LMFDB - Embedded newform 225.4.h.a.46.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("225.46");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			46.1
Character	$\chi$	$=$	225.46
Dual form			225.4.h.a.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.48860 + 4.58143i) q^{2} +(-12.3014 - 8.93752i) q^{4} +(-5.89885 + 9.49755i) q^{5} +1.13492 q^{7} +(28.0809 - 20.4020i) q^{8} +O(q^{10})$	\(q+(-1.48860 + 4.58143i) q^{2} +(-12.3014 - 8.93752i) q^{4} +(-5.89885 + 9.49755i) q^{5} +1.13492 q^{7} +(28.0809 - 20.4020i) q^{8} +(-34.7314 - 41.1632i) q^{10} +(17.7762 - 54.7096i) q^{11} +(-12.9726 - 39.9257i) q^{13} +(-1.68943 + 5.19954i) q^{14} +(14.0793 + 43.3315i) q^{16} +(-87.1630 + 63.3276i) q^{17} +(43.1077 - 31.3195i) q^{19} +(157.449 - 64.1125i) q^{20} +(224.187 + 162.881i) q^{22} +(5.32566 - 16.3907i) q^{23} +(-55.4071 - 112.049i) q^{25} +202.228 q^{26} +(-13.9611 - 10.1433i) q^{28} +(113.492 + 82.4568i) q^{29} +(196.544 - 142.798i) q^{31} +58.2010 q^{32} +(-160.380 - 493.600i) q^{34} +(-6.69471 + 10.7789i) q^{35} +(107.930 + 332.173i) q^{37} +(79.3184 + 244.117i) q^{38} +(28.1238 + 387.049i) q^{40} +(2.64330 + 8.13524i) q^{41} +111.804 q^{43} +(-707.642 + 514.132i) q^{44} +(67.1650 + 48.7982i) q^{46} +(-261.212 - 189.781i) q^{47} -341.712 q^{49} +(595.825 - 87.0474i) q^{50} +(-197.254 + 607.087i) q^{52} +(-332.211 - 241.366i) q^{53} +(414.748 + 491.555i) q^{55} +(31.8695 - 23.1546i) q^{56} +(-546.714 + 397.211i) q^{58} +(-205.936 - 633.807i) q^{59} +(91.5497 - 281.761i) q^{61} +(361.643 + 1113.02i) q^{62} +(-199.272 + 613.296i) q^{64} +(455.720 + 112.307i) q^{65} +(679.955 - 494.016i) q^{67} +1638.22 q^{68} +(-39.4172 - 46.7168i) q^{70} +(-45.5772 - 33.1138i) q^{71} +(66.9965 - 206.194i) q^{73} -1682.49 q^{74} -810.206 q^{76} +(20.1746 - 62.0909i) q^{77} +(-339.726 - 246.826i) q^{79} +(-494.595 - 121.888i) q^{80} -41.2059 q^{82} +(1179.19 - 856.729i) q^{83} +(-87.2959 - 1201.40i) q^{85} +(-166.431 + 512.222i) q^{86} +(-617.012 - 1898.97i) q^{88} +(378.815 - 1165.87i) q^{89} +(-14.7229 - 45.3123i) q^{91} +(-212.005 + 154.031i) q^{92} +(1258.31 - 914.215i) q^{94} +(43.1734 + 594.167i) q^{95} +(-419.892 - 305.069i) q^{97} +(508.671 - 1565.53i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.48860	+	4.58143i	−0.526298	+	1.61978i	0.235435	+	0.971890i	$0.424348\pi$
$2$	−1.48860	+	4.58143i	−0.526298	+	1.61978i	−0.761734	+	0.647890i	$0.775652\pi$
$3$		0			0
$3$		0			0
$4$	−12.3014	−	8.93752i	−1.53768	−	1.11719i
$5$	−5.89885	+	9.49755i	−0.527609	+	0.849487i
$5$	−5.89885	+	9.49755i	−0.527609	+	0.849487i
$6$		0			0
$7$	1.13492			0.0612798			0.0306399	−	0.999530i	$-0.490245\pi$
$7$	1.13492			0.0612798			0.0306399	+	0.999530i	$0.490245\pi$
$8$	28.0809	−	20.4020i	1.24101	−	0.901650i
$9$		0			0
$10$	−34.7314	−	41.1632i	−1.09830	−	1.30169i
$11$	17.7762	−	54.7096i	0.487249	−	1.49960i	−0.341449	−	0.939900i	$-0.610918\pi$
$11$	17.7762	−	54.7096i	0.487249	−	1.49960i	0.828697	−	0.559697i	$-0.189082\pi$
$12$		0			0
$13$	−12.9726	−	39.9257i	−0.276766	−	0.851799i	−0.988747	−	0.149600i	$-0.952201\pi$
$13$	−12.9726	−	39.9257i	−0.276766	−	0.851799i	0.711980	−	0.702200i	$-0.247799\pi$
$14$	−1.68943	+	5.19954i	−0.0322514	+	0.0992597i
$15$		0			0
$16$	14.0793	+	43.3315i	0.219988	+	0.677055i
$17$	−87.1630	+	63.3276i	−1.24354	+	0.903482i	−0.997829	−	0.0658616i	$-0.979020\pi$
$17$	−87.1630	+	63.3276i	−1.24354	+	0.903482i	−0.245708	+	0.969344i	$0.579020\pi$
$18$		0			0
$19$	43.1077	−	31.3195i	0.520504	−	0.378168i	−0.296290	−	0.955098i	$-0.595749\pi$
$19$	43.1077	−	31.3195i	0.520504	−	0.378168i	0.816794	+	0.576930i	$0.195749\pi$
$20$	157.449	−	64.1125i	1.76033	−	0.716800i
$21$		0			0
$22$	224.187	+	162.881i	2.17258	+	1.57847i
$23$	5.32566	−	16.3907i	0.0482816	−	0.148595i	−0.924009	−	0.382370i	$-0.875108\pi$
$23$	5.32566	−	16.3907i	0.0482816	−	0.148595i	0.972291	+	0.233775i	$0.0751079\pi$
$24$		0			0
$25$	−55.4071	−	112.049i	−0.443257	−	0.896395i
$26$	202.228			1.52539
$27$		0			0
$28$	−13.9611	−	10.1433i	−0.0942287	−	0.0684612i
$29$	113.492	+	82.4568i	0.726722	+	0.527994i	0.888525	−	0.458829i	$-0.151731\pi$
$29$	113.492	+	82.4568i	0.726722	+	0.527994i	−0.161803	+	0.986823i	$0.551731\pi$
$30$		0			0
$31$	196.544	−	142.798i	1.13872	−	0.827331i	0.151782	−	0.988414i	$-0.451499\pi$
$31$	196.544	−	142.798i	1.13872	−	0.827331i	0.986941	+	0.161083i	$0.0514988\pi$
$32$	58.2010			0.321518
$33$		0			0
$34$	−160.380	−	493.600i	−0.808971	−	2.48976i
$35$	−6.69471	+	10.7789i	−0.0323318	+	0.0520564i
$36$		0			0
$37$	107.930	+	332.173i	0.479554	+	1.47592i	0.839716	+	0.543026i	$0.182722\pi$
$37$	107.930	+	332.173i	0.479554	+	1.47592i	−0.360161	+	0.932890i	$0.617278\pi$
$38$	79.3184	+	244.117i	0.338609	+	1.04213i
$39$		0			0
$40$	28.1238	+	387.049i	0.111169	+	1.52994i
$41$	2.64330	+	8.13524i	0.0100686	+	0.0309881i	0.955965	−	0.293482i	$-0.0948141\pi$
$41$	2.64330	+	8.13524i	0.0100686	+	0.0309881i	−0.945896	+	0.324470i	$0.894814\pi$
$42$		0			0
$43$	111.804			0.396510			0.198255	−	0.980150i	$-0.436473\pi$
$43$	111.804			0.396510			0.198255	+	0.980150i	$0.436473\pi$
$44$	−707.642	+	514.132i	−2.42457	+	1.76155i
$45$		0			0
$46$	67.1650	+	48.7982i	0.215281	+	0.156411i
$47$	−261.212	−	189.781i	−0.810673	−	0.588988i	0.103353	−	0.994645i	$-0.467043\pi$
$47$	−261.212	−	189.781i	−0.810673	−	0.588988i	−0.914026	+	0.405656i	$0.867043\pi$
$48$		0			0
$49$	−341.712			−0.996245
$50$	595.825	−	87.0474i	1.68525	−	0.246207i
$51$		0			0
$52$	−197.254	+	607.087i	−0.526044	+	1.61900i
$53$	−332.211	−	241.366i	−0.860995	−	0.625549i	0.0671606	−	0.997742i	$-0.478606\pi$
$53$	−332.211	−	241.366i	−0.860995	−	0.625549i	−0.928155	+	0.372193i	$0.878606\pi$
$54$		0			0
$55$	414.748	+	491.555i	1.01681	+	1.20511i
$56$	31.8695	−	23.1546i	0.0760491	−	0.0552529i
$57$		0			0
$58$	−546.714	+	397.211i	−1.23771	+	0.899247i
$59$	−205.936	−	633.807i	−0.454417	−	1.39855i	−0.871818	−	0.489830i	$-0.837059\pi$
$59$	−205.936	−	633.807i	−0.454417	−	1.39855i	0.417401	−	0.908723i	$-0.362941\pi$
$60$		0			0
$61$	91.5497	−	281.761i	0.192160	−	0.591406i	−0.807838	−	0.589404i	$-0.799363\pi$
$61$	91.5497	−	281.761i	0.192160	−	0.591406i	0.999998	−	0.00200240i	$-0.000637386\pi$
$62$	361.643	+	1113.02i	0.740786	+	2.27990i
$63$		0			0
$64$	−199.272	+	613.296i	−0.389203	+	1.19784i
$65$	455.720	+	112.307i	0.869617	+	0.214308i
$66$		0			0
$67$	679.955	−	494.016i	1.23985	−	0.900801i	0.242258	−	0.970212i	$-0.422112\pi$
$67$	679.955	−	494.016i	1.23985	−	0.900801i	0.997588	+	0.0694110i	$0.0221120\pi$
$68$	1638.22			2.92152
$69$		0			0
$70$	−39.4172	−	46.7168i	−0.0673037	−	0.0797676i
$71$	−45.5772	−	33.1138i	−0.0761833	−	0.0553504i	0.549042	−	0.835795i	$-0.314993\pi$
$71$	−45.5772	−	33.1138i	−0.0761833	−	0.0553504i	−0.625225	+	0.780445i	$0.714993\pi$
$72$		0			0
$73$	66.9965	−	206.194i	0.107416	−	0.330592i	−0.882874	−	0.469610i	$-0.844395\pi$
$73$	66.9965	−	206.194i	0.107416	−	0.330592i	0.990290	+	0.139018i	$0.0443946\pi$
$74$	−1682.49			−2.64305
$75$		0			0
$76$	−810.206			−1.22285
$77$	20.1746	−	62.0909i	0.0298585	−	0.0918950i
$78$		0			0
$79$	−339.726	−	246.826i	−0.483825	−	0.351519i	0.318980	−	0.947762i	$-0.396660\pi$
$79$	−339.726	−	246.826i	−0.483825	−	0.351519i	−0.802805	+	0.596242i	$0.796660\pi$
$80$	−494.595	−	121.888i	−0.691217	−	0.170343i
