LMFDB - Embedded newform 675.2.u.a.49.1

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			49.1
Root			$0.342020 - 0.939693i$ of defining polynomial
Character	$\chi$	$=$	675.49
Dual form			675.2.u.a.124.1

$q$-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 $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

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	−0.916797	−	0.399354i	$-0.869234\pi$
$2$	−1.62760	−	1.93969i	−1.15088	−	1.37157i	−0.234087	−	0.972216i	$-0.575210\pi$
$3$	−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	−0.711849	−	0.702333i	$-0.752142\pi$
$7$	−3.01763	+	0.532089i	−1.14056	+	0.201111i	−0.428707	+	0.903444i	$0.641031\pi$
$8$	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	−0.618545	−	0.785750i	$-0.712277\pi$
$11$	−5.29813	−	1.92836i	−1.59745	−	0.581423i	−0.978903	+	0.204326i	$0.934500\pi$
$12$	5.85327	−	4.91147i	1.68969	−	1.41782i
$13$	−2.71686	+	3.23783i	−0.753521	+	0.898011i	−0.997420	−	0.0717893i	$-0.977129\pi$
$13$	−2.71686	+	3.23783i	−0.753521	+	0.898011i	0.243899	+	0.969801i	$0.421574\pi$
$14$	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	0.316286	−	0.948664i	$-0.397564\pi$
$17$	−1.43128	−	0.826352i	−0.347137	−	0.200420i	−0.663424	+	0.748244i	$0.730897\pi$
$18$	4.88279	−	5.81908i	1.15088	−	1.37157i
$19$	0.120615	+	0.208911i	0.0276709	+	0.0479274i	0.879529	−	0.475845i	$-0.157858\pi$
$19$	0.120615	+	0.208911i	0.0276709	+	0.0479274i	−0.851858	+	0.523772i	$0.824524\pi$
$20$		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	0.874559	−	0.484920i	$-0.161151\pi$
$23$	7.34013	+	1.29426i	1.53052	+	0.269872i	0.655964	+	0.754792i	$0.272262\pi$
$24$	−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	0.0985378	−	0.995133i	$-0.468583\pi$
$29$	5.90033	−	4.95096i	1.09566	−	0.919371i	0.997126	+	0.0757623i	$0.0241390\pi$
$30$		0			0
$31$	0.858441	−	4.86846i	0.154181	−	0.874401i	−0.805351	−	0.592799i	$-0.798023\pi$
$31$	0.858441	−	4.86846i	0.154181	−	0.874401i	0.959531	−	0.281602i	$-0.0908659\pi$
$32$	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	0.312144	−	0.950035i	$-0.398953\pi$
$37$	−2.15658	−	1.24510i	−0.354539	−	0.204693i	−0.666683	+	0.745342i	$0.732286\pi$
$38$	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	0.634199	−	0.773170i	$-0.281330\pi$
$41$	−0.109470	−	0.0918566i	−0.0170964	−	0.0143456i	−0.651296	+	0.758824i	$0.725774\pi$
$42$	−2.33359	−	13.2344i	−0.360080	−	2.04212i
$43$	−0.256867	+	0.705737i	−0.0391719	+	0.107624i	−0.957737	−	0.287647i	$-0.907127\pi$
$43$	−0.256867	+	0.705737i	−0.0391719	+	0.107624i	0.918565	+	0.395271i	$0.129349\pi$
$44$	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	0.170833	−	0.985300i	$-0.445354\pi$
$47$	4.58202	−	0.807934i	0.668356	−	0.117849i	0.497523	+	0.867451i	$0.334243\pi$
$48$	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	$0.312488\pi$
$53$			12.1061i			1.66290i	−0.555602	+	0.831448i	$0.687512\pi$
$54$	−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	−0.615228	−	0.788349i	$-0.710936\pi$
$59$	−4.45336	+	1.62089i	−0.579779	+	0.211022i	0.0354493	+	0.999371i	$0.488714\pi$
$60$		0			0
$61$	2.41488	+	13.6955i	0.309193	+	1.75352i	0.603078	+	0.797682i	$0.293941\pi$
$61$	2.41488	+	13.6955i	0.309193	+	1.75352i	−0.293885	+	0.955841i	$0.594948\pi$
$62$	−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	−0.394671	−	0.918822i	$-0.629141\pi$
$67$	4.73708	−	5.64543i	0.578726	−	0.689699i	0.973397	+	0.229123i	$0.0735859\pi$
