LMFDB - Embedded newform 225.4.h.a.136.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("225.46");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			136.7
Character	$\chi$	$=$	225.136
Dual form			225.4.h.a.91.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.76530 - 2.73565i) q^{2} +(4.22155 - 12.9926i) q^{4} +(-5.34090 - 9.82216i) q^{5} -26.0445 q^{7} +(-8.14206 - 25.0587i) q^{8} +O(q^{10})$	\(q+(3.76530 - 2.73565i) q^{2} +(4.22155 - 12.9926i) q^{4} +(-5.34090 - 9.82216i) q^{5} -26.0445 q^{7} +(-8.14206 - 25.0587i) q^{8} +(-46.9800 - 22.3725i) q^{10} +(2.03543 - 1.47883i) q^{11} +(-32.0534 - 23.2881i) q^{13} +(-98.0653 + 71.2486i) q^{14} +(-10.7917 - 7.84062i) q^{16} +(26.2638 + 80.8316i) q^{17} +(-44.1360 - 135.837i) q^{19} +(-150.162 + 27.9275i) q^{20} +(3.61845 - 11.1365i) q^{22} +(127.177 - 92.3993i) q^{23} +(-67.9495 + 104.918i) q^{25} -184.399 q^{26} +(-109.948 + 338.386i) q^{28} +(30.9737 - 95.3273i) q^{29} +(-53.5715 - 164.876i) q^{31} +148.703 q^{32} +(320.018 + 232.506i) q^{34} +(139.101 + 255.813i) q^{35} +(48.0520 + 34.9118i) q^{37} +(-537.786 - 390.725i) q^{38} +(-202.644 + 213.809i) q^{40} +(-287.546 - 208.914i) q^{41} +109.742 q^{43} +(-10.6211 - 32.6885i) q^{44} +(226.086 - 695.821i) q^{46} +(17.9575 - 55.2674i) q^{47} +335.317 q^{49} +(31.1696 + 580.935i) q^{50} +(-437.888 + 318.144i) q^{52} +(120.787 - 371.745i) q^{53} +(-25.3963 - 12.0941i) q^{55} +(212.056 + 652.641i) q^{56} +(-144.157 - 443.669i) q^{58} +(333.759 + 242.490i) q^{59} +(-290.142 + 210.800i) q^{61} +(-652.756 - 474.255i) q^{62} +(646.244 - 469.524i) q^{64} +(-57.5458 + 439.213i) q^{65} +(108.468 + 333.831i) q^{67} +1161.09 q^{68} +(1223.57 + 582.681i) q^{70} +(-52.7887 + 162.467i) q^{71} +(754.724 - 548.339i) q^{73} +276.437 q^{74} -1951.19 q^{76} +(-53.0119 + 38.5154i) q^{77} +(-405.819 + 1248.98i) q^{79} +(-19.3744 + 147.874i) q^{80} -1654.21 q^{82} +(202.066 + 621.896i) q^{83} +(653.668 - 689.680i) q^{85} +(413.211 - 300.216i) q^{86} +(-53.6301 - 38.9646i) q^{88} +(857.273 - 622.845i) q^{89} +(834.814 + 606.528i) q^{91} +(-663.624 - 2042.42i) q^{92} +(-83.5770 - 257.224i) q^{94} +(-1098.48 + 1159.00i) q^{95} +(198.234 - 610.103i) q^{97} +(1262.57 - 917.308i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10}) $ 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8	$ 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8} + 165 q^{10} - 19 q^{11} + 4 q^{13} + 24 q^{14} - 66 q^{16} - 208 q^{17} + 42 q^{19} - 295 q^{20} - 89 q^{22} - 32 q^{23} + 95 q^{25} - 206 q^{26} - 482 q^{28} + 716 q^{29} + 637 q^{31} + 844 q^{32} - 90 q^{34} - 430 q^{35} + 216 q^{37} - 2314 q^{38} - 500 q^{40} + 38 q^{41} - 1392 q^{43} - 603 q^{44} + 1622 q^{46} + 536 q^{47} + 162 q^{49} + 2265 q^{50} - 1922 q^{52} - 1672 q^{53} - 1000 q^{55} - 3000 q^{56} - 827 q^{58} - 973 q^{59} - 2712 q^{61} - 1057 q^{62} + 4439 q^{64} + 4360 q^{65} + 2768 q^{67} + 1370 q^{68} + 3230 q^{70} + 1074 q^{71} - 1018 q^{73} + 1414 q^{74} - 11408 q^{76} - 1607 q^{77} - 1820 q^{79} + 1290 q^{80} + 1772 q^{82} - 4045 q^{83} + 1850 q^{85} + 3986 q^{86} + 2407 q^{88} - 4542 q^{89} + 4412 q^{91} + 1089 q^{92} + 5137 q^{94} + 720 q^{95} - 5977 q^{97} + 10689 q^{98}+O(q^{100}) $ 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8 + 165 * q^10 - 19 * q^11 + 4 * q^13 + 24 * q^14 - 66 * q^16 - 208 * q^17 + 42 * q^19 - 295 * q^20 - 89 * q^22 - 32 * q^23 + 95 * q^25 - 206 * q^26 - 482 * q^28 + 716 * q^29 + 637 * q^31 + 844 * q^32 - 90 * q^34 - 430 * q^35 + 216 * q^37 - 2314 * q^38 - 500 * q^40 + 38 * q^41 - 1392 * q^43 - 603 * q^44 + 1622 * q^46 + 536 * q^47 + 162 * q^49 + 2265 * q^50 - 1922 * q^52 - 1672 * q^53 - 1000 * q^55 - 3000 * q^56 - 827 * q^58 - 973 * q^59 - 2712 * q^61 - 1057 * q^62 + 4439 * q^64 + 4360 * q^65 + 2768 * q^67 + 1370 * q^68 + 3230 * q^70 + 1074 * q^71 - 1018 * q^73 + 1414 * q^74 - 11408 * q^76 - 1607 * q^77 - 1820 * q^79 + 1290 * q^80 + 1772 * q^82 - 4045 * q^83 + 1850 * q^85 + 3986 * q^86 + 2407 * q^88 - 4542 * q^89 + 4412 * q^91 + 1089 * q^92 + 5137 * q^94 + 720 * q^95 - 5977 * q^97 + 10689 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	3.76530	−	2.73565i	1.33123	−	0.967198i	0.331515	−	0.943450i	$-0.392440\pi$
$2$	3.76530	−	2.73565i	1.33123	−	0.967198i	0.999718	−	0.0237477i	$-0.00755984\pi$
$3$		0			0
$3$		0			0
$4$	4.22155	−	12.9926i	0.527694	−	1.62407i
$5$	−5.34090	−	9.82216i	−0.477705	−	0.878520i
$5$	−5.34090	−	9.82216i	−0.477705	−	0.878520i
$6$		0			0
$7$	−26.0445			−1.40627			−0.703136	−	0.711056i	$-0.748217\pi$
$7$	−26.0445			−1.40627			−0.703136	+	0.711056i	$0.748217\pi$
$8$	−8.14206	−	25.0587i	−0.359832	−	1.10745i
$9$		0			0
$10$	−46.9800	−	22.3725i	−1.48564	−	0.707481i
$11$	2.03543	−	1.47883i	0.0557915	−	0.0405349i	−0.559540	−	0.828803i	$-0.689022\pi$
$11$	2.03543	−	1.47883i	0.0557915	−	0.0405349i	0.615331	+	0.788268i	$0.289022\pi$
$12$		0			0
$13$	−32.0534	−	23.2881i	−0.683846	−	0.496843i	0.190785	−	0.981632i	$-0.438897\pi$
$13$	−32.0534	−	23.2881i	−0.683846	−	0.496843i	−0.874632	+	0.484788i	$0.838897\pi$
$14$	−98.0653	+	71.2486i	−1.87208	+	1.36014i
$15$		0			0
$16$	−10.7917	−	7.84062i	−0.168620	−	0.122510i
$17$	26.2638	+	80.8316i	0.374700	+	1.15321i	0.943681	+	0.330857i	$0.107338\pi$
$17$	26.2638	+	80.8316i	0.374700	+	1.15321i	−0.568981	+	0.822351i	$0.692662\pi$
$18$		0			0
$19$	−44.1360	−	135.837i	−0.532921	−	1.64016i	−0.748099	−	0.663587i	$-0.769033\pi$
$19$	−44.1360	−	135.837i	−0.532921	−	1.64016i	0.215179	−	0.976575i	$-0.430967\pi$
$20$	−150.162	+	27.9275i	−1.67886	+	0.312239i
$21$		0			0
$22$	3.61845	−	11.1365i	0.0350662	−	0.107923i
$23$	127.177	−	92.3993i	1.15296	−	0.837678i	0.164092	−	0.986445i	$-0.447531\pi$
$23$	127.177	−	92.3993i	1.15296	−	0.837678i	0.988872	+	0.148768i	$0.0475306\pi$
$24$		0			0
$25$	−67.9495	+	104.918i	−0.543596	+	0.839347i
$26$	−184.399			−1.39090
$27$		0			0
$28$	−109.948	+	338.386i	−0.742081	+	2.28389i
$29$	30.9737	−	95.3273i	0.198334	−	0.610408i	−0.801588	−	0.597877i	$-0.796011\pi$
$29$	30.9737	−	95.3273i	0.198334	−	0.610408i	0.999921	−	0.0125312i	$-0.00398890\pi$
$30$		0			0
$31$	−53.5715	−	164.876i	−0.310378	−	0.955246i	−0.977615	−	0.210401i	$-0.932523\pi$
$31$	−53.5715	−	164.876i	−0.310378	−	0.955246i	0.667237	−	0.744846i	$-0.267477\pi$
$32$	148.703			0.821476
$33$		0			0
$34$	320.018	+	232.506i	1.61419	+	1.17278i
$35$	139.101	+	255.813i	0.671783	+	1.23544i
$36$		0			0
$37$	48.0520	+	34.9118i	0.213506	+	0.155121i	0.689398	−	0.724382i	$-0.257875\pi$
$37$	48.0520	+	34.9118i	0.213506	+	0.155121i	−0.475893	+	0.879503i	$0.657875\pi$
$38$	−537.786	−	390.725i	−2.29580	−	1.66800i
$39$		0			0
$40$	−202.644	+	213.809i	−0.801022	+	0.845153i
$41$	−287.546	−	208.914i	−1.09530	−	0.795779i	−0.115011	−	0.993364i	$-0.536690\pi$
$41$	−287.546	−	208.914i	−1.09530	−	0.795779i	−0.980286	+	0.197585i	$0.936690\pi$
$42$		0			0
$43$	109.742			0.389198			0.194599	−	0.980883i	$-0.437659\pi$
$43$	109.742			0.389198			0.194599	+	0.980883i	$0.437659\pi$
$44$	−10.6211	−	32.6885i	−0.0363908	−	0.112000i
$45$		0			0
$46$	226.086	−	695.821i	0.724665	−	2.23029i
$47$	17.9575	−	55.2674i	0.0557312	−	0.171523i	−0.919316	−	0.393520i	$-0.871257\pi$
$47$	17.9575	−	55.2674i	0.0557312	−	0.171523i	0.975047	+	0.221997i	$0.0712574\pi$
$48$		0			0
$49$	335.317			0.977600
$50$	31.1696	+	580.935i	0.0881610	+	1.64313i
$51$		0			0
$52$	−437.888	+	318.144i	−1.16777	+	0.848436i
$53$	120.787	−	371.745i	0.313045	−	0.963455i	−0.663506	−	0.748171i	$-0.730932\pi$