$81$		0			0
$82$	−41.2059			−0.0554930
$83$	1179.19	−	856.729i	1.55943	−	1.13299i	0.622951	−	0.782261i	$-0.285933\pi$
$83$	1179.19	−	856.729i	1.55943	−	1.13299i	0.936477	−	0.350730i	$-0.114067\pi$
$84$		0			0
$85$	−87.2959	−	1201.40i	−0.111395	−	1.53305i
$86$	−166.431	+	512.222i	−0.208683	+	0.642259i
$87$		0			0
$88$	−617.012	−	1898.97i	−0.747429	−	2.30035i
$89$	378.815	−	1165.87i	0.451172	−	1.38857i	−0.424398	−	0.905476i	$-0.639514\pi$
$89$	378.815	−	1165.87i	0.451172	−	1.38857i	0.875571	−	0.483090i	$-0.160486\pi$
$90$		0			0
$91$	−14.7229	−	45.3123i	−0.0169602	−	0.0521981i
$92$	−212.005	+	154.031i	−0.240251	+	0.174552i
$93$		0			0
$94$	1258.31	−	914.215i	1.38069	−	1.00313i
$95$	43.1734	+	594.167i	0.0466263	+	0.641687i
$96$		0			0
$97$	−419.892	−	305.069i	−0.439521	−	0.319331i	0.345924	−	0.938263i	$-0.387566\pi$
$97$	−419.892	−	305.069i	−0.439521	−	0.319331i	−0.785445	+	0.618932i	$0.787566\pi$
$98$	508.671	−	1565.53i	0.524322	−	1.61370i
$99$		0			0
$100$	−319.856	+	1873.57i	−0.319856	+	1.87357i
$101$	−1607.10			−1.58329			−0.791645	−	0.610981i	$-0.790775\pi$
$101$	−1607.10			−1.58329			−0.791645	+	0.610981i	$0.790775\pi$
$102$		0			0
$103$	281.943	+	204.844i	0.269715	+	0.195960i	0.714419	−	0.699718i	$-0.246691\pi$
$103$	281.943	+	204.844i	0.269715	+	0.195960i	−0.444704	+	0.895678i	$0.646691\pi$
$104$	−1178.85	−	856.483i	−1.11150	−	0.807549i
$105$		0			0
$106$	1600.33	−	1162.71i	1.46639	−	1.06540i
$107$	−1553.10			−1.40321			−0.701605	−	0.712566i	$-0.747533\pi$
$107$	−1553.10			−1.40321			−0.701605	+	0.712566i	$0.747533\pi$
$108$		0			0
$109$	113.099	+	348.082i	0.0993842	+	0.305873i	0.988371	−	0.152059i	$-0.0485903\pi$
$109$	113.099	+	348.082i	0.0993842	+	0.305873i	−0.888987	+	0.457932i	$0.848590\pi$
$110$	−2869.42	+	1168.41i	−2.48716	+	1.01276i
$111$		0			0
$112$	15.9788	+	49.1777i	0.0134808	+	0.0414898i
$113$	66.1339	+	203.539i	0.0550562	+	0.169446i	0.974803	−	0.223066i	$-0.0716064\pi$
$113$	66.1339	+	203.539i	0.0550562	+	0.169446i	−0.919747	+	0.392511i	$0.871606\pi$
$114$		0			0
$115$	124.256	+	147.267i	0.100756	+	0.119415i
$116$	−659.156	−	2028.67i	−0.527596	−	1.62377i
$117$		0			0
$118$	3210.30			2.50451
$119$	−98.9227	+	71.8716i	−0.0762036	+	0.0553652i
$120$		0			0
$121$	−1600.35	−	1162.72i	−1.20236	−	0.873569i
$122$	1154.59	+	838.857i	0.856815	+	0.622513i
$123$		0			0
$124$	−3694.04			−2.67528
$125$	1391.03	+	134.731i	0.995342	+	0.0964053i
$126$		0			0
$127$	240.890	−	741.384i	0.168311	−	0.518009i	−0.830954	−	0.556342i	$-0.812205\pi$
$127$	240.890	−	741.384i	0.168311	−	0.518009i	0.999265	+	0.0383324i	$0.0122046\pi$
$128$	−2136.45	−	1552.22i	−1.47529	−	1.07186i
$129$		0			0
$130$	−1192.91	+	1920.67i	−0.804810	+	1.29580i
$131$	686.007	−	498.413i	0.457532	−	0.332417i	−0.335030	−	0.942207i	$-0.608747\pi$
$131$	686.007	−	498.413i	0.457532	−	0.332417i	0.792562	+	0.609791i	$0.208747\pi$
$132$		0			0
$133$	48.9236	−	35.5451i	0.0318964	−	0.0231741i
$134$	1251.12	+	3850.56i	0.806570	+	2.48237i
$135$		0			0
$136$	−1155.61	+	3556.60i	−0.728622	+	2.24247i
$137$	392.708	+	1208.63i	0.244900	+	0.753724i	0.995653	+	0.0931411i	$0.0296908\pi$
$137$	392.708	+	1208.63i	0.244900	+	0.753724i	−0.750753	+	0.660583i	$0.770309\pi$
$138$		0			0
$139$	−211.761	+	651.733i	−0.129218	+	0.397692i	−0.994646	−	0.103341i	$-0.967047\pi$
$139$	−211.761	+	651.733i	−0.129218	+	0.397692i	0.865428	+	0.501033i	$0.167047\pi$
$140$	178.692	−	72.7624i	0.107873	−	0.0439253i
$141$		0			0
$142$	219.554	−	159.516i	0.129751	−	0.0942694i
$143$	−2414.92			−1.41221
$144$		0			0
$145$	−1452.61	+	591.496i	−0.831950	+	0.338766i
$146$	844.933	+	613.880i	0.478953	+	0.347980i
$147$		0			0
$148$	1641.11	−	5050.83i	0.911478	−	2.80524i
$149$	2370.55			1.30338			0.651688	−	0.758488i	$-0.274061\pi$
$149$	2370.55			1.30338			0.651688	+	0.758488i	$0.274061\pi$
$150$		0			0
$151$	−1177.98			−0.634850			−0.317425	−	0.948283i	$-0.602818\pi$
$151$	−1177.98			−0.634850			−0.317425	+	0.948283i	$0.602818\pi$
$152$	571.522	−	1758.96i	0.304978	−	0.938624i
$153$		0			0
$154$	254.433	+	184.857i	0.133135	+	0.0967284i
$155$	196.844	+	2709.03i	0.102006	+	1.40384i
$156$		0			0
$157$	1663.45			0.845593			0.422797	−	0.906225i	$-0.361048\pi$
$157$	1663.45			0.845593			0.422797	+	0.906225i	$0.361048\pi$
$158$	1636.53	−	1189.01i	0.824021	−	0.598686i
$159$		0			0
$160$	−343.319	+	552.767i	−0.169636	+	0.273126i
$161$	6.04418	−	18.6021i	0.00295868	−	0.00910589i
$162$		0			0
$163$	−383.350	−	1179.83i	−0.184211	−	0.566942i	0.815723	−	0.578442i	$-0.196339\pi$
$163$	−383.350	−	1179.83i	−0.184211	−	0.566942i	−0.999934	+	0.0115005i	$0.996339\pi$
$164$	40.1925	−	123.700i	0.0191372	−	0.0588984i
$165$		0			0
$166$	2169.71	+	6677.68i	1.01447	+	3.12222i
$167$	2942.59	−	2137.92i	1.36350	−	0.990642i	0.365288	−	0.930894i	$-0.380970\pi$
$167$	2942.59	−	2137.92i	1.36350	−	0.990642i	0.998214	−	0.0597477i	$-0.0190296\pi$
$168$		0			0
$169$	351.640	−	255.481i	0.160054	−	0.116286i
$170$	5634.06	+	1388.45i	2.54184	+	0.626409i
$171$		0			0
$172$	−1375.35	−	999.250i	−0.609706	−	0.442977i
$173$	−707.408	+	2177.18i	−0.310886	+	0.956808i	0.666529	+	0.745479i	$0.267779\pi$
$173$	−707.408	+	2177.18i	−0.310886	+	0.956808i	−0.977415	+	0.211329i	$0.932221\pi$
$174$		0			0
$175$	−62.8825	−	127.167i	−0.0271627	−	0.0549309i
$176$	2620.93			1.12250
$177$		0			0
$178$	4777.47	+	3471.03i	2.01172	+	1.46160i
$179$	−1828.26	−	1328.31i	−0.763409	−	0.554649i	0.136545	−	0.990634i	$-0.456400\pi$
$179$	−1828.26	−	1328.31i	−0.763409	−	0.554649i	−0.899954	+	0.435985i	$0.856400\pi$
$180$		0			0
$181$	41.7669	−	30.3454i	0.0171520	−	0.0124616i	−0.579176	−	0.815202i	$-0.696626\pi$
$181$	41.7669	−	30.3454i	0.0171520	−	0.0124616i	0.596328	+	0.802741i	$0.296626\pi$
$182$	229.512			0.0934755
$183$		0			0
$184$	−184.853	−	568.920i	−0.0740628	−	0.227942i
$185$	−3791.49	−	934.372i	−1.50679	−	0.371332i
$186$		0			0
$187$	1915.20	+	5894.38i	0.748948	+	2.30503i
$188$	1517.10	+	4669.17i	0.588544	+	1.81135i
$189$		0			0
$190$	−2786.40	−	686.679i	−1.06393	−	0.262194i
$191$	−542.383	−	1669.28i	−0.205473	−	0.632382i	−0.999694	−	0.0247522i	$-0.992120\pi$
$191$	−542.383	−	1669.28i	−0.205473	−	0.632382i	0.794220	−	0.607630i	$-0.207880\pi$
$192$		0			0
$193$	−4463.71			−1.66479			−0.832397	−	0.554180i	$-0.813032\pi$
$193$	−4463.71			−1.66479			−0.832397	+	0.554180i	$0.813032\pi$
$194$	2022.70	−	1469.58i	0.748565	−	0.543864i
$195$		0			0
$196$	4203.55	+	3054.06i	1.53191	+	1.11299i
$197$	−2859.82	−	2077.78i	−1.03428	−	0.751451i	−0.0651218	−	0.997877i	$-0.520744\pi$
$197$	−2859.82	−	2077.78i	−1.03428	−	0.751451i	−0.969161	+	0.246427i	$0.920744\pi$
$198$		0			0
$199$	−3943.80			−1.40487			−0.702434	−	0.711749i	$-0.747903\pi$
$199$	−3943.80			−1.40487			−0.702434	+	0.711749i	$0.747903\pi$
$200$	−3841.91	−	2016.04i	−1.35832	−	0.712776i
$201$		0			0
$202$	2392.32	−	7362.81i	0.833283	−	2.56458i
$203$	128.804	+	93.5816i	0.0445334	+	0.0323554i
$204$		0			0
$205$	−92.8574	−	22.8837i	−0.0316363	−	0.00779642i
$206$	−1358.18	+	986.774i	−0.459363	+	0.333746i
$207$		0			0
$208$	1547.39	−	1124.25i	0.515829	−	0.374772i
$209$	−947.189	−	2915.15i	−0.313485	−	0.964808i
$210$		0			0
$211$	−969.320	+	2983.26i	−0.316260	+	0.973347i	0.658973	+	0.752166i	$0.270991\pi$
