LMFDB - Embedded newform 975.2.o.c.476.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(476,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("975.476");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.o (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			476.1
Root			$-1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	975.476
Dual form			975.2.o.c.551.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 1.22474i) q^{2} +(1.22474 + 1.22474i) q^{3} -1.00000i q^{4} -3.00000 q^{6} +(0.224745 - 0.224745i) q^{7} +(-1.22474 - 1.22474i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.22474 + 1.22474i) q^{2} +(1.22474 + 1.22474i) q^{3} -1.00000i q^{4} -3.00000 q^{6} +(0.224745 - 0.224745i) q^{7} +(-1.22474 - 1.22474i) q^{8} +3.00000i q^{9} +(4.22474 + 4.22474i) q^{11} +(1.22474 - 1.22474i) q^{12} +(3.00000 - 2.00000i) q^{13} +0.550510i q^{14} +5.00000 q^{16} -3.00000 q^{17} +(-3.67423 - 3.67423i) q^{18} +(4.44949 + 4.44949i) q^{19} +0.550510 q^{21} -10.3485 q^{22} +6.00000 q^{23} -3.00000i q^{24} +(-1.22474 + 6.12372i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(-0.224745 - 0.224745i) q^{28} -1.89898i q^{29} +(-5.12372 - 5.12372i) q^{31} +(-3.67423 + 3.67423i) q^{32} +10.3485i q^{33} +(3.67423 - 3.67423i) q^{34} +3.00000 q^{36} +(-4.44949 + 4.44949i) q^{37} -10.8990 q^{38} +(6.12372 + 1.22474i) q^{39} +(-5.44949 + 5.44949i) q^{41} +(-0.674235 + 0.674235i) q^{42} -1.10102i q^{43} +(4.22474 - 4.22474i) q^{44} +(-7.34847 + 7.34847i) q^{46} +(-1.77526 - 1.77526i) q^{47} +(6.12372 + 6.12372i) q^{48} +6.89898i q^{49} +(-3.67423 - 3.67423i) q^{51} +(-2.00000 - 3.00000i) q^{52} -1.89898i q^{53} -9.00000i q^{54} -0.550510 q^{56} +10.8990i q^{57} +(2.32577 + 2.32577i) q^{58} +(-6.67423 - 6.67423i) q^{59} +12.7980 q^{61} +12.5505 q^{62} +(0.674235 + 0.674235i) q^{63} +1.00000i q^{64} +(-12.6742 - 12.6742i) q^{66} +(-4.67423 - 4.67423i) q^{67} +3.00000i q^{68} +(7.34847 + 7.34847i) q^{69} +(6.00000 - 6.00000i) q^{71} +(3.67423 - 3.67423i) q^{72} +(-6.44949 + 6.44949i) q^{73} -10.8990i q^{74} +(4.44949 - 4.44949i) q^{76} +1.89898 q^{77} +(-9.00000 + 6.00000i) q^{78} +3.55051 q^{79} -9.00000 q^{81} -13.3485i q^{82} +(-1.77526 + 1.77526i) q^{83} -0.550510i q^{84} +(1.34847 + 1.34847i) q^{86} +(2.32577 - 2.32577i) q^{87} -10.3485i q^{88} +(-0.550510 - 0.550510i) q^{89} +(0.224745 - 1.12372i) q^{91} -6.00000i q^{92} -12.5505i q^{93} +4.34847 q^{94} -9.00000 q^{96} +(6.44949 + 6.44949i) q^{97} +(-8.44949 - 8.44949i) q^{98} +(-12.6742 + 12.6742i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 12 q^{6} - 4 q^{7}+O(q^{10}) $ 4 * q - 12 * q^6 - 4 * q^7	$ 4 q - 12 q^{6} - 4 q^{7} + 12 q^{11} + 12 q^{13} + 20 q^{16} - 12 q^{17} + 8 q^{19} + 12 q^{21} - 12 q^{22} + 24 q^{23} + 4 q^{28} + 4 q^{31} + 12 q^{36} - 8 q^{37} - 24 q^{38} - 12 q^{41} + 12 q^{42} + 12 q^{44} - 12 q^{47} - 8 q^{52} - 12 q^{56} + 24 q^{58} - 12 q^{59} + 12 q^{61} + 60 q^{62} - 12 q^{63} - 36 q^{66} - 4 q^{67} + 24 q^{71} - 16 q^{73} + 8 q^{76} - 12 q^{77} - 36 q^{78} + 24 q^{79} - 36 q^{81} - 12 q^{83} - 24 q^{86} + 24 q^{87} - 12 q^{89} - 4 q^{91} - 12 q^{94} - 36 q^{96} + 16 q^{97} - 24 q^{98} - 36 q^{99}+O(q^{100}) $ 4 * q - 12 * q^6 - 4 * q^7 + 12 * q^11 + 12 * q^13 + 20 * q^16 - 12 * q^17 + 8 * q^19 + 12 * q^21 - 12 * q^22 + 24 * q^23 + 4 * q^28 + 4 * q^31 + 12 * q^36 - 8 * q^37 - 24 * q^38 - 12 * q^41 + 12 * q^42 + 12 * q^44 - 12 * q^47 - 8 * q^52 - 12 * q^56 + 24 * q^58 - 12 * q^59 + 12 * q^61 + 60 * q^62 - 12 * q^63 - 36 * q^66 - 4 * q^67 + 24 * q^71 - 16 * q^73 + 8 * q^76 - 12 * q^77 - 36 * q^78 + 24 * q^79 - 36 * q^81 - 12 * q^83 - 24 * q^86 + 24 * q^87 - 12 * q^89 - 4 * q^91 - 12 * q^94 - 36 * q^96 + 16 * q^97 - 24 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−1.22474	+	1.22474i	−0.866025	+	0.866025i	−0.992030	−	0.126004i	$-0.959785\pi$
$2$	−1.22474	+	1.22474i	−0.866025	+	0.866025i	0.126004	+	0.992030i	$0.459785\pi$
$3$	1.22474	+	1.22474i	0.707107	+	0.707107i
$3$	1.22474	+	1.22474i	0.707107	+	0.707107i
$4$		−	1.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	−3.00000			−1.22474
$7$	0.224745	−	0.224745i	0.0849456	−	0.0849456i	−0.663357	−	0.748303i	$-0.730869\pi$
$7$	0.224745	−	0.224745i	0.0849456	−	0.0849456i	0.748303	+	0.663357i	$0.230869\pi$
$8$	−1.22474	−	1.22474i	−0.433013	−	0.433013i
$9$			3.00000i			1.00000i
$10$		0			0
$11$	4.22474	+	4.22474i	1.27381	+	1.27381i	0.944074	+	0.329735i	$0.106959\pi$
$11$	4.22474	+	4.22474i	1.27381	+	1.27381i	0.329735	+	0.944074i	$0.393041\pi$
$12$	1.22474	−	1.22474i	0.353553	−	0.353553i
$13$	3.00000	−	2.00000i	0.832050	−	0.554700i
$13$	3.00000	−	2.00000i	0.832050	−	0.554700i
$14$			0.550510i			0.147130i
$15$		0			0
$16$	5.00000			1.25000
$17$	−3.00000			−0.727607			−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000			−0.727607			−0.363803	+	0.931476i	$0.618522\pi$
$18$	−3.67423	−	3.67423i	−0.866025	−	0.866025i
$19$	4.44949	+	4.44949i	1.02078	+	1.02078i	0.999779	+	0.0210036i	$0.00668613\pi$
$19$	4.44949	+	4.44949i	1.02078	+	1.02078i	0.0210036	+	0.999779i	$0.493314\pi$
$20$		0			0
$21$	0.550510			0.120131
$22$	−10.3485			−2.20630
$23$	6.00000			1.25109			0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000			1.25109			0.625543	+	0.780189i	$0.284877\pi$
$24$		−	3.00000i		−	0.612372i
$25$		0			0
$26$	−1.22474	+	6.12372i	−0.240192	+	1.20096i
$27$	−3.67423	+	3.67423i	−0.707107	+	0.707107i
$28$	−0.224745	−	0.224745i	−0.0424728	−	0.0424728i
$29$		−	1.89898i		−	0.352632i	−0.984334	−	0.176316i	$-0.943582\pi$
$29$		−	1.89898i		−	0.352632i	0.984334	−	0.176316i	$-0.0564180\pi$
$30$		0			0
$31$	−5.12372	−	5.12372i	−0.920248	−	0.920248i	0.0767986	−	0.997047i	$-0.475530\pi$
$31$	−5.12372	−	5.12372i	−0.920248	−	0.920248i	−0.997047	+	0.0767986i	$0.975530\pi$
$32$	−3.67423	+	3.67423i	−0.649519	+	0.649519i
$33$			10.3485i			1.80144i
$34$	3.67423	−	3.67423i	0.630126	−	0.630126i
$35$		0			0
$36$	3.00000			0.500000
$37$	−4.44949	+	4.44949i	−0.731492	+	0.731492i	−0.970915	−	0.239424i	$-0.923042\pi$
$37$	−4.44949	+	4.44949i	−0.731492	+	0.731492i	0.239424	+	0.970915i	$0.423042\pi$
$38$	−10.8990			−1.76805
$39$	6.12372	+	1.22474i	0.980581	+	0.196116i
$40$		0			0
$41$	−5.44949	+	5.44949i	−0.851067	+	0.851067i	−0.990265	−	0.139197i	$-0.955548\pi$
$41$	−5.44949	+	5.44949i	−0.851067	+	0.851067i	0.139197	+	0.990265i	$0.455548\pi$
$42$	−0.674235	+	0.674235i	−0.104037	+	0.104037i
$43$		−	1.10102i		−	0.167904i	−0.996470	−	0.0839520i	$-0.973246\pi$
$43$		−	1.10102i		−	0.167904i	0.996470	−	0.0839520i	$-0.0267543\pi$
$44$	4.22474	−	4.22474i	0.636904	−	0.636904i
$45$		0			0
$46$	−7.34847	+	7.34847i	−1.08347	+	1.08347i
$47$	−1.77526	−	1.77526i	−0.258948	−	0.258948i	0.565678	−	0.824626i	$-0.308614\pi$
$47$	−1.77526	−	1.77526i	−0.258948	−	0.258948i	−0.824626	+	0.565678i	$0.808614\pi$
$48$	6.12372	+	6.12372i	0.883883	+	0.883883i
$49$			6.89898i			0.985568i
$50$		0			0
$51$	−3.67423	−	3.67423i	−0.514496	−	0.514496i
$52$	−2.00000	−	3.00000i	−0.277350	−	0.416025i
$53$		−	1.89898i		−	0.260845i	−0.991459	−	0.130422i	$-0.958367\pi$
$53$		−	1.89898i		−	0.260845i	0.991459	−	0.130422i	$-0.0416334\pi$
$54$		−	9.00000i		−	1.22474i
$55$		0			0
$56$	−0.550510			−0.0735650
$57$			10.8990i			1.44361i
$58$	2.32577	+	2.32577i	0.305388	+	0.305388i
$59$	−6.67423	−	6.67423i	−0.868911	−	0.868911i	0.123441	−	0.992352i	$-0.460607\pi$
$59$	−6.67423	−	6.67423i	−0.868911	−	0.868911i	−0.992352	+	0.123441i	$0.960607\pi$
$60$		0			0
$61$	12.7980			1.63861			0.819305	−	0.573357i	$-0.194359\pi$
$61$	12.7980			1.63861			0.819305	+	0.573357i	$0.194359\pi$
