LMFDB - Embedded newform 225.4.h.a.91.2

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			91.2
Character	$\chi$	$=$	225.91
Dual form			225.4.h.a.136.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.25026 - 2.36146i) q^{2} +(2.51561 + 7.74226i) q^{4} +(6.00716 - 9.42943i) q^{5} +1.75849 q^{7} +(0.174670 - 0.537580i) q^{8} +O(q^{10})$	\(q+(-3.25026 - 2.36146i) q^{2} +(2.51561 + 7.74226i) q^{4} +(6.00716 - 9.42943i) q^{5} +1.75849 q^{7} +(0.174670 - 0.537580i) q^{8} +(-41.7920 + 16.4625i) q^{10} +(-18.9070 - 13.7367i) q^{11} +(43.1036 - 31.3166i) q^{13} +(-5.71556 - 4.15260i) q^{14} +(50.8505 - 36.9450i) q^{16} +(6.45676 - 19.8719i) q^{17} +(5.67829 - 17.4760i) q^{19} +(88.1167 + 22.7882i) q^{20} +(29.0140 + 89.2960i) q^{22} +(34.8681 + 25.3331i) q^{23} +(-52.8281 - 113.288i) q^{25} -214.051 q^{26} +(4.42368 + 13.6147i) q^{28} +(-41.2605 - 126.987i) q^{29} +(74.8546 - 230.379i) q^{31} -257.044 q^{32} +(-67.9127 + 49.3414i) q^{34} +(10.5635 - 16.5816i) q^{35} +(-288.826 + 209.844i) q^{37} +(-59.7247 + 43.3925i) q^{38} +(-4.01980 - 4.87637i) q^{40} +(-343.417 + 249.507i) q^{41} -93.5407 q^{43} +(58.7907 - 180.939i) q^{44} +(-53.5074 - 164.679i) q^{46} +(72.1996 + 222.207i) q^{47} -339.908 q^{49} +(-95.8194 + 492.968i) q^{50} +(350.893 + 254.939i) q^{52} +(8.66417 + 26.6656i) q^{53} +(-243.107 + 95.7633i) q^{55} +(0.307156 - 0.945330i) q^{56} +(-165.766 + 510.176i) q^{58} +(365.174 - 265.315i) q^{59} +(-696.837 - 506.281i) q^{61} +(-787.326 + 572.026i) q^{62} +(428.656 + 311.437i) q^{64} +(-36.3674 - 594.565i) q^{65} +(-191.985 + 590.868i) q^{67} +170.096 q^{68} +(-73.4909 + 28.9491i) q^{70} +(-292.011 - 898.717i) q^{71} +(556.132 + 404.054i) q^{73} +1434.30 q^{74} +149.588 q^{76} +(-33.2478 - 24.1559i) q^{77} +(-173.055 - 532.610i) q^{79} +(-42.9036 - 701.425i) q^{80} +1705.40 q^{82} +(290.880 - 895.238i) q^{83} +(-148.593 - 180.257i) q^{85} +(304.032 + 220.892i) q^{86} +(-10.6871 + 7.76462i) q^{88} +(912.809 + 663.195i) q^{89} +(75.7972 - 55.0699i) q^{91} +(-108.421 + 333.686i) q^{92} +(290.065 - 892.729i) q^{94} +(-130.678 - 158.524i) q^{95} +(-386.573 - 1189.75i) q^{97} +(1104.79 + 802.677i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

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

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 $

$2$	−3.25026	−	2.36146i	−1.14914	−	0.834901i	−0.160776	−	0.986991i	$-0.551400\pi$
$2$	−3.25026	−	2.36146i	−1.14914	−	0.834901i	−0.988367	+	0.152090i	$0.951400\pi$
$3$		0			0
$3$		0			0
$4$	2.51561	+	7.74226i	0.314452	+	0.967783i
$5$	6.00716	−	9.42943i	0.537296	−	0.843393i
$5$	6.00716	−	9.42943i	0.537296	−	0.843393i
$6$		0			0
$7$	1.75849			0.0949496			0.0474748	−	0.998872i	$-0.484883\pi$
$7$	1.75849			0.0949496			0.0474748	+	0.998872i	$0.484883\pi$
$8$	0.174670	−	0.537580i	0.00771941	−	0.0237579i
$9$		0			0
$10$	−41.7920	+	16.4625i	−1.32158	+	0.520590i
$11$	−18.9070	−	13.7367i	−0.518243	−	0.376526i	0.297699	−	0.954660i	$-0.403781\pi$
$11$	−18.9070	−	13.7367i	−0.518243	−	0.376526i	−0.815942	+	0.578134i	$0.803781\pi$
$12$		0			0
$13$	43.1036	−	31.3166i	0.919598	−	0.668127i	−0.0238256	−	0.999716i	$-0.507585\pi$
$13$	43.1036	−	31.3166i	0.919598	−	0.668127i	0.943424	+	0.331589i	$0.107585\pi$
$14$	−5.71556	−	4.15260i	−0.109111	−	0.0792735i
$15$		0			0
$16$	50.8505	−	36.9450i	0.794539	−	0.577266i
$17$	6.45676	−	19.8719i	0.0921173	−	0.283508i	−0.894374	−	0.447319i	$-0.852379\pi$
$17$	6.45676	−	19.8719i	0.0921173	−	0.283508i	0.986492	+	0.163811i	$0.0523788\pi$
$18$		0			0
$19$	5.67829	−	17.4760i	0.0685626	−	0.211014i	−0.910905	−	0.412617i	$-0.864615\pi$
$19$	5.67829	−	17.4760i	0.0685626	−	0.211014i	0.979467	+	0.201603i	$0.0646149\pi$
$20$	88.1167	+	22.7882i	0.985175	+	0.254780i
$21$		0			0
$22$	29.0140	+	89.2960i	0.281173	+	0.865363i
$23$	34.8681	+	25.3331i	0.316108	+	0.229666i	0.734513	−	0.678595i	$-0.237411\pi$
$23$	34.8681	+	25.3331i	0.316108	+	0.229666i	−0.418405	+	0.908261i	$0.637411\pi$
$24$		0			0
$25$	−52.8281	−	113.288i	−0.422625	−	0.906305i
$26$	−214.051			−1.61457
$27$		0			0
$28$	4.42368	+	13.6147i	0.0298571	+	0.0918906i
$29$	−41.2605	−	126.987i	−0.264203	−	0.813133i	−0.991876	−	0.127209i	$-0.959398\pi$
$29$	−41.2605	−	126.987i	−0.264203	−	0.813133i	0.727673	−	0.685924i	$-0.240602\pi$
$30$		0			0
$31$	74.8546	−	230.379i	0.433686	−	1.33475i	−0.460740	−	0.887535i	$-0.652416\pi$
$31$	74.8546	−	230.379i	0.433686	−	1.33475i	0.894427	−	0.447214i	$-0.147584\pi$
$32$	−257.044			−1.41998
$33$		0			0
$34$	−67.9127	+	49.3414i	−0.342557	+	0.248882i
$35$	10.5635	−	16.5816i	0.0510161	−	0.0800799i
$36$		0			0
$37$	−288.826	+	209.844i	−1.28332	+	0.932384i	−0.999648	−	0.0265384i	$-0.991552\pi$
$37$	−288.826	+	209.844i	−1.28332	+	0.932384i	−0.283669	+	0.958922i	$0.591552\pi$
$38$	−59.7247	+	43.3925i	−0.254964	+	0.185242i
$39$		0			0
$40$	−4.01980	−	4.87637i	−0.0158896	−	0.0192755i
$41$	−343.417	+	249.507i	−1.30812	+	0.950401i	−1.00000		0.000947731i	$-0.999698\pi$
$41$	−343.417	+	249.507i	−1.30812	+	0.950401i	−0.308116	+	0.951349i	$0.599698\pi$
$42$		0			0
$43$	−93.5407			−0.331740			−0.165870	−	0.986148i	$-0.553043\pi$
$43$	−93.5407			−0.331740			−0.165870	+	0.986148i	$0.553043\pi$
$44$	58.7907	−	180.939i	0.201432	−	0.619945i
$45$		0			0
$46$	−53.5074	−	164.679i	−0.171505	−	0.527838i
$47$	72.1996	+	222.207i	0.224072	+	0.689623i	0.998384	+	0.0568194i	$0.0180959\pi$
$47$	72.1996	+	222.207i	0.224072	+	0.689623i	−0.774312	+	0.632804i	$0.781904\pi$
$48$		0			0
$49$	−339.908			−0.990985
$50$	−95.8194	+	492.968i	−0.271018	+	1.39432i
$51$		0			0
$52$	350.893	+	254.939i	0.935771	+	0.679878i
$53$	8.66417	+	26.6656i	0.0224550	+	0.0691094i	0.961656	−	0.274258i	$-0.0884323\pi$
$53$	8.66417	+	26.6656i	0.0224550	+	0.0691094i	−0.939201	+	0.343368i	$0.888432\pi$
$54$		0			0
$55$	−243.107	+	95.7633i	−0.596009	+	0.234777i
$56$	0.307156	−	0.945330i	0.000732955	−	0.00225580i
$57$		0			0
$58$	−165.766	+	510.176i	−0.375279	+	1.15499i
$59$	365.174	−	265.315i	0.805790	−	0.585441i	−0.106817	−	0.994279i	$-0.534066\pi$
$59$	365.174	−	265.315i	0.805790	−	0.585441i	0.912607	+	0.408838i	$0.134066\pi$
$60$		0			0
$61$	−696.837	−	506.281i	−1.46264	−	1.06267i	−0.982667	−	0.185382i	$-0.940648\pi$
$61$	−696.837	−	506.281i	−1.46264	−	1.06267i	−0.479969	−	0.877285i	$-0.659352\pi$
$62$	−787.326	+	572.026i	−1.61275	+	1.17173i
$63$		0			0
$64$	428.656	+	311.437i	0.837218	+	0.608275i
$65$	−36.3674	−	594.565i	−0.0693972	−	1.13457i
$66$		0			0
$67$	−191.985	+	590.868i	−0.350070	+	1.07740i	0.608744	+	0.793367i	$0.291674\pi$
$67$	−191.985	+	590.868i	−0.350070	+	1.07740i	−0.958813	+	0.284037i	$0.908326\pi$
$68$	170.096			0.303340
$69$		0			0
$70$	−73.4909	+	28.9491i	−0.125483	+	0.0494298i
$71$	−292.011	−	898.717i	−0.488103	−	1.50223i	−0.827436	−	0.561560i	$-0.810201\pi$
$71$	−292.011	−	898.717i	−0.488103	−	1.50223i	0.339333	−	0.940666i	$-0.389799\pi$
$72$		0			0
$73$	556.132	+	404.054i	0.891649	+	0.647821i	0.936307	−	0.351182i	$-0.114220\pi$
$73$	556.132	+	404.054i	0.891649	+	0.647821i	−0.0446587	+	0.999002i	$0.514220\pi$
$74$	1434.30			2.25316
$75$		0			0
$76$	149.588			0.225775
$77$	−33.2478	−	24.1559i	−0.0492070	−	0.0357509i
$78$		0			0
$79$	−173.055	−	532.610i	−0.246459	−	0.758522i	−0.995393	−	0.0958781i	$-0.969434\pi$
$79$	−173.055	−	532.610i	−0.246459	−	0.758522i	0.748934	−	0.662644i	$-0.230566\pi$
