LMFDB - Embedded newform 276.2.i.a.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(13,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("276.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.i (of order $11$, degree $10$, 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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} + 43 x^{18} - 165 x^{17} + 538 x^{16} - 1433 x^{15} + 3444 x^{14} - 7370 x^{13} + \cdots + 529 $ x^20 - 8x^19 + 43x^18 - 165x^17 + 538x^16 - 1433x^15 + 3444x^14 - 7370x^13 + 15500x^12 - 28190x^11 + 41920x^10 - 33520x^9 - 13837x^8 + 78980x^7 - 92652x^6 - 52852x^5 + 177374x^4 + 151360x^3 + 115323x^2 + 12834*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			73.1
Root			$0.302381 + 2.10310i$ of defining polynomial
Character	$\chi$	$=$	276.73
Dual form			276.2.i.a.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 + 0.281733i) q^{3} +(-1.52130 - 0.977682i) q^{5} +(0.485296 + 3.37531i) q^{7} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.959493 + 0.281733i) q^{3} +(-1.52130 - 0.977682i) q^{5} +(0.485296 + 3.37531i) q^{7} +(0.841254 - 0.540641i) q^{9} +(-0.800715 + 1.75332i) q^{11} +(-0.753988 + 5.24410i) q^{13} +(1.73512 + 0.509479i) q^{15} +(0.496392 + 0.572867i) q^{17} +(-3.10335 + 3.58146i) q^{19} +(-1.41657 - 3.10186i) q^{21} +(3.36166 + 3.42041i) q^{23} +(-0.718574 - 1.57346i) q^{25} +(-0.654861 + 0.755750i) q^{27} +(-2.79381 - 3.22422i) q^{29} +(3.28356 + 0.964142i) q^{31} +(0.274313 - 1.90789i) q^{33} +(2.56170 - 5.60934i) q^{35} +(-3.09318 + 1.98787i) q^{37} +(-0.753988 - 5.24410i) q^{39} +(-5.92232 - 3.80604i) q^{41} +(3.52444 - 1.03487i) q^{43} -1.80838 q^{45} +10.3519 q^{47} +(-4.44075 + 1.30392i) q^{49} +(-0.637680 - 0.409812i) q^{51} +(-1.11911 - 7.78361i) q^{53} +(2.93232 - 1.88449i) q^{55} +(1.96863 - 4.31070i) q^{57} +(-1.53778 + 10.6955i) q^{59} +(12.3748 + 3.63356i) q^{61} +(2.23309 + 2.57712i) q^{63} +(6.27411 - 7.24071i) q^{65} +(-2.57750 - 5.64394i) q^{67} +(-4.18913 - 2.33477i) q^{69} +(-6.14490 - 13.4555i) q^{71} +(4.97621 - 5.74285i) q^{73} +(1.13276 + 1.30728i) q^{75} +(-6.30658 - 1.85178i) q^{77} +(-0.905219 + 6.29594i) q^{79} +(0.415415 - 0.909632i) q^{81} +(-8.22677 + 5.28702i) q^{83} +(-0.195081 - 1.35682i) q^{85} +(3.58901 + 2.30651i) q^{87} +(-10.6954 + 3.14044i) q^{89} -18.0664 q^{91} -3.42219 q^{93} +(8.22267 - 2.41439i) q^{95} +(6.41054 + 4.11980i) q^{97} +(0.274313 + 1.90789i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9	$ 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9} - 22 q^{13} + 7 q^{15} + 7 q^{17} + 19 q^{19} + 20 q^{23} + 20 q^{25} - 2 q^{27} + 32 q^{29} - 3 q^{31} + 11 q^{33} - 26 q^{35} - 10 q^{37} - 22 q^{39} - 40 q^{41} + 8 q^{43} - 4 q^{45} - 18 q^{47} - 34 q^{49} - 26 q^{51} - 34 q^{53} - 17 q^{55} - 3 q^{57} - 32 q^{59} + 32 q^{61} + 49 q^{65} + 35 q^{67} - 2 q^{69} + 33 q^{71} - q^{73} - 2 q^{75} - 50 q^{77} + 22 q^{79} - 2 q^{81} - 14 q^{83} - 9 q^{85} - 12 q^{87} + 10 q^{89} - 72 q^{91} + 30 q^{93} - 51 q^{95} - 4 q^{97} + 11 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9 - 22 * q^13 + 7 * q^15 + 7 * q^17 + 19 * q^19 + 20 * q^23 + 20 * q^25 - 2 * q^27 + 32 * q^29 - 3 * q^31 + 11 * q^33 - 26 * q^35 - 10 * q^37 - 22 * q^39 - 40 * q^41 + 8 * q^43 - 4 * q^45 - 18 * q^47 - 34 * q^49 - 26 * q^51 - 34 * q^53 - 17 * q^55 - 3 * q^57 - 32 * q^59 + 32 * q^61 + 49 * q^65 + 35 * q^67 - 2 * q^69 + 33 * q^71 - q^73 - 2 * q^75 - 50 * q^77 + 22 * q^79 - 2 * q^81 - 14 * q^83 - 9 * q^85 - 12 * q^87 + 10 * q^89 - 72 * q^91 + 30 * q^93 - 51 * q^95 - 4 * q^97 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$1$	$1$

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
$3$	−0.959493	+	0.281733i	−0.553964	+	0.162658i
$3$	−0.959493	+	0.281733i	−0.553964	+	0.162658i
$4$		0			0
$5$	−1.52130	−	0.977682i	−0.680348	−	0.437233i	0.154295	−	0.988025i	$-0.450689\pi$
$5$	−1.52130	−	0.977682i	−0.680348	−	0.437233i	−0.834643	+	0.550792i	$0.814326\pi$
$6$		0			0
$7$	0.485296	+	3.37531i	0.183425	+	1.27575i	0.848590	+	0.529051i	$0.177452\pi$
$7$	0.485296	+	3.37531i	0.183425	+	1.27575i	−0.665165	+	0.746696i	$0.731639\pi$
$8$		0			0
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$		0			0
$11$	−0.800715	+	1.75332i	−0.241425	+	0.528646i	−0.991094	−	0.133167i	$-0.957485\pi$
$11$	−0.800715	+	1.75332i	−0.241425	+	0.528646i	0.749669	+	0.661813i	$0.230213\pi$
$12$		0			0
$13$	−0.753988	+	5.24410i	−0.209119	+	1.45445i	0.566923	+	0.823771i	$0.308134\pi$
$13$	−0.753988	+	5.24410i	−0.209119	+	1.45445i	−0.776042	+	0.630682i	$0.782775\pi$
$14$		0			0
$15$	1.73512	+	0.509479i	0.448007	+	0.131547i
$16$		0			0
$17$	0.496392	+	0.572867i	0.120393	+	0.138941i	0.812746	−	0.582618i	$-0.197972\pi$
$17$	0.496392	+	0.572867i	0.120393	+	0.138941i	−0.692354	+	0.721558i	$0.743426\pi$
$18$		0			0
$19$	−3.10335	+	3.58146i	−0.711958	+	0.821643i	−0.990316	−	0.138834i	$-0.955664\pi$
$19$	−3.10335	+	3.58146i	−0.711958	+	0.821643i	0.278358	+	0.960477i	$0.410210\pi$
$20$		0			0
$21$	−1.41657	−	3.10186i	−0.309122	−	0.676882i
$22$		0			0
$23$	3.36166	+	3.42041i	0.700955	+	0.713206i
$23$	3.36166	+	3.42041i	0.700955	+	0.713206i
$24$		0			0
$25$	−0.718574	−	1.57346i	−0.143715	−	0.314691i
$26$		0			0
$27$	−0.654861	+	0.755750i	−0.126028	+	0.145444i
$28$		0			0
$29$	−2.79381	−	3.22422i	−0.518797	−	0.598723i	0.434532	−	0.900656i	$-0.356914\pi$
$29$	−2.79381	−	3.22422i	−0.518797	−	0.598723i	−0.953329	+	0.301933i	$0.902368\pi$
$30$		0			0
$31$	3.28356	+	0.964142i	0.589746	+	0.173165i	0.562971	−	0.826477i	$-0.309658\pi$
$31$	3.28356	+	0.964142i	0.589746	+	0.173165i	0.0267745	+	0.999641i	$0.491476\pi$
$32$		0			0
$33$	0.274313	−	1.90789i	0.0477517	−	0.332120i
$34$		0			0
$35$	2.56170	−	5.60934i	0.433006	−	0.948151i
$36$		0			0
$37$	−3.09318	+	1.98787i	−0.508516	+	0.326803i	−0.769614	−	0.638509i	$-0.779552\pi$
$37$	−3.09318	+	1.98787i	−0.508516	+	0.326803i	0.261099	+	0.965312i	$0.415915\pi$
$38$		0			0
$39$	−0.753988	−	5.24410i	−0.120735	−	0.839728i
$40$		0			0
$41$	−5.92232	−	3.80604i	−0.924911	−	0.594404i	−0.0108322	−	0.999941i	$-0.503448\pi$
$41$	−5.92232	−	3.80604i	−0.924911	−	0.594404i	−0.914079	+	0.405537i	$0.867084\pi$
$42$		0			0
$43$	3.52444	−	1.03487i	0.537472	−	0.157816i	−0.00172068	−	0.999999i	$-0.500548\pi$
$43$	3.52444	−	1.03487i	0.537472	−	0.157816i	0.539192	+	0.842183i	$0.318730\pi$
$44$		0			0
$45$	−1.80838			−0.269577
$46$		0			0
$47$	10.3519			1.50998			0.754989	−	0.655738i	$-0.227642\pi$
$47$	10.3519			1.50998			0.754989	+	0.655738i	$0.227642\pi$
$48$		0			0
$49$	−4.44075	+	1.30392i	−0.634393	+	0.186275i
$50$		0			0
$51$	−0.637680	−	0.409812i	−0.0892930	−	0.0573851i
$52$		0			0
$53$	−1.11911	−	7.78361i	−0.153722	−	1.06916i	−0.909910	−	0.414806i	$-0.863849\pi$
$53$	−1.11911	−	7.78361i	−0.153722	−	1.06916i	0.756187	−	0.654355i	$-0.227060\pi$
$54$		0			0
$55$	2.93232	−	1.88449i	0.395394	−	0.254104i
$56$		0			0
$57$	1.96863	−	4.31070i	0.260751	−	0.570966i
$58$		0			0
$59$	−1.53778	+	10.6955i	−0.200202	+	1.39244i	0.603480	+	0.797378i	$0.293780\pi$
