LMFDB - Embedded newform 100.4.i.a.29.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,4,Mod(9,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("100.9");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	100.i (of order $10$, 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:	$5.90019100057$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.7
Character	$\chi$	$=$	100.29
Dual form			100.4.i.a.69.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.08679 - 5.62498i) q^{3} +(-11.1568 + 0.725356i) q^{5} -19.2903i q^{7} +(-6.59510 - 20.2976i) q^{9} +O(q^{10})$	\(q+(4.08679 - 5.62498i) q^{3} +(-11.1568 + 0.725356i) q^{5} -19.2903i q^{7} +(-6.59510 - 20.2976i) q^{9} +(13.7774 - 42.4025i) q^{11} +(-62.4530 + 20.2922i) q^{13} +(-41.5153 + 65.7211i) q^{15} +(16.7373 + 23.0369i) q^{17} +(76.5456 - 55.6137i) q^{19} +(-108.508 - 78.8354i) q^{21} +(-112.604 - 36.5872i) q^{23} +(123.948 - 16.1853i) q^{25} +(37.4125 + 12.1561i) q^{27} +(-7.32137 - 5.31928i) q^{29} +(205.988 - 149.659i) q^{31} +(-182.208 - 250.788i) q^{33} +(13.9924 + 215.218i) q^{35} +(261.830 - 85.0736i) q^{37} +(-141.089 + 434.227i) q^{39} +(89.4467 + 275.289i) q^{41} +371.090i q^{43} +(88.3032 + 221.673i) q^{45} +(-94.9487 + 130.686i) q^{47} -29.1162 q^{49} +197.984 q^{51} +(94.9473 - 130.684i) q^{53} +(-122.955 + 483.070i) q^{55} -657.849i q^{57} +(60.1917 + 185.251i) q^{59} +(132.729 - 408.499i) q^{61} +(-391.548 + 127.222i) q^{63} +(682.056 - 271.696i) q^{65} +(-549.725 - 756.631i) q^{67} +(-665.990 + 483.870i) q^{69} +(781.193 + 567.570i) q^{71} +(267.559 + 86.9353i) q^{73} +(415.506 - 763.349i) q^{75} +(-817.958 - 265.771i) q^{77} +(-559.111 - 406.218i) q^{79} +(687.462 - 499.470i) q^{81} +(-391.465 - 538.805i) q^{83} +(-203.444 - 244.877i) q^{85} +(-59.8417 + 19.4438i) q^{87} +(-385.384 + 1186.09i) q^{89} +(391.443 + 1204.74i) q^{91} -1770.30i q^{93} +(-813.664 + 675.993i) q^{95} +(812.330 - 1118.08i) q^{97} -951.535 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 6 q^{5} + 122 q^{9}+O(q^{10}) $ 32 * q + 6 * q^5 + 122 * q^9	$ 32 q + 6 q^{5} + 122 q^{9} + 20 q^{11} + 68 q^{15} - 160 q^{17} + 2 q^{19} - 108 q^{21} + 290 q^{23} + 654 q^{25} + 600 q^{27} + 62 q^{29} - 378 q^{31} - 1280 q^{33} - 278 q^{35} + 680 q^{37} + 592 q^{39} - 528 q^{41} - 1044 q^{45} - 1810 q^{47} - 2796 q^{49} + 1664 q^{51} - 510 q^{53} - 1350 q^{55} + 144 q^{59} - 1346 q^{61} + 1660 q^{63} + 1142 q^{65} + 1890 q^{67} + 956 q^{69} + 786 q^{71} + 3720 q^{73} - 78 q^{75} + 2160 q^{77} + 896 q^{79} + 348 q^{81} + 570 q^{83} + 224 q^{85} + 3240 q^{87} - 2512 q^{89} - 2212 q^{91} + 1536 q^{95} - 2250 q^{97} - 2540 q^{99}+O(q^{100}) $ 32 * q + 6 * q^5 + 122 * q^9 + 20 * q^11 + 68 * q^15 - 160 * q^17 + 2 * q^19 - 108 * q^21 + 290 * q^23 + 654 * q^25 + 600 * q^27 + 62 * q^29 - 378 * q^31 - 1280 * q^33 - 278 * q^35 + 680 * q^37 + 592 * q^39 - 528 * q^41 - 1044 * q^45 - 1810 * q^47 - 2796 * q^49 + 1664 * q^51 - 510 * q^53 - 1350 * q^55 + 144 * q^59 - 1346 * q^61 + 1660 * q^63 + 1142 * q^65 + 1890 * q^67 + 956 * q^69 + 786 * q^71 + 3720 * q^73 - 78 * q^75 + 2160 * q^77 + 896 * q^79 + 348 * q^81 + 570 * q^83 + 224 * q^85 + 3240 * q^87 - 2512 * q^89 - 2212 * q^91 + 1536 * q^95 - 2250 * q^97 - 2540 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	4.08679	−	5.62498i	0.786502	−	1.08253i	−0.208032	−	0.978122i	$-0.566706\pi$
$3$	4.08679	−	5.62498i	0.786502	−	1.08253i	0.994535	−	0.104406i	$-0.0332940\pi$
$4$		0			0
$5$	−11.1568	+	0.725356i	−0.997893	+	0.0648778i
$5$	−11.1568	+	0.725356i	−0.997893	+	0.0648778i
$6$		0			0
$7$		−	19.2903i		−	1.04158i	−0.853685	−	0.520790i	$-0.825638\pi$
$7$		−	19.2903i		−	1.04158i	0.853685	−	0.520790i	$-0.174362\pi$
$8$		0			0
$9$	−6.59510	−	20.2976i	−0.244263	−	0.751765i
$10$		0			0
$11$	13.7774	−	42.4025i	0.377641	−	1.16226i	−0.564039	−	0.825748i	$-0.690753\pi$
$11$	13.7774	−	42.4025i	0.377641	−	1.16226i	0.941680	−	0.336511i	$-0.109247\pi$
$12$		0			0
$13$	−62.4530	+	20.2922i	−1.33241	+	0.432927i	−0.886739	−	0.462270i	$-0.847035\pi$
$13$	−62.4530	+	20.2922i	−1.33241	+	0.432927i	−0.445672	+	0.895196i	$0.647035\pi$
$14$		0			0
$15$	−41.5153	+	65.7211i	−0.714613	+	1.13127i
$16$		0			0
$17$	16.7373	+	23.0369i	0.238788	+	0.328663i	0.911545	−	0.411200i	$-0.134890\pi$
$17$	16.7373	+	23.0369i	0.238788	+	0.328663i	−0.672757	+	0.739863i	$0.734890\pi$
$18$		0			0
$19$	76.5456	−	55.6137i	0.924251	−	0.671508i	−0.0203272	−	0.999793i	$-0.506471\pi$
$19$	76.5456	−	55.6137i	0.924251	−	0.671508i	0.944579	+	0.328285i	$0.106471\pi$
$20$		0			0
$21$	−108.508	−	78.8354i	−1.12754	−	0.819204i
$22$		0			0
$23$	−112.604	−	36.5872i	−1.02085	−	0.331694i	−0.249683	−	0.968328i	$-0.580326\pi$
$23$	−112.604	−	36.5872i	−1.02085	−	0.331694i	−0.771166	+	0.636634i	$0.780326\pi$
$24$		0			0
$25$	123.948	−	16.1853i	0.991582	−	0.129482i
$26$		0			0
$27$	37.4125	+	12.1561i	0.266668	+	0.0866457i
$28$		0			0
$29$	−7.32137	−	5.31928i	−0.0468808	−	0.0340609i	0.564098	−	0.825708i	$-0.309224\pi$
$29$	−7.32137	−	5.31928i	−0.0468808	−	0.0340609i	−0.610979	+	0.791647i	$0.709224\pi$
$30$		0			0
$31$	205.988	−	149.659i	1.19344	−	0.867082i	0.199812	−	0.979834i	$-0.435967\pi$
$31$	205.988	−	149.659i	1.19344	−	0.867082i	0.993623	+	0.112753i	$0.0359668\pi$
$32$		0			0
$33$	−182.208	−	250.788i	−0.961162	−	1.32293i
$34$		0			0
$35$	13.9924	+	215.218i	0.0675754	+	1.03938i
$36$		0			0
$37$	261.830	−	85.0736i	1.16337	−	0.378001i	0.337203	−	0.941432i	$-0.390519\pi$
$37$	261.830	−	85.0736i	1.16337	−	0.378001i	0.826163	+	0.563431i	$0.190519\pi$
$38$		0			0
$39$	−141.089	+	434.227i	−0.579289	+	1.78287i
$40$		0			0
$41$	89.4467	+	275.289i	0.340713	+	1.04861i	0.963839	+	0.266485i	$0.0858623\pi$
$41$	89.4467	+	275.289i	0.340713	+	1.04861i	−0.623126	+	0.782121i	$0.714138\pi$
$42$		0			0
$43$			371.090i			1.31606i	0.752991	+	0.658031i	$0.228610\pi$
$43$			371.090i			1.31606i	−0.752991	+	0.658031i	$0.771390\pi$
$44$		0			0
$45$	88.3032	+	221.673i	0.292521	+	0.734333i
$46$		0			0
$47$	−94.9487	+	130.686i	−0.294674	+	0.405584i	−0.930525	−	0.366227i	$-0.880649\pi$
$47$	−94.9487	+	130.686i	−0.294674	+	0.405584i	0.635851	+	0.771812i	$0.280649\pi$
$48$		0			0
$49$	−29.1162			−0.0848869
$50$		0			0
$51$	197.984			0.543594
$52$		0			0
$53$	94.9473	−	130.684i	0.246076	−	0.338694i	−0.668056	−	0.744111i	$-0.732873\pi$
$53$	94.9473	−	130.684i	0.246076	−	0.338694i	0.914132	+	0.405416i	$0.132873\pi$
$54$		0			0
$55$	−122.955	+	483.070i	−0.301440	+	1.18431i
$56$		0			0
$57$		−	657.849i		−	1.52867i
$58$		0			0
$59$	60.1917	+	185.251i	0.132818	+	0.408773i	0.995244	−	0.0974103i	$-0.0310559\pi$
$59$	60.1917	+	185.251i	0.132818	+	0.408773i	−0.862426	+	0.506183i	$0.831056\pi$
$60$		0			0
$61$	132.729	−	408.499i	0.278594	−	0.857425i	−0.709652	−	0.704553i	$-0.751148\pi$
$61$	132.729	−	408.499i	0.278594	−	0.857425i	0.988246	−	0.152872i	$-0.0488523\pi$
$62$		0			0
$63$	−391.548	+	127.222i	−0.783022	+	0.254419i
