LMFDB - Embedded newform 735.2.d.e.589.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(589,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("735.589");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.d (of order $2$, degree $1$, 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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.2058981376.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 18x^{4} - 34x^{3} + 32x^{2} - 8x + 1 $ x^8 - 2x^7 + 2x^6 + 18x^4 - 34x^3 + 32x^2 - 8x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			589.1
Root			$0.769222 - 0.769222i$ of defining polynomial
Character	$\chi$	$=$	735.589
Dual form			735.2.d.e.589.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51658i q^{2} +1.00000i q^{3} -4.33317 q^{4} +(1.11922 - 1.93581i) q^{5} +2.51658 q^{6} +5.87162i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.51658i q^{2} +1.00000i q^{3} -4.33317 q^{4} +(1.11922 - 1.93581i) q^{5} +2.51658 q^{6} +5.87162i q^{8} -1.00000 q^{9} +(-4.87162 - 2.81659i) q^{10} +0.978135 q^{11} -4.33317i q^{12} -5.14977i q^{13} +(1.93581 + 1.11922i) q^{15} +6.11005 q^{16} -4.14977i q^{17} +2.51658i q^{18} -2.30001 q^{19} +(-4.84975 + 8.38820i) q^{20} -2.46156i q^{22} +5.07288i q^{23} -5.87162 q^{24} +(-2.49472 - 4.33317i) q^{25} -12.9598 q^{26} -1.00000i q^{27} -5.92664 q^{29} +(2.81659 - 4.87162i) q^{30} -0.633188 q^{31} -3.63319i q^{32} +0.978135i q^{33} -10.4432 q^{34} +4.33317 q^{36} -9.05502i q^{37} +5.78817i q^{38} +5.14977 q^{39} +(11.3663 + 6.57160i) q^{40} -2.65505 q^{41} +0.344947i q^{43} -4.23843 q^{44} +(-1.11922 + 1.93581i) q^{45} +12.7663 q^{46} -4.23843i q^{47} +6.11005i q^{48} +(-10.9048 + 6.27815i) q^{50} +4.14977 q^{51} +22.3148i q^{52} +7.63319i q^{53} -2.51658 q^{54} +(1.09474 - 1.89348i) q^{55} -2.30001i q^{57} +14.9149i q^{58} +1.81659 q^{59} +(-8.38820 - 4.84975i) q^{60} -0.656256 q^{61} +1.59347i q^{62} +3.07689 q^{64} +(-9.96897 - 5.76370i) q^{65} +2.46156 q^{66} +9.25982i q^{67} +17.9817i q^{68} -5.07288 q^{69} -5.49351 q^{71} -5.87162i q^{72} -5.37811i q^{73} -22.7877 q^{74} +(4.33317 - 2.49472i) q^{75} +9.96636 q^{76} -12.9598i q^{78} +10.8869 q^{79} +(6.83846 - 11.8279i) q^{80} +1.00000 q^{81} +6.68165i q^{82} -6.62663i q^{83} +(-8.03316 - 4.64448i) q^{85} +0.868086 q^{86} -5.92664i q^{87} +5.74324i q^{88} +16.3108 q^{89} +(4.87162 + 2.81659i) q^{90} -21.9817i q^{92} -0.633188i q^{93} -10.6663 q^{94} +(-2.57421 + 4.45239i) q^{95} +3.63319 q^{96} -1.53844i q^{97} -0.978135 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 2 q^{5} + 4 q^{6} - 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 + 2 * q^5 + 4 * q^6 - 8 * q^9	$ 8 q - 8 q^{4} + 2 q^{5} + 4 q^{6} - 8 q^{9} - 4 q^{10} - 2 q^{15} - 24 q^{19} + 4 q^{20} - 12 q^{24} + 4 q^{25} - 12 q^{26} + 12 q^{29} + 12 q^{30} + 16 q^{31} - 8 q^{34} + 8 q^{36} + 4 q^{39} + 32 q^{40} - 8 q^{41} - 20 q^{44} - 2 q^{45} + 32 q^{46} - 20 q^{50} - 4 q^{51} - 4 q^{54} - 4 q^{55} + 4 q^{59} - 16 q^{60} + 16 q^{61} + 8 q^{64} - 30 q^{65} + 28 q^{66} - 20 q^{69} - 28 q^{71} - 40 q^{74} + 8 q^{75} + 32 q^{76} + 16 q^{79} + 52 q^{80} + 8 q^{81} - 32 q^{85} + 48 q^{86} + 16 q^{89} + 4 q^{90} - 32 q^{94} + 22 q^{95} + 8 q^{96}+O(q^{100}) $ 8 * q - 8 * q^4 + 2 * q^5 + 4 * q^6 - 8 * q^9 - 4 * q^10 - 2 * q^15 - 24 * q^19 + 4 * q^20 - 12 * q^24 + 4 * q^25 - 12 * q^26 + 12 * q^29 + 12 * q^30 + 16 * q^31 - 8 * q^34 + 8 * q^36 + 4 * q^39 + 32 * q^40 - 8 * q^41 - 20 * q^44 - 2 * q^45 + 32 * q^46 - 20 * q^50 - 4 * q^51 - 4 * q^54 - 4 * q^55 + 4 * q^59 - 16 * q^60 + 16 * q^61 + 8 * q^64 - 30 * q^65 + 28 * q^66 - 20 * q^69 - 28 * q^71 - 40 * q^74 + 8 * q^75 + 32 * q^76 + 16 * q^79 + 52 * q^80 + 8 * q^81 - 32 * q^85 + 48 * q^86 + 16 * q^89 + 4 * q^90 - 32 * q^94 + 22 * q^95 + 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	2.51658i		−	1.77949i	−0.456457	−	0.889745i	$-0.650882\pi$
$2$		−	2.51658i		−	1.77949i	0.456457	−	0.889745i	$-0.349118\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−4.33317			−2.16659
$5$	1.11922	−	1.93581i	0.500528	−	0.865720i
$5$	1.11922	−	1.93581i	0.500528	−	0.865720i
$6$	2.51658			1.02739
$7$		0			0
$7$		0			0
$8$			5.87162i			2.07593i
$9$	−1.00000			−0.333333
$10$	−4.87162	−	2.81659i	−1.54054	−	0.890685i
$11$	0.978135			0.294919			0.147459	−	0.989068i	$-0.452890\pi$
$11$	0.978135			0.294919			0.147459	+	0.989068i	$0.452890\pi$
$12$		−	4.33317i		−	1.25088i
$13$		−	5.14977i		−	1.42829i	−0.699998	−	0.714144i	$-0.746816\pi$
$13$		−	5.14977i		−	1.42829i	0.699998	−	0.714144i	$-0.253184\pi$
$14$		0			0
$15$	1.93581	+	1.11922i	0.499824	+	0.288980i
$16$	6.11005			1.52751
$17$		−	4.14977i		−	1.00647i	−0.864151	−	0.503233i	$-0.832144\pi$
$17$		−	4.14977i		−	1.00647i	0.864151	−	0.503233i	$-0.167856\pi$
$18$			2.51658i			0.593164i
$19$	−2.30001			−0.527659			−0.263830	−	0.964569i	$-0.584986\pi$
$19$	−2.30001			−0.527659			−0.263830	+	0.964569i	$0.584986\pi$
$20$	−4.84975	+	8.38820i	−1.08444	+	1.87566i
$21$		0			0
$22$		−	2.46156i		−	0.524805i
$23$			5.07288i			1.05777i	0.848694	+	0.528884i	$0.177389\pi$
$23$			5.07288i			1.05777i	−0.848694	+	0.528884i	$0.822611\pi$
$24$	−5.87162			−1.19854
$25$	−2.49472	−	4.33317i	−0.498943	−	0.866635i
$26$	−12.9598			−2.54163
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	−5.92664			−1.10055			−0.550275	−	0.834983i	$-0.685477\pi$
$29$	−5.92664			−1.10055			−0.550275	+	0.834983i	$0.685477\pi$
$30$	2.81659	−	4.87162i	0.514237	−	0.889432i
$31$	−0.633188			−0.113724			−0.0568620	−	0.998382i	$-0.518110\pi$
$31$	−0.633188			−0.113724			−0.0568620	+	0.998382i	$0.518110\pi$
$32$		−	3.63319i		−	0.642263i
$33$			0.978135i			0.170271i
$34$	−10.4432			−1.79100
$35$		0			0
$36$	4.33317			0.722196
$37$		−	9.05502i		−	1.48864i	−0.667825	−	0.744318i	$-0.732775\pi$
$37$		−	9.05502i		−	1.48864i	0.667825	−	0.744318i	$-0.267225\pi$
$38$			5.78817i			0.938965i
$39$	5.14977			0.824623
$40$	11.3663	+	6.57160i	1.79718	+	1.03906i
$41$	−2.65505			−0.414650			−0.207325	−	0.978272i	$-0.566476\pi$
$41$	−2.65505			−0.414650			−0.207325	+	0.978272i	$0.566476\pi$
$42$		0			0
$43$			0.344947i			0.0526039i	0.999654	+	0.0263020i	$0.00837314\pi$
$43$			0.344947i			0.0526039i	−0.999654	+	0.0263020i	$0.991627\pi$
$44$	−4.23843			−0.638967
$45$	−1.11922	+	1.93581i	−0.166843	+	0.288573i
$46$	12.7663			1.88229
$47$		−	4.23843i		−	0.618239i	−0.951023	−	0.309119i	$-0.899966\pi$
$47$		−	4.23843i		−	0.618239i	0.951023	−	0.309119i	$-0.100034\pi$
$48$			6.11005i			0.881910i
$49$		0			0
$50$	−10.9048	+	6.27815i	−1.54217	+	0.887864i
$51$	4.14977			0.581084
$52$			22.3148i			3.09451i
$53$			7.63319i			1.04850i	0.851565	+	0.524250i	$0.175654\pi$
$53$			7.63319i			1.04850i	−0.851565	+	0.524250i	$0.824346\pi$
$54$	−2.51658			−0.342463
$55$	1.09474	−	1.89348i	0.147615	−	0.255317i
$56$		0			0
$57$		−	2.30001i		−	0.304644i
$58$			14.9149i			1.95842i
$59$	1.81659			0.236500			0.118250	−	0.992984i	$-0.462272\pi$
