LMFDB - Embedded newform 765.2.k.c.676.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [765,2,Mod(361,765)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(765, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("765.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 765 = 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	765.k (of order $4$, 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:	$6.10855575463$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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} + 26x^{14} + 277x^{12} + 1566x^{10} + 5064x^{8} + 9342x^{6} + 9109x^{4} + 3770x^{2} + 289 $ x^16 + 26x^14 + 277x^12 + 1566x^10 + 5064x^8 + 9342x^6 + 9109x^4 + 3770*x^2 + 289
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 255)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			676.6
Root			$1.67959i$ of defining polynomial
Character	$\chi$	$=$	765.676
Dual form			765.2.k.c.361.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.67959i q^{2} -0.821013 q^{4} +(0.707107 + 0.707107i) q^{5} +(3.02569 - 3.02569i) q^{7} +1.98021i q^{8} +O(q^{10})$	\(q+1.67959i q^{2} -0.821013 q^{4} +(0.707107 + 0.707107i) q^{5} +(3.02569 - 3.02569i) q^{7} +1.98021i q^{8} +(-1.18765 + 1.18765i) q^{10} +(2.89420 - 2.89420i) q^{11} +0.439079 q^{13} +(5.08191 + 5.08191i) q^{14} -4.96796 q^{16} +(2.30984 - 3.41535i) q^{17} -6.44189i q^{19} +(-0.580544 - 0.580544i) q^{20} +(4.86106 + 4.86106i) q^{22} +(-1.00915 + 1.00915i) q^{23} +1.00000i q^{25} +0.737471i q^{26} +(-2.48413 + 2.48413i) q^{28} +(-1.73422 - 1.73422i) q^{29} +(4.90418 + 4.90418i) q^{31} -4.38371i q^{32} +(5.73639 + 3.87957i) q^{34} +4.27897 q^{35} +(2.10567 + 2.10567i) q^{37} +10.8197 q^{38} +(-1.40022 + 1.40022i) q^{40} +(-7.91197 + 7.91197i) q^{41} +0.493885i q^{43} +(-2.37618 + 2.37618i) q^{44} +(-1.69496 - 1.69496i) q^{46} -9.32536 q^{47} -11.3096i q^{49} -1.67959 q^{50} -0.360489 q^{52} +10.4771i q^{53} +4.09302 q^{55} +(5.99150 + 5.99150i) q^{56} +(2.91277 - 2.91277i) q^{58} -1.57379i q^{59} +(-10.4634 + 10.4634i) q^{61} +(-8.23700 + 8.23700i) q^{62} -2.57311 q^{64} +(0.310476 + 0.310476i) q^{65} +8.59380 q^{67} +(-1.89641 + 2.80405i) q^{68} +7.18690i q^{70} +(-4.74540 - 4.74540i) q^{71} +(2.65402 + 2.65402i) q^{73} +(-3.53666 + 3.53666i) q^{74} +5.28888i q^{76} -17.5139i q^{77} +(-3.62038 + 3.62038i) q^{79} +(-3.51288 - 3.51288i) q^{80} +(-13.2888 - 13.2888i) q^{82} +4.41377i q^{83} +(4.04832 - 0.781718i) q^{85} -0.829523 q^{86} +(5.73113 + 5.73113i) q^{88} +1.96863 q^{89} +(1.32852 - 1.32852i) q^{91} +(0.828529 - 0.828529i) q^{92} -15.6628i q^{94} +(4.55511 - 4.55511i) q^{95} +(-0.619676 - 0.619676i) q^{97} +18.9954 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 20 q^{4} + 4 q^{7}+O(q^{10}) $ 16 * q - 20 * q^4 + 4 * q^7	$ 16 q - 20 q^{4} + 4 q^{7} - 4 q^{11} - 16 q^{13} + 16 q^{14} - 4 q^{16} + 12 q^{17} - 8 q^{20} - 20 q^{22} - 20 q^{23} - 8 q^{28} - 20 q^{29} - 12 q^{31} + 12 q^{34} - 4 q^{37} + 68 q^{38} + 12 q^{40} + 4 q^{41} + 44 q^{44} + 76 q^{46} - 40 q^{47} - 4 q^{50} + 72 q^{52} + 28 q^{56} + 20 q^{58} - 44 q^{61} + 36 q^{62} - 16 q^{64} + 4 q^{65} - 24 q^{67} - 48 q^{68} + 16 q^{71} + 12 q^{73} - 32 q^{74} - 24 q^{79} - 28 q^{82} + 8 q^{85} - 16 q^{86} + 116 q^{88} + 40 q^{89} + 84 q^{91} - 24 q^{92} - 16 q^{95} + 40 q^{97} - 56 q^{98}+O(q^{100}) $ 16 * q - 20 * q^4 + 4 * q^7 - 4 * q^11 - 16 * q^13 + 16 * q^14 - 4 * q^16 + 12 * q^17 - 8 * q^20 - 20 * q^22 - 20 * q^23 - 8 * q^28 - 20 * q^29 - 12 * q^31 + 12 * q^34 - 4 * q^37 + 68 * q^38 + 12 * q^40 + 4 * q^41 + 44 * q^44 + 76 * q^46 - 40 * q^47 - 4 * q^50 + 72 * q^52 + 28 * q^56 + 20 * q^58 - 44 * q^61 + 36 * q^62 - 16 * q^64 + 4 * q^65 - 24 * q^67 - 48 * q^68 + 16 * q^71 + 12 * q^73 - 32 * q^74 - 24 * q^79 - 28 * q^82 + 8 * q^85 - 16 * q^86 + 116 * q^88 + 40 * q^89 + 84 * q^91 - 24 * q^92 - 16 * q^95 + 40 * q^97 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/765\mathbb{Z}\right)^\times$.

$n$	$307$	$496$	$596$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$			1.67959i			1.18765i	0.804595	+	0.593824i	$0.202382\pi$
$2$			1.67959i			1.18765i	−0.804595	+	0.593824i	$0.797618\pi$
$3$		0			0
$3$		0			0
$4$	−0.821013			−0.410507
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$		0			0
$7$	3.02569	−	3.02569i	1.14360	−	1.14360i	0.155817	−	0.987786i	$-0.450199\pi$
$7$	3.02569	−	3.02569i	1.14360	−	1.14360i	0.987786	−	0.155817i	$-0.0498011\pi$
$8$			1.98021i			0.700110i
$9$		0			0
$10$	−1.18765	+	1.18765i	−0.375567	+	0.375567i
$11$	2.89420	−	2.89420i	0.872634	−	0.872634i	−0.120124	−	0.992759i	$-0.538329\pi$
$11$	2.89420	−	2.89420i	0.872634	−	0.872634i	0.992759	+	0.120124i	$0.0383294\pi$
$12$		0			0
$13$	0.439079			0.121779			0.0608893	−	0.998145i	$-0.480606\pi$
$13$	0.439079			0.121779			0.0608893	+	0.998145i	$0.480606\pi$
$14$	5.08191	+	5.08191i	1.35820	+	1.35820i
$15$		0			0
$16$	−4.96796			−1.24199
$17$	2.30984	−	3.41535i	0.560218	−	0.828345i
$17$	2.30984	−	3.41535i	0.560218	−	0.828345i
$18$		0			0
$19$		−	6.44189i		−	1.47787i	−0.673776	−	0.738936i	$-0.735329\pi$
$19$		−	6.44189i		−	1.47787i	0.673776	−	0.738936i	$-0.264671\pi$
$20$	−0.580544	−	0.580544i	−0.129814	−	0.129814i
$21$		0			0
$22$	4.86106	+	4.86106i	1.03638	+	1.03638i
$23$	−1.00915	+	1.00915i	−0.210423	+	0.210423i	−0.804447	−	0.594024i	$-0.797538\pi$
$23$	−1.00915	+	1.00915i	−0.210423	+	0.210423i	0.594024	+	0.804447i	$0.297538\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$			0.737471i			0.144630i
$27$		0			0
$28$	−2.48413	+	2.48413i	−0.469457	+	0.469457i
$29$	−1.73422	−	1.73422i	−0.322037	−	0.322037i	0.527511	−	0.849548i	$-0.323125\pi$
$29$	−1.73422	−	1.73422i	−0.322037	−	0.322037i	−0.849548	+	0.527511i	$0.823125\pi$
$30$		0			0
$31$	4.90418	+	4.90418i	0.880817	+	0.880817i	0.993618	−	0.112801i	$-0.0359822\pi$
$31$	4.90418	+	4.90418i	0.880817	+	0.880817i	−0.112801	+	0.993618i	$0.535982\pi$
$32$		−	4.38371i		−	0.774937i
$33$		0			0
$34$	5.73639	+	3.87957i	0.983782	+	0.665342i
$35$	4.27897			0.723278
$36$		0			0
$37$	2.10567	+	2.10567i	0.346170	+	0.346170i	0.858681	−	0.512511i	$-0.171284\pi$
$37$	2.10567	+	2.10567i	0.346170	+	0.346170i	−0.512511	+	0.858681i	$0.671284\pi$
$38$	10.8197			1.75519
$39$		0			0
$40$	−1.40022	+	1.40022i	−0.221394	+	0.221394i
$41$	−7.91197	+	7.91197i	−1.23564	+	1.23564i	−0.273878	+	0.961765i	$0.588306\pi$
$41$	−7.91197	+	7.91197i	−1.23564	+	1.23564i	−0.961765	+	0.273878i	$0.911694\pi$
$42$		0			0
$43$			0.493885i			0.0753168i	0.999291	+	0.0376584i	$0.0119899\pi$
$43$			0.493885i			0.0753168i	−0.999291	+	0.0376584i	$0.988010\pi$
$44$	−2.37618	+	2.37618i	−0.358222	+	0.358222i
$45$		0			0
$46$	−1.69496	−	1.69496i	−0.249909	−	0.249909i
$47$	−9.32536			−1.36024			−0.680122	−	0.733099i	$-0.738073\pi$
$47$	−9.32536			−1.36024			−0.680122	+	0.733099i	$0.738073\pi$
$48$		0			0
$49$		−	11.3096i		−	1.61566i
$50$	−1.67959			−0.237529
$51$		0			0
$52$	−0.360489			−0.0499909
$53$			10.4771i			1.43913i	0.694423	+	0.719567i	$0.255660\pi$
$53$			10.4771i			1.43913i	−0.694423	+	0.719567i	$0.744340\pi$
