LMFDB - Embedded newform 360.2.d.e.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(109,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, 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("360.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.839056.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 6x^{4} + 8x^{2} + 1 $ x^6 + 6x^4 + 8x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			109.1
Root			$-1.32132i$ of defining polynomial
Character	$\chi$	$=$	360.109
Dual form			360.2.d.e.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34067 - 0.450129i) q^{2} +(1.59477 + 1.20695i) q^{4} +(-0.254102 - 2.22158i) q^{5} -2.64265i q^{7} +(-1.59477 - 2.33596i) q^{8} +(-0.659335 + 3.09278i) q^{10} +1.51363i q^{11} -3.87086 q^{13} +(-1.18953 + 3.54291i) q^{14} +(1.08656 + 3.84959i) q^{16} +3.31415i q^{17} -7.08582i q^{19} +(2.27610 - 3.84959i) q^{20} +(0.681331 - 2.02927i) q^{22} -4.82778i q^{23} +(-4.87086 + 1.12902i) q^{25} +(5.18953 + 1.74239i) q^{26} +(3.18953 - 4.21441i) q^{28} -2.18513i q^{29} -7.36266 q^{31} +(0.276098 - 5.65011i) q^{32} +(1.49180 - 4.44317i) q^{34} +(-5.87086 + 0.671502i) q^{35} +7.87086 q^{37} +(-3.18953 + 9.49971i) q^{38} +(-4.78430 + 4.13648i) q^{40} -8.72532 q^{41} -1.01641 q^{43} +(-1.82687 + 2.41389i) q^{44} +(-2.17313 + 6.47244i) q^{46} -7.08582i q^{47} +0.0164068 q^{49} +(7.03840 + 0.678887i) q^{50} +(-6.17313 - 4.67192i) q^{52} +4.50820 q^{53} +(3.36266 - 0.384617i) q^{55} +(-6.17313 + 4.21441i) q^{56} +(-0.983593 + 2.92953i) q^{58} -6.79893i q^{59} -3.60104i q^{61} +(9.87086 + 3.31415i) q^{62} +(-2.91344 + 7.45063i) q^{64} +(0.983593 + 8.59945i) q^{65} +1.01641 q^{67} +(-4.00000 + 5.28530i) q^{68} +(8.17313 + 1.74239i) q^{70} +6.72532 q^{71} +15.5146i q^{73} +(-10.5522 - 3.54291i) q^{74} +(8.55220 - 11.3002i) q^{76} +4.00000 q^{77} +7.36266 q^{79} +(8.27610 - 3.39208i) q^{80} +(11.6977 + 3.92752i) q^{82} +7.74173 q^{83} +(7.36266 - 0.842131i) q^{85} +(1.36266 + 0.457515i) q^{86} +(3.53579 - 2.41389i) q^{88} +14.7581 q^{89} +10.2293i q^{91} +(5.82687 - 7.69919i) q^{92} +(-3.18953 + 9.49971i) q^{94} +(-15.7417 + 1.80052i) q^{95} -11.1444i q^{97} +(-0.0219960 - 0.00738516i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} + q^{4} - q^{8} - 11 q^{10} + 8 q^{13} + 10 q^{14} + q^{16} - 9 q^{20} - 10 q^{22} + 2 q^{25} + 14 q^{26} + 2 q^{28} - 16 q^{31} - 21 q^{32} + 12 q^{34} - 4 q^{35} + 16 q^{37} - 2 q^{38}+ \cdots + 21 q^{98}+O(q^{100}) $ 6 * q - q^2 + q^4 - q^8 - 11 * q^10 + 8 * q^13 + 10 * q^14 + q^16 - 9 * q^20 - 10 * q^22 + 2 * q^25 + 14 * q^26 + 2 * q^28 - 16 * q^31 - 21 * q^32 + 12 * q^34 - 4 * q^35 + 16 * q^37 - 2 * q^38 - 3 * q^40 + 4 * q^41 - 22 * q^44 - 2 * q^46 - 6 * q^49 + 15 * q^50 - 26 * q^52 + 24 * q^53 - 8 * q^55 - 26 * q^56 - 12 * q^58 + 28 * q^62 - 23 * q^64 + 12 * q^65 - 24 * q^68 + 38 * q^70 - 16 * q^71 - 18 * q^74 + 6 * q^76 + 24 * q^77 + 16 * q^79 + 27 * q^80 + 50 * q^82 - 16 * q^83 + 16 * q^85 - 20 * q^86 - 18 * q^88 + 20 * q^89 + 46 * q^92 - 2 * q^94 - 32 * q^95 + 21 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$-1$	$1$	$1$

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 $

$2$	−1.34067	−	0.450129i	−0.947994	−	0.318290i
$2$	−1.34067	−	0.450129i	−0.947994	−	0.318290i
$3$		0			0
$3$		0			0
$4$	1.59477	+	1.20695i	0.797384	+	0.603473i
$5$	−0.254102	−	2.22158i	−0.113638	−	0.993522i
$5$	−0.254102	−	2.22158i	−0.113638	−	0.993522i
$6$		0			0
$7$		−	2.64265i		−	0.998827i	−0.866364	−	0.499414i	$-0.833549\pi$
$7$		−	2.64265i		−	0.998827i	0.866364	−	0.499414i	$-0.166451\pi$
$8$	−1.59477	−	2.33596i	−0.563835	−	0.825887i
$9$		0			0
$10$	−0.659335	+	3.09278i	−0.208500	+	0.978022i
$11$			1.51363i			0.456377i	0.973617	+	0.228189i	$0.0732803\pi$
$11$			1.51363i			0.456377i	−0.973617	+	0.228189i	$0.926720\pi$
$12$		0			0
$13$	−3.87086			−1.07358			−0.536792	−	0.843714i	$-0.680364\pi$
$13$	−3.87086			−1.07358			−0.536792	+	0.843714i	$0.680364\pi$
$14$	−1.18953	+	3.54291i	−0.317916	+	0.946882i
$15$		0			0
$16$	1.08656	+	3.84959i	0.271641	+	0.962399i
$17$			3.31415i			0.803800i	0.915684	+	0.401900i	$0.131650\pi$
$17$			3.31415i			0.803800i	−0.915684	+	0.401900i	$0.868350\pi$
$18$		0			0
$19$		−	7.08582i		−	1.62560i	−0.582545	−	0.812799i	$-0.697943\pi$
$19$		−	7.08582i		−	1.62560i	0.582545	−	0.812799i	$-0.302057\pi$
$20$	2.27610	−	3.84959i	0.508951	−	0.860796i
$21$		0			0
$22$	0.681331	−	2.02927i	0.145260	−	0.432643i
$23$		−	4.82778i		−	1.00666i	−0.864094	−	0.503331i	$-0.832108\pi$
$23$		−	4.82778i		−	1.00666i	0.864094	−	0.503331i	$-0.167892\pi$
$24$		0			0
$25$	−4.87086	+	1.12902i	−0.974173	+	0.225803i
$26$	5.18953	+	1.74239i	1.01775	+	0.341711i
$27$		0			0
$28$	3.18953	−	4.21441i	0.602765	−	0.796448i
$29$		−	2.18513i		−	0.405769i	−0.979203	−	0.202885i	$-0.934968\pi$
$29$		−	2.18513i		−	0.405769i	0.979203	−	0.202885i	$-0.0650316\pi$
$30$		0			0
$31$	−7.36266			−1.32237			−0.661187	−	0.750222i	$-0.729947\pi$
$31$	−7.36266			−1.32237			−0.661187	+	0.750222i	$0.729947\pi$
$32$	0.276098	−	5.65011i	0.0488076	−	0.998808i
$33$		0			0
$34$	1.49180	−	4.44317i	0.255841	−	0.761997i
$35$	−5.87086	+	0.671502i	−0.992357	+	0.113504i
$36$		0			0
$37$	7.87086			1.29396			0.646981	−	0.762506i	$-0.276031\pi$
$37$	7.87086			1.29396			0.646981	+	0.762506i	$0.276031\pi$
$38$	−3.18953	+	9.49971i	−0.517411	+	1.54106i
$39$		0			0
$40$	−4.78430	+	4.13648i	−0.756464	+	0.654035i
$41$	−8.72532			−1.36267			−0.681333	−	0.731973i	$-0.738600\pi$
$41$	−8.72532			−1.36267			−0.681333	+	0.731973i	$0.738600\pi$
$42$		0			0
$43$	−1.01641			−0.155001			−0.0775003	−	0.996992i	$-0.524694\pi$
$43$	−1.01641			−0.155001			−0.0775003	+	0.996992i	$0.524694\pi$
$44$	−1.82687	+	2.41389i	−0.275411	+	0.363908i
$45$		0			0
$46$	−2.17313	+	6.47244i	−0.320410	+	0.954309i
$47$		−	7.08582i		−	1.03357i	−0.856114	−	0.516786i	$-0.827128\pi$
$47$		−	7.08582i		−	1.03357i	0.856114	−	0.516786i	$-0.172872\pi$
$48$		0			0
$49$	0.0164068			0.00234382
$50$	7.03840	+	0.678887i	0.995380	+	0.0960091i
$51$		0			0
$52$	−6.17313	−	4.67192i	−0.856059	−	0.647879i
$53$	4.50820			0.619249			0.309625	−	0.950859i	$-0.399797\pi$
$53$	4.50820			0.619249			0.309625	+	0.950859i	$0.399797\pi$
$54$		0			0
$55$	3.36266	−	0.384617i	0.453421	−	0.0518617i
$56$	−6.17313	+	4.21441i	−0.824919	+	0.563174i
$57$		0			0
$58$	−0.983593	+	2.92953i	−0.129152	+	0.384667i
$59$		−	6.79893i		−	0.885145i	−0.896733	−	0.442573i	$-0.854066\pi$
$59$		−	6.79893i		−	0.885145i	0.896733	−	0.442573i	$-0.145934\pi$
$60$		0			0
$61$		−	3.60104i		−	0.461065i	−0.973065	−	0.230533i	$-0.925953\pi$
$61$		−	3.60104i		−	0.461065i	0.973065	−	0.230533i	$-0.0740469\pi$
$62$	9.87086	+	3.31415i	1.25360	+	0.420898i
$63$		0			0
$64$	−2.91344	+	7.45063i	−0.364180	+	0.931329i
$65$	0.983593	+	8.59945i	0.122000	+	1.06663i
$66$		0			0
$67$	1.01641			0.124174			0.0620869	−	0.998071i	$-0.480224\pi$
$67$	1.01641			0.124174			0.0620869	+	0.998071i	$0.480224\pi$
$68$	−4.00000	+	5.28530i	−0.485071	+	0.640937i
$69$		0			0
$70$	8.17313	+	1.74239i	0.976876	+	0.208255i
$71$	6.72532			0.798149			0.399074	−	0.916919i	$-0.369331\pi$
