LMFDB - Embedded newform 99.4.f.b.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,4,Mod(37,99)]

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, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("99.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	99.f (of order $5$, 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:	$5.84118909057$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.682515625.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 $ x^8 - 3x^7 + 5x^6 + 2x^5 + 19x^4 + 28x^3 + 100x^2 + 88*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.1
Root			$-0.390899 + 1.20306i$ of defining polynomial
Character	$\chi$	$=$	99.91
Dual form			99.4.f.b.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.523388 + 0.380264i) q^{2} +(-2.34280 + 7.21040i) q^{4} +(-9.01441 - 6.54935i) q^{5} +(8.07696 - 24.8583i) q^{7} +(-3.11499 - 9.58696i) q^{8} +O(q^{10})$	\(q+(-0.523388 + 0.380264i) q^{2} +(-2.34280 + 7.21040i) q^{4} +(-9.01441 - 6.54935i) q^{5} +(8.07696 - 24.8583i) q^{7} +(-3.11499 - 9.58696i) q^{8} +7.20851 q^{10} +(36.0937 - 5.31471i) q^{11} +(43.2976 - 31.4576i) q^{13} +(5.22533 + 16.0819i) q^{14} +(-43.7924 - 31.8170i) q^{16} +(18.9494 + 13.7676i) q^{17} +(-21.8916 - 67.3756i) q^{19} +(68.3424 - 49.6537i) q^{20} +(-16.8700 + 16.5068i) q^{22} -164.114 q^{23} +(-0.261588 - 0.805085i) q^{25} +(-10.6993 + 32.9290i) q^{26} +(160.316 + 116.476i) q^{28} +(67.5495 - 207.896i) q^{29} +(62.0698 - 45.0964i) q^{31} +115.662 q^{32} -15.1532 q^{34} +(-235.615 + 171.184i) q^{35} +(-87.5569 + 269.472i) q^{37} +(37.0783 + 26.9390i) q^{38} +(-34.7085 + 106.822i) q^{40} +(-1.50043 - 4.61784i) q^{41} -333.848 q^{43} +(-46.2392 + 272.701i) q^{44} +(85.8951 - 62.4064i) q^{46} +(121.601 + 374.250i) q^{47} +(-275.206 - 199.949i) q^{49} +(0.443057 + 0.321899i) q^{50} +(125.384 + 385.892i) q^{52} +(123.029 - 89.3860i) q^{53} +(-360.171 - 188.481i) q^{55} -263.475 q^{56} +(43.7007 + 134.497i) q^{58} +(237.027 - 729.494i) q^{59} +(287.741 + 209.056i) q^{61} +(-15.3381 + 47.2058i) q^{62} +(289.803 - 210.554i) q^{64} -596.329 q^{65} +102.070 q^{67} +(-143.665 + 104.378i) q^{68} +(58.2228 - 179.191i) q^{70} +(504.157 + 366.292i) q^{71} +(-95.7190 + 294.593i) q^{73} +(-56.6443 - 174.333i) q^{74} +537.093 q^{76} +(159.412 - 940.155i) q^{77} +(517.284 - 375.829i) q^{79} +(186.381 + 573.623i) q^{80} +(2.54130 + 1.84636i) q^{82} +(233.374 + 169.556i) q^{83} +(-80.6493 - 248.213i) q^{85} +(174.732 - 126.950i) q^{86} +(-163.383 - 329.473i) q^{88} -184.513 q^{89} +(-432.269 - 1330.39i) q^{91} +(384.486 - 1183.32i) q^{92} +(-205.958 - 149.637i) q^{94} +(-243.926 + 750.727i) q^{95} +(-515.522 + 374.549i) q^{97} +220.073 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{2} - 16 q^{4} - 9 q^{5} + 3 q^{7} - 36 q^{8}+O(q^{10}) $ 8 * q + 6 * q^2 - 16 * q^4 - 9 * q^5 + 3 * q^7 - 36 * q^8	$ 8 q + 6 q^{2} - 16 q^{4} - 9 q^{5} + 3 q^{7} - 36 q^{8} + 8 q^{10} + 87 q^{11} + 171 q^{13} - 12 q^{14} + 44 q^{16} - 36 q^{17} + 324 q^{19} + 87 q^{20} - 521 q^{22} + 84 q^{23} + 263 q^{25} + 774 q^{26} + 387 q^{28} - 393 q^{29} + 15 q^{31} - 102 q^{32} - 712 q^{34} - 1002 q^{35} - 747 q^{37} + 36 q^{38} + 41 q^{40} - 159 q^{41} - 644 q^{43} - 219 q^{44} + 753 q^{46} + 351 q^{47} - 1967 q^{49} - 330 q^{50} + 2871 q^{52} + 531 q^{53} - 716 q^{55} - 1470 q^{56} - 1205 q^{58} + 1002 q^{59} + 1449 q^{61} - 99 q^{62} - 1118 q^{64} + 954 q^{65} - 518 q^{67} - 873 q^{68} + 26 q^{70} - 429 q^{71} + 2547 q^{73} - 468 q^{74} - 2276 q^{76} + 2697 q^{77} + 2805 q^{79} + 1620 q^{80} - 1631 q^{82} + 2553 q^{83} - 197 q^{85} + 1713 q^{86} + 2866 q^{88} - 1788 q^{89} + 2885 q^{91} - 423 q^{92} + 1159 q^{94} - 3009 q^{95} + 9 q^{97} - 5550 q^{98}+O(q^{100}) $ 8 * q + 6 * q^2 - 16 * q^4 - 9 * q^5 + 3 * q^7 - 36 * q^8 + 8 * q^10 + 87 * q^11 + 171 * q^13 - 12 * q^14 + 44 * q^16 - 36 * q^17 + 324 * q^19 + 87 * q^20 - 521 * q^22 + 84 * q^23 + 263 * q^25 + 774 * q^26 + 387 * q^28 - 393 * q^29 + 15 * q^31 - 102 * q^32 - 712 * q^34 - 1002 * q^35 - 747 * q^37 + 36 * q^38 + 41 * q^40 - 159 * q^41 - 644 * q^43 - 219 * q^44 + 753 * q^46 + 351 * q^47 - 1967 * q^49 - 330 * q^50 + 2871 * q^52 + 531 * q^53 - 716 * q^55 - 1470 * q^56 - 1205 * q^58 + 1002 * q^59 + 1449 * q^61 - 99 * q^62 - 1118 * q^64 + 954 * q^65 - 518 * q^67 - 873 * q^68 + 26 * q^70 - 429 * q^71 + 2547 * q^73 - 468 * q^74 - 2276 * q^76 + 2697 * q^77 + 2805 * q^79 + 1620 * q^80 - 1631 * q^82 + 2553 * q^83 - 197 * q^85 + 1713 * q^86 + 2866 * q^88 - 1788 * q^89 + 2885 * q^91 - 423 * q^92 + 1159 * q^94 - 3009 * q^95 + 9 * q^97 - 5550 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−0.523388	+	0.380264i	−0.185046	+	0.134443i	−0.676452	−	0.736487i	$-0.736483\pi$
$2$	−0.523388	+	0.380264i	−0.185046	+	0.134443i	0.491406	+	0.870931i	$0.336483\pi$
$3$		0			0
$3$		0			0
$4$	−2.34280	+	7.21040i	−0.292850	+	0.901300i
$5$	−9.01441	−	6.54935i	−0.806273	−	0.585792i	0.106475	−	0.994315i	$-0.466044\pi$
$5$	−9.01441	−	6.54935i	−0.806273	−	0.585792i	−0.912748	+	0.408524i	$0.866044\pi$
$6$		0			0
$7$	8.07696	−	24.8583i	0.436115	−	1.34222i	−0.455825	−	0.890069i	$-0.650656\pi$
$7$	8.07696	−	24.8583i	0.436115	−	1.34222i	0.891940	−	0.452154i	$-0.149344\pi$
$8$	−3.11499	−	9.58696i	−0.137664	−	0.423688i
$9$		0			0
$10$	7.20851			0.227953
$11$	36.0937	−	5.31471i	0.989332	−	0.145677i
$11$	36.0937	−	5.31471i	0.989332	−	0.145677i
$12$		0			0
$13$	43.2976	−	31.4576i	0.923738	−	0.671135i	−0.0207134	−	0.999785i	$-0.506594\pi$
$13$	43.2976	−	31.4576i	0.923738	−	0.671135i	0.944452	+	0.328650i	$0.106594\pi$
$14$	5.22533	+	16.0819i	0.0997521	+	0.307005i
$15$		0			0
$16$	−43.7924	−	31.8170i	−0.684255	−	0.497141i
$17$	18.9494	+	13.7676i	0.270348	+	0.196419i	0.714697	−	0.699435i	$-0.246565\pi$
$17$	18.9494	+	13.7676i	0.270348	+	0.196419i	−0.444349	+	0.895854i	$0.646565\pi$
$18$		0			0
$19$	−21.8916	−	67.3756i	−0.264331	−	0.813527i	−0.991847	−	0.127436i	$-0.959325\pi$
$19$	−21.8916	−	67.3756i	−0.264331	−	0.813527i	0.727516	−	0.686091i	$-0.240675\pi$
$20$	68.3424	−	49.6537i	0.764091	−	0.555145i
$21$		0			0
$22$	−16.8700	+	16.5068i	−0.163486	+	0.159966i
$23$	−164.114			−1.48783			−0.743914	−	0.668275i	$-0.767033\pi$
$23$	−164.114			−1.48783			−0.743914	+	0.668275i	$0.767033\pi$
$24$		0			0
$25$	−0.261588	−	0.805085i	−0.00209270	−	0.00644068i
$26$	−10.6993	+	32.9290i	−0.0807040	+	0.248381i
$27$		0			0
$28$	160.316	+	116.476i	1.08203	+	0.786141i
$29$	67.5495	−	207.896i	0.432539	−	1.33122i	−0.463049	−	0.886333i	$-0.653245\pi$
$29$	67.5495	−	207.896i	0.432539	−	1.33122i	0.895588	−	0.444885i	$-0.146755\pi$
$30$		0			0
$31$	62.0698	−	45.0964i	0.359615	−	0.261276i	−0.393276	−	0.919420i	$-0.628658\pi$
$31$	62.0698	−	45.0964i	0.359615	−	0.261276i	0.752892	+	0.658145i	$0.228658\pi$
$32$	115.662			0.638947
$33$		0			0
$34$	−15.1532			−0.0764340
$35$	−235.615	+	171.184i	−1.13789	+	0.826726i
$36$		0			0
$37$	−87.5569	+	269.472i	−0.389034	+	1.19732i	0.544477	+	0.838776i	$0.316728\pi$
$37$	−87.5569	+	269.472i	−0.389034	+	1.19732i	−0.933511	+	0.358548i	$0.883272\pi$
$38$	37.0783	+	26.9390i	0.158287	+	0.115002i
$39$		0			0
$40$	−34.7085	+	106.822i	−0.137198	+	0.422251i
$41$	−1.50043	−	4.61784i	−0.00571530	−	0.0175899i	0.948158	−	0.317799i	$-0.102944\pi$
$41$	−1.50043	−	4.61784i	−0.00571530	−	0.0175899i	−0.953874	+	0.300209i	$0.902944\pi$
$42$		0			0
$43$	−333.848			−1.18398			−0.591992	−	0.805944i	$-0.701658\pi$
$43$	−333.848			−1.18398			−0.591992	+	0.805944i	$0.701658\pi$
$44$	−46.2392	+	272.701i	−0.158428	+	0.934347i
$45$		0			0
$46$	85.8951	−	62.4064i	0.275316	−	0.200029i
$47$	121.601	+	374.250i	0.377390	+	1.16149i	0.941852	+	0.336029i	$0.109084\pi$
$47$	121.601	+	374.250i	0.377390	+	1.16149i	−0.564461	+	0.825459i	$0.690916\pi$
$48$		0			0
$49$	−275.206	−	199.949i	−0.802350	−	0.582941i