$53$	120.787	−	371.745i	0.313045	−	0.963455i	0.976552	−	0.215284i	$-0.0690676\pi$
$54$		0			0
$55$	−25.3963	−	12.0941i	−0.0622626	−	0.0296502i
$56$	212.056	+	652.641i	0.506021	+	1.55737i
$57$		0			0
$58$	−144.157	−	443.669i	−0.326357	−	1.00442i
$59$	333.759	+	242.490i	0.736470	+	0.535077i	0.891604	−	0.452817i	$-0.149581\pi$
$59$	333.759	+	242.490i	0.736470	+	0.535077i	−0.155134	+	0.987893i	$0.549581\pi$
$60$		0			0
$61$	−290.142	+	210.800i	−0.608998	+	0.442463i	−0.849061	−	0.528294i	$-0.822832\pi$
$61$	−290.142	+	210.800i	−0.608998	+	0.442463i	0.240064	+	0.970757i	$0.422832\pi$
$62$	−652.756	−	474.255i	−1.33710	−	0.971459i
$63$		0			0
$64$	646.244	−	469.524i	1.26220	−	0.917039i
$65$	−57.5458	+	439.213i	−0.109810	+	0.838118i
$66$		0			0
$67$	108.468	+	333.831i	0.197783	+	0.608715i	0.999933	+	0.0115915i	$0.00368977\pi$
$67$	108.468	+	333.831i	0.197783	+	0.608715i	−0.802149	+	0.597123i	$0.796310\pi$
$68$	1161.09			2.07062
$69$		0			0
$70$	1223.57	+	582.681i	2.08921	+	0.994910i
$71$	−52.7887	+	162.467i	−0.0882376	+	0.271567i	−0.985432	−	0.170068i	$-0.945601\pi$
$71$	−52.7887	+	162.467i	−0.0882376	+	0.271567i	0.897195	+	0.441635i	$0.145601\pi$
$72$		0			0
$73$	754.724	−	548.339i	1.21005	−	0.879154i	0.214817	−	0.976654i	$-0.431085\pi$
$73$	754.724	−	548.339i	1.21005	−	0.879154i	0.995236	+	0.0975001i	$0.0310846\pi$
$74$	276.437			0.434258
$75$		0			0
$76$	−1951.19			−2.94496
$77$	−53.0119	+	38.5154i	−0.0784580	+	0.0570030i
$78$		0			0
$79$	−405.819	+	1248.98i	−0.577952	+	1.77875i	0.0479457	+	0.998850i	$0.484733\pi$
$79$	−405.819	+	1248.98i	−0.577952	+	1.77875i	−0.625898	+	0.779905i	$0.715267\pi$
$80$	−19.3744	+	147.874i	−0.0270766	+	0.206660i
$81$		0			0
$82$	−1654.21			−2.22777
$83$	202.066	+	621.896i	0.267225	+	0.822433i	0.991173	+	0.132578i	$0.0423255\pi$
$83$	202.066	+	621.896i	0.267225	+	0.822433i	−0.723948	+	0.689855i	$0.757674\pi$
$84$		0			0
$85$	653.668	−	689.680i	0.834121	−	0.880075i
$86$	413.211	−	300.216i	0.518113	−	0.376431i
$87$		0			0
$88$	−53.6301	−	38.9646i	−0.0649658	−	0.0472004i
$89$	857.273	−	622.845i	1.02102	−	0.741814i	0.0545280	−	0.998512i	$-0.482635\pi$
$89$	857.273	−	622.845i	1.02102	−	0.741814i	0.966492	+	0.256698i	$0.0826346\pi$
$90$		0			0
$91$	834.814	+	606.528i	0.961674	+	0.698697i
$92$	−663.624	−	2042.42i	−0.752039	−	2.31454i
$93$		0			0
$94$	−83.5770	−	257.224i	−0.0917054	−	0.282240i
$95$	−1098.48	+	1159.00i	−1.18634	+	1.25169i
$96$		0			0
$97$	198.234	−	610.103i	0.207502	−	0.638624i	−0.792100	−	0.610392i	$-0.791012\pi$
$97$	198.234	−	610.103i	0.207502	−	0.638624i	0.999601	−	0.0282327i	$-0.00898793\pi$
$98$	1262.57	−	917.308i	1.30141	−	0.945532i
$99$		0			0
$100$	1076.31	+	1325.76i	1.07631	+	1.32576i
$101$	−864.030			−0.851229			−0.425615	−	0.904904i	$-0.639942\pi$
$101$	−864.030			−0.851229			−0.425615	+	0.904904i	$0.639942\pi$
$102$		0			0
$103$	566.152	−	1742.44i	0.541598	−	1.66687i	−0.187345	−	0.982294i	$-0.559988\pi$
$103$	566.152	−	1742.44i	0.541598	−	1.66687i	0.728944	−	0.684574i	$-0.240012\pi$
$104$	−322.589	+	992.828i	−0.304159	+	0.936104i
$105$		0			0
$106$	−562.163	−	1730.16i	−0.515115	−	1.58536i
$107$	1037.99			0.937816			0.468908	−	0.883247i	$-0.344648\pi$
$107$	1037.99			0.937816			0.468908	+	0.883247i	$0.344648\pi$
$108$		0			0
$109$	−1259.67	−	915.201i	−1.10692	−	0.804224i	−0.124743	−	0.992189i	$-0.539811\pi$
$109$	−1259.67	−	915.201i	−1.10692	−	0.804224i	−0.982176	+	0.187966i	$0.939811\pi$
$110$	−128.710	+	23.9377i	−0.111564	+	0.0207488i
$111$		0			0
$112$	281.064	+	204.205i	0.237126	+	0.172282i
$113$	−788.953	−	573.208i	−0.656800	−	0.477193i	0.208781	−	0.977963i	$-0.433051\pi$
$113$	−788.953	−	573.208i	−0.656800	−	0.477193i	−0.865581	+	0.500769i	$0.833051\pi$
$114$		0			0
$115$	−1586.80	−	755.654i	−1.28669	−	0.612740i
$116$	−1107.79	−	804.858i	−0.886689	−	0.644217i
$117$		0			0
$118$	1920.07			1.49794
$119$	−684.027	−	2105.22i	−0.526930	−	1.62172i
$120$		0			0
$121$	−409.346	+	1259.84i	−0.307547	+	0.946534i
$122$	−515.794	+	1587.45i	−0.382769	+	1.17804i
$123$		0			0
$124$	−2368.33			−1.71518
$125$	1393.44	+	107.052i	0.997062	+	0.0766002i
$126$		0			0
$127$	832.392	−	604.768i	0.581597	−	0.422555i	−0.257702	−	0.966224i	$-0.582965\pi$
$127$	832.392	−	604.768i	0.581597	−	0.422555i	0.839300	+	0.543669i	$0.182965\pi$
$128$	781.235	−	2404.39i	0.539469	−	1.66032i
$129$		0			0
$130$	984.855	+	1811.19i	0.664442	+	1.22194i
$131$	825.045	+	2539.23i	0.550264	+	1.69354i	0.708134	+	0.706078i	$0.249537\pi$
$131$	825.045	+	2539.23i	0.550264	+	1.69354i	−0.157870	+	0.987460i	$0.550463\pi$
$132$		0			0
$133$	1149.50	+	3537.80i	0.749431	+	2.30651i
$134$	1321.66	+	960.241i	0.852044	+	0.619046i
$135$		0			0
$136$	1811.69	−	1316.27i	1.14229	−	0.829921i
$137$	−986.533	−	716.758i	−0.615221	−	0.446984i	0.236028	−	0.971746i	$-0.424154\pi$
$137$	−986.533	−	716.758i	−0.615221	−	0.446984i	−0.851249	+	0.524762i	$0.824154\pi$
$138$		0			0
$139$	−708.126	+	514.484i	−0.432104	+	0.313942i	−0.782490	−	0.622664i	$-0.786051\pi$
$139$	−708.126	+	514.484i	−0.432104	+	0.313942i	0.350386	+	0.936606i	$0.386051\pi$
$140$	3910.90	−	727.357i	2.36094	−	0.439092i
$141$		0			0
$142$	245.687	+	756.148i	0.145194	+	0.446863i
$143$	−99.6816			−0.0582923
$144$		0			0
$145$	−1101.75	+	204.905i	−0.631001	+	0.117355i
$146$	1341.70	−	4129.32i	0.760546	−	2.34072i
$147$		0			0
$148$	656.449	−	476.938i	0.364593	−	0.264893i
$149$	819.633			0.450650			0.225325	−	0.974284i	$-0.427656\pi$
$149$	819.633			0.450650			0.225325	+	0.974284i	$0.427656\pi$
$150$		0			0
$151$	567.457			0.305821			0.152911	−	0.988240i	$-0.451135\pi$
$151$	567.457			0.305821			0.152911	+	0.988240i	$0.451135\pi$
$152$	−3044.53	+	2211.98i	−1.62463	+	1.18036i
$153$		0			0
$154$	−94.2409	+	290.044i	−0.0493126	+	0.151769i
$155$	−1333.32	+	1406.78i	−0.690934	+	0.729000i
$156$		0			0
$157$	−1643.63			−0.835516			−0.417758	−	0.908558i	$-0.637184\pi$
$157$	−1643.63			−0.835516			−0.417758	+	0.908558i	$0.637184\pi$
$158$	1888.75	+	5812.97i	0.951018	+	2.92693i
$159$		0			0
$160$	−794.208	−	1460.58i	−0.392423	−	0.721683i
$161$	−3312.26	+	2406.49i	−1.62138	+	1.17800i
$162$		0			0
$163$	1035.78	+	752.538i	0.497721	+	0.361615i	0.808146	−	0.588982i	$-0.200471\pi$
$163$	1035.78	+	752.538i	0.497721	+	0.361615i	−0.310425	+	0.950598i	$0.600471\pi$
$164$	−3928.23	+	2854.03i	−1.87039	+	1.35892i
$165$		0			0
$166$	2462.13	+	1788.84i	1.15119	+	0.836391i
$167$	487.198	+	1499.44i	0.225752	+	0.694792i	0.998214	+	0.0597320i	$0.0190246\pi$
$167$	487.198	+	1499.44i	0.225752	+	0.694792i	−0.772463	+	0.635060i	$0.780975\pi$
$168$		0			0
$169$	−193.829	−	596.545i	−0.0882246	−	0.271527i
$170$	574.531	−	4385.06i	0.259203	−	1.97834i
$171$		0			0
$172$	463.282	−	1425.83i	0.205377	−	0.632086i
$173$	1797.33	−	1305.83i	0.789874	−	0.573877i	−0.118052	−	0.993007i	$-0.537665\pi$
$173$	1797.33	−	1305.83i	0.789874	−	0.573877i	0.907926	+	0.419131i	$0.137665\pi$
$174$		0			0
$175$	1769.71	−	2732.55i	0.764444	−	1.18035i
$176$	−33.5607			−0.0143735
$177$		0			0
$178$	1524.00	−	4690.39i	0.641734	−	1.97506i
$179$	−931.708	+	2867.50i	−0.389045	+	1.19736i	0.544458	+	0.838788i	$0.316736\pi$
$179$	−931.708	+	2867.50i	−0.389045	+	1.19736i	−0.933503	+	0.358570i	$0.883264\pi$
$180$		0			0
$181$	764.093	+	2351.64i	0.313782	+	0.965722i	0.976253	+	0.216634i	$0.0695079\pi$
$181$	764.093	+	2351.64i	0.313782	+	0.965722i	−0.662471	+	0.749088i	$0.730492\pi$
$182$	4802.57			1.95599
$183$		0			0
$184$	−3350.88	−	2434.56i	−1.34256	−	0.975425i
$185$	86.2684	−	658.435i	0.0342842	−	0.261671i
