LMFDB - Embedded newform 225.4.k.a.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(49,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("225.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.k (of order $6$, degree $2$, not 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.303595776.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.2
Root			$-1.26217 + 1.18614i$ of defining polynomial
Character	$\chi$	$=$	225.49
Dual form			225.4.k.a.124.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.05446 + 1.18614i) q^{2} +(4.97494 - 1.50000i) q^{3} +(-1.18614 + 2.05446i) q^{4} +(-8.44158 + 8.98266i) q^{6} +(-6.38458 + 3.68614i) q^{7} -24.6060i q^{8} +(22.5000 - 14.9248i) q^{9} +O(q^{10})$	\(q+(-2.05446 + 1.18614i) q^{2} +(4.97494 - 1.50000i) q^{3} +(-1.18614 + 2.05446i) q^{4} +(-8.44158 + 8.98266i) q^{6} +(-6.38458 + 3.68614i) q^{7} -24.6060i q^{8} +(22.5000 - 14.9248i) q^{9} +(2.06930 + 3.58413i) q^{11} +(-2.81929 + 12.0000i) q^{12} +(68.3972 + 39.4891i) q^{13} +(8.74456 - 15.1460i) q^{14} +(19.6970 + 34.1162i) q^{16} +33.3070i q^{17} +(-28.5223 + 57.3505i) q^{18} -89.3070 q^{19} +(-26.2337 + 27.9152i) q^{21} +(-8.50256 - 4.90895i) q^{22} +(172.826 + 99.7812i) q^{23} +(-36.9090 - 122.413i) q^{24} -187.359 q^{26} +(89.5489 - 108.000i) q^{27} -17.4891i q^{28} +(25.2405 + 43.7179i) q^{29} +(3.00000 - 5.19615i) q^{31} +(89.5419 + 51.6970i) q^{32} +(15.6708 + 14.7269i) q^{33} +(-39.5068 - 68.4278i) q^{34} +(3.97420 + 63.9282i) q^{36} +290.277i q^{37} +(183.477 - 105.931i) q^{38} +(399.505 + 93.8602i) q^{39} +(26.6684 - 46.1911i) q^{41} +(20.7846 - 88.4674i) q^{42} +(-258.412 + 149.194i) q^{43} -9.81791 q^{44} -473.418 q^{46} +(362.782 - 209.452i) q^{47} +(149.166 + 140.181i) q^{48} +(-144.325 + 249.978i) q^{49} +(49.9605 + 165.700i) q^{51} +(-162.257 + 93.6793i) q^{52} +399.228i q^{53} +(-55.8710 + 328.099i) q^{54} +(90.7011 + 157.099i) q^{56} +(-444.297 + 133.961i) q^{57} +(-103.711 - 59.8776i) q^{58} +(49.1209 - 85.0799i) q^{59} +(341.797 + 592.011i) q^{61} +14.2337i q^{62} +(-88.6382 + 178.227i) q^{63} -560.432 q^{64} +(-49.6631 - 11.6679i) q^{66} +(195.289 + 112.750i) q^{67} +(-68.4278 - 39.5068i) q^{68} +(1009.47 + 237.166i) q^{69} +512.951 q^{71} +(-367.239 - 553.634i) q^{72} -994.318i q^{73} +(-344.310 - 596.362i) q^{74} +(105.931 - 183.477i) q^{76} +(-26.4232 - 15.2554i) q^{77} +(-932.097 + 281.038i) q^{78} +(-100.853 - 174.683i) q^{79} +(283.500 - 671.617i) q^{81} +126.530i q^{82} +(959.247 - 553.822i) q^{83} +(-26.2337 - 87.0073i) q^{84} +(353.931 - 613.026i) q^{86} +(191.147 + 179.633i) q^{87} +(88.1909 - 50.9171i) q^{88} -372.269 q^{89} -582.250 q^{91} +(-409.992 + 236.709i) q^{92} +(7.13058 - 30.3505i) q^{93} +(-496.880 + 860.622i) q^{94} +(523.011 + 122.877i) q^{96} +(120.578 - 69.6156i) q^{97} -684.758i q^{98} +(100.052 + 49.7590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} - 102 q^{6} + 180 q^{9}+O(q^{10}) $ 8 * q + 2 * q^4 - 102 * q^6 + 180 * q^9	$ 8 q + 2 q^{4} - 102 q^{6} + 180 q^{9} + 74 q^{11} + 24 q^{14} + 238 q^{16} - 140 q^{19} - 72 q^{21} - 54 q^{24} - 304 q^{26} + 650 q^{29} + 24 q^{31} - 902 q^{34} + 342 q^{36} + 1128 q^{39} - 476 q^{41} + 404 q^{44} - 984 q^{46} - 1258 q^{49} - 462 q^{51} - 1998 q^{54} + 312 q^{56} - 170 q^{59} + 494 q^{61} - 2852 q^{64} - 1776 q^{66} + 3078 q^{69} + 1576 q^{71} + 968 q^{74} + 790 q^{76} - 1680 q^{79} + 2268 q^{81} - 72 q^{84} + 2774 q^{86} + 4260 q^{89} - 2544 q^{91} + 1264 q^{94} + 48 q^{96} + 180 q^{99}+O(q^{100}) $ 8 * q + 2 * q^4 - 102 * q^6 + 180 * q^9 + 74 * q^11 + 24 * q^14 + 238 * q^16 - 140 * q^19 - 72 * q^21 - 54 * q^24 - 304 * q^26 + 650 * q^29 + 24 * q^31 - 902 * q^34 + 342 * q^36 + 1128 * q^39 - 476 * q^41 + 404 * q^44 - 984 * q^46 - 1258 * q^49 - 462 * q^51 - 1998 * q^54 + 312 * q^56 - 170 * q^59 + 494 * q^61 - 2852 * q^64 - 1776 * q^66 + 3078 * q^69 + 1576 * q^71 + 968 * q^74 + 790 * q^76 - 1680 * q^79 + 2268 * q^81 - 72 * q^84 + 2774 * q^86 + 4260 * q^89 - 2544 * q^91 + 1264 * q^94 + 48 * q^96 + 180 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−2.05446	+	1.18614i	−0.726360	+	0.419364i	−0.817089	−	0.576512i	$-0.804414\pi$
$2$	−2.05446	+	1.18614i	−0.726360	+	0.419364i	0.0907292	+	0.995876i	$0.471080\pi$
$3$	4.97494	−	1.50000i	0.957427	−	0.288675i
$3$	4.97494	−	1.50000i	0.957427	−	0.288675i
$4$	−1.18614	+	2.05446i	−0.148268	+	0.256807i
$5$		0			0
$5$		0			0
$6$	−8.44158	+	8.98266i	−0.574377	+	0.611193i
$7$	−6.38458	+	3.68614i	−0.344735	+	0.199033i	−0.662364	−	0.749182i	$-0.730447\pi$
$7$	−6.38458	+	3.68614i	−0.344735	+	0.199033i	0.317629	+	0.948215i	$0.397113\pi$
$8$		−	24.6060i		−	1.08744i
$9$	22.5000	−	14.9248i	0.833333	−	0.552771i
$10$		0			0
$11$	2.06930	+	3.58413i	0.0567197	+	0.0982414i	0.892991	−	0.450074i	$-0.148603\pi$
$11$	2.06930	+	3.58413i	0.0567197	+	0.0982414i	−0.836271	+	0.548316i	$0.815269\pi$
$12$	−2.81929	+	12.0000i	−0.0678216	+	0.288675i
$13$	68.3972	+	39.4891i	1.45923	+	0.842486i	0.998973	−	0.0453014i	$-0.0144248\pi$
$13$	68.3972	+	39.4891i	1.45923	+	0.842486i	0.460254	+	0.887787i	$0.347758\pi$
$14$	8.74456	−	15.1460i	0.166934	−	0.289139i
$15$		0			0
$16$	19.6970	+	34.1162i	0.307766	+	0.533066i
$17$			33.3070i			0.475185i	0.971365	+	0.237592i	$0.0763583\pi$
$17$			33.3070i			0.475185i	−0.971365	+	0.237592i	$0.923642\pi$
$18$	−28.5223	+	57.3505i	−0.373488	+	0.750981i
$19$	−89.3070			−1.07834			−0.539169	−	0.842197i	$-0.681262\pi$
$19$	−89.3070			−1.07834			−0.539169	+	0.842197i	$0.681262\pi$
$20$		0			0
$21$	−26.2337	+	27.9152i	−0.272603	+	0.290076i
$22$	−8.50256	−	4.90895i	−0.0823978	−	0.0475724i
$23$	172.826	+	99.7812i	1.56682	+	0.904601i	0.996537	+	0.0831494i	$0.0264979\pi$
$23$	172.826	+	99.7812i	1.56682	+	0.904601i	0.570278	+	0.821452i	$0.306835\pi$
$24$	−36.9090	−	122.413i	−0.313917	−	1.04114i
$25$		0			0
$26$	−187.359			−1.41323
$27$	89.5489	−	108.000i	0.638285	−	0.769800i
$28$		−	17.4891i		−	0.118041i
$29$	25.2405	+	43.7179i	0.161622	+	0.279938i	0.935451	−	0.353457i	$-0.114994\pi$
$29$	25.2405	+	43.7179i	0.161622	+	0.279938i	−0.773828	+	0.633395i	$0.781661\pi$
$30$		0			0
$31$	3.00000	−	5.19615i	0.0173812	−	0.0301050i	−0.857204	−	0.514977i	$-0.827800\pi$
$31$	3.00000	−	5.19615i	0.0173812	−	0.0301050i	0.874585	+	0.484872i	$0.161134\pi$
$32$	89.5419	+	51.6970i	0.494654	+	0.285588i
$33$	15.6708	+	14.7269i	0.0826648	+	0.0776854i
$34$	−39.5068	−	68.4278i	−0.199275	−	0.345155i
$35$		0			0
$36$	3.97420	+	63.9282i	0.0183991	+	0.295964i
$37$			290.277i			1.28976i	0.764282	+	0.644882i	$0.223094\pi$
$37$			290.277i			1.28976i	−0.764282	+	0.644882i	$0.776906\pi$
$38$	183.477	−	105.931i	0.783262	−	0.452217i
$39$	399.505	+	93.8602i	1.64031	+	0.385376i
$40$		0			0
$41$	26.6684	−	46.1911i	0.101583	−	0.175947i	−0.810754	−	0.585387i	$-0.800943\pi$
$41$	26.6684	−	46.1911i	0.101583	−	0.175947i	0.912337	+	0.409440i	$0.134276\pi$
$42$	20.7846	−	88.4674i	0.0763604	−	0.325019i
$43$	−258.412	+	149.194i	−0.916453	+	0.529114i	−0.882502	−	0.470309i	$-0.844142\pi$
$43$	−258.412	+	149.194i	−0.916453	+	0.529114i	−0.0339510	+	0.999424i	$0.510809\pi$
$44$	−9.81791			−0.0336388
$45$		0			0
$46$	−473.418			−1.51743
$47$	362.782	−	209.452i	1.12590	−	0.650038i	0.182998	−	0.983113i	$-0.441420\pi$
$47$	362.782	−	209.452i	1.12590	−	0.650038i	0.942900	+	0.333075i	$0.108086\pi$
$48$	149.166	+	140.181i	0.448546	+	0.421528i
$49$	−144.325	+	249.978i	−0.420772	+	0.728798i
$50$		0			0
$51$	49.9605	+	165.700i	0.137174	+	0.454955i
$52$	−162.257	+	93.6793i	−0.432712	+	0.249827i
$53$			399.228i			1.03468i	0.855779	+	0.517342i	$0.173078\pi$
$53$			399.228i			1.03468i	−0.855779	+	0.517342i	$0.826922\pi$
$54$	−55.8710	+	328.099i	−0.140798	+	0.826826i
$55$		0			0
$56$	90.7011	+	157.099i	0.216436	+	0.374879i
$57$	−444.297	+	133.961i	−1.03243	+	0.311290i
$58$	−103.711	−	59.8776i	−0.234792	−	0.135557i
$59$	49.1209	−	85.0799i	0.108390	−	0.187737i	−0.806728	−	0.590923i	$-0.798764\pi$
$59$	49.1209	−	85.0799i	0.108390	−	0.187737i	0.915118	+	0.403186i	$0.132097\pi$
$60$		0			0
$61$	341.797	+	592.011i	0.717421	+	1.24261i	0.962018	+	0.272985i	$0.0880109\pi$
$61$	341.797	+	592.011i	0.717421	+	1.24261i	−0.244597	+	0.969625i	$0.578656\pi$
