LMFDB - Embedded newform 225.4.k.c.124.4

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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 23x^{10} + 198x^{8} - 719x^{6} + 886x^{4} + 585x^{2} + 81 $ x^12 - 23x^10 + 198x^8 - 719x^6 + 886x^4 + 585*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			124.4
Root			$-1.98116 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	225.124
Dual form			225.4.k.c.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.151541 + 0.0874923i) q^{2} +(0.151541 - 5.19394i) q^{3} +(-3.98469 - 6.90169i) q^{4} +(0.477395 - 0.773837i) q^{6} +(-7.32979 - 4.23186i) q^{7} -2.79440i q^{8} +(-26.9541 - 1.57419i) q^{9} +O(q^{10})$	\(q+(0.151541 + 0.0874923i) q^{2} +(0.151541 - 5.19394i) q^{3} +(-3.98469 - 6.90169i) q^{4} +(0.477395 - 0.773837i) q^{6} +(-7.32979 - 4.23186i) q^{7} -2.79440i q^{8} +(-26.9541 - 1.57419i) q^{9} +(15.7541 - 27.2870i) q^{11} +(-36.4508 + 19.6504i) q^{12} +(-23.2697 + 13.4348i) q^{13} +(-0.740510 - 1.28260i) q^{14} +(-31.6330 + 54.7900i) q^{16} -44.3307i q^{17} +(-3.94692 - 2.59683i) q^{18} +90.2082 q^{19} +(-23.0908 + 37.4292i) q^{21} +(4.77480 - 2.75673i) q^{22} +(-168.232 + 97.1287i) q^{23} +(-14.5139 - 0.423466i) q^{24} -4.70176 q^{26} +(-12.2609 + 139.759i) q^{27} +67.4506i q^{28} +(1.87186 - 3.24215i) q^{29} +(125.832 + 217.947i) q^{31} +(-28.9476 + 16.7129i) q^{32} +(-139.339 - 85.9611i) q^{33} +(3.87859 - 6.71792i) q^{34} +(96.5390 + 192.301i) q^{36} -62.2293i q^{37} +(13.6703 + 7.89252i) q^{38} +(66.2532 + 122.898i) q^{39} +(102.173 + 176.969i) q^{41} +(-6.77397 + 3.65180i) q^{42} +(-456.968 - 263.831i) q^{43} -251.101 q^{44} -33.9920 q^{46} +(-134.864 - 77.8637i) q^{47} +(279.782 + 172.603i) q^{48} +(-135.683 - 235.009i) q^{49} +(-230.251 - 6.71792i) q^{51} +(185.445 + 107.067i) q^{52} +141.694i q^{53} +(-14.0859 + 20.1065i) q^{54} +(-11.8255 + 20.4823i) q^{56} +(13.6703 - 468.536i) q^{57} +(0.567326 - 0.327546i) q^{58} +(-246.923 - 427.683i) q^{59} +(379.742 - 657.732i) q^{61} +44.0373i q^{62} +(190.906 + 125.604i) q^{63} +500.280 q^{64} +(-13.5947 - 25.2178i) q^{66} +(-470.763 + 271.795i) q^{67} +(-305.956 + 176.644i) q^{68} +(478.987 + 888.505i) q^{69} -928.207 q^{71} +(-4.39891 + 75.3203i) q^{72} -608.739i q^{73} +(5.44459 - 9.43030i) q^{74} +(-359.452 - 622.589i) q^{76} +(-230.949 + 133.338i) q^{77} +(-0.712510 + 24.4207i) q^{78} +(307.420 - 532.467i) q^{79} +(724.044 + 84.8617i) q^{81} +35.7573i q^{82} +(931.246 + 537.655i) q^{83} +(350.334 + 10.2215i) q^{84} +(-46.1663 - 79.9623i) q^{86} +(-16.5559 - 10.2136i) q^{87} +(-76.2506 - 44.0233i) q^{88} -1505.15 q^{89} +227.416 q^{91} +(1340.70 + 774.055i) q^{92} +(1151.07 - 620.536i) q^{93} +(-13.6249 - 23.5991i) q^{94} +(82.4190 + 152.885i) q^{96} +(288.160 + 166.369i) q^{97} -47.4848i q^{98} +(-467.593 + 710.695i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 22 q^{4} + 168 q^{6} - 114 q^{9}+O(q^{10}) $ 12 * q + 22 * q^4 + 168 * q^6 - 114 * q^9	$ 12 q + 22 q^{4} + 168 q^{6} - 114 q^{9} - 28 q^{11} - 54 q^{14} + 26 q^{16} + 656 q^{19} - 288 q^{21} + 126 q^{24} + 1736 q^{26} - 670 q^{29} + 704 q^{31} - 104 q^{34} + 2172 q^{36} + 780 q^{39} - 374 q^{41} - 3928 q^{44} - 804 q^{46} + 860 q^{49} - 360 q^{51} - 1278 q^{54} - 1410 q^{56} - 596 q^{59} + 2878 q^{61} + 6276 q^{64} - 1932 q^{66} + 1746 q^{69} + 280 q^{71} - 640 q^{74} - 408 q^{76} - 764 q^{79} - 2502 q^{81} + 1818 q^{84} - 3160 q^{86} - 6876 q^{89} - 2840 q^{91} - 4154 q^{94} + 2310 q^{96} + 1524 q^{99}+O(q^{100}) $ 12 * q + 22 * q^4 + 168 * q^6 - 114 * q^9 - 28 * q^11 - 54 * q^14 + 26 * q^16 + 656 * q^19 - 288 * q^21 + 126 * q^24 + 1736 * q^26 - 670 * q^29 + 704 * q^31 - 104 * q^34 + 2172 * q^36 + 780 * q^39 - 374 * q^41 - 3928 * q^44 - 804 * q^46 + 860 * q^49 - 360 * q^51 - 1278 * q^54 - 1410 * q^56 - 596 * q^59 + 2878 * q^61 + 6276 * q^64 - 1932 * q^66 + 1746 * q^69 + 280 * q^71 - 640 * q^74 - 408 * q^76 - 764 * q^79 - 2502 * q^81 + 1818 * q^84 - 3160 * q^86 - 6876 * q^89 - 2840 * q^91 - 4154 * q^94 + 2310 * q^96 + 1524 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	0.151541	+	0.0874923i	0.0535779	+	0.0309332i	0.526550	−	0.850144i	$-0.323485\pi$
$2$	0.151541	+	0.0874923i	0.0535779	+	0.0309332i	−0.472972	+	0.881078i	$0.656819\pi$
$3$	0.151541	−	5.19394i	0.0291641	−	0.999575i
$3$	0.151541	−	5.19394i	0.0291641	−	0.999575i
$4$	−3.98469	−	6.90169i	−0.498086	−	0.862711i
$5$		0			0
$5$		0			0
$6$	0.477395	−	0.773837i	0.0324826	−	0.0526529i
$7$	−7.32979	−	4.23186i	−0.395772	−	0.228499i	0.288886	−	0.957363i	$-0.406715\pi$
$7$	−7.32979	−	4.23186i	−0.395772	−	0.228499i	−0.684658	+	0.728865i	$0.740048\pi$
$8$		−	2.79440i		−	0.123496i
$9$	−26.9541	−	1.57419i	−0.998299	−	0.0583034i
$10$		0			0
$11$	15.7541	−	27.2870i	0.431823	−	0.747939i	−0.565208	−	0.824949i	$-0.691204\pi$
$11$	15.7541	−	27.2870i	0.431823	−	0.747939i	0.997030	+	0.0770098i	$0.0245373\pi$
$12$	−36.4508	+	19.6504i	−0.876870	+	0.472714i
$13$	−23.2697	+	13.4348i	−0.496451	+	0.286626i	−0.727247	−	0.686376i	$-0.759200\pi$
$13$	−23.2697	+	13.4348i	−0.496451	+	0.286626i	0.230796	+	0.973002i	$0.425867\pi$
$14$	−0.740510	−	1.28260i	−0.0141364	−	0.0244850i
$15$		0			0
$16$	−31.6330	+	54.7900i	−0.494266	+	0.856094i
$17$		−	44.3307i		−	0.632457i	−0.948683	−	0.316229i	$-0.897583\pi$
$17$		−	44.3307i		−	0.632457i	0.948683	−	0.316229i	$-0.102417\pi$
$18$	−3.94692	−	2.59683i	−0.0516832	−	0.0340044i
$19$	90.2082			1.08922			0.544610	−	0.838689i	$-0.316678\pi$
$19$	90.2082			1.08922			0.544610	+	0.838689i	$0.316678\pi$
$20$		0			0
$21$	−23.0908	+	37.4292i	−0.239944	+	0.388939i
$22$	4.77480	−	2.75673i	0.0462723	−	0.0267153i
$23$	−168.232	+	97.1287i	−1.52516	+	0.880553i	−0.525608	+	0.850727i	$0.676162\pi$
$23$	−168.232	+	97.1287i	−1.52516	+	0.880553i	−0.999555	+	0.0298265i	$0.990505\pi$
$24$	−14.5139	−	0.423466i	−0.123443	−	0.00360165i
$25$		0			0
$26$	−4.70176			−0.0354650
$27$	−12.2609	+	139.759i	−0.0873931	+	0.996174i
$28$			67.4506i			0.455248i
$29$	1.87186	−	3.24215i	0.0119860	−	0.0207604i	−0.859970	−	0.510344i	$-0.829518\pi$
$29$	1.87186	−	3.24215i	0.0119860	−	0.0207604i	0.871956	+	0.489584i	$0.162851\pi$
$30$		0			0
$31$	125.832	+	217.947i	0.729035	+	1.26273i	0.957292	+	0.289124i	$0.0933641\pi$
$31$	125.832	+	217.947i	0.729035	+	1.26273i	−0.228257	+	0.973601i	$0.573303\pi$
$32$	−28.9476	+	16.7129i	−0.159914	+	0.0923265i
$33$	−139.339	−	85.9611i	−0.735027	−	0.453452i
$34$	3.87859	−	6.71792i	0.0195639	−	0.0338857i
$35$		0			0
$36$	96.5390	+	192.301i	0.446940	+	0.890283i
$37$		−	62.2293i		−	0.276498i	−0.990397	−	0.138249i	$-0.955853\pi$
$37$		−	62.2293i		−	0.276498i	0.990397	−	0.138249i	$-0.0441475\pi$
$38$	13.6703	+	7.89252i	0.0583581	+	0.0336931i
$39$	66.2532	+	122.898i	0.272026	+	0.504599i
$40$		0			0
$41$	102.173	+	176.969i	0.389188	+	0.674094i	0.992341	−	0.123532i	$-0.0394223\pi$
$41$	102.173	+	176.969i	0.389188	+	0.674094i	−0.603152	+	0.797626i	$0.706089\pi$
$42$	−6.77397	+	3.65180i	−0.0248868	+	0.0134163i
$43$	−456.968	−	263.831i	−1.62063	−	0.935669i	−0.986752	−	0.162233i	$-0.948130\pi$
$43$	−456.968	−	263.831i	−1.62063	−	0.935669i	−0.633874	−	0.773436i	$-0.718536\pi$
$44$	−251.101			−0.860340
$45$		0			0
$46$	−33.9920			−0.108953
$47$	−134.864	−	77.8637i	−0.418551	−	0.241651i	0.275906	−	0.961185i	$-0.411022\pi$
$47$	−134.864	−	77.8637i	−0.418551	−	0.241651i	−0.694457	+	0.719534i	$0.744355\pi$
$48$	279.782	+	172.603i	0.841315	+	0.519023i
$49$	−135.683	−	235.009i	−0.395577	−	0.685159i
$50$		0			0
$51$	−230.251	−	6.71792i	−0.632188	−	0.0184450i
$52$	185.445	+	107.067i	0.494551	+	0.285529i
$53$			141.694i			0.367230i	0.982998	+	0.183615i	$0.0587800\pi$
$53$			141.694i			0.367230i	−0.982998	+	0.183615i	$0.941220\pi$
$54$	−14.0859	+	20.1065i	−0.0354972	+	0.0506695i
$55$		0			0
$56$	−11.8255	+	20.4823i	−0.0282187	+	0.0488762i
$57$	13.6703	−	468.536i	0.0317661	−	1.08876i
$58$	0.567326	−	0.327546i	0.00128437	−	0.000741533i
$59$	−246.923	−	427.683i	−0.544857	−	0.943721i	−0.998616	−	0.0525961i	$-0.983250\pi$
$59$	−246.923	−	427.683i	−0.544857	−	0.943721i	0.453758	−	0.891125i	$-0.350083\pi$
$60$		0			0
$61$	379.742	−	657.732i	0.797065	−	1.38056i	−0.124455	−	0.992225i	$-0.539718\pi$
$61$	379.742	−	657.732i	0.797065	−	1.38056i	0.921520	−	0.388331i	$-0.126948\pi$
