LMFDB - Embedded newform 225.4.h.d.136.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("225.46");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			136.1
Character	$\chi$	$=$	225.136
Dual form			225.4.h.d.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.45962 + 3.24011i) q^{2} +(6.91782 - 21.2908i) q^{4} +(-7.22670 + 8.53082i) q^{5} -10.2696 q^{7} +(24.5064 + 75.4228i) q^{8} +O(q^{10})$	\(q+(-4.45962 + 3.24011i) q^{2} +(6.91782 - 21.2908i) q^{4} +(-7.22670 + 8.53082i) q^{5} -10.2696 q^{7} +(24.5064 + 75.4228i) q^{8} +(4.58760 - 61.4595i) q^{10} +(30.7071 - 22.3100i) q^{11} +(68.6194 + 49.8549i) q^{13} +(45.7987 - 33.2747i) q^{14} +(-208.778 - 151.686i) q^{16} +(0.731068 + 2.24999i) q^{17} +(18.4425 + 56.7600i) q^{19} +(131.635 + 212.877i) q^{20} +(-64.6553 + 198.988i) q^{22} +(-121.764 + 88.4666i) q^{23} +(-20.5497 - 123.299i) q^{25} -467.552 q^{26} +(-71.0434 + 218.649i) q^{28} +(-19.2720 + 59.3130i) q^{29} +(30.7798 + 94.7305i) q^{31} +788.118 q^{32} +(-10.5505 - 7.66539i) q^{34} +(74.2155 - 87.6083i) q^{35} +(-241.532 - 175.484i) q^{37} +(-266.155 - 193.373i) q^{38} +(-820.518 - 335.999i) q^{40} +(-166.007 - 120.611i) q^{41} +223.838 q^{43} +(-262.573 - 808.116i) q^{44} +(256.380 - 789.055i) q^{46} +(72.4695 - 223.038i) q^{47} -237.535 q^{49} +(491.146 + 483.285i) q^{50} +(1536.15 - 1116.08i) q^{52} +(-166.824 + 513.433i) q^{53} +(-31.5883 + 423.184i) q^{55} +(-251.671 - 774.564i) q^{56} +(-106.235 - 326.957i) q^{58} +(-554.190 - 402.642i) q^{59} +(8.59875 - 6.24736i) q^{61} +(-444.203 - 322.733i) q^{62} +(-1844.48 + 1340.10i) q^{64} +(-921.195 + 225.093i) q^{65} +(125.876 + 387.407i) q^{67} +52.9617 q^{68} +(-47.1130 + 631.166i) q^{70} +(-43.1539 + 132.814i) q^{71} +(-692.701 + 503.277i) q^{73} +1645.73 q^{74} +1336.05 q^{76} +(-315.350 + 229.115i) q^{77} +(-7.25535 + 22.3297i) q^{79} +(2802.79 - 684.858i) q^{80} +1131.12 q^{82} +(-242.596 - 746.633i) q^{83} +(-24.4775 - 10.0234i) q^{85} +(-998.231 + 725.257i) q^{86} +(2435.20 + 1769.28i) q^{88} +(-604.043 + 438.863i) q^{89} +(-704.696 - 511.991i) q^{91} +(1041.19 + 3204.45i) q^{92} +(399.481 + 1229.47i) q^{94} +(-617.487 - 252.858i) q^{95} +(132.515 - 407.841i) q^{97} +(1059.32 - 769.638i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) $ 64 * q - 72 * q^4 + 20 * q^7	$ 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97}+O(q^{100}) $ 64 * q - 72 * q^4 + 20 * q^7 + 50 * q^10 + 180 * q^13 - 244 * q^16 - 116 * q^19 - 210 * q^22 + 440 * q^25 + 980 * q^28 + 42 * q^31 + 40 * q^34 - 1170 * q^37 - 3040 * q^40 + 1040 * q^43 + 700 * q^46 + 4188 * q^49 + 3280 * q^52 + 2640 * q^55 - 4530 * q^58 + 88 * q^61 - 3018 * q^64 - 2860 * q^67 - 3720 * q^70 - 5280 * q^73 + 9288 * q^76 - 1144 * q^79 + 2840 * q^82 + 470 * q^85 + 7610 * q^88 - 1180 * q^91 + 2170 * q^94 + 2050 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−4.45962	+	3.24011i	−1.57671	+	1.14555i	−0.656372	+	0.754437i	$0.727910\pi$
$2$	−4.45962	+	3.24011i	−1.57671	+	1.14555i	−0.920343	+	0.391113i	$0.872090\pi$
$3$		0			0
$3$		0			0
$4$	6.91782	−	21.2908i	0.864727	−	2.66136i
$5$	−7.22670	+	8.53082i	−0.646376	+	0.763019i
$5$	−7.22670	+	8.53082i	−0.646376	+	0.763019i
$6$		0			0
$7$	−10.2696			−0.554508			−0.277254	−	0.960797i	$-0.589424\pi$
$7$	−10.2696			−0.554508			−0.277254	+	0.960797i	$0.589424\pi$
$8$	24.5064	+	75.4228i	1.08304	+	3.33325i
$9$		0			0
$10$	4.58760	−	61.4595i	0.145073	−	1.94352i
$11$	30.7071	−	22.3100i	0.841685	−	0.611520i	−0.0811559	−	0.996701i	$-0.525861\pi$
$11$	30.7071	−	22.3100i	0.841685	−	0.611520i	0.922841	+	0.385181i	$0.125861\pi$
$12$		0			0
$13$	68.6194	+	49.8549i	1.46397	+	1.06364i	0.982307	+	0.187280i	$0.0599671\pi$
$13$	68.6194	+	49.8549i	1.46397	+	1.06364i	0.481663	+	0.876356i	$0.340033\pi$
$14$	45.7987	−	33.2747i	0.874300	−	0.635216i
$15$		0			0
$16$	−208.778	−	151.686i	−3.26216	−	2.37010i
$17$	0.731068	+	2.24999i	0.0104300	+	0.0321002i	0.956136	−	0.292923i	$-0.0946279\pi$
$17$	0.731068	+	2.24999i	0.0104300	+	0.0321002i	−0.945706	+	0.325023i	$0.894628\pi$
$18$		0			0
$19$	18.4425	+	56.7600i	0.222684	+	0.685350i	0.998518	+	0.0544137i	$0.0173290\pi$
$19$	18.4425	+	56.7600i	0.222684	+	0.685350i	−0.775835	+	0.630936i	$0.782671\pi$
$20$	131.635	+	212.877i	1.47173	+	2.38004i
$21$		0			0
$22$	−64.6553	+	198.988i	−0.626570	+	1.92839i
$23$	−121.764	+	88.4666i	−1.10389	+	0.802024i	−0.981691	−	0.190481i	$-0.938995\pi$
$23$	−121.764	+	88.4666i	−1.10389	+	0.802024i	−0.122201	+	0.992505i	$0.538995\pi$
$24$		0			0
$25$	−20.5497	−	123.299i	−0.164397	−	0.986394i
$26$	−467.552			−3.52671
$27$		0			0
$28$	−71.0434	+	218.649i	−0.479498	+	1.47574i
$29$	−19.2720	+	59.3130i	−0.123404	+	0.379798i	−0.993607	−	0.112895i	$-0.963988\pi$
$29$	−19.2720	+	59.3130i	−0.123404	+	0.379798i	0.870203	+	0.492693i	$0.163988\pi$
$30$		0			0
$31$	30.7798	+	94.7305i	0.178330	+	0.548842i	0.999770	−	0.0214525i	$-0.00682906\pi$
$31$	30.7798	+	94.7305i	0.178330	+	0.548842i	−0.821440	+	0.570295i	$0.806829\pi$
$32$	788.118			4.35378
$33$		0			0
$34$	−10.5505	−	7.66539i	−0.0532176	−	0.0386648i
$35$	74.2155	−	87.6083i	0.358420	−	0.423100i
$36$		0			0
$37$	−241.532	−	175.484i	−1.07318	−	0.779711i	−0.0966991	−	0.995314i	$-0.530828\pi$
$37$	−241.532	−	175.484i	−1.07318	−	0.779711i	−0.976481	+	0.215603i	$0.930828\pi$
$38$	−266.155	−	193.373i	−1.13621	−	0.825506i
$39$		0			0
$40$	−820.518	−	335.999i	−3.24338	−	1.32815i
$41$	−166.007	−	120.611i	−0.632340	−	0.459422i	0.224870	−	0.974389i	$-0.427804\pi$
$41$	−166.007	−	120.611i	−0.632340	−	0.459422i	−0.857210	+	0.514967i	$0.827804\pi$
$42$		0			0
$43$	223.838			0.793835			0.396917	−	0.917854i	$-0.370080\pi$
$43$	223.838			0.793835			0.396917	+	0.917854i	$0.370080\pi$
$44$	−262.573	−	808.116i	−0.899644	−	2.76882i
$45$		0			0
$46$	256.380	−	789.055i	0.821763	−	2.52913i
$47$	72.4695	−	223.038i	0.224910	−	0.692201i	−0.773391	−	0.633929i	$-0.781441\pi$
$47$	72.4695	−	223.038i	0.224910	−	0.692201i	0.998301	−	0.0582718i	$-0.0185590\pi$
$48$		0			0
$49$	−237.535			−0.692521
$50$	491.146	+	483.285i	1.38917	+	1.36694i
$51$		0			0
$52$	1536.15	−	1116.08i	4.09665	−	2.97639i
$53$	−166.824	+	513.433i	−0.432360	+	1.33067i	0.463407	+	0.886146i	$0.346627\pi$
$53$	−166.824	+	513.433i	−0.432360	+	1.33067i	−0.895767	+	0.444523i	$0.853373\pi$
$54$		0			0
$55$	−31.5883	+	423.184i	−0.0774430	+	1.03749i
$56$	−251.671	−	774.564i	−0.600553	−	1.84831i
$57$		0			0
$58$	−106.235	−	326.957i	−0.240505	−	0.740199i
$59$	−554.190	−	402.642i	−1.22287	−	0.888468i	−0.226536	−	0.974003i	$-0.572740\pi$
$59$	−554.190	−	402.642i	−1.22287	−	0.888468i	−0.996335	+	0.0855353i	$0.972740\pi$
$60$		0			0
$61$	8.59875	−	6.24736i	0.0180485	−	0.0131130i	−0.578724	−	0.815523i	$-0.696449\pi$
$61$	8.59875	−	6.24736i	0.0180485	−	0.0131130i	0.596773	+	0.802410i	$0.296449\pi$
$62$	−444.203	−	322.733i	−0.909901	−	0.661082i
$63$		0			0
$64$	−1844.48	+	1340.10i	−3.60251	+	2.61738i
$65$	−921.195	+	225.093i	−1.75785	+	0.429529i
$66$		0			0
$67$	125.876	+	387.407i	0.229526	+	0.706408i	0.997801	+	0.0662876i	$0.0211155\pi$
$67$	125.876	+	387.407i	0.229526	+	0.706408i	−0.768275	+	0.640120i	$0.778885\pi$
$68$	52.9617			0.0944492
$69$		0			0
$70$	−47.1130	+	631.166i	−0.0804439	+	1.07770i
$71$	−43.1539	+	132.814i	−0.0721327	+	0.222002i	−0.980623	−	0.195904i	$-0.937236\pi$
$71$	−43.1539	+	132.814i	−0.0721327	+	0.222002i	0.908490	+	0.417906i	$0.137236\pi$