$50$	0.443057	+	0.321899i	0.00125315	+	0.000910469i
$51$		0			0
$52$	125.384	+	385.892i	0.334377	+	1.02911i
$53$	123.029	−	89.3860i	0.318856	−	0.231663i	−0.416831	−	0.908984i	$-0.636859\pi$
$53$	123.029	−	89.3860i	0.318856	−	0.231663i	0.735687	+	0.677321i	$0.236859\pi$
$54$		0			0
$55$	−360.171	−	188.481i	−0.883008	−	0.462087i
$56$	−263.475			−0.628721
$57$		0			0
$58$	43.7007	+	134.497i	0.0989341	+	0.304488i
$59$	237.027	−	729.494i	0.523021	−	1.60969i	−0.245174	−	0.969479i	$-0.578845\pi$
$59$	237.027	−	729.494i	0.523021	−	1.60969i	0.768195	−	0.640215i	$-0.221155\pi$
$60$		0			0
$61$	287.741	+	209.056i	0.603959	+	0.438802i	0.847282	−	0.531143i	$-0.178237\pi$
$61$	287.741	+	209.056i	0.603959	+	0.438802i	−0.243323	+	0.969945i	$0.578237\pi$
$62$	−15.3381	+	47.2058i	−0.0314184	+	0.0966959i
$63$		0			0
$64$	289.803	−	210.554i	0.566021	−	0.411238i
$65$	−596.329			−1.13793
$66$		0			0
$67$	102.070			0.186116			0.0930582	−	0.995661i	$-0.470336\pi$
$67$	102.070			0.186116			0.0930582	+	0.995661i	$0.470336\pi$
$68$	−143.665	+	104.378i	−0.256204	+	0.186143i
$69$		0			0
$70$	58.2228	−	179.191i	0.0994137	−	0.305964i
$71$	504.157	+	366.292i	0.842711	+	0.612265i	0.923127	−	0.384496i	$-0.125625\pi$
$71$	504.157	+	366.292i	0.842711	+	0.612265i	−0.0804159	+	0.996761i	$0.525625\pi$
$72$		0			0
$73$	−95.7190	+	294.593i	−0.153467	+	0.472322i	−0.998002	−	0.0631776i	$-0.979877\pi$
$73$	−95.7190	+	294.593i	−0.153467	+	0.472322i	0.844536	+	0.535499i	$0.179877\pi$
$74$	−56.6443	−	174.333i	−0.0889834	−	0.273863i
$75$		0			0
$76$	537.093			0.810642
$77$	159.412	−	940.155i	0.235932	−	1.39144i
$78$		0			0
$79$	517.284	−	375.829i	0.736697	−	0.535242i	−0.154978	−	0.987918i	$-0.549531\pi$
$79$	517.284	−	375.829i	0.736697	−	0.535242i	0.891675	+	0.452676i	$0.149531\pi$
$80$	186.381	+	573.623i	0.260476	+	0.801662i
$81$		0			0
$82$	2.54130	+	1.84636i	0.00342244	+	0.00248655i
$83$	233.374	+	169.556i	0.308628	+	0.224232i	0.731308	−	0.682048i	$-0.238910\pi$
$83$	233.374	+	169.556i	0.308628	+	0.224232i	−0.422679	+	0.906279i	$0.638910\pi$
$84$		0			0
$85$	−80.6493	−	248.213i	−0.102913	−	0.316735i
$86$	174.732	−	126.950i	0.219091	−	0.159179i
$87$		0			0
$88$	−163.383	−	329.473i	−0.197917	−	0.399113i
$89$	−184.513			−0.219756			−0.109878	−	0.993945i	$-0.535046\pi$
$89$	−184.513			−0.219756			−0.109878	+	0.993945i	$0.535046\pi$
$90$		0			0
$91$	−432.269	−	1330.39i	−0.497957	−	1.53255i
$92$	384.486	−	1183.32i	0.435711	−	1.34098i
$93$		0			0
$94$	−205.958	−	149.637i	−0.225989	−	0.164191i
$95$	−243.926	+	750.727i	−0.263434	+	0.810768i
$96$		0			0
$97$	−515.522	+	374.549i	−0.539622	+	0.392058i	−0.823945	−	0.566670i	$-0.808231\pi$
$97$	−515.522	+	374.549i	−0.539622	+	0.392058i	0.284323	+	0.958729i	$0.408231\pi$
$98$	220.073			0.226844
$99$		0			0
$100$	6.41783			0.00641783
$101$	−621.680	+	451.677i	−0.612470	+	0.444986i	−0.850283	−	0.526325i	$-0.823569\pi$
$101$	−621.680	+	451.677i	−0.612470	+	0.444986i	0.237813	+	0.971311i	$0.423569\pi$
$102$		0			0
$103$	354.197	−	1090.10i	0.338835	−	1.04283i	−0.625967	−	0.779850i	$-0.715295\pi$
$103$	354.197	−	1090.10i	0.338835	−	1.04283i	0.964802	−	0.262978i	$-0.0847046\pi$
$104$	−436.454	−	317.102i	−0.411518	−	0.298985i
$105$		0			0
$106$	−30.4018	+	93.5672i	−0.0278574	+	0.0857363i
$107$	230.941	+	710.765i	0.208654	+	0.642170i	0.999544	+	0.0302117i	$0.00961814\pi$
$107$	230.941	+	710.765i	0.208654	+	0.642170i	−0.790890	+	0.611959i	$0.790382\pi$
$108$		0			0
$109$	−742.910			−0.652825			−0.326412	−	0.945227i	$-0.605840\pi$
$109$	−742.910			−0.652825			−0.326412	+	0.945227i	$0.605840\pi$
$110$	260.182	−	38.3111i	0.225521	−	0.0332075i
$111$		0			0
$112$	−1144.63	+	831.620i	−0.965688	+	0.701613i
$113$	−561.797	−	1729.03i	−0.467694	−	1.43942i	−0.855562	−	0.517700i	$-0.826788\pi$
$113$	−561.797	−	1729.03i	−0.467694	−	1.43942i	0.387868	−	0.921715i	$-0.373212\pi$
$114$		0			0
$115$	1479.39	+	1074.84i	1.19960	+	0.871557i
$116$	1340.76	+	974.118i	1.07316	+	0.779694i
$117$		0			0
$118$	153.343	+	471.941i	0.119630	+	0.368184i
$119$	495.293	−	359.851i	0.381541	−	0.277206i
$120$		0			0
$121$	1274.51	−	383.655i	0.957557	−	0.288245i
$122$	−230.097			−0.170754
$123$		0			0
$124$	179.746	+	553.200i	0.130175	+	0.400636i
$125$	−433.314	+	1333.60i	−0.310054	+	0.954250i
$126$		0			0
$127$	1958.12	+	1422.66i	1.36815	+	0.994021i	0.997879	+	0.0650981i	$0.0207360\pi$
$127$	1958.12	+	1422.66i	1.36815	+	0.994021i	0.370274	+	0.928923i	$0.379264\pi$
$128$	−357.545	+	1100.41i	−0.246897	+	0.759871i
$129$		0			0
$130$	312.111	−	226.762i	0.210569	−	0.152987i
$131$	−1878.36			−1.25277			−0.626386	−	0.779513i	$-0.715467\pi$
$131$	−1878.36			−1.25277			−0.626386	+	0.779513i	$0.715467\pi$
$132$		0			0
$133$	−1851.66			−1.20721
$134$	−53.4221	+	38.8134i	−0.0344400	+	0.0250222i
$135$		0			0
$136$	72.9618	−	224.553i	0.0460031	−	0.141583i
$137$	−430.765	−	312.969i	−0.268633	−	0.195174i	0.445311	−	0.895376i	$-0.353093\pi$
$137$	−430.765	−	312.969i	−0.268633	−	0.195174i	−0.713944	+	0.700202i	$0.753093\pi$
$138$		0			0
$139$	−516.215	+	1588.75i	−0.314999	+	0.969466i	0.660756	+	0.750601i	$0.270236\pi$
$139$	−516.215	+	1588.75i	−0.314999	+	0.969466i	−0.975755	+	0.218866i	$0.929764\pi$
$140$	−682.308	−	2099.93i	−0.411897	−	1.26769i
$141$		0			0
$142$	−403.157			−0.238255
$143$	1395.58	−	1365.53i	0.816115	−	0.798543i
$144$		0			0
$145$	−1970.50	+	1431.65i	−1.12856	+	0.819947i
$146$	−61.9248	−	190.585i	−0.0351023	−	0.108034i
$147$		0			0
$148$	−1737.88	−	1262.64i	−0.965219	−	0.701273i
$149$	2432.65	+	1767.42i	1.33752	+	0.971763i	0.999531	+	0.0306124i	$0.00974574\pi$
$149$	2432.65	+	1767.42i	1.33752	+	0.971763i	0.337986	+	0.941151i	$0.390254\pi$
$150$		0			0
$151$	−767.053	−	2360.75i	−0.413390	−	1.27228i	−0.913683	−	0.406428i	$-0.866774\pi$
$151$	−767.053	−	2360.75i	−0.413390	−	1.27228i	0.500293	−	0.865856i	$-0.333226\pi$
$152$	−577.734	+	419.749i	−0.308292	+	0.223988i
$153$		0			0
$154$	274.072	+	552.685i	0.143411	+	0.289199i
$155$	−854.875			−0.443001
$156$		0			0
$157$	975.427	+	3002.06i	0.495844	+	1.52605i	0.815637	+	0.578564i	$0.196387\pi$
$157$	975.427	+	3002.06i	0.495844	+	1.52605i	−0.319792	+	0.947488i	$0.603613\pi$
$158$	−127.826	+	393.409i	−0.0643628	+	0.198088i
$159$		0			0
$160$	−1042.62	−	757.510i	−0.515166	−	0.374290i
$161$	−1325.54	+	4079.59i	−0.648864	+	1.99700i
$162$		0			0
$163$	667.571	−	485.019i	0.320787	−	0.233065i	−0.415724	−	0.909491i	$-0.636472\pi$
$163$	667.571	−	485.019i	0.320787	−	0.233065i	0.736511	+	0.676425i	$0.236472\pi$
$164$	36.8117			0.0175275
$165$		0			0
$166$	−186.621			−0.0872568
$167$	2792.71	−	2029.02i	1.29405	−	0.940184i	0.294173	−	0.955752i	$-0.404956\pi$
$167$	2792.71	−	2029.02i	1.29405	−	0.940184i	0.999879	+	0.0155686i	$0.00495583\pi$
$168$		0			0
$169$	206.195	−	634.604i	0.0938531	−	0.288850i
$170$	136.597	+	99.2437i	0.0616267	+	0.0447744i
$171$		0			0
$172$	782.139	−	2407.17i	0.346730	−	1.06712i
$173$	229.523	+	706.398i	0.100869	+	0.310442i	0.988739	−	0.149653i	$-0.0478155\pi$
$173$	229.523	+	706.398i	0.100869	+	0.310442i	−0.887870	+	0.460094i	$0.847816\pi$
$174$		0			0
$175$	−22.1259			−0.00955749
$176$	−1749.73	−	915.649i	−0.749378	−	0.392157i
$177$		0			0
$178$	96.5717	−	70.1635i	0.0406649	−	0.0295448i
$179$	726.105	+	2234.72i	0.303193	+	0.933133i	0.980345	+	0.197290i	$0.0632140\pi$
$179$	726.105	+	2234.72i	0.303193	+	0.933133i	−0.677152	+	0.735843i	$0.736786\pi$
$180$		0			0
$181$	2282.19	+	1658.11i	0.937202	+	0.680917i	0.947746	−	0.319027i	$-0.103356\pi$
$181$	2282.19	+	1658.11i	0.937202	+	0.680917i	−0.0105436	+	0.999944i	$0.503356\pi$
$182$	732.142	+	531.933i	0.298187	+	0.216645i
$183$		0			0
$184$	511.212	+	1573.35i	0.204821	+	0.630374i
$185$	2554.14	−	1855.69i	1.01505	−	0.737477i
$186$		0			0
$187$	757.126	+	396.212i	0.296078	+	0.154941i
