LMFDB - Embedded newform 3150.2.bp.c.899.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(899,3150)]

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, 3, 1]))

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

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

chi := DirichletCharacter("3150.899");

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.bp (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:	$25.1528766367$
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			899.4
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	3150.899
Dual form			3150.2.bp.c.1349.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.63896 - 0.189469i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.63896 - 0.189469i) q^{7} +1.00000 q^{8} +(2.55171 + 1.47323i) q^{11} -3.93185 q^{13} +(-1.48356 - 2.19067i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.346065 + 0.199801i) q^{17} +(-0.0305501 + 0.0176381i) q^{19} -2.94646i q^{22} +(1.86603 + 3.23205i) q^{23} +(1.96593 + 3.40508i) q^{26} +(-1.15539 + 2.38014i) q^{28} +8.89898i q^{29} +(0.717439 + 0.414214i) q^{31} +(-0.500000 + 0.866025i) q^{32} -0.399602i q^{34} +(6.86919 - 3.96593i) q^{37} +(0.0305501 + 0.0176381i) q^{38} +6.31079 q^{41} -3.03528i q^{43} +(-2.55171 + 1.47323i) q^{44} +(1.86603 - 3.23205i) q^{46} +(-5.02520 + 2.90130i) q^{47} +(6.92820 - 1.00000i) q^{49} +(1.96593 - 3.40508i) q^{52} +(2.14929 - 3.72268i) q^{53} +(2.63896 - 0.189469i) q^{56} +(7.70674 - 4.44949i) q^{58} +(-2.78522 + 4.82415i) q^{59} +(-9.97710 + 5.76028i) q^{61} -0.828427i q^{62} +1.00000 q^{64} +(-10.8420 - 6.25966i) q^{67} +(-0.346065 + 0.199801i) q^{68} -1.93426i q^{71} +(0.171573 - 0.297173i) q^{73} +(-6.86919 - 3.96593i) q^{74} -0.0352762i q^{76} +(7.01299 + 3.40433i) q^{77} +(4.15331 + 7.19375i) q^{79} +(-3.15539 - 5.46530i) q^{82} +10.3490i q^{83} +(-2.62863 + 1.51764i) q^{86} +(2.55171 + 1.47323i) q^{88} +(3.08604 + 5.34519i) q^{89} +(-10.3760 + 0.744963i) q^{91} -3.73205 q^{92} +(5.02520 + 2.90130i) q^{94} +15.6344 q^{97} +(-4.33013 - 5.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8	$ 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} + 24 q^{11} - 16 q^{13} - 4 q^{16} - 24 q^{17} + 8 q^{23} + 8 q^{26} - 4 q^{32} + 32 q^{41} - 24 q^{44} + 8 q^{46} - 12 q^{47} + 8 q^{52} - 4 q^{53} + 24 q^{59} + 8 q^{64} - 48 q^{67} + 24 q^{68} + 24 q^{73} + 4 q^{77} + 24 q^{79} - 16 q^{82} + 24 q^{88} + 16 q^{89} - 20 q^{91} - 16 q^{92} + 12 q^{94} + 48 q^{97}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 + 24 * q^11 - 16 * q^13 - 4 * q^16 - 24 * q^17 + 8 * q^23 + 8 * q^26 - 4 * q^32 + 32 * q^41 - 24 * q^44 + 8 * q^46 - 12 * q^47 + 8 * q^52 - 4 * q^53 + 24 * q^59 + 8 * q^64 - 48 * q^67 + 24 * q^68 + 24 * q^73 + 4 * q^77 + 24 * q^79 - 16 * q^82 + 24 * q^88 + 16 * q^89 - 20 * q^91 - 16 * q^92 + 12 * q^94 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.63896	−	0.189469i	0.997433	−	0.0716124i
$7$	2.63896	−	0.189469i	0.997433	−	0.0716124i
$8$	1.00000			0.353553
$9$		0			0
$10$		0			0
$11$	2.55171	+	1.47323i	0.769370	+	0.444196i	0.832650	−	0.553800i	$-0.186823\pi$
$11$	2.55171	+	1.47323i	0.769370	+	0.444196i	−0.0632797	+	0.997996i	$0.520156\pi$
$12$		0			0
$13$	−3.93185			−1.09050			−0.545250	−	0.838274i	$-0.683565\pi$
$13$	−3.93185			−1.09050			−0.545250	+	0.838274i	$0.683565\pi$
$14$	−1.48356	−	2.19067i	−0.396499	−	0.585481i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.346065	+	0.199801i	0.0839331	+	0.0484588i	0.541379	−	0.840779i	$-0.317902\pi$
$17$	0.346065	+	0.199801i	0.0839331	+	0.0484588i	−0.457446	+	0.889237i	$0.651236\pi$
$18$		0			0
$19$	−0.0305501	+	0.0176381i	−0.00700867	+	0.00404646i	−0.503500	−	0.863995i	$-0.667955\pi$
$19$	−0.0305501	+	0.0176381i	−0.00700867	+	0.00404646i	0.496492	+	0.868042i	$0.334621\pi$
$20$		0			0
$21$		0			0
$22$		−	2.94646i		−	0.628188i
$23$	1.86603	+	3.23205i	0.389093	+	0.673929i	0.992328	−	0.123635i	$-0.0394551\pi$
$23$	1.86603	+	3.23205i	0.389093	+	0.673929i	−0.603235	+	0.797564i	$0.706122\pi$
$24$		0			0
$25$		0			0
$26$	1.96593	+	3.40508i	0.385550	+	0.667792i
$27$		0			0
$28$	−1.15539	+	2.38014i	−0.218349	+	0.449804i
$29$			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	0.563042	−	0.826428i	$-0.309631\pi$
$31$	0.717439	+	0.414214i	0.128856	+	0.0743950i	−0.434187	+	0.900823i	$0.642964\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$		−	0.399602i		−	0.0685311i
$35$		0			0
$36$		0			0
$37$	6.86919	−	3.96593i	1.12929	−	0.651994i	0.185532	−	0.982638i	$-0.440599\pi$
$37$	6.86919	−	3.96593i	1.12929	−	0.651994i	0.943756	+	0.330644i	$0.107266\pi$
$38$	0.0305501	+	0.0176381i	0.00495588	+	0.00286128i
$39$		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
$43$		−	3.03528i		−	0.462875i	−0.972850	−	0.231438i	$-0.925657\pi$
$43$		−	3.03528i		−	0.462875i	0.972850	−	0.231438i	$-0.0743429\pi$
$44$	−2.55171	+	1.47323i	−0.384685	+	0.222098i
$45$		0			0
$46$	1.86603	−	3.23205i	0.275130	−	0.476540i
$47$	−5.02520	+	2.90130i	−0.733001	+	0.423198i	−0.819519	−	0.573052i	$-0.805759\pi$
$47$	−5.02520	+	2.90130i	−0.733001	+	0.423198i	0.0865180	+	0.996250i	$0.472426\pi$
$48$		0			0
$49$	6.92820	−	1.00000i	0.989743	−	0.142857i
$50$		0			0
$51$		0			0
$52$	1.96593	−	3.40508i	0.272625	−	0.472200i
$53$	2.14929	−	3.72268i	0.295228	−	0.511349i	−0.679810	−	0.733388i	$-0.737938\pi$
$53$	2.14929	−	3.72268i	0.295228	−	0.511349i	0.975038	+	0.222039i	$0.0712711\pi$
$54$		0			0
$55$		0			0
$56$	2.63896	−	0.189469i	0.352646	−	0.0253188i
$57$		0			0
$58$	7.70674	−	4.44949i	1.01194	−	0.584247i
$59$	−2.78522	+	4.82415i	−0.362605	+	0.628050i	−0.988389	−	0.151946i	$-0.951446\pi$
$59$	−2.78522	+	4.82415i	−0.362605	+	0.628050i	0.625784	+	0.779997i	$0.284779\pi$
$60$		0			0
$61$	−9.97710	+	5.76028i	−1.27744	+	0.737528i	−0.976376	−	0.216077i	$-0.930674\pi$
$61$	−9.97710	+	5.76028i	−1.27744	+	0.737528i	−0.301060	+	0.953605i	$0.597340\pi$
$62$		−	0.828427i		−	0.105210i
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−10.8420	−	6.25966i	−1.32457	−	0.764739i	−0.340113	−	0.940385i	$-0.610465\pi$
$67$	−10.8420	−	6.25966i	−1.32457	−	0.764739i	−0.984453	+	0.175646i	$0.943799\pi$
$68$	−0.346065	+	0.199801i	−0.0419666	+	0.0242294i
$69$		0			0
$70$		0			0
$71$		−	1.93426i		−	0.229554i	−0.993391	−	0.114777i	$-0.963385\pi$
$71$		−	1.93426i		−	0.229554i	0.993391	−	0.114777i	$-0.0366153\pi$
$72$		0			0
$73$	0.171573	−	0.297173i	0.0200811	−	0.0347815i	−0.855810	−	0.517290i	$-0.826941\pi$
$73$	0.171573	−	0.297173i	0.0200811	−	0.0347815i	0.875891	+	0.482508i	$0.160274\pi$
$74$	−6.86919	−	3.96593i	−0.798527	−	0.461030i
$75$		0			0