$64$		0			0
$65$	682.056	−	271.696i	1.30152	−	0.518458i
$66$		0			0
$67$	−549.725	−	756.631i	−1.00238	−	1.37966i	−0.923853	−	0.382748i	$-0.874978\pi$
$67$	−549.725	−	756.631i	−1.00238	−	1.37966i	−0.0785286	−	0.996912i	$-0.525022\pi$
$68$		0			0
$69$	−665.990	+	483.870i	−1.16197	+	0.844219i
$70$		0			0
$71$	781.193	+	567.570i	1.30578	+	0.948706i	0.999994	−	0.00339389i	$-0.00108031\pi$
$71$	781.193	+	567.570i	1.30578	+	0.948706i	0.305787	+	0.952100i	$0.401080\pi$
$72$		0			0
$73$	267.559	+	86.9353i	0.428979	+	0.139384i	0.515545	−	0.856862i	$-0.327589\pi$
$73$	267.559	+	86.9353i	0.428979	+	0.139384i	−0.0865664	+	0.996246i	$0.527589\pi$
$74$		0			0
$75$	415.506	−	763.349i	0.639713	−	1.17525i
$76$		0			0
$77$	−817.958	−	265.771i	−1.21058	−	0.393343i
$78$		0			0
$79$	−559.111	−	406.218i	−0.796264	−	0.578520i	0.113552	−	0.993532i	$-0.463777\pi$
$79$	−559.111	−	406.218i	−0.796264	−	0.578520i	−0.909816	+	0.415012i	$0.863777\pi$
$80$		0			0
$81$	687.462	−	499.470i	0.943021	−	0.685145i
$82$		0			0
$83$	−391.465	−	538.805i	−0.517697	−	0.712549i	0.467497	−	0.883995i	$-0.345156\pi$
$83$	−391.465	−	538.805i	−0.517697	−	0.712549i	−0.985193	+	0.171446i	$0.945156\pi$
$84$		0			0
$85$	−203.444	−	244.877i	−0.259608	−	0.312479i
$86$		0			0
$87$	−59.8417	+	19.4438i	−0.0737437	+	0.0239608i
$88$		0			0
$89$	−385.384	+	1186.09i	−0.458996	+	1.41264i	0.407384	+	0.913257i	$0.366441\pi$
$89$	−385.384	+	1186.09i	−0.458996	+	1.41264i	−0.866379	+	0.499386i	$0.833559\pi$
$90$		0			0
$91$	391.443	+	1204.74i	0.450927	+	1.38781i
$92$		0			0
$93$		−	1770.30i		−	1.97389i
$94$		0			0
$95$	−813.664	+	675.993i	−0.878738	+	0.730057i
$96$		0			0
$97$	812.330	−	1118.08i	0.850306	−	1.17035i	−0.133490	−	0.991050i	$-0.542618\pi$
$97$	812.330	−	1118.08i	0.850306	−	1.17035i	0.983795	−	0.179295i	$-0.0573817\pi$
$98$		0			0
$99$	−951.535			−0.965989
$100$		0			0
$101$	−1689.47			−1.66444			−0.832220	−	0.554446i	$-0.812930\pi$
$101$	−1689.47			−1.66444			−0.832220	+	0.554446i	$0.812930\pi$
$102$		0			0
$103$	−497.052	+	684.134i	−0.475495	+	0.654463i	−0.977631	−	0.210325i	$-0.932548\pi$
$103$	−497.052	+	684.134i	−0.475495	+	0.654463i	0.502136	+	0.864789i	$0.332548\pi$
$104$		0			0
$105$	1267.78	+	800.843i	1.17831	+	0.744326i
$106$		0			0
$107$		−	579.281i		−	0.523376i	−0.965153	−	0.261688i	$-0.915721\pi$
$107$		−	579.281i		−	0.523376i	0.965153	−	0.261688i	$-0.0842792\pi$
$108$		0			0
$109$	60.4006	+	185.894i	0.0530764	+	0.163352i	0.974081	−	0.226199i	$-0.0726300\pi$
$109$	60.4006	+	185.894i	0.0530764	+	0.163352i	−0.921005	+	0.389552i	$0.872630\pi$
$110$		0			0
$111$	591.505	−	1820.46i	0.505794	−	1.55667i
$112$		0			0
$113$	−1866.33	+	606.407i	−1.55371	+	0.504832i	−0.955119	−	0.296222i	$-0.904273\pi$
$113$	−1866.33	+	606.407i	−1.55371	+	0.504832i	−0.598593	+	0.801054i	$0.704273\pi$
$114$		0			0
$115$	1282.84	+	326.518i	1.04022	+	0.264765i
$116$		0			0
$117$	823.768	+	1133.82i	0.650918	+	0.895911i
$118$		0			0
$119$	444.389	−	322.868i	0.342328	−	0.248716i
$120$		0			0
$121$	−531.357	−	386.053i	−0.399216	−	0.290047i
$122$		0			0
$123$	1914.04	+	621.910i	1.40312	+	0.455900i
$124$		0			0
$125$	−1371.12	+	270.482i	−0.981092	+	0.193541i
$126$		0			0
$127$	868.951	+	282.339i	0.607142	+	0.197272i	0.596423	−	0.802670i	$-0.296588\pi$
$127$	868.951	+	282.339i	0.607142	+	0.197272i	0.0107186	+	0.999943i	$0.496588\pi$
$128$		0			0
$129$	2087.37	+	1516.56i	1.42467	+	1.03509i
$130$		0			0
$131$	1568.98	−	1139.93i	1.04643	−	0.760276i	0.0749003	−	0.997191i	$-0.476136\pi$
$131$	1568.98	−	1139.93i	1.04643	−	0.760276i	0.971530	+	0.236915i	$0.0761362\pi$
$132$		0			0
$133$	−1072.81	−	1476.59i	−0.699429	−	0.962681i
$134$		0			0
$135$	−426.221	−	108.485i	−0.271728	−	0.0691623i
$136$		0			0
$137$	−830.731	+	269.921i	−0.518059	+	0.168328i	−0.556364	−	0.830938i	$-0.687804\pi$
$137$	−830.731	+	269.921i	−0.518059	+	0.168328i	0.0383051	+	0.999266i	$0.487804\pi$
$138$		0			0
$139$	710.797	−	2187.61i	0.433734	−	1.33490i	−0.460644	−	0.887585i	$-0.652382\pi$
$139$	710.797	−	2187.61i	0.433734	−	1.33490i	0.894378	−	0.447311i	$-0.147618\pi$
$140$		0			0
$141$	347.069	+	1068.17i	0.207294	+	0.637986i
$142$		0			0
$143$			2927.74i			1.71210i
$144$		0			0
$145$	85.5413	+	54.0355i	0.0489918	+	0.0309476i
$146$		0			0
$147$	−118.992	+	163.778i	−0.0667638	+	0.0918924i
$148$		0			0
$149$	309.895			0.170387			0.0851933	−	0.996364i	$-0.472849\pi$
$149$	309.895			0.170387			0.0851933	+	0.996364i	$0.472849\pi$
$150$		0			0
$151$	−350.923			−0.189124			−0.0945621	−	0.995519i	$-0.530145\pi$
$151$	−350.923			−0.189124			−0.0945621	+	0.995519i	$0.530145\pi$
$152$		0			0
$153$	357.211	−	491.658i	0.188750	−	0.259792i
$154$		0			0
$155$	−2189.61	+	1819.13i	−1.13467	+	0.942682i
$156$		0			0
$157$			2730.00i			1.38776i	0.720093	+	0.693878i	$0.244099\pi$
$157$			2730.00i			1.38776i	−0.720093	+	0.693878i	$0.755901\pi$
$158$		0			0
$159$	−347.064	−	1068.15i	−0.173107	−	0.532768i
$160$		0			0
$161$	−705.779	+	2172.16i	−0.345485	+	1.06329i
$162$		0			0
$163$	−1522.57	+	494.713i	−0.731638	+	0.237723i	−0.651062	−	0.759025i	$-0.725676\pi$
$163$	−1522.57	+	494.713i	−0.731638	+	0.237723i	−0.0805761	+	0.996748i	$0.525676\pi$
$164$		0			0
$165$	2214.77	+	2665.82i	1.04497	+	1.25778i
$166$		0			0
$167$	345.118	+	475.014i	0.159916	+	0.220106i	0.881455	−	0.472268i	$-0.156565\pi$
$167$	345.118	+	475.014i	0.159916	+	0.220106i	−0.721538	+	0.692374i	$0.756565\pi$
$168$		0			0
$169$	1711.19	−	1243.25i	0.778877	−	0.565887i
$170$		0			0
$171$	−1633.65	−	1186.92i	−0.730576	−	0.530795i
$172$		0			0
$173$	2764.05	+	898.096i	1.21472	+	0.394688i	0.845158	−	0.534517i	$-0.179506\pi$
$173$	2764.05	+	898.096i	1.21472	+	0.394688i	0.369566	+	0.929205i	$0.379506\pi$
$174$		0			0
$175$	−312.219	−	2390.99i	−0.134866	−	1.03281i
$176$		0			0
$177$	1288.02	+	418.504i	0.546970	+	0.177721i
$178$		0			0
$179$	194.784	+	141.519i	0.0813341	+	0.0590927i	0.627709	−	0.778448i	$-0.283993\pi$
$179$	194.784	+	141.519i	0.0813341	+	0.0590927i	−0.546375	+	0.837541i	$0.683993\pi$
$180$		0			0
$181$	1158.32	−	841.568i	0.475675	−	0.345598i	−0.323974	−	0.946066i	$-0.605019\pi$
$181$	1158.32	−	841.568i	0.475675	−	0.345598i	0.799649	+	0.600468i	$0.205019\pi$
$182$		0			0
$183$	−1755.36	−	2416.05i	−0.709071	−	0.975952i
$184$		0			0
$185$	−2859.47	+	1139.07i	−1.13639	+	0.452681i
$186$		0			0
$187$	1207.42	−	392.315i	0.472167	−	0.153416i
$188$		0			0
$189$	234.494	−	721.699i	0.0902484	−	0.277756i
$190$		0			0
$191$	45.6319	+	140.440i	0.0172869	+	0.0532037i	0.959328	−	0.282294i	$-0.0910954\pi$
$191$	45.6319	+	140.440i	0.0172869	+	0.0532037i	−0.942041	+	0.335498i	$0.891095\pi$
$192$		0			0
$193$		−	169.522i		−	0.0632252i	−0.999500	−	0.0316126i	$-0.989936\pi$
$193$		−	169.522i		−	0.0632252i	0.999500	−	0.0316126i	$-0.0100643\pi$
$194$		0			0
$195$	1259.13	−	4946.91i	0.462400	−	1.81670i
$196$		0			0
$197$	−425.052	+	585.034i	−0.153724	+	0.211584i	−0.878932	−	0.476946i	$-0.841744\pi$
