LMFDB - Embedded newform 90.3.g.a.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [90,3,Mod(37,90)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(90, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("90.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 90 = 2 \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	90.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.45232237924$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	90.37
Dual form			90.3.g.a.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} +(-3.00000 + 4.00000i) q^{5} +(8.00000 + 8.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} +(-3.00000 + 4.00000i) q^{5} +(8.00000 + 8.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +(7.00000 - 1.00000i) q^{10} +4.00000 q^{11} +(-3.00000 + 3.00000i) q^{13} -16.0000i q^{14} -4.00000 q^{16} +(19.0000 + 19.0000i) q^{17} -8.00000i q^{19} +(-8.00000 - 6.00000i) q^{20} +(-4.00000 - 4.00000i) q^{22} +(-20.0000 + 20.0000i) q^{23} +(-7.00000 - 24.0000i) q^{25} +6.00000 q^{26} +(-16.0000 + 16.0000i) q^{28} -38.0000i q^{29} -44.0000 q^{31} +(4.00000 + 4.00000i) q^{32} -38.0000i q^{34} +(-56.0000 + 8.00000i) q^{35} +(-3.00000 - 3.00000i) q^{37} +(-8.00000 + 8.00000i) q^{38} +(2.00000 + 14.0000i) q^{40} +70.0000 q^{41} +(36.0000 - 36.0000i) q^{43} +8.00000i q^{44} +40.0000 q^{46} +79.0000i q^{49} +(-17.0000 + 31.0000i) q^{50} +(-6.00000 - 6.00000i) q^{52} +(17.0000 - 17.0000i) q^{53} +(-12.0000 + 16.0000i) q^{55} +32.0000 q^{56} +(-38.0000 + 38.0000i) q^{58} -92.0000i q^{59} +72.0000 q^{61} +(44.0000 + 44.0000i) q^{62} -8.00000i q^{64} +(-3.00000 - 21.0000i) q^{65} +(44.0000 + 44.0000i) q^{67} +(-38.0000 + 38.0000i) q^{68} +(64.0000 + 48.0000i) q^{70} -88.0000 q^{71} +(55.0000 - 55.0000i) q^{73} +6.00000i q^{74} +16.0000 q^{76} +(32.0000 + 32.0000i) q^{77} +12.0000i q^{79} +(12.0000 - 16.0000i) q^{80} +(-70.0000 - 70.0000i) q^{82} +(-24.0000 + 24.0000i) q^{83} +(-133.000 + 19.0000i) q^{85} -72.0000 q^{86} +(8.00000 - 8.00000i) q^{88} +26.0000i q^{89} -48.0000 q^{91} +(-40.0000 - 40.0000i) q^{92} +(32.0000 + 24.0000i) q^{95} +(-57.0000 - 57.0000i) q^{97} +(79.0000 - 79.0000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 6 q^{5} + 16 q^{7} + 4 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 - 6 * q^5 + 16 * q^7 + 4 * q^8	$ 2 q - 2 q^{2} - 6 q^{5} + 16 q^{7} + 4 q^{8} + 14 q^{10} + 8 q^{11} - 6 q^{13} - 8 q^{16} + 38 q^{17} - 16 q^{20} - 8 q^{22} - 40 q^{23} - 14 q^{25} + 12 q^{26} - 32 q^{28} - 88 q^{31} + 8 q^{32} - 112 q^{35} - 6 q^{37} - 16 q^{38} + 4 q^{40} + 140 q^{41} + 72 q^{43} + 80 q^{46} - 34 q^{50} - 12 q^{52} + 34 q^{53} - 24 q^{55} + 64 q^{56} - 76 q^{58} + 144 q^{61} + 88 q^{62} - 6 q^{65} + 88 q^{67} - 76 q^{68} + 128 q^{70} - 176 q^{71} + 110 q^{73} + 32 q^{76} + 64 q^{77} + 24 q^{80} - 140 q^{82} - 48 q^{83} - 266 q^{85} - 144 q^{86} + 16 q^{88} - 96 q^{91} - 80 q^{92} + 64 q^{95} - 114 q^{97} + 158 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 6 * q^5 + 16 * q^7 + 4 * q^8 + 14 * q^10 + 8 * q^11 - 6 * q^13 - 8 * q^16 + 38 * q^17 - 16 * q^20 - 8 * q^22 - 40 * q^23 - 14 * q^25 + 12 * q^26 - 32 * q^28 - 88 * q^31 + 8 * q^32 - 112 * q^35 - 6 * q^37 - 16 * q^38 + 4 * q^40 + 140 * q^41 + 72 * q^43 + 80 * q^46 - 34 * q^50 - 12 * q^52 + 34 * q^53 - 24 * q^55 + 64 * q^56 - 76 * q^58 + 144 * q^61 + 88 * q^62 - 6 * q^65 + 88 * q^67 - 76 * q^68 + 128 * q^70 - 176 * q^71 + 110 * q^73 + 32 * q^76 + 64 * q^77 + 24 * q^80 - 140 * q^82 - 48 * q^83 - 266 * q^85 - 144 * q^86 + 16 * q^88 - 96 * q^91 - 80 * q^92 + 64 * q^95 - 114 * q^97 + 158 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			2.00000i			0.500000i
$5$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$5$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$6$		0			0
$7$	8.00000	+	8.00000i	1.14286	+	1.14286i	0.987925	+	0.154932i	$0.0495158\pi$
$7$	8.00000	+	8.00000i	1.14286	+	1.14286i	0.154932	+	0.987925i	$0.450484\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$		0			0
$10$	7.00000	−	1.00000i	0.700000	−	0.100000i
$11$	4.00000			0.363636			0.181818	−	0.983332i	$-0.441802\pi$
$11$	4.00000			0.363636			0.181818	+	0.983332i	$0.441802\pi$
$12$		0			0
$13$	−3.00000	+	3.00000i	−0.230769	+	0.230769i	−0.813014	−	0.582245i	$-0.802175\pi$
$13$	−3.00000	+	3.00000i	−0.230769	+	0.230769i	0.582245	+	0.813014i	$0.302175\pi$
$14$		−	16.0000i		−	1.14286i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	19.0000	+	19.0000i	1.11765	+	1.11765i	0.992086	+	0.125561i	$0.0400731\pi$
$17$	19.0000	+	19.0000i	1.11765	+	1.11765i	0.125561	+	0.992086i	$0.459927\pi$
$18$		0			0
$19$		−	8.00000i		−	0.421053i	−0.977588	−	0.210526i	$-0.932482\pi$
$19$		−	8.00000i		−	0.421053i	0.977588	−	0.210526i	$-0.0675178\pi$
$20$	−8.00000	−	6.00000i	−0.400000	−	0.300000i
$21$		0			0
$22$	−4.00000	−	4.00000i	−0.181818	−	0.181818i
$23$	−20.0000	+	20.0000i	−0.869565	+	0.869565i	−0.992424	−	0.122859i	$-0.960794\pi$
$23$	−20.0000	+	20.0000i	−0.869565	+	0.869565i	0.122859	+	0.992424i	$0.460794\pi$
$24$		0			0
$25$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$26$	6.00000			0.230769
$27$		0			0
$28$	−16.0000	+	16.0000i	−0.571429	+	0.571429i
$29$		−	38.0000i		−	1.31034i	−0.755479	−	0.655172i	$-0.772596\pi$
$29$		−	38.0000i		−	1.31034i	0.755479	−	0.655172i	$-0.227404\pi$
$30$		0			0
$31$	−44.0000			−1.41935			−0.709677	−	0.704527i	$-0.751159\pi$
$31$	−44.0000			−1.41935			−0.709677	+	0.704527i	$0.751159\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$		0			0
$34$		−	38.0000i		−	1.11765i
$35$	−56.0000	+	8.00000i	−1.60000	+	0.228571i
$36$		0			0
$37$	−3.00000	−	3.00000i	−0.0810811	−	0.0810811i	0.665403	−	0.746484i	$-0.268260\pi$
$37$	−3.00000	−	3.00000i	−0.0810811	−	0.0810811i	−0.746484	+	0.665403i	$0.768260\pi$
$38$	−8.00000	+	8.00000i	−0.210526	+	0.210526i
$39$		0			0
$40$	2.00000	+	14.0000i	0.0500000	+	0.350000i
$41$	70.0000			1.70732			0.853659	−	0.520833i	$-0.174379\pi$
$41$	70.0000			1.70732			0.853659	+	0.520833i	$0.174379\pi$
$42$		0			0
$43$	36.0000	−	36.0000i	0.837209	−	0.837209i	−0.151281	−	0.988491i	$-0.548340\pi$
$43$	36.0000	−	36.0000i	0.837209	−	0.837209i	0.988491	+	0.151281i	$0.0483400\pi$
$44$			8.00000i			0.181818i
$45$		0			0
$46$	40.0000			0.869565
$47$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$47$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$48$		0			0
$49$			79.0000i			1.61224i
$50$	−17.0000	+	31.0000i	−0.340000	+	0.620000i
$51$		0			0
$52$	−6.00000	−	6.00000i	−0.115385	−	0.115385i
$53$	17.0000	−	17.0000i	0.320755	−	0.320755i	−0.528302	−	0.849057i	$-0.677171\pi$
$53$	17.0000	−	17.0000i	0.320755	−	0.320755i	0.849057	+	0.528302i	$0.177171\pi$
$54$		0			0
$55$	−12.0000	+	16.0000i	−0.218182	+	0.290909i
$56$	32.0000			0.571429
$57$		0			0
$58$	−38.0000	+	38.0000i	−0.655172	+	0.655172i
$59$		−	92.0000i		−	1.55932i	−0.626202	−	0.779661i	$-0.715391\pi$
$59$		−	92.0000i		−	1.55932i	0.626202	−	0.779661i	$-0.284609\pi$
$60$		0			0
$61$	72.0000			1.18033			0.590164	−	0.807283i	$-0.299063\pi$
$61$	72.0000			1.18033			0.590164	+	0.807283i	$0.299063\pi$
