LMFDB - Embedded newform 392.3.h.a.293.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(293,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("392.293");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.h (of order $2$, degree $1$, 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:	$10.6812263629$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			293.12
Character	$\chi$	$=$	392.293
Dual form			392.3.h.a.293.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.621472 + 1.90099i) q^{2} +3.40276 q^{3} +(-3.22755 - 2.36283i) q^{4} -4.31716 q^{5} +(-2.11472 + 6.46862i) q^{6} +(6.49755 - 4.66711i) q^{8} +2.57876 q^{9} +O(q^{10})$	\(q+(-0.621472 + 1.90099i) q^{2} +3.40276 q^{3} +(-3.22755 - 2.36283i) q^{4} -4.31716 q^{5} +(-2.11472 + 6.46862i) q^{6} +(6.49755 - 4.66711i) q^{8} +2.57876 q^{9} +(2.68300 - 8.20689i) q^{10} +17.8862i q^{11} +(-10.9826 - 8.04013i) q^{12} +3.25607 q^{13} -14.6903 q^{15} +(4.83409 + 15.2523i) q^{16} +15.7343i q^{17} +(-1.60263 + 4.90220i) q^{18} -1.55704 q^{19} +(13.9338 + 10.2007i) q^{20} +(-34.0014 - 11.1157i) q^{22} -41.4139 q^{23} +(22.1096 - 15.8810i) q^{24} -6.36211 q^{25} +(-2.02356 + 6.18976i) q^{26} -21.8499 q^{27} -3.74374i q^{29} +(9.12958 - 27.9261i) q^{30} +0.0167630i q^{31} +(-31.9987 - 0.289277i) q^{32} +60.8622i q^{33} +(-29.9109 - 9.77845i) q^{34} +(-8.32306 - 6.09316i) q^{36} -1.34839i q^{37} +(0.967659 - 2.95993i) q^{38} +11.0796 q^{39} +(-28.0510 + 20.1487i) q^{40} +70.3018i q^{41} +13.0380i q^{43} +(42.2619 - 57.7284i) q^{44} -11.1329 q^{45} +(25.7376 - 78.7274i) q^{46} +35.7723i q^{47} +(16.4493 + 51.8998i) q^{48} +(3.95387 - 12.0943i) q^{50} +53.5402i q^{51} +(-10.5091 - 7.69353i) q^{52} -45.9558i q^{53} +(13.5791 - 41.5365i) q^{54} -77.2174i q^{55} -5.29824 q^{57} +(7.11682 + 2.32663i) q^{58} +68.7017 q^{59} +(47.4135 + 34.7105i) q^{60} +96.0771 q^{61} +(-0.0318663 - 0.0104177i) q^{62} +(20.4362 - 60.6495i) q^{64} -14.0570 q^{65} +(-115.699 - 37.8242i) q^{66} -13.9497i q^{67} +(37.1775 - 50.7833i) q^{68} -140.921 q^{69} -75.7095 q^{71} +(16.7556 - 12.0353i) q^{72} +53.1487i q^{73} +(2.56328 + 0.837986i) q^{74} -21.6487 q^{75} +(5.02543 + 3.67902i) q^{76} +(-6.88567 + 21.0623i) q^{78} -23.3488 q^{79} +(-20.8696 - 65.8465i) q^{80} -97.5588 q^{81} +(-133.643 - 43.6906i) q^{82} +102.487 q^{83} -67.9277i q^{85} +(-24.7852 - 8.10278i) q^{86} -12.7390i q^{87} +(83.4766 + 116.216i) q^{88} -88.5638i q^{89} +(6.91880 - 21.1636i) q^{90} +(133.665 + 97.8538i) q^{92} +0.0570404i q^{93} +(-68.0029 - 22.2315i) q^{94} +6.72201 q^{95} +(-108.884 - 0.984338i) q^{96} -140.869i q^{97} +46.1241i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{2} + 8 q^{4} - 20 q^{8} + 64 q^{9}+O(q^{10}) $ 28 * q + 4 * q^2 + 8 * q^4 - 20 * q^8 + 64 * q^9	$ 28 q + 4 q^{2} + 8 q^{4} - 20 q^{8} + 64 q^{9} + 28 q^{15} - 32 q^{16} + 84 q^{18} - 92 q^{22} - 60 q^{23} + 64 q^{25} - 44 q^{30} - 176 q^{32} + 256 q^{36} + 40 q^{39} + 84 q^{44} - 136 q^{46} + 400 q^{50} + 124 q^{57} + 44 q^{58} + 124 q^{60} - 520 q^{64} + 104 q^{65} - 136 q^{71} - 192 q^{72} + 276 q^{74} - 956 q^{78} + 324 q^{79} + 36 q^{81} - 336 q^{86} - 100 q^{88} + 1020 q^{92} - 580 q^{95}+O(q^{100}) $ 28 * q + 4 * q^2 + 8 * q^4 - 20 * q^8 + 64 * q^9 + 28 * q^15 - 32 * q^16 + 84 * q^18 - 92 * q^22 - 60 * q^23 + 64 * q^25 - 44 * q^30 - 176 * q^32 + 256 * q^36 + 40 * q^39 + 84 * q^44 - 136 * q^46 + 400 * q^50 + 124 * q^57 + 44 * q^58 + 124 * q^60 - 520 * q^64 + 104 * q^65 - 136 * q^71 - 192 * q^72 + 276 * q^74 - 956 * q^78 + 324 * q^79 + 36 * q^81 - 336 * q^86 - 100 * q^88 + 1020 * q^92 - 580 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−0.621472	+	1.90099i	−0.310736	+	0.950496i
$2$	−0.621472	+	1.90099i	−0.310736	+	0.950496i
$3$	3.40276			1.13425			0.567126	−	0.823631i	$-0.308055\pi$
$3$	3.40276			1.13425			0.567126	+	0.823631i	$0.308055\pi$
$4$	−3.22755	−	2.36283i	−0.806886	−	0.590707i
$5$	−4.31716			−0.863433			−0.431716	−	0.902009i	$-0.642092\pi$
$5$	−4.31716			−0.863433			−0.431716	+	0.902009i	$0.642092\pi$
$6$	−2.11472	+	6.46862i	−0.352453	+	1.07810i
$7$		0			0
$7$		0			0
$8$	6.49755	−	4.66711i	0.812193	−	0.583389i
$9$	2.57876			0.286529
$10$	2.68300	−	8.20689i	0.268300	−	0.820689i
$11$			17.8862i			1.62601i	0.582254	+	0.813007i	$0.302171\pi$
$11$			17.8862i			1.62601i	−0.582254	+	0.813007i	$0.697829\pi$
$12$	−10.9826	−	8.04013i	−0.915213	−	0.670011i
$13$	3.25607			0.250467			0.125233	−	0.992127i	$-0.460032\pi$
$13$	3.25607			0.250467			0.125233	+	0.992127i	$0.460032\pi$
$14$		0			0
$15$	−14.6903			−0.979350
$16$	4.83409	+	15.2523i	0.302131	+	0.953266i
$17$			15.7343i			0.925550i	0.886476	+	0.462775i	$0.153146\pi$
$17$			15.7343i			0.925550i	−0.886476	+	0.462775i	$0.846854\pi$
$18$	−1.60263	+	4.90220i	−0.0890348	+	0.272344i
$19$	−1.55704			−0.0819496			−0.0409748	−	0.999160i	$-0.513046\pi$
$19$	−1.55704			−0.0819496			−0.0409748	+	0.999160i	$0.513046\pi$
$20$	13.9338	+	10.2007i	0.696692	+	0.510035i
$21$		0			0
$22$	−34.0014	−	11.1157i	−1.54552	−	0.505261i
$23$	−41.4139			−1.80060			−0.900301	−	0.435267i	$-0.856654\pi$
$23$	−41.4139			−1.80060			−0.900301	+	0.435267i	$0.856654\pi$
$24$	22.1096	−	15.8810i	0.921232	−	0.661710i
$25$	−6.36211			−0.254484
$26$	−2.02356	+	6.18976i	−0.0778291	+	0.238068i
$27$	−21.8499			−0.809257
$28$		0			0
$29$		−	3.74374i		−	0.129095i	−0.997915	−	0.0645473i	$-0.979440\pi$
$29$		−	3.74374i		−	0.129095i	0.997915	−	0.0645473i	$-0.0205603\pi$
$30$	9.12958	−	27.9261i	0.304319	−	0.930869i
$31$			0.0167630i			0.000540742i	1.00000		0.000270371i	$8.60617e-5\pi$
$31$			0.0167630i			0.000540742i	−1.00000		0.000270371i	$0.999914\pi$
$32$	−31.9987	−	0.289277i	−0.999959	−	0.00903989i
$33$			60.8622i			1.84431i
$34$	−29.9109	−	9.77845i	−0.879732	−	0.287602i
$35$		0			0
$36$	−8.32306	−	6.09316i	−0.231196	−	0.169254i
$37$		−	1.34839i		−	0.0364429i	−0.999834	−	0.0182215i	$-0.994200\pi$
$37$		−	1.34839i		−	0.0364429i	0.999834	−	0.0182215i	$-0.00580039\pi$
$38$	0.967659	−	2.95993i	0.0254647	−	0.0778928i
$39$	11.0796			0.284093
$40$	−28.0510	+	20.1487i	−0.701274	+	0.503717i
$41$			70.3018i			1.71468i	0.514753	+	0.857339i	$0.327884\pi$
$41$			70.3018i			1.71468i	−0.514753	+	0.857339i	$0.672116\pi$
$42$		0			0
$43$			13.0380i			0.303210i	0.988441	+	0.151605i	$0.0484442\pi$
$43$			13.0380i			0.303210i	−0.988441	+	0.151605i	$0.951556\pi$
$44$	42.2619	−	57.7284i	0.960498	−	1.31201i
$45$	−11.1329			−0.247398
$46$	25.7376	−	78.7274i	0.559512	−	1.71147i
$47$			35.7723i			0.761113i	0.924758	+	0.380557i	$0.124268\pi$
$47$			35.7723i			0.761113i	−0.924758	+	0.380557i	$0.875732\pi$
$48$	16.4493	+	51.8998i	0.342693	+	1.08124i
$49$		0			0
$50$	3.95387	−	12.0943i	0.0790774	−	0.241886i
$51$			53.5402i			1.04981i
$52$	−10.5091	−	7.69353i	−0.202098	−	0.147952i
$53$		−	45.9558i		−	0.867091i	−0.901132	−	0.433546i	$-0.857262\pi$
$53$		−	45.9558i		−	0.867091i	0.901132	−	0.433546i	$-0.142738\pi$
$54$	13.5791	−	41.5365i	0.251465	−	0.769195i
$55$		−	77.2174i		−	1.40395i
$56$		0			0
$57$	−5.29824			−0.0929516
$58$	7.11682	+	2.32663i	0.122704	+	0.0401143i
$59$	68.7017			1.16444			0.582218	−	0.813033i	$-0.302185\pi$
$59$	68.7017			1.16444			0.582218	+	0.813033i	$0.302185\pi$
$60$	47.4135	+	34.7105i	0.790224	+	0.578509i
$61$	96.0771			1.57503			0.787517	−	0.616292i	$-0.211366\pi$
$61$	96.0771			1.57503			0.787517	+	0.616292i	$0.211366\pi$
$62$	−0.0318663	−	0.0104177i	−0.000513973	−	0.000168028i
$63$		0			0
$64$	20.4362	−	60.6495i	0.319316	−	0.947648i
$65$	−14.0570			−0.216261