$71$	6.72532			0.798149			0.399074	+	0.916919i	$0.369331\pi$
$72$		0			0
$73$			15.5146i			1.81585i	0.419132	+	0.907925i	$0.362334\pi$
$73$			15.5146i			1.81585i	−0.419132	+	0.907925i	$0.637666\pi$
$74$	−10.5522	−	3.54291i	−1.22667	−	0.411855i
$75$		0			0
$76$	8.55220	−	11.3002i	0.981004	−	1.29622i
$77$	4.00000			0.455842
$78$		0			0
$79$	7.36266			0.828364			0.414182	−	0.910194i	$-0.364068\pi$
$79$	7.36266			0.828364			0.414182	+	0.910194i	$0.364068\pi$
$80$	8.27610	−	3.39208i	0.925296	−	0.379246i
$81$		0			0
$82$	11.6977	+	3.92752i	1.29180	+	0.433723i
$83$	7.74173			0.849765			0.424883	−	0.905248i	$-0.360315\pi$
$83$	7.74173			0.849765			0.424883	+	0.905248i	$0.360315\pi$
$84$		0			0
$85$	7.36266	−	0.842131i	0.798593	−	0.0913420i
$86$	1.36266	+	0.457515i	0.146940	+	0.0493351i
$87$		0			0
$88$	3.53579	−	2.41389i	0.376916	−	0.257322i
$89$	14.7581			1.56436			0.782180	−	0.623053i	$-0.214108\pi$
$89$	14.7581			1.56436			0.782180	+	0.623053i	$0.214108\pi$
$90$		0			0
$91$			10.2293i			1.07233i
$92$	5.82687	−	7.69919i	0.607493	−	0.802696i
$93$		0			0
$94$	−3.18953	+	9.49971i	−0.328975	+	0.979820i
$95$	−15.7417	+	1.80052i	−1.61507	+	0.184729i
$96$		0			0
$97$		−	11.1444i		−	1.13154i	−0.824563	−	0.565769i	$-0.808579\pi$
$97$		−	11.1444i		−	1.13154i	0.824563	−	0.565769i	$-0.191421\pi$
$98$	−0.0219960	−	0.00738516i	−0.00222193	−	0.000746014i
$99$		0			0
$100$	−9.13056	−	4.07835i	−0.913056	−	0.407835i
$101$			13.3295i			1.32633i	0.748471	+	0.663167i	$0.230788\pi$
$101$			13.3295i			1.32633i	−0.748471	+	0.663167i	$0.769212\pi$
$102$		0			0
$103$		−	0.958386i		−	0.0944326i	−0.998885	−	0.0472163i	$-0.984965\pi$
$103$		−	0.958386i		−	0.0944326i	0.998885	−	0.0472163i	$-0.0150350\pi$
$104$	6.17313	+	9.04219i	0.605325	+	0.886660i
$105$		0			0
$106$	−6.04399	−	2.02927i	−0.587044	−	0.197101i
$107$	−4.00000			−0.386695			−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000			−0.386695			−0.193347	+	0.981130i	$0.561934\pi$
$108$		0			0
$109$		−	0.769233i		−	0.0736792i	−0.999321	−	0.0368396i	$-0.988271\pi$
$109$		−	0.769233i		−	0.0736792i	0.999321	−	0.0368396i	$-0.0117291\pi$
$110$	−4.68133	−	0.997991i	−0.446347	−	0.0951547i
$111$		0			0
$112$	10.1731	−	2.87141i	0.961270	−	0.271322i
$113$			14.4585i			1.36014i	0.733146	+	0.680071i	$0.238051\pi$
$113$			14.4585i			1.36014i	−0.733146	+	0.680071i	$0.761949\pi$
$114$		0			0
$115$	−10.7253	+	1.22675i	−1.00014	+	0.114395i
$116$	2.63734	−	3.48478i	0.244871	−	0.323554i
$117$		0			0
$118$	−3.06040	+	9.11509i	−0.281733	+	0.839112i
$119$	8.75814			0.802857
$120$		0			0
$121$	8.70892			0.791720
$122$	−1.62093	+	4.82778i	−0.146752	+	0.437087i
$123$		0			0
$124$	−11.7417	−	8.88633i	−1.05444	−	0.798016i
$125$	3.74590	+	10.5341i	0.335043	+	0.942203i
$126$		0			0
$127$		−	11.5290i		−	1.02303i	−0.859274	−	0.511516i	$-0.829084\pi$
$127$		−	11.5290i		−	1.02303i	0.859274	−	0.511516i	$-0.170916\pi$
$128$	7.25969	−	8.67738i	0.641672	−	0.766979i
$129$		0			0
$130$	2.55220	−	11.9717i	0.223842	−	1.04999i
$131$		−	7.37270i		−	0.644156i	−0.946713	−	0.322078i	$-0.895619\pi$
$131$		−	7.37270i		−	0.644156i	0.946713	−	0.322078i	$-0.104381\pi$
$132$		0			0
$133$	−18.7253			−1.62369
$134$	−1.36266	−	0.457515i	−0.117716	−	0.0395232i
$135$		0			0
$136$	7.74173	−	5.28530i	0.663848	−	0.453211i
$137$		−	3.88792i		−	0.332167i	−0.986112	−	0.166084i	$-0.946888\pi$
$137$		−	3.88792i		−	0.332167i	0.986112	−	0.166084i	$-0.0531122\pi$
$138$		0			0
$139$			14.6291i			1.24083i	0.784275	+	0.620414i	$0.213035\pi$
$139$			14.6291i			1.24083i	−0.784275	+	0.620414i	$0.786965\pi$
$140$	−10.1731	−	6.01493i	−0.859786	−	0.508354i
$141$		0			0
$142$	−9.01641	−	3.02727i	−0.756640	−	0.254042i
$143$		−	5.85907i		−	0.489960i
$144$		0			0
$145$	−4.85446	+	0.555246i	−0.403141	+	0.0461107i
$146$	6.98359	−	20.7999i	0.577966	−	1.72141i
$147$		0			0
$148$	12.5522	+	9.49971i	1.03178	+	0.780871i
$149$		−	11.0715i		−	0.907010i	−0.891254	−	0.453505i	$-0.850173\pi$
$149$		−	11.0715i		−	0.907010i	0.891254	−	0.453505i	$-0.149827\pi$
$150$		0			0
$151$	0.637339			0.0518659			0.0259329	−	0.999664i	$-0.491744\pi$
$151$	0.637339			0.0518659			0.0259329	+	0.999664i	$0.491744\pi$
$152$	−16.5522	+	11.3002i	−1.34256	+	0.916569i
$153$		0			0
$154$	−5.36266	−	1.80052i	−0.432136	−	0.145090i
$155$	1.87086	+	16.3568i	0.150271	+	1.31381i
$156$		0			0
$157$	−0.129135			−0.0103061			−0.00515306	−	0.999987i	$-0.501640\pi$
$157$	−0.129135			−0.0103061			−0.00515306	+	0.999987i	$0.501640\pi$
$158$	−9.87086	−	3.31415i	−0.785284	−	0.263660i
$159$		0			0
$160$	−12.6224	+	0.822329i	−0.997885	+	0.0650108i
$161$	−12.7581			−1.00548
$162$		0			0
$163$	19.4835			1.52606			0.763031	−	0.646362i	$-0.223710\pi$
$163$	19.4835			1.52606			0.763031	+	0.646362i	$0.223710\pi$
$164$	−13.9149	−	10.5310i	−1.08657	−	0.822332i
$165$		0			0
$166$	−10.3791	−	3.48478i	−0.805572	−	0.270471i
$167$			1.80052i			0.139328i	0.997571	+	0.0696641i	$0.0221928\pi$
$167$			1.80052i			0.139328i	−0.997571	+	0.0696641i	$0.977807\pi$
$168$		0			0
$169$	1.98359			0.152584
$170$	−10.2499	−	2.18513i	−0.786134	−	0.167592i
$171$		0			0
$172$	−1.62093	−	1.22675i	−0.123595	−	0.0935386i
$173$	−23.2335			−1.76641			−0.883206	−	0.468985i	$-0.844620\pi$
$173$	−23.2335			−1.76641			−0.883206	+	0.468985i	$0.844620\pi$
$174$		0			0
$175$	2.98359	+	12.8720i	0.225538	+	0.973031i
$176$	−5.82687	+	1.64466i	−0.439217	+	0.123971i
$177$		0			0
$178$	−19.7857	−	6.64307i	−1.48300	−	0.497919i
$179$		−	2.85664i		−	0.213515i	−0.994285	−	0.106757i	$-0.965953\pi$
$179$		−	2.85664i		−	0.213515i	0.994285	−	0.106757i	$-0.0340468\pi$
$180$		0			0
$181$			5.28530i			0.392853i	0.980519	+	0.196427i	$0.0629337\pi$
$181$			5.28530i			0.392853i	−0.980519	+	0.196427i	$0.937066\pi$
$182$	4.60453	−	13.7141i	0.341310	−	1.01656i
$183$		0			0
$184$	−11.2775	+	7.69919i	−0.831390	+	0.567592i
$185$	−2.00000	−	17.4858i	−0.147043	−	1.28558i
$186$		0			0
$187$	−5.01641			−0.366836
$188$	8.55220	−	11.3002i	0.623733	−	0.824154i
$189$		0			0
$190$	21.9149	+	4.67192i	1.58987	+	0.338937i
$191$	5.96719			0.431770			0.215885	−	0.976419i	$-0.430736\pi$
$191$	5.96719			0.431770			0.215885	+	0.976419i	$0.430736\pi$
$192$		0			0
$193$		−	14.9409i		−	1.07547i	−0.843115	−	0.537733i	$-0.819281\pi$
$193$		−	14.9409i		−	1.07547i	0.843115	−	0.537733i	$-0.180719\pi$
$194$	−5.01641	+	14.9409i	−0.360157	+	1.07269i
$195$		0			0
$196$	0.0261649	+	0.0198021i	0.00186892	+	0.00141443i
$197$	3.23353			0.230379			0.115190	−	0.993344i	$-0.463252\pi$
$197$	3.23353			0.230379			0.115190	+	0.993344i	$0.463252\pi$
$198$		0			0
$199$	8.12080			0.575668			0.287834	−	0.957680i	$-0.407065\pi$
$199$	8.12080			0.575668			0.287834	+	0.957680i	$0.407065\pi$
$200$	10.4052	+	9.57764i	0.735761	+	0.677241i
$201$		0			0
$202$	6.00000	−	17.8704i	0.422159	−	1.25736i
$203$	−5.77454			−0.405293
$204$		0			0
$205$	2.21712	+	19.3840i	0.154850	+	1.35384i
$206$	−0.431398	+	1.28488i	−0.0300569	+	0.0895215i
$207$		0			0
$208$	−4.20594	−	14.9013i	−0.291630	−	1.03322i
$209$	10.7253			0.741886
$210$		0			0
$211$		−	13.7141i		−	0.944119i	−0.881567	−	0.472059i	$-0.843511\pi$
