LMFDB - Embedded newform 675.2.u.a.124.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(49,675)]

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, 9]))

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

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

chi := DirichletCharacter("675.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.u (of order $18$, degree $6$, not 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:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			124.1
Root			$0.342020 + 0.939693i$ of defining polynomial
Character	$\chi$	$=$	675.124
Dual form			675.2.u.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

$2$	−1.62760	+	1.93969i	−1.15088	+	1.37157i	−0.234087	+	0.972216i	$0.575210\pi$
$2$	−1.62760	+	1.93969i	−1.15088	+	1.37157i	−0.916797	+	0.399354i	$0.869234\pi$
$3$	−1.32683	+	1.11334i	−0.766044	+	0.642788i
$3$	−1.32683	+	1.11334i	−0.766044	+	0.642788i
$4$	−0.766044	−	4.34445i	−0.383022	−	2.17223i
$5$		0			0
$5$		0			0
$6$		−	4.38571i		−	1.79046i
$7$	−3.01763	−	0.532089i	−1.14056	−	0.201111i	−0.428707	−	0.903444i	$-0.641031\pi$
$7$	−3.01763	−	0.532089i	−1.14056	−	0.201111i	−0.711849	+	0.702333i	$0.752142\pi$
$8$	5.28801	+	3.05303i	1.86959	+	1.07941i
$9$	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	$0.712277\pi$
$12$	5.85327	+	4.91147i	1.68969	+	1.41782i
$13$	−2.71686	−	3.23783i	−0.753521	−	0.898011i	0.243899	−	0.969801i	$-0.421574\pi$
$13$	−2.71686	−	3.23783i	−0.753521	−	0.898011i	−0.997420	+	0.0717893i	$0.977129\pi$
$14$	5.94356	−	4.98724i	1.58848	−	1.33290i
$15$		0			0
$16$	−6.23783	+	2.27038i	−1.55946	+	0.567596i
$17$	−1.43128	+	0.826352i	−0.347137	+	0.200420i	−0.663424	−	0.748244i	$-0.730897\pi$
$17$	−1.43128	+	0.826352i	−0.347137	+	0.200420i	0.316286	+	0.948664i	$0.397564\pi$
$18$	4.88279	+	5.81908i	1.15088	+	1.37157i
$19$	0.120615	−	0.208911i	0.0276709	−	0.0479274i	−0.851858	−	0.523772i	$-0.824524\pi$
$19$	0.120615	−	0.208911i	0.0276709	−	0.0479274i	0.879529	+	0.475845i	$0.157858\pi$
$20$		0			0
$21$	4.59627	−	2.65366i	1.00299	−	0.579075i
$22$	4.88279	−	13.4153i	1.04101	−	2.86016i
$23$	7.34013	−	1.29426i	1.53052	−	0.269872i	0.655964	−	0.754792i	$-0.272262\pi$
$23$	7.34013	−	1.29426i	1.53052	−	0.269872i	0.874559	+	0.484920i	$0.161151\pi$
$24$	−10.4153	+	1.83651i	−2.12602	+	0.374875i
$25$		0			0
$26$	10.7023			2.09890
$27$	2.59808	+	4.50000i	0.500000	+	0.866025i
$28$			13.5175i			2.55458i
$29$	5.90033	+	4.95096i	1.09566	+	0.919371i	0.997126	−	0.0757623i	$-0.0241390\pi$
$29$	5.90033	+	4.95096i	1.09566	+	0.919371i	0.0985378	+	0.995133i	$0.468583\pi$
$30$		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	$0.798023\pi$
$32$	1.57202	−	4.31908i	0.277896	−	0.763512i
$33$	4.88279	−	8.45723i	0.849984	−	1.47222i
$34$	0.726682	−	4.12122i	0.124625	−	0.706783i
$35$		0			0
$36$	−13.2344			−2.20574
$37$	−2.15658	+	1.24510i	−0.354539	+	0.204693i	−0.666683	−	0.745342i	$-0.732286\pi$
$37$	−2.15658	+	1.24510i	−0.354539	+	0.204693i	0.312144	+	0.950035i	$0.398953\pi$
$38$	0.208911	+	0.573978i	0.0338898	+	0.0931115i
$39$	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	$0.281330\pi$
$42$	−2.33359	+	13.2344i	−0.360080	+	2.04212i
$43$	−0.256867	−	0.705737i	−0.0391719	−	0.107624i	0.918565	−	0.395271i	$-0.129349\pi$
$43$	−0.256867	−	0.705737i	−0.0391719	−	0.107624i	−0.957737	+	0.287647i	$0.907127\pi$
$44$	12.4363	+	21.5403i	1.87484	+	3.24732i
$45$		0			0
$46$	−9.43629	+	16.3441i	−1.39130	+	2.40981i
$47$	4.58202	+	0.807934i	0.668356	+	0.117849i	0.497523	−	0.867451i	$-0.334243\pi$
$47$	4.58202	+	0.807934i	0.668356	+	0.117849i	0.170833	+	0.985300i	$0.445354\pi$
$48$	5.74881	−	9.95723i	0.829769	−	1.43720i
$49$	2.24510	+	0.817150i	0.320729	+	0.116736i
$50$		0			0
$51$	0.979055	−	2.68993i	0.137095	−	0.376666i
$52$	−11.9854	+	14.2836i	−1.66207	+	1.98078i
$53$		−	12.1061i		−	1.66290i	−0.555602	−	0.831448i	$-0.687512\pi$
$53$		−	12.1061i		−	1.66290i	0.555602	−	0.831448i	$-0.312488\pi$
$54$	−12.9572	−	2.28471i	−1.76326	−	0.310910i
$55$		0			0
$56$	−14.3327	−	12.0266i	−1.91529	−	1.60712i
$57$	0.0725540	+	0.411474i	0.00961001	+	0.0545011i
$58$	−19.2067	+	3.38666i	−2.52196	+	0.444690i
$59$	−4.45336	−	1.62089i	−0.579779	−	0.211022i	0.0354493	−	0.999371i	$-0.488714\pi$
$59$	−4.45336	−	1.62089i	−0.579779	−	0.211022i	−0.615228	+	0.788349i	$0.710936\pi$
$60$		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	$-0.293941\pi$
$62$	−10.8405	−	6.25877i	−1.37675	−	0.794865i
$63$	−3.14403	+	8.63816i	−0.396111	+	1.08831i
$64$	−0.819078	−	1.41868i	−0.102385	−	0.177336i
$65$		0			0
$66$	8.45723	+	23.2361i	1.04101	+	2.86016i
$67$	4.73708	+	5.64543i	0.578726	+	0.689699i	0.973397	−	0.229123i	$-0.0735859\pi$
$67$	4.73708	+	5.64543i	0.578726	+	0.689699i	−0.394671	+	0.918822i	$0.629141\pi$
$68$	4.68647	+	5.58512i	0.568318	+	0.677296i
$69$	−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	$0.739392\pi$
$72$	11.7747	−	14.0326i	1.38766	−	1.65375i
$73$	−0.196312	−	0.113341i	−0.0229766	−	0.0132655i	0.488468	−	0.872582i	$-0.337556\pi$
$73$	−0.196312	−	0.113341i	−0.0229766	−	0.0132655i	−0.511444	+	0.859316i	$0.670889\pi$
$74$	1.09492	−	6.20961i	0.127282	−	0.721853i
$75$		0			0
$76$	−1.00000	−	0.363970i	−0.114708	−	0.0417502i
$77$	17.0138	−	3.00000i	1.93891	−	0.341882i
$78$	−14.2002	+	11.9153i	−1.60785	+	1.34915i
$79$	7.53596	+	6.32342i	0.847862	+	0.711440i	0.959318	−	0.282329i	$-0.0911070\pi$
