LMFDB - Embedded newform 675.2.l.a.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(76,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("675.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, 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:	$5.38990213644$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			151.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	675.151
Dual form			675.2.l.a.76.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.93969 - 1.62760i) q^{2} +(1.11334 + 1.32683i) q^{3} +(0.766044 + 4.34445i) q^{4} -4.38571i q^{6} +(0.532089 - 3.01763i) q^{7} +(3.05303 - 5.28801i) q^{8} +(-0.520945 + 2.95442i) q^{9} +O(q^{10})$	\(q+(-1.93969 - 1.62760i) q^{2} +(1.11334 + 1.32683i) q^{3} +(0.766044 + 4.34445i) q^{4} -4.38571i q^{6} +(0.532089 - 3.01763i) q^{7} +(3.05303 - 5.28801i) q^{8} +(-0.520945 + 2.95442i) q^{9} +(-5.29813 + 1.92836i) q^{11} +(-4.91147 + 5.85327i) q^{12} +(-3.23783 + 2.71686i) q^{13} +(-5.94356 + 4.98724i) q^{14} +(-6.23783 + 2.27038i) q^{16} +(-0.826352 - 1.43128i) q^{17} +(5.81908 - 4.88279i) q^{18} +(-0.120615 + 0.208911i) q^{19} +(4.59627 - 2.65366i) q^{21} +(13.4153 + 4.88279i) q^{22} +(-1.29426 - 7.34013i) q^{23} +(10.4153 - 1.83651i) q^{24} +10.7023 q^{26} +(-4.50000 + 2.59808i) q^{27} +13.5175 q^{28} +(-5.90033 - 4.95096i) q^{29} +(0.858441 + 4.86846i) q^{31} +(4.31908 + 1.57202i) q^{32} +(-8.45723 - 4.88279i) q^{33} +(-0.726682 + 4.12122i) q^{34} -13.2344 q^{36} +(-1.24510 - 2.15658i) q^{37} +(0.573978 - 0.208911i) q^{38} +(-7.20961 - 1.27125i) q^{39} +(-0.109470 + 0.0918566i) q^{41} +(-13.2344 - 2.33359i) q^{42} +(-0.705737 + 0.256867i) q^{43} +(-12.4363 - 21.5403i) q^{44} +(-9.43629 + 16.3441i) q^{46} +(-0.807934 + 4.58202i) q^{47} +(-9.95723 - 5.74881i) q^{48} +(-2.24510 - 0.817150i) q^{49} +(0.979055 - 2.68993i) q^{51} +(-14.2836 - 11.9854i) q^{52} -12.1061 q^{53} +(12.9572 + 2.28471i) q^{54} +(-14.3327 - 12.0266i) q^{56} +(-0.411474 + 0.0725540i) q^{57} +(3.38666 + 19.2067i) q^{58} +(4.45336 + 1.62089i) q^{59} +(2.41488 - 13.6955i) q^{61} +(6.25877 - 10.8405i) q^{62} +(8.63816 + 3.14403i) q^{63} +(0.819078 + 1.41868i) q^{64} +(8.45723 + 23.2361i) q^{66} +(-5.64543 + 4.73708i) q^{67} +(5.58512 - 4.68647i) q^{68} +(8.29813 - 9.88933i) q^{69} +(2.45084 + 4.24497i) q^{71} +(14.0326 + 11.7747i) q^{72} +(-0.113341 + 0.196312i) q^{73} +(-1.09492 + 6.20961i) q^{74} +(-1.00000 - 0.363970i) q^{76} +(3.00000 + 17.0138i) q^{77} +(11.9153 + 14.2002i) q^{78} +(-7.53596 - 6.32342i) q^{79} +(-8.45723 - 3.07818i) q^{81} +0.361844 q^{82} +(6.78493 + 5.69323i) q^{83} +(15.0496 + 17.9355i) q^{84} +(1.78699 + 0.650411i) q^{86} -13.3408i q^{87} +(-5.97818 + 33.9039i) q^{88} +(-3.33022 + 5.76811i) q^{89} +(6.47565 + 11.2162i) q^{91} +(30.8974 - 11.2457i) q^{92} +(-5.50387 + 6.55926i) q^{93} +(9.02481 - 7.57272i) q^{94} +(2.72281 + 7.48086i) q^{96} +(-8.95723 + 3.26017i) q^{97} +(3.02481 + 5.23913i) q^{98} +(-2.93717 - 16.6575i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 6 q^{7} + 6 q^{8}+O(q^{10}) $ 6 * q - 6 * q^2 - 6 * q^7 + 6 * q^8	$ 6 q - 6 q^{2} - 6 q^{7} + 6 q^{8} - 18 q^{11} - 9 q^{12} - 6 q^{14} - 18 q^{16} - 6 q^{17} + 18 q^{18} - 12 q^{19} + 36 q^{22} - 18 q^{23} + 18 q^{24} + 12 q^{26} - 27 q^{27} + 36 q^{28} - 21 q^{29} - 3 q^{31} + 9 q^{32} + 9 q^{34} - 18 q^{36} - 6 q^{37} - 12 q^{38} - 9 q^{39} - 18 q^{41} - 18 q^{42} + 6 q^{43} - 27 q^{44} - 9 q^{46} + 6 q^{47} - 9 q^{48} - 12 q^{49} + 9 q^{51} - 36 q^{52} - 48 q^{53} + 27 q^{54} - 48 q^{56} + 18 q^{57} + 27 q^{58} + 36 q^{61} + 15 q^{62} + 18 q^{63} - 12 q^{64} - 18 q^{67} + 12 q^{68} + 36 q^{69} + 3 q^{71} + 9 q^{72} + 6 q^{73} + 12 q^{74} - 6 q^{76} + 18 q^{77} + 27 q^{78} - 12 q^{79} + 36 q^{82} - 18 q^{83} + 36 q^{84} + 3 q^{86} + 18 q^{88} + 3 q^{89} + 63 q^{92} - 9 q^{93} + 27 q^{94} + 27 q^{96} - 3 q^{97} - 9 q^{98} - 27 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 - 6 * q^7 + 6 * q^8 - 18 * q^11 - 9 * q^12 - 6 * q^14 - 18 * q^16 - 6 * q^17 + 18 * q^18 - 12 * q^19 + 36 * q^22 - 18 * q^23 + 18 * q^24 + 12 * q^26 - 27 * q^27 + 36 * q^28 - 21 * q^29 - 3 * q^31 + 9 * q^32 + 9 * q^34 - 18 * q^36 - 6 * q^37 - 12 * q^38 - 9 * q^39 - 18 * q^41 - 18 * q^42 + 6 * q^43 - 27 * q^44 - 9 * q^46 + 6 * q^47 - 9 * q^48 - 12 * q^49 + 9 * q^51 - 36 * q^52 - 48 * q^53 + 27 * q^54 - 48 * q^56 + 18 * q^57 + 27 * q^58 + 36 * q^61 + 15 * q^62 + 18 * q^63 - 12 * q^64 - 18 * q^67 + 12 * q^68 + 36 * q^69 + 3 * q^71 + 9 * q^72 + 6 * q^73 + 12 * q^74 - 6 * q^76 + 18 * q^77 + 27 * q^78 - 12 * q^79 + 36 * q^82 - 18 * q^83 + 36 * q^84 + 3 * q^86 + 18 * q^88 + 3 * q^89 + 63 * q^92 - 9 * q^93 + 27 * q^94 + 27 * q^96 - 3 * q^97 - 9 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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 $

$2$	−1.93969	−	1.62760i	−1.37157	−	1.15088i	−0.972216	−	0.234087i	$-0.924790\pi$
$2$	−1.93969	−	1.62760i	−1.37157	−	1.15088i	−0.399354	−	0.916797i	$-0.630766\pi$
$3$	1.11334	+	1.32683i	0.642788	+	0.766044i
$3$	1.11334	+	1.32683i	0.642788	+	0.766044i
$4$	0.766044	+	4.34445i	0.383022	+	2.17223i
$5$		0			0
$5$		0			0
$6$		−	4.38571i		−	1.79046i
$7$	0.532089	−	3.01763i	0.201111	−	1.14056i	−0.702333	−	0.711849i	$-0.747858\pi$
$7$	0.532089	−	3.01763i	0.201111	−	1.14056i	0.903444	−	0.428707i	$-0.141031\pi$
$8$	3.05303	−	5.28801i	1.07941	−	1.86959i
$9$	−0.520945	+	2.95442i	−0.173648	+	0.984808i
$10$		0			0
$11$	−5.29813	+	1.92836i	−1.59745	+	0.581423i	−0.978903	−	0.204326i	$-0.934500\pi$
$11$	−5.29813	+	1.92836i	−1.59745	+	0.581423i	−0.618545	+	0.785750i	$0.712277\pi$
$12$	−4.91147	+	5.85327i	−1.41782	+	1.68969i
$13$	−3.23783	+	2.71686i	−0.898011	+	0.753521i	−0.969801	−	0.243899i	$-0.921574\pi$
$13$	−3.23783	+	2.71686i	−0.898011	+	0.753521i	0.0717893	+	0.997420i	$0.477129\pi$
$14$	−5.94356	+	4.98724i	−1.58848	+	1.33290i
$15$		0			0
$16$	−6.23783	+	2.27038i	−1.55946	+	0.567596i
$17$	−0.826352	−	1.43128i	−0.200420	−	0.347137i	0.748244	−	0.663424i	$-0.230897\pi$
$17$	−0.826352	−	1.43128i	−0.200420	−	0.347137i	−0.948664	+	0.316286i	$0.897564\pi$
$18$	5.81908	−	4.88279i	1.37157	−	1.15088i
$19$	−0.120615	+	0.208911i	−0.0276709	+	0.0479274i	−0.879529	−	0.475845i	$-0.842142\pi$
$19$	−0.120615	+	0.208911i	−0.0276709	+	0.0479274i	0.851858	+	0.523772i	$0.175476\pi$
$20$		0			0
$21$	4.59627	−	2.65366i	1.00299	−	0.579075i
$22$	13.4153	+	4.88279i	2.86016	+	1.04101i
$23$	−1.29426	−	7.34013i	−0.269872	−	1.53052i	−0.754792	−	0.655964i	$-0.772262\pi$
$23$	−1.29426	−	7.34013i	−0.269872	−	1.53052i	0.484920	−	0.874559i	$-0.338849\pi$
$24$	10.4153	−	1.83651i	2.12602	−	0.374875i
$25$		0			0
$26$	10.7023			2.09890
$27$	−4.50000	+	2.59808i	−0.866025	+	0.500000i
$28$	13.5175			2.55458
$29$	−5.90033	−	4.95096i	−1.09566	−	0.919371i	−0.0985378	−	0.995133i	$-0.531417\pi$
$29$	−5.90033	−	4.95096i	−1.09566	−	0.919371i	−0.997126	+	0.0757623i	$0.975861\pi$
$30$		0			0