$68$	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	−0.683153	−	0.730276i	$-0.739392\pi$
$71$	2.45084	−	4.24497i	0.290861	−	0.503786i	0.974014	+	0.226490i	$0.0727250\pi$
$72$	11.7747	+	14.0326i	1.38766	+	1.65375i
$73$	−0.196312	+	0.113341i	−0.0229766	+	0.0132655i	−0.511444	−	0.859316i	$-0.670889\pi$
$73$	−0.196312	+	0.113341i	−0.0229766	+	0.0132655i	0.488468	+	0.872582i	$0.337556\pi$
$74$	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	−0.111456	−	0.993769i	$-0.535551\pi$
$79$	7.53596	−	6.32342i	0.847862	−	0.711440i	0.959318	+	0.282329i	$0.0911070\pi$
$80$		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	0.356994	−	0.934107i	$-0.383802\pi$
$83$	−5.69323	−	6.78493i	−0.624913	−	0.744743i	−0.981907	+	0.189364i	$0.939357\pi$
$84$	−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	0.986774	−	0.162102i	$-0.0518273\pi$
$89$	3.33022	+	5.76811i	0.353003	+	0.611419i	−0.633771	+	0.773521i	$0.718494\pi$
$90$		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	−0.656827	−	0.754041i	$-0.728102\pi$
$97$	3.26017	−	8.95723i	0.331020	−	0.909469i	0.987847	−	0.155428i	$-0.0496758\pi$
$98$	−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	0.957999	−	0.286770i	$-0.0925816\pi$
$101$	−0.405078	−	2.29731i	−0.0403067	−	0.228591i	−0.998306	+	0.0581793i	$0.981470\pi$
$102$	3.62414	−	6.27719i	0.358843	−	0.621534i
$103$	6.37462	+	17.5141i	0.628110	+	1.72572i	0.686205	+	0.727408i	$0.259275\pi$
$103$	6.37462	+	17.5141i	0.628110	+	1.72572i	−0.0580946	+	0.998311i	$0.518503\pi$
$104$	−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	$-0.832272\pi$
$107$		−	10.4037i		−	1.00577i	0.864354	−	0.502883i	$-0.167728\pi$
$108$	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	0.772199	−	0.635381i	$-0.219157\pi$
$113$	−2.42107	−	6.65183i	−0.227755	−	0.625751i	−0.999954	+	0.00962978i	$0.996935\pi$
$114$	−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	−0.490599	−	0.871386i	$-0.663222\pi$
$127$	0.211239	−	0.121959i	0.0187444	−	0.0108221i	0.509343	+	0.860564i	$0.329888\pi$
$128$	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	−0.835755	−	0.549102i	$-0.814970\pi$
$131$	1.57263	−	8.91885i	0.137402	−	0.779243i	0.973157	−	0.230142i	$-0.0739190\pi$
$132$	−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	0.990265	−	0.139194i	$-0.0444513\pi$
$137$	7.97357	+	9.50253i	0.681228	+	0.811856i	−0.309037	+	0.951050i	$0.600007\pi$
$138$	−5.67626	+	32.1917i	−0.483195	+	2.74034i
$139$	−3.21823	+	18.2515i	−0.272966	+	1.54807i	0.472382	+	0.881394i	$0.343394\pi$
$139$	−3.21823	+	18.2515i	−0.272966	+	1.54807i	−0.745348	+	0.666675i	$0.767717\pi$
$140$		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	0.780292	−	0.625415i	$-0.215070\pi$
$149$	3.66044	+	3.07148i	0.299875	+	0.251625i	−0.480417	+	0.877040i	$0.659515\pi$
$150$		0			0
$151$	5.25877	+	1.91404i	0.427953	+	0.155762i	0.547011	−	0.837125i	$-0.315765\pi$
$151$	5.25877	+	1.91404i	0.427953	+	0.155762i	−0.119059	+	0.992887i	$0.537988\pi$
$152$	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	0.838705	+	0.544586i	$0.183313\pi$
$157$	6.84478	+	18.8059i	0.546273	+	1.50087i	−0.292432	+	0.956286i	$0.594465\pi$
$158$	−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	$0.127521\pi$
$163$			9.95811i			0.779979i	−0.920819	+	0.389990i	$0.872479\pi$
$164$	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	0.974481	−	0.224468i	$-0.0720646\pi$
