LMFDB - Embedded newform 2100.2.bo.i.1349.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2100.1349");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1349.7
Character	$\chi$	$=$	2100.1349
Dual form			2100.2.bo.i.1949.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.478563 + 1.66463i) q^{3} +(-2.33003 + 1.25338i) q^{7} +(-2.54196 - 1.59326i) q^{9} +O(q^{10})$	\(q+(-0.478563 + 1.66463i) q^{3} +(-2.33003 + 1.25338i) q^{7} +(-2.54196 - 1.59326i) q^{9} +(-4.63831 + 2.67793i) q^{11} -4.13670 q^{13} +(0.134025 - 0.0773793i) q^{17} +(3.40485 + 1.96579i) q^{19} +(-0.971337 - 4.47845i) q^{21} +(-2.99803 + 5.19273i) q^{23} +(3.86866 - 3.46893i) q^{27} -10.3150i q^{29} +(6.70071 - 3.86866i) q^{31} +(-2.23803 - 9.00261i) q^{33} +(9.07719 + 5.24072i) q^{37} +(1.97967 - 6.88606i) q^{39} +2.33876 q^{41} +1.78236i q^{43} +(3.11974 + 1.80118i) q^{47} +(3.85809 - 5.84082i) q^{49} +(0.0646682 + 0.260132i) q^{51} +(-2.47955 - 4.29470i) q^{53} +(-4.90174 + 4.72705i) q^{57} +(-5.27011 - 9.12810i) q^{59} +(-3.25602 - 1.87987i) q^{61} +(7.91979 + 0.526307i) q^{63} +(0.770225 - 0.444690i) q^{67} +(-7.20921 - 7.47564i) q^{69} -11.6200i q^{71} +(-6.12550 - 10.6097i) q^{73} +(7.45095 - 12.0532i) q^{77} +(-3.61147 + 6.25525i) q^{79} +(3.92307 + 8.09997i) q^{81} +5.14180i q^{83} +(17.1705 + 4.93635i) q^{87} +(-8.58428 + 14.8684i) q^{89} +(9.63865 - 5.18485i) q^{91} +(3.23316 + 13.0056i) q^{93} -4.28309 q^{97} +(16.0570 + 0.582836i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

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

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
$3$	−0.478563	+	1.66463i	−0.276298	+	0.961072i
$3$	−0.478563	+	1.66463i	−0.276298	+	0.961072i
$4$		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
$9$	−2.54196	−	1.59326i	−0.847318	−	0.531085i
$10$		0			0
$11$	−4.63831	+	2.67793i	−1.39850	+	0.807426i	−0.994236	−	0.107214i	$-0.965807\pi$
$11$	−4.63831	+	2.67793i	−1.39850	+	0.807426i	−0.404268	+	0.914641i	$0.632474\pi$
$12$		0			0
$13$	−4.13670			−1.14732			−0.573658	−	0.819095i	$-0.694476\pi$
$13$	−4.13670			−1.14732			−0.573658	+	0.819095i	$0.694476\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.134025	−	0.0773793i	0.0325058	−	0.0187672i	−0.483659	−	0.875257i	$-0.660693\pi$
$17$	0.134025	−	0.0773793i	0.0325058	−	0.0187672i	0.516165	+	0.856489i	$0.327359\pi$
$18$		0			0
$19$	3.40485	+	1.96579i	0.781126	+	0.450983i	0.836829	−	0.547464i	$-0.184407\pi$
$19$	3.40485	+	1.96579i	0.781126	+	0.450983i	−0.0557031	+	0.998447i	$0.517740\pi$
$20$		0			0
$21$	−0.971337	−	4.47845i	−0.211963	−	0.977278i
$22$		0			0
$23$	−2.99803	+	5.19273i	−0.625132	+	1.08276i	0.363384	+	0.931640i	$0.381621\pi$
$23$	−2.99803	+	5.19273i	−0.625132	+	1.08276i	−0.988515	+	0.151120i	$0.951712\pi$
$24$		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	0.242156	−	0.970237i	$-0.422146\pi$
$31$	6.70071	−	3.86866i	1.20348	−	0.694832i	0.961328	+	0.275406i	$0.0888122\pi$
$32$		0			0
$33$	−2.23803	−	9.00261i	−0.389591	−	1.56715i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	9.07719	+	5.24072i	1.49228	+	0.861569i	0.999961	−	0.00884571i	$-0.00281571\pi$
$37$	9.07719	+	5.24072i	1.49228	+	0.861569i	0.492320	+	0.870414i	$0.336149\pi$
$38$		0			0
$39$	1.97967	−	6.88606i	0.317001	−	1.10265i
$40$		0			0
$41$	2.33876			0.365253			0.182627	−	0.983182i	$-0.441540\pi$
$41$	2.33876			0.365253			0.182627	+	0.983182i	$0.441540\pi$
$42$		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	0.709965	−	0.704237i	$-0.248711\pi$
$47$	3.11974	+	1.80118i	0.455061	+	0.262729i	−0.254905	+	0.966966i	$0.582044\pi$
$48$		0			0
$49$	3.85809	−	5.84082i	0.551156	−	0.834402i
$50$		0			0
$51$	0.0646682	+	0.260132i	0.00905537	+	0.0364258i
$52$		0			0
$53$	−2.47955	−	4.29470i	−0.340592	−	0.589923i	0.643951	−	0.765067i	$-0.277294\pi$
$53$	−2.47955	−	4.29470i	−0.340592	−	0.589923i	−0.984543	+	0.175144i	$0.943961\pi$
$54$		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	−0.973087	−	0.230440i	$-0.925983\pi$
$59$	−5.27011	−	9.12810i	−0.686110	−	1.18838i	0.286976	−	0.957938i	$-0.407350\pi$
$60$		0			0
$61$	−3.25602	−	1.87987i	−0.416891	−	0.240692i	0.276855	−	0.960912i	$-0.410708\pi$
$61$	−3.25602	−	1.87987i	−0.416891	−	0.240692i	−0.693746	+	0.720219i	$0.744041\pi$
$62$		0			0
$63$	7.91979	+	0.526307i	0.997799	+	0.0663085i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	0.770225	−	0.444690i	0.0940980	−	0.0543275i	−0.452213	−	0.891910i	$-0.649365\pi$
$67$	0.770225	−	0.444690i	0.0940980	−	0.0543275i	0.546311	+	0.837583i	$0.316032\pi$
$68$		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	−0.962208	−	0.272314i	$-0.912211\pi$
$73$	−6.12550	−	10.6097i	−0.716935	−	1.24177i	0.245273	−	0.969454i	$-0.421122\pi$
$74$		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	−0.994474	−	0.104980i	$-0.966522\pi$