$31$	0.858441	+	4.86846i	0.154181	+	0.874401i	0.959531	+	0.281602i	$0.0908659\pi$
$31$	0.858441	+	4.86846i	0.154181	+	0.874401i	−0.805351	+	0.592799i	$0.798023\pi$
$32$	4.31908	+	1.57202i	0.763512	+	0.277896i
$33$	−8.45723	−	4.88279i	−1.47222	−	0.849984i
$34$	−0.726682	+	4.12122i	−0.124625	+	0.706783i
$35$		0			0
$36$	−13.2344			−2.20574
$37$	−1.24510	−	2.15658i	−0.204693	−	0.354539i	0.745342	−	0.666683i	$-0.232286\pi$
$37$	−1.24510	−	2.15658i	−0.204693	−	0.354539i	−0.950035	+	0.312144i	$0.898953\pi$
$38$	0.573978	−	0.208911i	0.0931115	−	0.0338898i
$39$	−7.20961	−	1.27125i	−1.15446	−	0.203563i
$40$		0			0
$41$	−0.109470	+	0.0918566i	−0.0170964	+	0.0143456i	−0.651296	−	0.758824i	$-0.725774\pi$
$41$	−0.109470	+	0.0918566i	−0.0170964	+	0.0143456i	0.634199	+	0.773170i	$0.281330\pi$
$42$	−13.2344	−	2.33359i	−2.04212	−	0.360080i
$43$	−0.705737	+	0.256867i	−0.107624	+	0.0391719i	−0.395271	−	0.918565i	$-0.629349\pi$
$43$	−0.705737	+	0.256867i	−0.107624	+	0.0391719i	0.287647	+	0.957737i	$0.407127\pi$
$44$	−12.4363	−	21.5403i	−1.87484	−	3.24732i
$45$		0			0
$46$	−9.43629	+	16.3441i	−1.39130	+	2.40981i
$47$	−0.807934	+	4.58202i	−0.117849	+	0.668356i	0.867451	+	0.497523i	$0.165757\pi$
$47$	−0.807934	+	4.58202i	−0.117849	+	0.668356i	−0.985300	+	0.170833i	$0.945354\pi$
$48$	−9.95723	−	5.74881i	−1.43720	−	0.829769i
$49$	−2.24510	−	0.817150i	−0.320729	−	0.116736i
$50$		0			0
$51$	0.979055	−	2.68993i	0.137095	−	0.376666i
$52$	−14.2836	−	11.9854i	−1.98078	−	1.66207i
$53$	−12.1061			−1.66290			−0.831448	−	0.555602i	$-0.812488\pi$
$53$	−12.1061			−1.66290			−0.831448	+	0.555602i	$0.812488\pi$
$54$	12.9572	+	2.28471i	1.76326	+	0.310910i
$55$		0			0
$56$	−14.3327	−	12.0266i	−1.91529	−	1.60712i
$57$	−0.411474	+	0.0725540i	−0.0545011	+	0.00961001i
$58$	3.38666	+	19.2067i	0.444690	+	2.52196i
$59$	4.45336	+	1.62089i	0.579779	+	0.211022i	0.615228	−	0.788349i	$-0.289064\pi$
$59$	4.45336	+	1.62089i	0.579779	+	0.211022i	−0.0354493	+	0.999371i	$0.511286\pi$
$60$		0			0
$61$	2.41488	−	13.6955i	0.309193	−	1.75352i	−0.293885	−	0.955841i	$-0.594948\pi$
$61$	2.41488	−	13.6955i	0.309193	−	1.75352i	0.603078	−	0.797682i	$-0.293941\pi$
$62$	6.25877	−	10.8405i	0.794865	−	1.37675i
$63$	8.63816	+	3.14403i	1.08831	+	0.396111i
$64$	0.819078	+	1.41868i	0.102385	+	0.177336i
$65$		0			0
$66$	8.45723	+	23.2361i	1.04101	+	2.86016i
$67$	−5.64543	+	4.73708i	−0.689699	+	0.578726i	−0.918822	−	0.394671i	$-0.870859\pi$
$67$	−5.64543	+	4.73708i	−0.689699	+	0.578726i	0.229123	+	0.973397i	$0.426414\pi$
$68$	5.58512	−	4.68647i	0.677296	−	0.568318i
$69$	8.29813	−	9.88933i	0.998978	−	1.19054i
$70$		0			0
$71$	2.45084	+	4.24497i	0.290861	+	0.503786i	0.974014	−	0.226490i	$-0.0727250\pi$
$71$	2.45084	+	4.24497i	0.290861	+	0.503786i	−0.683153	+	0.730276i	$0.739392\pi$
$72$	14.0326	+	11.7747i	1.65375	+	1.38766i
$73$	−0.113341	+	0.196312i	−0.0132655	+	0.0229766i	−0.872582	−	0.488468i	$-0.837556\pi$
$73$	−0.113341	+	0.196312i	−0.0132655	+	0.0229766i	0.859316	+	0.511444i	$0.170889\pi$
$74$	−1.09492	+	6.20961i	−0.127282	+	0.721853i
$75$		0			0
$76$	−1.00000	−	0.363970i	−0.114708	−	0.0417502i
$77$	3.00000	+	17.0138i	0.341882	+	1.93891i
$78$	11.9153	+	14.2002i	1.34915	+	1.60785i
$79$	−7.53596	−	6.32342i	−0.847862	−	0.711440i	0.111456	−	0.993769i	$-0.464449\pi$
$79$	−7.53596	−	6.32342i	−0.847862	−	0.711440i	−0.959318	+	0.282329i	$0.908893\pi$
$80$		0			0
$81$	−8.45723	−	3.07818i	−0.939693	−	0.342020i
$82$	0.361844			0.0399590
$83$	6.78493	+	5.69323i	0.744743	+	0.624913i	0.934107	−	0.356994i	$-0.116198\pi$
$83$	6.78493	+	5.69323i	0.744743	+	0.624913i	−0.189364	+	0.981907i	$0.560643\pi$
$84$	15.0496	+	17.9355i	1.64205	+	1.95692i
$85$		0			0
$86$	1.78699	+	0.650411i	0.192696	+	0.0701356i
$87$		−	13.3408i		−	1.43029i
$88$	−5.97818	+	33.9039i	−0.637276	+	3.61417i
$89$	−3.33022	+	5.76811i	−0.353003	+	0.611419i	−0.986774	−	0.162102i	$-0.948173\pi$
$89$	−3.33022	+	5.76811i	−0.353003	+	0.611419i	0.633771	+	0.773521i	$0.281506\pi$
$90$		0			0
$91$	6.47565	+	11.2162i	0.678833	+	1.17577i
$92$	30.8974	−	11.2457i	3.22128	−	1.17245i
$93$	−5.50387	+	6.55926i	−0.570725	+	0.680163i
$94$	9.02481	−	7.57272i	0.930839	−	0.781066i
$95$		0			0
$96$	2.72281	+	7.48086i	0.277896	+	0.763512i
$97$	−8.95723	+	3.26017i	−0.909469	+	0.331020i	−0.754041	−	0.656827i	$-0.771898\pi$
$97$	−8.95723	+	3.26017i	−0.909469	+	0.331020i	−0.155428	+	0.987847i	$0.549676\pi$
$98$	3.02481	+	5.23913i	0.305552	+	0.529232i
$99$	−2.93717	−	16.6575i	−0.295196	−	1.67414i
$100$		0			0
$101$	−0.405078	+	2.29731i	−0.0403067	+	0.228591i	−0.998306	−	0.0581793i	$-0.981470\pi$
$101$	−0.405078	+	2.29731i	−0.0403067	+	0.228591i	0.957999	+	0.286770i	$0.0925816\pi$
$102$	−6.27719	+	3.62414i	−0.621534	+	0.358843i
$103$	−17.5141	−	6.37462i	−1.72572	−	0.628110i	−0.727408	−	0.686205i	$-0.759275\pi$
$103$	−17.5141	−	6.37462i	−1.72572	−	0.628110i	−0.998311	+	0.0580946i	$0.981497\pi$
$104$	4.48158	+	25.4163i	0.439455	+	2.49227i
$105$		0			0
$106$	23.4820	+	19.7038i	2.28078	+	1.91380i
$107$	−10.4037			−1.00577			−0.502883	−	0.864354i	$-0.667728\pi$
$107$	−10.4037			−1.00577			−0.502883	+	0.864354i	$0.667728\pi$
$108$	−14.7344	−	17.5598i	−1.41782	−	1.68969i
$109$	0.147956			0.0141716			0.00708580	−	0.999975i	$-0.497745\pi$
$109$	0.147956			0.0141716			0.00708580	+	0.999975i	$0.497745\pi$
$110$		0			0
$111$	1.47519	−	4.05304i	0.140018	−	0.384697i
$112$	3.53209	+	20.0315i	0.333751	+	1.89280i
$113$	6.65183	+	2.42107i	0.625751	+	0.227755i	0.635381	−	0.772199i	$-0.280843\pi$
$113$	6.65183	+	2.42107i	0.625751	+	0.227755i	−0.00962978	+	0.999954i	$0.503065\pi$
$114$	0.916222	+	0.528981i	0.0858120	+	0.0495436i
$115$		0			0
$116$	16.9893	−	29.4264i	1.57742	−	2.73217i
$117$	−6.34002	−	10.9812i	−0.586135	−	1.01522i
$118$	−6.00000	−	10.3923i	−0.552345	−	0.956689i
$119$	−4.75877	+	1.73205i	−0.436236	+	0.158777i
$120$		0			0
$121$	15.9251	−	13.3628i	1.44774	−	1.21480i
$122$	−26.9748	+	22.6345i	−2.44218	+	2.04923i
$123$	−0.243756	−	0.0429807i	−0.0219787	−	0.00387544i
$124$	−20.4932	+	7.45891i	−1.84034	+	0.669830i
$125$		0			0
$126$	−11.6382	−	20.1579i	−1.03681	−	1.79581i
$127$	−0.121959	+	0.211239i	−0.0108221	+	0.0187444i	−0.871386	−	0.490599i	$-0.836778\pi$
$127$	−0.121959	+	0.211239i	−0.0108221	+	0.0187444i	0.860564	+	0.509343i	$0.170112\pi$
$128$	2.31655	−	13.1378i	0.204756	−	1.16123i
$129$	−1.12654	−	0.650411i	−0.0991867	−	0.0572655i
$130$		0			0
$131$	1.57263	+	8.91885i	0.137402	+	0.779243i	0.973157	+	0.230142i	$0.0739190\pi$
$131$	1.57263	+	8.91885i	0.137402	+	0.779243i	−0.835755	+	0.549102i	$0.814970\pi$
$132$	14.7344	−	40.4825i	1.28247	−	3.52355i
$133$	0.566237	+	0.475129i	0.0490990	+	0.0411989i
$134$	18.6604			1.61202
$135$		0			0
$136$	−10.0915			−0.865341
$137$	9.50253	+	7.97357i	0.811856	+	0.681228i	0.951050	−	0.309037i	$-0.100007\pi$
$137$	9.50253	+	7.97357i	0.811856	+	0.681228i	−0.139194	+	0.990265i	$0.544451\pi$