$62$			44.0373i			0.0902055i
$63$	190.906	+	125.604i	0.381776	+	0.251185i
$64$	500.280			0.977108
$65$		0			0
$66$	−13.5947	−	25.2178i	−0.0253545	−	0.0470317i
$67$	−470.763	+	271.795i	−0.858401	+	0.495598i	−0.863476	−	0.504389i	$-0.831718\pi$
$67$	−470.763	+	271.795i	−0.858401	+	0.495598i	0.00507574	+	0.999987i	$0.498384\pi$
$68$	−305.956	+	176.644i	−0.545627	+	0.315018i
$69$	478.987	+	888.505i	0.835699	+	1.55019i
$70$		0			0
$71$	−928.207			−1.55152			−0.775760	−	0.631028i	$-0.782633\pi$
$71$	−928.207			−1.55152			−0.775760	+	0.631028i	$0.782633\pi$
$72$	−4.39891	+	75.3203i	−0.00720024	+	0.123286i
$73$		−	608.739i		−	0.975993i	−0.872845	−	0.487997i	$-0.837728\pi$
$73$		−	608.739i		−	0.975993i	0.872845	−	0.487997i	$-0.162272\pi$
$74$	5.44459	−	9.43030i	0.00855298	−	0.0148142i
$75$		0			0
$76$	−359.452	−	622.589i	−0.542526	−	0.939682i
$77$	−230.949	+	133.338i	−0.341806	+	0.197342i
$78$	−0.712510	+	24.4207i	−0.00103431	+	0.0354500i
$79$	307.420	−	532.467i	0.437816	−	0.758319i	−0.559705	−	0.828692i	$-0.689085\pi$
$79$	307.420	−	532.467i	0.437816	−	0.758319i	0.997521	+	0.0703726i	$0.0224188\pi$
$80$		0			0
$81$	724.044	+	84.8617i	0.993201	+	0.116408i
$82$			35.7573i			0.0481553i
$83$	931.246	+	537.655i	1.23154	+	0.711028i	0.967350	−	0.253444i	$-0.0815634\pi$
$83$	931.246	+	537.655i	1.23154	+	0.711028i	0.264186	+	0.964472i	$0.414897\pi$
$84$	350.334	+	10.2215i	0.455055	+	0.0132769i
$85$		0			0
$86$	−46.1663	−	79.9623i	−0.0578865	−	0.100262i
$87$	−16.5559	−	10.2136i	−0.0204020	−	0.0125864i
$88$	−76.2506	−	44.0233i	−0.0923675	−	0.0533284i
$89$	−1505.15			−1.79265			−0.896324	−	0.443400i	$-0.853772\pi$
$89$	−1505.15			−1.79265			−0.896324	+	0.443400i	$0.853772\pi$
$90$		0			0
$91$	227.416			0.261975
$92$	1340.70	+	774.055i	1.51933	+	0.877183i
$93$	1151.07	−	620.536i	1.28345	−	0.691898i
$94$	−13.6249	−	23.5991i	−0.0149501	−	0.0258943i
$95$		0			0
$96$	82.4190	+	152.885i	0.0876234	+	0.162539i
$97$	288.160	+	166.369i	0.301631	+	0.174147i	0.643175	−	0.765719i	$-0.277617\pi$
$97$	288.160	+	166.369i	0.301631	+	0.174147i	−0.341544	+	0.939866i	$0.610950\pi$
$98$		−	47.4848i		−	0.0489458i
$99$	−467.593	+	710.695i	−0.474695	+	0.721490i
$100$		0			0
$101$	247.493	−	428.670i	0.243826	−	0.422319i	−0.717975	−	0.696069i	$-0.754931\pi$
$101$	247.493	−	428.670i	0.243826	−	0.422319i	0.961801	+	0.273750i	$0.0882640\pi$
$102$	−34.3047	−	21.1632i	−0.0333007	−	0.0205438i
$103$	545.622	−	315.015i	0.521959	−	0.301353i	−0.215777	−	0.976443i	$-0.569228\pi$
$103$	545.622	−	315.015i	0.521959	−	0.301353i	0.737736	+	0.675090i	$0.235895\pi$
$104$	37.5421	+	65.0248i	0.0353972	+	0.0613097i
$105$		0			0
$106$	−12.3971	+	21.4725i	−0.0113596	+	0.0196754i
$107$		−	1561.00i		−	1.41035i	−0.709034	−	0.705175i	$-0.750869\pi$
$107$		−	1561.00i		−	1.41035i	0.709034	−	0.705175i	$-0.249131\pi$
$108$	1013.43	−	472.277i	0.902939	−	0.420786i
$109$	936.140			0.822623			0.411311	−	0.911495i	$-0.365071\pi$
$109$	936.140			0.822623			0.411311	+	0.911495i	$0.365071\pi$
$110$		0			0
$111$	−323.215	−	9.43030i	−0.276381	−	0.00806382i
$112$	463.727	−	267.733i	0.391233	−	0.225878i
$113$	−1173.45	+	677.490i	−0.976890	+	0.564008i	−0.901330	−	0.433134i	$-0.857408\pi$
$113$	−1173.45	+	677.490i	−0.976890	+	0.564008i	−0.0755602	+	0.997141i	$0.524075\pi$
$114$	43.0649	−	69.8065i	0.0353807	−	0.0573506i
$115$		0			0
$116$	−29.8351			−0.0238803
$117$	648.363	−	325.491i	0.512318	−	0.257194i
$118$		−	86.4153i		−	0.0674167i
$119$	−187.601	+	324.935i	−0.144516	+	0.250309i
$120$		0			0
$121$	169.115	+	292.915i	0.127058	+	0.220071i
$122$	115.093	−	66.4490i	0.0854101	−	0.0493115i
$123$	934.648	−	503.862i	0.685157	−	0.369363i
$124$	1002.80	−	1736.90i	0.726244	−	1.25789i
$125$		0			0
$126$	17.9407	+	35.7370i	0.0126848	+	0.0252675i
$127$		−	1182.37i		−	0.826126i	−0.910702	−	0.413063i	$-0.864459\pi$
$127$		−	1182.37i		−	0.826126i	0.910702	−	0.413063i	$-0.135541\pi$
$128$	307.393	+	177.474i	0.212266	+	0.122552i
$129$	−1439.57	+	2333.48i	−0.982535	+	1.59265i
$130$		0			0
$131$	−1126.87	−	1951.80i	−0.751569	−	1.30176i	−0.947062	−	0.321050i	$-0.895964\pi$
$131$	−1126.87	−	1951.80i	−0.751569	−	1.30176i	0.195494	−	0.980705i	$-0.437369\pi$
$132$	−38.0522	+	1304.21i	−0.0250910	+	0.859974i
$133$	−661.207	−	381.748i	−0.431082	−	0.248885i
$134$	−95.1199			−0.0613217
$135$		0			0
$136$	−123.877			−0.0781059
$137$	−410.246	−	236.856i	−0.255837	−	0.147708i	0.366597	−	0.930380i	$-0.380523\pi$
$137$	−410.246	−	236.856i	−0.255837	−	0.147708i	−0.622434	+	0.782672i	$0.713856\pi$
$138$	−5.15119	+	176.553i	−0.00317753	+	0.108907i
$139$	−68.5193	−	118.679i	−0.0418110	−	0.0724188i	0.844363	−	0.535772i	$-0.179979\pi$
$139$	−68.5193	−	118.679i	−0.0418110	−	0.0724188i	−0.886174	+	0.463353i	$0.846646\pi$
$140$		0			0
$141$	−424.857	+	688.675i	−0.253755	+	0.411326i
$142$	−140.662	−	81.2110i	−0.0831272	−	0.0479935i
$143$			846.613i			0.495086i
$144$	938.889	−	1427.02i	0.543339	−	0.825820i
$145$		0			0
$146$	53.2600	−	92.2490i	0.0301906	−	0.0522917i
$147$	−1241.19	+	669.115i	−0.696404	+	0.375426i
$148$	−429.487	+	247.965i	−0.238538	+	0.137720i
$149$	−71.5553	−	123.937i	−0.0393426	−	0.0681433i	0.845684	−	0.533685i	$-0.179193\pi$
$149$	−71.5553	−	123.937i	−0.0393426	−	0.0681433i	−0.885026	+	0.465541i	$0.845860\pi$
$150$		0			0
$151$	−108.421	+	187.790i	−0.0584314	+	0.101206i	−0.893761	−	0.448543i	$-0.851943\pi$
$151$	−108.421	+	187.790i	−0.0584314	+	0.101206i	0.835330	+	0.549749i	$0.185277\pi$
$152$		−	252.077i		−	0.134514i
$153$	−69.7850	+	1194.89i	−0.0368744	+	0.631381i
$154$	−46.6644			−0.0244177
$155$		0			0
$156$	584.202	−	946.967i	0.299831	−	0.486013i
$157$	1167.78	−	674.215i	0.593622	−	0.342728i	−0.172906	−	0.984938i	$-0.555316\pi$
$157$	1167.78	−	674.215i	0.593622	−	0.342728i	0.766528	+	0.642211i	$0.221983\pi$
$158$	93.1736	−	53.7938i	0.0469145	−	0.0270861i
$159$	735.951	+	21.4725i	0.367074	+	0.0107099i
$160$		0			0
$161$	1644.14			0.804822
$162$	102.298	+	76.2083i	0.0496127	+	0.0369598i
$163$		−	1039.85i		−	0.499676i	−0.968288	−	0.249838i	$-0.919623\pi$
$163$		−	1039.85i		−	0.499676i	0.968288	−	0.249838i	$-0.0803774\pi$
$164$	814.254	−	1410.33i	0.387699	−	0.671514i
$165$		0			0
$166$	94.0813	+	162.954i	0.0439887	+	0.0761907i
$167$	−2881.31	+	1663.52i	−1.33510	+	0.770822i	−0.986077	−	0.166291i	$-0.946821\pi$
$167$	−2881.31	+	1663.52i	−1.33510	+	0.770822i	−0.349026	+	0.937113i	$0.613487\pi$
$168$	104.592	+	64.5248i	0.0480324	+	0.0296321i
$169$	−737.513	+	1277.41i	−0.335691	+	0.581434i
$170$		0			0
$171$	−2431.48	−	142.005i	−1.08737	−	0.0635052i
$172$			4205.13i			1.86418i
$173$	−1034.25	−	597.127i	−0.454525	−	0.262420i	0.255214	−	0.966885i	$-0.417854\pi$
$173$	−1034.25	−	597.127i	−0.454525	−	0.262420i	−0.709740	+	0.704464i	$0.751187\pi$
$174$	−1.61528	−	2.99630i	−0.000703760	−	0.00130545i
$175$		0			0
$176$	996.702	+	1726.34i	0.426871	+	0.739362i
$177$	−2258.78	+	1217.69i	−0.959210	+	0.517103i
$178$	−228.092	−	131.689i	−0.0960463	−	0.0554523i
$179$	−2323.70			−0.970288			−0.485144	−	0.874434i	$-0.661233\pi$
$179$	−2323.70			−0.970288			−0.485144	+	0.874434i	$0.661233\pi$
$180$		0			0
$181$	2527.12			1.03779			0.518893	−	0.854839i	$-0.326344\pi$
$181$	2527.12			1.03779			0.518893	+	0.854839i	$0.326344\pi$
$182$	34.4629	+	19.8972i	0.0140361	+	0.00810372i
$183$	−3358.68	−	2072.03i	−1.35672	−	0.836988i
$184$	271.416	+	470.106i	0.108745	+	0.188352i
$185$		0			0
$186$	228.727	+	6.67346i	0.0901671	+	0.00263076i
$187$	−1209.65	−	698.391i	−0.473039	−	0.273109i
$188$			1241.05i			0.481452i
$189$	681.311	−	972.520i	0.262212	−	0.374288i
$190$		0			0
$191$	−1194.43	+	2068.82i	−0.452493	+	0.783741i	−0.998540	−	0.0540134i	$-0.982799\pi$
$191$	−1194.43	+	2068.82i	−0.452493	+	0.783741i	0.546047	+	0.837754i	$0.316132\pi$
$192$	75.8129	−	2598.42i	0.0284965	−	0.976693i
$193$	−3072.64	+	1773.99i	−1.14597	+	0.661629i	−0.947903	−	0.318559i	$-0.896801\pi$
$193$	−3072.64	+	1773.99i	−1.14597	+	0.661629i	−0.198072	+	0.980188i	$0.563468\pi$
$194$	29.1120	+	50.4235i	0.0107738	+	0.0186608i
$195$		0			0
$196$	−1081.31	+	1872.88i	−0.394063	+	0.682536i
$197$		−	1239.26i		−	0.448192i	−0.974567	−	0.224096i	$-0.928057\pi$