$211$		−	13.7141i		−	0.944119i	0.881567	−	0.472059i	$-0.156489\pi$
$212$	7.18953	+	5.44116i	0.493779	+	0.373700i
$213$		0			0
$214$	5.36266	+	1.80052i	0.366584	+	0.123081i
$215$	0.258271	+	2.25803i	0.0176139	+	0.153997i
$216$		0			0
$217$			19.4569i			1.32082i
$218$	−0.346255	+	1.03128i	−0.0234513	+	0.0698474i
$219$		0			0
$220$	5.82687	+	3.44518i	0.392848	+	0.232274i
$221$		−	12.8286i		−	0.862947i
$222$		0			0
$223$		−	9.84472i		−	0.659251i	−0.944112	−	0.329626i	$-0.893077\pi$
$223$		−	9.84472i		−	0.659251i	0.944112	−	0.329626i	$-0.106923\pi$
$224$	−14.9313	−	0.729629i	−0.997637	−	0.0487504i
$225$		0			0
$226$	6.50820	−	19.3840i	0.432919	−	1.28941i
$227$	−5.70892			−0.378914			−0.189457	−	0.981889i	$-0.560673\pi$
$227$	−5.70892			−0.378914			−0.189457	+	0.981889i	$0.560673\pi$
$228$		0			0
$229$			0.769233i			0.0508324i	0.999677	+	0.0254162i	$0.00809109\pi$
$229$			0.769233i			0.0508324i	−0.999677	+	0.0254162i	$0.991909\pi$
$230$	14.9313	+	3.18312i	0.984538	+	0.209889i
$231$		0			0
$232$	−5.10439	+	3.48478i	−0.335120	+	0.228787i
$233$		−	18.4008i		−	1.20548i	−0.797939	−	0.602739i	$-0.794076\pi$
$233$		−	18.4008i		−	1.20548i	0.797939	−	0.602739i	$-0.205924\pi$
$234$		0			0
$235$	−15.7417	+	1.80052i	−1.02688	+	0.117453i
$236$	8.20594	−	10.8427i	0.534161	−	0.705800i
$237$		0			0
$238$	−11.7417	−	3.94229i	−0.761103	−	0.255541i
$239$	10.0328			0.648969			0.324484	−	0.945891i	$-0.394809\pi$
$239$	10.0328			0.648969			0.324484	+	0.945891i	$0.394809\pi$
$240$		0			0
$241$	10.7581			0.692992			0.346496	−	0.938051i	$-0.387371\pi$
$241$	10.7581			0.692992			0.346496	+	0.938051i	$0.387371\pi$
$242$	−11.6757	−	3.92014i	−0.750545	−	0.251996i
$243$		0			0
$244$	4.34625	−	5.74281i	0.278240	−	0.367646i
$245$	−0.00416898	−	0.0364490i	−0.000266347	−	0.00232864i
$246$		0			0
$247$			27.4282i			1.74522i
$248$	11.7417	+	17.1989i	0.745601	+	1.09213i
$249$		0			0
$250$	−0.280267	−	15.8089i	−0.0177256	−	0.999843i
$251$			12.6580i			0.798966i	0.916741	+	0.399483i	$0.130810\pi$
$251$			12.6580i			0.798966i	−0.916741	+	0.399483i	$0.869190\pi$
$252$		0			0
$253$	7.30749			0.459418
$254$	−5.18953	+	15.4565i	−0.325620	+	0.969827i
$255$		0			0
$256$	−13.6388	+	8.36566i	−0.852422	+	0.522854i
$257$		−	13.3110i		−	0.830316i	−0.909749	−	0.415158i	$-0.863726\pi$
$257$		−	13.3110i		−	0.830316i	0.909749	−	0.415158i	$-0.136274\pi$
$258$		0			0
$259$		−	20.7999i		−	1.29244i
$260$	−8.81047	+	14.9013i	−0.546402	+	0.924137i
$261$		0			0
$262$	−3.31867	+	9.88432i	−0.205028	+	0.610656i
$263$			18.4256i			1.13617i	0.822969	+	0.568087i	$0.192316\pi$
$263$			18.4256i			1.13617i	−0.822969	+	0.568087i	$0.807684\pi$
$264$		0			0
$265$	−1.14554	−	10.0153i	−0.0703701	−	0.615238i
$266$	25.1044	+	8.42882i	1.53925	+	0.516804i
$267$		0			0
$268$	1.62093	+	1.22675i	0.0990142	+	0.0749356i
$269$		−	3.86940i		−	0.235921i	−0.993018	−	0.117961i	$-0.962364\pi$
$269$		−	3.86940i		−	0.235921i	0.993018	−	0.117961i	$-0.0376357\pi$
$270$		0			0
$271$	−17.3955			−1.05670			−0.528350	−	0.849027i	$-0.677189\pi$
$271$	−17.3955			−1.05670			−0.528350	+	0.849027i	$0.677189\pi$
$272$	−12.7581	+	3.60104i	−0.773576	+	0.218345i
$273$		0			0
$274$	−1.75007	+	5.21240i	−0.105725	+	0.314893i
$275$	−1.70892	−	7.37270i	−0.103052	−	0.444591i
$276$		0			0
$277$	−0.887271			−0.0533110			−0.0266555	−	0.999645i	$-0.508486\pi$
$277$	−0.887271			−0.0533110			−0.0266555	+	0.999645i	$0.508486\pi$
$278$	6.58501	−	19.6128i	0.394943	−	1.17630i
$279$		0			0
$280$	10.9313	+	12.6432i	0.653268	+	0.755577i
$281$	13.4835			0.804356			0.402178	−	0.915562i	$-0.368253\pi$
$281$	13.4835			0.804356			0.402178	+	0.915562i	$0.368253\pi$
$282$		0			0
$283$	28.4342			1.69024			0.845120	−	0.534577i	$-0.179529\pi$
$283$	28.4342			1.69024			0.845120	+	0.534577i	$0.179529\pi$
$284$	10.7253	+	8.11710i	0.636431	+	0.481661i
$285$		0			0
$286$	−2.63734	+	7.85505i	−0.155949	+	0.464479i
$287$			23.0580i			1.36107i
$288$		0			0
$289$	6.01641			0.353906
$290$	6.75814	+	1.44073i	0.396851	+	0.0846029i
$291$		0			0
$292$	−18.7253	+	24.7422i	−1.09582	+	1.44793i
$293$	−7.99166			−0.466878			−0.233439	−	0.972371i	$-0.574998\pi$
$293$	−7.99166			−0.466878			−0.233439	+	0.972371i	$0.574998\pi$
$294$		0			0
$295$	−15.1044	+	1.72762i	−0.879412	+	0.100586i
$296$	−12.5522	−	18.3860i	−0.729582	−	1.06867i
$297$		0			0
$298$	−4.98359	+	14.8431i	−0.288692	+	0.859840i
$299$			18.6877i			1.08074i
$300$		0			0
$301$			2.68601i			0.154819i
$302$	−0.854458	−	0.286885i	−0.0491685	−	0.0165084i
$303$		0			0
$304$	27.2775	−	7.69919i	1.56447	−	0.441579i
$305$	−8.00000	+	0.915029i	−0.458079	+	0.0523944i
$306$		0			0
$307$	−17.4506			−0.995961			−0.497980	−	0.867188i	$-0.665925\pi$
$307$	−17.4506			−0.995961			−0.497980	+	0.867188i	$0.665925\pi$
$308$	6.37907	+	4.82778i	0.363481	+	0.275088i
$309$		0			0
$310$	4.85446	−	22.7711i	0.275715	−	1.29331i
$311$	−21.4506			−1.21635			−0.608177	−	0.793801i	$-0.708099\pi$
$311$	−21.4506			−1.21635			−0.608177	+	0.793801i	$0.708099\pi$
$312$		0			0
$313$		−	7.73879i		−	0.437422i	−0.975790	−	0.218711i	$-0.929815\pi$
$313$		−	7.73879i		−	0.437422i	0.975790	−	0.218711i	$-0.0701853\pi$
$314$	0.173127	+	0.0581276i	0.00977014	+	0.00328033i
$315$		0			0
$316$	11.7417	+	8.88633i	0.660524	+	0.499895i
$317$	11.2335			0.630938			0.315469	−	0.948936i	$-0.397838\pi$
$317$	11.2335			0.630938			0.315469	+	0.948936i	$0.397838\pi$
$318$		0			0
$319$	3.30749			0.185184
$320$	17.2925	+	4.57922i	0.966680	+	0.255986i
$321$		0			0
$322$	17.1044	+	5.74281i	0.953190	+	0.320034i
$323$	23.4835			1.30665
$324$		0			0
$325$	18.8545	−	4.37027i	1.04586	−	0.242419i
$326$	−26.1208	−	8.77008i	−1.44670	−	0.485730i
$327$		0			0
$328$	13.9149	+	20.3820i	0.768319	+	1.12541i
$329$	−18.7253			−1.03236
$330$		0			0
$331$			8.00084i			0.439766i	0.975526	+	0.219883i	$0.0705676\pi$
$331$			8.00084i			0.439766i	−0.975526	+	0.219883i	$0.929432\pi$
$332$	12.3463	+	9.34385i	0.677589	+	0.512810i
$333$		0			0
$334$	0.810466	−	2.41389i	0.0443467	−	0.132082i
$335$	−0.258271	−	2.25803i	−0.0141108	−	0.123369i
$336$		0			0
$337$		−	21.5692i		−	1.17495i	−0.809243	−	0.587474i	$-0.800123\pi$
$337$		−	21.5692i		−	1.17495i	0.809243	−	0.587474i	$-0.199877\pi$
$338$	−2.65933	−	0.892874i	−0.144649	−	0.0485659i
$339$		0			0
$340$	12.7581	+	7.54333i	0.691907	+	0.409095i
$341$		−	11.1444i		−	0.603501i
$342$		0			0
$343$		−	18.5419i		−	1.00117i
$344$	1.62093	+	2.37429i	0.0873948	+	0.128013i
$345$		0			0
$346$	31.1484	+	10.4581i	1.67455	+	0.562231i
$347$	21.7089			1.16540			0.582698	−	0.812689i	$-0.301997\pi$
$347$	21.7089			1.16540			0.582698	+	0.812689i	$0.301997\pi$
$348$		0			0
$349$		−	24.7422i		−	1.32442i	−0.749318	−	0.662211i	$-0.769618\pi$
$349$		−	24.7422i		−	1.32442i	0.749318	−	0.662211i	$-0.230382\pi$
$350$	1.79406	−	18.6000i	0.0958965	−	0.994213i
$351$		0			0
$352$	8.55220	+	0.417910i	0.455834	+	0.0222747i
$353$			3.31415i			0.176394i	0.996103	+	0.0881972i	$0.0281106\pi$
$353$			3.31415i			0.176394i	−0.996103	+	0.0881972i	$0.971889\pi$
$354$		0			0
$355$	−1.70892	−	14.9409i	−0.0906998	−	0.792979i
$356$	23.5358	+	17.8123i	1.24739	+	0.944048i
