LMFDB - Embedded newform 225.4.h.a.136.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(46,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("225.46");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.h (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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			136.1
Character	$\chi$	$=$	225.136
Dual form			225.4.h.a.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.87763 + 2.81726i) q^{2} +(4.62691 - 14.2402i) q^{4} +(-7.51887 - 8.27445i) q^{5} +0.140520 q^{7} +(10.3279 + 31.7859i) q^{8} +O(q^{10})$	\(q+(-3.87763 + 2.81726i) q^{2} +(4.62691 - 14.2402i) q^{4} +(-7.51887 - 8.27445i) q^{5} +0.140520 q^{7} +(10.3279 + 31.7859i) q^{8} +(52.4667 + 10.9026i) q^{10} +(38.3073 - 27.8319i) q^{11} +(-27.7836 - 20.1859i) q^{13} +(-0.544885 + 0.395882i) q^{14} +(-32.6895 - 23.7503i) q^{16} +(-5.10385 - 15.7080i) q^{17} +(28.1212 + 86.5481i) q^{19} +(-152.619 + 68.7848i) q^{20} +(-70.1318 + 215.843i) q^{22} +(-130.722 + 94.9752i) q^{23} +(-11.9331 + 124.429i) q^{25} +164.604 q^{26} +(0.650173 - 2.00103i) q^{28} +(3.81101 - 11.7291i) q^{29} +(-102.914 - 316.738i) q^{31} -73.7042 q^{32} +(64.0445 + 46.5310i) q^{34} +(-1.05655 - 1.16273i) q^{35} +(227.659 + 165.404i) q^{37} +(-352.872 - 256.377i) q^{38} +(185.357 - 324.451i) q^{40} +(101.620 + 73.8315i) q^{41} -529.821 q^{43} +(-219.086 - 674.278i) q^{44} +(239.322 - 736.558i) q^{46} +(-23.1983 + 71.3970i) q^{47} -342.980 q^{49} +(-304.278 - 516.109i) q^{50} +(-416.003 + 302.244i) q^{52} +(77.0767 - 237.218i) q^{53} +(-518.321 - 107.707i) q^{55} +(1.45127 + 4.46655i) q^{56} +(18.2662 + 56.2177i) q^{58} +(-217.273 - 157.858i) q^{59} +(-299.213 + 217.391i) q^{61} +(1291.40 + 938.256i) q^{62} +(547.314 - 397.647i) q^{64} +(41.8736 + 381.669i) q^{65} +(-54.5434 - 167.867i) q^{67} -247.300 q^{68} +(7.37262 + 1.53204i) q^{70} +(-223.142 + 686.762i) q^{71} +(1.97619 - 1.43579i) q^{73} -1348.77 q^{74} +1362.57 q^{76} +(5.38294 - 3.91094i) q^{77} +(187.778 - 577.921i) q^{79} +(49.2675 + 449.064i) q^{80} -602.049 q^{82} +(392.005 + 1206.47i) q^{83} +(-91.6001 + 160.338i) q^{85} +(2054.45 - 1492.65i) q^{86} +(1280.29 + 930.187i) q^{88} +(-1082.09 + 786.182i) q^{89} +(-3.90415 - 2.83653i) q^{91} +(747.623 + 2300.95i) q^{92} +(-111.190 - 342.207i) q^{94} +(504.698 - 883.431i) q^{95} +(-442.269 + 1361.16i) q^{97} +(1329.95 - 966.266i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10}) $ 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8	$ 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8} + 165 q^{10} - 19 q^{11} + 4 q^{13} + 24 q^{14} - 66 q^{16} - 208 q^{17} + 42 q^{19} - 295 q^{20} - 89 q^{22} - 32 q^{23} + 95 q^{25} - 206 q^{26} - 482 q^{28} + 716 q^{29} + 637 q^{31} + 844 q^{32} - 90 q^{34} - 430 q^{35} + 216 q^{37} - 2314 q^{38} - 500 q^{40} + 38 q^{41} - 1392 q^{43} - 603 q^{44} + 1622 q^{46} + 536 q^{47} + 162 q^{49} + 2265 q^{50} - 1922 q^{52} - 1672 q^{53} - 1000 q^{55} - 3000 q^{56} - 827 q^{58} - 973 q^{59} - 2712 q^{61} - 1057 q^{62} + 4439 q^{64} + 4360 q^{65} + 2768 q^{67} + 1370 q^{68} + 3230 q^{70} + 1074 q^{71} - 1018 q^{73} + 1414 q^{74} - 11408 q^{76} - 1607 q^{77} - 1820 q^{79} + 1290 q^{80} + 1772 q^{82} - 4045 q^{83} + 1850 q^{85} + 3986 q^{86} + 2407 q^{88} - 4542 q^{89} + 4412 q^{91} + 1089 q^{92} + 5137 q^{94} + 720 q^{95} - 5977 q^{97} + 10689 q^{98}+O(q^{100}) $ 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8 + 165 * q^10 - 19 * q^11 + 4 * q^13 + 24 * q^14 - 66 * q^16 - 208 * q^17 + 42 * q^19 - 295 * q^20 - 89 * q^22 - 32 * q^23 + 95 * q^25 - 206 * q^26 - 482 * q^28 + 716 * q^29 + 637 * q^31 + 844 * q^32 - 90 * q^34 - 430 * q^35 + 216 * q^37 - 2314 * q^38 - 500 * q^40 + 38 * q^41 - 1392 * q^43 - 603 * q^44 + 1622 * q^46 + 536 * q^47 + 162 * q^49 + 2265 * q^50 - 1922 * q^52 - 1672 * q^53 - 1000 * q^55 - 3000 * q^56 - 827 * q^58 - 973 * q^59 - 2712 * q^61 - 1057 * q^62 + 4439 * q^64 + 4360 * q^65 + 2768 * q^67 + 1370 * q^68 + 3230 * q^70 + 1074 * q^71 - 1018 * q^73 + 1414 * q^74 - 11408 * q^76 - 1607 * q^77 - 1820 * q^79 + 1290 * q^80 + 1772 * q^82 - 4045 * q^83 + 1850 * q^85 + 3986 * q^86 + 2407 * q^88 - 4542 * q^89 + 4412 * q^91 + 1089 * q^92 + 5137 * q^94 + 720 * q^95 - 5977 * q^97 + 10689 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−3.87763	+	2.81726i	−1.37095	+	0.996053i	−0.373287	+	0.927716i	$0.621769\pi$
$2$	−3.87763	+	2.81726i	−1.37095	+	0.996053i	−0.997662	+	0.0683371i	$0.978231\pi$
$3$		0			0
$3$		0			0
$4$	4.62691	−	14.2402i	0.578364	−	1.78002i
$5$	−7.51887	−	8.27445i	−0.672509	−	0.740089i
$5$	−7.51887	−	8.27445i	−0.672509	−	0.740089i
$6$		0			0
$7$	0.140520			0.00758737			0.00379368	−	0.999993i	$-0.498792\pi$
$7$	0.140520			0.00758737			0.00379368	+	0.999993i	$0.498792\pi$
$8$	10.3279	+	31.7859i	0.456431	+	1.40475i
$9$		0			0
$10$	52.4667	+	10.9026i	1.65914	+	0.344771i
$11$	38.3073	−	27.8319i	1.05001	−	0.762875i	0.0777938	−	0.996969i	$-0.475212\pi$
$11$	38.3073	−	27.8319i	1.05001	−	0.762875i	0.972214	+	0.234094i	$0.0752124\pi$
$12$		0			0
$13$	−27.7836	−	20.1859i	−0.592752	−	0.430660i	0.250547	−	0.968104i	$-0.419390\pi$
$13$	−27.7836	−	20.1859i	−0.592752	−	0.430660i	−0.843299	+	0.537445i	$0.819390\pi$
$14$	−0.544885	+	0.395882i	−0.0104019	+	0.00755742i
$15$		0			0
$16$	−32.6895	−	23.7503i	−0.510774	−	0.371099i
$17$	−5.10385	−	15.7080i	−0.0728156	−	0.224103i	0.908025	−	0.418916i	$-0.137590\pi$
$17$	−5.10385	−	15.7080i	−0.0728156	−	0.224103i	−0.980840	+	0.194813i	$0.937590\pi$
$18$		0			0
$19$	28.1212	+	86.5481i	0.339549	+	1.04503i	0.964437	+	0.264311i	$0.0851446\pi$
$19$	28.1212	+	86.5481i	0.339549	+	1.04503i	−0.624888	+	0.780714i	$0.714855\pi$
$20$	−152.619	+	68.7848i	−1.70633	+	0.769038i
$21$		0			0
$22$	−70.1318	+	215.843i	−0.679643	+	2.09173i
$23$	−130.722	+	94.9752i	−1.18511	+	0.861031i	−0.992739	−	0.120292i	$-0.961617\pi$
$23$	−130.722	+	94.9752i	−1.18511	+	0.861031i	−0.192368	+	0.981323i	$0.561617\pi$
$24$		0			0
$25$	−11.9331	+	124.429i	−0.0954645	+	0.995433i
$26$	164.604			1.24159
$27$		0			0
$28$	0.650173	−	2.00103i	0.00438826	−	0.0135057i
$29$	3.81101	−	11.7291i	0.0244030	−	0.0751048i	−0.938113	−	0.346328i	$-0.887428\pi$
$29$	3.81101	−	11.7291i	0.0244030	−	0.0751048i	0.962516	+	0.271224i	$0.0874283\pi$
$30$		0			0
$31$	−102.914	−	316.738i	−0.596257	−	1.83509i	−0.548366	−	0.836239i	$-0.684750\pi$
$31$	−102.914	−	316.738i	−0.596257	−	1.83509i	−0.0478915	−	0.998853i	$-0.515250\pi$
$32$	−73.7042			−0.407162
$33$		0			0
$34$	64.0445	+	46.5310i	0.323045	+	0.234706i
$35$	−1.05655	−	1.16273i	−0.00510257	−	0.00561533i
$36$		0			0
$37$	227.659	+	165.404i	1.01154	+	0.734926i	0.964531	−	0.263968i	$-0.0850315\pi$
$37$	227.659	+	165.404i	1.01154	+	0.734926i	0.0470077	+	0.998895i	$0.485031\pi$
$38$	−352.872	−	256.377i	−1.50641	−	1.09447i
$39$		0			0
$40$	185.357	−	324.451i	0.732687	−	1.28251i
$41$	101.620	+	73.8315i	0.387084	+	0.281233i	0.764259	−	0.644909i	$-0.223105\pi$
$41$	101.620	+	73.8315i	0.387084	+	0.281233i	−0.377176	+	0.926142i	$0.623105\pi$
$42$		0			0
$43$	−529.821			−1.87900			−0.939500	−	0.342549i	$-0.888710\pi$
$43$	−529.821			−1.87900			−0.939500	+	0.342549i	$0.888710\pi$
$44$	−219.086	−	674.278i	−0.750647	−	2.31025i
$45$		0			0
$46$	239.322	−	736.558i	0.767090	−	2.36086i
$47$	−23.1983	+	71.3970i	−0.0719962	+	0.221581i	−0.980579	−	0.196122i	$-0.937165\pi$
$47$	−23.1983	+	71.3970i	−0.0719962	+	0.221581i	0.908583	+	0.417704i	$0.137165\pi$
$48$		0			0
$49$	−342.980			−0.999942
$50$	−304.278	−	516.109i	−0.860627	−	1.45978i
$51$		0			0
$52$	−416.003	+	302.244i	−1.10941	+	0.806033i
$53$	77.0767	−	237.218i	0.199760	−	0.614799i	−0.800127	−	0.599830i	$-0.795235\pi$
$53$	77.0767	−	237.218i	0.199760	−	0.614799i	0.999888	−	0.0149695i	$-0.00476512\pi$
$54$		0			0
