LMFDB - Embedded newform 3150.2.bf.c.1601.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(1151,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("3150.1151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.bf (of order $6$, 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:	$25.1528766367$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1601.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	3150.1601
Dual form			3150.2.bf.c.1151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.189469 + 2.63896i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.189469 + 2.63896i) q^{7} -1.00000i q^{8} +(2.55171 - 1.47323i) q^{11} +3.93185i q^{13} +(1.48356 - 2.19067i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.199801 + 0.346065i) q^{17} +(0.0305501 + 0.0176381i) q^{19} -2.94646 q^{22} +(-3.23205 - 1.86603i) q^{23} +(1.96593 - 3.40508i) q^{26} +(-2.38014 + 1.15539i) q^{28} +8.89898i q^{29} +(0.717439 - 0.414214i) q^{31} +(0.866025 - 0.500000i) q^{32} -0.399602i q^{34} +(-3.96593 + 6.86919i) q^{37} +(-0.0176381 - 0.0305501i) q^{38} +6.31079 q^{41} +3.03528 q^{43} +(2.55171 + 1.47323i) q^{44} +(1.86603 + 3.23205i) q^{46} +(2.90130 - 5.02520i) q^{47} +(-6.92820 - 1.00000i) q^{49} +(-3.40508 + 1.96593i) q^{52} +(3.72268 - 2.14929i) q^{53} +(2.63896 + 0.189469i) q^{56} +(4.44949 - 7.70674i) q^{58} +(2.78522 + 4.82415i) q^{59} +(-9.97710 - 5.76028i) q^{61} -0.828427 q^{62} -1.00000 q^{64} +(-6.25966 - 10.8420i) q^{67} +(-0.199801 + 0.346065i) q^{68} +1.93426i q^{71} +(0.297173 - 0.171573i) q^{73} +(6.86919 - 3.96593i) q^{74} +0.0352762i q^{76} +(3.40433 + 7.01299i) q^{77} +(-4.15331 + 7.19375i) q^{79} +(-5.46530 - 3.15539i) q^{82} -10.3490 q^{83} +(-2.62863 - 1.51764i) q^{86} +(-1.47323 - 2.55171i) q^{88} +(-3.08604 + 5.34519i) q^{89} +(-10.3760 - 0.744963i) q^{91} -3.73205i q^{92} +(-5.02520 + 2.90130i) q^{94} +15.6344i q^{97} +(5.50000 + 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 8 q + 4 q^{4} + 24 q^{11} - 4 q^{16} - 12 q^{23} + 8 q^{26} - 24 q^{37} + 4 q^{38} + 32 q^{41} + 16 q^{43} + 24 q^{44} + 8 q^{46} + 8 q^{47} - 24 q^{53} + 16 q^{58} - 24 q^{59} + 16 q^{62} - 8 q^{64} + 24 q^{67} + 16 q^{77} - 24 q^{79} + 16 q^{83} - 16 q^{89} - 20 q^{91} - 12 q^{94} + 44 q^{98}+O(q^{100}) $ 8 * q + 4 * q^4 + 24 * q^11 - 4 * q^16 - 12 * q^23 + 8 * q^26 - 24 * q^37 + 4 * q^38 + 32 * q^41 + 16 * q^43 + 24 * q^44 + 8 * q^46 + 8 * q^47 - 24 * q^53 + 16 * q^58 - 24 * q^59 + 16 * q^62 - 8 * q^64 + 24 * q^67 + 16 * q^77 - 24 * q^79 + 16 * q^83 - 16 * q^89 - 20 * q^91 - 12 * q^94 + 44 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.189469	+	2.63896i	−0.0716124	+	0.997433i
$7$	−0.189469	+	2.63896i	−0.0716124	+	0.997433i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$		0			0
$11$	2.55171	−	1.47323i	0.769370	−	0.444196i	−0.0632797	−	0.997996i	$-0.520156\pi$
$11$	2.55171	−	1.47323i	0.769370	−	0.444196i	0.832650	+	0.553800i	$0.186823\pi$
$12$		0			0
$13$			3.93185i			1.09050i	0.838274	+	0.545250i	$0.183565\pi$
$13$			3.93185i			1.09050i	−0.838274	+	0.545250i	$0.816435\pi$
$14$	1.48356	−	2.19067i	0.396499	−	0.585481i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.199801	+	0.346065i	0.0484588	+	0.0839331i	0.889237	−	0.457446i	$-0.151236\pi$
$17$	0.199801	+	0.346065i	0.0484588	+	0.0839331i	−0.840779	+	0.541379i	$0.817902\pi$
$18$		0			0
$19$	0.0305501	+	0.0176381i	0.00700867	+	0.00404646i	0.503500	−	0.863995i	$-0.332045\pi$
$19$	0.0305501	+	0.0176381i	0.00700867	+	0.00404646i	−0.496492	+	0.868042i	$0.665379\pi$
$20$		0			0
$21$		0			0
$22$	−2.94646			−0.628188
$23$	−3.23205	−	1.86603i	−0.673929	−	0.389093i	0.123635	−	0.992328i	$-0.460545\pi$
$23$	−3.23205	−	1.86603i	−0.673929	−	0.389093i	−0.797564	+	0.603235i	$0.793878\pi$
$24$		0			0
$25$		0			0
$26$	1.96593	−	3.40508i	0.385550	−	0.667792i
$27$		0			0
$28$	−2.38014	+	1.15539i	−0.449804	+	0.218349i
$29$			8.89898i			1.65250i	0.563304	+	0.826250i	$0.309530\pi$
$29$			8.89898i			1.65250i	−0.563304	+	0.826250i	$0.690470\pi$
$30$		0			0
$31$	0.717439	−	0.414214i	0.128856	−	0.0743950i	−0.434187	−	0.900823i	$-0.642964\pi$
$31$	0.717439	−	0.414214i	0.128856	−	0.0743950i	0.563042	+	0.826428i	$0.309631\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$		−	0.399602i		−	0.0685311i
$35$		0			0
$36$		0			0
$37$	−3.96593	+	6.86919i	−0.651994	+	1.12929i	0.330644	+	0.943756i	$0.392734\pi$
$37$	−3.96593	+	6.86919i	−0.651994	+	1.12929i	−0.982638	+	0.185532i	$0.940599\pi$
$38$	−0.0176381	−	0.0305501i	−0.00286128	−	0.00495588i
$39$		0			0
$40$		0			0
$41$	6.31079			0.985580			0.492790	−	0.870148i	$-0.335977\pi$
$41$	6.31079			0.985580			0.492790	+	0.870148i	$0.335977\pi$
$42$		0			0
$43$	3.03528			0.462875			0.231438	−	0.972850i	$-0.425657\pi$
$43$	3.03528			0.462875			0.231438	+	0.972850i	$0.425657\pi$
$44$	2.55171	+	1.47323i	0.384685	+	0.222098i
$45$		0			0
$46$	1.86603	+	3.23205i	0.275130	+	0.476540i
$47$	2.90130	−	5.02520i	0.423198	−	0.733001i	−0.573052	−	0.819519i	$-0.694241\pi$
$47$	2.90130	−	5.02520i	0.423198	−	0.733001i	0.996250	+	0.0865180i	$0.0275740\pi$
$48$		0			0
$49$	−6.92820	−	1.00000i	−0.989743	−	0.142857i
$50$		0			0
$51$		0			0
$52$	−3.40508	+	1.96593i	−0.472200	+	0.272625i
$53$	3.72268	−	2.14929i	0.511349	−	0.295228i	−0.222039	−	0.975038i	$-0.571271\pi$
$53$	3.72268	−	2.14929i	0.511349	−	0.295228i	0.733388	+	0.679810i	$0.237938\pi$
$54$		0			0
$55$		0			0
$56$	2.63896	+	0.189469i	0.352646	+	0.0253188i
$57$		0			0
$58$	4.44949	−	7.70674i	0.584247	−	1.01194i
$59$	2.78522	+	4.82415i	0.362605	+	0.628050i	0.988389	−	0.151946i	$-0.0485540\pi$
$59$	2.78522	+	4.82415i	0.362605	+	0.628050i	−0.625784	+	0.779997i	$0.715221\pi$
$60$		0			0
$61$	−9.97710	−	5.76028i	−1.27744	−	0.737528i	−0.301060	−	0.953605i	$-0.597340\pi$
$61$	−9.97710	−	5.76028i	−1.27744	−	0.737528i	−0.976376	+	0.216077i	$0.930674\pi$
$62$	−0.828427			−0.105210
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	−6.25966	−	10.8420i	−0.764739	−	1.32457i	−0.940385	−	0.340113i	$-0.889535\pi$
$67$	−6.25966	−	10.8420i	−0.764739	−	1.32457i	0.175646	−	0.984453i	$-0.443799\pi$
$68$	−0.199801	+	0.346065i	−0.0242294	+	0.0419666i
$69$		0			0
$70$		0			0
$71$			1.93426i			0.229554i	0.993391	+	0.114777i	$0.0366153\pi$
$71$			1.93426i			0.229554i	−0.993391	+	0.114777i	$0.963385\pi$
$72$		0			0
$73$	0.297173	−	0.171573i	0.0347815	−	0.0200811i	−0.482508	−	0.875891i	$-0.660274\pi$
$73$	0.297173	−	0.171573i	0.0347815	−	0.0200811i	0.517290	+	0.855810i	$0.326941\pi$
$74$	6.86919	−	3.96593i	0.798527	−	0.461030i
$75$		0			0
$76$			0.0352762i			0.00404646i
$77$	3.40433	+	7.01299i	0.387959	+	0.799205i
$78$		0			0
$79$	−4.15331	+	7.19375i	−0.467284	+	0.809360i	−0.999301	−	0.0373736i	$-0.988101\pi$
