047\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−20.4157	−	11.7870i	−0.976613	−	0.563848i
$438$		0			0
$439$	−23.8206	+	13.7528i	−1.13689	+	0.656386i	−0.945660	−	0.325158i	$-0.894582\pi$
$439$	−23.8206	+	13.7528i	−1.13689	+	0.656386i	−0.191234	+	0.981544i	$0.561249\pi$
$440$		0			0
$441$	18.4319	+	10.0630i	0.877712	+	0.479189i
$442$		0			0
$443$	9.68708	+	16.7785i	0.460247	+	0.797171i	0.998973	−	0.0453099i	$-0.0144275\pi$
$443$	9.68708	+	16.7785i	0.460247	+	0.797171i	−0.538726	+	0.842481i	$0.681094\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	25.3864	−	24.4816i	1.20073	−	1.15794i
$448$		0			0
$449$		−	26.9504i		−	1.27187i	−0.771744	−	0.635934i	$-0.780615\pi$
$449$		−	26.9504i		−	1.27187i	0.771744	−	0.635934i	$-0.219385\pi$
$450$		0			0
$451$	−10.8479	−	6.26304i	−0.510808	−	0.294915i
$452$		0			0
$453$	5.44983	−	18.9566i	0.256056	−	0.890660i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	15.9124	−	9.18704i	0.744352	−	0.429752i	−0.0792977	−	0.996851i	$-0.525268\pi$
$457$	15.9124	−	9.18704i	0.744352	−	0.429752i	0.823649	+	0.567099i	$0.191934\pi$
$458$		0			0
$459$	−0.786920	+	0.165569i	−0.0367303	+	0.00772810i
$460$		0			0
$461$	−12.2344			−0.569814			−0.284907	−	0.958555i	$-0.591963\pi$
$461$	−12.2344			−0.569814			−0.284907	+	0.958555i	$0.591963\pi$
$462$		0			0
$463$			11.4136i			0.530433i	0.964189	+	0.265217i	$0.0854435\pi$
$463$			11.4136i			0.530433i	−0.964189	+	0.265217i	$0.914556\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.15336	−	0.665893i	0.0533711	−	0.0308138i	−0.473077	−	0.881021i	$-0.656857\pi$
$467$	1.15336	−	0.665893i	0.0533711	−	0.0308138i	0.526448	+	0.850207i	$0.323523\pi$
$468$		0			0
$469$	−1.23728	−	2.00152i	−0.0571325	−	0.0924218i
$470$		0			0
$471$	−3.26008	+	11.3398i	−0.150217	+	0.522511i
$472$		0			0
$473$	−4.77302	+	8.26712i	−0.219464	+	0.380123i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.539659	+	14.8675i	−0.0247093	+	0.680736i
$478$		0			0
$479$	−10.7342	+	18.5922i	−0.490458	+	0.849498i	−0.999940	−	0.0109835i	$-0.996504\pi$
$479$	−10.7342	+	18.5922i	−0.490458	+	0.849498i	0.509482	+	0.860481i	$0.329837\pi$
$480$		0			0
$481$	−37.5496	+	21.6793i	−1.71212	+	0.988491i
$482$		0			0
$483$	7.42790	+	26.4543i	0.337981	+	1.20371i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	24.0115	+	13.8630i	1.08807	+	0.628195i	0.933061	−	0.359719i	$-0.117127\pi$
$487$	24.0115	+	13.8630i	1.08807	+	0.628195i	0.155004	+	0.987914i	$0.450461\pi$
$488$		0			0
$489$	−9.86409	+	9.51254i	−0.446070	+	0.430172i
$490$		0			0
$491$			0.536100i			0.0241938i	0.999927	+	0.0120969i	$0.00385066\pi$
$491$			0.536100i			0.0241938i	−0.999927	+	0.0120969i	$0.996149\pi$
$492$		0			0
$493$	0.798164	−	1.38246i	0.0359475	−	0.0622629i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	14.5642	−	27.0749i	0.653293	−	1.21447i
$498$		0			0
$499$	−15.1191	−	26.1870i	−0.676823	−	1.17229i	−0.975933	−	0.218072i	$-0.930023\pi$
$499$	−15.1191	−	26.1870i	−0.676823	−	1.17229i	0.299110	−	0.954219i	$-0.403310\pi$
$500$		0			0
$501$	8.04420	+	32.3583i	0.359388	+	1.44566i
$502$		0			0
$503$		−	32.5176i		−	1.44989i	−0.688807	−	0.724945i	$-0.741865\pi$
$503$		−	32.5176i		−	1.44989i	0.688807	−	0.724945i	$-0.258135\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−6.91235	+	1.71839i	−0.306988	+	0.0763166i
$508$		0			0
$509$	13.1885	+	22.8432i	0.584570	+	1.01251i	0.994929	+	0.100581i	$0.0320702\pi$
