LMFDB - Embedded newform 350.4.j.h.149.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [350,4,Mod(149,350)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("350.149"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(350, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	350.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,24,0,24,0,0,112,0,52] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$20.6506685020$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 134x^{10} + 13467x^{8} - 530084x^{6} + 15364507x^{4} - 160351569x^{2} + 1275989841 $ x^12 - 134x^10 + 13467x^8 - 530084x^6 + 15364507x^4 - 160351569*x^2 + 1275989841
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.1
Root			$-5.13062 - 2.96216i$ of defining polynomial
Character	$\chi$	$=$	350.149
Dual form			350.4.j.h.249.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.73205 - 1.00000i) q^{2} +(-5.99664 + 3.46216i) q^{3} +(2.00000 + 3.46410i) q^{4} +13.8487 q^{6} +(-12.7473 + 13.4353i) q^{7} -8.00000i q^{8} +(10.4731 - 18.1400i) q^{9} +(-18.6814 - 32.3572i) q^{11} +(-23.9866 - 13.8487i) q^{12} +89.1041i q^{13} +(35.5142 - 10.5234i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(-60.7584 + 35.0789i) q^{17} +(-36.2800 + 20.9463i) q^{18} +(-62.7005 + 108.600i) q^{19} +(29.9255 - 124.700i) q^{21} +74.7257i q^{22} +(-5.42874 - 3.13428i) q^{23} +(27.6973 + 47.9731i) q^{24} +(89.1041 - 154.333i) q^{26} -41.9179i q^{27} +(-72.0358 - 17.2872i) q^{28} +95.4760 q^{29} +(108.882 + 188.588i) q^{31} +(27.7128 - 16.0000i) q^{32} +(224.052 + 129.356i) q^{33} +140.316 q^{34} +83.7851 q^{36} +(-182.580 - 105.413i) q^{37} +(217.201 - 125.401i) q^{38} +(-308.493 - 534.325i) q^{39} -12.2490 q^{41} +(-176.532 + 186.061i) q^{42} +131.746i q^{43} +(74.7257 - 129.429i) q^{44} +(6.26857 + 10.8575i) q^{46} +(-315.338 - 182.060i) q^{47} -110.789i q^{48} +(-18.0149 - 342.527i) q^{49} +(242.898 - 420.711i) q^{51} +(-308.666 + 178.208i) q^{52} +(431.676 - 249.228i) q^{53} +(-41.9179 + 72.6039i) q^{54} +(107.482 + 101.978i) q^{56} -868.318i q^{57} +(-165.369 - 95.4760i) q^{58} +(-179.014 - 310.061i) q^{59} +(77.3039 - 133.894i) q^{61} -435.526i q^{62} +(110.213 + 371.945i) q^{63} -64.0000 q^{64} +(-258.713 - 448.103i) q^{66} +(-58.4849 + 33.7663i) q^{67} +(-243.034 - 140.316i) q^{68} +43.4056 q^{69} -517.772 q^{71} +(-145.120 - 83.7851i) q^{72} +(584.365 - 337.383i) q^{73} +(210.826 + 365.161i) q^{74} -501.604 q^{76} +(672.866 + 161.475i) q^{77} +1233.97i q^{78} +(465.841 - 806.860i) q^{79} +(427.901 + 741.147i) q^{81} +(21.2159 + 12.2490i) q^{82} -1435.72i q^{83} +(491.824 - 145.735i) q^{84} +(131.746 - 228.191i) q^{86} +(-572.535 + 330.553i) q^{87} +(-258.857 + 149.451i) q^{88} +(-168.341 + 291.575i) q^{89} +(-1197.14 - 1135.83i) q^{91} -25.0743i q^{92} +(-1305.85 - 753.932i) q^{93} +(364.121 + 630.676i) q^{94} +(-110.789 + 191.893i) q^{96} +179.620i q^{97} +(-311.324 + 611.288i) q^{98} -782.613 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 24 q^{4} + 24 q^{6} + 112 q^{9} + 52 q^{11} + 16 q^{14} - 96 q^{16} - 36 q^{19} + 370 q^{21} + 48 q^{24} + 320 q^{26} + 1616 q^{29} + 1230 q^{31} + 240 q^{34} + 896 q^{36} - 180 q^{39} - 404 q^{41}+ \cdots + 228 q^{99}+O(q^{100}) $ 12 * q + 24 * q^4 + 24 * q^6 + 112 * q^9 + 52 * q^11 + 16 * q^14 - 96 * q^16 - 36 * q^19 + 370 * q^21 + 48 * q^24 + 320 * q^26 + 1616 * q^29 + 1230 * q^31 + 240 * q^34 + 896 * q^36 - 180 * q^39 - 404 * q^41 - 208 * q^44 + 212 * q^46 + 432 * q^49 + 678 * q^51 - 1296 * q^54 + 896 * q^56 - 182 * q^59 + 1294 * q^61 - 768 * q^64 - 1256 * q^66 + 6192 * q^69 + 2132 * q^71 + 1704 * q^74 - 288 * q^76 + 2842 * q^79 + 2786 * q^81 + 608 * q^84 + 996 * q^86 - 388 * q^89 - 7710 * q^91 - 1608 * q^94 - 192 * q^96 + 228 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−1.73205	−	1.00000i	−0.612372	−	0.353553i
$2$	−1.73205	−	1.00000i	−0.612372	−	0.353553i
$3$	−5.99664	+	3.46216i	−1.15405	+	0.666294i	−0.949872	−	0.312639i	$-0.898787\pi$
$3$	−5.99664	+	3.46216i	−1.15405	+	0.666294i	−0.204182	+	0.978933i	$0.565454\pi$
$4$	2.00000	+	3.46410i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	13.8487			0.942281
$7$	−12.7473	+	13.4353i	−0.688287	+	0.725438i
$7$	−12.7473	+	13.4353i	−0.688287	+	0.725438i
$8$		−	8.00000i		−	0.353553i
$9$	10.4731	−	18.1400i	0.387894	−	0.671852i
$10$		0			0
$11$	−18.6814	−	32.3572i	−0.512060	−	0.886914i	−0.999902	−	0.0139823i	$-0.995549\pi$
$11$	−18.6814	−	32.3572i	−0.512060	−	0.886914i	0.487842	−	0.872932i	$-0.337784\pi$
$12$	−23.9866	−	13.8487i	−0.577027	−	0.333147i
$13$			89.1041i			1.90100i	0.310722	+	0.950501i	$0.399429\pi$
$13$			89.1041i			1.90100i	−0.310722	+	0.950501i	$0.600571\pi$
$14$	35.5142	−	10.5234i	0.677969	−	0.200892i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−60.7584	+	35.0789i	−0.866828	+	0.500464i	−0.866293	−	0.499536i	$-0.833504\pi$
$17$	−60.7584	+	35.0789i	−0.866828	+	0.500464i	−0.000535451		1.00000i	$0.500170\pi$
$18$	−36.2800	+	20.9463i	−0.475071	+	0.274283i
$19$	−62.7005	+	108.600i	−0.757078	+	1.31130i	0.187256	+	0.982311i	$0.440041\pi$
$19$	−62.7005	+	108.600i	−0.757078	+	1.31130i	−0.944334	+	0.328987i	$0.893293\pi$
$20$		0			0
$21$	29.9255	−	124.700i	0.310966	−	1.29580i
$22$			74.7257i			0.724162i
$23$	−5.42874	−	3.13428i	−0.0492161	−	0.0284149i	0.475190	−	0.879883i	$-0.342379\pi$
$23$	−5.42874	−	3.13428i	−0.0492161	−	0.0284149i	−0.524406	+	0.851468i	$0.675713\pi$
$24$	27.6973	+	47.9731i	0.235570	+	0.408020i
$25$		0			0
$26$	89.1041	−	154.333i	0.672106	−	1.16412i
$27$		−	41.9179i		−	0.298781i
$28$	−72.0358	−	17.2872i	−0.486196	−	0.116677i
$29$	95.4760			0.611360			0.305680	−	0.952134i	$-0.401116\pi$
$29$	95.4760			0.611360			0.305680	+	0.952134i	$0.401116\pi$
$30$		0			0
$31$	108.882	+	188.588i	0.630829	+	1.09263i	0.987382	+	0.158354i	$0.0506186\pi$
$31$	108.882	+	188.588i	0.630829	+	1.09263i	−0.356553	+	0.934275i	$0.616048\pi$
$32$	27.7128	−	16.0000i	0.153093	−	0.0883883i
$33$	224.052	+	129.356i	1.18189	+	0.682365i
$34$	140.316			0.707762
$35$		0			0
$36$	83.7851			0.387894
$37$	−182.580	−	105.413i	−0.811244	−	0.468372i	0.0361435	−	0.999347i	$-0.488493\pi$
$37$	−182.580	−	105.413i	−0.811244	−	0.468372i	−0.847388	+	0.530975i	$0.821826\pi$
$38$	217.201	−	125.401i	0.927228	−	0.535335i
$39$	−308.493	−	534.325i	−1.26663	−	2.19386i
$40$		0			0
$41$	−12.2490			−0.0466578			−0.0233289	−	0.999728i	$-0.507426\pi$
$41$	−12.2490			−0.0466578			−0.0233289	+	0.999728i	$0.507426\pi$
$42$	−176.532	+	186.061i	−0.648560	+	0.683567i
$43$			131.746i			0.467235i	0.972329	+	0.233618i	$0.0750564\pi$
$43$			131.746i			0.467235i	−0.972329	+	0.233618i	$0.924944\pi$
$44$	74.7257	−	129.429i	0.256030	−	0.443457i
$45$		0			0
$46$	6.26857	+	10.8575i	0.0200924	+	0.0348010i
$47$	−315.338	−	182.060i	−0.978654	−	0.565026i	−0.0767907	−	0.997047i	$-0.524467\pi$
$47$	−315.338	−	182.060i	−0.978654	−	0.565026i	−0.901864	+	0.432021i	$0.857801\pi$
$48$		−	110.789i		−	0.333147i
$49$	−18.0149	−	342.527i	−0.0525216	−	0.998620i
$50$		0			0
$51$	242.898	−	420.711i	0.666911	−	1.15512i
$52$	−308.666	+	178.208i	−0.823158	+	0.475250i
$53$	431.676	−	249.228i	1.11878	−	0.645926i	0.177689	−	0.984087i	$-0.443138\pi$
$53$	431.676	−	249.228i	1.11878	−	0.645926i	0.941088	+	0.338160i	$0.109805\pi$
$54$	−41.9179	+	72.6039i	−0.105635	+	0.182966i
$55$		0			0
$56$	107.482	+	101.978i	0.256481	+	0.243346i
$57$		−	868.318i		−	2.01775i
$58$	−165.369	−	95.4760i	−0.374380	−	0.216149i
$59$	−179.014	−	310.061i	−0.395010	−	0.684177i	0.598093	−	0.801427i	$-0.295926\pi$
$59$	−179.014	−	310.061i	−0.395010	−	0.684177i	−0.993102	+	0.117250i	$0.962592\pi$
$60$		0			0
$61$	77.3039	−	133.894i	0.162258	−	0.281039i	−0.773420	−	0.633894i	$-0.781456\pi$
$61$	77.3039	−	133.894i	0.162258	−	0.281039i	0.935678	+	0.352854i	$0.114789\pi$
$62$		−	435.526i		−	0.892127i
$63$	110.213	+	371.945i	0.220405	+	0.743821i
$64$	−64.0000			−0.125000