$186$		0			0
$187$	172.994	+	125.688i	0.0676502	+	0.0491508i
$188$	−642.259	−	466.628i	−0.249157	−	0.181023i
$189$		0			0
$190$	−965.494	+	7369.04i	−0.368654	+	2.81372i
$191$	−518.536	−	376.738i	−0.196439	−	0.142722i	0.485218	−	0.874393i	$-0.338740\pi$
$191$	−518.536	−	376.738i	−0.196439	−	0.142722i	−0.681657	+	0.731672i	$0.738740\pi$
$192$		0			0
$193$	−658.953			−0.245764			−0.122882	−	0.992421i	$-0.539214\pi$
$193$	−658.953			−0.245764			−0.122882	+	0.992421i	$0.539214\pi$
$194$	−922.615	−	2839.52i	−0.341443	−	1.05085i
$195$		0			0
$196$	1415.56	−	4356.63i	0.515873	−	1.58769i
$197$	−865.948	+	2665.12i	−0.313179	+	0.963866i	0.663318	+	0.748337i	$0.269147\pi$
$197$	−865.948	+	2665.12i	−0.313179	+	0.963866i	−0.976498	+	0.215529i	$0.930853\pi$
$198$		0			0
$199$	−2715.89			−0.967459			−0.483729	−	0.875218i	$-0.660718\pi$
$199$	−2715.89			−0.967459			−0.483729	+	0.875218i	$0.660718\pi$
$200$	3182.36	+	848.474i	1.12514	+	0.299981i
$201$		0			0
$202$	−3253.33	+	2363.68i	−1.13318	+	0.823307i
$203$	−806.696	+	2482.75i	−0.278911	+	0.858400i
$204$		0			0
$205$	−516.235	+	3940.11i	−0.175880	+	1.34239i
$206$	−2634.96	−	8109.58i	−0.891197	−	2.74282i
$207$		0			0
$208$	163.317	+	502.637i	0.0544421	+	0.167556i
$209$	−290.715	−	211.217i	−0.0962162	−	0.0699051i
$210$		0			0
$211$	1402.23	−	1018.78i	0.457505	−	0.332397i	−0.335047	−	0.942201i	$-0.608752\pi$
$211$	1402.23	−	1018.78i	0.457505	−	0.332397i	0.792552	+	0.609805i	$0.208752\pi$
$212$	−4320.02	−	3138.68i	−1.39953	−	1.01682i
$213$		0			0
$214$	3908.34	−	2839.58i	1.24845	−	0.907053i
$215$	−586.122	−	1077.90i	−0.185922	−	0.341918i
$216$		0			0
$217$	1395.24	+	4294.12i	0.436476	+	1.34334i
$218$	−7246.68			−2.25141
$219$		0			0
$220$	−264.345	+	278.909i	−0.0810098	+	0.0854728i
$221$	1040.57	−	3202.56i	0.316727	−	0.974784i
$222$		0			0
$223$	−3541.18	+	2572.82i	−1.06338	+	0.772594i	−0.974712	−	0.223467i	$-0.928263\pi$
$223$	−3541.18	+	2572.82i	−1.06338	+	0.772594i	−0.0886732	+	0.996061i	$0.528263\pi$
$224$	−3872.90			−1.15522
$225$		0			0
$226$	−4538.74			−1.33589
$227$	−1819.26	+	1321.77i	−0.531931	+	0.386471i	−0.821080	−	0.570814i	$-0.806628\pi$
$227$	−1819.26	+	1321.77i	−0.531931	+	0.386471i	0.289148	+	0.957284i	$0.406628\pi$
$228$		0			0
$229$	693.843	−	2135.43i	0.200220	−	0.616215i	−0.799656	−	0.600459i	$-0.794985\pi$
$229$	693.843	−	2135.43i	0.200220	−	0.616215i	0.999876	−	0.0157557i	$-0.00501539\pi$
$230$	−8041.97	+	1495.66i	−2.30553	+	0.428787i
$231$		0			0
$232$	−2640.97			−0.747362
$233$	−218.901	−	673.707i	−0.0615479	−	0.189425i	0.915555	−	0.402193i	$-0.131752\pi$
$233$	−218.901	−	673.707i	−0.0615479	−	0.189425i	−0.977103	+	0.212768i	$0.931752\pi$
$234$		0			0
$235$	−638.754	+	118.797i	−0.177310	+	0.0329764i
$236$	4559.56	−	3312.71i	1.25763	−	0.913725i
$237$		0			0
$238$	−8334.70	−	6055.52i	−2.26999	−	1.64925i
$239$	4411.37	−	3205.04i	1.19392	−	0.867435i	0.200249	−	0.979745i	$-0.435825\pi$
$239$	4411.37	−	3205.04i	1.19392	−	0.867435i	0.993673	+	0.112309i	$0.0358248\pi$
$240$		0			0
$241$	−4628.17	−	3362.56i	−1.23704	−	0.898762i	−0.239642	−	0.970861i	$-0.577030\pi$
$241$	−4628.17	−	3362.56i	−1.23704	−	0.898762i	−0.997397	+	0.0720995i	$0.977030\pi$
$242$	1905.16	+	5863.48i	0.506068	+	1.55752i
$243$		0			0
$244$	1514.00	+	4659.60i	0.397228	+	1.22254i
$245$	−1790.89	−	3293.53i	−0.467004	−	0.858841i
$246$		0			0
$247$	−1748.67	+	5381.87i	−0.450468	+	1.38640i
$248$	−3695.40	+	2684.86i	−0.946202	+	0.687456i
$249$		0			0
$250$	5539.56	−	3408.87i	1.40141	−	0.862383i
$251$	−2045.23			−0.514319			−0.257159	−	0.966369i	$-0.582787\pi$
$251$	−2045.23			−0.514319			−0.257159	+	0.966369i	$0.582787\pi$
$252$		0			0
$253$	122.217	−	376.145i	0.0303704	−	0.0934705i
$254$	1479.77	−	4554.26i	0.365547	−	1.12504i
$255$		0			0
$256$	−1661.25	−	5112.79i	−0.405578	−	1.24824i
$257$	−407.547			−0.0989186			−0.0494593	−	0.998776i	$-0.515750\pi$
$257$	−407.547			−0.0989186			−0.0494593	+	0.998776i	$0.515750\pi$
$258$		0			0
$259$	−1251.49	−	909.262i	−0.300247	−	0.218142i
$260$	5463.58	+	2601.83i	1.30322	+	0.620610i
$261$		0			0
$262$	10053.0	+	7303.91i	2.37052	+	1.72228i
$263$	−717.991	−	521.651i	−0.168339	−	0.122306i	0.500426	−	0.865779i	$-0.333177\pi$
$263$	−717.991	−	521.651i	−0.168339	−	0.122306i	−0.668765	+	0.743474i	$0.733177\pi$
$264$		0			0
$265$	−4296.45	+	799.062i	−0.995958	+	0.185230i
$266$	14006.4	+	10176.2i	3.22852	+	2.34566i
$267$		0			0
$268$	4795.23			1.09297
$269$	−1864.45	−	5738.18i	−0.422592	−	1.30061i	−0.905281	−	0.424814i	$-0.860340\pi$
$269$	−1864.45	−	5738.18i	−0.422592	−	1.30061i	0.482688	−	0.875792i	$-0.339660\pi$
$270$		0			0
$271$	2019.40	−	6215.08i	0.452656	−	1.39313i	−0.421209	−	0.906964i	$-0.638394\pi$
$271$	2019.40	−	6215.08i	0.452656	−	1.39313i	0.873865	−	0.486169i	$-0.161606\pi$
$272$	350.339	−	1078.23i	0.0780972	−	0.240358i
$273$		0			0
$274$	−5675.39			−1.25132
$275$	16.8496	+	314.040i	0.00369480	+	0.0688630i
$276$		0			0
$277$	4454.88	−	3236.66i	0.966309	−	0.702064i	0.0117014	−	0.999932i	$-0.496275\pi$
$277$	4454.88	−	3236.66i	0.966309	−	0.702064i	0.954607	+	0.297867i	$0.0962753\pi$
$278$	−1258.86	+	3874.37i	−0.271587	+	0.835860i
$279$		0			0
$280$	5277.77	−	5568.54i	1.12645	−	1.18851i
$281$	2323.54	+	7151.11i	0.493276	+	1.51815i	0.819626	+	0.572898i	$0.194181\pi$
$281$	2323.54	+	7151.11i	0.493276	+	1.51815i	−0.326350	+	0.945249i	$0.605819\pi$
$282$		0			0
$283$	1384.45	+	4260.88i	0.290801	+	0.894994i	0.984600	+	0.174825i	$0.0559359\pi$
$283$	1384.45	+	4260.88i	0.290801	+	0.894994i	−0.693798	+	0.720169i	$0.744064\pi$
$284$	1888.02	+	1371.73i	0.394483	+	0.286609i
$285$		0			0
$286$	−375.331	+	272.694i	−0.0776006	+	0.0563802i
$287$	7489.00	+	5441.08i	1.54028	+	1.11908i
$288$		0			0
$289$	−1869.26	+	1358.09i	−0.380471	+	0.276429i
$290$	−3587.86	+	3785.52i	−0.726504	+	0.766529i
$291$		0			0
$292$	−3938.24	−	12120.7i	−0.789275	−	2.42914i
$293$	6672.17			1.33035			0.665174	−	0.746688i	$-0.268357\pi$
$293$	6672.17			1.33035			0.665174	+	0.746688i	$0.268357\pi$
$294$		0			0
$295$	599.201	−	4573.35i	0.118261	−	0.902612i
$296$	483.602	−	1488.37i	0.0949622	−	0.292264i
$297$		0			0
$298$	3086.16	−	2242.23i	0.599921	−	0.435868i
$299$	−6228.25			−1.20464
$300$		0			0
$301$	−2858.18			−0.547318
$302$	2136.65	−	1552.36i	0.407120	−	0.295790i
$303$		0			0
$304$	−588.742	+	1811.96i	−0.111075	+	0.341852i
$305$	3620.13	+	1723.95i	0.679634	+	0.323650i
$306$		0			0
$307$	5433.28			1.01008			0.505039	−	0.863097i	$-0.331478\pi$
$307$	5433.28			1.01008			0.505039	+	0.863097i	$0.331478\pi$
$308$	276.622	+	851.356i	0.0511754	+	0.157502i
$309$		0			0
$310$	−1171.90	+	8944.42i	−0.214708	+	1.63874i
$311$	415.035	−	301.541i	0.0756736	−	0.0549801i	−0.549305	−	0.835622i	$-0.685108\pi$
$311$	415.035	−	301.541i	0.0756736	−	0.0549801i	0.624979	+	0.780642i	$0.285108\pi$
$312$		0			0
$313$	806.159	+	585.709i	0.145581	+	0.105771i	0.658192	−	0.752850i	$-0.271322\pi$
$313$	806.159	+	585.709i	0.145581	+	0.105771i	−0.512611	+	0.858621i	$0.671322\pi$
$314$	−6188.75	+	4496.39i	−1.11227	+	0.808109i
$315$		0			0
$316$	14514.4	+	10545.3i	2.58385	+	1.87728i
$317$	−1322.77	−	4071.07i	−0.234366	−	0.721305i	−0.997205	−	0.0747164i	$-0.976195\pi$
$317$	−1322.77	−	4071.07i	−0.234366	−	0.721305i	0.762838	−	0.646589i	$-0.223805\pi$
$318$		0			0
$319$	−77.9278	−	239.837i	−0.0136775	−	0.0420950i
$320$	−8063.27	−	3839.83i	−1.40859	−	0.670791i
$321$		0			0
$322$	−5888.30	+	18122.3i	−1.01908	+	3.13639i
$323$	9820.71	−	7135.17i	1.69176	−	1.22914i
$324$		0			0