$59$	−1.53778	+	10.6955i	−0.200202	+	1.39244i	−0.803682	+	0.595059i	$0.797129\pi$
$60$		0			0
$61$	12.3748	+	3.63356i	1.58443	+	0.465229i	0.951158	−	0.308704i	$-0.0998951\pi$
$61$	12.3748	+	3.63356i	1.58443	+	0.465229i	0.633268	+	0.773933i	$0.281713\pi$
$62$		0			0
$63$	2.23309	+	2.57712i	0.281343	+	0.324687i
$64$		0			0
$65$	6.27411	−	7.24071i	0.778208	−	0.898100i
$66$		0			0
$67$	−2.57750	−	5.64394i	−0.314892	−	0.689517i	0.684321	−	0.729181i	$-0.260099\pi$
$67$	−2.57750	−	5.64394i	−0.314892	−	0.689517i	−0.999213	+	0.0396637i	$0.987371\pi$
$68$		0			0
$69$	−4.18913	−	2.33477i	−0.504312	−	0.281074i
$70$		0			0
$71$	−6.14490	−	13.4555i	−0.729266	−	1.59687i	−0.800445	−	0.599406i	$-0.795403\pi$
$71$	−6.14490	−	13.4555i	−0.729266	−	1.59687i	0.0711790	−	0.997464i	$-0.477324\pi$
$72$		0			0
$73$	4.97621	−	5.74285i	0.582421	−	0.672150i	−0.385702	−	0.922623i	$-0.626041\pi$
$73$	4.97621	−	5.74285i	0.582421	−	0.672150i	0.968124	+	0.250473i	$0.0805862\pi$
$74$		0			0
$75$	1.13276	+	1.30728i	0.130800	+	0.150951i
$76$		0			0
$77$	−6.30658	−	1.85178i	−0.718702	−	0.211030i
$78$		0			0
$79$	−0.905219	+	6.29594i	−0.101845	+	0.708348i	0.873365	+	0.487067i	$0.161933\pi$
$79$	−0.905219	+	6.29594i	−0.101845	+	0.708348i	−0.975210	+	0.221282i	$0.928976\pi$
$80$		0			0
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$		0			0
$83$	−8.22677	+	5.28702i	−0.903005	+	0.580326i	−0.907680	−	0.419663i	$-0.862148\pi$
$83$	−8.22677	+	5.28702i	−0.903005	+	0.580326i	0.00467489	+	0.999989i	$0.498512\pi$
$84$		0			0
$85$	−0.195081	−	1.35682i	−0.0211595	−	0.147168i
$86$		0			0
$87$	3.58901	+	2.30651i	0.384782	+	0.247284i
$88$		0			0
$89$	−10.6954	+	3.14044i	−1.13371	+	0.332886i	−0.794163	−	0.607704i	$-0.792091\pi$
$89$	−10.6954	+	3.14044i	−1.13371	+	0.332886i	−0.339543	+	0.940591i	$0.610272\pi$
$90$		0			0
$91$	−18.0664			−1.89387
$92$		0			0
$93$	−3.42219			−0.354864
$94$		0			0
$95$	8.22267	−	2.41439i	0.843628	−	0.247712i
$96$		0			0
$97$	6.41054	+	4.11980i	0.650892	+	0.418303i	0.823992	−	0.566601i	$-0.191742\pi$
$97$	6.41054	+	4.11980i	0.650892	+	0.418303i	−0.173100	+	0.984904i	$0.555378\pi$
$98$		0			0
$99$	0.274313	+	1.90789i	0.0275695	+	0.191750i
$100$		0			0
$101$	7.49704	−	4.81805i	0.745983	−	0.479414i	−0.111604	−	0.993753i	$-0.535599\pi$
$101$	7.49704	−	4.81805i	0.745983	−	0.479414i	0.857587	+	0.514339i	$0.171963\pi$
$102$		0			0
$103$	−0.367699	+	0.805149i	−0.0362305	+	0.0793337i	−0.926882	−	0.375353i	$-0.877521\pi$
$103$	−0.367699	+	0.805149i	−0.0362305	+	0.0793337i	0.890651	+	0.454687i	$0.150249\pi$
$104$		0			0
$105$	−0.877598	+	6.10383i	−0.0856448	+	0.595673i
$106$		0			0
$107$	7.59185	+	2.22917i	0.733932	+	0.215502i	0.627279	−	0.778794i	$-0.284168\pi$
$107$	7.59185	+	2.22917i	0.733932	+	0.215502i	0.106653	+	0.994296i	$0.465987\pi$
$108$		0			0
$109$	1.15251	+	1.33007i	0.110391	+	0.127398i	0.808256	−	0.588832i	$-0.200412\pi$
$109$	1.15251	+	1.33007i	0.110391	+	0.127398i	−0.697865	+	0.716229i	$0.745866\pi$
$110$		0			0
$111$	2.40784	−	2.77879i	0.228542	−	0.263751i
$112$		0			0
$113$	6.94750	+	15.2129i	0.653566	+	1.43111i	0.888398	+	0.459074i	$0.151819\pi$
$113$	6.94750	+	15.2129i	0.653566	+	1.43111i	−0.234832	+	0.972036i	$0.575454\pi$
$114$		0			0
$115$	−1.77003	−	8.49012i	−0.165056	−	0.791708i
$116$		0			0
$117$	2.20088	+	4.81926i	0.203471	+	0.445540i
$118$		0			0
$119$	−1.69271	+	1.95349i	−0.155170	+	0.179076i
$120$		0			0
$121$	4.77048	+	5.50543i	0.433680	+	0.500493i
$122$		0			0
$123$	6.75471	+	1.98336i	0.609052	+	0.178834i
$124$		0			0
$125$	−1.73197	+	12.0461i	−0.154912	+	1.07744i
$126$		0			0
$127$	0.531324	−	1.16344i	0.0471473	−	0.103238i	−0.884593	−	0.466365i	$-0.845563\pi$
$127$	0.531324	−	1.16344i	0.0471473	−	0.103238i	0.931740	+	0.363126i	$0.118291\pi$
$128$		0			0
$129$	−3.09012	+	1.98590i	−0.272070	+	0.174849i
$130$		0			0
$131$	1.43523	+	9.98224i	0.125397	+	0.872152i	0.951284	+	0.308317i	$0.0997657\pi$
$131$	1.43523	+	9.98224i	0.125397	+	0.872152i	−0.825887	+	0.563835i	$0.809325\pi$
$132$		0			0
$133$	−13.5946	−	8.73670i	−1.17880	−	0.757568i
$134$		0			0
$135$	1.73512	−	0.509479i	0.149336	−	0.0438489i
$136$		0			0
$137$	6.53140			0.558015			0.279007	−	0.960289i	$-0.409995\pi$
$137$	6.53140			0.558015			0.279007	+	0.960289i	$0.409995\pi$
$138$		0			0
$139$	−8.55305			−0.725461			−0.362730	−	0.931894i	$-0.618155\pi$
$139$	−8.55305			−0.725461			−0.362730	+	0.931894i	$0.618155\pi$
$140$		0			0
$141$	−9.93256	+	2.91646i	−0.836473	+	0.245610i
$142$		0			0
$143$	−8.59086	−	5.52101i	−0.718404	−	0.461690i
$144$		0			0
$145$	1.09796	+	7.63648i	0.0911806	+	0.634175i
$146$		0			0
$147$	3.89351	−	2.50221i	0.321132	−	0.206379i
$148$		0			0
$149$	1.34464	−	2.94435i	0.110157	−	0.241211i	−0.846523	−	0.532353i	$-0.821308\pi$
$149$	1.34464	−	2.94435i	0.110157	−	0.241211i	0.956680	+	0.291142i	$0.0940352\pi$
$150$		0			0
$151$	−1.00038	+	6.95781i	−0.0814100	+	0.566219i	0.907765	+	0.419479i	$0.137787\pi$
$151$	−1.00038	+	6.95781i	−0.0814100	+	0.566219i	−0.989175	+	0.146740i	$0.953122\pi$
$152$		0			0
$153$	0.727307	+	0.213556i	0.0587993	+	0.0172650i
$154$		0			0
$155$	−4.05267	−	4.67704i	−0.325519	−	0.375668i
$156$		0			0
$157$	13.1324	−	15.1556i	1.04808	−	1.20955i	0.0708217	−	0.997489i	$-0.477438\pi$
$157$	13.1324	−	15.1556i	1.04808	−	1.20955i	0.977257	−	0.212058i	$-0.0680167\pi$
$158$		0			0
$159$	3.26668	+	7.15303i	0.259065	+	0.567272i
$160$		0			0
$161$	−9.91356	+	13.0066i	−0.781298	+	1.02506i
$162$		0			0
$163$	−6.16725	−	13.5044i	−0.483056	−	1.05775i	−0.981612	−	0.190888i	$-0.938863\pi$
$163$	−6.16725	−	13.5044i	−0.483056	−	1.05775i	0.498556	−	0.866858i	$-0.333864\pi$
$164$		0			0
$165$	−2.28262	+	2.63428i	−0.177702	+	0.205079i
$166$		0			0
$167$	16.1307	+	18.6159i	1.24823	+	1.44054i	0.852961	+	0.521974i	$0.174804\pi$
$167$	16.1307	+	18.6159i	1.24823	+	1.44054i	0.395272	+	0.918564i	$0.370650\pi$
$168$		0			0
$169$	−14.4587	−	4.24546i	−1.11221	−	0.326574i
$170$		0			0
$171$	−0.674423	+	4.69071i	−0.0515744	+	0.358708i
$172$		0			0
$173$	−6.48345	+	14.1968i	−0.492928	+	1.07936i	0.485776	+	0.874083i	$0.338537\pi$
$173$	−6.48345	+	14.1968i	−0.492928	+	1.07936i	−0.978704	+	0.205278i	$0.934190\pi$
$174$		0			0
$175$	4.96218	−	3.18900i	0.375106	−	0.241066i
$176$		0			0
$177$	−1.53778	−	10.6955i	−0.115587	−	0.803924i
$178$		0			0
$179$	−15.2621	−	9.80838i	−1.14075	−	0.733113i	−0.172970	−	0.984927i	$-0.555336\pi$
$179$	−15.2621	−	9.80838i	−1.14075	−	0.733113i	−0.967775	+	0.251815i	$0.918973\pi$
$180$		0			0
$181$	25.5232	−	7.49429i	1.89712	−	0.557046i	0.906157	−	0.422942i	$-0.139003\pi$
$181$	25.5232	−	7.49429i	1.89712	−	0.557046i	0.990967	−	0.134103i	$-0.0428154\pi$
$182$		0			0
$183$	−12.8972			−0.953388
$184$		0			0
$185$	6.64917			0.488856
$186$		0			0
$187$	−1.40189	+	0.411631i	−0.102516	+	0.0301015i
$188$		0			0
$189$	−2.86869	−	1.84360i	−0.208667	−	0.134102i
$190$		0			0
$191$	3.52838	+	24.5404i	0.255305	+	1.77568i	0.565240	+	0.824927i	$0.308784\pi$
$191$	3.52838	+	24.5404i	0.255305	+	1.77568i	−0.309935	+	0.950758i	$0.600307\pi$
$192$		0			0
