LMFDB - Embedded newform 196.6.d.b.195.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,6,Mod(195,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("196.195");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	196.d (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:	$31.4352286833$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			195.22
Character	$\chi$	$=$	196.195
Dual form			196.6.d.b.195.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.64203 - 5.41329i) q^{2} +26.1637 q^{3} +(-26.6075 - 17.7776i) q^{4} +69.3681i q^{5} +(42.9616 - 141.632i) q^{6} +(-139.926 + 114.843i) q^{8} +441.538 q^{9} +O(q^{10})$	\(q+(1.64203 - 5.41329i) q^{2} +26.1637 q^{3} +(-26.6075 - 17.7776i) q^{4} +69.3681i q^{5} +(42.9616 - 141.632i) q^{6} +(-139.926 + 114.843i) q^{8} +441.538 q^{9} +(375.510 + 113.905i) q^{10} +513.527i q^{11} +(-696.150 - 465.127i) q^{12} +23.3349i q^{13} +1814.93i q^{15} +(391.915 + 946.033i) q^{16} -30.6492i q^{17} +(725.019 - 2390.18i) q^{18} +40.8156 q^{19} +(1233.20 - 1845.71i) q^{20} +(2779.87 + 843.226i) q^{22} +2460.71i q^{23} +(-3660.97 + 3004.71i) q^{24} -1686.94 q^{25} +(126.318 + 38.3165i) q^{26} +5194.49 q^{27} +6823.51 q^{29} +(9824.73 + 2980.16i) q^{30} +6008.57 q^{31} +(5764.69 - 568.139i) q^{32} +13435.8i q^{33} +(-165.913 - 50.3269i) q^{34} +(-11748.2 - 7849.48i) q^{36} -11247.1 q^{37} +(67.0204 - 220.947i) q^{38} +610.526i q^{39} +(-7966.43 - 9706.37i) q^{40} +10626.3i q^{41} -7944.77i q^{43} +(9129.26 - 13663.6i) q^{44} +30628.7i q^{45} +(13320.5 + 4040.56i) q^{46} -7844.39 q^{47} +(10254.0 + 24751.7i) q^{48} +(-2770.00 + 9131.89i) q^{50} -801.896i q^{51} +(414.837 - 620.882i) q^{52} +11227.9 q^{53} +(8529.51 - 28119.3i) q^{54} -35622.4 q^{55} +1067.89 q^{57} +(11204.4 - 36937.7i) q^{58} -9810.53 q^{59} +(32265.0 - 48290.6i) q^{60} -12712.9i q^{61} +(9866.25 - 32526.1i) q^{62} +(6390.29 - 32138.9i) q^{64} -1618.70 q^{65} +(72731.6 + 22061.9i) q^{66} -27848.6i q^{67} +(-544.869 + 815.498i) q^{68} +64381.2i q^{69} +35312.6i q^{71} +(-61782.5 + 50707.5i) q^{72} -54755.8i q^{73} +(-18468.1 + 60884.0i) q^{74} -44136.5 q^{75} +(-1086.00 - 725.602i) q^{76} +(3304.96 + 1002.50i) q^{78} -1571.07i q^{79} +(-65624.5 + 27186.4i) q^{80} +28613.2 q^{81} +(57523.0 + 17448.6i) q^{82} +47882.7 q^{83} +2126.08 q^{85} +(-43007.3 - 13045.5i) q^{86} +178528. q^{87} +(-58974.8 - 71855.5i) q^{88} -88136.1i q^{89} +(165802. + 50293.2i) q^{90} +(43745.5 - 65473.3i) q^{92} +157206. q^{93} +(-12880.7 + 42464.0i) q^{94} +2831.30i q^{95} +(150826. - 14864.6i) q^{96} -117064. i q^{97} +226742. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 24 q^{4} - 72 q^{8} + 2272 q^{9}+O(q^{10}) $ 36 * q + 24 * q^4 - 72 * q^8 + 2272 * q^9	$ 36 q + 24 q^{4} - 72 q^{8} + 2272 q^{9} - 1328 q^{16} + 3560 q^{18} + 13768 q^{22} - 15224 q^{25} + 176 q^{29} + 11672 q^{30} - 2320 q^{32} - 27920 q^{36} - 23444 q^{37} - 18192 q^{44} + 2080 q^{46} - 51168 q^{50} + 66972 q^{53} - 1668 q^{57} + 96872 q^{58} - 28624 q^{60} + 44544 q^{64} - 30712 q^{65} - 296128 q^{72} - 34304 q^{74} + 127704 q^{78} - 320804 q^{81} + 71212 q^{85} + 504992 q^{86} - 110536 q^{88} - 190176 q^{92} + 330324 q^{93}+O(q^{100}) $ 36 * q + 24 * q^4 - 72 * q^8 + 2272 * q^9 - 1328 * q^16 + 3560 * q^18 + 13768 * q^22 - 15224 * q^25 + 176 * q^29 + 11672 * q^30 - 2320 * q^32 - 27920 * q^36 - 23444 * q^37 - 18192 * q^44 + 2080 * q^46 - 51168 * q^50 + 66972 * q^53 - 1668 * q^57 + 96872 * q^58 - 28624 * q^60 + 44544 * q^64 - 30712 * q^65 - 296128 * q^72 - 34304 * q^74 + 127704 * q^78 - 320804 * q^81 + 71212 * q^85 + 504992 * q^86 - 110536 * q^88 - 190176 * q^92 + 330324 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.64203	−	5.41329i	0.290273	−	0.956944i
$2$	1.64203	−	5.41329i	0.290273	−	0.956944i
$3$	26.1637			1.67840			0.839201	−	0.543822i	$-0.183023\pi$
$3$	26.1637			1.67840			0.839201	+	0.543822i	$0.183023\pi$
$4$	−26.6075	−	17.7776i	−0.831484	−	0.555549i
$5$			69.3681i			1.24090i	0.784248	+	0.620448i	$0.213049\pi$
$5$			69.3681i			1.24090i	−0.784248	+	0.620448i	$0.786951\pi$
$6$	42.9616	−	141.632i	0.487194	−	1.60614i
$7$		0			0
$7$		0			0
$8$	−139.926	+	114.843i	−0.772987	+	0.634422i
$9$	441.538			1.81703
$10$	375.510	+	113.905i	1.18747	+	0.360198i
$11$			513.527i			1.27962i	0.768533	+	0.639810i	$0.220987\pi$
$11$			513.527i			1.27962i	−0.768533	+	0.639810i	$0.779013\pi$
$12$	−696.150	−	465.127i	−1.39556	−	0.932435i
$13$			23.3349i			0.0382954i	0.999817	+	0.0191477i	$0.00609528\pi$
$13$			23.3349i			0.0382954i	−0.999817	+	0.0191477i	$0.993905\pi$
$14$		0			0
$15$			1814.93i			2.08272i
$16$	391.915	+	946.033i	0.382730	+	0.923860i
$17$		−	30.6492i		−	0.0257215i	−0.999917	−	0.0128608i	$-0.995906\pi$
$17$		−	30.6492i		−	0.0257215i	0.999917	−	0.0128608i	$-0.00409382\pi$
$18$	725.019	−	2390.18i	0.527434	−	1.73880i
$19$	40.8156			0.0259383			0.0129692	−	0.999916i	$-0.495872\pi$
$19$	40.8156			0.0259383			0.0129692	+	0.999916i	$0.495872\pi$
$20$	1233.20	−	1845.71i	0.689378	−	1.03178i
$21$		0			0
$22$	2779.87	+	843.226i	1.22453	+	0.371439i
$23$			2460.71i			0.969931i	0.874533	+	0.484965i	$0.161168\pi$
$23$			2460.71i			0.969931i	−0.874533	+	0.484965i	$0.838832\pi$
$24$	−3660.97	+	3004.71i	−1.29738	+	1.06482i
$25$	−1686.94			−0.539820
$26$	126.318	+	38.3165i	0.0366466	+	0.0111161i
$27$	5194.49			1.37130
$28$		0			0
$29$	6823.51			1.50665			0.753326	−	0.657647i	$-0.228448\pi$
$29$	6823.51			1.50665			0.753326	+	0.657647i	$0.228448\pi$
$30$	9824.73	+	2980.16i	1.99305	+	0.604556i
$31$	6008.57			1.12297			0.561483	−	0.827488i	$-0.310231\pi$
$31$	6008.57			1.12297			0.561483	+	0.827488i	$0.310231\pi$
$32$	5764.69	−	568.139i	0.995179	−	0.0980798i
$33$			13435.8i			2.14772i
$34$	−165.913	−	50.3269i	−0.0246141	−	0.00746626i
$35$		0			0
$36$	−11748.2	−	7849.48i	−1.51083	−	1.00945i
$37$	−11247.1			−1.35063			−0.675316	−	0.737528i	$-0.735993\pi$
$37$	−11247.1			−1.35063			−0.675316	+	0.737528i	$0.735993\pi$
$38$	67.0204	−	220.947i	0.00752918	−	0.0248215i
$39$			610.526i			0.0642751i
$40$	−7966.43	−	9706.37i	−0.787252	−	0.959195i
$41$			10626.3i			0.987235i	0.869679	+	0.493618i	$0.164326\pi$
$41$			10626.3i			0.987235i	−0.869679	+	0.493618i	$0.835674\pi$
$42$		0			0
$43$		−	7944.77i		−	0.655254i	−0.944807	−	0.327627i	$-0.893751\pi$
$43$		−	7944.77i		−	0.655254i	0.944807	−	0.327627i	$-0.106249\pi$
$44$	9129.26	−	13663.6i	0.710893	−	1.06398i
$45$			30628.7i			2.25474i
$46$	13320.5	+	4040.56i	0.928170	+	0.281544i
$47$	−7844.39			−0.517982			−0.258991	−	0.965880i	$-0.583390\pi$
$47$	−7844.39			−0.517982			−0.258991	+	0.965880i	$0.583390\pi$
$48$	10254.0	+	24751.7i	0.642374	+	1.55061i
$49$		0			0
$50$	−2770.00	+	9131.89i	−0.156695	+	0.516578i
$51$		−	801.896i		−	0.0431711i
$52$	414.837	−	620.882i	0.0212750	−	0.0318420i
$53$	11227.9			0.549044			0.274522	−	0.961581i	$-0.411480\pi$
$53$	11227.9			0.549044			0.274522	+	0.961581i	$0.411480\pi$
$54$	8529.51	−	28119.3i	0.398052	−	1.31226i
$55$	−35622.4			−1.58788
$56$		0			0
$57$	1067.89			0.0435349
$58$	11204.4	−	36937.7i	0.437340	−	1.44178i
$59$	−9810.53			−0.366912			−0.183456	−	0.983028i	$-0.558729\pi$
$59$	−9810.53			−0.366912			−0.183456	+	0.983028i	$0.558729\pi$
$60$	32265.0	−	48290.6i	1.15705	−	1.73175i
$61$		−	12712.9i		−	0.437442i	−0.975787	−	0.218721i	$-0.929812\pi$
$61$		−	12712.9i		−	0.437442i	0.975787	−	0.218721i	$-0.0701884\pi$
$62$	9866.25	−	32526.1i	0.325966	−	1.07462i
$63$		0			0
$64$	6390.29	−	32138.9i	0.195016	−	0.980800i
$65$	−1618.70			−0.0475206
$66$	72731.6	+	22061.9i	2.05524	+	0.623423i
$67$		−	27848.6i		−	0.757908i	−0.925416	−	0.378954i	$-0.876284\pi$
