LMFDB - Embedded newform 2100.2.bi.l.1601.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 3, 0, 1]))

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

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

chi := DirichletCharacter("2100.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 9 x^{14} - 18 x^{13} + 32 x^{12} - 36 x^{11} + 51 x^{9} - 167 x^{8} + 153 x^{7} + \cdots + 6561 $ x^16 - 3x^15 + 9x^14 - 18x^13 + 32x^12 - 36x^11 + 51x^9 - 167x^8 + 153x^7 - 972x^5 + 2592x^4 - 4374x^3 + 6561x^2 - 6561*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1601.6
Root			$-0.417865 - 1.68089i$ of defining polynomial
Character	$\chi$	$=$	2100.1601
Dual form			2100.2.bi.l.101.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.417865 - 1.68089i) q^{3} +(-1.25338 - 2.33003i) q^{7} +(-2.65078 - 1.40477i) q^{9} +O(q^{10})$	\(q+(0.417865 - 1.68089i) q^{3} +(-1.25338 - 2.33003i) q^{7} +(-2.65078 - 1.40477i) q^{9} +(4.63831 - 2.67793i) q^{11} +4.13670i q^{13} +(-0.0773793 - 0.134025i) q^{17} +(-3.40485 - 1.96579i) q^{19} +(-4.44027 + 1.13315i) q^{21} +(-5.19273 - 2.99803i) q^{23} +(-3.46893 + 3.86866i) q^{27} -10.3150i q^{29} +(6.70071 - 3.86866i) q^{31} +(-2.56312 - 8.91550i) q^{33} +(-5.24072 + 9.07719i) q^{37} +(6.95334 + 1.72858i) q^{39} -2.33876 q^{41} +1.78236 q^{43} +(1.80118 - 3.11974i) q^{47} +(-3.85809 + 5.84082i) q^{49} +(-0.257615 + 0.0740617i) q^{51} +(4.29470 - 2.47955i) q^{53} +(-4.72705 + 4.90174i) q^{57} +(-5.27011 - 9.12810i) q^{59} +(-3.25602 - 1.87987i) q^{61} +(0.0492651 + 7.93710i) q^{63} +(0.444690 + 0.770225i) q^{67} +(-7.20921 + 7.47564i) q^{69} +11.6200i q^{71} +(-10.6097 + 6.12550i) q^{73} +(-12.0532 - 7.45095i) q^{77} +(3.61147 - 6.25525i) q^{79} +(5.05324 + 7.44747i) q^{81} -5.14180 q^{83} +(-17.3383 - 4.31026i) q^{87} +(-8.58428 + 14.8684i) q^{89} +(9.63865 - 5.18485i) q^{91} +(-3.70279 - 12.8797i) q^{93} -4.28309i q^{97} +(-16.0570 + 0.582836i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{3} - 6 q^{7} - 9 q^{9}+O(q^{10}) $ 16 * q - 3 * q^3 - 6 * q^7 - 9 * q^9	$ 16 q - 3 q^{3} - 6 q^{7} - 9 q^{9} - 18 q^{19} - 11 q^{21} - 18 q^{31} - 12 q^{33} + 6 q^{37} + 12 q^{39} - 4 q^{43} - 18 q^{49} - q^{51} - 6 q^{57} + 36 q^{61} - 19 q^{63} - 30 q^{67} - 54 q^{73} + 7 q^{81} - 81 q^{87} + 20 q^{91} + 34 q^{93} - 30 q^{99}+O(q^{100}) $ 16 * q - 3 * q^3 - 6 * q^7 - 9 * q^9 - 18 * q^19 - 11 * q^21 - 18 * q^31 - 12 * q^33 + 6 * q^37 + 12 * q^39 - 4 * q^43 - 18 * q^49 - q^51 - 6 * q^57 + 36 * q^61 - 19 * q^63 - 30 * q^67 - 54 * q^73 + 7 * q^81 - 81 * q^87 + 20 * q^91 + 34 * q^93 - 30 * 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
$3$	0.417865	−	1.68089i	0.241255	−	0.970462i
$3$	0.417865	−	1.68089i	0.241255	−	0.970462i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.25338	−	2.33003i	−0.473732	−	0.880669i
$7$	−1.25338	−	2.33003i	−0.473732	−	0.880669i
$8$		0			0
$9$	−2.65078	−	1.40477i	−0.883592	−	0.468257i
$10$		0			0
$11$	4.63831	−	2.67793i	1.39850	−	0.807426i	0.404268	−	0.914641i	$-0.367526\pi$
$11$	4.63831	−	2.67793i	1.39850	−	0.807426i	0.994236	+	0.107214i	$0.0341931\pi$
$12$		0			0
$13$			4.13670i			1.14732i	0.819095	+	0.573658i	$0.194476\pi$
$13$			4.13670i			1.14732i	−0.819095	+	0.573658i	$0.805524\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.0773793	−	0.134025i	−0.0187672	−	0.0325058i	0.856489	−	0.516165i	$-0.172641\pi$
$17$	−0.0773793	−	0.134025i	−0.0187672	−	0.0325058i	−0.875257	+	0.483659i	$0.839307\pi$
$18$		0			0
$19$	−3.40485	−	1.96579i	−0.781126	−	0.450983i	0.0557031	−	0.998447i	$-0.482260\pi$
$19$	−3.40485	−	1.96579i	−0.781126	−	0.450983i	−0.836829	+	0.547464i	$0.815593\pi$
$20$		0			0
$21$	−4.44027	+	1.13315i	−0.968946	+	0.247273i
$22$		0			0
$23$	−5.19273	−	2.99803i	−1.08276	−	0.625132i	−0.151120	−	0.988515i	$-0.548288\pi$
$23$	−5.19273	−	2.99803i	−1.08276	−	0.625132i	−0.931640	+	0.363384i	$0.881621\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.46893	+	3.86866i	−0.667596	+	0.744524i
$28$		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
$33$	−2.56312	−	8.91550i	−0.446181	−	1.55199i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−5.24072	+	9.07719i	−0.861569	+	1.49228i	0.00884571	+	0.999961i	$0.497184\pi$
$37$	−5.24072	+	9.07719i	−0.861569	+	1.49228i	−0.870414	+	0.492320i	$0.836149\pi$
$38$		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
$43$	1.78236			0.271807			0.135903	−	0.990722i	$-0.456606\pi$
$43$	1.78236			0.271807			0.135903	+	0.990722i	$0.456606\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.80118	−	3.11974i	0.262729	−	0.455061i	−0.704237	−	0.709965i	$-0.748711\pi$
$47$	1.80118	−	3.11974i	0.262729	−	0.455061i	0.966966	+	0.254905i	$0.0820440\pi$
$48$		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
$53$	4.29470	−	2.47955i	0.589923	−	0.340592i	−0.175144	−	0.984543i	$-0.556039\pi$
$53$	4.29470	−	2.47955i	0.589923	−	0.340592i	0.765067	+	0.643951i	$0.222706\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−4.72705	+	4.90174i	−0.626112	+	0.649251i
$58$		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