$66$	−115.699	−	37.8242i	−1.75301	−	0.573094i
$67$		−	13.9497i		−	0.208204i	−0.994567	−	0.104102i	$-0.966803\pi$
$67$		−	13.9497i		−	0.208204i	0.994567	−	0.104102i	$-0.0331969\pi$
$68$	37.1775	−	50.7833i	0.546729	−	0.746813i
$69$	−140.921			−2.04234
$70$		0			0
$71$	−75.7095			−1.06633			−0.533166	−	0.846011i	$-0.678998\pi$
$71$	−75.7095			−1.06633			−0.533166	+	0.846011i	$0.678998\pi$
$72$	16.7556	−	12.0353i	0.232717	−	0.167158i
$73$			53.1487i			0.728065i	0.931386	+	0.364033i	$0.118600\pi$
$73$			53.1487i			0.728065i	−0.931386	+	0.364033i	$0.881400\pi$
$74$	2.56328	+	0.837986i	0.0346389	+	0.0113241i
$75$	−21.6487			−0.288649
$76$	5.02543	+	3.67902i	0.0661240	+	0.0484082i
$77$		0			0
$78$	−6.88567	+	21.0623i	−0.0882778	+	0.270029i
$79$	−23.3488			−0.295554			−0.147777	−	0.989021i	$-0.547212\pi$
$79$	−23.3488			−0.295554			−0.147777	+	0.989021i	$0.547212\pi$
$80$	−20.8696	−	65.8465i	−0.260870	−	0.823081i
$81$	−97.5588			−1.20443
$82$	−133.643	−	43.6906i	−1.62979	−	0.532812i
$83$	102.487			1.23479			0.617393	−	0.786655i	$-0.288189\pi$
$83$	102.487			1.23479			0.617393	+	0.786655i	$0.288189\pi$
$84$		0			0
$85$		−	67.9277i		−	0.799150i
$86$	−24.7852	−	8.10278i	−0.288200	−	0.0942184i
$87$		−	12.7390i		−	0.146426i
$88$	83.4766	+	116.216i	0.948598	+	1.32064i
$89$		−	88.5638i		−	0.995099i	−0.867436	−	0.497549i	$-0.834233\pi$
$89$		−	88.5638i		−	0.995099i	0.867436	−	0.497549i	$-0.165767\pi$
$90$	6.91880	−	21.1636i	0.0768755	−	0.235151i
$91$		0			0
$92$	133.665	+	97.8538i	1.45288	+	1.06363i
$93$			0.0570404i			0.000613338i
$94$	−68.0029	−	22.2315i	−0.723435	−	0.236505i
$95$	6.72201			0.0707580
$96$	−108.884	−	0.984338i	−1.13421	−	0.0102535i
$97$		−	140.869i		−	1.45226i	−0.687558	−	0.726130i	$-0.741317\pi$
$97$		−	140.869i		−	1.45226i	0.687558	−	0.726130i	$-0.258683\pi$
$98$		0			0
$99$			46.1241i			0.465900i
$100$	20.5340	+	15.0326i	0.205340	+	0.150326i
$101$	−35.3977			−0.350472			−0.175236	−	0.984526i	$-0.556069\pi$
$101$	−35.3977			−0.350472			−0.175236	+	0.984526i	$0.556069\pi$
$102$	−101.779	−	33.2737i	−0.997838	−	0.326213i
$103$			100.650i			0.977181i	0.872513	+	0.488590i	$0.162489\pi$
$103$			100.650i			0.977181i	−0.872513	+	0.488590i	$0.837511\pi$
$104$	21.1565	−	15.1964i	0.203427	−	0.146119i
$105$		0			0
$106$	87.3617	+	28.5603i	0.824167	+	0.269437i
$107$			106.950i			0.999534i	0.866160	+	0.499767i	$0.166581\pi$
$107$			106.950i			0.999534i	−0.866160	+	0.499767i	$0.833419\pi$
$108$	70.5216	+	51.6276i	0.652978	+	0.478033i
$109$		−	52.6312i		−	0.482855i	−0.970419	−	0.241427i	$-0.922384\pi$
$109$		−	52.6312i		−	0.482855i	0.970419	−	0.241427i	$-0.0776156\pi$
$110$	146.790	+	47.9885i	1.33445	+	0.436259i
$111$		−	4.58824i		−	0.0413355i
$112$		0			0
$113$	45.4346			0.402076			0.201038	−	0.979583i	$-0.435568\pi$
$113$	45.4346			0.402076			0.201038	+	0.979583i	$0.435568\pi$
$114$	3.29271	−	10.0719i	0.0288834	−	0.0883501i
$115$	178.790			1.55470
$116$	−8.84581	+	12.0831i	−0.0762570	+	0.104165i
$117$	8.39662			0.0717659
$118$	−42.6962	+	130.601i	−0.361832	+	1.10679i
$119$		0			0
$120$	−95.4506	+	68.5610i	−0.795422	+	0.571342i
$121$	−198.914			−1.64392
$122$	−59.7092	+	182.642i	−0.489420	+	1.49706i
$123$			239.220i			1.94488i
$124$	0.0396081	−	0.0541033i	0.000319420	−	0.000436317i
$125$	135.395			1.08316
$126$		0			0
$127$	125.695			0.989723			0.494861	−	0.868972i	$-0.335219\pi$
$127$	125.695			0.989723			0.494861	+	0.868972i	$0.335219\pi$
$128$	102.594	+	76.5410i	0.801513	+	0.597977i
$129$			44.3653i			0.343917i
$130$	8.73602	−	26.7222i	0.0672001	−	0.205555i
$131$	113.301			0.864891			0.432446	−	0.901660i	$-0.357651\pi$
$131$	113.301			0.864891			0.432446	+	0.901660i	$0.357651\pi$
$132$	143.807	−	196.436i	1.08945	−	1.48815i
$133$		0			0
$134$	26.5182	+	8.66933i	0.197897	+	0.0646965i
$135$	94.3297			0.698738
$136$	73.4339	+	102.235i	0.539955	+	0.751725i
$137$	78.3358			0.571794			0.285897	−	0.958260i	$-0.407708\pi$
$137$	78.3358			0.571794			0.285897	+	0.958260i	$0.407708\pi$
$138$	87.5787	−	267.890i	0.634628	−	1.94123i
$139$	149.038			1.07222			0.536109	−	0.844149i	$-0.319894\pi$
$139$	149.038			1.07222			0.536109	+	0.844149i	$0.319894\pi$
$140$		0			0
$141$			121.725i			0.863295i
$142$	47.0513	−	143.923i	0.331348	−	1.01354i
$143$			58.2385i			0.407263i
$144$	12.4660	+	39.3319i	0.0865692	+	0.273138i
$145$			16.1623i			0.111464i
$146$	−101.035	−	33.0305i	−0.692023	−	0.226236i
$147$		0			0
$148$	−3.18601	+	4.35198i	−0.0215271	+	0.0294053i
$149$			85.2595i			0.572212i	0.958198	+	0.286106i	$0.0923609\pi$
$149$			85.2595i			0.572212i	−0.958198	+	0.286106i	$0.907639\pi$
$150$	13.4541	−	41.1540i	0.0896938	−	0.274360i
$151$	131.802			0.872864			0.436432	−	0.899737i	$-0.356242\pi$
$151$	131.802			0.872864			0.436432	+	0.899737i	$0.356242\pi$
$152$	−10.1170	+	7.26689i	−0.0665590	+	0.0478085i
$153$			40.5751i			0.265197i
$154$		0			0
$155$		−	0.0723686i		−	0.000466894i
$156$	−35.7599	−	26.1792i	−0.229230	−	0.167815i
$157$	−245.105			−1.56118			−0.780589	−	0.625045i	$-0.785081\pi$
$157$	−245.105			−1.56118			−0.780589	+	0.625045i	$0.785081\pi$
$158$	14.5106	−	44.3859i	0.0918393	−	0.280923i
$159$		−	156.377i		−	0.983501i
$160$	138.144	+	1.24885i	0.863397	+	0.00780534i
$161$		0			0
$162$	60.6301	−	185.459i	0.374260	−	1.14481i
$163$		−	240.281i		−	1.47411i	−0.675830	−	0.737057i	$-0.736215\pi$
$163$		−	240.281i		−	1.47411i	0.675830	−	0.737057i	$-0.263785\pi$
$164$	166.111	−	226.902i	1.01287	−	1.38355i
$165$		−	262.752i		−	1.59244i
$166$	−63.6930	+	194.828i	−0.383693	+	1.17366i
$167$			73.1965i			0.438302i	0.975691	+	0.219151i	$0.0703288\pi$
$167$			73.1965i			0.438302i	−0.975691	+	0.219151i	$0.929671\pi$
$168$		0			0
$169$	−158.398			−0.937266
$170$	129.130	+	42.2152i	0.759589	+	0.248325i
$171$	−4.01524			−0.0234809
$172$	30.8067	−	42.0809i	0.179108	−	0.244656i
$173$	37.0491			0.214157			0.107078	−	0.994251i	$-0.465850\pi$
$173$	37.0491			0.214157			0.107078	+	0.994251i	$0.465850\pi$
$174$	24.2168	+	7.91696i	0.139177	+	0.0454998i
$175$		0			0
$176$	−272.804	+	86.4634i	−1.55002	+	0.491269i
$177$	233.775			1.32076
$178$	168.359	+	55.0399i	0.945837	+	0.309213i
$179$			237.848i			1.32876i	0.747395	+	0.664379i	$0.231304\pi$
$179$			237.848i			1.32876i	−0.747395	+	0.664379i	$0.768696\pi$
$180$	35.9320	+	26.3052i	0.199622	+	0.146140i
$181$	−292.553			−1.61631			−0.808157	−	0.588966i	$-0.799535\pi$
$181$	−292.553			−1.61631			−0.808157	+	0.588966i	$0.799535\pi$
$182$		0			0
$183$	326.927			1.78649
$184$	−269.088	+	193.283i	−1.46244	+	1.05045i
$185$			5.82121i			0.0314660i
$186$	−0.108433	−	0.0354490i	−0.000582975	−	0.000190586i
$187$	−281.427			−1.50496
$188$	84.5238	−	115.457i	0.449595	−	0.614132i
$189$		0			0
$190$	−4.17754	+	12.7785i	−0.0219871	+	0.0672552i
$191$	141.227			0.739408			0.369704	−	0.929150i	$-0.379459\pi$
$191$	141.227			0.739408			0.369704	+	0.929150i	$0.379459\pi$
$192$	69.5394	−	206.376i	0.362185	−	1.07487i
$193$	−65.9598			−0.341761			−0.170880	−	0.985292i	$-0.554661\pi$
$193$	−65.9598			−0.341761			−0.170880	+	0.985292i	$0.554661\pi$
$194$	267.791	+	87.5462i	1.38037	+	0.451269i
$195$	−47.8325			−0.245295
$196$		0			0
$197$			199.421i			1.01229i	0.862448	+	0.506145i	$0.168930\pi$
$197$			199.421i			1.01229i	−0.862448	+	0.506145i	$0.831070\pi$
$198$	−87.6815	−	28.6648i	−0.442836	−	0.144772i
$199$		−	67.6920i		−	0.340161i	−0.985430	−	0.170080i	$-0.945597\pi$
$199$		−	67.6920i		−	0.340161i	0.985430	−	0.170080i	$-0.0544028\pi$
$200$	−41.3381	+	29.6926i	−0.206690	+	0.148463i