$79$	−4.15331	+	7.19375i	−0.467284	+	0.809360i	0.532017	+	0.846734i	$0.321434\pi$
$80$		0			0
$81$		0			0
$82$	−5.46530	−	3.15539i	−0.603542	−	0.348455i
$83$	−10.3490			−1.13595			−0.567974	−	0.823046i	$-0.692273\pi$
$83$	−10.3490			−1.13595			−0.567974	+	0.823046i	$0.692273\pi$
$84$		0			0
$85$		0			0
$86$	−2.62863	−	1.51764i	−0.283452	−	0.163651i
$87$		0			0
$88$	−1.47323	−	2.55171i	−0.157047	−	0.272013i
$89$	−3.08604	+	5.34519i	−0.327120	+	0.566589i	−0.981939	−	0.189197i	$-0.939411\pi$
$89$	−3.08604	+	5.34519i	−0.327120	+	0.566589i	0.654819	+	0.755786i	$0.272745\pi$
$90$		0			0
$91$	−10.3760	−	0.744963i	−1.08770	−	0.0780933i
$92$		−	3.73205i		−	0.389093i
$93$		0			0
$94$	−5.02520	+	2.90130i	−0.518310	+	0.299246i
$95$		0			0
$96$		0			0
$97$			15.6344i			1.58744i	0.608286	+	0.793718i	$0.291857\pi$
$97$			15.6344i			1.58744i	−0.608286	+	0.793718i	$0.708143\pi$
$98$	5.50000	+	4.33013i	0.555584	+	0.437409i
$99$		0			0
$100$		0			0
$101$	−9.02458	−	15.6310i	−0.897979	−	1.55535i	−0.830074	−	0.557654i	$-0.811702\pi$
$101$	−9.02458	−	15.6310i	−0.897979	−	1.55535i	−0.0679057	−	0.997692i	$-0.521632\pi$
$102$		0			0
$103$	7.37857	+	4.26002i	0.727032	+	0.419752i	0.817336	−	0.576162i	$-0.195450\pi$
$103$	7.37857	+	4.26002i	0.727032	+	0.419752i	−0.0903031	+	0.995914i	$0.528784\pi$
$104$	3.93185			0.385550
$105$		0			0
$106$	−4.29858			−0.417515
$107$	14.7702	+	8.52761i	1.42789	+	0.824395i	0.996954	−	0.0779862i	$-0.0248490\pi$
$107$	14.7702	+	8.52761i	1.42789	+	0.824395i	0.430939	+	0.902381i	$0.358182\pi$
$108$		0			0
$109$	5.84909	+	10.1309i	0.560241	+	0.970366i	0.997475	+	0.0710185i	$0.0226249\pi$
$109$	5.84909	+	10.1309i	0.560241	+	0.970366i	−0.437234	+	0.899348i	$0.644042\pi$
$110$		0			0
$111$		0			0
$112$	−2.19067	−	1.48356i	−0.206999	−	0.140184i
$113$		−	13.5546i		−	1.27511i	−0.770405	−	0.637554i	$-0.779946\pi$
$113$		−	13.5546i		−	1.27511i	0.770405	−	0.637554i	$-0.220054\pi$
$114$		0			0
$115$		0			0
$116$	−7.70674	+	4.44949i	−0.715553	+	0.413125i
$117$		0			0
$118$		−	5.57045i		−	0.512801i
$119$	−0.951108	+	0.461698i	−0.0871879	+	0.0423237i
$120$		0			0
$121$	−1.15918	+	2.00775i	−0.105380	+	0.182523i
$122$	5.76028	+	9.97710i	0.521511	+	0.903284i
$123$		0			0
$124$	0.717439	+	0.414214i	0.0644279	+	0.0371975i
$125$		0			0
$126$		0			0
$127$	−8.95983			−0.795056			−0.397528	−	0.917590i	$-0.630132\pi$
$127$	−8.95983			−0.795056			−0.397528	+	0.917590i	$0.630132\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$		0			0
$131$	−6.39047	+	11.0686i	−0.558338	+	0.967070i	0.439297	+	0.898342i	$0.355227\pi$
$131$	−6.39047	+	11.0686i	−0.558338	+	0.967070i	−0.997635	+	0.0687282i	$0.978106\pi$
$132$		0			0
$133$	−0.0523345	+	0.0772785i	−0.00453797	+	0.00670090i
$134$			12.5193i			1.08150i
$135$		0			0
$136$	0.346065	−	0.199801i	0.0296748	−	0.0171328i
$137$	4.78094	−	2.76028i	0.408464	−	0.235827i	−0.281666	−	0.959513i	$-0.590887\pi$
$137$	4.78094	−	2.76028i	0.408464	−	0.235827i	0.690129	+	0.723686i	$0.257554\pi$
$138$		0			0
$139$			21.8471i			1.85305i	0.376235	+	0.926524i	$0.377218\pi$
$139$			21.8471i			1.85305i	−0.376235	+	0.926524i	$0.622782\pi$
$140$		0			0
$141$		0			0
$142$	0.967128	−	1.67511i	0.0811596	−	0.140572i
$143$	5.79253	+	10.0330i	0.484396	+	0.838998i
$144$		0			0
$145$		0			0
$146$	−0.343146			−0.0283989
$147$		0			0
$148$	−7.93185			−0.651994
$149$	−18.6179	−	10.7491i	−1.52524	−	0.880598i	−0.999552	−	0.0299204i	$-0.990475\pi$
$149$	−18.6179	−	10.7491i	−1.52524	−	0.880598i	−0.525688	−	0.850677i	$-0.676192\pi$
$150$		0			0
$151$	−1.47531	−	2.55532i	−0.120059	−	0.207949i	0.799732	−	0.600358i	$-0.204975\pi$
$151$	−1.47531	−	2.55532i	−0.120059	−	0.207949i	−0.919791	+	0.392409i	$0.871642\pi$
$152$	0.0176381	−	0.0305501i	0.00143064	−	0.00247794i
$153$		0			0
$154$	0.558263	−	7.77559i	0.0449861	−	0.626575i
$155$		0			0
$156$		0			0
$157$	−19.4823	+	11.2481i	−1.55486	+	0.897698i	−0.557123	+	0.830430i	$0.688095\pi$
$157$	−19.4823	+	11.2481i	−1.55486	+	0.897698i	−0.997735	+	0.0672682i	$0.978572\pi$
$158$	7.19375	−	4.15331i	0.572304	−	0.330420i
$159$		0			0
$160$		0			0
$161$	5.53674	−	8.17569i	0.436356	−	0.644335i
$162$		0			0
$163$	11.4035	−	19.7515i	0.893192	−	1.54705i	0.0571664	−	0.998365i	$-0.481793\pi$
$163$	11.4035	−	19.7515i	0.893192	−	1.54705i	0.836026	−	0.548690i	$-0.184873\pi$
$164$	3.15539	+	5.46530i	0.246395	+	0.426769i
$165$		0			0
$166$	8.96248	+	5.17449i	0.695624	+	0.401618i
$167$	−8.84961			−0.684803			−0.342402	−	0.939554i	$-0.611240\pi$
$167$	−8.84961			−0.684803			−0.342402	+	0.939554i	$0.611240\pi$
$168$		0			0
$169$	−2.45946			−0.189189
$170$		0			0
$171$		0			0
$172$	1.51764	+	2.62863i	0.115719	+	0.200431i
$173$	−3.86843	+	6.70032i	−0.294111	+	0.509416i	−0.974778	−	0.223178i	$-0.928357\pi$
$173$	−3.86843	+	6.70032i	−0.294111	+	0.509416i	0.680667	+	0.732593i	$0.261690\pi$
$174$		0			0
$175$		0			0
$176$			2.94646i			0.222098i
$177$		0			0
$178$	5.34519	−	3.08604i	0.400639	−	0.231309i
$179$	−0.417291	+	0.240923i	−0.0311898	+	0.0180074i	−0.515514	−	0.856881i	$-0.672399\pi$
$179$	−0.417291	+	0.240923i	−0.0311898	+	0.0180074i	0.484324	+	0.874889i	$0.339066\pi$
$180$		0			0
$181$			2.44876i			0.182015i	0.995850	+	0.0910075i	$0.0290087\pi$
$181$			2.44876i			0.182015i	−0.995850	+	0.0910075i	$0.970991\pi$
$182$	8.61339	+	5.83315i	0.638467	+	0.432382i
$183$		0			0
$184$	−1.86603	+	3.23205i	−0.137565	+	0.238270i
$185$		0			0
$186$		0			0
$187$	1.01967	+	0.588706i	0.0745655	+	0.0430504i
$188$	5.80260			0.423198
$189$		0			0
$190$		0			0
$191$	3.89241	+	2.24728i	0.281645	+	0.162608i	0.634168	−	0.773195i	$-0.281343\pi$
$191$	3.89241	+	2.24728i	0.281645	+	0.162608i	−0.352523	+	0.935803i	$0.614676\pi$
$192$		0			0
$193$	−6.28497	−	10.8859i	−0.452402	−	0.783583i	0.546133	−	0.837698i	$-0.316099\pi$
$193$	−6.28497	−	10.8859i	−0.452402	−	0.783583i	−0.998535	+	0.0541158i	$0.982766\pi$
$194$	7.81722	−	13.5398i	0.561243	−	0.972102i
$195$		0			0
$196$	−2.59808	−	6.50000i	−0.185577	−	0.464286i
$197$			13.3748i			0.952916i	0.879197	+	0.476458i	$0.158080\pi$
$197$			13.3748i			0.952916i	−0.879197	+	0.476458i	$0.841920\pi$
$198$		0			0
$199$	−23.5169	+	13.5775i	−1.66707	+	0.962483i	−0.697864	+	0.716231i	$0.745866\pi$
$199$	−23.5169	+	13.5775i	−1.66707	+	0.962483i	−0.969206	+	0.246253i	$0.920801\pi$
$200$		0			0
$201$		0			0
$202$			18.0492i			1.26993i
$203$	−23.4840	−	1.68608i	−1.64826	−	0.118339i
$204$		0			0
$205$		0			0
$206$	−4.26002	−	7.37857i	−0.296810	−	0.514090i
$207$		0			0
$208$	−3.40508	−	1.96593i	−0.236100	−	0.136312i
$209$	0.103940			0.00718968
$210$		0			0
$211$	18.4183			1.26797			0.633984	−	0.773346i	$-0.281419\pi$
$211$	18.4183			1.26797			0.633984	+	0.773346i	$0.281419\pi$
$212$	3.72268	+	2.14929i	0.255675	+	0.147614i
$213$		0			0