$54$		0			0
$55$	4.09302			0.551902
$56$	5.99150	+	5.99150i	0.800649	+	0.800649i
$57$		0			0
$58$	2.91277	−	2.91277i	0.382466	−	0.382466i
$59$		−	1.57379i		−	0.204890i	−0.994739	−	0.102445i	$-0.967333\pi$
$59$		−	1.57379i		−	0.204890i	0.994739	−	0.102445i	$-0.0326666\pi$
$60$		0			0
$61$	−10.4634	+	10.4634i	−1.33970	+	1.33970i	−0.443345	+	0.896351i	$0.646208\pi$
$61$	−10.4634	+	10.4634i	−1.33970	+	1.33970i	−0.896351	+	0.443345i	$0.853792\pi$
$62$	−8.23700	+	8.23700i	−1.04610	+	1.04610i
$63$		0			0
$64$	−2.57311			−0.321639
$65$	0.310476	+	0.310476i	0.0385098	+	0.0385098i
$66$		0			0
$67$	8.59380			1.04990			0.524950	−	0.851133i	$-0.324084\pi$
$67$	8.59380			1.04990			0.524950	+	0.851133i	$0.324084\pi$
$68$	−1.89641	+	2.80405i	−0.229973	+	0.340041i
$69$		0			0
$70$			7.18690i			0.858999i
$71$	−4.74540	−	4.74540i	−0.563176	−	0.563176i	0.367032	−	0.930208i	$-0.380374\pi$
$71$	−4.74540	−	4.74540i	−0.563176	−	0.563176i	−0.930208	+	0.367032i	$0.880374\pi$
$72$		0			0
$73$	2.65402	+	2.65402i	0.310629	+	0.310629i	0.845153	−	0.534524i	$-0.179509\pi$
$73$	2.65402	+	2.65402i	0.310629	+	0.310629i	−0.534524	+	0.845153i	$0.679509\pi$
$74$	−3.53666	+	3.53666i	−0.411128	+	0.411128i
$75$		0			0
$76$			5.28888i			0.606676i
$77$		−	17.5139i		−	1.99589i
$78$		0			0
$79$	−3.62038	+	3.62038i	−0.407324	+	0.407324i	−0.880804	−	0.473480i	$-0.842998\pi$
$79$	−3.62038	+	3.62038i	−0.407324	+	0.407324i	0.473480	+	0.880804i	$0.342998\pi$
$80$	−3.51288	−	3.51288i	−0.392752	−	0.392752i
$81$		0			0
$82$	−13.2888	−	13.2888i	−1.46751	−	1.46751i
$83$			4.41377i			0.484474i	0.970217	+	0.242237i	$0.0778811\pi$
$83$			4.41377i			0.484474i	−0.970217	+	0.242237i	$0.922119\pi$
$84$		0			0
$85$	4.04832	−	0.781718i	0.439102	−	0.0847893i
$86$	−0.829523			−0.0894498
$87$		0			0
$88$	5.73113	+	5.73113i	0.610940	+	0.610940i
$89$	1.96863			0.208674			0.104337	−	0.994542i	$-0.466728\pi$
$89$	1.96863			0.208674			0.104337	+	0.994542i	$0.466728\pi$
$90$		0			0
$91$	1.32852	−	1.32852i	0.139266	−	0.139266i
$92$	0.828529	−	0.828529i	0.0863801	−	0.0863801i
$93$		0			0
$94$		−	15.6628i		−	1.61549i
$95$	4.55511	−	4.55511i	0.467344	−	0.467344i
$96$		0			0
$97$	−0.619676	−	0.619676i	−0.0629186	−	0.0629186i	0.674947	−	0.737866i	$-0.264166\pi$
$97$	−0.619676	−	0.619676i	−0.0629186	−	0.0629186i	−0.737866	+	0.674947i	$0.764166\pi$
$98$	18.9954			1.91883
$99$		0			0
$100$		−	0.821013i		−	0.0821013i
$101$	−11.5416			−1.14844			−0.574218	−	0.818702i	$-0.694694\pi$
$101$	−11.5416			−1.14844			−0.574218	+	0.818702i	$0.694694\pi$
$102$		0			0
$103$	8.50163			0.837690			0.418845	−	0.908058i	$-0.362435\pi$
$103$	8.50163			0.837690			0.418845	+	0.908058i	$0.362435\pi$
$104$			0.869469i			0.0852584i
$105$		0			0
$106$	−17.5971			−1.70918
$107$	5.71988	+	5.71988i	0.552962	+	0.552962i	0.927295	−	0.374332i	$-0.122128\pi$
$107$	5.71988	+	5.71988i	0.552962	+	0.552962i	−0.374332	+	0.927295i	$0.622128\pi$
$108$		0			0
$109$	−14.0284	+	14.0284i	−1.34368	+	1.34368i	−0.451309	+	0.892368i	$0.649043\pi$
$109$	−14.0284	+	14.0284i	−1.34368	+	1.34368i	−0.892368	+	0.451309i	$0.850957\pi$
$110$			6.87458i			0.655466i
$111$		0			0
$112$	−15.0315	+	15.0315i	−1.42034	+	1.42034i
$113$	7.28696	−	7.28696i	0.685500	−	0.685500i	−0.275734	−	0.961234i	$-0.588921\pi$
$113$	7.28696	−	7.28696i	0.685500	−	0.685500i	0.961234	+	0.275734i	$0.0889210\pi$
$114$		0			0
$115$	−1.42716			−0.133083
$116$	1.42382	+	1.42382i	0.132198	+	0.132198i
$117$		0			0
$118$	2.64332			0.243337
$119$	−3.34495	−	17.3227i	−0.306631	−	1.58797i
$120$		0			0
$121$		−	5.75280i		−	0.522982i
$122$	−17.5741	−	17.5741i	−1.59109	−	1.59109i
$123$		0			0
$124$	−4.02640	−	4.02640i	−0.361581	−	0.361581i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$		0			0
$127$		−	4.75054i		−	0.421542i	−0.977535	−	0.210771i	$-0.932403\pi$
$127$		−	4.75054i		−	0.421542i	0.977535	−	0.210771i	$-0.0675974\pi$
$128$		−	13.0892i		−	1.15693i
$129$		0			0
$130$	−0.521471	+	0.521471i	−0.0457360	+	0.0457360i
$131$	−13.3729	−	13.3729i	−1.16840	−	1.16840i	−0.982586	−	0.185810i	$-0.940509\pi$
$131$	−13.3729	−	13.3729i	−1.16840	−	1.16840i	−0.185810	−	0.982586i	$-0.559491\pi$
$132$		0			0
$133$	−19.4912	−	19.4912i	−1.69010	−	1.69010i
$134$			14.4340i			1.24691i
$135$		0			0
$136$	6.76312	+	4.57397i	0.579933	+	0.392214i
$137$	9.16489			0.783010			0.391505	−	0.920176i	$-0.371955\pi$
$137$	9.16489			0.783010			0.391505	+	0.920176i	$0.371955\pi$
$138$		0			0
$139$	2.71929	+	2.71929i	0.230647	+	0.230647i	0.812963	−	0.582316i	$-0.197853\pi$
$139$	2.71929	+	2.71929i	0.230647	+	0.230647i	−0.582316	+	0.812963i	$0.697853\pi$
$140$	−3.51309			−0.296910
$141$		0			0
$142$	7.97032	−	7.97032i	0.668854	−	0.668854i
$143$	1.27078	−	1.27078i	0.106268	−	0.106268i
$144$		0			0
$145$		−	2.45256i		−	0.203674i
$146$	−4.45765	+	4.45765i	−0.368918	+	0.368918i
$147$		0			0
$148$	−1.72878	−	1.72878i	−0.142105	−	0.142105i
$149$	19.0319			1.55916			0.779578	−	0.626305i	$-0.215434\pi$
$149$	19.0319			1.55916			0.779578	+	0.626305i	$0.215434\pi$
$150$		0			0
$151$			9.25373i			0.753058i	0.926405	+	0.376529i	$0.122882\pi$
$151$			9.25373i			0.753058i	−0.926405	+	0.376529i	$0.877118\pi$
$152$	12.7563			1.03467
$153$		0			0
$154$	29.4161			2.37042
$155$			6.93556i			0.557077i
$156$		0			0
$157$	−11.6598			−0.930551			−0.465275	−	0.885166i	$-0.654045\pi$
$157$	−11.6598			−0.930551			−0.465275	+	0.885166i	$0.654045\pi$
$158$	−6.08074	−	6.08074i	−0.483757	−	0.483757i
$159$		0			0
$160$	3.09975	−	3.09975i	0.245057	−	0.245057i
$161$			6.10678i			0.481281i
$162$		0			0
$163$	13.7525	−	13.7525i	1.07718	−	1.07718i	0.0804174	−	0.996761i	$-0.474375\pi$
$163$	13.7525	−	13.7525i	1.07718	−	1.07718i	0.996761	−	0.0804174i	$-0.0256253\pi$
$164$	6.49583	−	6.49583i	0.507239	−	0.507239i
$165$		0			0
$166$	−7.41330			−0.575384
$167$	−0.0611209	−	0.0611209i	−0.00472968	−	0.00472968i	0.704738	−	0.709468i	$-0.251065\pi$
$167$	−0.0611209	−	0.0611209i	−0.00472968	−	0.00472968i	−0.709468	+	0.704738i	$0.751065\pi$
$168$		0			0
$169$	−12.8072			−0.985170
$170$	1.31296	+	6.79951i	0.100700	+	0.521499i
$171$		0			0
$172$		−	0.405486i		−	0.0309180i
$173$	3.83923	+	3.83923i	0.291891	+	0.291891i	0.837827	−	0.545936i	$-0.183826\pi$
$173$	3.83923	+	3.83923i	0.291891	+	0.291891i	−0.545936	+	0.837827i	$0.683826\pi$
$174$		0			0
$175$	3.02569	+	3.02569i	0.228721	+	0.228721i
$176$	−14.3783	+	14.3783i	−1.08380	+	1.08380i
$177$		0			0
$178$			3.30648i			0.247831i
$179$			3.22062i			0.240720i	0.992730	+	0.120360i	$0.0384050\pi$
$179$			3.22062i			0.240720i	−0.992730	+	0.120360i	$0.961595\pi$
$180$		0			0
$181$	18.2577	−	18.2577i	1.35709	−	1.35709i	0.479599	−	0.877488i	$-0.340782\pi$
$181$	18.2577	−	18.2577i	1.35709	−	1.35709i	0.877488	−	0.479599i	$-0.159218\pi$
$182$	2.23136	+	2.23136i	0.165399	+	0.165399i
$183$		0			0
$184$	−1.99834	−	1.99834i	−0.147320	−	0.147320i
$185$			2.97787i			0.218937i
$186$		0			0
$187$	−3.19959	−	16.5699i	−0.233977	−	1.21171i
$188$	7.65624			0.558389
$189$		0			0
$190$	7.65070	+	7.65070i	0.555040	+	0.555040i
