LMFDB - Embedded newform 45.4.l.a.2.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,4,Mod(2,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("45.2");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	45.l (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.65508595026$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			2.14
Character	$\chi$	$=$	45.2
Dual form			45.4.l.a.23.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11026 + 4.14355i) q^{2} +(-4.87317 - 1.80338i) q^{3} +(-9.00816 + 5.20086i) q^{4} +(-9.88574 + 5.22228i) q^{5} +(2.06189 - 22.1945i) q^{6} +(-14.5845 + 3.90791i) q^{7} +(-7.28515 - 7.28515i) q^{8} +(20.4957 + 17.5763i) q^{9} +O(q^{10})$	\(q+(1.11026 + 4.14355i) q^{2} +(-4.87317 - 1.80338i) q^{3} +(-9.00816 + 5.20086i) q^{4} +(-9.88574 + 5.22228i) q^{5} +(2.06189 - 22.1945i) q^{6} +(-14.5845 + 3.90791i) q^{7} +(-7.28515 - 7.28515i) q^{8} +(20.4957 + 17.5763i) q^{9} +(-32.6146 - 35.1640i) q^{10} +(42.5632 + 24.5739i) q^{11} +(53.2775 - 9.09960i) q^{12} +(-33.7651 - 9.04733i) q^{13} +(-32.3853 - 56.0930i) q^{14} +(57.5927 - 7.62135i) q^{15} +(-19.5089 + 33.7905i) q^{16} +(18.9033 - 18.9033i) q^{17} +(-50.0730 + 104.439i) q^{18} +53.7656i q^{19} +(61.8920 - 98.4575i) q^{20} +(78.1204 + 7.25747i) q^{21} +(-54.5669 + 203.647i) q^{22} +(-45.7984 + 170.922i) q^{23} +(22.3639 + 48.6397i) q^{24} +(70.4556 - 103.252i) q^{25} -149.952i q^{26} +(-68.1821 - 122.614i) q^{27} +(111.055 - 111.055i) q^{28} +(110.003 - 190.531i) q^{29} +(95.5224 + 230.177i) q^{30} +(-22.1047 - 38.2864i) q^{31} +(-241.286 - 64.6525i) q^{32} +(-163.102 - 196.510i) q^{33} +(99.3145 + 57.3392i) q^{34} +(123.771 - 114.797i) q^{35} +(-276.040 - 51.7355i) q^{36} +(169.138 + 169.138i) q^{37} +(-222.781 + 59.6939i) q^{38} +(148.227 + 104.980i) q^{39} +(110.064 + 33.9740i) q^{40} +(42.1171 - 24.3163i) q^{41} +(56.6624 + 331.754i) q^{42} +(-92.3811 - 344.771i) q^{43} -511.222 q^{44} +(-294.403 - 66.7212i) q^{45} -759.073 q^{46} +(137.261 + 512.264i) q^{47} +(156.007 - 129.485i) q^{48} +(-99.6102 + 57.5100i) q^{49} +(506.055 + 177.300i) q^{50} +(-126.209 + 58.0293i) q^{51} +(351.215 - 94.1079i) q^{52} +(198.516 + 198.516i) q^{53} +(432.358 - 418.650i) q^{54} +(-549.101 - 20.6541i) q^{55} +(134.720 + 77.7807i) q^{56} +(96.9596 - 262.009i) q^{57} +(911.609 + 244.265i) q^{58} +(64.3921 + 111.530i) q^{59} +(-479.166 + 368.186i) q^{60} +(-33.4727 + 57.9764i) q^{61} +(134.100 - 134.100i) q^{62} +(-367.606 - 176.247i) q^{63} -759.421i q^{64} +(381.041 - 86.8911i) q^{65} +(633.166 - 894.000i) q^{66} +(18.6925 - 69.7613i) q^{67} +(-71.9705 + 268.597i) q^{68} +(531.420 - 750.341i) q^{69} +(613.086 + 385.395i) q^{70} +1038.75i q^{71} +(-21.2676 - 277.360i) q^{72} +(339.210 - 339.210i) q^{73} +(-513.044 + 888.619i) q^{74} +(-529.545 + 376.107i) q^{75} +(-279.627 - 484.329i) q^{76} +(-716.797 - 192.065i) q^{77} +(-270.421 + 730.744i) q^{78} +(297.681 + 171.866i) q^{79} +(16.3970 - 435.925i) q^{80} +(111.144 + 720.478i) q^{81} +(147.517 + 147.517i) q^{82} +(-841.890 + 225.584i) q^{83} +(-741.466 + 340.917i) q^{84} +(-88.1548 + 285.591i) q^{85} +(1326.01 - 765.572i) q^{86} +(-879.665 + 730.114i) q^{87} +(-131.055 - 489.104i) q^{88} +230.315 q^{89} +(-50.4019 - 1293.95i) q^{90} +527.804 q^{91} +(-476.383 - 1777.88i) q^{92} +(38.6751 + 226.440i) q^{93} +(-1970.20 + 1137.50i) q^{94} +(-280.779 - 531.512i) q^{95} +(1059.24 + 750.193i) q^{96} +(553.082 - 148.198i) q^{97} +(-348.889 - 348.889i) q^{98} +(440.442 + 1251.76i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) $ 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7	$ 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 8 q^{10} - 36 q^{11} - 138 q^{12} - 2 q^{13} - 96 q^{15} + 316 q^{16} - 480 q^{18} + 378 q^{20} + 480 q^{21} - 34 q^{22} + 306 q^{23} - 146 q^{25} + 180 q^{27} - 232 q^{28} - 1170 q^{30} - 4 q^{31} - 1770 q^{32} - 294 q^{33} - 216 q^{36} + 136 q^{37} + 114 q^{38} + 126 q^{40} + 1992 q^{41} + 1698 q^{42} - 2 q^{43} + 1134 q^{45} - 952 q^{46} + 3462 q^{47} + 4326 q^{48} + 666 q^{50} - 2496 q^{51} - 242 q^{52} + 284 q^{55} - 7128 q^{56} - 2544 q^{57} + 534 q^{58} + 1818 q^{60} + 32 q^{61} - 4038 q^{63} - 2094 q^{65} + 2892 q^{66} + 610 q^{67} - 2694 q^{68} + 498 q^{70} - 1854 q^{72} - 8 q^{73} - 6408 q^{75} + 1368 q^{76} - 6486 q^{77} + 1434 q^{78} + 3012 q^{81} - 3784 q^{82} + 2814 q^{83} - 1658 q^{85} + 12480 q^{86} + 4830 q^{87} - 1338 q^{88} + 13914 q^{90} + 992 q^{91} + 13152 q^{92} + 8310 q^{93} + 4284 q^{95} - 7932 q^{96} + 358 q^{97}+O(q^{100}) $ 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 8 * q^10 - 36 * q^11 - 138 * q^12 - 2 * q^13 - 96 * q^15 + 316 * q^16 - 480 * q^18 + 378 * q^20 + 480 * q^21 - 34 * q^22 + 306 * q^23 - 146 * q^25 + 180 * q^27 - 232 * q^28 - 1170 * q^30 - 4 * q^31 - 1770 * q^32 - 294 * q^33 - 216 * q^36 + 136 * q^37 + 114 * q^38 + 126 * q^40 + 1992 * q^41 + 1698 * q^42 - 2 * q^43 + 1134 * q^45 - 952 * q^46 + 3462 * q^47 + 4326 * q^48 + 666 * q^50 - 2496 * q^51 - 242 * q^52 + 284 * q^55 - 7128 * q^56 - 2544 * q^57 + 534 * q^58 + 1818 * q^60 + 32 * q^61 - 4038 * q^63 - 2094 * q^65 + 2892 * q^66 + 610 * q^67 - 2694 * q^68 + 498 * q^70 - 1854 * q^72 - 8 * q^73 - 6408 * q^75 + 1368 * q^76 - 6486 * q^77 + 1434 * q^78 + 3012 * q^81 - 3784 * q^82 + 2814 * q^83 - 1658 * q^85 + 12480 * q^86 + 4830 * q^87 - 1338 * q^88 + 13914 * q^90 + 992 * q^91 + 13152 * q^92 + 8310 * q^93 + 4284 * q^95 - 7932 * q^96 + 358 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.11026	+	4.14355i	0.392537	+	1.46497i	0.825935	+	0.563765i	$0.190648\pi$
$2$	1.11026	+	4.14355i	0.392537	+	1.46497i	−0.433398	+	0.901203i	$0.642686\pi$
$3$	−4.87317	−	1.80338i	−0.937843	−	0.347060i
$3$	−4.87317	−	1.80338i	−0.937843	−	0.347060i
$4$	−9.00816	+	5.20086i	−1.12602	+	0.650108i
$5$	−9.88574	+	5.22228i	−0.884207	+	0.467095i
$5$	−9.88574	+	5.22228i	−0.884207	+	0.467095i
$6$	2.06189	−	22.1945i	0.140294	−	1.51014i
$7$	−14.5845	+	3.90791i	−0.787490	+	0.211007i	−0.630084	−	0.776527i	$-0.716980\pi$
$7$	−14.5845	+	3.90791i	−0.787490	+	0.211007i	−0.157406	+	0.987534i	$0.550313\pi$
$8$	−7.28515	−	7.28515i	−0.321961	−	0.321961i
$9$	20.4957	+	17.5763i	0.759098	+	0.650976i
$10$	−32.6146	−	35.1640i	−1.03136	−	1.11198i
$11$	42.5632	+	24.5739i	1.16666	+	0.673573i	0.952892	−	0.303310i	$-0.0980919\pi$
$11$	42.5632	+	24.5739i	1.16666	+	0.673573i	0.213771	+	0.976884i	$0.431425\pi$
$12$	53.2775	−	9.09960i	1.28166	−	0.218902i
$13$	−33.7651	−	9.04733i	−0.720366	−	0.193021i	−0.120031	−	0.992770i	$-0.538299\pi$
$13$	−33.7651	−	9.04733i	−0.720366	−	0.193021i	−0.600335	+	0.799749i	$0.704966\pi$
$14$	−32.3853	−	56.0930i	−0.618238	−	1.07082i
$15$	57.5927	−	7.62135i	0.991357	−	0.131188i
$16$	−19.5089	+	33.7905i	−0.304827	+	0.527976i
$17$	18.9033	−	18.9033i	0.269690	−	0.269690i	−0.559285	−	0.828975i	$-0.688924\pi$
$17$	18.9033	−	18.9033i	0.269690	−	0.269690i	0.828975	+	0.559285i	$0.188924\pi$
$18$	−50.0730	+	104.439i	−0.655685	+	1.36759i
$19$			53.7656i			0.649193i	0.945853	+	0.324596i	$0.105228\pi$
$19$			53.7656i			0.649193i	−0.945853	+	0.324596i	$0.894772\pi$
$20$	61.8920	−	98.4575i	0.691973	−	1.10079i
$21$	78.1204	+	7.25747i	0.811774	+	0.0754148i
$22$	−54.5669	+	203.647i	−0.528805	+	1.97353i
$23$	−45.7984	+	170.922i	−0.415201	+	1.54955i	0.369231	+	0.929338i	$0.379621\pi$
$23$	−45.7984	+	170.922i	−0.415201	+	1.54955i	−0.784432	+	0.620214i	$0.787046\pi$
$24$	22.3639	+	48.6397i	0.190209	+	0.413689i
$25$	70.4556	−	103.252i	0.563645	−	0.826017i
$26$		−	149.952i		−	1.13108i
$27$	−68.1821	−	122.614i	−0.485987	−	0.873966i
$28$	111.055	−	111.055i	0.749552	−	0.749552i
$29$	110.003	−	190.531i	0.704382	−	1.22003i	−0.262532	−	0.964923i	$-0.584557\pi$
$29$	110.003	−	190.531i	0.704382	−	1.22003i	0.966914	−	0.255103i	$-0.0821092\pi$
$30$	95.5224	+	230.177i	0.581331	+	1.40081i
$31$	−22.1047	−	38.2864i	−0.128068	−	0.221821i	0.794860	−	0.606793i	$-0.207544\pi$
$31$	−22.1047	−	38.2864i	−0.128068	−	0.221821i	−0.922928	+	0.384972i	$0.874211\pi$
$32$	−241.286	−	64.6525i	−1.33293	−	0.357158i
$33$	−163.102	−	196.510i	−0.860376	−	1.03661i
$34$	99.3145	+	57.3392i	0.500950	+	0.289224i
$35$	123.771	−	114.797i	0.597744	−	0.554407i
$36$	−276.040	−	51.7355i	−1.27796	−	0.239516i
$37$	169.138	+	169.138i	0.751516	+	0.751516i	0.974762	−	0.223246i	$-0.0716654\pi$
$37$	169.138	+	169.138i	0.751516	+	0.751516i	−0.223246	+	0.974762i	$0.571665\pi$
$38$	−222.781	+	59.6939i	−0.951047	+	0.254832i
$39$	148.227	+	104.980i	0.608600	+	0.431034i
$40$	110.064	+	33.9740i	0.435067	+	0.134294i
$41$	42.1171	−	24.3163i	0.160429	−	0.0926237i	−0.417636	−	0.908614i	$-0.637141\pi$
$41$	42.1171	−	24.3163i	0.160429	−	0.0926237i	0.578065	+	0.815991i	$0.303808\pi$
$42$	56.6624	+	331.754i	0.208171	+	1.21883i
$43$	−92.3811	−	344.771i	−0.327628	−	1.22272i	−0.911644	−	0.410981i	$-0.865186\pi$
$43$	−92.3811	−	344.771i	−0.327628	−	1.22272i	0.584016	−	0.811742i	$-0.301480\pi$
$44$	−511.222			−1.75158
$45$	−294.403	−	66.7212i	−0.975268	−	0.221027i
$46$	−759.073			−2.43303
$47$	137.261	+	512.264i	0.425990	+	1.58982i	0.761751	+	0.647870i	$0.224340\pi$
$47$	137.261	+	512.264i	0.425990	+	1.58982i	−0.335761	+	0.941947i	$0.608993\pi$
$48$	156.007	−	129.485i	0.469119	−	0.389365i
$49$	−99.6102	+	57.5100i	−0.290409	+	0.167667i
$50$	506.055	+	177.300i	1.43134	+	0.501480i
$51$	−126.209	+	58.0293i	−0.346525	+	0.159328i
$52$	351.215	−	94.1079i	0.936631	−	0.250969i
$53$	198.516	+	198.516i	0.514496	+	0.514496i	0.915901	−	0.401405i	$-0.131478\pi$
$53$	198.516	+	198.516i	0.514496	+	0.514496i	−0.401405	+	0.915901i	$0.631478\pi$
$54$	432.358	−	418.650i	1.08956	−	1.05502i