$55$	−518.321	−	107.707i	−1.27074	−	0.264059i
$56$	1.45127	+	4.46655i	0.00346311	+	0.0106584i
$57$		0			0
$58$	18.2662	+	56.2177i	0.0413530	+	0.127272i
$59$	−217.273	−	157.858i	−0.479432	−	0.348328i	0.321674	−	0.946851i	$-0.395755\pi$
$59$	−217.273	−	157.858i	−0.479432	−	0.348328i	−0.801106	+	0.598523i	$0.795755\pi$
$60$		0			0
$61$	−299.213	+	217.391i	−0.628038	+	0.456296i	−0.855720	−	0.517439i	$-0.826885\pi$
$61$	−299.213	+	217.391i	−0.628038	+	0.456296i	0.227682	+	0.973736i	$0.426885\pi$
$62$	1291.40	+	938.256i	2.64529	+	1.92191i
$63$		0			0
$64$	547.314	−	397.647i	1.06897	−	0.776654i
$65$	41.8736	+	381.669i	0.0799042	+	0.728312i
$66$		0			0
$67$	−54.5434	−	167.867i	−0.0994558	−	0.306094i	0.888933	−	0.458036i	$-0.151447\pi$
$67$	−54.5434	−	167.867i	−0.0994558	−	0.306094i	−0.988389	+	0.151943i	$0.951447\pi$
$68$	−247.300			−0.441022
$69$		0			0
$70$	7.37262	+	1.53204i	0.0125885	+	0.00261590i
$71$	−223.142	+	686.762i	−0.372988	+	1.14794i	0.571839	+	0.820366i	$0.306230\pi$
$71$	−223.142	+	686.762i	−0.372988	+	1.14794i	−0.944826	+	0.327572i	$0.893770\pi$
$72$		0			0
$73$	1.97619	−	1.43579i	0.00316844	−	0.00230201i	−0.586200	−	0.810166i	$-0.699377\pi$
$73$	1.97619	−	1.43579i	0.00316844	−	0.00230201i	0.589368	+	0.807864i	$0.299377\pi$
$74$	−1348.77			−2.11879
$75$		0			0
$76$	1362.57			2.05655
$77$	5.38294	−	3.91094i	0.00796679	−	0.00578822i
$78$		0			0
$79$	187.778	−	577.921i	0.267426	−	0.823053i	−0.723698	−	0.690116i	$-0.757559\pi$
$79$	187.778	−	577.921i	0.267426	−	0.823053i	0.991125	−	0.132937i	$-0.0424407\pi$
$80$	49.2675	+	449.064i	0.0688535	+	0.627586i
$81$		0			0
$82$	−602.049			−0.810795
$83$	392.005	+	1206.47i	0.518411	+	1.59551i	0.776988	+	0.629515i	$0.216747\pi$
$83$	392.005	+	1206.47i	0.518411	+	1.59551i	−0.258577	+	0.965991i	$0.583253\pi$
$84$		0			0
$85$	−91.6001	+	160.338i	−0.116887	+	0.204601i
$86$	2054.45	−	1492.65i	2.57601	−	1.87158i
$87$		0			0
$88$	1280.29	+	930.187i	1.55091	+	1.12680i
$89$	−1082.09	+	786.182i	−1.28878	+	0.936350i	−0.999780	−	0.0209802i	$-0.993321\pi$
$89$	−1082.09	+	786.182i	−1.28878	+	0.936350i	−0.288996	+	0.957330i	$0.593321\pi$
$90$		0			0
$91$	−3.90415	−	2.83653i	−0.00449743	−	0.00326757i
$92$	747.623	+	2300.95i	0.847229	+	2.60750i
$93$		0			0
$94$	−111.190	−	342.207i	−0.122004	−	0.375489i
$95$	504.698	−	883.431i	0.545063	−	0.954086i
$96$		0			0
$97$	−442.269	+	1361.16i	−0.462944	+	1.42480i	0.398605	+	0.917122i	$0.369494\pi$
$97$	−442.269	+	1361.16i	−0.462944	+	1.42480i	−0.861550	+	0.507673i	$0.830506\pi$
$98$	1329.95	−	966.266i	1.37087	−	0.995996i
$99$		0			0
$100$	1716.68	+	745.651i	1.71668	+	0.745651i
$101$	374.102			0.368559			0.184280	−	0.982874i	$-0.441005\pi$
$101$	374.102			0.368559			0.184280	+	0.982874i	$0.441005\pi$
$102$		0			0
$103$	−623.556	+	1919.11i	−0.596512	+	1.83588i	−0.0494621	+	0.998776i	$0.515751\pi$
$103$	−623.556	+	1919.11i	−0.596512	+	1.83588i	−0.547050	+	0.837100i	$0.684249\pi$
$104$	354.683	−	1091.60i	0.334419	−	1.02923i
$105$		0			0
$106$	369.430	+	1136.99i	0.338511	+	1.04183i
$107$	−1679.71			−1.51761			−0.758804	−	0.651319i	$-0.774216\pi$
$107$	−1679.71			−1.51761			−0.758804	+	0.651319i	$0.774216\pi$
$108$		0			0
$109$	−16.3651	−	11.8899i	−0.0143806	−	0.0104481i	0.580572	−	0.814209i	$-0.302829\pi$
$109$	−16.3651	−	11.8899i	−0.0143806	−	0.0104481i	−0.594952	+	0.803761i	$0.702829\pi$
$110$	2313.30	−	1042.60i	2.00513	−	0.903707i
$111$		0			0
$112$	−4.59354	−	3.33740i	−0.00387543	−	0.00281567i
$113$	−519.810	−	377.664i	−0.432740	−	0.314404i	0.350004	−	0.936748i	$-0.386180\pi$
$113$	−519.810	−	377.664i	−0.432740	−	0.314404i	−0.782744	+	0.622344i	$0.786180\pi$
$114$		0			0
$115$	1768.75	+	367.548i	1.43423	+	0.298035i
$116$	−149.391	−	108.539i	−0.119574	−	0.0868757i
$117$		0			0
$118$	1287.23			1.00423
$119$	−0.717193	−	2.20729i	−0.000552479	−	0.00170035i
$120$		0			0
$121$	281.534	−	866.472i	0.211521	−	0.650993i
$122$	547.790	−	1685.92i	0.406513	−	1.25112i
$123$		0			0
$124$	−4986.58			−3.61135
$125$	1119.31	−	836.827i	0.800910	−	0.598785i
$126$		0			0
$127$	959.422	−	697.061i	0.670354	−	0.487041i	−0.199790	−	0.979839i	$-0.564026\pi$
$127$	959.422	−	697.061i	0.670354	−	0.487041i	0.870144	+	0.492798i	$0.164026\pi$
$128$	−819.798	+	2523.08i	−0.566099	+	1.74227i
$129$		0			0
$130$	−1237.63	−	1362.00i	−0.834982	−	0.918889i
$131$	68.9399	+	212.175i	0.0459794	+	0.141510i	0.971411	−	0.237406i	$-0.0762970\pi$
$131$	68.9399	+	212.175i	0.0459794	+	0.141510i	−0.925431	+	0.378916i	$0.876297\pi$
$132$		0			0
$133$	3.95159	+	12.1617i	0.00257629	+	0.00792900i
$134$	684.426	+	497.265i	0.441234	+	0.320575i
$135$		0			0
$136$	446.582	−	324.461i	0.281574	−	0.204575i
$137$	−1277.88	−	928.434i	−0.796910	−	0.578989i	0.113096	−	0.993584i	$-0.463923\pi$
$137$	−1277.88	−	928.434i	−0.796910	−	0.578989i	−0.910006	+	0.414595i	$0.863923\pi$
$138$		0			0
$139$	−1266.31	+	920.031i	−0.772715	+	0.561410i	−0.902784	−	0.430095i	$-0.858480\pi$
$139$	−1266.31	+	920.031i	−0.772715	+	0.561410i	0.130069	+	0.991505i	$0.458480\pi$
$140$	−21.4460	+	9.66565i	−0.0129465	+	0.00583497i
$141$		0			0
$142$	−1069.52	−	3291.66i	−0.632060	−	1.94528i
$143$	−1626.13			−0.950934
$144$		0			0
$145$	−125.706	+	56.6556i	−0.0719955	+	0.0324482i
$146$	−3.61796	+	11.1349i	−0.00205085	+	0.00631187i
$147$		0			0
$148$	3408.74	−	2476.59i	1.89322	−	1.37551i
$149$	−192.635			−0.105915			−0.0529574	−	0.998597i	$-0.516865\pi$
$149$	−192.635			−0.105915			−0.0529574	+	0.998597i	$0.516865\pi$
$150$		0			0
$151$	1052.83			0.567406			0.283703	−	0.958912i	$-0.408437\pi$
$151$	1052.83			0.567406			0.283703	+	0.958912i	$0.408437\pi$
$152$	−2460.57	+	1787.71i	−1.31302	+	0.953964i
$153$		0			0
$154$	−9.85492	+	30.3303i	−0.00515670	+	0.0158707i
$155$	−1847.03	+	3233.07i	−0.957143	+	1.67540i
$156$		0			0
$157$	2045.26			1.03968			0.519838	−	0.854265i	$-0.325992\pi$
$157$	2045.26			1.03968			0.519838	+	0.854265i	$0.325992\pi$
$158$	900.022	+	2769.98i	0.453177	+	1.39473i
$159$		0			0
$160$	554.172	+	609.862i	0.273820	+	0.301336i
$161$	−18.3691	+	13.3459i	−0.00899184	+	0.00653296i
$162$		0			0
$163$	−686.057	−	498.449i	−0.329669	−	0.239519i	0.410621	−	0.911806i	$-0.365312\pi$
$163$	−686.057	−	498.449i	−0.329669	−	0.239519i	−0.740290	+	0.672287i	$0.765312\pi$
$164$	1521.56	−	1105.48i	0.724475	−	0.526362i
$165$		0			0
$166$	−4918.99	−	3573.85i	−2.29992	−	1.67099i
$167$	−609.520	−	1875.91i	−0.282432	−	0.869235i	−0.987157	−	0.159755i	$-0.948930\pi$
$167$	−609.520	−	1875.91i	−0.282432	−	0.869235i	0.704725	−	0.709480i	$-0.251070\pi$
$168$		0			0
$169$	−314.456	−	967.796i	−0.143130	−	0.440508i
$170$	−96.5236	−	879.794i	−0.0435472	−	0.396924i
$171$		0			0
$172$	−2451.44	+	7544.74i	−1.08675	+	3.34466i
$173$	2190.53	−	1591.51i	0.962676	−	0.699425i	0.00890552	−	0.999960i	$-0.497165\pi$
$173$	2190.53	−	1591.51i	0.962676	−	0.699425i	0.953771	+	0.300535i	$0.0971652\pi$
$174$		0			0
$175$	−1.67683	+	17.4848i	−0.000724324	+	0.00755272i
$176$	−1913.26			−0.819419
$177$		0			0
$178$	1981.05	−	6097.05i	0.834191	−	2.56738i
$179$	−967.918	+	2978.95i	−0.404165	+	1.24389i	0.517425	+	0.855729i	$0.326891\pi$
$179$	−967.918	+	2978.95i	−0.404165	+	1.24389i	−0.921590	+	0.388164i	$0.873109\pi$
$180$		0			0
$181$	97.9741	+	301.533i	0.0402340	+	0.123828i	0.969156	−	0.246448i	$-0.0792634\pi$
$181$	97.9741	+	301.533i	0.0402340	+	0.123828i	−0.928922	+	0.370275i	$0.879263\pi$
$182$	23.1301			0.00942042
$183$		0			0
$184$	−4368.95	−	3174.23i	−1.75045	−	1.27178i
$185$	−343.113	−	3127.41i	−0.136358	−	1.24287i
$186$		0			0
$187$	−632.699	−	459.682i	−0.247420	−	0.179761i
$188$	909.369	+	660.695i	0.352779	+	0.256309i
$189$		0			0
$190$	531.826	+	4847.49i	0.203067	+	1.85091i
$191$	1358.71	+	987.161i	0.514727	+	0.373971i	0.814614	−	0.580004i	$-0.196949\pi$
$191$	1358.71	+	987.161i	0.514727	+	0.373971i	−0.299887	+	0.953975i	$0.596949\pi$