$138$	−32.1917	+	5.67626i	−2.74034	+	0.483195i
$139$	3.21823	+	18.2515i	0.272966	+	1.54807i	0.745348	+	0.666675i	$0.232283\pi$
$139$	3.21823	+	18.2515i	0.272966	+	1.54807i	−0.472382	+	0.881394i	$0.656606\pi$
$140$		0			0
$141$	−6.97906	+	4.02936i	−0.587742	+	0.339333i
$142$	2.15523	−	12.2229i	0.180863	−	1.02572i
$143$	11.9153	−	20.6380i	0.996411	−	1.72583i
$144$	−3.45811	−	19.6119i	−0.288176	−	1.63433i
$145$		0			0
$146$	0.539363	−	0.196312i	0.0446380	−	0.0162469i
$147$	−1.41534	−	3.88863i	−0.116736	−	0.320729i
$148$	8.41534	−	7.06131i	0.691737	−	0.580436i
$149$	−3.66044	+	3.07148i	−0.299875	+	0.251625i	−0.780292	−	0.625415i	$-0.784930\pi$
$149$	−3.66044	+	3.07148i	−0.299875	+	0.251625i	0.480417	+	0.877040i	$0.340485\pi$
$150$		0			0
$151$	5.25877	−	1.91404i	0.427953	−	0.155762i	−0.119059	−	0.992887i	$-0.537988\pi$
$151$	5.25877	−	1.91404i	0.427953	−	0.155762i	0.547011	+	0.837125i	$0.315765\pi$
$152$	0.736482	+	1.27562i	0.0597366	+	0.103467i
$153$	4.65910	−	1.69577i	0.376666	−	0.137095i
$154$	21.8726	−	37.8844i	1.76254	−	3.05281i
$155$		0			0
$156$		−	32.2956i		−	2.58572i
$157$	18.8059	+	6.84478i	1.50087	+	0.546273i	0.956286	−	0.292432i	$-0.0944646\pi$
$157$	18.8059	+	6.84478i	1.50087	+	0.546273i	0.544586	+	0.838705i	$0.316687\pi$
$158$	4.32547	+	24.5310i	0.344116	+	1.95158i
$159$	−13.4782	−	16.0627i	−1.06889	−	1.27385i
$160$		0			0
$161$	−22.8384			−1.79992
$162$	11.3944	+	19.7357i	0.895229	+	1.55058i
$163$	−9.95811			−0.779979			−0.389990	−	0.920819i	$-0.627521\pi$
$163$	−9.95811			−0.779979			−0.389990	+	0.920819i	$0.627521\pi$
$164$	−0.482926	−	0.405223i	−0.0377102	−	0.0316426i
$165$		0			0
$166$	−3.89440	−	22.0862i	−0.302264	−	1.71422i
$167$	2.97178	+	1.08164i	0.229963	+	0.0836998i	0.454432	−	0.890782i	$-0.349842\pi$
$167$	2.97178	+	1.08164i	0.229963	+	0.0836998i	−0.224468	+	0.974481i	$0.572065\pi$
$168$		−	32.4068i		−	2.50024i
$169$	0.844770	−	4.79093i	0.0649823	−	0.368533i
$170$		0			0
$171$	−0.554378	−	0.465178i	−0.0423943	−	0.0355731i
$172$	−1.65657	−	2.86927i	−0.126313	−	0.218780i
$173$	18.5608	−	6.75557i	1.41115	−	0.513616i	0.479682	−	0.877442i	$-0.340752\pi$
$173$	18.5608	−	6.75557i	1.41115	−	0.513616i	0.931467	+	0.363826i	$0.118530\pi$
$174$	−21.7135	+	25.8771i	−1.64609	+	1.96174i
$175$		0			0
$176$	28.6707	−	24.0576i	2.16114	−	1.81341i
$177$	2.80747	+	7.71345i	0.211022	+	0.579779i
$178$	15.8478	−	5.76811i	1.18784	−	0.432338i
$179$	4.05051	+	7.01568i	0.302749	+	0.524377i	0.976758	−	0.214347i	$-0.0687622\pi$
$179$	4.05051	+	7.01568i	0.302749	+	0.524377i	−0.674009	+	0.738724i	$0.735429\pi$
$180$		0			0
$181$	4.45723	−	7.72016i	0.331304	−	0.573835i	−0.651464	−	0.758679i	$-0.725845\pi$
$181$	4.45723	−	7.72016i	0.331304	−	0.573835i	0.982768	+	0.184845i	$0.0591782\pi$
$182$	5.69459	−	32.2956i	0.422111	−	2.39391i
$183$	20.8601	−	12.0436i	1.54202	−	0.890287i
$184$	−42.7661	−	15.5656i	−3.15276	−	1.14751i
$185$		0			0
$186$	21.3516	−	3.76487i	1.56558	−	0.276054i
$187$	7.13816	+	5.98962i	0.521994	+	0.438005i
$188$	−20.5253			−1.49696
$189$	5.44562	+	14.9617i	0.396111	+	1.08831i
$190$		0			0
$191$	−4.27584	−	3.58786i	−0.309389	−	0.259608i	0.474850	−	0.880067i	$-0.342502\pi$
$191$	−4.27584	−	3.58786i	−0.309389	−	0.259608i	−0.784240	+	0.620458i	$0.786947\pi$
$192$	−0.970437	+	2.66625i	−0.0700353	+	0.192420i
$193$	−4.39780	−	24.9412i	−0.316561	−	1.79531i	−0.563331	−	0.826232i	$-0.690480\pi$
$193$	−4.39780	−	24.9412i	−0.316561	−	1.79531i	0.246770	−	0.969074i	$-0.420631\pi$
$194$	22.6805	+	8.25503i	1.62837	+	0.592677i
$195$		0			0
$196$	1.83022	−	10.3797i	0.130730	−	0.741408i
$197$	2.44104	−	4.22800i	0.173917	−	0.301233i	−0.765869	−	0.642996i	$-0.777691\pi$
$197$	2.44104	−	4.22800i	0.173917	−	0.301233i	0.939786	+	0.341764i	$0.111024\pi$
$198$	−21.4145	+	37.0909i	−1.52186	+	2.63594i
$199$	−8.68092	−	15.0358i	−0.615374	−	1.06586i	−0.990319	−	0.138812i	$-0.955672\pi$
$199$	−8.68092	−	15.0358i	−0.615374	−	1.06586i	0.374944	−	0.927047i	$-0.377662\pi$
$200$		0			0
$201$	−12.5706	−	2.21653i	−0.886660	−	0.156342i
$202$	4.52481	−	3.79677i	0.318365	−	0.267140i
$203$	−18.0797	+	15.1706i	−1.26894	+	1.06477i
$204$	12.4363	+	2.19285i	0.870714	+	0.153530i
$205$		0			0
$206$	23.5967	+	40.8707i	1.64406	+	2.84760i
$207$	22.3601			1.55413
$208$	14.0287	−	24.2984i	0.972714	−	1.68479i
$209$	0.236177	−	1.33943i	0.0163367	−	0.0926501i
$210$		0			0
$211$	−10.7699	−	3.91993i	−0.741432	−	0.269859i	−0.0564359	−	0.998406i	$-0.517974\pi$
$211$	−10.7699	−	3.91993i	−0.741432	−	0.269859i	−0.684996	+	0.728547i	$0.740196\pi$
$212$	−9.27379	−	52.5942i	−0.636926	−	3.61219i
$213$	−2.90373	+	7.97794i	−0.198961	+	0.546640i
$214$	20.1800	+	16.9331i	1.37948	+	1.15752i
$215$		0			0
$216$			31.7281i			2.15882i
$217$	15.1480			1.02831
$218$	−0.286989	−	0.240812i	−0.0194373	−	0.0163099i
$219$	−0.386659	+	0.0681784i	−0.0261280	+	0.00460707i
$220$		0			0
$221$	6.56418	+	2.38917i	0.441554	+	0.160713i
$222$	−9.45811	+	5.46064i	−0.634787	+	0.366494i
$223$	−0.0765042	+	0.433877i	−0.00512310	+	0.0290545i	−0.987262	−	0.159102i	$-0.949140\pi$
$223$	−0.0765042	+	0.433877i	−0.00512310	+	0.0290545i	0.982139	+	0.188157i	$0.0602512\pi$
$224$	7.04189	−	12.1969i	0.470506	−	0.814940i
$225$		0			0
$226$	−8.96198	−	15.5226i	−0.596142	−	1.03255i
$227$	4.99273	−	1.81720i	0.331379	−	0.120612i	−0.170972	−	0.985276i	$-0.554691\pi$
$227$	4.99273	−	1.81720i	0.331379	−	0.120612i	0.502351	+	0.864664i	$0.332469\pi$
$228$	−0.630415	−	1.73205i	−0.0417502	−	0.114708i
$229$	0.0603074	−	0.0506039i	0.00398522	−	0.00334400i	−0.640793	−	0.767714i	$-0.721394\pi$
$229$	0.0603074	−	0.0506039i	0.00398522	−	0.00334400i	0.644778	+	0.764370i	$0.276950\pi$
$230$		0			0
$231$	−19.2344	+	22.9227i	−1.26553	+	1.50820i
$232$	−44.1946	+	16.0855i	−2.90152	+	1.05607i
$233$	−0.187319	−	0.324446i	−0.0122717	−	0.0212551i	0.859824	−	0.510590i	$-0.170573\pi$
$233$	−0.187319	−	0.324446i	−0.0122717	−	0.0212551i	−0.872096	+	0.489335i	$0.837240\pi$
$234$	−5.57532	+	31.6192i	−0.364470	+	2.06701i
$235$		0			0
$236$	−3.63041	+	20.5891i	−0.236320	+	1.34024i
$237$		−	17.0390i		−	1.10680i
$238$	12.0496	+	4.38571i	0.781061	+	0.284283i
$239$	−1.88666	−	10.6998i	−0.122038	−	0.692111i	−0.983023	−	0.183481i	$-0.941263\pi$
$239$	−1.88666	−	10.6998i	−0.122038	−	0.692111i	0.860985	−	0.508630i	$-0.169848\pi$
$240$		0			0
$241$	20.4893	+	17.1926i	1.31983	+	1.10747i	0.986341	+	0.164719i	$0.0526717\pi$
$241$	20.4893	+	17.1926i	1.31983	+	1.10747i	0.333493	+	0.942753i	$0.391773\pi$
$242$	−52.6391			−3.38377
$243$	−5.33157	−	14.6484i	−0.342020	−	0.939693i
$244$	61.3492			3.92748
$245$		0			0
$246$	0.402856	+	0.480105i	0.0256852	+	0.0306104i
$247$	−0.177052	−	1.00411i	−0.0112655	−	0.0638900i
$248$	28.3653	+	10.3241i	1.80120	+	0.655583i
$249$			15.3409i			0.972193i
$250$		0			0
$251$	2.99660	−	5.19026i	0.189143	−	0.327606i	−0.755821	−	0.654778i	$-0.772762\pi$
$251$	2.99660	−	5.19026i	0.189143	−	0.327606i	0.944965	+	0.327172i	$0.106096\pi$
