LMFDB - Embedded newform 1080.2.d.i.109.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1080,2,Mod(109,1080)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1080, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1080.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1080 = 2^{3} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1080.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:	$8.62384341830$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3x^{18} + 8x^{16} - 24x^{14} + 56x^{12} - 92x^{10} + 224x^{8} - 384x^{6} + 512x^{4} - 768x^{2} + 1024 $ x^20 - 3x^18 + 8x^16 - 24x^14 + 56x^12 - 92x^10 + 224x^8 - 384x^6 + 512x^4 - 768*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			109.16
Root			$-0.986501 + 1.01332i$ of defining polynomial
Character	$\chi$	$=$	1080.109
Dual form			1080.2.d.i.109.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.986501 + 1.01332i) q^{2} +(-0.0536316 + 1.99928i) q^{4} +(0.569524 + 2.16232i) q^{5} -4.64762i q^{7} +(-2.07882 + 1.91795i) q^{8} +O(q^{10})$	\(q+(0.986501 + 1.01332i) q^{2} +(-0.0536316 + 1.99928i) q^{4} +(0.569524 + 2.16232i) q^{5} -4.64762i q^{7} +(-2.07882 + 1.91795i) q^{8} +(-1.62929 + 2.71024i) q^{10} +3.44932i q^{11} -2.72863 q^{13} +(4.70952 - 4.58488i) q^{14} +(-3.99425 - 0.214449i) q^{16} +2.43191i q^{17} +7.45458i q^{19} +(-4.35364 + 1.02267i) q^{20} +(-3.49526 + 3.40276i) q^{22} +6.60396i q^{23} +(-4.35129 + 2.46299i) q^{25} +(-2.69180 - 2.76497i) q^{26} +(9.29190 + 0.249259i) q^{28} +0.952629i q^{29} +5.77397 q^{31} +(-3.72302 - 4.25900i) q^{32} +(-2.46430 + 2.39908i) q^{34} +(10.0497 - 2.64693i) q^{35} -0.0145540 q^{37} +(-7.55387 + 7.35395i) q^{38} +(-5.33116 - 3.40276i) q^{40} -4.42746 q^{41} +6.83386 q^{43} +(-6.89616 - 0.184993i) q^{44} +(-6.69191 + 6.51481i) q^{46} -6.05042i q^{47} -14.6004 q^{49} +(-6.78834 - 1.97950i) q^{50} +(0.146341 - 5.45530i) q^{52} +4.54964 q^{53} +(-7.45855 + 1.96447i) q^{55} +(8.91389 + 9.66156i) q^{56} +(-0.965317 + 0.939770i) q^{58} -9.70460i q^{59} -1.57648i q^{61} +(5.69603 + 5.85087i) q^{62} +(0.642962 - 7.97412i) q^{64} +(-1.55402 - 5.90018i) q^{65} -7.29776 q^{67} +(-4.86207 - 0.130427i) q^{68} +(12.5962 + 7.57231i) q^{70} +12.8649 q^{71} -3.38640i q^{73} +(-0.0143575 - 0.0147479i) q^{74} +(-14.9038 - 0.399801i) q^{76} +16.0311 q^{77} +5.03790 q^{79} +(-1.81111 - 8.75899i) q^{80} +(-4.36769 - 4.48643i) q^{82} +12.7427 q^{83} +(-5.25858 + 1.38503i) q^{85} +(6.74161 + 6.92488i) q^{86} +(-6.61561 - 7.17051i) q^{88} -0.535414 q^{89} +12.6816i q^{91} +(-13.2032 - 0.354181i) q^{92} +(6.13101 - 5.96874i) q^{94} +(-16.1192 + 4.24556i) q^{95} -9.22760i q^{97} +(-14.4033 - 14.7949i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{4}+O(q^{10}) $ 20 * q + 6 * q^4	$ 20 q + 6 q^{4} - 2 q^{10} - 4 q^{13} - 14 q^{16} - 34 q^{22} + 20 q^{25} + 20 q^{28} + 12 q^{31} + 6 q^{34} - 32 q^{37} - 6 q^{40} + 12 q^{43} + 2 q^{46} - 52 q^{49} - 50 q^{52} - 28 q^{55} + 6 q^{58} + 54 q^{64} + 12 q^{70} - 24 q^{76} + 36 q^{79} + 32 q^{82} - 44 q^{85} - 30 q^{88} - 22 q^{94}+O(q^{100}) $ 20 * q + 6 * q^4 - 2 * q^10 - 4 * q^13 - 14 * q^16 - 34 * q^22 + 20 * q^25 + 20 * q^28 + 12 * q^31 + 6 * q^34 - 32 * q^37 - 6 * q^40 + 12 * q^43 + 2 * q^46 - 52 * q^49 - 50 * q^52 - 28 * q^55 + 6 * q^58 + 54 * q^64 + 12 * q^70 - 24 * q^76 + 36 * q^79 + 32 * q^82 - 44 * q^85 - 30 * q^88 - 22 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$541$	$1001$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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 $

$2$	0.986501	+	1.01332i	0.697562	+	0.716525i
$2$	0.986501	+	1.01332i	0.697562	+	0.716525i
$3$		0			0
$3$		0			0
$4$	−0.0536316	+	1.99928i	−0.0268158	+	0.999640i
$5$	0.569524	+	2.16232i	0.254699	+	0.967020i
$5$	0.569524	+	2.16232i	0.254699	+	0.967020i
$6$		0			0
$7$		−	4.64762i		−	1.75664i	−0.478077	−	0.878318i	$-0.658666\pi$
$7$		−	4.64762i		−	1.75664i	0.478077	−	0.878318i	$-0.341334\pi$
$8$	−2.07882	+	1.91795i	−0.734973	+	0.678097i
$9$		0			0
$10$	−1.62929	+	2.71024i	−0.515226	+	0.857054i
$11$			3.44932i			1.04001i	0.854163	+	0.520005i	$0.174070\pi$
$11$			3.44932i			1.04001i	−0.854163	+	0.520005i	$0.825930\pi$
$12$		0			0
$13$	−2.72863			−0.756786			−0.378393	−	0.925645i	$-0.623523\pi$
$13$	−2.72863			−0.756786			−0.378393	+	0.925645i	$0.623523\pi$
$14$	4.70952	−	4.58488i	1.25867	−	1.22536i
$15$		0			0
$16$	−3.99425	−	0.214449i	−0.998562	−	0.0536123i
$17$			2.43191i			0.589825i	0.955524	+	0.294912i	$0.0952905\pi$
$17$			2.43191i			0.589825i	−0.955524	+	0.294912i	$0.904710\pi$
$18$		0			0
$19$			7.45458i			1.71020i	0.518465	+	0.855099i	$0.326504\pi$
$19$			7.45458i			1.71020i	−0.518465	+	0.855099i	$0.673496\pi$
$20$	−4.35364	+	1.02267i	−0.973503	+	0.228676i
$21$		0			0
$22$	−3.49526	+	3.40276i	−0.745193	+	0.725471i
$23$			6.60396i			1.37702i	0.725227	+	0.688510i	$0.241735\pi$
$23$			6.60396i			1.37702i	−0.725227	+	0.688510i	$0.758265\pi$
$24$		0			0
$25$	−4.35129	+	2.46299i	−0.870257	+	0.492598i
$26$	−2.69180	−	2.76497i	−0.527905	−	0.542256i
$27$		0			0
$28$	9.29190	+	0.249259i	1.75600	+	0.0471056i
$29$			0.952629i			0.176899i	0.996081	+	0.0884494i	$0.0281912\pi$
$29$			0.952629i			0.176899i	−0.996081	+	0.0884494i	$0.971809\pi$
$30$		0			0
$31$	5.77397			1.03704			0.518518	−	0.855067i	$-0.326484\pi$
$31$	5.77397			1.03704			0.518518	+	0.855067i	$0.326484\pi$
$32$	−3.72302	−	4.25900i	−0.658144	−	0.752892i
$33$		0			0
$34$	−2.46430	+	2.39908i	−0.422624	+	0.411439i
$35$	10.0497	−	2.64693i	1.69870	−	0.447413i
$36$		0			0
$37$	−0.0145540			−0.00239266			−0.00119633	−	0.999999i	$-0.500381\pi$
$37$	−0.0145540			−0.00239266			−0.00119633	+	0.999999i	$0.500381\pi$
$38$	−7.55387	+	7.35395i	−1.22540	+	1.19297i
$39$		0			0
$40$	−5.33116	−	3.40276i	−0.842930	−	0.538023i
$41$	−4.42746			−0.691453			−0.345727	−	0.938335i	$-0.612368\pi$
$41$	−4.42746			−0.691453			−0.345727	+	0.938335i	$0.612368\pi$
$42$		0			0
$43$	6.83386			1.04215			0.521077	−	0.853510i	$-0.325530\pi$
$43$	6.83386			1.04215			0.521077	+	0.853510i	$0.325530\pi$
$44$	−6.89616	−	0.184993i	−1.03964	−	0.0278887i
$45$		0			0
$46$	−6.69191	+	6.51481i	−0.986669	+	0.960556i
$47$		−	6.05042i		−	0.882544i	−0.897373	−	0.441272i	$-0.854527\pi$
$47$		−	6.05042i		−	0.882544i	0.897373	−	0.441272i	$-0.145473\pi$
$48$		0			0
$49$	−14.6004			−2.08577
$50$	−6.78834	−	1.97950i	−0.960016	−	0.279943i
$51$		0			0
$52$	0.146341	−	5.45530i	0.0202938	−	0.756514i
$53$	4.54964			0.624941			0.312470	−	0.949927i	$-0.398843\pi$
$53$	4.54964			0.624941			0.312470	+	0.949927i	$0.398843\pi$
$54$		0			0
$55$	−7.45855	+	1.96447i	−1.00571	+	0.264889i
$56$	8.91389	+	9.66156i	1.19117	+	1.29108i
$57$		0			0
$58$	−0.965317	+	0.939770i	−0.126752	+	0.123398i
$59$		−	9.70460i		−	1.26343i	−0.775200	−	0.631716i	$-0.782351\pi$
$59$		−	9.70460i		−	1.26343i	0.775200	−	0.631716i	$-0.217649\pi$
$60$		0			0
$61$		−	1.57648i		−	0.201847i	−0.994894	−	0.100924i	$-0.967820\pi$