$72$		0			0
$73$	−692.701	+	503.277i	−1.11061	+	0.806906i	−0.982760	−	0.184888i	$-0.940808\pi$
$73$	−692.701	+	503.277i	−1.11061	+	0.806906i	−0.127851	+	0.991793i	$0.540808\pi$
$74$	1645.73			2.58530
$75$		0			0
$76$	1336.05			2.01652
$77$	−315.350	+	229.115i	−0.466721	+	0.339092i
$78$		0			0
$79$	−7.25535	+	22.3297i	−0.0103328	+	0.0318011i	−0.956090	−	0.293073i	$-0.905322\pi$
$79$	−7.25535	+	22.3297i	−0.0103328	+	0.0318011i	0.945757	+	0.324874i	$0.105322\pi$
$80$	2802.79	−	684.858i	3.91701	−	0.957118i
$81$		0			0
$82$	1131.12			1.52331
$83$	−242.596	−	746.633i	−0.320823	−	0.987393i	−0.973291	−	0.229576i	$-0.926266\pi$
$83$	−242.596	−	746.633i	−0.320823	−	0.987393i	0.652467	−	0.757817i	$-0.273734\pi$
$84$		0			0
$85$	−24.4775	−	10.0234i	−0.0312348	−	0.0127905i
$86$	−998.231	+	725.257i	−1.25165	+	0.909378i
$87$		0			0
$88$	2435.20	+	1769.28i	2.94992	+	2.14325i
$89$	−604.043	+	438.863i	−0.719420	+	0.522690i	−0.886199	−	0.463305i	$-0.846664\pi$
$89$	−604.043	+	438.863i	−0.719420	+	0.522690i	0.166779	+	0.985994i	$0.446664\pi$
$90$		0			0
$91$	−704.696	−	511.991i	−0.811782	−	0.589794i
$92$	1041.19	+	3204.45i	1.17991	+	3.63138i
$93$		0			0
$94$	399.481	+	1229.47i	0.438333	+	1.34905i
$95$	−617.487	−	252.858i	−0.666872	−	0.273081i
$96$		0			0
$97$	132.515	−	407.841i	0.138710	−	0.426906i	−0.857438	−	0.514587i	$-0.827945\pi$
$97$	132.515	−	407.841i	0.138710	−	0.426906i	0.996149	+	0.0876802i	$0.0279454\pi$
$98$	1059.32	−	769.638i	1.09191	−	0.793318i
$99$		0			0
$100$	−2767.30	−	415.442i	−2.76730	−	0.415442i
$101$	437.662			0.431179			0.215589	−	0.976484i	$-0.430833\pi$
$101$	437.662			0.431179			0.215589	+	0.976484i	$0.430833\pi$
$102$		0			0
$103$	−332.320	+	1022.77i	−0.317907	+	0.978417i	0.656634	+	0.754209i	$0.271980\pi$
$103$	−332.320	+	1022.77i	−0.317907	+	0.978417i	−0.974541	+	0.224208i	$0.928020\pi$
$104$	−2078.59	+	6397.23i	−1.95983	+	6.03173i
$105$		0			0
$106$	−919.603	−	2830.25i	−0.842639	−	2.59338i
$107$	187.419			0.169331			0.0846656	−	0.996409i	$-0.473018\pi$
$107$	187.419			0.169331			0.0846656	+	0.996409i	$0.473018\pi$
$108$		0			0
$109$	236.110	+	171.544i	0.207479	+	0.150742i	0.686672	−	0.726967i	$-0.259071\pi$
$109$	236.110	+	171.544i	0.207479	+	0.150742i	−0.479193	+	0.877709i	$0.659071\pi$
$110$	−1230.29	−	1989.59i	−1.06640	−	1.72455i
$111$		0			0
$112$	2144.07	+	1557.76i	1.80889	+	1.31424i
$113$	−532.005	−	386.524i	−0.442892	−	0.321780i	0.343891	−	0.939010i	$-0.388255\pi$
$113$	−532.005	−	386.524i	−0.442892	−	0.321780i	−0.786783	+	0.617229i	$0.788255\pi$
$114$		0			0
$115$	125.258	−	1678.07i	0.101569	−	1.36070i
$116$	1129.50	+	820.633i	0.904068	+	0.656843i
$117$		0			0
$118$	3776.08			2.94590
$119$	−7.50779	−	23.1066i	−0.00578351	−	0.0177998i
$120$		0			0
$121$	33.8872	−	104.294i	0.0254600	−	0.0783578i
$122$	−18.1051	+	55.7217i	−0.0134357	+	0.0413509i
$123$		0			0
$124$	2229.82			1.61487
$125$	1200.35	+	715.741i	0.858900	+	0.512143i
$126$		0			0
$127$	−2195.33	+	1595.00i	−1.53389	+	1.11444i	−0.579865	+	0.814712i	$0.696895\pi$
$127$	−2195.33	+	1595.00i	−1.53389	+	1.11444i	−0.954026	+	0.299725i	$0.903105\pi$
$128$	1935.32	−	5956.29i	1.33640	−	4.11302i
$129$		0			0
$130$	3378.86	−	3988.60i	2.27958	−	2.69095i
$131$	652.854	+	2009.28i	0.435421	+	1.34009i	0.892655	+	0.450741i	$0.148840\pi$
$131$	652.854	+	2009.28i	0.435421	+	1.34009i	−0.457234	+	0.889346i	$0.651160\pi$
$132$		0			0
$133$	−189.397	−	582.904i	−0.123480	−	0.380032i
$134$	−1816.60	−	1319.84i	−1.17112	−	0.850870i
$135$		0			0
$136$	−151.785	+	110.278i	−0.0957019	+	0.0695315i
$137$	−2108.87	−	1532.19i	−1.31513	−	0.955500i	−0.999979	−	0.00645905i	$-0.997944\pi$
$137$	−2108.87	−	1532.19i	−1.31513	−	0.955500i	−0.315153	−	0.949041i	$-0.602056\pi$
$138$		0			0
$139$	−229.538	+	166.769i	−0.140066	+	0.101764i	−0.655612	−	0.755098i	$-0.727589\pi$
$139$	−229.538	+	166.769i	−0.140066	+	0.101764i	0.515546	+	0.856862i	$0.327589\pi$
$140$	−1351.85	−	2186.17i	−0.816084	−	1.31975i
$141$		0			0
$142$	−237.881	−	732.123i	−0.140581	−	0.432665i
$143$	3219.37			1.88264
$144$		0			0
$145$	−366.716	−	593.043i	−0.210028	−	0.339652i
$146$	1458.52	−	4488.85i	0.826765	−	2.54452i
$147$		0			0
$148$	−5407.07	+	3928.47i	−3.00310	+	2.18188i
$149$	2803.58			1.54146			0.770732	−	0.637160i	$-0.219891\pi$
$149$	2803.58			1.54146			0.770732	+	0.637160i	$0.219891\pi$
$150$		0			0
$151$	−2663.88			−1.43565			−0.717825	−	0.696224i	$-0.754862\pi$
$151$	−2663.88			−1.43565			−0.717825	+	0.696224i	$0.754862\pi$
$152$	−3829.04	+	2781.96i	−2.04327	+	1.48452i
$153$		0			0
$154$	663.985	−	2043.54i	0.347438	−	1.06930i
$155$	−1030.57	−	422.012i	−0.534045	−	0.218689i
$156$		0			0
$157$	−1281.52			−0.651441			−0.325720	−	0.945466i	$-0.605607\pi$
$157$	−1281.52			−0.651441			−0.325720	+	0.945466i	$0.605607\pi$
$158$	−39.9944	−	123.090i	−0.0201379	−	0.0619780i
$159$		0			0
$160$	−5695.49	+	6723.29i	−2.81418	+	3.32202i
$161$	1250.47	−	908.519i	0.612116	−	0.444729i
$162$		0			0
$163$	2234.46	+	1623.43i	1.07372	+	0.780103i	0.976577	−	0.215167i	$-0.0690296\pi$
$163$	2234.46	+	1623.43i	1.07372	+	0.780103i	0.0971430	+	0.995270i	$0.469030\pi$
$164$	−3716.32	+	2700.06i	−1.76949	+	1.28561i
$165$		0			0
$166$	3501.06	+	2543.67i	1.63696	+	1.18932i
$167$	−123.881	−	381.266i	−0.0574023	−	0.176666i	0.918244	−	0.396014i	$-0.129607\pi$
$167$	−123.881	−	381.266i	−0.0574023	−	0.176666i	−0.975647	+	0.219348i	$0.929607\pi$
$168$		0			0
$169$	1544.20	+	4752.56i	0.702868	+	2.16321i
$170$	141.637	−	34.6090i	0.0639005	−	0.0156140i
$171$		0			0
$172$	1548.47	−	4765.69i	0.686450	−	2.11268i
$173$	−1237.60	+	899.171i	−0.543892	+	0.395160i	−0.825528	−	0.564361i	$-0.809123\pi$
$173$	−1237.60	+	899.171i	−0.543892	+	0.395160i	0.281637	+	0.959521i	$0.409123\pi$
$174$		0			0
$175$	211.037	+	1266.24i	0.0911595	+	0.546963i
$176$	−9795.09			−4.19507
$177$		0			0
$178$	1271.84	−	3914.33i	0.535554	−	1.64826i
$179$	210.341	−	647.364i	0.0878305	−	0.270314i	−0.897489	−	0.441038i	$-0.854610\pi$
$179$	210.341	−	647.364i	0.0878305	−	0.270314i	0.985319	+	0.170723i	$0.0546105\pi$
$180$		0			0
$181$	−1.51674	−	4.66806i	−0.000622866	−	0.00191698i	0.950745	−	0.309975i	$-0.100321\pi$
$181$	−1.51674	−	4.66806i	−0.000622866	−	0.00191698i	−0.951367	+	0.308058i	$0.900321\pi$
$182$	4801.58			1.95559
$183$		0			0
$184$	−9656.38	−	7015.77i	−3.86890	−	2.81092i
$185$	3242.50	−	792.302i	1.28861	−	0.314871i
$186$		0			0
$187$	72.6463	+	52.7807i	0.0284087	+	0.0206401i
$188$	−4247.34	−	3085.87i	−1.64771	−	1.19713i
$189$		0			0
$190$	3573.05	−	873.071i	1.36430	−	0.333364i
$191$	895.191	+	650.395i	0.339130	+	0.246392i	0.744295	−	0.667851i	$-0.232786\pi$
$191$	895.191	+	650.395i	0.339130	+	0.246392i	−0.405165	+	0.914244i	$0.632786\pi$
$192$		0			0
$193$	−2999.41			−1.11866			−0.559332	−	0.828944i	$-0.688942\pi$
$193$	−2999.41			−1.11866			−0.559332	+	0.828944i	$0.688942\pi$
$194$	730.478	+	2248.18i	0.270336	+	0.832009i
$195$		0			0
$196$	−1643.22	+	5057.32i	−0.598842	+	1.84305i
$197$	−248.858	+	765.907i	−0.0900022	+	0.276998i	−0.985919	−	0.167224i	$-0.946520\pi$
$197$	−248.858	+	765.907i	−0.0900022	+	0.276998i	0.895917	+	0.444222i	$0.146520\pi$
$198$		0			0
$199$	2005.20			0.714295			0.357148	−	0.934048i	$-0.383749\pi$
$199$	2005.20			0.714295			0.357148	+	0.934048i	$0.383749\pi$
$200$	8795.98	−	4571.53i	3.10985	−	1.61628i
$201$		0			0
$202$	−1951.81	+	1418.07i	−0.679846	+	0.493937i