$167$	1.08164	+	2.97178i	0.0836998	+	0.229963i	−0.890782	+	0.454432i	$0.849842\pi$
$168$	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	−0.363826	−	0.931467i	$-0.618530\pi$
$173$	6.75557	−	18.5608i	0.513616	−	1.41115i	0.877442	−	0.479682i	$-0.159248\pi$
$174$	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	−0.976758	−	0.214347i	$-0.931238\pi$
$179$	−4.05051	+	7.01568i	−0.302749	+	0.524377i	0.674009	+	0.738724i	$0.264571\pi$
$180$		0			0
$181$	4.45723	+	7.72016i	0.331304	+	0.573835i	0.982768	−	0.184845i	$-0.0591782\pi$
$181$	4.45723	+	7.72016i	0.331304	+	0.573835i	−0.651464	+	0.758679i	$0.725845\pi$
$182$	−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	−0.784240	−	0.620458i	$-0.786947\pi$
$191$	−4.27584	+	3.58786i	−0.309389	+	0.259608i	0.474850	+	0.880067i	$0.342502\pi$
$192$	2.66625	−	0.970437i	0.192420	−	0.0700353i
$193$	24.9412	+	4.39780i	1.79531	+	0.316561i	0.969074	−	0.246770i	$-0.0793692\pi$
$193$	24.9412	+	4.39780i	1.79531	+	0.316561i	0.826232	+	0.563331i	$0.190480\pi$
$194$	−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	−0.642996	−	0.765869i	$-0.722309\pi$
$197$	−4.22800	+	2.44104i	−0.301233	+	0.173917i	0.341764	+	0.939786i	$0.388976\pi$
$198$	−37.0909	+	21.4145i	−2.63594	+	1.52186i
$199$	8.68092	−	15.0358i	0.615374	−	1.06586i	−0.374944	−	0.927047i	$-0.622338\pi$
$199$	8.68092	−	15.0358i	0.615374	−	1.06586i	0.990319	−	0.138812i	$-0.0443284\pi$
$200$		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	−0.684996	−	0.728547i	$-0.740196\pi$
$211$	−10.7699	+	3.91993i	−0.741432	+	0.269859i	−0.0564359	+	0.998406i	$0.517974\pi$
$212$	−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	−0.188157	−	0.982139i	$-0.560251\pi$
$223$	−0.433877	+	0.0765042i	−0.0290545	+	0.00512310i	0.159102	+	0.987262i	$0.449140\pi$
$224$	−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	−0.985276	−	0.170972i	$-0.945309\pi$
$227$	−1.81720	+	4.99273i	−0.120612	+	0.331379i	0.864664	+	0.502351i	$0.167531\pi$
$228$	1.73205	+	0.630415i	0.114708	+	0.0417502i
$229$	−0.0603074	−	0.0506039i	−0.00398522	−	0.00334400i	0.640793	−	0.767714i	$-0.278606\pi$
$229$	−0.0603074	−	0.0506039i	−0.00398522	−	0.00334400i	−0.644778	+	0.764370i	$0.723050\pi$
$230$		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	0.510590	−	0.859824i	$-0.329427\pi$
$233$	0.324446	+	0.187319i	0.0212551	+	0.0122717i	−0.489335	+	0.872096i	$0.662760\pi$
$234$	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	−0.860985	−	0.508630i	$-0.830152\pi$
$239$	1.88666	−	10.6998i	0.122038	−	0.692111i	0.983023	−	0.183481i	$-0.0587367\pi$
$240$		0			0
$241$	20.4893	−	17.1926i	1.31983	−	1.10747i	0.333493	−	0.942753i	$-0.391773\pi$
$241$	20.4893	−	17.1926i	1.31983	−	1.10747i	0.986341	−	0.164719i	$-0.0526717\pi$
$242$		−	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	0.944965	−	0.327172i	$-0.106096\pi$
$251$	2.99660	+	5.19026i	0.189143	+	0.327606i	−0.755821	+	0.654778i	$0.772762\pi$
$252$	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	−0.877795	−	0.479037i	$-0.840986\pi$
$257$	−4.06564	+	4.84524i	−0.253607	+	0.302238i	0.624187	+	0.781275i	$0.285430\pi$
$258$	−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	−0.159423	−	0.987210i	$-0.550963\pi$
$263$	0.460802	−	0.0812519i	0.0284143	−	0.00501021i	0.187837	+	0.982200i	$0.439852\pi$
$264$	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	−0.171829	−	0.985127i	$-0.554968\pi$