$79$	7.53596	+	6.32342i	0.847862	+	0.711440i	−0.111456	+	0.993769i	$0.535551\pi$
$80$		0			0
$81$	−8.45723	−	3.07818i	−0.939693	−	0.342020i
$82$		−	0.361844i		−	0.0399590i
$83$	−5.69323	+	6.78493i	−0.624913	+	0.744743i	−0.981907	−	0.189364i	$-0.939357\pi$
$83$	−5.69323	+	6.78493i	−0.624913	+	0.744743i	0.356994	+	0.934107i	$0.383802\pi$
$84$	−15.0496	−	17.9355i	−1.64205	−	1.95692i
$85$		0			0
$86$	1.78699	+	0.650411i	0.192696	+	0.0701356i
$87$	−13.3408			−1.43029
$88$	−33.9039	−	5.97818i	−3.61417	−	0.637276i
$89$	3.33022	−	5.76811i	0.353003	−	0.611419i	−0.633771	−	0.773521i	$-0.718494\pi$
$89$	3.33022	−	5.76811i	0.353003	−	0.611419i	0.986774	+	0.162102i	$0.0518273\pi$
$90$		0			0
$91$	6.47565	+	11.2162i	0.678833	+	1.17577i
$92$	−11.2457	−	30.8974i	−1.17245	−	3.22128i
$93$	−6.55926	−	5.50387i	−0.680163	−	0.570725i
$94$	−9.02481	+	7.57272i	−0.930839	+	0.781066i
$95$		0			0
$96$	2.72281	+	7.48086i	0.277896	+	0.763512i
$97$	3.26017	+	8.95723i	0.331020	+	0.909469i	0.987847	+	0.155428i	$0.0496758\pi$
$97$	3.26017	+	8.95723i	0.331020	+	0.909469i	−0.656827	+	0.754041i	$0.728102\pi$
$98$	−5.23913	+	3.02481i	−0.529232	+	0.305552i
$99$	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	$0.0925816\pi$
$102$	3.62414	+	6.27719i	0.358843	+	0.621534i
$103$	6.37462	−	17.5141i	0.628110	−	1.72572i	−0.0580946	−	0.998311i	$-0.518503\pi$
$103$	6.37462	−	17.5141i	0.628110	−	1.72572i	0.686205	−	0.727408i	$-0.259275\pi$
$104$	−4.48158	−	25.4163i	−0.439455	−	2.49227i
$105$		0			0
$106$	23.4820	+	19.7038i	2.28078	+	1.91380i
$107$			10.4037i			1.00577i	0.864354	+	0.502883i	$0.167728\pi$
$107$			10.4037i			1.00577i	−0.864354	+	0.502883i	$0.832272\pi$
$108$	17.5598	−	14.7344i	1.68969	−	1.41782i
$109$	−0.147956			−0.0141716			−0.00708580	−	0.999975i	$-0.502255\pi$
$109$	−0.147956			−0.0141716			−0.00708580	+	0.999975i	$0.502255\pi$
$110$		0			0
$111$	1.47519	−	4.05304i	0.140018	−	0.384697i
$112$	20.0315	−	3.53209i	1.89280	−	0.333751i
$113$	−2.42107	+	6.65183i	−0.227755	+	0.625751i	−0.999954	−	0.00962978i	$-0.996935\pi$
$113$	−2.42107	+	6.65183i	−0.227755	+	0.625751i	0.772199	+	0.635381i	$0.219157\pi$
$114$	−0.916222	−	0.528981i	−0.0858120	−	0.0495436i
$115$		0			0
$116$	16.9893	−	29.4264i	1.57742	−	2.73217i
$117$	−10.9812	+	6.34002i	−1.01522	+	0.586135i
$118$	10.3923	−	6.00000i	0.956689	−	0.552345i
$119$	4.75877	−	1.73205i	0.436236	−	0.158777i
$120$		0			0
$121$	15.9251	−	13.3628i	1.44774	−	1.21480i
$122$	22.6345	+	26.9748i	2.04923	+	2.44218i
$123$	0.0429807	−	0.243756i	0.00387544	−	0.0219787i
$124$	20.4932	−	7.45891i	1.84034	−	0.669830i
$125$		0			0
$126$	−11.6382	−	20.1579i	−1.03681	−	1.79581i
$127$	0.211239	+	0.121959i	0.0187444	+	0.0108221i	0.509343	−	0.860564i	$-0.329888\pi$
$127$	0.211239	+	0.121959i	0.0187444	+	0.0108221i	−0.490599	+	0.871386i	$0.663222\pi$
$128$	13.1378	+	2.31655i	1.16123	+	0.204756i
$129$	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	$0.814970\pi$
$132$	−40.4825	−	14.7344i	−3.52355	−	1.28247i
$133$	−0.475129	+	0.566237i	−0.0411989	+	0.0490990i
$134$	−18.6604			−1.61202
$135$		0			0
$136$	−10.0915			−0.865341
$137$	7.97357	−	9.50253i	0.681228	−	0.811856i	−0.309037	−	0.951050i	$-0.600007\pi$
$137$	7.97357	−	9.50253i	0.681228	−	0.811856i	0.990265	+	0.139194i	$0.0444513\pi$
$138$	−5.67626	−	32.1917i	−0.483195	−	2.74034i
$139$	−3.21823	−	18.2515i	−0.272966	−	1.54807i	−0.745348	−	0.666675i	$-0.767717\pi$
$139$	−3.21823	−	18.2515i	−0.272966	−	1.54807i	0.472382	−	0.881394i	$-0.343394\pi$
$140$		0			0
$141$	−6.97906	+	4.02936i	−0.587742	+	0.339333i
$142$	−12.2229	−	2.15523i	−1.02572	−	0.180863i
$143$	20.6380	+	11.9153i	1.72583	+	0.996411i
$144$	3.45811	+	19.6119i	0.288176	+	1.63433i
$145$		0			0
$146$	0.539363	−	0.196312i	0.0446380	−	0.0162469i
$147$	−3.88863	+	1.41534i	−0.320729	+	0.116736i
$148$	7.06131	+	8.41534i	0.580436	+	0.691737i
$149$	3.66044	−	3.07148i	0.299875	−	0.251625i	−0.480417	−	0.877040i	$-0.659515\pi$
$149$	3.66044	−	3.07148i	0.299875	−	0.251625i	0.780292	+	0.625415i	$0.215070\pi$
$150$		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	$0.315765\pi$
$152$	1.27562	−	0.736482i	0.103467	−	0.0597366i
$153$	1.69577	+	4.65910i	0.137095	+	0.376666i
$154$	−21.8726	+	37.8844i	−1.76254	+	3.05281i
$155$		0			0
$156$		−	32.2956i		−	2.58572i
$157$	6.84478	−	18.8059i	0.546273	−	1.50087i	−0.292432	−	0.956286i	$-0.594465\pi$
$157$	6.84478	−	18.8059i	0.546273	−	1.50087i	0.838705	−	0.544586i	$-0.183313\pi$
$158$	−24.5310	+	4.32547i	−1.95158	+	0.344116i
$159$	13.4782	+	16.0627i	1.06889	+	1.27385i
$160$		0			0
$161$	−22.8384			−1.79992
$162$	19.7357	−	11.3944i	1.55058	−	0.895229i
$163$		−	9.95811i		−	0.779979i	−0.920819	−	0.389990i	$-0.872479\pi$
$163$		−	9.95811i		−	0.779979i	0.920819	−	0.389990i	$-0.127521\pi$
$164$	0.482926	+	0.405223i	0.0377102	+	0.0316426i
$165$		0			0
$166$	−3.89440	−	22.0862i	−0.302264	−	1.71422i
$167$	1.08164	−	2.97178i	0.0836998	−	0.229963i	−0.890782	−	0.454432i	$-0.849842\pi$
$167$	1.08164	−	2.97178i	0.0836998	−	0.229963i	0.974481	+	0.224468i	$0.0720646\pi$
$168$	32.4068			2.50024
$169$	−0.844770	+	4.79093i	−0.0649823	+	0.368533i
$170$		0			0
$171$	−0.554378	−	0.465178i	−0.0423943	−	0.0355731i
$172$	−2.86927	+	1.65657i	−0.218780	+	0.126313i
$173$	6.75557	+	18.5608i	0.513616	+	1.41115i	0.877442	+	0.479682i	$0.159248\pi$