$62$			14.2337i			0.0291561i
$63$	−88.6382	+	178.227i	−0.177260	+	0.356420i
$64$	−560.432			−1.09459
$65$		0			0
$66$	−49.6631	−	11.6679i	−0.0926228	−	0.0217609i
$67$	195.289	+	112.750i	0.356094	+	0.205591i	0.667366	−	0.744730i	$-0.267422\pi$
$67$	195.289	+	112.750i	0.356094	+	0.205591i	−0.311272	+	0.950321i	$0.600755\pi$
$68$	−68.4278	−	39.5068i	−0.122031	−	0.0704545i
$69$	1009.47	+	237.166i	1.76125	+	0.413789i
$70$		0			0
$71$	512.951			0.857410			0.428705	−	0.903445i	$-0.358970\pi$
$71$	512.951			0.857410			0.428705	+	0.903445i	$0.358970\pi$
$72$	−367.239	−	553.634i	−0.601105	−	0.906200i
$73$		−	994.318i		−	1.59419i	−0.603852	−	0.797096i	$-0.706368\pi$
$73$		−	994.318i		−	1.59419i	0.603852	−	0.797096i	$-0.293632\pi$
$74$	−344.310	−	596.362i	−0.540881	−	0.936833i
$75$		0			0
$76$	105.931	−	183.477i	0.159883	−	0.276925i
$77$	−26.4232	−	15.2554i	−0.0391065	−	0.0225782i
$78$	−932.097	+	281.038i	−1.35307	+	0.407965i
$79$	−100.853	−	174.683i	−0.143631	−	0.248777i	0.785230	−	0.619204i	$-0.212545\pi$
$79$	−100.853	−	174.683i	−0.143631	−	0.248777i	−0.928862	+	0.370427i	$0.879211\pi$
$80$		0			0
$81$	283.500	−	671.617i	0.388889	−	0.921285i
$82$			126.530i			0.170401i
$83$	959.247	−	553.822i	1.26857	−	0.732408i	0.293850	−	0.955851i	$-0.405063\pi$
$83$	959.247	−	553.822i	1.26857	−	0.732408i	0.974717	+	0.223444i	$0.0717299\pi$
$84$	−26.2337	−	87.0073i	−0.0340754	−	0.113015i
$85$		0			0
$86$	353.931	−	613.026i	0.443783	−	0.768655i
$87$	191.147	+	179.633i	0.235553	+	0.221364i
$88$	88.1909	−	50.9171i	0.106832	−	0.0616793i
$89$	−372.269			−0.443375			−0.221688	−	0.975118i	$-0.571157\pi$
$89$	−372.269			−0.443375			−0.221688	+	0.975118i	$0.571157\pi$
$90$		0			0
$91$	−582.250			−0.670729
$92$	−409.992	+	236.709i	−0.464616	+	0.268246i
$93$	7.13058	−	30.3505i	0.00795061	−	0.0338409i
$94$	−496.880	+	860.622i	−0.545205	+	0.944323i
$95$		0			0
$96$	523.011	+	122.877i	0.556037	+	0.130636i
$97$	120.578	−	69.6156i	0.126215	−	0.0728700i	−0.435563	−	0.900158i	$-0.643451\pi$
$97$	120.578	−	69.6156i	0.126215	−	0.0728700i	0.561778	+	0.827288i	$0.310118\pi$
$98$		−	684.758i		−	0.705826i
$99$	100.052	+	49.7590i	0.101571	+	0.0505148i
$100$		0			0
$101$	−985.872	−	1707.58i	−0.971267	−	1.68228i	−0.691742	−	0.722145i	$-0.743156\pi$
$101$	−985.872	−	1707.58i	−0.971267	−	1.68228i	−0.279525	−	0.960139i	$-0.590177\pi$
$102$	−299.186	−	281.164i	−0.290429	−	0.272935i
$103$	−1569.85	−	906.353i	−1.50177	−	0.867045i	−0.999998	−	0.00204255i	$-0.999350\pi$
$103$	−1569.85	−	906.353i	−1.50177	−	0.867045i	−0.501768	−	0.865002i	$-0.667317\pi$
$104$	971.668	−	1682.98i	0.916153	−	1.58682i
$105$		0			0
$106$	−473.541	−	820.197i	−0.433909	−	0.751552i
$107$			259.217i			0.234201i	0.993120	+	0.117100i	$0.0373600\pi$
$107$			259.217i			0.234201i	−0.993120	+	0.117100i	$0.962640\pi$
$108$	115.664	+	312.077i	0.103053	+	0.278052i
$109$	−775.556			−0.681512			−0.340756	−	0.940152i	$-0.610683\pi$
$109$	−775.556			−0.681512			−0.340756	+	0.940152i	$0.610683\pi$
$110$		0			0
$111$	435.416	+	1444.11i	0.372323	+	1.23486i
$112$	−251.514	−	145.212i	−0.212195	−	0.122511i
$113$	186.417	+	107.628i	0.155191	+	0.0895997i	0.575585	−	0.817742i	$-0.304775\pi$
$113$	186.417	+	107.628i	0.155191	+	0.0895997i	−0.420393	+	0.907342i	$0.638108\pi$
$114$	753.892	−	802.215i	0.619373	−	0.659073i
$115$		0			0
$116$	−119.755			−0.0958534
$117$	2128.30	−	132.310i	1.68172	−	0.104547i
$118$			233.057i			0.181819i
$119$	−122.774	−	212.652i	−0.0945774	−	0.163813i
$120$		0			0
$121$	656.936	−	1137.85i	0.493566	−	0.854881i
$122$	−1404.42	−	810.840i	−1.04221	−	0.601721i
$123$	63.3872	−	269.800i	0.0464669	−	0.197781i
$124$	7.11684	+	12.3267i	0.00515412	+	0.00892721i
$125$		0			0
$126$	−29.2989	−	471.297i	−0.0207155	−	0.333226i
$127$		−	2424.76i		−	1.69420i	−0.531436	−	0.847098i	$-0.678348\pi$
$127$		−	2424.76i		−	1.69420i	0.531436	−	0.847098i	$-0.321652\pi$
$128$	435.048	−	251.175i	0.300415	−	0.173445i
$129$	−1061.79	+	1129.85i	−0.724694	+	0.771145i
$130$		0			0
$131$	−130.247	+	225.595i	−0.0868684	+	0.150461i	−0.906186	−	0.422880i	$-0.861019\pi$
$131$	−130.247	+	225.595i	−0.0868684	+	0.150461i	0.819317	+	0.573340i	$0.194353\pi$
$132$	−48.8435	+	14.7269i	−0.0322067	+	0.00971067i
$133$	570.188	−	329.198i	0.371741	−	0.214625i
$134$	−534.949			−0.344870
$135$		0			0
$136$	819.552			0.516735
$137$	350.427	−	202.319i	0.218533	−	0.126170i	−0.386738	−	0.922190i	$-0.626398\pi$
$137$	350.427	−	202.319i	0.218533	−	0.126170i	0.605271	+	0.796020i	$0.293065\pi$
$138$	−2355.23	+	710.127i	−1.45283	+	0.438044i
$139$	−883.841	+	1530.86i	−0.539327	+	0.934141i	0.459614	+	0.888119i	$0.347988\pi$
$139$	−883.841	+	1530.86i	−0.539327	+	0.934141i	−0.998940	+	0.0460221i	$0.985346\pi$
$140$		0			0
$141$	1490.64	−	1586.19i	0.890316	−	0.947383i
$142$	−1053.84	+	608.432i	−0.622788	+	0.359567i
$143$			326.859i			0.191142i
$144$	952.361	+	473.641i	0.551135	+	0.274098i
$145$		0			0
$146$	1179.40	+	2042.78i	0.668547	+	1.15796i
$147$	−343.040	+	1460.11i	−0.192472	+	0.819237i
$148$	−596.362	−	344.310i	−0.331220	−	0.191230i
$149$	960.344	−	1663.36i	0.528016	−	0.914551i	−0.471450	−	0.881893i	$-0.656269\pi$
$149$	960.344	−	1663.36i	0.528016	−	0.914551i	0.999467	−	0.0326584i	$-0.0103973\pi$
$150$		0			0
$151$	1262.28	+	2186.33i	0.680284	+	1.17829i	0.974894	+	0.222668i	$0.0714767\pi$
$151$	1262.28	+	2186.33i	0.680284	+	1.17829i	−0.294611	+	0.955617i	$0.595190\pi$
$152$			2197.49i			1.17263i
$153$	497.101	+	749.408i	0.262668	+	0.395987i
$154$	72.3804			0.0378739
$155$		0			0
$156$	−666.701	+	709.435i	−0.342172	+	0.364104i
$157$	1682.43	+	971.350i	0.855238	+	0.493772i	0.862415	−	0.506202i	$-0.168951\pi$
$157$	1682.43	+	971.350i	0.855238	+	0.493772i	−0.00717683	+	0.999974i	$0.502284\pi$
$158$	414.397	+	239.252i	0.208656	+	0.120468i
$159$	598.842	+	1986.13i	0.298687	+	0.990634i
$160$		0			0
$161$	−1471.23			−0.720181
$162$	214.193	+	1716.08i	0.103880	+	0.832270i
$163$		−	1051.21i		−	0.505134i	−0.967579	−	0.252567i	$-0.918725\pi$
$163$		−	1051.21i		−	0.505134i	0.967579	−	0.252567i	$-0.0812748\pi$
$164$	63.2650	+	109.578i	0.0301230	+	0.0521745i
$165$		0			0
$166$	−1313.82	+	2275.60i	−0.614291	+	1.06398i
$167$	−2439.11	−	1408.22i	−1.13020	−	0.652524i	−0.186218	−	0.982508i	$-0.559623\pi$
$167$	−2439.11	−	1408.22i	−1.13020	−	0.652524i	−0.943986	+	0.329985i	$0.892956\pi$
$168$	686.880	+	645.505i	0.315440	+	0.296439i
$169$	2020.28	+	3499.23i	0.919564	+	1.59273i
$170$		0			0
$171$	−2009.41	+	1332.89i	−0.898616	+	0.596074i
$172$		−	707.861i		−	0.313802i
$173$	−1249.20	+	721.225i	−0.548987	+	0.316958i	−0.748713	−	0.662894i	$-0.769328\pi$
$173$	−1249.20	+	721.225i	−0.548987	+	0.316958i	0.199726	+	0.979852i	$0.435995\pi$
$174$	−605.772	−	142.321i	−0.263928	−	0.0620075i
$175$		0			0
$176$	−81.5179	+	141.193i	−0.0349128	+	0.0604707i
$177$	116.754	−	496.948i	0.0495804	−	0.211033i
$178$	764.809	−	441.563i	0.322050	−	0.185936i
$179$	−1534.89			−0.640912			−0.320456	−	0.947263i	$-0.603836\pi$
$179$	−1534.89			−0.640912			−0.320456	+	0.947263i	$0.603836\pi$
$180$		0			0
$181$	−3650.43			−1.49908			−0.749542	−	0.661956i	$-0.769726\pi$
$181$	−3650.43			−1.49908			−0.749542	+	0.661956i	$0.769726\pi$
$182$	1196.21	−	690.630i	0.487191	−	0.281280i
$183$	2588.44	+	2432.52i	1.04559	+	0.982606i
$184$	2455.21	−	4252.56i	0.983700	−	1.70382i
$185$		0			0
$186$	21.3505	+	70.8117i	0.00841665	+	0.0279149i
$187$	−119.377	+	68.9221i	−0.0466828	+	0.0269523i
$188$			993.760i			0.385518i
$189$	−173.629	+	1019.62i	−0.0668235	+	0.392417i
$190$		0			0
$191$	−678.644	−	1175.45i	−0.257094	−	0.445300i	0.708368	−	0.705843i	$-0.249432\pi$
$191$	−678.644	−	1175.45i	−0.257094	−	0.445300i	−0.965462	+	0.260543i	$0.916098\pi$
$192$	−2788.11	+	840.648i	−1.04799	+	0.315982i
$193$	1561.48	+	901.520i	0.582371	+	0.336232i	0.762075	−	0.647488i	$-0.224181\pi$
$193$	1561.48	+	901.520i	0.582371	+	0.336232i	−0.179704	+	0.983721i	$0.557514\pi$
$194$	−165.148	+	286.044i	−0.0611181	+	0.105860i
$195$		0			0
$196$	−342.379	−	593.018i	−0.124774	−	0.216114i
$197$			263.403i			0.0952624i	0.998865	+	0.0476312i	$0.0151672\pi$
$197$			263.403i			0.0952624i	−0.998865	+	0.0476312i	$0.984833\pi$