$80$	−42.9036	−	701.425i	−0.0599596	−	0.980272i
$81$		0			0
$82$	1705.40			2.29670
$83$	290.880	−	895.238i	0.384678	−	1.18392i	−0.552036	−	0.833820i	$-0.686149\pi$
$83$	290.880	−	895.238i	0.384678	−	1.18392i	0.936714	−	0.350097i	$-0.113851\pi$
$84$		0			0
$85$	−148.593	−	180.257i	−0.189614	−	0.230019i
$86$	304.032	+	220.892i	0.381216	+	0.276970i
$87$		0			0
$88$	−10.6871	+	7.76462i	−0.0129460	+	0.00940581i
$89$	912.809	+	663.195i	1.08716	+	0.789871i	0.978918	−	0.204253i	$-0.0654766\pi$
$89$	912.809	+	663.195i	1.08716	+	0.789871i	0.108246	+	0.994124i	$0.465477\pi$
$90$		0			0
$91$	75.7972	−	55.0699i	0.0873155	−	0.0634384i
$92$	−108.421	+	333.686i	−0.122866	+	0.378143i
$93$		0			0
$94$	290.065	−	892.729i	0.318276	−	0.979553i
$95$	−130.678	−	158.524i	−0.141129	−	0.171202i
$96$		0			0
$97$	−386.573	−	1189.75i	−0.404645	−	1.24537i	−0.921191	−	0.389110i	$-0.872782\pi$
$97$	−386.573	−	1189.75i	−0.404645	−	1.24537i	0.516546	−	0.856260i	$-0.327218\pi$
$98$	1104.79	+	802.677i	1.13878	+	0.827374i
$99$		0			0
$100$	744.211	−	693.998i	0.744211	−	0.693998i
$101$	−665.647			−0.655785			−0.327893	−	0.944715i	$-0.606338\pi$
$101$	−665.647			−0.655785			−0.327893	+	0.944715i	$0.606338\pi$
$102$		0			0
$103$	89.4705	+	275.362i	0.0855902	+	0.263420i	0.984687	−	0.174330i	$-0.0557758\pi$
$103$	89.4705	+	275.362i	0.0855902	+	0.263420i	−0.899097	+	0.437749i	$0.855776\pi$
$104$	−9.30625	−	28.6417i	−0.00877455	−	0.0270053i
$105$		0			0
$106$	34.8087	−	107.130i	0.0318955	−	0.0981642i
$107$	−50.4077			−0.0455430			−0.0227715	−	0.999741i	$-0.507249\pi$
$107$	−50.4077			−0.0455430			−0.0227715	+	0.999741i	$0.507249\pi$
$108$		0			0
$109$	1299.92	−	944.450i	1.14229	−	0.829926i	0.154857	−	0.987937i	$-0.450508\pi$
$109$	1299.92	−	944.450i	1.14229	−	0.829926i	0.987437	+	0.158011i	$0.0505082\pi$
$110$	1016.30	+	262.830i	0.880915	+	0.227817i
$111$		0			0
$112$	89.4201	−	64.9675i	0.0754411	−	0.0548112i
$113$	−978.283	+	710.764i	−0.814417	+	0.591709i	−0.915108	−	0.403209i	$-0.867895\pi$
$113$	−978.283	+	710.764i	−0.814417	+	0.591709i	0.100691	+	0.994918i	$0.467895\pi$
$114$		0			0
$115$	448.335	−	176.606i	0.363543	−	0.143205i
$116$	879.369	−	638.899i	0.703857	−	0.511382i
$117$		0			0
$118$	−1813.44			−1.41475
$119$	11.3541	−	34.9445i	0.00874650	−	0.0269189i
$120$		0			0
$121$	−242.525	−	746.416i	−0.182213	−	0.560793i
$122$	1069.34	+	3291.10i	0.793555	+	2.44231i
$123$		0			0
$124$	1971.96			1.42812
$125$	−1385.59	−	182.400i	−0.991446	−	0.130515i
$126$		0			0
$127$	556.607	+	404.399i	0.388905	+	0.282556i	0.765007	−	0.644023i	$-0.222736\pi$
$127$	556.607	+	404.399i	0.388905	+	0.282556i	−0.376102	+	0.926578i	$0.622736\pi$
$128$	−22.3543	−	68.7996i	−0.0154364	−	0.0475085i
$129$		0			0
$130$	−1285.84	+	2018.38i	−0.867502	+	1.36172i
$131$	−453.558	+	1395.91i	−0.302500	+	0.931000i	0.678098	+	0.734972i	$0.262805\pi$
$131$	−453.558	+	1395.91i	−0.302500	+	0.931000i	−0.980598	+	0.196028i	$0.937195\pi$
$132$		0			0
$133$	9.98522	−	30.7314i	0.00650999	−	0.0200357i
$134$	2019.31	−	1467.12i	1.30181	−	0.945817i
$135$		0			0
$136$	−9.55491	−	6.94205i	−0.00602446	−	0.00437703i
$137$	2124.73	−	1543.71i	1.32502	−	0.962687i	0.325169	−	0.945656i	$-0.394579\pi$
$137$	2124.73	−	1543.71i	1.32502	−	0.962687i	0.999855	−	0.0170308i	$-0.00542133\pi$
$138$		0			0
$139$	2556.35	+	1857.30i	1.55990	+	1.13334i	0.936088	+	0.351765i	$0.114418\pi$
$139$	2556.35	+	1857.30i	1.55990	+	1.13334i	0.623816	+	0.781572i	$0.285582\pi$
$140$	154.953	+	40.0728i	0.0935420	+	0.0241912i
$141$		0			0
$142$	−1173.17	+	3610.64i	−0.693310	+	2.13379i
$143$	−1245.15			−0.728142
$144$		0			0
$145$	−1445.27	−	373.767i	−0.827746	−	0.214066i
$146$	−853.422	−	2626.56i	−0.483765	−	1.48888i
$147$		0			0
$148$	−2351.24	−	1708.28i	−1.30589	−	0.948782i
$149$	−1591.21			−0.874879			−0.437440	−	0.899248i	$-0.644115\pi$
$149$	−1591.21			−0.874879			−0.437440	+	0.899248i	$0.644115\pi$
$150$		0			0
$151$	1150.25			0.619909			0.309955	−	0.950751i	$-0.399686\pi$
$151$	1150.25			0.619909			0.309955	+	0.950751i	$0.399686\pi$
$152$	−8.40291	−	6.10507i	−0.00448399	−	0.00325781i
$153$		0			0
$154$	51.0209	+	157.026i	0.0266973	+	0.0821658i
$155$	−1722.68	−	2089.76i	−0.892701	−	1.08292i
$156$		0			0
$157$	−629.792			−0.320146			−0.160073	−	0.987105i	$-0.551173\pi$
$157$	−629.792			−0.320146			−0.160073	+	0.987105i	$0.551173\pi$
$158$	−695.258	+	2139.79i	−0.350075	+	1.07742i
$159$		0			0
$160$	−1544.10	+	2423.77i	−0.762949	+	1.19760i
$161$	61.3152	+	44.5481i	0.0300144	+	0.0218067i
$162$		0			0
$163$	−522.519	+	379.632i	−0.251085	+	0.182424i	−0.706207	−	0.708005i	$-0.749595\pi$
$163$	−522.519	+	379.632i	−0.251085	+	0.182424i	0.455123	+	0.890429i	$0.349595\pi$
$164$	−2795.65	−	2031.16i	−1.33112	−	0.967116i
$165$		0			0
$166$	−3059.50	+	2222.86i	−1.43050	+	1.03932i
$167$	1059.00	−	3259.28i	0.490707	−	1.51024i	−0.332834	−	0.942986i	$-0.608005\pi$
$167$	1059.00	−	3259.28i	0.490707	−	1.51024i	0.823541	−	0.567257i	$-0.191995\pi$
$168$		0			0
$169$	198.279	−	610.241i	0.0902500	−	0.277761i
$170$	57.2994	+	936.779i	0.0258509	+	0.422633i
$171$		0			0
$172$	−235.312	−	724.216i	−0.104316	−	0.321052i
$173$	895.187	+	650.392i	0.393409	+	0.285829i	0.766851	−	0.641825i	$-0.221822\pi$
$173$	895.187	+	650.392i	0.393409	+	0.285829i	−0.373442	+	0.927654i	$0.621822\pi$
$174$		0			0
$175$	−92.8978	−	199.216i	−0.0401281	−	0.0860533i
$176$	−1468.93			−0.629120
$177$		0			0
$178$	−1400.77	−	4311.12i	−0.589842	−	1.81535i
$179$	46.8362	+	144.147i	0.0195570	+	0.0601903i	0.960359	−	0.278767i	$-0.0899257\pi$
$179$	46.8362	+	144.147i	0.0195570	+	0.0601903i	−0.940802	+	0.338957i	$0.889926\pi$
$180$		0			0
$181$	855.398	−	2632.64i	0.351277	−	1.08112i	−0.606859	−	0.794809i	$-0.707571\pi$
$181$	855.398	−	2632.64i	0.351277	−	1.08112i	0.958137	−	0.286311i	$-0.0924292\pi$
$182$	−376.406			−0.153303
$183$		0			0
$184$	19.7090	−	14.3194i	0.00789656	−	0.00573718i
$185$	243.689	+	3984.03i	0.0968451	+	1.58331i
$186$		0			0
$187$	−395.052	+	287.022i	−0.154487	+	0.112241i
$188$	−1538.76	+	1117.98i	−0.596945	+	0.433706i
$189$		0			0
$190$	50.3910	+	823.835i	0.0192408	+	0.314565i
$191$	1921.46	−	1396.02i	0.727915	−	0.528861i	−0.160988	−	0.986956i	$-0.551468\pi$
$191$	1921.46	−	1396.02i	0.727915	−	0.528861i	0.888903	+	0.458095i	$0.151468\pi$
$192$		0			0
$193$	−1876.65			−0.699917			−0.349958	−	0.936765i	$-0.613804\pi$
$193$	−1876.65			−0.699917			−0.349958	+	0.936765i	$0.613804\pi$
$194$	−1553.08	+	4779.88i	−0.574765	+	1.76895i
$195$		0			0
$196$	−855.076	−	2631.65i	−0.311617	−	0.959058i
$197$	295.553	+	909.619i	0.106890	+	0.328973i	0.990169	−	0.139874i	$-0.0446697\pi$
$197$	295.553	+	909.619i	0.106890	+	0.328973i	−0.883280	+	0.468847i	$0.844670\pi$
$198$		0			0
$199$	−633.678			−0.225730			−0.112865	−	0.993610i	$-0.536003\pi$
$199$	−633.678			−0.225730			−0.112865	+	0.993610i	$0.536003\pi$
$200$	−70.1289	+	8.61128i	−0.0247943	+	0.00304455i
$201$		0			0
$202$	2163.53	+	1571.90i	0.753591	+	0.547516i
$203$	−72.5562	−	223.305i	−0.0250860	−	0.0772066i
$204$		0			0
$205$	289.748	+	4737.05i	0.0987165	+	1.61390i
$206$	359.452	−	1106.28i	0.121574	−	0.374166i
$207$		0			0
$208$	1034.85	−	3184.93i	0.344969	−	1.06171i
$209$	−347.422	+	252.417i	−0.114984	+	0.0835409i
$210$		0			0
$211$	662.435	+	481.287i	0.216132	+	0.157029i	0.690584	−	0.723252i	$-0.257354\pi$