$192$		0			0
$193$	−1449.62			−0.540653			−0.270326	−	0.962769i	$-0.587132\pi$
$193$	−1449.62			−0.540653			−0.270326	+	0.962769i	$0.587132\pi$
$194$	−2119.80	−	6524.08i	−0.784499	−	2.41444i
$195$		0			0
$196$	−1586.94	+	4884.09i	−0.578330	+	1.77992i
$197$	327.751	−	1008.71i	0.118535	−	0.364812i	−0.874133	−	0.485686i	$-0.838570\pi$
$197$	327.751	−	1008.71i	0.118535	−	0.364812i	0.992668	+	0.120874i	$0.0385698\pi$
$198$		0			0
$199$	−183.077			−0.0652159			−0.0326080	−	0.999468i	$-0.510381\pi$
$199$	−183.077			−0.0652159			−0.0326080	+	0.999468i	$0.510381\pi$
$200$	−4078.33	+	905.783i	−1.44191	+	0.320243i
$201$		0			0
$202$	−1450.63	+	1053.94i	−0.505276	+	0.367105i
$203$	0.535524	−	1.64817i	0.000185155	−	0.000569848i
$204$		0			0
$205$	−153.155	−	1395.98i	−0.0521797	−	0.475608i
$206$	−2988.71	−	9198.31i	−1.01084	−	3.11105i
$207$		0			0
$208$	428.809	+	1319.74i	0.142945	+	0.439940i
$209$	3486.04	+	2532.76i	1.15375	+	0.838251i
$210$		0			0
$211$	3968.01	−	2882.93i	1.29464	−	0.940611i	0.294751	−	0.955574i	$-0.404763\pi$
$211$	3968.01	−	2882.93i	1.29464	−	0.940611i	0.999888	+	0.0149634i	$0.00476319\pi$
$212$	−3021.39	−	2195.17i	−0.978821	−	0.711155i
$213$		0			0
$214$	6513.31	−	4732.20i	2.08056	−	1.51162i
$215$	3983.66	+	4383.98i	1.26364	+	1.39063i
$216$		0			0
$217$	−14.4615	−	44.5080i	−0.00452402	−	0.0139235i
$218$	96.9547			0.0301220
$219$		0			0
$220$	−3932.00	+	6882.63i	−1.20498	+	2.10921i
$221$	−175.278	+	539.451i	−0.0533507	+	0.164196i
$222$		0			0
$223$	3913.55	−	2843.36i	1.17521	−	0.853837i	0.183583	−	0.983004i	$-0.441230\pi$
$223$	3913.55	−	2843.36i	1.17521	−	0.853837i	0.991623	+	0.129167i	$0.0412303\pi$
$224$	−10.3569			−0.00308929
$225$		0			0
$226$	3079.61			0.906428
$227$	−36.2582	+	26.3431i	−0.0106015	+	0.00770244i	−0.593073	−	0.805148i	$-0.702086\pi$
$227$	−36.2582	+	26.3431i	−0.0106015	+	0.00770244i	0.582472	+	0.812851i	$0.302086\pi$
$228$		0			0
$229$	−1285.44	+	3956.19i	−0.370937	+	1.14163i	0.575243	+	0.817983i	$0.304908\pi$
$229$	−1285.44	+	3956.19i	−0.370937	+	1.14163i	−0.946179	+	0.323643i	$0.895092\pi$
$230$	−7894.04	+	3557.83i	−2.26312	+	1.01998i
$231$		0			0
$232$	412.179			0.116642
$233$	−910.177	−	2801.24i	−0.255913	−	0.787619i	−0.993648	−	0.112529i	$-0.964105\pi$
$233$	−910.177	−	2801.24i	−0.255913	−	0.787619i	0.737736	−	0.675090i	$-0.235895\pi$
$234$		0			0
$235$	765.196	−	344.872i	0.212408	−	0.0957318i
$236$	−3253.22	+	2363.61i	−0.897317	+	0.651939i
$237$		0			0
$238$	8.99953	+	6.53854i	0.00245106	+	0.00178080i
$239$	1759.24	−	1278.16i	0.476133	−	0.345931i	−0.323694	−	0.946162i	$-0.604925\pi$
$239$	1759.24	−	1278.16i	0.476133	−	0.345931i	0.799827	+	0.600231i	$0.204925\pi$
$240$		0			0
$241$	−1861.30	−	1352.31i	−0.497496	−	0.361452i	0.310564	−	0.950553i	$-0.399482\pi$
$241$	−1861.30	−	1352.31i	−0.497496	−	0.361452i	−0.808060	+	0.589100i	$0.799482\pi$
$242$	1349.40	+	4153.01i	0.358440	+	1.10316i
$243$		0			0
$244$	1711.25	+	5266.69i	0.448982	+	1.38182i
$245$	2578.83	+	2837.97i	0.672470	+	0.740047i
$246$		0			0
$247$	965.748	−	2972.27i	0.248782	−	0.765671i
$248$	9004.91	−	6542.45i	2.30569	−	1.67519i
$249$		0			0
$250$	−1982.69	+	6398.29i	−0.501586	+	1.61865i
$251$	−3368.55			−0.847096			−0.423548	−	0.905874i	$-0.639215\pi$
$251$	−3368.55			−0.847096			−0.423548	+	0.905874i	$0.639215\pi$
$252$		0			0
$253$	−2364.27	+	7276.49i	−0.587513	+	1.80818i
$254$	−1756.48	+	5405.89i	−0.433903	+	1.33542i
$255$		0			0
$256$	−2256.86	−	6945.91i	−0.550992	−	1.69578i
$257$	−404.905			−0.0982772			−0.0491386	−	0.998792i	$-0.515648\pi$
$257$	−404.905			−0.0982772			−0.0491386	+	0.998792i	$0.515648\pi$
$258$		0			0
$259$	31.9907	+	23.2426i	0.00767492	+	0.00557616i
$260$	5628.78	+	1169.66i	1.34262	+	0.278998i
$261$		0			0
$262$	−865.077	−	628.515i	−0.203987	−	0.148205i
$263$	−1225.42	−	890.319i	−0.287310	−	0.208743i	0.434790	−	0.900532i	$-0.356823\pi$
$263$	−1225.42	−	890.319i	−0.287310	−	0.208743i	−0.722100	+	0.691789i	$0.756823\pi$
$264$		0			0
$265$	−2542.38	+	1145.84i	−0.589347	+	0.265617i
$266$	−49.5856	−	36.0261i	−0.0114297	−	0.00830413i
$267$		0			0
$268$	−2642.83			−0.602374
$269$	584.624	+	1799.29i	0.132510	+	0.407823i	0.995194	−	0.0979190i	$-0.0312186\pi$
$269$	584.624	+	1799.29i	0.132510	+	0.407823i	−0.862685	+	0.505742i	$0.831219\pi$
$270$		0			0
$271$	−647.179	+	1991.81i	−0.145068	+	0.446472i	−0.997020	−	0.0771477i	$-0.975419\pi$
$271$	−647.179	+	1991.81i	−0.145068	+	0.446472i	0.851952	+	0.523620i	$0.175419\pi$
$272$	−206.229	+	634.707i	−0.0459722	+	0.141488i
$273$		0			0
$274$	7570.79			1.66923
$275$	3005.97	+	5098.66i	0.659153	+	1.11804i
$276$		0			0
$277$	1207.64	−	877.405i	0.261950	−	0.190318i	−0.449056	−	0.893504i	$-0.648240\pi$
$277$	1207.64	−	877.405i	0.261950	−	0.190318i	0.711006	+	0.703185i	$0.248240\pi$
$278$	2318.33	−	7135.08i	0.500159	−	1.53933i
$279$		0			0
$280$	26.0463	−	45.5919i	0.00555917	−	0.00973085i
$281$	−639.509	−	1968.21i	−0.135765	−	0.417841i	0.859943	−	0.510389i	$-0.170499\pi$
$281$	−639.509	−	1968.21i	−0.135765	−	0.417841i	−0.995708	+	0.0925483i	$0.970499\pi$
$282$		0			0
$283$	1050.32	+	3232.55i	0.220618	+	0.678992i	0.998707	+	0.0508383i	$0.0161893\pi$
$283$	1050.32	+	3232.55i	0.220618	+	0.678992i	−0.778089	+	0.628154i	$0.783811\pi$
$284$	8747.13	+	6355.17i	1.82763	+	1.32785i
$285$		0			0
$286$	6305.52	−	4581.23i	1.30368	−	0.947180i
$287$	14.2797	+	10.3748i	0.00293695	+	0.00213382i
$288$		0			0
$289$	3754.01	−	2727.45i	0.764097	−	0.555149i
$290$	327.829	−	573.837i	0.0663821	−	0.116196i
$291$		0			0
$292$	−11.3022	−	34.7846i	−0.00226511	−	0.00697128i
$293$	−7677.60			−1.53082			−0.765410	−	0.643543i	$-0.777464\pi$
$293$	−7677.60			−1.53082			−0.765410	+	0.643543i	$0.777464\pi$
$294$		0			0
$295$	327.459	+	2984.73i	0.0646285	+	0.589076i
$296$	−2906.28	+	8944.62i	−0.570690	+	1.75640i
$297$		0			0
$298$	746.968	−	542.704i	0.145204	−	0.105497i
$299$	5549.09			1.07329
$300$		0			0
$301$	−74.4505			−0.0142567
$302$	−4082.49	+	2966.11i	−0.777885	+	0.565166i
$303$		0			0
$304$	1136.28	−	3497.10i	0.214375	−	0.659779i
$305$	4048.54	+	841.288i	0.760061	+	0.157941i
$306$		0			0
$307$	−4507.90			−0.838043			−0.419022	−	0.907976i	$-0.637627\pi$
$307$	−4507.90			−0.838043			−0.419022	+	0.907976i	$0.637627\pi$
$308$	−30.7860	−	94.7495i	−0.00569543	−	0.0175287i
$309$		0			0
$310$	−1946.31	−	17740.2i	−0.356590	−	3.25025i
$311$	5715.86	−	4152.81i	1.04218	−	0.757185i	0.0714665	−	0.997443i	$-0.477232\pi$
$311$	5715.86	−	4152.81i	1.04218	−	0.757185i	0.970709	+	0.240258i	$0.0772321\pi$
$312$		0			0
$313$	−1669.65	−	1213.07i	−0.301516	−	0.219064i	0.426732	−	0.904378i	$-0.359665\pi$
$313$	−1669.65	−	1213.07i	−0.301516	−	0.219064i	−0.728247	+	0.685314i	$0.759665\pi$
$314$	−7930.75	+	5762.02i	−1.42534	+	1.03557i
$315$		0			0
$316$	−7360.86	−	5347.97i	−1.31038	−	0.952048i
$317$	−2656.46	−	8175.75i	−0.470668	−	1.44857i	−0.851712	−	0.524010i	$-0.824435\pi$
$317$	−2656.46	−	8175.75i	−0.470668	−	1.44857i	0.381044	−	0.924557i	$-0.375565\pi$
$318$		0			0
$319$	−180.453	−	555.378i	−0.0316722	−	0.0974771i
$320$	−7405.49	−	1538.87i	−1.29369	−	0.268829i
$321$		0			0
$322$	33.6295	−	103.501i	0.00582019	−	0.0179127i
$323$	1215.97	−	883.456i	0.209469	−	0.152188i
$324$		0			0
$325$	2843.26	−	3216.20i	0.485279	−	0.548932i
$326$	4064.54			0.690533
$327$		0			0
$328$	−1297.28	+	3992.61i	−0.218385	+	0.672119i
$329$	−3.25983	+	10.0327i	−0.000546262	+	0.00168122i
$330$		0			0
$331$	80.2294	+	246.921i	0.0133227	+	0.0410030i	0.957497	−	0.288444i	$-0.0931378\pi$
$331$	80.2294	+	246.921i	0.0133227	+	0.0410030i	−0.944174	+	0.329447i	$0.893138\pi$
$332$	18994.1			3.13986
$333$		0			0
$334$	7648.42	+	5556.90i	1.25300	+	0.910360i
$335$	−978.905	+	1713.49i	−0.159652	+	0.279457i
$336$		0			0