$173$	6.75557	+	18.5608i	0.513616	+	1.41115i	−0.363826	+	0.931467i	$0.618530\pi$
$174$	21.7135	−	25.8771i	1.64609	−	1.96174i
$175$		0			0
$176$	28.6707	−	24.0576i	2.16114	−	1.81341i
$177$	7.71345	−	2.80747i	0.579779	−	0.211022i
$178$	5.76811	+	15.8478i	0.432338	+	1.18784i
$179$	−4.05051	−	7.01568i	−0.302749	−	0.524377i	0.674009	−	0.738724i	$-0.264571\pi$
$179$	−4.05051	−	7.01568i	−0.302749	−	0.524377i	−0.976758	+	0.214347i	$0.931238\pi$
$180$		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	$0.0591782\pi$
$182$	−32.2956	−	5.69459i	−2.39391	−	0.422111i
$183$	12.0436	+	20.8601i	0.890287	+	1.54202i
$184$	42.7661	+	15.5656i	3.15276	+	1.14751i
$185$		0			0
$186$	21.3516	−	3.76487i	1.56558	−	0.276054i
$187$	5.98962	−	7.13816i	0.438005	−	0.521994i
$188$		−	20.5253i		−	1.49696i
$189$	−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	$0.786947\pi$
$192$	2.66625	+	0.970437i	0.192420	+	0.0700353i
$193$	24.9412	−	4.39780i	1.79531	−	0.316561i	0.826232	−	0.563331i	$-0.190480\pi$
$193$	24.9412	−	4.39780i	1.79531	−	0.316561i	0.969074	+	0.246770i	$0.0793692\pi$
$194$	−22.6805	−	8.25503i	−1.62837	−	0.592677i
$195$		0			0
$196$	1.83022	−	10.3797i	0.130730	−	0.741408i
$197$	−4.22800	−	2.44104i	−0.301233	−	0.173917i	0.341764	−	0.939786i	$-0.388976\pi$
$197$	−4.22800	−	2.44104i	−0.301233	−	0.173917i	−0.642996	+	0.765869i	$0.722309\pi$
$198$	−37.0909	−	21.4145i	−2.63594	−	1.52186i
$199$	8.68092	+	15.0358i	0.615374	+	1.06586i	0.990319	+	0.138812i	$0.0443284\pi$
$199$	8.68092	+	15.0358i	0.615374	+	1.06586i	−0.374944	+	0.927047i	$0.622338\pi$
$200$		0			0
$201$	−12.5706	−	2.21653i	−0.886660	−	0.156342i
$202$	−3.79677	−	4.52481i	−0.267140	−	0.318365i
$203$	−15.1706	−	18.0797i	−1.06477	−	1.26894i
$204$	−12.4363	−	2.19285i	−0.870714	−	0.153530i
$205$		0			0
$206$	23.5967	+	40.8707i	1.64406	+	2.84760i
$207$		−	22.3601i		−	1.55413i
$208$	24.2984	+	14.0287i	1.68479	+	0.972714i
$209$	−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	$0.740196\pi$
$212$	−52.5942	+	9.27379i	−3.61219	+	0.636926i
$213$	−7.97794	−	2.90373i	−0.546640	−	0.198961i
$214$	−20.1800	−	16.9331i	−1.37948	−	1.15752i
$215$		0			0
$216$			31.7281i			2.15882i
$217$		−	15.1480i		−	1.02831i
$218$	0.240812	−	0.286989i	0.0163099	−	0.0194373i
$219$	0.386659	−	0.0681784i	0.0261280	−	0.00460707i
$220$		0			0
$221$	6.56418	+	2.38917i	0.441554	+	0.160713i
$222$	5.46064	+	9.45811i	0.366494	+	0.634787i
$223$	−0.433877	−	0.0765042i	−0.0290545	−	0.00512310i	0.159102	−	0.987262i	$-0.449140\pi$
$223$	−0.433877	−	0.0765042i	−0.0290545	−	0.00512310i	−0.188157	+	0.982139i	$0.560251\pi$
$224$	−7.04189	+	12.1969i	−0.470506	+	0.814940i
$225$		0			0
$226$	−8.96198	−	15.5226i	−0.596142	−	1.03255i
$227$	−1.81720	−	4.99273i	−0.120612	−	0.331379i	0.864664	−	0.502351i	$-0.167531\pi$
$227$	−1.81720	−	4.99273i	−0.120612	−	0.331379i	−0.985276	+	0.170972i	$0.945309\pi$
$228$	1.73205	−	0.630415i	0.114708	−	0.0417502i
$229$	−0.0603074	+	0.0506039i	−0.00398522	+	0.00334400i	−0.644778	−	0.764370i	$-0.723050\pi$
$229$	−0.0603074	+	0.0506039i	−0.00398522	+	0.00334400i	0.640793	+	0.767714i	$0.278606\pi$
$230$		0			0
$231$	−19.2344	+	22.9227i	−1.26553	+	1.50820i
$232$	16.0855	+	44.1946i	1.05607	+	2.90152i
$233$	0.324446	−	0.187319i	0.0212551	−	0.0122717i	−0.489335	−	0.872096i	$-0.662760\pi$
$233$	0.324446	−	0.187319i	0.0212551	−	0.0122717i	0.510590	+	0.859824i	$0.329427\pi$
$234$	5.57532	−	31.6192i	0.364470	−	2.06701i
$235$		0			0
$236$	−3.63041	+	20.5891i	−0.236320	+	1.34024i
$237$	−17.0390			−1.10680
$238$	−4.38571	+	12.0496i	−0.284283	+	0.781061i
$239$	1.88666	+	10.6998i	0.122038	+	0.692111i	0.983023	+	0.183481i	$0.0587367\pi$
$239$	1.88666	+	10.6998i	0.122038	+	0.692111i	−0.860985	+	0.508630i	$0.830152\pi$
$240$		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	$0.391773\pi$
$242$			52.6391i			3.38377i
$243$	14.6484	−	5.33157i	0.939693	−	0.342020i
$244$	−61.3492			−3.92748
$245$		0			0
$246$	0.402856	+	0.480105i	0.0256852	+	0.0306104i
$247$	−1.00411	+	0.177052i	−0.0638900	+	0.0112655i
$248$	−10.3241	+	28.3653i	−0.655583	+	1.80120i
$249$		−	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	$0.106096\pi$
$252$	39.9365	+	7.04189i	2.51577	+	0.443597i
$253$	−36.3932	+	21.0116i	−2.28802	+	1.32099i
$254$	−0.580375	+	0.211239i	−0.0364159	+	0.0132543i
$255$		0			0
$256$	−23.3666	+	19.6069i	−1.46042	+	1.22543i
$257$	−4.06564	−	4.84524i	−0.253607	−	0.302238i	0.624187	−	0.781275i	$-0.285430\pi$
$257$	−4.06564	−	4.84524i	−0.253607	−	0.302238i	−0.877795	+	0.479037i	$0.840986\pi$
$258$	−3.09516	+	1.12654i	−0.192696	+	0.0701356i
$259$	7.17024	−	2.60976i	0.445537	−	0.162162i
$260$		0			0
$261$	17.7010	−	14.8529i	1.09566	−	0.919371i
$262$	−19.8594	−	11.4659i	−1.22692	−	0.708363i
$263$	0.460802	+	0.0812519i	0.0284143	+	0.00501021i	0.187837	−	0.982200i	$-0.439852\pi$
$263$	0.460802	+	0.0812519i	0.0284143	+	0.00501021i	−0.159423	+	0.987210i	$0.550963\pi$
$264$	51.6404	−	29.8146i	3.17825	−	1.83496i
$265$		0			0
$266$	−0.325008	−	1.84321i	−0.0199275	−	0.113014i
$267$	2.00324	+	11.3610i	0.122597	+	0.695280i
$268$	20.8975	−	24.9047i	1.27652	−	1.52129i
$269$	−1.84524			−0.112506			−0.0562530	−	0.998417i	$-0.517915\pi$
$269$	−1.84524			−0.112506			−0.0562530	+	0.998417i	$0.517915\pi$
$270$		0			0
$271$	−4.12567			−0.250616			−0.125308	−	0.992118i	$-0.539992\pi$