$193$	−3.96991	+	2.55131i	−0.285761	+	0.183647i	−0.675666	−	0.737208i	$-0.736144\pi$
$193$	−3.96991	+	2.55131i	−0.285761	+	0.183647i	0.389906	+	0.920855i	$0.372508\pi$
$194$		0			0
$195$	−3.98002	+	8.71503i	−0.285015	+	0.624096i
$196$		0			0
$197$	1.58426	−	11.0188i	0.112874	−	0.785055i	−0.852226	−	0.523174i	$-0.824748\pi$
$197$	1.58426	−	11.0188i	0.112874	−	0.785055i	0.965100	−	0.261882i	$-0.0843430\pi$
$198$		0			0
$199$	7.56852	+	2.22232i	0.536518	+	0.157536i	0.538756	−	0.842462i	$-0.318894\pi$
$199$	7.56852	+	2.22232i	0.536518	+	0.157536i	−0.00223844	+	0.999997i	$0.500713\pi$
$200$		0			0
$201$	4.06318	+	4.68915i	0.286594	+	0.330747i
$202$		0			0
$203$	9.52693	−	10.9947i	0.668660	−	0.771674i
$204$		0			0
$205$	5.28854	+	11.5803i	0.369368	+	0.808803i
$206$		0			0
$207$	4.67722	+	1.05999i	0.325090	+	0.0736741i
$208$		0			0
$209$	−3.79455	−	8.30890i	−0.262474	−	0.574738i
$210$		0			0
$211$	12.2185	−	14.1009i	0.841159	−	0.970749i	−0.158704	−	0.987326i	$-0.550732\pi$
$211$	12.2185	−	14.1009i	0.841159	−	0.970749i	0.999863	+	0.0165774i	$0.00527698\pi$
$212$		0			0
$213$	9.68683	+	11.1792i	0.663731	+	0.765986i
$214$		0			0
$215$	−6.37351	−	1.87143i	−0.434670	−	0.127631i
$216$		0			0
$217$	−1.66077	+	11.5509i	−0.112741	+	0.784129i
$218$		0			0
$219$	−3.15669	+	6.91219i	−0.213309	+	0.467082i
$220$		0			0
$221$	−3.37845	+	2.17120i	−0.227259	+	0.146050i
$222$		0			0
$223$	−3.29264	−	22.9008i	−0.220491	−	1.53355i	−0.736186	−	0.676779i	$-0.763375\pi$
$223$	−3.29264	−	22.9008i	−0.220491	−	1.53355i	0.515694	−	0.856773i	$-0.327534\pi$
$224$		0			0
$225$	−1.45518	−	0.935186i	−0.0970119	−	0.0623457i
$226$		0			0
$227$	−11.8332	+	3.47453i	−0.785394	+	0.230613i	−0.649753	−	0.760145i	$-0.725128\pi$
$227$	−11.8332	+	3.47453i	−0.785394	+	0.230613i	−0.135641	+	0.990758i	$0.543309\pi$
$228$		0			0
$229$	−11.4857			−0.758998			−0.379499	−	0.925192i	$-0.623904\pi$
$229$	−11.4857			−0.758998			−0.379499	+	0.925192i	$0.623904\pi$
$230$		0			0
$231$	6.57283			0.432460
$232$		0			0
$233$	5.13434	−	1.50758i	0.336362	−	0.0987647i	−0.109190	−	0.994021i	$-0.534826\pi$
$233$	5.13434	−	1.50758i	0.336362	−	0.0987647i	0.445552	+	0.895256i	$0.353008\pi$
$234$		0			0
$235$	−15.7484	−	10.1209i	−1.02731	−	0.660212i
$236$		0			0
$237$	−0.905219	−	6.29594i	−0.0588003	−	0.408965i
$238$		0			0
$239$	9.62507	−	6.18565i	0.622594	−	0.400117i	−0.190967	−	0.981596i	$-0.561162\pi$
$239$	9.62507	−	6.18565i	0.622594	−	0.400117i	0.813561	+	0.581480i	$0.197526\pi$
$240$		0			0
$241$	1.45687	−	3.19010i	0.0938452	−	0.205492i	−0.856888	−	0.515503i	$-0.827605\pi$
$241$	1.45687	−	3.19010i	0.0938452	−	0.205492i	0.950733	+	0.310010i	$0.100333\pi$
$242$		0			0
$243$	−0.142315	+	0.989821i	−0.00912950	+	0.0634971i
$244$		0			0
$245$	8.03055	+	2.35798i	0.513053	+	0.150646i
$246$		0			0
$247$	−16.4416	−	18.9747i	−1.04616	−	1.20733i
$248$		0			0
$249$	6.40400	−	7.39061i	0.405837	−	0.468361i
$250$		0			0
$251$	−4.91943	−	10.7720i	−0.310512	−	0.679925i	0.688460	−	0.725275i	$-0.258287\pi$
$251$	−4.91943	−	10.7720i	−0.310512	−	0.679925i	−0.998971	+	0.0453492i	$0.985560\pi$
$252$		0			0
$253$	−8.68881	+	3.15529i	−0.546261	+	0.198371i
$254$		0			0
$255$	0.569439	+	1.24690i	0.0356596	+	0.0780837i
$256$		0			0
$257$	16.7144	−	19.2895i	1.04262	−	1.20324i	0.0639142	−	0.997955i	$-0.479642\pi$
$257$	16.7144	−	19.2895i	1.04262	−	1.20324i	0.978702	−	0.205287i	$-0.0658129\pi$
$258$		0			0
$259$	−8.21077	−	9.47573i	−0.510192	−	0.588794i
$260$		0			0
$261$	−4.09345	−	1.20194i	−0.253378	−	0.0743985i
$262$		0			0
$263$	0.511613	−	3.55835i	0.0315474	−	0.219417i	−0.967949	−	0.251147i	$-0.919192\pi$
$263$	0.511613	−	3.55835i	0.0315474	−	0.219417i	0.999496	+	0.0317294i	$0.0101015\pi$
$264$		0			0
$265$	−5.90739	+	12.9354i	−0.362888	+	0.794614i
$266$		0			0
$267$	9.37736	−	6.02646i	0.573885	−	0.368814i
$268$		0			0
$269$	−2.30719	−	16.0468i	−0.140672	−	0.978393i	−0.930820	−	0.365478i	$-0.880906\pi$
$269$	−2.30719	−	16.0468i	−0.140672	−	0.978393i	0.790148	−	0.612915i	$-0.210003\pi$
$270$		0			0
$271$	−3.65183	−	2.34689i	−0.221833	−	0.142563i	0.425005	−	0.905191i	$-0.360272\pi$
$271$	−3.65183	−	2.34689i	−0.221833	−	0.142563i	−0.646838	+	0.762628i	$0.723909\pi$
$272$		0			0
$273$	17.3346	−	5.08989i	1.04914	−	0.308054i
$274$		0			0
$275$	3.33415			0.201057
$276$		0			0
$277$	28.6009			1.71846			0.859230	−	0.511589i	$-0.170943\pi$
$277$	28.6009			1.71846			0.859230	+	0.511589i	$0.170943\pi$
$278$		0			0
$279$	3.28356	−	0.964142i	0.196582	−	0.0577216i
$280$		0			0
$281$	−9.53062	−	6.12496i	−0.568549	−	0.365384i	0.224563	−	0.974459i	$-0.427904\pi$
$281$	−9.53062	−	6.12496i	−0.568549	−	0.365384i	−0.793113	+	0.609075i	$0.791541\pi$
$282$		0			0
$283$	0.759137	+	5.27992i	0.0451260	+	0.313858i	0.999865	+	0.0164143i	$0.00522508\pi$
$283$	0.759137	+	5.27992i	0.0451260	+	0.313858i	−0.954739	+	0.297444i	$0.903866\pi$
$284$		0			0
$285$	−7.20938	+	4.63319i	−0.427047	+	0.274446i
$286$		0			0
$287$	9.97249	−	21.8367i	0.588658	−	1.28898i
$288$		0			0
$289$	2.33758	−	16.2582i	0.137505	−	0.956367i
$290$		0			0
$291$	−7.31155	−	2.14687i	−0.428611	−	0.125851i
$292$		0			0
$293$	15.4905	+	17.8770i	0.904963	+	1.04438i	0.998809	+	0.0487965i	$0.0155386\pi$
$293$	15.4905	+	17.8770i	0.904963	+	1.04438i	−0.0938455	+	0.995587i	$0.529916\pi$
$294$		0			0
$295$	12.7963	−	14.7677i	0.745027	−	0.859806i
$296$		0			0
$297$	−0.800715	−	1.75332i	−0.0464622	−	0.101738i
$298$		0			0
$299$	−20.4717	+	15.0499i	−1.18391	+	0.870361i
$300$		0			0
$301$	5.20340	+	11.3939i	0.299919	+	0.656731i
$302$		0			0
$303$	−5.83595	+	6.73505i	−0.335267	+	0.386918i
$304$		0			0
$305$	−15.2733	−	17.6263i	−0.874547	−	1.00928i
$306$		0			0
$307$	18.7890	+	5.51696i	1.07235	+	0.314870i	0.769813	−	0.638269i	$-0.220349\pi$
$307$	18.7890	+	5.51696i	1.07235	+	0.314870i	0.302534	+	0.953139i	$0.402167\pi$
$308$		0			0
$309$	0.125968	−	0.876128i	0.00716608	−	0.0498412i
$310$		0			0
$311$	−0.797463	+	1.74620i	−0.0452200	+	0.0990179i	−0.930894	−	0.365290i	$-0.880970\pi$
$311$	−0.797463	+	1.74620i	−0.0452200	+	0.0990179i	0.885674	+	0.464308i	$0.153697\pi$
$312$		0			0
$313$	−10.6720	+	6.85849i	−0.603219	+	0.387665i	−0.806309	−	0.591495i	$-0.798538\pi$
$313$	−10.6720	+	6.85849i	−0.603219	+	0.387665i	0.203090	+	0.979160i	$0.434902\pi$
$314$		0			0
$315$	−0.877598	−	6.10383i	−0.0494471	−	0.343912i
$316$		0			0
$317$	2.62869	+	1.68936i	0.147642	+	0.0948838i	0.612376	−	0.790566i	$-0.290214\pi$
$317$	2.62869	+	1.68936i	0.147642	+	0.0948838i	−0.464734	+	0.885450i	$0.653850\pi$
$318$		0			0
$319$	7.89014	−	2.31675i	0.441763	−	0.129713i
$320$		0			0
$321$	−7.91236			−0.441625
$322$		0			0
$323$	−3.59218			−0.199874
$324$		0			0
$325$	8.79317	−	2.58191i	0.487757	−	0.143218i
$326$		0			0
$327$	−1.48055	−	0.951493i	−0.0818747	−	0.0526177i
$328$		0			0
$329$	5.02373	+	34.9408i	0.276967	+	1.92635i
$330$		0			0
$331$	−10.8260	+	6.95744i	−0.595050	+	0.382415i	−0.803225	−	0.595676i	$-0.796884\pi$
$331$	−10.8260	+	6.95744i	−0.595050	+	0.382415i	0.208175	+	0.978092i	$0.433248\pi$
$332$		0			0
$333$	−1.52743	+	3.34460i	−0.0837025	+	0.183283i
