LMFDB - Embedded newform 333.3.bu.c.19.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [333,3,Mod(19,333)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(333, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 35]))

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

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

chi := DirichletCharacter("333.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 333 = 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	333.bu (of order $36$, degree $12$, 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:	$9.07359280320$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 111)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			19.6
Character	$\chi$	$=$	333.19
Dual form			333.3.bu.c.298.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.10167 - 0.271361i) q^{2} +(5.60750 - 0.988754i) q^{4} +(2.11176 + 4.52869i) q^{5} +(2.70338 + 0.983949i) q^{7} +(5.09460 - 1.36510i) q^{8} +O(q^{10})$	\(q+(3.10167 - 0.271361i) q^{2} +(5.60750 - 0.988754i) q^{4} +(2.11176 + 4.52869i) q^{5} +(2.70338 + 0.983949i) q^{7} +(5.09460 - 1.36510i) q^{8} +(7.77891 + 13.4735i) q^{10} +(8.33897 + 4.81450i) q^{11} +(-4.61863 + 6.59608i) q^{13} +(8.65199 + 2.31829i) q^{14} +(-5.97111 + 2.17330i) q^{16} +(18.3347 - 12.8381i) q^{17} +(-14.4890 - 1.26763i) q^{19} +(16.3195 + 23.3066i) q^{20} +(27.1712 + 12.6701i) q^{22} +(8.58575 - 32.0425i) q^{23} +(0.0202017 - 0.0240755i) q^{25} +(-12.5355 + 21.7122i) q^{26} +(16.1321 + 2.84452i) q^{28} +(1.37880 + 5.14577i) q^{29} +(8.73864 - 8.73864i) q^{31} +(-37.0513 + 17.2773i) q^{32} +(53.3845 - 44.7949i) q^{34} +(1.25289 + 14.3206i) q^{35} +(-26.6087 + 25.7095i) q^{37} -45.2843 q^{38} +(16.9407 + 20.1891i) q^{40} +(-34.1422 + 6.02019i) q^{41} +(-8.79308 - 8.79308i) q^{43} +(51.5211 + 18.7522i) q^{44} +(17.9351 - 101.715i) q^{46} +(-11.2691 - 19.5187i) q^{47} +(-31.1961 - 26.1766i) q^{49} +(0.0561260 - 0.0801562i) q^{50} +(-19.3771 + 41.5542i) q^{52} +(90.8964 - 33.0836i) q^{53} +(-4.19348 + 47.9317i) q^{55} +(15.1158 + 1.32246i) q^{56} +(5.67296 + 15.5863i) q^{58} +(18.0061 + 8.39640i) q^{59} +(-62.1006 - 43.4833i) q^{61} +(24.7331 - 29.4757i) q^{62} +(-88.2206 + 50.9342i) q^{64} +(-39.6251 - 6.98697i) q^{65} +(22.6172 - 62.1402i) q^{67} +(90.1182 - 90.1182i) q^{68} +(7.77212 + 44.0779i) q^{70} +(-57.7715 + 48.4761i) q^{71} +42.7823i q^{73} +(-75.5550 + 86.9629i) q^{74} +(-82.5007 + 7.21788i) q^{76} +(17.8061 + 21.2205i) q^{77} +(-36.2729 - 77.7875i) q^{79} +(-22.4518 - 22.4518i) q^{80} +(-104.264 + 27.9375i) q^{82} +(-23.1080 + 131.052i) q^{83} +(96.8584 + 55.9212i) q^{85} +(-29.6593 - 24.8871i) q^{86} +(49.0560 + 13.1445i) q^{88} +(56.5674 - 121.309i) q^{89} +(-18.9761 + 13.2872i) q^{91} +(16.4625 - 188.167i) q^{92} +(-40.2498 - 57.4827i) q^{94} +(-24.8567 - 68.2933i) q^{95} +(-31.5679 + 117.813i) q^{97} +(-103.863 - 72.7259i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 18 q^{4} + 18 q^{5} - 66 q^{8}+O(q^{10}) $ 72 * q - 18 * q^4 + 18 * q^5 - 66 * q^8	$ 72 q - 18 q^{4} + 18 q^{5} - 66 q^{8} - 72 q^{13} - 42 q^{14} - 6 q^{16} + 24 q^{17} + 108 q^{19} + 354 q^{20} + 18 q^{25} + 30 q^{26} + 48 q^{28} + 156 q^{29} - 60 q^{31} + 192 q^{32} - 90 q^{34} - 24 q^{35} - 294 q^{37} + 120 q^{38} + 612 q^{40} - 300 q^{41} - 60 q^{43} - 174 q^{44} + 234 q^{46} - 66 q^{47} - 144 q^{49} + 252 q^{50} + 912 q^{52} - 234 q^{53} + 234 q^{55} - 312 q^{56} - 1014 q^{58} + 18 q^{59} - 720 q^{61} + 1092 q^{62} + 54 q^{64} + 54 q^{65} - 708 q^{67} + 408 q^{68} - 228 q^{70} - 234 q^{74} + 90 q^{76} + 18 q^{77} + 360 q^{79} - 924 q^{80} + 1134 q^{82} - 438 q^{83} - 756 q^{85} - 396 q^{86} + 684 q^{88} - 1470 q^{89} + 1170 q^{91} - 1602 q^{92} - 1008 q^{94} + 984 q^{95} - 774 q^{97} + 1038 q^{98}+O(q^{100}) $ 72 * q - 18 * q^4 + 18 * q^5 - 66 * q^8 - 72 * q^13 - 42 * q^14 - 6 * q^16 + 24 * q^17 + 108 * q^19 + 354 * q^20 + 18 * q^25 + 30 * q^26 + 48 * q^28 + 156 * q^29 - 60 * q^31 + 192 * q^32 - 90 * q^34 - 24 * q^35 - 294 * q^37 + 120 * q^38 + 612 * q^40 - 300 * q^41 - 60 * q^43 - 174 * q^44 + 234 * q^46 - 66 * q^47 - 144 * q^49 + 252 * q^50 + 912 * q^52 - 234 * q^53 + 234 * q^55 - 312 * q^56 - 1014 * q^58 + 18 * q^59 - 720 * q^61 + 1092 * q^62 + 54 * q^64 + 54 * q^65 - 708 * q^67 + 408 * q^68 - 228 * q^70 - 234 * q^74 + 90 * q^76 + 18 * q^77 + 360 * q^79 - 924 * q^80 + 1134 * q^82 - 438 * q^83 - 756 * q^85 - 396 * q^86 + 684 * q^88 - 1470 * q^89 + 1170 * q^91 - 1602 * q^92 - 1008 * q^94 + 984 * q^95 - 774 * q^97 + 1038 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/333\mathbb{Z}\right)^\times$.

$n$	$38$	$298$
$\chi(n)$	$1$	$e\left(\frac{35}{36}\right)$

Coefficient data

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

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

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

$2$	3.10167	−	0.271361i	1.55084	−	0.135681i	0.720702	−	0.693245i	$-0.243820\pi$
$2$	3.10167	−	0.271361i	1.55084	−	0.135681i	0.830134	+	0.557564i	$0.188264\pi$
$3$		0			0
$3$		0			0
$4$	5.60750	−	0.988754i	1.40188	−	0.247188i
$5$	2.11176	+	4.52869i	0.422353	+	0.905738i	0.996226	+	0.0867941i	$0.0276622\pi$
$5$	2.11176	+	4.52869i	0.422353	+	0.905738i	−0.573874	+	0.818944i	$0.694560\pi$
$6$		0			0
$7$	2.70338	+	0.983949i	0.386197	+	0.140564i	0.527819	−	0.849357i	$-0.323010\pi$
$7$	2.70338	+	0.983949i	0.386197	+	0.140564i	−0.141623	+	0.989921i	$0.545232\pi$
$8$	5.09460	−	1.36510i	0.636826	−	0.170637i
$9$		0			0
$10$	7.77891	+	13.4735i	0.777891	+	1.34735i
$11$	8.33897	+	4.81450i	0.758088	+	0.437682i	0.828609	−	0.559828i	$-0.189133\pi$
$11$	8.33897	+	4.81450i	0.758088	+	0.437682i	−0.0705210	+	0.997510i	$0.522466\pi$
$12$		0			0
$13$	−4.61863	+	6.59608i	−0.355279	+	0.507391i	−0.956516	−	0.291680i	$-0.905786\pi$
$13$	−4.61863	+	6.59608i	−0.355279	+	0.507391i	0.601237	+	0.799071i	$0.294675\pi$
$14$	8.65199	+	2.31829i	0.618000	+	0.165592i
$15$		0			0
$16$	−5.97111	+	2.17330i	−0.373194	+	0.135832i
$17$	18.3347	−	12.8381i	1.07851	−	0.755183i	0.107499	−	0.994205i	$-0.465716\pi$
$17$	18.3347	−	12.8381i	1.07851	−	0.755183i	0.971014	+	0.239022i	$0.0768270\pi$
$18$		0			0
$19$	−14.4890	−	1.26763i	−0.762581	−	0.0667172i	−0.300772	−	0.953696i	$-0.597244\pi$
$19$	−14.4890	−	1.26763i	−0.762581	−	0.0667172i	−0.461810	+	0.886979i	$0.652800\pi$
$20$	16.3195	+	23.3066i	0.815974	+	1.16533i
$21$		0			0
$22$	27.1712	+	12.6701i	1.23505	+	0.575915i
$23$	8.58575	−	32.0425i	0.373294	−	1.39315i	−0.482528	−	0.875880i	$-0.660281\pi$
$23$	8.58575	−	32.0425i	0.373294	−	1.39315i	0.855822	−	0.517270i	$-0.173052\pi$
$24$		0			0
$25$	0.0202017	−	0.0240755i	0.000808069	−	0.000963019i
$26$	−12.5355	+	21.7122i	−0.482136	+	0.835085i
$27$		0			0
$28$	16.1321	+	2.84452i	0.576145	+	0.101590i
$29$	1.37880	+	5.14577i	0.0475450	+	0.177440i	0.985615	−	0.169005i	$-0.0540554\pi$
$29$	1.37880	+	5.14577i	0.0475450	+	0.177440i	−0.938070	+	0.346445i	$0.887389\pi$
$30$		0			0
$31$	8.73864	−	8.73864i	0.281891	−	0.281891i	−0.551971	−	0.833863i	$-0.686124\pi$
$31$	8.73864	−	8.73864i	0.281891	−	0.281891i	0.833863	+	0.551971i	$0.186124\pi$
$32$	−37.0513	+	17.2773i	−1.15785	+	0.539916i
$33$		0			0
$34$	53.3845	−	44.7949i	1.57013	−	1.31750i
$35$	1.25289	+	14.3206i	0.0357969	+	0.409161i
$36$		0			0
$37$	−26.6087	+	25.7095i	−0.719155	+	0.694850i
$37$	−26.6087	+	25.7095i	−0.719155	+	0.694850i
$38$	−45.2843			−1.19169
$39$		0			0
$40$	16.9407	+	20.1891i	0.423517	+	0.504728i
$41$	−34.1422	+	6.02019i	−0.832736	+	0.146834i	−0.573733	−	0.819043i	$-0.694505\pi$
$41$	−34.1422	+	6.02019i	−0.832736	+	0.146834i	−0.259003	+	0.965876i	$0.583394\pi$
$42$		0			0
$43$	−8.79308	−	8.79308i	−0.204490	−	0.204490i	0.597431	−	0.801921i	$-0.296188\pi$
$43$	−8.79308	−	8.79308i	−0.204490	−	0.204490i	−0.801921	+	0.597431i	$0.796188\pi$
$44$	51.5211	+	18.7522i	1.17093	+	0.426185i
$45$		0			0
$46$	17.9351	−	101.715i	0.389894	−	2.21120i
$47$	−11.2691	−	19.5187i	−0.239769	−	0.415292i	0.720879	−	0.693061i	$-0.243738\pi$
$47$	−11.2691	−	19.5187i	−0.239769	−	0.415292i	−0.960648	+	0.277769i	$0.910405\pi$
