LMFDB - Embedded newform 99.3.k.b.46.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,3,Mod(19,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("99.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	99.k (of order $10$, degree $4$, 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:	$2.69755461717$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 21x^{14} + 227x^{12} - 1488x^{10} + 24225x^{8} - 62832x^{6} + 64372x^{4} + 7986x^{2} + 14641 $ x^16 - 21x^14 + 227x^12 - 1488x^10 + 24225x^8 - 62832x^6 + 64372x^4 + 7986*x^2 + 14641
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			46.3
Root			$0.386583 - 0.532086i$ of defining polynomial
Character	$\chi$	$=$	99.46
Dual form			99.3.k.b.28.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.625505 + 0.203239i) q^{2} +(-2.88612 - 2.09689i) q^{4} +(-2.50346 - 7.70484i) q^{5} +(-2.40175 + 3.30573i) q^{7} +(-2.92545 - 4.02653i) q^{8} +O(q^{10})$	\(q+(0.625505 + 0.203239i) q^{2} +(-2.88612 - 2.09689i) q^{4} +(-2.50346 - 7.70484i) q^{5} +(-2.40175 + 3.30573i) q^{7} +(-2.92545 - 4.02653i) q^{8} -5.32822i q^{10} +(-6.70179 - 8.72273i) q^{11} +(14.0643 + 4.56975i) q^{13} +(-2.17416 + 1.57962i) q^{14} +(3.39806 + 10.4582i) q^{16} +(28.0003 - 9.09786i) q^{17} +(-7.52161 - 10.3526i) q^{19} +(-8.93092 + 27.4865i) q^{20} +(-2.41921 - 6.81818i) q^{22} -12.6293 q^{23} +(-32.8719 + 23.8828i) q^{25} +(7.86851 + 5.71681i) q^{26} +(13.8635 - 4.50452i) q^{28} +(-7.85901 + 10.8170i) q^{29} +(10.9884 - 33.8187i) q^{31} +27.1405i q^{32} +19.3634 q^{34} +(31.4828 + 10.2294i) q^{35} +(14.5329 + 10.5587i) q^{37} +(-2.60075 - 8.00429i) q^{38} +(-23.7001 + 32.6203i) q^{40} +(9.51144 + 13.0914i) q^{41} -44.2415i q^{43} +(1.05159 + 39.2277i) q^{44} +(-7.89971 - 2.56677i) q^{46} +(7.76454 - 5.64127i) q^{47} +(9.98240 + 30.7227i) q^{49} +(-25.4155 + 8.25799i) q^{50} +(-31.0088 - 42.6800i) q^{52} +(17.8438 - 54.9177i) q^{53} +(-50.4296 + 73.4732i) q^{55} +20.3368 q^{56} +(-7.11429 + 5.16883i) q^{58} +(-81.1105 - 58.9302i) q^{59} +(79.0445 - 25.6831i) q^{61} +(13.7466 - 18.9205i) q^{62} +(8.07624 - 24.8561i) q^{64} -119.803i q^{65} +87.5688 q^{67} +(-99.8895 - 32.4561i) q^{68} +(17.6136 + 12.7971i) q^{70} +(21.1594 + 65.1219i) q^{71} +(-15.2790 + 21.0298i) q^{73} +(6.94443 + 9.55819i) q^{74} +45.6508i q^{76} +(44.9310 - 1.20448i) q^{77} +(-62.3915 - 20.2722i) q^{79} +(72.0716 - 52.3631i) q^{80} +(3.28878 + 10.1218i) q^{82} +(-83.0198 + 26.9748i) q^{83} +(-140.195 - 192.962i) q^{85} +(8.99160 - 27.6733i) q^{86} +(-15.5166 + 52.5028i) q^{88} +29.3444 q^{89} +(-48.8852 + 35.5172i) q^{91} +(36.4497 + 26.4823i) q^{92} +(6.00329 - 1.95059i) q^{94} +(-60.9352 + 83.8701i) q^{95} +(-11.3670 + 34.9841i) q^{97} +21.2460i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} + 30 q^{7}+O(q^{10}) $ 16 * q - 4 * q^4 + 30 * q^7	$ 16 q - 4 q^{4} + 30 q^{7} - 30 q^{13} - 176 q^{16} + 90 q^{22} - 74 q^{25} - 50 q^{28} + 130 q^{31} + 328 q^{34} + 90 q^{37} + 450 q^{40} - 370 q^{46} - 54 q^{49} - 790 q^{52} - 476 q^{55} - 630 q^{58} + 210 q^{61} + 1104 q^{64} + 300 q^{67} + 268 q^{70} - 170 q^{73} + 30 q^{79} + 90 q^{82} - 610 q^{85} - 600 q^{88} - 402 q^{91} + 1030 q^{94} + 870 q^{97}+O(q^{100}) $ 16 * q - 4 * q^4 + 30 * q^7 - 30 * q^13 - 176 * q^16 + 90 * q^22 - 74 * q^25 - 50 * q^28 + 130 * q^31 + 328 * q^34 + 90 * q^37 + 450 * q^40 - 370 * q^46 - 54 * q^49 - 790 * q^52 - 476 * q^55 - 630 * q^58 + 210 * q^61 + 1104 * q^64 + 300 * q^67 + 268 * q^70 - 170 * q^73 + 30 * q^79 + 90 * q^82 - 610 * q^85 - 600 * q^88 - 402 * q^91 + 1030 * q^94 + 870 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	0.625505	+	0.203239i	0.312753	+	0.101619i	0.461187	−	0.887303i	$-0.347424\pi$
$2$	0.625505	+	0.203239i	0.312753	+	0.101619i	−0.148435	+	0.988922i	$0.547424\pi$
$3$		0			0
$3$		0			0
$4$	−2.88612	−	2.09689i	−0.721529	−	0.524222i
$5$	−2.50346	−	7.70484i	−0.500691	−	1.54097i	−0.807896	−	0.589325i	$-0.799394\pi$
$5$	−2.50346	−	7.70484i	−0.500691	−	1.54097i	0.307205	−	0.951643i	$-0.400606\pi$
$6$		0			0
$7$	−2.40175	+	3.30573i	−0.343108	+	0.472247i	−0.945346	−	0.326069i	$-0.894276\pi$
$7$	−2.40175	+	3.30573i	−0.343108	+	0.472247i	0.602238	+	0.798316i	$0.294276\pi$
$8$	−2.92545	−	4.02653i	−0.365681	−	0.503316i
$9$		0			0
$10$		−	5.32822i		−	0.532822i
$11$	−6.70179	−	8.72273i	−0.609254	−	0.792975i
$11$	−6.70179	−	8.72273i	−0.609254	−	0.792975i
$12$		0			0
$13$	14.0643	+	4.56975i	1.08187	+	0.351520i	0.795098	−	0.606481i	$-0.207419\pi$
$13$	14.0643	+	4.56975i	1.08187	+	0.351520i	0.286768	+	0.958000i	$0.407419\pi$
$14$	−2.17416	+	1.57962i	−0.155297	+	0.112830i
$15$		0			0
$16$	3.39806	+	10.4582i	0.212379	+	0.653635i
$17$	28.0003	−	9.09786i	1.64708	−	0.535169i	0.668975	−	0.743285i	$-0.266733\pi$
$17$	28.0003	−	9.09786i	1.64708	−	0.535169i	0.978104	+	0.208116i	$0.0667332\pi$
$18$		0			0
$19$	−7.52161	−	10.3526i	−0.395874	−	0.544874i	0.563828	−	0.825892i	$-0.309328\pi$
$19$	−7.52161	−	10.3526i	−0.395874	−	0.544874i	−0.959702	+	0.281018i	$0.909328\pi$
$20$	−8.93092	+	27.4865i	−0.446546	+	1.37433i
$21$		0			0
$22$	−2.41921	−	6.81818i	−0.109964	−	0.309917i
$23$	−12.6293			−0.549101			−0.274551	−	0.961573i	$-0.588529\pi$
$23$	−12.6293			−0.549101			−0.274551	+	0.961573i	$0.588529\pi$
$24$		0			0
$25$	−32.8719	+	23.8828i	−1.31488	+	0.955314i
$26$	7.86851	+	5.71681i	0.302635	+	0.219877i
$27$		0			0
$28$	13.8635	−	4.50452i	0.495124	−	0.160876i
$29$	−7.85901	+	10.8170i	−0.271000	+	0.373000i	−0.922727	−	0.385454i	$-0.874045\pi$
$29$	−7.85901	+	10.8170i	−0.271000	+	0.373000i	0.651727	+	0.758454i	$0.274045\pi$
$30$		0			0
$31$	10.9884	−	33.8187i	0.354464	−	1.09093i	−0.601856	−	0.798604i	$-0.705572\pi$
$31$	10.9884	−	33.8187i	0.354464	−	1.09093i	0.956320	−	0.292322i	$-0.0944280\pi$
$32$			27.1405i			0.848141i
$33$		0			0
$34$	19.3634			0.569512
$35$	31.4828	+	10.2294i	0.899509	+	0.292268i
$36$		0			0
$37$	14.5329	+	10.5587i	0.392780	+	0.285371i	0.766594	−	0.642132i	$-0.221950\pi$
$37$	14.5329	+	10.5587i	0.392780	+	0.285371i	−0.373814	+	0.927504i	$0.621950\pi$
$38$	−2.60075	−	8.00429i	−0.0684408	−	0.210639i
$39$		0			0
$40$	−23.7001	+	32.6203i	−0.592502	+	0.815509i
$41$	9.51144	+	13.0914i	0.231986	+	0.319302i	0.909101	−	0.416576i	$-0.136770\pi$
$41$	9.51144	+	13.0914i	0.231986	+	0.319302i	−0.677115	+	0.735877i	$0.736770\pi$
$42$		0			0
$43$		−	44.2415i		−	1.02887i	−0.857529	−	0.514436i	$-0.828001\pi$
$43$		−	44.2415i		−	1.02887i	0.857529	−	0.514436i	$-0.171999\pi$
$44$	1.05159	+	39.2277i	0.0238998	+	0.891539i
$45$		0			0
$46$	−7.89971	−	2.56677i	−0.171733	−	0.0557994i
$47$	7.76454	−	5.64127i	0.165203	−	0.120027i	−0.502112	−	0.864803i	$-0.667443\pi$
$47$	7.76454	−	5.64127i	0.165203	−	0.120027i	0.667315	+	0.744776i	$0.267443\pi$
$48$		0			0
$49$	9.98240	+	30.7227i	0.203723	+	0.626994i
$50$	−25.4155	+	8.25799i	−0.508309	+	0.165160i
$51$		0			0
$52$	−31.0088	−	42.6800i	−0.596324	−	0.820769i
$53$	17.8438	−	54.9177i	0.336676	−	1.03618i	−0.629214	−	0.777232i	$-0.716623\pi$
$53$	17.8438	−	54.9177i	0.336676	−	1.03618i	0.965890	−	0.258951i	$-0.0833769\pi$
$54$		0			0
$55$	−50.4296	+	73.4732i	−0.916902	+	1.33588i
$56$	20.3368			0.363157
$57$		0			0
$58$	−7.11429	+	5.16883i	−0.122660	+	0.0891178i
$59$	−81.1105	−	58.9302i	−1.37475	−	0.998817i	−0.997349	−	0.0727685i	$-0.976817\pi$
$59$	−81.1105	−	58.9302i	−1.37475	−	0.998817i	−0.377405	−	0.926048i	$-0.623183\pi$
$60$		0			0
$61$	79.0445	−	25.6831i	1.29581	−	0.421035i	0.421690	−	0.906740i	$-0.361437\pi$
$61$	79.0445	−	25.6831i	1.29581	−	0.421035i	0.874123	+	0.485705i	$0.161437\pi$