$62$	12.5505			1.59392
$63$	0.674235	+	0.674235i	0.0849456	+	0.0849456i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−12.6742	−	12.6742i	−1.56009	−	1.56009i
$67$	−4.67423	−	4.67423i	−0.571049	−	0.571049i	0.361373	−	0.932421i	$-0.382308\pi$
$67$	−4.67423	−	4.67423i	−0.571049	−	0.571049i	−0.932421	+	0.361373i	$0.882308\pi$
$68$			3.00000i			0.363803i
$69$	7.34847	+	7.34847i	0.884652	+	0.884652i
$70$		0			0
$71$	6.00000	−	6.00000i	0.712069	−	0.712069i	−0.254899	−	0.966968i	$-0.582042\pi$
$71$	6.00000	−	6.00000i	0.712069	−	0.712069i	0.966968	+	0.254899i	$0.0820421\pi$
$72$	3.67423	−	3.67423i	0.433013	−	0.433013i
$73$	−6.44949	+	6.44949i	−0.754856	+	0.754856i	−0.975381	−	0.220526i	$-0.929223\pi$
$73$	−6.44949	+	6.44949i	−0.754856	+	0.754856i	0.220526	+	0.975381i	$0.429223\pi$
$74$		−	10.8990i		−	1.26698i
$75$		0			0
$76$	4.44949	−	4.44949i	0.510391	−	0.510391i
$77$	1.89898			0.216409
$78$	−9.00000	+	6.00000i	−1.01905	+	0.679366i
$79$	3.55051			0.399464			0.199732	−	0.979851i	$-0.435993\pi$
$79$	3.55051			0.399464			0.199732	+	0.979851i	$0.435993\pi$
$80$		0			0
$81$	−9.00000			−1.00000
$82$		−	13.3485i		−	1.47409i
$83$	−1.77526	+	1.77526i	−0.194860	+	0.194860i	−0.797792	−	0.602933i	$-0.793999\pi$
$83$	−1.77526	+	1.77526i	−0.194860	+	0.194860i	0.602933	+	0.797792i	$0.293999\pi$
$84$		−	0.550510i		−	0.0600656i
$85$		0			0
$86$	1.34847	+	1.34847i	0.145409	+	0.145409i
$87$	2.32577	−	2.32577i	0.249348	−	0.249348i
$88$		−	10.3485i		−	1.10315i
$89$	−0.550510	−	0.550510i	−0.0583540	−	0.0583540i	0.677328	−	0.735682i	$-0.263138\pi$
$89$	−0.550510	−	0.550510i	−0.0583540	−	0.0583540i	−0.735682	+	0.677328i	$0.763138\pi$
$90$		0			0
$91$	0.224745	−	1.12372i	0.0235597	−	0.117798i
$92$		−	6.00000i		−	0.625543i
$93$		−	12.5505i		−	1.30143i
$94$	4.34847			0.448510
$95$		0			0
$96$	−9.00000			−0.918559
$97$	6.44949	+	6.44949i	0.654846	+	0.654846i	0.954156	−	0.299310i	$-0.0967563\pi$
$97$	6.44949	+	6.44949i	0.654846	+	0.654846i	−0.299310	+	0.954156i	$0.596756\pi$
$98$	−8.44949	−	8.44949i	−0.853527	−	0.853527i
$99$	−12.6742	+	12.6742i	−1.27381	+	1.27381i
$100$		0			0
$101$	−3.00000			−0.298511			−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000			−0.298511			−0.149256	+	0.988799i	$0.547688\pi$
$102$	9.00000			0.891133
$103$			9.55051i			0.941040i	0.882389	+	0.470520i	$0.155934\pi$
$103$			9.55051i			0.941040i	−0.882389	+	0.470520i	$0.844066\pi$
$104$	−6.12372	−	1.22474i	−0.600481	−	0.120096i
$105$		0			0
$106$	2.32577	+	2.32577i	0.225898	+	0.225898i
$107$		−	1.34847i		−	0.130361i	−0.997873	−	0.0651807i	$-0.979238\pi$
$107$		−	1.34847i		−	0.130361i	0.997873	−	0.0651807i	$-0.0207624\pi$
$108$	3.67423	+	3.67423i	0.353553	+	0.353553i
$109$	−7.79796	−	7.79796i	−0.746909	−	0.746909i	0.226988	−	0.973897i	$-0.427112\pi$
$109$	−7.79796	−	7.79796i	−0.746909	−	0.746909i	−0.973897	+	0.226988i	$0.927112\pi$
$110$		0			0
$111$	−10.8990			−1.03449
$112$	1.12372	−	1.12372i	0.106182	−	0.106182i
$113$		−	16.8990i		−	1.58972i	−0.606791	−	0.794861i	$-0.707544\pi$
$113$		−	16.8990i		−	1.58972i	0.606791	−	0.794861i	$-0.292456\pi$
$114$	−13.3485	−	13.3485i	−1.25020	−	1.25020i
$115$		0			0
$116$	−1.89898			−0.176316
$117$	6.00000	+	9.00000i	0.554700	+	0.832050i
$118$	16.3485			1.50500
$119$	−0.674235	+	0.674235i	−0.0618070	+	0.0618070i
$120$		0			0
$121$			24.6969i			2.24518i
$122$	−15.6742	+	15.6742i	−1.41908	+	1.41908i
$123$	−13.3485			−1.20359
$124$	−5.12372	+	5.12372i	−0.460124	+	0.460124i
$125$		0			0
$126$	−1.65153			−0.147130
$127$		−	2.65153i		−	0.235285i	−0.993056	−	0.117643i	$-0.962466\pi$
$127$		−	2.65153i		−	0.235285i	0.993056	−	0.117643i	$-0.0375337\pi$
$128$	−8.57321	−	8.57321i	−0.757772	−	0.757772i
$129$	1.34847	−	1.34847i	0.118726	−	0.118726i
$130$		0			0
$131$		−	7.10102i		−	0.620419i	−0.950668	−	0.310210i	$-0.899601\pi$
$131$		−	7.10102i		−	0.620419i	0.950668	−	0.310210i	$-0.100399\pi$
$132$	10.3485			0.900719
$133$	2.00000			0.173422
$134$	11.4495			0.989085
$135$		0			0
$136$	3.67423	+	3.67423i	0.315063	+	0.315063i
$137$	−4.34847	−	4.34847i	−0.371515	−	0.371515i	0.496514	−	0.868029i	$-0.334613\pi$
$137$	−4.34847	−	4.34847i	−0.371515	−	0.371515i	−0.868029	+	0.496514i	$0.834613\pi$
$138$	−18.0000			−1.53226
$139$	9.34847			0.792927			0.396463	−	0.918051i	$-0.370237\pi$
$139$	9.34847			0.792927			0.396463	+	0.918051i	$0.370237\pi$
$140$		0			0
$141$		−	4.34847i		−	0.366207i
$142$			14.6969i			1.23334i
$143$	21.1237	+	4.22474i	1.76645	+	0.353291i
$144$			15.0000i			1.25000i
$145$		0			0
$146$		−	15.7980i		−	1.30745i
$147$	−8.44949	+	8.44949i	−0.696902	+	0.696902i
$148$	4.44949	+	4.44949i	0.365746	+	0.365746i
$149$	−14.4495	+	14.4495i	−1.18375	+	1.18375i	−0.204983	+	0.978766i	$0.565714\pi$
$149$	−14.4495	+	14.4495i	−1.18375	+	1.18375i	−0.978766	+	0.204983i	$0.934286\pi$
$150$		0			0
$151$	−1.57321	+	1.57321i	−0.128026	+	0.128026i	−0.768216	−	0.640190i	$-0.778856\pi$
$151$	−1.57321	+	1.57321i	−0.128026	+	0.128026i	0.640190	+	0.768216i	$0.278856\pi$
$152$		−	10.8990i		−	0.884024i
$153$		−	9.00000i		−	0.727607i
$154$	−2.32577	+	2.32577i	−0.187416	+	0.187416i
$155$		0			0
$156$	1.22474	−	6.12372i	0.0980581	−	0.490290i
$157$	7.00000			0.558661			0.279330	−	0.960195i	$-0.409888\pi$
$157$	7.00000			0.558661			0.279330	+	0.960195i	$0.409888\pi$
$158$	−4.34847	+	4.34847i	−0.345946	+	0.345946i
$159$	2.32577	−	2.32577i	0.184445	−	0.184445i
$160$		0			0
$161$	1.34847	−	1.34847i	0.106274	−	0.106274i
$162$	11.0227	−	11.0227i	0.866025	−	0.866025i
$163$	−9.34847	+	9.34847i	−0.732229	+	0.732229i	−0.971061	−	0.238832i	$-0.923235\pi$
$163$	−9.34847	+	9.34847i	−0.732229	+	0.732229i	0.238832	+	0.971061i	$0.423235\pi$
$164$	5.44949	+	5.44949i	0.425534	+	0.425534i
$165$		0			0
$166$		−	4.34847i		−	0.337507i
$167$	12.2474	+	12.2474i	0.947736	+	0.947736i	0.998700	−	0.0509644i	$-0.0162295\pi$
$167$	12.2474	+	12.2474i	0.947736	+	0.947736i	−0.0509644	+	0.998700i	$0.516230\pi$
$168$	−0.674235	−	0.674235i	−0.0520183	−	0.0520183i
$169$	5.00000	−	12.0000i	0.384615	−	0.923077i
$170$		0			0
$171$	−13.3485	+	13.3485i	−1.02078	+	1.02078i
$172$	−1.10102			−0.0839520
$173$	6.79796			0.516839			0.258420	−	0.966033i	$-0.416798\pi$
$173$	6.79796			0.516839			0.258420	+	0.966033i	$0.416798\pi$
$174$			5.69694i			0.431884i
$175$		0			0
$176$	21.1237	+	21.1237i	1.59226	+	1.59226i
$177$		−	16.3485i		−	1.22883i
$178$	1.34847			0.101072
$179$	12.2474			0.915417			0.457709	−	0.889102i	$-0.348670\pi$
$179$	12.2474			0.915417			0.457709	+	0.889102i	$0.348670\pi$
$180$		0			0
$181$		−	23.6969i		−	1.76138i	−0.473693	−	0.880690i	$-0.657080\pi$
$181$		−	23.6969i		−	1.76138i	0.473693	−	0.880690i	$-0.342920\pi$
$182$	1.10102	+	1.65153i	0.0816131	+	0.122420i
$183$	15.6742	+	15.6742i	1.15867	+	1.15867i
$184$	−7.34847	−	7.34847i	−0.541736	−	0.541736i
$185$		0			0
$186$	15.3712	+	15.3712i	1.12707	+	1.12707i
$187$	−12.6742	−	12.6742i	−0.926832	−	0.926832i
$188$	−1.77526	+	1.77526i	−0.129474	+	0.129474i
$189$			1.65153i			0.120131i
$190$		0			0
$191$		−	8.69694i		−	0.629288i	−0.949210	−	0.314644i	$-0.898115\pi$
$191$		−	8.69694i		−	0.629288i	0.949210	−	0.314644i	$-0.101885\pi$
$192$	−1.22474	+	1.22474i	−0.0883883	+	0.0883883i
$193$	1.44949	−	1.44949i	0.104337	−	0.104337i	−0.653011	−	0.757348i	$-0.726495\pi$
$193$	1.44949	−	1.44949i	0.104337	−	0.104337i	0.757348	+	0.653011i	$0.226495\pi$
$194$	−15.7980			−1.13423
$195$		0			0
$196$	6.89898			0.492784
$197$	9.24745	−	9.24745i	0.658853	−	0.658853i	−0.296255	−	0.955109i	$-0.595738\pi$
$197$	9.24745	−	9.24745i	0.658853	−	0.658853i	0.955109	+	0.296255i	$0.0957379\pi$