$48$		0			0
$49$	−31.1961	−	26.1766i	−0.636655	−	0.534217i
$50$	0.0561260	−	0.0801562i	0.00112252	−	0.00160312i
$51$		0			0
$52$	−19.3771	+	41.5542i	−0.372636	+	0.799120i
$53$	90.8964	−	33.0836i	1.71503	−	0.624218i	0.717636	−	0.696419i	$-0.245224\pi$
$53$	90.8964	−	33.0836i	1.71503	−	0.624218i	0.997390	+	0.0722003i	$0.0230021\pi$
$54$		0			0
$55$	−4.19348	+	47.9317i	−0.0762451	+	0.871485i
$56$	15.1158	+	1.32246i	0.269925	+	0.0236154i
$57$		0			0
$58$	5.67296	+	15.5863i	0.0978096	+	0.268730i
$59$	18.0061	+	8.39640i	0.305189	+	0.142312i	0.569179	−	0.822213i	$-0.307261\pi$
$59$	18.0061	+	8.39640i	0.305189	+	0.142312i	−0.263991	+	0.964525i	$0.585039\pi$
$60$		0			0
$61$	−62.1006	−	43.4833i	−1.01804	−	0.712841i	−0.0596276	−	0.998221i	$-0.518991\pi$
$61$	−62.1006	−	43.4833i	−1.01804	−	0.712841i	−0.958414	+	0.285380i	$0.907880\pi$
$62$	24.7331	−	29.4757i	0.398920	−	0.475415i
$63$		0			0
$64$	−88.2206	+	50.9342i	−1.37845	+	0.795847i
$65$	−39.6251	−	6.98697i	−0.609616	−	0.107492i
$66$		0			0
$67$	22.6172	−	62.1402i	0.337570	−	0.927466i	−0.648512	−	0.761205i	$-0.724608\pi$
$67$	22.6172	−	62.1402i	0.337570	−	0.927466i	0.986082	−	0.166261i	$-0.0531695\pi$
$68$	90.1182	−	90.1182i	1.32527	−	1.32527i
$69$		0			0
$70$	7.77212	+	44.0779i	0.111030	+	0.629684i
$71$	−57.7715	+	48.4761i	−0.813684	+	0.682762i	−0.951484	−	0.307698i	$-0.900441\pi$
$71$	−57.7715	+	48.4761i	−0.813684	+	0.682762i	0.137800	+	0.990460i	$0.455997\pi$
$72$		0			0
$73$			42.7823i			0.586058i	0.956103	+	0.293029i	$0.0946633\pi$
$73$			42.7823i			0.586058i	−0.956103	+	0.293029i	$0.905337\pi$
$74$	−75.5550	+	86.9629i	−1.02101	+	1.17517i
$75$		0			0
$76$	−82.5007	+	7.21788i	−1.08554	+	0.0949721i
$77$	17.8061	+	21.2205i	0.231249	+	0.275591i
$78$		0			0
$79$	−36.2729	−	77.7875i	−0.459151	−	0.984652i	−0.990502	−	0.137500i	$-0.956093\pi$
$79$	−36.2729	−	77.7875i	−0.459151	−	0.984652i	0.531351	−	0.847152i	$-0.321684\pi$
$80$	−22.4518	−	22.4518i	−0.280647	−	0.280647i
$81$		0			0
$82$	−104.264	+	27.9375i	−1.27151	+	0.340701i
$83$	−23.1080	+	131.052i	−0.278410	+	1.57894i	0.449508	+	0.893276i	$0.351599\pi$
$83$	−23.1080	+	131.052i	−0.278410	+	1.57894i	−0.727918	+	0.685664i	$0.759512\pi$
$84$		0			0
$85$	96.8584	+	55.9212i	1.13951	+	0.657897i
$86$	−29.6593	−	24.8871i	−0.344876	−	0.289385i
$87$		0			0
$88$	49.0560	+	13.1445i	0.557454	+	0.149369i
$89$	56.5674	−	121.309i	0.635588	−	1.36302i	−0.279646	−	0.960103i	$-0.590217\pi$
$89$	56.5674	−	121.309i	0.635588	−	1.36302i	0.915235	−	0.402921i	$-0.132005\pi$
$90$		0			0
$91$	−18.9761	+	13.2872i	−0.208529	+	0.146013i
$92$	16.4625	−	188.167i	0.178940	−	2.04530i
$93$		0			0
$94$	−40.2498	−	57.4827i	−0.428189	−	0.611518i
$95$	−24.8567	−	68.2933i	−0.261650	−	0.718877i
$96$		0			0
$97$	−31.5679	+	117.813i	−0.325442	+	1.21457i	0.588425	+	0.808552i	$0.299748\pi$
$97$	−31.5679	+	117.813i	−0.325442	+	1.21457i	−0.913867	+	0.406014i	$0.866918\pi$
$98$	−103.863	−	72.7259i	−1.05983	−	0.742101i
$99$		0			0
$100$	0.0894765	−	0.154978i	0.000894765	−	0.00154978i
$101$	−157.801	+	91.1063i	−1.56238	+	0.902043i	−0.565368	+	0.824838i	$0.691266\pi$
$101$	−157.801	+	91.1063i	−1.56238	+	0.902043i	−0.997015	+	0.0772042i	$0.975401\pi$
$102$		0			0
$103$	−28.6233	−	106.824i	−0.277896	−	1.03712i	−0.953876	−	0.300202i	$-0.902946\pi$
$103$	−28.6233	−	106.824i	−0.277896	−	1.03712i	0.675979	−	0.736920i	$-0.263721\pi$
$104$	−14.5258	+	39.9093i	−0.139671	+	0.383743i
$105$		0			0
$106$	272.953	−	127.280i	2.57503	−	1.20076i
$107$	−1.26502	−	7.17426i	−0.0118226	−	0.0670492i	0.978326	−	0.207072i	$-0.0663935\pi$
$107$	−1.26502	−	7.17426i	−0.0118226	−	0.0670492i	−0.990148	+	0.140023i	$0.955282\pi$
$108$		0			0
$109$	8.35870	+	95.5404i	0.0766853	+	0.876517i	0.932956	+	0.359990i	$0.117220\pi$
$109$	8.35870	+	95.5404i	0.0766853	+	0.876517i	−0.856271	+	0.516527i	$0.827225\pi$
$110$			149.806i			1.36188i
$111$		0			0
$112$	−18.2806			−0.163219
$113$	−28.5049	+	2.49385i	−0.252255	+	0.0220695i	−0.212582	−	0.977143i	$-0.568187\pi$
$113$	−28.5049	+	2.49385i	−0.252255	+	0.0220695i	−0.0396734	+	0.999213i	$0.512632\pi$
$114$		0			0
$115$	163.241	−	28.7839i	1.41949	−	0.250295i
$116$	12.8195	+	27.4916i	0.110513	+	0.236996i
$117$		0			0
$118$	58.1276	+	21.1567i	0.492607	+	0.179294i
$119$	62.1977	−	16.6658i	0.522670	−	0.140049i
$120$		0			0
$121$	−14.1411	−	24.4931i	−0.116869	−	0.202422i
$122$	−204.415	−	118.019i	−1.67554	−	0.967371i
$123$		0			0
$124$	40.3616	−	57.6423i	0.325496	−	0.464857i
$125$	120.817	+	32.3727i	0.966532	+	0.258981i
$126$		0			0
$127$	85.0924	−	30.9711i	0.670019	−	0.243867i	0.0154628	−	0.999880i	$-0.495078\pi$
$127$	85.0924	−	30.9711i	0.670019	−	0.243867i	0.654556	+	0.756014i	$0.272856\pi$
$128$	−125.857	+	88.1259i	−0.983256	+	0.688484i
$129$		0			0
$130$	−124.800	−	10.9186i	−0.959999	−	0.0839891i
$131$	101.701	+	145.244i	0.776346	+	1.10874i	0.991237	+	0.132098i	$0.0421715\pi$
$131$	101.701	+	145.244i	0.776346	+	1.10874i	−0.214891	+	0.976638i	$0.568940\pi$
$132$		0			0
$133$	−37.9221	−	17.6834i	−0.285128	−	0.132958i
$134$	53.2887	−	198.876i	0.397677	−	1.48415i
$135$		0			0
$136$	75.8829	−	90.4337i	0.557962	−	0.664954i
$137$	39.6379	−	68.6548i	0.289327	−	0.501130i	−0.684322	−	0.729180i	$-0.739902\pi$
$137$	39.6379	−	68.6548i	0.289327	−	0.501130i	0.973649	+	0.228050i	$0.0732350\pi$
$138$		0			0
$139$	201.116	+	35.4622i	1.44688	+	0.255124i	0.841260	−	0.540631i	$-0.181814\pi$
$139$	201.116	+	35.4622i	1.44688	+	0.255124i	0.605619	+	0.795755i	$0.292926\pi$
$140$	21.1852	+	79.0641i	0.151323	+	0.564744i
$141$		0			0
$142$	−166.034	+	166.034i	−1.16925	+	1.16925i
$143$	−70.2714	+	32.7681i	−0.491409	+	0.229148i
$144$		0			0
$145$	−20.3919	+	17.1108i	−0.140634	+	0.118006i
$146$	11.6094	+	132.697i	0.0795167	+	0.908881i
$147$		0			0
$148$	−123.788	+	170.475i	−0.836406	+	1.15186i
$149$	225.229			1.51160			0.755801	−	0.654801i	$-0.227248\pi$
$149$	225.229			1.51160			0.755801	+	0.654801i	$0.227248\pi$
$150$		0			0
$151$	−93.9846	−	112.006i	−0.622414	−	0.741765i	0.359069	−	0.933311i	$-0.383094\pi$
$151$	−93.9846	−	112.006i	−0.622414	−	0.741765i	−0.981484	+	0.191546i	$0.938650\pi$
$152$	−75.5464	+	13.3209i	−0.497016	+	0.0876373i
$153$		0			0
$154$	60.9872	+	60.9872i	0.396021	+	0.396021i
$155$	58.0285	+	21.1206i	0.374377	+	0.136262i
$156$		0			0
$157$	−28.3703	+	160.896i	−0.180703	+	1.02482i	0.750651	+	0.660699i	$0.229740\pi$
$157$	−28.3703	+	160.896i	−0.180703	+	1.02482i	−0.931353	+	0.364116i	$0.881371\pi$
$158$	−133.615	−	231.428i	−0.845665	−	1.46474i
$159$		0			0
$160$	−156.487	−	131.308i	−0.978044	−	0.820677i
$161$	54.7387	−	78.1749i	0.339992	−	0.485559i
$162$		0			0
$163$	26.4311	−	56.6817i	0.162154	−	0.347741i	−0.808396	−	0.588639i	$-0.799664\pi$
$163$	26.4311	−	56.6817i	0.162154	−	0.347741i	0.970550	+	0.240898i	$0.0774419\pi$
$164$	−185.500	+	67.5164i	−1.13110	+	0.411685i
$165$		0			0
$166$	−36.1110	+	412.751i	−0.217536	+	2.48645i
$167$	196.741	+	17.2126i	1.17809	+	0.103070i	0.659333	−	0.751851i	$-0.270839\pi$
$167$	196.741	+	17.2126i	1.17809	+	0.103070i	0.518759	+	0.854921i	$0.326394\pi$
$168$		0			0
$169$	35.6248	+	97.8784i	0.210798	+	0.579162i
$170$	315.598	+	147.166i	1.85646	+	0.865680i
$171$		0			0
$172$	−58.0014	−	40.6130i	−0.337217	−	0.236122i
$173$	−139.920	+	166.751i	−0.808788	+	0.963876i	−0.999843	−	0.0177034i	$-0.994365\pi$
$173$	−139.920	+	166.751i	−0.808788	+	0.963876i	0.191055	+	0.981579i	$0.438809\pi$
$174$		0			0
$175$	0.0783019	−	0.0452076i	0.000447440	−	0.000258329i
$176$	−60.2562	−	10.6248i	−0.342365	−	0.0603682i
$177$		0			0
$178$	142.535	−	391.611i	0.800758	−	2.20006i
$179$	172.557	−	172.557i	0.964003	−	0.964003i	−0.0353710	−	0.999374i	$-0.511261\pi$
$179$	172.557	−	172.557i	0.964003	−	0.964003i	0.999374	+	0.0353710i	$0.0112613\pi$
$180$		0			0
$181$	−43.2052	−	245.029i	−0.238703	−	1.35375i	−0.834674	−	0.550744i	$-0.814344\pi$
$181$	−43.2052	−	245.029i	−0.238703	−	1.35375i	0.595972	−	0.803006i	$-0.296767\pi$
$182$	−55.2520	+	46.3619i	−0.303582	+	0.254736i
$183$		0			0
$184$		−	174.964i		−	0.950892i
$185$	−172.621	−	66.2104i	−0.933089	−	0.357894i
