LMFDB - Embedded newform 261.3.s.a.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,3,Mod(10,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([0, 23]))

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

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

chi := DirichletCharacter("261.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	261.s (of order $28$, 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:	$7.11173489980$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{28})$
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	261.19
Dual form			261.3.s.a.55.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.448531 + 0.713833i) q^{2} +(1.42716 - 2.96352i) q^{4} +(-4.21883 - 0.962920i) q^{5} +(-10.1429 + 4.88457i) q^{7} +(6.10659 - 0.688048i) q^{8} +O(q^{10})$	\(q+(0.448531 + 0.713833i) q^{2} +(1.42716 - 2.96352i) q^{4} +(-4.21883 - 0.962920i) q^{5} +(-10.1429 + 4.88457i) q^{7} +(6.10659 - 0.688048i) q^{8} +(-1.20491 - 3.44344i) q^{10} +(-1.54207 - 0.173749i) q^{11} +(-11.3208 + 9.02803i) q^{13} +(-8.03618 - 5.04946i) q^{14} +(-4.97314 - 6.23612i) q^{16} +(-16.8448 + 16.8448i) q^{17} +(0.448791 - 0.157039i) q^{19} +(-8.87457 + 11.1284i) q^{20} +(-0.567637 - 1.17871i) q^{22} +(-1.55197 - 6.79962i) q^{23} +(-5.65292 - 2.72230i) q^{25} +(-11.5222 - 4.03180i) q^{26} +37.0298i q^{28} +(20.2766 + 20.7330i) q^{29} +(-7.88671 - 12.5516i) q^{31} +(10.3395 - 29.5486i) q^{32} +(-19.5798 - 4.46896i) q^{34} +(47.4946 - 10.8403i) q^{35} +(26.2932 - 2.96253i) q^{37} +(0.313396 + 0.249925i) q^{38} +(-26.4252 - 2.97741i) q^{40} +(-46.1225 - 46.1225i) q^{41} +(-53.7324 - 33.7623i) q^{43} +(-2.71568 + 4.32198i) q^{44} +(4.15769 - 4.15769i) q^{46} +(-5.72285 + 50.7917i) q^{47} +(48.4686 - 60.7777i) q^{49} +(-0.592241 - 5.25628i) q^{50} +(10.5982 + 46.4338i) q^{52} +(9.09960 - 39.8680i) q^{53} +(6.33841 + 2.21790i) q^{55} +(-58.5778 + 36.8069i) q^{56} +(-5.70521 + 23.7735i) q^{58} -23.8690 q^{59} +(23.8851 - 68.2596i) q^{61} +(5.42233 - 11.2596i) q^{62} +(-5.37487 + 1.22678i) q^{64} +(56.4537 - 27.1867i) q^{65} +(89.8491 + 71.6523i) q^{67} +(25.8798 + 73.9602i) q^{68} +(29.0410 + 29.0410i) q^{70} +(54.7070 - 43.6274i) q^{71} +(-43.5770 + 69.3524i) q^{73} +(13.9081 + 17.4402i) q^{74} +(0.175107 - 1.55412i) q^{76} +(16.4897 - 5.77000i) q^{77} +(12.9255 + 114.717i) q^{79} +(14.9759 + 31.0978i) q^{80} +(12.2364 - 53.6111i) q^{82} +(1.11626 + 0.537563i) q^{83} +(87.2856 - 54.8452i) q^{85} -53.4995i q^{86} -9.53632 q^{88} +(35.1684 + 55.9701i) q^{89} +(70.7277 - 146.868i) q^{91} +(-22.3657 - 5.10483i) q^{92} +(-38.8237 + 18.6965i) q^{94} +(-2.04459 + 0.230370i) q^{95} +(-26.0062 - 74.3215i) q^{97} +(65.1248 + 7.33780i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) $ 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8	$ 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) $ 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8 - 20 * q^10 + 8 * q^11 - 14 * q^13 - 26 * q^14 + 18 * q^16 + 26 * q^17 + 2 * q^19 - 46 * q^20 + 154 * q^22 - 56 * q^23 - 34 * q^25 - 110 * q^26 + 170 * q^29 - 88 * q^31 + 132 * q^32 - 224 * q^34 + 210 * q^35 - 56 * q^37 + 294 * q^38 - 492 * q^40 + 34 * q^41 + 176 * q^43 - 126 * q^44 + 744 * q^46 - 208 * q^47 + 506 * q^49 - 732 * q^50 + 690 * q^52 + 14 * q^53 + 284 * q^55 - 332 * q^56 - 508 * q^58 + 44 * q^59 - 30 * q^61 + 504 * q^62 - 896 * q^64 + 554 * q^65 - 574 * q^67 + 796 * q^68 - 1066 * q^70 - 224 * q^71 - 22 * q^73 - 820 * q^74 + 514 * q^76 - 436 * q^77 + 564 * q^79 - 1162 * q^80 - 18 * q^82 + 126 * q^83 + 38 * q^85 - 384 * q^88 + 160 * q^89 - 434 * q^91 + 1022 * q^92 - 2 * q^94 + 642 * q^95 + 604 * q^97 + 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{9}{28}\right)$	$1$

Coefficient data

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

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

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

$2$	0.448531	+	0.713833i	0.224266	+	0.356917i	0.939837	−	0.341623i	$-0.110977\pi$
$2$	0.448531	+	0.713833i	0.224266	+	0.356917i	−0.715572	+	0.698539i	$0.753834\pi$
$3$		0			0
$3$		0			0
$4$	1.42716	−	2.96352i	0.356789	−	0.740881i
$5$	−4.21883	−	0.962920i	−0.843766	−	0.192584i	−0.221275	−	0.975211i	$-0.571022\pi$
$5$	−4.21883	−	0.962920i	−0.843766	−	0.192584i	−0.622490	+	0.782627i	$0.713879\pi$
$6$		0			0
$7$	−10.1429	+	4.88457i	−1.44899	+	0.697795i	−0.982419	−	0.186690i	$-0.940224\pi$
$7$	−10.1429	+	4.88457i	−1.44899	+	0.697795i	−0.466568	+	0.884485i	$0.654510\pi$
$8$	6.10659	−	0.688048i	0.763324	−	0.0860060i
$9$		0			0
$10$	−1.20491	−	3.44344i	−0.120491	−	0.344344i
$11$	−1.54207	−	0.173749i	−0.140188	−	0.0157954i	0.0415917	−	0.999135i	$-0.486757\pi$
$11$	−1.54207	−	0.173749i	−0.140188	−	0.0157954i	−0.181780	+	0.983339i	$0.558186\pi$
$12$		0			0
$13$	−11.3208	+	9.02803i	−0.870830	+	0.694464i	−0.953266	−	0.302133i	$-0.902301\pi$
$13$	−11.3208	+	9.02803i	−0.870830	+	0.694464i	0.0824361	+	0.996596i	$0.473730\pi$
$14$	−8.03618	−	5.04946i	−0.574013	−	0.360676i
$15$		0			0
$16$	−4.97314	−	6.23612i	−0.310821	−	0.389757i
$17$	−16.8448	+	16.8448i	−0.990872	+	0.990872i	−0.999959	−	0.00908711i	$-0.997107\pi$
$17$	−16.8448	+	16.8448i	−0.990872	+	0.990872i	0.00908711	+	0.999959i	$0.497107\pi$
$18$		0			0
$19$	0.448791	−	0.157039i	0.0236206	−	0.00826520i	−0.318443	−	0.947942i	$-0.603160\pi$
$19$	0.448791	−	0.157039i	0.0236206	−	0.00826520i	0.342064	+	0.939677i	$0.388874\pi$
$20$	−8.87457	+	11.1284i	−0.443728	+	0.556418i
$21$		0			0
$22$	−0.567637	−	1.17871i	−0.0258017	−	0.0535777i
$23$	−1.55197	−	6.79962i	−0.0674769	−	0.295636i	0.929918	−	0.367766i	$-0.119877\pi$
$23$	−1.55197	−	6.79962i	−0.0674769	−	0.295636i	−0.997395	+	0.0721306i	$0.977020\pi$
$24$		0			0
$25$	−5.65292	−	2.72230i	−0.226117	−	0.108892i
$26$	−11.5222	−	4.03180i	−0.443163	−	0.155069i
$27$		0			0
$28$			37.0298i			1.32249i
$29$	20.2766	+	20.7330i	0.699195	+	0.714931i
$29$	20.2766	+	20.7330i	0.699195	+	0.714931i
$30$		0			0
$31$	−7.88671	−	12.5516i	−0.254410	−	0.404891i	0.694962	−	0.719047i	$-0.255421\pi$
$31$	−7.88671	−	12.5516i	−0.254410	−	0.404891i	−0.949371	+	0.314156i	$0.898279\pi$
$32$	10.3395	−	29.5486i	0.323110	−	0.923394i
$33$		0			0
$34$	−19.5798	−	4.46896i	−0.575877	−	0.131440i
$35$	47.4946	−	10.8403i	1.35699	−	0.309724i
$36$		0			0
$37$	26.2932	−	2.96253i	0.710627	−	0.0800685i	0.250751	−	0.968052i	$-0.419322\pi$
$37$	26.2932	−	2.96253i	0.710627	−	0.0800685i	0.459876	+	0.887983i	$0.347894\pi$
$38$	0.313396	+	0.249925i	0.00824727	+	0.00657698i
$39$		0			0
$40$	−26.4252	−	2.97741i	−0.660630	−	0.0744351i
$41$	−46.1225	−	46.1225i	−1.12494	−	1.12494i	−0.990988	−	0.133950i	$-0.957234\pi$
$41$	−46.1225	−	46.1225i	−1.12494	−	1.12494i	−0.133950	−	0.990988i	$-0.542766\pi$
$42$		0			0
$43$	−53.7324	−	33.7623i	−1.24959	−	0.785170i	−0.265721	−	0.964050i	$-0.585610\pi$
$43$	−53.7324	−	33.7623i	−1.24959	−	0.785170i	−0.983871	+	0.178880i	$0.942753\pi$
$44$	−2.71568	+	4.32198i	−0.0617200	+	0.0982268i
$45$		0			0
$46$	4.15769	−	4.15769i	0.0903845	−	0.0903845i
$47$	−5.72285	+	50.7917i	−0.121763	+	1.08067i	0.773085	+	0.634302i	$0.218713\pi$
$47$	−5.72285	+	50.7917i	−0.121763	+	1.08067i	−0.894848	+	0.446372i	$0.852716\pi$
$48$		0			0
$49$	48.4686	−	60.7777i	0.989155	−	1.24036i
$50$	−0.592241	−	5.25628i	−0.0118448	−	0.105126i
$51$		0			0
$52$	10.5982	+	46.4338i	0.203812	+	0.892958i
$53$	9.09960	−	39.8680i	0.171691	−	0.752226i	−0.813612	−	0.581408i	$-0.802502\pi$
$53$	9.09960	−	39.8680i	0.171691	−	0.752226i	0.985303	−	0.170818i	$-0.0546409\pi$
$54$		0			0
$55$	6.33841	+	2.21790i	0.115244	+	0.0403255i
$56$	−58.5778	+	36.8069i	−1.04603	+	0.657265i
$57$		0			0
$58$	−5.70521	+	23.7735i	−0.0983656	+	0.409889i
$59$	−23.8690			−0.404559			−0.202280	−	0.979328i	$-0.564835\pi$
$59$	−23.8690			−0.404559			−0.202280	+	0.979328i	$0.564835\pi$
$60$		0			0
