LMFDB - Embedded newform 261.3.s.a.55.3

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			55.3
Character	$\chi$	$=$	261.55
Dual form			261.3.s.a.19.3

$q$-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 $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{19}{28}\right)$	$1$

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	−0.715572	−	0.698539i	$-0.753834\pi$
$2$	0.448531	−	0.713833i	0.224266	−	0.356917i	0.939837	+	0.341623i	$0.110977\pi$
$3$		0			0
$3$		0			0
$4$	1.42716	+	2.96352i	0.356789	+	0.740881i
$5$	−4.21883	+	0.962920i	−0.843766	+	0.192584i	−0.622490	−	0.782627i	$-0.713879\pi$
$5$	−4.21883	+	0.962920i	−0.843766	+	0.192584i	−0.221275	+	0.975211i	$0.571022\pi$
$6$		0			0
$7$	−10.1429	−	4.88457i	−1.44899	−	0.697795i	−0.466568	−	0.884485i	$-0.654510\pi$
$7$	−10.1429	−	4.88457i	−1.44899	−	0.697795i	−0.982419	+	0.186690i	$0.940224\pi$
$8$	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	−0.181780	−	0.983339i	$-0.558186\pi$
$11$	−1.54207	+	0.173749i	−0.140188	+	0.0157954i	0.0415917	+	0.999135i	$0.486757\pi$
$12$		0			0
$13$	−11.3208	−	9.02803i	−0.870830	−	0.694464i	0.0824361	−	0.996596i	$-0.473730\pi$
$13$	−11.3208	−	9.02803i	−0.870830	−	0.694464i	−0.953266	+	0.302133i	$0.902301\pi$
$14$	−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	0.00908711	−	0.999959i	$-0.497107\pi$
$17$	−16.8448	−	16.8448i	−0.990872	−	0.990872i	−0.999959	+	0.00908711i	$0.997107\pi$
$18$		0			0
$19$	0.448791	+	0.157039i	0.0236206	+	0.00826520i	0.342064	−	0.939677i	$-0.388874\pi$
$19$	0.448791	+	0.157039i	0.0236206	+	0.00826520i	−0.318443	+	0.947942i	$0.603160\pi$
$20$	−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	−0.997395	−	0.0721306i	$-0.977020\pi$
$23$	−1.55197	+	6.79962i	−0.0674769	+	0.295636i	0.929918	+	0.367766i	$0.119877\pi$
$24$		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	−0.949371	−	0.314156i	$-0.898279\pi$
$31$	−7.88671	+	12.5516i	−0.254410	+	0.404891i	0.694962	+	0.719047i	$0.255421\pi$
$32$	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	0.459876	−	0.887983i	$-0.347894\pi$
$37$	26.2932	+	2.96253i	0.710627	+	0.0800685i	0.250751	+	0.968052i	$0.419322\pi$
$38$	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	−0.133950	+	0.990988i	$0.542766\pi$
$41$	−46.1225	+	46.1225i	−1.12494	+	1.12494i	−0.990988	+	0.133950i	$0.957234\pi$
$42$		0			0
$43$	−53.7324	+	33.7623i	−1.24959	+	0.785170i	−0.983871	−	0.178880i	$-0.942753\pi$
$43$	−53.7324	+	33.7623i	−1.24959	+	0.785170i	−0.265721	+	0.964050i	$0.585610\pi$
$44$	−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	−0.894848	−	0.446372i	$-0.852716\pi$
$47$	−5.72285	−	50.7917i	−0.121763	−	1.08067i	0.773085	−	0.634302i	$-0.218713\pi$
$48$		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	0.985303	+	0.170818i	$0.0546409\pi$
$53$	9.09960	+	39.8680i	0.171691	+	0.752226i	−0.813612	+	0.581408i	$0.802502\pi$
$54$		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	0.955957	+	0.293507i	$0.0948225\pi$
$61$	23.8851	+	68.2596i	0.391559	+	1.11901i	−0.564398	+	0.825503i	$0.690892\pi$
$62$	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	0.349866	−	0.936800i	$-0.386227\pi$
$67$	89.8491	−	71.6523i	1.34103	−	1.06944i	0.991165	−	0.132637i	$-0.0423445\pi$
$68$	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	0.927797	−	0.373085i	$-0.121700\pi$
$71$	54.7070	+	43.6274i	0.770521	+	0.614470i	−0.157276	+	0.987555i	$0.550271\pi$
$72$		0			0
$73$	−43.5770	−	69.3524i	−0.596945	−	0.950032i	−0.999401	−	0.0345932i	$-0.988986\pi$
$73$	−43.5770	−	69.3524i	−0.596945	−	0.950032i	0.402457	−	0.915439i	$-0.368156\pi$
$74$	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	−0.596653	−	0.802499i	$-0.703503\pi$
$79$	12.9255	−	114.717i	0.163613	−	1.45211i	0.760267	−	0.649611i	$-0.225068\pi$