$198$	−264.573	+	16.4476i	−0.0949614	+	0.00590344i
$199$	−492.853			−0.175565			−0.0877824	−	0.996140i	$-0.527978\pi$
$199$	−492.853			−0.175565			−0.0877824	+	0.996140i	$0.527978\pi$
$200$		0			0
$201$	1140.67	+	267.991i	0.400283	+	0.0940429i
$202$	4050.86	+	2338.77i	1.41098	+	0.814629i
$203$	−322.300	−	186.080i	−0.111434	−	0.0643363i
$204$	−399.684	−	93.9022i	−0.137174	−	0.0322278i
$205$		0			0
$206$	4300.25			1.45443
$207$	5377.80	−	334.320i	1.80572	−	0.112255i
$208$			3111.27i			1.03715i
$209$	−184.803	−	320.088i	−0.0611630	−	0.105937i
$210$		0			0
$211$	500.772	−	867.362i	0.163387	−	0.282994i	−0.772695	−	0.634778i	$-0.781092\pi$
$211$	500.772	−	867.362i	0.163387	−	0.282994i	0.936081	+	0.351784i	$0.114425\pi$
$212$	−820.197	−	473.541i	−0.265714	−	0.153410i
$213$	2551.90	−	769.426i	0.820907	−	0.247513i
$214$	−307.468	−	532.551i	−0.0982155	−	0.170114i
$215$		0			0
$216$	−2657.44	−	2203.44i	−0.837112	−	0.694097i
$217$			44.2337i			0.0138377i
$218$	1593.35	−	919.919i	0.495023	−	0.285802i
$219$	−1491.48	−	4946.67i	−0.460204	−	1.52632i
$220$		0			0
$221$	−1315.27	+	2278.11i	−0.400336	+	0.693403i
$222$	−2607.46	−	2450.40i	−0.788294	−	0.740810i
$223$	485.969	−	280.574i	0.145932	−	0.0842540i	−0.425256	−	0.905073i	$-0.639816\pi$
$223$	485.969	−	280.574i	0.145932	−	0.0842540i	0.571188	+	0.820819i	$0.306483\pi$
$224$	−762.250			−0.227366
$225$		0			0
$226$	−510.646			−0.150300
$227$	3383.09	−	1953.23i	0.989180	−	0.571103i	0.0841506	−	0.996453i	$-0.473182\pi$
$227$	3383.09	−	1953.23i	0.989180	−	0.571103i	0.905029	+	0.425350i	$0.139849\pi$
$228$	251.783	−	1071.68i	0.0731347	−	0.311290i
$229$	1498.45	−	2595.40i	0.432405	−	0.748947i	−0.564675	−	0.825313i	$-0.690999\pi$
$229$	1498.45	−	2595.40i	0.432405	−	0.748947i	0.997080	+	0.0763664i	$0.0243319\pi$
$230$		0			0
$231$	−154.337	−	36.2601i	−0.0439594	−	0.0103279i
$232$	1075.72	−	621.067i	0.304416	−	0.175755i
$233$			4194.30i			1.17930i	0.807658	+	0.589651i	$0.200735\pi$
$233$			4194.30i			1.17930i	−0.807658	+	0.589651i	$0.799265\pi$
$234$	−4215.57	+	2796.29i	−1.17769	+	0.781194i
$235$		0			0
$236$	116.529	+	201.833i	0.0321414	+	0.0556705i
$237$	−763.763	−	717.757i	−0.209332	−	0.196723i
$238$	504.469	+	291.255i	0.137394	+	0.0793247i
$239$	−83.2362	+	144.169i	−0.0225276	+	0.0390190i	−0.877069	−	0.480364i	$-0.840505\pi$
$239$	−83.2362	+	144.169i	−0.0225276	+	0.0390190i	0.854542	+	0.519383i	$0.173838\pi$
$240$		0			0
$241$	−307.272	−	532.210i	−0.0821291	−	0.142252i	0.822035	−	0.569437i	$-0.192839\pi$
$241$	−307.272	−	532.210i	−0.0821291	−	0.142252i	−0.904164	+	0.427185i	$0.859505\pi$
$242$			3116.87i			0.827935i
$243$	402.970	−	3766.50i	0.106381	−	0.994325i
$244$	−1621.68			−0.425481
$245$		0			0
$246$	189.795	+	629.479i	0.0491906	+	0.163147i
$247$	−6108.35	−	3526.66i	−1.57354	−	0.908485i
$248$	−127.856	−	73.8179i	−0.0327374	−	0.0189010i
$249$	3941.46	−	4194.10i	1.00313	−	1.06743i
$250$		0			0
$251$	−6136.16			−1.54307			−0.771536	−	0.636185i	$-0.780511\pi$
$251$	−6136.16			−1.54307			−0.771536	+	0.636185i	$0.780511\pi$
$252$	−261.022	−	393.505i	−0.0652493	−	0.0983671i
$253$			825.908i			0.205235i
$254$	2876.11	+	4981.57i	0.710485	+	1.23060i
$255$		0			0
$256$	1645.87	−	2850.73i	0.401824	−	0.695979i
$257$	4720.19	+	2725.20i	1.14567	+	0.661453i	0.947828	−	0.318781i	$-0.103273\pi$
$257$	4720.19	+	2725.20i	1.14567	+	0.661453i	0.197842	+	0.980234i	$0.436607\pi$
$258$	841.244	−	3580.66i	0.202998	−	0.864040i
$259$	−1070.00	−	1853.30i	−0.256705	−	0.444627i
$260$		0			0
$261$	1220.39	+	606.942i	0.289427	+	0.143942i
$262$		−	617.967i		−	0.145718i
$263$	−678.305	+	391.620i	−0.159035	+	0.0918186i	−0.577405	−	0.816458i	$-0.695935\pi$
$263$	−678.305	+	391.620i	−0.159035	+	0.0918186i	0.418371	+	0.908276i	$0.362601\pi$
$264$	362.369	−	385.596i	0.0844782	−	0.0898930i
$265$		0			0
$266$	−780.951	+	1352.65i	−0.180012	+	0.311790i
$267$	−1852.01	+	558.403i	−0.424499	+	0.127991i
$268$	−463.279	+	267.474i	−0.105594	+	0.0609649i
$269$	−141.019			−0.0319632			−0.0159816	−	0.999872i	$-0.505087\pi$
$269$	−141.019			−0.0319632			−0.0159816	+	0.999872i	$0.505087\pi$
$270$		0			0
$271$	6375.83			1.42917			0.714583	−	0.699551i	$-0.246616\pi$
$271$	6375.83			1.42917			0.714583	+	0.699551i	$0.246616\pi$
$272$	−1136.31	+	656.049i	−0.253305	+	0.146246i
$273$	−2896.66	+	873.375i	−0.642174	+	0.193623i
$274$	−479.958	+	831.312i	−0.105822	+	0.183290i
$275$		0			0
$276$	−1684.62	+	1792.60i	−0.367400	+	0.390949i
$277$	−5909.04	+	3411.59i	−1.28173	+	0.740008i	−0.977165	−	0.212482i	$-0.931845\pi$
$277$	−5909.04	+	3411.59i	−1.28173	+	0.740008i	−0.304567	+	0.952491i	$0.598512\pi$
$278$		−	4193.44i		−	0.904697i
$279$	−10.0516	−	161.688i	−0.00215689	−	0.0346953i
$280$		0			0
$281$	−294.846	−	510.689i	−0.0625945	−	0.108417i	0.833030	−	0.553228i	$-0.186604\pi$
$281$	−294.846	−	510.689i	−0.0625945	−	0.108417i	−0.895624	+	0.444811i	$0.853271\pi$
$282$	−1181.02	+	5026.86i	−0.249392	+	1.06151i
$283$	5175.39	+	2988.01i	1.08709	+	0.627629i	0.932799	−	0.360397i	$-0.117359\pi$
$283$	5175.39	+	2988.01i	1.08709	+	0.627629i	0.154286	+	0.988026i	$0.450692\pi$
$284$	−608.432	+	1053.84i	−0.127126	+	0.220189i
$285$		0			0
$286$	−387.701	−	671.517i	−0.0801581	−	0.138838i
$287$			393.214i			0.0808736i
$288$	2786.26	−	173.212i	0.570076	−	0.0354397i
$289$	3803.64			0.774199
$290$		0			0
$291$	495.443	−	527.200i	0.0998055	−	0.106203i
$292$	2042.78	+	1179.40i	0.409400	+	0.236367i
$293$	−6977.99	−	4028.74i	−1.39133	−	0.803282i	−0.397864	−	0.917445i	$-0.630248\pi$
$293$	−6977.99	−	4028.74i	−1.39133	−	0.803282i	−0.993462	+	0.114162i	$0.963582\pi$
$294$	−1027.14	−	3406.63i	−0.203755	−	0.675777i
$295$		0			0
$296$	7142.55			1.40254
$297$	572.389	+	97.4705i	0.111830	+	0.0190431i
$298$			4556.41i			0.885724i
$299$	7880.55	+	13649.5i	1.52423	+	2.64004i
$300$		0			0
$301$	1099.90	−	1905.09i	0.210622	−	0.364808i
$302$	−5186.59	−	2994.48i	−0.988261	−	0.570573i
$303$	−7466.02	−	7016.30i	−1.41555	−	1.33028i
$304$	−1759.08	−	3046.82i	−0.331876	−	0.574826i
$305$		0			0
$306$	−1910.18	−	949.994i	−0.356855	−	0.177476i
$307$			4546.58i			0.845235i	0.906308	+	0.422618i	$0.138889\pi$
$307$			4546.58i			0.845235i	−0.906308	+	0.422618i	$0.861111\pi$
$308$	62.6832	−	36.1902i	0.0115965	−	0.00669522i
$309$	−9169.43	−	2154.28i	−1.68813	−	0.396610i
$310$		0			0
$311$	2101.40	−	3639.73i	0.383149	−	0.663633i	−0.608362	−	0.793660i	$-0.708173\pi$
$311$	2101.40	−	3639.73i	0.383149	−	0.663633i	0.991510	+	0.130027i	$0.0415063\pi$
$312$	2309.52	−	9830.22i	0.419073	−	1.78374i
$313$	−6039.04	+	3486.64i	−1.09056	+	0.629637i	−0.933727	−	0.357987i	$-0.883463\pi$
$313$	−6039.04	+	3486.64i	−1.09056	+	0.629637i	−0.156838	+	0.987624i	$0.550130\pi$
$314$	−4608.63			−0.828281
$315$		0			0
$316$	478.505			0.0851835
$317$	6373.97	−	3680.02i	1.12933	−	0.652020i	0.185565	−	0.982632i	$-0.440589\pi$
$317$	6373.97	−	3680.02i	1.12933	−	0.652020i	0.943767	+	0.330612i	$0.107255\pi$
$318$	−3586.13	−	3370.12i	−0.632391	−	0.594298i
$319$	−104.460	+	180.930i	−0.0183343	+	0.0317560i
$320$		0			0
$321$	388.826	+	1289.59i	0.0676080	+	0.224230i
$322$	3022.58	−	1745.09i	0.523111	−	0.302018i
$323$		−	2974.55i		−	0.512410i
$324$	1043.54	+	1379.07i	0.178933	+	0.236466i
$325$		0			0
$326$	1246.88	+	2159.66i	0.211835	+	0.366909i
$327$	−3858.34	+	1163.33i	−0.652498	+	0.196736i
$328$	−1136.58	−	656.203i	−0.191332	−	0.110466i
$329$	−1544.14	+	2674.53i	−0.258758	+	0.448182i
$330$		0			0
$331$	3417.06	+	5918.52i	0.567428	+	0.982814i	0.996819	+	0.0796957i	$0.0253949\pi$
$331$	3417.06	+	5918.52i	0.567428	+	0.982814i	−0.429391	+	0.903119i	$0.641272\pi$
$332$			2627.64i			0.434369i
$333$	4332.33	+	6531.24i	0.712944	+	1.07480i
$334$	6681.39			1.09458
$335$		0			0
$336$	−1469.09	−	345.149i	−0.238528	−	0.0560399i
$337$	−6000.24	−	3464.24i	−0.969893	−	0.559968i	−0.0706891	−	0.997498i	$-0.522520\pi$
$337$	−6000.24	−	3464.24i	−0.969893	−	0.559968i	−0.899204	+	0.437531i	$0.855853\pi$
$338$	−8301.16	−	4792.68i	−1.33587	−	0.771264i
$339$	1088.85	+	255.816i	0.174449	+	0.0409853i
$340$		0			0
$341$	24.8316			0.00394341
$342$	2547.24	−	5121.81i	0.402746	−	0.809812i
$343$		−	4656.70i		−	0.733055i
$344$	3671.07	+	6358.48i	0.575380	+	0.996588i