$214$	−8.52761	−	14.7702i	−0.582935	−	1.00967i
$215$		0			0
$216$		0			0
$217$	0.957160	+	1.97177i	0.0649763	+	0.133853i
$218$		−	11.6982i		−	0.792301i
$219$		0			0
$220$		0			0
$221$	−1.36068	+	0.785587i	−0.0915290	+	0.0528443i
$222$		0			0
$223$			17.8045i			1.19228i	0.802881	+	0.596140i	$0.203300\pi$
$223$			17.8045i			1.19228i	−0.802881	+	0.596140i	$0.796700\pi$
$224$	1.15539	+	2.38014i	0.0771980	+	0.159030i
$225$		0			0
$226$	−6.77729	+	11.7386i	−0.450819	+	0.780841i
$227$	−0.856140	−	1.48288i	−0.0568240	−	0.0984220i	0.836214	−	0.548403i	$-0.184764\pi$
$227$	−0.856140	−	1.48288i	−0.0568240	−	0.0984220i	−0.893038	+	0.449981i	$0.851431\pi$
$228$		0			0
$229$	5.26142	+	3.03768i	0.347684	+	0.200736i	0.663665	−	0.748030i	$-0.269000\pi$
$229$	5.26142	+	3.03768i	0.347684	+	0.200736i	−0.315981	+	0.948766i	$0.602333\pi$
$230$		0			0
$231$		0			0
$232$	8.89898			0.584247
$233$	6.17109	+	3.56288i	0.404282	+	0.233412i	0.688330	−	0.725398i	$-0.258344\pi$
$233$	6.17109	+	3.56288i	0.404282	+	0.233412i	−0.284048	+	0.958810i	$0.591678\pi$
$234$		0			0
$235$		0			0
$236$	−2.78522	+	4.82415i	−0.181303	+	0.314025i
$237$		0			0
$238$	1.05453	+	0.0757120i	0.0683552	+	0.00490768i
$239$			18.7194i			1.21085i	0.795900	+	0.605427i	$0.206998\pi$
$239$			18.7194i			1.21085i	−0.795900	+	0.605427i	$0.793002\pi$
$240$		0			0
$241$	7.68036	−	4.43426i	0.494735	−	0.285636i	−0.231802	−	0.972763i	$-0.574462\pi$
$241$	7.68036	−	4.43426i	0.494735	−	0.285636i	0.726537	+	0.687128i	$0.241129\pi$
$242$	2.00775	−	1.15918i	0.129063	−	0.0745147i
$243$		0			0
$244$		−	11.5206i		−	0.737528i
$245$		0			0
$246$		0			0
$247$	−0.0693504	+	0.120118i	−0.00441266	+	0.00764295i
$248$	−0.414214	−	0.717439i	−0.0263026	−	0.0455574i
$249$		0			0
$250$		0			0
$251$	22.1738			1.39960			0.699798	−	0.714341i	$-0.253273\pi$
$251$	22.1738			1.39960			0.699798	+	0.714341i	$0.253273\pi$
$252$		0			0
$253$	−10.9964			−0.691335
$254$	7.75944	+	4.47992i	0.486871	+	0.281095i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	8.41662	−	14.5780i	0.525014	−	0.909351i	−0.474561	−	0.880222i	$-0.657393\pi$
$257$	8.41662	−	14.5780i	0.525014	−	0.909351i	0.999576	−	0.0291289i	$-0.00927332\pi$
$258$		0			0
$259$	−17.3761	−	11.7674i	−1.07970	−	0.731191i
$260$		0			0
$261$		0			0
$262$	11.0686	−	6.39047i	0.683822	−	0.394805i
$263$	−19.1562	+	11.0599i	−1.18122	+	0.681980i	−0.956297	−	0.292396i	$-0.905548\pi$
$263$	−19.1562	+	11.0599i	−1.18122	+	0.681980i	−0.224926	+	0.974376i	$0.572214\pi$
$264$		0			0
$265$		0			0
$266$	0.0839622	−	0.0407579i	0.00514805	−	0.00249903i
$267$		0			0
$268$	6.25966	−	10.8420i	0.382369	−	0.662283i
$269$	1.45049	+	2.51231i	0.0884377	+	0.153179i	0.906851	−	0.421452i	$-0.138479\pi$
$269$	1.45049	+	2.51231i	0.0884377	+	0.153179i	−0.818413	+	0.574630i	$0.805146\pi$
$270$		0			0
$271$	15.1244	+	8.73205i	0.918739	+	0.530434i	0.883233	−	0.468935i	$-0.155362\pi$
$271$	15.1244	+	8.73205i	0.918739	+	0.530434i	0.0355066	+	0.999369i	$0.488696\pi$
$272$	−0.399602			−0.0242294
$273$		0			0
$274$	−5.52056			−0.333509
$275$		0			0
$276$		0			0
$277$	2.28825	+	3.96336i	0.137488	+	0.238135i	0.926545	−	0.376184i	$-0.122764\pi$
$277$	2.28825	+	3.96336i	0.137488	+	0.238135i	−0.789057	+	0.614319i	$0.789431\pi$
$278$	10.9236	−	18.9202i	0.655152	−	1.13476i
$279$		0			0
$280$		0			0
$281$			9.55948i			0.570271i	0.958487	+	0.285135i	$0.0920386\pi$
$281$			9.55948i			0.570271i	−0.958487	+	0.285135i	$0.907961\pi$
$282$		0			0
$283$	−9.46238	+	5.46311i	−0.562480	+	0.324748i	−0.754140	−	0.656713i	$-0.771946\pi$
$283$	−9.46238	+	5.46311i	−0.562480	+	0.324748i	0.191660	+	0.981461i	$0.438613\pi$
$284$	−1.67511	+	0.967128i	−0.0993998	+	0.0573885i
$285$		0			0
$286$		−	11.5851i		−	0.685039i
$287$	−1.19570	+	16.6539i	−0.0705798	+	0.983049i
$288$		0			0
$289$	8.42016	−	14.5841i	0.495303	−	0.857891i
$290$		0			0
$291$		0			0
$292$	0.297173	+	0.171573i	0.0173907	+	0.0100405i
$293$	−16.2280			−0.948052			−0.474026	−	0.880511i	$-0.657200\pi$
$293$	−16.2280			−0.948052			−0.474026	+	0.880511i	$0.657200\pi$
$294$		0			0
$295$		0			0
$296$	6.86919	+	3.96593i	0.399263	+	0.230515i
$297$		0			0
$298$	10.7491	+	18.6179i	0.622677	+	1.07851i
$299$	7.33694	−	12.7079i	0.424306	−	0.734919i
$300$		0			0
$301$	−0.575090	+	8.00997i	−0.0331476	+	0.461687i
$302$			2.95063i			0.169790i
$303$		0			0
$304$	−0.0305501	+	0.0176381i	−0.00175217	+	0.00101161i
$305$		0			0
$306$		0			0
$307$			12.3782i			0.706462i	0.935536	+	0.353231i	$0.114917\pi$
$307$			12.3782i			0.706462i	−0.935536	+	0.353231i	$0.885083\pi$
$308$	−4.37127	+	6.45473i	−0.249076	+	0.367792i
$309$		0			0
$310$		0			0
$311$	11.4312	+	19.7995i	0.648206	+	1.12272i	0.983551	+	0.180630i	$0.0578136\pi$
$311$	11.4312	+	19.7995i	0.648206	+	1.12272i	−0.335346	+	0.942095i	$0.608853\pi$
$312$		0			0
$313$	30.1399	+	17.4013i	1.70361	+	0.983578i	0.942045	+	0.335487i	$0.108901\pi$
$313$	30.1399	+	17.4013i	1.70361	+	0.983578i	0.761563	+	0.648091i	$0.224432\pi$
$314$	22.4962			1.26954
$315$		0			0
$316$	−8.30663			−0.467284
$317$	−5.87780	−	3.39355i	−0.330130	−	0.190601i	0.325769	−	0.945449i	$-0.394377\pi$
$317$	−5.87780	−	3.39355i	−0.330130	−	0.190601i	−0.655899	+	0.754849i	$0.727710\pi$
$318$		0			0
$319$	13.1103	+	22.7076i	0.734034	+	1.27138i
$320$		0			0
$321$		0			0
$322$	−8.88280	+	4.31199i	−0.495019	+	0.240298i
$323$			0.0140964i			0.000784346i
$324$		0			0
$325$		0			0
$326$	−19.7515	+	11.4035i	−1.09393	+	0.631582i
$327$		0			0
$328$		−	6.31079i		−	0.348455i
$329$	12.7116	+	8.60853i	0.700813	+	0.474604i
$330$		0			0
$331$	−5.56985	+	9.64726i	−0.306147	+	0.530261i	−0.977516	−	0.210862i	$-0.932373\pi$
$331$	−5.56985	+	9.64726i	−0.306147	+	0.530261i	0.671369	+	0.741123i	$0.265706\pi$
$332$	−5.17449	−	8.96248i	−0.283987	−	0.491880i
$333$		0			0
$334$	7.66398	+	4.42480i	0.419355	+	0.242114i
$335$		0			0
$336$		0			0
$337$	−1.59111			−0.0866733			−0.0433366	−	0.999061i	$-0.513799\pi$
$337$	−1.59111			−0.0866733			−0.0433366	+	0.999061i	$0.513799\pi$
$338$	2.12995	+	1.22973i	0.115854	+	0.0668884i
$339$		0			0
$340$		0			0
$341$	1.22047	−	2.11391i	0.0660919	−	0.114475i
$342$		0			0
$343$	3.95164	−	18.0938i	0.213368	−	0.976972i
$344$		−	3.03528i		−	0.163651i
$345$		0			0
$346$	6.70032	−	3.86843i	0.360211	−	0.207968i
$347$	−13.3860	+	7.72840i	−0.718597	+	0.414882i	−0.814236	−	0.580534i	$-0.802844\pi$
$347$	−13.3860	+	7.72840i	−0.718597	+	0.414882i	0.0956388	+	0.995416i	$0.469511\pi$
$348$		0			0
$349$			0.585057i			0.0313174i	0.999877	+	0.0156587i	$0.00498452\pi$
$349$			0.585057i			0.0313174i	−0.999877	+	0.0156587i	$0.995015\pi$
$350$		0			0
$351$		0			0
$352$	1.47323	−	2.55171i	0.0785235	−	0.136007i
$353$	1.83788	+	3.18330i	0.0978204	+	0.169430i	0.910782	−	0.412887i	$-0.135480\pi$