$61$	23.8851	−	68.2596i	0.391559	−	1.11901i	−0.564398	−	0.825503i	$-0.690892\pi$
$61$	23.8851	−	68.2596i	0.391559	−	1.11901i	0.955957	−	0.293507i	$-0.0948225\pi$
$62$	5.42233	−	11.2596i	0.0874569	−	0.181606i
$63$		0			0
$64$	−5.37487	+	1.22678i	−0.0839824	+	0.0191684i
$65$	56.4537	−	27.1867i	0.868519	−	0.418257i
$66$		0			0
$67$	89.8491	+	71.6523i	1.34103	+	1.06944i	0.991165	+	0.132637i	$0.0423445\pi$
$67$	89.8491	+	71.6523i	1.34103	+	1.06944i	0.349866	+	0.936800i	$0.386227\pi$
$68$	25.8798	+	73.9602i	0.380585	+	1.08765i
$69$		0			0
$70$	29.0410	+	29.0410i	0.414872	+	0.414872i
$71$	54.7070	−	43.6274i	0.770521	−	0.614470i	−0.157276	−	0.987555i	$-0.550271\pi$
$71$	54.7070	−	43.6274i	0.770521	−	0.614470i	0.927797	+	0.373085i	$0.121700\pi$
$72$		0			0
$73$	−43.5770	+	69.3524i	−0.596945	+	0.950032i	0.402457	+	0.915439i	$0.368156\pi$
$73$	−43.5770	+	69.3524i	−0.596945	+	0.950032i	−0.999401	+	0.0345932i	$0.988986\pi$
$74$	13.9081	+	17.4402i	0.187947	+	0.235678i
$75$		0			0
$76$	0.175107	−	1.55412i	0.00230405	−	0.0204490i
$77$	16.4897	−	5.77000i	0.214152	−	0.0749351i
$78$		0			0
$79$	12.9255	+	114.717i	0.163613	+	1.45211i	0.760267	+	0.649611i	$0.225068\pi$
$79$	12.9255	+	114.717i	0.163613	+	1.45211i	−0.596653	+	0.802499i	$0.703503\pi$
$80$	14.9759	+	31.0978i	0.187199	+	0.388723i
$81$		0			0
$82$	12.2364	−	53.6111i	0.149224	−	0.653794i
$83$	1.11626	+	0.537563i	0.0134489	+	0.00647666i	0.440596	−	0.897705i	$-0.354767\pi$
$83$	1.11626	+	0.537563i	0.0134489	+	0.00647666i	−0.427147	+	0.904182i	$0.640481\pi$
$84$		0			0
$85$	87.2856	−	54.8452i	1.02689	−	0.645237i
$86$		−	53.4995i		−	0.622087i
$87$		0			0
$88$	−9.53632			−0.108367
$89$	35.1684	+	55.9701i	0.395150	+	0.628878i	0.983749	−	0.179547i	$-0.0574632\pi$
$89$	35.1684	+	55.9701i	0.395150	+	0.628878i	−0.588599	+	0.808425i	$0.700320\pi$
$90$		0			0
$91$	70.7277	−	146.868i	0.777227	−	1.61393i
$92$	−22.3657	−	5.10483i	−0.243106	−	0.0554873i
$93$		0			0
$94$	−38.8237	+	18.6965i	−0.413018	+	0.198899i
$95$	−2.04459	+	0.230370i	−0.0215220	+	0.00242495i
$96$		0			0
$97$	−26.0062	−	74.3215i	−0.268105	−	0.766201i	−0.996694	−	0.0812495i	$-0.974109\pi$
$97$	−26.0062	−	74.3215i	−0.268105	−	0.766201i	0.728588	−	0.684952i	$-0.240177\pi$
$98$	65.1248	+	7.33780i	0.664539	+	0.0748755i
$99$		0			0
$100$	−16.1352	+	12.8674i	−0.161352	+	0.128674i
$101$	−71.2798	−	44.7881i	−0.705741	−	0.443446i	0.130759	−	0.991414i	$-0.458259\pi$
$101$	−71.2798	−	44.7881i	−0.705741	−	0.443446i	−0.836499	+	0.547968i	$0.815402\pi$
$102$		0			0
$103$	30.3804	+	38.0958i	0.294955	+	0.369862i	0.907123	−	0.420866i	$-0.138274\pi$
$103$	30.3804	+	38.0958i	0.294955	+	0.369862i	−0.612168	+	0.790728i	$0.709702\pi$
$104$	−62.9197	+	62.9197i	−0.604997	+	0.604997i
$105$		0			0
$106$	32.5405	−	11.3864i	0.306986	−	0.107419i
$107$	−83.6309	+	104.870i	−0.781597	+	0.980092i	0.218394	+	0.975861i	$0.429918\pi$
$107$	−83.6309	+	104.870i	−0.781597	+	0.980092i	−0.999991	+	0.00423133i	$0.998653\pi$
$108$		0			0
$109$	8.81881	+	18.3125i	0.0809066	+	0.168004i	0.937498	−	0.347992i	$-0.113136\pi$
$109$	8.81881	+	18.3125i	0.0809066	+	0.168004i	−0.856591	+	0.515996i	$0.827422\pi$
$110$	1.25976	+	5.51936i	0.0114524	+	0.0501760i
$111$		0			0
$112$	80.9028	+	38.9607i	0.722347	+	0.347864i
$113$	−22.6341	−	7.92002i	−0.200302	−	0.0700886i	0.228264	−	0.973599i	$-0.426695\pi$
$113$	−22.6341	−	7.92002i	−0.200302	−	0.0700886i	−0.428566	+	0.903511i	$0.640981\pi$
$114$		0			0
$115$			30.1808i			0.262442i
$116$	90.3807	−	30.5010i	0.779144	−	0.262940i
$117$		0			0
$118$	−10.7060	−	17.0385i	−0.0907287	−	0.144394i
$119$	88.5758	−	253.135i	0.744334	−	2.12719i
$120$		0			0
$121$	−115.618	−	26.3892i	−0.955525	−	0.218092i
$122$	59.4392	−	13.5666i	0.487206	−	0.111202i
$123$		0			0
$124$	−48.4526	+	5.45930i	−0.390747	+	0.0440266i
$125$	105.808	+	84.3793i	0.846466	+	0.675034i
$126$		0			0
$127$	−8.21611	−	0.925733i	−0.0646938	−	0.00728924i	0.0795583	−	0.996830i	$-0.474649\pi$
$127$	−8.21611	−	0.925733i	−0.0646938	−	0.00728924i	−0.144252	+	0.989541i	$0.546078\pi$
$128$	−91.8315	−	91.8315i	−0.717433	−	0.717433i
$129$		0			0
$130$	44.7280	+	28.1045i	0.344062	+	0.216188i
$131$	−127.911	+	203.569i	−0.976419	+	1.55396i	−0.151694	+	0.988428i	$0.548473\pi$
$131$	−127.911	+	203.569i	−0.976419	+	1.55396i	−0.824725	+	0.565534i	$0.808670\pi$
$132$		0			0
$133$	−3.78498	+	3.78498i	−0.0284585	+	0.0284585i
$134$	−10.8476	+	96.2755i	−0.0809526	+	0.718474i
$135$		0			0
$136$	−91.2744	+	114.454i	−0.671135	+	0.841577i
$137$	−4.55051	−	40.3869i	−0.0332154	−	0.294795i	−0.999327	−	0.0366716i	$-0.988324\pi$
$137$	−4.55051	−	40.3869i	−0.0332154	−	0.294795i	0.966112	−	0.258123i	$-0.0831041\pi$
$138$		0			0
$139$	−12.4270	−	54.4464i	−0.0894032	−	0.391701i	0.910352	−	0.413835i	$-0.135811\pi$
$139$	−12.4270	−	54.4464i	−0.0894032	−	0.391701i	−0.999755	+	0.0221342i	$0.992954\pi$
$140$	35.6567	−	156.222i	0.254691	−	1.11587i
$141$		0			0
$142$	55.6805	+	19.4834i	0.392116	+	0.137207i
$143$	19.0260	−	11.9548i	0.133049	−	0.0836003i
$144$		0			0
$145$	−65.5794	−	106.994i	−0.452272	−	0.737888i
$146$	−69.0516			−0.472956
$147$		0			0
$148$	28.7450	−	82.1485i	0.194223	−	0.555058i
$149$	45.3207	−	94.1095i	0.304166	−	0.631607i	−0.691726	−	0.722161i	$-0.743149\pi$
$149$	45.3207	−	94.1095i	0.304166	−	0.631607i	0.995892	+	0.0905531i	$0.0288635\pi$
$150$		0			0
$151$	40.2640	−	9.18999i	0.266649	−	0.0608609i	−0.0871059	−	0.996199i	$-0.527762\pi$
$151$	40.2640	−	9.18999i	0.266649	−	0.0608609i	0.353755	+	0.935338i	$0.384905\pi$
$152$	2.63253	−	1.26776i	0.0173193	−	0.00834054i
$153$		0			0
$154$	11.5150	+	9.18289i	0.0747726	+	0.0596291i
$155$	21.1865	+	60.5474i	0.136687	+	0.390628i
$156$		0			0
$157$	−57.9484	−	57.9484i	−0.369098	−	0.369098i	0.498050	−	0.867148i	$-0.334050\pi$
$157$	−57.9484	−	57.9484i	−0.369098	−	0.369098i	−0.867148	+	0.498050i	$0.834050\pi$
$158$	−76.0911	+	60.6806i	−0.481589	+	0.384055i
$159$		0			0
$160$	−72.0736	+	114.704i	−0.450460	+	0.716903i
$161$	48.9547	+	61.3872i	0.304066	+	0.381287i
$162$		0			0
$163$	0.128402	−	1.13960i	0.000787743	−	0.00699141i	−0.993312	−	0.115459i	$-0.963166\pi$
$163$	0.128402	−	1.13960i	0.000787743	−	0.00699141i	0.994100	+	0.108468i	$0.0345945\pi$
$164$	−202.509	+	70.8610i	−1.23481	+	0.432079i
$165$		0			0
$166$	0.116947	+	1.03794i	0.000704503	+	0.00625264i
$167$	−84.8706	−	176.236i	−0.508207	−	1.05530i	−0.984397	−	0.175960i	$-0.943697\pi$
$167$	−84.8706	−	176.236i	−0.508207	−	1.05530i	0.476190	−	0.879342i	$-0.342017\pi$
$168$		0			0
$169$	9.04891	−	39.6459i	0.0535439	−	0.234591i
$170$	78.3006	+	37.7076i	0.460592	+	0.221809i
$171$		0			0
$172$	−176.740	+	111.053i	−1.02756	+	0.645658i
$173$			93.9168i			0.542872i	0.962457	+	0.271436i	$0.0874985\pi$
$173$			93.9168i			0.542872i	−0.962457	+	0.271436i	$0.912502\pi$
$174$		0			0
$175$	70.6344			0.403625
$176$	6.58539	+	10.4806i	0.0374170	+	0.0595488i
$177$		0			0
$178$	−24.1792	+	50.2087i	−0.135838	+	0.282071i
$179$	−168.864	−	38.5422i	−0.943376	−	0.215319i	−0.276945	−	0.960886i	$-0.589322\pi$
$179$	−168.864	−	38.5422i	−0.943376	−	0.215319i	−0.666431	+	0.745566i	$0.732179\pi$
$180$		0			0
$181$	−87.2784	+	42.0311i	−0.482201	+	0.232216i	−0.659160	−	0.752002i	$-0.729088\pi$
$181$	−87.2784	+	42.0311i	−0.482201	+	0.232216i	0.176959	+	0.984218i	$0.443374\pi$
$182$	136.563	−	15.3869i	0.750344	−	0.0845434i
$183$		0			0
$184$	−14.1557	−	40.4547i	−0.0769332	−	0.219862i
$185$	−113.779	−	12.8198i	−0.615023	−	0.0692964i
$186$		0			0
$187$	28.9026	−	23.0490i	0.154559	−	0.123257i
$188$	142.355	+	89.4475i	0.757207	+	0.475785i
$189$		0			0
$190$	−1.08151	−	1.35617i	−0.00569214	−	0.00713772i
$191$	253.146	−	253.146i	1.32537	−	1.32537i	0.416013	−	0.909359i	$-0.363427\pi$
$191$	253.146	−	253.146i	1.32537	−	1.32537i	0.909359	−	0.416013i	$-0.136573\pi$
$192$		0			0
$193$	−281.027	+	98.3354i	−1.45610	+	0.509510i	−0.938248	−	0.345963i	$-0.887552\pi$