$203$	197.916	−	609.122i	0.0684284	−	0.210601i
$204$		0			0
$205$	2228.59	−	544.555i	0.759277	−	0.185529i
$206$	−1831.88	−	5637.94i	−0.619578	−	1.90686i
$207$		0			0
$208$	−6763.94	−	20817.3i	−2.25478	−	6.93951i
$209$	1832.63	+	1331.48i	0.606534	+	0.440673i
$210$		0			0
$211$	2540.56	−	1845.83i	0.828908	−	0.602237i	−0.0903418	−	0.995911i	$-0.528796\pi$
$211$	2540.56	−	1845.83i	0.828908	−	0.602237i	0.919250	+	0.393674i	$0.128796\pi$
$212$	9777.36	+	7103.67i	3.16751	+	2.30133i
$213$		0			0
$214$	−835.816	+	607.256i	−0.266987	+	0.193977i
$215$	−1617.61	+	1909.52i	−0.513115	+	0.605711i
$216$		0			0
$217$	−316.097	−	972.847i	−0.0988851	−	0.304337i
$218$	−1608.78			−0.499818
$219$		0			0
$220$	8791.43	+	3600.05i	2.69417	+	1.10325i
$221$	−62.0079	+	190.841i	−0.0188738	+	0.0580875i
$222$		0			0
$223$	−2001.60	+	1454.25i	−0.601064	+	0.436698i	−0.846256	−	0.532776i	$-0.821149\pi$
$223$	−2001.60	+	1454.25i	−0.601064	+	0.436698i	0.245193	+	0.969474i	$0.421149\pi$
$224$	−8093.68			−2.41420
$225$		0			0
$226$	3624.92			1.06693
$227$	3754.41	−	2727.74i	1.09775	−	0.797560i	0.117057	−	0.993125i	$-0.462654\pi$
$227$	3754.41	−	2727.74i	1.09775	−	0.797560i	0.980691	+	0.195565i	$0.0626540\pi$
$228$		0			0
$229$	1787.22	−	5500.51i	0.515734	−	1.58727i	−0.266209	−	0.963915i	$-0.585771\pi$
$229$	1787.22	−	5500.51i	0.515734	−	1.58727i	0.781943	−	0.623350i	$-0.214229\pi$
$230$	4878.51	+	7889.39i	1.39861	+	2.26179i
$231$		0			0
$232$	−4945.84			−1.39961
$233$	775.748	+	2387.51i	0.218115	+	0.671290i	0.998918	+	0.0465122i	$0.0148106\pi$
$233$	775.748	+	2387.51i	0.218115	+	0.671290i	−0.780802	+	0.624778i	$0.785189\pi$
$234$		0			0
$235$	1378.98	+	2230.05i	0.382787	+	0.619032i
$236$	−12406.4	+	9013.76i	−3.42198	+	2.48621i
$237$		0			0
$238$	108.350	+	78.7207i	0.0295095	+	0.0214399i
$239$	1736.13	−	1261.37i	0.469877	−	0.341386i	−0.327516	−	0.944846i	$-0.606212\pi$
$239$	1736.13	−	1261.37i	0.469877	−	0.341386i	0.797393	+	0.603460i	$0.206212\pi$
$240$		0			0
$241$	−5582.38	−	4055.84i	−1.49209	−	1.08406i	−0.973404	−	0.229097i	$-0.926423\pi$
$241$	−5582.38	−	4055.84i	−1.49209	−	1.08406i	−0.518683	−	0.854967i	$-0.673577\pi$
$242$	186.800	+	574.911i	0.0496196	+	0.152714i
$243$		0			0
$244$	−73.5270	−	226.293i	−0.0192913	−	0.0593726i
$245$	1716.59	−	2026.37i	0.447629	−	0.528407i
$246$		0			0
$247$	−1564.26	+	4814.29i	−0.402961	+	1.24019i
$248$	−6390.54	+	4643.00i	−1.63629	+	1.18883i
$249$		0			0
$250$	−7672.18	+	697.323i	−1.94093	+	0.176410i
$251$	2610.76			0.656533			0.328266	−	0.944585i	$-0.393536\pi$
$251$	2610.76			0.656533			0.328266	+	0.944585i	$0.393536\pi$
$252$		0			0
$253$	−1765.32	+	5433.10i	−0.438675	+	1.35010i
$254$	4622.38	−	14226.2i	1.14186	−	3.51430i
$255$		0			0
$256$	5031.98	+	15486.9i	1.22851	+	3.78097i
$257$	−2896.67			−0.703072			−0.351536	−	0.936174i	$-0.614341\pi$
$257$	−2896.67			−0.703072			−0.351536	+	0.936174i	$0.614341\pi$
$258$		0			0
$259$	2480.45	+	1802.15i	0.595087	+	0.432356i
$260$	−1580.23	+	21170.2i	−0.376931	+	5.04969i
$261$		0			0
$262$	−9421.75	−	6845.31i	−2.22167	−	1.61414i
$263$	4107.74	+	2984.45i	0.963095	+	0.699730i	0.953868	−	0.300228i	$-0.0970626\pi$
$263$	4107.74	+	2984.45i	0.963095	+	0.699730i	0.00922790	+	0.999957i	$0.497063\pi$
$264$		0			0
$265$	−3174.41	−	5133.57i	−0.735859	−	1.19001i
$266$	2733.31	+	1985.87i	0.630038	+	0.457749i
$267$		0			0
$268$	9119.02			2.07848
$269$	−556.477	−	1712.66i	−0.126130	−	0.388188i	0.867975	−	0.496608i	$-0.165421\pi$
$269$	−556.477	−	1712.66i	−0.126130	−	0.388188i	−0.994105	+	0.108419i	$0.965421\pi$
$270$		0			0
$271$	1254.40	−	3860.63i	0.281177	−	0.865375i	−0.706341	−	0.707872i	$-0.749655\pi$
$271$	1254.40	−	3860.63i	0.281177	−	0.865375i	0.987518	−	0.157504i	$-0.0503446\pi$
$272$	188.662	−	580.643i	0.0420564	−	0.129436i
$273$		0			0
$274$	14369.2			3.16816
$275$	−3381.83	−	3327.70i	−0.741570	−	0.729701i
$276$		0			0
$277$	−2240.93	+	1628.13i	−0.486080	+	0.353158i	−0.803675	−	0.595069i	$-0.797125\pi$
$277$	−2240.93	+	1628.13i	−0.486080	+	0.353158i	0.317595	+	0.948227i	$0.397125\pi$
$278$	483.304	−	1487.46i	0.104269	−	0.320906i
$279$		0			0
$280$	8426.41	+	3450.58i	1.79848	+	0.736470i
$281$	−233.378	−	718.263i	−0.0495450	−	0.152484i	0.923223	−	0.384264i	$-0.125545\pi$
$281$	−233.378	−	718.263i	−0.0495450	−	0.152484i	−0.972768	+	0.231781i	$0.925545\pi$
$282$		0			0
$283$	826.993	+	2545.22i	0.173709	+	0.534621i	0.999572	−	0.0292494i	$-0.00931171\pi$
$283$	826.993	+	2545.22i	0.173709	+	0.534621i	−0.825863	+	0.563870i	$0.809312\pi$
$284$	2529.19	+	1837.56i	0.528450	+	0.383942i
$285$		0			0
$286$	−14357.2	+	10431.1i	−2.96838	+	2.15665i
$287$	1704.83	+	1238.63i	0.350637	+	0.254753i
$288$		0			0
$289$	3970.17	−	2884.50i	0.808095	−	0.587116i
$290$	3556.93	+	1456.55i	0.720243	+	0.294936i
$291$		0			0
$292$	5923.21	+	18229.8i	1.18709	+	3.65348i
$293$	−1248.58			−0.248951			−0.124475	−	0.992223i	$-0.539725\pi$
$293$	−1248.58			−0.248951			−0.124475	+	0.992223i	$0.539725\pi$
$294$		0			0
$295$	7439.83	−	1817.92i	1.46835	−	0.358790i
$296$	7316.38	−	22517.5i	1.43668	−	4.42163i
$297$		0			0
$298$	−12502.9	+	9083.89i	−2.43045	+	1.76582i
$299$	−12765.9			−2.46913
$300$		0			0
$301$	−2298.73			−0.440187
$302$	11879.9	−	8631.24i	2.26361	−	1.64461i
$303$		0			0
$304$	4759.34	−	14647.7i	0.897917	−	2.76350i
$305$	−8.84552	+	118.502i	−0.00166063	+	0.0222473i
$306$		0			0
$307$	−7222.69			−1.34274			−0.671369	−	0.741123i	$-0.734293\pi$
$307$	−7222.69			−1.34274			−0.671369	+	0.741123i	$0.734293\pi$
$308$	2696.53	+	8299.05i	0.498860	+	1.53533i
$309$		0			0
$310$	5963.30	−	1457.13i	1.09256	−	0.266965i
$311$	−5102.15	+	3706.93i	−0.930277	+	0.675886i	−0.946061	−	0.323989i	$-0.894976\pi$
$311$	−5102.15	+	3706.93i	−0.930277	+	0.675886i	0.0157835	+	0.999875i	$0.494976\pi$
$312$		0			0
$313$	4072.39	+	2958.77i	0.735417	+	0.534311i	0.891272	−	0.453468i	$-0.149814\pi$
$313$	4072.39	+	2958.77i	0.735417	+	0.534311i	−0.155856	+	0.987780i	$0.549814\pi$
$314$	5715.08	−	4152.25i	1.02714	−	0.746258i
$315$		0			0
$316$	425.227	+	308.945i	0.0756989	+	0.0549985i
$317$	−471.885	−	1452.31i	−0.0836079	−	0.257319i	0.900510	−	0.434836i	$-0.143194\pi$
$317$	−471.885	−	1452.31i	−0.0836079	−	0.257319i	−0.984118	+	0.177517i	$0.943194\pi$
$318$		0			0
$319$	731.488	+	2251.29i	0.128387	+	0.395134i
$320$	1897.42	−	25419.4i	0.331465	−	4.44059i
$321$		0			0
$322$	−2632.92	+	8103.30i	−0.455674	+	1.40242i
$323$	−114.227	+	82.9908i	−0.0196773	+	0.0142964i
$324$		0			0
$325$	4736.97	−	9485.23i	0.808492	−	1.61891i
$326$	−15224.9			−2.58660
$327$		0			0
$328$	5028.61	−	15476.5i	0.846519	−	2.60532i
$329$	−744.234	+	2290.52i	−0.124714	+	0.383831i
$330$		0			0
$331$	−29.4876	−	90.7536i	−0.00489664	−	0.0150703i	0.948578	−	0.316542i	$-0.102522\pi$
$331$	−29.4876	−	90.7536i	−0.00489664	−	0.0150703i	−0.953475	+	0.301472i	$0.902522\pi$
$332$	−17574.7			−2.90523
$333$		0			0
$334$	1787.80	+	1298.92i	0.292887	+	0.212795i
$335$	−4214.57	−	1725.85i	−0.687363	−	0.281472i
$336$		0			0
$337$	−6558.38	−	4764.94i	−1.06011	−	0.770216i	−0.0860028	−	0.996295i	$-0.527409\pi$
$337$	−6558.38	−	4764.94i	−1.06011	−	0.770216i	−0.974109	+	0.226079i	$0.927409\pi$
$338$	−22285.4	−	16191.3i	−3.58628	−	2.60559i
$339$		0			0
$340$	−382.738	+	451.806i	−0.0610497	+	0.0720666i
$341$	3058.60	+	2222.20i	0.485725	+	0.352900i
$342$		0			0
$343$	5961.87			0.938516
$344$	5485.44	+	16882.4i	0.859753	+	2.64605i
