LMFDB - Embedded newform 630.2.k.j.541.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(361,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("630.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.k (of order $3$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.1
Root			$1.32288 - 2.29129i$ of defining polynomial
Character	$\chi$	$=$	630.541
Dual form			630.2.k.j.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -2.64575 q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -2.64575 q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +(-0.322876 - 0.559237i) q^{11} -4.64575 q^{13} +(-1.32288 + 2.29129i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.64575 - 6.31463i) q^{17} +(-3.14575 + 5.44860i) q^{19} +1.00000 q^{20} -0.645751 q^{22} +(1.50000 - 2.59808i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-2.32288 + 4.02334i) q^{26} +(1.32288 + 2.29129i) q^{28} +(-1.00000 - 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} -7.29150 q^{34} +(1.32288 - 2.29129i) q^{35} +(-4.96863 + 8.60591i) q^{37} +(3.14575 + 5.44860i) q^{38} +(0.500000 - 0.866025i) q^{40} -6.64575 q^{41} +0.708497 q^{43} +(-0.322876 + 0.559237i) q^{44} +(-1.50000 - 2.59808i) q^{46} +(5.79150 - 10.0312i) q^{47} +7.00000 q^{49} -1.00000 q^{50} +(2.32288 + 4.02334i) q^{52} +(5.14575 + 8.91270i) q^{53} +0.645751 q^{55} +2.64575 q^{56} +(0.645751 + 1.11847i) q^{59} +(-0.354249 + 0.613577i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(2.32288 - 4.02334i) q^{65} +(-7.64575 - 13.2428i) q^{67} +(-3.64575 + 6.31463i) q^{68} +(-1.32288 - 2.29129i) q^{70} +13.2915 q^{71} +(-1.00000 - 1.73205i) q^{73} +(4.96863 + 8.60591i) q^{74} +6.29150 q^{76} +(0.854249 + 1.47960i) q^{77} +(-0.354249 + 0.613577i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-3.32288 + 5.75539i) q^{82} -4.70850 q^{83} +7.29150 q^{85} +(0.354249 - 0.613577i) q^{86} +(0.322876 + 0.559237i) q^{88} +(-7.29150 + 12.6293i) q^{89} +12.2915 q^{91} -3.00000 q^{92} +(-5.79150 - 10.0312i) q^{94} +(-3.14575 - 5.44860i) q^{95} -4.00000 q^{97} +(3.50000 - 6.06218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{8} + 2 q^{10} + 4 q^{11} - 8 q^{13} - 2 q^{16} - 4 q^{17} - 2 q^{19} + 4 q^{20} + 8 q^{22} + 6 q^{23} - 2 q^{25} - 4 q^{26} - 4 q^{31} + 2 q^{32} - 8 q^{34} - 4 q^{37} + 2 q^{38} + 2 q^{40} - 16 q^{41} + 24 q^{43} + 4 q^{44} - 6 q^{46} + 2 q^{47} + 28 q^{49} - 4 q^{50} + 4 q^{52} + 10 q^{53} - 8 q^{55} - 8 q^{59} - 12 q^{61} - 8 q^{62} + 4 q^{64} + 4 q^{65} - 20 q^{67} - 4 q^{68} + 32 q^{71} - 4 q^{73} + 4 q^{74} + 4 q^{76} + 14 q^{77} - 12 q^{79} - 2 q^{80} - 8 q^{82} - 40 q^{83} + 8 q^{85} + 12 q^{86} - 4 q^{88} - 8 q^{89} + 28 q^{91} - 12 q^{92} - 2 q^{94} - 2 q^{95} - 16 q^{97} + 14 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^8 + 2 * q^10 + 4 * q^11 - 8 * q^13 - 2 * q^16 - 4 * q^17 - 2 * q^19 + 4 * q^20 + 8 * q^22 + 6 * q^23 - 2 * q^25 - 4 * q^26 - 4 * q^31 + 2 * q^32 - 8 * q^34 - 4 * q^37 + 2 * q^38 + 2 * q^40 - 16 * q^41 + 24 * q^43 + 4 * q^44 - 6 * q^46 + 2 * q^47 + 28 * q^49 - 4 * q^50 + 4 * q^52 + 10 * q^53 - 8 * q^55 - 8 * q^59 - 12 * q^61 - 8 * q^62 + 4 * q^64 + 4 * q^65 - 20 * q^67 - 4 * q^68 + 32 * q^71 - 4 * q^73 + 4 * q^74 + 4 * q^76 + 14 * q^77 - 12 * q^79 - 2 * q^80 - 8 * q^82 - 40 * q^83 + 8 * q^85 + 12 * q^86 - 4 * q^88 - 8 * q^89 + 28 * q^91 - 12 * q^92 - 2 * q^94 - 2 * q^95 - 16 * q^97 + 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	−2.64575			−1.00000
$7$	−2.64575			−1.00000
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−0.322876	−	0.559237i	−0.0973507	−	0.168616i	0.813237	−	0.581933i	$-0.197704\pi$
$11$	−0.322876	−	0.559237i	−0.0973507	−	0.168616i	−0.910587	+	0.413317i	$0.864370\pi$
$12$		0			0
$13$	−4.64575			−1.28850			−0.644250	−	0.764815i	$-0.722830\pi$
$13$	−4.64575			−1.28850			−0.644250	+	0.764815i	$0.722830\pi$
$14$	−1.32288	+	2.29129i	−0.353553	+	0.612372i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.64575	−	6.31463i	−0.884225	−	1.53152i	−0.846600	−	0.532230i	$-0.821354\pi$
$17$	−3.64575	−	6.31463i	−0.884225	−	1.53152i	−0.0376247	−	0.999292i	$-0.511979\pi$
$18$		0			0
$19$	−3.14575	+	5.44860i	−0.721685	+	1.24999i	0.238639	+	0.971108i	$0.423299\pi$
$19$	−3.14575	+	5.44860i	−0.721685	+	1.24999i	−0.960324	+	0.278887i	$0.910035\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	−0.645751			−0.137675
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.32288	+	4.02334i	−0.455553	+	0.789042i
$27$		0			0
$28$	1.32288	+	2.29129i	0.250000	+	0.433013i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−7.29150			−1.25048
$35$	1.32288	−	2.29129i	0.223607	−	0.387298i
$36$		0			0
$37$	−4.96863	+	8.60591i	−0.816837	+	1.41480i	0.0911639	+	0.995836i	$0.470941\pi$
$37$	−4.96863	+	8.60591i	−0.816837	+	1.41480i	−0.908001	+	0.418968i	$0.862392\pi$
$38$	3.14575	+	5.44860i	0.510308	+	0.883880i
$39$		0			0
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−6.64575			−1.03789			−0.518946	−	0.854807i	$-0.673675\pi$
$41$	−6.64575			−1.03789			−0.518946	+	0.854807i	$0.673675\pi$
$42$		0			0
$43$	0.708497			0.108045			0.0540224	−	0.998540i	$-0.482796\pi$
$43$	0.708497			0.108045			0.0540224	+	0.998540i	$0.482796\pi$
$44$	−0.322876	+	0.559237i	−0.0486753	+	0.0843082i
$45$		0			0
$46$	−1.50000	−	2.59808i	−0.221163	−	0.383065i
$47$	5.79150	−	10.0312i	0.844777	−	1.46320i	−0.0410368	−	0.999158i	$-0.513066\pi$
$47$	5.79150	−	10.0312i	0.844777	−	1.46320i	0.885814	−	0.464040i	$-0.153601\pi$
$48$		0			0
$49$	7.00000			1.00000
$50$	−1.00000			−0.141421
$51$		0			0
$52$	2.32288	+	4.02334i	0.322125	+	0.557937i
$53$	5.14575	+	8.91270i	0.706823	+	1.22425i	0.966029	+	0.258432i	$0.0832057\pi$
$53$	5.14575	+	8.91270i	0.706823	+	1.22425i	−0.259206	+	0.965822i	$0.583461\pi$
$54$		0			0
$55$	0.645751			0.0870731
$56$	2.64575			0.353553
$57$		0			0
$58$		0			0
$59$	0.645751	+	1.11847i	0.0840697	+	0.145613i	0.904994	−	0.425423i	$-0.139875\pi$
$59$	0.645751	+	1.11847i	0.0840697	+	0.145613i	−0.820925	+	0.571036i	$0.806542\pi$
$60$		0			0
$61$	−0.354249	+	0.613577i	−0.0453569	+	0.0785604i	−0.887813	−	0.460205i	$-0.847776\pi$
$61$	−0.354249	+	0.613577i	−0.0453569	+	0.0785604i	0.842456	+	0.538766i	$0.181109\pi$
$62$	−2.00000			−0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	2.32288	−	4.02334i	0.288117	−	0.499034i
$66$		0			0
$67$	−7.64575	−	13.2428i	−0.934077	−	1.61787i	−0.776271	−	0.630399i	$-0.782891\pi$
$67$	−7.64575	−	13.2428i	−0.934077	−	1.61787i	−0.157806	−	0.987470i	$-0.550442\pi$
$68$	−3.64575	+	6.31463i	−0.442112	+	0.765761i
$69$		0			0
$70$	−1.32288	−	2.29129i	−0.158114	−	0.273861i
$71$	13.2915			1.57741			0.788706	−	0.614771i	$-0.210752\pi$
$71$	13.2915			1.57741			0.788706	+	0.614771i	$0.210752\pi$
$72$		0			0
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	0.801553	−	0.597924i	$-0.204008\pi$
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	−0.918594	+	0.395203i	$0.870674\pi$
$74$	4.96863	+	8.60591i	0.577591	+	1.00042i
$75$		0			0
$76$	6.29150			0.721685
