LMFDB - Embedded newform 1638.2.bj.f.1135.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(127,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1638.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.195105024.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 4x^{5} - 20x^{4} + 12x^{3} + 45x^{2} - 108x + 81 $ x^8 - 4x^7 + 5x^6 + 4x^5 - 20x^4 + 12x^3 + 45x^2 - 108*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1135.1
Root			$-1.58726 - 0.693255i$ of defining polynomial
Character	$\chi$	$=$	1638.1135
Dual form			1638.2.bj.f.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.78801i q^{5} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.78801i q^{5} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.894007 + 1.54846i) q^{10} +(-2.74922 - 1.58726i) q^{11} +(1.47952 - 3.28801i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.78052 - 4.81599i) q^{17} +(-5.36028 + 3.09476i) q^{19} +(1.54846 - 0.894007i) q^{20} +(1.58726 + 2.74922i) q^{22} +(-3.06678 + 5.31181i) q^{23} +1.80301 q^{25} +(-2.92531 + 2.10774i) q^{26} +(0.866025 + 0.500000i) q^{28} +(1.03880 - 1.79925i) q^{29} +5.63862i q^{31} +(0.866025 - 0.500000i) q^{32} +5.56103i q^{34} +(-0.894007 - 1.54846i) q^{35} +(-2.68202 - 1.54846i) q^{37} +6.18952 q^{38} -1.78801 q^{40} +(1.29768 + 0.749217i) q^{41} +(-4.81931 - 8.34729i) q^{43} -3.17452i q^{44} +(5.31181 - 3.06678i) q^{46} +10.5086i q^{47} +(0.500000 - 0.866025i) q^{49} +(-1.56145 - 0.901504i) q^{50} +(3.58726 - 0.362708i) q^{52} -3.60200 q^{53} +(-2.83804 + 4.91564i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(-1.79925 + 1.03880i) q^{58} +(2.40874 - 1.39069i) q^{59} +(-0.844395 - 1.46254i) q^{61} +(2.81931 - 4.88319i) q^{62} -1.00000 q^{64} +(-5.87901 - 2.64539i) q^{65} +(-10.0064 - 5.77720i) q^{67} +(2.78052 - 4.81599i) q^{68} +1.78801i q^{70} +(0.518313 - 0.299248i) q^{71} +0.423973i q^{73} +(1.54846 + 2.68202i) q^{74} +(-5.36028 - 3.09476i) q^{76} -3.17452 q^{77} +6.96254 q^{79} +(1.54846 + 0.894007i) q^{80} +(-0.749217 - 1.29768i) q^{82} +4.30228i q^{83} +(-8.61106 + 4.97160i) q^{85} +9.63862i q^{86} +(-1.58726 + 2.74922i) q^{88} +(14.1102 + 8.14654i) q^{89} +(-0.362708 - 3.58726i) q^{91} -6.13356 q^{92} +(5.25429 - 9.10069i) q^{94} +(5.53347 + 9.58425i) q^{95} +(-15.1461 + 8.74462i) q^{97} +(-0.866025 + 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 8 q + 4 q^{4} + 6 q^{10} - 6 q^{11} + 12 q^{13} - 8 q^{14} - 4 q^{16} - 2 q^{17} - 12 q^{19} + 6 q^{20} - 4 q^{22} - 8 q^{23} - 24 q^{25} - 6 q^{26} - 2 q^{29} + 6 q^{35} + 18 q^{37} + 4 q^{38} + 12 q^{40} - 12 q^{41} - 8 q^{43} + 18 q^{46} + 4 q^{49} - 12 q^{50} + 12 q^{52} + 12 q^{53} - 22 q^{55} - 4 q^{56} - 24 q^{58} - 18 q^{59} - 8 q^{61} - 8 q^{62} - 8 q^{64} - 46 q^{65} + 18 q^{67} + 2 q^{68} - 6 q^{71} + 6 q^{74} - 12 q^{76} + 8 q^{77} - 4 q^{79} + 6 q^{80} + 10 q^{82} - 54 q^{85} + 4 q^{88} + 18 q^{89} + 6 q^{91} - 16 q^{92} - 2 q^{94} + 50 q^{95} - 54 q^{97}+O(q^{100}) $ 8 * q + 4 * q^4 + 6 * q^10 - 6 * q^11 + 12 * q^13 - 8 * q^14 - 4 * q^16 - 2 * q^17 - 12 * q^19 + 6 * q^20 - 4 * q^22 - 8 * q^23 - 24 * q^25 - 6 * q^26 - 2 * q^29 + 6 * q^35 + 18 * q^37 + 4 * q^38 + 12 * q^40 - 12 * q^41 - 8 * q^43 + 18 * q^46 + 4 * q^49 - 12 * q^50 + 12 * q^52 + 12 * q^53 - 22 * q^55 - 4 * q^56 - 24 * q^58 - 18 * q^59 - 8 * q^61 - 8 * q^62 - 8 * q^64 - 46 * q^65 + 18 * q^67 + 2 * q^68 - 6 * q^71 + 6 * q^74 - 12 * q^76 + 8 * q^77 - 4 * q^79 + 6 * q^80 + 10 * q^82 - 54 * q^85 + 4 * q^88 + 18 * q^89 + 6 * q^91 - 16 * q^92 - 2 * q^94 + 50 * q^95 - 54 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		−	1.78801i		−	0.799624i	−0.916597	−	0.399812i	$-0.869075\pi$
$5$		−	1.78801i		−	0.799624i	0.916597	−	0.399812i	$-0.130925\pi$
$6$		0			0
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.894007	+	1.54846i	−0.282710	+	0.489668i
$11$	−2.74922	−	1.58726i	−0.828920	−	0.478577i	0.0245627	−	0.999698i	$-0.492181\pi$
$11$	−2.74922	−	1.58726i	−0.828920	−	0.478577i	−0.853483	+	0.521121i	$0.825514\pi$
$12$		0			0
$13$	1.47952	−	3.28801i	0.410344	−	0.911931i
$13$	1.47952	−	3.28801i	0.410344	−	0.911931i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.78052	−	4.81599i	−0.674374	−	1.16805i	−0.976651	−	0.214830i	$-0.931080\pi$
$17$	−2.78052	−	4.81599i	−0.674374	−	1.16805i	0.302277	−	0.953220i	$-0.402253\pi$
$18$		0			0
$19$	−5.36028	+	3.09476i	−1.22973	+	0.709986i	−0.966974	−	0.254875i	$-0.917966\pi$
$19$	−5.36028	+	3.09476i	−1.22973	+	0.709986i	−0.262758	+	0.964862i	$0.584632\pi$
$20$	1.54846	−	0.894007i	0.346247	−	0.199906i
$21$		0			0
$22$	1.58726	+	2.74922i	0.338405	+	0.586135i
$23$	−3.06678	+	5.31181i	−0.639467	+	1.10759i	0.346083	+	0.938204i	$0.387512\pi$
$23$	−3.06678	+	5.31181i	−0.639467	+	1.10759i	−0.985550	+	0.169386i	$0.945822\pi$
$24$		0			0
$25$	1.80301			0.360602
$26$	−2.92531	+	2.10774i	−0.573700	+	0.413363i
$27$		0			0
$28$	0.866025	+	0.500000i	0.163663	+	0.0944911i
$29$	1.03880	−	1.79925i	0.192900	−	0.334112i	−0.753310	−	0.657665i	$-0.771544\pi$
$29$	1.03880	−	1.79925i	0.192900	−	0.334112i	0.946210	+	0.323553i	$0.104877\pi$
$30$		0			0
$31$			5.63862i			1.01273i	0.862320	+	0.506363i	$0.169011\pi$
$31$			5.63862i			1.01273i	−0.862320	+	0.506363i	$0.830989\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$			5.56103i			0.953709i
$35$	−0.894007	−	1.54846i	−0.151115	−	0.261738i
$36$		0			0
$37$	−2.68202	−	1.54846i	−0.440921	−	0.254566i	0.263067	−	0.964778i	$-0.415266\pi$
$37$	−2.68202	−	1.54846i	−0.440921	−	0.254566i	−0.703988	+	0.710211i	$0.748599\pi$
$38$	6.18952			1.00407
$39$		0			0
$40$	−1.78801			−0.282710
$41$	1.29768	+	0.749217i	0.202664	+	0.117008i	0.597897	−	0.801573i	$-0.296003\pi$
$41$	1.29768	+	0.749217i	0.202664	+	0.117008i	−0.395234	+	0.918581i	$0.629336\pi$
$42$		0			0
$43$	−4.81931	−	8.34729i	−0.734938	−	1.27295i	−0.954750	−	0.297408i	$-0.903878\pi$
$43$	−4.81931	−	8.34729i	−0.734938	−	1.27295i	0.219812	−	0.975542i	$-0.429456\pi$
$44$		−	3.17452i		−	0.478577i
$45$		0			0
$46$	5.31181	−	3.06678i	0.783184	−	0.452172i
$47$			10.5086i			1.53283i	0.642344	+	0.766416i	$0.277962\pi$
$47$			10.5086i			1.53283i	−0.642344	+	0.766416i	$0.722038\pi$
$48$		0			0
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	−1.56145	−	0.901504i	−0.220823	−	0.127492i
$51$		0			0
$52$	3.58726	−	0.362708i	0.497464	−	0.0502985i
$53$	−3.60200			−0.494773			−0.247386	−	0.968917i	$-0.579572\pi$
$53$	−3.60200			−0.494773			−0.247386	+	0.968917i	$0.579572\pi$
$54$		0			0
$55$	−2.83804	+	4.91564i	−0.382682	+	0.662824i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$		0			0
$58$	−1.79925	+	1.03880i	−0.236253	+	0.136401i
$59$	2.40874	−	1.39069i	0.313592	−	0.181052i	−0.334941	−	0.942239i	$-0.608716\pi$
$59$	2.40874	−	1.39069i	0.313592	−	0.181052i	0.648533	+	0.761187i	$0.275383\pi$
$60$		0			0
$61$	−0.844395	−	1.46254i	−0.108114	−	0.187259i	0.806892	−	0.590699i	$-0.201148\pi$
$61$	−0.844395	−	1.46254i	−0.108114	−	0.187259i	−0.915006	+	0.403440i	$0.867814\pi$
$62$	2.81931	−	4.88319i	0.358053	−	0.620166i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−5.87901	−	2.64539i	−0.729202	−	0.328121i
$66$		0			0
$67$	−10.0064	−	5.77720i	−1.22248	−	0.705797i	−0.257031	−	0.966403i	$-0.582744\pi$
$67$	−10.0064	−	5.77720i	−1.22248	−	0.705797i	−0.965445	+	0.260606i	$0.916078\pi$