$59$	1.81659			0.236500			0.118250	+	0.992984i	$0.462272\pi$
$60$	−8.38820	−	4.84975i	−1.08291	−	0.626101i
$61$	−0.656256			−0.0840250			−0.0420125	−	0.999117i	$-0.513377\pi$
$61$	−0.656256			−0.0840250			−0.0420125	+	0.999117i	$0.513377\pi$
$62$			1.59347i			0.202371i
$63$		0			0
$64$	3.07689			0.384611
$65$	−9.96897	−	5.76370i	−1.23650	−	0.714899i
$66$	2.46156			0.302997
$67$			9.25982i			1.13127i	0.824657	+	0.565633i	$0.191368\pi$
$67$			9.25982i			1.13127i	−0.824657	+	0.565633i	$0.808632\pi$
$68$			17.9817i			2.18060i
$69$	−5.07288			−0.610703
$70$		0			0
$71$	−5.49351			−0.651960			−0.325980	−	0.945377i	$-0.605694\pi$
$71$	−5.49351			−0.651960			−0.325980	+	0.945377i	$0.605694\pi$
$72$		−	5.87162i		−	0.691977i
$73$		−	5.37811i		−	0.629460i	−0.949181	−	0.314730i	$-0.898086\pi$
$73$		−	5.37811i		−	0.629460i	0.949181	−	0.314730i	$-0.101914\pi$
$74$	−22.7877			−2.64902
$75$	4.33317	−	2.49472i	0.500352	−	0.288065i
$76$	9.96636			1.14322
$77$		0			0
$78$		−	12.9598i		−	1.46741i
$79$	10.8869			1.22487			0.612437	−	0.790519i	$-0.290189\pi$
$79$	10.8869			1.22487			0.612437	+	0.790519i	$0.290189\pi$
$80$	6.83846	−	11.8279i	0.764563	−	1.32240i
$81$	1.00000			0.111111
$82$			6.68165i			0.737865i
$83$		−	6.62663i		−	0.727367i	−0.931523	−	0.363683i	$-0.881519\pi$
$83$		−	6.62663i		−	0.727367i	0.931523	−	0.363683i	$-0.118481\pi$
$84$		0			0
$85$	−8.03316	−	4.64448i	−0.871318	−	0.503765i
$86$	0.868086			0.0936082
$87$		−	5.92664i		−	0.635403i
$88$			5.74324i			0.612231i
$89$	16.3108			1.72894			0.864472	−	0.502680i	$-0.167653\pi$
$89$	16.3108			1.72894			0.864472	+	0.502680i	$0.167653\pi$
$90$	4.87162	+	2.81659i	0.513514	+	0.296895i
$91$		0			0
$92$		−	21.9817i		−	2.29175i
$93$		−	0.633188i		−	0.0656586i
$94$	−10.6663			−1.10015
$95$	−2.57421	+	4.45239i	−0.264108	+	0.456805i
$96$	3.63319			0.370811
$97$		−	1.53844i		−	0.156205i	−0.996945	−	0.0781027i	$-0.975114\pi$
$97$		−	1.53844i		−	0.156205i	0.996945	−	0.0781027i	$-0.0248862\pi$
$98$		0			0
$99$	−0.978135			−0.0983063
$100$	10.8100	+	18.7764i	1.08100	+	1.87764i
$101$	5.51610			0.548873			0.274436	−	0.961605i	$-0.411509\pi$
$101$	5.51610			0.548873			0.274436	+	0.961605i	$0.411509\pi$
$102$		−	10.4432i		−	1.03403i
$103$		−	16.5213i		−	1.62789i	−0.580939	−	0.813947i	$-0.697315\pi$
$103$		−	16.5213i		−	1.62789i	0.580939	−	0.813947i	$-0.302685\pi$
$104$	30.2375			2.96503
$105$		0			0
$106$	19.2095			1.86579
$107$			2.38820i			0.230876i	0.993315	+	0.115438i	$0.0368271\pi$
$107$			2.38820i			0.230876i	−0.993315	+	0.115438i	$0.963173\pi$
$108$			4.33317i			0.416960i
$109$	18.1096			1.73458			0.867291	−	0.497801i	$-0.165859\pi$
$109$	18.1096			1.73458			0.867291	+	0.497801i	$0.165859\pi$
$110$	−4.76510	−	2.75501i	−0.454335	−	0.262680i
$111$	9.05502			0.859465
$112$		0			0
$113$			4.04373i			0.380402i	0.981745	+	0.190201i	$0.0609140\pi$
$113$			4.04373i			0.380402i	−0.981745	+	0.190201i	$0.939086\pi$
$114$	−5.78817			−0.542112
$115$	9.82013	+	5.67764i	0.915731	+	0.529443i
$116$	25.6812			2.38444
$117$			5.14977i			0.476096i
$118$		−	4.57160i		−	0.420850i
$119$		0			0
$120$	−6.57160	+	11.3663i	−0.599903	+	1.03760i
$121$	−10.0433			−0.913023
$122$			1.65152i			0.149522i
$123$		−	2.65505i		−	0.239398i
$124$	2.74372			0.246393
$125$	−11.1803	−	0.0204612i	−0.999998	−	0.00183011i
$126$		0			0
$127$		−	6.85023i		−	0.607860i	−0.952694	−	0.303930i	$-0.901701\pi$
$127$		−	6.85023i		−	0.607860i	0.952694	−	0.303930i	$-0.0982989\pi$
$128$		−	15.0096i		−	1.32667i
$129$	−0.344947			−0.0303709
$130$	−14.5048	+	25.0877i	−1.27216	+	2.20034i
$131$	4.02540			0.351701			0.175850	−	0.984417i	$-0.443733\pi$
$131$	4.02540			0.351701			0.175850	+	0.984417i	$0.443733\pi$
$132$		−	4.23843i		−	0.368908i
$133$		0			0
$134$	23.3031			2.01308
$135$	−1.93581	−	1.11922i	−0.166608	−	0.0963267i
$136$	24.3659			2.08935
$137$		−	11.2319i		−	0.959603i	−0.877377	−	0.479802i	$-0.840709\pi$
$137$		−	11.2319i		−	0.959603i	0.877377	−	0.479802i	$-0.159291\pi$
$138$			12.7663i			1.08674i
$139$	−4.98991			−0.423238			−0.211619	−	0.977352i	$-0.567874\pi$
$139$	−4.98991			−0.423238			−0.211619	+	0.977352i	$0.567874\pi$
$140$		0			0
$141$	4.23843			0.356940
$142$			13.8249i			1.16016i
$143$		−	5.03717i		−	0.421229i
$144$	−6.11005			−0.509171
$145$	−6.63319	+	11.4729i	−0.550856	+	0.952768i
$146$	−13.5344			−1.12012
$147$		0			0
$148$			39.2370i			3.22526i
$149$	14.4942			1.18741			0.593707	−	0.804681i	$-0.297664\pi$
$149$	14.4942			1.18741			0.593707	+	0.804681i	$0.297664\pi$
$150$	−6.27815	−	10.9048i	−0.512609	−	0.890371i
$151$	7.88692			0.641829			0.320914	−	0.947108i	$-0.396010\pi$
$151$	7.88692			0.641829			0.320914	+	0.947108i	$0.396010\pi$
$152$		−	13.5048i		−	1.09538i
$153$			4.14977i			0.335489i
$154$		0			0
$155$	−0.708674	+	1.22573i	−0.0569221	+	0.0984531i
$156$	−22.3148			−1.78662
$157$			6.55630i			0.523250i	0.965170	+	0.261625i	$0.0842583\pi$
$157$			6.55630i			0.523250i	−0.965170	+	0.261625i	$0.915742\pi$
$158$		−	27.3978i		−	2.17965i
$159$	−7.63319			−0.605351
$160$	−7.03316	−	4.06632i	−0.556020	−	0.321471i
$161$		0			0
$162$		−	2.51658i		−	0.197721i
$163$		−	12.2558i		−	0.959949i	−0.877282	−	0.479974i	$-0.840646\pi$
$163$		−	12.2558i		−	0.959949i	0.877282	−	0.479974i	$-0.159354\pi$
$164$	11.5048			0.898374
$165$	1.89348	+	1.09474i	0.147407	+	0.0852257i
$166$	−16.6764			−1.29434
$167$		−	2.13239i		−	0.165009i	−0.996591	−	0.0825047i	$-0.973708\pi$
$167$		−	2.13239i		−	0.165009i	0.996591	−	0.0825047i	$-0.0262920\pi$
$168$		0			0
$169$	−13.5201			−1.04001
$170$	−11.6882	+	20.2161i	−0.896445	+	1.55050i
$171$	2.30001			0.175886
$172$		−	1.49472i		−	0.113971i
$173$		−	11.5485i		−	0.878019i	−0.898482	−	0.439009i	$-0.855329\pi$
$173$		−	11.5485i		−	0.878019i	0.898482	−	0.439009i	$-0.144671\pi$
$174$	−14.9149			−1.13069
$175$		0			0
$176$	5.97645			0.450492
$177$			1.81659i			0.136544i
$178$		−	41.0475i		−	3.07664i
$179$	−8.89956			−0.665185			−0.332592	−	0.943071i	$-0.607923\pi$
$179$	−8.89956			−0.665185			−0.332592	+	0.943071i	$0.607923\pi$
$180$	4.84975	−	8.38820i	0.361479	−	0.625219i
$181$	3.17940			0.236323			0.118161	−	0.992994i	$-0.462300\pi$
$181$	3.17940			0.236323			0.118161	+	0.992994i	$0.462300\pi$
$182$		0			0
$183$		−	0.656256i		−	0.0485119i
$184$	−29.7860			−2.19585
$185$	−17.5288	−	10.1345i	−1.28874	−	0.745105i
$186$	−1.59347			−0.116839
$187$		−	4.05903i		−	0.296826i
$188$			18.3659i			1.33947i
$189$		0			0
$190$	11.2048	+	6.47821i	0.812881	+	0.469979i
$191$	−0.622618			−0.0450511			−0.0225255	−	0.999746i	$-0.507171\pi$
$191$	−0.622618			−0.0450511			−0.0225255	+	0.999746i	$0.507171\pi$
$192$			3.07689i			0.222055i
$193$		−	15.1877i		−	1.09323i	−0.837383	−	0.546616i	$-0.815916\pi$
$193$		−	15.1877i		−	1.09323i	0.837383	−	0.546616i	$-0.184084\pi$
$194$	−3.87162			−0.277966
$195$	5.76370	−	9.96897i	0.412747	−	0.713893i
$196$		0			0
$197$			23.9410i			1.70573i	0.522136	+	0.852863i	$0.325136\pi$
$197$			23.9410i			1.70573i	−0.522136	+	0.852863i	$0.674864\pi$