$63$	0.0492651	+	7.93710i	0.00620682	+	0.999981i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	0.444690	+	0.770225i	0.0543275	+	0.0940980i	0.891910	−	0.452213i	$-0.149365\pi$
$67$	0.444690	+	0.770225i	0.0543275	+	0.0940980i	−0.837583	+	0.546311i	$0.816032\pi$
$68$		0			0
$69$	−7.20921	+	7.47564i	−0.867887	+	0.899961i
$70$		0			0
$71$			11.6200i			1.37904i	0.724269	+	0.689518i	$0.242178\pi$
$71$			11.6200i			1.37904i	−0.724269	+	0.689518i	$0.757822\pi$
$72$		0			0
$73$	−10.6097	+	6.12550i	−1.24177	+	0.716935i	−0.969454	−	0.245273i	$-0.921122\pi$
$73$	−10.6097	+	6.12550i	−1.24177	+	0.716935i	−0.272314	+	0.962208i	$0.587789\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−12.0532	−	7.45095i	−1.37359	−	0.849115i
$78$		0			0
$79$	3.61147	−	6.25525i	0.406322	−	0.703770i	−0.588152	−	0.808750i	$-0.700144\pi$
$79$	3.61147	−	6.25525i	0.406322	−	0.703770i	0.994474	+	0.104980i	$0.0334778\pi$
$80$		0			0
$81$	5.05324	+	7.44747i	0.561471	+	0.827496i
$82$		0			0
$83$	−5.14180			−0.564386			−0.282193	−	0.959358i	$-0.591062\pi$
$83$	−5.14180			−0.564386			−0.282193	+	0.959358i	$0.591062\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−17.3383	−	4.31026i	−1.85886	−	0.462108i
$88$		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
$93$	−3.70279	−	12.8797i	−0.383962	−	1.33557i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	4.28309i		−	0.434882i	−0.976073	−	0.217441i	$-0.930229\pi$
$97$		−	4.28309i		−	0.434882i	0.976073	−	0.217441i	$-0.0697710\pi$
$98$		0			0
$99$	−16.0570	+	0.582836i	−1.61379	+	0.0585772i
$100$		0			0
$101$	3.04794	+	5.27919i	0.303282	+	0.525299i	0.976877	−	0.213801i	$-0.0685844\pi$
$101$	3.04794	+	5.27919i	0.303282	+	0.525299i	−0.673596	+	0.739100i	$0.735251\pi$
$102$		0			0
$103$	3.73132	+	2.15428i	0.367658	+	0.212267i	0.672435	−	0.740157i	$-0.265249\pi$
$103$	3.73132	+	2.15428i	0.367658	+	0.212267i	−0.304777	+	0.952424i	$0.598582\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−14.3579	−	8.28953i	−1.38803	−	0.801379i	−0.394936	−	0.918709i	$-0.629233\pi$
$107$	−14.3579	−	8.28953i	−1.38803	−	0.801379i	−0.993093	+	0.117330i	$0.962567\pi$
$108$		0			0
$109$	−1.92426	−	3.33292i	−0.184311	−	0.319236i	0.759033	−	0.651052i	$-0.225672\pi$
$109$	−1.92426	−	3.33292i	−0.184311	−	0.319236i	−0.943344	+	0.331816i	$0.892339\pi$
$110$		0			0
$111$	13.0678	+	12.6021i	1.24034	+	1.19614i
$112$		0			0
$113$		−	9.94281i		−	0.935341i	−0.883903	−	0.467671i	$-0.845093\pi$
$113$		−	9.94281i		−	0.935341i	0.883903	−	0.467671i	$-0.154907\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	5.81112	−	10.9655i	0.537238	−	1.01376i
$118$		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
$123$	−0.977287	+	3.93120i	−0.0881190	+	0.354464i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−4.64472			−0.412152			−0.206076	−	0.978536i	$-0.566069\pi$
$127$	−4.64472			−0.412152			−0.206076	+	0.978536i	$0.566069\pi$
$128$		0			0
$129$	0.744784	−	2.99594i	0.0655746	−	0.263778i
$130$		0			0
$131$	3.31417	−	5.74031i	0.289561	−	0.501534i	−0.684144	−	0.729347i	$-0.739824\pi$
$131$	3.31417	−	5.74031i	0.289561	−	0.501534i	0.973705	+	0.227813i	$0.0731575\pi$
$132$		0			0
$133$	−0.312794	+	10.3973i	−0.0271227	+	0.901559i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.08389	+	2.35783i	−0.348910	+	0.201443i	−0.664205	−	0.747550i	$-0.731230\pi$
$137$	−4.08389	+	2.35783i	−0.348910	+	0.201443i	0.315295	+	0.948994i	$0.397897\pi$
$138$		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
$143$	11.0778	+	19.1873i	0.926373	+	1.60452i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	8.20560	+	8.92570i	0.676787	+	0.736179i
$148$		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
$153$	0.0168412	+	0.463970i	0.00136153	+	0.0375098i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	5.89957	−	3.40612i	0.470837	−	0.271838i	−0.245753	−	0.969332i	$-0.579035\pi$
$157$	5.89957	−	3.40612i	0.470837	−	0.271838i	0.716590	+	0.697495i	$0.245702\pi$
$158$		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
$163$	−3.95589	+	6.85180i	−0.309849	+	0.536674i	−0.978329	−	0.207056i	$-0.933612\pi$
$163$	−3.95589	+	6.85180i	−0.309849	+	0.536674i	0.668480	+	0.743730i	$0.266945\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	19.2507			1.48966			0.744832	−	0.667252i	$-0.232530\pi$
$167$	19.2507			1.48966			0.744832	+	0.667252i	$0.232530\pi$
$168$		0			0
$169$	−4.11232			−0.316332
$170$		0			0
$171$	6.26402	+	9.99391i	0.479021	+	0.764253i
$172$		0			0
$173$	7.07129	−	12.2478i	0.537621	−	0.931186i	−0.461411	−	0.887186i	$-0.652657\pi$
$173$	7.07129	−	12.2478i	0.537621	−	0.931186i	0.999032	−	0.0439995i	$-0.0140100\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−17.5455	+	5.04416i	−1.31880	+	0.379142i
$178$		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
$183$	−4.52043	+	4.68749i	−0.334160	+	0.346509i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.717819	−	0.414433i	−0.0524921	−	0.0303063i
$188$		0			0
$189$	13.3620	+	3.23383i	0.971941	+	0.235226i
$190$		0			0
$191$	−2.00687	−	1.15867i	−0.145212	−	0.0838383i	0.425634	−	0.904896i	$-0.360051\pi$
$191$	−2.00687	−	1.15867i	−0.145212	−	0.0838383i	−0.570846	+	0.821057i	$0.693385\pi$
$192$		0			0
$193$	−8.93203	−	15.4707i	−0.642942	−	1.11361i	−0.984773	−	0.173846i	$-0.944380\pi$