$77$	0.854249	+	1.47960i	0.0973507	+	0.168616i
$78$		0			0
$79$	−0.354249	+	0.613577i	−0.0398561	+	0.0690328i	−0.885265	−	0.465086i	$-0.846023\pi$
$79$	−0.354249	+	0.613577i	−0.0398561	+	0.0690328i	0.845409	+	0.534119i	$0.179357\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$		0			0
$82$	−3.32288	+	5.75539i	−0.366950	+	0.635576i
$83$	−4.70850			−0.516825			−0.258412	−	0.966035i	$-0.583199\pi$
$83$	−4.70850			−0.516825			−0.258412	+	0.966035i	$0.583199\pi$
$84$		0			0
$85$	7.29150			0.790875
$86$	0.354249	−	0.613577i	0.0381996	−	0.0661637i
$87$		0			0
$88$	0.322876	+	0.559237i	0.0344187	+	0.0596149i
$89$	−7.29150	+	12.6293i	−0.772898	+	1.33870i	0.163071	+	0.986614i	$0.447860\pi$
$89$	−7.29150	+	12.6293i	−0.772898	+	1.33870i	−0.935968	+	0.352084i	$0.885473\pi$
$90$		0			0
$91$	12.2915			1.28850
$92$	−3.00000			−0.312772
$93$		0			0
$94$	−5.79150	−	10.0312i	−0.597348	−	1.03464i
$95$	−3.14575	−	5.44860i	−0.322747	−	0.559015i
$96$		0			0
$97$	−4.00000			−0.406138			−0.203069	−	0.979164i	$-0.565092\pi$
$97$	−4.00000			−0.406138			−0.203069	+	0.979164i	$0.565092\pi$
$98$	3.50000	−	6.06218i	0.353553	−	0.612372i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	−0.993258	−	0.115924i	$-0.963017\pi$
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	0.396236	−	0.918149i	$-0.370316\pi$
$102$		0			0
$103$	−3.35425	+	5.80973i	−0.330504	+	0.572450i	−0.982611	−	0.185677i	$-0.940552\pi$
$103$	−3.35425	+	5.80973i	−0.330504	+	0.572450i	0.652107	+	0.758127i	$0.273885\pi$
$104$	4.64575			0.455553
$105$		0			0
$106$	10.2915			0.999599
$107$	7.93725	−	13.7477i	0.767323	−	1.32904i	−0.171686	−	0.985152i	$-0.554922\pi$
$107$	7.93725	−	13.7477i	0.767323	−	1.32904i	0.939009	−	0.343891i	$-0.111745\pi$
$108$		0			0
$109$	0.291503	+	0.504897i	0.0279209	+	0.0483604i	0.879648	−	0.475625i	$-0.157778\pi$
$109$	0.291503	+	0.504897i	0.0279209	+	0.0483604i	−0.851727	+	0.523985i	$0.824445\pi$
$110$	0.322876	−	0.559237i	0.0307850	−	0.0533212i
$111$		0			0
$112$	1.32288	−	2.29129i	0.125000	−	0.216506i
$113$	−8.58301			−0.807421			−0.403711	−	0.914887i	$-0.632280\pi$
$113$	−8.58301			−0.807421			−0.403711	+	0.914887i	$0.632280\pi$
$114$		0			0
$115$	1.50000	+	2.59808i	0.139876	+	0.242272i
$116$		0			0
$117$		0			0
$118$	1.29150			0.118892
$119$	9.64575	+	16.7069i	0.884225	+	1.53152i
$120$		0			0
$121$	5.29150	−	9.16515i	0.481046	−	0.833196i
$122$	0.354249	+	0.613577i	0.0320722	+	0.0555506i
$123$		0			0
$124$	−1.00000	+	1.73205i	−0.0898027	+	0.155543i
$125$	1.00000			0.0894427
$126$		0			0
$127$	14.6458			1.29960			0.649800	−	0.760105i	$-0.274853\pi$
$127$	14.6458			1.29960			0.649800	+	0.760105i	$0.274853\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−2.32288	−	4.02334i	−0.203730	−	0.352870i
$131$	0.322876	−	0.559237i	0.0282098	−	0.0488608i	−0.851576	−	0.524231i	$-0.824353\pi$
$131$	0.322876	−	0.559237i	0.0282098	−	0.0488608i	0.879786	+	0.475371i	$0.157686\pi$
$132$		0			0
$133$	8.32288	−	14.4156i	0.721685	−	1.24999i
$134$	−15.2915			−1.32098
$135$		0			0
$136$	3.64575	+	6.31463i	0.312621	+	0.541475i
$137$	−7.93725	−	13.7477i	−0.678125	−	1.17455i	−0.975545	−	0.219801i	$-0.929459\pi$
$137$	−7.93725	−	13.7477i	−0.678125	−	1.17455i	0.297419	−	0.954747i	$-0.403874\pi$
$138$		0			0
$139$	10.5830			0.897639			0.448819	−	0.893622i	$-0.351845\pi$
$139$	10.5830			0.897639			0.448819	+	0.893622i	$0.351845\pi$
$140$	−2.64575			−0.223607
$141$		0			0
$142$	6.64575	−	11.5108i	0.557699	−	0.965963i
$143$	1.50000	+	2.59808i	0.125436	+	0.217262i
$144$		0			0
$145$		0			0
$146$	−2.00000			−0.165521
$147$		0			0
$148$	9.93725			0.816837
$149$	−4.93725	+	8.55157i	−0.404476	+	0.700572i	−0.994260	−	0.106988i	$-0.965879\pi$
$149$	−4.93725	+	8.55157i	−0.404476	+	0.700572i	0.589785	+	0.807561i	$0.299213\pi$
$150$		0			0
$151$	−7.00000	−	12.1244i	−0.569652	−	0.986666i	−0.996600	−	0.0823900i	$-0.973745\pi$
$151$	−7.00000	−	12.1244i	−0.569652	−	0.986666i	0.426948	−	0.904276i	$-0.359589\pi$
$152$	3.14575	−	5.44860i	0.255154	−	0.441940i
$153$		0			0
$154$	1.70850			0.137675
$155$	2.00000			0.160644
$156$		0			0
$157$	7.67712	+	13.2972i	0.612701	+	1.06123i	0.990783	+	0.135458i	$0.0432504\pi$
$157$	7.67712	+	13.2972i	0.612701	+	1.06123i	−0.378082	+	0.925772i	$0.623416\pi$
$158$	0.354249	+	0.613577i	0.0281825	+	0.0488135i
$159$		0			0
$160$	−1.00000			−0.0790569
$161$	−3.96863	+	6.87386i	−0.312772	+	0.541736i
$162$		0			0
$163$	−4.00000	+	6.92820i	−0.313304	+	0.542659i	−0.979076	−	0.203497i	$-0.934769\pi$
$163$	−4.00000	+	6.92820i	−0.313304	+	0.542659i	0.665771	+	0.746156i	$0.268103\pi$
$164$	3.32288	+	5.75539i	0.259473	+	0.449420i
$165$		0			0
$166$	−2.35425	+	4.07768i	−0.182725	+	0.316489i
$167$	−9.00000			−0.696441			−0.348220	−	0.937413i	$-0.613214\pi$
$167$	−9.00000			−0.696441			−0.348220	+	0.937413i	$0.613214\pi$
$168$		0			0
$169$	8.58301			0.660231
$170$	3.64575	−	6.31463i	0.279616	−	0.484310i
$171$		0			0
$172$	−0.354249	−	0.613577i	−0.0270112	−	0.0467848i
$173$	3.85425	−	6.67575i	0.293033	−	0.507548i	−0.681492	−	0.731825i	$-0.738669\pi$
$173$	3.85425	−	6.67575i	0.293033	−	0.507548i	0.974525	+	0.224277i	$0.0720021\pi$
$174$		0			0
$175$	1.32288	+	2.29129i	0.100000	+	0.173205i
$176$	0.645751			0.0486753
$177$		0			0
$178$	7.29150	+	12.6293i	0.546521	+	0.946603i
$179$	−5.03137	−	8.71459i	−0.376062	−	0.651359i	0.614423	−	0.788977i	$-0.289389\pi$
$179$	−5.03137	−	8.71459i	−0.376062	−	0.651359i	−0.990485	+	0.137617i	$0.956056\pi$
$180$		0			0
$181$	−11.2915			−0.839291			−0.419645	−	0.907688i	$-0.637846\pi$
$181$	−11.2915			−0.839291			−0.419645	+	0.907688i	$0.637846\pi$
$182$	6.14575	−	10.6448i	0.455553	−	0.789042i
$183$		0			0
$184$	−1.50000	+	2.59808i	−0.110581	+	0.191533i
$185$	−4.96863	−	8.60591i	−0.365301	−	0.632719i
$186$		0			0
$187$	−2.35425	+	4.07768i	−0.172160	+	0.298189i
$188$	−11.5830			−0.844777
$189$		0			0
$190$	−6.29150			−0.456434
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	−0.953912	−	0.300088i	$-0.902984\pi$
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	0.736839	+	0.676068i	$0.236317\pi$
$192$		0			0
$193$	−11.9373	−	20.6759i	−0.859262	−	1.48829i	−0.872634	−	0.488375i	$-0.837590\pi$
$193$	−11.9373	−	20.6759i	−0.859262	−	1.48829i	0.0133713	−	0.999911i	$-0.495744\pi$
$194$	−2.00000	+	3.46410i	−0.143592	+	0.248708i
$195$		0			0
$196$	−3.50000	−	6.06218i	−0.250000	−	0.433013i
$197$	4.29150			0.305757			0.152878	−	0.988245i	$-0.451146\pi$
$197$	4.29150			0.305757			0.152878	+	0.988245i	$0.451146\pi$
$198$		0			0
$199$	6.93725	+	12.0157i	0.491769	+	0.851769i	0.999955	−	0.00947853i	$-0.00301715\pi$
$199$	6.93725	+	12.0157i	0.491769	+	0.851769i	−0.508186	+	0.861247i	$0.669684\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$		0			0
$202$	−12.0000			−0.844317
$203$		0			0
$204$		0			0
$205$	3.32288	−	5.75539i	0.232080	−	0.401974i
$206$	3.35425	+	5.80973i	0.233702	+	0.404783i
$207$		0			0
$208$	2.32288	−	4.02334i	0.161062	−	0.278968i
$209$	4.06275			0.281026
$210$		0			0
$211$	−2.29150			−0.157754			−0.0788768	−	0.996884i	$-0.525133\pi$