$345$		0			0
$346$	2605.83	−	8019.93i	0.404886	−	1.24611i
$347$	−1980.24	+	6094.54i	−0.306353	+	0.942859i	0.672815	+	0.739811i	$0.265085\pi$
$347$	−1980.24	+	6094.54i	−0.306353	+	0.942859i	−0.979169	+	0.203048i	$0.934915\pi$
$348$		0			0
$349$	4849.33			0.743779			0.371890	−	0.928277i	$-0.378710\pi$
$349$	4849.33			0.743779			0.371890	+	0.928277i	$0.378710\pi$
$350$	−5043.89	−	4963.16i	−0.770306	−	0.757977i
$351$		0			0
$352$	24200.8	−	17582.9i	3.66451	−	2.66242i
$353$	3114.55	−	9585.60i	0.469606	−	1.44530i	−0.383491	−	0.923545i	$-0.625278\pi$
$353$	3114.55	−	9585.60i	0.469606	−	1.44530i	0.853097	−	0.521753i	$-0.174722\pi$
$354$		0			0
$355$	−821.152	−	1327.94i	−0.122767	−	0.198535i
$356$	5165.10	+	15896.6i	0.768961	+	2.36662i
$357$		0			0
$358$	1159.49	+	3568.53i	0.171175	+	0.526823i
$359$	6962.67	+	5058.68i	1.02361	+	0.743695i	0.967020	−	0.254702i	$-0.0819774\pi$
$359$	6962.67	+	5058.68i	1.02361	+	0.743695i	0.0565894	+	0.998398i	$0.481977\pi$
$360$		0			0
$361$	2667.47	−	1938.03i	0.388901	−	0.282553i
$362$	21.8891	+	15.9034i	0.00317808	+	0.00230901i
$363$		0			0
$364$	−15775.7	+	11461.7i	−2.27162	+	1.65043i
$365$	712.580	−	9546.34i	0.102187	−	1.36898i
$366$		0			0
$367$	−1844.02	−	5675.31i	−0.262281	−	0.807217i	−0.992307	−	0.123799i	$-0.960492\pi$
$367$	−1844.02	−	5675.31i	−0.262281	−	0.807217i	0.730027	−	0.683419i	$-0.239508\pi$
$368$	38840.8			5.50195
$369$		0			0
$370$	−11893.2	+	14039.4i	−1.67107	+	1.97263i
$371$	1713.22	−	5272.76i	0.239747	−	0.737866i
$372$		0			0
$373$	1798.36	−	1306.58i	0.249639	−	0.181374i	−0.455928	−	0.890017i	$-0.650692\pi$
$373$	1798.36	−	1306.58i	0.249639	−	0.181374i	0.705567	+	0.708643i	$0.250692\pi$
$374$	−494.990			−0.0684367
$375$		0			0
$376$	18598.1			2.55086
$377$	−4279.48	+	3109.22i	−0.584627	+	0.424756i
$378$		0			0
$379$	−2879.17	+	8861.17i	−0.390219	+	1.20097i	0.542404	+	0.840118i	$0.317514\pi$
$379$	−2879.17	+	8861.17i	−0.390219	+	1.20097i	−0.932623	+	0.360853i	$0.882486\pi$
$380$	−9655.24	+	11397.6i	−1.30343	+	1.53864i
$381$		0			0
$382$	−6099.56			−0.816965
$383$	505.859	+	1556.87i	0.0674888	+	0.207709i	0.979113	−	0.203315i	$-0.0651714\pi$
$383$	505.859	+	1556.87i	0.0674888	+	0.207709i	−0.911625	+	0.411024i	$0.865171\pi$
$384$		0			0
$385$	324.400	−	4345.94i	0.0429427	−	0.575298i
$386$	13376.2	−	9718.41i	1.76382	−	1.28149i
$387$		0			0
$388$	−7766.55	−	5642.73i	−1.01620	−	0.738315i
$389$	−7110.48	+	5166.06i	−0.926775	+	0.673341i	−0.945201	−	0.326489i	$-0.894134\pi$
$389$	−7110.48	+	5166.06i	−0.926775	+	0.673341i	0.0184260	+	0.999830i	$0.494134\pi$
$390$		0			0
$391$	−288.067	−	209.293i	−0.0372588	−	0.0270701i
$392$	−5821.11	−	17915.5i	−0.750027	−	2.30835i
$393$		0			0
$394$	−1371.81	−	4221.99i	−0.175408	−	0.539849i
$395$	−138.058	−	223.264i	−0.0175860	−	0.0284396i
$396$		0			0
$397$	−180.018	+	554.039i	−0.0227578	+	0.0700414i	−0.961790	−	0.273787i	$-0.911724\pi$
$397$	−180.018	+	554.039i	−0.0227578	+	0.0700414i	0.939033	+	0.343828i	$0.111724\pi$
$398$	−8942.43	+	6497.06i	−1.12624	+	0.818261i
$399$		0			0
$400$	−14412.5	+	28859.3i	−1.80156	+	3.60741i
$401$	−992.277			−0.123571			−0.0617855	−	0.998089i	$-0.519679\pi$
$401$	−992.277			−0.123571			−0.0617855	+	0.998089i	$0.519679\pi$
$402$		0			0
$403$	−2610.69	+	8034.88i	−0.322699	+	0.993166i
$404$	3027.67	−	9318.20i	0.372852	−	1.14752i
$405$		0			0
$406$	1090.99	+	3357.72i	0.133362	+	0.410446i
$407$	−11331.8			−1.38009
$408$		0			0
$409$	5490.11	+	3988.80i	0.663737	+	0.482233i	0.867923	−	0.496699i	$-0.165455\pi$
$409$	5490.11	+	3988.80i	0.663737	+	0.482233i	−0.204186	+	0.978932i	$0.565455\pi$
$410$	−8174.28	+	9649.39i	−0.984631	+	1.16232i
$411$		0			0
$412$	19476.8	+	14150.7i	2.32901	+	1.69213i
$413$	5691.32	+	4134.99i	0.678091	+	0.492662i
$414$		0			0
$415$	8122.55	+	3326.15i	0.960772	+	0.393432i
$416$	54080.2	+	39291.6i	6.37380	+	4.63084i
$417$		0			0
$418$	−12487.0			−1.46115
$419$	964.975	+	2969.89i	0.112511	+	0.346273i	0.991420	−	0.130717i	$-0.0417278\pi$
$419$	964.975	+	2969.89i	0.112511	+	0.346273i	−0.878909	+	0.476990i	$0.841728\pi$
$420$		0			0
$421$	142.552	−	438.731i	0.0165025	−	0.0507896i	−0.942466	−	0.334302i	$-0.891500\pi$
$421$	142.552	−	438.731i	0.0165025	−	0.0507896i	0.958969	+	0.283512i	$0.0914996\pi$
$422$	−5349.28	+	16463.4i	−0.617059	+	1.89911i
$423$		0			0
$424$	−42812.8			−4.90371
$425$	262.400	−	136.377i	0.0299488	−	0.0155653i
$426$		0			0
$427$	−88.3060	+	64.1580i	−0.0100080	+	0.00727125i
$428$	1296.53	−	3990.30i	0.146425	−	0.450651i
$429$		0			0
$430$	1026.88	−	13756.9i	0.115164	−	1.54283i
$431$	1736.93	+	5345.72i	0.194118	+	0.597434i	0.999986	+	0.00533830i	$0.00169924\pi$
$431$	1736.93	+	5345.72i	0.194118	+	0.597434i	−0.805868	+	0.592096i	$0.798301\pi$
$432$		0			0
$433$	−1082.14	−	3330.49i	−0.120102	−	0.369637i	0.872875	−	0.487945i	$-0.162253\pi$
$433$	−1082.14	−	3330.49i	−0.120102	−	0.369637i	−0.992977	+	0.118307i	$0.962253\pi$
$434$	4561.80	+	3314.34i	0.504547	+	0.366575i
$435$		0			0
$436$	5285.68	−	3840.27i	0.580592	−	0.421825i
$437$	−7266.99	−	5279.78i	−0.795486	−	0.577954i
$438$		0			0
$439$	1257.42	−	913.567i	0.136704	−	0.0993216i	−0.517331	−	0.855785i	$-0.673075\pi$
$439$	1257.42	−	913.567i	0.136704	−	0.0993216i	0.654036	+	0.756464i	$0.273075\pi$
$440$	−32691.8	+	7988.22i	−3.54210	+	0.865508i
$441$		0			0
$442$	−341.812	−	1051.99i	−0.0367836	−	0.113208i
$443$	−11004.5			−1.18023			−0.590114	−	0.807320i	$-0.700917\pi$
$443$	−11004.5			−1.18023			−0.590114	+	0.807320i	$0.700917\pi$
$444$		0			0
$445$	621.377	−	8324.51i	0.0661935	−	0.886785i
$446$	4214.47	−	12970.8i	0.447446	−	1.37710i
$447$		0			0
$448$	18942.2	−	13762.3i	1.99762	−	1.45135i
$449$	−7618.99			−0.800807			−0.400403	−	0.916339i	$-0.631130\pi$
$449$	−7618.99			−0.800807			−0.400403	+	0.916339i	$0.631130\pi$
$450$		0			0
$451$	−7788.43			−0.813177
$452$	−11909.7	+	8652.94i	−1.23935	+	0.900442i
$453$		0			0
$454$	−7905.08	+	24329.3i	−0.817189	+	2.51505i
$455$	9460.33	−	2311.62i	0.974741	−	0.238177i
$456$		0			0
$457$	4271.34			0.437210			0.218605	−	0.975813i	$-0.429849\pi$
$457$	4271.34			0.437210			0.218605	+	0.975813i	$0.429849\pi$
$458$	9851.88	+	30321.0i	1.00513	+	3.09346i
$459$		0			0
$460$	−34860.9	−	14275.4i	−3.53348	−	1.44694i
$461$	−7028.26	+	5106.33i	−0.710062	+	0.515890i	−0.883194	−	0.469009i	$-0.844611\pi$
$461$	−7028.26	+	5106.33i	−0.710062	+	0.515890i	0.173132	+	0.984899i	$0.444611\pi$
$462$		0			0
$463$	3448.43	+	2505.43i	0.346139	+	0.251484i	0.747247	−	0.664546i	$-0.231375\pi$
$463$	3448.43	+	2505.43i	0.346139	+	0.251484i	−0.401109	+	0.916030i	$0.631375\pi$
$464$	13020.5	−	9459.97i	1.30272	−	0.946483i
$465$		0			0
$466$	−11195.3	−	8133.87i	−1.11290	−	0.808571i
$467$	−3604.59	−	11093.8i	−0.357175	−	1.09927i	−0.954738	−	0.297449i	$-0.903864\pi$
$467$	−3604.59	−	11093.8i	−0.357175	−	1.09927i	0.597563	−	0.801822i	$-0.296136\pi$
$468$		0			0
$469$	−1292.70	−	3978.53i	−0.127274	−	0.391708i
$470$	−13375.3	−	5477.15i	−1.31268	−	0.537536i
$471$		0			0
$472$	16787.3	−	51665.8i	1.63707	−	5.03838i
$473$	6873.40	−	4993.82i	0.668159	−	0.485446i
$474$		0			0
$475$	6619.48	−	3440.34i	0.639416	−	0.332323i
$476$	−543.897			−0.0523728
$477$		0			0
$478$	−3655.50	+	11250.5i	−0.349788	+	1.07654i
$479$	−3624.76	+	11155.9i	−0.345761	+	1.06414i	0.615414	+	0.788204i	$0.288989\pi$
$479$	−3624.76	+	11155.9i	−0.345761	+	1.06414i	−0.961175	+	0.275939i	$0.911011\pi$