$61$		−	1.57648i		−	0.201847i	0.994894	−	0.100924i	$-0.0321798\pi$
$62$	5.69603	+	5.85087i	0.723396	+	0.743062i
$63$		0			0
$64$	0.642962	−	7.97412i	0.0803703	−	0.996765i
$65$	−1.55402	−	5.90018i	−0.192752	−	0.731827i
$66$		0			0
$67$	−7.29776			−0.891564			−0.445782	−	0.895142i	$-0.647074\pi$
$67$	−7.29776			−0.891564			−0.445782	+	0.895142i	$0.647074\pi$
$68$	−4.86207	−	0.130427i	−0.589613	−	0.0158166i
$69$		0			0
$70$	12.5962	+	7.57231i	1.50553	+	0.905065i
$71$	12.8649			1.52678			0.763392	−	0.645936i	$-0.223533\pi$
$71$	12.8649			1.52678			0.763392	+	0.645936i	$0.223533\pi$
$72$		0			0
$73$		−	3.38640i		−	0.396348i	−0.980167	−	0.198174i	$-0.936499\pi$
$73$		−	3.38640i		−	0.396348i	0.980167	−	0.198174i	$-0.0635011\pi$
$74$	−0.0143575	−	0.0147479i	−0.00166903	−	0.00171440i
$75$		0			0
$76$	−14.9038	−	0.399801i	−1.70958	−	0.0458603i
$77$	16.0311			1.82692
$78$		0			0
$79$	5.03790			0.566808			0.283404	−	0.959001i	$-0.408536\pi$
$79$	5.03790			0.566808			0.283404	+	0.959001i	$0.408536\pi$
$80$	−1.81111	−	8.75899i	−0.202488	−	0.979285i
$81$		0			0
$82$	−4.36769	−	4.48643i	−0.482331	−	0.495443i
$83$	12.7427			1.39870			0.699348	−	0.714781i	$-0.253474\pi$
$83$	12.7427			1.39870			0.699348	+	0.714781i	$0.253474\pi$
$84$		0			0
$85$	−5.25858	+	1.38503i	−0.570373	+	0.150228i
$86$	6.74161	+	6.92488i	0.726967	+	0.746729i
$87$		0			0
$88$	−6.61561	−	7.17051i	−0.705227	−	0.764379i
$89$	−0.535414			−0.0567537			−0.0283769	−	0.999597i	$-0.509034\pi$
$89$	−0.535414			−0.0567537			−0.0283769	+	0.999597i	$0.509034\pi$
$90$		0			0
$91$			12.6816i			1.32940i
$92$	−13.2032	−	0.354181i	−1.37652	−	0.0369259i
$93$		0			0
$94$	6.13101	−	5.96874i	0.632365	−	0.615629i
$95$	−16.1192	+	4.24556i	−1.65380	+	0.435585i
$96$		0			0
$97$		−	9.22760i		−	0.936921i	−0.883484	−	0.468461i	$-0.844809\pi$
$97$		−	9.22760i		−	0.936921i	0.883484	−	0.468461i	$-0.155191\pi$
$98$	−14.4033	−	14.7949i	−1.45495	−	1.49451i
$99$		0			0
$100$	−4.69084	−	8.83154i	−0.469084	−	0.883154i
$101$			10.2563i			1.02054i	0.860014	+	0.510270i	$0.170454\pi$
$101$			10.2563i			1.02054i	−0.860014	+	0.510270i	$0.829546\pi$
$102$		0			0
$103$			13.3327i			1.31371i	0.754018	+	0.656854i	$0.228113\pi$
$103$			13.3327i			1.31371i	−0.754018	+	0.656854i	$0.771887\pi$
$104$	5.67232	−	5.23337i	0.556217	−	0.513174i
$105$		0			0
$106$	4.48822	+	4.61024i	0.435935	+	0.447786i
$107$	−2.68478			−0.259547			−0.129774	−	0.991544i	$-0.541425\pi$
$107$	−2.68478			−0.259547			−0.129774	+	0.991544i	$0.541425\pi$
$108$		0			0
$109$		−	15.7670i		−	1.51020i	−0.655610	−	0.755100i	$-0.727588\pi$
$109$		−	15.7670i		−	1.51020i	0.655610	−	0.755100i	$-0.272412\pi$
$110$	−9.34850	−	5.61994i	−0.891345	−	0.535840i
$111$		0			0
$112$	−0.996679	+	18.5638i	−0.0941773	+	1.75411i
$113$		−	14.7770i		−	1.39010i	−0.718959	−	0.695052i	$-0.755381\pi$
$113$		−	14.7770i		−	1.39010i	0.718959	−	0.695052i	$-0.244619\pi$
$114$		0			0
$115$	−14.2799	+	3.76111i	−1.33161	+	0.350725i
$116$	−1.90457	−	0.0510910i	−0.176835	−	0.00474368i
$117$		0			0
$118$	9.83386	−	9.57360i	0.905280	−	0.881321i
$119$	11.3026			1.03611
$120$		0			0
$121$	−0.897818			−0.0816198
$122$	1.59747	−	1.55520i	0.144629	−	0.140801i
$123$		0			0
$124$	−0.309667	+	11.5438i	−0.0278089	+	1.03666i
$125$	−7.80394	−	8.00616i	−0.698006	−	0.716092i
$126$		0			0
$127$			2.84385i			0.252351i	0.992008	+	0.126175i	$0.0402702\pi$
$127$			2.84385i			0.252351i	−0.992008	+	0.126175i	$0.959730\pi$
$128$	8.71461	−	7.21495i	0.770270	−	0.637718i
$129$		0			0
$130$	4.44572	−	7.39525i	0.389916	−	0.648606i
$131$			17.9281i			1.56638i	0.621780	+	0.783192i	$0.286410\pi$
$131$			17.9281i			1.56638i	−0.621780	+	0.783192i	$0.713590\pi$
$132$		0			0
$133$	34.6461			3.00419
$134$	−7.19925	−	7.39496i	−0.621920	−	0.638828i
$135$		0			0
$136$	−4.66427	−	5.05550i	−0.399958	−	0.433505i
$137$			17.3365i			1.48116i	0.671970	+	0.740578i	$0.265448\pi$
$137$			17.3365i			1.48116i	−0.671970	+	0.740578i	$0.734552\pi$
$138$		0			0
$139$			8.31238i			0.705046i	0.935803	+	0.352523i	$0.114676\pi$
$139$			8.31238i			0.705046i	−0.935803	+	0.352523i	$0.885324\pi$
$140$	4.75298	+	20.2341i	0.401700	+	1.71009i
$141$		0			0
$142$	12.6912	+	13.0363i	1.06503	+	1.09398i
$143$		−	9.41192i		−	0.787064i
$144$		0			0
$145$	−2.05989	+	0.542545i	−0.171065	+	0.0450559i
$146$	3.43150	−	3.34068i	0.283993	−	0.276477i
$147$		0			0
$148$	0.000780555	−	0.0290976i	6.41612e−5	−	0.00239180i
$149$			5.82725i			0.477387i	0.971095	+	0.238693i	$0.0767190\pi$
$149$			5.82725i			0.477387i	−0.971095	+	0.238693i	$0.923281\pi$
$150$		0			0
$151$	13.9550			1.13564			0.567821	−	0.823152i	$-0.307787\pi$
$151$	13.9550			1.13564			0.567821	+	0.823152i	$0.307787\pi$
$152$	−14.2975	−	15.4967i	−1.15968	−	1.25695i
$153$		0			0
$154$	15.8147	+	16.2447i	1.27439	+	1.30903i
$155$	3.28841	+	12.4852i	0.264132	+	1.00283i
$156$		0			0
$157$	0.106247			0.00847944			0.00423972	−	0.999991i	$-0.498650\pi$
$157$	0.106247			0.00847944			0.00423972	+	0.999991i	$0.498650\pi$
$158$	4.96989	+	5.10500i	0.395383	+	0.406132i
$159$		0			0
$160$	7.08899	−	10.4760i	0.560434	−	0.828199i
$161$	30.6927			2.41892
$162$		0			0
$163$	−2.97089			−0.232698			−0.116349	−	0.993208i	$-0.537119\pi$
$163$	−2.97089			−0.232698			−0.116349	+	0.993208i	$0.537119\pi$
$164$	0.237452	−	8.85174i	0.0185419	−	0.691204i
$165$		0			0
$166$	12.5707	+	12.9125i	0.975677	+	1.00220i
$167$		−	20.9617i		−	1.62207i	−0.585000	−	0.811034i	$-0.698905\pi$
$167$		−	20.9617i		−	1.62207i	0.585000	−	0.811034i	$-0.301095\pi$
$168$		0			0
$169$	−5.55458			−0.427275
$170$	−6.59107	−	3.96228i	−0.505512	−	0.303893i
$171$		0			0
$172$	−0.366511	+	13.6628i	−0.0279462	+	1.04178i
$173$	8.31527			0.632198			0.316099	−	0.948726i	$-0.397627\pi$
$173$	8.31527			0.632198			0.316099	+	0.948726i	$0.397627\pi$
$174$		0			0
$175$	11.4470	+	20.2231i	0.865315	+	1.52872i
$176$	0.739704	−	13.7774i	0.0557573	−	1.03851i
$177$		0			0
$178$	−0.528186	−	0.542545i	−0.0395892	−	0.0406655i
$179$			3.31080i			0.247461i	0.992316	+	0.123730i	$0.0394858\pi$
$179$			3.31080i			0.247461i	−0.992316	+	0.123730i	$0.960514\pi$
$180$		0			0
$181$		−	10.5626i		−	0.785113i	−0.919728	−	0.392557i	$-0.871591\pi$
$181$		−	10.5626i		−	0.785113i	0.919728	−	0.392557i	$-0.128409\pi$
$182$	−12.8505	+	12.5105i	−0.952546	+	0.927336i
$183$		0			0
$184$	−12.6660	−	13.7284i	−0.933752	−	1.01207i
$185$	−0.00828885	−	0.0314705i	−0.000609409	−	0.00231376i
$186$		0			0
$187$	−8.38844			−0.613423
$188$	12.0965	+	0.324494i	0.882227	+	0.0236661i
$189$		0			0
$190$	−20.2037	−	12.1457i	−1.46573	−	0.881138i
$191$	−20.1575			−1.45855			−0.729273	−	0.684222i	$-0.760142\pi$
$191$	−20.1575			−1.45855			−0.729273	+	0.684222i	$0.760142\pi$
$192$		0			0
$193$			5.90885i			0.425328i	0.977125	+	0.212664i	$0.0682140\pi$
$193$			5.90885i			0.425328i	−0.977125	+	0.212664i	$0.931786\pi$
$194$	9.35051	−	9.10304i	0.671327	−	0.653560i
$195$		0			0
$196$	0.783042	−	29.1903i	0.0559316	−	2.08502i
$197$	19.6179			1.39772			0.698858	−	0.715261i	$-0.253692\pi$