$55$	−549.101	−	20.6541i	−1.34619	−	0.0506363i
$56$	134.720	+	77.7807i	0.321477	+	0.185605i
$57$	96.9596	−	262.009i	0.225309	−	0.608841i
$58$	911.609	+	244.265i	2.06379	+	0.552992i
$59$	64.3921	+	111.530i	0.142087	+	0.246102i	0.928282	−	0.371876i	$-0.121285\pi$
$59$	64.3921	+	111.530i	0.142087	+	0.246102i	−0.786195	+	0.617978i	$0.787952\pi$
$60$	−479.166	+	368.186i	−1.03100	+	0.792210i
$61$	−33.4727	+	57.9764i	−0.0702581	+	0.121691i	−0.899014	−	0.437919i	$-0.855716\pi$
$61$	−33.4727	+	57.9764i	−0.0702581	+	0.121691i	0.828756	+	0.559610i	$0.189049\pi$
$62$	134.100	−	134.100i	0.274689	−	0.274689i
$63$	−367.606	−	176.247i	−0.735143	−	0.352462i
$64$		−	759.421i		−	1.48324i
$65$	381.041	−	86.8911i	0.727112	−	0.165808i
$66$	633.166	−	894.000i	1.18087	−	1.66733i
$67$	18.6925	−	69.7613i	0.0340843	−	0.127204i	−0.946787	−	0.321860i	$-0.895692\pi$
$67$	18.6925	−	69.7613i	0.0340843	−	0.127204i	0.980872	+	0.194655i	$0.0623588\pi$
$68$	−71.9705	+	268.597i	−0.128349	+	0.479003i
$69$	531.420	−	750.341i	0.927181	−	1.30914i
$70$	613.086	+	385.395i	1.04682	+	0.658051i
$71$			1038.75i			1.73629i	0.496313	+	0.868143i	$0.334687\pi$
$71$			1038.75i			1.73629i	−0.496313	+	0.868143i	$0.665313\pi$
$72$	−21.2676	−	277.360i	−0.0348112	−	0.453989i
$73$	339.210	−	339.210i	0.543857	−	0.543857i	−0.380800	−	0.924657i	$-0.624351\pi$
$73$	339.210	−	339.210i	0.543857	−	0.543857i	0.924657	+	0.380800i	$0.124351\pi$
$74$	−513.044	+	888.619i	−0.805949	+	1.39594i
$75$	−529.545	+	376.107i	−0.815288	+	0.579055i
$76$	−279.627	−	484.329i	−0.422045	−	0.731004i
$77$	−716.797	−	192.065i	−1.06086	−	0.284258i
$78$	−270.421	+	730.744i	−0.392553	+	1.06078i
$79$	297.681	+	171.866i	0.423946	+	0.244766i	0.696764	−	0.717300i	$-0.254622\pi$
$79$	297.681	+	171.866i	0.423946	+	0.244766i	−0.272818	+	0.962066i	$0.587956\pi$
$80$	16.3970	−	435.925i	0.0229156	−	0.609223i
$81$	111.144	+	720.478i	0.152461	+	0.988310i
$82$	147.517	+	147.517i	0.198665	+	0.198665i
$83$	−841.890	+	225.584i	−1.11337	+	0.298326i	−0.768196	−	0.640214i	$-0.778845\pi$
$83$	−841.890	+	225.584i	−1.11337	+	0.298326i	−0.345170	+	0.938540i	$0.612179\pi$
$84$	−741.466	+	340.917i	−0.963102	+	0.442822i
$85$	−88.1548	+	285.591i	−0.112491	+	0.364432i
$86$	1326.01	−	765.572i	1.66264	−	0.959928i
$87$	−879.665	+	730.114i	−1.08402	+	0.899730i
$88$	−131.055	−	489.104i	−0.158756	−	0.592485i
$89$	230.315			0.274307			0.137153	−	0.990550i	$-0.456205\pi$
$89$	230.315			0.274307			0.137153	+	0.990550i	$0.456205\pi$
$90$	−50.4019	−	1293.95i	−0.0590314	−	1.51550i
$91$	527.804			0.608010
$92$	−476.383	−	1777.88i	−0.539851	−	2.01475i
$93$	38.6751	+	226.440i	0.0431228	+	0.252481i
$94$	−1970.20	+	1137.50i	−2.16181	+	1.24812i
$95$	−280.779	−	531.512i	−0.303234	−	0.574021i
$96$	1059.24	+	750.193i	1.12612	+	0.797565i
$97$	553.082	−	148.198i	0.578938	−	0.155126i	0.0425454	−	0.999095i	$-0.486453\pi$
$97$	553.082	−	148.198i	0.578938	−	0.155126i	0.536393	+	0.843969i	$0.319787\pi$
$98$	−348.889	−	348.889i	−0.359624	−	0.359624i
$99$	440.442	+	1251.76i	0.447132	+	1.27078i
$100$	−97.6755	+	1296.54i	−0.0976755	+	1.29654i
$101$	−122.461	−	70.7028i	−0.120647	−	0.0696554i	0.438462	−	0.898750i	$-0.355523\pi$
$101$	−122.461	−	70.7028i	−0.120647	−	0.0696554i	−0.559109	+	0.829094i	$0.688857\pi$
$102$	−380.572	−	458.526i	−0.369434	−	0.445106i
$103$	115.727	+	31.0089i	0.110708	+	0.0296641i	0.313748	−	0.949506i	$-0.398415\pi$
$103$	115.727	+	31.0089i	0.110708	+	0.0296641i	−0.203040	+	0.979170i	$0.565082\pi$
$104$	180.073	+	311.895i	0.169784	+	0.294075i
$105$	−810.178	+	336.221i	−0.753003	+	0.312493i
$106$	−602.157	+	1042.97i	−0.551761	+	0.955678i
$107$	940.778	−	940.778i	0.849985	−	0.849985i	−0.140146	−	0.990131i	$-0.544757\pi$
$107$	940.778	−	940.778i	0.849985	−	0.849985i	0.990131	+	0.140146i	$0.0447571\pi$
$108$	1251.89	+	749.921i	1.11540	+	0.668159i
$109$		−	1052.78i		−	0.925121i	−0.886588	−	0.462560i	$-0.846931\pi$
$109$		−	1052.78i		−	0.925121i	0.886588	−	0.462560i	$-0.153069\pi$
$110$	−524.064	−	2298.16i	−0.454251	−	1.99201i
$111$	−519.219	−	1129.26i	−0.443982	−	0.965625i
$112$	152.478	−	569.057i	0.128642	−	0.480097i
$113$	303.543	−	1132.84i	0.252699	−	0.943085i	−0.716657	−	0.697425i	$-0.754329\pi$
$113$	303.543	−	1132.84i	0.252699	−	0.943085i	0.969356	−	0.245659i	$-0.0790045\pi$
$114$	1193.30	+	110.859i	0.980374	+	0.0910779i
$115$	−439.851	−	1928.86i	−0.356663	−	1.56406i
$116$			2288.45i			1.83170i
$117$	−533.019	−	778.898i	−0.421176	−	0.615463i
$118$	−390.640	+	390.640i	−0.304757	+	0.304757i
$119$	−201.823	+	349.568i	−0.155471	+	0.269284i
$120$	−475.094	−	364.048i	−0.361416	−	0.276941i
$121$	542.252	+	939.209i	0.407402	+	0.705641i
$122$	−277.392	−	74.3270i	−0.205852	−	0.0551578i
$123$	−249.095	+	42.5446i	−0.182603	+	0.0311880i
$124$	398.245	+	229.927i	0.288415	+	0.166517i
$125$	−157.295	+	1388.66i	−0.112551	+	0.993646i
$126$	322.152	−	1718.88i	0.227774	−	1.21532i
$127$	2.78116	+	2.78116i	0.00194321	+	0.00194321i	0.708078	−	0.706135i	$-0.249563\pi$
$127$	2.78116	+	2.78116i	0.00194321	+	0.00194321i	−0.706135	+	0.708078i	$0.749563\pi$
$128$	1216.41	−	325.937i	0.839974	−	0.225070i
$129$	−171.563	+	1846.73i	−0.117095	+	1.26043i
$130$	783.093	+	1482.39i	0.528322	+	1.00011i
$131$	−455.461	+	262.961i	−0.303770	+	0.175381i	−0.644135	−	0.764912i	$-0.722783\pi$
$131$	−455.461	+	262.961i	−0.303770	+	0.175381i	0.340365	+	0.940293i	$0.389449\pi$
$132$	2491.27	+	921.926i	1.64271	+	0.607904i
$133$	−210.111	−	784.145i	−0.136984	−	0.511233i
$134$	309.813			0.199730
$135$	1314.35	+	856.064i	0.837938	+	0.545765i
$136$	−275.427			−0.173659
$137$	482.495	+	1800.69i	0.300893	+	1.12295i	0.936424	+	0.350871i	$0.114115\pi$
$137$	482.495	+	1800.69i	0.300893	+	1.12295i	−0.635531	+	0.772075i	$0.719219\pi$
$138$	3699.09	+	1368.89i	2.28180	+	0.844406i
$139$	2076.42	−	1198.82i	1.26705	−	0.731531i	0.292620	−	0.956229i	$-0.405473\pi$
$139$	2076.42	−	1198.82i	1.26705	−	0.731531i	0.974428	+	0.224698i	$0.0721395\pi$
$140$	−517.902	+	1677.82i	−0.312648	+	1.01287i
$141$	254.910	−	2743.89i	0.152250	−	1.63884i
$142$	−4304.10	+	1153.28i	−2.54360	+	0.681557i
$143$	−1214.82	−	1214.82i	−0.710410	−	0.710410i
$144$	−993.761	+	349.662i	−0.575093	+	0.202351i
$145$	−92.4565	+	2458.01i	−0.0529524	+	1.40777i
$146$	1782.15	+	1028.92i	1.01022	+	0.583249i
$147$	589.130	−	100.621i	0.330548	−	0.0564565i
$148$	−2403.28	−	643.958i	−1.33479	−	0.357655i
$149$	−1086.72	−	1882.25i	−0.597498	−	1.03490i	−0.993189	−	0.116513i	$-0.962828\pi$
$149$	−1086.72	−	1882.25i	−0.597498	−	1.03490i	0.395691	−	0.918384i	$-0.370505\pi$
$150$	−2146.36	−	1776.62i	−1.16833	−	0.967070i
$151$	−1316.04	+	2279.46i	−0.709260	+	1.22847i	0.255873	+	0.966711i	$0.417637\pi$
$151$	−1316.04	+	2279.46i	−0.709260	+	1.22847i	−0.965132	+	0.261763i	$0.915696\pi$
$152$	391.690	−	391.690i	0.209015	−	0.209015i
$153$	719.687	−	55.1846i	0.380282	−	0.0291595i
$154$		−	3183.33i		−	1.66571i
$155$	418.464	+	263.053i	0.216850	+	0.136316i
$156$	−1881.25	−	174.770i	−0.965514	−	0.0896974i
$157$	749.861	−	2798.52i	0.381181	−	1.42259i	−0.462919	−	0.886401i	$-0.653198\pi$
$157$	749.861	−	2798.52i	0.381181	−	1.42259i	0.844100	−	0.536186i	$-0.180135\pi$
$158$	−381.633	+	1424.28i	−0.192159	+	0.717147i
$159$	−609.404	−	1325.40i	−0.303955	−	0.661077i
$160$	2722.93	−	620.926i	1.34541	−	0.306803i
$161$		−	2671.79i		−	1.30787i
$162$	−2861.94	+	1260.45i	−1.38800	+	0.611298i
$163$	−1097.25	+	1097.25i	−0.527259	+	0.527259i	−0.919754	−	0.392495i	$-0.871612\pi$
$163$	−1097.25	+	1097.25i	−0.527259	+	0.527259i	0.392495	+	0.919754i	$0.371612\pi$
$164$	−252.932	+	438.091i	−0.120431	+	0.208592i
$165$	2638.62	+	1090.89i	1.24495	+	0.514700i
$166$	−1869.44	−	3237.96i	−0.874075	−	1.51394i
$167$	3359.65	+	900.215i	1.55675	+	0.417130i	0.931633	−	0.363401i	$-0.118384\pi$
$167$	3359.65	+	900.215i	1.55675	+	0.417130i	0.625117	+	0.780531i	$0.285051\pi$
$168$	−516.247	−	621.990i	−0.237079	−	0.285640i
$169$	−844.431	−	487.532i	−0.384356	−	0.221908i
$170$	−1281.24	−	48.1930i	−0.578038	−	0.0217426i
$171$	−945.002	+	1101.96i	−0.422609	+	0.492801i
$172$	2625.29	+	2625.29i	1.16382	+	1.16382i
$173$	854.813	−	229.047i	0.375666	−	0.100659i	−0.0660452	−	0.997817i	$-0.521038\pi$
$173$	854.813	−	229.047i	0.375666	−	0.100659i	0.441711	+	0.897157i	$0.354372\pi$
$174$	−4001.93	−	2834.32i	−1.74359	−	1.23488i
$175$	−624.062	+	1781.22i	−0.269569	+	0.769414i
$176$	−1660.73	+	958.821i	−0.711261	+	0.410647i
$177$	−112.663	−	659.631i	−0.0478432	−	0.280118i
$178$	255.710	+	954.321i	0.107676	+	0.401851i
$179$	1948.94			0.813803			0.406901	−	0.913472i	$-0.366609\pi$
$179$	1948.94			0.813803			0.406901	+	0.913472i	$0.366609\pi$
$180$	2999.04	−	930.116i	1.24186	−	0.385149i
$181$	1591.17			0.653431			0.326716	−	0.945123i	$-0.394058\pi$
$181$	1591.17			0.653431			0.326716	+	0.945123i	$0.394058\pi$
$182$	586.001	+	2186.98i	0.238666	+	0.890715i
$183$	267.672	−	222.165i	0.108125	−	0.0897428i
$184$	1578.84	−	911.544i	0.632574	−	0.365217i
$185$	−2555.34	−	788.768i	−1.01552	−	0.313467i
$186$	−895.326	+	411.660i	−0.352949	+	0.162281i
$187$	1269.11	−	340.058i	0.496293	−	0.132981i
$188$	−3900.68	−	3900.68i	−1.51323	−	1.51323i
$189$	1473.57	+	1521.82i	0.567123	+	0.585693i
$190$	1890.61	−	1753.54i	0.721892	−	0.669553i
$191$	−1725.63	−	996.295i	−0.653730	−	0.377431i	0.136154	−	0.990688i	$-0.456526\pi$
$191$	−1725.63	−	996.295i	−0.653730	−	0.377431i	−0.789884	+	0.613257i	$0.789859\pi$
$192$	−1369.52	+	3700.79i	−0.514775	+	1.39105i
$193$	2376.60	+	636.807i	0.886379	+	0.237504i	0.673157	−	0.739500i	$-0.264938\pi$
$193$	2376.60	+	636.807i	0.886379	+	0.237504i	0.213221	+	0.977004i	$0.431604\pi$
$194$	1228.13	+	2127.19i	0.454509	+	0.787233i
