LMFDB - Embedded newform 950.2.j.d.349.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(49,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("950.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	950.349
Dual form			950.2.j.d.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{7} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{7} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +5.00000 q^{11} +(-1.73205 - 1.00000i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} -3.00000i q^{18} +(0.500000 + 4.33013i) q^{19} +(-4.33013 + 2.50000i) q^{22} +(-0.866025 - 0.500000i) q^{23} +2.00000 q^{26} +(-0.866025 - 0.500000i) q^{28} +(3.00000 - 5.19615i) q^{29} +4.00000 q^{31} +(0.866025 + 0.500000i) q^{32} +(1.50000 + 2.59808i) q^{36} +11.0000i q^{37} +(-2.59808 - 3.50000i) q^{38} +(4.50000 + 7.79423i) q^{41} +(5.19615 - 3.00000i) q^{43} +(2.50000 - 4.33013i) q^{44} +1.00000 q^{46} +6.00000 q^{49} +(-1.73205 + 1.00000i) q^{52} +(-4.33013 - 2.50000i) q^{53} +1.00000 q^{56} +6.00000i q^{58} +(-3.46410 + 2.00000i) q^{62} +(2.59808 + 1.50000i) q^{63} -1.00000 q^{64} +(10.3923 + 6.00000i) q^{67} +(-3.00000 - 5.19615i) q^{71} +(-2.59808 - 1.50000i) q^{72} +(12.1244 - 7.00000i) q^{73} +(-5.50000 - 9.52628i) q^{74} +(4.00000 + 1.73205i) q^{76} -5.00000i q^{77} +(5.00000 + 8.66025i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-7.79423 - 4.50000i) q^{82} +14.0000i q^{83} +(-3.00000 + 5.19615i) q^{86} +5.00000i q^{88} +(-3.50000 + 6.06218i) q^{89} +(-1.00000 + 1.73205i) q^{91} +(-0.866025 + 0.500000i) q^{92} +(1.73205 - 1.00000i) q^{97} +(-5.19615 + 3.00000i) q^{98} +(-7.50000 + 12.9904i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 6 * q^9	$ 4 q + 2 q^{4} - 6 q^{9} + 20 q^{11} + 2 q^{14} - 2 q^{16} + 2 q^{19} + 8 q^{26} + 12 q^{29} + 16 q^{31} + 6 q^{36} + 18 q^{41} + 10 q^{44} + 4 q^{46} + 24 q^{49} + 4 q^{56} - 4 q^{64} - 12 q^{71} - 22 q^{74} + 16 q^{76} + 20 q^{79} - 18 q^{81} - 12 q^{86} - 14 q^{89} - 4 q^{91} - 30 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 - 6 * q^9 + 20 * q^11 + 2 * q^14 - 2 * q^16 + 2 * q^19 + 8 * q^26 + 12 * q^29 + 16 * q^31 + 6 * q^36 + 18 * q^41 + 10 * q^44 + 4 * q^46 + 24 * q^49 + 4 * q^56 - 4 * q^64 - 12 * q^71 - 22 * q^74 + 16 * q^76 + 20 * q^79 - 18 * q^81 - 12 * q^86 - 14 * q^89 - 4 * q^91 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$3$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	1.00000i		−	0.377964i	−0.981981	−	0.188982i	$-0.939481\pi$
$7$		−	1.00000i		−	0.377964i	0.981981	−	0.188982i	$-0.0605189\pi$
$8$			1.00000i			0.353553i
$9$	−1.50000	+	2.59808i	−0.500000	+	0.866025i
$10$		0			0
$11$	5.00000			1.50756			0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000			1.50756			0.753778	+	0.657129i	$0.228229\pi$
$12$		0			0
$13$	−1.73205	−	1.00000i	−0.480384	−	0.277350i	0.240192	−	0.970725i	$-0.422790\pi$
$13$	−1.73205	−	1.00000i	−0.480384	−	0.277350i	−0.720577	+	0.693375i	$0.756123\pi$
$14$	0.500000	+	0.866025i	0.133631	+	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$17$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$18$		−	3.00000i		−	0.707107i
$19$	0.500000	+	4.33013i	0.114708	+	0.993399i
$19$	0.500000	+	4.33013i	0.114708	+	0.993399i
$20$		0			0
$21$		0			0
$22$	−4.33013	+	2.50000i	−0.923186	+	0.533002i
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i	0.406986	−	0.913434i	$-0.366580\pi$
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i	−0.587565	+	0.809177i	$0.699913\pi$
$24$		0			0
$25$		0			0
$26$	2.00000			0.392232
$27$		0			0
$28$	−0.866025	−	0.500000i	−0.163663	−	0.0944911i
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	−0.440652	−	0.897678i	$-0.645253\pi$
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	0.997738	−	0.0672232i	$-0.0214140\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$			11.0000i			1.80839i	0.427121	+	0.904194i	$0.359528\pi$
$37$			11.0000i			1.80839i	−0.427121	+	0.904194i	$0.640472\pi$
$38$	−2.59808	−	3.50000i	−0.421464	−	0.567775i
$39$		0			0
$40$		0			0
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	0.967486	+	0.252924i	$0.0813924\pi$
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	−0.264704	+	0.964330i	$0.585274\pi$
$42$		0			0
$43$	5.19615	−	3.00000i	0.792406	−	0.457496i	−0.0484030	−	0.998828i	$-0.515413\pi$
$43$	5.19615	−	3.00000i	0.792406	−	0.457496i	0.840809	+	0.541332i	$0.182080\pi$
$44$	2.50000	−	4.33013i	0.376889	−	0.652791i
$45$		0			0
$46$	1.00000			0.147442
$47$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$47$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$48$		0			0
$49$	6.00000			0.857143
$50$		0			0
$51$		0			0
$52$	−1.73205	+	1.00000i	−0.240192	+	0.138675i
$53$	−4.33013	−	2.50000i	−0.594789	−	0.343401i	0.172200	−	0.985062i	$-0.444912\pi$
$53$	−4.33013	−	2.50000i	−0.594789	−	0.343401i	−0.766989	+	0.641661i	$0.778246\pi$
$54$		0			0
$55$		0			0
$56$	1.00000			0.133631
$57$		0			0
$58$			6.00000i			0.787839i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$61$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$62$	−3.46410	+	2.00000i	−0.439941	+	0.254000i
$63$	2.59808	+	1.50000i	0.327327	+	0.188982i
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	10.3923	+	6.00000i	1.26962	+	0.733017i	0.974916	−	0.222571i	$-0.0714450\pi$
$67$	10.3923	+	6.00000i	1.26962	+	0.733017i	0.294706	+	0.955588i	$0.404778\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	0.631260	−	0.775571i	$-0.282538\pi$
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	−0.987294	+	0.158901i	$0.949205\pi$
$72$	−2.59808	−	1.50000i	−0.306186	−	0.176777i
$73$	12.1244	−	7.00000i	1.41905	−	0.819288i	0.422833	−	0.906208i	$-0.361036\pi$
$73$	12.1244	−	7.00000i	1.41905	−	0.819288i	0.996215	+	0.0869195i	$0.0277023\pi$
$74$	−5.50000	−	9.52628i	−0.639362	−	1.10741i
$75$		0			0
$76$	4.00000	+	1.73205i	0.458831	+	0.198680i
$77$		−	5.00000i		−	0.569803i
$78$		0			0
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	0.997274	+	0.0737937i	$0.0235106\pi$
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	−0.434730	+	0.900561i	$0.643156\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−7.79423	−	4.50000i	−0.860729	−	0.496942i
$83$			14.0000i			1.53670i	0.640030	+	0.768350i	$0.278922\pi$
$83$			14.0000i			1.53670i	−0.640030	+	0.768350i	$0.721078\pi$
$84$		0			0
$85$		0			0
$86$	−3.00000	+	5.19615i	−0.323498	+	0.560316i
$87$		0			0
$88$			5.00000i			0.533002i
$89$	−3.50000	+	6.06218i	−0.370999	+	0.642590i	−0.989720	−	0.143022i	$-0.954318\pi$