$186$		0			0
$187$	214.702	−	18.7840i	1.14814	−	0.100449i
$188$	−82.4909	−	98.3088i	−0.438781	−	0.522919i
$189$		0			0
$190$	−95.6296	−	205.078i	−0.503314	−	1.07936i
$191$	−53.7988	−	53.7988i	−0.281669	−	0.281669i	0.552105	−	0.833774i	$-0.313825\pi$
$191$	−53.7988	−	53.7988i	−0.281669	−	0.281669i	−0.833774	+	0.552105i	$0.813825\pi$
$192$		0			0
$193$	−96.7817	+	25.9326i	−0.501460	+	0.134366i	−0.500677	−	0.865634i	$-0.666916\pi$
$193$	−96.7817	+	25.9326i	−0.501460	+	0.134366i	−0.000782315		1.00000i	$0.500249\pi$
$194$	−65.9433	+	373.983i	−0.339914	+	1.92775i
$195$		0			0
$196$	−200.814	−	115.940i	−1.02456	−	0.591532i
$197$	−203.411	−	170.682i	−1.03254	−	0.866408i	−0.0413932	−	0.999143i	$-0.513180\pi$
$197$	−203.411	−	170.682i	−1.03254	−	0.866408i	−0.991152	+	0.132735i	$0.957624\pi$
$198$		0			0
$199$	265.385	+	71.1096i	1.33359	+	0.357335i	0.854053	−	0.520187i	$-0.174138\pi$
$199$	265.385	+	71.1096i	1.33359	+	0.357335i	0.479538	+	0.877521i	$0.340804\pi$
$200$	0.0700545	−	0.150232i	0.000350272	−	0.000751162i
$201$		0			0
$202$	−464.723	+	325.403i	−2.30061	+	1.61091i
$203$	−1.33574	+	15.2676i	−0.00658002	+	0.0752099i
$204$		0			0
$205$	−99.3637	−	141.906i	−0.484701	−	0.692225i
$206$	−117.768	−	323.565i	−0.571689	−	1.57070i
$207$		0			0
$208$	13.2430	−	49.4236i	0.0636683	−	0.237613i
$209$	−114.721	−	80.3283i	−0.548903	−	0.384346i
$210$		0			0
$211$	−181.122	+	313.713i	−0.858398	+	1.48679i	0.0150578	+	0.999887i	$0.495207\pi$
$211$	−181.122	+	313.713i	−0.858398	+	1.48679i	−0.873456	+	0.486903i	$0.838127\pi$
$212$	476.990	−	275.390i	2.24995	−	1.29901i
$213$		0			0
$214$	−5.87048	−	21.9089i	−0.0274321	−	0.102378i
$215$	21.2522	−	58.3900i	0.0988475	−	0.271581i
$216$		0			0
$217$	32.2222	−	15.0255i	0.148489	−	0.0692417i
$218$	51.8519	+	294.067i	0.237853	+	1.34893i
$219$		0			0
$220$	23.8777	+	272.923i	0.108535	+	1.24056i
$221$			180.232i			0.815528i
$222$		0			0
$223$	203.596			0.912986			0.456493	−	0.889727i	$-0.349105\pi$
$223$	203.596			0.912986			0.456493	+	0.889727i	$0.349105\pi$
$224$	−117.164	+	10.2505i	−0.523052	+	0.0457611i
$225$		0			0
$226$	−87.7360	+	15.4702i	−0.388212	+	0.0684523i
$227$	51.3750	+	110.174i	0.226322	+	0.485349i	0.986375	−	0.164512i	$-0.0526050\pi$
$227$	51.3750	+	110.174i	0.226322	+	0.485349i	−0.760053	+	0.649861i	$0.774827\pi$
$228$		0			0
$229$	−251.407	−	91.5047i	−1.09785	−	0.399584i	−0.271326	−	0.962488i	$-0.587462\pi$
$229$	−251.407	−	91.5047i	−1.09785	−	0.399584i	−0.826523	+	0.562904i	$0.809684\pi$
$230$	498.511	−	133.576i	2.16744	−	0.580763i
$231$		0			0
$232$	14.0489	+	24.3334i	0.0605557	+	0.104886i
$233$	225.808	+	130.370i	0.969132	+	0.559529i	0.898972	−	0.438007i	$-0.144316\pi$
$233$	225.808	+	130.370i	0.969132	+	0.559529i	0.0701605	+	0.997536i	$0.477649\pi$
$234$		0			0
$235$	64.5965	−	92.2533i	0.274879	−	0.392567i
$236$	109.271	+	29.2792i	0.463014	+	0.124064i
$237$		0			0
$238$	188.394	−	68.5699i	0.791573	−	0.288109i
$239$	−94.8385	+	66.4066i	−0.396814	+	0.277852i	−0.754904	−	0.655835i	$-0.772317\pi$
$239$	−94.8385	+	66.4066i	−0.396814	+	0.277852i	0.358091	+	0.933687i	$0.383428\pi$
$240$		0			0
$241$	−46.2880	−	4.04968i	−0.192066	−	0.0168036i	−0.00928341	−	0.999957i	$-0.502955\pi$
$241$	−46.2880	−	4.04968i	−0.192066	−	0.0168036i	−0.182783	+	0.983153i	$0.558511\pi$
$242$	−50.5076	−	72.1323i	−0.208709	−	0.298067i
$243$		0			0
$244$	−391.223	−	182.430i	−1.60337	−	0.747666i
$245$	52.6671	−	196.556i	0.214968	−	0.802270i
$246$		0			0
$247$	75.2809	−	89.7163i	0.304781	−	0.363224i
$248$	32.5908	−	56.4490i	0.131415	−	0.227617i
$249$		0			0
$250$	383.518	+	67.6245i	1.53407	+	0.270498i
$251$	0.441106	+	1.64623i	0.00175739	+	0.00655868i	0.966799	−	0.255538i	$-0.0822527\pi$
$251$	0.441106	+	1.64623i	0.00175739	+	0.00655868i	−0.965042	+	0.262097i	$0.915586\pi$
$252$		0			0
$253$	225.865	−	225.865i	0.892747	−	0.892747i
$254$	255.524	−	119.153i	1.00600	−	0.469106i
$255$		0			0
$256$	−54.3099	+	45.5714i	−0.212148	+	0.178013i
$257$	39.3084	+	449.297i	0.152951	+	1.74824i	0.554306	+	0.832313i	$0.312984\pi$
$257$	39.3084	+	449.297i	0.152951	+	1.74824i	−0.401355	+	0.915923i	$0.631461\pi$
$258$		0			0
$259$	−97.2302	+	43.3207i	−0.375406	+	0.167262i
$260$	−229.106			−0.881177
$261$		0			0
$262$	354.858	+	422.903i	1.35442	+	1.61413i
$263$	112.739	−	19.8790i	0.428667	−	0.0755855i	0.0448477	−	0.998994i	$-0.485720\pi$
$263$	112.739	−	19.8790i	0.428667	−	0.0755855i	0.383819	+	0.923408i	$0.374609\pi$
$264$		0			0
$265$	341.777	+	341.777i	1.28972	+	1.28972i
$266$	−122.420	−	44.5574i	−0.460227	−	0.167509i
$267$		0			0
$268$	65.3845	−	370.814i	0.243972	−	1.38363i
$269$	9.65112	+	16.7162i	0.0358778	+	0.0621421i	0.883407	−	0.468607i	$-0.155244\pi$
$269$	9.65112	+	16.7162i	0.0358778	+	0.0621421i	−0.847529	+	0.530749i	$0.821911\pi$
$270$		0			0
$271$	310.333	+	260.401i	1.14514	+	0.960888i	0.999595	−	0.0284637i	$-0.00906149\pi$
$271$	310.333	+	260.401i	1.14514	+	0.960888i	0.145547	+	0.989351i	$0.453506\pi$
$272$	−81.5774	+	116.505i	−0.299917	+	0.428326i
$273$		0			0
$274$	104.313	−	223.701i	0.380706	−	0.816426i
$275$	0.284373	−	0.103503i	0.00103408	−	0.000376376i
$276$		0			0
$277$	−18.1093	+	206.990i	−0.0653766	+	0.747258i	0.890786	+	0.454422i	$0.150154\pi$
$277$	−18.1093	+	206.990i	−0.0653766	+	0.747258i	−0.956163	+	0.292835i	$0.905401\pi$
$278$	633.419	+	55.4170i	2.27849	+	0.199342i
$279$		0			0
$280$	25.9320	+	71.2476i	0.0926143	+	0.254456i
$281$	214.145	+	99.8577i	0.762083	+	0.355365i	0.764493	−	0.644632i	$-0.222989\pi$
$281$	214.145	+	99.8577i	0.762083	+	0.355365i	−0.00240983	+	0.999997i	$0.500767\pi$
$282$		0			0
$283$	54.6218	+	38.2466i	0.193010	+	0.135147i	0.666087	−	0.745874i	$-0.267968\pi$
$283$	54.6218	+	38.2466i	0.193010	+	0.135147i	−0.473077	+	0.881021i	$0.656857\pi$
$284$	−276.023	+	328.951i	−0.971912	+	1.15828i
$285$		0			0
$286$	−209.067	+	120.705i	−0.731003	+	0.422045i
$287$	−98.2227	−	17.3193i	−0.342239	−	0.0603460i
$288$		0			0
$289$	72.5010	−	199.195i	0.250869	−	0.689256i
$290$	−58.6057	+	58.6057i	−0.202089	+	0.202089i
$291$		0			0
$292$	42.3011	+	239.902i	0.144867	+	0.821581i
$293$	−189.609	+	159.101i	−0.647129	+	0.543006i	−0.906198	−	0.422853i	$-0.861029\pi$
$293$	−189.609	+	159.101i	−0.647129	+	0.543006i	0.259069	+	0.965859i	$0.416584\pi$
$294$		0			0
$295$			99.2754i			0.336527i
$296$	−100.465	+	167.303i	−0.339409	+	0.565213i
$297$		0			0
$298$	698.586	−	61.1183i	2.34425	−	0.205095i
$299$	171.700	+	204.625i	0.574249	+	0.684363i
$300$		0			0
$301$	−15.1191	−	32.4229i	−0.0502294	−	0.107717i
$302$	−321.903	−	321.903i	−1.06591	−	1.06591i
$303$		0			0
$304$	89.2706	−	23.9200i	0.293653	−	0.0786841i
$305$	65.7806	−	373.061i	0.215674	−	1.22315i
$306$		0			0
$307$	−363.891	−	210.093i	−1.18531	−	0.684341i	−0.228076	−	0.973643i	$-0.573243\pi$
$307$	−363.891	−	210.093i	−1.18531	−	0.684341i	−0.957238	+	0.289302i	$0.906577\pi$
$308$	120.830	+	101.388i	0.392305	+	0.329183i
$309$		0			0
$310$	185.717	+	49.7626i	0.599086	+	0.160525i
$311$	−123.440	+	264.718i	−0.396914	+	0.851184i	0.601709	+	0.798716i	$0.294487\pi$
$311$	−123.440	+	264.718i	−0.396914	+	0.851184i	−0.998623	+	0.0524688i	$0.983291\pi$
$312$		0			0
$313$	−45.5211	+	31.8743i	−0.145435	+	0.101835i	−0.644029	−	0.765001i	$-0.722739\pi$
$313$	−45.5211	+	31.8743i	−0.145435	+	0.101835i	0.498594	+	0.866835i	$0.333850\pi$
$314$	−44.3345	+	506.745i	−0.141193	+	1.61384i
$315$		0			0
$316$	−280.313	−	400.328i	−0.887066	−	1.26686i
$317$	−167.983	−	461.528i	−0.529914	−	1.45593i	−0.859173	−	0.511686i	$-0.829021\pi$
$317$	−167.983	−	461.528i	−0.529914	−	1.45593i	0.329259	−	0.944240i	$-0.393201\pi$
$318$		0			0
$319$	−13.2765	+	49.5486i	−0.0416192	+	0.155325i
$320$	−416.966	−	291.963i	−1.30302	−	0.912384i
$321$		0			0
$322$	148.568	−	257.327i	0.461391	−	0.799152i
$323$	−281.927	+	162.770i	−0.872838	+	0.503933i
$324$		0			0
$325$	0.0654996	+	0.244448i	0.000201537	+	0.000752148i
$326$	66.5995	−	182.981i	0.204293	−	0.561290i
$327$		0			0
$328$	−165.723	+	77.2778i	−0.505252	+	0.235603i
$329$	−11.2593	−	63.8547i	−0.0342228	−	0.194087i
