LMFDB - Embedded newform 90.3.g.d.73.2

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:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			73.2
Root			$-1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	90.73
Dual form			90.3.g.d.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(4.89898 - 1.00000i) q^{5} +(0.898979 - 0.898979i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(4.89898 - 1.00000i) q^{5} +(0.898979 - 0.898979i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-3.89898 + 5.89898i) q^{10} +13.7980 q^{11} +(12.7980 + 12.7980i) q^{13} +1.79796i q^{14} -4.00000 q^{16} +(-15.8990 + 15.8990i) q^{17} -25.7980i q^{19} +(-2.00000 - 9.79796i) q^{20} +(-13.7980 + 13.7980i) q^{22} +(-10.6969 - 10.6969i) q^{23} +(23.0000 - 9.79796i) q^{25} -25.5959 q^{26} +(-1.79796 - 1.79796i) q^{28} -25.7980i q^{29} -39.5959 q^{31} +(4.00000 - 4.00000i) q^{32} -31.7980i q^{34} +(3.50510 - 5.30306i) q^{35} +(-27.0000 + 27.0000i) q^{37} +(25.7980 + 25.7980i) q^{38} +(11.7980 + 7.79796i) q^{40} -17.7980 q^{41} +(-12.4949 - 12.4949i) q^{43} -27.5959i q^{44} +21.3939 q^{46} +(-9.30306 + 9.30306i) q^{47} +47.3837i q^{49} +(-13.2020 + 32.7980i) q^{50} +(25.5959 - 25.5959i) q^{52} +(19.0908 + 19.0908i) q^{53} +(67.5959 - 13.7980i) q^{55} +3.59592 q^{56} +(25.7980 + 25.7980i) q^{58} +20.0000i q^{59} +15.1918 q^{61} +(39.5959 - 39.5959i) q^{62} +8.00000i q^{64} +(75.4949 + 49.8990i) q^{65} +(-48.0908 + 48.0908i) q^{67} +(31.7980 + 31.7980i) q^{68} +(1.79796 + 8.80816i) q^{70} -6.20204 q^{71} +(-37.2020 - 37.2020i) q^{73} -54.0000i q^{74} -51.5959 q^{76} +(12.4041 - 12.4041i) q^{77} -115.373i q^{79} +(-19.5959 + 4.00000i) q^{80} +(17.7980 - 17.7980i) q^{82} +(-82.2929 - 82.2929i) q^{83} +(-61.9898 + 93.7878i) q^{85} +24.9898 q^{86} +(27.5959 + 27.5959i) q^{88} +117.394i q^{89} +23.0102 q^{91} +(-21.3939 + 21.3939i) q^{92} -18.6061i q^{94} +(-25.7980 - 126.384i) q^{95} +(81.9898 - 81.9898i) q^{97} +(-47.3837 - 47.3837i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 16 q^{7} + 8 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 - 16 * q^7 + 8 * q^8	$ 4 q - 4 q^{2} - 16 q^{7} + 8 q^{8} + 4 q^{10} + 16 q^{11} + 12 q^{13} - 16 q^{16} - 44 q^{17} - 8 q^{20} - 16 q^{22} + 16 q^{23} + 92 q^{25} - 24 q^{26} + 32 q^{28} - 80 q^{31} + 16 q^{32} + 112 q^{35} - 108 q^{37} + 64 q^{38} + 8 q^{40} - 32 q^{41} + 48 q^{43} - 32 q^{46} - 96 q^{47} - 92 q^{50} + 24 q^{52} - 100 q^{53} + 192 q^{55} - 64 q^{56} + 64 q^{58} - 96 q^{61} + 80 q^{62} + 204 q^{65} - 16 q^{67} + 88 q^{68} - 32 q^{70} - 64 q^{71} - 188 q^{73} - 128 q^{76} + 128 q^{77} + 32 q^{82} - 192 q^{83} - 52 q^{85} - 96 q^{86} + 32 q^{88} + 288 q^{91} + 32 q^{92} - 64 q^{95} + 132 q^{97} + 124 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 - 16 * q^7 + 8 * q^8 + 4 * q^10 + 16 * q^11 + 12 * q^13 - 16 * q^16 - 44 * q^17 - 8 * q^20 - 16 * q^22 + 16 * q^23 + 92 * q^25 - 24 * q^26 + 32 * q^28 - 80 * q^31 + 16 * q^32 + 112 * q^35 - 108 * q^37 + 64 * q^38 + 8 * q^40 - 32 * q^41 + 48 * q^43 - 32 * q^46 - 96 * q^47 - 92 * q^50 + 24 * q^52 - 100 * q^53 + 192 * q^55 - 64 * q^56 + 64 * q^58 - 96 * q^61 + 80 * q^62 + 204 * q^65 - 16 * q^67 + 88 * q^68 - 32 * q^70 - 64 * q^71 - 188 * q^73 - 128 * q^76 + 128 * q^77 + 32 * q^82 - 192 * q^83 - 52 * q^85 - 96 * q^86 + 32 * q^88 + 288 * q^91 + 32 * q^92 - 64 * q^95 + 132 * q^97 + 124 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$11$	$37$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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
$5$	4.89898	−	1.00000i	0.979796	−	0.200000i
$5$	4.89898	−	1.00000i	0.979796	−	0.200000i
$6$		0			0
$7$	0.898979	−	0.898979i	0.128426	−	0.128426i	−0.639972	−	0.768398i	$-0.721054\pi$
$7$	0.898979	−	0.898979i	0.128426	−	0.128426i	0.768398	+	0.639972i	$0.221054\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$		0			0
$10$	−3.89898	+	5.89898i	−0.389898	+	0.589898i
$11$	13.7980			1.25436			0.627180	−	0.778874i	$-0.284209\pi$
$11$	13.7980			1.25436			0.627180	+	0.778874i	$0.284209\pi$
$12$		0			0
$13$	12.7980	+	12.7980i	0.984458	+	0.984458i	0.999881	−	0.0154227i	$-0.00490939\pi$
$13$	12.7980	+	12.7980i	0.984458	+	0.984458i	−0.0154227	+	0.999881i	$0.504909\pi$
$14$			1.79796i			0.128426i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	−15.8990	+	15.8990i	−0.935234	+	0.935234i	−0.998027	−	0.0627925i	$-0.979999\pi$
$17$	−15.8990	+	15.8990i	−0.935234	+	0.935234i	0.0627925	+	0.998027i	$0.479999\pi$
$18$		0			0
$19$		−	25.7980i		−	1.35779i	−0.734237	−	0.678894i	$-0.762460\pi$
$19$		−	25.7980i		−	1.35779i	0.734237	−	0.678894i	$-0.237540\pi$
$20$	−2.00000	−	9.79796i	−0.100000	−	0.489898i
$21$		0			0
$22$	−13.7980	+	13.7980i	−0.627180	+	0.627180i
$23$	−10.6969	−	10.6969i	−0.465084	−	0.465084i	0.435233	−	0.900318i	$-0.356666\pi$
$23$	−10.6969	−	10.6969i	−0.465084	−	0.465084i	−0.900318	+	0.435233i	$0.856666\pi$
$24$		0			0
$25$	23.0000	−	9.79796i	0.920000	−	0.391918i
$26$	−25.5959			−0.984458
$27$		0			0
$28$	−1.79796	−	1.79796i	−0.0642128	−	0.0642128i
$29$		−	25.7980i		−	0.889585i	−0.895634	−	0.444792i	$-0.853277\pi$
$29$		−	25.7980i		−	0.889585i	0.895634	−	0.444792i	$-0.146723\pi$
$30$		0			0
$31$	−39.5959			−1.27729			−0.638644	−	0.769502i	$-0.720504\pi$
$31$	−39.5959			−1.27729			−0.638644	+	0.769502i	$0.720504\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$		0			0
$34$		−	31.7980i		−	0.935234i
$35$	3.50510	−	5.30306i	0.100146	−	0.151516i
$36$		0			0
$37$	−27.0000	+	27.0000i	−0.729730	+	0.729730i	−0.970566	−	0.240836i	$-0.922578\pi$
$37$	−27.0000	+	27.0000i	−0.729730	+	0.729730i	0.240836	+	0.970566i	$0.422578\pi$
$38$	25.7980	+	25.7980i	0.678894	+	0.678894i
$39$		0			0
$40$	11.7980	+	7.79796i	0.294949	+	0.194949i
$41$	−17.7980			−0.434097			−0.217048	−	0.976161i	$-0.569643\pi$
$41$	−17.7980			−0.434097			−0.217048	+	0.976161i	$0.569643\pi$
$42$		0			0
$43$	−12.4949	−	12.4949i	−0.290579	−	0.290579i	0.546730	−	0.837309i	$-0.315872\pi$
$43$	−12.4949	−	12.4949i	−0.290579	−	0.290579i	−0.837309	+	0.546730i	$0.815872\pi$
$44$		−	27.5959i		−	0.627180i
$45$		0			0
$46$	21.3939			0.465084
$47$	−9.30306	+	9.30306i	−0.197937	+	0.197937i	−0.799115	−	0.601178i	$-0.794698\pi$
$47$	−9.30306	+	9.30306i	−0.197937	+	0.197937i	0.601178	+	0.799115i	$0.294698\pi$
$48$		0			0
$49$			47.3837i			0.967014i
$50$	−13.2020	+	32.7980i	−0.264041	+	0.655959i
$51$		0			0
$52$	25.5959	−	25.5959i	0.492229	−	0.492229i
$53$	19.0908	+	19.0908i	0.360204	+	0.360204i	0.863888	−	0.503684i	$-0.168022\pi$
$53$	19.0908	+	19.0908i	0.360204	+	0.360204i	−0.503684	+	0.863888i	$0.668022\pi$
$54$		0			0
$55$	67.5959	−	13.7980i	1.22902	−	0.250872i
$56$	3.59592			0.0642128
$57$		0			0
$58$	25.7980	+	25.7980i	0.444792	+	0.444792i
$59$			20.0000i			0.338983i	0.985532	+	0.169492i	$0.0542125\pi$
$59$			20.0000i			0.338983i	−0.985532	+	0.169492i	$0.945787\pi$
$60$		0			0
$61$	15.1918			0.249046			0.124523	−	0.992217i	$-0.460260\pi$
$61$	15.1918			0.249046			0.124523	+	0.992217i	$0.460260\pi$
$62$	39.5959	−	39.5959i	0.638644	−	0.638644i
$63$		0			0
$64$			8.00000i			0.125000i
$65$	75.4949	+	49.8990i	1.16146	+	0.767677i
$66$		0			0
$67$	−48.0908	+	48.0908i	−0.717773	+	0.717773i	−0.968149	−	0.250375i	$-0.919446\pi$
