LMFDB - Embedded newform 760.2.q.f.201.3

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			201.3
Root			$0.689667 - 1.19454i$ of defining polynomial
Character	$\chi$	$=$	760.201
Dual form			760.2.q.f.121.3

$q$-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 $\left(\mathbb{Z}/760\mathbb{Z}\right)^\times$.

$n$	$191$	$381$	$401$	$457$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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	−0.663016	−	0.748605i	$-0.730724\pi$
$3$	0.548719	−	0.950409i	0.316803	−	0.548719i	0.979819	+	0.199886i	$0.0640572\pi$
$4$		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	0.993898	+	0.110305i	$0.0351826\pi$
$13$	2.13620	+	3.70001i	0.592475	+	1.02620i	−0.401422	+	0.915893i	$0.631484\pi$
$14$		0			0
$15$	0.548719	+	0.950409i	0.141679	+	0.245395i
$16$		0			0
$17$	0.602185	−	1.04302i	0.146051	−	0.252968i	−0.783713	−	0.621123i	$-0.786677\pi$
$17$	0.602185	−	1.04302i	0.146051	−	0.252968i	0.929765	+	0.368154i	$0.120010\pi$
$18$		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	0.888496	−	0.458884i	$-0.151751\pi$
$23$	0.224652	+	0.389109i	0.0468432	+	0.0811349i	−0.841653	+	0.540019i	$0.818417\pi$
$24$		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	0.998525	+	0.0542864i	$0.0172884\pi$
$29$	2.94179	+	5.09532i	0.546276	+	0.946178i	−0.452249	+	0.891892i	$0.649378\pi$
$30$		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	−0.987972	−	0.154631i	$-0.950581\pi$
$41$	−2.30559	+	3.99339i	−0.360072	+	0.623663i	0.627900	+	0.778294i	$0.283915\pi$
$42$		0			0
$43$	2.80084	−	4.85120i	0.427124	−	0.739800i	−0.569492	−	0.821997i	$-0.692860\pi$
$43$	2.80084	−	4.85120i	0.427124	−	0.739800i	0.996616	+	0.0821964i	$0.0261935\pi$
$44$		0			0
$45$	−1.79563			−0.267677
$46$		0			0
$47$	1.07375	+	1.85979i	0.156622	+	0.271278i	0.933649	−	0.358190i	$-0.116606\pi$
$47$	1.07375	+	1.85979i	0.156622	+	0.271278i	−0.777026	+	0.629468i	$0.783273\pi$
$48$		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	−0.972472	−	0.233020i	$-0.925139\pi$
$53$	−5.00899	−	8.67582i	−0.688037	−	1.19172i	0.284435	−	0.958695i	$-0.408194\pi$
$54$		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	−0.729617	−	0.683856i	$-0.760302\pi$
$59$	1.74691	−	3.02574i	0.227428	−	0.393917i	0.957045	+	0.289939i	$0.0936349\pi$
$60$		0			0
$61$	4.86984	+	8.43481i	0.623519	+	1.07997i	0.988825	+	0.149079i	$0.0476310\pi$
$61$	4.86984	+	8.43481i	0.623519	+	1.07997i	−0.365306	+	0.930887i	$0.619036\pi$
$62$		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	0.523996	−	0.851721i	$-0.324441\pi$
$67$	−3.89307	−	6.74299i	−0.475614	−	0.823787i	−0.999610	+	0.0279334i	$0.991107\pi$
$68$		0			0
$69$	0.493084			0.0593604
$70$		0			0
$71$	6.09827	−	10.5625i	0.723731	−	1.25354i	−0.235763	−	0.971811i	$-0.575759\pi$
$71$	6.09827	−	10.5625i	0.723731	−	1.25354i	0.959494	−	0.281729i	$-0.0909079\pi$
$72$		0			0
$73$	0.534015	−	0.924942i	0.0625018	−	0.108256i	−0.833081	−	0.553151i	$-0.813425\pi$
$73$	0.534015	−	0.924942i	0.0625018	−	0.108256i	0.895583	+	0.444894i	$0.146759\pi$
$74$		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	0.132078	+	0.991239i	$0.457835\pi$