$197$	19.6179			1.39772			0.698858	+	0.715261i	$0.253692\pi$
$198$		0			0
$199$	25.2228			1.78799			0.893997	−	0.448072i	$-0.147889\pi$
$199$	25.2228			1.78799			0.893997	+	0.448072i	$0.147889\pi$
$200$	4.32164	−	13.4656i	0.305586	−	0.952164i
$201$		0			0
$202$	−10.3929	+	10.1178i	−0.731242	+	0.711889i
$203$	4.42746			0.310747
$204$		0			0
$205$	−2.52154	−	9.57360i	−0.176112	−	0.668649i
$206$	−13.5103	+	13.1527i	−0.941304	+	0.916392i
$207$		0			0
$208$	10.8988	+	0.585153i	0.755697	+	0.0405730i
$209$	−25.7132			−1.77862
$210$		0			0
$211$		−	12.9089i		−	0.888688i	−0.895856	−	0.444344i	$-0.853437\pi$
$211$		−	12.9089i		−	0.888688i	0.895856	−	0.444344i	$-0.146563\pi$
$212$	−0.244004	+	9.09600i	−0.0167583	+	0.624716i
$213$		0			0
$214$	−2.64854	−	2.72054i	−0.181050	−	0.185972i
$215$	3.89205	+	14.7770i	0.265435	+	1.00778i
$216$		0			0
$217$		−	26.8352i		−	1.82169i
$218$	15.9770	−	15.5541i	1.08210	−	1.05346i
$219$		0			0
$220$	−3.52751	−	15.0171i	−0.237825	−	1.01245i
$221$		−	6.63578i		−	0.446371i
$222$		0			0
$223$		−	18.0621i		−	1.20953i	−0.796405	−	0.604764i	$-0.793267\pi$
$223$		−	18.0621i		−	1.20953i	0.796405	−	0.604764i	$-0.206733\pi$
$224$	−19.7942	+	17.3032i	−1.32256	+	1.15612i
$225$		0			0
$226$	14.9738	−	14.5775i	0.996045	−	0.969684i
$227$	−10.4646			−0.694562			−0.347281	−	0.937761i	$-0.612895\pi$
$227$	−10.4646			−0.694562			−0.347281	+	0.937761i	$0.612895\pi$
$228$		0			0
$229$		−	11.2813i		−	0.745489i	−0.927934	−	0.372745i	$-0.878417\pi$
$229$		−	11.2813i		−	0.745489i	0.927934	−	0.372745i	$-0.121583\pi$
$230$	−17.8983	−	10.7597i	−1.18018	−	0.709477i
$231$		0			0
$232$	−1.82709	−	1.98034i	−0.119954	−	0.130016i
$233$			9.78141i			0.640801i	0.947282	+	0.320401i	$0.103818\pi$
$233$			9.78141i			0.640801i	−0.947282	+	0.320401i	$0.896182\pi$
$234$		0			0
$235$	13.0830	−	3.44586i	0.853438	−	0.224783i
$236$	19.4022	+	0.520473i	1.26298	+	0.0338799i
$237$		0			0
$238$	11.1500	+	11.4531i	0.722749	+	0.742397i
$239$	−19.8650			−1.28496			−0.642480	−	0.766303i	$-0.722094\pi$
$239$	−19.8650			−1.28496			−0.642480	+	0.766303i	$0.722094\pi$
$240$		0			0
$241$	−14.8281			−0.955162			−0.477581	−	0.878588i	$-0.658486\pi$
$241$	−14.8281			−0.955162			−0.477581	+	0.878588i	$0.658486\pi$
$242$	−0.885698	−	0.909776i	−0.0569348	−	0.0584826i
$243$		0			0
$244$	3.15182	+	0.0845490i	0.201775	+	0.00541269i
$245$	−8.31527	−	31.5708i	−0.531243	−	2.01698i
$246$		0			0
$247$		−	20.3408i		−	1.29425i
$248$	−12.0030	+	11.0742i	−0.762193	+	0.703210i
$249$		0			0
$250$	0.414196	−	15.8060i	0.0261960	−	0.999657i
$251$			4.50463i			0.284330i	0.989843	+	0.142165i	$0.0454063\pi$
$251$			4.50463i			0.284330i	−0.989843	+	0.142165i	$0.954594\pi$
$252$		0			0
$253$	−22.7792			−1.43211
$254$	−2.88173	+	2.80546i	−0.180816	+	0.176030i
$255$		0			0
$256$	15.9080	+	1.71313i	0.994251	+	0.107070i
$257$			1.30180i			0.0812041i	0.999175	+	0.0406021i	$0.0129276\pi$
$257$			1.30180i			0.0812041i	−0.999175	+	0.0406021i	$0.987072\pi$
$258$		0			0
$259$			0.0676415i			0.00420304i
$260$	11.8795	−	2.79049i	0.736733	−	0.173059i
$261$		0			0
$262$	−18.1669	+	17.6861i	−1.12235	+	1.09265i
$263$			15.3436i			0.946125i	0.881029	+	0.473063i	$0.156852\pi$
$263$			15.3436i			0.946125i	−0.881029	+	0.473063i	$0.843148\pi$
$264$		0			0
$265$	2.59113	+	9.83779i	0.159172	+	0.604331i
$266$	34.1784	+	35.1075i	2.09561	+	2.15258i
$267$		0			0
$268$	0.391391	−	14.5903i	0.0239080	−	0.891243i
$269$			5.44946i			0.332260i	0.986104	+	0.166130i	$0.0531271\pi$
$269$			5.44946i			0.332260i	−0.986104	+	0.166130i	$0.946873\pi$
$270$		0			0
$271$	1.47181			0.0894063			0.0447032	−	0.999000i	$-0.485766\pi$
$271$	1.47181			0.0894063			0.0447032	+	0.999000i	$0.485766\pi$
$272$	0.521521	−	9.71365i	0.0316219	−	0.588977i
$273$		0			0
$274$	−17.5674	+	17.1025i	−1.06129	+	1.03320i
$275$	−8.49564	−	15.0090i	−0.512306	−	0.905076i
$276$		0			0
$277$	0.368259			0.0221266			0.0110633	−	0.999939i	$-0.496478\pi$
$277$	0.368259			0.0221266			0.0110633	+	0.999939i	$0.496478\pi$
$278$	−8.42309	+	8.20017i	−0.505183	+	0.491813i
$279$		0			0
$280$	−15.8147	+	24.7772i	−0.945111	+	1.48072i
$281$	28.8213			1.71933			0.859667	−	0.510856i	$-0.170671\pi$
$281$	28.8213			1.71933			0.859667	+	0.510856i	$0.170671\pi$
$282$		0			0
$283$	0.0291080			0.00173029			0.000865146	−	1.00000i	$-0.499725\pi$
$283$	0.0291080			0.00173029			0.000865146		1.00000i	$0.499725\pi$
$284$	−0.689965	+	25.7206i	−0.0409419	+	1.52623i
$285$		0			0
$286$	9.53728	−	9.28487i	0.563951	−	0.549026i
$287$			20.5772i			1.21463i
$288$		0			0
$289$	11.0858			0.652107
$290$	−2.58186	−	1.55211i	−0.151612	−	0.0911429i
$291$		0			0
$292$	6.77036	+	0.181618i	0.396205	+	0.0106284i
$293$	−16.2755			−0.950825			−0.475412	−	0.879763i	$-0.657701\pi$
$293$	−16.2755			−0.950825			−0.475412	+	0.879763i	$0.657701\pi$
$294$		0			0
$295$	20.9845	−	5.52700i	1.22176	−	0.321795i
$296$	0.0302551	−	0.0279138i	0.00175854	−	0.00162246i
$297$		0			0
$298$	−5.90486	+	5.74858i	−0.342059	+	0.333006i
$299$		−	18.0198i		−	1.04211i
$300$		0			0
$301$		−	31.7612i		−	1.83069i
$302$	13.7666	+	14.1409i	0.792180	+	0.813715i
$303$		0			0
$304$	1.59863	−	29.7754i	0.0916876	−	1.70774i
$305$	3.40885	−	0.897841i	0.195190	−	0.0514102i
$306$		0			0
$307$	29.1765			1.66519			0.832596	−	0.553880i	$-0.186853\pi$
$307$	29.1765			1.66519			0.832596	+	0.553880i	$0.186853\pi$
$308$	−0.859776	+	32.0508i	−0.0489903	+	1.82626i
$309$		0			0
$310$	−9.40746	+	15.6489i	−0.534308	+	0.888796i
$311$	17.5187			0.993393			0.496697	−	0.867924i	$-0.334546\pi$
$311$	17.5187			0.993393			0.496697	+	0.867924i	$0.334546\pi$
$312$		0			0
$313$			26.9029i			1.52064i	0.649549	+	0.760320i	$0.274958\pi$
$313$			26.9029i			1.52064i	−0.649549	+	0.760320i	$0.725042\pi$
$314$	0.104813	+	0.107662i	0.00591493	+	0.00607573i
$315$		0			0
$316$	−0.270190	+	10.0722i	−0.0151994	+	0.566604i
$317$	−8.31527			−0.467032			−0.233516	−	0.972353i	$-0.575023\pi$
$317$	−8.31527			−0.467032			−0.233516	+	0.972353i	$0.575023\pi$
$318$		0			0
$319$	−3.28592			−0.183976
$320$	17.6088	−	3.15116i	0.984362	−	0.176155i
$321$		0			0
$322$	30.2784	+	31.1015i	1.68735	+	1.73322i
$323$	−18.1289			−1.00872
$324$		0			0
$325$	11.8730	−	6.72059i	0.658598	−	0.372791i
$326$	−2.93079	−	3.01046i	−0.162321	−	0.166734i
$327$		0			0
$328$	9.20388	−	8.49163i	0.508199	−	0.468872i
$329$	−28.1201			−1.55031
$330$		0			0
$331$			34.3513i			1.88812i	0.329777	+	0.944059i	$0.393026\pi$
$331$			34.3513i			1.88812i	−0.329777	+	0.944059i	$0.606974\pi$
$332$	−0.683413	+	25.4763i	−0.0375072	+	1.39819i
$333$		0			0
$334$	21.2409	−	20.6788i	1.16225	−	1.13149i
$335$	−4.15625	−	15.7801i	−0.227080	−	0.862160i
$336$		0			0
$337$		−	13.7667i		−	0.749922i	−0.927041	−	0.374961i	$-0.877656\pi$
$337$		−	13.7667i		−	0.749922i	0.927041	−	0.374961i	$-0.122344\pi$
$338$	−5.47960	−	5.62856i	−0.298051	−	0.306153i
$339$		0			0
$340$	−2.48704	−	10.5877i	−0.134879	−	0.574196i
$341$			19.9163i			1.07853i
$342$		0			0
