LMFDB - Embedded newform 760.2.q.f.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [760,2,Mod(121,760)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(760, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("760.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 760 = 2^{3} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	760.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.06863055362$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.4601315889.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 $ x^8 - x^7 + 6x^6 - 3x^5 + 26x^4 - 14x^3 + 31x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.3
Root			$0.689667 + 1.19454i$ of defining polynomial
Character	$\chi$	$=$	760.121
Dual form			760.2.q.f.201.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.548719 + 0.950409i) q^{3} +(-0.500000 - 0.866025i) q^{5} -0.416295 q^{7} +(0.897815 - 1.55506i) q^{9} +2.17496 q^{11} +(2.13620 - 3.70001i) q^{13} +(0.548719 - 0.950409i) q^{15} +(0.602185 + 1.04302i) q^{17} +(-4.32112 - 0.572641i) q^{19} +(-0.228429 - 0.395651i) q^{21} +(0.224652 - 0.389109i) q^{23} +(-0.500000 + 0.866025i) q^{25} +5.26291 q^{27} +(2.94179 - 5.09532i) q^{29} +8.26291 q^{31} +(1.19344 + 2.06711i) q^{33} +(0.208148 + 0.360522i) q^{35} +6.80605 q^{37} +4.68870 q^{39} +(-2.30559 - 3.99339i) q^{41} +(2.80084 + 4.85120i) q^{43} -1.79563 q^{45} +(1.07375 - 1.85979i) q^{47} -6.82670 q^{49} +(-0.660861 + 1.14465i) q^{51} +(-5.00899 + 8.67582i) q^{53} +(-1.08748 - 1.88357i) q^{55} +(-1.82684 - 4.42105i) q^{57} +(1.74691 + 3.02574i) q^{59} +(4.86984 - 8.43481i) q^{61} +(-0.373756 + 0.647365i) q^{63} -4.27240 q^{65} +(-3.89307 + 6.74299i) q^{67} +0.493084 q^{69} +(6.09827 + 10.5625i) q^{71} +(0.534015 + 0.924942i) q^{73} -1.09744 q^{75} -0.905427 q^{77} +(-7.04300 - 12.1988i) q^{79} +(0.194414 + 0.336735i) q^{81} +9.73018 q^{83} +(0.602185 - 1.04302i) q^{85} +6.45686 q^{87} +(-4.19050 + 7.25815i) q^{89} +(-0.889291 + 1.54030i) q^{91} +(4.53402 + 7.85314i) q^{93} +(1.66464 + 4.02852i) q^{95} +(-3.91856 - 6.78714i) q^{97} +(1.95271 - 3.38220i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{3} - 4 q^{5} + 4 q^{7} - q^{9} - 8 q^{11} + q^{13} + q^{15} + 13 q^{17} + q^{19} + 12 q^{21} + 8 q^{23} - 4 q^{25} - 20 q^{27} - 3 q^{29} + 4 q^{31} - 15 q^{33} - 2 q^{35} + 20 q^{37} - 2 q^{39}+ \cdots + 30 q^{99}+O(q^{100}) $ 8 * q + q^3 - 4 * q^5 + 4 * q^7 - q^9 - 8 * q^11 + q^13 + q^15 + 13 * q^17 + q^19 + 12 * q^21 + 8 * q^23 - 4 * q^25 - 20 * q^27 - 3 * q^29 + 4 * q^31 - 15 * q^33 - 2 * q^35 + 20 * q^37 - 2 * q^39 - 8 * q^41 - 3 * q^43 + 2 * q^45 + 10 * q^47 + 12 * q^49 - 16 * q^51 - 11 * q^53 + 4 * q^55 - 29 * q^57 + q^59 - 25 * q^63 - 2 * q^65 - 8 * q^67 + 22 * q^69 - 4 * q^71 - 20 * q^73 - 2 * q^75 - 36 * q^77 - 3 * q^79 + 12 * q^81 - 30 * q^83 + 13 * q^85 + 24 * q^87 + 17 * q^89 - 4 * q^91 + 12 * q^93 + 4 * q^95 + 11 * q^97 + 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/760\mathbb{Z}\right)^\times$.

$n$	$191$	$381$	$401$	$457$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.548719	+	0.950409i	0.316803	+	0.548719i	0.979819	−	0.199886i	$-0.0640572\pi$
$3$	0.548719	+	0.950409i	0.316803	+	0.548719i	−0.663016	+	0.748605i	$0.730724\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−0.416295			−0.157345			−0.0786724	−	0.996901i	$-0.525068\pi$
$7$	−0.416295			−0.157345			−0.0786724	+	0.996901i	$0.525068\pi$
$8$		0			0
$9$	0.897815	−	1.55506i	0.299272	−	0.518354i
$10$		0			0
$11$	2.17496			0.655776			0.327888	−	0.944717i	$-0.393663\pi$
$11$	2.17496			0.655776			0.327888	+	0.944717i	$0.393663\pi$
$12$		0			0
$13$	2.13620	−	3.70001i	0.592475	−	1.02620i	−0.401422	−	0.915893i	$-0.631484\pi$
$13$	2.13620	−	3.70001i	0.592475	−	1.02620i	0.993898	−	0.110305i	$-0.0351826\pi$
$14$		0			0
$15$	0.548719	−	0.950409i	0.141679	−	0.245395i
$16$		0			0
$17$	0.602185	+	1.04302i	0.146051	+	0.252968i	0.929765	−	0.368154i	$-0.120010\pi$
$17$	0.602185	+	1.04302i	0.146051	+	0.252968i	−0.783713	+	0.621123i	$0.786677\pi$
$18$		0			0
$19$	−4.32112	−	0.572641i	−0.991333	−	0.131373i
$19$	−4.32112	−	0.572641i	−0.991333	−	0.131373i
$20$		0			0
$21$	−0.228429	−	0.395651i	−0.0498474	−	0.0863381i
$22$		0			0
$23$	0.224652	−	0.389109i	0.0468432	−	0.0811349i	−0.841653	−	0.540019i	$-0.818417\pi$
$23$	0.224652	−	0.389109i	0.0468432	−	0.0811349i	0.888496	+	0.458884i	$0.151751\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	5.26291			1.01285
$28$		0			0
$29$	2.94179	−	5.09532i	0.546276	−	0.946178i	−0.452249	−	0.891892i	$-0.649378\pi$
$29$	2.94179	−	5.09532i	0.546276	−	0.946178i	0.998525	−	0.0542864i	$-0.0172884\pi$
$30$		0			0
$31$	8.26291			1.48406			0.742031	−	0.670366i	$-0.233863\pi$
$31$	8.26291			1.48406			0.742031	+	0.670366i	$0.233863\pi$
$32$		0			0
$33$	1.19344	+	2.06711i	0.207752	+	0.359837i
$34$		0			0
$35$	0.208148	+	0.360522i	0.0351834	+	0.0609394i
$36$		0			0
$37$	6.80605			1.11891			0.559454	−	0.828862i	$-0.311011\pi$
$37$	6.80605			1.11891			0.559454	+	0.828862i	$0.311011\pi$
$38$		0			0
$39$	4.68870			0.750792
$40$		0			0
$41$	−2.30559	−	3.99339i	−0.360072	−	0.623663i	0.627900	−	0.778294i	$-0.283915\pi$
$41$	−2.30559	−	3.99339i	−0.360072	−	0.623663i	−0.987972	+	0.154631i	$0.950581\pi$
$42$		0			0
$43$	2.80084	+	4.85120i	0.427124	+	0.739800i	0.996616	−	0.0821964i	$-0.0261935\pi$
$43$	2.80084	+	4.85120i	0.427124	+	0.739800i	−0.569492	+	0.821997i	$0.692860\pi$
$44$		0			0
$45$	−1.79563			−0.267677
$46$		0			0
$47$	1.07375	−	1.85979i	0.156622	−	0.271278i	−0.777026	−	0.629468i	$-0.783273\pi$
$47$	1.07375	−	1.85979i	0.156622	−	0.271278i	0.933649	+	0.358190i	$0.116606\pi$
$48$		0			0
$49$	−6.82670			−0.975243
$50$		0			0
$51$	−0.660861	+	1.14465i	−0.0925391	+	0.160282i
$52$		0			0
$53$	−5.00899	+	8.67582i	−0.688037	+	1.19172i	0.284435	+	0.958695i	$0.408194\pi$
$53$	−5.00899	+	8.67582i	−0.688037	+	1.19172i	−0.972472	+	0.233020i	$0.925139\pi$
$54$		0			0
$55$	−1.08748	−	1.88357i	−0.146636	−	0.253981i
$56$		0			0
$57$	−1.82684	−	4.42105i	−0.241971	−	0.585583i
$58$		0			0
$59$	1.74691	+	3.02574i	0.227428	+	0.393917i	0.957045	−	0.289939i	$-0.0936349\pi$
$59$	1.74691	+	3.02574i	0.227428	+	0.393917i	−0.729617	+	0.683856i	$0.760302\pi$
$60$		0			0
$61$	4.86984	−	8.43481i	0.623519	−	1.07997i	−0.365306	−	0.930887i	$-0.619036\pi$
$61$	4.86984	−	8.43481i	0.623519	−	1.07997i	0.988825	−	0.149079i	$-0.0476310\pi$
$62$		0			0
$63$	−0.373756	+	0.647365i	−0.0470888	+	0.0815603i
$64$		0			0
$65$	−4.27240			−0.529926