$79$	−7.04300	+	12.1988i	−0.792400	+	1.37248i	−0.924477	+	0.381237i	$0.875498\pi$
$80$		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	0.553804	−	0.832647i	$-0.313176\pi$
$89$	−4.19050	−	7.25815i	−0.444192	−	0.769363i	−0.997996	+	0.0632844i	$0.979842\pi$
$90$		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	−0.993463	−	0.114156i	$-0.963584\pi$
$97$	−3.91856	+	6.78714i	−0.397869	+	0.689130i	0.595593	+	0.803286i	$0.296917\pi$
$98$		0			0
$99$	1.95271	+	3.38220i	0.196255	+	0.339924i
$100$		0			0
$101$	−0.470224	−	0.814452i	−0.0467891	−	0.0810410i	0.841682	−	0.539973i	$-0.181566\pi$
$101$	−0.470224	−	0.814452i	−0.0467891	−	0.0810410i	−0.888471	+	0.458932i	$0.848232\pi$
$102$		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	0.0961903	+	0.995363i	$0.469334\pi$
$109$	−8.49752	+	14.7181i	−0.813914	+	1.40974i	−0.910105	+	0.414378i	$0.863999\pi$
$110$		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	0.939770	−	0.341807i	$-0.111039\pi$
$127$	1.95944	+	3.39384i	0.173872	+	0.301155i	−0.765898	+	0.642962i	$0.777705\pi$
$128$		0			0
$129$	−3.07375	−	5.32389i	−0.270628	−	0.468742i
$130$		0			0
$131$	6.14178	−	10.6379i	0.536610	−	0.929435i	−0.462474	−	0.886633i	$-0.653038\pi$
$131$	6.14178	−	10.6379i	0.536610	−	0.929435i	0.999084	−	0.0428023i	$-0.0136286\pi$
$132$		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	0.565878	−	0.824489i	$-0.308537\pi$
$137$	−5.04577	−	8.73953i	−0.431089	−	0.746669i	−0.996967	+	0.0778202i	$0.975204\pi$
$138$		0			0
$139$	−1.41810	−	2.45621i	−0.120281	−	0.208333i	0.799597	−	0.600537i	$-0.205046\pi$
$139$	−1.41810	−	2.45621i	−0.120281	−	0.208333i	−0.919879	+	0.392203i	$0.871713\pi$
$140$		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	0.260759	+	0.965404i	$0.416027\pi$
$149$	−8.61398	+	14.9198i	−0.705685	+	1.22228i	−0.966444	+	0.256878i	$0.917306\pi$
$150$		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	−0.506881	−	0.862016i	$-0.669201\pi$
$157$	6.17837	−	10.7013i	0.493088	−	0.854053i	0.999968	+	0.00796326i	$0.00253481\pi$
$158$		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	−0.972993	−	0.230834i	$-0.925855\pi$
$167$	−8.87030	−	15.3638i	−0.686405	−	1.18889i	0.286589	−	0.958054i	$-0.407479\pi$
$168$		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	0.0683116	−	0.997664i	$-0.478239\pi$
$173$	11.8134	−	20.4615i	0.898158	−	1.55566i	0.829847	−	0.557992i	$-0.188428\pi$
$174$		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	0.999758	−	0.0219813i	$-0.00699743\pi$
$181$	6.46908	+	11.2048i	0.480843	+	0.832844i	−0.518916	+	0.854826i	$0.673664\pi$
$182$		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	−0.637713	−	0.770274i	$-0.720120\pi$
$193$	4.83763	−	8.37901i	0.348220	−	0.603135i	0.985933	+	0.167139i	$0.0534529\pi$
$194$		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	0.900117	−	0.435648i	$-0.143481\pi$
$199$	1.02664	+	1.77819i	0.0727764	+	0.126052i	−0.827341	+	0.561700i	$0.810147\pi$
$200$		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	−0.390031	−	0.920802i	$-0.627536\pi$