$357$		0			0
$358$	−1.28586	+	3.82979i	−0.0679596	+	0.202411i
$359$	−16.7581			−0.884461			−0.442230	−	0.896902i	$-0.645813\pi$
$359$	−16.7581			−0.884461			−0.442230	+	0.896902i	$0.645813\pi$
$360$		0			0
$361$	−31.2088			−1.64257
$362$	2.37907	−	7.08582i	0.125041	−	0.372422i
$363$		0			0
$364$	−12.3463	+	16.3134i	−0.647120	+	0.855055i
$365$	34.4671	−	3.94229i	1.80409	−	0.206349i
$366$		0			0
$367$			28.5324i			1.48938i	0.667411	+	0.744690i	$0.267403\pi$
$367$			28.5324i			1.48938i	−0.667411	+	0.744690i	$0.732597\pi$
$368$	18.5850	−	5.24569i	0.968811	−	0.273451i
$369$		0			0
$370$	−5.18953	+	24.3428i	−0.269791	+	1.26552i
$371$		−	11.9136i		−	0.618523i
$372$		0			0
$373$	−37.5798			−1.94581			−0.972904	−	0.231211i	$-0.925731\pi$
$373$	−37.5798			−1.94581			−0.972904	+	0.231211i	$0.925731\pi$
$374$	6.72532	+	2.25803i	0.347758	+	0.116760i
$375$		0			0
$376$	−16.5522	+	11.3002i	−0.853614	+	0.582765i
$377$			8.45836i			0.435628i
$378$		0			0
$379$			6.74456i			0.346445i	0.984883	+	0.173222i	$0.0554179\pi$
$379$			6.74456i			0.346445i	−0.984883	+	0.173222i	$0.944582\pi$
$380$	−27.2775	−	16.1280i	−1.39931	−	0.827349i
$381$		0			0
$382$	−8.00000	−	2.68601i	−0.409316	−	0.137428i
$383$			21.8312i			1.11552i	0.830001	+	0.557762i	$0.188340\pi$
$383$			21.8312i			1.11552i	−0.830001	+	0.557762i	$0.811660\pi$
$384$		0			0
$385$	−1.01641	−	8.88633i	−0.0518009	−	0.452889i
$386$	−6.72532	+	20.0307i	−0.342310	+	1.01954i
$387$		0			0
$388$	13.4506	−	17.7727i	0.682853	−	0.902270i
$389$			8.81344i			0.446859i	0.974720	+	0.223429i	$0.0717252\pi$
$389$			8.81344i			0.446859i	−0.974720	+	0.223429i	$0.928275\pi$
$390$		0			0
$391$	16.0000			0.809155
$392$	−0.0261649	−	0.0383256i	−0.00132153	−	0.00193573i
$393$		0			0
$394$	−4.33508	−	1.45551i	−0.218398	−	0.0733273i
$395$	−1.87086	−	16.3568i	−0.0941334	−	0.822998i
$396$		0			0
$397$	0.821644			0.0412372			0.0206186	−	0.999787i	$-0.493436\pi$
$397$	0.821644			0.0412372			0.0206186	+	0.999787i	$0.493436\pi$
$398$	−10.8873	−	3.65541i	−0.545730	−	0.183229i
$399$		0			0
$400$	−9.63876	−	17.5241i	−0.481938	−	0.876205i
$401$	12.7253			0.635472			0.317736	−	0.948179i	$-0.397077\pi$
$401$	12.7253			0.635472			0.317736	+	0.948179i	$0.397077\pi$
$402$		0			0
$403$	28.4999			1.41968
$404$	−16.0880	+	21.2574i	−0.800407	+	1.05760i
$405$		0			0
$406$	7.74173	+	2.59929i	0.384216	+	0.129001i
$407$			11.9136i			0.590535i
$408$		0			0
$409$	−2.25827			−0.111664			−0.0558321	−	0.998440i	$-0.517781\pi$
$409$	−2.25827			−0.111664			−0.0558321	+	0.998440i	$0.517781\pi$
$410$	5.75291	−	26.9855i	0.284116	−	1.33272i
$411$		0			0
$412$	1.15672	−	1.52840i	0.0569875	−	0.0752990i
$413$	−17.9672			−0.884107
$414$		0			0
$415$	−1.96719	−	17.1989i	−0.0965654	−	0.844261i
$416$	−1.06874	+	21.8708i	−0.0523991	+	1.07231i
$417$		0			0
$418$	−14.3791	−	4.82778i	−0.703303	−	0.236135i
$419$		−	33.4579i		−	1.63453i	−0.576264	−	0.817263i	$-0.695490\pi$
$419$		−	33.4579i		−	1.63453i	0.576264	−	0.817263i	$-0.304510\pi$
$420$		0			0
$421$		−	11.3398i		−	0.552669i	−0.961061	−	0.276335i	$-0.910880\pi$
$421$		−	11.3398i		−	0.552669i	0.961061	−	0.276335i	$-0.0891198\pi$
$422$	−6.17313	+	18.3860i	−0.300503	+	0.895018i
$423$		0			0
$424$	−7.18953	−	10.5310i	−0.349155	−	0.511430i
$425$	−3.74173	−	16.1428i	−0.181501	−	0.783040i
$426$		0			0
$427$	−9.51627			−0.460525
$428$	−6.37907	−	4.82778i	−0.308344	−	0.233360i
$429$		0			0
$430$	0.670152	−	3.14352i	0.0323176	−	0.151594i
$431$	−10.6597			−0.513459			−0.256730	−	0.966483i	$-0.582645\pi$
$431$	−10.6597			−0.513459			−0.256730	+	0.966483i	$0.582645\pi$
$432$		0			0
$433$			26.5132i			1.27414i	0.770805	+	0.637072i	$0.219854\pi$
$433$			26.5132i			1.27414i	−0.770805	+	0.637072i	$0.780146\pi$
$434$	8.75814	−	26.0852i	0.420404	−	1.25213i
$435$		0			0
$436$	0.928423	−	1.22675i	0.0444634	−	0.0587506i
$437$	−34.2088			−1.63643
$438$		0			0
$439$	−32.8789			−1.56923			−0.784613	−	0.619986i	$-0.787138\pi$
$439$	−32.8789			−1.56923			−0.784613	+	0.619986i	$0.787138\pi$
$440$	−6.26111	−	7.24167i	−0.298487	−	0.345233i
$441$		0			0
$442$	−5.77454	+	17.1989i	−0.274667	+	0.818068i
$443$	5.70892			0.271239			0.135619	−	0.990761i	$-0.456698\pi$
$443$	5.70892			0.271239			0.135619	+	0.990761i	$0.456698\pi$
$444$		0			0
$445$	−3.75007	−	32.7864i	−0.177770	−	1.55423i
$446$	−4.43140	+	13.1985i	−0.209833	+	0.624966i
$447$		0			0
$448$	19.6894	+	7.69919i	0.930237	+	0.363753i
$449$	−2.00000			−0.0943858			−0.0471929	−	0.998886i	$-0.515028\pi$
$449$	−2.00000			−0.0943858			−0.0471929	+	0.998886i	$0.515028\pi$
$450$		0			0
$451$		−	13.2069i		−	0.621890i
$452$	−17.4506	+	23.0580i	−0.820809	+	1.08456i
$453$		0			0
$454$	7.65375	+	2.56975i	0.359208	+	0.120604i
$455$	22.7253	−	2.59929i	1.06538	−	0.121857i
$456$		0			0
$457$			3.94229i			0.184413i	0.995740	+	0.0922064i	$0.0293920\pi$
$457$			3.94229i			0.184413i	−0.995740	+	0.0922064i	$0.970608\pi$
$458$	0.346255	−	1.03128i	0.0161794	−	0.0481888i
$459$		0			0
$460$	−18.5850	−	10.9885i	−0.866531	−	0.512342i
$461$			33.8969i			1.57874i	0.613920	+	0.789369i	$0.289592\pi$
$461$			33.8969i			1.57874i	−0.613920	+	0.789369i	$0.710408\pi$
$462$		0			0
$463$			22.8688i			1.06280i	0.847120	+	0.531402i	$0.178335\pi$
$463$			22.8688i			1.06280i	−0.847120	+	0.531402i	$0.821665\pi$
$464$	8.41188	−	2.37429i	0.390512	−	0.110224i
$465$		0			0
$466$	−8.28275	+	24.6693i	−0.383691	+	1.14278i
$467$	−15.7417			−0.728440			−0.364220	−	0.931313i	$-0.618664\pi$
$467$	−15.7417			−0.728440			−0.364220	+	0.931313i	$0.618664\pi$
$468$		0			0
$469$		−	2.68601i		−	0.124028i
$470$	21.9149	+	4.67192i	1.01086	+	0.215500i
$471$		0			0
$472$	−15.8820	+	10.8427i	−0.731030	+	0.499076i
$473$		−	1.53847i		−	0.0707388i
$474$		0			0
$475$	8.00000	+	34.5140i	0.367065	+	1.58361i
$476$	13.9672	+	10.5706i	0.640185	+	0.484502i
$477$		0			0
$478$	−13.4506	−	4.51606i	−0.615218	−	0.206560i
$479$	20.6925			0.945465			0.472732	−	0.881206i	$-0.343268\pi$
$479$	20.6925			0.945465			0.472732	+	0.881206i	$0.343268\pi$
$480$		0			0
$481$	−30.4671			−1.38918
$482$	−14.4231	−	4.84255i	−0.656952	−	0.220572i
$483$		0			0
$484$	13.8887	+	10.5112i	0.631304	+	0.477781i
$485$	−24.7581	+	2.83180i	−1.12421	+	0.128586i
$486$		0			0
$487$		−	30.8401i		−	1.39750i	−0.715366	−	0.698750i	$-0.753740\pi$
$487$		−	30.8401i		−	1.39750i	0.715366	−	0.698750i	$-0.246260\pi$
$488$	−8.41188	+	5.74281i	−0.380788	+	0.259965i
$489$		0			0
$490$	−0.0108175	+	0.0507425i	−0.000488687	+	0.00229231i
$491$			10.9737i			0.495238i	0.968858	+	0.247619i	$0.0796481\pi$
$491$			10.9737i			0.495238i	−0.968858	+	0.247619i	$0.920352\pi$
$492$		0			0
$493$	7.24186			0.326157
$494$	12.3463	−	36.7721i	0.555484	−	1.65445i
$495$		0			0
$496$	−8.00000	−	28.3433i	−0.359211	−	1.27265i
$497$		−	17.7727i		−	0.797213i
$498$		0			0
$499$		−	3.71729i		−	0.166409i	−0.996533	−	0.0832044i	$-0.973485\pi$
$499$		−	3.71729i		−	0.166409i	0.996533	−	0.0832044i	$-0.0265154\pi$
$500$	−6.74031	+	21.3206i	−0.301436	+	0.953486i
$501$		0			0
$502$	5.69774	−	16.9701i	0.254302	−	0.757414i
$503$		−	39.9451i		−	1.78107i	−0.454919	−	0.890533i	$-0.650332\pi$