$66$		0			0
$67$	−3.89307	+	6.74299i	−0.475614	+	0.823787i	−0.999610	−	0.0279334i	$-0.991107\pi$
$67$	−3.89307	+	6.74299i	−0.475614	+	0.823787i	0.523996	+	0.851721i	$0.324441\pi$
$68$		0			0
$69$	0.493084			0.0593604
$70$		0			0
$71$	6.09827	+	10.5625i	0.723731	+	1.25354i	0.959494	+	0.281729i	$0.0909079\pi$
$71$	6.09827	+	10.5625i	0.723731	+	1.25354i	−0.235763	+	0.971811i	$0.575759\pi$
$72$		0			0
$73$	0.534015	+	0.924942i	0.0625018	+	0.108256i	0.895583	−	0.444894i	$-0.146759\pi$
$73$	0.534015	+	0.924942i	0.0625018	+	0.108256i	−0.833081	+	0.553151i	$0.813425\pi$
$74$		0			0
$75$	−1.09744			−0.126721
$76$		0			0
$77$	−0.905427			−0.103183
$78$		0			0
$79$	−7.04300	−	12.1988i	−0.792400	−	1.37248i	−0.924477	−	0.381237i	$-0.875498\pi$
$79$	−7.04300	−	12.1988i	−0.792400	−	1.37248i	0.132078	−	0.991239i	$-0.457835\pi$
$80$		0			0
$81$	0.194414	+	0.336735i	0.0216016	+	0.0374150i
$82$		0			0
$83$	9.73018			1.06803			0.534013	−	0.845476i	$-0.320683\pi$
$83$	9.73018			1.06803			0.534013	+	0.845476i	$0.320683\pi$
$84$		0			0
$85$	0.602185	−	1.04302i	0.0653162	−	0.113131i
$86$		0			0
$87$	6.45686			0.692248
$88$		0			0
$89$	−4.19050	+	7.25815i	−0.444192	+	0.769363i	−0.997996	−	0.0632844i	$-0.979842\pi$
$89$	−4.19050	+	7.25815i	−0.444192	+	0.769363i	0.553804	+	0.832647i	$0.313176\pi$
$90$		0			0
$91$	−0.889291	+	1.54030i	−0.0932230	+	0.161467i
$92$		0			0
$93$	4.53402	+	7.85314i	0.470155	+	0.814333i
$94$		0			0
$95$	1.66464	+	4.02852i	0.170788	+	0.413318i
$96$		0			0
$97$	−3.91856	−	6.78714i	−0.397869	−	0.689130i	0.595593	−	0.803286i	$-0.296917\pi$
$97$	−3.91856	−	6.78714i	−0.397869	−	0.689130i	−0.993463	+	0.114156i	$0.963584\pi$
$98$		0			0
$99$	1.95271	−	3.38220i	0.196255	−	0.339924i
$100$		0			0
$101$	−0.470224	+	0.814452i	−0.0467891	+	0.0810410i	−0.888471	−	0.458932i	$-0.848232\pi$
$101$	−0.470224	+	0.814452i	−0.0467891	+	0.0810410i	0.841682	+	0.539973i	$0.181566\pi$
$102$		0			0
$103$	−5.55070			−0.546926			−0.273463	−	0.961882i	$-0.588169\pi$
$103$	−5.55070			−0.546926			−0.273463	+	0.961882i	$0.588169\pi$
$104$		0			0
$105$	−0.228429	+	0.395651i	−0.0222924	+	0.0386116i
$106$		0			0
$107$	−1.74557			−0.168751			−0.0843754	−	0.996434i	$-0.526889\pi$
$107$	−1.74557			−0.168751			−0.0843754	+	0.996434i	$0.526889\pi$
$108$		0			0
$109$	−8.49752	−	14.7181i	−0.813914	−	1.40974i	−0.910105	−	0.414378i	$-0.863999\pi$
$109$	−8.49752	−	14.7181i	−0.813914	−	1.40974i	0.0961903	−	0.995363i	$-0.469334\pi$
$110$		0			0
$111$	3.73461	+	6.46853i	0.354473	+	0.613966i
$112$		0			0
$113$	−10.9385			−1.02901			−0.514504	−	0.857488i	$-0.672024\pi$
$113$	−10.9385			−1.02901			−0.514504	+	0.857488i	$0.672024\pi$
$114$		0			0
$115$	−0.449305			−0.0418979
$116$		0			0
$117$	−3.83582	−	6.64384i	−0.354622	−	0.614223i
$118$		0			0
$119$	−0.250687	−	0.434203i	−0.0229804	−	0.0398033i
$120$		0			0
$121$	−6.26954			−0.569958
$122$		0			0
$123$	2.53024	−	4.38250i	0.228144	−	0.395157i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	1.95944	−	3.39384i	0.173872	−	0.301155i	−0.765898	−	0.642962i	$-0.777705\pi$
$127$	1.95944	−	3.39384i	0.173872	−	0.301155i	0.939770	+	0.341807i	$0.111039\pi$
$128$		0			0
$129$	−3.07375	+	5.32389i	−0.270628	+	0.468742i
$130$		0			0
$131$	6.14178	+	10.6379i	0.536610	+	0.929435i	0.999084	+	0.0428023i	$0.0136286\pi$
$131$	6.14178	+	10.6379i	0.536610	+	0.929435i	−0.462474	+	0.886633i	$0.653038\pi$
$132$		0			0
$133$	1.79886	+	0.238388i	0.155981	+	0.0206709i
$134$		0			0
$135$	−2.63145	−	4.55781i	−0.226479	−	0.392274i
$136$		0			0
$137$	−5.04577	+	8.73953i	−0.431089	+	0.746669i	−0.996967	−	0.0778202i	$-0.975204\pi$
$137$	−5.04577	+	8.73953i	−0.431089	+	0.746669i	0.565878	+	0.824489i	$0.308537\pi$
$138$		0			0
$139$	−1.41810	+	2.45621i	−0.120281	+	0.208333i	−0.919879	−	0.392203i	$-0.871713\pi$
$139$	−1.41810	+	2.45621i	−0.120281	+	0.208333i	0.799597	+	0.600537i	$0.205046\pi$
$140$		0			0
$141$	2.35674			0.198474
$142$		0			0
$143$	4.64616	−	8.04738i	0.388531	−	0.672956i
$144$		0			0
$145$	−5.88357			−0.488604
$146$		0			0
$147$	−3.74594	−	6.48816i	−0.308960	−	0.535134i
$148$		0			0
$149$	−8.61398	−	14.9198i	−0.705685	−	1.22228i	−0.966444	−	0.256878i	$-0.917306\pi$
$149$	−8.61398	−	14.9198i	−0.705685	−	1.22228i	0.260759	−	0.965404i	$-0.416027\pi$
$150$		0			0
$151$	−11.6586			−0.948760			−0.474380	−	0.880320i	$-0.657328\pi$
$151$	−11.6586			−0.948760			−0.474380	+	0.880320i	$0.657328\pi$
$152$		0			0
$153$	2.16260			0.174836
$154$		0			0
$155$	−4.13145	−	7.15589i	−0.331846	−	0.574775i
$156$		0			0
$157$	6.17837	+	10.7013i	0.493088	+	0.854053i	0.999968	−	0.00796326i	$-0.00253481\pi$
$157$	6.17837	+	10.7013i	0.493088	+	0.854053i	−0.506881	+	0.862016i	$0.669201\pi$
$158$		0			0
$159$	−10.9941			−0.871889
$160$		0			0
$161$	−0.0935217	+	0.161984i	−0.00737055	+	0.0127662i
$162$		0			0
$163$	3.64721			0.285671			0.142836	−	0.989746i	$-0.454378\pi$
$163$	3.64721			0.285671			0.142836	+	0.989746i	$0.454378\pi$
$164$		0			0
$165$	1.19344	−	2.06711i	0.0929095	−	0.160924i
$166$		0			0
$167$	−8.87030	+	15.3638i	−0.686405	+	1.18889i	0.286589	+	0.958054i	$0.407479\pi$
$167$	−8.87030	+	15.3638i	−0.686405	+	1.18889i	−0.972993	+	0.230834i	$0.925855\pi$
$168$		0			0
$169$	−2.62671	−	4.54959i	−0.202054	−	0.349968i
$170$		0			0
$171$	−4.77006	+	6.20548i	−0.364775	+	0.474545i
$172$		0			0
$173$	11.8134	+	20.4615i	0.898158	+	1.55566i	0.829847	+	0.557992i	$0.188428\pi$
$173$	11.8134	+	20.4615i	0.898158	+	1.55566i	0.0683116	+	0.997664i	$0.478239\pi$
$174$		0			0
$175$	0.208148	−	0.360522i	0.0157345	−	0.0272529i
$176$		0			0
$177$	−1.91713	+	3.32056i	−0.144100	+	0.249589i
$178$		0			0
$179$	−19.0991			−1.42753			−0.713767	−	0.700383i	$-0.753012\pi$
$179$	−19.0991			−1.42753			−0.713767	+	0.700383i	$0.753012\pi$
$180$		0			0
$181$	6.46908	−	11.2048i	0.480843	−	0.832844i	−0.518916	−	0.854826i	$-0.673664\pi$
$181$	6.46908	−	11.2048i	0.480843	−	0.832844i	0.999758	+	0.0219813i	$0.00699743\pi$
$182$		0			0
$183$	10.6887			0.790131
$184$		0			0
$185$	−3.40302	−	5.89421i	−0.250195	−	0.433351i
$186$		0			0
$187$	1.30973	+	2.26852i	0.0957770	+	0.165891i
$188$		0			0
$189$	−2.19092			−0.159366
$190$		0			0
$191$	−15.4824			−1.12027			−0.560133	−	0.828403i	$-0.689250\pi$
$191$	−15.4824			−1.12027			−0.560133	+	0.828403i	$0.689250\pi$
$192$		0			0
$193$	4.83763	+	8.37901i	0.348220	+	0.603135i	0.985933	−	0.167139i	$-0.0534529\pi$
$193$	4.83763	+	8.37901i	0.348220	+	0.603135i	−0.637713	+	0.770274i	$0.720120\pi$
$194$		0			0