$330$		0			0
$331$	40.8212	+	466.589i	0.123327	+	1.40963i	0.765678	+	0.643224i	$0.222403\pi$
$331$	40.8212	+	466.589i	0.123327	+	1.40963i	−0.642351	+	0.766410i	$0.722041\pi$
$332$			757.723i			2.28230i
$333$		0			0
$334$	614.898			1.84101
$335$	329.176	−	28.7992i	0.982615	−	0.0859676i
$336$		0			0
$337$	−573.183	+	101.068i	−1.70084	+	0.299904i	−0.937988	−	0.346668i	$-0.887313\pi$
$337$	−573.183	+	101.068i	−1.70084	+	0.299904i	−0.762853	+	0.646572i	$0.776202\pi$
$338$	137.057	+	293.919i	0.405494	+	0.869584i
$339$		0			0
$340$	598.426	+	217.809i	1.76008	+	0.640615i
$341$	114.943	−	30.7990i	0.337077	−	0.0903196i
$342$		0			0
$343$	−129.062	−	223.541i	−0.376273	−	0.651724i
$344$	−56.8006	−	32.7939i	−0.165118	−	0.0953310i
$345$		0			0
$346$	−388.737	+	555.174i	−1.12352	+	1.60455i
$347$	−113.522	−	30.4180i	−0.327152	−	0.0876601i	0.0915049	−	0.995805i	$-0.470832\pi$
$347$	−113.522	−	30.4180i	−0.327152	−	0.0876601i	−0.418657	+	0.908145i	$0.637499\pi$
$348$		0			0
$349$	226.522	−	82.4471i	0.649059	−	0.236238i	0.00355337	−	0.999994i	$-0.498869\pi$
$349$	226.522	−	82.4471i	0.649059	−	0.236238i	0.645506	+	0.763756i	$0.276647\pi$
$350$	0.230599	−	0.161467i	0.000658855	−	0.000461335i
$351$		0			0
$352$	−392.151	−	34.3088i	−1.11407	−	0.0974681i
$353$	−379.252	−	541.628i	−1.07437	−	1.53436i	−0.824320	−	0.566124i	$-0.808442\pi$
$353$	−379.252	−	541.628i	−1.07437	−	1.53436i	−0.250049	−	0.968233i	$-0.580447\pi$
$354$		0			0
$355$	−341.533	−	159.259i	−0.962064	−	0.448618i
$356$	197.257	−	736.172i	0.554092	−	2.06790i
$357$		0			0
$358$	488.389	−	582.039i	1.36421	−	1.62581i
$359$	262.364	−	454.428i	0.730819	−	1.26582i	−0.225715	−	0.974193i	$-0.572472\pi$
$359$	262.364	−	454.428i	0.730819	−	1.26582i	0.956534	−	0.291622i	$-0.0941950\pi$
$360$		0			0
$361$	−147.190	−	25.9536i	−0.407728	−	0.0718935i
$362$	−200.500	−	748.274i	−0.553866	−	2.06706i
$363$		0			0
$364$	−93.2707	+	93.2707i	−0.256238	+	0.256238i
$365$	−193.748	+	90.3460i	−0.530815	+	0.247523i
$366$		0			0
$367$	−304.599	+	255.589i	−0.829970	+	0.696427i	−0.955284	−	0.295690i	$-0.904451\pi$
$367$	−304.599	+	255.589i	−0.829970	+	0.696427i	0.125314	+	0.992117i	$0.460006\pi$
$368$	18.3716	+	209.988i	0.0499228	+	0.570621i
$369$		0			0
$370$	−553.382	−	158.520i	−1.49563	−	0.428433i
$371$	278.280			0.750080
$372$		0			0
$373$	−54.3230	−	64.7396i	−0.145638	−	0.173565i	0.688294	−	0.725432i	$-0.258360\pi$
$373$	−54.3230	−	64.7396i	−0.145638	−	0.173565i	−0.833932	+	0.551867i	$0.813916\pi$
$374$	660.837	−	116.523i	1.76694	−	0.311560i
$375$		0			0
$376$	−84.0567	−	84.0567i	−0.223555	−	0.223555i
$377$	−40.3101	−	14.6717i	−0.106923	−	0.0389169i
$378$		0			0
$379$	−24.9345	+	141.410i	−0.0657902	+	0.373115i	0.934081	+	0.357061i	$0.116221\pi$
$379$	−24.9345	+	141.410i	−0.0657902	+	0.373115i	−0.999871	+	0.0160533i	$0.994890\pi$
$380$	−206.909	−	358.378i	−0.544499	−	0.943099i
$381$		0			0
$382$	−181.465	−	152.267i	−0.475040	−	0.398606i
$383$	137.760	−	196.742i	0.359687	−	0.513687i	−0.598001	−	0.801496i	$-0.704038\pi$
$383$	137.760	−	196.742i	0.359687	−	0.513687i	0.957688	+	0.287809i	$0.0929268\pi$
$384$		0			0
$385$	−58.4989	+	125.451i	−0.151945	+	0.325847i
$386$	−293.148	+	106.697i	−0.759451	+	0.276418i
$387$		0			0
$388$	−60.5289	+	691.849i	−0.156002	+	1.78311i
$389$	−530.220	−	46.3882i	−1.36303	−	0.119250i	−0.617948	−	0.786219i	$-0.712036\pi$
$389$	−530.220	−	46.3882i	−1.36303	−	0.119250i	−0.745085	+	0.666969i	$0.767591\pi$
$390$		0			0
$391$	−253.947	−	697.714i	−0.649482	−	1.78444i
$392$	−194.665	−	90.7739i	−0.496595	−	0.231566i
$393$		0			0
$394$	−677.232	−	474.203i	−1.71886	−	1.20356i
$395$	275.676	−	328.537i	0.697913	−	0.831740i
$396$		0			0
$397$	71.6940	−	41.3925i	0.180589	−	0.104263i	−0.406980	−	0.913437i	$-0.633418\pi$
$397$	71.6940	−	41.3925i	0.180589	−	0.104263i	0.587570	+	0.809174i	$0.300085\pi$
$398$	842.432	+	148.544i	2.11666	+	0.373225i
$399$		0			0
$400$	−0.0683033	+	0.187662i	−0.000170758	+	0.000469154i
$401$	−31.6513	+	31.6513i	−0.0789309	+	0.0789309i	−0.745470	−	0.666539i	$-0.767775\pi$
$401$	−31.6513	+	31.6513i	−0.0789309	+	0.0789309i	0.666539	+	0.745470i	$0.267775\pi$
$402$		0			0
$403$	17.2803	+	98.0013i	0.0428791	+	0.243179i
$404$	−794.786	+	666.905i	−1.96729	+	1.65075i
$405$		0			0
$406$			47.7176i			0.117531i
$407$	−345.667	+	86.2825i	−0.849306	+	0.211996i
$408$		0			0
$409$	−191.115	+	16.7204i	−0.467274	+	0.0408812i	−0.318362	−	0.947969i	$-0.603133\pi$
$409$	−191.115	+	16.7204i	−0.467274	+	0.0408812i	−0.148912	+	0.988850i	$0.547577\pi$
$410$	−346.701	−	413.183i	−0.845613	−	1.00776i
$411$		0			0
$412$	−266.127	−	570.712i	−0.645941	−	1.38522i
$413$	40.4158	+	40.4158i	0.0978590	+	0.0978590i
$414$		0			0
$415$	−642.293	+	172.102i	−1.54769	+	0.414703i
$416$	57.1636	−	324.191i	0.137412	−	0.779305i
$417$		0			0
$418$	−377.624	−	218.021i	−0.903406	−	0.521582i
$419$	−173.017	−	145.179i	−0.412928	−	0.346488i	0.412537	−	0.910941i	$-0.364643\pi$
$419$	−173.017	−	145.179i	−0.412928	−	0.346488i	−0.825465	+	0.564453i	$0.809087\pi$
$420$		0			0
$421$	−327.755	−	87.8216i	−0.778515	−	0.208602i	−0.152385	−	0.988321i	$-0.548695\pi$
$421$	−327.755	−	87.8216i	−0.778515	−	0.208602i	−0.626130	+	0.779719i	$0.715362\pi$
$422$	−476.652	+	1022.18i	−1.12951	+	2.42223i
$423$		0			0
$424$	417.919	−	292.630i	0.985658	−	0.690165i
$425$	0.0613094	−	0.700769i	0.000144257	−	0.00164887i
$426$		0			0
$427$	−125.096	−	178.655i	−0.292965	−	0.418397i
$428$	−14.1872	−	38.9789i	−0.0331476	−	0.0910721i
$429$		0			0
$430$	50.0726	−	186.874i	0.116448	−	0.434590i
$431$	−259.320	−	181.578i	−0.601671	−	0.421295i	0.232660	−	0.972558i	$-0.425257\pi$
$431$	−259.320	−	181.578i	−0.601671	−	0.421295i	−0.834331	+	0.551263i	$0.814146\pi$
$432$		0			0
$433$	−140.290	+	242.989i	−0.323995	+	0.561176i	−0.981309	−	0.192441i	$-0.938360\pi$
$433$	−140.290	+	242.989i	−0.323995	+	0.561176i	0.657313	+	0.753618i	$0.271693\pi$
$434$	95.8654	−	55.3479i	0.220888	−	0.127530i
$435$		0			0
$436$	141.337	+	527.478i	0.324168	+	1.20981i
$437$	−165.017	+	453.381i	−0.377614	+	1.03749i
$438$		0			0
$439$	209.482	−	97.6831i	0.477180	−	0.222513i	−0.169121	−	0.985595i	$-0.554093\pi$
$439$	209.482	−	97.6831i	0.477180	−	0.222513i	0.646301	+	0.763083i	$0.276315\pi$
$440$	44.0672	+	249.917i	0.100153	+	0.567994i
$441$		0			0
$442$	48.9079	+	559.020i	0.110651	+	1.26475i
$443$			162.984i			0.367909i	0.982935	+	0.183954i	$0.0588899\pi$
$443$			162.984i			0.367909i	−0.982935	+	0.183954i	$0.941110\pi$
$444$		0			0
$445$	668.828			1.50298
$446$	631.487	−	55.2480i	1.41589	−	0.123874i
$447$		0			0
$448$	−288.610	+	50.8897i	−0.644219	+	0.113593i
$449$	−41.7587	−	89.5519i	−0.0930039	−	0.199447i	0.854303	−	0.519776i	$-0.173985\pi$
$449$	−41.7587	−	89.5519i	−0.0930039	−	0.199447i	−0.947307	+	0.320328i	$0.896207\pi$
$450$		0			0
$451$	−313.695	−	114.175i	−0.695553	−	0.253161i
$452$	−157.375	+	42.1686i	−0.348175	+	0.0932933i
$453$		0			0
$454$	189.246	+	327.783i	0.416840	+	0.721989i
$455$	−100.247	−	57.8774i	−0.220322	−	0.127203i
$456$		0			0
$457$	100.758	−	143.898i	0.220478	−	0.314875i	−0.693641	−	0.720320i	$-0.743995\pi$
$457$	100.758	−	143.898i	0.220478	−	0.314875i	0.914119	+	0.405446i	$0.132884\pi$
$458$	−804.614	−	215.596i	−1.75680	−	0.470733i
$459$		0			0
$460$	886.917	−	322.811i	1.92808	−	0.701764i
$461$	−299.734	+	209.876i	−0.650183	+	0.455263i	−0.851565	−	0.524250i	$-0.824346\pi$
$461$	−299.734	+	209.876i	−0.650183	+	0.455263i	0.201381	+	0.979513i	$0.435457\pi$
$462$		0			0
$463$	733.948	+	64.2121i	1.58520	+	0.138687i	0.845398	−	0.534136i	$-0.179363\pi$
$463$	733.948	+	64.2121i	1.58520	+	0.138687i	0.739803	+	0.672824i	$0.234919\pi$
$464$	−19.4163	−	27.7294i	−0.0418455	−	0.0597615i
$465$		0			0
$466$	735.759	+	343.090i	1.57888	+	0.736245i
$467$	−110.732	+	413.259i	−0.237114	+	0.884922i	0.740070	+	0.672530i	$0.234792\pi$
$467$	−110.732	+	413.259i	−0.237114	+	0.884922i	−0.977184	+	0.212393i	$0.931874\pi$
$468$		0			0
$469$	122.286	−	145.734i	0.260737	−	0.310734i
$470$	175.323	−	303.669i	0.373028	−	0.646103i
$471$		0			0
$472$	103.196	+	18.1962i	0.218636	+	0.0385514i