$193$	−8.93203	−	15.4707i	−0.642942	−	1.11361i	0.341831	−	0.939761i	$-0.388953\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	18.3849i		−	1.30987i	−0.755685	−	0.654936i	$-0.772696\pi$
$197$		−	18.3849i		−	1.30987i	0.755685	−	0.654936i	$-0.227304\pi$
$198$		0			0
$199$	−1.70763	+	0.985902i	−0.121051	+	0.0698887i	−0.559303	−	0.828963i	$-0.688931\pi$
$199$	−1.70763	+	0.985902i	−0.121051	+	0.0698887i	0.438252	+	0.898852i	$0.355598\pi$
$200$		0			0
$201$	1.48048	−	0.425624i	0.104425	−	0.0300212i
$202$		0			0
$203$	−24.0342	+	12.9285i	−1.68687	+	0.907405i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	9.55324	+	15.2417i	0.663996	+	1.05937i
$208$		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
$213$	19.5319	+	4.85558i	1.33830	+	0.332699i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−17.4126	−	10.7640i	−1.18205	−	0.730707i
$218$		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
$223$			15.3841i			1.03020i	0.857131	+	0.515099i	$0.172245\pi$
$223$			15.3841i			1.03020i	−0.857131	+	0.515099i	$0.827755\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.975410	+	1.68946i	0.0647402	+	0.112133i	0.896579	−	0.442884i	$-0.146045\pi$
$227$	0.975410	+	1.68946i	0.0647402	+	0.112133i	−0.831838	+	0.555018i	$0.812711\pi$
$228$		0			0
$229$	2.44750	+	1.41307i	0.161735	+	0.0933780i	0.578683	−	0.815553i	$-0.303567\pi$
$229$	2.44750	+	1.41307i	0.161735	+	0.0933780i	−0.416948	+	0.908930i	$0.636900\pi$
$230$		0			0
$231$	−17.5608	+	17.1466i	−1.15542	+	1.12817i
$232$		0			0
$233$	−3.80293	−	2.19563i	−0.249139	−	0.143840i	0.370231	−	0.928940i	$-0.379278\pi$
$233$	−3.80293	−	2.19563i	−0.249139	−	0.143840i	−0.619370	+	0.785099i	$0.712612\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−9.00527	−	8.68433i	−0.584955	−	0.564108i
$238$		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
$243$	14.6299	−	5.38190i	0.938511	−	0.345249i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	8.13190	−	14.0849i	0.517420	−	0.896198i
$248$		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
$253$	−32.1140			−2.01899
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.85563	+	15.3384i	−0.552399	+	0.956784i	0.445702	+	0.895182i	$0.352954\pi$
$257$	−8.85563	+	15.3384i	−0.552399	+	0.956784i	−0.998101	+	0.0616020i	$0.980379\pi$
$258$		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
$263$	−4.84912	+	2.79964i	−0.299010	+	0.172633i	−0.641998	−	0.766706i	$-0.721894\pi$
$263$	−4.84912	+	2.79964i	−0.299010	+	0.172633i	0.342988	+	0.939340i	$0.388561\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	21.4051	+	20.6422i	1.30997	+	1.26328i
$268$		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
$273$	−4.68750	−	18.3681i	−0.283701	−	1.11169i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−5.26868	−	9.12563i	−0.316565	−	0.548306i	0.663204	−	0.748438i	$-0.269196\pi$
$277$	−5.26868	−	9.12563i	−0.316565	−	0.548306i	−0.979769	+	0.200133i	$0.935863\pi$
$278$		0			0
$279$	−23.1967	+	0.841992i	−1.38875	+	0.0504087i
$280$		0			0
$281$		−	19.2208i		−	1.14662i	−0.819339	−	0.573309i	$-0.805660\pi$
$281$		−	19.2208i		−	1.14662i	0.819339	−	0.573309i	$-0.194340\pi$
$282$		0			0
$283$	15.5733	−	8.99126i	0.925738	−	0.534475i	0.0402770	−	0.999189i	$-0.487176\pi$
$283$	15.5733	−	8.99126i	0.925738	−	0.534475i	0.885461	+	0.464713i	$0.153843\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.93135	+	5.44939i	0.173032	+	0.321667i
$288$		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
$293$	25.2153			1.47309			0.736546	−	0.676388i	$-0.236456\pi$
$293$	25.2153			1.47309			0.736546	+	0.676388i	$0.236456\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−5.72998	+	27.2336i	−0.332487	+	1.58025i
$298$		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
$303$	10.1474	−	2.91726i	0.582951	−	0.167592i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	8.28693i		−	0.472960i	−0.971636	−	0.236480i	$-0.924006\pi$
$307$		−	8.28693i		−	0.472960i	0.971636	−	0.236480i	$-0.0759938\pi$
$308$		0			0
$309$	5.18029	−	5.37173i	0.294696	−	0.305587i
$310$		0			0
$311$	4.28958	+	7.42977i	0.243240	+	0.421304i	0.961635	−	0.274331i	$-0.0884564\pi$
$311$	4.28958	+	7.42977i	0.243240	+	0.421304i	−0.718395	+	0.695635i	$0.755123\pi$
$312$		0			0
$313$	0.807839	+	0.466406i	0.0456617	+	0.0263628i	0.522657	−	0.852543i	$-0.324941\pi$
$313$	0.807839	+	0.466406i	0.0456617	+	0.0263628i	−0.476995	+	0.878906i	$0.658274\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.58262	+	1.49108i	0.145054	+	0.0837472i	0.570771	−	0.821109i	$-0.306645\pi$
$317$	2.58262	+	1.49108i	0.145054	+	0.0837472i	−0.425716	+	0.904857i	$0.639978\pi$
$318$		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
$323$			0.608446i			0.0338549i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−6.40636	+	1.84176i	−0.354272	+	0.101850i
$328$		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
$333$	26.6433	−	16.6996i	1.46005	−	0.915133i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	36.4696			1.98663			0.993314	−	0.115448i	$-0.0368304\pi$
$337$	36.4696			1.98663			0.993314	+	0.115448i	$0.0368304\pi$
$338$		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
