LMFDB - Embedded newform 261.3.s.a.73.2

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			73.2
Character	$\chi$	$=$	261.73
Dual form			261.3.s.a.118.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415096 + 0.0467701i) q^{2} +(-3.72959 + 0.851255i) q^{4} +(-0.738700 - 0.589093i) q^{5} +(-0.577468 + 2.53005i) q^{7} +(3.08546 - 1.07965i) q^{8} +O(q^{10})$	\(q+(-0.415096 + 0.0467701i) q^{2} +(-3.72959 + 0.851255i) q^{4} +(-0.738700 - 0.589093i) q^{5} +(-0.577468 + 2.53005i) q^{7} +(3.08546 - 1.07965i) q^{8} +(0.334184 + 0.209981i) q^{10} +(8.65125 + 3.02720i) q^{11} +(-4.51239 - 9.37008i) q^{13} +(0.121374 - 1.07722i) q^{14} +(12.5564 - 6.04684i) q^{16} +(-21.4949 - 21.4949i) q^{17} +(14.2589 - 22.6929i) q^{19} +(3.25652 + 1.56826i) q^{20} +(-3.73269 - 0.851961i) q^{22} +(2.27710 + 2.85539i) q^{23} +(-5.36438 - 23.5029i) q^{25} +(2.31132 + 3.67844i) q^{26} -9.92764i q^{28} +(24.3191 - 15.7981i) q^{29} +(21.7090 - 2.44602i) q^{31} +(-16.0007 + 10.0539i) q^{32} +(9.92777 + 7.91713i) q^{34} +(1.91701 - 1.52877i) q^{35} +(-46.0478 + 16.1128i) q^{37} +(-4.85746 + 10.0866i) q^{38} +(-2.91524 - 1.02009i) q^{40} +(25.3355 - 25.3355i) q^{41} +(2.78030 - 24.6759i) q^{43} +(-34.8426 - 3.92581i) q^{44} +(-1.07876 - 1.07876i) q^{46} +(-7.49184 + 21.4104i) q^{47} +(38.0798 + 18.3383i) q^{49} +(3.32597 + 9.50507i) q^{50} +(24.8057 + 31.1054i) q^{52} +(18.6271 - 23.3576i) q^{53} +(-4.60737 - 7.33259i) q^{55} +(0.949813 + 8.42982i) q^{56} +(-9.35591 + 7.69514i) q^{58} -18.2577 q^{59} +(-78.8333 + 49.5342i) q^{61} +(-8.89694 + 2.03067i) q^{62} +(-37.4125 + 29.8355i) q^{64} +(-2.18655 + 9.57990i) q^{65} +(24.5454 - 50.9691i) q^{67} +(98.4648 + 61.8696i) q^{68} +(-0.724244 + 0.724244i) q^{70} +(-56.1438 - 116.584i) q^{71} +(47.2614 + 5.32509i) q^{73} +(18.3607 - 8.84204i) q^{74} +(-33.8624 + 96.7732i) q^{76} +(-12.6548 + 20.1400i) q^{77} +(-13.7375 - 39.2594i) q^{79} +(-12.8375 - 2.93009i) q^{80} +(-9.33174 + 11.7016i) q^{82} +(29.4538 + 129.046i) q^{83} +(3.21577 + 28.5408i) q^{85} +10.3729i q^{86} +29.9614 q^{88} +(-32.3276 + 3.64244i) q^{89} +(26.3125 - 6.00567i) q^{91} +(-10.9233 - 8.71105i) q^{92} +(2.10847 - 9.23779i) q^{94} +(-23.9012 + 8.36341i) q^{95} +(-36.1089 - 22.6888i) q^{97} +(-16.6645 - 5.83115i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{27}{28}\right)$	$1$

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 $

$2$	−0.415096	+	0.0467701i	−0.207548	+	0.0233851i	−0.215126	−	0.976586i	$-0.569016\pi$
$2$	−0.415096	+	0.0467701i	−0.207548	+	0.0233851i	0.00757815	+	0.999971i	$0.497588\pi$
$3$		0			0
$3$		0			0
$4$	−3.72959	+	0.851255i	−0.932398	+	0.212814i
$5$	−0.738700	−	0.589093i	−0.147740	−	0.117819i	0.546831	−	0.837243i	$-0.315834\pi$
$5$	−0.738700	−	0.589093i	−0.147740	−	0.117819i	−0.694571	+	0.719425i	$0.744406\pi$
$6$		0			0
$7$	−0.577468	+	2.53005i	−0.0824954	+	0.361436i	−0.999280	−	0.0379466i	$-0.987918\pi$
$7$	−0.577468	+	2.53005i	−0.0824954	+	0.361436i	0.916784	+	0.399383i	$0.130775\pi$
$8$	3.08546	−	1.07965i	0.385682	−	0.134956i
$9$		0			0
$10$	0.334184	+	0.209981i	0.0334184	+	0.0209981i
$11$	8.65125	+	3.02720i	0.786477	+	0.275200i	0.693489	−	0.720467i	$-0.256072\pi$
$11$	8.65125	+	3.02720i	0.786477	+	0.275200i	0.0929879	+	0.995667i	$0.470358\pi$
$12$		0			0
$13$	−4.51239	−	9.37008i	−0.347107	−	0.720775i	0.652198	−	0.758049i	$-0.273847\pi$
$13$	−4.51239	−	9.37008i	−0.347107	−	0.720775i	−0.999305	+	0.0372733i	$0.988133\pi$
$14$	0.121374	−	1.07722i	0.00866957	−	0.0769445i
$15$		0			0
$16$	12.5564	−	6.04684i	0.784774	−	0.377927i
$17$	−21.4949	−	21.4949i	−1.26441	−	1.26441i	−0.948936	−	0.315469i	$-0.897838\pi$
$17$	−21.4949	−	21.4949i	−1.26441	−	1.26441i	−0.315469	−	0.948936i	$-0.602162\pi$
$18$		0			0
$19$	14.2589	−	22.6929i	0.750467	−	1.19436i	−0.225030	−	0.974352i	$-0.572248\pi$
$19$	14.2589	−	22.6929i	0.750467	−	1.19436i	0.975498	−	0.220010i	$-0.0706090\pi$
$20$	3.25652	+	1.56826i	0.162826	+	0.0784128i
$21$		0			0
$22$	−3.73269	−	0.851961i	−0.169668	−	0.0387255i
$23$	2.27710	+	2.85539i	0.0990042	+	0.124147i	0.828866	−	0.559448i	$-0.188987\pi$
$23$	2.27710	+	2.85539i	0.0990042	+	0.124147i	−0.729861	+	0.683595i	$0.760415\pi$
$24$		0			0
$25$	−5.36438	−	23.5029i	−0.214575	−	0.940115i
$26$	2.31132	+	3.67844i	0.0888969	+	0.141479i
$27$		0			0
$28$		−	9.92764i		−	0.354558i
$29$	24.3191	−	15.7981i	0.838591	−	0.544761i
$29$	24.3191	−	15.7981i	0.838591	−	0.544761i
$30$		0			0
$31$	21.7090	−	2.44602i	0.700291	−	0.0789039i	0.245362	−	0.969431i	$-0.421093\pi$
$31$	21.7090	−	2.44602i	0.700291	−	0.0789039i	0.454929	+	0.890528i	$0.349665\pi$
$32$	−16.0007	+	10.0539i	−0.500022	+	0.314185i
$33$		0			0
$34$	9.92777	+	7.91713i	0.291993	+	0.232857i
$35$	1.91701	−	1.52877i	0.0547718	−	0.0436790i
$36$		0			0
$37$	−46.0478	+	16.1128i	−1.24454	+	0.435482i	−0.870608	−	0.491976i	$-0.836275\pi$
$37$	−46.0478	+	16.1128i	−1.24454	+	0.435482i	−0.373927	+	0.927458i	$0.621989\pi$
$38$	−4.85746	+	10.0866i	−0.127828	+	0.265437i
$39$		0			0
$40$	−2.91524	−	1.02009i	−0.0728810	−	0.0255021i
$41$	25.3355	−	25.3355i	0.617940	−	0.617940i	−0.327063	−	0.945003i	$-0.606059\pi$
$41$	25.3355	−	25.3355i	0.617940	−	0.617940i	0.945003	+	0.327063i	$0.106059\pi$
$42$		0			0
$43$	2.78030	−	24.6759i	0.0646582	−	0.573857i	−0.919057	−	0.394124i	$-0.871048\pi$
$43$	2.78030	−	24.6759i	0.0646582	−	0.573857i	0.983715	−	0.179733i	$-0.0575234\pi$
$44$	−34.8426	−	3.92581i	−0.791877	−	0.0892231i
$45$		0			0
$46$	−1.07876	−	1.07876i	−0.0234513	−	0.0234513i
$47$	−7.49184	+	21.4104i	−0.159401	+	0.455541i	−0.995690	−	0.0927479i	$-0.970435\pi$
$47$	−7.49184	+	21.4104i	−0.159401	+	0.455541i	0.836289	+	0.548289i	$0.184721\pi$
$48$		0			0
$49$	38.0798	+	18.3383i	0.777138	+	0.374250i
$50$	3.32597	+	9.50507i	0.0665193	+	0.190101i
$51$		0			0
$52$	24.8057	+	31.1054i	0.477033	+	0.598181i
$53$	18.6271	−	23.3576i	0.351454	−	0.440709i	−0.574409	−	0.818568i	$-0.694768\pi$
$53$	18.6271	−	23.3576i	0.351454	−	0.440709i	0.925863	+	0.377859i	$0.123340\pi$
$54$		0			0
$55$	−4.60737	−	7.33259i	−0.0837704	−	0.133320i
$56$	0.949813	+	8.42982i	0.0169609	+	0.150533i
$57$		0			0
$58$	−9.35591	+	7.69514i	−0.161309	+	0.132675i
$59$	−18.2577			−0.309453			−0.154726	−	0.987957i	$-0.549450\pi$
$59$	−18.2577			−0.309453			−0.154726	+	0.987957i	$0.549450\pi$
$60$		0			0
$61$	−78.8333	+	49.5342i	−1.29235	+	0.812037i	−0.989987	−	0.141156i	$-0.954918\pi$
$61$	−78.8333	+	49.5342i	−1.29235	+	0.812037i	−0.302362	+	0.953193i	$0.597775\pi$
$62$	−8.89694	+	2.03067i	−0.143499	+	0.0327527i
$63$		0			0
$64$	−37.4125	+	29.8355i	−0.584570	+	0.466179i
$65$	−2.18655	+	9.57990i	−0.0336392	+	0.147383i
$66$		0			0
$67$	24.5454	−	50.9691i	0.366349	−	0.760732i	−0.633567	−	0.773688i	$-0.718410\pi$
$67$	24.5454	−	50.9691i	0.366349	−	0.760732i	0.999916	+	0.0129558i	$0.00412406\pi$
$68$	98.4648	+	61.8696i	1.44801	+	0.909846i
$69$		0			0
$70$	−0.724244	+	0.724244i	−0.0103463	+	0.0103463i
$71$	−56.1438	−	116.584i	−0.790758	−	1.64203i	−0.766436	−	0.642321i	$-0.777972\pi$
$71$	−56.1438	−	116.584i	−0.790758	−	1.64203i	−0.0243218	−	0.999704i	$-0.507743\pi$
$72$		0			0
$73$	47.2614	+	5.32509i	0.647417	+	0.0729464i	0.429566	−	0.903036i	$-0.358667\pi$
$73$	47.2614	+	5.32509i	0.647417	+	0.0729464i	0.217851	+	0.975982i	$0.430095\pi$
$74$	18.3607	−	8.84204i	0.248117	−	0.119487i
$75$		0			0
$76$	−33.8624	+	96.7732i	−0.445558	+	1.27333i
$77$	−12.6548	+	20.1400i	−0.164348	+	0.261558i
$78$		0			0
$79$	−13.7375	−	39.2594i	−0.173892	−	0.496954i	0.823644	−	0.567107i	$-0.191937\pi$
$79$	−13.7375	−	39.2594i	−0.173892	−	0.496954i	−0.997536	+	0.0701522i	$0.977652\pi$