$76$		−	0.0352762i		−	0.00404646i
$77$	7.01299	+	3.40433i	0.799205	+	0.387959i
$78$		0			0
$79$	4.15331	+	7.19375i	0.467284	+	0.809360i	0.999301	−	0.0373736i	$-0.0118992\pi$
$79$	4.15331	+	7.19375i	0.467284	+	0.809360i	−0.532017	+	0.846734i	$0.678566\pi$
$80$		0			0
$81$		0			0
$82$	−3.15539	−	5.46530i	−0.348455	−	0.603542i
$83$			10.3490i			1.13595i	0.823046	+	0.567974i	$0.192273\pi$
$83$			10.3490i			1.13595i	−0.823046	+	0.567974i	$0.807727\pi$
$84$		0			0
$85$		0			0
$86$	−2.62863	+	1.51764i	−0.283452	+	0.163651i
$87$		0			0
$88$	2.55171	+	1.47323i	0.272013	+	0.157047i
$89$	3.08604	+	5.34519i	0.327120	+	0.566589i	0.981939	−	0.189197i	$-0.0605885\pi$
$89$	3.08604	+	5.34519i	0.327120	+	0.566589i	−0.654819	+	0.755786i	$0.727255\pi$
$90$		0			0
$91$	−10.3760	+	0.744963i	−1.08770	+	0.0780933i
$92$	−3.73205			−0.389093
$93$		0			0
$94$	5.02520	+	2.90130i	0.518310	+	0.299246i
$95$		0			0
$96$		0			0
$97$	15.6344			1.58744			0.793718	−	0.608286i	$-0.208143\pi$
$97$	15.6344			1.58744			0.793718	+	0.608286i	$0.208143\pi$
$98$	−4.33013	−	5.50000i	−0.437409	−	0.555584i
$99$		0			0
$100$		0			0
$101$	−9.02458	+	15.6310i	−0.897979	+	1.55535i	−0.0679057	+	0.997692i	$0.521632\pi$
$101$	−9.02458	+	15.6310i	−0.897979	+	1.55535i	−0.830074	+	0.557654i	$0.811702\pi$
$102$		0			0
$103$	−4.26002	−	7.37857i	−0.419752	−	0.727032i	0.576162	−	0.817336i	$-0.304550\pi$
$103$	−4.26002	−	7.37857i	−0.419752	−	0.727032i	−0.995914	+	0.0903031i	$0.971216\pi$
$104$	−3.93185			−0.385550
$105$		0			0
$106$	−4.29858			−0.417515
$107$	8.52761	+	14.7702i	0.824395	+	1.42789i	0.902381	+	0.430939i	$0.141818\pi$
$107$	8.52761	+	14.7702i	0.824395	+	1.42789i	−0.0779862	+	0.996954i	$0.524849\pi$
$108$		0			0
$109$	−5.84909	+	10.1309i	−0.560241	+	0.970366i	0.437234	+	0.899348i	$0.355958\pi$
$109$	−5.84909	+	10.1309i	−0.560241	+	0.970366i	−0.997475	+	0.0710185i	$0.977375\pi$
$110$		0			0
$111$		0			0
$112$	−1.48356	−	2.19067i	−0.140184	−	0.206999i
$113$	13.5546			1.27511			0.637554	−	0.770405i	$-0.279946\pi$
$113$	13.5546			1.27511			0.637554	+	0.770405i	$0.279946\pi$
$114$		0			0
$115$		0			0
$116$	−7.70674	−	4.44949i	−0.715553	−	0.413125i
$117$		0			0
$118$	5.57045			0.512801
$119$	0.951108	+	0.461698i	0.0871879	+	0.0423237i
$120$		0			0
$121$	−1.15918	−	2.00775i	−0.105380	−	0.182523i
$122$	9.97710	+	5.76028i	0.903284	+	0.521511i
$123$		0			0
$124$	−0.717439	+	0.414214i	−0.0644279	+	0.0371975i
$125$		0			0
$126$		0			0
$127$		−	8.95983i		−	0.795056i	−0.917590	−	0.397528i	$-0.869868\pi$
$127$		−	8.95983i		−	0.795056i	0.917590	−	0.397528i	$-0.130132\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$		0			0
$131$	−6.39047	−	11.0686i	−0.558338	−	0.967070i	−0.997635	−	0.0687282i	$-0.978106\pi$
$131$	−6.39047	−	11.0686i	−0.558338	−	0.967070i	0.439297	−	0.898342i	$-0.355227\pi$
$132$		0			0
$133$	−0.0772785	+	0.0523345i	−0.00670090	+	0.00453797i
$134$			12.5193i			1.08150i
$135$		0			0
$136$	0.346065	+	0.199801i	0.0296748	+	0.0171328i
$137$	−2.76028	+	4.78094i	−0.235827	+	0.408464i	−0.959513	−	0.281666i	$-0.909113\pi$
$137$	−2.76028	+	4.78094i	−0.235827	+	0.408464i	0.723686	+	0.690129i	$0.242446\pi$
$138$		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
$142$	−1.67511	+	0.967128i	−0.140572	+	0.0811596i
$143$	−10.0330	−	5.79253i	−0.838998	−	0.484396i
$144$		0			0
$145$		0			0
$146$	−0.343146			−0.0283989
$147$		0			0
$148$			7.93185i			0.651994i
$149$	18.6179	−	10.7491i	1.52524	−	0.880598i	0.525688	−	0.850677i	$-0.323808\pi$
$149$	18.6179	−	10.7491i	1.52524	−	0.880598i	0.999552	−	0.0299204i	$-0.00952537\pi$
$150$		0			0
$151$	−1.47531	+	2.55532i	−0.120059	+	0.207949i	−0.919791	−	0.392409i	$-0.871642\pi$
$151$	−1.47531	+	2.55532i	−0.120059	+	0.207949i	0.799732	+	0.600358i	$0.204975\pi$
$152$	−0.0305501	+	0.0176381i	−0.00247794	+	0.00143064i
$153$		0			0
$154$	−0.558263	−	7.77559i	−0.0449861	−	0.626575i
$155$		0			0
$156$		0			0
$157$	11.2481	−	19.4823i	0.897698	−	1.55486i	0.0672682	−	0.997735i	$-0.478572\pi$
$157$	11.2481	−	19.4823i	0.897698	−	1.55486i	0.830430	−	0.557123i	$-0.188095\pi$
$158$	4.15331	−	7.19375i	0.330420	−	0.572304i
$159$		0			0
$160$		0			0
$161$	5.53674	+	8.17569i	0.436356	+	0.644335i
$162$		0			0
$163$	19.7515	−	11.4035i	1.54705	−	0.893192i	0.548690	−	0.836026i	$-0.315127\pi$
$163$	19.7515	−	11.4035i	1.54705	−	0.893192i	0.998365	−	0.0571664i	$-0.0182066\pi$
$164$	−3.15539	+	5.46530i	−0.246395	+	0.426769i
$165$		0			0
$166$	8.96248	−	5.17449i	0.695624	−	0.401618i
$167$		−	8.84961i		−	0.684803i	−0.939554	−	0.342402i	$-0.888760\pi$
$167$		−	8.84961i		−	0.684803i	0.939554	−	0.342402i	$-0.111240\pi$
$168$		0			0
$169$	2.45946			0.189189
$170$		0			0
$171$		0			0
$172$	2.62863	+	1.51764i	0.200431	+	0.115719i
$173$	−6.70032	+	3.86843i	−0.509416	+	0.294111i	−0.732593	−	0.680667i	$-0.761690\pi$
$173$	−6.70032	+	3.86843i	−0.509416	+	0.294111i	0.223178	+	0.974778i	$0.428357\pi$
$174$		0			0
$175$		0			0
$176$		−	2.94646i		−	0.222098i
$177$		0			0
$178$	3.08604	−	5.34519i	0.231309	−	0.400639i
$179$	0.417291	+	0.240923i	0.0311898	+	0.0180074i	0.515514	−	0.856881i	$-0.327601\pi$
$179$	0.417291	+	0.240923i	0.0311898	+	0.0180074i	−0.484324	+	0.874889i	$0.660934\pi$
$180$		0			0
$181$		−	2.44876i		−	0.182015i	−0.995850	−	0.0910075i	$-0.970991\pi$
$181$		−	2.44876i		−	0.182015i	0.995850	−	0.0910075i	$-0.0290087\pi$
$182$	5.83315	+	8.61339i	0.432382	+	0.638467i
$183$		0			0
$184$	1.86603	+	3.23205i	0.137565	+	0.238270i
$185$		0			0
$186$		0			0
$187$	0.588706	+	1.01967i	0.0430504	+	0.0745655i
$188$		−	5.80260i		−	0.423198i
$189$		0			0
$190$		0			0
$191$	3.89241	−	2.24728i	0.281645	−	0.162608i	−0.352523	−	0.935803i	$-0.614676\pi$
$191$	3.89241	−	2.24728i	0.281645	−	0.162608i	0.634168	+	0.773195i	$0.281343\pi$
$192$		0			0
$193$	10.8859	+	6.28497i	0.783583	+	0.452402i	0.837698	−	0.546133i	$-0.183901\pi$
$193$	10.8859	+	6.28497i	0.783583	+	0.452402i	−0.0541158	+	0.998535i	$0.517234\pi$
$194$	−7.81722	−	13.5398i	−0.561243	−	0.972102i
$195$		0			0
$196$	−2.59808	+	6.50000i	−0.185577	+	0.464286i
$197$	13.3748			0.952916			0.476458	−	0.879197i	$-0.341920\pi$
$197$	13.3748			0.952916			0.476458	+	0.879197i	$0.341920\pi$
$198$		0			0
$199$	23.5169	+	13.5775i	1.66707	+	0.962483i	0.969206	+	0.246253i	$0.0791993\pi$
$199$	23.5169	+	13.5775i	1.66707	+	0.962483i	0.697864	+	0.716231i	$0.254134\pi$
$200$		0			0
$201$		0			0
$202$	18.0492			1.26993
$203$	1.68608	+	23.4840i	0.118339	+	1.64826i
$204$		0			0
$205$		0			0
$206$	−4.26002	+	7.37857i	−0.296810	+	0.514090i
$207$		0			0
$208$	1.96593	+	3.40508i	0.136312	+	0.236100i
$209$	−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	$0.281419\pi$