$191$	−9.54898			−0.690940			−0.345470	−	0.938430i	$-0.612280\pi$
$191$	−9.54898			−0.690940			−0.345470	+	0.938430i	$0.612280\pi$
$192$		0			0
$193$	0.852092	−	0.852092i	0.0613349	−	0.0613349i	−0.675774	−	0.737109i	$-0.736190\pi$
$193$	0.852092	−	0.852092i	0.0613349	−	0.0613349i	0.737109	+	0.675774i	$0.236190\pi$
$194$	1.04080	−	1.04080i	0.0747251	−	0.0747251i
$195$		0			0
$196$			9.28532i			0.663237i
$197$	10.1701	−	10.1701i	0.724592	−	0.724592i	−0.244945	−	0.969537i	$-0.578770\pi$
$197$	10.1701	−	10.1701i	0.724592	−	0.724592i	0.969537	+	0.244945i	$0.0787699\pi$
$198$		0			0
$199$	9.08259	+	9.08259i	0.643848	+	0.643848i	0.951499	−	0.307651i	$-0.0995430\pi$
$199$	9.08259	+	9.08259i	0.643848	+	0.643848i	−0.307651	+	0.951499i	$0.599543\pi$
$200$	−1.98021			−0.140022
$201$		0			0
$202$		−	19.3852i		−	1.36394i
$203$	−10.4944			−0.736564
$204$		0			0
$205$	−11.1892			−0.781489
$206$			14.2792i			0.994881i
$207$		0			0
$208$	−2.18133			−0.151248
$209$	−18.6441	−	18.6441i	−1.28964	−	1.28964i
$210$		0			0
$211$	−19.2917	+	19.2917i	−1.32810	+	1.32810i	−0.421067	+	0.907030i	$0.638344\pi$
$211$	−19.2917	+	19.2917i	−1.32810	+	1.32810i	−0.907030	+	0.421067i	$0.861656\pi$
$212$		−	8.60180i		−	0.590774i
$213$		0			0
$214$	−9.60704	+	9.60704i	−0.656724	+	0.656724i
$215$	−0.349229	+	0.349229i	−0.0238172	+	0.0238172i
$216$		0			0
$217$	29.6771			2.01461
$218$	−23.5619	−	23.5619i	−1.59581	−	1.59581i
$219$		0			0
$220$	−3.36042			−0.226560
$221$	1.01420	−	1.49961i	0.0682225	−	0.100875i
$222$		0			0
$223$			11.0021i			0.736755i	0.929676	+	0.368377i	$0.120087\pi$
$223$			11.0021i			0.736755i	−0.929676	+	0.368377i	$0.879913\pi$
$224$	−13.2637	−	13.2637i	−0.886220	−	0.886220i
$225$		0			0
$226$	12.2391	+	12.2391i	0.814132	+	0.814132i
$227$	10.7537	−	10.7537i	0.713746	−	0.713746i	−0.253571	−	0.967317i	$-0.581605\pi$
$227$	10.7537	−	10.7537i	0.713746	−	0.713746i	0.967317	+	0.253571i	$0.0816051\pi$
$228$		0			0
$229$		−	27.8444i		−	1.84001i	−0.391905	−	0.920006i	$-0.628184\pi$
$229$		−	27.8444i		−	1.84001i	0.391905	−	0.920006i	$-0.371816\pi$
$230$		−	2.39704i		−	0.158056i
$231$		0			0
$232$	3.43412	−	3.43412i	0.225461	−	0.225461i
$233$	4.03285	+	4.03285i	0.264201	+	0.264201i	0.826758	−	0.562557i	$-0.190182\pi$
$233$	4.03285	+	4.03285i	0.264201	+	0.264201i	−0.562557	+	0.826758i	$0.690182\pi$
$234$		0			0
$235$	−6.59402	−	6.59402i	−0.430147	−	0.430147i
$236$			1.29210i			0.0841086i
$237$		0			0
$238$	29.0949	−	5.61814i	1.88594	−	0.364170i
$239$	2.40695			0.155693			0.0778463	−	0.996965i	$-0.475196\pi$
$239$	2.40695			0.155693			0.0778463	+	0.996965i	$0.475196\pi$
$240$		0			0
$241$	−0.738168	−	0.738168i	−0.0475496	−	0.0475496i	0.682932	−	0.730482i	$-0.260704\pi$
$241$	−0.738168	−	0.738168i	−0.0475496	−	0.0475496i	−0.730482	+	0.682932i	$0.760704\pi$
$242$	9.66232			0.621118
$243$		0			0
$244$	8.59056	−	8.59056i	0.549954	−	0.549954i
$245$	7.99709	−	7.99709i	0.510915	−	0.510915i
$246$		0			0
$247$		−	2.82850i		−	0.179973i
$248$	−9.71131	+	9.71131i	−0.616669	+	0.616669i
$249$		0			0
$250$	−1.18765	−	1.18765i	−0.0751134	−	0.0751134i
$251$	3.38799			0.213848			0.106924	−	0.994267i	$-0.465900\pi$
$251$	3.38799			0.213848			0.106924	+	0.994267i	$0.465900\pi$
$252$		0			0
$253$			5.84139i			0.367245i
$254$	7.97894			0.500643
$255$		0			0
$256$	16.8382			1.05239
$257$			4.80677i			0.299838i	0.988698	+	0.149919i	$0.0479013\pi$
$257$			4.80677i			0.299838i	−0.988698	+	0.149919i	$0.952099\pi$
$258$		0			0
$259$	12.7422			0.791763
$260$	−0.254904	−	0.254904i	−0.0158085	−	0.0158085i
$261$		0			0
$262$	22.4609	−	22.4609i	1.38764	−	1.38764i
$263$			3.29766i			0.203343i	0.994818	+	0.101671i	$0.0324190\pi$
$263$			3.29766i			0.203343i	−0.994818	+	0.101671i	$0.967581\pi$
$264$		0			0
$265$	−7.40840	+	7.40840i	−0.455094	+	0.455094i
$266$	32.7371	−	32.7371i	2.00724	−	2.00724i
$267$		0			0
$268$	−7.05562			−0.430991
$269$	−17.7235	−	17.7235i	−1.08062	−	1.08062i	−0.996452	−	0.0841685i	$-0.973177\pi$
$269$	−17.7235	−	17.7235i	−1.08062	−	1.08062i	−0.0841685	−	0.996452i	$-0.526823\pi$
$270$		0			0
$271$	−4.04356			−0.245629			−0.122814	−	0.992430i	$-0.539192\pi$
$271$	−4.04356			−0.245629			−0.122814	+	0.992430i	$0.539192\pi$
$272$	−11.4752	+	16.9674i	−0.695786	+	1.02880i
$273$		0			0
$274$			15.3932i			0.929939i
$275$	2.89420	+	2.89420i	0.174527	+	0.174527i
$276$		0			0
$277$	−8.44251	−	8.44251i	−0.507261	−	0.507261i	0.406424	−	0.913685i	$-0.366776\pi$
$277$	−8.44251	−	8.44251i	−0.507261	−	0.507261i	−0.913685	+	0.406424i	$0.866776\pi$
$278$	−4.56728	+	4.56728i	−0.273927	+	0.273927i
$279$		0			0
$280$			8.47327i			0.506375i
$281$		−	31.4527i		−	1.87631i	−0.346216	−	0.938155i	$-0.612533\pi$
$281$		−	31.4527i		−	1.87631i	0.346216	−	0.938155i	$-0.387467\pi$
$282$		0			0
$283$	−9.75331	+	9.75331i	−0.579774	+	0.579774i	−0.934841	−	0.355067i	$-0.884458\pi$
$283$	−9.75331	+	9.75331i	−0.579774	+	0.579774i	0.355067	+	0.934841i	$0.384458\pi$
$284$	3.89604	+	3.89604i	0.231187	+	0.231187i
$285$		0			0
$286$	2.13439	+	2.13439i	0.126209	+	0.126209i
$287$			47.8783i			2.82617i
$288$		0			0
$289$	−6.32930	−	15.7778i	−0.372312	−	0.928108i
$290$	4.11928			0.241893
$291$		0			0
$292$	−2.17898	−	2.17898i	−0.127515	−	0.127515i
$293$	6.63195			0.387442			0.193721	−	0.981057i	$-0.437944\pi$
$293$	6.63195			0.387442			0.193721	+	0.981057i	$0.437944\pi$
$294$		0			0
$295$	1.11284	−	1.11284i	0.0647919	−	0.0647919i
$296$	−4.16968	+	4.16968i	−0.242358	+	0.242358i
$297$		0			0
$298$			31.9658i			1.85173i
$299$	−0.443098	+	0.443098i	−0.0256250	+	0.0256250i
$300$		0			0
$301$	1.49434	+	1.49434i	0.0861325	+	0.0861325i
$302$	−15.5424			−0.894367
$303$		0			0
$304$			32.0031i			1.83550i
$305$	−14.7974			−0.847298
$306$		0			0
$307$	−5.77161			−0.329403			−0.164702	−	0.986343i	$-0.552666\pi$
$307$	−5.77161			−0.329403			−0.164702	+	0.986343i	$0.552666\pi$
$308$			14.3791i			0.819328i
$309$		0			0
$310$	−11.6489			−0.661612
$311$	15.3055	+	15.3055i	0.867896	+	0.867896i	0.992239	−	0.124343i	$-0.0396824\pi$
$311$	15.3055	+	15.3055i	0.867896	+	0.867896i	−0.124343	+	0.992239i	$0.539682\pi$
$312$		0			0
$313$	−16.2354	+	16.2354i	−0.917681	+	0.917681i	−0.996860	−	0.0791790i	$-0.974770\pi$
$313$	−16.2354	+	16.2354i	−0.917681	+	0.917681i	0.0791790	+	0.996860i	$0.474770\pi$
$314$		−	19.5836i		−	1.10517i
$315$		0			0
$316$	2.97238	−	2.97238i	0.167209	−	0.167209i
$317$	−2.35908	+	2.35908i	−0.132499	+	0.132499i	−0.770246	−	0.637747i	$-0.779867\pi$
$317$	−2.35908	+	2.35908i	−0.132499	+	0.132499i	0.637747	+	0.770246i	$0.279867\pi$
$318$		0			0
$319$	−10.0384			−0.562040
$320$	−1.81947	−	1.81947i	−0.101711	−	0.101711i
$321$		0			0
$322$	−10.2569			−0.571593
$323$	−22.0013	−	14.8797i	−1.22419	−	0.827930i
$324$		0			0
$325$			0.439079i			0.0243557i
$326$	23.0985	+	23.0985i	1.27931	+	1.27931i
$327$		0			0
$328$	−15.6674	−	15.6674i	−0.865086	−	0.865086i
$329$	−28.2156	+	28.2156i	−1.55558	+	1.55558i
$330$		0			0
$331$			20.1831i			1.10936i	0.832062	+	0.554682i	$0.187160\pi$
$331$			20.1831i			1.10936i	−0.832062	+	0.554682i	$0.812840\pi$
