LMFDB - Embedded newform 228.3.g.a.115.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,3,Mod(115,228)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("228.115");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	228.g (of order $2$, degree $1$, 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:	$6.21255002741$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			115.19
Character	$\chi$	$=$	228.115
Dual form			228.3.g.a.115.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.234708 - 1.98618i) q^{2} +1.73205i q^{3} +(-3.88982 - 0.932347i) q^{4} -0.816108 q^{5} +(3.44017 + 0.406527i) q^{6} -3.29246i q^{7} +(-2.76478 + 7.50706i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(0.234708 - 1.98618i) q^{2} +1.73205i q^{3} +(-3.88982 - 0.932347i) q^{4} -0.816108 q^{5} +(3.44017 + 0.406527i) q^{6} -3.29246i q^{7} +(-2.76478 + 7.50706i) q^{8} -3.00000 q^{9} +(-0.191547 + 1.62094i) q^{10} -15.5683i q^{11} +(1.61487 - 6.73737i) q^{12} -19.7611 q^{13} +(-6.53941 - 0.772767i) q^{14} -1.41354i q^{15} +(14.2615 + 7.25333i) q^{16} -25.9240 q^{17} +(-0.704125 + 5.95854i) q^{18} +4.35890i q^{19} +(3.17452 + 0.760895i) q^{20} +5.70270 q^{21} +(-30.9214 - 3.65401i) q^{22} +10.1514i q^{23} +(-13.0026 - 4.78874i) q^{24} -24.3340 q^{25} +(-4.63810 + 39.2491i) q^{26} -5.19615i q^{27} +(-3.06971 + 12.8071i) q^{28} +29.6603 q^{29} +(-2.80755 - 0.331770i) q^{30} -55.0301i q^{31} +(17.7537 - 26.6234i) q^{32} +26.9651 q^{33} +(-6.08459 + 51.4898i) q^{34} +2.68700i q^{35} +(11.6695 + 2.79704i) q^{36} -61.1896 q^{37} +(8.65756 + 1.02307i) q^{38} -34.2273i q^{39} +(2.25636 - 6.12657i) q^{40} +53.7702 q^{41} +(1.33847 - 11.3266i) q^{42} +23.1601i q^{43} +(-14.5150 + 60.5579i) q^{44} +2.44832 q^{45} +(20.1624 + 2.38261i) q^{46} +28.3513i q^{47} +(-12.5631 + 24.7016i) q^{48} +38.1597 q^{49} +(-5.71139 + 48.3316i) q^{50} -44.9018i q^{51} +(76.8673 + 18.4242i) q^{52} +48.3999 q^{53} +(-10.3205 - 1.21958i) q^{54} +12.7054i q^{55} +(24.7167 + 9.10293i) q^{56} -7.54983 q^{57} +(6.96153 - 58.9108i) q^{58} -9.75362i q^{59} +(-1.31791 + 5.49842i) q^{60} -59.0626 q^{61} +(-109.300 - 12.9160i) q^{62} +9.87737i q^{63} +(-48.7120 - 41.5108i) q^{64} +16.1272 q^{65} +(6.32893 - 53.5575i) q^{66} -109.748i q^{67} +(100.840 + 24.1702i) q^{68} -17.5827 q^{69} +(5.33686 + 0.630661i) q^{70} +71.0816i q^{71} +(8.29435 - 22.5212i) q^{72} +70.6749 q^{73} +(-14.3617 + 121.534i) q^{74} -42.1477i q^{75} +(4.06400 - 16.9553i) q^{76} -51.2579 q^{77} +(-67.9815 - 8.03343i) q^{78} -85.1124i q^{79} +(-11.6389 - 5.91950i) q^{80} +9.00000 q^{81} +(12.6203 - 106.797i) q^{82} -99.6812i q^{83} +(-22.1825 - 5.31689i) q^{84} +21.1568 q^{85} +(46.0001 + 5.43587i) q^{86} +51.3732i q^{87} +(116.872 + 43.0429i) q^{88} -0.665467 q^{89} +(0.574642 - 4.86281i) q^{90} +65.0626i q^{91} +(9.46458 - 39.4870i) q^{92} +95.3150 q^{93} +(56.3108 + 6.65429i) q^{94} -3.55733i q^{95} +(46.1131 + 30.7503i) q^{96} -40.5229 q^{97} +(8.95641 - 75.7921i) q^{98} +46.7048i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{2} + 12 q^{4} + 8 q^{5} - 20 q^{8} - 108 q^{9}+O(q^{10}) $ 36 * q + 4 * q^2 + 12 * q^4 + 8 * q^5 - 20 * q^8 - 108 * q^9	$ 36 q + 4 q^{2} + 12 q^{4} + 8 q^{5} - 20 q^{8} - 108 q^{9} + 8 q^{10} + 24 q^{12} - 24 q^{13} - 12 q^{14} + 4 q^{16} - 40 q^{17} - 12 q^{18} - 80 q^{20} + 12 q^{22} + 36 q^{24} + 284 q^{25} - 112 q^{26} - 48 q^{28} + 104 q^{29} + 24 q^{30} + 44 q^{32} + 48 q^{33} + 140 q^{34} - 36 q^{36} - 184 q^{37} + 180 q^{40} - 200 q^{41} + 48 q^{42} + 96 q^{44} - 24 q^{45} - 28 q^{46} - 144 q^{48} - 332 q^{49} + 176 q^{50} + 276 q^{52} + 264 q^{53} - 192 q^{56} - 184 q^{58} - 180 q^{60} + 40 q^{61} - 240 q^{62} - 372 q^{64} + 176 q^{65} - 120 q^{66} - 104 q^{68} - 60 q^{70} + 60 q^{72} + 424 q^{73} - 104 q^{74} - 400 q^{77} - 180 q^{78} + 704 q^{80} + 324 q^{81} + 528 q^{82} + 312 q^{84} - 128 q^{85} + 668 q^{86} - 496 q^{88} - 520 q^{89} - 24 q^{90} - 456 q^{92} - 32 q^{94} + 300 q^{96} - 440 q^{97} - 472 q^{98}+O(q^{100}) $ 36 * q + 4 * q^2 + 12 * q^4 + 8 * q^5 - 20 * q^8 - 108 * q^9 + 8 * q^10 + 24 * q^12 - 24 * q^13 - 12 * q^14 + 4 * q^16 - 40 * q^17 - 12 * q^18 - 80 * q^20 + 12 * q^22 + 36 * q^24 + 284 * q^25 - 112 * q^26 - 48 * q^28 + 104 * q^29 + 24 * q^30 + 44 * q^32 + 48 * q^33 + 140 * q^34 - 36 * q^36 - 184 * q^37 + 180 * q^40 - 200 * q^41 + 48 * q^42 + 96 * q^44 - 24 * q^45 - 28 * q^46 - 144 * q^48 - 332 * q^49 + 176 * q^50 + 276 * q^52 + 264 * q^53 - 192 * q^56 - 184 * q^58 - 180 * q^60 + 40 * q^61 - 240 * q^62 - 372 * q^64 + 176 * q^65 - 120 * q^66 - 104 * q^68 - 60 * q^70 + 60 * q^72 + 424 * q^73 - 104 * q^74 - 400 * q^77 - 180 * q^78 + 704 * q^80 + 324 * q^81 + 528 * q^82 + 312 * q^84 - 128 * q^85 + 668 * q^86 - 496 * q^88 - 520 * q^89 - 24 * q^90 - 456 * q^92 - 32 * q^94 + 300 * q^96 - 440 * q^97 - 472 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.234708	−	1.98618i	0.117354	−	0.993090i
$2$	0.234708	−	1.98618i	0.117354	−	0.993090i
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	−3.88982	−	0.932347i	−0.972456	−	0.233087i
$5$	−0.816108			−0.163222			−0.0816108	−	0.996664i	$-0.526006\pi$
$5$	−0.816108			−0.163222			−0.0816108	+	0.996664i	$0.526006\pi$
$6$	3.44017	+	0.406527i	0.573361	+	0.0677545i
$7$		−	3.29246i		−	0.470351i	−0.971953	−	0.235175i	$-0.924434\pi$
$7$		−	3.29246i		−	0.470351i	0.971953	−	0.235175i	$-0.0755665\pi$
$8$	−2.76478	+	7.50706i	−0.345598	+	0.938383i
$9$	−3.00000			−0.333333
$10$	−0.191547	+	1.62094i	−0.0191547	+	0.162094i
$11$		−	15.5683i		−	1.41530i	−0.706564	−	0.707649i	$-0.749756\pi$
$11$		−	15.5683i		−	1.41530i	0.706564	−	0.707649i	$-0.250244\pi$
$12$	1.61487	−	6.73737i	0.134573	−	0.561448i
$13$	−19.7611			−1.52009			−0.760043	−	0.649873i	$-0.774822\pi$
$13$	−19.7611			−1.52009			−0.760043	+	0.649873i	$0.774822\pi$
$14$	−6.53941	−	0.772767i	−0.467101	−	0.0551977i
$15$		−	1.41354i		−	0.0942360i
$16$	14.2615	+	7.25333i	0.891341	+	0.453333i
$17$	−25.9240			−1.52494			−0.762472	−	0.647022i	$-0.776014\pi$
$17$	−25.9240			−1.52494			−0.762472	+	0.647022i	$0.776014\pi$
$18$	−0.704125	+	5.95854i	−0.0391181	+	0.331030i
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	3.17452	+	0.760895i	0.158726	+	0.0380448i
$21$	5.70270			0.271557
$22$	−30.9214	−	3.65401i	−1.40552	−	0.166091i
$23$			10.1514i			0.441363i	0.975346	+	0.220682i	$0.0708282\pi$
$23$			10.1514i			0.441363i	−0.975346	+	0.220682i	$0.929172\pi$
$24$	−13.0026	−	4.78874i	−0.541776	−	0.199531i
$25$	−24.3340			−0.973359
$26$	−4.63810	+	39.2491i	−0.178388	+	1.50958i
$27$		−	5.19615i		−	0.192450i
$28$	−3.06971	+	12.8071i	−0.109633	+	0.457396i
$29$	29.6603			1.02277			0.511385	−	0.859352i	$-0.329133\pi$
$29$	29.6603			1.02277			0.511385	+	0.859352i	$0.329133\pi$
$30$	−2.80755	−	0.331770i	−0.0935848	−	0.0110590i
$31$		−	55.0301i		−	1.77517i	−0.460648	−	0.887583i	$-0.652383\pi$
$31$		−	55.0301i		−	1.77517i	0.460648	−	0.887583i	$-0.347617\pi$
$32$	17.7537	−	26.6234i	0.554803	−	0.831982i
$33$	26.9651			0.817123
$34$	−6.08459	+	51.4898i	−0.178959	+	1.51441i
$35$			2.68700i			0.0767714i
$36$	11.6695	+	2.79704i	0.324152	+	0.0776955i
$37$	−61.1896			−1.65377			−0.826886	−	0.562369i	$-0.809890\pi$
$37$	−61.1896			−1.65377			−0.826886	+	0.562369i	$0.809890\pi$
$38$	8.65756	+	1.02307i	0.227830	+	0.0269229i
$39$		−	34.2273i		−	0.877622i
$40$	2.25636	−	6.12657i	0.0564090	−	0.153164i
$41$	53.7702			1.31147			0.655734	−	0.754992i	$-0.272359\pi$
$41$	53.7702			1.31147			0.655734	+	0.754992i	$0.272359\pi$
$42$	1.33847	−	11.3266i	0.0318684	−	0.269681i
$43$			23.1601i			0.538607i	0.963055	+	0.269304i	$0.0867935\pi$
$43$			23.1601i			0.538607i	−0.963055	+	0.269304i	$0.913207\pi$
$44$	−14.5150	+	60.5579i	−0.329887	+	1.37632i
$45$	2.44832			0.0544072
$46$	20.1624	+	2.38261i	0.438314	+	0.0517959i
$47$			28.3513i			0.603219i	0.953432	+	0.301609i	$0.0975239\pi$
$47$			28.3513i			0.603219i	−0.953432	+	0.301609i	$0.902476\pi$
$48$	−12.5631	+	24.7016i	−0.261732	+	0.514616i
$49$	38.1597			0.778770
$50$	−5.71139	+	48.3316i	−0.114228	+	0.966633i
$51$		−	44.9018i		−	0.880427i
$52$	76.8673	+	18.4242i	1.47822	+	0.354312i
$53$	48.3999			0.913206			0.456603	−	0.889671i	$-0.349066\pi$