$68$	2.78052	−	4.81599i	0.337187	−	0.584025i
$69$		0			0
$70$			1.78801i			0.213708i
$71$	0.518313	−	0.299248i	0.0615124	−	0.0355142i	−0.468928	−	0.883236i	$-0.655360\pi$
$71$	0.518313	−	0.299248i	0.0615124	−	0.0355142i	0.530441	+	0.847722i	$0.322026\pi$
$72$		0			0
$73$			0.423973i			0.0496223i	0.999692	+	0.0248112i	$0.00789845\pi$
$73$			0.423973i			0.0496223i	−0.999692	+	0.0248112i	$0.992102\pi$
$74$	1.54846	+	2.68202i	0.180005	+	0.311778i
$75$		0			0
$76$	−5.36028	−	3.09476i	−0.614866	−	0.354993i
$77$	−3.17452			−0.361770
$78$		0			0
$79$	6.96254			0.783346			0.391673	−	0.920104i	$-0.371896\pi$
$79$	6.96254			0.783346			0.391673	+	0.920104i	$0.371896\pi$
$80$	1.54846	+	0.894007i	0.173124	+	0.0999530i
$81$		0			0
$82$	−0.749217	−	1.29768i	−0.0827372	−	0.143305i
$83$			4.30228i			0.472237i	0.971724	+	0.236118i	$0.0758753\pi$
$83$			4.30228i			0.472237i	−0.971724	+	0.236118i	$0.924125\pi$
$84$		0			0
$85$	−8.61106	+	4.97160i	−0.934001	+	0.539246i
$86$			9.63862i			1.03936i
$87$		0			0
$88$	−1.58726	+	2.74922i	−0.169203	+	0.293068i
$89$	14.1102	+	8.14654i	1.49568	+	0.863532i	0.999988	−	0.00496618i	$-0.00158079\pi$
$89$	14.1102	+	8.14654i	1.49568	+	0.863532i	0.495693	+	0.868498i	$0.334914\pi$
$90$		0			0
$91$	−0.362708	−	3.58726i	−0.0380221	−	0.376047i
$92$	−6.13356			−0.639467
$93$		0			0
$94$	5.25429	−	9.10069i	0.541938	−	0.938665i
$95$	5.53347	+	9.58425i	0.567722	+	0.983323i
$96$		0			0
$97$	−15.1461	+	8.74462i	−1.53786	+	0.887881i	−0.538892	+	0.842375i	$0.681157\pi$
$97$	−15.1461	+	8.74462i	−1.53786	+	0.887881i	−0.998964	+	0.0455062i	$0.985510\pi$
$98$	−0.866025	+	0.500000i	−0.0874818	+	0.0505076i
$99$		0			0
$100$	0.901504	+	1.56145i	0.0901504	+	0.156145i
$101$	2.03433	−	3.52357i	0.202424	−	0.350608i	−0.746885	−	0.664953i	$-0.768452\pi$
$101$	2.03433	−	3.52357i	0.202424	−	0.350608i	0.949309	+	0.314345i	$0.101785\pi$
$102$		0			0
$103$	−18.0768			−1.78116			−0.890578	−	0.454831i	$-0.849700\pi$
$103$	−18.0768			−1.78116			−0.890578	+	0.454831i	$0.849700\pi$
$104$	−3.28801	−	1.47952i	−0.322416	−	0.145079i
$105$		0			0
$106$	3.11942	+	1.80100i	0.302985	+	0.174929i
$107$	−0.770847	+	1.33515i	−0.0745206	+	0.129073i	−0.900878	−	0.434073i	$-0.857076\pi$
$107$	−0.770847	+	1.33515i	−0.0745206	+	0.129073i	0.826357	+	0.563146i	$0.190409\pi$
$108$		0			0
$109$			7.37731i			0.706618i	0.935507	+	0.353309i	$0.114944\pi$
$109$			7.37731i			0.706618i	−0.935507	+	0.353309i	$0.885056\pi$
$110$	4.91564	−	2.83804i	0.468688	−	0.270597i
$111$		0			0
$112$			1.00000i			0.0944911i
$113$	−4.95660	−	8.58509i	−0.466278	−	0.807617i	0.532980	−	0.846128i	$-0.321072\pi$
$113$	−4.95660	−	8.58509i	−0.466278	−	0.807617i	−0.999258	+	0.0385104i	$0.987739\pi$
$114$		0			0
$115$	9.49759	+	5.48344i	0.885655	+	0.511333i
$116$	2.07759			0.192900
$117$		0			0
$118$	−2.78138			−0.256047
$119$	−4.81599	−	2.78052i	−0.441481	−	0.254889i
$120$		0			0
$121$	−0.461204	−	0.798828i	−0.0419276	−	0.0726208i
$122$			1.68879i			0.152896i
$123$		0			0
$124$	−4.88319	+	2.81931i	−0.438524	+	0.253182i
$125$		−	12.1639i		−	1.08797i
$126$		0			0
$127$	9.17452	−	15.8907i	0.814107	−	1.41008i	−0.0958600	−	0.995395i	$-0.530560\pi$
$127$	9.17452	−	15.8907i	0.814107	−	1.41008i	0.909967	−	0.414680i	$-0.136107\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	3.76868	+	5.23048i	0.330535	+	0.458744i
$131$	−5.91928			−0.517170			−0.258585	−	0.965989i	$-0.583256\pi$
$131$	−5.91928			−0.517170			−0.258585	+	0.965989i	$0.583256\pi$
$132$		0			0
$133$	−3.09476	+	5.36028i	−0.268350	+	0.464795i
$134$	5.77720	+	10.0064i	0.499074	+	0.864421i
$135$		0			0
$136$	−4.81599	+	2.78052i	−0.412968	+	0.238427i
$137$	−7.62363	+	4.40150i	−0.651331	+	0.376046i	−0.788966	−	0.614437i	$-0.789383\pi$
$137$	−7.62363	+	4.40150i	−0.651331	+	0.376046i	0.137635	+	0.990483i	$0.456050\pi$
$138$		0			0
$139$	−9.48720	−	16.4323i	−0.804694	−	1.39377i	−0.916498	−	0.400040i	$-0.868996\pi$
$139$	−9.48720	−	16.4323i	−0.804694	−	1.39377i	0.111804	−	0.993730i	$-0.464337\pi$
$140$	0.894007	−	1.54846i	0.0755574	−	0.130869i
$141$		0			0
$142$	−0.598496			−0.0502247
$143$	−9.28645	+	6.69108i	−0.776572	+	0.559537i
$144$		0			0
$145$	−3.21708	−	1.85738i	−0.267164	−	0.154247i
$146$	0.211987	−	0.367172i	0.0175441	−	0.0303873i
$147$		0			0
$148$		−	3.09693i		−	0.254566i
$149$	−12.0919	+	6.98127i	−0.990608	+	0.571928i	−0.905456	−	0.424440i	$-0.860471\pi$
$149$	−12.0919	+	6.98127i	−0.990608	+	0.571928i	−0.0851520	+	0.996368i	$0.527138\pi$
$150$		0			0
$151$			17.8426i			1.45201i	0.687688	+	0.726006i	$0.258626\pi$
$151$			17.8426i			1.45201i	−0.687688	+	0.726006i	$0.741374\pi$
$152$	3.09476	+	5.36028i	0.251018	+	0.434776i
$153$		0			0
$154$	2.74922	+	1.58726i	0.221538	+	0.127905i
$155$	10.0819			0.809800
$156$		0			0
$157$	4.57916			0.365457			0.182728	−	0.983163i	$-0.441507\pi$
$157$	4.57916			0.365457			0.182728	+	0.983163i	$0.441507\pi$
$158$	−6.02973	−	3.48127i	−0.479700	−	0.276955i
$159$		0			0
$160$	−0.894007	−	1.54846i	−0.0706774	−	0.122417i
$161$			6.13356i			0.483392i
$162$		0			0
$163$	10.6267	−	6.13531i	0.832344	−	0.480554i	−0.0223103	−	0.999751i	$-0.507102\pi$
$163$	10.6267	−	6.13531i	0.832344	−	0.480554i	0.854655	+	0.519197i	$0.173769\pi$
$164$			1.49843i			0.117008i
$165$		0			0
$166$	2.15114	−	3.72589i	0.166961	−	0.289185i
$167$	−14.4610	−	8.34904i	−1.11902	−	0.646068i	−0.177872	−	0.984054i	$-0.556921\pi$
$167$	−14.4610	−	8.34904i	−1.11902	−	0.646068i	−0.941151	+	0.337985i	$0.890255\pi$
$168$		0			0
$169$	−8.62206	−	9.72934i	−0.663236	−	0.748411i
$170$	9.94320			0.762609
$171$		0			0
$172$	4.81931	−	8.34729i	0.367469	−	0.636475i
$173$	−3.68865	−	6.38894i	−0.280443	−	0.485742i	0.691051	−	0.722806i	$-0.257148\pi$
$173$	−3.68865	−	6.38894i	−0.280443	−	0.485742i	−0.971494	+	0.237064i	$0.923815\pi$
$174$		0			0
$175$	1.56145	−	0.901504i	0.118035	−	0.0681473i
$176$	2.74922	−	1.58726i	0.207230	−	0.119644i
$177$		0			0
$178$	−8.14654	−	14.1102i	−0.610609	−	1.05761i
$179$	−9.91008	+	17.1648i	−0.740714	+	1.28295i	0.211457	+	0.977387i	$0.432179\pi$
$179$	−9.91008	+	17.1648i	−0.740714	+	1.28295i	−0.952171	+	0.305567i	$0.901154\pi$
$180$		0			0
$181$	−18.3266			−1.36220			−0.681102	−	0.732189i	$-0.738499\pi$
$181$	−18.3266			−1.36220			−0.681102	+	0.732189i	$0.738499\pi$
$182$	−1.47952	+	3.28801i	−0.109669	+	0.243724i
$183$		0			0
$184$	5.31181	+	3.06678i	0.391592	+	0.226086i
$185$	−2.76868	+	4.79549i	−0.203557	+	0.352571i
$186$		0			0
$187$			17.6536i			1.29096i
$188$	−9.10069	+	5.25429i	−0.663736	+	0.383208i
$189$		0			0
$190$		−	11.0669i		−	0.802880i
$191$	−7.51518	−	13.0167i	−0.543779	−	0.941854i	−0.998683	−	0.0513127i	$-0.983659\pi$
$191$	−7.51518	−	13.0167i	−0.543779	−	0.941854i	0.454903	−	0.890541i	$-0.349674\pi$
$192$		0			0
$193$	−4.72408	−	2.72745i	−0.340047	−	0.196326i	0.320246	−	0.947334i	$-0.396234\pi$
$193$	−4.72408	−	2.72745i	−0.340047	−	0.196326i	−0.660293	+	0.751008i	$0.729568\pi$
$194$	17.4892			1.25565
$195$		0			0
$196$	1.00000			0.0714286
$197$	6.60751	+	3.81485i	0.470766	+	0.271797i	0.716560	−	0.697525i	$-0.245716\pi$
$197$	6.60751	+	3.81485i	0.470766	+	0.271797i	−0.245795	+	0.969322i	$0.579049\pi$
$198$		0			0
$199$	2.99512	+	5.18769i	0.212318	+	0.367746i	0.952440	−	0.304727i	$-0.0985653\pi$