$195$	−2.34435	−	4.06053i	−0.167882	−	0.290781i
$196$		0			0
$197$	7.68567			0.547581			0.273791	−	0.961789i	$-0.411722\pi$
$197$	7.68567			0.547581			0.273791	+	0.961789i	$0.411722\pi$
$198$		0			0
$199$	1.02664	−	1.77819i	0.0727764	−	0.126052i	−0.827341	−	0.561700i	$-0.810147\pi$
$199$	1.02664	−	1.77819i	0.0727764	−	0.126052i	0.900117	+	0.435648i	$0.143481\pi$
$200$		0			0
$201$	−8.54480			−0.602704
$202$		0			0
$203$	−1.22465	+	2.12116i	−0.0859537	+	0.148876i
$204$		0			0
$205$	−2.30559	+	3.99339i	−0.161029	+	0.278911i
$206$		0			0
$207$	−0.403392	−	0.698696i	−0.0280377	−	0.0485627i
$208$		0			0
$209$	−9.39828	−	1.24547i	−0.650092	−	0.0861512i
$210$		0			0
$211$	8.75069	+	15.1566i	0.602422	+	1.04343i	0.992453	+	0.122624i	$0.0391309\pi$
$211$	8.75069	+	15.1566i	0.602422	+	1.04343i	−0.390031	+	0.920802i	$0.627536\pi$
$212$		0			0
$213$	−6.69247	+	11.5917i	−0.458561	+	0.794250i
$214$		0			0
$215$	2.80084	−	4.85120i	0.191016	−	0.330849i
$216$		0			0
$217$	−3.43981			−0.233510
$218$		0			0
$219$	−0.586049	+	1.01507i	−0.0396015	+	0.0685918i
$220$		0			0
$221$	5.14556			0.346128
$222$		0			0
$223$	−6.58928	−	11.4130i	−0.441251	−	0.764269i	0.556532	−	0.830826i	$-0.312132\pi$
$223$	−6.58928	−	11.4130i	−0.441251	−	0.764269i	−0.997783	+	0.0665573i	$0.978798\pi$
$224$		0			0
$225$	0.897815	+	1.55506i	0.0598543	+	0.103671i
$226$		0			0
$227$	−9.45520			−0.627563			−0.313782	−	0.949495i	$-0.601596\pi$
$227$	−9.45520			−0.627563			−0.313782	+	0.949495i	$0.601596\pi$
$228$		0			0
$229$	−4.93363			−0.326023			−0.163012	−	0.986624i	$-0.552121\pi$
$229$	−4.93363			−0.326023			−0.163012	+	0.986624i	$0.552121\pi$
$230$		0			0
$231$	−0.496825	−	0.860527i	−0.0326887	−	0.0566185i
$232$		0			0
$233$	10.5243	+	18.2287i	0.689473	+	1.19420i	0.972009	+	0.234945i	$0.0754911\pi$
$233$	10.5243	+	18.2287i	0.689473	+	1.19420i	−0.282536	+	0.959257i	$0.591176\pi$
$234$		0			0
$235$	−2.14750			−0.140087
$236$		0			0
$237$	7.72926	−	13.3875i	0.502069	−	0.869610i
$238$		0			0
$239$	−12.4047			−0.802393			−0.401197	−	0.915992i	$-0.631406\pi$
$239$	−12.4047			−0.802393			−0.401197	+	0.915992i	$0.631406\pi$
$240$		0			0
$241$	6.25097	−	10.8270i	0.402661	−	0.697429i	−0.591385	−	0.806389i	$-0.701419\pi$
$241$	6.25097	−	10.8270i	0.402661	−	0.697429i	0.994046	+	0.108960i	$0.0347521\pi$
$242$		0			0
$243$	7.68100	−	13.3039i	0.492737	−	0.853445i
$244$		0			0
$245$	3.41335	+	5.91209i	0.218071	+	0.377710i
$246$		0			0
$247$	−11.3496	+	14.7649i	−0.722155	+	0.939468i
$248$		0			0
$249$	5.33914	+	9.24766i	0.338354	+	0.586047i
$250$		0			0
$251$	0.815080	−	1.41176i	0.0514474	−	0.0891095i	−0.839155	−	0.543893i	$-0.816950\pi$
$251$	0.815080	−	1.41176i	0.0514474	−	0.0891095i	0.890602	+	0.454783i	$0.150283\pi$
$252$		0			0
$253$	0.488611	−	0.846298i	0.0307187	−	0.0532063i
$254$		0			0
$255$	1.32172			0.0827695
$256$		0			0
$257$	−6.56937	+	11.3785i	−0.409786	+	0.709770i	−0.994866	−	0.101206i	$-0.967730\pi$
$257$	−6.56937	+	11.3785i	−0.409786	+	0.709770i	0.585080	+	0.810976i	$0.301063\pi$
$258$		0			0
$259$	−2.83333			−0.176054
$260$		0			0
$261$	−5.28236	−	9.14931i	−0.326970	−	0.566328i
$262$		0			0
$263$	7.12491	+	12.3407i	0.439341	+	0.760960i	0.997639	−	0.0686803i	$-0.0218788\pi$
$263$	7.12491	+	12.3407i	0.439341	+	0.760960i	−0.558298	+	0.829640i	$0.688545\pi$
$264$		0			0
$265$	10.0180			0.615399
$266$		0			0
$267$	−9.19762			−0.562885
$268$		0			0
$269$	7.42053	+	12.8527i	0.452438	+	0.783646i	0.998537	−	0.0540751i	$-0.0172210\pi$
$269$	7.42053	+	12.8527i	0.452438	+	0.783646i	−0.546099	+	0.837721i	$0.683888\pi$
$270$		0			0
$271$	6.83826	+	11.8442i	0.415395	+	0.719485i	0.995470	−	0.0950781i	$-0.0303101\pi$
$271$	6.83826	+	11.8442i	0.415395	+	0.719485i	−0.580075	+	0.814563i	$0.696977\pi$
$272$		0			0
$273$	−1.95188			−0.118133
$274$		0			0
$275$	−1.08748	+	1.88357i	−0.0655776	+	0.113584i
$276$		0			0
$277$	25.5605			1.53578			0.767890	−	0.640581i	$-0.221307\pi$
$277$	25.5605			1.53578			0.767890	+	0.640581i	$0.221307\pi$
$278$		0			0
$279$	7.41856	−	12.8493i	0.444137	−	0.769269i
$280$		0			0
$281$	−11.0070	+	19.0647i	−0.656623	+	1.13730i	0.324861	+	0.945762i	$0.394682\pi$
$281$	−11.0070	+	19.0647i	−0.656623	+	1.13730i	−0.981484	+	0.191543i	$0.938651\pi$
$282$		0			0
$283$	0.169893	+	0.294263i	0.0100991	+	0.0174921i	0.871031	−	0.491228i	$-0.163452\pi$
$283$	0.169893	+	0.294263i	0.0100991	+	0.0174921i	−0.860932	+	0.508721i	$0.830119\pi$
$284$		0			0
$285$	−2.91533	+	3.79261i	−0.172689	+	0.224655i
$286$		0			0
$287$	0.959805	+	1.66243i	0.0566555	+	0.0981302i
$288$		0			0
$289$	7.77475	−	13.4663i	0.457338	−	0.792133i
$290$		0			0
$291$	4.30038	−	7.44847i	0.252093	−	0.436637i
$292$		0			0
$293$	3.36302			0.196470			0.0982349	−	0.995163i	$-0.468680\pi$
$293$	3.36302			0.196470			0.0982349	+	0.995163i	$0.468680\pi$
$294$		0			0
$295$	1.74691	−	3.02574i	0.101709	−	0.176165i
$296$		0			0
$297$	11.4466			0.664201
$298$		0			0
$299$	−0.959805	−	1.66243i	−0.0555070	−	0.0961409i
$300$		0			0
$301$	−1.16598	−	2.01953i	−0.0672058	−	0.116404i
$302$		0			0
$303$	−1.03208			−0.0592917
$304$		0			0
$305$	−9.73968			−0.557692
$306$		0			0
$307$	−9.28840	−	16.0880i	−0.530117	−	0.918189i	−0.999383	−	0.0351324i	$-0.988815\pi$
$307$	−9.28840	−	16.0880i	−0.530117	−	0.918189i	0.469266	−	0.883057i	$-0.344519\pi$
$308$		0			0
$309$	−3.04577	−	5.27543i	−0.173268	−	0.300109i
$310$		0			0
$311$	−13.4628			−0.763403			−0.381701	−	0.924286i	$-0.624662\pi$
$311$	−13.4628			−0.763403			−0.381701	+	0.924286i	$0.624662\pi$
$312$		0			0
$313$	−0.332510	+	0.575924i	−0.0187946	+	0.0325532i	−0.875270	−	0.483635i	$-0.839316\pi$
$313$	−0.332510	+	0.575924i	−0.0187946	+	0.0325532i	0.856475	+	0.516188i	$0.172650\pi$
$314$		0			0
$315$	0.747512			0.0421175
$316$		0			0
$317$	−0.458467	+	0.794088i	−0.0257501	+	0.0446004i	−0.878613	−	0.477534i	$-0.841531\pi$
$317$	−0.458467	+	0.794088i	−0.0257501	+	0.0446004i	0.852863	+	0.522134i	$0.174864\pi$
$318$		0			0
$319$	6.39828	−	11.0821i	0.358235	−	0.620481i
$320$		0			0
$321$	−0.957829	−	1.65901i	−0.0534608	−	0.0925968i
$322$		0			0
$323$	−2.00484	−	4.85183i	−0.111552	−	0.269963i
$324$		0			0
$325$	2.13620	+	3.70001i	0.118495	+	0.205240i
$326$		0			0
$327$	9.32550	−	16.1522i	0.515701	−	0.893221i
$328$		0			0
$329$	−0.446996	+	0.774220i	−0.0246437	+	0.0426841i
$330$		0			0
$331$	−3.93003			−0.216014			−0.108007	−	0.994150i	$-0.534447\pi$
$331$	−3.93003			−0.216014			−0.108007	+	0.994150i	$0.534447\pi$
$332$		0			0