$211$	662.435	+	481.287i	0.216132	+	0.157029i	−0.474452	+	0.880282i	$0.657354\pi$
$212$	−184.656	+	134.161i	−0.0598219	+	0.0434631i
$213$		0			0
$214$	163.838	+	119.036i	0.0523353	+	0.0380238i
$215$	−561.913	+	882.035i	−0.178243	+	0.279787i
$216$		0			0
$217$	131.631	−	405.119i	0.0411783	−	0.126734i
$218$	−6455.37			−2.00556
$219$		0			0
$220$	−1352.99	−	1641.29i	−0.414629	−	0.502981i
$221$	−344.009	−	1058.75i	−0.104708	−	0.322259i
$222$		0			0
$223$	2678.65	+	1946.15i	0.804375	+	0.584412i	0.912194	−	0.409758i	$-0.134387\pi$
$223$	2678.65	+	1946.15i	0.804375	+	0.584412i	−0.107819	+	0.994170i	$0.534387\pi$
$224$	−452.009			−0.134826
$225$		0			0
$226$	4858.12			1.42990
$227$	−797.992	−	579.775i	−0.233324	−	0.169520i	0.464980	−	0.885321i	$-0.346062\pi$
$227$	−797.992	−	579.775i	−0.233324	−	0.169520i	−0.698304	+	0.715801i	$0.746062\pi$
$228$		0			0
$229$	−110.060	−	338.730i	−0.0317597	−	0.0977464i	0.933920	−	0.357482i	$-0.116365\pi$
$229$	−110.060	−	338.730i	−0.0317597	−	0.0977464i	−0.965680	+	0.259736i	$0.916365\pi$
$230$	−1874.25	−	484.707i	−0.537324	−	0.138959i
$231$		0			0
$232$	−75.4726			−0.0213578
$233$	1574.73	−	4846.52i	0.442764	−	1.36269i	−0.442153	−	0.896940i	$-0.645785\pi$
$233$	1574.73	−	4846.52i	0.442764	−	1.36269i	0.884917	−	0.465748i	$-0.154215\pi$
$234$		0			0
$235$	2529.00	+	654.034i	0.702017	+	0.181551i
$236$	2972.77	+	2159.85i	0.819962	+	0.595737i
$237$		0			0
$238$	−119.424	+	86.7665i	−0.0325256	+	0.0236312i
$239$	−2414.42	−	1754.18i	−0.653455	−	0.474763i	0.210991	−	0.977488i	$-0.432331\pi$
$239$	−2414.42	−	1754.18i	−0.653455	−	0.474763i	−0.864446	+	0.502725i	$0.832331\pi$
$240$		0			0
$241$	−3533.35	+	2567.13i	−0.944411	+	0.686155i	−0.949478	−	0.313832i	$-0.898387\pi$
$241$	−3533.35	+	2567.13i	−0.944411	+	0.686155i	0.00506735	+	0.999987i	$0.498387\pi$
$242$	−974.357	+	2998.76i	−0.258818	+	0.796561i
$243$		0			0
$244$	2166.79	−	6668.70i	0.568502	−	1.74967i
$245$	−2041.88	+	3205.13i	−0.532453	+	0.835790i
$246$		0			0
$247$	−302.533	−	931.102i	−0.0779341	−	0.239857i
$248$	−110.772	−	80.4806i	−0.0283630	−	0.0206070i
$249$		0			0
$250$	4072.80	+	3864.86i	1.03035	+	0.977740i
$251$	6267.54			1.57611			0.788055	−	0.615605i	$-0.211088\pi$
$251$	6267.54			1.57611			0.788055	+	0.615605i	$0.211088\pi$
$252$		0			0
$253$	−311.256	−	957.946i	−0.0773457	−	0.238046i
$254$	−854.151	−	2628.81i	−0.211001	−	0.649394i
$255$		0			0
$256$	1220.05	−	3754.92i	0.297863	−	0.916727i
$257$	6002.51			1.45691			0.728456	−	0.685093i	$-0.240238\pi$
$257$	6002.51			1.45691			0.728456	+	0.685093i	$0.240238\pi$
$258$		0			0
$259$	−507.898	+	369.010i	−0.121850	+	0.0885295i
$260$	4511.79	−	1777.26i	1.07619	−	0.423927i
$261$		0			0
$262$	4770.56	−	3466.01i	1.12491	−	0.817294i
$263$	5375.15	−	3905.27i	1.26025	−	0.915626i	0.261481	−	0.965209i	$-0.415789\pi$
$263$	5375.15	−	3905.27i	1.26025	−	0.915626i	0.998770	+	0.0495832i	$0.0157893\pi$
$264$		0			0
$265$	303.488	+	78.4862i	0.0703514	+	0.0181938i
$266$	−105.025	+	76.3054i	−0.0242087	+	0.0175887i
$267$		0			0
$268$	−5057.62			−1.15277
$269$	−2613.50	+	8043.53i	−0.592372	+	1.82313i	−0.0249746	+	0.999688i	$0.507951\pi$
$269$	−2613.50	+	8043.53i	−0.592372	+	1.82313i	−0.567397	+	0.823444i	$0.692049\pi$
$270$		0			0
$271$	−2595.56	−	7988.32i	−0.581805	−	1.79061i	−0.611739	−	0.791060i	$-0.709530\pi$
$271$	−2595.56	−	7988.32i	−0.581805	−	1.79061i	0.0299337	−	0.999552i	$-0.490470\pi$
$272$	−405.837	−	1249.04i	−0.0904687	−	0.278434i
$273$		0			0
$274$	−10551.4			−2.32639
$275$	−557.387	+	2867.62i	−0.122224	+	0.628815i
$276$		0			0
$277$	−1269.42	−	922.289i	−0.275351	−	0.200054i	0.441536	−	0.897243i	$-0.354434\pi$
$277$	−1269.42	−	922.289i	−0.275351	−	0.200054i	−0.716887	+	0.697189i	$0.754434\pi$
$278$	−3922.89	−	12073.4i	−0.846328	−	2.60473i
$279$		0			0
$280$	−7.06878	−	8.57505i	−0.00150872	−	0.00183020i
$281$	462.238	−	1422.62i	0.0981311	−	0.302016i	−0.889926	−	0.456105i	$-0.849244\pi$
$281$	462.238	−	1422.62i	0.0981311	−	0.302016i	0.988057	+	0.154089i	$0.0492441\pi$
$282$		0			0
$283$	−1845.06	+	5678.52i	−0.387553	+	1.19277i	0.547058	+	0.837095i	$0.315748\pi$
$283$	−1845.06	+	5678.52i	−0.387553	+	1.19277i	−0.934611	+	0.355672i	$0.884252\pi$
$284$	6223.51	−	4521.65i	1.30034	−	0.944755i
$285$		0			0
$286$	4047.05	+	2940.36i	0.836739	+	0.607926i
$287$	−603.896	+	438.756i	−0.124205	+	0.0902402i
$288$		0			0
$289$	3621.50	+	2631.17i	0.737126	+	0.535553i
$290$	3814.88	+	4627.78i	0.772474	+	0.937079i
$291$		0			0
$292$	−1729.28	+	5322.16i	−0.346569	+	1.06663i
$293$	−1269.10			−0.253043			−0.126521	−	0.991964i	$-0.540381\pi$
$293$	−1269.10			−0.253043			−0.126521	+	0.991964i	$0.540381\pi$
$294$		0			0
$295$	−308.105	−	5037.17i	−0.0608088	−	0.994154i
$296$	62.3588	+	191.921i	0.0122450	+	0.0376864i
$297$		0			0
$298$	5171.86	+	3757.57i	1.00536	+	0.730437i
$299$	2296.28			0.444139
$300$		0			0
$301$	−164.490			−0.0314986
$302$	−3738.63	−	2716.27i	−0.712364	−	0.517563i
$303$		0			0
$304$	−356.907	−	1098.45i	−0.0673356	−	0.207238i
$305$	−8959.95	+	3529.46i	−1.68212	+	0.662610i
$306$		0			0
$307$	5218.55			0.970157			0.485078	−	0.874471i	$-0.338791\pi$
$307$	5218.55			0.970157			0.485078	+	0.874471i	$0.338791\pi$
$308$	103.383	−	318.180i	0.0191259	−	0.0588636i
$309$		0			0
$310$	664.284	+	10860.3i	0.121706	+	1.98975i
$311$	521.486	+	378.882i	0.0950828	+	0.0690817i	0.634311	−	0.773078i	$-0.281284\pi$
$311$	521.486	+	378.882i	0.0950828	+	0.0690817i	−0.539228	+	0.842160i	$0.681284\pi$
$312$		0			0
$313$	−746.588	+	542.428i	−0.134823	+	0.0979547i	−0.653153	−	0.757226i	$-0.726554\pi$
$313$	−746.588	+	542.428i	−0.134823	+	0.0979547i	0.518330	+	0.855181i	$0.326554\pi$
$314$	2046.99	+	1487.23i	0.367893	+	0.267290i
$315$		0			0
$316$	3688.26	−	2679.68i	0.656585	−	0.477037i
$317$	378.337	−	1164.40i	0.0670331	−	0.206307i	−0.911929	−	0.410347i	$-0.865407\pi$
$317$	378.337	−	1164.40i	0.0670331	−	0.206307i	0.978962	+	0.204041i	$0.0654075\pi$
$318$		0			0
$319$	−964.272	+	2967.72i	−0.169244	+	0.520880i
$320$	5511.67	−	2171.13i	0.962849	−	0.379281i
$321$		0			0
$322$	−94.0922	−	289.586i	−0.0162843	−	0.0501180i
$323$	−310.617	−	225.676i	−0.0535083	−	0.0388761i
$324$		0			0
$325$	−5824.88	−	3228.72i	−0.994172	−	0.551069i
$326$	2594.81			0.440838
$327$		0			0
$328$	74.1452	+	228.196i	0.0124817	+	0.0384146i
$329$	126.962	+	390.750i	0.0212756	+	0.0654794i
$330$		0			0
$331$	−3288.95	+	10122.3i	−0.546154	+	1.68089i	0.172076	+	0.985084i	$0.444953\pi$
$331$	−3288.95	+	10122.3i	−0.546154	+	1.68089i	−0.718230	+	0.695806i	$0.755047\pi$
$332$	7662.91			1.26674
$333$		0			0
$334$	−11138.7	+	8092.72i	−1.82479	+	1.32579i
$335$	4418.27	+	5359.75i	0.720584	+	0.874132i
$336$		0			0
$337$	3198.88	−	2324.12i	0.517074	−	0.375676i	−0.298426	−	0.954433i	$-0.596462\pi$
$337$	3198.88	−	2324.12i	0.517074	−	0.375676i	0.815501	+	0.578756i	$0.196462\pi$
$338$	−2085.52	+	1515.22i	−0.335613	+	0.243837i
$339$		0			0
$340$	1021.79	−	1603.91i	0.162984	−	0.255835i
$341$	−4579.92	+	3327.51i	−0.727322	+	0.528430i
$342$		0			0
$343$	−1200.89			−0.189043
$344$	−16.3388	+	50.2856i	−0.00256084	+	0.00788145i
$345$		0			0
$346$	−1373.72	−	4227.89i	−0.213445	−	0.656916i
$347$	−2928.61	−	9013.35i	−0.453073	−	1.39441i	−0.873383	−	0.487034i	$-0.838079\pi$
$347$	−2928.61	−	9013.35i	−0.453073	−	1.39441i	0.420310	−	0.907381i	$-0.361921\pi$