$195$	−2013.57	−	263.724i	−0.739462	−	0.0968497i
$196$	598.203	−	1036.12i	0.218004	−	0.377594i
$197$	497.126	−	497.126i	0.179790	−	0.179790i	−0.611474	−	0.791265i	$-0.709423\pi$
$197$	497.126	−	497.126i	0.179790	−	0.179790i	0.791265	+	0.611474i	$0.209423\pi$
$198$	−4697.75	+	3214.78i	−1.68613	+	1.15386i
$199$			1269.73i			0.452305i	0.974092	+	0.226152i	$0.0726148\pi$
$199$			1269.73i			0.452305i	−0.974092	+	0.226152i	$0.927385\pi$
$200$	−1265.49	+	238.927i	−0.447417	+	0.0844735i
$201$	−216.898	+	306.249i	−0.0761133	+	0.107468i
$202$	156.997	−	585.922i	0.0546846	−	0.204086i
$203$	−859.766	+	3208.69i	−0.297260	+	1.10939i
$204$	835.107	−	1179.13i	0.286614	−	0.404685i
$205$	−289.372	+	460.332i	−0.0985884	+	0.156834i
$206$			513.949i			0.173828i
$207$	−3942.85	+	2698.19i	−1.32390	+	0.905976i
$208$	964.434	−	964.434i	0.321498	−	0.321498i
$209$	−1321.23	+	2288.44i	−0.437279	+	0.757389i
$210$	−2292.66	−	2983.72i	−0.753374	−	0.980460i
$211$	−676.141	−	1171.11i	−0.220604	−	0.382098i	0.734387	−	0.678731i	$-0.237470\pi$
$211$	−676.141	−	1171.11i	−0.220604	−	0.382098i	−0.954992	+	0.296633i	$0.904136\pi$
$212$	−2820.72	−	755.809i	−0.913810	−	0.244855i
$213$	1873.25	−	5061.99i	0.602596	−	1.62836i
$214$	4942.67	+	2853.65i	1.57885	+	0.911550i
$215$	2713.74	+	2925.88i	0.860818	+	0.928107i
$216$	−396.544	+	1389.98i	−0.124914	+	0.437852i
$217$	472.006	+	472.006i	0.147658	+	0.147658i
$218$	4362.26	−	1168.86i	1.35527	−	0.363144i
$219$	−2264.76	+	1041.31i	−0.698804	+	0.321301i
$220$	5053.81	−	2669.74i	1.54876	−	0.818155i
$221$	−809.296	+	467.247i	−0.246331	+	0.142219i
$222$	4102.67	−	3405.18i	1.24033	−	1.02946i
$223$	−26.4940	−	98.8770i	−0.00795592	−	0.0296919i	0.961834	−	0.273634i	$-0.0882258\pi$
$223$	−26.4940	−	98.8770i	−0.00795592	−	0.0296919i	−0.969790	+	0.243943i	$0.921559\pi$
$224$	3771.70			1.12503
$225$	3258.83	−	877.867i	0.965579	−	0.260109i
$226$	5031.00			1.48078
$227$	−375.911	−	1402.92i	−0.109912	−	0.410198i	0.888944	−	0.458016i	$-0.151440\pi$
$227$	−375.911	−	1402.92i	−0.109912	−	0.410198i	−0.998856	+	0.0478183i	$0.984773\pi$
$228$	489.245	+	2864.49i	0.142110	+	0.832042i
$229$	−4802.27	+	2772.59i	−1.38578	+	0.800079i	−0.992836	−	0.119485i	$-0.961876\pi$
$229$	−4802.27	+	2772.59i	−1.38578	+	0.800079i	−0.392941	+	0.919564i	$0.628542\pi$
$230$	7503.99	−	3964.09i	2.15130	−	1.13645i
$231$	3146.71	+	2228.62i	0.896270	+	0.634773i
$232$	−2189.44	+	586.658i	−0.619585	+	0.166017i
$233$	−870.893	−	870.893i	−0.244867	−	0.244867i	0.573993	−	0.818860i	$-0.305394\pi$
$233$	−870.893	−	870.893i	−0.244867	−	0.244867i	−0.818860	+	0.573993i	$0.805394\pi$
$234$	2635.62	−	3073.37i	0.736306	−	0.858601i
$235$	−4032.11	−	4347.30i	−1.11926	−	1.20675i
$236$	−1160.11	−	669.790i	−0.319986	−	0.184744i
$237$	−1140.71	−	1374.37i	−0.312647	−	0.376687i
$238$	−1672.53	−	448.153i	−0.455521	−	0.122057i
$239$	45.9510	+	79.5895i	0.0124365	+	0.0215406i	0.872177	−	0.489191i	$-0.162708\pi$
$239$	45.9510	+	79.5895i	0.0124365	+	0.0215406i	−0.859740	+	0.510732i	$0.829375\pi$
$240$	−866.043	+	2094.77i	−0.232928	+	0.563403i
$241$	−979.248	+	1696.11i	−0.261738	+	0.453344i	−0.966704	−	0.255898i	$-0.917629\pi$
$241$	−979.248	+	1696.11i	−0.261738	+	0.453344i	0.704966	+	0.709241i	$0.250962\pi$
$242$	−3289.62	+	3289.62i	−0.873821	+	0.873821i
$243$	757.670	−	3711.45i	0.200019	−	0.979792i
$244$		−	696.348i		−	0.182701i
$245$	684.387	−	1088.72i	0.178465	−	0.283901i
$246$	−452.847	−	984.905i	−0.117368	−	0.255265i
$247$	486.435	−	1815.40i	0.125308	−	0.467656i
$248$	−117.886	+	439.958i	−0.0301847	+	0.112651i
$249$	4509.49	+	418.937i	1.14770	+	0.106623i
$250$	−5928.64	+	890.020i	−1.49984	+	0.225159i
$251$		−	1167.85i		−	0.293681i	−0.989160	−	0.146840i	$-0.953090\pi$
$251$		−	1167.85i		−	0.293681i	0.989160	−	0.146840i	$-0.0469104\pi$
$252$	4228.10	−	324.204i	1.05692	−	0.0810435i
$253$	−6149.55	+	6149.55i	−1.52814	+	1.52814i
$254$	−8.43606	+	14.6117i	−0.00208396	+	0.00360952i
$255$	944.623	−	1232.76i	0.231979	−	0.302739i
$256$	−336.610	−	583.026i	−0.0821802	−	0.142340i
$257$	−25.3091	−	6.78155i	−0.00614295	−	0.00164600i	0.255746	−	0.966744i	$-0.417679\pi$
$257$	−25.3091	−	6.78155i	−0.00614295	−	0.00164600i	−0.261889	+	0.965098i	$0.584346\pi$
$258$	−7842.49	+	1339.47i	−1.89245	+	0.323224i
$259$	−3127.77	−	1805.82i	−0.750387	−	0.433236i
$260$	−2980.57	+	2764.47i	−0.710949	+	0.659404i
$261$	5603.43	−	1971.61i	1.32890	−	0.467584i
$262$	−1595.27	−	1595.27i	−0.376169	−	0.376169i
$263$	−576.639	+	154.510i	−0.135198	+	0.0362262i	−0.325783	−	0.945444i	$-0.605628\pi$
$263$	−576.639	+	154.510i	−0.135198	+	0.0362262i	0.190585	+	0.981671i	$0.438961\pi$
$264$	−243.385	+	2619.83i	−0.0567399	+	0.610755i
$265$	−2999.18	−	925.771i	−0.695239	−	0.214603i
$266$	3015.87	−	1741.21i	0.695168	−	0.401356i
$267$	−1122.36	−	415.344i	−0.257257	−	0.0952009i
$268$	194.434	+	725.638i	0.0443170	+	0.165393i
$269$	−6123.85			−1.38802			−0.694011	−	0.719965i	$-0.744158\pi$
$269$	−6123.85			−1.38802			−0.694011	+	0.719965i	$0.744158\pi$
$270$	−2087.87	+	6396.56i	−0.470607	+	1.44179i
$271$	−122.463			−0.0274505			−0.0137253	−	0.999906i	$-0.504369\pi$
$271$	−122.463			−0.0274505			−0.0137253	+	0.999906i	$0.504369\pi$
$272$	269.968	+	1007.53i	0.0601809	+	0.224598i
$273$	−2572.08	−	951.830i	−0.570218	−	0.211016i
$274$	−6925.58	+	3998.49i	−1.52697	+	0.881596i
$275$	5536.13	−	2663.37i	1.21397	−	0.584027i
$276$	−884.701	+	9523.04i	−0.192945	+	2.07688i
$277$	−1496.60	+	401.012i	−0.324627	+	0.0869836i	−0.417452	−	0.908699i	$-0.637077\pi$
$277$	−1496.60	+	401.012i	−0.324627	+	0.0869836i	0.0928250	+	0.995682i	$0.470410\pi$
$278$	7272.76	+	7272.76i	1.56903	+	1.56903i
$279$	219.886	−	1173.23i	0.0471836	−	0.251753i
$280$	−1738.00	−	65.3738i	−0.370948	−	0.0139530i
$281$	−2397.24	−	1384.04i	−0.508922	−	0.293826i	0.223468	−	0.974711i	$-0.428262\pi$
$281$	−2397.24	−	1384.04i	−0.508922	−	0.293826i	−0.732390	+	0.680885i	$0.761595\pi$
$282$	11652.5	−	1990.20i	2.46062	−	0.420265i
$283$	5947.68	+	1593.68i	1.24930	+	0.334750i	0.822067	−	0.569391i	$-0.192821\pi$
$283$	5947.68	+	1593.68i	1.24930	+	0.334750i	0.427236	+	0.904140i	$0.359487\pi$
$284$	−5402.37	−	9357.18i	−1.12877	−	1.95509i
$285$	409.766	+	3096.50i	0.0851664	+	0.643582i
$286$	3684.91	−	6382.46i	0.761866	−	1.31959i
$287$	−519.232	+	519.232i	−0.106792	+	0.106792i
$288$	−3808.97	−	5566.03i	−0.779325	−	1.13882i
$289$			4198.33i			0.854535i
$290$	−10287.5	+	2345.94i	−2.08312	+	0.475028i
$291$	−2962.52	−	275.222i	−0.596791	−	0.0554426i
$292$	−1291.47	+	4819.85i	−0.258828	+	0.965960i
$293$	−1828.92	+	6825.62i	−0.364664	+	1.36094i	0.503212	+	0.864163i	$0.332152\pi$
$293$	−1828.92	+	6825.62i	−0.364664	+	1.36094i	−0.867876	+	0.496781i	$0.834515\pi$
$294$	1071.02	+	2329.38i	0.212459	+	0.462081i
$295$	−1219.01	−	766.287i	−0.240588	−	0.151237i
$296$		−	2464.39i		−	0.483918i
$297$	111.053	−	6894.35i	0.0216968	−	1.34697i
$298$	6592.65	−	6592.65i	1.28155	−	1.28155i
$299$	3092.77	−	5356.84i	0.598193	−	1.03610i
$300$	2814.15	−	6142.13i	0.541582	−	1.18205i
$301$	2694.67	+	4667.30i	0.516007	+	0.893750i
$302$	−10906.2	−	2922.31i	−2.07809	−	0.556821i
$303$	469.269	+	565.391i	0.0889730	+	0.107197i
$304$	−1816.76	−	1048.91i	−0.342758	−	0.197892i
$305$	28.1335	−	747.944i	0.00528169	−	0.140417i
$306$	1027.70	+	2920.79i	0.191993	+	0.545655i
$307$	496.221	+	496.221i	0.0922502	+	0.0922502i	0.751726	−	0.659476i	$-0.229222\pi$
$307$	496.221	+	496.221i	0.0922502	+	0.0922502i	−0.659476	+	0.751726i	$0.729222\pi$
$308$	7455.93	−	1997.81i	1.37935	−	0.369597i
$309$	−508.037	−	359.811i	−0.0935314	−	0.0662426i
$310$	−625.370	+	2025.98i	−0.114576	+	0.371188i
$311$	2763.77	−	1595.66i	0.503920	−	0.290938i	−0.226411	−	0.974032i	$-0.572699\pi$
$311$	2763.77	−	1595.66i	0.503920	−	0.290938i	0.730331	+	0.683094i	$0.239366\pi$
$312$	−315.061	−	1844.66i	−0.0571692	−	0.334722i
$313$	−1129.32	−	4214.66i	−0.203938	−	0.761108i	−0.989771	−	0.142669i	$-0.954432\pi$
$313$	−1129.32	−	4214.66i	−0.203938	−	0.761108i	0.785832	−	0.618440i	$-0.212235\pi$
$314$	12428.4			2.23367
$315$	4554.47	−	177.405i	0.814652	−	0.0317322i
$316$	−3575.42			−0.636496
$317$	−1041.92	−	3888.50i	−0.184606	−	0.688959i	−0.994715	−	0.102679i	$-0.967259\pi$
$317$	−1041.92	−	3888.50i	−0.184606	−	0.688959i	0.810109	−	0.586280i	$-0.199408\pi$
$318$	4815.28	−	3996.64i	0.849143	−	0.704781i
$319$	9364.18	−	5406.41i	1.64355	−	0.948906i
$320$	3965.91	+	7507.44i	0.692815	+	1.31150i
$321$	−6281.15	+	2888.00i	−1.09215	+	0.502156i
$322$	11070.7	−	2966.39i	1.91598	−	0.513386i
$323$	1016.35	+	1016.35i	0.175081	+	0.175081i
$324$	−4748.31	−	5912.13i	−0.814182	−	1.01374i
$325$	−3313.10	+	2848.88i	−0.565469	+	0.486239i
$326$	−5764.75	−	3328.28i	−0.979386	−	0.565449i
$327$	−1898.56	+	5130.39i	−0.321073	+	0.867618i
$328$	−483.977	−	129.681i	−0.0814731	−	0.0218306i
$329$	−4003.77	−	6934.73i	−0.670926	−	1.16208i
$330$	−1590.59	+	12144.4i	−0.265331	+	2.02584i
$331$	−324.017	+	561.214i	−0.0538054	+	0.0931937i	−0.891674	−	0.452679i	$-0.850468\pi$
$331$	−324.017	+	561.214i	−0.0538054	+	0.0931937i	0.837868	+	0.545873i	$0.183802\pi$
$332$	6410.65	−	6410.65i	1.05973	−	1.05973i
$333$	493.765	+	6439.41i	0.0812558	+	1.05969i
$334$			14920.4i			2.44433i
$335$	179.524	+	787.259i	0.0292789	+	0.128396i
$336$	−1769.28	+	2498.14i	−0.287268	+	0.405609i
$337$	−2911.92	+	10867.4i	−0.470689	+	1.75664i	0.166614	+	0.986022i	$0.446717\pi$
$337$	−2911.92	+	10867.4i	−0.470689	+	1.75664i	−0.637303	+	0.770614i	$0.719950\pi$
$338$	1082.58	−	4040.23i	0.174214	−	0.650177i
$339$	−3522.16	+	4973.12i	−0.564299	+	0.796764i
$340$	−691.209	−	3031.13i	−0.110253	−	0.483489i
$341$		−	2172.79i		−	0.345054i