$277$	0.0605553	−	0.0106775i	0.00363841	−	0.000641550i	0.175467	+	0.984485i	$0.443856\pi$
$278$	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	0.505969	−	0.862552i	$-0.331135\pi$
$281$	5.68479	+	2.06910i	0.339126	+	0.123432i	−0.166843	+	0.985984i	$0.553357\pi$
$282$	3.54336	+	20.0954i	0.211004	+	1.19666i
$283$	−5.37051	+	6.40033i	−0.319244	+	0.380460i	−0.901671	−	0.432423i	$-0.857659\pi$
$283$	−5.37051	+	6.40033i	−0.319244	+	0.380460i	0.582427	+	0.812883i	$0.302103\pi$
$284$	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	−0.182960	−	0.983120i	$-0.558568\pi$
$293$	−11.8303	−	2.08600i	−0.691133	−	0.121865i	−0.508173	+	0.861255i	$0.669679\pi$
$294$	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	0.742185	−	0.670195i	$-0.233789\pi$
$307$	9.33667	+	5.39053i	0.532872	+	0.307654i	−0.209313	+	0.977849i	$0.567123\pi$
$308$	−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	0.242326	−	0.970195i	$-0.422090\pi$
$311$	−11.8341	−	9.92998i	−0.671050	−	0.563078i	−0.913376	+	0.407117i	$0.866534\pi$
$312$	34.2433	−	28.7335i	1.93865	−	1.62672i
$313$	−1.58370	+	4.35117i	−0.0895157	+	0.245942i	−0.976370	−	0.216108i	$-0.930664\pi$
$313$	−1.58370	+	4.35117i	−0.0895157	+	0.245942i	0.886854	+	0.462050i	$0.152886\pi$
$314$	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	0.0455972	−	0.998960i	$-0.485481\pi$
$317$	7.65787	−	1.35029i	0.430109	−	0.0758398i	0.384512	+	0.923120i	$0.374370\pi$
$318$	−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	0.999375	+	0.0353621i	$0.0112585\pi$
$331$	1.31655	+	7.46654i	0.0723642	+	0.410398i	−0.927010	+	0.375036i	$0.877630\pi$
$332$	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	−0.394198	−	0.919025i	$-0.628978\pi$
$337$	10.6348	−	12.6741i	0.579317	−	0.690403i	0.973515	+	0.228622i	$0.0734221\pi$
$338$	−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	0.559982	−	0.828505i	$-0.310808\pi$
$347$	14.9550	+	2.63697i	0.802828	+	0.141560i	0.242846	+	0.970065i	$0.421919\pi$
$348$	10.2197	−	57.9586i	0.547832	−	3.10691i
$349$	−10.8191	+	9.07828i	−0.579132	+	0.485949i	−0.884662	−	0.466233i	$-0.845611\pi$
$349$	−10.8191	+	9.07828i	−0.579132	+	0.485949i	0.305530	+	0.952182i	$0.401166\pi$
$350$		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	0.832574	−	0.553914i	$-0.186866\pi$
$353$	2.67733	+	3.19072i	0.142500	+	0.169825i	−0.690074	+	0.723739i	$0.742422\pi$
$354$	−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	0.765816	−	0.643060i	$-0.222335\pi$
$359$	−3.29679	−	5.71021i	−0.173998	−	0.301373i	−0.939814	+	0.341686i	$0.889002\pi$
$360$		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	−0.999934	−	0.0114966i	$-0.996340\pi$
$367$	−4.34008	+	11.9243i	−0.226550	+	0.622442i	0.773384	+	0.633938i	$0.218563\pi$
$368$	−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	0.853537	−	0.521032i	$-0.174453\pi$
$373$	−2.61159	−	7.17530i	−0.135223	−	0.371523i	−0.988760	+	0.149509i	$0.952231\pi$
$374$	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	0.996571	−	0.0827443i	$-0.0263685\pi$
$383$	3.52201	+	9.67664i	0.179966	+	0.494453i	−0.816605	+	0.577198i	$0.804146\pi$
$384$	−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	0.438937	−	0.898518i	$-0.355355\pi$
$389$	3.89780	+	1.41868i	0.197626	+	0.0719302i	−0.241311	+	0.970448i	$0.577577\pi$
$390$		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	0.0644021	−	0.997924i	$-0.479486\pi$
$397$	19.1444	−	11.0530i	0.960831	−	0.554736i	0.896429	+	0.443188i	$0.146153\pi$