$188$	−2983.38			−1.15737
$189$		0			0
$190$	−157.806	−	485.678i	−0.0602551	−	0.185446i
$191$	1144.94	−	3523.78i	0.433745	−	1.33493i	−0.460622	−	0.887596i	$-0.652374\pi$
$191$	1144.94	−	3523.78i	0.433745	−	1.33493i	0.894367	−	0.447333i	$-0.147626\pi$
$192$		0			0
$193$	−2004.39	−	1456.28i	−0.747561	−	0.543135i	0.147509	−	0.989061i	$-0.452875\pi$
$193$	−2004.39	−	1456.28i	−0.747561	−	0.543135i	−0.895070	+	0.445926i	$0.852875\pi$
$194$	127.391	−	392.069i	0.0471450	−	0.145097i
$195$		0			0
$196$	2086.47	−	1515.91i	0.760374	−	0.552444i
$197$	−1713.08			−0.619551			−0.309775	−	0.950810i	$-0.600254\pi$
$197$	−1713.08			−0.619551			−0.309775	+	0.950810i	$0.600254\pi$
$198$		0			0
$199$	825.847			0.294185			0.147092	−	0.989123i	$-0.453009\pi$
$199$	825.847			0.294185			0.147092	+	0.989123i	$0.453009\pi$
$200$	−6.90347	+	5.01566i	−0.00244075	+	0.00177331i
$201$		0			0
$202$	153.624	−	472.805i	0.0535095	−	0.164685i
$203$	−4622.35	−	3358.33i	−1.59815	−	1.16113i
$204$		0			0
$205$	−16.7184	+	51.4539i	−0.00569592	+	0.0175302i
$206$	229.145	+	705.236i	0.0775014	+	0.238525i
$207$		0			0
$208$	−2896.99			−0.965722
$209$	−1148.23	−	2315.48i	−0.380023	−	0.766342i
$210$		0			0
$211$	2266.93	−	1647.02i	0.739629	−	0.537372i	−0.152966	−	0.988231i	$-0.548883\pi$
$211$	2266.93	−	1647.02i	0.739629	−	0.537372i	0.892595	+	0.450860i	$0.148883\pi$
$212$	356.276	+	1096.50i	0.115420	+	0.355228i
$213$		0			0
$214$	−391.150	−	284.187i	−0.124946	−	0.0907787i
$215$	3009.44	+	2186.48i	0.954614	+	0.693567i
$216$		0			0
$217$	−619.685	−	1907.19i	−0.193857	−	0.596630i
$218$	388.830	−	282.502i	0.120802	−	0.0877680i
$219$		0			0
$220$	2202.83	−	2155.40i	0.675068	−	0.660533i
$221$	1253.56			0.381555
$222$		0			0
$223$	682.251	+	2099.75i	0.204874	+	0.630538i	0.999719	+	0.0237244i	$0.00755241\pi$
$223$	682.251	+	2099.75i	0.204874	+	0.630538i	−0.794844	+	0.606813i	$0.792448\pi$
$224$	934.196	−	2875.16i	0.278654	−	0.857610i
$225$		0			0
$226$	951.527	+	691.325i	0.280065	+	0.203479i
$227$	733.649	−	2257.94i	0.214511	−	0.660197i	−0.784677	−	0.619905i	$-0.787171\pi$
$227$	733.649	−	2257.94i	0.214511	−	0.660197i	0.999188	−	0.0402921i	$-0.0128288\pi$
$228$		0			0
$229$	−346.279	+	251.587i	−0.0999248	+	0.0725996i	−0.636626	−	0.771173i	$-0.719670\pi$
$229$	−346.279	+	251.587i	−0.0999248	+	0.0725996i	0.536701	+	0.843773i	$0.319670\pi$
$230$	−1183.01			−0.339155
$231$		0			0
$232$	−2203.50			−0.623565
$233$	−2238.22	+	1626.16i	−0.629316	+	0.457225i	−0.856163	−	0.516705i	$-0.827158\pi$
$233$	−2238.22	+	1626.16i	−0.629316	+	0.457225i	0.226847	+	0.973930i	$0.427158\pi$
$234$		0			0
$235$	1354.93	−	4170.05i	0.376110	−	1.15755i
$236$	4704.63	+	3418.12i	1.29765	+	0.942799i
$237$		0			0
$238$	−122.392	+	376.684i	−0.0333340	+	0.102591i
$239$	1066.04	+	3280.94i	0.288521	+	0.887977i	0.985321	+	0.170711i	$0.0546065\pi$
$239$	1066.04	+	3280.94i	0.288521	+	0.887977i	−0.696800	+	0.717265i	$0.745394\pi$
$240$		0			0
$241$	1453.69			0.388549			0.194274	−	0.980947i	$-0.437765\pi$
$241$	1453.69			0.388549			0.194274	+	0.980947i	$0.437765\pi$
$242$	−521.172	+	685.449i	−0.138439	+	0.182076i
$243$		0			0
$244$	−2181.50	+	1584.95i	−0.572362	+	0.415845i
$245$	1171.28	+	3604.84i	0.305431	+	0.940020i
$246$		0			0
$247$	−3067.33	−	2228.54i	−0.790159	−	0.574084i
$248$	−625.684	−	454.586i	−0.160206	−	0.116396i
$249$		0			0
$250$	−280.330	−	862.766i	−0.0709184	−	0.218264i
$251$	2346.81	−	1705.06i	0.590158	−	0.428775i	−0.252214	−	0.967671i	$-0.581159\pi$
$251$	2346.81	−	1705.06i	0.590158	−	0.428775i	0.842372	+	0.538897i	$0.181159\pi$
$252$		0			0
$253$	−5923.46	+	872.215i	−1.47196	+	0.216742i
$254$	−1565.84			−0.386810
$255$		0			0
$256$	654.247	+	2013.57i	0.159728	+	0.491593i
$257$	−971.414	+	2989.70i	−0.235779	+	0.725652i	0.761238	+	0.648472i	$0.224592\pi$
$257$	−971.414	+	2989.70i	−0.235779	+	0.725652i	−0.997017	+	0.0771801i	$0.975408\pi$
$258$		0			0
$259$	5991.44	+	4353.03i	1.43741	+	1.04434i
$260$	1397.08	−	4299.77i	0.333243	−	1.02562i
$261$		0			0
$262$	983.112	−	714.273i	0.231820	−	0.168427i
$263$	−587.892			−0.137836			−0.0689182	−	0.997622i	$-0.521955\pi$
$263$	−587.892			−0.137836			−0.0689182	+	0.997622i	$0.521955\pi$
$264$		0			0
$265$	−1694.46			−0.392791
$266$	969.137	−	704.120i	0.223390	−	0.162302i
$267$		0			0
$268$	−239.129	+	735.964i	−0.0545042	+	0.167747i
$269$	−1303.12	−	946.775i	−0.295364	−	0.214594i	0.430227	−	0.902721i	$-0.358433\pi$
$269$	−1303.12	−	946.775i	−0.295364	−	0.214594i	−0.725591	+	0.688126i	$0.758433\pi$
$270$		0			0
$271$	−700.861	+	2157.03i	−0.157101	+	0.483506i	−0.998368	−	0.0571137i	$-0.981810\pi$
$271$	−700.861	+	2157.03i	−0.157101	+	0.483506i	0.841267	+	0.540620i	$0.181810\pi$
$272$	−391.798	−	1205.83i	−0.0873391	−	0.268802i
$273$		0			0
$274$	344.468			0.0759492
$275$	−13.7205	−	27.6682i	−0.00300864	−	0.00606711i
$276$		0			0
$277$	3930.39	−	2855.60i	0.852543	−	0.619409i	−0.0733031	−	0.997310i	$-0.523354\pi$
$277$	3930.39	−	2855.60i	0.852543	−	0.619409i	0.925846	+	0.377901i	$0.123354\pi$
$278$	−333.962	−	1027.83i	−0.0720493	−	0.221745i
$279$		0			0
$280$	2375.07	+	1725.59i	0.506921	+	0.368299i
$281$	−3948.13	−	2868.49i	−0.838170	−	0.608966i	0.0836886	−	0.996492i	$-0.473330\pi$
$281$	−3948.13	−	2868.49i	−0.838170	−	0.608966i	−0.921859	+	0.387526i	$0.873330\pi$
$282$		0			0
$283$	2061.42	+	6344.40i	0.432999	+	1.33264i	0.895123	+	0.445819i	$0.147088\pi$
$283$	2061.42	+	6344.40i	0.432999	+	1.33264i	−0.462124	+	0.886816i	$0.652912\pi$
$284$	−3822.25	+	2777.03i	−0.798623	+	0.580233i
$285$		0			0
$286$	−211.169	+	1245.39i	−0.0436597	+	0.257488i
$287$	−126.911			−0.0261021
$288$		0			0
$289$	−1348.67	−	4150.76i	−0.274510	−	0.844853i
$290$	486.931	−	1498.62i	0.0985986	−	0.303455i
$291$		0			0
$292$	−1899.88	−	1380.34i	−0.380761	−	0.276639i
$293$	−1675.44	+	5156.47i	−0.334062	+	1.02814i	0.633120	+	0.774054i	$0.281774\pi$
$293$	−1675.44	+	5156.47i	−0.334062	+	1.02814i	−0.967182	+	0.254084i	$0.918226\pi$
$294$		0			0
$295$	−6914.36	+	5023.58i	−1.36464	+	0.991472i
$296$	2856.16			0.560847
$297$		0			0
$298$	−1945.30			−0.378149
$299$	−7105.73	+	5162.61i	−1.37436	+	0.998534i
$300$		0			0
$301$	−2696.47	+	8298.89i	−0.516353	+	1.58917i
$302$	1299.17	+	943.904i	0.247546	+	0.179853i
$303$		0			0
$304$	−1185.00	+	3647.06i	−0.223568	+	0.688070i
$305$	−1224.63	−	3769.04i	−0.229909	−	0.707588i
$306$		0			0
$307$	4774.61			0.887627			0.443813	−	0.896119i	$-0.353625\pi$
$307$	4774.61			0.887627			0.443813	+	0.896119i	$0.353625\pi$
$308$	6405.42	+	3352.02i	1.18501	+	0.620128i
$309$		0			0
$310$	447.431	−	325.078i	0.0819754	−	0.0595586i
$311$	−273.472	−	841.659i	−0.0498622	−	0.153460i	0.923025	−	0.384740i	$-0.125709\pi$
$311$	−273.472	−	841.659i	−0.0498622	−	0.153460i	−0.972887	+	0.231280i	$0.925709\pi$
$312$		0			0
$313$	−5381.54	−	3909.92i	−0.971829	−	0.706075i	−0.0159614	−	0.999873i	$-0.505081\pi$
$313$	−5381.54	−	3909.92i	−0.971829	−	0.706075i	−0.955868	+	0.293797i	$0.905081\pi$
$314$	−1652.10	−	1200.32i	−0.296922	−	0.215726i
$315$		0			0
$316$	1497.98	+	4610.32i	0.266672	+	0.820731i
$317$	−1246.50	+	905.636i	−0.220853	+	0.160459i	−0.692711	−	0.721216i	$-0.743584\pi$
$317$	−1246.50	+	905.636i	−0.220853	+	0.160459i	0.471857	+	0.881675i	$0.343584\pi$
$318$		0			0
$319$	1333.20	−	7862.73i	0.233997	−	1.38003i
$320$	−3991.39			−0.697267
$321$		0			0
$322$	−857.548	−	2639.26i	−0.148414	−	0.456771i
$323$	512.764	−	1578.12i	0.0883311	−	0.271855i
$324$		0			0
$325$	−36.6521	−	26.6293i	−0.00625568	−	0.00454502i
$326$	−164.964	+	507.706i	−0.0280261	+	0.0862554i
$327$		0			0
$328$	−39.5972	+	28.7691i	−0.00666583	+	0.00484301i
$329$	10285.4			1.72356
$330$		0			0
$331$	3573.14			0.593346			0.296673	−	0.954979i	$-0.404123\pi$
$331$	3573.14			0.593346			0.296673	+	0.954979i	$0.404123\pi$
$332$	−1769.32	+	1285.49i	−0.292482	+	0.212501i