$343$	18.4449	+	1.66873i	0.995932	+	0.0901031i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.62881	+	2.09509i	−0.194805	+	0.112471i	−0.594230	−	0.804295i	$-0.702543\pi$
$347$	−3.62881	+	2.09509i	−0.194805	+	0.112471i	0.399425	+	0.916766i	$0.369210\pi$
$348$		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
$353$	−8.72220	−	15.1073i	−0.464236	−	0.804080i	0.534931	−	0.844896i	$-0.320338\pi$
$353$	−8.72220	−	15.1073i	−0.464236	−	0.804080i	−0.999167	+	0.0408157i	$0.987004\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	0.495455	+	0.507424i	0.0262223	+	0.0268557i
$358$		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
$363$	−22.0493	−	21.2634i	−1.15729	−	1.11604i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	23.1633	−	13.3734i	1.20912	−	0.698084i	0.246550	−	0.969130i	$-0.420703\pi$
$367$	23.1633	−	13.3734i	1.20912	−	0.698084i	0.962566	+	0.271046i	$0.0873696\pi$
$368$		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
$373$	2.56718	−	4.44649i	0.132924	−	0.230231i	−0.791879	−	0.610678i	$-0.790897\pi$
$373$	2.56718	−	4.44649i	0.132924	−	0.230231i	0.924802	+	0.380448i	$0.124230\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	42.6699			2.19761
$378$		0			0
$379$	−17.3320			−0.890284			−0.445142	−	0.895460i	$-0.646847\pi$
$379$	−17.3320			−0.890284			−0.445142	+	0.895460i	$0.646847\pi$
$380$		0			0
$381$	−1.94087	+	7.80726i	−0.0994336	+	0.399978i
$382$		0			0
$383$	10.8457	−	18.7852i	0.554188	−	0.959881i	−0.443779	−	0.896136i	$-0.646362\pi$
$383$	10.8457	−	18.7852i	0.554188	−	0.959881i	0.997966	−	0.0637447i	$-0.0203043\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−4.72463	−	2.50380i	−0.240166	−	0.127275i
$388$		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
$393$	−8.26396	−	7.96943i	−0.416861	−	0.402005i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	11.8800	+	6.85891i	0.596240	+	0.344239i	0.767561	−	0.640976i	$-0.221470\pi$
$397$	11.8800	+	6.85891i	0.596240	+	0.344239i	−0.171321	+	0.985215i	$0.554804\pi$
$398$		0			0
$399$	17.3460	+	4.87044i	0.868385	+	0.243827i
$400$		0			0
$401$	−16.4976	−	9.52487i	−0.823849	−	0.475649i	0.0278932	−	0.999611i	$-0.491120\pi$
$401$	−16.4976	−	9.52487i	−0.823849	−	0.475649i	−0.851742	+	0.523962i	$0.824453\pi$
$402$		0			0
$403$	16.0035	+	27.7189i	0.797191	+	1.38078i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			56.1371i			2.78261i
$408$		0			0
$409$	30.1428	−	17.4030i	1.49047	−	0.860521i	0.490526	−	0.871427i	$-0.336805\pi$
$409$	30.1428	−	17.4030i	1.49047	−	0.860521i	0.999941	+	0.0109054i	$0.00347135\pi$
$410$		0			0
$411$	2.25674	+	7.84982i	0.111317	+	0.387203i
$412$		0			0
$413$	−14.6633	+	23.7205i	−0.721535	+	1.16721i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	16.0739	+	3.99593i	0.787142	+	0.195682i
$418$		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
$423$	−9.15705	+	5.73949i	−0.445231	+	0.279063i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−0.299122	+	9.94282i	−0.0144755	+	0.481167i
$428$		0			0
$429$	36.8808	−	10.6029i	1.78062	−	0.511910i
$430$		0			0
$431$	−9.22781	+	5.32768i	−0.444488	+	0.256625i	−0.705499	−	0.708711i	$-0.749277\pi$
$431$	−9.22781	+	5.32768i	−0.444488	+	0.256625i	0.261012	+	0.965336i	$0.415944\pi$
$432$		0			0
$433$			25.5027i			1.22558i	0.790245	+	0.612791i	$0.209953\pi$
$433$			25.5027i			1.22558i	−0.790245	+	0.612791i	$0.790047\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	11.7870	+	20.4157i	0.563848	+	0.976613i
$438$		0			0
$439$	23.8206	+	13.7528i	1.13689	+	0.656386i	0.945660	−	0.325158i	$-0.105418\pi$
$439$	23.8206	+	13.7528i	1.13689	+	0.656386i	0.191234	+	0.981544i	$0.438751\pi$
$440$		0			0
$441$	18.4319	−	10.0630i	0.877712	−	0.479189i
$442$		0			0
$443$	16.7785	+	9.68708i	0.797171	+	0.460247i	0.842481	−	0.538726i	$-0.181094\pi$
$443$	16.7785	+	9.68708i	0.797171	+	0.460247i	−0.0453099	+	0.998973i	$0.514428\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	24.4816	−	25.3864i	1.15794	−	1.20073i
$448$		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
$453$	−18.9566	+	5.44983i	−0.890660	+	0.256056i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	9.18704	−	15.9124i	0.429752	−	0.744352i	−0.567099	−	0.823649i	$-0.691934\pi$
$457$	9.18704	−	15.9124i	0.429752	−	0.744352i	0.996851	+	0.0792977i	$0.0252678\pi$
$458$		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
$463$	11.4136			0.530433			0.265217	−	0.964189i	$-0.414556\pi$
$463$	11.4136			0.530433			0.265217	+	0.964189i	$0.414556\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	0.665893	−	1.15336i	0.0308138	−	0.0533711i	−0.850207	−	0.526448i	$-0.823523\pi$
$467$	0.665893	−	1.15336i	0.0308138	−	0.0533711i	0.881021	+	0.473077i	$0.156857\pi$
$468$		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
$473$	8.26712	−	4.77302i	0.380123	−	0.219464i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−14.8675	+	0.539659i	−0.680736	+	0.0247093i
$478$		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
$483$	26.4543	+	7.42790i	1.20371	+	0.337981i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−13.8630	−	24.0115i	−0.628195	−	1.08807i	−0.987914	−	0.155004i	$-0.950461\pi$