$337$	−5437.56	−	3950.62i	−0.878940	−	0.638587i	0.0540310	−	0.998539i	$-0.482793\pi$
$337$	−5437.56	−	3950.62i	−0.878940	−	0.638587i	−0.932971	+	0.359952i	$0.882793\pi$
$338$	3945.88	+	2866.85i	0.634993	+	0.461349i
$339$		0			0
$340$	1859.42	+	2046.27i	0.296591	+	0.326396i
$341$	−12757.8	−	9269.08i	−2.02602	−	1.47199i
$342$		0			0
$343$	−96.3940			−0.0151743
$344$	−5471.92	−	16840.8i	−0.857634	−	2.63953i
$345$		0			0
$346$	−4010.36	+	12342.6i	−0.623116	+	1.91775i
$347$	2206.24	−	6790.12i	0.341318	−	1.05047i	−0.622207	−	0.782853i	$-0.713764\pi$
$347$	2206.24	−	6790.12i	0.341318	−	1.05047i	0.963525	−	0.267617i	$-0.0862361\pi$
$348$		0			0
$349$	−11473.4			−1.75976			−0.879879	−	0.475198i	$-0.842376\pi$
$349$	−11473.4			−1.75976			−0.879879	+	0.475198i	$0.842376\pi$
$350$	−42.7571	−	72.5236i	−0.00652989	−	0.0110759i
$351$		0			0
$352$	−2823.41	+	2051.33i	−0.427523	+	0.310614i
$353$	−18.4180	+	56.6848i	−0.00277703	+	0.00854683i	−0.952435	−	0.304740i	$-0.901430\pi$
$353$	−18.4180	+	56.6848i	−0.00277703	+	0.00854683i	0.949658	+	0.313287i	$0.101430\pi$
$354$		0			0
$355$	7360.35	−	3317.29i	1.10041	−	0.495954i
$356$	6188.64	+	19046.7i	0.921341	+	2.83560i
$357$		0			0
$358$	−4639.25	−	14278.1i	−0.684893	−	2.10788i
$359$	−6311.85	−	4585.83i	−0.927930	−	0.674180i	0.0175554	−	0.999846i	$-0.494412\pi$
$359$	−6311.85	−	4585.83i	−0.927930	−	0.674180i	−0.945485	+	0.325666i	$0.894412\pi$
$360$		0			0
$361$	−1150.72	+	836.048i	−0.167768	+	0.121891i
$362$	−1229.41	−	893.216i	−0.178498	−	0.129686i
$363$		0			0
$364$	−58.4568	+	42.4713i	−0.00841749	+	0.00611567i
$365$	−26.7391	−	5.55641i	−0.00383449	−	0.000796810i
$366$		0			0
$367$	−489.265	−	1505.80i	−0.0695897	−	0.214175i	0.910213	−	0.414139i	$-0.135917\pi$
$367$	−489.265	−	1505.80i	−0.0695897	−	0.214175i	−0.979803	+	0.199964i	$0.935917\pi$
$368$	6528.94			0.924850
$369$		0			0
$370$	10141.2	+	11160.3i	1.42491	+	1.56810i
$371$	10.8308	−	33.3339i	0.00151566	−	0.00466471i
$372$		0			0
$373$	9045.77	−	6572.14i	1.25569	−	0.912312i	0.257152	−	0.966371i	$-0.417216\pi$
$373$	9045.77	−	6572.14i	1.25569	−	0.912312i	0.998538	+	0.0540593i	$0.0172160\pi$
$374$	3748.42			0.518252
$375$		0			0
$376$	−2509.01			−0.344128
$377$	−342.646	+	248.947i	−0.0468095	+	0.0340091i
$378$		0			0
$379$	−3622.62	+	11149.3i	−0.490980	+	1.51108i	0.332148	+	0.943227i	$0.392227\pi$
$379$	−3622.62	+	11149.3i	−0.490980	+	1.51108i	−0.823129	+	0.567855i	$0.807773\pi$
$380$	−10245.0	−	11274.5i	−1.38305	−	1.52203i
$381$		0			0
$382$	−8049.67			−1.07816
$383$	2865.21	+	8818.21i	0.382260	+	1.17647i	0.938449	+	0.345419i	$0.112263\pi$
$383$	2865.21	+	8818.21i	0.382260	+	1.17647i	−0.556189	+	0.831056i	$0.687737\pi$
$384$		0			0
$385$	−72.8345	−	15.1351i	−0.00964153	−	0.00200352i
$386$	5621.09	−	4083.96i	0.741207	−	0.538519i
$387$		0			0
$388$	17336.8	+	12596.0i	2.26841	+	1.64810i
$389$	−1085.01	+	788.308i	−0.141420	+	0.102748i	−0.656246	−	0.754547i	$-0.727857\pi$
$389$	−1085.01	+	788.308i	−0.141420	+	0.102748i	0.514826	+	0.857295i	$0.327857\pi$
$390$		0			0
$391$	2159.06	+	1568.65i	0.279254	+	0.202890i
$392$	−3542.25	−	10901.9i	−0.456405	−	1.40467i
$393$		0			0
$394$	1570.92	+	4834.78i	0.200867	+	0.618205i
$395$	−6193.86	+	2791.56i	−0.788979	+	0.355591i
$396$		0			0
$397$	3512.37	−	10810.0i	0.444032	−	1.36659i	−0.439510	−	0.898238i	$-0.644848\pi$
$397$	3512.37	−	10810.0i	0.444032	−	1.36659i	0.883542	−	0.468353i	$-0.155152\pi$
$398$	709.904	−	515.775i	0.0894077	−	0.0649585i
$399$		0			0
$400$	3345.32	−	3784.12i	0.418165	−	0.473015i
$401$	12421.7			1.54690			0.773451	−	0.633856i	$-0.218529\pi$
$401$	12421.7			1.54690			0.773451	+	0.633856i	$0.218529\pi$
$402$		0			0
$403$	−3534.33	+	10877.5i	−0.436867	+	1.34454i
$404$	1730.93	−	5327.27i	0.213161	−	0.656043i
$405$		0			0
$406$	2.56677	+	7.89972i	0.000313761	+	0.000965656i
$407$	13324.5			1.62278
$408$		0			0
$409$	−10450.7	−	7592.88i	−1.26346	−	0.917956i	−0.264536	−	0.964376i	$-0.585219\pi$
$409$	−10450.7	−	7592.88i	−1.26346	−	0.917956i	−0.998922	+	0.0464199i	$0.985219\pi$
$410$	4526.73	+	4981.62i	0.545266	+	0.600060i
$411$		0			0
$412$	24443.3	+	17759.1i	2.92289	+	2.12361i
$413$	−30.5312	−	22.1822i	−0.00363763	−	0.00264289i
$414$		0			0
$415$	7035.42	−	12314.9i	0.832181	−	1.45666i
$416$	2047.77	+	1487.79i	0.241346	+	0.175348i
$417$		0			0
$418$	−20653.0			−2.41668
$419$	1286.38	+	3959.06i	0.149985	+	0.461605i	0.997618	−	0.0689767i	$-0.0219734\pi$
$419$	1286.38	+	3959.06i	0.149985	+	0.461605i	−0.847634	+	0.530582i	$0.821973\pi$
$420$		0			0
$421$	−4618.97	+	14215.7i	−0.534714	+	1.64568i	0.209551	+	0.977798i	$0.432800\pi$
$421$	−4618.97	+	14215.7i	−0.534714	+	1.64568i	−0.744265	+	0.667884i	$0.767200\pi$
$422$	−7264.50	+	22357.8i	−0.837987	+	2.57906i
$423$		0			0
$424$	8336.21			0.954817
$425$	2015.44	−	447.622i	0.230031	−	0.0510891i
$426$		0			0
$427$	−42.0454	+	30.5478i	−0.00476515	+	0.00346209i
$428$	−7771.89	+	23919.4i	−0.877730	+	2.70137i
$429$		0			0
$430$	−27798.0	−	5776.44i	−3.11753	−	0.647825i
$431$	3943.96	+	12138.2i	0.440774	+	1.35656i	0.887052	+	0.461669i	$0.152749\pi$
$431$	3943.96	+	12138.2i	0.440774	+	1.35656i	−0.446278	+	0.894894i	$0.647251\pi$
$432$		0			0
$433$	240.260	+	739.444i	0.0266655	+	0.0820679i	0.963504	−	0.267695i	$-0.0862621\pi$
$433$	240.260	+	739.444i	0.0266655	+	0.0820679i	−0.936838	+	0.349763i	$0.886262\pi$
$434$	181.467	+	131.844i	0.0200708	+	0.0145823i
$435$		0			0
$436$	−245.034	+	178.028i	−0.0269151	+	0.0195550i
$437$	−11896.0	−	8642.94i	−1.30220	−	0.946105i
$438$		0			0
$439$	−8038.76	+	5840.50i	−0.873961	+	0.634970i	−0.931647	−	0.363365i	$-0.881628\pi$
$439$	−8038.76	+	5840.50i	−0.873961	+	0.634970i	0.0576858	+	0.998335i	$0.481628\pi$
$440$	−1929.57	−	17587.7i	−0.209065	−	1.90559i
$441$		0			0
$442$	−840.111	−	2585.60i	−0.0904073	−	0.278245i
$443$	−7139.86			−0.765745			−0.382873	−	0.923801i	$-0.625065\pi$
$443$	−7139.86			−0.765745			−0.382873	+	0.923801i	$0.625065\pi$
$444$		0			0
$445$	14641.3	+	3042.47i	1.55970	+	0.324106i
$446$	−7164.81	+	22051.0i	−0.760681	+	2.34114i
$447$		0			0
$448$	76.9086	−	55.8773i	0.00811069	−	0.00589276i
$449$	−10438.2			−1.09712			−0.548560	−	0.836111i	$-0.684824\pi$
$449$	−10438.2			−1.09712			−0.548560	+	0.836111i	$0.684824\pi$
$450$		0			0
$451$	5947.67			0.620986
$452$	−7783.11	+	5654.76i	−0.809926	+	0.588446i
$453$		0			0
$454$	66.3804	−	204.298i	0.00686208	−	0.0211193i
$455$	5.88407	+	53.6322i	0.000606263	+	0.00552597i
$456$		0			0
$457$	5039.76			0.515864			0.257932	−	0.966163i	$-0.416959\pi$
$457$	5039.76			0.515864			0.257932	+	0.966163i	$0.416959\pi$
$458$	−6161.15	−	18962.1i	−0.628584	−	1.93458i
$459$		0			0
$460$	13417.8	−	23486.7i	1.36002	−	2.38059i
$461$	1482.67	−	1077.22i	0.149794	−	0.108831i	−0.510364	−	0.859958i	$-0.670489\pi$
$461$	1482.67	−	1077.22i	0.149794	−	0.108831i	0.660158	+	0.751127i	$0.270489\pi$
$462$		0			0
$463$	−1527.01	−	1109.44i	−0.153275	−	0.111361i	0.508505	−	0.861059i	$-0.330198\pi$
$463$	−1527.01	−	1109.44i	−0.153275	−	0.111361i	−0.661779	+	0.749699i	$0.730198\pi$
$464$	−403.150	+	292.906i	−0.0403358	+	0.0293056i
$465$		0			0
$466$	11421.2	+	8297.96i	1.13535	+	0.824883i
$467$	1218.86	+	3751.27i	0.120775	+	0.371708i	0.993108	−	0.117205i	$-0.0373934\pi$
$467$	1218.86	+	3751.27i	0.120775	+	0.371708i	−0.872332	+	0.488913i	$0.837393\pi$
$468$		0			0
$469$	−7.66444	−	23.5887i	−0.000754608	−	0.00232244i
$470$	−1995.55	+	3493.05i	−0.195847	+	0.342813i
$471$		0			0
$472$	2773.69	−	8536.54i	0.270486	−	0.832470i
$473$	−20296.0	+	14745.9i	−1.97296	+	1.43344i
$474$		0			0
$475$	−11104.7	+	2466.31i	−1.07267	+	0.238236i
$476$	−34.7506			−0.00334620
$477$		0			0
$478$	−3220.76	+	9912.49i	−0.308189	+	0.948507i
$479$	3324.76	−	10232.6i	0.317144	−	0.976070i	−0.657718	−	0.753264i	$-0.728478\pi$
$479$	3324.76	−	10232.6i	0.317144	−	0.976070i	0.974863	−	0.222806i	$-0.0715217\pi$