$345$		0			0
$346$	1710.95	−	2963.45i	0.265842	−	0.460451i
$347$	−6530.35	−	3770.30i	−1.01028	−	0.583286i	−0.0990071	−	0.995087i	$-0.531567\pi$
$347$	−6530.35	−	3770.30i	−1.01028	−	0.583286i	−0.911274	+	0.411801i	$0.864900\pi$
$348$	−595.775	+	179.633i	−0.0917726	+	0.0276705i
$349$	−922.084	−	1597.10i	−0.141427	−	0.244959i	0.786607	−	0.617454i	$-0.211836\pi$
$349$	−922.084	−	1597.10i	−0.141427	−	0.244959i	−0.928034	+	0.372495i	$0.878502\pi$
$350$		0			0
$351$	10389.7	−	3850.69i	1.57995	−	0.585568i
$352$			427.906i			0.0647939i
$353$	−6146.61	+	3548.74i	−0.926773	+	0.535073i	−0.885789	−	0.464087i	$-0.846382\pi$
$353$	−6146.61	+	3548.74i	−0.926773	+	0.535073i	−0.0409833	+	0.999160i	$0.513049\pi$
$354$	349.586	+	1159.44i	0.0524866	+	0.174079i
$355$		0			0
$356$	441.563	−	764.809i	0.0657382	−	0.113862i
$357$	−929.772	−	873.766i	−0.137840	−	0.129537i
$358$	3153.37	−	1820.60i	0.465532	−	0.268775i
$359$	−7709.65			−1.13342			−0.566712	−	0.823916i	$-0.691785\pi$
$359$	−7709.65			−1.13342			−0.566712	+	0.823916i	$0.691785\pi$
$360$		0			0
$361$	1116.75			0.162815
$362$	7499.65	−	4329.92i	1.08888	−	0.628662i
$363$	1561.45	−	6646.12i	0.225770	−	0.960966i
$364$	690.630	−	1196.21i	0.0994474	−	0.172248i
$365$		0			0
$366$	−8203.14	−	1927.25i	−1.17154	−	0.275244i
$367$	4552.17	−	2628.19i	0.647469	−	0.373816i	−0.140017	−	0.990149i	$-0.544716\pi$
$367$	4552.17	−	2628.19i	0.647469	−	0.373816i	0.787486	+	0.616333i	$0.211382\pi$
$368$			7861.57i			1.11362i
$369$	−89.3535	−	1437.32i	−0.0126058	−	0.202775i
$370$		0			0
$371$	−1471.61	−	2548.91i	−0.205936	−	0.356692i
$372$	53.8960	+	50.6495i	0.00751176	+	0.00705928i
$373$	−862.955	−	498.227i	−0.119791	−	0.0691615i	0.438907	−	0.898532i	$-0.355366\pi$
$373$	−862.955	−	498.227i	−0.119791	−	0.0691615i	−0.558698	+	0.829371i	$0.688699\pi$
$374$	163.503	−	283.195i	0.0226057	−	0.0391542i
$375$		0			0
$376$	−5153.78	−	8926.61i	−0.706878	−	1.22435i
$377$			3986.90i			0.544658i
$378$	−852.705	−	2300.72i	−0.116028	−	0.313059i
$379$	2735.20			0.370707			0.185354	−	0.982672i	$-0.440657\pi$
$379$	2735.20			0.370707			0.185354	+	0.982672i	$0.440657\pi$
$380$		0			0
$381$	−3637.14	−	12063.0i	−0.489072	−	1.62207i
$382$	2788.49	+	1609.93i	0.373485	+	0.215632i
$383$	7741.80	+	4469.73i	1.03287	+	0.596325i	0.917804	−	0.397033i	$-0.129960\pi$
$383$	7741.80	+	4469.73i	1.03287	+	0.596325i	0.115062	+	0.993358i	$0.463293\pi$
$384$	1787.57	−	1902.15i	0.237557	−	0.252783i
$385$		0			0
$386$	−4277.32			−0.564015
$387$	−3587.57	+	7213.62i	−0.471232	+	0.947517i
$388$			330.295i			0.0432170i
$389$	−5566.93	−	9642.21i	−0.725590	−	1.25676i	−0.958731	−	0.284316i	$-0.908233\pi$
$389$	−5566.93	−	9642.21i	−0.725590	−	1.25676i	0.233140	−	0.972443i	$-0.425100\pi$
$390$		0			0
$391$	−3323.42	+	5756.33i	−0.429853	+	0.744527i
$392$	6150.95	+	3551.25i	0.792525	+	0.457564i
$393$	−309.580	+	1317.69i	−0.0397360	+	0.169132i
$394$	−312.433	−	541.150i	−0.0399496	−	0.0691948i
$395$		0			0
$396$	−220.903	+	146.530i	−0.0280323	+	0.0185945i
$397$			9479.40i			1.19838i	0.800606	+	0.599191i	$0.204511\pi$
$397$			9479.40i			1.19838i	−0.800606	+	0.599191i	$0.795489\pi$
$398$	1012.54	−	584.593i	0.127523	−	0.0736256i
$399$	2342.85	−	2493.02i	0.293958	−	0.312800i
$400$		0			0
$401$	−4713.80	+	8164.54i	−0.587022	+	1.01675i	0.407598	+	0.913162i	$0.366367\pi$
$401$	−4713.80	+	8164.54i	−0.587022	+	1.01675i	−0.994620	+	0.103591i	$0.966967\pi$
$402$	−2661.34	+	802.423i	−0.330188	+	0.0995553i
$403$	410.383	−	236.935i	0.0507261	−	0.0292868i
$404$	4677.53			0.576029
$405$		0			0
$406$	882.869			0.107921
$407$	−1040.39	+	600.670i	−0.126708	+	0.0731550i
$408$	4077.22	−	1229.33i	0.494736	−	0.149169i
$409$	204.093	−	353.500i	0.0246742	−	0.0427370i	−0.853425	−	0.521216i	$-0.825478\pi$
$409$	204.093	−	353.500i	0.0246742	−	0.0427370i	0.878099	+	0.478479i	$0.158812\pi$
$410$		0			0
$411$	1439.87	−	1532.17i	0.172807	−	0.183884i
$412$	3724.12	−	2150.12i	0.445326	−	0.257109i
$413$			724.266i			0.0862925i
$414$	−10651.9	+	7065.68i	−1.26452	+	0.838790i
$415$		0			0
$416$	4082.94	+	7071.86i	0.481208	+	0.833477i
$417$	−2100.77	+	8941.68i	−0.246703	+	1.05006i
$418$	759.338	+	438.404i	0.0888527	+	0.0512992i
$419$	4406.94	−	7633.05i	0.513826	−	0.889973i	−0.486045	−	0.873934i	$-0.661561\pi$
$419$	4406.94	−	7633.05i	0.513826	−	0.889973i	0.999871	−	0.0160393i	$-0.00510569\pi$
$420$		0			0
$421$	1174.68	+	2034.61i	0.135987	+	0.235537i	0.925974	−	0.377587i	$-0.123246\pi$
$421$	1174.68	+	2034.61i	0.135987	+	0.235537i	−0.789987	+	0.613124i	$0.789913\pi$
$422$			2375.94i			0.274074i
$423$	5036.56	−	10127.1i	0.578927	−	1.16406i
$424$	9823.40			1.12516
$425$		0			0
$426$	−4330.12	+	4607.66i	−0.492476	+	0.524042i
$427$	−4364.47	−	2519.83i	−0.494640	−	0.285581i
$428$	−532.551	−	307.468i	−0.0601444	−	0.0347244i
$429$	490.288	+	1626.10i	0.0551780	+	0.183005i
$430$		0			0
$431$	4481.16			0.500812			0.250406	−	0.968141i	$-0.419436\pi$
$431$	4481.16			0.500812			0.250406	+	0.968141i	$0.419436\pi$
$432$	5448.40	+	927.792i	0.606797	+	0.103330i
$433$			3422.69i			0.379871i	0.981797	+	0.189935i	$0.0608279\pi$
$433$			3422.69i			0.379871i	−0.981797	+	0.189935i	$0.939172\pi$
$434$	−52.4674	−	90.8762i	−0.00580303	−	0.0100511i
$435$		0			0
$436$	919.919	−	1593.35i	0.101046	−	0.175017i
$437$	−15434.6	−	8911.17i	−1.68956	−	0.975467i
$438$	8931.62	+	8393.61i	0.974359	+	0.915667i
$439$	−4064.59	−	7040.07i	−0.441896	−	0.765386i	0.555934	−	0.831226i	$-0.312361\pi$
$439$	−4064.59	−	7040.07i	−0.441896	−	0.765386i	−0.997830	+	0.0658402i	$0.979027\pi$
$440$		0			0
$441$	483.565	+	7778.52i	0.0522152	+	0.839922i
$442$		−	6240.36i		−	0.671547i
$443$	2035.83	−	1175.39i	0.218342	−	0.126060i	−0.386840	−	0.922147i	$-0.626434\pi$
$443$	2035.83	−	1175.39i	0.218342	−	0.126060i	0.605182	+	0.796087i	$0.293100\pi$
$444$	−3483.33	−	818.376i	−0.372323	−	0.0874739i
$445$		0			0
$446$	−665.601	+	1152.86i	−0.0706662	+	0.122397i
$447$	2282.60	−	9715.65i	0.241529	−	1.02804i
$448$	3578.12	−	2065.83i	0.377345	−	0.217860i
$449$	−4760.99			−0.500412			−0.250206	−	0.968193i	$-0.580498\pi$
$449$	−4760.99			−0.500412			−0.250206	+	0.968193i	$0.580498\pi$
$450$		0			0
$451$	220.740			0.0230471
$452$	−442.233	+	255.323i	−0.0460196	+	0.0265695i
$453$	9559.26	+	8983.44i	0.991464	+	0.931742i
$454$	−4633.61	+	8025.65i	−0.479000	+	0.829653i
$455$		0			0
$456$	3296.23	+	10932.4i	0.338509	+	1.12271i
$457$	−1930.44	+	1114.54i	−0.197598	+	0.114083i	−0.595535	−	0.803330i	$-0.703060\pi$
$457$	−1930.44	+	1114.54i	−0.197598	+	0.114083i	0.397937	+	0.917413i	$0.369726\pi$
$458$			7109.51i			0.725340i
$459$	3597.16	+	2982.61i	0.365797	+	0.303303i
$460$		0			0
$461$	−2868.31	−	4968.06i	−0.289784	−	0.501921i	0.683974	−	0.729507i	$-0.260250\pi$
$461$	−2868.31	−	4968.06i	−0.289784	−	0.501921i	−0.973758	+	0.227585i	$0.926917\pi$
$462$	360.088	−	108.571i	0.0362615	−	0.0109332i
$463$	3121.13	+	1801.99i	0.313286	+	0.180876i	0.648396	−	0.761303i	$-0.275440\pi$
$463$	3121.13	+	1801.99i	0.313286	+	0.180876i	−0.335110	+	0.942179i	$0.608773\pi$
$464$	−994.326	+	1722.22i	−0.0994836	+	0.172311i
$465$		0			0
$466$	−4975.03	−	8617.00i	−0.494557	−	0.856598i
$467$			3780.37i			0.374593i	0.982303	+	0.187296i	$0.0599725\pi$
$467$			3780.37i			0.374593i	−0.982303	+	0.187296i	$0.940028\pi$
$468$	−2252.64	+	4529.44i	−0.222497	+	0.447380i
$469$	−1662.45			−0.163677
$470$		0			0
$471$	9827.00	+	2308.76i	0.961368	+	0.225865i
$472$	−2093.47	−	1208.67i	−0.204152	−	0.117867i
$473$	−1069.46	−	617.454i	−0.103962	−	0.0600224i
$474$	2420.48	+	568.670i	0.234549	+	0.0551052i
$475$		0			0
$476$	582.511			0.0560911
$477$	5958.40	+	8982.63i	0.571943	+	0.862236i
$478$		−	394.920i		−	0.0377891i
$479$	−7230.58	−	12523.7i	−0.689715	−	1.19462i	−0.971930	−	0.235271i	$-0.924402\pi$
$479$	−7230.58	−	12523.7i	−0.689715	−	1.19462i	0.282215	−	0.959351i	$-0.408931\pi$
$480$		0			0
$481$	−11462.8	+	19854.1i	−1.08661	+	1.88206i
$482$	1262.55	+	728.935i	0.119311	+	0.0688840i
$483$	−7319.28	+	2206.85i	−0.689521	+	0.207898i
$484$	1558.44	+	2699.29i	0.146360	+	0.253502i
$485$		0			0
$486$	3639.71	+	8216.09i	0.339714	+	0.766850i
$487$		−	3581.74i		−	0.333273i	−0.986018	−	0.166636i	$-0.946709\pi$