$271$	−4.12567			−0.250616			−0.125308	+	0.992118i	$0.539992\pi$
$272$	7.05196	−	8.40420i	0.427588	−	0.509579i
$273$	−21.0795	−	7.67230i	−1.27579	−	0.464349i
$274$	5.45424	+	30.9325i	0.329503	+	1.86870i
$275$		0			0
$276$	49.3205	+	28.4752i	2.96874	+	1.71401i
$277$	0.0605553	+	0.0106775i	0.00363841	+	0.000641550i	0.175467	−	0.984485i	$-0.443856\pi$
$277$	0.0605553	+	0.0106775i	0.00363841	+	0.000641550i	−0.171829	+	0.985127i	$0.554968\pi$
$278$	40.6402	+	23.4636i	2.43744	+	1.40726i
$279$	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	$0.331135\pi$
$282$	3.54336	−	20.0954i	0.211004	−	1.19666i
$283$	−5.37051	−	6.40033i	−0.319244	−	0.380460i	0.582427	−	0.812883i	$-0.302103\pi$
$283$	−5.37051	−	6.40033i	−0.319244	−	0.380460i	−0.901671	+	0.432423i	$0.857659\pi$
$284$	16.5646	−	13.8994i	0.982931	−	0.824777i
$285$		0			0
$286$	−56.7024	+	20.6380i	−3.35288	+	1.22035i
$287$	0.379217	−	0.218941i	0.0223844	−	0.0129237i
$288$	−11.9415	−	6.89440i	−0.703657	−	0.406256i
$289$	−7.13429	+	12.3569i	−0.419664	+	0.726879i
$290$		0			0
$291$	−14.2981	−	8.25503i	−0.838171	−	0.483918i
$292$	−0.342020	+	0.939693i	−0.0200152	+	0.0549914i
$293$	−11.8303	+	2.08600i	−0.691133	+	0.121865i	−0.508173	−	0.861255i	$-0.669679\pi$
$293$	−11.8303	+	2.08600i	−0.691133	+	0.121865i	−0.182960	+	0.983120i	$0.558568\pi$
$294$	3.58378	−	9.84635i	0.209010	−	0.574251i
$295$		0			0
$296$	−15.2053			−0.883792
$297$	−22.4426	−	18.8316i	−1.30225	−	1.09272i
$298$			12.0993i			0.700891i
$299$	−24.1327	−	20.2497i	−1.39563	−	1.17107i
$300$		0			0
$301$	0.399615	+	2.26633i	0.0230334	+	0.130629i
$302$	−4.84651	+	13.3157i	−0.278885	+	0.766231i
$303$	−2.02022	−	3.49912i	−0.116059	−	0.201019i
$304$	−0.278066	+	1.57699i	−0.0159482	+	0.0904467i
$305$		0			0
$306$	−11.7973	−	4.29385i	−0.674404	−	0.245463i
$307$	9.33667	−	5.39053i	0.532872	−	0.307654i	−0.209313	−	0.977849i	$-0.567123\pi$
$307$	9.33667	−	5.39053i	0.532872	−	0.307654i	0.742185	+	0.670195i	$0.233789\pi$
$308$	−26.0667	−	71.6177i	−1.48529	−	4.08080i
$309$	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	$0.422090\pi$
$312$	34.2433	+	28.7335i	1.93865	+	1.62672i
$313$	−1.58370	−	4.35117i	−0.0895157	−	0.245942i	0.886854	−	0.462050i	$-0.152886\pi$
$313$	−1.58370	−	4.35117i	−0.0895157	−	0.245942i	−0.976370	+	0.216108i	$0.930664\pi$
$314$	25.3371	+	43.8851i	1.42985	+	2.47658i
$315$		0			0
$316$	21.6989	−	37.5836i	1.22066	−	2.11425i
$317$	7.65787	+	1.35029i	0.430109	+	0.0758398i	0.384512	−	0.923120i	$-0.374370\pi$
$317$	7.65787	+	1.35029i	0.430109	+	0.0758398i	0.0455972	+	0.998960i	$0.485481\pi$
$318$	−53.0937			−2.97734
$319$	−40.8080	−	14.8529i	−2.28481	−	0.831602i
$320$		0			0
$321$	−11.5829	−	13.8040i	−0.646494	−	0.770462i
$322$	37.1717	−	44.2995i	2.07150	−	2.46872i
$323$			0.398681i			0.0221832i
$324$	−6.89440	+	39.1001i	−0.383022	+	2.17223i
$325$		0			0
$326$	19.3157	+	16.2078i	1.06980	+	0.897666i
$327$	0.196312	−	0.164725i	0.0108561	−	0.00910933i
$328$	−0.859322	+	0.151522i	−0.0474481	+	0.00836638i
$329$	−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	$-0.0112585\pi$
$332$	33.8381	+	19.5364i	1.85711	+	1.07220i
$333$	2.55510	+	7.02007i	0.140018	+	0.384697i
$334$	4.00387	+	6.93491i	0.219082	+	0.379461i
$335$		0			0
$336$	−22.6459	+	26.9883i	−1.23543	+	1.47233i
$337$	10.6348	+	12.6741i	0.579317	+	0.690403i	0.973515	−	0.228622i	$-0.0734221\pi$
$337$	10.6348	+	12.6741i	0.579317	+	0.690403i	−0.394198	+	0.919025i	$0.628978\pi$
$338$	−7.91799	−	9.43629i	−0.430682	−	0.513266i
$339$	−4.19341	−	11.5213i	−0.227755	−	0.625751i
$340$		0			0
$341$	−13.9363	−	24.1384i	−0.754692	−	1.30717i
$342$	1.80460	−	0.318201i	0.0975819	−	0.0172063i
$343$	12.2355	+	7.06418i	0.660656	+	0.381430i
$344$	0.796322	−	4.51617i	0.0429348	−	0.243495i
$345$		0			0
$346$	−46.9975	−	17.1057i	−2.52660	−	0.919608i
$347$	14.9550	−	2.63697i	0.802828	−	0.141560i	0.242846	−	0.970065i	$-0.421919\pi$
$347$	14.9550	−	2.63697i	0.802828	−	0.141560i	0.559982	+	0.828505i	$0.310808\pi$
$348$	10.2197	+	57.9586i	0.547832	+	3.10691i
$349$	−10.8191	−	9.07828i	−0.579132	−	0.485949i	0.305530	−	0.952182i	$-0.401166\pi$
$349$	−10.8191	−	9.07828i	−0.579132	−	0.485949i	−0.884662	+	0.466233i	$0.845611\pi$
$350$		0			0
$351$	7.51161	−	20.6380i	0.400940	−	1.10157i
$352$			25.9145i			1.38125i
$353$	2.67733	−	3.19072i	0.142500	−	0.169825i	−0.690074	−	0.723739i	$-0.742422\pi$
$353$	2.67733	−	3.19072i	0.142500	−	0.169825i	0.832574	+	0.553914i	$0.186866\pi$
$354$	−7.10876	+	19.5311i	−0.377826	+	1.03807i
$355$		0			0
$356$	−27.6104	−	10.0494i	−1.46335	−	0.532615i
$357$	−4.38571	+	7.59627i	−0.232116	+	0.402037i
$358$	20.2009	+	3.56196i	1.06765	+	0.188255i
$359$	−3.29679	+	5.71021i	−0.173998	+	0.301373i	−0.939814	−	0.341686i	$-0.889002\pi$
$359$	−3.29679	+	5.71021i	−0.173998	+	0.301373i	0.765816	+	0.643060i	$0.222335\pi$
$360$		0			0
$361$	9.47090	+	16.4041i	0.498469	+	0.863373i
$362$	7.72016	+	21.2110i	0.405762	+	1.11482i
$363$	−6.25259	+	35.4602i	−0.328176	+	1.86118i
$364$	43.7674	−	36.7252i	2.29404	−	1.92493i
$365$		0			0
$366$	−60.0642	−	10.5909i	−3.13961	−	0.553598i
$367$	−4.34008	−	11.9243i	−0.226550	−	0.622442i	0.773384	−	0.633938i	$-0.218563\pi$
$367$	−4.34008	−	11.9243i	−0.226550	−	0.622442i	−0.999934	+	0.0114966i	$0.996340\pi$
$368$	−42.8480	+	24.7383i	−2.23361	+	1.28957i
$369$	0.214355	+	0.371274i	0.0111589	+	0.0193278i
$370$		0			0