$211$	−969.320	+	2983.26i	−0.316260	+	0.973347i	−0.975233	+	0.221180i	$0.929009\pi$
$212$	1929.47	+	5938.29i	0.625077	+	1.92379i
$213$		0			0
$214$	2311.93	−	7115.40i	0.738507	−	2.27289i
$215$	−659.515	+	1061.86i	−0.209202	+	0.336830i
$216$		0			0
$217$	223.062	−	162.064i	0.0697807	−	0.0506986i
$218$	−1763.07			−0.547753
$219$		0			0
$220$	−708.721	−	9753.65i	−0.217191	−	2.98905i
$221$	3659.13	+	2658.51i	1.11375	+	0.809190i
$222$		0			0
$223$	−722.791	+	2224.52i	−0.217048	+	0.668004i	0.781954	+	0.623336i	$0.214223\pi$
$223$	−722.791	+	2224.52i	−0.217048	+	0.668004i	−0.999002	+	0.0446682i	$0.985777\pi$
$224$	66.0533			0.0197026
$225$		0			0
$226$	−1030.95			−0.303441
$227$	−312.546	+	961.916i	−0.0913849	+	0.281254i	−0.986295	−	0.164993i	$-0.947240\pi$
$227$	−312.546	+	961.916i	−0.0913849	+	0.281254i	0.894910	+	0.446247i	$0.147240\pi$
$228$		0			0
$229$	2470.22	+	1794.72i	0.712825	+	0.517898i	0.884084	−	0.467328i	$-0.154783\pi$
$229$	2470.22	+	1794.72i	0.712825	+	0.517898i	−0.171259	+	0.985226i	$0.554783\pi$
$230$	−859.660	+	350.050i	−0.246454	+	0.100355i
$231$		0			0
$232$	4869.25			1.37794
$233$	−5180.23	+	3763.66i	−1.45652	+	1.05822i	−0.472262	+	0.881458i	$0.656562\pi$
$233$	−5180.23	+	3763.66i	−1.45652	+	1.05822i	−0.984254	+	0.176762i	$0.943438\pi$
$234$		0			0
$235$	3343.31	−	1361.38i	0.928057	−	0.377900i
$236$	−3131.35	+	9637.30i	−0.863701	+	2.65820i
$237$		0			0
$238$	−182.019	−	560.195i	−0.0495736	−	0.152572i
$239$	1184.49	−	3645.47i	0.320578	−	0.986636i	−0.652820	−	0.757513i	$-0.726414\pi$
$239$	1184.49	−	3645.47i	0.320578	−	0.986636i	0.973397	−	0.229123i	$-0.0735859\pi$
$240$		0			0
$241$	−1100.13	−	3385.84i	−0.294047	−	0.904984i	−0.983540	−	0.180691i	$-0.942166\pi$
$241$	−1100.13	−	3385.84i	−0.294047	−	0.904984i	0.689493	−	0.724293i	$-0.257834\pi$
$242$	7709.19	−	5601.05i	2.04779	−	1.48781i
$243$		0			0
$244$	−3644.44	+	2647.84i	−0.956194	+	0.694715i
$245$	2015.71	−	3245.43i	0.525628	−	0.846297i
$246$		0			0
$247$	−1809.67	−	1314.81i	−0.466182	−	0.338701i
$248$	2605.79	−	8019.80i	0.667209	−	2.05346i
$249$		0			0
$250$	−2687.95	+	6172.36i	−0.680002	+	1.56150i
$251$	−177.342			−0.0445964			−0.0222982	−	0.999751i	$-0.507098\pi$
$251$	−177.342			−0.0445964			−0.0222982	+	0.999751i	$0.507098\pi$
$252$		0			0
$253$	−802.058	−	582.729i	−0.199308	−	0.144806i
$254$	3038.01	+	2207.24i	0.750479	+	0.545255i
$255$		0			0
$256$	6118.11	−	4445.07i	1.49368	−	1.08522i
$257$	6061.58			1.47125			0.735624	−	0.677390i	$-0.236889\pi$
$257$	6061.58			1.47125			0.735624	+	0.677390i	$0.236889\pi$
$258$		0			0
$259$	122.491	+	376.989i	0.0293870	+	0.0904438i
$260$	−4602.27	−	5454.55i	−1.09777	−	1.30106i
$261$		0			0
$262$	1262.26	+	3884.83i	0.297643	+	0.916052i
$263$	−115.261	−	354.736i	−0.0270239	−	0.0831709i	0.936635	−	0.350307i	$-0.113923\pi$
$263$	−115.261	−	354.736i	−0.0270239	−	0.0831709i	−0.963659	+	0.267136i	$0.913923\pi$
$264$		0			0
$265$	4252.05	−	1731.41i	0.985665	−	0.401358i
$266$	90.0198	+	277.052i	0.0207499	+	0.0638616i
$267$		0			0
$268$	−12779.7			−2.91285
$269$	2193.25	−	1593.49i	0.497117	−	0.361177i	−0.310798	−	0.950476i	$-0.600596\pi$
$269$	2193.25	−	1593.49i	0.497117	−	0.361177i	0.807915	+	0.589299i	$0.200596\pi$
$270$		0			0
$271$	4446.04	+	3230.24i	0.996597	+	0.724070i	0.961356	−	0.275308i	$-0.0887800\pi$
$271$	4446.04	+	3230.24i	0.996597	+	0.724070i	0.0352415	+	0.999379i	$0.488780\pi$
$272$	−3971.27	−	2885.30i	−0.885271	−	0.643187i
$273$		0			0
$274$	−6121.83			−1.34976
$275$	−7115.11	+	1039.49i	−1.56021	+	0.227939i
$276$		0			0
$277$	−246.785	+	759.525i	−0.0535302	+	0.164749i	−0.974248	−	0.225481i	$-0.927605\pi$
$277$	−246.785	+	759.525i	−0.0535302	+	0.164749i	0.920717	+	0.390230i	$0.127605\pi$
$278$	−2670.64	−	1940.33i	−0.576167	−	0.418610i
$279$		0			0
$280$	31.9182	+	439.268i	0.00681241	+	0.0937546i
$281$	1608.31	−	1168.51i	0.341437	−	0.248069i	−0.403831	−	0.914834i	$-0.632322\pi$
$281$	1608.31	−	1168.51i	0.341437	−	0.248069i	0.745268	+	0.666765i	$0.232322\pi$
$282$		0			0
$283$	−710.307	+	516.068i	−0.149199	+	0.108399i	−0.659881	−	0.751370i	$-0.729393\pi$
$283$	−710.307	+	516.068i	−0.149199	+	0.108399i	0.510681	+	0.859770i	$0.329393\pi$
$284$	264.710	+	814.694i	0.0553087	+	0.170223i
$285$		0			0
$286$	3594.85	−	11063.8i	0.743244	−	2.28747i
$287$	2.99993	+	9.23283i	0.000617004	+	0.00189894i
$288$		0			0
$289$	2068.80	−	6367.10i	0.421086	−	1.29597i
$290$	−547.548	−	7535.53i	−0.110873	−	1.52587i
$291$		0			0
$292$	−2667.02	+	1937.70i	−0.534505	+	0.388341i
$293$	−115.531			−0.0230355			−0.0115178	−	0.999934i	$-0.503666\pi$
$293$	−115.531			−0.0230355			−0.0115178	+	0.999934i	$0.503666\pi$
$294$		0			0
$295$	7234.40	+	1782.84i	1.42781	+	0.351868i
$296$	9807.76	+	7125.75i	1.92589	+	1.39924i
$297$		0			0
$298$	−3528.79	+	10860.5i	−0.685964	+	2.11118i
$299$	−723.497			−0.139936
$300$		0			0
$301$	126.888			0.0242981
$302$	1753.53	−	5396.82i	0.334121	−	1.02832i
$303$		0			0
$304$	1964.05	+	1426.96i	0.370546	+	0.269217i
$305$	2136.00	+	2531.56i	0.401007	+	0.475269i
$306$		0			0
$307$	−4930.95			−0.916691			−0.458345	−	0.888774i	$-0.651558\pi$
$307$	−4930.95			−0.916691			−0.458345	+	0.888774i	$0.651558\pi$
$308$	−803.115	+	583.497i	−0.148577	+	0.107948i
$309$		0			0
$310$	−12704.3	−	3130.83i	−2.32759	−	0.573611i
$311$	−2153.35	+	6627.33i	−0.392622	+	1.20836i	0.538177	+	0.842832i	$0.319113\pi$
$311$	−2153.35	+	6627.33i	−0.392622	+	1.20836i	−0.930798	+	0.365533i	$0.880887\pi$
$312$		0			0
$313$	−1390.92	−	4280.82i	−0.251181	−	0.773054i	−0.994558	−	0.104182i	$-0.966777\pi$
$313$	−1390.92	−	4280.82i	−0.251181	−	0.773054i	0.743378	−	0.668872i	$-0.233223\pi$
$314$	−2476.21	+	7621.00i	−0.445034	+	1.36968i
$315$		0			0
$316$	1973.11	+	6072.62i	0.351254	+	1.08105i
$317$	−1803.33	+	1310.20i	−0.319512	+	0.232139i	−0.735967	−	0.677017i	$-0.763272\pi$
$317$	−1803.33	+	1310.20i	−0.319512	+	0.232139i	0.416455	+	0.909156i	$0.363272\pi$
$318$		0			0
$319$	6528.64	−	4743.33i	1.14587	−	0.832526i
$320$	−4649.34	−	5510.34i	−0.812206	−	0.962616i
$321$		0			0
$322$	76.2267	+	55.3819i	0.0131924	+	0.00958483i
$323$	−1774.00	+	5459.81i	−0.305597	+	0.940532i
$324$		0			0
$325$	−3754.87	+	3665.74i	−0.640870	+	0.625658i
$326$	5975.97			1.01527
$327$		0			0
$328$	240.202	+	174.517i	0.0404357	+	0.0293783i
$329$	−296.454	−	215.386i	−0.0496778	−	0.0360931i
$330$		0			0
$331$	−8241.86	+	5988.06i	−1.36862	+	0.994362i	−0.370778	+	0.928721i	$0.620909\pi$
$331$	−8241.86	+	5988.06i	−1.36862	+	0.994362i	−0.997843	+	0.0656406i	$0.979091\pi$
$332$	−22162.7			−3.66367
$333$		0			0
$334$	5414.39	+	16663.8i	0.887013	+	2.72995i
$335$	680.992	+	9372.03i	0.111064	+	1.52850i
$336$		0			0
$337$	490.028	+	1508.15i	0.0792092	+	0.243781i	0.982818	−	0.184578i	$-0.0590919\pi$
$337$	490.028	+	1508.15i	0.0792092	+	0.243781i	−0.903609	+	0.428359i	$0.859092\pi$
$338$	647.020	+	1991.32i	0.104122	+	0.320454i
$339$		0			0
$340$	−9663.63	+	15559.1i	−1.54142	+	2.48180i
$341$	−4318.60	−	13291.3i	−0.685822	−	2.11074i
$342$		0			0
$343$	−777.091			−0.122329
$344$	3139.56	−	2281.02i	0.492075	−	0.357513i
$345$		0			0
$346$	−8921.55	−	6481.88i	−1.38620	−	1.00713i
$347$	899.992	+	653.883i	0.139234	+	0.101159i	0.655222	−	0.755437i	$-0.272575\pi$
$347$	899.992	+	653.883i	0.139234	+	0.101159i	−0.515988	+	0.856596i	$0.672575\pi$