$199$	2.99512	+	5.18769i	0.212318	+	0.367746i	−0.740121	+	0.672473i	$0.765232\pi$
$200$		−	1.80301i		−	0.127492i
$201$		0			0
$202$	−3.52357	+	2.03433i	−0.247917	+	0.143135i
$203$		−	2.07759i		−	0.145818i
$204$		0			0
$205$	1.33961	−	2.32027i	0.0935624	−	0.162055i
$206$	15.6549	+	9.03838i	1.09073	+	0.629734i
$207$		0			0
$208$	2.10774	+	2.92531i	0.146146	+	0.202833i
$209$	19.6488			1.35913
$210$		0			0
$211$	1.38651	−	2.40150i	0.0954512	−	0.165326i	−0.814346	−	0.580380i	$-0.802904\pi$
$211$	1.38651	−	2.40150i	0.0954512	−	0.165326i	0.909797	+	0.415054i	$0.136237\pi$
$212$	−1.80100	−	3.11942i	−0.123693	−	0.214243i
$213$		0			0
$214$	1.33515	−	0.770847i	0.0912687	−	0.0526940i
$215$	−14.9251	+	8.61699i	−1.01788	+	0.587674i
$216$		0			0
$217$	2.81931	+	4.88319i	0.191387	+	0.331493i
$218$	3.68865	−	6.38894i	0.249827	−	0.432713i
$219$		0			0
$220$	−5.67609			−0.382682
$221$	−19.9489	+	2.01703i	−1.34191	+	0.135680i
$222$		0			0
$223$	19.5163	+	11.2677i	1.30691	+	0.754542i	0.981578	−	0.191060i	$-0.0611924\pi$
$223$	19.5163	+	11.2677i	1.30691	+	0.754542i	0.325327	+	0.945602i	$0.394526\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$		0			0
$226$			9.91321i			0.659417i
$227$	1.58616	−	0.915773i	0.105277	−	0.0607820i	−0.446437	−	0.894815i	$-0.647307\pi$
$227$	1.58616	−	0.915773i	0.105277	−	0.0607820i	0.551714	+	0.834033i	$0.313974\pi$
$228$		0			0
$229$			22.6060i			1.49385i	0.664910	+	0.746924i	$0.268470\pi$
$229$			22.6060i			1.49385i	−0.664910	+	0.746924i	$0.731530\pi$
$230$	−5.48344	−	9.49759i	−0.361567	−	0.626253i
$231$		0			0
$232$	−1.79925	−	1.03880i	−0.118126	−	0.0682003i
$233$	9.43897			0.618367			0.309184	−	0.951002i	$-0.399944\pi$
$233$	9.43897			0.618367			0.309184	+	0.951002i	$0.399944\pi$
$234$		0			0
$235$	18.7895			1.22569
$236$	2.40874	+	1.39069i	0.156796	+	0.0905262i
$237$		0			0
$238$	2.78052	+	4.81599i	0.180234	+	0.312175i
$239$		−	15.8757i		−	1.02692i	−0.858115	−	0.513458i	$-0.828364\pi$
$239$		−	15.8757i		−	1.02692i	0.858115	−	0.513458i	$-0.171636\pi$
$240$		0			0
$241$	20.7197	−	11.9625i	1.33467	−	0.770575i	0.348662	−	0.937248i	$-0.386636\pi$
$241$	20.7197	−	11.9625i	1.33467	−	0.770575i	0.986012	+	0.166674i	$0.0533027\pi$
$242$			0.922407i			0.0592946i
$243$		0			0
$244$	0.844395	−	1.46254i	0.0540569	−	0.0936293i
$245$	−1.54846	−	0.894007i	−0.0989278	−	0.0571160i
$246$		0			0
$247$	2.24499	+	22.2034i	0.142845	+	1.41277i
$248$	5.63862			0.358053
$249$		0			0
$250$	−6.08193	+	10.5342i	−0.384655	+	0.666243i
$251$	10.2618	+	17.7739i	0.647718	+	1.12188i	0.983667	+	0.180000i	$0.0576098\pi$
$251$	10.2618	+	17.7739i	0.647718	+	1.12188i	−0.335949	+	0.941880i	$0.609057\pi$
$252$		0			0
$253$	16.8625	−	9.73555i	1.06013	−	0.612069i
$254$	−15.8907	+	9.17452i	−0.997074	+	0.575661i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.413344	−	0.715933i	0.0257837	−	0.0446587i	−0.852846	−	0.522163i	$-0.825125\pi$
$257$	0.413344	−	0.715933i	0.0257837	−	0.0446587i	0.878629	+	0.477504i	$0.158459\pi$
$258$		0			0
$259$	−3.09693			−0.192434
$260$	−0.648527	−	6.41407i	−0.0402199	−	0.397784i
$261$		0			0
$262$	5.12624	+	2.95964i	0.316700	+	0.182847i
$263$	10.1805	−	17.6331i	0.627754	−	1.08730i	−0.360248	−	0.932857i	$-0.617308\pi$
$263$	10.1805	−	17.6331i	0.627754	−	1.08730i	0.988001	−	0.154445i	$-0.0493588\pi$
$264$		0			0
$265$			6.44042i			0.395632i
$266$	5.36028	−	3.09476i	0.328660	−	0.189752i
$267$		0			0
$268$		−	11.5544i		−	0.705797i
$269$	−10.2587	−	17.7687i	−0.625487	−	1.08338i	−0.988446	−	0.151570i	$-0.951567\pi$
$269$	−10.2587	−	17.7687i	−0.625487	−	1.08338i	0.362959	−	0.931805i	$-0.381766\pi$
$270$		0			0
$271$	−10.5495	−	6.09076i	−0.640837	−	0.369988i	0.144100	−	0.989563i	$-0.453971\pi$
$271$	−10.5495	−	6.09076i	−0.640837	−	0.369988i	−0.784937	+	0.619576i	$0.787305\pi$
$272$	5.56103			0.337187
$273$		0			0
$274$	8.80301			0.531809
$275$	−4.95686	−	2.86185i	−0.298910	−	0.172576i
$276$		0			0
$277$	4.31242	+	7.46933i	0.259108	+	0.448789i	0.966003	−	0.258530i	$-0.0832380\pi$
$277$	4.31242	+	7.46933i	0.259108	+	0.448789i	−0.706895	+	0.707318i	$0.749905\pi$
$278$			18.9744i			1.13801i
$279$		0			0
$280$	−1.54846	+	0.894007i	−0.0925385	+	0.0534271i
$281$		−	24.2922i		−	1.44915i	−0.689194	−	0.724577i	$-0.742035\pi$
$281$		−	24.2922i		−	1.44915i	0.689194	−	0.724577i	$-0.257965\pi$
$282$		0			0
$283$	5.36054	−	9.28472i	0.318651	−	0.551919i	−0.661556	−	0.749896i	$-0.730104\pi$
$283$	5.36054	−	9.28472i	0.318651	−	0.551919i	0.980207	+	0.197976i	$0.0634369\pi$
$284$	0.518313	+	0.299248i	0.0307562	+	0.0177571i
$285$		0			0
$286$	11.3878	−	1.15142i	0.673377	−	0.0680852i
$287$	1.49843			0.0884498
$288$		0			0
$289$	−6.96254	+	12.0595i	−0.409561	+	0.709380i
$290$	1.85738	+	3.21708i	0.109069	+	0.188913i
$291$		0			0
$292$	−0.367172	+	0.211987i	−0.0214871	+	0.0124056i
$293$	18.5571	−	10.7139i	1.08412	−	0.625914i	0.152112	−	0.988363i	$-0.451393\pi$
$293$	18.5571	−	10.7139i	1.08412	−	0.625914i	0.932004	+	0.362449i	$0.118059\pi$
$294$		0			0
$295$	−2.48657	−	4.30687i	−0.144774	−	0.250755i
$296$	−1.54846	+	2.68202i	−0.0900027	+	0.155889i
$297$		0			0
$298$	13.9625			0.808828
$299$	12.9280	+	17.9425i	0.747644	+	1.03764i
$300$		0			0
$301$	−8.34729	−	4.81931i	−0.481130	−	0.277781i
$302$	8.92131	−	15.4522i	0.513364	−	0.889172i
$303$		0			0
$304$		−	6.18952i		−	0.354993i
$305$	−2.61503	+	1.50979i	−0.149736	+	0.0864503i
$306$		0			0
$307$		−	7.59364i		−	0.433392i	−0.976239	−	0.216696i	$-0.930472\pi$
$307$		−	7.59364i		−	0.433392i	0.976239	−	0.216696i	$-0.0695280\pi$
$308$	−1.58726	−	2.74922i	−0.0904426	−	0.156651i
$309$		0			0
$310$	−8.73121	−	5.04097i	−0.495899	−	0.286308i
$311$	−25.6355			−1.45366			−0.726828	−	0.686820i	$-0.759006\pi$
$311$	−25.6355			−1.45366			−0.726828	+	0.686820i	$0.759006\pi$
$312$		0			0
$313$	−1.71308			−0.0968293			−0.0484146	−	0.998827i	$-0.515417\pi$
$313$	−1.71308			−0.0968293			−0.0484146	+	0.998827i	$0.515417\pi$
$314$	−3.96567	−	2.28958i	−0.223796	−	0.129208i
$315$		0			0
$316$	3.48127	+	6.02973i	0.195837	+	0.339199i
$317$		−	33.2098i		−	1.86525i	−0.360850	−	0.932624i	$-0.617513\pi$
$317$		−	33.2098i		−	1.86525i	0.360850	−	0.932624i	$-0.382487\pi$
$318$		0			0
$319$	−5.71175	+	3.29768i	−0.319797	+	0.184635i
$320$			1.78801i			0.0999530i
$321$		0			0
$322$	3.06678	−	5.31181i	0.170905	−	0.296016i
$323$	29.8087	+	17.2101i	1.65860	+	0.957593i
$324$		0			0
$325$	2.66758	−	5.92832i	0.147971	−	0.328844i
$326$	−12.2706			−0.679606
$327$		0			0
$328$	0.749217	−	1.29768i	0.0413686	−	0.0716525i
$329$	5.25429	+	9.10069i	0.289678	+	0.501737i
$330$		0			0
$331$	4.29537	−	2.47994i	0.236095	−	0.136310i	−0.377286	−	0.926097i	$-0.623142\pi$
$331$	4.29537	−	2.47994i	0.236095	−	0.136310i	0.613381	+	0.789787i	$0.289809\pi$
$332$	−3.72589	+	2.15114i	−0.204485	+	0.118059i
$333$		0			0
$334$	8.34904	+	14.4610i	0.456839	+	0.791269i
$335$	−10.3297	+	17.8916i	−0.564372	+	0.977521i
$336$		0			0
$337$	23.6174			1.28652			0.643260	−	0.765648i	$-0.277581\pi$
$337$	23.6174			1.28652			0.643260	+	0.765648i	$0.277581\pi$
$338$	2.60226	+	12.7369i	0.141544	+	0.692795i
$339$		0			0
$340$	−8.61106	−	4.97160i	−0.467000	−	0.269623i
$341$	8.94997	−	15.5018i	0.484668	−	0.839470i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	−8.34729	+	4.81931i	−0.450056	+	0.259840i