$89$	−3.50000	+	6.06218i	−0.370999	+	0.642590i	0.618720	+	0.785611i	$0.287651\pi$
$90$		0			0
$91$	−1.00000	+	1.73205i	−0.104828	+	0.181568i
$92$	−0.866025	+	0.500000i	−0.0902894	+	0.0521286i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	1.73205	−	1.00000i	0.175863	−	0.101535i	−0.409484	−	0.912317i	$-0.634291\pi$
$97$	1.73205	−	1.00000i	0.175863	−	0.101535i	0.585348	+	0.810782i	$0.300958\pi$
$98$	−5.19615	+	3.00000i	−0.524891	+	0.303046i
$99$	−7.50000	+	12.9904i	−0.753778	+	1.30558i
$100$		0			0
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	−0.999996	−	0.00286291i	$-0.999089\pi$
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	0.502477	+	0.864590i	$0.332422\pi$
$102$		0			0
$103$			13.0000i			1.28093i	0.767988	+	0.640464i	$0.221258\pi$
$103$			13.0000i			1.28093i	−0.767988	+	0.640464i	$0.778742\pi$
$104$	1.00000	−	1.73205i	0.0980581	−	0.169842i
$105$		0			0
$106$	5.00000			0.485643
$107$			4.00000i			0.386695i	0.981130	+	0.193347i	$0.0619344\pi$
$107$			4.00000i			0.386695i	−0.981130	+	0.193347i	$0.938066\pi$
$108$		0			0
$109$	2.00000	+	3.46410i	0.191565	+	0.331801i	0.945769	−	0.324840i	$-0.105310\pi$
$109$	2.00000	+	3.46410i	0.191565	+	0.331801i	−0.754204	+	0.656640i	$0.771977\pi$
$110$		0			0
$111$		0			0
$112$	−0.866025	+	0.500000i	−0.0818317	+	0.0472456i
$113$		−	12.0000i		−	1.12887i	−0.825479	−	0.564433i	$-0.809095\pi$
$113$		−	12.0000i		−	1.12887i	0.825479	−	0.564433i	$-0.190905\pi$
$114$		0			0
$115$		0			0
$116$	−3.00000	−	5.19615i	−0.278543	−	0.482451i
$117$	5.19615	−	3.00000i	0.480384	−	0.277350i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	14.0000			1.27273
$122$		0			0
$123$		0			0
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$		0			0
$126$	−3.00000			−0.267261
$127$	−12.9904	−	7.50000i	−1.15271	−	0.665517i	−0.203164	−	0.979145i	$-0.565122\pi$
$127$	−12.9904	−	7.50000i	−1.15271	−	0.665517i	−0.949546	+	0.313627i	$0.898456\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$		0			0
$131$	−0.500000	−	0.866025i	−0.0436852	−	0.0756650i	0.843356	−	0.537355i	$-0.180577\pi$
$131$	−0.500000	−	0.866025i	−0.0436852	−	0.0756650i	−0.887041	+	0.461690i	$0.847243\pi$
$132$		0			0
$133$	4.33013	−	0.500000i	0.375470	−	0.0433555i
$134$	−12.0000			−1.03664
$135$		0			0
$136$		0			0
$137$	10.3923	+	6.00000i	0.887875	+	0.512615i	0.873247	−	0.487278i	$-0.162010\pi$
$137$	10.3923	+	6.00000i	0.887875	+	0.512615i	0.0146279	+	0.999893i	$0.495344\pi$
$138$		0			0
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	−0.296866	−	0.954919i	$-0.595942\pi$
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	0.975417	−	0.220366i	$-0.0707252\pi$
$140$		0			0
$141$		0			0
$142$	5.19615	+	3.00000i	0.436051	+	0.251754i
$143$	−8.66025	−	5.00000i	−0.724207	−	0.418121i
$144$	3.00000			0.250000
$145$		0			0
$146$	−7.00000	+	12.1244i	−0.579324	+	1.00342i
$147$		0			0
$148$	9.52628	+	5.50000i	0.783055	+	0.452097i
$149$	−2.00000	−	3.46410i	−0.163846	−	0.283790i	0.772399	−	0.635138i	$-0.219057\pi$
$149$	−2.00000	−	3.46410i	−0.163846	−	0.283790i	−0.936245	+	0.351348i	$0.885723\pi$
$150$		0			0
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$	−4.33013	+	0.500000i	−0.351220	+	0.0405554i
$153$		0			0
$154$	2.50000	+	4.33013i	0.201456	+	0.348932i
$155$		0			0
$156$		0			0
$157$	18.1865	−	10.5000i	1.45144	−	0.837991i	0.452880	−	0.891572i	$-0.350397\pi$
$157$	18.1865	−	10.5000i	1.45144	−	0.837991i	0.998564	+	0.0535803i	$0.0170633\pi$
$158$	−8.66025	−	5.00000i	−0.688973	−	0.397779i
$159$		0			0
$160$		0			0
$161$	−0.500000	+	0.866025i	−0.0394055	+	0.0682524i
$162$	7.79423	+	4.50000i	0.612372	+	0.353553i
$163$			10.0000i			0.783260i	0.920123	+	0.391630i	$0.128089\pi$
$163$			10.0000i			0.783260i	−0.920123	+	0.391630i	$0.871911\pi$
$164$	9.00000			0.702782
$165$		0			0
$166$	−7.00000	−	12.1244i	−0.543305	−	0.941033i
$167$	−4.33013	−	2.50000i	−0.335075	−	0.193456i	0.323017	−	0.946393i	$-0.395303\pi$
$167$	−4.33013	−	2.50000i	−0.335075	−	0.193456i	−0.658092	+	0.752937i	$0.728636\pi$
$168$		0			0
$169$	−4.50000	−	7.79423i	−0.346154	−	0.599556i
$170$		0			0
$171$	−12.0000	−	5.19615i	−0.917663	−	0.397360i
$172$		−	6.00000i		−	0.457496i
$173$	0.866025	−	0.500000i	0.0658427	−	0.0380143i	−0.466717	−	0.884407i	$-0.654563\pi$
$173$	0.866025	−	0.500000i	0.0658427	−	0.0380143i	0.532560	+	0.846392i	$0.321230\pi$
$174$		0			0
$175$		0			0
$176$	−2.50000	−	4.33013i	−0.188445	−	0.326396i
$177$		0			0
$178$		−	7.00000i		−	0.524672i
$179$	−19.0000			−1.42013			−0.710063	−	0.704138i	$-0.751334\pi$
$179$	−19.0000			−1.42013			−0.710063	+	0.704138i	$0.751334\pi$
$180$		0			0
$181$	−1.00000	+	1.73205i	−0.0743294	+	0.128742i	−0.900794	−	0.434246i	$-0.857015\pi$
$181$	−1.00000	+	1.73205i	−0.0743294	+	0.128742i	0.826465	+	0.562988i	$0.190348\pi$
$182$		−	2.00000i		−	0.148250i
$183$		0			0
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−18.0000			−1.30243			−0.651217	−	0.758891i	$-0.725741\pi$
$191$	−18.0000			−1.30243			−0.651217	+	0.758891i	$0.725741\pi$
$192$		0			0
$193$	3.46410	−	2.00000i	0.249351	−	0.143963i	−0.370116	−	0.928986i	$-0.620682\pi$
$193$	3.46410	−	2.00000i	0.249351	−	0.143963i	0.619467	+	0.785022i	$0.287349\pi$
$194$	−1.00000	+	1.73205i	−0.0717958	+	0.124354i
$195$		0			0
$196$	3.00000	−	5.19615i	0.214286	−	0.371154i
$197$		−	23.0000i		−	1.63868i	−0.573306	−	0.819341i	$-0.694340\pi$
$197$		−	23.0000i		−	1.63868i	0.573306	−	0.819341i	$-0.305660\pi$
$198$		−	15.0000i		−	1.06600i
$199$	12.0000	−	20.7846i	0.850657	−	1.47338i	−0.0299585	−	0.999551i	$-0.509538\pi$
$199$	12.0000	−	20.7846i	0.850657	−	1.47338i	0.880616	−	0.473831i	$-0.157129\pi$
$200$		0			0
$201$		0			0
$202$		−	10.0000i		−	0.703598i
$203$	−5.19615	−	3.00000i	−0.364698	−	0.210559i
$204$		0			0
$205$		0			0
$206$	−6.50000	−	11.2583i	−0.452876	−	0.784405i
$207$	2.59808	−	1.50000i	0.180579	−	0.104257i
$208$			2.00000i			0.138675i
$209$	2.50000	+	21.6506i	0.172929	+	1.49761i
$210$		0			0
$211$	−6.50000	−	11.2583i	−0.447478	−	0.775055i	0.550743	−	0.834675i	$-0.314345\pi$
$211$	−6.50000	−	11.2583i	−0.447478	−	0.775055i	−0.998221	+	0.0596196i	$0.981011\pi$
$212$	−4.33013	+	2.50000i	−0.297394	+	0.171701i
$213$		0			0
$214$	−2.00000	−	3.46410i	−0.136717	−	0.236801i
$215$		0			0
$216$		0			0
$217$		−	4.00000i		−	0.271538i
$218$	−3.46410	−	2.00000i	−0.234619	−	0.135457i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−19.9186	+	11.5000i	−1.33385	+	0.770097i	−0.985887	−	0.167412i	$-0.946459\pi$
