LMFDB - Embedded newform 100.7.d.a.99.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,7,Mod(99,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("100.99");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	100.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$23.0054083620$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 7x^{2} + 16 $ x^4 - 7*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 4)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.4
Root			$-1.93649 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	100.99
Dual form			100.7.d.a.99.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.74597 + 2.00000i) q^{2} +30.9839 q^{3} +(56.0000 + 30.9839i) q^{4} +(240.000 + 61.9677i) q^{6} +309.839 q^{7} +(371.806 + 352.000i) q^{8} +231.000 q^{9} +O(q^{10})$	\(q+(7.74597 + 2.00000i) q^{2} +30.9839 q^{3} +(56.0000 + 30.9839i) q^{4} +(240.000 + 61.9677i) q^{6} +309.839 q^{7} +(371.806 + 352.000i) q^{8} +231.000 q^{9} +960.500i q^{11} +(1735.10 + 960.000i) q^{12} -1466.00i q^{13} +(2400.00 + 619.677i) q^{14} +(2176.00 + 3470.19i) q^{16} -4766.00i q^{17} +(1789.32 + 462.000i) q^{18} +7529.08i q^{19} +9600.00 q^{21} +(-1921.00 + 7440.00i) q^{22} +10472.5 q^{23} +(11520.0 + 10906.3i) q^{24} +(2932.00 - 11355.6i) q^{26} -15430.0 q^{27} +(17351.0 + 9600.00i) q^{28} -25498.0 q^{29} -41890.2i q^{31} +(9914.84 + 31232.0i) q^{32} +29760.0i q^{33} +(9532.00 - 36917.3i) q^{34} +(12936.0 + 7157.27i) q^{36} +1994.00i q^{37} +(-15058.2 + 58320.0i) q^{38} -45422.3i q^{39} +29362.0 q^{41} +(74361.3 + 19200.0i) q^{42} +21533.8 q^{43} +(-29760.0 + 53788.0i) q^{44} +(81120.0 + 20945.1i) q^{46} -7560.06 q^{47} +(67420.9 + 107520. i) q^{48} -21649.0 q^{49} -147669. i q^{51} +(45422.3 - 82096.0i) q^{52} +192854. i q^{53} +(-119520. - 30859.9i) q^{54} +(115200. + 109063. i) q^{56} +233280. i q^{57} +(-197507. - 50996.0i) q^{58} -78420.2i q^{59} -10918.0 q^{61} +(83780.4 - 324480. i) q^{62} +71572.7 q^{63} +(14336.0 + 261752. i) q^{64} +(-59520.0 + 230520. i) q^{66} -394146. q^{67} +(147669. - 266896. i) q^{68} +324480. q^{69} -532241. i q^{71} +(85887.3 + 81312.0i) q^{72} -288626. i q^{73} +(-3988.00 + 15445.5i) q^{74} +(-233280. + 421628. i) q^{76} +297600. i q^{77} +(90844.7 - 351840. i) q^{78} -310706. i q^{79} -646479. q^{81} +(227437. + 58724.0i) q^{82} +204153. q^{83} +(537600. + 297445. i) q^{84} +(166800. + 43067.6i) q^{86} -790027. q^{87} +(-338096. + 357120. i) q^{88} -310738. q^{89} -454223. i q^{91} +(586463. + 324480. i) q^{92} -1.29792e6i q^{93} +(-58560.0 - 15120.1i) q^{94} +(307200. + 967688. i) q^{96} -1.45709e6i q^{97} +(-167692. - 43298.0i) q^{98} +221875. