LMFDB - Embedded newform 676.2.e.f.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [676,2,Mod(529,676)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(676, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("676.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 676 = 2^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	676.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.39788717664$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.1
Root			$0.222521 + 0.385418i$ of defining polynomial
Character	$\chi$	$=$	676.529
Dual form			676.2.e.f.653.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.846011 + 1.46533i) q^{3} -1.19806 q^{5} +(2.14795 + 3.72036i) q^{7} +(0.0685317 + 0.118700i) q^{9} +(1.84601 - 3.19738i) q^{11} +(1.01357 - 1.75556i) q^{15} +(3.92543 + 6.79904i) q^{17} +(-2.32640 - 4.02944i) q^{19} -7.26875 q^{21} +(-1.85690 + 3.21624i) q^{23} -3.56465 q^{25} -5.30798 q^{27} +(-2.14795 + 3.72036i) q^{29} -2.91185 q^{31} +(3.12349 + 5.41004i) q^{33} +(-2.57338 - 4.45722i) q^{35} +(-4.01842 + 6.96010i) q^{37} +(4.05496 - 7.02339i) q^{41} +(-0.442353 - 0.766179i) q^{43} +(-0.0821052 - 0.142210i) q^{45} +4.58211 q^{47} +(-5.72737 + 9.92009i) q^{49} -13.2838 q^{51} +5.43296 q^{53} +(-2.21164 + 3.83067i) q^{55} +7.87263 q^{57} +(1.16487 + 2.01762i) q^{59} +(3.12833 + 5.41843i) q^{61} +(-0.294405 + 0.509924i) q^{63} +(-1.66756 + 2.88830i) q^{67} +(-3.14191 - 5.44194i) q^{69} +(-2.17845 - 3.77318i) q^{71} -3.82908 q^{73} +(3.01573 - 5.22340i) q^{75} +15.8605 q^{77} -10.5526 q^{79} +(4.28501 - 7.42186i) q^{81} -5.24698 q^{83} +(-4.70291 - 8.14567i) q^{85} +(-3.63437 - 6.29492i) q^{87} +(4.73341 - 8.19850i) q^{89} +(2.46346 - 4.26684i) q^{93} +(2.78717 + 4.82752i) q^{95} +(1.83997 + 3.18692i) q^{97} +0.506041 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 16 q^{5} - q^{7} - 5 q^{9} + 6 q^{11} + 10 q^{17} + 4 q^{19} - 28 q^{21} - 3 q^{23} + 22 q^{25} - 42 q^{27} + q^{29} - 10 q^{31} + 14 q^{33} + 12 q^{35} + 4 q^{37} + 25 q^{41} - 5 q^{43} + 11 q^{45}+ \cdots + 22 q^{99}+O(q^{100}) $ 6 * q - 16 * q^5 - q^7 - 5 * q^9 + 6 * q^11 + 10 * q^17 + 4 * q^19 - 28 * q^21 - 3 * q^23 + 22 * q^25 - 42 * q^27 + q^29 - 10 * q^31 + 14 * q^33 + 12 * q^35 + 4 * q^37 + 25 * q^41 - 5 * q^43 + 11 * q^45 + 16 * q^47 - 12 * q^49 - 14 * q^51 - 6 * q^53 - 16 * q^55 + 14 * q^57 + 9 * q^59 - 8 * q^61 - 18 * q^63 - 9 * q^67 + 14 * q^69 - 9 * q^71 - 2 * q^73 - 7 * q^75 + 24 * q^77 + 18 * q^79 + q^81 - 22 * q^83 - 15 * q^85 - 14 * q^87 + 25 * q^89 - 14 * q^93 - 27 * q^95 - 13 * q^97 + 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/676\mathbb{Z}\right)^\times$.

$n$	$339$	$509$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.846011	+	1.46533i	−0.488445	+	0.846011i	−0.999912	−	0.0132921i	$-0.995769\pi$
$3$	−0.846011	+	1.46533i	−0.488445	+	0.846011i	0.511467	+	0.859303i	$0.329102\pi$
$4$		0			0
$5$	−1.19806			−0.535790			−0.267895	−	0.963448i	$-0.586328\pi$
$5$	−1.19806			−0.535790			−0.267895	+	0.963448i	$0.586328\pi$
$6$		0			0
$7$	2.14795	+	3.72036i	0.811848	+	1.40616i	0.911569	+	0.411147i	$0.134872\pi$
$7$	2.14795	+	3.72036i	0.811848	+	1.40616i	−0.0997209	+	0.995015i	$0.531795\pi$
$8$		0			0
$9$	0.0685317	+	0.118700i	0.0228439	+	0.0395668i
$10$		0			0
$11$	1.84601	−	3.19738i	0.556593	−	0.964048i	−0.441184	−	0.897416i	$-0.645442\pi$
$11$	1.84601	−	3.19738i	0.556593	−	0.964048i	0.997778	−	0.0666312i	$-0.0212251\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$	1.01357	−	1.75556i	0.261704	−	0.453284i
$16$		0			0
$17$	3.92543	+	6.79904i	0.952056	+	1.64901i	0.740966	+	0.671543i	$0.234368\pi$
$17$	3.92543	+	6.79904i	0.952056	+	1.64901i	0.211090	+	0.977467i	$0.432299\pi$
$18$		0			0
$19$	−2.32640	−	4.02944i	−0.533712	−	0.924416i	−0.999225	−	0.0393749i	$-0.987463\pi$
$19$	−2.32640	−	4.02944i	−0.533712	−	0.924416i	0.465513	−	0.885041i	$-0.345870\pi$
$20$		0			0
$21$	−7.26875			−1.58617
$22$		0			0
$23$	−1.85690	+	3.21624i	−0.387190	+	0.670632i	−0.992070	−	0.125684i	$-0.959887\pi$
$23$	−1.85690	+	3.21624i	−0.387190	+	0.670632i	0.604881	+	0.796316i	$0.293221\pi$
$24$		0			0
$25$	−3.56465			−0.712929
$26$		0			0
$27$	−5.30798			−1.02152
$28$		0			0
$29$	−2.14795	+	3.72036i	−0.398864	+	0.690853i	−0.993586	−	0.113079i	$-0.963929\pi$
$29$	−2.14795	+	3.72036i	−0.398864	+	0.690853i	0.594722	+	0.803931i	$0.297262\pi$
$30$		0			0
$31$	−2.91185			−0.522984			−0.261492	−	0.965206i	$-0.584215\pi$
$31$	−2.91185			−0.522984			−0.261492	+	0.965206i	$0.584215\pi$
$32$		0			0
$33$	3.12349	+	5.41004i	0.543730	+	0.941768i
$34$		0			0
$35$	−2.57338	−	4.45722i	−0.434980	−	0.753407i
$36$		0			0
$37$	−4.01842	+	6.96010i	−0.660624	+	1.14423i	0.319828	+	0.947476i	$0.396375\pi$
$37$	−4.01842	+	6.96010i	−0.660624	+	1.14423i	−0.980452	+	0.196758i	$0.936959\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.05496	−	7.02339i	0.633278	−	1.09687i	−0.353599	−	0.935397i	$-0.615042\pi$
$41$	4.05496	−	7.02339i	0.633278	−	1.09687i	0.986877	−	0.161473i	$-0.0516244\pi$
$42$		0			0
$43$	−0.442353	−	0.766179i	−0.0674583	−	0.116841i	0.830324	−	0.557282i	$-0.188156\pi$
$43$	−0.442353	−	0.766179i	−0.0674583	−	0.116841i	−0.897782	+	0.440440i	$0.854822\pi$
$44$		0			0
$45$	−0.0821052	−	0.142210i	−0.0122395	−	0.0211995i
$46$		0			0
$47$	4.58211			0.668369			0.334184	−	0.942508i	$-0.391539\pi$
$47$	4.58211			0.668369			0.334184	+	0.942508i	$0.391539\pi$
$48$		0			0
$49$	−5.72737	+	9.92009i	−0.818195	+	1.41716i
$50$		0			0
$51$	−13.2838			−1.86011
$52$		0			0
$53$	5.43296			0.746274			0.373137	−	0.927776i	$-0.378282\pi$
$53$	5.43296			0.746274			0.373137	+	0.927776i	$0.378282\pi$
$54$		0			0
$55$	−2.21164	+	3.83067i	−0.298217	+	0.516527i
$56$		0			0
$57$	7.87263			1.04275
$58$		0			0
$59$	1.16487	+	2.01762i	0.151654	+	0.262672i	0.931836	−	0.362881i	$-0.118207\pi$
$59$	1.16487	+	2.01762i	0.151654	+	0.262672i	−0.780182	+	0.625553i	$0.784873\pi$
$60$		0			0
$61$	3.12833	+	5.41843i	0.400542	+	0.693759i	0.993791	−	0.111259i	$-0.0354885\pi$
$61$	3.12833	+	5.41843i	0.400542	+	0.693759i	−0.593249	+	0.805019i	$0.702155\pi$
$62$		0			0
$63$	−0.294405	+	0.509924i	−0.0370915	+	0.0642444i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−1.66756	+	2.88830i	−0.203725	+	0.352862i	−0.949726	−	0.313083i	$-0.898638\pi$
$67$	−1.66756	+	2.88830i	−0.203725	+	0.352862i	0.746001	+	0.665945i	$0.231972\pi$
$68$		0			0
$69$	−3.14191	−	5.44194i	−0.378241	−	0.655133i
$70$		0			0