$67$	−48.0908	+	48.0908i	−0.717773	+	0.717773i	0.250375	+	0.968149i	$0.419446\pi$
$68$	31.7980	+	31.7980i	0.467617	+	0.467617i
$69$		0			0
$70$	1.79796	+	8.80816i	0.0256851	+	0.125831i
$71$	−6.20204			−0.0873527			−0.0436763	−	0.999046i	$-0.513907\pi$
$71$	−6.20204			−0.0873527			−0.0436763	+	0.999046i	$0.513907\pi$
$72$		0			0
$73$	−37.2020	−	37.2020i	−0.509617	−	0.509617i	0.404792	−	0.914409i	$-0.367344\pi$
$73$	−37.2020	−	37.2020i	−0.509617	−	0.509617i	−0.914409	+	0.404792i	$0.867344\pi$
$74$		−	54.0000i		−	0.729730i
$75$		0			0
$76$	−51.5959			−0.678894
$77$	12.4041	−	12.4041i	0.161092	−	0.161092i
$78$		0			0
$79$		−	115.373i		−	1.46042i	−0.683221	−	0.730212i	$-0.739421\pi$
$79$		−	115.373i		−	1.46042i	0.683221	−	0.730212i	$-0.260579\pi$
$80$	−19.5959	+	4.00000i	−0.244949	+	0.0500000i
$81$		0			0
$82$	17.7980	−	17.7980i	0.217048	−	0.217048i
$83$	−82.2929	−	82.2929i	−0.991480	−	0.991480i	0.00848381	−	0.999964i	$-0.497299\pi$
$83$	−82.2929	−	82.2929i	−0.991480	−	0.991480i	−0.999964	+	0.00848381i	$0.997299\pi$
$84$		0			0
$85$	−61.9898	+	93.7878i	−0.729292	+	1.10339i
$86$	24.9898			0.290579
$87$		0			0
$88$	27.5959	+	27.5959i	0.313590	+	0.313590i
$89$			117.394i			1.31903i	0.751690	+	0.659516i	$0.229239\pi$
$89$			117.394i			1.31903i	−0.751690	+	0.659516i	$0.770761\pi$
$90$		0			0
$91$	23.0102			0.252859
$92$	−21.3939	+	21.3939i	−0.232542	+	0.232542i
$93$		0			0
$94$		−	18.6061i		−	0.197937i
$95$	−25.7980	−	126.384i	−0.271557	−	1.33035i
$96$		0			0
$97$	81.9898	−	81.9898i	0.845256	−	0.845256i	−0.144281	−	0.989537i	$-0.546087\pi$
$97$	81.9898	−	81.9898i	0.845256	−	0.845256i	0.989537	+	0.144281i	$0.0460870\pi$
$98$	−47.3837	−	47.3837i	−0.483507	−	0.483507i
$99$		0			0
$100$	−19.5959	−	46.0000i	−0.195959	−	0.460000i
$101$	−28.3837			−0.281026			−0.140513	−	0.990079i	$-0.544875\pi$
$101$	−28.3837			−0.281026			−0.140513	+	0.990079i	$0.544875\pi$
$102$		0			0
$103$	16.4949	+	16.4949i	0.160145	+	0.160145i	0.782631	−	0.622486i	$-0.213877\pi$
$103$	16.4949	+	16.4949i	0.160145	+	0.160145i	−0.622486	+	0.782631i	$0.713877\pi$
$104$			51.1918i			0.492229i
$105$		0			0
$106$	−38.1816			−0.360204
$107$	−15.1010	+	15.1010i	−0.141131	+	0.141131i	−0.774142	−	0.633011i	$-0.781819\pi$
$107$	−15.1010	+	15.1010i	−0.141131	+	0.141131i	0.633011	+	0.774142i	$0.281819\pi$
$108$		0			0
$109$			130.000i			1.19266i	0.802739	+	0.596330i	$0.203375\pi$
$109$			130.000i			1.19266i	−0.802739	+	0.596330i	$0.796625\pi$
$110$	−53.7980	+	81.3939i	−0.489072	+	0.739944i
$111$		0			0
$112$	−3.59592	+	3.59592i	−0.0321064	+	0.0321064i
$113$	−77.2929	−	77.2929i	−0.684008	−	0.684008i	0.276893	−	0.960901i	$-0.410695\pi$
$113$	−77.2929	−	77.2929i	−0.684008	−	0.684008i	−0.960901	+	0.276893i	$0.910695\pi$
$114$		0			0
$115$	−63.1010	−	41.7071i	−0.548705	−	0.362671i
$116$	−51.5959			−0.444792
$117$		0			0
$118$	−20.0000	−	20.0000i	−0.169492	−	0.169492i
$119$			28.5857i			0.240216i
$120$		0			0
$121$	69.3837			0.573419
$122$	−15.1918	+	15.1918i	−0.124523	+	0.124523i
$123$		0			0
$124$			79.1918i			0.638644i
$125$	102.879	−	71.0000i	0.823029	−	0.568000i
$126$		0			0
$127$	18.2929	−	18.2929i	0.144038	−	0.144038i	−0.631411	−	0.775449i	$-0.717524\pi$
$127$	18.2929	−	18.2929i	0.144038	−	0.144038i	0.775449	+	0.631411i	$0.217524\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−125.394	+	25.5959i	−0.964568	+	0.196892i
$131$	133.798			1.02136			0.510679	−	0.859771i	$-0.329394\pi$
$131$	133.798			1.02136			0.510679	+	0.859771i	$0.329394\pi$
$132$		0			0
$133$	−23.1918	−	23.1918i	−0.174375	−	0.174375i
$134$		−	96.1816i		−	0.717773i
$135$		0			0
$136$	−63.5959			−0.467617
$137$	−25.8990	+	25.8990i	−0.189044	+	0.189044i	−0.795283	−	0.606239i	$-0.792678\pi$
$137$	−25.8990	+	25.8990i	−0.189044	+	0.189044i	0.606239	+	0.795283i	$0.292678\pi$
$138$		0			0
$139$			54.2020i			0.389943i	0.980809	+	0.194971i	$0.0624614\pi$
$139$			54.2020i			0.389943i	−0.980809	+	0.194971i	$0.937539\pi$
$140$	−10.6061	−	7.01021i	−0.0757580	−	0.0500729i
$141$		0			0
$142$	6.20204	−	6.20204i	0.0436763	−	0.0436763i
$143$	176.586	+	176.586i	1.23487	+	1.23487i
$144$		0			0
$145$	−25.7980	−	126.384i	−0.177917	−	0.871612i
$146$	74.4041			0.509617
$147$		0			0
$148$	54.0000	+	54.0000i	0.364865	+	0.364865i
$149$		−	42.7673i		−	0.287029i	−0.989648	−	0.143515i	$-0.954160\pi$
$149$		−	42.7673i		−	0.287029i	0.989648	−	0.143515i	$-0.0458404\pi$
$150$		0			0
$151$	178.384			1.18135			0.590674	−	0.806910i	$-0.298862\pi$
$151$	178.384			1.18135			0.590674	+	0.806910i	$0.298862\pi$
$152$	51.5959	−	51.5959i	0.339447	−	0.339447i
$153$		0			0
$154$			24.8082i			0.161092i
$155$	−193.980	+	39.5959i	−1.25148	+	0.255458i
$156$		0			0
$157$	123.000	−	123.000i	0.783439	−	0.783439i	−0.196970	−	0.980410i	$-0.563110\pi$
$157$	123.000	−	123.000i	0.783439	−	0.783439i	0.980410	+	0.196970i	$0.0631102\pi$
$158$	115.373	+	115.373i	0.730212	+	0.730212i
$159$		0			0
$160$	15.5959	−	23.5959i	0.0974745	−	0.147474i
$161$	−19.2327			−0.119457
$162$		0			0
$163$	−63.5051	−	63.5051i	−0.389602	−	0.389602i	0.484944	−	0.874545i	$-0.338840\pi$
$163$	−63.5051	−	63.5051i	−0.389602	−	0.389602i	−0.874545	+	0.484944i	$0.838840\pi$
$164$			35.5959i			0.217048i
$165$		0			0
$166$	164.586			0.991480
$167$	48.6765	−	48.6765i	0.291476	−	0.291476i	−0.546187	−	0.837663i	$-0.683921\pi$
$167$	48.6765	−	48.6765i	0.291476	−	0.291476i	0.837663	+	0.546187i	$0.183921\pi$
$168$		0			0
$169$			158.576i			0.938317i
$170$	−31.7980	−	155.778i	−0.187047	−	0.916339i
$171$		0			0
$172$	−24.9898	+	24.9898i	−0.145290	+	0.145290i
$173$	−35.1112	−	35.1112i	−0.202955	−	0.202955i	0.598310	−	0.801265i	$-0.295839\pi$
$173$	−35.1112	−	35.1112i	−0.202955	−	0.202955i	−0.801265	+	0.598310i	$0.795839\pi$
$174$		0			0
$175$	11.8684	−	29.4847i	0.0678192	−	0.168484i
$176$	−55.1918			−0.313590
$177$		0			0
$178$	−117.394	−	117.394i	−0.659516	−	0.659516i
$179$			141.171i			0.788667i	0.918967	+	0.394334i	$0.129025\pi$
$179$			141.171i			0.788667i	−0.918967	+	0.394334i	$0.870975\pi$
$180$		0			0
$181$	58.8082			0.324907			0.162453	−	0.986716i	$-0.448059\pi$
$181$	58.8082			0.324907			0.162453	+	0.986716i	$0.448059\pi$
$182$	−23.0102	+	23.0102i	−0.126430	+	0.126430i
$183$		0			0
$184$		−	42.7878i		−	0.232542i
$185$	−105.272	+	159.272i	−0.569040	+	0.860932i
$186$		0			0
$187$	−219.373	+	219.373i	−1.17312	+	1.17312i
$188$	18.6061	+	18.6061i	0.0989687	+	0.0989687i
$189$		0			0
$190$	152.182	+	100.586i	0.800956	+	0.529398i
$191$	325.394			1.70363			0.851816	−	0.523840i	$-0.175501\pi$
$191$	325.394			1.70363			0.851816	+	0.523840i	$0.175501\pi$
$192$		0			0
$193$	−39.3837	−	39.3837i	−0.204060	−	0.204060i	0.597677	−	0.801737i	$-0.296091\pi$
$193$	−39.3837	−	39.3837i	−0.204060	−	0.204060i	−0.801737	+	0.597677i	$0.796091\pi$
$194$			163.980i			0.845256i
$195$		0			0
$196$	94.7673			0.483507
$197$	119.313	−	119.313i	0.605651	−	0.605651i	−0.336155	−	0.941807i	$-0.609127\pi$
$197$	119.313	−	119.313i	0.605651	−	0.605651i	0.941807	+	0.336155i	$0.109127\pi$
$198$		0			0
$199$			178.565i			0.897313i	0.893704	+	0.448657i	$0.148097\pi$
$199$			178.565i			0.897313i	−0.893704	+	0.448657i	$0.851903\pi$