$333$	6.11057	−	10.5838i	0.334857	−	0.579990i
$334$		0			0
$335$	7.78614			0.425402
$336$		0			0
$337$	−13.6517	−	23.6455i	−0.743657	−	1.28805i	−0.950819	−	0.309746i	$-0.899756\pi$
$337$	−13.6517	−	23.6455i	−0.743657	−	1.28805i	0.207162	−	0.978307i	$-0.433577\pi$
$338$		0			0
$339$	−6.00217	−	10.3961i	−0.325993	−	0.564637i
$340$		0			0
$341$	17.9715			0.973212
$342$		0			0
$343$	5.75599			0.310794
$344$		0			0
$345$	−0.246542	−	0.427023i	−0.0132734	−	0.0229902i
$346$		0			0
$347$	11.0637	+	19.1630i	0.593933	+	1.02872i	0.993697	+	0.112104i	$0.0357589\pi$
$347$	11.0637	+	19.1630i	0.593933	+	1.02872i	−0.399763	+	0.916618i	$0.630908\pi$
$348$		0			0
$349$	19.7812			1.05886			0.529431	−	0.848353i	$-0.322406\pi$
$349$	19.7812			1.05886			0.529431	+	0.848353i	$0.322406\pi$
$350$		0			0
$351$	11.2426	−	19.4728i	0.600087	−	1.03938i
$352$		0			0
$353$	16.4680			0.876504			0.438252	−	0.898852i	$-0.355598\pi$
$353$	16.4680			0.876504			0.438252	+	0.898852i	$0.355598\pi$
$354$		0			0
$355$	6.09827	−	10.5625i	0.323663	−	0.560600i
$356$		0			0
$357$	0.275114	−	0.476511i	0.0145606	−	0.0252196i
$358$		0			0
$359$	3.99101	+	6.91264i	0.210638	+	0.364835i	0.951914	−	0.306365i	$-0.0991127\pi$
$359$	3.99101	+	6.91264i	0.210638	+	0.364835i	−0.741277	+	0.671200i	$0.765779\pi$
$360$		0			0
$361$	18.3442	+	4.94890i	0.965482	+	0.260469i
$362$		0			0
$363$	−3.44021	−	5.95863i	−0.180564	−	0.312747i
$364$		0			0
$365$	0.534015	−	0.924942i	0.0279516	−	0.0484137i
$366$		0			0
$367$	−3.82397	+	6.62331i	−0.199610	+	0.345734i	−0.948402	−	0.317071i	$-0.897301\pi$
$367$	−3.82397	+	6.62331i	−0.199610	+	0.345734i	0.748792	+	0.662805i	$0.230634\pi$
$368$		0			0
$369$	−8.27996			−0.431037
$370$		0			0
$371$	2.08522	−	3.61170i	0.108259	−	0.187510i
$372$		0			0
$373$	30.6572			1.58737			0.793684	−	0.608330i	$-0.208160\pi$
$373$	30.6572			1.58737			0.793684	+	0.608330i	$0.208160\pi$
$374$		0			0
$375$	0.548719	+	0.950409i	0.0283357	+	0.0490789i
$376$		0			0
$377$	−12.5685	−	21.7693i	−0.647310	−	1.12117i
$378$		0			0
$379$	−32.4123			−1.66491			−0.832453	−	0.554096i	$-0.813064\pi$
$379$	−32.4123			−1.66491			−0.832453	+	0.554096i	$0.813064\pi$
$380$		0			0
$381$	4.30072			0.220333
$382$		0			0
$383$	−6.06569	−	10.5061i	−0.309942	−	0.536835i	0.668407	−	0.743795i	$-0.266976\pi$
$383$	−6.06569	−	10.5061i	−0.309942	−	0.536835i	−0.978349	+	0.206960i	$0.933643\pi$
$384$		0			0
$385$	0.452714	+	0.784123i	0.0230724	+	0.0399626i
$386$		0			0
$387$	10.0585			0.511304
$388$		0			0
$389$	4.06001	−	7.03215i	0.205851	−	0.356544i	−0.744553	−	0.667564i	$-0.767337\pi$
$389$	4.06001	−	7.03215i	0.205851	−	0.356544i	0.950404	+	0.311020i	$0.100670\pi$
$390$		0			0
$391$	0.541129			0.0273661
$392$		0			0
$393$	−6.74022	+	11.6744i	−0.339999	+	0.588896i
$394$		0			0
$395$	−7.04300	+	12.1988i	−0.354372	+	0.613790i
$396$		0			0
$397$	12.9848	+	22.4903i	0.651688	+	1.12876i	0.982713	+	0.185135i	$0.0592721\pi$
$397$	12.9848	+	22.4903i	0.651688	+	1.12876i	−0.331025	+	0.943622i	$0.607395\pi$
$398$		0			0
$399$	0.760504	+	1.84046i	0.0380728	+	0.0921385i
$400$		0			0
$401$	−1.47400	−	2.55304i	−0.0736081	−	0.127493i	0.826872	−	0.562390i	$-0.190118\pi$
$401$	−1.47400	−	2.55304i	−0.0736081	−	0.127493i	−0.900480	+	0.434897i	$0.856785\pi$
$402$		0			0
$403$	17.6512	−	30.5728i	0.879270	−	1.52294i
$404$		0			0
$405$	0.194414	−	0.336735i	0.00966051	−	0.0167325i
$406$		0			0
$407$	14.8029			0.733753
$408$		0			0
$409$	2.52301	−	4.36998i	0.124755	−	0.216081i	−0.796882	−	0.604135i	$-0.793519\pi$
$409$	2.52301	−	4.36998i	0.124755	−	0.216081i	0.921637	+	0.388053i	$0.126852\pi$
$410$		0			0
$411$	−11.0748			−0.546282
$412$		0			0
$413$	−0.727231	−	1.25960i	−0.0357847	−	0.0619809i
$414$		0			0
$415$	−4.86509	−	8.42659i	−0.238818	−	0.413645i
$416$		0			0
$417$	−3.11255			−0.152422
$418$		0			0
$419$	27.7613			1.35623			0.678113	−	0.734958i	$-0.262798\pi$
$419$	27.7613			1.35623			0.678113	+	0.734958i	$0.262798\pi$
$420$		0			0
$421$	4.65809	+	8.06805i	0.227021	+	0.393213i	0.956924	−	0.290339i	$-0.0937679\pi$
$421$	4.65809	+	8.06805i	0.227021	+	0.393213i	−0.729903	+	0.683551i	$0.760435\pi$
$422$		0			0
$423$	−1.92805	−	3.33949i	−0.0937451	−	0.162371i
$424$		0			0
$425$	−1.20437			−0.0584206
$426$		0			0
$427$	−2.02729	+	3.51137i	−0.0981075	+	0.169927i
$428$		0			0
$429$	10.1977			0.492352
$430$		0			0
$431$	−11.3656	+	19.6859i	−0.547463	+	0.948234i	0.450984	+	0.892532i	$0.351073\pi$
$431$	−11.3656	+	19.6859i	−0.547463	+	0.948234i	−0.998447	+	0.0557024i	$0.982260\pi$
$432$		0			0
$433$	−13.0700	+	22.6379i	−0.628104	+	1.08791i	0.359827	+	0.933019i	$0.382836\pi$
$433$	−13.0700	+	22.6379i	−0.628104	+	1.08791i	−0.987932	+	0.154890i	$0.950498\pi$
$434$		0			0
$435$	−3.22843	−	5.59180i	−0.154791	−	0.268106i
$436$		0			0
$437$	−1.19357	+	1.55274i	−0.0570962	+	0.0742778i
$438$		0			0
$439$	18.8272	+	32.6096i	0.898571	+	1.55637i	0.829321	+	0.558772i	$0.188727\pi$
$439$	18.8272	+	32.6096i	0.898571	+	1.55637i	0.0692500	+	0.997599i	$0.477939\pi$
$440$		0			0
$441$	−6.12911	+	10.6159i	−0.291862	+	0.505520i
$442$		0			0
$443$	11.6519	−	20.1817i	0.553599	−	0.958862i	−0.444412	−	0.895822i	$-0.646587\pi$
$443$	11.6519	−	20.1817i	0.553599	−	0.958862i	0.998011	−	0.0630391i	$-0.0200793\pi$
$444$		0			0
$445$	8.38099			0.397297
$446$		0			0
$447$	9.45331	−	16.3736i	0.447126	−	0.774445i
$448$		0			0
$449$	14.1926			0.669790			0.334895	−	0.942256i	$-0.391299\pi$
$449$	14.1926			0.669790			0.334895	+	0.942256i	$0.391299\pi$
$450$		0			0
$451$	−5.01456	−	8.68548i	−0.236127	−	0.408983i
$452$		0			0
$453$	−6.39727	−	11.0804i	−0.300570	−	0.520603i
$454$		0			0
$455$	1.77858			0.0833812
$456$		0			0
$457$	−8.95253			−0.418782			−0.209391	−	0.977832i	$-0.567148\pi$
$457$	−8.95253			−0.418782			−0.209391	+	0.977832i	$0.567148\pi$
$458$		0			0
$459$	3.16925	+	5.48929i	0.147928	+	0.256218i
$460$		0			0
$461$	5.02520	+	8.70391i	0.234047	+	0.405381i	0.958995	−	0.283422i	$-0.0914697\pi$
$461$	5.02520	+	8.70391i	0.234047	+	0.405381i	−0.724948	+	0.688803i	$0.758136\pi$
$462$		0			0
$463$	−23.0903			−1.07310			−0.536550	−	0.843869i	$-0.680273\pi$
$463$	−23.0903			−1.07310			−0.536550	+	0.843869i	$0.680273\pi$
$464$		0			0
$465$	4.53402	−	7.85314i	0.210260	−	0.364181i
$466$		0			0
$467$	37.9186			1.75466			0.877332	−	0.479885i	$-0.159321\pi$
$467$	37.9186			1.75466			0.877332	+	0.479885i	$0.159321\pi$
$468$		0			0
$469$	1.62067	−	2.80708i	0.0748354	−	0.129619i
$470$		0			0
$471$	−6.78038	+	11.7440i	−0.312424	+	0.541133i
