LMFDB - Embedded newform 63.6.e.f.46.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,6,Mod(37,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("63.37");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	63.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.1041806482$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 187x^{10} + 25399x^{8} + 1518438x^{6} + 66232188x^{4} + 1297462320x^{2} + 18380851776 $ x^12 + 187x^10 + 25399x^8 + 1518438x^6 + 66232188x^4 + 1297462320*x^2 + 18380851776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.6
Root			$5.31117 + 9.19921i$ of defining polynomial
Character	$\chi$	$=$	63.46
Dual form			63.6.e.f.37.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.31117 + 9.19921i) q^{2} +(-40.4170 + 70.0043i) q^{4} +(-33.7376 - 58.4352i) q^{5} +(-120.281 - 48.3679i) q^{7} -518.731 q^{8} +O(q^{10})$	\(q+(5.31117 + 9.19921i) q^{2} +(-40.4170 + 70.0043i) q^{4} +(-33.7376 - 58.4352i) q^{5} +(-120.281 - 48.3679i) q^{7} -518.731 q^{8} +(358.372 - 620.718i) q^{10} +(-261.323 + 452.625i) q^{11} +76.6331 q^{13} +(-193.887 - 1363.38i) q^{14} +(-1461.72 - 2531.78i) q^{16} +(-634.801 + 1099.51i) q^{17} +(946.362 + 1639.15i) q^{19} +5454.28 q^{20} -5551.73 q^{22} +(575.022 + 995.967i) q^{23} +(-713.945 + 1236.59i) q^{25} +(407.011 + 704.964i) q^{26} +(8247.36 - 6465.31i) q^{28} -3850.03 q^{29} +(5206.86 - 9018.55i) q^{31} +(7227.21 - 12517.9i) q^{32} -13486.1 q^{34} +(1231.60 + 8660.46i) q^{35} +(2801.14 + 4851.71i) q^{37} +(-10052.6 + 17411.6i) q^{38} +(17500.7 + 30312.1i) q^{40} -14232.7 q^{41} -14827.9 q^{43} +(-21123.8 - 36587.5i) q^{44} +(-6108.08 + 10579.5i) q^{46} +(5774.88 + 10002.4i) q^{47} +(12128.1 + 11635.5i) q^{49} -15167.5 q^{50} +(-3097.28 + 5364.64i) q^{52} +(2338.86 - 4051.02i) q^{53} +35265.6 q^{55} +(62393.5 + 25089.9i) q^{56} +(-20448.2 - 35417.3i) q^{58} +(-14551.0 + 25203.0i) q^{59} +(-5921.45 - 10256.2i) q^{61} +110618. q^{62} +59989.5 q^{64} +(-2585.41 - 4478.06i) q^{65} +(18106.3 - 31361.0i) q^{67} +(-51313.5 - 88877.6i) q^{68} +(-73128.1 + 57326.9i) q^{70} -13477.6 q^{71} +(-1304.23 + 2258.98i) q^{73} +(-29754.6 + 51536.5i) q^{74} -152996. q^{76} +(53324.8 - 41802.6i) q^{77} +(39160.2 + 67827.4i) q^{79} +(-98629.9 + 170832. i) q^{80} +(-75592.3 - 130930. i) q^{82} +16746.0 q^{83} +85666.5 q^{85} +(-78753.5 - 136405. i) q^{86} +(135557. - 234791. i) q^{88} +(-18384.2 - 31842.4i) q^{89} +(-9217.51 - 3706.58i) q^{91} -92962.7 q^{92} +(-61342.7 + 106249. i) q^{94} +(63855.9 - 110602. i) q^{95} +36133.4 q^{97} +(-42623.0 + 173367. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 182 q^{4} + 142 q^{7}+O(q^{10}) $ 12 * q - 182 * q^4 + 142 * q^7	$ 12 q - 182 q^{4} + 142 q^{7} + 686 q^{10} + 308 q^{13} - 1898 q^{16} + 9422 q^{19} - 18292 q^{22} - 7526 q^{25} + 37074 q^{28} + 23422 q^{31} - 55608 q^{34} - 18182 q^{37} + 69258 q^{40} - 87372 q^{43} + 25332 q^{46} + 30354 q^{49} + 34272 q^{52} - 96320 q^{55} - 89782 q^{58} - 16156 q^{61} + 380580 q^{64} + 144650 q^{67} - 187262 q^{70} - 100058 q^{73} - 685440 q^{76} + 101994 q^{79} + 75712 q^{82} + 602352 q^{85} + 752310 q^{88} - 282306 q^{91} - 120456 q^{94} - 866096 q^{97}+O(q^{100}) $ 12 * q - 182 * q^4 + 142 * q^7 + 686 * q^10 + 308 * q^13 - 1898 * q^16 + 9422 * q^19 - 18292 * q^22 - 7526 * q^25 + 37074 * q^28 + 23422 * q^31 - 55608 * q^34 - 18182 * q^37 + 69258 * q^40 - 87372 * q^43 + 25332 * q^46 + 30354 * q^49 + 34272 * q^52 - 96320 * q^55 - 89782 * q^58 - 16156 * q^61 + 380580 * q^64 + 144650 * q^67 - 187262 * q^70 - 100058 * q^73 - 685440 * q^76 + 101994 * q^79 + 75712 * q^82 + 602352 * q^85 + 752310 * q^88 - 282306 * q^91 - 120456 * q^94 - 866096 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	5.31117	+	9.19921i	0.938891	+	1.62621i	0.767545	+	0.640995i	$0.221478\pi$
$2$	5.31117	+	9.19921i	0.938891	+	1.62621i	0.171346	+	0.985211i	$0.445189\pi$
$3$		0			0
$3$		0			0
$4$	−40.4170	+	70.0043i	−1.26303	+	2.18763i
$5$	−33.7376	−	58.4352i	−0.603516	−	1.04532i	−0.992284	−	0.123984i	$-0.960433\pi$
$5$	−33.7376	−	58.4352i	−0.603516	−	1.04532i	0.388769	−	0.921335i	$-0.372901\pi$
$6$		0			0
$7$	−120.281	−	48.3679i	−0.927796	−	0.373089i
$7$	−120.281	−	48.3679i	−0.927796	−	0.373089i
$8$	−518.731			−2.86561
$9$		0			0
$10$	358.372	−	620.718i	1.13327	−	1.96288i
$11$	−261.323	+	452.625i	−0.651173	+	1.12787i	0.331665	+	0.943397i	$0.392390\pi$
$11$	−261.323	+	452.625i	−0.651173	+	1.12787i	−0.982839	+	0.184468i	$0.940944\pi$
$12$		0			0
$13$	76.6331			0.125764			0.0628822	−	0.998021i	$-0.479971\pi$
$13$	76.6331			0.125764			0.0628822	+	0.998021i	$0.479971\pi$
$14$	−193.887	−	1363.38i	−0.264379	−	1.85908i
$15$		0			0
$16$	−1461.72	−	2531.78i	−1.42746	−	2.47244i
$17$	−634.801	+	1099.51i	−0.532740	+	0.922733i	0.466529	+	0.884506i	$0.345504\pi$
$17$	−634.801	+	1099.51i	−0.532740	+	0.922733i	−0.999269	+	0.0382267i	$0.987829\pi$
$18$		0			0
$19$	946.362	+	1639.15i	0.601414	+	1.04168i	0.992607	+	0.121371i	$0.0387290\pi$
$19$	946.362	+	1639.15i	0.601414	+	1.04168i	−0.391193	+	0.920309i	$0.627938\pi$
$20$	5454.28			3.04904
$21$		0			0
$22$	−5551.73			−2.44552
$23$	575.022	+	995.967i	0.226655	+	0.392578i	0.956815	−	0.290699i	$-0.0938877\pi$
$23$	575.022	+	995.967i	0.226655	+	0.392578i	−0.730160	+	0.683276i	$0.760554\pi$
$24$		0			0
$25$	−713.945	+	1236.59i	−0.228462	+	0.395708i
$26$	407.011	+	704.964i	0.118079	+	0.204519i
$27$		0			0
$28$	8247.36	−	6465.31i	1.98802	−	1.55845i
$29$	−3850.03			−0.850099			−0.425049	−	0.905170i	$-0.639743\pi$
$29$	−3850.03			−0.850099			−0.425049	+	0.905170i	$0.639743\pi$
$30$		0			0
$31$	5206.86	−	9018.55i	0.973132	−	1.68551i	0.287165	−	0.957881i	$-0.407287\pi$
$31$	5206.86	−	9018.55i	0.973132	−	1.68551i	0.685967	−	0.727633i	$-0.259379\pi$
$32$	7227.21	−	12517.9i	1.24766	−	2.16101i
$33$		0			0
$34$	−13486.1			−2.00074
$35$	1231.60	+	8660.46i	0.169942	+	1.19501i
$36$		0			0
$37$	2801.14	+	4851.71i	0.336380	+	0.582627i	0.983749	−	0.179550i	$-0.0574641\pi$
$37$	2801.14	+	4851.71i	0.336380	+	0.582627i	−0.647369	+	0.762177i	$0.724131\pi$
$38$	−10052.6	+	17411.6i	−1.12932	+	1.95605i
$39$		0			0
$40$	17500.7	+	30312.1i	1.72944	+	2.99548i
$41$	−14232.7			−1.32229			−0.661147	−	0.750256i	$-0.729930\pi$
$41$	−14232.7			−1.32229			−0.661147	+	0.750256i	$0.729930\pi$
$42$		0			0
$43$	−14827.9			−1.22295			−0.611475	−	0.791264i	$-0.709424\pi$
$43$	−14827.9			−1.22295			−0.611475	+	0.791264i	$0.709424\pi$
$44$	−21123.8	−	36587.5i	−1.64490	−	2.84906i
$45$		0			0
$46$	−6108.08	+	10579.5i	−0.425608	+	0.737175i
$47$	5774.88	+	10002.4i	0.381328	+	0.660479i	0.991252	−	0.131981i	$-0.0421337\pi$
$47$	5774.88	+	10002.4i	0.381328	+	0.660479i	−0.609925	+	0.792459i	$0.708800\pi$
$48$		0			0
$49$	12128.1	+	11635.5i	0.721610	+	0.692300i
$50$	−15167.5			−0.858004
$51$		0			0
$52$	−3097.28	+	5364.64i	−0.158844	+	0.275127i
$53$	2338.86	−	4051.02i	0.114371	−	0.198096i	−0.803157	−	0.595767i	$-0.796848\pi$
$53$	2338.86	−	4051.02i	0.114371	−	0.198096i	0.917528	+	0.397671i	$0.130182\pi$
$54$		0			0
$55$	35265.6			1.57197
$56$	62393.5	+	25089.9i	2.65870	+	1.06913i
$57$		0			0
$58$	−20448.2	−	35417.3i	−0.798150	−	1.38244i
$59$	−14551.0	+	25203.0i	−0.544205	+	0.942590i	0.454452	+	0.890771i	$0.349835\pi$
$59$	−14551.0	+	25203.0i	−0.544205	+	0.942590i	−0.998656	+	0.0518189i	$0.983498\pi$
$60$		0			0
$61$	−5921.45	−	10256.2i	−0.203753	−	0.352910i	0.745982	−	0.665966i	$-0.231980\pi$
$61$	−5921.45	−	10256.2i	−0.203753	−	0.352910i	−0.949735	+	0.313056i	$0.898647\pi$
$62$	110618.			3.65466