$503$		−	39.9451i		−	1.78107i	0.454919	−	0.890533i	$-0.349668\pi$
$504$		0			0
$505$	29.6126	−	3.38705i	1.31774	−	0.150722i
$506$	−9.79690	−	3.28932i	−0.435525	−	0.146228i
$507$		0			0
$508$	13.9149	−	18.3860i	0.617372	−	0.815749i
$509$		−	0.0728979i		−	0.00323114i	−0.999999	−	0.00161557i	$-0.999486\pi$
$509$		−	0.0728979i		−	0.00323114i	0.999999	−	0.00161557i	$-0.000514253\pi$
$510$		0			0
$511$	40.9997			1.81372
$512$	22.0506	−	5.07634i	0.974510	−	0.224345i
$513$		0			0
$514$	−5.99166	+	17.8456i	−0.264281	+	0.787134i
$515$	−2.12914	+	0.243528i	−0.0938209	+	0.0107311i
$516$		0			0
$517$	10.7253			0.471699
$518$	−9.36266	+	27.8857i	−0.411372	+	1.22523i
$519$		0			0
$520$	18.5194	−	16.0118i	0.812129	−	0.702162i
$521$	11.9672			0.524292			0.262146	−	0.965028i	$-0.415570\pi$
$521$	11.9672			0.524292			0.262146	+	0.965028i	$0.415570\pi$
$522$		0			0
$523$	−16.0656			−0.702501			−0.351250	−	0.936282i	$-0.614243\pi$
$523$	−16.0656			−0.702501			−0.351250	+	0.936282i	$0.614243\pi$
$524$	8.89845	−	11.7577i	0.388731	−	0.513639i
$525$		0			0
$526$	8.29392	−	24.7026i	0.361632	−	1.07709i
$527$		−	24.4010i		−	1.06292i
$528$		0			0
$529$	−0.307491			−0.0133692
$530$	−2.97241	+	13.9429i	−0.129113	+	0.605640i
$531$		0			0
$532$	−29.8625	−	22.6004i	−1.29470	−	0.979854i
$533$	33.7745			1.46294
$534$		0			0
$535$	1.01641	+	8.88633i	0.0439431	+	0.384190i
$536$	−1.62093	−	2.37429i	−0.0700136	−	0.102554i
$537$		0			0
$538$	−1.74173	+	5.18757i	−0.0750913	+	0.223652i
$539$			0.0248338i			0.00106967i
$540$		0			0
$541$			15.8559i			0.681698i	0.940118	+	0.340849i	$0.110715\pi$
$541$			15.8559i			0.681698i	−0.940118	+	0.340849i	$0.889285\pi$
$542$	23.3215	+	7.83021i	1.00174	+	0.336337i
$543$		0			0
$544$	18.7253	+	0.915029i	0.802842	+	0.0392316i
$545$	−1.70892	+	0.195463i	−0.0732019	+	0.00837274i
$546$		0			0
$547$	−4.95078			−0.211680			−0.105840	−	0.994383i	$-0.533753\pi$
$547$	−4.95078			−0.211680			−0.105840	+	0.994383i	$0.533753\pi$
$548$	4.69251	−	6.20033i	0.200454	−	0.264865i
$549$		0			0
$550$	−1.02759	+	10.6536i	−0.0438164	+	0.454269i
$551$	−15.4835			−0.659618
$552$		0			0
$553$		−	19.4569i		−	0.827393i
$554$	1.18953	+	0.399387i	0.0505385	+	0.0169683i
$555$		0			0
$556$	−17.6566	+	23.3301i	−0.748806	+	0.989416i
$557$	−1.26634			−0.0536565			−0.0268283	−	0.999640i	$-0.508541\pi$
$557$	−1.26634			−0.0536565			−0.0268283	+	0.999640i	$0.508541\pi$
$558$		0			0
$559$	3.93437			0.166406
$560$	−8.96408	−	21.8708i	−0.378801	−	0.924211i
$561$		0			0
$562$	−18.0768	−	6.06930i	−0.762524	−	0.256018i
$563$	−5.70892			−0.240602			−0.120301	−	0.992737i	$-0.538386\pi$
$563$	−5.70892			−0.240602			−0.120301	+	0.992737i	$0.538386\pi$
$564$		0			0
$565$	32.1208	−	3.67393i	1.35133	−	0.154564i
$566$	−38.1208	−	12.7991i	−1.60234	−	0.537986i
$567$		0			0
$568$	−10.7253	−	15.7101i	−0.450025	−	0.659181i
$569$	−2.75814			−0.115627			−0.0578135	−	0.998327i	$-0.518413\pi$
$569$	−2.75814			−0.115627			−0.0578135	+	0.998327i	$0.518413\pi$
$570$		0			0
$571$			25.7735i			1.07859i	0.842118	+	0.539294i	$0.181309\pi$
$571$			25.7735i			1.07859i	−0.842118	+	0.539294i	$0.818691\pi$
$572$	7.07158	−	9.34385i	0.295677	−	0.390686i
$573$		0			0
$574$	10.3791	−	30.9130i	0.433214	−	1.29028i
$575$	5.45065	+	23.5155i	0.227308	+	0.980663i
$576$		0			0
$577$			32.7135i			1.36188i	0.732338	+	0.680941i	$0.238429\pi$
$577$			32.7135i			1.36188i	−0.732338	+	0.680941i	$0.761571\pi$
$578$	−8.06599	−	2.70816i	−0.335501	−	0.112645i
$579$		0			0
$580$	−8.41188	−	4.97358i	−0.349284	−	0.206517i
$581$		−	20.4587i		−	0.848769i
$582$		0			0
$583$			6.82376i			0.282611i
$584$	36.2416	−	24.7422i	1.49969	−	1.02384i
$585$		0			0
$586$	10.7141	+	3.59728i	0.442597	+	0.148602i
$587$	−43.4835			−1.79475			−0.897377	−	0.441264i	$-0.854530\pi$
$587$	−43.4835			−1.79475			−0.897377	+	0.441264i	$0.854530\pi$
$588$		0			0
$589$			52.1705i			2.14965i
$590$	21.0276	+	4.48277i	0.865692	+	0.184553i
$591$		0			0
$592$	8.55220	+	30.2996i	0.351493	+	1.24531i
$593$		−	7.83021i		−	0.321548i	−0.986991	−	0.160774i	$-0.948601\pi$
$593$		−	7.83021i		−	0.321548i	0.986991	−	0.160774i	$-0.0513991\pi$
$594$		0			0
$595$	−2.22546	−	19.4569i	−0.0912348	−	0.797656i
$596$	13.3627	−	17.6564i	0.547356	−	0.723235i
$597$		0			0
$598$	8.41188	−	25.0539i	0.343987	−	1.02453i
$599$	−32.7581			−1.33846			−0.669231	−	0.743055i	$-0.733376\pi$
$599$	−32.7581			−1.33846			−0.669231	+	0.743055i	$0.733376\pi$
$600$		0			0
$601$	17.8074			0.726377			0.363189	−	0.931716i	$-0.381688\pi$
$601$	17.8074			0.726377			0.363189	+	0.931716i	$0.381688\pi$
$602$	1.20905	−	3.60104i	0.0492772	−	0.146767i
$603$		0			0
$604$	1.01641	+	0.769233i	0.0413570	+	0.0312997i
$605$	−2.21295	−	19.3476i	−0.0899692	−	0.786591i
$606$		0			0
$607$			3.41188i			0.138484i	0.997600	+	0.0692420i	$0.0220581\pi$
$607$			3.41188i			0.138484i	−0.997600	+	0.0692420i	$0.977942\pi$
$608$	−40.0357	−	1.95638i	−1.62366	−	0.0793416i
$609$		0			0
$610$	11.1372	+	2.37429i	0.450932	+	0.0961321i
$611$			27.4282i			1.10963i
$612$		0			0
$613$	−36.6290			−1.47943			−0.739716	−	0.672920i	$-0.765040\pi$
$613$	−36.6290			−1.47943			−0.739716	+	0.672920i	$0.765040\pi$
$614$	23.3955	+	7.85505i	0.944165	+	0.317004i
$615$		0			0
$616$	−6.37907	−	9.34385i	−0.257020	−	0.376474i
$617$			40.3979i			1.62636i	0.582012	+	0.813180i	$0.302266\pi$
$617$			40.3979i			1.62636i	−0.582012	+	0.813180i	$0.697734\pi$
$618$		0			0
$619$			24.5172i			0.985430i	0.870191	+	0.492715i	$0.163996\pi$
$619$			24.5172i			0.985430i	−0.870191	+	0.492715i	$0.836004\pi$
$620$	−16.7581	+	28.3433i	−0.673023	+	1.13829i
$621$		0			0
$622$	28.7581	+	9.65557i	1.15310	+	0.387153i
$623$		−	39.0006i		−	1.56252i
$624$		0			0
$625$	22.4506	−	10.9986i	0.898026	−	0.439943i
$626$	−3.48346	+	10.3751i	−0.139227	+	0.414674i
$627$		0			0
$628$	−0.205941	−	0.155859i	−0.00821793	−	0.00621947i
$629$			26.0852i			1.04009i
$630$		0			0
$631$	18.7805			0.747640			0.373820	−	0.927501i	$-0.378048\pi$
$631$	18.7805			0.747640			0.373820	+	0.927501i	$0.378048\pi$
$632$	−11.7417	−	17.1989i	−0.467061	−	0.684135i
$633$		0			0
$634$	−15.0604	−	5.05654i	−0.598125	−	0.200821i
$635$	−25.6126	+	2.92953i	−1.01640	+	0.116255i
$636$		0			0
$637$	−0.0635083			−0.00251629
$638$	−4.43424	−	1.48880i	−0.175553	−	0.0589421i
$639$		0			0
$640$	−21.1222	−	13.9231i	−0.834929	−	0.550358i
$641$	15.5163			0.612856			0.306428	−	0.951894i	$-0.400866\pi$
$641$	15.5163			0.612856			0.306428	+	0.951894i	$0.400866\pi$
$642$		0			0
$643$	−17.4506			−0.688186			−0.344093	−	0.938936i	$-0.611814\pi$
$643$	−17.4506			−0.688186			−0.344093	+	0.938936i	$0.611814\pi$
$644$	−20.3463	−	15.3984i	−0.801755	−	0.606781i
$645$		0			0
$646$	−31.4835	−	10.5706i	−1.23870	−	0.415895i
$647$		−	13.1403i		−	0.516600i	−0.966065	−	0.258300i	$-0.916838\pi$
$647$		−	13.1403i		−	0.516600i	0.966065	−	0.258300i	$-0.0831624\pi$
$648$		0			0
$649$	10.2911			0.403960
$650$	−27.2447	−	2.62788i	−1.06863	−	0.103074i
$651$		0			0
$652$	31.0716	+	23.5155i	1.21686	+	0.920937i
$653$	−14.7993			−0.579141			−0.289570	−	0.957157i	$-0.593512\pi$