$480$		0			0
$481$	−2986.35	−	9191.03i	−0.283089	−	0.871258i
$482$	11027.2			1.04207
$483$		0			0
$484$	−11036.1	−	8018.17i	−1.03645	−	0.753022i
$485$	14588.2	−	6574.88i	1.36581	−	0.615567i
$486$		0			0
$487$	−2581.85	−	1875.82i	−0.240236	−	0.174542i	0.461153	−	0.887321i	$-0.347436\pi$
$487$	−2581.85	−	1875.82i	−0.240236	−	0.174542i	−0.701388	+	0.712779i	$0.747436\pi$
$488$	−10000.2	−	7265.56i	−0.927638	−	0.673968i
$489$		0			0
$490$	−17995.0	−	3739.38i	−1.65905	−	0.344751i
$491$	755.541	+	548.933i	0.0694442	+	0.0504541i	0.621966	−	0.783044i	$-0.286334\pi$
$491$	755.541	+	548.933i	0.0694442	+	0.0504541i	−0.552522	+	0.833499i	$0.686334\pi$
$492$		0			0
$493$	−203.692			−0.0186082
$494$	4628.84	+	14246.1i	0.421582	+	1.29750i
$495$		0			0
$496$	−4158.41	+	12798.3i	−0.376448	+	1.15859i
$497$	−31.3560	+	96.5037i	−0.00282999	+	0.00870983i
$498$		0			0
$499$	5499.10			0.493333			0.246667	−	0.969100i	$-0.420665\pi$
$499$	5499.10			0.493333			0.246667	+	0.969100i	$0.420665\pi$
$500$	−6737.63	−	19811.0i	−0.602632	−	1.77195i
$501$		0			0
$502$	13062.0	−	9490.09i	1.16133	−	0.843752i
$503$	3452.50	−	10625.7i	0.306042	−	0.941901i	−0.673244	−	0.739420i	$-0.735100\pi$
$503$	3452.50	−	10625.7i	0.306042	−	0.941901i	0.979286	−	0.202481i	$-0.0649004\pi$
$504$		0			0
$505$	−2812.82	−	3095.49i	−0.247859	−	0.272767i
$506$	−11332.0	−	34876.3i	−0.995591	−	3.06411i
$507$		0			0
$508$	−5487.10	−	16887.6i	−0.479234	−	1.47493i
$509$	−6938.79	−	5041.32i	−0.604236	−	0.439003i	0.243144	−	0.969990i	$-0.421821\pi$
$509$	−6938.79	−	5041.32i	−0.604236	−	0.439003i	−0.847380	+	0.530987i	$0.821821\pi$
$510$		0			0
$511$	0.277695	−	0.201757i	2.40401e−5	−	1.74662e-5i
$512$	11149.7	+	8100.70i	0.962403	+	0.699226i
$513$		0			0
$514$	1570.07	−	1140.72i	0.134733	−	0.0978893i
$515$	20568.0	−	9269.94i	1.75987	−	0.793170i
$516$		0			0
$517$	1098.45	+	3380.68i	0.0934425	+	0.287586i
$518$	−189.529			−0.0160761
$519$		0			0
$520$	−11699.2	+	5272.81i	−0.986625	+	0.444670i
$521$	6097.64	−	18766.6i	0.512750	−	1.57808i	−0.274589	−	0.961562i	$-0.588542\pi$
$521$	6097.64	−	18766.6i	0.512750	−	1.57808i	0.787339	−	0.616520i	$-0.211458\pi$
$522$		0			0
$523$	−13230.4	+	9612.48i	−1.10617	+	0.803680i	−0.982056	−	0.188588i	$-0.939609\pi$
$523$	−13230.4	+	9612.48i	−1.10617	+	0.803680i	−0.124114	+	0.992268i	$0.539609\pi$
$524$	3340.39			0.278484
$525$		0			0
$526$	7259.98			0.601807
$527$	−4450.07	+	3233.17i	−0.367833	+	0.267246i
$528$		0			0
$529$	4308.19	−	13259.2i	0.354088	−	1.08977i
$530$	6630.26	−	11605.7i	0.543396	−	0.951169i
$531$		0			0
$532$	191.469			0.0156038
$533$	−1333.02	−	4102.60i	−0.108329	−	0.333402i
$534$		0			0
$535$	12629.6	+	13898.7i	1.02060	+	1.12317i
$536$	4772.49	−	3467.42i	0.384590	−	0.279421i
$537$		0			0
$538$	−7336.02	−	5329.93i	−0.587878	−	0.427118i
$539$	−13138.6	+	9545.79i	−1.04995	+	0.762831i
$540$		0			0
$541$	−11519.4	−	8369.30i	−0.915445	−	0.665110i	0.0269410	−	0.999637i	$-0.491423\pi$
$541$	−11519.4	−	8369.30i	−0.915445	−	0.665110i	−0.942386	+	0.334527i	$0.891423\pi$
$542$	−3101.94	−	9546.78i	−0.245830	−	0.756585i
$543$		0			0
$544$	376.175	+	1157.75i	0.0296477	+	0.0912463i
$545$	24.6644	+	224.811i	0.00193854	+	0.0176694i
$546$		0			0
$547$	2168.92	−	6675.24i	0.169536	−	0.521778i	−0.829806	−	0.558052i	$-0.811549\pi$
$547$	2168.92	−	6675.24i	0.169536	−	0.521778i	0.999342	+	0.0362740i	$0.0115489\pi$
$548$	−19133.7	+	13901.4i	−1.49152	+	1.08365i
$549$		0			0
$550$	−26020.3	−	11302.1i	−2.01729	−	0.876225i
$551$	1122.30			0.0867725
$552$		0			0
$553$	26.3866	−	81.2095i	0.00202906	−	0.00624481i
$554$	−2210.92	+	6804.50i	−0.169554	+	0.521833i
$555$		0			0
$556$	7242.27	+	22289.4i	0.552411	+	1.70015i
$557$	−6144.57			−0.467421			−0.233711	−	0.972306i	$-0.575087\pi$
$557$	−6144.57			−0.467421			−0.233711	+	0.972306i	$0.575087\pi$
$558$		0			0
$559$	14720.3	+	10694.9i	1.11378	+	0.809209i
$560$	6.92307	+	63.1025i	0.000522416	+	0.00476173i
$561$		0			0
$562$	8024.74	+	5830.31i	0.602319	+	0.437610i
$563$	13890.4	+	10092.0i	1.03981	+	0.755463i	0.970248	−	0.242115i	$-0.0778410\pi$
$563$	13890.4	+	10092.0i	1.03981	+	0.755463i	0.0695583	+	0.997578i	$0.477841\pi$
$564$		0			0
$565$	783.423	+	7140.75i	0.0583343	+	0.531706i
$566$	−13179.7	−	9575.59i	−0.978769	−	0.711117i
$567$		0			0
$568$	−24133.9			−1.78281
$569$	4813.01	+	14812.9i	0.354608	+	1.09137i	0.956236	+	0.292595i	$0.0945188\pi$
$569$	4813.01	+	14812.9i	0.354608	+	1.09137i	−0.601629	+	0.798776i	$0.705481\pi$
$570$		0			0
$571$	−6553.52	+	20169.7i	−0.480309	+	1.47824i	0.358353	+	0.933586i	$0.383339\pi$
$571$	−6553.52	+	20169.7i	−0.480309	+	1.47824i	−0.838662	+	0.544653i	$0.816661\pi$
$572$	−7523.94	+	23156.3i	−0.549985	+	1.69268i
$573$		0			0
$574$	−84.5999			−0.00615180
$575$	−10257.8	−	17399.0i	−0.743963	−	1.26189i
$576$		0			0
$577$	1675.68	−	1217.45i	0.120900	−	0.0878392i	−0.525692	−	0.850675i	$-0.676194\pi$
$577$	1675.68	−	1217.45i	0.120900	−	0.0878392i	0.646592	+	0.762836i	$0.276194\pi$
$578$	−6872.72	+	21152.1i	−0.494580	+	1.52216i
$579$		0			0
$580$	225.152	+	2052.22i	0.0161189	+	0.146920i
$581$	55.0846	+	169.533i	0.00393338	+	0.0121057i
$582$		0			0
$583$	−3649.62	−	11232.4i	−0.259265	−	0.797936i
$584$	66.0477	+	47.9864i	0.00467992	+	0.00340016i
$585$		0			0
$586$	29770.9	−	21629.8i	2.09868	−	1.52478i
$587$	16771.4	+	12185.2i	1.17927	+	0.856789i	0.992089	−	0.125537i	$-0.0400652\pi$
$587$	16771.4	+	12185.2i	1.17927	+	0.856789i	0.187180	+	0.982326i	$0.440065\pi$
$588$		0			0
$589$	24519.0	−	17814.1i	1.71526	−	1.24621i
$590$	−9678.53	−	10651.1i	−0.675354	−	0.743220i
$591$		0			0
$592$	−3513.67	−	10814.0i	−0.243938	−	0.750763i
$593$	1924.00			0.133236			0.0666182	−	0.997779i	$-0.478779\pi$
$593$	1924.00			0.133236			0.0666182	+	0.997779i	$0.478779\pi$
$594$		0			0
$595$	−12.8717	+	22.5307i	−0.000886868	+	0.00155239i
$596$	−891.306	+	2743.16i	−0.0612572	+	0.188530i
$597$		0			0
$598$	−21517.3	+	15633.3i	−1.47142	+	1.06905i
$599$	8088.34			0.551720			0.275860	−	0.961198i	$-0.411037\pi$
$599$	8088.34			0.551720			0.275860	+	0.961198i	$0.411037\pi$
$600$		0			0
$601$	19953.8			1.35430			0.677149	−	0.735846i	$-0.263215\pi$
$601$	19953.8			1.35430			0.677149	+	0.735846i	$0.263215\pi$
$602$	288.692	−	209.747i	0.0195452	−	0.0142004i
$603$		0			0
$604$	4871.36	−	14992.5i	0.328167	−	1.00999i
$605$	−9286.40	+	4185.36i	−0.624043	+	0.281254i
$606$		0			0
$607$	−3633.68			−0.242976			−0.121488	−	0.992593i	$-0.538767\pi$
$607$	−3633.68			−0.242976			−0.121488	+	0.992593i	$0.538767\pi$
$608$	−2072.65	−	6378.95i	−0.138252	−	0.425495i
$609$		0			0
$610$	−18068.9	+	8143.59i	−1.19932	+	0.540532i
$611$	2085.75	−	1515.38i	0.138102	−	0.100337i
$612$		0			0
$613$	1279.79	+	929.823i	0.0843235	+	0.0612646i	0.629148	−	0.777285i	$-0.283404\pi$
$613$	1279.79	+	929.823i	0.0843235	+	0.0612646i	−0.544825	+	0.838550i	$0.683404\pi$
$614$	17480.0	−	12699.9i	1.14892	−	0.834736i
$615$		0			0
$616$	179.907	+	130.710i	0.0117673	+	0.00854944i
$617$	−1376.37	−	4236.04i	−0.0898065	−	0.276396i	0.896059	−	0.443935i	$-0.146418\pi$
$617$	−1376.37	−	4236.04i	−0.0898065	−	0.276396i	−0.985865	+	0.167539i	$0.946418\pi$
$618$		0			0
$619$	−812.796	−	2501.53i	−0.0527771	−	0.162431i	0.921194	−	0.389104i	$-0.127215\pi$
$619$	−812.796	−	2501.53i	−0.0527771	−	0.162431i	−0.973971	+	0.226673i	$0.927215\pi$
$620$	37493.4	+	41261.2i	2.42867	+	2.67272i
$621$		0			0
$622$	−10464.4	+	32206.2i	−0.674574	+	2.07612i
$623$	−152.055	+	110.474i	−0.00977841	+	0.00710443i
$624$		0			0
$625$	−15340.2	−	2969.64i	−0.981773	−	0.190057i
$626$	9891.85			0.631562
$627$		0			0
$628$	9463.21	−	29124.8i	0.601311	−	1.85064i
$629$	1436.23	−	4420.28i	0.0910436	−	0.280203i
$630$		0			0
$631$	−5221.29	−	16069.5i	−0.329407	−	1.01381i	−0.969412	−	0.245441i	$-0.921067\pi$