$345$		0			0
$346$			7.37731i			0.396607i
$347$	−3.58483	−	6.20911i	−0.192444	−	0.333323i	0.753616	−	0.657315i	$-0.228308\pi$
$347$	−3.58483	−	6.20911i	−0.192444	−	0.333323i	−0.946060	+	0.323993i	$0.894975\pi$
$348$		0			0
$349$	10.7155	+	6.18662i	0.573590	+	0.331162i	0.758582	−	0.651578i	$-0.225893\pi$
$349$	10.7155	+	6.18662i	0.573590	+	0.331162i	−0.184992	+	0.982740i	$0.559226\pi$
$350$	−1.80301			−0.0963749
$351$		0			0
$352$	−3.17452			−0.169203
$353$	−22.7018	−	13.1069i	−1.20830	−	0.697610i	−0.245909	−	0.969293i	$-0.579087\pi$
$353$	−22.7018	−	13.1069i	−1.20830	−	0.697610i	−0.962387	+	0.271683i	$0.912420\pi$
$354$		0			0
$355$	−0.535059	−	0.926750i	−0.0283980	−	0.0491868i
$356$			16.2931i			0.863532i
$357$		0			0
$358$	17.1648	−	9.91008i	0.907186	−	0.523764i
$359$			3.61956i			0.191033i	0.995428	+	0.0955165i	$0.0304503\pi$
$359$			3.61956i			0.191033i	−0.995428	+	0.0955165i	$0.969550\pi$
$360$		0			0
$361$	9.65506	−	16.7231i	0.508161	−	0.880161i
$362$	15.8713	+	9.16329i	0.834176	+	0.481612i
$363$		0			0
$364$	2.92531	−	2.10774i	0.153328	−	0.110476i
$365$	0.758070			0.0396792
$366$		0			0
$367$	4.03245	−	6.98440i	0.210492	−	0.364583i	−0.741377	−	0.671089i	$-0.765827\pi$
$367$	4.03245	−	6.98440i	0.210492	−	0.364583i	0.951869	+	0.306506i	$0.0991601\pi$
$368$	−3.06678	−	5.31181i	−0.159867	−	0.276897i
$369$		0			0
$370$	4.79549	−	2.76868i	0.249306	−	0.143937i
$371$	−3.11942	+	1.80100i	−0.161952	+	0.0935032i
$372$		0			0
$373$	−14.5851	−	25.2621i	−0.755187	−	1.30802i	−0.945281	−	0.326257i	$-0.894213\pi$
$373$	−14.5851	−	25.2621i	−0.755187	−	1.30802i	0.190094	−	0.981766i	$-0.439121\pi$
$374$	8.82681	−	15.2885i	0.456423	−	0.790549i
$375$		0			0
$376$	10.5086			0.541938
$377$	−4.37904	−	6.07759i	−0.225532	−	0.313012i
$378$		0			0
$379$	−23.3797	−	13.4983i	−1.20094	−	0.693361i	−0.240173	−	0.970730i	$-0.577204\pi$
$379$	−23.3797	−	13.4983i	−1.20094	−	0.693361i	−0.960763	+	0.277369i	$0.910538\pi$
$380$	−5.53347	+	9.58425i	−0.283861	+	0.491662i
$381$		0			0
$382$			15.0304i			0.769020i
$383$	−22.6159	+	13.0573i	−1.15562	+	0.667197i	−0.950250	−	0.311488i	$-0.899173\pi$
$383$	−22.6159	+	13.0573i	−1.15562	+	0.667197i	−0.205368	+	0.978685i	$0.565839\pi$
$384$		0			0
$385$			5.67609i			0.289280i
$386$	2.72745	+	4.72408i	0.138824	+	0.240450i
$387$		0			0
$388$	−15.1461	−	8.74462i	−0.768928	−	0.443941i
$389$	32.7110			1.65852			0.829258	−	0.558866i	$-0.188764\pi$
$389$	32.7110			1.65852			0.829258	+	0.558866i	$0.188764\pi$
$390$		0			0
$391$	34.1089			1.72496
$392$	−0.866025	−	0.500000i	−0.0437409	−	0.0252538i
$393$		0			0
$394$	−3.81485	−	6.60751i	−0.192189	−	0.332882i
$395$		−	12.4491i		−	0.626383i
$396$		0			0
$397$	−0.524826	+	0.303008i	−0.0263403	+	0.0152076i	−0.513112	−	0.858321i	$-0.671508\pi$
$397$	−0.524826	+	0.303008i	−0.0263403	+	0.0152076i	0.486772	+	0.873529i	$0.338174\pi$
$398$		−	5.99023i		−	0.300263i
$399$		0			0
$400$	−0.901504	+	1.56145i	−0.0450752	+	0.0780726i
$401$	−8.83963	−	5.10356i	−0.441430	−	0.254860i	0.262774	−	0.964857i	$-0.415363\pi$
$401$	−8.83963	−	5.10356i	−0.441430	−	0.254860i	−0.704204	+	0.709998i	$0.748696\pi$
$402$		0			0
$403$	18.5399	+	8.34244i	0.923537	+	0.415566i
$404$	4.06866			0.202424
$405$		0			0
$406$	−1.03880	+	1.79925i	−0.0515546	+	0.0892952i
$407$	4.91564	+	8.51413i	0.243659	+	0.422030i
$408$		0			0
$409$	8.01863	−	4.62956i	0.396496	−	0.228917i	−0.288475	−	0.957487i	$-0.593148\pi$
$409$	8.01863	−	4.62956i	0.396496	−	0.228917i	0.684971	+	0.728570i	$0.259815\pi$
$410$	−2.32027	+	1.33961i	−0.114590	+	0.0661586i
$411$		0			0
$412$	−9.03838	−	15.6549i	−0.445289	−	0.771263i
$413$	1.39069	−	2.40874i	0.0684313	−	0.118527i
$414$		0			0
$415$	7.69254			0.377612
$416$	−0.362708	−	3.58726i	−0.0177832	−	0.175880i
$417$		0			0
$418$	−17.0163	−	9.82438i	−0.832296	−	0.480526i
$419$	6.42444	−	11.1275i	0.313855	−	0.543612i	−0.665339	−	0.746542i	$-0.731713\pi$
$419$	6.42444	−	11.1275i	0.313855	−	0.543612i	0.979193	+	0.202930i	$0.0650462\pi$
$420$		0			0
$421$		−	7.21371i		−	0.351575i	−0.984428	−	0.175787i	$-0.943753\pi$
$421$		−	7.21371i		−	0.351575i	0.984428	−	0.175787i	$-0.0562471\pi$
$422$	−2.40150	+	1.38651i	−0.116903	+	0.0674942i
$423$		0			0
$424$			3.60200i			0.174929i
$425$	−5.01329	−	8.68328i	−0.243180	−	0.421201i
$426$		0			0
$427$	−1.46254	−	0.844395i	−0.0707771	−	0.0408632i
$428$	−1.54169			−0.0745206
$429$		0			0
$430$	17.2340			0.831097
$431$	5.17941	+	2.99033i	0.249483	+	0.144039i	0.619528	−	0.784975i	$-0.287324\pi$
$431$	5.17941	+	2.99033i	0.249483	+	0.144039i	−0.370044	+	0.929014i	$0.620658\pi$
$432$		0			0
$433$	6.30144	+	10.9144i	0.302828	+	0.524513i	0.976775	−	0.214266i	$-0.0687359\pi$
$433$	6.30144	+	10.9144i	0.302828	+	0.524513i	−0.673947	+	0.738779i	$0.735403\pi$
$434$		−	5.63862i		−	0.270663i
$435$		0			0
$436$	−6.38894	+	3.68865i	−0.305975	+	0.176655i
$437$		−	37.9637i		−	1.81605i
$438$		0			0
$439$	9.77965	−	16.9389i	0.466757	−	0.808447i	−0.532522	−	0.846416i	$-0.678755\pi$
$439$	9.77965	−	16.9389i	0.466757	−	0.808447i	0.999279	+	0.0379690i	$0.0120888\pi$
$440$	4.91564	+	2.83804i	0.234344	+	0.135298i
$441$		0			0
$442$	18.2847	+	8.22764i	0.869717	+	0.391349i
$443$	40.2601			1.91281			0.956407	−	0.292038i	$-0.0943335\pi$
$443$	40.2601			1.91281			0.956407	+	0.292038i	$0.0943335\pi$
$444$		0			0
$445$	14.5661	−	25.2293i	0.690500	−	1.19598i
$446$	−11.2677	−	19.5163i	−0.533542	−	0.924121i
$447$		0			0
$448$	−0.866025	+	0.500000i	−0.0409159	+	0.0236228i
$449$	24.7821	−	14.3079i	1.16954	−	0.675234i	0.215967	−	0.976401i	$-0.430710\pi$
$449$	24.7821	−	14.3079i	1.16954	−	0.675234i	0.953571	+	0.301167i	$0.0973762\pi$
$450$		0			0
$451$	−2.37841	−	4.11952i	−0.111995	−	0.193981i
$452$	4.95660	−	8.58509i	0.233139	−	0.403809i
$453$		0			0
$454$	−1.83155			−0.0859587
$455$	−6.41407	+	0.648527i	−0.300696	+	0.0304034i
$456$		0			0
$457$	5.49961	+	3.17520i	0.257261	+	0.148530i	0.623084	−	0.782155i	$-0.285879\pi$
$457$	5.49961	+	3.17520i	0.257261	+	0.148530i	−0.365824	+	0.930684i	$0.619213\pi$
$458$	11.3030	−	19.5774i	0.528155	−	0.914791i
$459$		0			0
$460$			10.9669i			0.511333i
$461$	−20.9785	+	12.1119i	−0.977065	+	0.564109i	−0.901383	−	0.433023i	$-0.857447\pi$
$461$	−20.9785	+	12.1119i	−0.977065	+	0.564109i	−0.0756821	+	0.997132i	$0.524113\pi$
$462$		0			0
$463$		−	17.3851i		−	0.807954i	−0.914769	−	0.403977i	$-0.867628\pi$
$463$		−	17.3851i		−	0.807954i	0.914769	−	0.403977i	$-0.132372\pi$
$464$	1.03880	+	1.79925i	0.0482249	+	0.0835280i
$465$		0			0
$466$	−8.17439	−	4.71948i	−0.378671	−	0.218626i
$467$	14.8537			0.687349			0.343675	−	0.939089i	$-0.388328\pi$
$467$	14.8537			0.687349			0.343675	+	0.939089i	$0.388328\pi$
$468$		0			0
$469$	−11.5544			−0.533532
$470$	−16.2722	−	9.39473i	−0.750579	−	0.433347i
$471$		0			0
$472$	−1.39069	−	2.40874i	−0.0640117	−	0.110871i
$473$			30.5980i			1.40690i
$474$		0			0
$475$	−9.66463	+	5.57988i	−0.443444	+	0.256022i
$476$		−	5.56103i		−	0.254889i
$477$		0			0
$478$	−7.93787	+	13.7488i	−0.363070	+	0.628855i
$479$	33.5014	+	19.3420i	1.53072	+	0.883759i	0.999329	+	0.0366302i	$0.0116624\pi$
$479$	33.5014	+	19.3420i	1.53072	+	0.883759i	0.531387	+	0.847129i	$0.321671\pi$
$480$		0			0
$481$	−9.05947	+	6.52754i	−0.413076	+	0.297630i
$482$	−23.9251			−1.08976
$483$		0			0