$211$	−2.29150			−0.157754			−0.0788768	+	0.996884i	$0.525133\pi$
$212$	5.14575	−	8.91270i	0.353412	−	0.612127i
$213$		0			0
$214$	−7.93725	−	13.7477i	−0.542580	−	0.939775i
$215$	−0.354249	+	0.613577i	−0.0241596	+	0.0418456i
$216$		0			0
$217$	2.64575	+	4.58258i	0.179605	+	0.311086i
$218$	0.583005			0.0394861
$219$		0			0
$220$	−0.322876	−	0.559237i	−0.0217683	−	0.0377038i
$221$	16.9373	+	29.3362i	1.13932	+	1.97337i
$222$		0			0
$223$	−5.29150			−0.354345			−0.177173	−	0.984180i	$-0.556695\pi$
$223$	−5.29150			−0.354345			−0.177173	+	0.984180i	$0.556695\pi$
$224$	−1.32288	−	2.29129i	−0.0883883	−	0.153093i
$225$		0			0
$226$	−4.29150	+	7.43310i	−0.285467	+	0.494442i
$227$	−3.64575	−	6.31463i	−0.241977	−	0.419116i	0.719300	−	0.694699i	$-0.244463\pi$
$227$	−3.64575	−	6.31463i	−0.241977	−	0.419116i	−0.961277	+	0.275583i	$0.911129\pi$
$228$		0			0
$229$	−3.35425	+	5.80973i	−0.221655	+	0.383918i	−0.955311	−	0.295604i	$-0.904479\pi$
$229$	−3.35425	+	5.80973i	−0.221655	+	0.383918i	0.733656	+	0.679521i	$0.237813\pi$
$230$	3.00000			0.197814
$231$		0			0
$232$		0			0
$233$	−13.9373	+	24.1400i	−0.913060	+	1.58147i	−0.103343	+	0.994646i	$0.532954\pi$
$233$	−13.9373	+	24.1400i	−0.913060	+	1.58147i	−0.809717	+	0.586820i	$0.800380\pi$
$234$		0			0
$235$	5.79150	+	10.0312i	0.377796	+	0.654362i
$236$	0.645751	−	1.11847i	0.0420348	−	0.0728065i
$237$		0			0
$238$	19.2915			1.25048
$239$	8.58301			0.555188			0.277594	−	0.960698i	$-0.410463\pi$
$239$	8.58301			0.555188			0.277594	+	0.960698i	$0.410463\pi$
$240$		0			0
$241$	2.20850	+	3.82523i	0.142262	+	0.246405i	0.928348	−	0.371712i	$-0.121229\pi$
$241$	2.20850	+	3.82523i	0.142262	+	0.246405i	−0.786086	+	0.618117i	$0.787896\pi$
$242$	−5.29150	−	9.16515i	−0.340151	−	0.589158i
$243$		0			0
$244$	0.708497			0.0453569
$245$	−3.50000	+	6.06218i	−0.223607	+	0.387298i
$246$		0			0
$247$	14.6144	−	25.3128i	0.929891	−	1.61062i
$248$	1.00000	+	1.73205i	0.0635001	+	0.109985i
$249$		0			0
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	1.93725			0.122278			0.0611392	−	0.998129i	$-0.480527\pi$
$251$	1.93725			0.122278			0.0611392	+	0.998129i	$0.480527\pi$
$252$		0			0
$253$	−1.93725			−0.121794
$254$	7.32288	−	12.6836i	0.459478	−	0.795839i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	8.35425	−	14.4700i	0.521124	−	0.902613i	−0.478574	−	0.878047i	$-0.658846\pi$
$257$	8.35425	−	14.4700i	0.521124	−	0.902613i	0.999698	−	0.0245658i	$-0.00782032\pi$
$258$		0			0
$259$	13.1458	−	22.7691i	0.816837	−	1.41480i
$260$	−4.64575			−0.288117
$261$		0			0
$262$	−0.322876	−	0.559237i	−0.0199473	−	0.0345498i
$263$	7.29150	+	12.6293i	0.449613	+	0.778753i	0.998361	−	0.0572351i	$-0.0182285\pi$
$263$	7.29150	+	12.6293i	0.449613	+	0.778753i	−0.548747	+	0.835988i	$0.684895\pi$
$264$		0			0
$265$	−10.2915			−0.632202
$266$	−8.32288	−	14.4156i	−0.510308	−	0.883880i
$267$		0			0
$268$	−7.64575	+	13.2428i	−0.467039	+	0.808935i
$269$	4.93725	+	8.55157i	0.301030	+	0.521399i	0.976369	−	0.216108i	$-0.0693363\pi$
$269$	4.93725	+	8.55157i	0.301030	+	0.521399i	−0.675340	+	0.737507i	$0.736003\pi$
$270$		0			0
$271$	−12.5830	+	21.7944i	−0.764363	+	1.32392i	0.176219	+	0.984351i	$0.443613\pi$
$271$	−12.5830	+	21.7944i	−0.764363	+	1.32392i	−0.940583	+	0.339565i	$0.889720\pi$
$272$	7.29150			0.442112
$273$		0			0
$274$	−15.8745			−0.959014
$275$	−0.322876	+	0.559237i	−0.0194701	+	0.0337233i
$276$		0			0
$277$	−2.70850	−	4.69126i	−0.162738	−	0.281870i	0.773112	−	0.634270i	$-0.218699\pi$
$277$	−2.70850	−	4.69126i	−0.162738	−	0.281870i	−0.935850	+	0.352400i	$0.885366\pi$
$278$	5.29150	−	9.16515i	0.317363	−	0.549689i
$279$		0			0
$280$	−1.32288	+	2.29129i	−0.0790569	+	0.136931i
$281$	−10.5203			−0.627586			−0.313793	−	0.949491i	$-0.601600\pi$
$281$	−10.5203			−0.627586			−0.313793	+	0.949491i	$0.601600\pi$
$282$		0			0
$283$	−11.9373	−	20.6759i	−0.709596	−	1.22906i	−0.965007	−	0.262224i	$-0.915544\pi$
$283$	−11.9373	−	20.6759i	−0.709596	−	1.22906i	0.255411	−	0.966833i	$-0.417789\pi$
$284$	−6.64575	−	11.5108i	−0.394353	−	0.683039i
$285$		0			0
$286$	3.00000			0.177394
$287$	17.5830			1.03789
$288$		0			0
$289$	−18.0830	+	31.3207i	−1.06371	+	1.84239i
$290$		0			0
$291$		0			0
$292$	−1.00000	+	1.73205i	−0.0585206	+	0.101361i
$293$	−22.2915			−1.30228			−0.651142	−	0.758956i	$-0.725710\pi$
$293$	−22.2915			−1.30228			−0.651142	+	0.758956i	$0.725710\pi$
$294$		0			0
$295$	−1.29150			−0.0751942
$296$	4.96863	−	8.60591i	0.288796	−	0.500209i
$297$		0			0
$298$	4.93725	+	8.55157i	0.286007	+	0.495379i
$299$	−6.96863	+	12.0700i	−0.403006	+	0.698027i
$300$		0			0
$301$	−1.87451			−0.108045
$302$	−14.0000			−0.805609
$303$		0			0
$304$	−3.14575	−	5.44860i	−0.180421	−	0.312499i
$305$	−0.354249	−	0.613577i	−0.0202842	−	0.0351333i
$306$		0			0
$307$	−23.2915			−1.32932			−0.664658	−	0.747148i	$-0.731423\pi$
$307$	−23.2915			−1.32932			−0.664658	+	0.747148i	$0.731423\pi$
$308$	0.854249	−	1.47960i	0.0486753	−	0.0843082i
$309$		0			0
$310$	1.00000	−	1.73205i	0.0567962	−	0.0983739i
$311$	4.93725	+	8.55157i	0.279966	+	0.484915i	0.971376	−	0.237547i	$-0.0763435\pi$
$311$	4.93725	+	8.55157i	0.279966	+	0.484915i	−0.691410	+	0.722463i	$0.743010\pi$
$312$		0			0
$313$	−14.9373	+	25.8721i	−0.844304	+	1.46238i	0.0419212	+	0.999121i	$0.486652\pi$
$313$	−14.9373	+	25.8721i	−0.844304	+	1.46238i	−0.886225	+	0.463256i	$0.846681\pi$
$314$	15.3542			0.866490
$315$		0			0
$316$	0.708497			0.0398561
$317$	−16.2915	+	28.2177i	−0.915022	+	1.58486i	−0.108153	+	0.994134i	$0.534494\pi$
$317$	−16.2915	+	28.2177i	−0.915022	+	1.58486i	−0.806869	+	0.590730i	$0.798840\pi$
$318$		0			0
$319$		0			0
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$		0			0
$322$	3.96863	+	6.87386i	0.221163	+	0.383065i
$323$	45.8745			2.55253
$324$		0			0
$325$	2.32288	+	4.02334i	0.128850	+	0.223175i
$326$	4.00000	+	6.92820i	0.221540	+	0.383718i
$327$		0			0
$328$	6.64575			0.366950
$329$	−15.3229	+	26.5400i	−0.844777	+	1.46320i
$330$		0			0
$331$	−14.7288	+	25.5110i	−0.809566	+	1.40221i	0.103599	+	0.994619i	$0.466964\pi$
$331$	−14.7288	+	25.5110i	−0.809566	+	1.40221i	−0.913165	+	0.407590i	$0.866369\pi$
$332$	2.35425	+	4.07768i	0.129206	+	0.223792i
$333$		0			0
$334$	−4.50000	+	7.79423i	−0.246229	+	0.426481i
$335$	15.2915			0.835464
$336$		0			0
$337$	0.708497			0.0385943			0.0192972	−	0.999814i	$-0.493857\pi$
$337$	0.708497			0.0385943			0.0192972	+	0.999814i	$0.493857\pi$
$338$	4.29150	−	7.43310i	0.233427	−	0.404307i
$339$		0			0
$340$	−3.64575	−	6.31463i	−0.197719	−	0.342459i
$341$	−0.645751	+	1.11847i	−0.0349694	+	0.0605688i
$342$		0			0
$343$	−18.5203			−1.00000
$344$	−0.708497			−0.0381996
$345$		0			0
$346$	−3.85425	−	6.67575i	−0.207206	−	0.358891i
$347$	0.645751	+	1.11847i	0.0346657	+	0.0600428i	0.882838	−	0.469678i	$-0.155630\pi$
$347$	0.645751	+	1.11847i	0.0346657	+	0.0600428i	−0.848172	+	0.529721i	$0.822297\pi$
$348$		0			0
$349$	22.5830			1.20884			0.604420	−	0.796666i	$-0.293405\pi$
$349$	22.5830			1.20884			0.604420	+	0.796666i	$0.293405\pi$