$371$	−6.44150	+	36.5316i	−0.334426	+	1.89663i
$372$	−18.8866	+	32.7126i	−0.979226	+	1.69607i
$373$	−2.61159	+	7.17530i	−0.135223	+	0.371523i	−0.988760	−	0.149509i	$-0.952231\pi$
$373$	−2.61159	+	7.17530i	−0.135223	+	0.371523i	0.853537	+	0.521032i	$0.174453\pi$
$374$	4.09714	+	23.2361i	0.211858	+	1.20151i
$375$		0			0
$376$	21.7631	+	18.2614i	1.12235	+	0.941761i
$377$		−	32.5553i		−	1.67668i
$378$	37.8844	+	13.7888i	1.94856	+	0.709219i
$379$	27.0838			1.39120			0.695600	−	0.718429i	$-0.255139\pi$
$379$	27.0838			1.39120			0.695600	+	0.718429i	$0.255139\pi$
$380$		0			0
$381$	−0.416060	+	0.0733626i	−0.0213154	+	0.00375848i
$382$	13.9187	−	2.45424i	0.712142	−	0.125570i
$383$	3.52201	−	9.67664i	0.179966	−	0.494453i	−0.816605	−	0.577198i	$-0.804146\pi$
$383$	3.52201	−	9.67664i	0.179966	−	0.494453i	0.996571	+	0.0827443i	$0.0263685\pi$
$384$	−20.0107	+	11.5532i	−1.02117	+	0.589572i
$385$		0			0
$386$	−32.0638	+	55.5361i	−1.63200	+	2.82671i
$387$	−2.21886	+	0.391245i	−0.112791	+	0.0198881i
$388$	36.4169	−	21.0253i	1.84879	−	1.06740i
$389$	3.89780	−	1.41868i	0.197626	−	0.0719302i	−0.241311	−	0.970448i	$-0.577577\pi$
$389$	3.89780	−	1.41868i	0.197626	−	0.0719302i	0.438937	+	0.898518i	$0.355355\pi$
$390$		0			0
$391$	−9.43629	+	7.91799i	−0.477214	+	0.400430i
$392$	9.37732	+	11.1755i	0.473626	+	0.564446i
$393$	−12.0163	−	10.0829i	−0.606144	−	0.508615i
$394$	11.6163	−	4.22800i	0.585222	−	0.213004i
$395$		0			0
$396$	70.1177	−	25.5208i	3.52355	−	1.28247i
$397$	19.1444	+	11.0530i	0.960831	+	0.554736i	0.896429	−	0.443188i	$-0.146153\pi$
$397$	19.1444	+	11.0530i	0.960831	+	0.554736i	0.0644021	+	0.997924i	$0.479486\pi$
$398$	−43.2939	−	7.63387i	−2.17012	−	0.382652i
$399$		−	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	$-0.193910\pi$
$402$	24.7592	−	20.7754i	1.23488	−	1.03618i
$403$	13.4310	−	16.0064i	0.669044	−	0.797335i
$404$	10.2909			0.511989
$405$		0			0
$406$	59.7606			2.96587
$407$	9.02482	−	10.7554i	0.447344	−	0.533124i
$408$	13.3897	−	11.2353i	0.662889	−	0.556230i
$409$	6.09199	+	34.5494i	0.301229	+	1.70836i	0.640743	+	0.767755i	$0.278626\pi$
$409$	6.09199	+	34.5494i	0.301229	+	1.70836i	−0.339514	+	0.940601i	$0.610263\pi$
$410$		0			0
$411$			21.4855i			1.05980i
$412$	−80.9726	−	14.2777i	−3.98923	−	0.703410i
$413$	12.5761	+	7.26083i	0.618831	+	0.357282i
$414$	43.3717	+	36.3932i	2.13160	+	1.78863i
$415$		0			0
$416$	−18.2554	+	6.64441i	−0.895043	+	0.325769i
$417$	24.5901	+	20.6336i	1.20418	+	1.01043i
$418$	−2.21368	−	2.63816i	−0.108274	−	0.129036i
$419$	−12.7665	+	10.7124i	−0.623685	+	0.523334i	−0.898959	−	0.438032i	$-0.855676\pi$
$419$	−12.7665	+	10.7124i	−0.623685	+	0.523334i	0.275275	+	0.961366i	$0.411231\pi$
$420$		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	$0.155764\pi$
$422$	25.1325	−	14.5103i	1.22343	−	0.706349i
$423$	4.77396	−	13.1163i	0.232118	−	0.637738i
$424$	36.9602	−	64.0170i	1.79495	−	3.10894i
$425$		0			0
$426$	18.6172	−	10.7487i	0.902007	−	0.520774i
$427$	−14.5744	+	40.0428i	−0.705304	+	1.93781i
$428$	45.1985	−	7.96972i	2.18475	−	0.385231i
$429$	−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	$0.617190\pi$
$432$	−26.4231	−	22.1716i	−1.27128	−	1.06673i
$433$		−	23.3919i		−	1.12414i	−0.827089	−	0.562071i	$-0.810005\pi$
$433$		−	23.3919i		−	1.12414i	0.827089	−	0.562071i	$-0.189995\pi$
$434$	29.3824	+	24.6547i	1.41040	+	1.18347i
$435$		0			0
$436$	0.113341	+	0.642788i	0.00542804	+	0.0307839i
$437$	0.614942	−	1.68954i	0.0294167	−	0.0808217i
$438$	−0.497079	+	0.860967i	−0.0237514	+	0.0411386i
$439$	4.55959	−	25.8587i	0.217617	−	1.23417i	−0.658689	−	0.752415i	$-0.728889\pi$
$439$	4.55959	−	25.8587i	0.217617	−	1.23417i	0.876306	−	0.481754i	$-0.160000\pi$
$440$		0			0
$441$	3.58378	−	6.20729i	0.170656	−	0.295585i
$442$	−15.3181	+	8.84389i	−0.728606	+	0.420661i
$443$	10.8554	+	29.8251i	0.515757	+	1.41703i	0.875153	+	0.483846i	$0.160761\pi$
$443$	10.8554	+	29.8251i	0.515757	+	1.41703i	−0.359396	+	0.933185i	$0.617017\pi$
$444$	−18.7383	−	3.30407i	−0.889280	−	0.156804i
$445$		0			0
$446$	0.854570	−	0.717070i	0.0404651	−	0.0339542i
$447$	−1.43718	+	8.15064i	−0.0679762	+	0.385512i
$448$	1.71680	+	4.71688i	0.0811114	+	0.222852i
$449$	−9.23695	−	15.9989i	−0.435919	−	0.755033i	0.561452	−	0.827510i	$-0.310243\pi$
$449$	−9.23695	−	15.9989i	−0.435919	−	0.755033i	−0.997370	+	0.0724765i	$0.976910\pi$
$450$		0			0
$451$	0.402856	−	0.697767i	0.0189697	−	0.0328566i
$452$	30.7532	+	5.42262i	1.44651	+	0.255059i
$453$	−4.84651	+	8.39440i	−0.227709	+	0.394403i
$454$	12.6420	+	4.60132i	0.593320	+	0.215951i
$455$		0			0
$456$	−0.872578	+	2.39739i	−0.0408622	+	0.112268i
$457$	−6.86998	+	8.18732i	−0.321364	+	0.382987i	−0.902406	−	0.430887i	$-0.858201\pi$
$457$	−6.86998	+	8.18732i	−0.321364	+	0.382987i	0.581042	+	0.813874i	$0.302645\pi$
$458$		−	0.199340i		−	0.00931457i
$459$	−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	$0.499694\pi$
$462$	−13.1571	−	74.6177i	−0.612125	−	3.47153i
$463$	−4.54077	+	0.800660i	−0.211027	+	0.0372098i	−0.278162	−	0.960534i	$-0.589725\pi$
$463$	−4.54077	+	0.800660i	−0.211027	+	0.0372098i	0.0671350	+	0.997744i	$0.478614\pi$
$464$	−48.0458	−	17.4872i	−2.23047	−	0.811825i
$465$		0			0
$466$	−0.164725	+	0.934204i	−0.00763075	+	0.0432762i
$467$	16.9310	+	9.77513i	0.783474	+	0.452339i	0.837660	−	0.546192i	$-0.183923\pi$
