LMFDB - Embedded newform 126.2.g.c.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(37,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("126.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.g (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:	$1.00611506547$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	126.109
Dual form			126.2.g.c.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(2.50000 - 4.33013i) q^{11} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(-4.00000 - 6.92820i) q^{19} -1.00000 q^{20} +5.00000 q^{22} +(-2.00000 - 3.46410i) q^{23} +(2.00000 - 3.46410i) q^{25} +(-2.50000 - 0.866025i) q^{28} +5.00000 q^{29} +(-1.50000 + 2.59808i) q^{31} +(0.500000 - 0.866025i) q^{32} -4.00000 q^{34} +(-2.00000 + 1.73205i) q^{35} +(2.00000 + 3.46410i) q^{37} +(4.00000 - 6.92820i) q^{38} +(-0.500000 - 0.866025i) q^{40} +2.00000 q^{43} +(2.50000 + 4.33013i) q^{44} +(2.00000 - 3.46410i) q^{46} +(-3.00000 - 5.19615i) q^{47} +(-6.50000 + 2.59808i) q^{49} +4.00000 q^{50} +(-4.50000 + 7.79423i) q^{53} +5.00000 q^{55} +(-0.500000 - 2.59808i) q^{56} +(2.50000 + 4.33013i) q^{58} +(-5.50000 + 9.52628i) q^{59} +(3.00000 + 5.19615i) q^{61} -3.00000 q^{62} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(-2.50000 - 0.866025i) q^{70} -2.00000 q^{71} +(-5.00000 + 8.66025i) q^{73} +(-2.00000 + 3.46410i) q^{74} +8.00000 q^{76} +(12.5000 + 4.33013i) q^{77} +(-1.50000 - 2.59808i) q^{79} +(0.500000 - 0.866025i) q^{80} +7.00000 q^{83} -4.00000 q^{85} +(1.00000 + 1.73205i) q^{86} +(-2.50000 + 4.33013i) q^{88} +(-3.00000 - 5.19615i) q^{89} +4.00000 q^{92} +(3.00000 - 5.19615i) q^{94} +(4.00000 - 6.92820i) q^{95} +7.00000 q^{97} +(-5.50000 - 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} + q^{5} + q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 + q^5 + q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} + q^{5} + q^{7} - 2 q^{8} - q^{10} + 5 q^{11} - 4 q^{14} - q^{16} - 4 q^{17} - 8 q^{19} - 2 q^{20} + 10 q^{22} - 4 q^{23} + 4 q^{25} - 5 q^{28} + 10 q^{29} - 3 q^{31} + q^{32} - 8 q^{34} - 4 q^{35} + 4 q^{37} + 8 q^{38} - q^{40} + 4 q^{43} + 5 q^{44} + 4 q^{46} - 6 q^{47} - 13 q^{49} + 8 q^{50} - 9 q^{53} + 10 q^{55} - q^{56} + 5 q^{58} - 11 q^{59} + 6 q^{61} - 6 q^{62} + 2 q^{64} + 2 q^{67} - 4 q^{68} - 5 q^{70} - 4 q^{71} - 10 q^{73} - 4 q^{74} + 16 q^{76} + 25 q^{77} - 3 q^{79} + q^{80} + 14 q^{83} - 8 q^{85} + 2 q^{86} - 5 q^{88} - 6 q^{89} + 8 q^{92} + 6 q^{94} + 8 q^{95} + 14 q^{97} - 11 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 + q^5 + q^7 - 2 * q^8 - q^10 + 5 * q^11 - 4 * q^14 - q^16 - 4 * q^17 - 8 * q^19 - 2 * q^20 + 10 * q^22 - 4 * q^23 + 4 * q^25 - 5 * q^28 + 10 * q^29 - 3 * q^31 + q^32 - 8 * q^34 - 4 * q^35 + 4 * q^37 + 8 * q^38 - q^40 + 4 * q^43 + 5 * q^44 + 4 * q^46 - 6 * q^47 - 13 * q^49 + 8 * q^50 - 9 * q^53 + 10 * q^55 - q^56 + 5 * q^58 - 11 * q^59 + 6 * q^61 - 6 * q^62 + 2 * q^64 + 2 * q^67 - 4 * q^68 - 5 * q^70 - 4 * q^71 - 10 * q^73 - 4 * q^74 + 16 * q^76 + 25 * q^77 - 3 * q^79 + q^80 + 14 * q^83 - 8 * q^85 + 2 * q^86 - 5 * q^88 - 6 * q^89 + 8 * q^92 + 6 * q^94 + 8 * q^95 + 14 * q^97 - 11 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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	0.955901	−	0.293691i	$-0.0948835\pi$
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	−0.732294	+	0.680989i	$0.761550\pi$
$6$		0			0
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	−0.192201	−	0.981356i	$-0.561563\pi$
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	0.945979	−	0.324227i	$-0.105104\pi$
$12$		0			0
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$	−2.00000	+	1.73205i	−0.534522	+	0.462910i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	−0.999853	−	0.0171533i	$-0.994540\pi$
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	0.514782	+	0.857321i	$0.327873\pi$
$18$		0			0
$19$	−4.00000	−	6.92820i	−0.917663	−	1.58944i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−4.00000	−	6.92820i	−0.917663	−	1.58944i	−0.114708	−	0.993399i	$-0.536593\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	5.00000			1.06600
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$		0			0
$27$		0			0
$28$	−2.50000	−	0.866025i	−0.472456	−	0.163663i
$29$	5.00000			0.928477			0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000			0.928477			0.464238	+	0.885710i	$0.346328\pi$
$30$		0			0
$31$	−1.50000	+	2.59808i	−0.269408	+	0.466628i	−0.968709	−	0.248199i	$-0.920161\pi$
$31$	−1.50000	+	2.59808i	−0.269408	+	0.466628i	0.699301	+	0.714827i	$0.253495\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−4.00000			−0.685994
$35$	−2.00000	+	1.73205i	−0.338062	+	0.292770i
$36$		0			0
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	0.982274	−	0.187453i	$-0.0600231\pi$
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	−0.653476	+	0.756948i	$0.726690\pi$
$38$	4.00000	−	6.92820i	0.648886	−	1.12390i
$39$		0			0
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	2.50000	+	4.33013i	0.376889	+	0.652791i
$45$		0			0
$46$	2.00000	−	3.46410i	0.294884	−	0.510754i
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$		0			0
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	4.00000			0.565685
$51$		0			0
$52$		0			0
$53$	−4.50000	+	7.79423i	−0.618123	+	1.07062i	0.371706	+	0.928351i	$0.378773\pi$
$53$	−4.50000	+	7.79423i	−0.618123	+	1.07062i	−0.989828	+	0.142269i	$0.954560\pi$
$54$		0			0
$55$	5.00000			0.674200
$56$	−0.500000	−	2.59808i	−0.0668153	−	0.347183i
$57$		0			0
$58$	2.50000	+	4.33013i	0.328266	+	0.568574i
$59$	−5.50000	+	9.52628i	−0.716039	+	1.24022i	0.246518	+	0.969138i	$0.420713\pi$
$59$	−5.50000	+	9.52628i	−0.716039	+	1.24022i	−0.962557	+	0.271078i	$0.912620\pi$
$60$		0			0
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	0.991645	−	0.128994i	$-0.0411748\pi$
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	−0.607535	+	0.794293i	$0.707841\pi$
$62$	−3.00000			−0.381000
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	−0.798454	−	0.602056i	$-0.794348\pi$
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	0.920623	+	0.390453i	$0.127682\pi$
$68$	−2.00000	−	3.46410i	−0.242536	−	0.420084i
$69$		0			0
$70$	−2.50000	−	0.866025i	−0.298807	−	0.103510i
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$		0			0
$73$	−5.00000	+	8.66025i	−0.585206	+	1.01361i	0.409644	+	0.912245i	$0.365653\pi$
$73$	−5.00000	+	8.66025i	−0.585206	+	1.01361i	−0.994850	+	0.101361i	$0.967680\pi$
$74$	−2.00000	+	3.46410i	−0.232495	+	0.402694i
$75$		0			0
$76$	8.00000			0.917663
$77$	12.5000	+	4.33013i	1.42451	+	0.493464i
$78$		0			0
$79$	−1.50000	−	2.59808i	−0.168763	−	0.292306i	0.769222	−	0.638982i	$-0.220644\pi$
$79$	−1.50000	−	2.59808i	−0.168763	−	0.292306i	−0.937985	+	0.346675i	$0.887311\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$		0			0
$82$		0			0
$83$	7.00000			0.768350			0.384175	−	0.923260i	$-0.374486\pi$
$83$	7.00000			0.768350			0.384175	+	0.923260i	$0.374486\pi$