$332$		−	3.62376i		−	0.198880i
$333$		0			0
$334$	0.102658	−	0.102658i	0.00561719	−	0.00561719i
$335$	6.07673	+	6.07673i	0.332007	+	0.332007i
$336$		0			0
$337$	13.7858	+	13.7858i	0.750958	+	0.750958i	0.974658	−	0.223700i	$-0.0718137\pi$
$337$	13.7858	+	13.7858i	0.750958	+	0.750958i	−0.223700	+	0.974658i	$0.571814\pi$
$338$		−	21.5108i		−	1.17003i
$339$		0			0
$340$	−3.32373	+	0.641801i	−0.180254	+	0.0348065i
$341$	28.3874			1.53726
$342$		0			0
$343$	−13.0395	−	13.0395i	−0.704066	−	0.704066i
$344$	−0.977997			−0.0527300
$345$		0			0
$346$	−6.44832	+	6.44832i	−0.346664	+	0.346664i
$347$	−8.80865	+	8.80865i	−0.472873	+	0.472873i	−0.902843	−	0.429970i	$-0.858524\pi$
$347$	−8.80865	+	8.80865i	−0.472873	+	0.472873i	0.429970	+	0.902843i	$0.358524\pi$
$348$		0			0
$349$			10.8409i			0.580300i	0.956981	+	0.290150i	$0.0937052\pi$
$349$			10.8409i			0.580300i	−0.956981	+	0.290150i	$0.906295\pi$
$350$	−5.08191	+	5.08191i	−0.271639	+	0.271639i
$351$		0			0
$352$	−12.6873	−	12.6873i	−0.676237	−	0.676237i
$353$	−31.6372			−1.68388			−0.841939	−	0.539572i	$-0.818586\pi$
$353$	−31.6372			−1.68388			−0.841939	+	0.539572i	$0.818586\pi$
$354$		0			0
$355$		−	6.71101i		−	0.356184i
$356$	−1.61627			−0.0856620
$357$		0			0
$358$	−5.40931			−0.285891
$359$			26.4835i			1.39775i	0.715246	+	0.698873i	$0.246315\pi$
$359$			26.4835i			1.39775i	−0.715246	+	0.698873i	$0.753685\pi$
$360$		0			0
$361$	−22.4980			−1.18410
$362$	30.6655	+	30.6655i	1.61174	+	1.61174i
$363$		0			0
$364$	−1.09073	+	1.09073i	−0.0571697	+	0.0571697i
$365$			3.75335i			0.196459i
$366$		0			0
$367$	−2.20683	+	2.20683i	−0.115196	+	0.115196i	−0.762355	−	0.647159i	$-0.775957\pi$
$367$	−2.20683	+	2.20683i	−0.115196	+	0.115196i	0.647159	+	0.762355i	$0.275957\pi$
$368$	5.01344	−	5.01344i	0.261344	−	0.261344i
$369$		0			0
$370$	−5.00159			−0.260020
$371$	31.7003	+	31.7003i	1.64580	+	1.64580i
$372$		0			0
$373$	−31.6271			−1.63759			−0.818794	−	0.574087i	$-0.805357\pi$
$373$	−31.6271			−1.63759			−0.818794	+	0.574087i	$0.805357\pi$
$374$	27.8305	−	5.37399i	1.43908	−	0.277882i
$375$		0			0
$376$		−	18.4662i		−	0.952321i
$377$	−0.761459	−	0.761459i	−0.0392171	−	0.0392171i
$378$		0			0
$379$	2.71215	+	2.71215i	0.139314	+	0.139314i	0.773324	−	0.634011i	$-0.218592\pi$
$379$	2.71215	+	2.71215i	0.139314	+	0.139314i	−0.634011	+	0.773324i	$0.718592\pi$
$380$	−3.73980	+	3.73980i	−0.191848	+	0.191848i
$381$		0			0
$382$		−	16.0383i		−	0.820593i
$383$			18.7593i			0.958557i	0.877663	+	0.479278i	$0.159102\pi$
$383$			18.7593i			0.958557i	−0.877663	+	0.479278i	$0.840898\pi$
$384$		0			0
$385$	12.3842	−	12.3842i	0.631157	−	0.631157i
$386$	1.43116	+	1.43116i	0.0728443	+	0.0728443i
$387$		0			0
$388$	0.508762	+	0.508762i	0.0258285	+	0.0258285i
$389$		−	4.21279i		−	0.213597i	−0.994281	−	0.106798i	$-0.965940\pi$
$389$		−	4.21279i		−	0.213597i	0.994281	−	0.106798i	$-0.0340600\pi$
$390$		0			0
$391$	1.11564	+	5.77761i	0.0564202	+	0.292186i
$392$	22.3954			1.13114
$393$		0			0
$394$	17.0816	+	17.0816i	0.860560	+	0.860560i
$395$	−5.11999			−0.257614
$396$		0			0
$397$	2.82201	−	2.82201i	0.141632	−	0.141632i	−0.632736	−	0.774368i	$-0.718068\pi$
$397$	2.82201	−	2.82201i	0.141632	−	0.141632i	0.774368	+	0.632736i	$0.218068\pi$
$398$	−15.2550	+	15.2550i	−0.764664	+	0.764664i
$399$		0			0
$400$		−	4.96796i		−	0.248398i
$401$	2.28769	−	2.28769i	0.114242	−	0.114242i	−0.647675	−	0.761917i	$-0.724259\pi$
$401$	2.28769	−	2.28769i	0.114242	−	0.114242i	0.761917	+	0.647675i	$0.224259\pi$
$402$		0			0
$403$	2.15332	+	2.15332i	0.107265	+	0.107265i
$404$	9.47584			0.471441
$405$		0			0
$406$		−	17.6263i		−	0.874778i
$407$	12.1885			0.604160
$408$		0			0
$409$	24.5939			1.21609			0.608044	−	0.793903i	$-0.291954\pi$
$409$	24.5939			1.21609			0.608044	+	0.793903i	$0.291954\pi$
$410$		−	18.7933i		−	0.928133i
$411$		0			0
$412$	−6.97995			−0.343877
$413$	−4.76180	−	4.76180i	−0.234313	−	0.234313i
$414$		0			0
$415$	−3.12100	+	3.12100i	−0.153204	+	0.153204i
$416$		−	1.92479i		−	0.0943707i
$417$		0			0
$418$	31.3144	−	31.3144i	1.53164	−	1.53164i
$419$	−2.22521	+	2.22521i	−0.108709	+	0.108709i	−0.759369	−	0.650660i	$-0.774492\pi$
$419$	−2.22521	+	2.22521i	−0.108709	+	0.108709i	0.650660	+	0.759369i	$0.274492\pi$
$420$		0			0
$421$	8.28666			0.403867			0.201934	−	0.979399i	$-0.435277\pi$
$421$	8.28666			0.403867			0.201934	+	0.979399i	$0.435277\pi$
$422$	−32.4021	−	32.4021i	−1.57731	−	1.57731i
$423$		0			0
$424$	−20.7468			−1.00755
$425$	3.41535	+	2.30984i	0.165669	+	0.112044i
$426$		0			0
$427$			63.3178i			3.06416i
$428$	−4.69610	−	4.69610i	−0.226995	−	0.226995i
$429$		0			0
$430$	−0.586561	−	0.586561i	−0.0282865	−	0.0282865i
$431$	−15.9341	+	15.9341i	−0.767518	+	0.767518i	−0.977669	−	0.210151i	$-0.932604\pi$
$431$	−15.9341	+	15.9341i	−0.767518	+	0.767518i	0.210151	+	0.977669i	$0.432604\pi$
$432$		0			0
$433$		−	8.12498i		−	0.390462i	−0.980757	−	0.195231i	$-0.937454\pi$
$433$		−	8.12498i		−	0.390462i	0.980757	−	0.195231i	$-0.0625456\pi$
$434$			49.8452i			2.39265i
$435$		0			0
$436$	11.5175	−	11.5175i	0.551588	−	0.551588i
$437$	6.50087	+	6.50087i	0.310979	+	0.310979i
$438$		0			0
$439$	−17.8550	−	17.8550i	−0.852172	−	0.852172i	0.138228	−	0.990400i	$-0.455859\pi$
$439$	−17.8550	−	17.8550i	−0.852172	−	0.852172i	−0.990400	+	0.138228i	$0.955859\pi$
$440$			8.10504i			0.386393i
$441$		0			0
$442$	2.51873	+	1.70344i	0.119804	+	0.0810243i
$443$	22.3918			1.06387			0.531934	−	0.846786i	$-0.321466\pi$
$443$	22.3918			1.06387			0.531934	+	0.846786i	$0.321466\pi$
$444$		0			0
$445$	1.39203	+	1.39203i	0.0659885	+	0.0659885i
$446$	−18.4790			−0.875005
$447$		0			0
$448$	−7.78544	+	7.78544i	−0.367827	+	0.367827i
$449$	18.6350	−	18.6350i	0.879439	−	0.879439i	−0.114037	−	0.993476i	$-0.536378\pi$
$449$	18.6350	−	18.6350i	0.879439	−	0.879439i	0.993476	+	0.114037i	$0.0363783\pi$
$450$		0			0
$451$			45.7977i			2.15653i
$452$	−5.98269	+	5.98269i	−0.281402	+	0.281402i
$453$		0			0
$454$	18.0617	+	18.0617i	0.847678	+	0.847678i
$455$	1.87881			0.0880798
$456$		0			0
$457$		−	4.12083i		−	0.192764i	−0.995344	−	0.0963822i	$-0.969273\pi$
$457$		−	4.12083i		−	0.192764i	0.995344	−	0.0963822i	$-0.0307271\pi$
$458$	46.7671			2.18529
$459$		0			0
$460$	1.17172			0.0546316
$461$		−	30.8842i		−	1.43842i	−0.694792	−	0.719211i	$-0.744504\pi$
$461$		−	30.8842i		−	1.43842i	0.694792	−	0.719211i	$-0.255496\pi$
$462$		0			0
$463$	−4.58314			−0.212996			−0.106498	−	0.994313i	$-0.533964\pi$
$463$	−4.58314			−0.212996			−0.106498	+	0.994313i	$0.533964\pi$
$464$	8.61554	+	8.61554i	0.399966	+	0.399966i
$465$		0			0
$466$	−6.77353	+	6.77353i	−0.313778	+	0.313778i
$467$		−	19.6867i		−	0.910993i	−0.890238	−	0.455496i	$-0.849462\pi$
$467$		−	19.6867i		−	0.910993i	0.890238	−	0.455496i	$-0.150538\pi$
$468$		0			0
$469$	26.0022	−	26.0022i	1.20067	−	1.20067i
$470$	11.0752	−	11.0752i	0.510863	−	0.510863i
$471$		0			0
$472$	3.11644			0.143446
$473$	1.42940	+	1.42940i	0.0657240	+	0.0657240i
$474$		0			0
$475$	6.44189			0.295574