$348$		0			0
$349$	5181.97			0.794798			0.397399	−	0.917646i	$-0.369913\pi$
$349$	5181.97			0.794798			0.397399	+	0.917646i	$0.369913\pi$
$350$	676.212	−	98.7916i	0.103272	−	0.0150875i
$351$		0			0
$352$	1034.59	−	3184.16i	0.156659	−	0.482148i
$353$	5808.98	+	4220.47i	0.875866	+	0.636354i	0.932155	−	0.362061i	$-0.117927\pi$
$353$	5808.98	+	4220.47i	0.875866	+	0.636354i	−0.0562885	+	0.998415i	$0.517927\pi$
$354$		0			0
$355$	583.353	−	237.539i	0.0872145	−	0.0355134i
$356$	−15080.0	+	10956.3i	−2.24505	+	1.63113i
$357$		0			0
$358$	8807.07	−	6398.71i	1.30019	−	0.944644i
$359$	1836.46	+	5652.03i	0.269985	+	0.830927i	0.990503	+	0.137491i	$0.0439039\pi$
$359$	1836.46	+	5652.03i	0.269985	+	0.830927i	−0.720518	+	0.693436i	$0.756096\pi$
$360$		0			0
$361$	−1242.19	+	3823.07i	−0.181104	+	0.557380i
$362$	76.8514	+	236.524i	0.0111581	+	0.0343410i
$363$		0			0
$364$	−223.867	+	688.993i	−0.0322358	+	0.0992117i
$365$	1563.14	+	1852.61i	0.224160	+	0.265672i
$366$		0			0
$367$	5556.35	−	4036.92i	0.790297	−	0.574184i	−0.117755	−	0.993043i	$-0.537570\pi$
$367$	5556.35	−	4036.92i	0.790297	−	0.574184i	0.908051	+	0.418859i	$0.137570\pi$
$368$	785.214			0.111229
$369$		0			0
$370$	9924.76	−	15979.5i	1.39450	−	2.24524i
$371$	−377.032	−	273.930i	−0.0527616	−	0.0383335i
$372$		0			0
$373$	1285.59	−	3956.65i	0.178460	−	0.549243i	−0.821315	−	0.570475i	$-0.806759\pi$
$373$	1285.59	−	3956.65i	0.178460	−	0.549243i	0.999775	+	0.0212324i	$0.00675900\pi$
$374$	−29855.6			−4.12780
$375$		0			0
$376$	−11207.0			−1.53712
$377$	1819.85	−	5600.93i	0.248613	−	0.765152i
$378$		0			0
$379$	−3141.87	−	2282.70i	−0.425823	−	0.309379i	0.354153	−	0.935187i	$-0.384769\pi$
$379$	−3141.87	−	2282.70i	−0.425823	−	0.309379i	−0.779977	+	0.625809i	$0.784769\pi$
$380$	4779.28	−	7694.97i	0.645190	−	1.03880i
$381$		0			0
$382$	8455.09			1.13246
$383$	−5339.64	+	3879.48i	−0.712384	+	0.517577i	−0.883942	−	0.467597i	$-0.845120\pi$
$383$	−5339.64	+	3879.48i	−0.712384	+	0.517577i	0.171558	+	0.985174i	$0.445120\pi$
$384$		0			0
$385$	470.705	+	557.874i	0.0623100	+	0.0738491i
$386$	6644.67	−	20450.2i	0.876178	−	2.69660i
$387$		0			0
$388$	2438.71	+	7505.58i	0.319090	+	0.982057i
$389$	2930.09	−	9017.90i	0.381907	−	1.17539i	−0.556793	−	0.830651i	$-0.687968\pi$
$389$	2930.09	−	9017.90i	0.381907	−	1.17539i	0.938699	−	0.344737i	$-0.112032\pi$
$390$		0			0
$391$	573.783	+	1765.92i	0.0742134	+	0.228405i
$392$	−9595.59	+	6971.61i	−1.23635	+	0.898264i
$393$		0			0
$394$	13776.3	−	10009.1i	1.76153	−	1.27982i
$395$	4348.23	−	1770.58i	0.553882	−	0.225538i
$396$		0			0
$397$	−601.345	−	436.903i	−0.0760217	−	0.0552330i	0.549125	−	0.835740i	$-0.314961\pi$
$397$	−601.345	−	436.903i	−0.0760217	−	0.0552330i	−0.625147	+	0.780507i	$0.714961\pi$
$398$	5870.73	−	18068.2i	0.739379	−	2.27558i
$399$		0			0
$400$	4075.18	−	3978.45i	0.509397	−	0.497306i
$401$	−8535.31			−1.06292			−0.531462	−	0.847082i	$-0.678357\pi$
$401$	−8535.31			−1.06292			−0.531462	+	0.847082i	$0.678357\pi$
$402$		0			0
$403$	−8251.00	−	5994.70i	−1.01988	−	0.740986i
$404$	19769.6	+	14363.5i	2.43459	+	1.76884i
$405$		0			0
$406$	−620.475	+	450.801i	−0.0758464	+	0.0551057i
$407$	20091.6			2.44694
$408$		0			0
$409$	775.388	+	2386.40i	0.0937420	+	0.288508i	0.986924	−	0.161188i	$-0.0515324\pi$
$409$	775.388	+	2386.40i	0.0937420	+	0.288508i	−0.893182	+	0.449696i	$0.851532\pi$
$410$	243.067	−	391.355i	0.0292786	−	0.0471406i
$411$		0			0
$412$	−1637.51	−	5039.75i	−0.195812	−	0.602647i
$413$	−233.721	−	719.318i	−0.0278466	−	0.0857030i
$414$		0			0
$415$	1180.99	+	16253.1i	0.139692	+	1.92249i
$416$	−755.021	−	2323.72i	−0.0889854	−	0.273869i
$417$		0			0
$418$	14765.5			1.72776
$419$	3826.64	−	2780.22i	0.446167	−	0.324159i	−0.341914	−	0.939731i	$-0.611075\pi$
$419$	3826.64	−	2780.22i	0.446167	−	0.324159i	0.788080	+	0.615572i	$0.211075\pi$
$420$		0			0
$421$	−6603.65	−	4797.83i	−0.764471	−	0.555421i	0.135807	−	0.990735i	$-0.456637\pi$
$421$	−6603.65	−	4797.83i	−0.764471	−	0.555421i	−0.900278	+	0.435315i	$0.856637\pi$
$422$	−12224.7	−	8881.75i	−1.41016	−	1.02454i
$423$		0			0
$424$	−14253.1			−1.63253
$425$	11925.3	+	6257.75i	1.36108	+	0.714225i
$426$		0			0
$427$	103.901	−	319.775i	0.0117755	−	0.0362412i
$428$	19105.3	+	13880.8i	2.15769	+	1.56765i
$429$		0			0
$430$	−3883.10	−	4602.21i	−0.435488	−	0.516135i
$431$	6205.97	−	4508.90i	0.693576	−	0.503912i	−0.184258	−	0.982878i	$-0.558988\pi$
$431$	6205.97	−	4508.90i	0.693576	−	0.503912i	0.877834	+	0.478966i	$0.158988\pi$
$432$		0			0
$433$	11113.5	−	8074.46i	1.23345	−	0.896152i	0.236304	−	0.971679i	$-0.424064\pi$
$433$	11113.5	−	8074.46i	1.23345	−	0.896152i	0.997144	+	0.0755267i	$0.0240638\pi$
$434$	410.435	+	1263.19i	0.0453952	+	0.139712i
$435$		0			0
$436$	1719.71	−	5292.73i	0.188897	−	0.581366i
$437$	−283.772	−	873.361i	−0.0310633	−	0.0956030i
$438$		0			0
$439$	3764.26	−	11585.2i	0.409245	−	1.25953i	−0.508054	−	0.861325i	$-0.669635\pi$
$439$	3764.26	−	11585.2i	0.409245	−	1.25953i	0.917298	−	0.398200i	$-0.130365\pi$
$440$	21675.2	+	5341.63i	2.34847	+	0.578755i
$441$		0			0
$442$	−17626.8	+	12806.6i	−1.89688	+	1.37816i
$443$	3654.36			0.391927			0.195964	−	0.980611i	$-0.437217\pi$
$443$	3654.36			0.391927			0.195964	+	0.980611i	$0.437217\pi$
$444$		0			0
$445$	8838.37	+	10475.1i	0.941526	+	1.11589i
$446$	−9115.54	−	6622.83i	−0.967788	−	0.703139i
$447$		0			0
$448$	−226.157	+	696.040i	−0.0238503	+	0.0734036i
$449$	−2365.17			−0.248595			−0.124297	−	0.992245i	$-0.539668\pi$
$449$	−2365.17			−0.248595			−0.124297	+	0.992245i	$0.539668\pi$
$450$		0			0
$451$	492.064			0.0513756
$452$	1005.59	−	3094.90i	0.104644	−	0.322061i
$453$		0			0
$454$	−3941.70	−	2863.81i	−0.407474	−	0.296047i
$455$	517.204	+	127.460i	0.0532899	+	0.0131327i
$456$		0			0
$457$	−2585.28			−0.264626			−0.132313	−	0.991208i	$-0.542240\pi$
$457$	−2585.28			−0.264626			−0.132313	+	0.991208i	$0.542240\pi$
$458$	−11899.6	+	8645.54i	−1.21404	+	0.882051i
$459$		0			0
$460$	−212.329	−	2922.14i	−0.0215215	−	0.296186i
$461$	−1225.83	+	3772.71i	−0.123845	+	0.381155i	−0.993689	−	0.112172i	$-0.964219\pi$
$461$	−1225.83	+	3772.71i	−0.123845	+	0.381155i	0.869844	+	0.493327i	$0.164219\pi$
$462$		0			0
$463$	1686.02	+	5189.05i	0.169236	+	0.520854i	0.999323	−	0.0367788i	$-0.0117097\pi$
$463$	1686.02	+	5189.05i	0.169236	+	0.520854i	−0.830088	+	0.557633i	$0.811710\pi$
$464$	−1975.09	+	6078.71i	−0.197611	+	0.608183i
$465$		0			0
$466$	−9531.66	−	29335.4i	−0.947523	−	2.91617i
$467$	−11900.1	+	8645.95i	−1.17917	+	0.856717i	−0.992078	−	0.125626i	$-0.959906\pi$
$467$	−11900.1	+	8645.95i	−1.17917	+	0.856717i	−0.187092	+	0.982342i	$0.559906\pi$
$468$		0			0
$469$	771.692	−	560.667i	0.0759775	−	0.0552009i
$470$	1260.23	+	17343.7i	0.123681	+	1.70214i
$471$		0			0
$472$	−18713.8	−	13596.4i	−1.82494	−	1.32590i
$473$	1987.45	−	6116.75i	0.193199	−	0.594606i
$474$		0			0
$475$	−5897.80	−	3094.86i	−0.569705	−	0.298951i
$476$	1859.25			0.179030
$477$		0			0
$478$	14938.3	+	10853.3i	1.42941	+	1.03853i
$479$	8289.24	+	6022.49i	0.790700	+	0.574477i	0.908171	−	0.418599i	$-0.137479\pi$
$479$	8289.24	+	6022.49i	0.790700	+	0.574477i	−0.117471	+	0.993076i	$0.537479\pi$
$480$		0			0
$481$	11862.1	−	8618.32i	1.12446	−	0.816968i
$482$	17149.6			1.62063
$483$		0			0
$484$	9294.74	+	28606.3i	0.872909	+	2.68654i