$80$	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	−0.427147	−	0.904182i	$-0.640481\pi$
$83$	1.11626	−	0.537563i	0.0134489	−	0.00647666i	0.440596	+	0.897705i	$0.354767\pi$
$84$		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	−0.588599	−	0.808425i	$-0.700320\pi$
$89$	35.1684	−	55.9701i	0.395150	−	0.628878i	0.983749	+	0.179547i	$0.0574632\pi$
$90$		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	0.728588	+	0.684952i	$0.240177\pi$
$97$	−26.0062	+	74.3215i	−0.268105	+	0.766201i	−0.996694	+	0.0812495i	$0.974109\pi$
$98$	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	−0.836499	−	0.547968i	$-0.815402\pi$
$101$	−71.2798	+	44.7881i	−0.705741	+	0.443446i	0.130759	+	0.991414i	$0.458259\pi$
$102$		0			0
$103$	30.3804	−	38.0958i	0.294955	−	0.369862i	−0.612168	−	0.790728i	$-0.709702\pi$
$103$	30.3804	−	38.0958i	0.294955	−	0.369862i	0.907123	+	0.420866i	$0.138274\pi$
$104$	−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	−0.999991	−	0.00423133i	$-0.998653\pi$
$107$	−83.6309	−	104.870i	−0.781597	−	0.980092i	0.218394	−	0.975861i	$-0.429918\pi$
$108$		0			0
$109$	8.81881	−	18.3125i	0.0809066	−	0.168004i	−0.856591	−	0.515996i	$-0.827422\pi$
$109$	8.81881	−	18.3125i	0.0809066	−	0.168004i	0.937498	+	0.347992i	$0.113136\pi$
$110$	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	−0.428566	−	0.903511i	$-0.640981\pi$
$113$	−22.6341	+	7.92002i	−0.200302	+	0.0700886i	0.228264	+	0.973599i	$0.426695\pi$
$114$		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	−0.144252	−	0.989541i	$-0.546078\pi$
$127$	−8.21611	+	0.925733i	−0.0646938	+	0.00728924i	0.0795583	+	0.996830i	$0.474649\pi$
$128$	−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	−0.824725	−	0.565534i	$-0.808670\pi$
$131$	−127.911	−	203.569i	−0.976419	−	1.55396i	−0.151694	−	0.988428i	$-0.548473\pi$
$132$		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	0.966112	+	0.258123i	$0.0831041\pi$
$137$	−4.55051	+	40.3869i	−0.0332154	+	0.294795i	−0.999327	+	0.0366716i	$0.988324\pi$
$138$		0			0
$139$	−12.4270	+	54.4464i	−0.0894032	+	0.391701i	−0.999755	−	0.0221342i	$-0.992954\pi$
$139$	−12.4270	+	54.4464i	−0.0894032	+	0.391701i	0.910352	+	0.413835i	$0.135811\pi$
$140$	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	0.995892	−	0.0905531i	$-0.0288635\pi$
$149$	45.3207	+	94.1095i	0.304166	+	0.631607i	−0.691726	+	0.722161i	$0.743149\pi$
$150$		0			0
$151$	40.2640	+	9.18999i	0.266649	+	0.0608609i	0.353755	−	0.935338i	$-0.384905\pi$
$151$	40.2640	+	9.18999i	0.266649	+	0.0608609i	−0.0871059	+	0.996199i	$0.527762\pi$
$152$	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	−0.867148	−	0.498050i	$-0.834050\pi$
$157$	−57.9484	+	57.9484i	−0.369098	+	0.369098i	0.498050	+	0.867148i	$0.334050\pi$
$158$	−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	0.994100	−	0.108468i	$-0.0345945\pi$
$163$	0.128402	+	1.13960i	0.000787743	+	0.00699141i	−0.993312	+	0.115459i	$0.963166\pi$
$164$	−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	0.476190	+	0.879342i	$0.342017\pi$
$167$	−84.8706	+	176.236i	−0.508207	+	1.05530i	−0.984397	+	0.175960i	$0.943697\pi$
$168$		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	$-0.912502\pi$
$173$		−	93.9168i		−	0.542872i	0.962457	−	0.271436i	$-0.0874985\pi$
$174$		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	−0.666431	−	0.745566i	$-0.732179\pi$
$179$	−168.864	+	38.5422i	−0.943376	+	0.215319i	−0.276945	+	0.960886i	$0.589322\pi$
$180$		0			0
$181$	−87.2784	−	42.0311i	−0.482201	−	0.232216i	0.176959	−	0.984218i	$-0.443374\pi$
$181$	−87.2784	−	42.0311i	−0.482201	−	0.232216i	−0.659160	+	0.752002i	$0.729088\pi$
$182$	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	0.909359	+	0.416013i	$0.136573\pi$