$398$	−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	0.820115	+	0.572199i	$0.193910\pi$
$401$	−2.92855	+	16.6086i	−0.146245	+	0.829395i	−0.966359	+	0.257196i	$0.917201\pi$
$402$	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	−0.339514	−	0.940601i	$-0.610263\pi$
$409$	6.09199	−	34.5494i	0.301229	−	1.70836i	0.640743	−	0.767755i	$-0.278626\pi$
$410$		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	0.275275	−	0.961366i	$-0.411231\pi$
$419$	−12.7665	−	10.7124i	−0.623685	−	0.523334i	−0.898959	+	0.438032i	$0.855676\pi$
$420$		0			0
$421$	25.7841	+	9.38463i	1.25664	+	0.457379i	0.882639	−	0.470051i	$-0.155764\pi$
$421$	25.7841	+	9.38463i	1.25664	+	0.457379i	0.373998	+	0.927429i	$0.377987\pi$
$422$	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	$0.189995\pi$
$433$			23.3919i			1.12414i	−0.827089	+	0.562071i	$0.810005\pi$
$434$	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	0.876306	+	0.481754i	$0.160000\pi$
$439$	4.55959	+	25.8587i	0.217617	+	1.23417i	−0.658689	+	0.752415i	$0.728889\pi$
$440$		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	−0.359396	−	0.933185i	$-0.617017\pi$
$443$	10.8554	−	29.8251i	0.515757	−	1.41703i	0.875153	−	0.483846i	$-0.160761\pi$
$444$	−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	−0.997370	−	0.0724765i	$-0.976910\pi$
$449$	−9.23695	+	15.9989i	−0.435919	+	0.755033i	0.561452	+	0.827510i	$0.310243\pi$
$450$		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	0.581042	−	0.813874i	$-0.302645\pi$
$457$	−6.86998	−	8.18732i	−0.321364	−	0.382987i	−0.902406	+	0.430887i	$0.858201\pi$
$458$			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	0.000959987	−	1.00000i	$-0.499694\pi$
$461$	21.1689	−	17.7628i	0.985934	−	0.827297i	0.984974	+	0.172703i	$0.0552500\pi$
$462$	−13.1571	+	74.6177i	−0.612125	+	3.47153i
$463$	−4.54077	−	0.800660i	−0.211027	−	0.0372098i	0.0671350	−	0.997744i	$-0.478614\pi$
$463$	−4.54077	−	0.800660i	−0.211027	−	0.0372098i	−0.278162	+	0.960534i	$0.589725\pi$
$464$	−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	−0.0541859	−	0.998531i	$-0.517256\pi$
$467$	16.9310	−	9.77513i	0.783474	−	0.452339i	0.837660	+	0.546192i	$0.183923\pi$
$468$	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	0.993353	−	0.115106i	$-0.0367209\pi$
$479$	0.449493	+	2.54920i	0.0205379	+	0.116476i	−0.972815	+	0.231582i	$0.925610\pi$
$480$		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	$-0.624801\pi$
$487$		−	40.7870i		−	1.84824i	0.382105	−	0.924119i	$-0.375199\pi$
$488$	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	−0.997278	−	0.0737387i	$-0.976507\pi$
$491$	−37.9761	+	13.8222i	−1.71384	+	0.623786i	−0.716561	+	0.697525i	$0.754285\pi$
$492$	−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	0.842256	−	0.539077i	$-0.181227\pi$
$499$	10.2226	+	8.57775i	0.457625	+	0.383993i	−0.384631	+	0.923070i	$0.625671\pi$
$500$		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	0.109082	−	0.994033i	$-0.465209\pi$
$503$	−15.6373	−	9.02822i	−0.697234	−	0.402548i	−0.806316	+	0.591484i	$0.798542\pi$
$504$	−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	0.739535	+	0.673118i	$0.235045\pi$
$509$	−4.18779	+	23.7501i	−0.185620	+	1.05271i	−0.925156	+	0.379588i	$0.876066\pi$
$510$		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	0.820259	+	0.571993i	$0.193829\pi$
$521$	20.6682	+	35.7983i	0.905490	+	1.56835i	0.0852310	+	0.996361i	$0.472837\pi$