$62$	44.0000	+	44.0000i	0.709677	+	0.709677i
$63$		0			0
$64$		−	8.00000i		−	0.125000i
$65$	−3.00000	−	21.0000i	−0.0461538	−	0.323077i
$66$		0			0
$67$	44.0000	+	44.0000i	0.656716	+	0.656716i	0.954602	−	0.297885i	$-0.0962813\pi$
$67$	44.0000	+	44.0000i	0.656716	+	0.656716i	−0.297885	+	0.954602i	$0.596281\pi$
$68$	−38.0000	+	38.0000i	−0.558824	+	0.558824i
$69$		0			0
$70$	64.0000	+	48.0000i	0.914286	+	0.685714i
$71$	−88.0000			−1.23944			−0.619718	−	0.784824i	$-0.712753\pi$
$71$	−88.0000			−1.23944			−0.619718	+	0.784824i	$0.712753\pi$
$72$		0			0
$73$	55.0000	−	55.0000i	0.753425	−	0.753425i	−0.221692	−	0.975117i	$-0.571158\pi$
$73$	55.0000	−	55.0000i	0.753425	−	0.753425i	0.975117	+	0.221692i	$0.0711580\pi$
$74$			6.00000i			0.0810811i
$75$		0			0
$76$	16.0000			0.210526
$77$	32.0000	+	32.0000i	0.415584	+	0.415584i
$78$		0			0
$79$			12.0000i			0.151899i	0.997112	+	0.0759494i	$0.0241987\pi$
$79$			12.0000i			0.151899i	−0.997112	+	0.0759494i	$0.975801\pi$
$80$	12.0000	−	16.0000i	0.150000	−	0.200000i
$81$		0			0
$82$	−70.0000	−	70.0000i	−0.853659	−	0.853659i
$83$	−24.0000	+	24.0000i	−0.289157	+	0.289157i	−0.836747	−	0.547590i	$-0.815545\pi$
$83$	−24.0000	+	24.0000i	−0.289157	+	0.289157i	0.547590	+	0.836747i	$0.315545\pi$
$84$		0			0
$85$	−133.000	+	19.0000i	−1.56471	+	0.223529i
$86$	−72.0000			−0.837209
$87$		0			0
$88$	8.00000	−	8.00000i	0.0909091	−	0.0909091i
$89$			26.0000i			0.292135i	0.989275	+	0.146067i	$0.0466616\pi$
$89$			26.0000i			0.292135i	−0.989275	+	0.146067i	$0.953338\pi$
$90$		0			0
$91$	−48.0000			−0.527473
$92$	−40.0000	−	40.0000i	−0.434783	−	0.434783i
$93$		0			0
$94$		0			0
$95$	32.0000	+	24.0000i	0.336842	+	0.252632i
$96$		0			0
$97$	−57.0000	−	57.0000i	−0.587629	−	0.587629i	0.349360	−	0.936989i	$-0.386399\pi$
$97$	−57.0000	−	57.0000i	−0.587629	−	0.587629i	−0.936989	+	0.349360i	$0.886399\pi$
$98$	79.0000	−	79.0000i	0.806122	−	0.806122i
$99$		0			0
$100$	48.0000	−	14.0000i	0.480000	−	0.140000i
$101$	56.0000			0.554455			0.277228	−	0.960804i	$-0.410584\pi$
$101$	56.0000			0.554455			0.277228	+	0.960804i	$0.410584\pi$
$102$		0			0
$103$	4.00000	−	4.00000i	0.0388350	−	0.0388350i	−0.687423	−	0.726258i	$-0.741258\pi$
$103$	4.00000	−	4.00000i	0.0388350	−	0.0388350i	0.726258	+	0.687423i	$0.241258\pi$
$104$			12.0000i			0.115385i
$105$		0			0
$106$	−34.0000			−0.320755
$107$	−68.0000	−	68.0000i	−0.635514	−	0.635514i	0.313932	−	0.949446i	$-0.398354\pi$
$107$	−68.0000	−	68.0000i	−0.635514	−	0.635514i	−0.949446	+	0.313932i	$0.898354\pi$
$108$		0			0
$109$		−	46.0000i		−	0.422018i	−0.977484	−	0.211009i	$-0.932325\pi$
$109$		−	46.0000i		−	0.422018i	0.977484	−	0.211009i	$-0.0676750\pi$
$110$	28.0000	−	4.00000i	0.254545	−	0.0363636i
$111$		0			0
$112$	−32.0000	−	32.0000i	−0.285714	−	0.285714i
$113$	53.0000	−	53.0000i	0.469027	−	0.469027i	−0.432573	−	0.901599i	$-0.642394\pi$
$113$	53.0000	−	53.0000i	0.469027	−	0.469027i	0.901599	+	0.432573i	$0.142394\pi$
$114$		0			0
$115$	−20.0000	−	140.000i	−0.173913	−	1.21739i
$116$	76.0000			0.655172
$117$		0			0
$118$	−92.0000	+	92.0000i	−0.779661	+	0.779661i
$119$			304.000i			2.55462i
$120$		0			0
$121$	−105.000			−0.867769
$122$	−72.0000	−	72.0000i	−0.590164	−	0.590164i
$123$		0			0
$124$		−	88.0000i		−	0.709677i
$125$	117.000	+	44.0000i	0.936000	+	0.352000i
$126$		0			0
$127$	68.0000	+	68.0000i	0.535433	+	0.535433i	0.922184	−	0.386751i	$-0.126403\pi$
$127$	68.0000	+	68.0000i	0.535433	+	0.535433i	−0.386751	+	0.922184i	$0.626403\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	−18.0000	+	24.0000i	−0.138462	+	0.184615i
$131$	−44.0000			−0.335878			−0.167939	−	0.985797i	$-0.553711\pi$
$131$	−44.0000			−0.335878			−0.167939	+	0.985797i	$0.553711\pi$
$132$		0			0
$133$	64.0000	−	64.0000i	0.481203	−	0.481203i
$134$		−	88.0000i		−	0.656716i
$135$		0			0
$136$	76.0000			0.558824
$137$	−69.0000	−	69.0000i	−0.503650	−	0.503650i	0.408920	−	0.912570i	$-0.365905\pi$
$137$	−69.0000	−	69.0000i	−0.503650	−	0.503650i	−0.912570	+	0.408920i	$0.865905\pi$
$138$		0			0
$139$			80.0000i			0.575540i	0.957700	+	0.287770i	$0.0929138\pi$
$139$			80.0000i			0.575540i	−0.957700	+	0.287770i	$0.907086\pi$
$140$	−16.0000	−	112.000i	−0.114286	−	0.800000i
$141$		0			0
$142$	88.0000	+	88.0000i	0.619718	+	0.619718i
$143$	−12.0000	+	12.0000i	−0.0839161	+	0.0839161i
$144$		0			0
$145$	152.000	+	114.000i	1.04828	+	0.786207i
$146$	−110.000			−0.753425
$147$		0			0
$148$	6.00000	−	6.00000i	0.0405405	−	0.0405405i
$149$			168.000i			1.12752i	0.825940	+	0.563758i	$0.190645\pi$
$149$			168.000i			1.12752i	−0.825940	+	0.563758i	$0.809355\pi$
$150$		0			0
$151$	4.00000			0.0264901			0.0132450	−	0.999912i	$-0.495784\pi$
$151$	4.00000			0.0264901			0.0132450	+	0.999912i	$0.495784\pi$
$152$	−16.0000	−	16.0000i	−0.105263	−	0.105263i
$153$		0			0
$154$		−	64.0000i		−	0.415584i
$155$	132.000	−	176.000i	0.851613	−	1.13548i
$156$		0			0
$157$	99.0000	+	99.0000i	0.630573	+	0.630573i	0.948212	−	0.317639i	$-0.102890\pi$
$157$	99.0000	+	99.0000i	0.630573	+	0.630573i	−0.317639	+	0.948212i	$0.602890\pi$
$158$	12.0000	−	12.0000i	0.0759494	−	0.0759494i
$159$		0			0
$160$	−28.0000	+	4.00000i	−0.175000	+	0.0250000i
$161$	−320.000			−1.98758
$162$		0			0
$163$	−160.000	+	160.000i	−0.981595	+	0.981595i	−0.999834	−	0.0182386i	$-0.994194\pi$
$163$	−160.000	+	160.000i	−0.981595	+	0.981595i	0.0182386	+	0.999834i	$0.494194\pi$
$164$			140.000i			0.853659i
$165$		0			0
$166$	48.0000			0.289157
$167$	56.0000	+	56.0000i	0.335329	+	0.335329i	0.854606	−	0.519277i	$-0.173799\pi$
$167$	56.0000	+	56.0000i	0.335329	+	0.335329i	−0.519277	+	0.854606i	$0.673799\pi$
$168$		0			0
$169$			151.000i			0.893491i
$170$	152.000	+	114.000i	0.894118	+	0.670588i
$171$		0			0
$172$	72.0000	+	72.0000i	0.418605	+	0.418605i
$173$	−41.0000	+	41.0000i	−0.236994	+	0.236994i	−0.815604	−	0.578610i	$-0.803595\pi$
$173$	−41.0000	+	41.0000i	−0.236994	+	0.236994i	0.578610	+	0.815604i	$0.303595\pi$
$174$		0			0
$175$	136.000	−	248.000i	0.777143	−	1.41714i
$176$	−16.0000			−0.0909091
$177$		0			0
$178$	26.0000	−	26.0000i	0.146067	−	0.146067i
$179$		−	172.000i		−	0.960894i	−0.877024	−	0.480447i	$-0.840474\pi$
$179$		−	172.000i		−	0.960894i	0.877024	−	0.480447i	$-0.159526\pi$
$180$		0			0
$181$	62.0000			0.342541			0.171271	−	0.985224i	$-0.445213\pi$
$181$	62.0000			0.342541			0.171271	+	0.985224i	$0.445213\pi$
$182$	48.0000	+	48.0000i	0.263736	+	0.263736i
$183$		0			0
$184$			80.0000i			0.434783i
$185$	21.0000	−	3.00000i	0.113514	−	0.0162162i
$186$		0			0
$187$	76.0000	+	76.0000i	0.406417	+	0.406417i
$188$		0			0
$189$		0			0
$190$	−8.00000	−	56.0000i	−0.0421053	−	0.294737i
$191$	248.000			1.29843			0.649215	−	0.760605i	$-0.275098\pi$
$191$	248.000			1.29843			0.649215	+	0.760605i	$0.275098\pi$
$192$		0			0
$193$	135.000	−	135.000i	0.699482	−	0.699482i	−0.264817	−	0.964299i	$-0.585312\pi$
$193$	135.000	−	135.000i	0.699482	−	0.699482i	0.964299	+	0.264817i	$0.0853115\pi$
$194$			114.000i			0.587629i
$195$		0			0
$196$	−158.000			−0.806122
$197$	−153.000	−	153.000i	−0.776650	−	0.776650i	0.202610	−	0.979260i	$-0.435058\pi$
$197$	−153.000	−	153.000i	−0.776650	−	0.776650i	−0.979260	+	0.202610i	$0.935058\pi$