$467$	16.9310	+	9.77513i	0.783474	+	0.452339i	−0.0541859	+	0.998531i	$0.517256\pi$
$468$	35.9561	+	42.8508i	1.66207	+	1.98078i
$469$	−11.2909	−	19.5563i	−0.521363	−	0.903028i
$470$		0			0
$471$	11.8555	+	32.5727i	0.546273	+	1.50087i
$472$	−18.6008	−	22.1676i	−0.856171	−	1.02034i
$473$	2.72183	+	3.24376i	0.125150	+	0.149148i
$474$	27.7327	−	33.0505i	1.27380	−	1.51806i
$475$		0			0
$476$	−11.1702	−	19.3474i	−0.511987	−	0.886788i
$477$	−35.7664	−	6.30659i	−1.63763	−	0.288759i
$478$	−23.8250	−	13.7554i	−1.08973	−	0.629156i
$479$	0.449493	−	2.54920i	0.0205379	−	0.116476i	−0.972815	−	0.231582i	$-0.925610\pi$
$479$	0.449493	−	2.54920i	0.0205379	−	0.116476i	0.993353	+	0.115106i	$0.0367209\pi$
$480$		0			0
$481$	9.89053	+	3.59986i	0.450969	+	0.164139i
$482$	−66.6967	+	11.7604i	−3.03795	+	0.535672i
$483$	30.3027	−	25.4270i	1.37882	−	1.15697i
$484$	−70.2534	−	58.9496i	−3.19333	−	2.67953i
$485$		0			0
$486$	−13.5000	+	37.0909i	−0.612372	+	1.68248i
$487$			40.7870i			1.84824i	0.382105	+	0.924119i	$0.375199\pi$
$487$			40.7870i			1.84824i	−0.382105	+	0.924119i	$0.624801\pi$
$488$	54.5826	−	65.0490i	2.47084	−	2.94463i
$489$	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	$0.976507\pi$
$492$	−1.09191			−0.0492271
$493$	−12.5363	−	2.21048i	−0.564606	−	0.0995552i
$494$	1.29086	−	2.23583i	0.0580785	−	0.100595i
$495$		0			0
$496$	−16.4081	−	28.4196i	−0.736744	−	1.27608i
$497$	−5.13701	−	14.1138i	−0.230426	−	0.633091i
$498$	29.7567	+	24.9688i	1.33343	+	1.11888i
$499$	10.2226	−	8.57775i	0.457625	−	0.383993i	−0.384631	−	0.923070i	$-0.625671\pi$
$499$	10.2226	−	8.57775i	0.457625	−	0.383993i	0.842256	+	0.539077i	$0.181227\pi$
$500$		0			0
$501$	1.87346	+	5.14728i	0.0836998	+	0.229963i
$502$	5.19026	+	14.2601i	0.231653	+	0.636460i
$503$	−15.6373	+	9.02822i	−0.697234	+	0.402548i	−0.806316	−	0.591484i	$-0.798542\pi$
$503$	−15.6373	+	9.02822i	−0.697234	+	0.402548i	0.109082	+	0.994033i	$0.465209\pi$
$504$	−42.9982	+	36.0798i	−1.91529	+	1.60712i
$505$		0			0
$506$	18.4773	−	104.790i	0.821416	−	4.65848i
$507$	−4.21307	−	7.29726i	−0.187109	−	0.324083i
$508$	0.368026	−	1.01114i	0.0163285	−	0.0448623i
$509$	−4.18779	−	23.7501i	−0.185620	−	1.05271i	−0.925156	−	0.379588i	$-0.876066\pi$
$509$	−4.18779	−	23.7501i	−0.185620	−	1.05271i	0.739535	−	0.673118i	$-0.235045\pi$
$510$		0			0
$511$	0.532089	+	0.446476i	0.0235382	+	0.0197509i
$512$		−	50.5553i		−	2.23425i
$513$	1.25347			0.0553418
$514$	16.0155			0.706413
$515$		0			0
$516$	1.96270	−	5.39246i	0.0864029	−	0.237390i
$517$	−25.8341	+	4.55525i	−1.13618	+	0.200340i
$518$	−6.60813	+	18.1557i	−0.290345	+	0.797716i
$519$	−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	$-0.193829\pi$
$522$			58.5090i			2.56087i
$523$	−5.66955	+	3.27332i	−0.247912	+	0.143132i	−0.618808	−	0.785542i	$-0.712384\pi$
$523$	−5.66955	+	3.27332i	−0.247912	+	0.143132i	0.370896	+	0.928675i	$0.379051\pi$
$524$	37.5428	−	13.6645i	1.64007	−	0.596935i
$525$		0			0
$526$	−0.907604	+	0.761570i	−0.0395734	+	0.0332060i
$527$	−5.25173	−	6.25877i	−0.228769	−	0.272636i
$528$	−11.2568	+	63.8405i	−0.489890	+	2.77830i
$529$	30.5895	−	11.1337i	1.32998	−	0.484072i
$530$		0			0
$531$	−7.10876	+	12.3127i	−0.308494	+	0.534327i
$532$	2.82396	+	1.63041i	0.122434	+	0.0706875i
$533$	0.594831	+	0.104885i	0.0257650	+	0.00454306i
$534$	−25.2973	−	14.6054i	−1.09472	−	0.632037i
$535$		0			0
$536$	7.81403	+	44.3155i	0.337514	+	1.91414i
$537$	13.1852	+	4.79901i	0.568982	+	0.207093i
$538$	3.00330	−	3.57919i	0.129481	−	0.154310i
$539$	−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	$0.726302\pi$
$542$	6.71492	−	8.00253i	0.288430	−	0.343738i
$543$	2.68118	+	15.2057i	0.115061	+	0.652541i
$544$	1.31908	+	7.48086i	0.0565550	+	0.320739i
$545$		0			0
$546$	49.1908	−	28.4003i	2.10517	−	1.21542i
$547$	−38.0907	−	6.71641i	−1.62864	−	0.287173i	−0.716664	−	0.697418i	$-0.754332\pi$
$547$	−38.0907	−	6.71641i	−1.62864	−	0.287173i	−0.911975	+	0.410245i	$0.865443\pi$
$548$	−47.3914	−	27.3614i	−2.02446	−	1.16882i
$549$	−39.2041	−	14.2691i	−1.67319	−	0.608992i
$550$		0			0
$551$	1.74598	−	0.635484i	0.0743811	−	0.0270725i
$552$	−74.0731	+	26.9604i	−3.15276	+	1.14751i
$553$	−19.3761	−	23.0915i	−0.823955	−	0.981951i
$554$	−0.119271	+	0.100080i	−0.00506732	+	0.00425199i
$555$		0			0
$556$	−76.8273	+	27.9629i	−3.25821	+	1.18589i
$557$	−12.8808	+	7.43676i	−0.545779	+	0.315105i	−0.747418	−	0.664354i	$-0.768707\pi$
$557$	−12.8808	+	7.43676i	−0.545779	+	0.315105i	0.201639	+	0.979460i	$0.435373\pi$
$558$	−24.1384	+	28.7670i	−1.02186	+	1.21780i
$559$	−1.58718	+	2.74908i	−0.0671306	+	0.116274i
$560$		0			0
$561$			16.1396i			0.681414i
$562$	−5.23913	+	14.3944i	−0.220999	+	0.607191i
$563$	−28.8485	+	5.08677i	−1.21582	+	0.214382i	−0.744525	−	0.667594i	$-0.767324\pi$
$563$	−28.8485	+	5.08677i	−1.21582	+	0.214382i	−0.471294	+	0.881976i	$0.656213\pi$
$564$	22.8516	+	27.2335i	0.962227	+	1.14674i
$565$		0			0
$566$	21.1557			0.889240
$567$	23.8829	+	13.7888i	1.00299	+	0.579075i
$568$			29.9299i			1.25583i
$569$	24.4127	+	20.4847i	1.02343	+	0.858761i	0.990055	−	0.140682i	$-0.0449294\pi$
$569$	24.4127	+	20.4847i	1.02343	+	0.858761i	0.0333769	+	0.999443i	$0.489374\pi$
$570$		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	$-0.164620\pi$
$572$	35.9561	−	98.7884i	1.50340	−	4.13055i
$573$	9.66782			0.403879
$574$	−0.192533	+	1.09191i	−0.00803619	+	0.0455755i
$575$		0			0