$197$		−	1239.26i		−	0.448192i	0.974567	−	0.224096i	$-0.0719430\pi$
$198$	−133.040	+	66.7887i	−0.0477512	+	0.0239720i
$199$	−516.657			−0.184044			−0.0920222	−	0.995757i	$-0.529333\pi$
$199$	−516.657			−0.184044			−0.0920222	+	0.995757i	$0.529333\pi$
$200$		0			0
$201$	1340.35	+	2486.30i	0.470353	+	0.872489i
$202$	75.0107	−	43.3074i	0.0261274	−	0.0150847i
$203$	−27.4406	+	15.8429i	−0.00948746	+	0.00547759i
$204$	871.114	+	1615.89i	0.298971	+	0.554583i
$205$		0			0
$206$	110.246			0.0372873
$207$	4687.43	−	2353.18i	1.57391	−	0.790133i
$208$		−	1699.93i		−	0.566678i
$209$	1421.15	−	2461.51i	0.470350	−	0.814670i
$210$		0			0
$211$	8.92159	+	15.4527i	0.00291084	+	0.00504173i	0.867477	−	0.497477i	$-0.165740\pi$
$211$	8.92159	+	15.4527i	0.00291084	+	0.00504173i	−0.864566	+	0.502519i	$0.832407\pi$
$212$	977.928	−	564.607i	0.316813	−	0.182912i
$213$	−140.662	+	4821.05i	−0.0452487	+	1.55086i
$214$	136.575	−	236.555i	0.0436266	−	0.0755635i
$215$		0			0
$216$	390.543	+	34.2618i	0.123024	+	0.0107927i
$217$		−	2130.01i		−	0.666334i
$218$	141.864	+	81.9050i	0.0440744	+	0.0254464i
$219$	−3161.76	−	92.2490i	−0.975578	−	0.0284640i
$220$		0			0
$221$	595.573	+	1031.56i	0.181279	+	0.313984i
$222$	−48.1554	−	29.7079i	−0.0145584	−	0.00898138i
$223$	856.978	+	494.777i	0.257343	+	0.148577i	0.623122	−	0.782125i	$-0.285864\pi$
$223$	856.978	+	494.777i	0.257343	+	0.148577i	−0.365779	+	0.930702i	$0.619197\pi$
$224$	282.906			0.0843860
$225$		0			0
$226$	−237.101			−0.0697863
$227$	2967.98	+	1713.57i	0.867806	+	0.501028i	0.866619	−	0.498971i	$-0.166289\pi$
$227$	2967.98	+	1713.57i	0.867806	+	0.501028i	0.00118754	+	0.999999i	$0.499622\pi$
$228$	−3288.16	+	1772.62i	−0.955104	+	0.514890i
$229$	549.805	+	952.290i	0.158656	+	0.274800i	0.934384	−	0.356267i	$-0.115951\pi$
$229$	549.805	+	952.290i	0.158656	+	0.274800i	−0.775728	+	0.631067i	$0.782617\pi$
$230$		0			0
$231$	657.554	+	1219.74i	0.187290	+	0.347416i
$232$	−9.05985	−	5.23071i	−0.00256383	−	0.00148023i
$233$		−	4459.91i		−	1.25399i	−0.779025	−	0.626993i	$-0.784285\pi$
$233$		−	4459.91i		−	1.25399i	0.779025	−	0.626993i	$-0.215715\pi$
$234$	126.732	+	7.40147i	0.0354047	+	0.00206773i
$235$		0			0
$236$	−1967.82	+	3408.37i	−0.542772	+	0.940109i
$237$	−2719.02	−	1677.41i	−0.745228	−	0.459745i
$238$	−56.8586	+	32.8273i	−0.0154857	+	0.00894067i
$239$	3272.23	+	5667.66i	0.885618	+	1.53394i	0.845003	+	0.534761i	$0.179598\pi$
$239$	3272.23	+	5667.66i	0.885618	+	1.53394i	0.0406148	+	0.999175i	$0.487068\pi$
$240$		0			0
$241$	105.162	−	182.147i	0.0281083	−	0.0486851i	−0.851629	−	0.524145i	$-0.824385\pi$
$241$	105.162	−	182.147i	0.0281083	−	0.0486851i	0.879737	+	0.475460i	$0.157718\pi$
$242$			59.1849i			0.0157213i
$243$	550.489	−	3747.78i	0.145325	−	0.989384i
$244$	−6052.61			−1.58803
$245$		0			0
$246$	185.722	+	5.41871i	0.0481349	+	0.00140441i
$247$	−2099.12	+	1211.93i	−0.540744	+	0.312199i
$248$	609.031	−	351.624i	0.155942	−	0.0900329i
$249$	2933.67	−	4755.36i	0.746642	−	1.21028i
$250$		0			0
$251$	816.143			0.205237			0.102618	−	0.994721i	$-0.467278\pi$
$251$	816.143			0.205237			0.102618	+	0.994721i	$0.467278\pi$
$252$	106.180	−	1818.07i	0.0265425	−	0.454474i
$253$			6120.71i			1.52097i
$254$	103.448	−	179.177i	0.0255547	−	0.0442621i
$255$		0			0
$256$	−1970.06	−	3412.25i	−0.480972	−	0.833069i
$257$	−3613.36	+	2086.17i	−0.877023	+	0.506350i	−0.869676	−	0.493623i	$-0.835672\pi$
$257$	−3613.36	+	2086.17i	−0.877023	+	0.506350i	−0.00734758	+	0.999973i	$0.502339\pi$
$258$	−422.316	+	227.667i	−0.101908	+	0.0549378i
$259$	−263.346	+	456.128i	−0.0631795	+	0.109430i
$260$		0			0
$261$	−55.5579	+	84.4425i	−0.0131760	+	0.0200263i
$262$		−	394.371i		−	0.0929937i
$263$	−2439.64	−	1408.52i	−0.571994	−	0.330241i	0.185951	−	0.982559i	$-0.440463\pi$
$263$	−2439.64	−	1408.52i	−0.571994	−	0.330241i	−0.757945	+	0.652318i	$0.773797\pi$
$264$	−240.209	+	389.370i	−0.0559995	+	0.0907729i
$265$		0			0
$266$	−66.8001	−	115.701i	−0.0153976	−	0.0266695i
$267$	−228.092	+	7817.66i	−0.0522810	+	1.79189i
$268$	3751.69	+	2166.04i	0.855115	+	0.493701i
$269$	102.610			0.0232573			0.0116287	−	0.999932i	$-0.496298\pi$
$269$	102.610			0.0232573			0.0116287	+	0.999932i	$0.496298\pi$
$270$		0			0
$271$	−3337.27			−0.748061			−0.374031	−	0.927416i	$-0.622025\pi$
$271$	−3337.27			−0.748061			−0.374031	+	0.927416i	$0.622025\pi$
$272$	2428.88	+	1402.31i	0.541443	+	0.312602i
$273$	34.4629	−	1181.19i	0.00764026	−	0.261863i
$274$	−41.4461	−	71.7867i	−0.00913814	−	0.0158277i
$275$		0			0
$276$	4223.57	−	6846.23i	0.921120	−	1.49310i
$277$	−548.959	−	316.941i	−0.119075	−	0.0687479i	0.439280	−	0.898350i	$-0.355234\pi$
$277$	−548.959	−	316.941i	−0.119075	−	0.0687479i	−0.558354	+	0.829603i	$0.688567\pi$
$278$		−	23.9796i		−	0.00517339i
$279$	−3048.59	−	6072.65i	−0.654173	−	1.30308i
$280$		0			0
$281$	3101.20	−	5371.44i	0.658370	−	1.14033i	−0.322667	−	0.946513i	$-0.604579\pi$
$281$	3101.20	−	5371.44i	0.658370	−	1.14033i	0.981037	−	0.193818i	$-0.0620872\pi$
$282$	−124.637	+	67.1909i	−0.0263193	+	0.0141885i
$283$	6477.98	−	3740.06i	1.36069	−	0.785596i	0.370976	−	0.928642i	$-0.379023\pi$
$283$	6477.98	−	3740.06i	1.36069	−	0.785596i	0.989716	+	0.143047i	$0.0456899\pi$
$284$	3698.62	+	6406.19i	0.772791	+	1.33851i
$285$		0			0
$286$	−74.0722	+	128.297i	−0.0153146	+	0.0265257i
$287$		−	1729.52i		−	0.355716i
$288$	806.564	−	404.911i	0.165025	−	0.0828459i
$289$	2947.79			0.599998
$290$		0			0
$291$	907.780	−	1471.47i	0.182869	−	0.296424i
$292$	−4201.33	+	2425.64i	−0.842000	+	0.486129i
$293$	4188.54	−	2418.26i	0.835144	−	0.482171i	−0.0204666	−	0.999791i	$-0.506515\pi$
$293$	4188.54	−	2418.26i	0.835144	−	0.482171i	0.855611	+	0.517620i	$0.173182\pi$
$294$	−246.633	−	7.19590i	−0.0489250	−	0.00142746i
$295$		0			0
$296$	−173.893			−0.0341464
$297$	3620.45	+	2536.35i	0.707339	+	0.495535i
$298$		−	25.0422i		−	0.00486796i
$299$	2609.81	−	4520.31i	0.504779	−	0.874303i
$300$		0			0
$301$	2232.99	+	3867.65i	0.427599	+	0.740623i
$302$	−32.8604	+	18.9719i	−0.00626126	+	0.00361494i
$303$	−2188.98	−	1350.42i	−0.415029	−	0.256039i
$304$	−2853.56	+	4942.51i	−0.538365	+	0.932475i
$305$		0			0
$306$	−115.119	+	174.970i	−0.0215063	+	0.0326874i
$307$		−	5611.86i		−	1.04328i	−0.853167	−	0.521638i	$-0.825321\pi$
$307$		−	5611.86i		−	1.04328i	0.853167	−	0.521638i	$-0.174679\pi$
$308$	1840.52	+	1062.63i	0.340498	+	0.196587i
$309$	−1553.49	−	2881.67i	−0.286002	−	0.530525i
$310$		0			0
$311$	−5460.70	−	9458.21i	−0.995653	−	1.72452i	−0.578489	−	0.815690i	$-0.696358\pi$
$311$	−5460.70	−	9458.21i	−0.995653	−	1.72452i	−0.417163	−	0.908831i	$-0.636976\pi$
$312$	343.424	−	185.138i	0.0623159	−	0.0335941i
$313$	4313.44	+	2490.36i	0.778946	+	0.449724i	0.836056	−	0.548643i	$-0.184856\pi$
$313$	4313.44	+	2490.36i	0.778946	+	0.449724i	−0.0571109	+	0.998368i	$0.518189\pi$
$314$	235.955			0.0424067
$315$		0			0
$316$	−4899.89			−0.872280
$317$	3252.90	+	1878.06i	0.576344	+	0.332752i	0.759679	−	0.650298i	$-0.225356\pi$
$317$	3252.90	+	1878.06i	0.576344	+	0.332752i	−0.183335	+	0.983050i	$0.558689\pi$
$318$	109.648	+	67.6440i	0.0193357	+	0.0119286i
$319$	−58.9789	−	102.154i	−0.0103517	−	0.0179296i
$320$		0			0
$321$	−8107.73	−	236.555i	−1.40975	−	0.0411316i
$322$	249.155	+	143.849i	0.0431206	+	0.0248957i
$323$		−	3998.99i		−	0.688885i
$324$	−2299.40	−	5335.27i	−0.394273	−	0.914827i
$325$		0			0
$326$	90.9788	−	157.580i	0.0154566	−	0.0267716i
$327$	141.864	−	4862.25i	0.0239911	−	0.822273i
$328$	494.520	−	285.511i	0.0832479	−	0.0480632i
$329$	659.016	+	1141.45i	0.110434	+	0.191277i
$330$		0			0
$331$	453.477	−	785.445i	0.0753031	−	0.130429i	−0.825915	−	0.563795i	$-0.809341\pi$
$331$	453.477	−	785.445i	0.0753031	−	0.130429i	0.901218	+	0.433366i	$0.142674\pi$
$332$		−	8569.55i		−	1.41661i
$333$	−97.9609	+	1677.33i	−0.0161208	+	0.276028i
$334$	−582.182			−0.0953759
$335$		0			0
$336$	−1320.32	−	2449.14i	−0.214372	−	0.397654i
$337$	8555.20	−	4939.35i	1.38288	−	0.798408i	0.390383	−	0.920653i	$-0.372343\pi$
$337$	8555.20	−	4939.35i	1.38288	−	0.798408i	0.992500	+	0.122245i	$0.0390093\pi$
$338$	−223.527	+	129.053i	−0.0359712	+	0.0207680i
$339$	3341.02	+	6197.48i	0.535278	+	0.992923i
$340$		0			0
$341$	7929.49			1.25925
$342$	−356.045	−	234.255i	−0.0562944	−	0.0370382i