$325$	4621.36	−	1780.57i	0.788760	−	0.303902i
$326$	5958.70			1.01234
$327$		0			0
$328$	−2893.90	+	8906.52i	−0.487162	+	1.49933i
$329$	−467.694	+	1439.41i	−0.0783732	+	0.241208i
$330$		0			0
$331$	−918.630	−	2827.25i	−0.152545	−	0.469486i	0.845359	−	0.534199i	$-0.179387\pi$
$331$	−918.630	−	2827.25i	−0.152545	−	0.469486i	−0.997904	+	0.0647132i	$0.979387\pi$
$332$	8933.07			1.47670
$333$		0			0
$334$	5936.39	+	4313.04i	0.972529	+	0.706584i
$335$	2699.62	−	2848.35i	0.440286	−	0.464543i
$336$		0			0
$337$	−1248.14	−	906.825i	−0.201752	−	0.146581i	0.482322	−	0.875994i	$-0.339794\pi$
$337$	−1248.14	−	906.825i	−0.201752	−	0.146581i	−0.684074	+	0.729413i	$0.739794\pi$
$338$	−2361.76	−	1715.92i	−0.380068	−	0.276136i
$339$		0			0
$340$	−6201.25	−	11404.4i	−0.989146	−	1.81908i
$341$	−352.865	−	256.371i	−0.0560373	−	0.0407135i
$342$		0			0
$343$	200.108			0.0315009
$344$	−893.526	−	2749.99i	−0.140046	−	0.431016i
$345$		0			0
$346$	3195.16	−	9833.70i	0.496454	−	1.52793i
$347$	1738.01	−	5349.05i	0.268880	−	0.827527i	−0.721894	−	0.692003i	$-0.756728\pi$
$347$	1738.01	−	5349.05i	0.268880	−	0.827527i	0.990774	−	0.135524i	$-0.0432717\pi$
$348$		0			0
$349$	3546.44			0.543945			0.271972	−	0.962305i	$-0.412324\pi$
$349$	3546.44			0.543945			0.271972	+	0.962305i	$0.412324\pi$
$350$	−811.798	−	15130.2i	−0.123978	−	2.31069i
$351$		0			0
$352$	302.675	−	219.906i	0.0458313	−	0.0332984i
$353$	592.091	−	1822.27i	0.0892742	−	0.274758i	−0.896445	−	0.443155i	$-0.853859\pi$
$353$	592.091	−	1822.27i	0.0892742	−	0.274758i	0.985719	+	0.168397i	$0.0538591\pi$
$354$		0			0
$355$	1877.72	−	349.221i	0.280729	−	0.0522105i
$356$	−4473.36	−	13767.6i	−0.665976	−	2.04966i
$357$		0			0
$358$	4336.32	+	13345.8i	0.640172	+	1.97025i
$359$	2130.22	+	1547.69i	0.313171	+	0.227532i	0.733256	−	0.679953i	$-0.238000\pi$
$359$	2130.22	+	1547.69i	0.313171	+	0.227532i	−0.420085	+	0.907485i	$0.638000\pi$
$360$		0			0
$361$	−10954.6	+	7958.96i	−1.59711	+	1.16037i
$362$	9310.28	+	6764.32i	1.35176	+	0.982112i
$363$		0			0
$364$	11404.6	−	8285.92i	1.64221	−	1.19313i
$365$	−9416.78	−	4484.39i	−1.35040	−	0.643079i
$366$		0			0
$367$	−2102.12	−	6469.65i	−0.298991	−	0.920199i	−0.981852	−	0.189650i	$-0.939265\pi$
$367$	−2102.12	−	6469.65i	−0.298991	−	0.920199i	0.682861	−	0.730548i	$-0.260735\pi$
$368$	−2096.92			−0.297037
$369$		0			0
$370$	−1476.42	−	2715.20i	−0.207447	−	0.381505i
$371$	−3145.85	+	9681.92i	−0.440227	+	1.35488i
$372$		0			0
$373$	5424.55	−	3941.17i	0.753010	−	0.547094i	−0.143748	−	0.989614i	$-0.545916\pi$
$373$	5424.55	−	3941.17i	0.753010	−	0.547094i	0.896758	+	0.442520i	$0.145916\pi$
$374$	995.212			0.137597
$375$		0			0
$376$	−1531.14			−0.210007
$377$	−3212.81	+	2334.24i	−0.438907	+	0.318885i
$378$		0			0
$379$	1202.29	−	3700.27i	0.162948	−	0.501504i	−0.835931	−	0.548835i	$-0.815072\pi$
$379$	1202.29	−	3700.27i	0.162948	−	0.501504i	0.998879	+	0.0473310i	$0.0150716\pi$
$380$	10421.1	+	19164.9i	1.40682	+	2.58721i
$381$		0			0
$382$	−2983.06			−0.399547
$383$	1743.53	+	5366.04i	0.232612	+	0.715906i	0.997429	+	0.0716588i	$0.0228293\pi$
$383$	1743.53	+	5366.04i	0.232612	+	0.715906i	−0.764817	+	0.644247i	$0.777171\pi$
$384$		0			0
$385$	661.435	+	314.984i	0.0875581	+	0.0416963i
$386$	−2481.15	+	1802.66i	−0.327169	+	0.237702i
$387$		0			0
$388$	−7089.96	−	5151.16i	−0.927676	−	0.673996i
$389$	−3785.35	+	2750.22i	−0.493380	+	0.358462i	−0.806483	−	0.591257i	$-0.798632\pi$
$389$	−3785.35	+	2750.22i	−0.493380	+	0.358462i	0.313102	+	0.949719i	$0.398632\pi$
$390$		0			0
$391$	10808.9	+	7853.14i	1.39803	+	1.01573i
$392$	−2730.17	−	8402.59i	−0.351771	−	1.08264i
$393$		0			0
$394$	4030.26	+	12403.9i	0.515334	+	1.58604i
$395$	14435.2	−	2684.68i	1.83876	−	0.341977i
$396$		0			0
$397$	2589.33	−	7969.14i	0.327342	−	1.00746i	−0.643030	−	0.765841i	$-0.722323\pi$
$397$	2589.33	−	7969.14i	0.327342	−	1.00746i	0.970372	−	0.241614i	$-0.0776769\pi$
$398$	−10226.1	+	7429.72i	−1.28791	+	0.935724i
$399$		0			0
$400$	1555.92	−	599.480i	0.194489	−	0.0749350i
$401$	−6042.30			−0.752464			−0.376232	−	0.926525i	$-0.622780\pi$
$401$	−6042.30			−0.752464			−0.376232	+	0.926525i	$0.622780\pi$
$402$		0			0
$403$	−2122.51	+	6532.42i	−0.262357	+	0.807451i
$404$	−3647.55	+	11226.0i	−0.449189	+	1.38246i
$405$		0			0
$406$	3754.49	+	11555.1i	0.458947	+	1.41249i
$407$	149.435			0.0181996
$408$		0			0
$409$	−5290.72	−	3843.93i	−0.639631	−	0.464719i	0.220092	−	0.975479i	$-0.429364\pi$
$409$	−5290.72	−	3843.93i	−0.639631	−	0.464719i	−0.859723	+	0.510760i	$0.829364\pi$
$410$	8834.99	+	16247.9i	1.06422	+	1.95714i
$411$		0			0
$412$	−20248.7	−	14711.6i	−2.42132	−	1.75919i
$413$	−8692.59	−	6315.54i	−1.03568	−	0.752463i
$414$		0			0
$415$	5029.14	−	5306.21i	0.594869	−	0.627642i
$416$	−4766.43	−	3463.01i	−0.561763	−	0.408145i
$417$		0			0
$418$	−1672.44			−0.195698
$419$	−4050.94	−	12467.5i	−0.472319	−	1.45365i	−0.849540	−	0.527525i	$-0.823120\pi$
$419$	−4050.94	−	12467.5i	−0.472319	−	1.45365i	0.377221	−	0.926123i	$-0.376880\pi$
$420$		0			0
$421$	1054.72	−	3246.11i	0.122100	−	0.375785i	−0.871262	−	0.490819i	$-0.836698\pi$
$421$	1054.72	−	3246.11i	0.122100	−	0.375785i	0.993362	+	0.115034i	$0.0366977\pi$
$422$	2492.79	−	7672.01i	0.287552	−	0.884995i
$423$		0			0
$424$	−10298.9			−1.17962
$425$	−10265.3	−	2736.91i	−1.17163	−	0.312376i
$426$		0			0
$427$	7556.60	−	5490.19i	0.856416	−	0.622223i
$428$	4381.93	−	13486.2i	0.494880	−	1.52308i
$429$		0			0
$430$	−5155.69	−	2455.20i	−0.578208	−	0.275350i
$431$	467.178	+	1437.83i	0.0522116	+	0.160691i	0.973762	−	0.227567i	$-0.0730771\pi$
$431$	467.178	+	1437.83i	0.0522116	+	0.160691i	−0.921551	+	0.388258i	$0.873077\pi$
$432$		0			0
$433$	−2665.17	−	8202.55i	−0.295797	−	0.910368i	−0.982953	−	0.183858i	$-0.941141\pi$
$433$	−2665.17	−	8202.55i	−0.295797	−	0.910368i	0.687156	−	0.726510i	$-0.258859\pi$
$434$	17000.7	+	12351.7i	1.88032	+	1.36613i
$435$		0			0
$436$	−17208.6	+	12502.8i	−1.89023	+	1.37333i
$437$	−18164.3	−	13197.1i	−1.98836	−	1.44463i
$438$		0			0
$439$	2854.86	−	2074.17i	0.310375	−	0.225501i	−0.421682	−	0.906744i	$-0.638560\pi$
$439$	2854.86	−	2074.17i	0.310375	−	0.225501i	0.732058	+	0.681243i	$0.238560\pi$
$440$	−96.2828	+	734.869i	−0.0104320	+	0.0796216i
$441$		0			0
$442$	−4843.00	−	14905.2i	−0.521172	−	1.60400i
$443$	9589.40			1.02846			0.514228	−	0.857653i	$-0.328078\pi$
$443$	9589.40			1.02846			0.514228	+	0.857653i	$0.328078\pi$
$444$		0			0
$445$	−10696.3	−	5093.71i	−1.13944	−	0.542618i
$446$	−6295.26	+	19374.8i	−0.668362	+	2.05701i
$447$		0			0
$448$	−16831.1	+	12228.5i	−1.77499	+	1.28961i
$449$	9820.81			1.03223			0.516117	−	0.856518i	$-0.327377\pi$
$449$	9820.81			1.03223			0.516117	+	0.856518i	$0.327377\pi$
$450$		0			0
$451$	−894.230			−0.0933650
$452$	−10778.1	+	7830.72i	−1.12159	+	0.814881i
$453$		0			0
$454$	−3234.15	+	9953.70i	−0.334331	+	1.02897i
$455$	1498.75	−	11439.1i	0.154423	−	1.17862i
$456$		0			0
$457$	1597.23			0.163491			0.0817455	−	0.996653i	$-0.473951\pi$
$457$	1597.23			0.163491			0.0817455	+	0.996653i	$0.473951\pi$
$458$	−3229.26	−	9938.63i	−0.329461	−	1.01398i
$459$		0			0
$460$	−16516.7	+	17426.6i	−1.67412	+	1.76635i
$461$	−3157.65	+	2294.17i	−0.319016	+	0.231779i	−0.735755	−	0.677247i	$-0.763173\pi$
$461$	−3157.65	+	2294.17i	−0.319016	+	0.231779i	0.416740	+	0.909026i	$0.363173\pi$
$462$		0			0
$463$	12670.8	+	9205.86i	1.27184	+	0.924044i	0.999274	−	0.0380937i	$-0.0121285\pi$
$463$	12670.8	+	9205.86i	1.27184	+	0.924044i	0.272563	+	0.962138i	$0.412129\pi$