$191$	253.146	+	253.146i	1.32537	+	1.32537i	0.416013	+	0.909359i	$0.363427\pi$
$192$		0			0
$193$	−281.027	−	98.3354i	−1.45610	−	0.509510i	−0.517848	−	0.855473i	$-0.673267\pi$
$193$	−281.027	−	98.3354i	−1.45610	−	0.509510i	−0.938248	+	0.345963i	$0.887552\pi$
$194$	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	−0.833716	−	0.552193i	$-0.813791\pi$
$197$	30.9336	−	135.529i	0.157024	−	0.687965i	0.990740	−	0.135773i	$-0.0433516\pi$
$198$		0			0
$199$	10.4281	−	5.02191i	0.0524025	−	0.0252357i	−0.407499	−	0.913206i	$-0.633599\pi$
$199$	10.4281	−	5.02191i	0.0524025	−	0.0252357i	0.459901	+	0.887970i	$0.347885\pi$
$200$	−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	−0.221629	−	0.975131i	$-0.571137\pi$
$211$	−138.139	−	15.5646i	−0.654688	−	0.0737657i	−0.433059	+	0.901365i	$0.642566\pi$
$212$	−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	0.916205	−	0.400711i	$-0.131237\pi$
$223$	71.7315	+	89.9485i	0.321666	+	0.403356i	−0.594539	+	0.804067i	$0.702665\pi$
$224$	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	−0.954373	−	0.298616i	$-0.903475\pi$
$227$	−50.8656	−	222.857i	−0.224077	−	0.981747i	0.730296	−	0.683131i	$-0.239382\pi$
$228$		0			0
$229$	−195.058	+	68.2538i	−0.851782	+	0.298051i	−0.720638	−	0.693312i	$-0.756151\pi$
$229$	−195.058	+	68.2538i	−0.851782	+	0.298051i	−0.131144	+	0.991363i	$0.541865\pi$
$230$	−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	0.105720	−	0.994396i	$-0.466285\pi$
$239$	−144.790	−	69.7270i	−0.605814	−	0.291745i	−0.711534	+	0.702651i	$0.751999\pi$
$240$		0			0
$241$	−152.244	+	121.410i	−0.631717	+	0.503777i	−0.886202	−	0.463300i	$-0.846665\pi$
$241$	−152.244	+	121.410i	−0.631717	+	0.503777i	0.254485	+	0.967077i	$0.418094\pi$
$242$	−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	0.870399	−	0.492347i	$-0.163861\pi$
$251$	312.227	+	109.253i	1.24393	+	0.435270i	0.373532	+	0.927617i	$0.378147\pi$
$252$		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	−0.712480	−	0.701692i	$-0.752428\pi$
$257$	−156.282	+	75.2612i	−0.608099	+	0.292845i	0.104381	+	0.994537i	$0.466714\pi$
$258$		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	−0.640614	−	0.767863i	$-0.721320\pi$
$263$	86.5688	−	137.774i	0.329159	−	0.523854i	0.969773	+	0.244010i	$0.0784628\pi$
$264$		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	0.0574202	−	0.998350i	$-0.481713\pi$
$269$	−29.2546	−	3.29620i	−0.108753	−	0.0122535i	−0.166173	+	0.986097i	$0.553141\pi$
$270$		0			0
$271$	168.083	−	480.355i	0.620234	−	1.77253i	−0.0146174	−	0.999893i	$-0.504653\pi$
$271$	168.083	−	480.355i	0.620234	−	1.77253i	0.634852	−	0.772634i	$-0.281061\pi$
$272$	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	−0.959813	−	0.280642i	$-0.909453\pi$
$277$	−130.918	+	164.166i	−0.472629	+	0.592657i	0.487184	+	0.873299i	$0.338024\pi$
$278$	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	0.959140	+	0.282931i	$0.0913067\pi$
$281$	287.055	+	359.956i	1.02155	+	1.28098i	0.0624084	+	0.998051i	$0.480122\pi$
$282$		0			0
$283$	194.833	−	404.574i	0.688455	−	1.42959i	−0.204237	−	0.978922i	$-0.565471\pi$
$283$	194.833	−	404.574i	0.688455	−	1.42959i	0.892691	−	0.450669i	$-0.148815\pi$
$284$	−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	0.863045	−	0.505126i	$-0.168554\pi$
$293$	−37.1090	−	106.051i	−0.126652	−	0.361950i	−0.989697	+	0.143176i	$0.954268\pi$
$294$		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	0.887752	−	0.460323i	$-0.152266\pi$
$307$	131.221	+	131.221i	0.427429	+	0.427429i	−0.460323	+	0.887752i	$0.652266\pi$
$308$	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	−0.493560	−	0.869712i	$-0.664305\pi$
$311$	56.3391	−	500.023i	0.181155	−	1.60779i	0.674714	−	0.738079i	$-0.264267\pi$
$312$		0			0