$476$	2.74625	+	14.2221i	0.125874	+	0.651870i
$477$		0			0
$478$			4.04268i			0.184908i
$479$	−8.69601	−	8.69601i	−0.397331	−	0.397331i	0.479960	−	0.877291i	$-0.340651\pi$
$479$	−8.69601	−	8.69601i	−0.397331	−	0.397331i	−0.877291	+	0.479960i	$0.840651\pi$
$480$		0			0
$481$	0.924556	+	0.924556i	0.0421561	+	0.0421561i
$482$	1.23982	−	1.23982i	0.0564721	−	0.0564721i
$483$		0			0
$484$			4.72312i			0.214687i
$485$		−	0.876354i		−	0.0397932i
$486$		0			0
$487$	−3.08371	+	3.08371i	−0.139736	+	0.139736i	−0.773515	−	0.633778i	$-0.781503\pi$
$487$	−3.08371	+	3.08371i	−0.139736	+	0.139736i	0.633778	+	0.773515i	$0.281503\pi$
$488$	−20.7197	−	20.7197i	−0.937935	−	0.937935i
$489$		0			0
$490$	13.4318	+	13.4318i	0.606787	+	0.606787i
$491$		−	15.9818i		−	0.721250i	−0.932711	−	0.360625i	$-0.882563\pi$
$491$		−	15.9818i		−	0.721250i	0.932711	−	0.360625i	$-0.117437\pi$
$492$		0			0
$493$	−9.92874	+	1.91721i	−0.447168	+	0.0863467i
$494$	4.75071			0.213745
$495$		0			0
$496$	−24.3638	−	24.3638i	−1.09397	−	1.09397i
$497$	−28.7162			−1.28810
$498$		0			0
$499$	18.7026	−	18.7026i	0.837241	−	0.837241i	−0.151254	−	0.988495i	$-0.548331\pi$
$499$	18.7026	−	18.7026i	0.837241	−	0.837241i	0.988495	+	0.151254i	$0.0483310\pi$
$500$	0.580544	−	0.580544i	0.0259627	−	0.0259627i
$501$		0			0
$502$			5.69042i			0.253976i
$503$	−9.05971	+	9.05971i	−0.403952	+	0.403952i	−0.879623	−	0.475671i	$-0.842205\pi$
$503$	−9.05971	+	9.05971i	−0.403952	+	0.403952i	0.475671	+	0.879623i	$0.342205\pi$
$504$		0			0
$505$	−8.16118	−	8.16118i	−0.363168	−	0.363168i
$506$	−9.81113			−0.436158
$507$		0			0
$508$			3.90025i			0.173046i
$509$	22.3411			0.990250			0.495125	−	0.868822i	$-0.335122\pi$
$509$	22.3411			0.990250			0.495125	+	0.868822i	$0.335122\pi$
$510$		0			0
$511$	16.0605			0.710473
$512$			2.10285i			0.0929338i
$513$		0			0
$514$	−8.07339			−0.356102
$515$	6.01156	+	6.01156i	0.264901	+	0.264901i
$516$		0			0
$517$	−26.9895	+	26.9895i	−1.18700	+	1.18700i
$518$			21.4017i			0.940335i
$519$		0			0
$520$	−0.614807	+	0.614807i	−0.0269611	+	0.0269611i
$521$	−8.92119	+	8.92119i	−0.390844	+	0.390844i	−0.874988	−	0.484144i	$-0.839131\pi$
$521$	−8.92119	+	8.92119i	−0.390844	+	0.390844i	0.484144	+	0.874988i	$0.339131\pi$
$522$		0			0
$523$	29.0702			1.27115			0.635575	−	0.772039i	$-0.280763\pi$
$523$	29.0702			1.27115			0.635575	+	0.772039i	$0.280763\pi$
$524$	10.9793	+	10.9793i	0.479634	+	0.479634i
$525$		0			0
$526$	−5.53871			−0.241499
$527$	28.0774	−	5.42165i	1.22307	−	0.236171i
$528$		0			0
$529$			20.9632i			0.911444i
$530$	−12.4431	−	12.4431i	−0.540492	−	0.540492i
$531$		0			0
$532$	16.0025	+	16.0025i	0.693796	+	0.693796i
$533$	−3.47398	+	3.47398i	−0.150475	+	0.150475i
$534$		0			0
$535$			8.08914i			0.349724i
$536$			17.0175i			0.735046i
$537$		0			0
$538$	29.7681	−	29.7681i	1.28340	−	1.28340i
$539$	−32.7322	−	32.7322i	−1.40988	−	1.40988i
$540$		0			0
$541$	12.9824	+	12.9824i	0.558157	+	0.558157i	0.928782	−	0.370626i	$-0.120857\pi$
$541$	12.9824	+	12.9824i	0.558157	+	0.558157i	−0.370626	+	0.928782i	$0.620857\pi$
$542$		−	6.79151i		−	0.291720i
$543$		0			0
$544$	−14.9719	−	10.1256i	−0.641915	−	0.434134i
$545$	−19.8391			−0.849816
$546$		0			0
$547$	−19.3595	−	19.3595i	−0.827753	−	0.827753i	0.159453	−	0.987206i	$-0.449027\pi$
$547$	−19.3595	−	19.3595i	−0.827753	−	0.827753i	−0.987206	+	0.159453i	$0.949027\pi$
$548$	−7.52450			−0.321431
$549$		0			0
$550$	−4.86106	+	4.86106i	−0.207276	+	0.207276i
$551$	−11.1717	+	11.1717i	−0.475929	+	0.475929i
$552$		0			0
$553$			21.9083i			0.931634i
$554$	14.1799	−	14.1799i	0.602447	−	0.602447i
$555$		0			0
$556$	−2.23257	−	2.23257i	−0.0946821	−	0.0946821i
$557$	19.2455			0.815460			0.407730	−	0.913103i	$-0.366320\pi$
$557$	19.2455			0.815460			0.407730	+	0.913103i	$0.366320\pi$
$558$		0			0
$559$			0.216854i			0.00917196i
$560$	−21.2578			−0.898305
$561$		0			0
$562$	52.8275			2.22839
$563$		−	14.0811i		−	0.593449i	−0.954963	−	0.296724i	$-0.904106\pi$
$563$		−	14.0811i		−	0.593449i	0.954963	−	0.296724i	$-0.0958943\pi$
$564$		0			0
$565$	10.3053			0.433548
$566$	−16.3815	−	16.3815i	−0.688567	−	0.688567i
$567$		0			0
$568$	9.39690	−	9.39690i	0.394285	−	0.394285i
$569$			8.35032i			0.350064i	0.984563	+	0.175032i	$0.0560029\pi$
$569$			8.35032i			0.350064i	−0.984563	+	0.175032i	$0.943997\pi$
$570$		0			0
$571$	10.3373	−	10.3373i	0.432602	−	0.432602i	−0.456911	−	0.889513i	$-0.651044\pi$
$571$	10.3373	−	10.3373i	0.432602	−	0.432602i	0.889513	+	0.456911i	$0.151044\pi$
$572$	−1.04333	+	1.04333i	−0.0436238	+	0.0436238i
$573$		0			0
$574$	−80.4158			−3.35649
$575$	−1.00915	−	1.00915i	−0.0420847	−	0.0420847i
$576$		0			0
$577$	38.4382			1.60020			0.800102	−	0.599864i	$-0.204779\pi$
$577$	38.4382			1.60020			0.800102	+	0.599864i	$0.204779\pi$
$578$	26.5002	−	10.6306i	1.10226	−	0.442175i
$579$		0			0
$580$			2.01358i			0.0836094i
$581$	13.3547	+	13.3547i	0.554046	+	0.554046i
$582$		0			0
$583$	30.3227	+	30.3227i	1.25584	+	1.25584i
$584$	−5.25551	+	5.25551i	−0.217475	+	0.217475i
$585$		0			0
$586$			11.1389i			0.460145i
$587$		−	9.20716i		−	0.380020i	−0.981782	−	0.190010i	$-0.939148\pi$
$587$		−	9.20716i		−	0.380020i	0.981782	−	0.190010i	$-0.0608521\pi$
$588$		0			0
$589$	31.5922	−	31.5922i	1.30173	−	1.30173i
$590$	1.86911	+	1.86911i	0.0769499	+	0.0769499i
$591$		0			0
$592$	−10.4609	−	10.4609i	−0.429941	−	0.429941i
$593$			17.3480i			0.712395i	0.934411	+	0.356198i	$0.115927\pi$
$593$			17.3480i			0.712395i	−0.934411	+	0.356198i	$0.884073\pi$
$594$		0			0
$595$	9.88373	−	14.6142i	0.405193	−	0.599124i
$596$	−15.6255			−0.640043
$597$		0			0
$598$	−0.744222	−	0.744222i	−0.0304335	−	0.0304335i
$599$	−21.2727			−0.869179			−0.434590	−	0.900629i	$-0.643107\pi$
$599$	−21.2727			−0.869179			−0.434590	+	0.900629i	$0.643107\pi$
$600$		0			0
$601$	4.97490	−	4.97490i	0.202930	−	0.202930i	−0.598324	−	0.801254i	$-0.704166\pi$
$601$	4.97490	−	4.97490i	0.202930	−	0.202930i	0.801254	+	0.598324i	$0.204166\pi$
$602$	−2.50988	+	2.50988i	−0.102295	+	0.102295i
$603$		0			0
$604$		−	7.59743i		−	0.309135i
$605$	4.06784	−	4.06784i	0.165381	−	0.165381i
$606$		0			0
$607$	−23.8730	−	23.8730i	−0.968974	−	0.968974i	0.0305587	−	0.999533i	$-0.490271\pi$
$607$	−23.8730	−	23.8730i	−0.968974	−	0.968974i	−0.999533	+	0.0305587i	$0.990271\pi$
$608$	−28.2394			−1.14526
$609$		0			0
$610$		−	24.8536i		−	1.00629i
$611$	−4.09457			−0.165648
$612$		0			0
$613$	9.45692			0.381961			0.190981	−	0.981594i	$-0.438833\pi$
$613$	9.45692			0.381961			0.190981	+	0.981594i	$0.438833\pi$
$614$		−	9.69392i		−	0.391215i
$615$		0			0
$616$	34.6812			1.39735
$617$	1.42550	+	1.42550i	0.0573883	+	0.0573883i	0.735219	−	0.677830i	$-0.237080\pi$
$617$	1.42550	+	1.42550i	0.0573883	+	0.0573883i	−0.677830	+	0.735219i	$0.737080\pi$
$618$		0			0
$619$	2.96801	−	2.96801i	0.119294	−	0.119294i	−0.644939	−	0.764234i	$-0.723117\pi$
$619$	2.96801	−	2.96801i	0.119294	−	0.119294i	0.764234	+	0.644939i	$0.223117\pi$
$620$		−	5.69418i		−	0.228684i
$621$		0			0
$622$	−25.7069	+	25.7069i	−1.03075	+	1.03075i
$623$	5.95645	−	5.95645i	0.238640	−	0.238640i
