LMFDB - Embedded newform 1026.2.h.g.505.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1026,2,Mod(505,1026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1026, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 4]))

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

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

chi := DirichletCharacter("1026.505");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1026 = 2 \cdot 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1026.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.19265124738$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 4 x^{16} - 6 x^{15} + x^{14} - 21 x^{13} - 12 x^{12} + 9 x^{10} + 135 x^{9} + 27 x^{8} + \cdots + 19683 $ x^18 + 4x^16 - 6x^15 + x^14 - 21x^13 - 12x^12 + 9x^10 + 135x^9 + 27x^8 - 324x^6 - 1701x^5 + 243x^4 - 4374x^3 + 8748x^2 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 342)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			505.1
Root			$-1.24302 - 1.20619i$ of defining polynomial
Character	$\chi$	$=$	1026.505
Dual form			1026.2.h.g.577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.94363 q^{5} +(1.02646 - 1.77787i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.94363 q^{5} +(1.02646 - 1.77787i) q^{7} +1.00000 q^{8} +(1.97181 + 3.41528i) q^{10} +(-2.58114 + 4.47067i) q^{11} +(-1.94128 + 3.36239i) q^{13} -2.05291 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.05469 - 3.55883i) q^{17} +(4.23814 + 1.01891i) q^{19} +(1.97181 - 3.41528i) q^{20} +5.16229 q^{22} +(2.60260 - 4.50783i) q^{23} +10.5522 q^{25} +3.88255 q^{26} +(1.02646 + 1.77787i) q^{28} +1.20243 q^{29} +(-4.20987 - 7.29170i) q^{31} +(-0.500000 + 0.866025i) q^{32} -4.10938 q^{34} +(-4.04796 + 7.01126i) q^{35} +0.435335 q^{37} +(-1.23667 - 4.17979i) q^{38} -3.94363 q^{40} -2.76709 q^{41} +(0.838250 + 1.45189i) q^{43} +(-2.58114 - 4.47067i) q^{44} -5.20520 q^{46} +7.13833 q^{47} +(1.39278 + 2.41236i) q^{49} +(-5.27609 - 9.13846i) q^{50} +(-1.94128 - 3.36239i) q^{52} +(0.708689 + 1.22749i) q^{53} +(10.1791 - 17.6307i) q^{55} +(1.02646 - 1.77787i) q^{56} +(-0.601213 - 1.04133i) q^{58} +14.4637 q^{59} -6.59332 q^{61} +(-4.20987 + 7.29170i) q^{62} +1.00000 q^{64} +(7.65567 - 13.2600i) q^{65} +(7.35934 - 12.7467i) q^{67} +(2.05469 + 3.55883i) q^{68} +8.09591 q^{70} +(2.20789 - 3.82418i) q^{71} +(5.08361 - 8.80507i) q^{73} +(-0.217668 - 0.377012i) q^{74} +(-3.00147 + 3.16088i) q^{76} +(5.29886 + 9.17789i) q^{77} +(0.998660 + 1.72973i) q^{79} +(1.97181 + 3.41528i) q^{80} +(1.38355 + 2.39637i) q^{82} +(2.63550 - 4.56482i) q^{83} +(-8.10293 + 14.0347i) q^{85} +(0.838250 - 1.45189i) q^{86} +(-2.58114 + 4.47067i) q^{88} +(0.817559 + 1.41605i) q^{89} +(3.98527 + 6.90269i) q^{91} +(2.60260 + 4.50783i) q^{92} +(-3.56916 - 6.18197i) q^{94} +(-16.7136 - 4.01820i) q^{95} +(2.23760 + 3.87564i) q^{97} +(1.39278 - 2.41236i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 9 q^{2} - 9 q^{4} + 5 q^{7} + 18 q^{8}+O(q^{10}) $ 18 * q - 9 * q^2 - 9 * q^4 + 5 * q^7 + 18 * q^8	$ 18 q - 9 q^{2} - 9 q^{4} + 5 q^{7} + 18 q^{8} - q^{11} + q^{13} - 10 q^{14} - 9 q^{16} + 5 q^{17} + 9 q^{19} + 2 q^{22} + 2 q^{23} + 18 q^{25} - 2 q^{26} + 5 q^{28} - 18 q^{29} + 4 q^{31} - 9 q^{32} - 10 q^{34} - 6 q^{35} + 20 q^{37} - 3 q^{38} + 2 q^{41} + 7 q^{43} - q^{44} - 4 q^{46} + 38 q^{47} + 6 q^{49} - 9 q^{50} + q^{52} + 10 q^{53} + 6 q^{55} + 5 q^{56} + 9 q^{58} - 10 q^{59} - 36 q^{61} + 4 q^{62} + 18 q^{64} + 45 q^{65} + 22 q^{67} + 5 q^{68} + 12 q^{70} - 11 q^{71} + 44 q^{73} - 10 q^{74} - 6 q^{76} + 2 q^{77} + 2 q^{79} - q^{82} + 7 q^{83} + 7 q^{86} - q^{88} - q^{89} - 25 q^{91} + 2 q^{92} - 19 q^{94} - 21 q^{95} + 6 q^{98}+O(q^{100}) $ 18 * q - 9 * q^2 - 9 * q^4 + 5 * q^7 + 18 * q^8 - q^11 + q^13 - 10 * q^14 - 9 * q^16 + 5 * q^17 + 9 * q^19 + 2 * q^22 + 2 * q^23 + 18 * q^25 - 2 * q^26 + 5 * q^28 - 18 * q^29 + 4 * q^31 - 9 * q^32 - 10 * q^34 - 6 * q^35 + 20 * q^37 - 3 * q^38 + 2 * q^41 + 7 * q^43 - q^44 - 4 * q^46 + 38 * q^47 + 6 * q^49 - 9 * q^50 + q^52 + 10 * q^53 + 6 * q^55 + 5 * q^56 + 9 * q^58 - 10 * q^59 - 36 * q^61 + 4 * q^62 + 18 * q^64 + 45 * q^65 + 22 * q^67 + 5 * q^68 + 12 * q^70 - 11 * q^71 + 44 * q^73 - 10 * q^74 - 6 * q^76 + 2 * q^77 + 2 * q^79 - q^82 + 7 * q^83 + 7 * q^86 - q^88 - q^89 - 25 * q^91 + 2 * q^92 - 19 * q^94 - 21 * q^95 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1026\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−3.94363			−1.76364			−0.881821	−	0.471583i	$-0.843683\pi$
$5$	−3.94363			−1.76364			−0.881821	+	0.471583i	$0.843683\pi$
$6$		0			0
$7$	1.02646	−	1.77787i	0.387964	−	0.671973i	−0.604212	−	0.796824i	$-0.706512\pi$
$7$	1.02646	−	1.77787i	0.387964	−	0.671973i	0.992176	+	0.124851i	$0.0398453\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	1.97181	+	3.41528i	0.623542	+	1.08001i
$11$	−2.58114	+	4.47067i	−0.778244	+	1.34796i	0.154708	+	0.987960i	$0.450556\pi$
$11$	−2.58114	+	4.47067i	−0.778244	+	1.34796i	−0.932953	+	0.359999i	$0.882777\pi$
$12$		0			0
$13$	−1.94128	+	3.36239i	−0.538413	+	0.932559i	0.460576	+	0.887620i	$0.347643\pi$
$13$	−1.94128	+	3.36239i	−0.538413	+	0.932559i	−0.998990	+	0.0449392i	$0.985691\pi$
$14$	−2.05291			−0.548663
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.05469	−	3.55883i	0.498335	−	0.863142i	−0.501663	−	0.865063i	$-0.667278\pi$
$17$	2.05469	−	3.55883i	0.498335	−	0.863142i	0.999998	+	0.00192099i	$0.000611471\pi$
$18$		0			0
$19$	4.23814	+	1.01891i	0.972296	+	0.233754i
$19$	4.23814	+	1.01891i	0.972296	+	0.233754i
$20$	1.97181	−	3.41528i	0.440911	−	0.763680i
$21$		0			0
$22$	5.16229			1.10060
$23$	2.60260	−	4.50783i	0.542679	−	0.939948i	−0.456070	−	0.889944i	$-0.650743\pi$
$23$	2.60260	−	4.50783i	0.542679	−	0.939948i	0.998749	−	0.0500039i	$-0.0159234\pi$
$24$		0			0
$25$	10.5522			2.11044
$26$	3.88255			0.761431
$27$		0			0
$28$	1.02646	+	1.77787i	0.193982	+	0.335986i
$29$	1.20243			0.223285			0.111642	−	0.993748i	$-0.464389\pi$
$29$	1.20243			0.223285			0.111642	+	0.993748i	$0.464389\pi$
$30$		0			0
$31$	−4.20987	−	7.29170i	−0.756114	−	1.30963i	−0.944818	−	0.327594i	$-0.893762\pi$
$31$	−4.20987	−	7.29170i	−0.756114	−	1.30963i	0.188704	−	0.982034i	$-0.439571\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−4.10938			−0.704753
$35$	−4.04796	+	7.01126i	−0.684229	+	1.18512i
$36$		0			0
$37$	0.435335			0.0715687			0.0357844	−	0.999360i	$-0.488607\pi$
$37$	0.435335			0.0715687			0.0357844	+	0.999360i	$0.488607\pi$
$38$	−1.23667	−	4.17979i	−0.200614	−	0.678052i
$39$		0			0
$40$	−3.94363			−0.623542
$41$	−2.76709			−0.432147			−0.216073	−	0.976377i	$-0.569325\pi$
$41$	−2.76709			−0.432147			−0.216073	+	0.976377i	$0.569325\pi$
$42$		0			0
$43$	0.838250	+	1.45189i	0.127832	+	0.221411i	0.922836	−	0.385192i	$-0.125865\pi$
$43$	0.838250	+	1.45189i	0.127832	+	0.221411i	−0.795004	+	0.606604i	$0.792532\pi$
$44$	−2.58114	−	4.47067i	−0.389122	−	0.673980i
$45$		0			0
$46$	−5.20520			−0.767464
$47$	7.13833			1.04123			0.520616	−	0.853791i	$-0.325702\pi$
$47$	7.13833			1.04123			0.520616	+	0.853791i	$0.325702\pi$
$48$		0			0
$49$	1.39278	+	2.41236i	0.198968	+	0.344623i
$50$	−5.27609	−	9.13846i	−0.746152	−	1.29237i
$51$		0			0
$52$	−1.94128	−	3.36239i	−0.269207	−	0.466280i
$53$	0.708689	+	1.22749i	0.0973460	+	0.168608i	0.910585	−	0.413321i	$-0.135631\pi$
$53$	0.708689	+	1.22749i	0.0973460	+	0.168608i	−0.813239	+	0.581929i	$0.802298\pi$