$80$	−12.8375	−	2.93009i	−0.160469	−	0.0366261i
$81$		0			0
$82$	−9.33174	+	11.7016i	−0.113802	+	0.142703i
$83$	29.4538	+	129.046i	0.354865	+	1.55477i	0.765786	+	0.643095i	$0.222350\pi$
$83$	29.4538	+	129.046i	0.354865	+	1.55477i	−0.410921	+	0.911671i	$0.634793\pi$
$84$		0			0
$85$	3.21577	+	28.5408i	0.0378326	+	0.335774i
$86$			10.3729i			0.120615i
$87$		0			0
$88$	29.9614			0.340470
$89$	−32.3276	+	3.64244i	−0.363231	+	0.0409263i	−0.291694	−	0.956512i	$-0.594219\pi$
$89$	−32.3276	+	3.64244i	−0.363231	+	0.0409263i	−0.0715370	+	0.997438i	$0.522790\pi$
$90$		0			0
$91$	26.3125	−	6.00567i	0.289149	−	0.0659963i
$92$	−10.9233	−	8.71105i	−0.118732	−	0.0946853i
$93$		0			0
$94$	2.10847	−	9.23779i	0.0224305	−	0.0982744i
$95$	−23.9012	+	8.36341i	−0.251592	+	0.0880359i
$96$		0			0
$97$	−36.1089	−	22.6888i	−0.372257	−	0.233905i	0.332890	−	0.942966i	$-0.391976\pi$
$97$	−36.1089	−	22.6888i	−0.372257	−	0.233905i	−0.705147	+	0.709061i	$0.749119\pi$
$98$	−16.6645	−	5.83115i	−0.170046	−	0.0595015i
$99$		0			0
$100$	40.0139	+	83.0897i	0.400139	+	0.830897i
$101$	−10.9637	+	97.3053i	−0.108551	+	0.963419i	0.814873	+	0.579639i	$0.196806\pi$
$101$	−10.9637	+	97.3053i	−0.108551	+	0.963419i	−0.923425	+	0.383780i	$0.874622\pi$
$102$		0			0
$103$	−66.1244	+	31.8438i	−0.641985	+	0.309164i	−0.726405	−	0.687267i	$-0.758810\pi$
$103$	−66.1244	+	31.8438i	−0.641985	+	0.309164i	0.0844205	+	0.996430i	$0.473096\pi$
$104$	−24.0392	−	24.0392i	−0.231146	−	0.231146i
$105$		0			0
$106$	−6.63959	+	10.5668i	−0.0626376	+	0.0996872i
$107$	−55.3820	−	26.6706i	−0.517589	−	0.249258i	0.156805	−	0.987630i	$-0.449881\pi$
$107$	−55.3820	−	26.6706i	−0.517589	−	0.249258i	−0.674394	+	0.738372i	$0.735595\pi$
$108$		0			0
$109$	154.567	+	35.2790i	1.41805	+	0.323660i	0.861755	−	0.507325i	$-0.169366\pi$
$109$	154.567	+	35.2790i	1.41805	+	0.323660i	0.556294	+	0.830985i	$0.312223\pi$
$110$	2.25545	+	2.82824i	0.0205041	+	0.0257113i
$111$		0			0
$112$	8.04790	+	35.2602i	0.0718562	+	0.314823i
$113$	46.5316	+	74.0546i	0.411784	+	0.655351i	0.986642	−	0.162902i	$-0.0520856\pi$
$113$	46.5316	+	74.0546i	0.411784	+	0.655351i	−0.574858	+	0.818253i	$0.694943\pi$
$114$		0			0
$115$		−	3.45070i		−	0.0300061i
$116$	−77.2523	+	79.6222i	−0.665968	+	0.686398i
$117$		0			0
$118$	7.57871	−	0.853915i	0.0642263	−	0.00723657i
$119$	66.7958	−	41.9706i	0.561309	−	0.352694i
$120$		0			0
$121$	−28.9215	−	23.0641i	−0.239020	−	0.190612i
$122$	30.4067	−	24.2485i	0.249235	−	0.198759i
$123$		0			0
$124$	−78.8837	+	27.6026i	−0.636159	+	0.222602i
$125$	−20.1314	+	41.8033i	−0.161051	+	0.334426i
$126$		0			0
$127$	−171.713	−	60.0851i	−1.35207	−	0.473111i	−0.445546	−	0.895259i	$-0.646990\pi$
$127$	−171.713	−	60.0851i	−1.35207	−	0.473111i	−0.906527	+	0.422148i	$0.861276\pi$
$128$	67.5837	−	67.5837i	0.527998	−	0.527998i
$129$		0			0
$130$	0.459576	−	4.07885i	0.00353520	−	0.0313757i
$131$	72.7489	+	8.19683i	0.555335	+	0.0625712i	0.385172	−	0.922845i	$-0.374142\pi$
$131$	72.7489	+	8.19683i	0.555335	+	0.0625712i	0.170163	+	0.985416i	$0.445571\pi$
$132$		0			0
$133$	49.1801	+	49.1801i	0.369775	+	0.369775i
$134$	−7.80488	+	22.3051i	−0.0582454	+	0.166456i
$135$		0			0
$136$	−89.5284	−	43.1146i	−0.658297	−	0.317019i
$137$	−65.2470	−	186.465i	−0.476255	−	1.36106i	−0.892188	−	0.451664i	$-0.850831\pi$
$137$	−65.2470	−	186.465i	−0.476255	−	1.36106i	0.415933	−	0.909395i	$-0.363455\pi$
$138$		0			0
$139$	−38.5551	−	48.3466i	−0.277375	−	0.347817i	0.623557	−	0.781778i	$-0.285687\pi$
$139$	−38.5551	−	48.3466i	−0.277375	−	0.347817i	−0.900932	+	0.433961i	$0.857116\pi$
$140$	−5.84830	+	7.33354i	−0.0417736	+	0.0523824i
$141$		0			0
$142$	28.7577	+	45.7677i	0.202519	+	0.322308i
$143$	−10.6727	−	94.7228i	−0.0746343	−	0.662397i
$144$		0			0
$145$	−27.2711	−	2.65621i	−0.188076	−	0.0183187i
$146$	−19.8671			−0.136076
$147$		0			0
$148$	158.023	−	99.2927i	1.06773	−	0.670897i
$149$	29.6561	−	6.76882i	0.199034	−	0.0454283i	−0.121841	−	0.992550i	$-0.538880\pi$
$149$	29.6561	−	6.76882i	0.199034	−	0.0454283i	0.320876	+	0.947121i	$0.396023\pi$
$150$		0			0
$151$	110.649	−	88.2399i	0.732777	−	0.584370i	−0.184399	−	0.982851i	$-0.559034\pi$
$151$	110.649	−	88.2399i	0.732777	−	0.584370i	0.917177	+	0.398481i	$0.130463\pi$
$152$	19.4948	−	85.4124i	0.128255	−	0.561924i
$153$		0			0
$154$	4.31101	−	8.95191i	0.0279936	−	0.0581293i
$155$	−17.4774	−	10.9818i	−0.112757	−	0.0708501i
$156$		0			0
$157$	19.5784	−	19.5784i	0.124703	−	0.124703i	−0.642001	−	0.766704i	$-0.721895\pi$
$157$	19.5784	−	19.5784i	0.124703	−	0.124703i	0.766704	+	0.642001i	$0.221895\pi$
$158$	7.53854	+	15.6539i	0.0477123	+	0.0990755i
$159$		0			0
$160$	17.7424	+	1.99909i	0.110890	+	0.0124943i
$161$	−8.53923	+	4.11228i	−0.0530387	+	0.0255421i
$162$		0			0
$163$	34.1257	−	97.5257i	0.209360	−	0.598317i	−0.790541	−	0.612410i	$-0.790200\pi$
$163$	34.1257	−	97.5257i	0.209360	−	0.598317i	0.999901	+	0.0140927i	$0.00448600\pi$
$164$	−72.9242	+	116.058i	−0.444660	+	0.707672i
$165$		0			0
$166$	−18.2617	−	52.1888i	−0.110010	−	0.314390i
$167$	262.410	+	59.8934i	1.57132	+	0.358643i	0.917414	−	0.397934i	$-0.130273\pi$
$167$	262.410	+	59.8934i	1.57132	+	0.358643i	0.653904	+	0.756577i	$0.273130\pi$
$168$		0			0
$169$	37.9331	−	47.5666i	0.224456	−	0.281459i
$170$	−2.66971	−	11.6968i	−0.0157042	−	0.0688045i
$171$		0			0
$172$	10.6361	+	94.3977i	0.0618376	+	0.548824i
$173$		−	126.379i		−	0.730512i	−0.930907	−	0.365256i	$-0.880981\pi$
$173$		−	126.379i		−	0.730512i	0.930907	−	0.365256i	$-0.119019\pi$
$174$		0			0
$175$	62.5612			0.357493
$176$	126.933	−	14.3020i	0.721213	−	0.0812612i
$177$		0			0
$178$	13.2487	−	3.02393i	0.0744309	−	0.0169884i
$179$	−220.984	−	176.229i	−1.23455	−	0.984520i	−0.999923	−	0.0124338i	$-0.996042\pi$
$179$	−220.984	−	176.229i	−1.23455	−	0.984520i	−0.234626	−	0.972086i	$-0.575386\pi$
$180$		0			0
$181$	51.3580	−	225.014i	0.283746	−	1.24317i	−0.609204	−	0.793014i	$-0.708511\pi$
$181$	51.3580	−	225.014i	0.283746	−	1.24317i	0.892949	−	0.450157i	$-0.148632\pi$
$182$	−10.6414	+	3.72357i	−0.0584690	+	0.0204592i
$183$		0			0
$184$	10.1087	+	6.35171i	0.0549386	+	0.0345202i
$185$	43.5075	+	15.2239i	0.235175	+	0.0822914i
$186$		0			0
$187$	−120.888	−	251.027i	−0.646461	−	1.34239i
$188$	9.71575	−	86.2297i	0.0516795	−	0.458669i
$189$		0			0
$190$	9.53017	−	4.58949i	0.0501588	−	0.0241552i
$191$	−68.5806	−	68.5806i	−0.359061	−	0.359061i	0.504406	−	0.863467i	$-0.331711\pi$
$191$	−68.5806	−	68.5806i	−0.359061	−	0.359061i	−0.863467	+	0.504406i	$0.831711\pi$
$192$		0			0
$193$	−16.7176	+	26.6059i	−0.0866198	+	0.137855i	−0.887224	−	0.461339i	$-0.847369\pi$
$193$	−16.7176	+	26.6059i	−0.0866198	+	0.137855i	0.800604	+	0.599194i	$0.204512\pi$
$194$	16.0499	+	7.72920i	0.0827312	+	0.0398413i
$195$		0			0
$196$	−157.633	−	35.9786i	−0.804248	−	0.183564i
$197$	63.4701	+	79.5889i	0.322183	+	0.404005i	0.916377	−	0.400317i	$-0.131100\pi$
$197$	63.4701	+	79.5889i	0.322183	+	0.404005i	−0.594194	+	0.804322i	$0.702529\pi$
$198$		0			0
$199$	34.8200	+	152.557i	0.174975	+	0.766616i	0.983902	+	0.178707i	$0.0571915\pi$
$199$	34.8200	+	152.557i	0.174975	+	0.766616i	−0.808927	+	0.587909i	$0.799951\pi$
$200$	−41.9264	−	66.7254i	−0.209632	−	0.333627i
$201$		0			0
$202$		−	40.9039i		−	0.202494i
$203$	25.9264	+	70.6516i	0.127716	+	0.348037i
$204$		0			0
$205$	−33.6403	+	3.79036i	−0.164099	+	0.0184895i
$206$	25.9587	−	16.3109i	0.126013	−	0.0791792i
$207$		0			0
$208$	−113.319	−	90.3686i	−0.544801	−	0.434465i
$209$	192.053	−	153.157i	0.918914	−	0.732810i
$210$		0			0