$201$		−	47.4674i		−	0.236156i
$202$	21.9987	−	67.2907i	0.108904	−	0.333122i
$203$		0			0
$204$	126.506	−	172.803i	0.620128	−	0.847075i
$205$		−	303.504i		−	1.48051i
$206$	−191.334	−	62.5509i	−0.928807	−	0.303645i
$207$	−106.796			−0.515924
$208$	15.7401	+	49.6624i	0.0756738	+	0.238762i
$209$		−	27.8495i		−	0.133251i
$210$		0			0
$211$			62.1464i			0.294533i	0.989097	+	0.147266i	$0.0470475\pi$
$211$			62.1464i			0.294533i	−0.989097	+	0.147266i	$0.952953\pi$
$212$	−108.586	+	148.325i	−0.512197	+	0.699644i
$213$	−257.621			−1.20949
$214$	−203.311	−	66.4665i	−0.950053	−	0.310591i
$215$		−	56.2874i		−	0.261802i
$216$	−141.971	+	101.976i	−0.657273	+	0.472111i
$217$		0			0
$218$	100.051	+	32.7088i	0.458952	+	0.150040i
$219$			180.852i			0.825810i
$220$	−182.451	+	249.223i	−0.829325	+	1.13283i
$221$			51.2321i			0.231820i
$222$	8.72221	+	2.85146i	0.0392892	+	0.0128444i
$223$			115.525i			0.518050i	0.965871	+	0.259025i	$0.0834012\pi$
$223$			115.525i			0.518050i	−0.965871	+	0.259025i	$0.916599\pi$
$224$		0			0
$225$	−16.4063			−0.0729171
$226$	−28.2363	+	86.3708i	−0.124940	+	0.382172i
$227$	−56.5064			−0.248927			−0.124463	−	0.992224i	$-0.539721\pi$
$227$	−56.5064			−0.248927			−0.124463	+	0.992224i	$0.539721\pi$
$228$	17.1003	+	12.5188i	0.0750014	+	0.0549071i
$229$	−118.339			−0.516765			−0.258383	−	0.966043i	$-0.583190\pi$
$229$	−118.339			−0.516765			−0.258383	+	0.966043i	$0.583190\pi$
$230$	−111.113	+	339.879i	−0.483101	+	1.47774i
$231$		0			0
$232$	−17.4724	−	24.3251i	−0.0753123	−	0.104850i
$233$	−24.6805			−0.105925			−0.0529625	−	0.998597i	$-0.516866\pi$
$233$	−24.6805			−0.105925			−0.0529625	+	0.998597i	$0.516866\pi$
$234$	−5.21826	+	15.9619i	−0.0223003	+	0.0682133i
$235$		−	154.435i		−	0.657170i
$236$	−221.738	−	162.330i	−0.939568	−	0.687840i
$237$	−79.4503			−0.335233
$238$		0			0
$239$	−251.189			−1.05100			−0.525499	−	0.850794i	$-0.676121\pi$
$239$	−251.189			−1.05100			−0.525499	+	0.850794i	$0.676121\pi$
$240$	−71.0141	−	224.060i	−0.295892	−	0.933582i
$241$		−	112.443i		−	0.466567i	−0.972409	−	0.233283i	$-0.925053\pi$
$241$		−	112.443i		−	0.466567i	0.972409	−	0.233283i	$-0.0749470\pi$
$242$	123.620	−	378.135i	0.510826	−	1.56254i
$243$	−135.320			−0.556871
$244$	−310.093	−	227.014i	−1.27087	−	0.930384i
$245$		0			0
$246$	−454.755	−	148.668i	−1.84860	−	0.604343i
$247$	−5.06984			−0.0205257
$248$	0.0782347	+	0.108918i	0.000315462	+	0.000439187i
$249$	348.739			1.40056
$250$	−84.1444	+	257.385i	−0.336578	+	1.02954i
$251$	121.248			0.483059			0.241529	−	0.970394i	$-0.422351\pi$
$251$	121.248			0.483059			0.241529	+	0.970394i	$0.422351\pi$
$252$		0			0
$253$		−	740.735i		−	2.92781i
$254$	−78.1158	+	238.945i	−0.307543	+	0.940728i
$255$		−	231.142i		−	0.906438i
$256$	−209.263	+	147.462i	−0.817434	+	0.576023i
$257$		−	104.775i		−	0.407684i	−0.979004	−	0.203842i	$-0.934657\pi$
$257$		−	104.775i		−	0.407684i	0.979004	−	0.203842i	$-0.0653430\pi$
$258$	−84.3381	−	27.5718i	−0.326892	−	0.106867i
$259$		0			0
$260$	45.3695	+	33.2142i	0.174498	+	0.127747i
$261$		−	9.65421i		−	0.0369893i
$262$	−70.4133	+	215.384i	−0.268753	+	0.822076i
$263$	−104.678			−0.398017			−0.199008	−	0.979998i	$-0.563772\pi$
$263$	−104.678			−0.398017			−0.199008	+	0.979998i	$0.563772\pi$
$264$	284.051	+	395.455i	1.07595	+	1.49794i
$265$			198.399i			0.748675i
$266$		0			0
$267$		−	301.361i		−	1.12869i
$268$	−32.9607	+	45.0232i	−0.122988	+	0.167997i
$269$	304.932			1.13358			0.566789	−	0.823863i	$-0.308185\pi$
$269$	304.932			1.13358			0.566789	+	0.823863i	$0.308185\pi$
$270$	−58.6233	+	179.320i	−0.217123	+	0.664148i
$271$			102.646i			0.378768i	0.981903	+	0.189384i	$0.0606491\pi$
$271$			102.646i			0.378768i	−0.981903	+	0.189384i	$0.939351\pi$
$272$	−239.984	+	76.0613i	−0.882295	+	0.279637i
$273$		0			0
$274$	−48.6835	+	148.916i	−0.177677	+	0.543488i
$275$		−	113.794i		−	0.413795i
$276$	454.830	+	332.973i	1.64793	+	1.20642i
$277$		−	16.6548i		−	0.0601256i	−0.999548	−	0.0300628i	$-0.990429\pi$
$277$		−	16.6548i		−	0.0601256i	0.999548	−	0.0300628i	$-0.00957073\pi$
$278$	−92.6232	+	283.321i	−0.333177	+	1.01914i
$279$			0.0432277i			0.000154938i
$280$		0			0
$281$	75.8291			0.269855			0.134927	−	0.990856i	$-0.456920\pi$
$281$	75.8291			0.269855			0.134927	+	0.990856i	$0.456920\pi$
$282$	−231.397	−	75.6484i	−0.820559	−	0.268257i
$283$	−87.3313			−0.308591			−0.154296	−	0.988025i	$-0.549311\pi$
$283$	−87.3313			−0.308591			−0.154296	+	0.988025i	$0.549311\pi$
$284$	244.356	+	178.889i	0.860408	+	0.629889i
$285$	22.8734			0.0802574
$286$	−110.711	−	36.1936i	−0.387102	−	0.126551i
$287$		0			0
$288$	−82.5169	−	0.745975i	−0.286517	−	0.00259019i
$289$	41.4304			0.143358
$290$	−30.7245	−	10.0444i	−0.105947	−	0.0346360i
$291$		−	479.344i		−	1.64723i
$292$	125.581	−	171.540i	0.430073	−	0.587466i
$293$	27.5057			0.0938760			0.0469380	−	0.998898i	$-0.485054\pi$
$293$	27.5057			0.0938760			0.0469380	+	0.998898i	$0.485054\pi$
$294$		0			0
$295$	−296.597			−1.00541
$296$	−6.29307	−	8.76122i	−0.0212604	−	0.0295987i
$297$		−	390.811i		−	1.31586i
$298$	−162.078	−	52.9864i	−0.543885	−	0.177807i
$299$	−134.846			−0.450991
$300$	69.8722	+	51.1522i	0.232907	+	0.170507i
$301$		0			0
$302$	−81.9115	+	250.555i	−0.271230	+	0.829654i
$303$	−120.450			−0.397524
$304$	−7.52689	−	23.7484i	−0.0247595	−	0.0781199i
$305$	−414.781			−1.35994
$306$	−77.1329	−	25.2163i	−0.252068	−	0.0824061i
$307$	247.996			0.807805			0.403902	−	0.914802i	$-0.367654\pi$
$307$	247.996			0.807805			0.403902	+	0.914802i	$0.367654\pi$
$308$		0			0
$309$			342.486i			1.10837i
$310$	0.137572	+	0.0449750i	0.000443781	+	0.000145081i
$311$		−	437.036i		−	1.40526i	−0.711556	−	0.702630i	$-0.752009\pi$
$311$		−	437.036i		−	1.40526i	0.711556	−	0.702630i	$-0.247991\pi$
$312$	71.9903	−	51.7097i	0.230738	−	0.165736i
$313$		−	82.8301i		−	0.264633i	−0.991208	−	0.132317i	$-0.957758\pi$
$313$		−	82.8301i		−	0.264633i	0.991208	−	0.132317i	$-0.0422415\pi$
$314$	152.326	−	465.943i	0.485114	−	1.48389i
$315$		0			0
$316$	75.3593	+	55.1691i	0.238479	+	0.174586i
$317$		−	244.536i		−	0.771408i	−0.922623	−	0.385704i	$-0.873959\pi$
$317$		−	244.536i		−	0.771408i	0.922623	−	0.385704i	$-0.126041\pi$
$318$	297.271	+	97.1837i	0.934814	+	0.305609i
$319$	66.9611			0.209910
$320$	−88.2264	+	261.834i	−0.275708	+	0.818230i
$321$			363.925i			1.13372i
$322$		0			0
$323$		−	24.4991i		−	0.0758485i
$324$	314.876	+	230.515i	0.971838	+	0.711465i
$325$	−20.7155			−0.0637399
$326$	456.772	+	149.328i	1.40114	+	0.458060i
$327$		−	179.091i		−	0.547679i
$328$	328.106	+	456.789i	1.00032	+	1.39265i
$329$		0			0
$330$	499.490	+	163.293i	1.51361	+	0.494828i
$331$		−	76.5472i		−	0.231261i	−0.993292	−	0.115630i	$-0.963111\pi$
$331$		−	76.5472i		−	0.231261i	0.993292	−	0.115630i	$-0.0368888\pi$
$332$	−330.782	−	242.160i	−0.996332	−	0.729397i
$333$		−	3.47717i		−	0.0104419i
$334$	−139.146	−	45.4896i	−0.416605	−	0.136196i
$335$			60.2230i			0.179770i
$336$		0			0
$337$	−38.2520			−0.113507			−0.0567537	−	0.998388i	$-0.518075\pi$
$337$	−38.2520			−0.113507			−0.0567537	+	0.998388i	$0.518075\pi$
$338$	98.4399	−	301.113i	0.291242	−	0.890868i
$339$	154.603			0.456056
$340$	−160.501	+	219.240i	−0.472063	+	0.644823i
$341$	−0.299825			−0.000879253
$342$	2.49536	−	7.63294i	0.00729637	−	0.0223185i
$343$		0			0
$344$	60.8500	+	84.7153i	0.176889	+	0.246265i
$345$	608.380			1.76342
$346$	−23.0250	+	70.4301i	−0.0665462	+	0.203555i
$347$			240.633i			0.693468i	0.937964	+	0.346734i	$0.112709\pi$
$347$			240.633i			0.693468i	−0.937964	+	0.346734i	$0.887291\pi$