$79$	−3.61147	+	6.25525i	−0.406322	+	0.703770i	0.588152	+	0.808750i	$0.299856\pi$
$80$		0			0
$81$	3.92307	+	8.09997i	0.435897	+	0.899997i
$82$		0			0
$83$			5.14180i			0.564386i	0.959358	+	0.282193i	$0.0910618\pi$
$83$			5.14180i			0.564386i	−0.959358	+	0.282193i	$0.908938\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	17.1705	+	4.93635i	1.84087	+	0.529233i
$88$		0			0
$89$	−8.58428	+	14.8684i	−0.909932	+	1.57605i	−0.0957761	+	0.995403i	$0.530533\pi$
$89$	−8.58428	+	14.8684i	−0.909932	+	1.57605i	−0.814156	+	0.580646i	$0.802800\pi$
$90$		0			0
$91$	9.63865	−	5.18485i	1.01041	−	0.543520i
$92$		0			0
$93$	3.23316	+	13.0056i	0.335263	+	1.34862i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−4.28309			−0.434882			−0.217441	−	0.976073i	$-0.569771\pi$
$97$	−4.28309			−0.434882			−0.217441	+	0.976073i	$0.569771\pi$
$98$		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	$-0.264749\pi$
$101$	−3.04794	−	5.27919i	−0.303282	−	0.525299i	−0.976877	+	0.213801i	$0.931416\pi$
$102$		0			0
$103$	−2.15428	+	3.73132i	−0.212267	+	0.367658i	−0.952424	−	0.304777i	$-0.901418\pi$
$103$	−2.15428	+	3.73132i	−0.212267	+	0.367658i	0.740157	+	0.672435i	$0.234751\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.28953	−	14.3579i	0.801379	−	1.38803i	−0.117330	−	0.993093i	$-0.537433\pi$
$107$	8.28953	−	14.3579i	0.801379	−	1.38803i	0.918709	−	0.394936i	$-0.129233\pi$
$108$		0			0
$109$	1.92426	+	3.33292i	0.184311	+	0.319236i	0.943344	−	0.331816i	$-0.107661\pi$
$109$	1.92426	+	3.33292i	0.184311	+	0.319236i	−0.759033	+	0.651052i	$0.774328\pi$
$110$		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
$117$	10.5153	+	6.59083i	0.972141	+	0.609322i
$118$		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
$123$	−1.11924	+	3.89316i	−0.100919	+	0.351035i
$124$		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
$129$	−2.96695	−	0.852969i	−0.261226	−	0.0750997i
$130$		0			0
$131$	−3.31417	+	5.74031i	−0.289561	+	0.501534i	−0.973705	−	0.227813i	$-0.926842\pi$
$131$	−3.31417	+	5.74031i	−0.289561	+	0.501534i	0.684144	+	0.729347i	$0.260176\pi$
$132$		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	0.747550	−	0.664205i	$-0.231230\pi$
$137$	−2.35783	−	4.08389i	−0.201443	−	0.348910i	−0.948994	+	0.315295i	$0.897897\pi$
$138$		0			0
$139$		−	9.56273i		−	0.811100i	−0.914073	−	0.405550i	$-0.867080\pi$
$139$		−	9.56273i		−	0.811100i	0.914073	−	0.405550i	$-0.132920\pi$
$140$		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
$147$	7.87643	+	9.21748i	0.649637	+	0.760245i
$148$		0			0
$149$	17.6339	+	10.1809i	1.44462	+	0.834054i	0.998153	−	0.0607437i	$-0.0193472\pi$
$149$	17.6339	+	10.1809i	1.44462	+	0.834054i	0.446471	+	0.894798i	$0.352681\pi$
$150$		0			0
$151$	−5.69396	−	9.86223i	−0.463368	−	0.802577i	0.535758	−	0.844371i	$-0.320026\pi$
$151$	−5.69396	−	9.86223i	−0.463368	−	0.802577i	−0.999126	+	0.0417947i	$0.986692\pi$
$152$		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	$-0.254298\pi$
$157$	−3.40612	−	5.89957i	−0.271838	−	0.470837i	−0.969332	+	0.245753i	$0.920965\pi$
$158$		0			0
$159$	8.33569	−	2.07223i	0.661063	−	0.164339i
$160$		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	$-0.433612\pi$
$163$	−6.85180	−	3.95589i	−0.536674	−	0.309849i	−0.743730	+	0.668480i	$0.766945\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			19.2507i			1.48966i	0.667252	+	0.744832i	$0.267470\pi$
$167$			19.2507i			1.48966i	−0.667252	+	0.744832i	$0.732530\pi$
$168$		0			0
$169$	4.11232			0.316332
$170$		0			0
$171$	−5.52297	−	10.4217i	−0.422352	−	0.796971i
$172$		0			0
$173$	−12.2478	−	7.07129i	−0.931186	−	0.537621i	−0.0439995	−	0.999032i	$-0.514010\pi$
$173$	−12.2478	−	7.07129i	−0.931186	−	0.537621i	−0.887186	+	0.461411i	$0.847343\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	17.7169	−	4.40439i	1.33169	−	0.331054i
$178$		0			0
$179$	−1.79606	+	1.03696i	−0.134244	+	0.0775058i	−0.565618	−	0.824667i	$-0.691362\pi$
$179$	−1.79606	+	1.03696i	−0.134244	+	0.0775058i	0.431374	+	0.902173i	$0.358029\pi$
$180$		0			0
$181$		−	21.7401i		−	1.61593i	−0.589231	−	0.807965i	$-0.700569\pi$
$181$		−	21.7401i		−	1.61593i	0.589231	−	0.807965i	$-0.299431\pi$
$182$		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
$189$	−4.66622	+	12.9316i	−0.339417	+	0.940636i
$190$		0			0
$191$	2.00687	+	1.15867i	0.145212	+	0.0838383i	0.570846	−	0.821057i	$-0.306615\pi$
$191$	2.00687	+	1.15867i	0.145212	+	0.0838383i	−0.425634	+	0.904896i	$0.639949\pi$
$192$		0			0
$193$	15.4707	−	8.93203i	1.11361	−	0.642942i	0.173846	−	0.984773i	$-0.444380\pi$
$193$	15.4707	−	8.93203i	1.11361	−	0.642942i	0.939761	+	0.341831i	$0.111047\pi$
$194$		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	−0.438252	−	0.898852i	$-0.644402\pi$
$199$	1.70763	−	0.985902i	0.121051	−	0.0698887i	0.559303	+	0.828963i	$0.311069\pi$