$472$		0			0
$473$	6.09172	+	10.5512i	0.280098	+	0.485143i
$474$		0			0
$475$	2.65648	−	3.45588i	0.121888	−	0.158567i
$476$		0			0
$477$	8.99428	+	15.5786i	0.411820	+	0.713293i
$478$		0			0
$479$	13.2015	−	22.8656i	0.603190	−	1.04476i	−0.389145	−	0.921177i	$-0.627229\pi$
$479$	13.2015	−	22.8656i	0.603190	−	1.04476i	0.992335	−	0.123579i	$-0.0394373\pi$
$480$		0			0
$481$	14.5391	−	25.1824i	0.662925	−	1.14822i
$482$		0			0
$483$	−0.205269			−0.00934005
$484$		0			0
$485$	−3.91856	+	6.78714i	−0.177933	+	0.308188i
$486$		0			0
$487$	−38.5718			−1.74786			−0.873928	−	0.486055i	$-0.838435\pi$
$487$	−38.5718			−1.74786			−0.873928	+	0.486055i	$0.838435\pi$
$488$		0			0
$489$	2.00129	+	3.46634i	0.0905016	+	0.156753i
$490$		0			0
$491$	1.09823	+	1.90220i	0.0495626	+	0.0858449i	0.889742	−	0.456463i	$-0.150884\pi$
$491$	1.09823	+	1.90220i	0.0495626	+	0.0858449i	−0.840180	+	0.542308i	$0.817551\pi$
$492$		0			0
$493$	7.08600			0.319138
$494$		0			0
$495$	−3.90543			−0.175536
$496$		0			0
$497$	−2.53868	−	4.39713i	−0.113875	−	0.197238i
$498$		0			0
$499$	−5.23705	−	9.07083i	−0.234442	−	0.406066i	0.724668	−	0.689098i	$-0.241993\pi$
$499$	−5.23705	−	9.07083i	−0.234442	−	0.406066i	−0.959111	+	0.283032i	$0.908660\pi$
$500$		0			0
$501$	−19.4692			−0.869821
$502$		0			0
$503$	3.55232	−	6.15280i	0.158390	−	0.274340i	−0.775898	−	0.630858i	$-0.782703\pi$
$503$	3.55232	−	6.15280i	0.158390	−	0.274340i	0.934288	+	0.356518i	$0.116036\pi$
$504$		0			0
$505$	0.940448			0.0418494
$506$		0			0
$507$	2.88265	−	4.99289i	0.128023	−	0.221742i
$508$		0			0
$509$	−7.28996	+	12.6266i	−0.323122	+	0.559663i	−0.981130	−	0.193347i	$-0.938066\pi$
$509$	−7.28996	+	12.6266i	−0.323122	+	0.559663i	0.658009	+	0.753010i	$0.271399\pi$
$510$		0			0
$511$	−0.222308	−	0.385049i	−0.00983433	−	0.0170336i
$512$		0			0
$513$	−22.7417	−	3.01376i	−1.00407	−	0.133061i
$514$		0			0
$515$	2.77535	+	4.80704i	0.122296	+	0.211824i
$516$		0			0
$517$	2.33536	−	4.04497i	0.102709	−	0.177897i
$518$		0			0
$519$	−12.9645	+	22.4552i	−0.569079	+	0.985673i
$520$		0			0
$521$	−0.438723			−0.0192208			−0.00961041	−	0.999954i	$-0.503059\pi$
$521$	−0.438723			−0.0192208			−0.00961041	+	0.999954i	$0.503059\pi$
$522$		0			0
$523$	−3.68672	+	6.38559i	−0.161209	+	0.279222i	−0.935303	−	0.353849i	$-0.884873\pi$
$523$	−3.68672	+	6.38559i	−0.161209	+	0.279222i	0.774094	+	0.633071i	$0.218206\pi$
$524$		0			0
$525$	0.456859			0.0199389
$526$		0			0
$527$	4.97580	+	8.61834i	0.216749	+	0.375421i
$528$		0			0
$529$	11.3991	+	19.7438i	0.495611	+	0.858424i
$530$		0			0
$531$	6.27361			0.272251
$532$		0			0
$533$	−19.7008			−0.853335
$534$		0			0
$535$	0.872786	+	1.51171i	0.0377338	+	0.0653569i
$536$		0			0
$537$	−10.4800	−	18.1520i	−0.452247	−	0.783315i
$538$		0			0
$539$	−14.8478			−0.639541
$540$		0			0
$541$	20.8239	−	36.0681i	0.895291	−	1.55069i	0.0618460	−	0.998086i	$-0.480301\pi$
$541$	20.8239	−	36.0681i	0.895291	−	1.55069i	0.833445	−	0.552603i	$-0.186365\pi$
$542$		0			0
$543$	14.1988			0.609330
$544$		0			0
$545$	−8.49752	+	14.7181i	−0.363994	+	0.630455i
$546$		0			0
$547$	−1.21890	+	2.11120i	−0.0521164	+	0.0902682i	−0.890907	−	0.454186i	$-0.849930\pi$
$547$	−1.21890	+	2.11120i	−0.0521164	+	0.0902682i	0.838790	+	0.544455i	$0.183263\pi$
$548$		0			0
$549$	−8.74443	−	15.1458i	−0.373203	−	0.646407i
$550$		0			0
$551$	−15.6296	+	20.3329i	−0.665844	+	0.866211i
$552$		0			0
$553$	2.93197	+	5.07832i	0.124680	+	0.215952i
$554$		0			0
$555$	3.73461	−	6.46853i	0.158525	−	0.274574i
$556$		0			0
$557$	11.5671	−	20.0347i	0.490112	−	0.848899i	−0.509823	−	0.860279i	$-0.670289\pi$
$557$	11.5671	−	20.0347i	0.490112	−	0.848899i	0.999935	+	0.0113802i	$0.00362251\pi$
$558$		0			0
$559$	23.9326			1.01224
$560$		0			0
$561$	−1.43735	+	2.48956i	−0.0606849	+	0.105109i
$562$		0			0
$563$	−14.1246			−0.595279			−0.297640	−	0.954678i	$-0.596199\pi$
$563$	−14.1246			−0.595279			−0.297640	+	0.954678i	$0.596199\pi$
$564$		0			0
$565$	5.46925	+	9.47303i	0.230093	+	0.398533i
$566$		0			0
$567$	−0.0809337	−	0.140181i	−0.00339889	−	0.00588706i
$568$		0			0
$569$	−8.74123			−0.366452			−0.183226	−	0.983071i	$-0.558654\pi$
$569$	−8.74123			−0.366452			−0.183226	+	0.983071i	$0.558654\pi$
$570$		0			0
$571$	10.8293			0.453191			0.226596	−	0.973989i	$-0.427240\pi$
$571$	10.8293			0.453191			0.226596	+	0.973989i	$0.427240\pi$
$572$		0			0
$573$	−8.49548	−	14.7146i	−0.354904	−	0.614711i
$574$		0			0
$575$	0.224652	+	0.389109i	0.00936865	+	0.0162270i
$576$		0			0
$577$	−29.6635			−1.23491			−0.617453	−	0.786608i	$-0.711835\pi$
$577$	−29.6635			−1.23491			−0.617453	+	0.786608i	$0.711835\pi$
$578$		0			0
$579$	−5.30899	+	9.19545i	−0.220634	+	0.382150i
$580$		0			0
$581$	−4.05063			−0.168049
$582$		0			0
$583$	−10.8944	+	18.8696i	−0.451198	+	0.781498i
$584$		0			0
$585$	−3.83582	+	6.64384i	−0.158592	+	0.274689i
$586$		0			0
$587$	22.7837	+	39.4624i	0.940382	+	1.62879i	0.764744	+	0.644334i	$0.222866\pi$
$587$	22.7837	+	39.4624i	0.940382	+	1.62879i	0.175638	+	0.984455i	$0.443801\pi$
$588$		0			0
$589$	−35.7050	−	4.73168i	−1.47120	−	0.194966i
$590$		0			0
$591$	4.21727	+	7.30453i	0.173475	+	0.300468i
$592$		0			0
$593$	−13.7567	+	23.8274i	−0.564921	+	0.978472i	0.432136	+	0.901808i	$0.357760\pi$
$593$	−13.7567	+	23.8274i	−0.564921	+	0.978472i	−0.997057	+	0.0766635i	$0.975573\pi$
$594$		0			0
$595$	−0.250687	+	0.434203i	−0.0102772	+	0.0178006i
$596$		0			0
$597$	2.25334			0.0922231
$598$		0			0
$599$	−1.81540	+	3.14437i	−0.0741754	+	0.128475i	−0.900727	−	0.434385i	$-0.856966\pi$
$599$	−1.81540	+	3.14437i	−0.0741754	+	0.128475i	0.826552	+	0.562860i	$0.190299\pi$
$600$		0			0
$601$	39.0016			1.59091			0.795454	−	0.606014i	$-0.207233\pi$
$601$	39.0016			1.59091			0.795454	+	0.606014i	$0.207233\pi$
$602$		0			0
$603$	6.99051	+	12.1079i	0.284675	+	0.493072i
$604$		0			0
$605$	3.13477	+	5.42958i	0.127446	+	0.220744i
$606$		0			0
$607$	−33.0870			−1.34296			−0.671480	−	0.741022i	$-0.734341\pi$
$607$	−33.0870			−1.34296			−0.671480	+	0.741022i	$0.734341\pi$
$608$		0			0
$609$	−2.68796			−0.108922
$610$		0			0
$611$	−4.58748	−	7.94575i	−0.185590	−	0.321451i
$612$		0			0
$613$	−11.5084	−	19.9331i	−0.464820	−	0.805092i	0.534374	−	0.845248i	$-0.320548\pi$
$613$	−11.5084	−	19.9331i	−0.464820	−	0.805092i	−0.999193	+	0.0401569i	$0.987214\pi$
$614$		0			0
$615$	−5.06048			−0.204058
$616$		0			0
$617$	1.58729	−	2.74927i	0.0639018	−	0.110681i	−0.832304	−	0.554319i	$-0.812979\pi$