$343$			5199.81i			0.818553i
$344$	−737.247	+	1276.95i	−0.115551	+	0.200141i
$345$		0			0
$346$	−104.488	−	180.979i	−0.0162350	−	0.0281199i
$347$	−3039.50	+	1754.86i	−0.470228	+	0.271486i	−0.716335	−	0.697757i	$-0.754182\pi$
$347$	−3039.50	+	1754.86i	−0.470228	+	0.271486i	0.246107	+	0.969243i	$0.420848\pi$
$348$	−4.52124	+	154.962i	−0.000696448	+	0.0238702i
$349$	−5196.48	+	9000.57i	−0.797024	+	1.38049i	0.124522	+	0.992217i	$0.460260\pi$
$349$	−5196.48	+	9000.57i	−0.797024	+	1.38049i	−0.921546	+	0.388269i	$0.873073\pi$
$350$		0			0
$351$	−1592.33	−	3416.88i	−0.242143	−	0.519600i
$352$			1053.19i			0.159475i
$353$	7002.16	+	4042.70i	1.05577	+	0.609550i	0.924259	−	0.381765i	$-0.124684\pi$
$353$	7002.16	+	4042.70i	1.05577	+	0.609550i	0.131512	+	0.991315i	$0.458017\pi$
$354$	−448.836	−	13.0955i	−0.0673881	−	0.00196615i
$355$		0			0
$356$	5997.56	+	10388.1i	0.892893	+	1.54654i
$357$	1659.26	+	1023.63i	0.245987	+	0.151754i
$358$	−352.136	−	203.306i	−0.0519860	−	0.0300141i
$359$	8189.49			1.20397			0.601984	−	0.798508i	$-0.294377\pi$
$359$	8189.49			1.20397			0.601984	+	0.798508i	$0.294377\pi$
$360$		0			0
$361$	1278.52			0.186400
$362$	382.962	+	221.103i	0.0556024	+	0.0321020i
$363$	1547.01	−	833.983i	0.223683	−	0.120586i
$364$	−906.184	−	1569.56i	−0.130486	−	0.226008i
$365$		0			0
$366$	−327.691	−	607.856i	−0.0467996	−	0.0868119i
$367$	7789.60	+	4497.33i	1.10794	+	0.639669i	0.938295	−	0.345836i	$-0.112405\pi$
$367$	7789.60	+	4497.33i	1.10794	+	0.639669i	0.169645	+	0.985505i	$0.445738\pi$
$368$		−	12289.9i		−	1.74091i
$369$	−2475.39	−	4930.86i	−0.349224	−	0.695638i
$370$		0			0
$371$	599.629	−	1038.59i	0.0839116	−	0.145339i
$372$	−8869.42	−	5471.71i	−1.23618	−	0.762621i
$373$	805.288	−	464.934i	0.111786	−	0.0645398i	−0.443064	−	0.896490i	$-0.646109\pi$
$373$	805.288	−	464.934i	0.111786	−	0.0645398i	0.554851	+	0.831950i	$0.312775\pi$
$374$	−122.208	−	211.670i	−0.0168963	−	0.0292652i
$375$		0			0
$376$	−217.582	+	376.863i	−0.0298429	+	0.0516894i
$377$			100.592i			0.0137420i
$378$	188.335	−	87.7673i	0.0256267	−	0.0119425i
$379$	−3449.71			−0.467546			−0.233773	−	0.972291i	$-0.575107\pi$
$379$	−3449.71			−0.467546			−0.233773	+	0.972291i	$0.575107\pi$
$380$		0			0
$381$	−6141.14	−	179.177i	−0.825775	−	0.0240932i
$382$	−362.012	+	209.007i	−0.0484872	+	0.0279941i
$383$	4629.89	−	2673.07i	0.617692	−	0.356625i	−0.158278	−	0.987395i	$-0.550594\pi$
$383$	4629.89	−	2673.07i	0.617692	−	0.356625i	0.775970	+	0.630770i	$0.217261\pi$
$384$	968.370	−	1569.69i	0.128690	−	0.208601i
$385$		0			0
$386$	−620.841			−0.0818652
$387$	11901.8	+	7830.66i	1.56332	+	1.02857i
$388$		−	2651.72i		−	0.346960i
$389$	3861.72	−	6688.70i	0.503334	−	0.871801i	−0.496658	−	0.867946i	$-0.665440\pi$
$389$	3861.72	−	6688.70i	0.503334	−	0.871801i	0.999993	−	0.00385448i	$-0.00122692\pi$
$390$		0			0
$391$	4305.78	+	7457.83i	0.556912	+	0.964600i
$392$	−656.709	+	379.151i	−0.0846144	+	0.0488521i
$393$	−10308.3	+	5557.14i	−1.32312	+	0.713284i
$394$	108.426	−	187.799i	0.0138640	−	0.0240132i
$395$		0			0
$396$	6768.20	+	395.282i	0.858876	+	0.0501607i
$397$			7125.03i			0.900744i	0.892841	+	0.450372i	$0.148709\pi$
$397$			7125.03i			0.900744i	−0.892841	+	0.450372i	$0.851291\pi$
$398$	−78.2948	−	45.2035i	−0.00986071	−	0.00569308i
$399$	−2082.98	+	3376.42i	−0.261352	+	0.423640i
$400$		0			0
$401$	896.547	+	1552.86i	0.111649	+	0.193382i	0.916435	−	0.400183i	$-0.131053\pi$
$401$	896.547	+	1552.86i	0.111649	+	0.193382i	−0.804786	+	0.593565i	$0.797720\pi$
$402$	−14.4146	+	494.047i	−0.00178839	+	0.0612956i
$403$	−5856.15	−	3381.05i	−0.723860	−	0.417921i
$404$	−3944.73			−0.485786
$405$		0			0
$406$	−5.54451			−0.000677757
$407$	−1698.05	−	980.369i	−0.206804	−	0.119398i
$408$	−18.7725	+	643.412i	−0.00227789	+	0.0780727i
$409$	1569.87	+	2719.09i	0.189792	+	0.328729i	0.945181	−	0.326548i	$-0.105885\pi$
$409$	1569.87	+	2719.09i	0.189792	+	0.328729i	−0.755389	+	0.655277i	$0.772552\pi$
$410$		0			0
$411$	−1292.38	+	2094.90i	−0.155106	+	0.251420i
$412$	−4348.27	−	2510.48i	−0.519961	−	0.300200i
$413$			4179.77i			0.497997i
$414$	916.224	+	53.5100i	0.108768	+	0.00635235i
$415$		0			0
$416$	449.068	−	777.808i	0.0529263	−	0.0916711i
$417$	−626.795	+	337.900i	−0.0736074	+	0.0396812i
$418$	430.726	−	248.680i	0.0504007	−	0.0290989i
$419$	1228.70	+	2128.17i	0.143260	+	0.248133i	0.928722	−	0.370776i	$-0.120908\pi$
$419$	1228.70	+	2128.17i	0.143260	+	0.248133i	−0.785463	+	0.618909i	$0.787575\pi$
$420$		0			0
$421$	1339.33	−	2319.80i	0.155048	−	0.268551i	−0.778029	−	0.628229i	$-0.783780\pi$
$421$	1339.33	−	2319.80i	0.155048	−	0.268551i	0.933076	+	0.359678i	$0.117113\pi$
$422$			3.12228i			0.000360167i
$423$	3512.56	+	2311.04i	0.403750	+	0.265643i
$424$	395.949			0.0453514
$425$		0			0
$426$	−443.121	+	718.281i	−0.0503974	+	0.0816921i
$427$	−5566.86	+	3214.03i	−0.630911	+	0.364257i
$428$	−10773.5	+	6220.09i	−1.21672	+	0.702476i
$429$	4397.26	+	128.297i	0.494876	+	0.0144388i
$430$		0			0
$431$	−9472.42			−1.05863			−0.529316	−	0.848425i	$-0.677551\pi$
$431$	−9472.42			−1.05863			−0.529316	+	0.848425i	$0.677551\pi$
$432$	−7269.57	−	5092.79i	−0.809623	−	0.567192i
$433$			4238.21i			0.470382i	0.971949	+	0.235191i	$0.0755715\pi$
$433$			4238.21i			0.470382i	−0.971949	+	0.235191i	$0.924428\pi$
$434$	186.360	−	322.784i	0.0206119	−	0.0357008i
$435$		0			0
$436$	−3730.23	−	6460.94i	−0.409737	−	0.709686i
$437$	−15175.9	+	8761.80i	−1.66124	+	0.959116i
$438$	−471.065	−	290.609i	−0.0513889	−	0.0317028i
$439$	2429.47	−	4207.96i	0.264128	−	0.457483i	−0.703207	−	0.710985i	$-0.748249\pi$
$439$	2429.47	−	4207.96i	0.264128	−	0.457483i	0.967335	+	0.253503i	$0.0815826\pi$
$440$		0			0
$441$	3287.25	+	6548.05i	0.354957	+	0.707057i
$442$			208.432i			0.0224301i
$443$	2022.82	+	1167.88i	0.216946	+	0.125254i	0.604535	−	0.796578i	$-0.293359\pi$
$443$	2022.82	+	1167.88i	0.216946	+	0.125254i	−0.387589	+	0.921832i	$0.626692\pi$
$444$	1222.83	+	2268.31i	0.130705	+	0.242453i
$445$		0			0
$446$	86.5783	+	149.958i	0.00919193	+	0.0159209i
$447$	−654.568	+	352.873i	−0.0692617	+	0.0373385i
$448$	−3666.94	−	2117.11i	−0.386712	−	0.223268i
$449$	−13290.5			−1.39692			−0.698460	−	0.715649i	$-0.746131\pi$
$449$	−13290.5			−1.39692			−0.698460	+	0.715649i	$0.746131\pi$
$450$		0			0
$451$	6438.58			0.672241
$452$	9351.64	+	5399.17i	0.973151	+	0.561849i
$453$	958.941	+	591.588i	0.0994591	+	0.0613582i
$454$	299.848	+	519.351i	0.0309968	+	0.0536880i
$455$		0			0
$456$	−1309.28	−	38.2001i	−0.134457	−	0.00392299i
$457$	−4481.35	−	2587.31i	−0.458706	−	0.264834i	0.252794	−	0.967520i	$-0.418650\pi$
$457$	−4481.35	−	2587.31i	−0.458706	−	0.264834i	−0.711500	+	0.702686i	$0.751984\pi$
$458$			192.415i			0.0196309i
$459$	6195.63	+	543.534i	0.630037	+	0.0552724i
$460$		0			0
$461$	−3170.44	+	5491.37i	−0.320309	+	0.554791i	−0.980552	−	0.196261i	$-0.937120\pi$
$461$	−3170.44	+	5491.37i	−0.320309	+	0.554791i	0.660243	+	0.751052i	$0.270453\pi$
$462$	−7.07157	+	242.372i	−0.000712119	+	0.0244073i
$463$	−2756.38	+	1591.40i	−0.276673	+	0.159737i	−0.631916	−	0.775036i	$-0.717731\pi$
$463$	−2756.38	+	1591.40i	−0.276673	+	0.159737i	0.355243	+	0.934774i	$0.384398\pi$
$464$	118.425	+	205.118i	0.0118486	+	0.0205223i
$465$		0			0
$466$	390.208	−	675.860i	0.0387898	−	0.0671859i
$467$		−	8576.23i		−	0.849808i	−0.905238	−	0.424904i	$-0.860308\pi$
$467$		−	8576.23i		−	0.849808i	0.905238	−	0.424904i	$-0.139692\pi$
$468$	−4829.96	−	3177.82i	−0.477062	−	0.313877i
$469$	4600.79			0.452974
$470$		0			0
$471$	−3324.87	−	6167.53i	−0.325269	−	0.603365i
$472$	−1195.11	+	690.000i	−0.116546	+	0.0672877i
$473$	−14398.3	+	8312.84i	−1.39965	+	0.808086i
$474$	−265.282	−	492.090i	−0.0257064	−	0.0476845i
$475$		0			0
$476$	2990.13			0.287925
$477$	223.054	−	3819.23i	0.0214107	−	0.366605i
$478$			1145.18i			0.109580i
$479$	1458.82	−	2526.76i	0.139155	−	0.241024i	−0.788022	−	0.615647i	$-0.788895\pi$
$479$	1458.82	−	2526.76i	0.139155	−	0.241024i	0.927177	+	0.374623i	$0.122228\pi$
$480$		0			0
$481$	836.037	+	1448.06i	0.0792516	+	0.137268i
$482$	31.8729	−	18.4018i	0.00301197	−	0.00173896i
$483$	249.155	−	8539.56i	0.0234719	−	0.804479i
$484$	1347.74	−	2334.35i	0.126572	−	0.219229i
$485$		0			0
$486$	411.324	−	519.779i	0.0383910	−	0.0485137i