$67$		−	27848.6i		−	0.757908i	0.925416	−	0.378954i	$-0.123716\pi$
$68$	−544.869	+	815.498i	−0.0142896	+	0.0213870i
$69$			64381.2i			1.62793i
$70$		0			0
$71$			35312.6i			0.831350i	0.909513	+	0.415675i	$0.136455\pi$
$71$			35312.6i			0.831350i	−0.909513	+	0.415675i	$0.863545\pi$
$72$	−61782.5	+	50707.5i	−1.40454	+	1.15276i
$73$		−	54755.8i		−	1.20261i	−0.799021	−	0.601303i	$-0.794649\pi$
$73$		−	54755.8i		−	1.20261i	0.799021	−	0.601303i	$-0.205351\pi$
$74$	−18468.1	+	60884.0i	−0.392052	+	1.29248i
$75$	−44136.5			−0.906035
$76$	−1086.00	−	725.602i	−0.0215673	−	0.0144100i
$77$		0			0
$78$	3304.96	+	1002.50i	0.0615076	+	0.0186573i
$79$		−	1571.07i		−	0.0283222i	−0.999900	−	0.0141611i	$-0.995492\pi$
$79$		−	1571.07i		−	0.0283222i	0.999900	−	0.0141611i	$-0.00450776\pi$
$80$	−65624.5	+	27186.4i	−1.14641	+	0.474928i
$81$	28613.2			0.484568
$82$	57523.0	+	17448.6i	0.944729	+	0.286567i
$83$	47882.7			0.762928			0.381464	−	0.924384i	$-0.375420\pi$
$83$	47882.7			0.762928			0.381464	+	0.924384i	$0.375420\pi$
$84$		0			0
$85$	2126.08			0.0319177
$86$	−43007.3	−	13045.5i	−0.627042	−	0.190202i
$87$	178528.			2.52877
$88$	−58974.8	−	71855.5i	−0.811820	−	0.989130i
$89$		−	88136.1i		−	1.17945i	−0.807605	−	0.589724i	$-0.799237\pi$
$89$		−	88136.1i		−	1.17945i	0.807605	−	0.589724i	$-0.200763\pi$
$90$	165802.	+	50293.2i	2.15766	+	0.654490i
$91$		0			0
$92$	43745.5	−	65473.3i	0.538844	−	0.806482i
$93$	157206.			1.88479
$94$	−12880.7	+	42464.0i	−0.150356	+	0.495680i
$95$			2831.30i			0.0321867i
$96$	150826.	−	14864.6i	1.67031	−	0.164617i
$97$		−	117064.i		−	1.26326i	−0.775269	−	0.631631i	$-0.782386\pi$
$97$		−	117064.i		−	1.26326i	0.775269	−	0.631631i	$-0.217614\pi$
$98$		0			0
$99$			226742.i			2.32511i
$100$	44885.2	+	29989.7i	0.448852	+	0.299897i
$101$			63250.6i			0.616966i	0.951230	+	0.308483i	$0.0998213\pi$
$101$			63250.6i			0.616966i	−0.951230	+	0.308483i	$0.900179\pi$
$102$	−4340.90	−	1316.74i	−0.0413123	−	0.0125314i
$103$	−58863.8			−0.546708			−0.273354	−	0.961914i	$-0.588133\pi$
$103$	−58863.8			−0.546708			−0.273354	+	0.961914i	$0.588133\pi$
$104$	−2679.84	−	3265.14i	−0.0242955	−	0.0296018i
$105$		0			0
$106$	18436.5	−	60779.7i	0.159372	−	0.525404i
$107$		−	70316.2i		−	0.593739i	−0.954918	−	0.296870i	$-0.904057\pi$
$107$		−	70316.2i		−	0.593739i	0.954918	−	0.296870i	$-0.0959427\pi$
$108$	−138212.	−	92345.5i	−1.14022	−	0.761827i
$109$	200963.			1.62013			0.810066	−	0.586339i	$-0.199431\pi$
$109$	200963.			1.62013			0.810066	+	0.586339i	$0.199431\pi$
$110$	−58493.0	+	192834.i	−0.460917	+	1.51951i
$111$	−294266.			−2.26690
$112$		0			0
$113$	98427.2			0.725135			0.362568	−	0.931957i	$-0.381900\pi$
$113$	98427.2			0.725135			0.362568	+	0.931957i	$0.381900\pi$
$114$	1753.50	−	5780.77i	0.0126370	−	0.0416604i
$115$	−170695.			−1.20358
$116$	−181556.	−	121305.i	−1.25276	−	0.837019i
$117$			10303.2i			0.0695839i
$118$	−16109.2	+	53107.3i	−0.106505	+	0.351115i
$119$		0			0
$120$	−208431.	−	253954.i	−1.32132	−	1.60991i
$121$	−102659.			−0.637430
$122$	−68818.7	−	20875.0i	−0.418607	−	0.126977i
$123$			278022.i			1.65698i
$124$	−159873.	−	106818.i	−0.933728	−	0.623863i
$125$			99755.6i			0.571035i
$126$		0			0
$127$		−	34726.6i		−	0.191053i	−0.995427	−	0.0955263i	$-0.969547\pi$
$127$		−	34726.6i		−	0.191053i	0.995427	−	0.0955263i	$-0.0304534\pi$
$128$	−163484.	−	87365.5i	−0.881963	−	0.471319i
$129$		−	207864.i		−	1.09978i
$130$	−2657.95	+	8762.48i	−0.0137939	+	0.0454746i
$131$	−379763.			−1.93346			−0.966728	−	0.255806i	$-0.917659\pi$
$131$	−379763.			−1.93346			−0.966728	+	0.255806i	$0.917659\pi$
$132$	238855.	−	357491.i	1.19316	−	1.78579i
$133$		0			0
$134$	−150753.	−	45728.2i	−0.725275	−	0.220000i
$135$			360332.i			1.70164i
$136$	3519.84	+	4288.61i	0.0163183	+	0.0198824i
$137$	−265973.			−1.21070			−0.605350	−	0.795959i	$-0.706967\pi$
$137$	−265973.			−1.21070			−0.605350	+	0.795959i	$0.706967\pi$
$138$	348514.	+	105716.i	1.55784	+	0.472544i
$139$	−395298.			−1.73535			−0.867676	−	0.497130i	$-0.834387\pi$
$139$	−395298.			−1.73535			−0.867676	+	0.497130i	$0.834387\pi$
$140$		0			0
$141$	−205238.			−0.869382
$142$	191157.	+	57984.4i	0.795555	+	0.241318i
$143$	−11983.1			−0.0490036
$144$	173046.	+	417710.i	0.695432	+	1.67868i
$145$			473334.i			1.86960i
$146$	−296409.	−	89910.7i	−1.15083	−	0.349084i
$147$		0			0
$148$	299257.	+	199947.i	1.12303	+	0.750343i
$149$	−39007.8			−0.143941			−0.0719707	−	0.997407i	$-0.522929\pi$
$149$	−39007.8			−0.143941			−0.0719707	+	0.997407i	$0.522929\pi$
$150$	−72473.5	+	238924.i	−0.262997	+	0.867025i
$151$			69297.0i			0.247327i	0.992324	+	0.123664i	$0.0394644\pi$
$151$			69297.0i			0.247327i	−0.992324	+	0.123664i	$0.960536\pi$
$152$	−5711.14	+	4687.37i	−0.0200500	+	0.0164558i
$153$		−	13532.8i		−	0.0467368i
$154$		0			0
$155$			416803.i			1.39348i
$156$	10853.7	−	16244.6i	0.0357080	−	0.0534437i
$157$			129707.i			0.419965i	0.977705	+	0.209983i	$0.0673407\pi$
$157$			129707.i			0.419965i	−0.977705	+	0.209983i	$0.932659\pi$
$158$	−8504.64	−	2579.74i	−0.0271027	−	0.00822115i
$159$	293762.			0.921516
$160$	39410.7	+	399886.i	0.121707	+	1.23491i
$161$		0			0
$162$	46983.8	−	154892.i	0.140657	−	0.463704i
$163$		−	311346.i		−	0.917854i	−0.888474	−	0.458927i	$-0.848234\pi$
$163$		−	311346.i		−	0.917854i	0.888474	−	0.458927i	$-0.151766\pi$
$164$	188909.	−	282738.i	0.548458	−	0.820870i
$165$	−932013.			−2.66509
$166$	78624.8	−	259203.i	0.221457	−	0.730079i
$167$	317064.			0.879742			0.439871	−	0.898061i	$-0.355024\pi$
$167$	317064.			0.879742			0.439871	+	0.898061i	$0.355024\pi$
$168$		0			0
$169$	370748.			0.998533
$170$	3491.09	−	11509.1i	0.00926485	−	0.0305435i
$171$	18021.6			0.0471307
$172$	−141239.	+	211390.i	−0.364026	+	0.544833i
$173$			446727.i			1.13482i	0.823435	+	0.567410i	$0.192055\pi$
$173$			446727.i			1.13482i	−0.823435	+	0.567410i	$0.807945\pi$
$174$	293149.	−	966425.i	0.734031	−	2.41989i
$175$		0			0
$176$	−485813.	+	201259.i	−1.18219	+	0.489749i
$177$	−256680.			−0.615826
$178$	−477106.	−	144722.i	−1.12867	−	0.342361i
$179$		−	493691.i		−	1.15166i	−0.817571	−	0.575828i	$-0.804680\pi$
$179$		−	493691.i		−	1.15166i	0.817571	−	0.575828i	$-0.195320\pi$
$180$	544504.	−	814952.i	1.25262	−	1.87478i
$181$			13246.9i			0.0300551i	0.999887	+	0.0150276i	$0.00478360\pi$
$181$			13246.9i			0.0300551i	−0.999887	+	0.0150276i	$0.995216\pi$
$182$		0			0
$183$		−	332616.i		−	0.734203i
$184$	−282595.	−	344316.i	−0.615346	−	0.749744i
$185$		−	780192.i		−	1.67599i
$186$	258137.	−	851003.i	0.547102	−	1.80364i
$187$	15739.2			0.0329138
$188$	208719.	+	139454.i	0.430694	+	0.287765i
$189$		0			0
$190$	15326.6	+	4649.08i	0.0308009	+	0.00934292i
$191$			890892.i			1.76702i	0.468412	+	0.883510i	$0.344826\pi$
$191$			890892.i			1.76702i	−0.468412	+	0.883510i	$0.655174\pi$
$192$	167194.	−	840871.i	0.327315	−	1.64618i
$193$	819556.			1.58375			0.791873	−	0.610686i	$-0.209106\pi$
$193$	819556.			1.58375			0.791873	+	0.610686i	$0.209106\pi$
$194$	−633701.	−	192222.i	−1.20887	−	0.366691i
$195$	−42351.0			−0.0797586
$196$		0			0
$197$	476248.			0.874314			0.437157	−	0.899385i	$-0.355985\pi$
$197$	476248.			0.874314			0.437157	+	0.899385i	$0.355985\pi$
$198$	1.22742e6	+	372317.i	2.22500	+	0.674916i
$199$	160769.			0.287786			0.143893	−	0.989593i	$-0.454038\pi$
$199$	160769.			0.287786			0.143893	+	0.989593i	$0.454038\pi$
$200$	236046.	−	193733.i	0.417274	−	0.342474i
$201$		−	728622.i		−	1.27207i
$202$	342394.	+	103859.i	0.590402	+	0.179088i
$203$		0			0
$204$	−14255.8	+	21336.4i	−0.0239837	+	0.0358960i
$205$	−737123.			−1.22506