$198$			2.46156i			0.174935i
$199$	13.9532			0.989119			0.494560	−	0.869144i	$-0.335329\pi$
$199$	13.9532			0.989119			0.494560	+	0.869144i	$0.335329\pi$
$200$	25.4427	−	14.6480i	1.79907	−	1.03577i
$201$	−9.25982			−0.653137
$202$		−	13.8817i		−	0.976714i
$203$		0			0
$204$	−17.9817			−1.25897
$205$	−2.97158	+	5.13968i	−0.207544	+	0.358971i
$206$	−41.5772			−2.89682
$207$		−	5.07288i		−	0.352589i
$208$		−	31.4653i		−	2.18173i
$209$	−2.24973			−0.155617
$210$		0			0
$211$	4.82315			0.332040			0.166020	−	0.986122i	$-0.446908\pi$
$211$	4.82315			0.332040			0.166020	+	0.986122i	$0.446908\pi$
$212$		−	33.0759i		−	2.27166i
$213$		−	5.49351i		−	0.376409i
$214$	6.01009			0.410841
$215$	0.667751	+	0.386070i	0.0455403	+	0.0263297i
$216$	5.87162			0.399513
$217$		0			0
$218$		−	45.5742i		−	3.08667i
$219$	5.37811			0.363419
$220$	−4.74372	+	8.20479i	−0.319821	+	0.553167i
$221$	−21.3703			−1.43752
$222$		−	22.7877i		−	1.52941i
$223$			15.8227i			1.05956i	0.848134	+	0.529782i	$0.177726\pi$
$223$			15.8227i			1.05956i	−0.848134	+	0.529782i	$0.822274\pi$
$224$		0			0
$225$	2.49472	+	4.33317i	0.166314	+	0.288878i
$226$	10.1764			0.676922
$227$			21.6983i			1.44017i	0.693887	+	0.720084i	$0.255897\pi$
$227$			21.6983i			1.44017i	−0.693887	+	0.720084i	$0.744103\pi$
$228$			9.96636i			0.660038i
$229$	−2.07689			−0.137245			−0.0686223	−	0.997643i	$-0.521860\pi$
$229$	−2.07689			−0.137245			−0.0686223	+	0.997643i	$0.521860\pi$
$230$	14.2882	−	24.7131i	0.942139	−	1.62954i
$231$		0			0
$232$		−	34.7990i		−	2.28467i
$233$			6.75902i			0.442798i	0.975183	+	0.221399i	$0.0710623\pi$
$233$			6.75902i			0.442798i	−0.975183	+	0.221399i	$0.928938\pi$
$234$	12.9598			0.847209
$235$	−8.20479	−	4.74372i	−0.535222	−	0.309446i
$236$	−7.87162			−0.512399
$237$			10.8869i			0.707182i
$238$		0			0
$239$	2.90478			0.187894			0.0939472	−	0.995577i	$-0.470051\pi$
$239$	2.90478			0.187894			0.0939472	+	0.995577i	$0.470051\pi$
$240$	11.8279	+	6.83846i	0.763487	+	0.441421i
$241$	8.89749			0.573138			0.286569	−	0.958060i	$-0.407485\pi$
$241$	8.89749			0.573138			0.286569	+	0.958060i	$0.407485\pi$
$242$			25.2746i			1.62472i
$243$			1.00000i			0.0641500i
$244$	2.84367			0.182047
$245$		0			0
$246$	−6.68165			−0.426007
$247$			11.8445i			0.753650i
$248$		−	3.71784i		−	0.236083i
$249$	6.62663			0.419946
$250$	−0.0514923	+	28.1362i	−0.00325666	+	1.77949i
$251$	21.1747			1.33653			0.668267	−	0.743921i	$-0.267036\pi$
$251$	21.1747			1.33653			0.668267	+	0.743921i	$0.267036\pi$
$252$		0			0
$253$			4.96196i			0.311956i
$254$	−17.2392			−1.08168
$255$	4.64448	−	8.03316i	0.290849	−	0.503056i
$256$	−31.6191			−1.97619
$257$		−	6.23442i		−	0.388892i	−0.980913	−	0.194446i	$-0.937709\pi$
$257$		−	6.23442i		−	0.388892i	0.980913	−	0.194446i	$-0.0622910\pi$
$258$			0.868086i			0.0540447i
$259$		0			0
$260$	43.1973	+	24.9751i	2.67898	+	1.54889i
$261$	5.92664			0.366850
$262$		−	10.1302i		−	0.625848i
$263$			28.0480i			1.72951i	0.502191	+	0.864756i	$0.332527\pi$
$263$			28.0480i			1.72951i	−0.502191	+	0.864756i	$0.667473\pi$
$264$	−5.74324			−0.353472
$265$	14.7764	+	8.54318i	0.907707	+	0.524803i
$266$		0			0
$267$			16.3108i			0.998207i
$268$		−	40.1244i		−	2.45099i
$269$	7.41830			0.452302			0.226151	−	0.974092i	$-0.427386\pi$
$269$	7.41830			0.452302			0.226151	+	0.974092i	$0.427386\pi$
$270$	−2.81659	+	4.87162i	−0.171412	+	0.296477i
$271$	31.2116			1.89597			0.947985	−	0.318316i	$-0.103117\pi$
$271$	31.2116			1.89597			0.947985	+	0.318316i	$0.103117\pi$
$272$		−	25.3553i		−	1.53739i
$273$		0			0
$274$	−28.2659			−1.70761
$275$	−2.44017	−	4.23843i	−0.147148	−	0.255587i
$276$	21.9817			1.32314
$277$		−	12.4526i		−	0.748204i	−0.927388	−	0.374102i	$-0.877951\pi$
$277$		−	12.4526i		−	0.748204i	0.927388	−	0.374102i	$-0.122049\pi$
$278$			12.5575i			0.753149i
$279$	0.633188			0.0379080
$280$		0			0
$281$	−0.0409225			−0.00244123			−0.00122061	−	0.999999i	$-0.500389\pi$
$281$	−0.0409225			−0.00244123			−0.00122061	+	0.999999i	$0.500389\pi$
$282$		−	10.6663i		−	0.635172i
$283$			10.8420i			0.644489i	0.946656	+	0.322245i	$0.104437\pi$
$283$			10.8420i			0.644489i	−0.946656	+	0.322245i	$0.895563\pi$
$284$	23.8043			1.41253
$285$	−4.45239	−	2.57421i	−0.263737	−	0.152483i
$286$	−12.6764			−0.749574
$287$		0			0
$288$			3.63319i			0.214088i
$289$	−0.220576			−0.0129750
$290$	28.8723	+	16.6929i	1.69544	+	0.980244i
$291$	1.53844			0.0901852
$292$			23.3043i			1.36378i
$293$			29.6455i			1.73191i	0.500125	+	0.865953i	$0.333287\pi$
$293$			29.6455i			1.73191i	−0.500125	+	0.865953i	$0.666713\pi$
$294$		0			0
$295$	2.03316	−	3.51658i	0.118375	−	0.204743i
$296$	53.1676			3.09031
$297$		−	0.978135i		−	0.0567572i
$298$		−	36.4759i		−	2.11299i
$299$	26.1242			1.51080
$300$	−18.7764	+	10.8100i	−1.08406	+	0.624118i
$301$		0			0
$302$		−	19.8481i		−	1.14213i
$303$			5.51610i			0.316892i
$304$	−14.0532			−0.806006
$305$	−0.734492	+	1.27039i	−0.0420569	+	0.0727421i
$306$	10.4432			0.596999
$307$		−	31.6055i		−	1.80382i	−0.431923	−	0.901910i	$-0.642165\pi$
$307$		−	31.6055i		−	1.80382i	0.431923	−	0.901910i	$-0.357835\pi$
$308$		0			0
$309$	16.5213			0.939865
$310$	3.08465	+	1.78343i	0.175196	+	0.101292i
$311$	−22.1703			−1.25716			−0.628581	−	0.777744i	$-0.716364\pi$
$311$	−22.1703			−1.25716			−0.628581	+	0.777744i	$0.716364\pi$
$312$			30.2375i			1.71186i
$313$			6.88572i			0.389204i	0.980882	+	0.194602i	$0.0623415\pi$
$313$			6.88572i			0.389204i	−0.980882	+	0.194602i	$0.937658\pi$
$314$	16.4995			0.931118
$315$		0			0
$316$	−47.1749			−2.65380
$317$			12.8387i			0.721094i	0.932741	+	0.360547i	$0.117410\pi$
$317$			12.8387i			0.721094i	−0.932741	+	0.360547i	$0.882590\pi$
$318$			19.2095i			1.07722i
$319$	−5.79706			−0.324573
$320$	3.44370	−	5.95627i	0.192509	−	0.332966i
$321$	−2.38820			−0.133296
$322$		0			0
$323$			9.54453i			0.531072i
$324$	−4.33317			−0.240732
$325$	−22.3148	+	12.8472i	−1.23780	+	0.712635i
$326$	−30.8427			−1.70822
$327$			18.1096i			1.00146i
$328$		−	15.5895i		−	0.860784i
$329$		0			0
$330$	2.75501	−	4.76510i	0.151658	−	0.262310i
$331$	−8.53357			−0.469047			−0.234524	−	0.972110i	$-0.575353\pi$
$331$	−8.53357			−0.469047			−0.234524	+	0.972110i	$0.575353\pi$
$332$			28.7143i			1.57590i
$333$			9.05502i			0.496212i
$334$	−5.36633			−0.293633
$335$	17.9252	+	10.3637i	0.979360	+	0.566231i
$336$		0			0
$337$		−	29.1131i		−	1.58589i	−0.609292	−	0.792946i	$-0.708546\pi$
$337$		−	29.1131i		−	1.58589i	0.609292	−	0.792946i	$-0.291454\pi$
$338$			34.0244i			1.85069i
$339$	−4.04373			−0.219625
$340$	34.8091	+	20.1254i	1.88779	+	1.09145i
$341$	−0.619344			−0.0335393
$342$		−	5.78817i		−	0.312988i
$343$		0			0
$344$	−2.02540			−0.109202
$345$	−5.67764	+	9.82013i	−0.305674	+	0.528698i
$346$	−29.0628			−1.56243
$347$		−	13.4427i		−	0.721644i	−0.932635	−	0.360822i	$-0.882496\pi$
$347$		−	13.4427i		−	0.721644i	0.932635	−	0.360822i	$-0.117504\pi$
$348$			25.6812i			1.37666i
$349$	−24.7397			−1.32429			−0.662144	−	0.749377i	$-0.730353\pi$