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 224 q^{4} + 960 q^{6} + 924 q^{9}+O(q^{10}) $ 4 * q + 224 * q^4 + 960 * q^6 + 924 * q^9	$ 4 q + 224 q^{4} + 960 q^{6} + 924 q^{9} + 9600 q^{14} + 8704 q^{16} + 38400 q^{21} + 46080 q^{24} + 11728 q^{26} - 101992 q^{29} + 38128 q^{34} + 51744 q^{36} + 117448 q^{41} - 119040 q^{44} + 324480 q^{46} - 86596 q^{49} - 478080 q^{54} + 460800 q^{56} - 43672 q^{61} + 57344 q^{64} - 238080 q^{66} + 1297920 q^{69} - 15952 q^{74} - 933120 q^{76} - 2585916 q^{81} + 2150400 q^{84} + 667200 q^{86} - 1242952 q^{89} - 234240 q^{94} + 1228800 q^{96}+O(q^{100}) $ 4 * q + 224 * q^4 + 960 * q^6 + 924 * q^9 + 9600 * q^14 + 8704 * q^16 + 38400 * q^21 + 46080 * q^24 + 11728 * q^26 - 101992 * q^29 + 38128 * q^34 + 51744 * q^36 + 117448 * q^41 - 119040 * q^44 + 324480 * q^46 - 86596 * q^49 - 478080 * q^54 + 460800 * q^56 - 43672 * q^61 + 57344 * q^64 - 238080 * q^66 + 1297920 * q^69 - 15952 * q^74 - 933120 * q^76 - 2585916 * q^81 + 2150400 * q^84 + 667200 * q^86 - 1242952 * q^89 - 234240 * q^94 + 1228800 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$-1$

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 $

$2$	7.74597	+	2.00000i	0.968246	+	0.250000i
$2$	7.74597	+	2.00000i	0.968246	+	0.250000i
$3$	30.9839			1.14755			0.573775	−	0.819013i	$-0.305478\pi$
$3$	30.9839			1.14755			0.573775	+	0.819013i	$0.305478\pi$
$4$	56.0000	+	30.9839i	0.875000	+	0.484123i
$5$		0			0
$5$		0			0
$6$	240.000	+	61.9677i	1.11111	+	0.286888i
$7$	309.839			0.903320			0.451660	−	0.892190i	$-0.350832\pi$
$7$	309.839			0.903320			0.451660	+	0.892190i	$0.350832\pi$
$8$	371.806	+	352.000i	0.726184	+	0.687500i
$9$	231.000			0.316872
$10$		0			0
$11$			960.500i			0.721638i	0.932636	+	0.360819i	$0.117503\pi$
$11$			960.500i			0.721638i	−0.932636	+	0.360819i	$0.882497\pi$
$12$	1735.10	+	960.000i	1.00411	+	0.555556i
$13$		−	1466.00i		−	0.667274i	−0.942702	−	0.333637i	$-0.891724\pi$
$13$		−	1466.00i		−	0.667274i	0.942702	−	0.333637i	$-0.108276\pi$
$14$	2400.00	+	619.677i	0.874636	+	0.225830i
$15$		0			0
$16$	2176.00	+	3470.19i	0.531250	+	0.847215i
$17$		−	4766.00i		−	0.970079i	−0.874492	−	0.485040i	$-0.838805\pi$
$17$		−	4766.00i		−	0.970079i	0.874492	−	0.485040i	$-0.161195\pi$
$18$	1789.32	+	462.000i	0.306810	+	0.0792181i
$19$			7529.08i			1.09769i	0.835923	+	0.548847i	$0.184933\pi$
$19$			7529.08i			1.09769i	−0.835923	+	0.548847i	$0.815067\pi$
$20$		0			0
$21$	9600.00			1.03661
$22$	−1921.00	+	7440.00i	−0.180409	+	0.698723i
$23$	10472.5			0.860734			0.430367	−	0.902654i	$-0.358384\pi$
$23$	10472.5			0.860734			0.430367	+	0.902654i	$0.358384\pi$
$24$	11520.0	+	10906.3i	0.833333	+	0.788941i
$25$		0			0
$26$	2932.00	−	11355.6i	0.166818	−	0.646085i
$27$	−15430.0			−0.783923
$28$	17351.0	+	9600.00i	0.790405	+	0.437318i
$29$	−25498.0			−1.04547			−0.522736	−	0.852495i	$-0.675089\pi$
