LMFDB - Embedded newform 225.4.h.a.46.4

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			46.4
Character	$\chi$	$=$	225.46
Dual form			225.4.h.a.181.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.177563 - 0.546483i) q^{2} +(6.20502 + 4.50821i) q^{4} +(9.45304 - 5.96993i) q^{5} -2.67744 q^{7} +(7.28438 - 5.29241i) q^{8} +O(q^{10})$	\(q+(0.177563 - 0.546483i) q^{2} +(6.20502 + 4.50821i) q^{4} +(9.45304 - 5.96993i) q^{5} -2.67744 q^{7} +(7.28438 - 5.29241i) q^{8} +(-1.58395 - 6.22597i) q^{10} +(19.4804 - 59.9545i) q^{11} +(4.38017 + 13.4808i) q^{13} +(-0.475414 + 1.46317i) q^{14} +(17.3621 + 53.4350i) q^{16} +(24.5906 - 17.8661i) q^{17} +(-22.2647 + 16.1762i) q^{19} +(85.5700 + 5.57276i) q^{20} +(-29.3052 - 21.2914i) q^{22} +(-35.9246 + 110.565i) q^{23} +(53.7199 - 112.868i) q^{25} +8.14478 q^{26} +(-16.6135 - 12.0704i) q^{28} +(-32.5312 - 23.6353i) q^{29} +(180.304 - 130.998i) q^{31} +104.316 q^{32} +(-5.39715 - 16.6107i) q^{34} +(-25.3099 + 15.9841i) q^{35} +(25.6160 + 78.8378i) q^{37} +(4.88665 + 15.0396i) q^{38} +(37.2642 - 93.5166i) q^{40} +(-44.5269 - 137.040i) q^{41} +433.956 q^{43} +(391.164 - 284.197i) q^{44} +(54.0428 + 39.2644i) q^{46} +(371.550 + 269.947i) q^{47} -335.831 q^{49} +(-52.1418 - 49.3982i) q^{50} +(-33.5952 + 103.395i) q^{52} +(-200.214 - 145.464i) q^{53} +(-173.775 - 683.049i) q^{55} +(-19.5034 + 14.1701i) q^{56} +(-18.6927 + 13.5810i) q^{58} +(-95.9388 - 295.269i) q^{59} +(0.644333 - 1.98305i) q^{61} +(-39.5730 - 121.793i) q^{62} +(-120.374 + 370.473i) q^{64} +(121.885 + 101.285i) q^{65} +(-529.476 + 384.687i) q^{67} +233.129 q^{68} +(4.24094 + 16.6696i) q^{70} +(-734.591 - 533.711i) q^{71} +(-271.486 + 835.547i) q^{73} +47.6320 q^{74} -211.079 q^{76} +(-52.1575 + 160.524i) q^{77} +(921.477 + 669.493i) q^{79} +(483.127 + 401.473i) q^{80} -82.7962 q^{82} +(-798.210 + 579.934i) q^{83} +(125.796 - 315.693i) q^{85} +(77.0546 - 237.150i) q^{86} +(-175.401 - 539.830i) q^{88} +(-305.549 + 940.383i) q^{89} +(-11.7276 - 36.0939i) q^{91} +(-721.361 + 524.100i) q^{92} +(213.495 - 155.113i) q^{94} +(-113.898 + 285.833i) q^{95} +(-1244.20 - 903.964i) q^{97} +(-59.6313 + 183.526i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.177563	−	0.546483i	0.0627781	−	0.193211i	−0.914748	−	0.404024i	$-0.867611\pi$
$2$	0.177563	−	0.546483i	0.0627781	−	0.193211i	0.977526	+	0.210813i	$0.0676112\pi$
$3$		0			0
$3$		0			0
$4$	6.20502	+	4.50821i	0.775628	+	0.563526i
$5$	9.45304	−	5.96993i	0.845506	−	0.533967i
$5$	9.45304	−	5.96993i	0.845506	−	0.533967i
$6$		0			0
$7$	−2.67744			−0.144568			−0.0722840	−	0.997384i	$-0.523029\pi$
$7$	−2.67744			−0.144568			−0.0722840	+	0.997384i	$0.523029\pi$
$8$	7.28438	−	5.29241i	0.321927	−	0.233894i
$9$		0			0
$10$	−1.58395	−	6.22597i	−0.0500891	−	0.196882i
$11$	19.4804	−	59.9545i	0.533960	−	1.64336i	−0.211924	−	0.977286i	$-0.567973\pi$
$11$	19.4804	−	59.9545i	0.533960	−	1.64336i	0.745885	−	0.666075i	$-0.232027\pi$
$12$		0			0
$13$	4.38017	+	13.4808i	0.0934493	+	0.287607i	0.986846	−	0.161660i	$-0.0516849\pi$
$13$	4.38017	+	13.4808i	0.0934493	+	0.287607i	−0.893397	+	0.449268i	$0.851685\pi$
$14$	−0.475414	+	1.46317i	−0.00907569	+	0.0279321i
$15$		0			0
$16$	17.3621	+	53.4350i	0.271282	+	0.834922i
$17$	24.5906	−	17.8661i	0.350829	−	0.254892i	−0.398388	−	0.917217i	$-0.630430\pi$
$17$	24.5906	−	17.8661i	0.350829	−	0.254892i	0.749217	+	0.662325i	$0.230430\pi$
$18$		0			0
$19$	−22.2647	+	16.1762i	−0.268835	+	0.195320i	−0.714033	−	0.700112i	$-0.753133\pi$
$19$	−22.2647	+	16.1762i	−0.268835	+	0.195320i	0.445198	+	0.895432i	$0.353133\pi$
$20$	85.5700	+	5.57276i	0.956702	+	0.0623054i
$21$		0			0
$22$	−29.3052	−	21.2914i	−0.283995	−	0.206334i
$23$	−35.9246	+	110.565i	−0.325687	+	1.00236i	0.645443	+	0.763809i	$0.276673\pi$
$23$	−35.9246	+	110.565i	−0.325687	+	1.00236i	−0.971130	+	0.238553i	$0.923327\pi$
$24$		0			0
$25$	53.7199	−	112.868i	0.429759	−	0.902944i
$26$	8.14478			0.0614355
$27$		0			0
$28$	−16.6135	−	12.0704i	−0.112131	−	0.0814678i
$29$	−32.5312	−	23.6353i	−0.208307	−	0.151344i	0.478740	−	0.877956i	$-0.341093\pi$
$29$	−32.5312	−	23.6353i	−0.208307	−	0.151344i	−0.687047	+	0.726613i	$0.741093\pi$
$30$		0			0
$31$	180.304	−	130.998i	1.04463	−	0.758967i	0.0734444	−	0.997299i	$-0.476601\pi$
$31$	180.304	−	130.998i	1.04463	−	0.758967i	0.971184	+	0.238333i	$0.0766008\pi$
$32$	104.316			0.576270
$33$		0			0
$34$	−5.39715	−	16.6107i	−0.0272236	−	0.0837857i
$35$	−25.3099	+	15.9841i	−0.122233	+	0.0771944i
$36$		0			0
$37$	25.6160	+	78.8378i	0.113817	+	0.350293i	0.991698	−	0.128585i	$-0.0410435\pi$
$37$	25.6160	+	78.8378i	0.113817	+	0.350293i	−0.877881	+	0.478878i	$0.841044\pi$
$38$	4.88665	+	15.0396i	0.0208610	+	0.0642037i
$39$		0			0
$40$	37.2642	−	93.5166i	0.147300	−	0.369657i
$41$	−44.5269	−	137.040i	−0.169608	−	0.522000i	0.829738	−	0.558153i	$-0.188490\pi$
$41$	−44.5269	−	137.040i	−0.169608	−	0.522000i	−0.999346	+	0.0361527i	$0.988490\pi$
$42$		0			0
$43$	433.956			1.53901			0.769507	−	0.638638i	$-0.220502\pi$
$43$	433.956			1.53901			0.769507	+	0.638638i	$0.220502\pi$
$44$	391.164	−	284.197i	1.34023	−	0.973736i
$45$		0			0
$46$	54.0428	+	39.2644i	0.173221	+	0.125853i
$47$	371.550	+	269.947i	1.15311	+	0.837783i	0.988891	−	0.148641i	$-0.0474898\pi$
$47$	371.550	+	269.947i	1.15311	+	0.837783i	0.164218	+	0.986424i	$0.447490\pi$
$48$		0			0
$49$	−335.831			−0.979100
$50$	−52.1418	−	49.3982i	−0.147479	−	0.139719i
$51$		0			0
$52$	−33.5952	+	103.395i	−0.0895925	+	0.275737i
$53$	−200.214	−	145.464i	−0.518897	−	0.377001i	0.297291	−	0.954787i	$-0.403917\pi$
$53$	−200.214	−	145.464i	−0.518897	−	0.377001i	−0.816188	+	0.577786i	$0.803917\pi$
$54$		0			0
$55$	−173.775	−	683.049i	−0.426034	−	1.67459i
$56$	−19.5034	+	14.1701i	−0.0465403	+	0.0338135i
$57$		0			0
$58$	−18.6927	+	13.5810i	−0.0423184	+	0.0307461i
$59$	−95.9388	−	295.269i	−0.211698	−	0.651539i	−0.999372	−	0.0354462i	$-0.988715\pi$
$59$	−95.9388	−	295.269i	−0.211698	−	0.651539i	0.787674	−	0.616092i	$-0.211285\pi$
$60$		0			0
$61$	0.644333	−	1.98305i	0.00135243	−	0.00416236i	−0.950378	−	0.311097i	$-0.899303\pi$
$61$	0.644333	−	1.98305i	0.00135243	−	0.00416236i	0.951730	+	0.306935i	$0.0993034\pi$
$62$	−39.5730	−	121.793i	−0.0810610	−	0.249480i
$63$		0			0
$64$	−120.374	+	370.473i	−0.235105	+	0.723580i
$65$	121.885	+	101.285i	0.232585	+	0.193275i
$66$		0			0
$67$	−529.476	+	384.687i	−0.965460	+	0.701448i	−0.954412	−	0.298491i	$-0.903517\pi$
$67$	−529.476	+	384.687i	−0.965460	+	0.701448i	−0.0110477	+	0.999939i	$0.503517\pi$
$68$	233.129			0.415751
$69$		0			0
$70$	4.24094	+	16.6696i	0.00724127	+	0.0284629i
$71$	−734.591	−	533.711i	−1.22789	−	0.892111i	−0.231156	−	0.972917i	$-0.574251\pi$
$71$	−734.591	−	533.711i	−1.22789	−	0.892111i	−0.996730	+	0.0808056i	$0.974251\pi$
$72$		0			0
$73$	−271.486	+	835.547i	−0.435274	+	1.33964i	0.457531	+	0.889194i	$0.348734\pi$
$73$	−271.486	+	835.547i	−0.435274	+	1.33964i	−0.892805	+	0.450443i	$0.851266\pi$
$74$	47.6320			0.0748258
$75$		0			0
$76$	−211.079			−0.318584
$77$	−52.1575	+	160.524i	−0.0771935	+	0.237577i
$78$		0			0
$79$	921.477	+	669.493i	1.31233	+	0.953466i	0.999994	+	0.00349520i	$0.00111256\pi$
$79$	921.477	+	669.493i	1.31233	+	0.953466i	0.312339	+	0.949971i	$0.398887\pi$
$80$	483.127	+	401.473i	0.675191	+	0.561075i
$81$		0			0
$82$	−82.7962			−0.111504