$212$	2.14929	+	3.72268i	0.147614	+	0.255675i
$213$		0			0
$214$	8.52761	−	14.7702i	0.582935	−	1.00967i
$215$		0			0
$216$		0			0
$217$	1.97177	+	0.957160i	0.133853	+	0.0649763i
$218$	11.6982			0.792301
$219$		0			0
$220$		0			0
$221$	−1.36068	−	0.785587i	−0.0915290	−	0.0528443i
$222$		0			0
$223$	−17.8045			−1.19228			−0.596140	−	0.802881i	$-0.703300\pi$
$223$	−17.8045			−1.19228			−0.596140	+	0.802881i	$0.703300\pi$
$224$	−1.15539	+	2.38014i	−0.0771980	+	0.159030i
$225$		0			0
$226$	−6.77729	−	11.7386i	−0.450819	−	0.780841i
$227$	−1.48288	−	0.856140i	−0.0984220	−	0.0568240i	0.449981	−	0.893038i	$-0.351431\pi$
$227$	−1.48288	−	0.856140i	−0.0984220	−	0.0568240i	−0.548403	+	0.836214i	$0.684764\pi$
$228$		0			0
$229$	−5.26142	+	3.03768i	−0.347684	+	0.200736i	−0.663665	−	0.748030i	$-0.731000\pi$
$229$	−5.26142	+	3.03768i	−0.347684	+	0.200736i	0.315981	+	0.948766i	$0.397667\pi$
$230$		0			0
$231$		0			0
$232$			8.89898i			0.584247i
$233$	−3.56288	−	6.17109i	−0.233412	−	0.404282i	0.725398	−	0.688330i	$-0.241656\pi$
$233$	−3.56288	−	6.17109i	−0.233412	−	0.404282i	−0.958810	+	0.284048i	$0.908322\pi$
$234$		0			0
$235$		0			0
$236$	−2.78522	−	4.82415i	−0.181303	−	0.314025i
$237$		0			0
$238$	−0.0757120	−	1.05453i	−0.00490768	−	0.0683552i
$239$			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	0.726537	−	0.687128i	$-0.241129\pi$
$241$	7.68036	+	4.43426i	0.494735	+	0.285636i	−0.231802	+	0.972763i	$0.574462\pi$
$242$	−1.15918	+	2.00775i	−0.0745147	+	0.129063i
$243$		0			0
$244$		−	11.5206i		−	0.737528i
$245$		0			0
$246$		0			0
$247$	0.120118	−	0.0693504i	0.00764295	−	0.00441266i
$248$	0.717439	+	0.414214i	0.0455574	+	0.0263026i
$249$		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
$253$			10.9964i			0.691335i
$254$	−7.75944	+	4.47992i	−0.486871	+	0.281095i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−14.5780	+	8.41662i	−0.909351	+	0.525014i	−0.880222	−	0.474561i	$-0.842607\pi$
$257$	−14.5780	+	8.41662i	−0.909351	+	0.525014i	−0.0291289	+	0.999576i	$0.509273\pi$
$258$		0			0
$259$	17.3761	−	11.7674i	1.07970	−	0.731191i
$260$		0			0
$261$		0			0
$262$	−6.39047	+	11.0686i	−0.394805	+	0.683822i
$263$	−11.0599	+	19.1562i	−0.681980	+	1.18122i	0.292396	+	0.956297i	$0.405548\pi$
$263$	−11.0599	+	19.1562i	−0.681980	+	1.18122i	−0.974376	+	0.224926i	$0.927786\pi$
$264$		0			0
$265$		0			0
$266$	0.0839622	+	0.0407579i	0.00514805	+	0.00249903i
$267$		0			0
$268$	10.8420	−	6.25966i	0.662283	−	0.382369i
$269$	−1.45049	+	2.51231i	−0.0884377	+	0.153179i	−0.906851	−	0.421452i	$-0.861521\pi$
$269$	−1.45049	+	2.51231i	−0.0884377	+	0.153179i	0.818413	+	0.574630i	$0.194854\pi$
$270$		0			0
$271$	15.1244	−	8.73205i	0.918739	−	0.530434i	0.0355066	−	0.999369i	$-0.488696\pi$
$271$	15.1244	−	8.73205i	0.918739	−	0.530434i	0.883233	+	0.468935i	$0.155362\pi$
$272$		−	0.399602i		−	0.0242294i
$273$		0			0
$274$	5.52056			0.333509
$275$		0			0
$276$		0			0
$277$	3.96336	+	2.28825i	0.238135	+	0.137488i	0.614319	−	0.789057i	$-0.289431\pi$
$277$	3.96336	+	2.28825i	0.238135	+	0.137488i	−0.376184	+	0.926545i	$0.622764\pi$
$278$	18.9202	−	10.9236i	1.13476	−	0.655152i
$279$		0			0
$280$		0			0
$281$		−	9.55948i		−	0.570271i	−0.958487	−	0.285135i	$-0.907961\pi$
$281$		−	9.55948i		−	0.570271i	0.958487	−	0.285135i	$-0.0920386\pi$
$282$		0			0
$283$	−5.46311	+	9.46238i	−0.324748	+	0.562480i	−0.981461	−	0.191660i	$-0.938613\pi$
$283$	−5.46311	+	9.46238i	−0.324748	+	0.562480i	0.656713	+	0.754140i	$0.271946\pi$
$284$	1.67511	+	0.967128i	0.0993998	+	0.0573885i
$285$		0			0
$286$			11.5851i			0.685039i
$287$	16.6539	−	1.19570i	0.983049	−	0.0705798i
$288$		0			0
$289$	−8.42016	−	14.5841i	−0.495303	−	0.857891i
$290$		0			0
$291$		0			0
$292$	0.171573	+	0.297173i	0.0100405	+	0.0173907i
$293$			16.2280i			0.948052i	0.880511	+	0.474026i	$0.157200\pi$
$293$			16.2280i			0.948052i	−0.880511	+	0.474026i	$0.842800\pi$
$294$		0			0
$295$		0			0
$296$	6.86919	−	3.96593i	0.399263	−	0.230515i
$297$		0			0
$298$	−18.6179	−	10.7491i	−1.07851	−	0.622677i
$299$	−7.33694	−	12.7079i	−0.424306	−	0.734919i
$300$		0			0
$301$	−0.575090	−	8.00997i	−0.0331476	−	0.461687i
$302$	2.95063			0.169790
$303$		0			0
$304$	0.0305501	+	0.0176381i	0.00175217	+	0.00101161i
$305$		0			0
$306$		0			0
$307$	12.3782			0.706462			0.353231	−	0.935536i	$-0.385083\pi$
$307$	12.3782			0.706462			0.353231	+	0.935536i	$0.385083\pi$
$308$	−6.45473	+	4.37127i	−0.367792	+	0.249076i
$309$		0			0
$310$		0			0
$311$	11.4312	−	19.7995i	0.648206	−	1.12272i	−0.335346	−	0.942095i	$-0.608853\pi$
$311$	11.4312	−	19.7995i	0.648206	−	1.12272i	0.983551	−	0.180630i	$-0.0578136\pi$
$312$		0			0
$313$	−17.4013	−	30.1399i	−0.983578	−	1.70361i	−0.648091	−	0.761563i	$-0.724432\pi$
$313$	−17.4013	−	30.1399i	−0.983578	−	1.70361i	−0.335487	−	0.942045i	$-0.608901\pi$
$314$	−22.4962			−1.26954
$315$		0			0
$316$	−8.30663			−0.467284
$317$	−3.39355	−	5.87780i	−0.190601	−	0.330130i	0.754849	−	0.655899i	$-0.227710\pi$
$317$	−3.39355	−	5.87780i	−0.190601	−	0.330130i	−0.945449	+	0.325769i	$0.894377\pi$
$318$		0			0
$319$	−13.1103	+	22.7076i	−0.734034	+	1.27138i
$320$		0			0
$321$		0			0
$322$	4.31199	−	8.88280i	0.240298	−	0.495019i
$323$	−0.0140964			−0.000784346
$324$		0			0
$325$		0			0
$326$	−19.7515	−	11.4035i	−1.09393	−	0.631582i
$327$		0			0
$328$	6.31079			0.348455
$329$	−12.7116	+	8.60853i	−0.700813	+	0.474604i
$330$		0			0
$331$	−5.56985	−	9.64726i	−0.306147	−	0.530261i	0.671369	−	0.741123i	$-0.265706\pi$
$331$	−5.56985	−	9.64726i	−0.306147	−	0.530261i	−0.977516	+	0.210862i	$0.932373\pi$
$332$	−8.96248	−	5.17449i	−0.491880	−	0.283987i
$333$		0			0
$334$	−7.66398	+	4.42480i	−0.419355	+	0.242114i
$335$		0			0
$336$		0			0
$337$		−	1.59111i		−	0.0866733i	−0.999061	−	0.0433366i	$-0.986201\pi$
$337$		−	1.59111i		−	0.0866733i	0.999061	−	0.0433366i	$-0.0137988\pi$
$338$	−1.22973	−	2.12995i	−0.0668884	−	0.115854i
$339$		0			0
$340$		0			0
$341$	1.22047	+	2.11391i	0.0660919	+	0.114475i
$342$		0			0
$343$	18.0938	−	3.95164i	0.976972	−	0.213368i
$344$		−	3.03528i		−	0.163651i
$345$		0			0
$346$	6.70032	+	3.86843i	0.360211	+	0.207968i
$347$	7.72840	−	13.3860i	0.414882	−	0.718597i	−0.580534	−	0.814236i	$-0.697156\pi$
$347$	7.72840	−	13.3860i	0.414882	−	0.718597i	0.995416	+	0.0956388i	$0.0304894\pi$
$348$		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
$352$	−2.55171	+	1.47323i	−0.136007	+	0.0785235i
$353$	−3.18330	−	1.83788i	−0.169430	−	0.0978204i	0.412887	−	0.910782i	$-0.364520\pi$
$353$	−3.18330	−	1.83788i	−0.169430	−	0.0978204i	−0.582317	+	0.812962i	$0.697854\pi$
$354$		0			0