$84$		0			0
$85$	−4.00000			−0.433861
$86$	1.00000	+	1.73205i	0.107833	+	0.186772i
$87$		0			0
$88$	−2.50000	+	4.33013i	−0.266501	+	0.461593i
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$		0			0
$91$		0			0
$92$	4.00000			0.417029
$93$		0			0
$94$	3.00000	−	5.19615i	0.309426	−	0.535942i
$95$	4.00000	−	6.92820i	0.410391	−	0.710819i
$96$		0			0
$97$	7.00000			0.710742			0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000			0.710742			0.355371	+	0.934725i	$0.384354\pi$
$98$	−5.50000	−	4.33013i	−0.555584	−	0.437409i
$99$		0			0
$100$	2.00000	+	3.46410i	0.200000	+	0.346410i
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	−0.502477	−	0.864590i	$-0.667578\pi$
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	0.999996	+	0.00286291i	$0.000911295\pi$
$102$		0			0
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$		0			0
$105$		0			0
$106$	−9.00000			−0.874157
$107$	1.50000	+	2.59808i	0.145010	+	0.251166i	0.929377	−	0.369132i	$-0.120345\pi$
$107$	1.50000	+	2.59808i	0.145010	+	0.251166i	−0.784366	+	0.620298i	$0.787012\pi$
$108$		0			0
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$	2.50000	+	4.33013i	0.238366	+	0.412861i
$111$		0			0
$112$	2.00000	−	1.73205i	0.188982	−	0.163663i
$113$	−16.0000			−1.50515			−0.752577	−	0.658505i	$-0.771189\pi$
$113$	−16.0000			−1.50515			−0.752577	+	0.658505i	$0.771189\pi$
$114$		0			0
$115$	2.00000	−	3.46410i	0.186501	−	0.323029i
$116$	−2.50000	+	4.33013i	−0.232119	+	0.402042i
$117$		0			0
$118$	−11.0000			−1.01263
$119$	−10.0000	−	3.46410i	−0.916698	−	0.317554i
$120$		0			0
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$	−3.00000	+	5.19615i	−0.271607	+	0.470438i
$123$		0			0
$124$	−1.50000	−	2.59808i	−0.134704	−	0.233314i
$125$	9.00000			0.804984
$126$		0			0
$127$	9.00000			0.798621			0.399310	−	0.916816i	$-0.369250\pi$
$127$	9.00000			0.798621			0.399310	+	0.916816i	$0.369250\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$		0			0
$131$	0.500000	+	0.866025i	0.0436852	+	0.0756650i	0.887041	−	0.461690i	$-0.152757\pi$
$131$	0.500000	+	0.866025i	0.0436852	+	0.0756650i	−0.843356	+	0.537355i	$0.819423\pi$
$132$		0			0
$133$	16.0000	−	13.8564i	1.38738	−	1.20150i
$134$	2.00000			0.172774
$135$		0			0
$136$	2.00000	−	3.46410i	0.171499	−	0.297044i
$137$	−1.00000	+	1.73205i	−0.0854358	+	0.147979i	−0.905577	−	0.424182i	$-0.860562\pi$
$137$	−1.00000	+	1.73205i	−0.0854358	+	0.147979i	0.820141	+	0.572161i	$0.193895\pi$
$138$		0			0
$139$	−14.0000			−1.18746			−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000			−1.18746			−0.593732	+	0.804663i	$0.702346\pi$
$140$	−0.500000	−	2.59808i	−0.0422577	−	0.219578i
$141$		0			0
$142$	−1.00000	−	1.73205i	−0.0839181	−	0.145350i
$143$		0			0
$144$		0			0
$145$	2.50000	+	4.33013i	0.207614	+	0.359597i
$146$	−10.0000			−0.827606
$147$		0			0
$148$	−4.00000			−0.328798
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	−0.953703	−	0.300750i	$-0.902763\pi$
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	0.216394	−	0.976306i	$-0.430570\pi$
$150$		0			0
$151$	−9.50000	+	16.4545i	−0.773099	+	1.33905i	0.162758	+	0.986666i	$0.447961\pi$
$151$	−9.50000	+	16.4545i	−0.773099	+	1.33905i	−0.935857	+	0.352381i	$0.885372\pi$
$152$	4.00000	+	6.92820i	0.324443	+	0.561951i
$153$		0			0
$154$	2.50000	+	12.9904i	0.201456	+	1.04679i
$155$	−3.00000			−0.240966
$156$		0			0
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	−0.775113	−	0.631822i	$-0.782307\pi$
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	0.934731	+	0.355357i	$0.115641\pi$
$158$	1.50000	−	2.59808i	0.119334	−	0.206692i
$159$		0			0
$160$	1.00000			0.0790569
$161$	8.00000	−	6.92820i	0.630488	−	0.546019i
$162$		0			0
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	0.933659	−	0.358162i	$-0.116597\pi$
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	−0.777007	+	0.629492i	$0.783263\pi$
$164$		0			0
$165$		0			0
$166$	3.50000	+	6.06218i	0.271653	+	0.470516i
$167$	14.0000			1.08335			0.541676	−	0.840587i	$-0.317790\pi$
$167$	14.0000			1.08335			0.541676	+	0.840587i	$0.317790\pi$
$168$		0			0
$169$	−13.0000			−1.00000
$170$	−2.00000	−	3.46410i	−0.153393	−	0.265684i
$171$		0			0
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	11.0000	+	19.0526i	0.836315	+	1.44854i	0.892956	+	0.450145i	$0.148628\pi$
$173$	11.0000	+	19.0526i	0.836315	+	1.44854i	−0.0566411	+	0.998395i	$0.518039\pi$
$174$		0			0
$175$	10.0000	+	3.46410i	0.755929	+	0.261861i
$176$	−5.00000			−0.376889
$177$		0			0
$178$	3.00000	−	5.19615i	0.224860	−	0.389468i
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$		0			0
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$		0			0
$184$	2.00000	+	3.46410i	0.147442	+	0.255377i
$185$	−2.00000	+	3.46410i	−0.147043	+	0.254686i
$186$		0			0
$187$	10.0000	+	17.3205i	0.731272	+	1.26660i
$188$	6.00000			0.437595
$189$		0			0
$190$	8.00000			0.580381
$191$	12.0000	+	20.7846i	0.868290	+	1.50392i	0.863743	+	0.503932i	$0.168114\pi$
$191$	12.0000	+	20.7846i	0.868290	+	1.50392i	0.00454614	+	0.999990i	$0.498553\pi$
$192$		0			0
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	−0.941865	−	0.335993i	$-0.890928\pi$
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	0.761911	+	0.647682i	$0.224262\pi$
$194$	3.50000	+	6.06218i	0.251285	+	0.435239i
$195$		0			0
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	−0.786389	−	0.617731i	$-0.788052\pi$
$199$	2.00000	−	3.46410i	0.141776	−	0.245564i	0.928166	+	0.372168i	$0.121385\pi$
$200$	−2.00000	+	3.46410i	−0.141421	+	0.244949i
$201$		0			0
$202$	10.0000			0.703598
$203$	2.50000	+	12.9904i	0.175466	+	0.911746i
$204$		0			0
$205$		0			0
$206$	4.00000	−	6.92820i	0.278693	−	0.482711i
$207$		0			0
$208$		0			0
$209$	−40.0000			−2.76686
$210$		0			0
$211$	2.00000			0.137686			0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000			0.137686			0.0688428	+	0.997628i	$0.478069\pi$
$212$	−4.50000	−	7.79423i	−0.309061	−	0.535310i
$213$		0			0
$214$	−1.50000	+	2.59808i	−0.102538	+	0.177601i
$215$	1.00000	+	1.73205i	0.0681994	+	0.118125i
$216$		0			0
$217$	−7.50000	−	2.59808i	−0.509133	−	0.176369i
$218$	2.00000			0.135457
$219$		0			0
$220$	−2.50000	+	4.33013i	−0.168550	+	0.291937i
$221$		0			0
$222$		0			0
$223$	−7.00000			−0.468755			−0.234377	−	0.972146i	$-0.575305\pi$
$223$	−7.00000			−0.468755			−0.234377	+	0.972146i	$0.575305\pi$
$224$	2.50000	+	0.866025i	0.167038	+	0.0578638i
$225$		0			0
$226$	−8.00000	−	13.8564i	−0.532152	−	0.921714i
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	−0.811943	−	0.583736i	$-0.801590\pi$
$227$	1.50000	−	2.59808i	0.0995585	−	0.172440i	0.911502	+	0.411296i	$0.134924\pi$
$228$		0			0
$229$	10.0000	+	17.3205i	0.660819	+	1.14457i	0.980401	+	0.197013i	$0.0631241\pi$
$229$	10.0000	+	17.3205i	0.660819	+	1.14457i	−0.319582	+	0.947559i	$0.603543\pi$
$230$	4.00000			0.263752
$231$		0			0
$232$	−5.00000			−0.328266
$233$	−2.00000	−	3.46410i	−0.131024	−	0.226941i	0.793047	−	0.609160i	$-0.208493\pi$