$83$	−798.210	+	579.934i	−1.05560	+	0.766940i	−0.973270	−	0.229665i	$-0.926237\pi$
$83$	−798.210	+	579.934i	−1.05560	+	0.766940i	−0.0823324	+	0.996605i	$0.526237\pi$
$84$		0			0
$85$	125.796	−	315.693i	0.160524	−	0.402844i
$86$	77.0546	−	237.150i	0.0966164	−	0.297355i
$87$		0			0
$88$	−175.401	−	539.830i	−0.212476	−	0.653932i
$89$	−305.549	+	940.383i	−0.363911	+	1.12000i	0.586748	+	0.809769i	$0.300408\pi$
$89$	−305.549	+	940.383i	−0.363911	+	1.12000i	−0.950660	+	0.310235i	$0.899592\pi$
$90$		0			0
$91$	−11.7276	−	36.0939i	−0.0135098	−	0.0415788i
$92$	−721.361	+	524.100i	−0.817469	+	0.593926i
$93$		0			0
$94$	213.495	−	155.113i	0.234259	−	0.170199i
$95$	−113.898	+	285.833i	−0.123007	+	0.308693i
$96$		0			0
$97$	−1244.20	−	903.964i	−1.30236	−	0.946223i	−0.302388	−	0.953185i	$-0.597784\pi$
$97$	−1244.20	−	903.964i	−1.30236	−	0.946223i	−0.999976	+	0.00696215i	$0.997784\pi$
$98$	−59.6313	+	183.526i	−0.0614660	+	0.189173i
$99$		0			0
$100$	842.166	−	458.167i	0.842166	−	0.458167i
$101$	266.284			0.262339			0.131170	−	0.991360i	$-0.458127\pi$
$101$	266.284			0.262339			0.131170	+	0.991360i	$0.458127\pi$
$102$		0			0
$103$	630.873	+	458.356i	0.603512	+	0.438477i	0.847124	−	0.531396i	$-0.178332\pi$
$103$	630.873	+	458.356i	0.603512	+	0.438477i	−0.243612	+	0.969873i	$0.578332\pi$
$104$	103.253	+	75.0174i	0.0973534	+	0.0707314i
$105$		0			0
$106$	−115.044	+	83.5847i	−0.105416	+	0.0765893i
$107$	−526.990			−0.476132			−0.238066	−	0.971249i	$-0.576513\pi$
$107$	−526.990			−0.476132			−0.238066	+	0.971249i	$0.576513\pi$
$108$		0			0
$109$	−18.0367	−	55.5114i	−0.0158496	−	0.0487800i	0.942819	−	0.333305i	$-0.108164\pi$
$109$	−18.0367	−	55.5114i	−0.0158496	−	0.0487800i	−0.958669	+	0.284525i	$0.908164\pi$
$110$	−404.131	−	26.3191i	−0.350294	−	0.0228130i
$111$		0			0
$112$	−46.4858	−	143.069i	−0.0392187	−	0.120703i
$113$	14.5997	+	44.9333i	0.0121542	+	0.0374068i	0.956950	−	0.290254i	$-0.0937397\pi$
$113$	14.5997	+	44.9333i	0.0121542	+	0.0374068i	−0.944795	+	0.327661i	$0.893740\pi$
$114$		0			0
$115$	320.466	+	1259.64i	0.259857	+	1.02141i
$116$	−95.3039	−	293.315i	−0.0762823	−	0.234773i
$117$		0			0
$118$	−178.395			−0.139174
$119$	−65.8397	+	47.8354i	−0.0507186	+	0.0368493i
$120$		0			0
$121$	−2138.26	−	1553.54i	−1.60651	−	1.16719i
$122$	−0.969296	−	0.704235i	−0.000719311	−	0.000522610i
$123$		0			0
$124$	1709.35			1.23794
$125$	−165.997	−	1387.65i	−0.118778	−	0.992921i
$126$		0			0
$127$	−485.405	+	1493.92i	−0.339155	+	1.04381i	0.625484	+	0.780237i	$0.284902\pi$
$127$	−485.405	+	1493.92i	−0.339155	+	1.04381i	−0.964639	+	0.263575i	$0.915098\pi$
$128$	856.231	+	622.088i	0.591257	+	0.429573i
$129$		0			0
$130$	76.9929	−	48.6238i	0.0519440	−	0.0328045i
$131$	−2344.50	+	1703.38i	−1.56366	+	1.13607i	−0.630741	+	0.775993i	$0.717249\pi$
$131$	−2344.50	+	1703.38i	−1.56366	+	1.13607i	−0.932923	+	0.360076i	$0.882751\pi$
$132$		0			0
$133$	59.6122	−	43.3108i	0.0388649	−	0.0282370i
$134$	116.210	+	357.656i	0.0749177	+	0.230573i
$135$		0			0
$136$	84.5724	−	260.287i	0.0533237	−	0.164113i
$137$	−402.958	−	1240.18i	−0.251292	−	0.773398i	−0.994538	−	0.104379i	$-0.966714\pi$
$137$	−402.958	−	1240.18i	−0.251292	−	0.773398i	0.743245	−	0.669019i	$-0.233286\pi$
$138$		0			0
$139$	381.913	−	1175.41i	0.233047	−	0.717243i	−0.764328	−	0.644828i	$-0.776929\pi$
$139$	381.913	−	1175.41i	0.233047	−	0.717243i	0.997375	−	0.0724158i	$-0.0230709\pi$
$140$	−229.108	−	14.9207i	−0.138308	−	0.00900736i
$141$		0			0
$142$	−422.101	+	306.674i	−0.249450	+	0.181236i
$143$	893.562			0.522541
$144$		0			0
$145$	−448.620	−	29.2165i	−0.256937	−	0.0167331i
$146$	408.407	+	296.725i	0.231507	+	0.168200i
$147$		0			0
$148$	−196.470	+	604.672i	−0.109120	+	0.335836i
$149$	810.211			0.445470			0.222735	−	0.974879i	$-0.428501\pi$
$149$	810.211			0.445470			0.222735	+	0.974879i	$0.428501\pi$
$150$		0			0
$151$	−3447.19			−1.85781			−0.928903	−	0.370324i	$-0.879247\pi$
$151$	−3447.19			−1.85781			−0.928903	+	0.370324i	$0.879247\pi$
$152$	−76.5730	+	235.667i	−0.0408611	+	0.125758i
$153$		0			0
$154$	78.4626	+	57.0064i	0.0410565	+	0.0298293i
$155$	922.366	−	2314.73i	0.477976	−	1.19951i
$156$		0			0
$157$	−804.338			−0.408873			−0.204437	−	0.978880i	$-0.565536\pi$
$157$	−804.338			−0.408873			−0.204437	+	0.978880i	$0.565536\pi$
$158$	529.487	−	384.695i	0.266606	−	0.193700i
$159$		0			0
$160$	986.104	−	622.760i	0.487240	−	0.307709i
$161$	96.1858	−	296.029i	0.0470839	−	0.144909i
$162$		0			0
$163$	976.108	+	3004.15i	0.469047	+	1.44358i	0.853821	+	0.520567i	$0.174280\pi$
$163$	976.108	+	3004.15i	0.469047	+	1.44358i	−0.384774	+	0.923011i	$0.625720\pi$
$164$	341.514	−	1051.07i	0.162608	−	0.500456i
$165$		0			0
$166$	175.191	+	539.184i	0.0819126	+	0.252101i
$167$	−2278.34	+	1655.31i	−1.05571	+	0.767018i	−0.973290	−	0.229580i	$-0.926265\pi$
$167$	−2278.34	+	1655.31i	−1.05571	+	0.767018i	−0.0824199	+	0.996598i	$0.526265\pi$
$168$		0			0
$169$	1614.86	−	1173.27i	0.735032	−	0.534032i
$170$	−150.184	−	124.801i	−0.0677565	−	0.0563048i
$171$		0			0
$172$	2692.70	+	1956.36i	1.19370	+	0.867276i
$173$	1133.19	−	3487.61i	0.498006	−	1.53270i	−0.314213	−	0.949352i	$-0.601741\pi$
$173$	1133.19	−	3487.61i	0.498006	−	1.53270i	0.812219	−	0.583352i	$-0.198259\pi$
$174$		0			0
$175$	−143.832	+	302.197i	−0.0621294	+	0.130537i
$176$	3541.89			1.51693
$177$		0			0
$178$	459.649	+	333.955i	0.193552	+	0.140623i
$179$	1965.97	+	1428.36i	0.820912	+	0.596427i	0.916974	−	0.398948i	$-0.130625\pi$
$179$	1965.97	+	1428.36i	0.820912	+	0.596427i	−0.0960617	+	0.995375i	$0.530625\pi$
$180$		0			0
$181$	2655.62	−	1929.42i	1.09056	−	0.792336i	0.111064	−	0.993813i	$-0.464574\pi$
$181$	2655.62	−	1929.42i	1.09056	−	0.792336i	0.979493	+	0.201477i	$0.0645743\pi$
$182$	−21.8071			−0.00888160
$183$		0			0
$184$	323.465	+	995.522i	0.129599	+	0.398863i
$185$	712.805	+	592.331i	0.283278	+	0.235400i
$186$		0			0
$187$	−592.120	−	1822.36i	−0.231551	−	0.712642i
$188$	1088.50	+	3350.05i	0.422271	+	1.29962i
$189$		0			0
$190$	135.979	+	112.997i	0.0519208	+	0.0431455i
$191$	−659.004	−	2028.21i	−0.249654	−	0.768355i	−0.994836	−	0.101494i	$-0.967638\pi$
$191$	−659.004	−	2028.21i	−0.249654	−	0.768355i	0.745183	−	0.666861i	$-0.232362\pi$
$192$		0			0
$193$	−3868.32			−1.44274			−0.721368	−	0.692552i	$-0.756486\pi$
$193$	−3868.32			−1.44274			−0.721368	+	0.692552i	$0.756486\pi$
$194$	−714.925	+	519.423i	−0.264581	+	0.192229i
$195$		0			0
$196$	−2083.84	−	1514.00i	−0.759417	−	0.551749i
$197$	−1428.32	−	1037.74i	−0.516568	−	0.375308i	0.298742	−	0.954334i	$-0.403433\pi$
$197$	−1428.32	−	1037.74i	−0.516568	−	0.375308i	−0.815309	+	0.579026i	$0.803433\pi$
$198$		0			0
$199$	3952.78			1.40807			0.704033	−	0.710167i	$-0.251381\pi$
$199$	3952.78			1.40807			0.704033	+	0.710167i	$0.251381\pi$
$200$	−206.027	−	1106.48i	−0.0728417	−	0.391200i
$201$		0			0
$202$	47.2823	−	145.520i	0.0164692	−	0.0506869i
$203$	87.1002	+	63.2820i	0.0301145	+	0.0218794i
$204$		0			0
$205$	−1239.03	−	1029.62i	−0.422135	−	0.350789i
$206$	362.504	−	263.374i	0.122606	−	0.0890784i
$207$		0			0
$208$	−644.296	+	468.109i	−0.214778	+	0.156046i
$209$	536.113	+	1649.99i	0.177434	+	0.546086i
$210$		0			0
$211$	1472.71	−	4532.54i	0.480501	−	1.47883i	−0.357891	−	0.933763i	$-0.616504\pi$
$211$	1472.71	−	4532.54i	0.480501	−	1.47883i	0.838392	−	0.545067i	$-0.183496\pi$