$54$		0			0
$55$	10.1791	−	17.6307i	1.37255	−	2.37732i
$56$	1.02646	−	1.77787i	0.137166	−	0.237578i
$57$		0			0
$58$	−0.601213	−	1.04133i	−0.0789431	−	0.136733i
$59$	14.4637			1.88301			0.941506	−	0.336997i	$-0.109411\pi$
$59$	14.4637			1.88301			0.941506	+	0.336997i	$0.109411\pi$
$60$		0			0
$61$	−6.59332			−0.844189			−0.422094	−	0.906552i	$-0.638705\pi$
$61$	−6.59332			−0.844189			−0.422094	+	0.906552i	$0.638705\pi$
$62$	−4.20987	+	7.29170i	−0.534653	+	0.926047i
$63$		0			0
$64$	1.00000			0.125000
$65$	7.65567	−	13.2600i	0.949569	−	1.64470i
$66$		0			0
$67$	7.35934	−	12.7467i	0.899086	−	1.55726i	0.0704222	−	0.997517i	$-0.477565\pi$
$67$	7.35934	−	12.7467i	0.899086	−	1.55726i	0.828664	−	0.559746i	$-0.189101\pi$
$68$	2.05469	+	3.55883i	0.249168	+	0.431571i
$69$		0			0
$70$	8.09591			0.967646
$71$	2.20789	−	3.82418i	0.262028	−	0.453847i	−0.704752	−	0.709453i	$-0.748942\pi$
$71$	2.20789	−	3.82418i	0.262028	−	0.453847i	0.966781	+	0.255607i	$0.0822752\pi$
$72$		0			0
$73$	5.08361	−	8.80507i	0.594991	−	1.03056i	−0.398557	−	0.917144i	$-0.630489\pi$
$73$	5.08361	−	8.80507i	0.594991	−	1.03056i	0.993548	−	0.113411i	$-0.0361778\pi$
$74$	−0.217668	−	0.377012i	−0.0253034	−	0.0438267i
$75$		0			0
$76$	−3.00147	+	3.16088i	−0.344292	+	0.362578i
$77$	5.29886	+	9.17789i	0.603861	+	1.04592i
$78$		0			0
$79$	0.998660	+	1.72973i	0.112358	+	0.194610i	0.916721	−	0.399529i	$-0.130826\pi$
$79$	0.998660	+	1.72973i	0.112358	+	0.194610i	−0.804363	+	0.594139i	$0.797493\pi$
$80$	1.97181	+	3.41528i	0.220455	+	0.381840i
$81$		0			0
$82$	1.38355	+	2.39637i	0.152787	+	0.264635i
$83$	2.63550	−	4.56482i	0.289284	−	0.501054i	−0.684355	−	0.729149i	$-0.739916\pi$
$83$	2.63550	−	4.56482i	0.289284	−	0.501054i	0.973639	+	0.228095i	$0.0732496\pi$
$84$		0			0
$85$	−8.10293	+	14.0347i	−0.878886	+	1.52227i
$86$	0.838250	−	1.45189i	0.0903908	−	0.156562i
$87$		0			0
$88$	−2.58114	+	4.47067i	−0.275151	+	0.476575i
$89$	0.817559	+	1.41605i	0.0866610	+	0.150101i	0.906098	−	0.423068i	$-0.139047\pi$
$89$	0.817559	+	1.41605i	0.0866610	+	0.150101i	−0.819437	+	0.573170i	$0.805714\pi$
$90$		0			0
$91$	3.98527	+	6.90269i	0.417770	+	0.723598i
$92$	2.60260	+	4.50783i	0.271340	+	0.469974i
$93$		0			0
$94$	−3.56916	−	6.18197i	−0.368131	−	0.637622i
$95$	−16.7136	−	4.01820i	−1.71478	−	0.412258i
$96$		0			0
$97$	2.23760	+	3.87564i	0.227194	+	0.393512i	0.956976	−	0.290169i	$-0.0937114\pi$
$97$	2.23760	+	3.87564i	0.227194	+	0.393512i	−0.729781	+	0.683681i	$0.760378\pi$
$98$	1.39278	−	2.41236i	0.140692	−	0.243686i
$99$		0			0
$100$	−5.27609	+	9.13846i	−0.527609	+	0.913846i
$101$	−4.30035			−0.427901			−0.213950	−	0.976845i	$-0.568633\pi$
$101$	−4.30035			−0.427901			−0.213950	+	0.976845i	$0.568633\pi$
$102$		0			0
$103$	7.26626	+	12.5855i	0.715965	+	1.24009i	0.962586	+	0.270976i	$0.0873465\pi$
$103$	7.26626	+	12.5855i	0.715965	+	1.24009i	−0.246621	+	0.969112i	$0.579320\pi$
$104$	−1.94128	+	3.36239i	−0.190358	+	0.329709i
$105$		0			0
$106$	0.708689	−	1.22749i	0.0688340	−	0.119224i
$107$	2.11280			0.204252			0.102126	−	0.994771i	$-0.467435\pi$
$107$	2.11280			0.204252			0.102126	+	0.994771i	$0.467435\pi$
$108$		0			0
$109$	4.80520	−	8.32285i	0.460255	−	0.797184i	−0.538719	−	0.842486i	$-0.681091\pi$
$109$	4.80520	−	8.32285i	0.460255	−	0.797184i	0.998973	+	0.0453014i	$0.0144248\pi$
$110$	−20.3581			−1.94107
$111$		0			0
$112$	−2.05291			−0.193982
$113$	3.49351	+	6.05094i	0.328642	+	0.569225i	0.982243	−	0.187615i	$-0.0600757\pi$
$113$	3.49351	+	6.05094i	0.328642	+	0.569225i	−0.653601	+	0.756840i	$0.726742\pi$
$114$		0			0
$115$	−10.2637	+	17.7772i	−0.957092	+	1.65773i
$116$	−0.601213	+	1.04133i	−0.0558212	+	0.0966852i
$117$		0			0
$118$	−7.23184	−	12.5259i	−0.665745	−	1.15310i
$119$	−4.21809	−	7.30595i	−0.386672	−	0.669736i
$120$		0			0
$121$	−7.82462	−	13.5526i	−0.711329	−	1.23206i
$122$	3.29666	+	5.70999i	0.298466	+	0.516958i
$123$		0			0
$124$	8.41973			0.756114
$125$	−21.8957			−1.95841
$126$		0			0
$127$	−1.73490	−	3.00493i	−0.153947	−	0.266645i	0.778728	−	0.627362i	$-0.215865\pi$
$127$	−1.73490	−	3.00493i	−0.153947	−	0.266645i	−0.932675	+	0.360717i	$0.882532\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−15.3113			−1.34289
$131$	−0.360455			−0.0314931			−0.0157466	−	0.999876i	$-0.505012\pi$
$131$	−0.360455			−0.0314931			−0.0157466	+	0.999876i	$0.505012\pi$
$132$		0			0
$133$	6.16175	−	6.48901i	0.534292	−	0.562668i
$134$	−14.7187			−1.27150
$135$		0			0
$136$	2.05469	−	3.55883i	0.176188	−	0.305167i
$137$	17.8295			1.52327			0.761637	−	0.648004i	$-0.224396\pi$
$137$	17.8295			1.52327			0.761637	+	0.648004i	$0.224396\pi$
$138$		0			0
$139$	−9.76105	+	16.9066i	−0.827922	+	1.43400i	0.0717438	+	0.997423i	$0.477144\pi$
$139$	−9.76105	+	16.9066i	−0.827922	+	1.43400i	−0.899666	+	0.436580i	$0.856190\pi$
$140$	−4.04796	−	7.01126i	−0.342115	−	0.592560i
$141$		0			0
$142$	−4.41578			−0.370564
$143$	−10.0214	−	17.3576i	−0.838034	−	1.45152i
$144$		0			0
$145$	−4.74192			−0.393795
$146$	−10.1672			−0.841445
$147$		0			0
$148$	−0.217668	+	0.377012i	−0.0178922	+	0.0309902i
$149$	18.7583			1.53674			0.768371	−	0.640005i	$-0.221068\pi$
$149$	18.7583			1.53674			0.768371	+	0.640005i	$0.221068\pi$
$150$		0			0
$151$	−2.80807	+	4.86372i	−0.228518	+	0.395804i	−0.957369	−	0.288868i	$-0.906721\pi$
$151$	−2.80807	+	4.86372i	−0.228518	+	0.395804i	0.728851	+	0.684672i	$0.240055\pi$
$152$	4.23814	+	1.01891i	0.343758	+	0.0826445i
$153$		0			0
$154$	5.29886	−	9.17789i	0.426994	−	0.739576i
$155$	16.6021	+	28.7557i	1.33352	+	2.30972i
$156$		0			0
$157$	−12.0730			−0.963529			−0.481765	−	0.876301i	$-0.660004\pi$
$157$	−12.0730			−0.963529			−0.481765	+	0.876301i	$0.660004\pi$
$158$	0.998660	−	1.72973i	0.0794491	−	0.137610i
$159$		0			0
$160$	1.97181	−	3.41528i	0.155885	−	0.270002i
$161$	−5.34290	−	9.25418i	−0.421080	−	0.729331i
$162$		0			0
$163$	−11.5204			−0.902351			−0.451175	−	0.892435i	$-0.648995\pi$
$163$	−11.5204			−0.902351			−0.451175	+	0.892435i	$0.648995\pi$
$164$	1.38355	−	2.39637i	0.108037	−	0.187125i
$165$		0			0
$166$	−5.27100			−0.409109
$167$	−9.37172	+	16.2323i	−0.725206	+	1.25609i	0.233683	+	0.972313i	$0.424922\pi$
$167$	−9.37172	+	16.2323i	−0.725206	+	1.25609i	−0.958889	+	0.283781i	$0.908411\pi$
$168$		0			0
$169$	−1.03711	−	1.79633i	−0.0797779	−	0.138179i
$170$	16.2059			1.24293
$171$		0			0
$172$	−1.67650			−0.127832
$173$	−0.723760	−	1.25359i	−0.0550265	−	0.0953087i	0.837200	−	0.546897i	$-0.184191\pi$
$173$	−0.723760	−	1.25359i	−0.0550265	−	0.0953087i	−0.892227	+	0.451588i	$0.850858\pi$
$174$		0			0
$175$	10.8313	−	18.7604i	0.818773	−	1.41816i
$176$	5.16229			0.389122
$177$		0			0
$178$	0.817559	−	1.41605i	0.0612786	−	0.106138i
$179$	−1.31420			−0.0982278			−0.0491139	−	0.998793i	$-0.515640\pi$
$179$	−1.31420			−0.0982278			−0.0491139	+	0.998793i	$0.515640\pi$
$180$		0			0
$181$	−5.35552	−	9.27604i	−0.398073	−	0.689482i	0.595415	−	0.803418i	$-0.296988\pi$
$181$	−5.35552	−	9.27604i	−0.398073	−	0.689482i	−0.993488	+	0.113936i	$0.963654\pi$
$182$	3.98527	−	6.90269i	0.295408	−	0.511661i
$183$		0			0
$184$	2.60260	−	4.50783i	0.191866	−	0.332322i
$185$	−1.71680			−0.126222
$186$		0			0
$187$	10.6069	+	18.3717i	0.775654	+	1.34347i
$188$	−3.56916	+	6.18197i	−0.260308	+	0.450867i
$189$		0			0
$190$	4.87696	+	16.4835i	0.353812	+	1.19584i
$191$	1.88682	−	3.26807i	0.136526	−	0.236469i	−0.789654	−	0.613553i	$-0.789740\pi$