$313$	−36.9386	+	161.838i	−0.118015	+	0.517056i	0.881018	+	0.473082i	$0.156859\pi$
$313$	−36.9386	+	161.838i	−0.118015	+	0.517056i	−0.999033	+	0.0439731i	$0.985998\pi$
$314$	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	0.506416	−	0.862290i	$-0.330970\pi$
$317$	−16.0893	−	10.1096i	−0.0507550	−	0.0318915i	−0.557171	+	0.830398i	$0.688113\pi$
$318$		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	−0.756694	−	0.653769i	$-0.773187\pi$
$331$	−34.0680	+	34.0680i	−0.102924	+	0.102924i	0.653769	+	0.756694i	$0.273187\pi$
$332$	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	0.974876	+	0.222748i	$0.0715027\pi$
$337$	24.9408	+	221.356i	0.0740083	+	0.656841i	−0.900868	+	0.434093i	$0.857069\pi$
$338$	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	$-0.804171\pi$
$347$		−	400.531i		−	1.15427i	0.816649	−	0.577134i	$-0.195829\pi$
$348$		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	−0.457609	−	0.889154i	$-0.651294\pi$
$353$	−170.891	+	39.0048i	−0.484111	+	0.110495i	−0.0265018	+	0.999649i	$0.508437\pi$
$354$		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	0.319435	−	0.947608i	$-0.396507\pi$
$359$	302.179	−	34.0473i	0.841723	−	0.0948394i	0.522288	+	0.852769i	$0.325078\pi$
$360$		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	0.466336	−	0.884608i	$-0.345574\pi$
$367$	102.535	+	35.8787i	0.279388	+	0.0977622i	−0.186948	+	0.982370i	$0.559860\pi$
$368$	−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	−0.877042	−	0.480414i	$-0.840486\pi$
$373$	−391.003	+	188.297i	−1.04826	+	0.504818i	−0.171223	+	0.985232i	$0.554772\pi$
$374$	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	−0.595963	−	0.803012i	$-0.703230\pi$
$379$	146.333	−	232.888i	0.386104	−	0.614481i	0.982067	+	0.188530i	$0.0603724\pi$
$380$	−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	0.491433	−	0.870915i	$-0.336473\pi$
$383$	213.072	+	48.6323i	0.556323	+	0.126977i	0.0648901	+	0.997892i	$0.479330\pi$
$384$		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	−0.739698	−	0.672939i	$-0.765032\pi$
$389$	−25.9695	+	25.9695i	−0.0667597	+	0.0667597i	0.672939	+	0.739698i	$0.265032\pi$
$390$		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	0.875942	−	0.482416i	$-0.160241\pi$
$397$	83.6502	+	104.894i	0.210706	+	0.264217i	−0.665236	+	0.746633i	$0.731669\pi$
$398$	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	−0.917236	−	0.398345i	$-0.869585\pi$
$401$	−105.732	−	463.241i	−0.263670	−	1.15521i	0.653566	−	0.756870i	$-0.273272\pi$
$402$		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	0.955080	−	0.296347i	$-0.0957684\pi$
$409$	9.65215	+	27.5843i	0.0235994	+	0.0674432i	−0.931481	+	0.363790i	$0.881483\pi$
$410$	−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	0.394758	−	0.918785i	$-0.370828\pi$
$419$	−173.110	−	138.050i	−0.413149	−	0.329476i	−0.807907	+	0.589309i	$0.799400\pi$
$420$		0			0
$421$	65.2084	+	103.779i	0.154889	+	0.246505i	0.915150	−	0.403113i	$-0.132072\pi$
$421$	65.2084	+	103.779i	0.154889	+	0.246505i	−0.760261	+	0.649618i	$0.774929\pi$
$422$	−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	−0.629013	−	0.777395i	$-0.716541\pi$
$431$	−178.177	+	85.8056i	−0.413404	+	0.199085i	0.215609	+	0.976480i	$0.430826\pi$
$432$		0			0
$433$	−148.885	−	93.5509i	−0.343846	−	0.216053i	0.349026	−	0.937113i	$-0.386512\pi$
$433$	−148.885	−	93.5509i	−0.343846	−	0.216053i	−0.692873	+	0.721060i	$0.743655\pi$
$434$		−	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	0.760511	−	0.649325i	$-0.224949\pi$
$439$	−97.1608	−	201.756i	−0.221323	−	0.459582i	−0.981834	+	0.189743i	$0.939234\pi$
$440$	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	−0.0854526	−	0.996342i	$-0.527234\pi$