$355$		0			0
$356$	−6.17209			−0.327120
$357$		0			0
$358$		−	0.481846i		−	0.0254664i
$359$	17.4069	−	10.0499i	0.918702	−	0.530413i	0.0354812	−	0.999370i	$-0.488704\pi$
$359$	17.4069	−	10.0499i	0.918702	−	0.530413i	0.883221	+	0.468958i	$0.155370\pi$
$360$		0			0
$361$	−9.49938	+	16.4534i	−0.499967	+	0.865969i
$362$	−2.12069	+	1.22438i	−0.111461	+	0.0643520i
$363$		0			0
$364$	4.54284	−	9.35835i	0.238110	−	0.490511i
$365$		0			0
$366$		0			0
$367$	−9.96885	+	17.2665i	−0.520369	+	0.901306i	0.479350	+	0.877624i	$0.340872\pi$
$367$	−9.96885	+	17.2665i	−0.520369	+	0.901306i	−0.999720	+	0.0236826i	$0.992461\pi$
$368$	1.86603	−	3.23205i	0.0972733	−	0.168482i
$369$		0			0
$370$		0			0
$371$	4.96656	−	10.2312i	0.257851	−	0.531179i
$372$		0			0
$373$	−29.2856	+	16.9081i	−1.51635	+	0.875467i	−0.516537	+	0.856265i	$0.672779\pi$
$373$	−29.2856	+	16.9081i	−1.51635	+	0.875467i	−0.999816	+	0.0192016i	$0.993888\pi$
$374$	0.588706	−	1.01967i	0.0304413	−	0.0527258i
$375$		0			0
$376$	−5.02520	+	2.90130i	−0.259155	+	0.149623i
$377$		−	34.9895i		−	1.80205i
$378$		0			0
$379$	−26.7614			−1.37464			−0.687321	−	0.726353i	$-0.741214\pi$
$379$	−26.7614			−1.37464			−0.687321	+	0.726353i	$0.741214\pi$
$380$		0			0
$381$		0			0
$382$	−3.89241	−	2.24728i	−0.199153	−	0.114981i
$383$	17.1310	−	9.89060i	0.875355	−	0.505386i	0.00623078	−	0.999981i	$-0.498017\pi$
$383$	17.1310	−	9.89060i	0.875355	−	0.505386i	0.869124	+	0.494594i	$0.164683\pi$
$384$		0			0
$385$		0			0
$386$		−	12.5699i		−	0.639793i
$387$		0			0
$388$	−7.81722	+	13.5398i	−0.396859	+	0.687380i
$389$	−4.49181	−	2.59335i	−0.227744	−	0.131488i	0.381787	−	0.924250i	$-0.375309\pi$
$389$	−4.49181	−	2.59335i	−0.227744	−	0.131488i	−0.609531	+	0.792762i	$0.708642\pi$
$390$		0			0
$391$			1.49133i			0.0754200i
$392$	6.92820	−	1.00000i	0.349927	−	0.0505076i
$393$		0			0
$394$	−6.68740	−	11.5829i	−0.336907	−	0.583539i
$395$		0			0
$396$		0			0
$397$	−2.88259	−	4.99280i	−0.144673	−	0.250581i	0.784578	−	0.620030i	$-0.212880\pi$
$397$	−2.88259	−	4.99280i	−0.144673	−	0.250581i	−0.929251	+	0.369449i	$0.879546\pi$
$398$		−	27.1550i		−	1.36116i
$399$		0			0
$400$		0			0
$401$	−15.4361	+	8.91202i	−0.770841	+	0.445045i	−0.833175	−	0.553010i	$-0.813479\pi$
$401$	−15.4361	+	8.91202i	−0.770841	+	0.445045i	0.0623335	+	0.998055i	$0.480146\pi$
$402$		0			0
$403$	−2.82086	−	1.62863i	−0.140517	−	0.0811277i
$404$	−9.02458	−	15.6310i	−0.448990	−	0.777673i
$405$		0			0
$406$	19.4947	−	13.2022i	0.967507	−	0.655214i
$407$	23.3709			1.15845
$408$		0			0
$409$	28.5617	+	16.4901i	1.41228	+	0.815382i	0.995603	−	0.0936705i	$-0.0298600\pi$
$409$	28.5617	+	16.4901i	1.41228	+	0.815382i	0.416681	+	0.909053i	$0.363193\pi$
$410$		0			0
$411$		0			0
$412$	8.52004			0.419752
$413$	−6.43606	+	13.2584i	−0.316698	+	0.652405i
$414$		0			0
$415$		0			0
$416$	1.96593	−	3.40508i	0.0963874	−	0.166948i
$417$		0			0
$418$	0.0519700	+	0.0900147i	0.00254194	+	0.00440276i
$419$	15.2287			0.743969			0.371985	−	0.928239i	$-0.378677\pi$
$419$	15.2287			0.743969			0.371985	+	0.928239i	$0.378677\pi$
$420$		0			0
$421$	16.9939			0.828234			0.414117	−	0.910224i	$-0.364090\pi$
$421$	16.9939			0.828234			0.414117	+	0.910224i	$0.364090\pi$
$422$	−9.20915	−	15.9507i	−0.448294	−	0.776468i
$423$		0			0
$424$	2.14929	−	3.72268i	0.104379	−	0.180789i
$425$		0			0
$426$		0			0
$427$	−25.2377	+	17.0915i	−1.22134	+	0.827115i
$428$	−17.0552			−0.824395
$429$		0			0
$430$		0			0
$431$	15.4818	+	8.93842i	0.745732	+	0.430549i	0.824150	−	0.566372i	$-0.191653\pi$
$431$	15.4818	+	8.93842i	0.745732	+	0.430549i	−0.0784178	+	0.996921i	$0.524987\pi$
$432$		0			0
$433$	−5.56388			−0.267383			−0.133691	−	0.991023i	$-0.542683\pi$
$433$	−5.56388			−0.267383			−0.133691	+	0.991023i	$0.542683\pi$
$434$	−0.156961	−	2.18618i	−0.00753437	−	0.104940i
$435$		0			0
$436$	−5.84909	−	10.1309i	−0.280121	−	0.485183i
$437$	−0.114014	−	0.0658262i	−0.00545405	−	0.00314890i
$438$		0			0
$439$	−9.53568	+	5.50543i	−0.455113	+	0.262760i	−0.709987	−	0.704214i	$-0.751299\pi$
$439$	−9.53568	+	5.50543i	−0.455113	+	0.262760i	0.254874	+	0.966974i	$0.417966\pi$
$440$		0			0
$441$		0			0
$442$			1.57117i			0.0747332i
$443$	8.49233	+	14.7091i	0.403483	+	0.698853i	0.994144	−	0.108067i	$-0.0344662\pi$
$443$	8.49233	+	14.7091i	0.403483	+	0.698853i	−0.590661	+	0.806920i	$0.701133\pi$
$444$		0			0
$445$		0			0
$446$	8.90226	+	15.4192i	0.421534	+	0.730119i
$447$		0			0
$448$	2.63896	−	0.189469i	0.124679	−	0.00895155i
$449$			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
$452$	−6.77729	+	11.7386i	−0.318777	+	0.552138i
$453$		0			0
$454$			1.71228i			0.0803612i
$455$		0			0
$456$		0			0
$457$	1.87783	−	1.08417i	0.0878414	−	0.0507153i	−0.455436	−	0.890269i	$-0.650517\pi$
$457$	1.87783	−	1.08417i	0.0878414	−	0.0507153i	0.543277	+	0.839553i	$0.317183\pi$
$458$	5.26142	+	3.03768i	0.245850	+	0.141941i
$459$		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
$463$			28.2133i			1.31118i	0.755115	+	0.655592i	$0.227581\pi$
$463$			28.2133i			1.31118i	−0.755115	+	0.655592i	$0.772419\pi$
$464$	7.70674	−	4.44949i	0.357777	−	0.206562i
$465$		0			0
$466$	−3.56288	+	6.17109i	−0.165047	+	0.285870i
$467$	3.64324	−	2.10342i	0.168589	−	0.0973349i	−0.413331	−	0.910581i	$-0.635635\pi$
$467$	3.64324	−	2.10342i	0.168589	−	0.0973349i	0.581920	+	0.813246i	$0.302302\pi$
$468$		0			0
$469$	−29.7977	−	14.4647i	−1.37593	−	0.667920i
$470$		0			0
$471$		0			0
$472$	−2.78522	+	4.82415i	−0.128200	+	0.222049i
$473$	4.47167	−	7.74515i	0.205607	−	0.356122i
$474$		0			0
$475$		0			0
$476$	−0.875396	+	0.592835i	−0.0401237	+	0.0271725i
$477$		0			0
$478$	16.2114	−	9.35968i	0.741494	−	0.428102i
$479$	7.35968	−	12.7473i	0.336272	−	0.582441i	−0.647456	−	0.762103i	$-0.724167\pi$
$479$	7.35968	−	12.7473i	0.336272	−	0.582441i	0.983728	+	0.179662i	$0.0575004\pi$
$480$		0			0
$481$	−27.0086	+	15.5934i	−1.23149	+	0.710999i
$482$		−	8.86851i		−	0.403950i
$483$		0			0
$484$	2.31835			0.105380
$485$		0			0
$486$		0			0
$487$	−1.62602	−	0.938784i	−0.0736821	−	0.0425404i	0.462706	−	0.886512i	$-0.346878\pi$
$487$	−1.62602	−	0.938784i	−0.0736821	−	0.0425404i	−0.536388	+	0.843971i	$0.680212\pi$
$488$	−9.97710	+	5.76028i	−0.451642	+	0.260756i
$489$		0			0
$490$		0			0
$491$		−	10.4281i		−	0.470613i	−0.971921	−	0.235307i	$-0.924391\pi$
$491$		−	10.4281i		−	0.470613i	0.971921	−	0.235307i	$-0.0756095\pi$
$492$		0			0
$493$	−1.77802	+	3.07963i	−0.0800782	+	0.138699i
$494$	−0.120118	−	0.0693504i	−0.00540438	−	0.00312022i
$495$		0			0
$496$		−	0.828427i		−	0.0371975i
$497$	−0.366481	−	5.10442i	−0.0164389	−	0.228965i
$498$		0			0