$480$		0			0
$481$	−7825.09	−	24083.2i	−0.741774	−	2.28295i
$482$	38036.7			3.59444
$483$		0			0
$484$	−1986.09	−	1442.98i	−0.186522	−	0.135516i
$485$	2521.56	+	4077.81i	0.236079	+	0.381781i
$486$		0			0
$487$	14474.6	+	10516.4i	1.34683	+	0.978529i	0.999163	+	0.0409109i	$0.0130260\pi$
$487$	14474.6	+	10516.4i	1.34683	+	0.978529i	0.347667	+	0.937618i	$0.386974\pi$
$488$	681.917	+	495.442i	0.0632560	+	0.0459582i
$489$		0			0
$490$	−1089.72	+	14598.8i	−0.100466	+	1.34593i
$491$	2171.48	+	1577.67i	0.199588	+	0.145009i	0.683090	−	0.730334i	$-0.260636\pi$
$491$	2171.48	+	1577.67i	0.199588	+	0.145009i	−0.483502	+	0.875343i	$0.660636\pi$
$492$		0			0
$493$	−147.543			−0.0134787
$494$	−8622.81	−	26538.3i	−0.785341	−	2.41703i
$495$		0			0
$496$	7943.17	−	24446.6i	0.719070	−	2.21307i
$497$	443.174	−	1363.95i	0.0399981	−	0.123102i
$498$		0			0
$499$	14708.6			1.31954			0.659768	−	0.751470i	$-0.270655\pi$
$499$	14708.6			1.31954			0.659768	+	0.751470i	$0.270655\pi$
$500$	23542.5	−	20605.1i	2.10571	−	1.84298i
$501$		0			0
$502$	−11643.0	+	8459.14i	−1.03516	+	0.752091i
$503$	2957.48	−	9102.18i	0.262162	−	0.806851i	−0.730172	−	0.683263i	$-0.760560\pi$
$503$	2957.48	−	9102.18i	0.262162	−	0.806851i	0.992334	−	0.123587i	$-0.0394399\pi$
$504$		0			0
$505$	−3162.85	+	3733.62i	−0.278703	+	0.328998i
$506$	−9731.16	−	29949.4i	−0.854946	−	2.63125i
$507$		0			0
$508$	18772.0	+	57774.4i	1.63952	+	5.04591i
$509$	4318.54	+	3137.61i	0.376063	+	0.273226i	0.759721	−	0.650250i	$-0.225336\pi$
$509$	4318.54	+	3137.61i	0.376063	+	0.273226i	−0.383658	+	0.923475i	$0.625336\pi$
$510$		0			0
$511$	7113.78	−	5168.47i	0.615842	−	0.447435i
$512$	−32086.0	−	23311.9i	−2.76956	−	2.01220i
$513$		0			0
$514$	12918.1	−	9385.53i	1.10854	−	0.805404i
$515$	−6323.53	−	10226.2i	−0.541064	−	0.874994i
$516$		0			0
$517$	−2750.66	−	8465.65i	−0.233992	−	0.720152i
$518$	−16901.0			−1.43357
$519$		0			0
$520$	−39552.3	−	63962.9i	−3.33554	−	5.39415i
$521$	−3719.00	+	11445.9i	−0.312730	+	0.962483i	0.663949	+	0.747778i	$0.268879\pi$
$521$	−3719.00	+	11445.9i	−0.312730	+	0.962483i	−0.976679	+	0.214705i	$0.931121\pi$
$522$		0			0
$523$	−6851.88	+	4978.18i	−0.572871	+	0.416215i	−0.836147	−	0.548505i	$-0.815197\pi$
$523$	−6851.88	+	4978.18i	−0.572871	+	0.416215i	0.263276	+	0.964721i	$0.415197\pi$
$524$	47295.5			3.94297
$525$		0			0
$526$	−27988.9			−2.32010
$527$	−190.641	+	138.509i	−0.0157580	+	0.0114488i
$528$		0			0
$529$	3240.28	−	9972.56i	0.266317	−	0.819640i
$530$	30790.0	+	12608.4i	2.52346	+	1.03334i
$531$		0			0
$532$	−13720.7			−1.11818
$533$	−5378.25	−	16552.5i	−0.437069	−	1.34516i
$534$		0			0
$535$	−1354.42	+	1598.83i	−0.109452	+	0.129203i
$536$	−26134.6	+	18987.9i	−2.10605	+	1.53013i
$537$		0			0
$538$	8030.88	+	5834.77i	0.643561	+	0.467574i
$539$	−7294.00	+	5299.40i	−0.582885	+	0.423491i
$540$		0			0
$541$	−659.860	−	479.416i	−0.0524391	−	0.0380993i	0.561257	−	0.827642i	$-0.310318\pi$
$541$	−659.860	−	479.416i	−0.0524391	−	0.0380993i	−0.613696	+	0.789542i	$0.710318\pi$
$542$	6914.73	+	21281.3i	0.547994	+	1.68655i
$543$		0			0
$544$	576.168	+	1773.26i	0.0454099	+	0.139757i
$545$	−3169.70	+	774.514i	−0.249129	+	0.0608744i
$546$		0			0
$547$	−5568.75	+	17138.8i	−0.435288	+	1.33968i	0.457504	+	0.889208i	$0.348744\pi$
$547$	−5568.75	+	17138.8i	−0.435288	+	1.33968i	−0.892792	+	0.450470i	$0.851256\pi$
$548$	−47210.3	+	34300.3i	−3.68016	+	2.67379i
$549$		0			0
$550$	25863.8	+	3882.80i	2.00515	+	0.301024i
$551$	−3722.03			−0.287775
$552$		0			0
$553$	74.5097	−	229.317i	0.00572961	−	0.0176339i
$554$	4718.38	−	14521.7i	0.361850	−	1.11366i
$555$		0			0
$556$	1962.76	+	6040.75i	0.149711	+	0.460764i
$557$	1620.65			0.123284			0.0616421	−	0.998098i	$-0.480366\pi$
$557$	1620.65			0.123284			0.0616421	+	0.998098i	$0.480366\pi$
$558$		0			0
$559$	15359.6	+	11159.4i	1.16215	+	0.844352i
$560$	−28783.6	+	7033.23i	−2.17201	+	0.530729i
$561$		0			0
$562$	3368.02	+	2447.01i	0.252796	+	0.183667i
$563$	4504.49	+	3272.70i	0.337197	+	0.244988i	0.743478	−	0.668760i	$-0.233175\pi$
$563$	4504.49	+	3272.70i	0.337197	+	0.244988i	−0.406281	+	0.913748i	$0.633175\pi$
$564$		0			0
$565$	7142.01	−	1745.14i	0.531799	−	0.129945i
$566$	−11934.9	−	8671.19i	−0.886325	−	0.643953i
$567$		0			0
$568$	−11074.7			−0.818109
$569$	−5525.12	−	17004.6i	−0.407074	−	1.25284i	−0.919151	−	0.393905i	$-0.871124\pi$
$569$	−5525.12	−	17004.6i	−0.407074	−	1.25284i	0.512077	−	0.858939i	$-0.328876\pi$
$570$		0			0
$571$	−2852.01	+	8777.58i	−0.209024	+	0.643310i	0.790500	+	0.612462i	$0.209821\pi$
$571$	−2852.01	+	8777.58i	−0.209024	+	0.643310i	−0.999524	+	0.0308481i	$0.990179\pi$
$572$	22271.0	−	68543.0i	1.62797	−	5.01036i
$573$		0			0
$574$	−11616.2			−0.844688
$575$	13410.1	+	13195.4i	0.972589	+	0.957022i
$576$		0			0
$577$	−5659.59	+	4111.93i	−0.408339	+	0.296676i	−0.772929	−	0.634492i	$-0.781209\pi$
$577$	−5659.59	+	4111.93i	−0.408339	+	0.296676i	0.364590	+	0.931168i	$0.381209\pi$
$578$	−8359.39	+	25727.6i	−0.601565	+	1.85143i
$579$		0			0
$580$	−15163.3	+	3705.13i	−1.08555	+	0.265253i
$581$	2491.37	+	7667.64i	0.177899	+	0.547517i
$582$		0			0
$583$	6332.00	+	19487.9i	0.449819	+	1.38440i
$584$	−54934.1	−	39912.0i	−3.89245	−	2.82803i
$585$		0			0
$586$	5568.18	−	4045.52i	0.392524	−	0.285186i
$587$	7151.24	+	5195.68i	0.502833	+	0.365330i	0.810098	−	0.586294i	$-0.199414\pi$
$587$	7151.24	+	5195.68i	0.502833	+	0.365330i	−0.307265	+	0.951624i	$0.599414\pi$
$588$		0			0
$589$	−4809.25	+	3494.13i	−0.336438	+	0.244436i
$590$	−27288.6	+	32213.1i	−1.90416	+	2.24778i
$591$		0			0
$592$	23808.3	+	73274.3i	1.65289	+	5.08709i
$593$	27529.3			1.90640			0.953198	−	0.302346i	$-0.0977698\pi$
$593$	27529.3			1.90640			0.953198	+	0.302346i	$0.0977698\pi$
$594$		0			0
$595$	251.375	+	102.937i	0.0173199	+	0.00709244i
$596$	19394.6	−	59690.6i	1.33295	−	4.10238i
$597$		0			0
$598$	56930.9	−	41362.7i	3.89311	−	2.82851i
$599$	18137.9			1.23722			0.618609	−	0.785699i	$-0.287696\pi$
$599$	18137.9			1.23722			0.618609	+	0.785699i	$0.287696\pi$
$600$		0			0
$601$	4362.42			0.296085			0.148042	−	0.988981i	$-0.452703\pi$
$601$	4362.42			0.296085			0.148042	+	0.988981i	$0.452703\pi$
$602$	10251.5	−	7448.12i	0.694050	−	0.504257i
$603$		0			0
$604$	−18428.2	+	56716.2i	−1.24145	+	3.82078i
$605$	644.822	+	1042.79i	0.0433318	+	0.0700750i
$606$		0			0
$607$	517.300			0.0345907			0.0172954	−	0.999850i	$-0.494494\pi$
$607$	517.300			0.0345907			0.0172954	+	0.999850i	$0.494494\pi$
$608$	14534.8	+	44733.6i	0.969515	+	2.98386i
$609$		0			0
$610$	−344.512	−	557.135i	−0.0228670	−	0.0369799i
$611$	16092.4	−	11691.8i	1.06551	−	0.774139i
$612$		0			0
$613$	−19128.8	−	13897.9i	−1.26037	−	0.915710i	−0.261591	−	0.965179i	$-0.584247\pi$
$613$	−19128.8	−	13897.9i	−1.26037	−	0.915710i	−0.998776	+	0.0494688i	$0.984247\pi$
$614$	32210.5	−	23402.3i	2.11712	−	1.53817i
$615$		0			0
$616$	−25008.6	−	18169.8i	−1.63576	−	1.18845i
$617$	5339.23	+	16432.5i	0.348378	+	1.07220i	0.959750	+	0.280854i	$0.0906178\pi$
$617$	5339.23	+	16432.5i	0.348378	+	1.07220i	−0.611372	+	0.791343i	$0.709382\pi$
$618$		0			0
$619$	−3492.66	−	10749.3i	−0.226788	−	0.697982i	−0.998105	−	0.0615307i	$-0.980402\pi$
$619$	−3492.66	−	10749.3i	−0.226788	−	0.697982i	0.771317	−	0.636451i	$-0.219598\pi$
$620$	−16114.3	+	19022.2i	−1.04381	+	1.23218i
$621$		0			0
$622$	10742.8	−	33063.0i	0.692520	−	2.13136i