$71$	−2.17845	−	3.77318i	−0.258534	−	0.447794i	0.707315	−	0.706898i	$-0.249906\pi$
$71$	−2.17845	−	3.77318i	−0.258534	−	0.447794i	−0.965849	+	0.259104i	$0.916573\pi$
$72$		0			0
$73$	−3.82908			−0.448160			−0.224080	−	0.974571i	$-0.571938\pi$
$73$	−3.82908			−0.448160			−0.224080	+	0.974571i	$0.571938\pi$
$74$		0			0
$75$	3.01573	−	5.22340i	0.348226	−	0.603146i
$76$		0			0
$77$	15.8605			1.80748
$78$		0			0
$79$	−10.5526			−1.18726			−0.593628	−	0.804739i	$-0.702305\pi$
$79$	−10.5526			−1.18726			−0.593628	+	0.804739i	$0.702305\pi$
$80$		0			0
$81$	4.28501	−	7.42186i	0.476112	−	0.824651i
$82$		0			0
$83$	−5.24698			−0.575931			−0.287965	−	0.957641i	$-0.592979\pi$
$83$	−5.24698			−0.575931			−0.287965	+	0.957641i	$0.592979\pi$
$84$		0			0
$85$	−4.70291	−	8.14567i	−0.510102	−	0.883522i
$86$		0			0
$87$	−3.63437	−	6.29492i	−0.389646	−	0.674886i
$88$		0			0
$89$	4.73341	−	8.19850i	0.501740	−	0.869039i	−0.498258	−	0.867029i	$-0.666027\pi$
$89$	4.73341	−	8.19850i	0.501740	−	0.869039i	0.999998	−	0.00201039i	$-0.000639928\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	2.46346	−	4.26684i	0.255449	−	0.442450i
$94$		0			0
$95$	2.78717	+	4.82752i	0.285957	+	0.495293i
$96$		0			0
$97$	1.83997	+	3.18692i	0.186821	+	0.323583i	0.944189	−	0.329406i	$-0.106848\pi$
$97$	1.83997	+	3.18692i	0.186821	+	0.323583i	−0.757368	+	0.652988i	$0.773515\pi$
$98$		0			0
$99$	0.506041			0.0508590
$100$		0			0
$101$	8.56249	−	14.8307i	0.852000	−	1.47571i	−0.0274011	−	0.999625i	$-0.508723\pi$
$101$	8.56249	−	14.8307i	0.852000	−	1.47571i	0.879401	−	0.476082i	$-0.157944\pi$
$102$		0			0
$103$	8.14675			0.802723			0.401362	−	0.915920i	$-0.368537\pi$
$103$	8.14675			0.802723			0.401362	+	0.915920i	$0.368537\pi$
$104$		0			0
$105$	8.70841			0.849854
$106$		0			0
$107$	−0.282323	+	0.488998i	−0.0272932	+	0.0472733i	−0.879349	−	0.476177i	$-0.842022\pi$
$107$	−0.282323	+	0.488998i	−0.0272932	+	0.0472733i	0.852056	+	0.523450i	$0.175355\pi$
$108$		0			0
$109$	−2.04354			−0.195736			−0.0978678	−	0.995199i	$-0.531202\pi$
$109$	−2.04354			−0.195736			−0.0978678	+	0.995199i	$0.531202\pi$
$110$		0			0
$111$	−6.79925	−	11.7766i	−0.645356	−	1.11779i
$112$		0			0
$113$	6.89224	+	11.9377i	0.648367	+	1.12301i	0.983513	+	0.180839i	$0.0578812\pi$
$113$	6.89224	+	11.9377i	0.648367	+	1.12301i	−0.335145	+	0.942166i	$0.608785\pi$
$114$		0			0
$115$	2.22468	−	3.85325i	0.207452	−	0.359318i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−16.8632	+	29.2080i	−1.54585	+	2.67749i
$120$		0			0
$121$	−1.31551	−	2.27853i	−0.119592	−	0.207139i
$122$		0			0
$123$	6.86108	+	11.8837i	0.618642	+	1.07152i
$124$		0			0
$125$	10.2610			0.917770
$126$		0			0
$127$	3.15399	−	5.46287i	0.279871	−	0.484751i	−0.691481	−	0.722394i	$-0.743042\pi$
$127$	3.15399	−	5.46287i	0.279871	−	0.484751i	0.971353	+	0.237643i	$0.0763749\pi$
$128$		0			0
$129$	1.49694			0.131798
$130$		0			0
$131$	14.2959			1.24904			0.624519	−	0.781009i	$-0.285295\pi$
$131$	14.2959			1.24904			0.624519	+	0.781009i	$0.285295\pi$
$132$		0			0
$133$	9.99396	−	17.3100i	0.866586	−	1.50097i
$134$		0			0
$135$	6.35929			0.547320
$136$		0			0
$137$	5.60388	+	9.70620i	0.478771	+	0.829256i	0.999704	−	0.0243416i	$-0.00774894\pi$
$137$	5.60388	+	9.70620i	0.478771	+	0.829256i	−0.520932	+	0.853598i	$0.674416\pi$
$138$		0			0
$139$	−2.28232	−	3.95310i	−0.193584	−	0.335298i	0.752851	−	0.658191i	$-0.228678\pi$
$139$	−2.28232	−	3.95310i	−0.193584	−	0.335298i	−0.946435	+	0.322893i	$0.895345\pi$
$140$		0			0
$141$	−3.87651	+	6.71431i	−0.326461	+	0.565447i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	2.57338	−	4.45722i	0.213707	−	0.370152i
$146$		0			0
$147$	−9.69083	−	16.7850i	−0.799286	−	1.38440i
$148$		0			0
$149$	10.8373	+	18.7707i	0.887825	+	1.53776i	0.842441	+	0.538788i	$0.181118\pi$
$149$	10.8373	+	18.7707i	0.887825	+	1.53776i	0.0453832	+	0.998970i	$0.485549\pi$
$150$		0			0
$151$	20.9758			1.70699			0.853495	−	0.521102i	$-0.174479\pi$
$151$	20.9758			1.70699			0.853495	+	0.521102i	$0.174479\pi$
$152$		0			0
$153$	−0.538032	+	0.931899i	−0.0434973	+	0.0753396i
$154$		0			0
$155$	3.48858			0.280210
$156$		0			0
$157$	3.62565			0.289358			0.144679	−	0.989479i	$-0.453785\pi$
$157$	3.62565			0.289358			0.144679	+	0.989479i	$0.453785\pi$
$158$		0			0
$159$	−4.59634	+	7.96110i	−0.364514	+	0.631356i
$160$		0			0
$161$	−15.9541			−1.25736
$162$		0			0
$163$	−10.8862	−	18.8554i	−0.852673	−	1.47687i	−0.878787	−	0.477214i	$-0.841647\pi$
$163$	−10.8862	−	18.8554i	−0.852673	−	1.47687i	0.0261143	−	0.999659i	$-0.491687\pi$
$164$		0			0
$165$	−3.74214	−	6.48157i	−0.291325	−	0.504589i
$166$		0			0
$167$	1.40581	−	2.43494i	0.108785	−	0.188421i	−0.806493	−	0.591243i	$-0.798637\pi$
$167$	1.40581	−	2.43494i	0.108785	−	0.188421i	0.915278	+	0.402822i	$0.131971\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	0.318864	−	0.552288i	0.0243841	−	0.0422345i
$172$		0			0
$173$	−3.50604	−	6.07264i	−0.266559	−	0.461694i	0.701412	−	0.712756i	$-0.252553\pi$
$173$	−3.50604	−	6.07264i	−0.266559	−	0.461694i	−0.967971	+	0.251062i	$0.919220\pi$
$174$		0			0
$175$	−7.65668	−	13.2618i	−0.578790	−	1.00249i
$176$		0			0
$177$	−3.94198			−0.296298
$178$		0			0
$179$	7.74309	−	13.4114i	0.578746	−	1.00242i	−0.416877	−	0.908963i	$-0.636876\pi$
$179$	7.74309	−	13.4114i	0.578746	−	1.00242i	0.995624	−	0.0934549i	$-0.0297911\pi$
$180$		0			0
$181$	5.67456			0.421787			0.210893	−	0.977509i	$-0.432363\pi$
$181$	5.67456			0.421787			0.210893	+	0.977509i	$0.432363\pi$
$182$		0			0
$183$	−10.5864			−0.782570
$184$		0			0
$185$	4.81431	−	8.33864i	0.353955	−	0.613069i
$186$		0			0
$187$	28.9855			2.11963
$188$		0			0
$189$	−11.4013	−	19.7476i	−0.829320	−	1.43642i
$190$		0			0
$191$	10.2932	+	17.8284i	0.744790	+	1.29001i	0.950293	+	0.311358i	$0.100784\pi$
$191$	10.2932	+	17.8284i	0.744790	+	1.29001i	−0.205502	+	0.978657i	$0.565883\pi$
$192$		0			0
$193$	−9.47650	+	16.4138i	−0.682133	+	1.18149i	0.292195	+	0.956359i	$0.405614\pi$
$193$	−9.47650	+	16.4138i	−0.682133	+	1.18149i	−0.974328	+	0.225131i	$0.927719\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.17025	+	2.02693i	−0.0833769	+	0.144413i	−0.904698	−	0.426052i	$-0.859904\pi$
$197$	−1.17025	+	2.02693i	−0.0833769	+	0.144413i	0.821321	+	0.570466i	$0.193237\pi$
$198$		0			0
$199$	−2.82036	−	4.88500i	−0.199930	−	0.346288i	0.748576	−	0.663049i	$-0.230738\pi$
$199$	−2.82036	−	4.88500i	−0.199930	−	0.346288i	−0.948505	+	0.316761i	$0.897405\pi$