$617$	1.58729	−	2.74927i	0.0639018	−	0.110681i	0.896206	+	0.443637i	$0.146312\pi$
$618$		0			0
$619$	26.9439			1.08297			0.541483	−	0.840712i	$-0.317863\pi$
$619$	26.9439			1.08297			0.541483	+	0.840712i	$0.317863\pi$
$620$		0			0
$621$	1.18232	−	2.04785i	0.0474450	−	0.0821772i
$622$		0			0
$623$	1.74448	−	3.02154i	0.0698913	−	0.121055i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−3.97330	−	9.61563i	−0.158678	−	0.384011i
$628$		0			0
$629$	4.09850	+	7.09882i	0.163418	+	0.283048i
$630$		0			0
$631$	3.82655	−	6.62778i	0.152333	−	0.263848i	−0.779752	−	0.626089i	$-0.784655\pi$
$631$	3.82655	−	6.62778i	0.152333	−	0.263848i	0.932085	+	0.362241i	$0.117988\pi$
$632$		0			0
$633$	−9.60334	+	16.6335i	−0.381698	+	0.661121i
$634$		0			0
$635$	−3.91887			−0.155516
$636$		0			0
$637$	−14.5832	+	25.2588i	−0.577807	+	1.00079i
$638$		0			0
$639$	21.9005			0.866369
$640$		0			0
$641$	−12.3983	−	21.4745i	−0.489704	−	0.848192i	0.510226	−	0.860040i	$-0.329562\pi$
$641$	−12.3983	−	21.4745i	−0.489704	−	0.848192i	−0.999930	+	0.0118484i	$0.996228\pi$
$642$		0			0
$643$	−5.33860	−	9.24672i	−0.210534	−	0.364655i	0.741348	−	0.671121i	$-0.234187\pi$
$643$	−5.33860	−	9.24672i	−0.210534	−	0.364655i	−0.951882	+	0.306466i	$0.900853\pi$
$644$		0			0
$645$	6.14750			0.242057
$646$		0			0
$647$	18.6515			0.733264			0.366632	−	0.930366i	$-0.380511\pi$
$647$	18.6515			0.733264			0.366632	+	0.930366i	$0.380511\pi$
$648$		0			0
$649$	3.79946	+	6.58087i	0.149142	+	0.258322i
$650$		0			0
$651$	−1.88749	−	3.26923i	−0.0739766	−	0.128131i
$652$		0			0
$653$	−38.6199			−1.51132			−0.755658	−	0.654967i	$-0.772683\pi$
$653$	−38.6199			−1.51132			−0.755658	+	0.654967i	$0.772683\pi$
$654$		0			0
$655$	6.14178	−	10.6379i	0.239979	−	0.415656i
$656$		0			0
$657$	1.91779			0.0748200
$658$		0			0
$659$	4.00416	−	6.93541i	0.155980	−	0.270165i	−0.777436	−	0.628963i	$-0.783480\pi$
$659$	4.00416	−	6.93541i	0.155980	−	0.270165i	0.933415	+	0.358798i	$0.116813\pi$
$660$		0			0
$661$	−0.174640	+	0.302485i	−0.00679271	+	0.0117653i	−0.869402	−	0.494106i	$-0.835496\pi$
$661$	−0.174640	+	0.302485i	−0.00679271	+	0.0117653i	0.862609	+	0.505871i	$0.168829\pi$
$662$		0			0
$663$	2.82346	+	4.89038i	0.109654	+	0.189927i
$664$		0			0
$665$	−0.692981	−	1.67705i	−0.0268727	−	0.0650334i
$666$		0			0
$667$	−1.32176	−	2.28935i	−0.0511787	−	0.0886441i
$668$		0			0
$669$	7.23133	−	12.5250i	0.279579	−	0.484246i
$670$		0			0
$671$	10.5917	−	18.3454i	0.408889	−	0.708216i
$672$		0			0
$673$	8.68870			0.334925			0.167462	−	0.985878i	$-0.446443\pi$
$673$	8.68870			0.334925			0.167462	+	0.985878i	$0.446443\pi$
$674$		0			0
$675$	−2.63145	+	4.55781i	−0.101285	+	0.175430i
$676$		0			0
$677$	−16.2105			−0.623019			−0.311509	−	0.950243i	$-0.600835\pi$
$677$	−16.2105			−0.623019			−0.311509	+	0.950243i	$0.600835\pi$
$678$		0			0
$679$	1.63128	+	2.82546i	0.0626027	+	0.108431i
$680$		0			0
$681$	−5.18825	−	8.98631i	−0.198814	−	0.344356i
$682$		0			0
$683$	−51.3904			−1.96640			−0.983199	−	0.182534i	$-0.941570\pi$
$683$	−51.3904			−1.96640			−0.983199	+	0.182534i	$0.941570\pi$
$684$		0			0
$685$	10.0915			0.385578
$686$		0			0
$687$	−2.70718	−	4.68897i	−0.103285	−	0.178895i
$688$		0			0
$689$	21.4004	+	37.0666i	0.815290	+	1.41212i
$690$		0			0
$691$	−27.0851			−1.03036			−0.515182	−	0.857081i	$-0.672276\pi$
$691$	−27.0851			−1.03036			−0.515182	+	0.857081i	$0.672276\pi$
$692$		0			0
$693$	−0.812906	+	1.40799i	−0.0308797	+	0.0534853i
$694$		0			0
$695$	2.83619			0.107583
$696$		0			0
$697$	2.77678	−	4.80952i	0.105178	−	0.182174i
$698$		0			0
$699$	−11.5498	+	20.0049i	−0.436854	+	0.756654i
$700$		0			0
$701$	−17.1154	−	29.6448i	−0.646442	−	1.11967i	−0.983967	−	0.178353i	$-0.942923\pi$
$701$	−17.1154	−	29.6448i	−0.646442	−	1.11967i	0.337525	−	0.941317i	$-0.390410\pi$
$702$		0			0
$703$	−29.4098	−	3.89743i	−1.10921	−	0.146994i
$704$		0			0
$705$	−1.17837	−	2.04100i	−0.0443801	−	0.0768685i
$706$		0			0
$707$	0.195752	−	0.339053i	0.00736202	−	0.0127514i
$708$		0			0
$709$	−12.2756	+	21.2619i	−0.461019	+	0.798509i	−0.999012	−	0.0444405i	$-0.985850\pi$
$709$	−12.2756	+	21.2619i	−0.461019	+	0.798509i	0.537993	+	0.842950i	$0.319183\pi$
$710$		0			0
$711$	−25.2932			−0.948571
$712$		0			0
$713$	1.85628	−	3.21517i	0.0695183	−	0.120409i
$714$		0			0
$715$	−9.29231			−0.347513
$716$		0			0
$717$	−6.80670	−	11.7895i	−0.254201	−	0.440289i
$718$		0			0
$719$	11.6389	+	20.1592i	0.434059	+	0.751812i	0.997218	−	0.0745364i	$-0.0237477\pi$
$719$	11.6389	+	20.1592i	0.434059	+	0.751812i	−0.563160	+	0.826348i	$0.690414\pi$
$720$		0			0
$721$	2.31073			0.0860560
$722$		0			0
$723$	13.7201			0.510257
$724$		0			0
$725$	2.94179	+	5.09532i	0.109255	+	0.189236i
$726$		0			0
$727$	7.74757	+	13.4192i	0.287341	+	0.497690i	0.973174	−	0.230069i	$-0.0738953\pi$
$727$	7.74757	+	13.4192i	0.287341	+	0.497690i	−0.685833	+	0.727759i	$0.740562\pi$
$728$		0			0
$729$	18.0253			0.667605
$730$		0			0
$731$	−3.37325	+	5.84264i	−0.124764	+	0.216098i
$732$		0			0
$733$	−50.4872			−1.86479			−0.932394	−	0.361444i	$-0.882284\pi$
$733$	−50.4872			−1.86479			−0.932394	+	0.361444i	$0.882284\pi$
$734$		0			0
$735$	−3.74594	+	6.48816i	−0.138171	+	0.239319i
$736$		0			0
$737$	−8.46728	+	14.6658i	−0.311896	+	0.540220i
$738$		0			0
$739$	13.8666	+	24.0177i	0.510091	+	0.883504i	0.999932	+	0.0116920i	$0.00372175\pi$
$739$	13.8666	+	24.0177i	0.510091	+	0.883504i	−0.489840	+	0.871812i	$0.662945\pi$
$740$		0			0
$741$	−20.2604	−	2.68494i	−0.744285	−	0.0986338i
$742$		0			0
$743$	−7.25410	−	12.5645i	−0.266127	−	0.460945i	0.701731	−	0.712442i	$-0.252411\pi$
$743$	−7.25410	−	12.5645i	−0.266127	−	0.460945i	−0.967858	+	0.251496i	$0.919077\pi$
$744$		0			0
$745$	−8.61398	+	14.9198i	−0.315592	+	0.546621i
$746$		0			0
$747$	8.73590	−	15.1310i	0.319630	−	0.553615i
$748$		0			0
$749$	0.726674			0.0265521
$750$		0			0
$751$	20.1708	−	34.9368i	0.736041	−	1.27486i	−0.218223	−	0.975899i	$-0.570026\pi$
$751$	20.1708	−	34.9368i	0.736041	−	1.27486i	0.954265	−	0.298962i	$-0.0966405\pi$
$752$		0			0
$753$	1.78900			0.0651948
$754$		0			0
$755$	5.82928	+	10.0966i	0.212149	+	0.367453i
$756$		0			0
$757$	−15.5498	−	26.9331i	−0.565168	−	0.978899i	−0.997034	−	0.0769617i	$-0.975478\pi$
$757$	−15.5498	−	26.9331i	−0.565168	−	0.978899i	0.431866	−	0.901938i	$-0.357855\pi$
$758$		0			0
$759$	1.07244			0.0389271
$760$		0			0
$761$	−39.8246			−1.44364			−0.721820	−	0.692081i	$-0.756694\pi$
$761$	−39.8246			−1.44364			−0.721820	+	0.692081i	$0.756694\pi$
$762$		0			0