$191$	1.88682	−	3.26807i	0.136526	−	0.236469i	0.926179	+	0.377084i	$0.123073\pi$
$192$		0			0
$193$	16.2305			1.16830			0.584150	−	0.811646i	$-0.301428\pi$
$193$	16.2305			1.16830			0.584150	+	0.811646i	$0.301428\pi$
$194$	2.23760	−	3.87564i	0.160651	−	0.278255i
$195$		0			0
$196$	−2.78556			−0.198968
$197$	20.6274			1.46964			0.734821	−	0.678261i	$-0.237266\pi$
$197$	20.6274			1.46964			0.734821	+	0.678261i	$0.237266\pi$
$198$		0			0
$199$	3.22792	+	5.59093i	0.228821	+	0.396330i	0.957459	−	0.288569i	$-0.0931795\pi$
$199$	3.22792	+	5.59093i	0.228821	+	0.396330i	−0.728638	+	0.684899i	$0.759846\pi$
$200$	10.5522			0.746152
$201$		0			0
$202$	2.15018	+	3.72421i	0.151286	+	0.262035i
$203$	1.23424	−	2.13776i	0.0866264	−	0.150041i
$204$		0			0
$205$	10.9124			0.762153
$206$	7.26626	−	12.5855i	0.506264	−	0.876875i
$207$		0			0
$208$	3.88255			0.269207
$209$	−15.4945	+	16.3174i	−1.07177	+	1.12870i
$210$		0			0
$211$	−0.405098			−0.0278881			−0.0139440	−	0.999903i	$-0.504439\pi$
$211$	−0.405098			−0.0278881			−0.0139440	+	0.999903i	$0.504439\pi$
$212$	−1.41738			−0.0973460
$213$		0			0
$214$	−1.05640	−	1.82974i	−0.0722141	−	0.125078i
$215$	−3.30574	−	5.72572i	−0.225450	−	0.390491i
$216$		0			0
$217$	−17.2850			−1.17338
$218$	−9.61040			−0.650898
$219$		0			0
$220$	10.1791	+	17.6307i	0.686273	+	1.18866i
$221$	7.97744	+	13.8173i	0.536621	+	0.929455i
$222$		0			0
$223$	4.20440	+	7.28224i	0.281547	+	0.487655i	0.971766	−	0.235946i	$-0.0758190\pi$
$223$	4.20440	+	7.28224i	0.281547	+	0.487655i	−0.690219	+	0.723601i	$0.742486\pi$
$224$	1.02646	+	1.77787i	0.0685829	+	0.118789i
$225$		0			0
$226$	3.49351	−	6.05094i	0.232385	−	0.402503i
$227$	−0.146997	+	0.254607i	−0.00975656	+	0.0168989i	−0.870862	−	0.491527i	$-0.836439\pi$
$227$	−0.146997	+	0.254607i	−0.00975656	+	0.0168989i	0.861106	+	0.508426i	$0.169772\pi$
$228$		0			0
$229$	−3.61171	−	6.25566i	−0.238668	−	0.413386i	0.721664	−	0.692243i	$-0.243378\pi$
$229$	−3.61171	−	6.25566i	−0.238668	−	0.413386i	−0.960332	+	0.278858i	$0.910044\pi$
$230$	20.5273			1.35353
$231$		0			0
$232$	1.20243			0.0789431
$233$	−9.39739	+	16.2768i	−0.615644	+	1.06633i	0.374627	+	0.927175i	$0.377771\pi$
$233$	−9.39739	+	16.2768i	−0.615644	+	1.06633i	−0.990271	+	0.139151i	$0.955563\pi$
$234$		0			0
$235$	−28.1509			−1.83636
$236$	−7.23184	+	12.5259i	−0.470753	+	0.815368i
$237$		0			0
$238$	−4.21809	+	7.30595i	−0.273418	+	0.473575i
$239$	1.67306	+	2.89782i	0.108221	+	0.187444i	0.915050	−	0.403341i	$-0.132151\pi$
$239$	1.67306	+	2.89782i	0.108221	+	0.187444i	−0.806829	+	0.590786i	$0.798818\pi$
$240$		0			0
$241$	−1.24755			−0.0803619			−0.0401810	−	0.999192i	$-0.512793\pi$
$241$	−1.24755			−0.0803619			−0.0401810	+	0.999192i	$0.512793\pi$
$242$	−7.82462	+	13.5526i	−0.502986	+	0.871197i
$243$		0			0
$244$	3.29666	−	5.70999i	0.211047	−	0.365544i
$245$	−5.49260	−	9.51346i	−0.350909	−	0.607793i
$246$		0			0
$247$	−11.6534	+	12.2723i	−0.741486	+	0.780867i
$248$	−4.20987	−	7.29170i	−0.267327	−	0.463024i
$249$		0			0
$250$	10.9479	+	18.9623i	0.692404	+	1.19928i
$251$	−2.56602	−	4.44447i	−0.161966	−	0.280532i	0.773608	−	0.633664i	$-0.218450\pi$
$251$	−2.56602	−	4.44447i	−0.161966	−	0.280532i	−0.935574	+	0.353132i	$0.885117\pi$
$252$		0			0
$253$	13.4354	+	23.2707i	0.844674	+	1.46302i
$254$	−1.73490	+	3.00493i	−0.108857	+	0.188546i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.13299	−	12.3547i	0.444943	−	0.770665i	−0.553105	−	0.833112i	$-0.686557\pi$
$257$	7.13299	−	12.3547i	0.444943	−	0.770665i	0.998048	+	0.0624470i	$0.0198904\pi$
$258$		0			0
$259$	0.446852	−	0.773971i	0.0277661	−	0.0480922i
$260$	7.65567	+	13.2600i	0.474784	+	0.822351i
$261$		0			0
$262$	0.180228	+	0.312163i	0.0111345	+	0.0192855i
$263$	0.251728	+	0.436005i	0.0155222	+	0.0268852i	0.873682	−	0.486497i	$-0.161726\pi$
$263$	0.251728	+	0.436005i	0.0155222	+	0.0268852i	−0.858160	+	0.513382i	$0.828392\pi$
$264$		0			0
$265$	−2.79481	−	4.84074i	−0.171684	−	0.297365i
$266$	−8.70052	−	2.09173i	−0.533463	−	0.128252i
$267$		0			0
$268$	7.35934	+	12.7467i	0.449543	+	0.778632i
$269$	−2.90769	+	5.03628i	−0.177285	+	0.307067i	−0.940950	−	0.338546i	$-0.890065\pi$
$269$	−2.90769	+	5.03628i	−0.177285	+	0.307067i	0.763664	+	0.645613i	$0.223398\pi$
$270$		0			0
$271$	16.2151	−	28.0854i	0.984997	−	1.70606i	0.343045	−	0.939319i	$-0.388542\pi$
$271$	16.2151	−	28.0854i	0.984997	−	1.70606i	0.641952	−	0.766745i	$-0.278125\pi$
$272$	−4.10938			−0.249168
$273$		0			0
$274$	−8.91473	−	15.4408i	−0.538558	−	0.932811i
$275$	−27.2367	+	47.1754i	−1.64244	+	2.84478i
$276$		0			0
$277$	9.88182	−	17.1158i	0.593741	−	1.02839i	−0.399982	−	0.916523i	$-0.630984\pi$
$277$	9.88182	−	17.1158i	0.593741	−	1.02839i	0.993723	−	0.111866i	$-0.0356829\pi$
$278$	19.5221			1.17086
$279$		0			0
$280$	−4.04796	+	7.01126i	−0.241912	+	0.419003i
$281$	−24.5308			−1.46338			−0.731692	−	0.681635i	$-0.761269\pi$
$281$	−24.5308			−1.46338			−0.731692	+	0.681635i	$0.761269\pi$
$282$		0			0
$283$	−2.74263			−0.163033			−0.0815163	−	0.996672i	$-0.525976\pi$
$283$	−2.74263			−0.163033			−0.0815163	+	0.996672i	$0.525976\pi$
$284$	2.20789	+	3.82418i	0.131014	+	0.226923i
$285$		0			0
$286$	−10.0214	+	17.3576i	−0.592580	+	1.02638i
$287$	−2.84029	+	4.91953i	−0.167657	+	0.290391i
$288$		0			0
$289$	0.0565005	+	0.0978617i	0.00332356	+	0.00575657i
$290$	2.37096	+	4.10662i	0.139227	+	0.241149i
$291$		0			0
$292$	5.08361	+	8.80507i	0.297496	+	0.515278i
$293$	−15.1403	−	26.2237i	−0.884504	−	1.53201i	−0.846281	−	0.532737i	$-0.821163\pi$
$293$	−15.1403	−	26.2237i	−0.884504	−	1.53201i	−0.0382235	−	0.999269i	$-0.512170\pi$
$294$		0			0
$295$	−57.0393			−3.32096
$296$	0.435335			0.0253034
$297$		0			0
$298$	−9.37916	−	16.2452i	−0.543320	−	0.941058i
$299$	10.1047	+	17.5019i	0.584371	+	1.01216i
$300$		0			0
$301$	3.44171			0.198377
$302$	5.61615			0.323173
$303$		0			0
$304$	−1.23667	−	4.17979i	−0.0709278	−	0.239727i
$305$	26.0016			1.48885
$306$		0			0
$307$	−8.15255	+	14.1206i	−0.465291	+	0.805907i	−0.999215	−	0.0396256i	$-0.987383\pi$
$307$	−8.15255	+	14.1206i	−0.465291	+	0.805907i	0.533924	+	0.845532i	$0.320717\pi$
$308$	−10.5977			−0.603861
$309$		0			0
$310$	16.6021	−	28.7557i	0.942938	−	1.63322i
$311$	−13.3270	−	23.0831i	−0.755706	−	1.30892i	−0.945022	−	0.327006i	$-0.893960\pi$
$311$	−13.3270	−	23.0831i	−0.755706	−	1.30892i	0.189316	−	0.981916i	$-0.439373\pi$
$312$		0			0
$313$	17.9803			1.01630			0.508152	−	0.861267i	$-0.330329\pi$
$313$	17.9803			1.01630			0.508152	+	0.861267i	$0.330329\pi$
$314$	6.03649	+	10.4555i	0.340659	+	0.590039i
$315$		0			0
$316$	−1.99732			−0.112358
$317$	−16.6493			−0.935115			−0.467558	−	0.883963i	$-0.654866\pi$
$317$	−16.6493			−0.935115			−0.467558	+	0.883963i	$0.654866\pi$
$318$		0			0
$319$	−3.10364	+	5.37565i	−0.173770	+	0.300979i
$320$	−3.94363			−0.220455
$321$		0			0
$322$	−5.34290	+	9.25418i	−0.297748	+	0.515715i
$323$	12.3342	−	12.9893i	0.686292	−	0.722742i
$324$		0			0
$325$	−20.4847	+	35.4806i	−1.13629	+	1.96811i
$326$	5.76022	+	9.97699i	0.319029	+	0.552575i
$327$		0			0
$328$	−2.76709			−0.152787
$329$	7.32717	−	12.6910i	0.403960	−	0.699679i
$330$		0			0
$331$	0.156160	−	0.270477i	0.00858333	−	0.0148668i	−0.861702	−	0.507415i	$-0.830601\pi$
$331$	0.156160	−	0.270477i	0.00858333	−	0.0148668i	0.870285	+	0.492548i	$0.163934\pi$
$332$	2.63550	+	4.56482i	0.144642	+	0.250527i