$350$	2.64575			0.141421
$351$		0			0
$352$	0.322876	−	0.559237i	0.0172093	−	0.0298074i
$353$	−6.00000	−	10.3923i	−0.319348	−	0.553127i	0.661004	−	0.750382i	$-0.270130\pi$
$353$	−6.00000	−	10.3923i	−0.319348	−	0.553127i	−0.980352	+	0.197256i	$0.936797\pi$
$354$		0			0
$355$	−6.64575	+	11.5108i	−0.352720	+	0.610929i
$356$	14.5830			0.772898
$357$		0			0
$358$	−10.0627			−0.531833
$359$	1.29150	−	2.23695i	0.0681629	−	0.118062i	−0.829930	−	0.557868i	$-0.811620\pi$
$359$	1.29150	−	2.23695i	0.0681629	−	0.118062i	0.898093	+	0.439806i	$0.144953\pi$
$360$		0			0
$361$	−10.2915	−	17.8254i	−0.541658	−	0.938179i
$362$	−5.64575	+	9.77873i	−0.296734	+	0.513959i
$363$		0			0
$364$	−6.14575	−	10.6448i	−0.322125	−	0.557937i
$365$	2.00000			0.104685
$366$		0			0
$367$	10.6771	+	18.4933i	0.557341	+	0.965344i	0.997717	+	0.0675300i	$0.0215119\pi$
$367$	10.6771	+	18.4933i	0.557341	+	0.965344i	−0.440376	+	0.897813i	$0.645155\pi$
$368$	1.50000	+	2.59808i	0.0781929	+	0.135434i
$369$		0			0
$370$	−9.93725			−0.516613
$371$	−13.6144	−	23.5808i	−0.706823	−	1.22425i
$372$		0			0
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	−0.809591	−	0.586994i	$-0.800311\pi$
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	0.913147	+	0.407630i	$0.133645\pi$
$374$	2.35425	+	4.07768i	0.121735	+	0.210852i
$375$		0			0
$376$	−5.79150	+	10.0312i	−0.298674	+	0.517318i
$377$		0			0
$378$		0			0
$379$	12.2915			0.631372			0.315686	−	0.948864i	$-0.397765\pi$
$379$	12.2915			0.631372			0.315686	+	0.948864i	$0.397765\pi$
$380$	−3.14575	+	5.44860i	−0.161374	+	0.279507i
$381$		0			0
$382$	3.00000	+	5.19615i	0.153493	+	0.265858i
$383$	10.5000	−	18.1865i	0.536525	−	0.929288i	−0.462563	−	0.886586i	$-0.653070\pi$
$383$	10.5000	−	18.1865i	0.536525	−	0.929288i	0.999088	−	0.0427020i	$-0.0135966\pi$
$384$		0			0
$385$	−1.70850			−0.0870731
$386$	−23.8745			−1.21518
$387$		0			0
$388$	2.00000	+	3.46410i	0.101535	+	0.175863i
$389$	−12.6458	−	21.9031i	−0.641165	−	1.11053i	−0.985173	−	0.171564i	$-0.945118\pi$
$389$	−12.6458	−	21.9031i	−0.641165	−	1.11053i	0.344008	−	0.938967i	$-0.388215\pi$
$390$		0			0
$391$	−21.8745			−1.10624
$392$	−7.00000			−0.353553
$393$		0			0
$394$	2.14575	−	3.71655i	0.108101	−	0.187237i
$395$	−0.354249	−	0.613577i	−0.0178242	−	0.0308724i
$396$		0			0
$397$	0.708497	−	1.22715i	0.0355585	−	0.0615891i	−0.847698	−	0.530478i	$-0.822012\pi$
$397$	0.708497	−	1.22715i	0.0355585	−	0.0615891i	0.883257	+	0.468889i	$0.155346\pi$
$398$	13.8745			0.695466
$399$		0			0
$400$	1.00000			0.0500000
$401$	4.61438	−	7.99234i	0.230431	−	0.399118i	−0.727504	−	0.686103i	$-0.759320\pi$
$401$	4.61438	−	7.99234i	0.230431	−	0.399118i	0.957935	+	0.286985i	$0.0926530\pi$
$402$		0			0
$403$	4.64575	+	8.04668i	0.231421	+	0.400834i
$404$	−6.00000	+	10.3923i	−0.298511	+	0.517036i
$405$		0			0
$406$		0			0
$407$	6.41699			0.318079
$408$		0			0
$409$	−5.70850	−	9.88741i	−0.282267	−	0.488901i	0.689676	−	0.724118i	$-0.257753\pi$
$409$	−5.70850	−	9.88741i	−0.282267	−	0.488901i	−0.971943	+	0.235218i	$0.924420\pi$
$410$	−3.32288	−	5.75539i	−0.164105	−	0.284238i
$411$		0			0
$412$	6.70850			0.330504
$413$	−1.70850	−	2.95920i	−0.0840697	−	0.145613i
$414$		0			0
$415$	2.35425	−	4.07768i	0.115566	−	0.200165i
$416$	−2.32288	−	4.02334i	−0.113888	−	0.197260i
$417$		0			0
$418$	2.03137	−	3.51844i	0.0993577	−	0.172093i
$419$	37.9373			1.85336			0.926678	−	0.375856i	$-0.122651\pi$
$419$	37.9373			1.85336			0.926678	+	0.375856i	$0.122651\pi$
$420$		0			0
$421$	−31.8745			−1.55347			−0.776734	−	0.629828i	$-0.783125\pi$
$421$	−31.8745			−1.55347			−0.776734	+	0.629828i	$0.783125\pi$
$422$	−1.14575	+	1.98450i	−0.0557743	+	0.0966039i
$423$		0			0
$424$	−5.14575	−	8.91270i	−0.249900	−	0.432839i
$425$	−3.64575	+	6.31463i	−0.176845	+	0.306304i
$426$		0			0
$427$	0.937254	−	1.62337i	0.0453569	−	0.0785604i
$428$	−15.8745			−0.767323
$429$		0			0
$430$	0.354249	+	0.613577i	0.0170834	+	0.0295893i
$431$	−16.9373	−	29.3362i	−0.815839	−	1.41307i	−0.908724	−	0.417397i	$-0.862942\pi$
$431$	−16.9373	−	29.3362i	−0.815839	−	1.41307i	0.0928852	−	0.995677i	$-0.470391\pi$
$432$		0			0
$433$	8.00000			0.384455			0.192228	−	0.981350i	$-0.438429\pi$
$433$	8.00000			0.384455			0.192228	+	0.981350i	$0.438429\pi$
$434$	5.29150			0.254000
$435$		0			0
$436$	0.291503	−	0.504897i	0.0139604	−	0.0241802i
$437$	9.43725	+	16.3458i	0.451445	+	0.781926i
$438$		0			0
$439$	4.58301	−	7.93800i	0.218735	−	0.378860i	−0.735687	−	0.677322i	$-0.763140\pi$
$439$	4.58301	−	7.93800i	0.218735	−	0.378860i	0.954421	+	0.298462i	$0.0964737\pi$
$440$	−0.645751			−0.0307850
$441$		0			0
$442$	33.8745			1.61125
$443$	−14.3542	+	24.8623i	−0.681991	+	1.18124i	0.292381	+	0.956302i	$0.405552\pi$
$443$	−14.3542	+	24.8623i	−0.681991	+	1.18124i	−0.974372	+	0.224941i	$0.927781\pi$
$444$		0			0
$445$	−7.29150	−	12.6293i	−0.345650	−	0.598684i
$446$	−2.64575	+	4.58258i	−0.125280	+	0.216991i
$447$		0			0
$448$	−2.64575			−0.125000
$449$	−23.8118			−1.12375			−0.561873	−	0.827223i	$-0.689919\pi$
$449$	−23.8118			−1.12375			−0.561873	+	0.827223i	$0.689919\pi$
$450$		0			0
$451$	2.14575	+	3.71655i	0.101039	+	0.175006i
$452$	4.29150	+	7.43310i	0.201855	+	0.349624i
$453$		0			0
$454$	−7.29150			−0.342207
$455$	−6.14575	+	10.6448i	−0.288117	+	0.499034i
$456$		0			0
$457$	8.64575	−	14.9749i	0.404431	−	0.700495i	−0.589824	−	0.807532i	$-0.700803\pi$
$457$	8.64575	−	14.9749i	0.404431	−	0.700495i	0.994255	+	0.107037i	$0.0341362\pi$
$458$	3.35425	+	5.80973i	0.156734	+	0.271471i
$459$		0			0
$460$	1.50000	−	2.59808i	0.0699379	−	0.121136i
$461$	−17.1660			−0.799501			−0.399750	−	0.916624i	$-0.630903\pi$
$461$	−17.1660			−0.799501			−0.399750	+	0.916624i	$0.630903\pi$
$462$		0			0
$463$	15.9373			0.740667			0.370334	−	0.928899i	$-0.379243\pi$
$463$	15.9373			0.740667			0.370334	+	0.928899i	$0.379243\pi$
$464$		0			0
$465$		0			0
$466$	13.9373	+	24.1400i	0.645631	+	1.11827i
$467$	−9.64575	+	16.7069i	−0.446352	+	0.773105i	−0.998145	−	0.0608764i	$-0.980610\pi$
$467$	−9.64575	+	16.7069i	−0.446352	+	0.773105i	0.551793	+	0.833981i	$0.313944\pi$
$468$		0			0
$469$	20.2288	+	35.0372i	0.934077	+	1.61787i
$470$	11.5830			0.534284
$471$		0			0
$472$	−0.645751	−	1.11847i	−0.0297231	−	0.0514819i
$473$	−0.228757	−	0.396218i	−0.0105182	−	0.0182181i
$474$		0			0
$475$	6.29150			0.288674
$476$	9.64575	−	16.7069i	0.442112	−	0.765761i
$477$		0			0
$478$	4.29150	−	7.43310i	0.196289	−	0.339982i
$479$	−18.8745	−	32.6916i	−0.862398	−	1.49372i	−0.869608	−	0.493744i	$-0.835628\pi$
$479$	−18.8745	−	32.6916i	−0.862398	−	1.49372i	0.00720924	−	0.999974i	$-0.497705\pi$
$480$		0			0
$481$	23.0830	−	39.9809i	1.05249	−	1.82297i
$482$	4.41699			0.201189
$483$		0			0
$484$	−10.5830			−0.481046
$485$	2.00000	−	3.46410i	0.0908153	−	0.157297i
$486$		0			0
$487$	−11.9373	−	20.6759i	−0.540929	−	0.936916i	−0.998851	−	0.0479237i	$-0.984740\pi$
$487$	−11.9373	−	20.6759i	−0.540929	−	0.936916i	0.457922	−	0.888992i	$-0.348594\pi$
$488$	0.354249	−	0.613577i	0.0160361	−	0.0277753i