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	−27.2688	−	27.2688i	−1.08988	−	1.08988i
$627$		0			0
$628$	9.57282			0.381997
$629$	12.0554	−	2.32786i	0.480680	−	0.0928177i
$630$		0			0
$631$		−	12.6345i		−	0.502973i	−0.967861	−	0.251486i	$-0.919081\pi$
$631$		−	12.6345i		−	0.502973i	0.967861	−	0.251486i	$-0.0809194\pi$
$632$	−7.16911	−	7.16911i	−0.285172	−	0.285172i
$633$		0			0
$634$	−3.96227	−	3.96227i	−0.157362	−	0.157362i
$635$	3.35914	−	3.35914i	0.133303	−	0.133303i
$636$		0			0
$637$		−	4.96580i		−	0.196752i
$638$		−	16.8603i		−	0.667506i
$639$		0			0
$640$	9.25545	−	9.25545i	0.365854	−	0.365854i
$641$	8.12982	+	8.12982i	0.321108	+	0.321108i	0.849192	−	0.528084i	$-0.177089\pi$
$641$	8.12982	+	8.12982i	0.321108	+	0.321108i	−0.528084	+	0.849192i	$0.677089\pi$
$642$		0			0
$643$	−14.2402	−	14.2402i	−0.561578	−	0.561578i	0.368177	−	0.929756i	$-0.379982\pi$
$643$	−14.2402	−	14.2402i	−0.561578	−	0.561578i	−0.929756	+	0.368177i	$0.879982\pi$
$644$		−	5.01374i		−	0.197569i
$645$		0			0
$646$	24.9918	−	36.9532i	0.983289	−	1.45390i
$647$	39.6327			1.55812			0.779061	−	0.626948i	$-0.215696\pi$
$647$	39.6327			1.55812			0.779061	+	0.626948i	$0.215696\pi$
$648$		0			0
$649$	−4.55486	−	4.55486i	−0.178794	−	0.178794i
$650$	−0.737471			−0.0289260
$651$		0			0
$652$	−11.2910	+	11.2910i	−0.442189	+	0.442189i
$653$	−1.84259	+	1.84259i	−0.0721062	+	0.0721062i	−0.742240	−	0.670134i	$-0.766237\pi$
$653$	−1.84259	+	1.84259i	−0.0721062	+	0.0721062i	0.670134	+	0.742240i	$0.266237\pi$
$654$		0			0
$655$		−	18.9121i		−	0.738958i
$656$	39.3064	−	39.3064i	1.53466	−	1.53466i
$657$		0			0
$658$	−47.3906	−	47.3906i	−1.84748	−	1.84748i
$659$	25.1852			0.981076			0.490538	−	0.871420i	$-0.336800\pi$
$659$	25.1852			0.981076			0.490538	+	0.871420i	$0.336800\pi$
$660$		0			0
$661$		−	24.1103i		−	0.937780i	−0.883256	−	0.468890i	$-0.844654\pi$
$661$		−	24.1103i		−	0.937780i	0.883256	−	0.468890i	$-0.155346\pi$
$662$	−33.8993			−1.31753
$663$		0			0
$664$	−8.74019			−0.339185
$665$		−	27.5647i		−	1.06891i
$666$		0			0
$667$	3.50019			0.135528
$668$	0.0501811	+	0.0501811i	0.00194156	+	0.00194156i
$669$		0			0
$670$	−10.2064	+	10.2064i	−0.394308	+	0.394308i
$671$			60.5661i			2.33813i
$672$		0			0
$673$	−32.2463	+	32.2463i	−1.24300	+	1.24300i	−0.284256	+	0.958748i	$0.591747\pi$
$673$	−32.2463	+	32.2463i	−1.24300	+	1.24300i	−0.958748	+	0.284256i	$0.908253\pi$
$674$	−23.1544	+	23.1544i	−0.891873	+	0.891873i
$675$		0			0
$676$	10.5149			0.404419
$677$	−34.7395	−	34.7395i	−1.33515	−	1.33515i	−0.900694	−	0.434455i	$-0.856941\pi$
$677$	−34.7395	−	34.7395i	−1.33515	−	1.33515i	−0.434455	−	0.900694i	$-0.643059\pi$
$678$		0			0
$679$	−3.74990			−0.143908
$680$	1.54797	+	8.01653i	0.0593618	+	0.307420i
$681$		0			0
$682$			47.6791i			1.82573i
$683$	10.7216	+	10.7216i	0.410250	+	0.410250i	0.881826	−	0.471575i	$-0.156314\pi$
$683$	10.7216	+	10.7216i	0.410250	+	0.410250i	−0.471575	+	0.881826i	$0.656314\pi$
$684$		0			0
$685$	6.48056	+	6.48056i	0.247609	+	0.247609i
$686$	21.9010	−	21.9010i	0.836183	−	0.836183i
$687$		0			0
$688$		−	2.45360i		−	0.0935427i
$689$			4.60025i			0.175256i
$690$		0			0
$691$	17.2465	−	17.2465i	0.656089	−	0.656089i	−0.298364	−	0.954452i	$-0.596441\pi$
$691$	17.2465	−	17.2465i	0.656089	−	0.656089i	0.954452	+	0.298364i	$0.0964408\pi$
$692$	−3.15206	−	3.15206i	−0.119823	−	0.119823i
$693$		0			0
$694$	−14.7949	−	14.7949i	−0.561606	−	0.561606i
$695$			3.84565i			0.145874i
$696$		0			0
$697$	8.74681	+	45.2976i	0.331309	+	1.71577i
$698$	−18.2082			−0.689192
$699$		0			0
$700$	−2.48413	−	2.48413i	−0.0938913	−	0.0938913i
$701$	−7.19617			−0.271796			−0.135898	−	0.990723i	$-0.543392\pi$
$701$	−7.19617			−0.271796			−0.135898	+	0.990723i	$0.543392\pi$
$702$		0			0
$703$	13.5645	−	13.5645i	0.511595	−	0.511595i
$704$	−7.44710	+	7.44710i	−0.280673	+	0.280673i
$705$		0			0
$706$		−	53.1375i		−	1.99985i
$707$	−34.9214	+	34.9214i	−1.31336	+	1.31336i
$708$		0			0
$709$	−10.0144	−	10.0144i	−0.376100	−	0.376100i	0.493593	−	0.869693i	$-0.335683\pi$
$709$	−10.0144	−	10.0144i	−0.376100	−	0.376100i	−0.869693	+	0.493593i	$0.835683\pi$
$710$	11.2717			0.423021
$711$		0			0
$712$			3.89829i			0.146095i
$713$	−9.89815			−0.370689
$714$		0			0
$715$	1.79716			0.0672099
$716$		−	2.64417i		−	0.0988173i
$717$		0			0
$718$	−44.4814			−1.66003
$719$	−19.2040	−	19.2040i	−0.716188	−	0.716188i	0.251634	−	0.967822i	$-0.419032\pi$
$719$	−19.2040	−	19.2040i	−0.716188	−	0.716188i	−0.967822	+	0.251634i	$0.919032\pi$
$720$		0			0
$721$	25.7233	−	25.7233i	0.957985	−	0.957985i
$722$		−	37.7873i		−	1.40630i
$723$		0			0
$724$	−14.9898	+	14.9898i	−0.557093	+	0.557093i
$725$	1.73422	−	1.73422i	0.0644073	−	0.0644073i
$726$		0			0
$727$	45.1922			1.67609			0.838043	−	0.545604i	$-0.183700\pi$
$727$	45.1922			1.67609			0.838043	+	0.545604i	$0.183700\pi$
$728$	2.63074	+	2.63074i	0.0975018	+	0.0975018i
$729$		0			0
$730$	−6.30407			−0.233324
$731$	1.68679	+	1.14079i	0.0623883	+	0.0421938i
$732$		0			0
$733$		−	33.2376i		−	1.22766i	−0.789439	−	0.613829i	$-0.789629\pi$
$733$		−	33.2376i		−	1.22766i	0.789439	−	0.613829i	$-0.210371\pi$
$734$	−3.70657	−	3.70657i	−0.136812	−	0.136812i
$735$		0			0
$736$	4.42384	+	4.42384i	0.163065	+	0.163065i
$737$	24.8722	−	24.8722i	0.916178	−	0.916178i
$738$		0			0
$739$			2.69704i			0.0992123i	0.998769	+	0.0496061i	$0.0157966\pi$
$739$			2.69704i			0.0992123i	−0.998769	+	0.0496061i	$0.984203\pi$
$740$		−	2.44487i		−	0.0898752i
$741$		0			0
$742$	−53.2435	+	53.2435i	−1.95463	+	1.95463i
$743$	16.6740	+	16.6740i	0.611708	+	0.611708i	0.943391	−	0.331683i	$-0.107616\pi$
$743$	16.6740	+	16.6740i	0.611708	+	0.611708i	−0.331683	+	0.943391i	$0.607616\pi$
$744$		0			0
$745$	13.4576	+	13.4576i	0.493048	+	0.493048i
$746$		−	53.1204i		−	1.94488i
$747$		0			0
$748$	2.62690	+	13.6041i	0.0960491	+	0.497414i
$749$	34.6132			1.26474
$750$		0			0
$751$	−10.2022	−	10.2022i	−0.372283	−	0.372283i	0.496025	−	0.868308i	$-0.334792\pi$
$751$	−10.2022	−	10.2022i	−0.372283	−	0.372283i	−0.868308	+	0.496025i	$0.834792\pi$
$752$	46.3280			1.68941
$753$		0			0
$754$	1.27894	−	1.27894i	0.0465761	−	0.0465761i
$755$	−6.54337	+	6.54337i	−0.238138	+	0.238138i
$756$		0			0
$757$			38.4795i			1.39856i	0.714847	+	0.699281i	$0.246497\pi$
$757$			38.4795i			1.39856i	−0.714847	+	0.699281i	$0.753503\pi$
$758$	−4.55529	+	4.55529i	−0.165456	+	0.165456i
$759$		0			0
$760$	9.02007	+	9.02007i	0.327192	+	0.327192i
$761$	2.89837			0.105066			0.0525329	−	0.998619i	$-0.483271\pi$
$761$	2.89837			0.105066			0.0525329	+	0.998619i	$0.483271\pi$
$762$		0			0
$763$			84.8911i			3.07327i
$764$	7.83984			0.283635
$765$		0			0
$766$	−31.5079			−1.13843
$767$		−	0.691018i		−	0.0249512i
$768$		0			0
$769$	−3.28681			−0.118525			−0.0592626	−	0.998242i	$-0.518875\pi$
$769$	−3.28681			−0.118525			−0.0592626	+	0.998242i	$0.518875\pi$
$770$	20.8003	+	20.8003i	0.749592	+	0.749592i
$771$		0			0
$772$	−0.699579	+	0.699579i	−0.0251784	+	0.0251784i
$773$		−	32.6253i		−	1.17345i	−0.809786	−	0.586725i	$-0.800417\pi$