$487$		−	3581.74i		−	0.333273i	0.986018	−	0.166636i	$-0.0532906\pi$
$488$	14567.0	−	8410.26i	1.35126	−	0.780153i
$489$	−1576.81	−	5229.69i	−0.145820	−	0.483629i
$490$		0			0
$491$	3507.69	−	6075.50i	0.322403	−	0.558419i	−0.658580	−	0.752511i	$-0.728843\pi$
$491$	3507.69	−	6075.50i	0.322403	−	0.558419i	0.980983	+	0.194092i	$0.0621760\pi$
$492$	479.107	+	450.247i	0.0439021	+	0.0412576i
$493$	−1456.11	+	840.687i	−0.133022	+	0.0768005i
$494$	16732.4			1.52394
$495$		0			0
$496$	236.364			0.0213973
$497$	−3274.98	+	1890.81i	−0.295579	+	0.170653i
$498$	−3122.77	+	13291.7i	−0.280993	+	1.19602i
$499$	1259.90	−	2182.21i	0.113028	−	0.195769i	−0.803962	−	0.594681i	$-0.797279\pi$
$499$	1259.90	−	2182.21i	0.113028	−	0.195769i	0.916990	+	0.398911i	$0.130612\pi$
$500$		0			0
$501$	−14246.8	−	3347.15i	−1.27046	−	0.298482i
$502$	12606.5	−	7278.35i	1.12083	−	0.647109i
$503$		−	4989.32i		−	0.442272i	−0.975243	−	0.221136i	$-0.929024\pi$
$503$		−	4989.32i		−	0.442272i	0.975243	−	0.221136i	$-0.0709764\pi$
$504$	4385.44	+	2181.03i	0.387586	+	0.192759i
$505$		0			0
$506$	−979.643	−	1696.79i	−0.0860681	−	0.149074i
$507$	15299.6	+	14378.0i	1.34020	+	1.25947i
$508$	4981.57	+	2876.11i	0.435081	+	0.251194i
$509$	2359.76	−	4087.22i	0.205490	−	0.355919i	−0.744799	−	0.667289i	$-0.767454\pi$
$509$	2359.76	−	4087.22i	0.205490	−	0.355919i	0.950289	+	0.311370i	$0.100788\pi$
$510$		0			0
$511$	3665.19	+	6348.30i	0.317297	+	0.549574i
$512$			11827.7i			1.02093i
$513$	−7997.34	+	9645.16i	−0.688287	+	0.830106i
$514$	−12929.9			−1.10956
$515$		0			0
$516$	−1061.79	−	3521.57i	−0.0905868	−	0.300442i
$517$	1501.41	+	866.839i	0.127721	+	0.0737399i
$518$	4396.55	+	2538.35i	0.372921	+	0.215306i
$519$	−5132.85	+	5461.85i	−0.434117	+	0.461943i
$520$		0			0
$521$	−10711.0			−0.900682			−0.450341	−	0.892857i	$-0.648698\pi$
$521$	−10711.0			−0.900682			−0.450341	+	0.892857i	$0.648698\pi$
$522$	−3227.16	+	200.622i	−0.270592	+	0.0168218i
$523$		−	10566.4i		−	0.883433i	−0.897155	−	0.441717i	$-0.854370\pi$
$523$		−	10566.4i		−	0.883433i	0.897155	−	0.441717i	$-0.145630\pi$
$524$	−308.983	−	535.175i	−0.0257595	−	0.0446168i
$525$		0			0
$526$	929.032	−	1609.13i	0.0770109	−	0.133387i
$527$	173.068	+	99.9211i	0.0143055	+	0.00825926i
$528$	−193.757	+	824.704i	−0.0159700	+	0.0679747i
$529$	13829.1	+	23952.7i	1.13661	+	1.96866i
$530$		0			0
$531$	−164.581	−	2647.42i	−0.0134505	−	0.216362i
$532$			1561.90i			0.127288i
$533$	3648.09	−	2106.23i	0.296466	−	0.171165i
$534$	3142.53	−	3343.96i	0.254664	−	0.270988i
$535$		0			0
$536$	2774.32	−	4805.26i	0.223568	−	0.387231i
$537$	−7635.99	+	2302.34i	−0.613626	+	0.185015i
$538$	289.718	−	167.269i	0.0232168	−	0.0134042i
$539$	−1194.60			−0.0954642
$540$		0			0
$541$	−6595.81			−0.524170			−0.262085	−	0.965045i	$-0.584410\pi$
$541$	−6595.81			−0.524170			−0.262085	+	0.965045i	$0.584410\pi$
$542$	−13098.9	+	7562.63i	−1.03809	+	0.599341i
$543$	−18160.7	+	5475.65i	−1.43526	+	0.432749i
$544$	−1721.87	+	2982.37i	−0.135707	+	0.235052i
$545$		0			0
$546$	4915.11	−	5230.15i	0.385251	−	0.409945i
$547$	5532.85	−	3194.39i	0.432482	−	0.249693i	−0.267922	−	0.963441i	$-0.586337\pi$
$547$	5532.85	−	3194.39i	0.432482	−	0.249693i	0.700403	+	0.713747i	$0.253003\pi$
$548$			959.916i			0.0748277i
$549$	16526.1	+	8218.97i	1.28473	+	0.638939i
$550$		0			0
$551$	−2254.16	−	3904.31i	−0.174284	−	0.301868i
$552$	5835.70	−	24839.0i	0.449971	−	1.91525i
$553$	1287.81	+	743.519i	0.0990296	+	0.0571748i
$554$	8093.24	−	14017.9i	0.620666	−	1.07502i
$555$		0			0
$556$	−2096.72	−	3631.62i	−0.159929	−	0.277006i
$557$		−	15992.4i		−	1.21655i	−0.793726	−	0.608276i	$-0.791862\pi$
$557$		−	15992.4i		−	1.21655i	0.793726	−	0.608276i	$-0.208138\pi$
$558$	212.435	+	320.258i	0.0161167	+	0.0242968i
$559$	−23566.2			−1.78308
$560$		0			0
$561$	−490.508	+	521.948i	−0.0369149	+	0.0392811i
$562$	1211.50	+	699.459i	0.0909323	+	0.0524998i
$563$	5500.23	+	3175.56i	0.411736	+	0.237716i	0.691535	−	0.722343i	$-0.256935\pi$
$563$	5500.23	+	3175.56i	0.411736	+	0.237716i	−0.279800	+	0.960058i	$0.590268\pi$
$564$	1490.64	+	4943.89i	0.111290	+	0.369106i
$565$		0			0
$566$	−14176.8			−1.05282
$567$	665.644	+	5333.01i	0.0493023	+	0.395001i
$568$		−	12621.7i		−	0.932382i
$569$	4810.21	+	8331.53i	0.354402	+	0.613842i	0.987015	−	0.160626i	$-0.0513512\pi$
$569$	4810.21	+	8331.53i	0.354402	+	0.613842i	−0.632614	+	0.774468i	$0.718018\pi$
$570$		0			0
$571$	2532.30	−	4386.08i	0.185593	−	0.321456i	−0.758183	−	0.652042i	$-0.773913\pi$
$571$	2532.30	−	4386.08i	0.185593	−	0.321456i	0.943776	+	0.330585i	$0.107246\pi$
$572$	−671.517	−	387.701i	−0.0490866	−	0.0283402i
$573$	−5139.38	−	4829.80i	−0.374696	−	0.352125i
$574$	−466.408	−	807.842i	−0.0339155	−	0.0587433i
$575$		0			0
$576$	−12609.7	+	8364.34i	−0.912161	+	0.605059i
$577$		−	11355.1i		−	0.819273i	−0.912249	−	0.409637i	$-0.865655\pi$
$577$		−	11355.1i		−	0.819273i	0.912249	−	0.409637i	$-0.134345\pi$
$578$	−7814.41	+	4511.65i	−0.562347	+	0.324671i
$579$	9120.54	+	2142.79i	0.654640	+	0.153802i
$580$		0			0
$581$	−4082.93	+	7071.84i	−0.291546	+	0.504973i
$582$	−392.533	+	1670.77i	−0.0279571	+	0.118996i
$583$	−1430.88	+	826.121i	−0.101649	+	0.0586869i
$584$	−24466.2			−1.73359
$585$		0			0
$586$	19114.6			1.34747
$587$	8687.96	−	5016.00i	0.610887	−	0.352696i	−0.162426	−	0.986721i	$-0.551932\pi$
$587$	8687.96	−	5016.00i	0.610887	−	0.352696i	0.773312	+	0.634025i	$0.218598\pi$
$588$	−2592.84	−	2436.66i	−0.181848	−	0.170895i
$589$	−267.921	+	464.053i	−0.0187428	+	0.0324634i
$590$		0			0
$591$	395.105	+	1310.41i	0.0274999	+	0.0912068i
$592$	−9903.16	+	5717.59i	−0.687530	+	0.396945i
$593$		−	1325.12i		−	0.0917643i	−0.998947	−	0.0458821i	$-0.985390\pi$
$593$		−	1325.12i		−	0.0917643i	0.998947	−	0.0458821i	$-0.0146099\pi$
$594$	−1291.56	+	478.685i	−0.0892145	+	0.0330651i
$595$		0			0
$596$	2278.21	+	3945.97i	0.156575	+	0.271197i
$597$	−2451.91	+	739.279i	−0.168091	+	0.0506812i
$598$	−32380.5	−	18694.9i	−2.21427	−	1.27841i
$599$	8285.78	−	14351.4i	0.565188	−	0.978935i	−0.431844	−	0.901948i	$-0.642137\pi$
$599$	8285.78	−	14351.4i	0.565188	−	0.978935i	0.997032	−	0.0769865i	$-0.0245298\pi$
$600$		0			0
$601$	−8604.49	−	14903.4i	−0.584001	−	1.01152i	−0.994999	−	0.0998833i	$-0.968153\pi$
$601$	−8604.49	−	14903.4i	−0.584001	−	1.01152i	0.410998	−	0.911636i	$-0.365180\pi$
$602$			5218.55i			0.353310i
$603$	6076.76	−	377.772i	0.410390	−	0.0255126i
$604$	−5988.96			−0.403456
$605$		0			0
$606$	23660.9	+	5558.92i	1.58607	+	0.372633i
$607$	3618.24	+	2088.99i	0.241944	+	0.139686i	0.616070	−	0.787692i	$-0.288724\pi$
$607$	3618.24	+	2088.99i	0.241944	+	0.139686i	−0.374126	+	0.927378i	$0.622057\pi$
$608$	−7996.72	−	4616.91i	−0.533404	−	0.307961i
$609$	−1882.54	−	442.287i	−0.125262	−	0.0294292i
$610$		0			0
$611$	33084.4			2.19059
$612$	−2129.26	+	132.369i	−0.140638	+	0.00874297i
$613$			14944.2i			0.984649i	0.870412	+	0.492324i	$0.163853\pi$
$613$			14944.2i			0.984649i	−0.870412	+	0.492324i	$0.836147\pi$
$614$	−5392.89	−	9340.75i	−0.354461	−	0.613945i
$615$		0			0
$616$	−375.375	+	650.168i	−0.0245524	+	0.0425260i
$617$	17756.0	+	10251.4i	1.15856	+	0.668893i	0.950958	−	0.309320i	$-0.100102\pi$
$617$	17756.0	+	10251.4i	1.15856	+	0.668893i	0.207600	+	0.978214i	$0.433435\pi$
$618$	21393.5	−	6450.37i	1.39251	−	0.419858i
$619$	1364.26	+	2362.97i	0.0885854	+	0.153434i	0.906913	−	0.421317i	$-0.138432\pi$
$619$	1364.26	+	2362.97i	0.0885854	+	0.153434i	−0.818328	+	0.574751i	$0.805099\pi$
$620$		0			0
$621$	26252.8	−	9729.93i	1.69644	−	0.628742i
$622$			9970.21i			0.642715i
$623$	2376.78	−	1372.23i	0.152847	−	0.0882463i
$624$	4666.91	+	15478.4i	0.299400	+	0.992999i
$625$		0			0
$626$	8271.29	−	14326.3i	0.528095	−	0.914687i
$627$	−1399.51	−	1315.21i	−0.0891407	−	0.0837712i
$628$	−3991.19	+	2304.32i	−0.253608	+	0.146421i
$629$	−9668.27			−0.612876
$630$		0			0
$631$	−3393.08			−0.214067			−0.107034	−	0.994255i	$-0.534135\pi$
$631$	−3393.08			−0.214067			−0.107034	+	0.994255i	$0.534135\pi$
$632$	−4298.25	+	2481.59i	−0.270530	+	0.156191i
$633$	1190.27	−	5066.23i	0.0747374	−	0.318112i
$634$	−8730.03	+	15120.9i	−0.546867	+	0.947202i
$635$		0			0
$636$	−4790.74	−	1125.54i	−0.298687	−	0.0701739i