$29$	−25498.0			−1.04547			−0.522736	+	0.852495i	$0.675089\pi$
$30$		0			0
$31$		−	41890.2i		−	1.40614i	−0.711123	−	0.703068i	$-0.751813\pi$
$31$		−	41890.2i		−	1.40614i	0.711123	−	0.703068i	$-0.248187\pi$
$32$	9914.84	+	31232.0i	0.302577	+	0.953125i
$33$			29760.0i			0.828116i
$34$	9532.00	−	36917.3i	0.242520	−	0.939275i
$35$		0			0
$36$	12936.0	+	7157.27i	0.277263	+	0.153405i
$37$			1994.00i			0.0393659i	0.999806	+	0.0196829i	$0.00626568\pi$
$37$			1994.00i			0.0393659i	−0.999806	+	0.0196829i	$0.993734\pi$
$38$	−15058.2	+	58320.0i	−0.274423	+	1.06284i
$39$		−	45422.3i		−	0.765730i
$40$		0			0
$41$	29362.0			0.426024			0.213012	−	0.977050i	$-0.431673\pi$
$41$	29362.0			0.426024			0.213012	+	0.977050i	$0.431673\pi$
$42$	74361.3	+	19200.0i	1.00369	+	0.259151i
$43$	21533.8			0.270841			0.135421	−	0.990788i	$-0.456761\pi$
$43$	21533.8			0.270841			0.135421	+	0.990788i	$0.456761\pi$
$44$	−29760.0	+	53788.0i	−0.349361	+	0.631433i
$45$		0			0
$46$	81120.0	+	20945.1i	0.833402	+	0.215183i
$47$	−7560.06			−0.0728168			−0.0364084	−	0.999337i	$-0.511592\pi$
$47$	−7560.06			−0.0728168			−0.0364084	+	0.999337i	$0.511592\pi$
$48$	67420.9	+	107520.i	0.609636	+	0.972222i
$49$	−21649.0			−0.184013
$50$		0			0
$51$		−	147669.i		−	1.11322i
$52$	45422.3	−	82096.0i	0.323042	−	0.583864i
$53$			192854.i			1.29539i	0.761899	+	0.647696i	$0.224267\pi$
$53$			192854.i			1.29539i	−0.761899	+	0.647696i	$0.775733\pi$
$54$	−119520.	−	30859.9i	−0.759031	−	0.195981i
$55$		0			0
$56$	115200.	+	109063.i	0.655977	+	0.621032i
$57$			233280.i			1.25966i
$58$	−197507.	−	50996.0i	−1.01227	−	0.261368i
$59$		−	78420.2i		−	0.381831i	−0.981606	−	0.190916i	$-0.938854\pi$
$59$		−	78420.2i		−	0.381831i	0.981606	−	0.190916i	$-0.0611457\pi$
$60$		0			0
$61$	−10918.0			−0.0481009			−0.0240505	−	0.999711i	$-0.507656\pi$
$61$	−10918.0			−0.0481009			−0.0240505	+	0.999711i	$0.507656\pi$
$62$	83780.4	−	324480.i	0.351534	−	1.36149i
$63$	71572.7			0.286237
$64$	14336.0	+	261752.i	0.0546875	+	0.998504i
$65$		0			0
$66$	−59520.0	+	230520.i	−0.207029	+	0.801820i
$67$	−394146.			−1.31049			−0.655243	−	0.755418i	$-0.727434\pi$
$67$	−394146.			−1.31049			−0.655243	+	0.755418i	$0.727434\pi$
$68$	147669.	−	266896.i	0.469638	−	0.848819i
$69$	324480.			0.987735
$70$		0			0
$71$		−	532241.i		−	1.48708i	−0.668694	−	0.743538i	$-0.733146\pi$
$71$		−	532241.i		−	1.48708i	0.668694	−	0.743538i	$-0.266854\pi$
$72$	85887.3	+	81312.0i	0.230108	+	0.217850i
$73$		−	288626.i		−	0.741937i	−0.928646	−	0.370968i	$-0.879026\pi$
$73$		−	288626.i		−	0.741937i	0.928646	−	0.370968i	$-0.120974\pi$
$74$	−3988.00	+	15445.5i	−0.00984147	+	0.0381159i
$75$		0			0
$76$	−233280.	+	421628.i	−0.531419	+	0.960482i
$77$			297600.i			0.651870i
$78$	90844.7	−	351840.i	0.191433	−	0.741415i