$252$	−7.04189	+	39.9365i	−0.443597	+	2.51577i
$253$	21.0116	+	36.3932i	1.32099	+	2.28802i
$254$	0.580375	−	0.211239i	0.0364159	−	0.0132543i
$255$		0			0
$256$	−23.3666	+	19.6069i	−1.46042	+	1.22543i
$257$	4.84524	−	4.06564i	0.302238	−	0.253607i	−0.479037	−	0.877795i	$-0.659014\pi$
$257$	4.84524	−	4.06564i	0.302238	−	0.253607i	0.781275	+	0.624187i	$0.214570\pi$
$258$	1.12654	+	3.09516i	0.0701356	+	0.192696i
$259$	−7.17024	+	2.60976i	−0.445537	+	0.162162i
$260$		0			0
$261$	17.7010	−	14.8529i	1.09566	−	0.919371i
$262$	11.4659	−	19.8594i	0.708363	−	1.22692i
$263$	0.0812519	−	0.460802i	0.00501021	−	0.0284143i	−0.982200	−	0.187837i	$-0.939852\pi$
$263$	0.0812519	−	0.460802i	0.00501021	−	0.0284143i	0.987210	+	0.159423i	$0.0509634\pi$
$264$	−51.6404	+	29.8146i	−3.17825	+	1.83496i
$265$		0			0
$266$	−0.325008	−	1.84321i	−0.0199275	−	0.113014i
$267$	−11.3610	+	2.00324i	−0.695280	+	0.122597i
$268$	−24.9047	−	20.8975i	−1.52129	−	1.27652i
$269$	1.84524			0.112506			0.0562530	−	0.998417i	$-0.482085\pi$
$269$	1.84524			0.112506			0.0562530	+	0.998417i	$0.482085\pi$
$270$		0			0
$271$	−4.12567			−0.250616			−0.125308	−	0.992118i	$-0.539992\pi$
$271$	−4.12567			−0.250616			−0.125308	+	0.992118i	$0.539992\pi$
$272$	8.40420	+	7.05196i	0.509579	+	0.427588i
$273$	−7.67230	+	21.0795i	−0.464349	+	1.27579i
$274$	−5.45424	−	30.9325i	−0.329503	−	1.86870i
$275$		0			0
$276$	49.3205	+	28.4752i	2.96874	+	1.71401i
$277$	−0.0106775	+	0.0605553i	−0.000641550	+	0.00363841i	−0.985127	−	0.171829i	$-0.945032\pi$
$277$	−0.0106775	+	0.0605553i	−0.000641550	+	0.00363841i	0.984485	+	0.175467i	$0.0561436\pi$
$278$	23.4636	−	40.6402i	1.40726	−	2.43744i
$279$	−14.8307			−0.887890
$280$		0			0
$281$	5.68479	−	2.06910i	0.339126	−	0.123432i	−0.166843	−	0.985984i	$-0.553357\pi$
$281$	5.68479	−	2.06910i	0.339126	−	0.123432i	0.505969	+	0.862552i	$0.331135\pi$
$282$	20.0954	+	3.54336i	1.19666	+	0.211004i
$283$	−6.40033	+	5.37051i	−0.380460	+	0.319244i	−0.812883	−	0.582427i	$-0.802103\pi$
$283$	−6.40033	+	5.37051i	−0.380460	+	0.319244i	0.432423	+	0.901671i	$0.357659\pi$
$284$	−16.5646	+	13.8994i	−0.982931	+	0.824777i
$285$		0			0
$286$	−56.7024	+	20.6380i	−3.35288	+	1.22035i
$287$	0.218941	+	0.379217i	0.0129237	+	0.0223844i
$288$	−6.89440	+	11.9415i	−0.406256	+	0.703657i
$289$	7.13429	−	12.3569i	0.419664	−	0.726879i
$290$		0			0
$291$	−14.2981	−	8.25503i	−0.838171	−	0.483918i
$292$	−0.939693	−	0.342020i	−0.0549914	−	0.0200152i
$293$	2.08600	+	11.8303i	0.121865	+	0.691133i	0.983120	+	0.182960i	$0.0585679\pi$
$293$	2.08600	+	11.8303i	0.121865	+	0.691133i	−0.861255	+	0.508173i	$0.830321\pi$
$294$	−3.58378	+	9.84635i	−0.209010	+	0.574251i
$295$		0			0
$296$	−15.2053			−0.883792
$297$	18.8316	−	22.4426i	1.09272	−	1.30225i
$298$	12.0993			0.700891
$299$	24.1327	+	20.2497i	1.39563	+	1.17107i
$300$		0			0
$301$	0.399615	+	2.26633i	0.0230334	+	0.130629i
$302$	−13.3157	−	4.84651i	−0.766231	−	0.278885i
$303$	−3.49912	+	2.02022i	−0.201019	+	0.116059i
$304$	0.278066	−	1.57699i	0.0159482	−	0.0904467i
$305$		0			0
$306$	−11.7973	−	4.29385i	−0.674404	−	0.245463i
$307$	5.39053	+	9.33667i	0.307654	+	0.532872i	0.977849	−	0.209313i	$-0.0671228\pi$
$307$	5.39053	+	9.33667i	0.307654	+	0.532872i	−0.670195	+	0.742185i	$0.733789\pi$
$308$	−71.6177	+	26.0667i	−4.08080	+	1.48529i
$309$	−11.0412	−	30.3354i	−0.628110	−	1.72572i
$310$		0			0
$311$	−11.8341	+	9.92998i	−0.671050	+	0.563078i	−0.913376	−	0.407117i	$-0.866534\pi$
$311$	−11.8341	+	9.92998i	−0.671050	+	0.563078i	0.242326	+	0.970195i	$0.422090\pi$
$312$	−28.7335	+	34.2433i	−1.62672	+	1.93865i
$313$	−4.35117	+	1.58370i	−0.245942	+	0.0895157i	−0.462050	−	0.886854i	$-0.652886\pi$
$313$	−4.35117	+	1.58370i	−0.245942	+	0.0895157i	0.216108	+	0.976370i	$0.430664\pi$
$314$	−25.3371	−	43.8851i	−1.42985	−	2.47658i
$315$		0			0
$316$	21.6989	−	37.5836i	1.22066	−	2.11425i
$317$	−1.35029	+	7.65787i	−0.0758398	+	0.430109i	0.923120	+	0.384512i	$0.125630\pi$
$317$	−1.35029	+	7.65787i	−0.0758398	+	0.430109i	−0.998960	+	0.0455972i	$0.985481\pi$
$318$			53.0937i			2.97734i
$319$	40.8080	+	14.8529i	2.28481	+	0.831602i
$320$		0			0
$321$	−11.5829	−	13.8040i	−0.646494	−	0.770462i
$322$	44.2995	+	37.1717i	2.46872	+	2.07150i
$323$	0.398681			0.0221832
$324$	6.89440	−	39.1001i	0.383022	−	2.17223i
$325$		0			0
$326$	19.3157	+	16.2078i	1.06980	+	0.897666i
$327$	0.164725	+	0.196312i	0.00910933	+	0.0108561i
$328$	0.151522	+	0.859322i	0.00836638	+	0.0474481i
$329$	13.3969	+	4.87608i	0.738596	+	0.268827i
$330$		0			0
$331$	1.31655	−	7.46654i	0.0723642	−	0.410398i	−0.927010	−	0.375036i	$-0.877630\pi$
$331$	1.31655	−	7.46654i	0.0723642	−	0.410398i	0.999375	−	0.0353621i	$-0.0112585\pi$
$332$	−19.5364	+	33.8381i	−1.07220	+	1.85711i
$333$	7.02007	−	2.55510i	0.384697	−	0.140018i
$334$	−4.00387	−	6.93491i	−0.219082	−	0.379461i
$335$		0			0
$336$	−22.6459	+	26.9883i	−1.23543	+	1.47233i
$337$	−12.6741	+	10.6348i	−0.690403	+	0.579317i	−0.919025	−	0.394198i	$-0.871022\pi$
$337$	−12.6741	+	10.6348i	−0.690403	+	0.579317i	0.228622	+	0.973515i	$0.426578\pi$
$338$	−9.43629	+	7.91799i	−0.513266	+	0.430682i
$339$	4.19341	+	11.5213i	0.227755	+	0.625751i
$340$		0			0
$341$	−13.9363	−	24.1384i	−0.754692	−	1.30717i
$342$	0.318201	+	1.80460i	0.0172063	+	0.0975819i
$343$	7.06418	−	12.2355i	0.381430	−	0.660656i
$344$	−0.796322	+	4.51617i	−0.0429348	+	0.243495i
$345$		0			0
$346$	−46.9975	−	17.1057i	−2.52660	−	0.919608i
$347$	2.63697	+	14.9550i	0.141560	+	0.802828i	0.970065	+	0.242846i	$0.0780808\pi$
$347$	2.63697	+	14.9550i	0.141560	+	0.802828i	−0.828505	+	0.559982i	$0.810808\pi$
$348$	57.9586	−	10.2197i	3.10691	−	0.547832i
$349$	10.8191	+	9.07828i	0.579132	+	0.485949i	0.884662	−	0.466233i	$-0.154389\pi$
$349$	10.8191	+	9.07828i	0.579132	+	0.485949i	−0.305530	+	0.952182i	$0.598834\pi$
$350$		0			0
$351$	7.51161	−	20.6380i	0.400940	−	1.10157i
$352$	−25.9145			−1.38125
$353$	−3.19072	−	2.67733i	−0.169825	−	0.142500i	0.553914	−	0.832574i	$-0.313134\pi$
$353$	−3.19072	−	2.67733i	−0.169825	−	0.142500i	−0.723739	+	0.690074i	$0.757578\pi$
$354$	7.10876	−	19.5311i	0.377826	−	1.03807i
$355$		0			0
$356$	−27.6104	−	10.0494i	−1.46335	−	0.532615i
$357$	−7.59627	−	4.38571i	−0.402037	−	0.232116i
$358$	3.56196	−	20.2009i	0.188255	−	1.06765i
$359$	3.29679	−	5.71021i	0.173998	−	0.301373i	−0.765816	−	0.643060i	$-0.777665\pi$
$359$	3.29679	−	5.71021i	0.173998	−	0.301373i	0.939814	+	0.341686i	$0.110998\pi$
$360$		0			0
$361$	9.47090	+	16.4041i	0.498469	+	0.863373i
$362$	−21.2110	+	7.72016i	−1.11482	+	0.405762i
$363$	35.4602	+	6.25259i	1.86118	+	0.328176i
$364$	−43.7674	+	36.7252i	−2.29404	+	1.92493i
$365$		0			0
$366$	−60.0642	−	10.5909i	−3.13961	−	0.553598i
$367$	11.9243	−	4.34008i	0.622442	−	0.226550i	−0.0114966	−	0.999934i	$-0.503660\pi$
$367$	11.9243	−	4.34008i	0.622442	−	0.226550i	0.633938	+	0.773384i	$0.281437\pi$
$368$	24.7383	+	42.8480i	1.28957	+	2.23361i