$349$	−24.7397			−1.32429			−0.662144	+	0.749377i	$0.730353\pi$
$350$		0			0
$351$	−5.14977			−0.274874
$352$		−	3.55375i		−	0.189415i
$353$			16.7550i			0.891779i	0.895088	+	0.445890i	$0.147113\pi$
$353$			16.7550i			0.891779i	−0.895088	+	0.445890i	$0.852887\pi$
$354$	4.57160			0.242978
$355$	−6.14842	+	10.6344i	−0.326324	+	0.564415i
$356$	−70.6777			−3.74591
$357$		0			0
$358$			22.3965i			1.18369i
$359$	32.4924			1.71488			0.857442	−	0.514581i	$-0.172052\pi$
$359$	32.4924			1.71488			0.857442	+	0.514581i	$0.172052\pi$
$360$	−11.3663	−	6.57160i	−0.599058	−	0.346354i
$361$	−13.7099			−0.721575
$362$		−	8.00120i		−	0.420534i
$363$		−	10.0433i		−	0.527134i
$364$		0			0
$365$	−10.4110	−	6.01926i	−0.544936	−	0.315062i
$366$	−1.65152			−0.0863264
$367$		−	23.9619i		−	1.25080i	−0.780304	−	0.625400i	$-0.784936\pi$
$367$		−	23.9619i		−	1.25080i	0.780304	−	0.625400i	$-0.215064\pi$
$368$			30.9955i			1.61575i
$369$	2.65505			0.138217
$370$	−25.5043	+	44.1126i	−1.32591	+	2.29331i
$371$		0			0
$372$			2.74372i			0.142255i
$373$			11.0754i			0.573464i	0.958011	+	0.286732i	$0.0925689\pi$
$373$			11.0754i			0.573464i	−0.958011	+	0.286732i	$0.907431\pi$
$374$	−10.2149			−0.528199
$375$	0.0204612	−	11.1803i	0.00105661	−	0.577349i
$376$	24.8864			1.28342
$377$			30.5208i			1.57190i
$378$		0			0
$379$	32.7423			1.68186			0.840929	−	0.541145i	$-0.182009\pi$
$379$	32.7423			1.68186			0.840929	+	0.541145i	$0.182009\pi$
$380$	11.1545	−	19.2930i	0.572214	−	0.989709i
$381$	6.85023			0.350948
$382$			1.56687i			0.0801680i
$383$			23.2523i			1.18814i	0.804414	+	0.594069i	$0.202479\pi$
$383$			23.2523i			1.18814i	−0.804414	+	0.594069i	$0.797521\pi$
$384$	15.0096			0.765956
$385$		0			0
$386$	−38.2210			−1.94540
$387$		−	0.344947i		−	0.0175346i
$388$			6.66635i			0.338433i
$389$	37.6262			1.90772			0.953861	−	0.300249i	$-0.0970699\pi$
$389$	37.6262			1.90772			0.953861	+	0.300249i	$0.0970699\pi$
$390$	−25.0877	−	14.5048i	−1.27037	−	0.734479i
$391$	21.0513			1.06461
$392$		0			0
$393$			4.02540i			0.203054i
$394$	60.2494			3.03532
$395$	12.1848	−	21.0750i	0.613084	−	1.06040i
$396$	4.23843			0.212989
$397$		−	0.0575740i		−	0.00288956i	−0.999999	−	0.00144478i	$-0.999540\pi$
$397$		−	0.0575740i		−	0.00288956i	0.999999	−	0.00144478i	$-0.000459887\pi$
$398$		−	35.1144i		−	1.76013i
$399$		0			0
$400$	−15.2428	−	26.4759i	−0.762142	−	1.32380i
$401$	−9.07593			−0.453230			−0.226615	−	0.973984i	$-0.572766\pi$
$401$	−9.07593			−0.453230			−0.226615	+	0.973984i	$0.572766\pi$
$402$			23.3031i			1.16225i
$403$			3.26077i			0.162431i
$404$	−23.9022			−1.18918
$405$	1.11922	−	1.93581i	0.0556142	−	0.0961911i
$406$		0			0
$407$		−	8.85704i		−	0.439027i
$408$			24.3659i			1.20629i
$409$	16.6120			0.821413			0.410706	−	0.911768i	$-0.365282\pi$
$409$	16.6120			0.821413			0.410706	+	0.911768i	$0.365282\pi$
$410$	12.9344	+	7.47821i	0.638785	+	0.369322i
$411$	11.2319			0.554027
$412$			71.5897i			3.52697i
$413$		0			0
$414$	−12.7663			−0.627430
$415$	−12.8279	−	7.41662i	−0.629696	−	0.364068i
$416$	−18.7101			−0.917337
$417$		−	4.98991i		−	0.244357i
$418$			5.66161i			0.276919i
$419$	−29.8759			−1.45953			−0.729766	−	0.683697i	$-0.760371\pi$
$419$	−29.8759			−1.45953			−0.729766	+	0.683697i	$0.760371\pi$
$420$		0			0
$421$	−19.3201			−0.941602			−0.470801	−	0.882239i	$-0.656035\pi$
$421$	−19.3201			−0.941602			−0.470801	+	0.882239i	$0.656035\pi$
$422$		−	12.1379i		−	0.590861i
$423$			4.23843i			0.206080i
$424$	−44.8192			−2.17661
$425$	−17.9817	+	10.3525i	−0.872239	+	0.502169i
$426$	−13.8249			−0.669817
$427$		0			0
$428$		−	10.3485i		−	0.500213i
$429$	5.03717			0.243197
$430$	0.971576	−	1.68045i	0.0468535	−	0.0810385i
$431$	−21.9962			−1.05952			−0.529761	−	0.848147i	$-0.677718\pi$
$431$	−21.9962			−1.05952			−0.529761	+	0.848147i	$0.677718\pi$
$432$		−	6.11005i		−	0.293970i
$433$			2.72706i			0.131054i	0.997851	+	0.0655272i	$0.0208729\pi$
$433$			2.72706i			0.131054i	−0.997851	+	0.0655272i	$0.979127\pi$
$434$		0			0
$435$	−11.4729	−	6.63319i	−0.550081	−	0.318037i
$436$	−78.4719			−3.75812
$437$		−	11.6677i		−	0.558142i
$438$		−	13.5344i		−	0.646700i
$439$	−7.54366			−0.360039			−0.180020	−	0.983663i	$-0.557616\pi$
$439$	−7.54366			−0.360039			−0.180020	+	0.983663i	$0.557616\pi$
$440$	11.1178	+	6.42792i	0.530021	+	0.306439i
$441$		0			0
$442$			53.7802i			2.55806i
$443$		−	10.4383i		−	0.495941i	−0.968768	−	0.247970i	$-0.920236\pi$
$443$		−	10.4383i		−	0.495941i	0.968768	−	0.247970i	$-0.0797636\pi$
$444$	−39.2370			−1.86211
$445$	18.2553	−	31.5747i	0.865386	−	1.49678i
$446$	39.8190			1.88549
$447$			14.4942i			0.685554i
$448$		0			0
$449$	1.73107			0.0816944			0.0408472	−	0.999165i	$-0.486994\pi$
$449$	1.73107			0.0816944			0.0408472	+	0.999165i	$0.486994\pi$
$450$	10.9048	−	6.27815i	0.514056	−	0.295955i
$451$	−2.59700			−0.122288
$452$		−	17.5222i		−	0.824174i
$453$			7.88692i			0.370560i
$454$	54.6055			2.56276
$455$		0			0
$456$	13.5048			0.632421
$457$		−	30.8614i		−	1.44364i	−0.692082	−	0.721819i	$-0.743306\pi$
$457$		−	30.8614i		−	1.44364i	0.692082	−	0.721819i	$-0.256694\pi$
$458$			5.22666i			0.244226i
$459$	−4.14977			−0.193695
$460$	−42.5523	−	24.6022i	−1.98401	−	1.14708i
$461$	−10.7294			−0.499718			−0.249859	−	0.968282i	$-0.580384\pi$
$461$	−10.7294			−0.499718			−0.249859	+	0.968282i	$0.580384\pi$
$462$		0			0
$463$			11.1060i			0.516141i	0.966126	+	0.258071i	$0.0830867\pi$
$463$			11.1060i			0.516141i	−0.966126	+	0.258071i	$0.916913\pi$
$464$	−36.2121			−1.68110
$465$	−1.22573	−	0.708674i	−0.0568420	−	0.0328640i
$466$	17.0096			0.787955
$467$			27.5895i			1.27669i	0.769751	+	0.638344i	$0.220380\pi$
$467$			27.5895i			1.27669i	−0.769751	+	0.638344i	$0.779620\pi$
$468$		−	22.3148i		−	1.03150i
$469$		0			0
$470$	−11.9379	+	20.6480i	−0.550656	+	0.952422i
$471$	−6.55630			−0.302098
$472$			10.6663i			0.490958i
$473$			0.337405i			0.0155139i
$474$	27.3978			1.25842
$475$	5.73788	+	9.96636i	0.263272	+	0.457288i
$476$		0			0
$477$		−	7.63319i		−	0.349500i
$478$		−	7.31011i		−	0.334356i
$479$	−10.0174			−0.457706			−0.228853	−	0.973461i	$-0.573497\pi$
$479$	−10.0174			−0.457706			−0.228853	+	0.973461i	$0.573497\pi$
$480$	4.06632	−	7.03316i	0.185601	−	0.321018i
$481$	−46.6313			−2.12620
$482$		−	22.3913i		−	1.01989i
$483$		0			0
$484$	43.5192			1.97814
$485$	−2.97814	−	1.72185i	−0.135230	−	0.0781852i
$486$	2.51658			0.114154
$487$			30.7341i			1.39270i	0.717704	+	0.696348i	$0.245193\pi$
$487$			30.7341i			1.39270i	−0.717704	+	0.696348i	$0.754807\pi$
$488$		−	3.85329i		−	0.174430i
$489$	12.2558			0.554227
$490$		0			0
$491$	4.14054			0.186860			0.0934301	−	0.995626i	$-0.470217\pi$
$491$	4.14054			0.186860			0.0934301	+	0.995626i	$0.470217\pi$
$492$			11.5048i			0.518677i
$493$			24.5942i			1.10767i
$494$	29.8077			1.34111
$495$	−1.09474	+	1.89348i	−0.0492051	+	0.0851057i
$496$	−3.86881			−0.173715
$497$		0			0
$498$		−	16.6764i		−	0.747289i