$197$	−425.052	+	585.034i	−0.153724	+	0.211584i	0.725208	+	0.688530i	$0.241744\pi$
$198$		0			0
$199$	−2376.34			−0.846503			−0.423252	−	0.906012i	$-0.639111\pi$
$199$	−2376.34			−0.846503			−0.423252	+	0.906012i	$0.639111\pi$
$200$		0			0
$201$	−6502.64			−2.28190
$202$		0			0
$203$	−102.611	+	141.231i	−0.0354771	+	0.0488301i
$204$		0			0
$205$	−1197.62	−	3006.46i	−0.408026	−	1.02429i
$206$		0			0
$207$			2526.89i			0.848459i
$208$		0			0
$209$	−1303.56	−	4011.94i	−0.431431	−	1.32781i
$210$		0			0
$211$	199.563	−	614.191i	0.0651112	−	0.200392i	−0.913208	−	0.407493i	$-0.866403\pi$
$211$	199.563	−	614.191i	0.0651112	−	0.200392i	0.978319	+	0.207101i	$0.0664030\pi$
$212$		0			0
$213$	6385.13	−	2074.66i	2.05400	−	0.667385i
$214$		0			0
$215$	−269.172	−	4140.17i	−0.0853832	−	1.31329i
$216$		0			0
$217$	−2886.97	−	3973.57i	−0.903134	−	1.24306i
$218$		0			0
$219$	1582.47	−	1149.73i	0.488279	−	0.354756i
$220$		0			0
$221$	−1512.76	−	1099.09i	−0.460450	−	0.334537i
$222$		0			0
$223$	4129.23	+	1341.67i	1.23997	+	0.402891i	0.854317	−	0.519752i	$-0.173975\pi$
$223$	4129.23	+	1341.67i	1.23997	+	0.402891i	0.385655	+	0.922643i	$0.373975\pi$
$224$		0			0
$225$	−1145.97	−	2409.10i	−0.339547	−	0.713808i
$226$		0			0
$227$	−14.3395	−	4.65918i	−0.00419271	−	0.00136229i	0.306920	−	0.951735i	$-0.400702\pi$
$227$	−14.3395	−	4.65918i	−0.00419271	−	0.00136229i	−0.311113	+	0.950373i	$0.600702\pi$
$228$		0			0
$229$	4708.23	+	3420.73i	1.35864	+	0.987109i	0.998530	+	0.0541986i	$0.0172604\pi$
$229$	4708.23	+	3420.73i	1.35864	+	0.987109i	0.360109	+	0.932910i	$0.382740\pi$
$230$		0			0
$231$	−4837.78	+	3514.85i	−1.37793	+	1.00113i
$232$		0			0
$233$	2900.42	+	3992.08i	0.815505	+	1.12245i	0.990451	+	0.137868i	$0.0440250\pi$
$233$	2900.42	+	3992.08i	0.815505	+	1.12245i	−0.174946	+	0.984578i	$0.555975\pi$
$234$		0			0
$235$	964.528	−	1526.90i	0.267740	−	0.423848i
$236$		0			0
$237$	−4569.93	+	1484.86i	−1.25253	+	0.406971i
$238$		0			0
$239$	−2030.23	+	6248.40i	−0.549475	+	1.69111i	0.160630	+	0.987015i	$0.448648\pi$
$239$	−2030.23	+	6248.40i	−0.549475	+	1.69111i	−0.710105	+	0.704096i	$0.751352\pi$
$240$		0			0
$241$	1675.48	+	5156.60i	0.447831	+	1.37828i	0.879349	+	0.476178i	$0.157978\pi$
$241$	1675.48	+	5156.60i	0.447831	+	1.37828i	−0.431518	+	0.902104i	$0.642022\pi$
$242$		0			0
$243$		−	4846.07i		−	1.27932i
$244$		0			0
$245$	324.843	−	21.1196i	0.0847081	−	0.00550728i
$246$		0			0
$247$	−3651.98	+	5026.52i	−0.940769	+	1.29486i
$248$		0			0
$249$	−4630.60			−1.17852
$250$		0			0
$251$	4769.82			1.19947			0.599737	−	0.800197i	$-0.295272\pi$
$251$	4769.82			1.19947			0.599737	+	0.800197i	$0.295272\pi$
$252$		0			0
$253$	−3102.78	+	4270.61i	−0.771028	+	1.06123i
$254$		0			0
$255$	−2208.86	+	143.609i	−0.542449	+	0.0352672i
$256$		0			0
$257$		−	5116.69i		−	1.24191i	−0.783847	−	0.620954i	$-0.786745\pi$
$257$		−	5116.69i		−	1.24191i	0.783847	−	0.620954i	$-0.213255\pi$
$258$		0			0
$259$	−1641.10	−	5050.78i	−0.393717	−	1.21174i
$260$		0			0
$261$	−59.6838	+	183.688i	−0.0141545	+	0.0435632i
$262$		0			0
$263$	−113.835	+	36.9872i	−0.0266896	+	0.00867197i	−0.322331	−	0.946627i	$-0.604467\pi$
$263$	−113.835	+	36.9872i	−0.0266896	+	0.00867197i	0.295642	+	0.955299i	$0.404467\pi$
$264$		0			0
$265$	−964.514	+	1526.88i	−0.223584	+	0.353945i
$266$		0			0
$267$	5096.75	+	7015.07i	1.16822	+	1.60792i
$268$		0			0
$269$	5675.64	−	4123.60i	1.28643	−	0.934647i	0.286705	−	0.958019i	$-0.407440\pi$
$269$	5675.64	−	4123.60i	1.28643	−	0.934647i	0.999727	+	0.0233720i	$0.00744020\pi$
$270$		0			0
$271$	5335.60	+	3876.54i	1.19599	+	0.868941i	0.993885	−	0.110422i	$-0.0352201\pi$
$271$	5335.60	+	3876.54i	1.19599	+	0.868941i	0.202110	+	0.979363i	$0.435220\pi$
$272$		0			0
$273$	8376.37	+	2721.65i	1.85700	+	0.603376i
$274$		0			0
$275$	1021.38	−	5478.69i	0.223970	−	1.20137i
$276$		0			0
$277$	−1919.00	−	623.521i	−0.416251	−	0.135248i	0.0934014	−	0.995629i	$-0.470226\pi$
$277$	−1919.00	−	623.521i	−0.416251	−	0.135248i	−0.509652	+	0.860380i	$0.670226\pi$
$278$		0			0
$279$	−4396.23	−	3194.05i	−0.943353	−	0.685386i
$280$		0			0
$281$	−6928.28	+	5033.69i	−1.47084	+	1.06863i	−0.490473	+	0.871456i	$0.663176\pi$
$281$	−6928.28	+	5033.69i	−1.47084	+	1.06863i	−0.980369	+	0.197173i	$0.936824\pi$
$282$		0			0
$283$	1292.69	+	1779.23i	0.271528	+	0.373726i	0.922905	−	0.385028i	$-0.125808\pi$
$283$	1292.69	+	1779.23i	0.271528	+	0.373726i	−0.651377	+	0.758754i	$0.725808\pi$
$284$		0			0
$285$	477.175	+	7339.48i	0.0991768	+	1.52545i
$286$		0			0
$287$	5310.40	−	1725.45i	1.09221	−	0.354879i
$288$		0			0
$289$	1267.64	−	3901.39i	0.258017	−	0.794095i
$290$		0			0
$291$	−2969.34	−	9138.68i	−0.598164	−	1.84096i
$292$		0			0
$293$		−	8283.16i		−	1.65156i	−0.563992	−	0.825780i	$-0.690735\pi$
$293$		−	8283.16i		−	1.65156i	0.563992	−	0.825780i	$-0.309265\pi$
$294$		0			0
$295$	−805.918	−	2023.14i	−0.159059	−	0.399295i
$296$		0			0
$297$	1030.90	−	1418.91i	0.201410	−	0.277216i
$298$		0			0
$299$	7774.88			1.50379
$300$		0			0
$301$	7158.44			1.37078
$302$		0			0
$303$	−6904.50	+	9503.22i	−1.30909	+	1.80180i
$304$		0			0
$305$	−1184.53	+	4653.81i	−0.222379	+	0.873693i
$306$		0			0
$307$			6066.86i			1.12786i	0.825821	+	0.563932i	$0.190712\pi$
$307$			6066.86i			1.12786i	−0.825821	+	0.563932i	$0.809288\pi$
$308$		0			0
$309$	1816.89	+	5591.82i	0.334496	+	1.02947i
$310$		0			0
$311$	−1307.07	+	4022.76i	−0.238319	+	0.733472i	0.758344	+	0.651854i	$0.226009\pi$
$311$	−1307.07	+	4022.76i	−0.238319	+	0.733472i	−0.996664	+	0.0816175i	$0.973991\pi$
$312$		0			0
$313$	−1395.13	+	453.305i	−0.251940	+	0.0818604i	−0.432265	−	0.901747i	$-0.642285\pi$
$313$	−1395.13	+	453.305i	−0.251940	+	0.0818604i	0.180324	+	0.983607i	$0.442285\pi$
$314$		0			0
$315$	4276.13	−	1703.40i	0.764866	−	0.304684i
$316$		0			0
$317$	−1187.29	−	1634.17i	−0.210363	−	0.289539i	0.690777	−	0.723068i	$-0.257268\pi$
$317$	−1187.29	−	1634.17i	−0.210363	−	0.289539i	−0.901140	+	0.433528i	$0.857268\pi$
$318$		0			0
$319$	−326.421	+	237.159i	−0.0572917	+	0.0416249i
$320$		0			0
$321$	−3258.45	−	2367.40i	−0.566569	−	0.411637i
$322$		0			0
$323$	2562.33	+	832.553i	0.441400	+	0.143419i
$324$		0			0
$325$	−7412.47	+	3525.99i	−1.26514	+	0.601806i
$326$		0			0
$327$	1292.49	+	419.957i	0.218578	+	0.0710204i
$328$		0			0
$329$	2520.97	+	1831.59i	0.422448	+	0.306926i
$330$		0			0
$331$	1800.35	−	1308.03i	0.298961	−	0.217208i	−0.428184	−	0.903691i	$-0.640847\pi$
$331$	1800.35	−	1308.03i	0.298961	−	0.217208i	0.727145	+	0.686484i	$0.240847\pi$
$332$		0			0
$333$	−3453.59	−	4753.46i	−0.568335	−	0.782246i
$334$		0			0
$335$	6681.99	+	8042.82i	1.08978	+	1.31172i
$336$		0			0
$337$	−270.895	+	88.0192i	−0.0437881	+	0.0142276i	−0.330829	−	0.943691i	$-0.607328\pi$
$337$	−270.895	+	88.0192i	−0.0437881	+	0.0142276i	0.287041	+	0.957918i	$0.407328\pi$
$338$		0			0
$339$	−4216.26	+	12976.3i	−0.675504	+	2.07899i
$340$		0			0