$53$	48.3999			0.913206			0.456603	+	0.889671i	$0.349066\pi$
$54$	−10.3205	−	1.21958i	−0.191120	−	0.0225848i
$55$			12.7054i			0.231007i
$56$	24.7167	+	9.10293i	0.441369	+	0.162552i
$57$	−7.54983			−0.132453
$58$	6.96153	−	58.9108i	0.120026	−	1.01570i
$59$		−	9.75362i		−	0.165316i	−0.996578	−	0.0826578i	$-0.973659\pi$
$59$		−	9.75362i		−	0.165316i	0.996578	−	0.0826578i	$-0.0263408\pi$
$60$	−1.31791	+	5.49842i	−0.0219652	+	0.0916404i
$61$	−59.0626			−0.968240			−0.484120	−	0.875002i	$-0.660860\pi$
$61$	−59.0626			−0.968240			−0.484120	+	0.875002i	$0.660860\pi$
$62$	−109.300	−	12.9160i	−1.76290	−	0.208323i
$63$			9.87737i			0.156784i
$64$	−48.7120	−	41.5108i	−0.761124	−	0.648606i
$65$	16.1272			0.248111
$66$	6.32893	−	53.5575i	0.0958928	−	0.811477i
$67$		−	109.748i		−	1.63803i	−0.573774	−	0.819014i	$-0.694521\pi$
$67$		−	109.748i		−	1.63803i	0.573774	−	0.819014i	$-0.305479\pi$
$68$	100.840	+	24.1702i	1.48294	+	0.355444i
$69$	−17.5827			−0.254821
$70$	5.33686	+	0.630661i	0.0762409	+	0.00900945i
$71$			71.0816i			1.00115i	0.865694	+	0.500574i	$0.166878\pi$
$71$			71.0816i			1.00115i	−0.865694	+	0.500574i	$0.833122\pi$
$72$	8.29435	−	22.5212i	0.115199	−	0.312794i
$73$	70.6749			0.968150			0.484075	−	0.875027i	$-0.339156\pi$
$73$	70.6749			0.968150			0.484075	+	0.875027i	$0.339156\pi$
$74$	−14.3617	+	121.534i	−0.194077	+	1.64235i
$75$		−	42.1477i		−	0.561969i
$76$	4.06400	−	16.9553i	0.0534737	−	0.223097i
$77$	−51.2579			−0.665687
$78$	−67.9815	−	8.03343i	−0.871558	−	0.102993i
$79$		−	85.1124i		−	1.07737i	−0.842506	−	0.538686i	$-0.818921\pi$
$79$		−	85.1124i		−	1.07737i	0.842506	−	0.538686i	$-0.181079\pi$
$80$	−11.6389	−	5.91950i	−0.145486	−	0.0739937i
$81$	9.00000			0.111111
$82$	12.6203	−	106.797i	0.153906	−	1.30241i
$83$		−	99.6812i		−	1.20098i	−0.799633	−	0.600489i	$-0.794973\pi$
$83$		−	99.6812i		−	1.20098i	0.799633	−	0.600489i	$-0.205027\pi$
$84$	−22.1825	−	5.31689i	−0.264077	−	0.0632964i
$85$	21.1568			0.248904
$86$	46.0001	+	5.43587i	0.534885	+	0.0632078i
$87$			51.3732i			0.590497i
$88$	116.872	+	43.0429i	1.32809	+	0.489124i
$89$	−0.665467			−0.00747715			−0.00373858	−	0.999993i	$-0.501190\pi$
$89$	−0.665467			−0.00747715			−0.00373858	+	0.999993i	$0.501190\pi$
$90$	0.574642	−	4.86281i	0.00638491	−	0.0540312i
$91$			65.0626i			0.714974i
$92$	9.46458	−	39.4870i	0.102876	−	0.429206i
$93$	95.3150			1.02489
$94$	56.3108	+	6.65429i	0.599051	+	0.0707903i
$95$		−	3.55733i		−	0.0374456i
$96$	46.1131	+	30.7503i	0.480345	+	0.320316i
$97$	−40.5229			−0.417762			−0.208881	−	0.977941i	$-0.566982\pi$
$97$	−40.5229			−0.417762			−0.208881	+	0.977941i	$0.566982\pi$
$98$	8.95641	−	75.7921i	0.0913919	−	0.773389i
$99$			46.7048i			0.471766i
$100$	94.6549	+	22.6877i	0.946549	+	0.226877i
$101$	66.0069			0.653534			0.326767	−	0.945105i	$-0.394041\pi$
$101$	66.0069			0.653534			0.326767	+	0.945105i	$0.394041\pi$
$102$	−89.1830	−	10.5388i	−0.874343	−	0.103322i
$103$			136.173i			1.32207i	0.750356	+	0.661035i	$0.229882\pi$
$103$			136.173i			1.32207i	−0.750356	+	0.661035i	$0.770118\pi$
$104$	54.6352	−	148.348i	0.525338	−	1.42642i
$105$	−4.65402			−0.0443240
$106$	11.3599	−	96.1309i	0.107169	−	0.906896i
$107$		−	54.1371i		−	0.505954i	−0.967472	−	0.252977i	$-0.918590\pi$
$107$		−	54.1371i		−	0.505954i	0.967472	−	0.252977i	$-0.0814097\pi$
$108$	−4.84461	+	20.2121i	−0.0448575	+	0.187149i
$109$	−113.235			−1.03885			−0.519426	−	0.854515i	$-0.673854\pi$
$109$	−113.235			−1.03885			−0.519426	+	0.854515i	$0.673854\pi$
$110$	25.2352	+	2.98206i	0.229411	+	0.0271097i
$111$		−	105.983i		−	0.954806i
$112$	23.8813	−	46.9552i	0.213226	−	0.419243i
$113$	−86.1843			−0.762693			−0.381347	−	0.924432i	$-0.624540\pi$
$113$	−86.1843			−0.762693			−0.381347	+	0.924432i	$0.624540\pi$
$114$	−1.77201	+	14.9953i	−0.0155439	+	0.131538i
$115$		−	8.28460i		−	0.0720400i
$116$	−115.373	−	27.6537i	−0.994599	−	0.238394i
$117$	59.2833			0.506695
$118$	−19.3724	−	2.28926i	−0.164173	−	0.0194005i
$119$			85.3538i			0.717259i
$120$	10.6115	+	3.90813i	0.0884294	+	0.0325678i
$121$	−121.371			−1.00307
$122$	−13.8625	+	117.309i	−0.113627	+	0.961549i
$123$			93.1327i			0.757176i
$124$	−51.3072	+	214.058i	−0.413767	+	1.72627i
$125$	40.2618			0.322095
$126$	19.6182	+	2.31830i	0.155700	+	0.0183992i
$127$			50.7676i			0.399745i	0.979822	+	0.199872i	$0.0640528\pi$
$127$			50.7676i			0.399745i	−0.979822	+	0.199872i	$0.935947\pi$
$128$	−93.8810	+	87.0078i	−0.733445	+	0.679748i
$129$	−40.1145			−0.310965
$130$	3.78519	−	32.0315i	0.0291168	−	0.246396i
$131$			139.546i			1.06523i	0.846357	+	0.532617i	$0.178791\pi$
$131$			139.546i			1.06523i	−0.846357	+	0.532617i	$0.821209\pi$
$132$	−104.889	−	25.1408i	−0.794616	−	0.190460i
$133$	14.3515			0.107906
$134$	−217.979	−	25.7587i	−1.62671	−	0.192229i
$135$			4.24062i			0.0314120i
$136$	71.6743	−	194.613i	0.527017	−	1.43098i
$137$	205.186			1.49771			0.748854	−	0.662735i	$-0.230604\pi$
$137$	205.186			1.49771			0.748854	+	0.662735i	$0.230604\pi$
$138$	−4.12680	+	34.9223i	−0.0299043	+	0.253060i
$139$			117.722i			0.846919i	0.905915	+	0.423459i	$0.139184\pi$
$139$			117.722i			0.846919i	−0.905915	+	0.423459i	$0.860816\pi$
$140$	2.50521	−	10.4520i	0.0178944	−	0.0746568i
$141$	−49.1059			−0.348269
$142$	141.181	+	16.6834i	0.994231	+	0.117489i
$143$			307.647i			2.15137i
$144$	−42.7844	−	21.7600i	−0.297114	−	0.151111i
$145$	−24.2060			−0.166938
$146$	16.5880	−	140.373i	0.113616	−	0.961460i
$147$			66.0946i			0.449623i
$148$	238.017	+	57.0499i	1.60822	+	0.385472i
$149$	−48.2812			−0.324035			−0.162017	−	0.986788i	$-0.551800\pi$
$149$	−48.2812			−0.324035			−0.162017	+	0.986788i	$0.551800\pi$
$150$	−83.7129	−	9.89241i	−0.558086	−	0.0659494i
$151$			51.4770i			0.340907i	0.985366	+	0.170454i	$0.0545233\pi$
$151$			51.4770i			0.340907i	−0.985366	+	0.170454i	$0.945477\pi$
$152$	−32.7225	−	12.0514i	−0.215280	−	0.0792856i
$153$	77.7721			0.508314
$154$	−12.0307	+	101.807i	−0.0781212	+	0.661087i
$155$			44.9105i			0.289745i
$156$	−31.9117	+	133.138i	−0.204562	+	0.853449i
$157$	−243.445			−1.55060			−0.775301	−	0.631592i	$-0.782402\pi$
$157$	−243.445			−1.55060			−0.775301	+	0.631592i	$0.782402\pi$
$158$	−169.049	−	19.9766i	−1.06993	−	0.126434i
$159$			83.8311i			0.527240i
$160$	−14.4889	+	21.7276i	−0.0905558	+	0.135797i
$161$	33.4229			0.207596
$162$	2.11238	−	17.8756i	0.0130394	−	0.110343i
$163$		−	195.049i		−	1.19662i	−0.801265	−	0.598309i	$-0.795840\pi$
$163$		−	195.049i		−	1.19662i	0.801265	−	0.598309i	$-0.204160\pi$
$164$	−209.157	−	50.1325i	−1.27535	−	0.305686i
$165$	−22.0064			−0.133372
$166$	−197.985	−	23.3960i	−1.19268	−	0.140940i
$167$		−	151.865i		−	0.909372i	−0.890652	−	0.454686i	$-0.849751\pi$
$167$		−	151.865i		−	0.909372i	0.890652	−	0.454686i	$-0.150249\pi$
$168$	−15.7667	+	42.8105i	−0.0938496	+	0.254825i
$169$	221.502			1.31066
$170$	4.96568	−	42.0212i	0.0292099	−	0.247184i
$171$		−	13.0767i		−	0.0764719i
$172$	21.5932	−	90.0887i	0.125542	−	0.523772i
$173$	−336.868			−1.94721			−0.973606	−	0.228237i	$-0.926704\pi$
$173$	−336.868			−1.94721			−0.973606	+	0.228237i	$0.926704\pi$
$174$	102.036	+	12.0577i	0.586416	+	0.0692973i
$175$			80.1185i			0.457820i
$176$	112.922	−	222.026i	0.641601	−	1.26151i
$177$	16.8938			0.0954450
$178$	−0.156191	+	1.32174i	−0.000877475	+	0.00742549i
$179$		−	142.007i		−	0.793333i	−0.917963	−	0.396667i	$-0.870167\pi$
$179$		−	142.007i		−	0.793333i	0.917963	−	0.396667i	$-0.129833\pi$
$180$	−9.52355	−	2.28269i	−0.0529086	−	0.0126816i
$181$	−95.1500			−0.525691			−0.262845	−	0.964838i	$-0.584661\pi$
$181$	−95.1500			−0.525691			−0.262845	+	0.964838i	$0.584661\pi$
$182$	129.226	+	15.2707i	0.710033	+	0.0839052i
$183$		−	102.299i		−	0.559013i
$184$	−76.2069	−	28.0663i	−0.414168	−	0.152534i
$185$	49.9373			0.269931
$186$	22.3712	−	189.313i	0.120275	−	1.01781i
$187$			403.593i			2.15825i
$188$	26.4332	−	110.282i	0.140602	−	0.586604i
$189$	−17.1081			−0.0905191
$190$	−7.06550	−	0.834936i	−0.0371868	−	0.00439440i
$191$		−	144.964i		−	0.758975i	−0.925197	−	0.379488i	$-0.876100\pi$
$191$		−	144.964i		−	0.758975i	0.925197	−	0.379488i	$-0.123900\pi$