$348$	−30.1002	+	41.1158i	−0.0864947	+	0.118149i
$349$	430.367			1.23314			0.616572	−	0.787298i	$-0.288521\pi$
$349$	430.367			1.23314			0.616572	+	0.787298i	$0.288521\pi$
$350$		0			0
$351$	−71.1449			−0.202692
$352$	5.17405	−	572.334i	0.0146990	−	1.62595i
$353$			307.093i			0.869951i	0.900442	+	0.434975i	$0.143243\pi$
$353$			307.093i			0.869951i	−0.900442	+	0.434975i	$0.856757\pi$
$354$	−145.285	+	444.405i	−0.410409	+	1.25538i
$355$	326.850			0.920705
$356$	−209.261	+	285.844i	−0.587811	+	0.802931i
$357$		0			0
$358$	−452.147	−	147.816i	−1.26298	−	0.412893i
$359$	461.760			1.28624			0.643120	−	0.765766i	$-0.277640\pi$
$359$	461.760			1.28624			0.643120	+	0.765766i	$0.277640\pi$
$360$	−72.3367	+	51.9585i	−0.200935	+	0.144329i
$361$	−358.576			−0.993284
$362$	181.814	−	556.141i	0.502247	−	1.53630i
$363$	−676.858			−1.86462
$364$		0			0
$365$		−	229.452i		−	0.628635i
$366$	−203.176	+	621.486i	−0.555126	+	1.69805i
$367$			626.943i			1.70829i	0.520034	+	0.854146i	$0.325919\pi$
$367$			626.943i			1.70829i	−0.520034	+	0.854146i	$0.674081\pi$
$368$	−200.199	−	631.655i	−0.544018	−	1.71645i
$369$			181.291i			0.491304i
$370$	−11.0661	−	3.61772i	−0.0299083	−	0.00977762i
$371$		0			0
$372$	0.134777	−	0.184100i	0.000362303	−	0.000494894i
$373$			412.594i			1.10615i	0.833132	+	0.553075i	$0.186546\pi$
$373$			412.594i			1.10615i	−0.833132	+	0.553075i	$0.813454\pi$
$374$	174.899	−	534.990i	0.467644	−	1.43046i
$375$	460.717			1.22858
$376$	166.953	+	232.432i	0.444025	+	0.618171i
$377$		−	12.1899i		−	0.0323339i
$378$		0			0
$379$			327.118i			0.863107i	0.902087	+	0.431554i	$0.142034\pi$
$379$			327.118i			0.863107i	−0.902087	+	0.431554i	$0.857966\pi$
$380$	−21.6956	−	15.8829i	−0.0570937	−	0.0417972i
$381$	427.709			1.12260
$382$	−87.7686	+	268.471i	−0.229761	+	0.702805i
$383$		−	248.865i		−	0.649777i	−0.945752	−	0.324889i	$-0.894673\pi$
$383$		−	248.865i		−	0.649777i	0.945752	−	0.324889i	$-0.105327\pi$
$384$	349.102	+	260.451i	0.909119	+	0.678257i
$385$		0			0
$386$	40.9922	−	125.389i	0.106197	−	0.324842i
$387$			33.6220i			0.0868785i
$388$	−332.849	+	454.662i	−0.857859	+	1.17181i
$389$			377.273i			0.969854i	0.874555	+	0.484927i	$0.161154\pi$
$389$			377.273i			0.969854i	−0.874555	+	0.484927i	$0.838846\pi$
$390$	29.7266	−	90.9292i	0.0762219	−	0.233152i
$391$		−	651.620i		−	1.66655i
$392$		0			0
$393$	385.535			0.981005
$394$	−379.098	−	123.935i	−0.962179	−	0.314555i
$395$	100.801			0.255191
$396$	108.983	−	148.868i	0.275210	−	0.375928i
$397$	−671.749			−1.69206			−0.846031	−	0.533133i	$-0.821014\pi$
$397$	−671.749			−1.69206			−0.846031	+	0.533133i	$0.821014\pi$
$398$	128.682	+	42.0687i	0.323322	+	0.105700i
$399$		0			0
$400$	−30.7550	−	97.0365i	−0.0768876	−	0.242591i
$401$	−470.400			−1.17307			−0.586534	−	0.809925i	$-0.699508\pi$
$401$	−470.400			−1.17307			−0.586534	+	0.809925i	$0.699508\pi$
$402$	90.2351	+	29.4996i	0.224465	+	0.0733822i
$403$			0.0545815i			0.000135438i
$404$	114.248	+	83.6386i	0.282791	+	0.207026i
$405$	421.177			1.03994
$406$		0			0
$407$	24.1175			0.0592567
$408$	249.878	+	347.880i	0.612445	+	0.852646i
$409$			66.6725i			0.163013i	0.996673	+	0.0815067i	$0.0259732\pi$
$409$			66.6725i			0.163013i	−0.996673	+	0.0815067i	$0.974027\pi$
$410$	576.959	+	188.619i	1.40722	+	0.460047i
$411$	266.558			0.648559
$412$	237.818	−	324.851i	0.577227	−	0.788474i
$413$		0			0
$414$	66.3709	−	203.019i	0.160316	−	0.490384i
$415$	−442.454			−1.06615
$416$	−104.190	−	0.941905i	−0.250457	−	0.00226419i
$417$	507.141			1.21617
$418$	52.9417	+	17.3077i	0.126655	+	0.0414060i
$419$	−437.380			−1.04387			−0.521933	−	0.852986i	$-0.674789\pi$
$419$	−437.380			−1.04387			−0.521933	+	0.852986i	$0.674789\pi$
$420$		0			0
$421$			703.800i			1.67173i	0.548933	+	0.835867i	$0.315034\pi$
$421$			703.800i			1.67173i	−0.548933	+	0.835867i	$0.684966\pi$
$422$	−118.140	−	38.6223i	−0.279952	−	0.0915219i
$423$			92.2482i			0.218081i
$424$	−214.481	−	298.600i	−0.505851	−	0.704246i
$425$		−	100.104i		−	0.235538i
$426$	160.104	−	489.736i	0.375832	−	1.14961i
$427$		0			0
$428$	252.705	−	345.186i	0.590431	−	0.806510i
$429$			198.172i			0.461939i
$430$	107.002	+	34.9810i	0.248842	+	0.0813512i
$431$	−549.738			−1.27549			−0.637747	−	0.770246i	$-0.720134\pi$
$431$	−549.738			−1.27549			−0.637747	+	0.770246i	$0.720134\pi$
$432$	−105.625	−	333.261i	−0.244501	−	0.771437i
$433$		−	355.012i		−	0.819890i	−0.912110	−	0.409945i	$-0.865548\pi$
$433$		−	355.012i		−	0.819890i	0.912110	−	0.409945i	$-0.134452\pi$
$434$		0			0
$435$			54.9965i			0.126429i
$436$	−124.358	+	169.869i	−0.285226	+	0.389609i
$437$	64.4832			0.147559
$438$	−343.799	−	112.395i	−0.784929	−	0.256609i
$439$			550.830i			1.25474i	0.778722	+	0.627369i	$0.215868\pi$
$439$			550.830i			1.25474i	−0.778722	+	0.627369i	$0.784132\pi$
$440$	−360.382	−	501.724i	−0.819050	−	1.14028i
$441$		0			0
$442$	−97.3919	−	31.8393i	−0.220344	−	0.0720347i
$443$		−	270.231i		−	0.610002i	−0.952352	−	0.305001i	$-0.901343\pi$
$443$		−	270.231i		−	0.610002i	0.952352	−	0.305001i	$-0.0986569\pi$
$444$	−10.8412	+	14.8087i	−0.0244172	+	0.0333530i
$445$			382.344i			0.859200i
$446$	−219.613	−	71.7957i	−0.492405	−	0.160977i
$447$			290.117i			0.649032i
$448$		0			0
$449$	455.397			1.01425			0.507124	−	0.861873i	$-0.330709\pi$
$449$	455.397			1.01425			0.507124	+	0.861873i	$0.330709\pi$
$450$	10.1961	−	31.1883i	0.0226580	−	0.0693074i
$451$	−1257.43			−2.78809
$452$	−146.642	−	107.354i	−0.324430	−	0.237509i
$453$	448.492			0.990048
$454$	35.1171	−	107.418i	0.0773505	−	0.236604i
$455$		0			0
$456$	−34.4256	+	24.7275i	−0.0754947	+	0.0542269i
$457$	−168.634			−0.369003			−0.184501	−	0.982832i	$-0.559067\pi$
$457$	−168.634			−0.369003			−0.184501	+	0.982832i	$0.559067\pi$
$458$	73.5446	−	224.962i	0.160578	−	0.491184i
$459$		−	343.794i		−	0.749007i
$460$	−577.054	−	422.451i	−1.25447	−	0.918371i
$461$	265.062			0.574971			0.287485	−	0.957785i	$-0.407181\pi$
$461$	265.062			0.574971			0.287485	+	0.957785i	$0.407181\pi$
$462$		0			0
$463$	97.4735			0.210526			0.105263	−	0.994444i	$-0.466432\pi$
$463$	97.4735			0.210526			0.105263	+	0.994444i	$0.466432\pi$
$464$	57.1005	−	18.0976i	0.123061	−	0.0390035i
$465$		−	0.246253i		−	0.000529576i
$466$	15.3383	−	46.9175i	0.0329147	−	0.100681i
$467$	74.1994			0.158885			0.0794427	−	0.996839i	$-0.474686\pi$
$467$	74.1994			0.158885			0.0794427	+	0.996839i	$0.474686\pi$
$468$	−27.1005	−	19.8398i	−0.0579070	−	0.0423926i
$469$		0			0
$470$	293.580	+	95.9770i	0.624638	+	0.204206i
$471$	−834.032			−1.77077
$472$	446.393	−	320.638i	0.945747	−	0.679319i
$473$	−233.201			−0.493024
$474$	49.3761	−	151.034i	0.104169	−	0.318638i
$475$	9.90608			0.0208549
$476$		0			0
$477$		−	118.509i		−	0.248447i
$478$	156.107	−	477.508i	0.326583	−	0.998970i
$479$			548.737i			1.14559i	0.819699	+	0.572794i	$0.194140\pi$
$479$			548.737i			1.14559i	−0.819699	+	0.572794i	$0.805860\pi$
$480$	470.069	+	4.24955i	0.979310	+	0.00885322i
$481$		−	4.39045i		−	0.00912775i
$482$	213.753	+	69.8799i	0.443470	+	0.144979i
$483$		0			0
$484$	642.006	+	470.001i	1.32646	+	0.971076i
$485$			608.155i			1.25393i
$486$	84.0974	−	257.242i	0.173040	−	0.529304i
$487$	567.876			1.16607			0.583034	−	0.812447i	$-0.301865\pi$
$487$	567.876			1.16607			0.583034	+	0.812447i	$0.301865\pi$
$488$	624.266	−	448.402i	1.27923	−	0.918857i
$489$		−	817.617i		−	1.67202i
$490$		0			0
$491$		−	78.8005i		−	0.160490i	−0.996775	−	0.0802449i	$-0.974430\pi$
$491$		−	78.8005i		−	0.160490i	0.996775	−	0.0802449i	$-0.0255702\pi$