$200$		0			0
$201$	0.371641	+	1.49495i	0.0262135	+	0.105446i
$202$		0			0
$203$	12.9285	+	24.0342i	0.907405	+	1.68687i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	15.8942	−	8.42307i	1.10472	−	0.585444i
$208$		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
$213$	19.3429	+	5.56088i	1.32535	+	0.381025i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−10.7640	+	17.4126i	−0.730707	+	1.18205i
$218$		0			0
$219$	20.5926	−	5.11926i	1.39152	−	0.345928i
$220$		0			0
$221$	−0.554421	+	0.320095i	−0.0372944	+	0.0215319i
$222$		0			0
$223$	−15.3841			−1.03020			−0.515099	−	0.857131i	$-0.672245\pi$
$223$	−15.3841			−1.03020			−0.515099	+	0.857131i	$0.672245\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.68946	+	0.975410i	−0.112133	+	0.0647402i	−0.555018	−	0.831838i	$-0.687289\pi$
$227$	−1.68946	+	0.975410i	−0.112133	+	0.0647402i	0.442884	+	0.896579i	$0.353955\pi$
$228$		0			0
$229$	−2.44750	−	1.41307i	−0.161735	−	0.0933780i	0.416948	−	0.908930i	$-0.363100\pi$
$229$	−2.44750	−	1.41307i	−0.161735	−	0.0933780i	−0.578683	+	0.815553i	$0.696433\pi$
$230$		0			0
$231$	16.4983	+	18.1713i	1.08551	+	1.19558i
$232$		0			0
$233$	−2.19563	+	3.80293i	−0.143840	+	0.249139i	−0.928940	−	0.370231i	$-0.879278\pi$
$233$	−2.19563	+	3.80293i	−0.143840	+	0.249139i	0.785099	+	0.619370i	$0.212612\pi$
$234$		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	−0.614160	−	0.789181i	$-0.710505\pi$
$241$	−3.69148	+	2.13128i	−0.237789	+	0.137288i	0.376371	+	0.926469i	$0.377172\pi$
$242$		0			0
$243$	−15.3609	+	2.65410i	−0.985399	+	0.170261i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−14.0849	−	8.13190i	−0.896198	−	0.517420i
$248$		0			0
$249$	−8.55917	−	2.46067i	−0.542415	−	0.155939i
$250$		0			0
$251$	3.87820			0.244790			0.122395	−	0.992481i	$-0.460943\pi$
$251$	3.87820			0.244790			0.122395	+	0.992481i	$0.460943\pi$
$252$		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	−0.0616020	−	0.998101i	$-0.519621\pi$
$257$	−15.3384	−	8.85563i	−0.956784	−	0.552399i	−0.895182	+	0.445702i	$0.852954\pi$
$258$		0			0
$259$	−27.7187	−	0.833896i	−1.72236	−	0.0518158i
$260$		0			0
$261$	−16.4344	+	26.2202i	−1.01726	+	1.62299i
$262$		0			0
$263$	2.79964	+	4.84912i	0.172633	+	0.299010i	0.939340	−	0.342988i	$-0.111439\pi$
$263$	2.79964	+	4.84912i	0.172633	+	0.299010i	−0.766706	+	0.641998i	$0.778106\pi$
$264$		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	0.999722	+	0.0235867i	$0.00750857\pi$
$269$	8.53335	+	14.7802i	0.520288	+	0.901165i	−0.479434	+	0.877578i	$0.659158\pi$
$270$		0			0
$271$	14.7661	+	8.52521i	0.896977	+	0.517870i	0.876218	−	0.481915i	$-0.160059\pi$
$271$	14.7661	+	8.52521i	0.896977	+	0.517870i	0.0207586	+	0.999785i	$0.493392\pi$
$272$		0			0
$273$	4.01813	+	18.5260i	0.243188	+	1.12125i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−9.12563	+	5.26868i	−0.548306	+	0.316565i	−0.748438	−	0.663204i	$-0.769196\pi$
$277$	−9.12563	+	5.26868i	−0.548306	+	0.316565i	0.200133	+	0.979769i	$0.435863\pi$
$278$		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	0.999189	+	0.0402770i	$0.0128240\pi$
$283$	8.99126	+	15.5733i	0.534475	+	0.925738i	−0.464713	+	0.885461i	$0.653843\pi$
$284$		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
$291$	2.04973	−	7.12974i	0.120157	−	0.417953i
$292$		0			0
$293$		−	25.2153i		−	1.47309i	−0.676388	−	0.736546i	$-0.736456\pi$
$293$		−	25.2153i		−	1.47309i	0.676388	−	0.736546i	$-0.263544\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−8.65449	+	26.4500i	−0.502184	+	1.53478i
$298$		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
$303$	10.2465	−	2.54726i	0.588646	−	0.146336i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−8.28693			−0.472960			−0.236480	−	0.971636i	$-0.575994\pi$
$307$	−8.28693			−0.472960			−0.236480	+	0.971636i	$0.575994\pi$
$308$		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	$-0.244877\pi$
$311$	−4.28958	−	7.42977i	−0.243240	−	0.421304i	−0.961635	+	0.274331i	$0.911544\pi$
$312$		0			0
$313$	−0.466406	+	0.807839i	−0.0263628	+	0.0456617i	−0.878906	−	0.476995i	$-0.841726\pi$
$313$	−0.466406	+	0.807839i	−0.0263628	+	0.0456617i	0.852543	+	0.522657i	$0.175059\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.49108	+	2.58262i	−0.0837472	+	0.145054i	−0.904857	−	0.425716i	$-0.860022\pi$
$317$	−1.49108	+	2.58262i	−0.0837472	+	0.145054i	0.821109	+	0.570771i	$0.193355\pi$
$318$		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
$327$	−6.46895	+	1.60817i	−0.357734	+	0.0889317i
$328$		0			0
$329$	−9.52665	−	0.286602i	−0.525221	−	0.0158009i
$330$		0			0
$331$	10.9541	−	18.9730i	0.602091	−	1.04285i	−0.390413	−	0.920640i	$-0.627668\pi$
$331$	10.9541	−	18.9730i	0.602091	−	1.04285i	0.992504	−	0.122213i	$-0.0389990\pi$
$332$		0			0
$333$	−14.7240	−	27.7840i	−0.806871	−	1.52255i