$198$		0			0
$199$		−	252.000i		−	1.26633i	−0.774016	−	0.633166i	$-0.781755\pi$
$199$		−	252.000i		−	1.26633i	0.774016	−	0.633166i	$-0.218245\pi$
$200$	−62.0000	−	34.0000i	−0.310000	−	0.170000i
$201$		0			0
$202$	−56.0000	−	56.0000i	−0.277228	−	0.277228i
$203$	304.000	−	304.000i	1.49754	−	1.49754i
$204$		0			0
$205$	−210.000	+	280.000i	−1.02439	+	1.36585i
$206$	−8.00000			−0.0388350
$207$		0			0
$208$	12.0000	−	12.0000i	0.0576923	−	0.0576923i
$209$		−	32.0000i		−	0.153110i
$210$		0			0
$211$	−64.0000			−0.303318			−0.151659	−	0.988433i	$-0.548461\pi$
$211$	−64.0000			−0.303318			−0.151659	+	0.988433i	$0.548461\pi$
$212$	34.0000	+	34.0000i	0.160377	+	0.160377i
$213$		0			0
$214$			136.000i			0.635514i
$215$	36.0000	+	252.000i	0.167442	+	1.17209i
$216$		0			0
$217$	−352.000	−	352.000i	−1.62212	−	1.62212i
$218$	−46.0000	+	46.0000i	−0.211009	+	0.211009i
$219$		0			0
$220$	−32.0000	−	24.0000i	−0.145455	−	0.109091i
$221$	−114.000			−0.515837
$222$		0			0
$223$	−228.000	+	228.000i	−1.02242	+	1.02242i	−0.0226787	+	0.999743i	$0.507219\pi$
$223$	−228.000	+	228.000i	−1.02242	+	1.02242i	−0.999743	+	0.0226787i	$0.992781\pi$
$224$			64.0000i			0.285714i
$225$		0			0
$226$	−106.000			−0.469027
$227$	−100.000	−	100.000i	−0.440529	−	0.440529i	0.451661	−	0.892190i	$-0.350832\pi$
$227$	−100.000	−	100.000i	−0.440529	−	0.440529i	−0.892190	+	0.451661i	$0.850832\pi$
$228$		0			0
$229$		−	312.000i		−	1.36245i	−0.732076	−	0.681223i	$-0.761449\pi$
$229$		−	312.000i		−	1.36245i	0.732076	−	0.681223i	$-0.238551\pi$
$230$	−120.000	+	160.000i	−0.521739	+	0.695652i
$231$		0			0
$232$	−76.0000	−	76.0000i	−0.327586	−	0.327586i
$233$	−93.0000	+	93.0000i	−0.399142	+	0.399142i	−0.877930	−	0.478789i	$-0.841076\pi$
$233$	−93.0000	+	93.0000i	−0.399142	+	0.399142i	0.478789	+	0.877930i	$0.341076\pi$
$234$		0			0
$235$		0			0
$236$	184.000			0.779661
$237$		0			0
$238$	304.000	−	304.000i	1.27731	−	1.27731i
$239$		−	96.0000i		−	0.401674i	−0.979625	−	0.200837i	$-0.935634\pi$
$239$		−	96.0000i		−	0.401674i	0.979625	−	0.200837i	$-0.0643661\pi$
$240$		0			0
$241$	160.000			0.663900			0.331950	−	0.943297i	$-0.392293\pi$
$241$	160.000			0.663900			0.331950	+	0.943297i	$0.392293\pi$
$242$	105.000	+	105.000i	0.433884	+	0.433884i
$243$		0			0
$244$			144.000i			0.590164i
$245$	−316.000	−	237.000i	−1.28980	−	0.967347i
$246$		0			0
$247$	24.0000	+	24.0000i	0.0971660	+	0.0971660i
$248$	−88.0000	+	88.0000i	−0.354839	+	0.354839i
$249$		0			0
$250$	−73.0000	−	161.000i	−0.292000	−	0.644000i
$251$	12.0000			0.0478088			0.0239044	−	0.999714i	$-0.492390\pi$
$251$	12.0000			0.0478088			0.0239044	+	0.999714i	$0.492390\pi$
$252$		0			0
$253$	−80.0000	+	80.0000i	−0.316206	+	0.316206i
$254$		−	136.000i		−	0.535433i
$255$		0			0
$256$	16.0000			0.0625000
$257$	101.000	+	101.000i	0.392996	+	0.392996i	0.875754	−	0.482758i	$-0.160365\pi$
$257$	101.000	+	101.000i	0.392996	+	0.392996i	−0.482758	+	0.875754i	$0.660365\pi$
$258$		0			0
$259$		−	48.0000i		−	0.185328i
$260$	42.0000	−	6.00000i	0.161538	−	0.0230769i
$261$		0			0
$262$	44.0000	+	44.0000i	0.167939	+	0.167939i
$263$	−208.000	+	208.000i	−0.790875	+	0.790875i	−0.981636	−	0.190762i	$-0.938904\pi$
$263$	−208.000	+	208.000i	−0.790875	+	0.790875i	0.190762	+	0.981636i	$0.438904\pi$
$264$		0			0
$265$	17.0000	+	119.000i	0.0641509	+	0.449057i
$266$	−128.000			−0.481203
$267$		0			0
$268$	−88.0000	+	88.0000i	−0.328358	+	0.328358i
$269$		−	296.000i		−	1.10037i	−0.835042	−	0.550186i	$-0.814557\pi$
$269$		−	296.000i		−	1.10037i	0.835042	−	0.550186i	$-0.185443\pi$
$270$		0			0
$271$	108.000			0.398524			0.199262	−	0.979946i	$-0.436146\pi$
$271$	108.000			0.398524			0.199262	+	0.979946i	$0.436146\pi$
$272$	−76.0000	−	76.0000i	−0.279412	−	0.279412i
$273$		0			0
$274$			138.000i			0.503650i
$275$	−28.0000	−	96.0000i	−0.101818	−	0.349091i
$276$		0			0
$277$	−243.000	−	243.000i	−0.877256	−	0.877256i	0.115994	−	0.993250i	$-0.462995\pi$
$277$	−243.000	−	243.000i	−0.877256	−	0.877256i	−0.993250	+	0.115994i	$0.962995\pi$
$278$	80.0000	−	80.0000i	0.287770	−	0.287770i
$279$		0			0
$280$	−96.0000	+	128.000i	−0.342857	+	0.457143i
$281$	378.000			1.34520			0.672598	−	0.740008i	$-0.265178\pi$
$281$	378.000			1.34520			0.672598	+	0.740008i	$0.265178\pi$
$282$		0			0
$283$	92.0000	−	92.0000i	0.325088	−	0.325088i	−0.525627	−	0.850715i	$-0.676169\pi$
$283$	92.0000	−	92.0000i	0.325088	−	0.325088i	0.850715	+	0.525627i	$0.176169\pi$
$284$		−	176.000i		−	0.619718i
$285$		0			0
$286$	24.0000			0.0839161
$287$	560.000	+	560.000i	1.95122	+	1.95122i
$288$		0			0
$289$			433.000i			1.49827i
$290$	−38.0000	−	266.000i	−0.131034	−	0.917241i
$291$		0			0
$292$	110.000	+	110.000i	0.376712	+	0.376712i
$293$	−279.000	+	279.000i	−0.952218	+	0.952218i	−0.998909	−	0.0466910i	$-0.985132\pi$
$293$	−279.000	+	279.000i	−0.952218	+	0.952218i	0.0466910	+	0.998909i	$0.485132\pi$
$294$		0			0
$295$	368.000	+	276.000i	1.24746	+	0.935593i
$296$	−12.0000			−0.0405405
$297$		0			0
$298$	168.000	−	168.000i	0.563758	−	0.563758i
$299$		−	120.000i		−	0.401338i
$300$		0			0
$301$	576.000			1.91362
$302$	−4.00000	−	4.00000i	−0.0132450	−	0.0132450i
$303$		0			0
$304$			32.0000i			0.105263i
$305$	−216.000	+	288.000i	−0.708197	+	0.944262i
$306$		0			0
$307$	216.000	+	216.000i	0.703583	+	0.703583i	0.965178	−	0.261595i	$-0.0842484\pi$
$307$	216.000	+	216.000i	0.703583	+	0.703583i	−0.261595	+	0.965178i	$0.584248\pi$
$308$	−64.0000	+	64.0000i	−0.207792	+	0.207792i
$309$		0			0
$310$	−308.000	+	44.0000i	−0.993548	+	0.141935i
$311$	272.000			0.874598			0.437299	−	0.899316i	$-0.355935\pi$
$311$	272.000			0.874598			0.437299	+	0.899316i	$0.355935\pi$
$312$		0			0
$313$	15.0000	−	15.0000i	0.0479233	−	0.0479233i	−0.682739	−	0.730662i	$-0.739211\pi$
$313$	15.0000	−	15.0000i	0.0479233	−	0.0479233i	0.730662	+	0.682739i	$0.239211\pi$
$314$		−	198.000i		−	0.630573i
$315$		0			0
$316$	−24.0000			−0.0759494
$317$	87.0000	+	87.0000i	0.274448	+	0.274448i	0.830888	−	0.556440i	$-0.187833\pi$
$317$	87.0000	+	87.0000i	0.274448	+	0.274448i	−0.556440	+	0.830888i	$0.687833\pi$
$318$		0			0
$319$		−	152.000i		−	0.476489i
$320$	32.0000	+	24.0000i	0.100000	+	0.0750000i
$321$		0			0
$322$	320.000	+	320.000i	0.993789	+	0.993789i
$323$	152.000	−	152.000i	0.470588	−	0.470588i
$324$		0			0
$325$	93.0000	+	51.0000i	0.286154	+	0.156923i
$326$	320.000			0.981595
$327$		0			0
$328$	140.000	−	140.000i	0.426829	−	0.426829i
$329$		0			0
$330$		0			0
$331$	−584.000			−1.76435			−0.882175	−	0.470921i	$-0.843922\pi$
$331$	−584.000			−1.76435			−0.882175	+	0.470921i	$0.843922\pi$
$332$	−48.0000	−	48.0000i	−0.144578	−	0.144578i
$333$		0			0
$334$		−	112.000i		−	0.335329i
$335$	−308.000	+	44.0000i	−0.919403	+	0.131343i
$336$		0			0
$337$	−129.000	−	129.000i	−0.382789	−	0.382789i	0.489317	−	0.872106i	$-0.337246\pi$
$337$	−129.000	−	129.000i	−0.382789	−	0.382789i	−0.872106	+	0.489317i	$0.837246\pi$
$338$	151.000	−	151.000i	0.446746	−	0.446746i
$339$		0			0
$340$	−38.0000	−	266.000i	−0.111765	−	0.782353i
$341$	−176.000			−0.516129
$342$		0			0
$343$	−240.000	+	240.000i	−0.699708	+	0.699708i