$343$			35.3237i			1.90730i
$344$	−14.2063	+	13.1070i	−0.765955	+	0.706681i
$345$		0			0
$346$	8.20302	+	8.42602i	0.440997	+	0.452986i
$347$	3.22019			0.172869			0.0864345	−	0.996258i	$-0.472453\pi$
$347$	3.22019			0.172869			0.0864345	+	0.996258i	$0.472453\pi$
$348$		0			0
$349$		−	4.95673i		−	0.265327i	−0.991161	−	0.132664i	$-0.957647\pi$
$349$		−	4.95673i		−	0.265327i	0.991161	−	0.132664i	$-0.0423530\pi$
$350$	−9.19996	+	31.5496i	−0.491759	+	1.68640i
$351$		0			0
$352$	14.6907	−	12.8419i	0.783015	−	0.684476i
$353$			8.53882i			0.454476i	0.973839	+	0.227238i	$0.0729695\pi$
$353$			8.53882i			0.454476i	−0.973839	+	0.227238i	$0.927031\pi$
$354$		0			0
$355$	7.32687	+	27.8181i	0.388870	+	1.47643i
$356$	0.0287151	−	1.07044i	0.00152190	−	0.0567333i
$357$		0			0
$358$	−3.35490	+	3.26611i	−0.177312	+	0.172619i
$359$	34.0933			1.79937			0.899687	−	0.436537i	$-0.143795\pi$
$359$	34.0933			1.79937			0.899687	+	0.436537i	$0.143795\pi$
$360$		0			0
$361$	−36.5707			−1.92478
$362$	10.7033	−	10.4200i	0.562553	−	0.547665i
$363$		0			0
$364$	−25.3542	−	0.680137i	−1.32892	−	0.0356488i
$365$	7.32248	−	1.92863i	0.383276	−	0.100949i
$366$		0			0
$367$		−	27.7238i		−	1.44717i	−0.690236	−	0.723584i	$-0.742493\pi$
$367$		−	27.7238i		−	1.44717i	0.690236	−	0.723584i	$-0.257507\pi$
$368$	1.41621	−	26.3778i	0.0738252	−	1.37504i
$369$		0			0
$370$	0.0237127	−	0.0394449i	0.00123276	−	0.00205064i
$371$		−	21.1450i		−	1.09779i
$372$		0			0
$373$	−7.78852			−0.403274			−0.201637	−	0.979460i	$-0.564626\pi$
$373$	−7.78852			−0.403274			−0.201637	+	0.979460i	$0.564626\pi$
$374$	−8.27520	−	8.50017i	−0.427901	−	0.439533i
$375$		0			0
$376$	11.6044	+	12.5777i	0.598450	+	0.648646i
$377$		−	2.59937i		−	0.133874i
$378$		0			0
$379$		−	11.6926i		−	0.600610i	−0.953843	−	0.300305i	$-0.902912\pi$
$379$		−	11.6926i		−	0.600610i	0.953843	−	0.300305i	$-0.0970884\pi$
$380$	−7.62357	−	32.4545i	−0.391081	−	1.66488i
$381$		0			0
$382$	−19.8854	−	20.4260i	−1.01743	−	1.04509i
$383$		−	7.84048i		−	0.400630i	−0.979732	−	0.200315i	$-0.935804\pi$
$383$		−	7.84048i		−	0.400630i	0.979732	−	0.200315i	$-0.0641965\pi$
$384$		0			0
$385$	9.13012	+	34.6645i	0.465314	+	1.76667i
$386$	−5.98755	+	5.82908i	−0.304758	+	0.296693i
$387$		0			0
$388$	18.4486	+	0.494891i	0.936584	+	0.0251243i
$389$			11.6081i			0.588556i	0.955720	+	0.294278i	$0.0950791\pi$
$389$			11.6081i			0.588556i	−0.955720	+	0.294278i	$0.904921\pi$
$390$		0			0
$391$	−16.0602			−0.812201
$392$	30.3515	−	28.0028i	1.53298	−	1.41435i
$393$		0			0
$394$	19.3530	+	19.8792i	0.974992	+	1.00150i
$395$	2.86920	+	10.8936i	0.144365	+	0.548115i
$396$		0			0
$397$	−14.8866			−0.747139			−0.373570	−	0.927602i	$-0.621866\pi$
$397$	−14.8866			−0.747139			−0.373570	+	0.927602i	$0.621866\pi$
$398$	24.8823	+	25.5587i	1.24724	+	1.28114i
$399$		0			0
$400$	17.9083	−	8.90466i	0.895415	−	0.445233i
$401$	−32.1779			−1.60689			−0.803444	−	0.595380i	$-0.797001\pi$
$401$	−32.1779			−1.60689			−0.803444	+	0.595380i	$0.797001\pi$
$402$		0			0
$403$	−15.7550			−0.784814
$404$	−20.5052	−	0.550062i	−1.02017	−	0.0273666i
$405$		0			0
$406$	4.36769	+	4.48643i	0.216765	+	0.222658i
$407$		−	0.0502015i		−	0.00248839i
$408$		0			0
$409$	13.3784			0.661520			0.330760	−	0.943715i	$-0.392695\pi$
$409$	13.3784			0.661520			0.330760	+	0.943715i	$0.392695\pi$
$410$	7.21361	−	11.9995i	0.356255	−	0.592613i
$411$		0			0
$412$	−26.6558	−	0.715053i	−1.31324	−	0.0352281i
$413$	−45.1033			−2.21939
$414$		0			0
$415$	7.25729	+	27.5539i	0.356246	+	1.35257i
$416$	10.1588	+	11.6212i	0.498074	+	0.569778i
$417$		0			0
$418$	−25.3661	−	26.0557i	−1.24070	−	1.27443i
$419$		−	12.2062i		−	0.596311i	−0.954517	−	0.298156i	$-0.903629\pi$
$419$		−	12.2062i		−	0.596311i	0.954517	−	0.298156i	$-0.0963714\pi$
$420$		0			0
$421$			30.1847i			1.47111i	0.677463	+	0.735557i	$0.263079\pi$
$421$			30.1847i			1.47111i	−0.677463	+	0.735557i	$0.736921\pi$
$422$	13.0809	−	12.7347i	0.636767	−	0.619914i
$423$		0			0
$424$	−9.45787	+	8.72596i	−0.459315	+	0.423770i
$425$	−5.98977	−	10.5819i	−0.290546	−	0.513299i
$426$		0			0
$427$	−7.32687			−0.354572
$428$	0.143989	−	5.36763i	0.00695997	−	0.259454i
$429$		0			0
$430$	−11.1343	+	18.5214i	−0.536945	+	0.893183i
$431$	10.4172			0.501780			0.250890	−	0.968016i	$-0.419277\pi$
$431$	10.4172			0.501780			0.250890	+	0.968016i	$0.419277\pi$
$432$		0			0
$433$		−	8.21015i		−	0.394555i	−0.980348	−	0.197277i	$-0.936790\pi$
$433$		−	8.21015i		−	0.394555i	0.980348	−	0.197277i	$-0.0632100\pi$
$434$	27.1926	−	26.4730i	1.30529	−	1.27074i
$435$		0			0
$436$	31.5226	+	0.845607i	1.50966	+	0.0404972i
$437$	−49.2297			−2.35498
$438$		0			0
$439$	−7.51548			−0.358694			−0.179347	−	0.983786i	$-0.557398\pi$
$439$	−7.51548			−0.358694			−0.179347	+	0.983786i	$0.557398\pi$
$440$	11.7372	−	18.3889i	0.559549	−	0.876655i
$441$		0			0
$442$	6.72417	−	6.54621i	0.319836	−	0.311371i
$443$	−2.81775			−0.133875			−0.0669376	−	0.997757i	$-0.521323\pi$
$443$	−2.81775			−0.133875			−0.0669376	+	0.997757i	$0.521323\pi$
$444$		0			0
$445$	−0.304931	−	1.15774i	−0.0144551	−	0.0548820i
$446$	18.3027	−	17.8183i	0.866657	−	0.843721i
$447$		0			0
$448$	−37.0607	−	2.98824i	−1.75095	−	0.141181i
$449$	13.2990			0.627617			0.313808	−	0.949486i	$-0.398395\pi$
$449$	13.2990			0.627617			0.313808	+	0.949486i	$0.398395\pi$
$450$		0			0
$451$		−	15.2717i		−	0.719118i
$452$	29.5434	+	0.792515i	1.38960	+	0.0372768i
$453$		0			0
$454$	−10.3234	−	10.6040i	−0.484500	−	0.497671i
$455$	−27.4218	+	7.22250i	−1.28555	+	0.338596i
$456$		0			0
$457$		−	6.92630i		−	0.323998i	−0.986791	−	0.161999i	$-0.948206\pi$
$457$		−	6.92630i		−	0.323998i	0.986791	−	0.161999i	$-0.0517942\pi$
$458$	11.4316	−	11.1290i	0.534162	−	0.520025i
$459$		0			0
$460$	−6.75366	−	28.7512i	−0.314891	−	1.34053i
$461$			4.08444i			0.190232i	0.995466	+	0.0951158i	$0.0303221\pi$
$461$			4.08444i			0.190232i	−0.995466	+	0.0951158i	$0.969678\pi$
$462$		0			0
$463$			0.448220i			0.0208305i	0.999946	+	0.0104153i	$0.00331534\pi$
$463$			0.448220i			0.0208305i	−0.999946	+	0.0104153i	$0.996685\pi$
$464$	0.204291	−	3.80504i	0.00948395	−	0.176644i
$465$		0			0
$466$	−9.91169	+	9.64937i	−0.459150	+	0.446998i
$467$	−11.4895			−0.531672			−0.265836	−	0.964018i	$-0.585648\pi$
$467$	−11.4895			−0.531672			−0.265836	+	0.964018i	$0.585648\pi$
$468$		0			0
$469$			33.9172i			1.56615i
$470$	16.3981	+	9.85788i	0.756388	+	0.454710i
$471$		0			0
$472$	18.6129	+	20.1741i	0.856729	+	0.928588i
$473$			23.5722i			1.08385i
$474$		0			0
$475$	−18.3605	−	32.4370i	−0.842440	−	1.48831i
$476$	−0.606176	+	22.5971i	−0.0277840	+	1.03573i
$477$		0			0
$478$	−19.5968	−	20.1296i	−0.896338	−	0.920705i
$479$	17.8112			0.813815			0.406907	−	0.913469i	$-0.366607\pi$
$479$	17.8112			0.813815			0.406907	+	0.913469i	$0.366607\pi$
$480$		0			0
$481$	0.0397125			0.00181073
$482$	−14.6279	−	15.0256i	−0.666284	−	0.684397i
$483$		0			0
$484$	0.0481514	−	1.79499i	0.00218870	−	0.0815905i
$485$	19.9531	−	5.25534i	0.906022	−	0.238633i