$333$		0			0
$334$	18.7434			1.02560
$335$	−29.0225	+	50.2684i	−1.58567	+	2.74646i
$336$		0			0
$337$	18.4676			1.00599			0.502997	−	0.864288i	$-0.332231\pi$
$337$	18.4676			1.00599			0.502997	+	0.864288i	$0.332231\pi$
$338$	−1.03711	+	1.79633i	−0.0564115	+	0.0977075i
$339$		0			0
$340$	−8.10293	−	14.0347i	−0.439443	−	0.761137i
$341$	43.4651			2.35377
$342$		0			0
$343$	20.0889			1.08470
$344$	0.838250	+	1.45189i	0.0451954	+	0.0782808i
$345$		0			0
$346$	−0.723760	+	1.25359i	−0.0389096	+	0.0673934i
$347$	−7.13618			−0.383090			−0.191545	−	0.981484i	$-0.561350\pi$
$347$	−7.13618			−0.383090			−0.191545	+	0.981484i	$0.561350\pi$
$348$		0			0
$349$	6.45792	−	11.1854i	0.345685	−	0.598743i	−0.639793	−	0.768547i	$-0.720980\pi$
$349$	6.45792	−	11.1854i	0.345685	−	0.598743i	0.985478	+	0.169804i	$0.0543134\pi$
$350$	−21.6627			−1.15792
$351$		0			0
$352$	−2.58114	−	4.47067i	−0.137575	−	0.238288i
$353$	13.1427	−	22.7639i	0.699518	−	1.21160i	−0.269116	−	0.963108i	$-0.586732\pi$
$353$	13.1427	−	22.7639i	0.699518	−	1.21160i	0.968634	−	0.248492i	$-0.0799351\pi$
$354$		0			0
$355$	−8.70710	+	15.0811i	−0.462125	+	0.800423i
$356$	−1.63512			−0.0866610
$357$		0			0
$358$	0.657100	+	1.13813i	0.0347288	+	0.0601520i
$359$	−7.54249	+	13.0640i	−0.398077	+	0.689490i	−0.993489	−	0.113931i	$-0.963656\pi$
$359$	−7.54249	+	13.0640i	−0.398077	+	0.689490i	0.595411	+	0.803421i	$0.296989\pi$
$360$		0			0
$361$	16.9236	+	8.63656i	0.890718	+	0.454556i
$362$	−5.35552	+	9.27604i	−0.281480	+	0.487538i
$363$		0			0
$364$	−7.97054			−0.417770
$365$	−20.0478	+	34.7239i	−1.04935	+	1.81753i
$366$		0			0
$367$	−30.4079			−1.58728			−0.793639	−	0.608389i	$-0.791816\pi$
$367$	−30.4079			−1.58728			−0.793639	+	0.608389i	$0.791816\pi$
$368$	−5.20520			−0.271340
$369$		0			0
$370$	0.858400	+	1.48679i	0.0446261	+	0.0772947i
$371$	2.90975			0.151067
$372$		0			0
$373$	−5.07447	−	8.78925i	−0.262746	−	0.455090i	0.704224	−	0.709977i	$-0.251295\pi$
$373$	−5.07447	−	8.78925i	−0.262746	−	0.455090i	−0.966971	+	0.254887i	$0.917962\pi$
$374$	10.6069	−	18.3717i	0.548470	−	0.949978i
$375$		0			0
$376$	7.13833			0.368131
$377$	−2.33424	+	4.04302i	−0.120220	+	0.208226i
$378$		0			0
$379$	7.53375			0.386983			0.193491	−	0.981102i	$-0.438019\pi$
$379$	7.53375			0.386983			0.193491	+	0.981102i	$0.438019\pi$
$380$	11.8367	−	12.4653i	0.607209	−	0.639458i
$381$		0			0
$382$	−3.77365			−0.193077
$383$	10.3678			0.529768			0.264884	−	0.964280i	$-0.414666\pi$
$383$	10.3678			0.529768			0.264884	+	0.964280i	$0.414666\pi$
$384$		0			0
$385$	−20.8967	−	36.1942i	−1.06500	−	1.84463i
$386$	−8.11527	−	14.0561i	−0.413056	−	0.715435i
$387$		0			0
$388$	−4.47521			−0.227194
$389$	38.1779			1.93570			0.967849	−	0.251532i	$-0.0809343\pi$
$389$	38.1779			1.93570			0.967849	+	0.251532i	$0.0809343\pi$
$390$		0			0
$391$	−10.6951	−	18.5244i	−0.540873	−	0.936819i
$392$	1.39278	+	2.41236i	0.0703460	+	0.121843i
$393$		0			0
$394$	−10.3137	−	17.8639i	−0.519597	−	0.899969i
$395$	−3.93834	−	6.82140i	−0.198159	−	0.343222i
$396$		0			0
$397$	1.98523	−	3.43851i	0.0996357	−	0.172574i	−0.811898	−	0.583799i	$-0.801566\pi$
$397$	1.98523	−	3.43851i	0.0996357	−	0.172574i	0.911534	+	0.411225i	$0.134899\pi$
$398$	3.22792	−	5.59093i	0.161801	−	0.280248i
$399$		0			0
$400$	−5.27609	−	9.13846i	−0.263805	−	0.456923i
$401$	2.86983			0.143312			0.0716562	−	0.997429i	$-0.477172\pi$
$401$	2.86983			0.143312			0.0716562	+	0.997429i	$0.477172\pi$
$402$		0			0
$403$	32.6901			1.62841
$404$	2.15018	−	3.72421i	0.106975	−	0.185286i
$405$		0			0
$406$	−2.46847			−0.122508
$407$	−1.12366	+	1.94624i	−0.0556980	+	0.0964717i
$408$		0			0
$409$	11.4136	−	19.7689i	0.564364	−	0.977508i	−0.432744	−	0.901517i	$-0.642455\pi$
$409$	11.4136	−	19.7689i	0.564364	−	0.977508i	0.997109	−	0.0759908i	$-0.0242120\pi$
$410$	−5.45618	−	9.45039i	−0.269462	−	0.466721i
$411$		0			0
$412$	−14.5325			−0.715965
$413$	14.8463	−	25.7146i	0.730540	−	1.26533i
$414$		0			0
$415$	−10.3934	+	18.0019i	−0.510193	+	0.883680i
$416$	−1.94128	−	3.36239i	−0.0951789	−	0.164855i
$417$		0			0
$418$	21.8785	+	5.25991i	1.07011	+	0.257270i
$419$	−6.81387	−	11.8020i	−0.332879	−	0.576564i	0.650196	−	0.759767i	$-0.274687\pi$
$419$	−6.81387	−	11.8020i	−0.332879	−	0.576564i	−0.983075	+	0.183203i	$0.941353\pi$
$420$		0			0
$421$	6.22588	+	10.7835i	0.303431	+	0.525557i	0.976911	−	0.213648i	$-0.0685346\pi$
$421$	6.22588	+	10.7835i	0.303431	+	0.525557i	−0.673480	+	0.739205i	$0.735201\pi$
$422$	0.202549	+	0.350825i	0.00985992	+	0.0170779i
$423$		0			0
$424$	0.708689	+	1.22749i	0.0344170	+	0.0596120i
$425$	21.6815	−	37.5534i	1.05171	−	1.82161i
$426$		0			0
$427$	−6.76775	+	11.7221i	−0.327515	+	0.567272i
$428$	−1.05640	+	1.82974i	−0.0510630	+	0.0884438i
$429$		0			0
$430$	−3.30574	+	5.72572i	−0.159417	+	0.276119i
$431$	12.6070	+	21.8359i	0.607256	+	1.05180i	0.991691	+	0.128646i	$0.0410630\pi$
$431$	12.6070	+	21.8359i	0.607256	+	1.05180i	−0.384435	+	0.923152i	$0.625604\pi$
$432$		0			0
$433$	−10.0557	−	17.4169i	−0.483244	−	0.837003i	0.516571	−	0.856244i	$-0.327208\pi$
$433$	−10.0557	−	17.4169i	−0.483244	−	0.837003i	−0.999815	+	0.0192414i	$0.993875\pi$
$434$	8.64248	+	14.9692i	0.414852	+	0.718545i
$435$		0			0
$436$	4.80520	+	8.32285i	0.230127	+	0.398592i
$437$	15.6232	−	16.4530i	0.747361	−	0.787054i
$438$		0			0
$439$	6.31870	+	10.9443i	0.301575	+	0.522343i	0.976493	−	0.215550i	$-0.0691543\pi$
$439$	6.31870	+	10.9443i	0.301575	+	0.522343i	−0.674918	+	0.737893i	$0.735821\pi$
$440$	10.1791	−	17.6307i	0.485268	−	0.840509i
$441$		0			0
$442$	7.97744	−	13.8173i	0.379448	−	0.657224i
$443$	22.0612			1.04816			0.524080	−	0.851669i	$-0.324409\pi$
$443$	22.0612			1.04816			0.524080	+	0.851669i	$0.324409\pi$
$444$		0			0
$445$	−3.22415	−	5.58438i	−0.152839	−	0.264725i
$446$	4.20440	−	7.28224i	0.199084	−	0.344824i
$447$		0			0
$448$	1.02646	−	1.77787i	0.0484955	−	0.0839966i
$449$	−32.2058			−1.51988			−0.759942	−	0.649990i	$-0.774773\pi$
$449$	−32.2058			−1.51988			−0.759942	+	0.649990i	$0.774773\pi$
$450$		0			0
$451$	7.14226	−	12.3708i	0.336316	−	0.582516i
$452$	−6.98702			−0.328642
$453$		0			0
$454$	0.293995			0.0137979
$455$	−15.7164	−	27.2216i	−0.736796	−	1.27617i
$456$		0			0
$457$	0.903329	−	1.56461i	0.0422559	−	0.0731894i	−0.844124	−	0.536148i	$-0.819879\pi$
$457$	0.903329	−	1.56461i	0.0422559	−	0.0731894i	0.886380	+	0.462959i	$0.153212\pi$
$458$	−3.61171	+	6.25566i	−0.168764	+	0.292308i
$459$		0			0
$460$	−10.2637	−	17.7772i	−0.478546	−	0.828866i
$461$	−11.7593	−	20.3677i	−0.547686	−	0.948620i	−0.998433	−	0.0559681i	$-0.982175\pi$
$461$	−11.7593	−	20.3677i	−0.547686	−	0.948620i	0.450746	−	0.892652i	$-0.351158\pi$
$462$		0			0
$463$	10.1793	+	17.6310i	0.473071	+	0.819382i	0.999525	−	0.0308210i	$-0.00981219\pi$
$463$	10.1793	+	17.6310i	0.473071	+	0.819382i	−0.526454	+	0.850203i	$0.676479\pi$
$464$	−0.601213	−	1.04133i	−0.0279106	−	0.0483426i
$465$		0			0
$466$	18.7948			0.870652
$467$	−22.2721			−1.03063			−0.515316	−	0.857000i	$-0.672325\pi$
$467$	−22.2721			−1.03063			−0.515316	+	0.857000i	$0.672325\pi$
$468$		0			0
$469$	−15.1081	−	26.1679i	−0.697626	−	1.20832i
$470$	14.0754	+	24.3794i	0.649252	+	1.12454i
$471$		0			0
$472$	14.4637			0.665745
$473$	−8.65458			−0.397938
$474$		0			0
$475$	44.7216	+	10.7517i	2.05197	+	0.493323i
$476$	8.43619			0.386672
$477$		0			0
$478$	1.67306	−	2.89782i	0.0765238	−	0.132543i