$443$	−172.978	−	19.4899i	−0.390470	−	0.0439954i	−0.305017	+	0.952347i	$0.598662\pi$
$444$		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	−0.0397845	−	0.999208i	$-0.512667\pi$
$449$	378.601	−	237.891i	0.843209	−	0.529823i	0.882994	+	0.469385i	$0.155524\pi$
$450$		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	−0.876501	−	0.481400i	$-0.840128\pi$
$457$	21.1875	−	43.9964i	0.0463622	−	0.0962722i	0.922863	+	0.385128i	$0.125843\pi$
$458$	−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	−0.841732	−	0.539895i	$-0.818464\pi$
$461$	−536.238	+	187.638i	−1.16321	+	0.407023i	−0.321474	+	0.946918i	$0.604178\pi$
$462$		0			0
$463$			50.1618i			0.108341i	0.998532	+	0.0541704i	$0.0172514\pi$
$463$			50.1618i			0.108341i	−0.998532	+	0.0541704i	$0.982749\pi$
$464$	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	0.991002	−	0.133850i	$-0.0427340\pi$
$467$	61.9948	+	177.171i	0.132751	+	0.379381i	−0.858250	+	0.513231i	$0.828448\pi$
$468$		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	0.829974	−	0.557802i	$-0.188355\pi$
$479$	−15.6633	−	24.9280i	−0.0327000	−	0.0520418i	−0.862674	+	0.505760i	$0.831212\pi$
$480$		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	−0.917552	−	0.397616i	$-0.869838\pi$
$487$	39.7649	−	174.221i	0.0816527	−	0.357744i	0.999205	+	0.0398716i	$0.0126949\pi$
$488$	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	0.165607	−	0.986192i	$-0.447042\pi$
$491$	−319.674	−	200.864i	−0.651066	−	0.409092i	−0.816674	+	0.577100i	$0.804184\pi$
$492$		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	−0.396707	−	0.917945i	$-0.629847\pi$
$499$	−575.053	−	131.252i	−1.15241	−	0.263030i	−0.755703	+	0.654915i	$0.772704\pi$
$500$	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	0.756313	+	0.654209i	$0.226999\pi$
$503$	−122.173	+	349.151i	−0.242889	+	0.694137i	−0.999203	+	0.0399278i	$0.987287\pi$
$504$		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	−0.316440	+	0.948613i	$0.602487\pi$
$509$	−595.965	+	747.316i	−1.17085	+	1.46820i	−0.854414	+	0.519592i	$0.826084\pi$
$510$		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	$0.0507225\pi$
$521$			165.340i			0.317352i	−0.987331	+	0.158676i	$0.949278\pi$
$522$		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	0.558879	−	0.829250i	$-0.311232\pi$
$541$	259.030	+	90.6386i	0.478799	+	0.167539i	−0.0800798	+	0.996788i	$0.525518\pi$
$542$	−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	0.0906647	−	0.995881i	$-0.471101\pi$
$547$	506.415	−	243.877i	0.925805	−	0.445844i	0.835140	+	0.550037i	$0.185387\pi$
$548$	−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	0.506887	−	0.862013i	$-0.330796\pi$
$557$	328.386	+	74.9521i	0.589563	+	0.134564i	0.0826759	+	0.996576i	$0.473653\pi$
$558$		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	−0.832181	−	0.554504i	$-0.812908\pi$
$563$	−156.332	+	156.332i	−0.277677	+	0.277677i	0.554504	+	0.832181i	$0.312908\pi$
$564$		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	0.983481	+	0.181014i	$0.0579379\pi$
$569$	36.9493	+	327.934i	0.0649373	+	0.576334i	−0.918543	+	0.395321i	$0.870634\pi$
$570$		0			0
$571$	126.849	+	159.064i	0.222153	+	0.278570i	0.880401	−	0.474231i	$-0.157274\pi$
$571$	126.849	+	159.064i	0.222153	+	0.278570i	−0.658248	+	0.752801i	$0.728702\pi$
$572$	−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	0.257223	−	0.966352i	$-0.417192\pi$
$577$	612.104	−	214.185i	1.06084	−	0.371204i	0.803616	+	0.595148i	$0.202907\pi$
$578$	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	0.922815	−	0.385244i	$-0.125883\pi$
$587$	702.630	+	338.369i	1.19698	+	0.576437i	0.274170	+	0.961681i	$0.411597\pi$
$588$		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	0.998694	−	0.0510897i	$-0.0162694\pi$