$489$		0			0
$490$	3.50000	+	6.06218i	0.158114	+	0.273861i
$491$	39.8745			1.79951			0.899756	−	0.436394i	$-0.143745\pi$
$491$	39.8745			1.79951			0.899756	+	0.436394i	$0.143745\pi$
$492$		0			0
$493$		0			0
$494$	−14.6144	−	25.3128i	−0.657532	−	1.13888i
$495$		0			0
$496$	2.00000			0.0898027
$497$	−35.1660			−1.57741
$498$		0			0
$499$	3.29150	−	5.70105i	0.147348	−	0.255214i	−0.782899	−	0.622149i	$-0.786260\pi$
$499$	3.29150	−	5.70105i	0.147348	−	0.255214i	0.930246	+	0.366935i	$0.119593\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$		0			0
$502$	0.968627	−	1.67771i	0.0432319	−	0.0748799i
$503$	−36.0000			−1.60516			−0.802580	−	0.596544i	$-0.796540\pi$
$503$	−36.0000			−1.60516			−0.802580	+	0.596544i	$0.796540\pi$
$504$		0			0
$505$	12.0000			0.533993
$506$	−0.968627	+	1.67771i	−0.0430607	+	0.0745834i
$507$		0			0
$508$	−7.32288	−	12.6836i	−0.324900	−	0.562743i
$509$	16.5203	−	28.6139i	0.732248	−	1.26829i	−0.223673	−	0.974664i	$-0.571805\pi$
$509$	16.5203	−	28.6139i	0.732248	−	1.26829i	0.955920	−	0.293626i	$-0.0948620\pi$
$510$		0			0
$511$	2.64575	+	4.58258i	0.117041	+	0.202721i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−8.35425	−	14.4700i	−0.368490	−	0.638244i
$515$	−3.35425	−	5.80973i	−0.147806	−	0.256007i
$516$		0			0
$517$	−7.47974			−0.328959
$518$	−13.1458	−	22.7691i	−0.577591	−	1.00042i
$519$		0			0
$520$	−2.32288	+	4.02334i	−0.101865	+	0.176435i
$521$	−4.61438	−	7.99234i	−0.202160	−	0.350151i	0.747064	−	0.664752i	$-0.231463\pi$
$521$	−4.61438	−	7.99234i	−0.202160	−	0.350151i	−0.949224	+	0.314601i	$0.898129\pi$
$522$		0			0
$523$	13.5830	−	23.5265i	0.593943	−	1.02874i	−0.399752	−	0.916623i	$-0.630904\pi$
$523$	13.5830	−	23.5265i	0.593943	−	1.02874i	0.993695	−	0.112117i	$-0.0357630\pi$
$524$	−0.645751			−0.0282098
$525$		0			0
$526$	14.5830			0.635849
$527$	−7.29150	+	12.6293i	−0.317623	+	0.550139i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	−5.14575	+	8.91270i	−0.223517	+	0.387143i
$531$		0			0
$532$	−16.6458			−0.721685
$533$	30.8745			1.33732
$534$		0			0
$535$	7.93725	+	13.7477i	0.343157	+	0.594366i
$536$	7.64575	+	13.2428i	0.330246	+	0.572003i
$537$		0			0
$538$	9.87451			0.425720
$539$	−2.26013	−	3.91466i	−0.0973507	−	0.168616i
$540$		0			0
$541$	5.22876	−	9.05647i	0.224802	−	0.389368i	−0.731458	−	0.681886i	$-0.761160\pi$
$541$	5.22876	−	9.05647i	0.224802	−	0.389368i	0.956260	+	0.292518i	$0.0944932\pi$
$542$	12.5830	+	21.7944i	0.540486	+	0.936150i
$543$		0			0
$544$	3.64575	−	6.31463i	0.156310	−	0.270737i
$545$	−0.583005			−0.0249732
$546$		0			0
$547$	−8.70850			−0.372348			−0.186174	−	0.982517i	$-0.559609\pi$
$547$	−8.70850			−0.372348			−0.186174	+	0.982517i	$0.559609\pi$
$548$	−7.93725	+	13.7477i	−0.339063	+	0.587274i
$549$		0			0
$550$	0.322876	+	0.559237i	0.0137675	+	0.0238459i
$551$		0			0
$552$		0			0
$553$	0.937254	−	1.62337i	0.0398561	−	0.0690328i
$554$	−5.41699			−0.230146
$555$		0			0
$556$	−5.29150	−	9.16515i	−0.224410	−	0.388689i
$557$	18.0203	+	31.2120i	0.763543	+	1.32250i	0.941014	+	0.338369i	$0.109875\pi$
$557$	18.0203	+	31.2120i	0.763543	+	1.32250i	−0.177471	+	0.984126i	$0.556791\pi$
$558$		0			0
$559$	−3.29150			−0.139216
$560$	1.32288	+	2.29129i	0.0559017	+	0.0968246i
$561$		0			0
$562$	−5.26013	+	9.11081i	−0.221885	+	0.384316i
$563$	−5.58301	−	9.67005i	−0.235296	−	0.407544i	0.724063	−	0.689734i	$-0.242272\pi$
$563$	−5.58301	−	9.67005i	−0.235296	−	0.407544i	−0.959359	+	0.282190i	$0.908939\pi$
$564$		0			0
$565$	4.29150	−	7.43310i	0.180545	−	0.312713i
$566$	−23.8745			−1.00352
$567$		0			0
$568$	−13.2915			−0.557699
$569$	17.9059	−	31.0139i	0.750654	−	1.30017i	−0.196853	−	0.980433i	$-0.563072\pi$
$569$	17.9059	−	31.0139i	0.750654	−	1.30017i	0.947506	−	0.319737i	$-0.103595\pi$
$570$		0			0
$571$	15.2915	+	26.4857i	0.639929	+	1.10839i	0.985448	+	0.169978i	$0.0543698\pi$
$571$	15.2915	+	26.4857i	0.639929	+	1.10839i	−0.345518	+	0.938412i	$0.612297\pi$
$572$	1.50000	−	2.59808i	0.0627182	−	0.108631i
$573$		0			0
$574$	8.79150	−	15.2273i	0.366950	−	0.635576i
$575$	−3.00000			−0.125109
$576$		0			0
$577$	13.5830	+	23.5265i	0.565468	+	0.979419i	0.997006	+	0.0773244i	$0.0246377\pi$
$577$	13.5830	+	23.5265i	0.565468	+	0.979419i	−0.431538	+	0.902095i	$0.642029\pi$
$578$	18.0830	+	31.3207i	0.752154	+	1.30277i
$579$		0			0
$580$		0			0
$581$	12.4575			0.516825
$582$		0			0
$583$	3.32288	−	5.75539i	0.137619	−	0.238364i
$584$	1.00000	+	1.73205i	0.0413803	+	0.0716728i
$585$		0			0
$586$	−11.1458	+	19.3050i	−0.460427	+	0.797483i
$587$	−8.58301			−0.354259			−0.177129	−	0.984188i	$-0.556681\pi$
$587$	−8.58301			−0.354259			−0.177129	+	0.984188i	$0.556681\pi$
$588$		0			0
$589$	12.5830			0.518474
$590$	−0.645751	+	1.11847i	−0.0265852	+	0.0460468i
$591$		0			0
$592$	−4.96863	−	8.60591i	−0.204209	−	0.353701i
$593$	16.9373	−	29.3362i	0.695530	−	1.20469i	−0.274472	−	0.961595i	$-0.588503\pi$
$593$	16.9373	−	29.3362i	0.695530	−	1.20469i	0.970002	−	0.243098i	$-0.0781635\pi$
$594$		0			0
$595$	−19.2915			−0.790875
$596$	9.87451			0.404476
$597$		0			0
$598$	6.96863	+	12.0700i	0.284968	+	0.493580i
$599$	−15.0000	−	25.9808i	−0.612883	−	1.06155i	−0.990752	−	0.135686i	$-0.956676\pi$
$599$	−15.0000	−	25.9808i	−0.612883	−	1.06155i	0.377869	−	0.925859i	$-0.376657\pi$
$600$		0			0
$601$	31.1660			1.27129			0.635644	−	0.771982i	$-0.280735\pi$
$601$	31.1660			1.27129			0.635644	+	0.771982i	$0.280735\pi$
$602$	−0.937254	+	1.62337i	−0.0381996	+	0.0661637i
$603$		0			0
$604$	−7.00000	+	12.1244i	−0.284826	+	0.493333i
$605$	5.29150	+	9.16515i	0.215130	+	0.372616i
$606$		0			0
$607$	18.6144	−	32.2410i	0.755534	−	1.30862i	−0.189574	−	0.981866i	$-0.560711\pi$
$607$	18.6144	−	32.2410i	0.755534	−	1.30862i	0.945108	−	0.326757i	$-0.105956\pi$
$608$	−6.29150			−0.255154
$609$		0			0
$610$	−0.708497			−0.0286862
$611$	−26.9059	+	46.6024i	−1.08850	+	1.88533i
$612$		0			0
$613$	8.32288	+	14.4156i	0.336158	+	0.582242i	0.983707	−	0.179782i	$-0.0575391\pi$
$613$	8.32288	+	14.4156i	0.336158	+	0.582242i	−0.647549	+	0.762024i	$0.724206\pi$
$614$	−11.6458	+	20.1710i	−0.469984	+	0.814037i
$615$		0			0
$616$	−0.854249	−	1.47960i	−0.0344187	−	0.0596149i
$617$	−4.70850			−0.189557			−0.0947785	−	0.995498i	$-0.530214\pi$
$617$	−4.70850			−0.189557			−0.0947785	+	0.995498i	$0.530214\pi$
$618$		0			0
$619$	−13.4373	−	23.2740i	−0.540089	−	0.935461i	−0.998898	−	0.0469266i	$-0.985057\pi$
$619$	−13.4373	−	23.2740i	−0.540089	−	0.935461i	0.458810	−	0.888535i	$-0.348276\pi$
$620$	−1.00000	−	1.73205i	−0.0401610	−	0.0695608i
$621$		0			0
$622$	9.87451			0.395932
$623$	19.2915	−	33.4139i	0.772898	−	1.33870i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	14.9373	+	25.8721i	0.597013	+	1.03406i
$627$		0			0
$628$	7.67712	−	13.2972i	0.306351	−	0.530615i
$629$	72.4575			2.88907
$630$		0			0
$631$	33.7490			1.34353			0.671764	−	0.740766i	$-0.265537\pi$
$631$	33.7490			1.34353			0.671764	+	0.740766i	$0.265537\pi$
$632$	0.354249	−	0.613577i	0.0140913	−	0.0244068i
$633$		0			0