$211$	−19.1966	+	6.71718i	−0.0909791	+	0.0318350i	−0.375385	−	0.926869i	$-0.622489\pi$
$211$	−19.1966	+	6.71718i	−0.0909791	+	0.0318350i	0.284406	+	0.958704i	$0.408204\pi$
$212$	−49.5881	+	102.971i	−0.233906	+	0.485711i
$213$		0			0
$214$	24.2363	+	8.48064i	0.113254	+	0.0396291i
$215$	−16.5902	+	16.5902i	−0.0771637	+	0.0771637i
$216$		0			0
$217$	−6.34771	+	56.3375i	−0.0292521	+	0.259620i
$218$	−65.8104	−	7.41505i	−0.301882	−	0.0340140i
$219$		0			0
$220$	23.4255	+	23.4255i	0.106480	+	0.106480i
$221$	−104.415	+	298.402i	−0.472468	+	1.35024i
$222$		0			0
$223$	228.933	+	110.248i	1.02661	+	0.494387i	0.869884	−	0.493256i	$-0.164193\pi$
$223$	228.933	+	110.248i	1.02661	+	0.494387i	0.156721	+	0.987643i	$0.449908\pi$
$224$	−16.1970	−	46.2884i	−0.0723081	−	0.206645i
$225$		0			0
$226$	−22.7787	−	28.5635i	−0.100791	−	0.126387i
$227$	−261.380	+	327.760i	−1.15145	+	1.44388i	−0.275617	+	0.961268i	$0.588882\pi$
$227$	−261.380	+	327.760i	−1.15145	+	1.44388i	−0.875836	+	0.482609i	$0.839689\pi$
$228$		0			0
$229$	140.386	+	223.424i	0.613041	+	0.975649i	0.998596	+	0.0529641i	$0.0168669\pi$
$229$	140.386	+	223.424i	0.613041	+	0.975649i	−0.385556	+	0.922685i	$0.625990\pi$
$230$	0.161390	+	1.43237i	0.000701694	+	0.00622771i
$231$		0			0
$232$	57.9793	−	75.0004i	0.249911	−	0.323277i
$233$	−233.305			−1.00131			−0.500654	−	0.865648i	$-0.666907\pi$
$233$	−233.305			−1.00131			−0.500654	+	0.865648i	$0.666907\pi$
$234$		0			0
$235$	18.1470	−	11.4025i	0.0772211	−	0.0485212i
$236$	68.0938	−	15.5420i	0.288533	−	0.0658558i
$237$		0			0
$238$	−25.7637	+	20.5459i	−0.108251	+	0.0863272i
$239$	−37.0417	+	162.290i	−0.154986	+	0.679038i	0.836406	+	0.548111i	$0.184653\pi$
$239$	−37.0417	+	162.290i	−0.154986	+	0.679038i	−0.991392	+	0.130928i	$0.958204\pi$
$240$		0			0
$241$	−119.624	+	248.401i	−0.496363	+	1.03071i	0.490841	+	0.871249i	$0.336689\pi$
$241$	−119.624	+	248.401i	−0.496363	+	1.03071i	−0.987204	+	0.159460i	$0.949025\pi$
$242$	13.0839	+	8.22116i	0.0540657	+	0.0339717i
$243$		0			0
$244$	251.850	−	251.850i	1.03217	−	1.03217i
$245$	−17.3266	−	35.9790i	−0.0707207	−	0.146853i
$246$		0			0
$247$	−276.976	−	31.2077i	−1.12136	−	0.126347i
$248$	64.3414	−	30.9852i	0.259441	−	0.124940i
$249$		0			0
$250$	6.40133	−	18.2940i	0.0256053	−	0.0731758i
$251$	222.330	−	353.836i	0.885777	−	1.40971i	−0.0262849	−	0.999654i	$-0.508368\pi$
$251$	222.330	−	353.836i	0.885777	−	1.40971i	0.912062	−	0.410052i	$-0.134489\pi$
$252$		0			0
$253$	11.0559	+	31.5959i	0.0436992	+	0.124885i
$254$	74.0878	+	16.9100i	0.291684	+	0.0665750i
$255$		0			0
$256$	94.4490	−	118.435i	0.368941	−	0.462638i
$257$	−2.48412	−	10.8836i	−0.00966583	−	0.0423487i	0.969865	−	0.243643i	$-0.0783425\pi$
$257$	−2.48412	−	10.8836i	−0.00966583	−	0.0423487i	−0.979531	+	0.201294i	$0.935485\pi$
$258$		0			0
$259$	−14.1752	−	125.808i	−0.0547303	−	0.485745i
$260$		−	37.5904i		−	0.144579i
$261$		0			0
$262$	−30.5812			−0.116722
$263$	325.997	−	36.7310i	1.23953	−	0.139662i	0.532246	−	0.846590i	$-0.321348\pi$
$263$	325.997	−	36.7310i	1.23953	−	0.139662i	0.707285	+	0.706928i	$0.249920\pi$
$264$		0			0
$265$	−27.5196	+	6.28117i	−0.103848	+	0.0237025i
$266$	−22.7146	−	18.1143i	−0.0853934	−	0.0680990i
$267$		0			0
$268$	−48.1567	+	210.988i	−0.179689	+	0.787270i
$269$	−292.071	+	102.200i	−1.08577	+	0.379926i	−0.813066	−	0.582172i	$-0.802203\pi$
$269$	−292.071	+	102.200i	−1.08577	+	0.379926i	−0.272702	+	0.962099i	$0.587917\pi$
$270$		0			0
$271$	16.8213	+	10.5695i	0.0620712	+	0.0390019i	0.562710	−	0.826654i	$-0.309759\pi$
$271$	16.8213	+	10.5695i	0.0620712	+	0.0390019i	−0.500639	+	0.865656i	$0.666902\pi$
$272$	−399.874	−	139.922i	−1.47013	−	0.514419i
$273$		0			0
$274$	35.8048	+	74.3494i	0.130674	+	0.271348i
$275$	24.7394	−	219.568i	0.0899615	−	0.798430i
$276$		0			0
$277$	−278.671	+	134.201i	−1.00603	+	0.484480i	−0.862981	−	0.505236i	$-0.831406\pi$
$277$	−278.671	+	134.201i	−1.00603	+	0.484480i	−0.143051	+	0.989715i	$0.545691\pi$
$278$	18.2653	+	18.2653i	0.0657024	+	0.0657024i
$279$		0			0
$280$	4.26433	−	6.78663i	0.0152297	−	0.0242380i
$281$	275.413	+	132.632i	0.980118	+	0.472000i	0.854146	−	0.520034i	$-0.174081\pi$
$281$	275.413	+	132.632i	0.980118	+	0.472000i	0.125972	+	0.992034i	$0.459795\pi$
$282$		0			0
$283$	−104.652	−	23.8861i	−0.369794	−	0.0844032i	0.0335853	−	0.999436i	$-0.489307\pi$
$283$	−104.652	−	23.8861i	−0.369794	−	0.0844032i	−0.403380	+	0.915033i	$0.632165\pi$
$284$	308.636	+	387.017i	1.08675	+	1.36274i
$285$		0			0
$286$	8.86040	+	38.8199i	0.0309804	+	0.135734i
$287$	49.4697	+	78.7306i	0.172368	+	0.274323i
$288$		0			0
$289$			635.060i			2.19744i
$290$	11.4444	−	0.172888i	0.0394633	−	0.000596165i
$291$		0			0
$292$	−180.799	+	20.3712i	−0.619175	+	0.0697642i
$293$	230.684	−	144.948i	0.787318	−	0.494705i	−0.0773772	−	0.997002i	$-0.524655\pi$
$293$	230.684	−	144.948i	0.787318	−	0.494705i	0.864695	+	0.502297i	$0.167512\pi$
$294$		0			0
$295$	13.4870	+	10.7555i	0.0457185	+	0.0364593i
$296$	−124.682	+	99.4308i	−0.421224	+	0.335915i
$297$		0			0
$298$	−11.9936	+	4.19673i	−0.0402469	+	0.0140830i
$299$	16.4801	−	34.2212i	0.0551173	−	0.114452i
$300$		0			0
$301$	60.8257	+	21.2838i	0.202079	+	0.0707104i
$302$	−41.8032	+	41.8032i	−0.138421	+	0.138421i
$303$		0			0
$304$	41.8199	−	371.162i	0.137565	−	1.22093i
$305$	87.4144	+	9.84924i	0.286605	+	0.0322926i
$306$		0			0
$307$	−134.403	−	134.403i	−0.437796	−	0.437796i	0.453473	−	0.891270i	$-0.350185\pi$
$307$	−134.403	−	134.403i	−0.437796	−	0.437796i	−0.891270	+	0.453473i	$0.850185\pi$
$308$	30.0530	−	85.8865i	0.0975746	−	0.278852i
$309$		0			0
$310$	7.76842	+	3.74108i	0.0250594	+	0.0120680i
$311$	−60.8757	−	173.973i	−0.195742	−	0.559398i	0.803619	−	0.595144i	$-0.202905\pi$
$311$	−60.8757	−	173.973i	−0.195742	−	0.559398i	−0.999361	+	0.0357461i	$0.988619\pi$
$312$		0			0
$313$	263.236	+	330.088i	0.841010	+	1.05459i	0.997756	+	0.0669540i	$0.0213281\pi$
$313$	263.236	+	330.088i	0.841010	+	1.05459i	−0.156746	+	0.987639i	$0.550101\pi$
$314$	−7.21125	+	9.04262i	−0.0229658	+	0.0287981i
$315$		0			0
$316$	84.6549	+	134.728i	0.267895	+	0.426353i
$317$	45.6880	+	405.492i	0.144126	+	1.27915i	0.832592	+	0.553886i	$0.186856\pi$
$317$	45.6880	+	405.492i	0.144126	+	1.27915i	−0.688466	+	0.725268i	$0.741716\pi$
$318$		0			0
$319$	258.215	−	63.0541i	0.809451	−	0.197662i
$320$	45.2125			0.141289
$321$		0			0
$322$	3.35227	−	2.10637i	0.0104108	−	0.00654153i
$323$	−794.274	+	181.288i	−2.45905	+	0.561263i
$324$		0			0
$325$	−196.018	+	156.319i	−0.603131	+	0.480981i
$326$	−9.60417	+	42.0786i	−0.0294607	+	0.129076i
$327$		0			0
$328$	50.8182	−	105.525i	0.154934	−	0.321723i
$329$	−49.8432	−	31.3186i	−0.151499	−	0.0951932i
$330$		0			0
$331$	53.9759	−	53.9759i	0.163069	−	0.163069i	−0.620856	−	0.783925i	$-0.713215\pi$
$331$	53.9759	−	53.9759i	0.163069	−	0.163069i	0.783925	+	0.620856i	$0.213215\pi$
$332$	−219.702	−	456.215i	−0.661752	−	1.37414i
$333$		0			0
$334$	−111.727	−	12.5886i	−0.334511	−	0.0376904i
$335$	−48.1572	+	23.1913i	−0.143753	+	0.0692277i
$336$		0			0
$337$	−100.512	+	287.246i	−0.298255	+	0.852363i	0.693063	+	0.720877i	$0.256261\pi$
$337$	−100.512	+	287.246i	−0.298255	+	0.852363i	−0.991318	+	0.131486i	$0.958025\pi$
$338$	−13.5212	+	21.5189i	−0.0400035	+	0.0636652i
$339$		0			0
$340$	−36.2890	−	103.708i	−0.106732	−	0.305024i
$341$	195.215	+	44.5565i	0.572478	+	0.130664i
$342$		0			0
$343$	−147.670	+	185.172i	−0.430525	+	0.539861i
$344$	−18.0627	−	79.1380i	−0.0525080	−	0.230052i
$345$		0			0
$346$	5.91075	+	52.4593i	0.0170831	+	0.151617i
$347$		−	3.76060i		−	0.0108375i	−0.999985	−	0.00541873i	$-0.998275\pi$