$353$	1.83788	+	3.18330i	0.0978204	+	0.169430i	−0.812962	+	0.582317i	$0.802146\pi$
$354$		0			0
$355$		0			0
$356$	−6.17209			−0.327120
$357$		0			0
$358$	0.481846			0.0254664
$359$	−17.4069	−	10.0499i	−0.918702	−	0.530413i	−0.0354812	−	0.999370i	$-0.511296\pi$
$359$	−17.4069	−	10.0499i	−0.918702	−	0.530413i	−0.883221	+	0.468958i	$0.844630\pi$
$360$		0			0
$361$	−9.49938	−	16.4534i	−0.499967	−	0.865969i
$362$	1.22438	−	2.12069i	0.0643520	−	0.111461i
$363$		0			0
$364$	−4.54284	−	9.35835i	−0.238110	−	0.490511i
$365$		0			0
$366$		0			0
$367$	17.2665	−	9.96885i	0.901306	−	0.520369i	0.0236826	−	0.999720i	$-0.492461\pi$
$367$	17.2665	−	9.96885i	0.901306	−	0.520369i	0.877624	+	0.479350i	$0.159128\pi$
$368$	3.23205	−	1.86603i	0.168482	−	0.0972733i
$369$		0			0
$370$		0			0
$371$	4.96656	+	10.2312i	0.257851	+	0.531179i
$372$		0			0
$373$	−16.9081	+	29.2856i	−0.875467	+	1.51635i	−0.0192016	+	0.999816i	$0.506112\pi$
$373$	−16.9081	+	29.2856i	−0.875467	+	1.51635i	−0.856265	+	0.516537i	$0.827221\pi$
$374$	−0.588706	−	1.01967i	−0.0304413	−	0.0527258i
$375$		0			0
$376$	−5.02520	−	2.90130i	−0.259155	−	0.149623i
$377$	−34.9895			−1.80205
$378$		0			0
$379$	26.7614			1.37464			0.687321	−	0.726353i	$-0.258786\pi$
$379$	26.7614			1.37464			0.687321	+	0.726353i	$0.258786\pi$
$380$		0			0
$381$		0			0
$382$	−2.24728	−	3.89241i	−0.114981	−	0.199153i
$383$	9.89060	−	17.1310i	0.505386	−	0.875355i	−0.494594	−	0.869124i	$-0.664683\pi$
$383$	9.89060	−	17.1310i	0.505386	−	0.875355i	0.999981	−	0.00623078i	$-0.00198333\pi$
$384$		0			0
$385$		0			0
$386$			12.5699i			0.639793i
$387$		0			0
$388$	−13.5398	+	7.81722i	−0.687380	+	0.396859i
$389$	4.49181	−	2.59335i	0.227744	−	0.131488i	−0.381787	−	0.924250i	$-0.624691\pi$
$389$	4.49181	−	2.59335i	0.227744	−	0.131488i	0.609531	+	0.792762i	$0.291358\pi$
$390$		0			0
$391$		−	1.49133i		−	0.0754200i
$392$	−1.00000	+	6.92820i	−0.0505076	+	0.349927i
$393$		0			0
$394$	6.68740	−	11.5829i	0.336907	−	0.583539i
$395$		0			0
$396$		0			0
$397$	−4.99280	−	2.88259i	−0.250581	−	0.144673i	0.369449	−	0.929251i	$-0.379546\pi$
$397$	−4.99280	−	2.88259i	−0.250581	−	0.144673i	−0.620030	+	0.784578i	$0.712880\pi$
$398$	27.1550			1.36116
$399$		0			0
$400$		0			0
$401$	−15.4361	−	8.91202i	−0.770841	−	0.445045i	0.0623335	−	0.998055i	$-0.480146\pi$
$401$	−15.4361	−	8.91202i	−0.770841	−	0.445045i	−0.833175	+	0.553010i	$0.813479\pi$
$402$		0			0
$403$	1.62863	+	2.82086i	0.0811277	+	0.140517i
$404$	9.02458	−	15.6310i	0.448990	−	0.777673i
$405$		0			0
$406$	19.4947	+	13.2022i	0.967507	+	0.655214i
$407$			23.3709i			1.15845i
$408$		0			0
$409$	−28.5617	+	16.4901i	−1.41228	+	0.815382i	−0.995603	−	0.0936705i	$-0.970140\pi$
$409$	−28.5617	+	16.4901i	−1.41228	+	0.815382i	−0.416681	+	0.909053i	$0.636807\pi$
$410$		0			0
$411$		0			0
$412$			8.52004i			0.419752i
$413$	−13.2584	+	6.43606i	−0.652405	+	0.316698i
$414$		0			0
$415$		0			0
$416$	1.96593	+	3.40508i	0.0963874	+	0.166948i
$417$		0			0
$418$	−0.0900147	−	0.0519700i	−0.00440276	−	0.00254194i
$419$	−15.2287			−0.743969			−0.371985	−	0.928239i	$-0.621323\pi$
$419$	−15.2287			−0.743969			−0.371985	+	0.928239i	$0.621323\pi$
$420$		0			0
$421$	16.9939			0.828234			0.414117	−	0.910224i	$-0.364090\pi$
$421$	16.9939			0.828234			0.414117	+	0.910224i	$0.364090\pi$
$422$	−15.9507	−	9.20915i	−0.776468	−	0.448294i
$423$		0			0
$424$	−2.14929	−	3.72268i	−0.104379	−	0.180789i
$425$		0			0
$426$		0			0
$427$	17.0915	−	25.2377i	0.827115	−	1.22134i
$428$			17.0552i			0.824395i
$429$		0			0
$430$		0			0
$431$	15.4818	−	8.93842i	0.745732	−	0.430549i	−0.0784178	−	0.996921i	$-0.524987\pi$
$431$	15.4818	−	8.93842i	0.745732	−	0.430549i	0.824150	+	0.566372i	$0.191653\pi$
$432$		0			0
$433$			5.56388i			0.267383i	0.991023	+	0.133691i	$0.0426831\pi$
$433$			5.56388i			0.267383i	−0.991023	+	0.133691i	$0.957317\pi$
$434$	0.156961	−	2.18618i	0.00753437	−	0.104940i
$435$		0			0
$436$	−5.84909	+	10.1309i	−0.280121	+	0.485183i
$437$	−0.0658262	−	0.114014i	−0.00314890	−	0.00545405i
$438$		0			0
$439$	9.53568	+	5.50543i	0.455113	+	0.262760i	0.709987	−	0.704214i	$-0.248701\pi$
$439$	9.53568	+	5.50543i	0.455113	+	0.262760i	−0.254874	+	0.966974i	$0.582034\pi$
$440$		0			0
$441$		0			0
$442$	1.57117			0.0747332
$443$	−14.7091	−	8.49233i	−0.698853	−	0.403483i	0.108067	−	0.994144i	$-0.465534\pi$
$443$	−14.7091	−	8.49233i	−0.698853	−	0.403483i	−0.806920	+	0.590661i	$0.798867\pi$
$444$		0			0
$445$		0			0
$446$	8.90226	−	15.4192i	0.421534	−	0.730119i
$447$		0			0
$448$	0.189469	−	2.63896i	0.00895155	−	0.124679i
$449$			12.5892i			0.594122i	0.954858	+	0.297061i	$0.0960065\pi$
$449$			12.5892i			0.594122i	−0.954858	+	0.297061i	$0.903994\pi$
$450$		0			0
$451$	16.1033	−	9.29725i	0.758276	−	0.437791i
$452$	11.7386	−	6.77729i	0.552138	−	0.318777i
$453$		0			0
$454$			1.71228i			0.0803612i
$455$		0			0
$456$		0			0
$457$	−1.08417	+	1.87783i	−0.0507153	+	0.0878414i	−0.890269	−	0.455436i	$-0.849483\pi$
$457$	−1.08417	+	1.87783i	−0.0507153	+	0.0878414i	0.839553	+	0.543277i	$0.182817\pi$
$458$	−3.03768	−	5.26142i	−0.141941	−	0.245850i
$459$		0			0
$460$		0			0
$461$	−34.3032			−1.59766			−0.798829	−	0.601558i	$-0.794547\pi$
$461$	−34.3032			−1.59766			−0.798829	+	0.601558i	$0.794547\pi$
$462$		0			0
$463$	−28.2133			−1.31118			−0.655592	−	0.755115i	$-0.727581\pi$
$463$	−28.2133			−1.31118			−0.655592	+	0.755115i	$0.727581\pi$
$464$	−7.70674	−	4.44949i	−0.357777	−	0.206562i
$465$		0			0
$466$	−3.56288	−	6.17109i	−0.165047	−	0.285870i
$467$	−2.10342	+	3.64324i	−0.0973349	+	0.168589i	−0.910581	−	0.413331i	$-0.864365\pi$
$467$	−2.10342	+	3.64324i	−0.0973349	+	0.168589i	0.813246	+	0.581920i	$0.197698\pi$
$468$		0			0
$469$	29.7977	−	14.4647i	1.37593	−	0.667920i
$470$		0			0
$471$		0			0
$472$	4.82415	−	2.78522i	0.222049	−	0.128200i
$473$	7.74515	−	4.47167i	0.356122	−	0.205607i
$474$		0			0
$475$		0			0
$476$	−0.875396	−	0.592835i	−0.0401237	−	0.0271725i
$477$		0			0
$478$	9.35968	−	16.2114i	0.428102	−	0.741494i
$479$	−7.35968	−	12.7473i	−0.336272	−	0.582441i	0.647456	−	0.762103i	$-0.275833\pi$
$479$	−7.35968	−	12.7473i	−0.336272	−	0.582441i	−0.983728	+	0.179662i	$0.942500\pi$
$480$		0			0
$481$	−27.0086	−	15.5934i	−1.23149	−	0.710999i
$482$	−8.86851			−0.403950
$483$		0			0
$484$	−2.31835			−0.105380
$485$		0			0
$486$		0			0
$487$	−0.938784	−	1.62602i	−0.0425404	−	0.0736821i	0.843971	−	0.536388i	$-0.180212\pi$
$487$	−0.938784	−	1.62602i	−0.0425404	−	0.0736821i	−0.886512	+	0.462706i	$0.846878\pi$
$488$	−5.76028	+	9.97710i	−0.260756	+	0.451642i
$489$		0			0
$490$		0			0
$491$			10.4281i			0.470613i	0.971921	+	0.235307i	$0.0756095\pi$
$491$			10.4281i			0.470613i	−0.971921	+	0.235307i	$0.924391\pi$
$492$		0			0