$63$		0			0
$64$	59989.5			1.83073
$65$	−2585.41	−	4478.06i	−0.0759008	−	0.131464i
$66$		0			0
$67$	18106.3	−	31361.0i	0.492768	−	0.853499i	−0.507197	−	0.861830i	$-0.669319\pi$
$67$	18106.3	−	31361.0i	0.492768	−	0.853499i	0.999965	+	0.00833093i	$0.00265185\pi$
$68$	−51313.5	−	88877.6i	−1.34573	−	2.33088i
$69$		0			0
$70$	−73128.1	+	57326.9i	−1.78377	+	1.39834i
$71$	−13477.6			−0.317298			−0.158649	−	0.987335i	$-0.550714\pi$
$71$	−13477.6			−0.317298			−0.158649	+	0.987335i	$0.550714\pi$
$72$		0			0
$73$	−1304.23	+	2258.98i	−0.0286448	+	0.0496142i	−0.879992	−	0.474988i	$-0.842452\pi$
$73$	−1304.23	+	2258.98i	−0.0286448	+	0.0496142i	0.851348	+	0.524602i	$0.175786\pi$
$74$	−29754.6	+	51536.5i	−0.631648	+	1.09405i
$75$		0			0
$76$	−152996.			−3.03842
$77$	53324.8	−	41802.6i	1.02495	−	0.803483i
$78$		0			0
$79$	39160.2	+	67827.4i	0.705955	+	1.22275i	0.966346	+	0.257246i	$0.0828151\pi$
$79$	39160.2	+	67827.4i	0.705955	+	1.22275i	−0.260391	+	0.965503i	$0.583852\pi$
$80$	−98629.9	+	170832.i	−1.72299	+	2.98431i
$81$		0			0
$82$	−75592.3	−	130930.i	−1.24149	−	2.15032i
$83$	16746.0			0.266819			0.133410	−	0.991061i	$-0.457407\pi$
$83$	16746.0			0.266819			0.133410	+	0.991061i	$0.457407\pi$
$84$		0			0
$85$	85666.5			1.28607
$86$	−78753.5	−	136405.i	−1.14822	−	1.98877i
$87$		0			0
$88$	135557.	−	234791.i	1.86601	−	3.23202i
$89$	−18384.2	−	31842.4i	−0.246020	−	0.426119i	0.716398	−	0.697692i	$-0.245790\pi$
$89$	−18384.2	−	31842.4i	−0.246020	−	0.426119i	−0.962418	+	0.271573i	$0.912456\pi$
$90$		0			0
$91$	−9217.51	−	3706.58i	−0.116684	−	0.0469213i
$92$	−92962.7			−1.14509
$93$		0			0
$94$	−61342.7	+	106249.i	−0.716050	+	1.24023i
$95$	63855.9	−	110602.i	0.725925	−	1.25734i
$96$		0			0
$97$	36133.4			0.389924			0.194962	−	0.980811i	$-0.437542\pi$
$97$	36133.4			0.389924			0.194962	+	0.980811i	$0.437542\pi$
$98$	−42623.0	+	173367.i	−0.448310	+	1.82348i
$99$		0			0
$100$	−57711.0	−	99958.4i	−0.577110	−	0.999584i
$101$	49337.6	−	85455.2i	0.481254	−	0.833557i	−0.518514	−	0.855069i	$-0.673515\pi$
$101$	49337.6	−	85455.2i	0.481254	−	0.833557i	0.999769	+	0.0215120i	$0.00684802\pi$
$102$		0			0
$103$	−3636.75	−	6299.03i	−0.0337769	−	0.0585034i	0.848643	−	0.528966i	$-0.177420\pi$
$103$	−3636.75	−	6299.03i	−0.0337769	−	0.0585034i	−0.882420	+	0.470463i	$0.844087\pi$
$104$	−39751.9			−0.360392
$105$		0			0
$106$	49688.3			0.429526
$107$	15476.8	+	26806.5i	0.130683	+	0.226350i	0.923940	−	0.382537i	$-0.124950\pi$
$107$	15476.8	+	26806.5i	0.130683	+	0.226350i	−0.793257	+	0.608887i	$0.791616\pi$
$108$		0			0
$109$	−56915.6	+	98580.8i	−0.458844	+	0.794742i	−0.998900	−	0.0468875i	$-0.985070\pi$
$109$	−56915.6	+	98580.8i	−0.458844	+	0.794742i	0.540056	+	0.841629i	$0.318403\pi$
$110$	187302.	+	324416.i	1.47591	+	2.55635i
$111$		0			0
$112$	53360.9	+	375226.i	0.401955	+	2.82649i
$113$	−894.559			−0.00659041			−0.00329521	−	0.999995i	$-0.501049\pi$
$113$	−894.559			−0.00659041			−0.00329521	+	0.999995i	$0.501049\pi$
$114$		0			0
$115$	38799.7	−	67203.0i	0.273579	−	0.473854i
$116$	155607.	−	269519.i	1.07370	−	1.85970i
$117$		0			0
$118$	−309131.			−2.04379
$119$	129535.	−	101546.i	0.838535	−	0.657348i
$120$		0			0
$121$	−56054.3	−	97088.9i	−0.348053	−	0.602846i
$122$	62899.6	−	108945.i	0.382603	−	0.662687i
$123$		0			0
$124$	420891.	+	729005.i	2.45819	+	4.25771i
$125$	−114513.			−0.655509
$126$		0			0
$127$	72325.9			0.397910			0.198955	−	0.980009i	$-0.436245\pi$
$127$	72325.9			0.397910			0.198955	+	0.980009i	$0.436245\pi$
$128$	87343.4	+	151283.i	0.471200	+	0.816142i
$129$		0			0
$130$	27463.1	−	47567.5i	0.142525	−	0.246861i
$131$	35084.0	+	60767.3i	0.178620	+	0.309380i	0.941408	−	0.337269i	$-0.109503\pi$
$131$	35084.0	+	60767.3i	0.178620	+	0.309380i	−0.762788	+	0.646649i	$0.776170\pi$
$132$		0			0
$133$	−34547.4	−	242932.i	−0.169350	−	1.19085i
$134$	384662.			1.85062
$135$		0			0
$136$	329291.	−	570348.i	1.52662	−	2.64419i
$137$	−186004.	+	322169.i	−0.846685	+	1.46650i	0.0374656	+	0.999298i	$0.488072\pi$
$137$	−186004.	+	322169.i	−0.846685	+	1.46650i	−0.884150	+	0.467203i	$0.845262\pi$
$138$		0			0
$139$	5566.26			0.0244358			0.0122179	−	0.999925i	$-0.496111\pi$
$139$	5566.26			0.0244358			0.0122179	+	0.999925i	$0.496111\pi$
$140$	−656047.	−	263812.i	−2.82888	−	1.13756i
$141$		0			0
$142$	−71581.9	−	123984.i	−0.297908	−	0.515992i
$143$	−20026.0	+	34686.1i	−0.0818944	+	0.141845i
$144$		0			0
$145$	129891.	+	224977.i	0.513048	+	0.888625i
$146$	−27707.8			−0.107577
$147$		0			0
$148$	−452854.			−1.69943
$149$	166957.	+	289178.i	0.616083	+	1.06709i	0.990193	+	0.139703i	$0.0446148\pi$
$149$	166957.	+	289178.i	0.616083	+	1.06709i	−0.374110	+	0.927384i	$0.622052\pi$
$150$		0			0
$151$	−37578.6	+	65088.1i	−0.134122	+	0.232305i	−0.925262	−	0.379330i	$-0.876155\pi$
$151$	−37578.6	+	65088.1i	−0.134122	+	0.232305i	0.791140	+	0.611635i	$0.209488\pi$
$152$	−490907.	−	850277.i	−1.72342	−	2.98505i
$153$		0			0
$154$	667768.	+	268525.i	2.26894	+	0.912396i
$155$	−702667.			−2.34920
$156$		0			0
$157$	−237792.	+	411868.i	−0.769926	+	1.33355i	0.167677	+	0.985842i	$0.446373\pi$
$157$	−237792.	+	411868.i	−0.769926	+	1.33355i	−0.937603	+	0.347708i	$0.886960\pi$
$158$	−415972.	+	720485.i	−1.32563	+	2.29606i
$159$		0			0
$160$	−975314.			−3.01193
$161$	−20991.4	−	147609.i	−0.0638231	−	0.448794i
$162$		0			0
$163$	−119611.	−	207173.i	−0.352617	−	0.610751i	0.634090	−	0.773259i	$-0.281375\pi$
$163$	−119611.	−	207173.i	−0.352617	−	0.610751i	−0.986707	+	0.162508i	$0.948042\pi$
$164$	575243.	−	996351.i	1.67010	−	2.89270i
$165$		0			0
$166$	88941.0	+	154050.i	0.250514	+	0.433903i
$167$	−111308.			−0.308842			−0.154421	−	0.988005i	$-0.549351\pi$
$167$	−111308.			−0.308842			−0.154421	+	0.988005i	$0.549351\pi$
$168$		0			0
$169$	−365420.			−0.984183
$170$	454989.	+	788064.i	1.20748	+	2.09141i
$171$		0			0
$172$	599299.	−	1.03802e6i	1.54462	−	2.67537i
$173$	349497.	+	605346.i	0.887826	+	1.53776i	0.842440	+	0.538791i	$0.181119\pi$
$173$	349497.	+	605346.i	0.887826	+	1.53776i	0.0453864	+	0.998970i	$0.485548\pi$
$174$		0			0
$175$	145685.	−	114206.i	0.359601	−	0.281900i
$176$	1.52793e6			3.71810
$177$		0			0
$178$	195284.	−	338241.i	0.461972	−	0.800159i
$179$	−51954.4	+	89987.7i	−0.121196	+	0.209918i	−0.920240	−	0.391355i	$-0.872006\pi$
$179$	−51954.4	+	89987.7i	−0.121196	+	0.209918i	0.799043	+	0.601273i	$0.205340\pi$
$180$		0			0
$181$	−415260.			−0.942159			−0.471079	−	0.882091i	$-0.656135\pi$
$181$	−415260.			−0.942159			−0.471079	+	0.882091i	$0.656135\pi$
$182$	−14858.1	−	104480.i	−0.0332495	−	0.233806i
$183$		0			0
$184$	−298282.	−	516639.i	−0.649504	−	1.12497i
$185$	189007.	−	327370.i	0.406021	−	0.703249i
$186$		0			0
$187$	−331777.	−	574654.i	−0.693812	−	1.20172i
$188$	−933613.			−1.92651
$189$		0			0
$190$	1.35660e6			2.72626
$191$	−285058.	−	493735.i	−0.565392	−	0.979287i	−0.997013	−	0.0772324i	$-0.975392\pi$
$191$	−285058.	−	493735.i	−0.565392	−	0.979287i	0.431621	−	0.902055i	$-0.357942\pi$
$192$		0			0
$193$	−148854.	+	257823.i	−0.287653	+	0.498229i	−0.973249	−	0.229753i	$-0.926208\pi$
$193$	−148854.	+	257823.i	−0.287653	+	0.498229i	0.685596	+	0.727982i	$0.259542\pi$
$194$	191911.	+	332399.i	0.366096	+	0.634097i
$195$		0			0
$196$	−1.30472e6	+	378747.i	−2.42591	+	0.704221i
$197$	410678.			0.753938			0.376969	−	0.926226i	$-0.376966\pi$
$197$	410678.			0.753938			0.376969	+	0.926226i	$0.376966\pi$
$198$		0			0
$199$	349672.	−	605650.i	0.625934	−	1.08415i	−0.362425	−	0.932013i	$-0.618051\pi$