$486$		0			0
$487$		−	14.4178i		−	0.653331i	−0.945140	−	0.326666i	$-0.894075\pi$
$487$		−	14.4178i		−	0.653331i	0.945140	−	0.326666i	$-0.105925\pi$
$488$	3.02360	+	3.27721i	0.136872	+	0.148352i
$489$		0			0
$490$	23.7882	−	39.5706i	1.07464	−	1.78762i
$491$			33.8880i			1.52934i	0.644421	+	0.764671i	$0.277099\pi$
$491$			33.8880i			1.52934i	−0.644421	+	0.764671i	$0.722901\pi$
$492$		0			0
$493$	−2.31671			−0.104339
$494$	20.6117	−	20.0662i	0.927365	−	0.902821i
$495$		0			0
$496$	−23.0627	−	1.23822i	−1.03554	−	0.0555979i
$497$		−	59.7912i		−	2.68200i
$498$		0			0
$499$			21.2213i			0.949996i	0.879987	+	0.474998i	$0.157551\pi$
$499$			21.2213i			0.949996i	−0.879987	+	0.474998i	$0.842449\pi$
$500$	16.4251	−	15.1729i	0.734552	−	0.678552i
$501$		0			0
$502$	−4.56463	+	4.44382i	−0.203729	+	0.198338i
$503$		−	14.6567i		−	0.653512i	−0.945109	−	0.326756i	$-0.894045\pi$
$503$		−	14.6567i		−	0.653512i	0.945109	−	0.326756i	$-0.105955\pi$
$504$		0			0
$505$	−22.1774	+	5.84121i	−0.986883	+	0.259930i
$506$	−22.4717	−	23.0826i	−0.998988	−	1.02615i
$507$		0			0
$508$	−5.68566	−	0.152520i	−0.252260	−	0.00676699i
$509$			35.6910i			1.58198i	0.611831	+	0.790989i	$0.290433\pi$
$509$			35.6910i			1.58198i	−0.611831	+	0.790989i	$0.709567\pi$
$510$		0			0
$511$	−15.7387			−0.696239
$512$	13.9573	+	17.8099i	0.616833	+	0.787094i
$513$		0			0
$514$	−1.31914	+	1.28423i	−0.0581848	+	0.0566449i
$515$	−28.8296	+	7.59328i	−1.27038	+	0.334600i
$516$		0			0
$517$	20.8698			0.917855
$518$	−0.0685425	+	0.0667284i	−0.00301158	+	0.00293188i
$519$		0			0
$520$	14.5468	+	9.28487i	0.637917	+	0.407168i
$521$	−1.87141			−0.0819880			−0.0409940	−	0.999159i	$-0.513052\pi$
$521$	−1.87141			−0.0819880			−0.0409940	+	0.999159i	$0.513052\pi$
$522$		0			0
$523$	9.43999			0.412782			0.206391	−	0.978470i	$-0.433828\pi$
$523$	9.43999			0.412782			0.206391	+	0.978470i	$0.433828\pi$
$524$	−35.8433	−	0.961512i	−1.56582	−	0.0420038i
$525$		0			0
$526$	−15.5479	+	15.1364i	−0.677922	+	0.659981i
$527$			14.0418i			0.611669i
$528$		0			0
$529$	−20.6122			−0.896184
$530$	−7.41267	+	12.3306i	−0.321986	+	0.535608i
$531$		0			0
$532$	−1.85812	+	69.2672i	−0.0805599	+	3.00311i
$533$	12.0809			0.523282
$534$		0			0
$535$	−1.52905	−	5.80536i	−0.0661064	−	0.250988i
$536$	15.1707	−	13.9967i	0.655275	−	0.604566i
$537$		0			0
$538$	−5.52205	+	5.37590i	−0.238072	+	0.231772i
$539$		−	50.3614i		−	2.16922i
$540$		0			0
$541$			13.9429i			0.599451i	0.954026	+	0.299725i	$0.0968950\pi$
$541$			13.9429i			0.599451i	−0.954026	+	0.299725i	$0.903105\pi$
$542$	1.45195	+	1.49142i	0.0623664	+	0.0640619i
$543$		0			0
$544$	10.3575	−	9.05406i	0.444075	−	0.388190i
$545$	34.0933	−	8.97966i	1.46039	−	0.384646i
$546$		0			0
$547$	−31.5443			−1.34874			−0.674369	−	0.738394i	$-0.735584\pi$
$547$	−31.5443			−1.34874			−0.674369	+	0.738394i	$0.735584\pi$
$548$	−34.6605	−	0.929783i	−1.48062	−	0.0397184i
$549$		0			0
$550$	6.82793	−	23.4152i	0.291144	−	0.998426i
$551$	−7.10145			−0.302532
$552$		0			0
$553$		−	23.4142i		−	0.995675i
$554$	0.363288	+	0.373164i	0.0154346	+	0.0158542i
$555$		0			0
$556$	−16.6188	−	0.445806i	−0.704793	−	0.0189064i
$557$	−27.5809			−1.16864			−0.584319	−	0.811524i	$-0.698638\pi$
$557$	−27.5809			−1.16864			−0.584319	+	0.811524i	$0.698638\pi$
$558$		0			0
$559$	−18.6471			−0.788687
$560$	−40.7085	+	8.41736i	−1.72025	+	0.355698i
$561$		0			0
$562$	28.4322	+	29.2052i	1.19934	+	1.23194i
$563$	−25.3066			−1.06654			−0.533272	−	0.845944i	$-0.679038\pi$
$563$	−25.3066			−1.06654			−0.533272	+	0.845944i	$0.679038\pi$
$564$		0			0
$565$	31.9527	−	8.41586i	1.34426	−	0.354058i
$566$	0.0287151	+	0.0294957i	0.00120699	+	0.00123980i
$567$		0			0
$568$	−26.7438	+	24.6742i	−1.12214	+	1.03531i
$569$	−29.9749			−1.25661			−0.628307	−	0.777966i	$-0.716252\pi$
$569$	−29.9749			−1.25661			−0.628307	+	0.777966i	$0.716252\pi$
$570$		0			0
$571$			4.56813i			0.191170i	0.995421	+	0.0955851i	$0.0304722\pi$
$571$			4.56813i			0.191170i	−0.995421	+	0.0955851i	$0.969528\pi$
$572$	18.8171	+	0.504776i	0.786781	+	0.0211058i
$573$		0			0
$574$	−20.8512	+	20.2994i	−0.870314	+	0.847280i
$575$	−16.2655	−	28.7357i	−0.678317	−	1.19836i
$576$		0			0
$577$		−	41.5109i		−	1.72812i	−0.503386	−	0.864061i	$-0.667913\pi$
$577$		−	41.5109i		−	1.72812i	0.503386	−	0.864061i	$-0.332087\pi$
$578$	10.9362	+	11.2335i	0.454885	+	0.467251i
$579$		0			0
$580$	−0.974224	−	4.14740i	−0.0404525	−	0.172211i
$581$		−	59.2234i		−	2.45700i
$582$		0			0
$583$			15.6932i			0.649944i
$584$	6.49493	+	7.03970i	0.268762	+	0.291305i
$585$		0			0
$586$	−16.0558	−	16.4923i	−0.663259	−	0.681290i
$587$	−10.1867			−0.420449			−0.210225	−	0.977653i	$-0.567420\pi$
$587$	−10.1867			−0.420449			−0.210225	+	0.977653i	$0.567420\pi$
$588$		0			0
$589$			43.0425i			1.77354i
$590$	26.3018	+	15.8116i	1.08283	+	0.650953i
$591$		0			0
$592$	0.0581323	+	0.00312110i	0.00238922	+	0.000128276i
$593$		−	39.8323i		−	1.63572i	−0.575419	−	0.817859i	$-0.695161\pi$
$593$		−	39.8323i		−	1.63572i	0.575419	−	0.817859i	$-0.304839\pi$
$594$		0			0
$595$	6.43710	+	24.4399i	0.263895	+	1.00194i
$596$	−11.6503	−	0.312524i	−0.477215	−	0.0128015i
$597$		0			0
$598$	18.2598	−	17.7765i	0.746697	−	0.726935i
$599$	8.95628			0.365944			0.182972	−	0.983118i	$-0.441428\pi$
$599$	8.95628			0.365944			0.182972	+	0.983118i	$0.441428\pi$
$600$		0			0
$601$	20.6214			0.841163			0.420582	−	0.907255i	$-0.361826\pi$
$601$	20.6214			0.841163			0.420582	+	0.907255i	$0.361826\pi$
$602$	32.1842	−	31.3325i	1.31173	−	1.27702i
$603$		0			0
$604$	−0.748429	+	27.9000i	−0.0304531	+	1.13523i
$605$	−0.511329	−	1.94137i	−0.0207885	−	0.0789280i
$606$		0			0
$607$		−	8.49475i		−	0.344791i	−0.985028	−	0.172396i	$-0.944849\pi$
$607$		−	8.49475i		−	0.344791i	0.985028	−	0.172396i	$-0.0551508\pi$
$608$	31.7491	−	27.7536i	1.28759	−	1.12556i
$609$		0			0
$610$	4.27264	+	2.56854i	0.172994	+	0.103997i
$611$			16.5094i			0.667897i
$612$		0			0
$613$	−22.7814			−0.920133			−0.460066	−	0.887885i	$-0.652174\pi$
$613$	−22.7814			−0.920133			−0.460066	+	0.887885i	$0.652174\pi$
$614$	28.7827	+	29.5651i	1.16157	+	1.19315i
$615$		0			0
$616$	−33.3258	+	30.7469i	−1.34274	+	1.23883i
$617$			22.5202i			0.906627i	0.891351	+	0.453314i	$0.149758\pi$
$617$			22.5202i			0.906627i	−0.891351	+	0.453314i	$0.850242\pi$
$618$		0			0
$619$		−	29.6649i		−	1.19233i	−0.802861	−	0.596167i	$-0.796690\pi$
$619$		−	29.6649i		−	1.19233i	0.802861	−	0.596167i	$-0.203310\pi$
$620$	−25.1378	+	5.90486i	−1.00956	+	0.237145i
$621$		0			0
$622$	17.2822	+	17.7520i	0.692953	+	0.711791i
$623$			2.48840i			0.0996957i
$624$		0			0
$625$	12.8674	−	21.4343i	0.514695	−	0.857374i
$626$	−27.2612	+	26.5397i	−1.08958	+	1.06074i
$627$		0			0
$628$	−0.00569820	+	0.212418i	−0.000227383	+	0.00847639i
$629$		−	0.0353940i		−	0.00141125i
$630$		0			0
$631$	−11.5211			−0.458647			−0.229323	−	0.973350i	$-0.573651\pi$
$631$	−11.5211			−0.458647			−0.229323	+	0.973350i	$0.573651\pi$