$233$	−2.00000	−	3.46410i	−0.131024	−	0.226941i	−0.924072	+	0.382219i	$0.875160\pi$
$234$		0			0
$235$	3.00000	−	5.19615i	0.195698	−	0.338960i
$236$	−5.50000	−	9.52628i	−0.358020	−	0.620108i
$237$		0			0
$238$	−2.00000	−	10.3923i	−0.129641	−	0.673633i
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$		0			0
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	−0.110963	−	0.993825i	$-0.535394\pi$
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	0.916159	−	0.400815i	$-0.131273\pi$
$242$	7.00000	−	12.1244i	0.449977	−	0.779383i
$243$		0			0
$244$	−6.00000			−0.384111
$245$	−5.50000	−	4.33013i	−0.351382	−	0.276642i
$246$		0			0
$247$		0			0
$248$	1.50000	−	2.59808i	0.0952501	−	0.164978i
$249$		0			0
$250$	4.50000	+	7.79423i	0.284605	+	0.492950i
$251$	−21.0000			−1.32551			−0.662754	−	0.748837i	$-0.730613\pi$
$251$	−21.0000			−1.32551			−0.662754	+	0.748837i	$0.730613\pi$
$252$		0			0
$253$	−20.0000			−1.25739
$254$	4.50000	+	7.79423i	0.282355	+	0.489053i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	0.757159	−	0.653231i	$-0.226587\pi$
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	−0.944294	+	0.329104i	$0.893253\pi$
$258$		0			0
$259$	−8.00000	+	6.92820i	−0.497096	+	0.430498i
$260$		0			0
$261$		0			0
$262$	−0.500000	+	0.866025i	−0.0308901	+	0.0535032i
$263$	−15.0000	+	25.9808i	−0.924940	+	1.60204i	−0.133281	+	0.991078i	$0.542551\pi$
$263$	−15.0000	+	25.9808i	−0.924940	+	1.60204i	−0.791658	+	0.610964i	$0.790782\pi$
$264$		0			0
$265$	−9.00000			−0.552866
$266$	20.0000	+	6.92820i	1.22628	+	0.424795i
$267$		0			0
$268$	1.00000	+	1.73205i	0.0610847	+	0.105802i
$269$	15.5000	−	26.8468i	0.945052	−	1.63688i	0.189404	−	0.981899i	$-0.439344\pi$
$269$	15.5000	−	26.8468i	0.945052	−	1.63688i	0.755648	−	0.654978i	$-0.227322\pi$
$270$		0			0
$271$	−7.50000	−	12.9904i	−0.455593	−	0.789109i	0.543130	−	0.839649i	$-0.317239\pi$
$271$	−7.50000	−	12.9904i	−0.455593	−	0.789109i	−0.998722	+	0.0505395i	$0.983906\pi$
$272$	4.00000			0.242536
$273$		0			0
$274$	−2.00000			−0.120824
$275$	−10.0000	−	17.3205i	−0.603023	−	1.04447i
$276$		0			0
$277$	8.00000	−	13.8564i	0.480673	−	0.832551i	−0.519081	−	0.854725i	$-0.673726\pi$
$277$	8.00000	−	13.8564i	0.480673	−	0.832551i	0.999754	+	0.0221745i	$0.00705893\pi$
$278$	−7.00000	−	12.1244i	−0.419832	−	0.727171i
$279$		0			0
$280$	2.00000	−	1.73205i	0.119523	−	0.103510i
$281$	−2.00000			−0.119310			−0.0596550	−	0.998219i	$-0.519000\pi$
$281$	−2.00000			−0.119310			−0.0596550	+	0.998219i	$0.519000\pi$
$282$		0			0
$283$	−5.00000	+	8.66025i	−0.297219	+	0.514799i	−0.975499	−	0.220005i	$-0.929393\pi$
$283$	−5.00000	+	8.66025i	−0.297219	+	0.514799i	0.678280	+	0.734804i	$0.262726\pi$
$284$	1.00000	−	1.73205i	0.0593391	−	0.102778i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	−2.50000	+	4.33013i	−0.146805	+	0.254274i
$291$		0			0
$292$	−5.00000	−	8.66025i	−0.292603	−	0.506803i
$293$	21.0000			1.22683			0.613417	−	0.789760i	$-0.289795\pi$
$293$	21.0000			1.22683			0.613417	+	0.789760i	$0.289795\pi$
$294$		0			0
$295$	−11.0000			−0.640445
$296$	−2.00000	−	3.46410i	−0.116248	−	0.201347i
$297$		0			0
$298$	9.00000	−	15.5885i	0.521356	−	0.903015i
$299$		0			0
$300$		0			0
$301$	1.00000	+	5.19615i	0.0576390	+	0.299501i
$302$	−19.0000			−1.09333
$303$		0			0
$304$	−4.00000	+	6.92820i	−0.229416	+	0.397360i
$305$	−3.00000	+	5.19615i	−0.171780	+	0.297531i
$306$		0			0
$307$	28.0000			1.59804			0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$	−10.0000	+	8.66025i	−0.569803	+	0.493464i
$309$		0			0
$310$	−1.50000	−	2.59808i	−0.0851943	−	0.147561i
$311$	−16.0000	+	27.7128i	−0.907277	+	1.57145i	−0.0894452	+	0.995992i	$0.528509\pi$
$311$	−16.0000	+	27.7128i	−0.907277	+	1.57145i	−0.817832	+	0.575458i	$0.804824\pi$
$312$		0			0
$313$	−0.500000	−	0.866025i	−0.0282617	−	0.0489506i	0.851549	−	0.524276i	$-0.175664\pi$
$313$	−0.500000	−	0.866025i	−0.0282617	−	0.0489506i	−0.879810	+	0.475325i	$0.842331\pi$
$314$	4.00000			0.225733
$315$		0			0
$316$	3.00000			0.168763
$317$	1.50000	+	2.59808i	0.0842484	+	0.145922i	0.905071	−	0.425261i	$-0.139818\pi$
$317$	1.50000	+	2.59808i	0.0842484	+	0.145922i	−0.820822	+	0.571184i	$0.806484\pi$
$318$		0			0
$319$	12.5000	−	21.6506i	0.699866	−	1.21220i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$		0			0
$322$	10.0000	+	3.46410i	0.557278	+	0.193047i
$323$	32.0000			1.78053
$324$		0			0
$325$		0			0
$326$	−2.00000	+	3.46410i	−0.110770	+	0.191859i
$327$		0			0
$328$		0			0
$329$	12.0000	−	10.3923i	0.661581	−	0.572946i
$330$		0			0
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	0.915742	−	0.401768i	$-0.131604\pi$
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	−0.805812	+	0.592172i	$0.798271\pi$
$332$	−3.50000	+	6.06218i	−0.192087	+	0.332705i
$333$		0			0
$334$	7.00000	+	12.1244i	0.383023	+	0.663415i
$335$	2.00000			0.109272
$336$		0			0
$337$	9.00000			0.490261			0.245131	−	0.969490i	$-0.421169\pi$
$337$	9.00000			0.490261			0.245131	+	0.969490i	$0.421169\pi$
$338$	−6.50000	−	11.2583i	−0.353553	−	0.612372i
$339$		0			0
$340$	2.00000	−	3.46410i	0.108465	−	0.187867i
$341$	7.50000	+	12.9904i	0.406148	+	0.703469i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	−2.00000			−0.107833
$345$		0			0
$346$	−11.0000	+	19.0526i	−0.591364	+	1.02427i
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$	2.00000	+	10.3923i	0.106904	+	0.555492i
$351$		0			0
$352$	−2.50000	−	4.33013i	−0.133250	−	0.230797i
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	−0.347024	−	0.937856i	$-0.612808\pi$
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	0.985719	−	0.168397i	$-0.0538590\pi$
$354$		0			0
$355$	−1.00000	−	1.73205i	−0.0530745	−	0.0919277i
$356$	6.00000			0.317999
$357$		0			0
$358$	12.0000			0.634220
$359$	5.00000	+	8.66025i	0.263890	+	0.457071i	0.967272	−	0.253741i	$-0.0816611\pi$
$359$	5.00000	+	8.66025i	0.263890	+	0.457071i	−0.703382	+	0.710812i	$0.748328\pi$
$360$		0			0
$361$	−22.5000	+	38.9711i	−1.18421	+	2.05111i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−10.0000			−0.523424
$366$		0			0
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	−0.997960	−	0.0638362i	$-0.979666\pi$
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	0.554264	+	0.832341i	$0.313000\pi$
$368$	−2.00000	+	3.46410i	−0.104257	+	0.180579i
$369$		0			0
$370$	−4.00000			−0.207950
$371$	−22.5000	−	7.79423i	−1.16814	−	0.404656i
$372$		0			0
$373$	16.0000	+	27.7128i	0.828449	+	1.43492i	0.899255	+	0.437425i	$0.144109\pi$
$373$	16.0000	+	27.7128i	0.828449	+	1.43492i	−0.0708063	+	0.997490i	$0.522557\pi$
$374$	−10.0000	+	17.3205i	−0.517088	+	0.895622i
$375$		0			0
$376$	3.00000	+	5.19615i	0.154713	+	0.267971i
$377$		0			0
$378$		0			0
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$	4.00000	+	6.92820i	0.205196	+	0.355409i
$381$		0			0
$382$	−12.0000	+	20.7846i	−0.613973	+	1.06343i
$383$	−17.0000	−	29.4449i	−0.868659	−	1.50456i	−0.863367	−	0.504576i	$-0.831649\pi$