$199$	349672.	−	605650.i	0.625934	−	1.08415i	0.988359	−	0.152137i	$-0.0486155\pi$
$200$	370345.	−	641457.i	0.654684	−	1.13395i
$201$		0			0
$202$	1.04816e6			1.80738
$203$	463086.	+	186218.i	0.788718	+	0.317162i
$204$		0			0
$205$	480177.	+	831691.i	0.798025	+	1.38222i
$206$	38630.8	−	66910.4i	0.0634257	−	0.109857i
$207$		0			0
$208$	−112016.	−	194018.i	−0.179524	−	0.310945i
$209$	−989226.			−1.56650
$210$		0			0
$211$	−58292.9			−0.0901384			−0.0450692	−	0.998984i	$-0.514351\pi$
$211$	−58292.9			−0.0901384			−0.0450692	+	0.998984i	$0.514351\pi$
$212$	189059.	+	327460.i	0.288907	+	0.500402i
$213$		0			0
$214$	−164399.	+	284748.i	−0.245395	+	0.425036i
$215$	500257.	+	866471.i	0.738069	+	1.27837i
$216$		0			0
$217$	−1.06250e6	+	832916.i	−1.53171	+	1.20075i
$218$	−1.20915e6			−1.72322
$219$		0			0
$220$	−1.42533e6	+	2.46875e6i	−1.98545	+	3.43890i
$221$	−48646.7	+	84258.6i	−0.0669997	+	0.116047i
$222$		0			0
$223$	25758.5			0.0346864			0.0173432	−	0.999850i	$-0.494479\pi$
$223$	25758.5			0.0346864			0.0173432	+	0.999850i	$0.494479\pi$
$224$	−1.47476e6	+	1.15610e6i	−1.96382	+	1.53949i
$225$		0			0
$226$	−4751.15	−	8229.23i	−0.00618768	−	0.0107174i
$227$	491123.	−	850649.i	0.632594	−	1.09569i	−0.354425	−	0.935084i	$-0.615323\pi$
$227$	491123.	−	850649.i	0.632594	−	1.09569i	0.987019	−	0.160601i	$-0.0513432\pi$
$228$		0			0
$229$	−259982.	−	450301.i	−0.327607	−	0.567433i	0.654429	−	0.756123i	$-0.272909\pi$
$229$	−259982.	−	450301.i	−0.327607	−	0.567433i	−0.982037	+	0.188691i	$0.939576\pi$
$230$	824286.			1.02744
$231$		0			0
$232$	1.99713e6			2.43605
$233$	−609703.	−	1.05604e6i	−0.735747	−	1.27435i	−0.954395	−	0.298547i	$-0.903498\pi$
$233$	−609703.	−	1.05604e6i	−0.735747	−	1.27435i	0.218648	−	0.975804i	$-0.429835\pi$
$234$		0			0
$235$	389660.	−	674912.i	0.460274	−	0.797218i
$236$	−1.17621e6	−	2.03726e6i	−1.37469	−	2.38104i
$237$		0			0
$238$	1.62213e6	+	652296.i	1.85628	+	0.746453i
$239$	−909357.			−1.02977			−0.514884	−	0.857260i	$-0.672165\pi$
$239$	−909357.			−1.02977			−0.514884	+	0.857260i	$0.672165\pi$
$240$		0			0
$241$	320798.	−	555638.i	0.355786	−	0.616240i	−0.631466	−	0.775404i	$-0.717546\pi$
$241$	320798.	−	555638.i	0.355786	−	0.616240i	0.987252	+	0.159164i	$0.0508798\pi$
$242$	595428.	−	1.03131e6i	0.653568	−	1.13201i
$243$		0			0
$244$	957308.			1.02938
$245$	270749.	−	1.10126e6i	0.288172	−	1.17213i
$246$		0			0
$247$	72522.6	+	125613.i	0.0756365	+	0.131006i
$248$	−2.70096e6	+	4.67820e6i	−2.78862	+	4.83003i
$249$		0			0
$250$	−608196.	−	1.05343e6i	−0.615451	−	1.06599i
$251$	1.92052e6			1.92413			0.962066	−	0.272816i	$-0.0879550\pi$
$251$	1.92052e6			1.92413			0.962066	+	0.272816i	$0.0879550\pi$
$252$		0			0
$253$	−601067.			−0.590366
$254$	384135.	+	665342.i	0.373594	+	0.647084i
$255$		0			0
$256$	32041.3	−	55497.2i	0.0305570	−	0.0529263i
$257$	493184.	+	854221.i	0.465775	+	0.806747i	0.999236	−	0.0390781i	$-0.0124421\pi$
$257$	493184.	+	854221.i	0.465775	+	0.806747i	−0.533461	+	0.845825i	$0.679109\pi$
$258$		0			0
$259$	−102257.	−	719054.i	−0.0947202	−	0.666058i
$260$	417978.			0.383460
$261$		0			0
$262$	−372674.	+	645491.i	−0.335410	+	0.580948i
$263$	−424509.	+	735272.i	−0.378441	+	0.655479i	−0.990836	−	0.135073i	$-0.956873\pi$
$263$	−424509.	+	735272.i	−0.378441	+	0.655479i	0.612395	+	0.790552i	$0.290206\pi$
$264$		0			0
$265$	−315630.			−0.276098
$266$	2.05130e6	−	1.60806e6i	1.77756	−	1.39347i
$267$		0			0
$268$	1.46360e6	+	2.53504e6i	1.24476	+	2.15599i
$269$	866792.	−	1.50133e6i	0.730355	−	1.26501i	−0.226377	−	0.974040i	$-0.572688\pi$
$269$	866792.	−	1.50133e6i	0.730355	−	1.26501i	0.956732	−	0.290972i	$-0.0939787\pi$
$270$		0			0
$271$	527825.	+	914221.i	0.436583	+	0.756184i	0.997423	−	0.0717397i	$-0.0228551\pi$
$271$	527825.	+	914221.i	0.436583	+	0.756184i	−0.560840	+	0.827924i	$0.689522\pi$
$272$	3.71161e6			3.04187
$273$		0			0
$274$	−3.95160e6			−3.17978
$275$	−373141.	−	646299.i	−0.297537	−	0.515349i
$276$		0			0
$277$	−812463.	+	1.40723e6i	−0.636216	+	1.10196i	0.350041	+	0.936735i	$0.386168\pi$
$277$	−812463.	+	1.40723e6i	−0.636216	+	1.10196i	−0.986256	+	0.165223i	$0.947166\pi$
$278$	29563.3	+	51205.2i	0.0229425	+	0.0397377i
$279$		0			0
$280$	−638872.	−	4.49245e6i	−0.486988	−	3.42443i
$281$	−1.56484e6			−1.18224			−0.591118	−	0.806585i	$-0.701313\pi$
$281$	−1.56484e6			−1.18224			−0.591118	+	0.806585i	$0.701313\pi$
$282$		0			0
$283$	347107.	−	601206.i	0.257630	−	0.446229i	−0.707976	−	0.706236i	$-0.750392\pi$
$283$	347107.	−	601206.i	0.257630	−	0.446229i	0.965607	+	0.260007i	$0.0837250\pi$
$284$	544725.	−	943491.i	0.400757	−	0.694132i
$285$		0			0
$286$	−425446.			−0.307560
$287$	1.71193e6	+	688406.i	1.22682	+	0.493333i
$288$		0			0
$289$	−96015.8	−	166304.i	−0.0676236	−	0.117127i
$290$	−1.37974e6	+	2.38978e6i	−0.963392	+	1.66864i
$291$		0			0
$292$	−105426.	−	182603.i	−0.0723585	−	0.125329i
$293$	999262.			0.680002			0.340001	−	0.940425i	$-0.389573\pi$
$293$	999262.			0.680002			0.340001	+	0.940425i	$0.389573\pi$
$294$		0			0
$295$	1.96366e6			1.31374
$296$	−1.45304e6	−	2.51673e6i	−0.963934	−	1.66958i
$297$		0			0
$298$	−1.77347e6	+	3.07175e6i	−1.15687	+	2.00376i
$299$	44065.7	+	76324.0i	0.0285051	+	0.0493723i
$300$		0			0
$301$	1.78352e6	+	717195.i	1.13465	+	0.456269i
$302$	−798346.			−0.503702
$303$		0			0
$304$	2.76664e6	−	4.79196e6i	1.71699	−	2.97392i
$305$	−399550.	+	692041.i	−0.245936	+	0.425973i
$306$		0			0
$307$	800764.			0.484907			0.242453	−	0.970163i	$-0.422048\pi$
$307$	800764.			0.484907			0.242453	+	0.970163i	$0.422048\pi$
$308$	771134.	+	5.42250e6i	0.463184	+	3.25704i
$309$		0			0
$310$	−3.73198e6	−	6.46398e6i	−2.20564	−	3.82029i
$311$	291472.	−	504844.i	0.170882	−	0.295976i	−0.767847	−	0.640634i	$-0.778672\pi$
$311$	291472.	−	504844.i	0.170882	−	0.295976i	0.938728	+	0.344658i	$0.112005\pi$
$312$		0			0
$313$	999546.	+	1.73126e6i	0.576689	+	0.998855i	0.995856	+	0.0909459i	$0.0289890\pi$
$313$	999546.	+	1.73126e6i	0.576689	+	0.998855i	−0.419166	+	0.907909i	$0.637678\pi$
$314$	−5.05182e6			−2.89150
$315$		0			0
$316$	−6.33095e6			−3.56657
$317$	−901038.	−	1.56064e6i	−0.503610	−	0.872279i	−0.999991	−	0.00417407i	$-0.998671\pi$
$317$	−901038.	−	1.56064e6i	−0.503610	−	0.872279i	0.496381	−	0.868105i	$-0.334662\pi$
$318$		0			0
$319$	1.00610e6	−	1.74262e6i	0.553561	−	0.958797i
$320$	−2.02390e6	−	3.50549e6i	−1.10488	−	1.91370i
$321$		0			0
$322$	1.24639e6	−	977079.i	0.669909	−	0.525158i
$323$	−2.40301e6			−1.28159
$324$		0			0
$325$	−54711.8	+	94763.6i	−0.0287324	+	0.0497660i
$326$	1.27055e6	−	2.20066e6i	0.662138	−	1.14686i
$327$		0			0
$328$	7.38295e6			3.78918
$329$	−210815.	−	1.48242e6i	−0.107377	−	0.755058i
$330$		0			0
$331$	−51885.5	−	89868.4i	−0.0260301	−	0.0450855i	0.852717	−	0.522373i	$-0.174953\pi$
$331$	−51885.5	−	89868.4i	−0.0260301	−	0.0450855i	−0.878747	+	0.477288i	$0.841620\pi$
$332$	−676824.	+	1.17229e6i	−0.337001	+	0.583702i
$333$		0			0
$334$	−591176.	−	1.02395e6i	−0.289969	−	0.502240i
$335$	−2.44345e6			−1.18957
$336$		0			0
$337$	961978.			0.461414			0.230707	−	0.973023i	$-0.425896\pi$
$337$	961978.			0.461414			0.230707	+	0.973023i	$0.425896\pi$
$338$	−1.94081e6	−	3.36158e6i	−0.924040	−	1.60048i
$339$		0			0
$340$	−3.46238e6	+	5.99702e6i	−1.62434	+	2.81344i
$341$	2.72135e6	+	4.71351e6i	1.26735	+	2.19512i
$342$		0			0
$343$	−895997.	−	1.98614e6i	−0.411217	−	0.911537i
$344$	7.69169e6			3.50450
$345$		0			0
$346$	−3.71247e6	+	6.43019e6i	−1.66714	+	2.88758i
$347$	−1.21674e6	+	2.10746e6i	−0.542468	+	0.939582i	0.456294	+	0.889829i	$0.349177\pi$