$341$	−3507.94	−	10796.3i	−0.557083	−	1.71453i
$342$		0			0
$343$		−	6054.92i		−	0.953163i
$344$		0			0
$345$	7079.33	−	5881.52i	1.10475	−	0.917826i
$346$		0			0
$347$	−271.077	+	373.105i	−0.0419371	+	0.0577215i	−0.829471	−	0.558550i	$-0.811358\pi$
$347$	−271.077	+	373.105i	−0.0419371	+	0.0577215i	0.787533	+	0.616272i	$0.211358\pi$
$348$		0			0
$349$	−527.686			−0.0809352			−0.0404676	−	0.999181i	$-0.512885\pi$
$349$	−527.686			−0.0809352			−0.0404676	+	0.999181i	$0.512885\pi$
$350$		0			0
$351$	−2583.20			−0.392823
$352$		0			0
$353$	−3842.83	+	5289.20i	−0.579413	+	0.797494i	−0.993631	−	0.112684i	$-0.964055\pi$
$353$	−3842.83	+	5289.20i	−0.579413	+	0.797494i	0.414217	+	0.910178i	$0.364055\pi$
$354$		0			0
$355$	−9127.29	−	5765.61i	−1.36458	−	0.861991i
$356$		0			0
$357$		−	3819.17i		−	0.566196i
$358$		0			0
$359$	−1597.57	−	4916.81i	−0.234865	−	0.722839i	−0.997139	−	0.0755856i	$-0.975917\pi$
$359$	−1597.57	−	4916.81i	−0.234865	−	0.722839i	0.762275	−	0.647254i	$-0.224083\pi$
$360$		0			0
$361$	646.808	−	1990.67i	0.0943007	−	0.290228i
$362$		0			0
$363$	−4343.08	+	1411.15i	−0.627969	+	0.204039i
$364$		0			0
$365$	−3048.16	−	775.842i	−0.437118	−	0.111259i
$366$		0			0
$367$	4323.07	+	5950.19i	0.614884	+	0.846315i	0.996968	−	0.0778125i	$-0.0247935\pi$
$367$	4323.07	+	5950.19i	0.614884	+	0.846315i	−0.382084	+	0.924128i	$0.624794\pi$
$368$		0			0
$369$	4997.80	−	3631.11i	0.705082	−	0.512272i
$370$		0			0
$371$	−2520.93	−	1831.56i	−0.352777	−	0.256307i
$372$		0			0
$373$	−8229.64	−	2673.97i	−1.14240	−	0.371188i	−0.324123	−	0.946015i	$-0.605069\pi$
$373$	−8229.64	−	2673.97i	−1.14240	−	0.371188i	−0.818275	+	0.574827i	$0.805069\pi$
$374$		0			0
$375$	−4082.01	+	8817.91i	−0.562118	+	1.21428i
$376$		0			0
$377$	565.181	+	183.639i	0.0772104	+	0.0250872i
$378$		0			0
$379$	−3589.30	−	2607.78i	−0.486464	−	0.353437i	0.317359	−	0.948306i	$-0.397204\pi$
$379$	−3589.30	−	2607.78i	−0.486464	−	0.353437i	−0.803823	+	0.594869i	$0.797204\pi$
$380$		0			0
$381$	5139.37	−	3733.97i	0.691071	−	0.502092i
$382$		0			0
$383$	−6497.58	−	8943.15i	−0.866869	−	1.19314i	−0.979888	−	0.199550i	$-0.936052\pi$
$383$	−6497.58	−	8943.15i	−0.866869	−	1.19314i	0.113019	−	0.993593i	$-0.463948\pi$
$384$		0			0
$385$	9318.56	+	2371.84i	1.23355	+	0.313974i
$386$		0			0
$387$	7532.25	−	2447.37i	0.989368	−	0.321465i
$388$		0			0
$389$	1561.28	−	4805.12i	0.203496	−	0.626296i	−0.796276	−	0.604934i	$-0.793200\pi$
$389$	1561.28	−	4805.12i	0.203496	−	0.626296i	0.999772	−	0.0213622i	$-0.00680033\pi$
$390$		0			0
$391$	−1041.83	−	3206.42i	−0.134751	−	0.414720i
$392$		0			0
$393$		−	13484.1i		−	1.73075i
$394$		0			0
$395$	6532.53	+	4126.53i	0.832120	+	0.525641i
$396$		0			0
$397$	5065.78	−	6972.44i	0.640413	−	0.881453i	−0.358224	−	0.933635i	$-0.616618\pi$
$397$	5065.78	−	6972.44i	0.640413	−	0.881453i	0.998638	+	0.0521825i	$0.0166178\pi$
$398$		0			0
$399$	−12690.1			−1.59223
$400$		0			0
$401$	11889.0			1.48057			0.740283	−	0.672296i	$-0.234692\pi$
$401$	11889.0			1.48057			0.740283	+	0.672296i	$0.234692\pi$
$402$		0			0
$403$	−9827.64	+	13526.6i	−1.21476	+	1.67198i
$404$		0			0
$405$	−7307.57	+	6071.14i	−0.896583	+	0.744882i
$406$		0			0
$407$		−	12274.3i		−	1.49488i
$408$		0			0
$409$	−3085.01	−	9494.69i	−0.372968	−	1.14788i	−0.944839	−	0.327534i	$-0.893782\pi$
$409$	−3085.01	−	9494.69i	−0.372968	−	1.14788i	0.571871	−	0.820343i	$-0.306218\pi$
$410$		0			0
$411$	−1876.72	+	5775.95i	−0.225235	+	0.693204i
$412$		0			0
$413$	3573.55	−	1161.12i	0.425770	−	0.138341i
$414$		0			0
$415$	4758.31	+	5727.38i	0.562835	+	0.677460i
$416$		0			0
$417$	−9400.37	−	12938.5i	−1.10393	−	1.51943i
$418$		0			0
$419$	−588.725	+	427.734i	−0.0686422	+	0.0498715i	−0.621577	−	0.783353i	$-0.713508\pi$
$419$	−588.725	+	427.734i	−0.0686422	+	0.0498715i	0.552935	+	0.833224i	$0.313508\pi$
$420$		0			0
$421$	3666.72	+	2664.03i	0.424477	+	0.308401i	0.779437	−	0.626481i	$-0.215505\pi$
$421$	3666.72	+	2664.03i	0.424477	+	0.308401i	−0.354959	+	0.934882i	$0.615505\pi$
$422$		0			0
$423$	3278.81	+	1065.35i	0.376882	+	0.122456i
$424$		0			0
$425$	2447.41	+	2584.47i	0.279334	+	0.294977i
$426$		0			0
$427$	−7880.07	−	2560.39i	−0.893076	−	0.290178i
$428$		0			0
$429$	16468.5	+	11965.0i	1.85339	+	1.34657i
$430$		0			0
$431$	8219.29	−	5971.66i	0.918583	−	0.667389i	−0.0245883	−	0.999698i	$-0.507827\pi$
$431$	8219.29	−	5971.66i	0.918583	−	0.667389i	0.943171	+	0.332308i	$0.107827\pi$
$432$		0			0
$433$	−1610.24	−	2216.30i	−0.178714	−	0.245978i	0.710257	−	0.703943i	$-0.248579\pi$
$433$	−1610.24	−	2216.30i	−0.178714	−	0.245978i	−0.888971	+	0.457964i	$0.848579\pi$
$434$		0			0
$435$	653.538	−	260.336i	0.0720339	−	0.0286946i
$436$		0			0
$437$	−10654.1	+	3461.72i	−1.16626	+	0.378940i
$438$		0			0
$439$	−5058.78	+	15569.3i	−0.549982	+	1.69267i	0.158856	+	0.987302i	$0.449219\pi$
$439$	−5058.78	+	15569.3i	−0.549982	+	1.69267i	−0.708839	+	0.705370i	$0.750781\pi$
$440$		0			0
$441$	192.024	+	590.990i	0.0207347	+	0.0638150i
$442$		0			0
$443$		−	492.196i		−	0.0527877i	−0.999652	−	0.0263938i	$-0.991598\pi$
$443$		−	492.196i		−	0.0527877i	0.999652	−	0.0263938i	$-0.00840239\pi$
$444$		0			0
$445$	3439.31	−	13512.5i	0.366379	−	1.43945i
$446$		0			0
$447$	1266.48	−	1743.15i	0.134009	−	0.184448i
$448$		0			0
$449$	−12533.9			−1.31739			−0.658697	−	0.752408i	$-0.728892\pi$
$449$	−12533.9			−1.31739			−0.658697	+	0.752408i	$0.728892\pi$
$450$		0			0
$451$	12905.3			1.34742
$452$		0			0
$453$	−1434.15	+	1973.94i	−0.148747	+	0.204732i
$454$		0			0
$455$	−5241.11	−	13157.1i	−0.540015	−	1.35563i
$456$		0			0
$457$			11948.8i			1.22307i	0.791218	+	0.611534i	$0.209447\pi$
$457$			11948.8i			1.22307i	−0.791218	+	0.611534i	$0.790553\pi$
$458$		0			0
$459$	346.146	+	1065.33i	0.0351998	+	0.108334i
$460$		0			0
$461$	−1484.80	+	4569.76i	−0.150009	+	0.461681i	−0.997621	−	0.0689360i	$-0.978040\pi$
$461$	−1484.80	+	4569.76i	−0.150009	+	0.461681i	0.847612	+	0.530617i	$0.178040\pi$
$462$		0			0
$463$	−5295.53	+	1720.62i	−0.531543	+	0.172709i	−0.562477	−	0.826813i	$-0.690152\pi$
$463$	−5295.53	+	1720.62i	−0.531543	+	0.172709i	0.0309347	+	0.999521i	$0.490152\pi$
$464$		0			0
$465$	1284.10	+	19750.9i	0.128062	+	1.96973i
$466$		0			0
$467$	−3113.92	−	4285.94i	−0.308555	−	0.424689i	0.626375	−	0.779522i	$-0.284538\pi$
$467$	−3113.92	−	4285.94i	−0.308555	−	0.424689i	−0.934930	+	0.354833i	$0.884538\pi$
$468$		0			0
$469$	−14595.7	+	10604.4i	−1.43702	+	1.04406i
$470$		0			0
$471$	15356.2	+	11156.9i	1.50228	+	1.09147i
$472$		0			0
$473$	15735.1	+	5112.66i	1.52960	+	0.496999i
$474$		0			0
$475$	8587.53	−	8132.10i	0.829522	−	0.785529i
$476$		0			0
$477$	−3278.76	−	1065.33i	−0.314726	−	0.102261i
$478$		0			0
$479$	5990.03	+	4352.01i	0.571381	+	0.415133i	0.835607	−	0.549328i	$-0.185116\pi$
$479$	5990.03	+	4352.01i	0.571381	+	0.415133i	−0.264225	+	0.964461i	$0.585116\pi$
$480$		0			0
$481$	−14625.7	+	10626.2i	−1.38644	+	1.00730i
$482$		0			0