$473$	−30.9909	−	115.659i	−0.0655198	−	0.244523i
$474$		0			0
$475$	−0.323223	+	0.323223i	−0.000680469	+	0.000680469i
$476$	332.295	−	154.952i	0.698099	−	0.325529i
$477$		0			0
$478$	−276.138	+	231.707i	−0.577694	+	0.484743i
$479$	61.3415	+	701.137i	0.128062	+	1.46375i	0.739873	+	0.672747i	$0.234886\pi$
$479$	61.3415	+	701.137i	0.128062	+	1.46375i	−0.611811	+	0.791004i	$0.709559\pi$
$480$		0			0
$481$	−46.6859	−	294.256i	−0.0970602	−	0.611758i
$482$	−144.669			−0.300144
$483$		0			0
$484$	−103.514	−	123.363i	−0.213872	−	0.254882i
$485$	−600.202	+	105.832i	−1.23753	+	0.218210i
$486$		0			0
$487$	−313.964	−	313.964i	−0.644690	−	0.644690i	0.307015	−	0.951705i	$-0.400670\pi$
$487$	−313.964	−	313.964i	−0.644690	−	0.644690i	−0.951705	+	0.307015i	$0.900670\pi$
$488$	−375.737	−	136.757i	−0.769952	−	0.280240i
$489$		0			0
$490$	110.018	−	623.945i	0.224527	−	1.27336i
$491$	158.428	+	274.405i	0.322663	+	0.558869i	0.981037	−	0.193822i	$-0.0620886\pi$
$491$	158.428	+	274.405i	0.322663	+	0.558869i	−0.658373	+	0.752691i	$0.728755\pi$
$492$		0			0
$493$	91.3419	+	76.6449i	0.185278	+	0.155466i
$494$	209.151	−	298.699i	0.423383	−	0.604653i
$495$		0			0
$496$	−33.1876	+	71.1710i	−0.0669105	+	0.143490i
$497$	−203.876	+	74.2049i	−0.410214	+	0.149306i
$498$		0			0
$499$	−23.7069	+	270.971i	−0.0475088	+	0.543028i	0.934726	+	0.355370i	$0.115645\pi$
$499$	−23.7069	+	270.971i	−0.0475088	+	0.543028i	−0.982234	+	0.187658i	$0.939910\pi$
$500$	709.487	+	62.0721i	1.41897	+	0.124144i
$501$		0			0
$502$	1.81489	+	4.98636i	0.00361531	+	0.00993299i
$503$	362.633	+	169.098i	0.720940	+	0.336180i	0.748222	−	0.663448i	$-0.230908\pi$
$503$	362.633	+	169.098i	0.720940	+	0.336180i	−0.0272826	+	0.999628i	$0.508685\pi$
$504$		0			0
$505$	−745.830	−	522.236i	−1.47689	−	1.03413i
$506$	639.268	−	761.850i	1.26338	−	1.50563i
$507$		0			0
$508$	446.533	−	257.806i	0.879002	−	0.507492i
$509$	−594.527	−	104.831i	−1.16803	−	0.205955i	−0.444196	−	0.895930i	$-0.646511\pi$
$509$	−594.527	−	104.831i	−1.16803	−	0.205955i	−0.723834	+	0.689975i	$0.757622\pi$
$510$		0			0
$511$	−42.0956	+	115.657i	−0.0823788	+	0.226334i
$512$	278.482	−	278.482i	0.543911	−	0.543911i
$513$		0			0
$514$	243.843	+	1382.90i	0.474403	+	2.69047i
$515$	423.325	−	355.212i	0.821991	−	0.689732i
$516$		0			0
$517$		−	217.021i		−	0.419770i
$518$	−289.821	+	160.751i	−0.559499	+	0.310330i
$519$		0			0
$520$	−211.412	+	18.4961i	−0.406561	+	0.0355695i
$521$	−242.530	−	289.036i	−0.465509	−	0.554772i	0.481305	−	0.876553i	$-0.340163\pi$
$521$	−242.530	−	289.036i	−0.465509	−	0.554772i	−0.946814	+	0.321781i	$0.895718\pi$
$522$		0			0
$523$	255.278	+	547.445i	0.488102	+	1.04674i	0.983969	+	0.178340i	$0.0570728\pi$
$523$	255.278	+	547.445i	0.488102	+	1.04674i	−0.495866	+	0.868399i	$0.665149\pi$
$524$	713.901	+	713.901i	1.36241	+	1.36241i
$525$		0			0
$526$	344.286	−	92.2512i	0.654536	−	0.175382i
$527$	48.0329	−	272.408i	0.0911440	−	0.516903i
$528$		0			0
$529$	−494.877	−	285.717i	−0.935496	−	0.540109i
$530$	1152.82	+	967.335i	2.17514	+	1.82516i
$531$		0			0
$532$	−230.133	−	61.6638i	−0.432580	−	0.115909i
$533$	117.980	−	253.010i	0.221351	−	0.474690i
$534$		0			0
$535$	29.8186	−	20.8792i	0.0557357	−	0.0390265i
$536$	30.3983	−	347.454i	0.0567133	−	0.648236i
$537$		0			0
$538$	34.4707	+	49.2293i	0.0640720	+	0.0915043i
$539$	−134.116	−	368.480i	−0.248823	−	0.683636i
$540$		0			0
$541$	104.883	−	391.427i	0.193868	−	0.723525i	−0.798689	−	0.601744i	$-0.794473\pi$
$541$	104.883	−	391.427i	0.193868	−	0.723525i	0.992557	−	0.121781i	$-0.0388606\pi$
$542$	1033.21	+	723.465i	1.90630	+	1.33481i
$543$		0			0
$544$	−457.517	+	792.443i	−0.841024	+	1.45670i
$545$	−415.021	+	239.613i	−0.761507	+	0.439656i
$546$		0			0
$547$	−116.612	−	435.203i	−0.213185	−	0.795618i	−0.986798	−	0.161959i	$-0.948219\pi$
$547$	−116.612	−	435.203i	−0.213185	−	0.795618i	0.773612	−	0.633659i	$-0.218448\pi$
$548$	154.387	−	424.174i	0.281728	−	0.774040i
$549$		0			0
$550$	0.853945	−	0.398201i	0.00155263	−	0.000724002i
$551$	−13.4546	−	76.3051i	−0.0244186	−	0.138485i
$552$		0			0
$553$	−21.5204	−	245.980i	−0.0389158	−	0.444809i
$554$			646.931i			1.16774i
$555$		0			0
$556$	1162.82			2.09141
$557$	−360.553	+	31.5443i	−0.647312	+	0.0566325i	−0.406084	−	0.913836i	$-0.633106\pi$
$557$	−360.553	+	31.5443i	−0.647312	+	0.0566325i	−0.241229	+	0.970468i	$0.577550\pi$
$558$		0			0
$559$	98.6118	−	17.3879i	0.176408	−	0.0311054i
$560$	−38.6042	−	82.7870i	−0.0689361	−	0.147834i
$561$		0			0
$562$	691.306	+	251.615i	1.23008	+	0.447713i
$563$	242.588	−	65.0013i	0.430885	−	0.115455i	−0.0368568	−	0.999321i	$-0.511735\pi$
$563$	242.588	−	65.0013i	0.430885	−	0.115455i	0.467741	+	0.883865i	$0.345068\pi$
$564$		0			0
$565$	−71.4894	−	123.823i	−0.126530	−	0.219156i
$566$	179.798	+	103.806i	0.317663	+	0.183403i
$567$		0			0
$568$	−228.149	+	325.830i	−0.401670	+	0.573644i
$569$	−504.580	−	135.202i	−0.886784	−	0.237613i	−0.213452	−	0.976954i	$-0.568471\pi$
$569$	−504.580	−	135.202i	−0.886784	−	0.237613i	−0.673332	+	0.739341i	$0.735137\pi$
$570$		0			0
$571$	659.638	−	240.089i	1.15523	−	0.420470i	0.307841	−	0.951438i	$-0.400394\pi$
$571$	659.638	−	240.089i	1.15523	−	0.420470i	0.847392	+	0.530968i	$0.178171\pi$
$572$	−361.648	+	253.228i	−0.632251	+	0.442707i
$573$		0			0
$574$	−309.354	−	27.0650i	−0.538945	−	0.0471516i
$575$	−0.597991	−	0.854020i	−0.00103998	−	0.00148525i
$576$		0			0
$577$	777.772	+	362.681i	1.34796	+	0.628563i	0.956527	−	0.291644i	$-0.0942022\pi$
$577$	777.772	+	362.681i	1.34796	+	0.628563i	0.391432	+	0.920207i	$0.371980\pi$
$578$	170.821	−	637.511i	0.295537	−	1.10296i
$579$		0			0
$580$	−97.4291	+	116.111i	−0.167981	+	0.200192i
$581$	−191.418	+	331.546i	−0.329463	+	0.570647i
$582$		0			0
$583$	917.263	+	161.738i	1.57335	+	0.277424i
$584$	58.4019	+	217.959i	0.100003	+	0.373217i
$585$		0			0
$586$	−544.931	+	544.931i	−0.929916	+	0.929916i
$587$	49.1446	−	22.9165i	0.0837217	−	0.0390401i	−0.380306	−	0.924861i	$-0.624181\pi$
$587$	49.1446	−	22.9165i	0.0837217	−	0.0390401i	0.464028	+	0.885820i	$0.346404\pi$
$588$		0			0
$589$	−137.692	+	115.537i	−0.233772	+	0.196158i
$590$	26.9395	+	307.920i	0.0456602	+	0.521898i
$591$		0			0
$592$	103.009	−	211.343i	0.174002	−	0.356998i
$593$	−17.9752			−0.0303123			−0.0151562	−	0.999885i	$-0.504825\pi$
$593$	−17.9752			−0.0303123			−0.0151562	+	0.999885i	$0.504825\pi$
$594$		0			0
$595$	206.821	+	246.480i	0.347598	+	0.414252i
$596$	1262.97	−	222.696i	2.11908	−	0.373651i
$597$		0			0
$598$	588.085	+	588.085i	0.983421	+	0.983421i
$599$	−85.2913	−	31.0435i	−0.142390	−	0.0518255i	0.269842	−	0.962905i	$-0.413028\pi$
$599$	−85.2913	−	31.0435i	−0.142390	−	0.0518255i	−0.412232	+	0.911079i	$0.635251\pi$
$600$		0			0
$601$	−91.6076	+	519.533i	−0.152425	+	0.864447i	0.808677	+	0.588253i	$0.200184\pi$
$601$	−91.6076	+	519.533i	−0.152425	+	0.864447i	−0.961102	+	0.276194i	$0.910927\pi$
$602$	−55.6927	−	96.4626i	−0.0925128	−	0.160237i
$603$		0			0
$604$	−637.765	−	535.149i	−1.05590	−	0.886008i
$605$	81.0591	−	115.764i	0.133982	−	0.191346i
$606$		0			0
$607$	−242.257	+	519.523i	−0.399106	+	0.855886i	0.599358	+	0.800481i	$0.295423\pi$
$607$	−242.257	+	519.523i	−0.399106	+	0.855886i	−0.998464	+	0.0554046i	$0.982355\pi$
$608$	558.739	−	203.364i	0.918979	−	0.334481i
$609$		0			0
$610$	102.796	−	1174.96i	0.168518	−	1.92617i
$611$	180.795	+	15.8175i	0.295900	+	0.0258879i
$612$		0			0
$613$	−329.858	−	906.278i	−0.538105	−	1.47843i	−0.849210	−	0.528055i	$-0.822921\pi$
$613$	−329.858	−	906.278i	−0.538105	−	1.47843i	0.311105	−	0.950375i	$-0.399301\pi$
$614$	−1185.68	−	552.893i	−1.93108	−	0.900477i
$615$		0			0
$616$	119.683	+	83.8031i	0.194291	+	0.136044i
$617$	−39.6754	+	47.2833i	−0.0643037	+	0.0766341i	−0.797237	−	0.603666i	$-0.793706\pi$
$617$	−39.6754	+	47.2833i	−0.0643037	+	0.0766341i	0.732934	+	0.680300i	$0.238151\pi$
$618$		0			0
$619$	250.262	−	144.489i	0.404300	−	0.233423i	−0.284038	−	0.958813i	$-0.591674\pi$
$619$	250.262	−	144.489i	0.404300	−	0.233423i	0.688338	+	0.725390i	$0.258341\pi$