$479$	−12.5387			−0.572906			−0.286453	−	0.958094i	$-0.592476\pi$
$479$	−12.5387			−0.572906			−0.286453	+	0.958094i	$0.592476\pi$
$480$		0			0
$481$	−0.845107	+	1.46377i	−0.0385335	+	0.0667421i
$482$	0.623776	+	1.08041i	0.0284122	+	0.0492114i
$483$		0			0
$484$	15.6492			0.711329
$485$	−8.82427	−	15.2841i	−0.400690	−	0.694015i
$486$		0			0
$487$	−3.92089			−0.177672			−0.0888362	−	0.996046i	$-0.528315\pi$
$487$	−3.92089			−0.177672			−0.0888362	+	0.996046i	$0.528315\pi$
$488$	−6.59332			−0.298466
$489$		0			0
$490$	−5.49260	+	9.51346i	−0.248130	+	0.429774i
$491$	14.7707			0.666591			0.333296	−	0.942822i	$-0.391839\pi$
$491$	14.7707			0.666591			0.333296	+	0.942822i	$0.391839\pi$
$492$		0			0
$493$	2.47061	−	4.27922i	0.111271	−	0.192727i
$494$	16.4548	+	3.95597i	0.740337	+	0.177988i
$495$		0			0
$496$	−4.20987	+	7.29170i	−0.189029	+	0.327407i
$497$	−4.53260	−	7.85070i	−0.203315	−	0.352152i
$498$		0			0
$499$	28.8355			1.29085			0.645427	−	0.763822i	$-0.276680\pi$
$499$	28.8355			1.29085			0.645427	+	0.763822i	$0.276680\pi$
$500$	10.9479	−	18.9623i	0.489603	−	0.848018i
$501$		0			0
$502$	−2.56602	+	4.44447i	−0.114527	+	0.198366i
$503$	−14.8533	−	25.7266i	−0.662275	−	1.14709i	−0.980016	−	0.198917i	$-0.936258\pi$
$503$	−14.8533	−	25.7266i	−0.662275	−	1.14709i	0.317741	−	0.948177i	$-0.397076\pi$
$504$		0			0
$505$	16.9590			0.754664
$506$	13.4354	−	23.2707i	0.597275	−	1.03451i
$507$		0			0
$508$	3.46980			0.153947
$509$	20.5543	−	35.6011i	0.911053	−	1.57799i	0.0984726	−	0.995140i	$-0.468604\pi$
$509$	20.5543	−	35.6011i	0.911053	−	1.57799i	0.812580	−	0.582850i	$-0.198062\pi$
$510$		0			0
$511$	−10.4362	−	18.0760i	−0.461670	−	0.799636i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−14.2660			−0.629245
$515$	−28.6554	−	49.6326i	−1.26271	−	2.18707i
$516$		0			0
$517$	−18.4251	+	31.9131i	−0.810333	+	1.40354i
$518$	−0.893705			−0.0392671
$519$		0			0
$520$	7.65567	−	13.2600i	0.335723	−	0.581490i
$521$	−24.1264			−1.05700			−0.528499	−	0.848934i	$-0.677245\pi$
$521$	−24.1264			−1.05700			−0.528499	+	0.848934i	$0.677245\pi$
$522$		0			0
$523$	20.8795	+	36.1644i	0.912998	+	1.58136i	0.809806	+	0.586697i	$0.199572\pi$
$523$	20.8795	+	36.1644i	0.912998	+	1.58136i	0.103191	+	0.994662i	$0.467095\pi$
$524$	0.180228	−	0.312163i	0.00787328	−	0.0136369i
$525$		0			0
$526$	0.251728	−	0.436005i	0.0109758	−	0.0190107i
$527$	−34.5999			−1.50719
$528$		0			0
$529$	−2.04703	−	3.54556i	−0.0890013	−	0.154155i
$530$	−2.79481	+	4.84074i	−0.121399	+	0.210268i
$531$		0			0
$532$	2.53877	+	8.58074i	0.110070	+	0.372022i
$533$	5.37169	−	9.30404i	0.232674	−	0.403003i
$534$		0			0
$535$	−8.33210			−0.360228
$536$	7.35934	−	12.7467i	0.317875	−	0.550576i
$537$		0			0
$538$	5.81539			0.250719
$539$	−14.3799			−0.619384
$540$		0			0
$541$	−7.32270	−	12.6833i	−0.314828	−	0.545297i	0.664573	−	0.747223i	$-0.268613\pi$
$541$	−7.32270	−	12.6833i	−0.314828	−	0.545297i	−0.979401	+	0.201926i	$0.935280\pi$
$542$	−32.4302			−1.39300
$543$		0			0
$544$	2.05469	+	3.55883i	0.0880941	+	0.152583i
$545$	−18.9499	+	32.8222i	−0.811725	+	1.40595i
$546$		0			0
$547$	−35.7961			−1.53053			−0.765265	−	0.643716i	$-0.777392\pi$
$547$	−35.7961			−1.53053			−0.765265	+	0.643716i	$0.777392\pi$
$548$	−8.91473	+	15.4408i	−0.380818	+	0.659597i
$549$		0			0
$550$	54.4734			2.32275
$551$	5.09605	+	1.22516i	0.217099	+	0.0521937i
$552$		0			0
$553$	4.10032			0.174363
$554$	−19.7636			−0.839676
$555$		0			0
$556$	−9.76105	−	16.9066i	−0.413961	−	0.717001i
$557$	4.75137	+	8.22962i	0.201322	+	0.348700i	0.948955	−	0.315413i	$-0.102143\pi$
$557$	4.75137	+	8.22962i	0.201322	+	0.348700i	−0.747633	+	0.664113i	$0.768810\pi$
$558$		0			0
$559$	−6.50910			−0.275306
$560$	8.09591			0.342115
$561$		0			0
$562$	12.2654	+	21.2443i	0.517385	+	0.896137i
$563$	14.2685	+	24.7138i	0.601346	+	1.04156i	0.992618	+	0.121286i	$0.0387020\pi$
$563$	14.2685	+	24.7138i	0.601346	+	1.04156i	−0.391272	+	0.920275i	$0.627965\pi$
$564$		0			0
$565$	−13.7771	−	23.8626i	−0.579607	−	1.00391i
$566$	1.37132	+	2.37519i	0.0576407	+	0.0998366i
$567$		0			0
$568$	2.20789	−	3.82418i	0.0926411	−	0.160459i
$569$	5.24159	−	9.07869i	0.219739	−	0.380599i	−0.734989	−	0.678079i	$-0.762813\pi$
$569$	5.24159	−	9.07869i	0.219739	−	0.380599i	0.954728	+	0.297480i	$0.0961462\pi$
$570$		0			0
$571$	−9.32650	−	16.1540i	−0.390302	−	0.676022i	0.602187	−	0.798355i	$-0.294296\pi$
$571$	−9.32650	−	16.1540i	−0.390302	−	0.676022i	−0.992489	+	0.122332i	$0.960963\pi$
$572$	20.0429			0.838034
$573$		0			0
$574$	5.68059			0.237103
$575$	27.4631	−	47.5675i	1.14529	−	1.98370i
$576$		0			0
$577$	34.6202			1.44126			0.720628	−	0.693322i	$-0.243853\pi$
$577$	34.6202			1.44126			0.720628	+	0.693322i	$0.243853\pi$
$578$	0.0565005	−	0.0978617i	0.00235011	−	0.00407051i
$579$		0			0
$580$	2.37096	−	4.10662i	0.0984487	−	0.170518i
$581$	−5.41045	−	9.37117i	−0.224463	−	0.388782i
$582$		0			0
$583$	−7.31692			−0.303036
$584$	5.08361	−	8.80507i	0.210361	−	0.364356i
$585$		0			0
$586$	−15.1403	+	26.2237i	−0.625439	+	1.08329i
$587$	−7.01522	−	12.1507i	−0.289549	−	0.501514i	0.684153	−	0.729339i	$-0.260172\pi$
$587$	−7.01522	−	12.1507i	−0.289549	−	0.501514i	−0.973702	+	0.227825i	$0.926839\pi$
$588$		0			0
$589$	−10.4124	−	35.1927i	−0.429036	−	1.45009i
$590$	28.5197	+	49.3975i	1.17414	+	2.03366i
$591$		0			0
$592$	−0.217668	−	0.377012i	−0.00894609	−	0.0154951i
$593$	11.3497	+	19.6582i	0.466075	+	0.807266i	0.999249	−	0.0387394i	$-0.0123342\pi$
$593$	11.3497	+	19.6582i	0.466075	+	0.807266i	−0.533174	+	0.846006i	$0.679001\pi$
$594$		0			0
$595$	16.6346	+	28.8119i	0.681951	+	1.18117i
$596$	−9.37916	+	16.2452i	−0.384185	+	0.665429i
$597$		0			0
$598$	10.1047	−	17.5019i	0.413213	−	0.715706i
$599$	4.75273	−	8.23197i	0.194191	−	0.336349i	−0.752444	−	0.658656i	$-0.771125\pi$
$599$	4.75273	−	8.23197i	0.194191	−	0.336349i	0.946635	+	0.322307i	$0.104458\pi$
$600$		0			0
$601$	9.68287	−	16.7712i	0.394973	−	0.684113i	−0.598125	−	0.801403i	$-0.704087\pi$
$601$	9.68287	−	16.7712i	0.394973	−	0.684113i	0.993098	+	0.117290i	$0.0374208\pi$
$602$	−1.72085	−	2.98060i	−0.0701367	−	0.121480i
$603$		0			0
$604$	−2.80807	−	4.86372i	−0.114259	−	0.197902i
$605$	30.8574	+	53.4465i	1.25453	+	2.17291i
$606$		0			0
$607$	−4.51935	−	7.82774i	−0.183435	−	0.317718i	0.759613	−	0.650375i	$-0.225388\pi$
$607$	−4.51935	−	7.82774i	−0.183435	−	0.317718i	−0.943048	+	0.332657i	$0.892055\pi$
$608$	−3.00147	+	3.16088i	−0.121726	+	0.128191i
$609$		0			0
$610$	−13.0008	−	22.5180i	−0.526387	−	0.911729i
$611$	−13.8575	+	24.0018i	−0.560613	+	0.971011i
$612$		0			0
$613$	−2.58989	+	4.48582i	−0.104605	+	0.181181i	−0.913577	−	0.406667i	$-0.866691\pi$
$613$	−2.58989	+	4.48582i	−0.104605	+	0.181181i	0.808972	+	0.587847i	$0.200024\pi$
$614$	16.3051			0.658020
$615$		0			0
$616$	5.29886	+	9.17789i	0.213497	+	0.369788i
$617$	−11.5792	+	20.0558i	−0.466161	+	0.807415i	−0.999253	−	0.0386424i	$-0.987697\pi$
$617$	−11.5792	+	20.0558i	−0.466161	+	0.807415i	0.533092	+	0.846057i	$0.321030\pi$
$618$		0			0
$619$	5.07677	−	8.79323i	0.204053	−	0.353430i	−0.745778	−	0.666195i	$-0.767922\pi$
$619$	5.07677	−	8.79323i	0.204053	−	0.353430i	0.949830	+	0.312765i	$0.101255\pi$
$620$	−33.2043			−1.33352
$621$		0			0
$622$	−13.3270	+	23.0831i	−0.534365	+	0.925548i
$623$	3.35675			0.134485
$624$		0			0
$625$	33.5876			1.34351
$626$	−8.99013	−	15.5714i	−0.359318	−	0.622357i
$627$		0			0