$193$	−281.027	+	98.3354i	−1.45610	+	0.509510i	−0.517848	+	0.855473i	$0.673267\pi$
$194$	41.3886	−	51.8996i	0.213343	−	0.267524i
$195$		0			0
$196$	−110.944	−	230.377i	−0.566040	−	1.17539i
$197$	30.9336	+	135.529i	0.157024	+	0.687965i	0.990740	+	0.135773i	$0.0433516\pi$
$197$	30.9336	+	135.529i	0.157024	+	0.687965i	−0.833716	+	0.552193i	$0.813791\pi$
$198$		0			0
$199$	10.4281	+	5.02191i	0.0524025	+	0.0252357i	0.459901	−	0.887970i	$-0.347885\pi$
$199$	10.4281	+	5.02191i	0.0524025	+	0.0252357i	−0.407499	+	0.913206i	$0.633599\pi$
$200$	−36.3932	−	12.7345i	−0.181966	−	0.0636726i
$201$		0			0
$202$		−	70.9707i		−	0.351340i
$203$	−306.936	−	111.250i	−1.51200	−	0.548032i
$204$		0			0
$205$	150.171	+	238.995i	0.732539	+	1.16583i
$206$	−13.5675	+	38.7736i	−0.0658616	+	0.188222i
$207$		0			0
$208$	112.600	+	25.7001i	0.541344	+	0.123558i
$209$	−0.719351	+	0.164187i	−0.00344187	+	0.000785585i
$210$		0			0
$211$	−138.139	+	15.5646i	−0.654688	+	0.0737657i	−0.433059	−	0.901365i	$-0.642566\pi$
$211$	−138.139	+	15.5646i	−0.654688	+	0.0737657i	−0.221629	+	0.975131i	$0.571137\pi$
$212$	−105.163	−	83.8647i	−0.496052	−	0.395588i
$213$		0			0
$214$	−112.371	−	12.6611i	−0.525096	−	0.0591642i
$215$	194.178	+	194.178i	0.903151	+	0.903151i
$216$		0			0
$217$	141.303	+	88.7868i	0.651168	+	0.409156i
$218$	−9.11653	+	14.5089i	−0.0418189	+	0.0665544i
$219$		0			0
$220$	15.6187	−	15.6187i	0.0709941	−	0.0709941i
$221$	38.6211	−	342.772i	0.174756	−	1.55100i
$222$		0			0
$223$	71.7315	−	89.9485i	0.321666	−	0.403356i	−0.594539	−	0.804067i	$-0.702665\pi$
$223$	71.7315	−	89.9485i	0.321666	−	0.403356i	0.916205	+	0.400711i	$0.131237\pi$
$224$	39.4595	+	350.213i	0.176159	+	1.56345i
$225$		0			0
$226$	−4.49853	−	19.7094i	−0.0199050	−	0.0872095i
$227$	−50.8656	+	222.857i	−0.224077	+	0.981747i	0.730296	+	0.683131i	$0.239382\pi$
$227$	−50.8656	+	222.857i	−0.224077	+	0.981747i	−0.954373	+	0.298616i	$0.903475\pi$
$228$		0			0
$229$	−195.058	−	68.2538i	−0.851782	−	0.298051i	−0.131144	−	0.991363i	$-0.541865\pi$
$229$	−195.058	−	68.2538i	−0.851782	−	0.298051i	−0.720638	+	0.693312i	$0.756151\pi$
$230$	−21.5441	+	13.5370i	−0.0936700	+	0.0588567i
$231$		0			0
$232$	138.086	+	112.657i	0.595200	+	0.485589i
$233$	−186.225			−0.799248			−0.399624	−	0.916679i	$-0.630859\pi$
$233$	−186.225			−0.799248			−0.399624	+	0.916679i	$0.630859\pi$
$234$		0			0
$235$	73.0520	−	208.771i	0.310860	−	0.888386i
$236$	−34.0648	+	70.7363i	−0.144342	+	0.299730i
$237$		0			0
$238$	220.425	−	50.3106i	0.926156	−	0.211389i
$239$	−144.790	+	69.7270i	−0.605814	+	0.291745i	−0.711534	−	0.702651i	$-0.751999\pi$
$239$	−144.790	+	69.7270i	−0.605814	+	0.291745i	0.105720	+	0.994396i	$0.466285\pi$
$240$		0			0
$241$	−152.244	−	121.410i	−0.631717	−	0.503777i	0.254485	−	0.967077i	$-0.418094\pi$
$241$	−152.244	−	121.410i	−0.631717	−	0.503777i	−0.886202	+	0.463300i	$0.846665\pi$
$242$	−33.0210	−	94.3687i	−0.136451	−	0.389953i
$243$		0			0
$244$	−168.201	−	168.201i	−0.689349	−	0.689349i
$245$	−263.005	+	209.739i	−1.07349	+	0.856079i
$246$		0			0
$247$	−3.66292	+	5.82950i	−0.0148296	+	0.0236012i
$248$	−56.7970	−	71.2212i	−0.229020	−	0.287182i
$249$		0			0
$250$	−12.7744	+	113.376i	−0.0510977	+	0.453505i
$251$	312.227	−	109.253i	1.24393	−	0.435270i	0.373532	−	0.927617i	$-0.378147\pi$
$251$	312.227	−	109.253i	1.24393	−	0.435270i	0.870399	+	0.492347i	$0.163861\pi$
$252$		0			0
$253$	1.21181	+	10.7551i	0.00478976	+	0.0425103i
$254$	−3.02436	−	6.28015i	−0.0119069	−	0.0247250i
$255$		0			0
$256$	19.4560	−	85.2421i	0.0759998	−	0.332977i
$257$	−156.282	−	75.2612i	−0.608099	−	0.292845i	0.104381	−	0.994537i	$-0.466714\pi$
$257$	−156.282	−	75.2612i	−0.608099	−	0.292845i	−0.712480	+	0.701692i	$0.752428\pi$
$258$		0			0
$259$	−252.219	+	158.480i	−0.973818	+	0.611891i
$260$		−	206.102i		−	0.792698i
$261$		0			0
$262$	−202.686			−0.773612
$263$	86.5688	+	137.774i	0.329159	+	0.523854i	0.969773	−	0.244010i	$-0.0784628\pi$
$263$	86.5688	+	137.774i	0.329159	+	0.523854i	−0.640614	+	0.767863i	$0.721320\pi$
$264$		0			0
$265$	−76.7793	+	159.434i	−0.289733	+	0.601637i
$266$	−4.39953	−	1.00416i	−0.0165396	−	0.00377505i
$267$		0			0
$268$	340.572	−	164.011i	1.27079	−	0.611980i
$269$	−29.2546	+	3.29620i	−0.108753	+	0.0122535i	−0.166173	−	0.986097i	$-0.553141\pi$
$269$	−29.2546	+	3.29620i	−0.108753	+	0.0122535i	0.0574202	+	0.998350i	$0.481713\pi$
$270$		0			0
$271$	168.083	+	480.355i	0.620234	+	1.77253i	0.634852	+	0.772634i	$0.281061\pi$
$271$	168.083	+	480.355i	0.620234	+	1.77253i	−0.0146174	+	0.999893i	$0.504653\pi$
$272$	188.818	+	21.2747i	0.694183	+	0.0782157i
$273$		0			0
$274$	26.7885	−	21.3631i	0.0977682	−	0.0779675i
$275$	8.24418	+	5.18016i	0.0299789	+	0.0188370i
$276$		0			0
$277$	−130.918	−	164.166i	−0.472629	−	0.592657i	0.487184	−	0.873299i	$-0.338024\pi$
$277$	−130.918	−	164.166i	−0.472629	−	0.592657i	−0.959813	+	0.280642i	$0.909453\pi$
$278$	33.2918	−	33.2918i	0.119755	−	0.119755i
$279$		0			0
$280$	282.572	−	98.8761i	1.00918	−	0.353129i
$281$	287.055	−	359.956i	1.02155	−	1.28098i	0.0624084	−	0.998051i	$-0.480122\pi$
$281$	287.055	−	359.956i	1.02155	−	1.28098i	0.959140	−	0.282931i	$-0.0913067\pi$
$282$		0			0
$283$	194.833	+	404.574i	0.688455	+	1.42959i	0.892691	+	0.450669i	$0.148815\pi$
$283$	194.833	+	404.574i	0.688455	+	1.42959i	−0.204237	+	0.978922i	$0.565471\pi$
$284$	−51.2152	−	224.389i	−0.180335	−	0.790101i
$285$		0			0
$286$	17.0675	+	8.21928i	0.0596766	+	0.0287388i
$287$	693.104	+	242.528i	2.41500	+	0.845044i
$288$		0			0
$289$		−	278.496i		−	0.963653i
$290$	46.9613	−	94.8028i	0.161936	−	0.326906i
$291$		0			0
$292$	143.336	+	228.118i	0.490877	+	0.781226i
$293$	−37.1090	+	106.051i	−0.126652	+	0.361950i	−0.989697	−	0.143176i	$-0.954268\pi$
$293$	−37.1090	+	106.051i	−0.126652	+	0.361950i	0.863045	+	0.505126i	$0.168554\pi$
$294$		0			0
$295$	100.699	+	22.9839i	0.341353	+	0.0779117i
$296$	158.524	−	36.1820i	0.535553	−	0.122236i
$297$		0			0
$298$	87.5063	−	9.85959i	0.293645	−	0.0330859i
$299$	78.9566	+	62.9658i	0.264069	+	0.210588i
$300$		0			0
$301$	709.918	+	79.9885i	2.35853	+	0.265743i
$302$	24.6198	+	24.6198i	0.0815224	+	0.0815224i
$303$		0			0
$304$	−3.21121	−	2.01774i	−0.0105632	−	0.00663730i
$305$	−166.496	+	264.976i	−0.545887	+	0.868774i
$306$		0			0
$307$	131.221	−	131.221i	0.427429	−	0.427429i	−0.460323	−	0.887752i	$-0.652266\pi$
$307$	131.221	−	131.221i	0.427429	−	0.427429i	0.887752	+	0.460323i	$0.152266\pi$
$308$	6.43389	−	57.1024i	0.0208893	−	0.185397i
$309$		0			0
$310$	−33.7180	+	42.2810i	−0.108768	+	0.136390i
$311$	56.3391	+	500.023i	0.181155	+	1.60779i	0.674714	+	0.738079i	$0.264267\pi$
$311$	56.3391	+	500.023i	0.181155	+	1.60779i	−0.493560	+	0.869712i	$0.664305\pi$
$312$		0			0
$313$	−36.9386	−	161.838i	−0.118015	−	0.517056i	−0.999033	−	0.0439731i	$-0.985998\pi$
$313$	−36.9386	−	161.838i	−0.118015	−	0.517056i	0.881018	−	0.473082i	$-0.156859\pi$
$314$	15.3738	−	67.3572i	0.0489613	−	0.214513i
$315$		0			0
$316$	358.412	+	125.414i	1.13422	+	0.396879i
$317$	−16.0893	+	10.1096i	−0.0507550	+	0.0318915i	−0.557171	−	0.830398i	$-0.688113\pi$
$317$	−16.0893	+	10.1096i	−0.0507550	+	0.0318915i	0.506416	+	0.862290i	$0.330970\pi$
$318$		0			0
$319$	−27.6656	−	35.4947i	−0.0867260	−	0.111269i
$320$	23.8570			0.0745530
$321$		0			0
$322$	−21.8625	+	62.4795i	−0.0678961	+	0.194036i
$323$	−4.91451	+	10.2051i	−0.0152152	+	0.0315947i
$324$		0			0
$325$	88.5726	−	20.2161i	0.272531	−	0.0622034i
$326$	0.871077	−	0.419489i	0.00267202	−	0.00128677i
$327$		0			0
$328$	−313.386	−	249.917i	−0.955444	−	0.761941i
$329$	−190.049	−	543.129i	−0.577657	−	1.65085i
$330$		0			0
$331$	−34.0680	−	34.0680i	−0.102924	−	0.102924i	0.653769	−	0.756694i	$-0.273187\pi$
$331$	−34.0680	−	34.0680i	−0.102924	−	0.102924i	−0.756694	+	0.653769i	$0.773187\pi$
$332$	3.18616	−	2.54088i	0.00959686	−	0.00765324i
$333$		0			0
$334$	87.7357	−	139.631i	0.262682	−	0.418056i