$493$	−3.07963	+	1.77802i	−0.138699	+	0.0800782i
$494$	0.120118	−	0.0693504i	0.00540438	−	0.00312022i
$495$		0			0
$496$			0.828427i			0.0371975i
$497$	−5.10442	−	0.366481i	−0.228965	−	0.0164389i
$498$		0			0
$499$	18.8822	−	32.7050i	0.845285	−	1.46408i	−0.0400890	−	0.999196i	$-0.512764\pi$
$499$	18.8822	−	32.7050i	0.845285	−	1.46408i	0.885374	−	0.464880i	$-0.153903\pi$
$500$		0			0
$501$		0			0
$502$	−19.2030	−	11.0869i	−0.857074	−	0.494832i
$503$	35.8895			1.60023			0.800116	−	0.599845i	$-0.204771\pi$
$503$	35.8895			1.60023			0.800116	+	0.599845i	$0.204771\pi$
$504$		0			0
$505$		0			0
$506$	9.52312	+	5.49818i	0.423354	+	0.244424i
$507$		0			0
$508$	−4.47992	−	7.75944i	−0.198764	−	0.344270i
$509$	8.58746	−	14.8739i	0.380633	−	0.659275i	−0.610520	−	0.792001i	$-0.709040\pi$
$509$	8.58746	−	14.8739i	0.380633	−	0.659275i	0.991153	+	0.132726i	$0.0423729\pi$
$510$		0			0
$511$	0.396469	+	0.816735i	0.0175387	+	0.0361302i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−14.5780	+	8.41662i	−0.643008	+	0.371241i
$515$		0			0
$516$		0			0
$517$		−	17.0972i		−	0.751932i
$518$	9.16442	+	18.8789i	0.402661	+	0.829492i
$519$		0			0
$520$		0			0
$521$	2.26539	+	3.92377i	0.0992484	+	0.171903i	0.911374	−	0.411580i	$-0.135023\pi$
$521$	2.26539	+	3.92377i	0.0992484	+	0.171903i	−0.812125	+	0.583483i	$0.801689\pi$
$522$		0			0
$523$	22.9267	+	13.2368i	1.00252	+	0.578803i	0.908992	−	0.416814i	$-0.136853\pi$
$523$	22.9267	+	13.2368i	1.00252	+	0.578803i	0.0935241	+	0.995617i	$0.470187\pi$
$524$	−12.7809			−0.558338
$525$		0			0
$526$	22.1197			0.964465
$527$	0.286690	+	0.165520i	0.0124884	+	0.00721018i
$528$		0			0
$529$	−4.53590	−	7.85641i	−0.197213	−	0.341583i
$530$		0			0
$531$		0			0
$532$	−0.0930924	−	0.00668373i	−0.00403607	−	0.000289777i
$533$			24.8131i			1.07477i
$534$		0			0
$535$		0			0
$536$	−10.8420	+	6.25966i	−0.468305	+	0.270376i
$537$		0			0
$538$		−	2.90097i		−	0.125070i
$539$	−19.1520	+	7.65514i	−0.824936	+	0.329730i
$540$		0			0
$541$	−3.16504	+	5.48201i	−0.136076	+	0.235690i	−0.926008	−	0.377504i	$-0.876782\pi$
$541$	−3.16504	+	5.48201i	−0.136076	+	0.235690i	0.789932	+	0.613194i	$0.210116\pi$
$542$	−8.73205	−	15.1244i	−0.375074	−	0.649647i
$543$		0			0
$544$	0.346065	+	0.199801i	0.0148374	+	0.00856639i
$545$		0			0
$546$		0			0
$547$	38.5271			1.64730			0.823651	−	0.567097i	$-0.191934\pi$
$547$	38.5271			1.64730			0.823651	+	0.567097i	$0.191934\pi$
$548$	4.78094	+	2.76028i	0.204232	+	0.117913i
$549$		0			0
$550$		0			0
$551$	−0.156961	+	0.271864i	−0.00668676	+	0.0115818i
$552$		0			0
$553$	−18.1971	−	12.3234i	−0.773819	−	0.524045i
$554$		−	4.57650i		−	0.194437i
$555$		0			0
$556$	−18.9202	+	10.9236i	−0.802393	+	0.463262i
$557$	8.00456	−	4.62144i	0.339164	−	0.195817i	−0.320738	−	0.947168i	$-0.603931\pi$
$557$	8.00456	−	4.62144i	0.339164	−	0.195817i	0.659902	+	0.751351i	$0.270598\pi$
$558$		0			0
$559$			11.9343i			0.504765i
$560$		0			0
$561$		0			0
$562$	4.77974	−	8.27875i	0.201621	−	0.349218i
$563$	13.3871	+	23.1872i	0.564201	+	0.977225i	0.997124	+	0.0757935i	$0.0241490\pi$
$563$	13.3871	+	23.1872i	0.564201	+	0.977225i	−0.432923	+	0.901431i	$0.642518\pi$
$564$		0			0
$565$		0			0
$566$	10.9262			0.459263
$567$		0			0
$568$	1.93426			0.0811596
$569$	−39.6604	−	22.8979i	−1.66265	−	0.959931i	−0.971443	−	0.237274i	$-0.923746\pi$
$569$	−39.6604	−	22.8979i	−1.66265	−	0.959931i	−0.691207	−	0.722657i	$-0.742921\pi$
$570$		0			0
$571$	−0.390149	−	0.675759i	−0.0163272	−	0.0282796i	0.857746	−	0.514073i	$-0.171864\pi$
$571$	−0.390149	−	0.675759i	−0.0163272	−	0.0282796i	−0.874074	+	0.485794i	$0.838531\pi$
$572$	−5.79253	+	10.0330i	−0.242198	+	0.419499i
$573$		0			0
$574$	9.36246	−	13.8249i	0.390781	−	0.577039i
$575$		0			0
$576$		0			0
$577$	9.74401	−	5.62571i	0.405648	−	0.234201i	−0.283270	−	0.959040i	$-0.591419\pi$
$577$	9.74401	−	5.62571i	0.405648	−	0.234201i	0.688918	+	0.724839i	$0.258086\pi$
$578$	−14.5841	+	8.42016i	−0.606620	+	0.350232i
$579$		0			0
$580$		0			0
$581$	1.96081	−	27.3105i	0.0813480	−	1.13303i
$582$		0			0
$583$	6.33281	−	10.9687i	0.262278	−	0.454279i
$584$	−0.171573	−	0.297173i	−0.00709974	−	0.0122971i
$585$		0			0
$586$	14.0539	+	8.11401i	0.580561	+	0.335187i
$587$	40.1593			1.65755			0.828775	−	0.559582i	$-0.189038\pi$
$587$	40.1593			1.65755			0.828775	+	0.559582i	$0.189038\pi$
$588$		0			0
$589$	0.0292237			0.00120414
$590$		0			0
$591$		0			0
$592$	−3.96593	−	6.86919i	−0.162999	−	0.282322i
$593$	9.54170	−	16.5267i	0.391831	−	0.678671i	−0.600860	−	0.799354i	$-0.705175\pi$
$593$	9.54170	−	16.5267i	0.391831	−	0.678671i	0.992691	+	0.120683i	$0.0385085\pi$
$594$		0			0
$595$		0			0
$596$		−	21.4981i		−	0.880598i
$597$		0			0
$598$	−12.7079	+	7.33694i	−0.519666	+	0.300030i
$599$	−24.6424	+	14.2273i	−1.00686	+	0.581312i	−0.910271	−	0.414013i	$-0.864127\pi$
$599$	−24.6424	+	14.2273i	−1.00686	+	0.581312i	−0.0965902	+	0.995324i	$0.530794\pi$
$600$		0			0
$601$			29.2553i			1.19335i	0.802484	+	0.596673i	$0.203511\pi$
$601$			29.2553i			1.19335i	−0.802484	+	0.596673i	$0.796489\pi$
$602$	4.50303	−	6.64929i	0.183530	−	0.271005i
$603$		0			0
$604$	1.47531	−	2.55532i	0.0600297	−	0.103974i
$605$		0			0
$606$		0			0
$607$	22.3712	+	12.9160i	0.908020	+	0.524246i	0.879794	−	0.475356i	$-0.157681\pi$
$607$	22.3712	+	12.9160i	0.908020	+	0.524246i	0.0282267	+	0.999602i	$0.491014\pi$
$608$	0.0352762			0.00143064
$609$		0			0
$610$		0			0
$611$	19.7583	+	11.4075i	0.799337	+	0.461498i
$612$		0			0
$613$	8.12216	+	14.0680i	0.328051	+	0.568201i	0.982125	−	0.188230i	$-0.0602749\pi$
$613$	8.12216	+	14.0680i	0.328051	+	0.568201i	−0.654074	+	0.756430i	$0.726942\pi$
$614$	6.18910	−	10.7198i	0.249772	−	0.432618i
$615$		0			0
$616$	7.01299	−	3.40433i	0.282562	−	0.137164i
$617$		−	31.8398i		−	1.28182i	−0.767615	−	0.640911i	$-0.778557\pi$
$617$		−	31.8398i		−	1.28182i	0.767615	−	0.640911i	$-0.221443\pi$
$618$		0			0
$619$	8.01055	−	4.62490i	0.321971	−	0.185890i	−0.330300	−	0.943876i	$-0.607150\pi$
$619$	8.01055	−	4.62490i	0.321971	−	0.185890i	0.652271	+	0.757986i	$0.273816\pi$
$620$		0			0
$621$		0			0
$622$		−	22.8625i		−	0.916701i
$623$	−13.5210	−	9.15669i	−0.541708	−	0.366855i
$624$		0			0
$625$		0			0
$626$	−17.4013	−	30.1399i	−0.695495	−	1.20463i
$627$		0			0
$628$	−19.4823	−	11.2481i	−0.777429	−	0.448849i
$629$	−3.16958			−0.126379
$630$		0			0
$631$	−10.3096			−0.410421			−0.205210	−	0.978718i	$-0.565788\pi$
$631$	−10.3096			−0.410421			−0.205210	+	0.978718i	$0.565788\pi$
$632$	7.19375	+	4.15331i	0.286152	+	0.165210i
$633$		0			0
$634$	3.39355	+	5.87780i	0.134775	+	0.233437i
$635$		0			0
$636$		0			0
$637$	3.93185	−	27.2407i	0.155786	−	1.07931i
$638$		−	26.2205i		−	1.03808i
$639$		0			0
$640$		0			0
$641$	−11.1181	+	6.41906i	−0.439140	+	0.253538i	−0.703233	−	0.710960i	$-0.748261\pi$