$212$	−586.551	−	1805.22i	−0.190021	−	0.584825i
$213$		0			0
$214$	−93.5741	+	287.991i	−0.0298906	+	0.0919939i
$215$	4102.20	−	2590.69i	1.30125	−	0.821783i
$216$		0			0
$217$	−482.751	+	350.739i	−0.151020	+	0.109722i
$218$	−33.5387			−0.0104199
$219$		0			0
$220$	2001.05	−	5021.75i	0.613231	−	1.53894i
$221$	348.560	+	253.244i	0.106094	+	0.0770816i
$222$		0			0
$223$	−679.879	+	2092.45i	−0.204162	+	0.628345i	0.795585	+	0.605842i	$0.207164\pi$
$223$	−679.879	+	2092.45i	−0.204162	+	0.628345i	−0.999747	+	0.0225031i	$0.992836\pi$
$224$	−279.300			−0.0833102
$225$		0			0
$226$	27.1477			0.00799042
$227$	−301.326	+	927.386i	−0.0881045	+	0.271158i	−0.985395	−	0.170282i	$-0.945532\pi$
$227$	−301.326	+	927.386i	−0.0881045	+	0.271158i	0.897291	+	0.441440i	$0.145532\pi$
$228$		0			0
$229$	−1289.94	−	937.197i	−0.372235	−	0.270444i	0.385902	−	0.922540i	$-0.373890\pi$
$229$	−1289.94	−	937.197i	−0.372235	−	0.270444i	−0.758137	+	0.652095i	$0.773890\pi$
$230$	745.274	+	48.5362i	0.213661	+	0.0139147i
$231$		0			0
$232$	−362.057			−0.102458
$233$	−3787.94	+	2752.10i	−1.06505	+	0.773802i	−0.975016	−	0.222137i	$-0.928697\pi$
$233$	−3787.94	+	2752.10i	−1.06505	+	0.773802i	−0.0900318	+	0.995939i	$0.528697\pi$
$234$		0			0
$235$	5123.84	+	333.691i	1.42231	+	0.0926282i
$236$	735.834	−	2264.66i	0.202961	−	0.624649i
$237$		0			0
$238$	14.4505	+	44.4741i	0.00393566	+	0.0121127i
$239$	−22.3460	+	68.7738i	−0.00604787	+	0.0186134i	−0.954035	−	0.299695i	$-0.903115\pi$
$239$	−22.3460	+	68.7738i	−0.00604787	+	0.0186134i	0.947987	+	0.318309i	$0.103115\pi$
$240$		0			0
$241$	566.484	+	1743.46i	0.151413	+	0.466000i	0.997780	−	0.0665998i	$-0.0212151\pi$
$241$	566.484	+	1743.46i	0.151413	+	0.466000i	−0.846367	+	0.532600i	$0.821215\pi$
$242$	−1228.66	+	892.672i	−0.326368	+	0.237120i
$243$		0			0
$244$	12.9381	−	9.40010i	0.00339459	−	0.00246631i
$245$	−3174.63	+	2004.89i	−0.827835	+	0.522807i
$246$		0			0
$247$	−315.591	−	229.290i	−0.0812979	−	0.0590664i
$248$	620.103	−	1908.48i	0.158776	−	0.488664i
$249$		0			0
$250$	−787.802	−	155.681i	−0.199300	−	0.0393844i
$251$	211.935			0.0532956			0.0266478	−	0.999645i	$-0.491517\pi$
$251$	211.935			0.0532956			0.0266478	+	0.999645i	$0.491517\pi$
$252$		0			0
$253$	5929.02	+	4307.69i	1.47334	+	1.07044i
$254$	730.214	+	530.531i	0.180385	+	0.131057i
$255$		0			0
$256$	−2029.15	+	1474.26i	−0.495398	+	0.359927i
$257$	7074.89			1.71720			0.858599	−	0.512648i	$-0.171335\pi$
$257$	7074.89			1.71720			0.858599	+	0.512648i	$0.171335\pi$
$258$		0			0
$259$	−68.5851	−	211.083i	−0.0164543	−	0.0506412i
$260$	299.686	+	1177.96i	0.0714836	+	0.280977i
$261$		0			0
$262$	514.572	+	1583.69i	0.121337	+	0.373437i
$263$	1562.26	+	4808.14i	0.366286	+	1.12731i	0.949172	+	0.314758i	$0.101923\pi$
$263$	1562.26	+	4808.14i	0.366286	+	1.12731i	−0.582886	+	0.812554i	$0.698077\pi$
$264$		0			0
$265$	−2761.04	−	179.814i	−0.640036	−	0.0416825i
$266$	−13.0837	−	40.2675i	−0.00301584	−	0.00928179i
$267$		0			0
$268$	−5019.66			−1.14412
$269$	1867.63	−	1356.91i	0.423314	−	0.307556i	−0.355656	−	0.934617i	$-0.615742\pi$
$269$	1867.63	−	1356.91i	0.423314	−	0.307556i	0.778970	+	0.627061i	$0.215742\pi$
$270$		0			0
$271$	475.680	+	345.602i	0.106625	+	0.0774679i	0.639820	−	0.768525i	$-0.279009\pi$
$271$	475.680	+	345.602i	0.106625	+	0.0774679i	−0.533195	+	0.845992i	$0.679009\pi$
$272$	1381.62	+	1003.81i	0.307989	+	0.223767i
$273$		0			0
$274$	−749.287			−0.165205
$275$	−5720.46	−	5419.47i	−1.25439	−	1.18839i
$276$		0			0
$277$	−936.066	+	2880.92i	−0.203042	+	0.624900i	0.796746	+	0.604315i	$0.206553\pi$
$277$	−936.066	+	2880.92i	−0.203042	+	0.624900i	−0.999788	+	0.0205857i	$0.993447\pi$
$278$	−574.527	−	417.419i	−0.123949	−	0.0900543i
$279$		0			0
$280$	−99.7724	+	250.385i	−0.0212948	+	0.0534405i
$281$	−4977.64	+	3616.47i	−1.05673	+	0.767759i	−0.973481	−	0.228770i	$-0.926530\pi$
$281$	−4977.64	+	3616.47i	−1.05673	+	0.767759i	−0.0832489	+	0.996529i	$0.526530\pi$
$282$		0			0
$283$	4502.63	−	3271.35i	0.945773	−	0.687144i	−0.00403070	−	0.999992i	$-0.501283\pi$
$283$	4502.63	−	3271.35i	0.945773	−	0.687144i	0.949803	+	0.312848i	$0.101283\pi$
$284$	−2152.07	−	6623.38i	−0.449654	−	1.38389i
$285$		0			0
$286$	158.664	−	488.316i	0.0328041	−	0.100961i
$287$	119.218	+	366.915i	0.0245199	+	0.0754645i
$288$		0			0
$289$	−1232.70	+	3793.86i	−0.250906	+	0.772209i
$290$	−95.6247	+	239.976i	−0.0193630	+	0.0485926i
$291$		0			0
$292$	−5451.40	+	3960.67i	−1.09253	+	0.793770i
$293$	−2865.97			−0.571440			−0.285720	−	0.958313i	$-0.592233\pi$
$293$	−2865.97			−0.571440			−0.285720	+	0.958313i	$0.592233\pi$
$294$		0			0
$295$	−2669.65	−	2218.44i	−0.526892	−	0.437840i
$296$	603.838	+	438.714i	0.118572	+	0.0861478i
$297$		0			0
$298$	143.864	−	442.767i	0.0279658	−	0.0860698i
$299$	−1647.85			−0.318722
$300$		0			0
$301$	−1161.89			−0.222492
$302$	−612.095	+	1883.83i	−0.116629	+	0.358948i
$303$		0			0
$304$	−1250.94	−	908.859i	−0.236007	−	0.171469i
$305$	−5.74779	−	22.5925i	−0.00107907	−	0.00424145i
$306$		0			0
$307$	−1957.38			−0.363888			−0.181944	−	0.983309i	$-0.558239\pi$
$307$	−1957.38			−0.363888			−0.181944	+	0.983309i	$0.558239\pi$
$308$	−1047.32	+	760.920i	−0.193755	+	0.140771i
$309$		0			0
$310$	−1101.18	−	915.069i	−0.201752	−	0.167653i
$311$	−1081.33	+	3327.99i	−0.197159	+	0.606794i	0.802785	+	0.596268i	$0.203351\pi$
$311$	−1081.33	+	3327.99i	−0.197159	+	0.606794i	−0.999945	+	0.0105260i	$0.996649\pi$
$312$		0			0
$313$	132.624	+	408.176i	0.0239501	+	0.0737107i	0.962317	−	0.271930i	$-0.0876618\pi$
$313$	132.624	+	408.176i	0.0239501	+	0.0737107i	−0.938367	+	0.345640i	$0.887662\pi$
$314$	−142.821	+	439.557i	−0.0256683	+	0.0789989i
$315$		0			0
$316$	2699.57	+	8308.43i	0.480579	+	1.47907i
$317$	3210.73	−	2332.73i	0.568873	−	0.413310i	−0.265823	−	0.964022i	$-0.585644\pi$
$317$	3210.73	−	2332.73i	0.568873	−	0.413310i	0.834696	+	0.550712i	$0.185644\pi$
$318$		0			0
$319$	−2050.77	+	1489.97i	−0.359940	+	0.261512i
$320$	1073.80	+	4220.72i	0.187585	+	0.737329i
$321$		0			0
$322$	−144.696	−	105.128i	−0.0250422	−	0.0181942i
$323$	−258.495	+	795.566i	−0.0445296	+	0.137048i
$324$		0			0
$325$	1756.85	+	229.805i	0.299854	+	0.0392225i
$326$	1815.04			0.308361
$327$		0			0
$328$	−1049.62	−	762.594i	−0.176694	−	0.128376i
$329$	−994.801	−	722.765i	−0.166703	−	0.121117i
$330$		0			0
$331$	4997.11	−	3630.61i	0.829807	−	0.602890i	−0.0896980	−	0.995969i	$-0.528590\pi$
$331$	4997.11	−	3630.61i	0.829807	−	0.602890i	0.919505	+	0.393079i	$0.128590\pi$
$332$	−7567.38			−1.25094
$333$		0			0
$334$	500.051	+	1539.00i	0.0819209	+	0.252127i
$335$	−2708.61	+	6797.40i	−0.441752	+	1.10860i
$336$		0			0
$337$	−2557.17	−	7870.15i	−0.413346	−	1.27215i	−0.913722	−	0.406341i	$-0.866805\pi$
$337$	−2557.17	−	7870.15i	−0.413346	−	1.27215i	0.500375	−	0.865809i	$-0.333195\pi$
$338$	−354.431	−	1090.83i	−0.0570370	−	0.175542i
$339$		0			0
$340$	2203.78	−	1391.77i	0.351520	−	0.221997i
$341$	−4341.55	−	13361.9i	−0.689466	−	2.12196i
$342$		0			0
$343$	1817.53			0.286114
$344$	3161.10	−	2296.67i	0.495450	−	0.359966i
$345$		0			0
$346$	−1704.71	−	1238.54i	−0.264872	−	0.192440i
$347$	3062.22	+	2224.83i	0.473743	+	0.344194i	0.798898	−	0.601466i	$-0.205417\pi$
$347$	3062.22	+	2224.83i	0.473743	+	0.344194i	−0.325156	+	0.945661i	$0.605417\pi$
$348$		0			0