$348$		0			0
$349$	5550.12			0.851264			0.425632	−	0.904896i	$-0.360052\pi$
$349$	5550.12			0.851264			0.425632	+	0.904896i	$0.360052\pi$
$350$	−168.498	+	866.879i	−0.0257331	+	0.132390i
$351$		0			0
$352$	4859.92	+	3530.94i	0.735894	+	0.534658i
$353$	3749.94	+	11541.1i	0.565408	+	1.74015i	0.666737	+	0.745294i	$0.267691\pi$
$353$	3749.94	+	11541.1i	0.565408	+	1.74015i	−0.101329	+	0.994853i	$0.532309\pi$
$354$		0			0
$355$	−10228.5	−	2645.24i	−1.52922	−	0.395478i
$356$	−2838.35	+	8735.55i	−0.422563	+	1.30051i
$357$		0			0
$358$	188.167	−	579.118i	0.0277791	−	0.0854954i
$359$	−970.423	+	705.053i	−0.142666	+	0.103653i	−0.656829	−	0.754040i	$-0.728103\pi$
$359$	−970.423	+	705.053i	−0.142666	+	0.103653i	0.514163	+	0.857692i	$0.328103\pi$
$360$		0			0
$361$	5275.88	+	3833.15i	0.769191	+	0.558850i
$362$	−8997.14	+	6536.80i	−1.30630	+	0.949080i
$363$		0			0
$364$	617.042	+	448.307i	0.0888511	+	0.0645541i
$365$	7150.77	−	2816.79i	1.02545	−	0.403939i
$366$		0			0
$367$	2597.49	−	7994.25i	0.369449	−	1.13705i	−0.577699	−	0.816250i	$-0.696049\pi$
$367$	2597.49	−	7994.25i	0.369449	−	1.13705i	0.947148	−	0.320797i	$-0.103951\pi$
$368$	2708.99			0.383739
$369$		0			0
$370$	8616.06	−	13524.6i	1.21062	−	1.90030i
$371$	15.2359	+	46.8912i	0.00213209	+	0.00656191i
$372$		0			0
$373$	4207.03	+	3056.58i	0.583999	+	0.424300i	0.840164	−	0.542333i	$-0.182459\pi$
$373$	4207.03	+	3056.58i	0.583999	+	0.424300i	−0.256165	+	0.966633i	$0.582459\pi$
$374$	1961.81			0.271238
$375$		0			0
$376$	132.065			0.0181137
$377$	−5755.27	−	4181.45i	−0.786237	−	0.571235i
$378$		0			0
$379$	129.200	+	397.637i	0.0175107	+	0.0538924i	0.959430	−	0.281947i	$-0.0909801\pi$
$379$	129.200	+	397.637i	0.0175107	+	0.0538924i	−0.941919	+	0.335839i	$0.890980\pi$
$380$	898.599	−	1410.53i	0.121308	−	0.190417i
$381$		0			0
$382$	−9541.88			−1.27802
$383$	−1016.74	+	3129.22i	−0.135648	+	0.417482i	−0.995690	−	0.0927410i	$-0.970437\pi$
$383$	−1016.74	+	3129.22i	−0.135648	+	0.417482i	0.860042	+	0.510223i	$0.170437\pi$
$384$		0			0
$385$	−427.501	+	168.399i	−0.0565908	+	0.0222920i
$386$	6099.60	+	4431.62i	0.804304	+	0.584361i
$387$		0			0
$388$	8238.89	−	5985.90i	1.07801	−	0.783217i
$389$	−1083.31	−	787.069i	−0.141198	−	0.102586i	0.514944	−	0.857224i	$-0.327813\pi$
$389$	−1083.31	−	787.069i	−0.141198	−	0.102586i	−0.656142	+	0.754638i	$0.727813\pi$
$390$		0			0
$391$	728.551	−	529.323i	0.0942312	−	0.0684629i
$392$	−59.3718	+	182.728i	−0.00764982	+	0.0235437i
$393$		0			0
$394$	1187.40	−	3654.44i	0.151828	−	0.467279i
$395$	−6061.77	−	1567.66i	−0.772154	−	0.199690i
$396$		0			0
$397$	287.218	+	883.966i	0.0363100	+	0.111751i	0.967569	−	0.252608i	$-0.0812883\pi$
$397$	287.218	+	883.966i	0.0363100	+	0.111751i	−0.931259	+	0.364359i	$0.881288\pi$
$398$	2059.62	+	1496.40i	0.259396	+	0.188462i
$399$		0			0
$400$	−6871.77	−	3809.02i	−0.858971	−	0.476127i
$401$	−6924.87			−0.862372			−0.431186	−	0.902263i	$-0.641905\pi$
$401$	−6924.87			−0.862372			−0.431186	+	0.902263i	$0.641905\pi$
$402$		0			0
$403$	−3988.17	−	12274.3i	−0.492965	−	1.51719i
$404$	−1674.51	−	5153.61i	−0.206213	−	0.634658i
$405$		0			0
$406$	−291.498	+	897.139i	−0.0356325	+	0.109666i
$407$	8343.41			1.01614
$408$		0			0
$409$	1445.15	−	1049.97i	0.174715	−	0.126938i	−0.496991	−	0.867756i	$-0.665562\pi$
$409$	1445.15	−	1049.97i	0.174715	−	0.126938i	0.671706	+	0.740818i	$0.265562\pi$
$410$	10244.6	−	16080.9i	1.23401	−	1.93702i
$411$		0			0
$412$	−1906.85	+	1385.41i	−0.228019	+	0.165665i
$413$	642.156	−	466.553i	0.0765095	−	0.0555874i
$414$		0			0
$415$	−6694.21	−	8120.67i	−0.791822	−	0.960549i
$416$	−11079.5	+	8049.72i	−1.30581	+	0.948726i
$417$		0			0
$418$	1725.29			0.201882
$419$	3116.71	−	9592.24i	0.363392	−	1.11841i	−0.587590	−	0.809159i	$-0.699923\pi$
$419$	3116.71	−	9592.24i	0.363392	−	1.11841i	0.950982	−	0.309246i	$-0.100077\pi$
$420$		0			0
$421$	−1421.64	−	4375.37i	−0.164576	−	0.506514i	0.834428	−	0.551116i	$-0.185798\pi$
$421$	−1421.64	−	4375.37i	−0.164576	−	0.506514i	−0.999005	+	0.0446022i	$0.985798\pi$
$422$	−1016.55	−	3128.62i	−0.117263	−	0.360898i
$423$		0			0
$424$	15.8483			0.00181523
$425$	−2592.34	+	318.319i	−0.295875	+	0.0363312i
$426$		0			0
$427$	−1225.38	−	890.291i	−0.138877	−	0.100900i
$428$	−126.806	−	390.270i	−0.0143211	−	0.0440757i
$429$		0			0
$430$	3909.25	−	1539.91i	0.438421	−	0.172700i
$431$	1757.68	−	5409.57i	0.196437	−	0.604570i	−0.803520	−	0.595278i	$-0.797042\pi$
$431$	1757.68	−	5409.57i	0.196437	−	0.604570i	0.999957	−	0.00929261i	$-0.00295797\pi$
$432$		0			0
$433$	−4358.21	+	13413.2i	−0.483700	+	1.48868i	0.350155	+	0.936692i	$0.386129\pi$
$433$	−4358.21	+	13413.2i	−0.483700	+	1.48868i	−0.833855	+	0.551984i	$0.813871\pi$
$434$	−1384.51	+	1005.90i	−0.153130	+	0.111255i
$435$		0			0
$436$	10582.3	+	7688.48i	1.16238	+	0.844521i
$437$	640.712	−	465.505i	0.0701360	−	0.0509568i
$438$		0			0
$439$	11289.8	+	8202.55i	1.22741	+	0.891768i	0.996694	−	0.0812521i	$-0.0258919\pi$
$439$	11289.8	+	8202.55i	1.22741	+	0.891768i	0.230720	+	0.973020i	$0.425892\pi$
$440$	9.01692	+	147.416i	0.000976965	+	0.0159723i
$441$		0			0
$442$	−1382.07	+	4253.58i	−0.148730	+	0.457743i
$443$	6671.65			0.715530			0.357765	−	0.933812i	$-0.383539\pi$
$443$	6671.65			0.715530			0.357765	+	0.933812i	$0.383539\pi$
$444$		0			0
$445$	11736.9	−	4623.35i	1.25030	−	0.492512i
$446$	−4110.57	−	12651.0i	−0.436415	−	1.34315i
$447$		0			0
$448$	753.787	+	547.659i	0.0794935	+	0.0577554i
$449$	5676.67			0.596656			0.298328	−	0.954463i	$-0.403571\pi$
$449$	5676.67			0.596656			0.298328	+	0.954463i	$0.403571\pi$
$450$		0			0
$451$	9920.39			1.03577
$452$	−7963.91	−	5786.12i	−0.828740	−	0.602115i
$453$		0			0
$454$	1224.57	+	3768.84i	0.126590	+	0.389605i
$455$	−63.9517	−	1045.54i	−0.00658924	−	0.107727i
$456$		0			0
$457$	−16775.1			−1.71708			−0.858539	−	0.512749i	$-0.828627\pi$
$457$	−16775.1			−1.71708			−0.858539	+	0.512749i	$0.828627\pi$
$458$	−442.172	+	1360.86i	−0.0451121	+	0.138841i
$459$		0			0
$460$	2495.16	+	3026.85i	0.252908	+	0.306799i
$461$	−1058.41	−	768.980i	−0.106931	−	0.0776897i	0.533035	−	0.846093i	$-0.321051\pi$
$461$	−1058.41	−	768.980i	−0.106931	−	0.0776897i	−0.639966	+	0.768404i	$0.721051\pi$
$462$		0			0
$463$	609.193	−	442.604i	0.0611481	−	0.0444267i	−0.556791	−	0.830652i	$-0.687968\pi$
$463$	609.193	−	442.604i	0.0611481	−	0.0444267i	0.617939	+	0.786226i	$0.287968\pi$
$464$	−6789.65	−	4932.97i	−0.679314	−	0.493550i
$465$		0			0
$466$	−16563.1	+	12033.8i	−1.64651	+	1.19626i
$467$	−4934.43	+	15186.6i	−0.488947	+	1.50482i	0.337236	+	0.941420i	$0.390508\pi$
$467$	−4934.43	+	15186.6i	−0.488947	+	1.50482i	−0.826182	+	0.563403i	$0.809492\pi$
$468$		0			0
$469$	−337.604	+	1039.04i	−0.0332390	+	0.102299i
$470$	−6675.45	−	8097.91i	−0.655140	−	0.794742i
$471$		0			0
$472$	−78.8427	−	242.653i	−0.00768862	−	0.0236632i
$473$	1768.57	+	1284.94i	0.171922	+	0.124909i
$474$		0			0
$475$	−2279.79	+	279.941i	−0.220219	+	0.0270412i
$476$	299.112			0.0288020
$477$		0			0
$478$	3705.09	+	11403.1i	0.354533	+	1.09114i
$479$	3394.70	+	10447.8i	0.323816	+	0.996602i	0.971972	+	0.235095i	$0.0755402\pi$
$479$	3394.70	+	10447.8i	0.323816	+	0.996602i	−0.648157	+	0.761507i	$0.724460\pi$
$480$		0			0
$481$	−5877.82	+	18090.1i	−0.557185	+	1.71484i
$482$	17546.5			1.65813
$483$		0			0