$211$	8.75069	−	15.1566i	0.602422	−	1.04343i	0.992453	−	0.122624i	$-0.0391309\pi$
$212$		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	−0.997783	−	0.0665573i	$-0.978798\pi$
$223$	−6.58928	+	11.4130i	−0.441251	+	0.764269i	0.556532	+	0.830826i	$0.312132\pi$
$224$		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	−0.282536	−	0.959257i	$-0.591176\pi$
$233$	10.5243	−	18.2287i	0.689473	−	1.19420i	0.972009	−	0.234945i	$-0.0754911\pi$
$234$		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	0.994046	−	0.108960i	$-0.0347521\pi$
$241$	6.25097	+	10.8270i	0.402661	+	0.697429i	−0.591385	+	0.806389i	$0.701419\pi$
$242$		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	0.890602	−	0.454783i	$-0.150283\pi$
$251$	0.815080	+	1.41176i	0.0514474	+	0.0891095i	−0.839155	+	0.543893i	$0.816950\pi$
$252$		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	0.585080	−	0.810976i	$-0.301063\pi$
$257$	−6.56937	−	11.3785i	−0.409786	−	0.709770i	−0.994866	+	0.101206i	$0.967730\pi$
$258$		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	−0.558298	−	0.829640i	$-0.688545\pi$
$263$	7.12491	−	12.3407i	0.439341	−	0.760960i	0.997639	+	0.0686803i	$0.0218788\pi$
$264$		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	−0.546099	−	0.837721i	$-0.683888\pi$
$269$	7.42053	−	12.8527i	0.452438	−	0.783646i	0.998537	+	0.0540751i	$0.0172210\pi$
$270$		0			0
$271$	6.83826	−	11.8442i	0.415395	−	0.719485i	−0.580075	−	0.814563i	$-0.696977\pi$
$271$	6.83826	−	11.8442i	0.415395	−	0.719485i	0.995470	+	0.0950781i	$0.0303101\pi$
$272$		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	−0.981484	−	0.191543i	$-0.938651\pi$
$281$	−11.0070	−	19.0647i	−0.656623	−	1.13730i	0.324861	−	0.945762i	$-0.394682\pi$
$282$		0			0
$283$	0.169893	−	0.294263i	0.0100991	−	0.0174921i	−0.860932	−	0.508721i	$-0.830119\pi$
$283$	0.169893	−	0.294263i	0.0100991	−	0.0174921i	0.871031	+	0.491228i	$0.163452\pi$
$284$		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	0.469266	+	0.883057i	$0.344519\pi$
$307$	−9.28840	+	16.0880i	−0.530117	+	0.918189i	−0.999383	+	0.0351324i	$0.988815\pi$
$308$		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	0.856475	−	0.516188i	$-0.172650\pi$
$313$	−0.332510	−	0.575924i	−0.0187946	−	0.0325532i	−0.875270	+	0.483635i	$0.839316\pi$
$314$		0			0
$315$	0.747512			0.0421175
$316$		0			0
$317$	−0.458467	−	0.794088i	−0.0257501	−	0.0446004i	0.852863	−	0.522134i	$-0.174864\pi$
$317$	−0.458467	−	0.794088i	−0.0257501	−	0.0446004i	−0.878613	+	0.477534i	$0.841531\pi$
$318$		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	0.207162	+	0.978307i	$0.433577\pi$
$337$	−13.6517	+	23.6455i	−0.743657	+	1.28805i	−0.950819	+	0.309746i	$0.899756\pi$
$338$		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	−0.399763	−	0.916618i	$-0.630908\pi$
$347$	11.0637	−	19.1630i	0.593933	−	1.02872i	0.993697	−	0.112104i	$-0.0357589\pi$
$348$		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	−0.741277	−	0.671200i	$-0.765779\pi$
$359$	3.99101	−	6.91264i	0.210638	−	0.364835i	0.951914	+	0.306365i	$0.0991127\pi$
$360$		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	0.748792	−	0.662805i	$-0.230634\pi$