$499$	1.54828			0.0693105			0.0346552	−	0.999399i	$-0.488967\pi$
$499$	1.54828			0.0693105			0.0346552	+	0.999399i	$0.488967\pi$
$500$	48.4463	+	0.0886621i	2.16658	+	0.00396509i
$501$	2.13239			0.0952682
$502$		−	53.2878i		−	2.37835i
$503$		−	15.1658i		−	0.676210i	−0.941108	−	0.338105i	$-0.890214\pi$
$503$		−	15.1658i		−	0.676210i	0.941108	−	0.338105i	$-0.109786\pi$
$504$		0			0
$505$	6.17370	−	10.6781i	0.274726	−	0.475170i
$506$	12.4872			0.555123
$507$		−	13.5201i		−	0.600449i
$508$			29.6832i			1.31698i
$509$	−20.4655			−0.907116			−0.453558	−	0.891227i	$-0.649846\pi$
$509$	−20.4655			−0.907116			−0.453558	+	0.891227i	$0.649846\pi$
$510$	−20.2161	−	11.6882i	−0.895183	−	0.517563i
$511$		0			0
$512$			49.5528i			2.18994i
$513$			2.30001i			0.101548i
$514$	−15.6894			−0.692030
$515$	−31.9821	−	18.4909i	−1.40930	−	0.814807i
$516$	1.49472			0.0658012
$517$		−	4.14576i		−	0.182330i
$518$		0			0
$519$	11.5485			0.506924
$520$	33.8422	−	58.5340i	1.48408	−	2.56688i
$521$	−2.74674			−0.120337			−0.0601685	−	0.998188i	$-0.519164\pi$
$521$	−2.74674			−0.120337			−0.0601685	+	0.998188i	$0.519164\pi$
$522$		−	14.9149i		−	0.652806i
$523$		−	39.8669i		−	1.74326i	−0.490166	−	0.871629i	$-0.663064\pi$
$523$		−	39.8669i		−	1.74326i	0.490166	−	0.871629i	$-0.336936\pi$
$524$	−17.4427			−0.761990
$525$		0			0
$526$	70.5850			3.07765
$527$			2.62758i			0.114459i
$528$			5.97645i			0.260092i
$529$	−2.73410			−0.118874
$530$	21.4996	−	37.1860i	0.933883	−	1.61526i
$531$	−1.81659			−0.0788335
$532$		0			0
$533$			13.6729i			0.592239i
$534$	41.0475			1.77630
$535$	4.62310	+	2.67291i	0.199874	+	0.115560i
$536$	−54.3701			−2.34843
$537$		−	8.89956i		−	0.384045i
$538$		−	18.6688i		−	0.804867i
$539$		0			0
$540$	8.38820	+	4.84975i	0.360971	+	0.208700i
$541$	26.4986			1.13927			0.569633	−	0.821899i	$-0.307085\pi$
$541$	26.4986			1.13927			0.569633	+	0.821899i	$0.307085\pi$
$542$		−	78.5465i		−	3.37386i
$543$			3.17940i			0.136441i
$544$	−15.0769			−0.646416
$545$	20.2685	−	35.0567i	0.868207	−	1.50166i
$546$		0			0
$547$		−	12.9090i		−	0.551950i	−0.961165	−	0.275975i	$-0.910999\pi$
$547$		−	12.9090i		−	0.551950i	0.961165	−	0.275975i	$-0.0890008\pi$
$548$			48.6696i			2.07906i
$549$	0.656256			0.0280083
$550$	−10.6663	+	6.14088i	−0.454815	+	0.261848i
$551$	13.6314			0.580716
$552$		−	29.7860i		−	1.26778i
$553$		0			0
$554$	−31.3379			−1.33142
$555$	10.1345	−	17.5288i	0.430186	−	0.744056i
$556$	21.6221			0.916983
$557$		−	7.18509i		−	0.304442i	−0.988346	−	0.152221i	$-0.951357\pi$
$557$		−	7.18509i		−	0.304442i	0.988346	−	0.152221i	$-0.0486425\pi$
$558$		−	1.59347i		−	0.0674569i
$559$	1.77640			0.0751336
$560$		0			0
$561$	4.05903			0.171373
$562$			0.102985i			0.00434415i
$563$		−	2.38700i		−	0.100600i	−0.998734	−	0.0502999i	$-0.983982\pi$
$563$		−	2.38700i		−	0.100600i	0.998734	−	0.0502999i	$-0.0160177\pi$
$564$	−18.3659			−0.773342
$565$	7.82789	+	4.52580i	0.329322	+	0.190402i
$566$	27.2847			1.14686
$567$		0			0
$568$		−	32.2558i		−	1.35342i
$569$	−29.8542			−1.25155			−0.625776	−	0.780003i	$-0.715217\pi$
$569$	−29.8542			−1.25155			−0.625776	+	0.780003i	$0.715217\pi$
$570$	−6.47821	+	11.2048i	−0.271342	+	0.469317i
$571$	−19.4634			−0.814518			−0.407259	−	0.913313i	$-0.633515\pi$
$571$	−19.4634			−0.814518			−0.407259	+	0.913313i	$0.633515\pi$
$572$			21.8269i			0.912630i
$573$		−	0.622618i		−	0.0260103i
$574$		0			0
$575$	21.9817	−	12.6554i	0.916699	−	0.527766i
$576$	−3.07689			−0.128204
$577$			3.96187i			0.164935i	0.996594	+	0.0824675i	$0.0262801\pi$
$577$			3.96187i			0.164935i	−0.996594	+	0.0824675i	$0.973720\pi$
$578$			0.555096i			0.0230890i
$579$	15.1877			0.631178
$580$	28.7428	−	49.7139i	1.19348	−	2.06426i
$581$		0			0
$582$		−	3.87162i		−	0.160484i
$583$			7.46629i			0.309222i
$584$	31.5782			1.30671
$585$	9.96897	+	5.76370i	0.412166	+	0.238300i
$586$	74.6052			3.08191
$587$		−	13.9419i		−	0.575446i	−0.957714	−	0.287723i	$-0.907102\pi$
$587$		−	13.9419i		−	0.575446i	0.957714	−	0.287723i	$-0.0928982\pi$
$588$		0			0
$589$	1.45634			0.0600075
$590$	−8.84975	−	5.11661i	−0.364339	−	0.210647i
$591$	−23.9410			−0.984801
$592$		−	55.3266i		−	2.27391i
$593$		−	38.4973i		−	1.58089i	−0.612530	−	0.790447i	$-0.709848\pi$
$593$		−	38.4973i		−	1.58089i	0.612530	−	0.790447i	$-0.290152\pi$
$594$	−2.46156			−0.100999
$595$		0			0
$596$	−62.8061			−2.57264
$597$			13.9532i			0.571068i
$598$		−	65.7435i		−	2.68845i
$599$	−17.4997			−0.715019			−0.357509	−	0.933910i	$-0.616374\pi$
$599$	−17.4997			−0.715019			−0.357509	+	0.933910i	$0.616374\pi$
$600$	14.6480	+	25.4427i	0.598003	+	1.03870i
$601$	−34.5192			−1.40807			−0.704033	−	0.710167i	$-0.748619\pi$
$601$	−34.5192			−1.40807			−0.704033	+	0.710167i	$0.748619\pi$
$602$		0			0
$603$		−	9.25982i		−	0.377089i
$604$	−34.1754			−1.39058
$605$	−11.2406	+	19.4418i	−0.456994	+	0.790422i
$606$	13.8817			0.563906
$607$		−	10.9156i		−	0.443050i	−0.975155	−	0.221525i	$-0.928897\pi$
$607$		−	10.9156i		−	0.443050i	0.975155	−	0.221525i	$-0.0711035\pi$
$608$			8.35639i			0.338896i
$609$		0			0
$610$	3.19703	+	1.84841i	0.129444	+	0.0748398i
$611$	−21.8269			−0.883023
$612$		−	17.9817i		−	0.726866i
$613$			26.1173i			1.05487i	0.849596	+	0.527435i	$0.176846\pi$
$613$			26.1173i			1.05487i	−0.849596	+	0.527435i	$0.823154\pi$
$614$	−79.5377			−3.20988
$615$	−5.13968	−	2.97158i	−0.207252	−	0.119825i
$616$		0			0
$617$			11.6689i			0.469772i	0.972023	+	0.234886i	$0.0754717\pi$
$617$			11.6689i			0.469772i	−0.972023	+	0.234886i	$0.924528\pi$
$618$		−	41.5772i		−	1.67248i
$619$	−0.823632			−0.0331046			−0.0165523	−	0.999863i	$-0.505269\pi$
$619$	−0.823632			−0.0331046			−0.0165523	+	0.999863i	$0.505269\pi$
$620$	3.07081	−	5.31131i	0.123327	−	0.213307i
$621$	5.07288			0.203568
$622$			55.7933i			2.23711i
$623$		0			0
$624$	31.4653			1.25962
$625$	−12.5528	+	21.6201i	−0.502112	+	0.864803i
$626$	17.3285			0.692585
$627$		−	2.24973i		−	0.0898454i
$628$		−	28.4096i		−	1.13367i
$629$	−37.5763			−1.49826
$630$		0			0
$631$	−20.5920			−0.819755			−0.409877	−	0.912141i	$-0.634429\pi$
$631$	−20.5920			−0.819755			−0.409877	+	0.912141i	$0.634429\pi$
$632$			63.9239i			2.54275i
$633$			4.82315i			0.191703i
$634$	32.3096			1.28318
$635$	−13.2607	−	7.66688i	−0.526237	−	0.304251i
$636$	33.0759			1.31155
$637$		0			0
$638$			14.5888i			0.577575i
$639$	5.49351			0.217320
$640$	−29.0557	−	16.7990i	−1.14853	−	0.664038i
$641$	29.6741			1.17206			0.586029	−	0.810290i	$-0.300690\pi$
$641$	29.6741			1.17206			0.586029	+	0.810290i	$0.300690\pi$
$642$			6.01009i			0.237199i
$643$			11.1286i			0.438870i	0.975627	+	0.219435i	$0.0704214\pi$
$643$			11.1286i			0.438870i	−0.975627	+	0.219435i	$0.929579\pi$
$644$		0			0
$645$	−0.386070	+	0.667751i	−0.0152015	+	0.0262927i
$646$	24.0196			0.945037
$647$			10.9234i			0.429442i	0.976675	+	0.214721i	$0.0688841\pi$
$647$			10.9234i			0.429442i	−0.976675	+	0.214721i	$0.931116\pi$
$648$			5.87162i			0.230659i
$649$	1.77687			0.0697484