$484$	0.461204	−	0.798828i	0.0209638	−	0.0363104i
$485$	15.6355	+	27.0815i	0.709971	+	1.22971i
$486$		0			0
$487$	22.2780	−	12.8622i	1.00951	−	0.582843i	0.0984640	−	0.995141i	$-0.468607\pi$
$487$	22.2780	−	12.8622i	1.00951	−	0.582843i	0.911049	+	0.412298i	$0.135274\pi$
$488$	−1.46254	+	0.844395i	−0.0662059	+	0.0382240i
$489$		0			0
$490$	0.894007	+	1.54846i	0.0403871	+	0.0699525i
$491$	9.17452	−	15.8907i	0.414040	−	0.717139i	−0.581287	−	0.813699i	$-0.697451\pi$
$491$	9.17452	−	15.8907i	0.414040	−	0.717139i	0.995327	+	0.0965597i	$0.0307839\pi$
$492$		0			0
$493$	−11.5536			−0.520346
$494$	9.15749	−	20.3512i	0.412015	−	0.915644i
$495$		0			0
$496$	−4.88319	−	2.81931i	−0.219262	−	0.126591i
$497$	0.299248	−	0.518313i	0.0134231	−	0.0232495i
$498$		0			0
$499$			17.8096i			0.797269i	0.917110	+	0.398635i	$0.130516\pi$
$499$			17.8096i			0.797269i	−0.917110	+	0.398635i	$0.869484\pi$
$500$	10.5342	−	6.08193i	0.471105	−	0.271992i
$501$		0			0
$502$		−	20.5236i		−	0.916012i
$503$	15.4711	+	26.7967i	0.689823	+	1.19481i	0.971895	+	0.235415i	$0.0756448\pi$
$503$	15.4711	+	26.7967i	0.689823	+	1.19481i	−0.282072	+	0.959393i	$0.591022\pi$
$504$		0			0
$505$	−6.30019	−	3.63741i	−0.280355	−	0.161863i
$506$	−19.4711			−0.865596
$507$		0			0
$508$	18.3490			0.814107
$509$	−11.9583	−	6.90414i	−0.530044	−	0.306021i	0.210991	−	0.977488i	$-0.432331\pi$
$509$	−11.9583	−	6.90414i	−0.530044	−	0.306021i	−0.741034	+	0.671467i	$0.765664\pi$
$510$		0			0
$511$	0.211987	+	0.367172i	0.00937774	+	0.0162427i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−0.715933	+	0.413344i	−0.0315784	+	0.0182318i
$515$			32.3215i			1.42425i
$516$		0			0
$517$	16.6798	−	28.8903i	0.733579	−	1.27060i
$518$	2.68202	+	1.54846i	0.117841	+	0.0680356i
$519$		0			0
$520$	−2.64539	+	5.87901i	−0.116008	+	0.257812i
$521$	11.4549			0.501848			0.250924	−	0.968007i	$-0.419266\pi$
$521$	11.4549			0.501848			0.250924	+	0.968007i	$0.419266\pi$
$522$		0			0
$523$	−0.465198	+	0.805747i	−0.0203417	+	0.0352329i	−0.876017	−	0.482280i	$-0.839809\pi$
$523$	−0.465198	+	0.805747i	−0.0203417	+	0.0352329i	0.855675	+	0.517513i	$0.173142\pi$
$524$	−2.95964	−	5.12624i	−0.129292	−	0.223941i
$525$		0			0
$526$	−17.6331	+	10.1805i	−0.768838	+	0.443889i
$527$	27.1556	−	15.6783i	1.18292	−	0.682957i
$528$		0			0
$529$	−7.31025	−	12.6617i	−0.317837	−	0.550510i
$530$	3.22021	−	5.57757i	0.139877	−	0.242274i
$531$		0			0
$532$	−6.18952			−0.268350
$533$	4.38338	−	3.15832i	0.189865	−	0.136802i
$534$		0			0
$535$	2.38726	+	1.37828i	0.103210	+	0.0595884i
$536$	−5.77720	+	10.0064i	−0.249537	+	0.432211i
$537$		0			0
$538$			20.5175i			0.884572i
$539$	−2.74922	+	1.58726i	−0.118417	+	0.0683682i
$540$		0			0
$541$			22.7965i			0.980097i	0.871695	+	0.490048i	$0.163021\pi$
$541$			22.7965i			0.980097i	−0.871695	+	0.490048i	$0.836979\pi$
$542$	6.09076	+	10.5495i	0.261621	+	0.453140i
$543$		0			0
$544$	−4.81599	−	2.78052i	−0.206484	−	0.119214i
$545$	13.1907			0.565029
$546$		0			0
$547$	31.6698			1.35410			0.677052	−	0.735935i	$-0.263257\pi$
$547$	31.6698			1.35410			0.677052	+	0.735935i	$0.263257\pi$
$548$	−7.62363	−	4.40150i	−0.325665	−	0.188023i
$549$		0			0
$550$	2.86185	+	4.95686i	0.122029	+	0.211361i
$551$			12.8593i			0.547824i
$552$		0			0
$553$	6.02973	−	3.48127i	0.256410	−	0.148039i
$554$		−	8.62484i		−	0.366434i
$555$		0			0
$556$	9.48720	−	16.4323i	0.402347	−	0.696885i
$557$	9.38623	+	5.41914i	0.397707	+	0.229616i	0.685494	−	0.728078i	$-0.259586\pi$
$557$	9.38623	+	5.41914i	0.397707	+	0.229616i	−0.287787	+	0.957694i	$0.592920\pi$
$558$		0			0
$559$	−34.5763	+	3.49601i	−1.46242	+	0.147865i
$560$	1.78801			0.0755574
$561$		0			0
$562$	−12.1461	+	21.0377i	−0.512353	+	0.887422i
$563$	−7.73626	−	13.3996i	−0.326044	−	0.564725i	0.655679	−	0.755040i	$-0.272383\pi$
$563$	−7.73626	−	13.3996i	−0.326044	−	0.564725i	−0.981723	+	0.190315i	$0.939049\pi$
$564$		0			0
$565$	−15.3503	+	8.86247i	−0.645790	+	0.372847i
$566$	−9.28472	+	5.36054i	−0.390266	+	0.225320i
$567$		0			0
$568$	−0.299248	−	0.518313i	−0.0125562	−	0.0217479i
$569$	−16.8667	+	29.2139i	−0.707088	+	1.22471i	0.258845	+	0.965919i	$0.416658\pi$
$569$	−16.8667	+	29.2139i	−0.707088	+	1.22471i	−0.965933	+	0.258793i	$0.916675\pi$
$570$		0			0
$571$	−43.6140			−1.82519			−0.912594	−	0.408868i	$-0.865924\pi$
$571$	−43.6140			−1.82519			−0.912594	+	0.408868i	$0.865924\pi$
$572$	−10.4379	−	4.69676i	−0.436429	−	0.196381i
$573$		0			0
$574$	−1.29768	−	0.749217i	−0.0541642	−	0.0312717i
$575$	−5.52943	+	9.57725i	−0.230593	+	0.399399i
$576$		0			0
$577$		−	10.8368i		−	0.451143i	−0.974227	−	0.225571i	$-0.927575\pi$
$577$		−	10.8368i		−	0.451143i	0.974227	−	0.225571i	$-0.0724249\pi$
$578$	12.0595	−	6.96254i	0.501608	−	0.289603i
$579$		0			0
$580$		−	3.71476i		−	0.154247i
$581$	2.15114	+	3.72589i	0.0892444	+	0.154576i
$582$		0			0
$583$	9.90268	+	5.71731i	0.410127	+	0.236787i
$584$	0.423973			0.0175441
$585$		0			0
$586$	−21.4278			−0.885176
$587$	−22.5632	−	13.0269i	−0.931284	−	0.537677i	−0.0440666	−	0.999029i	$-0.514031\pi$
$587$	−22.5632	−	13.0269i	−0.931284	−	0.537677i	−0.887217	+	0.461352i	$0.847365\pi$
$588$		0			0
$589$	−17.4502	−	30.2246i	−0.719022	−	1.24538i
$590$			4.97314i			0.204741i
$591$		0			0
$592$	2.68202	−	1.54846i	0.110230	−	0.0636415i
$593$		−	1.68393i		−	0.0691509i	−0.999402	−	0.0345754i	$-0.988992\pi$
$593$		−	1.68393i		−	0.0691509i	0.999402	−	0.0345754i	$-0.0110079\pi$
$594$		0			0
$595$	−4.97160	+	8.61106i	−0.203816	+	0.353019i
$596$	−12.0919	−	6.98127i	−0.495304	−	0.285964i
$597$		0			0
$598$	−2.22469	−	22.0027i	−0.0909743	−	0.899756i
$599$	6.54081			0.267250			0.133625	−	0.991032i	$-0.457338\pi$
$599$	6.54081			0.267250			0.133625	+	0.991032i	$0.457338\pi$
$600$		0			0
$601$	−19.2387	+	33.3224i	−0.784763	+	1.35925i	0.144377	+	0.989523i	$0.453882\pi$
$601$	−19.2387	+	33.3224i	−0.784763	+	1.35925i	−0.929140	+	0.369727i	$0.879451\pi$
$602$	4.81931	+	8.34729i	0.196420	+	0.340210i
$603$		0			0
$604$	−15.4522	+	8.92131i	−0.628740	+	0.363003i
$605$	−1.42832	+	0.824638i	−0.0580693	+	0.0335263i
$606$		0			0
$607$	4.71797	+	8.17176i	0.191496	+	0.331682i	0.945746	−	0.324906i	$-0.105333\pi$
$607$	4.71797	+	8.17176i	0.191496	+	0.331682i	−0.754250	+	0.656587i	$0.771999\pi$
$608$	−3.09476	+	5.36028i	−0.125509	+	0.217388i
$609$		0			0
$610$	3.01958			0.122259
$611$	34.5523	+	15.5476i	1.39784	+	0.628989i
$612$		0			0
$613$	−22.0191	−	12.7127i	−0.889342	−	0.513462i	−0.0156146	−	0.999878i	$-0.504970\pi$
$613$	−22.0191	−	12.7127i	−0.889342	−	0.513462i	−0.873727	+	0.486416i	$0.838304\pi$
$614$	−3.79682	+	6.57628i	−0.153227	+	0.265397i
$615$		0			0
$616$			3.17452i			0.127905i
$617$	−24.8545	+	14.3497i	−1.00060	+	0.577699i	−0.908427	−	0.418044i	$-0.862716\pi$
$617$	−24.8545	+	14.3497i	−1.00060	+	0.577699i	−0.0921772	+	0.995743i	$0.529383\pi$
$618$		0			0
$619$			9.61494i			0.386457i	0.981154	+	0.193229i	$0.0618959\pi$
$619$			9.61494i			0.386457i	−0.981154	+	0.193229i	$0.938104\pi$
$620$	5.04097	+	8.73121i	0.202450	+	0.350654i
$621$		0			0
$622$	22.2010	+	12.8177i	0.890178	+	0.513945i
$623$	16.2931			0.652769
$624$		0			0
$625$	−12.7341			−0.509365
$626$	1.48357	+	0.856542i	0.0592956	+	0.0342343i
$627$		0			0
$628$	2.28958	+	3.96567i	0.0913642	+	0.158247i
$629$			17.2221i			0.686691i
$630$		0			0