$383$	−17.0000	−	29.4449i	−0.868659	−	1.50456i	−0.00529229	−	0.999986i	$-0.501685\pi$
$384$		0			0
$385$	2.50000	+	12.9904i	0.127412	+	0.662051i
$386$	−5.00000			−0.254493
$387$		0			0
$388$	−3.50000	+	6.06218i	−0.177686	+	0.307760i
$389$	−1.00000	+	1.73205i	−0.0507020	+	0.0878185i	−0.890263	−	0.455448i	$-0.849479\pi$
$389$	−1.00000	+	1.73205i	−0.0507020	+	0.0878185i	0.839561	+	0.543266i	$0.182813\pi$
$390$		0			0
$391$	16.0000			0.809155
$392$	6.50000	−	2.59808i	0.328300	−	0.131223i
$393$		0			0
$394$	−1.00000	−	1.73205i	−0.0503793	−	0.0872595i
$395$	1.50000	−	2.59808i	0.0754732	−	0.130723i
$396$		0			0
$397$	−18.0000	−	31.1769i	−0.903394	−	1.56472i	−0.823058	−	0.567957i	$-0.807734\pi$
$397$	−18.0000	−	31.1769i	−0.903394	−	1.56472i	−0.0803356	−	0.996768i	$-0.525599\pi$
$398$	4.00000			0.200502
$399$		0			0
$400$	−4.00000			−0.200000
$401$	12.0000	+	20.7846i	0.599251	+	1.03793i	0.992932	+	0.118686i	$0.0378683\pi$
$401$	12.0000	+	20.7846i	0.599251	+	1.03793i	−0.393680	+	0.919247i	$0.628798\pi$
$402$		0			0
$403$		0			0
$404$	5.00000	+	8.66025i	0.248759	+	0.430864i
$405$		0			0
$406$	−10.0000	+	8.66025i	−0.496292	+	0.429801i
$407$	20.0000			0.991363
$408$		0			0
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	−0.371750	−	0.928333i	$-0.621242\pi$
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	0.989835	−	0.142222i	$-0.0454247\pi$
$410$		0			0
$411$		0			0
$412$	8.00000			0.394132
$413$	−27.5000	−	9.52628i	−1.35319	−	0.468758i
$414$		0			0
$415$	3.50000	+	6.06218i	0.171808	+	0.297581i
$416$		0			0
$417$		0			0
$418$	−20.0000	−	34.6410i	−0.978232	−	1.69435i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	30.0000			1.46211			0.731055	−	0.682318i	$-0.239028\pi$
$421$	30.0000			1.46211			0.731055	+	0.682318i	$0.239028\pi$
$422$	1.00000	+	1.73205i	0.0486792	+	0.0843149i
$423$		0			0
$424$	4.50000	−	7.79423i	0.218539	−	0.378521i
$425$	8.00000	+	13.8564i	0.388057	+	0.672134i
$426$		0			0
$427$	−12.0000	+	10.3923i	−0.580721	+	0.502919i
$428$	−3.00000			−0.145010
$429$		0			0
$430$	−1.00000	+	1.73205i	−0.0482243	+	0.0835269i
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	−0.684564	−	0.728953i	$-0.740007\pi$
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	0.973574	+	0.228373i	$0.0733406\pi$
$432$		0			0
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$	−1.50000	−	7.79423i	−0.0720023	−	0.374135i
$435$		0			0
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$	−16.0000	+	27.7128i	−0.765384	+	1.32568i
$438$		0			0
$439$	−7.50000	−	12.9904i	−0.357955	−	0.619997i	0.629664	−	0.776868i	$-0.283193\pi$
$439$	−7.50000	−	12.9904i	−0.357955	−	0.619997i	−0.987619	+	0.156871i	$0.949859\pi$
$440$	−5.00000			−0.238366
$441$		0			0
$442$		0			0
$443$	8.50000	+	14.7224i	0.403847	+	0.699484i	0.994187	−	0.107671i	$-0.0343394\pi$
$443$	8.50000	+	14.7224i	0.403847	+	0.699484i	−0.590339	+	0.807155i	$0.701006\pi$
$444$		0			0
$445$	3.00000	−	5.19615i	0.142214	−	0.246321i
$446$	−3.50000	−	6.06218i	−0.165730	−	0.287052i
$447$		0			0
$448$	0.500000	+	2.59808i	0.0236228	+	0.122748i
$449$	−16.0000			−0.755087			−0.377543	−	0.925992i	$-0.623231\pi$
$449$	−16.0000			−0.755087			−0.377543	+	0.925992i	$0.623231\pi$
$450$		0			0
$451$		0			0
$452$	8.00000	−	13.8564i	0.376288	−	0.651751i
$453$		0			0
$454$	3.00000			0.140797
$455$		0			0
$456$		0			0
$457$	−15.5000	−	26.8468i	−0.725059	−	1.25584i	−0.958950	−	0.283577i	$-0.908479\pi$
$457$	−15.5000	−	26.8468i	−0.725059	−	1.25584i	0.233890	−	0.972263i	$-0.424854\pi$
$458$	−10.0000	+	17.3205i	−0.467269	+	0.809334i
$459$		0			0
$460$	2.00000	+	3.46410i	0.0932505	+	0.161515i
$461$	14.0000			0.652045			0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000			0.652045			0.326023	+	0.945362i	$0.394291\pi$
$462$		0			0
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$	−2.50000	−	4.33013i	−0.116060	−	0.201021i
$465$		0			0
$466$	2.00000	−	3.46410i	0.0926482	−	0.160471i
$467$	−10.0000	−	17.3205i	−0.462745	−	0.801498i	0.536352	−	0.843995i	$-0.319802\pi$
$467$	−10.0000	−	17.3205i	−0.462745	−	0.801498i	−0.999097	+	0.0424970i	$0.986469\pi$
$468$		0			0
$469$	5.00000	+	1.73205i	0.230879	+	0.0799787i
$470$	6.00000			0.276759
$471$		0			0
$472$	5.50000	−	9.52628i	0.253158	−	0.438483i
$473$	5.00000	−	8.66025i	0.229900	−	0.398199i
$474$		0			0
$475$	−32.0000			−1.46826
$476$	8.00000	−	6.92820i	0.366679	−	0.317554i
$477$		0			0
$478$	6.00000	+	10.3923i	0.274434	+	0.475333i
$479$	19.0000	−	32.9090i	0.868132	−	1.50365i	0.00422900	−	0.999991i	$-0.498654\pi$
$479$	19.0000	−	32.9090i	0.868132	−	1.50365i	0.863903	−	0.503658i	$-0.168013\pi$
$480$		0			0
$481$		0			0
$482$	25.0000			1.13872
$483$		0			0
$484$	14.0000			0.636364
$485$	3.50000	+	6.06218i	0.158927	+	0.275269i
$486$		0			0
$487$	−2.50000	+	4.33013i	−0.113286	+	0.196217i	−0.917093	−	0.398673i	$-0.869471\pi$
$487$	−2.50000	+	4.33013i	−0.113286	+	0.196217i	0.803807	+	0.594890i	$0.202804\pi$
$488$	−3.00000	−	5.19615i	−0.135804	−	0.235219i
$489$		0			0
$490$	1.00000	−	6.92820i	0.0451754	−	0.312984i
$491$	−9.00000			−0.406164			−0.203082	−	0.979162i	$-0.565096\pi$
$491$	−9.00000			−0.406164			−0.203082	+	0.979162i	$0.565096\pi$
$492$		0			0
$493$	−10.0000	+	17.3205i	−0.450377	+	0.780076i
$494$		0			0
$495$		0			0
$496$	3.00000			0.134704
$497$	−1.00000	−	5.19615i	−0.0448561	−	0.233079i
$498$		0			0
$499$	−5.00000	−	8.66025i	−0.223831	−	0.387686i	0.732137	−	0.681157i	$-0.238523\pi$
$499$	−5.00000	−	8.66025i	−0.223831	−	0.387686i	−0.955968	+	0.293471i	$0.905190\pi$
$500$	−4.50000	+	7.79423i	−0.201246	+	0.348569i
$501$		0			0
$502$	−10.5000	−	18.1865i	−0.468638	−	0.811705i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	10.0000			0.444994
$506$	−10.0000	−	17.3205i	−0.444554	−	0.769991i
$507$		0			0
$508$	−4.50000	+	7.79423i	−0.199655	+	0.345813i
$509$	7.50000	+	12.9904i	0.332432	+	0.575789i	0.982988	−	0.183669i	$-0.0587976\pi$
$509$	7.50000	+	12.9904i	0.332432	+	0.575789i	−0.650556	+	0.759458i	$0.725464\pi$
$510$		0			0
$511$	−25.0000	−	8.66025i	−1.10593	−	0.383107i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	3.00000	−	5.19615i	0.132324	−	0.229192i
$515$	4.00000	−	6.92820i	0.176261	−	0.305293i
$516$		0			0
$517$	−30.0000			−1.31940
$518$	−10.0000	−	3.46410i	−0.439375	−	0.152204i
$519$		0			0
$520$		0			0
$521$	−9.00000	+	15.5885i	−0.394297	+	0.682943i	−0.993011	−	0.118020i	$-0.962345\pi$
$521$	−9.00000	+	15.5885i	−0.394297	+	0.682943i	0.598714	+	0.800963i	$0.295679\pi$
$522$		0			0
$523$	−4.00000	−	6.92820i	−0.174908	−	0.302949i	0.765222	−	0.643767i	$-0.222629\pi$
$523$	−4.00000	−	6.92820i	−0.174908	−	0.302949i	−0.940129	+	0.340818i	$0.889296\pi$
$524$	−1.00000			−0.0436852
$525$		0			0
$526$	−30.0000			−1.30806
$527$	−6.00000	−	10.3923i	−0.261364	−	0.452696i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	−4.50000	−	7.79423i	−0.195468	−	0.338560i
$531$		0			0
$532$	4.00000	+	20.7846i	0.173422	+	0.901127i
$533$		0			0
$534$		0			0