$192$	71.8988	−	84.3716i	0.374473	−	0.439435i
$193$	138.191			0.716014			0.358007	−	0.933719i	$-0.383456\pi$
$193$	138.191			0.716014			0.358007	+	0.933719i	$0.383456\pi$
$194$	−9.51107	+	80.4858i	−0.0490261	+	0.414875i
$195$			27.9331i			0.143247i
$196$	−148.435	−	35.5781i	−0.757320	−	0.181521i
$197$	−53.6721			−0.272447			−0.136223	−	0.990678i	$-0.543497\pi$
$197$	−53.6721			−0.272447			−0.136223	+	0.990678i	$0.543497\pi$
$198$	92.7642	+	10.9620i	0.468506	+	0.0553637i
$199$			73.7233i			0.370469i	0.982694	+	0.185234i	$0.0593044\pi$
$199$			73.7233i			0.370469i	−0.982694	+	0.185234i	$0.940696\pi$
$200$	67.2781	−	182.677i	0.336391	−	0.913383i
$201$	190.089			0.945715
$202$	15.4924	−	131.102i	0.0766949	−	0.649018i
$203$		−	97.6553i		−	0.481061i
$204$	−41.8640	+	174.660i	−0.205216	+	0.856176i
$205$	−43.8823			−0.214060
$206$	270.464	+	31.9610i	1.31293	+	0.155150i
$207$		−	30.4541i		−	0.147121i
$208$	−281.822	−	143.334i	−1.35492	−	0.689105i
$209$	67.8606			0.324692
$210$	−1.09234	+	9.24372i	−0.00520161	+	0.0440177i
$211$		−	333.141i		−	1.57887i	−0.613837	−	0.789433i	$-0.710375\pi$
$211$		−	333.141i		−	1.57887i	0.613837	−	0.789433i	$-0.289625\pi$
$212$	−188.267	−	45.1255i	−0.888052	−	0.212856i
$213$	−123.117			−0.578014
$214$	−107.526	−	12.7064i	−0.502458	−	0.0593758i
$215$		−	18.9011i		−	0.0879123i
$216$	39.0078	+	14.3662i	0.180592	+	0.0665103i
$217$	−181.184			−0.834951
$218$	−26.5772	+	224.905i	−0.121914	+	1.03167i
$219$			122.413i			0.558962i
$220$	11.8458	−	49.4217i	0.0538447	−	0.224644i
$221$	512.288			2.31804
$222$	−210.502	−	24.8752i	−0.948208	−	0.112051i
$223$			93.9611i			0.421350i	0.977556	+	0.210675i	$0.0675662\pi$
$223$			93.9611i			0.421350i	−0.977556	+	0.210675i	$0.932434\pi$
$224$	−87.6564	−	58.4533i	−0.391323	−	0.260952i
$225$	73.0019			0.324453
$226$	−20.2282	+	171.178i	−0.0895053	+	0.757423i
$227$			85.9987i			0.378849i	0.981895	+	0.189425i	$0.0606622\pi$
$227$			85.9987i			0.378849i	−0.981895	+	0.189425i	$0.939338\pi$
$228$	29.3675	+	7.03906i	0.128805	+	0.0308731i
$229$	−282.865			−1.23522			−0.617609	−	0.786485i	$-0.711899\pi$
$229$	−282.865			−1.23522			−0.617609	+	0.786485i	$0.711899\pi$
$230$	−16.4547	−	1.94447i	−0.0715422	−	0.00845420i
$231$		−	88.7813i		−	0.384334i
$232$	−82.0044	+	222.662i	−0.353467	+	0.959750i
$233$	−14.3935			−0.0617746			−0.0308873	−	0.999523i	$-0.509833\pi$
$233$	−14.3935			−0.0617746			−0.0308873	+	0.999523i	$0.509833\pi$
$234$	13.9143	−	117.747i	0.0594628	−	0.503194i
$235$		−	23.1377i		−	0.0984583i
$236$	−9.09375	+	37.9399i	−0.0385328	+	0.160762i
$237$	147.419			0.622021
$238$	169.528	+	20.0332i	0.712302	+	0.0841733i
$239$		−	405.618i		−	1.69715i	−0.529077	−	0.848574i	$-0.677462\pi$
$239$		−	405.618i		−	1.69715i	0.529077	−	0.848574i	$-0.322538\pi$
$240$	10.2529	−	20.1591i	0.0427203	−	0.0839964i
$241$	−68.6981			−0.285054			−0.142527	−	0.989791i	$-0.545523\pi$
$241$	−68.6981			−0.285054			−0.142527	+	0.989791i	$0.545523\pi$
$242$	−28.4869	+	241.065i	−0.117714	+	0.996138i
$243$			15.5885i			0.0641500i
$244$	229.743	+	55.0668i	0.941570	+	0.225684i
$245$	−31.1425			−0.127112
$246$	184.978	+	21.8590i	0.751944	+	0.0888579i
$247$		−	86.1367i		−	0.348732i
$248$	413.115	+	152.146i	1.66578	+	0.613493i
$249$	172.653			0.693385
$250$	9.44979	−	79.9673i	0.0377992	−	0.319869i
$251$		−	150.734i		−	0.600532i	−0.953856	−	0.300266i	$-0.902925\pi$
$251$		−	150.734i		−	0.600532i	0.953856	−	0.300266i	$-0.0970754\pi$
$252$	9.20913	−	38.4212i	0.0365442	−	0.152465i
$253$	158.039			0.624661
$254$	100.834	+	11.9156i	0.396983	+	0.0469117i
$255$			36.6447i			0.143705i
$256$	150.778	+	206.886i	0.588978	+	0.808149i
$257$	121.100			0.471206			0.235603	−	0.971849i	$-0.424293\pi$
$257$	121.100			0.471206			0.235603	+	0.971849i	$0.424293\pi$
$258$	−9.41521	+	79.6746i	−0.0364931	+	0.308816i
$259$			201.464i			0.777853i
$260$	−62.7320	−	15.0361i	−0.241277	−	0.0578313i
$261$	−88.9810			−0.340923
$262$	277.163	+	32.7525i	1.05787	+	0.125010i
$263$		−	330.124i		−	1.25522i	−0.778527	−	0.627611i	$-0.784033\pi$
$263$		−	330.124i		−	1.25522i	0.778527	−	0.627611i	$-0.215967\pi$
$264$	−74.5525	+	202.428i	−0.282396	+	0.766774i
$265$	−39.4995			−0.149055
$266$	3.36841	−	28.5046i	0.0126632	−	0.107160i
$267$		−	1.15262i		−	0.00431694i
$268$	−102.323	+	426.900i	−0.381802	+	1.59291i
$269$	−176.239			−0.655163			−0.327582	−	0.944823i	$-0.606234\pi$
$269$	−176.239			−0.655163			−0.327582	+	0.944823i	$0.606234\pi$
$270$	8.42264	+	0.995309i	0.0311949	+	0.00368633i
$271$			46.1948i			0.170460i	0.996361	+	0.0852302i	$0.0271626\pi$
$271$			46.1948i			0.170460i	−0.996361	+	0.0852302i	$0.972837\pi$
$272$	−369.715	−	188.036i	−1.35925	−	0.691307i
$273$	−112.692			−0.412790
$274$	48.1589	−	407.536i	0.175762	−	1.48736i
$275$			378.838i			1.37759i
$276$	68.3935	+	16.3931i	0.247802	+	0.0593954i
$277$	−95.3665			−0.344283			−0.172142	−	0.985072i	$-0.555069\pi$
$277$	−95.3665			−0.344283			−0.172142	+	0.985072i	$0.555069\pi$
$278$	233.817	+	27.6303i	0.841067	+	0.0993895i
$279$			165.090i			0.591722i
$280$	−20.1715	−	7.42897i	−0.0720410	−	0.0265320i
$281$	0.420799			0.00149750			0.000748752	−	1.00000i	$-0.499762\pi$
$281$	0.420799			0.00149750			0.000748752		1.00000i	$0.499762\pi$
$282$	−11.5256	+	97.5331i	−0.0408708	+	0.345862i
$283$			304.285i			1.07521i	0.843196	+	0.537606i	$0.180671\pi$
$283$			304.285i			1.07521i	−0.843196	+	0.537606i	$0.819329\pi$
$284$	66.2727	−	276.495i	0.233354	−	0.973573i
$285$	6.16148			0.0216192
$286$	611.042	+	72.2072i	2.13651	+	0.252473i
$287$		−	177.036i		−	0.616850i
$288$	−53.2611	+	79.8702i	−0.184934	+	0.277327i
$289$	383.056			1.32545
$290$	−5.68136	+	48.0775i	−0.0195909	+	0.165785i
$291$		−	70.1878i		−	0.241195i
$292$	−274.913	−	65.8935i	−0.941483	−	0.225663i
$293$	−391.175			−1.33507			−0.667534	−	0.744579i	$-0.732650\pi$
$293$	−391.175			−1.33507			−0.667534	+	0.744579i	$0.732650\pi$
$294$	131.276	+	15.5130i	0.446516	+	0.0527652i
$295$			7.96000i			0.0269831i
$296$	169.176	−	459.354i	0.571540	−	1.55187i
$297$	−80.8952			−0.272374
$298$	−11.3320	+	95.8952i	−0.0380269	+	0.321796i
$299$		−	200.602i		−	0.670910i
$300$	−39.2962	+	163.947i	−0.130987	+	0.546490i
$301$	76.2536			0.253334
$302$	102.243	+	12.0821i	0.338552	+	0.0400069i
$303$			114.327i			0.377318i
$304$	−31.6165	+	62.1643i	−0.104002	+	0.204488i
$305$	48.2015			0.158038
$306$	18.2538	−	154.469i	0.0596528	−	0.504802i
$307$		−	410.655i		−	1.33764i	−0.743424	−	0.668820i	$-0.766800\pi$
$307$		−	410.655i		−	1.33764i	0.743424	−	0.668820i	$-0.233200\pi$
$308$	199.384	+	47.7901i	0.647351	+	0.155163i
$309$	−235.859			−0.763297
$310$	89.2004	+	10.5409i	0.287743	+	0.0340028i
$311$			209.338i			0.673112i	0.941663	+	0.336556i	$0.109262\pi$
$311$			209.338i			0.673112i	−0.941663	+	0.336556i	$0.890738\pi$
$312$	256.946	+	94.6309i	0.823545	+	0.303304i
$313$	129.382			0.413361			0.206680	−	0.978409i	$-0.433734\pi$
$313$	129.382			0.413361			0.206680	+	0.978409i	$0.433734\pi$
$314$	−57.1385	+	483.525i	−0.181970	+	1.53989i
$315$		−	8.06100i		−	0.0255905i
$316$	−79.3543	+	331.072i	−0.251121	+	1.04770i
$317$	325.429			1.02659			0.513295	−	0.858212i	$-0.328425\pi$
$317$	325.429			1.02659			0.513295	+	0.858212i	$0.328425\pi$
$318$	166.504	+	19.6759i	0.523596	+	0.0618738i
$319$		−	461.760i		−	1.44752i
$320$	39.7542	+	33.8773i	0.124232	+	0.105866i
$321$	93.7682			0.292113
$322$	7.84464	−	66.3839i	0.0243622	−	0.206161i
$323$		−	113.000i		−	0.349846i
$324$	−35.0084	−	8.39112i	−0.108051	−	0.0258985i
$325$	480.866			1.47959
$326$	−387.402	−	45.7796i	−1.18835	−	0.140428i
$327$		−	196.129i		−	0.599781i
$328$	−148.663	+	403.656i	−0.453241	+	1.23066i
$329$	93.3454			0.283725
$330$	−5.16509	+	43.7087i	−0.0156518	+	0.132450i
$331$		−	174.484i		−	0.527141i	−0.964640	−	0.263570i	$-0.915100\pi$
$331$		−	174.484i		−	0.527141i	0.964640	−	0.263570i	$-0.0849001\pi$
$332$	−92.9374	+	387.742i	−0.279932	+	1.16790i
$333$	183.569			0.551258
$334$	−301.632	−	35.6440i	−0.903088	−	0.106719i
$335$			89.5660i			0.267361i
$336$	81.3289	+	41.3636i	0.242050	+	0.123106i
$337$	−156.874			−0.465502			−0.232751	−	0.972536i	$-0.574773\pi$
$337$	−156.874			−0.465502			−0.232751	+	0.972536i	$0.574773\pi$