$62$	13.7466	−	18.9205i	0.221719	−	0.305170i
$63$		0			0
$64$	8.07624	−	24.8561i	0.126191	−	0.388377i
$65$		−	119.803i		−	1.84312i
$66$		0			0
$67$	87.5688			1.30700			0.653499	−	0.756928i	$-0.273301\pi$
$67$	87.5688			1.30700			0.653499	+	0.756928i	$0.273301\pi$
$68$	−99.8895	−	32.4561i	−1.46896	−	0.477295i
$69$		0			0
$70$	17.6136	+	12.7971i	0.251624	+	0.182815i
$71$	21.1594	+	65.1219i	0.298019	+	0.917210i	0.982190	+	0.187888i	$0.0601642\pi$
$71$	21.1594	+	65.1219i	0.298019	+	0.917210i	−0.684171	+	0.729322i	$0.739836\pi$
$72$		0			0
$73$	−15.2790	+	21.0298i	−0.209302	+	0.288079i	−0.900742	−	0.434355i	$-0.856977\pi$
$73$	−15.2790	+	21.0298i	−0.209302	+	0.288079i	0.691440	+	0.722434i	$0.256977\pi$
$74$	6.94443	+	9.55819i	0.0938436	+	0.129165i
$75$		0			0
$76$			45.6508i			0.600668i
$77$	44.9310	−	1.20448i	0.583520	−	0.0156426i
$78$		0			0
$79$	−62.3915	−	20.2722i	−0.789766	−	0.256611i	−0.113762	−	0.993508i	$-0.536290\pi$
$79$	−62.3915	−	20.2722i	−0.789766	−	0.256611i	−0.676004	+	0.736898i	$0.736290\pi$
$80$	72.0716	−	52.3631i	0.900895	−	0.654538i
$81$		0			0
$82$	3.28878	+	10.1218i	0.0401070	+	0.123437i
$83$	−83.0198	+	26.9748i	−1.00024	+	0.324997i	−0.762961	−	0.646444i	$-0.776255\pi$
$83$	−83.0198	+	26.9748i	−1.00024	+	0.324997i	−0.237278	+	0.971442i	$0.576255\pi$
$84$		0			0
$85$	−140.195	−	192.962i	−1.64936	−	2.27014i
$86$	8.99160	−	27.6733i	0.104554	−	0.321783i
$87$		0			0
$88$	−15.5166	+	52.5028i	−0.176325	+	0.596623i
$89$	29.3444			0.329713			0.164856	−	0.986318i	$-0.447284\pi$
$89$	29.3444			0.329713			0.164856	+	0.986318i	$0.447284\pi$
$90$		0			0
$91$	−48.8852	+	35.5172i	−0.537200	+	0.390299i
$92$	36.4497	+	26.4823i	0.396193	+	0.287851i
$93$		0			0
$94$	6.00329	−	1.95059i	0.0638647	−	0.0207509i
$95$	−60.9352	+	83.8701i	−0.641423	+	0.882843i
$96$		0			0
$97$	−11.3670	+	34.9841i	−0.117186	+	0.360661i	−0.992397	−	0.123081i	$-0.960723\pi$
$97$	−11.3670	+	34.9841i	−0.117186	+	0.360661i	0.875211	+	0.483741i	$0.160723\pi$
$98$			21.2460i			0.216796i
$99$		0			0
$100$	144.952			1.44952
$101$	86.1862	+	28.0036i	0.853329	+	0.277263i	0.702840	−	0.711348i	$-0.251915\pi$
$101$	86.1862	+	28.0036i	0.853329	+	0.277263i	0.150489	+	0.988612i	$0.451915\pi$
$102$		0			0
$103$	124.184	+	90.2248i	1.20567	+	0.875969i	0.994830	−	0.101552i	$-0.0323809\pi$
$103$	124.184	+	90.2248i	1.20567	+	0.875969i	0.210838	+	0.977521i	$0.432381\pi$
$104$	−22.7440	−	69.9987i	−0.218692	−	0.673065i
$105$		0			0
$106$	22.3228	−	30.7247i	0.210593	−	0.289856i
$107$	39.6735	+	54.6059i	0.370780	+	0.510336i	0.953113	−	0.302615i	$-0.0978597\pi$
$107$	39.6735	+	54.6059i	0.370780	+	0.510336i	−0.582332	+	0.812951i	$0.697860\pi$
$108$		0			0
$109$		−	150.536i		−	1.38106i	−0.723304	−	0.690530i	$-0.757377\pi$
$109$		−	150.536i		−	1.38106i	0.723304	−	0.690530i	$-0.242623\pi$
$110$	−46.4766	+	35.7086i	−0.422515	+	0.324624i
$111$		0			0
$112$	−42.7331	−	13.8848i	−0.381546	−	0.123972i
$113$	−118.763	+	86.2867i	−1.05100	+	0.763599i	−0.972403	−	0.233307i	$-0.925045\pi$
$113$	−118.763	+	86.2867i	−1.05100	+	0.763599i	−0.0786011	+	0.996906i	$0.525045\pi$
$114$		0			0
$115$	31.6170	+	97.3070i	0.274930	+	0.846148i
$116$	45.3641	−	14.7397i	0.391070	−	0.127066i
$117$		0			0
$118$	−38.7581	−	53.3459i	−0.328458	−	0.452084i
$119$	−37.1748	+	114.412i	−0.312394	+	0.961449i
$120$		0			0
$121$	−31.1719	+	116.916i	−0.257619	+	0.966247i
$122$	54.6626			0.448054
$123$		0			0
$124$	−102.628	+	74.5634i	−0.827643	+	0.601318i
$125$	102.454	+	74.4369i	0.819629	+	0.595496i
$126$		0			0
$127$	61.3816	−	19.9441i	0.483320	−	0.157040i	−0.0572147	−	0.998362i	$-0.518222\pi$
$127$	61.3816	−	19.9441i	0.483320	−	0.157040i	0.540535	+	0.841322i	$0.318222\pi$
$128$	73.9146	−	101.735i	0.577458	−	0.794803i
$129$		0			0
$130$	24.3486	−	74.9374i	0.187297	−	0.576442i
$131$			222.809i			1.70083i	0.526110	+	0.850416i	$0.323650\pi$
$131$			222.809i			1.70083i	−0.526110	+	0.850416i	$0.676350\pi$
$132$		0			0
$133$	52.2879			0.393142
$134$	54.7747	+	17.7974i	0.408767	+	0.132816i
$135$		0			0
$136$	−118.546	−	86.1289i	−0.871664	−	0.633301i
$137$	15.7350	+	48.4274i	0.114854	+	0.353485i	0.991917	−	0.126892i	$-0.0405001\pi$
$137$	15.7350	+	48.4274i	0.114854	+	0.353485i	−0.877062	+	0.480376i	$0.840500\pi$
$138$		0			0
$139$	−78.0268	+	107.395i	−0.561344	+	0.772623i	−0.991497	−	0.130133i	$-0.958460\pi$
$139$	−78.0268	+	107.395i	−0.561344	+	0.772623i	0.430153	+	0.902756i	$0.358460\pi$
$140$	−69.4132	−	95.5391i	−0.495809	−	0.682422i
$141$		0			0
$142$			45.0345i			0.317144i
$143$	−54.3950	−	153.304i	−0.380385	−	1.07206i
$144$		0			0
$145$	103.018	+	33.4726i	0.710469	+	0.230845i
$146$	−13.8312	+	10.0489i	−0.0947341	+	0.0688283i
$147$		0			0
$148$	−19.8030	−	60.9475i	−0.133804	−	0.411808i
$149$	250.465	−	81.3809i	1.68097	−	0.546181i	0.695872	−	0.718166i	$-0.255018\pi$
$149$	250.465	−	81.3809i	1.68097	−	0.546181i	0.985100	+	0.171985i	$0.0550182\pi$
$150$		0			0
$151$	−29.6709	−	40.8385i	−0.196496	−	0.270453i	0.699387	−	0.714743i	$-0.253456\pi$
$151$	−29.6709	−	40.8385i	−0.196496	−	0.270453i	−0.895883	+	0.444289i	$0.853456\pi$
$152$	−19.6810	+	60.5720i	−0.129480	+	0.398500i
$153$		0			0
$154$	28.3494	+	8.37832i	0.184087	+	0.0544047i
$155$	−288.077			−1.85856
$156$		0			0
$157$	−24.3706	+	17.7063i	−0.155227	+	0.112779i	−0.662688	−	0.748896i	$-0.730584\pi$
$157$	−24.3706	+	17.7063i	−0.155227	+	0.112779i	0.507461	+	0.861675i	$0.330584\pi$
$158$	−34.9061	−	25.3608i	−0.220925	−	0.160511i
$159$		0			0
$160$	209.113	−	67.9451i	1.30696	−	0.424657i
$161$	30.3325	−	41.7491i	0.188401	−	0.259311i
$162$		0			0
$163$	31.7613	−	97.7512i	0.194855	−	0.599701i	−0.805124	−	0.593107i	$-0.797901\pi$
$163$	31.7613	−	97.7512i	0.194855	−	0.599701i	0.999978	−	0.00659367i	$-0.00209884\pi$
$164$		−	57.7276i		−	0.351998i
$165$		0			0
$166$	−57.4117			−0.345853
$167$	−126.936	−	41.2441i	−0.760098	−	0.246971i	−0.0967772	−	0.995306i	$-0.530853\pi$
$167$	−126.936	−	41.2441i	−0.760098	−	0.246971i	−0.663321	+	0.748335i	$0.730853\pi$
$168$		0			0
$169$	40.1968	+	29.2047i	0.237851	+	0.172809i
$170$	−48.4754	−	149.192i	−0.285150	−	0.877600i
$171$		0			0
$172$	−92.7695	+	127.686i	−0.539358	+	0.742362i
$173$	−144.968	−	199.531i	−0.837963	−	1.15336i	−0.986388	−	0.164433i	$-0.947421\pi$
$173$	−144.968	−	199.531i	−0.837963	−	1.15336i	0.148426	−	0.988924i	$-0.452579\pi$
$174$		0			0
$175$		−	166.026i		−	0.948722i
$176$	68.4505	−	99.7288i	0.388924	−	0.566641i
$177$		0			0
$178$	18.3551	+	5.96393i	0.103119	+	0.0335052i
$179$	53.5634	−	38.9161i	0.299237	−	0.217408i	−0.428028	−	0.903766i	$-0.640791\pi$
$179$	53.5634	−	38.9161i	0.299237	−	0.217408i	0.727264	+	0.686357i	$0.240791\pi$
$180$		0			0
$181$	48.9480	+	150.646i	0.270431	+	0.832301i	0.990392	+	0.138287i	$0.0441595\pi$
$181$	48.9480	+	150.646i	0.270431	+	0.832301i	−0.719961	+	0.694014i	$0.755840\pi$
$182$	−37.7964	+	12.2808i	−0.207673	+	0.0674770i
$183$		0			0
$184$	36.9464	+	50.8524i	0.200796	+	0.276372i
$185$	44.9711	−	138.407i	0.243087	−	0.748144i
$186$		0			0
$187$	−267.011	−	183.267i	−1.42786	−	0.980039i
$188$	−34.2385			−0.182120
$189$		0			0
$190$	−55.1609	+	40.0768i	−0.290321	+	0.210930i
$191$	120.402	+	87.4774i	0.630378	+	0.457997i	0.856531	−	0.516095i	$-0.172615\pi$
$191$	120.402	+	87.4774i	0.630378	+	0.457997i	−0.226153	+	0.974092i	$0.572615\pi$
$192$		0			0
$193$	−204.065	+	66.3048i	−1.05733	+	0.343548i	−0.785542	−	0.618809i	$-0.787616\pi$
$193$	−204.065	+	66.3048i	−1.05733	+	0.343548i	−0.271790	+	0.962357i	$0.587616\pi$
$194$	−14.2202	+	19.5725i	−0.0733003	+	0.100889i
$195$		0			0
$196$	35.6116	−	109.601i	0.181692	−	0.559190i