$631$	−5221.29	−	16069.5i	−0.329407	−	1.01381i	0.640004	−	0.768371i	$-0.278933\pi$
$632$	20309.1			1.27825
$633$		0			0
$634$	33334.0	+	24218.6i	2.08811	+	1.51710i
$635$	−12981.6	−	2697.58i	−0.811272	−	0.168583i
$636$		0			0
$637$	9529.22	+	6923.38i	0.592718	+	0.430635i
$638$	2264.38	+	1645.17i	0.140513	+	0.102089i
$639$		0			0
$640$	27041.1	−	12187.3i	1.67014	−	0.752730i
$641$	23303.3	+	16930.8i	1.43592	+	1.04326i	0.988875	+	0.148746i	$0.0475238\pi$
$641$	23303.3	+	16930.8i	1.43592	+	1.04326i	0.447046	+	0.894511i	$0.352476\pi$
$642$		0			0
$643$	10219.9			0.626801			0.313400	−	0.949621i	$-0.398532\pi$
$643$	10219.9			0.626801			0.313400	+	0.949621i	$0.398532\pi$
$644$	105.056	+	323.329i	0.00642824	+	0.0197841i
$645$		0			0
$646$	−2226.17	+	6851.44i	−0.135584	+	0.417285i
$647$	553.877	−	1704.66i	0.0336555	−	0.103581i	−0.932818	−	0.360349i	$-0.882658\pi$
$647$	553.877	−	1704.66i	0.0336555	−	0.103581i	0.966473	+	0.256768i	$0.0826576\pi$
$648$		0			0
$649$	−12716.6			−0.769138
$650$	−1964.22	+	20481.5i	−0.118528	+	1.23592i
$651$		0			0
$652$	−10272.3	+	7463.28i	−0.617017	+	0.448289i
$653$	4142.49	−	12749.3i	0.248252	−	0.764040i	−0.746833	−	0.665012i	$-0.768427\pi$
$653$	4142.49	−	12749.3i	0.248252	−	0.764040i	0.995085	−	0.0990282i	$-0.0315734\pi$
$654$		0			0
$655$	1237.28	−	2165.76i	0.0738086	−	0.129196i
$656$	−1568.40	−	4827.03i	−0.0933471	−	0.287293i
$657$		0			0
$658$	−15.6244	−	48.0869i	−0.000925687	−	0.00284897i
$659$	−12492.5	−	9076.37i	−0.738453	−	0.536518i	0.153773	−	0.988106i	$-0.450858\pi$
$659$	−12492.5	−	9076.37i	−0.738453	−	0.536518i	−0.892226	+	0.451589i	$0.850858\pi$
$660$		0			0
$661$	−3524.55	+	2560.74i	−0.207397	+	0.150682i	−0.686635	−	0.727002i	$-0.740913\pi$
$661$	−3524.55	+	2560.74i	−0.207397	+	0.150682i	0.479238	+	0.877685i	$0.340913\pi$
$662$	−1006.74	−	731.440i	−0.0591059	−	0.0429429i
$663$		0			0
$664$	−34300.0	+	24920.4i	−2.00467	+	1.45648i
$665$	70.9202	−	124.140i	0.00413559	−	0.00723900i
$666$		0			0
$667$	615.790	+	1895.21i	0.0357473	+	0.110019i
$668$	−29533.4			−1.71060
$669$		0			0
$670$	−1031.52	−	9402.12i	−0.0594793	−	0.542143i
$671$	−5411.64	+	16655.3i	−0.311347	+	0.958229i
$672$		0			0
$673$	14252.6	−	10355.1i	0.816341	−	0.593107i	−0.0993208	−	0.995055i	$-0.531667\pi$
$673$	14252.6	−	10355.1i	0.816341	−	0.593107i	0.915662	+	0.401949i	$0.131667\pi$
$674$	32214.8			1.84105
$675$		0			0
$676$	−15236.5			−0.866894
$677$	2665.42	−	1936.54i	0.151315	−	0.109937i	−0.509552	−	0.860440i	$-0.670189\pi$
$677$	2665.42	−	1936.54i	0.151315	−	0.109937i	0.660867	+	0.750503i	$0.270189\pi$
$678$		0			0
$679$	−62.1476	+	191.271i	−0.00351253	+	0.0108104i
$680$	−6042.52	−	1255.64i	−0.340765	−	0.0708111i
$681$		0			0
$682$	75583.4			4.24375
$683$	−1492.40	−	4593.13i	−0.0836091	−	0.257322i	0.900509	−	0.434837i	$-0.143194\pi$
$683$	−1492.40	−	4593.13i	−0.0836091	−	0.257322i	−0.984118	+	0.177515i	$0.943194\pi$
$684$		0			0
$685$	1925.94	+	17554.5i	0.107425	+	0.979159i
$686$	373.780	−	271.567i	0.0208032	−	0.0151144i
$687$		0			0
$688$	17319.6	+	12583.4i	0.959745	+	0.697295i
$689$	−6929.93	+	5034.89i	−0.383178	+	0.278395i
$690$		0			0
$691$	−18874.8	−	13713.3i	−1.03912	−	0.754964i	−0.0690054	−	0.997616i	$-0.521983\pi$
$691$	−18874.8	−	13713.3i	−1.03912	−	0.754964i	−0.970113	+	0.242652i	$0.921983\pi$
$692$	−12528.0	−	38557.3i	−0.688214	−	2.11811i
$693$		0			0
$694$	10574.6	+	32545.2i	0.578393	+	1.78011i
$695$	17134.0	+	3560.46i	0.935151	+	0.194325i
$696$		0			0
$697$	641.092	−	1973.08i	0.0348395	−	0.107225i
$698$	44489.5	−	32323.5i	2.41254	−	1.75281i
$699$		0			0
$700$	241.228	+	104.779i	0.0130251	+	0.00565753i
$701$	−27619.7			−1.48813			−0.744066	−	0.668106i	$-0.767105\pi$
$701$	−27619.7			−1.48813			−0.744066	+	0.668106i	$0.767105\pi$
$702$		0			0
$703$	−7913.36	+	24354.8i	−0.424549	+	1.30663i
$704$	9898.86	−	30465.6i	0.529939	−	1.63099i
$705$		0			0
$706$	−88.2778	−	271.691i	−0.00470592	−	0.0144833i
$707$	52.5688			0.00279640
$708$		0			0
$709$	−20888.3	−	15176.2i	−1.10645	−	0.803886i	−0.124352	−	0.992238i	$-0.539685\pi$
$709$	−20888.3	−	15176.2i	−1.10645	−	0.803886i	−0.982101	+	0.188353i	$0.939685\pi$
$710$	−19195.0	+	33599.3i	−1.01462	+	1.77600i
$711$		0			0
$712$	−36165.1	−	26275.5i	−1.90358	−	1.38303i
$713$	43535.5	+	31630.4i	2.28670	+	1.66138i
$714$		0			0
$715$	12226.6	+	13455.3i	0.639511	+	0.703776i
$716$	37942.2	+	27566.6i	1.98040	+	1.43884i
$717$		0			0
$718$	37394.5			1.94366
$719$	5049.02	+	15539.3i	0.261887	+	0.806005i	0.992394	+	0.123100i	$0.0392836\pi$
$719$	5049.02	+	15539.3i	0.261887	+	0.806005i	−0.730507	+	0.682905i	$0.760716\pi$
$720$		0			0
$721$	−87.6220	+	269.673i	−0.00452596	+	0.0139295i
$722$	2106.70	−	6483.77i	0.108592	−	0.334212i
$723$		0			0
$724$	4747.20			0.243685
$725$	1413.96	+	614.165i	0.0724321	+	0.0314614i
$726$		0			0
$727$	5895.72	−	4283.49i	0.300771	−	0.218523i	−0.427156	−	0.904178i	$-0.640484\pi$
$727$	5895.72	−	4283.49i	0.300771	−	0.218523i	0.727926	+	0.685655i	$0.240484\pi$
$728$	49.8401	−	153.392i	0.00253736	−	0.00780918i
$729$		0			0
$730$	119.338	−	53.7855i	0.00605056	−	0.00272697i
$731$	2704.13	+	8322.45i	0.136821	+	0.421090i
$732$		0			0
$733$	−3717.51	−	11441.3i	−0.187325	−	0.576528i	0.812656	−	0.582744i	$-0.198021\pi$
$733$	−3717.51	−	11441.3i	−0.187325	−	0.576528i	−0.999981	+	0.00621681i	$0.998021\pi$
$734$	6139.43	+	4460.56i	0.308734	+	0.224308i
$735$		0			0
$736$	9634.77	−	7000.07i	0.482530	−	0.350579i
$737$	−6761.48	−	4912.50i	−0.337941	−	0.245528i
$738$		0			0
$739$	12267.2	−	8912.61i	0.610629	−	0.443648i	−0.239007	−	0.971018i	$-0.576822\pi$
$739$	12267.2	−	8912.61i	0.610629	−	0.443648i	0.849636	+	0.527370i	$0.176822\pi$
$740$	−46122.3	−	9584.25i	−2.29120	−	0.476113i
$741$		0			0
$742$	51.9123	+	159.770i	0.00256841	+	0.00790475i
$743$	22772.8			1.12443			0.562216	−	0.826991i	$-0.309949\pi$
$743$	22772.8			1.12443			0.562216	+	0.826991i	$0.309949\pi$
$744$		0			0
$745$	1448.40	+	1593.95i	0.0712286	+	0.0783864i
$746$	−16560.7	+	50968.6i	−0.812776	+	2.50147i
$747$		0			0
$748$	−9473.39	+	6882.82i	−0.463077	+	0.336445i
$749$	−236.034			−0.0115147
$750$		0			0
$751$	−27855.5			−1.35348			−0.676739	−	0.736223i	$-0.736608\pi$
$751$	−27855.5			−1.35348			−0.676739	+	0.736223i	$0.736608\pi$
$752$	2454.05	−	1782.97i	0.119002	−	0.0864604i
$753$		0			0
$754$	627.306	−	1930.65i	0.0302986	−	0.0932495i
$755$	−7916.11	−	8711.61i	−0.381585	−	0.419931i
$756$		0			0
$757$	302.235			0.0145111			0.00725557	−	0.999974i	$-0.497690\pi$
$757$	302.235			0.0145111			0.00725557	+	0.999974i	$0.497690\pi$
$758$	−17363.3	−	53438.7i	−0.832009	−	2.56066i
$759$		0			0
$760$	33293.1	+	6918.32i	1.58904	+	0.330202i
$761$	−3638.31	+	2643.38i	−0.173309	+	0.125917i	−0.671058	−	0.741404i	$-0.734160\pi$
$761$	−3638.31	+	2643.38i	−0.173309	+	0.125917i	0.497749	+	0.867321i	$0.334160\pi$
$762$		0			0
$763$	−2.29962	−	1.67077i	−0.000109111	−	7.92739e-5i
$764$	20344.0	−	14780.7i	0.963375	−	0.699933i
$765$		0			0
$766$	−35953.5	−	26121.7i	−1.69589	−	1.23214i
$767$	2850.10	+	8771.71i	0.134174	+	0.412944i
$768$		0			0
$769$	753.619	+	2319.40i	0.0353397	+	0.108764i	0.967170	−	0.254129i	$-0.0817889\pi$
$769$	753.619	+	2319.40i	0.0353397	+	0.108764i	−0.931831	+	0.362894i	$0.881789\pi$
$770$	325.065	−	146.506i	0.0152137	−	0.00685676i
$771$		0			0
$772$	−6707.26	+	20642.8i	−0.312694	+	0.962372i
$773$	−30309.4	+	22021.1i	−1.41029	+	1.02464i	−0.417009	+	0.908902i	$0.636922\pi$
$773$	−30309.4	+	22021.1i	−1.41029	+	1.02464i	−0.993280	+	0.115733i	$0.963078\pi$
$774$		0			0
$775$	40639.5	−	9025.89i	1.88363	−	0.418348i
$776$	−47833.4			−2.21278
$777$		0			0
$778$	1986.41	−	6113.53i	0.0915375	−	0.281723i
$779$	−3532.29	+	10871.3i	−0.162461	+	0.500005i
$780$		0			0
$781$	10565.9	+	32518.4i	0.484094	+	1.48989i
$782$	−12791.3			−0.584932
$783$		0			0