$335$	−310.062	−	388.806i	−0.925560	−	1.16062i
$336$		0			0
$337$	24.9408	−	221.356i	0.0740083	−	0.656841i	−0.900868	−	0.434093i	$-0.857069\pi$
$337$	24.9408	−	221.356i	0.0740083	−	0.656841i	0.974876	−	0.222748i	$-0.0715027\pi$
$338$	32.3593	−	11.3230i	0.0957375	−	0.0335000i
$339$		0			0
$340$	−37.9646	−	336.946i	−0.111661	−	0.991016i
$341$	9.98099	+	20.7257i	0.0292698	+	0.0607793i
$342$		0			0
$343$	−71.9903	+	315.410i	−0.209884	+	0.919563i
$344$	−351.352	−	169.202i	−1.02137	−	0.491867i
$345$		0			0
$346$	−67.0409	+	42.1246i	−0.193760	+	0.121747i
$347$			400.531i			1.15427i	0.816649	+	0.577134i	$0.195829\pi$
$347$			400.531i			1.15427i	−0.816649	+	0.577134i	$0.804171\pi$
$348$		0			0
$349$	191.095			0.547550			0.273775	−	0.961794i	$-0.411728\pi$
$349$	191.095			0.547550			0.273775	+	0.961794i	$0.411728\pi$
$350$	31.6817	+	50.4212i	0.0905192	+	0.144060i
$351$		0			0
$352$	−21.0782	+	43.7694i	−0.0598814	+	0.124345i
$353$	−170.891	−	39.0048i	−0.484111	−	0.110495i	−0.0265018	−	0.999649i	$-0.508437\pi$
$353$	−170.891	−	39.0048i	−0.484111	−	0.110495i	−0.457609	+	0.889154i	$0.651294\pi$
$354$		0			0
$355$	−272.809	+	131.378i	−0.768476	+	0.370079i
$356$	216.060	−	24.3441i	0.606909	−	0.0683822i
$357$		0			0
$358$	−48.2282	−	137.828i	−0.134716	−	0.384995i
$359$	302.179	+	34.0473i	0.841723	+	0.0948394i	0.522288	−	0.852769i	$-0.325078\pi$
$359$	302.179	+	34.0473i	0.841723	+	0.0948394i	0.319435	+	0.947608i	$0.396507\pi$
$360$		0			0
$361$	−282.064	+	224.939i	−0.781342	+	0.623099i
$362$	−69.1502	−	43.4500i	−0.191023	−	0.120028i
$363$		0			0
$364$	−334.306	−	419.206i	−0.918423	−	1.15167i
$365$	250.625	−	250.625i	0.686643	−	0.686643i
$366$		0			0
$367$	102.535	−	35.8787i	0.279388	−	0.0977622i	−0.186948	−	0.982370i	$-0.559860\pi$
$367$	102.535	−	35.8787i	0.279388	−	0.0977622i	0.466336	+	0.884608i	$0.345574\pi$
$368$	−34.6851	+	43.4937i	−0.0942529	+	0.118189i
$369$		0			0
$370$	−41.8823	−	86.9695i	−0.113195	−	0.235053i
$371$	102.441	+	448.825i	0.276122	+	1.20977i
$372$		0			0
$373$	−391.003	−	188.297i	−1.04826	−	0.504818i	−0.171223	−	0.985232i	$-0.554772\pi$
$373$	−391.003	−	188.297i	−1.04826	−	0.504818i	−0.877042	+	0.480414i	$0.840486\pi$
$374$	29.4169	+	10.2934i	0.0786548	+	0.0275225i
$375$		0			0
$376$			314.102i			0.835377i
$377$	−416.726	−	51.6559i	−1.10537	−	0.137018i
$378$		0			0
$379$	146.333	+	232.888i	0.386104	+	0.614481i	0.982067	−	0.188530i	$-0.0603724\pi$
$379$	146.333	+	232.888i	0.386104	+	0.614481i	−0.595963	+	0.803012i	$0.703230\pi$
$380$	−2.23524	+	6.38796i	−0.00588222	+	0.0168104i
$381$		0			0
$382$	294.248	+	67.1601i	0.770282	+	0.175812i
$383$	213.072	−	48.6323i	0.556323	−	0.126977i	0.0648901	−	0.997892i	$-0.479330\pi$
$383$	213.072	−	48.6323i	0.556323	−	0.126977i	0.491433	+	0.870915i	$0.336473\pi$
$384$		0			0
$385$	−75.1234	+	8.46437i	−0.195126	+	0.0219854i
$386$	−196.244	−	156.500i	−0.508405	−	0.405439i
$387$		0			0
$388$	−257.368	−	28.9985i	−0.663321	−	0.0747383i
$389$	−25.9695	−	25.9695i	−0.0667597	−	0.0667597i	0.672939	−	0.739698i	$-0.265032\pi$
$389$	−25.9695	−	25.9695i	−0.0667597	−	0.0667597i	−0.739698	+	0.672939i	$0.765032\pi$
$390$		0			0
$391$	140.681	+	88.3957i	0.359798	+	0.226076i
$392$	254.160	−	404.493i	0.648367	−	1.03187i
$393$		0			0
$394$	−82.8705	+	82.8705i	−0.210331	+	0.210331i
$395$	55.9327	−	496.416i	0.141602	−	1.25675i
$396$		0			0
$397$	83.6502	−	104.894i	0.210706	−	0.264217i	−0.665236	−	0.746633i	$-0.731669\pi$
$397$	83.6502	−	104.894i	0.210706	−	0.264217i	0.875942	+	0.482416i	$0.160241\pi$
$398$	1.09252	+	9.69641i	0.00274503	+	0.0243628i
$399$		0			0
$400$	11.1362	+	48.7907i	0.0278404	+	0.121977i
$401$	−105.732	+	463.241i	−0.263670	+	1.15521i	0.653566	+	0.756870i	$0.273272\pi$
$401$	−105.732	+	463.241i	−0.263670	+	1.15521i	−0.917236	+	0.398345i	$0.869585\pi$
$402$		0			0
$403$	202.600	+	70.8928i	0.502730	+	0.175913i
$404$	−234.458	+	147.320i	−0.580342	+	0.364653i
$405$		0			0
$406$	−58.2561	−	269.000i	−0.143488	−	0.662562i
$407$	−41.0606			−0.100886
$408$		0			0
$409$	9.65215	−	27.5843i	0.0235994	−	0.0674432i	−0.931481	−	0.363790i	$-0.881483\pi$
$409$	9.65215	−	27.5843i	0.0235994	−	0.0674432i	0.955080	+	0.296347i	$0.0957684\pi$
$410$	−103.246	+	214.393i	−0.251821	+	0.522911i
$411$		0			0
$412$	156.255	−	35.6642i	0.379260	−	0.0865637i
$413$	242.101	−	116.590i	0.586201	−	0.282300i
$414$		0			0
$415$	−4.19168	−	3.34275i	−0.0101004	−	0.00805483i
$416$	149.714	+	427.859i	0.359890	+	1.02851i
$417$		0			0
$418$	−0.439854	−	0.439854i	−0.00105228	−	0.00105228i
$419$	−173.110	+	138.050i	−0.413149	+	0.329476i	−0.807907	−	0.589309i	$-0.799400\pi$
$419$	−173.110	+	138.050i	−0.413149	+	0.329476i	0.394758	+	0.918785i	$0.370828\pi$
$420$		0			0
$421$	65.2084	−	103.779i	0.154889	−	0.246505i	−0.760261	−	0.649618i	$-0.774929\pi$
$421$	65.2084	−	103.779i	0.154889	−	0.246505i	0.915150	+	0.403113i	$0.132072\pi$
$422$	−73.0702	−	91.6272i	−0.173152	−	0.217126i
$423$		0			0
$424$	28.1365	−	249.718i	0.0663597	−	0.588958i
$425$	141.079	−	49.3657i	0.331951	−	0.116155i
$426$		0			0
$427$	91.1546	+	809.019i	0.213477	+	1.89466i
$428$	191.430	+	397.508i	0.447266	+	0.928757i
$429$		0			0
$430$	−51.5157	+	225.705i	−0.119804	+	0.524895i
$431$	−178.177	−	85.8056i	−0.413404	−	0.199085i	0.215609	−	0.976480i	$-0.430826\pi$
$431$	−178.177	−	85.8056i	−0.413404	−	0.199085i	−0.629013	+	0.777395i	$0.716541\pi$
$432$		0			0
$433$	−148.885	+	93.5509i	−0.343846	+	0.216053i	−0.692873	−	0.721060i	$-0.743655\pi$
$433$	−148.885	+	93.5509i	−0.343846	+	0.216053i	0.349026	+	0.937113i	$0.386512\pi$
$434$			140.691i			0.324172i
$435$		0			0
$436$	66.8552			0.153338
$437$	−1.76431	−	2.80789i	−0.00403733	−	0.00642538i
$438$		0			0
$439$	−97.1608	+	201.756i	−0.221323	+	0.459582i	−0.981834	−	0.189743i	$-0.939234\pi$
$439$	−97.1608	+	201.756i	−0.221323	+	0.459582i	0.760511	+	0.649325i	$0.224949\pi$
$440$	40.2321	+	9.18271i	0.0914366	+	0.0208698i
$441$		0			0
$442$	262.005	−	126.175i	0.592771	−	0.285463i
$443$	−172.978	+	19.4899i	−0.390470	+	0.0439954i	−0.305017	−	0.952347i	$-0.598662\pi$
$443$	−172.978	+	19.4899i	−0.390470	+	0.0439954i	−0.0854526	+	0.996342i	$0.527234\pi$
$444$		0			0
$445$	−94.4746	−	269.993i	−0.212302	−	0.606725i
$446$	96.3820	+	10.8596i	0.216103	+	0.0243490i
$447$		0			0
$448$	48.5246	−	38.6970i	0.108314	−	0.0863773i
$449$	378.601	+	237.891i	0.843209	+	0.529823i	0.882994	−	0.469385i	$-0.155524\pi$
$449$	378.601	+	237.891i	0.843209	+	0.529823i	−0.0397845	+	0.999208i	$0.512667\pi$
$450$		0			0
$451$	63.1102	+	79.1376i	0.139934	+	0.175471i
$452$	−55.7736	+	55.7736i	−0.123393	+	0.123393i
$453$		0			0
$454$	−181.897	+	63.6486i	−0.400655	+	0.140195i
$455$	−439.810	+	551.504i	−0.966615	+	1.21210i
$456$		0			0
$457$	21.1875	+	43.9964i	0.0463622	+	0.0962722i	0.922863	−	0.385128i	$-0.125843\pi$
$457$	21.1875	+	43.9964i	0.0463622	+	0.0962722i	−0.876501	+	0.481400i	$0.840128\pi$
$458$	−38.7678	−	169.853i	−0.0846459	−	0.370858i
$459$		0			0
$460$	89.4416	+	43.0728i	0.194438	+	0.0936366i
$461$	−536.238	−	187.638i	−1.16321	−	0.407023i	−0.321474	−	0.946918i	$-0.604178\pi$
$461$	−536.238	−	187.638i	−1.16321	−	0.407023i	−0.841732	+	0.539895i	$0.818464\pi$
$462$		0			0
$463$		−	50.1618i		−	0.108341i	−0.998532	−	0.0541704i	$-0.982749\pi$
$463$		−	50.1618i		−	0.108341i	0.998532	−	0.0541704i	$-0.0172514\pi$
$464$	28.4549	−	229.556i	0.0613253	−	0.494732i
$465$		0			0
$466$	−83.5276	−	132.933i	−0.179244	−	0.285265i
$467$	61.9948	−	177.171i	0.132751	−	0.379381i	−0.858250	−	0.513231i	$-0.828448\pi$
$467$	61.9948	−	177.171i	0.132751	−	0.379381i	0.991002	+	0.133850i	$0.0427340\pi$
$468$		0			0
$469$	−1261.32	−	287.888i	−2.68938	−	0.613834i
$470$	181.794	−	41.4932i	0.386795	−	0.0882834i
$471$		0			0
$472$	−145.758	+	16.4230i	−0.308810	+	0.0347945i
$473$	76.9928	+	61.3997i	0.162775	+	0.129809i
$474$		0			0
$475$	−2.96449	−	0.334018i	−0.00624103	−	0.000703195i