$197$		−	54.8802i		−	0.278580i	−0.990252	−	0.139290i	$-0.955518\pi$
$197$		−	54.8802i		−	0.278580i	0.990252	−	0.139290i	$-0.0444820\pi$
$198$		0			0
$199$	−58.1547			−0.292235			−0.146117	−	0.989267i	$-0.546678\pi$
$199$	−58.1547			−0.292235			−0.146117	+	0.989267i	$0.546678\pi$
$200$	192.330	+	62.4918i	0.961650	+	0.312459i
$201$		0			0
$202$	48.2185	+	35.0328i	0.238705	+	0.173430i
$203$	−16.8827	−	51.9595i	−0.0831659	−	0.255958i
$204$		0			0
$205$	77.0555	−	106.058i	0.375880	−	0.517355i
$206$	59.3404	+	81.6750i	0.288060	+	0.396481i
$207$		0			0
$208$			162.615i			0.781801i
$209$	−39.8947	+	134.990i	−0.190884	+	0.645885i
$210$		0			0
$211$	215.270	+	69.9454i	1.02024	+	0.331495i	0.770923	−	0.636928i	$-0.219795\pi$
$211$	215.270	+	69.9454i	1.02024	+	0.331495i	0.249313	+	0.968423i	$0.419795\pi$
$212$	−166.656	+	121.082i	−0.786112	+	0.571144i
$213$		0			0
$214$	13.7179	+	42.2195i	0.0641025	+	0.197287i
$215$	−340.874	+	110.757i	−1.58546	+	0.515148i
$216$		0			0
$217$	85.4042	+	117.549i	0.393568	+	0.541700i
$218$	30.5947	−	94.1607i	0.140343	−	0.431930i
$219$		0			0
$220$	299.611	−	106.307i	1.36187	−	0.483215i
$221$	435.379			1.97004
$222$		0			0
$223$	66.7089	−	48.4669i	0.299143	−	0.217340i	−0.428081	−	0.903740i	$-0.640810\pi$
$223$	66.7089	−	48.4669i	0.299143	−	0.217340i	0.727224	+	0.686400i	$0.240810\pi$
$224$	−89.7192	−	65.1848i	−0.400532	−	0.291004i
$225$		0			0
$226$	−91.8240	+	29.8354i	−0.406301	+	0.132015i
$227$	103.962	−	143.092i	0.457984	−	0.630361i	−0.516105	−	0.856525i	$-0.672619\pi$
$227$	103.962	−	143.092i	0.457984	−	0.630361i	0.974089	+	0.226164i	$0.0726186\pi$
$228$		0			0
$229$	−0.902758	+	2.77840i	−0.00394217	+	0.0121328i	−0.953008	−	0.302944i	$-0.902030\pi$
$229$	−0.902758	+	2.77840i	−0.00394217	+	0.0121328i	0.949066	+	0.315077i	$0.102030\pi$
$230$			67.2918i			0.292573i
$231$		0			0
$232$	66.5461			0.286837
$233$	−280.090	−	91.0066i	−1.20210	−	0.390586i	−0.361568	−	0.932346i	$-0.617758\pi$
$233$	−280.090	−	91.0066i	−1.20210	−	0.390586i	−0.840533	+	0.541760i	$0.817758\pi$
$234$		0			0
$235$	−62.9033	−	45.7019i	−0.267674	−	0.194476i
$236$	110.524	+	340.159i	0.468323	+	1.44135i
$237$		0			0
$238$	−46.5061	+	64.0102i	−0.195404	+	0.268950i
$239$	201.543	+	277.400i	0.843275	+	1.16067i	0.985305	+	0.170806i	$0.0546373\pi$
$239$	201.543	+	277.400i	0.843275	+	1.16067i	−0.142029	+	0.989862i	$0.545363\pi$
$240$		0			0
$241$			43.2741i			0.179561i	0.995962	+	0.0897804i	$0.0286165\pi$
$241$			43.2741i			0.179561i	−0.995962	+	0.0897804i	$0.971383\pi$
$242$	−43.2600	+	66.7961i	−0.178760	+	0.276017i
$243$		0			0
$244$	−281.986	−	91.6230i	−1.15568	−	0.375504i
$245$	211.723	−	153.826i	0.864175	−	0.627860i
$246$		0			0
$247$	−58.4770	−	179.974i	−0.236749	−	0.728638i
$248$	−168.318	+	54.6898i	−0.678702	+	0.220524i
$249$		0			0
$250$	48.9568	+	67.3833i	0.195827	+	0.269533i
$251$	−36.1563	+	111.278i	−0.144049	+	0.443337i	−0.996887	−	0.0788375i	$-0.974879\pi$
$251$	−36.1563	+	111.278i	−0.144049	+	0.443337i	0.852838	+	0.522175i	$0.174879\pi$
$252$		0			0
$253$	84.6391	+	110.162i	0.334542	+	0.435423i
$254$	42.4479			0.167118
$255$		0			0
$256$	−17.6650	+	12.8344i	−0.0690040	+	0.0501344i
$257$	−22.8578	−	16.6072i	−0.0889409	−	0.0646193i	0.542426	−	0.840104i	$-0.317506\pi$
$257$	−22.8578	−	16.6072i	−0.0889409	−	0.0646193i	−0.631367	+	0.775484i	$0.717506\pi$
$258$		0			0
$259$	−69.8087	+	22.6822i	−0.269531	+	0.0875761i
$260$	−251.214	+	345.766i	−0.966206	+	1.32987i
$261$		0			0
$262$	−45.2835	+	139.368i	−0.172838	+	0.531940i
$263$		−	247.683i		−	0.941759i	−0.882198	−	0.470879i	$-0.843937\pi$
$263$		−	247.683i		−	0.941759i	0.882198	−	0.470879i	$-0.156063\pi$
$264$		0			0
$265$	−467.804			−1.76530
$266$	32.7064	+	10.6269i	0.122956	+	0.0399509i
$267$		0			0
$268$	−252.734	−	183.622i	−0.943037	−	0.685156i
$269$	85.7617	+	263.947i	0.318817	+	0.981217i	0.974155	+	0.225882i	$0.0725262\pi$
$269$	85.7617	+	263.947i	0.318817	+	0.981217i	−0.655338	+	0.755336i	$0.727474\pi$
$270$		0			0
$271$	232.311	−	319.749i	0.857238	−	1.17989i	−0.124984	−	0.992159i	$-0.539888\pi$
$271$	232.311	−	319.749i	0.857238	−	1.17989i	0.982221	−	0.187727i	$-0.0601122\pi$
$272$	190.294	+	261.917i	0.699610	+	0.962930i
$273$		0			0
$274$			33.4896i			0.122225i
$275$	428.624	+	126.675i	1.55863	+	0.460636i
$276$		0			0
$277$	199.908	+	64.9542i	0.721691	+	0.234492i	0.646756	−	0.762697i	$-0.276125\pi$
$277$	199.908	+	64.9542i	0.721691	+	0.234492i	0.0749347	+	0.997188i	$0.476125\pi$
$278$	−70.6329	+	51.3178i	−0.254075	+	0.184596i
$279$		0			0
$280$	−50.9123	−	156.692i	−0.181830	−	0.559614i
$281$	−24.8709	+	8.08106i	−0.0885087	+	0.0287582i	−0.352937	−	0.935647i	$-0.614817\pi$
$281$	−24.8709	+	8.08106i	−0.0885087	+	0.0287582i	0.264428	+	0.964405i	$0.414817\pi$
$282$		0			0
$283$	173.462	+	238.750i	0.612941	+	0.843641i	0.996815	−	0.0797445i	$-0.0254105\pi$
$283$	173.462	+	238.750i	0.612941	+	0.843641i	−0.383874	+	0.923385i	$0.625410\pi$
$284$	75.4848	−	232.318i	0.265791	−	0.818022i
$285$		0			0
$286$	−2.86699	−	106.948i	−0.0100244	−	0.373943i
$287$	−66.1206			−0.230385
$288$		0			0
$289$	467.442	−	339.617i	1.61745	−	1.17514i
$290$	57.6354	+	41.8745i	0.198743	+	0.144395i
$291$		0			0
$292$	88.1941	−	28.6560i	0.302035	−	0.0981370i
$293$	36.5499	−	50.3066i	0.124744	−	0.171695i	−0.742078	−	0.670314i	$-0.766159\pi$
$293$	36.5499	−	50.3066i	0.124744	−	0.171695i	0.866821	+	0.498619i	$0.166159\pi$
$294$		0			0
$295$	−250.992	+	772.473i	−0.850819	+	2.61855i
$296$		−	89.4060i		−	0.302047i
$297$		0			0
$298$	173.207			0.581231
$299$	−177.622	−	57.7129i	−0.594054	−	0.193020i
$300$		0			0
$301$	146.251	+	106.257i	0.485882	+	0.353014i
$302$	−10.2593	−	31.5749i	−0.0339713	−	0.104553i
$303$		0			0
$304$	82.7103	−	113.841i	0.272073	−	0.374477i
$305$	−395.769	−	544.729i	−1.29760	−	1.78600i
$306$		0			0
$307$		−	119.712i		−	0.389941i	−0.980809	−	0.194970i	$-0.937539\pi$
$307$		−	119.712i		−	0.389941i	0.980809	−	0.194970i	$-0.0624610\pi$
$308$	−132.202	−	90.7390i	−0.429227	−	0.294607i
$309$		0			0
$310$	−180.194	−	58.5484i	−0.581270	−	0.188866i
$311$	253.352	−	184.071i	0.814638	−	0.591869i	−0.100534	−	0.994934i	$-0.532055\pi$
$311$	253.352	−	184.071i	0.814638	−	0.591869i	0.915172	+	0.403065i	$0.132055\pi$
$312$		0			0
$313$	−121.315	−	373.369i	−0.387588	−	1.19287i	−0.934586	−	0.355738i	$-0.884230\pi$
$313$	−121.315	−	373.369i	−0.387588	−	1.19287i	0.546998	−	0.837134i	$-0.315770\pi$
$314$	−18.8426	+	6.12232i	−0.0600082	+	0.0194978i
$315$		0			0
$316$	137.561	+	189.336i	0.435319	+	0.599165i
$317$	−10.9585	+	33.7267i	−0.0345693	+	0.106393i	−0.966852	−	0.255337i	$-0.917814\pi$
$317$	−10.9585	+	33.7267i	−0.0345693	+	0.106393i	0.932283	+	0.361730i	$0.117814\pi$
$318$		0			0
$319$	147.023	−	3.94131i	0.460888	−	0.0123552i
$320$	−211.731			−0.661659
$321$		0			0
$322$	27.4582	−	19.9495i	0.0852739	−	0.0619551i
$323$	−304.794	−	221.446i	−0.943635	−	0.685591i
$324$		0			0
$325$	−571.458	+	185.678i	−1.75833	+	0.571317i
$326$	39.7337	−	54.6887i	0.121882	−	0.167757i
$327$		0			0
$328$	24.8876	−	76.5962i	0.0758768	−	0.233525i
$329$			39.2164i			0.119199i
$330$		0			0
$331$	−437.250			−1.32100			−0.660498	−	0.750828i	$-0.729655\pi$
$331$	−437.250			−1.32100			−0.660498	+	0.750828i	$0.729655\pi$
$332$	296.168	+	96.2308i	0.892072	+	0.289852i
$333$		0			0
$334$	−71.0169	−	51.5968i	−0.212625	−	0.154481i
$335$	−219.225	−	674.704i	−0.654402	−	2.01404i
$336$		0			0
$337$	96.3092	−	132.558i	0.285784	−	0.393348i	−0.641855	−	0.766826i	$-0.721835\pi$
$337$	96.3092	−	132.558i	0.285784	−	0.393348i	0.927639	+	0.373478i	$0.121835\pi$