$641$	−11.1181	+	6.41906i	−0.439140	+	0.253538i	0.264093	+	0.964497i	$0.414928\pi$
$642$		0			0
$643$			8.96224i			0.353436i	0.984262	+	0.176718i	$0.0565481\pi$
$643$			8.96224i			0.353436i	−0.984262	+	0.176718i	$0.943452\pi$
$644$	9.84873	+	0.707107i	0.388094	+	0.0278639i
$645$		0			0
$646$	0.00704821	−	0.0122079i	0.000277308	−	0.000480312i
$647$	−22.6852	−	39.2919i	−0.891846	−	1.54472i	−0.837660	−	0.546191i	$-0.816077\pi$
$647$	−22.6852	−	39.2919i	−0.891846	−	1.54472i	−0.0541854	−	0.998531i	$-0.517256\pi$
$648$		0			0
$649$	14.2142	+	8.20656i	0.557955	+	0.322136i
$650$		0			0
$651$		0			0
$652$	22.8070			0.893192
$653$	−28.4051	−	16.3997i	−1.11158	−	0.641769i	−0.172340	−	0.985038i	$-0.555133\pi$
$653$	−28.4051	−	16.3997i	−1.11158	−	0.641769i	−0.939237	+	0.343268i	$0.888466\pi$
$654$		0			0
$655$		0			0
$656$	−3.15539	+	5.46530i	−0.123197	+	0.213384i
$657$		0			0
$658$	−6.70430	−	13.8110i	−0.261361	−	0.538409i
$659$		−	18.7103i		−	0.728850i	−0.931233	−	0.364425i	$-0.881266\pi$
$659$		−	18.7103i		−	0.728850i	0.931233	−	0.364425i	$-0.118734\pi$
$660$		0			0
$661$	7.41761	−	4.28256i	0.288512	−	0.166572i	−0.348759	−	0.937213i	$-0.613397\pi$
$661$	7.41761	−	4.28256i	0.288512	−	0.166572i	0.637270	+	0.770640i	$0.280063\pi$
$662$	9.64726	−	5.56985i	0.374951	−	0.216478i
$663$		0			0
$664$			10.3490i			0.401618i
$665$		0			0
$666$		0			0
$667$	16.6057	−	28.7620i	0.642976	−	1.11367i
$668$	−4.42480	−	7.66398i	−0.171201	−	0.296528i
$669$		0			0
$670$		0			0
$671$	−33.9449			−1.31043
$672$		0			0
$673$	0.179617			0.00692372			0.00346186	−	0.999994i	$-0.498898\pi$
$673$	0.179617			0.00692372			0.00346186	+	0.999994i	$0.498898\pi$
$674$	1.37794	+	0.795555i	0.0530763	+	0.0306436i
$675$		0			0
$676$	−1.22973	−	2.12995i	−0.0472973	−	0.0819213i
$677$	20.7051	−	35.8623i	0.795763	−	1.37830i	−0.126591	−	0.991955i	$-0.540404\pi$
$677$	20.7051	−	35.8623i	0.795763	−	1.37830i	0.922354	−	0.386346i	$-0.126263\pi$
$678$		0			0
$679$	−41.2586	−	2.96224i	−1.58336	−	0.113680i
$680$		0			0
$681$		0			0
$682$	−2.11391	+	1.22047i	−0.0809457	+	0.0467340i
$683$	37.5900	−	21.7026i	1.43834	−	0.830427i	0.440608	−	0.897700i	$-0.354763\pi$
$683$	37.5900	−	21.7026i	1.43834	−	0.830427i	0.997735	+	0.0672723i	$0.0214296\pi$
$684$		0			0
$685$		0			0
$686$	−12.4691	+	13.6938i	−0.476073	+	0.522834i
$687$		0			0
$688$	−1.51764	+	2.62863i	−0.0578594	+	0.100215i
$689$	8.45069	+	14.6370i	0.321946	+	0.557626i
$690$		0			0
$691$	−16.8728	−	9.74150i	−0.641871	−	0.370584i	0.143464	−	0.989656i	$-0.454176\pi$
$691$	−16.8728	−	9.74150i	−0.641871	−	0.370584i	−0.785335	+	0.619071i	$0.787509\pi$
$692$	−7.73686			−0.294111
$693$		0			0
$694$	15.4568			0.586732
$695$		0			0
$696$		0			0
$697$	1.26090	+	2.18394i	0.0477600	+	0.0827228i
$698$	0.292529	−	0.506675i	0.0110724	−	0.0191779i
$699$		0			0
$700$		0			0
$701$		−	47.0245i		−	1.77609i	−0.459755	−	0.888046i	$-0.652063\pi$
$701$		−	47.0245i		−	1.77609i	0.459755	−	0.888046i	$-0.347937\pi$
$702$		0			0
$703$	−0.242319	+	0.139903i	−0.00913922	+	0.00527653i
$704$	−2.55171	+	1.47323i	−0.0961713	+	0.0555245i
$705$		0			0
$706$		−	3.67576i		−	0.138339i
$707$	42.9595	−	20.8539i	1.61566	−	0.784292i
$708$		0			0
$709$	24.2227	−	41.9549i	0.909701	−	1.57565i	0.0952213	−	0.995456i	$-0.469644\pi$
$709$	24.2227	−	41.9549i	0.909701	−	1.57565i	0.814480	−	0.580192i	$-0.197023\pi$
$710$		0			0
$711$		0			0
$712$	5.34519	+	3.08604i	0.200319	+	0.115654i
$713$	−3.09173			−0.115786
$714$		0			0
$715$		0			0
$716$	−0.417291	−	0.240923i	−0.0155949	−	0.00900372i
$717$		0			0
$718$	10.0499	+	17.4069i	0.375058	+	0.649620i
$719$	20.6632	−	35.7897i	0.770606	−	1.33473i	−0.166625	−	0.986020i	$-0.553287\pi$
$719$	20.6632	−	35.7897i	0.770606	−	1.33473i	0.937231	−	0.348709i	$-0.113380\pi$
$720$		0			0
$721$	−12.6400	+	18.6646i	−0.470739	+	0.695106i
$722$			18.9988i			0.707060i
$723$		0			0
$724$	−2.12069	+	1.22438i	−0.0788148	+	0.0455037i
$725$		0			0
$726$		0			0
$727$			16.7905i			0.622726i	0.950291	+	0.311363i	$0.100786\pi$
$727$			16.7905i			0.622726i	−0.950291	+	0.311363i	$0.899214\pi$
$728$	−0.744963	+	10.3760i	−0.0276102	+	0.384560i
$729$		0			0
$730$		0			0
$731$	0.606451	+	1.05040i	0.0224304	+	0.0388506i
$732$		0			0
$733$	26.6043	+	15.3600i	0.982652	+	0.567335i	0.903070	−	0.429494i	$-0.141308\pi$
$733$	26.6043	+	15.3600i	0.982652	+	0.567335i	0.0795826	+	0.996828i	$0.474641\pi$
$734$	−19.9377			−0.735914
$735$		0			0
$736$	−3.73205			−0.137565
$737$	−31.9457	−	18.4438i	−1.17673	−	0.679388i
$738$		0			0
$739$	−15.3876	−	26.6521i	−0.566041	−	0.980412i	−0.996952	−	0.0780176i	$-0.975141\pi$
$739$	−15.3876	−	26.6521i	−0.566041	−	0.980412i	0.430911	−	0.902395i	$-0.358192\pi$
$740$		0			0
$741$		0			0
$742$	0.814447	−	11.3438i	0.0298993	−	0.416443i
$743$			33.3616i			1.22392i	0.790889	+	0.611960i	$0.209619\pi$
$743$			33.3616i			1.22392i	−0.790889	+	0.611960i	$0.790381\pi$
$744$		0			0
$745$		0			0
$746$	29.2856	−	16.9081i	1.07222	−	0.619048i
$747$		0			0
$748$			1.17741i			0.0430504i
$749$	−25.3025	+	37.3624i	−0.924533	+	1.36519i
$750$		0			0
$751$	15.9452	−	27.6179i	0.581849	−	1.00779i	−0.413411	−	0.910545i	$-0.635663\pi$
$751$	15.9452	−	27.6179i	0.581849	−	1.00779i	0.995260	−	0.0972480i	$-0.0310040\pi$
$752$	2.90130	+	5.02520i	0.105800	+	0.183250i
$753$		0			0
$754$	30.3018	+	17.4947i	1.10353	+	0.637121i
$755$		0			0
$756$		0			0
$757$	10.9065			0.396404			0.198202	−	0.980161i	$-0.436490\pi$
$757$	10.9065			0.396404			0.198202	+	0.980161i	$0.436490\pi$
$758$	−23.1761	−	13.3807i	−0.841793	−	0.486010i
$759$		0			0
$760$		0			0
$761$	−12.2097	+	21.1479i	−0.442602	+	0.766610i	−0.997882	−	0.0650543i	$-0.979278\pi$
$761$	−12.2097	+	21.1479i	−0.442602	+	0.766610i	0.555280	+	0.831664i	$0.312611\pi$
$762$		0			0
$763$	−27.8433	+	13.5160i	−1.00800	+	0.489313i
$764$			4.49457i			0.162608i
$765$		0			0
$766$	−17.1310	+	9.89060i	−0.618969	+	0.357362i
$767$	−18.9678	+	10.9511i	−0.684889	+	0.395421i
$768$		0			0
$769$			22.9416i			0.827294i	0.910437	+	0.413647i	$0.135745\pi$
$769$			22.9416i			0.827294i	−0.910437	+	0.413647i	$0.864255\pi$
$770$		0			0
$771$		0			0
$772$	6.28497	−	10.8859i	0.226201	−	0.391791i
$773$	22.6837	+	39.2894i	0.815877	+	1.41314i	0.908696	+	0.417458i	$0.137079\pi$
$773$	22.6837	+	39.2894i	0.815877	+	1.41314i	−0.0928193	+	0.995683i	$0.529588\pi$
$774$		0			0
$775$		0			0
$776$	15.6344			0.561243
$777$		0			0
$778$	−5.18670			−0.185952
$779$	0.192795	+	0.111310i	0.00690760	+	0.00398810i
$780$		0			0
$781$	2.84961	+	4.93566i	0.101967	+	0.176612i
$782$	−0.745667	+	1.29153i	−0.0266650	+	0.0461851i
$783$		0			0
$784$	4.33013	−	5.50000i	0.154647	−	0.196429i
$785$		0			0
$786$		0			0
$787$	−2.89834	+	1.67335i	−0.103314	+	0.0596487i	−0.550767	−	0.834659i	$-0.685665\pi$