$367$	−3.82397	−	6.62331i	−0.199610	−	0.345734i	−0.948402	+	0.317071i	$0.897301\pi$
$368$		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	−0.978349	−	0.206960i	$-0.933643\pi$
$383$	−6.06569	+	10.5061i	−0.309942	+	0.536835i	0.668407	+	0.743795i	$0.266976\pi$
$384$		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	0.950404	−	0.311020i	$-0.100670\pi$
$389$	4.06001	+	7.03215i	0.205851	+	0.356544i	−0.744553	+	0.667564i	$0.767337\pi$
$390$		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	−0.331025	−	0.943622i	$-0.607395\pi$
$397$	12.9848	−	22.4903i	0.651688	−	1.12876i	0.982713	−	0.185135i	$-0.0592721\pi$
$398$		0			0
$399$	0.760504	−	1.84046i	0.0380728	−	0.0921385i
$400$		0			0
$401$	−1.47400	+	2.55304i	−0.0736081	+	0.127493i	−0.900480	−	0.434897i	$-0.856785\pi$
$401$	−1.47400	+	2.55304i	−0.0736081	+	0.127493i	0.826872	+	0.562390i	$0.190118\pi$
$402$		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	0.921637	−	0.388053i	$-0.126852\pi$
$409$	2.52301	+	4.36998i	0.124755	+	0.216081i	−0.796882	+	0.604135i	$0.793519\pi$
$410$		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	−0.729903	−	0.683551i	$-0.760435\pi$
$421$	4.65809	−	8.06805i	0.227021	−	0.393213i	0.956924	+	0.290339i	$0.0937679\pi$
$422$		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	−0.998447	−	0.0557024i	$-0.982260\pi$
$431$	−11.3656	−	19.6859i	−0.547463	−	0.948234i	0.450984	−	0.892532i	$-0.351073\pi$
$432$		0			0
$433$	−13.0700	−	22.6379i	−0.628104	−	1.08791i	−0.987932	−	0.154890i	$-0.950498\pi$
$433$	−13.0700	−	22.6379i	−0.628104	−	1.08791i	0.359827	−	0.933019i	$-0.382836\pi$
$434$		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	0.0692500	−	0.997599i	$-0.477939\pi$
$439$	18.8272	−	32.6096i	0.898571	−	1.55637i	0.829321	−	0.558772i	$-0.188727\pi$
$440$		0			0
$441$	−6.12911	−	10.6159i	−0.291862	−	0.505520i
$442$		0			0
$443$	11.6519	+	20.1817i	0.553599	+	0.958862i	0.998011	+	0.0630391i	$0.0200793\pi$
$443$	11.6519	+	20.1817i	0.553599	+	0.958862i	−0.444412	+	0.895822i	$0.646587\pi$
$444$		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	−0.724948	−	0.688803i	$-0.758136\pi$
$461$	5.02520	−	8.70391i	0.234047	−	0.405381i	0.958995	+	0.283422i	$0.0914697\pi$
$462$		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	0.992335	+	0.123579i	$0.0394373\pi$
$479$	13.2015	+	22.8656i	0.603190	+	1.04476i	−0.389145	+	0.921177i	$0.627229\pi$
$480$		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	−0.840180	−	0.542308i	$-0.817551\pi$
$491$	1.09823	−	1.90220i	0.0495626	−	0.0858449i	0.889742	+	0.456463i	$0.150884\pi$
$492$		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	−0.959111	−	0.283032i	$-0.908660\pi$
$499$	−5.23705	+	9.07083i	−0.234442	+	0.406066i	0.724668	+	0.689098i	$0.241993\pi$
$500$		0			0
$501$	−19.4692			−0.869821
$502$		0			0
$503$	3.55232	+	6.15280i	0.158390	+	0.274340i	0.934288	−	0.356518i	$-0.116036\pi$
$503$	3.55232	+	6.15280i	0.158390	+	0.274340i	−0.775898	+	0.630858i	$0.782703\pi$
$504$		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	0.658009	−	0.753010i	$-0.271399\pi$