$223$	−19.9186	+	11.5000i	−1.33385	+	0.770097i	−0.347960	+	0.937509i	$0.613126\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$		0			0
$226$	6.00000	+	10.3923i	0.399114	+	0.691286i
$227$			10.0000i			0.663723i	0.943328	+	0.331862i	$0.107677\pi$
$227$			10.0000i			0.663723i	−0.943328	+	0.331862i	$0.892323\pi$
$228$		0			0
$229$	−6.00000			−0.396491			−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000			−0.396491			−0.198246	+	0.980152i	$0.563524\pi$
$230$		0			0
$231$		0			0
$232$	5.19615	+	3.00000i	0.341144	+	0.196960i
$233$	8.66025	−	5.00000i	0.567352	−	0.327561i	−0.188739	−	0.982027i	$-0.560440\pi$
$233$	8.66025	−	5.00000i	0.567352	−	0.327561i	0.756091	+	0.654466i	$0.227107\pi$
$234$	−3.00000	+	5.19615i	−0.196116	+	0.339683i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$		0			0
$241$	9.00000	−	15.5885i	0.579741	−	1.00414i	−0.415768	−	0.909471i	$-0.636487\pi$
$241$	9.00000	−	15.5885i	0.579741	−	1.00414i	0.995509	−	0.0946700i	$-0.0301796\pi$
$242$	−12.1244	+	7.00000i	−0.779383	+	0.449977i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.46410	−	8.00000i	0.220416	−	0.509028i
$248$			4.00000i			0.254000i
$249$		0			0
$250$		0			0
$251$	6.00000	−	10.3923i	0.378717	−	0.655956i	−0.612159	−	0.790735i	$-0.709699\pi$
$251$	6.00000	−	10.3923i	0.378717	−	0.655956i	0.990876	+	0.134778i	$0.0430322\pi$
$252$	2.59808	−	1.50000i	0.163663	−	0.0944911i
$253$	−4.33013	−	2.50000i	−0.272233	−	0.157174i
$254$	15.0000			0.941184
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.1244	−	7.00000i	−0.756297	−	0.436648i	0.0716680	−	0.997429i	$-0.477168\pi$
$257$	−12.1244	−	7.00000i	−0.756297	−	0.436648i	−0.827964	+	0.560781i	$0.810501\pi$
$258$		0			0
$259$	11.0000			0.683507
$260$		0			0
$261$	9.00000	+	15.5885i	0.557086	+	0.964901i
$262$	0.866025	+	0.500000i	0.0535032	+	0.0308901i
$263$	9.52628	−	5.50000i	0.587416	−	0.339145i	−0.176659	−	0.984272i	$-0.556529\pi$
$263$	9.52628	−	5.50000i	0.587416	−	0.339145i	0.764075	+	0.645128i	$0.223196\pi$
$264$		0			0
$265$		0			0
$266$	−3.50000	+	2.59808i	−0.214599	+	0.159298i
$267$		0			0
$268$	10.3923	−	6.00000i	0.634811	−	0.366508i
$269$	−14.0000	−	24.2487i	−0.853595	−	1.47847i	−0.877942	−	0.478766i	$-0.841084\pi$
$269$	−14.0000	−	24.2487i	−0.853595	−	1.47847i	0.0243472	−	0.999704i	$-0.492249\pi$
$270$		0			0
$271$	3.00000	+	5.19615i	0.182237	+	0.315644i	0.942642	−	0.333805i	$-0.108333\pi$
$271$	3.00000	+	5.19615i	0.182237	+	0.315644i	−0.760405	+	0.649449i	$0.775000\pi$
$272$		0			0
$273$		0			0
$274$	−12.0000			−0.724947
$275$		0			0
$276$		0			0
$277$			2.00000i			0.120168i	0.998193	+	0.0600842i	$0.0191369\pi$
$277$			2.00000i			0.120168i	−0.998193	+	0.0600842i	$0.980863\pi$
$278$			16.0000i			0.959616i
$279$	−6.00000	+	10.3923i	−0.359211	+	0.622171i
$280$		0			0
$281$	7.50000	−	12.9904i	0.447412	−	0.774941i	−0.550804	−	0.834634i	$-0.685679\pi$
$281$	7.50000	−	12.9904i	0.447412	−	0.774941i	0.998217	+	0.0596933i	$0.0190123\pi$
$282$		0			0
$283$	−12.1244	+	7.00000i	−0.720718	+	0.416107i	−0.815017	−	0.579437i	$-0.803272\pi$
$283$	−12.1244	+	7.00000i	−0.720718	+	0.416107i	0.0942988	+	0.995544i	$0.469939\pi$
$284$	−6.00000			−0.356034
$285$		0			0
$286$	10.0000			0.591312
$287$	7.79423	−	4.50000i	0.460079	−	0.265627i
$288$	−2.59808	+	1.50000i	−0.153093	+	0.0883883i
$289$	−8.50000	+	14.7224i	−0.500000	+	0.866025i
$290$		0			0
$291$		0			0
$292$		−	14.0000i		−	0.819288i
$293$		−	21.0000i		−	1.22683i	−0.789760	−	0.613417i	$-0.789795\pi$
$293$		−	21.0000i		−	1.22683i	0.789760	−	0.613417i	$-0.210205\pi$
$294$		0			0
$295$		0			0
$296$	−11.0000			−0.639362
$297$		0			0
$298$	3.46410	+	2.00000i	0.200670	+	0.115857i
$299$	1.00000	+	1.73205i	0.0578315	+	0.100167i
$300$		0			0
$301$	−3.00000	−	5.19615i	−0.172917	−	0.299501i
$302$	13.8564	−	8.00000i	0.797347	−	0.460348i
$303$		0			0
$304$	3.50000	−	2.59808i	0.200739	−	0.149010i
$305$		0			0
$306$		0			0
$307$	1.73205	−	1.00000i	0.0988534	−	0.0570730i	−0.449758	−	0.893150i	$-0.648490\pi$
$307$	1.73205	−	1.00000i	0.0988534	−	0.0570730i	0.548612	+	0.836077i	$0.315157\pi$
$308$	−4.33013	−	2.50000i	−0.246732	−	0.142451i
$309$		0			0
$310$		0			0
$311$	4.00000			0.226819			0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000			0.226819			0.113410	+	0.993548i	$0.463823\pi$
$312$		0			0
$313$	24.2487	+	14.0000i	1.37062	+	0.791327i	0.991006	−	0.133819i	$-0.0427240\pi$
$313$	24.2487	+	14.0000i	1.37062	+	0.791327i	0.379612	+	0.925146i	$0.376057\pi$
$314$	−10.5000	+	18.1865i	−0.592549	+	1.02633i
$315$		0			0
$316$	10.0000			0.562544
$317$	−23.3827	−	13.5000i	−1.31330	−	0.758236i	−0.330661	−	0.943750i	$-0.607272\pi$
$317$	−23.3827	−	13.5000i	−1.31330	−	0.758236i	−0.982642	+	0.185514i	$0.940605\pi$
$318$		0			0
$319$	15.0000	−	25.9808i	0.839839	−	1.45464i
$320$		0			0
$321$		0			0
$322$		−	1.00000i		−	0.0557278i
$323$		0			0
$324$	−9.00000			−0.500000
$325$		0			0
$326$	−5.00000	−	8.66025i	−0.276924	−	0.479647i
$327$		0			0
$328$	−7.79423	+	4.50000i	−0.430364	+	0.248471i
$329$		0			0
$330$		0			0
$331$	−25.0000			−1.37412			−0.687062	−	0.726599i	$-0.741100\pi$
$331$	−25.0000			−1.37412			−0.687062	+	0.726599i	$0.741100\pi$
$332$	12.1244	+	7.00000i	0.665410	+	0.384175i
$333$	−28.5788	−	16.5000i	−1.56611	−	0.904194i
$334$	5.00000			0.273588
$335$		0			0
$336$		0			0
$337$	−5.19615	+	3.00000i	−0.283052	+	0.163420i	−0.634804	−	0.772673i	$-0.718919\pi$
$337$	−5.19615	+	3.00000i	−0.283052	+	0.163420i	0.351752	+	0.936093i	$0.385586\pi$
$338$	7.79423	+	4.50000i	0.423950	+	0.244768i
$339$		0			0
$340$		0			0
$341$	20.0000			1.08306
$342$	12.9904	−	1.50000i	0.702439	−	0.0811107i
$343$		−	13.0000i		−	0.701934i
$344$	3.00000	+	5.19615i	0.161749	+	0.280158i
$345$		0			0
$346$	−0.500000	+	0.866025i	−0.0268802	+	0.0465578i
$347$	−15.5885	+	9.00000i	−0.836832	+	0.483145i	−0.856186	−	0.516667i	$-0.827172\pi$
$347$	−15.5885	+	9.00000i	−0.836832	+	0.483145i	0.0193540	+	0.999813i	$0.493839\pi$
$348$		0			0
$349$	28.0000			1.49881			0.749403	−	0.662114i	$-0.230341\pi$
$349$	28.0000			1.49881			0.749403	+	0.662114i	$0.230341\pi$
$350$		0			0
$351$		0			0
$352$	4.33013	+	2.50000i	0.230797	+	0.133250i
$353$			4.00000i			0.212899i	0.994318	+	0.106449i	$0.0339482\pi$
$353$			4.00000i			0.212899i	−0.994318	+	0.106449i	$0.966052\pi$
$354$		0			0
$355$		0			0
$356$	3.50000	+	6.06218i	0.185500	+	0.321295i
$357$		0			0
$358$	16.4545	−	9.50000i	0.869646	−	0.502091i