$499$	−18.8822	−	32.7050i	−0.845285	−	1.46408i	−0.885374	−	0.464880i	$-0.846097\pi$
$499$	−18.8822	−	32.7050i	−0.845285	−	1.46408i	0.0400890	−	0.999196i	$-0.487236\pi$
$500$		0			0
$501$		0			0
$502$	−11.0869	−	19.2030i	−0.494832	−	0.857074i
$503$		−	35.8895i		−	1.60023i	−0.599845	−	0.800116i	$-0.704771\pi$
$503$		−	35.8895i		−	1.60023i	0.599845	−	0.800116i	$-0.295229\pi$
$504$		0			0
$505$		0			0
$506$	9.52312	−	5.49818i	0.423354	−	0.244424i
$507$		0			0
$508$	7.75944	+	4.47992i	0.344270	+	0.198764i
$509$	−8.58746	−	14.8739i	−0.380633	−	0.659275i	0.610520	−	0.792001i	$-0.290960\pi$
$509$	−8.58746	−	14.8739i	−0.380633	−	0.659275i	−0.991153	+	0.132726i	$0.957627\pi$
$510$		0			0
$511$	0.396469	−	0.816735i	0.0175387	−	0.0361302i
$512$	1.00000			0.0441942
$513$		0			0
$514$	14.5780	+	8.41662i	0.643008	+	0.371241i
$515$		0			0
$516$		0			0
$517$	−17.0972			−0.751932
$518$	−18.8789	−	9.16442i	−0.829492	−	0.402661i
$519$		0			0
$520$		0			0
$521$	2.26539	−	3.92377i	0.0992484	−	0.171903i	−0.812125	−	0.583483i	$-0.801689\pi$
$521$	2.26539	−	3.92377i	0.0992484	−	0.171903i	0.911374	+	0.411580i	$0.135023\pi$
$522$		0			0
$523$	−13.2368	−	22.9267i	−0.578803	−	1.00252i	−0.995617	−	0.0935241i	$-0.970187\pi$
$523$	−13.2368	−	22.9267i	−0.578803	−	1.00252i	0.416814	−	0.908992i	$-0.363147\pi$
$524$	12.7809			0.558338
$525$		0			0
$526$	22.1197			0.964465
$527$	0.165520	+	0.286690i	0.00721018	+	0.0124884i
$528$		0			0
$529$	4.53590	−	7.85641i	0.197213	−	0.341583i
$530$		0			0
$531$		0			0
$532$	−0.00668373	−	0.0930924i	−0.000289777	−	0.00403607i
$533$	−24.8131			−1.07477
$534$		0			0
$535$		0			0
$536$	−10.8420	−	6.25966i	−0.468305	−	0.270376i
$537$		0			0
$538$	2.90097			0.125070
$539$	19.1520	+	7.65514i	0.824936	+	0.329730i
$540$		0			0
$541$	−3.16504	−	5.48201i	−0.136076	−	0.235690i	0.789932	−	0.613194i	$-0.210116\pi$
$541$	−3.16504	−	5.48201i	−0.136076	−	0.235690i	−0.926008	+	0.377504i	$0.876782\pi$
$542$	−15.1244	−	8.73205i	−0.649647	−	0.375074i
$543$		0			0
$544$	−0.346065	+	0.199801i	−0.0148374	+	0.00856639i
$545$		0			0
$546$		0			0
$547$			38.5271i			1.64730i	0.567097	+	0.823651i	$0.308066\pi$
$547$			38.5271i			1.64730i	−0.567097	+	0.823651i	$0.691934\pi$
$548$	−2.76028	−	4.78094i	−0.117913	−	0.204232i
$549$		0			0
$550$		0			0
$551$	−0.156961	−	0.271864i	−0.00668676	−	0.0115818i
$552$		0			0
$553$	12.3234	+	18.1971i	0.524045	+	0.773819i
$554$		−	4.57650i		−	0.194437i
$555$		0			0
$556$	−18.9202	−	10.9236i	−0.802393	−	0.463262i
$557$	−4.62144	+	8.00456i	−0.195817	+	0.339164i	−0.947168	−	0.320738i	$-0.896069\pi$
$557$	−4.62144	+	8.00456i	−0.195817	+	0.339164i	0.751351	+	0.659902i	$0.229402\pi$
$558$		0			0
$559$			11.9343i			0.504765i
$560$		0			0
$561$		0			0
$562$	−8.27875	+	4.77974i	−0.349218	+	0.201621i
$563$	−23.1872	−	13.3871i	−0.977225	−	0.564201i	−0.0757935	−	0.997124i	$-0.524149\pi$
$563$	−23.1872	−	13.3871i	−0.977225	−	0.564201i	−0.901431	+	0.432923i	$0.857482\pi$
$564$		0			0
$565$		0			0
$566$	10.9262			0.459263
$567$		0			0
$568$		−	1.93426i		−	0.0811596i
$569$	39.6604	−	22.8979i	1.66265	−	0.959931i	0.691207	−	0.722657i	$-0.257079\pi$
$569$	39.6604	−	22.8979i	1.66265	−	0.959931i	0.971443	−	0.237274i	$-0.0762539\pi$
$570$		0			0
$571$	−0.390149	+	0.675759i	−0.0163272	+	0.0282796i	−0.874074	−	0.485794i	$-0.838531\pi$
$571$	−0.390149	+	0.675759i	−0.0163272	+	0.0282796i	0.857746	+	0.514073i	$0.171864\pi$
$572$	10.0330	−	5.79253i	0.419499	−	0.242198i
$573$		0			0
$574$	−9.36246	−	13.8249i	−0.390781	−	0.577039i
$575$		0			0
$576$		0			0
$577$	−5.62571	+	9.74401i	−0.234201	+	0.405648i	−0.959040	−	0.283270i	$-0.908581\pi$
$577$	−5.62571	+	9.74401i	−0.234201	+	0.405648i	0.724839	+	0.688918i	$0.241914\pi$
$578$	−8.42016	+	14.5841i	−0.350232	+	0.606620i
$579$		0			0
$580$		0			0
$581$	1.96081	+	27.3105i	0.0813480	+	1.13303i
$582$		0			0
$583$	10.9687	−	6.33281i	0.454279	−	0.262278i
$584$	0.171573	−	0.297173i	0.00709974	−	0.0122971i
$585$		0			0
$586$	14.0539	−	8.11401i	0.580561	−	0.335187i
$587$			40.1593i			1.65755i	0.559582	+	0.828775i	$0.310962\pi$
$587$			40.1593i			1.65755i	−0.559582	+	0.828775i	$0.689038\pi$
$588$		0			0
$589$	−0.0292237			−0.00120414
$590$		0			0
$591$		0			0
$592$	−6.86919	−	3.96593i	−0.282322	−	0.162999i
$593$	16.5267	−	9.54170i	0.678671	−	0.391831i	−0.120683	−	0.992691i	$-0.538509\pi$
$593$	16.5267	−	9.54170i	0.678671	−	0.391831i	0.799354	+	0.600860i	$0.205175\pi$
$594$		0			0
$595$		0			0
$596$			21.4981i			0.880598i
$597$		0			0
$598$	−7.33694	+	12.7079i	−0.300030	+	0.519666i
$599$	24.6424	+	14.2273i	1.00686	+	0.581312i	0.910271	−	0.414013i	$-0.135873\pi$
$599$	24.6424	+	14.2273i	1.00686	+	0.581312i	0.0965902	+	0.995324i	$0.469206\pi$
$600$		0			0
$601$		−	29.2553i		−	1.19335i	−0.802484	−	0.596673i	$-0.796489\pi$
$601$		−	29.2553i		−	1.19335i	0.802484	−	0.596673i	$-0.203511\pi$
$602$	−6.64929	+	4.50303i	−0.271005	+	0.183530i
$603$		0			0
$604$	−1.47531	−	2.55532i	−0.0600297	−	0.103974i
$605$		0			0
$606$		0			0
$607$	12.9160	+	22.3712i	0.524246	+	0.908020i	0.999602	+	0.0282267i	$0.00898603\pi$
$607$	12.9160	+	22.3712i	0.524246	+	0.908020i	−0.475356	+	0.879794i	$0.657681\pi$
$608$		−	0.0352762i		−	0.00143064i
$609$		0			0
$610$		0			0
$611$	19.7583	−	11.4075i	0.799337	−	0.461498i
$612$		0			0
$613$	−14.0680	−	8.12216i	−0.568201	−	0.328051i	0.188230	−	0.982125i	$-0.439725\pi$
$613$	−14.0680	−	8.12216i	−0.568201	−	0.328051i	−0.756430	+	0.654074i	$0.773058\pi$
$614$	−6.18910	−	10.7198i	−0.249772	−	0.432618i
$615$		0			0
$616$	7.01299	+	3.40433i	0.282562	+	0.137164i
$617$	−31.8398			−1.28182			−0.640911	−	0.767615i	$-0.721443\pi$
$617$	−31.8398			−1.28182			−0.640911	+	0.767615i	$0.721443\pi$
$618$		0			0
$619$	−8.01055	−	4.62490i	−0.321971	−	0.185890i	0.330300	−	0.943876i	$-0.392850\pi$
$619$	−8.01055	−	4.62490i	−0.321971	−	0.185890i	−0.652271	+	0.757986i	$0.726184\pi$
$620$		0			0
$621$		0			0
$622$	−22.8625			−0.916701
$623$	9.15669	+	13.5210i	0.366855	+	0.541708i
$624$		0			0
$625$		0			0
$626$	−17.4013	+	30.1399i	−0.695495	+	1.20463i
$627$		0			0
$628$	11.2481	+	19.4823i	0.448849	+	0.777429i
$629$	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	$0.565788\pi$
$632$	4.15331	+	7.19375i	0.165210	+	0.286152i
$633$		0			0
$634$	−3.39355	+	5.87780i	−0.134775	+	0.233437i
$635$		0			0
$636$		0			0
$637$	−27.2407	+	3.93185i	−1.07931	+	0.155786i
$638$	26.2205			1.03808
$639$		0			0
$640$		0			0
$641$	−11.1181	−	6.41906i	−0.439140	−	0.253538i	0.264093	−	0.964497i	$-0.414928\pi$
$641$	−11.1181	−	6.41906i	−0.439140	−	0.253538i	−0.703233	+	0.710960i	$0.748261\pi$
$642$		0			0