$492$	565.235	−	772.093i	1.14885	−	1.56929i
$493$	58.9053			0.119483
$494$	3.15076	−	9.63773i	0.00637806	−	0.0195096i
$495$		−	199.125i		−	0.402273i
$496$	−0.255674	+	0.0810339i	−0.000515471	+	0.000163375i
$497$		0			0
$498$	−216.732	+	662.951i	−0.435204	+	1.33123i
$499$			335.939i			0.673225i	0.941643	+	0.336612i	$0.109281\pi$
$499$			335.939i			0.673225i	−0.941643	+	0.336612i	$0.890719\pi$
$500$	−436.994	−	319.916i	−0.873989	−	0.639831i
$501$			249.070i			0.497146i
$502$	−75.3521	+	230.491i	−0.150104	+	0.459145i
$503$			274.052i			0.544836i	0.962179	+	0.272418i	$0.0878233\pi$
$503$			274.052i			0.544836i	−0.962179	+	0.272418i	$0.912177\pi$
$504$		0			0
$505$	152.817			0.302609
$506$	1408.13	+	460.346i	2.78287	+	0.909775i
$507$	−538.990			−1.06310
$508$	−405.686	−	296.995i	−0.798594	−	0.584636i
$509$	336.017			0.660152			0.330076	−	0.943954i	$-0.392926\pi$
$509$	336.017			0.660152			0.330076	+	0.943954i	$0.392926\pi$
$510$	439.398	+	143.648i	0.861566	+	0.281663i
$511$		0			0
$512$	−150.273	−	489.451i	−0.293501	−	0.955959i
$513$	34.0213			0.0663183
$514$	199.176	+	65.1147i	0.387503	+	0.126682i
$515$		−	434.521i		−	0.843730i
$516$	104.828	−	143.191i	0.203154	−	0.277502i
$517$	−639.829			−1.23758
$518$		0			0
$519$	126.069			0.242908
$520$	−91.3359	+	65.6054i	−0.175646	+	0.126164i
$521$			632.282i			1.21359i	0.794857	+	0.606796i	$0.207546\pi$
$521$			632.282i			1.21359i	−0.794857	+	0.606796i	$0.792454\pi$
$522$	18.3526	+	5.99982i	0.0351582	+	0.0114939i
$523$	779.246			1.48995			0.744977	−	0.667090i	$-0.232461\pi$
$523$	779.246			1.48995			0.744977	+	0.667090i	$0.232461\pi$
$524$	−365.683	−	267.710i	−0.697869	−	0.510897i
$525$		0			0
$526$	65.0547	−	198.993i	0.123678	−	0.378314i
$527$	−0.263755			−0.000500483
$528$	−928.287	+	294.214i	−1.75812	+	0.557223i
$529$	1186.11			2.24217
$530$	−377.155	−	123.299i	−0.711613	−	0.232640i
$531$	177.165			0.333644
$532$		0			0
$533$			228.907i			0.429470i
$534$	572.885	+	187.287i	1.07282	+	0.350726i
$535$		−	461.721i		−	0.863030i
$536$	−65.1046	−	90.6386i	−0.121464	−	0.169102i
$537$			809.338i			1.50715i
$538$	−189.507	+	579.674i	−0.352243	+	1.07746i
$539$		0			0
$540$	−304.453	−	222.885i	−0.563802	−	0.412750i
$541$		−	673.903i		−	1.24566i	−0.782356	−	0.622831i	$-0.785982\pi$
$541$		−	673.903i		−	1.24566i	0.782356	−	0.622831i	$-0.214018\pi$
$542$	−195.130	−	63.7917i	−0.360018	−	0.117697i
$543$	−995.487			−1.83331
$544$	4.55158	−	503.478i	0.00836687	−	0.925512i
$545$			227.217i			0.416913i
$546$		0			0
$547$			52.5329i			0.0960382i	0.998846	+	0.0480191i	$0.0152908\pi$
$547$			52.5329i			0.0960382i	−0.998846	+	0.0480191i	$0.984709\pi$
$548$	−252.832	−	185.094i	−0.461373	−	0.337763i
$549$	247.760			0.451293
$550$	216.321	+	70.7196i	0.393311	+	0.128581i
$551$			5.82917i			0.0105793i
$552$	−915.643	+	657.695i	−1.65877	+	1.19148i
$553$		0			0
$554$	31.6606	+	10.3505i	0.0571491	+	0.0186832i
$555$			19.8082i			0.0356904i
$556$	−481.028	−	352.152i	−0.865158	−	0.633367i
$557$			783.029i			1.40580i	0.711290	+	0.702899i	$0.248111\pi$
$557$			783.029i			1.40580i	−0.711290	+	0.702899i	$0.751889\pi$
$558$	−0.0821755	−	0.0268648i	−0.000147268	−	4.81448e-5i
$559$			42.4528i			0.0759441i
$560$		0			0
$561$	−957.628			−1.70700
$562$	−47.1257	+	144.151i	−0.0838535	+	0.256496i
$563$	892.403			1.58509			0.792543	−	0.609816i	$-0.208757\pi$
$563$	892.403			1.58509			0.792543	+	0.609816i	$0.208757\pi$
$564$	287.614	−	392.872i	0.509954	−	0.696581i
$565$	−196.149			−0.347166
$566$	54.2739	−	166.016i	0.0958903	−	0.293315i
$567$		0			0
$568$	−491.926	+	353.345i	−0.866067	+	0.622085i
$569$	−297.443			−0.522747			−0.261373	−	0.965238i	$-0.584175\pi$
$569$	−297.443			−0.522747			−0.261373	+	0.965238i	$0.584175\pi$
$570$	−14.2152	+	43.4821i	−0.0249389	+	0.0762844i
$571$		−	252.746i		−	0.442638i	−0.975202	−	0.221319i	$-0.928964\pi$
$571$		−	252.746i		−	0.442638i	0.975202	−	0.221319i	$-0.0710362\pi$
$572$	137.608	−	187.968i	0.240573	−	0.328615i
$573$	480.561			0.838676
$574$		0			0
$575$	263.479			0.458225
$576$	52.7000	−	156.400i	0.0914931	−	0.271528i
$577$		−	882.716i		−	1.52984i	−0.644127	−	0.764918i	$-0.722779\pi$
$577$		−	882.716i		−	1.52984i	0.644127	−	0.764918i	$-0.277221\pi$
$578$	−25.7478	+	78.7588i	−0.0445464	+	0.136261i
$579$	−224.445			−0.387643
$580$	38.1888	−	52.1647i	0.0658428	−	0.0899391i
$581$		0			0
$582$	911.229	+	297.899i	1.56568	+	0.511853i
$583$	821.973			1.40990
$584$	248.051	+	345.336i	0.424745	+	0.591329i
$585$	−36.2496			−0.0619650
$586$	−17.0940	+	52.2880i	−0.0291706	+	0.0892288i
$587$	66.7814			0.113767			0.0568836	−	0.998381i	$-0.481884\pi$
$587$	66.7814			0.113767			0.0568836	+	0.998381i	$0.481884\pi$
$588$		0			0
$589$		−	0.0261007i		−	4.43136e-5i
$590$	184.326	−	563.828i	0.312418	−	0.955640i
$591$			678.582i			1.14819i
$592$	20.5660	−	6.51824i	0.0347398	−	0.0110105i
$593$		−	360.164i		−	0.607360i	−0.952774	−	0.303680i	$-0.901785\pi$
$593$		−	360.164i		−	0.607360i	0.952774	−	0.303680i	$-0.0982153\pi$
$594$	742.929	+	242.878i	1.25072	+	0.408886i
$595$		0			0
$596$	201.454	−	275.179i	0.338009	−	0.461710i
$597$		−	230.340i		−	0.385828i
$598$	83.8033	−	256.342i	0.140139	−	0.428666i
$599$	−198.044			−0.330624			−0.165312	−	0.986241i	$-0.552863\pi$
$599$	−198.044			−0.330624			−0.165312	+	0.986241i	$0.552863\pi$
$600$	−140.663	+	101.037i	−0.234439	+	0.168395i
$601$		−	373.907i		−	0.622141i	−0.950387	−	0.311071i	$-0.899312\pi$
$601$		−	373.907i		−	0.622141i	0.950387	−	0.311071i	$-0.100688\pi$
$602$		0			0
$603$		−	35.9728i		−	0.0596565i
$604$	−425.398	−	311.426i	−0.704302	−	0.515606i
$605$	858.746			1.41942
$606$	74.8561	−	228.974i	0.123525	−	0.377845i
$607$			231.130i			0.380774i	0.981709	+	0.190387i	$0.0609743\pi$
$607$			231.130i			0.380774i	−0.981709	+	0.190387i	$0.939026\pi$
$608$	49.8234	+	0.450416i	0.0819463	+	0.000740816i
$609$		0			0
$610$	257.775	−	788.495i	0.422581	−	1.29261i
$611$			116.477i			0.190634i
$612$	95.8719	−	130.958i	0.156653	−	0.213983i
$613$		−	513.516i		−	0.837710i	−0.908053	−	0.418855i	$-0.862431\pi$
$613$		−	513.516i		−	0.837710i	0.908053	−	0.418855i	$-0.137569\pi$
$614$	−154.123	+	471.439i	−0.251014	+	0.767815i
$615$		−	1032.75i		−	1.67927i
$616$		0			0
$617$	−1119.01			−1.81363			−0.906815	−	0.421529i	$-0.861493\pi$
$617$	−1119.01			−1.81363			−0.906815	+	0.421529i	$0.861493\pi$
$618$	−651.064	−	212.846i	−1.05350	−	0.344410i
$619$	128.204			0.207114			0.103557	−	0.994624i	$-0.466978\pi$
$619$	128.204			0.207114			0.103557	+	0.994624i	$0.466978\pi$
$620$	−0.170994	+	0.233573i	−0.000275797	+	0.000376730i
$621$	904.890			1.45715
$622$	830.802	+	271.605i	1.33569	+	0.436665i
$623$		0			0
$624$	53.5599	+	168.989i	0.0858332	+	0.270816i
$625$	−425.471			−0.680753
$626$	157.459	+	51.4766i	0.251533	+	0.0822310i
$627$		−	94.7652i		−	0.151141i
$628$	791.087	+	579.140i	1.25969	+	0.922198i
$629$	21.2160			0.0337297
$630$		0			0
$631$	313.995			0.497615			0.248808	−	0.968553i	$-0.419961\pi$
$631$	313.995			0.497615			0.248808	+	0.968553i	$0.419961\pi$
$632$	−151.710	+	108.971i	−0.240047	+	0.172423i
$633$			211.469i			0.334075i
$634$	464.862	+	151.973i	0.733221	+	0.239704i
$635$	−542.645			−0.854559
$636$	−369.491	+	504.713i	−0.580961	+	0.793573i
$637$		0			0
$638$	−41.6145	+	127.293i	−0.0652264	+	0.199518i
$639$	−195.237			−0.305535
$640$	−442.914	−	330.440i	−0.692053	−	0.516313i
$641$	−231.188			−0.360668			−0.180334	−	0.983605i	$-0.557718\pi$
$641$	−231.188			−0.360668			−0.180334	+	0.983605i	$0.557718\pi$