$359$	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
$361$	−18.5000	+	4.33013i	−0.973684	+	0.227901i
$362$		−	2.00000i		−	0.105118i
$363$		0			0
$364$	1.00000	+	1.73205i	0.0524142	+	0.0907841i
$365$		0			0
$366$		0			0
$367$	−3.46410	−	2.00000i	−0.180825	−	0.104399i	0.406855	−	0.913493i	$-0.366625\pi$
$367$	−3.46410	−	2.00000i	−0.180825	−	0.104399i	−0.587680	+	0.809093i	$0.699959\pi$
$368$			1.00000i			0.0521286i
$369$	−27.0000			−1.40556
$370$		0			0
$371$	−2.50000	+	4.33013i	−0.129794	+	0.224809i
$372$		0			0
$373$			31.0000i			1.60512i	0.596572	+	0.802560i	$0.296529\pi$
$373$			31.0000i			1.60512i	−0.596572	+	0.802560i	$0.703471\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−10.3923	+	6.00000i	−0.535231	+	0.309016i
$378$		0			0
$379$	12.0000			0.616399			0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000			0.616399			0.308199	+	0.951322i	$0.400274\pi$
$380$		0			0
$381$		0			0
$382$	15.5885	−	9.00000i	0.797575	−	0.460480i
$383$	6.92820	−	4.00000i	0.354015	−	0.204390i	−0.312437	−	0.949938i	$-0.601145\pi$
$383$	6.92820	−	4.00000i	0.354015	−	0.204390i	0.666452	+	0.745548i	$0.267812\pi$
$384$		0			0
$385$		0			0
$386$	−2.00000	+	3.46410i	−0.101797	+	0.176318i
$387$			18.0000i			0.914991i
$388$		−	2.00000i		−	0.101535i
$389$	13.0000	−	22.5167i	0.659126	−	1.14164i	−0.321716	−	0.946836i	$-0.604260\pi$
$389$	13.0000	−	22.5167i	0.659126	−	1.14164i	0.980842	−	0.194804i	$-0.0624070\pi$
$390$		0			0
$391$		0			0
$392$			6.00000i			0.303046i
$393$		0			0
$394$	11.5000	+	19.9186i	0.579362	+	1.00348i
$395$		0			0
$396$	7.50000	+	12.9904i	0.376889	+	0.652791i
$397$	−25.1147	+	14.5000i	−1.26047	+	0.727734i	−0.973166	−	0.230105i	$-0.926093\pi$
$397$	−25.1147	+	14.5000i	−1.26047	+	0.727734i	−0.287307	+	0.957839i	$0.592760\pi$
$398$			24.0000i			1.20301i
$399$		0			0
$400$		0			0
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	0.998350	−	0.0574304i	$-0.0182907\pi$
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	−0.548911	+	0.835881i	$0.684957\pi$
$402$		0			0
$403$	−6.92820	−	4.00000i	−0.345118	−	0.199254i
$404$	5.00000	+	8.66025i	0.248759	+	0.430864i
$405$		0			0
$406$	6.00000			0.297775
$407$			55.0000i			2.72625i
$408$		0			0
$409$	−5.50000	+	9.52628i	−0.271957	+	0.471044i	−0.969363	−	0.245633i	$-0.921004\pi$
$409$	−5.50000	+	9.52628i	−0.271957	+	0.471044i	0.697406	+	0.716677i	$0.254338\pi$
$410$		0			0
$411$		0			0
$412$	11.2583	+	6.50000i	0.554658	+	0.320232i
$413$		0			0
$414$	−1.50000	+	2.59808i	−0.0737210	+	0.127688i
$415$		0			0
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$		0			0
$418$	−12.9904	−	17.5000i	−0.635380	−	0.855953i
$419$	7.00000			0.341972			0.170986	−	0.985273i	$-0.445305\pi$
$419$	7.00000			0.341972			0.170986	+	0.985273i	$0.445305\pi$
$420$		0			0
$421$	4.00000	+	6.92820i	0.194948	+	0.337660i	0.946883	−	0.321577i	$-0.104213\pi$
$421$	4.00000	+	6.92820i	0.194948	+	0.337660i	−0.751935	+	0.659237i	$0.770879\pi$
$422$	11.2583	+	6.50000i	0.548047	+	0.316415i
$423$		0			0
$424$	2.50000	−	4.33013i	0.121411	−	0.210290i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	3.46410	+	2.00000i	0.167444	+	0.0966736i
$429$		0			0
$430$		0			0
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	−0.973574	−	0.228373i	$-0.926659\pi$
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	0.684564	+	0.728953i	$0.259993\pi$
$432$		0			0
$433$	−1.73205	−	1.00000i	−0.0832370	−	0.0480569i	0.457804	−	0.889053i	$-0.348636\pi$
$433$	−1.73205	−	1.00000i	−0.0832370	−	0.0480569i	−0.541041	+	0.840996i	$0.681970\pi$
$434$	2.00000	+	3.46410i	0.0960031	+	0.166282i
$435$		0			0
$436$	4.00000			0.191565
$437$	1.73205	−	4.00000i	0.0828552	−	0.191346i
$438$		0			0
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	0.945552	−	0.325471i	$-0.105523\pi$
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	−0.754642	+	0.656136i	$0.772190\pi$
$440$		0			0
$441$	−9.00000	+	15.5885i	−0.428571	+	0.742307i
$442$		0			0
$443$	−31.1769	−	18.0000i	−1.48126	−	0.855206i	−0.481486	−	0.876454i	$-0.659903\pi$
$443$	−31.1769	−	18.0000i	−1.48126	−	0.855206i	−0.999774	+	0.0212481i	$0.993236\pi$
$444$		0			0
$445$		0			0
$446$	11.5000	−	19.9186i	0.544541	−	0.943172i
$447$		0			0
$448$			1.00000i			0.0472456i
$449$	19.0000			0.896665			0.448333	−	0.893867i	$-0.352018\pi$
$449$	19.0000			0.896665			0.448333	+	0.893867i	$0.352018\pi$
$450$		0			0
$451$	22.5000	+	38.9711i	1.05948	+	1.83508i
$452$	−10.3923	−	6.00000i	−0.488813	−	0.282216i
$453$		0			0
$454$	−5.00000	−	8.66025i	−0.234662	−	0.406446i
$455$		0			0
$456$		0			0
$457$			32.0000i			1.49690i	0.663193	+	0.748448i	$0.269201\pi$
$457$			32.0000i			1.49690i	−0.663193	+	0.748448i	$0.730799\pi$
$458$	5.19615	−	3.00000i	0.242800	−	0.140181i
$459$		0			0
$460$		0			0
$461$	15.0000	+	25.9808i	0.698620	+	1.21004i	0.968945	+	0.247276i	$0.0795353\pi$
$461$	15.0000	+	25.9808i	0.698620	+	1.21004i	−0.270326	+	0.962769i	$0.587131\pi$
$462$		0			0
$463$			37.0000i			1.71954i	0.510685	+	0.859768i	$0.329392\pi$
$463$			37.0000i			1.71954i	−0.510685	+	0.859768i	$0.670608\pi$
$464$	−6.00000			−0.278543
$465$		0			0
$466$	−5.00000	+	8.66025i	−0.231621	+	0.401179i
$467$		−	34.0000i		−	1.57333i	−0.617379	−	0.786666i	$-0.711805\pi$
$467$		−	34.0000i		−	1.57333i	0.617379	−	0.786666i	$-0.288195\pi$
$468$		−	6.00000i		−	0.277350i
$469$	6.00000	−	10.3923i	0.277054	−	0.479872i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	25.9808	−	15.0000i	1.19460	−	0.689701i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	12.9904	−	7.50000i	0.594789	−	0.343401i
$478$	13.8564	−	8.00000i	0.633777	−	0.365911i
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	−0.995023	−	0.0996406i	$-0.968231\pi$
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	0.583803	+	0.811895i	$0.301564\pi$
$480$		0			0
$481$	11.0000	−	19.0526i	0.501557	−	0.868722i
$482$			18.0000i			0.819878i
$483$		0			0
$484$	7.00000	−	12.1244i	0.318182	−	0.551107i
$485$		0			0
$486$		0			0
$487$			23.0000i			1.04223i	0.853487	+	0.521115i	$0.174484\pi$
$487$			23.0000i			1.04223i	−0.853487	+	0.521115i	$0.825516\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−13.5000	−	23.3827i	−0.609246	−	1.05525i	−0.991365	−	0.131132i	$-0.958139\pi$
$491$	−13.5000	−	23.3827i	−0.609246	−	1.05525i	0.382118	−	0.924113i	$-0.375195\pi$
$492$		0			0
$493$		0			0
$494$	1.00000	+	8.66025i	0.0449921	+	0.389643i
$495$		0			0
$496$	−2.00000	−	3.46410i	−0.0898027	−	0.155543i
$497$	−5.19615	+	3.00000i	−0.233079	+	0.134568i