$464$	−1081.68	+	785.890i	−0.108224	+	0.0786293i
$465$		0			0
$466$	−2667.25	−	1937.87i	−0.265146	−	0.192640i
$467$	1976.88	+	6084.21i	0.195887	+	0.602878i	0.999965	+	0.00835414i	$0.00265924\pi$
$467$	1976.88	+	6084.21i	0.195887	+	0.602878i	−0.804078	+	0.594523i	$0.797341\pi$
$468$		0			0
$469$	−2825.00	−	8694.46i	−0.278137	−	0.856019i
$470$	−2080.11	+	2194.71i	−0.204146	+	0.215393i
$471$		0			0
$472$	3359.00	−	10337.9i	0.327564	−	1.00814i
$473$	223.373	−	162.290i	0.0217139	−	0.0157761i
$474$		0			0
$475$	17250.8	+	4599.36i	1.66636	+	0.444280i
$476$	−30239.9			−2.91186
$477$		0			0
$478$	7842.22	−	24135.9i	0.750408	−	2.30952i
$479$	3178.50	−	9782.42i	0.303193	−	0.933132i	−0.677153	−	0.735843i	$-0.736786\pi$
$479$	3178.50	−	9782.42i	0.303193	−	0.933132i	0.980345	−	0.197289i	$-0.0632137\pi$
$480$		0			0
$481$	−727.197	−	2238.08i	−0.0689342	−	0.212158i
$482$	−26625.2			−2.51607
$483$		0			0
$484$	14640.5	+	10636.9i	1.37495	+	0.998960i
$485$	−7051.28	+	1311.41i	−0.660169	+	0.122780i
$486$		0			0
$487$	−1685.55	−	1224.62i	−0.156837	−	0.113949i	0.506599	−	0.862182i	$-0.330902\pi$
$487$	−1685.55	−	1224.62i	−0.156837	−	0.113949i	−0.663436	+	0.748233i	$0.730902\pi$
$488$	7644.73	+	5554.22i	0.709141	+	0.515221i
$489$		0			0
$490$	−15753.2	−	7501.87i	−1.45236	−	0.691633i
$491$	14323.2	+	10406.4i	1.31649	+	0.956487i	0.999969	+	0.00790172i	$0.00251522\pi$
$491$	14323.2	+	10406.4i	1.31649	+	0.956487i	0.316522	+	0.948585i	$0.397485\pi$
$492$		0			0
$493$	8518.94			0.778243
$494$	8138.61	+	25048.1i	0.741242	+	2.28131i
$495$		0			0
$496$	−714.605	+	2199.33i	−0.0646909	+	0.199098i
$497$	1374.86	−	4231.37i	0.124086	−	0.381897i
$498$		0			0
$499$	5018.92			0.450256			0.225128	−	0.974329i	$-0.427720\pi$
$499$	5018.92			0.450256			0.225128	+	0.974329i	$0.427720\pi$
$500$	7273.35	−	17652.4i	0.650548	−	1.57888i
$501$		0			0
$502$	−7700.91	+	5595.04i	−0.684678	+	0.497448i
$503$	3109.30	−	9569.44i	0.275620	−	0.848270i	−0.713435	−	0.700721i	$-0.752862\pi$
$503$	3109.30	−	9569.44i	0.275620	−	0.848270i	0.989055	−	0.147549i	$-0.0471384\pi$
$504$		0			0
$505$	4614.70	+	8486.64i	0.406636	+	0.747822i
$506$	−568.818	−	1750.64i	−0.0499744	−	0.153805i
$507$		0			0
$508$	−4343.53	−	13368.0i	−0.379356	−	1.16754i
$509$	−4301.55	−	3125.26i	−0.374584	−	0.272151i	0.384525	−	0.923114i	$-0.374365\pi$
$509$	−4301.55	−	3125.26i	−0.374584	−	0.272151i	−0.759109	+	0.650963i	$0.774365\pi$
$510$		0			0
$511$	−19656.4	+	14281.2i	−1.70166	+	1.23633i
$512$	−3879.49	−	2818.62i	−0.334865	−	0.243294i
$513$		0			0
$514$	−1534.53	+	1114.90i	−0.131684	+	0.0956738i
$515$	−20138.3	+	3745.35i	−1.72310	+	0.320466i
$516$		0			0
$517$	−45.1798	−	139.049i	−0.00384334	−	0.0118286i
$518$	−7199.66			−0.610685
$519$		0			0
$520$	11474.6	−	2134.08i	0.967685	−	0.179972i
$521$	1938.78	−	5966.95i	0.163032	−	0.501760i	−0.835854	−	0.548952i	$-0.815027\pi$
$521$	1938.78	−	5966.95i	0.163032	−	0.501760i	0.998886	+	0.0471916i	$0.0150271\pi$
$522$		0			0
$523$	−11374.4	+	8264.02i	−0.950994	+	0.690937i	−0.951042	−	0.309063i	$-0.899985\pi$
$523$	−11374.4	+	8264.02i	−0.950994	+	0.690937i	4.79448e−5		1.00000i	$0.499985\pi$
$524$	36474.1			3.04080
$525$		0			0
$526$	−4130.50			−0.342392
$527$	11920.2	−	8660.54i	0.985299	−	0.715862i
$528$		0			0
$529$	3876.48	−	11930.6i	0.318606	−	0.980568i
$530$	−13991.5	+	14762.3i	−1.14670	+	1.20987i
$531$		0			0
$532$	50817.9			4.14142
$533$	4351.59	+	13392.8i	0.353637	+	1.08838i
$534$		0			0
$535$	−5543.80	−	10195.3i	−0.447999	−	0.823890i
$536$	7482.20	−	5436.14i	0.602951	−	0.438070i
$537$		0			0
$538$	−22717.8	−	16505.5i	−1.82051	−	1.32268i
$539$	682.515	−	495.876i	0.0545417	−	0.0396269i
$540$		0			0
$541$	16286.0	+	11832.5i	1.29425	+	0.940328i	0.999882	−	0.0153633i	$-0.00489048\pi$
$541$	16286.0	+	11832.5i	1.29425	+	0.940328i	0.294369	+	0.955692i	$0.404890\pi$
$542$	−9398.62	−	28926.0i	−0.744844	−	2.29239i
$543$		0			0
$544$	3905.50	+	12019.9i	0.307807	+	0.947332i
$545$	−2261.49	+	17260.6i	−0.177746	+	1.35663i
$546$		0			0
$547$	−4085.46	+	12573.8i	−0.319345	+	0.982843i	0.654584	+	0.755989i	$0.272844\pi$
$547$	−4085.46	+	12573.8i	−0.319345	+	0.982843i	−0.973929	+	0.226854i	$0.927156\pi$
$548$	−13477.3	+	9791.80i	−1.05058	+	0.763293i
$549$		0			0
$550$	922.547	+	1136.36i	0.0715228	+	0.0880991i
$551$	−14316.0			−1.10686
$552$		0			0
$553$	10569.4	−	32529.2i	0.812758	−	2.50141i
$554$	7919.57	−	24373.9i	0.607347	−	1.86922i
$555$		0			0
$556$	3695.09	+	11372.3i	0.281846	+	0.867434i
$557$	14165.4			1.07757			0.538786	−	0.842442i	$-0.318883\pi$
$557$	14165.4			1.07757			0.538786	+	0.842442i	$0.318883\pi$
$558$		0			0
$559$	−3517.60	−	2555.69i	−0.266152	−	0.193370i
$560$	504.598	−	3851.30i	0.0380771	−	0.290620i
$561$		0			0
$562$	28311.7	+	20569.7i	2.12501	+	1.54391i
$563$	9115.09	+	6622.50i	0.682336	+	0.495746i	0.874132	−	0.485689i	$-0.161431\pi$
$563$	9115.09	+	6622.50i	0.682336	+	0.495746i	−0.191796	+	0.981435i	$0.561431\pi$
$564$		0			0
$565$	−1416.42	+	10810.7i	−0.105467	+	0.804970i
$566$	16869.1	+	12256.1i	1.25276	+	0.910183i
$567$		0			0
$568$	4501.02			0.332497
$569$	2287.20	+	7039.27i	0.168514	+	0.518632i	0.999278	−	0.0379926i	$-0.0120963\pi$
$569$	2287.20	+	7039.27i	0.168514	+	0.518632i	−0.830764	+	0.556624i	$0.812096\pi$
$570$		0			0
$571$	−4038.92	+	12430.5i	−0.296013	+	0.911035i	0.686866	+	0.726784i	$0.258986\pi$
$571$	−4038.92	+	12430.5i	−0.296013	+	0.911035i	−0.982879	+	0.184251i	$0.941014\pi$
$572$	−420.811	+	1295.12i	−0.0307605	+	0.0946710i
$573$		0			0
$574$	43083.2			3.13285
$575$	1052.79	+	19621.7i	0.0763552	+	1.42310i
$576$		0			0
$577$	−6647.54	+	4829.72i	−0.479620	+	0.348464i	−0.801179	−	0.598425i	$-0.795793\pi$
$577$	−6647.54	+	4829.72i	−0.479620	+	0.348464i	0.321559	+	0.946890i	$0.395793\pi$
$578$	−3323.04	+	10227.3i	−0.239135	+	0.735982i
$579$		0			0
$580$	−1988.83	+	15179.6i	−0.142382	+	1.08672i
$581$	−5262.71	−	16197.0i	−0.375790	−	1.15656i
$582$		0			0
$583$	−303.893	−	935.286i	−0.0215883	−	0.0664418i
$584$	−19885.7	−	14447.8i	−1.40903	−	1.02372i
$585$		0			0
$586$	25122.7	−	18252.7i	1.77100	−	1.28671i
$587$	16152.0	+	11735.1i	1.13572	+	0.825145i	0.986517	−	0.163662i	$-0.0523306\pi$
$587$	16152.0	+	11735.1i	1.13572	+	0.825145i	0.149199	+	0.988807i	$0.452331\pi$
$588$		0			0
$589$	−20031.8	+	14554.0i	−1.40135	+	1.01814i
$590$	−10254.9	−	18859.2i	−0.715572	−	1.31597i
$591$		0			0
$592$	−244.832	−	753.515i	−0.0169975	−	0.0523130i
$593$	14429.9			0.999267			0.499634	−	0.866237i	$-0.333468\pi$
$593$	14429.9			0.999267			0.499634	+	0.866237i	$0.333468\pi$
$594$		0			0
$595$	−17024.5	+	17962.4i	−1.17300	+	1.23762i
$596$	3460.12	−	10649.2i	0.237805	−	0.731890i
$597$		0			0
$598$	−23451.2	+	17038.3i	−1.60366	+	1.16513i
$599$	7838.61			0.534686			0.267343	−	0.963601i	$-0.413854\pi$
$599$	7838.61			0.534686			0.267343	+	0.963601i	$0.413854\pi$
$600$		0			0
$601$	−25163.3			−1.70787			−0.853937	−	0.520376i	$-0.825792\pi$
$601$	−25163.3			−1.70787			−0.853937	+	0.520376i	$0.825792\pi$
$602$	−10761.9	+	7818.97i	−0.728608	+	0.529365i
$603$		0			0
$604$	2395.55	−	7372.74i	0.161380	−	0.496677i
$605$	14560.6	−	2708.01i	0.978466	−	0.181977i
$606$		0			0
$607$	−563.698			−0.0376932			−0.0188466	−	0.999822i	$-0.505999\pi$
$607$	−563.698			−0.0376932			−0.0188466	+	0.999822i	$0.505999\pi$
$608$	−6563.16	−	20199.3i	−0.437781	−	1.34735i
$609$		0			0
$610$	18347.0	−	3412.21i	1.21778	−	0.226486i
$611$	−1862.67	+	1353.31i	−0.123332	+	0.0896057i
$612$		0			0
$613$	5449.70	+	3959.44i	0.359072	+	0.260881i	0.752665	−	0.658404i	$-0.228768\pi$