$347$	−1.21674e6	+	2.10746e6i	−0.542468	+	0.939582i	−0.998762	+	0.0497528i	$0.984157\pi$
$348$		0			0
$349$	−3.42269e6			−1.50419			−0.752096	−	0.659053i	$-0.770957\pi$
$349$	−3.42269e6			−1.50419			−0.752096	+	0.659053i	$0.770957\pi$
$350$	1.82437e6	+	733621.i	0.796053	+	0.320112i
$351$		0			0
$352$	3.77728e6	+	6.54244e6i	1.62488	+	2.81438i
$353$	−1.92748e6	+	3.33850e6i	−0.823292	+	1.42598i	0.0799253	+	0.996801i	$0.474532\pi$
$353$	−1.92748e6	+	3.33850e6i	−0.823292	+	1.42598i	−0.903218	+	0.429183i	$0.858802\pi$
$354$		0			0
$355$	454702.	+	787567.i	0.191494	+	0.331678i
$356$	2.97214e6			1.24292
$357$		0			0
$358$	−1.10375e6			−0.455161
$359$	1.24184e6	+	2.15094e6i	0.508547	+	0.880829i	0.999951	+	0.00989749i	$0.00315052\pi$
$359$	1.24184e6	+	2.15094e6i	0.508547	+	0.880829i	−0.491404	+	0.870932i	$0.663516\pi$
$360$		0			0
$361$	−553154.	+	958091.i	−0.223397	+	0.386936i
$362$	−2.20552e6	−	3.82007e6i	−0.884584	−	1.53214i
$363$		0			0
$364$	632020.	−	495456.i	0.250022	−	0.195998i
$365$	176005.			0.0691503
$366$		0			0
$367$	2.03612e6	−	3.52666e6i	0.789111	−	1.36678i	−0.137401	−	0.990516i	$-0.543875\pi$
$367$	2.03612e6	−	3.52666e6i	0.789111	−	1.36678i	0.926512	−	0.376265i	$-0.122792\pi$
$368$	1.68105e6	−	2.91166e6i	0.647083	−	1.12078i
$369$		0			0
$370$	4.01539e6			1.52484
$371$	−477260.	+	374136.i	−0.180020	+	0.141122i
$372$		0			0
$373$	2.34636e6	+	4.06402e6i	0.873218	+	1.51246i	0.858649	+	0.512565i	$0.171305\pi$
$373$	2.34636e6	+	4.06402e6i	0.873218	+	1.51246i	0.0145699	+	0.999894i	$0.495362\pi$
$374$	3.52424e6	−	6.10417e6i	1.30283	−	2.25656i
$375$		0			0
$376$	−2.99561e6	−	5.18854e6i	−1.09274	−	1.89267i
$377$	−295040.			−0.106912
$378$		0			0
$379$	5.04599e6			1.80446			0.902232	−	0.431251i	$-0.141928\pi$
$379$	5.04599e6			1.80446			0.902232	+	0.431251i	$0.141928\pi$
$380$	5.16173e6	+	8.94037e6i	1.83373	+	3.17612i
$381$		0			0
$382$	3.02798e6	−	5.24461e6i	1.06168	−	1.83889i
$383$	−826418.	−	1.43140e6i	−0.287874	−	0.498613i	0.685428	−	0.728141i	$-0.259615\pi$
$383$	−826418.	−	1.43140e6i	−0.287874	−	0.498613i	−0.973302	+	0.229528i	$0.926282\pi$
$384$		0			0
$385$	−4.24179e6	−	1.70572e6i	−1.45847	−	0.586485i
$386$	−3.16236e6			−1.08030
$387$		0			0
$388$	−1.46040e6	+	2.52950e6i	−0.492486	+	0.853011i
$389$	−1.45727e6	+	2.52407e6i	−0.488278	+	0.845722i	−0.999909	−	0.0134832i	$-0.995708\pi$
$389$	−1.45727e6	+	2.52407e6i	−0.488278	+	0.845722i	0.511631	+	0.859205i	$0.329041\pi$
$390$		0			0
$391$	−1.46010e6			−0.482992
$392$	−6.29122e6	−	6.03569e6i	−2.06785	−	1.98386i
$393$		0			0
$394$	2.18118e6	+	3.77791e6i	0.707865	+	1.22606i
$395$	2.64234e6	−	4.57666e6i	0.852109	−	1.47590i
$396$		0			0
$397$	237471.	+	411312.i	0.0756197	+	0.130977i	0.901356	−	0.433080i	$-0.142573\pi$
$397$	237471.	+	411312.i	0.0756197	+	0.130977i	−0.825736	+	0.564057i	$0.809240\pi$
$398$	7.42867e6			2.35073
$399$		0			0
$400$	4.17436e6			1.30449
$401$	−24440.9	−	42332.8i	−0.00759025	−	0.0131467i	0.862205	−	0.506559i	$-0.169083\pi$
$401$	−24440.9	−	42332.8i	−0.00759025	−	0.0131467i	−0.869796	+	0.493412i	$0.835749\pi$
$402$		0			0
$403$	399018.	−	691119.i	0.122385	−	0.211978i
$404$	3.98816e6	+	6.90769e6i	1.21568	+	2.10562i
$405$		0			0
$406$	746470.	+	5.24906e6i	0.224749	+	1.58040i
$407$	−2.92801e6			−0.876166
$408$		0			0
$409$	−1.86947e6	+	3.23802e6i	−0.552599	+	0.957130i	0.445487	+	0.895289i	$0.353031\pi$
$409$	−1.86947e6	+	3.23802e6i	−0.552599	+	0.957130i	−0.998086	+	0.0618416i	$0.980303\pi$
$410$	−5.10060e6	+	8.83450e6i	−1.49852	+	2.59551i
$411$		0			0
$412$	587946.			0.170645
$413$	2.96923e6	−	2.32765e6i	0.856581	−	0.671495i
$414$		0			0
$415$	−564970.	−	978557.i	−0.161029	−	0.278911i
$416$	553843.	−	959285.i	0.156911	−	0.271778i
$417$		0			0
$418$	−5.25395e6	−	9.10010e6i	−1.47077	−	2.54745i
$419$	−681425.			−0.189619			−0.0948097	−	0.995495i	$-0.530224\pi$
$419$	−681425.			−0.189619			−0.0948097	+	0.995495i	$0.530224\pi$
$420$		0			0
$421$	1.54803e6			0.425670			0.212835	−	0.977088i	$-0.431730\pi$
$421$	1.54803e6			0.425670			0.212835	+	0.977088i	$0.431730\pi$
$422$	−309604.	−	536249.i	−0.0846301	−	0.146584i
$423$		0			0
$424$	−1.21324e6	+	2.10139e6i	−0.327742	+	0.567665i
$425$	−906425.	−	1.56997e6i	−0.243422	−	0.421619i
$426$		0			0
$427$	216165.	+	1.52004e6i	0.0573741	+	0.403446i
$428$	−2.50210e6			−0.660229
$429$		0			0
$430$	−5.31390e6	+	9.20394e6i	−1.38593	+	2.40051i
$431$	3.18855e6	−	5.52273e6i	0.826799	−	1.43206i	−0.0737367	−	0.997278i	$-0.523492\pi$
$431$	3.18855e6	−	5.52273e6i	0.826799	−	1.43206i	0.900536	−	0.434781i	$-0.143174\pi$
$432$		0			0
$433$	1.32669e6			0.340056			0.170028	−	0.985439i	$-0.445614\pi$
$433$	1.32669e6			0.340056			0.170028	+	0.985439i	$0.445614\pi$
$434$	−1.33053e7	−	5.35036e6i	−3.39078	−	1.36351i
$435$		0			0
$436$	−4.60072e6	−	7.96868e6i	−1.15907	−	2.00757i
$437$	−1.08836e6	+	1.88509e6i	−0.272627	+	0.472203i
$438$		0			0
$439$	−1.92664e6	−	3.33704e6i	−0.477133	−	0.826419i	0.522523	−	0.852625i	$-0.324991\pi$
$439$	−1.92664e6	−	3.33704e6i	−0.477133	−	0.826419i	−0.999657	+	0.0262059i	$0.991657\pi$
$440$	−1.82934e7			−4.50466
$441$		0			0
$442$	−1.03348e6			−0.251622
$443$	645522.	+	1.11808e6i	0.156279	+	0.270684i	0.933524	−	0.358515i	$-0.116717\pi$
$443$	645522.	+	1.11808e6i	0.156279	+	0.270684i	−0.777245	+	0.629198i	$0.783383\pi$
$444$		0			0
$445$	−1.24048e6	+	2.14857e6i	−0.296954	+	0.514339i
$446$	136808.	+	236958.i	0.0325667	+	0.0564072i
$447$		0			0
$448$	−7.21560e6	−	2.90156e6i	−1.69855	−	0.683026i
$449$	7.49006e6			1.75335			0.876677	−	0.481080i	$-0.159755\pi$
$449$	7.49006e6			1.75335			0.876677	+	0.481080i	$0.159755\pi$
$450$		0			0
$451$	3.71934e6	−	6.44209e6i	0.861042	−	1.49137i
$452$	36155.4	−	62622.9i	0.00832390	−	0.0144174i
$453$		0			0
$454$	1.04337e7			2.37575
$455$	94381.7	+	663678.i	0.0213727	+	0.150289i
$456$		0			0
$457$	−249662.	−	432427.i	−0.0559193	−	0.0968550i	0.836711	−	0.547645i	$-0.184476\pi$
$457$	−249662.	−	432427.i	−0.0559193	−	0.0968550i	−0.892630	+	0.450790i	$0.851142\pi$
$458$	2.76161e6	−	4.78325e6i	0.615175	−	1.06551i
$459$		0			0
$460$	3.13633e6	+	5.43229e6i	0.691079	+	1.19698i
$461$	−5.34926e6			−1.17231			−0.586153	−	0.810200i	$-0.699358\pi$
$461$	−5.34926e6			−1.17231			−0.586153	+	0.810200i	$0.699358\pi$
$462$		0			0
$463$	−6.52516e6			−1.41462			−0.707308	−	0.706906i	$-0.750091\pi$
$463$	−6.52516e6			−1.41462			−0.707308	+	0.706906i	$0.750091\pi$
$464$	5.62768e6	+	9.74743e6i	1.21348	+	2.10182i
$465$		0			0
$466$	6.47647e6	−	1.12176e7i	1.38157	−	2.39295i
$467$	1.60324e6	+	2.77690e6i	0.340179	+	0.589207i	0.984466	−	0.175577i	$-0.0561791\pi$
$467$	1.60324e6	+	2.77690e6i	0.340179	+	0.589207i	−0.644287	+	0.764784i	$0.722846\pi$
$468$		0			0
$469$	−3.69471e6	+	2.89637e6i	−0.775619	+	0.608027i
$470$	8.27821e6			1.72859
$471$		0			0
$472$	7.54804e6	−	1.30736e7i	1.55948	−	2.70110i
$473$	3.87488e6	−	6.71149e6i	0.796352	−	1.37932i
$474$		0			0
$475$	−2.70260e6			−0.549602
$476$	1.87322e6	+	1.31722e7i	0.378941	+	2.66466i
$477$		0			0
$478$	−4.82975e6	−	8.36536e6i	−0.966840	−	1.67462i
$479$	4.43405e6	−	7.68001e6i	0.883003	−	1.52941i	0.0350175	−	0.999387i	$-0.488851\pi$
$479$	4.43405e6	−	7.68001e6i	0.883003	−	1.52941i	0.847985	−	0.530019i	$-0.177815\pi$
$480$		0			0
$481$	214660.	+	371801.i	0.0423046	+	0.0732737i
$482$	6.81525e6			1.33618
$483$		0			0
$484$	9.06218e6			1.75841
$485$	−1.21905e6	−	2.11146e6i	−0.235325	−	0.407595i
$486$		0			0
$487$	−2.92361e6	+	5.06384e6i	−0.558595	+	0.967515i	0.439019	+	0.898478i	$0.355326\pi$