$487$	−13.8630	−	24.0115i	−0.628195	−	1.08807i	0.359719	−	0.933061i	$-0.382873\pi$
$488$		0			0
$489$	9.86409	+	9.51254i	0.446070	+	0.430172i
$490$		0			0
$491$		−	0.536100i		−	0.0241938i	−0.999927	−	0.0120969i	$-0.996149\pi$
$491$		−	0.536100i		−	0.0241938i	0.999927	−	0.0120969i	$-0.00385066\pi$
$492$		0			0
$493$	−1.38246	+	0.798164i	−0.0622629	+	0.0359475i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	27.0749	−	14.5642i	1.21447	−	0.653293i
$498$		0			0
$499$	15.1191	−	26.1870i	0.676823	−	1.17229i	−0.299110	−	0.954219i	$-0.596690\pi$
$499$	15.1191	−	26.1870i	0.676823	−	1.17229i	0.975933	−	0.218072i	$-0.0699769\pi$
$500$		0			0
$501$	8.04420	−	32.3583i	0.359388	−	1.44566i
$502$		0			0
$503$	−32.5176			−1.44989			−0.724945	−	0.688807i	$-0.758135\pi$
$503$	−32.5176			−1.44989			−0.724945	+	0.688807i	$0.758135\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.71839	+	6.91235i	−0.0763166	+	0.306988i
$508$		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
$513$	19.4162	−	6.35301i	0.857245	−	0.280492i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	19.2938i		−	0.848538i
$518$		0			0
$519$	−17.6324	−	17.0040i	−0.773977	−	0.746393i
$520$		0			0
$521$	−5.39842	−	9.35035i	−0.236509	−	0.409646i	0.723201	−	0.690638i	$-0.242670\pi$
$521$	−5.39842	−	9.35035i	−0.236509	−	0.409646i	−0.959710	+	0.280992i	$0.909337\pi$
$522$		0			0
$523$	0.206455	+	0.119197i	0.00902764	+	0.00521211i	0.504507	−	0.863408i	$-0.331674\pi$
$523$	0.206455	+	0.119197i	0.00902764	+	0.00521211i	−0.495479	+	0.868620i	$0.665008\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.03699	−	0.598708i	−0.0451721	−	0.0260801i
$528$		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
$533$		−	9.67476i		−	0.419061i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.992498	+	3.45229i	0.0428294	+	0.148977i
$538$		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
$543$	−36.5427	−	9.08444i	−1.56820	−	0.389850i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	27.1549			1.16106			0.580529	−	0.814239i	$-0.302846\pi$
$547$	27.1549			1.16106			0.580529	+	0.814239i	$0.302846\pi$
$548$		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
$553$	−19.1015	−	0.574652i	−0.812277	−	0.0244367i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−20.7984	+	12.0080i	−0.881257	+	0.508794i	−0.871073	−	0.491154i	$-0.836575\pi$
$557$	−20.7984	+	12.0080i	−0.881257	+	0.508794i	−0.0101846	+	0.999948i	$0.503242\pi$
$558$		0			0
$559$			7.37308i			0.311848i
$560$		0			0
$561$	−0.996567	+	1.03340i	−0.0420751	+	0.0436300i
$562$		0			0
$563$	20.1487	+	34.8986i	0.849168	+	1.47080i	0.881952	+	0.471340i	$0.156229\pi$
$563$	20.1487	+	34.8986i	0.849168	+	1.47080i	−0.0327839	+	0.999462i	$0.510437\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	11.0192	−	21.1087i	0.462763	−	0.886482i
$568$		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
$573$	−2.78620	+	2.88916i	−0.116395	+	0.120697i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	25.5104	−	14.7284i	1.06201	−	0.613153i	0.136024	−	0.990706i	$-0.456568\pi$
$577$	25.5104	−	14.7284i	1.06201	−	0.613153i	0.925988	+	0.377552i	$0.123234\pi$
$578$		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
$583$	13.2801	−	23.0018i	0.550006	−	0.952638i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−45.9862			−1.89805			−0.949027	−	0.315195i	$-0.897930\pi$
$587$	−45.9862			−1.89805			−0.949027	+	0.315195i	$0.897930\pi$
$588$		0			0
$589$	−30.4199			−1.25343
$590$		0			0
$591$	−30.9030	−	7.68242i	−1.27118	−	0.316012i
$592$		0			0
$593$	−0.954084	+	1.65252i	−0.0391795	+	0.0678610i	−0.884950	−	0.465686i	$-0.845808\pi$
$593$	−0.954084	+	1.65252i	−0.0391795	+	0.0678610i	0.845771	+	0.533547i	$0.179141\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.943632	+	3.28231i	0.0386203	+	0.134336i
$598$		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
$603$	−0.0967842	−	2.66638i	−0.00394136	−	0.108583i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	15.4049	+	8.89399i	0.625264	+	0.360996i	0.778915	−	0.627129i	$-0.215770\pi$
$607$	15.4049	+	8.89399i	0.625264	+	0.360996i	−0.153652	+	0.988125i	$0.549103\pi$
$608$		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
$613$	−14.5074	−	25.1276i	−0.585950	−	1.01490i	−0.994756	−	0.102274i	$-0.967388\pi$
$613$	−14.5074	−	25.1276i	−0.585950	−	1.01490i	0.408806	−	0.912621i	$-0.365945\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	3.32967i		−	0.134047i	−0.997751	−	0.0670237i	$-0.978650\pi$
$617$		−	3.32967i		−	0.134047i	0.997751	−	0.0670237i	$-0.0213503\pi$
$618$		0			0
$619$	41.6135	−	24.0256i	1.67259	−	0.965669i	0.706406	−	0.707806i	$-0.250315\pi$
$619$	41.6135	−	24.0256i	1.67259	−	0.965669i	0.966182	−	0.257863i	$-0.0830182\pi$
$620$		0			0
$621$	29.6116	−	9.68897i	1.18827	−	0.388805i
$622$		0			0
$623$	45.4032	+	1.36592i	1.81904	+	0.0547244i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−8.79899	+	35.3945i	−0.351398	+	1.41352i
$628$		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
$633$	0.451160	−	1.81482i	0.0179320	−	0.0721327i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−24.1617	−	15.9598i	−0.957322	−	0.632350i