$206$	−96656.1	+	318647.i	−0.158694	+	0.523169i
$207$			1.08650e6i			1.76239i
$208$	−22075.5	+	9145.29i	−0.0353796	+	0.0146568i
$209$			20959.9i			0.0331912i
$210$		0			0
$211$			358539.i			0.554409i	0.960811	+	0.277205i	$0.0894080\pi$
$211$			358539.i			0.554409i	−0.960811	+	0.277205i	$0.910592\pi$
$212$	−298745.	−	199604.i	−0.456521	−	0.305021i
$213$			923908.i			1.39534i
$214$	−380642.	−	115461.i	−0.568175	−	0.172346i
$215$	551114.			0.813102
$216$	−726842.	+	596550.i	−1.06000	+	0.869986i
$217$		0			0
$218$	329988.	−	1.08787e6i	0.470280	−	1.55038i
$219$		−	1.43261e6i		−	2.01845i
$220$	947822.	+	633280.i	1.32029	+	0.882143i
$221$	715.195			0.000985018
$222$	−483194.	+	1.59295e6i	−0.658020	+	2.16930i
$223$	−349119.			−0.470123			−0.235062	−	0.971980i	$-0.575529\pi$
$223$	−349119.			−0.470123			−0.235062	+	0.971980i	$0.575529\pi$
$224$		0			0
$225$	−744848.			−0.980870
$226$	161620.	−	532815.i	0.210487	−	0.693914i
$227$	569267.			0.733249			0.366625	−	0.930369i	$-0.380513\pi$
$227$	569267.			0.733249			0.366625	+	0.930369i	$0.380513\pi$
$228$	−28413.7	−	18984.4i	−0.0361985	−	0.0241858i
$229$		−	466817.i		−	0.588245i	−0.955768	−	0.294122i	$-0.904973\pi$
$229$		−	466817.i		−	0.588245i	0.955768	−	0.294122i	$-0.0950273\pi$
$230$	−280286.	+	924021.i	−0.349367	+	1.15176i
$231$		0			0
$232$	−954783.	+	783631.i	−1.16462	+	0.955854i
$233$	274508.			0.331258			0.165629	−	0.986188i	$-0.447035\pi$
$233$	274508.			0.331258			0.165629	+	0.986188i	$0.447035\pi$
$234$	55774.4	+	16918.2i	0.0665879	+	0.0201983i
$235$		−	544151.i		−	0.642761i
$236$	261033.	+	174407.i	0.305082	+	0.203838i
$237$		−	41104.9i		−	0.0475360i
$238$		0			0
$239$		−	351475.i		−	0.398016i	−0.979998	−	0.199008i	$-0.936228\pi$
$239$		−	351475.i		−	0.398016i	0.979998	−	0.199008i	$-0.0637719\pi$
$240$	−1.71698e6	+	711298.i	−1.92414	+	0.797119i
$241$			986016.i			1.09356i	0.837278	+	0.546778i	$0.184146\pi$
$241$			986016.i			1.09356i	−0.837278	+	0.546778i	$0.815854\pi$
$242$	−168569.	+	555722.i	−0.185028	+	0.609985i
$243$	−513634.			−0.558005
$244$	−226005.	+	338258.i	−0.243020	+	0.363726i
$245$		0			0
$246$	1.50501e6	+	456520.i	1.58563	+	0.480975i
$247$			952.425i			0.000993318i
$248$	−840752.	+	690040.i	−0.868038	+	0.712435i
$249$	1.25279e6			1.28050
$250$	540006.	+	163802.i	0.546448	+	0.165756i
$251$	1.12447e6			1.12658			0.563292	−	0.826258i	$-0.309535\pi$
$251$	1.12447e6			1.12658			0.563292	+	0.826258i	$0.309535\pi$
$252$		0			0
$253$	−1.26364e6			−1.24114
$254$	−187985.	−	57022.1i	−0.182827	−	0.0554573i
$255$	55626.1			0.0535708
$256$	−741381.	+	741530.i	−0.707036	+	0.707178i
$257$		−	787911.i		−	0.744123i	−0.928208	−	0.372061i	$-0.878651\pi$
$257$		−	787911.i		−	0.744123i	0.928208	−	0.372061i	$-0.121349\pi$
$258$	−1.12523e6	−	341319.i	−1.05243	−	0.319236i
$259$		0			0
$260$	43069.4	+	28776.5i	0.0395126	+	0.0264000i
$261$	3.01284e6			2.73763
$262$	−623582.	+	2.05577e6i	−0.561229	+	1.85021i
$263$		−	1.41276e6i		−	1.25944i	−0.776822	−	0.629720i	$-0.783169\pi$
$263$		−	1.41276e6i		−	1.25944i	0.776822	−	0.629720i	$-0.216831\pi$
$264$	−1.54300e6	−	1.88000e6i	−1.36256	−	1.66016i
$265$			778856.i			0.681306i
$266$		0			0
$267$		−	2.30596e6i		−	1.97959i
$268$	−495081.	+	740981.i	−0.421055	+	0.630188i
$269$		−	1.62293e6i		−	1.36748i	−0.729728	−	0.683738i	$-0.760353\pi$
$269$		−	1.62293e6i		−	1.36748i	0.729728	−	0.683738i	$-0.239647\pi$
$270$	1.95058e6	+	591676.i	1.62838	+	0.493941i
$271$	−267223.			−0.221030			−0.110515	−	0.993874i	$-0.535250\pi$
$271$	−267223.			−0.221030			−0.110515	+	0.993874i	$0.535250\pi$
$272$	28995.2	−	12011.9i	0.0237631	−	0.00984441i
$273$		0			0
$274$	−436736.	+	1.43979e6i	−0.351433	+	1.15857i
$275$		−	866288.i		−	0.690766i
$276$	1.14454e6	−	1.71302e6i	0.904397	−	1.35360i
$277$	996310.			0.780180			0.390090	−	0.920777i	$-0.372444\pi$
$277$	996310.			0.780180			0.390090	+	0.920777i	$0.372444\pi$
$278$	−649091.	+	2.13986e6i	−0.503725	+	1.66064i
$279$	2.65301e6			2.04046
$280$		0			0
$281$	1.05479e6			0.796893			0.398446	−	0.917192i	$-0.369550\pi$
$281$	1.05479e6			0.796893			0.398446	+	0.917192i	$0.369550\pi$
$282$	−337007.	+	1.11101e6i	−0.252358	+	0.831949i
$283$	−2.35242e6			−1.74602			−0.873009	−	0.487703i	$-0.837835\pi$
$283$	−2.35242e6			−1.74602			−0.873009	+	0.487703i	$0.837835\pi$
$284$	627773.	−	939579.i	0.461856	−	0.691254i
$285$			74077.2i			0.0540222i
$286$	−19676.6	+	64867.9i	−0.0142244	+	0.0468937i
$287$		0			0
$288$	2.54533e6	−	250855.i	1.80827	−	0.178214i
$289$	1.41892e6			0.999338
$290$	2.56230e6	+	777229.i	1.78910	+	0.542693i
$291$		−	3.06282e6i		−	2.12026i
$292$	−973426.	+	1.45691e6i	−0.668107	+	0.999947i
$293$		−	971707.i		−	0.661251i	−0.943762	−	0.330625i	$-0.892740\pi$
$293$		−	971707.i		−	0.661251i	0.943762	−	0.330625i	$-0.107260\pi$
$294$		0			0
$295$		−	680538.i		−	0.455300i
$296$	1.57376e6	−	1.29165e6i	1.04402	−	0.856871i
$297$			2.66751e6i			1.75475i
$298$	−64052.0	+	211161.i	−0.0417823	+	0.137744i
$299$	−57420.3			−0.0371439
$300$	1.17436e6	+	784641.i	0.753353	+	0.503347i
$301$		0			0
$302$	375125.	+	113788.i	0.236678	+	0.0717923i
$303$			1.65487e6i			1.03552i
$304$	15996.2	+	38612.9i	0.00992737	+	0.0239634i
$305$	881871.			0.542819
$306$	−73257.0	−	22221.3i	−0.0447245	−	0.0135664i
$307$	−155431.			−0.0941221			−0.0470611	−	0.998892i	$-0.514986\pi$
$307$	−155431.			−0.0941221			−0.0470611	+	0.998892i	$0.514986\pi$
$308$		0			0
$309$	−1.54009e6			−0.917595
$310$	2.25628e6	+	684403.i	1.33349	+	0.404490i
$311$	−1.33376e6			−0.781948			−0.390974	−	0.920402i	$-0.627862\pi$
$311$	−1.33376e6			−0.781948			−0.390974	+	0.920402i	$0.627862\pi$
$312$	−70114.5	−	85428.1i	−0.0407776	−	0.0496838i
$313$		−	2.33361e6i		−	1.34638i	−0.739469	−	0.673191i	$-0.764923\pi$
$313$		−	2.33361e6i		−	1.34638i	0.739469	−	0.673191i	$-0.235077\pi$
$314$	702140.	+	212982.i	0.401883	+	0.121904i
$315$		0			0
$316$	−27929.7	+	41802.1i	−0.0157344	+	0.0235494i
$317$	−2.80985e6			−1.57049			−0.785244	−	0.619186i	$-0.787463\pi$
$317$	−2.80985e6			−1.57049			−0.785244	+	0.619186i	$0.787463\pi$
$318$	482366.	−	1.59022e6i	0.267491	−	0.881839i
$319$			3.50405e6i			1.92794i
$320$	2.22941e6	+	443283.i	1.21707	+	0.241995i
$321$		−	1.83973e6i		−	0.996533i
$322$		0			0
$323$		−	1250.96i		−	0.000667173i
$324$	−761326.	−	508674.i	−0.402910	−	0.269201i
$325$		−	39364.5i		−	0.0206727i
$326$	−1.68541e6	−	511239.i	−0.878335	−	0.266428i
$327$	5.25794e6			2.71923
$328$	−1.22035e6	−	1.48688e6i	−0.626324	−	0.763119i
$329$		0			0
$330$	−1.53039e6	+	5.04526e6i	−0.773603	+	2.55034i
$331$			1.65727e6i			0.831427i	0.909496	+	0.415713i	$0.136468\pi$
$331$			1.65727e6i			0.831427i	−0.909496	+	0.415713i	$0.863532\pi$
$332$	−1.27404e6	−	851238.i	−0.634362	−	0.423844i
$333$	−4.96603e6			−2.45414
$334$	520628.	−	1.71636e6i	0.255365	−	0.841864i
$335$	1.93181e6			0.940484
$336$		0			0
$337$	1.64034e6			0.786790			0.393395	−	0.919370i	$-0.371301\pi$
$337$	1.64034e6			0.786790			0.393395	+	0.919370i	$0.371301\pi$
$338$	608780.	−	2.00697e6i	0.289847	−	0.955541i
$339$	2.57522e6			1.21707
$340$	−56569.6	−	37796.5i	−0.0265391	−	0.0177319i
$341$			3.08556e6i			1.43697i
$342$	29592.1	−	97556.3i	0.0136807	−	0.0451014i
$343$		0			0
$344$	912399.	+	1.11168e6i	0.415708	+	0.506503i
$345$	−4.46601e6			−2.02009
$346$	2.41826e6	+	733539.i	1.08596	+	0.329407i
$347$		−	484035.i		−	0.215801i	−0.994162	−	0.107900i	$-0.965587\pi$
$347$		−	484035.i		−	0.215801i	0.994162	−	0.107900i	$-0.0344128\pi$
$348$	−4.75018e6	−	3.17380e6i	−2.10263	−	1.40485i
$349$			815617.i			0.358445i	0.983809	+	0.179223i	$0.0573582\pi$
$349$			815617.i			0.358445i	−0.983809	+	0.179223i	$0.942642\pi$