$628$	6.03649	−	10.4555i	0.240882	−	0.417220i
$629$	0.894479	−	1.54928i	0.0356652	−	0.0617740i
$630$		0			0
$631$	9.75519	+	16.8965i	0.388348	+	0.672638i	0.992227	−	0.124437i	$-0.0397126\pi$
$631$	9.75519	+	16.8965i	0.388348	+	0.672638i	−0.603880	+	0.797076i	$0.706379\pi$
$632$	0.998660	+	1.72973i	0.0397245	+	0.0688049i
$633$		0			0
$634$	8.32463	+	14.4187i	0.330613	+	0.572639i
$635$	6.84179	+	11.8503i	0.271508	+	0.470266i
$636$		0			0
$637$	−10.8151			−0.428509
$638$	6.20727			0.245748
$639$		0			0
$640$	1.97181	+	3.41528i	0.0779427	+	0.135001i
$641$	−15.9590	−	27.6417i	−0.630341	−	1.09178i	−0.987482	−	0.157732i	$-0.949582\pi$
$641$	−15.9590	−	27.6417i	−0.630341	−	1.09178i	0.357141	−	0.934050i	$-0.383751\pi$
$642$		0			0
$643$	−22.2365			−0.876922			−0.438461	−	0.898750i	$-0.644476\pi$
$643$	−22.2365			−0.876922			−0.438461	+	0.898750i	$0.644476\pi$
$644$	10.6858			0.421080
$645$		0			0
$646$	−17.4161	−	4.18709i	−0.685228	−	0.164739i
$647$	−28.7608			−1.13070			−0.565352	−	0.824850i	$-0.691260\pi$
$647$	−28.7608			−1.13070			−0.565352	+	0.824850i	$0.691260\pi$
$648$		0			0
$649$	−37.3329	+	64.6624i	−1.46544	+	2.53822i
$650$	40.9694			1.60695
$651$		0			0
$652$	5.76022	−	9.97699i	0.225588	−	0.390729i
$653$	14.1756	+	24.5528i	0.554733	+	0.960826i	0.997924	+	0.0643991i	$0.0205131\pi$
$653$	14.1756	+	24.5528i	0.554733	+	0.960826i	−0.443191	+	0.896427i	$0.646154\pi$
$654$		0			0
$655$	1.42150			0.0555426
$656$	1.38355	+	2.39637i	0.0540184	+	0.0935625i
$657$		0			0
$658$	−14.6543			−0.571286
$659$	−5.34029			−0.208028			−0.104014	−	0.994576i	$-0.533169\pi$
$659$	−5.34029			−0.208028			−0.104014	+	0.994576i	$0.533169\pi$
$660$		0			0
$661$	−8.59702	+	14.8905i	−0.334385	+	0.579172i	−0.983367	−	0.181632i	$-0.941862\pi$
$661$	−8.59702	+	14.8905i	−0.334385	+	0.579172i	0.648981	+	0.760804i	$0.275195\pi$
$662$	−0.312320			−0.0121387
$663$		0			0
$664$	2.63550	−	4.56482i	0.102277	−	0.177149i
$665$	−24.2996	+	25.5902i	−0.942300	+	0.992346i
$666$		0			0
$667$	3.12943	−	5.42033i	0.121172	−	0.209876i
$668$	−9.37172	−	16.2323i	−0.362603	−	0.628047i
$669$		0			0
$670$	58.0450			2.24247
$671$	17.0183	−	29.4766i	0.656985	−	1.13793i
$672$		0			0
$673$	−16.6703	+	28.8738i	−0.642594	+	1.11300i	0.342258	+	0.939606i	$0.388808\pi$
$673$	−16.6703	+	28.8738i	−0.642594	+	1.11300i	−0.984852	+	0.173399i	$0.944525\pi$
$674$	−9.23379	−	15.9934i	−0.355672	−	0.616043i
$675$		0			0
$676$	2.07422			0.0797779
$677$	5.50556	−	9.53591i	0.211596	−	0.366495i	−0.740618	−	0.671926i	$-0.765467\pi$
$677$	5.50556	−	9.53591i	0.211596	−	0.366495i	0.952214	+	0.305431i	$0.0988006\pi$
$678$		0			0
$679$	9.18720			0.352573
$680$	−8.10293	+	14.0347i	−0.310733	+	0.538205i
$681$		0			0
$682$	−21.7325	−	37.6419i	−0.832182	−	1.44138i
$683$	1.26949			0.0485758			0.0242879	−	0.999705i	$-0.492268\pi$
$683$	1.26949			0.0485758			0.0242879	+	0.999705i	$0.492268\pi$
$684$		0			0
$685$	−70.3127			−2.68651
$686$	−10.0444	−	17.3975i	−0.383498	−	0.664239i
$687$		0			0
$688$	0.838250	−	1.45189i	0.0319580	−	0.0553529i
$689$	−5.50305			−0.209649
$690$		0			0
$691$	5.66777	−	9.81687i	0.215612	−	0.373451i	−0.737850	−	0.674965i	$-0.764159\pi$
$691$	5.66777	−	9.81687i	0.215612	−	0.373451i	0.953462	+	0.301514i	$0.0974919\pi$
$692$	1.44752			0.0550265
$693$		0			0
$694$	3.56809	+	6.18011i	0.135443	+	0.234594i
$695$	38.4939	−	66.6735i	1.46016	−	2.52907i
$696$		0			0
$697$	−5.68551	+	9.84760i	−0.215354	+	0.373004i
$698$	−12.9158			−0.488872
$699$		0			0
$700$	10.8313	+	18.7604i	0.409386	+	0.709078i
$701$	4.81374	−	8.33765i	0.181813	−	0.314909i	−0.760685	−	0.649121i	$-0.775137\pi$
$701$	4.81374	−	8.33765i	0.181813	−	0.314909i	0.942498	+	0.334212i	$0.108470\pi$
$702$		0			0
$703$	1.84501	+	0.443567i	0.0695860	+	0.0167295i
$704$	−2.58114	+	4.47067i	−0.0972806	+	0.168495i
$705$		0			0
$706$	−26.2855			−0.989267
$707$	−4.41412	+	7.64548i	−0.166010	+	0.287538i
$708$		0			0
$709$	33.9784			1.27609			0.638043	−	0.770001i	$-0.279744\pi$
$709$	33.9784			1.27609			0.638043	+	0.770001i	$0.279744\pi$
$710$	17.4142			0.653543
$711$		0			0
$712$	0.817559	+	1.41605i	0.0306393	+	0.0530688i
$713$	−43.8263			−1.64131
$714$		0			0
$715$	39.5208	+	68.4520i	1.47799	+	2.55996i
$716$	0.657100	−	1.13813i	0.0245570	−	0.0425339i
$717$		0			0
$718$	15.0850			0.562966
$719$	12.7403	−	22.0668i	0.475132	−	0.822952i	−0.524463	−	0.851433i	$-0.675734\pi$
$719$	12.7403	−	22.0668i	0.475132	−	0.822952i	0.999594	+	0.0284813i	$0.00906712\pi$
$720$		0			0
$721$	29.8339			1.11107
$722$	−0.982344	−	18.9746i	−0.0365590	−	0.706161i
$723$		0			0
$724$	10.7110			0.398073
$725$	12.6882			0.471228
$726$		0			0
$727$	15.0657	+	26.0946i	0.558758	+	0.967797i	0.997601	+	0.0692328i	$0.0220551\pi$
$727$	15.0657	+	26.0946i	0.558758	+	0.967797i	−0.438843	+	0.898564i	$0.644612\pi$
$728$	3.98527	+	6.90269i	0.147704	+	0.255831i
$729$		0			0
$730$	40.0957			1.48401
$731$	6.88938			0.254813
$732$		0			0
$733$	−22.4900	−	38.9539i	−0.830688	−	1.43879i	−0.897494	−	0.441028i	$-0.854614\pi$
$733$	−22.4900	−	38.9539i	−0.830688	−	1.43879i	0.0668058	−	0.997766i	$-0.478719\pi$
$734$	15.2039	+	26.3340i	0.561188	+	0.972006i
$735$		0			0
$736$	2.60260	+	4.50783i	0.0959330	+	0.166161i
$737$	37.9910	+	65.8024i	1.39942	+	2.42386i
$738$		0			0
$739$	2.68302	−	4.64713i	0.0986965	−	0.170947i	−0.812449	−	0.583032i	$-0.801866\pi$
$739$	2.68302	−	4.64713i	0.0986965	−	0.170947i	0.911145	+	0.412085i	$0.135199\pi$
$740$	0.858400	−	1.48679i	0.0315554	−	0.0546556i
$741$		0			0
$742$	−1.45488	−	2.51992i	−0.0534102	−	0.0925091i
$743$	−19.3933			−0.711471			−0.355735	−	0.934587i	$-0.615770\pi$
$743$	−19.3933			−0.711471			−0.355735	+	0.934587i	$0.615770\pi$
$744$		0			0
$745$	−73.9758			−2.71026
$746$	−5.07447	+	8.78925i	−0.185790	+	0.321797i
$747$		0			0
$748$	−21.2138			−0.775654
$749$	2.16870	−	3.75629i	0.0792424	−	0.137252i
$750$		0			0
$751$	14.4724	−	25.0669i	0.528104	−	0.914703i	−0.471359	−	0.881941i	$-0.656236\pi$
$751$	14.4724	−	25.0669i	0.528104	−	0.914703i	0.999463	−	0.0327619i	$-0.0104303\pi$
$752$	−3.56916	−	6.18197i	−0.130154	−	0.225433i
$753$		0			0
$754$	4.66848			0.170016
$755$	11.0740	−	19.1807i	0.403024	−	0.698057i
$756$		0			0
$757$	18.7844	−	32.5355i	0.682729	−	1.18252i	−0.291415	−	0.956597i	$-0.594126\pi$
$757$	18.7844	−	32.5355i	0.682729	−	1.18252i	0.974145	−	0.225925i	$-0.0725405\pi$
$758$	−3.76687	−	6.52442i	−0.136819	−	0.236978i
$759$		0			0
$760$	−16.7136	−	4.01820i	−0.606267	−	0.145755i
$761$	−5.50420	−	9.53355i	−0.199527	−	0.345591i	0.748848	−	0.662742i	$-0.230607\pi$
$761$	−5.50420	−	9.53355i	−0.199527	−	0.345591i	−0.948375	+	0.317151i	$0.897274\pi$
$762$		0			0
$763$	−9.86464	−	17.0861i	−0.357124	−	0.618557i
$764$	1.88682	+	3.26807i	0.0682629	+	0.118235i
$765$		0			0
$766$	−5.18388	−	8.97875i	−0.187301	−	0.324415i
$767$	−28.0780	+	48.6325i	−1.01384	+	1.75602i
$768$		0			0
$769$	22.9703	−	39.7858i	0.828331	−	1.43471i	−0.0710158	−	0.997475i	$-0.522624\pi$
$769$	22.9703	−	39.7858i	0.828331	−	1.43471i	0.899347	−	0.437236i	$-0.144043\pi$
$770$	−20.8967	+	36.1942i	−0.753065	+	1.30435i
$771$		0			0
$772$	−8.11527	+	14.0561i	−0.292075	+	0.505889i
$773$	3.45316	+	5.98106i	0.124202	+	0.215124i	0.921421	−	0.388567i	$-0.127030\pi$
$773$	3.45316	+	5.98106i	0.124202	+	0.215124i	−0.797219	+	0.603690i	$0.793696\pi$
$774$		0			0
$775$	−44.4233	−	76.9434i	−1.59573	−	2.76389i