$509$	13.1885	+	22.8432i	0.584570	+	1.01251i	−0.410359	+	0.911924i	$0.634597\pi$
$510$		0			0
$511$	27.5705	−	17.0433i	1.21965	−	0.753952i
$512$		0			0
$513$	−6.35301	+	19.4162i	−0.280492	+	0.857245i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	19.2938			0.848538
$518$		0			0
$519$	17.6324	−	17.0040i	0.773977	−	0.746393i
$520$		0			0
$521$	−5.39842	+	9.35035i	−0.236509	+	0.409646i	−0.959710	−	0.280992i	$-0.909337\pi$
$521$	−5.39842	+	9.35035i	−0.236509	+	0.409646i	0.723201	+	0.690638i	$0.242670\pi$
$522$		0			0
$523$	0.119197	+	0.206455i	0.00521211	+	0.00902764i	0.868620	−	0.495479i	$-0.165008\pi$
$523$	0.119197	+	0.206455i	0.00521211	+	0.00902764i	−0.863408	+	0.504507i	$0.831674\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.598708	+	1.03699i	0.0260801	+	0.0451721i
$528$		0			0
$529$	−6.47632	+	11.2173i	−0.281579	+	0.487709i
$530$		0			0
$531$	1.14701	−	31.5999i	0.0497760	−	1.37132i
$532$		0			0
$533$	−9.67476			−0.419061
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−3.45229	−	0.992498i	−0.148977	−	0.0428294i
$538$		0			0
$539$	2.25374	+	37.4232i	0.0970753	+	1.61193i
$540$		0			0
$541$	−1.28056	−	2.21799i	−0.0550555	−	0.0953588i	0.837184	−	0.546921i	$-0.184200\pi$
$541$	−1.28056	−	2.21799i	−0.0550555	−	0.0953588i	−0.892240	+	0.451562i	$0.850867\pi$
$542$		0			0
$543$	−9.08444	−	36.5427i	−0.389850	−	1.56820i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	27.1549i		−	1.16106i	−0.814239	−	0.580529i	$-0.802846\pi$
$547$		−	27.1549i		−	1.16106i	0.814239	−	0.580529i	$-0.197154\pi$
$548$		0			0
$549$	−5.99022	+	9.55707i	−0.255656	+	0.407886i
$550$		0			0
$551$	−20.2770	−	35.1209i	−0.863831	−	1.49620i
$552$		0			0
$553$	−0.574652	−	19.1015i	−0.0244367	−	0.812277i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−12.0080	+	20.7984i	−0.508794	+	0.881257i	0.491154	+	0.871073i	$0.336575\pi$
$557$	−12.0080	+	20.7984i	−0.508794	+	0.881257i	−0.999948	+	0.0101846i	$0.996758\pi$
$558$		0			0
$559$			7.37308i			0.311848i
$560$		0			0
$561$	−0.996567	−	1.03340i	−0.0420751	−	0.0436300i
$562$		0			0
$563$	34.8986	+	20.1487i	1.47080	+	0.849168i	0.999462	−	0.0327839i	$-0.0104373\pi$
$563$	34.8986	+	20.1487i	1.47080	+	0.849168i	0.471340	+	0.881952i	$0.343771\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	21.1087	−	11.0192i	0.886482	−	0.462763i
$568$		0			0
$569$	4.46883	−	2.58008i	0.187343	−	0.108163i	−0.403395	−	0.915026i	$-0.632170\pi$
$569$	4.46883	−	2.58008i	0.187343	−	0.108163i	0.590738	+	0.806863i	$0.298837\pi$
$570$		0			0
$571$	0.841937	−	1.45828i	0.0352340	−	0.0610270i	−0.847871	−	0.530203i	$-0.822116\pi$
$571$	0.841937	−	1.45828i	0.0352340	−	0.0610270i	0.883105	+	0.469176i	$0.155449\pi$
$572$		0			0
$573$	2.88916	−	2.78620i	0.120697	−	0.116395i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	14.7284	−	25.5104i	0.613153	−	1.06201i	−0.377552	−	0.925988i	$-0.623234\pi$
$577$	14.7284	−	25.5104i	0.613153	−	1.06201i	0.990706	−	0.136024i	$-0.0434325\pi$
$578$		0			0
$579$	29.7370	+	8.54907i	1.23583	+	0.355287i
$580$		0			0
$581$	6.44461	−	11.9806i	0.267368	−	0.497037i
$582$		0			0
$583$	−23.0018	+	13.2801i	−0.952638	+	0.550006i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			45.9862i			1.89805i	0.315195	+	0.949027i	$0.397930\pi$
$587$			45.9862i			1.89805i	−0.315195	+	0.949027i	$0.602070\pi$
$588$		0			0
$589$	30.4199			1.25343
$590$		0			0
$591$	−30.9030	+	7.68242i	−1.27118	+	0.316012i
$592$		0			0