$65$		0			0
$66$	−258.713	−	448.103i	−0.482505	−	0.835723i
$67$	−58.4849	+	33.7663i	−0.106643	+	0.0615703i	−0.552373	−	0.833597i	$-0.686277\pi$
$67$	−58.4849	+	33.7663i	−0.106643	+	0.0615703i	0.445730	+	0.895167i	$0.352944\pi$
$68$	−243.034	−	140.316i	−0.433414	−	0.250232i
$69$	43.4056			0.0757307
$70$		0			0
$71$	−517.772			−0.865469			−0.432734	−	0.901521i	$-0.642451\pi$
$71$	−517.772			−0.865469			−0.432734	+	0.901521i	$0.642451\pi$
$72$	−145.120	−	83.7851i	−0.237536	−	0.137141i
$73$	584.365	−	337.383i	0.936914	−	0.540928i	0.0479224	−	0.998851i	$-0.484740\pi$
$73$	584.365	−	337.383i	0.936914	−	0.540928i	0.888992	+	0.457924i	$0.151407\pi$
$74$	210.826	+	365.161i	0.331189	+	0.573636i
$75$		0			0
$76$	−501.604			−0.757078
$77$	672.866	+	161.475i	0.995846	+	0.238984i
$78$			1233.97i			1.79128i
$79$	465.841	−	806.860i	0.663433	−	1.14910i	−0.316274	−	0.948668i	$-0.602432\pi$
$79$	465.841	−	806.860i	0.663433	−	1.14910i	0.979708	−	0.200432i	$-0.0642346\pi$
$80$		0			0
$81$	427.901	+	741.147i	0.586970	+	1.01666i
$82$	21.2159	+	12.2490i	0.0285720	+	0.0164960i
$83$		−	1435.72i		−	1.89868i	−0.314247	−	0.949341i	$-0.601752\pi$
$83$		−	1435.72i		−	1.89868i	0.314247	−	0.949341i	$-0.398248\pi$
$84$	491.824	−	145.735i	0.638838	−	0.189297i
$85$		0			0
$86$	131.746	−	228.191i	0.165193	−	0.286122i
$87$	−572.535	+	330.553i	−0.705543	+	0.407345i
$88$	−258.857	+	149.451i	−0.313572	+	0.181041i
$89$	−168.341	+	291.575i	−0.200495	+	0.347268i	−0.948688	−	0.316213i	$-0.897588\pi$
$89$	−168.341	+	291.575i	−0.200495	+	0.347268i	0.748193	+	0.663481i	$0.230922\pi$
$90$		0			0
$91$	−1197.14	−	1135.83i	−1.37906	−	1.30844i
$92$		−	25.0743i		−	0.0284149i
$93$	−1305.85	−	753.932i	−1.45602	−	0.840635i
$94$	364.121	+	630.676i	0.399534	+	0.692013i
$95$		0			0
$96$	−110.789	+	191.893i	−0.117785	+	0.204010i
$97$			179.620i			0.188016i	0.995571	+	0.0940082i	$0.0299680\pi$
$97$			179.620i			0.188016i	−0.995571	+	0.0940082i	$0.970032\pi$
$98$	−311.324	+	611.288i	−0.320903	+	0.630096i
$99$	−782.613			−0.794501
$100$		0			0
$101$	447.196	+	774.567i	0.440571	+	0.763092i	0.997732	−	0.0673130i	$-0.0214426\pi$
$101$	447.196	+	774.567i	0.440571	+	0.763092i	−0.557161	+	0.830405i	$0.688109\pi$
$102$	−841.422	+	485.795i	−0.816796	+	0.471578i
$103$	21.5459	+	12.4395i	0.0206114	+	0.0119000i	0.510270	−	0.860014i	$-0.329545\pi$
$103$	21.5459	+	12.4395i	0.0206114	+	0.0119000i	−0.489659	+	0.871914i	$0.662879\pi$
$104$	712.833			0.672106
$105$		0			0
$106$	−996.912			−0.913478
$107$	−999.214	−	576.897i	−0.902782	−	0.521221i	−0.0246802	−	0.999695i	$-0.507857\pi$
$107$	−999.214	−	576.897i	−0.902782	−	0.521221i	−0.878102	+	0.478474i	$0.841190\pi$
$108$	145.208	−	83.8358i	0.129376	−	0.0746954i
$109$	940.483	+	1628.96i	0.826440	+	1.43144i	0.900814	+	0.434205i	$0.142971\pi$
$109$	940.483	+	1628.96i	0.826440	+	1.43144i	−0.0743741	+	0.997230i	$0.523696\pi$
$110$		0			0
$111$	1459.83			1.24829
$112$	−84.1870	−	284.114i	−0.0710261	−	0.239698i
$113$			2073.98i			1.72658i	0.504709	+	0.863289i	$0.331600\pi$
$113$			2073.98i			1.72658i	−0.504709	+	0.863289i	$0.668400\pi$
$114$	−868.318	+	1503.97i	−0.713381	+	1.23561i
$115$		0			0
$116$	190.952	+	330.739i	0.152840	+	0.264727i
$117$	1616.35	+	933.200i	1.27719	+	0.737388i
$118$			716.054i			0.558628i
$119$	303.208	−	1263.47i	0.233571	−	0.973293i
$120$		0			0
$121$	−32.4914	+	56.2768i	−0.0244113	+	0.0422816i
$122$	−267.789	+	154.608i	−0.198725	+	0.114734i
$123$	73.4528	−	42.4080i	0.0538456	−	0.0310878i
$124$	−435.526	+	754.354i	−0.315415	+	0.546314i
$125$		0			0
$126$	181.051	−	754.441i	0.128010	−	0.533420i
$127$			75.3532i			0.0526497i	0.999653	+	0.0263249i	$0.00838043\pi$
$127$			75.3532i			0.0526497i	−0.999653	+	0.0263249i	$0.991620\pi$
$128$	110.851	+	64.0000i	0.0765466	+	0.0441942i
$129$	−456.127	−	790.035i	−0.311316	−	0.539215i
$130$		0			0
$131$	−1100.09	+	1905.41i	−0.733705	+	1.27082i	0.221584	+	0.975141i	$0.428877\pi$
$131$	−1100.09	+	1905.41i	−0.733705	+	1.27082i	−0.955289	+	0.295674i	$0.904456\pi$
$132$			1034.85i			0.682365i
$133$	−659.821	−	2226.76i	−0.430179	−	1.45176i
$134$	135.065			0.0870735
$135$		0			0
$136$	280.631	+	486.067i	0.176941	+	0.306470i
$137$	1780.12	−	1027.75i	1.11011	−	0.640925i	0.171256	−	0.985227i	$-0.445218\pi$
$137$	1780.12	−	1027.75i	1.11011	−	0.640925i	0.938859	+	0.344302i	$0.111884\pi$
$138$	−75.1807	−	43.4056i	−0.0463754	−	0.0267749i
$139$	453.942			0.276999			0.138499	−	0.990363i	$-0.455772\pi$
$139$	453.942			0.276999			0.138499	+	0.990363i	$0.455772\pi$
$140$		0			0
$141$	2521.29			1.50589
$142$	896.808	+	517.772i	0.529989	+	0.305989i
$143$	2883.16	−	1664.59i	1.68603	−	0.973427i
$144$	167.570	+	290.240i	0.0969735	+	0.167963i
$145$		0			0
$146$	−1349.53			−0.764987
$147$	1293.91	+	1991.64i	0.725987	+	1.11747i
$148$		−	843.303i		−	0.468372i
$149$	117.348	−	203.253i	0.0645204	−	0.111753i	−0.831961	−	0.554834i	$-0.812782\pi$
$149$	117.348	−	203.253i	0.0645204	−	0.111753i	0.896481	+	0.443082i	$0.146115\pi$
$150$		0			0
$151$	−173.010	−	299.662i	−0.0932407	−	0.161498i	0.815632	−	0.578571i	$-0.196389\pi$
$151$	−173.010	−	299.662i	−0.0932407	−	0.161498i	−0.908873	+	0.417073i	$0.863056\pi$
$152$	868.804	+	501.604i	0.463614	+	0.267668i
$153$			1469.55i			0.776508i
$154$	−1003.96	−	952.548i	−0.525335	−	0.498432i
$155$		0			0
$156$	1233.97	−	2137.30i	0.633313	−	1.09693i
$157$	2891.76	−	1669.56i	1.46999	−	0.848697i	0.470554	−	0.882371i	$-0.344054\pi$
$157$	2891.76	−	1669.56i	1.46999	−	0.848697i	0.999433	+	0.0336738i	$0.0107207\pi$
$158$	−1613.72	+	931.682i	−0.812536	+	0.469118i
$159$	−1725.74	+	2989.06i	−0.860753	+	1.49087i
$160$		0			0
$161$	111.312	−	32.9832i	0.0544881	−	0.0161456i
$162$		−	1711.61i		−	0.830101i
$163$	−2088.54	−	1205.82i	−1.00360	−	0.579430i	−0.0942896	−	0.995545i	$-0.530058\pi$
$163$	−2088.54	−	1205.82i	−1.00360	−	0.579430i	−0.909312	+	0.416115i	$0.863391\pi$
$164$	−24.4980	−	42.4317i	−0.0116645	−	0.0202034i
$165$		0			0
$166$	−1435.72	+	2486.74i	−0.671286	+	1.16270i
$167$			1296.58i			0.600791i	0.953815	+	0.300395i	$0.0971186\pi$
$167$			1296.58i			0.600791i	−0.953815	+	0.300395i	$0.902881\pi$
$168$	−997.598	−	239.404i	−0.458133	−	0.109943i
$169$	−5742.54			−2.61381
$170$		0			0
$171$	1313.34	+	2274.78i	0.587333	+	1.01729i
$172$	−456.382	+	263.493i	−0.202319	+	0.116809i
$173$	2376.82	+	1372.25i	1.04454	+	0.603067i	0.921117	−	0.389287i	$-0.127278\pi$
$173$	2376.82	+	1372.25i	1.04454	+	0.603067i	0.123426	+	0.992354i	$0.460612\pi$
$174$	1322.21			0.576073
$175$		0			0
$176$	597.806			0.256030
$177$	2146.96	+	1239.55i	0.911726	+	0.526385i
$178$	583.149	−	336.681i	0.245556	−	0.141772i
$179$	−702.721	−	1217.15i	−0.293429	−	0.508234i	0.681189	−	0.732108i	$-0.261463\pi$
$179$	−702.721	−	1217.15i	−0.293429	−	0.508234i	−0.974618	+	0.223873i	$0.928130\pi$
$180$		0			0
$181$	−637.919			−0.261967			−0.130984	−	0.991385i	$-0.541814\pi$
$181$	−637.919			−0.261967			−0.130984	+	0.991385i	$0.541814\pi$
$182$	937.676	+	3164.46i	0.381896	+	1.28882i
$183$			1070.55i			0.432446i
$184$	−25.0743	+	43.4299i	−0.0100462	+	0.0174005i
$185$		0			0
$186$	1507.86	+	2611.70i	0.594419	+	1.02956i
$187$	2270.11	+	1310.65i	0.887737	+	0.512535i
$188$		−	1456.48i		−	0.565026i
$189$	563.180	+	534.338i	0.216748	+	0.205647i
$190$		0			0
$191$	−1827.88	+	3165.98i	−0.692465	+	1.19938i	0.278563	+	0.960418i	$0.410142\pi$
$191$	−1827.88	+	3165.98i	−0.692465	+	1.19938i	−0.971028	+	0.238966i	$0.923191\pi$
$192$	383.785	−	221.578i	0.144257	−	0.0832867i
$193$	−3839.66	+	2216.83i	−1.43204	+	0.826792i	−0.997277	−	0.0737508i	$-0.976503\pi$
$193$	−3839.66	+	2216.83i	−1.43204	+	0.826792i	−0.434768	+	0.900542i	$0.643170\pi$
$194$	179.620	−	311.110i	0.0664739	−	0.115136i
$195$		0			0
$196$	1150.52	−	747.459i	0.419285	−	0.272397i
$197$		−	5283.75i		−	1.91092i	−0.295115	−	0.955462i	$-0.595358\pi$
$197$		−	5283.75i		−	1.91092i	0.295115	−	0.955462i	$-0.404642\pi$