$642$	−691.819	−	226.169i	−1.07760	−	0.352289i
$643$	−637.869			−0.992020			−0.496010	−	0.868317i	$-0.665202\pi$
$643$	−637.869			−0.992020			−0.496010	+	0.868317i	$0.665202\pi$
$644$		0			0
$645$		−	191.532i		−	0.296949i
$646$	46.5725	+	15.2255i	0.0720937	+	0.0235689i
$647$			677.187i			1.04666i	0.852131	+	0.523329i	$0.175310\pi$
$647$			677.187i			1.04666i	−0.852131	+	0.523329i	$0.824690\pi$
$648$	−633.893	+	455.318i	−0.978230	+	0.702651i
$649$			1228.81i			1.89339i
$650$	12.8741	−	39.3799i	0.0198063	−	0.0605845i
$651$		0			0
$652$	−567.742	+	775.517i	−0.870769	+	1.18944i
$653$			1057.73i			1.61980i	0.586567	+	0.809901i	$0.300479\pi$
$653$			1057.73i			1.61980i	−0.586567	+	0.809901i	$0.699521\pi$
$654$	340.451	+	111.300i	0.520567	+	0.170184i
$655$	−489.138			−0.746775
$656$	−1072.26	+	339.845i	−1.63454	+	0.518057i
$657$			137.058i			0.208612i
$658$		0			0
$659$		−	644.502i		−	0.978000i	−0.872284	−	0.489000i	$-0.837362\pi$
$659$		−	644.502i		−	0.978000i	0.872284	−	0.489000i	$-0.162638\pi$
$660$	−620.838	+	848.045i	−0.940664	+	1.28492i
$661$	1120.14			1.69461			0.847306	−	0.531105i	$-0.178223\pi$
$661$	1120.14			1.69461			0.847306	+	0.531105i	$0.178223\pi$
$662$	145.516	+	47.5720i	0.219812	+	0.0718610i
$663$			174.330i			0.262942i
$664$	665.916	−	478.319i	1.00289	−	0.720360i
$665$		0			0
$666$	6.61007	+	2.16096i	0.00992503	+	0.00324469i
$667$			155.043i			0.232448i
$668$	172.951	−	236.245i	0.258908	−	0.353660i
$669$			393.104i			0.587600i
$670$	−114.483	−	37.4269i	−0.170871	−	0.0558611i
$671$			1718.45i			2.56103i
$672$		0			0
$673$	−307.811			−0.457371			−0.228686	−	0.973500i	$-0.573443\pi$
$673$	−307.811			−0.457371			−0.228686	+	0.973500i	$0.573443\pi$
$674$	23.7726	−	72.7168i	0.0352709	−	0.107888i
$675$	139.012			0.205943
$676$	511.237	+	374.267i	0.756267	+	0.553650i
$677$	−1015.55			−1.50007			−0.750033	−	0.661400i	$-0.769963\pi$
$677$	−1015.55			−1.50007			−0.750033	+	0.661400i	$0.769963\pi$
$678$	−96.0814	+	293.899i	−0.141713	+	0.433479i
$679$		0			0
$680$	−317.026	−	441.364i	−0.466215	−	0.649064i
$681$	−192.278			−0.282346
$682$	0.186333	−	0.569966i	0.000273216	−	0.000835727i
$683$		−	970.203i		−	1.42050i	−0.703948	−	0.710251i	$-0.748581\pi$
$683$		−	970.203i		−	1.42050i	0.703948	−	0.710251i	$-0.251419\pi$
$684$	12.9594	+	9.48732i	0.0189464	+	0.0138703i
$685$	−338.188			−0.493706
$686$		0			0
$687$	−402.680			−0.586143
$688$	−198.860	+	63.0272i	−0.289040	+	0.0916092i
$689$		−	149.635i		−	0.217178i
$690$	−378.091	+	1156.53i	−0.547958	+	1.67613i
$691$	549.161			0.794734			0.397367	−	0.917660i	$-0.369924\pi$
$691$	549.161			0.794734			0.397367	+	0.917660i	$0.369924\pi$
$692$	−119.578	−	87.5407i	−0.172800	−	0.126504i
$693$		0			0
$694$	−457.442	−	149.547i	−0.659138	−	0.215485i
$695$	−643.423			−0.925788
$696$	−59.4545	−	82.7725i	−0.0854231	−	0.118926i
$697$	−1106.15			−1.58702
$698$	−267.461	+	818.125i	−0.383182	+	1.17210i
$699$	−83.9818			−0.120146
$700$		0			0
$701$			452.665i			0.645742i	0.946443	+	0.322871i	$0.104648\pi$
$701$			452.665i			0.645742i	−0.946443	+	0.322871i	$0.895352\pi$
$702$	44.2145	−	135.246i	0.0629837	−	0.192658i
$703$			2.09950i			0.00298649i
$704$	1084.79	+	365.525i	1.54089	+	0.519212i
$705$		−	525.505i		−	0.745397i
$706$	−583.781	−	190.849i	−0.826885	−	0.270325i
$707$		0			0
$708$	−754.520	−	552.371i	−1.06571	−	0.780185i
$709$			703.414i			0.992121i	0.868288	+	0.496060i	$0.165221\pi$
$709$			703.414i			0.992121i	−0.868288	+	0.496060i	$0.834779\pi$
$710$	−203.128	+	621.340i	−0.286096	+	0.875127i
$711$	−60.2109			−0.0846848
$712$	−413.337	−	575.447i	−0.580529	−	0.808212i
$713$		−	0.694220i		−	0.000973661i
$714$		0			0
$715$		−	251.425i		−	0.351644i
$716$	561.993	−	767.665i	0.784907	−	1.07216i
$717$	−854.734			−1.19210
$718$	−286.971	+	877.802i	−0.399681	+	1.22257i
$719$			62.4878i			0.0869093i	0.999055	+	0.0434546i	$0.0138364\pi$
$719$			62.4878i			0.0869093i	−0.999055	+	0.0434546i	$0.986164\pi$
$720$	−53.8176	−	169.802i	−0.0747467	−	0.235836i
$721$		0			0
$722$	222.845	−	681.650i	0.308649	−	0.944113i
$723$		−	382.615i		−	0.529205i
$724$	944.228	+	691.252i	1.30418	+	0.954768i
$725$			23.8181i			0.0328525i
$726$	420.648	−	1286.70i	0.579405	−	1.77232i
$727$			889.995i			1.22420i	0.790779	+	0.612101i	$0.209676\pi$
$727$			889.995i			1.22420i	−0.790779	+	0.612101i	$0.790324\pi$
$728$		0			0
$729$	417.569			0.572797
$730$	436.186	+	142.598i	0.597515	+	0.195340i
$731$	−205.145			−0.280636
$732$	−1055.17	−	772.472i	−1.44149	−	1.05529i
$733$	−912.254			−1.24455			−0.622274	−	0.782800i	$-0.713791\pi$
$733$	−912.254			−1.24455			−0.622274	+	0.782800i	$0.713791\pi$
$734$	−1191.81	−	389.628i	−1.62372	−	0.530828i
$735$		0			0
$736$	1325.19	+	11.9801i	1.80053	+	0.0162773i
$737$	249.506			0.338543
$738$	−344.633	−	112.667i	−0.466983	−	0.152666i
$739$			1248.83i			1.68989i	0.534852	+	0.844946i	$0.320367\pi$
$739$			1248.83i			1.68989i	−0.534852	+	0.844946i	$0.679633\pi$
$740$	13.7545	−	18.7882i	0.0185872	−	0.0253895i
$741$	−17.2514			−0.0232813
$742$		0			0
$743$	−305.880			−0.411682			−0.205841	−	0.978585i	$-0.565993\pi$
$743$	−305.880			−0.411682			−0.205841	+	0.978585i	$0.565993\pi$
$744$	0.266214	+	0.370623i	0.000357814	+	0.000498149i
$745$		−	368.079i		−	0.494066i
$746$	−784.337	−	256.415i	−1.05139	−	0.343720i
$747$	264.290			0.353802
$748$	908.318	+	664.963i	1.21433	+	0.888988i
$749$		0			0
$750$	−286.323	+	875.820i	−0.381764	+	1.16776i
$751$	517.791			0.689468			0.344734	−	0.938700i	$-0.387969\pi$
$751$	517.791			0.689468			0.344734	+	0.938700i	$0.387969\pi$
$752$	−545.609	+	172.927i	−0.725544	+	0.229956i
$753$	412.577			0.547911
$754$	23.1729	+	7.57567i	0.0307333	+	0.0100473i
$755$	−569.012			−0.753659
$756$		0			0
$757$		−	939.898i		−	1.24161i	−0.783965	−	0.620804i	$-0.786806\pi$
$757$		−	939.898i		−	1.24161i	0.783965	−	0.620804i	$-0.213194\pi$
$758$	−621.848	−	203.294i	−0.820380	−	0.268199i
$759$		−	2520.54i		−	3.32087i
$760$	43.6766	−	31.3723i	0.0574692	−	0.0412794i
$761$		−	1127.86i		−	1.48208i	−0.671461	−	0.741039i	$-0.734333\pi$
$761$		−	1127.86i		−	1.48208i	0.671461	−	0.741039i	$-0.265667\pi$
$762$	−265.809	+	813.072i	−0.348831	+	1.06702i
$763$		0			0
$764$	−455.816	−	333.695i	−0.596618	−	0.436773i
$765$		−	175.169i		−	0.228979i
$766$	473.090	+	154.662i	0.617611	+	0.201909i
$767$	223.698			0.291653
$768$	−712.071	+	501.777i	−0.927176	+	0.653355i
$769$			300.115i			0.390267i	0.980777	+	0.195133i	$0.0625139\pi$
$769$			300.115i			0.390267i	−0.980777	+	0.195133i	$0.937486\pi$
$770$		0			0
$771$		−	356.524i		−	0.462417i
$772$	212.888	+	155.852i	0.275762	+	0.201880i
$773$	−750.240			−0.970557			−0.485278	−	0.874360i	$-0.661282\pi$
$773$	−750.240			−0.970557			−0.485278	+	0.874360i	$0.661282\pi$
$774$	−63.9151	−	20.8951i	−0.0825777	−	0.0269963i
$775$		−	0.106648i		−	0.000137610i
$776$	−657.452	−	915.304i	−0.847231	−	1.17952i
$777$		0			0
$778$	−717.194	−	234.465i	−0.921843	−	0.301369i
$779$		−	109.463i		−	0.140517i
$780$	154.382	+	113.020i	0.197925	+	0.144897i
$781$		−	1354.15i		−	1.73387i
$782$	1238.72	+	404.964i	1.58405	+	0.517856i
$783$			81.8005i			0.104471i
$784$		0			0
$785$	1058.16			1.34797
$786$	−239.599	+	732.899i	−0.304834	+	0.932442i
$787$	−289.552			−0.367919			−0.183960	−	0.982934i	$-0.558892\pi$
$787$	−289.552			−0.367919			−0.183960	+	0.982934i	$0.558892\pi$
$788$	471.198	−	643.641i	0.597967	−	0.816804i
$789$	−356.195			−0.451452
$790$	−62.6447	+	191.621i	−0.0792971	+	0.242558i
$791$		0			0
$792$	215.266	+	299.693i	0.271801	+	0.378401i