$485$	5374.29	−	2188.39i	0.503163	−	0.204886i
$486$		0			0
$487$	1362.49	+	4193.32i	0.126777	+	0.390180i	0.994221	−	0.107356i	$-0.0342384\pi$
$487$	1362.49	+	4193.32i	0.126777	+	0.390180i	−0.867444	+	0.497536i	$0.834238\pi$
$488$	−3177.69	−	9779.91i	−0.294769	−	0.907204i
$489$		0			0
$490$	11868.1	+	14066.0i	1.09418	+	1.29681i
$491$	997.495	+	3069.97i	0.0916829	+	0.282171i	0.986375	−	0.164512i	$-0.0526050\pi$
$491$	997.495	+	3069.97i	0.0916829	+	0.282171i	−0.894692	+	0.446683i	$0.852605\pi$
$492$		0			0
$493$	−15114.1			−1.38074
$494$	8717.56	−	6333.68i	0.793971	−	0.576854i
$495$		0			0
$496$	8954.85	+	6506.08i	0.810654	+	0.588975i
$497$	−51.7263	−	37.5814i	−0.00466850	−	0.00339186i
$498$		0			0
$499$	−10683.6			−0.958442			−0.479221	−	0.877694i	$-0.659081\pi$
$499$	−10683.6			−0.958442			−0.479221	+	0.877694i	$0.659081\pi$
$500$	−15907.6	−	14089.8i	−1.42282	−	1.26023i
$501$		0			0
$502$	263.990	−	812.478i	0.0234710	−	0.0722364i
$503$	−5022.26	−	3648.89i	−0.445192	−	0.323451i	0.342503	−	0.939517i	$-0.388725\pi$
$503$	−5022.26	−	3648.89i	−0.445192	−	0.323451i	−0.787695	+	0.616066i	$0.788725\pi$
$504$		0			0
$505$	9480.04	−	15263.5i	0.835359	−	1.34498i
$506$	3863.67	−	2807.12i	0.339449	−	0.246624i
$507$		0			0
$508$	−9589.43	+	6967.13i	−0.837524	+	0.608497i
$509$	−6199.98	−	19081.6i	−0.539901	−	1.66164i	−0.732815	−	0.680428i	$-0.761794\pi$
$509$	−6199.98	−	19081.6i	−0.539901	−	1.66164i	0.192915	−	0.981216i	$-0.438206\pi$
$510$		0			0
$511$	76.0355	−	234.013i	0.00658241	−	0.0202586i
$512$	4728.95	+	14554.2i	0.408188	+	1.25627i
$513$		0			0
$514$	−9023.24	+	27770.7i	−0.774316	+	2.38310i
$515$	−3608.66	+	1469.43i	−0.308770	+	0.125730i
$516$		0			0
$517$	−15026.2	+	10917.2i	−1.27824	+	0.928699i
$518$	−1909.49			−0.161965
$519$		0			0
$520$	15088.3	−	6143.90i	1.27244	−	0.518131i
$521$	−8254.15	−	5996.99i	−0.694090	−	0.504286i	0.183912	−	0.982943i	$-0.441124\pi$
$521$	−8254.15	−	5996.99i	−0.694090	−	0.504286i	−0.878002	+	0.478657i	$0.841124\pi$
$522$		0			0
$523$	−1220.43	+	3756.09i	−0.102037	+	0.314039i	−0.989024	−	0.147757i	$-0.952795\pi$
$523$	−1220.43	+	3756.09i	−0.102037	+	0.314039i	0.886986	+	0.461796i	$0.152795\pi$
$524$	−12893.5			−1.07491
$525$		0			0
$526$	1796.77			0.148941
$527$	−8088.34	+	24893.4i	−0.668565	+	2.05763i
$528$		0			0
$529$	9603.02	+	6977.00i	0.789268	+	0.573436i
$530$	1602.77	+	22057.8i	0.131358	+	1.80779i
$531$		0			0
$532$	−919.516			−0.0749363
$533$	290.515	−	211.071i	0.0236090	−	0.0171529i
$534$		0			0
$535$	9161.49	−	14750.6i	0.740347	−	1.19201i
$536$	9014.86	−	27744.9i	0.726460	−	2.23581i
$537$		0			0
$538$	4035.59	+	12420.3i	0.323395	+	0.995307i
$539$	−6074.35	+	18694.9i	−0.485419	+	1.49397i
$540$		0			0
$541$	7294.75	+	22450.9i	0.579715	+	1.78418i	0.619531	+	0.784972i	$0.287323\pi$
$541$	7294.75	+	22450.9i	0.579715	+	1.78418i	−0.0398165	+	0.999207i	$0.512677\pi$
$542$	−21417.5	+	15560.7i	−1.69734	+	1.23319i
$543$		0			0
$544$	−5072.97	+	3685.73i	−0.399820	+	0.290486i
$545$	−3973.08	−	979.122i	−0.312271	−	0.0769559i
$546$		0			0
$547$	6142.58	+	4462.85i	0.480142	+	0.348844i	0.801381	−	0.598154i	$-0.204099\pi$
$547$	6142.58	+	4462.85i	0.480142	+	0.348844i	−0.321238	+	0.946998i	$0.604099\pi$
$548$	5971.28	−	18377.7i	0.465476	−	1.43259i
$549$		0			0
$550$	5829.19	−	34144.7i	0.451923	−	2.64716i
$551$	7474.88			0.577932
$552$		0			0
$553$	−385.561	−	280.127i	−0.0296487	−	0.0215410i
$554$	−3112.35	−	2261.25i	−0.238684	−	0.173414i
$555$		0			0
$556$	8429.84	−	6124.63i	0.642994	−	0.467163i
$557$	7392.19			0.562329			0.281164	−	0.959660i	$-0.409279\pi$
$557$	7392.19			0.562329			0.281164	+	0.959660i	$0.409279\pi$
$558$		0			0
$559$	−1450.39	−	4463.85i	−0.109741	−	0.337747i
$560$	−561.324	−	138.332i	−0.0423576	−	0.0104386i
$561$		0			0
$562$	2959.30	+	9107.80i	0.222119	+	0.683611i
$563$	−1841.88	−	5668.72i	−0.137879	−	0.424348i	0.858148	−	0.513403i	$-0.171615\pi$
$563$	−1841.88	−	5668.72i	−0.137879	−	0.424348i	−0.996027	+	0.0890546i	$0.971615\pi$
$564$		0			0
$565$	−2323.24	−	572.537i	−0.172990	−	0.0426315i
$566$	−1306.97	−	4022.44i	−0.0970601	−	0.298720i
$567$		0			0
$568$	−1955.44			−0.144451
$569$	1662.47	−	1207.85i	0.122486	−	0.0889910i	−0.524856	−	0.851191i	$-0.675881\pi$
$569$	1662.47	−	1207.85i	0.122486	−	0.0889910i	0.647341	+	0.762200i	$0.275881\pi$
$570$		0			0
$571$	−12161.4	−	8835.80i	−0.891314	−	0.647578i	0.0449061	−	0.998991i	$-0.485701\pi$
$571$	−12161.4	−	8835.80i	−0.891314	−	0.647578i	−0.936220	+	0.351414i	$0.885701\pi$
$572$	29707.0	+	21583.4i	2.17153	+	1.57771i
$573$		0			0
$574$	−46.7652			−0.00340060
$575$	−2131.64	+	311.424i	−0.154601	+	0.0225866i
$576$		0			0
$577$	2951.37	−	9083.39i	0.212942	−	0.655367i	−0.786352	−	0.617779i	$-0.788033\pi$
$577$	2951.37	−	9083.39i	0.212942	−	0.655367i	0.999293	−	0.0375877i	$-0.0119673\pi$
$578$	26090.8	+	18956.1i	1.87757	+	1.36413i
$579$		0			0
$580$	23155.7	+	5706.48i	1.65774	+	0.408532i
$581$	1338.28	−	972.317i	0.0955614	−	0.0694294i
$582$		0			0
$583$	−19110.5	+	13884.6i	−1.35759	+	0.986348i
$584$	−2325.45	−	7156.99i	−0.164773	−	0.507120i
$585$		0			0
$586$	171.980	−	529.299i	0.0121236	−	0.0373125i
$587$	484.653	+	1491.61i	0.0340780	+	0.104881i	0.966649	−	0.256106i	$-0.0824397\pi$
$587$	484.653	+	1491.61i	0.0340780	+	0.104881i	−0.932571	+	0.360987i	$0.882440\pi$
$588$		0			0
$589$	4000.20	−	12311.4i	0.279840	−	0.861258i
$590$	−18937.1	+	30490.0i	−1.32140	+	2.12755i
$591$		0			0
$592$	−12874.0	+	9353.50i	−0.893780	+	0.649369i
$593$	−11899.9			−0.824061			−0.412031	−	0.911170i	$-0.635180\pi$
$593$	−11899.9			−0.824061			−0.412031	+	0.911170i	$0.635180\pi$
$594$		0			0
$595$	−99.0737	−	1363.48i	−0.00682626	−	0.0939452i
$596$	−29161.2	−	21186.8i	−2.00417	−	1.45612i
$597$		0			0
$598$	1077.00	−	3314.65i	0.0736482	−	0.226666i
$599$	8134.32			0.554857			0.277428	−	0.960746i	$-0.410518\pi$
$599$	8134.32			0.554857			0.277428	+	0.960746i	$0.410518\pi$
$600$		0			0
$601$	20859.5			1.41577			0.707884	−	0.706329i	$-0.249650\pi$
$601$	20859.5			1.41577			0.707884	+	0.706329i	$0.249650\pi$
$602$	−188.885	+	581.329i	−0.0127880	+	0.0393575i
$603$		0			0
$604$	14490.8	+	10528.2i	0.976197	+	0.709248i
$605$	20483.2	−	8340.67i	1.37646	−	0.560490i
$606$		0			0
$607$	−8452.89			−0.565226			−0.282613	−	0.959234i	$-0.591201\pi$
$607$	−8452.89			−0.565226			−0.282613	+	0.959234i	$0.591201\pi$
$608$	2508.91	−	1822.83i	0.167352	−	0.121588i
$609$		0			0
$610$	−14777.8	+	6017.47i	−0.980880	+	0.399410i
$611$	−4188.55	+	12891.0i	−0.277333	+	0.853543i
$612$		0			0
$613$	2896.11	+	8913.32i	0.190820	+	0.587285i	1.00000		0.000276748i	$-8.80917e-5\pi$
$613$	2896.11	+	8913.32i	0.190820	+	0.587285i	−0.809180	+	0.587561i	$0.800088\pi$
$614$	7340.19	−	22590.8i	0.482453	−	1.48484i
$615$		0			0
$616$	−700.258	−	2155.17i	−0.0458023	−	0.140965i
$617$	−11678.2	+	8484.69i	−0.761986	+	0.553615i	−0.899519	−	0.436882i	$-0.856083\pi$
$617$	−11678.2	+	8484.69i	−0.761986	+	0.553615i	0.137533	+	0.990497i	$0.456083\pi$
$618$		0			0
$619$	−5412.65	+	3932.52i	−0.351458	+	0.255349i	−0.749481	−	0.662026i	$-0.769697\pi$
$619$	−5412.65	+	3932.52i	−0.351458	+	0.255349i	0.398022	+	0.917376i	$0.369697\pi$
$620$	21790.6	−	35084.3i	1.41150	−	2.27261i
$621$		0			0
$622$	−27157.2	−	19730.9i	−1.75065	−	1.27192i