$342$	−5615.23	−	2692.20i	−0.887828	−	0.425666i
$343$	4890.10	−	4890.10i	0.769798	−	0.769798i
$344$	−1838.70	+	3184.72i	−0.288186	+	0.499152i
$345$	−1335.00	+	10192.9i	−0.208330	+	1.59063i
$346$	1898.13	+	3287.66i	0.294926	+	0.510826i
$347$	9499.02	+	2545.25i	1.46955	+	0.393765i	0.902777	−	0.430109i	$-0.141525\pi$
$347$	9499.02	+	2545.25i	1.46955	+	0.393765i	0.566774	+	0.823874i	$0.308191\pi$
$348$	4126.94	−	11152.0i	0.635710	−	1.71785i
$349$	8795.71	+	5078.20i	1.34906	+	0.778883i	0.988117	−	0.153703i	$-0.0491200\pi$
$349$	8795.71	+	5078.20i	1.34906	+	0.778883i	0.360947	+	0.932586i	$0.382453\pi$
$350$	−8073.44	−	608.216i	−1.23298	−	0.0928872i
$351$	1192.85	+	4756.94i	0.181394	+	0.723381i
$352$	−8681.16	−	8681.16i	−1.31451	−	1.31451i
$353$	4215.36	−	1129.50i	0.635584	−	0.170304i	0.0733816	−	0.997304i	$-0.476621\pi$
$353$	4215.36	−	1129.50i	0.635584	−	0.170304i	0.562202	+	0.827000i	$0.309954\pi$
$354$	2608.13	−	1199.19i	0.391584	−	0.180045i
$355$	−5424.61	−	10268.8i	−0.811010	−	1.53524i
$356$	−2074.71	+	1197.83i	−0.308875	+	0.178329i
$357$	1613.92	−	1339.54i	0.239266	−	0.198589i
$358$	2163.84	+	8075.54i	0.319448	+	1.19219i
$359$	−5672.13			−0.833881			−0.416941	−	0.908934i	$-0.636898\pi$
$359$	−5672.13			−0.833881			−0.416941	+	0.908934i	$0.636898\pi$
$360$	1658.70	+	2630.84i	0.242836	+	0.385160i
$361$	3968.27			0.578549
$362$	1766.62	+	6593.12i	0.256496	+	0.957256i
$363$	−948.742	−	5554.81i	−0.137179	−	0.803174i
$364$	−4754.54	+	2745.04i	−0.684631	+	0.395272i
$365$	−1581.89	+	5124.80i	−0.226850	+	0.734915i
$366$	1217.74	+	862.451i	0.173913	+	0.123172i
$367$	−4082.14	+	1093.81i	−0.580616	+	0.155576i	−0.537161	−	0.843480i	$-0.680503\pi$
$367$	−4082.14	+	1093.81i	−0.580616	+	0.155576i	−0.0434549	+	0.999055i	$0.513836\pi$
$368$	−4882.05	−	4882.05i	−0.691562	−	0.691562i
$369$	1290.61	+	241.886i	0.182077	+	0.0341249i
$370$	431.208	−	11463.9i	0.0605877	−	1.61076i
$371$	−3671.04	−	2119.48i	−0.513723	−	0.296598i
$372$	−1526.07	−	1838.66i	−0.212697	−	0.256264i
$373$	−223.349	−	59.8461i	−0.0310042	−	0.00830755i	0.243284	−	0.969955i	$-0.421775\pi$
$373$	−223.349	−	59.8461i	−0.0310042	−	0.00830755i	−0.274288	+	0.961648i	$0.588442\pi$
$374$	2818.10	+	4881.09i	0.389627	+	0.674853i
$375$	3270.81	−	6483.53i	0.450410	−	0.892822i
$376$	2731.96	−	4731.89i	0.374707	−	0.649012i
$377$	−5438.07	+	5438.07i	−0.742904	+	0.742904i
$378$	−4669.69	+	7795.43i	−0.635404	+	1.06072i
$379$		−	7586.66i		−	1.02823i	−0.857720	−	0.514117i	$-0.828120\pi$
$379$		−	7586.66i		−	1.02823i	0.857720	−	0.514117i	$-0.171880\pi$
$380$	5293.62	+	3327.66i	0.714624	+	0.449224i
$381$	−8.53759	−	18.5685i	−0.00114802	−	0.00249684i
$382$	2212.30	−	8256.40i	0.296311	−	1.10585i
$383$	−1160.64	+	4331.56i	−0.154846	+	0.577891i	0.844273	+	0.535913i	$0.180033\pi$
$383$	−1160.64	+	4331.56i	−0.154846	+	0.577891i	−0.999119	+	0.0419781i	$0.986634\pi$
$384$	−6515.58	−	605.305i	−0.865877	−	0.0804410i
$385$	8089.09	−	1844.61i	1.07080	−	0.244181i
$386$			10554.6i			1.39175i
$387$	4166.40	−	8690.03i	0.547261	−	1.14144i
$388$	−4211.50	+	4211.50i	−0.551047	+	0.551047i
$389$	−1695.52	+	2936.72i	−0.220993	+	0.382771i	−0.955110	−	0.296252i	$-0.904263\pi$
$389$	−1695.52	+	2936.72i	−0.220993	+	0.382771i	0.734117	+	0.679023i	$0.237596\pi$
$390$	−1142.84	−	8636.16i	−0.148384	−	1.12130i
$391$	2365.25	+	4096.73i	0.305923	+	0.529874i
$392$	1144.64	+	306.706i	0.147483	+	0.0395179i
$393$	2693.76	−	460.084i	0.345756	−	0.0590539i
$394$	2611.81	+	1507.93i	0.333962	+	0.192813i
$395$	−3840.33	−	144.452i	−0.489185	−	0.0184004i
$396$	−10477.8	−	8985.41i	−1.32962	−	1.14024i
$397$	−1130.27	−	1130.27i	−0.142889	−	0.142889i	0.632044	−	0.774933i	$-0.282216\pi$
$397$	−1130.27	−	1130.27i	−0.142889	−	0.142889i	−0.774933	+	0.632044i	$0.782216\pi$
$398$	−5261.19	+	1409.73i	−0.662612	+	0.177546i
$399$	−390.202	+	4200.18i	−0.0489587	+	0.526998i
$400$	2114.42	+	4395.07i	0.264303	+	0.549383i
$401$	6469.25	−	3735.03i	0.805634	−	0.465133i	−0.0398035	−	0.999208i	$-0.512673\pi$
$401$	6469.25	−	3735.03i	0.805634	−	0.465133i	0.845437	+	0.534075i	$0.179340\pi$
$402$	−1509.77	−	558.710i	−0.187315	−	0.0693183i
$403$	399.977	+	1492.73i	0.0494399	+	0.184512i
$404$	1470.86			0.181134
$405$	−4861.27	−	6542.03i	−0.596441	−	0.802657i
$406$	−14249.9			−1.74190
$407$	3042.68	+	11355.4i	0.370565	+	1.38297i
$408$	1342.20	+	496.698i	0.162865	+	0.0602702i
$409$	8609.85	−	4970.90i	1.04090	−	0.600966i	0.120815	−	0.992675i	$-0.461449\pi$
$409$	8609.85	−	4970.90i	1.04090	−	0.600966i	0.920089	+	0.391709i	$0.128116\pi$
$410$	−2228.69	−	687.940i	−0.268456	−	0.0828657i
$411$	896.052	−	9645.22i	0.107540	−	1.15758i
$412$	−1203.76	+	322.547i	−0.143944	+	0.0385697i
$413$	−1374.98	−	1374.98i	−0.163822	−	0.163822i
$414$	−15557.7	−	13341.7i	−1.84691	−	1.58384i
$415$	7144.64	−	6626.64i	0.845100	−	0.783829i
$416$	7562.12	+	4365.99i	0.891258	+	0.514568i
$417$	−12280.7	+	2097.50i	−1.44218	+	0.246319i
$418$	−10949.2	−	2933.82i	−1.28120	−	0.343296i
$419$	1659.67	+	2874.63i	0.193508	+	0.335167i	0.946411	−	0.322966i	$-0.104680\pi$
$419$	1659.67	+	2874.63i	0.193508	+	0.335167i	−0.752902	+	0.658133i	$0.771347\pi$
$420$	5549.58	−	7242.36i	0.644742	−	0.841407i
$421$	5046.60	−	8740.97i	0.584219	−	1.01190i	−0.410753	−	0.911747i	$-0.634734\pi$
$421$	5046.60	−	8740.97i	0.584219	−	1.01190i	0.994972	−	0.100150i	$-0.0319324\pi$
$422$	4101.87	−	4101.87i	0.473165	−	0.473165i
$423$	−6190.48	+	12911.7i	−0.711564	+	1.48414i
$424$		−	2892.44i		−	0.331295i
$425$	−619.962	−	3283.65i	−0.0707590	−	0.374777i
$426$	23054.4	+	2141.78i	2.62204	+	0.243591i
$427$	261.617	−	976.367i	0.0296499	−	0.110655i
$428$	−3581.82	+	13367.5i	−0.404518	+	1.50968i
$429$	3729.26	+	8110.83i	0.419698	+	0.912808i
$430$	−9110.56	+	14493.0i	−1.02174	+	1.62539i
$431$		−	4785.97i		−	0.534877i	−0.963575	−	0.267439i	$-0.913823\pi$
$431$		−	4785.97i		−	0.534877i	0.963575	−	0.267439i	$-0.0861773\pi$
$432$	5473.34	+	88.1636i	0.609575	+	0.00981892i
$433$	−5732.64	+	5732.64i	−0.636243	+	0.636243i	−0.949627	−	0.313384i	$-0.898537\pi$
$433$	−5732.64	+	5732.64i	−0.636243	+	0.636243i	0.313384	+	0.949627i	$0.398537\pi$
$434$	−1431.73	+	2479.84i	−0.158353	+	0.274276i
$435$	4883.28	−	11811.6i	0.538242	−	1.30189i
$436$	5475.37	+	9483.62i	0.601428	+	1.04170i
$437$	−9189.71	−	2462.38i	−1.00596	−	0.269546i
$438$	−6829.18	−	8228.02i	−0.745002	−	0.897602i
$439$	−14876.1	−	8588.72i	−1.61731	−	0.933753i	−0.987613	−	0.156910i	$-0.949847\pi$
$439$	−14876.1	−	8588.72i	−1.61731	−	0.933753i	−0.629694	−	0.776843i	$-0.716820\pi$
$440$	3849.81	+	4150.75i	0.417119	+	0.449725i
$441$	−3052.39	−	572.079i	−0.329596	−	0.0617729i
$442$	−2834.60	−	2834.60i	−0.305041	−	0.305041i
$443$	6720.19	−	1800.67i	0.720736	−	0.193121i	0.120236	−	0.992745i	$-0.461635\pi$
$443$	6720.19	−	1800.67i	0.720736	−	0.193121i	0.600500	+	0.799625i	$0.294968\pi$
$444$	10550.3	+	7472.15i	1.12769	+	0.798677i
$445$	−2276.83	+	1202.77i	−0.242544	+	0.128127i
$446$	380.287	−	219.559i	0.0403747	−	0.0233103i
$447$	1901.35	+	11132.3i	0.201188	+	1.17794i
$448$	2967.75	+	11075.8i	0.312975	+	1.16804i
$449$	3397.64			0.357115			0.178558	−	0.983929i	$-0.442857\pi$
$449$	3397.64			0.357115			0.178558	+	0.983929i	$0.442857\pi$
$450$	7255.65	+	12528.5i	0.760077	+	1.31244i
$451$	2390.19			0.249555
$452$	3157.38	+	11783.5i	0.328563	+	1.22621i
$453$	10524.0	−	8734.86i	1.09153	−	0.905959i
$454$	5395.71	−	3115.21i	0.557782	−	0.322036i
$455$	−5217.73	+	2756.34i	−0.537607	+	0.283998i
$456$	−2615.14	+	1202.41i	−0.268564	+	0.123482i
$457$	8373.74	−	2243.74i	0.857127	−	0.229666i	0.196614	−	0.980481i	$-0.437005\pi$
$457$	8373.74	−	2243.74i	0.857127	−	0.229666i	0.660513	+	0.750815i	$0.270339\pi$
$458$	−16820.2	−	16820.2i	−1.71606	−	1.71606i
$459$	−3606.68	−	1028.94i	−0.366765	−	0.104634i
$460$	13994.0	+	15087.9i	1.41842	+	1.52930i
$461$	7004.05	+	4043.79i	0.707617	+	0.408543i	0.810178	−	0.586184i	$-0.199370\pi$
$461$	7004.05	+	4043.79i	0.707617	+	0.408543i	−0.102561	+	0.994727i	$0.532704\pi$
$462$	−5740.75	+	15512.9i	−0.578103	+	1.56218i
$463$	−7287.87	−	1952.78i	−0.731525	−	0.196012i	−0.126217	−	0.992003i	$-0.540284\pi$
$463$	−7287.87	−	1952.78i	−0.731525	−	0.196012i	−0.605308	+	0.795991i	$0.706950\pi$
$464$	4292.09	+	7434.12i	0.429430	+	0.743794i
$465$	−1564.86	−	2036.55i	−0.156062	−	0.203103i
$466$	2641.67	−	4575.51i	0.262603	−	0.454842i
$467$	9156.39	−	9156.39i	0.907296	−	0.907296i	−0.0887572	−	0.996053i	$-0.528290\pi$
$467$	9156.39	−	9156.39i	0.907296	−	0.907296i	0.996053	+	0.0887572i	$0.0282895\pi$
$468$	8852.46	+	4244.28i	0.874370	+	0.419214i
$469$			1090.48i			0.107364i
$470$	13536.6	−	21533.9i	1.32850	−	2.11337i
$471$	−8700.99	+	12285.4i	−0.851211	+	1.20187i
$472$	343.410	−	1281.62i	0.0334888	−	0.124982i
$473$	4540.33	−	16944.7i	0.441362	−	1.64719i
$474$	4428.27	−	6252.51i	0.429108	−	0.605881i
$475$	5551.41	+	3788.09i	0.536244	+	0.365914i
$476$		−	4198.62i		−	0.404293i
$477$	579.529	+	7557.90i	0.0556286	+	0.725477i
$478$	−278.766	+	278.766i	−0.0266746	+	0.0266746i
$479$	−383.279	+	663.859i	−0.0365605	+	0.0633246i	−0.883727	−	0.468003i	$-0.844973\pi$
$479$	−383.279	+	663.859i	−0.0365605	+	0.0633246i	0.847166	+	0.531328i	$0.178307\pi$
$480$	−14389.1	−	1884.58i	−1.36827	−	0.179206i
$481$	−4180.71	−	7241.20i	−0.396307	−	0.686425i
$482$	−8115.13	−	2174.44i	−0.766876	−	0.205484i
$483$	−4818.25	+	13020.1i	−0.453909	+	1.22657i
$484$	−9769.39	−	5640.36i	−0.917486	−	0.529711i
$485$	−4693.70	+	4353.39i	−0.439443	+	0.407582i
$486$	16219.8	−	981.234i	1.51388	−	0.0915837i
$487$	3894.85	+	3894.85i	0.362408	+	0.362408i	0.864699	−	0.502291i	$-0.167509\pi$