$535$	−1.50000	+	2.59808i	−0.0648507	+	0.112325i
$536$	−1.00000	+	1.73205i	−0.0431934	+	0.0748132i
$537$		0			0
$538$	31.0000			1.33650
$539$	−5.00000	+	34.6410i	−0.215365	+	1.49209i
$540$		0			0
$541$	9.00000	+	15.5885i	0.386940	+	0.670200i	0.992036	−	0.125952i	$-0.0401986\pi$
$541$	9.00000	+	15.5885i	0.386940	+	0.670200i	−0.605096	+	0.796152i	$0.706865\pi$
$542$	7.50000	−	12.9904i	0.322153	−	0.557985i
$543$		0			0
$544$	2.00000	+	3.46410i	0.0857493	+	0.148522i
$545$	2.00000			0.0856706
$546$		0			0
$547$	−12.0000			−0.513083			−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000			−0.513083			−0.256541	+	0.966533i	$0.582583\pi$
$548$	−1.00000	−	1.73205i	−0.0427179	−	0.0739895i
$549$		0			0
$550$	10.0000	−	17.3205i	0.426401	−	0.738549i
$551$	−20.0000	−	34.6410i	−0.852029	−	1.47576i
$552$		0			0
$553$	6.00000	−	5.19615i	0.255146	−	0.220963i
$554$	16.0000			0.679775
$555$		0			0
$556$	7.00000	−	12.1244i	0.296866	−	0.514187i
$557$	−11.5000	+	19.9186i	−0.487271	+	0.843978i	−0.999893	−	0.0146368i	$-0.995341\pi$
$557$	−11.5000	+	19.9186i	−0.487271	+	0.843978i	0.512622	+	0.858614i	$0.328674\pi$
$558$		0			0
$559$		0			0
$560$	2.50000	+	0.866025i	0.105644	+	0.0365963i
$561$		0			0
$562$	−1.00000	−	1.73205i	−0.0421825	−	0.0730622i
$563$	8.50000	−	14.7224i	0.358232	−	0.620477i	−0.629433	−	0.777055i	$-0.716713\pi$
$563$	8.50000	−	14.7224i	0.358232	−	0.620477i	0.987666	+	0.156578i	$0.0500463\pi$
$564$		0			0
$565$	−8.00000	−	13.8564i	−0.336563	−	0.582943i
$566$	−10.0000			−0.420331
$567$		0			0
$568$	2.00000			0.0839181
$569$	12.0000	+	20.7846i	0.503066	+	0.871336i	0.999994	+	0.00354413i	$0.00112814\pi$
$569$	12.0000	+	20.7846i	0.503066	+	0.871336i	−0.496928	+	0.867792i	$0.665539\pi$
$570$		0			0
$571$	15.0000	−	25.9808i	0.627730	−	1.08726i	−0.360276	−	0.932846i	$-0.617317\pi$
$571$	15.0000	−	25.9808i	0.627730	−	1.08726i	0.988006	−	0.154415i	$-0.0493493\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−16.0000			−0.667246
$576$		0			0
$577$	−15.5000	+	26.8468i	−0.645273	+	1.11765i	0.338965	+	0.940799i	$0.389923\pi$
$577$	−15.5000	+	26.8468i	−0.645273	+	1.11765i	−0.984238	+	0.176847i	$0.943410\pi$
$578$	−0.500000	+	0.866025i	−0.0207973	+	0.0360219i
$579$		0			0
$580$	−5.00000			−0.207614
$581$	3.50000	+	18.1865i	0.145204	+	0.754505i
$582$		0			0
$583$	22.5000	+	38.9711i	0.931855	+	1.61402i
$584$	5.00000	−	8.66025i	0.206901	−	0.358364i
$585$		0			0
$586$	10.5000	+	18.1865i	0.433751	+	0.751279i
$587$	−35.0000			−1.44460			−0.722302	−	0.691577i	$-0.756916\pi$
$587$	−35.0000			−1.44460			−0.722302	+	0.691577i	$0.756916\pi$
$588$		0			0
$589$	24.0000			0.988903
$590$	−5.50000	−	9.52628i	−0.226431	−	0.392191i
$591$		0			0
$592$	2.00000	−	3.46410i	0.0821995	−	0.142374i
$593$	18.0000	+	31.1769i	0.739171	+	1.28028i	0.952869	+	0.303383i	$0.0981160\pi$
$593$	18.0000	+	31.1769i	0.739171	+	1.28028i	−0.213697	+	0.976900i	$0.568551\pi$
$594$		0			0
$595$	−2.00000	−	10.3923i	−0.0819920	−	0.426043i
$596$	18.0000			0.737309
$597$		0			0
$598$		0			0
$599$	−15.0000	+	25.9808i	−0.612883	+	1.06155i	0.377869	+	0.925859i	$0.376657\pi$
$599$	−15.0000	+	25.9808i	−0.612883	+	1.06155i	−0.990752	+	0.135686i	$0.956676\pi$
$600$		0			0
$601$	35.0000			1.42768			0.713840	−	0.700309i	$-0.246954\pi$
$601$	35.0000			1.42768			0.713840	+	0.700309i	$0.246954\pi$
$602$	−4.00000	+	3.46410i	−0.163028	+	0.141186i
$603$		0			0
$604$	−9.50000	−	16.4545i	−0.386550	−	0.669523i
$605$	7.00000	−	12.1244i	0.284590	−	0.492925i
$606$		0			0
$607$	13.5000	+	23.3827i	0.547948	+	0.949074i	0.998415	+	0.0562808i	$0.0179242\pi$
$607$	13.5000	+	23.3827i	0.547948	+	0.949074i	−0.450467	+	0.892793i	$0.648742\pi$
$608$	−8.00000			−0.324443
$609$		0			0
$610$	−6.00000			−0.242933
$611$		0			0
$612$		0			0
$613$	−6.00000	+	10.3923i	−0.242338	+	0.419741i	−0.961380	−	0.275225i	$-0.911248\pi$
$613$	−6.00000	+	10.3923i	−0.242338	+	0.419741i	0.719042	+	0.694967i	$0.244581\pi$
$614$	14.0000	+	24.2487i	0.564994	+	0.978598i
$615$		0			0
$616$	−12.5000	−	4.33013i	−0.503639	−	0.174466i
$617$	−2.00000			−0.0805170			−0.0402585	−	0.999189i	$-0.512818\pi$
$617$	−2.00000			−0.0805170			−0.0402585	+	0.999189i	$0.512818\pi$
$618$		0			0
$619$	−5.00000	+	8.66025i	−0.200967	+	0.348085i	−0.948840	−	0.315757i	$-0.897742\pi$
$619$	−5.00000	+	8.66025i	−0.200967	+	0.348085i	0.747873	+	0.663842i	$0.231075\pi$
$620$	1.50000	−	2.59808i	0.0602414	−	0.104341i
$621$		0			0
$622$	−32.0000			−1.28308
$623$	12.0000	−	10.3923i	0.480770	−	0.416359i
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	0.500000	−	0.866025i	0.0199840	−	0.0346133i
$627$		0			0
$628$	2.00000	+	3.46410i	0.0798087	+	0.138233i
$629$	−16.0000			−0.637962
$630$		0			0
$631$	−19.0000			−0.756378			−0.378189	−	0.925728i	$-0.623453\pi$
$631$	−19.0000			−0.756378			−0.378189	+	0.925728i	$0.623453\pi$
$632$	1.50000	+	2.59808i	0.0596668	+	0.103346i
$633$		0			0
$634$	−1.50000	+	2.59808i	−0.0595726	+	0.103183i
$635$	4.50000	+	7.79423i	0.178577	+	0.309305i
$636$		0			0
$637$		0			0
$638$	25.0000			0.989759
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	13.0000	−	22.5167i	0.513469	−	0.889355i	−0.486409	−	0.873731i	$-0.661693\pi$
$641$	13.0000	−	22.5167i	0.513469	−	0.889355i	0.999878	−	0.0156233i	$-0.00497325\pi$
$642$		0			0
$643$	14.0000			0.552106			0.276053	−	0.961142i	$-0.410973\pi$
$643$	14.0000			0.552106			0.276053	+	0.961142i	$0.410973\pi$
$644$	2.00000	+	10.3923i	0.0788110	+	0.409514i
$645$		0			0
$646$	16.0000	+	27.7128i	0.629512	+	1.09035i
$647$	−9.00000	+	15.5885i	−0.353827	+	0.612845i	−0.986916	−	0.161233i	$-0.948453\pi$
$647$	−9.00000	+	15.5885i	−0.353827	+	0.612845i	0.633090	+	0.774078i	$0.281786\pi$
$648$		0			0
$649$	27.5000	+	47.6314i	1.07947	+	1.86970i
$650$		0			0
$651$		0			0
$652$	−4.00000			−0.156652
$653$	−19.5000	−	33.7750i	−0.763094	−	1.32172i	−0.941248	−	0.337715i	$-0.890346\pi$
$653$	−19.5000	−	33.7750i	−0.763094	−	1.32172i	0.178154	−	0.984003i	$-0.442987\pi$
$654$		0			0
$655$	−0.500000	+	0.866025i	−0.0195366	+	0.0338384i
$656$		0			0
$657$		0			0
$658$	15.0000	+	5.19615i	0.584761	+	0.202567i
$659$	40.0000			1.55818			0.779089	−	0.626913i	$-0.215682\pi$
$659$	40.0000			1.55818			0.779089	+	0.626913i	$0.215682\pi$
$660$		0			0
$661$	−5.00000	+	8.66025i	−0.194477	+	0.336845i	−0.946729	−	0.322031i	$-0.895634\pi$
$661$	−5.00000	+	8.66025i	−0.194477	+	0.336845i	0.752252	+	0.658876i	$0.228968\pi$
$662$	−2.00000	+	3.46410i	−0.0777322	+	0.134636i
$663$		0			0
$664$	−7.00000			−0.271653
$665$	20.0000	+	6.92820i	0.775567	+	0.268664i
$666$		0			0
$667$	−10.0000	−	17.3205i	−0.387202	−	0.670653i
$668$	−7.00000	+	12.1244i	−0.270838	+	0.469105i
$669$		0			0
$670$	1.00000	+	1.73205i	0.0386334	+	0.0669150i
$671$	30.0000			1.15814
$672$		0			0
$673$	−19.0000			−0.732396			−0.366198	−	0.930537i	$-0.619341\pi$
$673$	−19.0000			−0.732396			−0.366198	+	0.930537i	$0.619341\pi$
$674$	4.50000	+	7.79423i	0.173334	+	0.300222i
$675$		0			0