$198$		−	31.0454i		−	2.20630i
$199$			4.69694i			0.332957i	0.986045	+	0.166479i	$0.0532397\pi$
$199$			4.69694i			0.332957i	−0.986045	+	0.166479i	$0.946760\pi$
$200$		0			0
$201$		−	11.4495i		−	0.807585i
$202$	3.67423	−	3.67423i	0.258518	−	0.258518i
$203$	−0.426786	−	0.426786i	−0.0299545	−	0.0299545i
$204$	−3.67423	+	3.67423i	−0.257248	+	0.257248i
$205$		0			0
$206$	−11.6969	−	11.6969i	−0.814964	−	0.814964i
$207$			18.0000i			1.25109i
$208$	15.0000	−	10.0000i	1.04006	−	0.693375i
$209$			37.5959i			2.60056i
$210$		0			0
$211$	20.6969			1.42484			0.712418	−	0.701755i	$-0.247600\pi$
$211$	20.6969			1.42484			0.712418	+	0.701755i	$0.247600\pi$
$212$	−1.89898			−0.130422
$213$	14.6969			1.00702
$214$	1.65153	+	1.65153i	0.112896	+	0.112896i
$215$		0			0
$216$	9.00000			0.612372
$217$	−2.30306			−0.156342
$218$	19.1010			1.29368
$219$	−15.7980			−1.06753
$220$		0			0
$221$	−9.00000	+	6.00000i	−0.605406	+	0.403604i
$222$	13.3485	−	13.3485i	0.895891	−	0.895891i
$223$	−7.55051	−	7.55051i	−0.505620	−	0.505620i	0.407559	−	0.913179i	$-0.366380\pi$
$223$	−7.55051	−	7.55051i	−0.505620	−	0.505620i	−0.913179	+	0.407559i	$0.866380\pi$
$224$			1.65153i			0.110348i
$225$		0			0
$226$	20.6969	+	20.6969i	1.37674	+	1.37674i
$227$	10.2247	−	10.2247i	0.678640	−	0.678640i	−0.281052	−	0.959692i	$-0.590683\pi$
$227$	10.2247	−	10.2247i	0.678640	−	0.678640i	0.959692	+	0.281052i	$0.0906834\pi$
$228$	10.8990			0.721803
$229$	−10.2474	+	10.2474i	−0.677170	+	0.677170i	−0.959359	−	0.282189i	$-0.908940\pi$
$229$	−10.2474	+	10.2474i	−0.677170	+	0.677170i	0.282189	+	0.959359i	$0.408940\pi$
$230$		0			0
$231$	2.32577	+	2.32577i	0.153024	+	0.153024i
$232$	−2.32577	+	2.32577i	−0.152694	+	0.152694i
$233$	−8.20204			−0.537334			−0.268667	−	0.963233i	$-0.586583\pi$
$233$	−8.20204			−0.537334			−0.268667	+	0.963233i	$0.586583\pi$
$234$	−18.3712	−	3.67423i	−1.20096	−	0.240192i
$235$		0			0
$236$	−6.67423	+	6.67423i	−0.434456	+	0.434456i
$237$	4.34847	+	4.34847i	0.282463	+	0.282463i
$238$		−	1.65153i		−	0.107053i
$239$	10.2247	−	10.2247i	0.661384	−	0.661384i	−0.294322	−	0.955706i	$-0.595094\pi$
$239$	10.2247	−	10.2247i	0.661384	−	0.661384i	0.955706	+	0.294322i	$0.0950940\pi$
$240$		0			0
$241$	20.3485	−	20.3485i	1.31076	−	1.31076i	0.389905	−	0.920855i	$-0.372508\pi$
$241$	20.3485	−	20.3485i	1.31076	−	1.31076i	0.920855	−	0.389905i	$-0.127492\pi$
$242$	−30.2474	−	30.2474i	−1.94438	−	1.94438i
$243$	−11.0227	−	11.0227i	−0.707107	−	0.707107i
$244$		−	12.7980i		−	0.819305i
$245$		0			0
$246$	16.3485	−	16.3485i	1.04234	−	1.04234i
$247$	22.2474	+	4.44949i	1.41557	+	0.283114i
$248$			12.5505i			0.796958i
$249$	−4.34847			−0.275573
$250$		0			0
$251$	−14.4495			−0.912044			−0.456022	−	0.889969i	$-0.650726\pi$
$251$	−14.4495			−0.912044			−0.456022	+	0.889969i	$0.650726\pi$
$252$	0.674235	−	0.674235i	0.0424728	−	0.0424728i
$253$	25.3485	+	25.3485i	1.59364	+	1.59364i
$254$	3.24745	+	3.24745i	0.203763	+	0.203763i
$255$		0			0
$256$	19.0000			1.18750
$257$	28.5959			1.78376			0.891882	−	0.452268i	$-0.149385\pi$
$257$	28.5959			1.78376			0.891882	+	0.452268i	$0.149385\pi$
$258$			3.30306i			0.205640i
$259$			2.00000i			0.124274i
$260$		0			0
$261$	5.69694			0.352632
$262$	8.69694	+	8.69694i	0.537299	+	0.537299i
$263$			21.7980i			1.34412i	0.740497	+	0.672060i	$0.234590\pi$
$263$			21.7980i			1.34412i	−0.740497	+	0.672060i	$0.765410\pi$
$264$	12.6742	−	12.6742i	0.780045	−	0.780045i
$265$		0			0
$266$	−2.44949	+	2.44949i	−0.150188	+	0.150188i
$267$		−	1.34847i		−	0.0825250i
$268$	−4.67423	+	4.67423i	−0.285524	+	0.285524i
$269$			6.79796i			0.414479i	0.978290	+	0.207239i	$0.0664479\pi$
$269$			6.79796i			0.414479i	−0.978290	+	0.207239i	$0.933552\pi$
$270$		0			0
$271$	7.12372	−	7.12372i	0.432735	−	0.432735i	−0.456822	−	0.889558i	$-0.651013\pi$
$271$	7.12372	−	7.12372i	0.432735	−	0.432735i	0.889558	+	0.456822i	$0.151013\pi$
$272$	−15.0000			−0.909509
$273$	1.65153	−	1.10102i	0.0999552	−	0.0666368i
$274$	10.6515			0.643483
$275$		0			0
$276$	7.34847	−	7.34847i	0.442326	−	0.442326i
$277$		−	4.89898i		−	0.294351i	−0.989110	−	0.147176i	$-0.952982\pi$
$277$		−	4.89898i		−	0.294351i	0.989110	−	0.147176i	$-0.0470182\pi$
$278$	−11.4495	+	11.4495i	−0.686695	+	0.686695i
$279$	15.3712	−	15.3712i	0.920248	−	0.920248i
$280$		0			0
$281$	9.55051	+	9.55051i	0.569736	+	0.569736i	0.932054	−	0.362319i	$-0.118015\pi$
$281$	9.55051	+	9.55051i	0.569736	+	0.569736i	−0.362319	+	0.932054i	$0.618015\pi$
$282$	5.32577	+	5.32577i	0.317145	+	0.317145i
$283$			5.34847i			0.317933i	0.987284	+	0.158967i	$0.0508163\pi$
$283$			5.34847i			0.317933i	−0.987284	+	0.158967i	$0.949184\pi$
$284$	−6.00000	−	6.00000i	−0.356034	−	0.356034i
$285$		0			0
$286$	−31.0454	+	20.6969i	−1.83575	+	1.22384i
$287$			2.44949i			0.144589i
$288$	−11.0227	−	11.0227i	−0.649519	−	0.649519i
$289$	−8.00000			−0.470588
$290$		0			0
$291$			15.7980i			0.926093i
$292$	6.44949	+	6.44949i	0.377428	+	0.377428i
$293$	18.2474	+	18.2474i	1.06603	+	1.06603i	0.997660	+	0.0683671i	$0.0217789\pi$
$293$	18.2474	+	18.2474i	1.06603	+	1.06603i	0.0683671	+	0.997660i	$0.478221\pi$
$294$		−	20.6969i		−	1.20707i
$295$		0			0
$296$	10.8990			0.633490
$297$	−31.0454			−1.80144
$298$		−	35.3939i		−	2.05031i
$299$	18.0000	−	12.0000i	1.04097	−	0.693978i
$300$		0			0
$301$	−0.247449	−	0.247449i	−0.0142627	−	0.0142627i
$302$		−	3.85357i		−	0.221748i
$303$	−3.67423	−	3.67423i	−0.211079	−	0.211079i
$304$	22.2474	+	22.2474i	1.27598	+	1.27598i
$305$		0			0
$306$	11.0227	+	11.0227i	0.630126	+	0.630126i
$307$	−20.2474	+	20.2474i	−1.15558	+	1.15558i	−0.170168	+	0.985415i	$0.554431\pi$
$307$	−20.2474	+	20.2474i	−1.15558	+	1.15558i	−0.985415	+	0.170168i	$0.945569\pi$
$308$		−	1.89898i		−	0.108204i
$309$	−11.6969	+	11.6969i	−0.665416	+	0.665416i
$310$		0			0
$311$	15.5505			0.881789			0.440894	−	0.897559i	$-0.354661\pi$
$311$	15.5505			0.881789			0.440894	+	0.897559i	$0.354661\pi$
$312$	−6.00000	−	9.00000i	−0.339683	−	0.509525i
$313$	21.0000			1.18699			0.593495	−	0.804838i	$-0.297748\pi$
$313$	21.0000			1.18699			0.593495	+	0.804838i	$0.297748\pi$
$314$	−8.57321	+	8.57321i	−0.483814	+	0.483814i
$315$		0			0
$316$		−	3.55051i		−	0.199732i
$317$	12.7980	−	12.7980i	0.718805	−	0.718805i	−0.249556	−	0.968360i	$-0.580285\pi$
$317$	12.7980	−	12.7980i	0.718805	−	0.718805i	0.968360	+	0.249556i	$0.0802845\pi$
$318$			5.69694i			0.319468i
$319$	8.02270	−	8.02270i	0.449185	−	0.449185i
$320$		0			0
$321$	1.65153	−	1.65153i	0.0921795	−	0.0921795i
$322$			3.30306i			0.184072i
$323$	−13.3485	−	13.3485i	−0.742729	−	0.742729i
$324$			9.00000i			0.500000i
$325$		0			0
$326$		−	22.8990i		−	1.26826i
$327$		−	19.1010i		−	1.05629i
$328$	13.3485			0.737046
$329$	−0.797959			−0.0439929
$330$		0			0
$331$	−19.7980	−	19.7980i	−1.08819	−	1.08819i	−0.995715	−	0.0924797i	$-0.970521\pi$
$331$	−19.7980	−	19.7980i	−1.08819	−	1.08819i	−0.0924797	−	0.995715i	$-0.529479\pi$
$332$	1.77526	+	1.77526i	0.0974298	+	0.0974298i
$333$	−13.3485	−	13.3485i	−0.731492	−	0.731492i
$334$	−30.0000			−1.64153
$335$		0			0
$336$	2.75255			0.150164
$337$		−	17.0000i		−	0.926049i	−0.886345	−	0.463025i	$-0.846764\pi$
$337$		−	17.0000i		−	0.926049i	0.886345	−	0.463025i	$-0.153236\pi$
$338$	8.57321	+	20.8207i	0.466321	+	1.13249i
$339$	20.6969	−	20.6969i	1.12410	−	1.12410i
$340$		0			0
$341$		−	43.2929i		−	2.34444i
$342$		−	32.6969i		−	1.76805i
$343$	3.12372	+	3.12372i	0.168665	+	0.168665i
$344$	−1.34847	+	1.34847i	−0.0727046	+	0.0727046i
$345$		0			0
$346$	−8.32577	+	8.32577i	−0.447596	+	0.447596i