$369$	−0.214355	−	0.371274i	−0.0111589	−	0.0193278i
$370$		0			0
$371$	−6.44150	+	36.5316i	−0.334426	+	1.89663i
$372$	−32.7126	−	18.8866i	−1.69607	−	0.979226i
$373$	7.17530	+	2.61159i	0.371523	+	0.135223i	0.521032	−	0.853537i	$-0.325547\pi$
$373$	7.17530	+	2.61159i	0.371523	+	0.135223i	−0.149509	+	0.988760i	$0.547769\pi$
$374$	−4.09714	−	23.2361i	−0.211858	−	1.20151i
$375$		0			0
$376$	21.7631	+	18.2614i	1.12235	+	0.941761i
$377$	32.5553			1.67668
$378$	13.7888	−	37.8844i	0.709219	−	1.94856i
$379$	−27.0838			−1.39120			−0.695600	−	0.718429i	$-0.744861\pi$
$379$	−27.0838			−1.39120			−0.695600	+	0.718429i	$0.744861\pi$
$380$		0			0
$381$	−0.416060	+	0.0733626i	−0.0213154	+	0.00375848i
$382$	2.45424	+	13.9187i	0.125570	+	0.712142i
$383$	−9.67664	−	3.52201i	−0.494453	−	0.179966i	0.0827443	−	0.996571i	$-0.473632\pi$
$383$	−9.67664	−	3.52201i	−0.494453	−	0.179966i	−0.577198	+	0.816605i	$0.695854\pi$
$384$	20.0107	−	11.5532i	1.02117	−	0.589572i
$385$		0			0
$386$	−32.0638	+	55.5361i	−1.63200	+	2.82671i
$387$	−0.391245	−	2.21886i	−0.0198881	−	0.112791i
$388$	−21.0253	−	36.4169i	−1.06740	−	1.84879i
$389$	−3.89780	+	1.41868i	−0.197626	+	0.0719302i	−0.438937	−	0.898518i	$-0.644645\pi$
$389$	−3.89780	+	1.41868i	−0.197626	+	0.0719302i	0.241311	+	0.970448i	$0.422423\pi$
$390$		0			0
$391$	−9.43629	+	7.91799i	−0.477214	+	0.400430i
$392$	−11.1755	+	9.37732i	−0.564446	+	0.473626i
$393$	−10.0829	+	12.0163i	−0.508615	+	0.606144i
$394$	−11.6163	+	4.22800i	−0.585222	+	0.213004i
$395$		0			0
$396$	70.1177	−	25.5208i	3.52355	−	1.28247i
$397$	−11.0530	+	19.1444i	−0.554736	+	0.960831i	0.443188	+	0.896429i	$0.353847\pi$
$397$	−11.0530	+	19.1444i	−0.554736	+	0.960831i	−0.997924	+	0.0644021i	$0.979486\pi$
$398$	−7.63387	+	43.2939i	−0.382652	+	2.17012i
$399$			1.28028i			0.0640942i
$400$		0			0
$401$	−2.92855	−	16.6086i	−0.146245	−	0.829395i	−0.966359	−	0.257196i	$-0.917201\pi$
$401$	−2.92855	−	16.6086i	−0.146245	−	0.829395i	0.820115	−	0.572199i	$-0.193910\pi$
$402$	20.7754	+	24.7592i	1.03618	+	1.23488i
$403$	−16.0064	−	13.4310i	−0.797335	−	0.669044i
$404$	−10.2909			−0.511989
$405$		0			0
$406$	59.7606			2.96587
$407$	10.7554	+	9.02482i	0.533124	+	0.447344i
$408$	−11.2353	−	13.3897i	−0.556230	−	0.662889i
$409$	−6.09199	−	34.5494i	−0.301229	−	1.70836i	−0.640743	−	0.767755i	$-0.721374\pi$
$409$	−6.09199	−	34.5494i	−0.301229	−	1.70836i	0.339514	−	0.940601i	$-0.389737\pi$
$410$		0			0
$411$			21.4855i			1.05980i
$412$	14.2777	−	80.9726i	0.703410	−	3.98923i
$413$	7.26083	−	12.5761i	0.357282	−	0.618831i
$414$	−43.3717	−	36.3932i	−2.13160	−	1.78863i
$415$		0			0
$416$	−18.2554	+	6.64441i	−0.895043	+	0.325769i
$417$	−20.6336	+	24.5901i	−1.01043	+	1.20418i
$418$	−2.63816	+	2.21368i	−0.129036	+	0.108274i
$419$	12.7665	−	10.7124i	0.623685	−	0.523334i	−0.275275	−	0.961366i	$-0.588769\pi$
$419$	12.7665	−	10.7124i	0.623685	−	0.523334i	0.898959	+	0.438032i	$0.144324\pi$
$420$		0			0
$421$	25.7841	−	9.38463i	1.25664	−	0.457379i	0.373998	−	0.927429i	$-0.377987\pi$
$421$	25.7841	−	9.38463i	1.25664	−	0.457379i	0.882639	+	0.470051i	$0.155764\pi$
$422$	14.5103	+	25.1325i	0.706349	+	1.22343i
$423$	−13.1163	−	4.77396i	−0.637738	−	0.232118i
$424$	−36.9602	+	64.0170i	−1.79495	+	3.10894i
$425$		0			0
$426$	18.6172	−	10.7487i	0.902007	−	0.520774i
$427$	−40.0428	−	14.5744i	−1.93781	−	0.705304i
$428$	−7.96972	−	45.1985i	−0.385231	−	2.18475i
$429$	40.6489	−	7.16750i	1.96255	−	0.346050i
$430$		0			0
$431$	−14.9436			−0.719806			−0.359903	−	0.932990i	$-0.617190\pi$
$431$	−14.9436			−0.719806			−0.359903	+	0.932990i	$0.617190\pi$
$432$	22.1716	−	26.4231i	1.06673	−	1.27128i
$433$	−23.3919			−1.12414			−0.562071	−	0.827089i	$-0.689995\pi$
$433$	−23.3919			−1.12414			−0.562071	+	0.827089i	$0.689995\pi$
$434$	−29.3824	−	24.6547i	−1.41040	−	1.18347i
$435$		0			0
$436$	0.113341	+	0.642788i	0.00542804	+	0.0307839i
$437$	1.68954	+	0.614942i	0.0808217	+	0.0294167i
$438$	0.860967	+	0.497079i	0.0411386	+	0.0237514i
$439$	−4.55959	+	25.8587i	−0.217617	+	1.23417i	0.658689	+	0.752415i	$0.271111\pi$
$439$	−4.55959	+	25.8587i	−0.217617	+	1.23417i	−0.876306	+	0.481754i	$0.840000\pi$
$440$		0			0
$441$	3.58378	−	6.20729i	0.170656	−	0.295585i
$442$	−8.84389	−	15.3181i	−0.420661	−	0.728606i
$443$	29.8251	−	10.8554i	1.41703	−	0.515757i	0.483846	−	0.875153i	$-0.339239\pi$
$443$	29.8251	−	10.8554i	1.41703	−	0.515757i	0.933185	+	0.359396i	$0.117017\pi$
$444$	18.7383	+	3.30407i	0.889280	+	0.156804i
$445$		0			0
$446$	0.854570	−	0.717070i	0.0404651	−	0.0339542i
$447$	−8.15064	−	1.43718i	−0.385512	−	0.0679762i
$448$	4.71688	−	1.71680i	0.222852	−	0.0811114i
$449$	9.23695	+	15.9989i	0.435919	+	0.755033i	0.997370	−	0.0724765i	$-0.0230902\pi$
$449$	9.23695	+	15.9989i	0.435919	+	0.755033i	−0.561452	+	0.827510i	$0.689757\pi$
$450$		0			0
$451$	0.402856	−	0.697767i	0.0189697	−	0.0328566i
$452$	−5.42262	+	30.7532i	−0.255059	+	1.44651i
$453$	8.39440	+	4.84651i	0.394403	+	0.227709i
$454$	−12.6420	−	4.60132i	−0.593320	−	0.215951i
$455$		0			0
$456$	−0.872578	+	2.39739i	−0.0408622	+	0.112268i
$457$	−8.18732	−	6.86998i	−0.382987	−	0.321364i	0.430887	−	0.902406i	$-0.358201\pi$
$457$	−8.18732	−	6.86998i	−0.382987	−	0.321364i	−0.813874	+	0.581042i	$0.802645\pi$
$458$	−0.199340			−0.00931457
$459$	7.43717	+	4.29385i	0.347137	+	0.200420i
$460$		0			0
$461$	21.1689	+	17.7628i	0.985934	+	0.827297i	0.984974	−	0.172703i	$-0.0552500\pi$
$461$	21.1689	+	17.7628i	0.985934	+	0.827297i	0.000959987		1.00000i	$0.499694\pi$
$462$	74.6177	−	13.1571i	3.47153	−	0.612125i
$463$	0.800660	+	4.54077i	0.0372098	+	0.211027i	0.997744	−	0.0671350i	$-0.0213858\pi$
$463$	0.800660	+	4.54077i	0.0372098	+	0.211027i	−0.960534	+	0.278162i	$0.910275\pi$
$464$	48.0458	+	17.4872i	2.23047	+	0.811825i
$465$		0			0
$466$	−0.164725	+	0.934204i	−0.00763075	+	0.0432762i
$467$	−9.77513	+	16.9310i	−0.452339	+	0.783474i	−0.998531	−	0.0541859i	$-0.982744\pi$
$467$	−9.77513	+	16.9310i	−0.452339	+	0.783474i	0.546192	+	0.837660i	$0.316077\pi$
$468$	42.8508	−	35.9561i	1.98078	−	1.66207i
$469$	11.2909	+	19.5563i	0.521363	+	0.903028i
$470$		0			0
$471$	11.8555	+	32.5727i	0.546273	+	1.50087i
$472$	22.1676	−	18.6008i	1.02034	−	0.856171i
$473$	3.24376	−	2.72183i	0.149148	−	0.125150i
$474$	−27.7327	+	33.0505i	−1.27380	+	1.51806i
$475$		0			0
$476$	−11.1702	−	19.3474i	−0.511987	−	0.886788i
$477$	6.30659	−	35.7664i	0.288759	−	1.63763i
$478$	−13.7554	+	23.8250i	−0.629156	+	1.08973i
$479$	−0.449493	+	2.54920i	−0.0205379	+	0.116476i	−0.993353	−	0.115106i	$-0.963279\pi$
$479$	−0.449493	+	2.54920i	−0.0205379	+	0.116476i	0.972815	+	0.231582i	$0.0743902\pi$
$480$		0			0
$481$	9.89053	+	3.59986i	0.450969	+	0.164139i
$482$	−11.7604	−	66.6967i	−0.535672	−	3.03795i
$483$	−25.4270	−	30.3027i	−1.15697	−	1.37882i
$484$	70.2534	+	58.9496i	3.19333	+	2.67953i
$485$		0			0
$486$	−13.5000	+	37.0909i	−0.612372	+	1.68248i