$347$		−	3.76060i		−	0.0108375i	0.999985	−	0.00541873i	$-0.00172484\pi$
$348$		0			0
$349$	227.541			0.651979			0.325989	−	0.945373i	$-0.394303\pi$
$349$	227.541			0.651979			0.325989	+	0.945373i	$0.394303\pi$
$350$	−25.9689	+	2.92600i	−0.0741970	+	0.00835999i
$351$		0			0
$352$	−168.861	+	38.5415i	−0.479720	+	0.109493i
$353$	317.199	+	252.957i	0.898579	+	0.716593i	0.959548	−	0.281547i	$-0.0908474\pi$
$353$	317.199	+	252.957i	0.898579	+	0.716593i	−0.0609682	+	0.998140i	$0.519419\pi$
$354$		0			0
$355$	−27.2053	+	119.194i	−0.0766347	+	0.335759i
$356$	117.468	−	41.1039i	0.329967	−	0.115460i
$357$		0			0
$358$	99.9720	+	62.8166i	0.279251	+	0.175465i
$359$	237.999	+	83.2794i	0.662949	+	0.231976i	0.640717	−	0.767777i	$-0.278637\pi$
$359$	237.999	+	83.2794i	0.662949	+	0.231976i	0.0222319	+	0.999753i	$0.492923\pi$
$360$		0			0
$361$	−155.019	−	321.900i	−0.429415	−	0.891690i
$362$	−10.7946	+	95.8045i	−0.0298193	+	0.264653i
$363$		0			0
$364$	−93.0227	+	44.7974i	−0.255557	+	0.123070i
$365$	−31.7750	−	31.7750i	−0.0870549	−	0.0870549i
$366$		0			0
$367$	−246.647	+	392.537i	−0.672063	+	1.06958i	0.320429	+	0.947273i	$0.396173\pi$
$367$	−246.647	+	392.537i	−0.672063	+	1.06958i	−0.992492	+	0.122310i	$0.960970\pi$
$368$	45.8582	+	22.0841i	0.124615	+	0.0600112i
$369$		0			0
$370$	−18.7718	−	4.28454i	−0.0507346	−	0.0115799i
$371$	48.3394	+	60.6157i	0.130295	+	0.163385i
$372$		0			0
$373$	−55.7998	−	244.475i	−0.149597	−	0.655429i	−0.992997	−	0.118142i	$-0.962306\pi$
$373$	−55.7998	−	244.475i	−0.149597	−	0.655429i	0.843399	−	0.537287i	$-0.180551\pi$
$374$	61.9209	+	98.5465i	0.165564	+	0.263493i
$375$		0			0
$376$			74.1495i			0.197206i
$377$	−257.767	−	156.585i	−0.683731	−	0.415345i
$378$		0			0
$379$	487.332	−	54.9091i	1.28584	−	0.144879i	0.557545	−	0.830147i	$-0.311743\pi$
$379$	487.332	−	54.9091i	1.28584	−	0.144879i	0.728291	+	0.685268i	$0.240315\pi$
$380$	82.0226	−	51.5382i	0.215849	−	0.135627i
$381$		0			0
$382$	31.6751	+	25.2600i	0.0829190	+	0.0661257i
$383$	−172.689	+	137.715i	−0.450886	+	0.359570i	−0.822450	−	0.568838i	$-0.807393\pi$
$383$	−172.689	+	137.715i	−0.450886	+	0.359570i	0.371564	+	0.928407i	$0.378822\pi$
$384$		0			0
$385$	21.2124	−	7.42255i	0.0550972	−	0.0192794i
$386$	5.69506	−	11.8259i	0.0147540	−	0.0306371i
$387$		0			0
$388$	153.986	+	53.8819i	0.396870	+	0.138871i
$389$	291.445	−	291.445i	0.749217	−	0.749217i	−0.225115	−	0.974332i	$-0.572276\pi$
$389$	291.445	−	291.445i	0.749217	−	0.749217i	0.974332	+	0.225115i	$0.0722759\pi$
$390$		0			0
$391$	12.4303	−	110.322i	0.0317911	−	0.282154i
$392$	137.292	+	15.4691i	0.350236	+	0.0394621i
$393$		0			0
$394$	−30.0686	−	30.0686i	−0.0763162	−	0.0763162i
$395$	−12.9796	+	37.0935i	−0.0328597	+	0.0939077i
$396$		0			0
$397$	−65.4912	−	31.5389i	−0.164965	−	0.0794430i	0.349579	−	0.936907i	$-0.386325\pi$
$397$	−65.4912	−	31.5389i	−0.164965	−	0.0794430i	−0.514544	+	0.857464i	$0.672039\pi$
$398$	−21.5888	−	61.6972i	−0.0542431	−	0.155018i
$399$		0			0
$400$	−209.475	−	262.674i	−0.523688	−	0.656684i
$401$	−324.268	+	406.619i	−0.808649	+	1.01401i	0.190826	+	0.981624i	$0.438883\pi$
$401$	−324.268	+	406.619i	−0.808649	+	1.01401i	−0.999475	+	0.0323898i	$0.989688\pi$
$402$		0			0
$403$	−120.879	−	192.378i	−0.299948	−	0.477365i
$404$	−41.9416	−	372.242i	−0.103816	−	0.921392i
$405$		0			0
$406$	−14.0663	−	28.1146i	−0.0346462	−	0.0692479i
$407$	−447.148			−1.09864
$408$		0			0
$409$	250.417	−	157.347i	0.612266	−	0.384712i	−0.189909	−	0.981802i	$-0.560819\pi$
$409$	250.417	−	157.347i	0.612266	−	0.384712i	0.802174	+	0.597090i	$0.203676\pi$
$410$	13.7867	−	3.14673i	0.0336261	−	0.00767494i
$411$		0			0
$412$	219.510	−	175.053i	0.532791	−	0.424887i
$413$	10.5432	−	46.1929i	0.0255284	−	0.111847i
$414$		0			0
$415$	54.2624	−	112.677i	0.130753	−	0.271511i
$416$	166.407	+	104.561i	0.400018	+	0.251348i
$417$		0			0
$418$	−72.5574	+	72.5574i	−0.173582	+	0.173582i
$419$	−59.7192	−	124.008i	−0.142528	−	0.295962i	0.817469	−	0.575972i	$-0.195376\pi$
$419$	−59.7192	−	124.008i	−0.142528	−	0.295962i	−0.959997	+	0.280010i	$0.909662\pi$
$420$		0			0
$421$	432.517	+	48.7330i	1.02736	+	0.115755i	0.609523	−	0.792768i	$-0.291361\pi$
$421$	432.517	+	48.7330i	1.02736	+	0.115755i	0.417833	+	0.908524i	$0.362790\pi$
$422$	7.65428	−	3.68611i	0.0181381	−	0.00873485i
$423$		0			0
$424$	32.2550	−	92.1795i	0.0760731	−	0.217404i
$425$	−389.885	+	620.498i	−0.917376	+	1.46000i
$426$		0			0
$427$	−79.8005	−	228.057i	−0.186886	−	0.534091i
$428$	229.256	+	52.3262i	0.535645	+	0.122257i
$429$		0			0
$430$	6.11061	−	7.66246i	0.0142107	−	0.0178197i
$431$	−38.3560	−	168.049i	−0.0889930	−	0.389904i	0.910741	−	0.412979i	$-0.135512\pi$
$431$	−38.3560	−	168.049i	−0.0889930	−	0.389904i	−0.999734	+	0.0230748i	$0.992654\pi$
$432$		0			0
$433$	5.55493	+	49.3014i	0.0128289	+	0.113860i	0.998495	−	0.0548506i	$-0.0174682\pi$
$433$	5.55493	+	49.3014i	0.0128289	+	0.113860i	−0.985666	+	0.168711i	$0.946040\pi$
$434$		−	23.6824i		−	0.0545677i
$435$		0			0
$436$	−606.505			−1.39107
$437$	97.2658	−	10.9592i	0.222576	−	0.0250783i
$438$		0			0
$439$	190.067	−	43.3816i	0.432955	−	0.0988191i	−0.000488576	−	1.00000i	$-0.500156\pi$
$439$	190.067	−	43.3816i	0.432955	−	0.0988191i	0.433443	+	0.901181i	$0.357298\pi$
$440$	−22.1324	−	17.6500i	−0.0503010	−	0.0401137i
$441$		0			0
$442$	29.3862	−	128.749i	0.0664845	−	0.291288i
$443$	228.033	−	79.7920i	0.514746	−	0.180117i	−0.0603905	−	0.998175i	$-0.519235\pi$
$443$	228.033	−	79.7920i	0.514746	−	0.180117i	0.575137	+	0.818057i	$0.304949\pi$
$444$		0			0
$445$	26.0261	+	16.3533i	0.0584856	+	0.0367490i
$446$	−100.186	−	35.0565i	−0.224631	−	0.0786019i
$447$		0			0
$448$	−53.8807	−	111.884i	−0.120269	−	0.249742i
$449$	55.8565	−	495.740i	0.124402	−	1.10410i	−0.764059	−	0.645147i	$-0.776796\pi$
$449$	55.8565	−	495.740i	0.124402	−	1.10410i	0.888461	−	0.458952i	$-0.151775\pi$
$450$		0			0
$451$	295.880	−	142.488i	0.656053	−	0.315938i
$452$	−236.583	−	236.583i	−0.523415	−	0.523415i
$453$		0			0
$454$	93.1685	−	148.277i	0.205217	−	0.326601i
$455$	−22.9750	−	11.0642i	−0.0504944	−	0.0243168i
$456$		0			0
$457$	204.659	+	46.7120i	0.447831	+	0.102215i	0.440488	−	0.897759i	$-0.354805\pi$
$457$	204.659	+	46.7120i	0.447831	+	0.102215i	0.00734312	+	0.999973i	$0.497663\pi$
$458$	−68.7234	−	86.1764i	−0.150051	−	0.188158i
$459$		0			0
$460$	2.93743	+	12.8697i	0.00638571	+	0.0279776i
$461$	129.473	+	206.054i	0.280852	+	0.446973i	0.957124	−	0.289679i	$-0.0935486\pi$
$461$	129.473	+	206.054i	0.280852	+	0.446973i	−0.676272	+	0.736652i	$0.736406\pi$
$462$		0			0
$463$		−	710.071i		−	1.53363i	−0.641868	−	0.766815i	$-0.721840\pi$
$463$		−	710.071i		−	1.53363i	0.641868	−	0.766815i	$-0.278160\pi$
$464$	209.832	−	345.421i	0.452225	−	0.744441i
$465$		0			0
$466$	96.8439	−	10.9117i	0.207820	−	0.0234156i
$467$	676.037	−	424.782i	1.44762	−	0.909598i	0.447735	−	0.894166i	$-0.352231\pi$
$467$	676.037	−	424.782i	1.44762	−	0.909598i	0.999881	−	0.0154315i	$-0.00491219\pi$
$468$		0			0
$469$	114.780	+	91.5341i	0.244734	+	0.195169i
$470$	−6.99944	+	5.58187i	−0.0148924	+	0.0118763i
$471$		0			0
$472$	−56.3333	+	19.7119i	−0.119350	+	0.0417625i
$473$	98.7519	−	205.061i	0.208778	−	0.433532i
$474$		0			0
$475$	−609.838	−	213.391i	−1.28387	−	0.449245i
$476$	−213.393	+	213.393i	−0.448306	+	0.448306i
$477$		0			0
$478$	7.78553	−	69.0985i	0.0162877	−	0.144558i
$479$	483.953	+	54.5284i	1.01034	+	0.113838i	0.601587	−	0.798807i	$-0.294535\pi$
$479$	483.953	+	54.5284i	1.01034	+	0.113838i	0.408753	+	0.912645i	$0.365964\pi$
$480$		0			0
$481$	358.764	+	358.764i	0.745872	+	0.745872i