$632$	−10.4729	+	9.66242i	−0.416588	+	0.384350i
$633$		0			0
$634$	−8.20302	−	8.42602i	−0.325784	−	0.334640i
$635$	−6.14933	+	1.61964i	−0.244029	+	0.0642735i
$636$		0			0
$637$	39.8391			1.57848
$638$	−3.24157	−	3.32969i	−0.128335	−	0.131824i
$639$		0			0
$640$	20.5642	+	14.7347i	0.812873	+	0.582441i
$641$	37.5104			1.48157			0.740786	−	0.671741i	$-0.234453\pi$
$641$	37.5104			1.48157			0.740786	+	0.671741i	$0.234453\pi$
$642$		0			0
$643$	4.26865			0.168339			0.0841697	−	0.996451i	$-0.473176\pi$
$643$	4.26865			0.168339			0.0841697	+	0.996451i	$0.473176\pi$
$644$	−1.64610	+	61.3633i	−0.0648653	+	2.41805i
$645$		0			0
$646$	−17.8841	−	18.3703i	−0.703642	−	0.722771i
$647$			20.4696i			0.804744i	0.915476	+	0.402372i	$0.131814\pi$
$647$			20.4696i			0.804744i	−0.915476	+	0.402372i	$0.868186\pi$
$648$		0			0
$649$	33.4743			1.31398
$650$	18.5229	+	5.40132i	0.726527	+	0.211857i
$651$		0			0
$652$	0.159334	−	5.93965i	0.00623999	−	0.232615i
$653$	39.7754			1.55653			0.778266	−	0.627935i	$-0.216100\pi$
$653$	39.7754			1.55653			0.778266	+	0.627935i	$0.216100\pi$
$654$		0			0
$655$	−38.7663	+	10.2105i	−1.51473	+	0.398956i
$656$	17.6844	+	0.949465i	0.690459	+	0.0370704i
$657$		0			0
$658$	−27.7405	−	28.4946i	−1.08144	−	1.11084i
$659$		−	18.9629i		−	0.738688i	−0.929293	−	0.369344i	$-0.879582\pi$
$659$		−	18.9629i		−	0.738688i	0.929293	−	0.369344i	$-0.120418\pi$
$660$		0			0
$661$		−	15.5029i		−	0.602991i	−0.953468	−	0.301496i	$-0.902514\pi$
$661$		−	15.5029i		−	0.602991i	0.953468	−	0.301496i	$-0.0974859\pi$
$662$	−34.8088	+	33.8876i	−1.35288	+	1.31708i
$663$		0			0
$664$	−26.4898	+	24.4399i	−1.02800	+	0.948451i
$665$	19.7318	+	74.9160i	0.765165	+	2.90512i
$666$		0			0
$667$	−6.29112			−0.243593
$668$	41.9084	+	1.12421i	1.62148	+	0.0434970i
$669$		0			0
$670$	11.8902	−	19.7787i	0.459357	−	0.764118i
$671$	5.43778			0.209923
$672$		0			0
$673$			20.3980i			0.786285i	0.919478	+	0.393143i	$0.128612\pi$
$673$			20.3980i			0.786285i	−0.919478	+	0.393143i	$0.871388\pi$
$674$	13.9501	−	13.5809i	0.537337	−	0.523116i
$675$		0			0
$676$	0.297901	−	11.1052i	0.0114577	−	0.427122i
$677$	−19.6179			−0.753976			−0.376988	−	0.926218i	$-0.623040\pi$
$677$	−19.6179			−0.753976			−0.376988	+	0.926218i	$0.623040\pi$
$678$		0			0
$679$	−42.8864			−1.64583
$680$	8.27520	−	12.9649i	0.317340	−	0.497181i
$681$		0			0
$682$	−20.1815	+	19.6474i	−0.772791	+	0.752339i
$683$	0.245121			0.00937928			0.00468964	−	0.999989i	$-0.498507\pi$
$683$	0.245121			0.00937928			0.00468964	+	0.999989i	$0.498507\pi$
$684$		0			0
$685$	−37.4871	+	9.87354i	−1.43231	+	0.377249i
$686$	−35.7942	+	34.8469i	−1.36663	+	1.33046i
$687$		0			0
$688$	−27.2961	−	1.46552i	−1.04066	−	0.0558723i
$689$	−12.4143			−0.472946
$690$		0			0
$691$		−	30.9426i		−	1.17711i	−0.808456	−	0.588556i	$-0.799697\pi$
$691$		−	30.9426i		−	1.17711i	0.808456	−	0.588556i	$-0.200303\pi$
$692$	−0.445961	+	16.6246i	−0.0169529	+	0.631971i
$693$		0			0
$694$	3.17672	+	3.26308i	0.120587	+	0.123865i
$695$	−17.9740	+	4.73410i	−0.681794	+	0.179574i
$696$		0			0
$697$		−	10.7672i		−	0.407836i
$698$	5.02274	−	4.88981i	0.190114	−	0.185082i
$699$		0			0
$700$	−41.0456	+	21.8013i	−1.55138	+	0.824010i
$701$		−	39.7391i		−	1.50093i	−0.660913	−	0.750463i	$-0.729831\pi$
$701$		−	39.7391i		−	1.50093i	0.660913	−	0.750463i	$-0.270169\pi$
$702$		0			0
$703$		−	0.108494i		−	0.00409193i
$704$	27.5053	+	2.21778i	1.03665	+	0.0835858i
$705$		0			0
$706$	−8.65255	+	8.42355i	−0.325643	+	0.317025i
$707$	47.6674			1.79272
$708$		0			0
$709$		−	16.4653i		−	0.618368i	−0.951002	−	0.309184i	$-0.899944\pi$
$709$		−	16.4653i		−	0.618368i	0.951002	−	0.309184i	$-0.100056\pi$
$710$	−20.9606	+	34.8670i	−0.786639	+	1.30854i
$711$		0			0
$712$	1.11303	−	1.02689i	0.0417125	−	0.0384845i
$713$			38.1310i			1.42802i
$714$		0			0
$715$	20.3516	−	5.36031i	0.761107	−	0.200464i
$716$	−6.61922	−	0.177564i	−0.247372	−	0.00663586i
$717$		0			0
$718$	33.6330	+	34.5473i	1.25517	+	1.28930i
$719$	36.5409			1.36275			0.681373	−	0.731936i	$-0.261383\pi$
$719$	36.5409			1.36275			0.681373	+	0.731936i	$0.261383\pi$
$720$		0			0
$721$	61.9652			2.30771
$722$	−36.0771	−	37.0578i	−1.34265	−	1.37915i
$723$		0			0
$724$	21.1176	+	0.566490i	0.784831	+	0.0210534i
$725$	−2.34632	−	4.14516i	−0.0871400	−	0.153947i
$726$		0			0
$727$		−	34.0483i		−	1.26278i	−0.775464	−	0.631391i	$-0.782484\pi$
$727$		−	34.0483i		−	1.26278i	0.775464	−	0.631391i	$-0.217516\pi$
$728$	−24.3227	−	26.3628i	−0.901460	−	0.977071i
$729$		0			0
$730$	9.17796	+	5.51742i	0.339692	+	0.204209i
$731$			16.6193i			0.614688i
$732$		0			0
$733$	−1.45374			−0.0536951			−0.0268476	−	0.999640i	$-0.508547\pi$
$733$	−1.45374			−0.0536951			−0.0268476	+	0.999640i	$0.508547\pi$
$734$	28.0930	−	27.3495i	1.03693	−	1.00949i
$735$		0			0
$736$	28.1263	−	24.5867i	1.03675	−	0.906277i
$737$		−	25.1723i		−	0.927235i
$738$		0			0
$739$			1.21631i			0.0447427i	0.999750	+	0.0223713i	$0.00712161\pi$
$739$			1.21631i			0.0447427i	−0.999750	+	0.0223713i	$0.992878\pi$
$740$	0.0633629	−	0.0148839i	0.00232927	−	0.000547144i
$741$		0			0
$742$	21.4266	−	20.8596i	0.786596	−	0.765779i
$743$		−	25.6972i		−	0.942737i	−0.881936	−	0.471369i	$-0.843760\pi$
$743$		−	25.6972i		−	0.942737i	0.881936	−	0.471369i	$-0.156240\pi$
$744$		0			0
$745$	−12.6004	+	3.31875i	−0.461643	+	0.121590i
$746$	−7.68338	−	7.89226i	−0.281309	−	0.288956i
$747$		0			0
$748$	0.449885	−	16.7708i	0.0164494	−	0.613203i
$749$			12.4778i			0.455930i
$750$		0			0
$751$	44.5901			1.62712			0.813558	−	0.581483i	$-0.197527\pi$
$751$	44.5901			1.62712			0.813558	+	0.581483i	$0.197527\pi$
$752$	−1.29751	+	24.1669i	−0.0473152	+	0.881275i
$753$		0			0
$754$	2.63399	−	2.56428i	0.0959244	−	0.0933857i
$755$	7.94770	+	30.1752i	0.289246	+	1.09819i
$756$		0			0
$757$	−33.4148			−1.21448			−0.607241	−	0.794517i	$-0.707724\pi$
$757$	−33.4148			−1.21448			−0.607241	+	0.794517i	$0.707724\pi$
$758$	11.8484	−	11.5348i	0.430352	−	0.418962i
$759$		0			0
$760$	25.3661	−	39.7415i	0.920126	−	1.44158i
$761$	−9.94233			−0.360409			−0.180205	−	0.983629i	$-0.557676\pi$
$761$	−9.94233			−0.360409			−0.180205	+	0.983629i	$0.557676\pi$
$762$		0			0
$763$	−73.2788			−2.65287
$764$	1.08108	−	40.3005i	0.0391121	−	1.45802i
$765$		0			0
$766$	7.94490	−	7.73464i	0.287061	−	0.279464i
$767$			26.4803i			0.956147i
$768$		0			0
$769$	−18.4215			−0.664297			−0.332148	−	0.943227i	$-0.607773\pi$
$769$	−18.4215			−0.664297			−0.332148	+	0.943227i	$0.607773\pi$
$770$	−26.1193	+	43.4483i	−0.941276	+	1.56577i
$771$		0			0
$772$	−11.8134	−	0.316901i	−0.425175	−	0.0114055i
$773$	8.84837			0.318254			0.159127	−	0.987258i	$-0.449132\pi$
$773$	8.84837			0.318254			0.159127	+	0.987258i	$0.449132\pi$
$774$		0			0
$775$	−25.1242	+	14.2212i	−0.902487	+	0.510841i
$776$	17.6980	+	19.1825i	0.635323	+	0.688612i
$777$		0			0
$778$	−11.7627	+	11.4514i	−0.421715	+	0.410554i
$779$		−	33.0048i		−	1.18252i
$780$		0			0
$781$			44.3752i			1.58787i
$782$	−15.8434	−	16.2741i	−0.566560	−	0.581962i