$338$	19.2078	+	26.4372i	0.0568277	+	0.0782166i
$339$		0			0
$340$			850.885i			2.50260i
$341$	−368.633	+	130.798i	−1.08104	+	0.383571i
$342$		0			0
$343$	−315.956	−	102.660i	−0.921154	−	0.299301i
$344$	−178.140	+	129.426i	−0.517849	+	0.376239i
$345$		0			0
$346$	−50.1255	−	154.271i	−0.144871	−	0.445868i
$347$	475.145	−	154.384i	1.36929	−	0.444910i	0.470158	−	0.882582i	$-0.344197\pi$
$347$	475.145	−	154.384i	1.36929	−	0.444910i	0.899135	+	0.437672i	$0.144197\pi$
$348$		0			0
$349$	172.838	+	237.892i	0.495239	+	0.681638i	0.981344	−	0.192263i	$-0.0615825\pi$
$349$	172.838	+	237.892i	0.495239	+	0.681638i	−0.486104	+	0.873901i	$0.661583\pi$
$350$	33.7430	−	103.850i	0.0964086	−	0.296715i
$351$		0			0
$352$	236.739	−	181.890i	0.672555	−	0.516733i
$353$	−36.8161			−0.104295			−0.0521474	−	0.998639i	$-0.516607\pi$
$353$	−36.8161			−0.104295			−0.0521474	+	0.998639i	$0.516607\pi$
$354$		0			0
$355$	448.782	−	326.059i	1.26418	−	0.918477i
$356$	−84.6915	−	61.5320i	−0.237897	−	0.172843i
$357$		0			0
$358$	41.4134	−	13.4560i	0.115680	−	0.0375867i
$359$	219.070	−	301.524i	0.610224	−	0.839901i	−0.386372	−	0.922343i	$-0.626272\pi$
$359$	219.070	−	301.524i	0.610224	−	0.839901i	0.996596	+	0.0824421i	$0.0262719\pi$
$360$		0			0
$361$	60.9533	−	187.595i	0.168846	−	0.519654i
$362$			104.178i			0.287785i
$363$		0			0
$364$	215.564			0.592209
$365$	200.281	+	65.0754i	0.548716	+	0.178289i
$366$		0			0
$367$	172.545	+	125.361i	0.470150	+	0.341584i	0.797500	−	0.603319i	$-0.206156\pi$
$367$	172.545	+	125.361i	0.470150	+	0.341584i	−0.327350	+	0.944903i	$0.606156\pi$
$368$	−42.9152	−	132.079i	−0.116617	−	0.358912i
$369$		0			0
$370$	56.2593	−	77.4342i	0.152052	−	0.209282i
$371$	138.687	+	190.886i	0.373818	+	0.514517i
$372$		0			0
$373$			32.7478i			0.0877957i	0.999036	+	0.0438978i	$0.0139776\pi$
$373$			32.7478i			0.0877957i	−0.999036	+	0.0438978i	$0.986022\pi$
$374$	−129.770	−	168.902i	−0.346977	−	0.451609i
$375$		0			0
$376$	−45.4295	−	14.7609i	−0.120823	−	0.0392578i
$377$	−159.962	+	116.219i	−0.424303	+	0.308274i
$378$		0			0
$379$	167.782	+	516.378i	0.442695	+	1.36248i	0.884992	+	0.465607i	$0.154164\pi$
$379$	167.782	+	516.378i	0.442695	+	1.36248i	−0.442296	+	0.896869i	$0.645836\pi$
$380$	351.732	−	114.285i	0.925611	−	0.300749i
$381$		0			0
$382$	57.5334	+	79.1880i	0.150611	+	0.207298i
$383$	−184.991	+	569.343i	−0.483005	+	1.48654i	0.351845	+	0.936058i	$0.385554\pi$
$383$	−184.991	+	569.343i	−0.483005	+	1.48654i	−0.834850	+	0.550477i	$0.814446\pi$
$384$		0			0
$385$	−121.763	−	343.171i	−0.316268	−	0.891354i
$386$	−141.119			−0.365594
$387$		0			0
$388$	106.164	−	77.1328i	0.273619	−	0.198796i
$389$	178.494	+	129.684i	0.458854	+	0.333377i	0.793082	−	0.609115i	$-0.208475\pi$
$389$	178.494	+	129.684i	0.458854	+	0.333377i	−0.334228	+	0.942492i	$0.608475\pi$
$390$		0			0
$391$	−353.625	+	114.900i	−0.904413	+	0.293862i
$392$	94.5028	−	130.072i	0.241079	−	0.331816i
$393$		0			0
$394$	11.1538	−	34.3278i	0.0283091	−	0.0871265i
$395$			531.468i			1.34549i
$396$		0			0
$397$	−734.263			−1.84953			−0.924764	−	0.380541i	$-0.875738\pi$
$397$	−734.263			−1.84953			−0.924764	+	0.380541i	$0.875738\pi$
$398$	−36.3760	−	11.8193i	−0.0913971	−	0.0296967i
$399$		0			0
$400$	−361.471	−	262.624i	−0.903678	−	0.656561i
$401$	28.1108	+	86.5163i	0.0701019	+	0.215751i	0.979970	−	0.199147i	$-0.0638171\pi$
$401$	28.1108	+	86.5163i	0.0701019	+	0.215751i	−0.909868	+	0.414898i	$0.863817\pi$
$402$		0			0
$403$	309.087	−	425.421i	0.766964	−	1.05564i
$404$	−190.023	−	261.544i	−0.470354	−	0.647387i
$405$		0			0
$406$		−	35.9322i		−	0.0885029i
$407$	−5.29522	−	197.529i	−0.0130104	−	0.485328i
$408$		0			0
$409$	165.356	+	53.7274i	0.404293	+	0.131363i	0.504103	−	0.863644i	$-0.331823\pi$
$409$	165.356	+	53.7274i	0.404293	+	0.131363i	−0.0998094	+	0.995007i	$0.531823\pi$
$410$	69.7537	−	50.6790i	0.170131	−	0.123607i
$411$		0			0
$412$	−169.218	−	520.799i	−0.410723	−	1.26407i
$413$	389.615	−	126.593i	0.943377	−	0.306522i
$414$		0			0
$415$	415.673	+	572.125i	1.00162	+	1.37861i
$416$	−124.025	+	381.711i	−0.298138	+	0.917575i
$417$		0			0
$418$	−52.3895	+	76.3287i	−0.125334	+	0.182605i
$419$	−374.418			−0.893599			−0.446800	−	0.894634i	$-0.647436\pi$
$419$	−374.418			−0.893599			−0.446800	+	0.894634i	$0.647436\pi$
$420$		0			0
$421$	0.0922850	−	0.0670490i	0.000219204	−	0.000159261i	−0.587676	−	0.809097i	$-0.699957\pi$
$421$	0.0922850	−	0.0670490i	0.000219204	−	0.000159261i	0.587895	+	0.808937i	$0.299957\pi$
$422$	120.437	+	87.5024i	0.285395	+	0.207352i
$423$		0			0
$424$	−273.329	+	88.8100i	−0.644644	+	0.209458i
$425$	−703.142	+	967.792i	−1.65445	+	2.27716i
$426$		0			0
$427$	−104.944	+	322.984i	−0.245770	+	0.756404i
$428$		−	240.790i		−	0.562593i
$429$		0			0
$430$	−235.729			−0.548206
$431$	252.091	+	81.9092i	0.584897	+	0.190045i	0.586493	−	0.809954i	$-0.300508\pi$
$431$	252.091	+	81.9092i	0.584897	+	0.190045i	−0.00159618	+	0.999999i	$0.500508\pi$
$432$		0			0
$433$	145.782	+	105.917i	0.336679	+	0.244612i	0.743259	−	0.669003i	$-0.233279\pi$
$433$	145.782	+	105.917i	0.336679	+	0.244612i	−0.406580	+	0.913615i	$0.633279\pi$
$434$	29.5303	+	90.8848i	0.0680421	+	0.209412i
$435$		0			0
$436$	−315.656	+	434.463i	−0.723982	+	0.996475i
$437$	94.9928	+	130.746i	0.217375	+	0.299191i
$438$		0			0
$439$		−	410.931i		−	0.936062i	−0.883712	−	0.468031i	$-0.844963\pi$
$439$		−	410.931i		−	0.936062i	0.883712	−	0.468031i	$-0.155037\pi$
$440$	443.371	−	11.8856i	1.00766	−	0.0270128i
$441$		0			0
$442$	272.332	+	88.4860i	0.616135	+	0.200195i
$443$	17.7973	−	12.9305i	0.0401744	−	0.0291884i	−0.567517	−	0.823362i	$-0.692096\pi$
$443$	17.7973	−	12.9305i	0.0401744	−	0.0291884i	0.607691	+	0.794173i	$0.292096\pi$
$444$		0			0
$445$	−73.4625	−	226.094i	−0.165084	−	0.508077i
$446$	51.5771	−	16.7584i	0.115644	−	0.0375749i
$447$		0			0
$448$	62.7704	+	86.3961i	0.140113	+	0.192848i
$449$	−44.5645	+	137.155i	−0.0992528	+	0.305469i	−0.988339	−	0.152272i	$-0.951341\pi$
$449$	−44.5645	+	137.155i	−0.0992528	+	0.305469i	0.889086	+	0.457740i	$0.151341\pi$
$450$		0			0
$451$	50.4487	−	170.701i	0.111860	−	0.378495i
$452$	523.699			1.15863
$453$		0			0
$454$	94.1109	−	68.3756i	0.207293	−	0.150607i
$455$	396.037	+	287.737i	0.870410	+	0.632390i
$456$		0			0
$457$	699.008	−	227.122i	1.52956	−	0.496984i	0.581086	−	0.813842i	$-0.302628\pi$
$457$	699.008	−	227.122i	1.52956	−	0.496984i	0.948473	+	0.316859i	$0.102628\pi$
$458$	−1.12936	+	1.55443i	−0.00246585	+	0.00339395i
$459$		0			0
$460$	112.792	−	347.137i	0.245199	−	0.754645i
$461$			128.454i			0.278643i	0.990247	+	0.139321i	$0.0444921\pi$
$461$			128.454i			0.278643i	−0.990247	+	0.139321i	$0.955508\pi$
$462$		0			0
$463$	7.10283			0.0153409			0.00767044	−	0.999971i	$-0.497558\pi$
$463$	7.10283			0.0153409			0.00767044	+	0.999971i	$0.497558\pi$
$464$	−139.831	−	45.4340i	−0.301361	−	0.0979180i
$465$		0			0
$466$	−156.701	−	113.850i	−0.336269	−	0.244314i
$467$	88.2695	+	271.666i	0.189014	+	0.581725i	0.999994	−	0.00334813i	$-0.00106574\pi$
$467$	88.2695	+	271.666i	0.189014	+	0.581725i	−0.810980	+	0.585073i	$0.801066\pi$
$468$		0			0
$469$	−210.319	+	289.479i	−0.448441	+	0.617225i
$470$	−30.0579	−	41.3712i	−0.0639530	−	0.0880238i
$471$		0			0
$472$			498.991i			1.05718i
$473$	−385.907	+	296.498i	−0.815871	+	0.626845i
$474$		0			0
$475$	494.499	+	160.673i	1.04105	+	0.338258i
$476$	347.201	−	252.256i	0.729413	−	0.529950i
$477$		0			0
$478$	69.6876	+	214.476i	0.145790	+	0.448695i
$479$	−373.411	+	121.329i	−0.779564	+	0.253296i	−0.671654	−	0.740865i	$-0.734416\pi$