$613$	5449.70	+	3959.44i	0.359072	+	0.260881i	−0.393593	+	0.919285i	$0.628768\pi$
$614$	20457.9	−	14863.6i	1.34465	−	0.976945i
$615$		0			0
$616$	1396.77	+	1014.81i	0.0913595	+	0.0663766i
$617$	3151.55	+	9699.47i	0.205635	+	0.632878i	0.999687	+	0.0250287i	$0.00796772\pi$
$617$	3151.55	+	9699.47i	0.205635	+	0.632878i	−0.794052	+	0.607850i	$0.792032\pi$
$618$		0			0
$619$	2342.12	+	7208.30i	0.152080	+	0.468055i	0.997853	−	0.0654878i	$-0.0208604\pi$
$619$	2342.12	+	7208.30i	0.152080	+	0.468055i	−0.845773	+	0.533543i	$0.820860\pi$
$620$	12649.0	+	23262.1i	0.819348	+	1.50682i
$621$		0			0
$622$	737.821	−	2270.78i	0.0475626	−	0.146383i
$623$	−22327.3	+	16221.7i	−1.43583	+	1.04319i
$624$		0			0
$625$	−6390.73	−	14258.3i	−0.409006	−	0.912531i
$626$	4637.72			0.296103
$627$		0			0
$628$	−6938.67	+	21355.0i	−0.440896	+	1.35694i
$629$	−1559.95	+	4801.04i	−0.0988861	+	0.304340i
$630$		0			0
$631$	1413.93	+	4351.64i	0.0892042	+	0.274542i	0.985700	−	0.168510i	$-0.0538956\pi$
$631$	1413.93	+	4351.64i	0.0892042	+	0.274542i	−0.896496	+	0.443052i	$0.853896\pi$
$632$	34602.1			2.17784
$633$		0			0
$634$	−16117.6	−	11710.1i	−1.00964	−	0.733547i
$635$	−10385.9	−	4945.88i	−0.649055	−	0.309088i
$636$		0			0
$637$	−10748.0	−	7808.90i	−0.668528	−	0.485714i
$638$	−949.532	−	689.875i	−0.0589221	−	0.0428094i
$639$		0			0
$640$	−27788.8	+	5168.22i	−1.71633	+	0.319206i
$641$	−14330.6	−	10411.8i	−0.883034	−	0.641562i	0.0510186	−	0.998698i	$-0.483753\pi$
$641$	−14330.6	−	10411.8i	−0.883034	−	0.641562i	−0.934052	+	0.357136i	$0.883753\pi$
$642$		0			0
$643$	−13212.2			−0.810323			−0.405162	−	0.914245i	$-0.632785\pi$
$643$	−13212.2			−0.810323			−0.405162	+	0.914245i	$0.632785\pi$
$644$	17283.8	+	53193.9i	1.05757	+	3.25487i
$645$		0			0
$646$	17458.6	−	53732.0i	1.06331	−	3.27254i
$647$	−1302.73	+	4009.39i	−0.0791586	+	0.243625i	−0.982803	−	0.184659i	$-0.940882\pi$
$647$	−1302.73	+	4009.39i	−0.0791586	+	0.243625i	0.903644	+	0.428284i	$0.140882\pi$
$648$		0			0
$649$	1037.95			0.0627780
$650$	12529.8	−	19346.8i	0.756091	−	1.16745i
$651$		0			0
$652$	14150.0	−	10280.6i	0.849935	−	0.617514i
$653$	−8093.51	+	24909.3i	−0.485028	+	1.49276i	0.346911	+	0.937898i	$0.387230\pi$
$653$	−8093.51	+	24909.3i	−0.485028	+	1.49276i	−0.831940	+	0.554866i	$0.812770\pi$
$654$		0			0
$655$	20534.2	−	21665.5i	1.22494	−	1.29243i
$656$	1465.09	+	4509.08i	0.0871983	+	0.268369i
$657$		0			0
$658$	2176.72	+	6699.26i	0.128963	+	0.396906i
$659$	−10410.7	−	7563.80i	−0.615391	−	0.447107i	0.235918	−	0.971773i	$-0.424190\pi$
$659$	−10410.7	−	7563.80i	−0.615391	−	0.447107i	−0.851308	+	0.524666i	$0.824190\pi$
$660$		0			0
$661$	17474.6	−	12696.0i	1.02827	−	0.747078i	0.0603043	−	0.998180i	$-0.480793\pi$
$661$	17474.6	−	12696.0i	1.02827	−	0.747078i	0.967961	+	0.251102i	$0.0807929\pi$
$662$	−11193.3	−	8132.40i	−0.657159	−	0.477454i
$663$		0			0
$664$	13938.6	−	10127.0i	0.814645	−	0.591874i
$665$	28609.5	−	30185.6i	1.66831	−	1.76022i
$666$		0			0
$667$	−4869.04	−	14985.4i	−0.282654	−	0.869918i
$668$	21538.4			1.24752
$669$		0			0
$670$	2372.79	−	18110.1i	0.136819	−	1.04426i
$671$	−278.827	+	858.140i	−0.0160417	+	0.0493713i
$672$		0			0
$673$	−8553.18	+	6214.25i	−0.489897	+	0.355931i	−0.805145	−	0.593078i	$-0.797912\pi$
$673$	−8553.18	+	6214.25i	−0.489897	+	0.355931i	0.315248	+	0.949009i	$0.397912\pi$
$674$	−7180.37			−0.410352
$675$		0			0
$676$	−8568.93			−0.487536
$677$	−12670.0	+	9205.29i	−0.719272	+	0.522582i	−0.886152	−	0.463395i	$-0.846631\pi$
$677$	−12670.0	+	9205.29i	−0.719272	+	0.522582i	0.166879	+	0.985977i	$0.446631\pi$
$678$		0			0
$679$	−5162.92	+	15889.8i	−0.291804	+	0.898079i
$680$	−22604.7	−	10764.6i	−1.27478	−	0.607066i
$681$		0			0
$682$	−2029.98			−0.113977
$683$	−7323.05	−	22538.0i	−0.410261	−	1.26265i	−0.916421	−	0.400215i	$-0.868935\pi$
$683$	−7323.05	−	22538.0i	−0.410261	−	1.26265i	0.506160	−	0.862440i	$-0.331065\pi$
$684$		0			0
$685$	−1771.13	+	13518.0i	−0.0987906	+	0.754010i
$686$	753.466	−	547.425i	0.0419351	−	0.0304676i
$687$		0			0
$688$	−1184.30	−	860.446i	−0.0656266	−	0.0476805i
$689$	−12528.9	+	9102.77i	−0.692761	+	0.503320i
$690$		0			0
$691$	−3580.95	−	2601.71i	−0.197143	−	0.143233i	0.484835	−	0.874606i	$-0.338880\pi$
$691$	−3580.95	−	2601.71i	−0.197143	−	0.143233i	−0.681978	+	0.731373i	$0.738880\pi$
$692$	−9378.67	−	28864.6i	−0.515207	−	1.58564i
$693$		0			0
$694$	−8088.99	−	24895.3i	−0.442441	−	1.36169i
$695$	8835.37	+	4207.52i	0.482223	+	0.229641i
$696$		0			0
$697$	9334.84	−	28729.7i	0.507292	−	1.56128i
$698$	13353.4	−	9701.82i	0.724118	−	0.526102i
$699$		0			0
$700$	−28032.0	−	34528.7i	−1.51358	−	1.86438i
$701$	−5192.49			−0.279768			−0.139884	−	0.990168i	$-0.544673\pi$
$701$	−5192.49			−0.279768			−0.139884	+	0.990168i	$0.544673\pi$
$702$		0			0
$703$	2621.48	−	8068.10i	0.140642	−	0.432851i
$704$	621.041	−	1911.37i	0.0332477	−	0.102326i
$705$		0			0
$706$	−2755.69	−	8481.13i	−0.146900	−	0.452113i
$707$	22503.2			1.19706
$708$		0			0
$709$	906.237	+	658.420i	0.0480035	+	0.0348766i	0.611528	−	0.791223i	$-0.290555\pi$
$709$	906.237	+	658.420i	0.0480035	+	0.0348766i	−0.563525	+	0.826099i	$0.690555\pi$
$710$	6114.81	−	6451.69i	0.323218	−	0.341025i
$711$		0			0
$712$	−22587.6	−	16410.9i	−1.18892	−	0.863798i
$713$	−22047.5	−	16018.4i	−1.15804	−	0.841368i
$714$		0			0
$715$	532.390	+	979.089i	0.0278465	+	0.0512110i
$716$	33323.0	+	24210.6i	1.73930	+	1.26368i
$717$		0			0
$718$	12254.8			0.636973
$719$	−7041.08	−	21670.2i	−0.365213	−	1.12401i	−0.949848	−	0.312713i	$-0.898762\pi$
$719$	−7041.08	−	21670.2i	−0.365213	−	1.12401i	0.584635	−	0.811297i	$-0.301238\pi$
$720$		0			0
$721$	−14745.2	+	45380.9i	−0.761634	+	2.34407i
$722$	−19474.3	+	59935.7i	−1.00382	+	3.08944i
$723$		0			0
$724$	33779.5			1.73399
$725$	7896.94	+	9727.16i	0.404531	+	0.498286i
$726$		0			0
$727$	−25911.7	+	18825.9i	−1.32188	+	0.960406i	−0.321978	+	0.946747i	$0.604348\pi$
$727$	−25911.7	+	18825.9i	−1.32188	+	0.960406i	−0.999907	+	0.0136585i	$0.995652\pi$
$728$	8401.69	−	25857.7i	0.427730	−	1.31642i
$729$		0			0
$730$	−47724.7	+	8875.93i	−2.41969	+	0.450018i
$731$	2882.24	+	8870.62i	0.145832	+	0.448826i
$732$		0			0
$733$	6712.80	+	20659.9i	0.338258	+	1.04105i	0.965095	+	0.261901i	$0.0843492\pi$
$733$	6712.80	+	20659.9i	0.338258	+	1.04105i	−0.626837	+	0.779151i	$0.715651\pi$
$734$	−25613.8	−	18609.5i	−1.28804	−	0.935816i
$735$		0			0
$736$	18911.6	−	13740.0i	0.947132	−	0.688132i
$737$	714.458	+	519.084i	0.0357088	+	0.0259440i
$738$		0			0
$739$	−24270.5	+	17633.5i	−1.20812	+	0.877754i	−0.995059	−	0.0992837i	$-0.968345\pi$
$739$	−24270.5	+	17633.5i	−1.20812	+	0.877754i	−0.213066	+	0.977038i	$0.568345\pi$
$740$	−8190.60	−	3900.47i	−0.406882	−	0.193762i
$741$		0			0
$742$	14641.3	+	45061.2i	0.724391	+	2.22945i
$743$	5551.03			0.274088			0.137044	−	0.990565i	$-0.456240\pi$
$743$	5551.03			0.274088			0.137044	+	0.990565i	$0.456240\pi$
$744$		0			0
$745$	−4377.58	−	8050.56i	−0.215278	−	0.395906i
$746$	9643.40	−	29679.3i	0.473284	−	1.45662i
$747$		0			0
$748$	2363.31	−	1717.05i	0.115523	−	0.0839324i
$749$	−27033.9			−1.31882
$750$		0			0
$751$	5337.87			0.259363			0.129682	−	0.991556i	$-0.458604\pi$
$751$	5337.87			0.259363			0.129682	+	0.991556i	$0.458604\pi$
$752$	−627.122	+	455.631i	−0.0304106	+	0.0220946i
$753$		0			0
$754$	−5711.51	+	17578.2i	−0.275863	+	0.849020i
$755$	−3030.73	−	5573.66i	−0.146092	−	0.268670i
$756$		0			0
$757$	−17462.2			−0.838409			−0.419205	−	0.907892i	$-0.637691\pi$