$200$	65.5959	+	26.4041i	0.327980	+	0.132020i
$201$		0			0
$202$	28.3837	−	28.3837i	0.140513	−	0.140513i
$203$	−23.1918	−	23.1918i	−0.114245	−	0.114245i
$204$		0			0
$205$	−87.1918	+	17.7980i	−0.425326	+	0.0868193i
$206$	−32.9898			−0.160145
$207$		0			0
$208$	−51.1918	−	51.1918i	−0.246115	−	0.246115i
$209$		−	355.959i		−	1.70315i
$210$		0			0
$211$	−318.747			−1.51065			−0.755324	−	0.655351i	$-0.772521\pi$
$211$	−318.747			−1.51065			−0.755324	+	0.655351i	$0.772521\pi$
$212$	38.1816	−	38.1816i	0.180102	−	0.180102i
$213$		0			0
$214$		−	30.2020i		−	0.141131i
$215$	−73.7071	−	48.7173i	−0.342824	−	0.226592i
$216$		0			0
$217$	−35.5959	+	35.5959i	−0.164036	+	0.164036i
$218$	−130.000	−	130.000i	−0.596330	−	0.596330i
$219$		0			0
$220$	−27.5959	−	135.192i	−0.125436	−	0.614508i
$221$	−406.949			−1.84140
$222$		0			0
$223$	208.677	+	208.677i	0.935769	+	0.935769i	0.998058	−	0.0622890i	$-0.0198400\pi$
$223$	208.677	+	208.677i	0.935769	+	0.935769i	−0.0622890	+	0.998058i	$0.519840\pi$
$224$		−	7.19184i		−	0.0321064i
$225$		0			0
$226$	154.586			0.684008
$227$	−242.070	+	242.070i	−1.06639	+	1.06639i	−0.0687559	+	0.997634i	$0.521903\pi$
$227$	−242.070	+	242.070i	−1.06639	+	1.06639i	−0.997634	+	0.0687559i	$0.978097\pi$
$228$		0			0
$229$		−	413.939i		−	1.80759i	−0.427963	−	0.903796i	$-0.640769\pi$
$229$		−	413.939i		−	1.80759i	0.427963	−	0.903796i	$-0.359231\pi$
$230$	104.808	−	21.3939i	0.455688	−	0.0930169i
$231$		0			0
$232$	51.5959	−	51.5959i	0.222396	−	0.222396i
$233$	−64.2622	−	64.2622i	−0.275804	−	0.275804i	0.555628	−	0.831431i	$-0.312478\pi$
$233$	−64.2622	−	64.2622i	−0.275804	−	0.275804i	−0.831431	+	0.555628i	$0.812478\pi$
$234$		0			0
$235$	−36.2724	+	54.8786i	−0.154351	+	0.233526i
$236$	40.0000			0.169492
$237$		0			0
$238$	−28.5857	−	28.5857i	−0.120108	−	0.120108i
$239$		−	154.788i		−	0.647648i	−0.946117	−	0.323824i	$-0.895032\pi$
$239$		−	154.788i		−	0.647648i	0.946117	−	0.323824i	$-0.104968\pi$
$240$		0			0
$241$	−421.939			−1.75078			−0.875392	−	0.483414i	$-0.839396\pi$
$241$	−421.939			−1.75078			−0.875392	+	0.483414i	$0.839396\pi$
$242$	−69.3837	+	69.3837i	−0.286709	+	0.286709i
$243$		0			0
$244$		−	30.3837i		−	0.124523i
$245$	47.3837	+	232.132i	0.193403	+	0.947476i
$246$		0			0
$247$	330.161	−	330.161i	1.33669	−	1.33669i
$248$	−79.1918	−	79.1918i	−0.319322	−	0.319322i
$249$		0			0
$250$	−31.8786	+	173.879i	−0.127514	+	0.695514i
$251$	−392.586			−1.56409			−0.782043	−	0.623224i	$-0.785822\pi$
$251$	−392.586			−1.56409			−0.782043	+	0.623224i	$0.785822\pi$
$252$		0			0
$253$	−147.596	−	147.596i	−0.583383	−	0.583383i
$254$			36.5857i			0.144038i
$255$		0			0
$256$	16.0000			0.0625000
$257$	123.515	−	123.515i	0.480604	−	0.480604i	−0.424720	−	0.905325i	$-0.639628\pi$
$257$	123.515	−	123.515i	0.480604	−	0.480604i	0.905325	+	0.424720i	$0.139628\pi$
$258$		0			0
$259$			48.5449i			0.187432i
$260$	99.7980	−	150.990i	0.383838	−	0.580730i
$261$		0			0
$262$	−133.798	+	133.798i	−0.510679	+	0.510679i
$263$	−30.6969	−	30.6969i	−0.116718	−	0.116718i	0.646335	−	0.763054i	$-0.276301\pi$
$263$	−30.6969	−	30.6969i	−0.116718	−	0.116718i	−0.763054	+	0.646335i	$0.776301\pi$
$264$		0			0
$265$	112.616	+	74.4347i	0.424967	+	0.280886i
$266$	46.3837			0.174375
$267$		0			0
$268$	96.1816	+	96.1816i	0.358887	+	0.358887i
$269$			429.151i			1.59536i	0.603083	+	0.797678i	$0.293939\pi$
$269$			429.151i			1.59536i	−0.603083	+	0.797678i	$0.706061\pi$
$270$		0			0
$271$	220.727			0.814489			0.407245	−	0.913319i	$-0.366490\pi$
$271$	220.727			0.814489			0.407245	+	0.913319i	$0.366490\pi$
$272$	63.5959	−	63.5959i	0.233809	−	0.233809i
$273$		0			0
$274$		−	51.7980i		−	0.189044i
$275$	317.353	−	135.192i	1.15401	−	0.491607i
$276$		0			0
$277$	−45.9898	+	45.9898i	−0.166028	+	0.166028i	−0.785231	−	0.619203i	$-0.787456\pi$
$277$	−45.9898	+	45.9898i	−0.166028	+	0.166028i	0.619203	+	0.785231i	$0.287456\pi$
$278$	−54.2020	−	54.2020i	−0.194971	−	0.194971i
$279$		0			0
$280$	17.6163	−	3.59592i	0.0629155	−	0.0128426i
$281$	482.524			1.71717			0.858584	−	0.512672i	$-0.171344\pi$
$281$	482.524			1.71717			0.858584	+	0.512672i	$0.171344\pi$
$282$		0			0
$283$	271.283	+	271.283i	0.958596	+	0.958596i	0.999176	−	0.0405803i	$-0.0129207\pi$
$283$	271.283	+	271.283i	0.958596	+	0.958596i	−0.0405803	+	0.999176i	$0.512921\pi$
$284$			12.4041i			0.0436763i
$285$		0			0
$286$	−353.171			−1.23487
$287$	−16.0000	+	16.0000i	−0.0557491	+	0.0557491i
$288$		0			0
$289$		−	216.555i		−	0.749326i
$290$	152.182	+	100.586i	0.524764	+	0.346847i
$291$		0			0
$292$	−74.4041	+	74.4041i	−0.254809	+	0.254809i
$293$	149.091	+	149.091i	0.508842	+	0.508842i	0.914171	−	0.405329i	$-0.132843\pi$
$293$	149.091	+	149.091i	0.508842	+	0.508842i	−0.405329	+	0.914171i	$0.632843\pi$
$294$		0			0
$295$	20.0000	+	97.9796i	0.0677966	+	0.332134i
$296$	−108.000			−0.364865
$297$		0			0
$298$	42.7673	+	42.7673i	0.143515	+	0.143515i
$299$		−	273.798i		−	0.915712i
$300$		0			0
$301$	−22.4653			−0.0746356
$302$	−178.384	+	178.384i	−0.590674	+	0.590674i
$303$		0			0
$304$			103.192i			0.339447i
$305$	74.4245	−	15.1918i	0.244015	−	0.0498093i
$306$		0			0
$307$	−230.697	+	230.697i	−0.751456	+	0.751456i	−0.974751	−	0.223295i	$-0.928319\pi$
$307$	−230.697	+	230.697i	−0.751456	+	0.751456i	0.223295	+	0.974751i	$0.428319\pi$
$308$	−24.8082	−	24.8082i	−0.0805460	−	0.0805460i
$309$		0			0
$310$	154.384	−	233.576i	0.498012	−	0.753469i
$311$	47.7367			0.153494			0.0767472	−	0.997051i	$-0.475547\pi$
$311$	47.7367			0.153494			0.0767472	+	0.997051i	$0.475547\pi$
$312$		0			0
$313$	219.767	+	219.767i	0.702132	+	0.702132i	0.964868	−	0.262736i	$-0.0846247\pi$
$313$	219.767	+	219.767i	0.702132	+	0.702132i	−0.262736	+	0.964868i	$0.584625\pi$
$314$			246.000i			0.783439i
$315$		0			0
$316$	−230.747			−0.730212
$317$	332.828	−	332.828i	1.04993	−	1.04993i	0.0512429	−	0.998686i	$-0.483682\pi$
$317$	332.828	−	332.828i	1.04993	−	1.04993i	0.998686	−	0.0512429i	$-0.0163183\pi$
$318$		0			0
$319$		−	355.959i		−	1.11586i
$320$	8.00000	+	39.1918i	0.0250000	+	0.122474i
$321$		0			0
$322$	19.2327	−	19.2327i	0.0597287	−	0.0597287i
$323$	410.161	+	410.161i	1.26985	+	1.26985i
$324$		0			0
$325$	419.747	+	168.959i	1.29153	+	0.519874i
$326$	127.010			0.389602
$327$		0			0
$328$	−35.5959	−	35.5959i	−0.108524	−	0.108524i
$329$			16.7265i			0.0508405i
$330$		0			0
$331$	209.980			0.634379			0.317190	−	0.948362i	$-0.397261\pi$
$331$	209.980			0.634379			0.317190	+	0.948362i	$0.397261\pi$
$332$	−164.586	+	164.586i	−0.495740	+	0.495740i
$333$		0			0
$334$			97.3531i			0.291476i
$335$	−187.505	+	283.687i	−0.559717	+	0.846826i
$336$		0			0
$337$	88.3735	−	88.3735i	0.262236	−	0.262236i	−0.563726	−	0.825962i	$-0.690633\pi$
$337$	88.3735	−	88.3735i	0.262236	−	0.262236i	0.825962	+	0.563726i	$0.190633\pi$
$338$	−158.576	−	158.576i	−0.469158	−	0.469158i
$339$		0			0
$340$	187.576	+	123.980i	0.551693	+	0.364646i
$341$	−546.343			−1.60218
$342$		0			0
$343$	86.6469	+	86.6469i	0.252615	+	0.252615i
$344$		−	49.9796i		−	0.145290i
$345$		0			0
$346$	70.2225			0.202955
$347$	−212.495	+	212.495i	−0.612377	+	0.612377i	−0.943565	−	0.331188i	$-0.892551\pi$
$347$	−212.495	+	212.495i	−0.612377	+	0.612377i	0.331188	+	0.943565i	$0.392551\pi$