$593$	1.65252	−	0.954084i	0.0678610	−	0.0391795i	−0.465686	−	0.884950i	$-0.654192\pi$
$593$	1.65252	−	0.954084i	0.0678610	−	0.0391795i	0.533547	+	0.845771i	$0.320859\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−3.28231	−	0.943632i	−0.134336	−	0.0386203i
$598$		0			0
$599$	−18.2188	−	10.5186i	−0.744401	−	0.429780i	0.0792661	−	0.996853i	$-0.474742\pi$
$599$	−18.2188	−	10.5186i	−0.744401	−	0.429780i	−0.823667	+	0.567073i	$0.808076\pi$
$600$		0			0
$601$		−	30.3573i		−	1.23830i	−0.785273	−	0.619150i	$-0.787477\pi$
$601$		−	30.3573i		−	1.23830i	0.785273	−	0.619150i	$-0.212523\pi$
$602$		0			0
$603$	−2.66638	−	0.0967842i	−0.108583	−	0.00394136i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−8.89399	−	15.4049i	−0.360996	−	0.625264i	0.627129	−	0.778915i	$-0.284230\pi$
$607$	−8.89399	−	15.4049i	−0.360996	−	0.625264i	−0.988125	+	0.153652i	$0.950897\pi$
$608$		0			0
$609$	−11.6884	+	45.8012i	−0.473637	+	1.85596i
$610$		0			0
$611$	12.9054	−	7.45095i	0.522098	−	0.301433i
$612$		0			0
$613$	−25.1276	−	14.5074i	−1.01490	−	0.585950i	−0.102274	−	0.994756i	$-0.532612\pi$
$613$	−25.1276	−	14.5074i	−1.01490	−	0.585950i	−0.912621	+	0.408806i	$0.865945\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.32967			0.134047			0.0670237	−	0.997751i	$-0.478650\pi$
$617$	3.32967			0.134047			0.0670237	+	0.997751i	$0.478650\pi$
$618$		0			0
$619$	−41.6135	−	24.0256i	−1.67259	−	0.965669i	−0.966182	−	0.257863i	$-0.916982\pi$
$619$	−41.6135	−	24.0256i	−1.67259	−	0.965669i	−0.706406	−	0.707806i	$-0.749685\pi$
$620$		0			0
$621$	29.6116	+	9.68897i	1.18827	+	0.388805i
$622$		0			0
$623$	1.36592	+	45.4032i	0.0547244	+	1.81904i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−35.3945	+	8.79899i	−1.41352	+	0.351398i
$628$		0			0
$629$	−1.62209			−0.0646771
$630$		0			0
$631$	15.8726			0.631878			0.315939	−	0.948779i	$-0.397680\pi$
$631$	15.8726			0.631878			0.315939	+	0.948779i	$0.397680\pi$
$632$		0			0
$633$	−1.81482	+	0.451160i	−0.0721327	+	0.0179320i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	15.9598	+	24.1617i	0.632350	+	0.957322i
$638$		0			0
$639$	−16.3234	−	30.8019i	−0.645743	−	1.21851i
$640$		0			0
$641$	3.34785	+	1.93288i	0.132232	+	0.0763443i	0.564657	−	0.825326i	$-0.309009\pi$
$641$	3.34785	+	1.93288i	0.132232	+	0.0763443i	−0.432425	+	0.901670i	$0.642342\pi$
$642$		0			0
$643$	37.7423			1.48841			0.744206	−	0.667950i	$-0.232828\pi$
$643$	37.7423			1.48841			0.744206	+	0.667950i	$0.232828\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	18.9193	+	10.9230i	0.743793	+	0.429429i	0.823447	−	0.567393i	$-0.192048\pi$
$647$	18.9193	+	10.9230i	0.743793	+	0.429429i	−0.0796536	+	0.996823i	$0.525381\pi$
$648$		0			0
$649$	48.8888	−	28.2260i	1.91905	−	1.10797i
$650$		0			0
$651$	−25.3692	−	24.7708i	−0.994297	−	0.970844i
$652$		0			0
$653$	1.81473	+	3.14321i	0.0710159	+	0.123003i	0.899347	−	0.437236i	$-0.144043\pi$
$653$	1.81473	+	3.14321i	0.0710159	+	0.123003i	−0.828331	+	0.560239i	$0.810709\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	1.33318	−	36.7288i	0.0520123	−	1.43293i
$658$		0			0
$659$			22.4040i			0.872737i	0.899768	+	0.436369i	$0.143736\pi$
$659$			22.4040i			0.872737i	−0.899768	+	0.436369i	$0.856264\pi$
$660$		0			0
$661$	13.6525	+	7.88230i	0.531023	+	0.306586i	0.741433	−	0.671027i	$-0.234147\pi$
$661$	13.6525	+	7.88230i	0.531023	+	0.306586i	−0.210410	+	0.977613i	$0.567480\pi$
$662$		0			0
$663$	−1.06568	−	0.306371i	−0.0413875	−	0.0118985i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−53.5628	+	30.9245i	−2.07396	+	1.19740i