$637$	−19742.8	+	11398.5i	−1.22800	+	0.708988i
$638$		−	495.618i		−	0.0307550i
$639$	11541.4	−	7655.70i	0.714508	−	0.473951i
$640$		0			0
$641$	−6780.88	−	11744.8i	−0.417830	−	0.723702i	0.577891	−	0.816114i	$-0.303876\pi$
$641$	−6780.88	−	11744.8i	−0.417830	−	0.723702i	−0.995721	+	0.0924116i	$0.970542\pi$
$642$	−2328.46	−	2188.20i	−0.143142	−	0.134520i
$643$	−11229.7	−	6483.44i	−0.688731	−	0.397639i	0.114405	−	0.993434i	$-0.463504\pi$
$643$	−11229.7	−	6483.44i	−0.688731	−	0.397639i	−0.803137	+	0.595795i	$0.796837\pi$
$644$	1745.09	−	3022.58i	0.106780	−	0.184948i
$645$		0			0
$646$	3528.24	+	6111.09i	0.214886	+	0.372194i
$647$		−	25837.9i		−	1.57000i	−0.619495	−	0.785001i	$-0.712663\pi$
$647$		−	25837.9i		−	1.57000i	0.619495	−	0.785001i	$-0.287337\pi$
$648$	−16525.8	−	6975.79i	−1.00184	−	0.422894i
$649$	406.583			0.0245913
$650$		0			0
$651$	66.3505	+	220.060i	0.00399460	+	0.0132486i
$652$	2159.66	+	1246.88i	0.129722	+	0.0748950i
$653$	24479.8	+	14133.4i	1.46703	+	0.846989i	0.999319	−	0.0368938i	$-0.0117463\pi$
$653$	24479.8	+	14133.4i	1.46703	+	0.846989i	0.467709	+	0.883883i	$0.345080\pi$
$654$	6546.92	−	6966.56i	0.391445	−	0.416535i
$655$		0			0
$656$	2101.15			0.125055
$657$	−14840.0	−	22372.1i	−0.881223	−	1.32849i
$658$		−	7326.28i		−	0.434055i
$659$	−7978.92	−	13819.9i	−0.471646	−	0.816914i	0.527828	−	0.849351i	$-0.323007\pi$
$659$	−7978.92	−	13819.9i	−0.471646	−	0.816914i	−0.999474	+	0.0324369i	$0.989673\pi$
$660$		0			0
$661$	−12028.9	+	20834.6i	−0.707821	+	1.22598i	0.257843	+	0.966187i	$0.416988\pi$
$661$	−12028.9	+	20834.6i	−0.707821	+	1.22598i	−0.965664	+	0.259795i	$0.916345\pi$
$662$	−14040.4	−	8106.23i	−0.824314	−	0.475918i
$663$	−3126.20	+	13306.3i	−0.183125	+	0.779450i
$664$	−13627.3	−	23603.2i	−0.796450	−	1.37949i
$665$		0			0
$666$	−16647.6	−	8279.38i	−0.968588	−	0.481711i
$667$			10074.1i			0.584815i
$668$	5786.26	−	3340.70i	0.335145	−	0.193496i
$669$	1996.80	−	2124.79i	0.115397	−	0.122794i
$670$		0			0
$671$	−1414.56	+	2450.09i	−0.0813838	+	0.140961i
$672$	−3792.15	+	1143.37i	−0.217686	+	0.0656349i
$673$	1085.16	−	626.519i	0.0621545	−	0.0358849i	−0.468601	−	0.883410i	$-0.655242\pi$
$673$	1085.16	−	626.519i	0.0621545	−	0.0358849i	0.530755	+	0.847525i	$0.321908\pi$
$674$	16436.3			0.939321
$675$		0			0
$676$	−9585.35			−0.545366
$677$	−762.733	+	440.364i	−0.0433002	+	0.0249994i	−0.521494	−	0.853255i	$-0.674625\pi$
$677$	−762.733	+	440.364i	−0.0433002	+	0.0249994i	0.478194	+	0.878254i	$0.341292\pi$
$678$	−2540.43	+	765.970i	−0.143901	+	0.0433877i
$679$	−513.226	+	888.933i	−0.0290071	+	0.0502417i
$680$		0			0
$681$	13900.8	−	14791.8i	0.782204	−	0.832341i
$682$	−51.0153	+	29.4537i	−0.00286434	+	0.00165373i
$683$		−	26686.4i		−	1.49506i	−0.664227	−	0.747531i	$-0.731239\pi$
$683$		−	26686.4i		−	1.49506i	0.664227	−	0.747531i	$-0.268761\pi$
$684$	−354.924	−	5709.24i	−0.0198404	−	0.319149i
$685$		0			0
$686$	5523.50	+	9566.98i	0.307417	+	0.532462i
$687$	3561.62	−	15159.6i	0.197794	−	0.841886i
$688$	−10179.9	−	5877.36i	−0.564106	−	0.325687i
$689$	−15765.2	+	27306.1i	−0.871706	+	1.50984i
$690$		0			0
$691$	85.7060	+	148.447i	0.00471839	+	0.00817249i	0.868375	−	0.495908i	$-0.165165\pi$
$691$	85.7060	+	148.447i	0.00471839	+	0.00817249i	−0.863657	+	0.504081i	$0.831831\pi$
$692$		−	3421.90i		−	0.187978i
$693$	−822.206	+	51.1138i	−0.0450693	+	0.00280181i
$694$	17888.4			0.978437
$695$		0			0
$696$	4420.04	−	4703.35i	0.240720	−	0.256150i
$697$	1538.49	+	888.247i	0.0836075	+	0.0482708i
$698$	3788.76	+	2187.44i	0.205454	+	0.118619i
$699$	6291.44	+	20866.4i	0.340435	+	1.12910i
$700$		0			0
$701$	−14229.6			−0.766684			−0.383342	−	0.923607i	$-0.625227\pi$
$701$	−14229.6			−0.766684			−0.383342	+	0.923607i	$0.625227\pi$
$702$	−16777.8	+	20234.7i	−0.902045	+	1.08791i
$703$		−	25923.8i		−	1.39080i
$704$	−1159.70	−	2008.66i	−0.0620850	−	0.107534i
$705$		0			0
$706$	8418.62	−	14581.5i	0.448780	−	0.777310i
$707$	12588.8	+	7268.13i	0.669659	+	0.386628i
$708$	882.472	+	829.316i	0.0468437	+	0.0440220i
$709$	−3887.04	−	6732.55i	−0.205897	−	0.356624i	0.744521	−	0.667599i	$-0.232678\pi$
$709$	−3887.04	−	6732.55i	−0.205897	−	0.356624i	−0.950418	+	0.310975i	$0.899344\pi$
$710$		0			0
$711$	−4876.31	−	2425.15i	−0.257210	−	0.127919i
$712$			9160.03i			0.482144i
$713$	1036.96	−	598.687i	0.0544661	−	0.0314460i
$714$	2946.59	+	692.274i	0.154444	+	0.0362853i
$715$		0			0
$716$	1820.60	−	3153.37i	0.0950264	−	0.164591i
$717$	−197.841	+	842.088i	−0.0103047	+	0.0438610i
$718$	15839.1	−	9144.72i	0.823274	−	0.475318i
$719$	22091.8			1.14588			0.572939	−	0.819598i	$-0.305803\pi$
$719$	22091.8			1.14588			0.572939	+	0.819598i	$0.305803\pi$
$720$		0			0
$721$	13363.8			0.690282
$722$	−2294.31	+	1324.62i	−0.118262	+	0.0682786i
$723$	−2326.97	−	2186.81i	−0.119697	−	0.112487i
$724$	4329.92	−	7499.65i	0.222266	−	0.384975i
$725$		0			0
$726$	4675.31	+	15506.3i	0.239004	+	0.792687i
$727$	−5753.42	+	3321.74i	−0.293511	+	0.169459i	−0.639524	−	0.768771i	$-0.720869\pi$
$727$	−5753.42	+	3321.74i	−0.293511	+	0.169459i	0.346013	+	0.938230i	$0.387535\pi$
$728$			14326.8i			0.729378i
$729$	−3645.00	−	19342.6i	−0.185185	−	0.982704i
$730$		0			0
$731$	−4969.22	−	8606.94i	−0.251427	−	0.435484i
$732$	−8067.75	+	2432.52i	−0.407367	+	0.122826i
$733$	2704.43	+	1561.40i	0.136276	+	0.0786791i	0.566588	−	0.824001i	$-0.308263\pi$
$733$	2704.43	+	1561.40i	0.136276	+	0.0786791i	−0.430312	+	0.902680i	$0.641596\pi$
$734$	−6234.82	+	10799.0i	−0.313530	+	0.543050i
$735$		0			0
$736$	10316.8	+	17869.2i	0.516687	+	0.894928i
$737$			933.252i			0.0466442i
$738$	1888.44	+	2846.93i	0.0941929	+	0.142001i
$739$	−19549.5			−0.973127			−0.486563	−	0.873645i	$-0.661750\pi$
$739$	−19549.5			−0.973127			−0.486563	+	0.873645i	$0.661750\pi$
$740$		0			0
$741$	−35678.6	−	8382.37i	−1.76881	−	0.415566i
$742$	6046.72	+	3491.08i	0.299167	+	0.172724i
$743$	−8133.58	−	4695.92i	−0.401604	−	0.231866i	0.285572	−	0.958357i	$-0.407817\pi$
$743$	−8133.58	−	4695.92i	−0.401604	−	0.231866i	−0.687176	+	0.726491i	$0.741150\pi$
$744$	−746.804	−	175.455i	−0.0368000	−	0.00864582i
$745$		0			0
$746$	2363.87			0.116015
$747$	13317.4	−	26777.6i	0.652286	−	1.31157i
$748$		−	327.005i		−	0.0159846i
$749$	−955.512	−	1655.00i	−0.0466137	−	0.0807373i
$750$		0			0
$751$	9136.01	−	15824.0i	0.443912	−	0.768878i	−0.554064	−	0.832474i	$-0.686924\pi$
$751$	9136.01	−	15824.0i	0.443912	−	0.768878i	0.997976	+	0.0635962i	$0.0202570\pi$
$752$	14291.5	+	8251.18i	0.693026	+	0.400119i
$753$	−30527.0	+	9204.25i	−1.47738	+	0.445447i
$754$	−4729.03	−	8190.92i	−0.228410	−	0.395618i
$755$		0			0
$756$	−1888.83	−	1566.13i	−0.0908676	−	0.0753434i
$757$		−	2016.30i		−	0.0968082i	−0.998828	−	0.0484041i	$-0.984586\pi$
$757$		−	2016.30i		−	0.0968082i	0.998828	−	0.0484041i	$-0.0154135\pi$
$758$	−5619.36	+	3244.34i	−0.269267	+	0.155461i
$759$	1238.86	+	4108.84i	0.0592462	+	0.196497i
$760$		0			0
$761$	8846.39	−	15322.4i	0.421395	−	0.729877i	−0.574681	−	0.818377i	$-0.694874\pi$
$761$	8846.39	−	15322.4i	0.421395	−	0.729877i	0.996076	+	0.0885001i	$0.0282074\pi$
$762$	21780.8	+	20468.8i	1.03548	+	0.973107i
$763$	4951.60	−	2858.81i	0.234941	−	0.135643i
$764$	3219.87			0.152475
$765$		0			0
$766$	−21206.9			−1.00031
$767$	6719.46	−	3879.48i	0.316331	−	0.182634i
$768$	3912.00	−	16651.0i	0.183805	−	0.782346i
$769$	−4879.86	+	8452.16i	−0.228833	+	0.396350i	−0.957462	−	0.288558i	$-0.906824\pi$
$769$	−4879.86	+	8452.16i	−0.228833	+	0.396350i	0.728630	+	0.684908i	$0.240157\pi$
$770$		0			0
$771$	27570.4	+	6477.43i	1.28784	+	0.302567i
$772$	−3704.27	+	2138.66i	−0.172694	+	0.0997047i
$773$		−	10338.3i		−	0.481038i	−0.970644	−	0.240519i	$-0.922682\pi$
$773$		−	10338.3i		−	0.481038i	0.970644	−	0.240519i	$-0.0773177\pi$
$774$	−1185.86	−	19075.4i	−0.0550707	−	0.885856i
$775$		0			0
$776$	−1712.96	−	2966.93i	−0.0792418	−	0.137251i
$777$	−8103.14	−	7615.04i	−0.374130	−	0.351593i
$778$	22874.0	+	13206.3i	1.05408	+	0.608573i
$779$	−2381.68	+	4125.19i	−0.109541	+	0.189731i
$780$		0			0
$781$	1061.45	+	1838.48i	0.0486320	+	0.0842331i
$782$		−	15768.2i		−	0.721059i
$783$	6981.79	+	1188.91i	0.318657	+	0.0542633i
$784$	−11371.1			−0.517997
$785$		0			0