$347$			16.0454i			0.861363i	0.902504	+	0.430681i	$0.141727\pi$
$347$			16.0454i			0.861363i	−0.902504	+	0.430681i	$0.858273\pi$
$348$	−2.32577	−	2.32577i	−0.124674	−	0.124674i
$349$	9.89898	−	9.89898i	0.529880	−	0.529880i	−0.390656	−	0.920537i	$-0.627752\pi$
$349$	9.89898	−	9.89898i	0.529880	−	0.529880i	0.920537	+	0.390656i	$0.127752\pi$
$350$		0			0
$351$	−3.67423	+	18.3712i	−0.196116	+	0.980581i
$352$	−31.0454			−1.65473
$353$	7.10102	−	7.10102i	0.377949	−	0.377949i	−0.492413	−	0.870362i	$-0.663885\pi$
$353$	7.10102	−	7.10102i	0.377949	−	0.377949i	0.870362	+	0.492413i	$0.163885\pi$
$354$	20.0227	+	20.0227i	1.06419	+	1.06419i
$355$		0			0
$356$	−0.550510	+	0.550510i	−0.0291770	+	0.0291770i
$357$	−1.65153			−0.0874083
$358$	−15.0000	+	15.0000i	−0.792775	+	0.792775i
$359$	2.02270	+	2.02270i	0.106754	+	0.106754i	0.758466	−	0.651712i	$-0.225949\pi$
$359$	2.02270	+	2.02270i	0.106754	+	0.106754i	−0.651712	+	0.758466i	$0.725949\pi$
$360$		0			0
$361$			20.5959i			1.08400i
$362$	29.0227	+	29.0227i	1.52540	+	1.52540i
$363$	−30.2474	+	30.2474i	−1.58758	+	1.58758i
$364$	−1.12372	−	0.224745i	−0.0588992	−	0.0117798i
$365$		0			0
$366$	−38.3939			−2.00688
$367$	−6.04541			−0.315568			−0.157784	−	0.987474i	$-0.550435\pi$
$367$	−6.04541			−0.315568			−0.157784	+	0.987474i	$0.550435\pi$
$368$	30.0000			1.56386
$369$	−16.3485	−	16.3485i	−0.851067	−	0.851067i
$370$		0			0
$371$	−0.426786	−	0.426786i	−0.0221576	−	0.0221576i
$372$	−12.5505			−0.650714
$373$	−31.8990			−1.65167			−0.825833	−	0.563914i	$-0.809295\pi$
$373$	−31.8990			−1.65167			−0.825833	+	0.563914i	$0.809295\pi$
$374$	31.0454			1.60532
$375$		0			0
$376$			4.34847i			0.224255i
$377$	−3.79796	−	5.69694i	−0.195605	−	0.293407i
$378$	−2.02270	−	2.02270i	−0.104037	−	0.104037i
$379$	−26.6742	−	26.6742i	−1.37016	−	1.37016i	−0.860190	−	0.509973i	$-0.829655\pi$
$379$	−26.6742	−	26.6742i	−1.37016	−	1.37016i	−0.509973	−	0.860190i	$-0.670345\pi$
$380$		0			0
$381$	3.24745	−	3.24745i	0.166372	−	0.166372i
$382$	10.6515	+	10.6515i	0.544980	+	0.544980i
$383$	−10.6515	+	10.6515i	−0.544268	+	0.544268i	−0.924777	−	0.380509i	$-0.875749\pi$
$383$	−10.6515	+	10.6515i	−0.544268	+	0.544268i	0.380509	+	0.924777i	$0.375749\pi$
$384$		−	21.0000i		−	1.07165i
$385$		0			0
$386$			3.55051i			0.180716i
$387$	3.30306			0.167904
$388$	6.44949	−	6.44949i	0.327423	−	0.327423i
$389$	−31.5959			−1.60198			−0.800988	−	0.598680i	$-0.795692\pi$
$389$	−31.5959			−1.60198			−0.800988	+	0.598680i	$0.795692\pi$
$390$		0			0
$391$	−18.0000			−0.910299
$392$	8.44949	−	8.44949i	0.426764	−	0.426764i
$393$	8.69694	−	8.69694i	0.438703	−	0.438703i
$394$			22.6515i			1.14117i
$395$		0			0
$396$	12.6742	+	12.6742i	0.636904	+	0.636904i
$397$	9.89898	−	9.89898i	0.496816	−	0.496816i	−0.413630	−	0.910445i	$-0.635739\pi$
$397$	9.89898	−	9.89898i	0.496816	−	0.496816i	0.910445	+	0.413630i	$0.135739\pi$
$398$	−5.75255	−	5.75255i	−0.288349	−	0.288349i
$399$	2.44949	+	2.44949i	0.122628	+	0.122628i
$400$		0			0
$401$	−9.00000	−	9.00000i	−0.449439	−	0.449439i	0.445729	−	0.895168i	$-0.352944\pi$
$401$	−9.00000	−	9.00000i	−0.449439	−	0.449439i	−0.895168	+	0.445729i	$0.852944\pi$
$402$	14.0227	+	14.0227i	0.699389	+	0.699389i
$403$	−25.6186	−	5.12372i	−1.27615	−	0.255231i
$404$			3.00000i			0.149256i
$405$		0			0
$406$	1.04541			0.0518827
$407$	−37.5959			−1.86356
$408$			9.00000i			0.445566i
$409$	8.00000	+	8.00000i	0.395575	+	0.395575i	0.876669	−	0.481094i	$-0.159761\pi$
$409$	8.00000	+	8.00000i	0.395575	+	0.395575i	−0.481094	+	0.876669i	$0.659761\pi$
$410$		0			0
$411$		−	10.6515i		−	0.525401i
$412$	9.55051			0.470520
$413$	−3.00000			−0.147620
$414$	−22.0454	−	22.0454i	−1.08347	−	1.08347i
$415$		0			0
$416$	−3.67423	+	18.3712i	−0.180144	+	0.900721i
$417$	11.4495	+	11.4495i	0.560684	+	0.560684i
$418$	−46.0454	−	46.0454i	−2.25215	−	2.25215i
$419$		−	34.2929i		−	1.67532i	−0.546195	−	0.837658i	$-0.683924\pi$
$419$		−	34.2929i		−	1.67532i	0.546195	−	0.837658i	$-0.316076\pi$
$420$		0			0
$421$	−11.1010	−	11.1010i	−0.541031	−	0.541031i	0.382800	−	0.923831i	$-0.374960\pi$
$421$	−11.1010	−	11.1010i	−0.541031	−	0.541031i	−0.923831	+	0.382800i	$0.874960\pi$
$422$	−25.3485	+	25.3485i	−1.23394	+	1.23394i
$423$	5.32577	−	5.32577i	0.258948	−	0.258948i
$424$	−2.32577	+	2.32577i	−0.112949	+	0.112949i
$425$		0			0
$426$	−18.0000	+	18.0000i	−0.872103	+	0.872103i
$427$	2.87628	−	2.87628i	0.139193	−	0.139193i
$428$	−1.34847			−0.0651807
$429$	20.6969	+	31.0454i	0.999258	+	1.49889i
$430$		0			0
$431$	−22.0454	+	22.0454i	−1.06189	+	1.06189i	−0.0639359	+	0.997954i	$0.520365\pi$
$431$	−22.0454	+	22.0454i	−1.06189	+	1.06189i	−0.997954	+	0.0639359i	$0.979635\pi$
$432$	−18.3712	+	18.3712i	−0.883883	+	0.883883i
$433$			16.0000i			0.768911i	0.923144	+	0.384455i	$0.125611\pi$
$433$			16.0000i			0.768911i	−0.923144	+	0.384455i	$0.874389\pi$
$434$	2.82066	−	2.82066i	0.135396	−	0.135396i
$435$		0			0
$436$	−7.79796	+	7.79796i	−0.373455	+	0.373455i
$437$	26.6969	+	26.6969i	1.27709	+	1.27709i
$438$	19.3485	−	19.3485i	0.924506	−	0.924506i
$439$		−	20.4495i		−	0.976001i	−0.872843	−	0.488000i	$-0.837726\pi$
$439$		−	20.4495i		−	0.976001i	0.872843	−	0.488000i	$-0.162274\pi$
$440$		0			0
$441$	−20.6969			−0.985568
$442$	3.67423	−	18.3712i	0.174766	−	0.873828i
$443$		−	1.10102i		−	0.0523111i	−0.999658	−	0.0261555i	$-0.991673\pi$
$443$		−	1.10102i		−	0.0523111i	0.999658	−	0.0261555i	$-0.00832651\pi$
$444$			10.8990i			0.517243i
$445$		0			0
$446$	18.4949			0.875759
$447$	−35.3939			−1.67407
$448$	0.224745	+	0.224745i	0.0106182	+	0.0106182i
$449$	15.2474	+	15.2474i	0.719572	+	0.719572i	0.968517	−	0.248946i	$-0.0800841\pi$
$449$	15.2474	+	15.2474i	0.719572	+	0.719572i	−0.248946	+	0.968517i	$0.580084\pi$
$450$		0			0
$451$	−46.0454			−2.16819
$452$	−16.8990			−0.794861
$453$	−3.85357			−0.181057
$454$			25.0454i			1.17544i
$455$		0			0
$456$	13.3485	−	13.3485i	0.625099	−	0.625099i
$457$	18.6969	+	18.6969i	0.874606	+	0.874606i	0.992970	−	0.118364i	$-0.0377651\pi$
$457$	18.6969	+	18.6969i	0.874606	+	0.874606i	−0.118364	+	0.992970i	$0.537765\pi$
$458$		−	25.1010i		−	1.17289i
$459$	11.0227	−	11.0227i	0.514496	−	0.514496i
$460$		0			0
$461$	9.55051	−	9.55051i	0.444812	−	0.444812i	−0.448814	−	0.893625i	$-0.648153\pi$
$461$	9.55051	−	9.55051i	0.444812	−	0.444812i	0.893625	+	0.448814i	$0.148153\pi$
$462$	−5.69694			−0.265046
$463$	−2.42679	+	2.42679i	−0.112782	+	0.112782i	−0.761246	−	0.648463i	$-0.775412\pi$
$463$	−2.42679	+	2.42679i	−0.112782	+	0.112782i	0.648463	+	0.761246i	$0.275412\pi$
$464$		−	9.49490i		−	0.440790i
$465$		0			0
$466$	10.0454	−	10.0454i	0.465345	−	0.465345i
$467$	−0.247449			−0.0114506			−0.00572528	−	0.999984i	$-0.501822\pi$
$467$	−0.247449			−0.0114506			−0.00572528	+	0.999984i	$0.501822\pi$
$468$	9.00000	−	6.00000i	0.416025	−	0.277350i
$469$	−2.10102			−0.0970161
$470$		0			0
$471$	8.57321	+	8.57321i	0.395033	+	0.395033i
$472$			16.3485i			0.752499i
$473$	4.65153	−	4.65153i	0.213878	−	0.213878i
$474$	−10.6515			−0.489241
$475$		0			0
$476$	0.674235	+	0.674235i	0.0309035	+	0.0309035i
$477$	5.69694			0.260845
$478$			25.0454i			1.14555i
$479$	9.12372	+	9.12372i	0.416874	+	0.416874i	0.884125	−	0.467251i	$-0.154756\pi$
$479$	9.12372	+	9.12372i	0.416874	+	0.416874i	−0.467251	+	0.884125i	$0.654756\pi$
$480$		0			0
$481$	−4.44949	+	22.2474i	−0.202879	+	1.01440i
$482$			49.8434i			2.27030i
$483$	3.30306			0.150295
$484$	24.6969			1.12259
$485$		0			0
$486$	27.0000			1.22474
$487$	−23.3712	−	23.3712i	−1.05905	−	1.05905i	−0.998144	−	0.0609054i	$-0.980601\pi$