$350$		0			0
$351$			121213.i			0.0525147i
$352$	291754.	+	2.96032e6i	0.125505	+	1.27345i
$353$		−	1.51647e6i		−	0.647735i	−0.946102	−	0.323867i	$-0.895017\pi$
$353$		−	1.51647e6i		−	0.647735i	0.946102	−	0.323867i	$-0.104983\pi$
$354$	−421475.	+	1.38948e6i	−0.178757	+	0.589311i
$355$	−2.44957e6			−1.03162
$356$	−1.56685e6	+	2.34508e6i	−0.655241	+	0.980691i
$357$		0			0
$358$	−2.67249e6	−	810656.i	−1.10207	−	0.334294i
$359$		−	2.77751e6i		−	1.13742i	−0.822539	−	0.568709i	$-0.807443\pi$
$359$		−	2.77751e6i		−	1.13742i	0.822539	−	0.568709i	$-0.192557\pi$
$360$	−3.51748e6	−	4.28573e6i	−1.43046	−	1.74289i
$361$	−2.47443e6			−0.999327
$362$	71709.5	+	21751.8i	0.0287611	+	0.00872418i
$363$	−2.68593e6			−1.06986
$364$		0			0
$365$	3.79831e6			1.49231
$366$	−1.80055e6	−	546166.i	−0.702591	−	0.213119i
$367$	755297.			0.292720			0.146360	−	0.989231i	$-0.453244\pi$
$367$	755297.			0.292720			0.146360	+	0.989231i	$0.453244\pi$
$368$	−2.32791e6	+	964390.i	−0.896081	+	0.371222i
$369$			4.69190e6i			1.79384i
$370$	−4.22341e6	−	1.28110e6i	−1.60383	−	0.486495i
$371$		0			0
$372$	−4.18286e6	−	2.79475e6i	−1.56717	−	1.04709i
$373$	−1.76602e6			−0.657240			−0.328620	−	0.944462i	$-0.606584\pi$
$373$	−1.76602e6			−0.657240			−0.328620	+	0.944462i	$0.606584\pi$
$374$	25844.2	−	85200.9i	0.00955398	−	0.0314967i
$375$			2.60997e6i			0.958425i
$376$	1.09763e6	−	900872.i	0.400393	−	0.328619i
$377$			159226.i			0.0576979i
$378$		0			0
$379$		−	804078.i		−	0.287541i	−0.989611	−	0.143771i	$-0.954077\pi$
$379$		−	804078.i		−	0.287541i	0.989611	−	0.143771i	$-0.0459228\pi$
$380$	50333.6	−	75333.7i	0.0178813	−	0.0267627i
$381$		−	908575.i		−	0.320663i
$382$	4.82266e6	+	1.46287e6i	1.69094	+	0.512918i
$383$	5.33735e6			1.85921			0.929606	−	0.368555i	$-0.120147\pi$
$383$	5.33735e6			1.85921			0.929606	+	0.368555i	$0.120147\pi$
$384$	−4.27734e6	−	2.28580e6i	−1.48029	−	0.791062i
$385$		0			0
$386$	1.34574e6	−	4.43650e6i	0.459718	−	1.51556i
$387$		−	3.50792e6i		−	1.19062i
$388$	−2.08111e6	+	3.11478e6i	−0.701805	+	1.05038i
$389$	4.94891e6			1.65819			0.829097	−	0.559105i	$-0.188855\pi$
$389$	4.94891e6			1.65819			0.829097	+	0.559105i	$0.188855\pi$
$390$	−69541.7	+	229259.i	−0.0231517	+	0.0763245i
$391$	75418.8			0.0249481
$392$		0			0
$393$	−9.93600e6			−3.24511
$394$	782013.	−	2.57807e6i	0.253789	−	0.836670i
$395$	108982.			0.0351448
$396$	4.03092e6	−	6.03302e6i	1.29171	−	1.93329i
$397$		−	3.47467e6i		−	1.10646i	−0.833028	−	0.553231i	$-0.813395\pi$
$397$		−	3.47467e6i		−	1.10646i	0.833028	−	0.553231i	$-0.186605\pi$
$398$	263988.	−	870291.i	0.0835365	−	0.275395i
$399$		0			0
$400$	−661137.	−	1.59590e6i	−0.206605	−	0.498719i
$401$	1.33076e6			0.413274			0.206637	−	0.978418i	$-0.433748\pi$
$401$	1.33076e6			0.413274			0.206637	+	0.978418i	$0.433748\pi$
$402$	−3.94424e6	−	1.19642e6i	−1.21730	−	0.369248i
$403$			140209.i			0.0430045i
$404$	1.12444e6	−	1.68294e6i	0.342755	−	0.512997i
$405$			1.98485e6i			0.601298i
$406$		0			0
$407$		−	5.77570e6i		−	1.72830i
$408$	92092.0	+	112206.i	0.0273887	+	0.0333707i
$409$		−	6.34307e6i		−	1.87496i	−0.348043	−	0.937479i	$-0.613154\pi$
$409$		−	6.34307e6i		−	1.87496i	0.348043	−	0.937479i	$-0.386846\pi$
$410$	−1.21038e6	+	3.99027e6i	−0.355600	+	1.17231i
$411$	−6.95884e6			−2.03204
$412$	1.56622e6	+	1.04646e6i	0.454578	+	0.303723i
$413$		0			0
$414$	5.88153e6	+	1.78406e6i	1.68651	+	0.511575i
$415$			3.32153e6i			0.946713i
$416$	13257.4	+	134518.i	0.00375601	+	0.0381108i
$417$	−1.03425e7			−2.91262
$418$	113462.	+	34416.7i	0.0317621	+	0.00963450i
$419$	−2.73017e6			−0.759720			−0.379860	−	0.925044i	$-0.624028\pi$
$419$	−2.73017e6			−0.759720			−0.379860	+	0.925044i	$0.624028\pi$
$420$		0			0
$421$	4.79106e6			1.31743			0.658713	−	0.752394i	$-0.271101\pi$
$421$	4.79106e6			1.31743			0.658713	+	0.752394i	$0.271101\pi$
$422$	1.94088e6	+	588732.i	0.530538	+	0.160930i
$423$	−3.46360e6			−0.941189
$424$	−1.57106e6	+	1.28944e6i	−0.424404	+	0.348326i
$425$			51703.4i			0.0138850i
$426$	5.00138e6	+	1.51708e6i	1.33526	+	0.405029i
$427$		0			0
$428$	−1.25005e6	+	1.87094e6i	−0.329851	+	0.493685i
$429$	−313521.			−0.0822477
$430$	904945.	−	2.98334e6i	0.236021	−	0.778093i
$431$			2.19145e6i			0.568250i	0.958787	+	0.284125i	$0.0917030\pi$
$431$			2.19145e6i			0.568250i	−0.958787	+	0.284125i	$0.908297\pi$
$432$	2.03580e6	+	4.91416e6i	0.524839	+	1.26689i
$433$		−	3.11651e6i		−	0.798819i	−0.916773	−	0.399410i	$-0.869215\pi$
$433$		−	3.11651e6i		−	0.798819i	0.916773	−	0.399410i	$-0.130785\pi$
$434$		0			0
$435$			1.23842e7i			3.13793i
$436$	−5.34712e6	−	3.57264e6i	−1.34711	−	0.900063i
$437$			100435.i			0.0251584i
$438$	−7.75516e6	−	2.35240e6i	−1.93155	−	0.585902i
$439$	2.52732e6			0.625891			0.312945	−	0.949771i	$-0.398684\pi$
$439$	2.52732e6			0.625891			0.312945	+	0.949771i	$0.398684\pi$
$440$	4.98448e6	−	4.09097e6i	1.22741	−	1.00738i
$441$		0			0
$442$	1174.37	−	3871.56i	0.000285924	−	0.000942607i
$443$			2.39692e6i			0.580288i	0.956983	+	0.290144i	$0.0937032\pi$
$443$			2.39692e6i			0.580288i	−0.956983	+	0.290144i	$0.906297\pi$
$444$	7.82968e6	+	5.23134e6i	1.88489	+	1.25938i
$445$	6.11384e6			1.46357
$446$	−573264.	+	1.88988e6i	−0.136464	+	0.449882i
$447$	−1.02059e6			−0.241591
$448$		0			0
$449$	1.43941e6			0.336952			0.168476	−	0.985706i	$-0.446115\pi$
$449$	1.43941e6			0.336952			0.168476	+	0.985706i	$0.446115\pi$
$450$	−1.22306e6	+	4.03208e6i	−0.284720	+	0.938638i
$451$	−5.45687e6			−1.26329
$452$	−2.61890e6	−	1.74980e6i	−0.602938	−	0.402848i
$453$			1.81306e6i			0.415114i
$454$	934754.	−	3.08161e6i	0.212842	−	0.701679i
$455$		0			0
$456$	−149424.	+	122639.i	−0.0336519	+	0.0276195i
$457$	6.14672e6			1.37674			0.688372	−	0.725358i	$-0.258326\pi$
$457$	6.14672e6			1.37674			0.688372	+	0.725358i	$0.258326\pi$
$458$	−2.52702e6	−	766528.i	−0.562917	−	0.170751i
$459$		−	159207.i		−	0.0352721i
$460$	4.54176e6	+	3.03454e6i	1.00076	+	0.668649i
$461$			3.73235e6i			0.817955i	0.912544	+	0.408978i	$0.134115\pi$
$461$			3.73235e6i			0.817955i	−0.912544	+	0.408978i	$0.865885\pi$
$462$		0			0
$463$			2.51379e6i			0.544975i	0.962159	+	0.272487i	$0.0878463\pi$
$463$			2.51379e6i			0.544975i	−0.962159	+	0.272487i	$0.912154\pi$
$464$	2.67424e6	+	6.45527e6i	0.576641	+	1.39194i
$465$			1.09051e7i			2.33882i
$466$	450751.	−	1.48599e6i	0.0961550	−	0.316995i
$467$	−156360.			−0.0331768			−0.0165884	−	0.999862i	$-0.505280\pi$
$467$	−156360.			−0.0331768			−0.0165884	+	0.999862i	$0.505280\pi$
$468$	183167.	−	274143.i	0.0386573	−	0.0578579i
$469$		0			0
$470$	−2.94565e6	−	893512.i	−0.615087	−	0.186576i
$471$			3.39361e6i			0.704870i
$472$	1.37274e6	−	1.12667e6i	0.283618	−	0.232777i
$473$	4.07985e6			0.838477
$474$	−222513.	−	67495.4i	−0.0454893	−	0.0137984i
$475$	−68853.3			−0.0140020
$476$		0			0
$477$	4.95753e6			0.997630
$478$	−1.90264e6	−	577133.i	−0.380879	−	0.115533i
$479$	4.92664e6			0.981096			0.490548	−	0.871414i	$-0.336797\pi$
$479$	4.92664e6			0.981096			0.490548	+	0.871414i	$0.336797\pi$
$480$	1.03113e6	+	1.04625e7i	0.204273	+	2.07268i
$481$		−	262450.i		−	0.0517230i
$482$	5.33759e6	+	1.61907e6i	1.04647	+	0.317429i
$483$		0			0
$484$	2.73149e6	+	1.82502e6i	0.530012	+	0.354124i
$485$	8.12051e6			1.56758
$486$	−843402.	+	2.78045e6i	−0.161973	+	0.533979i
$487$		−	6.02881e6i		−	1.15188i	−0.817490	−	0.575942i	$-0.804635\pi$
$487$		−	6.02881e6i		−	1.15188i	0.817490	−	0.575942i	$-0.195365\pi$
$488$	1.45998e6	+	1.77886e6i	0.277523	+	0.338137i
$489$		−	8.14595e6i		−	1.54053i
$490$		0			0
$491$		−	5.51492e6i		−	1.03237i	−0.856477	−	0.516185i	$-0.827352\pi$
$491$		−	5.51492e6i		−	1.03237i	0.856477	−	0.516185i	$-0.172648\pi$