$623$	429.924	−	1323.17i	0.0276477	−	0.0850910i
$624$		0			0
$625$	−9485.11	+	12416.7i	−0.607047	+	0.794666i
$626$	21682.8			1.38437
$627$		0			0
$628$	−20462.9	−	14867.2i	−1.30025	−	0.944689i
$629$	−30443.2	−	22118.3i	−1.92981	−	1.40209i
$630$		0			0
$631$	3833.39	−	2785.12i	0.241846	−	0.175712i	−0.460259	−	0.887785i	$-0.652244\pi$
$631$	3833.39	−	2785.12i	0.241846	−	0.175712i	0.702105	+	0.712073i	$0.252244\pi$
$632$	−14575.6			−0.917381
$633$		0			0
$634$	−3318.15	−	10212.2i	−0.207855	−	0.639713i
$635$	5620.36	+	6661.18i	0.351239	+	0.416285i
$636$		0			0
$637$	4432.91	+	13643.1i	0.275727	+	0.848601i
$638$	12012.7	+	36971.4i	0.745437	+	2.29422i
$639$		0			0
$640$	27344.9	−	11134.7i	1.68891	−	0.687717i
$641$	7848.96	+	24156.6i	0.483643	+	1.48850i	0.833936	+	0.551861i	$0.186082\pi$
$641$	7848.96	+	24156.6i	0.483643	+	1.48850i	−0.350293	+	0.936640i	$0.613918\pi$
$642$		0			0
$643$	16102.4			0.987585			0.493792	−	0.869580i	$-0.335610\pi$
$643$	16102.4			0.987585			0.493792	+	0.869580i	$0.335610\pi$
$644$	−240.608	+	174.812i	−0.0147225	+	0.0106965i
$645$		0			0
$646$	−22373.0	−	16254.9i	−1.36262	−	0.990001i
$647$	4460.33	+	3240.62i	0.271026	+	0.196912i	0.714994	−	0.699131i	$-0.246430\pi$
$647$	4460.33	+	3240.62i	0.271026	+	0.196912i	−0.443968	+	0.896043i	$0.646430\pi$
$648$		0			0
$649$	−38336.1			−2.31868
$650$	−11204.9	−	22659.5i	−0.676139	−	1.36735i
$651$		0			0
$652$	−5829.00	+	17939.8i	−0.350125	+	1.07757i
$653$	−18331.3	−	13318.5i	−1.09856	−	0.798152i	−0.117737	−	0.993045i	$-0.537564\pi$
$653$	−18331.3	−	13318.5i	−1.09856	−	0.798152i	−0.980825	+	0.194893i	$0.937564\pi$
$654$		0			0
$655$	687.054	+	9455.46i	0.0409854	+	0.564054i
$656$	−315.297	+	229.076i	−0.0187656	+	0.0136340i
$657$		0			0
$658$	1428.08	−	1037.56i	0.0846082	−	0.0614715i
$659$	3685.07	+	11341.5i	0.217830	+	0.670412i	0.998941	+	0.0460194i	$0.0146536\pi$
$659$	3685.07	+	11341.5i	0.217830	+	0.670412i	−0.781110	+	0.624393i	$0.785346\pi$
$660$		0			0
$661$	3635.37	−	11188.5i	0.213918	−	0.658371i	−0.785311	−	0.619102i	$-0.787497\pi$
$661$	3635.37	−	11188.5i	0.213918	−	0.658371i	0.999229	−	0.0392697i	$-0.0125031\pi$
$662$	−15165.1	−	46673.3i	−0.890344	−	2.74020i
$663$		0			0
$664$	15633.7	−	48115.5i	0.913712	−	2.81211i
$665$	48.9983	+	674.330i	0.00285725	+	0.0393224i
$666$		0			0
$667$	1955.94	−	1421.08i	0.113545	−	0.0824951i
$668$	−55305.9			−3.20337
$669$		0			0
$670$	−43951.0	−	10831.3i	−2.53429	−	0.624550i
$671$	−13787.6	−	10017.3i	−0.793242	−	0.576324i
$672$		0			0
$673$	−2637.18	+	8116.41i	−0.151049	+	0.464880i	−0.997739	−	0.0672055i	$-0.978592\pi$
$673$	−2637.18	+	8116.41i	−0.151049	+	0.464880i	0.846690	+	0.532086i	$0.178592\pi$
$674$	−7638.94			−0.436559
$675$		0			0
$676$	−6609.05			−0.376027
$677$	6545.74	−	20145.7i	0.371600	−	1.14367i	−0.574144	−	0.818755i	$-0.694665\pi$
$677$	6545.74	−	20145.7i	0.371600	−	1.14367i	0.945744	−	0.324913i	$-0.105335\pi$
$678$		0			0
$679$	−476.542	−	346.228i	−0.0269337	−	0.0195685i
$680$	−26962.2	−	31955.3i	−1.52052	−	1.80210i
$681$		0			0
$682$	67321.7			3.77988
$683$	−468.681	+	340.517i	−0.0262571	+	0.0190769i	−0.600836	−	0.799372i	$-0.705166\pi$
$683$	−468.681	+	340.517i	−0.0262571	+	0.0190769i	0.574579	+	0.818449i	$0.305166\pi$
$684$		0			0
$685$	−13795.5	−	3399.77i	−0.769490	−	0.189633i
$686$	1156.78	−	3560.19i	0.0643818	−	0.198147i
$687$		0			0
$688$	1574.12	+	4844.63i	0.0872277	+	0.268459i
$689$	−5327.03	+	16394.9i	−0.294548	+	0.906526i
$690$		0			0
$691$	7285.23	+	22421.6i	0.401076	+	1.23438i	0.924128	+	0.382083i	$0.124793\pi$
$691$	7285.23	+	22421.6i	0.401076	+	1.23438i	−0.523052	+	0.852301i	$0.675207\pi$
$692$	28160.7	−	20460.0i	1.54698	−	1.12395i
$693$		0			0
$694$	−4335.44	+	3149.88i	−0.237134	+	0.172288i
$695$	−4940.72	−	5855.68i	−0.269658	−	0.319595i
$696$		0			0
$697$	−745.583	−	541.698i	−0.0405179	−	0.0294380i
$698$	−7713.87	+	23740.8i	−0.418301	+	1.28740i
$699$		0			0
$700$	−363.010	+	2126.35i	−0.0196007	+	0.114812i
$701$	−12531.0			−0.675162			−0.337581	−	0.941297i	$-0.609609\pi$
$701$	−12531.0			−0.675162			−0.337581	+	0.941297i	$0.609609\pi$
$702$		0			0
$703$	15056.1	+	10938.9i	0.807755	+	0.586868i
$704$	30010.9	+	21804.2i	1.60664	+	1.16730i
$705$		0			0
$706$	−27983.0	+	20330.8i	−1.49172	+	1.08380i
$707$	−1823.92			−0.0970236
$708$		0			0
$709$	−290.331	−	893.548i	−0.0153789	−	0.0473313i	0.943073	−	0.332587i	$-0.107921\pi$
$709$	−290.331	−	893.548i	−0.0153789	−	0.0473313i	−0.958451	+	0.285256i	$0.907921\pi$
$710$	219.889	+	3026.19i	0.0116230	+	0.159959i
$711$		0			0
$712$	−13148.7	−	40467.4i	−0.692089	−	2.13003i
$713$	−1293.83	−	3981.99i	−0.0679582	−	0.209154i
$714$		0			0
$715$	14245.3	−	22935.9i	0.745095	−	1.19965i
$716$	10618.4	+	32680.2i	0.554231	+	1.70575i
$717$		0			0
$718$	−28628.1			−1.48801
$719$	24719.7	−	17959.9i	1.28218	−	0.931562i	0.282568	−	0.959247i	$-0.408814\pi$
$719$	24719.7	−	17959.9i	1.28218	−	0.931562i	0.999617	+	0.0276857i	$0.00881375\pi$
$720$		0			0
$721$	319.982	+	232.481i	0.0165281	+	0.0120084i
$722$	−15666.0	−	11382.0i	−0.807519	−	0.586697i
$723$		0			0
$724$	−785.006			−0.0402963
$725$	2950.96	−	17285.4i	0.151167	−	0.885467i
$726$		0			0
$727$	−2352.48	+	7240.20i	−0.120012	+	0.369359i	−0.992959	−	0.118455i	$-0.962206\pi$
$727$	−2352.48	+	7240.20i	−0.120012	+	0.369359i	0.872947	+	0.487815i	$0.162206\pi$
$728$	−1337.89	−	972.037i	−0.0681122	−	0.0494864i
$729$		0			0
$730$	−10814.5	+	4403.61i	−0.548305	+	0.223267i
$731$	−9745.16	+	7080.27i	−0.493075	+	0.358240i
$732$		0			0
$733$	−4011.96	+	2914.86i	−0.202163	+	0.146880i	−0.684261	−	0.729238i	$-0.739875\pi$
$733$	−4011.96	+	2914.86i	−0.202163	+	0.146880i	0.482098	+	0.876117i	$0.339875\pi$
$734$	10223.7	+	31465.4i	0.514120	+	1.58230i
$735$		0			0
$736$	309.959	−	953.954i	0.0155234	−	0.0477761i
$737$	−14940.4	−	45981.8i	−0.746725	−	2.29818i
$738$		0			0
$739$	7589.41	−	23357.8i	0.377782	−	1.16269i	−0.563800	−	0.825911i	$-0.690661\pi$
$739$	7589.41	−	23357.8i	0.377782	−	1.16269i	0.941582	−	0.336783i	$-0.109339\pi$
$740$	38289.8	+	45380.7i	1.90211	+	2.25436i
$741$		0			0
$742$	1816.24	−	1319.58i	0.0898602	−	0.0652873i
$743$	1368.49			0.0675709			0.0337855	−	0.999429i	$-0.489244\pi$
$743$	1368.49			0.0675709			0.0337855	+	0.999429i	$0.489244\pi$
$744$		0			0
$745$	−13983.5	+	22514.4i	−0.687673	+	1.10720i
$746$	16213.4	+	11779.7i	0.795730	+	0.578131i
$747$		0			0
$748$	29121.4	−	89626.5i	1.42351	−	4.38111i
$749$	−1762.64			−0.0859884
$750$		0			0
$751$	3672.88			0.178462			0.0892312	−	0.996011i	$-0.471559\pi$
$751$	3672.88			0.178462			0.0892312	+	0.996011i	$0.471559\pi$
$752$	4545.85	−	13990.7i	0.220439	−	0.678441i
$753$		0			0
$754$	22951.2	+	16675.0i	1.10853	+	0.805397i
$755$	6948.71	−	11187.9i	0.334953	−	0.539297i
$756$		0			0
$757$	−31304.6			−1.50302			−0.751509	−	0.659722i	$-0.770674\pi$
$757$	−31304.6			−1.50302			−0.751509	+	0.659722i	$0.770674\pi$
$758$	15135.0	−	10996.2i	0.725236	−	0.526915i
$759$		0			0
$760$	13334.5	+	15803.9i	0.636440	+	0.754301i
$761$	1945.16	−	5986.58i	0.0926570	−	0.285169i	−0.893979	−	0.448109i	$-0.852098\pi$
$761$	1945.16	−	5986.58i	0.0926570	−	0.285169i	0.986636	+	0.162940i	$0.0520977\pi$
$762$		0			0
$763$	128.358	+	395.044i	0.00609024	+	0.0187438i
$764$	−8247.16	+	25382.1i	−0.390539	+	1.20195i
$765$		0			0