$593$	694.472	+	553.823i	1.17112	+	0.933934i	0.172422	+	0.985023i	$0.444841\pi$
$594$		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	0.198799	−	0.980040i	$-0.436296\pi$
$599$	−153.834	−	53.8288i	−0.256818	−	0.0898645i	−0.455617	+	0.890176i	$0.650581\pi$
$600$		0			0
$601$	56.1166	−	498.048i	0.0933720	−	0.828699i	−0.856518	−	0.516116i	$-0.827377\pi$
$601$	56.1166	−	498.048i	0.0933720	−	0.828699i	0.949890	−	0.312583i	$-0.101194\pi$
$602$	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	0.991535	−	0.129842i	$-0.0414471\pi$
$607$	791.990	+	497.641i	1.30476	+	0.819836i	0.313227	+	0.949678i	$0.398590\pi$
$608$			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	0.987673	−	0.156531i	$-0.0500312\pi$
$613$	152.936	+	317.575i	0.249488	+	0.518067i	−0.738185	+	0.674598i	$0.764317\pi$
$614$	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	0.761566	−	0.648087i	$-0.224431\pi$
$617$	839.013	+	94.5340i	1.35983	+	0.153216i	0.598260	+	0.801302i	$0.295859\pi$
$618$		0			0
$619$	−171.638	+	490.514i	−0.277283	+	0.792430i	0.718055	+	0.695986i	$0.245032\pi$
$619$	−171.638	+	490.514i	−0.277283	+	0.792430i	−0.995338	+	0.0964436i	$0.969253\pi$
$620$	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	−0.999768	−	0.0215372i	$-0.993144\pi$
$631$	−226.898	+	471.158i	−0.359584	+	0.746685i	0.640184	+	0.768222i	$0.278858\pi$
$632$	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	0.920415	+	0.390944i	$0.127851\pi$
$641$	284.960	+	814.368i	0.444555	+	1.27046i	−0.475860	+	0.879521i	$0.657863\pi$
$642$		0			0
$643$	221.189	−	50.4849i	0.343995	−	0.0785147i	−0.0470331	−	0.998893i	$-0.514977\pi$
$643$	221.189	−	50.4849i	0.343995	−	0.0785147i	0.391028	+	0.920379i	$0.372119\pi$
$644$	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	−0.977400	−	0.211398i	$-0.932198\pi$
$647$	−639.749	+	510.183i	−0.988794	+	0.788537i	−0.0113937	+	0.999935i	$0.503627\pi$
$648$		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	−0.994293	−	0.106685i	$-0.965976\pi$
$653$	−430.330	−	684.867i	−0.659005	−	1.04880i	0.335288	−	0.942116i	$-0.391166\pi$
$654$		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	−0.981391	−	0.192018i	$-0.938497\pi$
$659$	11.9427	−	105.994i	0.0181225	−	0.160841i	0.999514	+	0.0311765i	$0.00992540\pi$
$660$		0			0
$661$	58.7442	−	257.375i	0.0888717	−	0.389372i	−0.910856	−	0.412725i	$-0.864577\pi$
$661$	58.7442	−	257.375i	0.0888717	−	0.389372i	0.999727	+	0.0233529i	$0.00743414\pi$
$662$	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	0.506642	−	0.862156i	$-0.330887\pi$
$673$	396.421	+	90.4804i	0.589035	+	0.134443i	0.0823931	+	0.996600i	$0.473744\pi$
$674$	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	−0.746256	−	0.665659i	$-0.768150\pi$
$677$	170.754	−	487.988i	0.252222	−	0.720810i	0.998478	−	0.0551504i	$-0.0175638\pi$
$678$		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	−0.910359	−	0.413820i	$-0.864194\pi$
$683$	−207.865	+	260.654i	−0.304341	+	0.381631i	0.606018	+	0.795451i	$0.292766\pi$
$684$		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	0.994122	−	0.108266i	$-0.0345298\pi$
$691$	35.5687	+	155.837i	0.0514743	+	0.225523i	−0.942648	+	0.333789i	$0.891673\pi$
$692$	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	−0.903240	−	0.429135i	$-0.858818\pi$
$701$	−1073.12	+	244.932i	−1.53084	+	0.349404i	−0.627597	+	0.778539i	$0.715961\pi$
$702$		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	0.758859	−	0.651255i	$-0.225757\pi$
$709$	207.591	+	165.548i	0.292794	+	0.233496i	−0.466065	+	0.884751i	$0.654329\pi$
$710$	−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	−0.426279	−	0.904592i	$-0.640176\pi$
$719$	251.846	−	1103.41i	0.350273	−	1.53465i	0.776552	−	0.630054i	$-0.216967\pi$
$720$		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	−0.829007	−	0.559238i	$-0.811094\pi$