$479$	−373.411	+	121.329i	−0.779564	+	0.253296i	−0.107910	+	0.994161i	$0.534416\pi$
$480$		0			0
$481$	156.143	+	214.912i	0.324622	+	0.446803i
$482$	−8.79499	+	27.0682i	−0.0182469	+	0.0561581i
$483$		0			0
$484$	335.125	−	272.069i	0.692407	−	0.562126i
$485$	298.004			0.614440
$486$		0			0
$487$	−417.281	+	303.173i	−0.856841	+	0.622531i	−0.927024	−	0.375003i	$-0.877642\pi$
$487$	−417.281	+	303.173i	−0.856841	+	0.622531i	0.0701830	+	0.997534i	$0.477642\pi$
$488$	−334.654	−	243.141i	−0.685767	−	0.498239i
$489$		0			0
$490$	163.697	−	53.1884i	0.334076	−	0.108548i
$491$	181.495	−	249.807i	0.369644	−	0.508771i	−0.583160	−	0.812357i	$-0.698184\pi$
$491$	181.495	−	249.807i	0.369644	−	0.508771i	0.952804	+	0.303586i	$0.0981840\pi$
$492$		0			0
$493$	−121.643	+	374.380i	−0.246741	+	0.759392i
$494$		−	124.459i		−	0.251942i
$495$		0			0
$496$	391.021			0.788348
$497$	−266.095	−	86.4595i	−0.535402	−	0.173963i
$498$		0			0
$499$	−469.197	−	340.892i	−0.940275	−	0.683149i	0.00821221	−	0.999966i	$-0.497386\pi$
$499$	−469.197	−	340.892i	−0.940275	−	0.683149i	−0.948487	+	0.316817i	$0.897386\pi$
$500$	−139.607	−	429.668i	−0.279215	−	0.859335i
$501$		0			0
$502$	−45.2319	+	62.2564i	−0.0901034	+	0.124017i
$503$	458.978	+	631.728i	0.912480	+	1.25592i	0.966313	+	0.257371i	$0.0828564\pi$
$503$	458.978	+	631.728i	0.912480	+	1.25592i	−0.0538322	+	0.998550i	$0.517144\pi$
$504$		0			0
$505$		−	734.157i		−	1.45378i
$506$	30.5530	+	86.1089i	0.0603814	+	0.170176i
$507$		0			0
$508$	−218.975	−	71.1493i	−0.431053	−	0.140058i
$509$	−547.788	+	397.992i	−1.07621	+	0.781909i	−0.977017	−	0.213160i	$-0.931624\pi$
$509$	−547.788	+	397.992i	−1.07621	+	0.781909i	−0.0991877	+	0.995069i	$0.531624\pi$
$510$		0			0
$511$	−32.8223	−	101.017i	−0.0642315	−	0.197684i
$512$	−492.044	+	159.875i	−0.961023	+	0.312255i
$513$		0			0
$514$	−10.9225	−	15.0335i	−0.0212499	−	0.0292480i
$515$	384.279	−	1182.69i	0.746174	−	2.29649i
$516$		0			0
$517$	−101.244	−	29.9213i	−0.195829	−	0.0578750i
$518$	−48.2756			−0.0931961
$519$		0			0
$520$	−482.391	+	350.477i	−0.927675	+	0.673995i
$521$	−538.428	−	391.191i	−1.03345	−	0.750846i	−0.0644546	−	0.997921i	$-0.520531\pi$
$521$	−538.428	−	391.191i	−1.03345	−	0.750846i	−0.968997	+	0.247074i	$0.920531\pi$
$522$		0			0
$523$	−856.820	+	278.398i	−1.63828	+	0.532309i	−0.976153	−	0.217083i	$-0.930346\pi$
$523$	−856.820	+	278.398i	−1.63828	+	0.532309i	−0.662127	+	0.749392i	$0.730346\pi$
$524$	467.205	−	643.053i	0.891613	−	1.22720i
$525$		0			0
$526$	50.3387	−	154.927i	0.0957010	−	0.294537i
$527$		−	1046.91i		−	1.98654i
$528$		0			0
$529$	−369.500			−0.698488
$530$	−292.614	−	95.0759i	−0.552101	−	0.179389i
$531$		0			0
$532$	−150.909	−	109.642i	−0.283664	−	0.206094i
$533$	73.9469	+	227.585i	0.138737	+	0.426989i
$534$		0			0
$535$	321.409	−	442.382i	0.600765	−	0.826882i
$536$	−256.178	−	352.598i	−0.477944	−	0.657833i
$537$		0			0
$538$			182.531i			0.339276i
$539$	201.086	−	292.971i	0.373072	−	0.543545i
$540$		0			0
$541$	370.362	+	120.338i	0.684587	+	0.222436i	0.630603	−	0.776106i	$-0.282808\pi$
$541$	370.362	+	120.338i	0.684587	+	0.222436i	0.0539846	+	0.998542i	$0.482808\pi$
$542$	210.297	−	152.790i	0.388003	−	0.281900i
$543$		0			0
$544$	246.921	+	759.944i	0.453898	+	1.39696i
$545$	−1159.85	+	376.859i	−2.12817	+	0.691485i
$546$		0			0
$547$	−414.894	−	571.053i	−0.758490	−	1.04397i	−0.997338	−	0.0729151i	$-0.976770\pi$
$547$	−414.894	−	571.053i	−0.758490	−	1.04397i	0.238848	−	0.971057i	$-0.423230\pi$
$548$	56.1337	−	172.762i	0.102434	−	0.315259i
$549$		0			0
$550$	242.361	+	166.349i	0.440657	+	0.302453i
$551$	171.097			0.310520
$552$		0			0
$553$	216.863	−	157.561i	0.392158	−	0.284920i
$554$	111.842	+	81.2583i	0.201882	+	0.146676i
$555$		0			0
$556$	450.389	−	146.340i	0.810052	−	0.263202i
$557$	97.3073	−	133.932i	0.174699	−	0.240452i	−0.712684	−	0.701485i	$-0.752521\pi$
$557$	97.3073	−	133.932i	0.174699	−	0.240452i	0.887383	+	0.461032i	$0.152521\pi$
$558$		0			0
$559$	202.173	−	622.224i	0.361669	−	1.11310i
$560$			364.012i			0.650022i
$561$		0			0
$562$	−17.1993			−0.0306037
$563$	345.683	+	112.319i	0.614002	+	0.199501i	0.599475	−	0.800393i	$-0.295376\pi$
$563$	345.683	+	112.319i	0.614002	+	0.199501i	0.0145265	+	0.999894i	$0.495376\pi$
$564$		0			0
$565$	962.145	+	699.039i	1.70291	+	1.23724i
$566$	59.9782	+	184.594i	0.105968	+	0.326138i
$567$		0			0
$568$	200.315	−	275.709i	0.352667	−	0.485404i
$569$	−136.330	−	187.642i	−0.239596	−	0.329775i	0.672238	−	0.740335i	$-0.265333\pi$
$569$	−136.330	−	187.642i	−0.239596	−	0.329775i	−0.911834	+	0.410560i	$0.865333\pi$
$570$		0			0
$571$		−	306.665i		−	0.537067i	−0.963270	−	0.268533i	$-0.913461\pi$
$571$		−	306.665i		−	0.537067i	0.963270	−	0.268533i	$-0.0865390\pi$
$572$	−164.471	+	556.514i	−0.287537	+	0.972927i
$573$		0			0
$574$	−41.3588	−	13.4383i	−0.0720536	−	0.0234116i
$575$	415.150	−	301.624i	0.722000	−	0.524564i
$576$		0			0
$577$	26.3161	+	80.9927i	0.0456085	+	0.140369i	0.971268	−	0.237990i	$-0.0764886\pi$
$577$	26.3161	+	80.9927i	0.0456085	+	0.140369i	−0.925659	+	0.378359i	$0.876489\pi$
$578$	361.411	−	117.430i	0.625279	−	0.203165i
$579$		0			0
$580$	−227.134	−	312.623i	−0.391610	−	0.539005i
$581$	110.222	−	339.228i	0.189711	−	0.583869i
$582$		0			0
$583$	−598.618	+	212.400i	−1.02679	+	0.364323i
$584$	129.375			0.221532
$585$		0			0
$586$	33.0864	−	24.0387i	0.0564614	−	0.0410216i
$587$	−497.688	−	361.591i	−0.847849	−	0.615999i	0.0767029	−	0.997054i	$-0.475561\pi$
$587$	−497.688	−	361.591i	−0.847849	−	0.615999i	−0.924552	+	0.381055i	$0.875561\pi$
$588$		0			0
$589$	−432.762	+	140.613i	−0.734740	+	0.238732i
$590$	−313.993	+	432.174i	−0.532192	+	0.732499i
$591$		0			0
$592$	−61.0414	+	187.866i	−0.103110	+	0.317341i
$593$		−	74.4809i		−	0.125600i	−0.998026	−	0.0628001i	$-0.979997\pi$
$593$		−	74.4809i		−	0.125600i	0.998026	−	0.0628001i	$-0.0200030\pi$
$594$		0			0
$595$	974.595			1.63798
$596$	−893.517	−	290.321i	−1.49919	−	0.487116i
$597$		0			0
$598$	−99.3740	−	72.1994i	−0.166177	−	0.120735i
$599$	229.210	+	705.436i	0.382654	+	1.17769i	0.938168	+	0.346181i	$0.112522\pi$
$599$	229.210	+	705.436i	0.382654	+	1.17769i	−0.555513	+	0.831508i	$0.687478\pi$
$600$		0			0
$601$	−659.404	+	907.591i	−1.09718	+	1.51014i	−0.258104	+	0.966117i	$0.583098\pi$
$601$	−659.404	+	907.591i	−1.09718	+	1.51014i	−0.839073	+	0.544018i	$0.816902\pi$
$602$	69.8848	+	96.1882i	0.116088	+	0.159781i
$603$		0			0
$604$			180.081i			0.298147i
$605$	978.856	−	52.5188i	1.61794	−	0.0868080i
$606$		0			0
$607$	10.5343	+	3.42282i	0.0173548	+	0.00563891i	0.317682	−	0.948197i	$-0.397096\pi$
$607$	10.5343	+	3.42282i	0.0173548	+	0.00563891i	−0.300327	+	0.953836i	$0.597096\pi$
$608$	280.975	−	204.140i	0.462130	−	0.335757i
$609$		0			0
$610$	−136.845	−	421.167i	−0.224337	−	0.690437i
$611$	134.982	−	43.8582i	0.220919	−	0.0717811i
$612$		0			0
$613$	−439.604	−	605.064i	−0.717136	−	0.987053i	−0.999614	−	0.0277794i	$-0.991156\pi$
$613$	−439.604	−	605.064i	−0.717136	−	0.987053i	0.282478	−	0.959274i	$-0.408844\pi$
$614$	24.3301	−	74.8803i	0.0396255	−	0.121955i
$615$		0			0
$616$	−136.293	−	177.392i	−0.221255	−	0.287975i
$617$	−771.423			−1.25028			−0.625140	−	0.780513i	$-0.714958\pi$
$617$	−771.423			−1.25028			−0.625140	+	0.780513i	$0.714958\pi$
$618$		0			0
$619$	−141.847	+	103.058i	−0.229156	+	0.166491i	−0.696438	−	0.717617i	$-0.745233\pi$
$619$	−141.847	+	103.058i	−0.229156	+	0.166491i	0.467283	+	0.884108i	$0.345233\pi$
$620$	831.424	+	604.065i	1.34101	+	0.974298i
$621$		0			0
$622$	195.884	−	63.6465i	0.314925	−	0.102325i
$623$	−70.4781	+	97.0048i	−0.113127	+	0.155706i