$757$	−17462.2			−0.838409			−0.419205	+	0.907892i	$0.637691\pi$
$758$	−5595.65	−	17221.6i	−0.268131	−	0.825222i
$759$		0			0
$760$	37987.0	+	18089.9i	1.81307	+	0.863406i
$761$	11011.7	−	8000.49i	0.524540	−	0.381100i	−0.293772	−	0.955876i	$-0.594911\pi$
$761$	11011.7	−	8000.49i	0.524540	−	0.381100i	0.818311	+	0.574775i	$0.194911\pi$
$762$		0			0
$763$	32807.4	+	23836.0i	1.55663	+	1.13096i
$764$	−7083.83	+	5146.71i	−0.335450	+	0.243719i
$765$		0			0
$766$	21244.5	+	15435.1i	1.00208	+	0.728056i
$767$	−5050.96	−	15545.2i	−0.237783	−	0.731820i
$768$		0			0
$769$	−7403.09	−	22784.4i	−0.347155	−	1.06843i	−0.960420	−	0.278556i	$-0.910144\pi$
$769$	−7403.09	−	22784.4i	−0.347155	−	1.06843i	0.613265	−	0.789877i	$-0.289856\pi$
$770$	3352.19	−	623.446i	0.156889	−	0.0291785i
$771$		0			0
$772$	−2781.80	+	8561.50i	−0.129688	+	0.399139i
$773$	−28541.9	+	20736.9i	−1.32805	+	0.964883i	−0.328254	+	0.944590i	$0.606460\pi$
$773$	−28541.9	+	20736.9i	−1.32805	+	0.964883i	−0.999794	+	0.0202938i	$0.993540\pi$
$774$		0			0
$775$	20938.7	+	5582.62i	0.970504	+	0.258753i
$776$	−16902.4			−0.781909
$777$		0			0
$778$	−6729.34	+	20710.8i	−0.310101	+	0.954393i
$779$	−15687.1	+	48280.0i	−0.721501	+	2.22055i
$780$		0			0
$781$	132.813	+	408.756i	0.00608505	+	0.0187278i
$782$	62182.2			2.84352
$783$		0			0
$784$	−3618.63	−	2629.09i	−0.164843	−	0.119765i
$785$	8778.47	+	16144.0i	0.399130	+	0.734018i
$786$		0			0
$787$	3159.18	+	2295.28i	0.143091	+	0.103962i	0.657028	−	0.753866i	$-0.271813\pi$
$787$	3159.18	+	2295.28i	0.143091	+	0.103962i	−0.513937	+	0.857828i	$0.671813\pi$
$788$	30971.1	+	22501.8i	1.40013	+	1.01725i
$789$		0			0
$790$	47008.3	−	49598.1i	2.11706	−	2.23370i
$791$	20547.9	+	14928.9i	0.923640	+	0.671063i
$792$		0			0
$793$	14209.2			0.636296
$794$	−12051.2	−	37089.7i	−0.538640	−	1.65776i
$795$		0			0
$796$	−11465.3	+	35286.5i	−0.510522	+	1.57123i
$797$	−2083.71	+	6412.98i	−0.0926081	+	0.285018i	−0.986623	−	0.163019i	$-0.947877\pi$
$797$	−2083.71	+	6412.98i	−0.0926081	+	0.285018i	0.894015	+	0.448037i	$0.147877\pi$
$798$		0			0
$799$	4938.98			0.218684
$800$	−10104.3	+	15601.7i	−0.446551	+	0.689503i
$801$		0			0
$802$	−22751.1	+	16529.6i	−1.00171	+	0.727781i
$803$	725.291	−	2232.22i	0.0318742	−	0.0980986i
$804$		0			0
$805$	41327.4	+	19680.6i	1.80944	+	0.861679i
$806$	9878.51	+	30402.9i	0.431707	+	1.32866i
$807$		0			0
$808$	7034.98	+	21651.4i	0.306299	+	0.942692i
$809$	10584.5	+	7690.07i	0.459988	+	0.334201i	0.793527	−	0.608536i	$-0.208243\pi$
$809$	10584.5	+	7690.07i	0.459988	+	0.334201i	−0.333538	+	0.942736i	$0.608243\pi$
$810$		0			0
$811$	−6068.49	+	4409.01i	−0.262754	+	0.190902i	−0.711360	−	0.702828i	$-0.751921\pi$
$811$	−6068.49	+	4409.01i	−0.262754	+	0.190902i	0.448606	+	0.893729i	$0.351921\pi$
$812$	28851.9	+	20962.1i	1.24693	+	0.905944i
$813$		0			0
$814$	562.668	−	408.802i	0.0242279	−	0.0176026i
$815$	1859.55	−	14192.8i	0.0799228	−	0.610003i
$816$		0			0
$817$	−4843.58	−	14907.0i	−0.207412	−	0.638347i
$818$	−30436.8			−1.30097
$819$		0			0
$820$	49013.0	+	23340.6i	2.08733	+	0.994012i
$821$	7243.43	−	22293.0i	0.307914	−	0.947662i	−0.670660	−	0.741765i	$-0.733989\pi$
$821$	7243.43	−	22293.0i	0.307914	−	0.947662i	0.978574	−	0.205897i	$-0.0660111\pi$
$822$		0			0
$823$	5027.18	−	3652.46i	0.212924	−	0.154698i	−0.476212	−	0.879331i	$-0.657990\pi$
$823$	5027.18	−	3652.46i	0.212924	−	0.154698i	0.689136	+	0.724632i	$0.257990\pi$
$824$	−48272.8			−2.04085
$825$		0			0
$826$	−50007.3			−2.10651
$827$	−476.862	+	346.460i	−0.0200509	+	0.0145678i	−0.597766	−	0.801671i	$-0.703945\pi$
$827$	−476.862	+	346.460i	−0.0200509	+	0.0145678i	0.577715	+	0.816239i	$0.303945\pi$
$828$		0			0
$829$	12257.5	−	37724.7i	0.513534	−	1.58050i	−0.272399	−	0.962184i	$-0.587817\pi$
$829$	12257.5	−	37724.7i	0.513534	−	1.58050i	0.785933	−	0.618312i	$-0.212183\pi$
$830$	4420.28	−	33737.4i	0.184856	−	1.41089i
$831$		0			0
$832$	−31648.6			−1.31877
$833$	8806.68	+	27104.2i	0.366307	+	1.12738i
$834$		0			0
$835$	12125.7	−	12793.7i	0.502546	−	0.530233i
$836$	−3971.52	+	2885.48i	−0.164304	+	0.119374i
$837$		0			0
$838$	−49359.8	−	35862.0i	−2.03473	−	1.47832i
$839$	−4893.28	+	3555.18i	−0.201353	+	0.146291i	−0.683893	−	0.729583i	$-0.739714\pi$
$839$	−4893.28	+	3555.18i	−0.201353	+	0.146291i	0.482540	+	0.875874i	$0.339714\pi$
$840$		0			0
$841$	11603.2	+	8430.21i	0.475755	+	0.345656i
$842$	−4908.86	−	15107.9i	−0.200915	−	0.618352i
$843$		0			0
$844$	−7317.01	−	22519.4i	−0.298414	−	0.918425i
$845$	−4824.14	+	5089.91i	−0.196397	+	0.207217i
$846$		0			0
$847$	10661.2	−	32811.8i	0.432495	−	1.33108i
$848$	−4218.21	+	3064.71i	−0.170818	+	0.124107i
$849$		0			0
$850$	−46139.2	+	17777.0i	−1.86184	+	0.717349i
$851$	9336.93			0.376105
$852$		0			0
$853$	−9595.40	+	29531.6i	−0.385159	+	1.18540i	0.551207	+	0.834369i	$0.314168\pi$
$853$	−9595.40	+	29531.6i	−0.385159	+	1.18540i	−0.936365	+	0.351027i	$0.885832\pi$
$854$	13433.6	−	41344.4i	0.538277	−	1.65665i
$855$		0			0
$856$	−8451.38	−	26010.7i	−0.337456	−	1.03858i
$857$	−10170.1			−0.405371			−0.202685	−	0.979244i	$-0.564967\pi$
$857$	−10170.1			−0.405371			−0.202685	+	0.979244i	$0.564967\pi$
$858$		0			0
$859$	33431.4	+	24289.4i	1.32790	+	0.964775i	0.999797	+	0.0201332i	$0.00640904\pi$
$859$	33431.4	+	24289.4i	1.32790	+	0.964775i	0.328102	+	0.944642i	$0.393591\pi$
$860$	−16479.1	+	3064.82i	−0.653411	+	0.121523i
$861$		0			0
$862$	5692.45	+	4135.81i	0.224925	+	0.163418i
$863$	25007.4	+	18168.9i	0.986399	+	0.716661i	0.959130	−	0.282967i	$-0.0913188\pi$
$863$	25007.4	+	18168.9i	0.986399	+	0.716661i	0.0272693	+	0.999628i	$0.491319\pi$
$864$		0			0
$865$	−22425.4	−	10679.3i	−0.881489	−	0.419776i
$866$	−32474.4	−	23594.1i	−1.27428	−	0.925819i
$867$		0			0
$868$	61681.9			2.41200
$869$	1021.01	+	3142.36i	0.0398568	+	0.122667i
$870$		0			0
$871$	4297.52	−	13226.4i	0.167183	−	0.514535i
$872$	−12677.5	+	39017.2i	−0.492331	+	1.51524i
$873$		0			0
$874$	−104497.			−4.04422
$875$	−36291.4	−	2788.12i	−1.40214	−	0.107721i
$876$		0			0
$877$	8697.14	−	6318.84i	0.334871	−	0.243298i	−0.407624	−	0.913150i	$-0.633643\pi$
$877$	8697.14	−	6318.84i	0.334871	−	0.243298i	0.742494	+	0.669852i	$0.233643\pi$
$878$	5075.17	−	15619.8i	0.195078	−	0.600389i
$879$		0			0
$880$	179.244	+	329.638i	0.00686628	+	0.0126274i
$881$	6484.06	+	19955.9i	0.247961	+	0.763146i	0.995135	+	0.0985174i	$0.0314100\pi$
$881$	6484.06	+	19955.9i	0.247961	+	0.763146i	−0.747174	+	0.664628i	$0.768590\pi$
$882$		0			0
$883$	−9359.05	−	28804.2i	−0.356690	−	1.09778i	−0.955023	−	0.296531i	$-0.904170\pi$
$883$	−9359.05	−	28804.2i	−0.356690	−	1.09778i	0.598334	−	0.801247i	$-0.295830\pi$
$884$	−37216.7	−	27039.5i	−1.41599	−	1.02878i
$885$		0			0
$886$	36106.9	−	26233.2i	1.36912	−	0.994721i
$887$	14883.9	+	10813.8i	0.563418	+	0.409347i	0.832708	−	0.553712i	$-0.186789\pi$
$887$	14883.9	+	10813.8i	0.563418	+	0.409347i	−0.269290	+	0.963059i	$0.586789\pi$
$888$		0			0
$889$	−21679.3	+	15750.9i	−0.817884	+	0.594227i
$890$	−54209.3	+	10082.0i	−2.04169	+	0.379717i
$891$		0			0
$892$	18478.3	+	56870.4i	0.693609	+	2.13471i
$893$	−8299.91			−0.311026
$894$		0			0
$895$	33141.2	−	6163.67i	1.23775	−	0.230200i
$896$	−20346.9	+	62621.3i	−0.758640	+	2.33485i
$897$		0			0
$898$	36978.3	−	26866.3i	1.37414	−	0.998373i
$899$	−17376.5			−0.644649
$900$		0			0
$901$	33221.1			1.22836
$902$	−3367.04	+	2446.30i	−0.124291	+	0.0903024i
$903$		0			0
$904$	−7940.13	+	24437.2i	−0.292129	+	0.899081i
$905$	19017.2	−	20064.9i	0.698511	−	0.736994i
$906$		0			0