$200$		0			0
$201$	−2.82155	−	4.88707i	−0.199017	−	0.344707i
$202$		0			0
$203$	−18.4547			−1.29527
$204$		0			0
$205$	−4.85809	+	8.41446i	−0.339304	+	0.587692i
$206$		0			0
$207$	−0.509025			−0.0353797
$208$		0			0
$209$	−17.1782			−1.18824
$210$		0			0
$211$	−0.291053	+	0.504118i	−0.0200369	+	0.0347049i	−0.875870	−	0.482547i	$-0.839712\pi$
$211$	−0.291053	+	0.504118i	−0.0200369	+	0.0347049i	0.855833	+	0.517252i	$0.173045\pi$
$212$		0			0
$213$	7.37196			0.505118
$214$		0			0
$215$	0.529967	+	0.917930i	0.0361434	+	0.0626023i
$216$		0			0
$217$	−6.25451	−	10.8331i	−0.424584	−	0.735401i
$218$		0			0
$219$	3.23945	−	5.61089i	0.218902	−	0.379149i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	7.61476	−	13.1892i	0.509922	−	0.883211i	−0.490012	−	0.871716i	$-0.663008\pi$
$223$	7.61476	−	13.1892i	0.509922	−	0.883211i	0.999934	−	0.0114952i	$-0.00365911\pi$
$224$		0			0
$225$	−0.244291	−	0.423125i	−0.0162861	−	0.0282083i
$226$		0			0
$227$	−6.72617	−	11.6501i	−0.446432	−	0.773242i	0.551719	−	0.834030i	$-0.313972\pi$
$227$	−6.72617	−	11.6501i	−0.446432	−	0.773242i	−0.998151	+	0.0607879i	$0.980639\pi$
$228$		0			0
$229$	7.11529			0.470192			0.235096	−	0.971972i	$-0.424460\pi$
$229$	7.11529			0.470192			0.235096	+	0.971972i	$0.424460\pi$
$230$		0			0
$231$	−13.4182	+	23.2410i	−0.882852	+	1.52914i
$232$		0			0
$233$	7.36898			0.482758			0.241379	−	0.970431i	$-0.422400\pi$
$233$	7.36898			0.482758			0.241379	+	0.970431i	$0.422400\pi$
$234$		0			0
$235$	−5.48965			−0.358105
$236$		0			0
$237$	8.92758	−	15.4630i	0.579909	−	1.00443i
$238$		0			0
$239$	−8.34481			−0.539781			−0.269891	−	0.962891i	$-0.586988\pi$
$239$	−8.34481			−0.539781			−0.269891	+	0.962891i	$0.586988\pi$
$240$		0			0
$241$	3.24214	+	5.61554i	0.208844	+	0.361729i	0.951351	−	0.308110i	$-0.0996965\pi$
$241$	3.24214	+	5.61554i	0.208844	+	0.361729i	−0.742506	+	0.669839i	$0.766363\pi$
$242$		0			0
$243$	−0.711636	−	1.23259i	−0.0456515	−	0.0790706i
$244$		0			0
$245$	6.86174	−	11.8849i	0.438381	−	0.759297i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	4.43900	−	7.68858i	0.281310	−	0.487244i
$250$		0			0
$251$	3.63102	+	6.28912i	0.229188	+	0.396965i	0.957568	−	0.288208i	$-0.0930596\pi$
$251$	3.63102	+	6.28912i	0.229188	+	0.396965i	−0.728380	+	0.685174i	$0.759726\pi$
$252$		0			0
$253$	6.85570	+	11.8744i	0.431014	+	0.746538i
$254$		0			0
$255$	15.9148			0.996626
$256$		0			0
$257$	6.81820	−	11.8095i	0.425308	−	0.736654i	−0.571141	−	0.820852i	$-0.693499\pi$
$257$	6.81820	−	11.8095i	0.425308	−	0.736654i	0.996449	+	0.0841972i	$0.0268326\pi$
$258$		0			0
$259$	−34.5254			−2.14531
$260$		0			0
$261$	−0.588810			−0.0364464
$262$		0			0
$263$	−5.65615	+	9.79673i	−0.348773	+	0.604092i	−0.986032	−	0.166557i	$-0.946735\pi$
$263$	−5.65615	+	9.79673i	−0.348773	+	0.604092i	0.637259	+	0.770650i	$0.280068\pi$
$264$		0			0
$265$	−6.50902			−0.399846
$266$		0			0
$267$	8.00902	+	13.8720i	0.490144	+	0.848955i
$268$		0			0
$269$	−0.334593	−	0.579532i	−0.0204005	−	0.0353347i	0.855645	−	0.517563i	$-0.173161\pi$
$269$	−0.334593	−	0.579532i	−0.0204005	−	0.0353347i	−0.876045	+	0.482229i	$0.839827\pi$
$270$		0			0
$271$	−10.2051	+	17.6757i	−0.619913	+	1.07372i	0.369588	+	0.929196i	$0.379499\pi$
$271$	−10.2051	+	17.6757i	−0.619913	+	1.07372i	−0.989501	+	0.144526i	$0.953834\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−6.58038	+	11.3975i	−0.396812	+	0.687298i
$276$		0			0
$277$	1.24429	+	2.15518i	0.0747622	+	0.129492i	0.900983	−	0.433855i	$-0.142847\pi$
$277$	1.24429	+	2.15518i	0.0747622	+	0.129492i	−0.826221	+	0.563347i	$0.809514\pi$
$278$		0			0
$279$	−0.199554	−	0.345638i	−0.0119470	−	0.0206928i
$280$		0			0
$281$	−16.6310			−0.992124			−0.496062	−	0.868287i	$-0.665221\pi$
$281$	−16.6310			−0.992124			−0.496062	+	0.868287i	$0.665221\pi$
$282$		0			0
$283$	−1.43296	+	2.48196i	−0.0851806	+	0.147537i	−0.905468	−	0.424414i	$-0.860480\pi$
$283$	−1.43296	+	2.48196i	−0.0851806	+	0.147537i	0.820288	+	0.571951i	$0.193813\pi$
$284$		0			0
$285$	−9.43190			−0.558697
$286$		0			0
$287$	34.8394			2.05650
$288$		0			0
$289$	−22.3180	+	38.6558i	−1.31282	+	2.27387i
$290$		0			0
$291$	−6.22654			−0.365006
$292$		0			0
$293$	15.3855	+	26.6485i	0.898833	+	1.55682i	0.828988	+	0.559266i	$0.188917\pi$
$293$	15.3855	+	26.6485i	0.898833	+	1.55682i	0.0698441	+	0.997558i	$0.477750\pi$
$294$		0			0
$295$	−1.39559	−	2.41724i	−0.0812545	−	0.140737i
$296$		0			0
$297$	−9.79859	+	16.9716i	−0.568572	+	0.984795i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	1.90030	−	3.29142i	0.109532	−	0.189715i
$302$		0			0
$303$	14.4879	+	25.0938i	0.832309	+	1.44160i
$304$		0			0
$305$	−3.74794	−	6.49162i	−0.214606	−	0.371709i
$306$		0			0
$307$	−20.2392			−1.15511			−0.577556	−	0.816351i	$-0.695994\pi$
$307$	−20.2392			−1.15511			−0.577556	+	0.816351i	$0.695994\pi$
$308$		0			0
$309$	−6.89224	+	11.9377i	−0.392086	+	0.679113i
$310$		0			0
$311$	18.8442			1.06855			0.534277	−	0.845310i	$-0.320584\pi$
$311$	18.8442			1.06855			0.534277	+	0.845310i	$0.320584\pi$
$312$		0			0
$313$	4.87263			0.275417			0.137709	−	0.990473i	$-0.456026\pi$
$313$	4.87263			0.275417			0.137709	+	0.990473i	$0.456026\pi$
$314$		0			0
$315$	0.352716	−	0.610921i	0.0198733	−	0.0344215i
$316$		0			0
$317$	−13.2185			−0.742425			−0.371213	−	0.928548i	$-0.621058\pi$
$317$	−13.2185			−0.742425			−0.371213	+	0.928548i	$0.621058\pi$
$318$		0			0
$319$	7.93027	+	13.7356i	0.444010	+	0.769048i
$320$		0			0
$321$	−0.477697	−	0.827396i	−0.0266625	−	0.0461807i
$322$		0			0
$323$	18.2642	−	31.6345i	1.01625	−	1.76019i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	1.72886	−	2.99447i	0.0956060	−	0.165594i
$328$		0			0
$329$	9.84213	+	17.0471i	0.542614	+	0.939835i
$330$		0			0
$331$	10.9025	+	18.8836i	0.599253	+	1.03794i	0.992931	+	0.118689i	$0.0378692\pi$
$331$	10.9025	+	18.8836i	0.599253	+	1.03794i	−0.393678	+	0.919248i	$0.628798\pi$
$332$		0			0
$333$	−1.10156			−0.0603649
$334$		0			0
$335$	1.99784	−	3.46037i	0.109154	−	0.189060i
$336$		0			0
$337$	−10.1564			−0.553257			−0.276628	−	0.960977i	$-0.589217\pi$
$337$	−10.1564			−0.553257			−0.276628	+	0.960977i	$0.589217\pi$
$338$		0			0
$339$	−23.3236			−1.26677
$340$		0			0
$341$	−5.37531	+	9.31032i	−0.291090	+	0.504182i
$342$		0			0
$343$	−19.1371			−1.03330
$344$		0			0
$345$	3.76420	+	6.51979i	0.202658	+	0.351014i
$346$		0			0
$347$	−13.9417	−	24.1477i	−0.748429	−	1.29632i	−0.948575	−	0.316551i	$-0.897475\pi$