$484$	5168.85	−	3755.39i	0.485429	−	0.352685i
$485$	−13540.9	−	3501.85i	−1.26775	−	0.327858i
$486$		0			0
$487$	5088.72	−	3697.17i	0.473494	−	0.344014i	−0.325307	−	0.945608i	$-0.605468\pi$
$487$	5088.72	−	3697.17i	0.473494	−	0.344014i	0.798802	+	0.601595i	$0.205468\pi$
$488$	−393.883	+	286.173i	−0.0365374	+	0.0265460i
$489$		0			0
$490$	14205.4	−	5595.73i	1.30967	−	0.515896i
$491$	−10099.7	+	7337.84i	−0.928292	+	0.674444i	−0.945574	−	0.325407i	$-0.894499\pi$
$491$	−10099.7	+	7337.84i	−0.928292	+	0.674444i	0.0172817	+	0.999851i	$0.494499\pi$
$492$		0			0
$493$	−2789.87			−0.254867
$494$	−1215.44	+	3740.75i	−0.110699	+	0.340697i
$495$		0			0
$496$	−4704.96	−	14480.4i	−0.425925	−	1.31086i
$497$	−513.498	−	1580.39i	−0.0463452	−	0.142636i
$498$		0			0
$499$	−7074.89			−0.634700			−0.317350	−	0.948308i	$-0.602793\pi$
$499$	−7074.89			−0.634700			−0.317350	+	0.948308i	$0.602793\pi$
$500$	−2073.41	−	11186.4i	−0.185452	−	1.00055i
$501$		0			0
$502$	−20371.2	−	14800.5i	−1.81117	−	1.31589i
$503$	2675.62	+	8234.70i	0.237177	+	0.729955i	0.996825	+	0.0796208i	$0.0253709\pi$
$503$	2675.62	+	8234.70i	0.237177	+	0.729955i	−0.759649	+	0.650334i	$0.774629\pi$
$504$		0			0
$505$	−3998.64	+	6276.67i	−0.352351	+	0.553085i
$506$	−1250.48	+	3848.59i	−0.109863	+	0.338124i
$507$		0			0
$508$	−1730.75	+	5326.71i	−0.151161	+	0.465225i
$509$	−7331.00	+	5326.28i	−0.638391	+	0.463818i	−0.859297	−	0.511477i	$-0.829099\pi$
$509$	−7331.00	+	5326.28i	−0.638391	+	0.463818i	0.220906	+	0.975295i	$0.429099\pi$
$510$		0			0
$511$	977.953	+	710.525i	0.0846617	+	0.0615103i
$512$	−13300.7	+	9663.55i	−1.14808	+	0.834126i
$513$		0			0
$514$	−19509.7	−	14174.7i	−1.67420	−	1.21638i
$515$	3133.97	+	810.487i	0.268154	+	0.0693482i
$516$		0			0
$517$	1687.33	−	5193.06i	0.143537	−	0.441761i
$518$	2522.20			0.213937
$519$		0			0
$520$	−325.979	−	84.3026i	−0.0274906	−	0.00710945i
$521$	−3035.14	−	9341.21i	−0.255225	−	0.785500i	−0.993785	−	0.111314i	$-0.964494\pi$
$521$	−3035.14	−	9341.21i	−0.255225	−	0.785500i	0.738561	−	0.674187i	$-0.235506\pi$
$522$		0			0
$523$	16877.5	+	12262.2i	1.41109	+	1.02522i	0.993163	+	0.116735i	$0.0372428\pi$
$523$	16877.5	+	12262.2i	1.41109	+	1.02522i	0.417926	+	0.908481i	$0.362757\pi$
$524$	−11948.5			−0.996127
$525$		0			0
$526$	−26692.8			−2.21266
$527$	−4094.73	−	2975.00i	−0.338462	−	0.245907i
$528$		0			0
$529$	−3185.80	−	9804.87i	−0.261839	−	0.805858i
$530$	−801.075	−	971.775i	−0.0656537	−	0.0796438i
$531$		0			0
$532$	263.049			0.0214373
$533$	−6988.79	+	21509.3i	−0.567951	+	1.74797i
$534$		0			0
$535$	−302.807	+	475.316i	−0.0244701	+	0.0384106i
$536$	284.105	+	206.414i	0.0228945	+	0.0166338i
$537$		0			0
$538$	27489.0	−	19971.9i	2.20285	−	1.60047i
$539$	6426.63	+	4669.22i	0.513571	+	0.373131i
$540$		0			0
$541$	−6405.10	+	4653.58i	−0.509014	+	0.369821i	−0.812450	−	0.583031i	$-0.801866\pi$
$541$	−6405.10	+	4653.58i	−0.509014	+	0.369821i	0.303435	+	0.952852i	$0.401866\pi$
$542$	−10427.8	+	32093.5i	−0.826406	+	2.54342i
$543$		0			0
$544$	−1659.67	+	5107.93i	−0.130805	+	0.402575i
$545$	−1096.77	−	17931.0i	−0.0862029	−	1.40932i
$546$		0			0
$547$	−4314.05	−	13277.3i	−0.337213	−	1.03783i	−0.965622	−	0.259951i	$-0.916293\pi$
$547$	−4314.05	−	13277.3i	−0.337213	−	1.03783i	0.628409	−	0.777883i	$-0.283707\pi$
$548$	17296.8	+	12566.9i	1.34833	+	0.979617i
$549$		0			0
$550$	8583.42	−	8004.29i	0.665451	−	0.620553i
$551$	−2453.51			−0.189697
$552$		0			0
$553$	−304.316	−	936.589i	−0.0234012	−	0.0720214i
$554$	1948.01	+	5995.37i	0.149392	+	0.459781i
$555$		0			0
$556$	−7948.89	+	24464.2i	−0.606309	+	1.86603i
$557$	−1925.41			−0.146467			−0.0732337	−	0.997315i	$-0.523332\pi$
$557$	−1925.41			−0.146467			−0.0732337	+	0.997315i	$0.523332\pi$
$558$		0			0
$559$	−4031.94	+	2929.37i	−0.305068	+	0.221645i
$560$	−75.4457	−	1233.45i	−0.00569314	−	0.0930764i
$561$		0			0
$562$	−4861.86	+	3532.35i	−0.364920	+	0.265130i
$563$	10178.3	−	7394.94i	0.761922	−	0.553569i	−0.137577	−	0.990491i	$-0.543931\pi$
$563$	10178.3	−	7394.94i	0.761922	−	0.553569i	0.899499	+	0.436922i	$0.143931\pi$
$564$		0			0
$565$	825.398	+	13494.3i	0.0614598	+	1.00480i
$566$	19406.5	−	14099.7i	1.44120	−	1.04709i
$567$		0			0
$568$	−534.138			−0.0394576
$569$	−283.413	+	872.255i	−0.0208810	+	0.0642651i	−0.960954	−	0.276708i	$-0.910757\pi$
$569$	−283.413	+	872.255i	−0.0208810	+	0.0642651i	0.940073	+	0.340973i	$0.110757\pi$
$570$		0			0
$571$	−2458.12	−	7565.32i	−0.180156	−	0.554464i	0.819675	−	0.572829i	$-0.194154\pi$
$571$	−2458.12	−	7565.32i	−0.180156	−	0.554464i	−0.999831	+	0.0183647i	$0.994154\pi$
$572$	−3132.31	−	9640.25i	−0.228966	−	0.704683i
$573$		0			0
$574$	2998.92			0.218071
$575$	1027.93	−	5288.44i	0.0745522	−	0.383553i
$576$		0			0
$577$	370.660	+	269.300i	0.0267431	+	0.0194300i	0.601077	−	0.799191i	$-0.294739\pi$
$577$	370.660	+	269.300i	0.0267431	+	0.0194300i	−0.574333	+	0.818621i	$0.694739\pi$
$578$	−5557.43	−	17104.0i	−0.399929	−	1.23085i
$579$		0			0
$580$	−741.943	−	12129.9i	−0.0531164	−	0.868392i
$581$	511.511	−	1574.27i	0.0365250	−	0.112412i
$582$		0			0
$583$	202.485	−	623.183i	0.0143843	−	0.0442703i
$584$	314.351	−	228.389i	0.0222739	−	0.0161829i
$585$		0			0
$586$	4124.91	+	2996.92i	0.290782	+	0.211266i
$587$	3356.69	−	2438.78i	0.236023	−	0.171481i	−0.463487	−	0.886104i	$-0.653402\pi$
$587$	3356.69	−	2438.78i	0.236023	−	0.171481i	0.699510	+	0.714623i	$0.253402\pi$
$588$		0			0
$589$	−3601.05	−	2616.31i	−0.251916	−	0.183028i
$590$	−10893.6	+	17099.7i	−0.760142	+	1.19319i
$591$		0			0
$592$	−6934.23	+	21341.4i	−0.481411	+	1.48163i
$593$	−5267.14			−0.364748			−0.182374	−	0.983229i	$-0.558378\pi$
$593$	−5267.14			−0.364748			−0.182374	+	0.983229i	$0.558378\pi$
$594$		0			0
$595$	−261.300	−	316.980i	−0.0180038	−	0.0218402i
$596$	−4002.87	−	12319.6i	−0.275107	−	0.846693i
$597$		0			0
$598$	−7463.53	−	5422.57i	−0.510379	−	0.370812i
$599$	20272.2			1.38281			0.691403	−	0.722470i	$-0.256993\pi$
$599$	20272.2			1.38281			0.691403	+	0.722470i	$0.256993\pi$
$600$		0			0
$601$	11957.9			0.811601			0.405801	−	0.913962i	$-0.366993\pi$
$601$	11957.9			0.811601			0.405801	+	0.913962i	$0.366993\pi$
$602$	534.637	+	388.437i	0.0361963	+	0.0262982i
$603$		0			0
$604$	2893.59	+	8905.56i	0.194931	+	0.599937i
$605$	−8495.16	−	2196.96i	−0.570872	−	0.147635i
$606$		0			0
$607$	11679.0			0.780949			0.390474	−	0.920614i	$-0.372311\pi$
$607$	11679.0			0.780949			0.390474	+	0.920614i	$0.372311\pi$
$608$	−1459.57	+	4492.09i	−0.0973574	+	0.299635i
$609$		0			0
$610$	37456.9	+	9686.86i	2.48620	+	0.642966i
$611$	10070.8	+	7316.89i	0.666812	+	0.484467i
$612$		0			0
$613$	−1455.56	+	1057.53i	−0.0959045	+	0.0696787i	−0.634704	−	0.772755i	$-0.718878\pi$
$613$	−1455.56	+	1057.53i	−0.0959045	+	0.0696787i	0.538800	+	0.842434i	$0.318878\pi$
$614$	−16961.7	−	12323.4i	−1.11485	−	0.809985i
$615$		0			0
$616$	−18.7931	+	13.6540i	−0.00122922	+	0.000893078i
$617$	−263.588	+	811.240i	−0.0171988	+	0.0529324i	−0.959288	−	0.282431i	$-0.908859\pi$
$617$	−263.588	+	811.240i	−0.0171988	+	0.0529324i	0.942089	+	0.335364i	$0.108859\pi$
$618$		0			0
$619$	3148.18	−	9689.09i	0.204420	−	0.629140i	−0.795317	−	0.606194i	$-0.792696\pi$
$619$	3148.18	−	9689.09i	0.204420	−	0.629140i	0.999737	−	0.0229456i	$-0.00730446\pi$
$620$	11845.9	−	18594.4i	0.767324	−	1.20447i
$621$		0			0
$622$	−800.255	−	2462.93i	−0.0515873	−	0.158769i