$482$	38.0376	−	108.705i	0.0789161	−	0.225529i
$483$		0			0
$484$	127.499	+	61.4001i	0.263427	+	0.126860i
$485$	13.3079	+	38.0317i	0.0274389	+	0.0784159i
$486$		0			0
$487$	−72.6889	−	91.1490i	−0.149259	−	0.187164i	0.701581	−	0.712589i	$-0.252478\pi$
$487$	−72.6889	−	91.1490i	−0.149259	−	0.187164i	−0.850840	+	0.525425i	$0.823906\pi$
$488$	−189.757	+	237.948i	−0.388847	+	0.487598i
$489$		0			0
$490$	8.87495	+	14.1244i	0.0181121	+	0.0288253i
$491$	−75.7150	−	671.989i	−0.154206	−	1.36861i	−0.797650	−	0.603120i	$-0.793924\pi$
$491$	−75.7150	−	671.989i	−0.154206	−	1.36861i	0.643445	−	0.765493i	$-0.277505\pi$
$492$		0			0
$493$	−862.315	−	183.159i	−1.74912	−	0.371520i
$494$	116.431			0.235691
$495$		0			0
$496$	257.796	−	161.984i	0.519751	−	0.326581i
$497$	327.384	−	74.7233i	0.658721	−	0.150349i
$498$		0			0
$499$	−611.573	+	487.713i	−1.22560	+	0.977381i	−0.225602	+	0.974220i	$0.572435\pi$
$499$	−611.573	+	487.713i	−1.22560	+	0.977381i	−0.999995	+	0.00316117i	$0.998994\pi$
$500$	39.4967	−	173.046i	0.0789934	−	0.346093i
$501$		0			0
$502$	−75.7395	+	157.275i	−0.150875	+	0.313296i
$503$	418.298	+	262.834i	0.831606	+	0.522533i	0.879266	−	0.476331i	$-0.158033\pi$
$503$	418.298	+	262.834i	0.831606	+	0.522533i	−0.0476598	+	0.998864i	$0.515176\pi$
$504$		0			0
$505$	65.4208	−	65.4208i	0.129546	−	0.129546i
$506$	−6.06701	−	12.5983i	−0.0119901	−	0.0248978i
$507$		0			0
$508$	691.569	+	77.9211i	1.36136	+	0.153388i
$509$	−658.293	+	317.017i	−1.29331	+	0.622823i	−0.948775	−	0.315952i	$-0.897676\pi$
$509$	−658.293	+	317.017i	−1.29331	+	0.622823i	−0.344531	+	0.938775i	$0.611962\pi$
$510$		0			0
$511$	−40.7647	+	116.499i	−0.0797744	+	0.227982i
$512$	−237.068	+	377.292i	−0.463023	+	0.736898i
$513$		0			0
$514$	1.54018	+	4.40157i	0.00299645	+	0.00856337i
$515$	67.6051	+	15.4304i	0.131272	+	0.0299620i
$516$		0			0
$517$	−129.627	+	162.548i	−0.250730	+	0.314406i
$518$	11.7681	+	51.5595i	0.0227184	+	0.0995356i
$519$		0			0
$520$	3.59641	+	31.9190i	0.00691618	+	0.0613828i
$521$			412.503i			0.791753i	0.918304	+	0.395876i	$0.129559\pi$
$521$			412.503i			0.791753i	−0.918304	+	0.395876i	$0.870441\pi$
$522$		0			0
$523$	−54.7428			−0.104671			−0.0523354	−	0.998630i	$-0.516666\pi$
$523$	−54.7428			−0.104671			−0.0523354	+	0.998630i	$0.516666\pi$
$524$	−278.301	+	31.3570i	−0.531110	+	0.0598417i
$525$		0			0
$526$	−133.602	+	30.4938i	−0.253996	+	0.0579730i
$527$	−519.210	−	414.056i	−0.985219	−	0.785686i
$528$		0			0
$529$	114.745	−	502.733i	0.216910	−	0.950346i
$530$	11.1295	−	3.89439i	0.0209991	−	0.00734790i
$531$		0			0
$532$	−225.287	−	141.557i	−0.423471	−	0.266084i
$533$	−351.720	−	123.072i	−0.659887	−	0.230904i
$534$		0			0
$535$	25.1992	+	52.3267i	0.0471013	+	0.0978069i
$536$	20.7051	−	183.763i	0.0386290	−	0.342842i
$537$		0			0
$538$	116.458	−	56.0832i	0.216465	−	0.104244i
$539$	273.924	+	273.924i	0.508208	+	0.508208i
$540$		0			0
$541$	−6.00071	+	9.55008i	−0.0110919	+	0.0176526i	−0.852224	−	0.523177i	$-0.824747\pi$
$541$	−6.00071	+	9.55008i	−0.0110919	+	0.0176526i	0.841132	+	0.540829i	$0.181890\pi$
$542$	−7.47680	−	3.60064i	−0.0137948	−	0.00664324i
$543$		0			0
$544$	560.041	+	127.826i	1.02949	+	0.234974i
$545$	−93.3962	−	117.115i	−0.171369	−	0.214890i
$546$		0			0
$547$	−11.9903	−	52.5331i	−0.0219202	−	0.0960385i	0.962785	−	0.270270i	$-0.0871130\pi$
$547$	−11.9903	−	52.5331i	−0.0219202	−	0.0960385i	−0.984705	+	0.174232i	$0.944256\pi$
$548$	402.074	+	639.897i	0.733712	+	1.16770i
$549$		0			0
$550$			92.2991i			0.167817i
$551$	−11.7400	−	777.134i	−0.0213068	−	1.41041i
$552$		0			0
$553$	107.261	−	12.0854i	0.193962	−	0.0218543i
$554$	109.399	−	68.7398i	0.197471	−	0.124079i
$555$		0			0
$556$	184.950	+	147.493i	0.332644	+	0.265275i
$557$	−543.971	+	433.802i	−0.976608	+	0.778819i	−0.975233	−	0.221180i	$-0.929009\pi$
$557$	−543.971	+	433.802i	−0.976608	+	0.778819i	−0.00137506	+	0.999999i	$0.500438\pi$
$558$		0			0
$559$	−243.761	+	85.2955i	−0.436066	+	0.152586i
$560$	14.8265	−	30.7876i	0.0264760	−	0.0549779i
$561$		0			0
$562$	−120.526	−	42.1740i	−0.214460	−	0.0750426i
$563$	319.915	−	319.915i	0.568233	−	0.568233i	−0.363400	−	0.931633i	$-0.618384\pi$
$563$	319.915	−	319.915i	0.568233	−	0.568233i	0.931633	+	0.363400i	$0.118384\pi$
$564$		0			0
$565$	9.25221	−	82.1156i	0.0163756	−	0.145337i
$566$	44.5578	+	5.02045i	0.0787239	+	0.00887006i
$567$		0			0
$568$	−299.099	−	299.099i	−0.526582	−	0.526582i
$569$	−173.583	+	496.072i	−0.305067	+	0.871832i	0.684660	+	0.728863i	$0.259951\pi$
$569$	−173.583	+	496.072i	−0.305067	+	0.871832i	−0.989727	+	0.142969i	$0.954335\pi$
$570$		0			0
$571$	619.219	+	298.200i	1.08445	+	0.522242i	0.888736	−	0.458419i	$-0.151584\pi$
$571$	619.219	+	298.200i	1.08445	+	0.522242i	0.195711	+	0.980662i	$0.437299\pi$
$572$	120.438	+	344.192i	0.210556	+	0.601735i
$573$		0			0
$574$	−24.2170	−	30.3671i	−0.0421898	−	0.0529044i
$575$	54.8946	−	68.8357i	0.0954689	−	0.119714i
$576$		0			0
$577$	−30.2263	−	48.1049i	−0.0523853	−	0.0833707i	0.819505	−	0.573072i	$-0.194249\pi$
$577$	−30.2263	−	48.1049i	−0.0523853	−	0.0833707i	−0.871890	+	0.489702i	$0.837106\pi$
$578$	−29.7019	−	263.611i	−0.0513873	−	0.456075i
$579$		0			0
$580$	103.971	−	13.3081i	0.179261	−	0.0229449i
$581$	−343.501			−0.591223
$582$		0			0
$583$	231.855	−	145.684i	0.397694	−	0.249888i
$584$	151.572	−	34.5954i	0.259542	−	0.0592387i
$585$		0			0
$586$	−88.9769	+	70.9567i	−0.151838	+	0.121087i
$587$	71.8016	−	314.583i	0.122320	−	0.535917i	−0.876221	−	0.481910i	$-0.839943\pi$
$587$	71.8016	−	314.583i	0.122320	−	0.535917i	0.998541	−	0.0540076i	$-0.0171995\pi$
$588$		0			0
$589$	254.039	−	527.518i	0.431306	−	0.895616i
$590$	−6.10142	−	3.83378i	−0.0103414	−	0.00649793i
$591$		0			0
$592$	−480.762	+	480.762i	−0.812099	+	0.812099i
$593$	−209.288	−	434.591i	−0.352931	−	0.732869i	0.646621	−	0.762812i	$-0.276182\pi$
$593$	−209.288	−	434.591i	−0.352931	−	0.732869i	−0.999552	+	0.0299430i	$0.990467\pi$
$594$		0			0
$595$	−74.0666	−	8.34530i	−0.124482	−	0.0140257i
$596$	−104.843	+	50.4899i	−0.175912	+	0.0847146i
$597$		0			0
$598$	−5.24029	+	14.9759i	−0.00876302	+	0.0250433i
$599$	−452.046	+	719.427i	−0.754668	+	1.20105i	0.219586	+	0.975593i	$0.429529\pi$
$599$	−452.046	+	719.427i	−0.754668	+	1.20105i	−0.974254	+	0.225454i	$0.927613\pi$
$600$		0			0
$601$	241.988	+	691.562i	0.402642	+	1.15069i	0.949584	+	0.313514i	$0.101506\pi$
$601$	241.988	+	691.562i	0.402642	+	1.15069i	−0.546941	+	0.837171i	$0.684208\pi$
$602$	−26.2440	−	5.99001i	−0.0435946	−	0.00995019i
$603$		0			0
$604$	−337.563	+	423.290i	−0.558878	+	0.700811i
$605$	7.77737	+	34.0749i	0.0128552	+	0.0563221i
$606$		0			0
$607$	−27.7513	−	246.300i	−0.0457188	−	0.405766i	−0.995640	−	0.0932767i	$-0.970266\pi$
$607$	−27.7513	−	246.300i	−0.0457188	−	0.405766i	0.949921	−	0.312489i	$-0.101163\pi$
$608$			506.460i			0.832993i
$609$		0			0
$610$	−36.7461			−0.0602395
$611$	234.424	−	26.4132i	0.383672	−	0.0432295i
$612$		0			0
$613$	1.19680	−	0.273162i	0.00195236	−	0.000445614i	−0.221545	−	0.975150i	$-0.571110\pi$
$613$	1.19680	−	0.273162i	0.00195236	−	0.000445614i	0.223497	+	0.974705i	$0.428253\pi$
$614$	62.0765	+	49.5043i	0.101102	+	0.0806260i
$615$		0			0
$616$	−17.3017	+	75.8038i	−0.0280872	+	0.123058i
$617$	285.233	−	99.8075i	0.462291	−	0.161762i	−0.0890772	−	0.996025i	$-0.528392\pi$
$617$	285.233	−	99.8075i	0.462291	−	0.161762i	0.551368	+	0.834262i	$0.314106\pi$
$618$		0			0
$619$	−272.432	−	171.181i	−0.440117	−	0.276544i	0.293691	−	0.955900i	$-0.405116\pi$
$619$	−272.432	−	171.181i	−0.440117	−	0.276544i	−0.733808	+	0.679356i	$0.762259\pi$