$349$	−7094.08			−1.08807			−0.544037	−	0.839061i	$-0.683105\pi$
$349$	−7094.08			−1.08807			−0.544037	+	0.839061i	$0.683105\pi$
$350$	139.606	+	132.261i	0.0213208	+	0.0201989i
$351$		0			0
$352$	2032.12	−	6254.22i	0.307706	−	0.947020i
$353$	−1416.95	−	1029.47i	−0.213644	−	0.155222i	0.475817	−	0.879544i	$-0.342153\pi$
$353$	−1416.95	−	1029.47i	−0.213644	−	0.155222i	−0.689461	+	0.724323i	$0.742153\pi$
$354$		0			0
$355$	−10130.3	−	659.740i	−1.51454	−	0.0986348i
$356$	−6135.38	+	4457.62i	−0.913412	+	0.663633i
$357$		0			0
$358$	1129.66	−	820.744i	0.166772	−	0.121167i
$359$	101.297	+	311.759i	0.0148920	+	0.0458329i	0.958226	−	0.286011i	$-0.0923293\pi$
$359$	101.297	+	311.759i	0.0148920	+	0.0458329i	−0.943334	+	0.331844i	$0.892329\pi$
$360$		0			0
$361$	−1885.50	+	5802.98i	−0.274895	+	0.846039i
$362$	−582.856	−	1793.85i	−0.0846250	−	0.260449i
$363$		0			0
$364$	89.9489	−	276.834i	0.0129522	−	0.0398628i
$365$	2421.79	+	9519.21i	0.347294	+	1.36509i
$366$		0			0
$367$	4716.67	−	3426.86i	0.670867	−	0.487413i	−0.199448	−	0.979908i	$-0.563915\pi$
$367$	4716.67	−	3426.86i	0.670867	−	0.487413i	0.870315	+	0.492495i	$0.163915\pi$
$368$	−6531.74			−0.925246
$369$		0			0
$370$	450.267	−	284.360i	0.0632656	−	0.0399545i
$371$	536.061	+	389.471i	0.0750159	+	0.0545022i
$372$		0			0
$373$	887.259	−	2730.70i	0.123165	−	0.379063i	−0.870397	−	0.492350i	$-0.836138\pi$
$373$	887.259	−	2730.70i	0.123165	−	0.379063i	0.993562	+	0.113287i	$0.0361380\pi$
$374$	−1101.03			−0.152227
$375$		0			0
$376$	4135.18			0.567169
$377$	176.130	−	542.073i	0.0240615	−	0.0740535i
$378$		0			0
$379$	8973.27	+	6519.46i	1.21616	+	0.883594i	0.995776	−	0.0918182i	$-0.0292678\pi$
$379$	8973.27	+	6519.46i	1.21616	+	0.883594i	0.220387	+	0.975412i	$0.429268\pi$
$380$	−1995.33	+	1260.12i	−0.269364	+	0.170113i
$381$		0			0
$382$	−1225.39			−0.164127
$383$	579.752	−	421.215i	0.0773472	−	0.0561960i	−0.548440	−	0.836190i	$-0.684778\pi$
$383$	579.752	−	421.215i	0.0773472	−	0.0561960i	0.625787	+	0.779994i	$0.284778\pi$
$384$		0			0
$385$	465.272	+	1828.82i	0.0615908	+	0.242092i
$386$	−686.872	+	2113.97i	−0.0905722	+	0.278753i
$387$		0			0
$388$	−3645.02	−	11218.2i	−0.476928	−	1.46783i
$389$	−2338.83	+	7198.19i	−0.304842	+	0.938207i	0.674894	+	0.737915i	$0.264189\pi$
$389$	−2338.83	+	7198.19i	−0.304842	+	0.938207i	−0.979736	+	0.200293i	$0.935811\pi$
$390$		0			0
$391$	1091.95	+	3360.68i	0.141234	+	0.434673i
$392$	−2446.32	+	1777.36i	−0.315199	+	0.229005i
$393$		0			0
$394$	−820.724	+	596.291i	−0.104943	+	0.0762454i
$395$	12707.6	+	827.584i	1.61870	+	0.105418i
$396$		0			0
$397$	−576.649	−	418.960i	−0.0728997	−	0.0529648i	0.550739	−	0.834678i	$-0.314346\pi$
$397$	−576.649	−	418.960i	−0.0728997	−	0.0529648i	−0.623638	+	0.781713i	$0.714346\pi$
$398$	701.868	−	2160.13i	0.0883957	−	0.272054i
$399$		0			0
$400$	6963.79	+	910.899i	0.870473	+	0.113862i
$401$	5539.33			0.689828			0.344914	−	0.938634i	$-0.387908\pi$
$401$	5539.33			0.689828			0.344914	+	0.938634i	$0.387908\pi$
$402$		0			0
$403$	2555.72	+	1856.84i	0.315904	+	0.229518i
$404$	1652.30	+	1200.47i	0.203478	+	0.147835i
$405$		0			0
$406$	50.0484	−	36.3623i	0.00611788	−	0.00444490i
$407$	5225.69			0.636432
$408$		0			0
$409$	−2701.55	−	8314.52i	−0.326609	−	1.00520i	−0.970709	−	0.240258i	$-0.922768\pi$
$409$	−2701.55	−	8314.52i	−0.326609	−	1.00520i	0.644100	−	0.764941i	$-0.277232\pi$
$410$	−782.676	+	494.288i	−0.0942771	+	0.0595393i
$411$		0			0
$412$	1848.21	+	5688.21i	0.221007	+	0.680190i
$413$	256.870	+	790.564i	0.0306047	+	0.0941916i
$414$		0			0
$415$	−4083.35	+	10247.4i	−0.482997	+	1.21211i
$416$	456.922	+	1406.26i	0.0538521	+	0.165740i
$417$		0			0
$418$	996.884			0.116649
$419$	2623.21	−	1905.87i	0.305853	−	0.222215i	−0.424262	−	0.905539i	$-0.639467\pi$
$419$	2623.21	−	1905.87i	0.305853	−	0.222215i	0.730115	+	0.683324i	$0.239467\pi$
$420$		0			0
$421$	1410.17	+	1024.55i	0.163249	+	0.118607i	0.666410	−	0.745585i	$-0.267830\pi$
$421$	1410.17	+	1024.55i	0.163249	+	0.118607i	−0.503162	+	0.864192i	$0.667830\pi$
$422$	−2215.46	−	1609.63i	−0.255561	−	0.185676i
$423$		0			0
$424$	−2228.29			−0.255225
$425$	−695.508	−	3735.26i	−0.0793813	−	0.426321i
$426$		0			0
$427$	−1.72516	+	5.30950i	−0.000195518	+	0.000601744i
$428$	−3269.99	−	2375.78i	−0.369301	−	0.268313i
$429$		0			0
$430$	−687.366	−	2701.79i	−0.0770878	−	0.303005i
$431$	5437.70	−	3950.72i	0.607715	−	0.441531i	−0.240894	−	0.970551i	$-0.577441\pi$
$431$	5437.70	−	3950.72i	0.607715	−	0.441531i	0.848609	+	0.529021i	$0.177441\pi$
$432$		0			0
$433$	4669.15	−	3392.34i	0.518210	−	0.376502i	−0.297719	−	0.954654i	$-0.596226\pi$
$433$	4669.15	−	3392.34i	0.518210	−	0.376502i	0.815929	+	0.578152i	$0.196226\pi$
$434$	105.954	+	326.094i	0.0117188	+	0.0360668i
$435$		0			0
$436$	138.339	−	425.763i	0.0151955	−	0.0467668i
$437$	−988.668	−	3042.81i	−0.108225	−	0.333083i
$438$		0			0
$439$	−1919.93	+	5908.95i	−0.208732	+	0.642412i	0.790807	+	0.612065i	$0.209661\pi$
$439$	−1919.93	+	5908.95i	−0.208732	+	0.642412i	−0.999539	+	0.0303466i	$0.990339\pi$
$440$	−4880.82	−	4055.90i	−0.528827	−	0.439449i
$441$		0			0
$442$	200.285	−	145.516i	0.0215534	−	0.0156594i
$443$	6346.31			0.680638			0.340319	−	0.940310i	$-0.389465\pi$
$443$	6346.31			0.680638			0.340319	+	0.940310i	$0.389465\pi$
$444$		0			0
$445$	2725.65	+	10713.6i	0.290356	+	1.14129i
$446$	1022.77	+	743.085i	0.108586	+	0.0788926i
$447$		0			0
$448$	322.293	−	991.917i	0.0339887	−	0.104606i
$449$	2732.09			0.287161			0.143581	−	0.989639i	$-0.454138\pi$
$449$	2732.09			0.287161			0.143581	+	0.989639i	$0.454138\pi$
$450$		0			0
$451$	−9083.55			−0.948399
$452$	−111.977	+	344.631i	−0.0116526	+	0.0358630i
$453$		0			0
$454$	453.297	+	329.339i	0.0468596	+	0.0340455i
$455$	−326.340	−	271.184i	−0.0336243	−	0.0279413i
$456$		0			0
$457$	11572.5			1.18455			0.592276	−	0.805735i	$-0.298230\pi$
$457$	11572.5			1.18455			0.592276	+	0.805735i	$0.298230\pi$
$458$	−741.209	+	538.520i	−0.0756210	+	0.0549419i
$459$		0			0
$460$	−3690.22	+	9260.81i	−0.374038	+	0.938669i
$461$	1118.62	−	3442.75i	0.113013	−	0.347819i	−0.878514	−	0.477716i	$-0.841465\pi$
$461$	1118.62	−	3442.75i	0.113013	−	0.347819i	0.991527	+	0.129897i	$0.0414647\pi$
$462$		0			0
$463$	−3882.35	−	11948.7i	−0.389694	−	1.19935i	−0.933018	−	0.359831i	$-0.882834\pi$
$463$	−3882.35	−	11948.7i	−0.389694	−	1.19935i	0.543324	−	0.839523i	$-0.317166\pi$
$464$	698.143	−	2148.66i	0.0698502	−	0.214977i
$465$		0			0
$466$	831.377	+	2558.72i	0.0826455	+	0.254357i
$467$	14107.1	−	10249.4i	1.39786	−	1.01561i	0.402910	−	0.915240i	$-0.367999\pi$
$467$	14107.1	−	10249.4i	1.39786	−	1.01561i	0.994951	−	0.100366i	$-0.0320012\pi$
$468$		0			0
$469$	1417.64	−	1029.97i	0.139575	−	0.101407i
$470$	1092.16	−	2740.84i	0.107187	−	0.268991i
$471$		0			0
$472$	−2261.54	−	1643.11i	−0.220542	−	0.160233i
$473$	8453.64	−	26017.6i	0.821773	−	2.52916i
$474$		0			0
$475$	629.722	+	3381.95i	0.0608287	+	0.326683i
$476$	−624.189			−0.0601043
$477$		0			0
$478$	33.6159	+	24.4234i	0.00321665	+	0.00233703i
$479$	−555.095	−	403.300i	−0.0529497	−	0.0384702i	0.560996	−	0.827819i	$-0.310418\pi$
$479$	−555.095	−	403.300i	−0.0529497	−	0.0384702i	−0.613945	+	0.789349i	$0.710418\pi$
$480$		0			0
$481$	−950.593	+	690.646i	−0.0901108	+	0.0654693i
$482$	1053.36			0.0995417
$483$		0			0
$484$	−6264.27	−	19279.4i	−0.588305	−	1.81062i