$766$	−9824.98	−	30238.2i	−0.463435	−	1.42631i
$767$	−22633.6	+	16444.3i	−1.06552	+	0.774145i
$768$		0			0
$769$	19166.8	−	13925.5i	0.898794	−	0.653012i	−0.0393617	−	0.999225i	$-0.512532\pi$
$769$	19166.8	−	13925.5i	0.898794	−	0.653012i	0.938156	+	0.346213i	$0.112532\pi$
$770$	−3256.55	+	1326.05i	−0.152413	+	0.0620618i
$771$		0			0
$772$	54910.1	+	39894.5i	2.55992	+	1.85989i
$773$	4888.03	−	15043.8i	0.227439	−	0.699985i	−0.770596	−	0.637324i	$-0.780041\pi$
$773$	4888.03	−	15043.8i	0.227439	−	0.699985i	0.998035	−	0.0626608i	$-0.0199586\pi$
$774$		0			0
$775$	−26890.4	−	14110.7i	−1.24636	−	0.654025i
$776$	−18015.0			−0.833376
$777$		0			0
$778$	36953.2	+	26848.0i	1.70287	+	1.23721i
$779$	368.739	+	267.904i	0.0169595	+	0.0123218i
$780$		0			0
$781$	−2621.83	+	1904.87i	−0.120124	+	0.0872749i
$782$	−8944.58			−0.409025
$783$		0			0
$784$	−4811.05	−	14806.9i	−0.219162	−	0.674512i
$785$	−9812.47	+	15798.8i	−0.446143	+	0.718321i
$786$		0			0
$787$	−6438.28	−	19815.0i	−0.291614	−	0.897495i	−0.984338	−	0.176292i	$-0.943590\pi$
$787$	−6438.28	−	19815.0i	−0.291614	−	0.897495i	0.692724	−	0.721203i	$-0.256410\pi$
$788$	16609.7	+	51119.4i	0.750884	+	2.31098i
$789$		0			0
$790$	1639.03	+	22556.8i	0.0738151	+	1.01587i
$791$	75.0565	+	231.000i	0.00337383	+	0.0103836i
$792$		0			0
$793$	−12437.1			−0.556943
$794$	2896.80	−	2104.65i	0.129475	−	0.0940694i
$795$		0			0
$796$	48514.4	+	35247.8i	2.16024	+	1.56950i
$797$	−4320.40	−	3138.96i	−0.192016	−	0.139508i	0.487624	−	0.873054i	$-0.337864\pi$
$797$	−4320.40	−	3138.96i	−0.192016	−	0.139508i	−0.679639	+	0.733546i	$0.737864\pi$
$798$		0			0
$799$	34786.4			1.54024
$800$	−3224.75	−	6521.38i	−0.142515	−	0.288207i
$801$		0			0
$802$	12705.6	−	39103.9i	0.559416	−	1.72170i
$803$	−10089.9	−	7330.71i	−0.443416	−	0.322161i
$804$		0			0
$805$	141.020	+	167.136i	0.00617431	+	0.00731771i
$806$	39746.7	−	28877.7i	1.73700	−	1.26200i
$807$		0			0
$808$	−45128.8	+	32788.0i	−1.96488	+	1.42757i
$809$	7059.14	+	21725.8i	0.306782	+	0.944177i	0.979006	+	0.203830i	$0.0653388\pi$
$809$	7059.14	+	21725.8i	0.306782	+	0.944177i	−0.672225	+	0.740347i	$0.734661\pi$
$810$		0			0
$811$	−8571.67	+	26380.9i	−0.371137	+	1.14224i	0.574911	+	0.818216i	$0.305037\pi$
$811$	−8571.67	+	26380.9i	−0.371137	+	1.14224i	−0.946048	+	0.324026i	$0.894963\pi$
$812$	−748.088	−	2302.38i	−0.0323310	−	0.0995045i
$813$		0			0
$814$	−29908.3	+	92048.4i	−1.28782	+	3.96351i
$815$	13466.8	+	3318.76i	0.578801	+	0.142639i
$816$		0			0
$817$	4819.61	−	3501.65i	0.206385	−	0.149948i
$818$	−12087.4			−0.516656
$819$		0			0
$820$	937.756	+	1111.42i	0.0399364	+	0.0473322i
$821$	27799.6	+	20197.6i	1.18174	+	0.858588i	0.992367	−	0.123317i	$-0.0393531\pi$
$821$	27799.6	+	20197.6i	1.18174	+	0.858588i	0.189377	+	0.981904i	$0.439353\pi$
$822$		0			0
$823$	564.580	−	1737.60i	0.0239125	−	0.0735952i	−0.938388	−	0.345583i	$-0.887681\pi$
$823$	564.580	−	1737.60i	0.0239125	−	0.0735952i	0.962301	+	0.271988i	$0.0876811\pi$
$824$	12096.5			0.511408
$825$		0			0
$826$	3643.42			0.153476
$827$	−11181.6	+	34413.3i	−0.470158	+	1.44700i	0.382220	+	0.924072i	$0.375160\pi$
$827$	−11181.6	+	34413.3i	−0.470158	+	1.44700i	−0.852378	+	0.522927i	$0.824840\pi$
$828$		0			0
$829$	24199.3	+	17581.8i	1.01385	+	0.736602i	0.965012	−	0.262205i	$-0.0844497\pi$
$829$	24199.3	+	17581.8i	1.01385	+	0.736602i	0.0488331	+	0.998807i	$0.484450\pi$
$830$	−76220.5	−	18783.7i	−3.18753	−	0.785533i
$831$		0			0
$832$	27071.3			1.12804
$833$	29784.6	−	21639.8i	1.23887	−	0.900090i
$834$		0			0
$835$	2947.08	+	40558.7i	0.122141	+	1.68095i
$836$	−14402.4	+	44326.0i	−0.595834	+	1.83379i
$837$		0			0
$838$	7041.05	+	21670.1i	0.290249	+	0.893296i
$839$	7126.88	−	21934.3i	0.293263	−	0.902569i	−0.690537	−	0.723297i	$-0.742626\pi$
$839$	7126.88	−	21934.3i	0.293263	−	0.902569i	0.983800	−	0.179272i	$-0.0573743\pi$
$840$		0			0
$841$	−1455.30	−	4478.95i	−0.0596703	−	0.183646i
$842$	31811.1	−	23112.1i	1.30200	−	0.945958i
$843$		0			0
$844$	38587.0	−	28035.1i	1.57372	−	1.14337i
$845$	352.176	+	4846.76i	0.0143375	+	0.197318i
$846$		0			0
$847$	−1816.26	−	1319.59i	−0.0736806	−	0.0535321i
$848$	5781.45	−	17793.5i	0.234122	−	0.720554i
$849$		0			0
$850$	−46421.4	+	45319.5i	−1.87322	+	1.82876i
$851$	6019.34			0.242468
$852$		0			0
$853$	−23210.2	−	16863.2i	−0.931655	−	0.676887i	0.0147424	−	0.999891i	$-0.495307\pi$
$853$	−23210.2	−	16863.2i	−0.931655	−	0.676887i	−0.946398	+	0.323004i	$0.895307\pi$
$854$	1310.36	+	952.033i	0.0525054	+	0.0381474i
$855$		0			0
$856$	−43612.4	+	31686.3i	−1.74140	+	1.26520i
$857$	21086.4			0.840489			0.420244	−	0.907411i	$-0.361944\pi$
$857$	21086.4			0.840489			0.420244	+	0.907411i	$0.361944\pi$
$858$		0			0
$859$	1894.85	+	5831.76i	0.0752638	+	0.231638i	0.981610	−	0.190898i	$-0.0611400\pi$
$859$	1894.85	+	5831.76i	0.0752638	+	0.231638i	−0.906346	+	0.422536i	$0.861140\pi$
$860$	17603.4	−	7168.03i	0.697990	−	0.284218i
$861$		0			0
$862$	11419.0	+	35144.2i	0.451199	+	1.38865i
$863$	−10499.0	−	32312.7i	−0.414127	−	1.27455i	−0.913030	−	0.407893i	$-0.866264\pi$
$863$	−10499.0	−	32312.7i	−0.414127	−	1.27455i	0.498903	−	0.866658i	$-0.333736\pi$
$864$		0			0
$865$	−16505.0	−	19561.5i	−0.648770	−	0.768915i
$866$	20449.0	+	62935.6i	0.802408	+	2.46956i
$867$		0			0
$868$	−4192.43			−0.163940
$869$	−19542.8	+	14198.7i	−0.762881	+	0.554265i
$870$		0			0
$871$	−28544.7	−	20739.0i	−1.11045	−	0.806789i
$872$	10277.5	+	7467.02i	0.399128	+	0.289983i
$873$		0			0
$874$	4423.66			0.171204
$875$	1578.71	+	152.908i	0.0609943	+	0.00590770i
$876$		0			0
$877$	4323.58	−	13306.6i	0.166473	−	0.512352i	−0.832669	−	0.553772i	$-0.813188\pi$
$877$	4323.58	−	13306.6i	0.166473	−	0.512352i	0.999142	+	0.0414198i	$0.0131881\pi$
$878$	47473.4	+	34491.4i	1.82477	+	1.32577i
$879$		0			0
$880$	−15460.5	+	24892.4i	−0.592241	+	0.953548i
$881$	−15312.4	+	11125.1i	−0.585571	+	0.425442i	−0.840728	−	0.541457i	$-0.817873\pi$
$881$	−15312.4	+	11125.1i	−0.585571	+	0.425442i	0.255157	+	0.966900i	$0.417873\pi$
$882$		0			0
$883$	15102.6	−	10972.7i	0.575586	−	0.418188i	−0.261544	−	0.965192i	$-0.584232\pi$
$883$	15102.6	−	10972.7i	0.575586	−	0.418188i	0.837130	+	0.547004i	$0.184232\pi$
$884$	−21252.1	−	65407.1i	−0.808580	−	2.48855i
$885$		0			0
$886$	−5439.87	+	16742.2i	−0.206271	+	0.634836i
$887$	1007.72	+	3101.43i	0.0381463	+	0.117402i	0.968316	−	0.249727i	$-0.0803408\pi$
$887$	1007.72	+	3101.43i	0.0381463	+	0.117402i	−0.930170	+	0.367129i	$0.880341\pi$
$888$		0			0
$889$	273.390	−	841.409i	0.0103141	−	0.0317435i
$890$	−61147.9	+	24899.1i	−2.30301	+	0.937776i
$891$		0			0
$892$	28773.1	−	20904.9i	1.08004	−	0.784693i
$893$	−17204.1			−0.644695
$894$		0			0
$895$	23400.3	−	9528.48i	0.873949	−	0.355868i
$896$	−2424.70	−	1761.64i	−0.0904056	−	0.0656835i
$897$		0			0
$898$	3520.78	−	10835.8i	0.130835	−	0.402669i
$899$	34080.9			1.26436
$900$		0			0
$901$	44241.6			1.63585
$902$	−732.485	+	2254.36i	−0.0270389	+	0.0832171i
$903$		0			0
$904$	6009.71	+	4366.31i	0.221106	+	0.160643i
$905$	41.8306	+	575.687i	0.00153646	+	0.0211453i
$906$		0			0
$907$	−48067.7			−1.75972			−0.879858	−	0.475236i	$-0.842363\pi$
$907$	−48067.7			−1.75972			−0.879858	+	0.475236i	$0.842363\pi$
$908$	12441.9	−	9039.58i	0.454735	−	0.330384i
$909$		0			0
$910$	−1353.86	+	2179.80i	−0.0493185	+	0.0794062i