$783$		0			0
$784$	58.3176	+	3.13104i	2.08277	+	0.111823i
$785$	0.0605102	+	0.229741i	0.00215970	+	0.00819979i
$786$		0			0
$787$	51.0698			1.82044			0.910221	−	0.414122i	$-0.135911\pi$
$787$	51.0698			1.82044			0.910221	+	0.414122i	$0.135911\pi$
$788$	−1.05214	+	39.2216i	−0.0374808	+	1.39721i
$789$		0			0
$790$	−8.20819	+	13.6539i	−0.292034	+	0.485785i
$791$	−68.6780			−2.44191
$792$		0			0
$793$			4.30162i			0.152755i
$794$	−14.6857	−	15.0849i	−0.521176	−	0.535344i
$795$		0			0
$796$	−1.35274	+	50.4274i	−0.0479465	+	1.78735i
$797$	−22.1165			−0.783406			−0.391703	−	0.920092i	$-0.628114\pi$
$797$	−22.1165			−0.783406			−0.391703	+	0.920092i	$0.628114\pi$
$798$		0			0
$799$	14.7141			0.520547
$800$	26.6898	+	9.36236i	0.943627	+	0.331010i
$801$		0			0
$802$	−31.7435	−	32.6065i	−1.12090	−	1.15138i
$803$	11.6808			0.412205
$804$		0			0
$805$	17.4802	+	66.3675i	0.616097	+	2.33915i
$806$	−15.5423	−	15.9649i	−0.547456	−	0.562338i
$807$		0			0
$808$	−19.6710	−	21.3210i	−0.692024	−	0.750069i
$809$	−31.2943			−1.10025			−0.550125	−	0.835082i	$-0.685420\pi$
$809$	−31.2943			−1.10025			−0.550125	+	0.835082i	$0.685420\pi$
$810$		0			0
$811$			38.6529i			1.35729i	0.734468	+	0.678644i	$0.237432\pi$
$811$			38.6529i			1.35729i	−0.734468	+	0.678644i	$0.762568\pi$
$812$	−0.237452	+	8.85174i	−0.00833292	+	0.310635i
$813$		0			0
$814$	0.0508701	−	0.0495238i	0.00178300	−	0.00173581i
$815$	−1.69199	−	6.42403i	−0.0592680	−	0.225024i
$816$		0			0
$817$			50.9435i			1.78229i
$818$	13.1978	+	13.5566i	0.461451	+	0.473996i
$819$		0			0
$820$	19.2755	−	4.52783i	0.673131	−	0.158119i
$821$			22.8741i			0.798312i	0.916883	+	0.399156i	$0.130697\pi$
$821$			22.8741i			0.798312i	−0.916883	+	0.399156i	$0.869303\pi$
$822$		0			0
$823$		−	13.8894i		−	0.484154i	−0.970257	−	0.242077i	$-0.922171\pi$
$823$		−	13.8894i		−	0.484154i	0.970257	−	0.242077i	$-0.0778286\pi$
$824$	−25.5714	−	27.7162i	−0.890821	−	0.965540i
$825$		0			0
$826$	−44.4945	−	45.7041i	−1.54816	−	1.59025i
$827$	5.40695			0.188018			0.0940090	−	0.995571i	$-0.470032\pi$
$827$	5.40695			0.188018			0.0940090	+	0.995571i	$0.470032\pi$
$828$		0			0
$829$		−	39.9980i		−	1.38919i	−0.719401	−	0.694595i	$-0.755584\pi$
$829$		−	39.9980i		−	1.38919i	0.719401	−	0.694595i	$-0.244416\pi$
$830$	−20.7616	+	34.5359i	−0.720645	+	1.19876i
$831$		0			0
$832$	−1.75441	+	21.7584i	−0.0608231	+	0.754338i
$833$		−	35.5068i		−	1.23024i
$834$		0			0
$835$	45.3260	−	11.9382i	1.56857	−	0.413139i
$836$	1.37904	−	51.4080i	0.0476952	−	1.77798i
$837$		0			0
$838$	12.3688	−	12.0414i	0.427272	−	0.415964i
$839$	−5.92926			−0.204701			−0.102350	−	0.994748i	$-0.532636\pi$
$839$	−5.92926			−0.204701			−0.102350	+	0.994748i	$0.532636\pi$
$840$		0			0
$841$	28.0925			0.968707
$842$	−30.5868	+	29.7773i	−1.05409	+	1.02619i
$843$		0			0
$844$	25.8086	+	0.692327i	0.888368	+	0.0238309i
$845$	−3.16346	−	12.0108i	−0.108826	−	0.413184i
$846$		0			0
$847$			4.17272i			0.143376i
$848$	−18.1724	−	0.975666i	−0.624042	−	0.0335045i
$849$		0			0
$850$	4.81396	−	16.5086i	0.165118	−	0.566242i
$851$		−	0.0961140i		−	0.00329475i
$852$		0			0
$853$	−42.3909			−1.45144			−0.725719	−	0.687992i	$-0.758493\pi$
$853$	−42.3909			−1.45144			−0.725719	+	0.687992i	$0.758493\pi$
$854$	−7.22797	−	7.42446i	−0.247336	−	0.254060i
$855$		0			0
$856$	5.58116	−	5.14926i	0.190760	−	0.175998i
$857$			36.2443i			1.23808i	0.785359	+	0.619040i	$0.212478\pi$
$857$			36.2443i			1.23808i	−0.785359	+	0.619040i	$0.787522\pi$
$858$		0			0
$859$		−	35.9708i		−	1.22731i	−0.789575	−	0.613654i	$-0.789699\pi$
$859$		−	35.9708i		−	1.22731i	0.789575	−	0.613654i	$-0.210301\pi$
$860$	−29.7521	+	6.98878i	−1.01454	+	0.238315i
$861$		0			0
$862$	10.2766	+	10.5560i	0.350023	+	0.359538i
$863$			10.6372i			0.362095i	0.983474	+	0.181047i	$0.0579487\pi$
$863$			10.6372i			0.362095i	−0.983474	+	0.181047i	$0.942051\pi$
$864$		0			0
$865$	4.73574	+	17.9803i	0.161020	+	0.611349i
$866$	8.31951	−	8.09932i	0.282708	−	0.275226i
$867$		0			0
$868$	53.6511	+	1.43922i	1.82104	+	0.0488502i
$869$			17.3773i			0.589486i
$870$		0			0
$871$	19.9129			0.674723
$872$	30.2402	+	32.7766i	1.02406	+	1.10996i
$873$		0			0
$874$	−48.5651	−	49.8854i	−1.64274	−	1.68740i
$875$	−37.2096	+	36.2698i	−1.25791	+	1.22614i
$876$		0			0
$877$	−24.9628			−0.842933			−0.421466	−	0.906844i	$-0.638484\pi$
$877$	−24.9628			−0.842933			−0.421466	+	0.906844i	$0.638484\pi$
$878$	−7.41402	−	7.61558i	−0.250211	−	0.257013i
$879$		0			0
$880$	30.2126	−	6.24710i	1.01847	−	0.210590i
$881$	−22.0036			−0.741319			−0.370660	−	0.928769i	$-0.620868\pi$
$881$	−22.0036			−0.741319			−0.370660	+	0.928769i	$0.620868\pi$
$882$		0			0
$883$	43.4412			1.46191			0.730957	−	0.682424i	$-0.239074\pi$
$883$	43.4412			1.46191			0.730957	+	0.682424i	$0.239074\pi$
$884$	13.2668	+	0.355888i	0.446211	+	0.0119698i
$885$		0			0
$886$	−2.77971	−	2.85528i	−0.0933862	−	0.0959249i
$887$		−	13.5030i		−	0.453388i	−0.973966	−	0.226694i	$-0.927208\pi$
$887$		−	13.5030i		−	0.453388i	0.973966	−	0.226694i	$-0.0727917\pi$
$888$		0			0
$889$	13.2171			0.443289
$890$	0.872343	−	1.45110i	0.0292410	−	0.0486410i
$891$		0			0
$892$	36.1112	+	0.968700i	1.20909	+	0.0324345i
$893$	45.1033			1.50933
$894$		0			0
$895$	−7.15903	+	1.88558i	−0.239300	+	0.0630280i
$896$	−33.5324	−	40.5022i	−1.12024	−	1.35308i
$897$		0			0
$898$	13.1194	+	13.4761i	0.437801	+	0.449703i
$899$			5.50045i			0.183450i
$900$		0			0
$901$			11.0643i			0.368606i
$902$	15.4751	−	15.0656i	0.515266	−	0.501629i
$903$		0			0
$904$	28.3415	+	30.7187i	0.942625	+	1.02169i
$905$	22.8398	−	6.01566i	0.759220	−	0.199967i
$906$		0			0
$907$	28.8615			0.958330			0.479165	−	0.877725i	$-0.340939\pi$
$907$	28.8615			0.958330			0.479165	+	0.877725i	$0.340939\pi$
$908$	0.561235	−	20.9217i	0.0186252	−	0.694312i
$909$		0			0
$910$	−34.3703	−	20.6620i	−1.13937	−	0.684940i
$911$	−8.07091			−0.267401			−0.133701	−	0.991022i	$-0.542686\pi$
$911$	−8.07091			−0.267401			−0.133701	+	0.991022i	$0.542686\pi$
$912$		0			0
$913$			43.9538i			1.45466i
$914$	7.01855	−	6.83280i	0.232153	−	0.226009i
$915$		0			0
$916$	22.5545	+	0.605034i	0.745221	+	0.0199909i
$917$	83.3230			2.75157
$918$		0			0
$919$	−24.8108			−0.818434			−0.409217	−	0.912437i	$-0.634198\pi$
$919$	−24.8108			−0.818434			−0.409217	+	0.912437i	$0.634198\pi$
$920$	22.4717	−	35.2067i	0.740869	−	1.16073i
$921$		0			0
$922$	−4.13885	+	4.02931i	−0.136306	+	0.132698i
$923$	−35.1036			−1.15545
$924$		0			0
$925$	0.0633286	−	0.0358464i	0.00208223	−	0.00117862i
$926$	−0.454190	+	0.442169i	−0.0149256	+	0.0145306i
$927$		0			0
$928$	4.05725	−	3.54666i	0.133186	−	0.116425i
$929$	35.9207			1.17852			0.589260	−	0.807943i	$-0.299419\pi$
$929$	35.9207			1.17852			0.589260	+	0.807943i	$0.299419\pi$
$930$		0			0
$931$		−	108.840i		−	3.56708i
$932$	−19.5558	−	0.524593i	−0.640571	−	0.0171836i
$933$		0			0
$934$	−11.3344	−	11.6426i	−0.370874	−	0.380956i
$935$	−4.77742	−	18.1385i	−0.156238	−	0.593193i
$936$		0			0