$485$	−17158.1	−	1117.42i	−1.60641	−	0.104618i
$486$		0			0
$487$	1216.53	+	3744.08i	0.113195	+	0.348379i	0.991566	−	0.129600i	$-0.0413694\pi$
$487$	1216.53	+	3744.08i	0.113195	+	0.348379i	−0.878371	+	0.477979i	$0.841369\pi$
$488$	−5.80157	−	17.8554i	−0.000538165	−	0.00165630i
$489$		0			0
$490$	531.942	+	2090.88i	0.0490422	+	0.192768i
$491$	6027.95	+	18552.1i	0.554048	+	1.70518i	0.698445	+	0.715664i	$0.253876\pi$
$491$	6027.95	+	18552.1i	0.554048	+	1.70518i	−0.144397	+	0.989520i	$0.546124\pi$
$492$		0			0
$493$	−1222.23			−0.111656
$494$	−181.341	+	131.752i	−0.0165160	+	0.0119996i
$495$		0			0
$496$	10130.3	+	7360.12i	0.917067	+	0.666288i
$497$	1966.82	+	1428.98i	0.177513	+	0.128971i
$498$		0			0
$499$	−8132.04			−0.729539			−0.364770	−	0.931098i	$-0.618852\pi$
$499$	−8132.04			−0.729539			−0.364770	+	0.931098i	$0.618852\pi$
$500$	5225.80	−	9358.74i	0.467410	−	0.837071i
$501$		0			0
$502$	37.6318	−	115.819i	0.00334579	−	0.0102973i
$503$	17482.4	+	12701.7i	1.54971	+	1.12593i	0.943860	+	0.330345i	$0.107165\pi$
$503$	17482.4	+	12701.7i	1.54971	+	1.12593i	0.605845	+	0.795582i	$0.292835\pi$
$504$		0			0
$505$	2517.20	−	1589.70i	0.221809	−	0.140081i
$506$	3406.86	−	2475.23i	0.299315	−	0.217465i
$507$		0			0
$508$	−9746.86	+	7081.51i	−0.851274	+	0.618487i
$509$	−4650.20	−	14311.8i	−0.404944	−	1.24629i	−0.920942	−	0.389699i	$-0.872579\pi$
$509$	−4650.20	−	14311.8i	−0.404944	−	1.24629i	0.515999	−	0.856589i	$-0.327421\pi$
$510$		0			0
$511$	726.886	−	2237.12i	0.0629267	−	0.193668i
$512$	3061.77	+	9423.15i	0.264282	+	0.813376i
$513$		0			0
$514$	1256.24	−	3866.31i	0.107802	−	0.331782i
$515$	8700.01	+	566.590i	0.744405	+	0.0484795i
$516$		0			0
$517$	23422.5	−	17017.4i	1.99250	−	1.44763i
$518$	−127.532			−0.0108174
$519$		0			0
$520$	1423.90	+	92.7318i	0.120081	+	0.00782030i
$521$	6623.59	+	4812.32i	0.556977	+	0.404667i	0.830351	−	0.557240i	$-0.188140\pi$
$521$	6623.59	+	4812.32i	0.556977	+	0.404667i	−0.273375	+	0.961908i	$0.588140\pi$
$522$		0			0
$523$	4169.76	−	12833.2i	0.348625	−	1.07296i	−0.610989	−	0.791639i	$-0.709228\pi$
$523$	4169.76	−	12833.2i	0.348625	−	1.07296i	0.959614	−	0.281319i	$-0.0907720\pi$
$524$	−22226.9			−1.85303
$525$		0			0
$526$	2904.97			0.240804
$527$	2093.34	−	6442.65i	0.173031	−	0.532535i
$528$		0			0
$529$	−1090.64	−	792.396i	−0.0896392	−	0.0651267i
$530$	−588.525	+	1476.94i	−0.0482338	+	0.121045i
$531$		0			0
$532$	565.149			0.0460570
$533$	1652.37	−	1200.51i	0.134281	−	0.0975611i
$534$		0			0
$535$	−4981.66	+	3146.09i	−0.402572	+	0.254238i
$536$	−1820.98	+	5604.41i	−0.146743	+	0.451630i
$537$		0			0
$538$	−409.908	−	1261.57i	−0.0328483	−	0.101097i
$539$	−6542.13	+	20134.6i	−0.522801	+	1.60902i
$540$		0			0
$541$	−2450.73	−	7542.58i	−0.194760	−	0.599410i	−0.999979	−	0.00643276i	$-0.997952\pi$
$541$	−2450.73	−	7542.58i	−0.194760	−	0.599410i	0.805219	−	0.592977i	$-0.202048\pi$
$542$	273.329	−	198.585i	0.0216614	−	0.0157379i
$543$		0			0
$544$	2565.20	−	1863.72i	0.202172	−	0.146887i
$545$	−501.901	−	417.073i	−0.0394478	−	0.0327806i
$546$		0			0
$547$	11905.8	+	8650.05i	0.930629	+	0.676142i	0.946147	−	0.323738i	$-0.104940\pi$
$547$	11905.8	+	8650.05i	0.930629	+	0.676142i	−0.0155174	+	0.999880i	$0.504940\pi$
$548$	3090.62	−	9511.95i	0.240921	−	0.741479i
$549$		0			0
$550$	−3977.39	+	2163.84i	−0.308357	+	0.167757i
$551$	1106.63			0.0855606
$552$		0			0
$553$	−2467.20	−	1792.52i	−0.189721	−	0.137841i
$554$	1408.16	+	1023.09i	0.107991	+	0.0784601i
$555$		0			0
$556$	7668.77	−	5571.69i	0.584943	−	0.424986i
$557$	−22711.9			−1.72771			−0.863856	−	0.503739i	$-0.831957\pi$
$557$	−22711.9			−1.72771			−0.863856	+	0.503739i	$0.831957\pi$
$558$		0			0
$559$	1900.80	+	5850.06i	0.143820	+	0.442632i
$560$	−1293.54	−	1074.92i	−0.0976110	−	0.0811134i
$561$		0			0
$562$	1092.49	+	3362.35i	0.0820000	+	0.252370i
$563$	−715.529	−	2202.17i	−0.0535630	−	0.164850i	0.920697	−	0.390279i	$-0.127622\pi$
$563$	−715.529	−	2202.17i	−0.0535630	−	0.164850i	−0.974260	+	0.225429i	$0.927622\pi$
$564$		0			0
$565$	406.260	+	337.597i	0.0302504	+	0.0251377i
$566$	−988.238	−	3041.48i	−0.0733900	−	0.225871i
$567$		0			0
$568$	−8175.66			−0.603949
$569$	−5246.99	+	3812.16i	−0.386582	+	0.280868i	−0.764053	−	0.645153i	$-0.776794\pi$
$569$	−5246.99	+	3812.16i	−0.386582	+	0.280868i	0.377472	+	0.926021i	$0.376794\pi$
$570$		0			0
$571$	1237.96	+	899.434i	0.0907307	+	0.0659197i	0.632226	−	0.774784i	$-0.282142\pi$
$571$	1237.96	+	899.434i	0.0907307	+	0.0659197i	−0.541495	+	0.840704i	$0.682142\pi$
$572$	5544.57	+	4028.36i	0.405297	+	0.294466i
$573$		0			0
$574$	221.682			0.0161199
$575$	10549.3	+	9994.25i	0.765109	+	0.724851i
$576$		0			0
$577$	2455.32	−	7556.70i	0.177151	−	0.545216i	−0.822574	−	0.568658i	$-0.807463\pi$
$577$	2455.32	−	7556.70i	0.177151	−	0.545216i	0.999725	+	0.0234424i	$0.00746262\pi$
$578$	1854.40	+	1347.30i	0.133448	+	0.0969556i
$579$		0			0
$580$	−2651.98	−	2203.76i	−0.189858	−	0.157769i
$581$	2137.16	−	1552.74i	0.152606	−	0.110875i
$582$		0			0
$583$	−12621.5	+	9170.06i	−0.896619	+	0.651432i
$584$	2444.45	+	7523.26i	0.173206	+	0.533073i
$585$		0			0
$586$	−508.891	+	1566.21i	−0.0358739	+	0.110409i
$587$	863.957	+	2658.98i	0.0607484	+	0.186964i	0.976825	−	0.214038i	$-0.0686618\pi$
$587$	863.957	+	2658.98i	0.0607484	+	0.186964i	−0.916077	+	0.401003i	$0.868662\pi$
$588$		0			0
$589$	−1895.34	+	5833.26i	−0.132591	+	0.408074i
$590$	−1686.37	+	1065.01i	−0.117673	+	0.0743145i
$591$		0			0
$592$	−3767.95	+	2737.58i	−0.261591	+	0.190057i
$593$	−18900.9			−1.30889			−0.654443	−	0.756112i	$-0.727097\pi$
$593$	−18900.9			−1.30889			−0.654443	+	0.756112i	$0.727097\pi$
$594$		0			0
$595$	−336.812	+	845.248i	−0.0232066	+	0.0582383i
$596$	5027.38	+	3652.60i	0.345519	+	0.251034i
$597$		0			0
$598$	−292.598	+	900.524i	−0.0200087	+	0.0615806i
$599$	−5146.04			−0.351021			−0.175511	−	0.984478i	$-0.556158\pi$
$599$	−5146.04			−0.351021			−0.175511	+	0.984478i	$0.556158\pi$
$600$		0			0
$601$	−1011.92			−0.0686805			−0.0343403	−	0.999410i	$-0.510933\pi$
$601$	−1011.92			−0.0686805			−0.0343403	+	0.999410i	$0.510933\pi$
$602$	−206.309	+	634.953i	−0.0139676	+	0.0429879i
$603$		0			0
$604$	−21389.9	−	15540.7i	−1.44096	−	1.04692i
$605$	−29487.5	−	1920.38i	−1.98155	−	0.129049i
$606$		0			0
$607$	10173.3			0.680263			0.340131	−	0.940378i	$-0.389528\pi$
$607$	10173.3			0.680263			0.340131	+	0.940378i	$0.389528\pi$
$608$	−2322.56	+	1687.44i	−0.154922	+	0.112557i
$609$		0			0
$610$	−13.3670	−	0.870530i	−0.000887238	−	5.77815e-5i
$611$	−2011.64	+	6191.20i	−0.133195	+	0.409933i
$612$		0			0
$613$	6821.12	+	20993.3i	0.449433	+	1.38321i	0.877548	+	0.479489i	$0.159178\pi$
$613$	6821.12	+	20993.3i	0.449433	+	1.38321i	−0.428115	+	0.903724i	$0.640822\pi$
$614$	−347.559	+	1069.68i	−0.0228442	+	0.0703071i
$615$		0			0
$616$	469.626	+	1445.36i	0.0307171	+	0.0945376i
$617$	−18690.4	+	13579.4i	−1.21953	+	0.886039i	−0.996061	−	0.0886729i	$-0.971737\pi$
$617$	−18690.4	+	13579.4i	−1.21953	+	0.886039i	−0.223467	+	0.974712i	$0.571737\pi$
$618$		0			0
$619$	−1080.02	+	784.684i	−0.0701290	+	0.0509517i	−0.622297	−	0.782781i	$-0.713801\pi$
$619$	−1080.02	+	784.684i	−0.0701290	+	0.0509517i	0.552168	+	0.833733i	$0.313801\pi$
$620$	16158.6	−	10204.7i	1.04669	−	0.661019i
$621$		0			0
$622$	1626.69	+	1181.86i	0.104862	+	0.0761868i