$487$	3894.85	+	3894.85i	0.362408	+	0.362408i	−0.502291	+	0.864699i	$0.667509\pi$
$488$	666.221	−	178.513i	0.0618000	−	0.0165593i
$489$	7325.84	−	3368.33i	0.677476	−	0.311495i
$490$	5271.02	+	1627.03i	0.485960	+	0.150004i
$491$	−12685.9	+	7324.19i	−1.16600	+	0.673190i	−0.952734	−	0.303805i	$-0.901743\pi$
$491$	−12685.9	+	7324.19i	−1.16600	+	0.673190i	−0.213265	+	0.976994i	$0.568410\pi$
$492$	2022.62	−	1678.76i	0.185339	−	0.153830i
$493$	−1522.24	−	5681.09i	−0.139064	−	0.518993i
$494$	8062.27			0.734289
$495$	−10891.2	−	10074.5i	−0.988931	−	0.914778i
$496$	1724.96			0.156155
$497$	−4059.32	−	15149.6i	−0.366369	−	1.36731i
$498$	3270.83	+	19150.4i	0.294316	+	1.72320i
$499$	11810.8	−	6818.95i	1.05956	−	0.611739i	0.134252	−	0.990947i	$-0.457137\pi$
$499$	11810.8	−	6818.95i	1.05956	−	0.611739i	0.925311	+	0.379208i	$0.123803\pi$
$500$	−5805.31	−	13327.4i	−0.519243	−	1.19204i
$501$	−14748.7	−	10445.6i	−1.31522	−	0.931488i
$502$	4839.04	−	1296.62i	0.430233	−	0.115281i
$503$	12517.9	+	12517.9i	1.10964	+	1.10964i	0.993198	+	0.116438i	$0.0371477\pi$
$503$	12517.9	+	12517.9i	1.10964	+	1.10964i	0.116438	+	0.993198i	$0.462852\pi$
$504$	1394.08	+	3962.05i	0.123209	+	0.350166i
$505$	1579.85	+	59.4250i	0.139212	+	0.00523639i
$506$	−32308.6	−	18653.4i	−2.83852	−	1.63882i
$507$	3235.85	+	3898.66i	0.283450	+	0.341510i
$508$	−39.5175	−	10.5887i	−0.00345139	−	0.000924798i
$509$	3526.64	+	6108.32i	0.307103	+	0.531918i	0.977727	−	0.209879i	$-0.0673070\pi$
$509$	3526.64	+	6108.32i	0.307103	+	0.531918i	−0.670624	+	0.741797i	$0.733974\pi$
$510$	6156.79	+	2545.41i	0.534563	+	0.221005i
$511$	−3621.62	+	6272.83i	−0.313524	+	0.543040i
$512$	9165.88	−	9165.88i	0.791169	−	0.791169i
$513$	6592.41	−	3665.85i	0.567372	−	0.315499i
$514$		−	112.399i		−	0.00964534i
$515$	−1305.98	+	297.812i	−0.111745	+	0.0254819i
$516$	−8059.11	−	17527.9i	−0.687563	−	1.49539i
$517$	−6746.06	+	25176.6i	−0.573871	+	2.14172i
$518$	4009.86	−	14965.0i	0.340122	−	1.26935i
$519$	−4578.71	−	425.368i	−0.387251	−	0.0359760i
$520$	−3408.95	−	2142.92i	−0.287485	−	0.180718i
$521$			17522.3i			1.47344i	0.676196	+	0.736722i	$0.263627\pi$
$521$			17522.3i			1.47344i	−0.676196	+	0.736722i	$0.736373\pi$
$522$	14390.7	+	21029.1i	1.20664	+	1.76326i
$523$	−5784.54	+	5784.54i	−0.483633	+	0.483633i	−0.906290	−	0.422657i	$-0.861098\pi$
$523$	−5784.54	+	5784.54i	−0.483633	+	0.483633i	0.422657	+	0.906290i	$0.361098\pi$
$524$	2735.25	−	4737.58i	0.228034	−	0.394966i
$525$	6253.37	−	7554.76i	0.519847	−	0.628032i
$526$	−1280.44	−	2217.79i	−0.106140	−	0.183841i
$527$	−1141.59	−	305.889i	−0.0943615	−	0.0252841i
$528$	9822.13	−	1677.58i	0.809570	−	0.138272i
$529$	−16579.9	−	9572.40i	−1.36269	−	0.786751i
$530$	506.106	−	13455.1i	0.0414790	−	1.10274i
$531$	−640.539	+	3417.67i	−0.0523484	+	0.279311i
$532$	5970.95	+	5970.95i	0.486604	+	0.486604i
$533$	−1642.09	+	439.995i	−0.133446	+	0.0357567i
$534$	474.884	−	5111.71i	0.0384836	−	0.414243i
$535$	−4387.28	+	14213.3i	−0.354540	+	1.14859i
$536$	−644.399	+	372.044i	−0.0519287	+	0.0299811i
$537$	−9497.53	−	3514.68i	−0.763219	−	0.282439i
$538$	−6799.08	−	25374.5i	−0.544850	−	2.03341i
$539$	−5652.97			−0.451745
$540$	−16292.2	−	875.783i	−1.29834	−	0.0697921i
$541$	10105.8			0.803113			0.401557	−	0.915834i	$-0.368469\pi$
$541$	10105.8			0.803113			0.401557	+	0.915834i	$0.368469\pi$
$542$	−135.966	−	507.432i	−0.0107753	−	0.0402141i
$543$	−7754.07	−	2869.49i	−0.612816	−	0.226780i
$544$	−5783.25	+	3338.96i	−0.455799	+	0.263156i
$545$	5497.91	+	10407.5i	0.432119	+	0.817998i
$546$	1088.28	−	11714.3i	0.0853002	−	0.918182i
$547$	−635.040	+	170.158i	−0.0496386	+	0.0133006i	−0.283553	−	0.958957i	$-0.591513\pi$
$547$	−635.040	+	170.158i	−0.0496386	+	0.0133006i	0.233914	+	0.972257i	$0.424846\pi$
$548$	−13711.6	−	13711.6i	−1.06885	−	1.06885i
$549$	−1705.06	+	599.937i	−0.132550	+	0.0466388i
$550$	17182.4	+	19982.2i	1.33211	+	1.54917i
$551$	10244.0	+	5914.38i	0.792032	+	0.457280i
$552$	−9337.82	+	1594.87i	−0.720007	+	0.122975i
$553$	−5013.18	−	1343.28i	−0.385501	−	0.103295i
$554$	−3323.23	−	5756.00i	−0.254856	−	0.441424i
$555$	11030.2	+	8452.04i	0.843611	+	0.646431i
$556$	−12469.8	+	21598.4i	−0.951148	+	1.64744i
$557$	−6427.65	+	6427.65i	−0.488956	+	0.488956i	−0.907977	−	0.419021i	$-0.862373\pi$
$557$	−6427.65	+	6427.65i	−0.488956	+	0.488956i	0.419021	+	0.907977i	$0.362373\pi$
$558$	5105.46	−	391.479i	0.387332	−	0.0297001i
$559$			12477.0i			0.944046i
$560$	1464.41	+	6421.83i	0.110505	+	0.484593i
$561$	−6797.86	−	631.529i	−0.511597	−	0.0475280i
$562$	3073.31	−	11469.7i	0.230675	−	0.860892i
$563$	−970.932	+	3623.57i	−0.0726819	+	0.271253i	−0.992698	−	0.120629i	$-0.961509\pi$
$563$	−970.932	+	3623.57i	−0.0726819	+	0.271253i	0.920016	+	0.391881i	$0.128176\pi$
$564$	11974.3	+	26043.1i	0.893988	+	1.94435i
$565$	2915.25	+	12784.1i	0.217072	+	0.951917i
$566$			26413.9i			1.96159i
$567$	−4436.54	−	10073.5i	−0.328602	−	0.746114i
$568$	7567.41	−	7567.41i	0.559017	−	0.559017i
$569$	−4162.66	+	7209.93i	−0.306692	+	0.531206i	−0.977637	−	0.210302i	$-0.932555\pi$
$569$	−4162.66	+	7209.93i	−0.306692	+	0.531206i	0.670945	+	0.741507i	$0.265889\pi$
$570$	−12375.6	+	5135.82i	−0.909396	+	0.377396i
$571$	−13072.8	−	22642.7i	−0.958107	−	1.65949i	−0.727093	−	0.686539i	$-0.759129\pi$
$571$	−13072.8	−	22642.7i	−0.958107	−	1.65949i	−0.231013	−	0.972951i	$-0.574204\pi$
$572$	17261.5	+	4625.19i	1.26178	+	0.338093i
$573$	6612.62	+	7967.09i	0.482105	+	0.580855i
$574$	−2727.95	−	1574.98i	−0.198367	−	0.114527i
$575$	14421.3	+	16771.2i	1.04593	+	1.21636i
$576$	13347.8	−	15564.8i	0.965556	−	1.12593i
$577$	−17789.3	−	17789.3i	−1.28349	−	1.28349i	−0.938665	−	0.344829i	$-0.887937\pi$
$577$	−17789.3	−	17789.3i	−1.28349	−	1.28349i	−0.344829	−	0.938665i	$-0.612063\pi$
$578$	−17396.0	+	4661.25i	−1.25187	+	0.335437i
$579$	−10433.2	−	7389.17i	−0.748855	−	0.530369i
$580$	−11950.9	−	22623.0i	−0.855577	−	1.61960i
$581$	11397.0	−	6580.06i	0.813816	−	0.469857i
$582$	−2148.78	−	12580.9i	−0.153041	−	0.896043i
$583$	3571.17	+	13327.8i	0.253693	+	0.946794i
$584$	−4942.39			−0.350202
$585$	9336.91	+	4916.41i	0.659886	+	0.347468i
$586$	−30312.9			−2.13688
$587$	−1709.74	−	6380.84i	−0.120219	−	0.448664i	0.879405	−	0.476074i	$-0.157941\pi$
$587$	−1709.74	−	6380.84i	−0.120219	−	0.448664i	−0.999624	+	0.0274104i	$0.991274\pi$
$588$	−4783.66	+	3970.40i	−0.335501	+	0.278463i
$589$	2058.49	−	1188.47i	0.144005	−	0.0831411i
$590$	1821.74	−	5901.80i	0.127118	−	0.411819i
$591$	−3319.08	+	1526.07i	−0.231013	+	0.106217i
$592$	−9014.94	+	2415.55i	−0.625865	+	0.167700i
$593$	1466.22	+	1466.22i	0.101535	+	0.101535i	0.756050	−	0.654514i	$-0.227127\pi$
$593$	1466.22	+	1466.22i	0.101535	+	0.101535i	−0.654514	+	0.756050i	$0.727127\pi$
$594$	28690.4	−	7194.38i	1.98179	−	0.496951i
$595$	169.630	−	4509.72i	0.0116877	−	0.310723i
$596$	19578.6	+	11303.7i	1.34559	+	0.776877i
$597$	2289.80	−	6187.61i	0.156977	−	0.424191i
$598$	25630.2	+	6867.58i	1.75267	+	0.469626i
$599$	−8093.94	−	14019.1i	−0.552102	−	0.956269i	−0.998123	−	0.0612464i	$-0.980492\pi$
$599$	−8093.94	−	14019.1i	−0.552102	−	0.956269i	0.446020	−	0.895023i	$-0.352841\pi$
$600$	6597.81	+	1117.82i	0.448924	+	0.0760578i
$601$	−4667.92	+	8085.07i	−0.316819	+	0.548747i	−0.979823	−	0.199869i	$-0.935948\pi$
$601$	−4667.92	+	8085.07i	−0.316819	+	0.548747i	0.663003	+	0.748617i	$0.269282\pi$
$602$	−16347.4	+	16347.4i	−1.10676	+	1.10676i
$603$	1609.26	−	1101.26i	0.108680	−	0.0743726i
$604$		−	27378.3i		−	1.84438i
$605$	−10265.4	−	6452.98i	−0.689829	−	0.433638i
$606$	−1821.71	+	2572.18i	−0.122116	+	0.172422i
$607$	1299.92	−	4851.38i	0.0869230	−	0.324401i	−0.908748	−	0.417344i	$-0.862961\pi$
$607$	1299.92	−	4851.38i	0.0869230	−	0.324401i	0.995671	+	0.0929433i	$0.0296275\pi$
$608$	3476.07	−	12972.9i	0.231864	−	0.865329i
$609$	9976.27	−	14086.0i	0.663807	−	0.937265i
$610$	3130.38	−	713.841i	0.207779	−	0.0473813i
$611$		−	18538.5i		−	1.22747i
$612$	−6196.05	+	4240.10i	−0.409249	+	0.280059i
$613$	17030.5	−	17030.5i	1.12212	−	1.12212i	0.130693	−	0.991423i	$-0.458280\pi$
$613$	17030.5	−	17030.5i	1.12212	−	1.12212i	0.991423	−	0.130693i	$-0.0417204\pi$
$614$	−1505.18	+	2607.05i	−0.0989320	+	0.171355i
$615$	2240.31	−	1721.43i	0.146891	−	0.112870i
$616$	3822.75	+	6621.19i	0.250037	+	0.433077i
$617$	6255.15	+	1676.06i	0.408141	+	0.109361i	0.457047	−	0.889442i	$-0.348907\pi$
$617$	6255.15	+	1676.06i	0.408141	+	0.109361i	−0.0489065	+	0.998803i	$0.515574\pi$
$618$	926.844	−	2504.56i	0.0603287	−	0.163023i
$619$	10407.7	+	6008.87i	0.675799	+	0.390173i	0.798270	−	0.602300i	$-0.205749\pi$
$619$	10407.7	+	6008.87i	0.675799	+	0.390173i	−0.122472	+	0.992472i	$0.539082\pi$
$620$	−5137.69	−	193.251i	−0.332798	−	0.0125180i
$621$	24080.1	−	6038.29i	1.55604	−	0.390191i
$622$	9680.22	+	9680.22i	0.624022	+	0.624022i
$623$	−3359.03	+	900.049i	−0.216014	+	0.0578807i
$624$	−6439.10	+	2960.62i	−0.413093	+	0.189935i
$625$	−5697.00	−	14549.4i	−0.364608	−	0.931161i
$626$	16209.9	−	9358.77i	1.03495	−	0.597526i
$627$	10565.5	−	8769.27i	0.672959	−	0.558550i
$628$	7799.85	+	29109.4i	0.495618	+	1.84967i
$629$	6394.53			0.405352
$630$	5791.75	+	18674.7i	0.366268	+	1.18098i
$631$	1233.51			0.0778212			0.0389106	−	0.999243i	$-0.487611\pi$
$631$	1233.51			0.0778212			0.0389106	+	0.999243i	$0.487611\pi$
$632$	−916.580	−	3420.72i	−0.0576892	−	0.215299i
$633$	1183.00	+	6926.37i	0.0742812	+	0.434910i
$634$	14955.4	−	8634.51i	0.936838	−	0.540884i
$635$	−42.0178	−	12.9698i	−0.00262587	−	0.000810538i
$636$	12382.8	+	8770.01i	0.772031	+	0.546782i
$637$	3883.66	−	1040.62i	0.241564	−	0.0647268i
$638$	32798.5	+	32798.5i	2.03527	+	2.03527i
$639$	−18257.3	+	21289.8i	−1.13028	+	1.31801i