$487$	−40.7870			−1.84824			−0.924119	−	0.382105i	$-0.875199\pi$
$487$	−40.7870			−1.84824			−0.924119	+	0.382105i	$0.875199\pi$
$488$	−65.0490	−	54.5826i	−2.94463	−	2.47084i
$489$	−11.0868	−	13.2127i	−0.501361	−	0.597499i
$490$		0			0
$491$	−37.9761	−	13.8222i	−1.71384	−	0.623786i	−0.716561	−	0.697525i	$-0.754285\pi$
$491$	−37.9761	−	13.8222i	−1.71384	−	0.623786i	−0.997278	+	0.0737387i	$0.976507\pi$
$492$		−	1.09191i		−	0.0492271i
$493$	−2.21048	+	12.5363i	−0.0995552	+	0.564606i
$494$	−1.29086	+	2.23583i	−0.0580785	+	0.100595i
$495$		0			0
$496$	−16.4081	−	28.4196i	−0.736744	−	1.27608i
$497$	14.1138	−	5.13701i	0.633091	−	0.230426i
$498$	24.9688	−	29.7567i	1.11888	−	1.33343i
$499$	−10.2226	+	8.57775i	−0.457625	+	0.383993i	−0.842256	−	0.539077i	$-0.818773\pi$
$499$	−10.2226	+	8.57775i	−0.457625	+	0.383993i	0.384631	+	0.923070i	$0.374329\pi$
$500$		0			0
$501$	1.87346	+	5.14728i	0.0836998	+	0.229963i
$502$	−14.2601	+	5.19026i	−0.636460	+	0.231653i
$503$	9.02822	+	15.6373i	0.402548	+	0.697234i	0.994033	−	0.109082i	$-0.0347912\pi$
$503$	9.02822	+	15.6373i	0.402548	+	0.697234i	−0.591484	+	0.806316i	$0.701458\pi$
$504$	42.9982	−	36.0798i	1.91529	−	1.60712i
$505$		0			0
$506$	18.4773	−	104.790i	0.821416	−	4.65848i
$507$	7.29726	−	4.21307i	0.324083	−	0.187109i
$508$	−1.01114	−	0.368026i	−0.0448623	−	0.0163285i
$509$	4.18779	+	23.7501i	0.185620	+	1.05271i	0.925156	+	0.379588i	$0.123934\pi$
$509$	4.18779	+	23.7501i	0.185620	+	1.05271i	−0.739535	+	0.673118i	$0.764955\pi$
$510$		0			0
$511$	0.532089	+	0.446476i	0.0235382	+	0.0197509i
$512$	50.5553			2.23425
$513$		−	1.25347i		−	0.0553418i
$514$	−16.0155			−0.706413
$515$		0			0
$516$	1.96270	−	5.39246i	0.0864029	−	0.237390i
$517$	−4.55525	−	25.8341i	−0.200340	−	1.13618i
$518$	18.1557	+	6.60813i	0.797716	+	0.290345i
$519$	29.6279	+	17.1057i	1.30052	+	0.750857i
$520$		0			0
$521$	20.6682	−	35.7983i	0.905490	−	1.56835i	0.0852310	−	0.996361i	$-0.472837\pi$
$521$	20.6682	−	35.7983i	0.905490	−	1.56835i	0.820259	−	0.571993i	$-0.193829\pi$
$522$	−58.5090			−2.56087
$523$	3.27332	+	5.66955i	0.143132	+	0.247912i	0.928675	−	0.370896i	$-0.120949\pi$
$523$	3.27332	+	5.66955i	0.143132	+	0.247912i	−0.785542	+	0.618808i	$0.787616\pi$
$524$	−37.5428	+	13.6645i	−1.64007	+	0.596935i
$525$		0			0
$526$	−0.907604	+	0.761570i	−0.0395734	+	0.0332060i
$527$	6.25877	−	5.25173i	0.272636	−	0.228769i
$528$	63.8405	+	11.2568i	2.77830	+	0.489890i
$529$	−30.5895	+	11.1337i	−1.32998	+	0.484072i
$530$		0			0
$531$	−7.10876	+	12.3127i	−0.308494	+	0.534327i
$532$	−1.63041	+	2.82396i	−0.0706875	+	0.122434i
$533$	0.104885	−	0.594831i	0.00454306	−	0.0257650i
$534$	25.2973	+	14.6054i	1.09472	+	0.632037i
$535$		0			0
$536$	7.81403	+	44.3155i	0.337514	+	1.91414i
$537$	−4.79901	+	13.1852i	−0.207093	+	0.568982i
$538$	−3.57919	−	3.00330i	−0.154310	−	0.129481i
$539$	13.4706			0.580220
$540$		0			0
$541$	−30.3560			−1.30511			−0.652553	−	0.757743i	$-0.726302\pi$
$541$	−30.3560			−1.30511			−0.652553	+	0.757743i	$0.726302\pi$
$542$	8.00253	+	6.71492i	0.343738	+	0.288430i
$543$	15.2057	−	2.68118i	0.652541	−	0.115061i
$544$	−1.31908	−	7.48086i	−0.0565550	−	0.320739i
$545$		0			0
$546$	49.1908	−	28.4003i	2.10517	−	1.21542i
$547$	6.71641	−	38.0907i	0.287173	−	1.62864i	−0.410245	−	0.911975i	$-0.634557\pi$
$547$	6.71641	−	38.0907i	0.287173	−	1.62864i	0.697418	−	0.716664i	$-0.254332\pi$
$548$	−27.3614	+	47.3914i	−1.16882	+	2.02446i
$549$	39.2041	+	14.2691i	1.67319	+	0.608992i
$550$		0			0
$551$	1.74598	−	0.635484i	0.0743811	−	0.0270725i
$552$	−26.9604	−	74.0731i	−1.14751	−	3.15276i
$553$	−23.0915	+	19.3761i	−0.981951	+	0.823955i
$554$	0.119271	−	0.100080i	0.00506732	−	0.00425199i
$555$		0			0
$556$	−76.8273	+	27.9629i	−3.25821	+	1.18589i
$557$	−7.43676	−	12.8808i	−0.315105	−	0.545779i	0.664354	−	0.747418i	$-0.268707\pi$
$557$	−7.43676	−	12.8808i	−0.315105	−	0.545779i	−0.979460	+	0.201639i	$0.935373\pi$
$558$	28.7670	+	24.1384i	1.21780	+	1.02186i
$559$	1.58718	−	2.74908i	0.0671306	−	0.116274i
$560$		0			0
$561$			16.1396i			0.681414i
$562$	−14.3944	−	5.23913i	−0.607191	−	0.220999i
$563$	5.08677	+	28.8485i	0.214382	+	1.21582i	0.881976	+	0.471294i	$0.156213\pi$
$563$	5.08677	+	28.8485i	0.214382	+	1.21582i	−0.667594	+	0.744525i	$0.732676\pi$
$564$	−22.8516	−	27.2335i	−0.962227	−	1.14674i
$565$		0			0
$566$	21.1557			0.889240
$567$	−13.7888	+	23.8829i	−0.579075	+	1.00299i
$568$	29.9299			1.25583
$569$	−24.4127	−	20.4847i	−1.02343	−	0.858761i	−0.0333769	−	0.999443i	$-0.510626\pi$
$569$	−24.4127	−	20.4847i	−1.02343	−	0.858761i	−0.990055	+	0.140682i	$0.955071\pi$
$570$		0			0
$571$	−2.78817	−	15.8125i	−0.116681	−	0.661733i	−0.985904	−	0.167312i	$-0.946491\pi$
$571$	−2.78817	−	15.8125i	−0.116681	−	0.661733i	0.869223	−	0.494421i	$-0.164620\pi$
$572$	98.7884	+	35.9561i	4.13055	+	1.50340i
$573$		−	9.66782i		−	0.403879i
$574$	0.192533	−	1.09191i	0.00803619	−	0.0455755i
$575$		0			0
$576$	−4.61809	+	1.68085i	−0.192420	+	0.0700353i
$577$	1.13429	+	1.96464i	0.0472209	+	0.0817890i	0.888670	−	0.458548i	$-0.151630\pi$
$577$	1.13429	+	1.96464i	0.0472209	+	0.0817890i	−0.841449	+	0.540337i	$0.818297\pi$
$578$	−33.9504	+	12.3569i	−1.41215	+	0.513981i
$579$	28.1964	−	33.6032i	1.17180	−	1.39650i
$580$		0			0
$581$	20.7902	−	17.4451i	0.862524	−	0.723744i
$582$	14.2981	+	39.2838i	0.592677	+	1.62837i
$583$	64.1396	−	23.3449i	2.65639	−	0.966847i
$584$	0.692066	+	1.19869i	0.0286379	+	0.0496023i
$585$		0			0
$586$	15.2087	−	26.3423i	0.628267	−	1.08819i
$587$	−5.78564	+	32.8120i	−0.238799	+	1.35430i	0.595664	+	0.803234i	$0.296889\pi$
$587$	−5.78564	+	32.8120i	−0.238799	+	1.35430i	−0.834463	+	0.551064i	$0.814222\pi$
$588$	15.8097	−	9.12776i	0.651983	−	0.376422i
$589$	−1.12061	−	0.407870i	−0.0461741	−	0.0168060i
$590$		0			0
$591$	8.32753	−	1.46837i	0.342549	−	0.0604006i
$592$	12.6630	+	10.6255i	0.520445	+	0.436705i
$593$	−24.7793			−1.01756			−0.508782	−	0.860895i	$-0.669904\pi$
$593$	−24.7793			−1.01756			−0.508782	+	0.860895i	$0.669904\pi$
$594$	−73.0549	+	12.8816i	−2.99748	+	0.528536i
$595$		0			0
$596$	−16.1480	−	13.5497i	−0.661446	−	0.555019i
$597$	10.2851	−	28.2581i	0.420941	−	1.15653i
$598$	−13.8516	−	78.5565i	−0.566435	−	3.21241i
$599$	−35.9368	−	13.0799i	−1.46834	−	0.534431i	−0.520688	−	0.853747i	$-0.674324\pi$
$599$	−35.9368	−	13.0799i	−1.46834	−	0.534431i	−0.947648	+	0.319316i	$0.896547\pi$
$600$		0			0
$601$	7.80747	−	44.2783i	0.318473	−	1.80615i	−0.233575	−	0.972339i	$-0.575042\pi$
$601$	7.80747	−	44.2783i	0.318473	−	1.80615i	0.552048	−	0.833812i	$-0.313847\pi$
$602$	2.91353	−	5.04639i	0.118747	−	0.205675i
$603$	−11.0544	−	19.1467i	−0.450169	−	0.779716i
$604$	12.3439	+	21.3802i	0.502266	+	0.869950i
$605$		0			0
$606$	10.0753	+	1.77655i	0.409282	+	0.0721675i
$607$	12.1374	−	10.1845i	0.492644	−	0.413377i	−0.362329	−	0.932050i	$-0.618018\pi$
$607$	12.1374	−	10.1845i	0.492644	−	0.413377i	0.854973	+	0.518673i	$0.173574\pi$