$487$		−	14061.0i		−	1.30834i	−0.756346	−	0.654172i	$-0.773017\pi$
$487$		−	14061.0i		−	1.30834i	0.756346	−	0.654172i	$-0.226983\pi$
$488$	−1837.96	−	1061.15i	−0.170493	−	0.0984343i
$489$	−5400.92	−	157.580i	−0.499464	−	0.0145726i
$490$		0			0
$491$	466.331	+	807.709i	0.0428620	+	0.0742391i	0.886661	−	0.462421i	$-0.153019\pi$
$491$	466.331	+	807.709i	0.0428620	+	0.0742391i	−0.843799	+	0.536660i	$0.819686\pi$
$492$	−7201.78	−	4442.91i	−0.659921	−	0.407118i
$493$	−143.727	−	82.9806i	−0.0131301	−	0.00758065i
$494$	−424.137			−0.0386292
$495$		0			0
$496$	−15921.8			−1.44135
$497$	6803.57	+	3928.04i	0.614048	+	0.354521i
$498$	860.629	−	463.959i	0.0774412	−	0.0417480i
$499$	−7215.39	−	12497.4i	−0.647305	−	1.12117i	−0.983764	−	0.179467i	$-0.942563\pi$
$499$	−7215.39	−	12497.4i	−0.647305	−	1.12117i	0.336459	−	0.941698i	$-0.390771\pi$
$500$		0			0
$501$	8203.60	+	15217.4i	0.731557	+	1.35701i
$502$	123.679	+	71.4062i	0.0109962	+	0.00634864i
$503$			3230.55i			0.286368i	0.989696	+	0.143184i	$0.0457341\pi$
$503$			3230.55i			0.286368i	−0.989696	+	0.143184i	$0.954266\pi$
$504$	350.988	−	533.467i	0.0310203	−	0.0471478i
$505$		0			0
$506$	−535.515	+	927.539i	−0.0470485	+	0.0814904i
$507$	6523.03	+	4024.18i	0.571397	+	0.352505i
$508$	−8160.32	+	4711.36i	−0.712708	+	0.411482i
$509$	−180.378	−	312.424i	−0.0157075	−	0.0272062i	0.858065	−	0.513541i	$-0.171667\pi$
$509$	−180.378	−	312.424i	−0.0157075	−	0.0272062i	−0.873772	+	0.486335i	$0.838333\pi$
$510$		0			0
$511$	−2576.10	+	4461.93i	−0.223013	+	0.386270i
$512$		−	3529.04i		−	0.304615i
$513$	−1106.03	+	12607.4i	−0.0951903	+	1.08505i
$514$	−730.096			−0.0626521
$515$		0			0
$516$	21841.2	+	637.250i	1.86338	+	0.0543670i
$517$	−4249.33	+	2453.35i	−0.361480	+	0.208701i
$518$	−79.8154	+	46.0814i	−0.00677005	+	0.00390869i
$519$	−3258.18	+	5281.37i	−0.275565	+	0.446679i
$520$		0			0
$521$	−11698.8			−0.983747			−0.491873	−	0.870667i	$-0.663688\pi$
$521$	−11698.8			−0.983747			−0.491873	+	0.870667i	$0.663688\pi$
$522$	−15.8074	+	7.93562i	−0.00132542	+	0.000665388i
$523$		−	18557.3i		−	1.55154i	−0.631015	−	0.775770i	$-0.717362\pi$
$523$		−	18557.3i		−	1.55154i	0.631015	−	0.775770i	$-0.282638\pi$
$524$	−8980.49	+	15554.7i	−0.748692	+	1.29677i
$525$		0			0
$526$	−246.470	−	426.899i	−0.0204308	−	0.0353872i
$527$	9661.75	−	5578.21i	0.798619	−	0.461083i
$528$	9117.54	−	4915.20i	0.751496	−	0.405126i
$529$	12784.5	−	22143.3i	1.05075	−	1.81995i
$530$		0			0
$531$	5982.32	+	11916.5i	0.488909	+	0.973883i
$532$			6084.59i			0.495866i
$533$	−4755.07	−	2745.34i	−0.386426	−	0.223103i
$534$	−718.551	+	1164.74i	−0.0582298	+	0.0943882i
$535$		0			0
$536$	759.503	+	1315.50i	0.0612044	+	0.106009i
$537$	−352.136	+	12069.2i	−0.0282976	+	0.969875i
$538$	15.5496	+	8.97756i	0.00124608	+	0.000719424i
$539$	−8550.26			−0.683276
$540$		0			0
$541$	22755.3			1.80837			0.904185	−	0.427140i	$-0.140479\pi$
$541$	22755.3			1.80837			0.904185	+	0.427140i	$0.140479\pi$
$542$	−505.733	−	291.985i	−0.0400795	−	0.0231399i
$543$	382.962	−	13125.7i	0.0302661	−	1.03734i
$544$	740.893	+	1283.26i	0.0583925	+	0.101139i
$545$		0			0
$546$	108.567	−	175.983i	0.00850962	−	0.0137937i
$547$	−5021.30	−	2899.05i	−0.392496	−	0.226608i	0.290745	−	0.956801i	$-0.406097\pi$
$547$	−5021.30	−	2899.05i	−0.392496	−	0.226608i	−0.683241	+	0.730193i	$0.739430\pi$
$548$			3775.18i			0.294284i
$549$	−11271.0	+	17130.8i	−0.876200	+	1.33174i
$550$		0			0
$551$	168.857	−	292.468i	0.0130554	−	0.0226127i
$552$	2482.84	−	1338.48i	0.191443	−	0.103205i
$553$	−4506.65	+	2601.92i	−0.346550	+	0.200081i
$554$	−55.4599	−	96.0593i	−0.00425318	−	0.00736673i
$555$		0			0
$556$	−546.056	+	945.797i	−0.0416510	+	0.0721416i
$557$			15740.3i			1.19738i	0.800982	+	0.598688i	$0.204311\pi$
$557$			15740.3i			1.19738i	−0.800982	+	0.598688i	$0.795689\pi$
$558$	69.3231	−	1186.98i	0.00525929	−	0.0900521i
$559$	14178.0			1.07275
$560$		0			0
$561$	−3810.72	+	6177.01i	−0.286789	+	0.464873i
$562$	939.919	−	542.662i	0.0705482	−	0.0407310i
$563$	−3307.45	+	1909.56i	−0.247589	+	0.142946i	−0.618660	−	0.785659i	$-0.712324\pi$
$563$	−3307.45	+	1909.56i	−0.247589	+	0.142946i	0.371071	+	0.928605i	$0.378991\pi$
$564$	6445.94	+	188.070i	0.481247	+	0.0140411i
$565$		0			0
$566$	1308.91			0.0972040
$567$	−4947.97	−	3686.07i	−0.366482	−	0.273016i
$568$			2593.78i			0.191607i
$569$	4445.56	−	7699.93i	0.327535	−	0.567308i	−0.654487	−	0.756073i	$-0.727115\pi$
$569$	4445.56	−	7699.93i	0.327535	−	0.567308i	0.982022	+	0.188766i	$0.0604487\pi$
$570$		0			0
$571$	−4193.31	−	7263.03i	−0.307329	−	0.532309i	0.670448	−	0.741956i	$-0.266102\pi$
$571$	−4193.31	−	7263.03i	−0.307329	−	0.532309i	−0.977777	+	0.209647i	$0.932768\pi$
$572$	5843.06	−	3373.49i	0.427116	−	0.246596i
$573$	10564.3	+	6517.33i	0.770211	+	0.475158i
$574$	151.320	−	262.094i	0.0110034	−	0.0190585i
$575$		0			0
$576$	−13484.6	−	787.536i	−0.975446	−	0.0569687i
$577$			16922.3i			1.22095i	0.792037	+	0.610473i	$0.209021\pi$
$577$			16922.3i			1.22095i	−0.792037	+	0.610473i	$0.790979\pi$
$578$	446.711	+	257.909i	0.0321466	+	0.0185599i
$579$	8748.35	+	16227.9i	0.627926	+	1.16478i
$580$		0			0
$581$	−4550.56	−	7881.80i	−0.324938	−	0.562809i
$582$	266.309	−	143.565i	0.0189671	−	0.0102250i
$583$	3866.40	+	2232.27i	0.274666	+	0.158578i
$584$	−1701.06			−0.120531
$585$		0			0
$586$	846.315			0.0596603
$587$	−13197.0	−	7619.29i	−0.927936	−	0.535744i	−0.0417777	−	0.999127i	$-0.513302\pi$
$587$	−13197.0	−	7619.29i	−0.927936	−	0.535744i	−0.886158	+	0.463383i	$0.846635\pi$
$588$	9563.77	+	5900.07i	0.670754	+	0.413800i
$589$	11351.1	+	19660.6i	0.794079	+	1.37539i
$590$		0			0
$591$	−6436.66	−	187.799i	−0.448002	−	0.0130711i
$592$	3409.55	+	1968.50i	0.236709	+	0.136664i
$593$			16960.2i			1.17449i	0.809409	+	0.587245i	$0.199787\pi$
$593$			16960.2i			1.17449i	−0.809409	+	0.587245i	$0.800213\pi$
$594$	326.735	+	701.123i	0.0225692	+	0.0484300i
$595$		0			0
$596$	−570.252	+	987.705i	−0.0391920	+	0.0678825i
$597$	−78.2948	+	2683.49i	−0.00536749	+	0.183966i
$598$	790.986	−	456.676i	0.0540900	−	0.0312289i
$599$	−12456.1	−	21574.5i	−0.849651	−	1.47164i	−0.881520	−	0.472147i	$-0.843479\pi$
$599$	−12456.1	−	21574.5i	−0.849651	−	1.47164i	0.0318690	−	0.999492i	$-0.489854\pi$
$600$		0			0
$601$	2175.63	−	3768.31i	0.147664	−	0.255761i	−0.782700	−	0.622399i	$-0.786158\pi$
$601$	2175.63	−	3768.31i	0.147664	−	0.255761i	0.930364	+	0.366638i	$0.119491\pi$
$602$			781.476i			0.0529080i
$603$	13116.8	−	6584.91i	0.885835	−	0.444707i
$604$	1728.09			0.116416
$605$		0			0
$606$	−213.569	−	396.164i	−0.0143163	−	0.0265562i
$607$	24096.0	−	13911.8i	1.61125	−	0.930254i	0.622166	−	0.782885i	$-0.286253\pi$
$607$	24096.0	−	13911.8i	1.61125	−	0.930254i	0.989082	−	0.147369i	$-0.0470805\pi$
$608$	−2611.31	+	1507.64i	−0.174182	+	0.100564i
$609$	78.1285	+	144.926i	0.00519856	+	0.00964317i
$610$		0			0
$611$	4184.33			0.277054
$612$	8524.84	−	4279.64i	0.563066	−	0.282670i
$613$		−	20034.6i		−	1.32005i	−0.751244	−	0.660024i	$-0.770546\pi$
$613$		−	20034.6i		−	1.32005i	0.751244	−	0.660024i	$-0.229454\pi$
$614$	490.994	−	850.427i	0.0322719	−	0.0558965i
$615$		0			0
$616$	372.600	+	645.363i	0.0243709	+	0.0422117i
$617$	6541.86	−	3776.95i	0.426848	−	0.246441i	−0.271155	−	0.962536i	$-0.587405\pi$
$617$	6541.86	−	3776.95i	0.426848	−	0.246441i	0.698003	+	0.716095i	$0.254072\pi$
$618$	16.7067	−	572.609i	0.00108745	−	0.0372714i
$619$	6192.54	−	10725.8i	0.402099	−	0.696456i	−0.591880	−	0.806026i	$-0.701614\pi$
$619$	6192.54	−	10725.8i	0.402099	−	0.696456i	0.993979	+	0.109570i	$0.0349474\pi$
$620$		0			0
$621$	−11512.0	−	24702.8i	−0.743896	−	1.59628i
$622$		−	1911.08i		−	0.123195i
$623$	11032.4	+	6369.58i	0.709479	+	0.409618i
$624$	−8829.35	−	257.610i	−0.566437	−	0.0165267i
$625$		0			0
$626$	435.775	+	754.785i	0.0278228	+	0.0481906i
$627$	−12569.6	−	7754.40i	−0.800606	−	0.493909i
$628$	−9306.45	−	5373.08i	−0.591350	−	0.341416i
$629$	−2758.67			−0.174873
$630$		0			0
$631$	−1325.17			−0.0836043			−0.0418022	−	0.999126i	$-0.513310\pi$
$631$	−1325.17			−0.0836043			−0.0418022	+	0.999126i	$0.513310\pi$
$632$	−1487.92	−	859.053i	−0.0936494	−	0.0540685i
$633$	81.6122	−	43.9965i	0.00512447	−	0.00276257i
$634$	328.632	+	569.207i	0.0205862	+	0.0356563i