$620$	346.278	+	61.0582i	0.558513	+	0.0984809i
$621$		0			0
$622$	−311.037	+	854.566i	−0.500059	+	1.37390i
$623$	272.285	−	272.285i	0.437054	−	0.437054i
$624$		0			0
$625$	108.394	+	614.730i	0.173430	+	0.983568i
$626$	−132.542	+	111.216i	−0.211729	+	0.177662i
$627$		0			0
$628$			930.276i			1.48133i
$629$	−157.803	+	812.981i	−0.250879	+	1.29250i
$630$		0			0
$631$	381.360	−	33.3647i	0.604374	−	0.0528758i	0.219138	−	0.975694i	$-0.429676\pi$
$631$	381.360	−	33.3647i	0.604374	−	0.0528758i	0.385236	+	0.922818i	$0.374120\pi$
$632$	−290.983	−	346.780i	−0.460417	−	0.548703i
$633$		0			0
$634$	−646.268	−	1385.93i	−1.01935	−	2.18600i
$635$	319.953	+	319.953i	0.503864	+	0.503864i
$636$		0			0
$637$	316.746	−	84.8719i	0.497247	−	0.133237i
$638$	−27.7338	+	157.286i	−0.0434699	+	0.246530i
$639$		0			0
$640$	−664.875	−	383.866i	−1.03887	−	0.599790i
$641$	949.661	+	796.860i	1.48153	+	1.24315i	0.904531	+	0.426408i	$0.140221\pi$
$641$	949.661	+	796.860i	1.48153	+	1.24315i	0.577000	+	0.816744i	$0.304223\pi$
$642$		0			0
$643$	427.388	+	114.518i	0.664678	+	0.178100i	0.575356	−	0.817903i	$-0.304863\pi$
$643$	427.388	+	114.518i	0.664678	+	0.178100i	0.0893218	+	0.996003i	$0.471530\pi$
$644$	229.651	−	492.489i	0.356602	−	0.764735i
$645$		0			0
$646$	−830.274	+	581.364i	−1.28525	+	0.899945i
$647$	−29.2667	+	334.520i	−0.0452345	+	0.517033i	0.939450	+	0.342686i	$0.111337\pi$
$647$	−29.2667	+	334.520i	−0.0452345	+	0.517033i	−0.984684	+	0.174346i	$0.944219\pi$
$648$		0			0
$649$	109.728	+	156.708i	0.169073	+	0.241461i
$650$	0.269492	+	0.740423i	0.000414603	+	0.00113911i
$651$		0			0
$652$	92.1683	−	343.977i	0.141362	−	0.527572i
$653$	481.867	+	337.407i	0.737928	+	0.516703i	0.881062	−	0.473001i	$-0.156829\pi$
$653$	481.867	+	337.407i	0.737928	+	0.516703i	−0.143134	+	0.989703i	$0.545718\pi$
$654$		0			0
$655$	−442.998	+	767.295i	−0.676333	+	1.17144i
$656$	190.783	−	110.148i	0.290827	−	0.167909i
$657$		0			0
$658$	−52.2504	−	195.001i	−0.0794078	−	0.296354i
$659$	422.563	−	1160.98i	0.641219	−	1.76173i	−0.00664567	−	0.999978i	$-0.502115\pi$
$659$	422.563	−	1160.98i	0.641219	−	1.76173i	0.647864	−	0.761756i	$-0.275662\pi$
$660$		0			0
$661$	439.322	−	204.859i	0.664632	−	0.309923i	−0.0608674	−	0.998146i	$-0.519387\pi$
$661$	439.322	−	204.859i	0.664632	−	0.309923i	0.725499	+	0.688223i	$0.241609\pi$
$662$	253.228	+	1436.13i	0.382520	+	2.16938i
$663$		0			0
$664$	61.1723	+	699.203i	0.0921270	+	1.05302i
$665$		−	209.080i		−	0.314407i
$666$		0			0
$667$	176.721			0.264949
$668$	1120.25	−	98.0089i	1.67702	−	0.146720i
$669$		0			0
$670$	1013.18	−	178.651i	1.51221	−	0.266643i
$671$	−308.504	−	661.589i	−0.459768	−	0.985975i
$672$		0			0
$673$	−1072.46	−	390.342i	−1.59355	−	0.580003i	−0.615453	−	0.788174i	$-0.711027\pi$
$673$	−1072.46	−	390.342i	−1.59355	−	0.580003i	−0.978092	+	0.208171i	$0.933249\pi$
$674$	−1750.40	+	469.018i	−2.59703	+	0.695873i
$675$		0			0
$676$	296.544	+	513.629i	0.438674	+	0.759806i
$677$	223.030	+	128.767i	0.329439	+	0.190202i	0.655592	−	0.755115i	$-0.272419\pi$
$677$	223.030	+	128.767i	0.329439	+	0.190202i	−0.326153	+	0.945317i	$0.605752\pi$
$678$		0			0
$679$	−201.262	+	287.431i	−0.296409	+	0.423316i
$680$	569.793	+	152.676i	0.837931	+	0.224523i
$681$		0			0
$682$	348.159	−	126.720i	0.510497	−	0.185806i
$683$	568.498	−	398.067i	0.832354	−	0.582821i	−0.0778572	−	0.996965i	$-0.524808\pi$
$683$	568.498	−	398.067i	0.832354	−	0.582821i	0.910211	+	0.414144i	$0.135919\pi$
$684$		0			0
$685$	394.622	+	34.5249i	0.576090	+	0.0504014i
$686$	−460.968	−	658.330i	−0.671964	−	0.959665i
$687$		0			0
$688$	71.6144	+	33.3944i	0.104091	+	0.0485383i
$689$	−201.594	+	752.361i	−0.292590	+	1.09196i
$690$		0			0
$691$	−573.213	+	683.128i	−0.829541	+	0.988608i	0.170454	+	0.985366i	$0.445477\pi$
$691$	−573.213	+	683.128i	−0.829541	+	0.988608i	−0.999995	+	0.00324267i	$0.998968\pi$
$692$	−619.728	+	1073.40i	−0.895561	+	1.55116i
$693$		0			0
$694$	−360.361	−	63.5414i	−0.519253	−	0.0915583i
$695$	264.112	+	985.680i	0.380018	+	1.41825i
$696$		0			0
$697$	−548.699	+	548.699i	−0.787230	+	0.787230i
$698$	680.223	−	317.193i	0.974531	−	0.454431i
$699$		0			0
$700$	0.394379	−	0.330923i	0.000563399	−	0.000472748i
$701$	−11.5724	−	132.273i	−0.0165084	−	0.188692i	−0.999971	−	0.00758187i	$-0.997587\pi$
$701$	−11.5724	−	132.273i	−0.0165084	−	0.188692i	0.983463	−	0.181110i	$-0.0579690\pi$
$702$		0			0
$703$	418.125	−	338.776i	0.594772	−	0.481900i
$704$	−980.891			−1.39331
$705$		0			0
$706$	−1323.29	−	1577.04i	−1.87435	−	2.23377i
$707$	−516.239	+	91.0268i	−0.730182	+	0.128751i
$708$		0			0
$709$	323.577	+	323.577i	0.456386	+	0.456386i	0.897467	−	0.441081i	$-0.145405\pi$
$709$	323.577	+	323.577i	0.456386	+	0.456386i	−0.441081	+	0.897467i	$0.645405\pi$
$710$	−1102.54	−	401.292i	−1.55287	−	0.565199i
$711$		0			0
$712$	122.590	−	695.242i	0.172177	−	0.976463i
$713$	−204.980	−	355.035i	−0.287489	−	0.497946i
$714$		0			0
$715$	−296.793	−	249.039i	−0.415095	−	0.348306i
$716$	796.995	−	1138.23i	1.11312	−	1.58970i
$717$		0			0
$718$	690.453	−	1480.68i	0.961634	−	2.06223i
$719$	1075.53	−	391.461i	1.49587	−	0.544452i	0.540882	−	0.841098i	$-0.318091\pi$
$719$	1075.53	−	391.461i	1.49587	−	0.544452i	0.954987	+	0.296647i	$0.0958683\pi$
$720$		0			0
$721$	27.7294	−	316.948i	0.0384596	−	0.439596i
$722$	−463.578	−	40.5578i	−0.642074	−	0.0561742i
$723$		0			0
$724$	−484.546	−	1331.28i	−0.669263	−	1.83878i
$725$	0.151741	+	0.0707580i	0.000209298	+	9.75973e-5i
$726$		0			0
$727$	−1018.57	−	713.213i	−1.40106	−	0.981036i	−0.997823	−	0.0659421i	$-0.978995\pi$
$727$	−1018.57	−	713.213i	−1.40106	−	0.981036i	−0.403241	−	0.915094i	$-0.632116\pi$
$728$	−78.5374	+	93.5972i	−0.107881	+	0.128568i
$729$		0			0
$730$	−576.425	+	332.799i	−0.789623	+	0.455889i
$731$	−274.105	−	48.3321i	−0.374973	−	0.0661178i
$732$		0			0
$733$	63.3798	−	174.134i	0.0864663	−	0.237564i	−0.888922	−	0.458059i	$-0.848545\pi$
$733$	63.3798	−	174.134i	0.0864663	−	0.237564i	0.975388	+	0.220495i	$0.0707672\pi$
$734$	−875.409	+	875.409i	−1.19266	+	1.19266i
$735$		0			0
$736$	235.494	+	1335.55i	0.319965	+	1.81461i
$737$	487.778	−	409.295i	0.661843	−	0.555352i
$738$		0			0
$739$			449.272i			0.607946i	0.952681	+	0.303973i	$0.0983133\pi$
$739$			449.272i			0.607946i	−0.952681	+	0.303973i	$0.901687\pi$
$740$	−1033.44	−	200.595i	−1.39654	−	0.271074i
$741$		0			0
$742$	863.132	−	75.5143i	1.16325	−	0.101771i
$743$	−333.509	−	397.461i	−0.448868	−	0.534940i	0.493399	−	0.869803i	$-0.335754\pi$
$743$	−333.509	−	397.461i	−0.448868	−	0.534940i	−0.942267	+	0.334863i	$0.891310\pi$
$744$		0			0
$745$	475.630	+	1019.99i	0.638429	+	1.36912i
$746$	−186.060	−	186.060i	−0.249410	−	0.249410i
$747$		0			0
$748$	1185.37	−	317.618i	1.58472	−	0.424623i
$749$	3.63929	−	20.6394i	0.00485886	−	0.0275560i
$750$		0			0
$751$	−1074.63	−	620.436i	−1.43093	−	0.826146i	−0.433735	−	0.901040i	$-0.642805\pi$
$751$	−1074.63	−	620.436i	−1.43093	−	0.826146i	−0.997191	+	0.0748943i	$0.976138\pi$
$752$	109.709	+	92.0571i	0.145890	+	0.122416i
$753$		0			0
$754$	−129.010	−	34.5681i	−0.171101	−	0.0458463i
$755$	308.769	−	662.158i	0.408966	−	0.877030i
$756$		0			0
$757$	−344.276	+	241.064i	−0.454790	+	0.318447i	−0.778428	−	0.627734i	$-0.783983\pi$
$757$	−344.276	+	241.064i	−0.454790	+	0.318447i	0.323639	+	0.946181i	$0.395094\pi$
$758$	−38.9653	+	445.375i	−0.0514054	+	0.587566i
$759$		0			0
$760$	−219.862	−	313.996i	−0.289292	−	0.413152i
$761$	−156.669	−	430.444i	−0.205873	−	0.565630i	0.793188	−	0.608977i	$-0.208420\pi$
$761$	−156.669	−	430.444i	−0.205873	−	0.565630i	−0.999060	+	0.0433474i	$0.986198\pi$
$762$		0			0
$763$	−71.4101	+	266.506i	−0.0935912	+	0.349287i
$764$	−354.871	−	248.483i	−0.464491	−	0.325240i
$765$		0			0
$766$	373.899	−	647.612i	0.488119	−	0.845446i
$767$	−138.547	+	79.9901i	−0.180635	+	0.104290i
$768$		0			0
$769$	−2.76053	−	10.3024i	−0.00358976	−	0.0133972i	0.964108	−	0.265511i	$-0.0855408\pi$
$769$	−2.76053	−	10.3024i	−0.00358976	−	0.0133972i	−0.967697	+	0.252114i	$0.918874\pi$
$770$	−147.402	+	404.983i	−0.191431	+	0.525952i
$771$		0			0
$772$	−517.063	+	241.110i	−0.669770	+	0.312319i