$653$	−14.7993			−0.579141			−0.289570	+	0.957157i	$0.593512\pi$
$654$		0			0
$655$	−16.3791	+	1.87342i	−0.639983	+	0.0732004i
$656$	−9.48062	−	33.5890i	−0.370156	−	1.31143i
$657$		0			0
$658$	25.1044	+	8.42882i	0.978671	+	0.328590i
$659$			7.99614i			0.311485i	0.987798	+	0.155743i	$0.0497771\pi$
$659$			7.99614i			0.311485i	−0.987798	+	0.155743i	$0.950223\pi$
$660$		0			0
$661$		−	0.915029i		−	0.0355905i	−0.999842	−	0.0177953i	$-0.994335\pi$
$661$		−	0.915029i		−	0.0355905i	0.999842	−	0.0177953i	$-0.00566470\pi$
$662$	3.60142	−	10.7265i	0.139973	−	0.416896i
$663$		0			0
$664$	−12.3463	−	18.0844i	−0.479128	−	0.701810i
$665$	4.75814	+	41.5999i	0.184513	+	1.61317i
$666$		0			0
$667$	−10.5494			−0.408473
$668$	−2.17313	+	2.87141i	−0.0840808	+	0.111098i
$669$		0			0
$670$	−0.670152	+	3.14352i	−0.0258902	+	0.121445i
$671$	5.45065			0.210420
$672$		0			0
$673$			34.3978i			1.32594i	0.748647	+	0.662969i	$0.230704\pi$
$673$			34.3978i			1.32594i	−0.748647	+	0.662969i	$0.769296\pi$
$674$	−9.70892	+	28.9170i	−0.373973	+	1.11384i
$675$		0			0
$676$	3.16337	+	2.39409i	0.121668	+	0.0920804i
$677$	40.1676			1.54377			0.771884	−	0.635764i	$-0.219315\pi$
$677$	40.1676			1.54377			0.771884	+	0.635764i	$0.219315\pi$
$678$		0			0
$679$	−29.4506			−1.13021
$680$	−13.7089	−	15.8559i	−0.525713	−	0.608046i
$681$		0			0
$682$	−5.01641	+	14.9409i	−0.192088	+	0.572115i
$683$	33.2580			1.27258			0.636291	−	0.771449i	$-0.280468\pi$
$683$	33.2580			1.27258			0.636291	+	0.771449i	$0.280468\pi$
$684$		0			0
$685$	−8.63734	+	0.987927i	−0.330016	+	0.0377468i
$686$	−8.34625	+	24.8585i	−0.318661	+	0.949101i
$687$		0			0
$688$	−1.10439	−	3.91275i	−0.0421045	−	0.149172i
$689$	−17.4506			−0.664817
$690$		0			0
$691$		−	50.2241i		−	1.91062i	−0.295611	−	0.955308i	$-0.595523\pi$
$691$		−	50.2241i		−	1.91062i	0.295611	−	0.955308i	$-0.404477\pi$
$692$	−37.0521	−	28.0416i	−1.40851	−	1.06598i
$693$		0			0
$694$	−29.1044	−	9.77182i	−1.10479	−	0.370933i
$695$	32.4999	−	3.71729i	1.23279	−	0.141005i
$696$		0			0
$697$		−	28.9170i		−	1.09531i
$698$	−11.1372	+	33.1710i	−0.421549	+	1.25554i
$699$		0			0
$700$	−10.7777	+	24.1289i	−0.407357	+	0.911985i
$701$		−	23.7543i		−	0.897188i	−0.893736	−	0.448594i	$-0.851925\pi$
$701$		−	23.7543i		−	0.897188i	0.893736	−	0.448594i	$-0.148075\pi$
$702$		0			0
$703$		−	55.7715i		−	2.10346i
$704$	−11.2775	−	4.40987i	−0.425037	−	0.166203i
$705$		0			0
$706$	1.49180	−	4.44317i	0.0561445	−	0.167221i
$707$	35.2252			1.32478
$708$		0			0
$709$			36.3146i			1.36382i	0.731435	+	0.681911i	$0.238851\pi$
$709$			36.3146i			1.36382i	−0.731435	+	0.681911i	$0.761149\pi$
$710$	−4.43424	+	20.7999i	−0.166414	+	0.780608i
$711$		0			0
$712$	−23.5358	−	34.4744i	−0.882041	−	1.29198i
$713$			35.5453i			1.33118i
$714$		0			0
$715$	−13.0164	+	1.48880i	−0.486786	+	0.0556779i
$716$	3.44780	−	4.55567i	0.128851	−	0.170253i
$717$		0			0
$718$	22.4671	+	7.54333i	0.838463	+	0.281515i
$719$	30.7253			1.14586			0.572931	−	0.819604i	$-0.305806\pi$
$719$	30.7253			1.14586			0.572931	+	0.819604i	$0.305806\pi$
$720$		0			0
$721$	−2.53268			−0.0943219
$722$	41.8405	+	14.0480i	1.55714	+	0.522812i
$723$		0			0
$724$	−6.37907	+	8.42882i	−0.237076	+	0.313255i
$725$	2.46705	+	10.6435i	0.0916240	+	0.395289i
$726$		0			0
$727$		−	5.47445i		−	0.203036i	−0.994834	−	0.101518i	$-0.967630\pi$
$727$		−	5.47445i		−	0.203036i	0.994834	−	0.101518i	$-0.0323700\pi$
$728$	23.8953	−	16.3134i	0.885620	−	0.604615i
$729$		0			0
$730$	−47.9833	−	10.2293i	−1.77594	−	0.378605i
$731$		−	3.36852i		−	0.124589i
$732$		0			0
$733$	17.1455			0.633285			0.316643	−	0.948545i	$-0.397444\pi$
$733$	17.1455			0.633285			0.316643	+	0.948545i	$0.397444\pi$
$734$	12.8433	−	38.2524i	0.474054	−	1.41192i
$735$		0			0
$736$	−27.2775	−	1.33294i	−1.00546	−	0.0491328i
$737$			1.53847i			0.0566701i
$738$		0			0
$739$		−	11.6019i		−	0.426782i	−0.976967	−	0.213391i	$-0.931549\pi$
$739$		−	11.6019i		−	0.426782i	0.976967	−	0.213391i	$-0.0684508\pi$
$740$	17.9149	−	30.2996i	0.658563	−	1.11384i
$741$		0			0
$742$	−5.36266	+	15.9721i	−0.196869	+	0.586356i
$743$			23.6613i			0.868048i	0.900901	+	0.434024i	$0.142907\pi$
$743$			23.6613i			0.868048i	−0.900901	+	0.434024i	$0.857093\pi$
$744$		0			0
$745$	−24.5962	+	2.81328i	−0.901135	+	0.103071i
$746$	50.3819	+	16.9158i	1.84461	+	0.619330i
$747$		0			0
$748$	−8.00000	−	6.05453i	−0.292509	−	0.221376i
$749$			10.5706i			0.386241i
$750$		0			0
$751$	−11.4283			−0.417024			−0.208512	−	0.978020i	$-0.566862\pi$
$751$	−11.4283			−0.417024			−0.208512	+	0.978020i	$0.566862\pi$
$752$	27.2775	−	7.69919i	0.994709	−	0.280761i
$753$		0			0
$754$	3.80736	−	11.3398i	0.138656	−	0.412972i
$755$	−0.161949	−	1.41590i	−0.00589392	−	0.0515299i
$756$		0			0
$757$	19.1784			0.697049			0.348525	−	0.937300i	$-0.386683\pi$
$757$	19.1784			0.697049			0.348525	+	0.937300i	$0.386683\pi$
$758$	3.03592	−	9.04219i	0.110270	−	0.328427i
$759$		0			0
$760$	29.3103	+	33.9007i	1.06320	+	1.22971i
$761$	−4.03281			−0.146189			−0.0730947	−	0.997325i	$-0.523288\pi$
$761$	−4.03281			−0.146189			−0.0730947	+	0.997325i	$0.523288\pi$
$762$		0			0
$763$	−2.03281			−0.0735928
$764$	9.51627	+	7.20207i	0.344287	+	0.260562i
$765$		0			0
$766$	9.82687	−	29.2684i	0.355059	−	1.05751i
$767$			26.3177i			0.950279i
$768$		0			0
$769$	2.95078			0.106408			0.0532039	−	0.998584i	$-0.483057\pi$
$769$	2.95078			0.106408			0.0532039	+	0.998584i	$0.483057\pi$
$770$	−2.63734	+	12.3711i	−0.0950431	+	0.445824i
$771$		0			0
$772$	18.0328	−	23.8272i	0.649015	−	0.857560i
$773$	45.2663			1.62812			0.814059	−	0.580783i	$-0.197253\pi$
$773$	45.2663			1.62812			0.814059	+	0.580783i	$0.197253\pi$
$774$		0			0
$775$	35.8625	−	8.31256i	1.28822	−	0.298596i
$776$	−26.0328	+	17.7727i	−0.934524	+	0.638002i
$777$		0			0
$778$	3.96719	−	11.8159i	0.142231	−	0.423619i
$779$			61.8260i			2.21515i
$780$		0			0
$781$			10.1797i			0.364257i
$782$	−21.4506	−	7.20207i	−0.767074	−	0.257546i
$783$		0			0
$784$	0.0178270	+	0.0631594i	0.000636678	+	0.00225569i
$785$	0.0328135	+	0.286885i	0.00117116	+	0.0102394i
$786$		0			0
$787$	52.9997			1.88924			0.944618	−	0.328171i	$-0.106432\pi$
$787$	52.9997			1.88924			0.944618	+	0.328171i	$0.106432\pi$
$788$	5.15672	+	3.90269i	0.183701	+	0.139028i
$789$		0			0
$790$	−4.85446	+	22.7711i	−0.172714	+	0.810159i
$791$	38.2088			1.35855
$792$		0			0
$793$			13.9391i			0.494993i
$794$	−1.10155	−	0.369846i	−0.0390926	−	0.0131254i
$795$		0			0
$796$	12.9508	+	9.80136i	0.459028	+	0.347400i
$797$	16.5738			0.587075			0.293538	−	0.955948i	$-0.405167\pi$
$797$	16.5738			0.587075			0.293538	+	0.955948i	$0.405167\pi$
$798$		0			0
$799$	23.4835			0.830785
$800$	5.03423	+	27.8327i	0.177987	+	0.984033i
$801$		0			0
$802$	−17.0604	−	5.72804i	−0.602424	−	0.202264i
$803$	−23.4835			−0.828713
$804$		0			0
$805$	3.24186	+	28.3433i	0.114261	+	0.998969i
$806$	−38.2088	−	12.8286i	−1.34585	−	0.451869i
$807$		0			0
$808$	31.1372	−	21.2574i	1.09540	−	0.747834i
$809$	−37.5491			−1.32016			−0.660078	−	0.751197i	$-0.729477\pi$
$809$	−37.5491			−1.32016			−0.660078	+	0.751197i	$0.729477\pi$
$810$		0			0