$344$		−	144.000i		−	0.418605i
$345$		0			0
$346$	82.0000			0.236994
$347$	−260.000	−	260.000i	−0.749280	−	0.749280i	0.225064	−	0.974344i	$-0.427741\pi$
$347$	−260.000	−	260.000i	−0.749280	−	0.749280i	−0.974344	+	0.225064i	$0.927741\pi$
$348$		0			0
$349$			136.000i			0.389685i	0.980835	+	0.194842i	$0.0624195\pi$
$349$			136.000i			0.389685i	−0.980835	+	0.194842i	$0.937580\pi$
$350$	−384.000	+	112.000i	−1.09714	+	0.320000i
$351$		0			0
$352$	16.0000	+	16.0000i	0.0454545	+	0.0454545i
$353$	−75.0000	+	75.0000i	−0.212465	+	0.212465i	−0.805314	−	0.592849i	$-0.798003\pi$
$353$	−75.0000	+	75.0000i	−0.212465	+	0.212465i	0.592849	+	0.805314i	$0.298003\pi$
$354$		0			0
$355$	264.000	−	352.000i	0.743662	−	0.991549i
$356$	−52.0000			−0.146067
$357$		0			0
$358$	−172.000	+	172.000i	−0.480447	+	0.480447i
$359$			32.0000i			0.0891365i	0.999006	+	0.0445682i	$0.0141912\pi$
$359$			32.0000i			0.0891365i	−0.999006	+	0.0445682i	$0.985809\pi$
$360$		0			0
$361$	297.000			0.822715
$362$	−62.0000	−	62.0000i	−0.171271	−	0.171271i
$363$		0			0
$364$		−	96.0000i		−	0.263736i
$365$	55.0000	+	385.000i	0.150685	+	1.05479i
$366$		0			0
$367$	−16.0000	−	16.0000i	−0.0435967	−	0.0435967i	0.684972	−	0.728569i	$-0.259814\pi$
$367$	−16.0000	−	16.0000i	−0.0435967	−	0.0435967i	−0.728569	+	0.684972i	$0.759814\pi$
$368$	80.0000	−	80.0000i	0.217391	−	0.217391i
$369$		0			0
$370$	−24.0000	−	18.0000i	−0.0648649	−	0.0486486i
$371$	272.000			0.733154
$372$		0			0
$373$	−251.000	+	251.000i	−0.672922	+	0.672922i	−0.958389	−	0.285466i	$-0.907851\pi$
$373$	−251.000	+	251.000i	−0.672922	+	0.672922i	0.285466	+	0.958389i	$0.407851\pi$
$374$		−	152.000i		−	0.406417i
$375$		0			0
$376$		0			0
$377$	114.000	+	114.000i	0.302387	+	0.302387i
$378$		0			0
$379$		−	560.000i		−	1.47757i	−0.673940	−	0.738786i	$-0.735399\pi$
$379$		−	560.000i		−	1.47757i	0.673940	−	0.738786i	$-0.264601\pi$
$380$	−48.0000	+	64.0000i	−0.126316	+	0.168421i
$381$		0			0
$382$	−248.000	−	248.000i	−0.649215	−	0.649215i
$383$	−300.000	+	300.000i	−0.783290	+	0.783290i	−0.980384	−	0.197095i	$-0.936849\pi$
$383$	−300.000	+	300.000i	−0.783290	+	0.783290i	0.197095	+	0.980384i	$0.436849\pi$
$384$		0			0
$385$	−224.000	+	32.0000i	−0.581818	+	0.0831169i
$386$	−270.000			−0.699482
$387$		0			0
$388$	114.000	−	114.000i	0.293814	−	0.293814i
$389$		−	24.0000i		−	0.0616967i	−0.999524	−	0.0308483i	$-0.990179\pi$
$389$		−	24.0000i		−	0.0616967i	0.999524	−	0.0308483i	$-0.00982089\pi$
$390$		0			0
$391$	−760.000			−1.94373
$392$	158.000	+	158.000i	0.403061	+	0.403061i
$393$		0			0
$394$			306.000i			0.776650i
$395$	−48.0000	−	36.0000i	−0.121519	−	0.0911392i
$396$		0			0
$397$	−299.000	−	299.000i	−0.753149	−	0.753149i	0.221917	−	0.975066i	$-0.428769\pi$
$397$	−299.000	−	299.000i	−0.753149	−	0.753149i	−0.975066	+	0.221917i	$0.928769\pi$
$398$	−252.000	+	252.000i	−0.633166	+	0.633166i
$399$		0			0
$400$	28.0000	+	96.0000i	0.0700000	+	0.240000i
$401$	−144.000			−0.359102			−0.179551	−	0.983749i	$-0.557465\pi$
$401$	−144.000			−0.359102			−0.179551	+	0.983749i	$0.557465\pi$
$402$		0			0
$403$	132.000	−	132.000i	0.327543	−	0.327543i
$404$			112.000i			0.277228i
$405$		0			0
$406$	−608.000			−1.49754
$407$	−12.0000	−	12.0000i	−0.0294840	−	0.0294840i
$408$		0			0
$409$		−	354.000i		−	0.865526i	−0.901508	−	0.432763i	$-0.857539\pi$
$409$		−	354.000i		−	0.865526i	0.901508	−	0.432763i	$-0.142461\pi$
$410$	490.000	−	70.0000i	1.19512	−	0.170732i
$411$		0			0
$412$	8.00000	+	8.00000i	0.0194175	+	0.0194175i
$413$	736.000	−	736.000i	1.78208	−	1.78208i
$414$		0			0
$415$	−24.0000	−	168.000i	−0.0578313	−	0.404819i
$416$	−24.0000			−0.0576923
$417$		0			0
$418$	−32.0000	+	32.0000i	−0.0765550	+	0.0765550i
$419$		−	468.000i		−	1.11695i	−0.829523	−	0.558473i	$-0.811388\pi$
$419$		−	468.000i		−	1.11695i	0.829523	−	0.558473i	$-0.188612\pi$
$420$		0			0
$421$	104.000			0.247031			0.123515	−	0.992343i	$-0.460583\pi$
$421$	104.000			0.247031			0.123515	+	0.992343i	$0.460583\pi$
$422$	64.0000	+	64.0000i	0.151659	+	0.151659i
$423$		0			0
$424$		−	68.0000i		−	0.160377i
$425$	323.000	−	589.000i	0.760000	−	1.38588i
$426$		0			0
$427$	576.000	+	576.000i	1.34895	+	1.34895i
$428$	136.000	−	136.000i	0.317757	−	0.317757i
$429$		0			0
$430$	216.000	−	288.000i	0.502326	−	0.669767i
$431$	−680.000			−1.57773			−0.788863	−	0.614569i	$-0.789330\pi$
$431$	−680.000			−1.57773			−0.788863	+	0.614569i	$0.789330\pi$
$432$		0			0
$433$	41.0000	−	41.0000i	0.0946882	−	0.0946882i	−0.658176	−	0.752864i	$-0.728672\pi$
$433$	41.0000	−	41.0000i	0.0946882	−	0.0946882i	0.752864	+	0.658176i	$0.228672\pi$
$434$			704.000i			1.62212i
$435$		0			0
$436$	92.0000			0.211009
$437$	160.000	+	160.000i	0.366133	+	0.366133i
$438$		0			0
$439$		−	364.000i		−	0.829157i	−0.910014	−	0.414579i	$-0.863929\pi$
$439$		−	364.000i		−	0.829157i	0.910014	−	0.414579i	$-0.136071\pi$
$440$	8.00000	+	56.0000i	0.0181818	+	0.127273i
$441$		0			0
$442$	114.000	+	114.000i	0.257919	+	0.257919i
$443$	−372.000	+	372.000i	−0.839729	+	0.839729i	−0.988823	−	0.149094i	$-0.952364\pi$
$443$	−372.000	+	372.000i	−0.839729	+	0.839729i	0.149094	+	0.988823i	$0.452364\pi$
$444$		0			0
$445$	−104.000	−	78.0000i	−0.233708	−	0.175281i
$446$	456.000			1.02242
$447$		0			0
$448$	64.0000	−	64.0000i	0.142857	−	0.142857i
$449$		−	176.000i		−	0.391982i	−0.980606	−	0.195991i	$-0.937208\pi$
$449$		−	176.000i		−	0.391982i	0.980606	−	0.195991i	$-0.0627924\pi$
$450$		0			0
$451$	280.000			0.620843
$452$	106.000	+	106.000i	0.234513	+	0.234513i
$453$		0			0
$454$			200.000i			0.440529i
$455$	144.000	−	192.000i	0.316484	−	0.421978i
$456$		0			0
$457$	129.000	+	129.000i	0.282276	+	0.282276i	0.834016	−	0.551740i	$-0.186036\pi$
$457$	129.000	+	129.000i	0.282276	+	0.282276i	−0.551740	+	0.834016i	$0.686036\pi$
$458$	−312.000	+	312.000i	−0.681223	+	0.681223i
$459$		0			0
$460$	280.000	−	40.0000i	0.608696	−	0.0869565i
$461$	568.000			1.23210			0.616052	−	0.787705i	$-0.288731\pi$
$461$	568.000			1.23210			0.616052	+	0.787705i	$0.288731\pi$
$462$		0			0
$463$	−568.000	+	568.000i	−1.22678	+	1.22678i	−0.261608	+	0.965174i	$0.584253\pi$
$463$	−568.000	+	568.000i	−1.22678	+	1.22678i	−0.965174	+	0.261608i	$0.915747\pi$
$464$			152.000i			0.327586i
$465$		0			0
$466$	186.000			0.399142
$467$	−272.000	−	272.000i	−0.582441	−	0.582441i	0.353132	−	0.935573i	$-0.385117\pi$
$467$	−272.000	−	272.000i	−0.582441	−	0.582441i	−0.935573	+	0.353132i	$0.885117\pi$
$468$		0			0
$469$			704.000i			1.50107i
$470$		0			0
$471$		0			0
$472$	−184.000	−	184.000i	−0.389831	−	0.389831i
$473$	144.000	−	144.000i	0.304440	−	0.304440i
$474$		0			0
$475$	−192.000	+	56.0000i	−0.404211	+	0.117895i
$476$	−608.000			−1.27731
$477$		0			0
$478$	−96.0000	+	96.0000i	−0.200837	+	0.200837i
$479$			928.000i			1.93737i	0.248294	+	0.968685i	$0.420130\pi$
$479$			928.000i			1.93737i	−0.248294	+	0.968685i	$0.579870\pi$
$480$		0			0
$481$	18.0000			0.0374220
$482$	−160.000	−	160.000i	−0.331950	−	0.331950i
$483$		0			0
$484$		−	210.000i		−	0.433884i
$485$	399.000	−	57.0000i	0.822680	−	0.117526i
$486$		0			0