$483$	9334.01	+	12847.2i	0.879321	+	1.21028i
$484$		0			0
$485$	−8251.99	+	13063.4i	−0.772585	+	1.22305i
$486$		0			0
$487$	−3204.10	+	1041.08i	−0.298135	+	0.0968700i	−0.454265	−	0.890867i	$-0.650098\pi$
$487$	−3204.10	+	1041.08i	−0.298135	+	0.0968700i	0.156130	+	0.987737i	$0.450098\pi$
$488$		0			0
$489$	−3439.67	+	10586.2i	−0.318093	+	0.978988i
$490$		0			0
$491$	−727.225	−	2238.17i	−0.0668416	−	0.205717i	0.912057	−	0.410063i	$-0.134493\pi$
$491$	−727.225	−	2238.17i	−0.0668416	−	0.205717i	−0.978899	+	0.204346i	$0.934493\pi$
$492$		0			0
$493$		−	257.692i		−	0.0235413i
$494$		0			0
$495$	10616.1	−	690.202i	0.963954	−	0.0626713i
$496$		0			0
$497$	10948.6	−	15069.4i	0.988152	−	1.36007i
$498$		0			0
$499$	−12984.0			−1.16482			−0.582408	−	0.812897i	$-0.697889\pi$
$499$	−12984.0			−1.16482			−0.582408	+	0.812897i	$0.697889\pi$
$500$		0			0
$501$	4082.37			0.364046
$502$		0			0
$503$	5061.33	−	6966.33i	0.448656	−	0.617521i	−0.523453	−	0.852055i	$-0.675356\pi$
$503$	5061.33	−	6966.33i	0.448656	−	0.617521i	0.972108	+	0.234534i	$0.0753563\pi$
$504$		0			0
$505$	18849.0	−	1225.47i	1.66093	−	0.107985i
$506$		0			0
$507$		−	14706.3i		−	1.28823i
$508$		0			0
$509$	5335.16	+	16419.9i	0.464591	+	1.42986i	0.859496	+	0.511142i	$0.170777\pi$
$509$	5335.16	+	16419.9i	0.464591	+	1.42986i	−0.394905	+	0.918722i	$0.629223\pi$
$510$		0			0
$511$	1677.01	−	5161.30i	0.145179	−	0.446815i
$512$		0			0
$513$	3539.81	−	1150.15i	0.304652	−	0.0989873i
$514$		0			0
$515$	5049.26	−	7993.27i	0.432033	−	0.683933i
$516$		0			0
$517$	4233.25	+	5826.58i	0.360113	+	0.495653i
$518$		0			0
$519$	16347.9	−	11877.4i	1.38264	−	1.00455i
$520$		0			0
$521$	−6659.06	−	4838.09i	−0.559960	−	0.406834i	0.271485	−	0.962443i	$-0.412485\pi$
$521$	−6659.06	−	4838.09i	−0.559960	−	0.406834i	−0.831444	+	0.555608i	$0.812485\pi$
$522$		0			0
$523$	−13059.3	−	4243.24i	−1.09186	−	0.354768i	−0.292898	−	0.956144i	$-0.594620\pi$
$523$	−13059.3	−	4243.24i	−1.09186	−	0.354768i	−0.798967	+	0.601375i	$0.794620\pi$
$524$		0			0
$525$	−14725.2	−	8015.24i	−1.22412	−	0.666312i
$526$		0			0
$527$	6895.36	+	2240.44i	0.569955	+	0.185190i
$528$		0			0
$529$	1497.69	+	1088.14i	0.123095	+	0.0894334i
$530$		0			0
$531$	3363.19	−	2443.50i	0.274859	−	0.199696i
$532$		0			0
$533$	−11172.4	−	15377.5i	−0.907939	−	1.24967i
$534$		0			0
$535$	420.185	+	6462.92i	0.0339555	+	0.522273i
$536$		0			0
$537$	1592.08	−	517.297i	0.127939	−	0.0415699i
$538$		0			0
$539$	−401.146	+	1234.60i	−0.0320568	+	0.0986606i
$540$		0			0
$541$	3698.98	+	11384.3i	0.293958	+	0.904711i	0.983569	+	0.180531i	$0.0577816\pi$
$541$	3698.98	+	11384.3i	0.293958	+	0.904711i	−0.689611	+	0.724180i	$0.742218\pi$
$542$		0			0
$543$		−	9954.83i		−	0.786745i
$544$		0			0
$545$	−808.716	−	2030.17i	−0.0635625	−	0.159565i
$546$		0			0
$547$	−8198.56	+	11284.4i	−0.640850	+	0.882055i	−0.998661	−	0.0517393i	$-0.983523\pi$
$547$	−8198.56	+	11284.4i	−0.640850	+	0.882055i	0.357810	+	0.933794i	$0.383523\pi$
$548$		0			0
$549$	−9166.93			−0.712632
$550$		0			0
$551$	−856.244			−0.0662018
$552$		0			0
$553$	−7836.07	+	10785.4i	−0.602574	+	0.829372i
$554$		0			0
$555$	−5278.81	+	20739.6i	−0.403735	+	1.58621i
$556$		0			0
$557$			1521.86i			0.115769i	0.998323	+	0.0578846i	$0.0184356\pi$
$557$			1521.86i			0.115769i	−0.998323	+	0.0578846i	$0.981564\pi$
$558$		0			0
$559$	−7530.23	−	23175.7i	−0.569758	−	1.75353i
$560$		0			0
$561$	2727.71	−	8395.02i	0.205283	−	0.631797i
$562$		0			0
$563$	13224.9	−	4297.03i	0.989988	−	0.321667i	0.231130	−	0.972923i	$-0.425758\pi$
$563$	13224.9	−	4297.03i	0.989988	−	0.321667i	0.758858	+	0.651256i	$0.225758\pi$
$564$		0			0
$565$	20382.4	−	8119.31i	1.51769	−	0.604569i
$566$		0			0
$567$	−9634.94	−	13261.4i	−0.713632	−	0.982231i
$568$		0			0
$569$	−14765.1	+	10727.5i	−1.08785	+	0.790370i	−0.979035	−	0.203692i	$-0.934706\pi$
$569$	−14765.1	+	10727.5i	−1.08785	+	0.790370i	−0.108815	+	0.994062i	$0.534706\pi$
$570$		0			0
$571$	−3513.40	−	2552.63i	−0.257498	−	0.187083i	0.451545	−	0.892248i	$-0.350873\pi$
$571$	−3513.40	−	2552.63i	−0.257498	−	0.187083i	−0.709043	+	0.705165i	$0.750873\pi$
$572$		0			0
$573$	976.462	+	317.272i	0.0711907	+	0.0231313i
$574$		0			0
$575$	−14549.2	−	2712.37i	−1.05520	−	0.196720i
$576$		0			0
$577$	22652.4	+	7360.22i	1.63437	+	0.531040i	0.975271	−	0.221014i	$-0.0709368\pi$
$577$	22652.4	+	7360.22i	1.63437	+	0.531040i	0.659101	+	0.752054i	$0.270937\pi$
$578$		0			0
$579$	−953.558	−	692.800i	−0.0684430	−	0.0497268i
$580$		0			0
$581$	−10393.7	+	7551.48i	−0.742176	+	0.539222i
$582$		0			0
$583$	−4233.19	−	5826.49i	−0.300722	−	0.413908i
$584$		0			0
$585$	−10013.0	−	12052.3i	−0.707671	−	0.851794i
$586$		0			0
$587$	−159.182	+	51.7214i	−0.0111928	+	0.00363675i	−0.314608	−	0.949222i	$-0.601873\pi$
$587$	−159.182	+	51.7214i	−0.0111928	+	0.00363675i	0.303415	+	0.952858i	$0.401873\pi$
$588$		0			0
$589$	7444.39	−	22911.5i	0.520782	−	1.60280i
$590$		0			0
$591$	1553.71	+	4781.82i	0.108140	+	0.332822i
$592$		0			0
$593$			6327.72i			0.438193i	0.975703	+	0.219096i	$0.0703109\pi$
$593$			6327.72i			0.438193i	−0.975703	+	0.219096i	$0.929689\pi$
$594$		0			0
$595$	−4723.76	+	3924.51i	−0.325471	+	0.270402i
$596$		0			0
$597$	−9711.59	+	13366.9i	−0.665777	+	0.916363i
$598$		0			0
$599$	18597.2			1.26855			0.634275	−	0.773107i	$-0.281299\pi$
$599$	18597.2			1.26855			0.634275	+	0.773107i	$0.281299\pi$
$600$		0			0
$601$	−14146.3			−0.960134			−0.480067	−	0.877232i	$-0.659388\pi$
$601$	−14146.3			−0.960134			−0.480067	+	0.877232i	$0.659388\pi$
$602$		0			0
$603$	−11732.3	+	16148.2i	−0.792334	+	1.09055i
$604$		0			0
$605$	6208.26	+	3921.69i	0.417193	+	0.263536i
$606$		0			0
$607$			17908.3i			1.19749i	0.800941	+	0.598744i	$0.204333\pi$
$607$			17908.3i			1.19749i	−0.800941	+	0.598744i	$0.795667\pi$
$608$		0			0
$609$	375.076	+	1154.37i	0.0249571	+	0.0768099i
$610$		0			0
$611$	3277.93	−	10088.4i	0.217039	−	0.667977i
$612$		0			0
$613$	−12225.2	+	3972.21i	−0.805499	+	0.261722i	−0.682690	−	0.730708i	$-0.739190\pi$
$613$	−12225.2	+	3972.21i	−0.805499	+	0.261722i	−0.122809	+	0.992430i	$0.539190\pi$
$614$		0			0
$615$	−21805.7	−	5550.15i	−1.42974	−	0.363909i
$616$		0			0
$617$	4479.50	+	6165.50i	0.292282	+	0.402291i	0.929754	−	0.368182i	$-0.120020\pi$
$617$	4479.50	+	6165.50i	0.292282	+	0.402291i	−0.637472	+	0.770474i	$0.720020\pi$
$618$		0			0
$619$	16530.4	−	12010.0i	1.07337	−	0.779846i	0.0968512	−	0.995299i	$-0.469123\pi$
$619$	16530.4	−	12010.0i	1.07337	−	0.779846i	0.976514	+	0.215453i	$0.0691229\pi$
$620$		0			0
$621$	−3768.04	−	2737.64i	−0.243488	−	0.176904i
$622$		0			0
$623$	22880.0	+	7434.18i	1.47138	+	0.478080i
$624$		0			0
$625$	15101.1	−	4012.26i	0.966469	−	0.256785i
$626$		0			0
$627$	−27894.5	−	9063.46i	−1.77671	−	0.577288i
$628$		0			0
$629$	6342.16	+	4607.85i	0.402032	+	0.292094i
$630$		0			0
$631$	19440.4	−	14124.2i	1.22648	−	0.891089i	0.229858	−	0.973224i	$-0.426174\pi$