$522$		−	58.5090i		−	2.56087i
$523$	−5.66955	−	3.27332i	−0.247912	−	0.143132i	0.370896	−	0.928675i	$-0.379051\pi$
$523$	−5.66955	−	3.27332i	−0.247912	−	0.143132i	−0.618808	+	0.785542i	$0.712384\pi$
$524$	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	−0.911975	−	0.410245i	$-0.865443\pi$
$547$	−38.0907	+	6.71641i	−1.62864	+	0.287173i	−0.716664	+	0.697418i	$0.754332\pi$
$548$	−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	0.201639	−	0.979460i	$-0.435373\pi$
$557$	−12.8808	−	7.43676i	−0.545779	−	0.315105i	−0.747418	+	0.664354i	$0.768707\pi$
$558$	−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	−0.471294	−	0.881976i	$-0.656213\pi$
$563$	−28.8485	−	5.08677i	−1.21582	−	0.214382i	−0.744525	+	0.667594i	$0.767324\pi$
$564$	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	0.0333769	−	0.999443i	$-0.489374\pi$
$569$	24.4127	−	20.4847i	1.02343	−	0.858761i	0.990055	+	0.140682i	$0.0449294\pi$
$570$		0			0
$571$	−2.78817	+	15.8125i	−0.116681	+	0.661733i	0.869223	+	0.494421i	$0.164620\pi$
$571$	−2.78817	+	15.8125i	−0.116681	+	0.661733i	−0.985904	+	0.167312i	$0.946491\pi$
$572$	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	0.540337	−	0.841449i	$-0.318297\pi$
$577$	1.96464	+	1.13429i	0.0817890	+	0.0472209i	−0.458548	+	0.888670i	$0.651630\pi$
$578$	−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	0.551064	−	0.834463i	$-0.314222\pi$
$587$	32.8120	−	5.78564i	1.35430	−	0.238799i	0.803234	+	0.595664i	$0.203111\pi$
$588$	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	$0.169904\pi$
$593$			24.7793i			1.01756i	−0.860895	+	0.508782i	$0.830096\pi$
$594$	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	0.520688	−	0.853747i	$-0.325676\pi$
$599$	35.9368	−	13.0799i	1.46834	−	0.534431i	0.947648	+	0.319316i	$0.103453\pi$
$600$		0			0
$601$	7.80747	+	44.2783i	0.318473	+	1.80615i	0.552048	+	0.833812i	$0.313847\pi$
$601$	7.80747	+	44.2783i	0.318473	+	1.80615i	−0.233575	+	0.972339i	$0.575042\pi$
$602$	−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	−0.932050	−	0.362329i	$-0.881982\pi$
$607$	−10.1845	+	12.1374i	−0.413377	+	0.492644i	0.518673	+	0.854973i	$0.326426\pi$
$608$	−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	−0.817721	−	0.575615i	$-0.804763\pi$
$613$	−18.0265	+	10.4076i	−0.728083	+	0.420359i	0.0896372	+	0.995974i	$0.471429\pi$
$614$	−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	−0.454718	−	0.890635i	$-0.650260\pi$
$617$	−29.4752	−	5.19728i	−1.18663	−	0.209235i	−0.731911	+	0.681401i	$0.761371\pi$
$618$	−76.8119	+	27.9572i	−3.08983	+	1.12460i
$619$	2.69775	−	2.26368i	0.108432	−	0.0909850i	−0.586960	−	0.809616i	$-0.699675\pi$
$619$	2.69775	−	2.26368i	0.108432	−	0.0909850i	0.695392	+	0.718631i	$0.255231\pi$
$620$		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	−0.991015	−	0.133753i	$-0.957297\pi$
$631$	−9.53730	+	16.5191i	−0.379674	+	0.657615i	0.611341	+	0.791368i	$0.290631\pi$
$632$	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	0.999957	+	0.00927459i	$0.00295224\pi$
$641$	1.60711	+	9.11435i	0.0634769	+	0.359995i	−0.936480	+	0.350721i	$0.885937\pi$
$642$	45.6277			1.80078
$643$	9.77411	+	26.8542i	0.385453	+	1.05902i	0.969025	+	0.246963i	$0.0794326\pi$
$643$	9.77411	+	26.8542i	0.385453	+	1.05902i	−0.583571	+	0.812062i	$0.698345\pi$
$644$	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	$-0.859776\pi$
$647$		−	21.6928i		−	0.852833i	0.904527	−	0.426417i	$-0.140224\pi$