$676$	6.50000	−	11.2583i	0.250000	−	0.433013i
$677$	−13.5000	−	23.3827i	−0.518847	−	0.898670i	−0.999760	−	0.0219013i	$-0.993028\pi$
$677$	−13.5000	−	23.3827i	−0.518847	−	0.898670i	0.480913	−	0.876768i	$-0.340305\pi$
$678$		0			0
$679$	3.50000	+	18.1865i	0.134318	+	0.697935i
$680$	4.00000			0.153393
$681$		0			0
$682$	−7.50000	+	12.9904i	−0.287190	+	0.497427i
$683$	−4.50000	+	7.79423i	−0.172188	+	0.298238i	−0.939184	−	0.343413i	$-0.888417\pi$
$683$	−4.50000	+	7.79423i	−0.172188	+	0.298238i	0.766997	+	0.641651i	$0.221750\pi$
$684$		0			0
$685$	−2.00000			−0.0764161
$686$	8.50000	−	16.4545i	0.324532	−	0.628235i
$687$		0			0
$688$	−1.00000	−	1.73205i	−0.0381246	−	0.0660338i
$689$		0			0
$690$		0			0
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$	−22.0000			−0.836315
$693$		0			0
$694$	12.0000			0.455514
$695$	−7.00000	−	12.1244i	−0.265525	−	0.459903i
$696$		0			0
$697$		0			0
$698$	−7.00000	−	12.1244i	−0.264954	−	0.458914i
$699$		0			0
$700$	−8.00000	+	6.92820i	−0.302372	+	0.261861i
$701$	5.00000			0.188847			0.0944237	−	0.995532i	$-0.469899\pi$
$701$	5.00000			0.188847			0.0944237	+	0.995532i	$0.469899\pi$
$702$		0			0
$703$	16.0000	−	27.7128i	0.603451	−	1.04521i
$704$	2.50000	−	4.33013i	0.0942223	−	0.163198i
$705$		0			0
$706$	24.0000			0.903252
$707$	25.0000	+	8.66025i	0.940222	+	0.325702i
$708$		0			0
$709$	−19.0000	−	32.9090i	−0.713560	−	1.23592i	−0.963512	−	0.267664i	$-0.913748\pi$
$709$	−19.0000	−	32.9090i	−0.713560	−	1.23592i	0.249952	−	0.968258i	$-0.419585\pi$
$710$	1.00000	−	1.73205i	0.0375293	−	0.0650027i
$711$		0			0
$712$	3.00000	+	5.19615i	0.112430	+	0.194734i
$713$	12.0000			0.449404
$714$		0			0
$715$		0			0
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$		0			0
$718$	−5.00000	+	8.66025i	−0.186598	+	0.323198i
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	0.804648	−	0.593753i	$-0.202354\pi$
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	−0.916529	+	0.399969i	$0.869021\pi$
$720$		0			0
$721$	16.0000	−	13.8564i	0.595871	−	0.516040i
$722$	−45.0000			−1.67473
$723$		0			0
$724$		0			0
$725$	10.0000	−	17.3205i	0.371391	−	0.643268i
$726$		0			0
$727$	7.00000			0.259616			0.129808	−	0.991539i	$-0.458564\pi$
$727$	7.00000			0.259616			0.129808	+	0.991539i	$0.458564\pi$
$728$		0			0
$729$		0			0
$730$	−5.00000	−	8.66025i	−0.185058	−	0.320530i
$731$	−4.00000	+	6.92820i	−0.147945	+	0.256249i
$732$		0			0
$733$	3.00000	+	5.19615i	0.110808	+	0.191924i	0.916096	−	0.400959i	$-0.131323\pi$
$733$	3.00000	+	5.19615i	0.110808	+	0.191924i	−0.805289	+	0.592883i	$0.797990\pi$
$734$	−17.0000			−0.627481
$735$		0			0
$736$	−4.00000			−0.147442
$737$	−5.00000	−	8.66025i	−0.184177	−	0.319005i
$738$		0			0
$739$	15.0000	−	25.9808i	0.551784	−	0.955718i	−0.446362	−	0.894852i	$-0.647281\pi$
$739$	15.0000	−	25.9808i	0.551784	−	0.955718i	0.998146	−	0.0608653i	$-0.0193860\pi$
$740$	−2.00000	−	3.46410i	−0.0735215	−	0.127343i
$741$		0			0
$742$	−4.50000	−	23.3827i	−0.165200	−	0.858405i
$743$	−30.0000			−1.10059			−0.550297	−	0.834969i	$-0.685485\pi$
$743$	−30.0000			−1.10059			−0.550297	+	0.834969i	$0.685485\pi$
$744$		0			0
$745$	9.00000	−	15.5885i	0.329734	−	0.571117i
$746$	−16.0000	+	27.7128i	−0.585802	+	1.01464i
$747$		0			0
$748$	−20.0000			−0.731272
$749$	−6.00000	+	5.19615i	−0.219235	+	0.189863i
$750$		0			0
$751$	−22.5000	−	38.9711i	−0.821037	−	1.42208i	−0.904911	−	0.425601i	$-0.860063\pi$
$751$	−22.5000	−	38.9711i	−0.821037	−	1.42208i	0.0838743	−	0.996476i	$-0.473271\pi$
$752$	−3.00000	+	5.19615i	−0.109399	+	0.189484i
$753$		0			0
$754$		0			0
$755$	−19.0000			−0.691481
$756$		0			0
$757$	−54.0000			−1.96266			−0.981332	−	0.192323i	$-0.938398\pi$
$757$	−54.0000			−1.96266			−0.981332	+	0.192323i	$0.938398\pi$
$758$	8.00000	+	13.8564i	0.290573	+	0.503287i
$759$		0			0
$760$	−4.00000	+	6.92820i	−0.145095	+	0.251312i
$761$	4.00000	+	6.92820i	0.145000	+	0.251147i	0.929373	−	0.369142i	$-0.120348\pi$
$761$	4.00000	+	6.92820i	0.145000	+	0.251147i	−0.784373	+	0.620289i	$0.787015\pi$
$762$		0			0
$763$	5.00000	+	1.73205i	0.181012	+	0.0627044i
$764$	−24.0000			−0.868290
$765$		0			0
$766$	17.0000	−	29.4449i	0.614235	−	1.06389i
$767$		0			0
$768$		0			0
$769$	−35.0000			−1.26213			−0.631066	−	0.775729i	$-0.717382\pi$
$769$	−35.0000			−1.26213			−0.631066	+	0.775729i	$0.717382\pi$
$770$	−10.0000	+	8.66025i	−0.360375	+	0.312094i
$771$		0			0
$772$	−2.50000	−	4.33013i	−0.0899770	−	0.155845i
$773$	5.00000	−	8.66025i	0.179838	−	0.311488i	−0.761987	−	0.647592i	$-0.775776\pi$
$773$	5.00000	−	8.66025i	0.179838	−	0.311488i	0.941825	+	0.336104i	$0.109109\pi$
$774$		0			0
$775$	6.00000	+	10.3923i	0.215526	+	0.373303i
$776$	−7.00000			−0.251285
$777$		0			0
$778$	−2.00000			−0.0717035
$779$		0			0
$780$		0			0
$781$	−5.00000	+	8.66025i	−0.178914	+	0.309888i
$782$	8.00000	+	13.8564i	0.286079	+	0.495504i
$783$		0			0
$784$	5.50000	+	4.33013i	0.196429	+	0.154647i
$785$	4.00000			0.142766
$786$		0			0
$787$	9.00000	−	15.5885i	0.320815	−	0.555668i	−0.659841	−	0.751405i	$-0.729376\pi$
$787$	9.00000	−	15.5885i	0.320815	−	0.555668i	0.980656	+	0.195737i	$0.0627098\pi$
$788$	1.00000	−	1.73205i	0.0356235	−	0.0617018i
$789$		0			0
$790$	3.00000			0.106735
$791$	−8.00000	−	41.5692i	−0.284447	−	1.47803i
$792$		0			0
$793$		0			0
$794$	18.0000	−	31.1769i	0.638796	−	1.10643i
$795$		0			0
$796$	2.00000	+	3.46410i	0.0708881	+	0.122782i
$797$	−21.0000			−0.743858			−0.371929	−	0.928261i	$-0.621304\pi$
$797$	−21.0000			−0.743858			−0.371929	+	0.928261i	$0.621304\pi$
$798$		0			0
$799$	24.0000			0.849059
$800$	−2.00000	−	3.46410i	−0.0707107	−	0.122474i
$801$		0			0
$802$	−12.0000	+	20.7846i	−0.423735	+	0.733930i
$803$	25.0000	+	43.3013i	0.882231	+	1.52807i
$804$		0			0
$805$	10.0000	+	3.46410i	0.352454	+	0.122094i
$806$		0			0
$807$		0			0
$808$	−5.00000	+	8.66025i	−0.175899	+	0.304667i
$809$	20.0000	−	34.6410i	0.703163	−	1.21791i	−0.264188	−	0.964471i	$-0.585104\pi$
$809$	20.0000	−	34.6410i	0.703163	−	1.21791i	0.967351	−	0.253442i	$-0.0815627\pi$
$810$		0			0
$811$	−14.0000			−0.491606			−0.245803	−	0.969320i	$-0.579052\pi$
$811$	−14.0000			−0.491606			−0.245803	+	0.969320i	$0.579052\pi$
$812$	−12.5000	−	4.33013i	−0.438664	−	0.151958i
$813$		0			0
$814$	10.0000	+	17.3205i	0.350500	+	0.607083i
$815$	−2.00000	+	3.46410i	−0.0700569	+	0.121342i
$816$		0			0
$817$	−8.00000	−	13.8564i	−0.279885	−	0.484774i
$818$	25.0000			0.874105
$819$		0			0
$820$		0			0
$821$	−12.5000	−	21.6506i	−0.436253	−	0.755612i	0.561144	−	0.827718i	$-0.310361\pi$
$821$	−12.5000	−	21.6506i	−0.436253	−	0.755612i	−0.997397	+	0.0721058i	$0.977028\pi$
$822$		0			0
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	0.272292	+	0.962215i	$0.412218\pi$
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	−0.969448	+	0.245295i	$0.921115\pi$
$824$	4.00000	+	6.92820i	0.139347	+	0.241355i
$825$		0			0
$826$	−5.50000	−	28.5788i	−0.191369	−	0.994385i
$827$	−9.00000			−0.312961			−0.156480	−	0.987681i	$-0.550015\pi$