$773$	136.342	+	773.234i	0.176380	+	1.00030i	0.936538	+	0.350565i	$0.114010\pi$
$773$	136.342	+	773.234i	0.176380	+	1.00030i	−0.760158	+	0.649738i	$0.774878\pi$
$774$		0			0
$775$	−0.0338513	−	0.386923i	−4.36791e−5	−	0.000499255i
$776$			643.303i			0.828999i
$777$		0			0
$778$	−1657.16			−2.13002
$779$	502.319	−	43.9472i	0.644825	−	0.0564149i
$780$		0			0
$781$	−715.143	+	126.099i	−0.915676	+	0.161458i
$782$	−976.994	−	2095.17i	−1.24935	−	2.67925i
$783$		0			0
$784$	243.165	+	88.5048i	0.310159	+	0.112889i
$785$	−788.560	+	211.294i	−1.00453	+	0.269164i
$786$		0			0
$787$	111.678	+	193.432i	0.141903	+	0.245784i	0.928213	−	0.372048i	$-0.121344\pi$
$787$	111.678	+	193.432i	0.141903	+	0.245784i	−0.786310	+	0.617832i	$0.788011\pi$
$788$	−1309.39	−	755.978i	−1.66167	−	0.959363i
$789$		0			0
$790$	765.903	−	1093.82i	0.969498	−	1.38459i
$791$	−79.5132	−	21.3055i	−0.100522	−	0.0269349i
$792$		0			0
$793$	573.639	−	208.787i	0.723378	−	0.263288i
$794$	211.139	−	147.841i	0.265918	−	0.186198i
$795$		0			0
$796$	1558.45	+	136.347i	1.95786	+	0.171290i
$797$	86.9127	+	124.124i	0.109050	+	0.155739i	0.869967	−	0.493109i	$-0.164140\pi$
$797$	86.9127	+	124.124i	0.109050	+	0.155739i	−0.760918	+	0.648849i	$0.775251\pi$
$798$		0			0
$799$	−457.200	−	213.196i	−0.572215	−	0.266828i
$800$	−0.332541	+	1.24106i	−0.000415676	+	0.00155132i
$801$		0			0
$802$	−89.5830	+	106.761i	−0.111699	+	0.133118i
$803$	−205.975	+	356.760i	−0.256507	+	0.444284i
$804$		0			0
$805$	469.625	+	82.8076i	0.583385	+	0.102867i
$806$	80.1915	+	299.279i	0.0994931	+	0.371313i
$807$		0			0
$808$	−679.564	+	679.564i	−0.841044	+	0.841044i
$809$	402.169	−	187.534i	0.497118	−	0.231810i	−0.157855	−	0.987462i	$-0.550458\pi$
$809$	402.169	−	187.534i	0.497118	−	0.231810i	0.654973	+	0.755652i	$0.272680\pi$
$810$		0			0
$811$	1163.16	−	976.006i	1.43423	−	1.20346i	0.491069	−	0.871121i	$-0.336606\pi$
$811$	1163.16	−	976.006i	1.43423	−	1.20346i	0.943160	−	0.332340i	$-0.107838\pi$
$812$	7.60573	+	86.9339i	0.00936666	+	0.107061i
$813$		0			0
$814$	−1048.73	+	361.421i	−1.28837	+	0.444006i
$815$	312.510			0.383448
$816$		0			0
$817$	116.257	+	138.550i	0.142297	+	0.169583i
$818$	−588.239	+	103.722i	−0.719118	+	0.126800i
$819$		0			0
$820$	−697.492	−	697.492i	−0.850600	−	0.850600i
$821$	873.407	+	317.894i	1.06383	+	0.387204i	0.813867	−	0.581051i	$-0.197358\pi$
$821$	873.407	+	317.894i	1.06383	+	0.387204i	0.249966	+	0.968255i	$0.419580\pi$
$822$		0			0
$823$	147.930	−	838.954i	0.179745	−	1.01939i	−0.752778	−	0.658275i	$-0.771287\pi$
$823$	147.930	−	838.954i	0.179745	−	1.01939i	0.932523	−	0.361111i	$-0.117602\pi$
$824$	−291.649	−	505.151i	−0.353943	−	0.613047i
$825$		0			0
$826$	136.324	+	114.389i	0.165041	+	0.138486i
$827$	493.474	−	704.754i	0.596704	−	0.852182i	−0.401260	−	0.915964i	$-0.631428\pi$
$827$	493.474	−	704.754i	0.596704	−	0.852182i	0.997964	+	0.0637825i	$0.0203164\pi$
$828$		0			0
$829$	−576.502	+	1236.31i	−0.695419	+	1.49133i	0.167439	+	0.985882i	$0.446450\pi$
$829$	−576.502	+	1236.31i	−0.695419	+	1.49133i	−0.862857	+	0.505448i	$0.831327\pi$
$830$	−1945.48	+	708.097i	−2.34395	+	0.853129i
$831$		0			0
$832$	71.4919	−	817.156i	0.0859278	−	0.982159i
$833$	−908.030	−	79.4423i	−1.09007	−	0.0953689i
$834$		0			0
$835$	337.520	+	927.329i	0.404216	+	1.11057i
$836$	−722.721	−	337.010i	−0.864499	−	0.403123i
$837$		0			0
$838$	−576.038	−	403.346i	−0.687396	−	0.481320i
$839$	386.228	−	460.289i	0.460343	−	0.548616i	−0.485076	−	0.874472i	$-0.661208\pi$
$839$	386.228	−	460.289i	0.460343	−	0.548616i	0.945419	+	0.325856i	$0.105653\pi$
$840$		0			0
$841$	703.750	−	406.310i	0.836801	−	0.483127i
$842$	−1040.42	−	183.454i	−1.23565	−	0.217879i
$843$		0			0
$844$	−705.458	+	1938.23i	−0.835850	+	2.29648i
$845$	−368.030	+	368.030i	−0.435538	+	0.435538i
$846$		0			0
$847$	−14.1288	−	80.1282i	−0.0166810	−	0.0946024i
$848$	−470.851	+	395.091i	−0.555249	+	0.465909i
$849$		0			0
$850$		−	2.19019i		−	0.00257670i
$851$	595.338	+	1073.34i	0.699575	+	1.26127i
$852$		0			0
$853$	1049.60	−	91.8283i	1.23048	−	0.107653i	0.546694	−	0.837333i	$-0.315886\pi$
$853$	1049.60	−	91.8283i	1.23048	−	0.107653i	0.683789	+	0.729679i	$0.260331\pi$
$854$	−436.487	−	520.185i	−0.511109	−	0.609115i
$855$		0			0
$856$	−16.2383	−	34.8231i	−0.0189700	−	0.0406812i
$857$	129.284	+	129.284i	0.150857	+	0.150857i	0.778501	−	0.627644i	$-0.215981\pi$
$857$	129.284	+	129.284i	0.150857	+	0.150857i	−0.627644	+	0.778501i	$0.715981\pi$
$858$		0			0
$859$	349.556	−	93.6632i	0.406933	−	0.109037i	−0.0495452	−	0.998772i	$-0.515777\pi$
$859$	349.556	−	93.6632i	0.406933	−	0.109037i	0.456479	+	0.889734i	$0.349111\pi$
$860$	61.4385	−	348.435i	0.0714402	−	0.405157i
$861$		0			0
$862$	−853.600	−	492.826i	−0.990255	−	0.571724i
$863$	−537.981	−	451.420i	−0.623385	−	0.523082i	0.275481	−	0.961307i	$-0.411163\pi$
$863$	−537.981	−	451.420i	−0.623385	−	0.523082i	−0.898865	+	0.438225i	$0.855607\pi$
$864$		0			0
$865$	−1050.64	−	281.518i	−1.21461	−	0.325454i
$866$	−369.196	+	791.743i	−0.426323	+	0.914252i
$867$		0			0
$868$	165.830	−	116.115i	0.191048	−	0.133773i
$869$	72.0297	−	823.303i	0.0828880	−	0.947414i
$870$		0			0
$871$	305.422	+	436.187i	0.350656	+	0.500789i
$872$	173.006	+	475.330i	0.198401	+	0.545103i
$873$		0			0
$874$	−388.800	+	1451.02i	−0.444851	+	1.66021i
$875$	294.759	+	206.393i	0.336868	+	0.235877i
$876$		0			0
$877$	−305.856	+	529.758i	−0.348752	+	0.604057i	−0.986028	−	0.166579i	$-0.946728\pi$
$877$	−305.856	+	529.758i	−0.348752	+	0.604057i	0.637276	+	0.770636i	$0.280061\pi$
$878$	623.237	−	359.826i	0.709837	−	0.409825i
$879$		0			0
$880$	−79.1304	−	295.319i	−0.0899209	−	0.335590i
$881$	266.254	−	731.526i	0.302217	−	0.830336i	−0.691897	−	0.721997i	$-0.743225\pi$
$881$	266.254	−	731.526i	0.302217	−	0.830336i	0.994114	−	0.108339i	$-0.0345532\pi$
$882$		0			0
$883$	−385.426	+	179.727i	−0.436496	+	0.203542i	−0.628430	−	0.777866i	$-0.716302\pi$
$883$	−385.426	+	179.727i	−0.436496	+	0.203542i	0.191933	+	0.981408i	$0.438524\pi$
$884$	178.205	+	1010.65i	0.201589	+	1.14327i
$885$		0			0
$886$	44.2274	+	505.522i	0.0499181	+	0.570566i
$887$			324.900i			0.366291i	0.983086	+	0.183146i	$0.0586280\pi$
$887$			324.900i			0.366291i	−0.983086	+	0.183146i	$0.941372\pi$
$888$		0			0
$889$	260.511			0.293038
$890$	2074.49	−	181.494i	2.33088	−	0.203926i
$891$		0			0
$892$	1141.66	−	201.306i	1.27989	−	0.225680i
$893$	138.537	+	297.093i	0.155136	+	0.332691i
$894$		0			0
$895$	1145.85	+	417.057i	1.28028	+	0.465985i
$896$	−426.950	+	114.401i	−0.476506	+	0.127680i
$897$		0			0
$898$	−153.823	−	266.429i	−0.171295	−	0.296691i
$899$	57.0158	+	32.9181i	0.0634214	+	0.0366164i
$900$		0			0
$901$	1241.83	−	1773.52i	1.37828	−	1.96839i
$902$	−1003.96	−	269.010i	−1.11304	−	0.298238i
$903$		0			0
$904$	−141.817	+	51.6170i	−0.156877	+	0.0570985i
$905$	1018.42	−	713.105i	1.12533	−	0.787962i
$906$		0			0
$907$	−481.154	−	42.0956i	−0.530490	−	0.0464119i	−0.181235	−	0.983440i	$-0.558010\pi$
$907$	−481.154	−	42.0956i	−0.530490	−	0.0464119i	−0.349255	+	0.937028i	$0.613565\pi$
$908$	397.021	+	567.004i	0.437248	+	0.624454i
$909$		0			0
$910$	−326.638	−	152.314i	−0.358943	−	0.167378i
$911$	−216.688	+	808.690i	−0.237857	+	0.887695i	0.738983	+	0.673724i	$0.235306\pi$
$911$	−216.688	+	808.690i	−0.237857	+	0.887695i	−0.976840	+	0.213971i	$0.931360\pi$
$912$		0			0
$913$	−823.648	+	981.585i	−0.902133	+	1.07512i
$914$	273.471	−	473.666i	0.299202	−	0.518234i
$915$		0			0
$916$	−1500.24	−	264.533i	−1.63782	−	0.288792i
$917$	132.024	+	492.719i	0.143974	+	0.537317i
$918$		0			0
$919$	635.279	−	635.279i	0.691273	−	0.691273i	−0.271239	−	0.962512i	$-0.587434\pi$
$919$	635.279	−	635.279i	0.691273	−	0.691273i	0.962512	+	0.271239i	$0.0874335\pi$
$920$	792.358	−	369.483i	0.861259	−	0.401611i
$921$		0			0
$922$	−872.726	+	732.304i	−0.946557	+	0.794256i
$923$	−52.9270	−	604.959i	−0.0573424	−	0.655427i
$924$		0			0
$925$	0.0814254	+	1.15999i	8.80275e−5	+	0.00125405i
$926$	2293.89			2.47720
$927$		0			0
$928$	−139.991	−	166.835i	−0.150853	−	0.179779i