$498$		0			0
$499$	−19.5000	−	33.7750i	−0.872940	−	1.51198i	−0.858941	−	0.512074i	$-0.828877\pi$
$499$	−19.5000	−	33.7750i	−0.872940	−	1.51198i	−0.0139987	−	0.999902i	$-0.504456\pi$
$500$		0			0
$501$		0			0
$502$			12.0000i			0.535586i
$503$	28.5788	+	16.5000i	1.27427	+	0.735699i	0.975788	−	0.218718i	$-0.0701873\pi$
$503$	28.5788	+	16.5000i	1.27427	+	0.735699i	0.298479	+	0.954416i	$0.403521\pi$
$504$	−1.50000	+	2.59808i	−0.0668153	+	0.115728i
$505$		0			0
$506$	5.00000			0.222277
$507$		0			0
$508$	−12.9904	+	7.50000i	−0.576355	+	0.332759i
$509$	7.00000	−	12.1244i	0.310270	−	0.537403i	−0.668151	−	0.744026i	$-0.732914\pi$
$509$	7.00000	−	12.1244i	0.310270	−	0.537403i	0.978421	+	0.206623i	$0.0662474\pi$
$510$		0			0
$511$	−7.00000	−	12.1244i	−0.309662	−	0.536350i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	14.0000			0.617514
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−9.52628	+	5.50000i	−0.418561	+	0.241656i
$519$		0			0
$520$		0			0
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$	−15.5885	−	9.00000i	−0.682288	−	0.393919i
$523$	36.3731	+	21.0000i	1.59048	+	0.918266i	0.993224	+	0.116218i	$0.0370770\pi$
$523$	36.3731	+	21.0000i	1.59048	+	0.918266i	0.597259	+	0.802048i	$0.296256\pi$
$524$	−1.00000			−0.0436852
$525$		0			0
$526$	−5.50000	+	9.52628i	−0.239811	+	0.415366i
$527$		0			0
$528$		0			0
$529$	−11.0000	−	19.0526i	−0.478261	−	0.828372i
$530$		0			0
$531$		0			0
$532$	1.73205	−	4.00000i	0.0750939	−	0.173422i
$533$		−	18.0000i		−	0.779667i
$534$		0			0
$535$		0			0
$536$	−6.00000	+	10.3923i	−0.259161	+	0.448879i
$537$		0			0
$538$	24.2487	+	14.0000i	1.04544	+	0.603583i
$539$	30.0000			1.29219
$540$		0			0
$541$	10.0000	−	17.3205i	0.429934	−	0.744667i	−0.566933	−	0.823764i	$-0.691870\pi$
$541$	10.0000	−	17.3205i	0.429934	−	0.744667i	0.996867	+	0.0790969i	$0.0252036\pi$
$542$	−5.19615	−	3.00000i	−0.223194	−	0.128861i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−19.0526	−	11.0000i	−0.814629	−	0.470326i	0.0339321	−	0.999424i	$-0.489197\pi$
$547$	−19.0526	−	11.0000i	−0.814629	−	0.470326i	−0.848561	+	0.529098i	$0.822530\pi$
$548$	10.3923	−	6.00000i	0.443937	−	0.256307i
$549$		0			0
$550$		0			0
$551$	24.0000	+	10.3923i	1.02243	+	0.442727i
$552$		0			0
$553$	8.66025	−	5.00000i	0.368271	−	0.212622i
$554$	−1.00000	−	1.73205i	−0.0424859	−	0.0735878i
$555$		0			0
$556$	−8.00000	−	13.8564i	−0.339276	−	0.587643i
$557$	−7.79423	−	4.50000i	−0.330252	−	0.190671i	0.325701	−	0.945473i	$-0.394400\pi$
$557$	−7.79423	−	4.50000i	−0.330252	−	0.190671i	−0.655953	+	0.754802i	$0.727733\pi$
$558$		−	12.0000i		−	0.508001i
$559$	−12.0000			−0.507546
$560$		0			0
$561$		0			0
$562$			15.0000i			0.632737i
$563$			32.0000i			1.34864i	0.738440	+	0.674320i	$0.235563\pi$
$563$			32.0000i			1.34864i	−0.738440	+	0.674320i	$0.764437\pi$
$564$		0			0
$565$		0			0
$566$	7.00000	−	12.1244i	0.294232	−	0.509625i
$567$	−7.79423	+	4.50000i	−0.327327	+	0.188982i
$568$	5.19615	−	3.00000i	0.218026	−	0.125877i
$569$	−45.0000			−1.88650			−0.943249	−	0.332086i	$-0.892248\pi$
$569$	−45.0000			−1.88650			−0.943249	+	0.332086i	$0.892248\pi$
$570$		0			0
$571$	12.0000			0.502184			0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000			0.502184			0.251092	+	0.967963i	$0.419210\pi$
$572$	−8.66025	+	5.00000i	−0.362103	+	0.209061i
$573$		0			0
$574$	−4.50000	+	7.79423i	−0.187826	+	0.325325i
$575$		0			0
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$		−	32.0000i		−	1.33218i	−0.745873	−	0.666089i	$-0.767967\pi$
$577$		−	32.0000i		−	1.33218i	0.745873	−	0.666089i	$-0.232033\pi$
$578$		−	17.0000i		−	0.707107i
$579$		0			0
$580$		0			0
$581$	14.0000			0.580818
$582$		0			0
$583$	−21.6506	−	12.5000i	−0.896678	−	0.517697i
$584$	7.00000	+	12.1244i	0.289662	+	0.501709i
$585$		0			0
$586$	10.5000	+	18.1865i	0.433751	+	0.751279i
$587$	−10.3923	+	6.00000i	−0.428936	+	0.247647i	−0.698893	−	0.715226i	$-0.746324\pi$
$587$	−10.3923	+	6.00000i	−0.428936	+	0.247647i	0.269957	+	0.962872i	$0.412990\pi$
$588$		0			0
$589$	2.00000	+	17.3205i	0.0824086	+	0.713679i
$590$		0			0
$591$		0			0
$592$	9.52628	−	5.50000i	0.391528	−	0.226049i
$593$	−36.3731	−	21.0000i	−1.49366	−	0.862367i	−0.493689	−	0.869638i	$-0.664352\pi$
$593$	−36.3731	−	21.0000i	−1.49366	−	0.862367i	−0.999974	+	0.00727173i	$0.997685\pi$
$594$		0			0
$595$		0			0
$596$	−4.00000			−0.163846
$597$		0			0
$598$	−1.73205	−	1.00000i	−0.0708288	−	0.0408930i
$599$	−22.0000	+	38.1051i	−0.898896	+	1.55693i	−0.0699877	+	0.997548i	$0.522296\pi$
$599$	−22.0000	+	38.1051i	−0.898896	+	1.55693i	−0.828908	+	0.559385i	$0.811037\pi$
$600$		0			0
$601$	21.0000			0.856608			0.428304	−	0.903635i	$-0.359111\pi$
$601$	21.0000			0.856608			0.428304	+	0.903635i	$0.359111\pi$
$602$	5.19615	+	3.00000i	0.211779	+	0.122271i
$603$	−31.1769	+	18.0000i	−1.26962	+	0.733017i
$604$	−8.00000	+	13.8564i	−0.325515	+	0.563809i
$605$		0			0
$606$		0			0
$607$		−	13.0000i		−	0.527654i	−0.964570	−	0.263827i	$-0.915015\pi$
$607$		−	13.0000i		−	0.527654i	0.964570	−	0.263827i	$-0.0849848\pi$
$608$	−1.73205	+	4.00000i	−0.0702439	+	0.162221i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	21.6506	−	12.5000i	0.874461	−	0.504870i	0.00563283	−	0.999984i	$-0.498207\pi$
$613$	21.6506	−	12.5000i	0.874461	−	0.504870i	0.868828	+	0.495114i	$0.164874\pi$
$614$	−1.00000	+	1.73205i	−0.0403567	+	0.0698999i
$615$		0			0
$616$	5.00000			0.201456
$617$	17.3205	+	10.0000i	0.697297	+	0.402585i	0.806340	−	0.591452i	$-0.201445\pi$
$617$	17.3205	+	10.0000i	0.697297	+	0.402585i	−0.109043	+	0.994037i	$0.534779\pi$
$618$		0			0
$619$	45.0000			1.80870			0.904351	−	0.426789i	$-0.140355\pi$
$619$	45.0000			1.80870			0.904351	+	0.426789i	$0.140355\pi$
$620$		0			0
$621$		0			0
$622$	−3.46410	+	2.00000i	−0.138898	+	0.0801927i
$623$	6.06218	+	3.50000i	0.242876	+	0.140225i
$624$		0			0
$625$		0			0
$626$	−28.0000			−1.11911
$627$		0			0
$628$		−	21.0000i		−	0.837991i
$629$		0			0
$630$		0			0
$631$	11.0000	−	19.0526i	0.437903	−	0.758470i	−0.559625	−	0.828746i	$-0.689055\pi$
$631$	11.0000	−	19.0526i	0.437903	−	0.758470i	0.997528	+	0.0702759i	$0.0223880\pi$
$632$	−8.66025	+	5.00000i	−0.344486	+	0.198889i
$633$		0			0
$634$	27.0000			1.07231
$635$		0			0
$636$		0			0
$637$	−10.3923	−	6.00000i	−0.411758	−	0.237729i
$638$			30.0000i			1.18771i
$639$	18.0000			0.712069
$640$		0			0
$641$	5.00000	+	8.66025i	0.197488	+	0.342059i	0.947713	−	0.319123i	$-0.103388\pi$
$641$	5.00000	+	8.66025i	0.197488	+	0.342059i	−0.750225	+	0.661182i	$0.770055\pi$