$784$	11211.9	+	8145.90i	0.510745	+	0.371078i
$785$	−15378.0	−	16923.4i	−0.699191	−	0.769453i
$786$		0			0
$787$	−24527.6	−	17820.4i	−1.11095	−	0.807150i	−0.128134	−	0.991757i	$-0.540899\pi$
$787$	−24527.6	−	17820.4i	−1.11095	−	0.807150i	−0.982812	+	0.184607i	$0.940899\pi$
$788$	−12847.8	−	9334.46i	−0.580816	−	0.421988i
$789$		0			0
$790$	16152.9	−	28274.3i	0.727463	−	1.27336i
$791$	−73.0437	−	53.0694i	−0.00328336	−	0.00238550i
$792$		0			0
$793$	12701.4			0.568779
$794$	16834.8	+	51812.3i	0.752451	+	2.31581i
$795$		0			0
$796$	−847.079	+	2607.04i	−0.0377185	+	0.116086i
$797$	7301.19	−	22470.7i	0.324493	−	0.998688i	−0.647175	−	0.762341i	$-0.724050\pi$
$797$	7301.19	−	22470.7i	0.324493	−	0.998688i	0.971669	−	0.236347i	$-0.0759502\pi$
$798$		0			0
$799$	1239.91			0.0548996
$800$	879.517	−	9170.94i	0.0388695	−	0.405302i
$801$		0			0
$802$	−48166.6	+	34995.1i	−2.12072	+	1.54080i
$803$	35.7420	−	110.002i	0.00157074	−	0.00483425i
$804$		0			0
$805$	248.545	+	51.6478i	0.0108821	+	0.00226130i
$806$	−16940.1	−	52136.2i	−0.740309	−	2.27844i
$807$		0			0
$808$	3863.67	+	11891.1i	0.168222	+	0.517734i
$809$	−24729.0	−	17966.7i	−1.07469	−	0.780810i	−0.0979434	−	0.995192i	$-0.531226\pi$
$809$	−24729.0	−	17966.7i	−1.07469	−	0.780810i	−0.976750	+	0.214382i	$0.931226\pi$
$810$		0			0
$811$	−29914.5	+	21734.2i	−1.29524	+	0.941048i	−0.999897	−	0.0143423i	$-0.995435\pi$
$811$	−29914.5	+	21734.2i	−1.29524	+	0.941048i	−0.295345	+	0.955391i	$0.595435\pi$
$812$	−20.9924	−	15.2519i	−0.000907253	−	0.000659158i
$813$		0			0
$814$	−51667.6	+	37538.7i	−2.22475	+	1.61638i
$815$	1033.98	+	9424.52i	0.0444401	+	0.405063i
$816$		0			0
$817$	−14899.2	−	45855.0i	−0.638014	−	1.96360i
$818$	61915.1			2.64647
$819$		0			0
$820$	−20587.6	−	4278.12i	−0.876770	−	0.182193i
$821$	2935.36	−	9034.11i	0.124781	−	0.384035i	−0.869080	−	0.494671i	$-0.835289\pi$
$821$	2935.36	−	9034.11i	0.124781	−	0.384035i	0.993861	+	0.110636i	$0.0352887\pi$
$822$		0			0
$823$	3845.46	−	2793.89i	0.162873	−	0.118334i	−0.503363	−	0.864075i	$-0.667904\pi$
$823$	3845.46	−	2793.89i	0.162873	−	0.118334i	0.666236	+	0.745741i	$0.267904\pi$
$824$	−67440.5			−2.85121
$825$		0			0
$826$	180.882			0.00761947
$827$	10698.5	−	7772.89i	0.449845	−	0.326832i	−0.339690	−	0.940538i	$-0.610322\pi$
$827$	10698.5	−	7772.89i	0.449845	−	0.326832i	0.789535	+	0.613706i	$0.210322\pi$
$828$		0			0
$829$	−3155.27	+	9710.93i	−0.132192	+	0.406845i	−0.995143	−	0.0984431i	$-0.968614\pi$
$829$	−3155.27	+	9710.93i	−0.132192	+	0.406845i	0.862951	+	0.505288i	$0.168614\pi$
$830$	7413.57	+	67573.3i	0.310035	+	2.82591i
$831$		0			0
$832$	−23233.2			−0.968109
$833$	1750.52	+	5387.54i	0.0728114	+	0.224090i
$834$		0			0
$835$	−10939.2	+	19148.2i	−0.453374	+	0.793592i
$836$	52196.5	−	37923.0i	2.15939	−	1.56889i
$837$		0			0
$838$	−16141.8	−	11727.7i	−0.665405	−	0.483445i
$839$	−5438.55	+	3951.34i	−0.223790	+	0.162593i	−0.694031	−	0.719945i	$-0.744167\pi$
$839$	−5438.55	+	3951.34i	−0.223790	+	0.162593i	0.470241	+	0.882538i	$0.344167\pi$
$840$		0			0
$841$	19608.1	+	14246.1i	0.803972	+	0.584120i
$842$	−22138.8	−	68136.2i	−0.906120	−	2.78875i
$843$		0			0
$844$	−22693.7	−	69844.1i	−0.925533	−	2.84850i
$845$	−5643.63	+	9878.69i	−0.229759	+	0.402174i
$846$		0			0
$847$	39.5611	−	121.757i	0.00160488	−	0.00493933i
$848$	−8153.61	+	5923.94i	−0.330184	+	0.239893i
$849$		0			0
$850$	−6554.06	+	7413.74i	−0.264474	+	0.299164i
$851$	−45469.4			−1.83158
$852$		0			0
$853$	−1169.79	+	3600.24i	−0.0469552	+	0.144513i	−0.971785	−	0.235867i	$-0.924207\pi$
$853$	−1169.79	+	3600.24i	−0.0469552	+	0.144513i	0.924830	+	0.380381i	$0.124207\pi$
$854$	76.9754	−	236.906i	0.00308436	−	0.00949269i
$855$		0			0
$856$	−17347.9	−	53391.2i	−0.692684	−	2.13186i
$857$	−13421.7			−0.534979			−0.267489	−	0.963561i	$-0.586194\pi$
$857$	−13421.7			−0.534979			−0.267489	+	0.963561i	$0.586194\pi$
$858$		0			0
$859$	−398.008	−	289.170i	−0.0158089	−	0.0114859i	0.579853	−	0.814721i	$-0.303110\pi$
$859$	−398.008	−	289.170i	−0.0158089	−	0.0114859i	−0.595662	+	0.803235i	$0.703110\pi$
$860$	80860.6	−	36443.7i	3.20619	−	1.44502i
$861$		0			0
$862$	−49489.8	−	35956.5i	−1.95549	−	1.42075i
$863$	−6543.41	−	4754.07i	−0.258100	−	0.187521i	0.451209	−	0.892418i	$-0.350993\pi$
$863$	−6543.41	−	4754.07i	−0.258100	−	0.187521i	−0.709309	+	0.704898i	$0.750993\pi$
$864$		0			0
$865$	−29639.2	−	6159.05i	−1.16505	−	0.242097i
$866$	−3014.85	−	2190.41i	−0.118301	−	0.0859507i
$867$		0			0
$868$	−700.714			−0.0274007
$869$	−8891.36	−	27364.8i	−0.347087	−	1.06822i
$870$		0			0
$871$	−1873.15	+	5764.97i	−0.0728695	+	0.224269i
$872$	208.915	−	642.975i	0.00811326	−	0.0249701i
$873$		0			0
$874$	70477.7			2.72762
$875$	157.285	−	117.591i	0.00607680	−	0.00454320i
$876$		0			0
$877$	−9708.54	+	7053.67i	−0.373813	+	0.271591i	−0.758790	−	0.651335i	$-0.774209\pi$
$877$	−9708.54	+	7053.67i	−0.373813	+	0.271591i	0.384977	+	0.922926i	$0.374209\pi$
$878$	14717.1	−	45294.6i	0.565693	−	1.74102i
$879$		0			0
$880$	14385.6	+	15831.2i	0.551066	+	0.606443i
$881$	706.220	+	2173.52i	0.0270070	+	0.0831190i	0.963652	−	0.267162i	$-0.0860860\pi$
$881$	706.220	+	2173.52i	0.0270070	+	0.0831190i	−0.936645	+	0.350281i	$0.886086\pi$
$882$		0			0
$883$	5941.34	+	18285.6i	0.226435	+	0.696895i	0.998143	+	0.0609179i	$0.0194028\pi$
$883$	5941.34	+	18285.6i	0.226435	+	0.696895i	−0.771708	+	0.635977i	$0.780597\pi$
$884$	6870.87	+	4991.98i	0.261417	+	0.189930i
$885$		0			0
$886$	27685.8	−	20114.9i	1.04980	−	0.762723i
$887$	12097.1	+	8789.05i	0.457926	+	0.332703i	0.792717	−	0.609589i	$-0.208666\pi$
$887$	12097.1	+	8789.05i	0.457926	+	0.332703i	−0.334791	+	0.942292i	$0.608666\pi$
$888$		0			0
$889$	134.818	−	97.9510i	0.00508622	−	0.00369536i
$890$	−65345.0	+	29450.8i	−2.46109	+	1.10921i
$891$		0			0
$892$	−22382.3	−	68885.6i	−0.840151	−	2.58572i
$893$	−6831.64			−0.256005
$894$		0			0
$895$	31926.8	−	14389.3i	1.19240	−	0.537410i
$896$	−115.198	+	354.543i	−0.00429520	+	0.0132193i
$897$		0			0
$898$	40475.3	−	29407.0i	1.50410	−	1.09279i
$899$	−4107.26			−0.152375
$900$		0			0
$901$	−4119.61			−0.152324
$902$	−23062.9	+	16756.1i	−0.851340	+	0.618535i
$903$		0			0
$904$	6635.86	−	20423.1i	0.244143	−	0.751395i
$905$	1758.37	−	3077.87i	0.0645857	−	0.113052i
$906$		0			0
$907$	48744.8			1.78450			0.892251	−	0.451540i	$-0.149125\pi$
$907$	48744.8			1.78450			0.892251	+	0.451540i	$0.149125\pi$
$908$	207.367	+	638.210i	0.00757898	+	0.0233257i
$909$		0			0
$910$	−173.912	−	191.389i	−0.00633531	−	0.00697195i
$911$	−28367.9	+	20610.5i	−1.03169	+	0.749568i	−0.968647	−	0.248442i	$-0.920081\pi$
$911$	−28367.9	+	20610.5i	−1.03169	+	0.749568i	−0.0630456	+	0.998011i	$0.520081\pi$
$912$		0			0
$913$	48594.9	+	35306.3i	1.76151	+	1.27981i
$914$	−19542.3	+	14198.3i	−0.707224	+	0.513828i
$915$		0			0
$916$	50389.1	+	36609.8i	1.81758	+	1.32055i
$917$	9.68744	+	29.8149i	0.000348863	+	0.00107369i
$918$		0			0
$919$	−6229.66	−	19172.9i	−0.223610	−	0.688200i	−0.998430	−	0.0560183i	$-0.982159\pi$
$919$	−6229.66	−	19172.9i	−0.223610	−	0.688200i	0.774820	−	0.632182i	$-0.217841\pi$
$920$	6584.59	+	60017.3i	0.235965	+	2.15077i
$921$		0			0
$922$	−2714.43	+	8354.15i	−0.0969576	+	0.298405i
$923$	20062.6	−	14576.3i	0.715460	−	0.519812i
$924$		0			0
$925$	−23297.8	+	26353.7i	−0.828136	+	0.936760i
$926$	9046.76			0.321053
$927$		0			0
$928$	−280.888	+	864.483i	−0.00993598	+	0.0305798i
$929$	−6866.91	+	21134.2i	−0.242514	+	0.746383i	0.753521	+	0.657424i	$0.228354\pi$
$929$	−6866.91	+	21134.2i	−0.242514	+	0.746383i	−0.996035	+	0.0889586i	$0.971646\pi$
$930$		0			0
$931$	−9645.01	−	29684.3i	−0.339530	−	1.04497i
$932$	−44101.4			−1.54999
$933$		0			0
$934$	−15294.6	−	11112.2i	−0.535818	−	0.389295i
$935$	953.562	+	8691.53i	0.0333527	+	0.304004i
$936$		0			0