$487$	−23.3712	−	23.3712i	−1.05905	−	1.05905i	−0.0609054	−	0.998144i	$-0.519399\pi$
$488$	−15.6742	−	15.6742i	−0.709539	−	0.709539i
$489$	−22.8990			−1.03553
$490$		0			0
$491$	1.34847			0.0608556			0.0304278	−	0.999537i	$-0.490313\pi$
$491$	1.34847			0.0608556			0.0304278	+	0.999537i	$0.490313\pi$
$492$			13.3485i			0.601795i
$493$			5.69694i			0.256577i
$494$	−32.6969	+	21.7980i	−1.47110	+	0.980737i
$495$		0			0
$496$	−25.6186	−	25.6186i	−1.15031	−	1.15031i
$497$		−	2.69694i		−	0.120974i
$498$	5.32577	−	5.32577i	0.238653	−	0.238653i
$499$	15.5732	+	15.5732i	0.697153	+	0.697153i	0.963795	−	0.266643i	$-0.0859143\pi$
$499$	15.5732	+	15.5732i	0.697153	+	0.697153i	−0.266643	+	0.963795i	$0.585914\pi$
$500$		0			0
$501$			30.0000i			1.34030i
$502$	17.6969	−	17.6969i	0.789853	−	0.789853i
$503$			2.44949i			0.109217i	0.998508	+	0.0546087i	$0.0173911\pi$
$503$			2.44949i			0.109217i	−0.998508	+	0.0546087i	$0.982609\pi$
$504$		−	1.65153i		−	0.0735650i
$505$		0			0
$506$	−62.0908			−2.76027
$507$	20.8207	−	8.57321i	0.924678	−	0.380750i
$508$	−2.65153			−0.117643
$509$	23.4495	−	23.4495i	1.03938	−	1.03938i	0.0401882	−	0.999192i	$-0.487204\pi$
$509$	23.4495	−	23.4495i	1.03938	−	1.03938i	0.999192	−	0.0401882i	$-0.0127958\pi$
$510$		0			0
$511$			2.89898i			0.128243i
$512$	−6.12372	+	6.12372i	−0.270633	+	0.270633i
$513$	−32.6969			−1.44361
$514$	−35.0227	+	35.0227i	−1.54479	+	1.54479i
$515$		0			0
$516$	−1.34847	−	1.34847i	−0.0593630	−	0.0593630i
$517$		−	15.0000i		−	0.659699i
$518$	−2.44949	−	2.44949i	−0.107624	−	0.107624i
$519$	8.32577	+	8.32577i	0.365461	+	0.365461i
$520$		0			0
$521$			7.10102i			0.311101i	0.987828	+	0.155551i	$0.0497152\pi$
$521$			7.10102i			0.311101i	−0.987828	+	0.155551i	$0.950285\pi$
$522$	−6.97730	+	6.97730i	−0.305388	+	0.305388i
$523$	24.6969			1.07992			0.539961	−	0.841690i	$-0.318439\pi$
$523$	24.6969			1.07992			0.539961	+	0.841690i	$0.318439\pi$
$524$	−7.10102			−0.310210
$525$		0			0
$526$	−26.6969	−	26.6969i	−1.16404	−	1.16404i
$527$	15.3712	+	15.3712i	0.669579	+	0.669579i
$528$			51.7423i			2.25180i
$529$	13.0000			0.565217
$530$		0			0
$531$	20.0227	−	20.0227i	0.868911	−	0.868911i
$532$		−	2.00000i		−	0.0867110i
$533$	−5.44949	+	27.2474i	−0.236044	+	1.18022i
$534$	1.65153	+	1.65153i	0.0714687	+	0.0714687i
$535$		0			0
$536$			11.4495i			0.494543i
$537$	15.0000	+	15.0000i	0.647298	+	0.647298i
$538$	−8.32577	−	8.32577i	−0.358949	−	0.358949i
$539$	−29.1464	+	29.1464i	−1.25543	+	1.25543i
$540$		0			0
$541$	3.89898	−	3.89898i	0.167630	−	0.167630i	−0.618307	−	0.785937i	$-0.712181\pi$
$541$	3.89898	−	3.89898i	0.167630	−	0.167630i	0.785937	+	0.618307i	$0.212181\pi$
$542$			17.4495i			0.749520i
$543$	29.0227	−	29.0227i	1.24548	−	1.24548i
$544$	11.0227	−	11.0227i	0.472595	−	0.472595i
$545$		0			0
$546$	−0.674235	+	3.37117i	−0.0288546	+	0.144273i
$547$	32.0000			1.36822			0.684111	−	0.729378i	$-0.260191\pi$
$547$	32.0000			1.36822			0.684111	+	0.729378i	$0.260191\pi$
$548$	−4.34847	+	4.34847i	−0.185757	+	0.185757i
$549$			38.3939i			1.63861i
$550$		0			0
$551$	8.44949	−	8.44949i	0.359960	−	0.359960i
$552$		−	18.0000i		−	0.766131i
$553$	0.797959	−	0.797959i	0.0339327	−	0.0339327i
$554$	6.00000	+	6.00000i	0.254916	+	0.254916i
$555$		0			0
$556$		−	9.34847i		−	0.396463i
$557$	−18.5505	−	18.5505i	−0.786010	−	0.786010i	0.194827	−	0.980838i	$-0.437585\pi$
$557$	−18.5505	−	18.5505i	−0.786010	−	0.786010i	−0.980838	+	0.194827i	$0.937585\pi$
$558$			37.6515i			1.59392i
$559$	−2.20204	−	3.30306i	−0.0931364	−	0.139705i
$560$		0			0
$561$		−	31.0454i		−	1.31074i
$562$	−23.3939			−0.986811
$563$	4.04541			0.170494			0.0852468	−	0.996360i	$-0.472832\pi$
$563$	4.04541			0.170494			0.0852468	+	0.996360i	$0.472832\pi$
$564$	−4.34847			−0.183104
$565$		0			0
$566$	−6.55051	−	6.55051i	−0.275338	−	0.275338i
$567$	−2.02270	+	2.02270i	−0.0849456	+	0.0849456i
$568$	−14.6969			−0.616670
$569$	−7.89898			−0.331142			−0.165571	−	0.986198i	$-0.552947\pi$
$569$	−7.89898			−0.331142			−0.165571	+	0.986198i	$0.552947\pi$
$570$		0			0
$571$			9.34847i			0.391221i	0.980682	+	0.195611i	$0.0626689\pi$
$571$			9.34847i			0.391221i	−0.980682	+	0.195611i	$0.937331\pi$
$572$	4.22474	−	21.1237i	0.176645	−	0.883227i
$573$	10.6515	−	10.6515i	0.444974	−	0.444974i
$574$	−3.00000	−	3.00000i	−0.125218	−	0.125218i
$575$		0			0
$576$	−3.00000			−0.125000
$577$	−16.4495	−	16.4495i	−0.684801	−	0.684801i	0.276277	−	0.961078i	$-0.410899\pi$
$577$	−16.4495	−	16.4495i	−0.684801	−	0.684801i	−0.961078	+	0.276277i	$0.910899\pi$
$578$	9.79796	−	9.79796i	0.407541	−	0.407541i
$579$	3.55051			0.147554
$580$		0			0
$581$			0.797959i			0.0331049i
$582$	−19.3485	−	19.3485i	−0.802020	−	0.802020i
$583$	8.02270	−	8.02270i	0.332266	−	0.332266i
$584$	15.7980			0.653724
$585$		0			0
$586$	−44.6969			−1.84641
$587$	13.7753	−	13.7753i	0.568566	−	0.568566i	−0.363161	−	0.931726i	$-0.618302\pi$
$587$	13.7753	−	13.7753i	0.568566	−	0.568566i	0.931726	+	0.363161i	$0.118302\pi$
$588$	8.44949	+	8.44949i	0.348451	+	0.348451i
$589$		−	45.5959i		−	1.87875i
$590$		0			0
$591$	22.6515			0.931759
$592$	−22.2474	+	22.2474i	−0.914365	+	0.914365i
$593$	−10.5959	−	10.5959i	−0.435122	−	0.435122i	0.455244	−	0.890367i	$-0.349552\pi$
$593$	−10.5959	−	10.5959i	−0.435122	−	0.435122i	−0.890367	+	0.455244i	$0.849552\pi$
$594$	38.0227	−	38.0227i	1.56009	−	1.56009i
$595$		0			0
$596$	14.4495	+	14.4495i	0.591874	+	0.591874i
$597$	−5.75255	+	5.75255i	−0.235436	+	0.235436i
$598$	−7.34847	+	36.7423i	−0.300501	+	1.50251i
$599$		−	41.3939i		−	1.69131i	−0.533732	−	0.845654i	$-0.679211\pi$
$599$		−	41.3939i		−	1.69131i	0.533732	−	0.845654i	$-0.320789\pi$
$600$		0			0
$601$	19.8990			0.811696			0.405848	−	0.913941i	$-0.366976\pi$
$601$	19.8990			0.811696			0.405848	+	0.913941i	$0.366976\pi$
$602$	0.606123			0.0247037
$603$	14.0227	−	14.0227i	0.571049	−	0.571049i
$604$	1.57321	+	1.57321i	0.0640132	+	0.0640132i
$605$		0			0
$606$	9.00000			0.365600
$607$	−36.0454			−1.46304			−0.731519	−	0.681821i	$-0.761188\pi$
$607$	−36.0454			−1.46304			−0.731519	+	0.681821i	$0.761188\pi$
$608$	−32.6969			−1.32604
$609$		−	1.04541i		−	0.0423621i
$610$		0			0
$611$	−8.87628	−	1.77526i	−0.359096	−	0.0718191i
$612$	−9.00000			−0.363803
$613$	−19.1464	−	19.1464i	−0.773317	−	0.773317i	0.205368	−	0.978685i	$-0.434161\pi$
$613$	−19.1464	−	19.1464i	−0.773317	−	0.773317i	−0.978685	+	0.205368i	$0.934161\pi$
$614$		−	49.5959i		−	2.00153i
$615$		0			0
$616$	−2.32577	−	2.32577i	−0.0937078	−	0.0937078i
$617$	−11.6969	+	11.6969i	−0.470901	+	0.470901i	−0.902206	−	0.431305i	$-0.858053\pi$
$617$	−11.6969	+	11.6969i	−0.470901	+	0.470901i	0.431305	+	0.902206i	$0.358053\pi$
$618$		−	28.6515i		−	1.15253i
$619$	−10.2474	+	10.2474i	−0.411880	+	0.411880i	−0.882393	−	0.470513i	$-0.844069\pi$
$619$	−10.2474	+	10.2474i	−0.411880	+	0.411880i	0.470513	+	0.882393i	$0.344069\pi$
$620$		0			0
$621$	−22.0454	+	22.0454i	−0.884652	+	0.884652i
$622$	−19.0454	+	19.0454i	−0.763651	+	0.763651i
$623$	−0.247449			−0.00991382
$624$	30.6186	+	6.12372i	1.22573	+	0.245145i
$625$		0			0
$626$	−25.7196	+	25.7196i	−1.02796	+	1.02796i
$627$	−46.0454	+	46.0454i	−1.83888	+	1.83888i
$628$		−	7.00000i		−	0.279330i
$629$	13.3485	−	13.3485i	0.532238	−	0.532238i
$630$		0			0
$631$	−12.6969	+	12.6969i	−0.505457	+	0.505457i	−0.913129	−	0.407672i	$-0.866341\pi$
$631$	−12.6969	+	12.6969i	−0.505457	+	0.505457i	0.407672	+	0.913129i	$0.366341\pi$
$632$	−4.34847	−	4.34847i	−0.172973	−	0.172973i
$633$	25.3485	+	25.3485i	1.00751	+	1.00751i
$634$			31.3485i			1.24501i
$635$		0			0
$636$	−2.32577	−	2.32577i	−0.0922226	−	0.0922226i