$338$	51.9883	−	439.942i	0.153812	−	1.30160i
$339$		−	149.276i		−	0.440341i
$340$	−82.2963	−	19.7255i	−0.242048	−	0.0580161i
$341$	−856.725			−2.51239
$342$	−25.9727	−	3.06921i	−0.0759435	−	0.00897430i
$343$		−	286.970i		−	0.836646i
$344$	−173.864	−	64.0327i	−0.505420	−	0.186141i
$345$	14.3494			0.0415923
$346$	−79.0657	+	669.080i	−0.228513	+	1.93376i
$347$		−	227.553i		−	0.655772i	−0.944717	−	0.327886i	$-0.893664\pi$
$347$		−	227.553i		−	0.655772i	0.944717	−	0.327886i	$-0.106336\pi$
$348$	47.8976	−	199.833i	0.137637	−	0.574232i
$349$	405.125			1.16082			0.580408	−	0.814326i	$-0.302893\pi$
$349$	405.125			1.16082			0.580408	+	0.814326i	$0.302893\pi$
$350$	159.130	+	18.8045i	0.454657	+	0.0537271i
$351$			102.682i			0.292541i
$352$	−414.481	−	276.395i	−1.17750	−	0.785212i
$353$	480.596			1.36146			0.680730	−	0.732534i	$-0.261663\pi$
$353$	480.596			1.36146			0.680730	+	0.732534i	$0.261663\pi$
$354$	3.96511	−	33.5541i	0.0112009	−	0.0947855i
$355$		−	58.0102i		−	0.163409i
$356$	2.58855	+	0.620445i	0.00727120	+	0.00174282i
$357$	−147.837			−0.414109
$358$	−282.051	−	33.3302i	−0.787852	−	0.0931010i
$359$			315.194i			0.877979i	0.898492	+	0.438990i	$0.144663\pi$
$359$			315.194i			0.877979i	−0.898492	+	0.438990i	$0.855337\pi$
$360$	−6.76908	+	18.3797i	−0.0188030	+	0.0510548i
$361$	−19.0000			−0.0526316
$362$	−22.3325	+	188.985i	−0.0616920	+	0.522058i
$363$		−	210.221i		−	0.579122i
$364$	60.6609	−	253.082i	0.166651	−	0.695280i
$365$	−57.6784			−0.158023
$366$	−203.185	−	24.0105i	−0.555151	−	0.0656026i
$367$			88.3725i			0.240797i	0.992726	+	0.120398i	$0.0384172\pi$
$367$			88.3725i			0.240797i	−0.992726	+	0.120398i	$0.961583\pi$
$368$	−73.6311	+	144.773i	−0.200085	+	0.393405i
$369$	−161.311			−0.437156
$370$	11.7207	−	99.1845i	0.0316776	−	0.268066i
$371$		−	159.355i		−	0.429527i
$372$	−370.759	−	88.8666i	−0.996663	−	0.238889i
$373$	−211.889			−0.568066			−0.284033	−	0.958815i	$-0.591673\pi$
$373$	−211.889			−0.568066			−0.284033	+	0.958815i	$0.591673\pi$
$374$	801.608	+	94.7266i	2.14334	+	0.253280i
$375$			69.7355i			0.185961i
$376$	−212.835	−	78.3851i	−0.566050	−	0.208471i
$377$	−586.121			−1.55470
$378$	−4.01542	+	33.9798i	−0.0106228	+	0.0898936i
$379$		−	689.793i		−	1.82003i	−0.414571	−	0.910017i	$-0.636069\pi$
$379$		−	689.793i		−	1.82003i	0.414571	−	0.910017i	$-0.363931\pi$
$380$	−3.31667	+	13.8374i	−0.00872807	+	0.0364142i
$381$	−87.9321			−0.230793
$382$	−287.925	−	34.0243i	−0.753731	−	0.0890690i
$383$		−	315.466i		−	0.823670i	−0.911258	−	0.411835i	$-0.864888\pi$
$383$		−	315.466i		−	0.823670i	0.911258	−	0.411835i	$-0.135112\pi$
$384$	−150.702	−	162.607i	−0.392453	−	0.423455i
$385$	41.8320			0.108654
$386$	32.4345	−	274.472i	0.0840273	−	0.711067i
$387$		−	69.4803i		−	0.179536i
$388$	157.627	+	37.7814i	0.406255	+	0.0973748i
$389$	−432.460			−1.11172			−0.555861	−	0.831275i	$-0.687612\pi$
$389$	−432.460			−1.11172			−0.555861	+	0.831275i	$0.687612\pi$
$390$	55.4802	+	6.55614i	0.142257	+	0.0168106i
$391$		−	263.164i		−	0.673054i
$392$	−105.503	+	286.467i	−0.269141	+	0.730784i
$393$	−241.700			−0.615013
$394$	−12.5973	+	106.602i	−0.0319728	+	0.270564i
$395$			69.4609i			0.175850i
$396$	43.5451	−	181.674i	0.109962	−	0.458772i
$397$	50.4777			0.127148			0.0635739	−	0.997977i	$-0.479750\pi$
$397$	50.4777			0.127148			0.0635739	+	0.997977i	$0.479750\pi$
$398$	146.428	+	17.3035i	0.367909	+	0.0434761i
$399$			24.8575i			0.0622995i
$400$	−347.038	−	176.502i	−0.867595	−	0.441256i
$401$	−341.884			−0.852578			−0.426289	−	0.904587i	$-0.640179\pi$
$401$	−341.884			−0.852578			−0.426289	+	0.904587i	$0.640179\pi$
$402$	44.6154	−	377.551i	0.110984	−	0.939181i
$403$			1087.46i			2.69840i
$404$	−256.755	−	61.5413i	−0.635533	−	0.152330i
$405$	−7.34497			−0.0181357
$406$	−193.961	−	22.9205i	−0.477737	−	0.0564545i
$407$			952.617i			2.34058i
$408$	337.080	+	124.144i	0.826177	+	0.304274i
$409$	770.817			1.88464			0.942319	−	0.334717i	$-0.108641\pi$
$409$	770.817			1.88464			0.942319	+	0.334717i	$0.108641\pi$
$410$	−10.2995	+	87.1581i	−0.0251208	+	0.212581i
$411$			355.393i			0.864702i
$412$	126.961	−	529.689i	0.308157	−	1.28565i
$413$	−32.1134			−0.0777563
$414$	−60.4873	−	7.14783i	−0.146105	−	0.0172653i
$415$			81.3506i			0.196026i
$416$	−350.833	+	526.108i	−0.843348	+	1.26468i
$417$	−203.900			−0.488969
$418$	15.9274	−	134.783i	0.0381039	−	0.322448i
$419$		−	38.9943i		−	0.0930652i	−0.998917	−	0.0465326i	$-0.985183\pi$
$419$		−	38.9943i		−	0.0930652i	0.998917	−	0.0465326i	$-0.0148171\pi$
$420$	18.1033	+	4.33916i	0.0431031	+	0.0103313i
$421$	320.214			0.760603			0.380301	−	0.924863i	$-0.375820\pi$
$421$	320.214			0.760603			0.380301	+	0.924863i	$0.375820\pi$
$422$	−661.677	−	78.1909i	−1.56796	−	0.185287i
$423$		−	85.0539i		−	0.201073i
$424$	−133.815	+	363.341i	−0.315602	+	0.856937i
$425$	630.835			1.48432
$426$	−28.8966	+	244.532i	−0.0678323	+	0.574020i
$427$			194.461i			0.455412i
$428$	−50.4745	+	210.584i	−0.117931	+	0.492018i
$429$	−532.859			−1.24210
$430$	−37.5411	−	4.43626i	−0.0873048	−	0.0103169i
$431$			44.3676i			0.102941i	0.998675	+	0.0514706i	$0.0163908\pi$
$431$			44.3676i			0.102941i	−0.998675	+	0.0514706i	$0.983609\pi$
$432$	37.6894	−	74.1047i	0.0872440	−	0.171539i
$433$	−632.976			−1.46184			−0.730919	−	0.682465i	$-0.760908\pi$
$433$	−632.976			−1.46184			−0.730919	+	0.682465i	$0.760908\pi$
$434$	−42.5255	+	359.865i	−0.0979850	+	0.829181i
$435$		−	41.9261i		−	0.0963818i
$436$	440.464	+	105.574i	1.01024	+	0.242142i
$437$	−44.2487			−0.101256
$438$	243.133	+	28.7313i	0.555099	+	0.0655965i
$439$			75.6284i			0.172274i	0.996283	+	0.0861372i	$0.0274523\pi$
$439$			75.6284i			0.172274i	−0.996283	+	0.0861372i	$0.972548\pi$
$440$	−95.3802	−	35.1277i	−0.216773	−	0.0798356i
$441$	−114.479			−0.259590
$442$	120.238	−	1017.50i	0.272032	−	2.30203i
$443$		−	327.197i		−	0.738594i	−0.929311	−	0.369297i	$-0.879598\pi$
$443$		−	327.197i		−	0.738594i	0.929311	−	0.369297i	$-0.120402\pi$
$444$	−98.8133	+	412.257i	−0.222553	+	0.928507i
$445$	0.543092			0.00122043
$446$	186.624	+	22.0535i	0.418439	+	0.0494472i
$447$		−	83.6255i		−	0.187082i
$448$	−136.672	+	160.382i	−0.305072	+	0.357995i
$449$	−382.953			−0.852903			−0.426451	−	0.904511i	$-0.640236\pi$
$449$	−382.953			−0.852903			−0.426451	+	0.904511i	$0.640236\pi$
$450$	17.1342	−	144.995i	0.0380759	−	0.322211i
$451$		−	837.109i		−	1.85612i
$452$	335.242	+	80.3537i	0.741686	+	0.177774i
$453$	−89.1608			−0.196823
$454$	170.809	+	20.1846i	0.376231	+	0.0444595i
$455$		−	53.0981i		−	0.116699i
$456$	20.8737	−	56.6771i	0.0457756	−	0.124292i
$457$	114.895			0.251411			0.125705	−	0.992068i	$-0.459881\pi$
$457$	114.895			0.251411			0.125705	+	0.992068i	$0.459881\pi$
$458$	−66.3908	+	561.821i	−0.144958	+	1.22668i
$459$			134.705i			0.293476i
$460$	−7.72412	+	32.2256i	−0.0167916	+	0.0700557i
$461$	611.366			1.32617			0.663087	−	0.748542i	$-0.269246\pi$
$461$	611.366			1.32617			0.663087	+	0.748542i	$0.269246\pi$
$462$	−176.336	−	20.8377i	−0.381679	−	0.0451033i
$463$		−	3.69002i		−	0.00796981i	−0.999992	−	0.00398490i	$-0.998732\pi$
$463$		−	3.69002i		−	0.00796981i	0.999992	−	0.00398490i	$-0.00126844\pi$
$464$	423.000	+	215.136i	0.911637	+	0.463655i
$465$	−77.7873			−0.167285
$466$	−3.37827	+	28.5880i	−0.00724951	+	0.0613477i
$467$			616.338i			1.31978i	0.751362	+	0.659890i	$0.229397\pi$
$467$			616.338i			1.31978i	−0.751362	+	0.659890i	$0.770603\pi$
$468$	−230.602	−	55.2726i	−0.492739	−	0.118104i
$469$	−361.340			−0.770448
$470$	−45.9557	−	5.43061i	−0.0977780	−	0.0115545i
$471$		−	421.658i		−	0.895241i
$472$	73.2210	+	26.9666i	0.155129	+	0.0571327i
$473$	360.563			0.762290
$474$	34.6005	−	292.801i	0.0729968	−	0.617723i
$475$		−	106.069i		−	0.223304i
$476$	79.5793	−	332.011i	0.167183	−	0.697502i
$477$	−145.200			−0.304402
$478$	−805.631	−	95.2021i	−1.68542	−	0.199167i
$479$			192.403i			0.401676i	0.979624	+	0.200838i	$0.0643665\pi$
$479$			192.403i			0.401676i	−0.979624	+	0.200838i	$0.935634\pi$
$480$	−37.6333	−	25.0956i	−0.0784026	−	0.0522824i
$481$	1209.17			2.51388
$482$	−16.1240	+	136.447i	−0.0334523	+	0.283085i
$483$			57.8902i			0.119855i