$487$	−2.92361e6	+	5.06384e6i	−0.558595	+	0.967515i	−0.997614	+	0.0690371i	$0.978007\pi$
$488$	3.07164e6	+	5.32023e6i	0.583876	+	1.01130i
$489$		0			0
$490$	1.15687e7	−	3.35829e6i	2.17668	−	0.631871i
$491$	−114241.			−0.0213854			−0.0106927	−	0.999943i	$-0.503404\pi$
$491$	−114241.			−0.0213854			−0.0106927	+	0.999943i	$0.503404\pi$
$492$		0			0
$493$	2.44400e6	−	4.23314e6i	0.452881	−	0.784414i
$494$	−770360.	+	1.33430e6i	−0.142029	+	0.246001i
$495$		0			0
$496$	−3.04439e7			−5.55644
$497$	1.62110e6	+	651884.i	0.294388	+	0.118380i
$498$		0			0
$499$	4.67241e6	+	8.09285e6i	0.840020	+	1.45496i	0.889877	+	0.456200i	$0.150790\pi$
$499$	4.67241e6	+	8.09285e6i	0.840020	+	1.45496i	−0.0498573	+	0.998756i	$0.515877\pi$
$500$	4.62826e6	−	8.01638e6i	0.827928	−	1.43401i
$501$		0			0
$502$	1.02002e7	+	1.76673e7i	1.80655	+	3.12904i
$503$	−892118.			−0.157218			−0.0786091	−	0.996906i	$-0.525048\pi$
$503$	−892118.			−0.157218			−0.0786091	+	0.996906i	$0.525048\pi$
$504$		0			0
$505$	−6.65812e6			−1.16178
$506$	−3.19237e6	−	5.52934e6i	−0.554289	−	0.960057i
$507$		0			0
$508$	−2.92320e6	+	5.06313e6i	−0.502573	+	0.870481i
$509$	−3.42011e6	−	5.92381e6i	−0.585122	−	1.01346i	−0.994860	−	0.101257i	$-0.967713\pi$
$509$	−3.42011e6	−	5.92381e6i	−0.585122	−	1.01346i	0.409739	−	0.912203i	$-0.365620\pi$
$510$		0			0
$511$	266136.	−	208631.i	0.0450870	−	0.0353448i
$512$	6.27068e6			1.05716
$513$		0			0
$514$	−5.23877e6	+	9.07382e6i	−0.874624	+	1.51489i
$515$	−245390.	+	425028.i	−0.0407698	+	0.0706154i
$516$		0			0
$517$	−6.03644e6			−0.993241
$518$	6.07163e6	−	4.75970e6i	0.994216	−	0.779391i
$519$		0			0
$520$	1.34113e6	+	2.32291e6i	0.217502	+	0.376725i
$521$	−4.45943e6	+	7.72397e6i	−0.719756	+	1.24665i	0.241340	+	0.970441i	$0.422413\pi$
$521$	−4.45943e6	+	7.72397e6i	−0.719756	+	1.24665i	−0.961096	+	0.276214i	$0.910920\pi$
$522$		0			0
$523$	−305911.	−	529854.i	−0.0489037	−	0.0847036i	0.840537	−	0.541754i	$-0.182239\pi$
$523$	−305911.	−	529854.i	−0.0489037	−	0.0847036i	−0.889441	+	0.457050i	$0.848906\pi$
$524$	−5.67196e6			−0.902413
$525$		0			0
$526$	−9.01856e6			−1.42126
$527$	6.61064e6	+	1.14500e7i	1.03685	+	1.79588i
$528$		0			0
$529$	2.55687e6	−	4.42863e6i	0.397255	−	0.688066i
$530$	−1.67636e6	−	2.90354e6i	−0.259226	−	0.448992i
$531$		0			0
$532$	1.84026e7	+	7.40012e6i	2.81903	+	1.13360i
$533$	−1.09070e6			−0.166298
$534$		0			0
$535$	1.04430e6	−	1.80877e6i	0.157739	−	0.273212i
$536$	−9.39229e6	+	1.62679e7i	−1.41208	+	2.44580i
$537$		0			0
$538$	1.84147e7			2.74289
$539$	−8.43587e6	+	2.44886e6i	−1.25071	+	0.363071i
$540$		0			0
$541$	122172.	+	211607.i	0.0179464	+	0.0310840i	0.874859	−	0.484377i	$-0.160954\pi$
$541$	122172.	+	211607.i	0.0179464	+	0.0310840i	−0.856913	+	0.515461i	$0.827621\pi$
$542$	−5.60674e6	+	9.71116e6i	−0.819808	+	1.41995i
$543$		0			0
$544$	9.17568e6	+	1.58927e7i	1.32936	+	2.30251i
$545$	7.68078e6			1.10768
$546$		0			0
$547$	−7.55551e6			−1.07968			−0.539840	−	0.841767i	$-0.681515\pi$
$547$	−7.55551e6			−1.07968			−0.539840	+	0.841767i	$0.681515\pi$
$548$	−1.50355e7	−	2.60422e7i	−2.13878	−	3.70447i
$549$		0			0
$550$	3.96363e6	−	6.86520e6i	0.558709	−	0.967713i
$551$	−3.64353e6	−	6.31077e6i	−0.511261	−	0.885530i
$552$		0			0
$553$	−1.42956e6	−	1.00525e7i	−0.198788	−	1.39785i
$554$	−1.72605e7			−2.38935
$555$		0			0
$556$	−224972.	+	389662.i	−0.0308632	+	0.0534566i
$557$	−1.28638e6	+	2.22808e6i	−0.175684	+	0.304293i	−0.940398	−	0.340077i	$-0.889547\pi$
$557$	−1.28638e6	+	2.22808e6i	−0.175684	+	0.304293i	0.764714	+	0.644370i	$0.222880\pi$
$558$		0			0
$559$	−1.13631e6			−0.153804
$560$	2.01261e7	−	1.57773e7i	2.71200	−	2.12600i
$561$		0			0
$562$	−8.31113e6	−	1.43953e7i	−1.10999	−	1.92256i
$563$	−5.53466e6	+	9.58632e6i	−0.735903	+	1.27462i	0.218424	+	0.975854i	$0.429909\pi$
$563$	−5.53466e6	+	9.58632e6i	−0.735903	+	1.27462i	−0.954326	+	0.298767i	$0.903425\pi$
$564$		0			0
$565$	30180.2	+	52273.7i	0.00397742	+	0.00688909i
$566$	7.37416e6			0.967546
$567$		0			0
$568$	6.99126e6			0.909253
$569$	−1.55605e6	−	2.69515e6i	−0.201485	−	0.348982i	0.747522	−	0.664237i	$-0.231243\pi$
$569$	−1.55605e6	−	2.69515e6i	−0.201485	−	0.348982i	−0.949007	+	0.315255i	$0.897910\pi$
$570$		0			0
$571$	−2.86862e6	+	4.96859e6i	−0.368199	+	0.637739i	−0.989284	−	0.146004i	$-0.953359\pi$
$571$	−2.86862e6	+	4.96859e6i	−0.368199	+	0.637739i	0.621085	+	0.783743i	$0.286692\pi$
$572$	−1.61878e6	−	2.80381e6i	−0.206870	−	0.358310i
$573$		0			0
$574$	2.75953e6	+	1.94046e7i	0.349587	+	2.45825i
$575$	−1.64214e6			−0.207128
$576$		0			0
$577$	5.56528e6	−	9.63935e6i	0.695901	−	1.20534i	−0.273975	−	0.961737i	$-0.588338\pi$
$577$	5.56528e6	−	9.63935e6i	0.695901	−	1.20534i	0.969876	−	0.243599i	$-0.0783282\pi$
$578$	1.01991e6	−	1.76654e6i	0.126982	−	0.219940i
$579$		0			0
$580$	−2.09992e7			−2.59198
$581$	−2.01423e6	−	809970.i	−0.247554	−	0.0995472i
$582$		0			0
$583$	1.22240e6	+	2.11725e6i	0.148950	+	0.257989i
$584$	676542.	−	1.17180e6i	0.0820848	−	0.142175i
$585$		0			0
$586$	5.30725e6	+	9.19242e6i	0.638448	+	1.10582i
$587$	7.71211e6			0.923800			0.461900	−	0.886932i	$-0.347168\pi$
$587$	7.71211e6			0.923800			0.461900	+	0.886932i	$0.347168\pi$
$588$		0			0
$589$	1.97103e7			2.34102
$590$	1.04293e7	+	1.80641e7i	1.23346	+	2.13642i
$591$		0			0
$592$	8.18897e6	−	1.41837e7i	0.960340	−	1.66336i
$593$	−4.16650e6	−	7.21660e6i	−0.486558	−	0.842744i	0.513322	−	0.858196i	$-0.328415\pi$
$593$	−4.16650e6	−	7.21660e6i	−0.486558	−	0.842744i	−0.999881	+	0.0154520i	$0.995081\pi$
$594$		0			0
$595$	−1.03041e7	−	4.14351e6i	−1.19321	−	0.479817i
$596$	−2.69916e7			−3.11253
$597$		0			0
$598$	−468081.	+	810739.i	−0.0535264	+	0.0927104i
$599$	−2.66790e6	+	4.62094e6i	−0.303811	+	0.526216i	−0.976996	−	0.213258i	$-0.931592\pi$
$599$	−2.66790e6	+	4.62094e6i	−0.303811	+	0.526216i	0.673185	+	0.739474i	$0.264926\pi$
$600$		0			0
$601$	−7.53972e6			−0.851470			−0.425735	−	0.904848i	$-0.639984\pi$
$601$	−7.53972e6			−0.851470			−0.425735	+	0.904848i	$0.639984\pi$
$602$	2.87493e6	+	2.02161e7i	0.323323	+	2.27356i
$603$		0			0
$604$	−3.03763e6	−	5.26133e6i	−0.338799	−	0.586818i
$605$	−3.78227e6	+	6.55108e6i	−0.420111	+	0.727654i
$606$		0			0
$607$	4.84283e6	+	8.38802e6i	0.533491	+	0.924034i	0.999235	+	0.0391140i	$0.0124536\pi$
$607$	4.84283e6	+	8.38802e6i	0.533491	+	0.924034i	−0.465744	+	0.884920i	$0.654213\pi$
$608$	2.73582e7			3.00144
$609$		0			0
$610$	−8.48831e6			−0.923627
$611$	442547.	+	766513.i	0.0479574	+	0.0830647i
$612$		0			0
$613$	−6.83805e6	+	1.18438e7i	−0.734989	+	1.27304i	0.219739	+	0.975559i	$0.429479\pi$
$613$	−6.83805e6	+	1.18438e7i	−0.734989	+	1.27304i	−0.954728	+	0.297480i	$0.903854\pi$
$614$	4.25299e6	+	7.36639e6i	0.455275	+	0.788559i
$615$		0			0
$616$	−2.76612e7	+	2.16843e7i	−2.93711	+	2.30247i
$617$	1.53796e7			1.62642			0.813211	−	0.581969i	$-0.197717\pi$
$617$	1.53796e7			1.62642			0.813211	+	0.581969i	$0.197717\pi$
$618$		0			0
$619$	−2.70804e6	+	4.69046e6i	−0.284072	+	0.492027i	−0.972384	−	0.233388i	$-0.925019\pi$
$619$	−2.70804e6	+	4.69046e6i	−0.284072	+	0.492027i	0.688312	+	0.725415i	$0.258352\pi$
$620$	2.83997e7	−	4.91897e7i	2.96711	−	5.13919i
$621$		0			0
$622$	6.19223e6			0.641757
$623$	671125.	+	4.71925e6i	0.0692761	+	0.487139i
$624$		0			0
$625$	6.09446e6	+	1.05559e7i	0.624072	+	1.08092i
$626$	−1.06175e7	+	1.83901e7i	−1.08290	+	1.87563i
$627$		0			0
$628$	−1.92217e7	−	3.32930e7i	−1.94488	−	3.36863i
$629$	−7.11266e6			−0.716812
$630$		0			0
$631$	1.44178e7			1.44154			0.720770	−	0.693174i	$-0.243788\pi$
$631$	1.44178e7			1.44154			0.720770	+	0.693174i	$0.243788\pi$