$635$		0			0
$636$	−2784.34	−	5164.86i	−0.173595	−	0.322013i
$637$	6314.60	+	3645.74i	0.392769	+	0.226765i
$638$		−	20.6408i		−	0.00128084i
$639$	25019.0	+	1461.18i	1.54888	+	0.0904589i
$640$		0			0
$641$	11255.8	−	19495.6i	0.693568	−	1.20129i	−0.277094	−	0.960843i	$-0.589371\pi$
$641$	11255.8	−	19495.6i	0.693568	−	1.20129i	0.970661	−	0.240451i	$-0.0772955\pi$
$642$	−1207.96	−	745.212i	−0.0742590	−	0.0458118i
$643$	−4862.40	+	2807.31i	−0.298218	+	0.172176i	−0.641642	−	0.767004i	$-0.721747\pi$
$643$	−4862.40	+	2807.31i	−0.298218	+	0.172176i	0.343424	+	0.939180i	$0.388413\pi$
$644$	−6551.38	−	11347.3i	−0.400871	−	0.694328i
$645$		0			0
$646$	349.881	−	606.012i	0.0213094	−	0.0369090i
$647$		−	11753.6i		−	0.714188i	−0.934068	−	0.357094i	$-0.883768\pi$
$647$		−	11753.6i		−	0.714188i	0.934068	−	0.357094i	$-0.116232\pi$
$648$	237.137	−	2023.27i	0.0143760	−	0.122656i
$649$	−15560.2			−0.941127
$650$		0			0
$651$	−11063.2	−	322.784i	−0.666051	−	0.0194330i
$652$	−7176.71	+	4143.48i	−0.431076	+	0.248882i
$653$	22393.9	−	12929.1i	1.34202	−	0.774816i	0.354916	−	0.934898i	$-0.384509\pi$
$653$	22393.9	−	12929.1i	1.34202	−	0.774816i	0.987104	+	0.160082i	$0.0511760\pi$
$654$	446.908	−	724.420i	0.0267209	−	0.0433135i
$655$		0			0
$656$	−12928.1			−0.769450
$657$	−958.272	+	16408.0i	−0.0569037	+	0.974333i
$658$			230.635i			0.0136643i
$659$	−8847.75	+	15324.8i	−0.523004	+	0.905869i	0.476638	+	0.879100i	$0.341855\pi$
$659$	−8847.75	+	15324.8i	−0.523004	+	0.905869i	−0.999642	+	0.0267695i	$0.991478\pi$
$660$		0			0
$661$	−3115.05	−	5395.42i	−0.183300	−	0.317485i	0.759702	−	0.650271i	$-0.225345\pi$
$661$	−3115.05	−	5395.42i	−0.183300	−	0.317485i	−0.943002	+	0.332786i	$0.892011\pi$
$662$	137.441	−	79.3515i	0.00806916	−	0.00465873i
$663$	5448.13	−	2937.05i	0.319137	−	0.172044i
$664$	1502.42	−	2602.27i	0.0878091	−	0.152090i
$665$		0			0
$666$	−161.599	+	245.614i	−0.00940214	+	0.0142903i
$667$			727.243i			0.0422174i
$668$	22962.2	+	13257.2i	1.32999	+	0.767872i
$669$	2699.71	−	4376.12i	0.156019	−	0.252901i
$670$		0			0
$671$	−11965.0	−	20724.0i	−0.688381	−	1.19231i
$672$	42.8719	−	1469.40i	0.00246104	−	0.0843501i
$673$	−5240.91	−	3025.84i	−0.300182	−	0.173310i	0.342343	−	0.939575i	$-0.388780\pi$
$673$	−5240.91	−	3025.84i	−0.300182	−	0.173310i	−0.642524	+	0.766265i	$0.722113\pi$
$674$	1728.62			0.0987892
$675$		0			0
$676$	11755.0			0.668812
$677$	−24334.1	−	14049.3i	−1.38144	−	0.797576i	−0.389112	−	0.921190i	$-0.627218\pi$
$677$	−24334.1	−	14049.3i	−1.38144	−	0.797576i	−0.992330	+	0.123614i	$0.960551\pi$
$678$	−35.9305	+	1231.49i	−0.00203525	+	0.0697566i
$679$	−1408.10	−	2438.90i	−0.0795846	−	0.137845i
$680$		0			0
$681$	9349.93	−	15155.9i	0.526124	−	0.852825i
$682$	1201.64	+	693.769i	0.0674682	+	0.0389528i
$683$			8335.71i			0.466994i	0.972358	+	0.233497i	$0.0750169\pi$
$683$			8335.71i			0.466994i	−0.972358	+	0.233497i	$0.924983\pi$
$684$	8708.61	+	17347.1i	0.486816	+	0.969714i
$685$		0			0
$686$	−454.944	+	787.986i	−0.0253205	+	0.0438563i
$687$	5029.46	−	2711.34i	0.279310	−	0.150574i
$688$	28910.6	−	16691.5i	1.60204	−	0.924939i
$689$	−1903.63	−	3297.18i	−0.105258	−	0.182312i
$690$		0			0
$691$	8442.55	−	14622.9i	0.464790	−	0.805039i	−0.534402	−	0.845230i	$-0.679463\pi$
$691$	8442.55	−	14622.9i	0.464790	−	0.805039i	0.999192	+	0.0401909i	$0.0127966\pi$
$692$			9517.46i			0.522832i
$693$	6434.92	−	3230.46i	0.352731	−	0.177078i
$694$	−614.146			−0.0335917
$695$		0			0
$696$	−28.5409	+	46.2637i	−0.00155437	+	0.00251957i
$697$	7845.14	−	4529.39i	0.426335	−	0.246145i
$698$	−1574.96	+	909.305i	−0.0854057	+	0.0493090i
$699$	−23164.5	−	675.860i	−1.25345	−	0.0365714i
$700$		0			0
$701$	16875.2			0.909226			0.454613	−	0.890689i	$-0.349778\pi$
$701$	16875.2			0.909226			0.454613	+	0.890689i	$0.349778\pi$
$702$	57.6479	−	657.115i	0.00309940	−	0.0353293i
$703$		−	5613.59i		−	0.301167i
$704$	7881.47	−	13651.1i	0.421938	−	0.730817i
$705$		0			0
$706$	707.410	+	1225.27i	0.0377106	+	0.0653168i
$707$	−3628.14	+	2094.71i	−0.192999	+	0.111428i
$708$	17404.6	+	10737.3i	0.923879	+	0.569959i
$709$	−9503.71	+	16460.9i	−0.503412	+	0.871936i	0.496580	+	0.867991i	$0.334589\pi$
$709$	−9503.71	+	16460.9i	−0.503412	+	0.871936i	−0.999992	+	0.00394482i	$0.998744\pi$
$710$		0			0
$711$	−9124.43	+	13868.2i	−0.481284	+	0.731503i
$712$			4205.99i			0.221385i
$713$	−42337.9	−	24443.8i	−2.22379	−	1.28391i
$714$	161.887	+	300.295i	0.00848524	+	0.0157398i
$715$		0			0
$716$	9259.23	+	16037.4i	0.483287	+	0.837078i
$717$	29933.4	−	16136.9i	1.55911	−	0.840506i
$718$	1241.04	+	716.517i	0.0645061	+	0.0372426i
$719$	−17588.1			−0.912275			−0.456138	−	0.889909i	$-0.650767\pi$
$719$	−17588.1			−0.912275			−0.456138	+	0.889909i	$0.650767\pi$
$720$		0			0
$721$	−5332.40			−0.275435
$722$	193.748	+	111.861i	0.00998693	+	0.00576596i
$723$	−930.123	−	573.810i	−0.0478446	−	0.0295162i
$724$	−10069.8	−	17441.4i	−0.516907	−	0.895309i
$725$		0			0
$726$	307.403	+	8.96895i	0.0157146	+	0.000458497i
$727$	−4854.40	−	2802.69i	−0.247648	−	0.142979i	0.371039	−	0.928617i	$-0.379002\pi$
$727$	−4854.40	−	2802.69i	−0.247648	−	0.142979i	−0.618687	+	0.785638i	$0.712335\pi$
$728$		−	635.491i		−	0.0323528i
$729$	−19382.3	−	3427.15i	−0.984725	−	0.174117i
$730$		0			0
$731$	−11695.8	+	20257.7i	−0.591771	+	1.02498i
$732$	−917.220	+	31436.9i	−0.0463134	+	1.58735i
$733$	−12921.2	+	7460.04i	−0.651097	+	0.375911i	−0.788877	−	0.614552i	$-0.789337\pi$
$733$	−12921.2	+	7460.04i	−0.651097	+	0.375911i	0.137779	+	0.990463i	$0.456004\pi$
$734$	786.963	+	1363.06i	0.0395740	+	0.0685443i
$735$		0			0
$736$	3246.60	−	5623.27i	0.162597	−	0.281626i
$737$			17127.6i			0.856042i
$738$	56.2889	−	963.806i	0.00280762	−	0.0480734i
$739$	27418.8			1.36484			0.682421	−	0.730959i	$-0.260927\pi$
$739$	27418.8			1.36484			0.682421	+	0.730959i	$0.260927\pi$
$740$		0			0
$741$	5976.58	+	11086.4i	0.296296	+	0.549619i
$742$	181.737	−	104.926i	0.00899161	−	0.00519131i
$743$	21255.9	−	12272.1i	1.04953	−	0.605948i	0.127014	−	0.991901i	$-0.459461\pi$
$743$	21255.9	−	12272.1i	1.04953	−	0.605948i	0.922518	+	0.385953i	$0.126127\pi$
$744$	−1734.02	−	3216.56i	−0.0854467	−	0.158501i
$745$		0			0
$746$	162.712			0.00798569
$747$	−24254.5	−	15957.9i	−1.18799	−	0.781621i
$748$			11131.5i			0.544128i
$749$	−6605.92	+	11441.8i	−0.322263	+	0.558176i
$750$		0			0
$751$	−767.283	−	1328.97i	−0.0372817	−	0.0645738i	0.846782	−	0.531939i	$-0.178537\pi$
$751$	−767.283	−	1328.97i	−0.0372817	−	0.0645738i	−0.884064	+	0.467365i	$0.845203\pi$
$752$	8532.30	−	4926.13i	0.413752	−	0.238880i
$753$	123.679	−	4239.00i	0.00598555	−	0.205150i
$754$	−8.80102	+	15.2438i	−0.000425085	+	0.000736269i
$755$		0			0
$756$	−9426.85	−	827.005i	−0.453507	−	0.0397856i
$757$		−	18051.1i		−	0.866681i	−0.901230	−	0.433341i	$-0.857335\pi$
$757$		−	18051.1i		−	0.866681i	0.901230	−	0.433341i	$-0.142665\pi$
$758$	−522.773	−	301.823i	−0.0250501	−	0.0144627i
$759$	31790.6	+	927.539i	1.52032	+	0.0443578i
$760$		0			0
$761$	−6462.29	−	11193.0i	−0.307829	−	0.533176i	0.670058	−	0.742309i	$-0.266269\pi$
$761$	−6462.29	−	11193.0i	−0.307829	−	0.533176i	−0.977887	+	0.209133i	$0.932936\pi$
$762$	−914.958	−	564.455i	−0.0434980	−	0.0268347i
$763$	−6861.71	−	3961.61i	−0.325571	−	0.187968i
$764$	19037.8			0.901522
$765$		0			0
$766$	935.491			0.0441262
$767$	11491.6	+	6634.70i	0.540990	+	0.312341i
$768$	−18021.6	+	9715.30i	−0.846741	+	0.456472i
$769$	−1686.16	−	2920.51i	−0.0790695	−	0.136952i	0.823779	−	0.566911i	$-0.191862\pi$
$769$	−1686.16	−	2920.51i	−0.0790695	−	0.136952i	−0.902849	+	0.429958i	$0.858528\pi$
$770$		0			0
$771$	10287.9	+	19083.7i	0.480557	+	0.891418i
$772$	24487.0	+	14137.6i	1.14159	+	0.659097i
$773$			27152.6i			1.26341i	0.775211	+	0.631703i	$0.217644\pi$
$773$			27152.6i			1.26341i	−0.775211	+	0.631703i	$0.782356\pi$
$774$	1118.49	+	2227.99i	0.0519424	+	0.103467i
$775$		0			0
$776$	464.901	−	805.232i	0.0215064	−	0.0372502i
$777$	2329.19	+	1436.92i	0.107541	+	0.0663441i
$778$	1170.42	−	675.742i	0.0539352	−	0.0311395i
$779$	9216.83	+	15964.0i	0.423912	+	0.734236i
$780$		0			0
$781$	−14623.1	+	25327.9i	−0.669982	+	1.16044i
$782$			1506.89i			0.0689083i
$783$	430.170	+	301.361i	0.0196335	+	0.0137545i
$784$	17168.2			0.782080