$631$	19440.4	−	14124.2i	1.22648	−	0.891089i	0.996621	+	0.0821349i	$0.0261738\pi$
$632$		0			0
$633$	−2639.24	−	3632.61i	−0.165720	−	0.228093i
$634$		0			0
$635$	−9899.50	−	2519.70i	−0.618661	−	0.157467i
$636$		0			0
$637$	1818.39	−	590.832i	0.113104	−	0.0367498i
$638$		0			0
$639$	6368.28	−	19599.5i	0.394249	−	1.21337i
$640$		0			0
$641$	−5754.29	−	17709.9i	−0.354572	−	1.09126i	−0.956257	−	0.292528i	$-0.905504\pi$
$641$	−5754.29	−	17709.9i	−0.354572	−	1.09126i	0.601685	−	0.798734i	$-0.294496\pi$
$642$		0			0
$643$		−	5153.28i		−	0.316058i	−0.987434	−	0.158029i	$-0.949486\pi$
$643$		−	5153.28i		−	0.316058i	0.987434	−	0.158029i	$-0.0505140\pi$
$644$		0			0
$645$	−24388.4	−	15405.9i	−1.48883	−	0.940475i
$646$		0			0
$647$	−465.672	+	640.943i	−0.0282959	+	0.0389460i	−0.822931	−	0.568142i	$-0.807662\pi$
$647$	−465.672	+	640.943i	−0.0282959	+	0.0389460i	0.794635	+	0.607088i	$0.207662\pi$
$648$		0			0
$649$	8684.40			0.525258
$650$		0			0
$651$	−34149.7			−2.05596
$652$		0			0
$653$	8128.20	−	11187.5i	0.487107	−	0.670446i	−0.492744	−	0.870174i	$-0.664006\pi$
$653$	8128.20	−	11187.5i	0.487107	−	0.670446i	0.979851	+	0.199729i	$0.0640061\pi$
$654$		0			0
$655$	−16677.9	+	13856.0i	−0.994901	+	0.826565i
$656$		0			0
$657$		−	6004.17i		−	0.356537i
$658$		0			0
$659$	1277.13	+	3930.61i	0.0754932	+	0.232344i	0.981681	−	0.190531i	$-0.0610209\pi$
$659$	1277.13	+	3930.61i	0.0754932	+	0.232344i	−0.906188	+	0.422875i	$0.861021\pi$
$660$		0			0
$661$	3544.12	−	10907.7i	0.208548	−	0.641845i	−0.791001	−	0.611815i	$-0.790440\pi$
$661$	3544.12	−	10907.7i	0.208548	−	0.641845i	0.999549	−	0.0300299i	$-0.00956025\pi$
$662$		0			0
$663$	−12364.7	+	4017.53i	−0.724290	+	0.235336i
$664$		0			0
$665$	13040.1	+	15695.8i	0.760412	+	0.915275i
$666$		0			0
$667$	629.796	+	866.840i	0.0365604	+	0.0503211i
$668$		0			0
$669$	24422.2	−	17743.7i	1.41138	−	1.02543i
$670$		0			0
$671$	−15492.7	−	11256.1i	−0.891341	−	0.647597i
$672$		0			0
$673$	11411.3	+	3707.76i	0.653601	+	0.212368i	0.617001	−	0.786962i	$-0.288347\pi$
$673$	11411.3	+	3707.76i	0.653601	+	0.212368i	0.0365996	+	0.999330i	$0.488347\pi$
$674$		0			0
$675$	4833.94	+	901.184i	0.275642	+	0.0513875i
$676$		0			0
$677$	20196.8	+	6562.35i	1.14657	+	0.372543i	0.819850	−	0.572579i	$-0.194057\pi$
$677$	20196.8	+	6562.35i	1.14657	+	0.372543i	0.326719	+	0.945122i	$0.394057\pi$
$678$		0			0
$679$	−21568.1	−	15670.1i	−1.21901	−	0.885661i
$680$		0			0
$681$	−84.8102	+	61.6182i	−0.00477230	+	0.00346728i
$682$		0			0
$683$	4669.91	+	6427.58i	0.261624	+	0.360095i	0.919540	−	0.392997i	$-0.128562\pi$
$683$	4669.91	+	6427.58i	0.261624	+	0.360095i	−0.657916	+	0.753092i	$0.728562\pi$
$684$		0			0
$685$	9072.50	−	3614.02i	0.506047	−	0.201584i
$686$		0			0
$687$	38483.0	−	12503.9i	2.13715	−	0.694401i
$688$		0			0
$689$	−3277.88	+	10088.3i	−0.181244	+	0.557813i
$690$		0			0
$691$	7055.97	+	21716.0i	0.388454	+	1.19554i	0.933943	+	0.357421i	$0.116344\pi$
$691$	7055.97	+	21716.0i	0.388454	+	1.19554i	−0.545489	+	0.838118i	$0.683656\pi$
$692$		0			0
$693$			18355.4i			1.00615i
$694$		0			0
$695$	−6343.41	+	24922.3i	−0.346215	+	1.36022i
$696$		0			0
$697$	−4844.70	+	6668.16i	−0.263280	+	0.362374i
$698$		0			0
$699$	34308.8			1.85648
$700$		0			0
$701$	−23268.0			−1.25367			−0.626833	−	0.779154i	$-0.715649\pi$
$701$	−23268.0			−1.25367			−0.626833	+	0.779154i	$0.715649\pi$
$702$		0			0
$703$	15310.7	−	21073.3i	0.821412	−	1.13058i
$704$		0			0
$705$	−4646.98	−	11665.6i	−0.248249	−	0.623193i
$706$		0			0
$707$			32590.4i			1.73365i
$708$		0			0
$709$	−6143.21	−	18906.9i	−0.325407	−	1.00150i	−0.971257	−	0.238034i	$-0.923497\pi$
$709$	−6143.21	−	18906.9i	−0.325407	−	1.00150i	0.645850	−	0.763464i	$-0.276503\pi$
$710$		0			0
$711$	−4557.87	+	14027.7i	−0.240413	+	0.739914i
$712$		0			0
$713$	−28670.6	+	9315.65i	−1.50592	+	0.489304i
$714$		0			0
$715$	−2123.65	−	32664.2i	−0.111077	−	1.70849i
$716$		0			0
$717$	26850.0	+	36955.9i	1.39851	+	1.92488i
$718$		0			0
$719$	−12736.5	+	9253.59i	−0.660627	+	0.479973i	−0.866874	−	0.498526i	$-0.833875\pi$
$719$	−12736.5	+	9253.59i	−0.660627	+	0.479973i	0.206248	+	0.978500i	$0.433875\pi$
$720$		0			0
$721$	13197.2	+	9588.29i	0.681675	+	0.495266i
$722$		0			0
$723$	35853.1	+	11649.4i	1.84425	+	0.599233i
$724$		0			0
$725$	−993.561	−	540.815i	−0.0508964	−	0.0277039i
$726$		0			0
$727$	18470.7	+	6001.50i	0.942284	+	0.306167i	0.739576	−	0.673073i	$-0.235026\pi$
$727$	18470.7	+	6001.50i	0.942284	+	0.306167i	0.202708	+	0.979239i	$0.435026\pi$
$728$		0			0
$729$	−8697.54	−	6319.14i	−0.441881	−	0.321045i
$730$		0			0
$731$	−8548.76	+	6211.04i	−0.432541	+	0.314259i
$732$		0			0
$733$	8116.78	+	11171.8i	0.409004	+	0.562946i	0.962975	−	0.269590i	$-0.0868882\pi$
$733$	8116.78	+	11171.8i	0.409004	+	0.562946i	−0.553971	+	0.832536i	$0.686888\pi$
$734$		0			0
$735$	1208.77	−	1913.55i	0.0606613	−	0.0960303i
$736$		0			0
$737$	−39656.9	+	12885.3i	−1.98206	+	0.644011i
$738$		0			0
$739$	−4145.49	+	12758.5i	−0.206352	+	0.635087i	0.793303	+	0.608827i	$0.208360\pi$
$739$	−4145.49	+	12758.5i	−0.206352	+	0.635087i	−0.999655	+	0.0262596i	$0.991640\pi$
$740$		0			0
$741$	13349.2	+	41084.6i	0.661802	+	2.03682i
$742$		0			0
$743$		−	4792.10i		−	0.236615i	−0.992977	−	0.118308i	$-0.962253\pi$
$743$		−	4792.10i		−	0.236615i	0.992977	−	0.118308i	$-0.0377469\pi$
$744$		0			0
$745$	−3457.43	+	224.784i	−0.170028	+	0.0110543i
$746$		0			0
$747$	−8354.72	+	11499.3i	−0.409214	+	0.563235i
$748$		0			0
$749$	−11174.5			−0.545138
$750$		0			0
$751$	−19166.6			−0.931292			−0.465646	−	0.884971i	$-0.654178\pi$
$751$	−19166.6			−0.931292			−0.465646	+	0.884971i	$0.654178\pi$
$752$		0			0
$753$	19493.2	−	26830.1i	0.943389	−	1.29846i
$754$		0			0
$755$	3915.18	−	254.545i	0.188726	−	0.0122700i
$756$		0			0
$757$			1538.62i			0.0738734i	0.999318	+	0.0369367i	$0.0117600\pi$
$757$			1538.62i			0.0738734i	−0.999318	+	0.0369367i	$0.988240\pi$
$758$		0			0
$759$	11341.7	+	34906.2i	0.542395	+	1.66932i
$760$		0			0
$761$	−5877.13	+	18087.9i	−0.279955	+	0.861613i	0.707911	+	0.706302i	$0.249638\pi$
$761$	−5877.13	+	18087.9i	−0.279955	+	0.861613i	−0.987866	+	0.155311i	$0.950362\pi$
$762$		0			0
$763$	3585.95	−	1165.15i	0.170144	−	0.0552833i
$764$		0			0
$765$	−3628.70	+	5744.43i	−0.171498	+	0.271491i
$766$		0			0
$767$	−7518.30	−	10348.1i	−0.353938	−	0.487153i
$768$		0			0
$769$	−7660.48	+	5565.67i	−0.359225	+	0.260992i	−0.752729	−	0.658331i	$-0.771263\pi$
$769$	−7660.48	+	5565.67i	−0.359225	+	0.260992i	0.393504	+	0.919323i	$0.371263\pi$
$770$		0			0
$771$	−28781.3	−	20910.8i	−1.34440	−	0.976764i
$772$		0			0
$773$	4747.43	+	1542.53i	0.220897	+	0.0717737i	0.417375	−	0.908735i	$-0.362950\pi$
$773$	4747.43	+	1542.53i	0.220897	+	0.0717737i	−0.196478	+	0.980508i	$0.562950\pi$
$774$		0			0
$775$	23109.4	−	21883.8i	1.07112	−	1.01431i
$776$		0			0
$777$	−35117.3	−	11410.3i	−1.62140	−	0.526825i
$778$		0			0
$779$	22156.6	+	16097.7i	1.01905	+	0.740384i