$776$	2.23760	+	3.87564i	0.0803253	+	0.139128i
$777$		0			0
$778$	−19.0890	−	33.0631i	−0.684373	−	1.18537i
$779$	−11.7273	−	2.81941i	−0.420175	−	0.101016i
$780$		0			0
$781$	11.3978	+	19.7415i	0.407844	+	0.706407i
$782$	−10.6951	+	18.5244i	−0.382455	+	0.662431i
$783$		0			0
$784$	1.39278	−	2.41236i	0.0497421	−	0.0861559i
$785$	47.6113			1.69932
$786$		0			0
$787$	6.00458	+	10.4002i	0.214040	+	0.370728i	0.952975	−	0.303048i	$-0.0980044\pi$
$787$	6.00458	+	10.4002i	0.214040	+	0.370728i	−0.738935	+	0.673777i	$0.764671\pi$
$788$	−10.3137	+	17.8639i	−0.367411	+	0.636374i
$789$		0			0
$790$	−3.93834	+	6.82140i	−0.140120	+	0.242695i
$791$	14.3437			0.510005
$792$		0			0
$793$	12.7995	−	22.1693i	0.454522	−	0.787256i
$794$	−3.97045			−0.140906
$795$		0			0
$796$	−6.45585			−0.228821
$797$	−15.3351	−	26.5611i	−0.543195	−	0.940842i	−0.998718	−	0.0506179i	$-0.983881\pi$
$797$	−15.3351	−	26.5611i	−0.543195	−	0.940842i	0.455523	−	0.890224i	$-0.349452\pi$
$798$		0			0
$799$	14.6670	−	25.4041i	0.518883	−	0.898731i
$800$	−5.27609	+	9.13846i	−0.186538	+	0.323093i
$801$		0			0
$802$	−1.43491	−	2.48535i	−0.0506686	−	0.0877606i
$803$	26.2431	+	45.4543i	0.926097	+	1.60405i
$804$		0			0
$805$	21.0704	+	36.4950i	0.742634	+	1.28628i
$806$	−16.3450	−	28.3104i	−0.575729	−	0.997192i
$807$		0			0
$808$	−4.30035			−0.151286
$809$	−25.7750			−0.906200			−0.453100	−	0.891460i	$-0.649682\pi$
$809$	−25.7750			−0.906200			−0.453100	+	0.891460i	$0.649682\pi$
$810$		0			0
$811$	21.5979	+	37.4087i	0.758406	+	1.31360i	0.943663	+	0.330908i	$0.107355\pi$
$811$	21.5979	+	37.4087i	0.758406	+	1.31360i	−0.185257	+	0.982690i	$0.559312\pi$
$812$	1.23424	+	2.13776i	0.0433132	+	0.0750207i
$813$		0			0
$814$	2.24733			0.0787688
$815$	45.4323			1.59142
$816$		0			0
$817$	2.07327	+	7.00742i	0.0725347	+	0.245159i
$818$	−22.8271			−0.798132
$819$		0			0
$820$	−5.45618	+	9.45039i	−0.190538	+	0.330022i
$821$	−20.3884			−0.711562			−0.355781	−	0.934569i	$-0.615785\pi$
$821$	−20.3884			−0.711562			−0.355781	+	0.934569i	$0.615785\pi$
$822$		0			0
$823$	−9.55183	+	16.5442i	−0.332956	+	0.576696i	−0.983090	−	0.183123i	$-0.941379\pi$
$823$	−9.55183	+	16.5442i	−0.332956	+	0.576696i	0.650134	+	0.759819i	$0.274713\pi$
$824$	7.26626	+	12.5855i	0.253132	+	0.438437i
$825$		0			0
$826$	−29.6926			−1.03314
$827$	26.8606	+	46.5239i	0.934035	+	1.61780i	0.776346	+	0.630307i	$0.217071\pi$
$827$	26.8606	+	46.5239i	0.934035	+	1.61780i	0.157689	+	0.987489i	$0.449596\pi$
$828$		0			0
$829$	−23.0581			−0.800842			−0.400421	−	0.916331i	$-0.631136\pi$
$829$	−23.0581			−0.800842			−0.400421	+	0.916331i	$0.631136\pi$
$830$	20.7868			0.721522
$831$		0			0
$832$	−1.94128	+	3.36239i	−0.0673017	+	0.116570i
$833$	11.4469			0.396612
$834$		0			0
$835$	36.9586	−	64.0141i	1.27900	−	2.21530i
$836$	−6.38404	−	21.5773i	−0.220797	−	0.746266i
$837$		0			0
$838$	−6.81387	+	11.8020i	−0.235381	+	0.407692i
$839$	10.5602	+	18.2908i	0.364579	+	0.631470i	0.988709	−	0.149851i	$-0.0478795\pi$
$839$	10.5602	+	18.2908i	0.364579	+	0.631470i	−0.624129	+	0.781321i	$0.714546\pi$
$840$		0			0
$841$	−27.5542			−0.950144
$842$	6.22588	−	10.7835i	0.214558	−	0.371625i
$843$		0			0
$844$	0.202549	−	0.350825i	0.00697202	−	0.0120759i
$845$	4.08998	+	7.08406i	0.140700	+	0.243699i
$846$		0			0
$847$	−32.1265			−1.10388
$848$	0.708689	−	1.22749i	0.0243365	−	0.0421520i
$849$		0			0
$850$	−43.3629			−1.48734
$851$	1.13300	−	1.96242i	0.0388388	−	0.0672709i
$852$		0			0
$853$	−5.64078	−	9.77012i	−0.193137	−	0.334523i	0.753151	−	0.657847i	$-0.228533\pi$
$853$	−5.64078	−	9.77012i	−0.193137	−	0.334523i	−0.946288	+	0.323325i	$0.895199\pi$
$854$	13.5355			0.463175
$855$		0			0
$856$	2.11280			0.0722141
$857$	20.6391	+	35.7479i	0.705017	+	1.22113i	0.966685	+	0.255968i	$0.0823940\pi$
$857$	20.6391	+	35.7479i	0.705017	+	1.22113i	−0.261668	+	0.965158i	$0.584273\pi$
$858$		0			0
$859$	13.8230	−	23.9422i	0.471636	−	0.816897i	−0.527838	−	0.849345i	$-0.676997\pi$
$859$	13.8230	−	23.9422i	0.471636	−	0.816897i	0.999473	+	0.0324485i	$0.0103305\pi$
$860$	6.61149			0.225450
$861$		0			0
$862$	12.6070	−	21.8359i	0.429395	−	0.743733i
$863$	1.24809			0.0424856			0.0212428	−	0.999774i	$-0.493238\pi$
$863$	1.24809			0.0424856			0.0212428	+	0.999774i	$0.493238\pi$
$864$		0			0
$865$	2.85424	+	4.94369i	0.0970471	+	0.168090i
$866$	−10.0557	+	17.4169i	−0.341705	+	0.591850i
$867$		0			0
$868$	8.64248	−	14.9692i	0.293345	−	0.508088i
$869$	−10.3107			−0.349768
$870$		0			0
$871$	28.5730	+	49.4899i	0.968160	+	1.67690i
$872$	4.80520	−	8.32285i	0.162725	−	0.281847i
$873$		0			0
$874$	−22.0603	−	5.30362i	−0.746202	−	0.179398i
$875$	−22.4750	+	38.9278i	−0.759793	+	1.31600i
$876$		0			0
$877$	29.5234			0.996934			0.498467	−	0.866909i	$-0.333896\pi$
$877$	29.5234			0.996934			0.498467	+	0.866909i	$0.333896\pi$
$878$	6.31870	−	10.9443i	0.213246	−	0.369352i
$879$		0			0
$880$	−20.3581			−0.686273
$881$	23.3038			0.785125			0.392562	−	0.919725i	$-0.371589\pi$
$881$	23.3038			0.785125			0.392562	+	0.919725i	$0.371589\pi$
$882$		0			0
$883$	−14.9075	−	25.8206i	−0.501678	−	0.868931i	−0.999998	−	0.00193813i	$-0.999383\pi$
$883$	−14.9075	−	25.8206i	−0.501678	−	0.868931i	0.498321	−	0.866993i	$-0.333950\pi$
$884$	−15.9549			−0.536621
$885$		0			0
$886$	−11.0306	−	19.1056i	−0.370581	−	0.641865i
$887$	−18.2609	+	31.6289i	−0.613142	+	1.06199i	0.377565	+	0.925983i	$0.376761\pi$
$887$	−18.2609	+	31.6289i	−0.613142	+	1.06199i	−0.990707	+	0.136010i	$0.956572\pi$
$888$		0			0
$889$	−7.12318			−0.238904
$890$	−3.22415	+	5.58438i	−0.108074	+	0.187189i
$891$		0			0
$892$	−8.40880			−0.281547
$893$	30.2532	+	7.27331i	1.01239	+	0.243392i
$894$		0			0
$895$	5.18271			0.173239
$896$	−2.05291			−0.0685829
$897$		0			0
$898$	16.1029	+	27.8910i	0.537360	+	0.930736i
$899$	−5.06205	−	8.76773i	−0.168829	−	0.292420i
$900$		0			0
$901$	5.82455			0.194044
$902$	−14.2845			−0.475623
$903$		0			0
$904$	3.49351	+	6.05094i	0.116192	+	0.201251i
$905$	21.1202	+	36.5812i	0.702058	+	1.21600i
$906$		0			0
$907$	11.7699	+	20.3860i	0.390812	+	0.676906i	0.992557	−	0.121782i	$-0.0388610\pi$
$907$	11.7699	+	20.3860i	0.390812	+	0.676906i	−0.601745	+	0.798688i	$0.705528\pi$
$908$	−0.146997	−	0.254607i	−0.00487828	−	0.00844943i
$909$		0			0
$910$	−15.7164	+	27.2216i	−0.520994	+	0.902388i
$911$	1.39516	−	2.41648i	0.0462236	−	0.0800617i	−0.841988	−	0.539496i	$-0.818615\pi$
$911$	1.39516	−	2.41648i	0.0462236	−	0.0800617i	0.888212	+	0.459435i	$0.151948\pi$
$912$		0			0
$913$	13.6052	+	23.5649i	0.450267	+	0.779885i
$914$	−1.80666			−0.0597589
$915$		0			0
$916$	7.22342			0.238668
$917$	−0.369991	+	0.640843i	−0.0122182	+	0.0211625i
$918$		0			0
$919$	11.5145			0.379829			0.189914	−	0.981801i	$-0.439179\pi$
$919$	11.5145			0.379829			0.189914	+	0.981801i	$0.439179\pi$
$920$	−10.2637	+	17.7772i	−0.338383	+	0.586097i
$921$		0			0
$922$	−11.7593	+	20.3677i	−0.387273	+	0.670776i
$923$	8.57226	+	14.8476i	0.282159	+	0.488714i
$924$		0			0
$925$	4.59374			0.151041
$926$	10.1793	−	17.6310i	0.334511	−	0.579391i
$927$		0			0
$928$	−0.601213	+	1.04133i	−0.0197358	+	0.0341834i
$929$	−22.2283	−	38.5006i	−0.729288	−	1.26316i	−0.957184	−	0.289479i	$-0.906518\pi$
$929$	−22.2283	−	38.5006i	−0.729288	−	1.26316i	0.227896	−	0.973685i	$-0.426815\pi$
$930$		0			0
$931$	3.44481	+	11.6431i	0.112899	+	0.381586i
$932$	−9.39739	−	16.2768i	−0.307822	−	0.533163i
$933$		0			0
$934$	11.1361	+	19.2882i	0.364383	+	0.631130i