$624$		0			0
$625$	3.13803	−	9.65786i	0.00502085	−	0.0154526i
$626$		−	258.200i		−	0.412460i
$627$		0			0
$628$	107.465			0.171122
$629$	502.987	+	163.430i	0.799661	+	0.259826i
$630$		0			0
$631$	−214.772	−	156.041i	−0.340367	−	0.247291i	0.404450	−	0.914560i	$-0.367463\pi$
$631$	−214.772	−	156.041i	−0.340367	−	0.247291i	−0.744817	+	0.667269i	$0.767463\pi$
$632$	100.896	+	310.527i	0.159646	+	0.491340i
$633$		0			0
$634$	−13.7092	+	18.8690i	−0.0216233	+	0.0297619i
$635$	−307.332	−	423.007i	−0.483988	−	0.666152i
$636$		0			0
$637$			477.709i			0.749935i
$638$	92.7648	+	27.4155i	0.145399	+	0.0429711i
$639$		0			0
$640$	−968.892	−	314.812i	−1.51389	−	0.491894i
$641$	−925.226	+	672.216i	−1.44341	+	1.04870i	−0.456095	+	0.889931i	$0.650752\pi$
$641$	−925.226	+	672.216i	−1.44341	+	1.04870i	−0.987316	+	0.158768i	$0.949248\pi$
$642$		0			0
$643$	174.074	+	535.744i	0.270721	+	0.833195i	0.990320	+	0.138804i	$0.0443259\pi$
$643$	174.074	+	535.744i	0.270721	+	0.833195i	−0.719599	+	0.694390i	$0.755674\pi$
$644$	−175.086	+	56.8890i	−0.271873	+	0.0883370i
$645$		0			0
$646$	−145.644	−	200.462i	−0.225455	−	0.310312i
$647$	−17.5246	+	53.9352i	−0.0270859	+	0.0833620i	−0.963686	−	0.267039i	$-0.913955\pi$
$647$	−17.5246	+	53.9352i	−0.0270859	+	0.0833620i	0.936600	+	0.350401i	$0.113955\pi$
$648$		0			0
$649$	29.5536	+	1102.44i	0.0455371	+	1.69868i
$650$	−395.187			−0.607980
$651$		0			0
$652$	−296.640	+	215.522i	−0.454969	+	0.330555i
$653$	616.756	+	448.100i	0.944496	+	0.686217i	0.949499	−	0.313771i	$-0.101592\pi$
$653$	616.756	+	448.100i	0.944496	+	0.686217i	−0.00500247	+	0.999987i	$0.501592\pi$
$654$		0			0
$655$	1716.71	−	557.793i	2.62093	−	0.851592i
$656$	−104.591	+	143.957i	−0.159438	+	0.219447i
$657$		0			0
$658$	−7.97030	+	24.5301i	−0.0121129	+	0.0372797i
$659$			1137.55i			1.72617i	0.505056	+	0.863086i	$0.331472\pi$
$659$			1137.55i			1.72617i	−0.505056	+	0.863086i	$0.668528\pi$
$660$		0			0
$661$	814.127			1.23166			0.615829	−	0.787879i	$-0.288821\pi$
$661$	814.127			1.23166			0.615829	+	0.787879i	$0.288821\pi$
$662$	−273.502	−	88.8661i	−0.413145	−	0.134239i
$663$		0			0
$664$	351.485	+	255.369i	0.529345	+	0.384591i
$665$	−130.901	−	402.870i	−0.196843	−	0.605820i
$666$		0			0
$667$	99.2540	−	136.611i	0.148807	−	0.204815i
$668$	279.869	+	385.207i	0.418965	+	0.576656i
$669$		0			0
$670$		−	466.586i		−	0.696397i
$671$	−753.767	−	517.361i	−1.12335	−	0.771030i
$672$		0			0
$673$	−301.768	−	98.0504i	−0.448393	−	0.145692i	0.0761119	−	0.997099i	$-0.475749\pi$
$673$	−301.768	−	98.0504i	−0.448393	−	0.145692i	−0.524504	+	0.851408i	$0.675749\pi$
$674$	87.1829	−	63.3421i	0.129352	−	0.0939794i
$675$		0			0
$676$	−54.7737	−	168.576i	−0.0810262	−	0.249373i
$677$	467.770	−	151.988i	0.690946	−	0.224502i	0.0575647	−	0.998342i	$-0.481666\pi$
$677$	467.770	−	151.988i	0.690946	−	0.224502i	0.633381	+	0.773840i	$0.281666\pi$
$678$		0			0
$679$	−88.3471	−	121.599i	−0.130114	−	0.179086i
$680$	−366.835	+	1129.00i	−0.539463	+	1.66030i
$681$		0			0
$682$	−257.165	+	6.89392i	−0.377075	+	0.0101084i
$683$	1267.89			1.85635			0.928176	−	0.372142i	$-0.121376\pi$
$683$	1267.89			1.85635			0.928176	+	0.372142i	$0.121376\pi$
$684$		0			0
$685$	333.734	−	242.472i	0.487203	−	0.353973i
$686$	−176.767	−	128.429i	−0.257678	−	0.187214i
$687$		0			0
$688$	462.685	−	150.335i	0.672507	−	0.218511i
$689$	501.921	−	690.835i	0.728477	−	1.00266i
$690$		0			0
$691$	−71.8167	+	221.029i	−0.103932	+	0.319868i	−0.989478	−	0.144682i	$-0.953784\pi$
$691$	−71.8167	+	221.029i	−0.103932	+	0.319868i	0.885547	+	0.464550i	$0.153784\pi$
$692$			879.850i			1.27146i
$693$		0			0
$694$	328.582			0.473461
$695$	1022.80	+	332.326i	1.47165	+	0.478167i
$696$		0			0
$697$	385.427	+	280.029i	0.552980	+	0.401763i
$698$	59.7625	+	183.930i	0.0856196	+	0.263510i
$699$		0			0
$700$	−348.138	+	479.171i	−0.497341	+	0.684531i
$701$	260.786	+	358.941i	0.372020	+	0.512041i	0.953448	−	0.301556i	$-0.0975061\pi$
$701$	260.786	+	358.941i	0.372020	+	0.512041i	−0.581429	+	0.813597i	$0.697506\pi$
$702$		0			0
$703$		−	229.872i		−	0.326987i
$704$	−270.938	+	96.1337i	−0.384856	+	0.136554i
$705$		0			0
$706$	−23.0286	−	7.48246i	−0.0326185	−	0.0105984i
$707$	−299.570	+	217.650i	−0.423720	+	0.307851i
$708$		0			0
$709$	−126.852	−	390.411i	−0.178917	−	0.550650i	0.820874	−	0.571110i	$-0.193487\pi$
$709$	−126.852	−	390.411i	−0.178917	−	0.550650i	−0.999791	+	0.0204599i	$0.993487\pi$
$710$	346.984	−	112.742i	0.488709	−	0.158791i
$711$		0			0
$712$	−85.8456	−	118.156i	−0.120570	−	0.165950i
$713$	−138.776	+	427.108i	−0.194636	+	0.599029i
$714$		0			0
$715$	−1045.01	+	802.896i	−1.46155	+	1.12293i
$716$	−236.193			−0.329878
$717$		0			0
$718$	198.311	−	144.081i	0.276199	−	0.200671i
$719$	187.845	+	136.477i	0.261259	+	0.189815i	0.710702	−	0.703493i	$-0.248378\pi$
$719$	187.845	+	136.477i	0.261259	+	0.189815i	−0.449443	+	0.893309i	$0.648378\pi$
$720$		0			0
$721$	−596.517	+	193.820i	−0.827347	+	0.268821i
$722$	76.2532	−	104.954i	0.105614	−	0.145365i
$723$		0			0
$724$	174.619	−	537.422i	0.241186	−	0.742295i
$725$		−	543.271i		−	0.749339i
$726$		0			0
$727$	−523.474			−0.720047			−0.360024	−	0.932943i	$-0.617231\pi$
$727$	−523.474			−0.720047			−0.360024	+	0.932943i	$0.617231\pi$
$728$	286.022	+	92.9342i	0.392888	+	0.127657i
$729$		0			0
$730$	112.051	+	81.4100i	0.153495	+	0.111521i
$731$	−402.504	−	1238.78i	−0.550620	−	1.69464i
$732$		0			0
$733$	186.056	−	256.084i	0.253828	−	0.349365i	−0.663019	−	0.748602i	$-0.730725\pi$
$733$	186.056	−	256.084i	0.253828	−	0.349365i	0.916847	+	0.399238i	$0.130725\pi$
$734$	82.4495	+	113.482i	0.112329	+	0.154608i
$735$		0			0
$736$		−	342.766i		−	0.465715i
$737$	−586.868	−	763.839i	−0.796293	−	1.03642i
$738$		0			0
$739$	−671.840	−	218.294i	−0.909120	−	0.295391i	−0.183124	−	0.983090i	$-0.558621\pi$
$739$	−671.840	−	218.294i	−0.909120	−	0.295391i	−0.725996	+	0.687699i	$0.758621\pi$
$740$	−420.015	+	305.159i	−0.567588	+	0.412377i
$741$		0			0
$742$	47.9538	+	147.586i	0.0646277	+	0.198904i
$743$	306.573	−	99.6115i	0.412615	−	0.134067i	−0.0953515	−	0.995444i	$-0.530398\pi$
$743$	306.573	−	99.6115i	0.412615	−	0.134067i	0.507966	+	0.861377i	$0.330398\pi$
$744$		0			0
$745$	−1254.05	−	1726.06i	−1.68329	−	2.31686i
$746$	−6.65563	+	20.4839i	−0.00892175	+	0.0274583i
$747$		0			0
$748$	386.333	+	1088.82i	0.516489	+	1.45565i
$749$	−275.798			−0.368222
$750$		0			0
$751$	−1067.26	+	775.408i	−1.42112	+	1.03250i	−0.429530	+	0.903053i	$0.641321\pi$
$751$	−1067.26	+	775.408i	−1.42112	+	1.03250i	−0.991586	+	0.129448i	$0.958679\pi$
$752$	85.3817	+	62.0334i	0.113539	+	0.0824913i
$753$		0			0
$754$	−123.677	+	40.1852i	−0.164028	+	0.0532961i
$755$	−240.374	+	330.847i	−0.318376	+	0.438208i
$756$		0			0
$757$	281.697	−	866.976i	0.372123	−	1.14528i	−0.573275	−	0.819363i	$-0.694328\pi$
$757$	281.697	−	866.976i	0.372123	−	1.14528i	0.945399	−	0.325915i	$-0.105672\pi$
$758$			357.097i			0.471104i
$759$		0			0
$760$	515.968			0.678905
$761$	−166.965	−	54.2501i	−0.219402	−	0.0712879i	0.197254	−	0.980352i	$-0.436798\pi$
$761$	−166.965	−	54.2501i	−0.219402	−	0.0712879i	−0.416655	+	0.909065i	$0.636798\pi$
$762$		0			0
$763$	497.630	+	361.549i	0.652201	+	0.473852i
$764$	−164.065	−	504.940i	−0.214745	−	0.660916i
$765$		0			0
$766$	−231.425	+	318.530i	−0.302122	+	0.415835i
$767$	−871.462	−	1199.46i	−1.13620	−	1.56384i
$768$		0			0
$769$		−	692.657i		−	0.900725i	−0.892846	−	0.450362i	$-0.851295\pi$
$769$		−	692.657i		−	0.900725i	0.892846	−	0.450362i	$-0.148705\pi$
$770$	−6.41775	−	239.402i	−0.00833473	−	0.310912i
$771$		0			0