$640$	−10323.0	+	9574.57i	−0.637582	+	0.591356i
$641$	22917.1	+	13231.2i	1.41212	+	0.815291i	0.995588	−	0.0938285i	$-0.0299105\pi$
$641$	22917.1	+	13231.2i	1.41212	+	0.815291i	0.416536	+	0.909119i	$0.363244\pi$
$642$	−18940.3	−	22819.9i	−1.16435	−	1.40285i
$643$	−23058.6	−	6178.54i	−1.41422	−	0.378939i	−0.530791	−	0.847503i	$-0.678105\pi$
$643$	−23058.6	−	6178.54i	−1.41422	−	0.378939i	−0.883430	+	0.468564i	$0.844772\pi$
$644$	13895.6	+	24067.9i	0.850255	+	1.47269i
$645$	−7948.09	−	19152.2i	−0.485203	−	1.16917i
$646$	−3082.88	+	5339.70i	−0.187762	+	0.325213i
$647$	11613.4	−	11613.4i	0.705670	−	0.705670i	−0.259951	−	0.965622i	$-0.583706\pi$
$647$	11613.4	−	11613.4i	0.705670	−	0.705670i	0.965622	+	0.259951i	$0.0837065\pi$
$648$	4439.09	−	6058.49i	0.269111	−	0.367284i
$649$			6329.46i			0.382825i
$650$	−15482.9	−	10565.0i	−0.934292	−	0.637528i
$651$	−1448.96	−	3151.38i	−0.0872340	−	0.189727i
$652$	4177.55	−	15590.8i	0.250929	−	0.936479i
$653$	−4917.23	+	18351.3i	−0.294680	+	1.09976i	0.646791	+	0.762667i	$0.276111\pi$
$653$	−4917.23	+	18351.3i	−0.294680	+	1.09976i	−0.941471	+	0.337094i	$0.890556\pi$
$654$	−23365.9	−	2170.72i	−1.39706	−	0.129789i
$655$	3129.32	−	4978.10i	0.186676	−	0.296963i
$656$			1897.54i			0.112937i
$657$	12914.4	−	990.260i	0.766879	−	0.0588032i
$658$	24289.2	−	24289.2i	1.43904	−	1.43904i
$659$	−10618.4	+	18391.6i	−0.627670	+	1.08716i	0.360348	+	0.932818i	$0.382658\pi$
$659$	−10618.4	+	18391.6i	−0.627670	+	1.08716i	−0.988018	+	0.154338i	$0.950675\pi$
$660$	−29442.6	+	3896.20i	−1.73644	+	0.229787i
$661$	7686.03	+	13312.6i	0.452272	+	0.783359i	0.998527	−	0.0542605i	$-0.0172801\pi$
$661$	7686.03	+	13312.6i	0.452272	+	0.783359i	−0.546254	+	0.837619i	$0.683947\pi$
$662$	−2685.16	−	719.488i	−0.157646	−	0.0422412i
$663$	4786.46	−	817.511i	0.280378	−	0.0478876i
$664$	7776.70	+	4489.88i	0.454510	+	0.262411i
$665$	6172.12	+	6654.59i	0.359917	+	0.388051i
$666$	−26133.9	+	9195.38i	−1.52052	+	0.535006i
$667$	27528.0	+	27528.0i	1.59803	+	1.59803i
$668$	−34946.1	+	9363.79i	−2.02411	+	0.542359i
$669$	−49.2027	+	529.624i	−0.00284347	+	0.0306075i
$670$	−3062.73	+	1617.93i	−0.176603	+	0.0932927i
$671$	−2849.41	+	1645.11i	−0.163935	+	0.0946479i
$672$	−18380.2	−	6801.80i	−1.05510	−	0.390454i
$673$	−7929.17	−	29592.1i	−0.454156	−	1.69493i	−0.690557	−	0.723278i	$-0.742635\pi$
$673$	−7929.17	−	29592.1i	−0.454156	−	1.69493i	0.236401	−	0.971656i	$-0.424032\pi$
$674$	−48262.8			−2.75818
$675$	−17464.0	−	1598.90i	−0.995835	−	0.0911730i
$676$	10142.4			0.577057
$677$	−8227.98	−	30707.2i	−0.467100	−	1.74324i	−0.649831	−	0.760079i	$-0.725160\pi$
$677$	−8227.98	−	30707.2i	−0.467100	−	1.74324i	0.182731	−	0.983163i	$-0.441506\pi$
$678$	−24516.9	−	9072.79i	−1.38874	−	0.513921i
$679$	−7487.30	+	4322.79i	−0.423175	+	0.244320i
$680$	2722.80	−	1438.35i	0.153551	−	0.0811153i
$681$	−698.112	+	7514.57i	−0.0392830	+	0.422847i
$682$	9003.09	−	2412.37i	0.505493	−	0.135446i
$683$	−10544.6	−	10544.6i	−0.590742	−	0.590742i	0.347090	−	0.937832i	$-0.387170\pi$
$683$	−10544.6	−	10544.6i	−0.590742	−	0.590742i	−0.937832	+	0.347090i	$0.887170\pi$
$684$	2781.59	−	14841.5i	0.155492	−	0.829646i
$685$	−14173.5	−	15281.5i	−0.790574	−	0.852372i
$686$	25691.7	+	14833.1i	1.42990	+	0.825555i
$687$	28402.3	−	4851.02i	1.57732	−	0.269400i
$688$	13452.2	+	3604.51i	0.745438	+	0.199739i
$689$	−4906.87	−	8498.95i	−0.271316	−	0.469933i
$690$	−43717.0	+	5785.16i	−2.41200	+	0.319184i
$691$	1725.29	−	2988.28i	0.0949825	−	0.164515i	−0.814619	−	0.579997i	$-0.803054\pi$
$691$	1725.29	−	2988.28i	0.0949825	−	0.164515i	0.909601	+	0.415482i	$0.136387\pi$
$692$	−6509.06	+	6509.06i	−0.357568	+	0.357568i
$693$	−11315.4	−	16535.2i	−0.620256	−	0.906377i
$694$			42185.6i			2.30741i
$695$	−14266.4	+	22694.9i	−0.778640	+	1.23866i
$696$	11727.5	+	1089.50i	0.638691	+	0.0593351i
$697$	336.493	−	1255.81i	0.0182864	−	0.0682457i
$698$	−11276.3	+	42083.6i	−0.611481	+	2.28208i
$699$	2673.46	+	5814.56i	0.144663	+	0.314631i
$700$	−3642.22	−	19291.2i	−0.196661	−	1.04162i
$701$		−	33118.2i		−	1.78439i	−0.451650	−	0.892195i	$-0.649165\pi$
$701$		−	33118.2i		−	1.78439i	0.451650	−	0.892195i	$-0.350835\pi$
$702$	−18386.3	+	10224.1i	−0.988526	+	0.549691i
$703$	−9093.79	+	9093.79i	−0.487879	+	0.487879i
$704$	18661.9	−	32323.4i	0.999074	−	1.73045i
$705$	11809.4	+	28456.5i	0.630874	+	1.52019i
$706$	9360.31	+	16212.5i	0.498980	+	0.864259i
$707$	2062.33	+	552.601i	0.109706	+	0.0293956i
$708$	4445.53	+	5356.12i	0.235979	+	0.284315i
$709$	24955.0	+	14407.8i	1.32187	+	0.763181i	0.984027	−	0.178021i	$-0.0569696\pi$
$709$	24955.0	+	14407.8i	1.32187	+	0.763181i	0.337842	+	0.941203i	$0.390303\pi$
$710$	36526.4	−	33878.2i	1.93072	−	1.79074i
$711$	3080.39	+	8754.66i	0.162481	+	0.461780i
$712$	−1677.88	−	1677.88i	−0.0883161	−	0.0883161i
$713$	7556.35	−	2024.72i	0.396897	−	0.106348i
$714$	7342.35	+	5200.13i	0.384846	+	0.272563i
$715$	18353.6	+	5665.28i	0.959978	+	0.296321i
$716$	−17556.4	+	10136.2i	−0.916358	+	0.529060i
$717$	−80.3973	−	470.720i	−0.00418758	−	0.0245180i
$718$	−6297.55	−	23502.8i	−0.327329	−	1.22161i
$719$	−11652.8			−0.604418			−0.302209	−	0.953242i	$-0.597724\pi$
$719$	−11652.8			−0.604418			−0.302209	+	0.953242i	$0.597724\pi$
$720$	7998.03	−	8646.36i	0.413985	−	0.447543i
$721$	−1809.00			−0.0934407
$722$	4405.82	+	16442.7i	0.227102	+	0.847555i
$723$	7830.76	−	6499.47i	0.402807	−	0.334326i
$724$	−14333.6	+	8275.48i	−0.735777	+	0.424801i
$725$	−11922.4	−	24782.1i	−0.610741	−	1.26949i
$726$	21963.3	−	10098.5i	1.12278	−	0.516238i
$727$	−12169.8	+	3260.88i	−0.620841	+	0.166354i	−0.555510	−	0.831510i	$-0.687477\pi$
$727$	−12169.8	+	3260.88i	−0.620841	+	0.166354i	−0.0653308	+	0.997864i	$0.520810\pi$
$728$	−3845.13	−	3845.13i	−0.195755	−	0.195755i
$729$	−10385.4	+	16720.2i	−0.527633	+	0.849472i
$730$	−22991.2	−	864.800i	−1.16567	−	0.0438461i
$731$	−8263.62	−	4771.00i	−0.418113	−	0.241398i
$732$	−1255.78	+	3393.43i	−0.0634084	+	0.171345i
$733$	26234.6	+	7029.55i	1.32196	+	0.354219i	0.849713	−	0.527246i	$-0.176775\pi$
$733$	26234.6	+	7029.55i	1.32196	+	0.354219i	0.472250	+	0.881465i	$0.343442\pi$
$734$	−9064.49	−	15700.2i	−0.455826	−	0.789514i
$735$	−5298.51	+	4071.31i	−0.265903	+	0.204317i
$736$	22101.0	−	38280.1i	1.10687	−	1.91715i
$737$	2509.92	−	2509.92i	0.125446	−	0.125446i
$738$	430.648	+	5616.27i	0.0214802	+	0.280132i
$739$		−	18361.9i		−	0.914008i	−0.889465	−	0.457004i	$-0.848923\pi$
$739$		−	18361.9i		−	0.914008i	0.889465	−	0.457004i	$-0.151077\pi$
$740$	27121.2	−	6184.61i	1.34729	−	0.307231i
$741$	−5644.33	+	7969.53i	−0.279824	+	0.395098i
$742$	4706.35	−	17564.3i	0.232851	−	0.869013i
$743$	3625.64	−	13531.1i	0.179020	−	0.668112i	−0.816812	−	0.576904i	$-0.804261\pi$
$743$	3625.64	−	13531.1i	0.179020	−	0.668112i	0.995832	−	0.0912077i	$-0.0290727\pi$
$744$	1367.89	−	1931.40i	0.0674051	−	0.0951728i
$745$	20572.6	+	12932.3i	1.01171	+	0.635975i
$746$		−	991.903i		−	0.0486811i
$747$	−21220.0	−	10173.9i	−1.03936	−	0.498316i
$748$	−9663.78	+	9663.78i	−0.472384	+	0.472384i
$749$	−10044.3	+	17397.3i	−0.490002	+	0.848708i
$750$	30496.3	+	6354.35i	1.48476	+	0.309371i
$751$	−12757.5	−	22096.6i	−0.619876	−	1.07366i	−0.989508	−	0.144478i	$-0.953850\pi$
$751$	−12757.5	−	22096.6i	−0.619876	−	1.07366i	0.369632	−	0.929178i	$-0.379484\pi$
$752$	−19987.5	−	5355.62i	−0.969239	−	0.259707i
$753$	−2106.07	+	5691.12i	−0.101925	+	0.275426i
$754$	−28570.6	−	16495.3i	−1.37995	−	0.796713i
$755$	1106.12	−	29406.9i	0.0533190	−	1.41752i
$756$	−21188.9	−	6044.95i	−1.01936	−	0.290810i
$757$	−14733.2	−	14733.2i	−0.707382	−	0.707382i	0.258602	−	0.965984i	$-0.416738\pi$
$757$	−14733.2	−	14733.2i	−0.707382	−	0.707382i	−0.965984	+	0.258602i	$0.916738\pi$
$758$	31435.7	−	8423.18i	1.50633	−	0.403620i
$759$	41057.8	−	18877.9i	1.96351	−	0.902797i
$760$	−1826.63	+	5917.66i	−0.0871827	+	0.282442i
$761$	1768.38	−	1020.97i	0.0842361	−	0.0486337i	−0.457290	−	0.889317i	$-0.651180\pi$
$761$	1768.38	−	1020.97i	0.0842361	−	0.0486337i	0.541526	+	0.840684i	$0.317847\pi$
$762$	67.4608	−	55.9919i	0.00320715	−	0.00266191i
$763$	4114.18	+	15354.3i	0.195207	+	0.728523i
$764$	20726.4			0.981484
$765$	−6826.44	+	4303.94i	−0.322628	+	0.203411i
$766$	−19236.7			−0.907375
$767$	−1165.15	−	4348.41i	−0.0548517	−	0.204709i
$768$	588.944	+	3448.22i	0.0276715	+	0.162014i
$769$	−7810.71	+	4509.51i	−0.366270	+	0.211466i	−0.671828	−	0.740708i	$-0.734490\pi$
$769$	−7810.71	+	4509.51i	−0.366270	+	0.211466i	0.305558	+	0.952174i	$0.401157\pi$
$770$	16624.2	+	31469.6i	0.778046	+	1.47284i
$771$	111.106	+	78.6896i	0.00518986	+	0.00367566i
$772$	−24720.7	+	6623.89i	−1.15248	+	0.308807i
$773$	−12401.6	−	12401.6i	−0.577042	−	0.577042i	0.357045	−	0.934087i	$-0.383784\pi$
$773$	−12401.6	−	12401.6i	−0.577042	−	0.577042i	−0.934087	+	0.357045i	$0.883784\pi$
$774$	40633.4	+	7615.51i	1.88700	+	0.353661i
$775$	−5510.56	−	415.140i	−0.255413	−	0.0192416i
$776$	−5108.93	−	2949.64i	−0.236340	−	0.136451i
$777$	11985.6	+	14440.6i	0.553386	+	0.666737i
$778$	−14050.9	−	3764.94i	−0.647494	−	0.173496i
$779$	1307.38	+	2264.45i	0.0601306	+	0.104149i
$780$	19510.2	−	8096.66i	0.895612	−	0.371675i
$781$	−25526.0	+	44212.3i	−1.16952	+	2.02566i
$782$	−14349.0	+	14349.0i	−0.656162	+	0.656162i
$783$	−30862.0	−	497.120i	−1.40858	−	0.0226892i
$784$		−	4487.83i		−	0.204438i
$785$	7201.71	+	31581.4i	0.327440	+	1.43591i
$786$	4897.16	+	10650.9i	0.222234	+	0.483341i
$787$	−8582.02	+	32028.5i	−0.388712	+	1.45069i	0.443521	+	0.896264i	$0.353729\pi$
$787$	−8582.02	+	32028.5i	−0.388712	+	1.45069i	−0.832232	+	0.554427i	$0.812937\pi$
$788$	−1892.70	+	7063.67i	−0.0855645	+	0.319331i
$789$	3088.70	+	286.944i	0.139367	+	0.0129474i