$780$		0			0
$781$	34829.2	−	25304.9i	1.59576	−	1.15939i
$782$		0			0
$783$	−209.249	−	288.007i	−0.00955039	−	0.0131450i
$784$		0			0
$785$	−1980.22	−	30458.0i	−0.0900346	−	1.38483i
$786$		0			0
$787$	−26458.3	+	8596.81i	−1.19839	+	0.389382i	−0.839169	−	0.543870i	$-0.816958\pi$
$787$	−26458.3	+	8596.81i	−1.19839	+	0.389382i	−0.359224	+	0.933252i	$0.616958\pi$
$788$		0			0
$789$	−257.167	+	791.478i	−0.0116038	+	0.0357127i
$790$		0			0
$791$	11697.8	+	36002.1i	0.525822	+	1.61831i
$792$		0			0
$793$			28205.3i			1.26305i
$794$		0			0
$795$	4646.91	+	11665.4i	0.207307	+	0.520414i
$796$		0			0
$797$	9081.75	−	12500.0i	0.403629	−	0.555547i	−0.558021	−	0.829827i	$-0.688439\pi$
$797$	9081.75	−	12500.0i	0.403629	−	0.555547i	0.961650	+	0.274279i	$0.0884393\pi$
$798$		0			0
$799$	−4599.78			−0.203665
$800$		0			0
$801$	26616.5			1.17409
$802$		0			0
$803$	7372.55	−	10147.4i	0.324000	−	0.445947i
$804$		0			0
$805$	6298.63	−	24746.3i	0.275773	−	1.08347i
$806$		0			0
$807$		−	48777.6i		−	2.12770i
$808$		0			0
$809$	−13271.0	−	40843.8i	−0.576740	−	1.77502i	−0.630178	−	0.776451i	$-0.717018\pi$
$809$	−13271.0	−	40843.8i	−0.576740	−	1.77502i	0.0534378	−	0.998571i	$-0.482982\pi$
$810$		0			0
$811$	−7059.52	+	21727.0i	−0.305664	+	0.940736i	0.673765	+	0.738946i	$0.264676\pi$
$811$	−7059.52	+	21727.0i	−0.305664	+	0.940736i	−0.979429	+	0.201791i	$0.935324\pi$
$812$		0			0
$813$	43610.9	−	14170.0i	1.88131	−	0.611273i
$814$		0			0
$815$	16628.2	−	6623.82i	0.714673	−	0.284690i
$816$		0			0
$817$	20637.7	+	28405.3i	0.883746	+	1.21637i
$818$		0			0
$819$	21871.7	−	15890.7i	0.933163	−	0.677982i
$820$		0			0
$821$	−18221.7	−	13238.8i	−0.774594	−	0.562775i	0.128758	−	0.991676i	$-0.458901\pi$
$821$	−18221.7	−	13238.8i	−0.774594	−	0.562775i	−0.903352	+	0.428901i	$0.858901\pi$
$822$		0			0
$823$	−12239.1	−	3976.72i	−0.518382	−	0.168432i	0.0381291	−	0.999273i	$-0.487860\pi$
$823$	−12239.1	−	3976.72i	−0.518382	−	0.168432i	−0.556511	+	0.830840i	$0.687860\pi$
$824$		0			0
$825$	−26643.3	−	28135.5i	−1.12437	−	1.18734i
$826$		0			0
$827$	−19694.3	−	6399.07i	−0.828100	−	0.269066i	−0.135855	−	0.990729i	$-0.543378\pi$
$827$	−19694.3	−	6399.07i	−0.828100	−	0.269066i	−0.692245	+	0.721663i	$0.743378\pi$
$828$		0			0
$829$	−17113.7	−	12433.9i	−0.716990	−	0.520924i	0.168431	−	0.985713i	$-0.446130\pi$
$829$	−17113.7	−	12433.9i	−0.716990	−	0.520924i	−0.885421	+	0.464790i	$0.846130\pi$
$830$		0			0
$831$	−11349.8	+	8246.14i	−0.473792	+	0.344230i
$832$		0			0
$833$	−487.327	−	670.747i	−0.0202699	−	0.0278992i
$834$		0			0
$835$	−4194.96	−	5049.30i	−0.173860	−	0.209267i
$836$		0			0
$837$	9525.78	−	3095.11i	0.393380	−	0.127817i
$838$		0			0
$839$	34.6829	−	106.743i	0.00142716	−	0.00439235i	−0.950340	−	0.311212i	$-0.899265\pi$
$839$	34.6829	−	106.743i	0.00142716	−	0.00439235i	0.951768	+	0.306820i	$0.0992650\pi$
$840$		0			0
$841$	−7511.31	−	23117.4i	−0.307979	−	0.947863i
$842$		0			0
$843$			59543.1i			2.43271i
$844$		0			0
$845$	−18189.6	+	15111.9i	−0.740522	+	0.615227i
$846$		0			0
$847$	−7447.09	+	10250.0i	−0.302107	+	0.415815i
$848$		0			0
$849$	15291.1			0.618126
$850$		0			0
$851$	−32595.6			−1.31300
$852$		0			0
$853$	−3291.14	+	4529.86i	−0.132106	+	0.181828i	−0.869945	−	0.493148i	$-0.835846\pi$
$853$	−3291.14	+	4529.86i	−0.132106	+	0.181828i	0.737840	+	0.674976i	$0.235846\pi$
$854$		0			0
$855$	19087.3	+	12057.2i	0.763474	+	0.482278i
$856$		0			0
$857$			6823.85i			0.271993i	0.990709	+	0.135997i	$0.0434237\pi$
$857$			6823.85i			0.271993i	−0.990709	+	0.135997i	$0.956576\pi$
$858$		0			0
$859$	3683.03	+	11335.2i	0.146290	+	0.450235i	0.997175	−	0.0751180i	$-0.0239334\pi$
$859$	3683.03	+	11335.2i	0.146290	+	0.450235i	−0.850885	+	0.525353i	$0.823933\pi$
$860$		0			0
$861$	11996.8	−	36922.5i	0.474856	−	1.46146i
$862$		0			0
$863$	33188.1	−	10783.5i	1.30908	−	0.425346i	0.430348	−	0.902663i	$-0.358391\pi$
$863$	33188.1	−	10783.5i	1.30908	−	0.425346i	0.878731	+	0.477318i	$0.158391\pi$
$864$		0			0
$865$	−31489.4	−	8014.94i	−1.23777	−	0.315047i
$866$		0			0
$867$	−16764.7	−	23074.6i	−0.656699	−	0.903868i
$868$		0			0
$869$	−24927.8	+	18111.1i	−0.973092	+	0.706993i
$870$		0			0
$871$	49685.7	+	36098.7i	1.93288	+	1.40432i
$872$		0			0
$873$	−28051.7	−	9114.56i	−1.08752	−	0.353357i
$874$		0			0
$875$	5217.68	+	26449.3i	0.201588	+	1.02189i
$876$		0			0
$877$	−22346.8	−	7260.90i	−0.860429	−	0.279570i	−0.154622	−	0.987974i	$-0.549416\pi$
$877$	−22346.8	−	7260.90i	−0.860429	−	0.279570i	−0.705808	+	0.708403i	$0.749416\pi$
$878$		0			0
$879$	−46592.6	−	33851.5i	−1.78786	−	1.29896i
$880$		0			0
$881$	−7758.19	+	5636.66i	−0.296686	+	0.215555i	−0.726163	−	0.687523i	$-0.758698\pi$
$881$	−7758.19	+	5636.66i	−0.296686	+	0.215555i	0.429477	+	0.903078i	$0.358698\pi$
$882$		0			0
$883$	−18540.4	−	25518.6i	−0.706606	−	0.972560i	−0.999863	−	0.0165261i	$-0.994739\pi$
$883$	−18540.4	−	25518.6i	−0.706606	−	0.972560i	0.293258	−	0.956033i	$-0.405261\pi$
$884$		0			0
$885$	−14673.8	−	3734.88i	−0.557348	−	0.141861i
$886$		0			0
$887$	29814.7	−	9687.39i	1.12861	−	0.366709i	0.315565	−	0.948904i	$-0.397806\pi$
$887$	29814.7	−	9687.39i	1.12861	−	0.366709i	0.813049	+	0.582195i	$0.197806\pi$
$888$		0			0
$889$	5446.42	−	16762.3i	0.205475	−	0.632386i
$890$		0			0
$891$	−11707.4	−	36031.6i	−0.440192	−	1.35477i
$892$		0			0
$893$			15283.9i			0.572738i
$894$		0			0
$895$	−2275.81	−	1437.60i	−0.0849966	−	0.0536914i
$896$		0			0
$897$	31774.3	−	43733.5i	1.18273	−	1.62789i
$898$		0			0
$899$	−2304.19			−0.0854828
$900$		0			0
$901$	4599.71			0.170076
$902$		0			0
$903$	29255.0	−	40266.0i	1.07812	−	1.48391i
$904$		0			0
$905$	−12312.7	+	10229.4i	−0.452251	+	0.375731i
$906$		0			0
$907$			16725.2i			0.612294i	0.951984	+	0.306147i	$0.0990399\pi$
$907$			16725.2i			0.612294i	−0.951984	+	0.306147i	$0.900960\pi$
$908$		0			0
$909$	11142.2	+	34292.2i	0.406561	+	1.25127i
$910$		0			0
$911$	1684.10	−	5183.13i	0.0612478	−	0.188501i	−0.915751	−	0.401746i	$-0.868403\pi$
$911$	1684.10	−	5183.13i	0.0612478	−	0.188501i	0.976999	+	0.213245i	$0.0684033\pi$
$912$		0			0
$913$	−28240.1	+	9175.76i	−1.02367	+	0.332610i
$914$		0			0
$915$	21336.7	+	25682.0i	0.770895	+	0.927893i
$916$		0			0
$917$	−21989.6	−	30266.1i	−0.791888	−	1.08994i
$918$		0			0
$919$	−23909.8	+	17371.5i	−0.858229	+	0.623540i	−0.927403	−	0.374065i	$-0.877964\pi$
$919$	−23909.8	+	17371.5i	−0.858229	+	0.623540i	0.0691738	+	0.997605i	$0.477964\pi$
$920$		0			0
$921$	34126.0	+	24794.0i	1.22094	+	0.887067i
$922$		0			0
$923$	−60305.1	−	19594.3i	−2.15056	−	0.698759i
$924$		0			0
$925$	31076.3	−	14782.5i	1.10463	−	0.525454i
$926$		0			0
$927$	17164.4	+	5577.06i	0.608148	+	0.197599i
$928$		0			0
$929$	15126.7	+	10990.2i	0.534221	+	0.388134i	0.821934	−	0.569582i	$-0.192895\pi$
$929$	15126.7	+	10990.2i	0.534221	+	0.388134i	−0.287713	+	0.957717i	$0.592895\pi$
$930$		0			0
$931$	−2228.72	+	1619.26i	−0.0784568	+	0.0570022i
$932$		0			0