$907$	−22143.3			−0.810648			−0.405324	−	0.914173i	$-0.632841\pi$
$907$	−22143.3			−0.810648			−0.405324	+	0.914173i	$0.632841\pi$
$908$	9493.11	+	29216.8i	0.346960	+	1.06783i
$909$		0			0
$910$	−25650.1	−	47171.6i	−0.934386	−	1.71838i
$911$	34301.6	−	24921.6i	1.24749	−	0.906354i	0.249416	−	0.968396i	$-0.419761\pi$
$911$	34301.6	−	24921.6i	1.24749	−	0.906354i	0.998074	+	0.0620423i	$0.0197614\pi$
$912$		0			0
$913$	1330.97	+	967.006i	0.0482461	+	0.0350528i
$914$	6014.06	−	4369.47i	0.217645	−	0.158128i
$915$		0			0
$916$	−24815.7	−	18029.6i	−0.895123	−	0.650345i
$917$	−21487.9	−	66133.0i	−0.773820	−	2.38157i
$918$		0			0
$919$	3571.54	+	10992.1i	0.128198	+	0.394554i	0.994470	−	0.105019i	$-0.0334903\pi$
$919$	3571.54	+	10992.1i	0.128198	+	0.394554i	−0.866272	+	0.499573i	$0.833490\pi$
$920$	−6015.88	+	45915.7i	−0.215585	+	1.64543i
$921$		0			0
$922$	−5613.45	+	17276.4i	−0.200509	+	0.617103i
$923$	5475.61	−	3978.26i	0.195267	−	0.141870i
$924$		0			0
$925$	−6928.00	+	2669.30i	−0.246261	+	0.0948821i
$926$	72893.2			2.58685
$927$		0			0
$928$	4605.88	−	14175.5i	0.162926	−	0.501435i
$929$	5028.90	−	15477.4i	0.177603	−	0.546605i	−0.822140	−	0.569285i	$-0.807220\pi$
$929$	5028.90	−	15477.4i	0.177603	−	0.546605i	0.999743	+	0.0226802i	$0.00721996\pi$
$930$		0			0
$931$	−14799.5	−	45548.3i	−0.520983	−	1.60342i
$932$	−9677.31			−0.340119
$933$		0			0
$934$	24087.8	+	17500.8i	0.843873	+	0.613109i
$935$	310.579	−	2370.46i	0.0108631	−	0.0829116i
$936$		0			0
$937$	32106.5	+	23326.8i	1.11940	+	0.813289i	0.984118	−	0.177518i	$-0.0568068\pi$
$937$	32106.5	+	23326.8i	1.11940	+	0.813289i	0.135279	+	0.990808i	$0.456807\pi$
$938$	−34421.9	−	25009.0i	−1.19820	−	0.870547i
$939$		0			0
$940$	−1153.05	+	8800.58i	−0.0400090	+	0.305365i
$941$	−17490.0	−	12707.2i	−0.605905	−	0.440216i	0.242065	−	0.970260i	$-0.422175\pi$
$941$	−17490.0	−	12707.2i	−0.605905	−	0.440216i	−0.847970	+	0.530044i	$0.822175\pi$
$942$		0			0
$943$	−55872.7			−1.92944
$944$	−1700.55	−	5233.76i	−0.0586316	−	0.180449i
$945$		0			0
$946$	397.097	−	1222.14i	0.0136477	−	0.0420033i
$947$	−952.900	+	2932.73i	−0.0326981	+	0.100634i	−0.966074	−	0.258267i	$-0.916849\pi$
$947$	−952.900	+	2932.73i	−0.0326981	+	0.100634i	0.933375	+	0.358901i	$0.116849\pi$
$948$		0			0
$949$	−36961.2			−1.26429
$950$	77536.5	−	29874.1i	2.64802	−	1.02026i
$951$		0			0
$952$	−47184.6	+	34281.6i	−1.60637	+	1.16709i
$953$	−11047.2	+	33999.8i	−0.375503	+	1.15568i	0.567636	+	0.823280i	$0.307858\pi$
$953$	−11047.2	+	33999.8i	−0.375503	+	1.15568i	−0.943139	+	0.332399i	$0.892142\pi$
$954$		0			0
$955$	−930.933	+	7105.26i	−0.0315438	+	0.240755i
$956$	−23019.0	−	70845.3i	−0.778754	−	2.39676i
$957$		0			0
$958$	−14793.3	−	45529.0i	−0.498902	−	1.53546i
$959$	25693.8	+	18667.6i	0.865167	+	0.628581i
$960$		0			0
$961$	−212.830	+	154.630i	−0.00714411	+	0.00519050i
$962$	−8860.72	−	6437.69i	−0.296966	−	0.215758i
$963$		0			0
$964$	−63226.4	+	45936.7i	−2.11243	+	1.53477i
$965$	3519.40	+	6472.33i	0.117403	+	0.215909i
$966$		0			0
$967$	−7301.83	−	22472.7i	−0.242824	−	0.747337i	−0.995987	−	0.0895018i	$-0.971473\pi$
$967$	−7301.83	−	22472.7i	−0.242824	−	0.747337i	0.753162	−	0.657835i	$-0.228527\pi$
$968$	34902.7			1.15890
$969$		0			0
$970$	−22962.6	+	24227.7i	−0.760087	+	0.801962i
$971$	−4862.36	+	14964.8i	−0.160701	+	0.494586i	−0.998694	−	0.0510947i	$-0.983729\pi$
$971$	−4862.36	+	14964.8i	−0.160701	+	0.494586i	0.837993	+	0.545681i	$0.183729\pi$
$972$		0			0
$973$	18442.8	−	13399.5i	0.607656	−	0.441488i
$974$	−9696.74			−0.318997
$975$		0			0
$976$	4783.93			0.156895
$977$	−3368.51	+	2447.37i	−0.110305	+	0.0801414i	−0.641570	−	0.767064i	$-0.721717\pi$
$977$	−3368.51	+	2447.37i	−0.110305	+	0.0801414i	0.531265	+	0.847206i	$0.321717\pi$
$978$		0			0
$979$	823.840	−	2535.52i	0.0268948	−	0.0827738i
$980$	−50351.9	+	9364.54i	−1.64126	+	0.305244i
$981$		0			0
$982$	82399.4			2.67767
$983$	12435.4	+	38272.1i	0.403485	+	1.24180i	0.922153	+	0.386825i	$0.126428\pi$
$983$	12435.4	+	38272.1i	0.403485	+	1.24180i	−0.518668	+	0.854976i	$0.673572\pi$
$984$		0			0
$985$	30802.1	−	5728.64i	0.996383	−	0.185309i
$986$	32076.3	−	23304.8i	1.03602	−	0.752715i
$987$		0			0
$988$	62542.3	+	45439.6i	2.01390	+	1.46319i
$989$	13956.6	−	10140.1i	0.448731	−	0.326022i
$990$		0			0
$991$	−42247.3	−	30694.5i	−1.35422	−	0.983896i	−0.998789	−	0.0491928i	$-0.984335\pi$
$991$	−42247.3	−	30694.5i	−1.35422	−	0.983896i	−0.355428	−	0.934704i	$-0.615665\pi$
$992$	−7966.25	−	24517.6i	−0.254968	−	0.784712i
$993$		0			0
$994$	−6398.81	−	19693.5i	−0.204183	−	0.628410i
$995$	14505.3	+	26675.9i	0.462160	+	0.849932i
$996$		0			0
$997$	−17687.7	+	54437.1i	−0.561860	+	1.72923i	0.115240	+	0.993338i	$0.463236\pi$
$997$	−17687.7	+	54437.1i	−0.561860	+	1.72923i	−0.677100	+	0.735891i	$0.736764\pi$
$998$	18897.7	−	13730.0i	0.599396	−	0.435487i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.a.136.7		28
3.2	odd	2		75.4.g.b.61.1	yes	28
25.16	even	5	inner	225.4.h.a.91.7		28
75.29	odd	10		1875.4.a.f.1.2		14
75.41	odd	10		75.4.g.b.16.1	✓	28
75.71	odd	10		1875.4.a.g.1.13		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.4.g.b.16.1	✓	28	75.41	odd	10
75.4.g.b.61.1	yes	28	3.2	odd	2
225.4.h.a.91.7		28	25.16	even	5	inner
225.4.h.a.136.7		28	1.1	even	1	trivial
1875.4.a.f.1.2		14	75.29	odd	10
1875.4.a.g.1.13		14	75.71	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(3.76530 - 2.73565i) q^{2} +(4.22155 - 12.9926i) q^{4} +(-5.34090 - 9.82216i) q^{5} -26.0445 q^{7} +(-8.14206 - 25.0587i) q^{8} +O(q^{10})\)	\(q+(3.76530 - 2.73565i) q^{2} +(4.22155 - 12.9926i) q^{4} +(-5.34090 - 9.82216i) q^{5} -26.0445 q^{7} +(-8.14206 - 25.0587i) q^{8} +(-46.9800 - 22.3725i) q^{10} +(2.03543 - 1.47883i) q^{11} +(-32.0534 - 23.2881i) q^{13} +(-98.0653 + 71.2486i) q^{14} +(-10.7917 - 7.84062i) q^{16} +(26.2638 + 80.8316i) q^{17} +(-44.1360 - 135.837i) q^{19} +(-150.162 + 27.9275i) q^{20} +(3.61845 - 11.1365i) q^{22} +(127.177 - 92.3993i) q^{23} +(-67.9495 + 104.918i) q^{25} -184.399 q^{26} +(-109.948 + 338.386i) q^{28} +(30.9737 - 95.3273i) q^{29} +(-53.5715 - 164.876i) q^{31} +148.703 q^{32} +(320.018 + 232.506i) q^{34} +(139.101 + 255.813i) q^{35} +(48.0520 + 34.9118i) q^{37} +(-537.786 - 390.725i) q^{38} +(-202.644 + 213.809i) q^{40} +(-287.546 - 208.914i) q^{41} +109.742 q^{43} +(-10.6211 - 32.6885i) q^{44} +(226.086 - 695.821i) q^{46} +(17.9575 - 55.2674i) q^{47} +335.317 q^{49} +(31.1696 + 580.935i) q^{50} +(-437.888 + 318.144i) q^{52} +(120.787 - 371.745i) q^{53} +(-25.3963 - 12.0941i) q^{55} +(212.056 + 652.641i) q^{56} +(-144.157 - 443.669i) q^{58} +(333.759 + 242.490i) q^{59} +(-290.142 + 210.800i) q^{61} +(-652.756 - 474.255i) q^{62} +(646.244 - 469.524i) q^{64} +(-57.5458 + 439.213i) q^{65} +(108.468 + 333.831i) q^{67} +1161.09 q^{68} +(1223.57 + 582.681i) q^{70} +(-52.7887 + 162.467i) q^{71} +(754.724 - 548.339i) q^{73} +276.437 q^{74} -1951.19 q^{76} +(-53.0119 + 38.5154i) q^{77} +(-405.819 + 1248.98i) q^{79} +(-19.3744 + 147.874i) q^{80} -1654.21 q^{82} +(202.066 + 621.896i) q^{83} +(653.668 - 689.680i) q^{85} +(413.211 - 300.216i) q^{86} +(-53.6301 - 38.9646i) q^{88} +(857.273 - 622.845i) q^{89} +(834.814 + 606.528i) q^{91} +(-663.624 - 2042.42i) q^{92} +(-83.5770 - 257.224i) q^{94} +(-1098.48 + 1159.00i) q^{95} +(198.234 - 610.103i) q^{97} +(1262.57 - 917.308i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10}) \) 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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