$347$	−13.9417	−	24.1477i	−0.748429	−	1.29632i	0.200146	−	0.979766i	$-0.435858\pi$
$348$		0			0
$349$	17.7104	−	30.6754i	0.948018	−	1.64202i	0.198426	−	0.980116i	$-0.436417\pi$
$349$	17.7104	−	30.6754i	0.948018	−	1.64202i	0.749593	−	0.661900i	$-0.230249\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	4.49516	−	7.78584i	0.239253	−	0.414398i	−0.721247	−	0.692678i	$-0.756431\pi$
$353$	4.49516	−	7.78584i	0.239253	−	0.414398i	0.960500	+	0.278279i	$0.0897641\pi$
$354$		0			0
$355$	2.60992	+	4.52051i	0.138520	+	0.239924i
$356$		0			0
$357$	−28.5330	−	49.4205i	−1.51012	−	2.61561i
$358$		0			0
$359$	−4.83446			−0.255153			−0.127577	−	0.991829i	$-0.540720\pi$
$359$	−4.83446			−0.255153			−0.127577	+	0.991829i	$0.540720\pi$
$360$		0			0
$361$	−1.32424	+	2.29365i	−0.0696969	+	0.120719i
$362$		0			0
$363$	4.45175			0.233656
$364$		0			0
$365$	4.58748			0.240120
$366$		0			0
$367$	14.2039	−	24.6018i	0.741436	−	1.28420i	−0.210406	−	0.977614i	$-0.567479\pi$
$367$	14.2039	−	24.6018i	0.741436	−	1.28420i	0.951842	−	0.306590i	$-0.0991881\pi$
$368$		0			0
$369$	1.11157			0.0578661
$370$		0			0
$371$	11.6697	+	20.2125i	0.605862	+	1.04938i
$372$		0			0
$373$	13.1984	+	22.8602i	0.683385	+	1.18366i	0.973941	+	0.226800i	$0.0728263\pi$
$373$	13.1984	+	22.8602i	0.683385	+	1.18366i	−0.290556	+	0.956858i	$0.593840\pi$
$374$		0			0
$375$	−8.68090	+	15.0358i	−0.448280	+	0.776443i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	9.93080	−	17.2007i	0.510111	−	0.883538i	−0.489820	−	0.871823i	$-0.662938\pi$
$379$	9.93080	−	17.2007i	0.510111	−	0.883538i	0.999931	−	0.0117150i	$-0.00372908\pi$
$380$		0			0
$381$	5.33662	+	9.24329i	0.273403	+	0.473548i
$382$		0			0
$383$	0.109916	+	0.190381i	0.00561646	+	0.00972799i	0.868820	−	0.495128i	$-0.164879\pi$
$383$	0.109916	+	0.190381i	0.00561646	+	0.00972799i	−0.863204	+	0.504856i	$0.831546\pi$
$384$		0			0
$385$	−19.0019			−0.968427
$386$		0			0
$387$	0.0606304	−	0.105015i	0.00308202	−	0.00533821i
$388$		0			0
$389$	−10.0543			−0.509773			−0.254886	−	0.966971i	$-0.582038\pi$
$389$	−10.0543			−0.509773			−0.254886	+	0.966971i	$0.582038\pi$
$390$		0			0
$391$	−29.1564			−1.47450
$392$		0			0
$393$	−12.0945	+	20.9483i	−0.610086	+	1.05670i
$394$		0			0
$395$	12.6426			0.636120
$396$		0			0
$397$	2.88016	+	4.98858i	0.144551	+	0.250370i	0.929205	−	0.369564i	$-0.120493\pi$
$397$	2.88016	+	4.98858i	0.144551	+	0.250370i	−0.784654	+	0.619934i	$0.787160\pi$
$398$		0			0
$399$	16.9100	+	29.2890i	0.846559	+	1.46628i
$400$		0			0
$401$	17.4650	−	30.2502i	0.872158	−	1.51062i	0.0123985	−	0.999923i	$-0.496053\pi$
$401$	17.4650	−	30.2502i	0.872158	−	1.51062i	0.859760	−	0.510699i	$-0.170613\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−5.13371	+	8.89185i	−0.255096	+	0.441839i
$406$		0			0
$407$	14.8361	+	25.6969i	0.735397	+	1.27375i
$408$		0			0
$409$	−5.92208	−	10.2573i	−0.292828	−	0.507193i	0.681649	−	0.731679i	$-0.261263\pi$
$409$	−5.92208	−	10.2573i	−0.292828	−	0.507193i	−0.974477	+	0.224486i	$0.927930\pi$
$410$		0			0
$411$	−18.9638			−0.935413
$412$		0			0
$413$	−5.00418	+	8.66749i	−0.246240	+	0.426500i
$414$		0			0
$415$	6.28621			0.308578
$416$		0			0
$417$	7.72348			0.378220
$418$		0			0
$419$	−5.37651	+	9.31239i	−0.262660	+	0.454940i	−0.966948	−	0.254974i	$-0.917933\pi$
$419$	−5.37651	+	9.31239i	−0.262660	+	0.454940i	0.704288	+	0.709914i	$0.251266\pi$
$420$		0			0
$421$	37.6722			1.83603			0.918015	−	0.396547i	$-0.129791\pi$
$421$	37.6722			1.83603			0.918015	+	0.396547i	$0.129791\pi$
$422$		0			0
$423$	0.314019	+	0.543897i	0.0152681	+	0.0264452i
$424$		0			0
$425$	−13.9928	−	24.2362i	−0.678749	−	1.17563i
$426$		0			0
$427$	−13.4390	+	23.2770i	−0.650359	+	1.12645i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	11.6564	−	20.1895i	0.561471	−	0.972496i	−0.435897	−	0.899996i	$-0.643569\pi$
$431$	11.6564	−	20.1895i	0.561471	−	0.972496i	0.997368	−	0.0724999i	$-0.0230977\pi$
$432$		0			0
$433$	−11.6184	−	20.1237i	−0.558345	−	0.967082i	−0.997635	−	0.0687366i	$-0.978103\pi$
$433$	−11.6184	−	20.1237i	−0.558345	−	0.967082i	0.439290	−	0.898345i	$-0.355230\pi$
$434$		0			0
$435$	4.35421	+	7.54171i	0.208768	+	0.361597i
$436$		0			0
$437$	17.2795			0.826591
$438$		0			0
$439$	−9.30947	+	16.1245i	−0.444317	+	0.769579i	−0.998004	−	0.0631452i	$-0.979887\pi$
$439$	−9.30947	+	16.1245i	−0.444317	+	0.769579i	0.553688	+	0.832724i	$0.313220\pi$
$440$		0			0
$441$	−1.57002			−0.0747630
$442$		0			0
$443$	27.0180			1.28367			0.641833	−	0.766844i	$-0.278174\pi$
$443$	27.0180			1.28367			0.641833	+	0.766844i	$0.278174\pi$
$444$		0			0
$445$	−5.67092	+	9.82231i	−0.268827	+	0.465622i
$446$		0			0
$447$	−36.6738			−1.73461
$448$		0			0
$449$	−15.3354	−	26.5617i	−0.723723	−	1.25353i	−0.959497	−	0.281718i	$-0.909096\pi$
$449$	−15.3354	−	26.5617i	−0.723723	−	1.25353i	0.235774	−	0.971808i	$-0.424237\pi$
$450$		0			0
$451$	−14.9710	−	25.9305i	−0.704957	−	1.22102i
$452$		0			0
$453$	−17.7458	+	30.7366i	−0.833770	+	1.44413i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−8.72132	+	15.1058i	−0.407966	+	0.706618i	−0.994662	−	0.103189i	$-0.967095\pi$
$457$	−8.72132	+	15.1058i	−0.407966	+	0.706618i	0.586695	+	0.809808i	$0.300429\pi$
$458$		0			0
$459$	−20.8361	−	36.0892i	−0.972545	−	1.68450i
$460$		0			0
$461$	13.5184	+	23.4146i	0.629615	+	1.09053i	0.987629	+	0.156810i	$0.0501209\pi$
$461$	13.5184	+	23.4146i	0.629615	+	1.09053i	−0.358013	+	0.933716i	$0.616546\pi$
$462$		0			0
$463$	7.90408			0.367334			0.183667	−	0.982989i	$-0.441203\pi$
$463$	7.90408			0.367334			0.183667	+	0.982989i	$0.441203\pi$
$464$		0			0
$465$	−2.95138	+	5.11194i	−0.136867	+	0.237060i
$466$		0			0
$467$	−14.7845			−0.684144			−0.342072	−	0.939674i	$-0.611129\pi$
$467$	−14.7845			−0.684144			−0.342072	+	0.939674i	$0.611129\pi$
$468$		0			0
$469$	−14.3274			−0.661576
$470$		0			0
$471$	−3.06734	+	5.31278i	−0.141335	+	0.244800i
$472$		0			0
$473$	−3.26636			−0.150187
$474$		0			0
$475$	8.29278	+	14.3635i	0.380499	+	0.659043i
$476$		0			0
$477$	0.372330	+	0.644894i	0.0170478	+	0.0295277i
$478$		0			0
$479$	−5.76122	+	9.97872i	−0.263237	+	0.455939i	−0.967100	−	0.254396i	$-0.918123\pi$
$479$	−5.76122	+	9.97872i	−0.263237	+	0.455939i	0.703863	+	0.710335i	$0.251457\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	13.4973	−	23.3780i	0.614149	−	1.06374i
$484$		0			0
$485$	−2.20440	−	3.81813i	−0.100097	−	0.173372i
$486$		0			0