$348$		0			0
$349$		−	280.000i		−	0.802292i	−0.916014	−	0.401146i	$-0.868612\pi$
$349$		−	280.000i		−	0.802292i	0.916014	−	0.401146i	$-0.131388\pi$
$350$	17.6163	+	41.3531i	0.0503324	+	0.118152i
$351$		0			0
$352$	55.1918	−	55.1918i	0.156795	−	0.156795i
$353$	−212.505	−	212.505i	−0.601997	−	0.601997i	0.338845	−	0.940842i	$-0.389964\pi$
$353$	−212.505	−	212.505i	−0.601997	−	0.601997i	−0.940842	+	0.338845i	$0.889964\pi$
$354$		0			0
$355$	−30.3837	+	6.20204i	−0.0855878	+	0.0174705i
$356$	234.788			0.659516
$357$		0			0
$358$	−141.171	−	141.171i	−0.394334	−	0.394334i
$359$		−	633.090i		−	1.76348i	−0.471734	−	0.881741i	$-0.656372\pi$
$359$		−	633.090i		−	1.76348i	0.471734	−	0.881741i	$-0.343628\pi$
$360$		0			0
$361$	−304.535			−0.843586
$362$	−58.8082	+	58.8082i	−0.162453	+	0.162453i
$363$		0			0
$364$		−	46.0204i		−	0.126430i
$365$	−219.454	−	145.050i	−0.601244	−	0.397397i
$366$		0			0
$367$	−267.505	+	267.505i	−0.728897	+	0.728897i	−0.970400	−	0.241503i	$-0.922360\pi$
$367$	−267.505	+	267.505i	−0.728897	+	0.728897i	0.241503	+	0.970400i	$0.422360\pi$
$368$	42.7878	+	42.7878i	0.116271	+	0.116271i
$369$		0			0
$370$	−54.0000	−	264.545i	−0.145946	−	0.714986i
$371$	34.3245			0.0925189
$372$		0			0
$373$	−376.939	−	376.939i	−1.01056	−	1.01056i	−0.999944	−	0.0106161i	$-0.996621\pi$
$373$	−376.939	−	376.939i	−1.01056	−	1.01056i	−0.0106161	−	0.999944i	$-0.503379\pi$
$374$		−	438.747i		−	1.17312i
$375$		0			0
$376$	−37.2122			−0.0989687
$377$	330.161	−	330.161i	0.875759	−	0.875759i
$378$		0			0
$379$		−	167.818i		−	0.442793i	−0.975184	−	0.221396i	$-0.928939\pi$
$379$		−	167.818i		−	0.442793i	0.975184	−	0.221396i	$-0.0710614\pi$
$380$	−252.767	+	51.5959i	−0.665177	+	0.135779i
$381$		0			0
$382$	−325.394	+	325.394i	−0.851816	+	0.851816i
$383$	478.293	+	478.293i	1.24881	+	1.24881i	0.956248	+	0.292559i	$0.0945068\pi$
$383$	478.293	+	478.293i	1.24881	+	1.24881i	0.292559	+	0.956248i	$0.405493\pi$
$384$		0			0
$385$	48.3633	−	73.1714i	0.125619	−	0.190056i
$386$	78.7673			0.204060
$387$		0			0
$388$	−163.980	−	163.980i	−0.422628	−	0.422628i
$389$			169.151i			0.434836i	0.976079	+	0.217418i	$0.0697634\pi$
$389$			169.151i			0.434836i	−0.976079	+	0.217418i	$0.930237\pi$
$390$		0			0
$391$	340.141			0.869925
$392$	−94.7673	+	94.7673i	−0.241753	+	0.241753i
$393$		0			0
$394$			238.627i			0.605651i
$395$	−115.373	−	565.212i	−0.292085	−	1.43092i
$396$		0			0
$397$	−69.3429	+	69.3429i	−0.174667	+	0.174667i	−0.789026	−	0.614359i	$-0.789415\pi$
$397$	−69.3429	+	69.3429i	−0.174667	+	0.174667i	0.614359	+	0.789026i	$0.289415\pi$
$398$	−178.565	−	178.565i	−0.448657	−	0.448657i
$399$		0			0
$400$	−92.0000	+	39.1918i	−0.230000	+	0.0979796i
$401$	−414.767			−1.03433			−0.517166	−	0.855885i	$-0.673013\pi$
$401$	−414.767			−1.03433			−0.517166	+	0.855885i	$0.673013\pi$
$402$		0			0
$403$	−506.747	−	506.747i	−1.25744	−	1.25744i
$404$			56.7673i			0.140513i
$405$		0			0
$406$	46.3837			0.114245
$407$	−372.545	+	372.545i	−0.915344	+	0.915344i
$408$		0			0
$409$			605.110i			1.47949i	0.672889	+	0.739744i	$0.265053\pi$
$409$			605.110i			1.47949i	−0.672889	+	0.739744i	$0.734947\pi$
$410$	69.3939	−	104.990i	0.169253	−	0.256073i
$411$		0			0
$412$	32.9898	−	32.9898i	0.0800723	−	0.0800723i
$413$	17.9796	+	17.9796i	0.0435341	+	0.0435341i
$414$		0			0
$415$	−485.444	−	320.858i	−1.16974	−	0.773152i
$416$	102.384			0.246115
$417$		0			0
$418$	355.959	+	355.959i	0.851577	+	0.851577i
$419$		−	15.9592i		−	0.0380887i	−0.999819	−	0.0190444i	$-0.993938\pi$
$419$		−	15.9592i		−	0.0380887i	0.999819	−	0.0190444i	$-0.00606238\pi$
$420$		0			0
$421$	433.171			1.02891			0.514455	−	0.857517i	$-0.327994\pi$
$421$	433.171			1.02891			0.514455	+	0.857517i	$0.327994\pi$
$422$	318.747	−	318.747i	0.755324	−	0.755324i
$423$		0			0
$424$			76.3633i			0.180102i
$425$	−209.899	+	521.454i	−0.493880	+	1.22695i
$426$		0			0
$427$	13.6571	−	13.6571i	0.0319840	−	0.0319840i
$428$	30.2020	+	30.2020i	0.0705655	+	0.0705655i
$429$		0			0
$430$	122.424	−	24.9898i	0.284708	−	0.0581158i
$431$	−24.1816			−0.0561059			−0.0280529	−	0.999606i	$-0.508931\pi$
$431$	−24.1816			−0.0561059			−0.0280529	+	0.999606i	$0.508931\pi$
$432$		0			0
$433$	528.918	+	528.918i	1.22152	+	1.22152i	0.967091	+	0.254429i	$0.0818875\pi$
$433$	528.918	+	528.918i	1.22152	+	1.22152i	0.254429	+	0.967091i	$0.418112\pi$
$434$		−	71.1918i		−	0.164036i
$435$		0			0
$436$	260.000			0.596330
$437$	−275.959	+	275.959i	−0.631486	+	0.631486i
$438$		0			0
$439$			44.6265i			0.101655i	0.998707	+	0.0508275i	$0.0161859\pi$
$439$			44.6265i			0.101655i	−0.998707	+	0.0508275i	$0.983814\pi$
$440$	162.788	+	107.596i	0.369972	+	0.244536i
$441$		0			0
$442$	406.949	−	406.949i	0.920699	−	0.920699i
$443$	−311.283	−	311.283i	−0.702670	−	0.702670i	0.262313	−	0.964983i	$-0.415515\pi$
$443$	−311.283	−	311.283i	−0.702670	−	0.702670i	−0.964983	+	0.262313i	$0.915515\pi$
$444$		0			0
$445$	117.394	+	575.110i	0.263806	+	1.29238i
$446$	−417.353			−0.935769
$447$		0			0
$448$	7.19184	+	7.19184i	0.0160532	+	0.0160532i
$449$			141.273i			0.314640i	0.987548	+	0.157320i	$0.0502855\pi$
$449$			141.273i			0.314640i	−0.987548	+	0.157320i	$0.949715\pi$
$450$		0			0
$451$	−245.576			−0.544513
$452$	−154.586	+	154.586i	−0.342004	+	0.342004i
$453$		0			0
$454$		−	484.141i		−	1.06639i
$455$	112.727	−	23.0102i	0.247751	−	0.0505719i
$456$		0			0
$457$	20.3939	−	20.3939i	0.0446256	−	0.0446256i	−0.684442	−	0.729067i	$-0.739954\pi$
$457$	20.3939	−	20.3939i	0.0446256	−	0.0446256i	0.729067	+	0.684442i	$0.239954\pi$
$458$	413.939	+	413.939i	0.903796	+	0.903796i
$459$		0			0
$460$	−83.4143	+	126.202i	−0.181335	+	0.274352i
$461$	626.727			1.35949			0.679747	−	0.733447i	$-0.262090\pi$
$461$	626.727			1.35949			0.679747	+	0.733447i	$0.262090\pi$
$462$		0			0
$463$	−314.515	−	314.515i	−0.679299	−	0.679299i	0.280543	−	0.959842i	$-0.409486\pi$
$463$	−314.515	−	314.515i	−0.679299	−	0.679299i	−0.959842	+	0.280543i	$0.909486\pi$
$464$			103.192i			0.222396i
$465$		0			0
$466$	128.524			0.275804
$467$	−46.6969	+	46.6969i	−0.0999934	+	0.0999934i	−0.755334	−	0.655340i	$-0.772525\pi$
$467$	−46.6969	+	46.6969i	−0.0999934	+	0.0999934i	0.655340	+	0.755334i	$0.272525\pi$
$468$		0			0
$469$			86.4653i			0.184361i
$470$	−18.6061	−	91.1510i	−0.0395875	−	0.193938i
$471$		0			0
$472$	−40.0000	+	40.0000i	−0.0847458	+	0.0847458i
$473$	−172.404	−	172.404i	−0.364491	−	0.364491i
$474$		0			0
$475$	−252.767	−	593.353i	−0.532142	−	1.24916i
$476$	57.1714			0.120108
$477$		0			0
$478$	154.788	+	154.788i	0.323824	+	0.323824i
$479$		−	71.2735i		−	0.148796i	−0.997229	−	0.0743982i	$-0.976296\pi$
$479$		−	71.2735i		−	0.148796i	0.997229	−	0.0743982i	$-0.0237036\pi$
$480$		0			0
$481$	−691.090			−1.43678
$482$	421.939	−	421.939i	0.875392	−	0.875392i
$483$		0			0
$484$		−	138.767i		−	0.286709i
$485$	319.677	−	483.656i	0.659127	−	0.997229i
$486$		0			0
$487$	295.423	−	295.423i	0.606619	−	0.606619i	−0.335442	−	0.942061i	$-0.608886\pi$
$487$	295.423	−	295.423i	0.606619	−	0.606619i	0.942061	+	0.335442i	$0.108886\pi$
$488$	30.3837	+	30.3837i	0.0622616	+	0.0622616i
$489$		0			0
$490$	−279.515	−	184.748i	−0.570439	−	0.377037i