$668$		0			0
$669$	−25.8590	+	6.42849i	−0.999767	+	0.248540i
$670$		0			0
$671$	−20.1366			−0.777365
$672$		0			0
$673$			8.84031i			0.340769i	0.985378	+	0.170385i	$0.0545010\pi$
$673$			8.84031i			0.340769i	−0.985378	+	0.170385i	$0.945499\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	13.5519	−	7.82417i	0.520840	−	0.300707i	−0.216438	−	0.976296i	$-0.569444\pi$
$677$	13.5519	−	7.82417i	0.520840	−	0.300707i	0.737278	+	0.675589i	$0.236111\pi$
$678$		0			0
$679$	9.97974	+	5.36833i	0.382987	+	0.206018i
$680$		0			0
$681$	3.24738	+	0.933590i	0.124440	+	0.0357752i
$682$		0			0
$683$	−18.9193	+	32.7691i	−0.723926	+	1.25388i	0.235489	+	0.971877i	$0.424331\pi$
$683$	−18.9193	+	32.7691i	−0.723926	+	1.25388i	−0.959415	+	0.281999i	$0.909002\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	3.52351	−	3.39793i	0.134430	−	0.129639i
$688$		0			0
$689$	−10.2572	+	17.7659i	−0.390766	+	0.676827i
$690$		0			0
$691$	−14.5792	+	8.41732i	−0.554620	+	0.320210i	−0.750983	−	0.660321i	$-0.770420\pi$
$691$	−14.5792	+	8.41732i	−0.554620	+	0.320210i	0.196363	+	0.980531i	$0.437087\pi$
$692$		0			0
$693$	36.6828	+	21.4835i	1.39347	+	0.816091i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−0.313452	−	0.180972i	−0.0118729	−	0.00685480i
$698$		0			0
$699$	5.27972	+	5.47484i	0.199697	+	0.207077i
$700$		0			0
$701$			28.2554i			1.06719i	0.845740	+	0.533596i	$0.179160\pi$
$701$			28.2554i			1.06719i	−0.845740	+	0.533596i	$0.820840\pi$
$702$		0			0
$703$	−20.6043	+	35.6877i	−0.777106	+	1.34599i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	13.7186	−	8.48046i	0.515942	−	0.318940i
$708$		0			0
$709$	7.40632	+	12.8281i	0.278150	+	0.481770i	0.970925	−	0.239384i	$-0.0769454\pi$
$709$	7.40632	+	12.8281i	0.278150	+	0.481770i	−0.692775	+	0.721154i	$0.743612\pi$
$710$		0			0
$711$	−18.3604	−	11.5080i	−0.688568	−	0.431583i
$712$		0			0
$713$		−	46.3934i		−	1.73744i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	7.38467	+	29.7053i	0.275786	+	1.10937i
$718$		0			0
$719$	−10.1406	−	17.5640i	−0.378179	−	0.655025i	0.612618	−	0.790379i	$-0.290116\pi$
$719$	−10.1406	−	17.5640i	−0.378179	−	0.655025i	−0.990797	+	0.135353i	$0.956783\pi$
$720$		0			0
$721$	0.342786	+	11.3942i	0.0127660	+	0.424342i
$722$		0			0
$723$	7.09555	+	2.03990i	0.263886	+	0.0758646i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	2.81854			0.104534			0.0522670	−	0.998633i	$-0.483355\pi$
$727$	2.81854			0.104534			0.0522670	+	0.998633i	$0.483355\pi$
$728$		0			0
$729$	2.93304	−	26.8402i	0.108631	−	0.994082i
$730$		0			0
$731$	−0.137917	+	0.238880i	−0.00510106	+	0.00883530i
$732$		0			0
$733$	−17.4457	−	30.2169i	−0.644372	−	1.11609i	−0.984446	−	0.175687i	$-0.943785\pi$
$733$	−17.4457	−	30.2169i	−0.644372	−	1.11609i	0.340074	−	0.940399i	$-0.389548\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.38170	−	4.12522i	−0.0877309	−	0.151954i
$738$		0			0
$739$	−13.4220	+	23.2476i	−0.493737	+	0.855177i	−0.999974	−	0.00721695i	$-0.997703\pi$
$739$	−13.4220	+	23.2476i	−0.493737	+	0.855177i	0.506237	+	0.862394i	$0.331036\pi$
$740$		0			0
$741$	−20.2770	+	19.5544i	−0.744896	+	0.718348i
$742$		0			0
$743$	−2.24499			−0.0823607			−0.0411804	−	0.999152i	$-0.513112\pi$
$743$	−2.24499			−0.0823607			−0.0411804	+	0.999152i	$0.513112\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−7.22305	−	13.6298i	−0.264277	−	0.498687i
$748$		0			0