$198$	1355.53	+	782.613i	0.486530	+	0.280898i
$199$	−2202.45	−	3814.76i	−0.784562	−	1.35890i	−0.929261	−	0.369425i	$-0.879555\pi$
$199$	−2202.45	−	3814.76i	−0.784562	−	1.35890i	0.144699	−	0.989476i	$-0.453779\pi$
$200$		0			0
$201$	233.809	−	404.969i	0.0820477	−	0.142111i
$202$		−	1788.78i		−	0.623062i
$203$	−1217.06	+	1282.75i	−0.420791	+	0.443504i
$204$	1943.18			0.666911
$205$		0			0
$206$	−24.8790	−	43.0917i	−0.00841458	−	0.0145745i
$207$	−113.712	+	65.6516i	−0.0381813	+	0.0220440i
$208$	−1234.66	−	712.833i	−0.411579	−	0.237625i
$209$	4685.34			1.55068
$210$		0			0
$211$	−1667.99			−0.544213			−0.272107	−	0.962267i	$-0.587720\pi$
$211$	−1667.99			−0.544213			−0.272107	+	0.962267i	$0.587720\pi$
$212$	1726.70	+	996.912i	0.559389	+	0.322963i
$213$	3104.90	−	1792.61i	0.998798	−	0.576656i
$214$	1153.79	+	1998.43i	0.368559	+	0.638363i
$215$		0			0
$216$	−335.343			−0.105635
$217$	−3921.69	−	941.128i	−1.22683	−	0.294414i
$218$		−	3761.93i		−	1.16876i
$219$	−2336.15	+	4046.33i	−0.720833	+	1.24852i
$220$		0			0
$221$	−3125.67	−	5413.82i	−0.951382	−	1.64784i
$222$	−2528.49	−	1459.83i	−0.764420	−	0.441338i
$223$			3706.93i			1.11316i	0.830795	+	0.556579i	$0.187886\pi$
$223$			3706.93i			1.11316i	−0.830795	+	0.556579i	$0.812114\pi$
$224$	−138.297	+	576.286i	−0.0412517	+	0.171896i
$225$		0			0
$226$	2073.98	−	3592.23i	0.610438	−	1.05731i
$227$	−4121.78	+	2379.71i	−1.20517	+	0.695802i	−0.961699	−	0.274107i	$-0.911618\pi$
$227$	−4121.78	+	2379.71i	−1.20517	+	0.695802i	−0.243466	+	0.969909i	$0.578284\pi$
$228$	3007.94	−	1736.64i	0.873709	−	0.504436i
$229$	−304.691	+	527.740i	−0.0879238	+	0.152288i	−0.906633	−	0.421919i	$-0.861357\pi$
$229$	−304.691	+	527.740i	−0.0879238	+	0.152288i	0.818710	+	0.574208i	$0.194690\pi$
$230$		0			0
$231$	−4593.99	+	1361.26i	−1.30849	+	0.387726i
$232$		−	763.808i		−	0.216149i
$233$	−2740.07	−	1581.98i	−0.770419	−	0.444802i	0.0626048	−	0.998038i	$-0.480059\pi$
$233$	−2740.07	−	1581.98i	−0.770419	−	0.444802i	−0.833024	+	0.553237i	$0.813393\pi$
$234$	−1866.40	−	3232.70i	−0.521412	−	0.903112i
$235$		0			0
$236$	716.054	−	1240.24i	0.197505	−	0.342089i
$237$			6451.27i			1.76817i
$238$	−1788.64	+	1885.18i	−0.487144	+	0.513438i
$239$	5180.13			1.40199			0.700993	−	0.713168i	$-0.252741\pi$
$239$	5180.13			1.40199			0.700993	+	0.713168i	$0.252741\pi$
$240$		0			0
$241$	−1027.16	−	1779.09i	−0.274544	−	0.475523i	0.695476	−	0.718549i	$-0.255193\pi$
$241$	−1027.16	−	1779.09i	−0.274544	−	0.475523i	−0.970020	+	0.243026i	$0.921860\pi$
$242$	112.554	−	64.9828i	0.0298976	−	0.0172614i
$243$	−4151.79	−	2397.04i	−1.09604	−	0.632798i
$244$	618.431			0.162258
$245$		0			0
$246$	−169.632			−0.0439648
$247$	−9676.75	−	5586.87i	−2.49278	−	1.43921i
$248$	1508.71	−	871.053i	0.386303	−	0.223032i
$249$	4970.69	+	8609.49i	1.26508	+	2.19118i
$250$		0			0
$251$	2455.16			0.617403			0.308701	−	0.951159i	$-0.400106\pi$
$251$	2455.16			0.617403			0.308701	+	0.951159i	$0.400106\pi$
$252$	−1068.03	+	1125.68i	−0.266983	+	0.281393i
$253$			234.212i			0.0582006i
$254$	75.3532	−	130.516i	0.0186145	−	0.0322413i
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	3195.72	+	1845.05i	0.775655	+	0.447825i	0.834888	−	0.550419i	$-0.185532\pi$
$257$	3195.72	+	1845.05i	0.775655	+	0.447825i	−0.0592330	+	0.998244i	$0.518865\pi$
$258$			1824.51i			0.440267i
$259$	3743.65	−	1109.30i	0.898144	−	0.266133i
$260$		0			0
$261$	999.934	−	1731.94i	0.237143	−	0.410744i
$262$	3810.83	−	2200.18i	0.898602	−	0.518808i
$263$	4516.44	−	2607.57i	1.05892	−	0.611367i	0.133786	−	0.991010i	$-0.457287\pi$
$263$	4516.44	−	2607.57i	1.05892	−	0.611367i	0.925133	+	0.379643i	$0.123953\pi$
$264$	1034.85	−	1792.41i	0.241252	−	0.417861i
$265$		0			0
$266$	−1083.92	+	4516.68i	−0.249846	+	1.04111i
$267$		−	2331.29i		−	0.534355i
$268$	−233.940	−	135.065i	−0.0533214	−	0.0307851i
$269$	−1817.19	−	3147.47i	−0.411882	−	0.713400i	0.583214	−	0.812319i	$-0.301795\pi$
$269$	−1817.19	−	3147.47i	−0.411882	−	0.713400i	−0.995096	+	0.0989184i	$0.968462\pi$
$270$		0			0
$271$	101.418	−	175.660i	0.0227331	−	0.0393749i	−0.854435	−	0.519558i	$-0.826097\pi$
$271$	101.418	−	175.660i	0.0227331	−	0.0393749i	0.877168	+	0.480183i	$0.159430\pi$
$272$		−	1122.52i		−	0.250232i
$273$	11111.3	+	2666.49i	2.46331	+	0.591147i
$274$	−4111.01			−0.906405
$275$		0			0
$276$	86.8112	+	150.361i	0.0189327	+	0.0327924i
$277$	661.640	−	381.998i	0.143517	−	0.0828593i	−0.426522	−	0.904477i	$-0.640261\pi$
$277$	661.640	−	381.998i	0.143517	−	0.0828593i	0.570039	+	0.821618i	$0.306928\pi$
$278$	−786.250	−	453.942i	−0.169626	−	0.0979338i
$279$	4561.33			0.978780
$280$		0			0
$281$	1451.40			0.308125			0.154063	−	0.988061i	$-0.450764\pi$
$281$	1451.40			0.308125			0.154063	+	0.988061i	$0.450764\pi$
$282$	−4367.00	−	2521.29i	−0.922168	−	0.532414i
$283$	−6633.56	+	3829.89i	−1.39337	+	0.804464i	−0.993687	−	0.112189i	$-0.964214\pi$
$283$	−6633.56	+	3829.89i	−1.39337	+	0.804464i	−0.399685	+	0.916652i	$0.630881\pi$
$284$	−1035.54	−	1793.62i	−0.216367	−	0.374759i
$285$		0			0
$286$	−6658.37			−1.37663
$287$	156.141	−	164.569i	0.0321140	−	0.0338474i
$288$		−	670.281i		−	0.137141i
$289$	4.55786	−	7.89445i	0.000927715	−	0.00160685i
$290$		0			0
$291$	−621.872	−	1077.11i	−0.125274	−	0.216981i
$292$	2337.46	+	1349.53i	0.468457	+	0.270464i
$293$			4222.68i			0.841952i	0.907072	+	0.420976i	$0.138312\pi$
$293$			4222.68i			0.841952i	−0.907072	+	0.420976i	$0.861688\pi$
$294$	−249.482	−	4743.53i	−0.0494901	−	0.940981i
$295$		0			0
$296$	−843.303	+	1460.64i	−0.165595	+	0.286818i
$297$	−1356.34	+	783.086i	−0.264994	+	0.152994i
$298$	−406.506	+	234.696i	−0.0790210	+	0.0456228i
$299$	279.277	−	483.723i	0.0540168	−	0.0935599i
$300$		0			0
$301$	−1770.05	−	1679.40i	−0.338950	−	0.321592i
$302$			692.040i			0.131862i
$303$	−5363.35	−	3096.53i	−1.01689	−	0.587099i
$304$	−1003.21	−	1737.61i	−0.189270	−	0.327825i
$305$		0			0
$306$	1469.55	−	2545.33i	0.274537	−	0.475512i
$307$		−	1243.11i		−	0.231101i	−0.993302	−	0.115551i	$-0.963137\pi$
$307$		−	1243.11i		−	0.231101i	0.993302	−	0.115551i	$-0.0368633\pi$
$308$	786.367	+	2653.82i	0.145479	+	0.490960i
$309$	−172.270			−0.0317156
$310$		0			0
$311$	684.344	+	1185.32i	0.124777	+	0.216120i	0.921646	−	0.388033i	$-0.126845\pi$
$311$	684.344	+	1185.32i	0.124777	+	0.216120i	−0.796869	+	0.604152i	$0.793512\pi$
$312$	−4274.60	+	2467.94i	−0.775646	+	0.447820i
$313$	−2780.51	−	1605.33i	−0.502121	−	0.289900i	0.227468	−	0.973786i	$-0.426955\pi$
$313$	−2780.51	−	1605.33i	−0.502121	−	0.289900i	−0.729589	+	0.683886i	$0.760289\pi$
$314$	−6678.24			−1.20024
$315$		0			0
$316$	3726.73			0.663433
$317$	−6624.32	−	3824.55i	−1.17369	−	0.677628i	−0.219141	−	0.975693i	$-0.570326\pi$
$317$	−6624.32	−	3824.55i	−1.17369	−	0.677628i	−0.954546	+	0.298065i	$0.903659\pi$
$318$	5978.12	−	3451.47i	1.05420	−	0.608644i
$319$	−1783.63	−	3089.33i	−0.313053	−	0.542224i
$320$		0			0
$321$	7989.24			1.38915
$322$	−225.781	−	54.1829i	−0.0390753	−	0.00937732i
$323$		−	8797.86i		−	1.51556i
$324$	−1711.61	+	2964.59i	−0.293485	+	0.508331i
$325$		0			0
$326$	2411.64	+	4177.08i	0.409719	+	0.709653i
$327$	−11279.5	−	6512.21i	−1.90751	−	1.10130i
$328$			97.9919i			0.0164960i
$329$	6465.73	−	1915.89i	1.08349	−	0.321053i
$330$		0			0
$331$	3958.64	−	6856.57i	0.657362	−	1.13858i	−0.323934	−	0.946080i	$-0.605006\pi$
$331$	3958.64	−	6856.57i	0.657362	−	1.13858i	0.981296	−	0.192504i	$-0.0616609\pi$
$332$	4973.48	−	2871.44i	0.822154	−	0.474671i
$333$	−3824.38	+	2208.01i	−0.629354	+	0.363358i
$334$	1296.58	−	2245.73i	0.212412	−	0.367908i
$335$		0			0
$336$	1488.49	+	1412.26i	0.241677	+	0.229301i
$337$			6878.10i			1.11179i	0.831252	+	0.555896i	$0.187625\pi$
$337$			6878.10i			1.11179i	−0.831252	+	0.555896i	$0.812375\pi$
$338$	9946.37	+	5742.54i	1.60062	+	0.924121i
$339$	−7180.45	−	12436.9i	−1.15041	−	1.99257i
$340$		0			0
$341$	4068.13	−	7046.20i	0.646045	−	1.11898i
$342$		−	5253.37i		−	0.830614i