$933$	17286.2	+	23792.4i	0.606565	+	0.834864i
$934$		0			0
$935$	−13186.4	+	5252.78i	−0.461219	+	0.183726i
$936$		0			0
$937$	−22174.7	+	7205.01i	−0.773124	+	0.251203i	−0.668902	−	0.743351i	$-0.733235\pi$
$937$	−22174.7	+	7205.01i	−0.773124	+	0.251203i	−0.104222	+	0.994554i	$0.533235\pi$
$938$		0			0
$939$	−3151.76	+	9700.13i	−0.109536	+	0.337116i
$940$		0			0
$941$	6290.36	+	19359.7i	0.217917	+	0.670680i	0.998934	+	0.0461693i	$0.0147014\pi$
$941$	6290.36	+	19359.7i	0.217917	+	0.670680i	−0.781017	+	0.624510i	$0.785299\pi$
$942$		0			0
$943$		−	34271.2i		−	1.18348i
$944$		0			0
$945$	−2092.71	+	8221.93i	−0.0720380	+	0.283026i
$946$		0			0
$947$	−21156.9	+	29120.0i	−0.725984	+	0.999231i	0.273320	+	0.961923i	$0.411878\pi$
$947$	−21156.9	+	29120.0i	−0.725984	+	0.999231i	−0.999304	+	0.0373075i	$0.988122\pi$
$948$		0			0
$949$	−18474.0			−0.631919
$950$		0			0
$951$	−14044.4			−0.478885
$952$		0			0
$953$	475.581	−	654.582i	0.0161654	−	0.0222497i	−0.800858	−	0.598855i	$-0.795623\pi$
$953$	475.581	−	654.582i	0.0161654	−	0.0222497i	0.817023	+	0.576605i	$0.195623\pi$
$954$		0			0
$955$	−610.974	−	1533.76i	−0.0207023	−	0.0519701i
$956$		0			0
$957$			2805.33i			0.0947579i
$958$		0			0
$959$	5206.86	+	16025.1i	0.175327	+	0.539600i
$960$		0			0
$961$	10827.3	−	33322.9i	0.363441	−	1.11856i
$962$		0			0
$963$	−11758.0	+	3820.42i	−0.393456	+	0.127841i
$964$		0			0
$965$	122.964	+	1891.32i	0.00410191	+	0.0630920i
$966$		0			0
$967$	−5371.49	−	7393.22i	−0.178630	−	0.245863i	0.710307	−	0.703892i	$-0.248556\pi$
$967$	−5371.49	−	7393.22i	−0.178630	−	0.245863i	−0.888938	+	0.458028i	$0.848556\pi$
$968$		0			0
$969$	15154.8	−	11010.6i	0.502417	−	0.365028i
$970$		0			0
$971$	−17470.0	−	12692.7i	−0.577385	−	0.419494i	0.260396	−	0.965502i	$-0.416147\pi$
$971$	−17470.0	−	12692.7i	−0.577385	−	0.419494i	−0.837780	+	0.546008i	$0.816147\pi$
$972$		0			0
$973$	−42199.7	−	13711.5i	−1.39040	−	0.451768i
$974$		0			0
$975$	−10459.5	+	56105.0i	−0.343563	+	1.84287i
$976$		0			0
$977$	47385.4	+	15396.5i	1.55168	+	0.504172i	0.954571	−	0.297985i	$-0.0963146\pi$
$977$	47385.4	+	15396.5i	1.55168	+	0.504172i	0.597113	+	0.802157i	$0.296315\pi$
$978$		0			0
$979$	44983.6	+	32682.5i	1.46852	+	1.06694i
$980$		0			0
$981$	3374.86	−	2451.98i	0.109838	−	0.0798019i
$982$		0			0
$983$	19350.5	+	26633.7i	0.627859	+	0.864174i	0.997895	−	0.0648435i	$-0.0206548\pi$
$983$	19350.5	+	26633.7i	0.627859	+	0.864174i	−0.370036	+	0.929017i	$0.620655\pi$
$984$		0			0
$985$	4317.86	−	6835.42i	0.139674	−	0.221111i
$986$		0			0
$987$	20605.3	−	6695.07i	0.664513	−	0.215913i
$988$		0			0
$989$	13577.1	−	41786.1i	0.436530	−	1.34350i
$990$		0			0
$991$	−11232.5	−	34570.2i	−0.360054	−	1.10813i	−0.953021	−	0.302905i	$-0.902044\pi$
$991$	−11232.5	−	34570.2i	−0.360054	−	1.10813i	0.592967	−	0.805227i	$-0.297956\pi$
$992$		0			0
$993$		−	15472.5i		−	0.494468i
$994$		0			0
$995$	26512.3	−	1723.69i	0.844720	−	0.0549193i
$996$		0			0
$997$	4839.58	−	6661.11i	0.153732	−	0.211594i	−0.725203	−	0.688535i	$-0.758254\pi$
$997$	4839.58	−	6661.11i	0.153732	−	0.211594i	0.878936	+	0.476940i	$0.158254\pi$
$998$		0			0
$999$	10829.9			0.342985

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.4.i.a.29.7	✓	32
5.2	odd	4		500.4.g.b.101.4		64
5.3	odd	4		500.4.g.b.101.13		64
5.4	even	2		500.4.i.a.149.2		32
25.6	even	5		500.4.i.a.349.2		32
25.8	odd	20		500.4.g.b.401.13		64
25.12	odd	20		2500.4.a.g.1.26		32
25.13	odd	20		2500.4.a.g.1.7		32
25.17	odd	20		500.4.g.b.401.4		64
25.19	even	10	inner	100.4.i.a.69.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.4.i.a.29.7	✓	32	1.1	even	1	trivial
100.4.i.a.69.7	yes	32	25.19	even	10	inner
500.4.g.b.101.4		64	5.2	odd	4
500.4.g.b.101.13		64	5.3	odd	4
500.4.g.b.401.4		64	25.17	odd	20
500.4.g.b.401.13		64	25.8	odd	20
500.4.i.a.149.2		32	5.4	even	2
500.4.i.a.349.2		32	25.6	even	5
2500.4.a.g.1.7		32	25.13	odd	20
2500.4.a.g.1.26		32	25.12	odd	20

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	100.i (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(4.08679 - 5.62498i) q^{3} +(-11.1568 + 0.725356i) q^{5} -19.2903i q^{7} +(-6.59510 - 20.2976i) q^{9} +O(q^{10})\)	\(q+(4.08679 - 5.62498i) q^{3} +(-11.1568 + 0.725356i) q^{5} -19.2903i q^{7} +(-6.59510 - 20.2976i) q^{9} +(13.7774 - 42.4025i) q^{11} +(-62.4530 + 20.2922i) q^{13} +(-41.5153 + 65.7211i) q^{15} +(16.7373 + 23.0369i) q^{17} +(76.5456 - 55.6137i) q^{19} +(-108.508 - 78.8354i) q^{21} +(-112.604 - 36.5872i) q^{23} +(123.948 - 16.1853i) q^{25} +(37.4125 + 12.1561i) q^{27} +(-7.32137 - 5.31928i) q^{29} +(205.988 - 149.659i) q^{31} +(-182.208 - 250.788i) q^{33} +(13.9924 + 215.218i) q^{35} +(261.830 - 85.0736i) q^{37} +(-141.089 + 434.227i) q^{39} +(89.4467 + 275.289i) q^{41} +371.090i q^{43} +(88.3032 + 221.673i) q^{45} +(-94.9487 + 130.686i) q^{47} -29.1162 q^{49} +197.984 q^{51} +(94.9473 - 130.684i) q^{53} +(-122.955 + 483.070i) q^{55} -657.849i q^{57} +(60.1917 + 185.251i) q^{59} +(132.729 - 408.499i) q^{61} +(-391.548 + 127.222i) q^{63} +(682.056 - 271.696i) q^{65} +(-549.725 - 756.631i) q^{67} +(-665.990 + 483.870i) q^{69} +(781.193 + 567.570i) q^{71} +(267.559 + 86.9353i) q^{73} +(415.506 - 763.349i) q^{75} +(-817.958 - 265.771i) q^{77} +(-559.111 - 406.218i) q^{79} +(687.462 - 499.470i) q^{81} +(-391.465 - 538.805i) q^{83} +(-203.444 - 244.877i) q^{85} +(-59.8417 + 19.4438i) q^{87} +(-385.384 + 1186.09i) q^{89} +(391.443 + 1204.74i) q^{91} -1770.30i q^{93} +(-813.664 + 675.993i) q^{95} +(812.330 - 1118.08i) q^{97} -951.535 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 6 q^{5} + 122 q^{9}+O(q^{10}) \) 32 * q + 6 * q^5 + 122 * q^9	\( 32 q + 6 q^{5} + 122 q^{9} + 20 q^{11} + 68 q^{15} - 160 q^{17} + 2 q^{19} - 108 q^{21} + 290 q^{23} + 654 q^{25} + 600 q^{27} + 62 q^{29} - 378 q^{31} - 1280 q^{33} - 278 q^{35} + 680 q^{37} + 592 q^{39} - 528 q^{41} - 1044 q^{45} - 1810 q^{47} - 2796 q^{49} + 1664 q^{51} - 510 q^{53} - 1350 q^{55} + 144 q^{59} - 1346 q^{61} + 1660 q^{63} + 1142 q^{65} + 1890 q^{67} + 956 q^{69} + 786 q^{71} + 3720 q^{73} - 78 q^{75} + 2160 q^{77} + 896 q^{79} + 348 q^{81} + 570 q^{83} + 224 q^{85} + 3240 q^{87} - 2512 q^{89} - 2212 q^{91} + 1536 q^{95} - 2250 q^{97} - 2540 q^{99}+O(q^{100}) \) 32 * q + 6 * q^5 + 122 * q^9 + 20 * q^11 + 68 * q^15 - 160 * q^17 + 2 * q^19 - 108 * q^21 + 290 * q^23 + 654 * q^25 + 600 * q^27 + 62 * q^29 - 378 * q^31 - 1280 * q^33 - 278 * q^35 + 680 * q^37 + 592 * q^39 - 528 * q^41 - 1044 * q^45 - 1810 * q^47 - 2796 * q^49 + 1664 * q^51 - 510 * q^53 - 1350 * q^55 + 144 * q^59 - 1346 * q^61 + 1660 * q^63 + 1142 * q^65 + 1890 * q^67 + 956 * q^69 + 786 * q^71 + 3720 * q^73 - 78 * q^75 + 2160 * q^77 + 896 * q^79 + 348 * q^81 + 570 * q^83 + 224 * q^85 + 3240 * q^87 - 2512 * q^89 - 2212 * q^91 + 1536 * q^95 - 2250 * q^97 - 2540 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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