$476$	−623.760	−	623.760i	−1.31042	−	1.31042i
$477$		0			0
$478$	−114.716	−	72.0809i	−0.239992	−	0.150797i
$479$	−15.6633	+	24.9280i	−0.0327000	+	0.0520418i	−0.862674	−	0.505760i	$-0.831212\pi$
$479$	−15.6633	+	24.9280i	−0.0327000	+	0.0520418i	0.829974	+	0.557802i	$0.188355\pi$
$480$		0			0
$481$	−270.914	+	270.914i	−0.563231	+	0.563231i
$482$	18.3807	−	163.133i	0.0381342	−	0.338450i
$483$		0			0
$484$	−243.211	+	304.977i	−0.502501	+	0.630117i
$485$	38.1501	+	338.592i	0.0786600	+	0.698127i
$486$		0			0
$487$	39.7649	+	174.221i	0.0816527	+	0.357744i	0.999205	−	0.0398716i	$-0.0126949\pi$
$487$	39.7649	+	174.221i	0.0816527	+	0.357744i	−0.917552	+	0.397616i	$0.869838\pi$
$488$	98.8905	−	433.268i	0.202645	−	0.887844i
$489$		0			0
$490$	−267.685	−	93.6669i	−0.546295	−	0.191157i
$491$	−319.674	+	200.864i	−0.651066	+	0.409092i	−0.816674	−	0.577100i	$-0.804184\pi$
$491$	−319.674	+	200.864i	−0.651066	+	0.409092i	0.165607	+	0.986192i	$0.447042\pi$
$492$		0			0
$493$	−690.800	−	7.68743i	−1.40122	−	0.0155932i
$494$	−5.80422			−0.0117494
$495$		0			0
$496$	−39.0517	+	111.603i	−0.0787333	+	0.225007i
$497$	−341.787	+	709.728i	−0.687701	+	1.42803i
$498$		0			0
$499$	−575.053	+	131.252i	−1.15241	+	0.263030i	−0.755703	−	0.654915i	$-0.772704\pi$
$499$	−575.053	+	131.252i	−1.15241	+	0.263030i	−0.396707	+	0.917945i	$0.629847\pi$
$500$	401.065	−	193.143i	0.802130	−	0.386286i
$501$		0			0
$502$	218.032	+	173.875i	0.434326	+	0.346364i
$503$	−122.173	−	349.151i	−0.242889	−	0.694137i	−0.999203	−	0.0399278i	$-0.987287\pi$
$503$	−122.173	−	349.151i	−0.242889	−	0.694137i	0.756313	−	0.654209i	$-0.226999\pi$
$504$		0			0
$505$	257.590	+	257.590i	0.510079	+	0.510079i
$506$	−7.13382	+	5.68903i	−0.0140985	+	0.0112432i
$507$		0			0
$508$	−14.4691	+	23.0275i	−0.0284825	+	0.0453296i
$509$	−595.965	−	747.316i	−1.17085	−	1.46820i	−0.854414	−	0.519592i	$-0.826084\pi$
$509$	−595.965	−	747.316i	−1.17085	−	1.46820i	−0.316440	−	0.948613i	$-0.602487\pi$
$510$		0			0
$511$	103.241	−	916.289i	0.202037	−	1.79313i
$512$	−420.751	+	147.227i	−0.821779	+	0.287553i
$513$		0			0
$514$	−16.3732	−	145.316i	−0.0318544	−	0.282716i
$515$	−91.4863	−	189.973i	−0.177643	−	0.368880i
$516$		0			0
$517$	17.6500	−	77.3298i	0.0341393	−	0.149574i
$518$	−226.256	−	108.959i	−0.436788	−	0.210346i
$519$		0			0
$520$	326.034	−	204.861i	0.626989	−	0.393963i
$521$		−	165.340i		−	0.317352i	−0.987331	−	0.158676i	$-0.949278\pi$
$521$		−	165.340i		−	0.317352i	0.987331	−	0.158676i	$-0.0507225\pi$
$522$		0			0
$523$	−680.975			−1.30205			−0.651027	−	0.759054i	$-0.725662\pi$
$523$	−680.975			−1.30205			−0.651027	+	0.759054i	$0.725662\pi$
$524$	420.732	+	669.592i	0.802924	+	1.27785i
$525$		0			0
$526$	−59.5185	+	123.591i	−0.113153	+	0.234965i
$527$	344.280	+	78.5796i	0.653283	+	0.149107i
$528$		0			0
$529$	432.786	−	208.419i	0.818122	−	0.393987i
$530$	−148.247	+	16.7034i	−0.279712	+	0.0315159i
$531$		0			0
$532$	5.81511	+	16.6186i	0.0109307	+	0.0312380i
$533$	938.537	+	105.748i	1.76086	+	0.198401i
$534$		0			0
$535$	453.806	−	361.898i	0.848235	−	0.676445i
$536$	597.972	+	375.731i	1.11562	+	0.700990i
$537$		0			0
$538$	−15.4745	−	19.4044i	−0.0287630	−	0.0360677i
$539$	−85.3018	+	85.3018i	−0.158259	+	0.158259i
$540$		0			0
$541$	259.030	−	90.6386i	0.478799	−	0.167539i	−0.0800798	−	0.996788i	$-0.525518\pi$
$541$	259.030	−	90.6386i	0.478799	−	0.167539i	0.558879	+	0.829250i	$0.311232\pi$
$542$	−267.503	+	335.438i	−0.493547	+	0.618889i
$543$		0			0
$544$	323.574	+	671.908i	0.594805	+	1.23513i
$545$	−19.5716	−	85.7489i	−0.0359113	−	0.157337i
$546$		0			0
$547$	506.415	+	243.877i	0.925805	+	0.445844i	0.835140	−	0.550037i	$-0.185387\pi$
$547$	506.415	+	243.877i	0.925805	+	0.445844i	0.0906647	+	0.995881i	$0.471101\pi$
$548$	−126.182	−	44.1529i	−0.230259	−	0.0805711i
$549$		0			0
$550$			8.20844i			0.0149244i
$551$	12.3559	+	6.12057i	0.0224244	+	0.0111081i
$552$		0			0
$553$	−691.443	−	1100.43i	−1.25035	−	1.98992i
$554$	58.4664	−	167.087i	0.105535	−	0.301602i
$555$		0			0
$556$	−179.089	−	40.8758i	−0.322102	−	0.0735176i
$557$	328.386	−	74.9521i	0.589563	−	0.134564i	0.0826759	−	0.996576i	$-0.473653\pi$
$557$	328.386	−	74.9521i	0.589563	−	0.134564i	0.506887	+	0.862013i	$0.330796\pi$
$558$		0			0
$559$	913.101	−	102.882i	1.63345	−	0.184046i
$560$	−303.799	−	242.272i	−0.542498	−	0.432628i
$561$		0			0
$562$	385.702	+	43.4581i	0.686302	+	0.0773276i
$563$	−156.332	−	156.332i	−0.277677	−	0.277677i	0.554504	−	0.832181i	$-0.312908\pi$
$563$	−156.332	−	156.332i	−0.277677	−	0.277677i	−0.832181	+	0.554504i	$0.812908\pi$
$564$		0			0
$565$	87.8631	+	55.2080i	0.155510	+	0.0977133i
$566$	−201.410	+	320.542i	−0.355848	+	0.566329i
$567$		0			0
$568$	304.056	−	304.056i	0.535309	−	0.535309i
$569$	36.9493	−	327.934i	0.0649373	−	0.576334i	−0.918543	−	0.395321i	$-0.870634\pi$
$569$	36.9493	−	327.934i	0.0649373	−	0.576334i	0.983481	−	0.181014i	$-0.0579379\pi$
$570$		0			0
$571$	126.849	−	159.064i	0.222153	−	0.278570i	−0.658248	−	0.752801i	$-0.728702\pi$
$571$	126.849	−	159.064i	0.222153	−	0.278570i	0.880401	+	0.474231i	$0.157274\pi$
$572$	−8.27532	−	73.4455i	−0.0144673	−	0.128401i
$573$		0			0
$574$	137.755	+	603.542i	0.239990	+	1.05147i
$575$	−9.73747	+	42.6627i	−0.0169347	+	0.0741959i
$576$		0			0
$577$	612.104	+	214.185i	1.06084	+	0.371204i	0.803616	−	0.595148i	$-0.202907\pi$
$577$	612.104	+	214.185i	1.06084	+	0.371204i	0.257223	+	0.966352i	$0.417192\pi$
$578$	198.799	−	124.914i	0.343944	−	0.216114i
$579$		0			0
$580$	−410.671	+	41.6492i	−0.708053	+	0.0718090i
$581$	−13.9479			−0.0240067
$582$		0			0
$583$	−20.9592	+	59.8980i	−0.0359506	+	0.102741i
$584$	−218.389	+	453.490i	−0.373954	+	0.776523i
$585$		0			0
$586$	−92.3475	+	21.0777i	−0.157590	+	0.0359688i
$587$	702.630	−	338.369i	1.19698	−	0.576437i	0.274170	−	0.961681i	$-0.411597\pi$
$587$	702.630	−	338.369i	1.19698	−	0.576437i	0.922815	+	0.385244i	$0.125883\pi$
$588$		0			0
$589$	−5.51058	−	4.39454i	−0.00935582	−	0.00746101i
$590$	28.7600	+	82.1915i	0.0487458	+	0.139308i
$591$		0			0
$592$	−149.234	−	149.234i	−0.252085	−	0.252085i
$593$	694.472	−	553.823i	1.17112	−	0.933934i	0.172422	−	0.985023i	$-0.444841\pi$
$593$	694.472	−	553.823i	1.17112	−	0.933934i	0.998694	+	0.0510897i	$0.0162694\pi$
$594$		0			0
$595$	−617.435	+	982.642i	−1.03771	+	1.65150i
$596$	−214.216	−	268.618i	−0.359423	−	0.450702i
$597$		0			0
$598$	−9.53258	+	84.6040i	−0.0159408	+	0.141478i
$599$	−153.834	+	53.8288i	−0.256818	+	0.0898645i	−0.455617	−	0.890176i	$-0.650581\pi$
$599$	−153.834	+	53.8288i	−0.256818	+	0.0898645i	0.198799	+	0.980040i	$0.436296\pi$
$600$		0			0
$601$	56.1166	+	498.048i	0.0933720	+	0.828699i	0.949890	+	0.312583i	$0.101194\pi$
$601$	56.1166	+	498.048i	0.0933720	+	0.828699i	−0.856518	+	0.516116i	$0.827377\pi$
$602$	261.322	+	542.640i	0.434089	+	0.901395i
$603$		0			0
$604$	30.2283	−	132.439i	0.0500468	−	0.219270i
$605$	462.364	+	222.663i	0.764238	+	0.368038i
$606$		0			0
$607$	791.990	−	497.641i	1.30476	−	0.819836i	0.313227	−	0.949678i	$-0.398590\pi$
$607$	791.990	−	497.641i	1.30476	−	0.819836i	0.991535	+	0.129842i	$0.0414471\pi$
$608$		−	14.8849i		−	0.0244817i
$609$		0			0
$610$	−263.827			−0.432504
$611$	−393.761	−	626.668i	−0.644454	−	1.02564i
$612$		0			0
$613$	152.936	−	317.575i	0.249488	−	0.518067i	−0.738185	−	0.674598i	$-0.764317\pi$
$613$	152.936	−	317.575i	0.249488	−	0.518067i	0.987673	+	0.156531i	$0.0500312\pi$
$614$	152.526	+	34.8131i	0.248414	+	0.0566989i
$615$		0			0
$616$	96.7260	−	46.5808i	0.157023	−	0.0756182i
$617$	839.013	−	94.5340i	1.35983	−	0.153216i	0.598260	−	0.801302i	$-0.295859\pi$
$617$	839.013	−	94.5340i	1.35983	−	0.153216i	0.761566	+	0.648087i	$0.224431\pi$
$618$		0			0
$619$	−171.638	−	490.514i	−0.277283	−	0.792430i	−0.995338	−	0.0964436i	$-0.969253\pi$
$619$	−171.638	−	490.514i	−0.277283	−	0.792430i	0.718055	−	0.695986i	$-0.245032\pi$