$631$	29.9445	−	17.2885i	1.19207	−	0.688244i	0.233297	−	0.972406i	$-0.425049\pi$
$631$	29.9445	−	17.2885i	1.19207	−	0.688244i	0.958776	+	0.284162i	$0.0917153\pi$
$632$		−	6.96254i		−	0.276955i
$633$		0			0
$634$	−16.6049	+	28.7605i	−0.659465	+	1.14223i
$635$	−28.4129	−	16.4042i	−1.12753	−	0.650980i
$636$		0			0
$637$	−2.10774	−	2.92531i	−0.0835119	−	0.115905i
$638$	6.59536			0.261113
$639$		0			0
$640$	0.894007	−	1.54846i	0.0353387	−	0.0612085i
$641$	−3.25646	−	5.64035i	−0.128622	−	0.222780i	0.794521	−	0.607237i	$-0.207722\pi$
$641$	−3.25646	−	5.64035i	−0.128622	−	0.222780i	−0.923143	+	0.384457i	$0.874389\pi$
$642$		0			0
$643$	−21.8991	+	12.6435i	−0.863617	+	0.498609i	−0.865222	−	0.501389i	$-0.832822\pi$
$643$	−21.8991	+	12.6435i	−0.863617	+	0.498609i	0.00160504	+	0.999999i	$0.499489\pi$
$644$	−5.31181	+	3.06678i	−0.209315	+	0.120848i
$645$		0			0
$646$	−17.2101	−	29.8087i	−0.677120	−	1.17281i
$647$	−5.95794	+	10.3194i	−0.234231	+	0.405699i	−0.959049	−	0.283241i	$-0.908590\pi$
$647$	−5.95794	+	10.3194i	−0.234231	+	0.405699i	0.724818	+	0.688940i	$0.241924\pi$
$648$		0			0
$649$	−8.82955			−0.346590
$650$	−5.27435	+	3.80028i	−0.206877	+	0.149059i
$651$		0			0
$652$	10.6267	+	6.13531i	0.416172	+	0.240277i
$653$	20.7508	−	35.9415i	0.812043	−	1.40650i	−0.0993891	−	0.995049i	$-0.531689\pi$
$653$	20.7508	−	35.9415i	0.812043	−	1.40650i	0.911432	−	0.411451i	$-0.134978\pi$
$654$		0			0
$655$			10.5837i			0.413541i
$656$	−1.29768	+	0.749217i	−0.0506660	+	0.0292520i
$657$		0			0
$658$		−	10.5086i		−	0.409667i
$659$	7.86778	+	13.6274i	0.306485	+	0.530848i	0.977591	−	0.210514i	$-0.0675137\pi$
$659$	7.86778	+	13.6274i	0.306485	+	0.530848i	−0.671106	+	0.741362i	$0.734180\pi$
$660$		0			0
$661$	−22.6071	−	13.0522i	−0.879315	−	0.507673i	−0.00888248	−	0.999961i	$-0.502827\pi$
$661$	−22.6071	−	13.0522i	−0.879315	−	0.507673i	−0.870432	+	0.492288i	$0.836161\pi$
$662$	−4.95987			−0.192771
$663$		0			0
$664$	4.30228			0.166961
$665$	9.58425	+	5.53347i	0.371661	+	0.214579i
$666$		0			0
$667$	6.37151	+	11.0358i	0.246706	+	0.427307i
$668$		−	16.6981i		−	0.646068i
$669$		0			0
$670$	17.8916	−	10.3297i	0.691212	−	0.399071i
$671$			5.36110i			0.206963i
$672$		0			0
$673$	0.620853	−	1.07535i	0.0239321	−	0.0414516i	−0.853811	−	0.520583i	$-0.825715\pi$
$673$	0.620853	−	1.07535i	0.0239321	−	0.0414516i	0.877743	+	0.479131i	$0.159048\pi$
$674$	−20.4532	−	11.8087i	−0.787829	−	0.454853i
$675$		0			0
$676$	4.11482	−	12.3316i	0.158262	−	0.474292i
$677$	−29.2845			−1.12550			−0.562748	−	0.826629i	$-0.690256\pi$
$677$	−29.2845			−1.12550			−0.562748	+	0.826629i	$0.690256\pi$
$678$		0			0
$679$	−8.74462	+	15.1461i	−0.335588	+	0.581255i
$680$	4.97160	+	8.61106i	0.190652	+	0.330219i
$681$		0			0
$682$	−15.5018	+	8.94997i	−0.593595	+	0.342712i
$683$	37.0486	−	21.3900i	1.41762	−	0.818466i	0.421535	−	0.906812i	$-0.361491\pi$
$683$	37.0486	−	21.3900i	1.41762	−	0.818466i	0.996090	+	0.0883461i	$0.0281581\pi$
$684$		0			0
$685$	7.86995	+	13.6311i	0.300695	+	0.520819i
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$		0			0
$688$	9.63862			0.367469
$689$	−5.32922	+	11.8434i	−0.203027	+	0.451198i
$690$		0			0
$691$	−16.3649	−	9.44827i	−0.622549	−	0.359429i	0.155312	−	0.987866i	$-0.450362\pi$
$691$	−16.3649	−	9.44827i	−0.622549	−	0.359429i	−0.777861	+	0.628437i	$0.783695\pi$
$692$	3.68865	−	6.38894i	0.140222	−	0.242871i
$693$		0			0
$694$			7.16967i			0.272157i
$695$	−29.3812	+	16.9632i	−1.11449	+	0.643452i
$696$		0			0
$697$		−	8.33284i		−	0.315629i
$698$	−6.18662	−	10.7155i	−0.234167	−	0.405589i
$699$		0			0
$700$	1.56145	+	0.901504i	0.0590173	+	0.0340737i
$701$	3.35161			0.126589			0.0632943	−	0.997995i	$-0.479839\pi$
$701$	3.35161			0.126589			0.0632943	+	0.997995i	$0.479839\pi$
$702$		0			0
$703$	19.1685			0.722954
$704$	2.74922	+	1.58726i	0.103615	+	0.0598222i
$705$		0			0
$706$	13.1069	+	22.7018i	0.493285	+	0.854395i
$707$		−	4.06866i		−	0.153018i
$708$		0			0
$709$	31.8468	−	18.3867i	1.19603	−	0.690529i	0.236363	−	0.971665i	$-0.424045\pi$
$709$	31.8468	−	18.3867i	1.19603	−	0.690529i	0.959668	+	0.281136i	$0.0907113\pi$
$710$			1.07012i			0.0401608i
$711$		0			0
$712$	8.14654	−	14.1102i	0.305305	−	0.528803i
$713$	−29.9513	−	17.2924i	−1.12169	−	0.647606i
$714$		0			0
$715$	11.9637	+	16.6043i	0.447419	+	0.620965i
$716$	−19.8202			−0.740714
$717$		0			0
$718$	1.80978	−	3.13463i	0.0675404	−	0.116983i
$719$	−8.08486	−	14.0034i	−0.301514	−	0.522238i	0.674965	−	0.737850i	$-0.264159\pi$
$719$	−8.08486	−	14.0034i	−0.301514	−	0.522238i	−0.976479	+	0.215612i	$0.930825\pi$
$720$		0			0
$721$	−15.6549	+	9.03838i	−0.583020	+	0.336607i
$722$	−16.7231	+	9.65506i	−0.622368	+	0.359324i
$723$		0			0
$724$	−9.16329	−	15.8713i	−0.340551	−	0.589851i
$725$	1.87296	−	3.24406i	0.0695599	−	0.120481i
$726$		0			0
$727$	27.2522			1.01073			0.505363	−	0.862907i	$-0.331358\pi$
$727$	27.2522			1.01073			0.505363	+	0.862907i	$0.331358\pi$
$728$	−3.58726	+	0.362708i	−0.132953	+	0.0134429i
$729$		0			0
$730$	−0.656508	−	0.379035i	−0.0242984	−	0.0140287i
$731$	−26.8003	+	46.4196i	−0.991247	+	1.71689i
$732$		0			0
$733$			39.6734i			1.46537i	0.680567	+	0.732686i	$0.261733\pi$
$733$			39.6734i			1.46537i	−0.680567	+	0.732686i	$0.738267\pi$
$734$	−6.98440	+	4.03245i	−0.257799	+	0.148840i
$735$		0			0
$736$			6.13356i			0.226086i
$737$	18.3398	+	31.7655i	0.675557	+	1.17010i
$738$		0			0
$739$	−22.0125	−	12.7089i	−0.809742	−	0.467505i	0.0371244	−	0.999311i	$-0.488180\pi$
$739$	−22.0125	−	12.7089i	−0.809742	−	0.467505i	−0.846866	+	0.531806i	$0.821514\pi$
$740$	−5.53735			−0.203557
$741$		0			0
$742$	3.60200			0.132234
$743$	21.5143	+	12.4213i	0.789285	+	0.455694i	0.839711	−	0.543034i	$-0.182725\pi$
$743$	21.5143	+	12.4213i	0.789285	+	0.455694i	−0.0504260	+	0.998728i	$0.516058\pi$
$744$		0			0
$745$	12.4826	+	21.6205i	0.457327	+	0.792114i
$746$			29.1702i			1.06800i
$747$		0			0
$748$	−15.2885	+	8.82681i	−0.559002	+	0.322740i
$749$			1.54169i			0.0563323i
$750$		0			0
$751$	−22.7211	+	39.3540i	−0.829103	+	1.43605i	0.0696398	+	0.997572i	$0.477815\pi$
$751$	−22.7211	+	39.3540i	−0.829103	+	1.43605i	−0.898743	+	0.438476i	$0.855518\pi$
$752$	−9.10069	−	5.25429i	−0.331868	−	0.191604i
$753$		0			0
$754$	0.753559	+	7.45287i	0.0274430	+	0.271417i
$755$	31.9028			1.16106
$756$		0			0
$757$	−3.20643	+	5.55369i	−0.116540	+	0.201852i	−0.918394	−	0.395667i	$-0.870514\pi$
$757$	−3.20643	+	5.55369i	−0.116540	+	0.201852i	0.801855	+	0.597519i	$0.203847\pi$
$758$	13.4983	+	23.3797i	0.490280	+	0.849190i
$759$		0			0
$760$	9.58425	−	5.53347i	0.347657	−	0.200720i
$761$	−27.8313	+	16.0684i	−1.00888	+	0.582479i	−0.910864	−	0.412706i	$-0.864584\pi$
$761$	−27.8313	+	16.0684i	−1.00888	+	0.582479i	−0.0980185	+	0.995185i	$0.531250\pi$
$762$		0			0
$763$	3.68865	+	6.38894i	0.133538	+	0.231295i
$764$	7.51518	−	13.0167i	0.271890	−	0.470927i
$765$		0			0
$766$	26.1146			0.943558
$767$	−1.00883	−	9.97753i	−0.0364267	−	0.360268i
$768$		0			0
$769$	−33.7551	−	19.4885i	−1.21724	−	0.702774i	−0.252914	−	0.967489i	$-0.581389\pi$
$769$	−33.7551	−	19.4885i	−1.21724	−	0.702774i	−0.964327	+	0.264714i	$0.914722\pi$
$770$	2.83804	−	4.91564i	0.102276	−	0.177147i
$771$		0			0
$772$		−	5.45490i		−	0.196326i
$773$	−2.09922	+	1.21199i	−0.0755038	+	0.0435921i	−0.537277	−	0.843406i	$-0.680547\pi$