$623$	6203.29	−	4506.96i	0.398924	−	0.289835i
$624$		0			0
$625$	−14780.4	+	5067.52i	−0.945947	+	0.324321i
$626$	−27748.1			−1.77162
$627$		0			0
$628$	−8865.30	+	27284.6i	−0.563319	+	1.73372i
$629$	218.261	−	671.737i	0.0138356	−	0.0425817i
$630$		0			0
$631$	2922.36	+	8994.09i	0.184370	+	0.567431i	0.999937	−	0.0112310i	$-0.00357500\pi$
$631$	2922.36	+	8994.09i	0.184370	+	0.567431i	−0.815567	+	0.578662i	$0.803575\pi$
$632$	−1861.97			−0.117192
$633$		0			0
$634$	6810.08	+	4947.81i	0.426597	+	0.309941i
$635$	2258.33	−	30254.6i	0.141133	−	1.89073i
$636$		0			0
$637$	−16299.5	−	11842.3i	−1.01383	−	0.736591i
$638$	−10556.6	−	7669.79i	−0.655076	−	0.475941i
$639$		0			0
$640$	36826.1	+	59554.1i	2.27450	+	3.67825i
$641$	19522.0	+	14183.5i	1.20292	+	0.873972i	0.994569	−	0.104082i	$-0.0331904\pi$
$641$	19522.0	+	14183.5i	1.20292	+	0.873972i	0.208351	+	0.978054i	$0.433190\pi$
$642$		0			0
$643$	−7261.29			−0.445346			−0.222673	−	0.974893i	$-0.571478\pi$
$643$	−7261.29			−0.445346			−0.222673	+	0.974893i	$0.571478\pi$
$644$	−10692.6	−	32908.5i	−0.654268	−	2.01363i
$645$		0			0
$646$	240.511	−	740.216i	0.0146482	−	0.0450827i
$647$	4009.28	−	12339.3i	0.243618	−	0.749780i	−0.752242	−	0.658887i	$-0.771028\pi$
$647$	4009.28	−	12339.3i	0.243618	−	0.749780i	0.995861	−	0.0908936i	$-0.0289723\pi$
$648$		0			0
$649$	−26000.5			−1.57259
$650$	9608.03	+	57648.8i	0.579782	+	3.47873i
$651$		0			0
$652$	50021.8	−	36343.0i	3.00461	−	2.18298i
$653$	−1507.85	+	4640.67i	−0.0903622	+	0.278106i	−0.986017	−	0.166643i	$-0.946707\pi$
$653$	−1507.85	+	4640.67i	−0.0903622	+	0.278106i	0.895655	+	0.444749i	$0.146707\pi$
$654$		0			0
$655$	−21858.8	−	8951.07i	−1.30396	−	0.533965i
$656$	16363.6	+	50362.0i	0.973920	+	2.99742i
$657$		0			0
$658$	−4102.52	−	12626.2i	−0.243059	−	0.748058i
$659$	−4666.14	−	3390.15i	−0.275823	−	0.200397i	0.441271	−	0.897374i	$-0.354528\pi$
$659$	−4666.14	−	3390.15i	−0.275823	−	0.200397i	−0.717093	+	0.696977i	$0.754528\pi$
$660$		0			0
$661$	−5147.38	+	3739.79i	−0.302889	+	0.220062i	−0.728839	−	0.684685i	$-0.759940\pi$
$661$	−5147.38	+	3739.79i	−0.302889	+	0.220062i	0.425950	+	0.904747i	$0.359940\pi$
$662$	425.555	+	309.184i	0.0249844	+	0.0181522i
$663$		0			0
$664$	50368.0	−	36594.5i	2.94376	−	2.13877i
$665$	6341.36	+	2596.76i	0.369786	+	0.151426i
$666$		0			0
$667$	−2900.59	−	8927.10i	−0.168383	−	0.518229i
$668$	−8974.46			−0.519809
$669$		0			0
$670$	24387.3	−	5959.02i	1.40622	−	0.343607i
$671$	124.664	−	383.676i	0.00717228	−	0.0220740i
$672$		0			0
$673$	18566.9	−	13489.7i	1.06345	−	0.772643i	0.0887275	−	0.996056i	$-0.471720\pi$
$673$	18566.9	−	13489.7i	1.06345	−	0.772643i	0.974724	+	0.223413i	$0.0717200\pi$
$674$	44686.8			2.55382
$675$		0			0
$676$	111869.			6.36485
$677$	5512.10	−	4004.77i	0.312921	−	0.227350i	−0.420228	−	0.907418i	$-0.638050\pi$
$677$	5512.10	−	4004.77i	0.312921	−	0.227350i	0.733149	+	0.680068i	$0.238050\pi$
$678$		0			0
$679$	−1360.88	+	4188.37i	−0.0769159	+	0.236723i
$680$	156.141	−	2091.80i	0.00880549	−	0.117966i
$681$		0			0
$682$	−20840.4			−1.17011
$683$	5916.94	+	18210.5i	0.331487	+	1.02021i	0.968427	+	0.249298i	$0.0801997\pi$
$683$	5916.94	+	18210.5i	0.331487	+	1.02021i	−0.636940	+	0.770913i	$0.719800\pi$
$684$		0			0
$685$	28311.0	−	6917.76i	1.57913	−	0.385860i
$686$	−26587.7	+	19317.1i	−1.47977	+	1.07512i
$687$		0			0
$688$	−46732.4	−	33953.1i	−2.58962	−	1.88147i
$689$	−37044.6	+	26914.5i	−2.04831	+	1.48818i
$690$		0			0
$691$	16033.3	+	11648.9i	0.882684	+	0.641307i	0.933960	−	0.357377i	$-0.116329\pi$
$691$	16033.3	+	11648.9i	0.882684	+	0.641307i	−0.0512762	+	0.998685i	$0.516329\pi$
$692$	10582.6	+	32569.9i	0.581345	+	1.78919i
$693$		0			0
$694$	−10915.8	−	33595.5i	−0.597060	−	1.83756i
$695$	236.126	−	3163.34i	0.0128874	−	0.172651i
$696$		0			0
$697$	150.012	−	461.690i	0.00815225	−	0.0250900i
$698$	−21626.2	+	15712.4i	−1.17273	+	0.852037i
$699$		0			0
$700$	28419.2	+	4266.43i	1.53449	+	0.230366i
$701$	−4498.76			−0.242391			−0.121195	−	0.992629i	$-0.538673\pi$
$701$	−4498.76			−0.242391			−0.121195	+	0.992629i	$0.538673\pi$
$702$		0			0
$703$	5506.00	−	16945.7i	0.295395	−	0.909133i
$704$	−26741.2	+	82300.9i	−1.43160	+	4.40601i
$705$		0			0
$706$	17168.6	+	52839.6i	0.915227	+	2.81678i
$707$	−4494.63			−0.239092
$708$		0			0
$709$	−22081.4	−	16043.1i	−1.16965	−	0.849804i	−0.178687	−	0.983906i	$-0.557185\pi$
$709$	−22081.4	−	16043.1i	−1.16965	−	0.849804i	−0.990968	+	0.134102i	$0.957185\pi$
$710$	7964.71	+	3261.51i	0.421000	+	0.172398i
$711$		0			0
$712$	−47903.1	−	34803.7i	−2.52141	−	1.83191i
$713$	−12128.4	−	8811.77i	−0.637041	−	0.462838i
$714$		0			0
$715$	−23265.4	+	27463.8i	−1.21689	+	1.43649i
$716$	−12327.8	−	8956.69i	−0.643453	−	0.467496i
$717$		0			0
$718$	−47441.5			−2.46588
$719$	7802.13	+	24012.5i	0.404687	+	1.24550i	0.921156	+	0.389193i	$0.127246\pi$
$719$	7802.13	+	24012.5i	0.404687	+	1.24550i	−0.516469	+	0.856306i	$0.672754\pi$
$720$		0			0
$721$	3412.80	−	10503.5i	0.176282	−	0.542540i
$722$	−5616.49	+	17285.8i	−0.289507	+	0.891011i
$723$		0			0
$724$	−109.879			−0.00564038
$725$	7709.28	+	1157.36i	0.394918	+	0.0592871i
$726$		0			0
$727$	8585.09	−	6237.43i	0.437969	−	0.318203i	−0.346859	−	0.937917i	$-0.612752\pi$
$727$	8585.09	−	6237.43i	0.437969	−	0.318203i	0.784827	+	0.619715i	$0.212752\pi$
$728$	21346.3	−	65697.2i	1.08674	−	3.34464i
$729$		0			0
$730$	27753.3	+	44881.9i	1.40712	+	2.27555i
$731$	163.640	+	503.633i	0.00827969	+	0.0254823i
$732$		0			0
$733$	3623.79	+	11152.9i	0.182603	+	0.561993i	0.999899	−	0.0142249i	$-0.00452807\pi$
$733$	3623.79	+	11152.9i	0.182603	+	0.561993i	−0.817296	+	0.576218i	$0.804528\pi$
$734$	26612.2	+	19334.9i	1.33825	+	0.972296i
$735$		0			0
$736$	−95964.3	+	69722.1i	−4.80610	+	3.49184i
$737$	12508.3	+	9087.85i	0.625171	+	0.454213i
$738$		0			0
$739$	−10455.8	+	7596.57i	−0.520463	+	0.378138i	−0.816778	−	0.576952i	$-0.804242\pi$
$739$	−10455.8	+	7596.57i	−0.520463	+	0.378138i	0.296315	+	0.955090i	$0.404242\pi$
$740$	5562.24	−	74516.5i	0.276313	−	3.70173i
$741$		0			0
$742$	9443.97	+	29065.6i	0.467250	+	1.43805i
$743$	30684.8			1.51510			0.757548	−	0.652780i	$-0.226397\pi$
$743$	30684.8			1.51510			0.757548	+	0.652780i	$0.226397\pi$
$744$		0			0
$745$	−20260.6	+	23916.8i	−0.996364	+	1.17617i
$746$	−3786.53	+	11653.7i	−0.185838	+	0.571949i
$747$		0			0
$748$	1626.30	−	1181.58i	0.0794965	−	0.0577576i
$749$	−1924.72			−0.0938955
$750$		0			0
$751$	905.662			0.0440054			0.0220027	−	0.999758i	$-0.492996\pi$
$751$	905.662			0.0440054			0.0220027	+	0.999758i	$0.492996\pi$
$752$	−48961.9	+	35572.9i	−2.37428	+	1.72501i
$753$		0			0
$754$	9010.65	−	27731.9i	0.435210	−	1.33944i
$755$	19251.0	−	22725.0i	0.927969	−	1.09543i
$756$		0			0
$757$	16397.3			0.787280			0.393640	−	0.919265i	$-0.371216\pi$
$757$	16397.3			0.787280			0.393640	+	0.919265i	$0.371216\pi$
$758$	−15871.1	−	48846.3i	−0.760508	−	2.34060i
$759$		0			0
$760$	3938.93	−	52769.3i	0.188000	−	2.51861i
$761$	11350.4	−	8246.52i	0.540671	−	0.392820i	−0.283663	−	0.958924i	$-0.591550\pi$
$761$	11350.4	−	8246.52i	0.540671	−	0.392820i	0.824334	+	0.566104i	$0.191550\pi$
$762$		0			0
$763$	−2424.76	−	1761.69i	−0.115049	−	0.0835878i
$764$	20040.2	−	14560.1i	0.948992	−	0.689483i
$765$		0			0
$766$	−7300.38	−	5304.04i	−0.344352	−	0.250186i
$767$	−17954.5	−	55258.2i	−0.845239	−	2.60138i
$768$		0			0
$769$	10100.4	+	31085.7i	0.473639	+	1.45771i	0.847784	+	0.530341i	$0.177936\pi$