$334$		0			0
$335$	−1.59682	+	11.1061i	−0.0872436	+	0.606792i
$336$		0			0
$337$	14.8281	+	4.35393i	0.807739	+	0.237174i	0.659429	−	0.751767i	$-0.270798\pi$
$337$	14.8281	+	4.35393i	0.807739	+	0.237174i	0.148311	+	0.988941i	$0.452616\pi$
$338$		0			0
$339$	−10.9520	−	12.6393i	−0.594834	−	0.686475i
$340$		0			0
$341$	−4.31965	+	4.98514i	−0.233922	+	0.269960i
$342$		0			0
$343$	3.35979	+	7.35691i	0.181412	+	0.397236i
$344$		0			0
$345$	4.09027	+	7.64754i	0.220213	+	0.411730i
$346$		0			0
$347$	−7.54167	−	16.5140i	−0.404858	−	0.886516i	−0.996754	−	0.0805017i	$-0.974348\pi$
$347$	−7.54167	−	16.5140i	−0.404858	−	0.886516i	0.591896	−	0.806014i	$-0.298380\pi$
$348$		0			0
$349$	−14.3287	+	16.5361i	−0.766995	+	0.885160i	−0.996099	−	0.0882423i	$-0.971875\pi$
$349$	−14.3287	+	16.5361i	−0.766995	+	0.885160i	0.229104	+	0.973402i	$0.426420\pi$
$350$		0			0
$351$	−3.46947	−	4.00398i	−0.185187	−	0.213717i
$352$		0			0
$353$	−11.6096	−	3.40888i	−0.617916	−	0.181436i	−0.0422305	−	0.999108i	$-0.513446\pi$
$353$	−11.6096	−	3.40888i	−0.617916	−	0.181436i	−0.575685	+	0.817672i	$0.695265\pi$
$354$		0			0
$355$	−3.80691	+	26.4776i	−0.202050	+	1.40529i
$356$		0			0
$357$	1.07378	−	2.35125i	0.0568304	−	0.124441i
$358$		0			0
$359$	−2.98260	+	1.91680i	−0.157415	+	0.101165i	−0.616977	−	0.786981i	$-0.711643\pi$
$359$	−2.98260	+	1.91680i	−0.157415	+	0.101165i	0.459562	+	0.888146i	$0.348007\pi$
$360$		0			0
$361$	−0.492073	−	3.42244i	−0.0258986	−	0.180129i
$362$		0			0
$363$	−6.12830	−	3.93842i	−0.321652	−	0.206713i
$364$		0			0
$365$	−13.1850	+	3.87147i	−0.690135	+	0.202642i
$366$		0			0
$367$	−26.1379			−1.36439			−0.682194	−	0.731171i	$-0.738974\pi$
$367$	−26.1379			−1.36439			−0.682194	+	0.731171i	$0.738974\pi$
$368$		0			0
$369$	−7.03987			−0.366481
$370$		0			0
$371$	25.7290	−	7.55472i	1.33578	−	0.392221i
$372$		0			0
$373$	12.1660	+	7.81858i	0.629929	+	0.404831i	0.816283	−	0.577652i	$-0.196031\pi$
$373$	12.1660	+	7.81858i	0.629929	+	0.404831i	−0.186354	+	0.982483i	$0.559667\pi$
$374$		0			0
$375$	−1.73197	−	12.0461i	−0.0894384	−	0.622058i
$376$		0			0
$377$	19.0147	−	12.2200i	0.979305	−	0.629361i
$378$		0			0
$379$	−11.6229	+	25.4505i	−0.597026	+	1.30730i	0.334076	+	0.942546i	$0.391576\pi$
$379$	−11.6229	+	25.4505i	−0.597026	+	1.30730i	−0.931102	+	0.364758i	$0.881152\pi$
$380$		0			0
$381$	−0.182023	+	1.26600i	−0.00932534	+	0.0648592i
$382$		0			0
$383$	17.7316	+	5.20645i	0.906040	+	0.266037i	0.701373	−	0.712794i	$-0.252571\pi$
$383$	17.7316	+	5.20645i	0.906040	+	0.266037i	0.204667	+	0.978832i	$0.434389\pi$
$384$		0			0
$385$	7.78377	+	8.98295i	0.396698	+	0.457814i
$386$		0			0
$387$	2.40545	−	2.77604i	0.122276	−	0.141114i
$388$		0			0
$389$	10.6824	+	23.3913i	0.541621	+	1.18598i	0.960586	+	0.277982i	$0.0896656\pi$
$389$	10.6824	+	23.3913i	0.541621	+	1.18598i	−0.418965	+	0.908002i	$0.637607\pi$
$390$		0			0
$391$	−0.290741	+	3.62365i	−0.0147034	+	0.183256i
$392$		0			0
$393$	−4.18941	−	9.17354i	−0.211328	−	0.462744i
$394$		0			0
$395$	7.53254	−	8.69302i	0.379003	−	0.437393i
$396$		0			0
$397$	18.2955	+	21.1141i	0.918225	+	1.05969i	0.998021	+	0.0628775i	$0.0200277\pi$
$397$	18.2955	+	21.1141i	0.918225	+	1.05969i	−0.0797958	+	0.996811i	$0.525427\pi$
$398$		0			0
$399$	15.5053	+	4.55277i	0.776237	+	0.227924i
$400$		0			0
$401$	−3.47619	+	24.1775i	−0.173593	+	1.20737i	0.697623	+	0.716465i	$0.254241\pi$
$401$	−3.47619	+	24.1775i	−0.173593	+	1.20737i	−0.871216	+	0.490900i	$0.836668\pi$
$402$		0			0
$403$	−7.53183	+	16.4924i	−0.375187	+	0.821545i
$404$		0			0
$405$	−1.52130	+	0.977682i	−0.0755942	+	0.0485814i
$406$		0			0
$407$	−1.00861	−	7.01505i	−0.0499950	−	0.347723i
$408$		0			0
$409$	−30.4357	−	19.5599i	−1.50495	−	0.967173i	−0.994212	−	0.107437i	$-0.965736\pi$
$409$	−30.4357	−	19.5599i	−1.50495	−	0.967173i	−0.510738	−	0.859736i	$-0.670628\pi$
$410$		0			0
$411$	−6.26683	+	1.84011i	−0.309120	+	0.0907658i
$412$		0			0
$413$	−36.8470			−1.81312
$414$		0			0
$415$	17.6844			0.868095
$416$		0			0
$417$	8.20660	−	2.40967i	0.401879	−	0.118002i
$418$		0			0
$419$	6.96574	+	4.47661i	0.340299	+	0.218697i	0.699617	−	0.714519i	$-0.253354\pi$
$419$	6.96574	+	4.47661i	0.340299	+	0.218697i	−0.359318	+	0.933215i	$0.616991\pi$
$420$		0			0
$421$	−5.08820	−	35.3892i	−0.247984	−	1.72476i	−0.609836	−	0.792528i	$-0.708765\pi$
$421$	−5.08820	−	35.3892i	−0.247984	−	1.72476i	0.361852	−	0.932236i	$-0.382145\pi$
$422$		0			0
$423$	8.70856	−	5.59665i	0.423425	−	0.272119i
$424$		0			0
$425$	0.544687	−	1.19270i	0.0264212	−	0.0578544i
$426$		0			0
$427$	−6.25896	+	43.5320i	−0.302892	+	2.10666i
$428$		0			0
$429$	9.79832	+	2.87705i	0.473067	+	0.138905i
$430$		0			0
$431$	−14.2907	−	16.4924i	−0.688361	−	0.794411i	0.298770	−	0.954325i	$-0.403424\pi$
$431$	−14.2907	−	16.4924i	−0.688361	−	0.794411i	−0.987131	+	0.159914i	$0.948878\pi$
$432$		0			0
$433$	−19.9066	+	22.9735i	−0.956651	+	1.10403i	0.0378476	+	0.999284i	$0.487950\pi$
$433$	−19.9066	+	22.9735i	−0.956651	+	1.10403i	−0.994499	+	0.104751i	$0.966596\pi$
$434$		0			0
$435$	−3.20493	−	7.01782i	−0.153665	−	0.336479i
$436$		0			0
$437$	−22.6825	+	1.42490i	−1.08505	+	0.0681621i
$438$		0			0
$439$	8.60356	+	18.8392i	0.410626	+	0.899145i	0.996081	+	0.0884405i	$0.0281883\pi$
$439$	8.60356	+	18.8392i	0.410626	+	0.899145i	−0.585456	+	0.810704i	$0.699084\pi$
$440$		0			0
$441$	−3.03084	+	3.49778i	−0.144326	+	0.166561i
$442$		0			0
$443$	−16.1133	−	18.5958i	−0.765567	−	0.883512i	0.230412	−	0.973093i	$-0.425993\pi$
$443$	−16.1133	−	18.5958i	−0.765567	−	0.883512i	−0.995980	+	0.0895812i	$0.971447\pi$
$444$		0			0
$445$	19.3412	+	5.67910i	0.916863	+	0.269215i
$446$		0			0
$447$	−0.460654	+	3.20392i	−0.0217882	+	0.151540i
$448$		0			0
$449$	16.3387	−	35.7767i	0.771070	−	1.68841i	0.0467864	−	0.998905i	$-0.485102\pi$
$449$	16.3387	−	35.7767i	0.771070	−	1.68841i	0.724283	−	0.689502i	$-0.242171\pi$
$450$		0			0
$451$	11.4153	−	7.33617i	0.537525	−	0.345447i
$452$		0			0
$453$	−1.00038	−	6.95781i	−0.0470021	−	0.326907i
$454$		0			0
$455$	27.4844	+	17.6632i	1.28849	+	0.828063i
$456$		0			0
$457$	−16.4781	+	4.83841i	−0.770814	+	0.226331i	−0.643412	−	0.765520i	$-0.722482\pi$
$457$	−16.4781	+	4.83841i	−0.770814	+	0.226331i	−0.127401	+	0.991851i	$0.540664\pi$
$458$		0			0
$459$	−0.758011			−0.0353809
$460$		0			0
$461$	1.59212			0.0741524			0.0370762	−	0.999312i	$-0.488196\pi$
$461$	1.59212			0.0741524			0.0370762	+	0.999312i	$0.488196\pi$
$462$		0			0
$463$	14.0004	−	4.11088i	0.650653	−	0.191049i	0.0602827	−	0.998181i	$-0.480800\pi$
$463$	14.0004	−	4.11088i	0.650653	−	0.191049i	0.590371	+	0.807132i	$0.298982\pi$
$464$		0			0
$465$	5.20619	+	3.34581i	0.241431	+	0.155158i
$466$		0			0
$467$	4.20501	+	29.2465i	0.194585	+	1.35337i	0.819681	+	0.572820i	$0.194150\pi$
$467$	4.20501	+	29.2465i	0.194585	+	1.35337i	−0.625097	+	0.780547i	$0.714940\pi$
$468$		0			0
$469$	17.7992	−	11.4388i	0.821890	−	0.528197i
$470$		0			0
$471$	−8.33061	+	18.2415i	−0.383854	+	0.840524i
$472$		0			0
$473$	−1.00761	+	7.00810i	−0.0463301	+	0.322233i
$474$		0			0