$650$	32.3310	+	56.1571i	1.26813	+	2.20266i
$651$		0			0
$652$			53.1065i			2.07981i
$653$			7.17076i			0.280614i	0.990108	+	0.140307i	$0.0448089\pi$
$653$			7.17076i			0.280614i	−0.990108	+	0.140307i	$0.955191\pi$
$654$	45.5742			1.78209
$655$	4.50528	−	7.79240i	0.176036	−	0.304474i
$656$	−16.2225			−0.633382
$657$			5.37811i			0.209820i
$658$		0			0
$659$	−14.1232			−0.550161			−0.275080	−	0.961421i	$-0.588704\pi$
$659$	−14.1232			−0.550161			−0.275080	+	0.961421i	$0.588704\pi$
$660$	−8.20479	−	4.74372i	−0.319371	−	0.184649i
$661$	−28.9217			−1.12492			−0.562461	−	0.826824i	$-0.690146\pi$
$661$	−28.9217			−1.12492			−0.562461	+	0.826824i	$0.690146\pi$
$662$			21.4754i			0.834665i
$663$		−	21.3703i		−	0.829955i
$664$	38.9090			1.50996
$665$		0			0
$666$	22.7877			0.883005
$667$		−	30.0651i		−	1.16413i
$668$			9.24002i			0.357507i
$669$	−15.8227			−0.611740
$670$	26.0811	−	45.1103i	1.00760	−	1.74276i
$671$	−0.641907			−0.0247806
$672$		0			0
$673$			14.4081i			0.555392i	0.960669	+	0.277696i	$0.0895709\pi$
$673$			14.4081i			0.555392i	−0.960669	+	0.277696i	$0.910429\pi$
$674$	−73.2654			−2.82208
$675$	−4.33317	+	2.49472i	−0.166784	+	0.0960216i
$676$	58.5850			2.25327
$677$			30.1366i			1.15825i	0.815240	+	0.579123i	$0.196605\pi$
$677$			30.1366i			1.15825i	−0.815240	+	0.579123i	$0.803395\pi$
$678$			10.1764i			0.390821i
$679$		0			0
$680$	27.2706	−	47.1676i	1.04578	−	1.80880i
$681$	−21.6983			−0.831481
$682$			1.55863i			0.0596830i
$683$			15.5168i			0.593735i	0.954919	+	0.296868i	$0.0959420\pi$
$683$			15.5168i			0.593735i	−0.954919	+	0.296868i	$0.904058\pi$
$684$	−9.96636			−0.381073
$685$	−21.7428	−	12.5709i	−0.830748	−	0.480309i
$686$		0			0
$687$		−	2.07689i		−	0.0792383i
$688$			2.10764i			0.0803531i
$689$	39.3092			1.49756
$690$	24.7131	+	14.2882i	0.940813	+	0.543944i
$691$	−45.7835			−1.74168			−0.870842	−	0.491562i	$-0.836426\pi$
$691$	−45.7835			−1.74168			−0.870842	+	0.491562i	$0.836426\pi$
$692$			50.0418i			1.90230i
$693$		0			0
$694$	−33.8297			−1.28416
$695$	−5.58478	+	9.65951i	−0.211843	+	0.366406i
$696$	34.7990			1.31905
$697$			11.0179i			0.417331i
$698$			62.2595i			2.35656i
$699$	−6.75902			−0.255650
$700$		0			0
$701$	24.0419			0.908050			0.454025	−	0.890989i	$-0.349988\pi$
$701$	24.0419			0.908050			0.454025	+	0.890989i	$0.349988\pi$
$702$			12.9598i			0.489136i
$703$			20.8267i			0.785493i
$704$	3.00961			0.113429
$705$	4.74372	−	8.20479i	0.178659	−	0.309010i
$706$	42.1653			1.58691
$707$		0			0
$708$		−	7.87162i		−	0.295834i
$709$	−18.3971			−0.690917			−0.345459	−	0.938434i	$-0.612277\pi$
$709$	−18.3971			−0.690917			−0.345459	+	0.938434i	$0.612277\pi$
$710$	26.7623	+	15.4730i	1.00437	+	0.580691i
$711$	−10.8869			−0.408292
$712$			95.7710i			3.58917i
$713$		−	3.21209i		−	0.120294i
$714$		0			0
$715$	−9.75100	−	5.63768i	−0.364667	−	0.210837i
$716$	38.5634			1.44118
$717$			2.90478i			0.108481i
$718$		−	81.7697i		−	3.05162i
$719$	−16.2455			−0.605855			−0.302927	−	0.953014i	$-0.597964\pi$
$719$	−16.2455			−0.605855			−0.302927	+	0.953014i	$0.597964\pi$
$720$	−6.83846	+	11.8279i	−0.254854	+	0.440799i
$721$		0			0
$722$			34.5021i			1.28404i
$723$			8.89749i			0.330901i
$724$	−13.7769			−0.512014
$725$	14.7853	+	25.6812i	0.549112	+	0.953775i
$726$	−25.2746			−0.938030
$727$		−	42.6977i		−	1.58357i	−0.610800	−	0.791785i	$-0.709152\pi$
$727$		−	42.6977i		−	1.58357i	0.610800	−	0.791785i	$-0.290848\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−15.1479	+	26.2001i	−0.560651	+	0.969709i
$731$	1.43145			0.0529441
$732$			2.84367i			0.105105i
$733$			46.7120i			1.72535i	0.505760	+	0.862674i	$0.331212\pi$
$733$			46.7120i			1.72535i	−0.505760	+	0.862674i	$0.668788\pi$
$734$	−60.3020			−2.22579
$735$		0			0
$736$	18.4307			0.679366
$737$			9.05735i			0.333632i
$738$		−	6.68165i		−	0.245955i
$739$	−7.04821			−0.259272			−0.129636	−	0.991562i	$-0.541381\pi$
$739$	−7.04821			−0.259272			−0.129636	+	0.991562i	$0.541381\pi$
$740$	75.9553	+	43.9146i	2.79217	+	1.61433i
$741$	−11.8445			−0.435120
$742$		0			0
$743$		−	8.55510i		−	0.313856i	−0.987610	−	0.156928i	$-0.949841\pi$
$743$		−	8.55510i		−	0.313856i	0.987610	−	0.156928i	$-0.0501591\pi$
$744$	3.71784			0.136303
$745$	16.2222	−	28.0581i	0.594334	−	1.02797i
$746$	27.8722			1.02047
$747$			6.62663i			0.242456i
$748$			17.5885i			0.643099i
$749$		0			0
$750$	−28.1362	−	0.0514923i	−1.02739	−	0.00188023i
$751$	−2.97645			−0.108612			−0.0543062	−	0.998524i	$-0.517295\pi$
$751$	−2.97645			−0.108612			−0.0543062	+	0.998524i	$0.517295\pi$
$752$		−	25.8970i		−	0.944367i
$753$			21.1747i			0.771648i
$754$	76.8081			2.79719
$755$	8.82716	−	15.2676i	0.321253	−	0.555644i
$756$		0			0
$757$		−	43.6750i		−	1.58740i	−0.608313	−	0.793698i	$-0.708153\pi$
$757$		−	43.6750i		−	1.58740i	0.608313	−	0.793698i	$-0.291847\pi$
$758$		−	82.3986i		−	2.99285i
$759$	−4.96196			−0.180108
$760$	−26.1427	−	15.1148i	−0.948296	−	0.548271i
$761$	−26.7256			−0.968803			−0.484402	−	0.874846i	$-0.660963\pi$
$761$	−26.7256			−0.968803			−0.484402	+	0.874846i	$0.660963\pi$
$762$		−	17.2392i		−	0.624509i
$763$		0			0
$764$	2.69791			0.0976071
$765$	8.03316	+	4.64448i	0.290439	+	0.167922i
$766$	58.5163			2.11428
$767$		−	9.35504i		−	0.337791i
$768$		−	31.6191i		−	1.14096i
$769$	−4.04661			−0.145925			−0.0729623	−	0.997335i	$-0.523245\pi$
$769$	−4.04661			−0.145925			−0.0729623	+	0.997335i	$0.523245\pi$
$770$		0			0
$771$	6.23442			0.224527
$772$			65.8108i			2.36858i
$773$		−	6.31105i		−	0.226993i	−0.993538	−	0.113496i	$-0.963795\pi$
$773$		−	6.31105i		−	0.226993i	0.993538	−	0.113496i	$-0.0362050\pi$
$774$	−0.868086			−0.0312027
$775$	1.57962	+	2.74372i	0.0567418	+	0.0985572i
$776$	9.03316			0.324272
$777$		0			0
$778$		−	94.6892i		−	3.39477i
$779$	6.10666			0.218794
$780$	−24.9751	+	43.1973i	−0.894252	+	1.54671i
$781$	−5.37340			−0.192275
$782$		−	52.9772i		−	1.89446i
$783$			5.92664i			0.211801i
$784$		0			0
$785$	12.6917	+	7.33791i	0.452988	+	0.261901i
$786$	10.1302			0.361333
$787$			29.9755i			1.06851i	0.845323	+	0.534256i	$0.179408\pi$
$787$			29.9755i			1.06851i	−0.845323	+	0.534256i	$0.820592\pi$
$788$		−	103.740i		−	3.69560i
$789$	−28.0480			−0.998535
$790$	−53.0369	−	30.6640i	−1.88697	−	1.09098i
$791$		0			0
$792$		−	5.74324i		−	0.204077i
$793$			3.37957i			0.120012i
$794$	−0.144890			−0.00514194
$795$	−8.54318	+	14.7764i	−0.302995	+	0.524065i
$796$	−60.4618			−2.14301
$797$			0.676527i			0.0239638i	0.999928	+	0.0119819i	$0.00381405\pi$
$797$			0.676527i			0.0239638i	−0.999928	+	0.0119819i	$0.996186\pi$
$798$		0			0
$799$	−17.5885			−0.622236
$800$	−15.7432	+	9.06377i	−0.556607	+	0.320453i
$801$	−16.3108			−0.576315
$802$			22.8403i			0.806519i
$803$		−	5.26052i		−	0.185640i
$804$	40.1244			1.41508
$805$		0			0
$806$	8.20600			0.289044
$807$			7.41830i			0.261137i
$808$			32.3884i			1.13942i
$809$	50.1223			1.76221			0.881104	−	0.472923i	$-0.156801\pi$
$809$	50.1223			1.76221			0.881104	+	0.472923i	$0.156801\pi$