$484$	472.113	+	113.160i	0.975441	+	0.233802i
$485$	33.0711			0.0681878
$486$	30.9615	+	3.65874i	0.0637068	+	0.00752828i
$487$		−	204.582i		−	0.420087i	−0.977692	−	0.210043i	$-0.932639\pi$
$487$		−	204.582i		−	0.420087i	0.977692	−	0.210043i	$-0.0673606\pi$
$488$	163.295	−	443.387i	0.334621	−	0.908579i
$489$	337.834			0.690868
$490$	−7.30940	+	61.8545i	−0.0149171	+	0.126234i
$491$			511.737i			1.04223i	0.853485	+	0.521117i	$0.174484\pi$
$491$			511.737i			1.04223i	−0.853485	+	0.521117i	$0.825516\pi$
$492$	86.8320	−	362.270i	0.176488	−	0.736321i
$493$	−768.916			−1.55967
$494$	−171.083	−	20.2170i	−0.346322	−	0.0409251i
$495$		−	38.1162i		−	0.0770024i
$496$	399.152	−	784.810i	0.804741	−	1.58228i
$497$	234.033			0.470891
$498$	40.5231	−	342.920i	0.0813717	−	0.688594i
$499$			519.962i			1.04201i	0.853554	+	0.521004i	$0.174442\pi$
$499$			519.962i			1.04201i	−0.853554	+	0.521004i	$0.825558\pi$
$500$	−156.611	−	37.5380i	−0.313223	−	0.0750760i
$501$	263.038			0.525026
$502$	−299.384	−	35.3784i	−0.596382	−	0.0704749i
$503$			936.121i			1.86108i	0.366196	+	0.930538i	$0.380660\pi$
$503$			936.121i			1.86108i	−0.366196	+	0.930538i	$0.619340\pi$
$504$	−74.1500	−	27.3088i	−0.147123	−	0.0541841i
$505$	−53.8687			−0.106671
$506$	37.0931	−	313.894i	0.0733066	−	0.620344i
$507$			383.652i			0.756710i
$508$	47.3330	−	197.477i	0.0931752	−	0.388734i
$509$	−835.038			−1.64055			−0.820273	−	0.571972i	$-0.806178\pi$
$509$	−835.038			−1.64055			−0.820273	+	0.571972i	$0.806178\pi$
$510$	72.7829	+	8.60081i	0.142712	+	0.0168643i
$511$		−	232.694i		−	0.455370i
$512$	446.302	−	250.915i	0.871684	−	0.490069i
$513$	22.6495			0.0441511
$514$	28.4232	−	240.526i	0.0552980	−	0.467950i
$515$		−	111.132i		−	0.215790i
$516$	156.038	+	37.4006i	0.302400	+	0.0724818i
$517$	441.381			0.853735
$518$	400.144	+	47.2853i	0.772479	+	0.0912844i
$519$		−	583.472i		−	1.12422i
$520$	−44.5882	+	121.068i	−0.0857465	+	0.232823i
$521$	553.366			1.06212			0.531061	−	0.847333i	$-0.321793\pi$
$521$	553.366			1.06212			0.531061	+	0.847333i	$0.321793\pi$
$522$	−20.8846	+	176.732i	−0.0400088	+	0.338568i
$523$			914.696i			1.74894i	0.485080	+	0.874470i	$0.338791\pi$
$523$			914.696i			1.74894i	−0.485080	+	0.874470i	$0.661209\pi$
$524$	130.105	−	542.808i	0.248292	−	1.03589i
$525$	−138.769			−0.264323
$526$	−655.685	−	77.4828i	−1.24655	−	0.147306i
$527$			1426.60i			2.70703i
$528$	384.561	+	195.586i	0.728335	+	0.370429i
$529$	425.950			0.805198
$530$	−9.27087	+	78.4532i	−0.0174922	+	0.148025i
$531$			29.2609i			0.0551052i
$532$	−55.8247	−	13.3806i	−0.104934	−	0.0251514i
$533$	−1062.56			−1.99354
$534$	−2.28931	−	0.270530i	−0.00428711	−	0.000506611i
$535$			44.1817i			0.0825826i
$536$	823.884	+	303.429i	1.53710	+	0.566099i
$537$	245.963			0.458031
$538$	−41.3648	+	350.042i	−0.0768862	+	0.650636i
$539$		−	594.081i		−	1.10219i
$540$	3.95373	−	16.4953i	0.00732172	−	0.0305468i
$541$	44.8570			0.0829149			0.0414574	−	0.999140i	$-0.486800\pi$
$541$	44.8570			0.0829149			0.0414574	+	0.999140i	$0.486800\pi$
$542$	91.7512	+	10.8423i	0.169283	+	0.0200043i
$543$		−	164.805i		−	0.303508i
$544$	−460.248	+	690.186i	−0.846043	+	1.26872i
$545$	92.4118			0.169563
$546$	−26.4497	+	223.826i	−0.0484427	+	0.409938i
$547$			900.669i			1.64656i	0.567634	+	0.823281i	$0.307859\pi$
$547$			900.669i			1.64656i	−0.567634	+	0.823281i	$0.692141\pi$
$548$	−798.137	−	191.304i	−1.45646	−	0.349096i
$549$	177.188			0.322747
$550$	752.441	+	88.9165i	1.36807	+	0.161666i
$551$			129.286i			0.234640i
$552$	48.6123	−	131.994i	0.0880657	−	0.239120i
$553$	−280.229			−0.506743
$554$	−22.3833	+	189.415i	−0.0404031	+	0.341904i
$555$			86.4939i			0.155845i
$556$	109.757	−	457.917i	0.197405	−	0.823591i
$557$	50.4140			0.0905098			0.0452549	−	0.998975i	$-0.485590\pi$
$557$	50.4140			0.0905098			0.0452549	+	0.998975i	$0.485590\pi$
$558$	327.899	+	38.7481i	0.587633	+	0.0694411i
$559$		−	457.670i		−	0.818729i
$560$	−19.4897	+	38.3205i	−0.0348030	+	0.0684295i
$561$	−699.043			−1.24607
$562$	0.0987650	−	0.835782i	0.000175738	−	0.00148716i
$563$		−	489.115i		−	0.868765i	−0.900729	−	0.434382i	$-0.856967\pi$
$563$		−	489.115i		−	0.868765i	0.900729	−	0.434382i	$-0.143033\pi$
$564$	191.013	+	45.7837i	0.338676	+	0.0811767i
$565$	70.3357			0.124488
$566$	604.364	+	71.4182i	1.06778	+	0.126181i
$567$		−	29.6321i		−	0.0522612i
$568$	−533.614	−	196.525i	−0.939461	−	0.345995i
$569$	65.9166			0.115846			0.0579232	−	0.998321i	$-0.481552\pi$
$569$	65.9166			0.115846			0.0579232	+	0.998321i	$0.481552\pi$
$570$	1.44615	−	12.2378i	0.00253711	−	0.0214698i
$571$			532.211i			0.932069i	0.884767	+	0.466034i	$0.154318\pi$
$571$			532.211i			0.932069i	−0.884767	+	0.466034i	$0.845682\pi$
$572$	286.833	−	1196.69i	0.501457	−	2.09212i
$573$	251.086			0.438195
$574$	−351.625	−	41.5518i	−0.612588	−	0.0723900i
$575$		−	247.023i		−	0.429605i
$576$	146.136	+	124.532i	0.253708	+	0.216202i
$577$	−46.5639			−0.0807000			−0.0403500	−	0.999186i	$-0.512847\pi$
$577$	−46.5639			−0.0807000			−0.0403500	+	0.999186i	$0.512847\pi$
$578$	89.9064	−	760.818i	0.155547	−	1.31629i
$579$			239.353i			0.413391i
$580$	94.1572	+	22.5684i	0.162340	+	0.0389110i
$581$	−328.196			−0.564881
$582$	−139.406	−	16.4737i	−0.239528	−	0.0283053i
$583$		−	753.503i		−	1.29246i
$584$	−195.401	+	530.561i	−0.334590	+	0.908495i
$585$	−48.3816			−0.0827036
$586$	−91.8121	+	776.944i	−0.156676	+	1.32584i
$587$			160.827i			0.273981i	0.990572	+	0.136991i	$0.0437430\pi$
$587$			160.827i			0.273981i	−0.990572	+	0.136991i	$0.956257\pi$
$588$	61.6231	−	257.096i	0.104801	−	0.437239i
$589$	239.871			0.407251
$590$	15.8100	+	1.86828i	0.0267966	+	0.00316658i
$591$		−	92.9627i		−	0.157297i
$592$	−872.653	−	443.828i	−1.47408	−	0.749710i
$593$	1035.41			1.74605			0.873027	−	0.487672i	$-0.162154\pi$
$593$	1035.41			1.74605			0.873027	+	0.487672i	$0.162154\pi$
$594$	−18.9868	+	160.672i	−0.0319643	+	0.270492i
$595$		−	69.6579i		−	0.117072i
$596$	187.805	+	45.0148i	0.315110	+	0.0755282i
$597$	−127.692			−0.213890
$598$	−398.432	−	47.0830i	−0.666274	−	0.0787341i
$599$		−	717.950i		−	1.19858i	−0.800532	−	0.599291i	$-0.795449\pi$
$599$		−	717.950i		−	1.19858i	0.800532	−	0.599291i	$-0.204551\pi$
$600$	316.405	+	116.529i	0.527342	+	0.194215i
$601$	788.330			1.31170			0.655848	−	0.754893i	$-0.272311\pi$
$601$	788.330			1.31170			0.655848	+	0.754893i	$0.272311\pi$
$602$	17.8974	−	151.453i	0.0297299	−	0.251584i
$603$			329.243i			0.546009i
$604$	47.9944	−	200.236i	0.0794609	−	0.331517i
$605$	99.0521			0.163722
$606$	227.075	+	26.8336i	0.374711	+	0.0442798i
$607$			43.3374i			0.0713960i	0.999363	+	0.0356980i	$0.0113654\pi$
$607$			43.3374i			0.0713960i	−0.999363	+	0.0356980i	$0.988635\pi$
$608$	116.049	+	77.3866i	0.190870	+	0.127281i
$609$	169.144			0.277741
$610$	11.3133	−	95.7368i	0.0185464	−	0.156946i
$611$		−	560.253i		−	0.916944i
$612$	−302.520	−	72.5106i	−0.494313	−	0.118481i
$613$	246.168			0.401579			0.200790	−	0.979634i	$-0.435649\pi$
$613$	246.168			0.401579			0.200790	+	0.979634i	$0.435649\pi$
$614$	−815.636	−	96.3843i	−1.32840	−	0.156978i
$615$		−	76.0063i		−	0.123588i
$616$	141.717	−	384.796i	0.230060	−	0.624669i
$617$	−1188.91			−1.92693			−0.963464	−	0.267839i	$-0.913691\pi$
$617$	−1188.91			−1.92693			−0.963464	+	0.267839i	$0.913691\pi$
$618$	−55.3580	+	468.458i	−0.0895761	+	0.758023i
$619$		−	72.3812i		−	0.116932i	−0.998289	−	0.0584662i	$-0.981379\pi$
$619$		−	72.3812i		−	0.116932i	0.998289	−	0.0584662i	$-0.0186210\pi$
$620$	41.8722	−	174.694i	0.0675358	−	0.281765i
$621$	52.7480			0.0849404
$622$	415.783	+	49.1334i	0.668461	+	0.0789925i
$623$			2.19102i			0.00351689i
$624$	248.261	−	488.131i	0.397855	−	0.782261i
$625$	575.491			0.920786
$626$	30.3670	−	256.976i	0.0485096	−	0.410505i
$627$			117.538i			0.187461i
$628$	946.956	+	226.975i	1.50789	+	0.361425i
$629$	1586.28			2.52191
$630$	−16.0106	−	1.89198i	−0.0254136	−	0.00300315i
$631$			77.0505i			0.122108i	0.998134	+	0.0610542i	$0.0194463\pi$
$631$			77.0505i			0.122108i	−0.998134	+	0.0610542i	$0.980554\pi$
$632$	638.944	+	235.317i	1.01099	+	0.372338i
$633$	577.017			0.911559
$634$	76.3809	−	646.360i	0.120475	−	1.01950i