$634$	16.2915	+	28.2177i	0.647018	+	1.12067i
$635$	−7.32288	+	12.6836i	−0.290599	+	0.503333i
$636$		0			0
$637$	−32.5203			−1.28850
$638$		0			0
$639$		0			0
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−6.55163	−	11.3478i	−0.258774	−	0.448210i	0.707140	−	0.707074i	$-0.249985\pi$
$641$	−6.55163	−	11.3478i	−0.258774	−	0.448210i	−0.965914	+	0.258864i	$0.916652\pi$
$642$		0			0
$643$	6.70850			0.264557			0.132279	−	0.991213i	$-0.457771\pi$
$643$	6.70850			0.264557			0.132279	+	0.991213i	$0.457771\pi$
$644$	7.93725			0.312772
$645$		0			0
$646$	22.9373	−	39.7285i	0.902454	−	1.56310i
$647$	7.08301	+	12.2681i	0.278462	+	0.482310i	0.971003	−	0.239069i	$-0.0768421\pi$
$647$	7.08301	+	12.2681i	0.278462	+	0.482310i	−0.692541	+	0.721379i	$0.743509\pi$
$648$		0			0
$649$	0.416995	−	0.722256i	0.0163685	−	0.0283510i
$650$	4.64575			0.182221
$651$		0			0
$652$	8.00000			0.313304
$653$	7.72876	−	13.3866i	0.302450	−	0.523858i	−0.674241	−	0.738512i	$-0.735529\pi$
$653$	7.72876	−	13.3866i	0.302450	−	0.523858i	0.976690	+	0.214654i	$0.0688623\pi$
$654$		0			0
$655$	0.322876	+	0.559237i	0.0126158	+	0.0218512i
$656$	3.32288	−	5.75539i	0.129736	−	0.224710i
$657$		0			0
$658$	15.3229	+	26.5400i	0.597348	+	1.03464i
$659$	−13.2915			−0.517763			−0.258882	−	0.965909i	$-0.583354\pi$
$659$	−13.2915			−0.517763			−0.258882	+	0.965909i	$0.583354\pi$
$660$		0			0
$661$	−11.2915	−	19.5575i	−0.439189	−	0.760697i	0.558439	−	0.829546i	$-0.311401\pi$
$661$	−11.2915	−	19.5575i	−0.439189	−	0.760697i	−0.997627	+	0.0688490i	$0.978067\pi$
$662$	14.7288	+	25.5110i	0.572449	+	0.991511i
$663$		0			0
$664$	4.70850			0.182725
$665$	8.32288	+	14.4156i	0.322747	+	0.559015i
$666$		0			0
$667$		0			0
$668$	4.50000	+	7.79423i	0.174110	+	0.301568i
$669$		0			0
$670$	7.64575	−	13.2428i	0.295381	−	0.511615i
$671$	0.457513			0.0176621
$672$		0			0
$673$	−1.41699			−0.0546211			−0.0273106	−	0.999627i	$-0.508694\pi$
$673$	−1.41699			−0.0546211			−0.0273106	+	0.999627i	$0.508694\pi$
$674$	0.354249	−	0.613577i	0.0136451	−	0.0236341i
$675$		0			0
$676$	−4.29150	−	7.43310i	−0.165058	−	0.285888i
$677$	8.56275	−	14.8311i	0.329093	−	0.570006i	−0.653239	−	0.757152i	$-0.726590\pi$
$677$	8.56275	−	14.8311i	0.329093	−	0.570006i	0.982332	+	0.187146i	$0.0599237\pi$
$678$		0			0
$679$	10.5830			0.406138
$680$	−7.29150			−0.279616
$681$		0			0
$682$	0.645751	+	1.11847i	0.0247271	+	0.0428286i
$683$	−14.5830	−	25.2585i	−0.558003	−	0.966490i	−0.997663	−	0.0683255i	$-0.978234\pi$
$683$	−14.5830	−	25.2585i	−0.558003	−	0.966490i	0.439660	−	0.898164i	$-0.355099\pi$
$684$		0			0
$685$	15.8745			0.606534
$686$	−9.26013	+	16.0390i	−0.353553	+	0.612372i
$687$		0			0
$688$	−0.354249	+	0.613577i	−0.0135056	+	0.0233924i
$689$	−23.9059	−	41.4062i	−0.910742	−	1.57745i
$690$		0			0
$691$	6.70850	−	11.6195i	0.255203	−	0.442025i	−0.709747	−	0.704456i	$-0.751191\pi$
$691$	6.70850	−	11.6195i	0.255203	−	0.442025i	0.964951	+	0.262431i	$0.0845243\pi$
$692$	−7.70850			−0.293033
$693$		0			0
$694$	1.29150			0.0490248
$695$	−5.29150	+	9.16515i	−0.200718	+	0.347654i
$696$		0			0
$697$	24.2288	+	41.9654i	0.917730	+	1.58955i
$698$	11.2915	−	19.5575i	0.427390	−	0.740261i
$699$		0			0
$700$	1.32288	−	2.29129i	0.0500000	−	0.0866025i
$701$	30.4575			1.15036			0.575182	−	0.818025i	$-0.304931\pi$
$701$	30.4575			1.15036			0.575182	+	0.818025i	$0.304931\pi$
$702$		0			0
$703$	−31.2601	−	54.1441i	−1.17900	−	2.04208i
$704$	−0.322876	−	0.559237i	−0.0121688	−	0.0210770i
$705$		0			0
$706$	−12.0000			−0.451626
$707$	15.8745	+	27.4955i	0.597022	+	1.03407i
$708$		0			0
$709$	10.5830	−	18.3303i	0.397453	−	0.688409i	−0.595958	−	0.803016i	$-0.703227\pi$
$709$	10.5830	−	18.3303i	0.397453	−	0.688409i	0.993411	+	0.114607i	$0.0365608\pi$
$710$	6.64575	+	11.5108i	0.249411	+	0.431992i
$711$		0			0
$712$	7.29150	−	12.6293i	0.273261	−	0.473301i
$713$	−6.00000			−0.224702
$714$		0			0
$715$	−3.00000			−0.112194
$716$	−5.03137	+	8.71459i	−0.188031	+	0.325680i
$717$		0			0
$718$	−1.29150	−	2.23695i	−0.0481984	−	0.0834822i
$719$	−10.0627	+	17.4292i	−0.375277	+	0.649999i	−0.990368	−	0.138457i	$-0.955786\pi$
$719$	−10.0627	+	17.4292i	−0.375277	+	0.649999i	0.615091	+	0.788456i	$0.289119\pi$
$720$		0			0
$721$	8.87451	−	15.3711i	0.330504	−	0.572450i
$722$	−20.5830			−0.766020
$723$		0			0
$724$	5.64575	+	9.77873i	0.209823	+	0.363424i
$725$		0			0
$726$		0			0
$727$	25.3542			0.940337			0.470169	−	0.882577i	$-0.344193\pi$
$727$	25.3542			0.940337			0.470169	+	0.882577i	$0.344193\pi$
$728$	−12.2915			−0.455553
$729$		0			0
$730$	1.00000	−	1.73205i	0.0370117	−	0.0641061i
$731$	−2.58301	−	4.47390i	−0.0955359	−	0.165473i
$732$		0			0
$733$	−24.2601	+	42.0198i	−0.896068	+	1.55204i	−0.0635915	+	0.997976i	$0.520255\pi$
$733$	−24.2601	+	42.0198i	−0.896068	+	1.55204i	−0.832477	+	0.554060i	$0.813078\pi$
$734$	21.3542			0.788200
$735$		0			0
$736$	3.00000			0.110581
$737$	−4.93725	+	8.55157i	−0.181866	+	0.315001i
$738$		0			0
$739$	16.1458	+	27.9653i	0.593931	+	1.02872i	0.993697	+	0.112101i	$0.0357582\pi$
$739$	16.1458	+	27.9653i	0.593931	+	1.02872i	−0.399766	+	0.916617i	$0.630909\pi$
$740$	−4.96863	+	8.60591i	−0.182650	+	0.316360i
$741$		0			0
$742$	−27.2288			−0.999599
$743$	−34.7490			−1.27482			−0.637409	−	0.770526i	$-0.719994\pi$
$743$	−34.7490			−1.27482			−0.637409	+	0.770526i	$0.719994\pi$
$744$		0			0
$745$	−4.93725	−	8.55157i	−0.180887	−	0.313305i
$746$	−2.00000	−	3.46410i	−0.0732252	−	0.126830i
$747$		0			0
$748$	4.70850			0.172160
$749$	−21.0000	+	36.3731i	−0.767323	+	1.32904i
$750$		0			0
$751$	−17.9373	+	31.0682i	−0.654540	+	1.13370i	0.327469	+	0.944862i	$0.393804\pi$
$751$	−17.9373	+	31.0682i	−0.654540	+	1.13370i	−0.982009	+	0.188834i	$0.939529\pi$
$752$	5.79150	+	10.0312i	0.211194	+	0.365799i
$753$		0			0
$754$		0			0
$755$	14.0000			0.509512
$756$		0			0
$757$	−9.16601			−0.333144			−0.166572	−	0.986029i	$-0.553270\pi$
$757$	−9.16601			−0.333144			−0.166572	+	0.986029i	$0.553270\pi$
$758$	6.14575	−	10.6448i	0.223224	−	0.386635i
$759$		0			0
$760$	3.14575	+	5.44860i	0.114108	+	0.197642i
$761$	14.0314	−	24.3031i	0.508637	−	0.880985i	−0.491313	−	0.870983i	$-0.663483\pi$
$761$	14.0314	−	24.3031i	0.508637	−	0.880985i	0.999950	−	0.0100019i	$-0.00318375\pi$
$762$		0			0
$763$	−0.771243	−	1.33583i	−0.0279209	−	0.0483604i
$764$	6.00000			0.217072
$765$		0			0
$766$	−10.5000	−	18.1865i	−0.379380	−	0.657106i
$767$	−3.00000	−	5.19615i	−0.108324	−	0.187622i
$768$		0			0
$769$	−12.1660			−0.438718			−0.219359	−	0.975644i	$-0.570397\pi$
$769$	−12.1660			−0.438718			−0.219359	+	0.975644i	$0.570397\pi$
$770$	−0.854249	+	1.47960i	−0.0307850	+	0.0533212i
$771$		0			0
$772$	−11.9373	+	20.6759i	−0.429631	+	0.744143i
$773$	9.43725	+	16.3458i	0.339434	+	0.587918i	0.984326	−	0.176356i	$-0.0564310\pi$
$773$	9.43725	+	16.3458i	0.339434	+	0.587918i	−0.644892	+	0.764274i	$0.723098\pi$
$774$		0			0
$775$	−1.00000	+	1.73205i	−0.0359211	+	0.0622171i
$776$	4.00000			0.143592
$777$		0			0
$778$	−25.2915			−0.906744
$779$	20.9059	−	36.2100i	0.749031	−	1.29736i