$637$	13.7980	+	20.6969i	0.546695	+	0.820043i
$638$			19.6515i			0.778012i
$639$	18.0000	+	18.0000i	0.712069	+	0.712069i
$640$		0			0
$641$	35.6969			1.40994			0.704972	−	0.709235i	$-0.250959\pi$
$641$	35.6969			1.40994			0.704972	+	0.709235i	$0.250959\pi$
$642$			4.04541i			0.159660i
$643$	−12.6969	−	12.6969i	−0.500718	−	0.500718i	0.410943	−	0.911661i	$-0.365200\pi$
$643$	−12.6969	−	12.6969i	−0.500718	−	0.500718i	−0.911661	+	0.410943i	$0.865200\pi$
$644$	−1.34847	−	1.34847i	−0.0531371	−	0.0531371i
$645$		0			0
$646$	32.6969			1.28644
$647$	−21.5505			−0.847238			−0.423619	−	0.905840i	$-0.639240\pi$
$647$	−21.5505			−0.847238			−0.423619	+	0.905840i	$0.639240\pi$
$648$	11.0227	+	11.0227i	0.433013	+	0.433013i
$649$		−	56.3939i		−	2.21365i
$650$		0			0
$651$	−2.82066	−	2.82066i	−0.110550	−	0.110550i
$652$	9.34847	+	9.34847i	0.366114	+	0.366114i
$653$			5.20204i			0.203572i	0.994806	+	0.101786i	$0.0324556\pi$
$653$			5.20204i			0.203572i	−0.994806	+	0.101786i	$0.967544\pi$
$654$	23.3939	+	23.3939i	0.914773	+	0.914773i
$655$		0			0
$656$	−27.2474	+	27.2474i	−1.06383	+	1.06383i
$657$	−19.3485	−	19.3485i	−0.754856	−	0.754856i
$658$	0.977296	−	0.977296i	0.0380990	−	0.0380990i
$659$		−	6.24745i		−	0.243366i	−0.992569	−	0.121683i	$-0.961171\pi$
$659$		−	6.24745i		−	0.243366i	0.992569	−	0.121683i	$-0.0388291\pi$
$660$		0			0
$661$	8.89898	−	8.89898i	0.346130	−	0.346130i	−0.512536	−	0.858666i	$-0.671294\pi$
$661$	8.89898	−	8.89898i	0.346130	−	0.346130i	0.858666	+	0.512536i	$0.171294\pi$
$662$	48.4949			1.88481
$663$	−18.3712	−	3.67423i	−0.713477	−	0.142695i
$664$	4.34847			0.168753
$665$		0			0
$666$	32.6969			1.26698
$667$		−	11.3939i		−	0.441173i
$668$	12.2474	−	12.2474i	0.473868	−	0.473868i
$669$		−	18.4949i		−	0.715054i
$670$		0			0
$671$	54.0681	+	54.0681i	2.08728	+	2.08728i
$672$	−2.02270	+	2.02270i	−0.0780275	+	0.0780275i
$673$		−	10.5959i		−	0.408443i	−0.978925	−	0.204221i	$-0.934534\pi$
$673$		−	10.5959i		−	0.408443i	0.978925	−	0.204221i	$-0.0654662\pi$
$674$	20.8207	+	20.8207i	0.801982	+	0.801982i
$675$		0			0
$676$	−12.0000	−	5.00000i	−0.461538	−	0.192308i
$677$		−	36.4949i		−	1.40261i	−0.712860	−	0.701306i	$-0.752600\pi$
$677$		−	36.4949i		−	1.40261i	0.712860	−	0.701306i	$-0.247400\pi$
$678$			50.6969i			1.94700i
$679$	2.89898			0.111253
$680$		0			0
$681$	25.0454			0.959742
$682$	53.0227	+	53.0227i	2.03034	+	2.03034i
$683$	−0.921683	−	0.921683i	−0.0352672	−	0.0352672i	0.689253	−	0.724520i	$-0.257939\pi$
$683$	−0.921683	−	0.921683i	−0.0352672	−	0.0352672i	−0.724520	+	0.689253i	$0.757939\pi$
$684$	13.3485	+	13.3485i	0.510391	+	0.510391i
$685$		0			0
$686$	−7.65153			−0.292137
$687$	−25.1010			−0.957664
$688$		−	5.50510i		−	0.209880i
$689$	−3.79796	−	5.69694i	−0.144691	−	0.217036i
$690$		0			0
$691$	−8.67423	−	8.67423i	−0.329983	−	0.329983i	0.522597	−	0.852580i	$-0.324963\pi$
$691$	−8.67423	−	8.67423i	−0.329983	−	0.329983i	−0.852580	+	0.522597i	$0.824963\pi$
$692$		−	6.79796i		−	0.258420i
$693$			5.69694i			0.216409i
$694$	−19.6515	−	19.6515i	−0.745962	−	0.745962i
$695$		0			0
$696$	−5.69694			−0.215942
$697$	16.3485	−	16.3485i	0.619242	−	0.619242i
$698$			24.2474i			0.917779i
$699$	−10.0454	−	10.0454i	−0.379952	−	0.379952i
$700$		0			0
$701$	11.2020			0.423095			0.211548	−	0.977368i	$-0.432150\pi$
$701$	11.2020			0.423095			0.211548	+	0.977368i	$0.432150\pi$
$702$	−18.0000	−	27.0000i	−0.679366	−	1.01905i
$703$	−39.5959			−1.49339
$704$	−4.22474	+	4.22474i	−0.159226	+	0.159226i
$705$		0			0
$706$			17.3939i			0.654627i
$707$	−0.674235	+	0.674235i	−0.0253572	+	0.0253572i
$708$	−16.3485			−0.614413
$709$	−5.24745	+	5.24745i	−0.197072	+	0.197072i	−0.798744	−	0.601672i	$-0.794502\pi$
$709$	−5.24745	+	5.24745i	−0.197072	+	0.197072i	0.601672	+	0.798744i	$0.294502\pi$
$710$		0			0
$711$			10.6515i			0.399464i
$712$			1.34847i			0.0505360i
$713$	−30.7423	−	30.7423i	−1.15131	−	1.15131i
$714$	2.02270	−	2.02270i	0.0756978	−	0.0756978i
$715$		0			0
$716$		−	12.2474i		−	0.457709i
$717$	25.0454			0.935338
$718$	−4.95459			−0.184904
$719$	−17.3939			−0.648682			−0.324341	−	0.945940i	$-0.605143\pi$
$719$	−17.3939			−0.648682			−0.324341	+	0.945940i	$0.605143\pi$
$720$		0			0
$721$	2.14643	+	2.14643i	0.0799372	+	0.0799372i
$722$	−25.2247	−	25.2247i	−0.938768	−	0.938768i
$723$	49.8434			1.85369
$724$	−23.6969			−0.880690
$725$		0			0
$726$		−	74.0908i		−	2.74977i
$727$		−	30.0454i		−	1.11432i	−0.830404	−	0.557161i	$-0.811891\pi$
$727$		−	30.0454i		−	1.11432i	0.830404	−	0.557161i	$-0.188109\pi$
$728$	−1.65153	+	1.10102i	−0.0612098	+	0.0408065i
$729$		−	27.0000i		−	1.00000i
$730$		0			0
$731$			3.30306i			0.122168i
$732$	15.6742	−	15.6742i	0.579336	−	0.579336i
$733$	20.3485	+	20.3485i	0.751588	+	0.751588i	0.974776	−	0.223188i	$-0.0716463\pi$
$733$	20.3485	+	20.3485i	0.751588	+	0.751588i	−0.223188	+	0.974776i	$0.571646\pi$
$734$	7.40408	−	7.40408i	0.273290	−	0.273290i
$735$		0			0
$736$	−22.0454	+	22.0454i	−0.812605	+	0.812605i
$737$		−	39.4949i		−	1.45481i
$738$	40.0454			1.47409
$739$	16.0227	−	16.0227i	0.589405	−	0.589405i	−0.348066	−	0.937470i	$-0.613161\pi$
$739$	16.0227	−	16.0227i	0.589405	−	0.589405i	0.937470	+	0.348066i	$0.113161\pi$
$740$		0			0
$741$	21.7980	+	32.6969i	0.800768	+	1.20115i
$742$	1.04541			0.0383781
$743$	−6.92168	+	6.92168i	−0.253932	+	0.253932i	−0.822581	−	0.568649i	$-0.807466\pi$
$743$	−6.92168	+	6.92168i	−0.253932	+	0.253932i	0.568649	+	0.822581i	$0.307466\pi$
$744$	−15.3712	+	15.3712i	−0.563535	+	0.563535i
$745$		0			0
$746$	39.0681	−	39.0681i	1.43039	−	1.43039i
$747$	−5.32577	−	5.32577i	−0.194860	−	0.194860i
$748$	−12.6742	+	12.6742i	−0.463416	+	0.463416i
$749$	−0.303062	−	0.303062i	−0.0110736	−	0.0110736i
$750$		0			0
$751$		−	54.4949i		−	1.98855i	−0.106865	−	0.994274i	$-0.534081\pi$
$751$		−	54.4949i		−	1.98855i	0.106865	−	0.994274i	$-0.465919\pi$
$752$	−8.87628	−	8.87628i	−0.323684	−	0.323684i
$753$	−17.6969	−	17.6969i	−0.644912	−	0.644912i
$754$	11.6288	+	2.32577i	0.423497	+	0.0846994i
$755$		0			0
$756$	1.65153			0.0600656
$757$	21.4949			0.781245			0.390623	−	0.920551i	$-0.372260\pi$
$757$	21.4949			0.781245			0.390623	+	0.920551i	$0.372260\pi$
$758$	65.3383			2.37319
$759$			62.0908i			2.25375i
$760$		0			0
$761$	15.4949	+	15.4949i	0.561690	+	0.561690i	0.929787	−	0.368098i	$-0.119991\pi$
$761$	15.4949	+	15.4949i	0.561690	+	0.561690i	−0.368098	+	0.929787i	$0.619991\pi$
$762$			7.95459i			0.288164i
$763$	−3.50510			−0.126893
$764$	−8.69694			−0.314644
$765$		0			0
$766$		−	26.0908i		−	0.942699i
$767$	−33.3712	−	6.67423i	−1.20496	−	0.240993i
$768$	23.2702	+	23.2702i	0.839689	+	0.839689i
$769$	−10.6969	−	10.6969i	−0.385741	−	0.385741i	0.487424	−	0.873165i	$-0.337937\pi$
$769$	−10.6969	−	10.6969i	−0.385741	−	0.385741i	−0.873165	+	0.487424i	$0.837937\pi$
$770$		0			0
$771$	35.0227	+	35.0227i	1.26131	+	1.26131i
$772$	−1.44949	−	1.44949i	−0.0521683	−	0.0521683i
$773$	35.1464	−	35.1464i	1.26413	−	1.26413i	0.315056	−	0.949073i	$-0.397977\pi$
$773$	35.1464	−	35.1464i	1.26413	−	1.26413i	0.949073	−	0.315056i	$-0.102023\pi$
$774$	−4.04541	+	4.04541i	−0.145409	+	0.145409i
$775$		0			0
$776$		−	15.7980i		−	0.567114i
$777$	−2.44949	+	2.44949i	−0.0878750	+	0.0878750i
$778$	38.6969	−	38.6969i	1.38735	−	1.38735i
$779$	−48.4949			−1.73751
$780$		0			0
$781$	50.6969			1.81408
$782$	22.0454	−	22.0454i	0.788342	−	0.788342i
$783$	6.97730	+	6.97730i	0.249348	+	0.249348i
$784$			34.4949i			1.23196i
$785$		0			0
$786$			21.3031i			0.759855i
$787$	9.57321	−	9.57321i	0.341248	−	0.341248i	−0.515588	−	0.856836i	$-0.672427\pi$