$620$	74.5319	+	26.0798i	0.120213	+	0.0420642i
$621$		0			0
$622$	33.4060	+	69.3683i	0.0537074	+	0.111525i
$623$	9.45256	−	83.8938i	0.0151727	−	0.134661i
$624$		0			0
$625$	−503.501	+	242.473i	−0.805601	+	0.387957i
$626$	−124.707	−	124.707i	−0.199212	−	0.199212i
$627$		0			0
$628$	−56.3533	+	89.6858i	−0.0897346	+	0.142812i
$629$	1336.14	+	643.449i	2.12422	+	1.02297i
$630$		0			0
$631$	680.376	+	155.291i	1.07825	+	0.246103i	0.724527	−	0.689247i	$-0.242058\pi$
$631$	680.376	+	155.291i	1.07825	+	0.246103i	0.353723	+	0.935350i	$0.384916\pi$
$632$	−84.7726	−	106.301i	−0.134134	−	0.168199i
$633$		0			0
$634$	−37.9298	−	166.181i	−0.0598262	−	0.262116i
$635$	91.4488	+	145.540i	0.144014	+	0.229197i
$636$		0			0
$637$		−	439.560i		−	0.690047i
$638$	−104.235	+	38.2503i	−0.163378	+	0.0599534i
$639$		0			0
$640$	−89.7372	+	10.1110i	−0.140214	+	0.0157984i
$641$	989.853	−	621.966i	1.54423	−	0.970306i	0.553748	−	0.832684i	$-0.313197\pi$
$641$	989.853	−	621.966i	1.54423	−	0.970306i	0.990485	−	0.137621i	$-0.0439457\pi$
$642$		0			0
$643$	−234.086	−	186.677i	−0.364052	−	0.290322i	0.424330	−	0.905508i	$-0.360510\pi$
$643$	−234.086	−	186.677i	−0.364052	−	0.290322i	−0.788382	+	0.615186i	$0.789081\pi$
$644$	28.3473	−	22.6062i	0.0440175	−	0.0351028i
$645$		0			0
$646$	321.221	−	112.400i	0.497247	−	0.173994i
$647$	−493.455	+	1024.67i	−0.762681	+	1.58372i	0.0484269	+	0.998827i	$0.484579\pi$
$647$	−493.455	+	1024.67i	−0.762681	+	1.58372i	−0.811108	+	0.584897i	$0.801135\pi$
$648$		0			0
$649$	−157.952	−	55.2698i	−0.243377	−	0.0851614i
$650$	74.0552	−	74.0552i	0.113931	−	0.113931i
$651$		0			0
$652$	−44.2558	+	392.781i	−0.0678770	+	0.602425i
$653$	−609.259	−	68.6470i	−0.933015	−	0.105126i	−0.367648	−	0.929965i	$-0.619837\pi$
$653$	−609.259	−	68.6470i	−0.933015	−	0.105126i	−0.565367	+	0.824839i	$0.691265\pi$
$654$		0			0
$655$	−48.9109	−	48.9109i	−0.0746731	−	0.0746731i
$656$	164.923	−	471.322i	0.251407	−	0.718479i
$657$		0			0
$658$	22.1545	+	10.6691i	0.0336695	+	0.0162144i
$659$	−176.059	−	503.147i	−0.267161	−	0.763501i	−0.996820	−	0.0796900i	$-0.974607\pi$
$659$	−176.059	−	503.147i	−0.267161	−	0.763501i	0.729659	−	0.683811i	$-0.239679\pi$
$660$		0			0
$661$	620.208	+	777.717i	0.938288	+	1.17658i	0.984098	+	0.177626i	$0.0568417\pi$
$661$	620.208	+	777.717i	0.938288	+	1.17658i	−0.0458100	+	0.998950i	$0.514587\pi$
$662$	−19.8808	+	24.9297i	−0.0300314	+	0.0376581i
$663$		0			0
$664$	230.202	+	366.365i	0.346690	+	0.551754i
$665$	−7.35765	−	65.3010i	−0.0110641	−	0.0981970i
$666$		0			0
$667$	100.487	+	33.4669i	0.150655	+	0.0501752i
$668$	−1029.67			−1.54142
$669$		0			0
$670$	18.9052	−	11.8789i	0.0282168	−	0.0177298i
$671$	−831.957	+	189.889i	−1.23988	+	0.282994i
$672$		0			0
$673$	314.226	−	250.587i	0.466903	−	0.372343i	−0.361594	−	0.932336i	$-0.617767\pi$
$673$	314.226	−	250.587i	0.466903	−	0.372343i	0.828498	+	0.559992i	$0.189196\pi$
$674$	28.2876	−	123.936i	0.0419697	−	0.183881i
$675$		0			0
$676$	−100.984	+	209.695i	−0.149384	+	0.310199i
$677$	−424.331	−	266.625i	−0.626781	−	0.393833i	0.180858	−	0.983509i	$-0.442112\pi$
$677$	−424.331	−	266.625i	−0.626781	−	0.393833i	−0.807640	+	0.589676i	$0.799255\pi$
$678$		0			0
$679$	78.2555	−	78.2555i	0.115251	−	0.115251i
$680$	40.7361	+	84.5893i	0.0599060	+	0.124396i
$681$		0			0
$682$	−83.1169	−	9.36503i	−0.121872	−	0.0137317i
$683$	344.482	−	165.894i	0.504366	−	0.242890i	−0.164358	−	0.986401i	$-0.552555\pi$
$683$	344.482	−	165.894i	0.504366	−	0.242890i	0.668724	+	0.743511i	$0.266841\pi$
$684$		0			0
$685$	−61.6474	+	176.178i	−0.0899963	+	0.257195i
$686$	52.6368	−	83.7709i	0.0767300	−	0.122115i
$687$		0			0
$688$	−114.300	−	326.652i	−0.166134	−	0.474784i
$689$	−302.915	−	69.1384i	−0.439645	−	0.100346i
$690$		0			0
$691$	−495.980	+	621.939i	−0.717771	+	0.900056i	−0.998209	−	0.0598158i	$-0.980949\pi$
$691$	−495.980	+	621.939i	−0.717771	+	0.900056i	0.280439	+	0.959872i	$0.409520\pi$
$692$	107.580	+	471.341i	0.155463	+	0.681129i
$693$		0			0
$694$	0.175884	+	1.56101i	0.000253435	+	0.00224930i
$695$			58.4262i			0.0840664i
$696$		0			0
$697$	−1089.17			−1.56265
$698$	−94.4513	+	10.6421i	−0.135317	+	0.0152466i
$699$		0			0
$700$	−233.328	+	53.2556i	−0.333326	+	0.0760794i
$701$	825.456	+	658.279i	1.17754	+	0.939057i	0.998993	−	0.0448739i	$-0.0142886\pi$
$701$	825.456	+	658.279i	1.17754	+	0.939057i	0.178548	+	0.983931i	$0.442860\pi$
$702$		0			0
$703$	−290.944	+	1274.71i	−0.413860	+	1.81324i
$704$	−413.983	+	144.859i	−0.588044	+	0.205765i
$705$		0			0
$706$	−143.499	−	90.1663i	−0.203256	−	0.127714i
$707$	−239.856	−	83.9294i	−0.339259	−	0.118712i
$708$		0			0
$709$	313.200	+	650.367i	0.441749	+	0.917301i	0.996364	+	0.0851945i	$0.0271512\pi$
$709$	313.200	+	650.367i	0.441749	+	0.917301i	−0.554615	+	0.832107i	$0.687135\pi$
$710$	5.71810	−	50.7495i	0.00805366	−	0.0714782i
$711$		0			0
$712$	−95.8127	+	46.1410i	−0.134568	+	0.0648048i
$713$	56.4179	+	56.4179i	0.0791275	+	0.0791275i
$714$		0			0
$715$	−47.9167	+	76.2589i	−0.0670163	+	0.106656i
$716$	974.197	+	469.149i	1.36061	+	0.655236i
$717$		0			0
$718$	−102.687	−	23.4377i	−0.143019	−	0.0326431i
$719$	684.608	+	858.472i	0.952167	+	1.19398i	0.980924	+	0.194394i	$0.0622739\pi$
$719$	684.608	+	858.472i	0.952167	+	1.19398i	−0.0287562	+	0.999586i	$0.509155\pi$
$720$		0			0
$721$	−42.3818	−	185.687i	−0.0587820	−	0.257541i
$722$	79.4031	+	126.369i	0.109977	+	0.175027i
$723$		0			0
$724$			882.929i			1.21952i
$725$	−501.757	−	486.823i	−0.692079	−	0.671480i
$726$		0			0
$727$	31.1294	−	3.50744i	0.0428190	−	0.00482454i	−0.0905290	−	0.995894i	$-0.528856\pi$
$727$	31.1294	−	3.50744i	0.0428190	−	0.00482454i	0.133348	+	0.991069i	$0.457427\pi$
$728$	74.7022	−	46.9385i	0.102613	−	0.0644759i
$729$		0			0
$730$	14.6758	+	11.7036i	0.0201039	+	0.0160323i
$731$	−590.167	+	470.643i	−0.807342	+	0.643834i
$732$		0			0
$733$	143.446	−	50.1941i	0.195698	−	0.0684776i	−0.230651	−	0.973037i	$-0.574085\pi$
$733$	143.446	−	50.1941i	0.195698	−	0.0684776i	0.426348	+	0.904559i	$0.359800\pi$
$734$	84.0234	−	174.476i	0.114473	−	0.237706i
$735$		0			0
$736$	−65.1430	−	22.7945i	−0.0885095	−	0.0309708i
$737$	366.642	−	366.642i	0.497479	−	0.497479i
$738$		0			0
$739$	125.579	−	1114.55i	0.169931	−	1.50818i	−0.562191	−	0.827008i	$-0.690041\pi$
$739$	125.579	−	1114.55i	0.169931	−	1.50818i	0.732122	−	0.681174i	$-0.238530\pi$
$740$	−175.225	−	19.7431i	−0.236790	−	0.0266798i
$741$		0			0
$742$	−22.9005	−	22.9005i	−0.0308632	−	0.0308632i
$743$	63.5004	−	181.474i	0.0854649	−	0.244245i	−0.893217	−	0.449625i	$-0.851558\pi$
$743$	63.5004	−	181.474i	0.0854649	−	0.244245i	0.978682	+	0.205381i	$0.0658432\pi$
$744$		0			0
$745$	−25.8944	−	12.4701i	−0.0347576	−	0.0167384i
$746$	34.5965	+	98.8710i	0.0463759	+	0.132535i
$747$		0			0
$748$	664.552	+	833.322i	0.888439	+	1.11407i
$749$	99.4592	−	124.718i	0.132789	−	0.166513i
$750$		0			0
$751$	−192.970	−	307.110i	−0.256950	−	0.408934i	0.693191	−	0.720754i	$-0.256204\pi$
$751$	−192.970	−	307.110i	−0.256950	−	0.408934i	−0.950141	+	0.311820i	$0.899061\pi$
$752$	35.3950	+	314.140i	0.0470679	+	0.417739i
$753$		0			0
$754$	114.322	+	52.9422i	0.151620	+	0.0702151i
$755$	−133.718			−0.177110
$756$		0			0
$757$	−145.660	+	91.5245i	−0.192418	+	0.120904i	−0.624796	−	0.780788i	$-0.714818\pi$
$757$	−145.660	+	91.5245i	−0.192418	+	0.120904i	0.432377	+	0.901693i	$0.357675\pi$
$758$	−199.722	+	45.5852i	−0.263485	+	0.0601387i
$759$		0			0
$760$	−64.7167	+	51.6098i	−0.0851536	+	0.0679077i
$761$	64.7556	−	283.713i	0.0850928	−	0.372816i	−0.914395	−	0.404824i	$-0.867333\pi$