$79$		−	310706.i		−	0.630186i	−0.949061	−	0.315093i	$-0.897964\pi$
$79$		−	310706.i		−	0.630186i	0.949061	−	0.315093i	$-0.102036\pi$
$80$		0			0
$81$	−646479.			−1.21646
$82$	227437.	+	58724.0i	0.412496	+	0.106506i
$83$	204153.			0.357043			0.178522	−	0.983936i	$-0.442869\pi$
$83$	204153.			0.357043			0.178522	+	0.983936i	$0.442869\pi$
$84$	537600.	+	297445.i	0.907029	+	0.501844i
$85$		0			0
$86$	166800.	+	43067.6i	0.262241	+	0.0677104i
$87$	−790027.			−1.19973
$88$	−338096.	+	357120.i	−0.496126	+	0.524042i
$89$	−310738.			−0.440783			−0.220391	−	0.975412i	$-0.570733\pi$
$89$	−310738.			−0.440783			−0.220391	+	0.975412i	$0.570733\pi$
$90$		0			0
$91$		−	454223.i		−	0.602761i
$92$	586463.	+	324480.i	0.753142	+	0.416701i
$93$		−	1.29792e6i		−	1.61361i
$94$	−58560.0	−	15120.1i	−0.0705046	−	0.0182042i
$95$		0			0
$96$	307200.	+	967688.i	0.347222	+	1.09376i
$97$		−	1.45709e6i		−	1.59650i	−0.602324	−	0.798252i	$-0.705758\pi$
$97$		−	1.45709e6i		−	1.59650i	0.602324	−	0.798252i	$-0.294242\pi$
$98$	−167692.	−	43298.0i	−0.178170	−	0.0460034i
$99$			221875.i			0.228667i
$100$		0			0
$101$	−639158.			−0.620360			−0.310180	−	0.950678i	$-0.600389\pi$
$101$	−639158.			−0.620360			−0.310180	+	0.950678i	$0.600389\pi$
$102$	295338.	−	1.14384e6i	0.278304	−	1.07787i
$103$	−1.38913e6			−1.27125			−0.635626	−	0.771997i	$-0.719258\pi$
$103$	−1.38913e6			−1.27125			−0.635626	+	0.771997i	$0.719258\pi$
$104$	516032.	−	545068.i	0.458751	−	0.484564i
$105$		0			0
$106$	−385708.	+	1.49384e6i	−0.323848	+	1.25426i
$107$	−1.14935e6			−0.938209			−0.469105	−	0.883143i	$-0.655423\pi$
$107$	−1.14935e6			−0.938209			−0.469105	+	0.883143i	$0.655423\pi$
$108$	−864078.	−	478080.i	−0.685933	−	0.379515i
$109$	−1.53574e6			−1.18587			−0.592936	−	0.805250i	$-0.702031\pi$
$109$	−1.53574e6			−1.18587			−0.592936	+	0.805250i	$0.702031\pi$
$110$		0			0
$111$			61781.8i			0.0451743i
$112$	674209.	+	1.07520e6i	0.479889	+	0.765306i
$113$			601694.i			0.417004i	0.978022	+	0.208502i	$0.0668588\pi$
$113$			601694.i			0.417004i	−0.978022	+	0.208502i	$0.933141\pi$
$114$	−466560.	+	1.80698e6i	−0.314915	+	1.21966i
$115$		0			0
$116$	−1.42789e6	−	790027.i	−0.914787	−	0.506137i
$117$		−	338646.i		−	0.211441i
$118$	156840.	−	607440.i	0.0954579	−	0.369707i
$119$		−	1.47669e6i		−	0.876292i
$120$		0			0
$121$	849001.			0.479239
$122$	−84570.5	−	21836.0i	−0.0465735	−	0.0120252i
$123$	909748.			0.488884
$124$	1.29792e6	−	2.34585e6i	0.680743	−	1.23037i
$125$		0			0
$126$	554400.	+	143145.i	0.277148	+	0.0715593i
$127$	1.67462e6			0.817531			0.408765	−	0.912640i	$-0.365959\pi$
$127$	1.67462e6			0.817531			0.408765	+	0.912640i	$0.365959\pi$
$128$	−412457.	+	2.05619e6i	−0.196675	+	0.980469i
$129$	667200.			0.310804
$130$		0			0