$334$		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
$339$	4.75826	−	16.5511i	0.258433	−	0.898930i
$340$		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	0.804295	−	0.594230i	$-0.202543\pi$
$347$	−2.09509	−	3.62881i	−0.112471	−	0.194805i	−0.916766	+	0.399425i	$0.869210\pi$
$348$		0			0
$349$		−	22.2897i		−	1.19314i	−0.802560	−	0.596571i	$-0.796530\pi$
$349$		−	22.2897i		−	1.19314i	0.802560	−	0.596571i	$-0.203470\pi$
$350$		0			0
$351$	−16.0035	+	14.3499i	−0.854203	+	0.765943i
$352$		0			0
$353$	−15.1073	+	8.72220i	−0.804080	+	0.464236i	−0.844896	−	0.534931i	$-0.820338\pi$
$353$	−15.1073	+	8.72220i	−0.804080	+	0.464236i	0.0408157	+	0.999167i	$0.487004\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.476723	−	0.525062i	−0.0252308	−	0.0277892i
$358$		0			0
$359$	25.2564	+	14.5818i	1.33298	+	0.769599i	0.985756	−	0.168182i	$-0.0537896\pi$
$359$	25.2564	+	14.5818i	1.33298	+	0.769599i	0.347228	+	0.937781i	$0.387123\pi$
$360$		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	−0.969130	−	0.246550i	$-0.920703\pi$
$367$	−13.3734	−	23.1633i	−0.698084	−	1.20912i	0.271046	−	0.962566i	$-0.412630\pi$
$368$		0			0
$369$	−5.94503	−	3.72625i	−0.309486	−	0.193981i
$370$		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	$-0.290897\pi$
$373$	4.44649	+	2.56718i	0.230231	+	0.132924i	−0.380448	+	0.924802i	$0.624230\pi$
$374$		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
$381$	−7.73172	−	2.22279i	−0.396108	−	0.113877i
$382$		0			0
$383$	−18.7852	−	10.8457i	−0.959881	−	0.554188i	−0.0637447	−	0.997966i	$-0.520304\pi$
$383$	−18.7852	−	10.8457i	−0.959881	−	0.554188i	−0.896136	+	0.443779i	$0.853638\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.83975	−	4.53067i	0.144353	−	0.230307i
$388$		0			0
$389$	11.6759	−	6.74110i	0.591993	−	0.341787i	−0.173892	−	0.984765i	$-0.555634\pi$
$389$	11.6759	−	6.74110i	0.591993	−	0.341787i	0.765885	+	0.642977i	$0.222301\pi$
$390$		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	$-0.721470\pi$
$397$	6.85891	−	11.8800i	0.344239	−	0.596240i	0.985215	+	0.171321i	$0.0548036\pi$
$398$		0			0
$399$	5.49644	−	17.1579i	0.275166	−	0.858969i
$400$		0			0
$401$	16.4976	+	9.52487i	0.823849	+	0.475649i	0.851742	−	0.523962i	$-0.175547\pi$
$401$	16.4976	+	9.52487i	0.823849	+	0.475649i	−0.0278932	+	0.999611i	$0.508880\pi$
$402$		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	−0.999941	−	0.0109054i	$-0.996529\pi$
$409$	−30.1428	+	17.4030i	−1.49047	+	0.860521i	−0.490526	+	0.871427i	$0.663195\pi$
$410$		0			0
$411$	7.92652	−	1.97051i	0.390986	−	0.0971983i
$412$		0			0
$413$	23.7205	+	14.6633i	1.16721	+	0.721535i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	15.9184	+	4.57637i	0.779526	+	0.224106i
$418$		0			0
$419$	−19.7934			−0.966971			−0.483486	−	0.875352i	$-0.660629\pi$
$419$	−19.7934			−0.966971			−0.483486	+	0.875352i	$0.660629\pi$
$420$		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
$423$	−5.06049	−	9.54906i	−0.246050	−	0.464291i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	9.94282	+	0.299122i	0.481167	+	0.0144755i
$428$		0			0
$429$	9.25806	+	37.2411i	0.446983	+	1.79802i
$430$		0			0
$431$	9.22781	−	5.32768i	0.444488	−	0.256625i	−0.261012	−	0.965336i	$-0.584056\pi$
$431$	9.22781	−	5.32768i	0.444488	−	0.256625i	0.705499	+	0.708711i	$0.250723\pi$
$432$		0			0
$433$	−25.5027			−1.22558			−0.612791	−	0.790245i	$-0.709953\pi$
$433$	−25.5027			−1.22558			−0.612791	+	0.790245i	$0.709953\pi$
$434$		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	−0.191234	−	0.981544i	$-0.561249\pi$
$439$	−23.8206	−	13.7528i	−1.13689	−	0.656386i	−0.945660	+	0.325158i	$0.894582\pi$
$440$		0			0
$441$	−19.1130	+	8.70016i	−0.910143	+	0.414294i
$442$		0			0
$443$	9.68708	−	16.7785i	0.460247	−	0.797171i	−0.538726	−	0.842481i	$-0.681094\pi$
$443$	9.68708	−	16.7785i	0.460247	−	0.797171i	0.998973	+	0.0453099i	$0.0144275\pi$
$444$		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
$453$	19.1418	−	4.75861i	0.899362	−	0.223579i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−15.9124	−	9.18704i	−0.744352	−	0.429752i	0.0792977	−	0.996851i	$-0.474732\pi$
$457$	−15.9124	−	9.18704i	−0.744352	−	0.429752i	−0.823649	+	0.567099i	$0.808066\pi$
$458$		0			0
$459$	0.250073	−	0.764277i	0.0116724	−	0.0356734i
$460$		0			0
$461$	12.2344			0.569814			0.284907	−	0.958555i	$-0.408037\pi$
$461$	12.2344			0.569814			0.284907	+	0.958555i	$0.408037\pi$
$462$		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	0.526448	−	0.850207i	$-0.323523\pi$
$467$	1.15336	+	0.665893i	0.0533711	+	0.0308138i	−0.473077	+	0.881021i	$0.656857\pi$
$468$		0			0
$469$	−1.23728	+	2.00152i	−0.0571325	+	0.0924218i
$470$		0			0
$471$	11.4506	−	2.84659i	0.527616	−	0.131164i
$472$		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	$-0.00349621\pi$