$642$		0			0
$643$	−13.8564	+	8.00000i	−0.546443	+	0.315489i	−0.747686	−	0.664052i	$-0.768835\pi$
$643$	−13.8564	+	8.00000i	−0.546443	+	0.315489i	0.201243	+	0.979541i	$0.435502\pi$
$644$	0.500000	+	0.866025i	0.0197028	+	0.0341262i
$645$		0			0
$646$		0			0
$647$			3.00000i			0.117942i	0.998260	+	0.0589711i	$0.0187820\pi$
$647$			3.00000i			0.117942i	−0.998260	+	0.0589711i	$0.981218\pi$
$648$	7.79423	−	4.50000i	0.306186	−	0.176777i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	8.66025	+	5.00000i	0.339162	+	0.195815i
$653$		−	25.0000i		−	0.978326i	−0.872192	−	0.489163i	$-0.837302\pi$
$653$		−	25.0000i		−	0.978326i	0.872192	−	0.489163i	$-0.162698\pi$
$654$		0			0
$655$		0			0
$656$	4.50000	−	7.79423i	0.175695	−	0.304314i
$657$			42.0000i			1.63858i
$658$		0			0
$659$	−7.50000	+	12.9904i	−0.292159	+	0.506033i	−0.974320	−	0.225168i	$-0.927707\pi$
$659$	−7.50000	+	12.9904i	−0.292159	+	0.506033i	0.682161	+	0.731202i	$0.261040\pi$
$660$		0			0
$661$	−12.0000	+	20.7846i	−0.466746	+	0.808428i	−0.999278	−	0.0379819i	$-0.987907\pi$
$661$	−12.0000	+	20.7846i	−0.466746	+	0.808428i	0.532533	+	0.846410i	$0.321240\pi$
$662$	21.6506	−	12.5000i	0.841476	−	0.485826i
$663$		0			0
$664$	−14.0000			−0.543305
$665$		0			0
$666$	33.0000			1.27872
$667$	−5.19615	+	3.00000i	−0.201196	+	0.116160i
$668$	−4.33013	+	2.50000i	−0.167538	+	0.0967279i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$			16.0000i			0.616755i	0.951264	+	0.308377i	$0.0997859\pi$
$673$			16.0000i			0.616755i	−0.951264	+	0.308377i	$0.900214\pi$
$674$	3.00000	−	5.19615i	0.115556	−	0.200148i
$675$		0			0
$676$	−9.00000			−0.346154
$677$		−	27.0000i		−	1.03769i	−0.854867	−	0.518847i	$-0.826361\pi$
$677$		−	27.0000i		−	1.03769i	0.854867	−	0.518847i	$-0.173639\pi$
$678$		0			0
$679$	−1.00000	−	1.73205i	−0.0383765	−	0.0664700i
$680$		0			0
$681$		0			0
$682$	−17.3205	+	10.0000i	−0.663237	+	0.382920i
$683$		−	44.0000i		−	1.68361i	−0.539779	−	0.841807i	$-0.681492\pi$
$683$		−	44.0000i		−	1.68361i	0.539779	−	0.841807i	$-0.318508\pi$
$684$	−10.5000	+	7.79423i	−0.401478	+	0.298020i
$685$		0			0
$686$	6.50000	+	11.2583i	0.248171	+	0.429845i
$687$		0			0
$688$	−5.19615	−	3.00000i	−0.198101	−	0.114374i
$689$	5.00000	+	8.66025i	0.190485	+	0.329929i
$690$		0			0
$691$	−15.0000			−0.570627			−0.285313	−	0.958434i	$-0.592098\pi$
$691$	−15.0000			−0.570627			−0.285313	+	0.958434i	$0.592098\pi$
$692$		−	1.00000i		−	0.0380143i
$693$	12.9904	+	7.50000i	0.493464	+	0.284901i
$694$	9.00000	−	15.5885i	0.341635	−	0.591730i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−24.2487	+	14.0000i	−0.917827	+	0.529908i
$699$		0			0
$700$		0			0
$701$	−3.00000	−	5.19615i	−0.113308	−	0.196256i	0.803794	−	0.594908i	$-0.202811\pi$
$701$	−3.00000	−	5.19615i	−0.113308	−	0.196256i	−0.917102	+	0.398652i	$0.869478\pi$
$702$		0			0
$703$	−47.6314	+	5.50000i	−1.79645	+	0.207436i
$704$	−5.00000			−0.188445
$705$		0			0
$706$	−2.00000	−	3.46410i	−0.0752710	−	0.130373i
$707$	8.66025	+	5.00000i	0.325702	+	0.188044i
$708$		0			0
$709$	4.00000	−	6.92820i	0.150223	−	0.260194i	−0.781086	−	0.624423i	$-0.785334\pi$
$709$	4.00000	−	6.92820i	0.150223	−	0.260194i	0.931309	+	0.364229i	$0.118667\pi$
$710$		0			0
$711$	−30.0000			−1.12509
$712$	−6.06218	−	3.50000i	−0.227190	−	0.131168i
$713$	−3.46410	−	2.00000i	−0.129732	−	0.0749006i
$714$		0			0
$715$		0			0
$716$	−9.50000	+	16.4545i	−0.355032	+	0.614933i
$717$		0			0
$718$	−8.66025	−	5.00000i	−0.323198	−	0.186598i
$719$	−24.0000	−	41.5692i	−0.895049	−	1.55027i	−0.833744	−	0.552151i	$-0.813807\pi$
$719$	−24.0000	−	41.5692i	−0.895049	−	1.55027i	−0.0613050	−	0.998119i	$-0.519526\pi$
$720$		0			0
$721$	13.0000			0.484145
$722$	13.8564	−	13.0000i	0.515682	−	0.483810i
$723$		0			0
$724$	1.00000	+	1.73205i	0.0371647	+	0.0643712i
$725$		0			0
$726$		0			0
$727$	13.8564	−	8.00000i	0.513906	−	0.296704i	−0.220532	−	0.975380i	$-0.570779\pi$
$727$	13.8564	−	8.00000i	0.513906	−	0.296704i	0.734438	+	0.678676i	$0.237446\pi$
$728$	−1.73205	−	1.00000i	−0.0641941	−	0.0370625i
$729$	27.0000			1.00000
$730$		0			0
$731$		0			0
$732$		0			0
$733$		−	15.0000i		−	0.554038i	−0.960864	−	0.277019i	$-0.910654\pi$
$733$		−	15.0000i		−	0.554038i	0.960864	−	0.277019i	$-0.0893464\pi$
$734$	4.00000			0.147643
$735$		0			0
$736$	−0.500000	−	0.866025i	−0.0184302	−	0.0319221i
$737$	51.9615	+	30.0000i	1.91403	+	1.10506i
$738$	23.3827	−	13.5000i	0.860729	−	0.496942i
$739$	−15.5000	−	26.8468i	−0.570177	−	0.987575i	−0.996547	−	0.0830265i	$-0.973541\pi$
$739$	−15.5000	−	26.8468i	−0.570177	−	0.987575i	0.426371	−	0.904549i	$-0.359792\pi$
$740$		0			0
$741$		0			0
$742$		−	5.00000i		−	0.183556i
$743$	−12.9904	+	7.50000i	−0.476571	+	0.275148i	−0.718986	−	0.695024i	$-0.755394\pi$
$743$	−12.9904	+	7.50000i	−0.476571	+	0.275148i	0.242415	+	0.970173i	$0.422060\pi$
$744$		0			0
$745$		0			0
$746$	−15.5000	−	26.8468i	−0.567495	−	0.982931i
$747$	−36.3731	−	21.0000i	−1.33082	−	0.768350i
$748$		0			0
$749$	4.00000			0.146157
$750$		0			0
$751$	10.0000	−	17.3205i	0.364905	−	0.632034i	−0.623856	−	0.781540i	$-0.714435\pi$
$751$	10.0000	−	17.3205i	0.364905	−	0.632034i	0.988761	+	0.149505i	$0.0477681\pi$
$752$		0			0
$753$		0			0
$754$	6.00000	−	10.3923i	0.218507	−	0.378465i
$755$		0			0
$756$		0			0
$757$	12.9904	−	7.50000i	0.472143	−	0.272592i	−0.244993	−	0.969525i	$-0.578786\pi$
$757$	12.9904	−	7.50000i	0.472143	−	0.272592i	0.717137	+	0.696933i	$0.245452\pi$
$758$	−10.3923	+	6.00000i	−0.377466	+	0.217930i
$759$		0			0
$760$		0			0
$761$	−43.0000			−1.55875			−0.779374	−	0.626559i	$-0.784463\pi$
$761$	−43.0000			−1.55875			−0.779374	+	0.626559i	$0.784463\pi$
$762$		0			0
$763$	3.46410	−	2.00000i	0.125409	−	0.0724049i
$764$	−9.00000	+	15.5885i	−0.325609	+	0.563971i
$765$		0			0
$766$	−4.00000	+	6.92820i	−0.144526	+	0.250326i
$767$		0			0
$768$		0			0
$769$	−13.0000	+	22.5167i	−0.468792	+	0.811972i	−0.999364	−	0.0356685i	$-0.988644\pi$
$769$	−13.0000	+	22.5167i	−0.468792	+	0.811972i	0.530572	+	0.847640i	$0.321977\pi$
$770$		0			0
$771$		0			0
$772$		−	4.00000i		−	0.143963i
$773$	−38.9711	−	22.5000i	−1.40169	−	0.809269i	−0.407128	−	0.913371i	$-0.633470\pi$
$773$	−38.9711	−	22.5000i	−1.40169	−	0.809269i	−0.994567	+	0.104102i	$0.966803\pi$
$774$	−9.00000	−	15.5885i	−0.323498	−	0.560316i
$775$		0			0
$776$	1.00000	+	1.73205i	0.0358979	+	0.0621770i
$777$		0			0
$778$			26.0000i			0.932145i
$779$	−31.5000	+	23.3827i	−1.12860	+	0.837772i
$780$		0			0