$509$	−7.28996	−	12.6266i	−0.323122	−	0.559663i	−0.981130	+	0.193347i	$0.938066\pi$
$510$		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	0.774094	−	0.633071i	$-0.218206\pi$
$523$	−3.68672	−	6.38559i	−0.161209	−	0.279222i	−0.935303	+	0.353849i	$0.884873\pi$
$524$		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	0.833445	+	0.552603i	$0.186365\pi$
$541$	20.8239	+	36.0681i	0.895291	+	1.55069i	0.0618460	+	0.998086i	$0.480301\pi$
$542$		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	0.838790	−	0.544455i	$-0.183263\pi$
$547$	−1.21890	−	2.11120i	−0.0521164	−	0.0902682i	−0.890907	+	0.454186i	$0.849930\pi$
$548$		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	0.999935	−	0.0113802i	$-0.00362251\pi$
$557$	11.5671	+	20.0347i	0.490112	+	0.848899i	−0.509823	+	0.860279i	$0.670289\pi$
$558$		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	0.175638	−	0.984455i	$-0.443801\pi$
$587$	22.7837	−	39.4624i	0.940382	−	1.62879i	0.764744	−	0.644334i	$-0.222866\pi$
$588$		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	−0.997057	−	0.0766635i	$-0.975573\pi$
$593$	−13.7567	−	23.8274i	−0.564921	−	0.978472i	0.432136	−	0.901808i	$-0.357760\pi$
$594$		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	0.826552	−	0.562860i	$-0.190299\pi$
$599$	−1.81540	−	3.14437i	−0.0741754	−	0.128475i	−0.900727	+	0.434385i	$0.856966\pi$
$600$		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	−0.999193	−	0.0401569i	$-0.987214\pi$
$613$	−11.5084	+	19.9331i	−0.464820	+	0.805092i	0.534374	+	0.845248i	$0.320548\pi$
$614$		0			0
$615$	−5.06048			−0.204058
$616$		0			0
$617$	1.58729	+	2.74927i	0.0639018	+	0.110681i	0.896206	−	0.443637i	$-0.146312\pi$
$617$	1.58729	+	2.74927i	0.0639018	+	0.110681i	−0.832304	+	0.554319i	$0.812979\pi$
$618$		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	0.932085	−	0.362241i	$-0.117988\pi$
$631$	3.82655	+	6.62778i	0.152333	+	0.263848i	−0.779752	+	0.626089i	$0.784655\pi$
$632$		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	−0.999930	−	0.0118484i	$-0.996228\pi$
$641$	−12.3983	+	21.4745i	−0.489704	+	0.848192i	0.510226	+	0.860040i	$0.329562\pi$
$642$		0			0
$643$	−5.33860	+	9.24672i	−0.210534	+	0.364655i	−0.951882	−	0.306466i	$-0.900853\pi$
$643$	−5.33860	+	9.24672i	−0.210534	+	0.364655i	0.741348	+	0.671121i	$0.234187\pi$
$644$		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	0.933415	−	0.358798i	$-0.116813\pi$
$659$	4.00416	+	6.93541i	0.155980	+	0.270165i	−0.777436	+	0.628963i	$0.783480\pi$
$660$		0			0
$661$	−0.174640	−	0.302485i	−0.00679271	−	0.0117653i	0.862609	−	0.505871i	$-0.168829\pi$
$661$	−0.174640	−	0.302485i	−0.00679271	−	0.0117653i	−0.869402	+	0.494106i	$0.835496\pi$
$662$		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	0.337525	+	0.941317i	$0.390410\pi$
$701$	−17.1154	+	29.6448i	−0.646442	+	1.11967i	−0.983967	+	0.178353i	$0.942923\pi$
$702$		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	0.537993	−	0.842950i	$-0.319183\pi$
$709$	−12.2756	−	21.2619i	−0.461019	−	0.798509i	−0.999012	+	0.0444405i	$0.985850\pi$
$710$		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	−0.563160	−	0.826348i	$-0.690414\pi$