$475$	7.86526	+	2.30945i	0.360883	+	0.105965i
$476$		0			0
$477$	−5.14960	−	5.94295i	−0.235784	−	0.272109i
$478$		0			0
$479$	−2.07544	+	2.39519i	−0.0948293	+	0.109439i	−0.801181	−	0.598423i	$-0.795794\pi$
$479$	−2.07544	+	2.39519i	−0.0948293	+	0.109439i	0.706351	+	0.707861i	$0.250340\pi$
$480$		0			0
$481$	−8.09235	−	17.7198i	−0.368979	−	0.807952i
$482$		0			0
$483$	5.84762	−	15.2727i	0.266076	−	0.694931i
$484$		0			0
$485$	−5.72452	−	12.5349i	−0.259937	−	0.569183i
$486$		0			0
$487$	−20.8452	+	24.0567i	−0.944586	+	1.09011i	0.0512256	+	0.998687i	$0.483687\pi$
$487$	−20.8452	+	24.0567i	−0.944586	+	1.09011i	−0.995812	+	0.0914238i	$0.970858\pi$
$488$		0			0
$489$	9.72205	+	11.2198i	0.439647	+	0.507379i
$490$		0			0
$491$	−10.7015	−	3.14225i	−0.482953	−	0.141808i	0.0311880	−	0.999514i	$-0.490071\pi$
$491$	−10.7015	−	3.14225i	−0.482953	−	0.141808i	−0.514141	+	0.857706i	$0.671889\pi$
$492$		0			0
$493$	0.460228	−	3.20096i	0.0207276	−	0.144164i
$494$		0			0
$495$	1.44799	−	3.17066i	0.0650825	−	0.142511i
$496$		0			0
$497$	42.4343	−	27.2708i	1.90344	−	1.22326i
$498$		0			0
$499$	−0.553581	−	3.85024i	−0.0247817	−	0.172360i	0.973672	−	0.227955i	$-0.0732038\pi$
$499$	−0.553581	−	3.85024i	−0.0247817	−	0.172360i	−0.998453	+	0.0555942i	$0.982295\pi$
$500$		0			0
$501$	−20.7220	−	13.3172i	−0.925791	−	0.594970i
$502$		0			0
$503$	−36.0920	+	10.5976i	−1.60926	+	0.472523i	−0.958105	−	0.286418i	$-0.907536\pi$
$503$	−36.0920	+	10.5976i	−1.60926	+	0.472523i	−0.651160	+	0.758940i	$0.725717\pi$
$504$		0			0
$505$	−16.1158			−0.717143
$506$		0			0
$507$	15.0691			0.669243
$508$		0			0
$509$	−18.9608	+	5.56740i	−0.840424	+	0.246771i	−0.673489	−	0.739197i	$-0.735205\pi$
$509$	−18.9608	+	5.56740i	−0.840424	+	0.246771i	−0.166935	+	0.985968i	$0.553387\pi$
$510$		0			0
$511$	21.7988	+	14.0093i	0.964324	+	0.619733i
$512$		0			0
$513$	−0.674423	−	4.69071i	−0.0297765	−	0.207100i
$514$		0			0
$515$	1.34656	−	0.865383i	0.0593366	−	0.0381333i
$516$		0			0
$517$	−8.28891	+	18.1502i	−0.364546	+	0.798244i
$518$		0			0
$519$	2.22113	−	15.4483i	0.0974969	−	0.678106i
$520$		0			0
$521$	−26.3779	−	7.74525i	−1.15564	−	0.339326i	−0.352901	−	0.935660i	$-0.614805\pi$
$521$	−26.3779	−	7.74525i	−1.15564	−	0.339326i	−0.802736	+	0.596335i	$0.796623\pi$
$522$		0			0
$523$	5.32266	+	6.14267i	0.232744	+	0.268600i	0.860093	−	0.510138i	$-0.170406\pi$
$523$	5.32266	+	6.14267i	0.232744	+	0.268600i	−0.627349	+	0.778738i	$0.715860\pi$
$524$		0			0
$525$	−3.86274	+	4.45783i	−0.168584	+	0.194556i
$526$		0			0
$527$	1.07761	+	2.35964i	0.0469414	+	0.102787i
$528$		0			0
$529$	−0.398477	+	22.9965i	−0.0173251	+	0.999850i
$530$		0			0
$531$	4.48877	+	9.82903i	0.194796	+	0.426544i
$532$		0			0
$533$	24.4246	−	28.1875i	1.05795	−	1.22094i
$534$		0			0
$535$	−9.37009	−	10.8137i	−0.405104	−	0.467515i
$536$		0			0
$537$	17.4072	+	5.11123i	0.751178	+	0.220566i
$538$		0			0
$539$	1.26958	−	8.83013i	0.0546847	−	0.380341i
$540$		0			0
$541$	9.72352	−	21.2915i	0.418047	−	0.915395i	−0.577070	−	0.816695i	$-0.695804\pi$
$541$	9.72352	−	21.2915i	0.418047	−	0.915395i	0.995117	−	0.0987006i	$-0.0314686\pi$
$542$		0			0
$543$	−22.3779	+	14.3814i	−0.960329	+	0.617166i
$544$		0			0
$545$	−0.452935	−	3.15023i	−0.0194016	−	0.134941i
$546$		0			0
$547$	13.7794	+	8.85546i	0.589163	+	0.378632i	0.800992	−	0.598675i	$-0.204306\pi$
$547$	13.7794	+	8.85546i	0.589163	+	0.378632i	−0.211829	+	0.977307i	$0.567942\pi$
$548$		0			0
$549$	12.3748	−	3.63356i	0.528142	−	0.155076i
$550$		0			0
$551$	20.2176			0.861298
$552$		0			0
$553$	−21.6900			−0.922354
$554$		0			0
$555$	−6.37983	+	1.87329i	−0.270809	+	0.0795166i
$556$		0			0
$557$	16.0768	+	10.3319i	0.681196	+	0.437778i	0.834946	−	0.550332i	$-0.185499\pi$
$557$	16.0768	+	10.3319i	0.681196	+	0.437778i	−0.153750	+	0.988110i	$0.549135\pi$
$558$		0			0
$559$	2.76957	+	19.2628i	0.117140	+	0.814729i
$560$		0			0
$561$	1.22913	−	0.789915i	0.0518940	−	0.0333502i
$562$		0			0
$563$	8.42062	−	18.4386i	0.354887	−	0.777094i	−0.645030	−	0.764158i	$-0.723155\pi$
$563$	8.42062	−	18.4386i	0.354887	−	0.777094i	0.999916	−	0.0129360i	$-0.00411778\pi$
$564$		0			0
$565$	4.30413	−	29.9359i	0.181076	−	1.25941i
$566$		0			0
$567$	3.27189	+	0.960713i	0.137406	+	0.0403462i
$568$		0			0
$569$	12.1549	+	14.0276i	0.509562	+	0.588066i	0.950986	−	0.309233i	$-0.100072\pi$
$569$	12.1549	+	14.0276i	0.509562	+	0.588066i	−0.441425	+	0.897298i	$0.645527\pi$
$570$		0			0
$571$	30.6110	−	35.3269i	1.28103	−	1.47839i	0.483191	−	0.875515i	$-0.339478\pi$
$571$	30.6110	−	35.3269i	1.28103	−	1.47839i	0.797838	−	0.602872i	$-0.205977\pi$
$572$		0			0
$573$	−10.2993	−	22.5523i	−0.430260	−	0.942137i
$574$		0			0
$575$	2.96628	−	7.74725i	0.123702	−	0.323083i
$576$		0			0
$577$	−14.8811	−	32.5851i	−0.619509	−	1.35653i	−0.915876	−	0.401461i	$-0.868503\pi$
$577$	−14.8811	−	32.5851i	−0.619509	−	1.35653i	0.296368	−	0.955074i	$-0.404225\pi$
$578$		0			0
$579$	3.09032	−	3.56642i	0.128429	−	0.148215i
$580$		0			0
$581$	−21.8378	−	25.2021i	−0.905983	−	1.04556i
$582$		0			0
$583$	14.5433	+	4.27029i	0.602320	+	0.176857i
$584$		0			0
$585$	1.36349	−	9.48331i	0.0563736	−	0.392087i
$586$		0			0
$587$	0.00770622	−	0.0168743i	0.000318070	−	0.000696476i	−0.909473	−	0.415763i	$-0.863515\pi$
$587$	0.00770622	−	0.0168743i	0.000318070	−	0.000696476i	0.909791	+	0.415067i	$0.136242\pi$
$588$		0			0
$589$	−13.6431	+	8.76788i	−0.562154	+	0.361274i
$590$		0			0
$591$	1.58426	+	11.0188i	0.0651678	+	0.453252i
$592$		0			0
$593$	−5.46726	−	3.51359i	−0.224513	−	0.144286i	0.423549	−	0.905873i	$-0.360784\pi$
$593$	−5.46726	−	3.51359i	−0.224513	−	0.144286i	−0.648063	+	0.761587i	$0.724420\pi$
$594$		0			0
$595$	4.48501	−	1.31692i	0.183867	−	0.0539883i
$596$		0			0
$597$	−7.88804			−0.322836
$598$		0			0
$599$	−7.49989			−0.306437			−0.153219	−	0.988192i	$-0.548964\pi$
$599$	−7.49989			−0.306437			−0.153219	+	0.988192i	$0.548964\pi$
$600$		0			0
$601$	−24.6872	+	7.24882i	−1.00701	+	0.295686i	−0.743331	−	0.668924i	$-0.766755\pi$
$601$	−24.6872	+	7.24882i	−1.00701	+	0.295686i	−0.263682	+	0.964610i	$0.584937\pi$
$602$		0			0
$603$	−5.21968	−	3.35448i	−0.212562	−	0.136605i
$604$		0			0
$605$	−1.87479	−	13.0394i	−0.0762210	−	0.530129i
$606$		0			0
$607$	24.3740	−	15.6642i	0.989309	−	0.635790i	0.0573502	−	0.998354i	$-0.481735\pi$
$607$	24.3740	−	15.6642i	0.989309	−	0.635790i	0.931959	+	0.362564i	$0.118098\pi$
$608$		0			0
$609$	−6.04347	+	13.2334i	−0.244894	+	0.536242i
$610$		0			0
$611$	−7.80520	+	54.2863i	−0.315765	+	2.19619i
$612$		0			0
$613$	−2.25859	−	0.663181i	−0.0912235	−	0.0267856i	0.235802	−	0.971801i	$-0.424228\pi$
$613$	−2.25859	−	0.663181i	−0.0912235	−	0.0267856i	−0.327026	+	0.945015i	$0.606046\pi$
$614$		0			0
$615$	−8.33686	−	9.62125i	−0.336175	−	0.387966i
$616$		0			0
$617$	−9.99989	+	11.5405i	−0.402580	+	0.464603i	−0.920452	−	0.390856i	$-0.872179\pi$
$617$	−9.99989	+	11.5405i	−0.402580	+	0.464603i	0.517871	+	0.855458i	$0.326725\pi$
$618$		0			0
$619$	−4.77631	−	10.4587i	−0.191976	−	0.420369i	0.789028	−	0.614358i	$-0.210585\pi$