$643$	−8.96224			−0.353436			−0.176718	−	0.984262i	$-0.556548\pi$
$643$	−8.96224			−0.353436			−0.176718	+	0.984262i	$0.556548\pi$
$644$	−9.84873	+	0.707107i	−0.388094	+	0.0278639i
$645$		0			0
$646$	0.00704821	+	0.0122079i	0.000277308	+	0.000480312i
$647$	−39.2919	−	22.6852i	−1.54472	−	0.891846i	−0.998531	−	0.0541854i	$-0.982744\pi$
$647$	−39.2919	−	22.6852i	−1.54472	−	0.891846i	−0.546191	−	0.837660i	$-0.683923\pi$
$648$		0			0
$649$	−14.2142	+	8.20656i	−0.557955	+	0.322136i
$650$		0			0
$651$		0			0
$652$			22.8070i			0.893192i
$653$	16.3997	+	28.4051i	0.641769	+	1.11158i	0.985038	+	0.172340i	$0.0551326\pi$
$653$	16.3997	+	28.4051i	0.641769	+	1.11158i	−0.343268	+	0.939237i	$0.611534\pi$
$654$		0			0
$655$		0			0
$656$	−3.15539	−	5.46530i	−0.123197	−	0.213384i
$657$		0			0
$658$	13.8110	+	6.70430i	0.538409	+	0.261361i
$659$		−	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	0.637270	−	0.770640i	$-0.280063\pi$
$661$	7.41761	+	4.28256i	0.288512	+	0.166572i	−0.348759	+	0.937213i	$0.613397\pi$
$662$	−5.56985	+	9.64726i	−0.216478	+	0.374951i
$663$		0			0
$664$			10.3490i			0.401618i
$665$		0			0
$666$		0			0
$667$	−28.7620	+	16.6057i	−1.11367	+	0.642976i
$668$	7.66398	+	4.42480i	0.296528	+	0.171201i
$669$		0			0
$670$		0			0
$671$	−33.9449			−1.31043
$672$		0			0
$673$		−	0.179617i		−	0.00692372i	−0.999994	−	0.00346186i	$-0.998898\pi$
$673$		−	0.179617i		−	0.00692372i	0.999994	−	0.00346186i	$-0.00110195\pi$
$674$	−1.37794	+	0.795555i	−0.0530763	+	0.0306436i
$675$		0			0
$676$	−1.22973	+	2.12995i	−0.0472973	+	0.0819213i
$677$	−35.8623	+	20.7051i	−1.37830	+	0.795763i	−0.991955	−	0.126591i	$-0.959596\pi$
$677$	−35.8623	+	20.7051i	−1.37830	+	0.795763i	−0.386346	+	0.922354i	$0.626263\pi$
$678$		0			0
$679$	41.2586	−	2.96224i	1.58336	−	0.113680i
$680$		0			0
$681$		0			0
$682$	1.22047	−	2.11391i	0.0467340	−	0.0809457i
$683$	21.7026	−	37.5900i	0.830427	−	1.43834i	−0.0672723	−	0.997735i	$-0.521430\pi$
$683$	21.7026	−	37.5900i	0.830427	−	1.43834i	0.897700	−	0.440608i	$-0.145237\pi$
$684$		0			0
$685$		0			0
$686$	−12.4691	−	13.6938i	−0.476073	−	0.522834i
$687$		0			0
$688$	−2.62863	+	1.51764i	−0.100215	+	0.0578594i
$689$	−8.45069	+	14.6370i	−0.321946	+	0.557626i
$690$		0			0
$691$	−16.8728	+	9.74150i	−0.641871	+	0.370584i	−0.785335	−	0.619071i	$-0.787509\pi$
$691$	−16.8728	+	9.74150i	−0.641871	+	0.370584i	0.143464	+	0.989656i	$0.454176\pi$
$692$		−	7.73686i		−	0.294111i
$693$		0			0
$694$	−15.4568			−0.586732
$695$		0			0
$696$		0			0
$697$	2.18394	+	1.26090i	0.0827228	+	0.0477600i
$698$	0.506675	−	0.292529i	0.0191779	−	0.0110724i
$699$		0			0
$700$		0			0
$701$			47.0245i			1.77609i	0.459755	+	0.888046i	$0.347937\pi$
$701$			47.0245i			1.77609i	−0.459755	+	0.888046i	$0.652063\pi$
$702$		0			0
$703$	−0.139903	+	0.242319i	−0.00527653	+	0.00913922i
$704$	2.55171	+	1.47323i	0.0961713	+	0.0555245i
$705$		0			0
$706$			3.67576i			0.138339i
$707$	−20.8539	+	42.9595i	−0.784292	+	1.61566i
$708$		0			0
$709$	−24.2227	−	41.9549i	−0.909701	−	1.57565i	−0.814480	−	0.580192i	$-0.802977\pi$
$709$	−24.2227	−	41.9549i	−0.909701	−	1.57565i	−0.0952213	−	0.995456i	$-0.530356\pi$
$710$		0			0
$711$		0			0
$712$	3.08604	+	5.34519i	0.115654	+	0.200319i
$713$			3.09173i			0.115786i
$714$		0			0
$715$		0			0
$716$	−0.417291	+	0.240923i	−0.0155949	+	0.00900372i
$717$		0			0
$718$	−17.4069	−	10.0499i	−0.649620	−	0.375058i
$719$	−20.6632	−	35.7897i	−0.770606	−	1.33473i	−0.937231	−	0.348709i	$-0.886620\pi$
$719$	−20.6632	−	35.7897i	−0.770606	−	1.33473i	0.166625	−	0.986020i	$-0.446713\pi$
$720$		0			0
$721$	−12.6400	−	18.6646i	−0.470739	−	0.695106i
$722$	18.9988			0.707060
$723$		0			0
$724$	2.12069	+	1.22438i	0.0788148	+	0.0455037i
$725$		0			0
$726$		0			0
$727$	16.7905			0.622726			0.311363	−	0.950291i	$-0.399214\pi$
$727$	16.7905			0.622726			0.311363	+	0.950291i	$0.399214\pi$
$728$	−10.3760	+	0.744963i	−0.384560	+	0.0276102i
$729$		0			0
$730$		0			0
$731$	0.606451	−	1.05040i	0.0224304	−	0.0388506i
$732$		0			0
$733$	−15.3600	−	26.6043i	−0.567335	−	0.982652i	−0.996828	−	0.0795826i	$-0.974641\pi$
$733$	−15.3600	−	26.6043i	−0.567335	−	0.982652i	0.429494	−	0.903070i	$-0.358692\pi$
$734$	19.9377			0.735914
$735$		0			0
$736$	−3.73205			−0.137565
$737$	−18.4438	−	31.9457i	−0.679388	−	1.17673i
$738$		0			0
$739$	15.3876	−	26.6521i	0.566041	−	0.980412i	−0.430911	−	0.902395i	$-0.641808\pi$
$739$	15.3876	−	26.6521i	0.566041	−	0.980412i	0.996952	−	0.0780176i	$-0.0248590\pi$
$740$		0			0
$741$		0			0
$742$	−11.3438	+	0.814447i	−0.416443	+	0.0298993i
$743$	−33.3616			−1.22392			−0.611960	−	0.790889i	$-0.709619\pi$
$743$	−33.3616			−1.22392			−0.611960	+	0.790889i	$0.709619\pi$
$744$		0			0
$745$		0			0
$746$	29.2856	+	16.9081i	1.07222	+	0.619048i
$747$		0			0
$748$	−1.17741			−0.0430504
$749$	25.3025	+	37.3624i	0.924533	+	1.36519i
$750$		0			0
$751$	15.9452	+	27.6179i	0.581849	+	1.00779i	0.995260	+	0.0972480i	$0.0310040\pi$
$751$	15.9452	+	27.6179i	0.581849	+	1.00779i	−0.413411	+	0.910545i	$0.635663\pi$
$752$	5.02520	+	2.90130i	0.183250	+	0.105800i
$753$		0			0
$754$	−30.3018	+	17.4947i	−1.10353	+	0.637121i
$755$		0			0
$756$		0			0
$757$			10.9065i			0.396404i	0.980161	+	0.198202i	$0.0635102\pi$
$757$			10.9065i			0.396404i	−0.980161	+	0.198202i	$0.936490\pi$
$758$	13.3807	+	23.1761i	0.486010	+	0.841793i
$759$		0			0
$760$		0			0
$761$	−12.2097	−	21.1479i	−0.442602	−	0.766610i	0.555280	−	0.831664i	$-0.312611\pi$
$761$	−12.2097	−	21.1479i	−0.442602	−	0.766610i	−0.997882	+	0.0650543i	$0.979278\pi$
$762$		0			0
$763$	−13.5160	+	27.8433i	−0.489313	+	1.00800i
$764$			4.49457i			0.162608i
$765$		0			0
$766$	−17.1310	−	9.89060i	−0.618969	−	0.357362i
$767$	10.9511	−	18.9678i	0.395421	−	0.684889i
$768$		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
$772$	−10.8859	+	6.28497i	−0.391791	+	0.226201i
$773$	−39.2894	−	22.6837i	−1.41314	−	0.815877i	−0.417458	−	0.908696i	$-0.637079\pi$
$773$	−39.2894	−	22.6837i	−1.41314	−	0.815877i	−0.995683	+	0.0928193i	$0.970412\pi$
$774$		0			0
$775$		0			0
$776$	15.6344			0.561243
$777$		0			0
$778$			5.18670i			0.185952i
$779$	−0.192795	+	0.111310i	−0.00690760	+	0.00398810i
$780$		0			0
$781$	2.84961	−	4.93566i	0.101967	−	0.176612i
$782$	1.29153	−	0.745667i	0.0461851	−	0.0266650i
$783$		0			0
$784$	−4.33013	−	5.50000i	−0.154647	−	0.196429i
$785$		0			0
$786$		0			0
$787$	1.67335	−	2.89834i	0.0596487	−	0.103314i	−0.834659	−	0.550767i	$-0.814335\pi$
$787$	1.67335	−	2.89834i	0.0596487	−	0.103314i	0.894308	+	0.447452i	$0.147669\pi$
$788$	−6.68740	+	11.5829i	−0.238229	+	0.412625i
$789$		0			0
$790$		0			0
$791$	35.7700	−	2.56817i	1.27183	−	0.0913136i