$793$	312.834			0.394494
$794$	417.473	−	1276.99i	0.525785	−	1.60830i
$795$			675.103i			0.849186i
$796$	−159.945	+	218.479i	−0.200935	+	0.274471i
$797$	1086.57			1.36332			0.681659	−	0.731670i	$-0.261259\pi$
$797$	1086.57			1.36332			0.681659	+	0.731670i	$0.261259\pi$
$798$		0			0
$799$	−562.854			−0.704448
$800$	203.579	+	1.84041i	0.254474	+	0.00230051i
$801$		−	228.385i		−	0.285124i
$802$	292.340	−	894.227i	0.364514	−	1.11500i
$803$	−950.627			−1.18384
$804$	−112.157	+	153.203i	−0.139499	+	0.190551i
$805$		0			0
$806$	−0.103759	−	0.0339208i	−0.000128733	−	4.20854e-5i
$807$	1037.61			1.28576
$808$	−229.998	+	165.205i	−0.284651	+	0.204461i
$809$	181.949			0.224906			0.112453	−	0.993657i	$-0.464129\pi$
$809$	181.949			0.224906			0.112453	+	0.993657i	$0.464129\pi$
$810$	−261.750	+	800.655i	−0.323148	+	0.988463i
$811$	1005.31			1.23960			0.619799	−	0.784760i	$-0.287214\pi$
$811$	1005.31			1.23960			0.619799	+	0.784760i	$0.287214\pi$
$812$		0			0
$813$			349.280i			0.429619i
$814$	−14.9883	+	45.8472i	−0.0184132	+	0.0563233i
$815$			1037.33i			1.27280i
$816$	−816.609	+	258.818i	−1.00075	+	0.317179i
$817$		−	20.3008i		−	0.0248480i
$818$	−126.744	−	41.4351i	−0.154944	−	0.0506541i
$819$		0			0
$820$	−717.128	+	979.573i	−0.874546	+	1.19460i
$821$		−	982.661i		−	1.19691i	−0.801158	−	0.598453i	$-0.795782\pi$
$821$		−	982.661i		−	1.19691i	0.801158	−	0.598453i	$-0.204218\pi$
$822$	−165.658	+	506.724i	−0.201531	+	0.616453i
$823$	1485.01			1.80439			0.902194	−	0.431331i	$-0.141956\pi$
$823$	1485.01			1.80439			0.902194	+	0.431331i	$0.141956\pi$
$824$	469.743	+	653.975i	0.570076	+	0.793660i
$825$		−	387.212i		−	0.469348i
$826$		0			0
$827$			708.113i			0.856243i	0.903721	+	0.428121i	$0.140824\pi$
$827$			708.113i			0.856243i	−0.903721	+	0.428121i	$0.859176\pi$
$828$	344.690	+	252.341i	0.416292	+	0.304760i
$829$	−150.033			−0.180980			−0.0904902	−	0.995897i	$-0.528843\pi$
$829$	−150.033			−0.180980			−0.0904902	+	0.995897i	$0.528843\pi$
$830$	274.973	−	841.102i	0.331293	−	1.01338i
$831$		−	56.6722i		−	0.0681976i
$832$	66.5417	−	197.479i	0.0799780	−	0.237354i
$833$		0			0
$834$	−315.174	+	964.072i	−0.377907	+	1.15596i
$835$		−	316.001i		−	0.378445i
$836$	−65.8036	+	89.8856i	−0.0787124	+	0.107519i
$837$		−	0.366270i		−	0.000437599i
$838$	271.819	−	831.456i	0.324367	−	0.992191i
$839$		−	1106.41i		−	1.31873i	−0.751824	−	0.659364i	$-0.770826\pi$
$839$		−	1106.41i		−	1.31873i	0.751824	−	0.659364i	$-0.229174\pi$
$840$		0			0
$841$	826.984			0.983335
$842$	−1337.92	−	437.392i	−1.58898	−	0.519468i
$843$	258.028			0.306083
$844$	146.841	−	200.580i	0.173983	−	0.237654i
$845$	683.830			0.809266
$846$	−175.363	−	57.3297i	−0.207285	−	0.0677656i
$847$		0			0
$848$	700.931	−	222.155i	0.826569	−	0.261975i
$849$	−297.167			−0.350020
$850$	190.296	+	62.2116i	0.223878	+	0.0731901i
$851$			55.8420i			0.0656192i
$852$	831.484	+	608.714i	0.975920	+	0.714453i
$853$	−1243.82			−1.45817			−0.729086	−	0.684423i	$-0.760054\pi$
$853$	−1243.82			−1.45817			−0.729086	+	0.684423i	$0.760054\pi$
$854$		0			0
$855$	17.3344			0.0202742
$856$	499.148	+	694.913i	0.583117	+	0.811815i
$857$		−	283.652i		−	0.330982i	−0.986211	−	0.165491i	$-0.947079\pi$
$857$		−	283.652i		−	0.330982i	0.986211	−	0.165491i	$-0.0529209\pi$
$858$	−376.723	−	123.158i	−0.439071	−	0.143541i
$859$	911.799			1.06147			0.530733	−	0.847539i	$-0.321917\pi$
$859$	911.799			1.06147			0.530733	+	0.847539i	$0.321917\pi$
$860$	−132.997	+	181.670i	−0.154648	+	0.211244i
$861$		0			0
$862$	341.647	−	1045.05i	0.396342	−	1.21235i
$863$	−873.816			−1.01253			−0.506266	−	0.862377i	$-0.668975\pi$
$863$	−873.816			−1.01253			−0.506266	+	0.862377i	$0.668975\pi$
$864$	699.169	+	6.32067i	0.809224	+	0.00731559i
$865$	−159.947			−0.184910
$866$	674.876	+	220.630i	0.779303	+	0.254769i
$867$	140.978			0.162604
$868$		0			0
$869$		−	417.620i		−	0.480575i
$870$	−104.548	−	34.1788i	−0.120170	−	0.0392860i
$871$		−	45.4211i		−	0.0521482i
$872$	−245.635	−	341.973i	−0.281692	−	0.392171i
$873$		−	363.268i		−	0.416114i
$874$	−40.0745	+	122.582i	−0.0458518	+	0.140254i
$875$		0			0
$876$	427.323	−	583.709i	0.487811	−	0.666334i
$877$		−	634.480i		−	0.723467i	−0.932282	−	0.361733i	$-0.882185\pi$
$877$		−	634.480i		−	0.723467i	0.932282	−	0.361733i	$-0.117815\pi$
$878$	−1047.12	−	342.325i	−1.19262	−	0.389892i
$879$	93.5951			0.106479
$880$	1177.74	−	373.276i	1.33834	−	0.424178i
$881$			670.044i			0.760549i	0.924874	+	0.380274i	$0.124170\pi$
$881$			670.044i			0.760549i	−0.924874	+	0.380274i	$0.875830\pi$
$882$		0			0
$883$			875.514i			0.991522i	0.868459	+	0.495761i	$0.165111\pi$
$883$			875.514i			0.991522i	−0.868459	+	0.495761i	$0.834889\pi$
$884$	121.053	−	165.354i	0.136937	−	0.187052i
$885$	−1009.25			−1.14039
$886$	513.707	+	167.941i	0.579805	+	0.189550i
$887$			986.289i			1.11194i	0.831203	+	0.555969i	$0.187653\pi$
$887$			986.289i			1.11194i	−0.831203	+	0.555969i	$0.812347\pi$
$888$	−21.4138	−	29.8123i	−0.0241146	−	0.0335724i
$889$		0			0
$890$	−726.833	−	237.616i	−0.816667	−	0.266985i
$891$		−	1744.95i		−	1.95842i
$892$	272.966	−	372.863i	0.306016	−	0.418008i
$893$		−	55.6991i		−	0.0623730i
$894$	−551.511	−	180.300i	−0.616903	−	0.201678i
$895$		−	1026.83i		−	1.14729i
$896$		0			0
$897$	−458.850			−0.511538
$898$	−283.017	+	865.707i	−0.315163	+	0.964039i
$899$	0.0627563			6.98068e−5
$900$	52.9522	+	38.7653i	0.0588358	+	0.0430726i
$901$	723.085			0.802536
$902$	781.457	−	2390.36i	0.866360	−	2.65007i
$903$		0			0
$904$	295.213	−	212.048i	0.326564	−	0.234567i
$905$	1263.00			1.39558
$906$	−278.725	+	852.579i	−0.307643	+	0.941037i
$907$		−	866.709i		−	0.955578i	−0.878475	−	0.477789i	$-0.841438\pi$
$907$		−	866.709i		−	0.955578i	0.878475	−	0.477789i	$-0.158562\pi$
$908$	182.377	+	133.515i	0.200856	+	0.147043i
$909$	−91.2820			−0.100420
$910$		0			0
$911$	−128.713			−0.141288			−0.0706438	−	0.997502i	$-0.522505\pi$
$911$	−128.713			−0.141288			−0.0706438	+	0.997502i	$0.522505\pi$
$912$	−25.6122	−	80.8102i	−0.0280836	−	0.0886076i
$913$			1833.10i			2.00778i
$914$	104.802	−	320.573i	0.114662	−	0.350736i
$915$	−1411.40			−1.54251
$916$	381.945	+	279.615i	0.416971	+	0.305257i
$917$		0			0
$918$	653.550	+	213.659i	0.711929	+	0.232743i
$919$	860.175			0.935990			0.467995	−	0.883731i	$-0.344977\pi$
$919$	860.175			0.935990			0.467995	+	0.883731i	$0.344977\pi$
$920$	1161.70	−	834.434i	1.26272	−	0.906994i
$921$	843.871			0.916255
$922$	−164.728	+	503.880i	−0.178664	+	0.546508i
$923$	−246.515			−0.267081
$924$		0			0
$925$			8.57859i			0.00927415i
$926$	−60.5770	+	185.296i	−0.0654180	+	0.200104i
$927$			259.551i			0.279990i
$928$	−1.08298	+	119.795i	−0.00116700	+	0.129089i
$929$			233.279i			0.251107i	0.992087	+	0.125554i	$0.0400707\pi$
$929$			233.279i			0.251107i	−0.992087	+	0.125554i	$0.959929\pi$
$930$	0.468124	+	0.153039i	0.000503360	+	0.000164558i
$931$		0			0
$932$	79.6575	+	58.3158i	0.0854694	+	0.0625706i
$933$		−	1487.13i		−	1.59392i
$934$	−46.1129	+	141.053i	−0.0493714	+	0.151020i
$935$	1214.97			1.29943
$936$	54.5574	−	39.1879i	0.0582878	−	0.0418674i
$937$			1426.29i			1.52219i	0.648641	+	0.761095i	$0.275338\pi$
$937$			1426.29i			1.52219i	−0.648641	+	0.761095i	$0.724662\pi$
$938$		0			0
$939$		−	281.851i		−	0.300161i
$940$	−364.903	+	498.446i	−0.388195	+	0.530262i
$941$	−1270.85			−1.35053			−0.675265	−	0.737575i	$-0.735971\pi$
$941$	−1270.85			−1.35053			−0.675265	+	0.737575i	$0.735971\pi$
$942$	518.328	−	1585.49i	0.550242	−	1.68311i
$943$		−	2911.47i		−	3.08745i