$773$	−2.09922	+	1.21199i	−0.0755038	+	0.0435921i	0.461773	+	0.886998i	$0.347214\pi$
$774$		0			0
$775$			10.1665i			0.365191i
$776$	8.74462	+	15.1461i	0.313913	+	0.543714i
$777$		0			0
$778$	−28.3286	−	16.3555i	−1.01563	−	0.586374i
$779$	−9.27458			−0.332296
$780$		0			0
$781$	−1.89994			−0.0679851
$782$	−29.5392	−	17.0544i	−1.05632	−	0.609866i
$783$		0			0
$784$	0.500000	+	0.866025i	0.0178571	+	0.0309295i
$785$		−	8.18760i		−	0.292228i
$786$		0			0
$787$	−43.9662	+	25.3839i	−1.56722	+	0.904837i	−0.570733	+	0.821136i	$0.693341\pi$
$787$	−43.9662	+	25.3839i	−1.56722	+	0.904837i	−0.996491	+	0.0837017i	$0.973326\pi$
$788$			7.62970i			0.271797i
$789$		0			0
$790$	−6.22455	+	10.7812i	−0.221460	+	0.383579i
$791$	−8.58509	−	4.95660i	−0.305251	−	0.176237i
$792$		0			0
$793$	−6.05813	+	0.612538i	−0.215131	+	0.0217519i
$794$	0.606017			0.0215067
$795$		0			0
$796$	−2.99512	+	5.18769i	−0.106159	+	0.183873i
$797$	−13.6044	−	23.5636i	−0.481894	−	0.834664i	0.517890	−	0.855447i	$-0.326717\pi$
$797$	−13.6044	−	23.5636i	−0.481894	−	0.834664i	−0.999784	+	0.0207828i	$0.993384\pi$
$798$		0			0
$799$	50.6092	−	29.2193i	1.79043	−	1.03370i
$800$	1.56145	−	0.901504i	0.0552056	−	0.0318730i
$801$		0			0
$802$	5.10356	+	8.83963i	0.180213	+	0.312138i
$803$	0.672957	−	1.16559i	0.0237481	−	0.0411329i
$804$		0			0
$805$	10.9669			0.386532
$806$	−11.8848	−	16.4947i	−0.418624	−	0.581001i
$807$		0			0
$808$	−3.52357	−	2.03433i	−0.123959	−	0.0715676i
$809$	−21.7049	+	37.5939i	−0.763102	+	1.32173i	0.178142	+	0.984005i	$0.442991\pi$
$809$	−21.7049	+	37.5939i	−0.763102	+	1.32173i	−0.941244	+	0.337727i	$0.890342\pi$
$810$		0			0
$811$			38.1252i			1.33876i	0.742922	+	0.669378i	$0.233439\pi$
$811$			38.1252i			1.33876i	−0.742922	+	0.669378i	$0.766561\pi$
$812$	1.79925	−	1.03880i	0.0631412	−	0.0364546i
$813$		0			0
$814$		−	9.83127i		−	0.344586i
$815$	−10.9700	−	19.0006i	−0.384263	−	0.665562i
$816$		0			0
$817$	51.6657	+	29.8292i	1.80755	+	1.04359i
$818$	−9.25912			−0.323738
$819$		0			0
$820$	2.67922			0.0935624
$821$	−21.2937	−	12.2939i	−0.743157	−	0.429062i	0.0800593	−	0.996790i	$-0.474489\pi$
$821$	−21.2937	−	12.2939i	−0.743157	−	0.429062i	−0.823216	+	0.567728i	$0.807822\pi$
$822$		0			0
$823$	−15.6465	−	27.1005i	−0.545402	−	0.944663i	−0.998582	−	0.0532443i	$-0.983044\pi$
$823$	−15.6465	−	27.1005i	−0.545402	−	0.944663i	0.453180	−	0.891419i	$-0.350290\pi$
$824$			18.0768i			0.629734i
$825$		0			0
$826$	−2.40874	+	1.39069i	−0.0838109	+	0.0483883i
$827$			10.9236i			0.379851i	0.981798	+	0.189926i	$0.0608247\pi$
$827$			10.9236i			0.379851i	−0.981798	+	0.189926i	$0.939175\pi$
$828$		0			0
$829$	21.8838	−	37.9039i	0.760057	−	1.31646i	−0.182763	−	0.983157i	$-0.558504\pi$
$829$	21.8838	−	37.9039i	0.760057	−	1.31646i	0.942820	−	0.333301i	$-0.108163\pi$
$830$	−6.66193	−	3.84627i	−0.231239	−	0.133506i
$831$		0			0
$832$	−1.47952	+	3.28801i	−0.0512930	+	0.113991i
$833$	−5.56103			−0.192678
$834$		0			0
$835$	−14.9282	+	25.8564i	−0.516612	+	0.894798i
$836$	9.82438	+	17.0163i	0.339783	+	0.588522i
$837$		0			0
$838$	−11.1275	+	6.42444i	−0.384392	+	0.221929i
$839$	16.7145	−	9.65012i	0.577048	−	0.333159i	−0.182911	−	0.983129i	$-0.558552\pi$
$839$	16.7145	−	9.65012i	0.577048	−	0.333159i	0.759959	+	0.649970i	$0.225219\pi$
$840$		0			0
$841$	12.3418	+	21.3766i	0.425579	+	0.737125i
$842$	−3.60686	+	6.24726i	−0.124300	+	0.215295i
$843$		0			0
$844$	2.77302			0.0954512
$845$	−17.3962	+	15.4164i	−0.598447	+	0.530339i
$846$		0			0
$847$	−0.798828	−	0.461204i	−0.0274481	−	0.0158471i
$848$	1.80100	−	3.11942i	0.0618466	−	0.107121i
$849$		0			0
$850$			10.0266i			0.343909i
$851$	16.4503	−	9.49759i	0.563910	−	0.325573i
$852$		0			0
$853$		−	28.9164i		−	0.990078i	−0.868871	−	0.495039i	$-0.835154\pi$
$853$		−	28.9164i		−	0.990078i	0.868871	−	0.495039i	$-0.164846\pi$
$854$	0.844395	+	1.46254i	0.0288946	+	0.0500469i
$855$		0			0
$856$	1.33515	+	0.770847i	0.0456344	+	0.0263470i
$857$	16.6946			0.570278			0.285139	−	0.958486i	$-0.407960\pi$
$857$	16.6946			0.570278			0.285139	+	0.958486i	$0.407960\pi$
$858$		0			0
$859$	27.5825			0.941103			0.470552	−	0.882372i	$-0.344055\pi$
$859$	27.5825			0.941103			0.470552	+	0.882372i	$0.344055\pi$
$860$	−14.9251	−	8.61699i	−0.508941	−	0.293837i
$861$		0			0
$862$	−2.99033	−	5.17941i	−0.101851	−	0.176411i
$863$		−	31.9313i		−	1.08696i	−0.839424	−	0.543478i	$-0.817107\pi$
$863$		−	31.9313i		−	1.08696i	0.839424	−	0.543478i	$-0.182893\pi$
$864$		0			0
$865$	−11.4235	+	6.59536i	−0.388411	+	0.224249i
$866$		−	12.6029i		−	0.428263i
$867$		0			0
$868$	−2.81931	+	4.88319i	−0.0956937	+	0.165746i
$869$	−19.1415	−	11.0514i	−0.649332	−	0.374892i
$870$		0			0
$871$	−33.8001	+	24.3537i	−1.14527	+	0.825194i
$872$	7.37731			0.249827
$873$		0			0
$874$	−18.9819	+	32.8776i	−0.642071	+	1.11210i
$875$	−6.08193	−	10.5342i	−0.205607	−	0.356122i
$876$		0			0
$877$	25.6513	−	14.8098i	0.866183	−	0.500091i	0.000104747	−	1.00000i	$-0.499967\pi$
$877$	25.6513	−	14.8098i	0.866183	−	0.500091i	0.866078	+	0.499909i	$0.166633\pi$
$878$	−16.9389	+	9.77965i	−0.571659	+	0.330047i
$879$		0			0
$880$	−2.83804	−	4.91564i	−0.0956704	−	0.165706i
$881$	5.04872	−	8.74464i	0.170096	−	0.294615i	−0.768357	−	0.640021i	$-0.778926\pi$
$881$	5.04872	−	8.74464i	0.170096	−	0.294615i	0.938453	+	0.345407i	$0.112259\pi$
$882$		0			0
$883$	46.5103			1.56520			0.782598	−	0.622527i	$-0.213894\pi$
$883$	46.5103			1.56520			0.782598	+	0.622527i	$0.213894\pi$
$884$	−11.7212	−	16.2677i	−0.394228	−	0.547142i
$885$		0			0
$886$	−34.8662	−	20.1300i	−1.17135	−	0.676282i
$887$	−13.2691	+	22.9828i	−0.445534	+	0.771688i	−0.998089	−	0.0617884i	$-0.980320\pi$
$887$	−13.2691	+	22.9828i	−0.445534	+	0.771688i	0.552555	+	0.833476i	$0.313653\pi$
$888$		0			0
$889$		−	18.3490i		−	0.615407i
$890$	−25.2293	+	14.5661i	−0.845687	+	0.488258i
$891$		0			0
$892$			22.5354i			0.754542i
$893$	−32.5215	−	56.3289i	−1.08829	−	1.88497i
$894$		0			0
$895$	30.6908	+	17.7193i	1.02588	+	0.592292i
$896$	1.00000			0.0334077
$897$		0			0
$898$	−28.6159			−0.954924
$899$	10.1453	+	5.85738i	0.338364	+	0.195355i
$900$		0			0
$901$	10.0154	+	17.3472i	0.333662	+	0.577919i
$902$			4.75681i			0.158385i
$903$		0			0
$904$	−8.58509	+	4.95660i	−0.285536	+	0.164854i
$905$			32.7682i			1.08925i
$906$		0			0
$907$	−11.8195	+	20.4721i	−0.392462	+	0.679763i	−0.992774	−	0.120002i	$-0.961710\pi$
$907$	−11.8195	+	20.4721i	−0.392462	+	0.679763i	0.600312	+	0.799766i	$0.295043\pi$
$908$	1.58616	+	0.915773i	0.0526387	+	0.0303910i
$909$		0			0
$910$	5.87901	+	2.64539i	0.194887	+	0.0876940i
$911$	1.46896			0.0486688			0.0243344	−	0.999704i	$-0.492253\pi$
$911$	1.46896			0.0486688			0.0243344	+	0.999704i	$0.492253\pi$
$912$		0			0
$913$	6.82884	−	11.8279i	0.226002	−	0.391447i
$914$	−3.17520	−	5.49961i	−0.105026	−	0.181911i
$915$		0			0
$916$	−19.5774	+	11.3030i	−0.646855	+	0.373462i
$917$	−5.12624	+	2.95964i	−0.169283	+	0.0977359i
$918$		0			0
$919$	−21.5188	−	37.2717i	−0.709841	−	1.22948i	−0.964916	−	0.262559i	$-0.915434\pi$
$919$	−21.5188	−	37.2717i	−0.709841	−	1.22948i	0.255075	−	0.966921i	$-0.417900\pi$
$920$	5.48344	−	9.49759i	0.180784	−	0.313126i
$921$		0			0
$922$	24.2238			0.797770
$923$	−0.217079	−	2.14696i	−0.00714525	−	0.0706681i
$924$		0			0