$343$	4831.59	+	4124.24i	0.760587	+	0.649236i
$344$	1053.97			0.165193
$345$		0			0
$346$	−2744.51	−	4753.63i	−0.426433	−	0.738603i
$347$	−1231.19	+	710.830i	−0.190472	+	0.109969i	−0.592204	−	0.805788i	$-0.701742\pi$
$347$	−1231.19	+	710.830i	−0.190472	+	0.109969i	0.401731	+	0.915758i	$0.368409\pi$
$348$	−2290.14	−	1322.21i	−0.352772	−	0.203673i
$349$	−2837.74			−0.435246			−0.217623	−	0.976033i	$-0.569830\pi$
$349$	−2837.74			−0.435246			−0.217623	+	0.976033i	$0.569830\pi$
$350$		0			0
$351$	3735.05			0.567984
$352$	−1035.43	−	597.806i	−0.156786	−	0.0905203i
$353$	3099.34	−	1789.41i	0.467313	−	0.269803i	−0.247801	−	0.968811i	$-0.579708\pi$
$353$	3099.34	−	1789.41i	0.467313	−	0.269803i	0.715114	+	0.699008i	$0.246375\pi$
$354$	−2479.10	−	4293.92i	−0.372210	−	0.644687i
$355$		0			0
$356$	−1346.73			−0.200495
$357$	2556.10	+	8626.32i	0.378945	+	1.27886i
$358$			2810.88i			0.414972i
$359$	−3060.74	+	5301.35i	−0.449971	+	0.779373i	−0.998384	−	0.0568352i	$-0.981899\pi$
$359$	−3060.74	+	5301.35i	−0.449971	+	0.779373i	0.548413	+	0.836208i	$0.315232\pi$
$360$		0			0
$361$	−4433.21	−	7678.55i	−0.646335	−	1.11948i
$362$	1104.91	+	637.919i	0.160422	+	0.0926195i
$363$		−	449.962i		−	0.0650603i
$364$	1540.36	−	6418.68i	0.221804	−	0.924259i
$365$		0			0
$366$	1070.55	−	1854.25i	0.152893	−	0.264818i
$367$	10554.1	−	6093.41i	1.50114	−	0.866686i	0.501145	−	0.865364i	$-0.332912\pi$
$367$	10554.1	−	6093.41i	1.50114	−	0.866686i	0.999999	−	0.00132220i	$-0.000420871\pi$
$368$	86.8598	−	50.1485i	0.0123040	−	0.00710373i
$369$	−128.285	+	222.197i	−0.0180983	+	0.0313472i
$370$		0			0
$371$	−2154.22	+	8976.67i	−0.301460	+	1.25619i
$372$		−	6031.45i		−	0.840635i
$373$	9047.28	+	5223.45i	1.25590	+	0.725094i	0.972275	−	0.233841i	$-0.0751296\pi$
$373$	9047.28	+	5223.45i	1.25590	+	0.725094i	0.283625	+	0.958935i	$0.408463\pi$
$374$	−2621.30	−	4540.22i	−0.362417	−	0.627725i
$375$		0			0
$376$	−1456.48	+	2522.70i	−0.199767	+	0.346007i
$377$			8507.30i			1.16220i
$378$	−441.118	−	1488.68i	−0.0600229	−	0.202565i
$379$	10274.0			1.39246			0.696229	−	0.717820i	$-0.254860\pi$
$379$	10274.0			1.39246			0.696229	+	0.717820i	$0.254860\pi$
$380$		0			0
$381$	−260.885	−	451.866i	−0.0350802	−	0.0607607i
$382$	6331.96	−	3655.76i	0.848093	−	0.489647i
$383$	5618.50	+	3243.84i	0.749587	+	0.432774i	0.825545	−	0.564337i	$-0.190868\pi$
$383$	5618.50	+	3243.84i	0.749587	+	0.432774i	−0.0759577	+	0.997111i	$0.524201\pi$
$384$	−886.314			−0.117785
$385$		0			0
$386$	8867.31			1.16926
$387$	2389.88	+	1379.80i	0.313913	+	0.181238i
$388$	−622.220	+	359.239i	−0.0814135	+	0.0470041i
$389$	−1853.16	−	3209.77i	−0.241540	−	0.418360i	0.719613	−	0.694375i	$-0.244319\pi$
$389$	−1853.16	−	3209.77i	−0.241540	−	0.418360i	−0.961153	+	0.276016i	$0.910986\pi$
$390$		0			0
$391$	439.789			0.0568825
$392$	−2740.21	+	144.119i	−0.353065	+	0.0185692i
$393$		−	15234.8i		−	1.95545i
$394$	−5283.75	+	9151.73i	−0.675613	+	1.17020i
$395$		0			0
$396$	−1565.23	−	2711.05i	−0.198625	−	0.344029i
$397$	−8036.94	−	4640.13i	−1.01603	−	0.586603i	−0.103076	−	0.994673i	$-0.532868\pi$
$397$	−8036.94	−	4640.13i	−1.01603	−	0.586603i	−0.912951	+	0.408070i	$0.866202\pi$
$398$			8809.81i			1.10954i
$399$	11666.1	+	11068.7i	1.46375	+	1.38879i
$400$		0			0
$401$	1209.54	−	2094.98i	0.150627	−	0.260894i	−0.780831	−	0.624742i	$-0.785204\pi$
$401$	1209.54	−	2094.98i	0.150627	−	0.260894i	0.931458	+	0.363848i	$0.118537\pi$
$402$	−809.937	+	467.617i	−0.100488	+	0.0580165i
$403$	−16804.0	+	9701.79i	−2.07709	+	1.19921i
$404$	−1788.78	+	3098.27i	−0.220286	+	0.381546i
$405$		0			0
$406$	3390.75	−	1004.73i	0.414484	−	0.122818i
$407$			7877.05i			0.959339i
$408$	−3365.69	−	1943.18i	−0.408398	−	0.235789i
$409$	−2497.99	−	4326.65i	−0.302000	−	0.523079i	0.674589	−	0.738193i	$-0.264321\pi$
$409$	−2497.99	−	4326.65i	−0.302000	−	0.523079i	−0.976589	+	0.215115i	$0.930988\pi$
$410$		0			0
$411$	−7116.48	+	12326.1i	−0.854088	+	1.47932i
$412$			99.5161i			0.0119000i
$413$	6447.69	+	1547.32i	0.768209	+	0.184355i
$414$	262.606			0.0311749
$415$		0			0
$416$	1425.67	+	2469.32i	0.168026	+	0.291030i
$417$	−2722.13	+	1571.62i	−0.319672	+	0.184562i
$418$	−8115.25	−	4685.34i	−0.949593	−	0.548248i
$419$	10746.6			1.25300			0.626500	−	0.779421i	$-0.284487\pi$
$419$	10746.6			1.25300			0.626500	+	0.779421i	$0.284487\pi$
$420$		0			0
$421$	8561.10			0.991075			0.495538	−	0.868587i	$-0.334971\pi$
$421$	8561.10			0.991075			0.495538	+	0.868587i	$0.334971\pi$
$422$	2889.04	+	1667.99i	0.333261	+	0.192408i
$423$	−6605.16	+	3813.49i	−0.759229	+	0.438341i
$424$	−1993.82	−	3453.40i	−0.228369	−	0.395547i
$425$		0			0
$426$	−7170.45			−0.815515
$427$	813.498	+	2745.39i	0.0921965	+	0.311144i
$428$		−	4615.17i		−	0.521221i
$429$	−11526.2	+	19963.9i	−1.29718	+	2.24678i
$430$		0			0
$431$	2617.95	+	4534.43i	0.292581	+	0.506765i	0.974419	−	0.224738i	$-0.0721526\pi$
$431$	2617.95	+	4534.43i	0.292581	+	0.506765i	−0.681838	+	0.731503i	$0.738819\pi$
$432$	580.831	+	335.343i	0.0646881	+	0.0373477i
$433$			3809.88i			0.422844i	0.977395	+	0.211422i	$0.0678094\pi$
$433$			3809.88i			0.422844i	−0.977395	+	0.211422i	$0.932191\pi$
$434$	5851.43	+	5551.77i	0.647183	+	0.614040i
$435$		0			0
$436$	−3761.93	+	6515.86i	−0.413220	+	0.715718i
$437$	680.769	−	393.042i	0.0745209	−	0.0430246i
$438$	8092.66	−	4672.30i	0.882837	−	0.509706i
$439$	−6266.39	+	10853.7i	−0.681272	+	1.18000i	0.293320	+	0.956014i	$0.405240\pi$
$439$	−6266.39	+	10853.7i	−0.681272	+	1.18000i	−0.974593	+	0.223984i	$0.928094\pi$
$440$		0			0
$441$	−6402.11	−	3260.54i	−0.691298	−	0.352072i
$442$			12502.7i			1.34546i
$443$	−15410.4	−	8897.20i	−1.65275	−	0.954218i	−0.975933	−	0.218071i	$-0.930024\pi$
$443$	−15410.4	−	8897.20i	−1.65275	−	0.954218i	−0.676821	−	0.736147i	$-0.736643\pi$
$444$	2919.65	+	5056.99i	0.312073	+	0.540527i
$445$		0			0
$446$	3706.93	−	6420.59i	0.393561	−	0.681667i
$447$			1625.11i			0.171958i
$448$	815.824	−	859.860i	0.0860359	−	0.0906798i
$449$	−12203.4			−1.28266			−0.641331	−	0.767265i	$-0.721617\pi$
$449$	−12203.4			−1.28266			−0.641331	+	0.767265i	$0.721617\pi$
$450$		0			0
$451$	228.828	+	396.343i	0.0238916	+	0.0413815i
$452$	−7184.47	+	4147.96i	−0.747631	+	0.431645i
$453$	2074.96	+	1197.98i	0.215210	+	0.124251i
$454$	9518.85			0.984013
$455$		0			0
$456$	−6946.54			−0.713381
$457$	4113.22	+	2374.77i	0.421024	+	0.243079i	0.695516	−	0.718511i	$-0.255176\pi$
$457$	4113.22	+	2374.77i	0.421024	+	0.243079i	−0.274491	+	0.961590i	$0.588509\pi$
$458$	1055.48	−	609.382i	0.107684	−	0.0621715i
$459$	1470.43	+	2546.86i	0.149529	+	0.258992i
$460$		0			0
$461$	−13208.0			−1.33440			−0.667199	−	0.744880i	$-0.732507\pi$
$461$	−13208.0			−1.33440			−0.667199	+	0.744880i	$0.732507\pi$
$462$	9318.28	+	2236.21i	0.938367	+	0.225190i
$463$			11987.9i			1.20329i	0.798763	+	0.601645i	$0.205488\pi$
$463$			11987.9i			1.20329i	−0.798763	+	0.601645i	$0.794512\pi$
$464$	−763.808	+	1322.95i	−0.0764200	+	0.132363i
$465$		0			0
$466$	3163.96	+	5480.13i	0.314522	+	0.544769i
$467$	4487.07	+	2590.61i	0.444619	+	0.256701i	0.705555	−	0.708655i	$-0.250698\pi$
$467$	4487.07	+	2590.61i	0.444619	+	0.256701i	−0.260936	+	0.965356i	$0.584031\pi$
$468$			7465.60i			0.737388i
$469$	291.862	−	1216.19i	0.0287355	−	0.119741i
$470$		0			0
$471$	−11560.6	+	20023.5i	−1.13096	+	1.95889i
$472$	−2480.49	+	1432.11i	−0.241893	+	0.139657i
$473$	4262.94	−	2461.21i	0.414398	−	0.239253i
$474$	6451.27	−	11173.9i	0.625141	−	1.08278i
$475$		0			0
$476$	4983.20	−	1476.59i	0.479841	−	0.142184i
$477$		−	10440.8i		−	1.00220i
$478$	−8972.24	−	5180.13i	−0.858537	−	0.495677i
$479$	−66.9992	−	116.046i	−0.00639096	−	0.0110695i	0.862812	−	0.505525i	$-0.168701\pi$
$479$	−66.9992	−	116.046i	−0.00639096	−	0.0110695i	−0.869203	+	0.494455i	$0.835368\pi$
$480$		0			0
$481$	9392.72	−	16268.7i	0.890376	−	1.54218i
$482$			4108.63i			0.388263i
$483$	−553.302	+	583.167i	−0.0521245	+	0.0549380i