$635$		−	41.4318i		−	0.0652470i
$636$	78.1596	−	326.088i	0.122893	−	0.512717i
$637$	−754.079			−1.18380
$638$	−917.139	−	108.379i	−1.43752	−	0.169873i
$639$		−	213.245i		−	0.333716i
$640$	76.6170	−	71.0077i	0.119714	−	0.110950i
$641$	201.980			0.315101			0.157551	−	0.987511i	$-0.449640\pi$
$641$	201.980			0.315101			0.157551	+	0.987511i	$0.449640\pi$
$642$	22.0082	−	186.240i	0.0342807	−	0.290094i
$643$			9.64366i			0.0149979i	0.999972	+	0.00749896i	$0.00238701\pi$
$643$			9.64366i			0.0149979i	−0.999972	+	0.00749896i	$0.997613\pi$
$644$	−130.009	−	31.1617i	−0.201878	−	0.0483878i
$645$	32.7377			0.0507562
$646$	−224.439	−	26.5221i	−0.347429	−	0.0410559i
$647$			218.107i			0.337105i	0.985693	+	0.168553i	$0.0539093\pi$
$647$			218.107i			0.337105i	−0.985693	+	0.168553i	$0.946091\pi$
$648$	−24.8830	+	67.5636i	−0.0383998	+	0.104265i
$649$	−151.847			−0.233971
$650$	112.863	−	955.087i	0.173636	−	1.46936i
$651$		−	313.820i		−	0.482059i
$652$	−181.853	+	758.705i	−0.278916	+	1.16366i
$653$	57.2745			0.0877098			0.0438549	−	0.999038i	$-0.486036\pi$
$653$	57.2745			0.0877098			0.0438549	+	0.999038i	$0.486036\pi$
$654$	−389.547	−	46.0330i	−0.595637	−	0.0703869i
$655$		−	113.884i		−	0.173869i
$656$	766.841	+	390.013i	1.16897	+	0.594532i
$657$	−212.025			−0.322717
$658$	21.9089	−	185.401i	0.0332963	−	0.281764i
$659$			19.7250i			0.0299317i	0.999888	+	0.0149658i	$0.00476395\pi$
$659$			19.7250i			0.0299317i	−0.999888	+	0.0149658i	$0.995236\pi$
$660$	85.6010	+	20.5176i	0.129698	+	0.0310872i
$661$	−2.20237			−0.00333187			−0.00166594	−	0.999999i	$-0.500530\pi$
$661$	−2.20237			−0.00333187			−0.00166594	+	0.999999i	$0.500530\pi$
$662$	−346.556	−	40.9528i	−0.523498	−	0.0618622i
$663$			887.309i			1.33832i
$664$	748.313	+	275.597i	1.12698	+	0.415056i
$665$	−11.7124			−0.0176126
$666$	43.0851	−	364.601i	0.0646924	−	0.547448i
$667$			301.093i			0.451413i
$668$	−141.591	+	590.729i	−0.211962	+	0.884324i
$669$	−162.745			−0.243267
$670$	177.894	+	21.0219i	0.265514	+	0.0313760i
$671$			919.503i			1.37035i
$672$	101.244	−	151.825i	0.150661	−	0.225931i
$673$	−1086.02			−1.61370			−0.806849	−	0.590757i	$-0.798829\pi$
$673$	−1086.02			−1.61370			−0.806849	+	0.590757i	$0.798829\pi$
$674$	−36.8197	+	311.581i	−0.0546287	+	0.462286i
$675$			126.443i			0.187323i
$676$	−861.602	−	206.516i	−1.27456	−	0.305497i
$677$	666.722			0.984818			0.492409	−	0.870364i	$-0.336116\pi$
$677$	666.722			0.984818			0.492409	+	0.870364i	$0.336116\pi$
$678$	−296.488	−	35.0363i	−0.437298	−	0.0516759i
$679$			133.420i			0.196495i
$680$	−58.4940	+	158.825i	−0.0860206	+	0.233567i
$681$	−148.954			−0.218729
$682$	−201.080	+	1701.61i	−0.294839	+	2.49503i
$683$		−	1048.18i		−	1.53467i	−0.641244	−	0.767337i	$-0.721581\pi$
$683$		−	1048.18i		−	1.53467i	0.641244	−	0.767337i	$-0.278419\pi$
$684$	−12.1920	+	50.8660i	−0.0178246	+	0.0743656i
$685$	−167.454			−0.244458
$686$	−569.973	−	67.3542i	−0.830865	−	0.0981839i
$687$		−	489.936i		−	0.713153i
$688$	−167.988	+	330.297i	−0.244168	+	0.480083i
$689$	−956.436			−1.38815
$690$	3.36791	−	28.5004i	0.00488103	−	0.0413049i
$691$		−	316.159i		−	0.457538i	−0.973481	−	0.228769i	$-0.926530\pi$
$691$		−	316.159i		−	0.457538i	0.973481	−	0.228769i	$-0.0734700\pi$
$692$	1310.36	+	314.077i	1.89358	+	0.453869i
$693$	153.774			0.221896
$694$	−451.961	−	53.4086i	−0.651240	−	0.0769576i
$695$		−	96.0736i		−	0.138235i
$696$	−385.662	−	142.036i	−0.554112	−	0.204074i
$697$	−1393.94			−1.99991
$698$	95.0861	−	804.650i	0.136227	−	1.15279i
$699$		−	24.9302i		−	0.0356656i
$700$	74.6982	−	311.647i	0.106712	−	0.445210i
$701$	1185.64			1.69136			0.845681	−	0.533689i	$-0.179195\pi$
$701$	1185.64			1.69136			0.845681	+	0.533689i	$0.179195\pi$
$702$	203.944	+	24.1003i	0.290519	+	0.0343309i
$703$		−	266.719i		−	0.379401i
$704$	−646.252	+	758.361i	−0.917971	+	1.07722i
$705$	40.0757			0.0568449
$706$	112.800	−	954.549i	0.159773	−	1.35205i
$707$		−	217.325i		−	0.307390i
$708$	−65.7138	−	15.7508i	−0.0928160	−	0.0222469i
$709$	278.105			0.392249			0.196125	−	0.980579i	$-0.437164\pi$
$709$	278.105			0.392249			0.196125	+	0.980579i	$0.437164\pi$
$710$	−115.219	−	13.6155i	−0.162280	−	0.0191767i
$711$			255.337i			0.359124i
$712$	1.83987	−	4.99570i	0.00258409	−	0.00701643i
$713$	558.631			0.783493
$714$	−34.6986	+	293.631i	−0.0485975	+	0.411248i
$715$		−	251.073i		−	0.351151i
$716$	−132.399	+	552.381i	−0.184915	+	0.771482i
$717$	702.552			0.979849
$718$	626.033	+	73.9788i	0.871912	+	0.103035i
$719$		−	572.825i		−	0.796697i	−0.917234	−	0.398348i	$-0.869584\pi$
$719$		−	572.825i		−	0.796697i	0.917234	−	0.398348i	$-0.130416\pi$
$720$	34.9167	+	17.7585i	0.0484954	+	0.0246646i
$721$	448.344			0.621836
$722$	−4.45946	+	37.7374i	−0.00617654	+	0.0522679i
$723$		−	118.989i		−	0.164576i
$724$	370.117	+	88.7128i	0.511211	+	0.122531i
$725$	−721.754			−0.995522
$726$	−417.538	−	49.3407i	−0.575121	−	0.0679624i
$727$			460.935i			0.634023i	0.948422	+	0.317011i	$0.102679\pi$
$727$			460.935i			0.634023i	−0.948422	+	0.317011i	$0.897321\pi$
$728$	−488.429	−	179.884i	−0.670919	−	0.247093i
$729$	−27.0000			−0.0370370
$730$	−13.5376	+	114.560i	−0.0185447	+	0.156931i
$731$		−	600.404i		−	0.821345i
$732$	−95.3785	+	397.927i	−0.130299	+	0.543616i
$733$	−169.890			−0.231774			−0.115887	−	0.993262i	$-0.536971\pi$
$733$	−169.890			−0.231774			−0.115887	+	0.993262i	$0.536971\pi$
$734$	175.524	+	20.7418i	0.239133	+	0.0282585i
$735$		−	53.9403i		−	0.0733882i
$736$	270.264	+	180.224i	0.367206	+	0.244870i
$737$	−1708.58			−2.31830
$738$	−37.8610	+	320.392i	−0.0513021	+	0.434135i
$739$		−	746.208i		−	1.00975i	−0.863191	−	0.504877i	$-0.831538\pi$
$739$		−	746.208i		−	1.00975i	0.863191	−	0.504877i	$-0.168462\pi$
$740$	−194.247	−	46.5589i	−0.262496	−	0.0629174i
$741$	149.193			0.201340
$742$	−316.507	−	37.4019i	−0.426559	−	0.0504068i
$743$		−	329.818i		−	0.443900i	−0.975058	−	0.221950i	$-0.928758\pi$
$743$		−	329.818i		−	0.443900i	0.975058	−	0.221950i	$-0.0712421\pi$
$744$	−263.525	+	715.536i	−0.354201	+	0.961741i
$745$	39.4027			0.0528895
$746$	−49.7320	+	420.849i	−0.0666649	+	0.564141i
$747$			299.044i			0.400326i
$748$	376.288	−	1569.90i	0.503059	−	2.09880i
$749$	−178.244			−0.237976
$750$	138.507	+	16.3675i	0.184676	+	0.0218234i
$751$		−	122.104i		−	0.162589i	−0.996690	−	0.0812945i	$-0.974095\pi$
$751$		−	122.104i		−	0.162589i	0.996690	−	0.0812945i	$-0.0259054\pi$
$752$	−205.641	+	404.331i	−0.273459	+	0.537674i
$753$	261.078			0.346717
$754$	−137.568	+	1164.14i	−0.182450	+	1.54396i
$755$		−	42.0108i		−	0.0556434i
$756$	66.5475	+	15.9507i	0.0880258	+	0.0210988i
$757$	−947.703			−1.25192			−0.625960	−	0.779855i	$-0.715293\pi$
$757$	−947.703			−1.25192			−0.625960	+	0.779855i	$0.715293\pi$
$758$	−1370.05	−	161.900i	−1.80746	−	0.213589i
$759$			273.732i			0.360648i
$760$	26.7051	+	9.83525i	0.0351383	+	0.0129411i
$761$	−1205.38			−1.58394			−0.791970	−	0.610560i	$-0.790944\pi$
$761$	−1205.38			−1.58394			−0.791970	+	0.610560i	$0.790944\pi$
$762$	−20.6384	+	174.649i	−0.0270845	+	0.229198i
$763$			372.821i			0.488625i
$764$	−135.157	+	563.886i	−0.176907	+	0.738070i
$765$	−63.4704			−0.0829679
$766$	−626.571	−	74.0424i	−0.817978	−	0.0966611i
$767$			192.742i			0.251294i
$768$	−358.337	+	261.156i	−0.466585	+	0.340047i
$769$	−1269.08			−1.65031			−0.825153	−	0.564910i	$-0.808911\pi$
$769$	−1269.08			−1.65031			−0.825153	+	0.564910i	$0.808911\pi$
$770$	9.81831	−	83.0858i	0.0127511	−	0.107904i
$771$			209.751i			0.272051i
$772$	−537.538	−	128.842i	−0.696293	−	0.166893i
$773$	163.663			0.211725			0.105863	−	0.994381i	$-0.466240\pi$
$773$	163.663			0.211725			0.105863	+	0.994381i	$0.466240\pi$
$774$	−138.000	−	16.3076i	−0.178295	−	0.0210693i
$775$			1339.10i			1.72787i
$776$	112.037	−	304.208i	0.144378	−	0.392021i
$777$	−348.946			−0.449094
$778$	−101.502	+	858.944i	−0.130465	+	1.10404i
$779$			234.379i			0.300871i
$780$	26.0434	−	108.655i	0.0333889	−	0.139301i
$781$	1106.62			1.41692
$782$	−522.691	−	61.7669i	−0.668403	−	0.0789857i
$783$		−	154.120i		−	0.196832i
$784$	544.213	+	276.785i	0.694150	+	0.353042i
$785$	198.677			0.253092
$786$	−56.7290	+	480.060i	−0.0721744	+	0.610763i