$131$		−	2.84454e6i		−	1.26531i	−0.774433	−	0.632656i	$-0.781965\pi$
$131$		−	2.84454e6i		−	1.26531i	0.774433	−	0.632656i	$-0.218035\pi$
$132$	−922080.	+	1.66656e6i	−0.400910	+	0.724601i
$133$			2.33280e6i			0.991568i
$134$	−3.05304e6	−	788292.i	−1.26887	−	0.327622i
$135$		0			0
$136$	1.67763e6	−	1.77203e6i	0.666930	−	0.704456i
$137$			3.81003e6i			1.48172i	0.671658	+	0.740862i	$0.265583\pi$
$137$			3.81003e6i			1.48172i	−0.671658	+	0.740862i	$0.734417\pi$
$138$	2.51341e6	+	648960.i	0.956371	+	0.246934i
$139$			138839.i			0.0516971i	0.999666	+	0.0258485i	$0.00822877\pi$
$139$			138839.i			0.0516971i	−0.999666	+	0.0258485i	$0.991771\pi$
$140$		0			0
$141$	−234240.			−0.0835610
$142$	1.06448e6	−	4.12272e6i	0.371769	−	1.43986i
$143$	1.40809e6			0.481530
$144$	502656.	+	801615.i	0.168338	+	0.268459i
$145$		0			0
$146$	577252.	−	2.23569e6i	0.185484	−	0.718377i
$147$	−670770.			−0.211165
$148$	−61781.8	+	111664.i	−0.0190579	+	0.0344451i
$149$	3.27426e6			0.989816			0.494908	−	0.868945i	$-0.335202\pi$
$149$	3.27426e6			0.989816			0.494908	+	0.868945i	$0.335202\pi$
$150$		0			0
$151$			5.59352e6i			1.62463i	0.583220	+	0.812314i	$0.301793\pi$
$151$			5.59352e6i			1.62463i	−0.583220	+	0.812314i	$0.698207\pi$
$152$	−2.65024e6	+	2.79936e6i	−0.754664	+	0.797128i
$153$		−	1.10095e6i		−	0.307391i
$154$	−595200.	+	2.30520e6i	−0.162967	+	0.631170i
$155$		0			0
$156$	1.40736e6	−	2.54365e6i	0.370708	−	0.670014i
$157$			816794.i			0.211064i	0.994416	+	0.105532i	$0.0336545\pi$
$157$			816794.i			0.211064i	−0.994416	+	0.105532i	$0.966345\pi$
$158$	621412.	−	2.40672e6i	0.157546	−	0.610175i
$159$			5.97536e6i			1.48653i
$160$		0			0
$161$	3.24480e6			0.777518
$162$	−5.00760e6	−	1.29296e6i	−1.17784	−	0.304116i
$163$	1.84593e6			0.426237			0.213119	−	0.977026i	$-0.431638\pi$
$163$	1.84593e6			0.426237			0.213119	+	0.977026i	$0.431638\pi$
$164$	1.64427e6	+	909748.i	0.372771	+	0.206248i
$165$		0			0
$166$	1.58136e6	+	408305.i	0.345706	+	0.0892608i
$167$	7.96515e6			1.71019			0.855095	−	0.518471i	$-0.173499\pi$
$167$	7.96515e6			1.71019			0.855095	+	0.518471i	$0.173499\pi$
$168$	3.56934e6	+	3.37920e6i	0.752766	+	0.712666i
$169$	2.67765e6			0.554746
$170$		0			0
$171$			1.73922e6i			0.347829i
$172$	1.20589e6	+	667200.i	0.236986	+	0.131121i
$173$			5.12653e6i			0.990115i	0.868860	+	0.495057i	$0.164853\pi$
$173$			5.12653e6i			0.990115i	−0.868860	+	0.495057i	$0.835147\pi$
$174$	−6.11952e6	−	1.58005e6i	−1.16163	−	0.299933i
$175$		0			0
$176$	−3.33312e6	+	2.09005e6i	−0.611382	+	0.383370i
$177$		−	2.42976e6i		−	0.438171i
$178$	−2.40697e6	−	621476.i	−0.426786	−	0.110196i
$179$		−	2.33411e6i		−	0.406969i	−0.979078	−	0.203485i	$-0.934773\pi$
$179$		−	2.33411e6i		−	0.406969i	0.979078	−	0.203485i	$-0.0652267\pi$
$180$		0			0