$484$	−259.931			−0.0244113
$485$		0			0
$486$	4794.07	+	8303.58i	0.447456	+	0.775017i
$487$	2873.78	−	1659.18i	0.267399	−	0.154383i	−0.360306	−	0.932834i	$-0.617328\pi$
$487$	2873.78	−	1659.18i	0.267399	−	0.154383i	0.627705	+	0.778451i	$0.283994\pi$
$488$	−1071.15	−	618.431i	−0.0993624	−	0.0573669i
$489$	16699.0			1.54428
$490$		0			0
$491$	−2195.90			−0.201832			−0.100916	−	0.994895i	$-0.532177\pi$
$491$	−2195.90			−0.201832			−0.100916	+	0.994895i	$0.532177\pi$
$492$	293.811	+	169.632i	0.0269228	+	0.0155439i
$493$	−5800.97	+	3349.19i	−0.529945	+	0.305964i
$494$	11173.7	+	19353.5i	1.01767	+	1.76266i
$495$		0			0
$496$	−3484.21			−0.315415
$497$	6600.18	−	6956.43i	0.595691	−	0.627844i
$498$		−	19882.8i		−	1.78909i
$499$	5844.81	−	10123.5i	0.524348	−	0.908197i	−0.475250	−	0.879851i	$-0.657642\pi$
$499$	5844.81	−	10123.5i	0.524348	−	0.908197i	0.999598	−	0.0283465i	$-0.00902418\pi$
$500$		0			0
$501$	−4488.96	−	7775.10i	−0.400303	−	0.693345i
$502$	−4252.46	−	2455.16i	−0.378081	−	0.218285i
$503$		−	9289.98i		−	0.823498i	−0.911297	−	0.411749i	$-0.864918\pi$
$503$		−	9289.98i		−	0.823498i	0.911297	−	0.411749i	$-0.135082\pi$
$504$	2975.56	−	881.703i	0.262980	−	0.0779249i
$505$		0			0
$506$	234.212	−	405.666i	0.0205770	−	0.0356404i
$507$	34435.9	−	19881.6i	3.01648	−	1.74156i
$508$	−261.031	+	150.706i	−0.0227980	+	0.0131624i
$509$	−3345.31	+	5794.25i	−0.291313	+	0.504569i	−0.974120	−	0.226029i	$-0.927425\pi$
$509$	−3345.31	+	5794.25i	−0.291313	+	0.504569i	0.682807	+	0.730598i	$0.260759\pi$
$510$		0			0
$511$	−2916.20	+	12151.8i	−0.252456	+	1.05199i
$512$			512.000i			0.0441942i
$513$	4552.30	+	2628.27i	0.391792	+	0.226201i
$514$	−3690.10	−	6391.44i	−0.316660	−	0.548471i
$515$		0			0
$516$	1824.51	−	3160.14i	0.155658	−	0.269607i
$517$			13604.6i			1.15731i
$518$	−7593.50	−	1822.29i	−0.644091	−	0.154569i
$519$	−19003.9			−1.60728
$520$		0			0
$521$	514.047	+	890.355i	0.0432261	+	0.0748698i	0.886829	−	0.462098i	$-0.152903\pi$
$521$	514.047	+	890.355i	0.0432261	+	0.0748698i	−0.843603	+	0.536968i	$0.819570\pi$
$522$	−3463.87	+	1999.87i	−0.290440	+	0.167686i
$523$	535.434	+	309.133i	0.0447665	+	0.0258460i	0.522216	−	0.852813i	$-0.325105\pi$
$523$	535.434	+	309.133i	0.0447665	+	0.0258460i	−0.477450	+	0.878659i	$0.658439\pi$
$524$	−8800.73			−0.733705
$525$		0			0
$526$	−10430.3			−0.864603
$527$	−13230.9	−	7638.89i	−1.09364	−	0.631414i
$528$	−3584.83	+	2069.70i	−0.295473	+	0.170591i
$529$	−6063.85	−	10502.9i	−0.498385	−	0.863228i
$530$		0			0
$531$	−7499.34			−0.612888
$532$	6394.08	−	6739.21i	0.521087	−	0.549214i
$533$		−	1091.43i		−	0.0886966i
$534$	−2331.29	+	4037.92i	−0.188923	+	0.327224i
$535$		0			0
$536$	270.130	+	467.879i	0.0217684	+	0.0377039i
$537$	8427.93	+	4865.87i	0.677267	+	0.391020i
$538$			7268.77i			0.582489i
$539$	−10746.7	+	6981.80i	−0.858796	+	0.557936i
$540$		0			0
$541$	417.761	−	723.584i	0.0331996	−	0.0575033i	−0.848948	−	0.528476i	$-0.822764\pi$
$541$	417.761	−	723.584i	0.0331996	−	0.0575033i	0.882148	+	0.470973i	$0.156097\pi$
$542$	−351.321	+	202.835i	−0.0278423	+	0.0160747i
$543$	3825.37	−	2208.58i	0.302325	−	0.174547i
$544$	−1122.52	+	1944.27i	−0.0884703	+	0.153235i
$545$		0			0
$546$	−16578.8	−	15729.7i	−1.29946	−	1.23291i
$547$		−	1100.23i		−	0.0860011i	−0.999075	−	0.0430005i	$-0.986308\pi$
$547$		−	1100.23i		−	0.0860011i	0.999075	−	0.0430005i	$-0.0136917\pi$
$548$	7120.47	+	4111.01i	0.555057	+	0.320462i
$549$	−1619.23	−	2804.59i	−0.125878	−	0.218027i
$550$		0			0
$551$	−5986.40	+	10368.7i	−0.462848	+	0.801676i
$552$		−	347.245i		−	0.0267749i
$553$	4902.22	+	16544.0i	0.376969	+	1.27219i
$554$	−1527.99			−0.117181
$555$		0			0
$556$	907.883	+	1572.50i	0.0692497	+	0.119944i
$557$	5195.85	−	2999.82i	0.395251	−	0.228199i	−0.289182	−	0.957274i	$-0.593383\pi$
$557$	5195.85	−	2999.82i	0.395251	−	0.228199i	0.684433	+	0.729076i	$0.260050\pi$
$558$	−7900.46	−	4561.33i	−0.599378	−	0.346051i
$559$	−11739.1			−0.888215
$560$		0			0
$561$	−18150.7			−1.36600
$562$	−2513.90	−	1451.40i	−0.188687	−	0.108939i
$563$	20866.2	−	12047.1i	1.56200	−	0.901819i	0.564940	−	0.825132i	$-0.308899\pi$
$563$	20866.2	−	12047.1i	1.56200	−	0.901819i	0.997055	−	0.0766870i	$-0.0244342\pi$
$564$	5042.58	+	8734.01i	0.376473	+	0.652071i
$565$		0			0
$566$	15319.6			1.13768
$567$	−15412.1	−	3698.60i	−1.14153	−	0.273945i
$568$			4142.18i			0.305989i
$569$	2754.95	−	4771.72i	0.202977	−	0.351566i	−0.746510	−	0.665375i	$-0.768272\pi$
$569$	2754.95	−	4771.72i	0.202977	−	0.351566i	0.949486	+	0.313809i	$0.101605\pi$
$570$		0			0
$571$	2219.12	+	3843.63i	0.162640	+	0.281700i	0.935815	−	0.352493i	$-0.114666\pi$
$571$	2219.12	+	3843.63i	0.162640	+	0.281700i	−0.773175	+	0.634193i	$0.781333\pi$
$572$	11532.6	+	6658.37i	0.843013	+	0.486714i
$573$		−	25313.7i		−	1.84554i
$574$	−435.013	+	128.901i	−0.0316326	+	0.00937319i
$575$		0			0
$576$	−670.281	+	1160.96i	−0.0484868	+	0.0839816i
$577$	7968.86	−	4600.82i	0.574953	−	0.331949i	−0.184172	−	0.982894i	$-0.558960\pi$
$577$	7968.86	−	4600.82i	0.574953	−	0.331949i	0.759125	+	0.650945i	$0.225627\pi$
$578$	−15.7889	+	9.11573i	−0.00113621	+	0.000655994i
$579$	15350.0	−	26587.0i	1.10177	−	1.90832i
$580$		0			0
$581$	19289.3	+	18301.5i	1.37738	+	1.30684i
$582$			2487.49i			0.177164i
$583$	−16128.6	−	9311.87i	−1.14576	−	0.661506i
$584$	−2699.07	−	4674.92i	−0.191247	−	0.331249i
$585$		0			0
$586$	4222.68	−	7313.90i	0.297675	−	0.515588i
$587$		−	5551.42i		−	0.390343i	−0.980769	−	0.195172i	$-0.937474\pi$
$587$		−	5551.42i		−	0.390343i	0.980769	−	0.195172i	$-0.0625264\pi$
$588$	−4311.42	+	8465.52i	−0.302381	+	0.593728i
$589$	−27307.7			−1.91035
$590$		0			0
$591$	18293.2	+	31684.8i	1.27324	+	2.20531i
$592$	2921.29	−	1686.61i	0.202811	−	0.117093i
$593$	4841.68	+	2795.34i	0.335285	+	0.193577i	0.658185	−	0.752856i	$-0.271325\pi$
$593$	4841.68	+	2795.34i	0.335285	+	0.193577i	−0.322900	+	0.946433i	$0.604658\pi$
$594$	3132.34			0.216366
$595$		0			0
$596$	938.786			0.0645204
$597$	26414.6	+	15250.5i	1.81085	+	1.04550i
$598$	−967.445	+	558.555i	−0.0661568	+	0.0381957i
$599$	6837.67	+	11843.2i	0.466410	+	0.807846i	0.999264	−	0.0383614i	$-0.0122138\pi$
$599$	6837.67	+	11843.2i	0.466410	+	0.807846i	−0.532854	+	0.846207i	$0.678880\pi$
$600$		0			0
$601$	−4508.67			−0.306011			−0.153005	−	0.988225i	$-0.548895\pi$
$601$	−4508.67			−0.306011			−0.153005	+	0.988225i	$0.548895\pi$
$602$	1386.42	+	4678.86i	0.0938639	+	0.316771i
$603$			1414.56i			0.0955310i
$604$	692.040	−	1198.65i	0.0466204	−	0.0807488i
$605$		0			0
$606$	6193.06	+	10726.7i	0.415142	+	0.719047i
$607$	3146.33	+	1816.53i	0.210388	+	0.121468i	0.601492	−	0.798879i	$-0.294573\pi$
$607$	3146.33	+	1816.53i	0.210388	+	0.121468i	−0.391104	+	0.920347i	$0.627907\pi$
$608$			4012.83i			0.267668i
$609$	2857.17	−	11905.8i	0.190112	−	0.792199i
$610$		0			0
$611$	16222.3	−	28097.9i	1.07412	−	1.86042i
$612$	−5090.65	+	2939.09i	−0.336238	+	0.194127i
$613$	−10313.7	+	5954.63i	−0.679555	+	0.392341i	−0.799687	−	0.600417i	$-0.795001\pi$
$613$	−10313.7	+	5954.63i	−0.679555	+	0.392341i	0.120132	+	0.992758i	$0.461668\pi$
$614$	−1243.11	+	2153.13i	−0.0817067	+	0.141520i
$615$		0			0
$616$	1291.80	−	5382.92i	0.0844935	−	0.352085i
$617$			5510.74i			0.359569i	0.983706	+	0.179784i	$0.0575400\pi$
$617$			5510.74i			0.359569i	−0.983706	+	0.179784i	$0.942460\pi$
$618$	298.381	+	172.270i	0.0194218	+	0.0112132i
$619$	−10467.7	−	18130.6i	−0.679699	−	1.17727i	−0.975072	−	0.221891i	$-0.928777\pi$
$619$	−10467.7	−	18130.6i	−0.679699	−	1.17727i	0.295373	−	0.955382i	$-0.404556\pi$
$620$		0			0
$621$	−131.383	+	227.561i	−0.00848985	+	0.0147049i
$622$		−	2737.38i		−	0.176461i
$623$	−1771.51	−	5978.49i	−0.113923	−	0.384467i
$624$	9871.77			0.633313
$625$		0			0
$626$	3210.66	+	5561.03i	0.204990	+	0.355053i
$627$	−28096.3	+	16221.4i	−1.78957	+	1.03321i
$628$	11567.1	+	6678.24i	0.734993	+	0.424349i
$629$	14791.1			0.937613