$719$	11.6389	−	20.1592i	0.434059	−	0.751812i	0.997218	+	0.0745364i	$0.0237477\pi$
$720$		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	−0.685833	−	0.727759i	$-0.740562\pi$
$727$	7.74757	−	13.4192i	0.287341	−	0.497690i	0.973174	+	0.230069i	$0.0738953\pi$
$728$		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	−0.489840	−	0.871812i	$-0.662945\pi$
$739$	13.8666	−	24.0177i	0.510091	−	0.883504i	0.999932	−	0.0116920i	$-0.00372175\pi$
$740$		0			0
$741$	−20.2604	+	2.68494i	−0.744285	+	0.0986338i
$742$		0			0
$743$	−7.25410	+	12.5645i	−0.266127	+	0.460945i	−0.967858	−	0.251496i	$-0.919077\pi$
$743$	−7.25410	+	12.5645i	−0.266127	+	0.460945i	0.701731	+	0.712442i	$0.252411\pi$
$744$		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	0.954265	+	0.298962i	$0.0966405\pi$
$751$	20.1708	+	34.9368i	0.736041	+	1.27486i	−0.218223	+	0.975899i	$0.570026\pi$
$752$		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	0.431866	+	0.901938i	$0.357855\pi$
$757$	−15.5498	+	26.9331i	−0.565168	+	0.978899i	−0.997034	+	0.0769617i	$0.975478\pi$
$758$		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	0.987889	+	0.155160i	$0.0495893\pi$
$769$	17.4238	+	30.1789i	0.628317	+	1.08828i	−0.359572	+	0.933117i	$0.617077\pi$
$770$		0			0
$771$	−14.4190			−0.519286
$772$		0			0
$773$	23.2918	+	40.3427i	0.837749	+	1.45102i	0.891772	+	0.452485i	$0.149462\pi$
$773$	23.2918	+	40.3427i	0.837749	+	1.45102i	−0.0540228	+	0.998540i	$0.517204\pi$
$774$		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	0.861833	−	0.507193i	$-0.169317\pi$
$811$	−0.237093	−	0.410657i	−0.00832546	−	0.0144201i	−0.870158	+	0.492773i	$0.835983\pi$
$812$		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	−0.989399	−	0.145226i	$-0.953609\pi$
$821$	−17.7783	−	30.7930i	−0.620469	−	1.07468i	0.368930	−	0.929457i	$-0.379724\pi$
$822$		0			0
$823$	−5.86006	−	10.1499i	−0.204269	−	0.353804i	0.745631	−	0.666359i	$-0.232148\pi$
$823$	−5.86006	−	10.1499i	−0.204269	−	0.353804i	−0.949900	+	0.312555i	$0.898815\pi$
$824$		0			0
$825$	−2.38689			−0.0831008
$826$		0			0
$827$	−16.8590	−	29.2007i	−0.586245	−	1.01541i	−0.994719	−	0.102636i	$-0.967272\pi$
$827$	−16.8590	−	29.2007i	−0.586245	−	1.01541i	0.408474	−	0.912770i	$-0.366061\pi$
$828$		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	−0.753562	−	0.657377i	$-0.771666\pi$
$839$	5.57657	−	9.65890i	0.192525	−	0.333462i	0.946086	+	0.323915i	$0.104999\pi$
$840$		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	−0.971621	−	0.236545i	$-0.923985\pi$
$853$	−8.20566	+	14.2126i	−0.280957	+	0.486631i	0.690664	+	0.723176i	$0.257318\pi$
$854$		0			0
$855$	7.75913	−	1.02825i	0.265357	−	0.0351655i
$856$		0			0
$857$	−8.76891	+	15.1882i	−0.299540	+	0.518819i	−0.976031	−	0.217632i	$-0.930167\pi$
$857$	−8.76891	+	15.1882i	−0.299540	+	0.518819i	0.676491	+	0.736451i	$0.263500\pi$
$858$		0			0
$859$	−15.7784	−	27.3290i	−0.538352	−	0.932453i	−0.998993	−	0.0448664i	$-0.985714\pi$
$859$	−15.7784	−	27.3290i	−0.538352	−	0.932453i	0.460641	−	0.887587i	$-0.347620\pi$
$860$		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	−0.312837	−	0.949807i	$-0.601279\pi$