$487$	252.000	+	252.000i	0.517454	+	0.517454i	0.916800	−	0.399346i	$-0.130763\pi$
$487$	252.000	+	252.000i	0.517454	+	0.517454i	−0.399346	+	0.916800i	$0.630763\pi$
$488$	144.000	−	144.000i	0.295082	−	0.295082i
$489$		0			0
$490$	79.0000	+	553.000i	0.161224	+	1.12857i
$491$	−844.000			−1.71894			−0.859470	−	0.511185i	$-0.829207\pi$
$491$	−844.000			−1.71894			−0.859470	+	0.511185i	$0.829207\pi$
$492$		0			0
$493$	722.000	−	722.000i	1.46450	−	1.46450i
$494$		−	48.0000i		−	0.0971660i
$495$		0			0
$496$	176.000			0.354839
$497$	−704.000	−	704.000i	−1.41650	−	1.41650i
$498$		0			0
$499$			872.000i			1.74749i	0.486380	+	0.873747i	$0.338317\pi$
$499$			872.000i			1.74749i	−0.486380	+	0.873747i	$0.661683\pi$
$500$	−88.0000	+	234.000i	−0.176000	+	0.468000i
$501$		0			0
$502$	−12.0000	−	12.0000i	−0.0239044	−	0.0239044i
$503$	480.000	−	480.000i	0.954274	−	0.954274i	−0.0447250	−	0.998999i	$-0.514241\pi$
$503$	480.000	−	480.000i	0.954274	−	0.954274i	0.998999	+	0.0447250i	$0.0142412\pi$
$504$		0			0
$505$	−168.000	+	224.000i	−0.332673	+	0.443564i
$506$	160.000			0.316206
$507$		0			0
$508$	−136.000	+	136.000i	−0.267717	+	0.267717i
$509$			694.000i			1.36346i	0.731605	+	0.681729i	$0.238772\pi$
$509$			694.000i			1.36346i	−0.731605	+	0.681729i	$0.761228\pi$
$510$		0			0
$511$	880.000			1.72211
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$		0			0
$514$		−	202.000i		−	0.392996i
$515$	4.00000	+	28.0000i	0.00776699	+	0.0543689i
$516$		0			0
$517$		0			0
$518$	−48.0000	+	48.0000i	−0.0926641	+	0.0926641i
$519$		0			0
$520$	−48.0000	−	36.0000i	−0.0923077	−	0.0692308i
$521$	528.000			1.01344			0.506718	−	0.862112i	$-0.330859\pi$
$521$	528.000			1.01344			0.506718	+	0.862112i	$0.330859\pi$
$522$		0			0
$523$	552.000	−	552.000i	1.05545	−	1.05545i	0.0570797	−	0.998370i	$-0.481821\pi$
$523$	552.000	−	552.000i	1.05545	−	1.05545i	0.998370	−	0.0570797i	$-0.0181789\pi$
$524$		−	88.0000i		−	0.167939i
$525$		0			0
$526$	416.000			0.790875
$527$	−836.000	−	836.000i	−1.58634	−	1.58634i
$528$		0			0
$529$		−	271.000i		−	0.512287i
$530$	102.000	−	136.000i	0.192453	−	0.256604i
$531$		0			0
$532$	128.000	+	128.000i	0.240602	+	0.240602i
$533$	−210.000	+	210.000i	−0.393996	+	0.393996i
$534$		0			0
$535$	476.000	−	68.0000i	0.889720	−	0.127103i
$536$	176.000			0.328358
$537$		0			0
$538$	−296.000	+	296.000i	−0.550186	+	0.550186i
$539$			316.000i			0.586271i
$540$		0			0
$541$	−782.000			−1.44547			−0.722736	−	0.691125i	$-0.757116\pi$
$541$	−782.000			−1.44547			−0.722736	+	0.691125i	$0.757116\pi$
$542$	−108.000	−	108.000i	−0.199262	−	0.199262i
$543$		0			0
$544$			152.000i			0.279412i
$545$	184.000	+	138.000i	0.337615	+	0.253211i
$546$		0			0
$547$	−420.000	−	420.000i	−0.767824	−	0.767824i	0.209899	−	0.977723i	$-0.432687\pi$
$547$	−420.000	−	420.000i	−0.767824	−	0.767824i	−0.977723	+	0.209899i	$0.932687\pi$
$548$	138.000	−	138.000i	0.251825	−	0.251825i
$549$		0			0
$550$	−68.0000	+	124.000i	−0.123636	+	0.225455i
$551$	−304.000			−0.551724
$552$		0			0
$553$	−96.0000	+	96.0000i	−0.173599	+	0.173599i
$554$			486.000i			0.877256i
$555$		0			0
$556$	−160.000			−0.287770
$557$	417.000	+	417.000i	0.748654	+	0.748654i	0.974226	−	0.225573i	$-0.0724254\pi$
$557$	417.000	+	417.000i	0.748654	+	0.748654i	−0.225573	+	0.974226i	$0.572425\pi$
$558$		0			0
$559$			216.000i			0.386404i
$560$	224.000	−	32.0000i	0.400000	−	0.0571429i
$561$		0			0
$562$	−378.000	−	378.000i	−0.672598	−	0.672598i
$563$	228.000	−	228.000i	0.404973	−	0.404973i	−0.475008	−	0.879981i	$-0.657555\pi$
$563$	228.000	−	228.000i	0.404973	−	0.404973i	0.879981	+	0.475008i	$0.157555\pi$
$564$		0			0
$565$	53.0000	+	371.000i	0.0938053	+	0.656637i
$566$	−184.000			−0.325088
$567$		0			0
$568$	−176.000	+	176.000i	−0.309859	+	0.309859i
$569$			368.000i			0.646749i	0.946271	+	0.323374i	$0.104817\pi$
$569$			368.000i			0.646749i	−0.946271	+	0.323374i	$0.895183\pi$
$570$		0			0
$571$	−736.000			−1.28897			−0.644483	−	0.764618i	$-0.722928\pi$
$571$	−736.000			−1.28897			−0.644483	+	0.764618i	$0.722928\pi$
$572$	−24.0000	−	24.0000i	−0.0419580	−	0.0419580i
$573$		0			0
$574$		−	1120.00i		−	1.95122i
$575$	620.000	+	340.000i	1.07826	+	0.591304i
$576$		0			0
$577$	−113.000	−	113.000i	−0.195841	−	0.195841i	0.602374	−	0.798214i	$-0.294222\pi$
$577$	−113.000	−	113.000i	−0.195841	−	0.195841i	−0.798214	+	0.602374i	$0.794222\pi$
$578$	433.000	−	433.000i	0.749135	−	0.749135i
$579$		0			0
$580$	−228.000	+	304.000i	−0.393103	+	0.524138i
$581$	−384.000			−0.660929
$582$		0			0
$583$	68.0000	−	68.0000i	0.116638	−	0.116638i
$584$		−	220.000i		−	0.376712i
$585$		0			0
$586$	558.000			0.952218
$587$	684.000	+	684.000i	1.16525	+	1.16525i	0.983310	+	0.181937i	$0.0582366\pi$
$587$	684.000	+	684.000i	1.16525	+	1.16525i	0.181937	+	0.983310i	$0.441763\pi$
$588$		0			0
$589$			352.000i			0.597623i
$590$	−92.0000	−	644.000i	−0.155932	−	1.09153i
$591$		0			0
$592$	12.0000	+	12.0000i	0.0202703	+	0.0202703i
$593$	−149.000	+	149.000i	−0.251265	+	0.251265i	−0.821489	−	0.570224i	$-0.806856\pi$
$593$	−149.000	+	149.000i	−0.251265	+	0.251265i	0.570224	+	0.821489i	$0.306856\pi$
$594$		0			0
$595$	−1216.00	−	912.000i	−2.04370	−	1.53277i
$596$	−336.000			−0.563758
$597$		0			0
$598$	−120.000	+	120.000i	−0.200669	+	0.200669i
$599$		−	152.000i		−	0.253756i	−0.991918	−	0.126878i	$-0.959504\pi$
$599$		−	152.000i		−	0.253756i	0.991918	−	0.126878i	$-0.0404957\pi$
$600$		0			0
$601$	320.000			0.532446			0.266223	−	0.963911i	$-0.414224\pi$
$601$	320.000			0.532446			0.266223	+	0.963911i	$0.414224\pi$
$602$	−576.000	−	576.000i	−0.956811	−	0.956811i
$603$		0			0
$604$			8.00000i			0.0132450i
$605$	315.000	−	420.000i	0.520661	−	0.694215i
$606$		0			0
$607$	−528.000	−	528.000i	−0.869852	−	0.869852i	0.122604	−	0.992456i	$-0.460876\pi$
$607$	−528.000	−	528.000i	−0.869852	−	0.869852i	−0.992456	+	0.122604i	$0.960876\pi$
$608$	32.0000	−	32.0000i	0.0526316	−	0.0526316i
$609$		0			0
$610$	504.000	−	72.0000i	0.826230	−	0.118033i
$611$		0			0
$612$		0			0
$613$	771.000	−	771.000i	1.25775	−	1.25775i	0.305583	−	0.952165i	$-0.401148\pi$
$613$	771.000	−	771.000i	1.25775	−	1.25775i	0.952165	−	0.305583i	$-0.0988515\pi$
$614$		−	432.000i		−	0.703583i
$615$		0			0
$616$	128.000			0.207792
$617$	675.000	+	675.000i	1.09400	+	1.09400i	0.995097	+	0.0989065i	$0.0315345\pi$
$617$	675.000	+	675.000i	1.09400	+	1.09400i	0.0989065	+	0.995097i	$0.468466\pi$
$618$		0			0
$619$			600.000i			0.969305i	0.874707	+	0.484653i	$0.161054\pi$
$619$			600.000i			0.969305i	−0.874707	+	0.484653i	$0.838946\pi$
$620$	352.000	+	264.000i	0.567742	+	0.425806i
$621$		0			0
$622$	−272.000	−	272.000i	−0.437299	−	0.437299i
$623$	−208.000	+	208.000i	−0.333868	+	0.333868i
$624$		0			0
$625$	−527.000	+	336.000i	−0.843200	+	0.537600i
$626$	−30.0000			−0.0479233
$627$		0			0
$628$	−198.000	+	198.000i	−0.315287	+	0.315287i
$629$		−	114.000i		−	0.181240i
$630$		0			0
$631$	−20.0000			−0.0316957			−0.0158479	−	0.999874i	$-0.505045\pi$
$631$	−20.0000			−0.0316957			−0.0158479	+	0.999874i	$0.505045\pi$
$632$	24.0000	+	24.0000i	0.0379747	+	0.0379747i
$633$		0			0
$634$		−	174.000i		−	0.274448i