$630$		0			0
$631$	−1538.74			−0.0970780			−0.0485390	−	0.998821i	$-0.515457\pi$
$631$	−1538.74			−0.0970780			−0.0485390	+	0.998821i	$0.515457\pi$
$632$	−6454.88	−	3726.73i	−0.406268	−	0.234559i
$633$	10002.3	−	5774.84i	0.628051	−	0.362606i
$634$	7649.10	+	13248.6i	0.479156	+	0.829922i
$635$		0			0
$636$	−13805.9			−0.860753
$637$	30520.5	−	1605.20i	1.89838	−	0.0998436i
$638$			7134.51i			0.442724i
$639$	−5422.71	+	9392.40i	−0.335710	+	0.581467i
$640$		0			0
$641$	2961.16	+	5128.88i	0.182463	+	0.316035i	0.942719	−	0.333589i	$-0.108260\pi$
$641$	2961.16	+	5128.88i	0.182463	+	0.316035i	−0.760256	+	0.649624i	$0.774926\pi$
$642$	−13837.8	−	7989.24i	−0.850675	−	0.491137i
$643$		−	22967.5i		−	1.40863i	−0.709887	−	0.704315i	$-0.751254\pi$
$643$		−	22967.5i		−	1.40863i	0.709887	−	0.704315i	$-0.248746\pi$
$644$	336.880	+	319.628i	0.0206133	+	0.0195576i
$645$		0			0
$646$	−8797.86	+	15238.3i	−0.535832	+	0.928088i
$647$	−12397.0	+	7157.41i	−0.753287	+	0.434910i	−0.826880	−	0.562378i	$-0.809887\pi$
$647$	−12397.0	+	7157.41i	−0.753287	+	0.434910i	0.0735935	+	0.997288i	$0.476553\pi$
$648$	5929.18	−	3423.21i	0.359444	−	0.207525i
$649$	−6688.46	+	11584.8i	−0.404538	+	0.700680i
$650$		0			0
$651$	26775.3	−	7933.91i	1.61199	−	0.477656i
$652$		−	9646.55i		−	0.579430i
$653$	−14019.3	−	8094.03i	−0.840148	−	0.485060i	0.0171665	−	0.999853i	$-0.494535\pi$
$653$	−14019.3	−	8094.03i	−0.840148	−	0.485060i	−0.857315	+	0.514793i	$0.827869\pi$
$654$	13024.4	+	22559.0i	0.778739	+	1.34882i
$655$		0			0
$656$	97.9919	−	169.727i	0.00583223	−	0.0101017i
$657$		−	14133.8i		−	0.839291i
$658$	−13114.9	−	3147.31i	−0.777007	−	0.186466i
$659$	−5303.87			−0.313519			−0.156760	−	0.987637i	$-0.550105\pi$
$659$	−5303.87			−0.313519			−0.156760	+	0.987637i	$0.550105\pi$
$660$		0			0
$661$	−11168.3	−	19344.0i	−0.657180	−	1.13827i	−0.981343	−	0.192267i	$-0.938416\pi$
$661$	−11168.3	−	19344.0i	−0.657180	−	1.13827i	0.324163	−	0.946001i	$-0.394917\pi$
$662$	−13713.1	+	7917.29i	−0.805100	+	0.464825i
$663$	37487.1	+	21643.2i	2.19589	+	1.26780i
$664$	−11485.8			−0.671286
$665$		0			0
$666$	8832.03			0.513865
$667$	−518.314	−	299.249i	−0.0300888	−	0.0173718i
$668$	−4491.47	+	2593.15i	−0.260150	+	0.150198i
$669$	−12834.0	−	22229.1i	−0.741690	−	1.28464i
$670$		0			0
$671$	−5776.59			−0.332344
$672$	−1165.88	−	3934.59i	−0.0669266	−	0.225863i
$673$			22907.3i			1.31206i	0.754737	+	0.656028i	$0.227765\pi$
$673$			22907.3i			1.31206i	−0.754737	+	0.656028i	$0.772235\pi$
$674$	6878.10	−	11913.2i	0.393078	−	0.680831i
$675$		0			0
$676$	−11485.1	−	19892.7i	−0.653452	−	1.13181i
$677$	−28005.0	−	16168.7i	−1.58984	−	0.917894i	−0.993332	−	0.115286i	$-0.963222\pi$
$677$	−28005.0	−	16168.7i	−1.58984	−	0.917894i	−0.596507	−	0.802608i	$-0.703445\pi$
$678$			28721.8i			1.62692i
$679$	−2413.24	−	2289.66i	−0.136394	−	0.129409i
$680$		0			0
$681$	16477.9	−	28540.6i	0.927217	−	1.60599i
$682$	−14092.4	+	8136.25i	−0.791241	+	0.456823i
$683$	−21369.2	+	12337.5i	−1.19718	+	0.691190i	−0.959925	−	0.280258i	$-0.909580\pi$
$683$	−21369.2	+	12337.5i	−1.19718	+	0.691190i	−0.237252	+	0.971448i	$0.576247\pi$
$684$	−5253.37	+	9099.11i	−0.293666	+	0.508645i
$685$		0			0
$686$	−4244.32	−	11975.0i	−0.236223	−	0.666482i
$687$		−	4219.56i		−	0.234332i
$688$	−1825.53	−	1053.97i	−0.101159	−	0.0584044i
$689$	22207.2	+	38464.0i	1.22791	+	2.12680i
$690$		0			0
$691$	6430.41	−	11137.8i	0.354015	−	0.613172i	−0.632934	−	0.774206i	$-0.718149\pi$
$691$	6430.41	−	11137.8i	0.354015	−	0.613172i	0.986949	+	0.161034i	$0.0514828\pi$
$692$			10978.0i			0.603067i
$693$	9976.17	−	10514.6i	0.546845	−	0.576361i
$694$	2843.32			0.155520
$695$		0			0
$696$	2644.43	+	4580.28i	0.144018	+	0.249447i
$697$	744.229	−	429.681i	0.0404443	−	0.0233505i
$698$	4915.11	+	2837.74i	0.266533	+	0.153883i
$699$	21908.3			1.18547
$700$		0			0
$701$	−2157.68			−0.116254			−0.0581272	−	0.998309i	$-0.518513\pi$
$701$	−2157.68			−0.116254			−0.0581272	+	0.998309i	$0.518513\pi$
$702$	−6469.30	−	3735.05i	−0.347818	−	0.200813i
$703$	22895.8	−	13218.9i	1.22835	−	0.709189i
$704$	1195.61	+	2070.86i	0.0640075	+	0.110864i
$705$		0			0
$706$	−7157.63			−0.381559
$707$	−16107.1	−	3865.38i	−0.856815	−	0.205619i
$708$			9916.39i			0.526385i
$709$	9274.61	−	16064.1i	0.491277	−	0.850916i	−0.508673	−	0.860960i	$-0.669864\pi$
$709$	9274.61	−	16064.1i	0.491277	−	0.850916i	0.999950	+	0.0100437i	$0.00319707\pi$
$710$		0			0
$711$	−9757.64	−	16900.7i	−0.514684	−	0.891458i
$712$	2332.60	+	1346.73i	0.122778	+	0.0708858i
$713$		−	1365.06i		−	0.0716999i
$714$	4199.02	−	17497.3i	0.220090	−	0.917116i
$715$		0			0
$716$	2810.88	−	4868.59i	0.146715	−	0.254117i
$717$	−31063.4	+	17934.4i	−1.61797	+	0.934134i
$718$	10602.7	−	6121.48i	0.551100	−	0.318178i
$719$	12886.3	−	22319.7i	0.668398	−	1.15770i	−0.309954	−	0.950751i	$-0.600314\pi$
$719$	12886.3	−	22319.7i	0.668398	−	1.15770i	0.978352	−	0.206947i	$-0.0663528\pi$
$720$		0			0
$721$	−441.779	+	130.906i	−0.0228193	+	0.00676169i
$722$			17732.8i			0.914056i
$723$	12319.0	+	7112.37i	0.633676	+	0.365853i
$724$	−1275.84	−	2209.81i	−0.0654919	−	0.113435i
$725$		0			0
$726$	−449.962	+	779.357i	−0.0230023	+	0.0398411i
$727$			24295.8i			1.23945i	0.784818	+	0.619727i	$0.212757\pi$
$727$			24295.8i			1.23945i	−0.784818	+	0.619727i	$0.787243\pi$
$728$	−9086.66	+	9577.12i	−0.462602	+	0.487571i
$729$	10089.1			0.512577
$730$		0			0
$731$	−4621.51	−	8004.70i	−0.233834	−	0.405013i
$732$	−3708.51	+	2141.11i	−0.187255	+	0.108112i
$733$	5314.61	+	3068.39i	0.267803	+	0.154616i	0.627889	−	0.778303i	$-0.283919\pi$
$733$	5314.61	+	3068.39i	0.267803	+	0.154616i	−0.360086	+	0.932919i	$0.617253\pi$
$734$	−24373.7			−1.22568
$735$		0			0
$736$	−200.594			−0.0100462
$737$	2185.16	+	1261.60i	0.109215	+	0.0630554i
$738$	444.394	−	256.571i	0.0221658	−	0.0127974i
$739$	−11801.0	−	20439.9i	−0.587424	−	1.01745i	−0.994568	−	0.104085i	$-0.966809\pi$
$739$	−11801.0	−	20439.9i	−0.587424	−	1.01745i	0.407144	−	0.913364i	$-0.366525\pi$
$740$		0			0
$741$	77370.6			3.83574
$742$	12707.9	−	13393.8i	0.628735	−	0.662672i
$743$			6486.83i			0.320294i	0.987093	+	0.160147i	$0.0511969\pi$
$743$			6486.83i			0.320294i	−0.987093	+	0.160147i	$0.948803\pi$
$744$	−6031.45	+	10446.8i	−0.297209	+	0.514782i
$745$		0			0
$746$	−10446.9	−	18094.6i	−0.512719	−	0.888055i
$747$	−26044.0	−	15036.5i	−1.27563	−	0.736488i
$748$			10485.2i			0.512535i
$749$	20488.0	−	6070.90i	0.999487	−	0.296163i
$750$		0			0
$751$	1296.11	−	2244.93i	0.0629770	−	0.109079i	−0.832818	−	0.553547i	$-0.813274\pi$
$751$	1296.11	−	2244.93i	0.0629770	−	0.109079i	0.895795	+	0.444468i	$0.146607\pi$
$752$	5045.41	−	2912.97i	0.244664	−	0.141257i
$753$	−14722.7	+	8500.15i	−0.712516	+	0.411372i
$754$	8507.30	−	14735.1i	0.410899	−	0.711697i
$755$		0			0
$756$	−724.642	+	3019.59i	−0.0348611	+	0.145266i
$757$		−	24578.4i		−	1.18007i	−0.807376	−	0.590037i	$-0.799113\pi$
$757$		−	24578.4i		−	1.18007i	0.807376	−	0.590037i	$-0.200887\pi$
$758$	−17795.1	−	10274.0i	−0.852703	−	0.492308i
$759$	−810.878	−	1404.48i	−0.0387787	−	0.0671667i
$760$		0			0
$761$	−18977.3	+	32869.6i	−0.903976	+	1.56573i	−0.0816895	+	0.996658i	$0.526032\pi$
$761$	−18977.3	+	32869.6i	−0.903976	+	1.56573i	−0.822286	+	0.569074i	$0.807302\pi$
$762$			1043.54i			0.0496109i
$763$	−33874.2	−	8129.15i	−1.60725	−	0.385708i
$764$	−14623.0			−0.692465
$765$		0			0
$766$	−6487.68	−	11237.0i	−0.306018	−	0.530038i
$767$	27627.7	−	15950.8i	1.30062	−	0.750915i
$768$	1535.14	+	886.314i	0.0721284	+	0.0416433i
$769$	3017.80			0.141514			0.0707572	−	0.997494i	$-0.477458\pi$
$769$	3017.80			0.141514			0.0707572	+	0.997494i	$0.477458\pi$
$770$		0			0
$771$	−25551.4			−1.19353
$772$	−15358.6	−	8867.31i	−0.716022	−	0.413396i
$773$	88.7300	−	51.2283i	0.00412858	−	0.00238364i	−0.497934	−	0.867215i	$-0.665908\pi$
$773$	88.7300	−	51.2283i	0.00412858	−	0.00238364i	0.502063	+	0.864831i	$0.332575\pi$