$638$		0			0
$639$	16.3234	−	30.8019i	0.645743	−	1.21851i
$640$		0			0
$641$	3.34785	−	1.93288i	0.132232	−	0.0763443i	−0.432425	−	0.901670i	$-0.642342\pi$
$641$	3.34785	−	1.93288i	0.132232	−	0.0763443i	0.564657	+	0.825326i	$0.309009\pi$
$642$		0			0
$643$			37.7423i			1.48841i	0.667950	+	0.744206i	$0.267172\pi$
$643$			37.7423i			1.48841i	−0.667950	+	0.744206i	$0.732828\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−10.9230	−	18.9193i	−0.429429	−	0.743793i	0.567393	−	0.823447i	$-0.307952\pi$
$647$	−10.9230	−	18.9193i	−0.429429	−	0.743793i	−0.996823	+	0.0796536i	$0.974619\pi$
$648$		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
$653$	3.14321	+	1.81473i	0.123003	+	0.0710159i	0.560239	−	0.828331i	$-0.310709\pi$
$653$	3.14321	+	1.81473i	0.123003	+	0.0710159i	−0.437236	+	0.899347i	$0.644043\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	36.7288	−	1.33318i	1.43293	−	0.0520123i
$658$		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
$663$	−0.306371	−	1.06568i	−0.0118985	−	0.0413875i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−30.9245	+	53.5628i	−1.19740	+	2.07396i
$668$		0			0
$669$	25.8590	+	6.42849i	0.999767	+	0.248540i
$670$		0			0
$671$	−20.1366			−0.777365
$672$		0			0
$673$	8.84031			0.340769			0.170385	−	0.985378i	$-0.445499\pi$
$673$	8.84031			0.340769			0.170385	+	0.985378i	$0.445499\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	7.82417	−	13.5519i	0.300707	−	0.520840i	−0.675589	−	0.737278i	$-0.736111\pi$
$677$	7.82417	−	13.5519i	0.300707	−	0.520840i	0.976296	+	0.216438i	$0.0694439\pi$
$678$		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
$683$	32.7691	−	18.9193i	1.25388	−	0.723926i	0.281999	−	0.959415i	$-0.409002\pi$
$683$	32.7691	−	18.9193i	1.25388	−	0.723926i	0.971877	+	0.235489i	$0.0756691\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	3.39793	−	3.52351i	0.129639	−	0.134430i
$688$		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
$693$	21.4835	+	36.6828i	0.816091	+	1.39347i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	0.180972	+	0.313452i	0.00685480	+	0.0118729i
$698$		0			0
$699$	−5.27972	+	5.47484i	−0.199697	+	0.207077i
$700$		0			0
$701$		−	28.2554i		−	1.06719i	−0.845740	−	0.533596i	$-0.820840\pi$
$701$		−	28.2554i		−	1.06719i	0.845740	−	0.533596i	$-0.179160\pi$
$702$		0			0
$703$	35.6877	−	20.6043i	1.34599	−	0.777106i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	8.48046	−	13.7186i	0.318940	−	0.515942i
$708$		0			0
$709$	−7.40632	+	12.8281i	−0.278150	+	0.481770i	−0.970925	−	0.239384i	$-0.923055\pi$
$709$	−7.40632	+	12.8281i	−0.278150	+	0.481770i	0.692775	+	0.721154i	$0.256388\pi$
$710$		0			0
$711$	−18.3604	+	11.5080i	−0.688568	+	0.431583i
$712$		0			0
$713$	−46.3934			−1.73744
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−29.7053	−	7.38467i	−1.10937	−	0.275786i
$718$		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
$723$	2.03990	+	7.09555i	0.0758646	+	0.263886i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	2.81854i		−	0.104534i	−0.998633	−	0.0522670i	$-0.983355\pi$
$727$		−	2.81854i		−	0.104534i	0.998633	−	0.0522670i	$-0.0166447\pi$
$728$		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
$733$	−30.2169	−	17.4457i	−1.11609	−	0.644372i	−0.175687	−	0.984446i	$-0.556215\pi$
$733$	−30.2169	−	17.4457i	−1.11609	−	0.644372i	−0.940399	+	0.340074i	$0.889548\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.12522	+	2.38170i	0.151954	+	0.0877309i
$738$		0			0
$739$	13.4220	+	23.2476i	0.493737	+	0.855177i	0.999974	−	0.00721695i	$-0.00229725\pi$
$739$	13.4220	+	23.2476i	0.493737	+	0.855177i	−0.506237	+	0.862394i	$0.668964\pi$
$740$		0			0
$741$	−20.2770	−	19.5544i	−0.744896	−	0.718348i
$742$		0			0
$743$		−	2.24499i		−	0.0823607i	−0.999152	−	0.0411804i	$-0.986888\pi$
$743$		−	2.24499i		−	0.0823607i	0.999152	−	0.0411804i	$-0.0131118\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	13.6298	+	7.22305i	0.498687	+	0.264277i
$748$		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
$753$	−1.62056	+	6.51882i	−0.0590566	+	0.237559i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	25.5473			0.928532			0.464266	−	0.885696i	$-0.346318\pi$
$757$	25.5473			0.928532			0.464266	+	0.885696i	$0.346318\pi$
$758$		0			0
$759$	−13.4193	+	53.9801i	−0.487091	+	1.95935i
$760$		0			0
$761$	−2.16163	+	3.74406i	−0.0783591	+	0.135722i	−0.902542	−	0.430602i	$-0.858301\pi$
$761$	−2.16163	+	3.74406i	−0.0783591	+	0.135722i	0.824183	+	0.566324i	$0.191635\pi$
$762$		0			0
$763$	−5.35399	+	8.66100i	−0.193827	+	0.313549i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	37.7603	−	21.8009i	1.36344	−	0.787185i
$768$		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
$773$	−5.19273	−	8.99408i	−0.186770	−	0.323494i	0.757402	−	0.652949i	$-0.226468\pi$
$773$	−5.19273	−	8.99408i	−0.186770	−	0.323494i	−0.944171	+	0.329455i	$0.893135\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	12.9844	−	46.2437i	0.465812	−	1.65898i
$778$		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
$783$	39.9050	+	35.7819i	1.42609	+	1.27874i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−37.1681	+	21.4590i	−1.32490	+	0.764931i	−0.984506	−	0.175352i	$-0.943894\pi$