$827$	−9.00000			−0.312961			−0.156480	+	0.987681i	$0.550015\pi$
$828$		0			0
$829$	16.0000	−	27.7128i	0.555703	−	0.962506i	−0.442145	−	0.896943i	$-0.645783\pi$
$829$	16.0000	−	27.7128i	0.555703	−	0.962506i	0.997848	−	0.0655624i	$-0.0208842\pi$
$830$	−3.50000	+	6.06218i	−0.121487	+	0.210421i
$831$		0			0
$832$		0			0
$833$	4.00000	−	27.7128i	0.138592	−	0.960192i
$834$		0			0
$835$	7.00000	+	12.1244i	0.242245	+	0.419581i
$836$	20.0000	−	34.6410i	0.691714	−	1.19808i
$837$		0			0
$838$		0			0
$839$	28.0000			0.966667			0.483334	−	0.875436i	$-0.339426\pi$
$839$	28.0000			0.966667			0.483334	+	0.875436i	$0.339426\pi$
$840$		0			0
$841$	−4.00000			−0.137931
$842$	15.0000	+	25.9808i	0.516934	+	0.895356i
$843$		0			0
$844$	−1.00000	+	1.73205i	−0.0344214	+	0.0596196i
$845$	−6.50000	−	11.2583i	−0.223607	−	0.387298i
$846$		0			0
$847$	28.0000	−	24.2487i	0.962091	−	0.833196i
$848$	9.00000			0.309061
$849$		0			0
$850$	−8.00000	+	13.8564i	−0.274398	+	0.475271i
$851$	8.00000	−	13.8564i	0.274236	−	0.474991i
$852$		0			0
$853$	14.0000			0.479351			0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000			0.479351			0.239675	+	0.970853i	$0.422959\pi$
$854$	−15.0000	−	5.19615i	−0.513289	−	0.177809i
$855$		0			0
$856$	−1.50000	−	2.59808i	−0.0512689	−	0.0888004i
$857$	−9.00000	+	15.5885i	−0.307434	+	0.532492i	−0.977800	−	0.209539i	$-0.932804\pi$
$857$	−9.00000	+	15.5885i	−0.307434	+	0.532492i	0.670366	+	0.742030i	$0.266137\pi$
$858$		0			0
$859$	17.0000	+	29.4449i	0.580033	+	1.00465i	0.995475	+	0.0950262i	$0.0302935\pi$
$859$	17.0000	+	29.4449i	0.580033	+	1.00465i	−0.415442	+	0.909620i	$0.636373\pi$
$860$	−2.00000			−0.0681994
$861$		0			0
$862$	12.0000			0.408722
$863$	5.00000	+	8.66025i	0.170202	+	0.294798i	0.938490	−	0.345305i	$-0.112225\pi$
$863$	5.00000	+	8.66025i	0.170202	+	0.294798i	−0.768288	+	0.640104i	$0.778891\pi$
$864$		0			0
$865$	−11.0000	+	19.0526i	−0.374011	+	0.647806i
$866$	7.00000	+	12.1244i	0.237870	+	0.412002i
$867$		0			0
$868$	6.00000	−	5.19615i	0.203653	−	0.176369i
$869$	−15.0000			−0.508840
$870$		0			0
$871$		0			0
$872$	−1.00000	+	1.73205i	−0.0338643	+	0.0586546i
$873$		0			0
$874$	−32.0000			−1.08242
$875$	4.50000	+	23.3827i	0.152128	+	0.790479i
$876$		0			0
$877$	16.0000	+	27.7128i	0.540282	+	0.935795i	0.998888	+	0.0471555i	$0.0150156\pi$
$877$	16.0000	+	27.7128i	0.540282	+	0.935795i	−0.458606	+	0.888640i	$0.651651\pi$
$878$	7.50000	−	12.9904i	0.253113	−	0.438404i
$879$		0			0
$880$	−2.50000	−	4.33013i	−0.0842750	−	0.145969i
$881$	42.0000			1.41502			0.707508	−	0.706705i	$-0.249819\pi$
$881$	42.0000			1.41502			0.707508	+	0.706705i	$0.249819\pi$
$882$		0			0
$883$	−40.0000			−1.34611			−0.673054	−	0.739594i	$-0.735018\pi$
$883$	−40.0000			−1.34611			−0.673054	+	0.739594i	$0.735018\pi$
$884$		0			0
$885$		0			0
$886$	−8.50000	+	14.7224i	−0.285563	+	0.494610i
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	0.992149	+	0.125061i	$0.0399128\pi$
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	−0.387768	+	0.921757i	$0.626754\pi$
$888$		0			0
$889$	4.50000	+	23.3827i	0.150925	+	0.784230i
$890$	6.00000			0.201120
$891$		0			0
$892$	3.50000	−	6.06218i	0.117189	−	0.202977i
$893$	−24.0000	+	41.5692i	−0.803129	+	1.39106i
$894$		0			0
$895$	12.0000			0.401116
$896$	−2.00000	+	1.73205i	−0.0668153	+	0.0578638i
$897$		0			0
$898$	−8.00000	−	13.8564i	−0.266963	−	0.462394i
$899$	−7.50000	+	12.9904i	−0.250139	+	0.433253i
$900$		0			0
$901$	−18.0000	−	31.1769i	−0.599667	−	1.03865i
$902$		0			0
$903$		0			0
$904$	16.0000			0.532152
$905$		0			0
$906$		0			0
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	−0.948278	−	0.317441i	$-0.897176\pi$
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	0.749051	+	0.662512i	$0.230510\pi$
$908$	1.50000	+	2.59808i	0.0497792	+	0.0862202i
$909$		0			0
$910$		0			0
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$		0			0
$913$	17.5000	−	30.3109i	0.579165	−	1.00314i
$914$	15.5000	−	26.8468i	0.512694	−	0.888013i
$915$		0			0
$916$	−20.0000			−0.660819
$917$	−2.00000	+	1.73205i	−0.0660458	+	0.0571974i
$918$		0			0
$919$	16.0000	+	27.7128i	0.527791	+	0.914161i	0.999475	+	0.0323936i	$0.0103130\pi$
$919$	16.0000	+	27.7128i	0.527791	+	0.914161i	−0.471684	+	0.881768i	$0.656354\pi$
$920$	−2.00000	+	3.46410i	−0.0659380	+	0.114208i
$921$		0			0
$922$	7.00000	+	12.1244i	0.230533	+	0.399294i
$923$		0			0
$924$		0			0
$925$	16.0000			0.526077
$926$	8.00000	+	13.8564i	0.262896	+	0.455350i
$927$		0			0
$928$	2.50000	−	4.33013i	0.0820665	−	0.142143i
$929$	−3.00000	−	5.19615i	−0.0984268	−	0.170480i	0.812607	−	0.582812i	$-0.198048\pi$
$929$	−3.00000	−	5.19615i	−0.0984268	−	0.170480i	−0.911034	+	0.412332i	$0.864714\pi$
$930$		0			0
$931$	44.0000	+	34.6410i	1.44204	+	1.13531i
$932$	4.00000			0.131024
$933$		0			0
$934$	10.0000	−	17.3205i	0.327210	−	0.566744i
$935$	−10.0000	+	17.3205i	−0.327035	+	0.566441i
$936$		0			0
$937$	35.0000			1.14340			0.571700	−	0.820463i	$-0.306284\pi$
$937$	35.0000			1.14340			0.571700	+	0.820463i	$0.306284\pi$
$938$	1.00000	+	5.19615i	0.0326512	+	0.169660i
$939$		0			0
$940$	3.00000	+	5.19615i	0.0978492	+	0.169480i
$941$	−5.50000	+	9.52628i	−0.179295	+	0.310548i	−0.941639	−	0.336624i	$-0.890715\pi$
$941$	−5.50000	+	9.52628i	−0.179295	+	0.310548i	0.762344	+	0.647172i	$0.224048\pi$
$942$		0			0
$943$		0			0
$944$	11.0000			0.358020
$945$		0			0
$946$	10.0000			0.325128
$947$	−16.0000	−	27.7128i	−0.519930	−	0.900545i	−0.999732	−	0.0231683i	$-0.992625\pi$
$947$	−16.0000	−	27.7128i	−0.519930	−	0.900545i	0.479801	−	0.877377i	$-0.340709\pi$
$948$		0			0
$949$		0			0
$950$	−16.0000	−	27.7128i	−0.519109	−	0.899122i
$951$		0			0
$952$	10.0000	+	3.46410i	0.324102	+	0.112272i
$953$	−2.00000			−0.0647864			−0.0323932	−	0.999475i	$-0.510313\pi$
$953$	−2.00000			−0.0647864			−0.0323932	+	0.999475i	$0.510313\pi$
$954$		0			0
$955$	−12.0000	+	20.7846i	−0.388311	+	0.672574i
$956$	−6.00000	+	10.3923i	−0.194054	+	0.336111i
$957$		0			0
$958$	38.0000			1.22772
$959$	−5.00000	−	1.73205i	−0.161458	−	0.0559308i
$960$		0			0
$961$	11.0000	+	19.0526i	0.354839	+	0.614599i
$962$		0			0
$963$		0			0
$964$	12.5000	+	21.6506i	0.402598	+	0.697320i
$965$	−5.00000			−0.160956
$966$		0			0
$967$	−61.0000			−1.96163			−0.980814	−	0.194946i	$-0.937547\pi$
$967$	−61.0000			−1.96163			−0.980814	+	0.194946i	$0.937547\pi$
$968$	7.00000	+	12.1244i	0.224989	+	0.389692i
$969$		0			0
$970$	−3.50000	+	6.06218i	−0.112378	+	0.194645i
$971$	7.50000	+	12.9904i	0.240686	+	0.416881i	0.960910	−	0.276861i	$-0.0892941\pi$
$971$	7.50000	+	12.9904i	0.240686	+	0.416881i	−0.720224	+	0.693742i	$0.755961\pi$
$972$		0			0
$973$	−7.00000	−	36.3731i	−0.224410	−	1.16607i
$974$	−5.00000			−0.160210
$975$		0			0
$976$	3.00000	−	5.19615i	0.0960277	−	0.166325i
$977$	−15.0000	+	25.9808i	−0.479893	+	0.831198i	−0.999734	−	0.0230645i	$-0.992658\pi$
$977$	−15.0000	+	25.9808i	−0.479893	+	0.831198i	0.519841	+	0.854263i	$0.325991\pi$
$978$		0			0
$979$	−30.0000			−0.958804