$487$	−16.3708	−	28.3550i	−0.741830	−	1.28489i	−0.951661	−	0.307150i	$-0.900625\pi$
$487$	−16.3708	−	28.3550i	−0.741830	−	1.28489i	0.209831	−	0.977738i	$-0.432709\pi$
$488$		0			0
$489$	36.8394			1.66593
$490$		0			0
$491$	−0.0534662	+	0.0926061i	−0.00241289	+	0.00417926i	−0.867229	−	0.497909i	$-0.834101\pi$
$491$	−0.0534662	+	0.0926061i	−0.00241289	+	0.00417926i	0.864816	+	0.502088i	$0.167435\pi$
$492$		0			0
$493$	−33.7265			−1.51896
$494$		0			0
$495$	−0.606268			−0.0272497
$496$		0			0
$497$	9.35839	−	16.2092i	0.419781	−	0.727082i
$498$		0			0
$499$	−5.58402			−0.249975			−0.124988	−	0.992158i	$-0.539889\pi$
$499$	−5.58402			−0.249975			−0.124988	+	0.992158i	$0.539889\pi$
$500$		0			0
$501$	2.37867	+	4.11997i	0.106271	+	0.184067i
$502$		0			0
$503$	6.65668	+	11.5297i	0.296807	+	0.514084i	0.975404	−	0.220427i	$-0.0707450\pi$
$503$	6.65668	+	11.5297i	0.296807	+	0.514084i	−0.678597	+	0.734511i	$0.737412\pi$
$504$		0			0
$505$	−10.2584	+	17.7681i	−0.456493	+	0.790669i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−11.7630	+	20.3741i	−0.521386	+	0.903067i	0.478305	+	0.878194i	$0.341251\pi$
$509$	−11.7630	+	20.3741i	−0.521386	+	0.903067i	−0.999691	+	0.0248731i	$0.992082\pi$
$510$		0			0
$511$	−8.22468	−	14.2456i	−0.363838	−	0.630186i
$512$		0			0
$513$	12.3485	+	21.3882i	0.545198	+	0.944311i
$514$		0			0
$515$	−9.76032			−0.430091
$516$		0			0
$517$	8.45862	−	14.6508i	0.372009	−	0.644339i
$518$		0			0
$519$	11.8646			0.520798
$520$		0			0
$521$	−9.20046			−0.403079			−0.201540	−	0.979480i	$-0.564594\pi$
$521$	−9.20046			−0.403079			−0.201540	+	0.979480i	$0.564594\pi$
$522$		0			0
$523$	17.7805	−	30.7967i	0.777485	−	1.34664i	−0.155902	−	0.987773i	$-0.549828\pi$
$523$	17.7805	−	30.7967i	0.777485	−	1.34664i	0.933387	−	0.358872i	$-0.116838\pi$
$524$		0			0
$525$	25.9105			1.13083
$526$		0			0
$527$	−11.4303	−	19.7978i	−0.497910	−	0.862406i
$528$		0			0
$529$	4.60388	+	7.97415i	0.200168	+	0.346702i
$530$		0			0
$531$	−0.159662	+	0.276542i	−0.00692872	+	0.0120009i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	0.338241	−	0.585851i	0.0146234	−	0.0253285i
$536$		0			0
$537$	13.1015	+	22.6924i	0.565371	+	0.979251i
$538$		0			0
$539$	21.1456	+	36.6252i	0.910804	+	1.57756i
$540$		0			0
$541$	−20.1943			−0.868223			−0.434111	−	0.900859i	$-0.642938\pi$
$541$	−20.1943			−0.868223			−0.434111	+	0.900859i	$0.642938\pi$
$542$		0			0
$543$	−4.80074	+	8.31513i	−0.206020	+	0.356836i
$544$		0			0
$545$	2.44829			0.104873
$546$		0			0
$547$	20.2218			0.864620			0.432310	−	0.901725i	$-0.357699\pi$
$547$	20.2218			0.864620			0.432310	+	0.901725i	$0.357699\pi$
$548$		0			0
$549$	−0.428780	+	0.742669i	−0.0182999	+	0.0316963i
$550$		0			0
$551$	19.9879			0.851514
$552$		0			0
$553$	−22.6664	−	39.2593i	−0.963872	−	1.66948i
$554$		0			0
$555$	8.14592	+	14.1092i	0.345775	+	0.598900i
$556$		0			0
$557$	2.78836	−	4.82959i	0.118147	−	0.204636i	−0.800886	−	0.598816i	$-0.795638\pi$
$557$	2.78836	−	4.82959i	0.118147	−	0.204636i	0.919033	+	0.394180i	$0.128971\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−24.5221	+	42.4735i	−1.03532	+	1.79323i
$562$		0			0
$563$	−7.35205	−	12.7341i	−0.309852	−	0.536679i	0.668478	−	0.743732i	$-0.266946\pi$
$563$	−7.35205	−	12.7341i	−0.309852	−	0.536679i	−0.978330	+	0.207053i	$0.933613\pi$
$564$		0			0
$565$	−8.25733	−	14.3021i	−0.347389	−	0.601695i
$566$		0			0
$567$	36.8159			1.54612
$568$		0			0
$569$	0.897084	−	1.55380i	0.0376077	−	0.0651385i	−0.846609	−	0.532216i	$-0.821360\pi$
$569$	0.897084	−	1.55380i	0.0376077	−	0.0651385i	0.884217	+	0.467077i	$0.154693\pi$
$570$		0			0
$571$	38.8025			1.62384			0.811918	−	0.583772i	$-0.198424\pi$
$571$	38.8025			1.62384			0.811918	+	0.583772i	$0.198424\pi$
$572$		0			0
$573$	−34.8327			−1.45516
$574$		0			0
$575$	6.61918	−	11.4648i	0.276039	−	0.478113i
$576$		0			0
$577$	19.3230			0.804429			0.402214	−	0.915545i	$-0.368241\pi$
$577$	19.3230			0.804429			0.402214	+	0.915545i	$0.368241\pi$
$578$		0			0
$579$	−16.0344	−	27.7725i	−0.666369	−	1.15418i
$580$		0			0
$581$	−11.2702	−	19.5206i	−0.467568	−	0.809852i
$582$		0			0
$583$	10.0293	−	17.3713i	0.415371	−	0.719444i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	13.1027	−	22.6945i	0.540805	−	0.936702i	−0.458053	−	0.888925i	$-0.651453\pi$
$587$	13.1027	−	22.6945i	0.540805	−	0.936702i	0.998858	−	0.0477774i	$-0.0152138\pi$
$588$		0			0
$589$	6.77413	+	11.7331i	0.279123	+	0.483455i
$590$		0			0
$591$	−1.98009	−	3.42962i	−0.0814500	−	0.141076i
$592$		0			0
$593$	10.5676			0.433961			0.216980	−	0.976176i	$-0.430379\pi$
$593$	10.5676			0.433961			0.216980	+	0.976176i	$0.430379\pi$
$594$		0			0
$595$	20.2032	−	34.9930i	0.828251	−	1.43457i
$596$		0			0
$597$	9.54420			0.390618
$598$		0			0
$599$	−2.50663			−0.102418			−0.0512091	−	0.998688i	$-0.516307\pi$
$599$	−2.50663			−0.102418			−0.0512091	+	0.998688i	$0.516307\pi$
$600$		0			0
$601$	12.6685	−	21.9425i	0.516760	−	0.895054i	−0.483051	−	0.875592i	$-0.660471\pi$
$601$	12.6685	−	21.9425i	0.516760	−	0.895054i	0.999811	−	0.0194619i	$-0.00619531\pi$
$602$		0			0
$603$	−0.457123			−0.0186155
$604$		0			0
$605$	1.57606	+	2.72982i	0.0640761	+	0.110983i
$606$		0			0
$607$	2.31312	+	4.00644i	0.0938866	+	0.162616i	0.909143	−	0.416483i	$-0.136738\pi$
$607$	2.31312	+	4.00644i	0.0938866	+	0.162616i	−0.815257	+	0.579100i	$0.803404\pi$
$608$		0			0
$609$	15.6129	−	27.0423i	0.632667	−	1.09581i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−10.2714	+	17.7907i	−0.414859	+	0.718558i	−0.995414	−	0.0956639i	$-0.969503\pi$
$613$	−10.2714	+	17.7907i	−0.414859	+	0.718558i	0.580554	+	0.814222i	$0.302836\pi$
$614$		0			0
$615$	−8.22000	−	14.2375i	−0.331462	−	0.574109i
$616$		0			0
$617$	−11.9940	−	20.7741i	−0.482859	−	0.836336i	0.516948	−	0.856017i	$-0.327068\pi$
$617$	−11.9940	−	20.7741i	−0.482859	−	0.836336i	−0.999806	+	0.0196813i	$0.993735\pi$
$618$		0			0
$619$	−33.1153			−1.33102			−0.665508	−	0.746391i	$-0.731785\pi$
$619$	−33.1153			−1.33102			−0.665508	+	0.746391i	$0.731785\pi$
$620$		0			0
$621$	9.85636	−	17.0717i	0.395522	−	0.685065i
$622$		0			0
$623$	40.6684			1.62935
$624$		0			0
$625$	5.52994			0.221198
$626$		0			0
$627$	14.5330	−	25.1718i	0.580390	−	1.00527i
$628$		0			0
$629$	−63.0960			−2.51580
$630$		0			0
$631$	−7.15668	−	12.3957i	−0.284903	−	0.493466i	0.687683	−	0.726011i	$-0.258628\pi$
$631$	−7.15668	−	12.3957i	−0.284903	−	0.493466i	−0.972586	+	0.232545i	$0.925295\pi$