$492$	4.94256e6	−	7.39746e6i	0.920532	−	1.37775i
$493$		−	209135.i		−	0.0387534i
$494$	5155.76	+	1563.91i	0.000950550	+	0.000288333i
$495$	−1.57287e7			−2.88522
$496$	2.35485e6	+	5.68430e6i	0.429793	+	1.03746i
$497$		0			0
$498$	2.05711e6	−	6.78171e6i	0.371694	−	1.22537i
$499$			2.46560e6i			0.443273i	0.975129	+	0.221636i	$0.0711398\pi$
$499$			2.46560e6i			0.443273i	−0.975129	+	0.221636i	$0.928860\pi$
$500$	1.77341e6	−	2.65425e6i	0.317238	−	0.474806i
$501$	8.29555e6			1.47656
$502$	1.84641e6	−	6.08708e6i	0.327016	−	1.07808i
$503$	−4.44315e6			−0.783016			−0.391508	−	0.920175i	$-0.628047\pi$
$503$	−4.44315e6			−0.783016			−0.391508	+	0.920175i	$0.628047\pi$
$504$		0			0
$505$	−4.38758e6			−0.765590
$506$	−2.07494e6	+	6.84045e6i	−0.360270	+	1.18771i
$507$	9.70015e6			1.67594
$508$	−617355.	+	923987.i	−0.106139	+	0.158857i
$509$		−	3.87559e6i		−	0.663046i	−0.943447	−	0.331523i	$-0.892438\pi$
$509$		−	3.87559e6i		−	0.663046i	0.943447	−	0.331523i	$-0.107562\pi$
$510$	91339.7	−	301120.i	0.0155501	−	0.0512642i
$511$		0			0
$512$	2.79675e6	+	5.23092e6i	0.471497	+	0.881868i
$513$	212016.			0.0355693
$514$	−4.26520e6	−	1.29377e6i	−0.712084	−	0.215998i
$515$		−	4.08327e6i		−	0.678407i
$516$	−3.69532e6	+	5.53074e6i	−0.610982	+	0.914449i
$517$		−	4.02831e6i		−	0.662821i
$518$		0			0
$519$			1.16880e7i			1.90468i
$520$	226497.	−	185895.i	0.0367328	−	0.0301481i
$521$		−	3.35203e6i		−	0.541021i	−0.962717	−	0.270511i	$-0.912808\pi$
$521$		−	3.35203e6i		−	0.541021i	0.962717	−	0.270511i	$-0.0871925\pi$
$522$	4.94718e6	−	1.63094e7i	0.794659	−	2.61976i
$523$	−6.04485e6			−0.966342			−0.483171	−	0.875526i	$-0.660515\pi$
$523$	−6.04485e6			−0.966342			−0.483171	+	0.875526i	$0.660515\pi$
$524$	1.01045e7	+	6.75127e6i	1.60764	+	1.07413i
$525$		0			0
$526$	−7.64766e6	−	2.31979e6i	−1.20521	−	0.365581i
$527$		−	184158.i		−	0.0288844i
$528$	−1.27107e7	+	5.26568e6i	−1.98419	+	0.821996i
$529$	381249.			0.0592339
$530$	4.21617e6	+	1.27890e6i	0.651972	+	0.197765i
$531$	−4.33172e6			−0.666691
$532$		0			0
$533$	−247962.			−0.0378066
$534$	−1.24829e7	−	3.78646e6i	−1.89435	−	0.574620i
$535$	4.87770e6			0.736768
$536$	3.19821e6	+	3.89673e6i	0.480834	+	0.585853i
$537$		−	1.29168e7i		−	1.93294i
$538$	−8.78541e6	−	2.66490e6i	−1.30860	−	0.396941i
$539$		0			0
$540$	6.40583e6	−	9.58753e6i	0.945347	−	1.41489i
$541$	−3.19042e6			−0.468656			−0.234328	−	0.972158i	$-0.575289\pi$
$541$	−3.19042e6			−0.468656			−0.234328	+	0.972158i	$0.575289\pi$
$542$	−438789.	+	1.44656e6i	−0.0641589	+	0.211513i
$543$			346588.i			0.0504446i
$544$	−17413.0	−	176683.i	−0.00252276	−	0.0255975i
$545$			1.39404e7i			2.01041i
$546$		0			0
$547$			6.68501e6i			0.955286i	0.878554	+	0.477643i	$0.158509\pi$
$547$			6.68501e6i			0.955286i	−0.878554	+	0.477643i	$0.841491\pi$
$548$	7.07688e6	+	4.72836e6i	1.00668	+	0.672604i
$549$		−	5.61323e6i		−	0.794845i
$550$	−4.68947e6	−	1.42247e6i	−0.661024	−	0.200510i
$551$	278505.			0.0390800
$552$	−7.39372e6	−	9.00858e6i	−1.03280	−	1.25837i
$553$		0			0
$554$	1.63597e6	−	5.39332e6i	0.226465	−	0.746589i
$555$		−	2.04127e7i		−	2.81299i
$556$	1.05179e7	+	7.02744e6i	1.44292	+	0.964074i
$557$	1.74226e6			0.237945			0.118972	−	0.992898i	$-0.462040\pi$
$557$	1.74226e6			0.237945			0.118972	+	0.992898i	$0.462040\pi$
$558$	4.35633e6	−	1.43615e7i	0.592291	−	1.95261i
$559$	185390.			0.0250932
$560$		0			0
$561$	411795.			0.0552426
$562$	1.73200e6	−	5.70988e6i	0.231316	−	0.762582i
$563$	−6.82985e6			−0.908114			−0.454057	−	0.890973i	$-0.650024\pi$
$563$	−6.82985e6			−0.908114			−0.454057	+	0.890973i	$0.650024\pi$
$564$	5.46087e6	+	3.64864e6i	0.722877	+	0.482984i
$565$			6.82771e6i			0.899817i
$566$	−3.86275e6	+	1.27343e7i	−0.506822	+	1.67084i
$567$		0			0
$568$	−4.05540e6	−	4.94113e6i	−0.527427	−	0.642622i
$569$	−7.29403e6			−0.944467			−0.472233	−	0.881474i	$-0.656552\pi$
$569$	−7.29403e6			−0.944467			−0.472233	+	0.881474i	$0.656552\pi$
$570$	401002.	+	121637.i	0.0516962	+	0.0156812i
$571$			1.05741e7i			1.35723i	0.734496	+	0.678613i	$0.237419\pi$
$571$			1.05741e7i			1.35723i	−0.734496	+	0.678613i	$0.762581\pi$
$572$	318839.	+	213030.i	0.0407457	+	0.0272239i
$573$			2.33090e7i			2.96577i
$574$		0			0
$575$		−	4.15107e6i		−	0.523589i
$576$	2.82156e6	−	1.41905e7i	0.354350	−	1.78214i
$577$			8.99832e6i			1.12518i	0.826736	+	0.562590i	$0.190195\pi$
$577$			8.99832e6i			1.12518i	−0.826736	+	0.562590i	$0.809805\pi$
$578$	2.32991e6	−	7.68102e6i	0.290081	−	0.956311i
$579$	2.14426e7			2.65816
$580$	8.41474e6	−	1.25942e7i	1.03865	−	1.55454i
$581$		0			0
$582$	−1.65800e7	−	5.02925e6i	−2.02897	−	0.615454i
$583$			5.76581e6i			0.702568i
$584$	6.28831e6	+	7.66174e6i	0.762960	+	0.929598i
$585$	−714716.			−0.0863463
$586$	−5.26014e6	−	1.59557e6i	−0.632780	−	0.191943i
$587$	3.22085e6			0.385812			0.192906	−	0.981217i	$-0.438209\pi$
$587$	3.22085e6			0.385812			0.192906	+	0.981217i	$0.438209\pi$
$588$		0			0
$589$	245243.			0.0291278
$590$	−3.68395e6	−	1.11746e6i	−0.435696	−	0.132161i
$591$	1.24604e7			1.46745
$592$	−4.40792e6	−	1.06401e7i	−0.516927	−	1.24780i
$593$			1.06697e7i			1.24600i	0.782223	+	0.622998i	$0.214086\pi$
$593$			1.06697e7i			1.24600i	−0.782223	+	0.622998i	$0.785914\pi$
$594$	1.44400e7	+	4.38013e6i	1.67920	+	0.509356i
$595$		0			0
$596$	1.03790e6	+	693464.i	0.119685	+	0.0799666i
$597$	4.20631e6			0.483021
$598$	−94285.9	+	310833.i	−0.0107819	+	0.0355446i
$599$			1.21184e7i			1.37999i	0.723813	+	0.689996i	$0.242388\pi$
$599$			1.21184e7i			1.37999i	−0.723813	+	0.689996i	$0.757612\pi$
$600$	6.17583e6	−	5.06876e6i	0.700353	−	0.574809i
$601$		−	5.44705e6i		−	0.615142i	−0.951525	−	0.307571i	$-0.900484\pi$
$601$		−	5.44705e6i		−	0.615142i	0.951525	−	0.307571i	$-0.0995162\pi$
$602$		0			0
$603$		−	1.22962e7i		−	1.37714i
$604$	1.23193e6	−	1.84382e6i	0.137402	−	0.205649i
$605$		−	7.12124e6i		−	0.790983i
$606$	8.95829e6	+	2.71734e6i	0.990931	+	0.300582i
$607$	−9.91654e6			−1.09242			−0.546208	−	0.837649i	$-0.683929\pi$
$607$	−9.91654e6			−1.09242			−0.546208	+	0.837649i	$0.683929\pi$
$608$	235289.	−	23188.9i	0.0258132	−	0.00254402i
$609$		0			0
$610$	1.44806e6	−	4.77382e6i	0.157566	−	0.519448i
$611$		−	183048.i		−	0.0198363i
$612$	−240580.	+	360074.i	−0.0259646	+	0.0388609i
$613$	−5.42686e6			−0.583307			−0.291653	−	0.956524i	$-0.594205\pi$
$613$	−5.42686e6			−0.583307			−0.291653	+	0.956524i	$0.594205\pi$
$614$	−255222.	+	841394.i	−0.0273211	+	0.0900696i
$615$	−1.92859e7			−2.05613
$616$		0			0
$617$	4.41338e6			0.466722			0.233361	−	0.972390i	$-0.425028\pi$
$617$	4.41338e6			0.466722			0.233361	+	0.972390i	$0.425028\pi$
$618$	−2.52888e6	+	8.33698e6i	−0.266353	+	0.878087i
$619$	3.92243e6			0.411461			0.205730	−	0.978609i	$-0.434043\pi$
$619$	3.92243e6			0.411461			0.205730	+	0.978609i	$0.434043\pi$
$620$	7.40975e6	−	1.10901e7i	0.774149	−	1.15866i
$621$			1.27821e7i			1.33007i
$622$	−2.19008e6	+	7.22005e6i	−0.226978	+	0.748280i
$623$		0			0
$624$	−577578.	+	239275.i	−0.0593812	+	0.0246000i
$625$	−1.21915e7			−1.24841
$626$	−1.26325e7	−	3.83186e6i	−1.28841	−	0.390818i
$627$			548388.i			0.0557081i
$628$	2.30587e6	−	3.45117e6i	0.233311	−	0.349194i
$629$			344715.i			0.0347403i
$630$		0			0
$631$			8.21028e6i			0.820889i	0.911886	+	0.410445i	$0.134626\pi$
$631$			8.21028e6i			0.820889i	−0.911886	+	0.410445i	$0.865374\pi$
$632$	180425.	+	219832.i	0.0179682	+	0.0218927i
$633$			9.38070e6i			0.930521i
$634$	−4.61386e6	+	1.52105e7i	−0.455870	+	1.50287i
$635$	2.40892e6			0.237076
$636$	−7.81627e6	−	5.22238e6i	−0.766226	−	0.511948i
$637$		0			0
$638$	1.89685e7	+	5.75376e6i	1.84493	+	0.559629i