$787$			785.121i			0.997612i	0.866714	+	0.498806i	$0.166228\pi$
$787$			785.121i			0.997612i	−0.866714	+	0.498806i	$0.833772\pi$
$788$	208.775	+	50.0410i	0.264943	+	0.0635037i
$789$	571.791			0.724703
$790$	137.962	+	16.3031i	0.174635	+	0.0206368i
$791$			283.758i			0.358733i
$792$	−350.616	−	129.129i	−0.442697	−	0.163041i
$793$	1167.14			1.47181
$794$	11.8475	−	100.258i	0.0149213	−	0.126269i
$795$		−	68.4152i		−	0.0860569i
$796$	68.7356	−	286.770i	0.0863513	−	0.360264i
$797$	45.3468			0.0568969			0.0284484	−	0.999595i	$-0.490943\pi$
$797$	45.3468			0.0568969			0.0284484	+	0.999595i	$0.490943\pi$
$798$	49.3715	+	5.83427i	0.0618690	+	0.00731111i
$799$		−	734.980i		−	0.919875i
$800$	−432.018	+	647.853i	−0.540022	+	0.809817i
$801$	1.99640			0.00249238
$802$	−80.2430	+	679.043i	−0.100054	+	0.846687i
$803$		−	1100.29i		−	1.37022i
$804$	−739.412	−	177.229i	−0.919667	−	0.220434i
$805$	−27.2767			−0.0338841
$806$	2159.89	+	255.235i	2.67976	+	0.316669i
$807$		−	305.255i		−	0.378259i
$808$	−182.495	+	495.518i	−0.225860	+	0.613265i
$809$	1235.45			1.52713			0.763563	−	0.645733i	$-0.223448\pi$
$809$	1235.45			1.52713			0.763563	+	0.645733i	$0.223448\pi$
$810$	−1.72393	+	14.5884i	−0.00212830	+	0.0180104i
$811$		−	637.594i		−	0.786183i	−0.919499	−	0.393091i	$-0.871406\pi$
$811$		−	637.594i		−	0.786183i	0.919499	−	0.393091i	$-0.128594\pi$
$812$	−91.0486	+	379.862i	−0.112129	+	0.467810i
$813$	−80.0117			−0.0984154
$814$	1892.07	+	223.587i	2.32441	+	0.274677i
$815$			159.181i			0.195314i
$816$	325.687	−	640.365i	0.399126	−	0.784760i
$817$	−100.953			−0.123565
$818$	180.917	−	1530.98i	0.221170	−	1.87161i
$819$		−	195.188i		−	0.238325i
$820$	170.694	+	40.9135i	0.208164	+	0.0498945i
$821$	505.166			0.615306			0.307653	−	0.951499i	$-0.400456\pi$
$821$	505.166			0.615306			0.307653	+	0.951499i	$0.400456\pi$
$822$	705.874	+	83.4136i	0.858727	+	0.101476i
$823$		−	1431.07i		−	1.73885i	−0.494066	−	0.869424i	$-0.664490\pi$
$823$		−	1431.07i		−	1.73885i	0.494066	−	0.869424i	$-0.335510\pi$
$824$	−1022.26	−	376.489i	−1.24061	−	0.456904i
$825$	−656.167			−0.795354
$826$	−7.53728	+	63.7829i	−0.00912503	+	0.0772190i
$827$			1327.13i			1.60475i	0.596819	+	0.802376i	$0.296431\pi$
$827$			1327.13i			1.60475i	−0.596819	+	0.802376i	$0.703569\pi$
$828$	−28.3937	+	118.461i	−0.0342920	+	0.143069i
$829$	−847.691			−1.02255			−0.511273	−	0.859418i	$-0.670826\pi$
$829$	−847.691			−1.02255			−0.511273	+	0.859418i	$0.670826\pi$
$830$	161.577	+	19.0937i	0.194671	+	0.0230044i
$831$		−	165.180i		−	0.198772i
$832$	962.602	+	820.299i	1.15697	+	0.985937i
$833$	−989.254			−1.18758
$834$	−47.8570	+	404.982i	−0.0573825	+	0.485590i
$835$			123.938i			0.148429i
$836$	−263.966	−	63.2696i	−0.315748	−	0.0756813i
$837$	−285.945			−0.341631
$838$	−77.4498	−	9.15230i	−0.0924221	−	0.0109216i
$839$			123.848i			0.147613i	0.997273	+	0.0738067i	$0.0235148\pi$
$839$			123.848i			0.147613i	−0.997273	+	0.0738067i	$0.976485\pi$
$840$	12.8674	−	34.9380i	0.0153183	−	0.0415929i
$841$	38.7353			0.0460586
$842$	75.1569	−	636.002i	0.0892600	−	0.755347i
$843$			0.728845i			0.000864585i
$844$	−310.603	+	1295.86i	−0.368012	+	1.53538i
$845$	−180.769			−0.213928
$846$	−168.932	−	19.9629i	−0.199684	−	0.0235968i
$847$			399.610i			0.471794i
$848$	690.253	+	351.060i	0.813978	+	0.413986i
$849$	−527.037			−0.620774
$850$	148.062	−	1252.95i	0.174191	−	1.47406i
$851$		−	621.157i		−	0.729915i
$852$	478.903	+	114.788i	0.562093	+	0.134727i
$853$	−872.815			−1.02323			−0.511615	−	0.859215i	$-0.670952\pi$
$853$	−872.815			−1.02323			−0.511615	+	0.859215i	$0.670952\pi$
$854$	386.235	+	45.6417i	0.452265	+	0.0534446i
$855$			10.6720i			0.0124819i
$856$	406.410	+	149.677i	0.474778	+	0.174857i
$857$	521.820			0.608892			0.304446	−	0.952530i	$-0.401529\pi$
$857$	521.820			0.608892			0.304446	+	0.952530i	$0.401529\pi$
$858$	−125.067	+	1058.36i	−0.145765	+	1.23351i
$859$		−	1135.45i		−	1.32183i	−0.750463	−	0.660913i	$-0.770169\pi$
$859$		−	1135.45i		−	1.32183i	0.750463	−	0.660913i	$-0.229831\pi$
$860$	−17.6224	+	73.5221i	−0.0204912	+	0.0854908i
$861$	306.635			0.356139
$862$	88.1221	+	10.4135i	0.102230	+	0.0120806i
$863$		−	1549.63i		−	1.79563i	−0.440375	−	0.897814i	$-0.645154\pi$
$863$		−	1549.63i		−	1.79563i	0.440375	−	0.897814i	$-0.354846\pi$
$864$	−138.339	−	92.2509i	−0.160115	−	0.106772i
$865$	274.920			0.317827
$866$	−148.565	+	1257.20i	−0.171553	+	1.45174i
$867$			663.472i			0.765250i
$868$	704.775	+	168.927i	0.811953	+	0.194616i
$869$	−1325.05			−1.52480
$870$	−83.2727	−	9.84040i	−0.0957158	−	0.0113108i
$871$			2168.74i			2.48994i
$872$	313.070	−	850.061i	0.359025	−	0.974841i
$873$	121.569			0.139254
$874$	−10.3856	+	87.8860i	−0.0118828	+	0.100556i
$875$		−	132.560i		−	0.151498i
$876$	114.131	−	476.163i	0.130286	−	0.543565i
$877$	1053.54			1.20130			0.600652	−	0.799511i	$-0.294908\pi$
$877$	1053.54			1.20130			0.600652	+	0.799511i	$0.294908\pi$
$878$	150.212	+	17.7506i	0.171084	+	0.0202171i
$879$		−	677.535i		−	0.770802i
$880$	−92.1564	+	181.197i	−0.104723	+	0.205906i
$881$	−911.357			−1.03446			−0.517229	−	0.855847i	$-0.673036\pi$
$881$	−911.357			−1.03446			−0.517229	+	0.855847i	$0.673036\pi$
$882$	−26.8692	+	227.376i	−0.0304640	+	0.257796i
$883$		−	865.793i		−	0.980513i	−0.871578	−	0.490257i	$-0.836903\pi$
$883$		−	865.793i		−	0.980513i	0.871578	−	0.490257i	$-0.163097\pi$
$884$	−1992.71	−	477.630i	−2.25420	−	0.540305i
$885$	−13.7871			−0.0155787
$886$	−649.873	−	76.7960i	−0.733491	−	0.0866772i
$887$		−	192.516i		−	0.217042i	−0.994094	−	0.108521i	$-0.965389\pi$
$887$		−	192.516i		−	0.217042i	0.994094	−	0.108521i	$-0.0346115\pi$
$888$	795.624	+	293.021i	0.895974	+	0.329979i
$889$	167.150			0.188020
$890$	0.127468	−	1.07868i	0.000143223	−	0.00121200i
$891$		−	140.115i		−	0.157255i
$892$	87.6043	−	365.492i	0.0982111	−	0.409744i
$893$	−123.580			−0.138388
$894$	−166.095	−	19.6276i	−0.185789	−	0.0219548i
$895$			115.893i			0.129489i
$896$	286.469	+	309.099i	0.319720	+	0.344977i
$897$	347.453			0.387350
$898$	−89.8824	+	760.614i	−0.100092	+	0.847009i
$899$		−	1632.21i		−	1.81559i
$900$	−283.965	−	68.0631i	−0.315516	−	0.0756256i
$901$	−1254.72			−1.39259
$902$	−1662.65	−	196.477i	−1.84329	−	0.217823i
$903$			132.075i			0.146263i
$904$	238.281	−	646.991i	0.263585	−	0.715698i
$905$	77.6527			0.0858040
$906$	−20.9268	+	177.089i	−0.0230980	+	0.195463i
$907$		−	1212.58i		−	1.33691i	−0.743753	−	0.668454i	$-0.766956\pi$
$907$		−	1212.58i		−	1.33691i	0.743753	−	0.668454i	$-0.233044\pi$
$908$	80.1806	−	334.520i	0.0883046	−	0.368414i
$909$	−198.021			−0.217845
$910$	−105.462	−	12.4626i	−0.115893	−	0.0136951i
$911$			1735.98i			1.90558i	0.303638	+	0.952788i	$0.401799\pi$
$911$			1735.98i			1.90558i	−0.303638	+	0.952788i	$0.598201\pi$
$912$	−107.672	−	54.7614i	−0.118061	−	0.0600454i
$913$	−1551.86			−1.69974
$914$	26.9667	−	228.201i	0.0295041	−	0.249673i
$915$			83.4874i			0.0912430i
$916$	1100.29	+	263.728i	1.20120	+	0.287913i
$917$	459.448			0.501034
$918$	267.549	+	31.6165i	0.291448	+	0.0344406i
$919$			90.7816i			0.0987831i	0.998779	+	0.0493915i	$0.0157282\pi$
$919$			90.7816i			0.0987831i	−0.998779	+	0.0493915i	$0.984272\pi$
$920$	62.1930	+	22.9051i	0.0676011	+	0.0248969i
$921$	711.276			0.772287
$922$	143.493	−	1214.28i	0.155632	−	1.31701i
$923$		−	1404.65i		−	1.52183i
$924$	−82.7749	+	345.343i	−0.0895832	+	0.373748i
$925$	1488.99			1.60971
$926$	−7.32905	−	0.866079i	−0.00791474	−	0.000935291i
$927$		−	408.519i		−	0.440690i
$928$	526.581	−	789.659i	0.567436	−	0.850926i
$929$	1015.99			1.09364			0.546819	−	0.837251i	$-0.315839\pi$
$929$	1015.99			1.09364			0.546819	+	0.837251i	$0.315839\pi$
$930$	−18.2573	+	154.500i	−0.0196315	+	0.166129i
$931$			166.334i			0.178662i
$932$	55.9881	+	13.4197i	0.0600731	+	0.0143988i
$933$	−362.584			−0.388621
$934$	1224.16	+	144.660i	1.31066	+	0.154882i
$935$		−	329.375i		−	0.352273i
$936$	−163.906	+	445.044i	−0.175113	+	0.475474i
$937$	1054.20			1.12508			0.562538	−	0.826771i	$-0.309825\pi$
$937$	1054.20			1.12508			0.562538	+	0.826771i	$0.309825\pi$
$938$	−84.8095	+	717.686i	−0.0904153	+	0.765124i
$939$			224.096i			0.238654i
$940$	−21.5724	+	90.0016i	−0.0229493	+	0.0957464i