$781$	−15.0000	−	25.9808i	−0.536742	−	0.929665i
$782$		0			0
$783$		0			0
$784$	−3.00000	−	5.19615i	−0.107143	−	0.185577i
$785$		0			0
$786$		0			0
$787$		−	18.0000i		−	0.641631i	−0.947142	−	0.320815i	$-0.896043\pi$
$787$		−	18.0000i		−	0.641631i	0.947142	−	0.320815i	$-0.103957\pi$
$788$	−19.9186	−	11.5000i	−0.709570	−	0.409671i
$789$		0			0
$790$		0			0
$791$	−12.0000			−0.426671
$792$	−12.9904	−	7.50000i	−0.461593	−	0.266501i
$793$		0			0
$794$	14.5000	−	25.1147i	0.514586	−	0.891289i
$795$		0			0
$796$	−12.0000	−	20.7846i	−0.425329	−	0.736691i
$797$		−	49.0000i		−	1.73567i	−0.496853	−	0.867835i	$-0.665511\pi$
$797$		−	49.0000i		−	1.73567i	0.496853	−	0.867835i	$-0.334489\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−10.5000	−	18.1865i	−0.370999	−	0.642590i
$802$	−15.5885	−	9.00000i	−0.550448	−	0.317801i
$803$	60.6218	−	35.0000i	2.13930	−	1.23512i
$804$		0			0
$805$		0			0
$806$	8.00000			0.281788
$807$		0			0
$808$	−8.66025	−	5.00000i	−0.304667	−	0.175899i
$809$	2.00000			0.0703163			0.0351581	−	0.999382i	$-0.488807\pi$
$809$	2.00000			0.0703163			0.0351581	+	0.999382i	$0.488807\pi$
$810$		0			0
$811$	2.50000	−	4.33013i	0.0877869	−	0.152051i	−0.818788	−	0.574095i	$-0.805354\pi$
$811$	2.50000	−	4.33013i	0.0877869	−	0.152051i	0.906575	+	0.422044i	$0.138687\pi$
$812$	−5.19615	+	3.00000i	−0.182349	+	0.105279i
$813$		0			0
$814$	−27.5000	−	47.6314i	−0.963875	−	1.66948i
$815$		0			0
$816$		0			0
$817$	15.5885	+	21.0000i	0.545371	+	0.734697i
$818$		−	11.0000i		−	0.384606i
$819$	−3.00000	−	5.19615i	−0.104828	−	0.181568i
$820$		0			0
$821$	−25.0000	+	43.3013i	−0.872506	+	1.51122i	−0.0131101	+	0.999914i	$0.504173\pi$
$821$	−25.0000	+	43.3013i	−0.872506	+	1.51122i	−0.859396	+	0.511311i	$0.829160\pi$
$822$		0			0
$823$	32.0429	+	18.5000i	1.11695	+	0.644869i	0.940620	−	0.339462i	$-0.110245\pi$
$823$	32.0429	+	18.5000i	1.11695	+	0.644869i	0.176327	+	0.984332i	$0.443578\pi$
$824$	−13.0000			−0.452876
$825$		0			0
$826$		0			0
$827$	5.19615	+	3.00000i	0.180688	+	0.104320i	0.587616	−	0.809140i	$-0.300067\pi$
$827$	5.19615	+	3.00000i	0.180688	+	0.104320i	−0.406928	+	0.913460i	$0.633400\pi$
$828$		−	3.00000i		−	0.104257i
$829$	52.0000			1.80603			0.903017	−	0.429604i	$-0.141347\pi$
$829$	52.0000			1.80603			0.903017	+	0.429604i	$0.141347\pi$
$830$		0			0
$831$		0			0
$832$	1.73205	+	1.00000i	0.0600481	+	0.0346688i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	20.0000	+	8.66025i	0.691714	+	0.299521i
$837$		0			0
$838$	−6.06218	+	3.50000i	−0.209414	+	0.120905i
$839$	13.0000	+	22.5167i	0.448810	+	0.777361i	0.998309	−	0.0581329i	$-0.0185147\pi$
$839$	13.0000	+	22.5167i	0.448810	+	0.777361i	−0.549499	+	0.835494i	$0.685181\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	−6.92820	−	4.00000i	−0.238762	−	0.137849i
$843$		0			0
$844$	−13.0000			−0.447478
$845$		0			0
$846$		0			0
$847$		−	14.0000i		−	0.481046i
$848$			5.00000i			0.171701i
$849$		0			0
$850$		0			0
$851$	5.50000	−	9.52628i	0.188538	−	0.326557i
$852$		0			0
$853$	46.7654	−	27.0000i	1.60122	−	0.924462i	0.609971	−	0.792424i	$-0.291181\pi$
$853$	46.7654	−	27.0000i	1.60122	−	0.924462i	0.991245	−	0.132039i	$-0.0421524\pi$
$854$		0			0
$855$		0			0
$856$	−4.00000			−0.136717
$857$	24.2487	−	14.0000i	0.828320	−	0.478231i	−0.0249570	−	0.999689i	$-0.507945\pi$
$857$	24.2487	−	14.0000i	0.828320	−	0.478231i	0.853277	+	0.521458i	$0.174612\pi$
$858$		0			0
$859$	−24.5000	+	42.4352i	−0.835929	+	1.44787i	0.0573424	+	0.998355i	$0.481737\pi$
$859$	−24.5000	+	42.4352i	−0.835929	+	1.44787i	−0.893272	+	0.449517i	$0.851596\pi$
$860$		0			0
$861$		0			0
$862$		−	12.0000i		−	0.408722i
$863$			17.0000i			0.578687i	0.957225	+	0.289343i	$0.0934369\pi$
$863$			17.0000i			0.578687i	−0.957225	+	0.289343i	$0.906563\pi$
$864$		0			0
$865$		0			0
$866$	2.00000			0.0679628
$867$		0			0
$868$	−3.46410	−	2.00000i	−0.117579	−	0.0678844i
$869$	25.0000	+	43.3013i	0.848067	+	1.46889i
$870$		0			0
$871$	−12.0000	−	20.7846i	−0.406604	−	0.704260i
$872$	−3.46410	+	2.00000i	−0.117309	+	0.0677285i
$873$			6.00000i			0.203069i
$874$	0.500000	+	4.33013i	0.0169128	+	0.146469i
$875$		0			0
$876$		0			0
$877$	−2.59808	+	1.50000i	−0.0877308	+	0.0506514i	−0.543224	−	0.839588i	$-0.682796\pi$
$877$	−2.59808	+	1.50000i	−0.0877308	+	0.0506514i	0.455493	+	0.890239i	$0.349463\pi$
$878$	−6.92820	−	4.00000i	−0.233816	−	0.134993i
$879$		0			0
$880$		0			0
$881$	−35.0000			−1.17918			−0.589590	−	0.807703i	$-0.700711\pi$
$881$	−35.0000			−1.17918			−0.589590	+	0.807703i	$0.700711\pi$
$882$		−	18.0000i		−	0.606092i
$883$	31.1769	+	18.0000i	1.04919	+	0.605748i	0.922422	−	0.386185i	$-0.126207\pi$
$883$	31.1769	+	18.0000i	1.04919	+	0.605748i	0.126765	+	0.991933i	$0.459541\pi$
$884$		0			0
$885$		0			0
$886$	36.0000			1.20944
$887$	48.4974	+	28.0000i	1.62838	+	0.940148i	0.984575	+	0.174962i	$0.0559801\pi$
$887$	48.4974	+	28.0000i	1.62838	+	0.940148i	0.643809	+	0.765186i	$0.277353\pi$
$888$		0			0
$889$	−7.50000	+	12.9904i	−0.251542	+	0.435683i
$890$		0			0
$891$	−22.5000	−	38.9711i	−0.753778	−	1.30558i
$892$			23.0000i			0.770097i
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−0.500000	−	0.866025i	−0.0167038	−	0.0289319i
$897$		0			0
$898$	−16.4545	+	9.50000i	−0.549093	+	0.317019i
$899$	12.0000	−	20.7846i	0.400222	−	0.693206i
$900$		0			0
$901$		0			0
$902$	−38.9711	−	22.5000i	−1.29760	−	0.749168i
$903$		0			0
$904$	12.0000			0.399114
$905$		0			0
$906$		0			0
$907$	8.66025	−	5.00000i	0.287559	−	0.166022i	−0.349281	−	0.937018i	$-0.613574\pi$
$907$	8.66025	−	5.00000i	0.287559	−	0.166022i	0.636841	+	0.770996i	$0.280241\pi$
$908$	8.66025	+	5.00000i	0.287401	+	0.165931i
$909$	−15.0000	−	25.9808i	−0.497519	−	0.861727i
$910$		0			0
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$		0			0
$913$			70.0000i			2.31666i
$914$	−16.0000	−	27.7128i	−0.529233	−	0.916658i
$915$		0			0
$916$	−3.00000	+	5.19615i	−0.0991228	+	0.171686i
$917$	−0.866025	+	0.500000i	−0.0285987	+	0.0165115i
$918$		0			0
$919$	−10.0000			−0.329870			−0.164935	−	0.986304i	$-0.552741\pi$
$919$	−10.0000			−0.329870			−0.164935	+	0.986304i	$0.552741\pi$
$920$		0			0
$921$		0			0
$922$	−25.9808	−	15.0000i	−0.855631	−	0.493999i
$923$			12.0000i			0.394985i
$924$		0			0
$925$		0			0
$926$	−18.5000	−	32.0429i	−0.607948	−	1.05300i
$927$	−33.7750	−	19.5000i	−1.10932	−	0.640464i
$928$	5.19615	−	3.00000i	0.170572	−	0.0984798i
$929$	−13.5000	−	23.3827i	−0.442921	−	0.767161i	0.554984	−	0.831861i	$-0.312724\pi$