$635$	−476.000	+	68.0000i	−0.749606	+	0.107087i
$636$		0			0
$637$	−237.000	−	237.000i	−0.372057	−	0.372057i
$638$	−152.000	+	152.000i	−0.238245	+	0.238245i
$639$		0			0
$640$	−8.00000	−	56.0000i	−0.0125000	−	0.0875000i
$641$	−694.000			−1.08268			−0.541342	−	0.840803i	$-0.682083\pi$
$641$	−694.000			−1.08268			−0.541342	+	0.840803i	$0.682083\pi$
$642$		0			0
$643$	−168.000	+	168.000i	−0.261275	+	0.261275i	−0.825572	−	0.564297i	$-0.809147\pi$
$643$	−168.000	+	168.000i	−0.261275	+	0.261275i	0.564297	+	0.825572i	$0.309147\pi$
$644$		−	640.000i		−	0.993789i
$645$		0			0
$646$	−304.000			−0.470588
$647$	−328.000	−	328.000i	−0.506955	−	0.506955i	0.406635	−	0.913591i	$-0.366702\pi$
$647$	−328.000	−	328.000i	−0.506955	−	0.506955i	−0.913591	+	0.406635i	$0.866702\pi$
$648$		0			0
$649$		−	368.000i		−	0.567026i
$650$	−42.0000	−	144.000i	−0.0646154	−	0.221538i
$651$		0			0
$652$	−320.000	−	320.000i	−0.490798	−	0.490798i
$653$	81.0000	−	81.0000i	0.124043	−	0.124043i	−0.642360	−	0.766403i	$-0.722045\pi$
$653$	81.0000	−	81.0000i	0.124043	−	0.124043i	0.766403	+	0.642360i	$0.222045\pi$
$654$		0			0
$655$	132.000	−	176.000i	0.201527	−	0.268702i
$656$	−280.000			−0.426829
$657$		0			0
$658$		0			0
$659$			500.000i			0.758725i	0.925248	+	0.379363i	$0.123857\pi$
$659$			500.000i			0.758725i	−0.925248	+	0.379363i	$0.876143\pi$
$660$		0			0
$661$	−568.000			−0.859304			−0.429652	−	0.902995i	$-0.641364\pi$
$661$	−568.000			−0.859304			−0.429652	+	0.902995i	$0.641364\pi$
$662$	584.000	+	584.000i	0.882175	+	0.882175i
$663$		0			0
$664$			96.0000i			0.144578i
$665$	64.0000	+	448.000i	0.0962406	+	0.673684i
$666$		0			0
$667$	760.000	+	760.000i	1.13943	+	1.13943i
$668$	−112.000	+	112.000i	−0.167665	+	0.167665i
$669$		0			0
$670$	352.000	+	264.000i	0.525373	+	0.394030i
$671$	288.000			0.429210
$672$		0			0
$673$	73.0000	−	73.0000i	0.108470	−	0.108470i	−0.650789	−	0.759259i	$-0.725562\pi$
$673$	73.0000	−	73.0000i	0.108470	−	0.108470i	0.759259	+	0.650789i	$0.225562\pi$
$674$			258.000i			0.382789i
$675$		0			0
$676$	−302.000			−0.446746
$677$	−839.000	−	839.000i	−1.23929	−	1.23929i	−0.960291	−	0.279000i	$-0.909997\pi$
$677$	−839.000	−	839.000i	−1.23929	−	1.23929i	−0.279000	−	0.960291i	$-0.590003\pi$
$678$		0			0
$679$		−	912.000i		−	1.34315i
$680$	−228.000	+	304.000i	−0.335294	+	0.447059i
$681$		0			0
$682$	176.000	+	176.000i	0.258065	+	0.258065i
$683$	−744.000	+	744.000i	−1.08931	+	1.08931i	−0.0937126	+	0.995599i	$0.529873\pi$
$683$	−744.000	+	744.000i	−1.08931	+	1.08931i	−0.995599	+	0.0937126i	$0.970127\pi$
$684$		0			0
$685$	483.000	−	69.0000i	0.705109	−	0.100730i
$686$	480.000			0.699708
$687$		0			0
$688$	−144.000	+	144.000i	−0.209302	+	0.209302i
$689$			102.000i			0.148041i
$690$		0			0
$691$	504.000			0.729378			0.364689	−	0.931129i	$-0.381175\pi$
$691$	504.000			0.729378			0.364689	+	0.931129i	$0.381175\pi$
$692$	−82.0000	−	82.0000i	−0.118497	−	0.118497i
$693$		0			0
$694$			520.000i			0.749280i
$695$	−320.000	−	240.000i	−0.460432	−	0.345324i
$696$		0			0
$697$	1330.00	+	1330.00i	1.90818	+	1.90818i
$698$	136.000	−	136.000i	0.194842	−	0.194842i
$699$		0			0
$700$	496.000	+	272.000i	0.708571	+	0.388571i
$701$	298.000			0.425107			0.212553	−	0.977149i	$-0.431822\pi$
$701$	298.000			0.425107			0.212553	+	0.977149i	$0.431822\pi$
$702$		0			0
$703$	−24.0000	+	24.0000i	−0.0341394	+	0.0341394i
$704$		−	32.0000i		−	0.0454545i
$705$		0			0
$706$	150.000			0.212465
$707$	448.000	+	448.000i	0.633663	+	0.633663i
$708$		0			0
$709$			472.000i			0.665726i	0.942975	+	0.332863i	$0.108015\pi$
$709$			472.000i			0.665726i	−0.942975	+	0.332863i	$0.891985\pi$
$710$	−616.000	+	88.0000i	−0.867606	+	0.123944i
$711$		0			0
$712$	52.0000	+	52.0000i	0.0730337	+	0.0730337i
$713$	880.000	−	880.000i	1.23422	−	1.23422i
$714$		0			0
$715$	−12.0000	−	84.0000i	−0.0167832	−	0.117483i
$716$	344.000			0.480447
$717$		0			0
$718$	32.0000	−	32.0000i	0.0445682	−	0.0445682i
$719$		−	872.000i		−	1.21280i	−0.795161	−	0.606398i	$-0.792614\pi$
$719$		−	872.000i		−	1.21280i	0.795161	−	0.606398i	$-0.207386\pi$
$720$		0			0
$721$	64.0000			0.0887656
$722$	−297.000	−	297.000i	−0.411357	−	0.411357i
$723$		0			0
$724$			124.000i			0.171271i
$725$	−912.000	+	266.000i	−1.25793	+	0.366897i
$726$		0			0
$727$	−60.0000	−	60.0000i	−0.0825309	−	0.0825309i	0.664636	−	0.747167i	$-0.268587\pi$
$727$	−60.0000	−	60.0000i	−0.0825309	−	0.0825309i	−0.747167	+	0.664636i	$0.768587\pi$
$728$	−96.0000	+	96.0000i	−0.131868	+	0.131868i
$729$		0			0
$730$	330.000	−	440.000i	0.452055	−	0.602740i
$731$	1368.00			1.87141
$732$		0			0
$733$	−581.000	+	581.000i	−0.792633	+	0.792633i	−0.981922	−	0.189289i	$-0.939382\pi$
$733$	−581.000	+	581.000i	−0.792633	+	0.792633i	0.189289	+	0.981922i	$0.439382\pi$
$734$			32.0000i			0.0435967i
$735$		0			0
$736$	−160.000			−0.217391
$737$	176.000	+	176.000i	0.238806	+	0.238806i
$738$		0			0
$739$			1160.00i			1.56969i	0.619693	+	0.784844i	$0.287257\pi$
$739$			1160.00i			1.56969i	−0.619693	+	0.784844i	$0.712743\pi$
$740$	6.00000	+	42.0000i	0.00810811	+	0.0567568i
$741$		0			0
$742$	−272.000	−	272.000i	−0.366577	−	0.366577i
$743$	380.000	−	380.000i	0.511440	−	0.511440i	−0.403527	−	0.914968i	$-0.632216\pi$
$743$	380.000	−	380.000i	0.511440	−	0.511440i	0.914968	+	0.403527i	$0.132216\pi$
$744$		0			0
$745$	−672.000	−	504.000i	−0.902013	−	0.676510i
$746$	502.000			0.672922
$747$		0			0
$748$	−152.000	+	152.000i	−0.203209	+	0.203209i
$749$		−	1088.00i		−	1.45260i
$750$		0			0
$751$	780.000			1.03862			0.519308	−	0.854587i	$-0.326190\pi$
$751$	780.000			1.03862			0.519308	+	0.854587i	$0.326190\pi$
$752$		0			0
$753$		0			0
$754$		−	228.000i		−	0.302387i
$755$	−12.0000	+	16.0000i	−0.0158940	+	0.0211921i
$756$		0			0
$757$	285.000	+	285.000i	0.376486	+	0.376486i	0.869833	−	0.493347i	$-0.164227\pi$
$757$	285.000	+	285.000i	0.376486	+	0.376486i	−0.493347	+	0.869833i	$0.664227\pi$
$758$	−560.000	+	560.000i	−0.738786	+	0.738786i
$759$		0			0
$760$	112.000	−	16.0000i	0.147368	−	0.0210526i
$761$	304.000			0.399474			0.199737	−	0.979850i	$-0.435991\pi$
$761$	304.000			0.399474			0.199737	+	0.979850i	$0.435991\pi$
$762$		0			0
$763$	368.000	−	368.000i	0.482307	−	0.482307i
$764$			496.000i			0.649215i
$765$		0			0
$766$	600.000			0.783290
$767$	276.000	+	276.000i	0.359844	+	0.359844i
$768$		0			0
$769$		−	1072.00i		−	1.39402i	−0.717062	−	0.697009i	$-0.754514\pi$
$769$		−	1072.00i		−	1.39402i	0.717062	−	0.697009i	$-0.245486\pi$
$770$	256.000	+	192.000i	0.332468	+	0.249351i
$771$		0			0
$772$	270.000	+	270.000i	0.349741	+	0.349741i
$773$	−897.000	+	897.000i	−1.16041	+	1.16041i	−0.176029	+	0.984385i	$0.556325\pi$
$773$	−897.000	+	897.000i	−1.16041	+	1.16041i	−0.984385	+	0.176029i	$0.943675\pi$
$774$		0			0
$775$	308.000	+	1056.00i	0.397419	+	1.36258i
$776$	−228.000			−0.293814
$777$		0			0
$778$	−24.0000	+	24.0000i	−0.0308483	+	0.0308483i
$779$		−	560.000i		−	0.718870i
$780$		0			0
$781$	−352.000			−0.450704
$782$	760.000	+	760.000i	0.971867	+	0.971867i
$783$		0			0
$784$		−	316.000i		−	0.403061i
$785$	−693.000	+	99.0000i	−0.882803	+	0.126115i
$786$		0			0