$787$	−37.1681	+	21.4590i	−1.32490	+	0.764931i	−0.340394	+	0.940283i	$0.610560\pi$
$788$		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
$793$	7.77645	−	13.4692i	0.276150	−	0.478306i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	19.3628			0.685866			0.342933	−	0.939360i	$-0.388580\pi$
$797$	19.3628			0.685866			0.342933	+	0.939360i	$0.388580\pi$
$798$		0			0
$799$	−0.557497			−0.0197228
$800$		0			0
$801$	43.6417	−	27.3539i	1.54200	−	0.966503i
$802$		0			0
$803$	−32.8073	+	56.8239i	−1.15774	+	2.00527i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	28.4097	−	8.16749i	1.00007	−	0.287509i
$808$		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
$813$	20.5002	−	21.2578i	0.718973	−	0.745543i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−6.06865	−	3.50374i	−0.212315	−	0.122580i
$818$		0			0
$819$	−32.8334	+	0.203795i	−1.14729	+	0.00712118i
$820$		0			0
$821$	39.9212	+	23.0485i	1.39326	+	0.804400i	0.993675	−	0.112296i	$-0.0358204\pi$
$821$	39.9212	+	23.0485i	1.39326	+	0.804400i	0.399586	+	0.916696i	$0.369154\pi$
$822$		0			0
$823$	−11.2425	−	19.4726i	−0.391889	−	0.678772i	0.600809	−	0.799392i	$-0.294845\pi$
$823$	−11.2425	−	19.4726i	−0.391889	−	0.678772i	−0.992699	+	0.120620i	$0.961512\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			52.2536i			1.81704i	0.417846	+	0.908518i	$0.362785\pi$
$827$			52.2536i			1.81704i	−0.417846	+	0.908518i	$0.637215\pi$
$828$		0			0
$829$	3.26705	−	1.88623i	0.113469	−	0.0655115i	−0.442191	−	0.896921i	$-0.645799\pi$
$829$	3.26705	−	1.88623i	0.113469	−	0.0655115i	0.555661	+	0.831409i	$0.312465\pi$
$830$		0			0
$831$	−17.5408	+	5.04279i	−0.608483	+	0.174933i
$832$		0			0
$833$	1.08135	+	0.0651222i	0.0374666	+	0.00225635i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−8.27779	+	39.3429i	−0.286122	+	1.35989i
$838$		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
$843$	−32.3081	−	8.03171i	−1.11275	−	0.276627i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−46.7696	−	1.40703i	−1.60702	−	0.0483460i
$848$		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
$853$		−	3.21298i		−	0.110010i	−0.998486	−	0.0550051i	$-0.982482\pi$
$853$		−	3.21298i		−	0.110010i	0.998486	−	0.0550051i	$-0.0175175\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−24.0555	−	41.6653i	−0.821720	−	1.42326i	−0.904400	−	0.426685i	$-0.859681\pi$
$857$	−24.0555	−	41.6653i	−0.821720	−	1.42326i	0.0826803	−	0.996576i	$-0.473652\pi$
$858$		0			0
$859$	10.4266	+	6.01978i	0.355750	+	0.205392i	0.667215	−	0.744865i	$-0.267486\pi$
$859$	10.4266	+	6.01978i	0.355750	+	0.205392i	−0.311465	+	0.950258i	$0.600820\pi$
$860$		0			0
$861$	10.3847	−	2.65017i	0.353911	−	0.0903174i
$862$		0			0
$863$	6.51239	+	3.75993i	0.221684	+	0.127989i	0.606730	−	0.794908i	$-0.292481\pi$
$863$	6.51239	+	3.75993i	0.221684	+	0.127989i	−0.385046	+	0.922898i	$0.625814\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−21.1651	−	20.4108i	−0.718803	−	0.693186i
$868$		0			0
$869$		−	38.6851i		−	1.31230i
$870$		0			0
$871$	−3.18619	+	1.83955i	−0.107960	+	0.0623308i
$872$		0			0
$873$	−6.01676	+	11.3535i	−0.203636	+	0.384259i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−16.6367	+	28.8156i	−0.561781	+	0.973033i	0.435560	+	0.900160i	$0.356550\pi$
$877$	−16.6367	+	28.8156i	−0.561781	+	0.973033i	−0.997341	+	0.0728736i	$0.976783\pi$
$878$		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
$883$	−51.3120			−1.72679			−0.863393	−	0.504533i	$-0.831665\pi$
$883$	−51.3120			−1.72679			−0.863393	+	0.504533i	$0.831665\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	9.94659	−	17.2280i	0.333974	−	0.578460i	−0.649313	−	0.760521i	$-0.724944\pi$
$887$	9.94659	−	17.2280i	0.333974	−	0.578460i	0.983287	+	0.182061i	$0.0582770\pi$
$888$		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
$893$	−12.2655	+	7.08149i	−0.410450	+	0.236973i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−30.9245	−	29.8224i	−1.03254	−	0.995740i
$898$		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
$903$	−7.91414	+	2.01967i	−0.263366	+	0.0672106i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−21.4200	−	37.1005i	−0.711239	−	1.23190i	−0.964392	−	0.264476i	$-0.914801\pi$
$907$	−21.4200	−	37.1005i	−0.711239	−	1.23190i	0.253153	−	0.967426i	$-0.418532\pi$
$908$		0			0
$909$	−0.663367	−	18.2756i	−0.0220025	−	0.606164i
$910$		0			0
$911$		−	28.5359i		−	0.945437i	−0.881213	−	0.472719i	$-0.843273\pi$
$911$		−	28.5359i		−	0.945437i	0.881213	−	0.472719i	$-0.156727\pi$
$912$		0			0
$913$	−23.8493	+	13.7694i	−0.789296	+	0.455700i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−17.5290	−	0.527347i	−0.578859	−	0.0174145i
$918$		0			0
$919$	4.41160	−	7.64112i	0.145525	−	0.252057i	−0.784043	−	0.620706i	$-0.786846\pi$
$919$	4.41160	−	7.64112i	0.145525	−	0.252057i	0.929569	+	0.368649i	$0.120179\pi$
$920$		0			0
$921$	−13.9294	−	3.46282i	−0.458990	−	0.114104i
$922$		0			0
$923$	−48.0683			−1.58219
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−6.86463	−	10.9521i	−0.225464	−	0.359716i
$928$		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