$811$			32.1102i			1.12754i	0.825931	+	0.563771i	$0.190650\pi$
$811$			32.1102i			1.12754i	−0.825931	+	0.563771i	$0.809350\pi$
$812$	−9.20905	−	6.96956i	−0.323174	−	0.244584i
$813$		0			0
$814$	5.36266	−	15.9721i	0.187961	−	0.559824i
$815$	−4.95078	−	43.2841i	−0.173418	−	1.51618i
$816$		0			0
$817$			7.20207i			0.251969i
$818$	3.02759	+	1.01651i	0.105857	+	0.0355416i
$819$		0			0
$820$	−19.8597	+	33.5890i	−0.693530	+	1.17298i
$821$		−	29.3809i		−	1.02540i	−0.858568	−	0.512699i	$-0.828646\pi$
$821$		−	29.3809i		−	1.02540i	0.858568	−	0.512699i	$-0.171354\pi$
$822$		0			0
$823$			28.3866i			0.989495i	0.869037	+	0.494748i	$0.164740\pi$
$823$			28.3866i			0.989495i	−0.869037	+	0.494748i	$0.835260\pi$
$824$	−2.23875	+	1.52840i	−0.0779907	+	0.0532444i
$825$		0			0
$826$	24.0880	+	8.08756i	0.838128	+	0.281402i
$827$	−1.45065			−0.0504439			−0.0252219	−	0.999682i	$-0.508029\pi$
$827$	−1.45065			−0.0504439			−0.0252219	+	0.999682i	$0.508029\pi$
$828$		0			0
$829$		−	37.4621i		−	1.30111i	−0.759458	−	0.650556i	$-0.774536\pi$
$829$		−	37.4621i		−	1.30111i	0.759458	−	0.650556i	$-0.225464\pi$
$830$	−5.10439	+	23.9435i	−0.177176	+	0.831089i
$831$		0			0
$832$	11.2775	−	28.8404i	0.390978	−	0.999860i
$833$			0.0543744i			0.00188396i
$834$		0			0
$835$	4.00000	−	0.457515i	0.138426	−	0.0158329i
$836$	17.1044	+	12.9449i	0.591568	+	0.447708i
$837$		0			0
$838$	−15.0604	+	44.8559i	−0.520253	+	1.54952i
$839$	−48.7581			−1.68332			−0.841659	−	0.540010i	$-0.818421\pi$
$839$	−48.7581			−1.68332			−0.841659	+	0.540010i	$0.818421\pi$
$840$		0			0
$841$	24.2252			0.835351
$842$	−5.10439	+	15.2029i	−0.175909	+	0.523927i
$843$		0			0
$844$	16.5522	−	21.8708i	0.569750	−	0.752825i
$845$	−0.504034	−	4.40672i	−0.0173393	−	0.151596i
$846$		0			0
$847$		−	23.0146i		−	0.790791i
$848$	4.89845	+	17.3548i	0.168213	+	0.595965i
$849$		0			0
$850$	−2.24993	+	23.3263i	−0.0771721	+	0.800086i
$851$		−	37.9988i		−	1.30258i
$852$		0			0
$853$	4.37073			0.149651			0.0748255	−	0.997197i	$-0.476160\pi$
$853$	4.37073			0.149651			0.0748255	+	0.997197i	$0.476160\pi$
$854$	12.7581	+	4.28355i	0.436574	+	0.146580i
$855$		0			0
$856$	6.37907	+	9.34385i	0.218032	+	0.319366i
$857$			20.5130i			0.700712i	0.936617	+	0.350356i	$0.113939\pi$
$857$			20.5130i			0.700712i	−0.936617	+	0.350356i	$0.886061\pi$
$858$		0			0
$859$			10.1131i			0.345054i	0.985005	+	0.172527i	$0.0551932\pi$
$859$			10.1131i			0.345054i	−0.985005	+	0.172527i	$0.944807\pi$
$860$	−2.31344	+	3.91275i	−0.0788877	+	0.133424i
$861$		0			0
$862$	14.2911	+	4.79824i	0.486756	+	0.163429i
$863$		−	13.2861i		−	0.452266i	−0.974096	−	0.226133i	$-0.927392\pi$
$863$		−	13.2861i		−	0.452266i	0.974096	−	0.226133i	$-0.0726083\pi$
$864$		0			0
$865$	5.90368	+	51.6152i	0.200731	+	1.75497i
$866$	11.9344	−	35.5453i	0.405547	−	1.20788i
$867$		0			0
$868$	−23.4835	+	31.0293i	−0.797081	+	1.05320i
$869$			11.1444i			0.378047i
$870$		0			0
$871$	−3.93437			−0.133311
$872$	−1.79690	+	1.22675i	−0.0608507	+	0.0415429i
$873$		0			0
$874$	45.8625	+	15.3984i	1.55132	+	0.520858i
$875$	27.8381	−	9.89909i	0.941098	−	0.334650i
$876$		0			0
$877$	−33.6454			−1.13612			−0.568062	−	0.822986i	$-0.692307\pi$
$877$	−33.6454			−1.13612			−0.568062	+	0.822986i	$0.692307\pi$
$878$	44.0796	+	14.7998i	1.48762	+	0.499468i
$879$		0			0
$880$	5.13436	+	12.5270i	0.173079	+	0.422284i
$881$	32.7909			1.10476			0.552378	−	0.833594i	$-0.313721\pi$
$881$	32.7909			1.10476			0.552378	+	0.833594i	$0.313721\pi$
$882$		0			0
$883$	−33.4506			−1.12570			−0.562852	−	0.826558i	$-0.690296\pi$
$883$	−33.4506			−1.12570			−0.562852	+	0.826558i	$0.690296\pi$
$884$	15.4835	−	20.4587i	0.520765	−	0.688100i
$885$		0			0
$886$	−7.65375	−	2.56975i	−0.257133	−	0.0863325i
$887$		−	34.8924i		−	1.17157i	−0.810466	−	0.585785i	$-0.800786\pi$
$887$		−	34.8924i		−	1.17157i	0.810466	−	0.585785i	$-0.199214\pi$
$888$		0			0
$889$	−30.4671			−1.02183
$890$	−9.73055	+	45.6436i	−0.326169	+	1.52998i
$891$		0			0
$892$	11.8820	−	15.7000i	0.397840	−	0.525676i
$893$	−50.2088			−1.68017
$894$		0			0
$895$	−6.34625	+	0.725876i	−0.212132	+	0.0242634i
$896$	−22.9313	−	19.1848i	−0.766080	−	0.640920i
$897$		0			0
$898$	2.68133	+	0.900259i	0.0894772	+	0.0300420i
$899$			16.0884i			0.536578i
$900$		0			0
$901$			14.9409i			0.497752i
$902$	−5.94483	+	17.7061i	−0.197941	+	0.589548i
$903$		0			0
$904$	33.7745	−	23.0580i	1.12332	−	0.766896i
$905$	11.7417	−	1.34300i	0.390308	−	0.0446429i
$906$		0			0
$907$	30.9836			1.02879			0.514397	−	0.857552i	$-0.328016\pi$
$907$	30.9836			1.02879			0.514397	+	0.857552i	$0.328016\pi$
$908$	−9.10439	−	6.89035i	−0.302140	−	0.228664i
$909$		0			0
$910$	−31.6371	−	6.74456i	−1.04876	−	0.223580i
$911$	−16.0000			−0.530104			−0.265052	−	0.964234i	$-0.585389\pi$
$911$	−16.0000			−0.530104			−0.265052	+	0.964234i	$0.585389\pi$
$912$		0			0
$913$			11.7181i			0.387814i
$914$	1.77454	−	5.28530i	0.0586967	−	0.174822i
$915$		0			0
$916$	−0.928423	+	1.22675i	−0.0306760	+	0.0405329i
$917$	−19.4835			−0.643400
$918$		0			0
$919$	15.6043			0.514737			0.257368	−	0.966313i	$-0.417145\pi$
$919$	15.6043			0.514737			0.257368	+	0.966313i	$0.417145\pi$
$920$	19.9700	+	23.0976i	0.658392	+	0.761504i
$921$		0			0
$922$	15.2580	−	45.4444i	0.502496	−	1.49663i
$923$	−26.0328			−0.856880
$924$		0			0
$925$	−38.3379	+	8.88633i	−1.26054	+	0.292181i
$926$	10.2939	−	30.6594i	0.338279	−	1.00753i
$927$		0			0
$928$	−12.3463	−	0.603310i	−0.405286	−	0.0198046i
$929$	−38.9341			−1.27739			−0.638693	−	0.769461i	$-0.720525\pi$
$929$	−38.9341			−1.27739			−0.638693	+	0.769461i	$0.720525\pi$
$930$		0			0
$931$		−	0.116255i		−	0.00381011i
$932$	22.2088	−	29.3450i	0.727473	−	0.961228i
$933$		0			0
$934$	21.1044	+	7.08582i	0.690557	+	0.231855i
$935$	1.27468	+	11.1444i	0.0416864	+	0.364460i
$936$		0			0
$937$		−	19.6027i		−	0.640393i	−0.947351	−	0.320197i	$-0.896251\pi$
$937$		−	19.6027i		−	0.640393i	0.947351	−	0.320197i	$-0.103749\pi$
$938$	−1.20905	+	3.60104i	−0.0394769	+	0.117578i
$939$		0			0
$940$	−27.2775	−	16.1280i	−0.889695	−	0.526038i
$941$			25.0476i			0.816530i	0.912864	+	0.408265i	$0.133866\pi$
$941$			25.0476i			0.816530i	−0.912864	+	0.408265i	$0.866134\pi$
$942$		0			0
$943$			42.1240i			1.37175i
$944$	26.1731	−	7.38747i	0.851863	−	0.240442i
$945$		0			0
$946$	−0.692509	+	2.06257i	−0.0225154	+	0.0670599i
$947$	−7.93437			−0.257832			−0.128916	−	0.991655i	$-0.541150\pi$
$947$	−7.93437			−0.257832			−0.128916	+	0.991655i	$0.541150\pi$
$948$		0			0
$949$		−	60.0550i		−	1.94947i
$950$	4.81047	−	49.8728i	0.156072	−	1.61809i
$951$		0			0
$952$	−13.9672	−	20.4587i	−0.452679	−	0.663069i
$953$			11.4809i			0.371903i	0.982559	+	0.185952i	$0.0595368\pi$
$953$			11.4809i			0.371903i	−0.982559	+	0.185952i	$0.940463\pi$
$954$		0			0
$955$	−1.51627	−	13.2566i	−0.0490654	−	0.428974i
$956$	16.0000	+	12.1091i	0.517477	+	0.391635i
$957$		0			0
$958$	−27.7417	−	9.31431i	−0.896295	−	0.300932i
$959$	−10.2744			−0.331778
$960$		0			0
$961$	23.2088			0.748670
$962$	40.8461	+	13.7141i	1.31693	+	0.442161i
$963$		0			0
$964$	17.1567	+	12.9845i	0.552581	+	0.418202i
$965$	−33.1924	+	3.79650i	−1.06850	+	0.122214i