$619$	−4.77631	−	10.4587i	−0.191976	−	0.420369i	−0.981004	+	0.193988i	$0.937858\pi$
$620$		0			0
$621$	−4.78640	+	0.300678i	−0.192071	+	0.0120658i
$622$		0			0
$623$	−15.7904	−	34.5761i	−0.632628	−	1.38526i
$624$		0			0
$625$	8.74830	−	10.0961i	0.349932	−	0.403843i
$626$		0			0
$627$	5.98173	+	6.90328i	0.238887	+	0.275690i
$628$		0			0
$629$	−2.67421	−	0.785219i	−0.106628	−	0.0313087i
$630$		0			0
$631$	2.01067	−	13.9845i	0.0800436	−	0.556715i	−0.909854	−	0.414929i	$-0.863806\pi$
$631$	2.01067	−	13.9845i	0.0800436	−	0.556715i	0.989897	−	0.141786i	$-0.0452845\pi$
$632$		0			0
$633$	−7.75090	+	16.9721i	−0.308071	+	0.674581i
$634$		0			0
$635$	−1.94578	+	1.25047i	−0.0772158	+	0.0496235i
$636$		0			0
$637$	−3.48963	−	24.2709i	−0.138264	−	0.961648i
$638$		0			0
$639$	−12.4440	−	7.99727i	−0.492277	−	0.316367i
$640$		0			0
$641$	23.8830	−	7.01267i	0.943320	−	0.276984i	0.226317	−	0.974054i	$-0.427331\pi$
$641$	23.8830	−	7.01267i	0.943320	−	0.276984i	0.717003	+	0.697070i	$0.245513\pi$
$642$		0			0
$643$	23.5235			0.927678			0.463839	−	0.885919i	$-0.346472\pi$
$643$	23.5235			0.927678			0.463839	+	0.885919i	$0.346472\pi$
$644$		0			0
$645$	6.64258			0.261551
$646$		0			0
$647$	19.2110	−	5.64087i	0.755264	−	0.221766i	0.118637	−	0.992938i	$-0.462147\pi$
$647$	19.2110	−	5.64087i	0.755264	−	0.221766i	0.636627	+	0.771172i	$0.280329\pi$
$648$		0			0
$649$	−17.5213	−	11.2603i	−0.687773	−	0.442005i
$650$		0			0
$651$	−1.66077	−	11.5509i	−0.0650909	−	0.452717i
$652$		0			0
$653$	−6.28245	+	4.03749i	−0.245851	+	0.157999i	−0.657764	−	0.753224i	$-0.728497\pi$
$653$	−6.28245	+	4.03749i	−0.245851	+	0.157999i	0.411912	+	0.911224i	$0.364861\pi$
$654$		0			0
$655$	7.57604	−	16.5892i	0.296020	−	0.648194i
$656$		0			0
$657$	1.08143	−	7.52154i	0.0421907	−	0.293443i
$658$		0			0
$659$	−10.4634	−	3.07234i	−0.407597	−	0.119681i	0.0715057	−	0.997440i	$-0.477220\pi$
$659$	−10.4634	−	3.07234i	−0.407597	−	0.119681i	−0.479102	+	0.877759i	$0.659038\pi$
$660$		0			0
$661$	−11.3039	−	13.0454i	−0.439672	−	0.507409i	0.492057	−	0.870563i	$-0.336245\pi$
$661$	−11.3039	−	13.0454i	−0.439672	−	0.507409i	−0.931729	+	0.363154i	$0.881700\pi$
$662$		0			0
$663$	2.62990	−	3.03506i	0.102137	−	0.117872i
$664$		0			0
$665$	12.1398	+	26.5824i	0.470759	+	1.03082i
$666$		0			0
$667$	1.63636	−	20.3947i	0.0633600	−	0.789687i
$668$		0			0
$669$	9.61117	+	21.0455i	0.371589	+	0.813667i
$670$		0			0
$671$	−16.2794	+	18.7875i	−0.628461	+	0.725283i
$672$		0			0
$673$	4.61892	+	5.33051i	0.178046	+	0.205476i	0.837757	−	0.546043i	$-0.183867\pi$
$673$	4.61892	+	5.33051i	0.178046	+	0.205476i	−0.659711	+	0.751520i	$0.729321\pi$
$674$		0			0
$675$	1.65971	+	0.487333i	0.0638821	+	0.0187575i
$676$		0			0
$677$	−3.71912	+	25.8671i	−0.142937	+	0.994152i	0.784488	+	0.620144i	$0.212926\pi$
$677$	−3.71912	+	25.8671i	−0.142937	+	0.994152i	−0.927426	+	0.374008i	$0.877983\pi$
$678$		0			0
$679$	−10.7946	+	23.6369i	−0.414259	+	0.907100i
$680$		0			0
$681$	10.3749	−	6.66757i	0.397569	−	0.255502i
$682$		0			0
$683$	0.601211	+	4.18151i	0.0230047	+	0.160001i	0.998086	−	0.0618487i	$-0.0196996\pi$
$683$	0.601211	+	4.18151i	0.0230047	+	0.160001i	−0.975081	+	0.221850i	$0.928791\pi$
$684$		0			0
$685$	−9.93623	−	6.38563i	−0.379644	−	0.243982i
$686$		0			0
$687$	11.0205	−	3.23590i	0.420457	−	0.123457i
$688$		0			0
$689$	41.6619			1.58719
$690$		0			0
$691$	35.2154			1.33966			0.669829	−	0.742516i	$-0.266367\pi$
$691$	35.2154			1.33966			0.669829	+	0.742516i	$0.266367\pi$
$692$		0			0
$693$	−6.30658	+	1.85178i	−0.239567	+	0.0703433i
$694$		0			0
$695$	13.0118	+	8.36217i	0.493565	+	0.317195i
$696$		0			0
$697$	−0.759435	−	5.28199i	−0.0287657	−	0.200070i
$698$		0			0
$699$	−4.50163	+	2.89302i	−0.170267	+	0.109424i
$700$		0			0
$701$	16.0954	−	35.2441i	0.607917	−	1.33115i	−0.316073	−	0.948735i	$-0.602365\pi$
$701$	16.0954	−	35.2441i	0.607917	−	1.33115i	0.923990	−	0.382417i	$-0.124908\pi$
$702$		0			0
$703$	2.47976	−	17.2471i	0.0935261	−	0.650488i
$704$		0			0
$705$	17.9618	+	5.27406i	0.676481	+	0.198633i
$706$		0			0
$707$	19.9007	+	22.9666i	0.748443	+	0.863749i
$708$		0			0
$709$	9.24611	−	10.6706i	0.347245	−	0.400742i	−0.555081	−	0.831796i	$-0.687313\pi$
$709$	9.24611	−	10.6706i	0.347245	−	0.400742i	0.902326	+	0.431054i	$0.141858\pi$
$710$		0			0
$711$	2.64232	+	5.78588i	0.0990948	+	0.216987i
$712$		0			0
$713$	7.74047	+	14.4723i	0.289883	+	0.541991i
$714$		0			0
$715$	7.67151	+	16.7983i	0.286898	+	0.628220i
$716$		0			0
$717$	−7.49248	+	8.64679i	−0.279812	+	0.322920i
$718$		0			0
$719$	−31.2454	−	36.0591i	−1.16526	−	1.34478i	−0.927666	−	0.373412i	$-0.878188\pi$
$719$	−31.2454	−	36.0591i	−1.16526	−	1.34478i	−0.237590	−	0.971365i	$-0.576358\pi$
$720$		0			0
$721$	−2.89607	−	0.850363i	−0.107855	−	0.0316692i
$722$		0			0
$723$	−0.499101	+	3.47132i	−0.0185618	+	0.129100i
$724$		0			0
$725$	−3.06562	+	6.71278i	−0.113854	+	0.249306i
$726$		0			0
$727$	−30.9527	+	19.8921i	−1.14797	+	0.737756i	−0.969234	−	0.246141i	$-0.920837\pi$
$727$	−30.9527	+	19.8921i	−1.14797	+	0.737756i	−0.178736	+	0.983897i	$0.557201\pi$
$728$		0			0
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$		0			0
$731$	2.34234	+	1.50533i	0.0866347	+	0.0556768i
$732$		0			0
$733$	−23.7585	+	6.97613i	−0.877541	+	0.257669i	−0.689320	−	0.724457i	$-0.742090\pi$
$733$	−23.7585	+	6.97613i	−0.877541	+	0.257669i	−0.188221	+	0.982127i	$0.560272\pi$
$734$		0			0
$735$	−8.36958			−0.308717
$736$		0			0
$737$	11.9595			0.440533
$738$		0			0
$739$	−18.0128	+	5.28903i	−0.662611	+	0.194560i	−0.595710	−	0.803199i	$-0.703129\pi$
$739$	−18.0128	+	5.28903i	−0.662611	+	0.194560i	−0.0669010	+	0.997760i	$0.521311\pi$
$740$		0			0
$741$	21.1214	+	13.5739i	0.775915	+	0.498650i
$742$		0			0
$743$	4.33086	+	30.1218i	0.158884	+	1.10506i	0.900695	+	0.434452i	$0.143058\pi$
$743$	4.33086	+	30.1218i	0.158884	+	1.10506i	−0.741811	+	0.670609i	$0.766033\pi$
$744$		0			0
$745$	−4.92425	+	3.16462i	−0.180411	+	0.115943i
$746$		0			0
$747$	−4.06242	+	8.89545i	−0.148636	+	0.325468i
$748$		0			0
$749$	−3.83984	+	26.7067i	−0.140305	+	0.975840i
$750$		0			0
$751$	−34.7928	−	10.2161i	−1.26961	−	0.372790i	−0.423545	−	0.905875i	$-0.639215\pi$
$751$	−34.7928	−	10.2161i	−1.26961	−	0.372790i	−0.846062	+	0.533085i	$0.821033\pi$
$752$		0			0
$753$	7.75499	+	8.94974i	0.282608	+	0.326147i
$754$		0			0
$755$	8.32442	−	9.60689i	0.302957	−	0.349631i
$756$		0			0
$757$	−18.1304	−	39.7001i	−0.658961	−	1.44292i	−0.883487	−	0.468456i	$-0.844811\pi$
$757$	−18.1304	−	39.7001i	−0.658961	−	1.44292i	0.224526	−	0.974468i	$-0.427917\pi$
$758$		0			0
$759$	7.44791	−	5.47540i	0.270342	−	0.198744i
$760$		0			0
$761$	−1.29149	−	2.82797i	−0.0468164	−	0.102514i	0.884779	−	0.466012i	$-0.154310\pi$
$761$	−1.29149	−	2.82797i	−0.0468164	−	0.102514i	−0.931595	+	0.363498i	$0.881582\pi$
$762$		0			0
$763$	−3.93009	+	4.53557i	−0.142279	+	0.164198i
$764$		0			0
$765$	−0.897664	−	1.03596i	−0.0324551	−	0.0374552i
$766$		0			0
$767$	−54.9289	−	16.1286i	−1.98337	−	0.582369i
$768$		0			0
$769$	6.34944	−	44.1613i	0.228967	−	1.59250i	−0.473508	−	0.880790i	$-0.657012\pi$