$774$	−2759.59	−	4779.76i	−0.128155	−	0.221970i
$775$		0			0
$776$	1436.96			0.0664739
$777$	−18608.8	+	19613.2i	−0.859184	+	0.905560i
$778$			7412.65i			0.341589i
$779$	768.018	−	1330.25i	0.0353236	−	0.0611823i
$780$		0			0
$781$	9672.73	+	16753.7i	0.443172	+	0.767597i
$782$	−761.737	−	439.789i	−0.0348333	−	0.0201110i
$783$		−	4002.15i		−	0.182663i
$784$	4890.31	+	2490.59i	0.222773	+	0.113456i
$785$		0			0
$786$	−15234.8	+	26387.4i	−0.691357	+	1.19747i
$787$	−10756.0	+	6209.98i	−0.487179	+	0.281273i	−0.723403	−	0.690426i	$-0.757423\pi$
$787$	−10756.0	+	6209.98i	−0.487179	+	0.281273i	0.236224	+	0.971699i	$0.424090\pi$
$788$	18303.5	−	10567.5i	0.827454	−	0.477731i
$789$	−18055.6	+	31273.3i	−0.814700	+	1.41110i
$790$		0			0
$791$	−27864.5	−	26437.5i	−1.25253	−	1.18838i
$792$			6260.90i			0.280898i
$793$	11930.5	+	6888.09i	0.534256	+	0.308453i
$794$	9280.26	+	16073.9i	0.414791	+	0.718439i
$795$		0			0
$796$	8809.81	−	15259.0i	0.392281	−	0.679450i
$797$		−	40547.2i		−	1.80208i	−0.433739	−	0.901039i	$-0.642806\pi$
$797$		−	40547.2i		−	1.80208i	0.433739	−	0.901039i	$-0.357194\pi$
$798$	−9137.63	−	30837.6i	−0.405349	−	1.36797i
$799$	25545.9			1.13110
$800$		0			0
$801$	3526.11	+	6107.41i	0.155542	+	0.269406i
$802$	−4189.97	+	2419.08i	−0.184480	+	0.106510i
$803$	−21833.5	−	12605.6i	−0.959513	−	0.553975i
$804$	1870.47			0.0820477
$805$		0			0
$806$	38807.2			1.69594
$807$	21794.1	+	12582.8i	0.950668	+	0.548868i
$808$	6196.53	−	3577.57i	0.269794	−	0.155765i
$809$	−3553.58	−	6154.97i	−0.154434	−	0.267487i	0.778419	−	0.627745i	$-0.216022\pi$
$809$	−3553.58	−	6154.97i	−0.154434	−	0.267487i	−0.932853	+	0.360258i	$0.882689\pi$
$810$		0			0
$811$	−21314.5			−0.922876			−0.461438	−	0.887172i	$-0.652666\pi$
$811$	−21314.5			−0.922876			−0.461438	+	0.887172i	$0.652666\pi$
$812$	−6877.69	−	1650.51i	−0.297241	−	0.0713320i
$813$			1404.50i			0.0605877i
$814$	7877.05	−	13643.5i	0.339177	−	0.587473i
$815$		0			0
$816$	3886.36	+	6731.38i	0.166728	+	0.288781i
$817$	−14307.7	−	8260.56i	−0.612685	−	0.353734i
$818$			9991.98i			0.427092i
$819$	−33141.8	+	9820.41i	−1.41400	+	0.418990i
$820$		0			0
$821$	−1442.44	+	2498.39i	−0.0613175	+	0.106205i	−0.895055	−	0.445957i	$-0.852864\pi$
$821$	−1442.44	+	2498.39i	−0.0613175	+	0.106205i	0.833737	+	0.552162i	$0.186197\pi$
$822$	24652.2	−	14233.0i	1.04604	−	0.603932i
$823$	15960.2	−	9214.61i	0.675986	−	0.390281i	−0.122355	−	0.992486i	$-0.539045\pi$
$823$	15960.2	−	9214.61i	0.675986	−	0.390281i	0.798341	+	0.602205i	$0.205711\pi$
$824$	99.5161	−	172.367i	0.00420729	−	0.00728724i
$825$		0			0
$826$	−9620.41	−	9127.73i	−0.405250	−	0.384497i
$827$			2056.14i			0.0864559i	0.999065	+	0.0432280i	$0.0137642\pi$
$827$			2056.14i			0.0864559i	−0.999065	+	0.0432280i	$0.986236\pi$
$828$	−454.848	−	262.606i	−0.0190906	−	0.0110220i
$829$	−3935.80	−	6817.00i	−0.164893	−	0.285602i	0.771725	−	0.635957i	$-0.219394\pi$
$829$	−3935.80	−	6817.00i	−0.164893	−	0.285602i	−0.936617	+	0.350355i	$0.886061\pi$
$830$		0			0
$831$	−2645.08	+	4581.41i	−0.110417	+	0.191248i
$832$		−	5702.66i		−	0.237625i
$833$	13110.0	+	20179.4i	0.545300	+	0.839347i
$834$	6286.48			0.261011
$835$		0			0
$836$	9370.68	+	16230.5i	0.387670	+	0.671464i
$837$	7905.23	−	4564.09i	0.326457	−	0.188480i
$838$	−18613.7	−	10746.6i	−0.767303	−	0.443003i
$839$	−34220.8			−1.40815			−0.704073	−	0.710128i	$-0.748637\pi$
$839$	−34220.8			−1.40815			−0.704073	+	0.710128i	$0.748637\pi$
$840$		0			0
$841$	−15273.3			−0.626239
$842$	−14828.3	−	8561.10i	−0.606907	−	0.350398i
$843$	−8703.52	+	5024.98i	−0.355593	+	0.205302i
$844$	−3335.97	−	5778.08i	−0.136053	−	0.235651i
$845$		0			0
$846$	15254.0			0.619908
$847$	−341.919	−	1153.91i	−0.0138707	−	0.0468107i
$848$			7975.30i			0.322963i
$849$	26519.4	−	45932.9i	1.07202	−	1.85679i
$850$		0			0
$851$	660.788	+	1144.52i	0.0266175	+	0.0461029i
$852$	12419.6	+	7170.45i	0.499399	+	0.288328i
$853$		−	33509.6i		−	1.34507i	−0.740065	−	0.672536i	$-0.765205\pi$
$853$		−	33509.6i		−	1.34507i	0.740065	−	0.672536i	$-0.234795\pi$
$854$	1336.37	−	5568.65i	0.0535474	−	0.223132i
$855$		0			0
$856$	−4615.17	+	7993.71i	−0.184280	+	0.319182i
$857$	7460.58	−	4307.37i	0.297373	−	0.171688i	−0.343889	−	0.939010i	$-0.611744\pi$
$857$	7460.58	−	4307.37i	0.297373	−	0.171688i	0.641262	+	0.767322i	$0.278411\pi$
$858$	39927.8	−	23052.3i	1.58871	−	0.917243i
$859$	2181.74	−	3778.89i	0.0866589	−	0.150098i	−0.819438	−	0.573168i	$-0.805714\pi$
$859$	2181.74	−	3778.89i	0.0866589	−	0.150098i	0.906097	+	0.423070i	$0.139048\pi$
$860$		0			0
$861$	−366.557	+	1527.45i	−0.0145090	+	0.0604590i
$862$		−	10471.8i		−	0.413772i
$863$	14780.2	+	8533.33i	0.582992	+	0.336591i	0.762322	−	0.647198i	$-0.224059\pi$
$863$	14780.2	+	8533.33i	0.582992	+	0.336591i	−0.179329	+	0.983789i	$0.557393\pi$
$864$	−670.686	−	1161.66i	−0.0264088	−	0.0457414i
$865$		0			0
$866$	3809.88	−	6598.91i	0.149498	−	0.258938i
$867$			63.1203i			0.00247252i
$868$	−4583.21	−	15467.4i	−0.179221	−	0.604835i
$869$	−34810.3			−1.35887
$870$		0			0
$871$	−3008.71	−	5211.24i	−0.117045	−	0.202728i
$872$	13031.7	−	7523.86i	0.506089	−	0.292191i
$873$	3258.30	+	1881.18i	0.126319	+	0.0729305i
$874$	−1572.17			−0.0608460
$875$		0			0
$876$	−18689.2			−0.720833
$877$	23258.4	+	13428.2i	0.895530	+	0.517034i	0.875747	−	0.482770i	$-0.160369\pi$
$877$	23258.4	+	13428.2i	0.895530	+	0.517034i	0.0197825	+	0.999804i	$0.493703\pi$
$878$	21707.4	−	12532.8i	0.834385	−	0.481732i
$879$	−14619.6	−	25321.9i	−0.560987	−	0.971658i
$880$		0			0
$881$	−27044.5			−1.03423			−0.517113	−	0.855917i	$-0.672993\pi$
$881$	−27044.5			−1.03423			−0.517113	+	0.855917i	$0.672993\pi$
$882$	7828.24	+	12049.5i	0.298856	+	0.460010i
$883$			48010.9i			1.82978i	0.403702	+	0.914890i	$0.367723\pi$
$883$			48010.9i			1.82978i	−0.403702	+	0.914890i	$0.632277\pi$
$884$	12502.7	−	21655.3i	0.475691	−	0.823921i
$885$		0			0
$886$	17794.4	+	30820.8i	0.674734	+	1.16867i
$887$	−3367.12	−	1944.01i	−0.127460	−	0.0735889i	0.434914	−	0.900472i	$-0.356779\pi$
$887$	−3367.12	−	1944.01i	−0.127460	−	0.0735889i	−0.562374	+	0.826883i	$0.690112\pi$
$888$		−	11678.6i		−	0.441338i
$889$	−1012.39	−	960.547i	−0.0381941	−	0.0362381i
$890$		0			0
$891$	15987.6	−	27691.4i	0.601128	−	1.04118i
$892$	−12841.2	+	7413.86i	−0.482012	+	0.278290i
$893$	39543.7	−	22830.6i	1.48184	−	0.855538i
$894$	1625.11	−	2814.78i	0.0607964	−	0.105302i
$895$		0			0
$896$	−2272.91	+	673.496i	−0.0847462	+	0.0251115i
$897$			3867.62i			0.143964i
$898$	21136.9	+	12203.4i	0.785466	+	0.453489i
$899$	10395.6	+	18005.7i	0.385664	+	0.667990i
$900$		0			0
$901$	−17485.3	+	30285.4i	−0.646525	+	1.11981i
$902$		−	915.314i		−	0.0337878i
$903$	16428.7	+	3942.57i	0.605442	+	0.145294i
$904$	16591.8			0.610438
$905$		0			0
$906$	−2395.95	−	4149.91i	−0.0878590	−	0.152176i
$907$	−8001.08	+	4619.43i	−0.292912	+	0.169113i	−0.639255	−	0.768995i	$-0.720757\pi$
$907$	−8001.08	+	4619.43i	−0.292912	+	0.169113i	0.346342	+	0.938108i	$0.387424\pi$
$908$	−16487.1	−	9518.85i	−0.602583	−	0.347901i
$909$	18734.2			0.683580
$910$		0			0
$911$	−54171.6			−1.97013			−0.985064	−	0.172190i	$-0.944916\pi$
$911$	−54171.6			−1.97013			−0.985064	+	0.172190i	$0.944916\pi$
$912$	12031.8	+	6946.54i	0.436855	+	0.252218i
$913$	−46455.8	+	26821.3i	−1.68397	+	0.972240i
$914$	−4749.53	−	8226.43i	−0.171883	−	0.297709i
$915$		0			0
$916$	−2437.53			−0.0879238
$917$	−11576.7	−	39068.9i	−0.416898	−	1.40694i
$918$		−	5881.73i		−	0.211466i
$919$	−9701.77	+	16804.0i	−0.348239	+	0.603168i	−0.985937	−	0.167119i	$-0.946554\pi$
$919$	−9701.77	+	16804.0i	−0.348239	+	0.603168i	0.637698	+	0.770287i	$0.279887\pi$
$920$		0			0
$921$	4303.85	+	7454.49i	0.153981	+	0.266704i
$922$	22876.9	+	13208.0i	0.817148	+	0.471781i
$923$		−	46135.6i		−	1.64526i
$924$	−13903.5	−	13191.5i	−0.495014	−	0.469663i
$925$		0			0
$926$	11987.9	−	20763.6i	0.425427	−	0.736862i
$927$	451.306	−	260.562i	0.0159901	−	0.00923189i