$479$	10.7342	+	18.5922i	0.490458	+	0.849498i	−0.509482	+	0.860481i	$0.670163\pi$
$480$		0			0
$481$	−37.5496	−	21.6793i	−1.71212	−	0.988491i
$482$		0			0
$483$	26.1675	+	8.38261i	1.19066	+	0.381422i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−24.0115	+	13.8630i	−1.08807	+	0.628195i	−0.933061	−	0.359719i	$-0.882873\pi$
$487$	−24.0115	+	13.8630i	−1.08807	+	0.628195i	−0.155004	+	0.987914i	$0.549539\pi$
$488$		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	0.299110	+	0.954219i	$0.403310\pi$
$499$	−15.1191	+	26.1870i	−0.676823	+	1.17229i	−0.975933	+	0.218072i	$0.930023\pi$
$500$		0			0
$501$	−32.0452	−	9.21267i	−1.43167	−	0.411592i
$502$		0			0
$503$			32.5176i			1.44989i	0.688807	+	0.724945i	$0.258135\pi$
$503$			32.5176i			1.44989i	−0.688807	+	0.724945i	$0.741865\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.96800	+	6.84547i	−0.0874021	+	0.304018i
$508$		0			0
$509$	−13.1885	+	22.8432i	−0.584570	+	1.01251i	0.410359	+	0.911924i	$0.365403\pi$
$509$	−13.1885	+	22.8432i	−0.584570	+	1.01251i	−0.994929	+	0.100581i	$0.967930\pi$
$510$		0			0
$511$	27.5705	+	17.0433i	1.21965	+	0.753952i
$512$		0			0
$513$	19.9914	−	4.20621i	0.882642	−	0.185709i
$514$		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	$-0.0906633\pi$
$521$	5.39842	+	9.35035i	0.236509	+	0.409646i	−0.723201	+	0.690638i	$0.757330\pi$
$522$		0			0
$523$	−0.119197	+	0.206455i	−0.00521211	+	0.00902764i	−0.868620	−	0.495479i	$-0.834992\pi$
$523$	−0.119197	+	0.206455i	−0.00521211	+	0.00902764i	0.863408	+	0.504507i	$0.168326\pi$
$524$		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
$537$	−0.866616	−	3.48602i	−0.0373972	−	0.150433i
$538$		0			0
$539$	−2.25374	+	37.4232i	−0.0970753	+	1.61193i
$540$		0			0
$541$	−1.28056	+	2.21799i	−0.0550555	+	0.0953588i	−0.892240	−	0.451562i	$-0.850867\pi$
$541$	−1.28056	+	2.21799i	−0.0550555	+	0.0953588i	0.837184	+	0.546921i	$0.184200\pi$
$542$		0			0
$543$	36.1891	+	10.4040i	1.55302	+	0.446479i
$544$		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
$549$	5.28156	+	9.96621i	0.225411	+	0.425348i
$550$		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	−0.999948	−	0.0101846i	$-0.996758\pi$
$557$	−12.0080	−	20.7984i	−0.508794	−	0.881257i	0.491154	−	0.871073i	$-0.336575\pi$
$558$		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	0.471340	−	0.881952i	$-0.343771\pi$
$563$	34.8986	−	20.1487i	1.47080	−	0.849168i	0.999462	+	0.0327839i	$0.0104373\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−19.2932	−	13.9561i	−0.810238	−	0.586101i
$568$		0			0
$569$	−4.46883	−	2.58008i	−0.187343	−	0.108163i	0.403395	−	0.915026i	$-0.367830\pi$
$569$	−4.46883	−	2.58008i	−0.187343	−	0.108163i	−0.590738	+	0.806863i	$0.701163\pi$
$570$		0			0
$571$	0.841937	+	1.45828i	0.0352340	+	0.0610270i	0.883105	−	0.469176i	$-0.155449\pi$
$571$	0.841937	+	1.45828i	0.0352340	+	0.0610270i	−0.847871	+	0.530203i	$0.822116\pi$
$572$		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	−0.990706	−	0.136024i	$-0.956568\pi$
$577$	−14.7284	−	25.5104i	−0.613153	−	1.06201i	0.377552	−	0.925988i	$-0.376766\pi$
$578$		0			0
$579$	7.46477	+	30.0275i	0.310225	+	1.24790i
$580$		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	$-0.602070\pi$
$587$		−	45.9862i		−	1.89805i	0.315195	−	0.949027i	$-0.397930\pi$
$588$		0			0
$589$	30.4199			1.25343
$590$		0			0
$591$	−8.79834	+	30.6040i	−0.361915	+	1.25888i
$592$		0			0
$593$	1.65252	+	0.954084i	0.0678610	+	0.0391795i	0.533547	−	0.845771i	$-0.320859\pi$
$593$	1.65252	+	0.954084i	0.0678610	+	0.0391795i	−0.465686	+	0.884950i	$0.654192\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.823948	+	3.31438i	0.0337219	+	0.135649i
$598$		0			0
$599$	18.2188	−	10.5186i	0.744401	−	0.429780i	−0.0792661	−	0.996853i	$-0.525258\pi$
$599$	18.2188	−	10.5186i	0.744401	−	0.429780i	0.823667	+	0.567073i	$0.191924\pi$
$600$		0			0
$601$			30.3573i			1.23830i	0.785273	+	0.619150i	$0.212523\pi$
$601$			30.3573i			1.23830i	−0.785273	+	0.619150i	$0.787477\pi$
$602$		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	$-0.715770\pi$
$607$	8.89399	−	15.4049i	0.360996	−	0.625264i	0.988125	+	0.153652i	$0.0491034\pi$
$608$		0			0
$609$	−46.1950	+	10.0193i	−1.87192	+	0.406002i
$610$		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	$-0.467388\pi$
$613$	25.1276	−	14.5074i	1.01490	−	0.585950i	0.912621	+	0.408806i	$0.134055\pi$
$614$		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	−0.706406	+	0.707806i	$0.749685\pi$
$619$	−41.6135	+	24.0256i	−1.67259	+	0.965669i	−0.966182	+	0.257863i	$0.916982\pi$
$620$		0			0
$621$	6.41489	+	30.4889i	0.257421	+	1.22348i
$622$		0			0
$623$	1.36592	−	45.4032i	0.0547244	−	1.81904i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	10.0771	−	35.0520i	0.402441	−	1.39984i
$628$		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