$769$	10100.4	+	31085.7i	0.473639	+	1.45771i	−0.374145	+	0.927370i	$0.622064\pi$
$770$	12634.6	+	20432.4i	0.591324	+	0.956274i
$771$		0			0
$772$	−20749.4	+	63860.0i	−0.967339	+	2.97716i
$773$	15750.7	−	11443.6i	0.732878	−	0.532467i	−0.157595	−	0.987504i	$-0.550374\pi$
$773$	15750.7	−	11443.6i	0.732878	−	0.532467i	0.890472	+	0.455037i	$0.150374\pi$
$774$		0			0
$775$	11047.7	−	5741.81i	0.512058	−	0.266131i
$776$	34007.9			1.57321
$777$		0			0
$778$	14971.5	−	46077.4i	0.689913	−	2.12333i
$779$	3784.32	−	11646.9i	0.174053	−	0.535680i
$780$		0			0
$781$	1637.95	+	5041.09i	0.0750454	+	0.230966i
$782$	1962.80			0.0897566
$783$		0			0
$784$	49592.1	+	36030.8i	2.25912	+	1.64134i
$785$	9261.14	−	10932.4i	0.421076	−	0.497062i
$786$		0			0
$787$	2802.30	+	2035.99i	0.126927	+	0.0922177i	0.649437	−	0.760415i	$-0.275004\pi$
$787$	2802.30	+	2035.99i	0.126927	+	0.0922177i	−0.522511	+	0.852633i	$0.675004\pi$
$788$	14585.3	+	10596.8i	0.659364	+	0.479056i
$789$		0			0
$790$	1339.09	+	548.350i	0.0603070	+	0.0246955i
$791$	5463.49	+	3969.46i	0.245587	+	0.178430i
$792$		0			0
$793$	901.503			0.0403699
$794$	−992.332	−	3054.09i	−0.0443534	−	0.136506i
$795$		0			0
$796$	13871.6	−	42692.4i	0.617670	−	1.90099i
$797$	−9560.52	+	29424.2i	−0.424907	+	1.30773i	0.478176	+	0.878264i	$0.341298\pi$
$797$	−9560.52	+	29424.2i	−0.424907	+	1.30773i	−0.903083	+	0.429465i	$0.858702\pi$
$798$		0			0
$799$	554.815			0.0245656
$800$	−16195.6	−	97174.4i	−0.715749	−	4.29454i
$801$		0			0
$802$	4425.18	−	3215.08i	0.194836	−	0.141557i
$803$	−10042.7	+	30908.3i	−0.441345	+	1.35832i
$804$		0			0
$805$	−1286.35	+	17233.1i	−0.0563205	+	0.754518i
$806$	−14391.2	−	44291.5i	−0.628917	−	1.93561i
$807$		0			0
$808$	10725.5	+	33009.7i	0.466983	+	1.43723i
$809$	14508.1	+	10540.7i	0.630503	+	0.458087i	0.856574	−	0.516024i	$-0.172588\pi$
$809$	14508.1	+	10540.7i	0.630503	+	0.458087i	−0.226072	+	0.974111i	$0.572588\pi$
$810$		0			0
$811$	−34775.5	+	25265.9i	−1.50571	+	1.09396i	−0.537677	+	0.843151i	$0.680698\pi$
$811$	−34775.5	+	25265.9i	−1.50571	+	1.09396i	−0.968035	+	0.250814i	$0.919302\pi$
$812$	−11599.6	−	8427.59i	−0.501312	−	0.364225i
$813$		0			0
$814$	50535.5	−	36716.2i	2.17601	−	1.58096i
$815$	−29997.0	+	7329.73i	−1.28926	+	0.315030i
$816$		0			0
$817$	4128.11	+	12705.0i	0.176774	+	0.544054i
$818$	−37407.9			−1.59895
$819$		0			0
$820$	3822.97	−	51215.8i	0.162810	−	2.18114i
$821$	−2288.17	+	7042.28i	−0.0972690	+	0.299363i	−0.987838	−	0.155484i	$-0.950306\pi$
$821$	−2288.17	+	7042.28i	−0.0972690	+	0.299363i	0.890569	+	0.454847i	$0.150306\pi$
$822$		0			0
$823$	−15069.7	+	10948.8i	−0.638271	+	0.463731i	−0.859256	−	0.511546i	$-0.829073\pi$
$823$	−15069.7	+	10948.8i	−0.638271	+	0.463731i	0.220985	+	0.975277i	$0.429073\pi$
$824$	−85284.5			−3.60561
$825$		0			0
$826$	−38778.9			−1.63353
$827$	−25563.0	+	18572.6i	−1.07487	+	0.780935i	−0.976780	−	0.214243i	$-0.931272\pi$
$827$	−25563.0	+	18572.6i	−1.07487	+	0.780935i	−0.0980846	+	0.995178i	$0.531272\pi$
$828$		0			0
$829$	6120.97	−	18838.4i	0.256442	−	0.789246i	−0.737101	−	0.675783i	$-0.763806\pi$
$829$	6120.97	−	18838.4i	0.256442	−	0.789246i	0.993542	−	0.113463i	$-0.0361944\pi$
$830$	−47000.6	+	11484.6i	−1.96556	+	0.480283i
$831$		0			0
$832$	−193378.			−8.05790
$833$	−173.654	−	534.452i	−0.00722300	−	0.0222301i
$834$		0			0
$835$	4147.76	+	1698.49i	0.171903	+	0.0703936i
$836$	41026.2	−	29807.3i	1.69727	−	1.23314i
$837$		0			0
$838$	−13926.2	−	10118.0i	−0.574071	−	0.417087i
$839$	−19266.9	+	13998.3i	−0.792811	+	0.576011i	−0.908796	−	0.417240i	$-0.862998\pi$
$839$	−19266.9	+	13998.3i	−0.792811	+	0.576011i	0.115985	+	0.993251i	$0.462998\pi$
$840$		0			0
$841$	16584.5	+	12049.3i	0.679999	+	0.494048i
$842$	785.805	+	2418.46i	0.0321622	+	0.0989852i
$843$		0			0
$844$	−21724.1	−	66859.9i	−0.885988	−	2.72679i
$845$	−51702.7	−	21172.0i	−2.10489	−	0.861941i
$846$		0			0
$847$	−348.009	+	1071.06i	−0.0141178	+	0.0434500i
$848$	112710.	−	81888.7i	4.56424	−	3.31612i
$849$		0			0
$850$	−728.328	+	1458.39i	−0.0293899	+	0.0588499i
$851$	44934.3			1.81002
$852$		0			0
$853$	1369.14	−	4213.77i	0.0549570	−	0.169140i	−0.919810	−	0.392363i	$-0.871658\pi$
$853$	1369.14	−	4213.77i	0.0549570	−	0.169140i	0.974767	+	0.223223i	$0.0716577\pi$
$854$	185.932	−	572.241i	0.00745021	−	0.0229294i
$855$		0			0
$856$	4592.95	+	14135.6i	0.183392	+	0.564423i
$857$	−44014.5			−1.75439			−0.877193	−	0.480139i	$-0.840586\pi$
$857$	−44014.5			−1.75439			−0.877193	+	0.480139i	$0.840586\pi$
$858$		0			0
$859$	−17060.8	−	12395.4i	−0.677655	−	0.492345i	0.194924	−	0.980818i	$-0.437554\pi$
$859$	−17060.8	−	12395.4i	−0.677655	−	0.492345i	−0.872579	+	0.488473i	$0.837554\pi$
$860$	29464.9	+	47649.9i	1.16831	+	1.88936i
$861$		0			0
$862$	−25066.7	−	18212.0i	−0.990459	−	0.719611i
$863$	−21255.2	−	15442.8i	−0.838397	−	0.609131i	0.0835257	−	0.996506i	$-0.473382\pi$
$863$	−21255.2	−	15442.8i	−0.838397	−	0.609131i	−0.921922	+	0.387375i	$0.873382\pi$
$864$		0			0
$865$	1273.12	−	17055.8i	0.0500432	−	0.670422i
$866$	15617.1	+	11346.5i	0.612805	+	0.445229i
$867$		0			0
$868$	−22899.4			−0.895458
$869$	275.384	+	847.546i	0.0107500	+	0.0330852i
$870$		0			0
$871$	−10676.6	+	32859.2i	−0.415342	+	1.27829i
$872$	−7152.12	+	22012.0i	−0.277754	+	0.854839i
$873$		0			0
$874$	49515.1			1.91633
$875$	−12327.1	−	7350.39i	−0.476267	−	0.283987i
$876$		0			0
$877$	−10779.6	+	7831.87i	−0.415055	+	0.301555i	−0.775645	−	0.631169i	$-0.782575\pi$
$877$	−10779.6	+	7831.87i	−0.415055	+	0.301555i	0.360590	+	0.932724i	$0.382575\pi$
$878$	−2647.55	+	8148.33i	−0.101766	+	0.313204i
$879$		0			0
$880$	70786.2	−	83560.2i	2.71159	−	3.20092i
$881$	−2311.73	−	7114.76i	−0.0884041	−	0.272080i	0.897075	−	0.441879i	$-0.145688\pi$
$881$	−2311.73	−	7114.76i	−0.0884041	−	0.272080i	−0.985479	+	0.169799i	$0.945688\pi$
$882$		0			0
$883$	−9621.24	−	29611.1i	−0.366682	−	1.12853i	−0.948921	−	0.315514i	$-0.897823\pi$
$883$	−9621.24	−	29611.1i	−0.366682	−	1.12853i	0.582238	−	0.813018i	$-0.302177\pi$
$884$	3634.20	+	2640.40i	0.138271	+	0.100460i
$885$		0			0
$886$	49076.1	−	35655.8i	1.86088	−	1.35201i
$887$	−13092.2	−	9512.01i	−0.495594	−	0.360070i	0.311738	−	0.950168i	$-0.399089\pi$
$887$	−13092.2	−	9512.01i	−0.495594	−	0.360070i	−0.807331	+	0.590098i	$0.799089\pi$
$888$		0			0
$889$	22545.2	−	16380.1i	0.850554	−	0.617964i
$890$	24201.2	+	39137.5i	0.911489	+	1.47404i
$891$		0			0
$892$	17115.5	+	52676.0i	0.642454	+	1.97727i
$893$	13996.2			0.524484
$894$		0			0
$895$	4002.47	+	6472.69i	0.149484	+	0.241741i
$896$	−19875.0	+	61168.8i	−0.741044	+	2.28070i
$897$		0			0
$898$	33977.8	−	24686.3i	1.26264	−	0.917364i
$899$	−6211.94			−0.230456
$900$		0			0
$901$	−1277.18			−0.0472243
$902$	34733.5	−	25235.3i	1.28215	−	0.931535i
$903$		0			0
$904$	16115.2	−	49597.6i	0.592904	−	1.82477i
$905$	50.7834	+	20.7956i	0.00186530	+	0.000763833i
$906$		0			0
$907$	35038.5			1.28273			0.641364	−	0.767236i	$-0.278369\pi$
$907$	35038.5			1.28273			0.641364	+	0.767236i	$0.278369\pi$
$908$	−32103.5	−	98804.5i	−1.17334	−	3.61117i
$909$		0			0
$910$	−34699.6	+	40961.4i	−1.26404	+	1.49215i
$911$	−35570.5	+	25843.5i	−1.29364	+	0.939883i	−0.999872	−	0.0159950i	$-0.994908\pi$
$911$	−35570.5	+	25843.5i	−1.29364	+	0.939883i	−0.293765	+	0.955878i	$0.594908\pi$
$912$		0			0
$913$	−24106.8	−	17514.6i	−0.873843	−	0.634884i
$914$	−19048.6	+	13839.6i	−0.689355	+	0.500846i