$786$	−926.950	−	3074.35i	−0.0420652	−	0.139514i
$787$	4093.95	+	2363.64i	0.185430	+	0.107058i	0.589842	−	0.807519i	$-0.299190\pi$
$787$	4093.95	+	2363.64i	0.185430	+	0.107058i	−0.404411	+	0.914577i	$0.632524\pi$
$788$	−541.150	−	312.433i	−0.0244640	−	0.0141243i
$789$	−2787.10	+	2965.74i	−0.125758	+	0.133819i
$790$		0			0
$791$	−1586.92			−0.0713331
$792$	1224.37	−	2461.87i	0.0549319	−	0.110453i
$793$			53989.1i			2.41767i
$794$	−11243.9	−	19475.0i	−0.502558	−	0.870456i
$795$		0			0
$796$	584.593	−	1012.54i	0.0260306	−	0.0450863i
$797$	24420.9	+	14099.4i	1.08536	+	0.626634i	0.932338	−	0.361588i	$-0.117765\pi$
$797$	24420.9	+	14099.4i	1.08536	+	0.626634i	0.153025	+	0.988222i	$0.451099\pi$
$798$	−1856.21	+	7900.76i	−0.0823423	+	0.350481i
$799$	6976.24	+	12083.2i	0.308888	+	0.535010i
$800$		0			0
$801$	−8376.04	+	5556.04i	−0.369479	+	0.245085i
$802$		−	22364.9i		−	0.984704i
$803$	3563.76	−	2057.54i	0.156616	−	0.0904221i
$804$	−1903.57	+	2025.59i	−0.0834998	+	0.0888519i
$805$		0			0
$806$	−562.076	+	973.544i	−0.0245636	+	0.0425454i
$807$	−701.562	+	211.529i	−0.0306024	+	0.00922697i
$808$	−42016.7	+	24258.3i	−1.82938	+	1.05619i
$809$	27310.5			1.18688			0.593439	−	0.804879i	$-0.297770\pi$
$809$	27310.5			1.18688			0.593439	+	0.804879i	$0.297770\pi$
$810$		0			0
$811$	−18045.0			−0.781312			−0.390656	−	0.920537i	$-0.627752\pi$
$811$	−18045.0			−0.781312			−0.390656	+	0.920537i	$0.627752\pi$
$812$	764.587	−	441.435i	0.0330440	−	0.0190780i
$813$	31719.3	−	9563.74i	1.36832	−	0.412565i
$814$	1424.96	−	2468.10i	0.0613572	−	0.106274i
$815$		0			0
$816$	−4669.00	+	4968.27i	−0.200304	+	0.213142i
$817$	23078.0	−	13324.1i	0.988246	−	0.570564i
$818$			968.333i			0.0413899i
$819$	−13100.6	+	8689.97i	−0.558941	+	0.370760i
$820$		0			0
$821$	6288.85	+	10892.6i	0.267335	+	0.463038i	0.968173	−	0.250283i	$-0.0805235\pi$
$821$	6288.85	+	10892.6i	0.267335	+	0.463038i	−0.700837	+	0.713321i	$0.747190\pi$
$822$	−1140.79	+	4855.66i	−0.0484060	+	0.206035i
$823$	30283.6	+	17484.2i	1.28265	+	0.740537i	0.977332	−	0.211714i	$-0.0679045\pi$
$823$	30283.6	+	17484.2i	1.28265	+	0.740537i	0.305316	+	0.952251i	$0.401238\pi$
$824$	−22301.7	+	38627.7i	−0.942860	+	1.63308i
$825$		0			0
$826$	−859.081	−	1487.97i	−0.0361880	−	0.0626794i
$827$			6735.01i			0.283191i	0.989925	+	0.141596i	$0.0452233\pi$
$827$			6735.01i			0.283191i	−0.989925	+	0.141596i	$0.954777\pi$
$828$	−5691.99	+	11445.0i	−0.238901	+	0.480364i
$829$	2867.97			0.120155			0.0600777	−	0.998194i	$-0.480865\pi$
$829$	2867.97			0.120155			0.0600777	+	0.998194i	$0.480865\pi$
$830$		0			0
$831$	−24279.7	+	25836.0i	−1.01354	+	1.07851i
$832$	−38332.0	−	22131.0i	−1.59726	−	0.922179i
$833$	−8326.02	−	4807.03i	−0.346314	−	0.199944i
$834$	−6290.16	−	20862.1i	−0.261163	−	0.866181i
$835$		0			0
$836$	876.808			0.0362740
$837$	−292.538	−	789.310i	−0.0120807	−	0.0325956i
$838$			20909.0i			0.861921i
$839$	13927.9	+	24123.8i	0.573116	+	0.992666i	0.996244	+	0.0865958i	$0.0275989\pi$
$839$	13927.9	+	24123.8i	0.573116	+	0.992666i	−0.423128	+	0.906070i	$0.639068\pi$
$840$		0			0
$841$	10920.3	−	18914.6i	0.447756	−	0.775537i
$842$	−4826.67	−	2786.68i	−0.197551	−	0.114056i
$843$	−2232.88	−	2098.38i	−0.0912270	−	0.0857318i
$844$	1187.97	+	2057.63i	0.0484499	+	0.0839176i
$845$		0			0
$846$	1664.81	+	26779.8i	0.0676566	+	1.08831i
$847$			9686.23i			0.392943i
$848$	−13620.2	+	7863.60i	−0.551554	+	0.318440i
$849$	30229.3	+	7102.09i	1.22199	+	0.287094i
$850$		0			0
$851$	−28964.2	+	50167.5i	−1.16672	+	2.02082i
$852$	−1446.16	+	6155.41i	−0.0581509	+	0.247513i
$853$	9462.29	−	5463.05i	0.379815	−	0.219287i	−0.297923	−	0.954590i	$-0.596294\pi$
$853$	9462.29	−	5463.05i	0.379815	−	0.219287i	0.677738	+	0.735304i	$0.262960\pi$
$854$	11955.5			0.479049
$855$		0			0
$856$	6378.30			0.254680
$857$	−39117.7	+	22584.6i	−1.55920	+	0.900206i	−0.561869	+	0.827226i	$0.689918\pi$
$857$	−39117.7	+	22584.6i	−1.55920	+	0.900206i	−0.997333	+	0.0729799i	$0.976749\pi$
$858$	−2936.06	−	2759.20i	−0.116825	−	0.109788i
$859$	−3525.95	+	6107.12i	−0.140051	+	0.242576i	−0.927516	−	0.373784i	$-0.878060\pi$
$859$	−3525.95	+	6107.12i	−0.140051	+	0.242576i	0.787465	+	0.616360i	$0.211393\pi$
$860$		0			0
$861$	589.822	+	1956.22i	0.0233462	+	0.0774306i
$862$	−9206.35	+	5315.29i	−0.363770	+	0.210022i
$863$			6882.52i			0.271476i	0.990745	+	0.135738i	$0.0433405\pi$
$863$			6882.52i			0.271476i	−0.990745	+	0.135738i	$0.956659\pi$
$864$	13601.6	−	5041.11i	0.535576	−	0.198498i
$865$		0			0
$866$	−4059.80	−	7031.77i	−0.159304	−	0.275923i
$867$	18922.9	−	5705.46i	0.741239	−	0.223492i
$868$	−90.8762	−	52.4674i	−0.00355362	−	0.00205168i
$869$	417.391	−	722.942i	0.0162935	−	0.0282211i
$870$		0			0
$871$	8904.79	+	15423.5i	0.346415	+	0.600008i
$872$			19083.3i			0.741104i
$873$	1674.00	−	3365.95i	0.0648984	−	0.130493i
$874$	42279.6			1.63630
$875$		0			0
$876$	11931.8	+	2803.27i	0.460204	+	0.108121i
$877$	32362.2	+	18684.3i	1.24606	+	0.719413i	0.970321	−	0.241820i	$-0.0777443\pi$
$877$	32362.2	+	18684.3i	1.24606	+	0.719413i	0.275738	+	0.961233i	$0.411078\pi$
$878$	16701.0	+	9642.35i	0.641951	+	0.370630i
$879$	−40758.2	−	9575.76i	−1.56398	−	0.367443i
$880$		0			0
$881$	−23880.5			−0.913229			−0.456614	−	0.889665i	$-0.650938\pi$
$881$	−23880.5			−0.913229			−0.456614	+	0.889665i	$0.650938\pi$
$882$	−10219.9	−	15407.0i	−0.390160	−	0.588189i
$883$		−	33107.0i		−	1.26177i	−0.775878	−	0.630883i	$-0.782693\pi$
$883$		−	33107.0i		−	1.26177i	0.775878	−	0.630883i	$-0.217307\pi$
$884$	−3120.18	−	5404.31i	−0.118714	−	0.205618i
$885$		0			0
$886$	−2788.36	+	4829.57i	−0.105730	+	0.183129i
$887$	9787.95	+	5651.07i	0.370515	+	0.213917i	0.673684	−	0.739020i	$-0.264711\pi$
$887$	9787.95	+	5651.07i	0.370515	+	0.213917i	−0.303168	+	0.952937i	$0.598044\pi$
$888$	35533.7	−	10713.8i	1.34283	−	0.404879i
$889$	8938.02	+	15481.1i	0.337201	+	0.584049i
$890$		0			0
$891$	2993.80	−	373.674i	0.112566	−	0.0140500i
$892$			1331.20i			0.0499686i
$893$	−32399.0	+	18705.6i	−1.21410	+	0.700961i
$894$	6834.62	+	22667.9i	0.255687	+	0.848016i
$895$		0			0
$896$	−1851.73	+	3207.30i	−0.0690425	+	0.119585i
$897$	59679.5	+	56084.6i	2.22145	+	2.08764i
$898$	9781.25	−	5647.21i	0.363479	−	0.209855i
$899$	302.886			0.0112367
$900$		0			0
$901$	−13297.1			−0.491666
$902$	−453.500	+	261.828i	−0.0167405	+	0.00966511i
$903$	2614.31	−	11127.5i	0.0963443	−	0.410079i
$904$	2648.28	−	4586.96i	0.0974343	−	0.168761i
$905$		0			0
$906$	−30294.7	−	7117.47i	−1.11090	−	0.260996i
$907$	−3431.40	+	1981.12i	−0.125620	+	0.0725270i	−0.561493	−	0.827481i	$-0.689773\pi$
$907$	−3431.40	+	1981.12i	−0.125620	+	0.0725270i	0.435873	+	0.900008i	$0.356440\pi$
$908$			9267.22i			0.338704i
$909$	−47667.4	−	23706.6i	−1.73931	−	0.865015i
$910$		0			0
$911$	17023.1	+	29484.8i	0.619100	+	1.07231i	0.989650	+	0.143500i	$0.0458356\pi$
$911$	17023.1	+	29484.8i	0.619100	+	1.07231i	−0.370551	+	0.928812i	$0.620831\pi$
$912$	−13321.6	−	12519.1i	−0.483685	−	0.454550i
$913$	3969.93	+	2292.04i	0.143905	+	0.0830838i
$914$	2644.01	−	4579.56i	0.0956849	−	0.165731i
$915$		0			0
$916$	3554.76	+	6157.02i	0.128223	+	0.222089i
$917$		−	1920.44i		−	0.0691587i
$918$	−10928.0	−	1860.90i	−0.392895	−	0.0669050i
$919$	35121.5			1.26066			0.630332	−	0.776326i	$-0.282919\pi$
$919$	35121.5			1.26066			0.630332	+	0.776326i	$0.282919\pi$
$920$		0			0
$921$	6819.87	+	22619.0i	0.243998	+	0.809251i
$922$	11785.6	+	6804.44i	0.420975	+	0.243050i
$923$	35084.4	+	20256.0i	1.25116	+	0.722355i
$924$	257.560	−	274.069i	0.00917002	−	0.00975779i
$925$		0			0
$926$	−8549.64			−0.303411
$927$	−48848.8	+	3036.76i	−1.73075	+	0.107595i
$928$			5219.44i			0.184630i
$929$	12228.9	+	21181.1i	0.431881	+	0.748039i	0.997035	−	0.0769459i	$-0.0245169\pi$
$929$	12228.9	+	21181.1i	0.431881	+	0.748039i	−0.565155	+	0.824985i	$0.691184\pi$
$930$		0			0
$931$	12889.2	−	22324.8i	0.453735	−	0.785891i
$932$	−8617.00	−	4975.03i	−0.302853	−	0.174852i
$933$	4994.73	−	21259.5i	0.175263	−	0.745986i
$934$	−4484.05	−	7766.61i	−0.157091	−	0.272089i
$935$		0			0
$936$	−3255.61	−	52369.0i	−0.113689	−	1.82878i
$937$		−	41877.5i		−	1.46006i	−0.683413	−	0.730032i	$-0.739505\pi$
$937$		−	41877.5i		−	1.46006i	0.683413	−	0.730032i	$-0.260495\pi$