$763$	3.53748	+	6.12709i	0.128065	+	0.221816i
$764$		0			0
$765$	−1.08130	−	1.87287i	−0.0390945	−	0.0677137i
$766$		0			0
$767$	14.9270			0.538983
$768$		0			0
$769$	17.4238	−	30.1789i	0.628317	−	1.08828i	−0.359572	−	0.933117i	$-0.617077\pi$
$769$	17.4238	−	30.1789i	0.628317	−	1.08828i	0.987889	−	0.155160i	$-0.0495893\pi$
$770$		0			0
$771$	−14.4190			−0.519286
$772$		0			0
$773$	23.2918	−	40.3427i	0.837749	−	1.45102i	−0.0540228	−	0.998540i	$-0.517204\pi$
$773$	23.2918	−	40.3427i	0.837749	−	1.45102i	0.891772	−	0.452485i	$-0.149462\pi$
$774$		0			0
$775$	−4.13145	+	7.15589i	−0.148406	+	0.257047i
$776$		0			0
$777$	−1.55470	−	2.69282i	−0.0557746	−	0.0966044i
$778$		0			0
$779$	7.67593	+	18.5762i	0.275019	+	0.665562i
$780$		0			0
$781$	13.2635	+	22.9731i	0.474606	+	0.822041i
$782$		0			0
$783$	15.4823	−	26.8162i	0.553294	−	0.958333i
$784$		0			0
$785$	6.17837	−	10.7013i	0.220516	−	0.381944i
$786$		0			0
$787$	−42.2991			−1.50780			−0.753901	−	0.656988i	$-0.771830\pi$
$787$	−42.2991			−1.50780			−0.753901	+	0.656988i	$0.771830\pi$
$788$		0			0
$789$	−7.81914	+	13.5432i	−0.278369	+	0.482149i
$790$		0			0
$791$	4.55365			0.161909
$792$		0			0
$793$	−20.8059	−	36.0369i	−0.738839	−	1.27971i
$794$		0			0
$795$	5.49705	+	9.52118i	0.194960	+	0.337681i
$796$		0			0
$797$	15.5910			0.552262			0.276131	−	0.961120i	$-0.410948\pi$
$797$	15.5910			0.552262			0.276131	+	0.961120i	$0.410948\pi$
$798$		0			0
$799$	2.58638			0.0914996
$800$		0			0
$801$	7.52458	+	13.0330i	0.265868	+	0.460497i
$802$		0			0
$803$	1.16146	+	2.01171i	0.0409872	+	0.0709918i
$804$		0			0
$805$	0.187043			0.00659242
$806$		0			0
$807$	−8.14358	+	14.1051i	−0.286668	+	0.496523i
$808$		0			0
$809$	37.1857			1.30738			0.653689	−	0.756763i	$-0.273220\pi$
$809$	37.1857			1.30738			0.653689	+	0.756763i	$0.273220\pi$
$810$		0			0
$811$	−0.237093	+	0.410657i	−0.00832546	+	0.0144201i	−0.870158	−	0.492773i	$-0.835983\pi$
$811$	−0.237093	+	0.410657i	−0.00832546	+	0.0144201i	0.861833	+	0.507193i	$0.169317\pi$
$812$		0			0
$813$	−7.50457	+	12.9983i	−0.263197	+	0.455870i
$814$		0			0
$815$	−1.82360	−	3.15858i	−0.0638781	−	0.110640i
$816$		0			0
$817$	−9.32477	−	22.5665i	−0.326232	−	0.789501i
$818$		0			0
$819$	1.59684	+	2.76580i	0.0557980	+	0.0966449i
$820$		0			0
$821$	−17.7783	+	30.7930i	−0.620469	+	1.07468i	0.368930	+	0.929457i	$0.379724\pi$
$821$	−17.7783	+	30.7930i	−0.620469	+	1.07468i	−0.989399	+	0.145226i	$0.953609\pi$
$822$		0			0
$823$	−5.86006	+	10.1499i	−0.204269	+	0.353804i	−0.949900	−	0.312555i	$-0.898815\pi$
$823$	−5.86006	+	10.1499i	−0.204269	+	0.353804i	0.745631	+	0.666359i	$0.232148\pi$
$824$		0			0
$825$	−2.38689			−0.0831008
$826$		0			0
$827$	−16.8590	+	29.2007i	−0.586245	+	1.01541i	0.408474	+	0.912770i	$0.366061\pi$
$827$	−16.8590	+	29.2007i	−0.586245	+	1.01541i	−0.994719	+	0.102636i	$0.967272\pi$
$828$		0			0
$829$	−24.1483			−0.838706			−0.419353	−	0.907823i	$-0.637743\pi$
$829$	−24.1483			−0.838706			−0.419353	+	0.907823i	$0.637743\pi$
$830$		0			0
$831$	14.0255	+	24.2929i	0.486540	+	0.842712i
$832$		0			0
$833$	−4.11094	−	7.12035i	−0.142436	−	0.246706i
$834$		0			0
$835$	17.7406			0.613939
$836$		0			0
$837$	43.4869			1.50313
$838$		0			0
$839$	5.57657	+	9.65890i	0.192525	+	0.333462i	0.946086	−	0.323915i	$-0.104999\pi$
$839$	5.57657	+	9.65890i	0.192525	+	0.333462i	−0.753562	+	0.657377i	$0.771666\pi$
$840$		0			0
$841$	−2.80822	−	4.86398i	−0.0968351	−	0.167723i
$842$		0			0
$843$	−24.1590			−0.832081
$844$		0			0
$845$	−2.62671	+	4.54959i	−0.0903614	+	0.156511i
$846$		0			0
$847$	2.60998			0.0896799
$848$		0			0
$849$	−0.186447	+	0.322936i	−0.00639885	+	0.0110831i
$850$		0			0
$851$	1.52899	−	2.64830i	0.0524133	−	0.0907824i
$852$		0			0
$853$	−8.20566	−	14.2126i	−0.280957	−	0.486631i	0.690664	−	0.723176i	$-0.257318\pi$
$853$	−8.20566	−	14.2126i	−0.280957	−	0.486631i	−0.971621	+	0.236545i	$0.923985\pi$
$854$		0			0
$855$	7.75913	+	1.02825i	0.265357	+	0.0351655i
$856$		0			0
$857$	−8.76891	−	15.1882i	−0.299540	−	0.518819i	0.676491	−	0.736451i	$-0.263500\pi$
$857$	−8.76891	−	15.1882i	−0.299540	−	0.518819i	−0.976031	+	0.217632i	$0.930167\pi$
$858$		0			0
$859$	−15.7784	+	27.3290i	−0.538352	+	0.932453i	0.460641	+	0.887587i	$0.347620\pi$
$859$	−15.7784	+	27.3290i	−0.538352	+	0.932453i	−0.998993	+	0.0448664i	$0.985714\pi$
$860$		0			0
$861$	−1.05333	+	1.82442i	−0.0358973	+	0.0621759i
$862$		0			0
$863$	−44.3106			−1.50835			−0.754175	−	0.656674i	$-0.771963\pi$
$863$	−44.3106			−1.50835			−0.754175	+	0.656674i	$0.771963\pi$
$864$		0			0
$865$	11.8134	−	20.4615i	0.401669	−	0.695710i
$866$		0			0
$867$	17.0646			0.579544
$868$		0			0
$869$	−15.3183	−	26.5320i	−0.519637	−	0.900037i
$870$		0			0
$871$	16.6327	+	28.8088i	0.563579	+	0.976148i
$872$		0			0
$873$	−14.0726			−0.476284
$874$		0			0
$875$	−0.416295			−0.0140734
$876$		0			0
$877$	19.7271	+	34.1684i	0.666138	+	1.15379i	0.978975	+	0.203979i	$0.0653873\pi$
$877$	19.7271	+	34.1684i	0.666138	+	1.15379i	−0.312837	+	0.949807i	$0.601279\pi$
$878$		0			0
$879$	1.84535	+	3.19625i	0.0622423	+	0.107807i
$880$		0			0
$881$	−40.9584			−1.37992			−0.689962	−	0.723845i	$-0.742373\pi$
$881$	−40.9584			−1.37992			−0.689962	+	0.723845i	$0.742373\pi$
$882$		0			0
$883$	12.9561	−	22.4406i	0.436007	−	0.755186i	−0.561370	−	0.827565i	$-0.689726\pi$
$883$	12.9561	−	22.4406i	0.436007	−	0.755186i	0.997377	+	0.0723788i	$0.0230591\pi$
$884$		0			0
$885$	3.83425			0.128887
$886$		0			0
$887$	−0.731933	+	1.26774i	−0.0245759	+	0.0425667i	−0.878052	−	0.478566i	$-0.841157\pi$
$887$	−0.731933	+	1.26774i	−0.0245759	+	0.0425667i	0.853476	+	0.521132i	$0.174490\pi$
$888$		0			0
$889$	−0.815705	+	1.41284i	−0.0273579	+	0.0473852i
$890$		0			0
$891$	0.422843	+	0.732386i	0.0141658	+	0.0245359i
$892$		0			0
$893$	−5.70478	+	7.42149i	−0.190903	+	0.248351i
$894$		0			0
$895$	9.54955	+	16.5403i	0.319206	+	0.552881i
$896$		0			0
$897$	1.05333	−	1.82442i	0.0351696	−	0.0609155i
$898$		0			0
$899$	24.3077	−	42.1022i	0.810708	−	1.40419i
$900$		0			0
$901$	−12.0654			−0.401955
$902$		0			0
$903$	1.27959	−	2.21631i	0.0425820	−	0.0737542i
$904$		0			0
$905$	−12.9382			−0.430079
$906$		0			0
$907$	15.2809	+	26.4673i	0.507393	+	0.878831i	0.999963	+	0.00855819i	$0.00272419\pi$
$907$	15.2809	+	26.4673i	0.507393	+	0.878831i	−0.492570	+	0.870273i	$0.663942\pi$
$908$		0			0
$909$	0.844348	+	1.46245i	0.0280053	+	0.0485065i
$910$		0			0
$911$	−15.5638			−0.515651			−0.257826	−	0.966191i	$-0.583006\pi$
$911$	−15.5638			−0.515651			−0.257826	+	0.966191i	$0.583006\pi$