$772$	727.989	+	236.538i	0.942991	+	0.306396i
$773$	339.099	−	246.370i	0.438679	−	0.318719i	−0.346431	−	0.938076i	$-0.612606\pi$
$773$	339.099	−	246.370i	0.438679	−	0.318719i	0.785110	+	0.619357i	$0.212606\pi$
$774$		0			0
$775$	446.479	+	1374.12i	0.576101	+	1.77306i
$776$	174.118	−	56.5744i	0.224379	−	0.0729051i
$777$		0			0
$778$	85.2923	+	117.395i	0.109630	+	0.150893i
$779$	63.9885	−	196.936i	0.0821418	−	0.252806i
$780$		0			0
$781$	426.235	−	621.001i	0.545755	−	0.795136i
$782$	−244.547			−0.312720
$783$		0			0
$784$	−287.382	+	208.795i	−0.366558	+	0.266320i
$785$	197.435	+	143.445i	0.251510	+	0.182732i
$786$		0			0
$787$	936.899	−	304.417i	1.19047	−	0.386807i	0.354222	−	0.935161i	$-0.384746\pi$
$787$	936.899	−	304.417i	1.19047	−	0.386807i	0.836246	+	0.548355i	$0.184746\pi$
$788$	−115.078	+	158.391i	−0.146038	+	0.201003i
$789$		0			0
$790$	−108.015	+	332.436i	−0.136728	+	0.420805i
$791$		−	599.839i		−	0.758330i
$792$		0			0
$793$	1229.07			1.54990
$794$	−459.285	−	149.231i	−0.578445	−	0.187948i
$795$		0			0
$796$	167.841	+	121.944i	0.210856	+	0.153196i
$797$	−231.830	−	713.499i	−0.290878	−	0.895230i	−0.984575	−	0.174963i	$-0.944019\pi$
$797$	−231.830	−	713.499i	−0.290878	−	0.895230i	0.693697	−	0.720267i	$-0.255981\pi$
$798$		0			0
$799$	166.086	−	228.598i	0.207868	−	0.286105i
$800$	−648.193	−	892.161i	−0.810241	−	1.11520i
$801$		0			0
$802$			59.8296i			0.0746005i
$803$	285.834	−	7.66245i	0.355957	−	0.00954228i
$804$		0			0
$805$	−397.607	−	129.190i	−0.493921	−	0.160485i
$806$	279.797	−	203.285i	0.347143	−	0.252214i
$807$		0			0
$808$	−139.376	−	428.954i	−0.172495	−	0.530884i
$809$	694.235	−	225.571i	0.858140	−	0.278827i	0.153288	−	0.988181i	$-0.451014\pi$
$809$	694.235	−	225.571i	0.858140	−	0.278827i	0.704851	+	0.709355i	$0.251014\pi$
$810$		0			0
$811$	−14.0885	−	19.3911i	−0.0173717	−	0.0239101i	0.800243	−	0.599676i	$-0.204704\pi$
$811$	−14.0885	−	19.3911i	−0.0173717	−	0.0239101i	−0.817615	+	0.575766i	$0.804704\pi$
$812$	−60.2279	+	185.362i	−0.0741723	+	0.228279i
$813$		0			0
$814$	36.8333	−	124.631i	0.0452498	−	0.153110i
$815$	−832.671			−1.02168
$816$		0			0
$817$	−458.015	+	332.767i	−0.560606	+	0.407304i
$818$	92.5115	+	67.2135i	0.113095	+	0.0821681i
$819$		0			0
$820$	−444.782	+	144.519i	−0.542418	+	0.176242i
$821$	1.54301	−	2.12377i	0.00187943	−	0.00258681i	−0.808076	−	0.589078i	$-0.799491\pi$
$821$	1.54301	−	2.12377i	0.00187943	−	0.00258681i	0.809956	+	0.586491i	$0.199491\pi$
$822$		0			0
$823$	10.4352	−	32.1162i	0.0126795	−	0.0390233i	−0.944517	−	0.328464i	$-0.893469\pi$
$823$	10.4352	−	32.1162i	0.0126795	−	0.0390233i	0.957196	+	0.289440i	$0.0934692\pi$
$824$		−	763.978i		−	0.927157i
$825$		0			0
$826$	269.435			0.326192
$827$	−1132.85	−	368.086i	−1.36984	−	0.445086i	−0.470521	−	0.882389i	$-0.655934\pi$
$827$	−1132.85	−	368.086i	−1.36984	−	0.445086i	−0.899314	+	0.437303i	$0.855934\pi$
$828$		0			0
$829$	−380.631	−	276.544i	−0.459144	−	0.333588i	0.334051	−	0.942555i	$-0.391584\pi$
$829$	−380.631	−	276.544i	−0.459144	−	0.333588i	−0.793195	+	0.608967i	$0.791584\pi$
$830$	143.728	+	442.348i	0.173166	+	0.532949i
$831$		0			0
$832$	227.173	−	312.676i	0.273044	−	0.375813i
$833$	559.022	+	769.427i	0.671094	+	0.923682i
$834$		0			0
$835$			1081.28i			1.29494i
$836$	398.199	−	305.942i	0.476315	−	0.365960i
$837$		0			0
$838$	−234.200	−	76.0963i	−0.279475	−	0.0908071i
$839$	439.290	−	319.163i	0.523588	−	0.380409i	−0.294366	−	0.955693i	$-0.595108\pi$
$839$	439.290	−	319.163i	0.523588	−	0.380409i	0.817954	+	0.575284i	$0.195108\pi$
$840$		0			0
$841$	204.640	+	629.817i	0.243329	+	0.748890i
$842$	0.0713517	−	0.0231836i	8.47408e−5	−	2.75339e-5i
$843$		0			0
$844$	−474.626	−	653.267i	−0.562353	−	0.774013i
$845$	124.387	−	382.823i	0.147203	−	0.453044i
$846$		0			0
$847$	−311.625	−	383.849i	−0.367916	−	0.453186i
$848$	634.973			0.748789
$849$		0			0
$850$	−636.512	+	462.453i	−0.748838	+	0.544062i
$851$	−183.540	−	133.350i	−0.215676	−	0.156698i
$852$		0			0
$853$	411.114	−	133.579i	0.481962	−	0.156599i	−0.0579514	−	0.998319i	$-0.518457\pi$
$853$	411.114	−	133.579i	0.481962	−	0.156599i	0.539914	+	0.841720i	$0.318457\pi$
$854$	−131.286	+	180.700i	−0.153731	+	0.211592i
$855$		0			0
$856$	103.810	−	319.493i	0.121273	−	0.373240i
$857$			267.129i			0.311703i	0.987781	+	0.155851i	$0.0498121\pi$
$857$			267.129i			0.311703i	−0.987781	+	0.155851i	$0.950188\pi$
$858$		0			0
$859$	537.909			0.626203			0.313102	−	0.949720i	$-0.398632\pi$
$859$	537.909			0.626203			0.313102	+	0.949720i	$0.398632\pi$
$860$	1216.05	+	395.118i	1.41401	+	0.459439i
$861$		0			0
$862$	141.037	+	102.469i	0.163616	+	0.118874i
$863$	351.588	+	1082.08i	0.407402	+	1.25386i	0.918872	+	0.394555i	$0.129101\pi$
$863$	351.588	+	1082.08i	0.407402	+	1.25386i	−0.511470	+	0.859301i	$0.670899\pi$
$864$		0			0
$865$	−1174.43	+	1616.47i	−1.35773	+	1.86875i
$866$	69.6610	+	95.8802i	0.0804400	+	0.110716i
$867$		0			0
$868$		−	518.343i		−	0.597169i
$869$	241.306	+	680.084i	0.277682	+	0.782606i
$870$		0			0
$871$	1231.59	+	400.168i	1.41400	+	0.459435i
$872$	−606.136	+	440.384i	−0.695110	+	0.505027i
$873$		0			0
$874$	32.8457	+	101.089i	0.0375809	+	0.115662i
$875$	−492.137	+	159.905i	−0.562442	+	0.182748i
$876$		0			0
$877$	−399.155	−	549.389i	−0.455136	−	0.626442i	0.518355	−	0.855166i	$-0.326545\pi$
$877$	−399.155	−	549.389i	−0.455136	−	0.626442i	−0.973491	+	0.228724i	$0.926545\pi$
$878$	83.5172	−	257.040i	0.0951222	−	0.292756i
$879$		0			0
$880$	−939.758	−	277.734i	−1.06791	−	0.315607i
$881$	−419.212			−0.475837			−0.237918	−	0.971285i	$-0.576465\pi$
$881$	−419.212			−0.475837			−0.237918	+	0.971285i	$0.576465\pi$
$882$		0			0
$883$	292.750	−	212.695i	0.331540	−	0.240878i	−0.409544	−	0.912290i	$-0.634312\pi$
$883$	292.750	−	212.695i	0.331540	−	0.240878i	0.741084	+	0.671413i	$0.234312\pi$
$884$	−1256.56	−	912.941i	−1.42144	−	1.03274i
$885$		0			0
$886$	13.7602	−	4.47097i	0.0155308	−	0.00504625i
$887$	−24.9623	+	34.3576i	−0.0281424	+	0.0387346i	−0.822856	−	0.568249i	$-0.807621\pi$
$887$	−24.9623	+	34.3576i	−0.0281424	+	0.0387346i	0.794714	+	0.606984i	$0.207621\pi$
$888$		0			0
$889$	−81.4937	+	250.812i	−0.0916690	+	0.282128i
$890$		−	156.354i		−	0.175678i
$891$		0			0
$892$	−294.159			−0.329775
$893$	−116.804	−	37.9518i	−0.130799	−	0.0424992i
$894$		0			0
$895$	−433.936	−	315.273i	−0.484844	−	0.352260i
$896$	158.783	+	488.683i	0.177213	+	0.545406i
$897$		0			0
$898$	−55.7506	+	76.7342i	−0.0620831	+	0.0854501i
$899$	279.460	+	384.643i	0.310856	+	0.427857i
$900$		0			0
$901$		−	1700.06i		−	1.88685i
$902$	66.2491	−	96.5214i	0.0734469	−	0.107008i
$903$		0			0
$904$	694.872	+	225.778i	0.768664	+	0.249754i
$905$	1038.17	−	754.274i	1.14715	−	0.833451i
$906$		0			0
$907$	−19.0536	−	58.6409i	−0.0210073	−	0.0646537i	0.940003	−	0.341165i	$-0.110822\pi$
$907$	−19.0536	−	58.6409i	−0.0210073	−	0.0646537i	−0.961011	+	0.276512i	$0.910822\pi$
$908$	−600.096	+	194.983i	−0.660898	+	0.214739i
$909$		0			0
$910$	189.243	+	260.471i	0.207960	+	0.286232i
$911$	−83.8172	+	257.963i	−0.0920057	+	0.283165i	−0.986462	−	0.163991i	$-0.947563\pi$
$911$	−83.8172	+	257.963i	−0.0920057	+	0.283165i	0.894456	+	0.447156i	$0.147563\pi$
$912$		0			0
$913$	791.675	+	543.380i	0.867114	+	0.595159i
$914$	483.393			0.528877
$915$		0			0
$916$	8.43146	−	6.12581i	0.00920465	−	0.00668757i
$917$	−736.546	−	535.132i	−0.803213	−	0.583568i
$918$		0			0
$919$	119.898	−	38.9574i	0.130466	−	0.0423910i	−0.243056	−	0.970012i	$-0.578150\pi$
$919$	119.898	−	38.9574i	0.130466	−	0.0423910i	0.373522	+	0.927621i	$0.378150\pi$
$920$	299.316	−	411.973i	0.325343	−	0.447797i