$938$	3415.43	−	1971.90i	0.118889	−	0.0686404i
$939$	−24813.9	+	26404.4i	−0.862375	+	0.917651i
$940$		0			0
$941$	4599.48	−	7966.54i	0.159340	−	0.275985i	−0.775291	−	0.631604i	$-0.782397\pi$
$941$	4599.48	−	7966.54i	0.159340	−	0.275985i	0.934631	+	0.355619i	$0.115730\pi$
$942$	−22927.7	+	6912.95i	−0.793018	+	0.239104i
$943$	9218.01	−	5322.02i	0.318324	−	0.183785i
$944$	3870.14			0.133435
$945$		0			0
$946$	2929.55			0.100685
$947$	−18155.0	+	10481.8i	−0.622976	+	0.359675i	−0.778027	−	0.628231i	$-0.783779\pi$
$947$	−18155.0	+	10481.8i	−0.622976	+	0.359675i	0.155051	+	0.987906i	$0.450446\pi$
$948$	2380.53	−	717.757i	0.0815570	−	0.0245904i
$949$	39264.7	−	68008.5i	1.34308	−	2.32629i
$950$		0			0
$951$	26190.1	−	27868.8i	0.893030	−	0.950271i
$952$	−5232.50	+	3020.98i	−0.178137	+	0.102847i
$953$		−	27943.7i		−	0.949828i	−0.880032	−	0.474914i	$-0.842479\pi$
$953$		−	27943.7i		−	0.949828i	0.880032	−	0.474914i	$-0.157521\pi$
$954$	−22895.9	−	11386.9i	−0.777027	−	0.386441i
$955$		0			0
$956$	−197.460	−	342.010i	−0.00668024	−	0.0115705i
$957$	−248.287	+	1056.81i	−0.00838662	+	0.0356967i
$958$	29709.8	+	17153.0i	1.00196	+	0.578484i
$959$	−1491.55	+	2583.45i	−0.0502240	+	0.0869905i
$960$		0			0
$961$	14877.5	+	25768.6i	0.499396	+	0.864979i
$962$		−	54385.9i		−	1.82274i
$963$	3868.77	+	5832.39i	0.129459	+	0.195167i
$964$	1457.87			0.0487084
$965$		0			0
$966$	12419.5	−	13215.6i	0.413655	−	0.440170i
$967$	1942.95	+	1121.76i	0.0646132	+	0.0373045i	0.531959	−	0.846770i	$-0.321456\pi$
$967$	1942.95	+	1121.76i	0.0646132	+	0.0373045i	−0.467345	+	0.884075i	$0.654790\pi$
$968$	−27997.8	−	16164.5i	−0.929632	−	0.536723i
$969$	−4461.83	−	14798.2i	−0.147920	−	0.490595i
$970$		0			0
$971$	57345.0			1.89525			0.947626	−	0.319381i	$-0.103475\pi$
$971$	57345.0			1.89525			0.947626	+	0.319381i	$0.103475\pi$
$972$	7260.13	+	5295.48i	0.239577	+	0.174746i
$973$		−	13031.8i		−	0.429375i
$974$	4248.44	+	7358.52i	0.139763	+	0.242076i
$975$		0			0
$976$	−13464.8	+	23321.7i	−0.441595	+	0.764866i
$977$	16273.4	+	9395.44i	0.532888	+	0.307663i	0.742192	−	0.670188i	$-0.233786\pi$
$977$	16273.4	+	9395.44i	0.532888	+	0.307663i	−0.209304	+	0.977851i	$0.567120\pi$
$978$	9442.63	+	8873.84i	0.308734	+	0.290137i
$979$	−770.334	−	1334.26i	−0.0251481	−	0.0435578i
$980$		0			0
$981$	−17450.0	+	11575.0i	−0.567927	+	0.376720i
$982$			16642.5i			0.540817i
$983$	−29962.4	+	17298.8i	−0.972181	+	0.561289i	−0.899900	−	0.436096i	$-0.856361\pi$
$983$	−29962.4	+	17298.8i	−0.972181	+	0.561289i	−0.0722803	+	0.997384i	$0.523028\pi$
$984$	−6638.70	−	1559.70i	−0.215075	−	0.0505300i
$985$		0			0
$986$	1994.35	−	3454.31i	0.0644147	−	0.111570i
$987$	−3670.21	+	15621.8i	−0.118363	+	0.503798i
$988$	14490.7	−	8366.22i	0.466611	−	0.269398i
$989$	−59547.1			−1.91455
$990$		0			0
$991$	−45026.3			−1.44330			−0.721649	−	0.692259i	$-0.756616\pi$
$991$	−45026.3			−1.44330			−0.721649	+	0.692259i	$0.756616\pi$
$992$	537.251	−	310.182i	0.0171953	−	0.00992771i
$993$	25877.5	+	24318.7i	0.826985	+	0.777171i
$994$	4485.53	−	7769.17i	0.143131	−	0.247911i
$995$		0			0
$996$	3941.46	+	13072.4i	0.125392	+	0.415877i
$997$	10368.1	−	5986.04i	0.329350	−	0.190150i	−0.326202	−	0.945300i	$-0.605769\pi$
$997$	10368.1	−	5986.04i	0.329350	−	0.190150i	0.655552	+	0.755150i	$0.272436\pi$
$998$			5977.66i			0.189599i
$999$	31349.9	+	25994.0i	0.992861	+	0.823237i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.k.a.49.2		8
5.2	odd	4		45.4.e.a.31.1	yes	4
5.3	odd	4		225.4.e.a.76.2		4
5.4	even	2	inner	225.4.k.a.49.3		8
9.7	even	3	inner	225.4.k.a.124.3		8
15.2	even	4		135.4.e.a.91.2		4
45.2	even	12		135.4.e.a.46.2		4
45.7	odd	12		45.4.e.a.16.1	✓	4
45.13	odd	12		2025.4.a.l.1.1		2
45.22	odd	12		405.4.a.d.1.2		2
45.23	even	12		2025.4.a.j.1.2		2
45.32	even	12		405.4.a.e.1.1		2
45.34	even	6	inner	225.4.k.a.124.2		8
45.43	odd	12		225.4.e.a.151.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.a.16.1	✓	4	45.7	odd	12
45.4.e.a.31.1	yes	4	5.2	odd	4
135.4.e.a.46.2		4	45.2	even	12
135.4.e.a.91.2		4	15.2	even	4
225.4.e.a.76.2		4	5.3	odd	4
225.4.e.a.151.2		4	45.43	odd	12
225.4.k.a.49.2		8	1.1	even	1	trivial
225.4.k.a.49.3		8	5.4	even	2	inner
225.4.k.a.124.2		8	45.34	even	6	inner
225.4.k.a.124.3		8	9.7	even	3	inner
405.4.a.d.1.2		2	45.22	odd	12
405.4.a.e.1.1		2	45.32	even	12
2025.4.a.j.1.2		2	45.23	even	12
2025.4.a.l.1.1		2	45.13	odd	12

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.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.05446 + 1.18614i) q^{2} +(4.97494 - 1.50000i) q^{3} +(-1.18614 + 2.05446i) q^{4} +(-8.44158 + 8.98266i) q^{6} +(-6.38458 + 3.68614i) q^{7} -24.6060i q^{8} +(22.5000 - 14.9248i) q^{9} +O(q^{10})\)	\(q+(-2.05446 + 1.18614i) q^{2} +(4.97494 - 1.50000i) q^{3} +(-1.18614 + 2.05446i) q^{4} +(-8.44158 + 8.98266i) q^{6} +(-6.38458 + 3.68614i) q^{7} -24.6060i q^{8} +(22.5000 - 14.9248i) q^{9} +(2.06930 + 3.58413i) q^{11} +(-2.81929 + 12.0000i) q^{12} +(68.3972 + 39.4891i) q^{13} +(8.74456 - 15.1460i) q^{14} +(19.6970 + 34.1162i) q^{16} +33.3070i q^{17} +(-28.5223 + 57.3505i) q^{18} -89.3070 q^{19} +(-26.2337 + 27.9152i) q^{21} +(-8.50256 - 4.90895i) q^{22} +(172.826 + 99.7812i) q^{23} +(-36.9090 - 122.413i) q^{24} -187.359 q^{26} +(89.5489 - 108.000i) q^{27} -17.4891i q^{28} +(25.2405 + 43.7179i) q^{29} +(3.00000 - 5.19615i) q^{31} +(89.5419 + 51.6970i) q^{32} +(15.6708 + 14.7269i) q^{33} +(-39.5068 - 68.4278i) q^{34} +(3.97420 + 63.9282i) q^{36} +290.277i q^{37} +(183.477 - 105.931i) q^{38} +(399.505 + 93.8602i) q^{39} +(26.6684 - 46.1911i) q^{41} +(20.7846 - 88.4674i) q^{42} +(-258.412 + 149.194i) q^{43} -9.81791 q^{44} -473.418 q^{46} +(362.782 - 209.452i) q^{47} +(149.166 + 140.181i) q^{48} +(-144.325 + 249.978i) q^{49} +(49.9605 + 165.700i) q^{51} +(-162.257 + 93.6793i) q^{52} +399.228i q^{53} +(-55.8710 + 328.099i) q^{54} +(90.7011 + 157.099i) q^{56} +(-444.297 + 133.961i) q^{57} +(-103.711 - 59.8776i) q^{58} +(49.1209 - 85.0799i) q^{59} +(341.797 + 592.011i) q^{61} +14.2337i q^{62} +(-88.6382 + 178.227i) q^{63} -560.432 q^{64} +(-49.6631 - 11.6679i) q^{66} +(195.289 + 112.750i) q^{67} +(-68.4278 - 39.5068i) q^{68} +(1009.47 + 237.166i) q^{69} +512.951 q^{71} +(-367.239 - 553.634i) q^{72} -994.318i q^{73} +(-344.310 - 596.362i) q^{74} +(105.931 - 183.477i) q^{76} +(-26.4232 - 15.2554i) q^{77} +(-932.097 + 281.038i) q^{78} +(-100.853 - 174.683i) q^{79} +(283.500 - 671.617i) q^{81} +126.530i q^{82} +(959.247 - 553.822i) q^{83} +(-26.2337 - 87.0073i) q^{84} +(353.931 - 613.026i) q^{86} +(191.147 + 179.633i) q^{87} +(88.1909 - 50.9171i) q^{88} -372.269 q^{89} -582.250 q^{91} +(-409.992 + 236.709i) q^{92} +(7.13058 - 30.3505i) q^{93} +(-496.880 + 860.622i) q^{94} +(523.011 + 122.877i) q^{96} +(120.578 - 69.6156i) q^{97} -684.758i q^{98} +(100.052 + 49.7590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} - 102 q^{6} + 180 q^{9}+O(q^{10}) \) 8 * q + 2 * q^4 - 102 * q^6 + 180 * q^9	\( 8 q + 2 q^{4} - 102 q^{6} + 180 q^{9} + 74 q^{11} + 24 q^{14} + 238 q^{16} - 140 q^{19} - 72 q^{21} - 54 q^{24} - 304 q^{26} + 650 q^{29} + 24 q^{31} - 902 q^{34} + 342 q^{36} + 1128 q^{39} - 476 q^{41} + 404 q^{44} - 984 q^{46} - 1258 q^{49} - 462 q^{51} - 1998 q^{54} + 312 q^{56} - 170 q^{59} + 494 q^{61} - 2852 q^{64} - 1776 q^{66} + 3078 q^{69} + 1576 q^{71} + 968 q^{74} + 790 q^{76} - 1680 q^{79} + 2268 q^{81} - 72 q^{84} + 2774 q^{86} + 4260 q^{89} - 2544 q^{91} + 1264 q^{94} + 48 q^{96} + 180 q^{99}+O(q^{100}) \) 8 * q + 2 * q^4 - 102 * q^6 + 180 * q^9 + 74 * q^11 + 24 * q^14 + 238 * q^16 - 140 * q^19 - 72 * q^21 - 54 * q^24 - 304 * q^26 + 650 * q^29 + 24 * q^31 - 902 * q^34 + 342 * q^36 + 1128 * q^39 - 476 * q^41 + 404 * q^44 - 984 * q^46 - 1258 * q^49 - 462 * q^51 - 1998 * q^54 + 312 * q^56 - 170 * q^59 + 494 * q^61 - 2852 * q^64 - 1776 * q^66 + 3078 * q^69 + 1576 * q^71 + 968 * q^74 + 790 * q^76 - 1680 * q^79 + 2268 * q^81 - 72 * q^84 + 2774 * q^86 + 4260 * q^89 - 2544 * q^91 + 1264 * q^94 + 48 * q^96 + 180 * q^99

Introduction

L-functions

Modular forms

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Database

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