$632$	−2.03136e7	−	3.51842e7i	−2.02299	−	3.50392i
$633$		0			0
$634$	9.57112e6	−	1.65777e7i	0.945670	−	1.63795i
$635$	−2.44010e6	−	4.22638e6i	−0.240145	−	0.415943i
$636$		0			0
$637$	929413.	+	891663.i	0.0907528	+	0.0870667i
$638$	2.13743e7			2.07893
$639$		0			0
$640$	5.89350e6	−	1.02078e7i	0.568753	−	0.985109i
$641$	−3.06909e6	+	5.31582e6i	−0.295029	+	0.511005i	−0.974992	−	0.222242i	$-0.928663\pi$
$641$	−3.06909e6	+	5.31582e6i	−0.295029	+	0.511005i	0.679963	+	0.733247i	$0.261996\pi$
$642$		0			0
$643$	−402177.			−0.0383610			−0.0191805	−	0.999816i	$-0.506106\pi$
$643$	−402177.			−0.0383610			−0.0191805	+	0.999816i	$0.506106\pi$
$644$	1.11817e7	+	4.49641e6i	1.06241	+	0.427219i
$645$		0			0
$646$	−1.27628e7	−	2.21058e7i	−1.20327	−	2.08413i
$647$	−6.64081e6	+	1.15022e7i	−0.623678	+	1.08024i	0.365117	+	0.930961i	$0.381029\pi$
$647$	−6.64081e6	+	1.15022e7i	−0.623678	+	1.08024i	−0.988795	+	0.149280i	$0.952304\pi$
$648$		0			0
$649$	−7.60502e6	−	1.31723e7i	−0.708743	−	1.22758i
$650$	−1.16233e6			−0.107906
$651$		0			0
$652$	1.93373e7			1.78147
$653$	−5.63657e6	−	9.76282e6i	−0.517287	−	0.895968i	−0.999798	−	0.0200780i	$-0.993609\pi$
$653$	−5.63657e6	−	9.76282e6i	−0.517287	−	0.895968i	0.482511	−	0.875890i	$-0.339725\pi$
$654$		0			0
$655$	2.36730e6	−	4.10028e6i	0.215601	−	0.373431i
$656$	2.08043e7	+	3.60341e7i	1.88753	+	3.26929i
$657$		0			0
$658$	1.25174e7	−	9.81269e6i	1.12707	−	0.883534i
$659$	9.29624e6			0.833861			0.416930	−	0.908938i	$-0.363106\pi$
$659$	9.29624e6			0.833861			0.416930	+	0.908938i	$0.363106\pi$
$660$		0			0
$661$	314386.	−	544533.i	0.0279872	−	0.0484753i	−0.851693	−	0.524042i	$-0.824424\pi$
$661$	314386.	−	544533.i	0.0279872	−	0.0484753i	0.879680	+	0.475566i	$0.157757\pi$
$662$	551146.	−	954612.i	0.0488789	−	0.0846607i
$663$		0			0
$664$	−8.68669e6			−0.764599
$665$	−1.30302e7	+	1.02147e7i	−1.14261	+	0.895720i
$666$		0			0
$667$	−2.21385e6	−	3.83451e6i	−0.192679	−	0.333730i
$668$	4.49874e6	−	7.79205e6i	0.390077	−	0.675633i
$669$		0			0
$670$	−1.29776e7	−	2.24778e7i	−1.11688	−	1.93449i
$671$	6.18965e6			0.530713
$672$		0			0
$673$	5.15635e6			0.438838			0.219419	−	0.975631i	$-0.429584\pi$
$673$	5.15635e6			0.438838			0.219419	+	0.975631i	$0.429584\pi$
$674$	5.10923e6	+	8.84944e6i	0.433217	+	0.750354i
$675$		0			0
$676$	1.47692e7	−	2.55810e7i	1.24305	−	2.15303i
$677$	3.28149e6	+	5.68370e6i	0.275169	+	0.476606i	0.970178	−	0.242395i	$-0.0779330\pi$
$677$	3.28149e6	+	5.68370e6i	0.275169	+	0.476606i	−0.695009	+	0.719001i	$0.744600\pi$
$678$		0			0
$679$	−4.34617e6	−	1.74770e6i	−0.361770	−	0.145476i
$680$	−4.44379e7			−3.68537
$681$		0			0
$682$	−2.89071e7	+	5.00685e7i	−2.37982	+	4.12196i
$683$	1.00766e7	−	1.74532e7i	0.826540	−	1.43161i	−0.0741975	−	0.997244i	$-0.523640\pi$
$683$	1.00766e7	−	1.74532e7i	0.826540	−	1.43161i	0.900737	−	0.434365i	$-0.143027\pi$
$684$		0			0
$685$	2.51013e7			2.04395
$686$	1.35121e7	−	1.87912e7i	1.09626	−	1.52456i
$687$		0			0
$688$	2.16743e7	+	3.75410e7i	1.74572	+	3.02367i
$689$	179234.	−	310442.i	0.0143838	−	0.0249134i
$690$		0			0
$691$	5.05979e6	+	8.76382e6i	0.403123	+	0.698229i	0.994101	−	0.108458i	$-0.0345914\pi$
$691$	5.05979e6	+	8.76382e6i	0.403123	+	0.698229i	−0.590978	+	0.806688i	$0.701258\pi$
$692$	−5.65024e7			−4.48541
$693$		0			0
$694$	−2.58492e7			−2.03727
$695$	−187792.	−	325265.i	−0.0147474	−	0.0255432i
$696$		0			0
$697$	9.03494e6	−	1.56490e7i	0.704439	−	1.22012i
$698$	−1.81785e7	−	3.14860e7i	−1.41227	−	2.44613i
$699$		0			0
$700$	2.10677e6	+	1.48145e7i	0.162507	+	1.14272i
$701$	−3.27446e6			−0.251678			−0.125839	−	0.992051i	$-0.540162\pi$
$701$	−3.27446e6			−0.251678			−0.125839	+	0.992051i	$0.540162\pi$
$702$		0			0
$703$	−5.30178e6	+	9.18295e6i	−0.404607	+	0.700800i
$704$	−1.56767e7	+	2.71528e7i	−1.19212	+	2.06482i
$705$		0			0
$706$	−4.09488e7			−3.09193
$707$	−1.00677e7	+	7.89230e6i	−0.757496	+	0.593820i
$708$		0			0
$709$	−2.99723e6	−	5.19136e6i	−0.223926	−	0.387851i	0.732071	−	0.681229i	$-0.238554\pi$
$709$	−2.99723e6	−	5.19136e6i	−0.223926	−	0.387851i	−0.955997	+	0.293377i	$0.905221\pi$
$710$	−4.83000e6	+	8.36580e6i	−0.359585	+	0.622819i
$711$		0			0
$712$	9.53647e6	+	1.65177e7i	0.704998	+	1.22109i
$713$	1.19762e7			0.882260
$714$		0			0
$715$	2.70251e6			0.197698
$716$	−4.19968e6	−	7.27406e6i	−0.306150	−	0.530267i
$717$		0			0
$718$	−1.31913e7	+	2.28480e7i	−0.954940	+	1.65400i
$719$	−1.23868e7	−	2.14546e7i	−0.893590	−	1.54774i	−0.835541	−	0.549429i	$-0.814845\pi$
$719$	−1.23868e7	−	2.14546e7i	−0.893590	−	1.54774i	−0.0580490	−	0.998314i	$-0.518488\pi$
$720$		0			0
$721$	132761.	+	933557.i	0.00951115	+	0.0668810i
$722$	−1.17516e7			−0.838983
$723$		0			0
$724$	1.67836e7	−	2.90700e7i	1.18998	−	2.06110i
$725$	2.74871e6	−	4.76091e6i	0.194215	−	0.336391i
$726$		0			0
$727$	−1.16194e7			−0.815357			−0.407678	−	0.913126i	$-0.633662\pi$
$727$	−1.16194e7			−0.815357			−0.407678	+	0.913126i	$0.633662\pi$
$728$	4.78141e6	+	1.92272e6i	0.334370	+	0.134458i
$729$		0			0
$730$	934794.	+	1.61911e6i	0.0649245	+	0.112453i
$731$	9.41277e6	−	1.63034e7i	0.651514	−	1.12846i
$732$		0			0
$733$	6.37168e6	+	1.10361e7i	0.438020	+	0.758674i	0.997537	−	0.0701457i	$-0.0223464\pi$
$733$	6.37168e6	+	1.10361e7i	0.438020	+	0.758674i	−0.559516	+	0.828819i	$0.689013\pi$
$734$	4.32567e7			2.96356
$735$		0			0
$736$	1.66232e7			1.13115
$737$	9.46319e6	+	1.63907e7i	0.641754	+	1.11155i
$738$		0			0
$739$	−6.04589e6	+	1.04718e7i	−0.407238	+	0.705358i	−0.994579	−	0.103982i	$-0.966842\pi$
$739$	−6.04589e6	+	1.04718e7i	−0.407238	+	0.705358i	0.587341	+	0.809340i	$0.300175\pi$
$740$	1.52782e7	+	2.64626e7i	1.02563	+	1.77645i
$741$		0			0
$742$	−5.97656e6	−	2.40332e6i	−0.398512	−	0.160251i
$743$	9.79136e6			0.650685			0.325343	−	0.945596i	$-0.394520\pi$
$743$	9.79136e6			0.650685			0.325343	+	0.945596i	$0.394520\pi$
$744$		0			0
$745$	1.12654e7	−	1.95123e7i	0.743632	−	1.28801i
$746$	−2.49238e7	+	4.31694e7i	−1.63971	+	2.84007i
$747$		0			0
$748$	5.36376e7			3.50522
$749$	−564986.	−	3.97290e6i	−0.0367988	−	0.258763i
$750$		0			0
$751$	8.76513e6	+	1.51816e7i	0.567098	+	0.982243i	0.996851	+	0.0792967i	$0.0252674\pi$
$751$	8.76513e6	+	1.51816e7i	0.567098	+	0.982243i	−0.429753	+	0.902947i	$0.641399\pi$
$752$	1.68825e7	−	2.92414e7i	1.08866	−	1.88562i
$753$		0			0
$754$	−1.56701e6	−	2.71413e6i	−0.100379	−	0.173861i
$755$	5.07125e6			0.323778
$756$		0			0
$757$	6.01558e6			0.381538			0.190769	−	0.981635i	$-0.438902\pi$
$757$	6.01558e6			0.381538			0.190769	+	0.981635i	$0.438902\pi$
$758$	2.68001e7	+	4.64191e7i	1.69419	+	2.93443i
$759$		0			0
$760$	−3.31240e7	+	5.73725e7i	−2.08022	+	3.60305i
$761$	−6.38402e6	−	1.10575e7i	−0.399607	−	0.692139i	0.594071	−	0.804413i	$-0.297520\pi$
$761$	−6.38402e6	−	1.10575e7i	−0.399607	−	0.692139i	−0.993677	+	0.112274i	$0.964187\pi$
$762$		0			0
$763$	1.16140e7	−	9.10452e6i	0.722223	−	0.566168i
$764$	4.60847e7			2.85643
$765$		0			0
$766$	8.77849e6	−	1.52048e7i	0.540565	−	0.936286i
$767$	−1.11509e6	+	1.93139e6i	−0.0684416	+	0.118544i
$768$		0			0
$769$	−6.32718e6			−0.385829			−0.192914	−	0.981216i	$-0.561794\pi$
$769$	−6.32718e6			−0.385829			−0.192914	+	0.981216i	$0.561794\pi$
$770$	−6.83754e6	−	4.80805e7i	−0.415597	−	2.92242i
$771$		0			0
$772$	−1.20325e7	−	2.08409e7i	−0.726628	−	1.25856i
$773$	8.10085e6	−	1.40311e7i	0.487620	−	0.844583i	−0.512279	−	0.858819i	$-0.671198\pi$
$773$	8.10085e6	−	1.40311e7i	0.487620	−	0.844583i	0.999899	+	0.0142365i	$0.00453179\pi$
$774$		0			0
$775$	7.43482e6	+	1.28775e7i	0.444648	+	0.770153i