$912$		0			0
$913$	21.1628			0.700386
$914$		0			0
$915$	−5.34435	−	9.25668i	−0.176679	−	0.306016i
$916$		0			0
$917$	−2.55679	−	4.42850i	−0.0844328	−	0.146242i
$918$		0			0
$919$	−30.8127			−1.01642			−0.508208	−	0.861234i	$-0.669692\pi$
$919$	−30.8127			−1.01642			−0.508208	+	0.861234i	$0.669692\pi$
$920$		0			0
$921$	10.1934	−	17.6556i	0.335885	−	0.581771i
$922$		0			0
$923$	52.1085			1.71517
$924$		0			0
$925$	−3.40302	+	5.89421i	−0.111891	+	0.193800i
$926$		0			0
$927$	−4.98350	+	8.63167i	−0.163679	+	0.283501i
$928$		0			0
$929$	7.38016	+	12.7828i	0.242135	+	0.419391i	0.961322	−	0.275426i	$-0.0888189\pi$
$929$	7.38016	+	12.7828i	0.242135	+	0.419391i	−0.719187	+	0.694817i	$0.755486\pi$
$930$		0			0
$931$	29.4990	+	3.90925i	0.966790	+	0.128120i
$932$		0			0
$933$	−7.38727	−	12.7951i	−0.241848	−	0.418894i
$934$		0			0
$935$	1.30973	−	2.26852i	0.0428328	−	0.0741886i
$936$		0			0
$937$	23.9700	−	41.5172i	0.783064	−	1.35631i	−0.147084	−	0.989124i	$-0.546989\pi$
$937$	23.9700	−	41.5172i	0.783064	−	1.35631i	0.930149	−	0.367183i	$-0.119678\pi$
$938$		0			0
$939$	−0.729818			−0.0238167
$940$		0			0
$941$	6.46031	−	11.1896i	0.210600	−	0.364770i	−0.741302	−	0.671171i	$-0.765792\pi$
$941$	6.46031	−	11.1896i	0.210600	−	0.364770i	0.951903	+	0.306401i	$0.0991249\pi$
$942$		0			0
$943$	−2.07182			−0.0674678
$944$		0			0
$945$	1.09546	+	1.89740i	0.0356354	+	0.0617223i
$946$		0			0
$947$	−25.8847	−	44.8336i	−0.841139	−	1.45690i	−0.888932	−	0.458039i	$-0.848552\pi$
$947$	−25.8847	−	44.8336i	−0.841139	−	1.45690i	0.0477927	−	0.998857i	$-0.484781\pi$
$948$		0			0
$949$	4.56305			0.148123
$950$		0			0
$951$	−1.00628			−0.0326308
$952$		0			0
$953$	5.60652	+	9.71078i	0.181613	+	0.314563i	0.942430	−	0.334404i	$-0.108535\pi$
$953$	5.60652	+	9.71078i	0.181613	+	0.314563i	−0.760817	+	0.648966i	$0.775202\pi$
$954$		0			0
$955$	7.74119	+	13.4081i	0.250499	+	0.433877i
$956$		0			0
$957$	14.0434			0.453960
$958$		0			0
$959$	2.10053	−	3.63823i	0.0678297	−	0.117485i
$960$		0			0
$961$	37.2756			1.20244
$962$		0			0
$963$	−1.56720	+	2.71447i	−0.0505023	+	0.0874726i
$964$		0			0
$965$	4.83763	−	8.37901i	0.155729	−	0.269730i
$966$		0			0
$967$	4.73120	+	8.19468i	0.152145	+	0.263523i	0.932016	−	0.362418i	$-0.118049\pi$
$967$	4.73120	+	8.19468i	0.152145	+	0.263523i	−0.779871	+	0.625941i	$0.784715\pi$
$968$		0			0
$969$	3.51113	−	4.56771i	0.112794	−	0.146736i
$970$		0			0
$971$	18.0401	+	31.2464i	0.578934	+	1.00274i	0.995602	+	0.0936844i	$0.0298645\pi$
$971$	18.0401	+	31.2464i	0.578934	+	1.00274i	−0.416668	+	0.909059i	$0.636802\pi$
$972$		0			0
$973$	0.590347	−	1.02251i	0.0189257	−	0.0327802i
$974$		0			0
$975$	−2.34435	+	4.06053i	−0.0750792	+	0.130041i
$976$		0			0
$977$	−11.3853			−0.364249			−0.182125	−	0.983275i	$-0.558297\pi$
$977$	−11.3853			−0.364249			−0.182125	+	0.983275i	$0.558297\pi$
$978$		0			0
$979$	−9.11418	+	15.7862i	−0.291290	+	0.504530i
$980$		0			0
$981$	−30.5168			−0.974326
$982$		0			0
$983$	−7.27761	−	12.6052i	−0.232120	−	0.402043i	0.726312	−	0.687365i	$-0.241233\pi$
$983$	−7.27761	−	12.6052i	−0.232120	−	0.402043i	−0.958432	+	0.285322i	$0.907899\pi$
$984$		0			0
$985$	−3.84283	−	6.65598i	−0.122443	−	0.212077i
$986$		0			0
$987$	−0.981102			−0.0312288
$988$		0			0
$989$	2.51686			0.0800315
$990$		0			0
$991$	−20.2836	−	35.1322i	−0.644328	−	1.11601i	−0.984456	−	0.175630i	$-0.943804\pi$
$991$	−20.2836	−	35.1322i	−0.644328	−	1.11601i	0.340128	−	0.940379i	$-0.389530\pi$
$992$		0			0
$993$	−2.15648	−	3.73514i	−0.0684339	−	0.118531i
$994$		0			0
$995$	−2.05327			−0.0650932
$996$		0			0
$997$	−25.0152	+	43.3275i	−0.792238	+	1.37220i	0.132340	+	0.991204i	$0.457751\pi$
$997$	−25.0152	+	43.3275i	−0.792238	+	1.37220i	−0.924578	+	0.380992i	$0.875583\pi$
$998$		0			0
$999$	35.8196			1.13328

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	760.2.q.f.121.3	✓	8
4.3	odd	2		1520.2.q.k.881.2		8
19.11	even	3	inner	760.2.q.f.201.3	yes	8
76.11	odd	6		1520.2.q.k.961.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
760.2.q.f.121.3	✓	8	1.1	even	1	trivial
760.2.q.f.201.3	yes	8	19.11	even	3	inner
1520.2.q.k.881.2		8	4.3	odd	2
1520.2.q.k.961.2		8	76.11	odd	6

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:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.548719 + 0.950409i) q^{3} +(-0.500000 - 0.866025i) q^{5} -0.416295 q^{7} +(0.897815 - 1.55506i) q^{9} +2.17496 q^{11} +(2.13620 - 3.70001i) q^{13} +(0.548719 - 0.950409i) q^{15} +(0.602185 + 1.04302i) q^{17} +(-4.32112 - 0.572641i) q^{19} +(-0.228429 - 0.395651i) q^{21} +(0.224652 - 0.389109i) q^{23} +(-0.500000 + 0.866025i) q^{25} +5.26291 q^{27} +(2.94179 - 5.09532i) q^{29} +8.26291 q^{31} +(1.19344 + 2.06711i) q^{33} +(0.208148 + 0.360522i) q^{35} +6.80605 q^{37} +4.68870 q^{39} +(-2.30559 - 3.99339i) q^{41} +(2.80084 + 4.85120i) q^{43} -1.79563 q^{45} +(1.07375 - 1.85979i) q^{47} -6.82670 q^{49} +(-0.660861 + 1.14465i) q^{51} +(-5.00899 + 8.67582i) q^{53} +(-1.08748 - 1.88357i) q^{55} +(-1.82684 - 4.42105i) q^{57} +(1.74691 + 3.02574i) q^{59} +(4.86984 - 8.43481i) q^{61} +(-0.373756 + 0.647365i) q^{63} -4.27240 q^{65} +(-3.89307 + 6.74299i) q^{67} +0.493084 q^{69} +(6.09827 + 10.5625i) q^{71} +(0.534015 + 0.924942i) q^{73} -1.09744 q^{75} -0.905427 q^{77} +(-7.04300 - 12.1988i) q^{79} +(0.194414 + 0.336735i) q^{81} +9.73018 q^{83} +(0.602185 - 1.04302i) q^{85} +6.45686 q^{87} +(-4.19050 + 7.25815i) q^{89} +(-0.889291 + 1.54030i) q^{91} +(4.53402 + 7.85314i) q^{93} +(1.66464 + 4.02852i) q^{95} +(-3.91856 - 6.78714i) q^{97} +(1.95271 - 3.38220i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{3} - 4 q^{5} + 4 q^{7} - q^{9} - 8 q^{11} + q^{13} + q^{15} + 13 q^{17} + q^{19} + 12 q^{21} + 8 q^{23} - 4 q^{25} - 20 q^{27} - 3 q^{29} + 4 q^{31} - 15 q^{33} - 2 q^{35} + 20 q^{37} - 2 q^{39}+ \cdots + 30 q^{99}+O(q^{100}) \) 8 * q + q^3 - 4 * q^5 + 4 * q^7 - q^9 - 8 * q^11 + q^13 + q^15 + 13 * q^17 + q^19 + 12 * q^21 + 8 * q^23 - 4 * q^25 - 20 * q^27 - 3 * q^29 + 4 * q^31 - 15 * q^33 - 2 * q^35 + 20 * q^37 - 2 * q^39 - 8 * q^41 - 3 * q^43 + 2 * q^45 + 10 * q^47 + 12 * q^49 - 16 * q^51 - 11 * q^53 + 4 * q^55 - 29 * q^57 + q^59 - 25 * q^63 - 2 * q^65 - 8 * q^67 + 22 * q^69 - 4 * q^71 - 20 * q^73 - 2 * q^75 - 36 * q^77 - 3 * q^79 + 12 * q^81 - 30 * q^83 + 13 * q^85 + 24 * q^87 + 17 * q^89 - 4 * q^91 + 12 * q^93 + 4 * q^95 + 11 * q^97 + 30 * q^99

Introduction

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