$648$	−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	0.955115	+	0.296237i	$0.0957317\pi$
$653$	10.5760	+	29.0574i	0.413872	+	1.13710i	−0.541243	+	0.840866i	$0.682046\pi$
$654$		−	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	0.926074	−	0.377343i	$-0.123162\pi$
$659$	35.7581	+	13.0149i	1.39294	+	0.506987i	0.466862	+	0.884330i	$0.345384\pi$
$660$		0			0
$661$	−20.7271	−	17.3921i	−0.806193	−	0.676476i	0.143503	−	0.989650i	$-0.454163\pi$
$661$	−20.7271	−	17.3921i	−0.806193	−	0.676476i	−0.949696	+	0.313174i	$0.898608\pi$
$662$	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	0.234420	−	0.972135i	$-0.424681\pi$
$673$	−19.8109	−	23.6097i	−0.763653	−	0.910087i	−0.998073	+	0.0620488i	$0.980237\pi$
$674$	−41.8931			−1.61366
$675$		0			0
$676$	21.4611			0.825427
$677$	−29.9708	−	35.7178i	−1.15187	−	1.37275i	−0.916105	−	0.400937i	$-0.868685\pi$
$677$	−29.9708	−	35.7178i	−1.15187	−	1.37275i	−0.235766	−	0.971810i	$-0.575760\pi$
$678$	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	−0.991352	−	0.131231i	$-0.958107\pi$
$683$	−35.8923	+	20.7224i	−1.37338	+	0.792921i	−0.382027	+	0.924151i	$0.624774\pi$
$684$	−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	0.245320	−	0.969442i	$-0.421107\pi$
$691$	−4.99185	−	1.81688i	−0.189899	−	0.0691175i	−0.435219	+	0.900325i	$0.643329\pi$
$692$	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	−0.960704	−	0.277575i	$-0.910469\pi$
$709$	−4.07057	−	23.0854i	−0.152874	−	0.866989i	0.807830	−	0.589415i	$-0.200642\pi$
$710$		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	−0.999921	−	0.0126038i	$-0.995988\pi$
$719$	−13.1133	+	22.7130i	−0.489045	+	0.847051i	0.510875	+	0.859655i	$0.329321\pi$
$720$		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	0.943836	−	0.330413i	$-0.107188\pi$
$727$	12.2559	+	14.6061i	0.454548	+	0.541709i	−0.489289	+	0.872122i	$0.662744\pi$
$728$		−	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	0.294972	−	0.955506i	$-0.404690\pi$
$733$	6.64268	+	1.17128i	0.245353	+	0.0432624i	−0.0496191	+	0.998768i	$0.515801\pi$
$734$	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	0.317592	+	0.948228i	$0.397126\pi$
$739$	−18.0069	+	31.1888i	−0.662393	+	1.14730i	−0.979985	+	0.199071i	$0.936208\pi$
$740$		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	0.154152	+	0.988047i	$0.450735\pi$
$743$	−23.0508	+	27.4709i	−0.845653	+	1.00781i	−0.999805	+	0.0197626i	$0.993709\pi$
$744$	−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	0.657392	−	0.753549i	$-0.271660\pi$
$751$	45.0899	−	16.4114i	1.64535	−	0.598860i	0.987963	+	0.154689i	$0.0494376\pi$
$752$	−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	$-0.854945\pi$
$757$		−	24.2172i		−	0.880189i	0.897952	−	0.440094i	$-0.145055\pi$
$758$	−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	0.564523	−	0.825417i	$-0.309060\pi$
$761$	42.1391	−	15.3374i	1.52754	−	0.555979i	0.963018	+	0.269438i	$0.0868379\pi$
$762$	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	0.630395	−	0.776275i	$-0.282893\pi$
$769$	−0.682733	−	0.572881i	−0.0246200	−	0.0206586i	−0.655015	+	0.755616i	$0.727338\pi$
$770$		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	0.895408	−	0.445247i	$-0.146884\pi$
$773$	26.6217	+	15.3701i	0.957516	+	0.552822i	0.0621086	+	0.998069i	$0.480217\pi$

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

Introduction

L-functions

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