$333$		0			0
$334$	−690.108	+	2123.93i	−0.113057	+	0.347954i
$335$	−920.098	−	668.490i	−0.150061	−	0.109025i
$336$		0			0
$337$	363.720	−	1119.42i	0.0587926	−	0.180945i	−0.917347	−	0.398088i	$-0.869674\pi$
$337$	363.720	−	1119.42i	0.0587926	−	0.180945i	0.976140	+	0.217143i	$0.0696738\pi$
$338$	133.397	+	410.552i	0.0214669	+	0.0660684i
$339$		0			0
$340$	1978.66			0.315612
$341$	2000.66	−	1957.58i	0.317717	−	0.310876i
$342$		0			0
$343$	59.7704	−	43.4257i	0.00940903	−	0.00683606i
$344$	1039.93	+	3200.58i	0.162992	+	0.501639i
$345$		0			0
$346$	−388.747	−	282.441i	−0.0604022	−	0.0438848i
$347$	4623.91	+	3359.46i	0.715344	+	0.519728i	0.884893	−	0.465794i	$-0.154231\pi$
$347$	4623.91	+	3359.46i	0.715344	+	0.519728i	−0.169549	+	0.985522i	$0.554231\pi$
$348$		0			0
$349$	−2843.25	−	8750.62i	−0.436091	−	1.34215i	−0.891965	−	0.452105i	$-0.850673\pi$
$349$	−2843.25	−	8750.62i	−0.436091	−	1.34215i	0.455874	−	0.890044i	$-0.349327\pi$
$350$	11.5804	−	8.41367i	0.00176857	−	0.00128494i
$351$		0			0
$352$	4174.66	−	614.709i	0.632131	−	0.0930798i
$353$	−844.785			−0.127375			−0.0636875	−	0.997970i	$-0.520286\pi$
$353$	−844.785			−0.127375			−0.0636875	+	0.997970i	$0.520286\pi$
$354$		0			0
$355$	−2145.71	−	6603.80i	−0.320795	−	0.987306i
$356$	432.277	−	1330.41i	0.0643556	−	0.198066i
$357$		0			0
$358$	−1229.82	−	893.515i	−0.181558	−	0.131910i
$359$	2857.69	−	8795.08i	0.420121	−	1.29300i	−0.487469	−	0.873140i	$-0.662080\pi$
$359$	2857.69	−	8795.08i	0.420121	−	1.29300i	0.907590	−	0.419858i	$-0.137920\pi$
$360$		0			0
$361$	1488.82	−	1081.69i	0.217061	−	0.157704i
$362$	−1824.99			−0.264970
$363$		0			0
$364$	10605.3			1.52712
$365$	2792.24	−	2028.68i	0.400418	−	0.290921i
$366$		0			0
$367$	1001.85	−	3083.37i	0.142496	−	0.438558i	−0.854184	−	0.519970i	$-0.825943\pi$
$367$	1001.85	−	3083.37i	0.142496	−	0.438558i	0.996681	+	0.0814122i	$0.0259430\pi$
$368$	7186.92	+	5221.60i	1.01805	+	0.739660i
$369$		0			0
$370$	−631.155	+	1942.49i	−0.0886815	+	0.272934i
$371$	−1228.28	−	3780.27i	−0.171885	−	0.529008i
$372$		0			0
$373$	−3319.48			−0.460794			−0.230397	−	0.973097i	$-0.574002\pi$
$373$	−3319.48			−0.460794			−0.230397	+	0.973097i	$0.574002\pi$
$374$	−546.936	+	80.5349i	−0.0756186	+	0.0111347i
$375$		0			0
$376$	3209.13	−	2331.57i	0.440155	−	0.319791i
$377$	−3615.17	−	11126.3i	−0.493874	−	1.51999i
$378$		0			0
$379$	−718.800	−	522.239i	−0.0974202	−	0.0707799i	0.538009	−	0.842939i	$-0.319177\pi$
$379$	−718.800	−	522.239i	−0.0974202	−	0.0707799i	−0.635429	+	0.772159i	$0.719177\pi$
$380$	−4841.57	−	3517.61i	−0.653598	−	0.474867i
$381$		0			0
$382$	740.714	+	2279.68i	0.0992100	+	0.305337i
$383$	−2726.60	+	1980.99i	−0.363767	+	0.264292i	−0.754622	−	0.656160i	$-0.772180\pi$
$383$	−2726.60	+	1980.99i	−0.363767	+	0.264292i	0.390854	+	0.920453i	$0.372180\pi$
$384$		0			0
$385$	−7594.41	+	7430.89i	−1.00532	+	0.983671i
$386$	1602.84			0.211354
$387$		0			0
$388$	−1492.88	−	4594.62i	−0.195334	−	0.601176i
$389$	−1482.84	+	4563.71i	−0.193272	+	0.594831i	0.806720	+	0.590934i	$0.201241\pi$
$389$	−1482.84	+	4563.71i	−0.193272	+	0.594831i	−0.999992	+	0.00389744i	$0.998759\pi$
$390$		0			0
$391$	−3109.86	−	2259.45i	−0.402231	−	0.292238i
$392$	−1059.64	+	3261.23i	−0.136530	+	0.420196i
$393$		0			0
$394$	896.603	−	651.420i	0.114645	−	0.0832946i
$395$	−7124.45			−0.907519
$396$		0			0
$397$	3560.10			0.450066			0.225033	−	0.974351i	$-0.427751\pi$
$397$	3560.10			0.450066			0.225033	+	0.974351i	$0.427751\pi$
$398$	−432.238	+	314.040i	−0.0544376	+	0.0395512i
$399$		0			0
$400$	−14.1598	+	43.5795i	−0.00176998	+	0.00544744i
$401$	2926.55	+	2126.26i	0.364451	+	0.264789i	0.754906	−	0.655833i	$-0.227682\pi$
$401$	2926.55	+	2126.26i	0.364451	+	0.264789i	−0.390455	+	0.920622i	$0.627682\pi$
$402$		0			0
$403$	1268.85	−	3905.13i	0.156839	−	0.482701i
$404$	−1800.30	−	5540.75i	−0.221704	−	0.682334i
$405$		0			0
$406$	3696.33			0.451837
$407$	−1728.08	+	10191.6i	−0.210462	+	1.24122i
$408$		0			0
$409$	−137.720	+	100.060i	−0.0166500	+	0.0120969i	−0.596079	−	0.802926i	$-0.703276\pi$
$409$	−137.720	+	100.060i	−0.0166500	+	0.0120969i	0.579429	+	0.815023i	$0.303276\pi$
$410$	−10.8159	−	33.2878i	−0.00130282	−	0.00400967i
$411$		0			0
$412$	7030.28	+	5107.80i	0.840673	+	0.610784i
$413$	−16219.5	−	11784.2i	−1.93247	−	1.40402i
$414$		0			0
$415$	−993.247	−	3056.90i	−0.117486	−	0.361584i
$416$	5007.88	−	3638.44i	0.590220	−	0.428820i
$417$		0			0
$418$	1481.47	+	775.266i	0.173351	+	0.0907165i
$419$	17029.2			1.98552			0.992759	−	0.120126i	$-0.0383298\pi$
$419$	17029.2			1.98552			0.992759	+	0.120126i	$0.0383298\pi$
$420$		0			0
$421$	3297.86	+	10149.8i	0.381776	+	1.17499i	0.938792	+	0.344484i	$0.111946\pi$
$421$	3297.86	+	10149.8i	0.381776	+	1.17499i	−0.557016	+	0.830502i	$0.688054\pi$
$422$	−560.181	+	1724.06i	−0.0646189	+	0.198877i
$423$		0			0
$424$	−1240.18	−	901.040i	−0.142048	−	0.103204i
$425$	6.12712	−	18.8573i	0.000699316	−	0.00215227i
$426$		0			0
$427$	7520.86	−	5464.23i	0.852366	−	0.619280i
$428$	−5665.95			−0.639893
$429$		0			0
$430$	−2406.54			−0.269893
$431$	13944.8	−	10131.5i	1.55847	−	1.13229i	0.621212	−	0.783643i	$-0.286641\pi$
$431$	13944.8	−	10131.5i	1.55847	−	1.13229i	0.937253	−	0.348649i	$-0.113359\pi$
$432$		0			0
$433$	−2083.79	+	6413.24i	−0.231271	+	0.711780i	0.766323	+	0.642456i	$0.222084\pi$
$433$	−2083.79	+	6413.24i	−0.231271	+	0.711780i	−0.997594	+	0.0693242i	$0.977916\pi$
$434$	1049.57	+	762.559i	0.116085	+	0.0843410i
$435$		0			0
$436$	1740.49	−	5356.68i	0.191180	−	0.588391i
$437$	3592.72	+	11057.2i	0.393279	+	1.21039i
$438$		0			0
$439$	−10414.5			−1.13224			−0.566122	−	0.824321i	$-0.691557\pi$
$439$	−10414.5			−1.13224			−0.566122	+	0.824321i	$0.691557\pi$
$440$	−685.032	+	4040.06i	−0.0742218	+	0.437733i
$441$		0			0
$442$	−656.098	+	476.683i	−0.0706050	+	0.0512975i
$443$	−1873.47	−	5765.94i	−0.200928	−	0.618393i	−0.999856	−	0.0169660i	$-0.994599\pi$
$443$	−1873.47	−	5765.94i	−0.200928	−	0.618393i	0.798928	−	0.601426i	$-0.205401\pi$
$444$		0			0
$445$	1663.27	+	1208.44i	0.177183	+	0.128731i
$446$	−1155.54	−	839.550i	−0.122683	−	0.0891342i
$447$		0			0
$448$	−2893.30	−	8904.65i	−0.305124	−	0.939074i
$449$	−7622.53	+	5538.10i	−0.801180	+	0.582091i	−0.911260	−	0.411832i	$-0.864889\pi$
$449$	−7622.53	+	5538.10i	−0.801180	+	0.582091i	0.110080	+	0.993923i	$0.464889\pi$
$450$		0			0
$451$	−78.6984	−	158.701i	−0.00821677	−	0.0165697i
$452$	13783.2			1.43431
$453$		0			0
$454$	474.629	+	1460.76i	0.0490649	+	0.151006i
$455$	−4816.52	+	14823.7i	−0.496268	+	1.52736i
$456$		0			0
$457$	−933.726	−	678.392i	−0.0955752	−	0.0694394i	0.538971	−	0.842324i	$-0.318813\pi$
$457$	−933.726	−	678.392i	−0.0955752	−	0.0694394i	−0.634547	+	0.772885i	$0.718813\pi$
$458$	85.5692	−	263.355i	0.00873010	−	0.0268685i
$459$		0			0
$460$	−11215.9	+	8148.84i	−1.13684	+	0.825960i
$461$	5162.80			0.521595			0.260798	−	0.965393i	$-0.416014\pi$
$461$	5162.80			0.521595			0.260798	+	0.965393i	$0.416014\pi$
$462$		0			0
$463$	−7080.69			−0.710729			−0.355365	−	0.934728i	$-0.615643\pi$
$463$	−7080.69			−0.710729			−0.355365	+	0.934728i	$0.615643\pi$
$464$	−9572.78	+	6955.03i	−0.957769	+	0.695860i
$465$		0			0
$466$	553.087	−	1702.23i	0.0549813	−	0.169215i
$467$	−8364.95	−	6077.49i	−0.828873	−	0.602212i	0.0903671	−	0.995909i	$-0.471196\pi$
$467$	−8364.95	−	6077.49i	−0.828873	−	0.602212i	−0.919240	+	0.393697i	$0.871196\pi$
$468$		0			0
$469$	824.413	−	2537.28i	0.0811681	−	0.249810i
$470$	876.563	+	2697.78i	0.0860273	+	0.264765i
$471$		0			0
$472$	−7731.96			−0.754009
$473$	−12049.8	+	1774.30i	−1.17135	+	0.172479i
$474$		0			0
$475$	−48.5165	+	35.2493i	−0.00468650	+	0.00340494i
$476$	1434.30	+	4414.32i	0.138111	+	0.425063i
$477$		0			0
$478$	−1805.58	−	1311.83i	−0.172772	−	0.125526i