$877$	19.7271	−	34.1684i	0.666138	−	1.15379i	0.978975	−	0.203979i	$-0.0653873\pi$
$878$		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	0.997377	−	0.0723788i	$-0.0230591\pi$
$883$	12.9561	+	22.4406i	0.436007	+	0.755186i	−0.561370	+	0.827565i	$0.689726\pi$
$884$		0			0
$885$	3.83425			0.128887
$886$		0			0
$887$	−0.731933	−	1.26774i	−0.0245759	−	0.0425667i	0.853476	−	0.521132i	$-0.174490\pi$
$887$	−0.731933	−	1.26774i	−0.0245759	−	0.0425667i	−0.878052	+	0.478566i	$0.841157\pi$
$888$		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	−0.492570	−	0.870273i	$-0.663942\pi$
$907$	15.2809	−	26.4673i	0.507393	−	0.878831i	0.999963	−	0.00855819i	$-0.00272419\pi$
$908$		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	−0.719187	−	0.694817i	$-0.755486\pi$
$929$	7.38016	−	12.7828i	0.242135	−	0.419391i	0.961322	+	0.275426i	$0.0888189\pi$
$930$		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	0.930149	+	0.367183i	$0.119678\pi$
$937$	23.9700	+	41.5172i	0.783064	+	1.35631i	−0.147084	+	0.989124i	$0.546989\pi$
$938$		0			0
$939$	−0.729818			−0.0238167
$940$		0			0
$941$	6.46031	+	11.1896i	0.210600	+	0.364770i	0.951903	−	0.306401i	$-0.0991249\pi$
$941$	6.46031	+	11.1896i	0.210600	+	0.364770i	−0.741302	+	0.671171i	$0.765792\pi$
$942$		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	0.0477927	+	0.998857i	$0.484781\pi$
$947$	−25.8847	+	44.8336i	−0.841139	+	1.45690i	−0.888932	+	0.458039i	$0.848552\pi$
$948$		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	−0.760817	−	0.648966i	$-0.775202\pi$
$953$	5.60652	−	9.71078i	0.181613	−	0.314563i	0.942430	+	0.334404i	$0.108535\pi$
$954$		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	−0.779871	−	0.625941i	$-0.784715\pi$
$967$	4.73120	−	8.19468i	0.152145	−	0.263523i	0.932016	+	0.362418i	$0.118049\pi$
$968$		0			0
$969$	3.51113	+	4.56771i	0.112794	+	0.146736i
$970$		0			0
$971$	18.0401	−	31.2464i	0.578934	−	1.00274i	−0.416668	−	0.909059i	$-0.636802\pi$
$971$	18.0401	−	31.2464i	0.578934	−	1.00274i	0.995602	−	0.0936844i	$-0.0298645\pi$
$972$		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	−0.958432	−	0.285322i	$-0.907899\pi$
$983$	−7.27761	+	12.6052i	−0.232120	+	0.402043i	0.726312	+	0.687365i	$0.241233\pi$
$984$		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	0.340128	+	0.940379i	$0.389530\pi$
$991$	−20.2836	+	35.1322i	−0.644328	+	1.11601i	−0.984456	+	0.175630i	$0.943804\pi$
$992$		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	−0.924578	−	0.380992i	$-0.875583\pi$
$997$	−25.0152	−	43.3275i	−0.792238	−	1.37220i	0.132340	−	0.991204i	$-0.457751\pi$
$998$		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.201.3	yes	8
4.3	odd	2		1520.2.q.k.961.2		8
19.7	even	3	inner	760.2.q.f.121.3	✓	8
76.7	odd	6		1520.2.q.k.881.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
760.2.q.f.121.3	✓	8	19.7	even	3	inner
760.2.q.f.201.3	yes	8	1.1	even	1	trivial
1520.2.q.k.881.2		8	76.7	odd	6
1520.2.q.k.961.2		8	4.3	odd	2

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

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