$792$		0			0
$793$	39.2285	−	22.6486i	1.39304	−	0.804274i
$794$	−2.88259	+	4.99280i	−0.102299	+	0.177188i
$795$		0			0
$796$	−23.5169	+	13.5775i	−0.833535	+	0.481242i
$797$		−	36.5402i		−	1.29432i	−0.762354	−	0.647160i	$-0.775956\pi$
$797$		−	36.5402i		−	1.29432i	0.762354	−	0.647160i	$-0.224044\pi$
$798$		0			0
$799$	−2.31873			−0.0820308
$800$		0			0
$801$		0			0
$802$	15.4361	+	8.91202i	0.545067	+	0.314695i
$803$	0.875609	−	0.505533i	0.0308996	−	0.0178399i
$804$		0			0
$805$		0			0
$806$			3.25725i			0.114732i
$807$		0			0
$808$	−9.02458	+	15.6310i	−0.317484	+	0.549898i
$809$	−41.5179	−	23.9704i	−1.45969	−	0.842753i	−0.460696	−	0.887558i	$-0.652400\pi$
$809$	−41.5179	−	23.9704i	−1.45969	−	0.842753i	−0.998996	+	0.0448048i	$0.985733\pi$
$810$		0			0
$811$			49.6994i			1.74518i	0.488452	+	0.872591i	$0.337562\pi$
$811$			49.6994i			1.74518i	−0.488452	+	0.872591i	$0.662438\pi$
$812$	−21.1808	−	10.2818i	−0.743301	−	0.360822i
$813$		0			0
$814$	−11.6855	−	20.2398i	−0.409575	−	0.709405i
$815$		0			0
$816$		0			0
$817$	0.0535365	+	0.0927279i	0.00187300	+	0.00324414i
$818$		−	32.9802i		−	1.15312i
$819$		0			0
$820$		0			0
$821$	−19.6520	+	11.3461i	−0.685858	+	0.395980i	−0.802059	−	0.597245i	$-0.796262\pi$
$821$	−19.6520	+	11.3461i	−0.685858	+	0.395980i	0.116200	+	0.993226i	$0.462929\pi$
$822$		0			0
$823$	2.76628	+	1.59711i	0.0964266	+	0.0556719i	0.547438	−	0.836846i	$-0.315603\pi$
$823$	2.76628	+	1.59711i	0.0964266	+	0.0556719i	−0.451011	+	0.892518i	$0.648937\pi$
$824$	−4.26002	−	7.37857i	−0.148405	−	0.257045i
$825$		0			0
$826$	14.7002	−	1.05543i	0.511484	−	0.0367229i
$827$	29.7259			1.03367			0.516836	−	0.856084i	$-0.327110\pi$
$827$	29.7259			1.03367			0.516836	+	0.856084i	$0.327110\pi$
$828$		0			0
$829$	−26.8588	−	15.5069i	−0.932845	−	0.538578i	−0.0451348	−	0.998981i	$-0.514372\pi$
$829$	−26.8588	−	15.5069i	−0.932845	−	0.538578i	−0.887710	+	0.460403i	$0.847705\pi$
$830$		0			0
$831$		0			0
$832$	−3.93185			−0.136312
$833$	2.59741	+	1.03820i	0.0899950	+	0.0359713i
$834$		0			0
$835$		0			0
$836$	0.0519700	−	0.0900147i	0.00179742	−	0.00311322i
$837$		0			0
$838$	−7.61434	−	13.1884i	−0.263033	−	0.455586i
$839$	35.8462			1.23755			0.618773	−	0.785570i	$-0.287630\pi$
$839$	35.8462			1.23755			0.618773	+	0.785570i	$0.287630\pi$
$840$		0			0
$841$	−50.1918			−1.73075
$842$	−8.49697	−	14.7172i	−0.292825	−	0.507188i
$843$		0			0
$844$	−9.20915	+	15.9507i	−0.316992	+	0.549046i
$845$		0			0
$846$		0			0
$847$	−3.43942	−	5.07875i	−0.118180	−	0.174508i
$848$	−4.29858			−0.147614
$849$		0			0
$850$		0			0
$851$	25.6361	+	14.8010i	0.878796	+	0.507373i
$852$		0			0
$853$	22.8818			0.783456			0.391728	−	0.920081i	$-0.371877\pi$
$853$	22.8818			0.783456			0.391728	+	0.920081i	$0.371877\pi$
$854$	27.4205	+	13.3108i	0.938311	+	0.455486i
$855$		0			0
$856$	8.52761	+	14.7702i	0.291468	+	0.504837i
$857$	−29.2012	−	16.8593i	−0.997494	−	0.575904i	−0.0899883	−	0.995943i	$-0.528683\pi$
$857$	−29.2012	−	16.8593i	−0.997494	−	0.575904i	−0.907506	+	0.420039i	$0.862016\pi$
$858$		0			0
$859$	−16.3926	+	9.46427i	−0.559308	+	0.322917i	−0.752868	−	0.658172i	$-0.771330\pi$
$859$	−16.3926	+	9.46427i	−0.559308	+	0.322917i	0.193560	+	0.981088i	$0.437997\pi$
$860$		0			0
$861$		0			0
$862$		−	17.8768i		−	0.608888i
$863$	2.62854	+	4.55277i	0.0894767	+	0.154978i	0.907290	−	0.420505i	$-0.138147\pi$
$863$	2.62854	+	4.55277i	0.0894767	+	0.154978i	−0.817813	+	0.575484i	$0.804814\pi$
$864$		0			0
$865$		0			0
$866$	2.78194	+	4.81846i	0.0945341	+	0.163738i
$867$		0			0
$868$	−1.81481	+	1.22902i	−0.0615987	+	0.0417158i
$869$			24.4752i			0.830263i
$870$		0			0
$871$	42.6293	+	24.6120i	1.44444	+	0.833947i
$872$	−5.84909	+	10.1309i	−0.198075	+	0.343076i
$873$		0			0
$874$			0.131652i			0.00445321i
$875$		0			0
$876$		0			0
$877$	35.2170	−	20.3326i	1.18919	−	0.686582i	0.231071	−	0.972937i	$-0.425777\pi$
$877$	35.2170	−	20.3326i	1.18919	−	0.686582i	0.958124	+	0.286355i	$0.0924437\pi$
$878$	9.53568	+	5.50543i	0.321814	+	0.185799i
$879$		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
$883$			11.0436i			0.371647i	0.982583	+	0.185823i	$0.0594952\pi$
$883$			11.0436i			0.371647i	−0.982583	+	0.185823i	$0.940505\pi$
$884$	1.36068	−	0.785587i	0.0457645	−	0.0264222i
$885$		0			0
$886$	8.49233	−	14.7091i	0.285305	−	0.494163i
$887$	−20.8698	+	12.0492i	−0.700738	+	0.404571i	−0.807622	−	0.589700i	$-0.799246\pi$
$887$	−20.8698	+	12.0492i	−0.700738	+	0.404571i	0.106884	+	0.994271i	$0.465913\pi$
$888$		0			0
$889$	−1.69761	−	23.6446i	−0.0569359	−	0.793015i
$890$		0			0
$891$		0			0
$892$	8.90226	−	15.4192i	0.298070	−	0.516272i
$893$	0.102347	−	0.177270i	0.00342491	−	0.00593211i
$894$		0			0
$895$		0			0
$896$	−1.48356	−	2.19067i	−0.0495624	−	0.0731852i
$897$		0			0
$898$	10.9026	−	6.29461i	0.363824	−	0.210054i
$899$	−3.68608	+	6.38447i	−0.122938	+	0.212934i
$900$		0			0
$901$	1.48759	−	0.858860i	0.0495588	−	0.0286128i
$902$		−	18.5945i		−	0.619129i
$903$		0			0
$904$	13.5546			0.450819
$905$		0			0
$906$		0			0
$907$	−14.0338	−	8.10243i	−0.465985	−	0.269037i	0.248572	−	0.968613i	$-0.420039\pi$
$907$	−14.0338	−	8.10243i	−0.465985	−	0.269037i	−0.714558	+	0.699577i	$0.753372\pi$
$908$	1.48288	−	0.856140i	0.0492110	−	0.0284120i
$909$		0			0
$910$		0			0
$911$			21.4586i			0.710955i	0.934685	+	0.355477i	$0.115682\pi$
$911$			21.4586i			0.710955i	−0.934685	+	0.355477i	$0.884318\pi$
$912$		0			0
$913$	−15.2465	+	26.4076i	−0.504584	+	0.873965i
$914$	−1.87783	−	1.08417i	−0.0621133	−	0.0358611i
$915$		0			0
$916$		−	6.07536i		−	0.200736i
$917$	−18.9613	−	27.9988i	−0.626159	−	0.924603i
$918$		0			0
$919$	−29.5164	−	51.1240i	−0.973657	−	1.68642i	−0.684297	−	0.729203i	$-0.739891\pi$
$919$	−29.5164	−	51.1240i	−0.973657	−	1.68642i	−0.289360	−	0.957220i	$-0.593442\pi$
$920$		0			0
$921$		0			0
$922$	17.1516	+	29.7074i	0.564857	+	0.978362i
$923$			7.60521i			0.250328i
$924$		0			0
$925$		0			0
$926$	24.4335	−	14.1067i	0.802933	−	0.463574i
$927$		0			0
$928$	−7.70674	−	4.44949i	−0.252986	−	0.146062i
$929$	−12.3197	−	21.3383i	−0.404195	−	0.700087i	0.590032	−	0.807380i	$-0.299115\pi$
$929$	−12.3197	−	21.3383i	−0.404195	−	0.700087i	−0.994227	+	0.107293i	$0.965782\pi$
$930$		0			0
$931$	−0.194019	+	0.152750i	−0.00635872	+	0.00500619i
$932$	7.12576			0.233412
$933$		0			0
$934$	−3.64324	−	2.10342i	−0.119210	−	0.0688262i
$935$		0			0
$936$		0			0
$937$	−52.5496			−1.71672			−0.858360	−	0.513048i	$-0.828516\pi$
$937$	−52.5496			−1.71672			−0.858360	+	0.513048i	$0.828516\pi$
$938$	2.37202	+	33.0379i	0.0774491	+	1.07873i
$939$		0			0
$940$		0			0
$941$	−0.752551	+	1.30346i	−0.0245325	+	0.0424915i	−0.878031	−	0.478604i	$-0.841143\pi$