$915$		0			0
$916$	−104747.	−	76103.0i	−3.77831	−	2.74510i
$917$	−6704.56	−	20634.5i	−0.241444	−	0.743088i
$918$		0			0
$919$	−3690.53	−	11358.3i	−0.132469	−	0.407698i	0.862719	−	0.505684i	$-0.168760\pi$
$919$	−3690.53	−	11358.3i	−0.132469	−	0.407698i	−0.995188	+	0.0979860i	$0.968760\pi$
$920$	129634.	−	31676.0i	4.64555	−	1.13514i
$921$		0			0
$922$	14798.3	−	45544.6i	0.528587	−	1.62682i
$923$	−9582.63	+	6962.19i	−0.341729	+	0.248281i
$924$		0			0
$925$	−16673.6	+	33386.9i	−0.592675	+	1.18676i
$926$	−23496.6			−0.833850
$927$		0			0
$928$	−15188.6	+	46745.7i	−0.537274	+	1.65356i
$929$	12525.1	−	38548.3i	0.442342	−	1.36139i	−0.443031	−	0.896506i	$-0.646097\pi$
$929$	12525.1	−	38548.3i	0.442342	−	1.36139i	0.885373	−	0.464882i	$-0.153903\pi$
$930$		0			0
$931$	−4380.72	−	13482.5i	−0.154213	−	0.474619i
$932$	56198.5			1.97515
$933$		0			0
$934$	52020.2	+	37794.9i	1.82243	+	1.32408i
$935$	−975.255	+	238.303i	−0.0341115	+	0.00833512i
$936$		0			0
$937$	18362.9	+	13341.4i	0.640223	+	0.465149i	0.859927	−	0.510417i	$-0.170509\pi$
$937$	18362.9	+	13341.4i	0.640223	+	0.465149i	−0.219704	+	0.975567i	$0.570509\pi$
$938$	18655.8	+	13554.2i	0.649396	+	0.471814i
$939$		0			0
$940$	57019.3	−	13932.6i	1.97847	−	0.483438i
$941$	−22281.6	−	16188.5i	−0.771902	−	0.560819i	0.130636	−	0.991430i	$-0.458298\pi$
$941$	−22281.6	−	16188.5i	−0.771902	−	0.560819i	−0.902538	+	0.430611i	$0.858298\pi$
$942$		0			0
$943$	30883.7			1.06650
$944$	54627.5	+	168126.i	1.88345	+	5.79665i
$945$		0			0
$946$	−14472.3	+	44541.1i	−0.497393	+	1.53082i
$947$	−7079.74	+	21789.2i	−0.242936	+	0.747681i	0.753033	+	0.657983i	$0.228590\pi$
$947$	−7079.74	+	21789.2i	−0.242936	+	0.747681i	−0.995969	+	0.0896978i	$0.971410\pi$
$948$		0			0
$949$	−72623.6			−2.48415
$950$	−18373.3	+	36790.5i	−0.627484	+	1.25646i
$951$		0			0
$952$	1558.78	−	1132.52i	0.0530675	−	0.0385558i
$953$	2829.91	−	8709.57i	0.0961907	−	0.296045i	−0.891371	−	0.453274i	$-0.850256\pi$
$953$	2829.91	−	8709.57i	0.0961907	−	0.296045i	0.987562	+	0.157229i	$0.0502561\pi$
$954$		0			0
$955$	−12017.7	+	2936.51i	−0.407207	+	0.0995007i
$956$	−14845.4	−	45689.5i	−0.502234	−	1.54572i
$957$		0			0
$958$	−19981.1	−	61495.6i	−0.673863	−	2.07394i
$959$	21657.3	+	15735.0i	0.729251	+	0.529832i
$960$		0			0
$961$	16074.9	−	11679.1i	0.539591	−	0.392036i
$962$	112929.	+	82047.7i	3.78480	+	2.74982i
$963$		0			0
$964$	−124970.	+	90796.1i	−4.17533	+	3.03355i
$965$	21675.8	−	25587.4i	0.723077	−	0.853563i
$966$		0			0
$967$	−6420.60	−	19760.6i	−0.213519	−	0.657143i	−0.999255	−	0.0385819i	$-0.987716\pi$
$967$	−6420.60	−	19760.6i	−0.213519	−	0.657143i	0.785737	−	0.618561i	$-0.212284\pi$
$968$	8696.61			0.288760
$969$		0			0
$970$	−24457.7	−	10015.3i	−0.809578	−	0.331519i
$971$	−16763.2	+	51591.8i	−0.554023	+	1.70511i	0.144486	+	0.989507i	$0.453847\pi$
$971$	−16763.2	+	51591.8i	−0.554023	+	1.70511i	−0.698509	+	0.715601i	$0.746153\pi$
$972$		0			0
$973$	2357.27	−	1712.66i	0.0776678	−	0.0564289i
$974$	−98625.4			−3.24452
$975$		0			0
$976$	−2742.87			−0.0899561
$977$	32418.2	−	23553.2i	1.06157	−	0.771273i	0.0871884	−	0.996192i	$-0.472212\pi$
$977$	32418.2	−	23553.2i	1.06157	−	0.771273i	0.974377	+	0.224919i	$0.0722118\pi$
$978$		0			0
$979$	−8757.37	+	26952.4i	−0.285890	+	0.879880i
$980$	−31268.0	−	50565.7i	−1.01920	−	1.64823i
$981$		0			0
$982$	−14795.8			−0.480808
$983$	−405.472	−	1247.91i	−0.0131562	−	0.0404906i	0.944263	−	0.329192i	$-0.106776\pi$
$983$	−405.472	−	1247.91i	−0.0131562	−	0.0404906i	−0.957419	+	0.288702i	$0.906776\pi$
$984$		0			0
$985$	−4735.39	−	7657.95i	−0.153180	−	0.247718i
$986$	657.986	−	478.055i	0.0212521	−	0.0154405i
$987$		0			0
$988$	91679.0	+	66608.7i	2.95212	+	2.14484i
$989$	−27255.3	+	19802.1i	−0.876308	+	0.636675i
$990$		0			0
$991$	47714.3	+	34666.5i	1.52946	+	1.11122i	0.956538	+	0.291607i	$0.0941899\pi$
$991$	47714.3	+	34666.5i	1.52946	+	1.11122i	0.572921	+	0.819611i	$0.305810\pi$
$992$	24258.1	+	74658.9i	0.776408	+	2.38954i
$993$		0			0
$994$	2442.95	+	7518.63i	0.0779534	+	0.239916i
$995$	−14491.0	+	17106.0i	−0.461703	+	0.545021i
$996$		0			0
$997$	13358.3	−	41112.6i	0.424334	−	1.30597i	−0.479296	−	0.877653i	$-0.659108\pi$
$997$	13358.3	−	41112.6i	0.424334	−	1.30597i	0.903630	−	0.428313i	$-0.140892\pi$
$998$	−65594.9	+	47657.5i	−2.08053	+	1.51159i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.h.d.136.1	yes	64
3.2	odd	2	inner	225.4.h.d.136.16	yes	64
25.16	even	5	inner	225.4.h.d.91.1	✓	64
75.41	odd	10	inner	225.4.h.d.91.16	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.4.h.d.91.1	✓	64	25.16	even	5	inner
225.4.h.d.91.16	yes	64	75.41	odd	10	inner
225.4.h.d.136.1	yes	64	1.1	even	1	trivial
225.4.h.d.136.16	yes	64	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-4.45962 + 3.24011i) q^{2} +(6.91782 - 21.2908i) q^{4} +(-7.22670 + 8.53082i) q^{5} -10.2696 q^{7} +(24.5064 + 75.4228i) q^{8} +O(q^{10})\)	\(q+(-4.45962 + 3.24011i) q^{2} +(6.91782 - 21.2908i) q^{4} +(-7.22670 + 8.53082i) q^{5} -10.2696 q^{7} +(24.5064 + 75.4228i) q^{8} +(4.58760 - 61.4595i) q^{10} +(30.7071 - 22.3100i) q^{11} +(68.6194 + 49.8549i) q^{13} +(45.7987 - 33.2747i) q^{14} +(-208.778 - 151.686i) q^{16} +(0.731068 + 2.24999i) q^{17} +(18.4425 + 56.7600i) q^{19} +(131.635 + 212.877i) q^{20} +(-64.6553 + 198.988i) q^{22} +(-121.764 + 88.4666i) q^{23} +(-20.5497 - 123.299i) q^{25} -467.552 q^{26} +(-71.0434 + 218.649i) q^{28} +(-19.2720 + 59.3130i) q^{29} +(30.7798 + 94.7305i) q^{31} +788.118 q^{32} +(-10.5505 - 7.66539i) q^{34} +(74.2155 - 87.6083i) q^{35} +(-241.532 - 175.484i) q^{37} +(-266.155 - 193.373i) q^{38} +(-820.518 - 335.999i) q^{40} +(-166.007 - 120.611i) q^{41} +223.838 q^{43} +(-262.573 - 808.116i) q^{44} +(256.380 - 789.055i) q^{46} +(72.4695 - 223.038i) q^{47} -237.535 q^{49} +(491.146 + 483.285i) q^{50} +(1536.15 - 1116.08i) q^{52} +(-166.824 + 513.433i) q^{53} +(-31.5883 + 423.184i) q^{55} +(-251.671 - 774.564i) q^{56} +(-106.235 - 326.957i) q^{58} +(-554.190 - 402.642i) q^{59} +(8.59875 - 6.24736i) q^{61} +(-444.203 - 322.733i) q^{62} +(-1844.48 + 1340.10i) q^{64} +(-921.195 + 225.093i) q^{65} +(125.876 + 387.407i) q^{67} +52.9617 q^{68} +(-47.1130 + 631.166i) q^{70} +(-43.1539 + 132.814i) q^{71} +(-692.701 + 503.277i) q^{73} +1645.73 q^{74} +1336.05 q^{76} +(-315.350 + 229.115i) q^{77} +(-7.25535 + 22.3297i) q^{79} +(2802.79 - 684.858i) q^{80} +1131.12 q^{82} +(-242.596 - 746.633i) q^{83} +(-24.4775 - 10.0234i) q^{85} +(-998.231 + 725.257i) q^{86} +(2435.20 + 1769.28i) q^{88} +(-604.043 + 438.863i) q^{89} +(-704.696 - 511.991i) q^{91} +(1041.19 + 3204.45i) q^{92} +(399.481 + 1229.47i) q^{94} +(-617.487 - 252.858i) q^{95} +(132.515 - 407.841i) q^{97} +(1059.32 - 769.638i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) \) 64 * q - 72 * q^4 + 20 * q^7	\( 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97}+O(q^{100}) \) 64 * q - 72 * q^4 + 20 * q^7 + 50 * q^10 + 180 * q^13 - 244 * q^16 - 116 * q^19 - 210 * q^22 + 440 * q^25 + 980 * q^28 + 42 * q^31 + 40 * q^34 - 1170 * q^37 - 3040 * q^40 + 1040 * q^43 + 700 * q^46 + 4188 * q^49 + 3280 * q^52 + 2640 * q^55 - 4530 * q^58 + 88 * q^61 - 3018 * q^64 - 2860 * q^67 - 3720 * q^70 - 5280 * q^73 + 9288 * q^76 - 1144 * q^79 + 2840 * q^82 + 470 * q^85 + 7610 * q^88 - 1180 * q^91 + 2170 * q^94 + 2050 * q^97

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