$632$		0			0
$633$	−0.492467	−	0.852978i	−0.0195738	−	0.0339028i
$634$		0			0
$635$	−3.77868	+	6.54486i	−0.149952	+	0.259725i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	0.298585	−	0.517165i	0.0118119	−	0.0204587i
$640$		0			0
$641$	−21.3686	−	37.0115i	−0.844009	−	1.46187i	−0.886479	−	0.462769i	$-0.846856\pi$
$641$	−21.3686	−	37.0115i	−0.844009	−	1.46187i	0.0424695	−	0.999098i	$-0.486477\pi$
$642$		0			0
$643$	14.4831	+	25.0854i	0.571157	+	0.989272i	0.996448	+	0.0842157i	$0.0268385\pi$
$643$	14.4831	+	25.0854i	0.571157	+	0.989272i	−0.425291	+	0.905057i	$0.639828\pi$
$644$		0			0
$645$	−1.79343			−0.0706163
$646$		0			0
$647$	23.3056	−	40.3665i	0.916237	−	1.58697i	0.111157	−	0.993803i	$-0.464544\pi$
$647$	23.3056	−	40.3665i	0.916237	−	1.58697i	0.805080	−	0.593166i	$-0.202122\pi$
$648$		0			0
$649$	8.60148			0.337638
$650$		0			0
$651$	21.1655			0.829543
$652$		0			0
$653$	−17.0504	+	29.5322i	−0.667234	+	1.15568i	0.311440	+	0.950266i	$0.399189\pi$
$653$	−17.0504	+	29.5322i	−0.667234	+	1.15568i	−0.978674	+	0.205418i	$0.934145\pi$
$654$		0			0
$655$	−17.1274			−0.669222
$656$		0			0
$657$	−0.262414	−	0.454514i	−0.0102377	−	0.0177323i
$658$		0			0
$659$	20.7983	+	36.0238i	0.810189	+	1.40329i	0.912732	+	0.408559i	$0.133969\pi$
$659$	20.7983	+	36.0238i	0.810189	+	1.40329i	−0.102543	+	0.994729i	$0.532698\pi$
$660$		0			0
$661$	5.37681	−	9.31290i	0.209134	−	0.362230i	−0.742308	−	0.670058i	$-0.766269\pi$
$661$	5.37681	−	9.31290i	0.209134	−	0.362230i	0.951442	+	0.307829i	$0.0996023\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−11.9734	+	20.7385i	−0.464308	+	0.804205i
$666$		0			0
$667$	−7.97703	−	13.8166i	−0.308872	−	0.534982i
$668$		0			0
$669$	12.8843	+	22.3163i	0.498137	+	0.862799i
$670$		0			0
$671$	23.0998			0.891756
$672$		0			0
$673$	1.58306	−	2.74195i	0.0610227	−	0.105694i	−0.833900	−	0.551915i	$-0.813897\pi$
$673$	1.58306	−	2.74195i	0.0610227	−	0.105694i	0.894923	+	0.446221i	$0.147230\pi$
$674$		0			0
$675$	18.9211			0.728272
$676$		0			0
$677$	25.8323			0.992817			0.496409	−	0.868089i	$-0.334652\pi$
$677$	25.8323			0.992817			0.496409	+	0.868089i	$0.334652\pi$
$678$		0			0
$679$	−7.90432	+	13.6907i	−0.303340	+	0.525400i
$680$		0			0
$681$	22.7616			0.872228
$682$		0			0
$683$	0.832437	+	1.44182i	0.0318523	+	0.0551698i	0.881512	−	0.472161i	$-0.156526\pi$
$683$	0.832437	+	1.44182i	0.0318523	+	0.0551698i	−0.849660	+	0.527331i	$0.823193\pi$
$684$		0			0
$685$	−6.71379	−	11.6286i	−0.256521	−	0.444307i
$686$		0			0
$687$	−6.01961	+	10.4263i	−0.229663	+	0.397787i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−12.5003	+	21.6511i	−0.475534	+	0.823648i	−0.999607	−	0.0280245i	$-0.991078\pi$
$691$	−12.5003	+	21.6511i	−0.475534	+	0.823648i	0.524074	+	0.851673i	$0.324412\pi$
$692$		0			0
$693$	1.08695	+	1.88265i	0.0412898	+	0.0715160i
$694$		0			0
$695$	2.73437	+	4.73606i	0.103720	+	0.179649i
$696$		0			0
$697$	63.6698			2.41166
$698$		0			0
$699$	−6.23423	+	10.7980i	−0.235800	+	0.408418i
$700$		0			0
$701$	−6.01208			−0.227073			−0.113537	−	0.993534i	$-0.536218\pi$
$701$	−6.01208			−0.227073			−0.113537	+	0.993534i	$0.536218\pi$
$702$		0			0
$703$	37.3937			1.41033
$704$		0			0
$705$	4.64430	−	8.04416i	0.174914	−	0.302961i
$706$		0			0
$707$	73.5672			2.76678
$708$		0			0
$709$	−8.06584	−	13.9705i	−0.302919	−	0.524671i	0.673877	−	0.738844i	$-0.264628\pi$
$709$	−8.06584	−	13.9705i	−0.302919	−	0.524671i	−0.976796	+	0.214172i	$0.931295\pi$
$710$		0			0
$711$	−0.723185	−	1.25259i	−0.0271216	−	0.0469759i
$712$		0			0
$713$	5.40701	−	9.36522i	0.202494	−	0.350730i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	7.05980	−	12.2279i	0.263653	−	0.456661i
$718$		0			0
$719$	8.79039	+	15.2254i	0.327826	+	0.567812i	0.982080	−	0.188463i	$-0.0603506\pi$
$719$	8.79039	+	15.2254i	0.327826	+	0.567812i	−0.654254	+	0.756275i	$0.727017\pi$
$720$		0			0
$721$	17.4988	+	30.3088i	0.651689	+	1.12876i
$722$		0			0
$723$	−10.9715			−0.408035
$724$		0			0
$725$	7.65668	−	13.2618i	0.284362	−	0.492529i
$726$		0			0
$727$	4.18731			0.155299			0.0776493	−	0.996981i	$-0.475259\pi$
$727$	4.18731			0.155299			0.0776493	+	0.996981i	$0.475259\pi$
$728$		0			0
$729$	28.1183			1.04142
$730$		0			0
$731$	3.47285	−	6.01516i	0.128448	−	0.222479i
$732$		0			0
$733$	−24.7821			−0.915347			−0.457674	−	0.889120i	$-0.651317\pi$
$733$	−24.7821			−0.915347			−0.457674	+	0.889120i	$0.651317\pi$
$734$		0			0
$735$	11.6102	+	20.1095i	0.428249	+	0.741749i
$736$		0			0
$737$	6.15668	+	10.6637i	0.226784	+	0.392802i
$738$		0			0
$739$	11.4179	−	19.7764i	0.420014	−	0.727486i	−0.575926	−	0.817502i	$-0.695358\pi$
$739$	11.4179	−	19.7764i	0.420014	−	0.727486i	0.995940	+	0.0900160i	$0.0286918\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−17.6462	+	30.5641i	−0.647377	+	1.12129i	0.336370	+	0.941730i	$0.390801\pi$
$743$	−17.6462	+	30.5641i	−0.647377	+	1.12129i	−0.983747	+	0.179560i	$0.942533\pi$
$744$		0			0
$745$	−12.9837	−	22.4885i	−0.475687	−	0.823915i
$746$		0			0
$747$	−0.359584	−	0.622818i	−0.0131565	−	0.0227877i
$748$		0			0
$749$	−2.42566			−0.0886319
$750$		0			0
$751$	−25.7482	+	44.5973i	−0.939566	+	1.62738i	−0.173285	+	0.984872i	$0.555438\pi$
$751$	−25.7482	+	44.5973i	−0.939566	+	1.62738i	−0.766281	+	0.642505i	$0.777895\pi$
$752$		0			0
$753$	−12.2875			−0.447783
$754$		0			0
$755$	−25.1304			−0.914587
$756$		0			0
$757$	−8.42692	+	14.5959i	−0.306282	+	0.530495i	−0.977546	−	0.210723i	$-0.932418\pi$
$757$	−8.42692	+	14.5959i	−0.306282	+	0.530495i	0.671264	+	0.741218i	$0.265752\pi$
$758$		0			0
$759$	−23.2000			−0.842106
$760$		0			0
$761$	3.95981	+	6.85860i	0.143543	+	0.248624i	0.928828	−	0.370510i	$-0.120817\pi$
$761$	3.95981	+	6.85860i	0.143543	+	0.248624i	−0.785285	+	0.619134i	$0.787484\pi$
$762$		0			0
$763$	−4.38942	−	7.60270i	−0.158908	−	0.275236i
$764$		0			0
$765$	0.644596	−	1.11647i	0.0233054	−	0.0403662i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	8.00216	−	13.8601i	0.288565	−	0.499809i	−0.684902	−	0.728635i	$-0.740155\pi$
$769$	8.00216	−	13.8601i	0.288565	−	0.499809i	0.973467	+	0.228825i	$0.0734885\pi$
$770$		0			0
$771$	11.5365	+	19.9819i	0.415478	+	0.719630i
$772$		0			0
$773$	−19.2540	−	33.3489i	−0.692518	−	1.19948i	−0.971010	−	0.239037i	$-0.923168\pi$
$773$	−19.2540	−	33.3489i	−0.692518	−	1.19948i	0.278493	−	0.960438i	$-0.410165\pi$
$774$		0			0
$775$	10.3797			0.372851
$776$		0			0
$777$	29.2089	−	50.5913i	1.04786	−	1.81495i