$608$	−0.849356	+	0.712694i	−0.0344459	+	0.0289036i
$609$	−40.2576	−	7.09851i	−1.63132	−	0.287646i
$610$		0			0
$611$	−9.83275	−	17.0308i	−0.397790	−	0.688993i
$612$	10.9363	+	18.9422i	0.442073	+	0.765693i
$613$	−10.4076	+	18.0265i	−0.420359	+	0.728083i	−0.995974	−	0.0896372i	$-0.971429\pi$
$613$	−10.4076	+	18.0265i	−0.420359	+	0.728083i	0.575615	+	0.817721i	$0.304763\pi$
$614$	4.74035	−	26.8839i	0.191305	−	1.08494i
$615$		0			0
$616$	99.1285	+	36.0798i	3.99400	+	1.45370i
$617$	−5.19728	−	29.4752i	−0.209235	−	1.18663i	−0.890635	−	0.454718i	$-0.849740\pi$
$617$	−5.19728	−	29.4752i	−0.209235	−	1.18663i	0.681401	−	0.731911i	$-0.261371\pi$
$618$	−27.9572	+	76.8119i	−1.12460	+	3.08983i
$619$	−2.69775	−	2.26368i	−0.108432	−	0.0909850i	0.586960	−	0.809616i	$-0.300325\pi$
$619$	−2.69775	−	2.26368i	−0.108432	−	0.0909850i	−0.695392	+	0.718631i	$0.744769\pi$
$620$		0			0
$621$	24.8944	+	29.6680i	0.998978	+	1.19054i
$622$	39.1165			1.56843
$623$	15.6340	+	13.1185i	0.626364	+	0.525582i
$624$	47.8585	−	8.43874i	1.91587	−	0.337820i
$625$		0			0
$626$	11.0175	+	4.01006i	0.440349	+	0.160274i
$627$	2.04013	−	1.17787i	0.0814751	−	0.0470397i
$628$	−15.3307	+	86.9447i	−0.611761	+	3.46947i
$629$	−2.05778	+	3.56418i	−0.0820491	+	0.142113i
$630$		0			0
$631$	−9.53730	−	16.5191i	−0.379674	−	0.657615i	0.611341	−	0.791368i	$-0.290631\pi$
$631$	−9.53730	−	16.5191i	−0.379674	−	0.657615i	−0.991015	+	0.133753i	$0.957297\pi$
$632$	−56.4458	+	20.5446i	−2.24529	+	0.817221i
$633$	−6.78952	−	18.6540i	−0.269859	−	0.741432i
$634$	15.0831	−	12.6562i	0.599025	−	0.502642i
$635$		0			0
$636$	59.4586	−	70.8600i	2.35769	−	2.80978i
$637$	9.48932	−	3.45383i	0.375981	−	0.136846i
$638$	−54.9805	−	95.2289i	−2.17670	−	3.77015i
$639$	−13.8182	+	5.02941i	−0.546640	+	0.198961i
$640$		0			0
$641$	1.60711	−	9.11435i	0.0634769	−	0.359995i	−0.936480	−	0.350721i	$-0.885937\pi$
$641$	1.60711	−	9.11435i	0.0634769	−	0.359995i	0.999957	−	0.00927459i	$-0.00295224\pi$
$642$			45.6277i			1.80078i
$643$	−26.8542	−	9.77411i	−1.05902	−	0.385453i	−0.246963	−	0.969025i	$-0.579433\pi$
$643$	−26.8542	−	9.77411i	−1.05902	−	0.385453i	−0.812062	+	0.583571i	$0.801655\pi$
$644$	−17.4953	−	99.2205i	−0.689410	−	3.90984i
$645$		0			0
$646$	−0.773318	−	0.648891i	−0.0304258	−	0.0255303i
$647$	−21.6928			−0.852833			−0.426417	−	0.904527i	$-0.640224\pi$
$647$	−21.6928			−0.852833			−0.426417	+	0.904527i	$0.640224\pi$
$648$	−42.0977	+	35.3241i	−1.65375	+	1.38766i
$649$	−26.7202			−1.04886
$650$		0			0
$651$	16.8648	+	20.0987i	0.660985	+	0.787731i
$652$	−7.62836	−	43.2626i	−0.298749	−	1.69429i
$653$	−29.0574	−	10.5760i	−1.13710	−	0.413872i	−0.296237	−	0.955115i	$-0.595732\pi$
$653$	−29.0574	−	10.5760i	−1.13710	−	0.413872i	−0.840866	+	0.541243i	$0.817954\pi$
$654$		−	0.648891i		−	0.0253737i
$655$		0			0
$656$	0.474308	−	0.821525i	0.0185186	−	0.0320752i
$657$	−0.520945	−	0.437124i	−0.0203240	−	0.0170538i
$658$	−18.0496	−	31.2629i	−0.703648	−	1.21875i
$659$	−35.7581	+	13.0149i	−1.39294	+	0.506987i	−0.926074	−	0.377343i	$-0.876838\pi$
$659$	−35.7581	+	13.0149i	−1.39294	+	0.506987i	−0.466862	+	0.884330i	$0.654616\pi$
$660$		0			0
$661$	−20.7271	+	17.3921i	−0.806193	+	0.676476i	−0.949696	−	0.313174i	$-0.898608\pi$
$661$	−20.7271	+	17.3921i	−0.806193	+	0.676476i	0.143503	+	0.989650i	$0.454163\pi$
$662$	−14.7062	+	12.3400i	−0.571573	+	0.479607i
$663$	4.13816	+	11.3695i	0.160713	+	0.441554i
$664$	50.8205	−	18.4971i	1.97222	−	0.717828i
$665$		0			0
$666$	−17.7754	−	6.46973i	−0.688784	−	0.250697i
$667$	−28.7041	+	49.7170i	−1.11143	+	1.92505i
$668$	−2.42262	+	13.7394i	−0.0937339	+	0.531591i
$669$	−0.660855	+	0.381545i	−0.0255501	+	0.0147514i
$670$		0			0
$671$	13.6155	+	77.2171i	0.525619	+	2.98093i
$672$	24.0232	−	4.23594i	0.926716	−	0.163405i
$673$	23.6097	+	19.8109i	0.910087	+	0.763653i	0.972135	−	0.234420i	$-0.0753190\pi$
$673$	23.6097	+	19.8109i	0.910087	+	0.763653i	−0.0620488	+	0.998073i	$0.519763\pi$
$674$	41.8931			1.61366
$675$		0			0
$676$	21.4611			0.825427
$677$	−35.7178	−	29.9708i	−1.37275	−	1.15187i	−0.971810	−	0.235766i	$-0.924240\pi$
$677$	−35.7178	−	29.9708i	−1.37275	−	1.15187i	−0.400937	−	0.916105i	$-0.631315\pi$
$678$	10.6181	−	29.1730i	0.407785	−	1.12038i
$679$	5.07192	+	28.7643i	0.194642	+	1.10387i
$680$		0			0
$681$	7.96972	+	4.60132i	0.305400	+	0.176323i
$682$	−12.2554	+	69.5036i	−0.469282	+	2.66143i
$683$	−20.7224	+	35.8923i	−0.792921	+	1.37338i	0.131231	+	0.991352i	$0.458107\pi$
$683$	−20.7224	+	35.8923i	−0.792921	+	1.37338i	−0.924151	+	0.382027i	$0.875226\pi$
$684$	1.59627	−	2.76481i	0.0610348	−	0.105715i
$685$		0			0
$686$	−33.6168	+	12.2355i	−1.28350	+	0.467154i
$687$	0.134285	+	0.0236781i	0.00512330	+	0.000903377i
$688$	3.81908	−	3.20459i	0.145601	−	0.122174i
$689$	39.1973	−	32.8905i	1.49330	−	1.25303i
$690$		0			0
$691$	−4.99185	+	1.81688i	−0.189899	+	0.0691175i	−0.435219	−	0.900325i	$-0.643329\pi$
$691$	−4.99185	+	1.81688i	−0.189899	+	0.0691175i	0.245320	+	0.969442i	$0.421107\pi$
$692$	43.5676	+	75.4614i	1.65619	+	2.86861i
$693$	−51.8289			−1.96882
$694$	19.2258	−	33.3001i	0.729802	−	1.26405i
$695$		0			0
$696$	−70.5464	−	40.7300i	−2.67406	−	1.54387i
$697$	0.221934	+	0.0807773i	0.00840634	+	0.00305966i
$698$	−6.20991	−	35.2182i	−0.235049	−	1.33303i
$699$	0.221934	−	0.609758i	0.00839431	−	0.0230632i
$700$		0			0
$701$	9.66962			0.365216			0.182608	−	0.983186i	$-0.441546\pi$
$701$	9.66962			0.365216			0.182608	+	0.983186i	$0.441546\pi$
$702$	−48.1605	+	27.8055i	−1.81770	+	1.04945i
$703$	0.600710			0.0226562
$704$	−7.07532	−	5.93690i	−0.266661	−	0.223755i
$705$		0			0
$706$	1.83140	+	10.3864i	0.0689258	+	0.390898i
$707$	6.71688	+	2.44474i	0.252614	+	0.0919441i
$708$	−31.3601	+	18.1058i	−1.17858	+	0.680456i
$709$	4.07057	−	23.0854i	0.152874	−	0.866989i	−0.807830	−	0.589415i	$-0.799358\pi$
$709$	4.07057	−	23.0854i	0.152874	−	0.866989i	0.960704	−	0.277575i	$-0.0895305\pi$
$710$		0			0
$711$	22.6079	−	18.9703i	0.847862	−	0.711440i
$712$	20.3346	+	35.2205i	0.762070	+	1.31994i
$713$	34.6241	−	12.6021i	1.29668	−	0.471954i
$714$	7.59627	+	20.8706i	0.284283	+	0.781061i
$715$		0			0
$716$	−27.3764	+	22.9716i	−1.02311	+	0.858488i
$717$	12.0963	−	14.4158i	0.451743	−	0.538367i
$718$	−15.6887	+	5.71021i	−0.585496	+	0.213103i
$719$	13.1133	+	22.7130i	0.489045	+	0.847051i	0.999921	−	0.0126038i	$-0.00401201\pi$
$719$	13.1133	+	22.7130i	0.489045	+	0.847051i	−0.510875	+	0.859655i	$0.670679\pi$
$720$		0			0
$721$	−28.5553	+	49.4592i	−1.06346	+	1.84196i
$722$	8.32857	−	47.2337i	0.309957	−	1.75786i
$723$			46.3270i			1.72292i
$724$	36.9543	+	13.4503i	1.37340	+	0.499875i
$725$		0			0
$726$	−58.6052	−	69.8430i	−2.17504	−	2.59212i
$727$	14.6061	+	12.2559i	0.541709	+	0.454548i	0.872122	−	0.489289i	$-0.162744\pi$
$727$	14.6061	+	12.2559i	0.541709	+	0.454548i	−0.330413	+	0.943836i	$0.607188\pi$
$728$	79.0815			2.93096
$729$	13.5000	−	23.3827i	0.500000	−	0.866025i
$730$		0			0