$776$	−1.87435e7			−1.11737
$777$		0			0
$778$	−3.09593e7			−1.83376
$779$	−1.34693e7	−	2.33295e7i	−0.795246	−	1.37741i
$780$		0			0
$781$	3.52202e6	−	6.10031e6i	0.206616	−	0.357869i
$782$	−7.75482e6	−	1.34318e7i	−0.453477	−	0.785445i
$783$		0			0
$784$	1.17306e7	−	4.77135e7i	0.681599	−	2.77237i
$785$	3.20901e7			1.85865
$786$		0			0
$787$	9.82736e6	−	1.70215e7i	0.565588	−	0.979627i	−0.431407	−	0.902158i	$-0.641983\pi$
$787$	9.82736e6	−	1.70215e7i	0.565588	−	0.979627i	0.996995	−	0.0774697i	$-0.0246841\pi$
$788$	−1.65984e7	+	2.87492e7i	−0.952247	+	1.64934i
$789$		0			0
$790$	5.61356e7			3.20015
$791$	107599.	+	43267.9i	0.00611456	+	0.00245881i
$792$		0			0
$793$	−453779.	−	785967.i	−0.0256248	−	0.0443835i
$794$	−2.52250e6	+	4.36910e6i	−0.141997	+	0.245946i
$795$		0			0
$796$	2.82654e7	+	4.89571e7i	1.58115	+	2.73863i
$797$	6.39709e6			0.356728			0.178364	−	0.983965i	$-0.442920\pi$
$797$	6.39709e6			0.356728			0.178364	+	0.983965i	$0.442920\pi$
$798$		0			0
$799$	−1.46636e7			−0.812593
$800$	1.03197e7	+	1.78742e7i	0.570086	+	0.987418i
$801$		0			0
$802$	259619.	−	449674.i	0.0142528	−	0.0246866i
$803$	−681649.	−	1.18065e6i	−0.0373054	−	0.0646149i
$804$		0			0
$805$	−7.91734e6	+	6.20659e6i	−0.430615	+	0.337570i
$806$	8.47700e6			0.459626
$807$		0			0
$808$	−2.55929e7	+	4.43283e7i	−1.37909	+	2.38865i
$809$	1.19353e7	−	2.06725e7i	0.641152	−	1.11051i	−0.344024	−	0.938961i	$-0.611790\pi$
$809$	1.19353e7	−	2.06725e7i	0.641152	−	1.11051i	0.985176	−	0.171547i	$-0.0548765\pi$
$810$		0			0
$811$	−3.15356e7			−1.68364			−0.841819	−	0.539759i	$-0.818515\pi$
$811$	−3.15356e7			−1.68364			−0.841819	+	0.539759i	$0.818515\pi$
$812$	−3.17526e7	+	2.48916e7i	−1.69001	+	1.32484i
$813$		0			0
$814$	−1.55511e7	−	2.69354e7i	−0.822624	−	1.42483i
$815$	−8.07079e6	+	1.39790e7i	−0.425620	+	0.737196i
$816$		0			0
$817$	−1.40326e7	−	2.43051e7i	−0.735499	−	1.27392i
$818$	−3.97163e7			−2.07532
$819$		0			0
$820$	−7.76292e7			−4.03172
$821$	1.17152e7	+	2.02914e7i	0.606587	+	1.05064i	0.991798	+	0.127812i	$0.0407953\pi$
$821$	1.17152e7	+	2.02914e7i	0.606587	+	1.05064i	−0.385211	+	0.922829i	$0.625871\pi$
$822$		0			0
$823$	−1.85920e7	+	3.22022e7i	−0.956810	+	1.65724i	−0.226641	+	0.973978i	$0.572774\pi$
$823$	−1.85920e7	+	3.22022e7i	−0.956810	+	1.65724i	−0.730170	+	0.683266i	$0.760559\pi$
$824$	1.88649e6	+	3.26750e6i	0.0967915	+	0.167648i
$825$		0			0
$826$	3.71826e7	+	1.49520e7i	1.89622	+	0.762517i
$827$	−494429.			−0.0251386			−0.0125693	−	0.999921i	$-0.504001\pi$
$827$	−494429.			−0.0251386			−0.0125693	+	0.999921i	$0.504001\pi$
$828$		0			0
$829$	6.67122e6	−	1.15549e7i	0.337147	−	0.583955i	−0.646748	−	0.762704i	$-0.723872\pi$
$829$	6.67122e6	−	1.15549e7i	0.337147	−	0.583955i	0.983895	+	0.178749i	$0.0572049\pi$
$830$	6.00130e6	−	1.03946e7i	0.302378	−	0.523734i
$831$		0			0
$832$	4.59718e6			0.230241
$833$	−2.04922e7	+	5.94871e6i	−1.02324	+	0.297037i
$834$		0			0
$835$	3.75527e6	+	6.50431e6i	0.186391	+	0.322838i
$836$	3.99816e7	−	6.92501e7i	1.97854	−	3.42693i
$837$		0			0
$838$	−3.61916e6	−	6.26857e6i	−0.178032	−	0.308360i
$839$	−1.74957e7			−0.858075			−0.429038	−	0.903287i	$-0.641147\pi$
$839$	−1.74957e7			−0.858075			−0.429038	+	0.903287i	$0.641147\pi$
$840$		0			0
$841$	−5.68840e6			−0.277332
$842$	8.22183e6	+	1.42406e7i	0.399658	+	0.692228i
$843$		0			0
$844$	2.35603e6	−	4.08076e6i	0.113848	−	0.197190i
$845$	1.23284e7	+	2.13534e7i	0.593970	+	1.02879i
$846$		0			0
$847$	2.04629e6	+	1.43892e7i	0.0980073	+	0.689172i
$848$	−1.36751e7			−0.653040
$849$		0			0
$850$	9.62835e6	−	1.66768e7i	0.457093	−	0.791709i
$851$	−3.22143e6	+	5.57968e6i	−0.152484	+	0.264110i
$852$		0			0
$853$	1.83938e7			0.865565			0.432782	−	0.901498i	$-0.357532\pi$
$853$	1.83938e7			0.865565			0.432782	+	0.901498i	$0.357532\pi$
$854$	−1.28351e7	+	1.00617e7i	−0.602218	+	0.472094i
$855$		0			0
$856$	−8.02827e6	−	1.39054e7i	−0.374488	−	0.648632i
$857$	−1.82575e6	+	3.16230e6i	−0.0849161	+	0.147079i	−0.905355	−	0.424655i	$-0.860396\pi$
$857$	−1.82575e6	+	3.16230e6i	−0.0849161	+	0.147079i	0.820439	+	0.571734i	$0.193729\pi$
$858$		0			0
$859$	2.56392e6	+	4.44085e6i	0.118556	+	0.205344i	0.919195	−	0.393802i	$-0.128840\pi$
$859$	2.56392e6	+	4.44085e6i	0.118556	+	0.205344i	−0.800640	+	0.599146i	$0.795507\pi$
$860$	−8.08756e7			−3.72882
$861$		0			0
$862$	6.77397e7			3.10510
$863$	−9.82446e6	−	1.70165e7i	−0.449037	−	0.777755i	0.549287	−	0.835634i	$-0.314899\pi$
$863$	−9.82446e6	−	1.70165e7i	−0.449037	−	0.777755i	−0.998324	+	0.0578794i	$0.981566\pi$
$864$		0			0
$865$	2.35823e7	−	4.08458e7i	1.07163	−	1.85612i
$866$	7.04629e6	+	1.22045e7i	0.319276	+	0.553002i
$867$		0			0
$868$	−1.53648e7	−	1.08043e8i	−0.692195	−	4.86741i
$869$	−4.09339e7			−1.83880
$870$		0			0
$871$	1.38754e6	−	2.40329e6i	0.0619727	−	0.107340i
$872$	2.95239e7	−	5.11369e7i	1.31487	−	2.27742i
$873$		0			0
$874$	−2.31218e7			−1.02387
$875$	1.37737e7	+	5.53874e6i	0.608178	+	0.244563i
$876$		0			0
$877$	1.53780e7	+	2.66354e7i	0.675150	+	1.16939i	0.976425	+	0.215856i	$0.0692543\pi$
$877$	1.53780e7	+	2.66354e7i	0.675150	+	1.16939i	−0.301276	+	0.953537i	$0.597412\pi$
$878$	2.04654e7	−	3.54472e7i	0.895952	−	1.55183i
$879$		0			0
$880$	−5.15486e7	−	8.92848e7i	−2.24393	−	3.88661i
$881$	−3.34518e7			−1.45204			−0.726022	−	0.687671i	$-0.758633\pi$
$881$	−3.34518e7			−1.45204			−0.726022	+	0.687671i	$0.758633\pi$
$882$		0			0
$883$	−2.87952e7			−1.24285			−0.621425	−	0.783474i	$-0.713446\pi$
$883$	−2.87952e7			−1.24285			−0.621425	+	0.783474i	$0.713446\pi$
$884$	−3.93231e6	−	6.81096e6i	−0.169245	−	0.293142i
$885$		0			0
$886$	−6.85695e6	+	1.18766e7i	−0.293458	+	0.508285i
$887$	8.41826e6	+	1.45809e7i	0.359264	+	0.622263i	0.987838	−	0.155487i	$-0.0496945\pi$
$887$	8.41826e6	+	1.45809e7i	0.359264	+	0.622263i	−0.628574	+	0.777750i	$0.716361\pi$
$888$		0			0
$889$	−8.69944e6	−	3.49825e6i	−0.369179	−	0.148456i
$890$	−2.63536e7			−1.11523
$891$		0			0
$892$	−1.04108e6	+	1.80321e6i	−0.0438100	+	0.0758811i
$893$	−1.09303e7	+	1.89318e7i	−0.458671	+	0.794442i
$894$		0			0
$895$	7.01126e6			0.292576
$896$	−3.18851e6	−	2.24211e7i	−0.132684	−	0.933012i
$897$		0			0
$898$	3.97810e7	+	6.89027e7i	1.64621	+	2.85131i
$899$	−2.00466e7	+	3.47217e7i	−0.827258	+	1.43285i
$900$		0			0
$901$	2.96942e6	+	5.14319e6i	0.121860	+	0.211067i
$902$	7.90161e7			3.23370
$903$		0			0
$904$	464035.			0.0188856
$905$	1.40099e7	+	2.42658e7i	0.568608	+	0.984857i
$906$		0			0
$907$	−4.87803e6	+	8.44899e6i	−0.196891	+	0.341025i	−0.947519	−	0.319700i	$-0.896418\pi$
$907$	−4.87803e6	+	8.44899e6i	−0.196891	+	0.341025i	0.750628	+	0.660725i	$0.229751\pi$
$908$	3.96994e7	+	6.87614e7i	1.59797	+	2.76777i
$909$		0			0
$910$	−5.60403e6	+	4.39314e6i	−0.224335	+	0.175862i
$911$	3.67934e7			1.46884			0.734420	−	0.678696i	$-0.237454\pi$
$911$	3.67934e7			1.46884			0.734420	+	0.678696i	$0.237454\pi$
$912$		0			0
$913$	−4.37613e6	+	7.57968e6i	−0.173745	+	0.300936i
$914$	2.65199e6	−	4.59338e6i	0.105004	−	0.181872i
$915$		0			0
$916$	4.20307e7			1.65511
$917$	−1.28076e6	−	9.00610e6i	−0.0502972	−	0.353683i
$918$		0			0
$919$	−8.60891e6	−	1.49111e7i	−0.336248	−	0.582398i	0.647476	−	0.762086i	$-0.275825\pi$
$919$	−8.60891e6	−	1.49111e7i	−0.336248	−	0.582398i	−0.983724	+	0.179688i	$0.942491\pi$
$920$	−2.01266e7	+	3.48603e7i	−0.783972	+	1.35788i
$921$		0			0
$922$	−2.84108e7	−	4.92089e7i	−1.10067	−	1.90641i
$923$	−1.03283e6			−0.0399048
$924$		0			0
$925$	−7.99943e6			−0.307400
$926$	−3.46562e7	−	6.00263e7i	−1.32817	−	2.30046i
$927$		0			0