$639$			1.55919e7i			1.51059i
$640$	6.06038e6	−	1.13406e7i	0.584857	−	1.09442i
$641$	−8.07881e6			−0.776609			−0.388304	−	0.921531i	$-0.626939\pi$
$641$	−8.07881e6			−0.776609			−0.388304	+	0.921531i	$0.626939\pi$
$642$	−9.95900e6	−	3.02089e6i	−0.953626	−	0.289266i
$643$	2.05710e7			1.96213			0.981066	−	0.193675i	$-0.0620406\pi$
$643$	2.05710e7			1.96213			0.981066	+	0.193675i	$0.0620406\pi$
$644$		0			0
$645$	1.44192e7			1.36471
$646$	−6771.84	−	2054.12i	−0.000638448	−	0.000193662i
$647$	−1.36372e7			−1.28075			−0.640373	−	0.768064i	$-0.721220\pi$
$647$	−1.36372e7			−1.28075			−0.640373	+	0.768064i	$0.721220\pi$
$648$	−4.00372e6	+	3.28602e6i	−0.374564	+	0.307421i
$649$		−	5.03797e6i		−	0.469509i
$650$	−213091.	−	64637.7i	−0.0197826	−	0.00600070i
$651$		0			0
$652$	−5.53497e6	+	8.28412e6i	−0.509913	+	0.763181i
$653$	−1.89923e7			−1.74299			−0.871494	−	0.490407i	$-0.836848\pi$
$653$	−1.89923e7			−1.74299			−0.871494	+	0.490407i	$0.836848\pi$
$654$	8.63369e6	−	2.84628e7i	0.789318	−	2.60215i
$655$		−	2.63434e7i		−	2.39922i
$656$	−1.00528e7	+	4.16459e6i	−0.912067	+	0.377844i
$657$		−	2.41768e7i		−	2.18517i
$658$		0			0
$659$			5.44490e6i			0.488401i	0.969725	+	0.244200i	$0.0785254\pi$
$659$			5.44490e6i			0.488401i	−0.969725	+	0.244200i	$0.921475\pi$
$660$	2.47985e7	+	1.65689e7i	2.21598	+	1.48059i
$661$			511327.i			0.0455192i	0.999741	+	0.0227596i	$0.00724524\pi$
$661$			511327.i			0.0455192i	−0.999741	+	0.0227596i	$0.992755\pi$
$662$	8.97130e6	+	2.72129e6i	0.795629	+	0.241340i
$663$	18712.1			0.00165325
$664$	−6.70001e6	+	5.49898e6i	−0.589733	+	0.484018i
$665$		0			0
$666$	−8.15438e6	+	2.68826e7i	−0.712369	+	2.34847i
$667$			1.67907e7i			1.46135i
$668$	−8.43627e6	−	5.63663e6i	−0.731491	−	0.488740i
$669$	−9.13425e6			−0.789055
$670$	3.17208e6	−	1.04574e7i	0.272997	−	0.899991i
$671$	6.52842e6			0.559760
$672$		0			0
$673$	−1.66700e7			−1.41873			−0.709364	−	0.704843i	$-0.751018\pi$
$673$	−1.66700e7			−1.41873			−0.709364	+	0.704843i	$0.751018\pi$
$674$	2.69349e6	−	8.87963e6i	0.228384	−	0.752914i
$675$	−8.76279e6			−0.740258
$676$	−9.86468e6	−	6.59101e6i	−0.830264	−	0.554735i
$677$			973622.i			0.0816429i	0.999166	+	0.0408215i	$0.0129975\pi$
$677$			973622.i			0.0816429i	−0.999166	+	0.0408215i	$0.987003\pi$
$678$	4.22858e6	−	1.39404e7i	0.353281	−	1.16467i
$679$		0			0
$680$	−297493.	+	244165.i	−0.0246720	+	0.0202493i
$681$	1.48941e7			1.23069
$682$	1.67030e7	+	5.06658e6i	1.37510	+	0.417113i
$683$		−	5.76002e6i		−	0.472468i	−0.971696	−	0.236234i	$-0.924087\pi$
$683$		−	5.76002e6i		−	0.472468i	0.971696	−	0.236234i	$-0.0759131\pi$
$684$	−479510.	−	320381.i	−0.0391884	−	0.0261834i
$685$		−	1.84501e7i		−	1.50235i
$686$		0			0
$687$		−	1.22137e7i		−	0.987311i
$688$	7.51601e6	−	3.11368e6i	0.605363	−	0.250785i
$689$			262001.i			0.0210259i
$690$	−7.33332e6	+	2.41758e7i	−0.586378	+	1.93312i
$691$	−3.72684e6			−0.296925			−0.148462	−	0.988918i	$-0.547432\pi$
$691$	−3.72684e6			−0.296925			−0.148462	+	0.988918i	$0.547432\pi$
$692$	7.94172e6	−	1.18863e7i	0.630448	−	0.943584i
$693$		0			0
$694$	−2.62022e6	−	794800.i	−0.206509	−	0.0626410i
$695$		−	2.74211e7i		−	2.15339i
$696$	−2.49806e7	+	2.05027e7i	−1.95470	+	1.60431i
$697$	325686.			0.0253932
$698$	4.41517e6	+	1.33927e6i	0.343012	+	0.104047i
$699$	7.18215e6			0.555983
$700$		0			0
$701$	1.74156e7			1.33858			0.669289	−	0.743002i	$-0.266599\pi$
$701$	1.74156e7			1.33858			0.669289	+	0.743002i	$0.266599\pi$
$702$	656160.	+	199035.i	0.0502536	+	0.0152436i
$703$	−459057.			−0.0350331
$704$	1.65042e7	+	3.28159e6i	1.25505	+	0.249547i
$705$		−	1.42370e7i		−	1.07881i
$706$	−8.20910e6	−	2.49009e6i	−0.619846	−	0.188020i
$707$		0			0
$708$	6.82959e6	+	4.56314e6i	0.512049	+	0.342122i
$709$	1.04824e7			0.783147			0.391573	−	0.920147i	$-0.371931\pi$
$709$	1.04824e7			0.783147			0.391573	+	0.920147i	$0.371931\pi$
$710$	−4.02227e6	+	1.32602e7i	−0.299451	+	0.987201i
$711$		−	693686.i		−	0.0514622i
$712$	1.01218e7	+	1.23325e7i	0.748268	+	0.911697i
$713$			1.47853e7i			1.08920i
$714$		0			0
$715$		−	831244.i		−	0.0608084i
$716$	−8.77663e6	+	1.31359e7i	−0.639802	+	0.957583i
$717$		−	9.19589e6i		−	0.668030i
$718$	−1.50355e7	−	4.56076e6i	−1.08845	−	0.330161i
$719$	1.78933e6			0.129082			0.0645412	−	0.997915i	$-0.479442\pi$
$719$	1.78933e6			0.129082			0.0645412	+	0.997915i	$0.479442\pi$
$720$	−2.89757e7	+	1.20039e7i	−2.08307	+	0.862958i
$721$		0			0
$722$	−4.06309e6	+	1.33948e7i	−0.290077	+	0.956300i
$723$			2.57978e7i			1.83543i
$724$	235498.	−	352467.i	0.0166971	−	0.0249903i
$725$	−1.15108e7			−0.813321
$726$	−4.41038e6	+	1.45397e7i	−0.310552	+	1.02380i
$727$	−5.13734e6			−0.360498			−0.180249	−	0.983621i	$-0.557690\pi$
$727$	−5.13734e6			−0.360498			−0.180249	+	0.983621i	$0.557690\pi$
$728$		0			0
$729$	−2.03916e7			−1.42112
$730$	6.23694e6	−	2.05614e7i	0.433176	−	1.42805i
$731$	−243501.			−0.0168542
$732$	−5.91311e6	+	8.85008e6i	−0.407886	+	0.610477i
$733$			2.74447e7i			1.88668i	0.331823	+	0.943342i	$0.392336\pi$
$733$			2.74447e7i			1.88668i	−0.331823	+	0.943342i	$0.607664\pi$
$734$	1.24022e6	−	4.08864e6i	0.0849687	−	0.280117i
$735$		0			0
$736$	1.39802e6	+	1.41852e7i	0.0951306	+	0.965255i
$737$	1.43010e7			0.969835
$738$	2.53986e7	+	7.70424e6i	1.71660	+	0.520701i
$739$			2.57113e7i			1.73186i	0.500162	+	0.865932i	$0.333274\pi$
$739$			2.57113e7i			1.73186i	−0.500162	+	0.865932i	$0.666726\pi$
$740$	−1.38699e7	+	2.07589e7i	−0.931096	+	1.39356i
$741$			24919.0i			0.00166719i
$742$		0			0
$743$		−	1.13613e7i		−	0.755016i	−0.926006	−	0.377508i	$-0.876781\pi$
$743$		−	1.13613e7i		−	0.755016i	0.926006	−	0.377508i	$-0.123219\pi$
$744$	−2.19972e7	+	1.80540e7i	−1.45692	+	1.19575i
$745$		−	2.70590e6i		−	0.178616i
$746$	−2.89986e6	+	9.55999e6i	−0.190779	+	0.628942i
$747$	2.11420e7			1.38626
$748$	−418780.	−	279805.i	−0.0273673	−	0.0182853i
$749$		0			0
$750$	1.41286e7	+	4.28566e6i	0.917159	+	0.278205i
$751$		−	2.19835e7i		−	1.42232i	−0.703032	−	0.711158i	$-0.748171\pi$
$751$		−	2.19835e7i		−	1.42232i	0.703032	−	0.711158i	$-0.251829\pi$
$752$	−3.07434e6	−	7.42105e6i	−0.198247	−	0.478543i
$753$	2.94203e7			1.89086
$754$	861935.	+	261453.i	0.0552136	+	0.0167481i
$755$	−4.80700e6			−0.306907
$756$		0			0
$757$	−2.19968e7			−1.39515			−0.697573	−	0.716513i	$-0.745737\pi$
$757$	−2.19968e7			−1.39515			−0.697573	+	0.716513i	$0.745737\pi$
$758$	−4.35271e6	−	1.32032e6i	−0.275161	−	0.0834654i
$759$	−3.30615e7			−2.08314
$760$	−325154.	−	396171.i	−0.0204200	−	0.0248799i
$761$		−	1.70822e7i		−	1.06926i	−0.845087	−	0.534629i	$-0.820451\pi$
$761$		−	1.70822e7i		−	1.06926i	0.845087	−	0.534629i	$-0.179549\pi$
$762$	−4.91839e6	−	1.49191e6i	−0.306856	−	0.0930796i
$763$		0			0
$764$	1.58379e7	−	2.37044e7i	0.981667	−	1.46925i
$765$	938745.			0.0579955
$766$	8.76409e6	−	2.88926e7i	0.539678	−	1.77916i
$767$		−	228927.i		−	0.0140511i
$768$	−1.93972e7	+	1.94012e7i	−1.18669	+	1.18693i
$769$		−	9.64197e6i		−	0.587963i	−0.955811	−	0.293981i	$-0.905020\pi$
$769$		−	9.64197e6i		−	0.587963i	0.955811	−	0.293981i	$-0.0949804\pi$
$770$		0			0
$771$		−	2.06147e7i		−	1.24894i
$772$	−2.18063e7	−	1.45697e7i	−1.31686	−	0.879849i
$773$			1.98984e6i			0.119776i	0.998205	+	0.0598878i	$0.0190743\pi$
$773$			1.98984e6i			0.119776i	−0.998205	+	0.0598878i	$0.980926\pi$
$774$	−1.89894e7	−	5.76011e6i	−1.13935	−	0.345603i
$775$	−1.01361e7			−0.606200
$776$	1.34439e7	+	1.63802e7i	0.801442	+	0.976485i
$777$		0			0
$778$	8.12626e6	−	2.67899e7i	0.481328	−	1.58680i
$779$			433716.i			0.0256072i
$780$	1.12685e6	+	752899.i	0.0663180	+	0.0443098i
$781$	−1.81340e7			−1.06381