$761$	64.7556	−	283.713i	0.0850928	−	0.372816i	0.999488	+	0.0320077i	$0.0101901\pi$
$762$		0			0
$763$	−178.515	+	370.691i	−0.233965	+	0.485833i
$764$	314.157	+	197.398i	0.411201	+	0.258374i
$765$		0			0
$766$	65.2418	−	65.2418i	0.0851721	−	0.0851721i
$767$	82.3859	+	171.076i	0.107413	+	0.223046i
$768$		0			0
$769$	−609.620	−	68.6876i	−0.792743	−	0.0893207i	−0.293700	−	0.955898i	$-0.594887\pi$
$769$	−609.620	−	68.6876i	−0.792743	−	0.0893207i	−0.499043	+	0.866577i	$0.666315\pi$
$770$	−8.45805	+	4.07318i	−0.0109845	+	0.00528985i
$771$		0			0
$772$	39.7015	−	113.460i	0.0514268	−	0.146969i
$773$	70.0120	−	111.423i	0.0905718	−	0.144144i	−0.798365	−	0.602173i	$-0.794302\pi$
$773$	70.0120	−	111.423i	0.0905718	−	0.144144i	0.888937	+	0.458029i	$0.151444\pi$
$774$		0			0
$775$	−173.944	−	497.103i	−0.224444	−	0.641424i
$776$	−135.908	−	31.0202i	−0.175140	−	0.0399745i
$777$		0			0
$778$	−107.347	+	134.609i	−0.137978	+	0.173019i
$779$	−213.680	−	936.192i	−0.274300	−	1.20179i
$780$		0			0
$781$	−132.791	−	1178.55i	−0.170027	−	1.50903i
$782$			46.3757i			0.0593040i
$783$		0			0
$784$	589.033			0.751318
$785$	−25.9961	+	2.92906i	−0.0331160	+	0.00373128i
$786$		0			0
$787$	−729.969	+	166.611i	−0.927534	+	0.211704i	−0.659499	−	0.751705i	$-0.729232\pi$
$787$	−729.969	+	166.611i	−0.927534	+	0.211704i	−0.268035	+	0.963409i	$0.586374\pi$
$788$	−304.468	−	242.805i	−0.386381	−	0.308128i
$789$		0			0
$790$	3.65291	−	16.0045i	0.00462394	−	0.0202588i
$791$	−214.233	+	74.9632i	−0.270838	+	0.0947702i
$792$		0			0
$793$	819.867	+	515.156i	1.03388	+	0.649630i
$794$	28.6602	+	10.0287i	0.0360960	+	0.0126305i
$795$		0			0
$796$	−259.729	−	539.333i	−0.326293	−	0.677554i
$797$	145.956	−	1295.40i	0.183132	−	1.62534i	−0.480298	−	0.877105i	$-0.659471\pi$
$797$	145.956	−	1295.40i	0.183132	−	1.62534i	0.663430	−	0.748238i	$-0.269100\pi$
$798$		0			0
$799$	621.251	−	299.179i	0.777536	−	0.374442i
$800$	322.130	+	322.130i	0.402662	+	0.402662i
$801$		0			0
$802$	115.585	−	183.952i	0.144121	−	0.229367i
$803$	392.750	+	189.139i	0.489104	+	0.235540i
$804$		0			0
$805$	8.73044	+	1.99267i	0.0108453	+	0.00247536i
$806$	59.1740	+	74.2019i	0.0734169	+	0.0920619i
$807$		0			0
$808$	71.2275	+	312.068i	0.0881529	+	0.386223i
$809$	471.755	+	750.793i	0.583133	+	0.928051i	0.999819	+	0.0190007i	$0.00604849\pi$
$809$	471.755	+	750.793i	0.583133	+	0.928051i	−0.416686	+	0.909050i	$0.636809\pi$
$810$		0			0
$811$		−	1145.79i		−	1.41281i	−0.707806	−	0.706407i	$-0.750315\pi$
$811$		−	1145.79i		−	1.41281i	0.707806	−	0.706407i	$-0.249685\pi$
$812$	−156.838	−	241.432i	−0.193150	−	0.297330i
$813$		0			0
$814$	185.610	−	20.9132i	0.228021	−	0.0256919i
$815$	−82.6604	+	51.9390i	−0.101424	+	0.0637288i
$816$		0			0
$817$	−520.322	−	414.943i	−0.636869	−	0.507886i
$818$	−96.5879	+	77.0263i	−0.118078	+	0.0941642i
$819$		0			0
$820$	122.238	−	42.7730i	0.149071	−	0.0521622i
$821$	−215.229	+	446.927i	−0.262155	+	0.544370i	−0.989949	−	0.141426i	$-0.954831\pi$
$821$	−215.229	+	446.927i	−0.262155	+	0.544370i	0.727794	+	0.685795i	$0.240546\pi$
$822$		0			0
$823$	1480.63	+	518.096i	1.79907	+	0.629521i	0.999584	+	0.0288316i	$0.00917867\pi$
$823$	1480.63	+	518.096i	1.79907	+	0.629521i	0.799483	+	0.600689i	$0.205107\pi$
$824$	−169.644	+	169.644i	−0.205878	+	0.205878i
$825$		0			0
$826$	−2.21601	+	19.6676i	−0.00268282	+	0.0238107i
$827$	373.230	+	42.0530i	0.451306	+	0.0508500i	0.334693	−	0.942327i	$-0.391367\pi$
$827$	373.230	+	42.0530i	0.451306	+	0.0508500i	0.116614	+	0.993177i	$0.462796\pi$
$828$		0			0
$829$	12.6142	+	12.6142i	0.0152162	+	0.0152162i	0.714674	−	0.699458i	$-0.246575\pi$
$829$	12.6142	+	12.6142i	0.0152162	+	0.0152162i	−0.699458	+	0.714674i	$0.746575\pi$
$830$	−17.2542	+	49.3097i	−0.0207882	+	0.0594093i
$831$		0			0
$832$	448.380	+	215.929i	0.538919	+	0.259530i
$833$	−424.342	−	1212.70i	−0.509414	−	1.45582i
$834$		0			0
$835$	−158.559	−	198.827i	−0.189892	−	0.238117i
$836$	−585.904	+	734.700i	−0.700842	+	0.878828i
$837$		0			0
$838$	30.5891	+	48.6823i	0.0365025	+	0.0580934i
$839$	−40.7280	−	361.471i	−0.0485435	−	0.430835i	−0.994354	−	0.106116i	$-0.966159\pi$
$839$	−40.7280	−	361.471i	−0.0485435	−	0.430835i	0.945810	−	0.324720i	$-0.105270\pi$
$840$		0			0
$841$	341.842	−	768.391i	0.406470	−	0.913664i
$842$	−181.816			−0.215933
$843$		0			0
$844$	65.8775	−	41.3936i	0.0780539	−	0.0490445i
$845$	−56.0423	+	12.7913i	−0.0663223	+	0.0151376i
$846$		0			0
$847$	75.0545	−	59.8540i	0.0886122	−	0.0706659i
$848$	92.6490	−	405.922i	0.109256	−	0.478681i
$849$		0			0
$850$	132.819	−	275.802i	0.156258	−	0.324472i
$851$	−150.864	−	94.7939i	−0.177278	−	0.111391i
$852$		0			0
$853$	797.728	−	797.728i	0.935202	−	0.935202i	−0.0628224	−	0.998025i	$-0.520010\pi$
$853$	797.728	−	797.728i	0.935202	−	0.935202i	0.998025	+	0.0628224i	$0.0200102\pi$
$854$	43.7912	+	90.9333i	0.0512777	+	0.106479i
$855$		0			0
$856$	−199.674	−	22.4978i	−0.233263	−	0.0262825i
$857$	−608.706	+	293.137i	−0.710275	+	0.342051i	−0.753892	−	0.656998i	$-0.771826\pi$
$857$	−608.706	+	293.137i	−0.710275	+	0.342051i	0.0436173	+	0.999048i	$0.486112\pi$
$858$		0			0
$859$	296.164	−	846.388i	0.344777	−	0.985317i	−0.632722	−	0.774379i	$-0.718062\pi$
$859$	296.164	−	846.388i	0.344777	−	0.985317i	0.977499	−	0.210938i	$-0.0676519\pi$
$860$	47.7522	−	75.9972i	0.0555258	−	0.0883688i
$861$		0			0
$862$	23.7811	+	67.9624i	0.0275883	+	0.0788427i
$863$	623.656	+	142.345i	0.722660	+	0.164942i	0.568004	−	0.823026i	$-0.307716\pi$
$863$	623.656	+	142.345i	0.722660	+	0.164942i	0.154656	+	0.987968i	$0.450573\pi$
$864$		0			0
$865$	−74.4488	+	93.3558i	−0.0860680	+	0.107926i
$866$	−4.61166	−	20.2050i	−0.00532525	−	0.0233314i
$867$		0			0
$868$	−24.2832	−	215.519i	−0.0279760	−	0.248294i
$869$		−	381.229i		−	0.438698i
$870$		0			0
$871$	−588.343			−0.675480
$872$	514.999	−	58.0265i	0.590596	−	0.0665442i
$873$		0			0
$874$	−39.8621	+	9.09827i	−0.0456089	+	0.0104099i
$875$	−94.1392	−	75.0735i	−0.107588	−	0.0857983i
$876$		0			0
$877$	210.603	−	922.713i	0.240140	−	1.05212i	−0.700748	−	0.713409i	$-0.747150\pi$
$877$	210.603	−	922.713i	0.240140	−	1.05212i	0.940889	−	0.338716i	$-0.109992\pi$
$878$	−76.8673	+	26.8970i	−0.0875481	+	0.0306344i
$879$		0			0
$880$	−102.191	−	64.2108i	−0.116126	−	0.0729668i
$881$	−609.457	−	213.258i	−0.691778	−	0.242064i	−0.0385856	−	0.999255i	$-0.512285\pi$
$881$	−609.457	−	213.258i	−0.691778	−	0.242064i	−0.653193	+	0.757192i	$0.726571\pi$
$882$		0			0
$883$	−670.866	−	1393.07i	−0.759758	−	1.57765i	−0.815192	−	0.579191i	$-0.803368\pi$
$883$	−670.866	−	1393.07i	−0.759758	−	1.57765i	0.0554336	−	0.998462i	$-0.482346\pi$
$884$	135.411	−	1201.80i	0.153180	−	1.35951i
$885$		0			0
$886$	−90.9236	+	43.7865i	−0.102623	+	0.0494204i
$887$	−229.854	−	229.854i	−0.259137	−	0.259137i	0.565566	−	0.824703i	$-0.308658\pi$
$887$	−229.854	−	229.854i	−0.259137	−	0.259137i	−0.824703	+	0.565566i	$0.808658\pi$
$888$		0			0
$889$	251.177	−	399.746i	0.282539	−	0.449658i
$890$	−11.5682	−	5.57095i	−0.0129980	−	0.00625949i
$891$		0			0
$892$	−947.677	−	216.301i	−1.06242	−	0.242490i
$893$	379.039	+	475.300i	0.424456	+	0.532251i
$894$		0			0
$895$	59.4256	+	260.361i	0.0663973	+	0.290906i
$896$	131.963	+	210.018i	0.147280	+	0.234395i
$897$		0			0
$898$			208.393i			0.232063i
$899$	489.303	−	402.446i	0.544274	−	0.447660i
$900$		0			0
$901$	−902.455	+	101.682i	−1.00162	+	0.112855i
$902$	−116.154	+	72.9847i	−0.128774	+	0.0809143i
$903$		0			0
$904$	223.524	+	178.255i	0.247261	+	0.197184i
$905$	−170.492	+	135.963i	−0.188389	+	0.150235i
$906$		0			0
$907$	418.178	−	146.327i	0.461056	−	0.161331i	−0.0897489	−	0.995964i	$-0.528606\pi$