$479$	4098.81	+	2977.96i	0.390980	+	0.284064i	0.765857	−	0.643011i	$-0.222315\pi$
$479$	4098.81	+	2977.96i	0.390980	+	0.284064i	−0.374877	+	0.927075i	$0.622315\pi$
$480$		0			0
$481$	4685.94	+	14421.8i	0.444200	+	1.36711i
$482$	−760.843	+	552.785i	−0.0718993	+	0.0522379i
$483$		0			0
$484$	−219.615	+	10088.5i	−0.0206250	+	0.947459i
$485$	7100.18			0.664747
$486$		0			0
$487$	1899.42	+	5845.80i	0.176737	+	0.543939i	0.999709	−	0.0241426i	$-0.00768559\pi$
$487$	1899.42	+	5845.80i	0.176737	+	0.543939i	−0.822972	+	0.568082i	$0.807686\pi$
$488$	1107.90	−	3409.77i	0.102771	−	0.316297i
$489$		0			0
$490$	−1983.83	−	1441.33i	−0.182898	−	0.132883i
$491$	−489.927	+	1507.84i	−0.0450307	+	0.138590i	−0.971044	−	0.238901i	$-0.923213\pi$
$491$	−489.927	+	1507.84i	−0.0450307	+	0.138590i	0.926013	+	0.377491i	$0.123213\pi$
$492$		0			0
$493$	4142.25	−	3009.52i	0.378413	−	0.274933i
$494$	2452.84			0.223397
$495$		0			0
$496$	−4153.02			−0.375960
$497$	13177.5	−	9573.98i	1.18931	−	0.864088i
$498$		0			0
$499$	324.409	−	998.427i	0.0291033	−	0.0895706i	−0.935450	−	0.353459i	$-0.885005\pi$
$499$	324.409	−	998.427i	0.0291033	−	0.0895706i	0.964553	+	0.263889i	$0.0850052\pi$
$500$	−8600.65	−	6248.74i	−0.769266	−	0.558904i
$501$		0			0
$502$	−579.922	+	1784.82i	−0.0515601	+	0.158686i
$503$	2970.82	+	9143.24i	0.263345	+	0.810491i	0.992070	+	0.125685i	$0.0401130\pi$
$503$	2970.82	+	9143.24i	0.263345	+	0.810491i	−0.728726	+	0.684806i	$0.759887\pi$
$504$		0			0
$505$	8562.27			0.754487
$506$	2768.60	−	2708.98i	0.243240	−	0.238002i
$507$		0			0
$508$	−14845.4	+	10785.8i	−1.29657	+	0.942017i
$509$	−482.077	−	1483.68i	−0.0419798	−	0.129200i	0.927870	−	0.372904i	$-0.121638\pi$
$509$	−482.077	−	1483.68i	−0.0419798	−	0.129200i	−0.969850	+	0.243703i	$0.921638\pi$
$510$		0			0
$511$	6549.96	+	4758.83i	0.567032	+	0.411973i
$512$	−8596.63	−	6245.82i	−0.742033	−	0.539119i
$513$		0			0
$514$	−628.449	−	1934.17i	−0.0539294	−	0.165978i
$515$	−10332.3	+	7506.89i	−0.884073	+	0.642317i
$516$		0			0
$517$	6378.06	+	12861.8i	0.542566	+	1.09412i
$518$	−4791.15			−0.406392
$519$		0			0
$520$	1857.56	+	5716.98i	0.156653	+	0.482127i
$521$	−3668.79	+	11291.4i	−0.308507	+	0.949488i	0.669838	+	0.742508i	$0.266364\pi$
$521$	−3668.79	+	11291.4i	−0.308507	+	0.949488i	−0.978345	+	0.206981i	$0.933636\pi$
$522$		0			0
$523$	−7071.20	−	5137.53i	−0.591209	−	0.429538i	0.251539	−	0.967847i	$-0.419063\pi$
$523$	−7071.20	−	5137.53i	−0.591209	−	0.429538i	−0.842748	+	0.538309i	$0.819063\pi$
$524$	4400.63	−	13543.7i	0.366875	−	1.12912i
$525$		0			0
$526$	307.696	−	223.554i	0.0255060	−	0.0185312i
$527$	1797.06			0.148541
$528$		0			0
$529$	14766.3			1.21363
$530$	886.858	−	644.340i	0.0726843	−	0.0528082i
$531$		0			0
$532$	4338.08	−	13351.2i	0.353533	−	1.08806i
$533$	−210.231	−	152.742i	−0.0170846	−	0.0124127i
$534$		0			0
$535$	2573.25	−	7919.64i	0.207946	−	0.639992i
$536$	−317.946	−	978.538i	−0.0256216	−	0.0788552i
$537$		0			0
$538$	1042.06			0.0835066
$539$	−10995.9	−	5754.25i	−0.878712	−	0.459839i
$540$		0			0
$541$	7589.57	−	5514.15i	0.603145	−	0.438210i	−0.243849	−	0.969813i	$-0.578410\pi$
$541$	7589.57	−	5514.15i	0.603145	−	0.438210i	0.846994	+	0.531603i	$0.178410\pi$
$542$	−453.417	−	1395.48i	−0.0359335	−	0.110592i
$543$		0			0
$544$	2191.73	+	1592.38i	0.172738	+	0.125502i
$545$	6696.89	+	4865.58i	0.526355	+	0.382419i
$546$		0			0
$547$	74.4993	+	229.285i	0.00582333	+	0.0179224i	0.953926	−	0.300042i	$-0.0970007\pi$
$547$	74.4993	+	229.285i	0.00582333	+	0.0179224i	−0.948103	+	0.317964i	$0.897001\pi$
$548$	3265.83	−	2372.77i	0.254579	−	0.184963i
$549$		0			0
$550$	17.7023	+	9.26382i	0.00137242	+	0.000718201i
$551$	−15485.9			−1.19731
$552$		0			0
$553$	−5164.40	−	15894.4i	−0.397129	−	1.22224i
$554$	−971.240	+	2989.17i	−0.0744838	+	0.229238i
$555$		0			0
$556$	−10246.1	−	7444.24i	−0.781533	−	0.567817i
$557$	2796.81	−	8607.70i	0.212755	−	0.654793i	−0.786550	−	0.617526i	$-0.788135\pi$
$557$	2796.81	−	8607.70i	0.212755	−	0.654793i	0.999305	−	0.0372668i	$-0.0118652\pi$
$558$		0			0
$559$	−14454.8	+	10502.0i	−1.09369	+	0.794613i
$560$	15764.7			1.18961
$561$		0			0
$562$	3157.19			0.236971
$563$	17478.7	−	12699.0i	1.30842	−	0.950622i	0.308420	−	0.951250i	$-0.400200\pi$
$563$	17478.7	−	12699.0i	1.30842	−	0.950622i	1.00000		0.000627893i	$0.000199864\pi$
$564$		0			0
$565$	−6259.78	+	19265.6i	−0.466108	+	1.43453i
$566$	−3491.47	−	2536.70i	−0.259289	−	0.188384i
$567$		0			0
$568$	1941.18	−	5974.33i	0.143398	−	0.441333i
$569$	−902.599	−	2777.92i	−0.0665008	−	0.204668i	0.912285	−	0.409557i	$-0.134317\pi$
$569$	−902.599	−	2777.92i	−0.0665008	−	0.204668i	−0.978785	+	0.204889i	$0.934317\pi$
$570$		0			0
$571$	17676.0			1.29548			0.647741	−	0.761861i	$-0.275714\pi$
$571$	17676.0			1.29548			0.647741	+	0.761861i	$0.275714\pi$
$572$	6576.47	+	13261.9i	0.480727	+	0.969418i
$573$		0			0
$574$	66.4235	−	48.2595i	0.00483008	−	0.00350926i
$575$	42.9301	+	132.125i	0.00311358	+	0.00958262i
$576$		0			0
$577$	−3392.48	−	2464.78i	−0.244767	−	0.177834i	0.458637	−	0.888624i	$-0.348338\pi$
$577$	−3392.48	−	2464.78i	−0.244767	−	0.177834i	−0.703404	+	0.710790i	$0.748338\pi$
$578$	2284.26	+	1659.61i	0.164382	+	0.119430i
$579$		0			0
$580$	−5706.30	−	17562.2i	−0.408519	−	1.25729i
$581$	6099.84	−	4431.79i	0.435566	−	0.316457i
$582$		0			0
$583$	3965.52	−	3880.14i	0.281707	−	0.275641i
$584$	3122.41			0.221244
$585$		0			0
$586$	−1083.91	−	3335.95i	−0.0764097	−	0.235165i
$587$	−8165.92	+	25132.1i	−0.574180	+	1.76714i	0.0647745	+	0.997900i	$0.479367\pi$
$587$	−8165.92	+	25132.1i	−0.574180	+	1.76714i	−0.638955	+	0.769245i	$0.720633\pi$
$588$		0			0
$589$	−4397.21	−	3194.76i	−0.307612	−	0.223493i
$590$	1708.61	−	5258.56i	0.119224	−	0.366935i
$591$		0			0
$592$	12408.1	−	9015.03i	0.861437	−	0.625871i
$593$	13972.0			0.967555			0.483778	−	0.875191i	$-0.339264\pi$
$593$	13972.0			0.967555			0.483778	+	0.875191i	$0.339264\pi$
$594$		0			0
$595$	−6821.56			−0.470011
$596$	−18443.0	+	13399.6i	−1.26754	+	0.920924i
$597$		0			0
$598$	1755.90	−	5404.10i	0.120074	−	0.369549i
$599$	1460.87	+	1061.38i	0.0996486	+	0.0723989i	0.636494	−	0.771282i	$-0.280384\pi$
$599$	1460.87	+	1061.38i	0.0996486	+	0.0723989i	−0.536845	+	0.843681i	$0.680384\pi$
$600$		0			0
$601$	7977.94	−	24553.6i	0.541476	−	1.66649i	−0.187748	−	0.982217i	$-0.560119\pi$
$601$	7977.94	−	24553.6i	0.541476	−	1.66649i	0.729224	−	0.684275i	$-0.239881\pi$
$602$	−1744.46	−	5368.91i	−0.118105	−	0.363489i
$603$		0			0
$604$	18819.0			1.26777
$605$	−14001.6	−	4888.78i	−0.940904	−	0.328524i
$606$		0			0
$607$	−21298.4	+	15474.2i	−1.42418	+	1.03473i	−0.433115	+	0.901339i	$0.642586\pi$
$607$	−21298.4	+	15474.2i	−1.42418	+	1.03473i	−0.991064	+	0.133388i	$0.957414\pi$
$608$	−2532.03	−	7792.78i	−0.168894	−	0.519801i
$609$		0			0
$610$	2074.19	+	1506.98i	0.137674	+	0.100026i
$611$	17038.0	+	12378.8i	1.12813	+	0.819631i
$612$		0			0
$613$	5780.29	+	17789.9i	0.380855	+	1.17215i	0.939443	+	0.342705i	$0.111343\pi$
$613$	5780.29	+	17789.9i	0.380855	+	1.17215i	−0.558589	+	0.829445i	$0.688657\pi$
$614$	−2498.97	+	1815.61i	−0.164251	+	0.119336i
$615$		0			0
$616$	−9509.79	+	1400.29i	−0.622014	+	0.0915900i
$617$	14282.3			0.931903			0.465952	−	0.884810i	$-0.345712\pi$
$617$	14282.3			0.931903			0.465952	+	0.884810i	$0.345712\pi$
$618$		0			0
$619$	−2242.48	−	6901.65i	−0.145611	−	0.448143i	0.851478	−	0.524390i	$-0.175706\pi$
$619$	−2242.48	−	6901.65i	−0.145611	−	0.448143i	−0.997089	+	0.0762464i	$0.975706\pi$
$620$	2002.80	−	6163.99i	0.129733	−	0.399277i
$621$		0			0
$622$	463.184	+	336.523i	0.0298585	+	0.0216935i
$623$	−1490.30	+	4586.67i	−0.0958389	+	0.294962i
$624$		0			0
$625$	12554.7	−	9121.53i	0.803501	−	0.583778i
$626$	4303.43			0.274760
$627$		0			0
$628$	−23931.3			−1.52064
$629$	−5369.14	+	3900.91i	−0.340352	+	0.247280i
$630$		0			0