$576$	−4.61809	+	1.68085i	−0.192420	+	0.0700353i
$577$	1.96464	−	1.13429i	0.0817890	−	0.0472209i	−0.458548	−	0.888670i	$-0.651630\pi$
$577$	1.96464	−	1.13429i	0.0817890	−	0.0472209i	0.540337	+	0.841449i	$0.318297\pi$
$578$	−12.3569	−	33.9504i	−0.513981	−	1.41215i
$579$	−28.1964	+	33.6032i	−1.17180	+	1.39650i
$580$		0			0
$581$	20.7902	−	17.4451i	0.862524	−	0.723744i
$582$	39.2838	−	14.2981i	1.62837	−	0.592677i
$583$	23.3449	+	64.1396i	0.966847	+	2.65639i
$584$	−0.692066	−	1.19869i	−0.0286379	−	0.0496023i
$585$		0			0
$586$	15.2087	−	26.3423i	0.628267	−	1.08819i
$587$	32.8120	+	5.78564i	1.35430	+	0.238799i	0.803234	−	0.595664i	$-0.203111\pi$
$587$	32.8120	+	5.78564i	1.35430	+	0.238799i	0.551064	+	0.834463i	$0.314222\pi$
$588$	9.12776	+	15.8097i	0.376422	+	0.651983i
$589$	1.12061	+	0.407870i	0.0461741	+	0.0168060i
$590$		0			0
$591$	8.32753	−	1.46837i	0.342549	−	0.0604006i
$592$	10.6255	−	12.6630i	0.436705	−	0.520445i
$593$		−	24.7793i		−	1.01756i	−0.860895	−	0.508782i	$-0.830096\pi$
$593$		−	24.7793i		−	1.01756i	0.860895	−	0.508782i	$-0.169904\pi$
$594$	73.0549	−	12.8816i	2.99748	−	0.528536i
$595$		0			0
$596$	−16.1480	−	13.5497i	−0.661446	−	0.555019i
$597$	−28.2581	−	10.2851i	−1.15653	−	0.420941i
$598$	78.5565	−	13.8516i	3.21241	−	0.566435i
$599$	35.9368	+	13.0799i	1.46834	+	0.534431i	0.947648	−	0.319316i	$-0.103453\pi$
$599$	35.9368	+	13.0799i	1.46834	+	0.534431i	0.520688	+	0.853747i	$0.325676\pi$
$600$		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	$-0.313847\pi$
$602$	−5.04639	−	2.91353i	−0.205675	−	0.118747i
$603$	19.1467	−	11.0544i	0.779716	−	0.450169i
$604$	−12.3439	−	21.3802i	−0.502266	−	0.869950i
$605$		0			0
$606$	10.0753	+	1.77655i	0.409282	+	0.0721675i
$607$	−10.1845	−	12.1374i	−0.413377	−	0.492644i	0.518673	−	0.854973i	$-0.326426\pi$
$607$	−10.1845	−	12.1374i	−0.413377	−	0.492644i	−0.932050	+	0.362329i	$0.881982\pi$
$608$	−0.712694	−	0.849356i	−0.0289036	−	0.0344459i
$609$	40.2576	+	7.09851i	1.63132	+	0.287646i
$610$		0			0
$611$	−9.83275	−	17.0308i	−0.397790	−	0.688993i
$612$	18.9422	−	10.9363i	0.765693	−	0.442073i
$613$	−18.0265	−	10.4076i	−0.728083	−	0.420359i	0.0896372	−	0.995974i	$-0.471429\pi$
$613$	−18.0265	−	10.4076i	−0.728083	−	0.420359i	−0.817721	+	0.575615i	$0.804763\pi$
$614$	−4.74035	+	26.8839i	−0.191305	+	1.08494i
$615$		0			0
$616$	99.1285	+	36.0798i	3.99400	+	1.45370i
$617$	−29.4752	+	5.19728i	−1.18663	+	0.209235i	−0.731911	−	0.681401i	$-0.761371\pi$
$617$	−29.4752	+	5.19728i	−1.18663	+	0.209235i	−0.454718	+	0.890635i	$0.650260\pi$
$618$	−76.8119	−	27.9572i	−3.08983	−	1.12460i
$619$	2.69775	+	2.26368i	0.108432	+	0.0909850i	0.695392	−	0.718631i	$-0.255231\pi$
$619$	2.69775	+	2.26368i	0.108432	+	0.0909850i	−0.586960	+	0.809616i	$0.699675\pi$
$620$		0			0
$621$	24.8944	+	29.6680i	0.998978	+	1.19054i
$622$		−	39.1165i		−	1.56843i
$623$	−13.1185	+	15.6340i	−0.525582	+	0.626364i
$624$	−47.8585	+	8.43874i	−1.91587	+	0.337820i
$625$		0			0
$626$	11.0175	+	4.01006i	0.440349	+	0.160274i
$627$	−1.17787	−	2.04013i	−0.0470397	−	0.0814751i
$628$	−86.9447	−	15.3307i	−3.46947	−	0.611761i
$629$	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	$0.957297\pi$
$632$	20.5446	+	56.4458i	0.817221	+	2.24529i
$633$	18.6540	−	6.78952i	0.741432	−	0.269859i
$634$	−15.0831	+	12.6562i	−0.599025	+	0.502642i
$635$		0			0
$636$	59.4586	−	70.8600i	2.35769	−	2.80978i
$637$	−3.45383	−	9.48932i	−0.136846	−	0.375981i
$638$	95.2289	−	54.9805i	3.77015	−	2.17670i
$639$	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	$-0.00295224\pi$
$642$	45.6277			1.80078
$643$	9.77411	−	26.8542i	0.385453	−	1.05902i	−0.583571	−	0.812062i	$-0.698345\pi$
$643$	9.77411	−	26.8542i	0.385453	−	1.05902i	0.969025	−	0.246963i	$-0.0794326\pi$
$644$	17.4953	+	99.2205i	0.689410	+	3.90984i
$645$		0			0
$646$	−0.773318	−	0.648891i	−0.0304258	−	0.0255303i
$647$			21.6928i			0.852833i	0.904527	+	0.426417i	$0.140224\pi$
$647$			21.6928i			0.852833i	−0.904527	+	0.426417i	$0.859776\pi$
$648$	−35.3241	−	42.0977i	−1.38766	−	1.65375i
$649$	26.7202			1.04886
$650$		0			0
$651$	16.8648	+	20.0987i	0.660985	+	0.787731i
$652$	−43.2626	+	7.62836i	−1.69429	+	0.298749i
$653$	10.5760	−	29.0574i	0.413872	−	1.13710i	−0.541243	−	0.840866i	$-0.682046\pi$
$653$	10.5760	−	29.0574i	0.413872	−	1.13710i	0.955115	−	0.296237i	$-0.0957317\pi$
$654$			0.648891i			0.0253737i
$655$		0			0
$656$	0.474308	−	0.821525i	0.0185186	−	0.0320752i
$657$	−0.437124	+	0.520945i	−0.0170538	+	0.0203240i
$658$	31.2629	−	18.0496i	1.21875	−	0.703648i
$659$	35.7581	−	13.0149i	1.39294	−	0.506987i	0.466862	−	0.884330i	$-0.345384\pi$
$659$	35.7581	−	13.0149i	1.39294	−	0.506987i	0.926074	+	0.377343i	$0.123162\pi$
$660$		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	$0.454163\pi$
$662$	12.3400	+	14.7062i	0.479607	+	0.571573i
$663$	−11.3695	+	4.13816i	−0.441554	+	0.160713i
$664$	−50.8205	+	18.4971i	−1.97222	+	0.717828i
$665$		0			0
$666$	−17.7754	−	6.46973i	−0.688784	−	0.250697i
$667$	49.7170	+	28.7041i	1.92505	+	1.11143i
$668$	−13.7394	−	2.42262i	−0.531591	−	0.0937339i
$669$	0.660855	−	0.381545i	0.0255501	−	0.0147514i
$670$		0			0
$671$	13.6155	+	77.2171i	0.525619	+	2.98093i
$672$	−4.23594	−	24.0232i	−0.163405	−	0.926716i
$673$	−19.8109	+	23.6097i	−0.763653	+	0.910087i	−0.998073	−	0.0620488i	$-0.980237\pi$
$673$	−19.8109	+	23.6097i	−0.763653	+	0.910087i	0.234420	+	0.972135i	$0.424681\pi$