$925$	−4.83570	−	2.79190i	−0.158997	−	0.0917970i
$926$	−8.69255	+	15.0559i	−0.285655	+	0.494769i
$927$		0			0
$928$		−	2.07759i		−	0.0682003i
$929$	1.48827	−	0.859255i	0.0488286	−	0.0281912i	−0.475387	−	0.879777i	$-0.657692\pi$
$929$	1.48827	−	0.859255i	0.0488286	−	0.0281912i	0.524216	+	0.851586i	$0.324359\pi$
$930$		0			0
$931$			6.18952i			0.202853i
$932$	4.71948	+	8.17439i	0.154592	+	0.267761i
$933$		0			0
$934$	−12.8637	−	7.42687i	−0.420914	−	0.243015i
$935$	31.5649			1.03228
$936$		0			0
$937$	−20.0024			−0.653451			−0.326725	−	0.945119i	$-0.605945\pi$
$937$	−20.0024			−0.653451			−0.326725	+	0.945119i	$0.605945\pi$
$938$	10.0064	+	5.77720i	0.326721	+	0.188632i
$939$		0			0
$940$	9.39473	+	16.2722i	0.306422	+	0.530739i
$941$			11.8846i			0.387428i	0.981058	+	0.193714i	$0.0620533\pi$
$941$			11.8846i			0.387428i	−0.981058	+	0.193714i	$0.937947\pi$
$942$		0			0
$943$	−7.95940	+	4.59536i	−0.259194	+	0.149646i
$944$			2.78138i			0.0905262i
$945$		0			0
$946$	15.2990	−	26.4987i	0.497414	−	0.861546i
$947$	−5.34394	−	3.08532i	−0.173655	−	0.100260i	0.410653	−	0.911792i	$-0.365301\pi$
$947$	−5.34394	−	3.08532i	−0.173655	−	0.100260i	−0.584308	+	0.811532i	$0.698634\pi$
$948$		0			0
$949$	1.39403	+	0.627276i	0.0452521	+	0.0203622i
$950$	11.1598			0.362070
$951$		0			0
$952$	−2.78052	+	4.81599i	−0.0901170	+	0.156087i
$953$	−20.5361	−	35.5696i	−0.665231	−	1.15221i	−0.979223	−	0.202788i	$-0.935000\pi$
$953$	−20.5361	−	35.5696i	−0.665231	−	1.15221i	0.313992	−	0.949426i	$-0.398333\pi$
$954$		0			0
$955$	−23.2740	+	13.4372i	−0.753129	+	0.434819i
$956$	13.7488	−	7.93787i	0.444668	−	0.256729i
$957$		0			0
$958$	−19.3420	−	33.5014i	−0.624912	−	1.08238i
$959$	−4.40150	+	7.62363i	−0.142132	+	0.246180i
$960$		0			0
$961$	−0.794081			−0.0256155
$962$	11.1095	−	1.12328i	0.358185	−	0.0362160i
$963$		0			0
$964$	20.7197	+	11.9625i	0.667337	+	0.385287i
$965$	−4.87672	+	8.44672i	−0.156987	+	0.271910i
$966$		0			0
$967$			34.4847i			1.10895i	0.832199	+	0.554477i	$0.187081\pi$
$967$			34.4847i			1.10895i	−0.832199	+	0.554477i	$0.812919\pi$
$968$	−0.798828	+	0.461204i	−0.0256753	+	0.0148236i
$969$		0			0
$970$		−	31.2710i		−	1.00405i
$971$	1.94777	+	3.37364i	0.0625071	+	0.108265i	0.895585	−	0.444890i	$-0.146757\pi$
$971$	1.94777	+	3.37364i	0.0625071	+	0.108265i	−0.833078	+	0.553155i	$0.813424\pi$
$972$		0			0
$973$	−16.4323	−	9.48720i	−0.526796	−	0.304146i
$974$	−25.7244			−0.824264
$975$		0			0
$976$	1.68879			0.0540569
$977$	−45.7455	−	26.4112i	−1.46353	−	0.844968i	−0.464356	−	0.885649i	$-0.653714\pi$
$977$	−45.7455	−	26.4112i	−1.46353	−	0.844968i	−0.999172	+	0.0406804i	$0.987047\pi$
$978$		0			0
$979$	−25.8614	−	44.7932i	−0.826533	−	1.43160i
$980$		−	1.78801i		−	0.0571160i
$981$		0			0
$982$	−15.8907	+	9.17452i	−0.507094	+	0.292771i
$983$		−	40.2176i		−	1.28274i	−0.767231	−	0.641371i	$-0.778366\pi$
$983$		−	40.2176i		−	1.28274i	0.767231	−	0.641371i	$-0.221634\pi$
$984$		0			0
$985$	6.82100	−	11.8143i	0.217335	−	0.376435i
$986$	10.0057	+	5.77678i	0.318646	+	0.183970i
$987$		0			0
$988$	−18.1062	+	13.0459i	−0.576036	+	0.415046i
$989$	59.1190			1.87988
$990$		0			0
$991$	−18.5909	+	32.2004i	−0.590559	+	1.02288i	0.403598	+	0.914937i	$0.367760\pi$
$991$	−18.5909	+	32.2004i	−0.590559	+	1.02288i	−0.994157	+	0.107942i	$0.965574\pi$
$992$	2.81931	+	4.88319i	0.0895132	+	0.155041i
$993$		0			0
$994$	−0.518313	+	0.299248i	−0.0164399	+	0.00949157i
$995$	9.27567	−	5.35531i	0.294058	−	0.169775i
$996$		0			0
$997$	0.0370447	+	0.0641633i	0.00117322	+	0.00203207i	0.866611	−	0.498984i	$-0.166293\pi$
$997$	0.0370447	+	0.0641633i	0.00117322	+	0.00203207i	−0.865438	+	0.501016i	$0.832960\pi$
$998$	8.90482	−	15.4236i	0.281877	−	0.488226i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.bj.f.1135.1		8
3.2	odd	2		546.2.s.e.43.4	✓	8
13.10	even	6	inner	1638.2.bj.f.127.2		8
39.20	even	12		7098.2.a.co.1.1		4
39.23	odd	6		546.2.s.e.127.3	yes	8
39.32	even	12		7098.2.a.cn.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.s.e.43.4	✓	8	3.2	odd	2
546.2.s.e.127.3	yes	8	39.23	odd	6
1638.2.bj.f.127.2		8	13.10	even	6	inner
1638.2.bj.f.1135.1		8	1.1	even	1	trivial
7098.2.a.cn.1.4		4	39.32	even	12
7098.2.a.co.1.1		4	39.20	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.78801i q^{5} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.78801i q^{5} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.894007 + 1.54846i) q^{10} +(-2.74922 - 1.58726i) q^{11} +(1.47952 - 3.28801i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.78052 - 4.81599i) q^{17} +(-5.36028 + 3.09476i) q^{19} +(1.54846 - 0.894007i) q^{20} +(1.58726 + 2.74922i) q^{22} +(-3.06678 + 5.31181i) q^{23} +1.80301 q^{25} +(-2.92531 + 2.10774i) q^{26} +(0.866025 + 0.500000i) q^{28} +(1.03880 - 1.79925i) q^{29} +5.63862i q^{31} +(0.866025 - 0.500000i) q^{32} +5.56103i q^{34} +(-0.894007 - 1.54846i) q^{35} +(-2.68202 - 1.54846i) q^{37} +6.18952 q^{38} -1.78801 q^{40} +(1.29768 + 0.749217i) q^{41} +(-4.81931 - 8.34729i) q^{43} -3.17452i q^{44} +(5.31181 - 3.06678i) q^{46} +10.5086i q^{47} +(0.500000 - 0.866025i) q^{49} +(-1.56145 - 0.901504i) q^{50} +(3.58726 - 0.362708i) q^{52} -3.60200 q^{53} +(-2.83804 + 4.91564i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(-1.79925 + 1.03880i) q^{58} +(2.40874 - 1.39069i) q^{59} +(-0.844395 - 1.46254i) q^{61} +(2.81931 - 4.88319i) q^{62} -1.00000 q^{64} +(-5.87901 - 2.64539i) q^{65} +(-10.0064 - 5.77720i) q^{67} +(2.78052 - 4.81599i) q^{68} +1.78801i q^{70} +(0.518313 - 0.299248i) q^{71} +0.423973i q^{73} +(1.54846 + 2.68202i) q^{74} +(-5.36028 - 3.09476i) q^{76} -3.17452 q^{77} +6.96254 q^{79} +(1.54846 + 0.894007i) q^{80} +(-0.749217 - 1.29768i) q^{82} +4.30228i q^{83} +(-8.61106 + 4.97160i) q^{85} +9.63862i q^{86} +(-1.58726 + 2.74922i) q^{88} +(14.1102 + 8.14654i) q^{89} +(-0.362708 - 3.58726i) q^{91} -6.13356 q^{92} +(5.25429 - 9.10069i) q^{94} +(5.53347 + 9.58425i) q^{95} +(-15.1461 + 8.74462i) q^{97} +(-0.866025 + 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 8 * q + 4 * q^4	\( 8 q + 4 q^{4} + 6 q^{10} - 6 q^{11} + 12 q^{13} - 8 q^{14} - 4 q^{16} - 2 q^{17} - 12 q^{19} + 6 q^{20} - 4 q^{22} - 8 q^{23} - 24 q^{25} - 6 q^{26} - 2 q^{29} + 6 q^{35} + 18 q^{37} + 4 q^{38} + 12 q^{40} - 12 q^{41} - 8 q^{43} + 18 q^{46} + 4 q^{49} - 12 q^{50} + 12 q^{52} + 12 q^{53} - 22 q^{55} - 4 q^{56} - 24 q^{58} - 18 q^{59} - 8 q^{61} - 8 q^{62} - 8 q^{64} - 46 q^{65} + 18 q^{67} + 2 q^{68} - 6 q^{71} + 6 q^{74} - 12 q^{76} + 8 q^{77} - 4 q^{79} + 6 q^{80} + 10 q^{82} - 54 q^{85} + 4 q^{88} + 18 q^{89} + 6 q^{91} - 16 q^{92} - 2 q^{94} + 50 q^{95} - 54 q^{97}+O(q^{100}) \) 8 * q + 4 * q^4 + 6 * q^10 - 6 * q^11 + 12 * q^13 - 8 * q^14 - 4 * q^16 - 2 * q^17 - 12 * q^19 + 6 * q^20 - 4 * q^22 - 8 * q^23 - 24 * q^25 - 6 * q^26 - 2 * q^29 + 6 * q^35 + 18 * q^37 + 4 * q^38 + 12 * q^40 - 12 * q^41 - 8 * q^43 + 18 * q^46 + 4 * q^49 - 12 * q^50 + 12 * q^52 + 12 * q^53 - 22 * q^55 - 4 * q^56 - 24 * q^58 - 18 * q^59 - 8 * q^61 - 8 * q^62 - 8 * q^64 - 46 * q^65 + 18 * q^67 + 2 * q^68 - 6 * q^71 + 6 * q^74 - 12 * q^76 + 8 * q^77 - 4 * q^79 + 6 * q^80 + 10 * q^82 - 54 * q^85 + 4 * q^88 + 18 * q^89 + 6 * q^91 - 16 * q^92 - 2 * q^94 + 50 * q^95 - 54 * q^97

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