$935$	−41.8297	−	72.4511i	−1.36798	−	2.36940i
$936$		0			0
$937$	0.0937801	+	0.162432i	0.00306366	+	0.00530642i	0.867553	−	0.497344i	$-0.165691\pi$
$937$	0.0937801	+	0.162432i	0.00306366	+	0.00530642i	−0.864490	+	0.502651i	$0.832358\pi$
$938$	−15.1081	+	26.1679i	−0.493296	+	0.854413i
$939$		0			0
$940$	14.0754	−	24.3794i	0.459090	−	0.795168i
$941$	−21.8085	+	37.7734i	−0.710936	+	1.23138i	0.253570	+	0.967317i	$0.418395\pi$
$941$	−21.8085	+	37.7734i	−0.710936	+	1.23138i	−0.964506	+	0.264060i	$0.914938\pi$
$942$		0			0
$943$	−7.20162	+	12.4736i	−0.234517	+	0.406196i
$944$	−7.23184	−	12.5259i	−0.235376	−	0.407684i
$945$		0			0
$946$	4.32729	+	7.49509i	0.140692	+	0.243686i
$947$	−5.22901	−	9.05691i	−0.169920	−	0.294310i	0.768472	−	0.639884i	$-0.221018\pi$
$947$	−5.22901	−	9.05691i	−0.169920	−	0.294310i	−0.938392	+	0.345574i	$0.887684\pi$
$948$		0			0
$949$	19.7374	+	34.1861i	0.640702	+	1.10973i
$950$	−13.0495	−	44.1059i	−0.423383	−	1.43098i
$951$		0			0
$952$	−4.21809	−	7.30595i	−0.136709	−	0.236787i
$953$	17.3582	−	30.0652i	0.562286	−	0.973908i	−0.435011	−	0.900425i	$-0.643255\pi$
$953$	17.3582	−	30.0652i	0.562286	−	0.973908i	0.997297	−	0.0734823i	$-0.0234112\pi$
$954$		0			0
$955$	−7.44092	+	12.8881i	−0.240783	+	0.417048i
$956$	−3.34611			−0.108221
$957$		0			0
$958$	6.26933	+	10.8588i	0.202553	+	0.350832i
$959$	18.3011	−	31.6985i	0.590975	−	1.02360i
$960$		0			0
$961$	−19.9459	+	34.5474i	−0.643417	+	1.11443i
$962$	1.69021			0.0544947
$963$		0			0
$964$	0.623776	−	1.08041i	0.0200905	−	0.0347977i
$965$	−64.0072			−2.06046
$966$		0			0
$967$	20.7731			0.668019			0.334009	−	0.942570i	$-0.391598\pi$
$967$	20.7731			0.668019			0.334009	+	0.942570i	$0.391598\pi$
$968$	−7.82462	−	13.5526i	−0.251493	−	0.435598i
$969$		0			0
$970$	−8.82427	+	15.2841i	−0.283330	+	0.490743i
$971$	−20.2792	+	35.1246i	−0.650791	+	1.12720i	0.332141	+	0.943230i	$0.392229\pi$
$971$	−20.2792	+	35.1246i	−0.650791	+	1.12720i	−0.982931	+	0.183973i	$0.941104\pi$
$972$		0			0
$973$	20.0386	+	34.7078i	0.642407	+	1.11268i
$974$	1.96044	+	3.39559i	0.0628167	+	0.108802i
$975$		0			0
$976$	3.29666	+	5.70999i	0.105524	+	0.182772i
$977$	30.3147	+	52.5066i	0.969852	+	1.67983i	0.695970	+	0.718071i	$0.254974\pi$
$977$	30.3147	+	52.5066i	0.969852	+	1.67983i	0.273882	+	0.961763i	$0.411692\pi$
$978$		0			0
$979$	−8.44095			−0.269774
$980$	10.9852			0.350909
$981$		0			0
$982$	−7.38534	−	12.7918i	−0.235676	−	0.408202i
$983$	−0.200134	−	0.346643i	−0.00638329	−	0.0110562i	0.862816	−	0.505518i	$-0.168699\pi$
$983$	−0.200134	−	0.346643i	−0.00638329	−	0.0110562i	−0.869199	+	0.494462i	$0.835365\pi$
$984$		0			0
$985$	−81.3468			−2.59192
$986$	−4.94122			−0.157361
$987$		0			0
$988$	−4.80143	−	16.2283i	−0.152754	−	0.516290i
$989$	8.72651			0.277487
$990$		0			0
$991$	−26.5252	+	45.9431i	−0.842602	+	1.45943i	0.0450855	+	0.998983i	$0.485644\pi$
$991$	−26.5252	+	45.9431i	−0.842602	+	1.45943i	−0.887688	+	0.460446i	$0.847689\pi$
$992$	8.41973			0.267327
$993$		0			0
$994$	−4.53260	+	7.85070i	−0.143765	+	0.249009i
$995$	−12.7297	−	22.0485i	−0.403559	−	0.698985i
$996$		0			0
$997$	8.39861			0.265987			0.132993	−	0.991117i	$-0.457541\pi$
$997$	8.39861			0.265987			0.132993	+	0.991117i	$0.457541\pi$
$998$	−14.4177	−	24.9723i	−0.456386	−	0.790483i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1026.2.h.g.505.1		18
3.2	odd	2		342.2.h.g.277.2	yes	18
9.4	even	3		1026.2.f.g.847.9		18
9.5	odd	6		342.2.f.g.49.5	yes	18
19.7	even	3		1026.2.f.g.235.9		18
57.26	odd	6		342.2.f.g.7.5	✓	18
171.121	even	3	inner	1026.2.h.g.577.1		18
171.140	odd	6		342.2.h.g.121.2	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.f.g.7.5	✓	18	57.26	odd	6
342.2.f.g.49.5	yes	18	9.5	odd	6
342.2.h.g.121.2	yes	18	171.140	odd	6
342.2.h.g.277.2	yes	18	3.2	odd	2
1026.2.f.g.235.9		18	19.7	even	3
1026.2.f.g.847.9		18	9.4	even	3
1026.2.h.g.505.1		18	1.1	even	1	trivial
1026.2.h.g.577.1		18	171.121	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1026 = 2 \cdot 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1026.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.94363 q^{5} +(1.02646 - 1.77787i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.94363 q^{5} +(1.02646 - 1.77787i) q^{7} +1.00000 q^{8} +(1.97181 + 3.41528i) q^{10} +(-2.58114 + 4.47067i) q^{11} +(-1.94128 + 3.36239i) q^{13} -2.05291 q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.05469 - 3.55883i) q^{17} +(4.23814 + 1.01891i) q^{19} +(1.97181 - 3.41528i) q^{20} +5.16229 q^{22} +(2.60260 - 4.50783i) q^{23} +10.5522 q^{25} +3.88255 q^{26} +(1.02646 + 1.77787i) q^{28} +1.20243 q^{29} +(-4.20987 - 7.29170i) q^{31} +(-0.500000 + 0.866025i) q^{32} -4.10938 q^{34} +(-4.04796 + 7.01126i) q^{35} +0.435335 q^{37} +(-1.23667 - 4.17979i) q^{38} -3.94363 q^{40} -2.76709 q^{41} +(0.838250 + 1.45189i) q^{43} +(-2.58114 - 4.47067i) q^{44} -5.20520 q^{46} +7.13833 q^{47} +(1.39278 + 2.41236i) q^{49} +(-5.27609 - 9.13846i) q^{50} +(-1.94128 - 3.36239i) q^{52} +(0.708689 + 1.22749i) q^{53} +(10.1791 - 17.6307i) q^{55} +(1.02646 - 1.77787i) q^{56} +(-0.601213 - 1.04133i) q^{58} +14.4637 q^{59} -6.59332 q^{61} +(-4.20987 + 7.29170i) q^{62} +1.00000 q^{64} +(7.65567 - 13.2600i) q^{65} +(7.35934 - 12.7467i) q^{67} +(2.05469 + 3.55883i) q^{68} +8.09591 q^{70} +(2.20789 - 3.82418i) q^{71} +(5.08361 - 8.80507i) q^{73} +(-0.217668 - 0.377012i) q^{74} +(-3.00147 + 3.16088i) q^{76} +(5.29886 + 9.17789i) q^{77} +(0.998660 + 1.72973i) q^{79} +(1.97181 + 3.41528i) q^{80} +(1.38355 + 2.39637i) q^{82} +(2.63550 - 4.56482i) q^{83} +(-8.10293 + 14.0347i) q^{85} +(0.838250 - 1.45189i) q^{86} +(-2.58114 + 4.47067i) q^{88} +(0.817559 + 1.41605i) q^{89} +(3.98527 + 6.90269i) q^{91} +(2.60260 + 4.50783i) q^{92} +(-3.56916 - 6.18197i) q^{94} +(-16.7136 - 4.01820i) q^{95} +(2.23760 + 3.87564i) q^{97} +(1.39278 - 2.41236i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 9 q^{2} - 9 q^{4} + 5 q^{7} + 18 q^{8}+O(q^{10}) \) 18 * q - 9 * q^2 - 9 * q^4 + 5 * q^7 + 18 * q^8	\( 18 q - 9 q^{2} - 9 q^{4} + 5 q^{7} + 18 q^{8} - q^{11} + q^{13} - 10 q^{14} - 9 q^{16} + 5 q^{17} + 9 q^{19} + 2 q^{22} + 2 q^{23} + 18 q^{25} - 2 q^{26} + 5 q^{28} - 18 q^{29} + 4 q^{31} - 9 q^{32} - 10 q^{34} - 6 q^{35} + 20 q^{37} - 3 q^{38} + 2 q^{41} + 7 q^{43} - q^{44} - 4 q^{46} + 38 q^{47} + 6 q^{49} - 9 q^{50} + q^{52} + 10 q^{53} + 6 q^{55} + 5 q^{56} + 9 q^{58} - 10 q^{59} - 36 q^{61} + 4 q^{62} + 18 q^{64} + 45 q^{65} + 22 q^{67} + 5 q^{68} + 12 q^{70} - 11 q^{71} + 44 q^{73} - 10 q^{74} - 6 q^{76} + 2 q^{77} + 2 q^{79} - q^{82} + 7 q^{83} + 7 q^{86} - q^{88} - q^{89} - 25 q^{91} + 2 q^{92} - 19 q^{94} - 21 q^{95} + 6 q^{98}+O(q^{100}) \) 18 * q - 9 * q^2 - 9 * q^4 + 5 * q^7 + 18 * q^8 - q^11 + q^13 - 10 * q^14 - 9 * q^16 + 5 * q^17 + 9 * q^19 + 2 * q^22 + 2 * q^23 + 18 * q^25 - 2 * q^26 + 5 * q^28 - 18 * q^29 + 4 * q^31 - 9 * q^32 - 10 * q^34 - 6 * q^35 + 20 * q^37 - 3 * q^38 + 2 * q^41 + 7 * q^43 - q^44 - 4 * q^46 + 38 * q^47 + 6 * q^49 - 9 * q^50 + q^52 + 10 * q^53 + 6 * q^55 + 5 * q^56 + 9 * q^58 - 10 * q^59 - 36 * q^61 + 4 * q^62 + 18 * q^64 + 45 * q^65 + 22 * q^67 + 5 * q^68 + 12 * q^70 - 11 * q^71 + 44 * q^73 - 10 * q^74 - 6 * q^76 + 2 * q^77 + 2 * q^79 - q^82 + 7 * q^83 + 7 * q^86 - q^88 - q^89 - 25 * q^91 + 2 * q^92 - 19 * q^94 - 21 * q^95 + 6 * q^98

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