$921$		0			0
$922$	−26.1069	+	80.3488i	−0.0283155	+	0.0871462i
$923$			1012.58i			1.09706i
$924$		0			0
$925$	−729.895			−0.789076
$926$	4.44286	+	1.44357i	0.00479790	+	0.00155893i
$927$		0			0
$928$	−293.579	−	213.298i	−0.316357	−	0.229847i
$929$	85.0652	+	261.804i	0.0915664	+	0.281813i	0.986344	−	0.164700i	$-0.0526657\pi$
$929$	85.0652	+	261.804i	0.0915664	+	0.281813i	−0.894777	+	0.446513i	$0.852666\pi$
$930$		0			0
$931$	242.976	−	334.428i	0.260984	−	0.359214i
$932$	617.541	+	849.972i	0.662597	+	0.911987i
$933$		0			0
$934$			187.868i			0.201144i
$935$	−743.597	+	2516.08i	−0.795291	+	2.69099i
$936$		0			0
$937$	1469.07	+	477.330i	1.56784	+	0.509424i	0.958889	−	0.283781i	$-0.0915888\pi$
$937$	1469.07	+	477.330i	1.56784	+	0.509424i	0.608955	+	0.793204i	$0.291589\pi$
$938$	−190.389	+	138.325i	−0.202973	+	0.147469i
$939$		0			0
$940$	85.7145	+	263.802i	0.0911857	+	0.280641i
$941$	−1018.35	+	330.882i	−1.08220	+	0.351628i	−0.795228	−	0.606310i	$-0.792649\pi$
$941$	−1018.35	+	330.882i	−1.08220	+	0.351628i	−0.286973	+	0.957939i	$0.592649\pi$
$942$		0			0
$943$	−120.123	−	165.335i	−0.127384	−	0.175329i
$944$	340.683	−	1048.51i	0.360893	−	1.11071i
$945$		0			0
$946$	−301.647	+	107.030i	−0.318865	+	0.113139i
$947$	1480.48			1.56333			0.781667	−	0.623696i	$-0.214370\pi$
$947$	1480.48			1.56333			0.781667	+	0.623696i	$0.214370\pi$
$948$		0			0
$949$	−310.989	+	225.947i	−0.327702	+	0.238089i
$950$	276.657	+	201.003i	0.291218	+	0.211582i
$951$		0			0
$952$	569.438	−	185.022i	0.598149	−	0.194350i
$953$	254.489	−	350.274i	0.267040	−	0.367549i	−0.654348	−	0.756194i	$-0.727057\pi$
$953$	254.489	−	350.274i	0.267040	−	0.367549i	0.921388	+	0.388645i	$0.127057\pi$
$954$		0			0
$955$	372.578	−	1146.68i	0.390134	−	1.20071i
$956$		−	1223.22i		−	1.27952i
$957$		0			0
$958$	−258.229			−0.269550
$959$	−197.880	−	64.2950i	−0.206339	−	0.0670437i
$960$		0			0
$961$	−245.497	−	178.364i	−0.255460	−	0.185602i
$962$	53.9897	+	166.163i	0.0561223	+	0.172727i
$963$		0			0
$964$	90.7410	−	124.894i	0.0941297	−	0.129558i
$965$	1021.74	+	1406.30i	1.05879	+	1.45730i
$966$		0			0
$967$			211.542i			0.218761i	0.994000	+	0.109381i	$0.0348867\pi$
$967$			211.542i			0.218761i	−0.994000	+	0.109381i	$0.965113\pi$
$968$	561.957	−	216.516i	0.580534	−	0.223674i
$969$		0			0
$970$	186.403	+	60.5659i	0.192168	+	0.0624391i
$971$	−1125.89	+	818.004i	−1.15951	+	0.842434i	−0.989716	−	0.143045i	$-0.954311\pi$
$971$	−1125.89	+	818.004i	−1.15951	+	0.842434i	−0.169795	+	0.985479i	$0.554311\pi$
$972$		0			0
$973$	−167.617	−	515.871i	−0.172268	−	0.530186i
$974$	−322.628	+	104.828i	−0.331240	+	0.107627i
$975$		0			0
$976$	537.196	+	739.388i	0.550406	+	0.757569i
$977$	10.0534	−	30.9411i	0.0102900	−	0.0316695i	−0.945780	−	0.324809i	$-0.894700\pi$
$977$	10.0534	−	30.9411i	0.0102900	−	0.0316695i	0.956070	+	0.293139i	$0.0947000\pi$
$978$		0			0
$979$	−196.660	−	255.964i	−0.200879	−	0.261454i
$980$	−933.613			−0.952666
$981$		0			0
$982$	164.296	−	119.368i	0.167308	−	0.121556i
$983$	980.893	+	712.660i	0.997856	+	0.724985i	0.961627	−	0.274359i	$-0.0884655\pi$
$983$	980.893	+	712.660i	0.997856	+	0.724985i	0.0362286	+	0.999344i	$0.488466\pi$
$984$		0			0
$985$	−422.843	+	137.390i	−0.429283	+	0.139482i
$986$	−152.177	+	209.454i	−0.154338	+	0.212428i
$987$		0			0
$988$	−208.613	+	642.044i	−0.211147	+	0.649843i
$989$			558.741i			0.564955i
$990$		0			0
$991$	−106.677			−0.107645			−0.0538227	−	0.998551i	$-0.517141\pi$
$991$	−106.677			−0.107645			−0.0538227	+	0.998551i	$0.517141\pi$
$992$	917.858	+	298.230i	0.925260	+	0.300635i
$993$		0			0
$994$	−148.872	−	108.162i	−0.149770	−	0.108815i
$995$	145.588	+	448.073i	0.146319	+	0.450324i
$996$		0			0
$997$	−759.309	+	1045.10i	−0.761593	+	1.04824i	0.235486	+	0.971878i	$0.424332\pi$
$997$	−759.309	+	1045.10i	−0.761593	+	1.04824i	−0.997080	+	0.0763658i	$0.975668\pi$
$998$	−224.203	−	308.588i	−0.224652	−	0.309207i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.3.k.b.46.3	yes	16
3.2	odd	2	inner	99.3.k.b.46.2	yes	16
11.4	even	5		1089.3.c.l.604.9		16
11.6	odd	10	inner	99.3.k.b.28.3	yes	16
11.7	odd	10		1089.3.c.l.604.7		16
33.17	even	10	inner	99.3.k.b.28.2	✓	16
33.26	odd	10		1089.3.c.l.604.8		16
33.29	even	10		1089.3.c.l.604.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.3.k.b.28.2	✓	16	33.17	even	10	inner
99.3.k.b.28.3	yes	16	11.6	odd	10	inner
99.3.k.b.46.2	yes	16	3.2	odd	2	inner
99.3.k.b.46.3	yes	16	1.1	even	1	trivial
1089.3.c.l.604.7		16	11.7	odd	10
1089.3.c.l.604.8		16	33.26	odd	10
1089.3.c.l.604.9		16	11.4	even	5
1089.3.c.l.604.10		16	33.29	even	10

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	99.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.625505 + 0.203239i) q^{2} +(-2.88612 - 2.09689i) q^{4} +(-2.50346 - 7.70484i) q^{5} +(-2.40175 + 3.30573i) q^{7} +(-2.92545 - 4.02653i) q^{8} +O(q^{10})\)	\(q+(0.625505 + 0.203239i) q^{2} +(-2.88612 - 2.09689i) q^{4} +(-2.50346 - 7.70484i) q^{5} +(-2.40175 + 3.30573i) q^{7} +(-2.92545 - 4.02653i) q^{8} -5.32822i q^{10} +(-6.70179 - 8.72273i) q^{11} +(14.0643 + 4.56975i) q^{13} +(-2.17416 + 1.57962i) q^{14} +(3.39806 + 10.4582i) q^{16} +(28.0003 - 9.09786i) q^{17} +(-7.52161 - 10.3526i) q^{19} +(-8.93092 + 27.4865i) q^{20} +(-2.41921 - 6.81818i) q^{22} -12.6293 q^{23} +(-32.8719 + 23.8828i) q^{25} +(7.86851 + 5.71681i) q^{26} +(13.8635 - 4.50452i) q^{28} +(-7.85901 + 10.8170i) q^{29} +(10.9884 - 33.8187i) q^{31} +27.1405i q^{32} +19.3634 q^{34} +(31.4828 + 10.2294i) q^{35} +(14.5329 + 10.5587i) q^{37} +(-2.60075 - 8.00429i) q^{38} +(-23.7001 + 32.6203i) q^{40} +(9.51144 + 13.0914i) q^{41} -44.2415i q^{43} +(1.05159 + 39.2277i) q^{44} +(-7.89971 - 2.56677i) q^{46} +(7.76454 - 5.64127i) q^{47} +(9.98240 + 30.7227i) q^{49} +(-25.4155 + 8.25799i) q^{50} +(-31.0088 - 42.6800i) q^{52} +(17.8438 - 54.9177i) q^{53} +(-50.4296 + 73.4732i) q^{55} +20.3368 q^{56} +(-7.11429 + 5.16883i) q^{58} +(-81.1105 - 58.9302i) q^{59} +(79.0445 - 25.6831i) q^{61} +(13.7466 - 18.9205i) q^{62} +(8.07624 - 24.8561i) q^{64} -119.803i q^{65} +87.5688 q^{67} +(-99.8895 - 32.4561i) q^{68} +(17.6136 + 12.7971i) q^{70} +(21.1594 + 65.1219i) q^{71} +(-15.2790 + 21.0298i) q^{73} +(6.94443 + 9.55819i) q^{74} +45.6508i q^{76} +(44.9310 - 1.20448i) q^{77} +(-62.3915 - 20.2722i) q^{79} +(72.0716 - 52.3631i) q^{80} +(3.28878 + 10.1218i) q^{82} +(-83.0198 + 26.9748i) q^{83} +(-140.195 - 192.962i) q^{85} +(8.99160 - 27.6733i) q^{86} +(-15.5166 + 52.5028i) q^{88} +29.3444 q^{89} +(-48.8852 + 35.5172i) q^{91} +(36.4497 + 26.4823i) q^{92} +(6.00329 - 1.95059i) q^{94} +(-60.9352 + 83.8701i) q^{95} +(-11.3670 + 34.9841i) q^{97} +21.2460i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} + 30 q^{7}+O(q^{10}) \) 16 * q - 4 * q^4 + 30 * q^7	\( 16 q - 4 q^{4} + 30 q^{7} - 30 q^{13} - 176 q^{16} + 90 q^{22} - 74 q^{25} - 50 q^{28} + 130 q^{31} + 328 q^{34} + 90 q^{37} + 450 q^{40} - 370 q^{46} - 54 q^{49} - 790 q^{52} - 476 q^{55} - 630 q^{58} + 210 q^{61} + 1104 q^{64} + 300 q^{67} + 268 q^{70} - 170 q^{73} + 30 q^{79} + 90 q^{82} - 610 q^{85} - 600 q^{88} - 402 q^{91} + 1030 q^{94} + 870 q^{97}+O(q^{100}) \) 16 * q - 4 * q^4 + 30 * q^7 - 30 * q^13 - 176 * q^16 + 90 * q^22 - 74 * q^25 - 50 * q^28 + 130 * q^31 + 328 * q^34 + 90 * q^37 + 450 * q^40 - 370 * q^46 - 54 * q^49 - 790 * q^52 - 476 * q^55 - 630 * q^58 + 210 * q^61 + 1104 * q^64 + 300 * q^67 + 268 * q^70 - 170 * q^73 + 30 * q^79 + 90 * q^82 - 610 * q^85 - 600 * q^88 - 402 * q^91 + 1030 * q^94 + 870 * q^97

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