$620$	209.670	+	23.6241i	0.338177	+	0.0381034i
$621$		0			0
$622$	−331.663	+	264.493i	−0.533221	+	0.425229i
$623$	−630.100	−	395.918i	−1.01140	−	0.635502i
$624$		0			0
$625$	−267.338	−	335.231i	−0.427741	−	0.536370i
$626$	98.9575	−	98.9575i	0.158079	−	0.158079i
$627$		0			0
$628$	−254.433	+	89.0300i	−0.405148	+	0.141767i
$629$	−393.001	+	492.808i	−0.624803	+	0.783478i
$630$		0			0
$631$	−226.898	−	471.158i	−0.359584	−	0.746685i	0.640184	−	0.768222i	$-0.278858\pi$
$631$	−226.898	−	471.158i	−0.359584	−	0.746685i	−0.999768	+	0.0215372i	$0.993144\pi$
$632$	157.861	+	691.635i	0.249780	+	1.09436i
$633$		0			0
$634$	−14.4331	−	6.95062i	−0.0227652	−	0.0109631i
$635$	33.7709	+	11.8170i	0.0531826	+	0.0186094i
$636$		0			0
$637$			1125.63i			1.76708i
$638$	12.9284	−	35.6691i	0.0202640	−	0.0559077i
$639$		0			0
$640$	298.995	+	475.848i	0.467179	+	0.743512i
$641$	284.960	−	814.368i	0.444555	−	1.27046i	−0.475860	−	0.879521i	$-0.657863\pi$
$641$	284.960	−	814.368i	0.444555	−	1.27046i	0.920415	−	0.390944i	$-0.127851\pi$
$642$		0			0
$643$	221.189	+	50.4849i	0.343995	+	0.0785147i	0.391028	−	0.920379i	$-0.372119\pi$
$643$	221.189	+	50.4849i	0.343995	+	0.0785147i	−0.0470331	+	0.998893i	$0.514977\pi$
$644$	251.788	−	57.4691i	0.390976	−	0.0892377i
$645$		0			0
$646$	−9.48905	+	1.06916i	−0.0146889	+	0.00165504i
$647$	−639.749	−	510.183i	−0.988794	−	0.788537i	−0.0113937	−	0.999935i	$-0.503627\pi$
$647$	−639.749	−	510.183i	−0.988794	−	0.788537i	−0.977400	+	0.211398i	$0.932198\pi$
$648$		0			0
$649$	36.8076	+	4.14722i	0.0567143	+	0.00639017i
$650$	54.1585	+	54.1585i	0.0833208	+	0.0833208i
$651$		0			0
$652$	−3.19398	−	2.00691i	−0.00489875	−	0.00307809i
$653$	−430.330	+	684.867i	−0.659005	+	1.04880i	0.335288	+	0.942116i	$0.391166\pi$
$653$	−430.330	+	684.867i	−0.659005	+	1.04880i	−0.994293	+	0.106685i	$0.965976\pi$
$654$		0			0
$655$	735.655	−	735.655i	1.12314	−	1.12314i
$656$	−58.2517	+	516.998i	−0.0887984	+	0.788107i
$657$		0			0
$658$	302.461	−	379.274i	0.459667	−	0.576404i
$659$	11.9427	+	105.994i	0.0181225	+	0.160841i	0.999514	−	0.0311765i	$-0.00992540\pi$
$659$	11.9427	+	105.994i	0.0181225	+	0.160841i	−0.981391	+	0.192018i	$0.938497\pi$
$660$		0			0
$661$	58.7442	+	257.375i	0.0888717	+	0.389372i	0.999727	−	0.0233529i	$-0.00743414\pi$
$661$	58.7442	+	257.375i	0.0888717	+	0.389372i	−0.910856	+	0.412725i	$0.864577\pi$
$662$	9.03830	−	39.5994i	0.0136530	−	0.0598178i
$663$		0			0
$664$	7.18642	+	2.51464i	0.0108229	+	0.00378710i
$665$	19.6128	−	12.3236i	0.0294930	−	0.0185317i
$666$		0			0
$667$	109.508	−	170.050i	0.164180	−	0.254948i
$668$	−643.402			−0.963176
$669$		0			0
$670$	138.470	−	395.724i	0.206672	−	0.590634i
$671$	−48.6924	+	101.111i	−0.0725669	+	0.150687i
$672$		0			0
$673$	396.421	−	90.4804i	0.589035	−	0.134443i	0.0823931	−	0.996600i	$-0.473744\pi$
$673$	396.421	−	90.4804i	0.589035	−	0.134443i	0.506642	+	0.862156i	$0.330887\pi$
$674$	169.198	−	81.4813i	0.251035	−	0.120892i
$675$		0			0
$676$	−104.577	−	83.3976i	−0.154700	−	0.123369i
$677$	170.754	+	487.988i	0.252222	+	0.720810i	0.998478	+	0.0551504i	$0.0175638\pi$
$677$	170.754	+	487.988i	0.252222	+	0.720810i	−0.746256	+	0.665659i	$0.768150\pi$
$678$		0			0
$679$	626.807	+	626.807i	0.923133	+	0.923133i
$680$	495.282	−	394.974i	0.728355	−	0.580844i
$681$		0			0
$682$	−10.3179	+	16.4209i	−0.0151289	+	0.0240776i
$683$	−207.865	−	260.654i	−0.304341	−	0.381631i	0.606018	−	0.795451i	$-0.292766\pi$
$683$	−207.865	−	260.654i	−0.304341	−	0.381631i	−0.910359	+	0.413820i	$0.864194\pi$
$684$		0			0
$685$	−19.6915	+	174.767i	−0.0287468	+	0.255135i
$686$	−257.440	+	90.0822i	−0.375277	+	0.131315i
$687$		0			0
$688$	56.6730	+	502.986i	0.0823735	+	0.731085i
$689$	256.914	+	533.488i	0.372880	+	0.774293i
$690$		0			0
$691$	35.5687	−	155.837i	0.0514743	−	0.225523i	−0.942648	−	0.333789i	$-0.891673\pi$
$691$	35.5687	−	155.837i	0.0514743	−	0.225523i	0.994122	+	0.108266i	$0.0345298\pi$
$692$	278.325	+	134.034i	0.402203	+	0.193691i
$693$		0			0
$694$	−285.912	+	179.651i	−0.411978	+	0.258863i
$695$			241.666i			0.347722i
$696$		0			0
$697$	1553.85			2.22934
$698$	85.7120	+	136.410i	0.122797	+	0.195430i
$699$		0			0
$700$	100.806	−	209.327i	0.144009	−	0.299038i
$701$	−1073.12	−	244.932i	−1.53084	−	0.349404i	−0.627597	−	0.778539i	$-0.715961\pi$
$701$	−1073.12	−	244.932i	−1.53084	−	0.349404i	−0.903240	+	0.429135i	$0.858818\pi$
$702$		0			0
$703$	11.3349	−	5.45861i	0.0161237	−	0.00776474i
$704$	8.50156	−	0.957896i	0.0120761	−	0.00136065i
$705$		0			0
$706$	−48.8070	−	139.483i	−0.0691318	−	0.197567i
$707$	941.755	+	106.110i	1.33204	+	0.150085i
$708$		0			0
$709$	207.591	−	165.548i	0.292794	−	0.233496i	−0.466065	−	0.884751i	$-0.654329\pi$
$709$	207.591	−	165.548i	0.292794	−	0.233496i	0.758859	+	0.651255i	$0.225757\pi$
$710$	−216.145	−	135.813i	−0.304430	−	0.191286i
$711$		0			0
$712$	253.269	+	317.589i	0.355715	+	0.446052i
$713$	−73.1063	+	73.1063i	−0.102533	+	0.102533i
$714$		0			0
$715$	−91.7790	+	32.1149i	−0.128362	+	0.0449159i
$716$	−355.217	+	445.428i	−0.496113	+	0.622106i
$717$		0			0
$718$	111.232	+	230.976i	0.154920	+	0.321694i
$719$	251.846	+	1103.41i	0.350273	+	1.53465i	0.776552	+	0.630054i	$0.216967\pi$
$719$	251.846	+	1103.41i	0.350273	+	1.53465i	−0.426279	+	0.904592i	$0.640176\pi$
$720$		0			0
$721$	−494.226	−	238.007i	−0.685474	−	0.330107i
$722$	−287.083	−	100.455i	−0.397623	−	0.139134i
$723$		0			0
$724$			318.636i			0.440106i
$725$	−58.1808	−	172.401i	−0.0802493	−	0.237795i
$726$		0			0
$727$	25.1121	+	39.9657i	0.0345421	+	0.0549734i	0.863549	−	0.504265i	$-0.168237\pi$
$727$	25.1121	+	39.9657i	0.0345421	+	0.0549734i	−0.829007	+	0.559238i	$0.811094\pi$
$728$	330.853	−	945.524i	0.454469	−	1.29880i
$729$		0			0
$730$	291.317	+	66.4912i	0.399064	+	0.0910838i
$731$	1473.83	−	336.393i	2.01619	−	0.460182i
$732$		0			0
$733$	117.112	−	13.1954i	0.159771	−	0.0180019i	−0.0317165	−	0.999497i	$-0.510097\pi$
$733$	117.112	−	13.1954i	0.159771	−	0.0180019i	0.191488	+	0.981495i	$0.438669\pi$
$734$	71.6018	+	57.1005i	0.0975501	+	0.0777936i
$735$		0			0
$736$	−216.966	−	24.4462i	−0.294791	−	0.0332149i
$737$	−126.104	−	126.104i	−0.171104	−	0.171104i
$738$		0			0
$739$	−954.623	−	599.830i	−1.29178	−	0.811677i	−0.301864	−	0.953351i	$-0.597609\pi$
$739$	−954.623	−	599.830i	−1.29178	−	0.811677i	−0.989913	+	0.141674i	$0.954752\pi$
$740$	−200.373	+	318.891i	−0.270774	+	0.430934i
$741$		0			0
$742$	−274.438	+	274.438i	−0.369862	+	0.369862i
$743$	−84.0696	+	746.139i	−0.113149	+	1.00422i	0.800950	+	0.598732i	$0.204328\pi$
$743$	−84.0696	+	746.139i	−0.113149	+	1.00422i	−0.914098	+	0.405492i	$0.867100\pi$
$744$		0			0
$745$	−281.820	+	353.392i	−0.378282	+	0.474351i
$746$	−40.9643	−	363.568i	−0.0549119	−	0.487356i
$747$		0			0
$748$	−27.0578	−	118.548i	−0.0361736	−	0.158487i
$749$	336.017	−	1472.19i	0.448621	−	1.96554i
$750$		0			0
$751$	−1157.37	−	404.983i	−1.54111	−	0.539258i	−0.579808	−	0.814753i	$-0.696873\pi$
$751$	−1157.37	−	404.983i	−1.54111	−	0.539258i	−0.961303	+	0.275495i	$0.911158\pi$
$752$	345.203	−	216.906i	0.459047	−	0.288438i
$753$		0			0
$754$	−150.041	−	320.642i	−0.198993	−	0.425255i
$755$	−178.716			−0.236710
$756$		0			0
$757$	347.068	−	991.864i	0.458478	−	1.31026i	−0.450263	−	0.892896i	$-0.648670\pi$
$757$	347.068	−	991.864i	0.458478	−	1.31026i	0.908741	−	0.417360i	$-0.137045\pi$
$758$	−100.608	+	208.915i	−0.132729	+	0.275614i
$759$		0			0
$760$	−12.3270	+	2.81355i	−0.0162197	+	0.00370204i
$761$	−147.446	+	71.0065i	−0.193754	+	0.0933068i	−0.528245	−	0.849092i	$-0.677150\pi$
$761$	−147.446	+	71.0065i	−0.193754	+	0.0933068i	0.334491	+	0.942399i	$0.391435\pi$
$762$		0			0
$763$	−178.897	−	142.665i	−0.234465	−	0.186980i
$764$	−388.925	−	1111.48i	−0.509064	−	1.45482i
$765$		0			0
$766$	130.285	+	130.285i	0.170084	+	0.170084i
$767$	270.216	−	215.490i	0.352302	−	0.280952i
$768$		0			0