$785$		0			0
$786$	−2048.34	−	59.7635i	−0.0929541	−	0.00271208i
$787$	−21834.3	+	12606.0i	−0.988957	+	0.570974i	−0.904962	−	0.425492i	$-0.860101\pi$
$787$	−21834.3	+	12606.0i	−0.988957	+	0.570974i	−0.0839943	+	0.996466i	$0.526768\pi$
$788$	−8553.01	+	4938.08i	−0.386660	+	0.223238i
$789$	−7685.50	+	12457.9i	−0.346782	+	0.562120i
$790$		0			0
$791$	11468.2			0.515500
$792$	1985.96	+	1306.64i	0.0891011	+	0.0586230i
$793$			20407.0i			0.913838i
$794$	−623.386	+	1079.74i	−0.0278629	+	0.0482599i
$795$		0			0
$796$	2058.72	+	3565.80i	0.0916700	+	0.158777i
$797$	33928.2	−	19588.5i	1.50790	−	0.870588i	0.507945	−	0.861390i	$-0.330405\pi$
$797$	33928.2	−	19588.5i	1.50790	−	0.870588i	0.999958	−	0.00919851i	$-0.00292802\pi$
$798$	−611.068	+	329.422i	−0.0271072	+	0.0146133i
$799$	−3451.75	+	5978.61i	−0.152834	+	0.264716i
$800$		0			0
$801$	40569.9	+	2369.40i	1.78960	+	0.104517i
$802$			313.764i			0.0138147i
$803$	−16610.6	−	9590.16i	−0.729983	−	0.421456i
$804$	11818.8	−	19157.8i	0.518430	−	0.840353i
$805$		0			0
$806$	−591.631	−	1024.74i	−0.0258552	−	0.0447826i
$807$	15.5496	−	532.949i	0.000678279	−	0.0232474i
$808$	−1197.87	−	691.593i	−0.0521548	−	0.0301116i
$809$	36739.0			1.59663			0.798316	−	0.602239i	$-0.205725\pi$
$809$	36739.0			1.59663			0.798316	+	0.602239i	$0.205725\pi$
$810$		0			0
$811$	−29660.0			−1.28422			−0.642111	−	0.766611i	$-0.721941\pi$
$811$	−29660.0			−1.28422			−0.642111	+	0.766611i	$0.721941\pi$
$812$	218.685	+	126.258i	0.00945115	+	0.00545662i
$813$	−505.733	+	17333.6i	−0.0218165	+	0.747743i
$814$	−171.549	−	297.132i	−0.00738674	−	0.0127942i
$815$		0			0
$816$	7651.61	−	12402.9i	0.328260	−	0.532096i
$817$	−41222.2	−	23799.7i	−1.76522	−	1.01915i
$818$			549.405i			0.0234835i
$819$	−6129.80	−	357.997i	−0.261529	−	0.0152740i
$820$		0			0
$821$	−10056.6	+	17418.6i	−0.427501	+	0.740453i	−0.996650	−	0.0817808i	$-0.973939\pi$
$821$	−10056.6	+	17418.6i	−0.427501	+	0.740453i	0.569149	+	0.822234i	$0.307273\pi$
$822$	−379.137	+	204.390i	−0.0160875	+	0.00867265i
$823$	−4654.06	+	2687.02i	−0.197121	+	0.113808i	−0.595312	−	0.803495i	$-0.702971\pi$
$823$	−4654.06	+	2687.02i	−0.197121	+	0.113808i	0.398191	+	0.917303i	$0.369638\pi$
$824$	−880.277	−	1524.68i	−0.0372159	−	0.0644598i
$825$		0			0
$826$	−365.697	+	633.406i	−0.0154046	+	0.0266816i
$827$			27865.2i			1.17167i	0.810432	+	0.585833i	$0.199233\pi$
$827$			27865.2i			1.17167i	−0.810432	+	0.585833i	$0.800767\pi$
$828$	−34918.9	−	22974.5i	−1.46560	−	0.964273i
$829$	−24363.1			−1.02070			−0.510352	−	0.859965i	$-0.670485\pi$
$829$	−24363.1			−1.02070			−0.510352	+	0.859965i	$0.670485\pi$
$830$		0			0
$831$	−1729.36	+	2803.23i	−0.0721913	+	0.117019i
$832$	−11641.4	+	6721.15i	−0.485086	+	0.280065i
$833$	−10418.1	+	6014.91i	−0.433333	+	0.250185i
$834$	−124.549	−	3.63390i	−0.00517119	−	0.000150877i
$835$		0			0
$836$	−22651.4			−0.937099
$837$	−32003.0	+	14914.0i	−1.32161	+	0.615892i
$838$			430.007i			0.0177259i
$839$	−17765.3	+	30770.4i	−0.731020	+	1.26616i	0.225428	+	0.974260i	$0.427622\pi$
$839$	−17765.3	+	30770.4i	−0.731020	+	1.26616i	−0.956448	+	0.291903i	$0.905711\pi$
$840$		0			0
$841$	12187.5	+	21109.4i	0.499713	+	0.865528i
$842$	405.928	−	234.363i	0.0166143	−	0.00959226i
$843$	−27429.0	−	16921.4i	−1.12065	−	0.691347i
$844$	71.0996	−	123.148i	0.00289970	−	0.00502243i
$845$		0			0
$846$	330.098	+	657.540i	0.0134149	+	0.0267219i
$847$		−	2862.68i		−	0.116131i
$848$	−7763.42	−	4482.22i	−0.314383	−	0.181509i
$849$	−18444.0	−	34213.0i	−0.745578	−	1.38302i
$850$		0			0
$851$	6044.25	+	10468.9i	0.243471	+	0.421705i
$852$	33833.9	−	18239.6i	1.36048	−	0.733426i
$853$	29832.4	+	17223.8i	1.19747	+	0.691360i	0.959991	−	0.280032i	$-0.0903452\pi$
$853$	29832.4	+	17223.8i	1.19747	+	0.691360i	0.237480	+	0.971392i	$0.423679\pi$
$854$	−1124.81			−0.0450705
$855$		0			0
$856$	−4362.05			−0.174173
$857$	−17326.4	−	10003.4i	−0.690618	−	0.398729i	0.113225	−	0.993569i	$-0.463882\pi$
$857$	−17326.4	−	10003.4i	−0.690618	−	0.398729i	−0.803844	+	0.594841i	$0.797215\pi$
$858$	655.141	+	404.169i	0.0260678	+	0.0160817i
$859$	893.190	+	1547.05i	0.0354776	+	0.0614490i	0.883219	−	0.468961i	$-0.155371\pi$
$859$	893.190	+	1547.05i	0.0354776	+	0.0614490i	−0.847741	+	0.530410i	$0.822038\pi$
$860$		0			0
$861$	−8983.04	−	262.094i	−0.355565	−	0.0103741i
$862$	−1435.46	−	828.764i	−0.0567192	−	0.0327469i
$863$		−	12151.9i		−	0.479322i	−0.970857	−	0.239661i	$-0.922964\pi$
$863$		−	12151.9i		−	0.479322i	0.970857	−	0.239661i	$-0.0770363\pi$
$864$	−1980.86	−	4250.61i	−0.0779978	−	0.167371i
$865$		0			0
$866$	−370.811	+	642.263i	−0.0145504	+	0.0252021i
$867$	446.711	−	15310.7i	0.0174984	−	0.599743i
$868$	−14700.7	+	8487.43i	−0.574854	+	0.331892i
$869$	−9686.27	−	16777.1i	−0.378118	−	0.654919i
$870$		0			0
$871$	7303.02	−	12649.2i	0.284102	−	0.492080i
$872$		−	2615.94i		−	0.101591i
$873$	−7505.18	−	4937.94i	−0.290964	−	0.191436i
$874$	−3066.36			−0.118674
$875$		0			0
$876$	11961.9	+	22189.0i	0.461366	+	0.855819i
$877$	−16344.7	+	9436.64i	−0.629330	+	0.363344i	−0.780493	−	0.625165i	$-0.785032\pi$
$877$	−16344.7	+	9436.64i	−0.629330	+	0.363344i	0.151163	+	0.988509i	$0.451698\pi$
$878$	736.328	−	425.119i	0.0283028	−	0.0163406i
$879$	−11925.5	−	22121.5i	−0.457609	−	0.848851i
$880$		0			0
$881$	23587.2			0.902014			0.451007	−	0.892520i	$-0.351065\pi$
$881$	23587.2			0.902014			0.451007	+	0.892520i	$0.351065\pi$
$882$	−74.7502	+	1279.91i	−0.00285371	+	0.0488625i
$883$			29504.5i			1.12447i	0.826978	+	0.562234i	$0.190058\pi$
$883$			29504.5i			1.12447i	−0.826978	+	0.562234i	$0.809942\pi$
$884$	4746.35	−	8220.92i	0.180585	−	0.312782i
$885$		0			0
$886$	204.360	+	353.963i	0.00774901	+	0.0134217i
$887$	2144.31	−	1238.02i	0.0811714	−	0.0468643i	−0.458865	−	0.888506i	$-0.651744\pi$
$887$	2144.31	−	1238.02i	0.0811714	−	0.0468643i	0.540036	+	0.841642i	$0.318410\pi$
$888$	−26.3520	+	903.192i	−0.000995850	+	0.0341319i
$889$	−5003.60	+	8666.49i	−0.188769	+	0.326957i
$890$		0			0
$891$	13722.3	−	18420.0i	0.515953	−	0.692586i
$892$		−	7886.13i		−	0.296017i
$893$	−12165.8	−	7023.94i	−0.455894	−	0.263211i
$894$	−130.068	−	3.79492i	−0.00486589	−	0.000141970i
$895$		0			0
$896$	−1502.09	−	2601.69i	−0.0560058	−	0.0970048i
$897$	−23082.8	−	14240.2i	−0.859210	−	0.530063i
$898$	−2014.06	−	1162.82i	−0.0748440	−	0.0432112i
$899$	942.157			0.0349529
$900$		0			0
$901$	6281.40			0.232257
$902$	975.709	+	563.326i	0.0360173	+	0.0207946i
$903$	20426.7	−	11011.9i	0.752778	−	0.405817i
$904$	1893.17	+	3279.07i	0.0696527	+	0.120642i
$905$		0			0
$906$	93.5595	+	173.550i	0.00343080	+	0.00636403i
$907$	23167.1	+	13375.5i	0.848126	+	0.489666i	0.860018	−	0.510264i	$-0.170452\pi$
$907$	23167.1	+	13375.5i	0.848126	+	0.489666i	−0.0118922	+	0.999929i	$0.503785\pi$
$908$		−	27312.1i		−	0.998221i
$909$	−7345.75	+	11164.8i	−0.268034	+	0.407385i
$910$		0			0
$911$	−6334.11	+	10971.0i	−0.230360	+	0.398996i	−0.957914	−	0.287055i	$-0.907324\pi$
$911$	−6334.11	+	10971.0i	−0.230360	+	0.398996i	0.727554	+	0.686051i	$0.240657\pi$
$912$	25238.7	+	15570.2i	0.916377	+	0.565330i
$913$	29341.9	−	16940.6i	1.06361	−	0.614076i
$914$	−452.739	−	784.167i	−0.0163843	−	0.0283785i
$915$		0			0
$916$	4381.61	−	7589.16i	0.158048	−	0.273748i
$917$			19075.1i			0.686930i
$918$	891.337	+	624.437i	0.0320463	+	0.0224504i
$919$	−46565.5			−1.67144			−0.835721	−	0.549155i	$-0.814950\pi$
$919$	−46565.5			−1.67144			−0.835721	+	0.549155i	$0.814950\pi$
$920$		0			0
$921$	−29147.7	−	850.427i	−1.04283	−	0.0304262i
$922$	−960.905	+	554.779i	−0.0343229	+	0.0198163i
$923$	21599.1	−	12470.3i	0.770253	−	0.444706i
$924$	5798.13	−	9398.53i	0.206433	−	0.334620i
$925$		0			0
$926$	−556.940			−0.0197648
$927$	−15202.6	+	7632.03i	−0.538641	+	0.270408i
$928$			125.136i			0.00442651i
$929$	2305.46	−	3993.17i	0.0814205	−	0.141024i	−0.822440	−	0.568852i	$-0.807388\pi$
$929$	2305.46	−	3993.17i	0.0814205	−	0.141024i	0.903860	+	0.427828i	$0.140721\pi$
$930$		0			0
$931$	−12239.7	−	21199.8i	−0.430870	−	0.746289i
$932$	−30780.9	+	17771.4i	−1.08183	+	0.624593i
$933$	−49952.9	+	26929.3i	−1.75283	+	0.944935i
$934$	750.354	−	1299.65i	0.0262873	−	0.0455309i
$935$		0			0
$936$	−909.551	−	1811.78i	−0.0317624	−	0.0632692i