$787$	9.57321	−	9.57321i	0.341248	−	0.341248i	0.856836	+	0.515588i	$0.172427\pi$
$788$	−9.24745	−	9.24745i	−0.329427	−	0.329427i
$789$	−26.6969	+	26.6969i	−0.950436	+	0.950436i
$790$		0			0
$791$	−3.79796	−	3.79796i	−0.135040	−	0.135040i
$792$	31.0454			1.10315
$793$	38.3939	−	25.5959i	1.36341	−	0.908938i
$794$			24.2474i			0.860510i
$795$		0			0
$796$	4.69694			0.166479
$797$	−18.7980			−0.665858			−0.332929	−	0.942952i	$-0.608037\pi$
$797$	−18.7980			−0.665858			−0.332929	+	0.942952i	$0.608037\pi$
$798$	−6.00000			−0.212398
$799$	5.32577	+	5.32577i	0.188412	+	0.188412i
$800$		0			0
$801$	1.65153	−	1.65153i	0.0583540	−	0.0583540i
$802$	22.0454			0.778450
$803$	−54.4949			−1.92308
$804$	−11.4495			−0.403792
$805$		0			0
$806$	37.6515	−	25.1010i	1.32622	−	0.884146i
$807$	−8.32577	+	8.32577i	−0.293081	+	0.293081i
$808$	3.67423	+	3.67423i	0.129259	+	0.129259i
$809$		−	34.2929i		−	1.20567i	−0.797865	−	0.602836i	$-0.794037\pi$
$809$		−	34.2929i		−	1.20567i	0.797865	−	0.602836i	$-0.205963\pi$
$810$		0			0
$811$	−5.77526	−	5.77526i	−0.202797	−	0.202797i	0.598400	−	0.801197i	$-0.295803\pi$
$811$	−5.77526	−	5.77526i	−0.202797	−	0.202797i	−0.801197	+	0.598400i	$0.795803\pi$
$812$	−0.426786	+	0.426786i	−0.0149772	+	0.0149772i
$813$	17.4495			0.611980
$814$	46.0454	−	46.0454i	1.61389	−	1.61389i
$815$		0			0
$816$	−18.3712	−	18.3712i	−0.643120	−	0.643120i
$817$	4.89898	−	4.89898i	0.171394	−	0.171394i
$818$	−19.5959			−0.685155
$819$	3.37117	+	0.674235i	0.117798	+	0.0235597i
$820$		0			0
$821$	−0.303062	+	0.303062i	−0.0105769	+	0.0105769i	−0.712375	−	0.701799i	$-0.752381\pi$
$821$	−0.303062	+	0.303062i	−0.0105769	+	0.0105769i	0.701799	+	0.712375i	$0.252381\pi$
$822$	13.0454	+	13.0454i	0.455011	+	0.455011i
$823$			14.6969i			0.512303i	0.966637	+	0.256152i	$0.0824546\pi$
$823$			14.6969i			0.512303i	−0.966637	+	0.256152i	$0.917545\pi$
$824$	11.6969	−	11.6969i	0.407482	−	0.407482i
$825$		0			0
$826$	3.67423	−	3.67423i	0.127843	−	0.127843i
$827$	15.9773	+	15.9773i	0.555585	+	0.555585i	0.928047	−	0.372462i	$-0.121486\pi$
$827$	15.9773	+	15.9773i	0.555585	+	0.555585i	−0.372462	+	0.928047i	$0.621486\pi$
$828$	18.0000			0.625543
$829$			39.6969i			1.37873i	0.724413	+	0.689366i	$0.242111\pi$
$829$			39.6969i			1.37873i	−0.724413	+	0.689366i	$0.757889\pi$
$830$		0			0
$831$	6.00000	−	6.00000i	0.208138	−	0.208138i
$832$	2.00000	+	3.00000i	0.0693375	+	0.104006i
$833$		−	20.6969i		−	0.717106i
$834$	−28.0454			−0.971133
$835$		0			0
$836$	37.5959			1.30028
$837$	37.6515			1.30143
$838$	42.0000	+	42.0000i	1.45087	+	1.45087i
$839$	37.3485	+	37.3485i	1.28941	+	1.28941i	0.935144	+	0.354269i	$0.115270\pi$
$839$	37.3485	+	37.3485i	1.28941	+	1.28941i	0.354269	+	0.935144i	$0.384730\pi$
$840$		0			0
$841$	25.3939			0.875651
$842$	27.1918			0.937093
$843$			23.3939i			0.805728i
$844$		−	20.6969i		−	0.712418i
$845$		0			0
$846$			13.0454i			0.448510i
$847$	5.55051	+	5.55051i	0.190718	+	0.190718i
$848$		−	9.49490i		−	0.326056i
$849$	−6.55051	+	6.55051i	−0.224813	+	0.224813i
$850$		0			0
$851$	−26.6969	+	26.6969i	−0.915159	+	0.915159i
$852$		−	14.6969i		−	0.503509i
$853$	5.65153	−	5.65153i	0.193505	−	0.193505i	−0.603704	−	0.797209i	$-0.706309\pi$
$853$	5.65153	−	5.65153i	0.193505	−	0.193505i	0.797209	+	0.603704i	$0.206309\pi$
$854$			7.04541i			0.241089i
$855$		0			0
$856$	−1.65153	+	1.65153i	−0.0564482	+	0.0564482i
$857$	−49.5959			−1.69416			−0.847082	−	0.531462i	$-0.821643\pi$
$857$	−49.5959			−1.69416			−0.847082	+	0.531462i	$0.821643\pi$
$858$	−63.3712	−	12.6742i	−2.16346	−	0.432691i
$859$	1.59592			0.0544520			0.0272260	−	0.999629i	$-0.491333\pi$
$859$	1.59592			0.0544520			0.0272260	+	0.999629i	$0.491333\pi$
$860$		0			0
$861$	−3.00000	+	3.00000i	−0.102240	+	0.102240i
$862$		−	54.0000i		−	1.83925i
$863$	8.87628	−	8.87628i	0.302152	−	0.302152i	−0.539703	−	0.841855i	$-0.681464\pi$
$863$	8.87628	−	8.87628i	0.302152	−	0.302152i	0.841855	+	0.539703i	$0.181464\pi$
$864$		−	27.0000i		−	0.918559i
$865$		0			0
$866$	−19.5959	−	19.5959i	−0.665896	−	0.665896i
$867$	−9.79796	−	9.79796i	−0.332756	−	0.332756i
$868$			2.30306i			0.0781710i
$869$	15.0000	+	15.0000i	0.508840	+	0.508840i
$870$		0			0
$871$	−23.3712	−	4.67423i	−0.791902	−	0.158380i
$872$			19.1010i			0.646842i
$873$	−19.3485	+	19.3485i	−0.654846	+	0.654846i
$874$	−65.3939			−2.21198
$875$		0			0
$876$			15.7980i			0.533764i
$877$	15.9444	+	15.9444i	0.538404	+	0.538404i	0.923060	−	0.384656i	$-0.125680\pi$
$877$	15.9444	+	15.9444i	0.538404	+	0.538404i	−0.384656	+	0.923060i	$0.625680\pi$
$878$	25.0454	+	25.0454i	0.845242	+	0.845242i
$879$			44.6969i			1.50759i
$880$		0			0
$881$	4.10102			0.138167			0.0690834	−	0.997611i	$-0.477993\pi$
$881$	4.10102			0.138167			0.0690834	+	0.997611i	$0.477993\pi$
$882$	25.3485	−	25.3485i	0.853527	−	0.853527i
$883$		−	42.6969i		−	1.43687i	−0.695596	−	0.718433i	$-0.744860\pi$
$883$		−	42.6969i		−	1.43687i	0.695596	−	0.718433i	$-0.255140\pi$
$884$	6.00000	+	9.00000i	0.201802	+	0.302703i
$885$		0			0
$886$	1.34847	+	1.34847i	0.0453027	+	0.0453027i
$887$		−	1.34847i		−	0.0452772i	−0.999744	−	0.0226386i	$-0.992793\pi$
$887$		−	1.34847i		−	0.0452772i	0.999744	−	0.0226386i	$-0.00720670\pi$
$888$	13.3485	+	13.3485i	0.447945	+	0.447945i
$889$	−0.595918	−	0.595918i	−0.0199864	−	0.0199864i
$890$		0			0
$891$	−38.0227	−	38.0227i	−1.27381	−	1.27381i
$892$	−7.55051	+	7.55051i	−0.252810	+	0.252810i
$893$		−	15.7980i		−	0.528659i
$894$	43.3485	−	43.3485i	1.44979	−	1.44979i
$895$		0			0
$896$	−3.85357			−0.128739
$897$	36.7423	+	7.34847i	1.22679	+	0.245358i
$898$	−37.3485			−1.24633
$899$	−9.72985	+	9.72985i	−0.324509	+	0.324509i
$900$		0			0
$901$			5.69694i			0.189793i
$902$	56.3939	−	56.3939i	1.87771	−	1.87771i
$903$		−	0.606123i		−	0.0201705i
$904$	−20.6969	+	20.6969i	−0.688370	+	0.688370i
$905$		0			0
$906$	4.71964	−	4.71964i	0.156800	−	0.156800i
$907$			46.6969i			1.55055i	0.631626	+	0.775273i	$0.282388\pi$
$907$			46.6969i			1.55055i	−0.631626	+	0.775273i	$0.717612\pi$
$908$	−10.2247	−	10.2247i	−0.339320	−	0.339320i
$909$		−	9.00000i		−	0.298511i
$910$		0			0
$911$			35.1464i			1.16445i	0.813027	+	0.582227i	$0.197818\pi$
$911$			35.1464i			1.16445i	−0.813027	+	0.582227i	$0.802182\pi$
$912$			54.4949i			1.80451i
$913$	−15.0000			−0.496428
$914$	−45.7980			−1.51486
$915$		0			0
$916$	10.2474	+	10.2474i	0.338585	+	0.338585i
$917$	−1.59592	−	1.59592i	−0.0527019	−	0.0527019i
$918$			27.0000i			0.891133i
$919$	−15.7980			−0.521127			−0.260563	−	0.965457i	$-0.583908\pi$
$919$	−15.7980			−0.521127			−0.260563	+	0.965457i	$0.583908\pi$
$920$		0			0
$921$	−49.5959			−1.63424
$922$			23.3939i			0.770436i
$923$	6.00000	−	30.0000i	0.197492	−	0.987462i
$924$	2.32577	−	2.32577i	0.0765121	−	0.0765121i
$925$		0			0
$926$		−	5.94439i		−	0.195345i
$927$	−28.6515			−0.941040
$928$	6.97730	+	6.97730i	0.229041	+	0.229041i
$929$	−20.3939	+	20.3939i	−0.669101	+	0.669101i	−0.957508	−	0.288407i	$-0.906875\pi$
$929$	−20.3939	+	20.3939i	−0.669101	+	0.669101i	0.288407	+	0.957508i	$0.406875\pi$
$930$		0			0
$931$	−30.6969	+	30.6969i	−1.00605	+	1.00605i
$932$			8.20204i			0.268667i
$933$	19.0454	+	19.0454i	0.623519	+	0.623519i
$934$	0.303062	−	0.303062i	0.00991648	−	0.00991648i
$935$		0			0
$936$	3.67423	−	18.3712i	0.120096	−	0.600481i
$937$	−1.40408			−0.0458694			−0.0229347	−	0.999737i	$-0.507301\pi$
$937$	−1.40408			−0.0458694			−0.0229347	+	0.999737i	$0.507301\pi$
$938$	2.57321	−	2.57321i	0.0840184	−	0.0840184i
$939$	25.7196	+	25.7196i	0.839329	+	0.839329i
$940$		0			0