$929$	−13.5000	−	23.3827i	−0.442921	−	0.767161i	−0.997905	+	0.0646999i	$0.979391\pi$
$930$		0			0
$931$	3.00000	+	25.9808i	0.0983210	+	0.851485i
$932$		−	10.0000i		−	0.327561i
$933$		0			0
$934$	17.0000	+	29.4449i	0.556257	+	0.963465i
$935$		0			0
$936$	3.00000	+	5.19615i	0.0980581	+	0.169842i
$937$	1.73205	+	1.00000i	0.0565836	+	0.0326686i	0.528025	−	0.849229i	$-0.322933\pi$
$937$	1.73205	+	1.00000i	0.0565836	+	0.0326686i	−0.471441	+	0.881897i	$0.656266\pi$
$938$			12.0000i			0.391814i
$939$		0			0
$940$		0			0
$941$	9.00000	−	15.5885i	0.293392	−	0.508169i	−0.681218	−	0.732081i	$-0.738549\pi$
$941$	9.00000	−	15.5885i	0.293392	−	0.508169i	0.974609	+	0.223912i	$0.0718827\pi$
$942$		0			0
$943$		−	9.00000i		−	0.293080i
$944$		0			0
$945$		0			0
$946$	−15.0000	+	25.9808i	−0.487692	+	0.844707i
$947$	51.9615	−	30.0000i	1.68852	−	0.974869i	0.732872	−	0.680367i	$-0.238179\pi$
$947$	51.9615	−	30.0000i	1.68852	−	0.974869i	0.955651	−	0.294502i	$-0.0951539\pi$
$948$		0			0
$949$	−28.0000			−0.908918
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−31.1769	+	18.0000i	−1.00992	+	0.583077i	−0.911168	−	0.412035i	$-0.864818\pi$
$953$	−31.1769	+	18.0000i	−1.00992	+	0.583077i	−0.0987513	+	0.995112i	$0.531485\pi$
$954$	−7.50000	+	12.9904i	−0.242821	+	0.420579i
$955$		0			0
$956$	−8.00000	+	13.8564i	−0.258738	+	0.448148i
$957$		0			0
$958$		−	18.0000i		−	0.581554i
$959$	6.00000	−	10.3923i	0.193750	−	0.335585i
$960$		0			0
$961$	−15.0000			−0.483871
$962$			22.0000i			0.709308i
$963$	−10.3923	−	6.00000i	−0.334887	−	0.193347i
$964$	−9.00000	−	15.5885i	−0.289870	−	0.502070i
$965$		0			0
$966$		0			0
$967$	6.92820	−	4.00000i	0.222796	−	0.128631i	−0.384448	−	0.923147i	$-0.625608\pi$
$967$	6.92820	−	4.00000i	0.222796	−	0.128631i	0.607244	+	0.794515i	$0.292275\pi$
$968$			14.0000i			0.449977i
$969$		0			0
$970$		0			0
$971$	10.0000	+	17.3205i	0.320915	+	0.555842i	0.980677	−	0.195633i	$-0.0626762\pi$
$971$	10.0000	+	17.3205i	0.320915	+	0.555842i	−0.659762	+	0.751475i	$0.729343\pi$
$972$		0			0
$973$	−13.8564	−	8.00000i	−0.444216	−	0.256468i
$974$	−11.5000	−	19.9186i	−0.368484	−	0.638233i
$975$		0			0
$976$		0			0
$977$			2.00000i			0.0639857i	0.999488	+	0.0319928i	$0.0101854\pi$
$977$			2.00000i			0.0639857i	−0.999488	+	0.0319928i	$0.989815\pi$
$978$		0			0
$979$	−17.5000	+	30.3109i	−0.559302	+	0.968740i
$980$		0			0
$981$	−12.0000			−0.383131
$982$	23.3827	+	13.5000i	0.746171	+	0.430802i
$983$	18.1865	−	10.5000i	0.580060	−	0.334898i	−0.181097	−	0.983465i	$-0.557965\pi$
$983$	18.1865	−	10.5000i	0.580060	−	0.334898i	0.761157	+	0.648567i	$0.224631\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−5.19615	−	7.00000i	−0.165312	−	0.222700i
$989$	−6.00000			−0.190789
$990$		0			0
$991$	−9.00000	−	15.5885i	−0.285894	−	0.495184i	0.686931	−	0.726722i	$-0.258957\pi$
$991$	−9.00000	−	15.5885i	−0.285894	−	0.495184i	−0.972826	+	0.231539i	$0.925624\pi$
$992$	3.46410	+	2.00000i	0.109985	+	0.0635001i
$993$		0			0
$994$	3.00000	−	5.19615i	0.0951542	−	0.164812i
$995$		0			0
$996$		0			0
$997$	−45.8993	−	26.5000i	−1.45365	−	0.839263i	−0.454961	−	0.890511i	$-0.650347\pi$
$997$	−45.8993	−	26.5000i	−1.45365	−	0.839263i	−0.998686	+	0.0512480i	$0.983680\pi$
$998$	33.7750	+	19.5000i	1.06913	+	0.617262i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.j.d.349.1		4
5.2	odd	4		190.2.e.a.121.1	yes	2
5.3	odd	4		950.2.e.f.501.1		2
5.4	even	2	inner	950.2.j.d.349.2		4
15.2	even	4		1710.2.l.h.1261.1		2
19.11	even	3	inner	950.2.j.d.49.2		4
20.7	even	4		1520.2.q.f.881.1		2
95.7	odd	12		3610.2.a.g.1.1		1
95.12	even	12		3610.2.a.c.1.1		1
95.49	even	6	inner	950.2.j.d.49.1		4
95.68	odd	12		950.2.e.f.201.1		2
95.87	odd	12		190.2.e.a.11.1	✓	2
285.182	even	12		1710.2.l.h.1531.1		2
380.87	even	12		1520.2.q.f.961.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.e.a.11.1	✓	2	95.87	odd	12
190.2.e.a.121.1	yes	2	5.2	odd	4
950.2.e.f.201.1		2	95.68	odd	12
950.2.e.f.501.1		2	5.3	odd	4
950.2.j.d.49.1		4	95.49	even	6	inner
950.2.j.d.49.2		4	19.11	even	3	inner
950.2.j.d.349.1		4	1.1	even	1	trivial
950.2.j.d.349.2		4	5.4	even	2	inner
1520.2.q.f.881.1		2	20.7	even	4
1520.2.q.f.961.1		2	380.87	even	12
1710.2.l.h.1261.1		2	15.2	even	4
1710.2.l.h.1531.1		2	285.182	even	12
3610.2.a.c.1.1		1	95.12	even	12
3610.2.a.g.1.1		1	95.7	odd	12

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{7} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{7} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +5.00000 q^{11} +(-1.73205 - 1.00000i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} -3.00000i q^{18} +(0.500000 + 4.33013i) q^{19} +(-4.33013 + 2.50000i) q^{22} +(-0.866025 - 0.500000i) q^{23} +2.00000 q^{26} +(-0.866025 - 0.500000i) q^{28} +(3.00000 - 5.19615i) q^{29} +4.00000 q^{31} +(0.866025 + 0.500000i) q^{32} +(1.50000 + 2.59808i) q^{36} +11.0000i q^{37} +(-2.59808 - 3.50000i) q^{38} +(4.50000 + 7.79423i) q^{41} +(5.19615 - 3.00000i) q^{43} +(2.50000 - 4.33013i) q^{44} +1.00000 q^{46} +6.00000 q^{49} +(-1.73205 + 1.00000i) q^{52} +(-4.33013 - 2.50000i) q^{53} +1.00000 q^{56} +6.00000i q^{58} +(-3.46410 + 2.00000i) q^{62} +(2.59808 + 1.50000i) q^{63} -1.00000 q^{64} +(10.3923 + 6.00000i) q^{67} +(-3.00000 - 5.19615i) q^{71} +(-2.59808 - 1.50000i) q^{72} +(12.1244 - 7.00000i) q^{73} +(-5.50000 - 9.52628i) q^{74} +(4.00000 + 1.73205i) q^{76} -5.00000i q^{77} +(5.00000 + 8.66025i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-7.79423 - 4.50000i) q^{82} +14.0000i q^{83} +(-3.00000 + 5.19615i) q^{86} +5.00000i q^{88} +(-3.50000 + 6.06218i) q^{89} +(-1.00000 + 1.73205i) q^{91} +(-0.866025 + 0.500000i) q^{92} +(1.73205 - 1.00000i) q^{97} +(-5.19615 + 3.00000i) q^{98} +(-7.50000 + 12.9904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 6 * q^9	\( 4 q + 2 q^{4} - 6 q^{9} + 20 q^{11} + 2 q^{14} - 2 q^{16} + 2 q^{19} + 8 q^{26} + 12 q^{29} + 16 q^{31} + 6 q^{36} + 18 q^{41} + 10 q^{44} + 4 q^{46} + 24 q^{49} + 4 q^{56} - 4 q^{64} - 12 q^{71} - 22 q^{74} + 16 q^{76} + 20 q^{79} - 18 q^{81} - 12 q^{86} - 14 q^{89} - 4 q^{91} - 30 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 - 6 * q^9 + 20 * q^11 + 2 * q^14 - 2 * q^16 + 2 * q^19 + 8 * q^26 + 12 * q^29 + 16 * q^31 + 6 * q^36 + 18 * q^41 + 10 * q^44 + 4 * q^46 + 24 * q^49 + 4 * q^56 - 4 * q^64 - 12 * q^71 - 22 * q^74 + 16 * q^76 + 20 * q^79 - 18 * q^81 - 12 * q^86 - 14 * q^89 - 4 * q^91 - 30 * q^99

Introduction

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