$749$	1.31902	+	43.8442i	0.0481959	+	1.60203i
$750$		0			0
$751$	−1.56634	−	2.71297i	−0.0571564	−	0.0989978i	0.836031	−	0.548682i	$-0.184870\pi$
$751$	−1.56634	−	2.71297i	−0.0571564	−	0.0989978i	−0.893188	+	0.449684i	$0.851537\pi$
$752$		0			0
$753$	6.51882	−	1.62056i	0.237559	−	0.0590566i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	25.5473i		−	0.928532i	−0.885696	−	0.464266i	$-0.846318\pi$
$757$		−	25.5473i		−	0.928532i	0.885696	−	0.464266i	$-0.153682\pi$
$758$		0			0
$759$	13.4193	+	53.9801i	0.487091	+	1.95935i
$760$		0			0
$761$	−2.16163	−	3.74406i	−0.0783591	−	0.135722i	0.824183	−	0.566324i	$-0.191635\pi$
$761$	−2.16163	−	3.74406i	−0.0783591	−	0.135722i	−0.902542	+	0.430602i	$0.858301\pi$
$762$		0			0
$763$	8.66100	−	5.35399i	0.313549	−	0.193827i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	21.8009	−	37.7603i	0.787185	−	1.36344i
$768$		0			0
$769$			34.4529i			1.24240i	0.783650	+	0.621202i	$0.213355\pi$
$769$			34.4529i			1.24240i	−0.783650	+	0.621202i	$0.786645\pi$
$770$		0			0
$771$	22.0817	−	21.2947i	0.795253	−	0.766911i
$772$		0			0
$773$	−8.99408	−	5.19273i	−0.323494	−	0.186770i	0.329455	−	0.944171i	$-0.393135\pi$
$773$	−8.99408	−	5.19273i	−0.323494	−	0.186770i	−0.652949	+	0.757402i	$0.726468\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	46.2437	−	12.9844i	1.65898	−	0.465812i
$778$		0			0
$779$	−7.96313	+	4.59752i	−0.285309	+	0.164723i
$780$		0			0
$781$	31.1174	−	53.8970i	1.11347	−	1.92859i
$782$		0			0
$783$	35.7819	+	39.9050i	1.27874	+	1.42609i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−21.4590	+	37.1681i	−0.764931	+	1.32490i	0.175352	+	0.984506i	$0.443894\pi$
$787$	−21.4590	+	37.1681i	−0.764931	+	1.32490i	−0.940283	+	0.340394i	$0.889440\pi$
$788$		0			0
$789$	−2.67961	+	9.32071i	−0.0953966	+	0.331826i
$790$		0			0
$791$	−23.1671	−	12.4621i	−0.823726	−	0.443101i
$792$		0			0
$793$	−13.4692	+	7.77645i	−0.478306	+	0.276150i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	19.3628i		−	0.685866i	−0.939360	−	0.342933i	$-0.888580\pi$
$797$		−	19.3628i		−	0.685866i	0.939360	−	0.342933i	$-0.111420\pi$
$798$		0			0
$799$	0.557497			0.0197228
$800$		0			0
$801$	43.6417	+	27.3539i	1.54200	+	0.966503i
$802$		0			0
$803$	56.8239	−	32.8073i	2.00527	−	1.15774i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	8.16749	−	28.4097i	0.287509	−	1.00007i
$808$		0			0
$809$	0.120667	+	0.0696669i	0.00424241	+	0.00244936i	0.502120	−	0.864798i	$-0.332554\pi$
$809$	0.120667	+	0.0696669i	0.00424241	+	0.00244936i	−0.497877	+	0.867247i	$0.665887\pi$
$810$		0			0
$811$			43.5559i			1.52945i	0.644354	+	0.764727i	$0.277126\pi$
$811$			43.5559i			1.52945i	−0.644354	+	0.764727i	$0.722874\pi$
$812$		0			0
$813$	−21.2578	+	20.5002i	−0.745543	+	0.718973i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	3.50374	+	6.06865i	0.122580	+	0.212315i
$818$		0			0
$819$	32.8334	+	0.203795i	1.14729	+	0.00712118i
$820$		0			0
$821$	39.9212	−	23.0485i	1.39326	−	0.804400i	0.399586	−	0.916696i	$-0.369154\pi$
$821$	39.9212	−	23.0485i	1.39326	−	0.804400i	0.993675	+	0.112296i	$0.0358204\pi$
$822$		0			0
$823$	−19.4726	−	11.2425i	−0.678772	−	0.391889i	0.120620	−	0.992699i	$-0.461512\pi$
$823$	−19.4726	−	11.2425i	−0.678772	−	0.391889i	−0.799392	+	0.600809i	$0.794845\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−52.2536			−1.81704			−0.908518	−	0.417846i	$-0.862785\pi$
$827$	−52.2536			−1.81704			−0.908518	+	0.417846i	$0.862785\pi$