$727$	25.1121	−	39.9657i	0.0345421	−	0.0549734i	0.863549	+	0.504265i	$0.168237\pi$
$728$	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	0.191488	−	0.981495i	$-0.438669\pi$
$733$	117.112	+	13.1954i	0.159771	+	0.0180019i	−0.0317165	+	0.999497i	$0.510097\pi$
$734$	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	−0.989913	−	0.141674i	$-0.954752\pi$
$739$	−954.623	+	599.830i	−1.29178	+	0.811677i	−0.301864	+	0.953351i	$0.597609\pi$
$740$	−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	−0.914098	−	0.405492i	$-0.867100\pi$
$743$	−84.0696	−	746.139i	−0.113149	−	1.00422i	0.800950	−	0.598732i	$-0.204328\pi$
$744$		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	−0.961303	−	0.275495i	$-0.911158\pi$
$751$	−1157.37	+	404.983i	−1.54111	+	0.539258i	−0.579808	+	0.814753i	$0.696873\pi$
$752$	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	0.908741	+	0.417360i	$0.137045\pi$
$757$	347.068	+	991.864i	0.458478	+	1.31026i	−0.450263	+	0.892896i	$0.648670\pi$
$758$	−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	0.334491	−	0.942399i	$-0.391435\pi$
$761$	−147.446	−	71.0065i	−0.193754	−	0.0933068i	−0.528245	+	0.849092i	$0.677150\pi$
$762$		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	0.999711	+	0.0240371i	$0.00765197\pi$
$769$	451.872	+	719.149i	0.587609	+	0.935175i	−0.412102	+	0.911138i	$0.635205\pi$
$770$	−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	−0.521897	−	0.853008i	$-0.674776\pi$
$773$	−1129.95	−	395.387i	−1.46177	−	0.511497i	−0.939878	+	0.341511i	$0.889061\pi$
$774$		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	−0.705371	−	0.708839i	$-0.749219\pi$
$787$	−645.160	−	1339.69i	−0.819772	−	1.70227i	−0.114401	−	0.993435i	$-0.536495\pi$
$788$	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	−0.450491	−	0.892781i	$-0.648751\pi$
$797$	126.257	−	79.3327i	0.158416	−	0.0995391i	0.608907	+	0.793242i	$0.291608\pi$
$798$		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	−0.966088	−	0.258214i	$-0.916866\pi$
$809$	−1262.37	+	441.723i	−1.56041	+	0.546012i	−0.594324	+	0.804226i	$0.702580\pi$
$810$		0			0
$811$			1098.94i			1.35504i	0.735502	+	0.677522i	$0.236946\pi$
$811$			1098.94i			1.35504i	−0.735502	+	0.677522i	$0.763054\pi$
$812$	−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	−0.229490	−	0.973311i	$-0.573706\pi$
$821$	548.717	−	437.587i	0.668352	−	0.532993i	0.897842	+	0.440318i	$0.145134\pi$
$822$		0			0
$823$	1160.52	−	130.760i	1.41011	−	0.158882i	0.626158	−	0.779696i	$-0.284627\pi$
$823$	1160.52	−	130.760i	1.41011	−	0.158882i	0.783957	+	0.620815i	$0.213198\pi$
$824$	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	0.725703	−	0.688008i	$-0.241515\pi$
$827$	−172.877	−	275.132i	−0.209041	−	0.332687i	−0.934744	+	0.355321i	$0.884372\pi$
$828$		0			0
$829$	−428.233	−	428.233i	−0.516566	−	0.516566i	0.399964	−	0.916531i	$-0.369022\pi$
$829$	−428.233	−	428.233i	−0.516566	−	0.516566i	−0.916531	+	0.399964i	$0.869022\pi$
$830$	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	0.912315	−	0.409489i	$-0.134293\pi$
$839$	788.003	+	495.135i	0.939217	+	0.590149i	0.0269021	+	0.999638i	$0.491436\pi$
$840$		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	−0.138067	+	0.990423i	$0.544089\pi$
$853$	−962.602	+	962.602i	−1.12849	+	1.12849i	−0.990423	+	0.138067i	$0.955911\pi$
$854$	−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	−0.872740	−	0.488185i	$-0.837659\pi$
$857$	−173.622	+	217.715i	−0.202592	+	0.254043i	0.670148	+	0.742228i	$0.266231\pi$
$858$		0			0
$859$	85.2609	+	756.711i	0.0992560	+	0.880921i	0.940391	+	0.340096i	$0.110459\pi$
$859$	85.2609	+	756.711i	0.0992560	+	0.880921i	−0.841135	+	0.540825i	$0.818112\pi$