$633$	−0.516694	+	1.79726i	−0.0205368	+	0.0714347i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−15.9598	+	24.1617i	−0.632350	+	0.957322i
$638$		0			0
$639$	−18.5136	+	29.5374i	−0.732385	+	1.16848i
$640$		0			0
$641$	−3.34785	+	1.93288i	−0.132232	+	0.0763443i	−0.564657	−	0.825326i	$-0.690991\pi$
$641$	−3.34785	+	1.93288i	−0.132232	+	0.0763443i	0.432425	+	0.901670i	$0.357658\pi$
$642$		0			0
$643$	−37.7423			−1.48841			−0.744206	−	0.667950i	$-0.767172\pi$
$643$	−37.7423			−1.48841			−0.744206	+	0.667950i	$0.767172\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	18.9193	−	10.9230i	0.743793	−	0.429429i	−0.0796536	−	0.996823i	$-0.525381\pi$
$647$	18.9193	−	10.9230i	0.743793	−	0.429429i	0.823447	+	0.567393i	$0.192048\pi$
$648$		0			0
$649$	48.8888	+	28.2260i	1.91905	+	1.10797i
$650$		0			0
$651$	−23.8342	−	26.2510i	−0.934138	−	1.02886i
$652$		0			0
$653$	1.81473	−	3.14321i	0.0710159	−	0.123003i	−0.828331	−	0.560239i	$-0.810709\pi$
$653$	1.81473	−	3.14321i	0.0710159	−	0.123003i	0.899347	+	0.437236i	$0.144043\pi$
$654$		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	−0.210410	−	0.977613i	$-0.567480\pi$
$661$	13.6525	−	7.88230i	0.531023	−	0.306586i	0.741433	+	0.671027i	$0.234147\pi$
$662$		0			0
$663$	−0.267513	−	1.07609i	−0.0103894	−	0.0417919i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	53.5628	+	30.9245i	2.07396	+	1.19740i
$668$		0			0
$669$	7.36227	−	25.6088i	0.284642	−	0.990094i
$670$		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	0.737278	−	0.675589i	$-0.236111\pi$
$677$	13.5519	+	7.82417i	0.520840	+	0.300707i	−0.216438	+	0.976296i	$0.569444\pi$
$678$		0			0
$679$	9.97974	−	5.36833i	0.382987	−	0.206018i
$680$		0			0
$681$	−0.815180	−	3.27911i	−0.0312378	−	0.125656i
$682$		0			0
$683$	−18.9193	−	32.7691i	−0.723926	−	1.25388i	−0.959415	−	0.281999i	$-0.909002\pi$
$683$	−18.9193	−	32.7691i	−0.723926	−	1.25388i	0.235489	−	0.971877i	$-0.424331\pi$
$684$		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	0.196363	−	0.980531i	$-0.437087\pi$
$691$	−14.5792	−	8.41732i	−0.554620	−	0.320210i	−0.750983	+	0.660321i	$0.770420\pi$
$692$		0			0
$693$	−38.1438	+	18.7675i	−1.44896	+	0.712917i
$694$		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	−0.692775	−	0.721154i	$-0.743612\pi$
$709$	7.40632	−	12.8281i	0.278150	−	0.481770i	0.970925	+	0.239384i	$0.0769454\pi$
$710$		0			0
$711$	19.1464	−	10.1466i	0.718046	−	0.380526i
$712$		0			0
$713$			46.3934i			1.73744i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	29.4179	+	8.45734i	1.09863	+	0.315845i
$718$		0			0
$719$	10.1406	−	17.5640i	0.378179	−	0.655025i	−0.612618	−	0.790379i	$-0.709884\pi$
$719$	10.1406	−	17.5640i	0.378179	−	0.655025i	0.990797	+	0.135353i	$0.0432170\pi$
$720$		0			0
$721$	0.342786	−	11.3942i	0.0127660	−	0.424342i
$722$		0			0
$723$	−1.78117	−	7.16488i	−0.0662425	−	0.266465i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−2.81854			−0.104534			−0.0522670	−	0.998633i	$-0.516645\pi$
$727$	−2.81854			−0.104534			−0.0522670	+	0.998633i	$0.516645\pi$
$728$		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	−0.340074	−	0.940399i	$-0.610452\pi$
$733$	17.4457	−	30.2169i	0.644372	−	1.11609i	0.984446	−	0.175687i	$-0.0562146\pi$
$734$		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	0.506237	−	0.862394i	$-0.331036\pi$
$739$	−13.4220	−	23.2476i	−0.493737	−	0.855177i	−0.999974	+	0.00721695i	$0.997703\pi$
$740$		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
$747$	8.19220	−	13.0702i	0.299737	−	0.478215i
$748$		0			0
$749$	−1.31902	+	43.8442i	−0.0481959	+	1.60203i
$750$		0			0
$751$	−1.56634	+	2.71297i	−0.0571564	+	0.0989978i	−0.893188	−	0.449684i	$-0.851537\pi$
$751$	−1.56634	+	2.71297i	−0.0571564	+	0.0989978i	0.836031	+	0.548682i	$0.184870\pi$
$752$		0			0
$753$	−1.85596	+	6.45575i	−0.0676350	+	0.235261i
$754$		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
$759$	53.4578	+	15.3686i	1.94040	+	0.557844i
$760$		0			0
$761$	2.16163	−	3.74406i	0.0783591	−	0.135722i	−0.824183	−	0.566324i	$-0.808365\pi$
$761$	2.16163	−	3.74406i	0.0783591	−	0.135722i	0.902542	+	0.430602i	$0.141699\pi$
$762$		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	$-0.786645\pi$
$769$		−	34.4529i		−	1.24240i	0.783650	−	0.621202i	$-0.213355\pi$
$770$		0			0
$771$	22.0817	−	21.2947i	0.795253	−	0.766911i
$772$		0			0
$773$	−8.99408	+	5.19273i	−0.323494	+	0.186770i	−0.652949	−	0.757402i	$-0.726468\pi$
$773$	−8.99408	+	5.19273i	−0.323494	+	0.186770i	0.329455	+	0.944171i	$0.393135\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	14.6533	−	45.7422i	0.525683	−	1.64099i
$778$		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	0.940283	+	0.340394i	$0.110560\pi$
$787$	21.4590	+	37.1681i	0.764931	+	1.32490i	−0.175352	+	0.984506i	$0.556106\pi$
$788$		0			0