$623$	1605.17	+	1166.22i	0.103226	+	0.0749979i
$624$		0			0
$625$	−10043.4	+	11969.6i	−0.642776	+	0.766054i
$626$	3707.53			0.236713
$627$		0			0
$628$	−1584.31	−	4876.01i	−0.100670	−	0.309831i
$629$	2305.12	+	7094.42i	0.146123	+	0.449719i
$630$		0			0
$631$	4782.62	−	14719.4i	0.301732	−	0.928636i	−0.679144	−	0.734005i	$-0.737649\pi$
$631$	4782.62	−	14719.4i	0.301732	−	0.928636i	0.980877	−	0.194631i	$-0.0623510\pi$
$632$	−316.548			−0.0199234
$633$		0			0
$634$	−3979.37	+	2891.18i	−0.249276	+	0.181110i
$635$	7156.88	−	2819.20i	0.447263	−	0.176183i
$636$		0			0
$637$	−14651.2	+	10644.7i	−0.911308	+	0.662104i
$638$	10142.3	−	7368.80i	0.629368	−	0.457263i
$639$		0			0
$640$	−783.027	−	202.501i	−0.0483623	−	0.0125071i
$641$	13634.8	−	9906.26i	0.840159	−	0.610411i	−0.0822559	−	0.996611i	$-0.526212\pi$
$641$	13634.8	−	9906.26i	0.840159	−	0.610411i	0.922415	+	0.386200i	$0.126212\pi$
$642$		0			0
$643$	25045.6			1.53608			0.768041	−	0.640401i	$-0.221232\pi$
$643$	25045.6			1.53608			0.768041	+	0.640401i	$0.221232\pi$
$644$	−190.658	+	586.784i	−0.0116661	+	0.0359045i
$645$		0			0
$646$	476.662	+	1467.02i	0.0290310	+	0.0893482i
$647$	−1897.40	−	5839.59i	−0.115293	−	0.354835i	0.876715	−	0.481010i	$-0.159730\pi$
$647$	−1897.40	−	5839.59i	−0.115293	−	0.354835i	−0.992008	+	0.126175i	$0.959730\pi$
$648$		0			0
$649$	−10548.9			−0.638029
$650$	11307.9	+	24249.4i	0.682357	+	1.46329i
$651$		0			0
$652$	−4253.66	−	3090.47i	−0.255500	−	0.185632i
$653$	3287.26	+	10117.1i	0.196999	+	0.606300i	0.999947	+	0.0102520i	$0.00326337\pi$
$653$	3287.26	+	10117.1i	0.196999	+	0.606300i	−0.802949	+	0.596048i	$0.796737\pi$
$654$		0			0
$655$	10438.0	+	12662.2i	0.622667	+	0.755350i
$656$	−8244.87	+	25375.1i	−0.490714	+	1.51026i
$657$		0			0
$658$	510.077	−	1569.86i	0.0302202	−	0.0930081i
$659$	5132.96	−	3729.31i	0.303417	−	0.220445i	−0.425650	−	0.904888i	$-0.639954\pi$
$659$	5132.96	−	3729.31i	0.303417	−	0.220445i	0.729067	+	0.684443i	$0.239954\pi$
$660$		0			0
$661$	25521.9	+	18542.7i	1.50179	+	1.09112i	0.969660	+	0.244456i	$0.0786093\pi$
$661$	25521.9	+	18542.7i	1.50179	+	1.09112i	0.532133	+	0.846661i	$0.321391\pi$
$662$	34593.4	−	25133.6i	2.03098	−	1.47560i
$663$		0			0
$664$	−430.454	−	312.743i	−0.0251579	−	0.0182783i
$665$	−229.796	−	278.763i	−0.0134002	−	0.0162556i
$666$		0			0
$667$	1778.30	−	5473.04i	0.103232	−	0.317717i
$668$	27898.2			1.61589
$669$		0			0
$670$	−1703.74	−	27854.1i	−0.0982404	−	1.60612i
$671$	6220.43	+	19144.5i	0.357879	+	1.10144i
$672$		0			0
$673$	−12123.9	−	8808.54i	−0.694417	−	0.504523i	0.183692	−	0.982984i	$-0.441195\pi$
$673$	−12123.9	−	8808.54i	−0.694417	−	0.504523i	−0.878109	+	0.478460i	$0.841195\pi$
$674$	−15885.5			−0.907844
$675$		0			0
$676$	5223.44			0.297192
$677$	446.032	+	324.061i	0.0253211	+	0.0183969i	0.600374	−	0.799719i	$-0.295018\pi$
$677$	446.032	+	324.061i	0.0253211	+	0.0183969i	−0.575053	+	0.818116i	$0.695018\pi$
$678$		0			0
$679$	−679.786	−	2092.17i	−0.0384209	−	0.118247i
$680$	−122.857	+	48.3953i	−0.00692848	+	0.00272923i
$681$		0			0
$682$	22743.7			1.27698
$683$	733.082	−	2256.19i	0.0410697	−	0.126400i	−0.928419	−	0.371534i	$-0.878832\pi$
$683$	733.082	−	2256.19i	0.0410697	−	0.126400i	0.969489	+	0.245134i	$0.0788320\pi$
$684$		0			0
$685$	−1792.68	−	29308.3i	−0.0999926	−	1.63476i
$686$	3903.20	+	2835.84i	0.217237	+	0.157832i
$687$		0			0
$688$	−4756.59	+	3455.86i	−0.263580	+	0.191502i
$689$	1208.53	+	878.049i	0.0668235	+	0.0485501i
$690$		0			0
$691$	−9105.79	+	6615.74i	−0.501303	+	0.364218i	−0.809514	−	0.587100i	$-0.800270\pi$
$691$	−9105.79	+	6615.74i	−0.501303	+	0.364218i	0.308211	+	0.951318i	$0.400270\pi$
$692$	−2783.56	+	8566.91i	−0.152912	+	0.470614i
$693$		0			0
$694$	−11765.8	+	36211.6i	−0.643553	+	1.98065i
$695$	32869.6	−	12947.8i	1.79398	−	0.706675i
$696$		0			0
$697$	2740.81	+	8435.34i	0.148946	+	0.458409i
$698$	−18039.4	−	13106.4i	−0.978224	−	0.710721i
$699$		0			0
$700$	1308.69	−	1220.39i	0.0706625	−	0.0658948i
$701$	−19255.2			−1.03746			−0.518729	−	0.854939i	$-0.673595\pi$
$701$	−19255.2			−1.03746			−0.518729	+	0.854939i	$0.673595\pi$
$702$		0			0
$703$	2027.20	+	6239.08i	0.108759	+	0.334724i
$704$	−3826.47	−	11776.7i	−0.204852	−	0.630468i
$705$		0			0
$706$	15065.6	−	46367.0i	0.803115	−	2.47174i
$707$	−1170.53			−0.0622666
$708$		0			0
$709$	20142.8	−	14634.6i	1.06697	−	0.775196i	0.0916013	−	0.995796i	$-0.470801\pi$
$709$	20142.8	−	14634.6i	1.06697	−	0.775196i	0.975364	+	0.220600i	$0.0708015\pi$
$710$	26998.8	+	32752.0i	1.42711	+	1.73121i
$711$		0			0
$712$	515.961	−	374.868i	0.0271579	−	0.0197314i
$713$	8446.24	−	6136.56i	0.443639	−	0.322322i
$714$		0			0
$715$	−7479.79	+	11741.0i	−0.391228	+	0.614110i
$716$	−998.203	+	725.237i	−0.0521014	+	0.0378539i
$717$		0			0
$718$	4819.08			0.250483
$719$	11440.9	−	35211.4i	0.593425	−	1.82637i	0.0310094	−	0.999519i	$-0.490128\pi$
$719$	11440.9	−	35211.4i	0.593425	−	1.82637i	0.562415	−	0.826855i	$-0.309872\pi$
$720$		0			0
$721$	157.333	+	484.222i	0.00812676	+	0.0250116i
$722$	−8096.19	−	24917.5i	−0.417326	−	1.28440i
$723$		0			0
$724$	22534.5			1.15675
$725$	−12206.4	+	11382.8i	−0.625287	+	0.583099i
$726$		0			0
$727$	−21547.9	−	15655.5i	−1.09927	−	0.798665i	−0.118328	−	0.992975i	$-0.537754\pi$
$727$	−21547.9	−	15655.5i	−1.09927	−	0.798665i	−0.980940	+	0.194309i	$0.937754\pi$
$728$	−16.3650	−	50.3662i	−0.000833140	−	0.00256414i
$729$		0			0
$730$	−29893.6	−	7730.90i	−1.51563	−	0.391963i
$731$	−603.969	+	1858.83i	−0.0305590	+	0.0940508i
$732$		0			0
$733$	−448.738	+	1381.07i	−0.0226119	+	0.0695922i	−0.961726	−	0.274014i	$-0.911649\pi$
$733$	−448.738	+	1381.07i	−0.0226119	+	0.0695922i	0.939114	+	0.343606i	$0.111649\pi$
$734$	−27320.6	+	19849.6i	−1.37387	+	0.998176i
$735$		0			0
$736$	−8962.61	−	6511.72i	−0.448867	−	0.326121i
$737$	11746.5	−	8534.30i	0.587091	−	0.426547i
$738$		0			0
$739$	−4718.01	−	3427.83i	−0.234851	−	0.170629i	0.464135	−	0.885764i	$-0.346365\pi$
$739$	−4718.01	−	3427.83i	−0.234851	−	0.170629i	−0.698986	+	0.715135i	$0.746365\pi$
$740$	−30232.4	+	11909.0i	−1.50184	+	0.591599i
$741$		0			0
$742$	61.2108	−	188.388i	0.00302846	−	0.00932066i
$743$	−34683.6			−1.71254			−0.856271	−	0.516527i	$-0.827225\pi$
$743$	−34683.6			−1.71254			−0.856271	+	0.516527i	$0.827225\pi$
$744$		0			0
$745$	−9558.65	+	15004.2i	−0.470070	+	0.737868i
$746$	−6455.97	−	19869.4i	−0.316849	−	0.975162i
$747$		0			0
$748$	−3216.00	−	2336.56i	−0.157204	−	0.114215i
$749$	−88.6415			−0.00432429
$750$		0			0
$751$	34364.2			1.66973			0.834865	−	0.550455i	$-0.185546\pi$
$751$	34364.2			1.66973			0.834865	+	0.550455i	$0.185546\pi$
$752$	11880.8	+	8631.94i	0.576130	+	0.418583i
$753$		0			0
$754$	8831.84	+	27181.6i	0.426574	+	1.31286i
$755$	6909.75	−	10846.2i	0.333075	−	0.522827i
$756$		0			0
$757$	32402.5			1.55573			0.777865	−	0.628431i	$-0.216303\pi$
$757$	32402.5			1.55573			0.777865	+	0.628431i	$0.216303\pi$
$758$	519.067	−	1597.52i	0.0248725	−	0.0765497i
$759$		0			0
$760$	−108.045	+	42.5605i	−0.00515684	+	0.00203136i
$761$	17626.1	+	12806.1i	0.839613	+	0.610015i	0.922263	−	0.386564i	$-0.126338\pi$
$761$	17626.1	+	12806.1i	0.839613	+	0.610015i	−0.0826493	+	0.996579i	$0.526338\pi$
$762$		0			0
$763$	2285.90	−	1660.81i	0.108460	−	0.0788011i
$764$	15642.0	+	11364.6i	0.740716	+	0.538162i
$765$		0			0