$623$	818.087	−	2517.81i	0.0526099	−	0.161917i
$624$		0			0
$625$	−9853.35	−	12126.5i	−0.630614	−	0.776096i
$626$	246.610			0.0157453
$627$		0			0
$628$	−4990.93	−	3626.12i	−0.317133	−	0.230411i
$629$	2038.44	+	1481.01i	0.129218	+	0.0938820i
$630$		0			0
$631$	5073.00	−	3685.75i	0.320052	−	0.232531i	−0.416146	−	0.909298i	$-0.636619\pi$
$631$	5073.00	−	3685.75i	0.320052	−	0.232531i	0.736198	+	0.676767i	$0.236619\pi$
$632$	10255.6			0.645485
$633$		0			0
$634$	−704.692	−	2168.82i	−0.0441434	−	0.135859i
$635$	4330.06	+	17019.9i	0.270603	+	1.06365i
$636$		0			0
$637$	−1471.00	−	4527.27i	−0.0914962	−	0.281596i
$638$	450.102	+	1385.27i	0.0279306	+	0.0859616i
$639$		0			0
$640$	11807.8	+	768.986i	0.729288	+	0.0474951i
$641$	−2824.44	−	8692.72i	−0.174038	−	0.535635i	0.825550	−	0.564329i	$-0.190865\pi$
$641$	−2824.44	−	8692.72i	−0.174038	−	0.535635i	−0.999588	+	0.0286942i	$0.990865\pi$
$642$		0			0
$643$	−12262.8			−0.752095			−0.376047	−	0.926600i	$-0.622717\pi$
$643$	−12262.8			−0.752095			−0.376047	+	0.926600i	$0.622717\pi$
$644$	1931.40	−	1403.24i	0.118180	−	0.0858626i
$645$		0			0
$646$	388.864	+	282.527i	0.0236837	+	0.0172072i
$647$	−13172.3	−	9570.20i	−0.800394	−	0.581520i	0.110636	−	0.993861i	$-0.464711\pi$
$647$	−13172.3	−	9570.20i	−0.800394	−	0.581520i	−0.911030	+	0.412341i	$0.864711\pi$
$648$		0			0
$649$	−19571.7			−1.18375
$650$	437.537	−	919.284i	0.0264025	−	0.0554728i
$651$		0			0
$652$	−7486.58	+	23041.3i	−0.449689	+	1.38400i
$653$	3811.13	+	2768.95i	0.228393	+	0.165938i	0.696097	−	0.717948i	$-0.254918\pi$
$653$	3811.13	+	2768.95i	0.228393	+	0.165938i	−0.467703	+	0.883886i	$0.654918\pi$
$654$		0			0
$655$	−11993.6	+	30098.6i	−0.715464	+	1.79550i
$656$	6549.63	−	4758.59i	0.389817	−	0.283219i
$657$		0			0
$658$	−571.619	+	415.306i	−0.0338663	+	0.0246053i
$659$	−5153.02	−	15859.4i	−0.304603	−	0.937471i	−0.979825	−	0.199857i	$-0.935952\pi$
$659$	−5153.02	−	15859.4i	−0.304603	−	0.937471i	0.675222	−	0.737614i	$-0.264048\pi$
$660$		0			0
$661$	−5801.03	+	17853.7i	−0.341352	+	1.05057i	0.622156	+	0.782894i	$0.286257\pi$
$661$	−5801.03	+	17853.7i	−0.341352	+	1.05057i	−0.963508	+	0.267680i	$0.913743\pi$
$662$	−1096.77	−	3375.50i	−0.0643913	−	0.198176i
$663$		0			0
$664$	−2745.22	+	8448.91i	−0.160444	+	0.493797i
$665$	304.954	−	765.299i	0.0177829	−	0.0446271i
$666$		0			0
$667$	3781.90	−	2747.71i	0.219544	−	0.159508i
$668$	−21599.7			−1.25107
$669$		0			0
$670$	3233.72	+	2687.18i	0.186462	+	0.154947i
$671$	−106.341	−	77.2614i	−0.00611812	−	0.00444507i
$672$		0			0
$673$	9259.20	−	28496.9i	0.530336	−	1.63221i	−0.223181	−	0.974777i	$-0.571644\pi$
$673$	9259.20	−	28496.9i	0.530336	−	1.63221i	0.753517	−	0.657429i	$-0.228356\pi$
$674$	−4754.96			−0.271742
$675$		0			0
$676$	15309.6			0.871052
$677$	6669.63	−	20527.0i	0.378633	−	1.16531i	−0.562362	−	0.826891i	$-0.690107\pi$
$677$	6669.63	−	20527.0i	0.378633	−	1.16531i	0.940995	−	0.338421i	$-0.109893\pi$
$678$		0			0
$679$	3331.26	+	2420.30i	0.188280	+	0.136793i
$680$	−754.429	−	2965.40i	−0.0425456	−	0.167232i
$681$		0			0
$682$	−8072.96			−0.453269
$683$	4810.04	−	3494.70i	0.269474	−	0.195784i	−0.444839	−	0.895610i	$-0.646739\pi$
$683$	4810.04	−	3494.70i	0.269474	−	0.195784i	0.714313	+	0.699826i	$0.246739\pi$
$684$		0			0
$685$	−11213.0	−	9317.82i	−0.625438	−	0.519731i
$686$	322.726	−	993.248i	0.0179617	−	0.0552804i
$687$		0			0
$688$	7534.37	+	23188.4i	0.417508	+	1.28496i
$689$	1084.00	−	3336.20i	0.0599377	−	0.184469i
$690$		0			0
$691$	−4660.89	−	14344.7i	−0.256597	−	0.789725i	−0.993511	−	0.113738i	$-0.963718\pi$
$691$	−4660.89	−	14344.7i	−0.256597	−	0.789725i	0.736914	−	0.675987i	$-0.236282\pi$
$692$	22754.4	−	16532.0i	1.24999	−	0.908168i
$693$		0			0
$694$	1759.57	−	1278.40i	0.0962427	−	0.0699244i
$695$	−3406.86	−	13391.2i	−0.185942	−	0.730872i
$696$		0			0
$697$	−3543.31	−	2574.37i	−0.192557	−	0.139901i
$698$	−1259.65	+	3876.80i	−0.0683071	+	0.210228i
$699$		0			0
$700$	−2254.84	+	1226.71i	−0.121750	+	0.0662363i
$701$	−29869.3			−1.60934			−0.804671	−	0.593722i	$-0.797658\pi$
$701$	−29869.3			−1.60934			−0.804671	+	0.593722i	$0.797658\pi$
$702$		0			0
$703$	−1845.63	−	1340.93i	−0.0990174	−	0.0719403i
$704$	19866.6	+	14433.9i	1.06357	+	0.772726i
$705$		0			0
$706$	−814.186	+	591.541i	−0.0434027	+	0.0315339i
$707$	−712.959			−0.0379259
$708$		0			0
$709$	3546.30	+	10914.4i	0.187848	+	0.578136i	0.999986	−	0.00532961i	$-0.00169648\pi$
$709$	3546.30	+	10914.4i	0.187848	+	0.578136i	−0.812138	+	0.583465i	$0.801696\pi$
$710$	−2159.31	+	5418.91i	−0.114137	+	0.286434i
$711$		0			0
$712$	2751.16	+	8467.19i	0.144809	+	0.445676i
$713$	8006.43	+	24641.2i	0.420537	+	1.29428i
$714$		0			0
$715$	8446.87	−	5334.50i	0.441811	−	0.279020i
$716$	5759.52	+	17726.0i	0.300619	+	0.925211i
$717$		0			0
$718$	188.358			0.00979031
$719$	7033.06	−	5109.81i	0.364797	−	0.265040i	−0.390253	−	0.920707i	$-0.627613\pi$
$719$	7033.06	−	5109.81i	0.364797	−	0.265040i	0.755050	+	0.655667i	$0.227613\pi$
$720$		0			0
$721$	−1689.12	−	1227.22i	−0.0872484	−	0.0633897i
$722$	2836.44	+	2060.79i	0.146207	+	0.106225i
$723$		0			0
$724$	25176.4			1.29237
$725$	−4415.24	+	2402.05i	−0.226177	+	0.123048i
$726$		0			0
$727$	4671.47	−	14377.3i	0.238315	−	0.733459i	−0.758349	−	0.651849i	$-0.773994\pi$
$727$	4671.47	−	14377.3i	0.238315	−	0.733459i	0.996664	−	0.0816103i	$-0.0260063\pi$
$728$	−276.452	−	200.854i	−0.0140742	−	0.0102255i
$729$		0			0
$730$	5632.11	+	366.792i	0.285553	+	0.0185967i
$731$	10671.2	−	7753.11i	0.539931	−	0.392283i
$732$		0			0
$733$	27204.2	−	19765.0i	1.37082	−	0.995959i	0.373148	−	0.927772i	$-0.378278\pi$
$733$	27204.2	−	19765.0i	1.37082	−	0.995959i	0.997673	−	0.0681872i	$-0.0217215\pi$
$734$	−1035.22	−	3186.06i	−0.0520579	−	0.160218i
$735$		0			0
$736$	−3747.51	+	11533.7i	−0.187684	+	0.577631i
$737$	12749.3	+	39238.4i	0.637215	+	1.96115i
$738$		0			0
$739$	−2946.68	+	9068.95i	−0.146678	+	0.451430i	−0.997223	−	0.0744731i	$-0.976273\pi$
$739$	−2946.68	+	9068.95i	−0.146678	+	0.451430i	0.850545	+	0.525903i	$0.176273\pi$
$740$	1752.61	+	6888.90i	0.0870640	+	0.342218i
$741$		0			0
$742$	308.024	−	223.793i	0.0152398	−	0.0110724i
$743$	−39282.1			−1.93960			−0.969798	−	0.243909i	$-0.921570\pi$
$743$	−39282.1			−1.93960			−0.969798	+	0.243909i	$0.921570\pi$
$744$		0			0
$745$	7658.96	−	4836.90i	0.376648	−	0.237866i
$746$	−1334.74	−	969.744i	−0.0655070	−	0.0475936i
$747$		0			0
$748$	4541.46	−	13977.2i	0.221995	−	0.683230i
$749$	1410.98			0.0688333
$750$		0			0
$751$	15625.4			0.759226			0.379613	−	0.925145i	$-0.376057\pi$
$751$	15625.4			0.759226			0.379613	+	0.925145i	$0.376057\pi$
$752$	−7973.73	+	24540.6i	−0.386665	+	1.19003i
$753$		0			0
$754$	−264.960	−	192.504i	−0.0127974	−	0.00929788i
$755$	−32586.4	+	20579.5i	−1.57078	+	0.992006i
$756$		0			0
$757$	−28389.3			−1.36305			−0.681524	−	0.731796i	$-0.738682\pi$
$757$	−28389.3			−1.36305			−0.681524	+	0.731796i	$0.738682\pi$
$758$	5156.10	−	3746.13i	0.247069	−	0.179506i
$759$		0			0
$760$	683.070	+	2684.91i	0.0326021	+	0.128147i
$761$	2807.36	−	8640.18i	0.133728	−	0.411572i	−0.861662	−	0.507482i	$-0.830576\pi$
$761$	2807.36	−	8640.18i	0.133728	−	0.411572i	0.995390	+	0.0959105i	$0.0305763\pi$
$762$		0			0
$763$	48.2922	+	148.628i	0.00229134	+	0.00705203i
$764$	5054.45	−	15556.0i	0.239350	−	0.736644i
$765$		0			0
$766$	−127.244	−	391.617i	−0.00600198	−	0.0184722i