$810$	−4.87162	−	2.81659i	−0.171171	−	0.0989650i
$811$	36.4884			1.28128			0.640641	−	0.767841i	$-0.278669\pi$
$811$	36.4884			1.28128			0.640641	+	0.767841i	$0.278669\pi$
$812$		0			0
$813$			31.2116i			1.09464i
$814$	−22.2894			−0.781245
$815$	−23.7249	−	13.7169i	−0.831047	−	0.480481i
$816$	25.3553			0.887613
$817$		−	0.793383i		−	0.0277570i
$818$		−	41.8055i		−	1.46170i
$819$		0			0
$820$	12.8764	−	22.2711i	0.449662	−	0.777741i
$821$	38.7308			1.35172			0.675858	−	0.737032i	$-0.263773\pi$
$821$	38.7308			1.35172			0.675858	+	0.737032i	$0.263773\pi$
$822$		−	28.2659i		−	0.985886i
$823$			20.9812i			0.731358i	0.930741	+	0.365679i	$0.119163\pi$
$823$			20.9812i			0.731358i	−0.930741	+	0.365679i	$0.880837\pi$
$824$	97.0069			3.37939
$825$	4.23843	−	2.44017i	0.147563	−	0.0849558i
$826$		0			0
$827$		−	37.8114i		−	1.31483i	−0.753528	−	0.657416i	$-0.771650\pi$
$827$		−	37.8114i		−	1.31483i	0.753528	−	0.657416i	$-0.228350\pi$
$828$			21.9817i			0.763916i
$829$	−53.3181			−1.85182			−0.925908	−	0.377750i	$-0.876698\pi$
$829$	−53.3181			−1.85182			−0.925908	+	0.377750i	$0.876698\pi$
$830$	−18.6645	+	32.2824i	−0.647855	+	1.12054i
$831$	12.4526			0.431976
$832$		−	15.8453i		−	0.549336i
$833$		0			0
$834$	−12.5575			−0.434831
$835$	−4.12790	−	2.38660i	−0.142852	−	0.0825919i
$836$	9.74845			0.337157
$837$			0.633188i			0.0218862i
$838$			75.1850i			2.59722i
$839$	52.6452			1.81752			0.908758	−	0.417324i	$-0.137032\pi$
$839$	52.6452			1.81752			0.908758	+	0.417324i	$0.137032\pi$
$840$		0			0
$841$	6.12510			0.211210
$842$			48.6205i			1.67557i
$843$		−	0.0409225i		−	0.00140944i
$844$	−20.8996			−0.719393
$845$	−15.1319	+	26.1724i	−0.520554	+	0.900356i
$846$	10.6663			0.366717
$847$		0			0
$848$			46.6392i			1.60160i
$849$	−10.8420			−0.372096
$850$	26.0529	+	45.2523i	0.893606	+	1.55214i
$851$	45.9350			1.57463
$852$			23.8043i			0.815523i
$853$			5.01225i			0.171616i	0.996312	+	0.0858081i	$0.0273472\pi$
$853$			5.01225i			0.171616i	−0.996312	+	0.0858081i	$0.972653\pi$
$854$		0			0
$855$	2.57421	−	4.45239i	0.0880362	−	0.152268i
$856$	−14.0226			−0.479282
$857$		−	38.4212i		−	1.31244i	−0.754568	−	0.656222i	$-0.772154\pi$
$857$		−	38.4212i		−	1.31244i	0.754568	−	0.656222i	$-0.227846\pi$
$858$		−	12.6764i		−	0.432767i
$859$	23.3418			0.796413			0.398207	−	0.917296i	$-0.369633\pi$
$859$	23.3418			0.796413			0.398207	+	0.917296i	$0.369633\pi$
$860$	−2.89348	−	1.67291i	−0.0986670	−	0.0570457i
$861$		0			0
$862$			55.3553i			1.88541i
$863$		−	54.3757i		−	1.85097i	−0.378783	−	0.925486i	$-0.623657\pi$
$863$		−	54.3757i		−	1.85097i	0.378783	−	0.925486i	$-0.376343\pi$
$864$	−3.63319			−0.123604
$865$	−22.3558	−	12.9253i	−0.760119	−	0.439473i
$866$	6.86287			0.233210
$867$		−	0.220576i		−	0.00749114i
$868$		0			0
$869$	10.6489			0.361239
$870$	−16.6929	+	28.8723i	−0.565944	+	0.978864i
$871$	47.6859			1.61578
$872$			106.332i			3.60087i
$873$			1.53844i			0.0520685i
$874$	−29.3627			−0.993208
$875$		0			0
$876$	−23.3043			−0.787378
$877$		−	28.4557i		−	0.960881i	−0.877027	−	0.480441i	$-0.840477\pi$
$877$		−	28.4557i		−	0.960881i	0.877027	−	0.480441i	$-0.159523\pi$
$878$			18.9842i			0.640686i
$879$	−29.6455			−0.999917
$880$	6.68894	−	11.5693i	0.225484	−	0.390000i
$881$	6.50466			0.219148			0.109574	−	0.993979i	$-0.465051\pi$
$881$	6.50466			0.219148			0.109574	+	0.993979i	$0.465051\pi$
$882$		0			0
$883$		−	34.7640i		−	1.16990i	−0.811069	−	0.584951i	$-0.801114\pi$
$883$		−	34.7640i		−	1.16990i	0.811069	−	0.584951i	$-0.198886\pi$
$884$	92.6014			3.11452
$885$	3.51658	+	2.03316i	0.118209	+	0.0683439i
$886$	−26.2689			−0.882522
$887$		−	29.3541i		−	0.985614i	−0.870139	−	0.492807i	$-0.835971\pi$
$887$		−	29.3541i		−	0.985614i	0.870139	−	0.492807i	$-0.164029\pi$
$888$			53.1676i			1.78419i
$889$		0			0
$890$	−79.4601	−	45.9410i	−2.66351	−	1.53995i
$891$	0.978135			0.0327688
$892$		−	68.5624i		−	2.29564i
$893$			9.74845i			0.326219i
$894$	36.4759			1.21994
$895$	−9.96053	+	17.2279i	−0.332944	+	0.575864i
$896$		0			0
$897$			26.1242i			0.872260i
$898$		−	4.35639i		−	0.145374i
$899$	3.75268			0.125159
$900$	−10.8100	−	18.7764i	−0.360334	−	0.625880i
$901$	31.6760			1.05528
$902$			6.53556i			0.217610i
$903$		0			0
$904$	−23.7432			−0.789688
$905$	3.55843	−	6.15470i	0.118286	−	0.204589i
$906$	19.8481			0.659408
$907$			36.2871i			1.20489i	0.798159	+	0.602447i	$0.205808\pi$
$907$			36.2871i			1.20489i	−0.798159	+	0.602447i	$0.794192\pi$
$908$		−	94.0225i		−	3.12025i
$909$	−5.51610			−0.182958
$910$		0			0
$911$	51.6732			1.71201			0.856004	−	0.516968i	$-0.172940\pi$
$911$	51.6732			1.71201			0.856004	+	0.516968i	$0.172940\pi$
$912$		−	14.0532i		−	0.465348i
$913$		−	6.48174i		−	0.214514i
$914$	−77.6653			−2.56894
$915$	−1.27039	−	0.734492i	−0.0419977	−	0.0242816i
$916$	8.99952			0.297353
$917$		0			0
$918$			10.4432i			0.344678i
$919$	41.0377			1.35371			0.676854	−	0.736117i	$-0.263343\pi$
$919$	41.0377			1.35371			0.676854	+	0.736117i	$0.263343\pi$
$920$	−33.3370	+	57.6600i	−1.09909	+	1.90100i
$921$	31.6055			1.04144
$922$			27.0014i			0.889243i
$923$			28.2903i			0.931187i
$924$		0			0
$925$	−39.2370	+	22.5897i	−1.29010	+	0.742745i
$926$	27.9492			0.918469
$927$			16.5213i			0.542631i
$928$			21.5326i			0.706843i
$929$	−2.98520			−0.0979412			−0.0489706	−	0.998800i	$-0.515594\pi$
$929$	−2.98520			−0.0979412			−0.0489706	+	0.998800i	$0.515594\pi$
$930$	−1.78343	+	3.08465i	−0.0584811	+	0.101150i
$931$		0			0
$932$		−	29.2880i		−	0.959361i
$933$		−	22.1703i		−	0.725823i
$934$	69.4311			2.27185
$935$	−7.85752	−	4.54293i	−0.256968	−	0.148570i
$936$	−30.2375			−0.988343
$937$		−	26.1169i		−	0.853201i	−0.904440	−	0.426601i	$-0.859711\pi$
$937$		−	26.1169i		−	0.853201i	0.904440	−	0.426601i	$-0.140289\pi$
$938$		0			0
$939$	−6.88572			−0.224707
$940$	35.5528	+	20.5553i	1.15960	+	0.670441i
$941$	−10.2116			−0.332889			−0.166444	−	0.986051i	$-0.553229\pi$
$941$	−10.2116			−0.332889			−0.166444	+	0.986051i	$0.553229\pi$
$942$			16.4995i			0.537581i
$943$		−	13.4688i		−	0.438603i
$944$	11.0995			0.361257
$945$		0			0
$946$	0.849106			0.0276068
$947$			46.5444i			1.51249i	0.654289	+	0.756245i	$0.272968\pi$
$947$			46.5444i			1.51249i	−0.654289	+	0.756245i	$0.727032\pi$
$948$		−	47.1749i		−	1.53217i
$949$	−27.6960			−0.899050
$950$	25.0811	−	14.4398i	0.813740	−	0.468490i
$951$	−12.8387			−0.416324
$952$		0			0
$953$		−	30.6348i		−	0.992358i	−0.868220	−	0.496179i	$-0.834736\pi$
$953$		−	30.6348i		−	0.992358i	0.868220	−	0.496179i	$-0.165264\pi$
$954$	−19.2095			−0.621931
$955$	−0.696844	+	1.20527i	−0.0225493	+	0.0390016i
$956$	−12.5869			−0.407090
$957$		−	5.79706i		−	0.187392i
$958$			25.2095i			0.814483i
$959$		0			0
$960$	5.95627	+	3.44370i	0.192238	+	0.111145i
$961$	−30.5991			−0.987067
$962$			117.351i			3.78356i
$963$		−	2.38820i		−	0.0769586i
$964$	−38.5544			−1.24175
$965$	−29.4004	−	16.9983i	−0.946433	−	0.547193i
$966$		0			0
$967$			57.4401i			1.84715i	0.383419	+	0.923575i	$0.374747\pi$