$766$	10694.2	−	7769.79i	0.504435	−	0.366493i
$767$	7431.57	−	22872.0i	0.349854	−	1.07674i
$768$		0			0
$769$	2619.17	−	8060.98i	0.122821	−	0.378006i	−0.870676	−	0.491856i	$-0.836319\pi$
$769$	2619.17	−	8060.98i	0.122821	−	0.378006i	0.993498	+	0.113851i	$0.0363186\pi$
$770$	1787.16	+	462.183i	0.0836425	+	0.0216311i
$771$		0			0
$772$	−4720.91	−	14529.5i	−0.220090	−	0.677367i
$773$	−31767.7	−	23080.6i	−1.47815	−	1.07394i	−0.978148	−	0.207909i	$-0.933334\pi$
$773$	−31767.7	−	23080.6i	−1.47815	−	1.07394i	−0.499997	−	0.866027i	$-0.666666\pi$
$774$		0			0
$775$	−30053.6	+	3690.34i	−1.39298	+	0.171046i
$776$	−707.109			−0.0327110
$777$		0			0
$778$	1662.41	+	5116.37i	0.0766070	+	0.235772i
$779$	2410.36	+	7418.32i	0.110860	+	0.341193i
$780$		0			0
$781$	−6824.39	+	21003.3i	−0.312671	+	0.962301i
$782$	−3617.95			−0.165445
$783$		0			0
$784$	−17284.5	+	12557.9i	−0.787376	+	0.572062i
$785$	−3783.26	+	5938.58i	−0.172013	+	0.270009i
$786$		0			0
$787$	18390.8	−	13361.7i	0.832988	−	0.605202i	−0.0874148	−	0.996172i	$-0.527861\pi$
$787$	18390.8	−	13361.7i	0.832988	−	0.605202i	0.920403	+	0.390970i	$0.127861\pi$
$788$	−6299.01	+	4576.50i	−0.284763	+	0.206892i
$789$		0			0
$790$	16000.4	+	19409.9i	0.720594	+	0.874144i
$791$	−1720.30	+	1249.87i	−0.0773286	+	0.0561825i
$792$		0			0
$793$	−45891.1			−2.05503
$794$	1153.91	−	3551.38i	0.0515753	−	0.158733i
$795$		0			0
$796$	−1594.09	−	4906.10i	−0.0709811	−	0.218457i
$797$	1044.21	+	3213.74i	0.0464088	+	0.142831i	0.971576	−	0.236729i	$-0.0760753\pi$
$797$	1044.21	+	3213.74i	0.0464088	+	0.142831i	−0.925167	+	0.379560i	$0.876075\pi$
$798$		0			0
$799$	4881.85			0.216154
$800$	13579.1	+	29120.0i	0.600118	+	1.28693i
$801$		0			0
$802$	22507.6	+	16352.8i	0.990988	+	0.719995i
$803$	−4964.41	−	15278.9i	−0.218170	−	0.671457i
$804$		0			0
$805$	788.392	−	310.559i	0.0345182	−	0.0135972i
$806$	−16022.7	+	49312.7i	−0.700217	+	2.15505i
$807$		0			0
$808$	−116.269	+	357.838i	−0.00506228	+	0.0155801i
$809$	−14579.2	+	10592.4i	−0.633592	+	0.460332i	−0.857643	−	0.514246i	$-0.828072\pi$
$809$	−14579.2	+	10592.4i	−0.633592	+	0.460332i	0.224051	+	0.974577i	$0.428072\pi$
$810$		0			0
$811$	−12216.1	−	8875.54i	−0.528935	−	0.384294i	0.291024	−	0.956716i	$-0.406004\pi$
$811$	−12216.1	−	8875.54i	−0.528935	−	0.384294i	−0.819959	+	0.572422i	$0.806004\pi$
$812$	1546.36	−	1123.50i	0.0668309	−	0.0485555i
$813$		0			0
$814$	−27118.3	−	19702.6i	−1.16768	−	0.848373i
$815$	440.860	+	7207.56i	0.0189480	+	0.309779i
$816$		0			0
$817$	−531.151	+	1634.72i	−0.0227450	+	0.0700018i
$818$	−7176.59			−0.306752
$819$		0			0
$820$	−35946.6	+	14159.9i	−1.53087	+	0.603030i
$821$	−2037.95	−	6272.15i	−0.0866319	−	0.266626i	0.898351	−	0.439279i	$-0.144766\pi$
$821$	−2037.95	−	6272.15i	−0.0866319	−	0.266626i	−0.984983	+	0.172653i	$0.944766\pi$
$822$		0			0
$823$	2390.87	+	1737.07i	0.101264	+	0.0735728i	0.637265	−	0.770645i	$-0.280066\pi$
$823$	2390.87	+	1737.07i	0.101264	+	0.0735728i	−0.536001	+	0.844217i	$0.680066\pi$
$824$	163.657			0.00691901
$825$		0			0
$826$	−3188.92			−0.134330
$827$	−22700.6	−	16493.0i	−0.954508	−	0.693491i	−0.00263938	−	0.999997i	$-0.500840\pi$
$827$	−22700.6	−	16493.0i	−0.954508	−	0.693491i	−0.951869	+	0.306506i	$0.900840\pi$
$828$		0			0
$829$	−5507.82	−	16951.3i	−0.230753	−	0.710186i	−0.997656	−	0.0684227i	$-0.978203\pi$
$829$	−5507.82	−	16951.3i	−0.230753	−	0.710186i	0.766903	−	0.641763i	$-0.221797\pi$
$830$	2581.37	+	42202.4i	0.107952	+	1.76490i
$831$		0			0
$832$	28229.7			1.17631
$833$	−2194.70	+	6754.60i	−0.0912868	+	0.280952i
$834$		0			0
$835$	−24371.5	−	29564.8i	−1.01007	−	1.22531i
$836$	−2828.26	−	2054.85i	−0.117006	−	0.0850101i
$837$		0			0
$838$	−32781.8	+	23817.4i	−1.35135	+	0.981810i
$839$	8554.12	+	6214.93i	0.351992	+	0.255737i	0.749704	−	0.661773i	$-0.230196\pi$
$839$	8554.12	+	6214.93i	0.351992	+	0.255737i	−0.397712	+	0.917510i	$0.630196\pi$
$840$		0			0
$841$	5307.90	−	3856.41i	0.217635	−	0.158121i
$842$	−5711.52	+	17578.3i	−0.233767	+	0.719462i
$843$		0			0
$844$	−2059.82	+	6339.47i	−0.0840070	+	0.258547i
$845$	−4563.13	−	5535.47i	−0.185771	−	0.225356i
$846$		0			0
$847$	−426.478	−	1312.57i	−0.0173010	−	0.0532471i
$848$	1425.74	+	1035.86i	0.0577359	+	0.0419476i
$849$		0			0
$850$	9177.50	+	5087.08i	0.370336	+	0.205277i
$851$	−15386.8			−0.619804
$852$		0			0
$853$	−12989.5	−	39977.6i	−0.521397	−	1.60470i	−0.771331	−	0.636434i	$-0.780409\pi$
$853$	−12989.5	−	39977.6i	−0.521397	−	1.60470i	0.249934	−	0.968263i	$-0.419591\pi$
$854$	1880.43	+	5787.37i	0.0753477	+	0.231896i
$855$		0			0
$856$	−8.80473	+	27.0982i	−0.000351565	+	0.00108201i
$857$	−13137.5			−0.523649			−0.261824	−	0.965116i	$-0.584324\pi$
$857$	−13137.5			−0.523649			−0.261824	+	0.965116i	$0.584324\pi$
$858$		0			0
$859$	−15419.0	+	11202.6i	−0.612445	+	0.444967i	−0.850274	−	0.526340i	$-0.823564\pi$
$859$	−15419.0	+	11202.6i	−0.612445	+	0.444967i	0.237830	+	0.971307i	$0.423564\pi$
$860$	−8242.50	−	2131.62i	−0.326822	−	0.0845206i
$861$		0			0
$862$	−18487.4	+	13431.9i	−0.730490	+	0.530732i
$863$	−12671.9	+	9206.66i	−0.499833	+	0.363150i	−0.808953	−	0.587873i	$-0.799965\pi$
$863$	−12671.9	+	9206.66i	−0.499833	+	0.363150i	0.309120	+	0.951023i	$0.399965\pi$
$864$		0			0
$865$	11510.4	−	4534.10i	0.452444	−	0.178224i
$866$	45840.0	−	33304.7i	1.79874	−	1.30686i
$867$		0			0
$868$	3467.67			0.135599
$869$	−4044.36	+	12447.3i	−0.157877	+	0.485897i
$870$		0			0
$871$	10228.7	+	31480.8i	0.397919	+	1.22467i
$872$	−280.659	−	863.780i	−0.0108995	−	0.0335451i
$873$		0			0
$874$	−3181.75			−0.123140
$875$	−2436.54	−	320.750i	−0.0941374	−	0.0123924i
$876$		0			0
$877$	−8267.03	−	6006.35i	−0.318310	−	0.231266i	0.417144	−	0.908840i	$-0.363031\pi$
$877$	−8267.03	−	6006.35i	−0.318310	−	0.231266i	−0.735454	+	0.677575i	$0.763031\pi$
$878$	−17325.0	−	53320.9i	−0.665935	−	2.04954i
$879$		0			0
$880$	−8824.12	+	13851.2i	−0.338024	+	0.530595i
$881$	4273.32	−	13151.9i	0.163419	−	0.502950i	−0.835498	−	0.549494i	$-0.814821\pi$
$881$	4273.32	−	13151.9i	0.163419	−	0.502950i	0.998916	+	0.0465434i	$0.0148206\pi$
$882$		0			0
$883$	−12703.5	+	39097.3i	−0.484152	+	1.49007i	0.349054	+	0.937103i	$0.386503\pi$
$883$	−12703.5	+	39097.3i	−0.484152	+	1.49007i	−0.833206	+	0.552963i	$0.813497\pi$
$884$	7331.73	−	5326.82i	0.278951	−	0.202670i
$885$		0			0
$886$	−21684.6	−	15754.8i	−0.822246	−	0.597396i
$887$	−28268.5	+	20538.3i	−1.07008	+	0.777461i	−0.975927	−	0.218097i	$-0.930015\pi$
$887$	−28268.5	+	20538.3i	−1.07008	+	0.777461i	−0.0941557	+	0.995557i	$0.530015\pi$
$888$		0			0
$889$	978.789	+	711.132i	0.0369263	+	0.0268286i
$890$	−49066.0	−	12689.1i	−1.84797	−	0.477911i
$891$		0			0
$892$	−8329.17	+	25634.6i	−0.312647	+	0.962229i
$893$	4293.26			0.160883
$894$		0			0
$895$	1640.58	+	424.276i	0.0612720	+	0.0158458i
$896$	−39.3099	−	120.983i	−0.00146568	−	0.00451091i
$897$		0			0
$898$	−18450.7	−	13405.2i	−0.685642	−	0.498148i
$899$	−32343.6			−1.19991
$900$		0			0
$901$	585.837			0.0216615
$902$	−32243.9	−	23426.6i	−1.19025	−	0.864766i
$903$		0			0
$904$	211.216	+	650.055i	0.00777094	+	0.0239165i
$905$	−19685.8	−	23880.6i	−0.723070	−	0.877147i
$906$		0			0
$907$	32117.9			1.17581			0.587903	−	0.808932i	$-0.299954\pi$
$907$	32117.9			1.17581			0.587903	+	0.808932i	$0.299954\pi$
$908$	2481.33	−	7636.75i	0.0906892	−	0.279113i
$909$		0			0