$787$	−2.89834	+	1.67335i	−0.103314	+	0.0596487i	0.447452	+	0.894308i	$0.352331\pi$
$788$	−11.5829	+	6.68740i	−0.412625	+	0.238229i
$789$		0			0
$790$		0			0
$791$	35.7700	+	2.56817i	1.27183	+	0.0913136i
$792$		0			0
$793$	22.6486	−	39.2285i	0.804274	−	1.39304i
$794$	2.88259	+	4.99280i	0.102299	+	0.177188i
$795$		0			0
$796$	−23.5169	−	13.5775i	−0.833535	−	0.481242i
$797$	−36.5402			−1.29432			−0.647160	−	0.762354i	$-0.724044\pi$
$797$	−36.5402			−1.29432			−0.647160	+	0.762354i	$0.724044\pi$
$798$		0			0
$799$	2.31873			0.0820308
$800$		0			0
$801$		0			0
$802$	8.91202	+	15.4361i	0.314695	+	0.545067i
$803$	0.505533	−	0.875609i	0.0178399	−	0.0308996i
$804$		0			0
$805$		0			0
$806$		−	3.25725i		−	0.114732i
$807$		0			0
$808$	−15.6310	+	9.02458i	−0.549898	+	0.317484i
$809$	41.5179	−	23.9704i	1.45969	−	0.842753i	0.460696	−	0.887558i	$-0.347600\pi$
$809$	41.5179	−	23.9704i	1.45969	−	0.842753i	0.998996	+	0.0448048i	$0.0142666\pi$
$810$		0			0
$811$		−	49.6994i		−	1.74518i	−0.488452	−	0.872591i	$-0.662438\pi$
$811$		−	49.6994i		−	1.74518i	0.488452	−	0.872591i	$-0.337562\pi$
$812$	−10.2818	−	21.1808i	−0.360822	−	0.743301i
$813$		0			0
$814$	11.6855	−	20.2398i	0.409575	−	0.709405i
$815$		0			0
$816$		0			0
$817$	0.0927279	+	0.0535365i	0.00324414	+	0.00187300i
$818$	32.9802			1.15312
$819$		0			0
$820$		0			0
$821$	−19.6520	−	11.3461i	−0.685858	−	0.395980i	0.116200	−	0.993226i	$-0.462929\pi$
$821$	−19.6520	−	11.3461i	−0.685858	−	0.395980i	−0.802059	+	0.597245i	$0.796262\pi$
$822$		0			0
$823$	−1.59711	−	2.76628i	−0.0556719	−	0.0964266i	0.836846	−	0.547438i	$-0.184397\pi$
$823$	−1.59711	−	2.76628i	−0.0556719	−	0.0964266i	−0.892518	+	0.451011i	$0.851063\pi$
$824$	4.26002	−	7.37857i	0.148405	−	0.257045i
$825$		0			0
$826$	14.7002	+	1.05543i	0.511484	+	0.0367229i
$827$			29.7259i			1.03367i	0.856084	+	0.516836i	$0.172890\pi$
$827$			29.7259i			1.03367i	−0.856084	+	0.516836i	$0.827110\pi$
$828$		0			0
$829$	26.8588	−	15.5069i	0.932845	−	0.538578i	0.0451348	−	0.998981i	$-0.485628\pi$
$829$	26.8588	−	15.5069i	0.932845	−	0.538578i	0.887710	+	0.460403i	$0.152295\pi$
$830$		0			0
$831$		0			0
$832$		−	3.93185i		−	0.136312i
$833$	−1.03820	−	2.59741i	−0.0359713	−	0.0899950i
$834$		0			0
$835$		0			0
$836$	0.0519700	+	0.0900147i	0.00179742	+	0.00311322i
$837$		0			0
$838$	13.1884	+	7.61434i	0.455586	+	0.263033i
$839$	−35.8462			−1.23755			−0.618773	−	0.785570i	$-0.712370\pi$
$839$	−35.8462			−1.23755			−0.618773	+	0.785570i	$0.712370\pi$
$840$		0			0
$841$	−50.1918			−1.73075
$842$	−14.7172	−	8.49697i	−0.507188	−	0.292825i
$843$		0			0
$844$	9.20915	+	15.9507i	0.316992	+	0.549046i
$845$		0			0
$846$		0			0
$847$	−5.07875	−	3.43942i	−0.174508	−	0.118180i
$848$			4.29858i			0.147614i
$849$		0			0
$850$		0			0
$851$	25.6361	−	14.8010i	0.878796	−	0.507373i
$852$		0			0
$853$		−	22.8818i		−	0.783456i	−0.920081	−	0.391728i	$-0.871877\pi$
$853$		−	22.8818i		−	0.783456i	0.920081	−	0.391728i	$-0.128123\pi$
$854$	−27.4205	+	13.3108i	−0.938311	+	0.455486i
$855$		0			0
$856$	8.52761	−	14.7702i	0.291468	−	0.504837i
$857$	−16.8593	−	29.2012i	−0.575904	−	0.997494i	−0.995943	−	0.0899883i	$-0.971317\pi$
$857$	−16.8593	−	29.2012i	−0.575904	−	0.997494i	0.420039	−	0.907506i	$-0.362016\pi$
$858$		0			0
$859$	16.3926	+	9.46427i	0.559308	+	0.322917i	0.752868	−	0.658172i	$-0.228670\pi$
$859$	16.3926	+	9.46427i	0.559308	+	0.322917i	−0.193560	+	0.981088i	$0.562003\pi$
$860$		0			0
$861$		0			0
$862$	−17.8768			−0.608888
$863$	−4.55277	−	2.62854i	−0.154978	−	0.0894767i	0.420505	−	0.907290i	$-0.361853\pi$
$863$	−4.55277	−	2.62854i	−0.154978	−	0.0894767i	−0.575484	+	0.817813i	$0.695186\pi$
$864$		0			0
$865$		0			0
$866$	2.78194	−	4.81846i	0.0945341	−	0.163738i
$867$		0			0
$868$	−1.22902	+	1.81481i	−0.0417158	+	0.0615987i
$869$			24.4752i			0.830263i
$870$		0			0
$871$	42.6293	−	24.6120i	1.44444	−	0.833947i
$872$	10.1309	−	5.84909i	0.343076	−	0.198075i
$873$		0			0
$874$			0.131652i			0.00445321i
$875$		0			0
$876$		0			0
$877$	−20.3326	+	35.2170i	−0.686582	+	1.18919i	0.286355	+	0.958124i	$0.407556\pi$
$877$	−20.3326	+	35.2170i	−0.686582	+	1.18919i	−0.972937	+	0.231071i	$0.925777\pi$
$878$	−5.50543	−	9.53568i	−0.185799	−	0.321814i
$879$		0			0
$880$		0			0
$881$	−1.01828			−0.0343067			−0.0171533	−	0.999853i	$-0.505460\pi$
$881$	−1.01828			−0.0343067			−0.0171533	+	0.999853i	$0.505460\pi$
$882$		0			0
$883$	−11.0436			−0.371647			−0.185823	−	0.982583i	$-0.559495\pi$
$883$	−11.0436			−0.371647			−0.185823	+	0.982583i	$0.559495\pi$
$884$	−1.36068	−	0.785587i	−0.0457645	−	0.0264222i
$885$		0			0
$886$	8.49233	+	14.7091i	0.285305	+	0.494163i
$887$	12.0492	−	20.8698i	0.404571	−	0.700738i	−0.589700	−	0.807622i	$-0.700754\pi$
$887$	12.0492	−	20.8698i	0.404571	−	0.700738i	0.994271	+	0.106884i	$0.0340875\pi$
$888$		0			0
$889$	1.69761	−	23.6446i	0.0569359	−	0.793015i
$890$		0			0
$891$		0			0
$892$	−15.4192	+	8.90226i	−0.516272	+	0.298070i
$893$	0.177270	−	0.102347i	0.00593211	−	0.00342491i
$894$		0			0
$895$		0			0
$896$	−1.48356	+	2.19067i	−0.0495624	+	0.0731852i
$897$		0			0
$898$	6.29461	−	10.9026i	0.210054	−	0.363824i
$899$	3.68608	+	6.38447i	0.122938	+	0.212934i
$900$		0			0
$901$	1.48759	+	0.858860i	0.0495588	+	0.0286128i
$902$	−18.5945			−0.619129
$903$		0			0
$904$	−13.5546			−0.450819
$905$		0			0
$906$		0			0
$907$	−8.10243	−	14.0338i	−0.269037	−	0.465985i	0.699577	−	0.714558i	$-0.253372\pi$
$907$	−8.10243	−	14.0338i	−0.269037	−	0.465985i	−0.968613	+	0.248572i	$0.920039\pi$
$908$	0.856140	−	1.48288i	0.0284120	−	0.0492110i
$909$		0			0
$910$		0			0
$911$		−	21.4586i		−	0.710955i	−0.934685	−	0.355477i	$-0.884318\pi$
$911$		−	21.4586i		−	0.710955i	0.934685	−	0.355477i	$-0.115682\pi$
$912$		0			0
$913$	−26.4076	+	15.2465i	−0.873965	+	0.504584i
$914$	1.87783	−	1.08417i	0.0621133	−	0.0358611i
$915$		0			0
$916$			6.07536i			0.200736i
$917$	−27.9988	−	18.9613i	−0.924603	−	0.626159i
$918$		0			0
$919$	29.5164	−	51.1240i	0.973657	−	1.68642i	0.289360	−	0.957220i	$-0.406558\pi$
$919$	29.5164	−	51.1240i	0.973657	−	1.68642i	0.684297	−	0.729203i	$-0.260109\pi$
$920$		0			0
$921$		0			0
$922$	29.7074	+	17.1516i	0.978362	+	0.564857i
$923$	−7.60521			−0.250328
$924$		0			0
$925$		0			0
$926$	24.4335	+	14.1067i	0.802933	+	0.463574i
$927$		0			0
$928$	4.44949	+	7.70674i	0.146062	+	0.252986i
$929$	12.3197	−	21.3383i	0.404195	−	0.700087i	−0.590032	−	0.807380i	$-0.700885\pi$
$929$	12.3197	−	21.3383i	0.404195	−	0.700087i	0.994227	+	0.107293i	$0.0342183\pi$
$930$		0			0
$931$	−0.194019	−	0.152750i	−0.00635872	−	0.00500619i
$932$			7.12576i			0.233412i
$933$		0			0
$934$	3.64324	−	2.10342i	0.119210	−	0.0688262i
$935$		0			0
$936$		0			0