$674$	−41.8931			−1.61366
$675$		0			0
$676$	21.4611			0.825427
$677$	−29.9708	+	35.7178i	−1.15187	+	1.37275i	−0.235766	+	0.971810i	$0.575760\pi$
$677$	−29.9708	+	35.7178i	−1.15187	+	1.37275i	−0.916105	+	0.400937i	$0.868685\pi$
$678$	29.1730	+	10.6181i	1.12038	+	0.407785i
$679$	−5.07192	−	28.7643i	−0.194642	−	1.10387i
$680$		0			0
$681$	7.96972	+	4.60132i	0.305400	+	0.176323i
$682$	69.5036	+	12.2554i	2.66143	+	0.469282i
$683$	−35.8923	−	20.7224i	−1.37338	−	0.792921i	−0.382027	−	0.924151i	$-0.624774\pi$
$683$	−35.8923	−	20.7224i	−1.37338	−	0.792921i	−0.991352	+	0.131231i	$0.958107\pi$
$684$	−1.59627	+	2.76481i	−0.0610348	+	0.105715i
$685$		0			0
$686$	−33.6168	+	12.2355i	−1.28350	+	0.467154i
$687$	0.0236781	−	0.134285i	0.000903377	−	0.00512330i
$688$	3.20459	+	3.81908i	0.122174	+	0.145601i
$689$	−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	$0.421107\pi$
$692$	75.4614	−	43.5676i	2.86861	−	1.65619i
$693$		−	51.8289i		−	1.96882i
$694$	−19.2258	+	33.3001i	−0.729802	+	1.26405i
$695$		0			0
$696$	−70.5464	−	40.7300i	−2.67406	−	1.54387i
$697$	0.0807773	−	0.221934i	0.00305966	−	0.00840634i
$698$	35.2182	−	6.20991i	1.33303	−	0.235049i
$699$	−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	$0.441546\pi$
$702$	27.8055	+	48.1605i	1.04945	+	1.81770i
$703$			0.600710i			0.0226562i
$704$	7.07532	+	5.93690i	0.266661	+	0.223755i
$705$		0			0
$706$	1.83140	+	10.3864i	0.0689258	+	0.390898i
$707$	2.44474	−	6.71688i	0.0919441	−	0.252614i
$708$	−18.1058	−	31.3601i	−0.680456	−	1.17858i
$709$	−4.07057	+	23.0854i	−0.152874	+	0.866989i	0.807830	+	0.589415i	$0.200642\pi$
$709$	−4.07057	+	23.0854i	−0.152874	+	0.866989i	−0.960704	+	0.277575i	$0.910469\pi$
$710$		0			0
$711$	22.6079	−	18.9703i	0.847862	−	0.711440i
$712$	35.2205	−	20.3346i	1.31994	−	0.762070i
$713$	12.6021	+	34.6241i	0.471954	+	1.29668i
$714$	−7.59627	−	20.8706i	−0.284283	−	0.781061i
$715$		0			0
$716$	−27.3764	+	22.9716i	−1.02311	+	0.858488i
$717$	−14.4158	−	12.0963i	−0.538367	−	0.451743i
$718$	−5.71021	−	15.6887i	−0.213103	−	0.585496i
$719$	−13.1133	−	22.7130i	−0.489045	−	0.847051i	0.510875	−	0.859655i	$-0.329321\pi$
$719$	−13.1133	−	22.7130i	−0.489045	−	0.847051i	−0.999921	+	0.0126038i	$0.995988\pi$
$720$		0			0
$721$	−28.5553	+	49.4592i	−1.06346	+	1.84196i
$722$	−47.2337	−	8.32857i	−1.75786	−	0.309957i
$723$	−46.3270			−1.72292
$724$	−36.9543	−	13.4503i	−1.37340	−	0.499875i
$725$		0			0
$726$	−58.6052	−	69.8430i	−2.17504	−	2.59212i
$727$	12.2559	−	14.6061i	0.454548	−	0.541709i	−0.489289	−	0.872122i	$-0.662744\pi$
$727$	12.2559	−	14.6061i	0.454548	−	0.541709i	0.943836	+	0.330413i	$0.107188\pi$
$728$			79.0815i			2.93096i
$729$	−13.5000	+	23.3827i	−0.500000	+	0.866025i
$730$		0			0
$731$	0.950837	+	0.797847i	0.0351680	+	0.0295094i
$732$	81.3998	−	68.3025i	3.00862	−	2.52453i
$733$	6.64268	−	1.17128i	0.245353	−	0.0432624i	−0.0496191	−	0.998768i	$-0.515801\pi$
$733$	6.64268	−	1.17128i	0.245353	−	0.0432624i	0.294972	+	0.955506i	$0.404690\pi$
$734$	30.1933	+	10.9895i	1.11446	+	0.405629i
$735$		0			0
$736$	5.94878	−	33.7372i	0.219275	−	1.24357i
$737$	−35.9841	−	20.7754i	−1.32549	−	0.765273i
$738$	−1.06904	−	0.188501i	−0.0393519	−	0.00693881i
$739$	−18.0069	−	31.1888i	−0.662393	−	1.14730i	−0.979985	−	0.199071i	$-0.936208\pi$
$739$	−18.0069	−	31.1888i	−0.662393	−	1.14730i	0.317592	−	0.948228i	$-0.397126\pi$
$740$		0			0
$741$	1.13516	−	1.35283i	0.0417012	−	0.0496976i
$742$	−60.3759	−	71.9532i	−2.21647	−	2.64148i
$743$	−23.0508	−	27.4709i	−0.845653	−	1.00781i	−0.999805	−	0.0197626i	$-0.993709\pi$
$743$	−23.0508	−	27.4709i	−0.845653	−	1.00781i	0.154152	−	0.988047i	$-0.450735\pi$
$744$	−17.8819	−	49.1301i	−0.655583	−	1.80120i
$745$		0			0
$746$	−9.66725	−	16.7442i	−0.353943	−	0.613048i
$747$	17.0797	+	20.3548i	0.624913	+	0.744743i
$748$	−35.5997	−	20.5535i	−1.30165	−	0.751510i
$749$	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	$0.271660\pi$
$752$	−30.4162	+	5.36319i	−1.10916	+	0.195575i
$753$	1.80256	+	10.2228i	0.0656888	+	0.372540i
$754$	63.1473	+	52.9869i	2.29969	+	1.92967i
$755$		0			0
$756$	−60.8289	+	35.1196i	−2.21233	+	1.27729i
$757$			24.2172i			0.880189i	0.897952	+	0.440094i	$0.145055\pi$
$757$			24.2172i			0.880189i	−0.897952	+	0.440094i	$0.854945\pi$
$758$	−44.0814	+	52.5342i	−1.60111	+	1.90813i
$759$	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	$0.309060\pi$
$762$	0.534876	−	0.926433i	0.0193765	−	0.0335611i
$763$	0.446476	+	0.0787257i	0.0161635	+	0.00285006i
$764$	−12.3118	+	21.3247i	−0.445425	+	0.771499i
$765$		0			0
$766$	13.0373	+	22.5813i	0.471057	+	0.815895i
$767$	6.85099	+	18.8229i	0.247375	+	0.679657i
$768$	9.17431	−	52.0301i	0.331049	−	1.87747i
$769$	−0.682733	+	0.572881i	−0.0246200	+	0.0206586i	−0.655015	−	0.755616i	$-0.727338\pi$
$769$	−0.682733	+	0.572881i	−0.0246200	+	0.0206586i	0.630395	+	0.776275i	$0.282893\pi$
$770$		0			0
$771$	10.7888	+	1.90236i	0.388549	+	0.0685117i
$772$	−38.2121	−	104.987i	−1.37528	−	3.77856i
$773$	26.6217	−	15.3701i	0.957516	−	0.552822i	0.0621086	−	0.998069i	$-0.480217\pi$
$773$	26.6217	−	15.3701i	0.957516	−	0.552822i	0.895408	+	0.445247i

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.u (of order \(18\), degree \(6\), not minimal)

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

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