$828$		0			0
$829$	−3.26705	−	1.88623i	−0.113469	−	0.0655115i	0.442191	−	0.896921i	$-0.354201\pi$
$829$	−3.26705	−	1.88623i	−0.113469	−	0.0655115i	−0.555661	+	0.831409i	$0.687535\pi$
$830$		0			0
$831$	−17.5408	−	5.04279i	−0.608483	−	0.174933i
$832$		0			0
$833$	0.0651222	+	1.08135i	0.00225635	+	0.0374666i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−39.3429	+	8.27779i	−1.35989	+	0.286122i
$838$		0			0
$839$	40.7191			1.40578			0.702890	−	0.711299i	$-0.251893\pi$
$839$	40.7191			1.40578			0.702890	+	0.711299i	$0.251893\pi$
$840$		0			0
$841$	−77.3983			−2.66891
$842$		0			0
$843$	−8.03171	−	32.3081i	−0.276627	−	1.11275i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	1.40703	+	46.7696i	0.0483460	+	1.60702i
$848$		0			0
$849$	8.60577	−	29.9342i	0.295349	−	1.02734i
$850$		0			0
$851$	54.4273	+	31.4236i	1.86574	+	1.07719i
$852$		0			0
$853$	−3.21298			−0.110010			−0.0550051	−	0.998486i	$-0.517518\pi$
$853$	−3.21298			−0.110010			−0.0550051	+	0.998486i	$0.517518\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	41.6653	+	24.0555i	1.42326	+	0.821720i	0.996576	−	0.0826803i	$-0.0263480\pi$
$857$	41.6653	+	24.0555i	1.42326	+	0.821720i	0.426685	+	0.904400i	$0.359681\pi$
$858$		0			0
$859$	−10.4266	+	6.01978i	−0.355750	+	0.205392i	−0.667215	−	0.744865i	$-0.732514\pi$
$859$	−10.4266	+	6.01978i	−0.355750	+	0.205392i	0.311465	+	0.950258i	$0.399180\pi$
$860$		0			0
$861$	10.3847	+	2.65017i	0.353911	+	0.0903174i
$862$		0			0
$863$	3.75993	+	6.51239i	0.127989	+	0.221684i	0.922898	−	0.385046i	$-0.125814\pi$
$863$	3.75993	+	6.51239i	0.127989	+	0.221684i	−0.794908	+	0.606730i	$0.792481\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	20.4108	+	21.1651i	0.693186	+	0.718803i
$868$		0			0
$869$		−	38.6851i		−	1.31230i
$870$		0			0
$871$	−3.18619	−	1.83955i	−0.107960	−	0.0623308i
$872$		0			0
$873$	11.3535	−	6.01676i	0.384259	−	0.203636i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−28.8156	+	16.6367i	−0.973033	+	0.561781i	−0.900160	−	0.435560i	$-0.856550\pi$
$877$	−28.8156	+	16.6367i	−0.973033	+	0.561781i	−0.0728736	+	0.997341i	$0.523217\pi$
$878$		0			0
$879$	−10.5366	−	42.3841i	−0.355390	−	1.42958i
$880$		0			0
$881$	19.9614			0.672515			0.336258	−	0.941770i	$-0.390839\pi$
$881$	19.9614			0.672515			0.336258	+	0.941770i	$0.390839\pi$
$882$		0			0
$883$		−	51.3120i		−	1.72679i	−0.504533	−	0.863393i	$-0.668335\pi$
$883$		−	51.3120i		−	1.72679i	0.504533	−	0.863393i	$-0.331665\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	17.2280	−	9.94659i	0.578460	−	0.333974i	−0.182061	−	0.983287i	$-0.558277\pi$
$887$	17.2280	−	9.94659i	0.578460	−	0.333974i	0.760521	+	0.649313i	$0.224944\pi$
$888$		0			0
$889$	−5.82158	+	10.8223i	−0.195250	+	0.362970i
$890$		0			0
$891$	43.3823	−	21.0114i	1.45336	−	0.703910i
$892$		0			0
$893$	7.08149	−	12.2655i	0.236973	−	0.410450i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	29.8224	+	30.9245i	0.995740	+	1.03254i
$898$		0			0
$899$	39.9050	−	69.1176i	1.33091	−	2.30520i
$900$		0			0
$901$	−0.664642	+	0.383731i	−0.0221424	+	0.0127839i
$902$		0			0
$903$	2.01967	−	7.91414i	0.0672106	−	0.263366i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	37.1005	+	21.4200i	1.23190	+	0.711239i	0.967426	−	0.253153i	$-0.0814676\pi$
$907$	37.1005	+	21.4200i	1.23190	+	0.711239i	0.264476	+	0.964392i	$0.414801\pi$
$908$		0			0
$909$	0.663367	−	18.2756i	0.0220025	−	0.606164i
$910$		0			0