$181$	9.69156e6			1.63440			0.817199	−	0.576355i	$-0.195525\pi$
$181$	9.69156e6			1.63440			0.817199	+	0.576355i	$0.195525\pi$
$182$	908447.	−	3.51840e6i	0.150690	−	0.583621i
$183$	−338282.			−0.0551983
$184$	3.89376e6	+	3.68634e6i	0.625051	+	0.591754i
$185$		0			0
$186$	2.59584e6	−	1.00536e7i	0.403403	−	1.56237i
$187$	4.57774e6			0.700046
$188$	−423364.	−	234240.i	−0.0637147	−	0.0352523i
$189$	−4.78080e6			−0.708134
$190$		0			0
$191$			1.14164e7i			1.63844i	0.573479	+	0.819220i	$0.305593\pi$
$191$			1.14164e7i			1.63844i	−0.573479	+	0.819220i	$0.694407\pi$
$192$	444185.	+	8.11008e6i	0.0627567	+	1.14583i
$193$			2.43033e6i			0.338060i	0.985611	+	0.169030i	$0.0540635\pi$
$193$			2.43033e6i			0.338060i	−0.985611	+	0.169030i	$0.945936\pi$
$194$	2.91417e6	−	1.12865e7i	0.399126	−	1.54581i
$195$		0			0
$196$	−1.21234e6	−	670770.i	−0.161012	−	0.0890851i
$197$		−	2.23065e6i		−	0.291764i	−0.989302	−	0.145882i	$-0.953398\pi$
$197$		−	2.23065e6i		−	0.291764i	0.989302	−	0.145882i	$-0.0466020\pi$
$198$	−443751.	+	1.71864e6i	−0.0571668	+	0.221406i
$199$			4.89576e6i			0.621242i	0.950534	+	0.310621i	$0.100537\pi$
$199$			4.89576e6i			0.621242i	−0.950534	+	0.310621i	$0.899463\pi$
$200$		0			0
$201$	−1.22122e7			−1.50385
$202$	−4.95090e6	−	1.27832e6i	−0.600661	−	0.155090i
$203$	−7.90027e6			−0.944395
$204$	4.57536e6	−	8.26947e6i	0.538933	−	0.974063i
$205$		0			0
$206$	−1.07602e7	−	2.77826e6i	−1.23088	−	0.317813i
$207$	2.41916e6			0.272743
$208$	5.08730e6	−	3.19002e6i	0.565324	−	0.354489i
$209$	−7.23168e6			−0.792137
$210$		0			0
$211$		−	3.90951e6i		−	0.416174i	−0.978110	−	0.208087i	$-0.933276\pi$
$211$		−	3.90951e6i		−	0.416174i	0.978110	−	0.208087i	$-0.0667238\pi$
$212$	−5.97536e6	+	1.07998e7i	−0.627129	+	1.13347i
$213$		−	1.64909e7i		−	1.70650i
$214$	−8.90280e6	−	2.29869e6i	−0.908417	−	0.234552i
$215$		0			0
$216$	−5.73696e6	−	5.43135e6i	−0.569273	−	0.538947i
$217$		−	1.29792e7i		−	1.27019i
$218$	−1.18958e7	−	3.07148e6i	−1.14822	−	0.296468i
$219$		−	8.94275e6i		−	0.851410i
$220$		0			0
$221$	−6.98696e6			−0.647308
$222$	−123564.	+	478560.i	−0.0112936	+	0.0437399i
$223$	−3.33114e6			−0.300385			−0.150192	−	0.988657i	$-0.547989\pi$
$223$	−3.33114e6			−0.300385			−0.150192	+	0.988657i	$0.547989\pi$
$224$	3.07200e6	+	9.67688e6i	0.273324	+	0.860977i
$225$		0			0
$226$	−1.20339e6	+	4.66070e6i	−0.104251	+	0.403763i
$227$	−1.35033e7			−1.15442			−0.577208	−	0.816597i	$-0.695858\pi$
$227$	−1.35033e7			−1.15442			−0.577208	+	0.816597i	$0.695858\pi$
$228$	−7.22792e6	+	1.30637e7i	−0.609830	+	1.10220i
$229$	−1.59598e6			−0.132899			−0.0664493	−	0.997790i	$-0.521167\pi$
$229$	−1.59598e6			−0.132899			−0.0664493	+	0.997790i	$0.521167\pi$
$230$		0			0
$231$			9.22080e6i			0.748053i