$778$		0			0
$779$	−37.7338			−1.35195
$780$		0			0
$781$	−16.0858			−0.575594
$782$		0			0
$783$	11.4013	−	19.7476i	0.407448	−	0.705721i
$784$		0			0
$785$	−4.34375			−0.155035
$786$		0			0
$787$	8.29201	+	14.3622i	0.295578	+	0.511957i	0.975119	−	0.221681i	$-0.0711543\pi$
$787$	8.29201	+	14.3622i	0.295578	+	0.511957i	−0.679541	+	0.733638i	$0.737821\pi$
$788$		0			0
$789$	−9.57032	−	16.5763i	−0.340712	−	0.590131i
$790$		0			0
$791$	−29.6084	+	51.2832i	−1.05275	+	1.82342i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	5.50670	−	9.53789i	0.195303	−	0.338274i
$796$		0			0
$797$	−18.9432	−	32.8106i	−0.671002	−	1.16221i	−0.977620	−	0.210377i	$-0.932531\pi$
$797$	−18.9432	−	32.8106i	−0.671002	−	1.16221i	0.306618	−	0.951833i	$-0.400802\pi$
$798$		0			0
$799$	17.9867	+	31.1539i	0.636324	+	1.10215i
$800$		0			0
$801$	1.29755			0.0458468
$802$		0			0
$803$	−7.06853	+	12.2431i	−0.249443	+	0.432048i
$804$		0			0
$805$	19.1140			0.673679
$806$		0			0
$807$	1.13228			0.0398581
$808$		0			0
$809$	24.0683	−	41.6875i	0.846196	−	1.46565i	−0.0383822	−	0.999263i	$-0.512220\pi$
$809$	24.0683	−	41.6875i	0.846196	−	1.46565i	0.884578	−	0.466392i	$-0.154446\pi$
$810$		0			0
$811$	−38.7743			−1.36155			−0.680775	−	0.732492i	$-0.738357\pi$
$811$	−38.7743			−1.36155			−0.680775	+	0.732492i	$0.738357\pi$
$812$		0			0
$813$	−17.2672	−	29.9076i	−0.605587	−	1.04891i
$814$		0			0
$815$	13.0423	+	22.5900i	0.456853	+	0.791293i
$816$		0			0
$817$	−2.05818	+	3.56487i	−0.0720066	+	0.124719i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	12.7865	−	22.1469i	0.446252	−	0.772931i	−0.551886	−	0.833919i	$-0.686092\pi$
$821$	12.7865	−	22.1469i	0.446252	−	0.772931i	0.998138	+	0.0609880i	$0.0194252\pi$
$822$		0			0
$823$	17.9983	+	31.1739i	0.627380	+	1.08665i	0.988075	+	0.153971i	$0.0492062\pi$
$823$	17.9983	+	31.1739i	0.627380	+	1.08665i	−0.360695	+	0.932684i	$0.617461\pi$
$824$		0			0
$825$	−11.1341	−	19.2849i	−0.387641	−	0.671414i
$826$		0			0
$827$	−46.2495			−1.60825			−0.804126	−	0.594459i	$-0.797366\pi$
$827$	−46.2495			−1.60825			−0.804126	+	0.594459i	$0.797366\pi$
$828$		0			0
$829$	−19.5981	+	33.9450i	−0.680671	+	1.17896i	0.294105	+	0.955773i	$0.404978\pi$
$829$	−19.5981	+	33.9450i	−0.680671	+	1.17896i	−0.974776	+	0.223184i	$0.928355\pi$
$830$		0			0
$831$	−4.21073			−0.146069
$832$		0			0
$833$	−89.9294			−3.11587
$834$		0			0
$835$	−1.68425	+	2.91721i	−0.0582859	+	0.100954i
$836$		0			0
$837$	15.4561			0.534240
$838$		0			0
$839$	−14.6136	−	25.3114i	−0.504516	−	0.873848i	−0.999986	−	0.00522281i	$-0.998338\pi$
$839$	−14.6136	−	25.3114i	−0.504516	−	0.873848i	0.495470	−	0.868625i	$-0.334996\pi$
$840$		0			0
$841$	5.27263	+	9.13247i	0.181815	+	0.314913i
$842$		0			0
$843$	14.0700	−	24.3700i	0.484597	−	0.839347i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	5.65130	−	9.78834i	0.194181	−	0.336331i
$848$		0			0
$849$	−2.42460	−	4.19953i	−0.0832120	−	0.144127i
$850$		0			0
$851$	−14.9236	−	25.8484i	−0.511573	−	0.886071i
$852$		0			0
$853$	−14.9638			−0.512349			−0.256175	−	0.966631i	$-0.582462\pi$
$853$	−14.9638			−0.512349			−0.256175	+	0.966631i	$0.582462\pi$
$854$		0			0
$855$	−0.382019	+	0.661675i	−0.0130648	+	0.0226288i
$856$		0			0
$857$	10.0537			0.343428			0.171714	−	0.985147i	$-0.445070\pi$
$857$	10.0537			0.343428			0.171714	+	0.985147i	$0.445070\pi$
$858$		0			0
$859$	4.52409			0.154360			0.0771800	−	0.997017i	$-0.475408\pi$
$859$	4.52409			0.154360			0.0771800	+	0.997017i	$0.475408\pi$
$860$		0			0
$861$	−29.4745	+	51.0513i	−1.00449	+	1.73982i
$862$		0			0
$863$	38.6582			1.31594			0.657970	−	0.753044i	$-0.271415\pi$
$863$	38.6582			1.31594			0.657970	+	0.753044i	$0.271415\pi$
$864$		0			0
$865$	4.20046	+	7.27540i	0.142820	+	0.247371i
$866$		0			0
$867$	−37.7625	−	65.4065i	−1.28248	−	2.22132i
$868$		0			0
$869$	−19.4801	+	33.7406i	−0.660819	+	1.14457i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.252192	+	0.436810i	−0.00853542	+	0.0147838i
$874$		0			0
$875$	22.0401	+	38.1745i	0.745090	+	1.29053i
$876$		0			0
$877$	−22.4100	−	38.8152i	−0.756732	−	1.31070i	−0.944509	−	0.328486i	$-0.893462\pi$
$877$	−22.4100	−	38.8152i	−0.756732	−	1.31070i	0.187777	−	0.982212i	$-0.439872\pi$
$878$		0			0
$879$	−52.0653			−1.75612
$880$		0			0
$881$	−17.5945	+	30.4745i	−0.592773	+	1.02671i	0.401084	+	0.916041i	$0.368634\pi$
$881$	−17.5945	+	30.4745i	−0.592773	+	1.02671i	−0.993857	+	0.110672i	$0.964700\pi$
$882$		0			0
$883$	−34.6262			−1.16527			−0.582633	−	0.812736i	$-0.697977\pi$
$883$	−34.6262			−1.16527			−0.582633	+	0.812736i	$0.697977\pi$
$884$		0			0
$885$	4.72274			0.158753
$886$		0			0
$887$	−1.05280	+	1.82351i	−0.0353496	+	0.0612274i	−0.883159	−	0.469074i	$-0.844588\pi$
$887$	−1.05280	+	1.82351i	−0.0353496	+	0.0612274i	0.847809	+	0.530301i	$0.177921\pi$
$888$		0			0
$889$	27.0984			0.908852
$890$		0			0
$891$	−15.8204	−	27.4017i	−0.530002	−	0.917990i
$892$		0			0
$893$	−10.6598	−	18.4633i	−0.356716	−	0.617851i
$894$		0			0
$895$	−9.27671	+	16.0677i	−0.310086	+	0.537085i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	6.25451	−	10.8331i	0.208600	−	0.361305i
$900$		0			0
$901$	21.3267	+	36.9389i	0.710495	+	1.23061i
$902$		0			0
$903$	3.21536	+	5.56916i	0.107000	+	0.185330i
$904$		0			0
$905$	−6.79848			−0.225989
$906$		0			0
$907$	8.21864	−	14.2351i	0.272895	−	0.472669i	−0.696707	−	0.717356i	$-0.745352\pi$
$907$	8.21864	−	14.2351i	0.272895	−	0.472669i	0.969602	+	0.244688i	$0.0786854\pi$
$908$		0			0
$909$	2.34721			0.0778519
$910$		0			0
$911$	−12.5623			−0.416206			−0.208103	−	0.978107i	$-0.566729\pi$
$911$	−12.5623			−0.416206			−0.208103	+	0.978107i	$0.566729\pi$
$912$		0			0
$913$	−9.68598	+	16.7766i	−0.320559	+	0.555225i
$914$		0			0
$915$	12.6832			0.419293
$916$		0			0
$917$	30.7068	+	53.1858i	1.01403	+	1.75635i
$918$		0			0
$919$	18.1441	+	31.4264i	0.598517	+	1.03666i	0.993040	+	0.117776i	$0.0375766\pi$
$919$	18.1441	+	31.4264i	0.598517	+	1.03666i	−0.394523	+	0.918886i	$0.629090\pi$
$920$		0			0
$921$	17.1226	−	29.6572i	0.564208	−	0.977238i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	14.3242	−	24.8103i	0.470978	−	0.815758i
$926$		0			0
$927$	0.558311	+	0.967022i	0.0183373	+	0.0317612i
$928$		0			0
$929$	10.7860	+	18.6819i	0.353876	+	0.612932i	0.986925	−	0.161180i	$-0.0515301\pi$
$929$	10.7860	+	18.6819i	0.353876	+	0.612932i	−0.633049	+	0.774112i	$0.718197\pi$
$930$		0			0
$931$	53.2965			1.74672
$932$		0			0