$928$	−2.78250e7	+	4.81943e7i	−1.06063	+	1.83707i
$929$	−2.45280e7	−	4.24837e7i	−0.932443	−	1.61504i	−0.779132	−	0.626860i	$-0.784340\pi$
$929$	−2.45280e7	−	4.24837e7i	−0.932443	−	1.61504i	−0.153311	−	0.988178i	$-0.548994\pi$
$930$		0			0
$931$	−7.59471e6	+	3.08911e7i	−0.287169	+	1.16804i
$932$	9.85694e7			3.71708
$933$		0			0
$934$	−1.70302e7	+	2.94971e7i	−0.638781	+	1.10640i
$935$	−2.23867e7	+	3.87748e7i	−0.837453	+	1.45051i
$936$		0			0
$937$	−2.80929e7			−1.04532			−0.522658	−	0.852542i	$-0.675060\pi$
$937$	−2.80929e7			−1.04532			−0.522658	+	0.852542i	$0.675060\pi$
$938$	−4.62676e7	−	1.86053e7i	−1.71700	−	0.690446i
$939$		0			0
$940$	3.14978e7	+	5.45558e7i	1.16268	+	2.01382i
$941$	1.14001e7	−	1.97455e7i	0.419695	−	0.726932i	−0.576214	−	0.817299i	$-0.695470\pi$
$941$	1.14001e7	−	1.97455e7i	0.419695	−	0.726932i	0.995909	+	0.0903664i	$0.0288038\pi$
$942$		0			0
$943$	−8.18412e6	−	1.41753e7i	−0.299704	−	0.519103i
$944$	8.50780e7			3.10733
$945$		0			0
$946$	8.23205e7			2.99075
$947$	2.17751e7	+	3.77156e7i	0.789016	+	1.36662i	0.926570	+	0.376122i	$0.122743\pi$
$947$	2.17751e7	+	3.77156e7i	0.789016	+	1.36662i	−0.137554	+	0.990494i	$0.543924\pi$
$948$		0			0
$949$	−99946.8	+	173113.i	−0.00360249	+	0.00623970i
$950$	−1.43540e7	−	2.48618e7i	−0.516016	−	0.893766i
$951$		0			0
$952$	−6.71940e7	+	5.26750e7i	−2.40291	+	1.88370i
$953$	−4.54239e7			−1.62014			−0.810069	−	0.586335i	$-0.800570\pi$
$953$	−4.54239e7			−1.62014			−0.810069	+	0.586335i	$0.800570\pi$
$954$		0			0
$955$	−1.92343e7	+	3.33148e7i	−0.682446	+	1.18203i
$956$	3.67535e7	−	6.36589e7i	1.30063	−	2.25276i
$957$		0			0
$958$	9.42000e7			3.31617
$959$	3.79554e7	−	2.97542e7i	1.33269	−	1.04472i
$960$		0			0
$961$	−3.99082e7	−	6.91231e7i	−1.39397	−	2.41443i
$962$	−2.28019e6	+	3.94940e6i	−0.0794388	+	0.137592i
$963$		0			0
$964$	2.59314e7	+	4.49145e7i	0.898738	+	1.55666i
$965$	2.00879e7			0.694411
$966$		0			0
$967$	5.43677e6			0.186971			0.0934855	−	0.995621i	$-0.470199\pi$
$967$	5.43677e6			0.186971			0.0934855	+	0.995621i	$0.470199\pi$
$968$	2.90771e7	+	5.03630e7i	0.997385	+	1.72752i
$969$		0			0
$970$	1.29492e7	−	2.24287e7i	0.441889	−	0.765375i
$971$	1.81352e7	+	3.14112e7i	0.617270	+	1.06914i	0.989982	+	0.141196i	$0.0450949\pi$
$971$	1.81352e7	+	3.14112e7i	0.617270	+	1.06914i	−0.372711	+	0.927947i	$0.621572\pi$
$972$		0			0
$973$	−669516.	−	269228.i	−0.0226714	−	0.00911672i
$974$	−6.21111e7			−2.09784
$975$		0			0
$976$	−1.73110e7	+	2.99836e7i	−0.581699	+	1.00753i
$977$	−2.53656e6	+	4.39345e6i	−0.0850175	+	0.147255i	−0.905399	−	0.424562i	$-0.860428\pi$
$977$	−2.53656e6	+	4.39345e6i	−0.0850175	+	0.147255i	0.820381	+	0.571817i	$0.193761\pi$
$978$		0			0
$979$	1.92169e7			0.640807
$980$	6.61500e7	+	6.34632e7i	2.20021	+	2.11085i
$981$		0			0
$982$	−606751.	−	1.05092e6i	−0.0200785	−	0.0347770i
$983$	−457830.	+	792984.i	−0.0151119	+	0.0261747i	−0.873482	−	0.486856i	$-0.838144\pi$
$983$	−457830.	+	792984.i	−0.0151119	+	0.0261747i	0.858371	+	0.513030i	$0.171477\pi$
$984$		0			0
$985$	−1.38553e7	−	2.39980e7i	−0.455013	−	0.788106i
$986$	5.19220e7			1.70082
$987$		0			0
$988$	−1.17246e7			−0.382125
$989$	−8.52637e6	−	1.47681e7i	−0.277187	−	0.480103i
$990$		0			0
$991$	1.41993e7	−	2.45939e7i	0.459285	−	0.795505i	−0.539638	−	0.841897i	$-0.681439\pi$
$991$	1.41993e7	−	2.45939e7i	0.459285	−	0.795505i	0.998923	+	0.0463917i	$0.0147722\pi$
$992$	−7.52622e7	−	1.30358e8i	−2.42827	−	4.20589i
$993$		0			0
$994$	2.61313e6	+	1.83751e7i	0.0838871	+	0.589881i
$995$	−4.71884e7			−1.51104
$996$		0			0
$997$	−2.72243e7	+	4.71539e7i	−0.867399	+	1.50238i	−0.00275387	+	0.999996i	$0.500877\pi$
$997$	−2.72243e7	+	4.71539e7i	−0.867399	+	1.50238i	−0.864645	+	0.502383i	$0.832457\pi$
$998$	−4.96319e7	+	8.59650e7i	−1.57737	+	2.73209i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.6.e.f.46.6	yes	12
3.2	odd	2	inner	63.6.e.f.46.1	yes	12
7.2	even	3	inner	63.6.e.f.37.6	yes	12
7.3	odd	6		441.6.a.bd.1.1		6
7.4	even	3		441.6.a.bc.1.1		6
21.2	odd	6	inner	63.6.e.f.37.1	✓	12
21.11	odd	6		441.6.a.bc.1.6		6
21.17	even	6		441.6.a.bd.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.6.e.f.37.1	✓	12	21.2	odd	6	inner
63.6.e.f.37.6	yes	12	7.2	even	3	inner
63.6.e.f.46.1	yes	12	3.2	odd	2	inner
63.6.e.f.46.6	yes	12	1.1	even	1	trivial
441.6.a.bc.1.1		6	7.4	even	3
441.6.a.bc.1.6		6	21.11	odd	6
441.6.a.bd.1.1		6	7.3	odd	6
441.6.a.bd.1.6		6	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	63.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(5.31117 + 9.19921i) q^{2} +(-40.4170 + 70.0043i) q^{4} +(-33.7376 - 58.4352i) q^{5} +(-120.281 - 48.3679i) q^{7} -518.731 q^{8} +O(q^{10})\)	\(q+(5.31117 + 9.19921i) q^{2} +(-40.4170 + 70.0043i) q^{4} +(-33.7376 - 58.4352i) q^{5} +(-120.281 - 48.3679i) q^{7} -518.731 q^{8} +(358.372 - 620.718i) q^{10} +(-261.323 + 452.625i) q^{11} +76.6331 q^{13} +(-193.887 - 1363.38i) q^{14} +(-1461.72 - 2531.78i) q^{16} +(-634.801 + 1099.51i) q^{17} +(946.362 + 1639.15i) q^{19} +5454.28 q^{20} -5551.73 q^{22} +(575.022 + 995.967i) q^{23} +(-713.945 + 1236.59i) q^{25} +(407.011 + 704.964i) q^{26} +(8247.36 - 6465.31i) q^{28} -3850.03 q^{29} +(5206.86 - 9018.55i) q^{31} +(7227.21 - 12517.9i) q^{32} -13486.1 q^{34} +(1231.60 + 8660.46i) q^{35} +(2801.14 + 4851.71i) q^{37} +(-10052.6 + 17411.6i) q^{38} +(17500.7 + 30312.1i) q^{40} -14232.7 q^{41} -14827.9 q^{43} +(-21123.8 - 36587.5i) q^{44} +(-6108.08 + 10579.5i) q^{46} +(5774.88 + 10002.4i) q^{47} +(12128.1 + 11635.5i) q^{49} -15167.5 q^{50} +(-3097.28 + 5364.64i) q^{52} +(2338.86 - 4051.02i) q^{53} +35265.6 q^{55} +(62393.5 + 25089.9i) q^{56} +(-20448.2 - 35417.3i) q^{58} +(-14551.0 + 25203.0i) q^{59} +(-5921.45 - 10256.2i) q^{61} +110618. q^{62} +59989.5 q^{64} +(-2585.41 - 4478.06i) q^{65} +(18106.3 - 31361.0i) q^{67} +(-51313.5 - 88877.6i) q^{68} +(-73128.1 + 57326.9i) q^{70} -13477.6 q^{71} +(-1304.23 + 2258.98i) q^{73} +(-29754.6 + 51536.5i) q^{74} -152996. q^{76} +(53324.8 - 41802.6i) q^{77} +(39160.2 + 67827.4i) q^{79} +(-98629.9 + 170832. i) q^{80} +(-75592.3 - 130930. i) q^{82} +16746.0 q^{83} +85666.5 q^{85} +(-78753.5 - 136405. i) q^{86} +(135557. - 234791. i) q^{88} +(-18384.2 - 31842.4i) q^{89} +(-9217.51 - 3706.58i) q^{91} -92962.7 q^{92} +(-61342.7 + 106249. i) q^{94} +(63855.9 - 110602. i) q^{95} +36133.4 q^{97} +(-42623.0 + 173367. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 182 q^{4} + 142 q^{7}+O(q^{10}) \) 12 * q - 182 * q^4 + 142 * q^7	\( 12 q - 182 q^{4} + 142 q^{7} + 686 q^{10} + 308 q^{13} - 1898 q^{16} + 9422 q^{19} - 18292 q^{22} - 7526 q^{25} + 37074 q^{28} + 23422 q^{31} - 55608 q^{34} - 18182 q^{37} + 69258 q^{40} - 87372 q^{43} + 25332 q^{46} + 30354 q^{49} + 34272 q^{52} - 96320 q^{55} - 89782 q^{58} - 16156 q^{61} + 380580 q^{64} + 144650 q^{67} - 187262 q^{70} - 100058 q^{73} - 685440 q^{76} + 101994 q^{79} + 75712 q^{82} + 602352 q^{85} + 752310 q^{88} - 282306 q^{91} - 120456 q^{94} - 866096 q^{97}+O(q^{100}) \) 12 * q - 182 * q^4 + 142 * q^7 + 686 * q^10 + 308 * q^13 - 1898 * q^16 + 9422 * q^19 - 18292 * q^22 - 7526 * q^25 + 37074 * q^28 + 23422 * q^31 - 55608 * q^34 - 18182 * q^37 + 69258 * q^40 - 87372 * q^43 + 25332 * q^46 + 30354 * q^49 + 34272 * q^52 - 96320 * q^55 - 89782 * q^58 - 16156 * q^61 + 380580 * q^64 + 144650 * q^67 - 187262 * q^70 - 100058 * q^73 - 685440 * q^76 + 101994 * q^79 + 75712 * q^82 + 602352 * q^85 + 752310 * q^88 - 282306 * q^91 - 120456 * q^94 - 866096 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more