$937$		−	52.5496i		−	1.71672i	−0.513048	−	0.858360i	$-0.671484\pi$
$937$		−	52.5496i		−	1.71672i	0.513048	−	0.858360i	$-0.328516\pi$
$938$	−33.0379	−	2.37202i	−1.07873	−	0.0774491i
$939$		0			0
$940$		0			0
$941$	−0.752551	−	1.30346i	−0.0245325	−	0.0424915i	0.853499	−	0.521095i	$-0.174476\pi$
$941$	−0.752551	−	1.30346i	−0.0245325	−	0.0424915i	−0.878031	+	0.478604i	$0.841143\pi$
$942$		0			0
$943$	−20.3968	−	11.7761i	−0.664211	−	0.383482i
$944$	−5.57045			−0.181303
$945$		0			0
$946$	−8.94333			−0.290773
$947$	−9.84136	−	5.68191i	−0.319801	−	0.184637i	0.331503	−	0.943454i	$-0.392444\pi$
$947$	−9.84136	−	5.68191i	−0.319801	−	0.184637i	−0.651304	+	0.758817i	$0.725778\pi$
$948$		0			0
$949$	0.674599	+	1.16844i	0.0218984	+	0.0379292i
$950$		0			0
$951$		0			0
$952$	0.461698	+	0.951108i	0.0149637	+	0.0308256i
$953$		−	21.9184i		−	0.710006i	−0.934865	−	0.355003i	$-0.884480\pi$
$953$		−	21.9184i		−	0.710006i	0.934865	−	0.355003i	$-0.115520\pi$
$954$		0			0
$955$		0			0
$956$	−16.2114	+	9.35968i	−0.524316	+	0.302714i
$957$		0			0
$958$			14.7194i			0.475561i
$959$	6.37842	+	13.1397i	0.205970	+	0.424303i
$960$		0			0
$961$	−15.1569	+	26.2524i	−0.488931	+	0.846853i
$962$	15.5934	+	27.0086i	0.502752	+	0.870793i
$963$		0			0
$964$	7.68036	+	4.43426i	0.247368	+	0.142818i
$965$		0			0
$966$		0			0
$967$	−21.6634			−0.696649			−0.348324	−	0.937374i	$-0.613249\pi$
$967$	−21.6634			−0.696649			−0.348324	+	0.937374i	$0.613249\pi$
$968$	2.00775	+	1.15918i	0.0645316	+	0.0372573i
$969$		0			0
$970$		0			0
$971$	−0.0858379	+	0.148676i	−0.00275467	+	0.00477123i	−0.867399	−	0.497612i	$-0.834210\pi$
$971$	−0.0858379	+	0.148676i	−0.00275467	+	0.00477123i	0.864645	+	0.502384i	$0.167544\pi$
$972$		0			0
$973$	−57.6536	−	4.13934i	−1.84829	−	0.132701i
$974$			1.87757i			0.0601612i
$975$		0			0
$976$	9.97710	−	5.76028i	0.319359	−	0.184382i
$977$	−9.72792	+	5.61642i	−0.311224	+	0.179685i	−0.647474	−	0.762088i	$-0.724175\pi$
$977$	−9.72792	+	5.61642i	−0.311224	+	0.179685i	0.336250	+	0.941773i	$0.390841\pi$
$978$		0			0
$979$			18.1858i			0.581222i
$980$		0			0
$981$		0			0
$982$	5.21405	−	9.03100i	0.166387	−	0.288191i
$983$	13.3960	+	23.2026i	0.427267	+	0.740048i	0.996629	−	0.0820385i	$-0.0261430\pi$
$983$	13.3960	+	23.2026i	0.427267	+	0.740048i	−0.569362	+	0.822087i	$0.692810\pi$
$984$		0			0
$985$		0			0
$986$	3.55605			0.113248
$987$		0			0
$988$	−0.138701			−0.00441266
$989$	−9.81017	−	5.66390i	−0.311945	−	0.180102i
$990$		0			0
$991$	−6.99635	−	12.1180i	−0.222246	−	0.384942i	0.733243	−	0.679966i	$-0.238006\pi$
$991$	−6.99635	−	12.1180i	−0.222246	−	0.384942i	−0.955490	+	0.295024i	$0.904672\pi$
$992$	0.414214	−	0.717439i	0.0131513	−	0.0227787i
$993$		0			0
$994$	4.23732	+	2.86959i	0.134400	+	0.0910179i
$995$		0			0
$996$		0			0
$997$	−34.2497	+	19.7740i	−1.08470	+	0.626250i	−0.932160	−	0.362047i	$-0.882078\pi$
$997$	−34.2497	+	19.7740i	−1.08470	+	0.626250i	−0.152538	+	0.988298i	$0.548745\pi$
$998$	−32.7050	+	18.8822i	−1.03526	+	0.597707i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.bf.c.1601.1		8
3.2	odd	2		3150.2.bf.b.1601.3		8
5.2	odd	4		3150.2.bp.f.1349.1		8
5.3	odd	4		3150.2.bp.c.1349.4		8
5.4	even	2		630.2.be.b.341.4	yes	8
7.3	odd	6		3150.2.bf.b.1151.3		8
15.2	even	4		3150.2.bp.a.1349.1		8
15.8	even	4		3150.2.bp.d.1349.4		8
15.14	odd	2		630.2.be.a.341.2	✓	8
21.17	even	6	inner	3150.2.bf.c.1151.1		8
35.3	even	12		3150.2.bp.a.899.1		8
35.9	even	6		4410.2.b.b.881.3		8
35.17	even	12		3150.2.bp.d.899.4		8
35.19	odd	6		4410.2.b.e.881.3		8
35.24	odd	6		630.2.be.a.521.2	yes	8
105.17	odd	12		3150.2.bp.c.899.4		8
105.38	odd	12		3150.2.bp.f.899.1		8
105.44	odd	6		4410.2.b.e.881.6		8
105.59	even	6		630.2.be.b.521.4	yes	8
105.89	even	6		4410.2.b.b.881.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.be.a.341.2	✓	8	15.14	odd	2
630.2.be.a.521.2	yes	8	35.24	odd	6
630.2.be.b.341.4	yes	8	5.4	even	2
630.2.be.b.521.4	yes	8	105.59	even	6
3150.2.bf.b.1151.3		8	7.3	odd	6
3150.2.bf.b.1601.3		8	3.2	odd	2
3150.2.bf.c.1151.1		8	21.17	even	6	inner
3150.2.bf.c.1601.1		8	1.1	even	1	trivial
3150.2.bp.a.899.1		8	35.3	even	12
3150.2.bp.a.1349.1		8	15.2	even	4
3150.2.bp.c.899.4		8	105.17	odd	12
3150.2.bp.c.1349.4		8	5.3	odd	4
3150.2.bp.d.899.4		8	35.17	even	12
3150.2.bp.d.1349.4		8	15.8	even	4
3150.2.bp.f.899.1		8	105.38	odd	12
3150.2.bp.f.1349.1		8	5.2	odd	4
4410.2.b.b.881.3		8	35.9	even	6
4410.2.b.b.881.6		8	105.89	even	6
4410.2.b.e.881.3		8	35.19	odd	6
4410.2.b.e.881.6		8	105.44	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:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.189469 + 2.63896i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.189469 + 2.63896i) q^{7} -1.00000i q^{8} +(2.55171 - 1.47323i) q^{11} +3.93185i q^{13} +(1.48356 - 2.19067i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.199801 + 0.346065i) q^{17} +(0.0305501 + 0.0176381i) q^{19} -2.94646 q^{22} +(-3.23205 - 1.86603i) q^{23} +(1.96593 - 3.40508i) q^{26} +(-2.38014 + 1.15539i) q^{28} +8.89898i q^{29} +(0.717439 - 0.414214i) q^{31} +(0.866025 - 0.500000i) q^{32} -0.399602i q^{34} +(-3.96593 + 6.86919i) q^{37} +(-0.0176381 - 0.0305501i) q^{38} +6.31079 q^{41} +3.03528 q^{43} +(2.55171 + 1.47323i) q^{44} +(1.86603 + 3.23205i) q^{46} +(2.90130 - 5.02520i) q^{47} +(-6.92820 - 1.00000i) q^{49} +(-3.40508 + 1.96593i) q^{52} +(3.72268 - 2.14929i) q^{53} +(2.63896 + 0.189469i) q^{56} +(4.44949 - 7.70674i) q^{58} +(2.78522 + 4.82415i) q^{59} +(-9.97710 - 5.76028i) q^{61} -0.828427 q^{62} -1.00000 q^{64} +(-6.25966 - 10.8420i) q^{67} +(-0.199801 + 0.346065i) q^{68} +1.93426i q^{71} +(0.297173 - 0.171573i) q^{73} +(6.86919 - 3.96593i) q^{74} +0.0352762i q^{76} +(3.40433 + 7.01299i) q^{77} +(-4.15331 + 7.19375i) q^{79} +(-5.46530 - 3.15539i) q^{82} -10.3490 q^{83} +(-2.62863 - 1.51764i) q^{86} +(-1.47323 - 2.55171i) q^{88} +(-3.08604 + 5.34519i) q^{89} +(-10.3760 - 0.744963i) q^{91} -3.73205i q^{92} +(-5.02520 + 2.90130i) q^{94} +15.6344i q^{97} +(5.50000 + 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 8 * q + 4 * q^4	\( 8 q + 4 q^{4} + 24 q^{11} - 4 q^{16} - 12 q^{23} + 8 q^{26} - 24 q^{37} + 4 q^{38} + 32 q^{41} + 16 q^{43} + 24 q^{44} + 8 q^{46} + 8 q^{47} - 24 q^{53} + 16 q^{58} - 24 q^{59} + 16 q^{62} - 8 q^{64} + 24 q^{67} + 16 q^{77} - 24 q^{79} + 16 q^{83} - 16 q^{89} - 20 q^{91} - 12 q^{94} + 44 q^{98}+O(q^{100}) \) 8 * q + 4 * q^4 + 24 * q^11 - 4 * q^16 - 12 * q^23 + 8 * q^26 - 24 * q^37 + 4 * q^38 + 32 * q^41 + 16 * q^43 + 24 * q^44 + 8 * q^46 + 8 * q^47 - 24 * q^53 + 16 * q^58 - 24 * q^59 + 16 * q^62 - 8 * q^64 + 24 * q^67 + 16 * q^77 - 24 * q^79 + 16 * q^83 - 16 * q^89 - 20 * q^91 - 12 * q^94 + 44 * q^98

Introduction

L-functions

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