$787$	328.000	+	328.000i	0.416773	+	0.416773i	0.884090	−	0.467317i	$-0.154779\pi$
$787$	328.000	+	328.000i	0.416773	+	0.416773i	−0.467317	+	0.884090i	$0.654779\pi$
$788$	306.000	−	306.000i	0.388325	−	0.388325i
$789$		0			0
$790$	12.0000	+	84.0000i	0.0151899	+	0.106329i
$791$	848.000			1.07206
$792$		0			0
$793$	−216.000	+	216.000i	−0.272383	+	0.272383i
$794$			598.000i			0.753149i
$795$		0			0
$796$	504.000			0.633166
$797$	−87.0000	−	87.0000i	−0.109159	−	0.109159i	0.650418	−	0.759577i	$-0.274594\pi$
$797$	−87.0000	−	87.0000i	−0.109159	−	0.109159i	−0.759577	+	0.650418i	$0.774594\pi$
$798$		0			0
$799$		0			0
$800$	68.0000	−	124.000i	0.0850000	−	0.155000i
$801$		0			0
$802$	144.000	+	144.000i	0.179551	+	0.179551i
$803$	220.000	−	220.000i	0.273973	−	0.273973i
$804$		0			0
$805$	960.000	−	1280.00i	1.19255	−	1.59006i
$806$	−264.000			−0.327543
$807$		0			0
$808$	112.000	−	112.000i	0.138614	−	0.138614i
$809$		−	922.000i		−	1.13968i	−0.821756	−	0.569839i	$-0.807005\pi$
$809$		−	922.000i		−	1.13968i	0.821756	−	0.569839i	$-0.192995\pi$
$810$		0			0
$811$	−1312.00			−1.61776			−0.808878	−	0.587977i	$-0.799925\pi$
$811$	−1312.00			−1.61776			−0.808878	+	0.587977i	$0.799925\pi$
$812$	608.000	+	608.000i	0.748768	+	0.748768i
$813$		0			0
$814$			24.0000i			0.0294840i
$815$	−160.000	−	1120.00i	−0.196319	−	1.37423i
$816$		0			0
$817$	−288.000	−	288.000i	−0.352509	−	0.352509i
$818$	−354.000	+	354.000i	−0.432763	+	0.432763i
$819$		0			0
$820$	−560.000	−	420.000i	−0.682927	−	0.512195i
$821$	−950.000			−1.15713			−0.578563	−	0.815638i	$-0.696386\pi$
$821$	−950.000			−1.15713			−0.578563	+	0.815638i	$0.696386\pi$
$822$		0			0
$823$	68.0000	−	68.0000i	0.0826245	−	0.0826245i	−0.664587	−	0.747211i	$-0.731392\pi$
$823$	68.0000	−	68.0000i	0.0826245	−	0.0826245i	0.747211	+	0.664587i	$0.231392\pi$
$824$		−	16.0000i		−	0.0194175i
$825$		0			0
$826$	−1472.00			−1.78208
$827$	264.000	+	264.000i	0.319226	+	0.319226i	0.848470	−	0.529244i	$-0.177524\pi$
$827$	264.000	+	264.000i	0.319226	+	0.319226i	−0.529244	+	0.848470i	$0.677524\pi$
$828$		0			0
$829$		−	178.000i		−	0.214717i	−0.994220	−	0.107358i	$-0.965761\pi$
$829$		−	178.000i		−	0.214717i	0.994220	−	0.107358i	$-0.0342392\pi$
$830$	−144.000	+	192.000i	−0.173494	+	0.231325i
$831$		0			0
$832$	24.0000	+	24.0000i	0.0288462	+	0.0288462i
$833$	−1501.00	+	1501.00i	−1.80192	+	1.80192i
$834$		0			0
$835$	−392.000	+	56.0000i	−0.469461	+	0.0670659i
$836$	64.0000			0.0765550
$837$		0			0
$838$	−468.000	+	468.000i	−0.558473	+	0.558473i
$839$		−	1576.00i		−	1.87843i	−0.343334	−	0.939213i	$-0.611556\pi$
$839$		−	1576.00i		−	1.87843i	0.343334	−	0.939213i	$-0.388444\pi$
$840$		0			0
$841$	−603.000			−0.717004
$842$	−104.000	−	104.000i	−0.123515	−	0.123515i
$843$		0			0
$844$		−	128.000i		−	0.151659i
$845$	−604.000	−	453.000i	−0.714793	−	0.536095i
$846$		0			0
$847$	−840.000	−	840.000i	−0.991736	−	0.991736i
$848$	−68.0000	+	68.0000i	−0.0801887	+	0.0801887i
$849$		0			0
$850$	−912.000	+	266.000i	−1.07294	+	0.312941i
$851$	120.000			0.141011
$852$		0			0
$853$	−509.000	+	509.000i	−0.596717	+	0.596717i	−0.939438	−	0.342720i	$-0.888652\pi$
$853$	−509.000	+	509.000i	−0.596717	+	0.596717i	0.342720	+	0.939438i	$0.388652\pi$
$854$		−	1152.00i		−	1.34895i
$855$		0			0
$856$	−272.000			−0.317757
$857$	357.000	+	357.000i	0.416569	+	0.416569i	0.884019	−	0.467450i	$-0.154827\pi$
$857$	357.000	+	357.000i	0.416569	+	0.416569i	−0.467450	+	0.884019i	$0.654827\pi$
$858$		0			0
$859$		−	520.000i		−	0.605355i	−0.953093	−	0.302678i	$-0.902119\pi$
$859$		−	520.000i		−	0.605355i	0.953093	−	0.302678i	$-0.0978805\pi$
$860$	−504.000	+	72.0000i	−0.586047	+	0.0837209i
$861$		0			0
$862$	680.000	+	680.000i	0.788863	+	0.788863i
$863$	952.000	−	952.000i	1.10313	−	1.10313i	0.109098	−	0.994031i	$-0.465204\pi$
$863$	952.000	−	952.000i	1.10313	−	1.10313i	0.994031	−	0.109098i	$-0.0347961\pi$
$864$		0			0
$865$	−41.0000	−	287.000i	−0.0473988	−	0.331792i
$866$	−82.0000			−0.0946882
$867$		0			0
$868$	704.000	−	704.000i	0.811060	−	0.811060i
$869$			48.0000i			0.0552359i
$870$		0			0
$871$	−264.000			−0.303100
$872$	−92.0000	−	92.0000i	−0.105505	−	0.105505i
$873$		0			0
$874$		−	320.000i		−	0.366133i
$875$	584.000	+	1288.00i	0.667429	+	1.47200i
$876$		0			0
$877$	−717.000	−	717.000i	−0.817560	−	0.817560i	0.168194	−	0.985754i	$-0.446206\pi$
$877$	−717.000	−	717.000i	−0.817560	−	0.817560i	−0.985754	+	0.168194i	$0.946206\pi$
$878$	−364.000	+	364.000i	−0.414579	+	0.414579i
$879$		0			0
$880$	48.0000	−	64.0000i	0.0545455	−	0.0727273i
$881$	−554.000			−0.628831			−0.314415	−	0.949285i	$-0.601808\pi$
$881$	−554.000			−0.628831			−0.314415	+	0.949285i	$0.601808\pi$
$882$		0			0
$883$	952.000	−	952.000i	1.07814	−	1.07814i	0.0814666	−	0.996676i	$-0.474040\pi$
$883$	952.000	−	952.000i	1.07814	−	1.07814i	0.996676	−	0.0814666i	$-0.0259604\pi$
$884$		−	228.000i		−	0.257919i
$885$		0			0
$886$	744.000			0.839729
$887$	648.000	+	648.000i	0.730552	+	0.730552i	0.970729	−	0.240177i	$-0.0772054\pi$
$887$	648.000	+	648.000i	0.730552	+	0.730552i	−0.240177	+	0.970729i	$0.577205\pi$
$888$		0			0
$889$			1088.00i			1.22385i
$890$	26.0000	+	182.000i	0.0292135	+	0.204494i
$891$		0			0
$892$	−456.000	−	456.000i	−0.511211	−	0.511211i
$893$		0			0
$894$		0			0
$895$	688.000	+	516.000i	0.768715	+	0.576536i
$896$	−128.000			−0.142857
$897$		0			0
$898$	−176.000	+	176.000i	−0.195991	+	0.195991i
$899$			1672.00i			1.85984i
$900$		0			0
$901$	646.000			0.716981
$902$	−280.000	−	280.000i	−0.310421	−	0.310421i
$903$		0			0
$904$		−	212.000i		−	0.234513i
$905$	−186.000	+	248.000i	−0.205525	+	0.274033i
$906$		0			0
$907$	−740.000	−	740.000i	−0.815877	−	0.815877i	0.169631	−	0.985508i	$-0.445742\pi$
$907$	−740.000	−	740.000i	−0.815877	−	0.815877i	−0.985508	+	0.169631i	$0.945742\pi$
$908$	200.000	−	200.000i	0.220264	−	0.220264i
$909$		0			0
$910$	−336.000	+	48.0000i	−0.369231	+	0.0527473i
$911$	−520.000			−0.570801			−0.285401	−	0.958408i	$-0.592127\pi$
$911$	−520.000			−0.570801			−0.285401	+	0.958408i	$0.592127\pi$
$912$		0			0
$913$	−96.0000	+	96.0000i	−0.105148	+	0.105148i
$914$		−	258.000i		−	0.282276i
$915$		0			0
$916$	624.000			0.681223
$917$	−352.000	−	352.000i	−0.383860	−	0.383860i
$918$		0			0
$919$		−	844.000i		−	0.918390i	−0.888336	−	0.459195i	$-0.848138\pi$
$919$		−	844.000i		−	0.918390i	0.888336	−	0.459195i	$-0.151862\pi$
$920$	−320.000	−	240.000i	−0.347826	−	0.260870i
$921$		0			0
$922$	−568.000	−	568.000i	−0.616052	−	0.616052i
$923$	264.000	−	264.000i	0.286024	−	0.286024i
$924$		0			0
$925$	−51.0000	+	93.0000i	−0.0551351	+	0.100541i
$926$	1136.00			1.22678
$927$		0			0
$928$	152.000	−	152.000i	0.163793	−	0.163793i
$929$			208.000i			0.223897i	0.993714	+	0.111948i	$0.0357091\pi$
$929$			208.000i			0.223897i	−0.993714	+	0.111948i	$0.964291\pi$
$930$		0			0
$931$	632.000			0.678840
$932$	−186.000	−	186.000i	−0.199571	−	0.199571i
$933$		0			0
$934$			544.000i			0.582441i
$935$	−532.000	+	76.0000i	−0.568984	+	0.0812834i
$936$		0			0
$937$	7.00000	+	7.00000i	0.00747065	+	0.00747065i	0.710832	−	0.703362i	$-0.248319\pi$
$937$	7.00000	+	7.00000i	0.00747065	+	0.00747065i	−0.703362	+	0.710832i	$0.748319\pi$