$790$	−3665.23	−	16073.0i	−0.165067	−	0.723863i
$791$			17708.1i			0.795991i
$792$	5910.60	−	12328.0i	0.265182	−	0.553100i
$793$	1654.74	−	1654.74i	0.0741004	−	0.0741004i
$794$	3428.45	−	5938.26i	0.153238	−	0.265417i
$795$	12946.0	+	9920.10i	0.577545	+	0.442553i
$796$	−6603.69	−	11437.9i	−0.294047	−	0.509305i
$797$	−8323.68	−	2230.32i	−0.369937	−	0.0991243i	0.0690608	−	0.997612i	$-0.478000\pi$
$797$	−8323.68	−	2230.32i	−0.369937	−	0.0991243i	−0.438998	+	0.898488i	$0.644666\pi$
$798$	−17836.9	+	3046.48i	−0.791253	+	0.135143i
$799$	12278.2	+	7088.80i	0.543642	+	0.313872i
$800$	−23675.5	+	20358.2i	−1.04632	+	0.899713i
$801$	4720.45	+	4048.09i	0.208226	+	0.178567i
$802$	22658.9	+	22658.9i	0.997646	+	0.997646i
$803$	22773.6	−	6102.17i	1.00083	−	0.268170i
$804$	361.088	−	3886.80i	0.0158390	−	0.170494i
$805$	13952.8	+	26412.6i	0.610898	+	1.15643i
$806$	−5741.14	+	3314.65i	−0.250897	+	0.144856i
$807$	29842.6	+	11043.6i	1.30175	+	0.481727i
$808$	377.065	+	1407.23i	0.0164172	+	0.0612699i
$809$	23450.0			1.01911			0.509554	−	0.860439i	$-0.329810\pi$
$809$	23450.0			1.01911			0.509554	+	0.860439i	$0.329810\pi$
$810$	21710.0	−	27406.3i	0.941741	−	1.18884i
$811$	12488.0			0.540705			0.270352	−	0.962761i	$-0.412860\pi$
$811$	12488.0			0.540705			0.270352	+	0.962761i	$0.412860\pi$
$812$	−8943.05	−	33375.9i	−0.386502	−	1.44244i
$813$	596.783	+	220.847i	0.0257443	+	0.00952699i
$814$	−43673.7	+	25215.0i	−1.88054	+	1.08573i
$815$	5116.98	−	16577.3i	0.219926	−	0.712486i
$816$	501.364	−	5396.75i	0.0215089	−	0.231524i
$817$	18536.8	−	4966.92i	0.793783	−	0.212693i
$818$	30156.4	+	30156.4i	1.28899	+	1.28899i
$819$	10817.7	+	9276.87i	0.461539	+	0.395800i
$820$	212.586	−	5651.73i	0.00905346	−	0.240691i
$821$	−7534.17	−	4349.85i	−0.320273	−	0.184910i	0.331241	−	0.943546i	$-0.392533\pi$
$821$	−7534.17	−	4349.85i	−0.320273	−	0.184910i	−0.651514	+	0.758636i	$0.725866\pi$
$822$	40960.3	−	6995.88i	1.73802	−	0.296848i
$823$	29156.6	+	7812.50i	1.23492	+	0.330895i	0.816492	−	0.577356i	$-0.195916\pi$
$823$	29156.6	+	7812.50i	1.23492	+	0.330895i	0.418425	+	0.908251i	$0.362582\pi$
$824$	−617.183	−	1068.99i	−0.0260930	−	0.0451943i
$825$	−31781.6	+	2995.36i	−1.34120	+	0.126406i
$826$	4170.72	−	7223.89i	0.175687	−	0.304299i
$827$	−26730.4	+	26730.4i	−1.12395	+	1.12395i	−0.132810	+	0.991141i	$0.542400\pi$
$827$	−26730.4	+	26730.4i	−1.12395	+	1.12395i	−0.991141	+	0.132810i	$0.957600\pi$
$828$	21484.9	−	44812.0i	0.901755	−	1.88083i
$829$		−	39741.7i		−	1.66500i	−0.554025	−	0.832500i	$-0.686909\pi$
$829$		−	39741.7i		−	1.66500i	0.554025	−	0.832500i	$-0.313091\pi$
$830$	35390.3	+	22246.9i	1.48002	+	0.930363i
$831$	8016.35	+	744.728i	0.334638	+	0.0310883i
$832$	−6870.73	+	25641.9i	−0.286298	+	1.06848i
$833$	−795.833	+	2970.09i	−0.0331020	+	0.123538i
$834$	−22325.9	−	48557.0i	−0.926957	−	2.01605i
$835$	−37913.8	+	8645.72i	−1.57133	+	0.358320i
$836$		−	27486.1i		−	1.13711i
$837$	−3187.31	+	5320.80i	−0.131624	+	0.219730i
$838$	−10068.5	+	10068.5i	−0.415049	+	0.415049i
$839$	14713.2	−	25484.1i	0.605431	−	1.04864i	−0.386552	−	0.922268i	$-0.626334\pi$
$839$	14713.2	−	25484.1i	0.605431	−	1.04864i	0.991983	−	0.126370i	$-0.0403328\pi$
$840$	8351.68	+	3452.85i	0.343048	+	0.141827i
$841$	−12006.9	−	20796.6i	−0.492309	−	0.852704i
$842$	41821.7	+	11206.1i	1.71172	+	0.458655i
$843$	9186.19	+	11067.8i	0.375314	+	0.452190i
$844$	12181.6	+	7033.04i	0.496810	+	0.286833i
$845$	10893.8	+	409.766i	0.443503	+	0.0166821i
$846$	−60373.5	−	11315.2i	−2.45353	−	0.459840i
$847$	−11578.8	−	11578.8i	−0.469721	−	0.469721i
$848$	−10580.8	+	2835.11i	−0.428473	+	0.114809i
$849$	−26110.1	−	18492.2i	−1.05547	−	0.747526i
$850$	12917.7	−	6214.56i	0.521261	−	0.250774i
$851$	−36655.6	+	21163.1i	−1.47654	+	0.852482i
$852$	9452.17	+	55341.7i	0.380077	+	2.22532i
$853$	−4857.73	−	18129.3i	−0.194989	−	0.727709i	−0.992270	−	0.124100i	$-0.960396\pi$
$853$	−4857.73	−	18129.3i	−0.194989	−	0.727709i	0.797281	−	0.603609i	$-0.206271\pi$
$854$	4336.09			0.173745
$855$	3587.30	−	15828.8i	0.143489	−	0.633137i
$856$	−13707.4			−0.547324
$857$	4197.56	+	15665.5i	0.167312	+	0.624415i	0.997734	+	0.0672811i	$0.0214324\pi$
$857$	4197.56	+	15665.5i	0.167312	+	0.624415i	−0.830422	+	0.557134i	$0.811901\pi$
$858$	−29467.2	+	24457.5i	−1.17249	+	0.973155i
$859$	601.750	−	347.420i	0.0239016	−	0.0137996i	−0.488002	−	0.872843i	$-0.662274\pi$
$859$	601.750	−	347.420i	0.0239016	−	0.0137996i	0.511903	+	0.859043i	$0.328941\pi$
$860$	−39662.9	−	12242.9i	−1.57267	−	0.485443i
$861$	3466.68	−	1593.94i	0.137217	−	0.0630908i
$862$	19830.9	−	5313.68i	0.783578	−	0.209959i
$863$	−15470.7	−	15470.7i	−0.610228	−	0.610228i	0.332777	−	0.943006i	$-0.392014\pi$
$863$	−15470.7	−	15470.7i	−0.610228	−	0.610228i	−0.943006	+	0.332777i	$0.892014\pi$
$864$	8524.11	+	33993.2i	0.335644	+	1.33851i
$865$	−7254.32	+	6728.37i	−0.285149	+	0.264476i
$866$	−30118.3	−	17388.8i	−1.18182	−	0.682327i
$867$	7571.18	−	20459.2i	0.296575	−	0.801420i
$868$	−6706.75	−	1797.07i	−0.262260	−	0.0702724i
$869$	8446.85	+	14630.4i	0.329735	+	0.571118i
$870$	54363.6	+	7120.18i	2.11850	+	0.277467i
$871$	−1262.31	+	2186.38i	−0.0491063	+	0.0850547i
$872$	−7669.67	+	7669.67i	−0.297853	+	0.297853i
$873$	13940.6	+	6683.75i	0.540454	+	0.259119i
$874$		−	40812.0i		−	1.57950i
$875$	−3132.70	−	20867.7i	−0.121034	−	0.806236i
$876$	14985.6	−	21158.9i	0.577986	−	0.816090i
$877$	5050.52	−	18848.8i	0.194463	−	0.725746i	−0.797942	−	0.602734i	$-0.794078\pi$
$877$	5050.52	−	18848.8i	0.194463	−	0.725746i	0.992405	−	0.123012i	$-0.0392553\pi$
$878$	19071.5	−	71175.7i	0.733065	−	2.73584i
$879$	21221.8	−	29964.2i	0.814327	−	1.14979i
$880$	11410.3	−	18151.4i	0.437091	−	0.695323i
$881$		−	22685.6i		−	0.867533i	−0.901025	−	0.433766i	$-0.857184\pi$
$881$		−	22685.6i		−	0.867533i	0.901025	−	0.433766i	$-0.142816\pi$
$882$	−1018.51	−	13282.9i	−0.0388834	−	0.507096i
$883$	−6561.23	+	6561.23i	−0.250060	+	0.250060i	−0.820995	−	0.570935i	$-0.806581\pi$
$883$	−6561.23	+	6561.23i	−0.250060	+	0.250060i	0.570935	+	0.820995i	$0.306581\pi$
$884$	4860.18	−	8418.08i	0.184916	−	0.320284i
$885$	4558.53	+	5932.58i	0.173145	+	0.225335i
$886$	14922.3	+	25846.3i	0.565831	+	0.980048i
$887$	12631.0	+	3384.46i	0.478137	+	0.128116i	0.489835	−	0.871815i	$-0.337057\pi$
$887$	12631.0	+	3384.46i	0.478137	+	0.128116i	−0.0116982	+	0.999932i	$0.503724\pi$
$888$	−4444.22	+	12009.4i	−0.167949	+	0.453839i
$889$	−51.4304	−	29.6933i	−0.00194029	−	0.00112023i
$890$	−7511.61	−	8098.78i	−0.282910	−	0.305024i
$891$	−12974.3	+	33397.1i	−0.487829	+	1.25572i
$892$	752.908	+	752.908i	0.0282615	+	0.0282615i
$893$	−27542.2	+	7379.90i	−1.03210	+	0.276550i
$894$	−44016.2	+	20238.1i	−1.64667	+	0.757118i
$895$	−19266.7	+	10177.9i	−0.719570	+	0.380123i
$896$	−16467.1	+	9507.27i	−0.613980	+	0.354482i
$897$	−24732.0	+	20527.4i	−0.920601	+	0.764091i
$898$	3772.27	+	14078.3i	0.140181	+	0.523162i
$899$	−9726.35			−0.360836
$900$	−24790.4	+	24856.7i	−0.918163	+	0.920619i
$901$	7505.21			0.277508
$902$	2653.73	+	9903.87i	0.0979597	+	0.365591i
$903$	−4714.68	−	27604.1i	−0.173748	−	1.01728i
$904$	−10464.3	+	6041.54i	−0.384996	+	0.222277i
$905$	−15729.9	+	8309.55i	−0.577769	+	0.305214i
$906$	47877.8	+	33908.9i	1.75567	+	1.24343i
$907$	−12250.7	+	3282.57i	−0.448488	+	0.120172i	−0.475992	−	0.879450i	$-0.657911\pi$
$907$	−12250.7	+	3282.57i	−0.448488	+	0.120172i	0.0275041	+	0.999622i	$0.491244\pi$
$908$	10682.7	+	10682.7i	0.390436	+	0.390436i
$909$	−1267.22	−	3601.52i	−0.0462387	−	0.131413i
$910$	−17214.1	−	18559.7i	−0.627079	−	0.676097i
$911$	−19788.0	−	11424.6i	−0.719655	−	0.415493i	0.0949706	−	0.995480i	$-0.469724\pi$
$911$	−19788.0	−	11424.6i	−0.719655	−	0.415493i	−0.814626	+	0.579987i	$0.803058\pi$
$912$	6961.82	+	8387.82i	0.252773	+	0.304549i
$913$	−41377.0	−	11086.9i	−1.49987	−	0.401888i
$914$	18594.1	+	32205.9i	0.672908	+	1.16551i
$915$	−1485.92	+	3594.12i	−0.0536865	+	0.129856i
$916$	28839.8	−	49951.9i	1.04028	−	1.80181i
$917$	5615.06	−	5615.06i	0.202209	−	0.202209i
$918$	259.124	−	16086.9i	0.00931631	−	0.578372i
$919$			34032.1i			1.22156i	0.791800	+	0.610780i	$0.209144\pi$
$919$			34032.1i			1.22156i	−0.791800	+	0.610780i	$0.790856\pi$
$920$	−10847.7	+	17256.4i	−0.388736	+	0.618399i
$921$	−1523.30	−	3313.04i	−0.0544998	−	0.118533i
$922$	−8979.34	+	33511.3i	−0.320736	+	1.19700i
$923$	9397.87	−	35073.3i	0.335140	−	1.25076i
$924$	−39936.8	−	3710.18i	−1.42189	−	0.132095i
$925$	29380.5	−	5547.12i	1.04435	−	0.197177i
$926$		−	32365.8i		−	1.14860i
$927$	1826.88	+	2669.61i	0.0647276	+	0.0945861i
$928$	−38860.6	+	38860.6i	−1.37463	+	1.37463i
$929$	10629.2	−	18410.4i	0.375386	−	0.650188i	−0.614998	−	0.788528i	$-0.710843\pi$
$929$	10629.2	−	18410.4i	0.375386	−	0.650188i	0.990385	+	0.138340i	$0.0441767\pi$
$930$	6701.15	−	8745.20i	0.236279	−	0.308351i
$931$	−3092.05	−	5355.60i	−0.108849	−	0.188531i
$932$	12374.5	+	3315.75i	0.434916	+	0.116535i
$933$	−16345.9	+	2791.82i	−0.573570	+	0.0979638i
$934$	48106.0	+	27774.0i	1.68531	+	0.973012i
$935$	−10770.2	+	9989.38i	−0.376711	+	0.349399i
$936$	−1791.27	+	9557.51i	−0.0625528	+	0.333757i
$937$	−376.587	−	376.587i	−0.0131297	−	0.0131297i	0.700511	−	0.713641i	$-0.252955\pi$
$937$	−376.587	−	376.587i	−0.0131297	−	0.0131297i	−0.713641	+	0.700511i	$0.752955\pi$
$938$	−4518.48	+	1210.72i	−0.157285	+	0.0421445i
$939$	−2097.28	+	22575.4i	−0.0728883	+	0.784579i
$940$	58931.6	+	18190.7i	2.04483	+	0.631186i
$941$	24030.3	−	13873.9i	0.832481	−	0.480633i	−0.0222206	−	0.999753i	$-0.507074\pi$
$941$	24030.3	−	13873.9i	0.832481	−	0.480633i	0.854701	+	0.519120i	$0.173740\pi$
$942$	−60565.6	−	22413.0i	−2.09483	−	0.775219i