$491$	910.080			1.85352			0.926761	−	0.375651i	$-0.122581\pi$
$491$	910.080			1.85352			0.926761	+	0.375651i	$0.122581\pi$
$492$		0			0
$493$	410.161	+	410.161i	0.831970	+	0.831970i
$494$			660.322i			1.33669i
$495$		0			0
$496$	158.384			0.319322
$497$	−5.57551	+	5.57551i	−0.0112183	+	0.0112183i
$498$		0			0
$499$			970.161i			1.94421i	0.234544	+	0.972105i	$0.424640\pi$
$499$			970.161i			1.94421i	−0.234544	+	0.972105i	$0.575360\pi$
$500$	−142.000	−	205.757i	−0.284000	−	0.411514i
$501$		0			0
$502$	392.586	−	392.586i	0.782043	−	0.782043i
$503$	−276.817	−	276.817i	−0.550333	−	0.550333i	0.376204	−	0.926537i	$-0.377229\pi$
$503$	−276.817	−	276.817i	−0.550333	−	0.550333i	−0.926537	+	0.376204i	$0.877229\pi$
$504$		0			0
$505$	−139.051	+	28.3837i	−0.275349	+	0.0562053i
$506$	295.192			0.583383
$507$		0			0
$508$	−36.5857	−	36.5857i	−0.0720191	−	0.0720191i
$509$			900.059i			1.76829i	0.467213	+	0.884145i	$0.345258\pi$
$509$			900.059i			1.76829i	−0.467213	+	0.884145i	$0.654742\pi$
$510$		0			0
$511$	−66.8877			−0.130896
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$		0			0
$514$			247.031i			0.480604i
$515$	97.3031	+	64.3133i	0.188938	+	0.124880i
$516$		0			0
$517$	−128.363	+	128.363i	−0.248285	+	0.248285i
$518$	−48.5449	−	48.5449i	−0.0937160	−	0.0937160i
$519$		0			0
$520$	51.1918	+	250.788i	0.0984458	+	0.482284i
$521$	239.494			0.459681			0.229841	−	0.973228i	$-0.426180\pi$
$521$	239.494			0.459681			0.229841	+	0.973228i	$0.426180\pi$
$522$		0			0
$523$	12.7173	+	12.7173i	0.0243162	+	0.0243162i	0.719160	−	0.694844i	$-0.244527\pi$
$523$	12.7173	+	12.7173i	0.0243162	+	0.0243162i	−0.694844	+	0.719160i	$0.744527\pi$
$524$		−	267.596i		−	0.510679i
$525$		0			0
$526$	61.3939			0.116718
$527$	629.535	−	629.535i	1.19456	−	1.19456i
$528$		0			0
$529$		−	300.151i		−	0.567393i
$530$	−187.051	+	38.1816i	−0.352926	+	0.0720408i
$531$		0			0
$532$	−46.3837	+	46.3837i	−0.0871874	+	0.0871874i
$533$	−227.778	−	227.778i	−0.427350	−	0.427350i
$534$		0			0
$535$	−58.8786	+	89.0806i	−0.110053	+	0.166506i
$536$	−192.363			−0.358887
$537$		0			0
$538$	−429.151	−	429.151i	−0.797678	−	0.797678i
$539$			653.798i			1.21298i
$540$		0			0
$541$	477.110			0.881904			0.440952	−	0.897531i	$-0.354641\pi$
$541$	477.110			0.881904			0.440952	+	0.897531i	$0.354641\pi$
$542$	−220.727	+	220.727i	−0.407245	+	0.407245i
$543$		0			0
$544$			127.192i			0.233809i
$545$	130.000	+	636.867i	0.238532	+	1.16856i
$546$		0			0
$547$	720.372	−	720.372i	1.31695	−	1.31695i	0.400775	−	0.916177i	$-0.368741\pi$
$547$	720.372	−	720.372i	1.31695	−	1.31695i	0.916177	−	0.400775i	$-0.131259\pi$
$548$	51.7980	+	51.7980i	0.0945218	+	0.0945218i
$549$		0			0
$550$	−182.161	+	452.545i	−0.331202	+	0.822809i
$551$	−665.535			−1.20787
$552$		0			0
$553$	−103.718	−	103.718i	−0.187556	−	0.187556i
$554$		−	91.9796i		−	0.166028i
$555$		0			0
$556$	108.404			0.194971
$557$	139.899	−	139.899i	0.251165	−	0.251165i	−0.570283	−	0.821448i	$-0.693166\pi$
$557$	139.899	−	139.899i	0.251165	−	0.251165i	0.821448	+	0.570283i	$0.193166\pi$
$558$		0			0
$559$		−	319.818i		−	0.572126i
$560$	−14.0204	+	21.2122i	−0.0250364	+	0.0378790i
$561$		0			0
$562$	−482.524	+	482.524i	−0.858584	+	0.858584i
$563$	−461.121	−	461.121i	−0.819043	−	0.819043i	0.166926	−	0.985969i	$-0.446616\pi$
$563$	−461.121	−	461.121i	−0.819043	−	0.819043i	−0.985969	+	0.166926i	$0.946616\pi$
$564$		0			0
$565$	−455.949	−	301.363i	−0.806989	−	0.533386i
$566$	−542.565			−0.958596
$567$		0			0
$568$	−12.4041	−	12.4041i	−0.0218382	−	0.0218382i
$569$		−	31.4939i		−	0.0553495i	−0.999617	−	0.0276748i	$-0.991190\pi$
$569$		−	31.4939i		−	0.0553495i	0.999617	−	0.0276748i	$-0.00881027\pi$
$570$		0			0
$571$	139.233			0.243840			0.121920	−	0.992540i	$-0.461095\pi$
$571$	139.233			0.243840			0.121920	+	0.992540i	$0.461095\pi$
$572$	353.171	−	353.171i	0.617433	−	0.617433i
$573$		0			0
$574$		−	32.0000i		−	0.0557491i
$575$	−350.838	−	141.221i	−0.610153	−	0.245602i
$576$		0			0
$577$	463.000	−	463.000i	0.802426	−	0.802426i	−0.181048	−	0.983474i	$-0.557949\pi$
$577$	463.000	−	463.000i	0.802426	−	0.802426i	0.983474	+	0.181048i	$0.0579489\pi$
$578$	216.555	+	216.555i	0.374663	+	0.374663i
$579$		0			0
$580$	−252.767	+	51.5959i	−0.435806	+	0.0889585i
$581$	−147.959			−0.254663
$582$		0			0
$583$	263.414	+	263.414i	0.451826	+	0.451826i
$584$		−	148.808i		−	0.254809i
$585$		0			0
$586$	−298.182			−0.508842
$587$	−464.091	+	464.091i	−0.790615	+	0.790615i	−0.981594	−	0.190979i	$-0.938834\pi$
$587$	−464.091	+	464.091i	−0.790615	+	0.790615i	0.190979	+	0.981594i	$0.438834\pi$
$588$		0			0
$589$			1021.49i			1.73429i
$590$	−117.980	−	77.9796i	−0.199965	−	0.132169i
$591$		0			0
$592$	108.000	−	108.000i	0.182432	−	0.182432i
$593$	−120.646	−	120.646i	−0.203450	−	0.203450i	0.598026	−	0.801476i	$-0.295952\pi$
$593$	−120.646	−	120.646i	−0.203450	−	0.203450i	−0.801476	+	0.598026i	$0.795952\pi$
$594$		0			0
$595$	28.5857	+	140.041i	0.0480432	+	0.235363i
$596$	−85.5347			−0.143515
$597$		0			0
$598$	273.798	+	273.798i	0.457856	+	0.457856i
$599$		−	157.131i		−	0.262322i	−0.991361	−	0.131161i	$-0.958130\pi$
$599$		−	157.131i		−	0.262322i	0.991361	−	0.131161i	$-0.0418704\pi$
$600$		0			0
$601$	550.302			0.915644			0.457822	−	0.889044i	$-0.348630\pi$
$601$	550.302			0.915644			0.457822	+	0.889044i	$0.348630\pi$
$602$	22.4653	−	22.4653i	0.0373178	−	0.0373178i
$603$		0			0
$604$		−	356.767i		−	0.590674i
$605$	339.909	−	69.3837i	0.561833	−	0.114684i
$606$		0			0
$607$	−182.030	+	182.030i	−0.299884	+	0.299884i	−0.840968	−	0.541084i	$-0.818014\pi$
$607$	−182.030	+	182.030i	−0.299884	+	0.299884i	0.541084	+	0.840968i	$0.318014\pi$
$608$	−103.192	−	103.192i	−0.169723	−	0.169723i
$609$		0			0
$610$	−59.2327	+	89.6163i	−0.0971027	+	0.146912i
$611$	−238.120			−0.389722
$612$		0			0
$613$	−788.110	−	788.110i	−1.28566	−	1.28566i	−0.937396	−	0.348265i	$-0.886771\pi$
$613$	−788.110	−	788.110i	−1.28566	−	1.28566i	−0.348265	−	0.937396i	$-0.613229\pi$
$614$		−	461.394i		−	0.751456i
$615$		0			0
$616$	49.6163			0.0805460
$617$	−356.221	+	356.221i	−0.577344	+	0.577344i	−0.934171	−	0.356826i	$-0.883859\pi$
$617$	−356.221	+	356.221i	−0.577344	+	0.577344i	0.356826	+	0.934171i	$0.383859\pi$
$618$		0			0
$619$			73.8796i			0.119353i	0.998218	+	0.0596766i	$0.0190069\pi$
$619$			73.8796i			0.119353i	−0.998218	+	0.0596766i	$0.980993\pi$
$620$	79.1918	+	387.959i	0.127729	+	0.625741i
$621$		0			0
$622$	−47.7367	+	47.7367i	−0.0767472	+	0.0767472i
$623$	105.535	+	105.535i	0.169398	+	0.169398i
$624$		0			0
$625$	433.000	−	450.706i	0.692800	−	0.721130i
$626$	−439.535			−0.702132
$627$		0			0
$628$	−246.000	−	246.000i	−0.391720	−	0.391720i
$629$		−	858.545i		−	1.36494i
$630$		0			0
$631$	−45.9796			−0.0728678			−0.0364339	−	0.999336i	$-0.511600\pi$
$631$	−45.9796			−0.0728678			−0.0364339	+	0.999336i	$0.511600\pi$
$632$	230.747	−	230.747i	0.365106	−	0.365106i
$633$		0			0
$634$			665.655i			1.04993i
$635$	71.3235	−	107.909i	0.112320	−	0.169936i
$636$		0			0
$637$	−606.414	+	606.414i	−0.951985	+	0.951985i
$638$	355.959	+	355.959i	0.557930	+	0.557930i
$639$		0			0
$640$	−47.1918	−	31.1918i	−0.0737372	−	0.0487372i
$641$	789.757			1.23207			0.616035	−	0.787719i	$-0.288738\pi$