$782$	123840.	−	408264.i	0.00724176	−	0.0238740i
$783$	3.54447e7			2.06608
$784$		0			0
$785$	−8.99751e6			−0.521133
$786$	−1.63152e7	+	5.37865e7i	−0.941968	+	3.10539i
$787$	−1.45609e7			−0.838012			−0.419006	−	0.907984i	$-0.637621\pi$
$787$	−1.45609e7			−0.838012			−0.419006	+	0.907984i	$0.637621\pi$
$788$	−1.26718e7	−	8.46653e6i	−0.726978	−	0.485725i
$789$		−	3.69629e7i		−	2.11385i
$790$	178952.	−	589951.i	0.0102016	−	0.0336316i
$791$		0			0
$792$	−2.60396e7	−	3.17269e7i	−1.47510	−	1.79728i
$793$	296654.			0.0167520
$794$	−1.88094e7	−	5.70550e6i	−1.05882	−	0.321176i
$795$			2.03777e7i			1.14350i
$796$	−4.27766e6	−	2.85809e6i	−0.239290	−	0.159879i
$797$			2.06913e6i			0.115383i	0.998334	+	0.0576916i	$0.0183740\pi$
$797$			2.06913e6i			0.115383i	−0.998334	+	0.0576916i	$0.981626\pi$
$798$		0			0
$799$			240425.i			0.0133233i
$800$	−9.72468e6	+	958415.i	−0.537218	+	0.0529455i
$801$		−	3.89154e7i		−	2.14309i
$802$	2.18514e6	−	7.20378e6i	0.119962	−	0.395480i
$803$	2.81186e7			1.53888
$804$	−1.29531e7	+	1.93868e7i	−0.706700	+	1.05771i
$805$		0			0
$806$	758993.	+	230228.i	0.0411529	+	0.0124830i
$807$		−	4.24619e7i		−	2.29517i
$808$	−7.26387e6	−	8.85037e6i	−0.391417	−	0.476906i
$809$	1.12690e7			0.605359			0.302680	−	0.953092i	$-0.402119\pi$
$809$	1.12690e7			0.605359			0.302680	+	0.953092i	$0.402119\pi$
$810$	1.07446e7	+	3.25918e6i	0.575408	+	0.174540i
$811$	−3.36555e7			−1.79682			−0.898408	−	0.439161i	$-0.855276\pi$
$811$	−3.36555e7			−1.79682			−0.898408	+	0.439161i	$0.855276\pi$
$812$		0			0
$813$	−6.99154e6			−0.370977
$814$	−3.12655e7	−	9.48387e6i	−1.65388	−	0.501677i
$815$	2.15975e7			1.13896
$816$	758620.	−	314276.i	0.0398840	−	0.0165229i
$817$		−	324270.i		−	0.0169962i
$818$	−3.43369e7	−	1.04155e7i	−1.79423	−	0.544249i
$819$		0			0
$820$	1.96130e7	+	1.31043e7i	1.01861	+	0.680578i
$821$	2.55262e7			1.32169			0.660844	−	0.750523i	$-0.270199\pi$
$821$	2.55262e7			1.32169			0.660844	+	0.750523i	$0.270199\pi$
$822$	−1.14266e7	+	3.76702e7i	−0.589846	+	1.94455i
$823$		−	2.01076e7i		−	1.03481i	−0.855740	−	0.517406i	$-0.826898\pi$
$823$		−	2.01076e7i		−	1.03481i	0.855740	−	0.517406i	$-0.173102\pi$
$824$	8.23655e6	−	6.76008e6i	0.422598	−	0.346844i
$825$		−	2.26653e7i		−	1.15938i
$826$		0			0
$827$		−	1.14644e7i		−	0.582890i	−0.956588	−	0.291445i	$-0.905864\pi$
$827$		−	1.14644e7i		−	0.582890i	0.956588	−	0.291445i	$-0.0941361\pi$
$828$	1.93153e7	−	2.89090e7i	0.979097	−	1.46540i
$829$			1.69125e7i			0.854718i	0.904082	+	0.427359i	$0.140556\pi$
$829$			1.69125e7i			0.854718i	−0.904082	+	0.427359i	$0.859444\pi$
$830$	1.79804e7	+	5.45406e6i	0.905951	+	0.274805i
$831$	2.60671e7			1.30946
$832$	749956.	+	149117.i	0.0375602	+	0.00746823i
$833$		0			0
$834$	−1.69826e7	+	5.59867e7i	−0.845453	+	2.78721i
$835$			2.19941e7i			1.09167i
$836$	372616.	−	557689.i	0.0184393	−	0.0275979i
$837$	3.12115e7			1.53993
$838$	−4.48301e6	+	1.47792e7i	−0.220526	+	0.727010i
$839$	4.18113e6			0.205064			0.102532	−	0.994730i	$-0.467306\pi$
$839$	4.18113e6			0.205064			0.102532	+	0.994730i	$0.467306\pi$
$840$		0			0
$841$	2.60491e7			1.27000
$842$	7.86706e6	−	2.59354e7i	0.382413	−	1.26070i
$843$	2.75972e7			1.33751
$844$	6.37396e6	−	9.53982e6i	0.308002	−	0.460982i
$845$			2.57181e7i			1.23908i
$846$	−5.68733e6	+	1.87495e7i	−0.273201	+	0.900665i
$847$		0			0
$848$	4.40037e6	+	1.06219e7i	0.210136	+	0.507240i
$849$	−6.15480e7			−2.93052
$850$	279885.	+	84898.5i	0.0132872	+	0.00403044i
$851$		−	2.76759e7i		−	1.31002i
$852$	1.64248e7	−	2.45829e7i	0.775180	−	1.16020i
$853$			3.92830e7i			1.84855i	0.381721	+	0.924277i	$0.375331\pi$
$853$			3.92830e7i			1.84855i	−0.381721	+	0.924277i	$0.624669\pi$
$854$		0			0
$855$			1.25013e6i			0.0584842i
$856$	8.07530e6	+	9.83903e6i	0.376682	+	0.458952i
$857$			3.15295e7i			1.46644i	0.679991	+	0.733221i	$0.261984\pi$
$857$			3.15295e7i			1.46644i	−0.679991	+	0.733221i	$0.738016\pi$
$858$	−514812.	+	1.69718e6i	−0.0238743	+	0.0787065i
$859$	−3.94120e7			−1.82241			−0.911203	−	0.411957i	$-0.864845\pi$
$859$	−3.94120e7			−1.82241			−0.911203	+	0.411957i	$0.864845\pi$
$860$	−1.46637e7	−	9.79746e6i	−0.676081	−	0.451718i
$861$		0			0
$862$	1.18630e7	+	3.59843e6i	0.543783	+	0.164947i
$863$		−	1.35160e7i		−	0.617760i	−0.951101	−	0.308880i	$-0.900046\pi$
$863$		−	1.35160e7i		−	0.617760i	0.951101	−	0.308880i	$-0.0999542\pi$
$864$	2.99446e7	−	2.95119e6i	1.36469	−	0.134497i
$865$	−3.09886e7			−1.40819
$866$	−1.68706e7	−	5.11740e6i	−0.764425	−	0.231875i
$867$	3.71241e7			1.67729
$868$		0			0
$869$	806784.			0.0362416
$870$	6.70391e7	+	2.03352e7i	3.00283	+	0.910856i
$871$	649843.			0.0290244
$872$	−2.81199e7	+	2.30792e7i	−1.25234	+	1.02785i
$873$		−	5.16882e7i		−	2.29539i
$874$	543685.	+	164918.i	0.0240752	+	0.00730279i
$875$		0			0
$876$	−2.54684e7	+	3.81183e7i	−1.12135	+	1.67831i
$877$	1.91830e7			0.842205			0.421102	−	0.907013i	$-0.361643\pi$
$877$	1.91830e7			0.842205			0.421102	+	0.907013i	$0.361643\pi$
$878$	4.14993e6	−	1.36811e7i	0.181679	−	0.598942i
$879$		−	2.54234e7i		−	1.10984i
$880$	−1.39610e7	−	3.37000e7i	−0.607727	−	1.46697i
$881$		−	3.94549e7i		−	1.71262i	−0.516460	−	0.856311i	$-0.672751\pi$
$881$		−	3.94549e7i		−	1.71262i	0.516460	−	0.856311i	$-0.327249\pi$
$882$		0			0
$883$			1.23808e7i			0.534375i	0.963645	+	0.267188i	$0.0860943\pi$
$883$			1.23808e7i			0.534375i	−0.963645	+	0.267188i	$0.913906\pi$
$884$	−19029.5	−	12714.4i	−0.000819026	−	0.000547226i
$885$		−	1.78054e7i		−	0.764175i
$886$	1.29752e7	+	3.93581e6i	0.555303	+	0.168442i
$887$	−4.52782e6			−0.193232			−0.0966162	−	0.995322i	$-0.530802\pi$
$887$	−4.52782e6			−0.193232			−0.0966162	+	0.995322i	$0.530802\pi$
$888$	4.11753e7	−	3.37943e7i	1.75228	−	1.43817i
$889$		0			0
$890$	1.00391e7	−	3.30960e7i	0.424835	−	1.40056i
$891$			1.46937e7i			0.620063i
$892$	9.28918e6	+	6.20650e6i	0.390900	+	0.261177i
$893$	−320173.			−0.0134356
$894$	−1.67584e6	+	5.52474e6i	−0.0701274	+	0.231189i
$895$	3.42464e7			1.42908
$896$		0			0
$897$	−1.50233e6			−0.0623424
$898$	2.36355e6	−	7.79193e6i	0.0978079	−	0.322444i
$899$	4.09995e7			1.69192
$900$	1.98185e7	+	1.32416e7i	0.815577	+	0.544922i
$901$		−	344125.i		−	0.0141223i
$902$	−8.96034e6	+	2.95396e7i	−0.366698	+	1.20889i
$903$		0			0
$904$	−1.37725e7	+	1.13036e7i	−0.560520	+	0.460042i
$905$	−918914.			−0.0372953
$906$	9.81465e6	+	2.97711e6i	0.397241	+	0.120496i
$907$			2.03106e7i			0.819793i	0.912132	+	0.409897i	$0.134435\pi$
$907$			2.03106e7i			0.819793i	−0.912132	+	0.409897i	$0.865565\pi$
$908$	−1.51468e7	−	1.01202e7i	−0.609685	−	0.407356i
$909$			2.79276e7i			1.12105i
$910$		0			0
$911$			3.63393e7i			1.45071i	0.688376	+	0.725354i	$0.258324\pi$
$911$			3.63393e7i			1.45071i	−0.688376	+	0.725354i	$0.741676\pi$
$912$	418521.	+	1.01025e6i	0.0166621	+	0.0402201i
$913$			2.45890e7i			0.976258i
$914$	1.00931e7	−	3.32740e7i	0.399631	−	1.31747i
$915$	2.30730e7			0.911068
$916$	−8.29888e6	+	1.24208e7i	−0.326799	+	0.489116i
$917$		0			0
$918$	−861835.	−	261423.i	−0.0337534	−	0.0102385i
$919$			2.02622e7i			0.791404i	0.918379	+	0.395702i	$0.129499\pi$
$919$			2.02622e7i			0.791404i	−0.918379	+	0.395702i	$0.870501\pi$
$920$	2.38846e7	−	1.96031e7i	0.930353	−	0.763580i
$921$	−4.06665e6			−0.157975
$922$	2.02043e7	+	6.12862e6i	0.782737	+	0.237430i
$923$	−824015.			−0.0318369
$924$		0			0
$925$	1.89732e7			0.729099
$926$	1.36079e7	+	4.12772e6i	0.521510	+	0.158191i
$927$	−2.59906e7			−0.993384
$928$	3.93354e7	−	3.87670e6i	1.49939	−	0.147772i
$929$			1.34475e7i			0.511212i	0.966781	+	0.255606i	$0.0822749\pi$
$929$			1.34475e7i			0.511212i	−0.966781	+	0.255606i	$0.917725\pi$
$930$	5.90325e7	+	1.79065e7i	2.23812	+	0.678896i