$773$		−	32.6253i		−	1.17345i	0.809786	−	0.586725i	$-0.199583\pi$
$774$		0			0
$775$	−4.90418	+	4.90418i	−0.176163	+	0.176163i
$776$	1.22709	−	1.22709i	0.0440500	−	0.0440500i
$777$		0			0
$778$	7.07575			0.253678
$779$	50.9681	+	50.9681i	1.82612	+	1.82612i
$780$		0			0
$781$	−27.4683			−0.982893
$782$	−9.70399	+	1.87381i	−0.347014	+	0.0670073i
$783$		0			0
$784$			56.1856i			2.00663i
$785$	−8.24470	−	8.24470i	−0.294266	−	0.294266i
$786$		0			0
$787$	−36.7438	−	36.7438i	−1.30977	−	1.30977i	−0.921576	−	0.388198i	$-0.873098\pi$
$787$	−36.7438	−	36.7438i	−1.30977	−	1.30977i	−0.388198	−	0.921576i	$-0.626902\pi$
$788$	−8.34981	+	8.34981i	−0.297450	+	0.297450i
$789$		0			0
$790$		−	8.59946i		−	0.305955i
$791$		−	44.0962i		−	1.56788i
$792$		0			0
$793$	−4.59424	+	4.59424i	−0.163146	+	0.163146i
$794$	4.73981	+	4.73981i	0.168209	+	0.168209i
$795$		0			0
$796$	−7.45693	−	7.45693i	−0.264304	−	0.264304i
$797$			25.3890i			0.899324i	0.893199	+	0.449662i	$0.148456\pi$
$797$			25.3890i			0.899324i	−0.893199	+	0.449662i	$0.851544\pi$
$798$		0			0
$799$	−21.5401	+	31.8494i	−0.762033	+	1.12675i
$800$	4.38371			0.154987
$801$		0			0
$802$	3.84237	+	3.84237i	0.135679	+	0.135679i
$803$	15.3625			0.542131
$804$		0			0
$805$	−4.31814	+	4.31814i	−0.152195	+	0.152195i
$806$	−3.61669	+	3.61669i	−0.127392	+	0.127392i
$807$		0			0
$808$		−	22.8549i		−	0.804033i
$809$	−29.9146	+	29.9146i	−1.05174	+	1.05174i	−0.0531551	+	0.998586i	$0.516928\pi$
$809$	−29.9146	+	29.9146i	−1.05174	+	1.05174i	−0.998586	+	0.0531551i	$0.983072\pi$
$810$		0			0
$811$	−39.8486	−	39.8486i	−1.39927	−	1.39927i	−0.802149	−	0.597124i	$-0.796310\pi$
$811$	−39.8486	−	39.8486i	−1.39927	−	1.39927i	−0.597124	−	0.802149i	$-0.703690\pi$
$812$	8.61606			0.302364
$813$		0			0
$814$			20.4716i			0.717530i
$815$	19.4490			0.681268
$816$		0			0
$817$	3.18155			0.111308
$818$			41.3076i			1.44428i
$819$		0			0
$820$	9.18649			0.320806
$821$	−22.2328	−	22.2328i	−0.775930	−	0.775930i	0.203206	−	0.979136i	$-0.434864\pi$
$821$	−22.2328	−	22.2328i	−0.775930	−	0.775930i	−0.979136	+	0.203206i	$0.934864\pi$
$822$		0			0
$823$	8.49023	−	8.49023i	0.295951	−	0.295951i	−0.543475	−	0.839425i	$-0.682892\pi$
$823$	8.49023	−	8.49023i	0.295951	−	0.295951i	0.839425	+	0.543475i	$0.182892\pi$
$824$			16.8350i			0.586476i
$825$		0			0
$826$	7.99785	−	7.99785i	0.278281	−	0.278281i
$827$	−29.6994	+	29.6994i	−1.03275	+	1.03275i	−0.0333056	+	0.999445i	$0.510603\pi$
$827$	−29.6994	+	29.6994i	−1.03275	+	1.03275i	−0.999445	+	0.0333056i	$0.989397\pi$
$828$		0			0
$829$	15.0504			0.522721			0.261361	−	0.965241i	$-0.415829\pi$
$829$	15.0504			0.522721			0.261361	+	0.965241i	$0.415829\pi$
$830$	−5.24200	−	5.24200i	−0.181952	−	0.181952i
$831$		0			0
$832$	−1.12980			−0.0391687
$833$	−38.6263	−	26.1233i	−1.33832	−	0.905120i
$834$		0			0
$835$		−	0.0864381i		−	0.00299131i
$836$	15.3071	+	15.3071i	0.529406	+	0.529406i
$837$		0			0
$838$	−3.73744	−	3.73744i	−0.129108	−	0.129108i
$839$	30.1459	−	30.1459i	1.04075	−	1.04075i	0.0416172	−	0.999134i	$-0.486749\pi$
$839$	30.1459	−	30.1459i	1.04075	−	1.04075i	0.999134	−	0.0416172i	$-0.0132510\pi$
$840$		0			0
$841$		−	22.9850i		−	0.792585i
$842$			13.9182i			0.479652i
$843$		0			0
$844$	15.8388	−	15.8388i	0.545192	−	0.545192i
$845$	−9.05606	−	9.05606i	−0.311538	−	0.311538i
$846$		0			0
$847$	−17.4062	−	17.4062i	−0.598083	−	0.598083i
$848$		−	52.0496i		−	1.78739i
$849$		0			0
$850$	−3.87957	+	5.73639i	−0.133068	+	0.196756i
$851$	−4.24990			−0.145685
$852$		0			0
$853$	−36.0478	−	36.0478i	−1.23425	−	1.23425i	−0.962314	−	0.271940i	$-0.912335\pi$
$853$	−36.0478	−	36.0478i	−1.23425	−	1.23425i	−0.271940	−	0.962314i	$-0.587665\pi$
$854$	−106.348			−3.63914
$855$		0			0
$856$	−11.3266	+	11.3266i	−0.387135	+	0.387135i
$857$	−4.87787	+	4.87787i	−0.166625	+	0.166625i	−0.785494	−	0.618869i	$-0.787591\pi$
$857$	−4.87787	+	4.87787i	−0.166625	+	0.166625i	0.618869	+	0.785494i	$0.287591\pi$
$858$		0			0
$859$		−	28.3337i		−	0.966734i	−0.875418	−	0.483367i	$-0.839414\pi$
$859$		−	28.3337i		−	0.966734i	0.875418	−	0.483367i	$-0.160586\pi$
$860$	0.286722	−	0.286722i	0.00977714	−	0.00977714i
$861$		0			0
$862$	−26.7627	−	26.7627i	−0.911541	−	0.911541i
$863$	13.1218			0.446671			0.223336	−	0.974742i	$-0.428305\pi$
$863$	13.1218			0.446671			0.223336	+	0.974742i	$0.428305\pi$
$864$		0			0
$865$			5.42949i			0.184608i
$866$	13.6466			0.463731
$867$		0			0
$868$	−24.3652			−0.827010
$869$			20.9562i			0.710890i
$870$		0			0
$871$	3.77335			0.127855
$872$	−27.7792	−	27.7792i	−0.940722	−	0.940722i
$873$		0			0
$874$	−10.9188	+	10.9188i	−0.369333	+	0.369333i
$875$			4.27897i			0.144656i
$876$		0			0
$877$	−12.0189	+	12.0189i	−0.405851	+	0.405851i	−0.880289	−	0.474438i	$-0.842651\pi$
$877$	−12.0189	+	12.0189i	−0.405851	+	0.405851i	0.474438	+	0.880289i	$0.342651\pi$
$878$	29.9890	−	29.9890i	1.01208	−	1.01208i
$879$		0			0
$880$	−20.3340			−0.685458
$881$	−5.40774	−	5.40774i	−0.182191	−	0.182191i	0.610119	−	0.792310i	$-0.291122\pi$
$881$	−5.40774	−	5.40774i	−0.182191	−	0.182191i	−0.792310	+	0.610119i	$0.791122\pi$
$882$		0			0
$883$	−8.85537			−0.298007			−0.149004	−	0.988837i	$-0.547607\pi$
$883$	−8.85537			−0.298007			−0.149004	+	0.988837i	$0.547607\pi$
$884$	−0.832672	+	1.23120i	−0.0280058	+	0.0414097i
$885$		0			0
$886$			37.6090i			1.26350i
$887$	22.2304	+	22.2304i	0.746422	+	0.746422i	0.973805	−	0.227383i	$-0.0730170\pi$
$887$	22.2304	+	22.2304i	0.746422	+	0.746422i	−0.227383	+	0.973805i	$0.573017\pi$
$888$		0			0
$889$	−14.3736	−	14.3736i	−0.482077	−	0.482077i
$890$	−2.33803	+	2.33803i	−0.0783711	+	0.0783711i
$891$		0			0
$892$		−	9.03286i		−	0.302443i
$893$			60.0730i			2.01027i
$894$		0			0
$895$	−2.27732	+	2.27732i	−0.0761225	+	0.0761225i
$896$	−39.6038	−	39.6038i	−1.32307	−	1.32307i
$897$		0			0
$898$	31.2991	+	31.2991i	1.04446	+	1.04446i
$899$		−	17.0099i		−	0.567310i
$900$		0			0
$901$	35.7829	+	24.2003i	1.19210	+	0.806229i
$902$	−76.9212			−2.56119
$903$		0			0
$904$	14.4297	+	14.4297i	0.479925	+	0.479925i
$905$	25.8203			0.858297
$906$		0			0
$907$	37.5975	−	37.5975i	1.24840	−	1.24840i	0.291979	−	0.956425i	$-0.405686\pi$
$907$	37.5975	−	37.5975i	1.24840	−	1.24840i	0.956425	−	0.291979i	$-0.0943137\pi$
$908$	−8.82890	+	8.82890i	−0.292997	+	0.292997i
$909$		0			0
$910$			3.15562i			0.104608i
$911$	−6.28836	+	6.28836i	−0.208343	+	0.208343i	−0.803563	−	0.595220i	$-0.797065\pi$
$911$	−6.28836	+	6.28836i	−0.208343	+	0.208343i	0.595220	+	0.803563i	$0.297065\pi$
$912$		0			0
$913$	12.7743	+	12.7743i	0.422768	+	0.422768i
$914$	6.92130			0.228936
$915$		0			0
$916$			22.8606i			0.755337i
$917$	−80.9245			−2.67236
$918$		0			0
$919$	28.9192			0.953956			0.476978	−	0.878915i	$-0.341732\pi$
$919$	28.9192			0.953956			0.476978	+	0.878915i	$0.341732\pi$
$920$		−	2.82608i		−	0.0931731i
$921$		0			0
$922$	51.8727			1.70834
$923$	−2.08361	−	2.08361i	−0.0685827	−	0.0685827i
$924$		0			0
$925$	−2.10567	+	2.10567i	−0.0692341	+	0.0692341i
$926$		−	7.69778i		−	0.252965i
$927$		0			0