$937$		−	6625.43i		−	0.230996i	−0.993308	−	0.115498i	$-0.963154\pi$
$937$		−	6625.43i		−	0.230996i	0.993308	−	0.115498i	$-0.0368464\pi$
$938$	697.209	+	402.534i	0.0242694	+	0.0140119i
$939$	13588.5	−	22026.4i	0.472250	−	0.765498i
$940$		0			0
$941$	21721.3	+	37622.4i	0.752491	+	1.30335i	0.946612	+	0.322375i	$0.104481\pi$
$941$	21721.3	+	37622.4i	0.752491	+	1.30335i	−0.194121	+	0.980978i	$0.562185\pi$
$942$	35.7568	−	1225.53i	0.00123675	−	0.0423886i
$943$	−34377.4	−	19847.8i	−1.18715	−	0.685402i
$944$	31243.7			1.07722
$945$		0			0
$946$	−2909.24			−0.0999868
$947$	−28511.7	−	16461.2i	−0.978357	−	0.564855i	−0.0765835	−	0.997063i	$-0.524401\pi$
$947$	−28511.7	−	16461.2i	−0.978357	−	0.564855i	−0.901774	+	0.432208i	$0.857735\pi$
$948$	−742.536	+	25449.8i	−0.0254393	+	0.871909i
$949$	8178.28	+	14165.2i	0.279745	+	0.484533i
$950$		0			0
$951$	10247.5	−	16610.8i	0.349419	−	0.566394i
$952$	907.996	+	524.232i	0.0309121	+	0.0178471i
$953$		−	20253.5i		−	0.688430i	−0.938891	−	0.344215i	$-0.888145\pi$
$953$		−	20253.5i		−	0.688430i	0.938891	−	0.344215i	$-0.111855\pi$
$954$	367.955	−	559.255i	0.0124874	−	0.0189796i
$955$		0			0
$956$	26077.6	−	45167.8i	0.882229	−	1.52806i
$957$	−539.522	+	290.853i	−0.0182239	+	0.00982437i
$958$	442.144	−	255.272i	0.0149113	−	0.00860904i
$959$	2004.68	+	3472.20i	0.0675020	+	0.116917i
$960$		0			0
$961$	−16771.8	+	29049.7i	−0.562983	+	0.975116i
$962$			292.587i			0.00980602i
$963$	−2457.31	+	42075.3i	−0.0822282	+	1.40795i
$964$	−1676.16			−0.0560015
$965$		0			0
$966$	784.903	−	1272.30i	0.0261427	−	0.0423762i
$967$	2803.43	−	1618.56i	0.0932289	−	0.0538257i	−0.452661	−	0.891683i	$-0.649525\pi$
$967$	2803.43	−	1618.56i	0.0932289	−	0.0538257i	0.545890	+	0.837857i	$0.316192\pi$
$968$	818.521	−	472.573i	0.0271780	−	0.0156912i
$969$	−20770.5	−	606.012i	−0.688592	−	0.0200907i
$970$		0			0
$971$	−1731.06			−0.0572114			−0.0286057	−	0.999591i	$-0.509107\pi$
$971$	−1731.06			−0.0572114			−0.0286057	+	0.999591i	$0.509107\pi$
$972$	−28059.5	+	11134.4i	−0.925936	+	0.367425i
$973$			1159.86i			0.0382151i
$974$	1230.23	−	2130.81i	0.0404712	−	0.0700982i
$975$		0			0
$976$	24024.8	+	41612.1i	0.787924	+	1.36472i
$977$	29918.5	−	17273.4i	0.979710	−	0.565636i	0.0775275	−	0.996990i	$-0.475297\pi$
$977$	29918.5	−	17273.4i	0.979710	−	0.565636i	0.902183	+	0.431354i	$0.141964\pi$
$978$	−804.674	−	496.418i	−0.0263094	−	0.0162308i
$979$	−23712.3	+	41071.0i	−0.774106	+	1.34079i
$980$		0			0
$981$	−25232.8	−	1473.66i	−0.821224	−	0.0479617i
$982$			163.201i			0.00530343i
$983$	17713.0	+	10226.6i	0.574726	+	0.331818i	0.759035	−	0.651050i	$-0.225671\pi$
$983$	17713.0	+	10226.6i	0.574726	+	0.331818i	−0.184309	+	0.982868i	$0.559005\pi$
$984$	−1407.99	−	2611.78i	−0.0456149	−	0.0846142i
$985$		0			0
$986$	−14.5203	−	25.1500i	−0.000468987	−	0.000812310i
$987$	6028.49	−	3249.91i	0.194416	−	0.104808i
$988$	16728.7	+	9658.31i	0.538675	+	0.311004i
$989$	102502.			3.29563
$990$		0			0
$991$	−5387.77			−0.172703			−0.0863513	−	0.996265i	$-0.527521\pi$
$991$	−5387.77			−0.172703			−0.0863513	+	0.996265i	$0.527521\pi$
$992$	−7285.05	−	4206.03i	−0.233166	−	0.134618i
$993$	−4010.84	−	2474.36i	−0.128177	−	0.0790750i
$994$	687.347	+	1190.52i	0.0219329	+	0.0379889i
$995$		0			0
$996$	−44509.8	−	1298.64i	−1.41601	−	0.0413142i
$997$	18918.2	+	10922.4i	0.600949	+	0.346958i	0.769415	−	0.638750i	$-0.220548\pi$
$997$	18918.2	+	10922.4i	0.600949	+	0.346958i	−0.168466	+	0.985707i	$0.553881\pi$
$998$		−	2525.16i		−	0.0800929i
$999$	8697.13	+	762.988i	0.275440	+	0.0241640i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.k.c.124.4		12
5.2	odd	4		225.4.e.c.151.2		6
5.3	odd	4		45.4.e.b.16.2	✓	6
5.4	even	2	inner	225.4.k.c.124.3		12
9.4	even	3	inner	225.4.k.c.49.3		12
15.8	even	4		135.4.e.b.46.2		6
45.2	even	12		2025.4.a.q.1.2		3
45.4	even	6	inner	225.4.k.c.49.4		12
45.7	odd	12		2025.4.a.s.1.2		3
45.13	odd	12		45.4.e.b.31.2	yes	6
45.22	odd	12		225.4.e.c.76.2		6
45.23	even	12		135.4.e.b.91.2		6
45.38	even	12		405.4.a.j.1.2		3
45.43	odd	12		405.4.a.h.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.b.16.2	✓	6	5.3	odd	4
45.4.e.b.31.2	yes	6	45.13	odd	12
135.4.e.b.46.2		6	15.8	even	4
135.4.e.b.91.2		6	45.23	even	12
225.4.e.c.76.2		6	45.22	odd	12
225.4.e.c.151.2		6	5.2	odd	4
225.4.k.c.49.3		12	9.4	even	3	inner
225.4.k.c.49.4		12	45.4	even	6	inner
225.4.k.c.124.3		12	5.4	even	2	inner
225.4.k.c.124.4		12	1.1	even	1	trivial
405.4.a.h.1.2		3	45.43	odd	12
405.4.a.j.1.2		3	45.38	even	12
2025.4.a.q.1.2		3	45.2	even	12
2025.4.a.s.1.2		3	45.7	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)

\(f(q)\)	\(=\)	\(q+(0.151541 + 0.0874923i) q^{2} +(0.151541 - 5.19394i) q^{3} +(-3.98469 - 6.90169i) q^{4} +(0.477395 - 0.773837i) q^{6} +(-7.32979 - 4.23186i) q^{7} -2.79440i q^{8} +(-26.9541 - 1.57419i) q^{9} +O(q^{10})\)	\(q+(0.151541 + 0.0874923i) q^{2} +(0.151541 - 5.19394i) q^{3} +(-3.98469 - 6.90169i) q^{4} +(0.477395 - 0.773837i) q^{6} +(-7.32979 - 4.23186i) q^{7} -2.79440i q^{8} +(-26.9541 - 1.57419i) q^{9} +(15.7541 - 27.2870i) q^{11} +(-36.4508 + 19.6504i) q^{12} +(-23.2697 + 13.4348i) q^{13} +(-0.740510 - 1.28260i) q^{14} +(-31.6330 + 54.7900i) q^{16} -44.3307i q^{17} +(-3.94692 - 2.59683i) q^{18} +90.2082 q^{19} +(-23.0908 + 37.4292i) q^{21} +(4.77480 - 2.75673i) q^{22} +(-168.232 + 97.1287i) q^{23} +(-14.5139 - 0.423466i) q^{24} -4.70176 q^{26} +(-12.2609 + 139.759i) q^{27} +67.4506i q^{28} +(1.87186 - 3.24215i) q^{29} +(125.832 + 217.947i) q^{31} +(-28.9476 + 16.7129i) q^{32} +(-139.339 - 85.9611i) q^{33} +(3.87859 - 6.71792i) q^{34} +(96.5390 + 192.301i) q^{36} -62.2293i q^{37} +(13.6703 + 7.89252i) q^{38} +(66.2532 + 122.898i) q^{39} +(102.173 + 176.969i) q^{41} +(-6.77397 + 3.65180i) q^{42} +(-456.968 - 263.831i) q^{43} -251.101 q^{44} -33.9920 q^{46} +(-134.864 - 77.8637i) q^{47} +(279.782 + 172.603i) q^{48} +(-135.683 - 235.009i) q^{49} +(-230.251 - 6.71792i) q^{51} +(185.445 + 107.067i) q^{52} +141.694i q^{53} +(-14.0859 + 20.1065i) q^{54} +(-11.8255 + 20.4823i) q^{56} +(13.6703 - 468.536i) q^{57} +(0.567326 - 0.327546i) q^{58} +(-246.923 - 427.683i) q^{59} +(379.742 - 657.732i) q^{61} +44.0373i q^{62} +(190.906 + 125.604i) q^{63} +500.280 q^{64} +(-13.5947 - 25.2178i) q^{66} +(-470.763 + 271.795i) q^{67} +(-305.956 + 176.644i) q^{68} +(478.987 + 888.505i) q^{69} -928.207 q^{71} +(-4.39891 + 75.3203i) q^{72} -608.739i q^{73} +(5.44459 - 9.43030i) q^{74} +(-359.452 - 622.589i) q^{76} +(-230.949 + 133.338i) q^{77} +(-0.712510 + 24.4207i) q^{78} +(307.420 - 532.467i) q^{79} +(724.044 + 84.8617i) q^{81} +35.7573i q^{82} +(931.246 + 537.655i) q^{83} +(350.334 + 10.2215i) q^{84} +(-46.1663 - 79.9623i) q^{86} +(-16.5559 - 10.2136i) q^{87} +(-76.2506 - 44.0233i) q^{88} -1505.15 q^{89} +227.416 q^{91} +(1340.70 + 774.055i) q^{92} +(1151.07 - 620.536i) q^{93} +(-13.6249 - 23.5991i) q^{94} +(82.4190 + 152.885i) q^{96} +(288.160 + 166.369i) q^{97} -47.4848i q^{98} +(-467.593 + 710.695i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 22 q^{4} + 168 q^{6} - 114 q^{9}+O(q^{10}) \) 12 * q + 22 * q^4 + 168 * q^6 - 114 * q^9	\( 12 q + 22 q^{4} + 168 q^{6} - 114 q^{9} - 28 q^{11} - 54 q^{14} + 26 q^{16} + 656 q^{19} - 288 q^{21} + 126 q^{24} + 1736 q^{26} - 670 q^{29} + 704 q^{31} - 104 q^{34} + 2172 q^{36} + 780 q^{39} - 374 q^{41} - 3928 q^{44} - 804 q^{46} + 860 q^{49} - 360 q^{51} - 1278 q^{54} - 1410 q^{56} - 596 q^{59} + 2878 q^{61} + 6276 q^{64} - 1932 q^{66} + 1746 q^{69} + 280 q^{71} - 640 q^{74} - 408 q^{76} - 764 q^{79} - 2502 q^{81} + 1818 q^{84} - 3160 q^{86} - 6876 q^{89} - 2840 q^{91} - 4154 q^{94} + 2310 q^{96} + 1524 q^{99}+O(q^{100}) \) 12 * q + 22 * q^4 + 168 * q^6 - 114 * q^9 - 28 * q^11 - 54 * q^14 + 26 * q^16 + 656 * q^19 - 288 * q^21 + 126 * q^24 + 1736 * q^26 - 670 * q^29 + 704 * q^31 - 104 * q^34 + 2172 * q^36 + 780 * q^39 - 374 * q^41 - 3928 * q^44 - 804 * q^46 + 860 * q^49 - 360 * q^51 - 1278 * q^54 - 1410 * q^56 - 596 * q^59 + 2878 * q^61 + 6276 * q^64 - 1932 * q^66 + 1746 * q^69 + 280 * q^71 - 640 * q^74 - 408 * q^76 - 764 * q^79 - 2502 * q^81 + 1818 * q^84 - 3160 * q^86 - 6876 * q^89 - 2840 * q^91 - 4154 * q^94 + 2310 * q^96 + 1524 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more