$631$	−46.7826	+	143.982i	−0.00295149	+	0.00908374i	−0.952521	−	0.304472i	$-0.901520\pi$
$631$	−46.7826	+	143.982i	−0.00295149	+	0.00908374i	0.949570	+	0.313555i	$0.101520\pi$
$632$	−5214.39	−	3788.48i	−0.328192	−	0.238446i
$633$		0			0
$634$	308.023	−	947.998i	0.0192952	−	0.0593846i
$635$	−8333.82	−	25648.9i	−0.520815	−	1.60290i
$636$		0			0
$637$	−18205.7			−1.13239
$638$	2292.13	+	4622.23i	0.142236	+	0.286827i
$639$		0			0
$640$	10430.0	−	7577.86i	0.644192	−	0.468033i
$641$	−6323.77	−	19462.6i	−0.389663	−	1.19926i	−0.933041	−	0.359771i	$-0.882855\pi$
$641$	−6323.77	−	19462.6i	−0.389663	−	1.19926i	0.543378	−	0.839488i	$-0.317145\pi$
$642$		0			0
$643$	−1007.21	−	731.783i	−0.0617739	−	0.0448813i	0.556470	−	0.830868i	$-0.312155\pi$
$643$	−1007.21	−	731.783i	−0.0617739	−	0.0448813i	−0.618244	+	0.785987i	$0.712155\pi$
$644$	−26310.0	−	19115.3i	−1.60987	−	1.16964i
$645$		0			0
$646$	331.729	+	1020.96i	0.0202039	+	0.0621811i
$647$	−272.538	+	198.010i	−0.0165604	+	0.0120318i	−0.596035	−	0.802959i	$-0.703258\pi$
$647$	−272.538	+	198.010i	−0.0165604	+	0.0120318i	0.579474	+	0.814991i	$0.303258\pi$
$648$		0			0
$649$	4678.13	−	27589.8i	0.282947	−	1.66871i
$650$	29.3095			0.00176863
$651$		0			0
$652$	1933.19	+	5949.76i	0.116119	+	0.357378i
$653$	4353.14	−	13397.6i	0.260875	−	0.802892i	−0.731739	−	0.681584i	$-0.761291\pi$
$653$	4353.14	−	13397.6i	0.260875	−	0.802892i	0.992615	−	0.121308i	$-0.0387088\pi$
$654$		0			0
$655$	16932.3	+	12302.0i	1.01008	+	0.733864i
$656$	−81.2186	+	249.965i	−0.00483393	+	0.0148773i
$657$		0			0
$658$	−5383.25	+	3911.16i	−0.318938	+	0.231722i
$659$	−4111.66			−0.243046			−0.121523	−	0.992589i	$-0.538778\pi$
$659$	−4111.66			−0.243046			−0.121523	+	0.992589i	$0.538778\pi$
$660$		0			0
$661$	22986.9			1.35263			0.676314	−	0.736614i	$-0.263576\pi$
$661$	22986.9			1.35263			0.676314	+	0.736614i	$0.263576\pi$
$662$	−1870.14	+	1358.73i	−0.109796	+	0.0797715i
$663$		0			0
$664$	898.570	−	2765.52i	0.0525170	−	0.161631i
$665$	16691.6	+	12127.2i	0.973344	+	0.707176i
$666$		0			0
$667$	−11085.8	+	34118.5i	−0.643543	+	1.98062i
$668$	8087.31	+	24890.2i	0.468424	+	1.44166i
$669$		0			0
$670$	735.771			0.0424258
$671$	11496.7	+	6016.35i	0.661439	+	0.346138i
$672$		0			0
$673$	13127.9	−	9538.01i	0.751924	−	0.546305i	−0.144499	−	0.989505i	$-0.546157\pi$
$673$	13127.9	−	9538.01i	0.751924	−	0.546305i	0.896423	+	0.443200i	$0.146157\pi$
$674$	235.306	+	724.198i	0.0134476	+	0.0413873i
$675$		0			0
$676$	4092.67	+	2973.50i	0.232856	+	0.169180i
$677$	−10994.8	−	7988.20i	−0.624173	−	0.453488i	0.230204	−	0.973142i	$-0.426061\pi$
$677$	−10994.8	−	7988.20i	−0.624173	−	0.453488i	−0.854377	+	0.519654i	$0.826061\pi$
$678$		0			0
$679$	5146.80	+	15840.2i	0.290893	+	0.895276i
$680$	−2128.39	+	1546.36i	−0.120029	+	0.0872063i
$681$		0			0
$682$	−302.723	+	1785.35i	−0.0169969	+	0.100241i
$683$	−10864.9			−0.608688			−0.304344	−	0.952562i	$-0.598437\pi$
$683$	−10864.9			−0.608688			−0.304344	+	0.952562i	$0.598437\pi$
$684$		0			0
$685$	1833.35	+	5642.47i	0.102261	+	0.314726i
$686$	−14.7699	+	45.4570i	−0.000822036	+	0.00252997i
$687$		0			0
$688$	14620.0	+	10622.0i	0.810147	+	0.588606i
$689$	2515.01	−	7740.41i	0.139063	−	0.427991i
$690$		0			0
$691$	−9632.06	+	6998.10i	−0.530276	+	0.385268i	−0.820461	−	0.571702i	$-0.806283\pi$
$691$	−9632.06	+	6998.10i	−0.530276	+	0.385268i	0.290185	+	0.956971i	$0.406283\pi$
$692$	−5631.14			−0.309341
$693$		0			0
$694$	−3697.58			−0.202245
$695$	15058.6	−	10940.7i	0.821880	−	0.597131i
$696$		0			0
$697$	35.1442	−	108.163i	0.00190987	−	0.00587799i
$698$	4815.67	+	3498.79i	0.261140	+	0.189729i
$699$		0			0
$700$	51.8366	−	159.537i	0.00279891	−	0.00861417i
$701$	9510.30	+	29269.7i	0.512410	+	1.57703i	0.787946	+	0.615744i	$0.211144\pi$
$701$	9510.30	+	29269.7i	0.512410	+	1.57703i	−0.275537	+	0.961291i	$0.588856\pi$
$702$		0			0
$703$	20072.6			1.07689
$704$	9341.02	−	9139.89i	0.500075	−	0.489308i
$705$		0			0
$706$	442.151	−	321.241i	0.0235702	−	0.0171247i
$707$	6206.65	+	19102.1i	0.330163	+	1.01614i
$708$		0			0
$709$	−18051.0	−	13114.8i	−0.956163	−	0.694693i	−0.00390691	−	0.999992i	$-0.501244\pi$
$709$	−18051.0	−	13114.8i	−0.956163	−	0.694693i	−0.952257	+	0.305299i	$0.901244\pi$
$710$	3634.22	+	2640.42i	0.192099	+	0.139568i
$711$		0			0
$712$	574.755	+	1768.91i	0.0302526	+	0.0931080i
$713$	−10186.5	+	7400.93i	−0.535046	+	0.388733i
$714$		0			0
$715$	−21523.7	+	3169.31i	−1.12579	+	0.165770i
$716$	−17814.3			−0.929823
$717$		0			0
$718$	1848.77	+	5689.91i	0.0960937	+	0.295746i
$719$	288.595	−	888.205i	0.0149691	−	0.0460702i	−0.943293	−	0.331961i	$-0.892290\pi$
$719$	288.595	−	888.205i	0.0149691	−	0.0460702i	0.958262	+	0.285891i	$0.0922896\pi$
$720$		0			0
$721$	−24237.3	−	17609.5i	−1.25194	−	0.909585i
$722$	−367.904	+	1132.29i	−0.0189639	+	0.0583650i
$723$		0			0
$724$	−17302.3	+	12570.9i	−0.888170	+	0.645294i
$725$	−185.044			−0.00947912
$726$		0			0
$727$	2130.84			0.108705			0.0543526	−	0.998522i	$-0.482691\pi$
$727$	2130.84			0.108705			0.0543526	+	0.998522i	$0.482691\pi$
$728$	−11407.9	+	8288.29i	−0.580774	+	0.421957i
$729$		0			0
$730$	−689.992	+	2123.58i	−0.0349832	+	0.107667i
$731$	−6326.23	−	4596.27i	−0.320087	−	0.232557i
$732$		0			0
$733$	−10219.1	+	31451.1i	−0.514939	+	1.58482i	0.268454	+	0.963293i	$0.413487\pi$
$733$	−10219.1	+	31451.1i	−0.514939	+	1.58482i	−0.783393	+	0.621527i	$0.786513\pi$
$734$	648.139	+	1994.77i	0.0325930	+	0.100311i
$735$		0			0
$736$	−18981.7			−0.950644
$737$	3684.07	−	542.471i	0.184131	−	0.0271128i
$738$		0			0
$739$	−3698.98	+	2687.47i	−0.184126	+	0.133775i	−0.676030	−	0.736874i	$-0.736301\pi$
$739$	−3698.98	+	2687.47i	−0.184126	+	0.133775i	0.491904	+	0.870649i	$0.336301\pi$
$740$	7396.44	+	22763.9i	0.367431	+	1.13083i
$741$		0			0
$742$	2080.37	+	1511.48i	0.102928	+	0.0747817i
$743$	−14937.1	−	10852.5i	−0.737537	−	0.535852i	0.154402	−	0.988008i	$-0.450655\pi$
$743$	−14937.1	−	10852.5i	−0.737537	−	0.535852i	−0.891939	+	0.452156i	$0.850655\pi$
$744$		0			0
$745$	−10353.4	−	31864.5i	−0.509153	−	1.56701i
$746$	1737.37	−	1262.28i	0.0852678	−	0.0619507i
$747$		0			0
$748$	−4630.64	+	4530.94i	−0.226354	+	0.221481i
$749$	19533.7			0.952933
$750$		0			0
$751$	−8719.88	−	26837.0i	−0.423692	−	1.30399i	−0.904241	−	0.427023i	$-0.859562\pi$
$751$	−8719.88	−	26837.0i	−0.423692	−	1.30399i	0.480549	−	0.876968i	$-0.340438\pi$
$752$	6582.31	−	20258.3i	0.319192	−	0.982371i
$753$		0			0
$754$	6123.08	+	4448.68i	0.295742	+	0.214869i
$755$	−8546.83	+	26304.4i	−0.411988	+	1.26797i
$756$		0			0
$757$	−7135.09	+	5183.95i	−0.342575	+	0.248895i	−0.745747	−	0.666229i	$-0.767907\pi$
$757$	−7135.09	+	5183.95i	−0.342575	+	0.248895i	0.403173	+	0.915124i	$0.367907\pi$
$758$	574.799			0.0275431
$759$		0			0
$760$	7957.01			0.379778
$761$	−23670.8	+	17197.8i	−1.12755	+	0.819212i	−0.985336	−	0.170624i	$-0.945421\pi$
$761$	−23670.8	+	17197.8i	−1.12755	+	0.819212i	−0.142212	+	0.989836i	$0.545421\pi$
$762$		0			0
$763$	−6000.45	+	18467.5i	−0.284706	+	0.876236i
$764$	22725.5	+	16511.0i	1.07615	+	0.781869i
$765$		0			0
$766$	673.772	−	2073.66i	0.0317811	−	0.0978123i
$767$	−12685.4	−	39041.6i	−0.597188	−	1.83795i
$768$		0			0
$769$	−19322.0			−0.906074			−0.453037	−	0.891492i	$-0.649659\pi$
$769$	−19322.0			−0.906074			−0.453037	+	0.891492i	$0.649659\pi$
$770$	1149.13	−	6777.12i	0.0537814	−	0.317182i
$771$		0			0
$772$	15196.2	−	11040.7i	0.708451	−	0.514720i
$773$	5164.93	+	15896.0i	0.240323	+	0.739638i	0.996371	+	0.0851216i	$0.0271279\pi$
$773$	5164.93	+	15896.0i	0.240323	+	0.739638i	−0.756048	+	0.654517i	$0.772872\pi$
$774$		0			0
$775$	−52.5431	−	38.1748i	−0.00243536	−	0.00176939i
$776$	5196.63	+	3775.57i	0.240397	+	0.174659i
$777$		0			0
$778$	−959.313	−	2952.46i	−0.0442070	−	0.136055i
$779$	−278.283	+	202.184i	−0.0127991	+	0.00929911i