$910$	−2261.13	+	3549.29i	−0.0823690	+	0.129294i
$911$	31846.4	+	23137.8i	1.15820	+	0.841480i	0.989549	−	0.144196i	$-0.0460597\pi$
$911$	31846.4	+	23137.8i	1.15820	+	0.841480i	0.168649	+	0.985676i	$0.446060\pi$
$912$		0			0
$913$	−17797.3	+	12930.5i	−0.645132	+	0.468716i
$914$	54523.4	+	39613.6i	1.97317	+	1.43359i
$915$		0			0
$916$	2345.67	−	1704.23i	0.0846103	−	0.0614730i
$917$	−797.577	+	2454.69i	−0.0287223	+	0.0883981i
$918$		0			0
$919$	−5488.96	+	16893.3i	−0.197023	+	0.606374i	0.802924	+	0.596081i	$0.203276\pi$
$919$	−5488.96	+	16893.3i	−0.197023	+	0.606374i	−0.999947	+	0.0102930i	$0.996724\pi$
$920$	−16.6289	−	271.864i	−0.000595911	−	0.00974247i
$921$		0			0
$922$	1624.20	+	4998.78i	0.0580154	+	0.178553i
$923$	−40731.4	−	29593.1i	−1.45254	−	1.05533i
$924$		0			0
$925$	39031.0	+	21634.9i	1.38739	+	0.769027i
$926$	−3025.23			−0.107360
$927$		0			0
$928$	10605.7	+	32641.1i	0.375162	+	1.15463i
$929$	−13935.4	−	42888.9i	−0.492150	−	1.51468i	−0.821352	−	0.570422i	$-0.806780\pi$
$929$	−13935.4	−	42888.9i	−0.492150	−	1.51468i	0.329202	−	0.944260i	$-0.393220\pi$
$930$		0			0
$931$	−1930.09	+	5940.22i	−0.0679445	+	0.209112i
$932$	41484.4			1.45801
$933$		0			0
$934$	51900.7	−	37708.1i	1.81825	−	1.32103i
$935$	333.314	+	5449.30i	0.0116583	+	0.190600i
$936$		0			0
$937$	−10238.8	+	7438.95i	−0.356978	+	0.259360i	−0.751791	−	0.659402i	$-0.770810\pi$
$937$	−10238.8	+	7438.95i	−0.356978	+	0.259360i	0.394813	+	0.918762i	$0.370810\pi$
$938$	3550.94	−	2579.91i	0.123606	−	0.0898049i
$939$		0			0
$940$	1298.29	+	21225.5i	0.0450483	+	0.736488i
$941$	4376.92	−	3180.02i	0.151630	−	0.110165i	−0.509384	−	0.860539i	$-0.670127\pi$
$941$	4376.92	−	3180.02i	0.151630	−	0.110165i	0.661013	+	0.750374i	$0.270127\pi$
$942$		0			0
$943$	−18295.1			−0.631781
$944$	8767.23	−	26982.8i	0.302276	−	0.930311i
$945$		0			0
$946$	−2713.99	−	8352.81i	−0.0932764	−	0.287075i
$947$	7945.09	+	24452.5i	0.272630	+	0.839069i	0.989837	+	0.142209i	$0.0454204\pi$
$947$	7945.09	+	24452.5i	0.272630	+	0.839069i	−0.717207	+	0.696861i	$0.754580\pi$
$948$		0			0
$949$	36624.9			1.25279
$950$	8071.00	+	4473.75i	0.275640	+	0.152787i
$951$		0			0
$952$	−16.8022	−	12.2075i	−0.000572020	−	0.000415597i
$953$	11813.1	+	36357.0i	0.401536	+	1.23580i	0.923753	+	0.382988i	$0.125105\pi$
$953$	11813.1	+	36357.0i	0.401536	+	1.23580i	−0.522217	+	0.852813i	$0.674895\pi$
$954$		0			0
$955$	−1621.17	−	26504.3i	−0.0549319	−	0.898074i
$956$	7507.56	−	23105.9i	0.253987	−	0.781693i
$957$		0			0
$958$	13638.4	−	41974.6i	0.459954	−	1.41559i
$959$	3736.33	−	2714.60i	0.125811	−	0.0914067i
$960$		0			0
$961$	−23369.7	−	16979.1i	−0.784455	−	0.569940i
$962$	61823.4	−	44917.3i	2.07200	−	1.50540i
$963$		0			0
$964$	−28763.9	−	20898.2i	−0.961020	−	0.698222i
$965$	−11273.3	+	17695.7i	−0.376063	+	0.590305i
$966$		0			0
$967$	6480.65	−	19945.4i	0.215516	−	0.663289i	−0.783601	−	0.621265i	$-0.786619\pi$
$967$	6480.65	−	19945.4i	0.215516	−	0.663289i	0.999117	−	0.0420246i	$-0.0133808\pi$
$968$	−443.620			−0.0147298
$969$		0			0
$970$	35742.0	+	43358.1i	1.18310	+	1.43520i
$971$	−1186.94	−	3653.02i	−0.0392283	−	0.120732i	0.929525	−	0.368760i	$-0.120218\pi$
$971$	−1186.94	−	3653.02i	−0.0392283	−	0.120732i	−0.968753	+	0.248028i	$0.920218\pi$
$972$		0			0
$973$	4495.32	+	3266.04i	0.148112	+	0.107610i
$974$	−25270.4			−0.831330
$975$		0			0
$976$	−54139.1			−1.77556
$977$	14326.9	+	10409.1i	0.469150	+	0.340857i	0.797110	−	0.603834i	$-0.206361\pi$
$977$	14326.9	+	10409.1i	0.469150	+	0.340857i	−0.327960	+	0.944692i	$0.606361\pi$
$978$		0			0
$979$	−8148.35	−	25078.0i	−0.266008	−	0.818690i
$980$	−29951.6	−	7745.88i	−0.976293	−	0.252483i
$981$		0			0
$982$	50154.6			1.62983
$983$	17635.0	−	54274.9i	0.572196	−	1.76104i	−0.0733397	−	0.997307i	$-0.523366\pi$
$983$	17635.0	−	54274.9i	0.572196	−	1.76104i	0.645535	−	0.763730i	$-0.276634\pi$
$984$		0			0
$985$	10352.6	+	2677.33i	0.334885	+	0.0866058i
$986$	9067.82	+	6588.16i	0.292879	+	0.212789i
$987$		0			0
$988$	6447.78	−	4684.58i	0.207623	−	0.150847i
$989$	−3261.58	−	2369.68i	−0.104866	−	0.0761894i
$990$		0			0
$991$	37113.9	−	26964.8i	1.18967	−	0.864344i	0.196438	−	0.980516i	$-0.437062\pi$
$991$	37113.9	−	26964.8i	1.18967	−	0.864344i	0.993229	+	0.116172i	$0.0370624\pi$
$992$	−19240.9	+	59217.4i	−0.615825	+	1.89532i
$993$		0			0
$994$	−2063.00	+	6349.27i	−0.0658295	+	0.202602i
$995$	−3806.60	+	5975.22i	−0.121284	+	0.190379i
$996$		0			0
$997$	−11563.9	−	35590.2i	−0.367336	−	1.13054i	−0.948505	−	0.316761i	$-0.897405\pi$
$997$	−11563.9	−	35590.2i	−0.367336	−	1.13054i	0.581170	−	0.813782i	$-0.302595\pi$
$998$	22995.3	+	16707.0i	0.729361	+	0.529912i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.a.91.2		28
3.2	odd	2		75.4.g.b.16.6	✓	28
25.11	even	5	inner	225.4.h.a.136.2		28
75.11	odd	10		75.4.g.b.61.6	yes	28
75.44	odd	10		1875.4.a.f.1.12		14
75.56	odd	10		1875.4.a.g.1.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.4.g.b.16.6	✓	28	3.2	odd	2
75.4.g.b.61.6	yes	28	75.11	odd	10
225.4.h.a.91.2		28	1.1	even	1	trivial
225.4.h.a.136.2		28	25.11	even	5	inner
1875.4.a.f.1.12		14	75.44	odd	10
1875.4.a.g.1.3		14	75.56	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)

\(f(q)\)	\(=\)	\(q+(-3.25026 - 2.36146i) q^{2} +(2.51561 + 7.74226i) q^{4} +(6.00716 - 9.42943i) q^{5} +1.75849 q^{7} +(0.174670 - 0.537580i) q^{8} +O(q^{10})\)	\(q+(-3.25026 - 2.36146i) q^{2} +(2.51561 + 7.74226i) q^{4} +(6.00716 - 9.42943i) q^{5} +1.75849 q^{7} +(0.174670 - 0.537580i) q^{8} +(-41.7920 + 16.4625i) q^{10} +(-18.9070 - 13.7367i) q^{11} +(43.1036 - 31.3166i) q^{13} +(-5.71556 - 4.15260i) q^{14} +(50.8505 - 36.9450i) q^{16} +(6.45676 - 19.8719i) q^{17} +(5.67829 - 17.4760i) q^{19} +(88.1167 + 22.7882i) q^{20} +(29.0140 + 89.2960i) q^{22} +(34.8681 + 25.3331i) q^{23} +(-52.8281 - 113.288i) q^{25} -214.051 q^{26} +(4.42368 + 13.6147i) q^{28} +(-41.2605 - 126.987i) q^{29} +(74.8546 - 230.379i) q^{31} -257.044 q^{32} +(-67.9127 + 49.3414i) q^{34} +(10.5635 - 16.5816i) q^{35} +(-288.826 + 209.844i) q^{37} +(-59.7247 + 43.3925i) q^{38} +(-4.01980 - 4.87637i) q^{40} +(-343.417 + 249.507i) q^{41} -93.5407 q^{43} +(58.7907 - 180.939i) q^{44} +(-53.5074 - 164.679i) q^{46} +(72.1996 + 222.207i) q^{47} -339.908 q^{49} +(-95.8194 + 492.968i) q^{50} +(350.893 + 254.939i) q^{52} +(8.66417 + 26.6656i) q^{53} +(-243.107 + 95.7633i) q^{55} +(0.307156 - 0.945330i) q^{56} +(-165.766 + 510.176i) q^{58} +(365.174 - 265.315i) q^{59} +(-696.837 - 506.281i) q^{61} +(-787.326 + 572.026i) q^{62} +(428.656 + 311.437i) q^{64} +(-36.3674 - 594.565i) q^{65} +(-191.985 + 590.868i) q^{67} +170.096 q^{68} +(-73.4909 + 28.9491i) q^{70} +(-292.011 - 898.717i) q^{71} +(556.132 + 404.054i) q^{73} +1434.30 q^{74} +149.588 q^{76} +(-33.2478 - 24.1559i) q^{77} +(-173.055 - 532.610i) q^{79} +(-42.9036 - 701.425i) q^{80} +1705.40 q^{82} +(290.880 - 895.238i) q^{83} +(-148.593 - 180.257i) q^{85} +(304.032 + 220.892i) q^{86} +(-10.6871 + 7.76462i) q^{88} +(912.809 + 663.195i) q^{89} +(75.7972 - 55.0699i) q^{91} +(-108.421 + 333.686i) q^{92} +(290.065 - 892.729i) q^{94} +(-130.678 - 158.524i) q^{95} +(-386.573 - 1189.75i) q^{97} +(1104.79 + 802.677i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10}) \) 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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