$980$	6.50000	−	2.59808i	0.207635	−	0.0829925i
$981$		0			0
$982$	−4.50000	−	7.79423i	−0.143601	−	0.248724i
$983$	−30.0000	+	51.9615i	−0.956851	+	1.65732i	−0.226778	+	0.973946i	$0.572819\pi$
$983$	−30.0000	+	51.9615i	−0.956851	+	1.65732i	−0.730073	+	0.683369i	$0.760514\pi$
$984$		0			0
$985$	−1.00000	−	1.73205i	−0.0318626	−	0.0551877i
$986$	−20.0000			−0.636930
$987$		0			0
$988$		0			0
$989$	−4.00000	−	6.92820i	−0.127193	−	0.220304i
$990$		0			0
$991$	−23.5000	+	40.7032i	−0.746502	+	1.29298i	0.202988	+	0.979181i	$0.434935\pi$
$991$	−23.5000	+	40.7032i	−0.746502	+	1.29298i	−0.949490	+	0.313798i	$0.898398\pi$
$992$	1.50000	+	2.59808i	0.0476250	+	0.0824890i
$993$		0			0
$994$	4.00000	−	3.46410i	0.126872	−	0.109875i
$995$	4.00000			0.126809
$996$		0			0
$997$	−19.0000	+	32.9090i	−0.601736	+	1.04224i	0.390822	+	0.920466i	$0.372191\pi$
$997$	−19.0000	+	32.9090i	−0.601736	+	1.04224i	−0.992558	+	0.121771i	$0.961143\pi$
$998$	5.00000	−	8.66025i	0.158272	−	0.274136i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.g.c.109.1		2
3.2	odd	2		42.2.e.a.25.1	✓	2
4.3	odd	2		1008.2.s.k.865.1		2
7.2	even	3	inner	126.2.g.c.37.1		2
7.3	odd	6		882.2.a.d.1.1		1
7.4	even	3		882.2.a.c.1.1		1
7.5	odd	6		882.2.g.i.667.1		2
7.6	odd	2		882.2.g.i.361.1		2
9.2	odd	6		1134.2.h.e.109.1		2
9.4	even	3		1134.2.e.e.865.1		2
9.5	odd	6		1134.2.e.l.865.1		2
9.7	even	3		1134.2.h.l.109.1		2
12.11	even	2		336.2.q.b.193.1		2
15.2	even	4		1050.2.o.a.949.2		4
15.8	even	4		1050.2.o.a.949.1		4
15.14	odd	2		1050.2.i.l.151.1		2
21.2	odd	6		42.2.e.a.37.1	yes	2
21.5	even	6		294.2.e.b.79.1		2
21.11	odd	6		294.2.a.e.1.1		1
21.17	even	6		294.2.a.f.1.1		1
21.20	even	2		294.2.e.b.67.1		2
24.5	odd	2		1344.2.q.g.193.1		2
24.11	even	2		1344.2.q.s.193.1		2
28.3	even	6		7056.2.a.bl.1.1		1
28.11	odd	6		7056.2.a.w.1.1		1
28.23	odd	6		1008.2.s.k.289.1		2
63.2	odd	6		1134.2.e.l.919.1		2
63.16	even	3		1134.2.e.e.919.1		2
63.23	odd	6		1134.2.h.e.541.1		2
63.58	even	3		1134.2.h.l.541.1		2
84.11	even	6		2352.2.a.t.1.1		1
84.23	even	6		336.2.q.b.289.1		2
84.47	odd	6		2352.2.q.u.961.1		2
84.59	odd	6		2352.2.a.f.1.1		1
84.83	odd	2		2352.2.q.u.1537.1		2
105.2	even	12		1050.2.o.a.499.1		4
105.23	even	12		1050.2.o.a.499.2		4
105.44	odd	6		1050.2.i.l.751.1		2
105.59	even	6		7350.2.a.q.1.1		1
105.74	odd	6		7350.2.a.bl.1.1		1
168.11	even	6		9408.2.a.q.1.1		1
168.53	odd	6		9408.2.a.ce.1.1		1
168.59	odd	6		9408.2.a.cr.1.1		1
168.101	even	6		9408.2.a.z.1.1		1
168.107	even	6		1344.2.q.s.961.1		2
168.149	odd	6		1344.2.q.g.961.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.e.a.25.1	✓	2	3.2	odd	2
42.2.e.a.37.1	yes	2	21.2	odd	6
126.2.g.c.37.1		2	7.2	even	3	inner
126.2.g.c.109.1		2	1.1	even	1	trivial
294.2.a.e.1.1		1	21.11	odd	6
294.2.a.f.1.1		1	21.17	even	6
294.2.e.b.67.1		2	21.20	even	2
294.2.e.b.79.1		2	21.5	even	6
336.2.q.b.193.1		2	12.11	even	2
336.2.q.b.289.1		2	84.23	even	6
882.2.a.c.1.1		1	7.4	even	3
882.2.a.d.1.1		1	7.3	odd	6
882.2.g.i.361.1		2	7.6	odd	2
882.2.g.i.667.1		2	7.5	odd	6
1008.2.s.k.289.1		2	28.23	odd	6
1008.2.s.k.865.1		2	4.3	odd	2
1050.2.i.l.151.1		2	15.14	odd	2
1050.2.i.l.751.1		2	105.44	odd	6
1050.2.o.a.499.1		4	105.2	even	12
1050.2.o.a.499.2		4	105.23	even	12
1050.2.o.a.949.1		4	15.8	even	4
1050.2.o.a.949.2		4	15.2	even	4
1134.2.e.e.865.1		2	9.4	even	3
1134.2.e.e.919.1		2	63.16	even	3
1134.2.e.l.865.1		2	9.5	odd	6
1134.2.e.l.919.1		2	63.2	odd	6
1134.2.h.e.109.1		2	9.2	odd	6
1134.2.h.e.541.1		2	63.23	odd	6
1134.2.h.l.109.1		2	9.7	even	3
1134.2.h.l.541.1		2	63.58	even	3
1344.2.q.g.193.1		2	24.5	odd	2
1344.2.q.g.961.1		2	168.149	odd	6
1344.2.q.s.193.1		2	24.11	even	2
1344.2.q.s.961.1		2	168.107	even	6
2352.2.a.f.1.1		1	84.59	odd	6
2352.2.a.t.1.1		1	84.11	even	6
2352.2.q.u.961.1		2	84.47	odd	6
2352.2.q.u.1537.1		2	84.83	odd	2
7056.2.a.w.1.1		1	28.11	odd	6
7056.2.a.bl.1.1		1	28.3	even	6
7350.2.a.q.1.1		1	105.59	even	6
7350.2.a.bl.1.1		1	105.74	odd	6
9408.2.a.q.1.1		1	168.11	even	6
9408.2.a.z.1.1		1	168.101	even	6
9408.2.a.ce.1.1		1	168.53	odd	6
9408.2.a.cr.1.1		1	168.59	odd	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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{10} +(2.50000 - 4.33013i) q^{11} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(-4.00000 - 6.92820i) q^{19} -1.00000 q^{20} +5.00000 q^{22} +(-2.00000 - 3.46410i) q^{23} +(2.00000 - 3.46410i) q^{25} +(-2.50000 - 0.866025i) q^{28} +5.00000 q^{29} +(-1.50000 + 2.59808i) q^{31} +(0.500000 - 0.866025i) q^{32} -4.00000 q^{34} +(-2.00000 + 1.73205i) q^{35} +(2.00000 + 3.46410i) q^{37} +(4.00000 - 6.92820i) q^{38} +(-0.500000 - 0.866025i) q^{40} +2.00000 q^{43} +(2.50000 + 4.33013i) q^{44} +(2.00000 - 3.46410i) q^{46} +(-3.00000 - 5.19615i) q^{47} +(-6.50000 + 2.59808i) q^{49} +4.00000 q^{50} +(-4.50000 + 7.79423i) q^{53} +5.00000 q^{55} +(-0.500000 - 2.59808i) q^{56} +(2.50000 + 4.33013i) q^{58} +(-5.50000 + 9.52628i) q^{59} +(3.00000 + 5.19615i) q^{61} -3.00000 q^{62} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(-2.50000 - 0.866025i) q^{70} -2.00000 q^{71} +(-5.00000 + 8.66025i) q^{73} +(-2.00000 + 3.46410i) q^{74} +8.00000 q^{76} +(12.5000 + 4.33013i) q^{77} +(-1.50000 - 2.59808i) q^{79} +(0.500000 - 0.866025i) q^{80} +7.00000 q^{83} -4.00000 q^{85} +(1.00000 + 1.73205i) q^{86} +(-2.50000 + 4.33013i) q^{88} +(-3.00000 - 5.19615i) q^{89} +4.00000 q^{92} +(3.00000 - 5.19615i) q^{94} +(4.00000 - 6.92820i) q^{95} +7.00000 q^{97} +(-5.50000 - 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} + q^{5} + q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 + q^5 + q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} + q^{5} + q^{7} - 2 q^{8} - q^{10} + 5 q^{11} - 4 q^{14} - q^{16} - 4 q^{17} - 8 q^{19} - 2 q^{20} + 10 q^{22} - 4 q^{23} + 4 q^{25} - 5 q^{28} + 10 q^{29} - 3 q^{31} + q^{32} - 8 q^{34} - 4 q^{35} + 4 q^{37} + 8 q^{38} - q^{40} + 4 q^{43} + 5 q^{44} + 4 q^{46} - 6 q^{47} - 13 q^{49} + 8 q^{50} - 9 q^{53} + 10 q^{55} - q^{56} + 5 q^{58} - 11 q^{59} + 6 q^{61} - 6 q^{62} + 2 q^{64} + 2 q^{67} - 4 q^{68} - 5 q^{70} - 4 q^{71} - 10 q^{73} - 4 q^{74} + 16 q^{76} + 25 q^{77} - 3 q^{79} + q^{80} + 14 q^{83} - 8 q^{85} + 2 q^{86} - 5 q^{88} - 6 q^{89} + 8 q^{92} + 6 q^{94} + 8 q^{95} + 14 q^{97} - 11 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 + q^5 + q^7 - 2 * q^8 - q^10 + 5 * q^11 - 4 * q^14 - q^16 - 4 * q^17 - 8 * q^19 - 2 * q^20 + 10 * q^22 - 4 * q^23 + 4 * q^25 - 5 * q^28 + 10 * q^29 - 3 * q^31 + q^32 - 8 * q^34 - 4 * q^35 + 4 * q^37 + 8 * q^38 - q^40 + 4 * q^43 + 5 * q^44 + 4 * q^46 - 6 * q^47 - 13 * q^49 + 8 * q^50 - 9 * q^53 + 10 * q^55 - q^56 + 5 * q^58 - 11 * q^59 + 6 * q^61 - 6 * q^62 + 2 * q^64 + 2 * q^67 - 4 * q^68 - 5 * q^70 - 4 * q^71 - 10 * q^73 - 4 * q^74 + 16 * q^76 + 25 * q^77 - 3 * q^79 + q^80 + 14 * q^83 - 8 * q^85 + 2 * q^86 - 5 * q^88 - 6 * q^89 + 8 * q^92 + 6 * q^94 + 8 * q^95 + 14 * q^97 - 11 * q^98

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