$937$	−6572.08	−	4774.90i	−0.229136	−	0.166477i	0.467293	−	0.884102i	$-0.345229\pi$
$937$	−6572.08	−	4774.90i	−0.229136	−	0.166477i	−0.696430	+	0.717625i	$0.745229\pi$
$938$	96.1755	+	69.8756i	0.00334781	+	0.00243232i
$939$		0			0
$940$	−1370.54	−	12492.2i	−0.0475554	−	0.433458i
$941$	−33838.2	−	24584.9i	−1.17226	−	0.851694i	−0.180979	−	0.983487i	$-0.557927\pi$
$941$	−33838.2	−	24584.9i	−1.17226	−	0.851694i	−0.991277	+	0.131793i	$0.957927\pi$
$942$		0			0
$943$	−20296.2			−0.700885
$944$	3353.37	+	10320.6i	0.115617	+	0.355834i
$945$		0			0
$946$	37157.3	−	114359.i	1.27705	−	3.93035i
$947$	−10149.2	+	31236.0i	−0.348263	+	1.07184i	0.611551	+	0.791205i	$0.290546\pi$
$947$	−10149.2	+	31236.0i	−0.348263	+	1.07184i	−0.959814	+	0.280638i	$0.909454\pi$
$948$		0			0
$949$	−83.8885			−0.00286948
$950$	36111.6	−	40848.2i	1.23328	−	1.39504i
$951$		0			0
$952$	62.7537	−	45.5932i	0.00213641	−	0.00155219i
$953$	3887.24	−	11963.7i	0.132130	−	0.406655i	−0.863002	−	0.505200i	$-0.831419\pi$
$953$	3887.24	−	11963.7i	0.132130	−	0.406655i	0.995133	+	0.0985447i	$0.0314187\pi$
$954$		0			0
$955$	−2047.76	−	18664.9i	−0.0693863	−	0.632442i
$956$	−10061.4	−	30965.8i	−0.340386	−	1.04760i
$957$		0			0
$958$	15935.6	+	49044.8i	0.537429	+	1.65404i
$959$	−179.568	−	130.464i	−0.00604645	−	0.00439300i
$960$		0			0
$961$	−65630.2	+	47683.1i	−2.20302	+	1.60059i
$962$	37473.5	+	27226.1i	1.25592	+	0.912479i
$963$		0			0
$964$	−27869.2	+	20248.1i	−0.931126	+	0.676502i
$965$	10899.5	+	11994.8i	0.363593	+	0.400131i
$966$		0			0
$967$	12942.6	+	39833.2i	0.430409	+	1.32466i	0.897718	+	0.440570i	$0.145223\pi$
$967$	12942.6	+	39833.2i	0.430409	+	1.32466i	−0.467309	+	0.884094i	$0.654777\pi$
$968$	30449.2			1.01103
$969$		0			0
$970$	−38044.6	+	66593.9i	−1.25932	+	2.20433i
$971$	−17116.5	+	52679.3i	−0.565701	+	1.74105i	0.100159	+	0.994971i	$0.468065\pi$
$971$	−17116.5	+	52679.3i	−0.565701	+	1.74105i	−0.665860	+	0.746077i	$0.731935\pi$
$972$		0			0
$973$	−177.942	+	129.283i	−0.00586287	+	0.00425963i
$974$	15296.2			0.503204
$975$		0			0
$976$	14944.2			0.490117
$977$	−28690.5	+	20844.9i	−0.939498	+	0.682585i	−0.948300	−	0.317376i	$-0.897198\pi$
$977$	−28690.5	+	20844.9i	−0.939498	+	0.682585i	0.00880161	+	0.999961i	$0.497198\pi$
$978$		0			0
$979$	−19570.9	+	60233.0i	−0.638906	+	1.96635i
$980$	52345.2	−	23591.8i	1.70623	−	0.768994i
$981$		0			0
$982$	−4476.20			−0.145459
$983$	10713.9	+	32974.0i	0.347630	+	1.06989i	0.960161	+	0.279448i	$0.0901515\pi$
$983$	10713.9	+	32974.0i	0.347630	+	1.06989i	−0.612531	+	0.790447i	$0.709849\pi$
$984$		0			0
$985$	−10810.9	+	4872.43i	−0.349709	+	0.157613i
$986$	789.842	−	573.854i	0.0255108	−	0.0185347i
$987$		0			0
$988$	−37857.1	−	27504.8i	−1.21902	−	0.885673i
$989$	69259.4	−	50319.9i	2.22682	−	1.61788i
$990$		0			0
$991$	30160.4	+	21912.8i	0.966778	+	0.702405i	0.954715	−	0.297522i	$-0.0961603\pi$
$991$	30160.4	+	21912.8i	0.966778	+	0.702405i	0.0120626	+	0.999927i	$0.496160\pi$
$992$	7585.22	+	23344.9i	0.242773	+	0.747179i
$993$		0			0
$994$	−150.290	−	462.544i	−0.00479567	−	0.0147596i
$995$	1376.53	+	1514.86i	0.0438583	+	0.0482656i
$996$		0			0
$997$	−10625.0	+	32700.3i	−0.337509	+	1.03875i	0.627964	+	0.778242i	$0.283889\pi$
$997$	−10625.0	+	32700.3i	−0.337509	+	1.03875i	−0.965473	+	0.260503i	$0.916111\pi$
$998$	−21323.5	+	15492.4i	−0.676335	+	0.491386i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.a.136.1		28
3.2	odd	2		75.4.g.b.61.7	yes	28
25.16	even	5	inner	225.4.h.a.91.1		28
75.29	odd	10		1875.4.a.f.1.13		14
75.41	odd	10		75.4.g.b.16.7	✓	28
75.71	odd	10		1875.4.a.g.1.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.4.g.b.16.7	✓	28	75.41	odd	10
75.4.g.b.61.7	yes	28	3.2	odd	2
225.4.h.a.91.1		28	25.16	even	5	inner
225.4.h.a.136.1		28	1.1	even	1	trivial
1875.4.a.f.1.13		14	75.29	odd	10
1875.4.a.g.1.2		14	75.71	odd	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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.87763 + 2.81726i) q^{2} +(4.62691 - 14.2402i) q^{4} +(-7.51887 - 8.27445i) q^{5} +0.140520 q^{7} +(10.3279 + 31.7859i) q^{8} +O(q^{10})\)	\(q+(-3.87763 + 2.81726i) q^{2} +(4.62691 - 14.2402i) q^{4} +(-7.51887 - 8.27445i) q^{5} +0.140520 q^{7} +(10.3279 + 31.7859i) q^{8} +(52.4667 + 10.9026i) q^{10} +(38.3073 - 27.8319i) q^{11} +(-27.7836 - 20.1859i) q^{13} +(-0.544885 + 0.395882i) q^{14} +(-32.6895 - 23.7503i) q^{16} +(-5.10385 - 15.7080i) q^{17} +(28.1212 + 86.5481i) q^{19} +(-152.619 + 68.7848i) q^{20} +(-70.1318 + 215.843i) q^{22} +(-130.722 + 94.9752i) q^{23} +(-11.9331 + 124.429i) q^{25} +164.604 q^{26} +(0.650173 - 2.00103i) q^{28} +(3.81101 - 11.7291i) q^{29} +(-102.914 - 316.738i) q^{31} -73.7042 q^{32} +(64.0445 + 46.5310i) q^{34} +(-1.05655 - 1.16273i) q^{35} +(227.659 + 165.404i) q^{37} +(-352.872 - 256.377i) q^{38} +(185.357 - 324.451i) q^{40} +(101.620 + 73.8315i) q^{41} -529.821 q^{43} +(-219.086 - 674.278i) q^{44} +(239.322 - 736.558i) q^{46} +(-23.1983 + 71.3970i) q^{47} -342.980 q^{49} +(-304.278 - 516.109i) q^{50} +(-416.003 + 302.244i) q^{52} +(77.0767 - 237.218i) q^{53} +(-518.321 - 107.707i) q^{55} +(1.45127 + 4.46655i) q^{56} +(18.2662 + 56.2177i) q^{58} +(-217.273 - 157.858i) q^{59} +(-299.213 + 217.391i) q^{61} +(1291.40 + 938.256i) q^{62} +(547.314 - 397.647i) q^{64} +(41.8736 + 381.669i) q^{65} +(-54.5434 - 167.867i) q^{67} -247.300 q^{68} +(7.37262 + 1.53204i) q^{70} +(-223.142 + 686.762i) q^{71} +(1.97619 - 1.43579i) q^{73} -1348.77 q^{74} +1362.57 q^{76} +(5.38294 - 3.91094i) q^{77} +(187.778 - 577.921i) q^{79} +(49.2675 + 449.064i) q^{80} -602.049 q^{82} +(392.005 + 1206.47i) q^{83} +(-91.6001 + 160.338i) q^{85} +(2054.45 - 1492.65i) q^{86} +(1280.29 + 930.187i) q^{88} +(-1082.09 + 786.182i) q^{89} +(-3.90415 - 2.83653i) q^{91} +(747.623 + 2300.95i) q^{92} +(-111.190 - 342.207i) q^{94} +(504.698 - 883.431i) q^{95} +(-442.269 + 1361.16i) q^{97} +(1329.95 - 966.266i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10}) \) 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8	\( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8} + 165 q^{10} - 19 q^{11} + 4 q^{13} + 24 q^{14} - 66 q^{16} - 208 q^{17} + 42 q^{19} - 295 q^{20} - 89 q^{22} - 32 q^{23} + 95 q^{25} - 206 q^{26} - 482 q^{28} + 716 q^{29} + 637 q^{31} + 844 q^{32} - 90 q^{34} - 430 q^{35} + 216 q^{37} - 2314 q^{38} - 500 q^{40} + 38 q^{41} - 1392 q^{43} - 603 q^{44} + 1622 q^{46} + 536 q^{47} + 162 q^{49} + 2265 q^{50} - 1922 q^{52} - 1672 q^{53} - 1000 q^{55} - 3000 q^{56} - 827 q^{58} - 973 q^{59} - 2712 q^{61} - 1057 q^{62} + 4439 q^{64} + 4360 q^{65} + 2768 q^{67} + 1370 q^{68} + 3230 q^{70} + 1074 q^{71} - 1018 q^{73} + 1414 q^{74} - 11408 q^{76} - 1607 q^{77} - 1820 q^{79} + 1290 q^{80} + 1772 q^{82} - 4045 q^{83} + 1850 q^{85} + 3986 q^{86} + 2407 q^{88} - 4542 q^{89} + 4412 q^{91} + 1089 q^{92} + 5137 q^{94} + 720 q^{95} - 5977 q^{97} + 10689 q^{98}+O(q^{100}) \) 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8 + 165 * q^10 - 19 * q^11 + 4 * q^13 + 24 * q^14 - 66 * q^16 - 208 * q^17 + 42 * q^19 - 295 * q^20 - 89 * q^22 - 32 * q^23 + 95 * q^25 - 206 * q^26 - 482 * q^28 + 716 * q^29 + 637 * q^31 + 844 * q^32 - 90 * q^34 - 430 * q^35 + 216 * q^37 - 2314 * q^38 - 500 * q^40 + 38 * q^41 - 1392 * q^43 - 603 * q^44 + 1622 * q^46 + 536 * q^47 + 162 * q^49 + 2265 * q^50 - 1922 * q^52 - 1672 * q^53 - 1000 * q^55 - 3000 * q^56 - 827 * q^58 - 973 * q^59 - 2712 * q^61 - 1057 * q^62 + 4439 * q^64 + 4360 * q^65 + 2768 * q^67 + 1370 * q^68 + 3230 * q^70 + 1074 * q^71 - 1018 * q^73 + 1414 * q^74 - 11408 * q^76 - 1607 * q^77 - 1820 * q^79 + 1290 * q^80 + 1772 * q^82 - 4045 * q^83 + 1850 * q^85 + 3986 * q^86 + 2407 * q^88 - 4542 * q^89 + 4412 * q^91 + 1089 * q^92 + 5137 * q^94 + 720 * q^95 - 5977 * q^97 + 10689 * q^98

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