$933$	−15.9424	+	27.6130i	−0.521929	+	0.904008i
$934$		0			0
$935$	−34.7265			−1.13568
$936$		0			0
$937$	5.95599			0.194574			0.0972868	−	0.995256i	$-0.468984\pi$
$937$	5.95599			0.194574			0.0972868	+	0.995256i	$0.468984\pi$
$938$		0			0
$939$	−4.12229	+	7.14002i	−0.134526	+	0.233006i
$940$		0			0
$941$	−46.8431			−1.52704			−0.763520	−	0.645784i	$-0.776531\pi$
$941$	−46.8431			−1.52704			−0.763520	+	0.645784i	$0.776531\pi$
$942$		0			0
$943$	15.0593	+	26.0834i	0.490397	+	0.849393i
$944$		0			0
$945$	13.6594	+	23.6588i	0.444341	+	0.769621i
$946$		0			0
$947$	−21.5911	+	37.3969i	−0.701617	+	1.21524i	0.266281	+	0.963895i	$0.414205\pi$
$947$	−21.5911	+	37.3969i	−0.701617	+	1.21524i	−0.967898	+	0.251342i	$0.919128\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	11.1830	−	19.3695i	0.362634	−	0.628100i
$952$		0			0
$953$	−17.9203	−	31.0390i	−0.580497	−	1.00545i	−0.995420	−	0.0955939i	$-0.969525\pi$
$953$	−17.9203	−	31.0390i	−0.580497	−	1.00545i	0.414923	−	0.909856i	$-0.363808\pi$
$954$		0			0
$955$	−12.3319	−	21.3595i	−0.399051	−	0.691177i
$956$		0			0
$957$	−26.8364			−0.867497
$958$		0			0
$959$	−24.0737	+	41.6968i	−0.777379	+	1.34646i
$960$		0			0
$961$	−22.5211			−0.726487
$962$		0			0
$963$	−0.0773924			−0.00249393
$964$		0			0
$965$	11.3534	−	19.6647i	0.365480	−	0.633030i
$966$		0			0
$967$	13.9815			0.449614			0.224807	−	0.974403i	$-0.427825\pi$
$967$	13.9815			0.449614			0.224807	+	0.974403i	$0.427825\pi$
$968$		0			0
$969$	30.9034	+	53.5263i	0.992761	+	1.71951i
$970$		0			0
$971$	20.3049	+	35.1692i	0.651616	+	1.12863i	0.982731	+	0.185041i	$0.0592419\pi$
$971$	20.3049	+	35.1692i	0.651616	+	1.12863i	−0.331115	+	0.943590i	$0.607425\pi$
$972$		0			0
$973$	9.80463	−	16.9821i	0.314322	−	0.544421i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	7.47985	−	12.9555i	0.239302	−	0.414483i	−0.721212	−	0.692714i	$-0.756415\pi$
$977$	7.47985	−	12.9555i	0.239302	−	0.414483i	0.960514	+	0.278231i	$0.0897482\pi$
$978$		0			0
$979$	−17.4758	−	30.2690i	−0.558530	−	0.967403i
$980$		0			0
$981$	−0.140047	−	0.242569i	−0.00447136	−	0.00774463i
$982$		0			0
$983$	25.4722			0.812437			0.406218	−	0.913776i	$-0.366847\pi$
$983$	25.4722			0.812437			0.406218	+	0.913776i	$0.366847\pi$
$984$		0			0
$985$	1.40203	−	2.42839i	0.0446725	−	0.0773751i
$986$		0			0
$987$	−33.3062			−1.06015
$988$		0			0
$989$	3.28562			0.104477
$990$		0			0
$991$	−10.5902	+	18.3427i	−0.336408	+	0.582675i	−0.983754	−	0.179520i	$-0.942545\pi$
$991$	−10.5902	+	18.3427i	−0.336408	+	0.582675i	0.647346	+	0.762196i	$0.275879\pi$
$992$		0			0
$993$	−36.8944			−1.17081
$994$		0			0
$995$	3.37896	+	5.85253i	0.107120	+	0.185538i
$996$		0			0
$997$	−26.2977	−	45.5489i	−0.832856	−	1.44255i	−0.895764	−	0.444530i	$-0.853371\pi$
$997$	−26.2977	−	45.5489i	−0.832856	−	1.44255i	0.0629081	−	0.998019i	$-0.479962\pi$
$998$		0			0
$999$	21.3297	−	36.9441i	0.674841	−	1.16886i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	676.2.e.f.529.1		6
13.2	odd	12		676.2.h.e.361.2		12
13.3	even	3	inner	676.2.e.f.653.1		6
13.4	even	6		676.2.a.h.1.3	yes	3
13.5	odd	4		676.2.h.e.485.2		12
13.6	odd	12		676.2.d.e.337.6		6
13.7	odd	12		676.2.d.e.337.5		6
13.8	odd	4		676.2.h.e.485.1		12
13.9	even	3		676.2.a.g.1.3	✓	3
13.10	even	6		676.2.e.g.653.1		6
13.11	odd	12		676.2.h.e.361.1		12
13.12	even	2		676.2.e.g.529.1		6
39.17	odd	6		6084.2.a.x.1.3		3
39.20	even	12		6084.2.b.p.4393.4		6
39.32	even	12		6084.2.b.p.4393.3		6
39.35	odd	6		6084.2.a.bc.1.1		3
52.7	even	12		2704.2.f.n.337.1		6
52.19	even	12		2704.2.f.n.337.2		6
52.35	odd	6		2704.2.a.x.1.1		3
52.43	odd	6		2704.2.a.y.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
676.2.a.g.1.3	✓	3	13.9	even	3
676.2.a.h.1.3	yes	3	13.4	even	6
676.2.d.e.337.5		6	13.7	odd	12
676.2.d.e.337.6		6	13.6	odd	12
676.2.e.f.529.1		6	1.1	even	1	trivial
676.2.e.f.653.1		6	13.3	even	3	inner
676.2.e.g.529.1		6	13.12	even	2
676.2.e.g.653.1		6	13.10	even	6
676.2.h.e.361.1		12	13.11	odd	12
676.2.h.e.361.2		12	13.2	odd	12
676.2.h.e.485.1		12	13.8	odd	4
676.2.h.e.485.2		12	13.5	odd	4
2704.2.a.x.1.1		3	52.35	odd	6
2704.2.a.y.1.1		3	52.43	odd	6
2704.2.f.n.337.1		6	52.7	even	12
2704.2.f.n.337.2		6	52.19	even	12
6084.2.a.x.1.3		3	39.17	odd	6
6084.2.a.bc.1.1		3	39.35	odd	6
6084.2.b.p.4393.3		6	39.32	even	12
6084.2.b.p.4393.4		6	39.20	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	676.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.846011 + 1.46533i) q^{3} -1.19806 q^{5} +(2.14795 + 3.72036i) q^{7} +(0.0685317 + 0.118700i) q^{9} +(1.84601 - 3.19738i) q^{11} +(1.01357 - 1.75556i) q^{15} +(3.92543 + 6.79904i) q^{17} +(-2.32640 - 4.02944i) q^{19} -7.26875 q^{21} +(-1.85690 + 3.21624i) q^{23} -3.56465 q^{25} -5.30798 q^{27} +(-2.14795 + 3.72036i) q^{29} -2.91185 q^{31} +(3.12349 + 5.41004i) q^{33} +(-2.57338 - 4.45722i) q^{35} +(-4.01842 + 6.96010i) q^{37} +(4.05496 - 7.02339i) q^{41} +(-0.442353 - 0.766179i) q^{43} +(-0.0821052 - 0.142210i) q^{45} +4.58211 q^{47} +(-5.72737 + 9.92009i) q^{49} -13.2838 q^{51} +5.43296 q^{53} +(-2.21164 + 3.83067i) q^{55} +7.87263 q^{57} +(1.16487 + 2.01762i) q^{59} +(3.12833 + 5.41843i) q^{61} +(-0.294405 + 0.509924i) q^{63} +(-1.66756 + 2.88830i) q^{67} +(-3.14191 - 5.44194i) q^{69} +(-2.17845 - 3.77318i) q^{71} -3.82908 q^{73} +(3.01573 - 5.22340i) q^{75} +15.8605 q^{77} -10.5526 q^{79} +(4.28501 - 7.42186i) q^{81} -5.24698 q^{83} +(-4.70291 - 8.14567i) q^{85} +(-3.63437 - 6.29492i) q^{87} +(4.73341 - 8.19850i) q^{89} +(2.46346 - 4.26684i) q^{93} +(2.78717 + 4.82752i) q^{95} +(1.83997 + 3.18692i) q^{97} +0.506041 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 16 q^{5} - q^{7} - 5 q^{9} + 6 q^{11} + 10 q^{17} + 4 q^{19} - 28 q^{21} - 3 q^{23} + 22 q^{25} - 42 q^{27} + q^{29} - 10 q^{31} + 14 q^{33} + 12 q^{35} + 4 q^{37} + 25 q^{41} - 5 q^{43} + 11 q^{45}+ \cdots + 22 q^{99}+O(q^{100}) \) 6 * q - 16 * q^5 - q^7 - 5 * q^9 + 6 * q^11 + 10 * q^17 + 4 * q^19 - 28 * q^21 - 3 * q^23 + 22 * q^25 - 42 * q^27 + q^29 - 10 * q^31 + 14 * q^33 + 12 * q^35 + 4 * q^37 + 25 * q^41 - 5 * q^43 + 11 * q^45 + 16 * q^47 - 12 * q^49 - 14 * q^51 - 6 * q^53 - 16 * q^55 + 14 * q^57 + 9 * q^59 - 8 * q^61 - 18 * q^63 - 9 * q^67 + 14 * q^69 - 9 * q^71 - 2 * q^73 - 7 * q^75 + 24 * q^77 + 18 * q^79 + q^81 - 22 * q^83 - 15 * q^85 - 14 * q^87 + 25 * q^89 - 14 * q^93 - 27 * q^95 - 13 * q^97 + 22 * q^99

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