$944$	332.111	+	1047.86i	0.351812	+	1.11002i
$945$		0			0
$946$	144.928	−	443.312i	0.153200	−	0.468618i
$947$			1632.17i			1.72352i	0.507318	+	0.861759i	$0.330637\pi$
$947$			1632.17i			1.72352i	−0.507318	+	0.861759i	$0.669363\pi$
$948$	256.429	+	187.727i	0.270495	+	0.198025i
$949$			173.056i			0.182356i
$950$	−6.15635	+	18.8314i	−0.00648037	+	0.0198225i
$951$		−	832.098i		−	0.874972i
$952$		0			0
$953$	95.9158			0.100646			0.0503231	−	0.998733i	$-0.483975\pi$
$953$	95.9158			0.100646			0.0503231	+	0.998733i	$0.483975\pi$
$954$	225.285	+	73.6500i	0.236148	+	0.0772013i
$955$	−609.700			−0.638429
$956$	810.723	+	593.515i	0.848036	+	0.620832i
$957$	227.853			0.238090
$958$	−1043.14	−	341.024i	−1.08888	−	0.355975i
$959$		0			0
$960$	−300.213	+	890.957i	−0.312722	+	0.928080i
$961$	961.000			1.00000
$962$	8.34620	+	2.72854i	0.00867589	+	0.00283632i
$963$			275.799i			0.286395i
$964$	−265.683	+	362.914i	−0.275604	+	0.376466i
$965$	284.759			0.295087
$966$		0			0
$967$	1419.97			1.46843			0.734216	−	0.678916i	$-0.237550\pi$
$967$	1419.97			1.46843			0.734216	+	0.678916i	$0.237550\pi$
$968$	−1292.46	+	928.355i	−1.33518	+	0.959045i
$969$		−	83.3644i		−	0.0860313i
$970$	−1156.10	−	377.951i	−1.19185	−	0.389641i
$971$	−659.635			−0.679336			−0.339668	−	0.940545i	$-0.610315\pi$
$971$	−659.635			−0.679336			−0.339668	+	0.940545i	$0.610315\pi$
$972$	436.750	+	319.737i	0.449332	+	0.328948i
$973$		0			0
$974$	−352.919	+	1079.53i	−0.362340	+	1.10834i
$975$	−70.4897			−0.0722971
$976$	464.446	+	1465.39i	0.475867	+	1.50143i
$977$	−1914.30			−1.95937			−0.979683	−	0.200550i	$-0.935727\pi$
$977$	−1914.30			−1.95937			−0.979683	+	0.200550i	$0.935727\pi$
$978$	1554.28	+	508.126i	1.58925	+	0.519556i
$979$	1584.07			1.61804
$980$		0			0
$981$		−	135.723i		−	0.138352i
$982$	149.799	+	48.9723i	0.152545	+	0.0498699i
$983$		−	223.613i		−	0.227480i	−0.993511	−	0.113740i	$-0.963717\pi$
$983$		−	223.613i		−	0.227480i	0.993511	−	0.113740i	$-0.0362831\pi$
$984$	1116.47	+	1554.34i	1.13462	+	1.57962i
$985$		−	860.934i		−	0.874045i
$986$	−36.6080	+	111.979i	−0.0371278	+	0.113569i
$987$		0			0
$988$	16.3631	+	11.9792i	0.0165619	+	0.0121247i
$989$		−	539.956i		−	0.545961i
$990$	378.535	+	123.751i	0.382359	+	0.125001i
$991$	−1472.74			−1.48612			−0.743058	−	0.669227i	$-0.766626\pi$
$991$	−1472.74			−1.48612			−0.743058	+	0.669227i	$0.766626\pi$
$992$	0.00484914	−	0.536394i	4.88825e−6	−	0.000540720i
$993$		−	260.472i		−	0.262308i
$994$		0			0
$995$			292.237i			0.293706i
$996$	−1125.57	−	824.011i	−1.13009	−	0.827320i
$997$	−106.896			−0.107218			−0.0536088	−	0.998562i	$-0.517072\pi$
$997$	−106.896			−0.107218			−0.0536088	+	0.998562i	$0.517072\pi$
$998$	−638.618	−	208.777i	−0.639898	−	0.209195i
$999$			29.4622i			0.0294917i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.h.a.293.12		28
4.3	odd	2		1568.3.h.a.881.7		28
7.2	even	3		56.3.j.a.45.14	yes	28
7.3	odd	6		56.3.j.a.5.5	✓	28
7.4	even	3		392.3.j.e.117.5		28
7.5	odd	6		392.3.j.e.325.14		28
7.6	odd	2	inner	392.3.h.a.293.11		28
8.3	odd	2		1568.3.h.a.881.22		28
8.5	even	2	inner	392.3.h.a.293.9		28
28.3	even	6		224.3.n.a.145.4		28
28.23	odd	6		224.3.n.a.17.11		28
28.27	even	2		1568.3.h.a.881.21		28
56.3	even	6		224.3.n.a.145.11		28
56.5	odd	6		392.3.j.e.325.5		28
56.13	odd	2	inner	392.3.h.a.293.10		28
56.27	even	2		1568.3.h.a.881.8		28
56.37	even	6		56.3.j.a.45.5	yes	28
56.45	odd	6		56.3.j.a.5.14	yes	28
56.51	odd	6		224.3.n.a.17.4		28
56.53	even	6		392.3.j.e.117.14		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.j.a.5.5	✓	28	7.3	odd	6
56.3.j.a.5.14	yes	28	56.45	odd	6
56.3.j.a.45.5	yes	28	56.37	even	6
56.3.j.a.45.14	yes	28	7.2	even	3
224.3.n.a.17.4		28	56.51	odd	6
224.3.n.a.17.11		28	28.23	odd	6
224.3.n.a.145.4		28	28.3	even	6
224.3.n.a.145.11		28	56.3	even	6
392.3.h.a.293.9		28	8.5	even	2	inner
392.3.h.a.293.10		28	56.13	odd	2	inner
392.3.h.a.293.11		28	7.6	odd	2	inner
392.3.h.a.293.12		28	1.1	even	1	trivial
392.3.j.e.117.5		28	7.4	even	3
392.3.j.e.117.14		28	56.53	even	6
392.3.j.e.325.5		28	56.5	odd	6
392.3.j.e.325.14		28	7.5	odd	6
1568.3.h.a.881.7		28	4.3	odd	2
1568.3.h.a.881.8		28	56.27	even	2
1568.3.h.a.881.21		28	28.27	even	2
1568.3.h.a.881.22		28	8.3	odd	2

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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.621472 + 1.90099i) q^{2} +3.40276 q^{3} +(-3.22755 - 2.36283i) q^{4} -4.31716 q^{5} +(-2.11472 + 6.46862i) q^{6} +(6.49755 - 4.66711i) q^{8} +2.57876 q^{9} +O(q^{10})\)	\(q+(-0.621472 + 1.90099i) q^{2} +3.40276 q^{3} +(-3.22755 - 2.36283i) q^{4} -4.31716 q^{5} +(-2.11472 + 6.46862i) q^{6} +(6.49755 - 4.66711i) q^{8} +2.57876 q^{9} +(2.68300 - 8.20689i) q^{10} +17.8862i q^{11} +(-10.9826 - 8.04013i) q^{12} +3.25607 q^{13} -14.6903 q^{15} +(4.83409 + 15.2523i) q^{16} +15.7343i q^{17} +(-1.60263 + 4.90220i) q^{18} -1.55704 q^{19} +(13.9338 + 10.2007i) q^{20} +(-34.0014 - 11.1157i) q^{22} -41.4139 q^{23} +(22.1096 - 15.8810i) q^{24} -6.36211 q^{25} +(-2.02356 + 6.18976i) q^{26} -21.8499 q^{27} -3.74374i q^{29} +(9.12958 - 27.9261i) q^{30} +0.0167630i q^{31} +(-31.9987 - 0.289277i) q^{32} +60.8622i q^{33} +(-29.9109 - 9.77845i) q^{34} +(-8.32306 - 6.09316i) q^{36} -1.34839i q^{37} +(0.967659 - 2.95993i) q^{38} +11.0796 q^{39} +(-28.0510 + 20.1487i) q^{40} +70.3018i q^{41} +13.0380i q^{43} +(42.2619 - 57.7284i) q^{44} -11.1329 q^{45} +(25.7376 - 78.7274i) q^{46} +35.7723i q^{47} +(16.4493 + 51.8998i) q^{48} +(3.95387 - 12.0943i) q^{50} +53.5402i q^{51} +(-10.5091 - 7.69353i) q^{52} -45.9558i q^{53} +(13.5791 - 41.5365i) q^{54} -77.2174i q^{55} -5.29824 q^{57} +(7.11682 + 2.32663i) q^{58} +68.7017 q^{59} +(47.4135 + 34.7105i) q^{60} +96.0771 q^{61} +(-0.0318663 - 0.0104177i) q^{62} +(20.4362 - 60.6495i) q^{64} -14.0570 q^{65} +(-115.699 - 37.8242i) q^{66} -13.9497i q^{67} +(37.1775 - 50.7833i) q^{68} -140.921 q^{69} -75.7095 q^{71} +(16.7556 - 12.0353i) q^{72} +53.1487i q^{73} +(2.56328 + 0.837986i) q^{74} -21.6487 q^{75} +(5.02543 + 3.67902i) q^{76} +(-6.88567 + 21.0623i) q^{78} -23.3488 q^{79} +(-20.8696 - 65.8465i) q^{80} -97.5588 q^{81} +(-133.643 - 43.6906i) q^{82} +102.487 q^{83} -67.9277i q^{85} +(-24.7852 - 8.10278i) q^{86} -12.7390i q^{87} +(83.4766 + 116.216i) q^{88} -88.5638i q^{89} +(6.91880 - 21.1636i) q^{90} +(133.665 + 97.8538i) q^{92} +0.0570404i q^{93} +(-68.0029 - 22.2315i) q^{94} +6.72201 q^{95} +(-108.884 - 0.984338i) q^{96} -140.869i q^{97} +46.1241i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} + 8 q^{4} - 20 q^{8} + 64 q^{9}+O(q^{10}) \) 28 * q + 4 * q^2 + 8 * q^4 - 20 * q^8 + 64 * q^9	\( 28 q + 4 q^{2} + 8 q^{4} - 20 q^{8} + 64 q^{9} + 28 q^{15} - 32 q^{16} + 84 q^{18} - 92 q^{22} - 60 q^{23} + 64 q^{25} - 44 q^{30} - 176 q^{32} + 256 q^{36} + 40 q^{39} + 84 q^{44} - 136 q^{46} + 400 q^{50} + 124 q^{57} + 44 q^{58} + 124 q^{60} - 520 q^{64} + 104 q^{65} - 136 q^{71} - 192 q^{72} + 276 q^{74} - 956 q^{78} + 324 q^{79} + 36 q^{81} - 336 q^{86} - 100 q^{88} + 1020 q^{92} - 580 q^{95}+O(q^{100}) \) 28 * q + 4 * q^2 + 8 * q^4 - 20 * q^8 + 64 * q^9 + 28 * q^15 - 32 * q^16 + 84 * q^18 - 92 * q^22 - 60 * q^23 + 64 * q^25 - 44 * q^30 - 176 * q^32 + 256 * q^36 + 40 * q^39 + 84 * q^44 - 136 * q^46 + 400 * q^50 + 124 * q^57 + 44 * q^58 + 124 * q^60 - 520 * q^64 + 104 * q^65 - 136 * q^71 - 192 * q^72 + 276 * q^74 - 956 * q^78 + 324 * q^79 + 36 * q^81 - 336 * q^86 - 100 * q^88 + 1020 * q^92 - 580 * q^95

Introduction

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