$641$	789.757			1.23207			0.616035	+	0.787719i	$0.288738\pi$
$642$		0			0
$643$	−530.474	−	530.474i	−0.824999	−	0.824999i	0.161821	−	0.986820i	$-0.448263\pi$
$643$	−530.474	−	530.474i	−0.824999	−	0.824999i	−0.986820	+	0.161821i	$0.948263\pi$
$644$			38.4653i			0.0597287i
$645$		0			0
$646$	−820.322			−1.26985
$647$	135.323	−	135.323i	0.209155	−	0.209155i	−0.594753	−	0.803908i	$-0.702750\pi$
$647$	135.323	−	135.323i	0.209155	−	0.209155i	0.803908	+	0.594753i	$0.202750\pi$
$648$		0			0
$649$			275.959i			0.425207i
$650$	−588.706	+	250.788i	−0.905702	+	0.385827i
$651$		0			0
$652$	−127.010	+	127.010i	−0.194801	+	0.194801i
$653$	49.8377	+	49.8377i	0.0763212	+	0.0763212i	0.744237	−	0.667916i	$-0.232813\pi$
$653$	49.8377	+	49.8377i	0.0763212	+	0.0763212i	−0.667916	+	0.744237i	$0.732813\pi$
$654$		0			0
$655$	655.473	−	133.798i	1.00072	−	0.204272i
$656$	71.1918			0.108524
$657$		0			0
$658$	−16.7265	−	16.7265i	−0.0254202	−	0.0254202i
$659$		−	209.576i		−	0.318020i	−0.987277	−	0.159010i	$-0.949170\pi$
$659$		−	209.576i		−	0.318020i	0.987277	−	0.159010i	$-0.0508303\pi$
$660$		0			0
$661$	−119.273			−0.180444			−0.0902220	−	0.995922i	$-0.528758\pi$
$661$	−119.273			−0.180444			−0.0902220	+	0.995922i	$0.528758\pi$
$662$	−209.980	+	209.980i	−0.317190	+	0.317190i
$663$		0			0
$664$		−	329.171i		−	0.495740i
$665$	−136.808	−	90.4245i	−0.205727	−	0.135977i
$666$		0			0
$667$	−275.959	+	275.959i	−0.413732	+	0.413732i
$668$	−97.3531	−	97.3531i	−0.145738	−	0.145738i
$669$		0			0
$670$	−96.1816	−	471.192i	−0.143555	−	0.703271i
$671$	209.616			0.312394
$672$		0			0
$673$	−468.857	−	468.857i	−0.696667	−	0.696667i	0.267023	−	0.963690i	$-0.413960\pi$
$673$	−468.857	−	468.857i	−0.696667	−	0.696667i	−0.963690	+	0.267023i	$0.913960\pi$
$674$			176.747i			0.262236i
$675$		0			0
$676$	317.151			0.469158
$677$	654.160	−	654.160i	0.966263	−	0.966263i	−0.0331860	−	0.999449i	$-0.510565\pi$
$677$	654.160	−	654.160i	0.966263	−	0.966263i	0.999449	+	0.0331860i	$0.0105654\pi$
$678$		0			0
$679$		−	147.414i		−	0.217105i
$680$	−311.555	+	63.5959i	−0.458169	+	0.0935234i
$681$		0			0
$682$	546.343	−	546.343i	0.801089	−	0.801089i
$683$	−286.070	−	286.070i	−0.418844	−	0.418844i	0.465961	−	0.884805i	$-0.345709\pi$
$683$	−286.070	−	286.070i	−0.418844	−	0.418844i	−0.884805	+	0.465961i	$0.845709\pi$
$684$		0			0
$685$	−100.980	+	152.778i	−0.147415	+	0.223033i
$686$	−173.294			−0.252615
$687$		0			0
$688$	49.9796	+	49.9796i	0.0726448	+	0.0726448i
$689$			488.647i			0.709212i
$690$		0			0
$691$	738.706			1.06904			0.534520	−	0.845156i	$-0.320493\pi$
$691$	738.706			1.06904			0.534520	+	0.845156i	$0.320493\pi$
$692$	−70.2225	+	70.2225i	−0.101478	+	0.101478i
$693$		0			0
$694$		−	424.990i		−	0.612377i
$695$	54.2020	+	265.535i	0.0779885	+	0.382064i
$696$		0			0
$697$	282.969	−	282.969i	0.405982	−	0.405982i
$698$	280.000	+	280.000i	0.401146	+	0.401146i
$699$		0			0
$700$	−58.9694	−	23.7367i	−0.0842420	−	0.0339096i
$701$	−475.778			−0.678713			−0.339356	−	0.940658i	$-0.610209\pi$
$701$	−475.778			−0.678713			−0.339356	+	0.940658i	$0.610209\pi$
$702$		0			0
$703$	696.545	+	696.545i	0.990818	+	0.990818i
$704$			110.384i			0.156795i
$705$		0			0
$706$	425.010			0.601997
$707$	−25.5163	+	25.5163i	−0.0360910	+	0.0360910i
$708$		0			0
$709$		−	504.363i		−	0.711373i	−0.934605	−	0.355686i	$-0.884247\pi$
$709$		−	504.363i		−	0.711373i	0.934605	−	0.355686i	$-0.115753\pi$
$710$	24.1816	−	36.5857i	0.0340586	−	0.0515292i
$711$		0			0
$712$	−234.788	+	234.788i	−0.329758	+	0.329758i
$713$	423.555	+	423.555i	0.594046	+	0.594046i
$714$		0			0
$715$	1041.68	+	688.504i	1.45689	+	0.962943i
$716$	282.343			0.394334
$717$		0			0
$718$	633.090	+	633.090i	0.881741	+	0.881741i
$719$			481.816i			0.670120i	0.942197	+	0.335060i	$0.108757\pi$
$719$			481.816i			0.670120i	−0.942197	+	0.335060i	$0.891243\pi$
$720$		0			0
$721$	29.6571			0.0411334
$722$	304.535	−	304.535i	0.421793	−	0.421793i
$723$		0			0
$724$		−	117.616i		−	0.162453i
$725$	−252.767	−	593.353i	−0.348645	−	0.818418i
$726$		0			0
$727$	−782.352	+	782.352i	−1.07614	+	1.07614i	−0.0792856	+	0.996852i	$0.525264\pi$
$727$	−782.352	+	782.352i	−1.07614	+	1.07614i	−0.996852	+	0.0792856i	$0.974736\pi$
$728$	46.0204	+	46.0204i	0.0632148	+	0.0632148i
$729$		0			0
$730$	364.504	−	74.4041i	0.499321	−	0.101923i
$731$	397.312			0.543519
$732$		0			0
$733$	537.586	+	537.586i	0.733405	+	0.733405i	0.971293	−	0.237888i	$-0.0764551\pi$
$733$	537.586	+	537.586i	0.733405	+	0.733405i	−0.237888	+	0.971293i	$0.576455\pi$
$734$		−	535.010i		−	0.728897i
$735$		0			0
$736$	−85.5755			−0.116271
$737$	−663.555	+	663.555i	−0.900346	+	0.900346i
$738$		0			0
$739$		−	833.353i		−	1.12768i	−0.825885	−	0.563838i	$-0.809324\pi$
$739$		−	833.353i		−	1.12768i	0.825885	−	0.563838i	$-0.190676\pi$
$740$	318.545	+	210.545i	0.430466	+	0.284520i
$741$		0			0
$742$	−34.3245	+	34.3245i	−0.0462594	+	0.0462594i
$743$	991.383	+	991.383i	1.33430	+	1.33430i	0.901484	+	0.432813i	$0.142479\pi$
$743$	991.383	+	991.383i	1.33430	+	1.33430i	0.432813	+	0.901484i	$0.357521\pi$
$744$		0			0
$745$	−42.7673	−	209.516i	−0.0574058	−	0.281230i
$746$	753.878			1.01056
$747$		0			0
$748$	438.747	+	438.747i	0.586560	+	0.586560i
$749$			27.1510i			0.0362497i
$750$		0			0
$751$	−1276.73			−1.70004			−0.850018	−	0.526754i	$-0.823409\pi$
$751$	−1276.73			−1.70004			−0.850018	+	0.526754i	$0.823409\pi$
$752$	37.2122	−	37.2122i	0.0494844	−	0.0494844i
$753$		0			0
$754$			660.322i			0.875759i
$755$	873.898	−	178.384i	1.15748	−	0.236270i
$756$		0			0
$757$	−36.0918	+	36.0918i	−0.0476775	+	0.0476775i	−0.730544	−	0.682866i	$-0.760733\pi$
$757$	−36.0918	+	36.0918i	−0.0476775	+	0.0476775i	0.682866	+	0.730544i	$0.260733\pi$
$758$	167.818	+	167.818i	0.221396	+	0.221396i
$759$		0			0
$760$	201.171	−	304.363i	0.264699	−	0.400478i
$761$	−716.261			−0.941211			−0.470605	−	0.882344i	$-0.655964\pi$
$761$	−716.261			−0.941211			−0.470605	+	0.882344i	$0.655964\pi$
$762$		0			0
$763$	116.867	+	116.867i	0.153168	+	0.153168i
$764$		−	650.788i		−	0.851816i
$765$		0			0
$766$	−956.586			−1.24881
$767$	−255.959	+	255.959i	−0.333715	+	0.333715i
$768$		0			0
$769$		−	389.576i		−	0.506600i	−0.967388	−	0.253300i	$-0.918484\pi$
$769$		−	389.576i		−	0.506600i	0.967388	−	0.253300i	$-0.0815160\pi$
$770$	24.8082	+	121.535i	0.0322184	+	0.157837i
$771$		0			0
$772$	−78.7673	+	78.7673i	−0.102030	+	0.102030i
$773$	409.677	+	409.677i	0.529983	+	0.529983i	0.920567	−	0.390585i	$-0.127727\pi$
$773$	409.677	+	409.677i	0.529983	+	0.529983i	−0.390585	+	0.920567i	$0.627727\pi$
$774$		0			0
$775$	−910.706	+	387.959i	−1.17510	+	0.500592i
$776$	327.959			0.422628
$777$		0			0
$778$	−169.151	−	169.151i	−0.217418	−	0.217418i
$779$			459.151i			0.589411i
$780$		0			0
$781$	−85.5755			−0.109572
$782$	−340.141	+	340.141i	−0.434963	+	0.434963i
$783$		0			0
$784$		−	189.535i		−	0.241753i
$785$	479.574	−	725.574i	0.610923	−	0.924299i
$786$		0			0
$787$	−383.142	+	383.142i	−0.486838	+	0.486838i	−0.907307	−	0.420469i	$-0.861866\pi$
$787$	−383.142	+	383.142i	−0.486838	+	0.486838i	0.420469	+	0.907307i	$0.361866\pi$
$788$	−238.627	−	238.627i	−0.302826	−	0.302826i
$789$		0			0
$790$	680.586	+	449.839i	0.861501	+	0.569416i