$769$	6.34944	−	44.1613i	0.228967	−	1.59250i	0.702475	−	0.711709i	$-0.252078\pi$
$770$		0			0
$771$	−10.6029	+	23.2171i	−0.381854	+	0.836143i
$772$		0			0
$773$	14.3965	−	9.25209i	0.517807	−	0.332774i	−0.255497	−	0.966810i	$-0.582239\pi$
$773$	14.3965	−	9.25209i	0.517807	−	0.332774i	0.773304	+	0.634035i	$0.218603\pi$
$774$		0			0
$775$	−0.842448	−	5.85936i	−0.0302616	−	0.210474i
$776$		0			0
$777$	10.5478	+	6.77866i	0.378400	+	0.243183i
$778$		0			0
$779$	32.0102	−	9.39905i	1.14689	−	0.336756i
$780$		0			0
$781$	28.5121			1.02024
$782$		0			0
$783$	4.26626			0.152464
$784$		0			0
$785$	−34.7957	+	10.2169i	−1.24191	+	0.364658i
$786$		0			0
$787$	−36.8248	−	23.6658i	−1.31266	−	0.843596i	−0.318131	−	0.948047i	$-0.603055\pi$
$787$	−36.8248	−	23.6658i	−1.31266	−	0.843596i	−0.994530	+	0.104451i	$0.966692\pi$
$788$		0			0
$789$	0.511613	+	3.55835i	0.0182139	+	0.126681i
$790$		0			0
$791$	−47.9767	+	30.8327i	−1.70585	+	1.09629i
$792$		0			0
$793$	−28.3852	+	62.1549i	−1.00799	+	2.20718i
$794$		0			0
$795$	2.02378	−	14.0757i	0.0717761	−	0.499214i
$796$		0			0
$797$	−27.6054	−	8.10566i	−0.977832	−	0.287117i	−0.246503	−	0.969142i	$-0.579281\pi$
$797$	−27.6054	−	8.10566i	−0.977832	−	0.287117i	−0.731329	+	0.682025i	$0.761100\pi$
$798$		0			0
$799$	5.13859	+	5.93025i	0.181790	+	0.209797i
$800$		0			0
$801$	−7.29966	+	8.42426i	−0.257921	+	0.297657i
$802$		0			0
$803$	6.08454	+	13.3233i	0.214719	+	0.470168i
$804$		0			0
$805$	27.7978	−	10.0946i	0.979744	−	0.355788i
$806$		0			0
$807$	6.73465	+	14.7468i	0.237071	+	0.519113i
$808$		0			0
$809$	8.71151	−	10.0536i	0.306280	−	0.353466i	−0.581654	−	0.813436i	$-0.697594\pi$
$809$	8.71151	−	10.0536i	0.306280	−	0.353466i	0.887935	+	0.459970i	$0.152140\pi$
$810$		0			0
$811$	30.0940	+	34.7303i	1.05674	+	1.21955i	0.974840	+	0.222907i	$0.0715545\pi$
$811$	30.0940	+	34.7303i	1.05674	+	1.21955i	0.0819035	+	0.996640i	$0.473900\pi$
$812$		0			0
$813$	4.16510	+	1.22298i	0.146077	+	0.0428919i
$814$		0			0
$815$	−3.82075	+	26.5739i	−0.133835	+	0.930842i
$816$		0			0
$817$	−7.23123	+	15.8342i	−0.252989	+	0.553968i
$818$		0			0
$819$	−15.1984	+	9.76742i	−0.531075	+	0.341301i
$820$		0			0
$821$	6.84569	+	47.6128i	0.238916	+	1.66170i	0.657451	+	0.753498i	$0.271635\pi$
$821$	6.84569	+	47.6128i	0.238916	+	1.66170i	−0.418534	+	0.908201i	$0.637456\pi$
$822$		0			0
$823$	24.2085	+	15.5579i	0.843856	+	0.542313i	0.889653	−	0.456637i	$-0.150946\pi$
$823$	24.2085	+	15.5579i	0.843856	+	0.542313i	−0.0457968	+	0.998951i	$0.514583\pi$
$824$		0			0
$825$	−3.19909	+	0.939338i	−0.111378	+	0.0327035i
$826$		0			0
$827$	47.0915			1.63753			0.818766	−	0.574128i	$-0.194659\pi$
$827$	47.0915			1.63753			0.818766	+	0.574128i	$0.194659\pi$
$828$		0			0
$829$	−27.9669			−0.971330			−0.485665	−	0.874145i	$-0.661423\pi$
$829$	−27.9669			−0.971330			−0.485665	+	0.874145i	$0.661423\pi$
$830$		0			0
$831$	−27.4423	+	8.05780i	−0.951964	+	0.279522i
$832$		0			0
$833$	−2.95133	−	1.89670i	−0.102257	−	0.0657169i
$834$		0			0
$835$	−6.33934	−	44.0911i	−0.219382	−	1.52584i
$836$		0			0
$837$	−2.87893	+	1.85017i	−0.0995103	+	0.0639514i
$838$		0			0
$839$	7.71830	−	16.9007i	0.266465	−	0.583477i	−0.728347	−	0.685209i	$-0.759711\pi$
$839$	7.71830	−	16.9007i	0.266465	−	0.583477i	0.994812	+	0.101731i	$0.0324382\pi$
$840$		0			0
$841$	1.53686	−	10.6891i	0.0529952	−	0.368590i
$842$		0			0
$843$	10.8702	+	3.19177i	0.374388	+	0.109930i
$844$		0			0
$845$	17.8454	+	20.5947i	0.613899	+	0.708478i
$846$		0			0
$847$	−16.2674	+	18.7736i	−0.558955	+	0.645069i
$848$		0			0
$849$	−2.21591	−	4.85217i	−0.0760499	−	0.166526i
$850$		0			0
$851$	−17.1975	−	3.89743i	−0.589524	−	0.133602i
$852$		0			0
$853$	18.1531	+	39.7498i	0.621551	+	1.36101i	0.914386	+	0.404844i	$0.132674\pi$
$853$	18.1531	+	39.7498i	0.621551	+	1.36101i	−0.292834	+	0.956163i	$0.594598\pi$
$854$		0			0
$855$	5.61203	−	6.47663i	0.191927	−	0.221496i
$856$		0			0
$857$	23.5393	+	27.1658i	0.804087	+	0.927966i	0.998598	−	0.0529347i	$-0.0168575\pi$
$857$	23.5393	+	27.1658i	0.804087	+	0.927966i	−0.194511	+	0.980900i	$0.562312\pi$
$858$		0			0
$859$	26.6711	+	7.83135i	0.910008	+	0.267202i	0.703044	−	0.711146i	$-0.251824\pi$
$859$	26.6711	+	7.83135i	0.910008	+	0.267202i	0.206964	+	0.978349i	$0.433642\pi$
$860$		0			0
$861$	−3.41642	+	23.7618i	−0.116431	+	0.809798i
$862$		0			0
$863$	−2.79661	+	6.12373i	−0.0951979	+	0.208454i	−0.951240	−	0.308452i	$-0.900189\pi$
$863$	−2.79661	+	6.12373i	−0.0951979	+	0.208454i	0.856042	+	0.516906i	$0.172916\pi$
$864$		0			0
$865$	23.7432	−	15.2589i	0.807294	−	0.518817i
$866$		0			0
$867$	2.33758	+	16.2582i	0.0793884	+	0.552158i
$868$		0			0
$869$	−10.3140	−	6.62839i	−0.349878	−	0.224853i
$870$		0			0
$871$	31.5408	−	9.26122i	1.06872	−	0.313804i
$872$		0			0
$873$	7.62022			0.257906
$874$		0			0
$875$	−41.4998			−1.40295
$876$		0			0
$877$	−12.0177	+	3.52871i	−0.405808	+	0.119156i	−0.478265	−	0.878216i	$-0.658734\pi$
$877$	−12.0177	+	3.52871i	−0.405808	+	0.119156i	0.0724571	+	0.997372i	$0.476916\pi$
$878$		0			0
$879$	−19.8995	−	12.7886i	−0.671194	−	0.431350i
$880$		0			0
$881$	4.25497	+	29.5939i	0.143353	+	0.997045i	0.926792	+	0.375576i	$0.122555\pi$
$881$	4.25497	+	29.5939i	0.143353	+	0.997045i	−0.783438	+	0.621470i	$0.786536\pi$
$882$		0			0
$883$	16.2520	−	10.4445i	0.546923	−	0.351486i	−0.237818	−	0.971310i	$-0.576432\pi$
$883$	16.2520	−	10.4445i	0.546923	−	0.351486i	0.784741	+	0.619824i	$0.212796\pi$
$884$		0			0
$885$	−8.11738	+	17.7746i	−0.272863	+	0.597486i
$886$		0			0
$887$	7.50812	−	52.2201i	0.252098	−	1.75338i	−0.333474	−	0.942759i	$-0.608221\pi$
$887$	7.50812	−	52.2201i	0.252098	−	1.75338i	0.585572	−	0.810620i	$-0.300870\pi$
$888$		0			0
$889$	4.18481	+	1.22877i	0.140354	+	0.0412116i
$890$		0			0
$891$	1.26225	+	1.45671i	0.0422869	+	0.0488017i
$892$		0			0
$893$	−32.1255	+	37.0748i	−1.07504	+	1.24066i
$894$		0			0
$895$	13.6289	+	29.8430i	0.455562	+	0.997543i
$896$		0			0
$897$	15.4024	−	20.2078i	0.514270	−	0.674720i
$898$		0			0
$899$	−6.06504	−	13.2806i	−0.202280	−	0.442932i
$900$		0			0
$901$	3.90345	−	4.50483i	0.130043	−	0.150078i
$902$		0			0
$903$	−8.20264	−	9.46636i	−0.272967	−	0.315021i
$904$		0			0
$905$	−46.1555	−	13.5525i	−1.53426	−	0.450500i
$906$		0			0
$907$	−0.829035	+	5.76607i	−0.0275277	+	0.191459i	−0.998945	−	0.0459181i	$-0.985379\pi$
$907$	−0.829035	+	5.76607i	−0.0275277	+	0.191459i	0.971418	+	0.237377i	$0.0762878\pi$
$908$		0			0
$909$	3.70207	−	8.10641i	0.122790	−	0.268873i
$910$		0			0
$911$	−30.2223	+	19.4227i	−1.00131	+	0.643503i	−0.935130	−	0.354305i	$-0.884717\pi$
$911$	−30.2223	+	19.4227i	−1.00131	+	0.643503i	−0.0661796	+	0.997808i	$0.521081\pi$
$912$		0			0
$913$	−2.68255	−	18.6576i	−0.0887795	−	0.617475i
$914$		0			0
$915$	19.6205	+	12.6094i	0.648635	+	0.416852i
$916$		0			0
$917$	−32.9966	+	9.68868i	−1.08964	+	0.319949i
$918$		0			0
$919$	−5.76019			−0.190011			−0.0950055	−	0.995477i	$-0.530287\pi$
$919$	−5.76019			−0.190011			−0.0950055	+	0.995477i	$0.530287\pi$
$920$		0			0
$921$	−19.5823			−0.645257
$922$		0			0