$938$	704.000	−	704.000i	0.750533	−	0.750533i
$939$		0			0
$940$		0			0
$941$	1752.00			1.86185			0.930925	−	0.365212i	$-0.119003\pi$
$941$	1752.00			1.86185			0.930925	+	0.365212i	$0.119003\pi$
$942$		0			0
$943$	−1400.00	+	1400.00i	−1.48462	+	1.48462i
$944$			368.000i			0.389831i
$945$		0			0
$946$	−288.000			−0.304440
$947$	224.000	+	224.000i	0.236536	+	0.236536i	0.815414	−	0.578878i	$-0.196509\pi$
$947$	224.000	+	224.000i	0.236536	+	0.236536i	−0.578878	+	0.815414i	$0.696509\pi$
$948$		0			0
$949$			330.000i			0.347734i
$950$	248.000	+	136.000i	0.261053	+	0.143158i
$951$		0			0
$952$	608.000	+	608.000i	0.638655	+	0.638655i
$953$	645.000	−	645.000i	0.676810	−	0.676810i	−0.282467	−	0.959277i	$-0.591153\pi$
$953$	645.000	−	645.000i	0.676810	−	0.676810i	0.959277	+	0.282467i	$0.0911528\pi$
$954$		0			0
$955$	−744.000	+	992.000i	−0.779058	+	1.03874i
$956$	192.000			0.200837
$957$		0			0
$958$	928.000	−	928.000i	0.968685	−	0.968685i
$959$		−	1104.00i		−	1.15120i
$960$		0			0
$961$	975.000			1.01457
$962$	−18.0000	−	18.0000i	−0.0187110	−	0.0187110i
$963$		0			0
$964$			320.000i			0.331950i
$965$	135.000	+	945.000i	0.139896	+	0.979275i
$966$		0			0
$967$	−92.0000	−	92.0000i	−0.0951396	−	0.0951396i	0.657935	−	0.753075i	$-0.271430\pi$
$967$	−92.0000	−	92.0000i	−0.0951396	−	0.0951396i	−0.753075	+	0.657935i	$0.771430\pi$
$968$	−210.000	+	210.000i	−0.216942	+	0.216942i
$969$		0			0
$970$	−456.000	−	342.000i	−0.470103	−	0.352577i
$971$	−4.00000			−0.00411946			−0.00205973	−	0.999998i	$-0.500656\pi$
$971$	−4.00000			−0.00411946			−0.00205973	+	0.999998i	$0.500656\pi$
$972$		0			0
$973$	−640.000	+	640.000i	−0.657760	+	0.657760i
$974$		−	504.000i		−	0.517454i
$975$		0			0
$976$	−288.000			−0.295082
$977$	−1011.00	−	1011.00i	−1.03480	−	1.03480i	−0.999372	−	0.0354282i	$-0.988720\pi$
$977$	−1011.00	−	1011.00i	−1.03480	−	1.03480i	−0.0354282	−	0.999372i	$-0.511280\pi$
$978$		0			0
$979$			104.000i			0.106231i
$980$	474.000	−	632.000i	0.483673	−	0.644898i
$981$		0			0
$982$	844.000	+	844.000i	0.859470	+	0.859470i
$983$	−604.000	+	604.000i	−0.614446	+	0.614446i	−0.944101	−	0.329656i	$-0.893067\pi$
$983$	−604.000	+	604.000i	−0.614446	+	0.614446i	0.329656	+	0.944101i	$0.393067\pi$
$984$		0			0
$985$	1071.00	−	153.000i	1.08731	−	0.155330i
$986$	−1444.00			−1.46450
$987$		0			0
$988$	−48.0000	+	48.0000i	−0.0485830	+	0.0485830i
$989$			1440.00i			1.45602i
$990$		0			0
$991$	652.000			0.657921			0.328961	−	0.944344i	$-0.393302\pi$
$991$	652.000			0.657921			0.328961	+	0.944344i	$0.393302\pi$
$992$	−176.000	−	176.000i	−0.177419	−	0.177419i
$993$		0			0
$994$			1408.00i			1.41650i
$995$	1008.00	+	756.000i	1.01307	+	0.759799i
$996$		0			0
$997$	1051.00	+	1051.00i	1.05416	+	1.05416i	0.998447	+	0.0557158i	$0.0177441\pi$
$997$	1051.00	+	1051.00i	1.05416	+	1.05416i	0.0557158	+	0.998447i	$0.482256\pi$
$998$	872.000	−	872.000i	0.873747	−	0.873747i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.3.g.a.37.1	✓	2
3.2	odd	2		90.3.g.c.37.1	yes	2
4.3	odd	2		720.3.bh.b.577.1		2
5.2	odd	4		450.3.g.d.343.1		2
5.3	odd	4	inner	90.3.g.a.73.1	yes	2
5.4	even	2		450.3.g.d.307.1		2
12.11	even	2		720.3.bh.d.577.1		2
15.2	even	4		450.3.g.a.343.1		2
15.8	even	4		90.3.g.c.73.1	yes	2
15.14	odd	2		450.3.g.a.307.1		2
20.3	even	4		720.3.bh.b.433.1		2
60.23	odd	4		720.3.bh.d.433.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.3.g.a.37.1	✓	2	1.1	even	1	trivial
90.3.g.a.73.1	yes	2	5.3	odd	4	inner
90.3.g.c.37.1	yes	2	3.2	odd	2
90.3.g.c.73.1	yes	2	15.8	even	4
450.3.g.a.307.1		2	15.14	odd	2
450.3.g.a.343.1		2	15.2	even	4
450.3.g.d.307.1		2	5.4	even	2
450.3.g.d.343.1		2	5.2	odd	4
720.3.bh.b.433.1		2	20.3	even	4
720.3.bh.b.577.1		2	4.3	odd	2
720.3.bh.d.433.1		2	60.23	odd	4
720.3.bh.d.577.1		2	12.11	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:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	90.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} +(-3.00000 + 4.00000i) q^{5} +(8.00000 + 8.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} +(-3.00000 + 4.00000i) q^{5} +(8.00000 + 8.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +(7.00000 - 1.00000i) q^{10} +4.00000 q^{11} +(-3.00000 + 3.00000i) q^{13} -16.0000i q^{14} -4.00000 q^{16} +(19.0000 + 19.0000i) q^{17} -8.00000i q^{19} +(-8.00000 - 6.00000i) q^{20} +(-4.00000 - 4.00000i) q^{22} +(-20.0000 + 20.0000i) q^{23} +(-7.00000 - 24.0000i) q^{25} +6.00000 q^{26} +(-16.0000 + 16.0000i) q^{28} -38.0000i q^{29} -44.0000 q^{31} +(4.00000 + 4.00000i) q^{32} -38.0000i q^{34} +(-56.0000 + 8.00000i) q^{35} +(-3.00000 - 3.00000i) q^{37} +(-8.00000 + 8.00000i) q^{38} +(2.00000 + 14.0000i) q^{40} +70.0000 q^{41} +(36.0000 - 36.0000i) q^{43} +8.00000i q^{44} +40.0000 q^{46} +79.0000i q^{49} +(-17.0000 + 31.0000i) q^{50} +(-6.00000 - 6.00000i) q^{52} +(17.0000 - 17.0000i) q^{53} +(-12.0000 + 16.0000i) q^{55} +32.0000 q^{56} +(-38.0000 + 38.0000i) q^{58} -92.0000i q^{59} +72.0000 q^{61} +(44.0000 + 44.0000i) q^{62} -8.00000i q^{64} +(-3.00000 - 21.0000i) q^{65} +(44.0000 + 44.0000i) q^{67} +(-38.0000 + 38.0000i) q^{68} +(64.0000 + 48.0000i) q^{70} -88.0000 q^{71} +(55.0000 - 55.0000i) q^{73} +6.00000i q^{74} +16.0000 q^{76} +(32.0000 + 32.0000i) q^{77} +12.0000i q^{79} +(12.0000 - 16.0000i) q^{80} +(-70.0000 - 70.0000i) q^{82} +(-24.0000 + 24.0000i) q^{83} +(-133.000 + 19.0000i) q^{85} -72.0000 q^{86} +(8.00000 - 8.00000i) q^{88} +26.0000i q^{89} -48.0000 q^{91} +(-40.0000 - 40.0000i) q^{92} +(32.0000 + 24.0000i) q^{95} +(-57.0000 - 57.0000i) q^{97} +(79.0000 - 79.0000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 6 q^{5} + 16 q^{7} + 4 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 - 6 * q^5 + 16 * q^7 + 4 * q^8	\( 2 q - 2 q^{2} - 6 q^{5} + 16 q^{7} + 4 q^{8} + 14 q^{10} + 8 q^{11} - 6 q^{13} - 8 q^{16} + 38 q^{17} - 16 q^{20} - 8 q^{22} - 40 q^{23} - 14 q^{25} + 12 q^{26} - 32 q^{28} - 88 q^{31} + 8 q^{32} - 112 q^{35} - 6 q^{37} - 16 q^{38} + 4 q^{40} + 140 q^{41} + 72 q^{43} + 80 q^{46} - 34 q^{50} - 12 q^{52} + 34 q^{53} - 24 q^{55} + 64 q^{56} - 76 q^{58} + 144 q^{61} + 88 q^{62} - 6 q^{65} + 88 q^{67} - 76 q^{68} + 128 q^{70} - 176 q^{71} + 110 q^{73} + 32 q^{76} + 64 q^{77} + 24 q^{80} - 140 q^{82} - 48 q^{83} - 266 q^{85} - 144 q^{86} + 16 q^{88} - 96 q^{91} - 80 q^{92} + 64 q^{95} - 114 q^{97} + 158 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 6 * q^5 + 16 * q^7 + 4 * q^8 + 14 * q^10 + 8 * q^11 - 6 * q^13 - 8 * q^16 + 38 * q^17 - 16 * q^20 - 8 * q^22 - 40 * q^23 - 14 * q^25 + 12 * q^26 - 32 * q^28 - 88 * q^31 + 8 * q^32 - 112 * q^35 - 6 * q^37 - 16 * q^38 + 4 * q^40 + 140 * q^41 + 72 * q^43 + 80 * q^46 - 34 * q^50 - 12 * q^52 + 34 * q^53 - 24 * q^55 + 64 * q^56 - 76 * q^58 + 144 * q^61 + 88 * q^62 - 6 * q^65 + 88 * q^67 - 76 * q^68 + 128 * q^70 - 176 * q^71 + 110 * q^73 + 32 * q^76 + 64 * q^77 + 24 * q^80 - 140 * q^82 - 48 * q^83 - 266 * q^85 - 144 * q^86 + 16 * q^88 - 96 * q^91 - 80 * q^92 + 64 * q^95 - 114 * q^97 + 158 * q^98

Introduction

L-functions

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