$911$	−1590.55	+	4895.21i	−0.0578456	+	0.178030i	−0.975804	−	0.218645i	$-0.929836\pi$
$911$	−1590.55	+	4895.21i	−0.0578456	+	0.178030i	0.917959	+	0.396676i	$0.129836\pi$
$912$		0			0
$913$	−25909.8	−	79742.3i	−0.939201	−	2.89056i
$914$	3848.43	−	11844.3i	0.139272	−	0.428636i
$915$		0			0
$916$	−14346.9	−	44155.4i	−0.517507	−	1.59272i
$917$	778.561	−	565.658i	0.0280375	−	0.0203704i
$918$		0			0
$919$	6570.90	−	4774.04i	0.235858	−	0.171361i	−0.463578	−	0.886056i	$-0.653435\pi$
$919$	6570.90	−	4774.04i	0.235858	−	0.171361i	0.699436	+	0.714695i	$0.253435\pi$
$920$	6493.77	+	1600.32i	0.232710	+	0.0573489i
$921$		0			0
$922$	−15459.6	−	11232.1i	−0.552209	−	0.401203i
$923$	−730.833	+	2249.27i	−0.0260625	+	0.0802120i
$924$		0			0
$925$	31239.7	−	30498.2i	1.11044	−	1.08408i
$926$	−26283.1			−0.932738
$927$		0			0
$928$	6605.35	+	4799.07i	0.233654	+	0.169760i
$929$	27225.7	+	19780.6i	0.961514	+	0.698581i	0.953502	−	0.301387i	$-0.0974497\pi$
$929$	27225.7	+	19780.6i	0.961514	+	0.698581i	0.00801191	+	0.999968i	$0.497450\pi$
$930$		0			0
$931$	−14730.4	+	10702.3i	−0.518549	+	0.376748i
$932$	97362.1			3.42189
$933$		0			0
$934$	−21896.3	−	67389.9i	−0.767098	−	2.36088i
$935$	−67279.7	−	16580.4i	−2.35324	−	0.579931i
$936$		0			0
$937$	−7711.66	−	23734.1i	−0.268868	−	0.827490i	−0.990777	−	0.135502i	$-0.956735\pi$
$937$	−7711.66	−	23734.1i	−0.268868	−	0.827490i	0.721909	−	0.691988i	$-0.243265\pi$
$938$	1419.92	+	4370.06i	0.0494264	+	0.152119i
$939$		0			0
$940$	−53294.9	−	13133.9i	−1.84924	−	0.455726i
$941$	2477.84	+	7626.00i	0.0858398	+	0.264188i	0.984758	−	0.173928i	$-0.0556460\pi$
$941$	2477.84	+	7626.00i	0.0858398	+	0.264188i	−0.898919	+	0.438116i	$0.855646\pi$
$942$		0			0
$943$	147.419			0.00509082
$944$	24564.4	−	17847.1i	0.846930	−	0.615331i
$945$		0			0
$946$	25064.9	+	18210.8i	0.861450	+	0.625880i
$947$	−27325.7	−	19853.3i	−0.937663	−	0.681252i	0.0101939	−	0.999948i	$-0.496755\pi$
$947$	−27325.7	−	19853.3i	−0.937663	−	0.681252i	−0.947857	+	0.318696i	$0.896755\pi$
$948$		0			0
$949$	−9101.56			−0.311327
$950$	22958.3	−	22413.4i	0.784070	−	0.765459i
$951$		0			0
$952$	−1311.52	+	4036.44i	−0.0446498	+	0.137418i
$953$	37642.9	+	27349.2i	1.27951	+	0.929619i	0.999538	−	0.0303891i	$-0.00967463\pi$
$953$	37642.9	+	27349.2i	1.27951	+	0.929619i	0.279973	+	0.960008i	$0.409675\pi$
$954$		0			0
$955$	19053.5	+	4695.54i	0.645610	+	0.159104i
$956$	−47152.4	+	34258.2i	−1.59521	+	1.15899i
$957$		0			0
$958$	−39930.9	+	29011.5i	−1.34667	+	0.978413i
$959$	445.691	+	1371.69i	0.0150074	+	0.0461880i
$960$		0			0
$961$	9032.54	−	27799.3i	0.303197	−	0.933144i
$962$	21826.3	+	67174.6i	0.731507	+	2.25135i
$963$		0			0
$964$	−16727.9	+	51483.1i	−0.558889	+	1.72008i
$965$	26330.8	−	42394.4i	0.878360	−	1.41422i
$966$		0			0
$967$	1507.34	−	1095.15i	0.0501269	−	0.0364194i	−0.562440	−	0.826838i	$-0.690137\pi$
$967$	1507.34	−	1095.15i	0.0501269	−	0.0364194i	0.612567	+	0.790419i	$0.290137\pi$
$968$	−68661.1			−2.27980
$969$		0			0
$970$	2025.79	+	27879.6i	0.0670558	+	0.922844i
$971$	38541.6	+	28002.1i	1.27380	+	0.925468i	0.999347	−	0.0361332i	$-0.0115040\pi$
$971$	38541.6	+	28002.1i	1.27380	+	0.925468i	0.274451	+	0.961601i	$0.411504\pi$
$972$		0			0
$973$	−240.331	+	739.662i	−0.00791845	+	0.0243705i
$974$	−21239.6			−0.698728
$975$		0			0
$976$	13498.1			0.442688
$977$	18632.2	−	57344.1i	0.610131	−	1.87779i	0.153454	−	0.988156i	$-0.450960\pi$
$977$	18632.2	−	57344.1i	0.610131	−	1.87779i	0.456676	−	0.889633i	$-0.349040\pi$
$978$		0			0
$979$	−57050.6	−	41449.7i	−1.86246	−	1.35315i
$980$	−53802.2	+	21908.0i	−1.75372	+	0.714108i
$981$		0			0
$982$	−15549.7			−0.505308
$983$	17385.6	−	12631.4i	0.564104	−	0.409846i	−0.268855	−	0.963181i	$-0.586645\pi$
$983$	17385.6	−	12631.4i	0.564104	−	0.409846i	0.832959	+	0.553335i	$0.186645\pi$
$984$		0			0
$985$	36603.5	−	14904.8i	1.18405	−	0.482138i
$986$	22498.8	−	69244.1i	0.726681	−	2.23649i
$987$		0			0
$988$	10510.5	+	32348.0i	0.338445	+	1.04163i
$989$	595.429	−	1832.54i	0.0191441	−	0.0589196i
$990$		0			0
$991$	8390.86	+	25824.4i	0.268965	+	0.827789i	0.990753	+	0.135675i	$0.0433204\pi$
$991$	8390.86	+	25824.4i	0.268965	+	0.827789i	−0.721788	+	0.692114i	$0.756680\pi$
$992$	11439.1	−	8310.98i	0.366120	−	0.266002i
$993$		0			0
$994$	249.176	−	181.037i	0.00795109	−	0.00577681i
$995$	23263.9	−	37456.5i	0.741221	−	1.19342i
$996$		0			0
$997$	19732.5	+	14336.5i	0.626816	+	0.455409i	0.855296	−	0.518140i	$-0.173375\pi$
$997$	19732.5	+	14336.5i	0.626816	+	0.455409i	−0.228479	+	0.973549i	$0.573375\pi$
$998$	15903.5	−	48946.1i	0.504427	−	1.55247i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.a.46.1		28
3.2	odd	2		75.4.g.b.46.7	yes	28
25.6	even	5	inner	225.4.h.a.181.1		28
75.41	odd	10		1875.4.a.g.1.14		14
75.56	odd	10		75.4.g.b.31.7	✓	28
75.59	odd	10		1875.4.a.f.1.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.4.g.b.31.7	✓	28	75.56	odd	10
75.4.g.b.46.7	yes	28	3.2	odd	2
225.4.h.a.46.1		28	1.1	even	1	trivial
225.4.h.a.181.1		28	25.6	even	5	inner
1875.4.a.f.1.1		14	75.59	odd	10
1875.4.a.g.1.14		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)

\(f(q)\)	\(=\)	\(q+(-1.48860 + 4.58143i) q^{2} +(-12.3014 - 8.93752i) q^{4} +(-5.89885 + 9.49755i) q^{5} +1.13492 q^{7} +(28.0809 - 20.4020i) q^{8} +O(q^{10})\)	\(q+(-1.48860 + 4.58143i) q^{2} +(-12.3014 - 8.93752i) q^{4} +(-5.89885 + 9.49755i) q^{5} +1.13492 q^{7} +(28.0809 - 20.4020i) q^{8} +(-34.7314 - 41.1632i) q^{10} +(17.7762 - 54.7096i) q^{11} +(-12.9726 - 39.9257i) q^{13} +(-1.68943 + 5.19954i) q^{14} +(14.0793 + 43.3315i) q^{16} +(-87.1630 + 63.3276i) q^{17} +(43.1077 - 31.3195i) q^{19} +(157.449 - 64.1125i) q^{20} +(224.187 + 162.881i) q^{22} +(5.32566 - 16.3907i) q^{23} +(-55.4071 - 112.049i) q^{25} +202.228 q^{26} +(-13.9611 - 10.1433i) q^{28} +(113.492 + 82.4568i) q^{29} +(196.544 - 142.798i) q^{31} +58.2010 q^{32} +(-160.380 - 493.600i) q^{34} +(-6.69471 + 10.7789i) q^{35} +(107.930 + 332.173i) q^{37} +(79.3184 + 244.117i) q^{38} +(28.1238 + 387.049i) q^{40} +(2.64330 + 8.13524i) q^{41} +111.804 q^{43} +(-707.642 + 514.132i) q^{44} +(67.1650 + 48.7982i) q^{46} +(-261.212 - 189.781i) q^{47} -341.712 q^{49} +(595.825 - 87.0474i) q^{50} +(-197.254 + 607.087i) q^{52} +(-332.211 - 241.366i) q^{53} +(414.748 + 491.555i) q^{55} +(31.8695 - 23.1546i) q^{56} +(-546.714 + 397.211i) q^{58} +(-205.936 - 633.807i) q^{59} +(91.5497 - 281.761i) q^{61} +(361.643 + 1113.02i) q^{62} +(-199.272 + 613.296i) q^{64} +(455.720 + 112.307i) q^{65} +(679.955 - 494.016i) q^{67} +1638.22 q^{68} +(-39.4172 - 46.7168i) q^{70} +(-45.5772 - 33.1138i) q^{71} +(66.9965 - 206.194i) q^{73} -1682.49 q^{74} -810.206 q^{76} +(20.1746 - 62.0909i) q^{77} +(-339.726 - 246.826i) q^{79} +(-494.595 - 121.888i) q^{80} -41.2059 q^{82} +(1179.19 - 856.729i) q^{83} +(-87.2959 - 1201.40i) q^{85} +(-166.431 + 512.222i) q^{86} +(-617.012 - 1898.97i) q^{88} +(378.815 - 1165.87i) q^{89} +(-14.7229 - 45.3123i) q^{91} +(-212.005 + 154.031i) q^{92} +(1258.31 - 914.215i) q^{94} +(43.1734 + 594.167i) q^{95} +(-419.892 - 305.069i) q^{97} +(508.671 - 1565.53i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10}) \) 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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