$933$	14.2811	−	4.10567i	0.467542	−	0.134414i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			16.3198i			0.533144i	0.963815	+	0.266572i	$0.0858911\pi$
$937$			16.3198i			0.533144i	−0.963815	+	0.266572i	$0.914109\pi$
$938$		0			0
$939$	1.12154	−	1.16299i	0.0366002	−	0.0379528i
$940$		0			0
$941$	3.80594	+	6.59208i	0.124070	+	0.214896i	0.921369	−	0.388689i	$-0.127072\pi$
$941$	3.80594	+	6.59208i	0.124070	+	0.214896i	−0.797299	+	0.603585i	$0.793739\pi$
$942$		0			0
$943$	12.1446	+	7.01167i	0.395481	+	0.228331i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−19.9034	−	11.4912i	−0.646774	−	0.373415i	0.140445	−	0.990088i	$-0.455147\pi$
$947$	−19.9034	−	11.4912i	−0.646774	−	0.373415i	−0.787219	+	0.616673i	$0.788480\pi$
$948$		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
$953$		−	40.5633i		−	1.31397i	−0.753902	−	0.656986i	$-0.771831\pi$
$953$		−	40.5633i		−	1.31397i	0.753902	−	0.656986i	$-0.228169\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−91.9630	+	26.4384i	−2.97274	+	0.854633i
$958$		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
$963$	26.4147	+	42.1432i	0.851201	+	1.35805i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−3.10140			−0.0997343			−0.0498672	−	0.998756i	$-0.515880\pi$
$967$	−3.10140			−0.0997343			−0.0498672	+	0.998756i	$0.515880\pi$
$968$		0			0
$969$	1.02273	+	0.254249i	0.0328549	+	0.00816764i
$970$		0			0
$971$	−22.5212	+	39.0078i	−0.722739	+	1.25182i	0.237159	+	0.971471i	$0.423784\pi$
$971$	−22.5212	+	39.0078i	−0.722739	+	1.25182i	−0.959898	+	0.280350i	$0.909550\pi$
$972$		0			0
$973$	22.2815	−	11.9857i	0.714311	−	0.384244i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−21.8598	+	12.6207i	−0.699356	+	0.403773i	−0.807108	−	0.590404i	$-0.798968\pi$
$977$	−21.8598	+	12.6207i	−0.699356	+	0.403773i	0.107751	+	0.994178i	$0.465635\pi$
$978$		0			0
$979$			91.9525i			2.93881i
$980$		0			0
$981$	0.418805	+	11.5380i	0.0133714	+	0.368379i
$982$		0			0
$983$	−30.1759	−	52.2661i	−0.962461	−	1.66703i	−0.716288	−	0.697805i	$-0.754160\pi$
$983$	−30.1759	−	52.2661i	−0.962461	−	1.66703i	−0.246173	−	0.969226i	$-0.579173\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−4.46260	+	15.8935i	−0.142046	+	0.505895i
$988$		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
$993$	−27.3142	−	26.3408i	−0.866792	−	0.835900i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	23.3385	−	13.4745i	0.739138	−	0.426742i	−0.0826177	−	0.996581i	$-0.526328\pi$
$997$	23.3385	−	13.4745i	0.739138	−	0.426742i	0.821756	+	0.569840i	$0.192995\pi$
$998$		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.bi.l.1601.6	yes	16
3.2	odd	2	inner	2100.2.bi.l.1601.8	yes	16
5.2	odd	4		2100.2.bo.i.1349.2		32
5.3	odd	4		2100.2.bo.i.1349.15		32
5.4	even	2		2100.2.bi.m.1601.3	yes	16
7.3	odd	6	inner	2100.2.bi.l.101.8	yes	16
15.2	even	4		2100.2.bo.i.1349.10		32
15.8	even	4		2100.2.bo.i.1349.7		32
15.14	odd	2		2100.2.bi.m.1601.1	yes	16
21.17	even	6	inner	2100.2.bi.l.101.6	✓	16
35.3	even	12		2100.2.bo.i.1949.10		32
35.17	even	12		2100.2.bo.i.1949.7		32
35.24	odd	6		2100.2.bi.m.101.1	yes	16
105.17	odd	12		2100.2.bo.i.1949.15		32
105.38	odd	12		2100.2.bo.i.1949.2		32
105.59	even	6		2100.2.bi.m.101.3	yes	16

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.417865 - 1.68089i) q^{3} +(-1.25338 - 2.33003i) q^{7} +(-2.65078 - 1.40477i) q^{9} +O(q^{10})\)	\(q+(0.417865 - 1.68089i) q^{3} +(-1.25338 - 2.33003i) q^{7} +(-2.65078 - 1.40477i) q^{9} +(4.63831 - 2.67793i) q^{11} +4.13670i q^{13} +(-0.0773793 - 0.134025i) q^{17} +(-3.40485 - 1.96579i) q^{19} +(-4.44027 + 1.13315i) q^{21} +(-5.19273 - 2.99803i) q^{23} +(-3.46893 + 3.86866i) q^{27} -10.3150i q^{29} +(6.70071 - 3.86866i) q^{31} +(-2.56312 - 8.91550i) q^{33} +(-5.24072 + 9.07719i) q^{37} +(6.95334 + 1.72858i) q^{39} -2.33876 q^{41} +1.78236 q^{43} +(1.80118 - 3.11974i) q^{47} +(-3.85809 + 5.84082i) q^{49} +(-0.257615 + 0.0740617i) q^{51} +(4.29470 - 2.47955i) q^{53} +(-4.72705 + 4.90174i) q^{57} +(-5.27011 - 9.12810i) q^{59} +(-3.25602 - 1.87987i) q^{61} +(0.0492651 + 7.93710i) q^{63} +(0.444690 + 0.770225i) q^{67} +(-7.20921 + 7.47564i) q^{69} +11.6200i q^{71} +(-10.6097 + 6.12550i) q^{73} +(-12.0532 - 7.45095i) q^{77} +(3.61147 - 6.25525i) q^{79} +(5.05324 + 7.44747i) q^{81} -5.14180 q^{83} +(-17.3383 - 4.31026i) q^{87} +(-8.58428 + 14.8684i) q^{89} +(9.63865 - 5.18485i) q^{91} +(-3.70279 - 12.8797i) q^{93} -4.28309i q^{97} +(-16.0570 + 0.582836i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{3} - 6 q^{7} - 9 q^{9}+O(q^{10}) \) 16 * q - 3 * q^3 - 6 * q^7 - 9 * q^9	\( 16 q - 3 q^{3} - 6 q^{7} - 9 q^{9} - 18 q^{19} - 11 q^{21} - 18 q^{31} - 12 q^{33} + 6 q^{37} + 12 q^{39} - 4 q^{43} - 18 q^{49} - q^{51} - 6 q^{57} + 36 q^{61} - 19 q^{63} - 30 q^{67} - 54 q^{73} + 7 q^{81} - 81 q^{87} + 20 q^{91} + 34 q^{93} - 30 q^{99}+O(q^{100}) \) 16 * q - 3 * q^3 - 6 * q^7 - 9 * q^9 - 18 * q^19 - 11 * q^21 - 18 * q^31 - 12 * q^33 + 6 * q^37 + 12 * q^39 - 4 * q^43 - 18 * q^49 - q^51 - 6 * q^57 + 36 * q^61 - 19 * q^63 - 30 * q^67 - 54 * q^73 + 7 * q^81 - 81 * q^87 + 20 * q^91 + 34 * q^93 - 30 * q^99

Introduction

L-functions

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