$789$	−9.41178	+	2.33975i	−0.335068	+	0.0832972i
$790$		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	$0.111420\pi$
$797$			19.3628i			0.685866i	−0.939360	+	0.342933i	$0.888580\pi$
$798$		0			0
$799$	0.557497			0.0197228
$800$		0			0
$801$	45.5101	−	24.1179i	1.60802	−	0.852164i
$802$		0			0
$803$	56.8239	+	32.8073i	2.00527	+	1.15774i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−28.6872	+	7.13158i	−1.00984	+	0.251043i
$808$		0			0
$809$	−0.120667	+	0.0696669i	−0.00424241	+	0.00244936i	−0.502120	−	0.864798i	$-0.667446\pi$
$809$	−0.120667	+	0.0696669i	−0.00424241	+	0.00244936i	0.497877	+	0.867247i	$0.334113\pi$
$810$		0			0
$811$		−	43.5559i		−	1.52945i	−0.644354	−	0.764727i	$-0.722874\pi$
$811$		−	43.5559i		−	1.52945i	0.644354	−	0.764727i	$-0.277126\pi$
$812$		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
$819$	−32.7618	−	2.17718i	−1.14479	−	0.0760767i
$820$		0			0
$821$	−39.9212	−	23.0485i	−1.39326	−	0.804400i	−0.399586	−	0.916696i	$-0.630846\pi$
$821$	−39.9212	−	23.0485i	−1.39326	−	0.804400i	−0.993675	+	0.112296i	$0.964180\pi$
$822$		0			0
$823$	19.4726	−	11.2425i	0.678772	−	0.391889i	−0.120620	−	0.992699i	$-0.538488\pi$
$823$	19.4726	−	11.2425i	0.678772	−	0.391889i	0.799392	+	0.600809i	$0.205155\pi$
$824$		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	−0.555661	−	0.831409i	$-0.687535\pi$
$829$	−3.26705	+	1.88623i	−0.113469	+	0.0655115i	0.442191	+	0.896921i	$0.354201\pi$
$830$		0			0
$831$	−4.40320	−	17.7121i	−0.152745	−	0.614428i
$832$		0			0
$833$	0.0651222	−	1.08135i	0.00225635	−	0.0374666i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	12.5027	−	38.2108i	0.432155	−	1.32076i
$838$		0			0
$839$	−40.7191			−1.40578			−0.702890	−	0.711299i	$-0.748107\pi$
$839$	−40.7191			−1.40578			−0.702890	+	0.711299i	$0.748107\pi$
$840$		0			0
$841$	−77.3983			−2.66891
$842$		0			0
$843$	−31.9955	−	9.19837i	−1.10198	−	0.316809i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−1.40703	+	46.7696i	−0.0483460	+	1.60702i
$848$		0			0
$849$	−30.2266	+	7.51427i	−1.03738	+	0.257889i
$850$		0			0
$851$	−54.4273	+	31.4236i	−1.86574	+	1.07719i
$852$		0			0
$853$	3.21298			0.110010			0.0550051	−	0.998486i	$-0.482482\pi$
$853$	3.21298			0.110010			0.0550051	+	0.998486i	$0.482482\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	41.6653	−	24.0555i	1.42326	−	0.821720i	0.426685	−	0.904400i	$-0.359681\pi$
$857$	41.6653	−	24.0555i	1.42326	−	0.821720i	0.996576	+	0.0826803i	$0.0263480\pi$
$858$		0			0
$859$	−10.4266	−	6.01978i	−0.355750	−	0.205392i	0.311465	−	0.950258i	$-0.399180\pi$
$859$	−10.4266	−	6.01978i	−0.355750	−	0.205392i	−0.667215	+	0.744865i	$0.732514\pi$
$860$		0			0
$861$	−2.27173	−	10.4740i	−0.0774202	−	0.356954i
$862$		0			0
$863$	3.75993	−	6.51239i	0.127989	−	0.221684i	−0.794908	−	0.606730i	$-0.792481\pi$
$863$	3.75993	−	6.51239i	0.127989	−	0.221684i	0.922898	+	0.385046i	$0.125814\pi$
$864$		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
$873$	10.8874	+	6.82406i	0.368484	+	0.230959i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	28.8156	+	16.6367i	0.973033	+	0.561781i	0.900160	−	0.435560i	$-0.143450\pi$
$877$	28.8156	+	16.6367i	0.973033	+	0.561781i	0.0728736	+	0.997341i	$0.476783\pi$
$878$		0			0
$879$	41.9740	+	12.0671i	1.41575	+	0.407013i
$880$		0			0
$881$	−19.9614			−0.672515			−0.336258	−	0.941770i	$-0.609161\pi$
$881$	−19.9614			−0.672515			−0.336258	+	0.941770i	$0.609161\pi$
$882$		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	0.760521	−	0.649313i	$-0.224944\pi$
$887$	17.2280	+	9.94659i	0.578460	+	0.333974i	−0.182061	+	0.983287i	$0.558277\pi$
$888$		0			0
$889$	−5.82158	−	10.8223i	−0.195250	−	0.362970i
$890$		0			0
$891$	−39.8876	−	27.0645i	−1.33628	−	0.906694i
$892$		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
$903$	7.98219	−	1.73127i	0.265631	−	0.0576130i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−37.1005	+	21.4200i	−1.23190	+	0.711239i	−0.967426	−	0.253153i	$-0.918532\pi$
$907$	−37.1005	+	21.4200i	−1.23190	+	0.711239i	−0.264476	+	0.964392i	$0.585199\pi$
$908$		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	−0.929569	−	0.368649i	$-0.879821\pi$
$919$	−4.41160	+	7.64112i	−0.145525	+	0.252057i	0.784043	+	0.620706i	$0.213154\pi$
$920$		0			0
$921$	3.96582	−	13.7946i	0.130678	−	0.454549i
$922$		0			0
$923$			48.0683i			1.58219i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	11.4210	−	6.05253i	0.375115	−	0.198791i
$928$		0			0
$929$	27.1691	−	47.0583i	0.891389	−	1.54393i	0.0531782	−	0.998585i	$-0.483065\pi$
$929$	27.1691	−	47.0583i	0.891389	−	1.54393i	0.838211	−	0.545346i	$-0.183602\pi$
$930$		0			0
$931$	24.6180	−	12.3029i	0.806824	−	0.403211i
$932$		0			0
$933$	14.4206	−	3.58493i	0.472110	−	0.117365i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	16.3198			0.533144			0.266572	−	0.963815i	$-0.414109\pi$