$928$	−7.60231	+	7.60231i	−0.249558	+	0.249558i
$929$	−34.3154	+	34.3154i	−1.12585	+	1.12585i	−0.135008	+	0.990845i	$0.543106\pi$
$929$	−34.3154	+	34.3154i	−1.12585	+	1.12585i	−0.990845	+	0.135008i	$0.956894\pi$
$930$		0			0
$931$	−72.8552			−2.38773
$932$	−3.31103	−	3.31103i	−0.108456	−	0.108456i
$933$		0			0
$934$	33.0656			1.08194
$935$	9.45421	−	13.9791i	0.309186	−	0.457166i
$936$		0			0
$937$		−	32.4360i		−	1.05964i	−0.848111	−	0.529819i	$-0.822260\pi$
$937$		−	32.4360i		−	1.05964i	0.848111	−	0.529819i	$-0.177740\pi$
$938$	43.6729	+	43.6729i	1.42597	+	1.42597i
$939$		0			0
$940$	5.41378	+	5.41378i	0.176578	+	0.176578i
$941$	20.1918	−	20.1918i	0.658232	−	0.658232i	−0.296729	−	0.954962i	$-0.595896\pi$
$941$	20.1918	−	20.1918i	0.658232	−	0.658232i	0.954962	+	0.296729i	$0.0958959\pi$
$942$		0			0
$943$		−	15.9688i		−	0.520016i
$944$			7.81853i			0.254471i
$945$		0			0
$946$	−2.40081	+	2.40081i	−0.0780569	+	0.0780569i
$947$	11.1514	+	11.1514i	0.362372	+	0.362372i	0.864686	−	0.502313i	$-0.167518\pi$
$947$	11.1514	+	11.1514i	0.362372	+	0.362372i	−0.502313	+	0.864686i	$0.667518\pi$
$948$		0			0
$949$	1.16532	+	1.16532i	0.0378280	+	0.0378280i
$950$			10.8197i			0.351038i
$951$		0			0
$952$	34.3025	−	6.62371i	1.11175	−	0.214676i
$953$	30.9064			1.00116			0.500578	−	0.865691i	$-0.333121\pi$
$953$	30.9064			1.00116			0.500578	+	0.865691i	$0.333121\pi$
$954$		0			0
$955$	−6.75215	−	6.75215i	−0.218494	−	0.218494i
$956$	−1.97614			−0.0639128
$957$		0			0
$958$	14.6057	−	14.6057i	0.471889	−	0.471889i
$959$	27.7301	−	27.7301i	0.895452	−	0.895452i
$960$		0			0
$961$			17.1020i			0.551676i
$962$	−1.55287	+	1.55287i	−0.0500666	+	0.0500666i
$963$		0			0
$964$	0.606045	+	0.606045i	0.0195194	+	0.0195194i
$965$	1.20504			0.0387916
$966$		0			0
$967$			26.7198i			0.859251i	0.903007	+	0.429625i	$0.141354\pi$
$967$			26.7198i			0.859251i	−0.903007	+	0.429625i	$0.858646\pi$
$968$	11.3918			0.366145
$969$		0			0
$970$	1.47191			0.0472603
$971$			16.3232i			0.523838i	0.965090	+	0.261919i	$0.0843553\pi$
$971$			16.3232i			0.523838i	−0.965090	+	0.261919i	$0.915645\pi$
$972$		0			0
$973$	16.4554			0.527537
$974$	−5.17936	−	5.17936i	−0.165958	−	0.165958i
$975$		0			0
$976$	51.9816	−	51.9816i	1.66389	−	1.66389i
$977$		−	19.0849i		−	0.610581i	−0.952259	−	0.305290i	$-0.901246\pi$
$977$		−	19.0849i		−	0.610581i	0.952259	−	0.305290i	$-0.0987535\pi$
$978$		0			0
$979$	5.69760	−	5.69760i	0.182096	−	0.182096i
$980$	−6.56571	+	6.56571i	−0.209734	+	0.209734i
$981$		0			0
$982$	26.8429			0.856590
$983$	21.1600	+	21.1600i	0.674900	+	0.674900i	0.958842	−	0.283942i	$-0.0916422\pi$
$983$	21.1600	+	21.1600i	0.674900	+	0.674900i	−0.283942	+	0.958842i	$0.591642\pi$
$984$		0			0
$985$	14.3827			0.458272
$986$	−3.22012	−	16.6762i	−0.102549	−	0.531078i
$987$		0			0
$988$			2.32223i			0.0738801i
$989$	−0.498406	−	0.498406i	−0.0158484	−	0.0158484i
$990$		0			0
$991$	24.5654	+	24.5654i	0.780347	+	0.780347i	0.979889	−	0.199542i	$-0.0639456\pi$
$991$	24.5654	+	24.5654i	0.780347	+	0.780347i	−0.199542	+	0.979889i	$0.563946\pi$
$992$	21.4985	−	21.4985i	0.682577	−	0.682577i
$993$		0			0
$994$		−	48.2314i		−	1.52981i
$995$			12.8447i			0.407205i
$996$		0			0
$997$	−34.0611	+	34.0611i	−1.07873	+	1.07873i	−0.0821015	+	0.996624i	$0.526163\pi$
$997$	−34.0611	+	34.0611i	−1.07873	+	1.07873i	−0.996624	+	0.0821015i	$0.973837\pi$
$998$	31.4126	+	31.4126i	0.994348	+	0.994348i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	765.2.k.c.676.6		16
3.2	odd	2		255.2.j.b.166.3	yes	16
17.4	even	4	inner	765.2.k.c.361.3		16
51.2	odd	8		4335.2.a.bf.1.6		8
51.32	odd	8		4335.2.a.bg.1.6		8
51.38	odd	4		255.2.j.b.106.6	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
255.2.j.b.106.6	✓	16	51.38	odd	4
255.2.j.b.166.3	yes	16	3.2	odd	2
765.2.k.c.361.3		16	17.4	even	4	inner
765.2.k.c.676.6		16	1.1	even	1	trivial
4335.2.a.bf.1.6		8	51.2	odd	8
4335.2.a.bg.1.6		8	51.32	odd	8

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:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	765.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.67959i q^{2} -0.821013 q^{4} +(0.707107 + 0.707107i) q^{5} +(3.02569 - 3.02569i) q^{7} +1.98021i q^{8} +O(q^{10})\)	\(q+1.67959i q^{2} -0.821013 q^{4} +(0.707107 + 0.707107i) q^{5} +(3.02569 - 3.02569i) q^{7} +1.98021i q^{8} +(-1.18765 + 1.18765i) q^{10} +(2.89420 - 2.89420i) q^{11} +0.439079 q^{13} +(5.08191 + 5.08191i) q^{14} -4.96796 q^{16} +(2.30984 - 3.41535i) q^{17} -6.44189i q^{19} +(-0.580544 - 0.580544i) q^{20} +(4.86106 + 4.86106i) q^{22} +(-1.00915 + 1.00915i) q^{23} +1.00000i q^{25} +0.737471i q^{26} +(-2.48413 + 2.48413i) q^{28} +(-1.73422 - 1.73422i) q^{29} +(4.90418 + 4.90418i) q^{31} -4.38371i q^{32} +(5.73639 + 3.87957i) q^{34} +4.27897 q^{35} +(2.10567 + 2.10567i) q^{37} +10.8197 q^{38} +(-1.40022 + 1.40022i) q^{40} +(-7.91197 + 7.91197i) q^{41} +0.493885i q^{43} +(-2.37618 + 2.37618i) q^{44} +(-1.69496 - 1.69496i) q^{46} -9.32536 q^{47} -11.3096i q^{49} -1.67959 q^{50} -0.360489 q^{52} +10.4771i q^{53} +4.09302 q^{55} +(5.99150 + 5.99150i) q^{56} +(2.91277 - 2.91277i) q^{58} -1.57379i q^{59} +(-10.4634 + 10.4634i) q^{61} +(-8.23700 + 8.23700i) q^{62} -2.57311 q^{64} +(0.310476 + 0.310476i) q^{65} +8.59380 q^{67} +(-1.89641 + 2.80405i) q^{68} +7.18690i q^{70} +(-4.74540 - 4.74540i) q^{71} +(2.65402 + 2.65402i) q^{73} +(-3.53666 + 3.53666i) q^{74} +5.28888i q^{76} -17.5139i q^{77} +(-3.62038 + 3.62038i) q^{79} +(-3.51288 - 3.51288i) q^{80} +(-13.2888 - 13.2888i) q^{82} +4.41377i q^{83} +(4.04832 - 0.781718i) q^{85} -0.829523 q^{86} +(5.73113 + 5.73113i) q^{88} +1.96863 q^{89} +(1.32852 - 1.32852i) q^{91} +(0.828529 - 0.828529i) q^{92} -15.6628i q^{94} +(4.55511 - 4.55511i) q^{95} +(-0.619676 - 0.619676i) q^{97} +18.9954 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 20 q^{4} + 4 q^{7}+O(q^{10}) \) 16 * q - 20 * q^4 + 4 * q^7	\( 16 q - 20 q^{4} + 4 q^{7} - 4 q^{11} - 16 q^{13} + 16 q^{14} - 4 q^{16} + 12 q^{17} - 8 q^{20} - 20 q^{22} - 20 q^{23} - 8 q^{28} - 20 q^{29} - 12 q^{31} + 12 q^{34} - 4 q^{37} + 68 q^{38} + 12 q^{40} + 4 q^{41} + 44 q^{44} + 76 q^{46} - 40 q^{47} - 4 q^{50} + 72 q^{52} + 28 q^{56} + 20 q^{58} - 44 q^{61} + 36 q^{62} - 16 q^{64} + 4 q^{65} - 24 q^{67} - 48 q^{68} + 16 q^{71} + 12 q^{73} - 32 q^{74} - 24 q^{79} - 28 q^{82} + 8 q^{85} - 16 q^{86} + 116 q^{88} + 40 q^{89} + 84 q^{91} - 24 q^{92} - 16 q^{95} + 40 q^{97} - 56 q^{98}+O(q^{100}) \) 16 * q - 20 * q^4 + 4 * q^7 - 4 * q^11 - 16 * q^13 + 16 * q^14 - 4 * q^16 + 12 * q^17 - 8 * q^20 - 20 * q^22 - 20 * q^23 - 8 * q^28 - 20 * q^29 - 12 * q^31 + 12 * q^34 - 4 * q^37 + 68 * q^38 + 12 * q^40 + 4 * q^41 + 44 * q^44 + 76 * q^46 - 40 * q^47 - 4 * q^50 + 72 * q^52 + 28 * q^56 + 20 * q^58 - 44 * q^61 + 36 * q^62 - 16 * q^64 + 4 * q^65 - 24 * q^67 - 48 * q^68 + 16 * q^71 + 12 * q^73 - 32 * q^74 - 24 * q^79 - 28 * q^82 + 8 * q^85 - 16 * q^86 + 116 * q^88 + 40 * q^89 + 84 * q^91 - 24 * q^92 - 16 * q^95 + 40 * q^97 - 56 * q^98

Introduction

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