$780$		0			0
$781$	20143.6	+	10541.4i	0.922914	+	0.482970i
$782$	2486.85			0.113721
$783$		0			0
$784$	5690.14	+	17512.5i	0.259209	+	0.797762i
$785$	10868.6	−	33450.2i	0.494163	−	1.52088i
$786$		0			0
$787$	14855.6	+	10793.2i	0.672865	+	0.488865i	0.870983	−	0.491313i	$-0.163483\pi$
$787$	14855.6	+	10793.2i	0.672865	+	0.488865i	−0.198118	+	0.980178i	$0.563483\pi$
$788$	4013.39	−	12352.0i	0.181436	−	0.558401i
$789$		0			0
$790$	3728.85	−	2709.17i	0.167932	−	0.122010i
$791$	−47518.5			−2.13598
$792$		0			0
$793$	19034.9			0.852396
$794$	−1863.31	+	1353.78i	−0.0832828	+	0.0605085i
$795$		0			0
$796$	−1934.80	+	5954.69i	−0.0861520	+	0.265149i
$797$	−10888.0	−	7910.57i	−0.483904	−	0.351577i	0.318931	−	0.947778i	$-0.396676\pi$
$797$	−10888.0	−	7910.57i	−0.483904	−	0.351577i	−0.802835	+	0.596201i	$0.796676\pi$
$798$		0			0
$799$	−2848.24	+	8765.98i	−0.126112	+	0.388133i
$800$	−30.2557	−	93.1176i	−0.00133713	−	0.00411525i
$801$		0			0
$802$	−2340.26			−0.103039
$803$	−1889.18	+	11141.7i	−0.0830232	+	0.489640i
$804$		0			0
$805$	38667.6	−	28093.6i	1.69299	−	1.23003i
$806$	820.877	+	2526.40i	0.0358736	+	0.110408i
$807$		0			0
$808$	6266.74	+	4553.05i	0.272850	+	0.198237i
$809$	17140.3	+	12453.2i	0.744898	+	0.541200i	0.894241	−	0.447585i	$-0.147716\pi$
$809$	17140.3	+	12453.2i	0.744898	+	0.541200i	−0.149343	+	0.988785i	$0.547716\pi$
$810$		0			0
$811$	4326.78	+	13316.5i	0.187341	+	0.576578i	0.999981	−	0.00618924i	$-0.00197011\pi$
$811$	4326.78	+	13316.5i	0.187341	+	0.576578i	−0.812639	+	0.582767i	$0.801970\pi$
$812$	35044.2	−	25461.1i	1.51454	−	1.10038i
$813$		0			0
$814$	−2971.03	−	5991.28i	−0.127930	−	0.257978i
$815$	−9194.32			−0.395169
$816$		0			0
$817$	7308.47	+	22493.2i	0.312963	+	0.963202i
$818$	34.0321	−	104.740i	0.00145465	−	0.00447696i
$819$		0			0
$820$	−331.836	−	241.093i	−0.0141320	−	0.0102675i
$821$	−10375.0	+	31931.0i	−0.441036	+	1.35737i	0.445738	+	0.895164i	$0.352941\pi$
$821$	−10375.0	+	31931.0i	−0.441036	+	1.35737i	−0.886773	+	0.462205i	$0.847059\pi$
$822$		0			0
$823$	12079.5	−	8776.26i	0.511621	−	0.371715i	−0.301817	−	0.953366i	$-0.597593\pi$
$823$	12079.5	−	8776.26i	0.511621	−	0.371715i	0.813438	+	0.581651i	$0.197593\pi$
$824$	−11554.1			−0.488479
$825$		0			0
$826$	12970.2			0.546357
$827$	7429.44	−	5397.80i	0.312390	−	0.226965i	−0.420531	−	0.907278i	$-0.638156\pi$
$827$	7429.44	−	5397.80i	0.312390	−	0.226965i	0.732921	+	0.680313i	$0.238156\pi$
$828$		0			0
$829$	5484.93	−	16880.9i	0.229794	−	0.707234i	−0.767975	−	0.640480i	$-0.778736\pi$
$829$	5484.93	−	16880.9i	0.229794	−	0.707234i	0.997769	−	0.0667543i	$-0.0212644\pi$
$830$	1682.28	+	1222.25i	0.0703528	+	0.0511143i
$831$		0			0
$832$	5924.25	−	18233.0i	0.246859	−	0.759753i
$833$	−2462.19	−	7577.84i	−0.102413	−	0.315194i
$834$		0			0
$835$	−38463.4			−1.59411
$836$	19385.7	−	2854.49i	0.801994	−	0.118092i
$837$		0			0
$838$	−8912.89	+	6475.59i	−0.367411	+	0.266940i
$839$	−3114.36	−	9585.01i	−0.128152	−	0.394412i	0.866310	−	0.499507i	$-0.166485\pi$
$839$	−3114.36	−	9585.01i	−0.128152	−	0.394412i	−0.994462	+	0.105095i	$0.966485\pi$
$840$		0			0
$841$	−18926.7	−	13751.0i	−0.776033	−	0.563821i
$842$	−5585.65	−	4058.21i	−0.228615	−	0.166099i
$843$		0			0
$844$	6564.70	+	20204.1i	0.267733	+	0.823997i
$845$	−6014.97	+	4370.13i	−0.244877	+	0.177914i
$846$		0			0
$847$	757.136	−	34780.9i	0.0307149	−	1.41096i
$848$	−8231.74			−0.333348
$849$		0			0
$850$	3.96390	+	12.1996i	0.000159954	+	0.000492287i
$851$	14369.3	−	44224.1i	0.578816	−	1.78141i
$852$		0			0
$853$	5770.57	+	4192.57i	0.231630	+	0.168289i	0.697546	−	0.716540i	$-0.254275\pi$
$853$	5770.57	+	4192.57i	0.231630	+	0.168289i	−0.465916	+	0.884829i	$0.654275\pi$
$854$	−1858.48	+	5719.82i	−0.0744684	+	0.229190i
$855$		0			0
$856$	6094.69	−	4428.05i	0.243355	−	0.176808i
$857$	−11652.5			−0.464458			−0.232229	−	0.972661i	$-0.574602\pi$
$857$	−11652.5			−0.464458			−0.232229	+	0.972661i	$0.574602\pi$
$858$		0			0
$859$	−38407.9			−1.52557			−0.762783	−	0.646655i	$-0.776167\pi$
$859$	−38407.9			−1.52557			−0.762783	+	0.646655i	$0.776167\pi$
$860$	−22815.9	+	16576.8i	−0.904671	+	0.657282i
$861$		0			0
$862$	−3445.91	+	10605.4i	−0.136158	+	0.419051i
$863$	−1891.32	−	1374.12i	−0.0746017	−	0.0542013i	0.549859	−	0.835257i	$-0.314681\pi$
$863$	−1891.32	−	1374.12i	−0.0746017	−	0.0542013i	−0.624461	+	0.781056i	$0.714681\pi$
$864$		0			0
$865$	2557.44	−	7870.98i	0.100527	−	0.309389i
$866$	−1348.09	−	4149.00i	−0.0528984	−	0.162805i
$867$		0			0
$868$	15203.4			0.594514
$869$	16673.3	−	16314.3i	0.650866	−	0.636851i
$870$		0			0
$871$	4419.38	−	3210.87i	0.171923	−	0.124909i
$872$	2314.16	+	7122.25i	0.0898707	+	0.276594i
$873$		0			0
$874$	−6085.05	−	4421.05i	−0.235503	−	0.171103i
$875$	29651.3	+	21542.9i	1.14560	+	0.832325i
$876$		0			0
$877$	−6096.23	−	18762.3i	−0.234726	−	0.722413i	−0.997158	−	0.0753442i	$-0.975994\pi$
$877$	−6096.23	−	18762.3i	−0.234726	−	0.722413i	0.762431	−	0.647069i	$-0.224006\pi$
$878$	5450.81	−	3960.24i	0.209517	−	0.152223i
$879$		0			0
$880$	9775.83	+	19713.6i	0.374481	+	0.755165i
$881$	−10669.9			−0.408036			−0.204018	−	0.978967i	$-0.565400\pi$
$881$	−10669.9			−0.408036			−0.204018	+	0.978967i	$0.565400\pi$
$882$		0			0
$883$	−9947.39	−	30614.9i	−0.379112	−	1.16679i	−0.940662	−	0.339345i	$-0.889795\pi$
$883$	−9947.39	−	30614.9i	−0.379112	−	1.16679i	0.561549	−	0.827443i	$-0.310205\pi$
$884$	−2936.84	+	9038.67i	−0.111738	+	0.343895i
$885$		0			0
$886$	3173.13	+	2305.41i	0.120320	+	0.0874174i
$887$	−193.766	+	596.350i	−0.00733486	+	0.0225744i	−0.954657	−	0.297708i	$-0.903778\pi$
$887$	−193.766	+	596.350i	−0.00733486	+	0.0225744i	0.947322	+	0.320282i	$0.103778\pi$
$888$		0			0
$889$	51180.6	−	37184.9i	1.93087	−	1.40286i
$890$	−1330.06			−0.0500941
$891$		0			0
$892$	−16738.4			−0.628301
$893$	22553.2	−	16385.9i	0.845146	−	0.614035i
$894$		0			0
$895$	8090.56	−	24900.2i	0.302165	−	0.929968i
$896$	24466.5	+	17775.9i	0.912241	+	0.662782i
$897$		0			0
$898$	1883.61	−	5797.15i	0.0699964	−	0.215427i
$899$	−5182.57	−	15950.3i	−0.192267	−	0.591738i
$900$		0			0
$901$	3561.97			0.131705
$902$	101.538	+	53.1358i	0.00374816	+	0.00196145i
$903$		0			0
$904$	−14826.2	+	10771.9i	−0.545477	+	0.396313i
$905$	−9713.04	−	29893.7i	−0.356765	−	1.09801i
$906$		0			0
$907$	−37985.9	−	27598.4i	−1.39063	−	1.01035i	−0.995796	−	0.0916008i	$-0.970802\pi$
$907$	−37985.9	−	27598.4i	−1.39063	−	1.01035i	−0.394835	−	0.918752i	$-0.629198\pi$
$908$	14561.9	+	10579.8i	0.532216	+	0.386678i
$909$		0			0
$910$	−3116.02	−	9590.11i	−0.113511	−	0.349351i
$911$	8224.34	−	5975.33i	0.299105	−	0.217312i	−0.428103	−	0.903730i	$-0.640818\pi$
$911$	8224.34	−	5975.33i	0.299105	−	0.217312i	0.727208	+	0.686418i	$0.240818\pi$
$912$		0			0
$913$	9324.48	+	4879.60i	0.338001	+	0.176880i
$914$	746.669			0.0270215
$915$		0			0
$916$	−1002.78	−	3086.23i	−0.0361710	−	0.111323i
$917$	−15171.4	+	46692.9i	−0.546353	+	1.68150i
$918$		0			0
$919$	18876.9	+	13714.9i	0.677576	+	0.492287i	0.872552	−	0.488520i	$-0.162463\pi$
$919$	18876.9	+	13714.9i	0.677576	+	0.492287i	−0.194977	+	0.980808i	$0.562463\pi$
$920$	5696.14	−	17530.9i	0.204126	−	0.628236i
$921$		0			0
$922$	−2702.15	+	1963.22i	−0.0965189	+	0.0701251i
$923$	33351.4			1.18936
$924$		0			0
$925$	239.852			0.00852571
$926$	3705.95	−	2692.53i	0.131517	−	0.0955529i
$927$		0			0
$928$	7812.90	−	24045.6i	0.276369	−	0.850578i
$929$	−24108.2	−	17515.6i	−0.851415	−	0.618589i	0.0741212	−	0.997249i	$-0.476385\pi$
$929$	−24108.2	−	17515.6i	−0.851415	−	0.618589i	−0.925536	+	0.378660i	$0.876385\pi$
$930$		0			0
$931$	−7446.96	+	22919.4i	−0.262153	+	0.806823i
$932$	−6481.58	−	19948.2i	−0.227802	−	0.701101i
$933$		0			0
$934$	6689.16			0.234343
$935$	−4230.11	−	8530.30i	−0.147957	−	0.298364i
$936$		0			0
$937$	−29762.2	+	21623.5i	−1.03766	+	0.753904i	−0.969827	−	0.243792i	$-0.921608\pi$