$929$	141.977	−	25.0343i	0.152828	−	0.0269476i	−0.0967109	−	0.995313i	$-0.530832\pi$
$929$	141.977	−	25.0343i	0.152828	−	0.0269476i	0.249538	+	0.968365i	$0.419721\pi$
$930$		0			0
$931$	418.819	+	418.819i	0.449860	+	0.449860i
$932$	1395.12	+	507.783i	1.49691	+	0.544831i
$933$		0			0
$934$	−231.313	+	1311.84i	−0.247659	+	1.40454i
$935$	538.466	+	932.650i	0.575899	+	0.997487i
$936$		0			0
$937$	1240.87	+	1041.22i	1.32430	+	1.11122i	0.985373	+	0.170411i	$0.0545096\pi$
$937$	1240.87	+	1041.22i	1.32430	+	1.11122i	0.338930	+	0.940811i	$0.389935\pi$
$938$	339.743	−	485.203i	0.362199	−	0.517274i
$939$		0			0
$940$	271.009	−	581.181i	0.288307	−	0.618277i
$941$	264.623	−	96.3150i	0.281215	−	0.102354i	−0.197562	−	0.980290i	$-0.563302\pi$
$941$	264.623	−	96.3150i	0.281215	−	0.102354i	0.478777	+	0.877936i	$0.341080\pi$
$942$		0			0
$943$	−100.235	+	1145.69i	−0.106293	+	1.21494i
$944$	−125.764	−	11.0030i	−0.133225	−	0.0116557i
$945$		0			0
$946$	−127.509	−	350.328i	−0.134787	−	0.370326i
$947$	1114.71	+	519.798i	1.17710	+	0.548889i	0.909930	−	0.414761i	$-0.136135\pi$
$947$	1114.71	+	519.798i	1.17710	+	0.548889i	0.267166	+	0.963650i	$0.413913\pi$
$948$		0			0
$949$	−282.195	−	197.595i	−0.297361	−	0.208214i
$950$	−0.914821	+	1.09024i	−0.000962969	+	0.00114762i
$951$		0			0
$952$	294.122	−	169.812i	0.308952	−	0.178373i
$953$	1365.44	+	240.764i	1.43278	+	0.252638i	0.835542	−	0.549427i	$-0.185154\pi$
$953$	1365.44	+	240.764i	1.43278	+	0.252638i	0.597237	+	0.802065i	$0.296265\pi$
$954$		0			0
$955$	130.028	−	357.249i	0.136155	−	0.374082i
$956$	−466.147	+	466.147i	−0.487602	+	0.487602i
$957$		0			0
$958$	380.522	+	2158.05i	0.397205	+	2.25266i
$959$	174.709	−	146.598i	0.182178	−	0.152866i
$960$		0			0
$961$			808.272i			0.841074i
$962$	−224.654	−	900.016i	−0.233528	−	0.935568i
$963$		0			0
$964$	−263.564	+	23.0589i	−0.273407	+	0.0239200i
$965$	−321.821	−	383.531i	−0.333493	−	0.397441i
$966$		0			0
$967$	−175.866	−	377.146i	−0.181868	−	0.390017i	0.794145	−	0.607728i	$-0.207919\pi$
$967$	−175.866	−	377.146i	−0.181868	−	0.390017i	−0.976013	+	0.217711i	$0.930141\pi$
$968$	−105.479	−	105.479i	−0.108966	−	0.108966i
$969$		0			0
$970$	−1832.91	+	491.127i	−1.88960	+	0.506316i
$971$	303.997	−	1724.05i	0.313076	−	1.77554i	−0.269735	−	0.962935i	$-0.586936\pi$
$971$	303.997	−	1724.05i	0.313076	−	1.77554i	0.582811	−	0.812608i	$-0.301953\pi$
$972$		0			0
$973$	508.800	+	293.756i	0.522919	+	0.301907i
$974$	−1059.01	−	888.615i	−1.08728	−	0.912336i
$975$		0			0
$976$	465.311	+	124.680i	0.476754	+	0.127746i
$977$	437.152	−	937.474i	0.447443	−	0.959544i	−0.545182	−	0.838318i	$-0.683540\pi$
$977$	437.152	−	937.474i	0.447443	−	0.959544i	0.992625	−	0.121226i	$-0.0386827\pi$
$978$		0			0
$979$	1055.76	−	739.249i	1.07840	−	0.755106i
$980$	100.985	−	1154.26i	0.103046	−	1.17782i
$981$		0			0
$982$	565.853	+	808.122i	0.576225	+	0.822935i
$983$	101.846	+	279.821i	0.103608	+	0.284660i	0.980655	−	0.195744i	$-0.0627122\pi$
$983$	101.846	+	279.821i	0.103608	+	0.284660i	−0.877047	+	0.480404i	$0.840490\pi$
$984$		0			0
$985$	343.411	−	1281.63i	0.348641	−	1.30114i
$986$	304.111	+	212.941i	0.308429	+	0.215964i
$987$		0			0
$988$	333.430	−	577.518i	0.337480	−	0.584533i
$989$	−357.247	+	206.257i	−0.361220	+	0.208551i
$990$		0			0
$991$	−298.760	−	1114.99i	−0.301473	−	1.12511i	−0.935939	−	0.352163i	$-0.885446\pi$
$991$	−298.760	−	1114.99i	−0.301473	−	1.12511i	0.634465	−	0.772951i	$-0.281220\pi$
$992$	−172.798	+	474.758i	−0.174191	+	0.478587i
$993$		0			0
$994$	−612.221	+	285.483i	−0.615916	+	0.287206i
$995$	238.396	+	1352.01i	0.239594	+	1.35880i
$996$		0			0
$997$	−74.6783	−	853.577i	−0.0749030	−	0.856146i	−0.936983	−	0.349374i	$-0.886394\pi$
$997$	−74.6783	−	853.577i	−0.0749030	−	0.856146i	0.862080	−	0.506772i	$-0.169161\pi$
$998$			846.896i			0.848593i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	333.3.bu.c.19.6		72
3.2	odd	2		111.3.r.a.19.1	✓	72
37.2	odd	36	inner	333.3.bu.c.298.6		72
111.2	even	36		111.3.r.a.76.1	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
111.3.r.a.19.1	✓	72	3.2	odd	2
111.3.r.a.76.1	yes	72	111.2	even	36
333.3.bu.c.19.6		72	1.1	even	1	trivial
333.3.bu.c.298.6		72	37.2	odd	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	333.bu (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(3.10167 - 0.271361i) q^{2} +(5.60750 - 0.988754i) q^{4} +(2.11176 + 4.52869i) q^{5} +(2.70338 + 0.983949i) q^{7} +(5.09460 - 1.36510i) q^{8} +O(q^{10})\)	\(q+(3.10167 - 0.271361i) q^{2} +(5.60750 - 0.988754i) q^{4} +(2.11176 + 4.52869i) q^{5} +(2.70338 + 0.983949i) q^{7} +(5.09460 - 1.36510i) q^{8} +(7.77891 + 13.4735i) q^{10} +(8.33897 + 4.81450i) q^{11} +(-4.61863 + 6.59608i) q^{13} +(8.65199 + 2.31829i) q^{14} +(-5.97111 + 2.17330i) q^{16} +(18.3347 - 12.8381i) q^{17} +(-14.4890 - 1.26763i) q^{19} +(16.3195 + 23.3066i) q^{20} +(27.1712 + 12.6701i) q^{22} +(8.58575 - 32.0425i) q^{23} +(0.0202017 - 0.0240755i) q^{25} +(-12.5355 + 21.7122i) q^{26} +(16.1321 + 2.84452i) q^{28} +(1.37880 + 5.14577i) q^{29} +(8.73864 - 8.73864i) q^{31} +(-37.0513 + 17.2773i) q^{32} +(53.3845 - 44.7949i) q^{34} +(1.25289 + 14.3206i) q^{35} +(-26.6087 + 25.7095i) q^{37} -45.2843 q^{38} +(16.9407 + 20.1891i) q^{40} +(-34.1422 + 6.02019i) q^{41} +(-8.79308 - 8.79308i) q^{43} +(51.5211 + 18.7522i) q^{44} +(17.9351 - 101.715i) q^{46} +(-11.2691 - 19.5187i) q^{47} +(-31.1961 - 26.1766i) q^{49} +(0.0561260 - 0.0801562i) q^{50} +(-19.3771 + 41.5542i) q^{52} +(90.8964 - 33.0836i) q^{53} +(-4.19348 + 47.9317i) q^{55} +(15.1158 + 1.32246i) q^{56} +(5.67296 + 15.5863i) q^{58} +(18.0061 + 8.39640i) q^{59} +(-62.1006 - 43.4833i) q^{61} +(24.7331 - 29.4757i) q^{62} +(-88.2206 + 50.9342i) q^{64} +(-39.6251 - 6.98697i) q^{65} +(22.6172 - 62.1402i) q^{67} +(90.1182 - 90.1182i) q^{68} +(7.77212 + 44.0779i) q^{70} +(-57.7715 + 48.4761i) q^{71} +42.7823i q^{73} +(-75.5550 + 86.9629i) q^{74} +(-82.5007 + 7.21788i) q^{76} +(17.8061 + 21.2205i) q^{77} +(-36.2729 - 77.7875i) q^{79} +(-22.4518 - 22.4518i) q^{80} +(-104.264 + 27.9375i) q^{82} +(-23.1080 + 131.052i) q^{83} +(96.8584 + 55.9212i) q^{85} +(-29.6593 - 24.8871i) q^{86} +(49.0560 + 13.1445i) q^{88} +(56.5674 - 121.309i) q^{89} +(-18.9761 + 13.2872i) q^{91} +(16.4625 - 188.167i) q^{92} +(-40.2498 - 57.4827i) q^{94} +(-24.8567 - 68.2933i) q^{95} +(-31.5679 + 117.813i) q^{97} +(-103.863 - 72.7259i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 18 q^{4} + 18 q^{5} - 66 q^{8}+O(q^{10}) \) 72 * q - 18 * q^4 + 18 * q^5 - 66 * q^8	\( 72 q - 18 q^{4} + 18 q^{5} - 66 q^{8} - 72 q^{13} - 42 q^{14} - 6 q^{16} + 24 q^{17} + 108 q^{19} + 354 q^{20} + 18 q^{25} + 30 q^{26} + 48 q^{28} + 156 q^{29} - 60 q^{31} + 192 q^{32} - 90 q^{34} - 24 q^{35} - 294 q^{37} + 120 q^{38} + 612 q^{40} - 300 q^{41} - 60 q^{43} - 174 q^{44} + 234 q^{46} - 66 q^{47} - 144 q^{49} + 252 q^{50} + 912 q^{52} - 234 q^{53} + 234 q^{55} - 312 q^{56} - 1014 q^{58} + 18 q^{59} - 720 q^{61} + 1092 q^{62} + 54 q^{64} + 54 q^{65} - 708 q^{67} + 408 q^{68} - 228 q^{70} - 234 q^{74} + 90 q^{76} + 18 q^{77} + 360 q^{79} - 924 q^{80} + 1134 q^{82} - 438 q^{83} - 756 q^{85} - 396 q^{86} + 684 q^{88} - 1470 q^{89} + 1170 q^{91} - 1602 q^{92} - 1008 q^{94} + 984 q^{95} - 774 q^{97} + 1038 q^{98}+O(q^{100}) \) 72 * q - 18 * q^4 + 18 * q^5 - 66 * q^8 - 72 * q^13 - 42 * q^14 - 6 * q^16 + 24 * q^17 + 108 * q^19 + 354 * q^20 + 18 * q^25 + 30 * q^26 + 48 * q^28 + 156 * q^29 - 60 * q^31 + 192 * q^32 - 90 * q^34 - 24 * q^35 - 294 * q^37 + 120 * q^38 + 612 * q^40 - 300 * q^41 - 60 * q^43 - 174 * q^44 + 234 * q^46 - 66 * q^47 - 144 * q^49 + 252 * q^50 + 912 * q^52 - 234 * q^53 + 234 * q^55 - 312 * q^56 - 1014 * q^58 + 18 * q^59 - 720 * q^61 + 1092 * q^62 + 54 * q^64 + 54 * q^65 - 708 * q^67 + 408 * q^68 - 228 * q^70 - 234 * q^74 + 90 * q^76 + 18 * q^77 + 360 * q^79 - 924 * q^80 + 1134 * q^82 - 438 * q^83 - 756 * q^85 - 396 * q^86 + 684 * q^88 - 1470 * q^89 + 1170 * q^91 - 1602 * q^92 - 1008 * q^94 + 984 * q^95 - 774 * q^97 + 1038 * q^98

Introduction

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