$911$			28.5359i			0.945437i	0.881213	+	0.472719i	$0.156727\pi$
$911$			28.5359i			0.945437i	−0.881213	+	0.472719i	$0.843273\pi$
$912$		0			0
$913$	13.7694	−	23.8493i	0.455700	−	0.789296i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.527347	+	17.5290i	0.0174145	+	0.578859i
$918$		0			0
$919$	−4.41160	−	7.64112i	−0.145525	−	0.252057i	0.784043	−	0.620706i	$-0.213154\pi$
$919$	−4.41160	−	7.64112i	−0.145525	−	0.252057i	−0.929569	+	0.368649i	$0.879821\pi$
$920$		0			0
$921$	−13.9294	+	3.46282i	−0.458990	+	0.114104i
$922$		0			0
$923$		−	48.0683i		−	1.58219i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	10.9521	+	6.86463i	0.359716	+	0.225464i
$928$		0			0
$929$	−27.1691	−	47.0583i	−0.891389	−	1.54393i	−0.838211	−	0.545346i	$-0.816398\pi$
$929$	−27.1691	−	47.0583i	−0.891389	−	1.54393i	−0.0531782	−	0.998585i	$-0.516935\pi$
$930$		0			0
$931$	24.6180	+	12.3029i	0.806824	+	0.403211i
$932$		0			0
$933$	−4.10567	+	14.2811i	−0.134414	+	0.467542i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−16.3198			−0.533144			−0.266572	−	0.963815i	$-0.585891\pi$
$937$	−16.3198			−0.533144			−0.266572	+	0.963815i	$0.585891\pi$
$938$		0			0
$939$	−1.12154	−	1.16299i	−0.0366002	−	0.0379528i
$940$		0			0
$941$	3.80594	−	6.59208i	0.124070	−	0.214896i	−0.797299	−	0.603585i	$-0.793739\pi$
$941$	3.80594	−	6.59208i	0.124070	−	0.214896i	0.921369	+	0.388689i	$0.127072\pi$
$942$		0			0
$943$	7.01167	+	12.1446i	0.228331	+	0.395481i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	11.4912	+	19.9034i	0.373415	+	0.646774i	0.990088	−	0.140445i	$-0.0448533\pi$
$947$	11.4912	+	19.9034i	0.373415	+	0.646774i	−0.616673	+	0.787219i	$0.711520\pi$
$948$		0			0
$949$	25.3394	−	43.8891i	0.822551	−	1.42470i
$950$		0			0
$951$	3.58552	+	3.71803i	0.116269	+	0.120565i
$952$		0			0
$953$	−40.5633			−1.31397			−0.656986	−	0.753902i	$-0.728169\pi$
$953$	−40.5633			−1.31397			−0.656986	+	0.753902i	$0.728169\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−26.4384	+	91.9630i	−0.854633	+	2.97274i
$958$		0			0
$959$	−10.6125	+	6.56034i	−0.342695	+	0.211844i
$960$		0			0
$961$	14.4330	+	24.9988i	0.465582	+	0.806412i
$962$		0			0
$963$	42.1432	+	26.4147i	1.35805	+	0.851201i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			3.10140i			0.0997343i	0.998756	+	0.0498672i	$0.0158798\pi$
$967$			3.10140i			0.0997343i	−0.998756	+	0.0498672i	$0.984120\pi$
$968$		0			0
$969$	−1.02273	+	0.254249i	−0.0328549	+	0.00816764i
$970$		0			0
$971$	−22.5212	−	39.0078i	−0.722739	−	1.25182i	−0.959898	−	0.280350i	$-0.909550\pi$
$971$	−22.5212	−	39.0078i	−0.722739	−	1.25182i	0.237159	−	0.971471i	$-0.423784\pi$
$972$		0			0
$973$	−11.9857	+	22.2815i	−0.384244	+	0.714311i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−12.6207	+	21.8598i	−0.403773	+	0.699356i	−0.994178	−	0.107751i	$-0.965635\pi$
$977$	−12.6207	+	21.8598i	−0.403773	+	0.699356i	0.590404	+	0.807108i	$0.298968\pi$
$978$		0			0
$979$			91.9525i			2.93881i
$980$		0			0
$981$	0.418805	−	11.5380i	0.0133714	−	0.368379i
$982$		0			0
$983$	−52.2661	−	30.1759i	−1.66703	−	0.962461i	−0.969226	−	0.246173i	$-0.920827\pi$
$983$	−52.2661	−	30.1759i	−1.66703	−	0.962461i	−0.697805	−	0.716288i	$-0.745840\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−15.8935	+	4.46260i	−0.505895	+	0.142046i
$988$		0			0
$989$	9.25530	−	5.34355i	0.294301	−	0.169915i
$990$		0			0
$991$	4.93445	−	8.54672i	0.156748	−	0.271495i	−0.776946	−	0.629567i	$-0.783232\pi$