$923$	75.1950	−	22.0792i	2.47507	−	0.726747i
$924$		0			0
$925$	5.35050	+	3.43856i	0.175923	+	0.113059i
$926$		0			0
$927$	0.125968	+	0.876128i	0.00413734	+	0.0287758i
$928$		0			0
$929$	16.6393	−	10.6934i	0.545917	−	0.350839i	−0.238432	−	0.971159i	$-0.576634\pi$
$929$	16.6393	−	10.6934i	0.545917	−	0.350839i	0.784349	+	0.620320i	$0.212997\pi$
$930$		0			0
$931$	9.11127	−	19.9509i	0.298610	−	0.653864i
$932$		0			0
$933$	0.273199	−	1.90014i	0.00894412	−	0.0622077i
$934$		0			0
$935$	2.53514	+	0.744384i	0.0829080	+	0.0243440i
$936$		0			0
$937$	−0.359201	−	0.414540i	−0.0117346	−	0.0135424i	0.749852	−	0.661606i	$-0.230125\pi$
$937$	−0.359201	−	0.414540i	−0.0117346	−	0.0135424i	−0.761587	+	0.648063i	$0.775579\pi$
$938$		0			0
$939$	8.30747	−	9.58733i	0.271104	−	0.312871i
$940$		0			0
$941$	18.7468	+	41.0498i	0.611129	+	1.33819i	0.921799	+	0.387669i	$0.126719\pi$
$941$	18.7468	+	41.0498i	0.611129	+	1.33819i	−0.310670	+	0.950518i	$0.600553\pi$
$942$		0			0
$943$	−6.89058	−	33.0514i	−0.224388	−	1.07630i
$944$		0			0
$945$	2.56170	+	5.60934i	0.0833320	+	0.182472i
$946$		0			0
$947$	−2.55059	+	2.94354i	−0.0828832	+	0.0956523i	−0.795676	−	0.605722i	$-0.792884\pi$
$947$	−2.55059	+	2.94354i	−0.0828832	+	0.0956523i	0.712793	+	0.701374i	$0.247430\pi$
$948$		0			0
$949$	26.3641	+	30.4258i	0.855815	+	0.987663i
$950$		0			0
$951$	−2.99816	−	0.880339i	−0.0972220	−	0.0285470i
$952$		0			0
$953$	6.86795	−	47.7677i	0.222475	−	1.54735i	−0.506157	−	0.862441i	$-0.668934\pi$
$953$	6.86795	−	47.7677i	0.222475	−	1.54735i	0.728632	−	0.684905i	$-0.240157\pi$
$954$		0			0
$955$	18.6250	−	40.7831i	0.602692	−	1.31971i
$956$		0			0
$957$	−6.91783	+	4.44582i	−0.223622	+	0.143713i
$958$		0			0
$959$	3.16966	+	22.0455i	0.102354	+	0.711886i
$960$		0			0
$961$	−16.2266	−	10.4282i	−0.523440	−	0.336394i
$962$		0			0
$963$	7.59185	−	2.22917i	0.244644	−	0.0718340i
$964$		0			0
$965$	8.53381			0.274713
$966$		0			0
$967$	−52.3950			−1.68491			−0.842456	−	0.538766i	$-0.818891\pi$
$967$	−52.3950			−1.68491			−0.842456	+	0.538766i	$0.818891\pi$
$968$		0			0
$969$	3.44667	−	1.01203i	0.110723	−	0.0325112i
$970$		0			0
$971$	0.372738	+	0.239544i	0.0119617	+	0.00768733i	0.546608	−	0.837389i	$-0.315919\pi$
$971$	0.372738	+	0.239544i	0.0119617	+	0.00768733i	−0.534646	+	0.845076i	$0.679555\pi$
$972$		0			0
$973$	−4.15077	−	28.8692i	−0.133067	−	0.925504i
$974$		0			0
$975$	−7.70957	+	4.95464i	−0.246904	+	0.158676i
$976$		0			0
$977$	21.8870	−	47.9259i	0.700228	−	1.53329i	−0.139467	−	0.990227i	$-0.544539\pi$
$977$	21.8870	−	47.9259i	0.700228	−	1.53329i	0.839695	−	0.543058i	$-0.182734\pi$
$978$		0			0
$979$	3.05773	−	21.2670i	0.0977255	−	0.679696i
$980$		0			0
$981$	1.68865	+	0.495831i	0.0539143	+	0.0158307i
$982$		0			0
$983$	−10.4554	−	12.0662i	−0.333475	−	0.384851i	0.564104	−	0.825704i	$-0.309222\pi$
$983$	−10.4554	−	12.0662i	−0.333475	−	0.384851i	−0.897580	+	0.440853i	$0.854676\pi$
$984$		0			0
$985$	−13.1830	+	15.2140i	−0.420046	+	0.484758i
$986$		0			0
$987$	−14.6642	−	32.1101i	−0.466767	−	1.02208i
$988$		0			0
$989$	15.3876	+	8.57617i	0.489299	+	0.272706i
$990$		0			0
$991$	−9.03107	−	19.7753i	−0.286881	−	0.628183i	0.710244	−	0.703956i	$-0.248585\pi$
$991$	−9.03107	−	19.7753i	−0.286881	−	0.628183i	−0.997125	+	0.0757732i	$0.975857\pi$
$992$		0			0
$993$	8.42732	−	9.72565i	0.267433	−	0.308634i
$994$		0			0
$995$	−9.34129	−	10.7804i	−0.296139	−	0.341762i
$996$		0			0
$997$	−30.8973	−	9.07225i	−0.978526	−	0.287321i	−0.246910	−	0.969038i	$-0.579415\pi$
$997$	−30.8973	−	9.07225i	−0.978526	−	0.287321i	−0.731616	+	0.681717i	$0.761233\pi$
$998$		0			0
$999$	0.523273	−	3.63944i	0.0165556	−	0.115147i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.i.a.73.1	✓	20
3.2	odd	2		828.2.q.c.73.2		20
23.6	even	11	inner	276.2.i.a.121.1	yes	20
23.11	odd	22		6348.2.a.t.1.8		10
23.12	even	11		6348.2.a.s.1.3		10
69.29	odd	22		828.2.q.c.397.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.i.a.73.1	✓	20	1.1	even	1	trivial
276.2.i.a.121.1	yes	20	23.6	even	11	inner
828.2.q.c.73.2		20	3.2	odd	2
828.2.q.c.397.2		20	69.29	odd	22
6348.2.a.s.1.3		10	23.12	even	11
6348.2.a.t.1.8		10	23.11	odd	22

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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 + 0.281733i) q^{3} +(-1.52130 - 0.977682i) q^{5} +(0.485296 + 3.37531i) q^{7} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.959493 + 0.281733i) q^{3} +(-1.52130 - 0.977682i) q^{5} +(0.485296 + 3.37531i) q^{7} +(0.841254 - 0.540641i) q^{9} +(-0.800715 + 1.75332i) q^{11} +(-0.753988 + 5.24410i) q^{13} +(1.73512 + 0.509479i) q^{15} +(0.496392 + 0.572867i) q^{17} +(-3.10335 + 3.58146i) q^{19} +(-1.41657 - 3.10186i) q^{21} +(3.36166 + 3.42041i) q^{23} +(-0.718574 - 1.57346i) q^{25} +(-0.654861 + 0.755750i) q^{27} +(-2.79381 - 3.22422i) q^{29} +(3.28356 + 0.964142i) q^{31} +(0.274313 - 1.90789i) q^{33} +(2.56170 - 5.60934i) q^{35} +(-3.09318 + 1.98787i) q^{37} +(-0.753988 - 5.24410i) q^{39} +(-5.92232 - 3.80604i) q^{41} +(3.52444 - 1.03487i) q^{43} -1.80838 q^{45} +10.3519 q^{47} +(-4.44075 + 1.30392i) q^{49} +(-0.637680 - 0.409812i) q^{51} +(-1.11911 - 7.78361i) q^{53} +(2.93232 - 1.88449i) q^{55} +(1.96863 - 4.31070i) q^{57} +(-1.53778 + 10.6955i) q^{59} +(12.3748 + 3.63356i) q^{61} +(2.23309 + 2.57712i) q^{63} +(6.27411 - 7.24071i) q^{65} +(-2.57750 - 5.64394i) q^{67} +(-4.18913 - 2.33477i) q^{69} +(-6.14490 - 13.4555i) q^{71} +(4.97621 - 5.74285i) q^{73} +(1.13276 + 1.30728i) q^{75} +(-6.30658 - 1.85178i) q^{77} +(-0.905219 + 6.29594i) q^{79} +(0.415415 - 0.909632i) q^{81} +(-8.22677 + 5.28702i) q^{83} +(-0.195081 - 1.35682i) q^{85} +(3.58901 + 2.30651i) q^{87} +(-10.6954 + 3.14044i) q^{89} -18.0664 q^{91} -3.42219 q^{93} +(8.22267 - 2.41439i) q^{95} +(6.41054 + 4.11980i) q^{97} +(0.274313 + 1.90789i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9	\( 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9} - 22 q^{13} + 7 q^{15} + 7 q^{17} + 19 q^{19} + 20 q^{23} + 20 q^{25} - 2 q^{27} + 32 q^{29} - 3 q^{31} + 11 q^{33} - 26 q^{35} - 10 q^{37} - 22 q^{39} - 40 q^{41} + 8 q^{43} - 4 q^{45} - 18 q^{47} - 34 q^{49} - 26 q^{51} - 34 q^{53} - 17 q^{55} - 3 q^{57} - 32 q^{59} + 32 q^{61} + 49 q^{65} + 35 q^{67} - 2 q^{69} + 33 q^{71} - q^{73} - 2 q^{75} - 50 q^{77} + 22 q^{79} - 2 q^{81} - 14 q^{83} - 9 q^{85} - 12 q^{87} + 10 q^{89} - 72 q^{91} + 30 q^{93} - 51 q^{95} - 4 q^{97} + 11 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9 - 22 * q^13 + 7 * q^15 + 7 * q^17 + 19 * q^19 + 20 * q^23 + 20 * q^25 - 2 * q^27 + 32 * q^29 - 3 * q^31 + 11 * q^33 - 26 * q^35 - 10 * q^37 - 22 * q^39 - 40 * q^41 + 8 * q^43 - 4 * q^45 - 18 * q^47 - 34 * q^49 - 26 * q^51 - 34 * q^53 - 17 * q^55 - 3 * q^57 - 32 * q^59 + 32 * q^61 + 49 * q^65 + 35 * q^67 - 2 * q^69 + 33 * q^71 - q^73 - 2 * q^75 - 50 * q^77 + 22 * q^79 - 2 * q^81 - 14 * q^83 - 9 * q^85 - 12 * q^87 + 10 * q^89 - 72 * q^91 + 30 * q^93 - 51 * q^95 - 4 * q^97 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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