$928$	2645.91	−	1527.62i	0.0935951	−	0.0540371i
$929$	−19554.1	+	33868.7i	−0.690581	+	1.19612i	0.281067	+	0.959688i	$0.409312\pi$
$929$	−19554.1	+	33868.7i	−0.690581	+	1.19612i	−0.971648	+	0.236433i	$0.924022\pi$
$930$		0			0
$931$	38328.1	+	19520.2i	1.34925	+	0.687162i
$932$		−	12655.8i		−	0.444802i
$933$	−8207.53	−	4738.62i	−0.287998	−	0.166276i
$934$	−5181.23	−	8974.15i	−0.181515	−	0.314393i
$935$		0			0
$936$	7465.60	−	12930.8i	0.260706	−	0.451556i
$937$			624.451i			0.0217715i	0.999941	+	0.0108858i	$0.00346512\pi$
$937$			624.451i			0.0217715i	−0.999941	+	0.0108858i	$0.996535\pi$
$938$	−1721.71	+	1814.64i	−0.0599316	+	0.0631665i
$939$	22231.7			0.772634
$940$		0			0
$941$	−26762.7	−	46354.4i	−0.927141	−	1.60586i	−0.788081	−	0.615571i	$-0.788925\pi$
$941$	−26762.7	−	46354.4i	−0.927141	−	1.60586i	−0.139060	−	0.990284i	$-0.544408\pi$
$942$	40047.0	−	23121.2i	1.38514	−	0.799712i
$943$	66.4965	+	38.3918i	0.00229631	+	0.00132578i
$944$	5728.43			0.197505
$945$		0			0
$946$	−9844.83			−0.338354
$947$	2464.76	+	1423.03i	0.0845766	+	0.0488303i	0.541692	−	0.840577i	$-0.317784\pi$
$947$	2464.76	+	1423.03i	0.0845766	+	0.0488303i	−0.457115	+	0.889407i	$0.651117\pi$
$948$	−22347.9	+	12902.5i	−0.765638	+	0.442041i
$949$	30062.2	+	52069.3i	1.02830	+	1.78108i
$950$		0			0
$951$	52964.9			1.80600
$952$	−10107.7	−	2425.66i	−0.344111	−	0.0825800i
$953$		−	29720.3i		−	1.01021i	−0.863057	−	0.505107i	$-0.831453\pi$
$953$		−	29720.3i		−	1.01021i	0.863057	−	0.505107i	$-0.168547\pi$
$954$	−10440.8	+	18084.0i	−0.354333	+	0.613722i
$955$		0			0
$956$	10360.3	+	17944.5i	0.350496	+	0.607077i
$957$	21391.6	+	12350.4i	0.722561	+	0.417171i
$958$			267.997i			0.00903819i
$959$	−8883.46	+	37017.4i	−0.299126	+	1.24646i
$960$		0			0
$961$	−8814.90	+	15267.9i	−0.295891	+	0.512499i
$962$	−32537.3	+	18785.4i	−1.09048	+	0.629591i
$963$	−20929.8	+	12083.8i	−0.700368	+	0.404358i
$964$	4108.63	−	7116.35i	0.137272	−	0.237762i
$965$		0			0
$966$	1541.52	−	456.773i	0.0513431	−	0.0152137i
$967$			7604.19i			0.252879i	0.991974	+	0.126440i	$0.0403550\pi$
$967$			7604.19i			0.252879i	−0.991974	+	0.126440i	$0.959645\pi$
$968$	450.214	+	259.931i	0.0149488	+	0.00863069i
$969$	30459.6	+	52757.6i	1.00981	+	1.74904i
$970$		0			0
$971$	−13172.5	+	22815.5i	−0.435352	+	0.754052i	−0.997324	−	0.0731043i	$-0.976709\pi$
$971$	−13172.5	+	22815.5i	−0.435352	+	0.754052i	0.561972	+	0.827156i	$0.310043\pi$
$972$		−	19176.3i		−	0.632798i
$973$	−5786.51	+	6098.84i	−0.190655	+	0.200946i
$974$	−6636.72			−0.218331
$975$		0			0
$976$	1236.86	+	2142.31i	0.0405645	+	0.0702598i
$977$	11683.5	−	6745.48i	0.382588	−	0.220888i	−0.296355	−	0.955078i	$-0.595771\pi$
$977$	11683.5	−	6745.48i	0.382588	−	0.220888i	0.678944	+	0.734190i	$0.262438\pi$
$978$	−28923.5	−	16699.0i	−0.945675	−	0.545986i
$979$	12579.4			0.410663
$980$		0			0
$981$	39399.3			1.28228
$982$	3803.41	+	2195.90i	0.123597	+	0.0713585i
$983$	−25032.3	+	14452.4i	−0.812214	+	0.468932i	−0.847724	−	0.530437i	$-0.822028\pi$
$983$	−25032.3	+	14452.4i	−0.812214	+	0.468932i	0.0355102	+	0.999369i	$0.488694\pi$
$984$	−339.264	−	587.622i	−0.0109912	−	0.0190373i
$985$		0			0
$986$	13396.8			0.432698
$987$	−32139.5	+	33874.3i	−1.03649	+	1.09243i
$988$		−	44695.0i		−	1.43921i
$989$	412.930	−	715.216i	0.0132765	−	0.0229955i
$990$		0			0
$991$	4600.88	+	7968.95i	0.147479	+	0.255441i	0.930295	−	0.366812i	$-0.119551\pi$
$991$	4600.88	+	7968.95i	0.147479	+	0.255441i	−0.782816	+	0.622253i	$0.786217\pi$
$992$	6034.83	+	3484.21i	0.193151	+	0.111516i
$993$			54821.9i			1.75198i
$994$	−18388.3	+	5448.71i	−0.586761	+	0.173866i
$995$		0			0
$996$	−19882.8	+	34438.0i	−0.632540	+	1.09559i
$997$	−31788.7	+	18353.2i	−1.00979	+	0.583000i	−0.911129	−	0.412121i	$-0.864788\pi$
$997$	−31788.7	+	18353.2i	−1.00979	+	0.583000i	−0.0986572	+	0.995121i	$0.531455\pi$
$998$	−20247.0	+	11689.6i	−0.642192	+	0.370770i
$999$	−4418.68	+	7653.39i	−0.139941	+	0.242385i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.4.j.h.149.1		12
5.2	odd	4		350.4.e.j.51.3	yes	6
5.3	odd	4		350.4.e.i.51.1	✓	6
5.4	even	2	inner	350.4.j.h.149.6		12
7.4	even	3	inner	350.4.j.h.249.6		12
35.2	odd	12		2450.4.a.cc.1.1		3
35.4	even	6	inner	350.4.j.h.249.1		12
35.12	even	12		2450.4.a.cd.1.3		3
35.18	odd	12		350.4.e.i.151.1	yes	6
35.23	odd	12		2450.4.a.ci.1.3		3
35.32	odd	12		350.4.e.j.151.3	yes	6
35.33	even	12		2450.4.a.ch.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.4.e.i.51.1	✓	6	5.3	odd	4
350.4.e.i.151.1	yes	6	35.18	odd	12
350.4.e.j.51.3	yes	6	5.2	odd	4
350.4.e.j.151.3	yes	6	35.32	odd	12
350.4.j.h.149.1		12	1.1	even	1	trivial
350.4.j.h.149.6		12	5.4	even	2	inner
350.4.j.h.249.1		12	35.4	even	6	inner
350.4.j.h.249.6		12	7.4	even	3	inner
2450.4.a.cc.1.1		3	35.2	odd	12
2450.4.a.cd.1.3		3	35.12	even	12
2450.4.a.ch.1.1		3	35.33	even	12
2450.4.a.ci.1.3		3	35.23	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	350.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 - 1.00000i) q^{2} +(-5.99664 + 3.46216i) q^{3} +(2.00000 + 3.46410i) q^{4} +13.8487 q^{6} +(-12.7473 + 13.4353i) q^{7} -8.00000i q^{8} +(10.4731 - 18.1400i) q^{9} +(-18.6814 - 32.3572i) q^{11} +(-23.9866 - 13.8487i) q^{12} +89.1041i q^{13} +(35.5142 - 10.5234i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(-60.7584 + 35.0789i) q^{17} +(-36.2800 + 20.9463i) q^{18} +(-62.7005 + 108.600i) q^{19} +(29.9255 - 124.700i) q^{21} +74.7257i q^{22} +(-5.42874 - 3.13428i) q^{23} +(27.6973 + 47.9731i) q^{24} +(89.1041 - 154.333i) q^{26} -41.9179i q^{27} +(-72.0358 - 17.2872i) q^{28} +95.4760 q^{29} +(108.882 + 188.588i) q^{31} +(27.7128 - 16.0000i) q^{32} +(224.052 + 129.356i) q^{33} +140.316 q^{34} +83.7851 q^{36} +(-182.580 - 105.413i) q^{37} +(217.201 - 125.401i) q^{38} +(-308.493 - 534.325i) q^{39} -12.2490 q^{41} +(-176.532 + 186.061i) q^{42} +131.746i q^{43} +(74.7257 - 129.429i) q^{44} +(6.26857 + 10.8575i) q^{46} +(-315.338 - 182.060i) q^{47} -110.789i q^{48} +(-18.0149 - 342.527i) q^{49} +(242.898 - 420.711i) q^{51} +(-308.666 + 178.208i) q^{52} +(431.676 - 249.228i) q^{53} +(-41.9179 + 72.6039i) q^{54} +(107.482 + 101.978i) q^{56} -868.318i q^{57} +(-165.369 - 95.4760i) q^{58} +(-179.014 - 310.061i) q^{59} +(77.3039 - 133.894i) q^{61} -435.526i q^{62} +(110.213 + 371.945i) q^{63} -64.0000 q^{64} +(-258.713 - 448.103i) q^{66} +(-58.4849 + 33.7663i) q^{67} +(-243.034 - 140.316i) q^{68} +43.4056 q^{69} -517.772 q^{71} +(-145.120 - 83.7851i) q^{72} +(584.365 - 337.383i) q^{73} +(210.826 + 365.161i) q^{74} -501.604 q^{76} +(672.866 + 161.475i) q^{77} +1233.97i q^{78} +(465.841 - 806.860i) q^{79} +(427.901 + 741.147i) q^{81} +(21.2159 + 12.2490i) q^{82} -1435.72i q^{83} +(491.824 - 145.735i) q^{84} +(131.746 - 228.191i) q^{86} +(-572.535 + 330.553i) q^{87} +(-258.857 + 149.451i) q^{88} +(-168.341 + 291.575i) q^{89} +(-1197.14 - 1135.83i) q^{91} -25.0743i q^{92} +(-1305.85 - 753.932i) q^{93} +(364.121 + 630.676i) q^{94} +(-110.789 + 191.893i) q^{96} +179.620i q^{97} +(-311.324 + 611.288i) q^{98} -782.613 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 24 q^{4} + 24 q^{6} + 112 q^{9} + 52 q^{11} + 16 q^{14} - 96 q^{16} - 36 q^{19} + 370 q^{21} + 48 q^{24} + 320 q^{26} + 1616 q^{29} + 1230 q^{31} + 240 q^{34} + 896 q^{36} - 180 q^{39} - 404 q^{41}+ \cdots + 228 q^{99}+O(q^{100}) \) 12 * q + 24 * q^4 + 24 * q^6 + 112 * q^9 + 52 * q^11 + 16 * q^14 - 96 * q^16 - 36 * q^19 + 370 * q^21 + 48 * q^24 + 320 * q^26 + 1616 * q^29 + 1230 * q^31 + 240 * q^34 + 896 * q^36 - 180 * q^39 - 404 * q^41 - 208 * q^44 + 212 * q^46 + 432 * q^49 + 678 * q^51 - 1296 * q^54 + 896 * q^56 - 182 * q^59 + 1294 * q^61 - 768 * q^64 - 1256 * q^66 + 6192 * q^69 + 2132 * q^71 + 1704 * q^74 - 288 * q^76 + 2842 * q^79 + 2786 * q^81 + 608 * q^84 + 996 * q^86 - 388 * q^89 - 7710 * q^91 - 1608 * q^94 - 192 * q^96 + 228 * q^99

Introduction

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