$966$		0			0
$967$		−	15.8993i		−	0.511285i	−0.966771	−	0.255643i	$-0.917713\pi$
$967$		−	15.8993i		−	0.511285i	0.966771	−	0.255643i	$-0.0822871\pi$
$968$	−13.8887	−	20.3437i	−0.446399	−	0.653871i
$969$		0			0
$970$	34.4671	+	7.34787i	1.10667	+	0.235926i
$971$		−	40.6600i		−	1.30484i	−0.757857	−	0.652421i	$-0.773754\pi$
$971$		−	40.6600i		−	1.30484i	0.757857	−	0.652421i	$-0.226246\pi$
$972$		0			0
$973$	38.6597			1.23937
$974$	−13.8820	+	41.3463i	−0.444809	+	1.32482i
$975$		0			0
$976$	13.8625	−	3.91275i	0.443729	−	0.125244i
$977$		−	26.5676i		−	0.849972i	−0.905200	−	0.424986i	$-0.860279\pi$
$977$		−	26.5676i		−	0.849972i	0.905200	−	0.424986i	$-0.139721\pi$
$978$		0			0
$979$			22.3384i			0.713938i
$980$	0.0373434	−	0.0631594i	0.00119289	−	0.00201755i
$981$		0			0
$982$	4.93960	−	14.7121i	0.157629	−	0.469482i
$983$		−	9.88057i		−	0.315141i	−0.987508	−	0.157571i	$-0.949634\pi$
$983$		−	9.88057i		−	0.315141i	0.987508	−	0.157571i	$-0.0503662\pi$
$984$		0			0
$985$	−0.821644	−	7.18355i	−0.0261798	−	0.228887i
$986$	−9.70892	−	3.25978i	−0.309195	−	0.103812i
$987$		0			0
$988$	−33.1044	+	43.7416i	−1.05319	+	1.39161i
$989$			4.90699i			0.156033i
$990$		0			0
$991$	−53.0549			−1.68534			−0.842672	−	0.538427i	$-0.819019\pi$
$991$	−53.0549			−1.68534			−0.842672	+	0.538427i	$0.819019\pi$
$992$	−2.03281	+	41.5999i	−0.0645419	+	1.32080i
$993$		0			0
$994$	−8.00000	+	23.8272i	−0.253745	+	0.755753i
$995$	−2.06351	−	18.0410i	−0.0654176	−	0.571939i
$996$		0			0
$997$	32.3051			1.02311			0.511556	−	0.859250i	$-0.329069\pi$
$997$	32.3051			1.02311			0.511556	+	0.859250i	$0.329069\pi$
$998$	−1.67326	+	4.98364i	−0.0529662	+	0.157754i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.d.e.109.1		6
3.2	odd	2		120.2.d.b.109.6	yes	6
4.3	odd	2		1440.2.d.f.1009.3		6
5.2	odd	4		1800.2.k.u.901.7		12
5.3	odd	4		1800.2.k.u.901.6		12
5.4	even	2		360.2.d.f.109.6		6
8.3	odd	2		1440.2.d.e.1009.4		6
8.5	even	2		360.2.d.f.109.5		6
12.11	even	2		480.2.d.b.49.4		6
15.2	even	4		600.2.k.f.301.6		12
15.8	even	4		600.2.k.f.301.7		12
15.14	odd	2		120.2.d.a.109.1	✓	6
20.3	even	4		7200.2.k.u.3601.9		12
20.7	even	4		7200.2.k.u.3601.3		12
20.19	odd	2		1440.2.d.e.1009.3		6
24.5	odd	2		120.2.d.a.109.2	yes	6
24.11	even	2		480.2.d.a.49.3		6
40.3	even	4		7200.2.k.u.3601.10		12
40.13	odd	4		1800.2.k.u.901.5		12
40.19	odd	2		1440.2.d.f.1009.4		6
40.27	even	4		7200.2.k.u.3601.4		12
40.29	even	2	inner	360.2.d.e.109.2		6
40.37	odd	4		1800.2.k.u.901.8		12
48.5	odd	4		3840.2.f.l.769.7		12
48.11	even	4		3840.2.f.m.769.1		12
48.29	odd	4		3840.2.f.l.769.6		12
48.35	even	4		3840.2.f.m.769.12		12
60.23	odd	4		2400.2.k.f.1201.11		12
60.47	odd	4		2400.2.k.f.1201.2		12
60.59	even	2		480.2.d.a.49.4		6
120.29	odd	2		120.2.d.b.109.5	yes	6
120.53	even	4		600.2.k.f.301.8		12
120.59	even	2		480.2.d.b.49.3		6
120.77	even	4		600.2.k.f.301.5		12
120.83	odd	4		2400.2.k.f.1201.5		12
120.107	odd	4		2400.2.k.f.1201.8		12
240.29	odd	4		3840.2.f.l.769.12		12
240.59	even	4		3840.2.f.m.769.7		12
240.149	odd	4		3840.2.f.l.769.1		12
240.179	even	4		3840.2.f.m.769.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.d.a.109.1	✓	6	15.14	odd	2
120.2.d.a.109.2	yes	6	24.5	odd	2
120.2.d.b.109.5	yes	6	120.29	odd	2
120.2.d.b.109.6	yes	6	3.2	odd	2
360.2.d.e.109.1		6	1.1	even	1	trivial
360.2.d.e.109.2		6	40.29	even	2	inner
360.2.d.f.109.5		6	8.5	even	2
360.2.d.f.109.6		6	5.4	even	2
480.2.d.a.49.3		6	24.11	even	2
480.2.d.a.49.4		6	60.59	even	2
480.2.d.b.49.3		6	120.59	even	2
480.2.d.b.49.4		6	12.11	even	2
600.2.k.f.301.5		12	120.77	even	4
600.2.k.f.301.6		12	15.2	even	4
600.2.k.f.301.7		12	15.8	even	4
600.2.k.f.301.8		12	120.53	even	4
1440.2.d.e.1009.3		6	20.19	odd	2
1440.2.d.e.1009.4		6	8.3	odd	2
1440.2.d.f.1009.3		6	4.3	odd	2
1440.2.d.f.1009.4		6	40.19	odd	2
1800.2.k.u.901.5		12	40.13	odd	4
1800.2.k.u.901.6		12	5.3	odd	4
1800.2.k.u.901.7		12	5.2	odd	4
1800.2.k.u.901.8		12	40.37	odd	4
2400.2.k.f.1201.2		12	60.47	odd	4
2400.2.k.f.1201.5		12	120.83	odd	4
2400.2.k.f.1201.8		12	120.107	odd	4
2400.2.k.f.1201.11		12	60.23	odd	4
3840.2.f.l.769.1		12	240.149	odd	4
3840.2.f.l.769.6		12	48.29	odd	4
3840.2.f.l.769.7		12	48.5	odd	4
3840.2.f.l.769.12		12	240.29	odd	4
3840.2.f.m.769.1		12	48.11	even	4
3840.2.f.m.769.6		12	240.179	even	4
3840.2.f.m.769.7		12	240.59	even	4
3840.2.f.m.769.12		12	48.35	even	4
7200.2.k.u.3601.3		12	20.7	even	4
7200.2.k.u.3601.4		12	40.27	even	4
7200.2.k.u.3601.9		12	20.3	even	4
7200.2.k.u.3601.10		12	40.3	even	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34067 - 0.450129i) q^{2} +(1.59477 + 1.20695i) q^{4} +(-0.254102 - 2.22158i) q^{5} -2.64265i q^{7} +(-1.59477 - 2.33596i) q^{8} +(-0.659335 + 3.09278i) q^{10} +1.51363i q^{11} -3.87086 q^{13} +(-1.18953 + 3.54291i) q^{14} +(1.08656 + 3.84959i) q^{16} +3.31415i q^{17} -7.08582i q^{19} +(2.27610 - 3.84959i) q^{20} +(0.681331 - 2.02927i) q^{22} -4.82778i q^{23} +(-4.87086 + 1.12902i) q^{25} +(5.18953 + 1.74239i) q^{26} +(3.18953 - 4.21441i) q^{28} -2.18513i q^{29} -7.36266 q^{31} +(0.276098 - 5.65011i) q^{32} +(1.49180 - 4.44317i) q^{34} +(-5.87086 + 0.671502i) q^{35} +7.87086 q^{37} +(-3.18953 + 9.49971i) q^{38} +(-4.78430 + 4.13648i) q^{40} -8.72532 q^{41} -1.01641 q^{43} +(-1.82687 + 2.41389i) q^{44} +(-2.17313 + 6.47244i) q^{46} -7.08582i q^{47} +0.0164068 q^{49} +(7.03840 + 0.678887i) q^{50} +(-6.17313 - 4.67192i) q^{52} +4.50820 q^{53} +(3.36266 - 0.384617i) q^{55} +(-6.17313 + 4.21441i) q^{56} +(-0.983593 + 2.92953i) q^{58} -6.79893i q^{59} -3.60104i q^{61} +(9.87086 + 3.31415i) q^{62} +(-2.91344 + 7.45063i) q^{64} +(0.983593 + 8.59945i) q^{65} +1.01641 q^{67} +(-4.00000 + 5.28530i) q^{68} +(8.17313 + 1.74239i) q^{70} +6.72532 q^{71} +15.5146i q^{73} +(-10.5522 - 3.54291i) q^{74} +(8.55220 - 11.3002i) q^{76} +4.00000 q^{77} +7.36266 q^{79} +(8.27610 - 3.39208i) q^{80} +(11.6977 + 3.92752i) q^{82} +7.74173 q^{83} +(7.36266 - 0.842131i) q^{85} +(1.36266 + 0.457515i) q^{86} +(3.53579 - 2.41389i) q^{88} +14.7581 q^{89} +10.2293i q^{91} +(5.82687 - 7.69919i) q^{92} +(-3.18953 + 9.49971i) q^{94} +(-15.7417 + 1.80052i) q^{95} -11.1444i q^{97} +(-0.0219960 - 0.00738516i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} + q^{4} - q^{8} - 11 q^{10} + 8 q^{13} + 10 q^{14} + q^{16} - 9 q^{20} - 10 q^{22} + 2 q^{25} + 14 q^{26} + 2 q^{28} - 16 q^{31} - 21 q^{32} + 12 q^{34} - 4 q^{35} + 16 q^{37} - 2 q^{38}+ \cdots + 21 q^{98}+O(q^{100}) \) 6 * q - q^2 + q^4 - q^8 - 11 * q^10 + 8 * q^13 + 10 * q^14 + q^16 - 9 * q^20 - 10 * q^22 + 2 * q^25 + 14 * q^26 + 2 * q^28 - 16 * q^31 - 21 * q^32 + 12 * q^34 - 4 * q^35 + 16 * q^37 - 2 * q^38 - 3 * q^40 + 4 * q^41 - 22 * q^44 - 2 * q^46 - 6 * q^49 + 15 * q^50 - 26 * q^52 + 24 * q^53 - 8 * q^55 - 26 * q^56 - 12 * q^58 + 28 * q^62 - 23 * q^64 + 12 * q^65 - 24 * q^68 + 38 * q^70 - 16 * q^71 - 18 * q^74 + 6 * q^76 + 24 * q^77 + 16 * q^79 + 27 * q^80 + 50 * q^82 - 16 * q^83 + 16 * q^85 - 20 * q^86 - 18 * q^88 + 20 * q^89 + 46 * q^92 - 2 * q^94 - 32 * q^95 + 21 * q^98

Introduction

L-functions

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