$769$	451.872	−	719.149i	0.587609	−	0.935175i	−0.412102	−	0.911138i	$-0.635205\pi$
$769$	451.872	−	719.149i	0.587609	−	0.935175i	0.999711	−	0.0240371i	$-0.00765197\pi$
$770$	−39.7373	−	49.8290i	−0.0516069	−	0.0647130i
$771$		0			0
$772$	−109.650	+	973.169i	−0.142033	+	1.26058i
$773$	−1129.95	+	395.387i	−1.46177	+	0.511497i	−0.939878	−	0.341511i	$-0.889061\pi$
$773$	−1129.95	+	395.387i	−1.46177	+	0.511497i	−0.521897	+	0.853008i	$0.674776\pi$
$774$		0			0
$775$	10.4136	+	92.4234i	0.0134369	+	0.119256i
$776$	−209.946	−	435.958i	−0.270549	−	0.561801i
$777$		0			0
$778$	6.88977	−	30.1860i	0.00885574	−	0.0387995i
$779$	−27.9424	−	13.4563i	−0.0358695	−	0.0172739i
$780$		0			0
$781$	−91.9420	+	57.7710i	−0.117723	+	0.0739706i
$782$			140.071i			0.179119i
$783$		0			0
$784$	−620.058			−0.790890
$785$	188.675	+	300.274i	0.240350	+	0.382515i
$786$		0			0
$787$	−645.160	+	1339.69i	−0.819772	+	1.70227i	−0.114401	+	0.993435i	$0.536495\pi$
$787$	−645.160	+	1339.69i	−0.819772	+	1.70227i	−0.705371	+	0.708839i	$0.749219\pi$
$788$	445.791	+	101.749i	0.565725	+	0.129123i
$789$		0			0
$790$	379.446	−	182.731i	0.480311	−	0.231306i
$791$	268.262	−	30.2258i	0.339142	−	0.0382122i
$792$		0			0
$793$	345.852	+	988.387i	0.436131	+	1.24639i
$794$	112.397	+	12.6640i	0.141557	+	0.0159497i
$795$		0			0
$796$	29.7651	−	23.7369i	0.0373933	−	0.0298202i
$797$	126.257	+	79.3327i	0.158416	+	0.0995391i	0.608907	−	0.793242i	$-0.291608\pi$
$797$	126.257	+	79.3327i	0.158416	+	0.0995391i	−0.450491	+	0.892781i	$0.648751\pi$
$798$		0			0
$799$	−759.176	−	951.977i	−0.950158	−	1.19146i
$800$	−138.889	+	138.889i	−0.173611	+	0.173611i
$801$		0			0
$802$	−378.101	+	132.303i	−0.471447	+	0.164967i
$803$	79.2485	−	99.3745i	0.0986905	−	0.123754i
$804$		0			0
$805$	−147.420	−	306.122i	−0.183131	−	0.380275i
$806$	40.2668	+	176.420i	0.0499588	+	0.218884i
$807$		0			0
$808$	−466.093	−	224.459i	−0.576848	−	0.277795i
$809$	−1262.37	−	441.723i	−1.56041	−	0.546012i	−0.594324	−	0.804226i	$-0.702580\pi$
$809$	−1262.37	−	441.723i	−1.56041	−	0.546012i	−0.966088	+	0.258214i	$0.916866\pi$
$810$		0			0
$811$		−	1098.94i		−	1.35504i	−0.735502	−	0.677522i	$-0.763054\pi$
$811$		−	1098.94i		−	1.35504i	0.735502	−	0.677522i	$-0.236946\pi$
$812$	−767.739	+	750.840i	−0.945491	+	0.924679i
$813$		0			0
$814$	−18.4170	−	29.3104i	−0.0226253	−	0.0360079i
$815$	−1.63905	+	4.68414i	−0.00201111	+	0.00574741i
$816$		0			0
$817$	−29.4166	−	6.71416i	−0.0360057	−	0.00821806i
$818$	24.0199	−	5.48238i	0.0293641	−	0.00670217i
$819$		0			0
$820$	922.584	−	103.950i	1.12510	−	0.126769i
$821$	548.717	+	437.587i	0.668352	+	0.532993i	0.897842	−	0.440318i	$-0.145134\pi$
$821$	548.717	+	437.587i	0.668352	+	0.532993i	−0.229490	+	0.973311i	$0.573706\pi$
$822$		0			0
$823$	1160.52	+	130.760i	1.41011	+	0.158882i	0.783957	−	0.620815i	$-0.213198\pi$
$823$	1160.52	+	130.760i	1.41011	+	0.158882i	0.626158	+	0.779696i	$0.284627\pi$
$824$	211.732	+	211.732i	0.256956	+	0.256956i
$825$		0			0
$826$	191.816	+	120.526i	0.232222	+	0.145915i
$827$	−172.877	+	275.132i	−0.209041	+	0.332687i	−0.934744	−	0.355321i	$-0.884372\pi$
$827$	−172.877	+	275.132i	−0.209041	+	0.332687i	0.725703	+	0.688008i	$0.241515\pi$
$828$		0			0
$829$	−428.233	+	428.233i	−0.516566	+	0.516566i	−0.916531	−	0.399964i	$-0.869022\pi$
$829$	−428.233	+	428.233i	−0.516566	+	0.516566i	0.399964	+	0.916531i	$0.369022\pi$
$830$	0.506070	−	4.49149i	0.000609722	−	0.00541144i
$831$		0			0
$832$	49.7724	−	62.4126i	0.0598226	−	0.0750152i
$833$	207.345	+	1840.23i	0.248913	+	2.20916i
$834$		0			0
$835$	188.354	+	825.231i	0.225573	+	0.988301i
$836$	−0.540055	+	2.36613i	−0.000645998	+	0.00283030i
$837$		0			0
$838$	−176.190	−	61.6515i	−0.210251	−	0.0735698i
$839$	788.003	−	495.135i	0.939217	−	0.590149i	0.0269021	−	0.999638i	$-0.491436\pi$
$839$	788.003	−	495.135i	0.939217	−	0.590149i	0.912315	+	0.409489i	$0.134293\pi$
$840$		0			0
$841$	−18.7155	+	840.792i	−0.0222538	+	0.999752i
$842$	103.329			0.122718
$843$		0			0
$844$	−151.021	+	431.592i	−0.178934	+	0.511365i
$845$	−76.3516	+	158.546i	−0.0903569	+	0.187628i
$846$		0			0
$847$	1301.61	−	297.083i	1.53673	−	0.350748i
$848$	−293.875	+	141.523i	−0.346550	+	0.166890i
$849$		0			0
$850$	98.5173	+	78.5649i	0.115903	+	0.0924293i
$851$	−60.9503	−	174.186i	−0.0716220	−	0.204684i
$852$		0			0
$853$	−962.602	−	962.602i	−1.12849	−	1.12849i	−0.990423	−	0.138067i	$-0.955911\pi$
$853$	−962.602	−	962.602i	−1.12849	−	1.12849i	−0.138067	−	0.990423i	$-0.544089\pi$
$854$	−536.619	+	427.939i	−0.628360	+	0.501100i
$855$		0			0
$856$	−438.544	+	697.940i	−0.512318	+	0.815350i
$857$	−173.622	−	217.715i	−0.202592	−	0.254043i	0.670148	−	0.742228i	$-0.266231\pi$
$857$	−173.622	−	217.715i	−0.202592	−	0.254043i	−0.872740	+	0.488185i	$0.837659\pi$
$858$		0			0
$859$	85.2609	−	756.711i	0.0992560	−	0.880921i	−0.841135	−	0.540825i	$-0.818112\pi$
$859$	85.2609	−	756.711i	0.0992560	−	0.880921i	0.940391	−	0.340096i	$-0.110459\pi$
$860$	852.571	−	298.328i	0.991362	−	0.346893i
$861$		0			0
$862$	−18.6671	−	165.675i	−0.0216556	−	0.192199i
$863$	−566.520	−	1176.39i	−0.656454	−	1.36314i	−0.917470	−	0.397806i	$-0.869772\pi$
$863$	−566.520	−	1176.39i	−0.656454	−	1.36314i	0.261016	−	0.965335i	$-0.415943\pi$
$864$		0			0
$865$	90.4344	−	396.219i	0.104548	−	0.458056i
$866$	−133.559	−	64.3188i	−0.154226	−	0.0742712i
$867$		0			0
$868$	464.784	−	292.043i	0.535465	−	0.336455i
$869$		−	179.146i		−	0.206152i
$870$		0			0
$871$	−1664.04			−1.91049
$872$	66.4528	+	105.759i	0.0762073	+	0.121283i
$873$		0			0
$874$	1.21302	−	2.51885i	0.00138789	−	0.00288198i
$875$	−1485.36	−	339.024i	−1.69755	−	0.387456i
$876$		0			0
$877$	−810.161	+	390.153i	−0.923787	+	0.444872i	−0.834422	−	0.551126i	$-0.814198\pi$
$877$	−810.161	+	390.153i	−0.923787	+	0.444872i	−0.0893654	+	0.995999i	$0.528484\pi$
$878$	−187.600	+	21.1375i	−0.213668	+	0.0240746i
$879$		0			0
$880$	−17.6907	−	50.5570i	−0.0201030	−	0.0574511i
$881$	270.422	+	30.4692i	0.306949	+	0.0345848i	0.264096	−	0.964497i	$-0.414927\pi$
$881$	270.422	+	30.4692i	0.306949	+	0.0345848i	0.0428534	+	0.999081i	$0.486355\pi$
$882$		0			0
$883$	33.8605	−	27.0028i	0.0383471	−	0.0305808i	−0.604129	−	0.796887i	$-0.706479\pi$
$883$	33.8605	−	27.0028i	0.0383471	−	0.0305808i	0.642476	+	0.766306i	$0.277907\pi$
$884$	−960.694	−	603.644i	−1.08676	−	0.682855i
$885$		0			0
$886$	−91.4986	−	114.736i	−0.103272	−	0.129498i
$887$	235.123	−	235.123i	0.265076	−	0.265076i	−0.562036	−	0.827113i	$-0.689982\pi$
$887$	235.123	−	235.123i	0.265076	−	0.265076i	0.827113	+	0.562036i	$0.189982\pi$
$888$		0			0
$889$	87.8570	−	30.7425i	0.0988268	−	0.0345810i
$890$	150.355	−	188.539i	0.168938	−	0.211842i
$891$		0			0
$892$	−164.192	−	340.949i	−0.184072	−	0.382229i
$893$	5.40790	+	23.6936i	0.00605588	+	0.0265326i
$894$		0			0
$895$	675.297	+	325.206i	0.754521	+	0.363358i
$896$	1380.00	+	482.881i	1.54017	+	0.538930i
$897$		0			0
$898$			376.959i			0.419777i
$899$	100.317	−	418.020i	0.111587	−	0.464983i
$900$		0			0
$901$	518.287	+	824.850i	0.575236	+	0.915482i
$902$	−28.1842	+	80.5458i	−0.0312463	+	0.0892969i
$903$		0			0
$904$	−143.667	−	32.7910i	−0.158923	−	0.0362732i
$905$	408.685	−	93.2797i	0.451586	−	0.103071i
$906$		0			0
$907$	−1313.77	+	148.026i	−1.44847	+	0.163204i	−0.800899	−	0.598799i	$-0.795645\pi$
$907$	−1313.77	+	148.026i	−1.44847	+	0.163204i	−0.647574	+	0.762003i	$0.724216\pi$
$908$	587.848	+	468.793i	0.647409	+	0.516292i
$909$		0			0
$910$	−590.950	−	66.5841i	−0.649396	−	0.0731693i
$911$	508.410	+	508.410i	0.558079	+	0.558079i	0.928760	−	0.370681i	$-0.120876\pi$
$911$	508.410	+	508.410i	0.558079	+	0.558079i	−0.370681	+	0.928760i	$0.620876\pi$
$912$		0			0
$913$	−1.62795	−	1.02291i	−0.00178307	−	0.00112038i
$914$	−21.9028	+	34.8581i	−0.0239637	+	0.0381380i
$915$		0			0
$916$	−480.650	+	480.650i	−0.524727	+	0.524727i
$917$	303.042	−	2689.57i	0.330471	−	2.93301i
$918$		0			0