$991$	4.93445	−	8.54672i	0.156748	−	0.271495i	0.933694	+	0.358072i	$0.116566\pi$
$992$		0			0
$993$	−26.3408	−	27.3142i	−0.835900	−	0.866792i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	13.4745	−	23.3385i	0.426742	−	0.739138i	−0.569840	−	0.821756i	$-0.692995\pi$
$997$	13.4745	−	23.3385i	0.426742	−	0.739138i	0.996581	+	0.0826177i	$0.0263280\pi$
$998$		0			0
$999$	16.9369	−	51.7627i	0.535859	−	1.63770i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bo.i.1949.2		32
3.2	odd	2	inner	2100.2.bo.i.1949.10		32
5.2	odd	4		2100.2.bi.l.101.6	✓	16
5.3	odd	4		2100.2.bi.m.101.3	yes	16
5.4	even	2	inner	2100.2.bo.i.1949.15		32
7.5	odd	6	inner	2100.2.bo.i.1349.7		32
15.2	even	4		2100.2.bi.l.101.8	yes	16
15.8	even	4		2100.2.bi.m.101.1	yes	16
15.14	odd	2	inner	2100.2.bo.i.1949.7		32
21.5	even	6	inner	2100.2.bo.i.1349.15		32
35.12	even	12		2100.2.bi.l.1601.8	yes	16
35.19	odd	6	inner	2100.2.bo.i.1349.10		32
35.33	even	12		2100.2.bi.m.1601.1	yes	16
105.47	odd	12		2100.2.bi.l.1601.6	yes	16
105.68	odd	12		2100.2.bi.m.1601.3	yes	16
105.89	even	6	inner	2100.2.bo.i.1349.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.bi.l.101.6	✓	16	5.2	odd	4
2100.2.bi.l.101.8	yes	16	15.2	even	4
2100.2.bi.l.1601.6	yes	16	105.47	odd	12
2100.2.bi.l.1601.8	yes	16	35.12	even	12
2100.2.bi.m.101.1	yes	16	15.8	even	4
2100.2.bi.m.101.3	yes	16	5.3	odd	4
2100.2.bi.m.1601.1	yes	16	35.33	even	12
2100.2.bi.m.1601.3	yes	16	105.68	odd	12
2100.2.bo.i.1349.2		32	105.89	even	6	inner
2100.2.bo.i.1349.7		32	7.5	odd	6	inner
2100.2.bo.i.1349.10		32	35.19	odd	6	inner
2100.2.bo.i.1349.15		32	21.5	even	6	inner
2100.2.bo.i.1949.2		32	1.1	even	1	trivial
2100.2.bo.i.1949.7		32	15.14	odd	2	inner
2100.2.bo.i.1949.10		32	3.2	odd	2	inner
2100.2.bo.i.1949.15		32	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.68089 + 0.417865i) q^{3} +(2.33003 + 1.25338i) q^{7} +(2.65078 - 1.40477i) q^{9} +O(q^{10})\)	\(q+(-1.68089 + 0.417865i) q^{3} +(2.33003 + 1.25338i) q^{7} +(2.65078 - 1.40477i) q^{9} +(4.63831 + 2.67793i) q^{11} +4.13670 q^{13} +(0.134025 + 0.0773793i) q^{17} +(3.40485 - 1.96579i) q^{19} +(-4.44027 - 1.13315i) q^{21} +(-2.99803 - 5.19273i) q^{23} +(-3.86866 + 3.46893i) q^{27} -10.3150i q^{29} +(6.70071 + 3.86866i) q^{31} +(-8.91550 - 2.56312i) q^{33} +(-9.07719 + 5.24072i) q^{37} +(-6.95334 + 1.72858i) q^{39} -2.33876 q^{41} +1.78236i q^{43} +(3.11974 - 1.80118i) q^{47} +(3.85809 + 5.84082i) q^{49} +(-0.257615 - 0.0740617i) q^{51} +(-2.47955 + 4.29470i) q^{53} +(-4.90174 + 4.72705i) q^{57} +(5.27011 - 9.12810i) q^{59} +(-3.25602 + 1.87987i) q^{61} +(7.93710 + 0.0492651i) q^{63} +(-0.770225 - 0.444690i) q^{67} +(7.20921 + 7.47564i) q^{69} -11.6200i q^{71} +(6.12550 - 10.6097i) q^{73} +(7.45095 + 12.0532i) q^{77} +(-3.61147 - 6.25525i) q^{79} +(5.05324 - 7.44747i) q^{81} -5.14180i q^{83} +(4.31026 + 17.3383i) q^{87} +(8.58428 + 14.8684i) q^{89} +(9.63865 + 5.18485i) q^{91} +(-12.8797 - 3.70279i) q^{93} +4.28309 q^{97} +(16.0570 + 0.582836i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 18 q^{9}+O(q^{10}) \) 32 * q + 18 * q^9	\( 32 q + 18 q^{9} + 36 q^{19} - 22 q^{21} - 36 q^{31} - 24 q^{39} + 36 q^{49} - 2 q^{51} + 72 q^{61} + 14 q^{81} + 40 q^{91} + 60 q^{99}+O(q^{100}) \) 32 * q + 18 * q^9 + 36 * q^19 - 22 * q^21 - 36 * q^31 - 24 * q^39 + 36 * q^49 - 2 * q^51 + 72 * q^61 + 14 * q^81 + 40 * q^91 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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