$767$	3560.23	−	2586.66i	0.167604	−	0.121772i
$768$		0			0
$769$	−10201.3	+	7411.64i	−0.478370	+	0.347556i	−0.800694	−	0.599073i	$-0.795536\pi$
$769$	−10201.3	+	7411.64i	−0.478370	+	0.347556i	0.322324	+	0.946629i	$0.395536\pi$
$770$	1082.03	+	70.4677i	0.0506413	+	0.00329803i
$771$		0			0
$772$	−24003.0	−	17439.2i	−1.11903	−	0.813020i
$773$	3920.38	−	12065.7i	0.182415	−	0.561414i	−0.817480	−	0.575957i	$-0.804629\pi$
$773$	3920.38	−	12065.7i	0.182415	−	0.561414i	0.999894	+	0.0145432i	$0.00462941\pi$
$774$		0			0
$775$	−5099.61	−	27387.7i	−0.236366	−	1.26941i
$776$	−13847.4			−0.640582
$777$		0			0
$778$	3518.40	+	2556.27i	0.162135	+	0.117798i
$779$	3208.16	+	2330.87i	0.147554	+	0.107204i
$780$		0			0
$781$	−46308.6	+	33645.1i	−2.12170	+	1.54151i
$782$	2030.45			0.0928499
$783$		0			0
$784$	−5830.73	−	17945.1i	−0.265613	−	0.817472i
$785$	−7603.43	+	4801.84i	−0.345705	+	0.218325i
$786$		0			0
$787$	−1803.51	−	5550.62i	−0.0816875	−	0.251408i	0.901869	−	0.432010i	$-0.142195\pi$
$787$	−1803.51	−	5550.62i	−0.0816875	−	0.251408i	−0.983556	+	0.180602i	$0.942195\pi$
$788$	−4184.43	−	12878.4i	−0.189168	−	0.582199i
$789$		0			0
$790$	2708.66	−	6797.53i	0.121987	−	0.306133i
$791$	−39.0898	−	120.306i	−0.00175711	−	0.00540782i
$792$		0			0
$793$	29.5554			0.00132351
$794$	−331.346	+	240.737i	−0.0148099	+	0.0107600i
$795$		0			0
$796$	24527.1	+	17820.0i	1.09213	+	0.793483i
$797$	−8363.61	−	6076.52i	−0.371712	−	0.270064i	0.386209	−	0.922411i	$-0.373784\pi$
$797$	−8363.61	−	6076.52i	−0.371712	−	0.270064i	−0.757920	+	0.652347i	$0.773784\pi$
$798$		0			0
$799$	13959.5			0.618089
$800$	5603.85	−	11773.9i	0.247657	−	0.520340i
$801$		0			0
$802$	983.581	−	3027.15i	0.0433060	−	0.133282i
$803$	44806.2	+	32553.6i	1.96909	+	1.43063i
$804$		0			0
$805$	−858.027	−	3372.60i	−0.0375670	−	0.147663i
$806$	1468.53	−	1066.95i	0.0641772	−	0.0466275i
$807$		0			0
$808$	1939.72	−	1409.29i	0.0844542	−	0.0613595i
$809$	−7061.41	−	21732.8i	−0.306880	−	0.944480i	−0.978969	−	0.204009i	$-0.934603\pi$
$809$	−7061.41	−	21732.8i	−0.306880	−	0.944480i	0.672089	−	0.740470i	$-0.265397\pi$
$810$		0			0
$811$	5199.66	−	16002.9i	0.225135	−	0.692895i	−0.773142	−	0.634232i	$-0.781316\pi$
$811$	5199.66	−	16002.9i	0.225135	−	0.692895i	0.998278	−	0.0586630i	$-0.0186837\pi$
$812$	255.170	+	785.333i	0.0110280	+	0.0339406i
$813$		0			0
$814$	927.891	−	2855.75i	0.0399540	−	0.122966i
$815$	27161.8	+	22571.1i	1.16740	+	0.970098i
$816$		0			0
$817$	−9661.88	+	7019.77i	−0.413741	+	0.300600i
$818$	−5023.44			−0.214719
$819$		0			0
$820$	−3046.48	−	11974.6i	−0.129741	−	0.509966i
$821$	−31598.7	−	22957.8i	−1.34324	−	0.975924i	−0.999318	−	0.0369280i	$-0.988243\pi$
$821$	−31598.7	−	22957.8i	−1.34324	−	0.975924i	−0.343927	−	0.938996i	$-0.611757\pi$
$822$		0			0
$823$	4474.49	−	13771.0i	0.189515	−	0.583267i	−0.810482	−	0.585764i	$-0.800795\pi$
$823$	4474.49	−	13771.0i	0.189515	−	0.583267i	0.999997	+	0.00249670i	$0.000794724\pi$
$824$	7021.32			0.296844
$825$		0			0
$826$	477.641			0.0201202
$827$	6978.44	−	21477.4i	0.293427	−	0.903075i	−0.690318	−	0.723506i	$-0.742530\pi$
$827$	6978.44	−	21477.4i	0.293427	−	0.903075i	0.983745	−	0.179570i	$-0.0574705\pi$
$828$		0			0
$829$	24825.2	+	18036.5i	1.04006	+	0.755651i	0.970298	−	0.241912i	$-0.0777746\pi$
$829$	24825.2	+	18036.5i	1.04006	+	0.755651i	0.0697666	+	0.997563i	$0.477775\pi$
$830$	4874.98	+	4051.04i	0.203871	+	0.169414i
$831$		0			0
$832$	−5521.52			−0.230077
$833$	−8258.29	+	6000.00i	−0.343497	+	0.249565i
$834$		0			0
$835$	−11655.2	+	29249.3i	−0.483046	+	1.21223i
$836$	−4111.90	+	12655.1i	−0.170111	+	0.523548i
$837$		0			0
$838$	−575.743	−	1771.95i	−0.0237335	−	0.0730443i
$839$	−8848.60	+	27233.2i	−0.364109	+	1.12061i	0.586428	+	0.810002i	$0.300534\pi$
$839$	−8848.60	+	27233.2i	−0.364109	+	1.12061i	−0.950537	+	0.310612i	$0.899466\pi$
$840$		0			0
$841$	−7036.96	−	21657.5i	−0.288530	−	0.888005i
$842$	810.295	−	588.714i	0.0331646	−	0.0240955i
$843$		0			0
$844$	29571.9	−	21485.2i	1.20605	−	0.876247i
$845$	8261.05	−	20731.6i	0.336318	−	0.844009i
$846$		0			0
$847$	5725.05	+	4159.49i	0.232249	+	0.168739i
$848$	4296.74	−	13224.0i	0.173998	−	0.535512i
$849$		0			0
$850$	−2164.75	−	283.161i	−0.0873534	−	0.0114263i
$851$	−9636.91			−0.388189
$852$		0			0
$853$	25308.6	+	18387.8i	1.01589	+	0.738084i	0.965435	−	0.260642i	$-0.0839343\pi$
$853$	25308.6	+	18387.8i	1.01589	+	0.738084i	0.0504504	+	0.998727i	$0.483934\pi$
$854$	2.59523	+	1.88554i	0.000103989	+	7.55526e-5i
$855$		0			0
$856$	−3838.80	+	2789.05i	−0.153280	+	0.111364i
$857$	18790.1			0.748958			0.374479	−	0.927235i	$-0.377822\pi$
$857$	18790.1			0.748958			0.374479	+	0.927235i	$0.377822\pi$
$858$		0			0
$859$	13511.0	+	41582.7i	0.536659	+	1.65167i	0.740036	+	0.672567i	$0.234808\pi$
$859$	13511.0	+	41582.7i	0.536659	+	1.65167i	−0.203377	+	0.979101i	$0.565192\pi$
$860$	37133.6	+	2418.33i	1.47238	+	0.0958889i
$861$		0			0
$862$	−1193.47	−	3673.12i	−0.0471574	−	0.145136i
$863$	1918.14	+	5903.42i	0.0756596	+	0.232856i	0.981733	−	0.190265i	$-0.0609346\pi$
$863$	1918.14	+	5903.42i	0.0756596	+	0.232856i	−0.906073	+	0.423121i	$0.860935\pi$
$864$		0			0
$865$	−10108.7	−	39733.6i	−0.397346	−	1.56183i
$866$	−1024.79	−	3153.97i	−0.0402120	−	0.123760i
$867$		0			0
$868$	−4576.69			−0.178966
$869$	58089.9	−	42204.8i	2.26762	−	1.64752i
$870$		0			0
$871$	−7505.08	−	5452.76i	−0.291963	−	0.212124i
$872$	−425.175	−	308.908i	−0.0165118	−	0.0119965i
$873$		0			0
$874$	−1838.39			−0.0711495
$875$	444.447	+	3715.34i	0.0171715	+	0.143544i
$876$		0			0
$877$	2031.80	−	6253.24i	0.0782315	−	0.240772i	−0.904291	−	0.426917i	$-0.859600\pi$
$877$	2031.80	−	6253.24i	0.0782315	−	0.240772i	0.982522	+	0.186145i	$0.0595996\pi$
$878$	2888.23	+	2098.42i	0.111017	+	0.0806588i
$879$		0			0
$880$	33481.6	−	21144.8i	1.28257	−	0.809991i
$881$	41653.2	−	30262.8i	1.59289	−	1.15730i	0.693217	−	0.720729i	$-0.256193\pi$
$881$	41653.2	−	30262.8i	1.59289	−	1.15730i	0.899670	−	0.436571i	$-0.143807\pi$
$882$		0			0
$883$	−30274.1	+	21995.4i	−1.15380	+	0.838285i	−0.988982	−	0.148039i	$-0.952704\pi$
$883$	−30274.1	+	21995.4i	−1.15380	+	0.838285i	−0.164819	+	0.986324i	$0.552704\pi$
$884$	1021.15	+	3142.77i	0.0388517	+	0.119573i
$885$		0			0
$886$	1126.87	−	3468.15i	0.0427291	−	0.131507i
$887$	−12836.0	−	39505.1i	−0.485897	−	1.49544i	−0.830678	−	0.556753i	$-0.812047\pi$
$887$	−12836.0	−	39505.1i	−0.485897	−	1.49544i	0.344781	−	0.938683i	$-0.387953\pi$
$888$		0			0
$889$	1299.64	−	3999.88i	0.0490310	−	0.150902i
$890$	6338.77	+	412.814i	0.238737	+	0.0155478i
$891$		0			0
$892$	−13651.9	+	9918.67i	−0.512442	+	0.372311i
$893$	−12639.2			−0.473632
$894$		0			0
$895$	27111.6	+	1765.65i	1.01256	+	0.0659430i
$896$	−2292.50	−	1665.60i	−0.0854767	−	0.0621025i
$897$		0			0
$898$	485.119	−	1493.04i	0.0180274	−	0.0554827i
$899$	−8961.68			−0.332468
$900$		0			0
$901$	−7522.27			−0.278139
$902$	−1612.90	+	4964.01i	−0.0595386	+	0.183241i
$903$		0			0
$904$	344.155	+	250.043i	0.0126620	+	0.00919947i
$905$	13585.2	−	34092.8i	0.498991	−	1.25225i
$906$		0			0
$907$	−14471.6			−0.529792			−0.264896	−	0.964277i	$-0.585338\pi$
$907$	−14471.6			−0.529792			−0.264896	+	0.964277i	$0.585338\pi$
$908$	−6050.59	+	4396.01i	−0.221141	+	0.160668i
$909$		0			0
$910$	−206.144	+	130.187i	−0.00750944	+	0.00474248i