$941$	−6.24745	+	6.24745i	−0.203661	+	0.203661i	−0.801567	−	0.597906i	$-0.796000\pi$
$941$	−6.24745	+	6.24745i	−0.203661	+	0.203661i	0.597906	+	0.801567i	$0.296000\pi$
$942$	−21.0000			−0.684217
$943$	−32.6969	+	32.6969i	−1.06476	+	1.06476i
$944$	−33.3712	−	33.3712i	−1.08614	−	1.08614i
$945$		0			0
$946$			11.3939i			0.370447i
$947$	33.3712	+	33.3712i	1.08442	+	1.08442i	0.996092	+	0.0883258i	$0.0281517\pi$
$947$	33.3712	+	33.3712i	1.08442	+	1.08442i	0.0883258	+	0.996092i	$0.471848\pi$
$948$	4.34847	−	4.34847i	0.141232	−	0.141232i
$949$	−6.44949	+	32.2474i	−0.209359	+	1.04680i
$950$		0			0
$951$	31.3485			1.01654
$952$	1.65153			0.0535264
$953$	−47.6969			−1.54506			−0.772528	−	0.634981i	$-0.781008\pi$
$953$	−47.6969			−1.54506			−0.772528	+	0.634981i	$0.781008\pi$
$954$	−6.97730	+	6.97730i	−0.225898	+	0.225898i
$955$		0			0
$956$	−10.2247	−	10.2247i	−0.330692	−	0.330692i
$957$	19.6515			0.635244
$958$	−22.3485			−0.722046
$959$	−1.95459			−0.0631171
$960$		0			0
$961$			21.5051i			0.693713i
$962$	−21.7980	−	32.6969i	−0.702794	−	1.05419i
$963$	4.04541			0.130361
$964$	−20.3485	−	20.3485i	−0.655380	−	0.655380i
$965$		0			0
$966$	−4.04541	+	4.04541i	−0.130159	+	0.130159i
$967$	26.9217	+	26.9217i	0.865743	+	0.865743i	0.991998	−	0.126255i	$-0.0402957\pi$
$967$	26.9217	+	26.9217i	0.865743	+	0.865743i	−0.126255	+	0.991998i	$0.540296\pi$
$968$	30.2474	−	30.2474i	0.972190	−	0.972190i
$969$		−	32.6969i		−	1.05038i
$970$		0			0
$971$		−	42.2474i		−	1.35579i	−0.735161	−	0.677893i	$-0.762893\pi$
$971$		−	42.2474i		−	1.35579i	0.735161	−	0.677893i	$-0.237107\pi$
$972$	−11.0227	+	11.0227i	−0.353553	+	0.353553i
$973$	2.10102	−	2.10102i	0.0673556	−	0.0673556i
$974$	57.2474			1.83433
$975$		0			0
$976$	63.9898			2.04826
$977$	−13.6515	+	13.6515i	−0.436751	+	0.436751i	−0.890917	−	0.454166i	$-0.849937\pi$
$977$	−13.6515	+	13.6515i	−0.436751	+	0.436751i	0.454166	+	0.890917i	$0.349937\pi$
$978$	28.0454	−	28.0454i	0.896793	−	0.896793i
$979$		−	4.65153i		−	0.148664i
$980$		0			0
$981$	23.3939	−	23.3939i	0.746909	−	0.746909i
$982$	−1.65153	+	1.65153i	−0.0527025	+	0.0527025i
$983$	−0.921683	−	0.921683i	−0.0293971	−	0.0293971i	0.692255	−	0.721653i	$-0.256617\pi$
$983$	−0.921683	−	0.921683i	−0.0293971	−	0.0293971i	−0.721653	+	0.692255i	$0.756617\pi$
$984$	16.3485	+	16.3485i	0.521170	+	0.521170i
$985$		0			0
$986$	−6.97730	−	6.97730i	−0.222202	−	0.222202i
$987$	−0.977296	−	0.977296i	−0.0311077	−	0.0311077i
$988$	4.44949	−	22.2474i	0.141557	−	0.707786i
$989$		−	6.60612i		−	0.210062i
$990$		0			0
$991$	2.00000			0.0635321			0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000			0.0635321			0.0317660	+	0.999495i	$0.489887\pi$
$992$	37.6515			1.19544
$993$		−	48.4949i		−	1.53894i
$994$	3.30306	+	3.30306i	0.104767	+	0.104767i
$995$		0			0
$996$			4.34847i			0.137787i
$997$	−49.0908			−1.55472			−0.777361	−	0.629055i	$-0.783442\pi$
$997$	−49.0908			−1.55472			−0.777361	+	0.629055i	$0.783442\pi$
$998$	−38.1464			−1.20750
$999$		−	32.6969i		−	1.03449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.o.c.476.1	✓	4
3.2	odd	2		975.2.o.f.476.2	yes	4
5.2	odd	4		975.2.n.a.749.1		4
5.3	odd	4		975.2.n.b.749.2		4
5.4	even	2		975.2.o.d.476.2	yes	4
13.5	odd	4		975.2.o.f.551.2	yes	4
15.2	even	4		975.2.n.f.749.2		4
15.8	even	4		975.2.n.i.749.1		4
15.14	odd	2		975.2.o.g.476.1	yes	4
39.5	even	4	inner	975.2.o.c.551.1	yes	4
65.18	even	4		975.2.n.f.824.2		4
65.44	odd	4		975.2.o.g.551.1	yes	4
65.57	even	4		975.2.n.i.824.1		4
195.44	even	4		975.2.o.d.551.2	yes	4
195.83	odd	4		975.2.n.a.824.1		4
195.122	odd	4		975.2.n.b.824.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.n.a.749.1		4	5.2	odd	4
975.2.n.a.824.1		4	195.83	odd	4
975.2.n.b.749.2		4	5.3	odd	4
975.2.n.b.824.2		4	195.122	odd	4
975.2.n.f.749.2		4	15.2	even	4
975.2.n.f.824.2		4	65.18	even	4
975.2.n.i.749.1		4	15.8	even	4
975.2.n.i.824.1		4	65.57	even	4
975.2.o.c.476.1	✓	4	1.1	even	1	trivial
975.2.o.c.551.1	yes	4	39.5	even	4	inner
975.2.o.d.476.2	yes	4	5.4	even	2
975.2.o.d.551.2	yes	4	195.44	even	4
975.2.o.f.476.2	yes	4	3.2	odd	2
975.2.o.f.551.2	yes	4	13.5	odd	4
975.2.o.g.476.1	yes	4	15.14	odd	2
975.2.o.g.551.1	yes	4	65.44	odd	4

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 1.22474i) q^{2} +(1.22474 + 1.22474i) q^{3} -1.00000i q^{4} -3.00000 q^{6} +(0.224745 - 0.224745i) q^{7} +(-1.22474 - 1.22474i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.22474 + 1.22474i) q^{2} +(1.22474 + 1.22474i) q^{3} -1.00000i q^{4} -3.00000 q^{6} +(0.224745 - 0.224745i) q^{7} +(-1.22474 - 1.22474i) q^{8} +3.00000i q^{9} +(4.22474 + 4.22474i) q^{11} +(1.22474 - 1.22474i) q^{12} +(3.00000 - 2.00000i) q^{13} +0.550510i q^{14} +5.00000 q^{16} -3.00000 q^{17} +(-3.67423 - 3.67423i) q^{18} +(4.44949 + 4.44949i) q^{19} +0.550510 q^{21} -10.3485 q^{22} +6.00000 q^{23} -3.00000i q^{24} +(-1.22474 + 6.12372i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(-0.224745 - 0.224745i) q^{28} -1.89898i q^{29} +(-5.12372 - 5.12372i) q^{31} +(-3.67423 + 3.67423i) q^{32} +10.3485i q^{33} +(3.67423 - 3.67423i) q^{34} +3.00000 q^{36} +(-4.44949 + 4.44949i) q^{37} -10.8990 q^{38} +(6.12372 + 1.22474i) q^{39} +(-5.44949 + 5.44949i) q^{41} +(-0.674235 + 0.674235i) q^{42} -1.10102i q^{43} +(4.22474 - 4.22474i) q^{44} +(-7.34847 + 7.34847i) q^{46} +(-1.77526 - 1.77526i) q^{47} +(6.12372 + 6.12372i) q^{48} +6.89898i q^{49} +(-3.67423 - 3.67423i) q^{51} +(-2.00000 - 3.00000i) q^{52} -1.89898i q^{53} -9.00000i q^{54} -0.550510 q^{56} +10.8990i q^{57} +(2.32577 + 2.32577i) q^{58} +(-6.67423 - 6.67423i) q^{59} +12.7980 q^{61} +12.5505 q^{62} +(0.674235 + 0.674235i) q^{63} +1.00000i q^{64} +(-12.6742 - 12.6742i) q^{66} +(-4.67423 - 4.67423i) q^{67} +3.00000i q^{68} +(7.34847 + 7.34847i) q^{69} +(6.00000 - 6.00000i) q^{71} +(3.67423 - 3.67423i) q^{72} +(-6.44949 + 6.44949i) q^{73} -10.8990i q^{74} +(4.44949 - 4.44949i) q^{76} +1.89898 q^{77} +(-9.00000 + 6.00000i) q^{78} +3.55051 q^{79} -9.00000 q^{81} -13.3485i q^{82} +(-1.77526 + 1.77526i) q^{83} -0.550510i q^{84} +(1.34847 + 1.34847i) q^{86} +(2.32577 - 2.32577i) q^{87} -10.3485i q^{88} +(-0.550510 - 0.550510i) q^{89} +(0.224745 - 1.12372i) q^{91} -6.00000i q^{92} -12.5505i q^{93} +4.34847 q^{94} -9.00000 q^{96} +(6.44949 + 6.44949i) q^{97} +(-8.44949 - 8.44949i) q^{98} +(-12.6742 + 12.6742i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 12 q^{6} - 4 q^{7}+O(q^{10}) \) 4 * q - 12 * q^6 - 4 * q^7	\( 4 q - 12 q^{6} - 4 q^{7} + 12 q^{11} + 12 q^{13} + 20 q^{16} - 12 q^{17} + 8 q^{19} + 12 q^{21} - 12 q^{22} + 24 q^{23} + 4 q^{28} + 4 q^{31} + 12 q^{36} - 8 q^{37} - 24 q^{38} - 12 q^{41} + 12 q^{42} + 12 q^{44} - 12 q^{47} - 8 q^{52} - 12 q^{56} + 24 q^{58} - 12 q^{59} + 12 q^{61} + 60 q^{62} - 12 q^{63} - 36 q^{66} - 4 q^{67} + 24 q^{71} - 16 q^{73} + 8 q^{76} - 12 q^{77} - 36 q^{78} + 24 q^{79} - 36 q^{81} - 12 q^{83} - 24 q^{86} + 24 q^{87} - 12 q^{89} - 4 q^{91} - 12 q^{94} - 36 q^{96} + 16 q^{97} - 24 q^{98} - 36 q^{99}+O(q^{100}) \) 4 * q - 12 * q^6 - 4 * q^7 + 12 * q^11 + 12 * q^13 + 20 * q^16 - 12 * q^17 + 8 * q^19 + 12 * q^21 - 12 * q^22 + 24 * q^23 + 4 * q^28 + 4 * q^31 + 12 * q^36 - 8 * q^37 - 24 * q^38 - 12 * q^41 + 12 * q^42 + 12 * q^44 - 12 * q^47 - 8 * q^52 - 12 * q^56 + 24 * q^58 - 12 * q^59 + 12 * q^61 + 60 * q^62 - 12 * q^63 - 36 * q^66 - 4 * q^67 + 24 * q^71 - 16 * q^73 + 8 * q^76 - 12 * q^77 - 36 * q^78 + 24 * q^79 - 36 * q^81 - 12 * q^83 - 24 * q^86 + 24 * q^87 - 12 * q^89 - 4 * q^91 - 12 * q^94 - 36 * q^96 + 16 * q^97 - 24 * q^98 - 36 * q^99

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