$780$		0			0
$781$	−4.29150	−	7.43310i	−0.153562	−	0.265977i
$782$	−10.9373	+	18.9439i	−0.391115	+	0.677432i
$783$		0			0
$784$	−3.50000	+	6.06218i	−0.125000	+	0.216506i
$785$	−15.3542			−0.548017
$786$		0			0
$787$	−7.22876	−	12.5206i	−0.257677	−	0.446310i	0.707942	−	0.706271i	$-0.249624\pi$
$787$	−7.22876	−	12.5206i	−0.257677	−	0.446310i	−0.965619	+	0.259960i	$0.916290\pi$
$788$	−2.14575	−	3.71655i	−0.0764392	−	0.132397i
$789$		0			0
$790$	−0.708497			−0.0252072
$791$	22.7085			0.807421
$792$		0			0
$793$	1.64575	−	2.85052i	0.0584423	−	0.101225i
$794$	−0.708497	−	1.22715i	−0.0251436	−	0.0435500i
$795$		0			0
$796$	6.93725	−	12.0157i	0.245884	−	0.425884i
$797$	25.7490			0.912077			0.456038	−	0.889960i	$-0.349268\pi$
$797$	25.7490			0.912077			0.456038	+	0.889960i	$0.349268\pi$
$798$		0			0
$799$	−84.4575			−2.98789
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$		0			0
$802$	−4.61438	−	7.99234i	−0.162939	−	0.282219i
$803$	−0.645751	+	1.11847i	−0.0227881	+	0.0394701i
$804$		0			0
$805$	−3.96863	−	6.87386i	−0.139876	−	0.242272i
$806$	9.29150			0.327279
$807$		0			0
$808$	6.00000	+	10.3923i	0.211079	+	0.365600i
$809$	−17.9059	−	31.0139i	−0.629537	−	1.09039i	−0.987645	−	0.156710i	$-0.949911\pi$
$809$	−17.9059	−	31.0139i	−0.629537	−	1.09039i	0.358107	−	0.933680i	$-0.383422\pi$
$810$		0			0
$811$	14.8745			0.522315			0.261157	−	0.965296i	$-0.415896\pi$
$811$	14.8745			0.522315			0.261157	+	0.965296i	$0.415896\pi$
$812$		0			0
$813$		0			0
$814$	3.20850	−	5.55728i	0.112458	−	0.194783i
$815$	−4.00000	−	6.92820i	−0.140114	−	0.242684i
$816$		0			0
$817$	−2.22876	+	3.86032i	−0.0779743	+	0.135055i
$818$	−11.4170			−0.399186
$819$		0			0
$820$	−6.64575			−0.232080
$821$	7.93725	−	13.7477i	0.277012	−	0.479799i	−0.693629	−	0.720333i	$-0.743989\pi$
$821$	7.93725	−	13.7477i	0.277012	−	0.479799i	0.970641	+	0.240534i	$0.0773225\pi$
$822$		0			0
$823$	14.6458	+	25.3672i	0.510519	+	0.884244i	0.999926	+	0.0121890i	$0.00387996\pi$
$823$	14.6458	+	25.3672i	0.510519	+	0.884244i	−0.489407	+	0.872056i	$0.662787\pi$
$824$	3.35425	−	5.80973i	0.116851	−	0.202392i
$825$		0			0
$826$	−3.41699			−0.118892
$827$	27.4170			0.953382			0.476691	−	0.879071i	$-0.341836\pi$
$827$	27.4170			0.953382			0.476691	+	0.879071i	$0.341836\pi$
$828$		0			0
$829$	−20.9373	−	36.2644i	−0.727181	−	1.25951i	−0.958070	−	0.286534i	$-0.907497\pi$
$829$	−20.9373	−	36.2644i	−0.727181	−	1.25951i	0.230889	−	0.972980i	$-0.425837\pi$
$830$	−2.35425	−	4.07768i	−0.0817172	−	0.141538i
$831$		0			0
$832$	−4.64575			−0.161062
$833$	−25.5203	−	44.2024i	−0.884225	−	1.53152i
$834$		0			0
$835$	4.50000	−	7.79423i	0.155729	−	0.269730i
$836$	−2.03137	−	3.51844i	−0.0702565	−	0.121688i
$837$		0			0
$838$	18.9686	−	32.8546i	0.655260	−	1.13494i
$839$	−12.4575			−0.430081			−0.215041	−	0.976605i	$-0.568988\pi$
$839$	−12.4575			−0.430081			−0.215041	+	0.976605i	$0.568988\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	−15.9373	+	27.6041i	−0.549234	+	0.951301i
$843$		0			0
$844$	1.14575	+	1.98450i	0.0394384	+	0.0683093i
$845$	−4.29150	+	7.43310i	−0.147632	+	0.255706i
$846$		0			0
$847$	−14.0000	+	24.2487i	−0.481046	+	0.833196i
$848$	−10.2915			−0.353412
$849$		0			0
$850$	3.64575	+	6.31463i	0.125048	+	0.216590i
$851$	14.9059	+	25.8177i	0.510967	+	0.885021i
$852$		0			0
$853$	2.18824			0.0749238			0.0374619	−	0.999298i	$-0.488073\pi$
$853$	2.18824			0.0749238			0.0374619	+	0.999298i	$0.488073\pi$
$854$	−0.937254	−	1.62337i	−0.0320722	−	0.0555506i
$855$		0			0
$856$	−7.93725	+	13.7477i	−0.271290	+	0.469888i
$857$	−7.93725	−	13.7477i	−0.271131	−	0.469613i	0.698020	−	0.716078i	$-0.254064\pi$
$857$	−7.93725	−	13.7477i	−0.271131	−	0.469613i	−0.969152	+	0.246464i	$0.920731\pi$
$858$		0			0
$859$	−0.583005	+	1.00979i	−0.0198919	+	0.0344538i	−0.875800	−	0.482674i	$-0.839666\pi$
$859$	−0.583005	+	1.00979i	−0.0198919	+	0.0344538i	0.855908	+	0.517128i	$0.172999\pi$
$860$	0.708497			0.0241596
$861$		0			0
$862$	−33.8745			−1.15377
$863$	10.0830	−	17.4643i	0.343229	−	0.594491i	−0.641801	−	0.766871i	$-0.721812\pi$
$863$	10.0830	−	17.4643i	0.343229	−	0.594491i	0.985030	+	0.172380i	$0.0551458\pi$
$864$		0			0
$865$	3.85425	+	6.67575i	0.131048	+	0.226982i
$866$	4.00000	−	6.92820i	0.135926	−	0.235430i
$867$		0			0
$868$	2.64575	−	4.58258i	0.0898027	−	0.155543i
$869$	0.457513			0.0155201
$870$		0			0
$871$	35.5203	+	61.5229i	1.20356	+	2.08462i
$872$	−0.291503	−	0.504897i	−0.00987152	−	0.0170980i
$873$		0			0
$874$	18.8745			0.638440
$875$	−2.64575			−0.0894427
$876$		0			0
$877$	−14.8431	+	25.7091i	−0.501217	+	0.868133i	0.498782	+	0.866727i	$0.333781\pi$
$877$	−14.8431	+	25.7091i	−0.501217	+	0.868133i	−0.999999	+	0.00140590i	$0.999552\pi$
$878$	−4.58301	−	7.93800i	−0.154669	−	0.267894i
$879$		0			0
$880$	−0.322876	+	0.559237i	−0.0108841	+	0.0188519i
$881$	−42.6458			−1.43677			−0.718386	−	0.695645i	$-0.755119\pi$
$881$	−42.6458			−1.43677			−0.718386	+	0.695645i	$0.755119\pi$
$882$		0			0
$883$	11.4170			0.384212			0.192106	−	0.981374i	$-0.438468\pi$
$883$	11.4170			0.384212			0.192106	+	0.981374i	$0.438468\pi$
$884$	16.9373	−	29.3362i	0.569661	−	0.986683i
$885$		0			0
$886$	14.3542	+	24.8623i	0.482240	+	0.835265i
$887$	−20.5830	+	35.6508i	−0.691110	+	1.19704i	0.280365	+	0.959893i	$0.409545\pi$
$887$	−20.5830	+	35.6508i	−0.691110	+	1.19704i	−0.971475	+	0.237144i	$0.923789\pi$
$888$		0			0
$889$	−38.7490			−1.29960
$890$	−14.5830			−0.488823
$891$		0			0
$892$	2.64575	+	4.58258i	0.0885863	+	0.153436i
$893$	36.4373	+	63.1112i	1.21933	+	2.11193i
$894$		0			0
$895$	10.0627			0.336361
$896$	−1.32288	+	2.29129i	−0.0441942	+	0.0765466i
$897$		0			0
$898$	−11.9059	+	20.6216i	−0.397304	+	0.688151i
$899$		0			0
$900$		0			0
$901$	37.5203	−	64.9870i	1.24998	−	2.16503i
$902$	4.29150			0.142891
$903$		0			0
$904$	8.58301			0.285467
$905$	5.64575	−	9.77873i	0.187671	−	0.325056i
$906$		0			0
$907$	−10.8745	−	18.8352i	−0.361082	−	0.625413i	0.627057	−	0.778973i	$-0.284259\pi$
$907$	−10.8745	−	18.8352i	−0.361082	−	0.625413i	−0.988139	+	0.153561i	$0.950926\pi$
$908$	−3.64575	+	6.31463i	−0.120989	+	0.209558i
$909$		0			0
$910$	6.14575	+	10.6448i	0.203730	+	0.352870i
$911$	−47.6235			−1.57784			−0.788919	−	0.614497i	$-0.789359\pi$
$911$	−47.6235			−1.57784			−0.788919	+	0.614497i	$0.789359\pi$
$912$		0			0
$913$	1.52026	+	2.63317i	0.0503132	+	0.0871451i
$914$	−8.64575	−	14.9749i	−0.285976	−	0.495325i
$915$		0			0
$916$	6.70850			0.221655
$917$	−0.854249	+	1.47960i	−0.0282098	+	0.0488608i
$918$		0			0
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	−0.924427	−	0.381358i	$-0.875456\pi$
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	0.792480	+	0.609898i	$0.208790\pi$
$920$	−1.50000	−	2.59808i	−0.0494535	−	0.0856560i
$921$		0			0
$922$	−8.58301	+	14.8662i	−0.282666	+	0.489592i
$923$	−61.7490			−2.03249
$924$		0			0
$925$	9.93725			0.326735
$926$	7.96863	−	13.8021i	0.261865	−	0.453564i
$927$		0			0
$928$		0			0
$929$	6.55163	−	11.3478i	0.214952	−	0.372308i	−0.738306	−	0.674466i	$-0.764374\pi$