$911$	6104.65	−	18788.2i	0.222015	−	0.683293i	−0.776565	−	0.630037i	$-0.783040\pi$
$911$	6104.65	−	18788.2i	0.222015	−	0.683293i	0.998581	−	0.0532566i	$-0.0169601\pi$
$912$		0			0
$913$	19220.2	+	59153.7i	0.696709	+	2.14425i
$914$	2054.86	−	6324.19i	0.0743639	−	0.228868i
$915$		0			0
$916$	−3779.03	−	11630.7i	−0.136313	−	0.419528i
$917$	6277.25	−	4560.69i	0.226056	−	0.164239i
$918$		0			0
$919$	−7114.39	+	5168.90i	−0.255367	+	0.185535i	−0.708102	−	0.706110i	$-0.750448\pi$
$919$	−7114.39	+	5168.90i	−0.255367	+	0.185535i	0.452735	+	0.891645i	$0.350448\pi$
$920$	9000.92	+	7479.65i	0.322556	+	0.268040i
$921$		0			0
$922$	−1682.78	−	1222.61i	−0.0601077	−	0.0436708i
$923$	3977.21	−	12240.6i	0.141833	−	0.436516i
$924$		0			0
$925$	10274.3	+	1343.94i	0.365209	+	0.0477713i
$926$	−7219.10			−0.256193
$927$		0			0
$928$	−3393.53	−	2465.54i	−0.120041	−	0.0872149i
$929$	25055.7	+	18204.0i	0.884876	+	0.642900i	0.934537	−	0.355866i	$-0.115814\pi$
$929$	25055.7	+	18204.0i	0.884876	+	0.642900i	−0.0496611	+	0.998766i	$0.515814\pi$
$930$		0			0
$931$	7477.17	−	5432.48i	0.263216	−	0.191238i
$932$	−35911.3			−1.26214
$933$		0			0
$934$	−3096.24	−	9529.24i	−0.108471	−	0.333840i
$935$	−16476.7	−	13691.9i	−0.576305	−	0.478902i
$936$		0			0
$937$	−8534.11	−	26265.3i	−0.297542	−	0.915741i	−0.982356	−	0.187022i	$-0.940116\pi$
$937$	−8534.11	−	26265.3i	−0.297542	−	0.915741i	0.684813	−	0.728718i	$-0.259884\pi$
$938$	−311.144	−	957.601i	−0.0108307	−	0.0333335i
$939$		0			0
$940$	30289.2	+	25169.9i	1.05098	+	0.873354i
$941$	7954.59	+	24481.7i	0.275571	+	0.848120i	0.989068	+	0.147462i	$0.0471104\pi$
$941$	7954.59	+	24481.7i	0.275571	+	0.848120i	−0.713497	+	0.700659i	$0.752890\pi$
$942$		0			0
$943$	16751.3			0.578472
$944$	14112.0	−	10253.0i	0.486554	−	0.353502i
$945$		0			0
$946$	−12717.1	−	9239.54i	−0.437072	−	0.317551i
$947$	−7972.65	−	5792.47i	−0.273576	−	0.198764i	0.442535	−	0.896751i	$-0.354079\pi$
$947$	−7972.65	−	5792.47i	−0.273576	−	0.198764i	−0.716111	+	0.697987i	$0.754079\pi$
$948$		0			0
$949$	−12453.0			−0.425965
$950$	1960.00	+	256.378i	0.0669375	+	0.00875578i
$951$		0			0
$952$	−226.437	+	696.902i	−0.00770890	+	0.0237255i
$953$	13751.8	+	9991.27i	0.467434	+	0.339611i	0.796440	−	0.604717i	$-0.206714\pi$
$953$	13751.8	+	9991.27i	0.467434	+	0.339611i	−0.329006	+	0.944328i	$0.606714\pi$
$954$		0			0
$955$	−18337.8	−	15238.5i	−0.621359	−	0.516341i
$956$	−448.704	+	326.003i	−0.0151801	+	0.0110290i
$957$		0			0
$958$	−318.961	+	231.739i	−0.0107570	+	0.00781538i
$959$	1078.89	+	3320.50i	0.0363288	+	0.111809i
$960$		0			0
$961$	6142.91	−	18905.9i	0.206200	−	0.634619i
$962$	208.636	+	642.116i	0.00699242	+	0.0215204i
$963$		0			0
$964$	−4344.83	+	13372.0i	−0.145164	+	0.446767i
$965$	−36567.4	+	23093.6i	−1.21984	+	0.770373i
$966$		0			0
$967$	−35433.3	+	25743.8i	−1.17835	+	0.856118i	−0.991984	−	0.126364i	$-0.959669\pi$
$967$	−35433.3	+	25743.8i	−1.17835	+	0.856118i	−0.186361	+	0.982481i	$0.559669\pi$
$968$	−23797.8			−0.790177
$969$		0			0
$970$	−3657.29	+	9178.18i	−0.121060	+	0.303808i
$971$	10419.1	+	7569.90i	0.344350	+	0.250185i	0.746495	−	0.665391i	$-0.231735\pi$
$971$	10419.1	+	7569.90i	0.344350	+	0.250185i	−0.402145	+	0.915576i	$0.631735\pi$
$972$		0			0
$973$	−1022.55	+	3147.08i	−0.0336910	+	0.103690i
$974$	2262.09			0.0744168
$975$		0			0
$976$	117.151			0.00384214
$977$	−13718.8	+	42222.0i	−0.449234	+	1.38260i	0.428538	+	0.903524i	$0.359029\pi$
$977$	−13718.8	+	42222.0i	−0.449234	+	1.38260i	−0.877773	+	0.479078i	$0.840971\pi$
$978$		0			0
$979$	50428.0	+	36638.1i	1.64626	+	1.19608i
$980$	−28737.1	−	1871.51i	−0.936707	−	0.0610032i
$981$		0			0
$982$	11208.8			0.364242
$983$	−5150.84	+	3742.31i	−0.167127	+	0.121425i	−0.668205	−	0.743977i	$-0.732937\pi$
$983$	−5150.84	+	3742.31i	−0.167127	+	0.121425i	0.501078	+	0.865402i	$0.332937\pi$
$984$		0			0
$985$	−19697.2	−	1282.78i	−0.637163	−	0.0414954i
$986$	−217.024	+	667.930i	−0.00700958	+	0.0215733i
$987$		0			0
$988$	−924.560	−	2845.50i	−0.0297714	−	0.0916271i
$989$	−15589.7	+	47980.1i	−0.501237	+	1.54265i
$990$		0			0
$991$	−12252.9	−	37710.5i	−0.392760	−	1.20879i	−0.930692	−	0.365804i	$-0.880794\pi$
$991$	−12252.9	−	37710.5i	−0.392760	−	1.20879i	0.537932	−	0.842988i	$-0.319206\pi$
$992$	18808.6	−	13665.2i	0.601988	−	0.437370i
$993$		0			0
$994$	1130.15	−	821.100i	0.0360625	−	0.0262009i
$995$	37365.8	−	23597.8i	1.19053	−	0.751860i
$996$		0			0
$997$	27866.6	+	20246.3i	0.885200	+	0.643135i	0.934622	−	0.355643i	$-0.115738\pi$
$997$	27866.6	+	20246.3i	0.885200	+	0.643135i	−0.0494223	+	0.998778i	$0.515738\pi$
$998$	−1443.95	+	4444.02i	−0.0457991	+	0.140955i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.a.46.4		28
3.2	odd	2		75.4.g.b.46.4	yes	28
25.6	even	5	inner	225.4.h.a.181.4		28
75.41	odd	10		1875.4.a.g.1.7		14
75.56	odd	10		75.4.g.b.31.4	✓	28
75.59	odd	10		1875.4.a.f.1.8		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.4.g.b.31.4	✓	28	75.56	odd	10
75.4.g.b.46.4	yes	28	3.2	odd	2
225.4.h.a.46.4		28	1.1	even	1	trivial
225.4.h.a.181.4		28	25.6	even	5	inner
1875.4.a.f.1.8		14	75.59	odd	10
1875.4.a.g.1.7		14	75.41	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)

\(f(q)\)	\(=\)	\(q+(0.177563 - 0.546483i) q^{2} +(6.20502 + 4.50821i) q^{4} +(9.45304 - 5.96993i) q^{5} -2.67744 q^{7} +(7.28438 - 5.29241i) q^{8} +O(q^{10})\)	\(q+(0.177563 - 0.546483i) q^{2} +(6.20502 + 4.50821i) q^{4} +(9.45304 - 5.96993i) q^{5} -2.67744 q^{7} +(7.28438 - 5.29241i) q^{8} +(-1.58395 - 6.22597i) q^{10} +(19.4804 - 59.9545i) q^{11} +(4.38017 + 13.4808i) q^{13} +(-0.475414 + 1.46317i) q^{14} +(17.3621 + 53.4350i) q^{16} +(24.5906 - 17.8661i) q^{17} +(-22.2647 + 16.1762i) q^{19} +(85.5700 + 5.57276i) q^{20} +(-29.3052 - 21.2914i) q^{22} +(-35.9246 + 110.565i) q^{23} +(53.7199 - 112.868i) q^{25} +8.14478 q^{26} +(-16.6135 - 12.0704i) q^{28} +(-32.5312 - 23.6353i) q^{29} +(180.304 - 130.998i) q^{31} +104.316 q^{32} +(-5.39715 - 16.6107i) q^{34} +(-25.3099 + 15.9841i) q^{35} +(25.6160 + 78.8378i) q^{37} +(4.88665 + 15.0396i) q^{38} +(37.2642 - 93.5166i) q^{40} +(-44.5269 - 137.040i) q^{41} +433.956 q^{43} +(391.164 - 284.197i) q^{44} +(54.0428 + 39.2644i) q^{46} +(371.550 + 269.947i) q^{47} -335.831 q^{49} +(-52.1418 - 49.3982i) q^{50} +(-33.5952 + 103.395i) q^{52} +(-200.214 - 145.464i) q^{53} +(-173.775 - 683.049i) q^{55} +(-19.5034 + 14.1701i) q^{56} +(-18.6927 + 13.5810i) q^{58} +(-95.9388 - 295.269i) q^{59} +(0.644333 - 1.98305i) q^{61} +(-39.5730 - 121.793i) q^{62} +(-120.374 + 370.473i) q^{64} +(121.885 + 101.285i) q^{65} +(-529.476 + 384.687i) q^{67} +233.129 q^{68} +(4.24094 + 16.6696i) q^{70} +(-734.591 - 533.711i) q^{71} +(-271.486 + 835.547i) q^{73} +47.6320 q^{74} -211.079 q^{76} +(-52.1575 + 160.524i) q^{77} +(921.477 + 669.493i) q^{79} +(483.127 + 401.473i) q^{80} -82.7962 q^{82} +(-798.210 + 579.934i) q^{83} +(125.796 - 315.693i) q^{85} +(77.0546 - 237.150i) q^{86} +(-175.401 - 539.830i) q^{88} +(-305.549 + 940.383i) q^{89} +(-11.7276 - 36.0939i) q^{91} +(-721.361 + 524.100i) q^{92} +(213.495 - 155.113i) q^{94} +(-113.898 + 285.833i) q^{95} +(-1244.20 - 903.964i) q^{97} +(-59.6313 + 183.526i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10}) \) 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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