$860$	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	0.261016	+	0.965335i	$0.415943\pi$
$863$	−566.520	+	1176.39i	−0.656454	+	1.36314i	−0.917470	+	0.397806i	$0.869772\pi$
$864$		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	−0.0893654	−	0.995999i	$-0.528484\pi$
$877$	−810.161	−	390.153i	−0.923787	−	0.444872i	−0.834422	+	0.551126i	$0.814198\pi$
$878$	−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	0.0428534	−	0.999081i	$-0.486355\pi$
$881$	270.422	−	30.4692i	0.306949	−	0.0345848i	0.264096	+	0.964497i	$0.414927\pi$
$882$		0			0
$883$	33.8605	+	27.0028i	0.0383471	+	0.0305808i	0.642476	−	0.766306i	$-0.277907\pi$
$883$	33.8605	+	27.0028i	0.0383471	+	0.0305808i	−0.604129	+	0.796887i	$0.706479\pi$
$884$	−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	0.827113	−	0.562036i	$-0.189982\pi$
$887$	235.123	+	235.123i	0.265076	+	0.265076i	−0.562036	+	0.827113i	$0.689982\pi$
$888$		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	−0.647574	−	0.762003i	$-0.724216\pi$
$907$	−1313.77	−	148.026i	−1.44847	−	0.163204i	−0.800899	+	0.598799i	$0.795645\pi$
$908$	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	−0.370681	−	0.928760i	$-0.620876\pi$
$911$	508.410	−	508.410i	0.558079	−	0.558079i	0.928760	+	0.370681i	$0.120876\pi$
$912$		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	−0.974104	−	0.226098i	$-0.927403\pi$
$919$	−898.576	−	1126.78i	−0.977776	−	1.22609i	−0.00367108	−	0.999993i	$-0.501169\pi$
$920$	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	−0.0342755	−	0.999412i	$-0.510912\pi$
$937$	873.708	−	696.759i	0.932453	−	0.743606i	0.966728	+	0.255806i	$0.0823409\pi$
$938$	−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	−0.171815	−	0.985129i	$-0.554963\pi$
$941$	−1101.42	−	878.352i	−1.17048	−	0.933424i	−0.998662	+	0.0517051i	$0.983534\pi$
$942$		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	0.290146	−	0.956982i	$-0.406296\pi$
$947$	−75.4551	−	26.4029i	−0.0796780	−	0.0278805i	−0.369824	+	0.929102i	$0.620582\pi$
$948$		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	−0.974563	−	0.224115i	$-0.928051\pi$
$953$	−1340.84	+	645.717i	−1.40697	+	0.677562i	−0.432409	+	0.901677i	$0.642336\pi$
$954$		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	0.378449	+	0.925622i	$0.376458\pi$
$967$	−478.230	+	1366.70i	−0.494550	+	1.41334i	−0.872999	+	0.487721i	$0.837828\pi$
$968$	−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	−0.372596	−	0.927994i	$-0.621532\pi$
$971$	293.082	−	184.155i	0.301835	−	0.189655i	0.674430	+	0.738338i	$0.264389\pi$
$972$		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	1.00000		0.000687874i	$0.000218957\pi$
$977$	760.252	+	953.326i	0.778150	+	0.975769i	−0.221850	+	0.975081i	$0.571210\pi$
$978$		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	−0.00459679	−	0.999989i	$-0.501463\pi$
$983$	604.833	−	211.640i	0.615293	−	0.215300i	0.619889	+	0.784689i	$0.287177\pi$
$984$		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	0.377829	−	0.925876i	$-0.376671\pi$
$991$	1109.88	−	253.324i	1.11996	−	0.255624i	0.742134	+	0.670251i	$0.233814\pi$
$992$	−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	0.277928	−	0.960602i	$-0.410352\pi$
$997$	760.354	−	85.6713i	0.762642	−	0.0859291i	0.484714	+	0.874673i	$0.338924\pi$
$998$	−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.55.3		48
3.2	odd	2		29.3.f.a.26.2	yes	48
29.19	odd	28	inner	261.3.s.a.19.3		48
87.77	even	28		29.3.f.a.19.2	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.f.a.19.2	✓	48	87.77	even	28
29.3.f.a.26.2	yes	48	3.2	odd	2
261.3.s.a.19.3		48	29.19	odd	28	inner
261.3.s.a.55.3		48	1.1	even	1	trivial

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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