$929$	6.55163	−	11.3478i	0.214952	−	0.372308i	0.953258	+	0.302158i	$0.0977071\pi$
$930$		0			0
$931$	−22.0203	+	38.1402i	−0.721685	+	1.24999i
$932$	27.8745			0.913060
$933$		0			0
$934$	9.64575	+	16.7069i	0.315619	+	0.546667i
$935$	−2.35425	−	4.07768i	−0.0769922	−	0.133354i
$936$		0			0
$937$	−57.6235			−1.88248			−0.941239	−	0.337741i	$-0.890337\pi$
$937$	−57.6235			−1.88248			−0.941239	+	0.337741i	$0.890337\pi$
$938$	40.4575			1.32098
$939$		0			0
$940$	5.79150	−	10.0312i	0.188898	−	0.327181i
$941$	−1.70850	−	2.95920i	−0.0556954	−	0.0964673i	0.836833	−	0.547458i	$-0.184404\pi$
$941$	−1.70850	−	2.95920i	−0.0556954	−	0.0964673i	−0.892529	+	0.450990i	$0.851071\pi$
$942$		0			0
$943$	−9.96863	+	17.2662i	−0.324623	+	0.562264i
$944$	−1.29150			−0.0420348
$945$		0			0
$946$	−0.457513			−0.0148750
$947$	−22.5203	+	39.0062i	−0.731810	+	1.26753i	0.224299	+	0.974520i	$0.427991\pi$
$947$	−22.5203	+	39.0062i	−0.731810	+	1.26753i	−0.956109	+	0.293012i	$0.905342\pi$
$948$		0			0
$949$	4.64575	+	8.04668i	0.150807	+	0.261206i
$950$	3.14575	−	5.44860i	0.102062	−	0.176776i
$951$		0			0
$952$	−9.64575	−	16.7069i	−0.312621	−	0.541475i
$953$		0			0			−	1.00000i	$-0.5\pi$
$953$		0			0				1.00000i	$0.5\pi$
$954$		0			0
$955$	−3.00000	−	5.19615i	−0.0970777	−	0.168144i
$956$	−4.29150	−	7.43310i	−0.138797	−	0.240404i
$957$		0			0
$958$	−37.7490			−1.21962
$959$	21.0000	+	36.3731i	0.678125	+	1.17455i
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	−23.0830	−	39.9809i	−0.744226	−	1.28904i
$963$		0			0
$964$	2.20850	−	3.82523i	0.0711309	−	0.123202i
$965$	23.8745			0.768548
$966$		0			0
$967$	−29.2915			−0.941951			−0.470976	−	0.882146i	$-0.656098\pi$
$967$	−29.2915			−0.941951			−0.470976	+	0.882146i	$0.656098\pi$
$968$	−5.29150	+	9.16515i	−0.170075	+	0.294579i
$969$		0			0
$970$	−2.00000	−	3.46410i	−0.0642161	−	0.111226i
$971$	26.9059	−	46.6024i	0.863451	−	1.49554i	−0.00512643	−	0.999987i	$-0.501632\pi$
$971$	26.9059	−	46.6024i	0.863451	−	1.49554i	0.868577	−	0.495554i	$-0.165035\pi$
$972$		0			0
$973$	−28.0000			−0.897639
$974$	−23.8745			−0.764989
$975$		0			0
$976$	−0.354249	−	0.613577i	−0.0113392	−	0.0196401i
$977$	21.0000	+	36.3731i	0.671850	+	1.16368i	0.977379	+	0.211495i	$0.0678332\pi$
$977$	21.0000	+	36.3731i	0.671850	+	1.16368i	−0.305530	+	0.952183i	$0.598833\pi$
$978$		0			0
$979$	9.41699			0.300968
$980$	7.00000			0.223607
$981$		0			0
$982$	19.9373	−	34.5323i	0.636223	−	1.10197i
$983$	24.6660	+	42.7228i	0.786724	+	1.36265i	0.927964	+	0.372670i	$0.121558\pi$
$983$	24.6660	+	42.7228i	0.786724	+	1.36265i	−0.141240	+	0.989975i	$0.545109\pi$
$984$		0			0
$985$	−2.14575	+	3.71655i	−0.0683693	+	0.118419i
$986$		0			0
$987$		0			0
$988$	−29.2288			−0.929891
$989$	1.06275	−	1.84073i	0.0337934	−	0.0585318i
$990$		0			0
$991$	2.64575	+	4.58258i	0.0840451	+	0.145570i	0.904984	−	0.425446i	$-0.139883\pi$
$991$	2.64575	+	4.58258i	0.0840451	+	0.145570i	−0.820939	+	0.571016i	$0.806549\pi$
$992$	1.00000	−	1.73205i	0.0317500	−	0.0549927i
$993$		0			0
$994$	−17.5830	+	30.4547i	−0.557699	+	0.965963i
$995$	−13.8745			−0.439851
$996$		0			0
$997$	23.8745	+	41.3519i	0.756113	+	1.30963i	0.944819	+	0.327593i	$0.106237\pi$
$997$	23.8745	+	41.3519i	0.756113	+	1.30963i	−0.188706	+	0.982034i	$0.560429\pi$
$998$	−3.29150	−	5.70105i	−0.104191	−	0.180464i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.k.j.541.1	yes	4
3.2	odd	2		630.2.k.i.541.1	yes	4
7.2	even	3		4410.2.a.bq.1.2		2
7.4	even	3	inner	630.2.k.j.361.1	yes	4
7.5	odd	6		4410.2.a.bo.1.2		2
21.2	odd	6		4410.2.a.bv.1.1		2
21.5	even	6		4410.2.a.ca.1.1		2
21.11	odd	6		630.2.k.i.361.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.k.i.361.1	✓	4	21.11	odd	6
630.2.k.i.541.1	yes	4	3.2	odd	2
630.2.k.j.361.1	yes	4	7.4	even	3	inner
630.2.k.j.541.1	yes	4	1.1	even	1	trivial
4410.2.a.bo.1.2		2	7.5	odd	6
4410.2.a.bq.1.2		2	7.2	even	3
4410.2.a.bv.1.1		2	21.2	odd	6
4410.2.a.ca.1.1		2	21.5	even	6

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -2.64575 q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -2.64575 q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +(-0.322876 - 0.559237i) q^{11} -4.64575 q^{13} +(-1.32288 + 2.29129i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.64575 - 6.31463i) q^{17} +(-3.14575 + 5.44860i) q^{19} +1.00000 q^{20} -0.645751 q^{22} +(1.50000 - 2.59808i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-2.32288 + 4.02334i) q^{26} +(1.32288 + 2.29129i) q^{28} +(-1.00000 - 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} -7.29150 q^{34} +(1.32288 - 2.29129i) q^{35} +(-4.96863 + 8.60591i) q^{37} +(3.14575 + 5.44860i) q^{38} +(0.500000 - 0.866025i) q^{40} -6.64575 q^{41} +0.708497 q^{43} +(-0.322876 + 0.559237i) q^{44} +(-1.50000 - 2.59808i) q^{46} +(5.79150 - 10.0312i) q^{47} +7.00000 q^{49} -1.00000 q^{50} +(2.32288 + 4.02334i) q^{52} +(5.14575 + 8.91270i) q^{53} +0.645751 q^{55} +2.64575 q^{56} +(0.645751 + 1.11847i) q^{59} +(-0.354249 + 0.613577i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(2.32288 - 4.02334i) q^{65} +(-7.64575 - 13.2428i) q^{67} +(-3.64575 + 6.31463i) q^{68} +(-1.32288 - 2.29129i) q^{70} +13.2915 q^{71} +(-1.00000 - 1.73205i) q^{73} +(4.96863 + 8.60591i) q^{74} +6.29150 q^{76} +(0.854249 + 1.47960i) q^{77} +(-0.354249 + 0.613577i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-3.32288 + 5.75539i) q^{82} -4.70850 q^{83} +7.29150 q^{85} +(0.354249 - 0.613577i) q^{86} +(0.322876 + 0.559237i) q^{88} +(-7.29150 + 12.6293i) q^{89} +12.2915 q^{91} -3.00000 q^{92} +(-5.79150 - 10.0312i) q^{94} +(-3.14575 - 5.44860i) q^{95} -4.00000 q^{97} +(3.50000 - 6.06218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{8} + 2 q^{10} + 4 q^{11} - 8 q^{13} - 2 q^{16} - 4 q^{17} - 2 q^{19} + 4 q^{20} + 8 q^{22} + 6 q^{23} - 2 q^{25} - 4 q^{26} - 4 q^{31} + 2 q^{32} - 8 q^{34} - 4 q^{37} + 2 q^{38} + 2 q^{40} - 16 q^{41} + 24 q^{43} + 4 q^{44} - 6 q^{46} + 2 q^{47} + 28 q^{49} - 4 q^{50} + 4 q^{52} + 10 q^{53} - 8 q^{55} - 8 q^{59} - 12 q^{61} - 8 q^{62} + 4 q^{64} + 4 q^{65} - 20 q^{67} - 4 q^{68} + 32 q^{71} - 4 q^{73} + 4 q^{74} + 4 q^{76} + 14 q^{77} - 12 q^{79} - 2 q^{80} - 8 q^{82} - 40 q^{83} + 8 q^{85} + 12 q^{86} - 4 q^{88} - 8 q^{89} + 28 q^{91} - 12 q^{92} - 2 q^{94} - 2 q^{95} - 16 q^{97} + 14 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^8 + 2 * q^10 + 4 * q^11 - 8 * q^13 - 2 * q^16 - 4 * q^17 - 2 * q^19 + 4 * q^20 + 8 * q^22 + 6 * q^23 - 2 * q^25 - 4 * q^26 - 4 * q^31 + 2 * q^32 - 8 * q^34 - 4 * q^37 + 2 * q^38 + 2 * q^40 - 16 * q^41 + 24 * q^43 + 4 * q^44 - 6 * q^46 + 2 * q^47 + 28 * q^49 - 4 * q^50 + 4 * q^52 + 10 * q^53 - 8 * q^55 - 8 * q^59 - 12 * q^61 - 8 * q^62 + 4 * q^64 + 4 * q^65 - 20 * q^67 - 4 * q^68 + 32 * q^71 - 4 * q^73 + 4 * q^74 + 4 * q^76 + 14 * q^77 - 12 * q^79 - 2 * q^80 - 8 * q^82 - 40 * q^83 + 8 * q^85 + 12 * q^86 - 4 * q^88 - 8 * q^89 + 28 * q^91 - 12 * q^92 - 2 * q^94 - 2 * q^95 - 16 * q^97 + 14 * q^98

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