$731$	0.950837	+	0.797847i	0.0351680	+	0.0295094i
$732$	68.3025	+	81.3998i	2.52453	+	3.00862i
$733$	−1.17128	−	6.64268i	−0.0432624	−	0.245353i	0.955506	−	0.294972i	$-0.0953104\pi$
$733$	−1.17128	−	6.64268i	−0.0432624	−	0.245353i	−0.998768	+	0.0496191i	$0.984199\pi$
$734$	−30.1933	−	10.9895i	−1.11446	−	0.405629i
$735$		0			0
$736$	5.94878	−	33.7372i	0.219275	−	1.24357i
$737$	20.7754	−	35.9841i	0.765273	−	1.32549i
$738$	−0.188501	+	1.06904i	−0.00693881	+	0.0393519i
$739$	18.0069	+	31.1888i	0.662393	+	1.14730i	0.979985	+	0.199071i	$0.0637925\pi$
$739$	18.0069	+	31.1888i	0.662393	+	1.14730i	−0.317592	+	0.948228i	$0.602874\pi$
$740$		0			0
$741$	1.13516	−	1.35283i	0.0417012	−	0.0496976i
$742$	71.9532	−	60.3759i	2.64148	−	2.21647i
$743$	−27.4709	+	23.0508i	−1.00781	+	0.845653i	−0.988047	−	0.154152i	$-0.950735\pi$
$743$	−27.4709	+	23.0508i	−1.00781	+	0.845653i	−0.0197626	+	0.999805i	$0.506291\pi$
$744$	17.8819	+	49.1301i	0.655583	+	1.80120i
$745$		0			0
$746$	−9.66725	−	16.7442i	−0.353943	−	0.613048i
$747$	−20.3548	+	17.0797i	−0.744743	+	0.624913i
$748$	−20.5535	+	35.5997i	−0.751510	+	1.30165i
$749$	−5.53571	+	31.3946i	−0.202270	+	1.14713i
$750$		0			0
$751$	45.0899	+	16.4114i	1.64535	+	0.598860i	0.987963	−	0.154689i	$-0.0494376\pi$
$751$	45.0899	+	16.4114i	1.64535	+	0.598860i	0.657392	+	0.753549i	$0.271660\pi$
$752$	−5.36319	−	30.4162i	−0.195575	−	1.10916i
$753$	10.2228	−	1.80256i	0.372540	−	0.0656888i
$754$	−63.1473	−	52.9869i	−2.29969	−	1.92967i
$755$		0			0
$756$	−60.8289	+	35.1196i	−2.21233	+	1.27729i
$757$	−24.2172			−0.880189			−0.440094	−	0.897952i	$-0.645055\pi$
$757$	−24.2172			−0.880189			−0.440094	+	0.897952i	$0.645055\pi$
$758$	52.5342	+	44.0814i	1.90813	+	1.60111i
$759$	−24.8944	+	68.3968i	−0.903609	+	2.48265i
$760$		0			0
$761$	42.1391	+	15.3374i	1.52754	+	0.555979i	0.963018	−	0.269438i	$-0.0868379\pi$
$761$	42.1391	+	15.3374i	1.52754	+	0.555979i	0.564523	+	0.825417i	$0.309060\pi$
$762$	0.926433	+	0.534876i	0.0335611	+	0.0193765i
$763$	0.0787257	−	0.446476i	0.00285006	−	0.0161635i
$764$	12.3118	−	21.3247i	0.445425	−	0.771499i
$765$		0			0
$766$	13.0373	+	22.5813i	0.471057	+	0.815895i
$767$	−18.8229	+	6.85099i	−0.679657	+	0.247375i
$768$	−52.0301	−	9.17431i	−1.87747	−	0.331049i
$769$	0.682733	−	0.572881i	0.0246200	−	0.0206586i	−0.630395	−	0.776275i	$-0.717107\pi$
$769$	0.682733	−	0.572881i	0.0246200	−	0.0206586i	0.655015	+	0.755616i	$0.272662\pi$
$770$		0			0
$771$	10.7888	+	1.90236i	0.388549	+	0.0685117i
$772$	104.987	−	38.2121i	3.77856	−	1.37528i
$773$	−15.3701	−	26.6217i

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.93969 - 1.62760i) q^{2} +(1.11334 + 1.32683i) q^{3} +(0.766044 + 4.34445i) q^{4} -4.38571i q^{6} +(0.532089 - 3.01763i) q^{7} +(3.05303 - 5.28801i) q^{8} +(-0.520945 + 2.95442i) q^{9} +O(q^{10})\)	\(q+(-1.93969 - 1.62760i) q^{2} +(1.11334 + 1.32683i) q^{3} +(0.766044 + 4.34445i) q^{4} -4.38571i q^{6} +(0.532089 - 3.01763i) q^{7} +(3.05303 - 5.28801i) q^{8} +(-0.520945 + 2.95442i) q^{9} +(-5.29813 + 1.92836i) q^{11} +(-4.91147 + 5.85327i) q^{12} +(-3.23783 + 2.71686i) q^{13} +(-5.94356 + 4.98724i) q^{14} +(-6.23783 + 2.27038i) q^{16} +(-0.826352 - 1.43128i) q^{17} +(5.81908 - 4.88279i) q^{18} +(-0.120615 + 0.208911i) q^{19} +(4.59627 - 2.65366i) q^{21} +(13.4153 + 4.88279i) q^{22} +(-1.29426 - 7.34013i) q^{23} +(10.4153 - 1.83651i) q^{24} +10.7023 q^{26} +(-4.50000 + 2.59808i) q^{27} +13.5175 q^{28} +(-5.90033 - 4.95096i) q^{29} +(0.858441 + 4.86846i) q^{31} +(4.31908 + 1.57202i) q^{32} +(-8.45723 - 4.88279i) q^{33} +(-0.726682 + 4.12122i) q^{34} -13.2344 q^{36} +(-1.24510 - 2.15658i) q^{37} +(0.573978 - 0.208911i) q^{38} +(-7.20961 - 1.27125i) q^{39} +(-0.109470 + 0.0918566i) q^{41} +(-13.2344 - 2.33359i) q^{42} +(-0.705737 + 0.256867i) q^{43} +(-12.4363 - 21.5403i) q^{44} +(-9.43629 + 16.3441i) q^{46} +(-0.807934 + 4.58202i) q^{47} +(-9.95723 - 5.74881i) q^{48} +(-2.24510 - 0.817150i) q^{49} +(0.979055 - 2.68993i) q^{51} +(-14.2836 - 11.9854i) q^{52} -12.1061 q^{53} +(12.9572 + 2.28471i) q^{54} +(-14.3327 - 12.0266i) q^{56} +(-0.411474 + 0.0725540i) q^{57} +(3.38666 + 19.2067i) q^{58} +(4.45336 + 1.62089i) q^{59} +(2.41488 - 13.6955i) q^{61} +(6.25877 - 10.8405i) q^{62} +(8.63816 + 3.14403i) q^{63} +(0.819078 + 1.41868i) q^{64} +(8.45723 + 23.2361i) q^{66} +(-5.64543 + 4.73708i) q^{67} +(5.58512 - 4.68647i) q^{68} +(8.29813 - 9.88933i) q^{69} +(2.45084 + 4.24497i) q^{71} +(14.0326 + 11.7747i) q^{72} +(-0.113341 + 0.196312i) q^{73} +(-1.09492 + 6.20961i) q^{74} +(-1.00000 - 0.363970i) q^{76} +(3.00000 + 17.0138i) q^{77} +(11.9153 + 14.2002i) q^{78} +(-7.53596 - 6.32342i) q^{79} +(-8.45723 - 3.07818i) q^{81} +0.361844 q^{82} +(6.78493 + 5.69323i) q^{83} +(15.0496 + 17.9355i) q^{84} +(1.78699 + 0.650411i) q^{86} -13.3408i q^{87} +(-5.97818 + 33.9039i) q^{88} +(-3.33022 + 5.76811i) q^{89} +(6.47565 + 11.2162i) q^{91} +(30.8974 - 11.2457i) q^{92} +(-5.50387 + 6.55926i) q^{93} +(9.02481 - 7.57272i) q^{94} +(2.72281 + 7.48086i) q^{96} +(-8.95723 + 3.26017i) q^{97} +(3.02481 + 5.23913i) q^{98} +(-2.93717 - 16.6575i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) 6 * q - 6 * q^2 - 6 * q^7 + 6 * q^8	\( 6 q - 6 q^{2} - 6 q^{7} + 6 q^{8} - 18 q^{11} - 9 q^{12} - 6 q^{14} - 18 q^{16} - 6 q^{17} + 18 q^{18} - 12 q^{19} + 36 q^{22} - 18 q^{23} + 18 q^{24} + 12 q^{26} - 27 q^{27} + 36 q^{28} - 21 q^{29} - 3 q^{31} + 9 q^{32} + 9 q^{34} - 18 q^{36} - 6 q^{37} - 12 q^{38} - 9 q^{39} - 18 q^{41} - 18 q^{42} + 6 q^{43} - 27 q^{44} - 9 q^{46} + 6 q^{47} - 9 q^{48} - 12 q^{49} + 9 q^{51} - 36 q^{52} - 48 q^{53} + 27 q^{54} - 48 q^{56} + 18 q^{57} + 27 q^{58} + 36 q^{61} + 15 q^{62} + 18 q^{63} - 12 q^{64} - 18 q^{67} + 12 q^{68} + 36 q^{69} + 3 q^{71} + 9 q^{72} + 6 q^{73} + 12 q^{74} - 6 q^{76} + 18 q^{77} + 27 q^{78} - 12 q^{79} + 36 q^{82} - 18 q^{83} + 36 q^{84} + 3 q^{86} + 18 q^{88} + 3 q^{89} + 63 q^{92} - 9 q^{93} + 27 q^{94} + 27 q^{96} - 3 q^{97} - 9 q^{98} - 27 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 6 * q^7 + 6 * q^8 - 18 * q^11 - 9 * q^12 - 6 * q^14 - 18 * q^16 - 6 * q^17 + 18 * q^18 - 12 * q^19 + 36 * q^22 - 18 * q^23 + 18 * q^24 + 12 * q^26 - 27 * q^27 + 36 * q^28 - 21 * q^29 - 3 * q^31 + 9 * q^32 + 9 * q^34 - 18 * q^36 - 6 * q^37 - 12 * q^38 - 9 * q^39 - 18 * q^41 - 18 * q^42 + 6 * q^43 - 27 * q^44 - 9 * q^46 + 6 * q^47 - 9 * q^48 - 12 * q^49 + 9 * q^51 - 36 * q^52 - 48 * q^53 + 27 * q^54 - 48 * q^56 + 18 * q^57 + 27 * q^58 + 36 * q^61 + 15 * q^62 + 18 * q^63 - 12 * q^64 - 18 * q^67 + 12 * q^68 + 36 * q^69 + 3 * q^71 + 9 * q^72 + 6 * q^73 + 12 * q^74 - 6 * q^76 + 18 * q^77 + 27 * q^78 - 12 * q^79 + 36 * q^82 - 18 * q^83 + 36 * q^84 + 3 * q^86 + 18 * q^88 + 3 * q^89 + 63 * q^92 - 9 * q^93 + 27 * q^94 + 27 * q^96 - 3 * q^97 - 9 * q^98 - 27 * q^99

Introduction

L-functions

Modular forms

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