$937$	−29762.2	+	21623.5i	−1.03766	+	0.753904i	−0.0678330	+	0.997697i	$0.521608\pi$
$938$	533.348	+	1641.48i	0.0185655	+	0.0571387i
$939$		0			0
$940$	26893.4	+	19539.2i	0.933155	+	0.677977i
$941$	34764.8	+	25258.1i	1.20436	+	0.875018i	0.994706	−	0.102758i	$-0.0327668\pi$
$941$	34764.8	+	25258.1i	1.20436	+	0.875018i	0.209652	+	0.977776i	$0.432767\pi$
$942$		0			0
$943$	246.241	+	757.851i	0.00850339	+	0.0261707i
$944$	−33590.3	+	24404.8i	−1.15812	+	0.841427i
$945$		0			0
$946$	5632.01	−	5510.74i	0.193565	−	0.189397i
$947$	−12592.4			−0.432099			−0.216049	−	0.976382i	$-0.569317\pi$
$947$	−12592.4			−0.432099			−0.216049	+	0.976382i	$0.569317\pi$
$948$		0			0
$949$	5122.77	+	15766.3i	0.175229	+	0.539298i
$950$	11.9889	−	36.8981i	0.000409444	−	0.00126014i
$951$		0			0
$952$	−4992.71	−	3627.42i	−0.169973	−	0.123493i
$953$	507.019	−	1560.44i	0.0172340	−	0.0530407i	−0.942070	−	0.335417i	$-0.891123\pi$
$953$	507.019	−	1560.44i	0.0172340	−	0.0530407i	0.959304	+	0.282376i	$0.0911227\pi$
$954$		0			0
$955$	−33399.4	+	24266.1i	−1.13171	+	0.822233i
$956$	−26154.4			−0.884827
$957$		0			0
$958$	−3277.68			−0.110540
$959$	−11259.2	+	8180.26i	−0.379121	+	0.275448i
$960$		0			0
$961$	−7386.94	+	22734.7i	−0.247959	+	0.763139i
$962$	−7936.66	−	5766.32i	−0.265996	−	0.193258i
$963$		0			0
$964$	−3405.70	+	10481.7i	−0.113787	+	0.350199i
$965$	8530.74	+	26254.9i	0.284574	+	0.875830i
$966$		0			0
$967$	13354.3			0.444100			0.222050	−	0.975035i	$-0.428725\pi$
$967$	13354.3			0.444100			0.222050	+	0.975035i	$0.428725\pi$
$968$	−7648.16	−	11023.6i	−0.253947	−	0.366024i
$969$		0			0
$970$	−3716.15	+	2699.94i	−0.123009	+	0.0893709i
$971$	4498.14	+	13843.8i	0.148663	+	0.457539i	0.997464	−	0.0711746i	$-0.0226747\pi$
$971$	4498.14	+	13843.8i	0.148663	+	0.457539i	−0.848801	+	0.528713i	$0.822675\pi$
$972$		0			0
$973$	35324.1	+	25664.5i	1.16386	+	0.845597i
$974$	−3217.08	−	2337.34i	−0.105833	−	0.0768925i
$975$		0			0
$976$	−5949.32	−	18310.1i	−0.195116	−	0.600505i
$977$	14858.3	−	10795.2i	0.486549	−	0.353498i	−0.317307	−	0.948323i	$-0.602778\pi$
$977$	14858.3	−	10795.2i	0.486549	−	0.353498i	0.803856	+	0.594825i	$0.202778\pi$
$978$		0			0
$979$	−6659.74	+	980.631i	−0.217412	+	0.0320134i
$980$	−28736.4			−0.936686
$981$		0			0
$982$	−316.955	−	975.486i	−0.0102998	−	0.0316996i
$983$	−6560.07	+	20189.8i	−0.212852	+	0.655092i	0.786447	+	0.617658i	$0.211918\pi$
$983$	−6560.07	+	20189.8i	−0.212852	+	0.655092i	−0.999299	+	0.0374338i	$0.988082\pi$
$984$		0			0
$985$	15442.4	+	11219.5i	0.499527	+	0.362928i
$986$	−1023.59	+	3150.29i	−0.0330607	+	0.101750i
$987$		0			0
$988$	23254.8	−	16895.6i	0.748821	−	0.544050i
$989$	54788.9			1.76156
$990$		0			0
$991$	−11835.8			−0.379391			−0.189695	−	0.981843i	$-0.560750\pi$
$991$	−11835.8			−0.379391			−0.189695	+	0.981843i	$0.560750\pi$
$992$	7179.11	−	5215.93i	0.229775	−	0.166941i
$993$		0			0
$994$	−3256.28	+	10021.8i	−0.103906	+	0.319791i
$995$	−7444.52	−	5408.76i	−0.237193	−	0.172331i
$996$		0			0
$997$	−4218.71	+	12983.9i	−0.134010	+	0.412441i	−0.995435	−	0.0954448i	$-0.969573\pi$
$997$	−4218.71	+	12983.9i	−0.134010	+	0.412441i	0.861425	+	0.507885i	$0.169573\pi$
$998$	209.874	+	645.926i	0.00665676	+	0.0204874i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.4.f.b.91.1		8
3.2	odd	2		33.4.e.b.25.2	yes	8
11.2	odd	10		1089.4.a.z.1.2		4
11.4	even	5	inner	99.4.f.b.37.1		8
11.9	even	5		1089.4.a.bg.1.3		4
33.2	even	10		363.4.a.t.1.3		4
33.20	odd	10		363.4.a.p.1.2		4
33.26	odd	10		33.4.e.b.4.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.e.b.4.2	✓	8	33.26	odd	10
33.4.e.b.25.2	yes	8	3.2	odd	2
99.4.f.b.37.1		8	11.4	even	5	inner
99.4.f.b.91.1		8	1.1	even	1	trivial
363.4.a.p.1.2		4	33.20	odd	10
363.4.a.t.1.3		4	33.2	even	10
1089.4.a.z.1.2		4	11.2	odd	10
1089.4.a.bg.1.3		4	11.9	even	5

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.523388 + 0.380264i) q^{2} +(-2.34280 + 7.21040i) q^{4} +(-9.01441 - 6.54935i) q^{5} +(8.07696 - 24.8583i) q^{7} +(-3.11499 - 9.58696i) q^{8} +O(q^{10})\)	\(q+(-0.523388 + 0.380264i) q^{2} +(-2.34280 + 7.21040i) q^{4} +(-9.01441 - 6.54935i) q^{5} +(8.07696 - 24.8583i) q^{7} +(-3.11499 - 9.58696i) q^{8} +7.20851 q^{10} +(36.0937 - 5.31471i) q^{11} +(43.2976 - 31.4576i) q^{13} +(5.22533 + 16.0819i) q^{14} +(-43.7924 - 31.8170i) q^{16} +(18.9494 + 13.7676i) q^{17} +(-21.8916 - 67.3756i) q^{19} +(68.3424 - 49.6537i) q^{20} +(-16.8700 + 16.5068i) q^{22} -164.114 q^{23} +(-0.261588 - 0.805085i) q^{25} +(-10.6993 + 32.9290i) q^{26} +(160.316 + 116.476i) q^{28} +(67.5495 - 207.896i) q^{29} +(62.0698 - 45.0964i) q^{31} +115.662 q^{32} -15.1532 q^{34} +(-235.615 + 171.184i) q^{35} +(-87.5569 + 269.472i) q^{37} +(37.0783 + 26.9390i) q^{38} +(-34.7085 + 106.822i) q^{40} +(-1.50043 - 4.61784i) q^{41} -333.848 q^{43} +(-46.2392 + 272.701i) q^{44} +(85.8951 - 62.4064i) q^{46} +(121.601 + 374.250i) q^{47} +(-275.206 - 199.949i) q^{49} +(0.443057 + 0.321899i) q^{50} +(125.384 + 385.892i) q^{52} +(123.029 - 89.3860i) q^{53} +(-360.171 - 188.481i) q^{55} -263.475 q^{56} +(43.7007 + 134.497i) q^{58} +(237.027 - 729.494i) q^{59} +(287.741 + 209.056i) q^{61} +(-15.3381 + 47.2058i) q^{62} +(289.803 - 210.554i) q^{64} -596.329 q^{65} +102.070 q^{67} +(-143.665 + 104.378i) q^{68} +(58.2228 - 179.191i) q^{70} +(504.157 + 366.292i) q^{71} +(-95.7190 + 294.593i) q^{73} +(-56.6443 - 174.333i) q^{74} +537.093 q^{76} +(159.412 - 940.155i) q^{77} +(517.284 - 375.829i) q^{79} +(186.381 + 573.623i) q^{80} +(2.54130 + 1.84636i) q^{82} +(233.374 + 169.556i) q^{83} +(-80.6493 - 248.213i) q^{85} +(174.732 - 126.950i) q^{86} +(-163.383 - 329.473i) q^{88} -184.513 q^{89} +(-432.269 - 1330.39i) q^{91} +(384.486 - 1183.32i) q^{92} +(-205.958 - 149.637i) q^{94} +(-243.926 + 750.727i) q^{95} +(-515.522 + 374.549i) q^{97} +220.073 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{2} - 16 q^{4} - 9 q^{5} + 3 q^{7} - 36 q^{8}+O(q^{10}) \) 8 * q + 6 * q^2 - 16 * q^4 - 9 * q^5 + 3 * q^7 - 36 * q^8	\( 8 q + 6 q^{2} - 16 q^{4} - 9 q^{5} + 3 q^{7} - 36 q^{8} + 8 q^{10} + 87 q^{11} + 171 q^{13} - 12 q^{14} + 44 q^{16} - 36 q^{17} + 324 q^{19} + 87 q^{20} - 521 q^{22} + 84 q^{23} + 263 q^{25} + 774 q^{26} + 387 q^{28} - 393 q^{29} + 15 q^{31} - 102 q^{32} - 712 q^{34} - 1002 q^{35} - 747 q^{37} + 36 q^{38} + 41 q^{40} - 159 q^{41} - 644 q^{43} - 219 q^{44} + 753 q^{46} + 351 q^{47} - 1967 q^{49} - 330 q^{50} + 2871 q^{52} + 531 q^{53} - 716 q^{55} - 1470 q^{56} - 1205 q^{58} + 1002 q^{59} + 1449 q^{61} - 99 q^{62} - 1118 q^{64} + 954 q^{65} - 518 q^{67} - 873 q^{68} + 26 q^{70} - 429 q^{71} + 2547 q^{73} - 468 q^{74} - 2276 q^{76} + 2697 q^{77} + 2805 q^{79} + 1620 q^{80} - 1631 q^{82} + 2553 q^{83} - 197 q^{85} + 1713 q^{86} + 2866 q^{88} - 1788 q^{89} + 2885 q^{91} - 423 q^{92} + 1159 q^{94} - 3009 q^{95} + 9 q^{97} - 5550 q^{98}+O(q^{100}) \) 8 * q + 6 * q^2 - 16 * q^4 - 9 * q^5 + 3 * q^7 - 36 * q^8 + 8 * q^10 + 87 * q^11 + 171 * q^13 - 12 * q^14 + 44 * q^16 - 36 * q^17 + 324 * q^19 + 87 * q^20 - 521 * q^22 + 84 * q^23 + 263 * q^25 + 774 * q^26 + 387 * q^28 - 393 * q^29 + 15 * q^31 - 102 * q^32 - 712 * q^34 - 1002 * q^35 - 747 * q^37 + 36 * q^38 + 41 * q^40 - 159 * q^41 - 644 * q^43 - 219 * q^44 + 753 * q^46 + 351 * q^47 - 1967 * q^49 - 330 * q^50 + 2871 * q^52 + 531 * q^53 - 716 * q^55 - 1470 * q^56 - 1205 * q^58 + 1002 * q^59 + 1449 * q^61 - 99 * q^62 - 1118 * q^64 + 954 * q^65 - 518 * q^67 - 873 * q^68 + 26 * q^70 - 429 * q^71 + 2547 * q^73 - 468 * q^74 - 2276 * q^76 + 2697 * q^77 + 2805 * q^79 + 1620 * q^80 - 1631 * q^82 + 2553 * q^83 - 197 * q^85 + 1713 * q^86 + 2866 * q^88 - 1788 * q^89 + 2885 * q^91 - 423 * q^92 + 1159 * q^94 - 3009 * q^95 + 9 * q^97 - 5550 * q^98

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