$791$	−138.969			−0.175688
$792$		0			0
$793$	194.424	+	194.424i	0.245176	+	0.245176i
$794$		−	138.686i		−	0.174667i
$795$		0			0
$796$	357.131			0.448657
$797$	−563.191	+	563.191i	−0.706638	+	0.706638i	−0.965827	−	0.259188i	$-0.916545\pi$
$797$	−563.191	+	563.191i	−0.706638	+	0.706638i	0.259188	+	0.965827i	$0.416545\pi$
$798$		0			0
$799$		−	295.818i		−	0.370236i
$800$	52.8082	−	131.192i	0.0660102	−	0.163990i
$801$		0			0
$802$	414.767	−	414.767i	0.517166	−	0.517166i
$803$	−513.312	−	513.312i	−0.639243	−	0.639243i
$804$		0			0
$805$	−94.2204	+	19.2327i	−0.117044	+	0.0238915i
$806$	1013.49			1.25744
$807$		0			0
$808$	−56.7673	−	56.7673i	−0.0702566	−	0.0702566i
$809$		−	770.161i		−	0.951992i	−0.879448	−	0.475996i	$-0.842088\pi$
$809$		−	770.161i		−	0.951992i	0.879448	−	0.475996i	$-0.157912\pi$
$810$		0			0
$811$	13.4939			0.0166386			0.00831928	−	0.999965i	$-0.497352\pi$
$811$	13.4939			0.0166386			0.00831928	+	0.999965i	$0.497352\pi$
$812$	−46.3837	+	46.3837i	−0.0571227	+	0.0571227i
$813$		0			0
$814$		−	745.090i		−	0.915344i
$815$	−374.615	−	247.605i	−0.459651	−	0.303810i
$816$		0			0
$817$	−322.343	+	322.343i	−0.394544	+	0.394544i
$818$	−605.110	−	605.110i	−0.739744	−	0.739744i
$819$		0			0
$820$	35.5959	+	174.384i	0.0434097	+	0.212663i
$821$	−741.312			−0.902938			−0.451469	−	0.892287i	$-0.649100\pi$
$821$	−741.312			−0.902938			−0.451469	+	0.892287i	$0.649100\pi$
$822$		0			0
$823$	−196.272	−	196.272i	−0.238484	−	0.238484i	0.577738	−	0.816222i	$-0.303936\pi$
$823$	−196.272	−	196.272i	−0.238484	−	0.238484i	−0.816222	+	0.577738i	$0.803936\pi$
$824$			65.9796i			0.0800723i
$825$		0			0
$826$	−35.9592			−0.0435341
$827$	20.5357	−	20.5357i	0.0248316	−	0.0248316i	−0.694582	−	0.719414i	$-0.744411\pi$
$827$	20.5357	−	20.5357i	0.0248316	−	0.0248316i	0.719414	+	0.694582i	$0.244411\pi$
$828$		0			0
$829$		−	264.465i		−	0.319017i	−0.987197	−	0.159509i	$-0.949009\pi$
$829$		−	264.465i		−	0.319017i	0.987197	−	0.159509i	$-0.0509910\pi$
$830$	806.302	−	164.586i	0.971448	−	0.198296i
$831$		0			0
$832$	−102.384	+	102.384i	−0.123057	+	0.123057i
$833$	−753.352	−	753.352i	−0.904384	−	0.904384i
$834$		0			0
$835$	189.789	−	287.142i	0.227292	−	0.343882i
$836$	−711.918			−0.851577
$837$		0			0
$838$	15.9592	+	15.9592i	0.0190444	+	0.0190444i
$839$			353.090i			0.420846i	0.977610	+	0.210423i	$0.0674841\pi$
$839$			353.090i			0.420846i	−0.977610	+	0.210423i	$0.932516\pi$
$840$		0			0
$841$	175.465			0.208639
$842$	−433.171	+	433.171i	−0.514455	+	0.514455i
$843$		0			0
$844$			637.494i			0.755324i
$845$	158.576	+	776.858i	0.187663	+	0.919359i
$846$		0			0
$847$	62.3745	−	62.3745i	0.0736417	−	0.0736417i
$848$	−76.3633	−	76.3633i	−0.0900510	−	0.0900510i
$849$		0			0
$850$	−311.555	−	731.353i	−0.366535	−	0.860415i
$851$	577.635			0.678772
$852$		0			0
$853$	19.4449	+	19.4449i	0.0227959	+	0.0227959i	0.718413	−	0.695617i	$-0.244869\pi$
$853$	19.4449	+	19.4449i	0.0227959	+	0.0227959i	−0.695617	+	0.718413i	$0.744869\pi$
$854$			27.3143i			0.0319840i
$855$		0			0
$856$	−60.4041			−0.0705655
$857$	−602.444	+	602.444i	−0.702968	+	0.702968i	−0.965047	−	0.262078i	$-0.915592\pi$
$857$	−602.444	+	602.444i	−0.702968	+	0.702968i	0.262078	+	0.965047i	$0.415592\pi$
$858$		0			0
$859$		−	1099.53i		−	1.28001i	−0.768369	−	0.640007i	$-0.778931\pi$
$859$		−	1099.53i		−	1.28001i	0.768369	−	0.640007i	$-0.221069\pi$
$860$	−97.4347	+	147.414i	−0.113296	+	0.171412i
$861$		0			0
$862$	24.1816	−	24.1816i	0.0280529	−	0.0280529i
$863$	−694.797	−	694.797i	−0.805095	−	0.805095i	0.178792	−	0.983887i	$-0.442781\pi$
$863$	−694.797	−	694.797i	−0.805095	−	0.805095i	−0.983887	+	0.178792i	$0.942781\pi$
$864$		0			0
$865$	−207.120	−	136.898i	−0.239446	−	0.158264i
$866$	−1057.84			−1.22152
$867$		0			0
$868$	71.1918	+	71.1918i	0.0820182	+	0.0820182i
$869$		−	1591.92i		−	1.83190i
$870$		0			0
$871$	−1230.93			−1.41324
$872$	−260.000	+	260.000i	−0.298165	+	0.298165i
$873$		0			0
$874$		−	551.918i		−	0.631486i
$875$	28.6582	−	156.313i	0.0327522	−	0.178644i
$876$		0			0
$877$	1092.90	−	1092.90i	1.24618	−	1.24618i	0.288783	−	0.957394i	$-0.406749\pi$
$877$	1092.90	−	1092.90i	1.24618	−	1.24618i	0.957394	−	0.288783i	$-0.0932507\pi$
$878$	−44.6265	−	44.6265i	−0.0508275	−	0.0508275i
$879$		0			0
$880$	−270.384	+	55.1918i	−0.307254	+	0.0627180i
$881$	−138.443			−0.157143			−0.0785714	−	0.996908i	$-0.525036\pi$
$881$	−138.443			−0.157143			−0.0785714	+	0.996908i	$0.525036\pi$
$882$		0			0
$883$	1008.41	+	1008.41i	1.14203	+	1.14203i	0.988078	+	0.153953i	$0.0492003\pi$
$883$	1008.41	+	1008.41i	1.14203	+	1.14203i	0.153953	+	0.988078i	$0.450800\pi$
$884$			813.898i			0.920699i
$885$		0			0
$886$	622.565			0.702670
$887$	639.687	−	639.687i	0.721180	−	0.721180i	−0.247666	−	0.968846i	$-0.579663\pi$
$887$	639.687	−	639.687i	0.721180	−	0.721180i	0.968846	+	0.247666i	$0.0796634\pi$
$888$		0			0
$889$		−	32.8898i		−	0.0369964i
$890$	−692.504	−	457.716i	−0.778094	−	0.514288i
$891$		0			0
$892$	417.353	−	417.353i	0.467885	−	0.467885i
$893$	240.000	+	240.000i	0.268757	+	0.268757i
$894$		0			0
$895$	141.171	+	691.596i	0.157733	+	0.772733i
$896$	−14.3837			−0.0160532
$897$		0			0
$898$	−141.273	−	141.273i	−0.157320	−	0.157320i
$899$			1021.49i			1.13626i
$900$		0			0
$901$	−607.049			−0.673750
$902$	245.576	−	245.576i	0.272257	−	0.272257i
$903$		0			0
$904$		−	309.171i		−	0.342004i
$905$	288.100	−	58.8082i	0.318343	−	0.0649814i
$906$		0			0
$907$	−893.303	+	893.303i	−0.984899	+	0.984899i	−0.999888	−	0.0149890i	$-0.995229\pi$
$907$	−893.303	+	893.303i	−0.984899	+	0.984899i	0.0149890	+	0.999888i	$0.495229\pi$
$908$	484.141	+	484.141i	0.533195	+	0.533195i
$909$		0			0
$910$	−89.7163	+	135.737i	−0.0985894	+	0.149161i
$911$	−1045.03			−1.14712			−0.573562	−	0.819162i	$-0.694439\pi$
$911$	−1045.03			−1.14712			−0.573562	+	0.819162i	$0.694439\pi$
$912$		0			0
$913$	−1135.47	−	1135.47i	−1.24367	−	1.24367i
$914$			40.7878i			0.0446256i
$915$		0			0
$916$	−827.878			−0.903796
$917$	120.282	−	120.282i	0.131169	−	0.131169i
$918$		0			0
$919$			803.573i			0.874400i	0.899364	+	0.437200i	$0.144030\pi$
$919$			803.573i			0.874400i	−0.899364	+	0.437200i	$0.855970\pi$
$920$	−42.7878	−	209.616i	−0.0465084	−	0.227844i
$921$		0			0
$922$	−626.727	+	626.727i	−0.679747	+	0.679747i
$923$	−79.3735	−	79.3735i	−0.0859951	−	0.0859951i
$924$		0			0
$925$	−356.455	+	885.545i	−0.385357	+	0.957346i
$926$	629.031			0.679299
$927$		0			0
$928$	−103.192	−	103.192i	−0.111198	−	0.111198i
$929$		−	1270.64i		−	1.36776i	−0.729597	−	0.683878i	$-0.760292\pi$
$929$		−	1270.64i		−	1.36776i	0.729597	−	0.683878i	$-0.239708\pi$
$930$		0			0
$931$	1222.40			1.31300
$932$	−128.524	+	128.524i	−0.137902	+	0.137902i
$933$		0			0
$934$		−	93.3939i		−	0.0999934i
$935$	−855.333	+	1294.08i	−0.914794	+	1.38404i
$936$		0			0
$937$	−970.616	+	970.616i	−1.03588	+	1.03588i	−0.0365445	+	0.999332i	$0.511635\pi$
$937$	−970.616	+	970.616i	−1.03588	+	1.03588i	−0.999332	+	0.0365445i	$0.988365\pi$
$938$	−86.4653	−	86.4653i	−0.0921805	−	0.0921805i
$939$		0			0
$940$	109.757	+	72.5449i	0.116763	+	0.0771754i
$941$	431.616			0.458678			0.229339	−	0.973347i	$-0.426344\pi$
$941$	431.616			0.458678			0.229339	+	0.973347i	$0.426344\pi$