$941$	346.337			0.368052			0.184026	−	0.982921i	$-0.441087\pi$
$941$	346.337			0.368052			0.184026	+	0.982921i	$0.441087\pi$
$942$	−837.489	−	98.9668i	−0.889055	−	0.105060i
$943$			545.840i			0.578834i
$944$	70.7462	−	139.101i	0.0749430	−	0.147353i
$945$	13.9621			0.0147747
$946$	84.6272	−	716.143i	0.0894579	−	0.757022i
$947$		−	139.649i		−	0.147464i	−0.997278	−	0.0737321i	$-0.976509\pi$
$947$		−	139.649i		−	0.147464i	0.997278	−	0.0737321i	$-0.0234910\pi$
$948$	−573.434	−	137.446i	−0.604888	−	0.144985i
$949$	−1396.62			−1.47167
$950$	−210.673	−	24.8954i	−0.221761	−	0.0262056i
$951$			563.659i			0.592702i
$952$	−640.756	−	235.985i	−0.673063	−	0.247883i
$953$	1808.86			1.89807			0.949033	−	0.315176i	$-0.102063\pi$
$953$	1808.86			1.89807			0.949033	+	0.315176i	$0.102063\pi$
$954$	−34.0796	+	288.393i	−0.0357228	+	0.302299i
$955$			118.306i			0.123881i
$956$	−378.177	+	1577.78i	−0.395583	+	1.65040i
$957$	799.792			0.835729
$958$	382.147	+	45.1586i	0.398901	+	0.0471384i
$959$		−	675.566i		−	0.704448i
$960$	−58.6772	+	68.8563i	−0.0611220	+	0.0717253i
$961$	−2067.32			−2.15121
$962$	283.803	−	2401.64i	0.295014	−	2.49651i
$963$			162.411i			0.168651i
$964$	267.224	+	64.0505i	0.277203	+	0.0664424i
$965$	−112.779			−0.116869
$966$	114.980	+	13.5873i	0.119027	+	0.0140655i
$967$		−	497.195i		−	0.514163i	−0.966390	−	0.257081i	$-0.917239\pi$
$967$		−	497.195i		−	0.514163i	0.966390	−	0.257081i	$-0.0827609\pi$
$968$	335.565	−	911.142i	0.346659	−	0.941263i
$969$	195.722			0.201984
$970$	7.76206	−	65.6851i	0.00800212	−	0.0677166i
$971$		−	173.070i		−	0.178239i	−0.996021	−	0.0891197i	$-0.971595\pi$
$971$		−	173.070i		−	0.178239i	0.996021	−	0.0891197i	$-0.0284054\pi$
$972$	14.5338	−	60.6364i	0.0149525	−	0.0623831i
$973$	387.594			0.398349
$974$	−406.337	−	48.0172i	−0.417184	−	0.0492990i
$975$			832.885i			0.854241i
$976$	−842.319	−	428.400i	−0.863032	−	0.438935i
$977$	752.733			0.770454			0.385227	−	0.922822i	$-0.374123\pi$
$977$	752.733			0.770454			0.385227	+	0.922822i	$0.374123\pi$
$978$	79.2926	−	671.000i	0.0810762	−	0.686094i
$979$			10.3602i			0.0105824i
$980$	121.139	+	29.0356i	0.123611	+	0.0296281i
$981$	339.705			0.346284
$982$	1016.40	+	120.109i	1.03503	+	0.122311i
$983$		−	582.973i		−	0.593055i	−0.955024	−	0.296527i	$-0.904171\pi$
$983$		−	582.973i		−	0.593055i	0.955024	−	0.296527i	$-0.0958286\pi$
$984$	−699.153	−	257.492i	−0.710521	−	0.261679i
$985$	43.8022			0.0444692
$986$	−180.471	+	1527.20i	−0.183033	+	1.54889i
$987$			161.679i			0.163808i
$988$	−80.3093	+	335.057i	−0.0812847	+	0.339126i
$989$	−235.107			−0.237721
$990$	−75.7056	−	8.94619i	−0.0764703	−	0.00903656i
$991$			66.2484i			0.0668501i	0.999441	+	0.0334250i	$0.0106415\pi$
$991$			66.2484i			0.0668501i	−0.999441	+	0.0334250i	$0.989358\pi$
$992$	−1465.09	−	976.989i	−1.47691	−	0.984868i
$993$	302.214			0.304345
$994$	54.9295	−	464.832i	0.0552611	−	0.467637i
$995$		−	60.1661i		−	0.0604685i
$996$	−671.589	−	160.972i	−0.674287	−	0.161619i
$997$	929.638			0.932435			0.466218	−	0.884670i	$-0.345616\pi$
$997$	929.638			0.932435			0.466218	+	0.884670i	$0.345616\pi$
$998$	1032.74	+	122.040i	1.03481	+	0.122284i
$999$			317.950i			0.318269i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.3.g.a.115.19	✓	36
3.2	odd	2		684.3.g.c.343.18		36
4.3	odd	2	inner	228.3.g.a.115.20	yes	36
12.11	even	2		684.3.g.c.343.17		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.3.g.a.115.19	✓	36	1.1	even	1	trivial
228.3.g.a.115.20	yes	36	4.3	odd	2	inner
684.3.g.c.343.17		36	12.11	even	2
684.3.g.c.343.18		36	3.2	odd	2

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:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	228.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.234708 - 1.98618i) q^{2} +1.73205i q^{3} +(-3.88982 - 0.932347i) q^{4} -0.816108 q^{5} +(3.44017 + 0.406527i) q^{6} -3.29246i q^{7} +(-2.76478 + 7.50706i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(0.234708 - 1.98618i) q^{2} +1.73205i q^{3} +(-3.88982 - 0.932347i) q^{4} -0.816108 q^{5} +(3.44017 + 0.406527i) q^{6} -3.29246i q^{7} +(-2.76478 + 7.50706i) q^{8} -3.00000 q^{9} +(-0.191547 + 1.62094i) q^{10} -15.5683i q^{11} +(1.61487 - 6.73737i) q^{12} -19.7611 q^{13} +(-6.53941 - 0.772767i) q^{14} -1.41354i q^{15} +(14.2615 + 7.25333i) q^{16} -25.9240 q^{17} +(-0.704125 + 5.95854i) q^{18} +4.35890i q^{19} +(3.17452 + 0.760895i) q^{20} +5.70270 q^{21} +(-30.9214 - 3.65401i) q^{22} +10.1514i q^{23} +(-13.0026 - 4.78874i) q^{24} -24.3340 q^{25} +(-4.63810 + 39.2491i) q^{26} -5.19615i q^{27} +(-3.06971 + 12.8071i) q^{28} +29.6603 q^{29} +(-2.80755 - 0.331770i) q^{30} -55.0301i q^{31} +(17.7537 - 26.6234i) q^{32} +26.9651 q^{33} +(-6.08459 + 51.4898i) q^{34} +2.68700i q^{35} +(11.6695 + 2.79704i) q^{36} -61.1896 q^{37} +(8.65756 + 1.02307i) q^{38} -34.2273i q^{39} +(2.25636 - 6.12657i) q^{40} +53.7702 q^{41} +(1.33847 - 11.3266i) q^{42} +23.1601i q^{43} +(-14.5150 + 60.5579i) q^{44} +2.44832 q^{45} +(20.1624 + 2.38261i) q^{46} +28.3513i q^{47} +(-12.5631 + 24.7016i) q^{48} +38.1597 q^{49} +(-5.71139 + 48.3316i) q^{50} -44.9018i q^{51} +(76.8673 + 18.4242i) q^{52} +48.3999 q^{53} +(-10.3205 - 1.21958i) q^{54} +12.7054i q^{55} +(24.7167 + 9.10293i) q^{56} -7.54983 q^{57} +(6.96153 - 58.9108i) q^{58} -9.75362i q^{59} +(-1.31791 + 5.49842i) q^{60} -59.0626 q^{61} +(-109.300 - 12.9160i) q^{62} +9.87737i q^{63} +(-48.7120 - 41.5108i) q^{64} +16.1272 q^{65} +(6.32893 - 53.5575i) q^{66} -109.748i q^{67} +(100.840 + 24.1702i) q^{68} -17.5827 q^{69} +(5.33686 + 0.630661i) q^{70} +71.0816i q^{71} +(8.29435 - 22.5212i) q^{72} +70.6749 q^{73} +(-14.3617 + 121.534i) q^{74} -42.1477i q^{75} +(4.06400 - 16.9553i) q^{76} -51.2579 q^{77} +(-67.9815 - 8.03343i) q^{78} -85.1124i q^{79} +(-11.6389 - 5.91950i) q^{80} +9.00000 q^{81} +(12.6203 - 106.797i) q^{82} -99.6812i q^{83} +(-22.1825 - 5.31689i) q^{84} +21.1568 q^{85} +(46.0001 + 5.43587i) q^{86} +51.3732i q^{87} +(116.872 + 43.0429i) q^{88} -0.665467 q^{89} +(0.574642 - 4.86281i) q^{90} +65.0626i q^{91} +(9.46458 - 39.4870i) q^{92} +95.3150 q^{93} +(56.3108 + 6.65429i) q^{94} -3.55733i q^{95} +(46.1131 + 30.7503i) q^{96} -40.5229 q^{97} +(8.95641 - 75.7921i) q^{98} +46.7048i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{2} + 12 q^{4} + 8 q^{5} - 20 q^{8} - 108 q^{9}+O(q^{10}) \) 36 * q + 4 * q^2 + 12 * q^4 + 8 * q^5 - 20 * q^8 - 108 * q^9	\( 36 q + 4 q^{2} + 12 q^{4} + 8 q^{5} - 20 q^{8} - 108 q^{9} + 8 q^{10} + 24 q^{12} - 24 q^{13} - 12 q^{14} + 4 q^{16} - 40 q^{17} - 12 q^{18} - 80 q^{20} + 12 q^{22} + 36 q^{24} + 284 q^{25} - 112 q^{26} - 48 q^{28} + 104 q^{29} + 24 q^{30} + 44 q^{32} + 48 q^{33} + 140 q^{34} - 36 q^{36} - 184 q^{37} + 180 q^{40} - 200 q^{41} + 48 q^{42} + 96 q^{44} - 24 q^{45} - 28 q^{46} - 144 q^{48} - 332 q^{49} + 176 q^{50} + 276 q^{52} + 264 q^{53} - 192 q^{56} - 184 q^{58} - 180 q^{60} + 40 q^{61} - 240 q^{62} - 372 q^{64} + 176 q^{65} - 120 q^{66} - 104 q^{68} - 60 q^{70} + 60 q^{72} + 424 q^{73} - 104 q^{74} - 400 q^{77} - 180 q^{78} + 704 q^{80} + 324 q^{81} + 528 q^{82} + 312 q^{84} - 128 q^{85} + 668 q^{86} - 496 q^{88} - 520 q^{89} - 24 q^{90} - 456 q^{92} - 32 q^{94} + 300 q^{96} - 440 q^{97} - 472 q^{98}+O(q^{100}) \) 36 * q + 4 * q^2 + 12 * q^4 + 8 * q^5 - 20 * q^8 - 108 * q^9 + 8 * q^10 + 24 * q^12 - 24 * q^13 - 12 * q^14 + 4 * q^16 - 40 * q^17 - 12 * q^18 - 80 * q^20 + 12 * q^22 + 36 * q^24 + 284 * q^25 - 112 * q^26 - 48 * q^28 + 104 * q^29 + 24 * q^30 + 44 * q^32 + 48 * q^33 + 140 * q^34 - 36 * q^36 - 184 * q^37 + 180 * q^40 - 200 * q^41 + 48 * q^42 + 96 * q^44 - 24 * q^45 - 28 * q^46 - 144 * q^48 - 332 * q^49 + 176 * q^50 + 276 * q^52 + 264 * q^53 - 192 * q^56 - 184 * q^58 - 180 * q^60 + 40 * q^61 - 240 * q^62 - 372 * q^64 + 176 * q^65 - 120 * q^66 - 104 * q^68 - 60 * q^70 + 60 * q^72 + 424 * q^73 - 104 * q^74 - 400 * q^77 - 180 * q^78 + 704 * q^80 + 324 * q^81 + 528 * q^82 + 312 * q^84 - 128 * q^85 + 668 * q^86 - 496 * q^88 - 520 * q^89 - 24 * q^90 - 456 * q^92 - 32 * q^94 + 300 * q^96 - 440 * q^97 - 472 * q^98

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