$967$			57.4401i			1.84715i	−0.383419	+	0.923575i	$0.625253\pi$
$968$		−	58.9701i		−	1.89537i
$969$	−9.54453			−0.306614
$970$	−4.33317	+	7.49472i	−0.139130	+	0.240641i
$971$	−48.1816			−1.54622			−0.773110	−	0.634272i	$-0.781300\pi$
$971$	−48.1816			−1.54622			−0.773110	+	0.634272i	$0.781300\pi$
$972$		−	4.33317i		−	0.138987i
$973$		0			0
$974$	77.3449			2.47829
$975$	−12.8472	−	22.3148i	−0.411440	−	0.714647i
$976$	−4.00976			−0.128349
$977$		−	13.7523i		−	0.439977i	−0.975503	−	0.219988i	$-0.929398\pi$
$977$		−	13.7523i		−	0.439977i	0.975503	−	0.219988i	$-0.0706019\pi$
$978$		−	30.8427i		−	0.986241i
$979$	15.9542			0.509898
$980$		0			0
$981$	−18.1096			−0.578194
$982$		−	10.4200i		−	0.332516i
$983$		−	38.1944i		−	1.21821i	−0.793089	−	0.609106i	$-0.791528\pi$
$983$		−	38.1944i		−	1.21821i	0.793089	−	0.609106i	$-0.208472\pi$
$984$	15.5895			0.496974
$985$	46.3452	+	26.7951i	1.47668	+	0.853764i
$986$	61.8933			1.97108
$987$		0			0
$988$		−	51.3245i		−	1.63285i
$989$	−1.74987			−0.0556428
$990$	4.76510	+	2.75501i	0.151445	+	0.0875600i
$991$	39.5200			1.25539			0.627697	−	0.778458i	$-0.283998\pi$
$991$	39.5200			1.25539			0.627697	+	0.778458i	$0.283998\pi$
$992$			2.30049i			0.0730407i
$993$		−	8.53357i		−	0.270805i
$994$		0			0
$995$	15.6167	−	27.0108i	0.495082	−	0.856300i
$996$	−28.7143			−0.909849
$997$		−	11.5290i		−	0.365126i	−0.983194	−	0.182563i	$-0.941561\pi$
$997$		−	11.5290i		−	0.365126i	0.983194	−	0.182563i	$-0.0584393\pi$
$998$		−	3.89637i		−	0.123337i
$999$	−9.05502			−0.286488

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.d.e.589.1		8
3.2	odd	2		2205.2.d.o.1324.8		8
5.2	odd	4		3675.2.a.cb.1.4		4
5.3	odd	4		3675.2.a.bn.1.1		4
5.4	even	2	inner	735.2.d.e.589.8		8
7.2	even	3		735.2.q.g.214.1		16
7.3	odd	6		105.2.q.a.79.8	yes	16
7.4	even	3		735.2.q.g.79.8		16
7.5	odd	6		105.2.q.a.4.1	✓	16
7.6	odd	2		735.2.d.d.589.1		8
15.14	odd	2		2205.2.d.o.1324.1		8
21.5	even	6		315.2.bf.b.109.8		16
21.17	even	6		315.2.bf.b.289.1		16
21.20	even	2		2205.2.d.s.1324.8		8
28.3	even	6		1680.2.di.d.289.5		16
28.19	even	6		1680.2.di.d.529.4		16
35.3	even	12		525.2.i.k.226.4		8
35.4	even	6		735.2.q.g.79.1		16
35.9	even	6		735.2.q.g.214.8		16
35.12	even	12		525.2.i.h.151.1		8
35.13	even	4		3675.2.a.bp.1.1		4
35.17	even	12		525.2.i.h.226.1		8
35.19	odd	6		105.2.q.a.4.8	yes	16
35.24	odd	6		105.2.q.a.79.1	yes	16
35.27	even	4		3675.2.a.bz.1.4		4
35.33	even	12		525.2.i.k.151.4		8
35.34	odd	2		735.2.d.d.589.8		8
105.59	even	6		315.2.bf.b.289.8		16
105.89	even	6		315.2.bf.b.109.1		16
105.104	even	2		2205.2.d.s.1324.1		8
140.19	even	6		1680.2.di.d.529.5		16
140.59	even	6		1680.2.di.d.289.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.1	✓	16	7.5	odd	6
105.2.q.a.4.8	yes	16	35.19	odd	6
105.2.q.a.79.1	yes	16	35.24	odd	6
105.2.q.a.79.8	yes	16	7.3	odd	6
315.2.bf.b.109.1		16	105.89	even	6
315.2.bf.b.109.8		16	21.5	even	6
315.2.bf.b.289.1		16	21.17	even	6
315.2.bf.b.289.8		16	105.59	even	6
525.2.i.h.151.1		8	35.12	even	12
525.2.i.h.226.1		8	35.17	even	12
525.2.i.k.151.4		8	35.33	even	12
525.2.i.k.226.4		8	35.3	even	12
735.2.d.d.589.1		8	7.6	odd	2
735.2.d.d.589.8		8	35.34	odd	2
735.2.d.e.589.1		8	1.1	even	1	trivial
735.2.d.e.589.8		8	5.4	even	2	inner
735.2.q.g.79.1		16	35.4	even	6
735.2.q.g.79.8		16	7.4	even	3
735.2.q.g.214.1		16	7.2	even	3
735.2.q.g.214.8		16	35.9	even	6
1680.2.di.d.289.4		16	140.59	even	6
1680.2.di.d.289.5		16	28.3	even	6
1680.2.di.d.529.4		16	28.19	even	6
1680.2.di.d.529.5		16	140.19	even	6
2205.2.d.o.1324.1		8	15.14	odd	2
2205.2.d.o.1324.8		8	3.2	odd	2
2205.2.d.s.1324.1		8	105.104	even	2
2205.2.d.s.1324.8		8	21.20	even	2
3675.2.a.bn.1.1		4	5.3	odd	4
3675.2.a.bp.1.1		4	35.13	even	4
3675.2.a.bz.1.4		4	35.27	even	4
3675.2.a.cb.1.4		4	5.2	odd	4

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.51658i q^{2} +1.00000i q^{3} -4.33317 q^{4} +(1.11922 - 1.93581i) q^{5} +2.51658 q^{6} +5.87162i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.51658i q^{2} +1.00000i q^{3} -4.33317 q^{4} +(1.11922 - 1.93581i) q^{5} +2.51658 q^{6} +5.87162i q^{8} -1.00000 q^{9} +(-4.87162 - 2.81659i) q^{10} +0.978135 q^{11} -4.33317i q^{12} -5.14977i q^{13} +(1.93581 + 1.11922i) q^{15} +6.11005 q^{16} -4.14977i q^{17} +2.51658i q^{18} -2.30001 q^{19} +(-4.84975 + 8.38820i) q^{20} -2.46156i q^{22} +5.07288i q^{23} -5.87162 q^{24} +(-2.49472 - 4.33317i) q^{25} -12.9598 q^{26} -1.00000i q^{27} -5.92664 q^{29} +(2.81659 - 4.87162i) q^{30} -0.633188 q^{31} -3.63319i q^{32} +0.978135i q^{33} -10.4432 q^{34} +4.33317 q^{36} -9.05502i q^{37} +5.78817i q^{38} +5.14977 q^{39} +(11.3663 + 6.57160i) q^{40} -2.65505 q^{41} +0.344947i q^{43} -4.23843 q^{44} +(-1.11922 + 1.93581i) q^{45} +12.7663 q^{46} -4.23843i q^{47} +6.11005i q^{48} +(-10.9048 + 6.27815i) q^{50} +4.14977 q^{51} +22.3148i q^{52} +7.63319i q^{53} -2.51658 q^{54} +(1.09474 - 1.89348i) q^{55} -2.30001i q^{57} +14.9149i q^{58} +1.81659 q^{59} +(-8.38820 - 4.84975i) q^{60} -0.656256 q^{61} +1.59347i q^{62} +3.07689 q^{64} +(-9.96897 - 5.76370i) q^{65} +2.46156 q^{66} +9.25982i q^{67} +17.9817i q^{68} -5.07288 q^{69} -5.49351 q^{71} -5.87162i q^{72} -5.37811i q^{73} -22.7877 q^{74} +(4.33317 - 2.49472i) q^{75} +9.96636 q^{76} -12.9598i q^{78} +10.8869 q^{79} +(6.83846 - 11.8279i) q^{80} +1.00000 q^{81} +6.68165i q^{82} -6.62663i q^{83} +(-8.03316 - 4.64448i) q^{85} +0.868086 q^{86} -5.92664i q^{87} +5.74324i q^{88} +16.3108 q^{89} +(4.87162 + 2.81659i) q^{90} -21.9817i q^{92} -0.633188i q^{93} -10.6663 q^{94} +(-2.57421 + 4.45239i) q^{95} +3.63319 q^{96} -1.53844i q^{97} -0.978135 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 2 q^{5} + 4 q^{6} - 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 + 2 * q^5 + 4 * q^6 - 8 * q^9	\( 8 q - 8 q^{4} + 2 q^{5} + 4 q^{6} - 8 q^{9} - 4 q^{10} - 2 q^{15} - 24 q^{19} + 4 q^{20} - 12 q^{24} + 4 q^{25} - 12 q^{26} + 12 q^{29} + 12 q^{30} + 16 q^{31} - 8 q^{34} + 8 q^{36} + 4 q^{39} + 32 q^{40} - 8 q^{41} - 20 q^{44} - 2 q^{45} + 32 q^{46} - 20 q^{50} - 4 q^{51} - 4 q^{54} - 4 q^{55} + 4 q^{59} - 16 q^{60} + 16 q^{61} + 8 q^{64} - 30 q^{65} + 28 q^{66} - 20 q^{69} - 28 q^{71} - 40 q^{74} + 8 q^{75} + 32 q^{76} + 16 q^{79} + 52 q^{80} + 8 q^{81} - 32 q^{85} + 48 q^{86} + 16 q^{89} + 4 q^{90} - 32 q^{94} + 22 q^{95} + 8 q^{96}+O(q^{100}) \) 8 * q - 8 * q^4 + 2 * q^5 + 4 * q^6 - 8 * q^9 - 4 * q^10 - 2 * q^15 - 24 * q^19 + 4 * q^20 - 12 * q^24 + 4 * q^25 - 12 * q^26 + 12 * q^29 + 12 * q^30 + 16 * q^31 - 8 * q^34 + 8 * q^36 + 4 * q^39 + 32 * q^40 - 8 * q^41 - 20 * q^44 - 2 * q^45 + 32 * q^46 - 20 * q^50 - 4 * q^51 - 4 * q^54 - 4 * q^55 + 4 * q^59 - 16 * q^60 + 16 * q^61 + 8 * q^64 - 30 * q^65 + 28 * q^66 - 20 * q^69 - 28 * q^71 - 40 * q^74 + 8 * q^75 + 32 * q^76 + 16 * q^79 + 52 * q^80 + 8 * q^81 - 32 * q^85 + 48 * q^86 + 16 * q^89 + 4 * q^90 - 32 * q^94 + 22 * q^95 + 8 * q^96

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