$943$	2227.30	+	8312.38i	0.0769149	+	0.287050i
$944$	−5024.89			−0.173248
$945$	−22514.7	−	7348.91i	−0.775029	−	0.252974i
$946$	75252.4			2.58633
$947$	3256.28	+	12152.6i	0.111737	+	0.417008i	0.999022	−	0.0442131i	$-0.0140781\pi$
$947$	3256.28	+	12152.6i	0.111737	+	0.417008i	−0.887285	+	0.461221i	$0.847411\pi$
$948$	17423.6	+	6447.82i	0.596933	+	0.220903i
$949$	−14522.4	+	8384.52i	−0.496752	+	0.286800i
$950$	−9532.63	+	27208.3i	−0.325557	+	0.929216i
$951$	−1934.97	+	20828.3i	−0.0659788	+	0.710204i
$952$	4016.97	−	1076.34i	0.136755	−	0.0366434i
$953$	1723.37	+	1723.37i	0.0585787	+	0.0585787i	0.735789	−	0.677211i	$-0.236811\pi$
$953$	1723.37	+	1723.37i	0.0585787	+	0.0585787i	−0.677211	+	0.735789i	$0.736811\pi$
$954$	−30673.1	+	10792.6i	−1.04096	+	0.366271i
$955$	22262.1	+	837.375i	0.754329	+	0.0283736i
$956$	−827.868	−	477.970i	−0.0280075	−	0.0161701i
$957$	−55383.1	+	9459.24i	−1.87072	+	0.319513i
$958$	−3176.28	−	851.080i	−0.107120	−	0.0287027i
$959$	−14073.9	−	24376.7i	−0.473900	−	0.820819i
$960$	−5787.81	−	43737.1i	−0.194584	−	1.47043i
$961$	13918.3	−	24107.1i	0.467197	−	0.809209i
$962$	25362.6	−	25362.6i	0.850025	−	0.850025i
$963$	35817.3	−	2746.42i	1.19854	−	0.0919025i
$964$		−	20371.7i		−	0.680632i
$965$	−26820.0	+	6115.93i	−0.894679	+	0.204020i
$966$	−59299.0	−	5508.95i	−1.97507	−	0.183486i
$967$	8142.30	−	30387.5i	0.270774	−	1.01054i	−0.687846	−	0.725856i	$-0.741444\pi$
$967$	8142.30	−	30387.5i	0.270774	−	1.01054i	0.958621	−	0.284687i	$-0.0918897\pi$
$968$	2891.88	−	10792.7i	0.0960214	−	0.358357i
$969$	−3119.98	−	6785.69i	−0.103435	−	0.224962i
$970$	−23249.8	−	14615.2i	−0.769593	−	0.483778i
$971$			51764.9i			1.71083i	0.517943	+	0.855415i	$0.326698\pi$
$971$			51764.9i			1.71083i	−0.517943	+	0.855415i	$0.673302\pi$
$972$	12477.5	+	37373.9i	0.411746	+	1.23330i
$973$	−25598.7	+	25598.7i	−0.843430	+	0.843430i
$974$	−11814.2	+	20462.8i	−0.388657	+	0.673174i
$975$	21282.9	−	7908.33i	0.699076	−	0.259763i
$976$	−1306.03	−	2262.12i	−0.0428331	−	0.0741891i
$977$	36283.3	+	9722.09i	1.18813	+	0.318359i	0.798148	−	0.602462i	$-0.205813\pi$
$977$	36283.3	+	9722.09i	1.18813	+	0.318359i	0.389985	+	0.920821i	$0.372480\pi$
$978$	22090.5	+	26615.3i	0.722265	+	0.870208i
$979$	9802.93	+	5659.73i	0.320024	+	0.184766i
$980$	−502.783	+	13366.8i	−0.0163886	+	0.435700i
$981$	18504.0	−	21577.4i	0.602231	−	0.702258i
$982$	−44432.8	−	44432.8i	−1.44390	−	1.44390i
$983$	−49244.5	+	13195.0i	−1.59782	+	0.428134i	−0.944382	−	0.328849i	$-0.893339\pi$
$983$	−49244.5	+	13195.0i	−1.59782	+	0.428134i	−0.653435	+	0.756983i	$0.726673\pi$
$984$	2124.64	+	1504.75i	0.0688324	+	0.0487498i
$985$	−2318.33	+	7510.58i	−0.0749929	+	0.242951i
$986$	21849.8	−	12615.0i	0.705720	−	0.407448i
$987$	7005.12	+	41014.4i	0.225912	+	1.32270i
$988$	5059.76	+	18883.3i	0.162928	+	0.608054i
$989$	63159.8			2.03070
$990$	29652.2	−	56313.4i	0.951929	−	1.80784i
$991$	61805.9			1.98116			0.990580	−	0.136936i	$-0.0437255\pi$
$991$	61805.9			1.98116			0.990580	+	0.136936i	$0.0437255\pi$
$992$	2858.24	+	10667.1i	0.0914812	+	0.341413i
$993$	2591.07	−	2150.57i	0.0828048	−	0.0687273i
$994$	58266.3	−	33640.1i	1.85925	−	1.07344i
$995$	−6630.88	−	12552.2i	−0.211269	−	0.399931i
$996$	−42801.0	+	19679.4i	−1.36165	+	0.626070i
$997$	−11218.8	+	3006.06i	−0.356371	+	0.0954892i	−0.432562	−	0.901604i	$-0.642390\pi$
$997$	−11218.8	+	3006.06i	−0.356371	+	0.0954892i	0.0761919	+	0.997093i	$0.475724\pi$
$998$	41367.7	+	41367.7i	1.31210	+	1.31210i
$999$	9206.49	−	32270.8i	0.291572	−	1.02203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.4.l.a.2.14	✓	64
3.2	odd	2		135.4.m.a.62.3		64
5.2	odd	4		225.4.p.b.218.3		64
5.3	odd	4	inner	45.4.l.a.38.14	yes	64
5.4	even	2		225.4.p.b.182.3		64
9.4	even	3		135.4.m.a.17.3		64
9.5	odd	6	inner	45.4.l.a.32.14	yes	64
15.8	even	4		135.4.m.a.8.3		64
45.13	odd	12		135.4.m.a.98.3		64
45.14	odd	6		225.4.p.b.32.3		64
45.23	even	12	inner	45.4.l.a.23.14	yes	64
45.32	even	12		225.4.p.b.68.3		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.l.a.2.14	✓	64	1.1	even	1	trivial
45.4.l.a.23.14	yes	64	45.23	even	12	inner
45.4.l.a.32.14	yes	64	9.5	odd	6	inner
45.4.l.a.38.14	yes	64	5.3	odd	4	inner
135.4.m.a.8.3		64	15.8	even	4
135.4.m.a.17.3		64	9.4	even	3
135.4.m.a.62.3		64	3.2	odd	2
135.4.m.a.98.3		64	45.13	odd	12
225.4.p.b.32.3		64	45.14	odd	6
225.4.p.b.68.3		64	45.32	even	12
225.4.p.b.182.3		64	5.4	even	2
225.4.p.b.218.3		64	5.2	odd	4

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	45.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11026 + 4.14355i) q^{2} +(-4.87317 - 1.80338i) q^{3} +(-9.00816 + 5.20086i) q^{4} +(-9.88574 + 5.22228i) q^{5} +(2.06189 - 22.1945i) q^{6} +(-14.5845 + 3.90791i) q^{7} +(-7.28515 - 7.28515i) q^{8} +(20.4957 + 17.5763i) q^{9} +O(q^{10})\)	\(q+(1.11026 + 4.14355i) q^{2} +(-4.87317 - 1.80338i) q^{3} +(-9.00816 + 5.20086i) q^{4} +(-9.88574 + 5.22228i) q^{5} +(2.06189 - 22.1945i) q^{6} +(-14.5845 + 3.90791i) q^{7} +(-7.28515 - 7.28515i) q^{8} +(20.4957 + 17.5763i) q^{9} +(-32.6146 - 35.1640i) q^{10} +(42.5632 + 24.5739i) q^{11} +(53.2775 - 9.09960i) q^{12} +(-33.7651 - 9.04733i) q^{13} +(-32.3853 - 56.0930i) q^{14} +(57.5927 - 7.62135i) q^{15} +(-19.5089 + 33.7905i) q^{16} +(18.9033 - 18.9033i) q^{17} +(-50.0730 + 104.439i) q^{18} +53.7656i q^{19} +(61.8920 - 98.4575i) q^{20} +(78.1204 + 7.25747i) q^{21} +(-54.5669 + 203.647i) q^{22} +(-45.7984 + 170.922i) q^{23} +(22.3639 + 48.6397i) q^{24} +(70.4556 - 103.252i) q^{25} -149.952i q^{26} +(-68.1821 - 122.614i) q^{27} +(111.055 - 111.055i) q^{28} +(110.003 - 190.531i) q^{29} +(95.5224 + 230.177i) q^{30} +(-22.1047 - 38.2864i) q^{31} +(-241.286 - 64.6525i) q^{32} +(-163.102 - 196.510i) q^{33} +(99.3145 + 57.3392i) q^{34} +(123.771 - 114.797i) q^{35} +(-276.040 - 51.7355i) q^{36} +(169.138 + 169.138i) q^{37} +(-222.781 + 59.6939i) q^{38} +(148.227 + 104.980i) q^{39} +(110.064 + 33.9740i) q^{40} +(42.1171 - 24.3163i) q^{41} +(56.6624 + 331.754i) q^{42} +(-92.3811 - 344.771i) q^{43} -511.222 q^{44} +(-294.403 - 66.7212i) q^{45} -759.073 q^{46} +(137.261 + 512.264i) q^{47} +(156.007 - 129.485i) q^{48} +(-99.6102 + 57.5100i) q^{49} +(506.055 + 177.300i) q^{50} +(-126.209 + 58.0293i) q^{51} +(351.215 - 94.1079i) q^{52} +(198.516 + 198.516i) q^{53} +(432.358 - 418.650i) q^{54} +(-549.101 - 20.6541i) q^{55} +(134.720 + 77.7807i) q^{56} +(96.9596 - 262.009i) q^{57} +(911.609 + 244.265i) q^{58} +(64.3921 + 111.530i) q^{59} +(-479.166 + 368.186i) q^{60} +(-33.4727 + 57.9764i) q^{61} +(134.100 - 134.100i) q^{62} +(-367.606 - 176.247i) q^{63} -759.421i q^{64} +(381.041 - 86.8911i) q^{65} +(633.166 - 894.000i) q^{66} +(18.6925 - 69.7613i) q^{67} +(-71.9705 + 268.597i) q^{68} +(531.420 - 750.341i) q^{69} +(613.086 + 385.395i) q^{70} +1038.75i q^{71} +(-21.2676 - 277.360i) q^{72} +(339.210 - 339.210i) q^{73} +(-513.044 + 888.619i) q^{74} +(-529.545 + 376.107i) q^{75} +(-279.627 - 484.329i) q^{76} +(-716.797 - 192.065i) q^{77} +(-270.421 + 730.744i) q^{78} +(297.681 + 171.866i) q^{79} +(16.3970 - 435.925i) q^{80} +(111.144 + 720.478i) q^{81} +(147.517 + 147.517i) q^{82} +(-841.890 + 225.584i) q^{83} +(-741.466 + 340.917i) q^{84} +(-88.1548 + 285.591i) q^{85} +(1326.01 - 765.572i) q^{86} +(-879.665 + 730.114i) q^{87} +(-131.055 - 489.104i) q^{88} +230.315 q^{89} +(-50.4019 - 1293.95i) q^{90} +527.804 q^{91} +(-476.383 - 1777.88i) q^{92} +(38.6751 + 226.440i) q^{93} +(-1970.20 + 1137.50i) q^{94} +(-280.779 - 531.512i) q^{95} +(1059.24 + 750.193i) q^{96} +(553.082 - 148.198i) q^{97} +(-348.889 - 348.889i) q^{98} +(440.442 + 1251.76i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) \) 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7	\( 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 8 q^{10} - 36 q^{11} - 138 q^{12} - 2 q^{13} - 96 q^{15} + 316 q^{16} - 480 q^{18} + 378 q^{20} + 480 q^{21} - 34 q^{22} + 306 q^{23} - 146 q^{25} + 180 q^{27} - 232 q^{28} - 1170 q^{30} - 4 q^{31} - 1770 q^{32} - 294 q^{33} - 216 q^{36} + 136 q^{37} + 114 q^{38} + 126 q^{40} + 1992 q^{41} + 1698 q^{42} - 2 q^{43} + 1134 q^{45} - 952 q^{46} + 3462 q^{47} + 4326 q^{48} + 666 q^{50} - 2496 q^{51} - 242 q^{52} + 284 q^{55} - 7128 q^{56} - 2544 q^{57} + 534 q^{58} + 1818 q^{60} + 32 q^{61} - 4038 q^{63} - 2094 q^{65} + 2892 q^{66} + 610 q^{67} - 2694 q^{68} + 498 q^{70} - 1854 q^{72} - 8 q^{73} - 6408 q^{75} + 1368 q^{76} - 6486 q^{77} + 1434 q^{78} + 3012 q^{81} - 3784 q^{82} + 2814 q^{83} - 1658 q^{85} + 12480 q^{86} + 4830 q^{87} - 1338 q^{88} + 13914 q^{90} + 992 q^{91} + 13152 q^{92} + 8310 q^{93} + 4284 q^{95} - 7932 q^{96} + 358 q^{97}+O(q^{100}) \) 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 8 * q^10 - 36 * q^11 - 138 * q^12 - 2 * q^13 - 96 * q^15 + 316 * q^16 - 480 * q^18 + 378 * q^20 + 480 * q^21 - 34 * q^22 + 306 * q^23 - 146 * q^25 + 180 * q^27 - 232 * q^28 - 1170 * q^30 - 4 * q^31 - 1770 * q^32 - 294 * q^33 - 216 * q^36 + 136 * q^37 + 114 * q^38 + 126 * q^40 + 1992 * q^41 + 1698 * q^42 - 2 * q^43 + 1134 * q^45 - 952 * q^46 + 3462 * q^47 + 4326 * q^48 + 666 * q^50 - 2496 * q^51 - 242 * q^52 + 284 * q^55 - 7128 * q^56 - 2544 * q^57 + 534 * q^58 + 1818 * q^60 + 32 * q^61 - 4038 * q^63 - 2094 * q^65 + 2892 * q^66 + 610 * q^67 - 2694 * q^68 + 498 * q^70 - 1854 * q^72 - 8 * q^73 - 6408 * q^75 + 1368 * q^76 - 6486 * q^77 + 1434 * q^78 + 3012 * q^81 - 3784 * q^82 + 2814 * q^83 - 1658 * q^85 + 12480 * q^86 + 4830 * q^87 - 1338 * q^88 + 13914 * q^90 + 992 * q^91 + 13152 * q^92 + 8310 * q^93 + 4284 * q^95 - 7932 * q^96 + 358 * q^97

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