$919$	−898.576	+	1126.78i	−0.977776	+	1.22609i	−0.00367108	+	0.999993i	$0.501169\pi$
$919$	−898.576	+	1126.78i	−0.977776	+	1.22609i	−0.974104	+	0.226098i	$0.927403\pi$
$920$	20.7659	+	184.302i	0.0225716	+	0.200328i
$921$		0			0
$922$	−106.577	−	466.946i	−0.115594	−	0.506449i
$923$	−225.457	+	987.792i	−0.244266	+	1.07020i
$924$		0			0
$925$	−156.698	−	54.8312i	−0.169404	−	0.0592769i
$926$	35.8071	−	22.4991i	0.0386686	−	0.0242971i
$927$		0			0
$928$	822.282	−	384.778i	0.886080	−	0.414631i
$929$	−905.489			−0.974692			−0.487346	−	0.873209i	$-0.662035\pi$
$929$	−905.489			−0.974692			−0.487346	+	0.873209i	$0.662035\pi$
$930$		0			0
$931$	12.2078	−	34.8879i	0.0131126	−	0.0374736i
$932$	−265.772	+	551.881i	−0.285163	+	0.592147i
$933$		0			0
$934$	154.277	−	35.2128i	0.165179	−	0.0377010i
$935$	−144.129	+	69.4091i	−0.154149	+	0.0742343i
$936$		0			0
$937$	873.708	+	696.759i	0.932453	+	0.743606i	0.966728	−	0.255806i	$-0.0823409\pi$
$937$	873.708	+	696.759i	0.932453	+	0.743606i	−0.0342755	+	0.999412i	$0.510912\pi$
$938$	−360.238	−	1029.50i	−0.384049	−	1.09755i
$939$		0			0
$940$	−514.440	−	514.440i	−0.547277	−	0.547277i
$941$	−1101.42	+	878.352i	−1.17048	+	0.933424i	−0.998662	−	0.0517051i	$-0.983534\pi$
$941$	−1101.42	+	878.352i	−1.17048	+	0.933424i	−0.171815	+	0.985129i	$0.554963\pi$
$942$		0			0
$943$	−242.035	+	385.196i	−0.256664	+	0.408479i
$944$	118.704	+	148.850i	0.125746	+	0.157680i
$945$		0			0
$946$	−9.29548	+	82.4997i	−0.00982609	+	0.0872090i
$947$	−75.4551	+	26.4029i	−0.0796780	+	0.0278805i	−0.369824	−	0.929102i	$-0.620582\pi$
$947$	−75.4551	+	26.4029i	−0.0796780	+	0.0278805i	0.290146	+	0.956982i	$0.406296\pi$
$948$		0			0
$949$	−132.789	−	1178.54i	−0.139925	−	1.24187i
$950$	−1.09123	−	2.26597i	−0.00114867	−	0.00238523i
$951$		0			0
$952$	366.727	−	1606.74i	0.385218	−	1.68775i
$953$	−1340.84	−	645.717i	−1.40697	−	0.677562i	−0.432409	−	0.901677i	$-0.642336\pi$
$953$	−1340.84	−	645.717i	−1.40697	−	0.677562i	−0.974563	+	0.224115i	$0.928051\pi$
$954$		0			0
$955$	−1311.74	+	824.220i	−1.37355	+	0.863058i
$956$			528.599i			0.552927i
$957$		0			0
$958$	−24.8199			−0.0259081
$959$	243.428	+	387.414i	0.253835	+	0.403977i
$960$		0			0
$961$	321.619	−	667.849i	0.334671	−	0.694952i
$962$	−314.901	−	71.8740i	−0.327340	−	0.0747131i
$963$		0			0
$964$	−577.078	+	277.906i	−0.598628	+	0.288284i
$965$	1280.29	−	144.254i	1.32673	−	0.149486i
$966$		0			0
$967$	−478.230	−	1366.70i	−0.494550	−	1.41334i	−0.872999	−	0.487721i	$-0.837828\pi$
$967$	−478.230	−	1366.70i	−0.494550	−	1.41334i	0.378449	−	0.925622i	$-0.376458\pi$
$968$	−724.192	−	81.5968i	−0.748132	−	0.0842943i
$969$		0			0
$970$	−224.586	+	179.102i	−0.231532	+	0.184641i
$971$	293.082	+	184.155i	0.301835	+	0.189655i	0.674430	−	0.738338i	$-0.264389\pi$
$971$	293.082	+	184.155i	0.301835	+	0.189655i	−0.372596	+	0.927994i	$0.621532\pi$
$972$		0			0
$973$	391.994	+	491.545i	0.402871	+	0.505185i
$974$	−106.529	+	106.529i	−0.109373	+	0.109373i
$975$		0			0
$976$	−544.459	+	190.514i	−0.557847	+	0.195199i
$977$	760.252	−	953.326i	0.778150	−	0.975769i	−0.221850	−	0.975081i	$-0.571210\pi$
$977$	760.252	−	953.326i	0.778150	−	0.975769i	1.00000		0.000687874i	$-0.000218957\pi$
$978$		0			0
$979$	−44.5072	−	92.4201i	−0.0454619	−	0.0944026i
$980$	246.218	+	1078.75i	0.251243	+	1.10077i
$981$		0			0
$982$	−286.767	−	138.100i	−0.292024	−	0.140631i
$983$	604.833	+	211.640i	0.615293	+	0.215300i	0.619889	−	0.784689i	$-0.287177\pi$
$983$	604.833	+	211.640i	0.615293	+	0.215300i	−0.00459679	+	0.999989i	$0.501463\pi$
$984$		0			0
$985$		−	601.561i		−	0.610722i
$986$	−304.358	−	496.564i	−0.308679	−	0.503615i
$987$		0			0
$988$	12.0483	+	19.1748i	0.0121946	+	0.0194076i
$989$	−146.180	+	417.758i	−0.147806	+	0.422405i
$990$		0			0
$991$	1109.88	+	253.324i	1.11996	+	0.255624i	0.742134	−	0.670251i	$-0.233814\pi$
$991$	1109.88	+	253.324i	1.11996	+	0.255624i	0.377829	+	0.925876i	$0.376671\pi$
$992$	−452.428	+	103.264i	−0.456076	+	0.104096i
$993$		0			0
$994$	−659.930	+	74.3562i	−0.663913	+	0.0748051i
$995$	−39.1587	−	31.2280i	−0.0393554	−	0.0313849i
$996$		0			0
$997$	760.354	+	85.6713i	0.762642	+	0.0859291i	0.484714	−	0.874673i	$-0.338924\pi$
$997$	760.354	+	85.6713i	0.762642	+	0.0859291i	0.277928	+	0.960602i	$0.410352\pi$
$998$	−351.621	−	351.621i	−0.352326	−	0.352326i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.3.s.a.19.3		48
3.2	odd	2		29.3.f.a.19.2	✓	48
29.26	odd	28	inner	261.3.s.a.55.3		48
87.26	even	28		29.3.f.a.26.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.f.a.19.2	✓	48	3.2	odd	2
29.3.f.a.26.2	yes	48	87.26	even	28
261.3.s.a.19.3		48	1.1	even	1	trivial
261.3.s.a.55.3		48	29.26	odd	28	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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	261.s (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.448531 + 0.713833i) q^{2} +(1.42716 - 2.96352i) q^{4} +(-4.21883 - 0.962920i) q^{5} +(-10.1429 + 4.88457i) q^{7} +(6.10659 - 0.688048i) q^{8} +O(q^{10})\)	\(q+(0.448531 + 0.713833i) q^{2} +(1.42716 - 2.96352i) q^{4} +(-4.21883 - 0.962920i) q^{5} +(-10.1429 + 4.88457i) q^{7} +(6.10659 - 0.688048i) q^{8} +(-1.20491 - 3.44344i) q^{10} +(-1.54207 - 0.173749i) q^{11} +(-11.3208 + 9.02803i) q^{13} +(-8.03618 - 5.04946i) q^{14} +(-4.97314 - 6.23612i) q^{16} +(-16.8448 + 16.8448i) q^{17} +(0.448791 - 0.157039i) q^{19} +(-8.87457 + 11.1284i) q^{20} +(-0.567637 - 1.17871i) q^{22} +(-1.55197 - 6.79962i) q^{23} +(-5.65292 - 2.72230i) q^{25} +(-11.5222 - 4.03180i) q^{26} +37.0298i q^{28} +(20.2766 + 20.7330i) q^{29} +(-7.88671 - 12.5516i) q^{31} +(10.3395 - 29.5486i) q^{32} +(-19.5798 - 4.46896i) q^{34} +(47.4946 - 10.8403i) q^{35} +(26.2932 - 2.96253i) q^{37} +(0.313396 + 0.249925i) q^{38} +(-26.4252 - 2.97741i) q^{40} +(-46.1225 - 46.1225i) q^{41} +(-53.7324 - 33.7623i) q^{43} +(-2.71568 + 4.32198i) q^{44} +(4.15769 - 4.15769i) q^{46} +(-5.72285 + 50.7917i) q^{47} +(48.4686 - 60.7777i) q^{49} +(-0.592241 - 5.25628i) q^{50} +(10.5982 + 46.4338i) q^{52} +(9.09960 - 39.8680i) q^{53} +(6.33841 + 2.21790i) q^{55} +(-58.5778 + 36.8069i) q^{56} +(-5.70521 + 23.7735i) q^{58} -23.8690 q^{59} +(23.8851 - 68.2596i) q^{61} +(5.42233 - 11.2596i) q^{62} +(-5.37487 + 1.22678i) q^{64} +(56.4537 - 27.1867i) q^{65} +(89.8491 + 71.6523i) q^{67} +(25.8798 + 73.9602i) q^{68} +(29.0410 + 29.0410i) q^{70} +(54.7070 - 43.6274i) q^{71} +(-43.5770 + 69.3524i) q^{73} +(13.9081 + 17.4402i) q^{74} +(0.175107 - 1.55412i) q^{76} +(16.4897 - 5.77000i) q^{77} +(12.9255 + 114.717i) q^{79} +(14.9759 + 31.0978i) q^{80} +(12.2364 - 53.6111i) q^{82} +(1.11626 + 0.537563i) q^{83} +(87.2856 - 54.8452i) q^{85} -53.4995i q^{86} -9.53632 q^{88} +(35.1684 + 55.9701i) q^{89} +(70.7277 - 146.868i) q^{91} +(-22.3657 - 5.10483i) q^{92} +(-38.8237 + 18.6965i) q^{94} +(-2.04459 + 0.230370i) q^{95} +(-26.0062 - 74.3215i) q^{97} +(65.1248 + 7.33780i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) \) 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) \) 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8 - 20 * q^10 + 8 * q^11 - 14 * q^13 - 26 * q^14 + 18 * q^16 + 26 * q^17 + 2 * q^19 - 46 * q^20 + 154 * q^22 - 56 * q^23 - 34 * q^25 - 110 * q^26 + 170 * q^29 - 88 * q^31 + 132 * q^32 - 224 * q^34 + 210 * q^35 - 56 * q^37 + 294 * q^38 - 492 * q^40 + 34 * q^41 + 176 * q^43 - 126 * q^44 + 744 * q^46 - 208 * q^47 + 506 * q^49 - 732 * q^50 + 690 * q^52 + 14 * q^53 + 284 * q^55 - 332 * q^56 - 508 * q^58 + 44 * q^59 - 30 * q^61 + 504 * q^62 - 896 * q^64 + 554 * q^65 - 574 * q^67 + 796 * q^68 - 1066 * q^70 - 224 * q^71 - 22 * q^73 - 820 * q^74 + 514 * q^76 - 436 * q^77 + 564 * q^79 - 1162 * q^80 - 18 * q^82 + 126 * q^83 + 38 * q^85 - 384 * q^88 + 160 * q^89 - 434 * q^91 + 1022 * q^92 - 2 * q^94 + 642 * q^95 + 604 * q^97 + 102 * q^98

Introduction

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