$931$		0			0
$932$	−7.30398e6	−	4.88010e6i	−0.275435	−	0.184030i
$933$	−3.48962e7			−1.31242
$934$	−256748.	+	846423.i	−0.00963030	+	0.0317483i
$935$			1.09180e6i			0.0408426i
$936$	−1.18325e6	−	1.44169e6i	−0.0441456	−	0.0537874i
$937$		−	2.83110e7i		−	1.05343i	−0.850042	−	0.526715i	$-0.823423\pi$
$937$		−	2.83110e7i		−	1.05343i	0.850042	−	0.526715i	$-0.176577\pi$
$938$		0			0
$939$		−	6.10559e7i		−	2.25977i
$940$	−9.67369e6	+	1.44785e7i	−0.357086	+	0.534446i
$941$			3.01113e7i			1.10855i	0.832334	+	0.554275i	$0.187004\pi$
$941$			3.01113e7i			1.10855i	−0.832334	+	0.554275i	$0.812996\pi$
$942$	1.83706e7	+	5.57240e6i	0.674521	+	0.204604i
$943$	−2.61481e7			−0.957550
$944$	−3.84490e6	−	9.28108e6i	−0.140428	−	0.338976i
$945$		0			0
$946$	6.69923e6	−	2.20854e7i	0.243387	−	0.802376i
$947$			2.42548e7i			0.878867i	0.898275	+	0.439434i	$0.144821\pi$
$947$			2.42548e7i			0.878867i	−0.898275	+	0.439434i	$0.855179\pi$
$948$	−730745.	+	1.09370e6i	−0.0264086	+	0.0395254i
$949$	1.27772e6			0.0460543
$950$	−113059.	+	372723.i	−0.00406441	+	0.0133992i
$951$	−7.35160e7			−2.63591
$952$		0			0
$953$	−4.03858e7			−1.44044			−0.720222	−	0.693743i	$-0.755960\pi$
$953$	−4.03858e7			−1.44044			−0.720222	+	0.693743i	$0.755960\pi$
$954$	8.14041e6	−	2.68366e7i	0.289585	−	0.954676i
$955$	−6.17995e7			−2.19269
$956$	−6.24838e6	+	9.35187e6i	−0.221117	+	0.330943i
$957$			9.16790e7i			3.23586i
$958$	8.08968e6	−	2.66693e7i	0.284785	−	0.938854i
$959$		0			0
$960$	5.83296e7	+	1.15979e7i	2.04273	+	0.406164i
$961$	7.47372e6			0.261053
$962$	−1.42072e6	−	430951.i	−0.0494960	−	0.0150138i
$963$		−	3.10473e7i		−	1.07884i
$964$	1.75290e7	−	2.62354e7i	0.607524	−	0.909274i
$965$			5.68511e7i			1.96526i
$966$		0			0
$967$		−	2.57888e7i		−	0.886882i	−0.896304	−	0.443441i	$-0.853758\pi$
$967$		−	2.57888e7i		−	0.886882i	0.896304	−	0.443441i	$-0.146242\pi$
$968$	1.43646e7	−	1.17896e7i	0.492725	−	0.404400i
$969$		−	32729.8i		−	0.00111978i
$970$	1.33341e7	−	4.39587e7i	0.455025	−	1.50008i
$971$	4.70949e7			1.60297			0.801487	−	0.598013i	$-0.204043\pi$
$971$	4.70949e7			1.60297			0.801487	+	0.598013i	$0.204043\pi$
$972$	1.36665e7	+	9.13116e6i	0.463972	+	0.309999i
$973$		0			0
$974$	−3.26357e7	−	9.89948e6i	−1.10229	−	0.334361i
$975$		−	1.02992e6i		−	0.0346970i
$976$	1.20268e7	−	4.98238e6i	0.404135	−	0.167422i
$977$	−3.70369e7			−1.24136			−0.620680	−	0.784064i	$-0.713143\pi$
$977$	−3.70369e7			−1.24136			−0.620680	+	0.784064i	$0.713143\pi$
$978$	−4.40964e7	−	1.33759e7i	−1.47420	−	0.447173i
$979$	4.52602e7			1.50925
$980$		0			0
$981$	8.87329e7			2.94383
$982$	−2.98539e7	−	9.05567e6i	−0.987921	−	0.299669i
$983$	8.94769e6			0.295343			0.147672	−	0.989036i	$-0.452822\pi$
$983$	8.94769e6			0.295343			0.147672	+	0.989036i	$0.452822\pi$
$984$	−3.19288e7	−	3.89024e7i	−1.05122	−	1.28082i
$985$			3.30364e7i			1.08493i
$986$	−1.13211e6	−	343406.i	−0.0370848	−	0.0112491i
$987$		0			0
$988$	16931.8	−	25341.6i	0.000551837	−	0.000825928i
$989$	1.95498e7			0.635552
$990$	−2.58269e7	+	8.51438e7i	−0.837499	+	2.76099i
$991$			3.89683e7i			1.26046i	0.776410	+	0.630228i	$0.217039\pi$
$991$			3.89683e7i			1.26046i	−0.776410	+	0.630228i	$0.782961\pi$
$992$	3.46375e7	−	3.41370e6i	1.11755	−	0.110140i
$993$			4.33604e7i			1.39547i
$994$		0			0
$995$			1.11523e7i			0.357113i
$996$	−3.33335e7	−	2.22715e7i	−1.06471	−	0.711380i
$997$			6.76935e6i			0.215680i	0.994168	+	0.107840i	$0.0343934\pi$
$997$			6.76935e6i			0.215680i	−0.994168	+	0.107840i	$0.965607\pi$
$998$	1.33470e7	+	4.04859e6i	0.424187	+	0.128670i
$999$	−5.84231e7			−1.85213

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.6.d.b.195.22		36
4.3	odd	2	inner	196.6.d.b.195.23		36
7.4	even	3		28.6.f.a.19.14	yes	36
7.5	odd	6		28.6.f.a.3.2	✓	36
7.6	odd	2	inner	196.6.d.b.195.21		36
28.11	odd	6		28.6.f.a.19.2	yes	36
28.19	even	6		28.6.f.a.3.14	yes	36
28.27	even	2	inner	196.6.d.b.195.24		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.6.f.a.3.2	✓	36	7.5	odd	6
28.6.f.a.3.14	yes	36	28.19	even	6
28.6.f.a.19.2	yes	36	28.11	odd	6
28.6.f.a.19.14	yes	36	7.4	even	3
196.6.d.b.195.21		36	7.6	odd	2	inner
196.6.d.b.195.22		36	1.1	even	1	trivial
196.6.d.b.195.23		36	4.3	odd	2	inner
196.6.d.b.195.24		36	28.27	even	2	inner

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	196.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.64203 - 5.41329i) q^{2} +26.1637 q^{3} +(-26.6075 - 17.7776i) q^{4} +69.3681i q^{5} +(42.9616 - 141.632i) q^{6} +(-139.926 + 114.843i) q^{8} +441.538 q^{9} +O(q^{10})\)	\(q+(1.64203 - 5.41329i) q^{2} +26.1637 q^{3} +(-26.6075 - 17.7776i) q^{4} +69.3681i q^{5} +(42.9616 - 141.632i) q^{6} +(-139.926 + 114.843i) q^{8} +441.538 q^{9} +(375.510 + 113.905i) q^{10} +513.527i q^{11} +(-696.150 - 465.127i) q^{12} +23.3349i q^{13} +1814.93i q^{15} +(391.915 + 946.033i) q^{16} -30.6492i q^{17} +(725.019 - 2390.18i) q^{18} +40.8156 q^{19} +(1233.20 - 1845.71i) q^{20} +(2779.87 + 843.226i) q^{22} +2460.71i q^{23} +(-3660.97 + 3004.71i) q^{24} -1686.94 q^{25} +(126.318 + 38.3165i) q^{26} +5194.49 q^{27} +6823.51 q^{29} +(9824.73 + 2980.16i) q^{30} +6008.57 q^{31} +(5764.69 - 568.139i) q^{32} +13435.8i q^{33} +(-165.913 - 50.3269i) q^{34} +(-11748.2 - 7849.48i) q^{36} -11247.1 q^{37} +(67.0204 - 220.947i) q^{38} +610.526i q^{39} +(-7966.43 - 9706.37i) q^{40} +10626.3i q^{41} -7944.77i q^{43} +(9129.26 - 13663.6i) q^{44} +30628.7i q^{45} +(13320.5 + 4040.56i) q^{46} -7844.39 q^{47} +(10254.0 + 24751.7i) q^{48} +(-2770.00 + 9131.89i) q^{50} -801.896i q^{51} +(414.837 - 620.882i) q^{52} +11227.9 q^{53} +(8529.51 - 28119.3i) q^{54} -35622.4 q^{55} +1067.89 q^{57} +(11204.4 - 36937.7i) q^{58} -9810.53 q^{59} +(32265.0 - 48290.6i) q^{60} -12712.9i q^{61} +(9866.25 - 32526.1i) q^{62} +(6390.29 - 32138.9i) q^{64} -1618.70 q^{65} +(72731.6 + 22061.9i) q^{66} -27848.6i q^{67} +(-544.869 + 815.498i) q^{68} +64381.2i q^{69} +35312.6i q^{71} +(-61782.5 + 50707.5i) q^{72} -54755.8i q^{73} +(-18468.1 + 60884.0i) q^{74} -44136.5 q^{75} +(-1086.00 - 725.602i) q^{76} +(3304.96 + 1002.50i) q^{78} -1571.07i q^{79} +(-65624.5 + 27186.4i) q^{80} +28613.2 q^{81} +(57523.0 + 17448.6i) q^{82} +47882.7 q^{83} +2126.08 q^{85} +(-43007.3 - 13045.5i) q^{86} +178528. q^{87} +(-58974.8 - 71855.5i) q^{88} -88136.1i q^{89} +(165802. + 50293.2i) q^{90} +(43745.5 - 65473.3i) q^{92} +157206. q^{93} +(-12880.7 + 42464.0i) q^{94} +2831.30i q^{95} +(150826. - 14864.6i) q^{96} -117064. i q^{97} +226742. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 24 q^{4} - 72 q^{8} + 2272 q^{9}+O(q^{10}) \) 36 * q + 24 * q^4 - 72 * q^8 + 2272 * q^9	\( 36 q + 24 q^{4} - 72 q^{8} + 2272 q^{9} - 1328 q^{16} + 3560 q^{18} + 13768 q^{22} - 15224 q^{25} + 176 q^{29} + 11672 q^{30} - 2320 q^{32} - 27920 q^{36} - 23444 q^{37} - 18192 q^{44} + 2080 q^{46} - 51168 q^{50} + 66972 q^{53} - 1668 q^{57} + 96872 q^{58} - 28624 q^{60} + 44544 q^{64} - 30712 q^{65} - 296128 q^{72} - 34304 q^{74} + 127704 q^{78} - 320804 q^{81} + 71212 q^{85} + 504992 q^{86} - 110536 q^{88} - 190176 q^{92} + 330324 q^{93}+O(q^{100}) \) 36 * q + 24 * q^4 - 72 * q^8 + 2272 * q^9 - 1328 * q^16 + 3560 * q^18 + 13768 * q^22 - 15224 * q^25 + 176 * q^29 + 11672 * q^30 - 2320 * q^32 - 27920 * q^36 - 23444 * q^37 - 18192 * q^44 + 2080 * q^46 - 51168 * q^50 + 66972 * q^53 - 1668 * q^57 + 96872 * q^58 - 28624 * q^60 + 44544 * q^64 - 30712 * q^65 - 296128 * q^72 - 34304 * q^74 + 127704 * q^78 - 320804 * q^81 + 71212 * q^85 + 504992 * q^86 - 110536 * q^88 - 190176 * q^92 + 330324 * q^93

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