$907$	418.178	−	146.327i	0.461056	−	0.161331i	0.550805	+	0.834634i	$0.314321\pi$
$908$	695.833	−	1444.91i	0.766336	−	1.59131i
$909$		0			0
$910$	10.0543	+	3.51815i	0.0110487	+	0.00386610i
$911$	−76.1750	+	76.1750i	−0.0836169	+	0.0836169i	−0.747678	−	0.664061i	$-0.768831\pi$
$911$	−76.1750	+	76.1750i	−0.0836169	+	0.0836169i	0.664061	+	0.747678i	$0.268831\pi$
$912$		0			0
$913$	−135.835	+	1205.57i	−0.148779	+	1.32045i
$914$	−87.1379	−	9.81808i	−0.0953369	−	0.0107419i
$915$		0			0
$916$	−713.774	−	713.774i	−0.779230	−	0.779230i
$917$	−62.7485	+	179.325i	−0.0684281	+	0.195556i
$918$		0			0
$919$	265.995	+	128.097i	0.289440	+	0.139387i	0.572970	−	0.819577i	$-0.305791\pi$
$919$	265.995	+	128.097i	0.289440	+	0.139387i	−0.283530	+	0.958963i	$0.591506\pi$
$920$	−3.72554	−	10.6470i	−0.00404950	−	0.0115728i
$921$		0			0
$922$	−63.3808	−	79.4770i	−0.0687427	−	0.0862007i
$923$	−839.056	+	1052.14i	−0.909054	+	1.13992i
$924$		0			0
$925$	625.715	+	995.820i	0.676449	+	1.07656i
$926$	33.2101	+	294.748i	0.0358641	+	0.318302i
$927$		0			0
$928$	−230.291	+	497.283i	−0.248159	+	0.535865i
$929$	1710.91			1.84167			0.920834	−	0.389954i	$-0.127509\pi$
$929$	1710.91			1.84167			0.920834	+	0.389954i	$0.127509\pi$
$930$		0			0
$931$	959.123	−	602.657i	1.03021	−	0.647322i
$932$	870.131	−	198.602i	0.933617	−	0.213092i
$933$		0			0
$934$	−260.753	+	207.944i	−0.279179	+	0.222638i
$935$	−58.5782	+	256.648i	−0.0626505	+	0.274490i
$936$		0			0
$937$	−276.504	+	574.166i	−0.295095	+	0.612770i	−0.994821	−	0.101641i	$-0.967591\pi$
$937$	−276.504	+	574.166i	−0.295095	+	0.612770i	0.699727	+	0.714411i	$0.253305\pi$
$938$	−51.9259	−	32.6272i	−0.0553581	−	0.0347838i
$939$		0			0
$940$	−57.9744	+	57.9744i	−0.0616749	+	0.0616749i
$941$	−287.782	−	597.585i	−0.305825	−	0.635053i	0.690249	−	0.723572i	$-0.257501\pi$
$941$	−287.782	−	597.585i	−0.305825	−	0.635053i	−0.996074	+	0.0885189i	$0.971787\pi$
$942$		0			0
$943$	130.034	+	14.6513i	0.137894	+	0.0155369i
$944$	−229.251	+	110.401i	−0.242850	+	0.116951i
$945$		0			0
$946$	−31.4009	+	89.7385i	−0.0331933	+	0.0948610i
$947$	−147.849	+	235.300i	−0.156123	+	0.248468i	−0.915622	−	0.402040i	$-0.868301\pi$
$947$	−147.849	+	235.300i	−0.156123	+	0.248468i	0.759499	+	0.650508i	$0.225444\pi$
$948$		0			0
$949$	−163.366	−	466.872i	−0.172145	−	0.491962i
$950$	263.122	+	60.0558i	0.276970	+	0.0632167i
$951$		0			0
$952$	160.782	−	201.614i	0.168889	−	0.211780i
$953$	−82.1839	−	360.071i	−0.0862370	−	0.377829i	0.913331	−	0.407218i	$-0.133501\pi$
$953$	−82.1839	−	360.071i	−0.0862370	−	0.377829i	−0.999568	+	0.0293889i	$0.990644\pi$
$954$		0			0
$955$	10.2601	+	91.0608i	0.0107435	+	0.0953516i
$956$		−	636.808i		−	0.666117i
$957$		0			0
$958$	−203.438			−0.212356
$959$	509.444	−	57.4006i	0.531224	−	0.0598546i
$960$		0			0
$961$	−471.607	+	107.641i	−0.490746	+	0.112009i
$962$	−165.701	−	132.142i	−0.172247	−	0.137362i
$963$		0			0
$964$	234.695	−	1028.26i	0.243459	−	1.06666i
$965$	28.0227	−	9.80556i	0.0290390	−	0.0101612i
$966$		0			0
$967$	1069.74	+	672.164i	1.10625	+	0.695102i	0.955947	−	0.293538i	$-0.0948329\pi$
$967$	1069.74	+	672.164i	1.10625	+	0.695102i	0.150301	+	0.988640i	$0.451976\pi$
$968$	−114.137	−	39.9382i	−0.117910	−	0.0412585i
$969$		0			0
$970$	−7.30280	−	15.1644i	−0.00752866	−	0.0156334i
$971$	−47.2445	+	419.307i	−0.0486555	+	0.431830i	0.945644	+	0.325204i	$0.105433\pi$
$971$	−47.2445	+	419.307i	−0.0486555	+	0.431830i	−0.994299	+	0.106625i	$0.965995\pi$
$972$		0			0
$973$	144.584	−	69.6278i	0.148596	−	0.0715599i
$974$	34.4360	+	34.4360i	0.0353552	+	0.0353552i
$975$		0			0
$976$	−690.336	+	1098.66i	−0.707311	+	1.12568i
$977$	−1121.97	−	540.311i	−1.14838	−	0.553031i	−0.239833	−	0.970814i	$-0.577093\pi$
$977$	−1121.97	−	540.311i	−1.14838	−	0.553031i	−0.908547	+	0.417784i	$0.862807\pi$
$978$		0			0
$979$	−290.700	−	66.3505i	−0.296936	−	0.0677737i
$980$	95.2484	+	119.438i	0.0971923	+	0.121875i
$981$		0			0
$982$	62.8580	+	275.399i	0.0640102	+	0.280447i
$983$	293.062	+	466.406i	0.298131	+	0.474472i	0.961876	−	0.273487i	$-0.0881769\pi$
$983$	293.062	+	466.406i	0.298131	+	0.474472i	−0.663745	+	0.747959i	$0.731034\pi$
$984$		0			0
$985$		−	96.1821i		−	0.0976468i
$986$	366.510	+	35.6982i	0.371714	+	0.0362051i
$987$		0			0
$988$	1059.57	−	119.385i	1.07244	−	0.120835i
$989$	76.7902	−	48.2505i	0.0776443	−	0.0487871i
$990$		0			0
$991$	258.790	+	206.378i	0.261140	+	0.208252i	0.745303	−	0.666725i	$-0.232305\pi$
$991$	258.790	+	206.378i	0.261140	+	0.208252i	−0.484164	+	0.874977i	$0.660876\pi$
$992$	−322.768	+	257.399i	−0.325371	+	0.259475i
$993$		0			0
$994$	−132.401	+	46.3292i	−0.133200	+	0.0466088i
$995$	64.1485	−	133.206i	0.0644709	−	0.133875i
$996$		0			0
$997$	−1064.53	−	372.496i	−1.06773	−	0.373616i	−0.261494	−	0.965205i	$-0.584215\pi$
$997$	−1064.53	−	372.496i	−1.06773	−	0.373616i	−0.806240	+	0.591589i	$0.798501\pi$
$998$	231.051	−	231.051i	0.231514	−	0.231514i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.3.s.a.73.2		48
3.2	odd	2		29.3.f.a.15.3	yes	48
29.2	odd	28	inner	261.3.s.a.118.2		48
87.2	even	28		29.3.f.a.2.3	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.f.a.2.3	✓	48	87.2	even	28
29.3.f.a.15.3	yes	48	3.2	odd	2
261.3.s.a.73.2		48	1.1	even	1	trivial
261.3.s.a.118.2		48	29.2	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)

\(f(q)\)	\(=\)	\(q+(-0.415096 + 0.0467701i) q^{2} +(-3.72959 + 0.851255i) q^{4} +(-0.738700 - 0.589093i) q^{5} +(-0.577468 + 2.53005i) q^{7} +(3.08546 - 1.07965i) q^{8} +O(q^{10})\)	\(q+(-0.415096 + 0.0467701i) q^{2} +(-3.72959 + 0.851255i) q^{4} +(-0.738700 - 0.589093i) q^{5} +(-0.577468 + 2.53005i) q^{7} +(3.08546 - 1.07965i) q^{8} +(0.334184 + 0.209981i) q^{10} +(8.65125 + 3.02720i) q^{11} +(-4.51239 - 9.37008i) q^{13} +(0.121374 - 1.07722i) q^{14} +(12.5564 - 6.04684i) q^{16} +(-21.4949 - 21.4949i) q^{17} +(14.2589 - 22.6929i) q^{19} +(3.25652 + 1.56826i) q^{20} +(-3.73269 - 0.851961i) q^{22} +(2.27710 + 2.85539i) q^{23} +(-5.36438 - 23.5029i) q^{25} +(2.31132 + 3.67844i) q^{26} -9.92764i q^{28} +(24.3191 - 15.7981i) q^{29} +(21.7090 - 2.44602i) q^{31} +(-16.0007 + 10.0539i) q^{32} +(9.92777 + 7.91713i) q^{34} +(1.91701 - 1.52877i) q^{35} +(-46.0478 + 16.1128i) q^{37} +(-4.85746 + 10.0866i) q^{38} +(-2.91524 - 1.02009i) q^{40} +(25.3355 - 25.3355i) q^{41} +(2.78030 - 24.6759i) q^{43} +(-34.8426 - 3.92581i) q^{44} +(-1.07876 - 1.07876i) q^{46} +(-7.49184 + 21.4104i) q^{47} +(38.0798 + 18.3383i) q^{49} +(3.32597 + 9.50507i) q^{50} +(24.8057 + 31.1054i) q^{52} +(18.6271 - 23.3576i) q^{53} +(-4.60737 - 7.33259i) q^{55} +(0.949813 + 8.42982i) q^{56} +(-9.35591 + 7.69514i) q^{58} -18.2577 q^{59} +(-78.8333 + 49.5342i) q^{61} +(-8.89694 + 2.03067i) q^{62} +(-37.4125 + 29.8355i) q^{64} +(-2.18655 + 9.57990i) q^{65} +(24.5454 - 50.9691i) q^{67} +(98.4648 + 61.8696i) q^{68} +(-0.724244 + 0.724244i) q^{70} +(-56.1438 - 116.584i) q^{71} +(47.2614 + 5.32509i) q^{73} +(18.3607 - 8.84204i) q^{74} +(-33.8624 + 96.7732i) q^{76} +(-12.6548 + 20.1400i) q^{77} +(-13.7375 - 39.2594i) q^{79} +(-12.8375 - 2.93009i) q^{80} +(-9.33174 + 11.7016i) q^{82} +(29.4538 + 129.046i) q^{83} +(3.21577 + 28.5408i) q^{85} +10.3729i q^{86} +29.9614 q^{88} +(-32.3276 + 3.64244i) q^{89} +(26.3125 - 6.00567i) q^{91} +(-10.9233 - 8.71105i) q^{92} +(2.10847 - 9.23779i) q^{94} +(-23.9012 + 8.36341i) q^{95} +(-36.1089 - 22.6888i) q^{97} +(-16.6645 - 5.83115i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) \) 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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