$941$	−0.752551	+	1.30346i	−0.0245325	+	0.0424915i	0.853499	+	0.521095i	$0.174476\pi$
$942$		0			0
$943$	11.7761	+	20.3968i	0.383482	+	0.664211i
$944$	5.57045			0.181303
$945$		0			0
$946$	−8.94333			−0.290773
$947$	−5.68191	−	9.84136i	−0.184637	−	0.319801i	0.758817	−	0.651304i	$-0.225778\pi$
$947$	−5.68191	−	9.84136i	−0.184637	−	0.319801i	−0.943454	+	0.331503i	$0.892444\pi$
$948$		0			0
$949$	−0.674599	+	1.16844i	−0.0218984	+	0.0379292i
$950$		0			0
$951$		0			0
$952$	0.951108	+	0.461698i	0.0308256	+	0.0149637i
$953$	21.9184			0.710006			0.355003	−	0.934865i	$-0.384480\pi$
$953$	21.9184			0.710006			0.355003	+	0.934865i	$0.384480\pi$
$954$		0			0
$955$		0			0
$956$	−16.2114	−	9.35968i	−0.524316	−	0.302714i
$957$		0			0
$958$	−14.7194			−0.475561
$959$	−6.37842	+	13.1397i	−0.205970	+	0.424303i
$960$		0			0
$961$	−15.1569	−	26.2524i	−0.488931	−	0.846853i
$962$	27.0086	+	15.5934i	0.870793	+	0.502752i
$963$		0			0
$964$	−7.68036	+	4.43426i	−0.247368	+	0.142818i
$965$		0			0
$966$		0			0
$967$		−	21.6634i		−	0.696649i	−0.937374	−	0.348324i	$-0.886751\pi$
$967$		−	21.6634i		−	0.696649i	0.937374	−	0.348324i	$-0.113249\pi$
$968$	−1.15918	−	2.00775i	−0.0372573	−	0.0645316i
$969$		0			0
$970$		0			0
$971$	−0.0858379	−	0.148676i	−0.00275467	−	0.00477123i	0.864645	−	0.502384i	$-0.167544\pi$
$971$	−0.0858379	−	0.148676i	−0.00275467	−	0.00477123i	−0.867399	+	0.497612i	$0.834210\pi$
$972$		0			0
$973$	4.13934	+	57.6536i	0.132701	+	1.84829i
$974$			1.87757i			0.0601612i
$975$		0			0
$976$	9.97710	+	5.76028i	0.319359	+	0.184382i
$977$	5.61642	−	9.72792i	0.179685	−	0.311224i	−0.762088	−	0.647474i	$-0.775825\pi$
$977$	5.61642	−	9.72792i	0.179685	−	0.311224i	0.941773	+	0.336250i	$0.109159\pi$
$978$		0			0
$979$			18.1858i			0.581222i
$980$		0			0
$981$		0			0
$982$	−9.03100	+	5.21405i	−0.288191	+	0.166387i
$983$	−23.2026	−	13.3960i	−0.740048	−	0.427267i	0.0820385	−	0.996629i	$-0.473857\pi$
$983$	−23.2026	−	13.3960i	−0.740048	−	0.427267i	−0.822087	+	0.569362i	$0.807190\pi$
$984$		0			0
$985$		0			0
$986$	3.55605			0.113248
$987$		0			0
$988$			0.138701i			0.00441266i
$989$	9.81017	−	5.66390i	0.311945	−	0.180102i
$990$		0			0
$991$	−6.99635	+	12.1180i	−0.222246	+	0.384942i	−0.955490	−	0.295024i	$-0.904672\pi$
$991$	−6.99635	+	12.1180i	−0.222246	+	0.384942i	0.733243	+	0.679966i	$0.238006\pi$
$992$	−0.717439	+	0.414214i	−0.0227787	+	0.0131513i
$993$		0			0
$994$	−4.23732	+	2.86959i	−0.134400	+	0.0910179i
$995$		0			0
$996$		0			0
$997$	19.7740	−	34.2497i	0.626250	−	1.08470i	−0.362047	−	0.932160i	$-0.617922\pi$
$997$	19.7740	−	34.2497i	0.626250	−	1.08470i	0.988298	−	0.152538i	$-0.0487445\pi$
$998$	−18.8822	+	32.7050i	−0.597707	+	1.03526i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.bp.c.899.4		8
3.2	odd	2		3150.2.bp.d.899.4		8
5.2	odd	4		630.2.be.b.521.4	yes	8
5.3	odd	4		3150.2.bf.c.1151.1		8
5.4	even	2		3150.2.bp.f.899.1		8
7.5	odd	6		3150.2.bp.a.1349.1		8
15.2	even	4		630.2.be.a.521.2	yes	8
15.8	even	4		3150.2.bf.b.1151.3		8
15.14	odd	2		3150.2.bp.a.899.1		8
21.5	even	6		3150.2.bp.f.1349.1		8
35.12	even	12		630.2.be.a.341.2	✓	8
35.17	even	12		4410.2.b.e.881.6		8
35.19	odd	6		3150.2.bp.d.1349.4		8
35.32	odd	12		4410.2.b.b.881.6		8
35.33	even	12		3150.2.bf.b.1601.3		8
105.17	odd	12		4410.2.b.b.881.3		8
105.32	even	12		4410.2.b.e.881.3		8
105.47	odd	12		630.2.be.b.341.4	yes	8
105.68	odd	12		3150.2.bf.c.1601.1		8
105.89	even	6	inner	3150.2.bp.c.1349.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.be.a.341.2	✓	8	35.12	even	12
630.2.be.a.521.2	yes	8	15.2	even	4
630.2.be.b.341.4	yes	8	105.47	odd	12
630.2.be.b.521.4	yes	8	5.2	odd	4
3150.2.bf.b.1151.3		8	15.8	even	4
3150.2.bf.b.1601.3		8	35.33	even	12
3150.2.bf.c.1151.1		8	5.3	odd	4
3150.2.bf.c.1601.1		8	105.68	odd	12
3150.2.bp.a.899.1		8	15.14	odd	2
3150.2.bp.a.1349.1		8	7.5	odd	6
3150.2.bp.c.899.4		8	1.1	even	1	trivial
3150.2.bp.c.1349.4		8	105.89	even	6	inner
3150.2.bp.d.899.4		8	3.2	odd	2
3150.2.bp.d.1349.4		8	35.19	odd	6
3150.2.bp.f.899.1		8	5.4	even	2
3150.2.bp.f.1349.1		8	21.5	even	6
4410.2.b.b.881.3		8	105.17	odd	12
4410.2.b.b.881.6		8	35.32	odd	12
4410.2.b.e.881.3		8	105.32	even	12
4410.2.b.e.881.6		8	35.17	even	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:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.bp (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.63896 - 0.189469i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(2.63896 - 0.189469i) q^{7} +1.00000 q^{8} +(2.55171 + 1.47323i) q^{11} -3.93185 q^{13} +(-1.48356 - 2.19067i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.346065 + 0.199801i) q^{17} +(-0.0305501 + 0.0176381i) q^{19} -2.94646i q^{22} +(1.86603 + 3.23205i) q^{23} +(1.96593 + 3.40508i) q^{26} +(-1.15539 + 2.38014i) q^{28} +8.89898i q^{29} +(0.717439 + 0.414214i) q^{31} +(-0.500000 + 0.866025i) q^{32} -0.399602i q^{34} +(6.86919 - 3.96593i) q^{37} +(0.0305501 + 0.0176381i) q^{38} +6.31079 q^{41} -3.03528i q^{43} +(-2.55171 + 1.47323i) q^{44} +(1.86603 - 3.23205i) q^{46} +(-5.02520 + 2.90130i) q^{47} +(6.92820 - 1.00000i) q^{49} +(1.96593 - 3.40508i) q^{52} +(2.14929 - 3.72268i) q^{53} +(2.63896 - 0.189469i) q^{56} +(7.70674 - 4.44949i) q^{58} +(-2.78522 + 4.82415i) q^{59} +(-9.97710 + 5.76028i) q^{61} -0.828427i q^{62} +1.00000 q^{64} +(-10.8420 - 6.25966i) q^{67} +(-0.346065 + 0.199801i) q^{68} -1.93426i q^{71} +(0.171573 - 0.297173i) q^{73} +(-6.86919 - 3.96593i) q^{74} -0.0352762i q^{76} +(7.01299 + 3.40433i) q^{77} +(4.15331 + 7.19375i) q^{79} +(-3.15539 - 5.46530i) q^{82} +10.3490i q^{83} +(-2.62863 + 1.51764i) q^{86} +(2.55171 + 1.47323i) q^{88} +(3.08604 + 5.34519i) q^{89} +(-10.3760 + 0.744963i) q^{91} -3.73205 q^{92} +(5.02520 + 2.90130i) q^{94} +15.6344 q^{97} +(-4.33013 - 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} + 24 q^{11} - 16 q^{13} - 4 q^{16} - 24 q^{17} + 8 q^{23} + 8 q^{26} - 4 q^{32} + 32 q^{41} - 24 q^{44} + 8 q^{46} - 12 q^{47} + 8 q^{52} - 4 q^{53} + 24 q^{59} + 8 q^{64} - 48 q^{67} + 24 q^{68} + 24 q^{73} + 4 q^{77} + 24 q^{79} - 16 q^{82} + 24 q^{88} + 16 q^{89} - 20 q^{91} - 16 q^{92} + 12 q^{94} + 48 q^{97}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 + 24 * q^11 - 16 * q^13 - 4 * q^16 - 24 * q^17 + 8 * q^23 + 8 * q^26 - 4 * q^32 + 32 * q^41 - 24 * q^44 + 8 * q^46 - 12 * q^47 + 8 * q^52 - 4 * q^53 + 24 * q^59 + 8 * q^64 - 48 * q^67 + 24 * q^68 + 24 * q^73 + 4 * q^77 + 24 * q^79 - 16 * q^82 + 24 * q^88 + 16 * q^89 - 20 * q^91 - 16 * q^92 + 12 * q^94 + 48 * q^97

Introduction

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