$942$		0			0
$943$	190.384	+	190.384i	0.201891	+	0.201891i
$944$		−	80.0000i		−	0.0847458i
$945$		0			0
$946$	344.808			0.364491
$947$	721.121	−	721.121i	0.761480	−	0.761480i	−0.215110	−	0.976590i	$-0.569011\pi$
$947$	721.121	−	721.121i	0.761480	−	0.761480i	0.976590	+	0.215110i	$0.0690110\pi$
$948$		0			0
$949$		−	952.220i		−	1.00339i
$950$	846.120	+	340.586i	0.890653	+	0.358511i
$951$		0			0
$952$	−57.1714	+	57.1714i	−0.0600540	+	0.0600540i
$953$	737.291	+	737.291i	0.773652	+	0.773652i	0.978743	−	0.205091i	$-0.0657489\pi$
$953$	737.291	+	737.291i	0.773652	+	0.773652i	−0.205091	+	0.978743i	$0.565749\pi$
$954$		0			0
$955$	1594.10	−	325.394i	1.66921	−	0.340727i
$956$	−309.576			−0.323824
$957$		0			0
$958$	71.2735	+	71.2735i	0.0743982	+	0.0743982i
$959$			46.5653i			0.0485561i
$960$		0			0
$961$	606.837			0.631464
$962$	691.090	−	691.090i	0.718389	−	0.718389i
$963$		0			0
$964$			843.878i			0.875392i
$965$	−232.323	−	153.556i	−0.240750	−	0.159126i
$966$		0			0
$967$	958.879	−	958.879i	0.991601	−	0.991601i	−0.00836361	−	0.999965i	$-0.502662\pi$
$967$	958.879	−	958.879i	0.991601	−	0.991601i	0.999965	+	0.00836361i	$0.00266225\pi$
$968$	138.767	+	138.767i	0.143355	+	0.143355i
$969$		0			0
$970$	163.980	+	803.333i	0.169051	+	0.828178i
$971$	1507.86			1.55289			0.776444	−	0.630186i	$-0.217021\pi$
$971$	1507.86			1.55289			0.776444	+	0.630186i	$0.217021\pi$
$972$		0			0
$973$	48.7265	+	48.7265i	0.0500786	+	0.0500786i
$974$			590.847i			0.606619i
$975$		0			0
$976$	−60.7673			−0.0622616
$977$	373.838	−	373.838i	0.382638	−	0.382638i	−0.489413	−	0.872052i	$-0.662789\pi$
$977$	373.838	−	373.838i	0.382638	−	0.382638i	0.872052	+	0.489413i	$0.162789\pi$
$978$		0			0
$979$			1619.80i			1.65454i
$980$	464.263	−	94.7673i	0.473738	−	0.0967014i
$981$		0			0
$982$	−910.080	+	910.080i	−0.926761	+	0.926761i
$983$	1319.46	+	1319.46i	1.34228	+	1.34228i	0.893783	+	0.448501i	$0.148042\pi$
$983$	1319.46	+	1319.46i	1.34228	+	1.34228i	0.448501	+	0.893783i	$0.351958\pi$
$984$		0			0
$985$	465.200	−	703.827i	0.472284	−	0.714545i
$986$	−820.322			−0.831970
$987$		0			0
$988$	−660.322	−	660.322i	−0.668343	−	0.668343i
$989$			267.314i			0.270287i
$990$		0			0
$991$	−315.029			−0.317890			−0.158945	−	0.987287i	$-0.550809\pi$
$991$	−315.029			−0.317890			−0.158945	+	0.987287i	$0.550809\pi$
$992$	−158.384	+	158.384i	−0.159661	+	0.159661i
$993$		0			0
$994$		−	11.1510i		−	0.0112183i
$995$	178.565	+	874.788i	0.179463	+	0.879184i
$996$		0			0
$997$	1009.38	−	1009.38i	1.01242	−	1.01242i	0.0124991	−	0.999922i	$-0.496021\pi$
$997$	1009.38	−	1009.38i	1.01242	−	1.01242i	0.999922	−	0.0124991i	$-0.00397868\pi$
$998$	−970.161	−	970.161i	−0.972105	−	0.972105i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.3.g.d.73.2		4
3.2	odd	2		30.3.f.a.13.2	yes	4
4.3	odd	2		720.3.bh.i.433.2		4
5.2	odd	4	inner	90.3.g.d.37.2		4
5.3	odd	4		450.3.g.j.307.1		4
5.4	even	2		450.3.g.j.343.1		4
12.11	even	2		240.3.bg.b.193.1		4
15.2	even	4		30.3.f.a.7.2	✓	4
15.8	even	4		150.3.f.b.7.1		4
15.14	odd	2		150.3.f.b.43.1		4
20.7	even	4		720.3.bh.i.577.2		4
24.5	odd	2		960.3.bg.e.193.1		4
24.11	even	2		960.3.bg.g.193.2		4
60.23	odd	4		1200.3.bg.d.1057.2		4
60.47	odd	4		240.3.bg.b.97.1		4
60.59	even	2		1200.3.bg.d.193.2		4
120.77	even	4		960.3.bg.e.577.1		4
120.107	odd	4		960.3.bg.g.577.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.3.f.a.7.2	✓	4	15.2	even	4
30.3.f.a.13.2	yes	4	3.2	odd	2
90.3.g.d.37.2		4	5.2	odd	4	inner
90.3.g.d.73.2		4	1.1	even	1	trivial
150.3.f.b.7.1		4	15.8	even	4
150.3.f.b.43.1		4	15.14	odd	2
240.3.bg.b.97.1		4	60.47	odd	4
240.3.bg.b.193.1		4	12.11	even	2
450.3.g.j.307.1		4	5.3	odd	4
450.3.g.j.343.1		4	5.4	even	2
720.3.bh.i.433.2		4	4.3	odd	2
720.3.bh.i.577.2		4	20.7	even	4
960.3.bg.e.193.1		4	24.5	odd	2
960.3.bg.e.577.1		4	120.77	even	4
960.3.bg.g.193.2		4	24.11	even	2
960.3.bg.g.577.2		4	120.107	odd	4
1200.3.bg.d.193.2		4	60.59	even	2
1200.3.bg.d.1057.2		4	60.23	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(4.89898 - 1.00000i) q^{5} +(0.898979 - 0.898979i) q^{7} +(2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(4.89898 - 1.00000i) q^{5} +(0.898979 - 0.898979i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-3.89898 + 5.89898i) q^{10} +13.7980 q^{11} +(12.7980 + 12.7980i) q^{13} +1.79796i q^{14} -4.00000 q^{16} +(-15.8990 + 15.8990i) q^{17} -25.7980i q^{19} +(-2.00000 - 9.79796i) q^{20} +(-13.7980 + 13.7980i) q^{22} +(-10.6969 - 10.6969i) q^{23} +(23.0000 - 9.79796i) q^{25} -25.5959 q^{26} +(-1.79796 - 1.79796i) q^{28} -25.7980i q^{29} -39.5959 q^{31} +(4.00000 - 4.00000i) q^{32} -31.7980i q^{34} +(3.50510 - 5.30306i) q^{35} +(-27.0000 + 27.0000i) q^{37} +(25.7980 + 25.7980i) q^{38} +(11.7980 + 7.79796i) q^{40} -17.7980 q^{41} +(-12.4949 - 12.4949i) q^{43} -27.5959i q^{44} +21.3939 q^{46} +(-9.30306 + 9.30306i) q^{47} +47.3837i q^{49} +(-13.2020 + 32.7980i) q^{50} +(25.5959 - 25.5959i) q^{52} +(19.0908 + 19.0908i) q^{53} +(67.5959 - 13.7980i) q^{55} +3.59592 q^{56} +(25.7980 + 25.7980i) q^{58} +20.0000i q^{59} +15.1918 q^{61} +(39.5959 - 39.5959i) q^{62} +8.00000i q^{64} +(75.4949 + 49.8990i) q^{65} +(-48.0908 + 48.0908i) q^{67} +(31.7980 + 31.7980i) q^{68} +(1.79796 + 8.80816i) q^{70} -6.20204 q^{71} +(-37.2020 - 37.2020i) q^{73} -54.0000i q^{74} -51.5959 q^{76} +(12.4041 - 12.4041i) q^{77} -115.373i q^{79} +(-19.5959 + 4.00000i) q^{80} +(17.7980 - 17.7980i) q^{82} +(-82.2929 - 82.2929i) q^{83} +(-61.9898 + 93.7878i) q^{85} +24.9898 q^{86} +(27.5959 + 27.5959i) q^{88} +117.394i q^{89} +23.0102 q^{91} +(-21.3939 + 21.3939i) q^{92} -18.6061i q^{94} +(-25.7980 - 126.384i) q^{95} +(81.9898 - 81.9898i) q^{97} +(-47.3837 - 47.3837i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 16 q^{7} + 8 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 - 16 * q^7 + 8 * q^8	\( 4 q - 4 q^{2} - 16 q^{7} + 8 q^{8} + 4 q^{10} + 16 q^{11} + 12 q^{13} - 16 q^{16} - 44 q^{17} - 8 q^{20} - 16 q^{22} + 16 q^{23} + 92 q^{25} - 24 q^{26} + 32 q^{28} - 80 q^{31} + 16 q^{32} + 112 q^{35} - 108 q^{37} + 64 q^{38} + 8 q^{40} - 32 q^{41} + 48 q^{43} - 32 q^{46} - 96 q^{47} - 92 q^{50} + 24 q^{52} - 100 q^{53} + 192 q^{55} - 64 q^{56} + 64 q^{58} - 96 q^{61} + 80 q^{62} + 204 q^{65} - 16 q^{67} + 88 q^{68} - 32 q^{70} - 64 q^{71} - 188 q^{73} - 128 q^{76} + 128 q^{77} + 32 q^{82} - 192 q^{83} - 52 q^{85} - 96 q^{86} + 32 q^{88} + 288 q^{91} + 32 q^{92} - 64 q^{95} + 132 q^{97} + 124 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 - 16 * q^7 + 8 * q^8 + 4 * q^10 + 16 * q^11 + 12 * q^13 - 16 * q^16 - 44 * q^17 - 8 * q^20 - 16 * q^22 + 16 * q^23 + 92 * q^25 - 24 * q^26 + 32 * q^28 - 80 * q^31 + 16 * q^32 + 112 * q^35 - 108 * q^37 + 64 * q^38 + 8 * q^40 - 32 * q^41 + 48 * q^43 - 32 * q^46 - 96 * q^47 - 92 * q^50 + 24 * q^52 - 100 * q^53 + 192 * q^55 - 64 * q^56 + 64 * q^58 - 96 * q^61 + 80 * q^62 + 204 * q^65 - 16 * q^67 + 88 * q^68 - 32 * q^70 - 64 * q^71 - 188 * q^73 - 128 * q^76 + 128 * q^77 + 32 * q^82 - 192 * q^83 - 52 * q^85 - 96 * q^86 + 32 * q^88 + 288 * q^91 + 32 * q^92 - 64 * q^95 + 132 * q^97 + 124 * q^98

Introduction

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