$937$			4.68847i			0.153166i	0.997063	+	0.0765829i	$0.0244010\pi$
$937$			4.68847i			0.153166i	−0.997063	+	0.0765829i	$0.975599\pi$
$938$	−34.3690	+	33.4594i	−1.12219	+	1.09249i
$939$		0			0
$940$	6.18758	+	26.3413i	0.201817	+	0.859159i
$941$			20.5630i			0.670334i	0.942159	+	0.335167i	$0.108793\pi$
$941$			20.5630i			0.670334i	−0.942159	+	0.335167i	$0.891207\pi$
$942$		0			0
$943$		−	29.2387i		−	0.952145i
$944$	−2.08114	+	38.7626i	−0.0677355	+	1.26161i
$945$		0			0
$946$	−23.8861	+	23.2540i	−0.776606	+	0.756052i
$947$	54.1452			1.75948			0.879741	−	0.475454i	$-0.157716\pi$
$947$	54.1452			1.75948			0.879741	+	0.475454i	$0.157716\pi$
$948$		0			0
$949$			9.24022i			0.299950i
$950$	14.7563	−	50.6042i	0.478759	−	1.64182i
$951$		0			0
$952$	−23.4960	+	21.6778i	−0.761511	+	0.702581i
$953$			16.0455i			0.519766i	0.965640	+	0.259883i	$0.0836840\pi$
$953$			16.0455i			0.519766i	−0.965640	+	0.259883i	$0.916316\pi$
$954$		0			0
$955$	−11.4802	−	43.5871i	−0.371490	−	1.41044i
$956$	1.06539	−	39.7157i	0.0344572	−	1.28450i
$957$		0			0
$958$	17.5708	+	18.0484i	0.567686	+	0.583118i
$959$	80.5734			2.60185
$960$		0			0
$961$	2.33871			0.0754422
$962$	0.0391764	+	0.0402414i	0.00126310	+	0.00129744i
$963$		0			0
$964$	0.795254	−	29.6455i	0.0256134	−	0.954818i
$965$	−12.7768	+	3.36523i	−0.411301	+	0.108331i
$966$		0			0
$967$		−	21.2724i		−	0.684073i	−0.939687	−	0.342037i	$-0.888883\pi$
$967$		−	21.2724i		−	0.684073i	0.939687	−	0.342037i	$-0.111117\pi$
$968$	1.86640	−	1.72197i	0.0599884	−	0.0553461i
$969$		0			0
$970$	25.0090	+	15.0344i	0.802992	+	0.482726i
$971$		−	38.8345i		−	1.24626i	−0.782119	−	0.623129i	$-0.785861\pi$
$971$		−	38.8345i		−	1.24626i	0.782119	−	0.623129i	$-0.214139\pi$
$972$		0			0
$973$	38.6328			1.23851
$974$	14.6098	−	14.2231i	0.468128	−	0.455739i
$975$		0			0
$976$	−0.338074	+	6.29684i	−0.0108215	+	0.201557i
$977$		−	2.30475i		−	0.0737356i	−0.999320	−	0.0368678i	$-0.988262\pi$
$977$		−	2.30475i		−	0.0737356i	0.999320	−	0.0368678i	$-0.0117381\pi$
$978$		0			0
$979$		−	1.84681i		−	0.0590244i
$980$	63.5648	−	14.9314i	2.03050	−	0.476965i
$981$		0			0
$982$	−34.3393	+	33.4305i	−1.09581	+	1.06681i
$983$			40.4209i			1.28922i	0.764509	+	0.644612i	$0.222981\pi$
$983$			40.4209i			1.28922i	−0.764509	+	0.644612i	$0.777019\pi$
$984$		0			0
$985$	11.1728	+	42.4202i	0.355996	+	1.35162i
$986$	−2.28544	−	2.34757i	−0.0727831	−	0.0747617i
$987$		0			0
$988$	40.6669	+	1.09091i	1.29379	+	0.0347064i
$989$			45.1305i			1.43507i
$990$		0			0
$991$	−44.6069			−1.41699			−0.708493	−	0.705718i	$-0.750625\pi$
$991$	−44.6069			−1.41699			−0.708493	+	0.705718i	$0.750625\pi$
$992$	−21.4966	−	24.5913i	−0.682518	−	0.780776i
$993$		0			0
$994$	60.5876	−	58.9841i	1.92172	−	1.87086i
$995$	14.3650	+	54.5398i	0.455400	+	1.72903i
$996$		0			0
$997$	−18.3783			−0.582046			−0.291023	−	0.956716i	$-0.593996\pi$
$997$	−18.3783			−0.582046			−0.291023	+	0.956716i	$0.593996\pi$
$998$	−21.5040	+	20.9348i	−0.680696	+	0.662681i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1080.2.d.i.109.16	yes	20
3.2	odd	2	inner	1080.2.d.i.109.5	✓	20
4.3	odd	2		4320.2.d.i.3889.12		20
5.4	even	2		1080.2.d.j.109.5	yes	20
8.3	odd	2		4320.2.d.j.3889.9		20
8.5	even	2		1080.2.d.j.109.6	yes	20
12.11	even	2		4320.2.d.i.3889.9		20
15.14	odd	2		1080.2.d.j.109.16	yes	20
20.19	odd	2		4320.2.d.j.3889.10		20
24.5	odd	2		1080.2.d.j.109.15	yes	20
24.11	even	2		4320.2.d.j.3889.12		20
40.19	odd	2		4320.2.d.i.3889.11		20
40.29	even	2	inner	1080.2.d.i.109.15	yes	20
60.59	even	2		4320.2.d.j.3889.11		20
120.29	odd	2	inner	1080.2.d.i.109.6	yes	20
120.59	even	2		4320.2.d.i.3889.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1080.2.d.i.109.5	✓	20	3.2	odd	2	inner
1080.2.d.i.109.6	yes	20	120.29	odd	2	inner
1080.2.d.i.109.15	yes	20	40.29	even	2	inner
1080.2.d.i.109.16	yes	20	1.1	even	1	trivial
1080.2.d.j.109.5	yes	20	5.4	even	2
1080.2.d.j.109.6	yes	20	8.5	even	2
1080.2.d.j.109.15	yes	20	24.5	odd	2
1080.2.d.j.109.16	yes	20	15.14	odd	2
4320.2.d.i.3889.9		20	12.11	even	2
4320.2.d.i.3889.10		20	120.59	even	2
4320.2.d.i.3889.11		20	40.19	odd	2
4320.2.d.i.3889.12		20	4.3	odd	2
4320.2.d.j.3889.9		20	8.3	odd	2
4320.2.d.j.3889.10		20	20.19	odd	2
4320.2.d.j.3889.11		20	60.59	even	2
4320.2.d.j.3889.12		20	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1080.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.986501 + 1.01332i) q^{2} +(-0.0536316 + 1.99928i) q^{4} +(0.569524 + 2.16232i) q^{5} -4.64762i q^{7} +(-2.07882 + 1.91795i) q^{8} +O(q^{10})\)	\(q+(0.986501 + 1.01332i) q^{2} +(-0.0536316 + 1.99928i) q^{4} +(0.569524 + 2.16232i) q^{5} -4.64762i q^{7} +(-2.07882 + 1.91795i) q^{8} +(-1.62929 + 2.71024i) q^{10} +3.44932i q^{11} -2.72863 q^{13} +(4.70952 - 4.58488i) q^{14} +(-3.99425 - 0.214449i) q^{16} +2.43191i q^{17} +7.45458i q^{19} +(-4.35364 + 1.02267i) q^{20} +(-3.49526 + 3.40276i) q^{22} +6.60396i q^{23} +(-4.35129 + 2.46299i) q^{25} +(-2.69180 - 2.76497i) q^{26} +(9.29190 + 0.249259i) q^{28} +0.952629i q^{29} +5.77397 q^{31} +(-3.72302 - 4.25900i) q^{32} +(-2.46430 + 2.39908i) q^{34} +(10.0497 - 2.64693i) q^{35} -0.0145540 q^{37} +(-7.55387 + 7.35395i) q^{38} +(-5.33116 - 3.40276i) q^{40} -4.42746 q^{41} +6.83386 q^{43} +(-6.89616 - 0.184993i) q^{44} +(-6.69191 + 6.51481i) q^{46} -6.05042i q^{47} -14.6004 q^{49} +(-6.78834 - 1.97950i) q^{50} +(0.146341 - 5.45530i) q^{52} +4.54964 q^{53} +(-7.45855 + 1.96447i) q^{55} +(8.91389 + 9.66156i) q^{56} +(-0.965317 + 0.939770i) q^{58} -9.70460i q^{59} -1.57648i q^{61} +(5.69603 + 5.85087i) q^{62} +(0.642962 - 7.97412i) q^{64} +(-1.55402 - 5.90018i) q^{65} -7.29776 q^{67} +(-4.86207 - 0.130427i) q^{68} +(12.5962 + 7.57231i) q^{70} +12.8649 q^{71} -3.38640i q^{73} +(-0.0143575 - 0.0147479i) q^{74} +(-14.9038 - 0.399801i) q^{76} +16.0311 q^{77} +5.03790 q^{79} +(-1.81111 - 8.75899i) q^{80} +(-4.36769 - 4.48643i) q^{82} +12.7427 q^{83} +(-5.25858 + 1.38503i) q^{85} +(6.74161 + 6.92488i) q^{86} +(-6.61561 - 7.17051i) q^{88} -0.535414 q^{89} +12.6816i q^{91} +(-13.2032 - 0.354181i) q^{92} +(6.13101 - 5.96874i) q^{94} +(-16.1192 + 4.24556i) q^{95} -9.22760i q^{97} +(-14.4033 - 14.7949i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{4}+O(q^{10}) \) 20 * q + 6 * q^4	\( 20 q + 6 q^{4} - 2 q^{10} - 4 q^{13} - 14 q^{16} - 34 q^{22} + 20 q^{25} + 20 q^{28} + 12 q^{31} + 6 q^{34} - 32 q^{37} - 6 q^{40} + 12 q^{43} + 2 q^{46} - 52 q^{49} - 50 q^{52} - 28 q^{55} + 6 q^{58} + 54 q^{64} + 12 q^{70} - 24 q^{76} + 36 q^{79} + 32 q^{82} - 44 q^{85} - 30 q^{88} - 22 q^{94}+O(q^{100}) \) 20 * q + 6 * q^4 - 2 * q^10 - 4 * q^13 - 14 * q^16 - 34 * q^22 + 20 * q^25 + 20 * q^28 + 12 * q^31 + 6 * q^34 - 32 * q^37 - 6 * q^40 + 12 * q^43 + 2 * q^46 - 52 * q^49 - 50 * q^52 - 28 * q^55 + 6 * q^58 + 54 * q^64 + 12 * q^70 - 24 * q^76 + 36 * q^79 + 32 * q^82 - 44 * q^85 - 30 * q^88 - 22 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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