$937$	16.3198			0.533144			0.266572	+	0.963815i	$0.414109\pi$
$938$		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	$-0.206261\pi$
$941$	−3.80594	−	6.59208i	−0.124070	−	0.214896i	−0.921369	+	0.388689i	$0.872928\pi$
$942$		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	−0.616673	−	0.787219i	$-0.711520\pi$
$947$	11.4912	−	19.9034i	0.373415	−	0.646774i	0.990088	+	0.140445i	$0.0448533\pi$
$948$		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
$957$	−92.8615	+	23.0852i	−3.00179	+	0.746237i
$958$		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
$963$	−43.9474	+	23.2898i	−1.41618	+	0.750502i
$964$		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
$969$	−0.291180	+	1.01284i	−0.00935404	+	0.0325370i
$970$		0			0
$971$	22.5212	−	39.0078i	0.722739	−	1.25182i	−0.237159	−	0.971471i	$-0.576216\pi$
$971$	22.5212	−	39.0078i	0.722739	−	1.25182i	0.959898	−	0.280350i	$-0.0904505\pi$
$972$		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	0.590404	−	0.807108i	$-0.298968\pi$
$977$	−12.6207	−	21.8598i	−0.403773	−	0.699356i	−0.994178	+	0.107751i	$0.965635\pi$
$978$		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	−0.697805	+	0.716288i	$0.745840\pi$
$983$	−52.2661	+	30.1759i	−1.66703	+	0.962461i	−0.969226	+	0.246173i	$0.920827\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	5.03618	−	15.7211i	0.160303	−	0.500409i
$988$		0			0
$989$	−9.25530	−	5.34355i	−0.294301	−	0.169915i
$990$		0			0
$991$	4.93445	+	8.54672i	0.156748	+	0.271495i	0.933694	−	0.358072i	$-0.116566\pi$
$991$	4.93445	+	8.54672i	0.156748	+	0.271495i	−0.776946	+	0.629567i	$0.783232\pi$
$992$		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	$-0.307005\pi$
$997$	−13.4745	−	23.3385i	−0.426742	−	0.739138i	−0.996581	+	0.0826177i	$0.973672\pi$
$998$		0			0
$999$	53.2962	−	11.2136i	1.68622	−	0.354782i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bo.i.1349.7		32
3.2	odd	2	inner	2100.2.bo.i.1349.15		32
5.2	odd	4		2100.2.bi.l.1601.8	yes	16
5.3	odd	4		2100.2.bi.m.1601.1	yes	16
5.4	even	2	inner	2100.2.bo.i.1349.10		32
7.3	odd	6	inner	2100.2.bo.i.1949.2		32
15.2	even	4		2100.2.bi.l.1601.6	yes	16
15.8	even	4		2100.2.bi.m.1601.3	yes	16
15.14	odd	2	inner	2100.2.bo.i.1349.2		32
21.17	even	6	inner	2100.2.bo.i.1949.10		32
35.3	even	12		2100.2.bi.m.101.3	yes	16
35.17	even	12		2100.2.bi.l.101.6	✓	16
35.24	odd	6	inner	2100.2.bo.i.1949.15		32
105.17	odd	12		2100.2.bi.l.101.8	yes	16
105.38	odd	12		2100.2.bi.m.101.1	yes	16
105.59	even	6	inner	2100.2.bo.i.1949.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.bi.l.101.6	✓	16	35.17	even	12
2100.2.bi.l.101.8	yes	16	105.17	odd	12
2100.2.bi.l.1601.6	yes	16	15.2	even	4
2100.2.bi.l.1601.8	yes	16	5.2	odd	4
2100.2.bi.m.101.1	yes	16	105.38	odd	12
2100.2.bi.m.101.3	yes	16	35.3	even	12
2100.2.bi.m.1601.1	yes	16	5.3	odd	4
2100.2.bi.m.1601.3	yes	16	15.8	even	4
2100.2.bo.i.1349.2		32	15.14	odd	2	inner
2100.2.bo.i.1349.7		32	1.1	even	1	trivial
2100.2.bo.i.1349.10		32	5.4	even	2	inner
2100.2.bo.i.1349.15		32	3.2	odd	2	inner
2100.2.bo.i.1949.2		32	7.3	odd	6	inner
2100.2.bo.i.1949.7		32	105.59	even	6	inner
2100.2.bo.i.1949.10		32	21.17	even	6	inner
2100.2.bo.i.1949.15		32	35.24	odd	6	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)

\(f(q)\)	\(=\)	\(q+(-0.478563 + 1.66463i) q^{3} +(-2.33003 + 1.25338i) q^{7} +(-2.54196 - 1.59326i) q^{9} +O(q^{10})\)	\(q+(-0.478563 + 1.66463i) q^{3} +(-2.33003 + 1.25338i) q^{7} +(-2.54196 - 1.59326i) q^{9} +(-4.63831 + 2.67793i) q^{11} -4.13670 q^{13} +(0.134025 - 0.0773793i) q^{17} +(3.40485 + 1.96579i) q^{19} +(-0.971337 - 4.47845i) q^{21} +(-2.99803 + 5.19273i) q^{23} +(3.86866 - 3.46893i) q^{27} -10.3150i q^{29} +(6.70071 - 3.86866i) q^{31} +(-2.23803 - 9.00261i) q^{33} +(9.07719 + 5.24072i) q^{37} +(1.97967 - 6.88606i) q^{39} +2.33876 q^{41} +1.78236i q^{43} +(3.11974 + 1.80118i) q^{47} +(3.85809 - 5.84082i) q^{49} +(0.0646682 + 0.260132i) q^{51} +(-2.47955 - 4.29470i) q^{53} +(-4.90174 + 4.72705i) q^{57} +(-5.27011 - 9.12810i) q^{59} +(-3.25602 - 1.87987i) q^{61} +(7.91979 + 0.526307i) q^{63} +(0.770225 - 0.444690i) q^{67} +(-7.20921 - 7.47564i) q^{69} -11.6200i q^{71} +(-6.12550 - 10.6097i) q^{73} +(7.45095 - 12.0532i) q^{77} +(-3.61147 + 6.25525i) q^{79} +(3.92307 + 8.09997i) q^{81} +5.14180i q^{83} +(17.1705 + 4.93635i) q^{87} +(-8.58428 + 14.8684i) q^{89} +(9.63865 - 5.18485i) q^{91} +(3.23316 + 13.0056i) q^{93} -4.28309 q^{97} +(16.0570 + 0.582836i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 18 q^{9}+O(q^{10}) \) 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

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Representations

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Database

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