$232$	−9.48032e6	−	8.97530e6i	−0.759205	−	0.718762i
$233$		−	8.04383e6i		−	0.635909i	−0.948106	−	0.317954i	$-0.897004\pi$
$233$		−	8.04383e6i		−	0.635909i	0.948106	−	0.317954i	$-0.102996\pi$
$234$	677292.	−	2.62314e6i	0.0528601	−	0.204726i
$235$		0			0
$236$	2.42976e6	−	4.39153e6i	0.184853	−	0.334103i
$237$		−	9.62688e6i		−	0.723170i
$238$	2.95338e6	−	1.14384e7i	0.219073	−	0.848466i
$239$			1.12532e7i			0.824296i	0.911117	+	0.412148i	$0.135221\pi$
$239$			1.12532e7i			0.824296i	−0.911117	+	0.412148i	$0.864779\pi$
$240$		0			0
$241$	5.05104e6			0.360853			0.180426	−	0.983589i	$-0.442252\pi$
$241$	5.05104e6			0.360853			0.180426	+	0.983589i	$0.442252\pi$
$242$	6.57633e6	+	1.69800e6i	0.464021	+	0.119810i
$243$	−8.78197e6			−0.612031
$244$	−611408.	−	338282.i	−0.0420883	−	0.0232868i
$245$		0			0
$246$	7.04688e6	+	1.81950e6i	0.473360	+	0.122221i
$247$	1.10376e7			0.732462
$248$	1.47453e7	−	1.55750e7i	0.966718	−	1.02111i
$249$	6.32544e6			0.409725
$250$		0			0
$251$		−	4.71590e6i		−	0.298225i	−0.988820	−	0.149112i	$-0.952358\pi$
$251$		−	4.71590e6i		−	0.298225i	0.988820	−	0.149112i	$-0.0476416\pi$
$252$	4.00807e6	+	2.21760e6i	0.250457	+	0.138574i
$253$			1.00589e7i			0.621138i
$254$	1.29715e7	+	3.34923e6i	0.791571	+	0.204383i
$255$		0			0
$256$	−7.30726e6	+	1.51023e7i	−0.435547	+	0.900166i
$257$			2.34552e7i			1.38178i	0.722958	+	0.690892i	$0.242782\pi$
$257$			2.34552e7i			1.38178i	−0.722958	+	0.690892i	$0.757218\pi$
$258$	5.16811e6	+	1.33440e6i	0.300935	+	0.0777011i
$259$			617818.i			0.0355600i
$260$		0			0
$261$	−5.89004e6			−0.331281
$262$	5.68907e6	−	2.20337e7i	0.316328	−	1.22513i
$263$	2.16993e7			1.19283			0.596415	−	0.802676i	$-0.296591\pi$
$263$	2.16993e7			1.19283			0.596415	+	0.802676i	$0.296591\pi$
$264$	−1.04755e7	+	1.10650e7i	−0.569330	+	0.601365i
$265$		0			0
$266$	−4.66560e6	+	1.80698e7i	−0.247892	+	0.960082i
$267$	−9.62786e6			−0.505820
$268$	−2.20722e7	−	1.22122e7i	−1.14668	−	0.634436i
$269$	2.94278e7			1.51182			0.755911	−	0.654674i	$-0.227194\pi$
$269$	2.94278e7			1.51182			0.755911	+	0.654674i	$0.227194\pi$
$270$		0			0
$271$			8.51474e6i			0.427822i	0.976853	+	0.213911i	$0.0686203\pi$
$271$			8.51474e6i			0.427822i	−0.976853	+	0.213911i	$0.931380\pi$
$272$	1.65389e7	−	1.03708e7i	0.821866	−	0.515355i
$273$		−	1.40736e7i		−	0.691699i
$274$	−7.62007e6	+	2.95124e7i	−0.370431	+	1.43467i
$275$		0			0
$276$	1.81709e7	+	1.00536e7i	0.864269	+	0.478185i
$277$			2.76226e7i			1.29965i	0.760085	+	0.649824i	$0.225157\pi$
$277$			2.76226e7i			1.29965i	−0.760085	+	0.649824i	$0.774843\pi$
$278$	−277677.	+	1.07544e6i	−0.0129243	+	0.0500555i
$279$		−	9.67663e6i		−	0.445566i
$280$		0			0
$281$	8.64008e6			0.389403			0.194701	−	0.980863i	$-0.437626\pi$
$281$	8.64008e6			0.389403			0.194701	+	0.980863i	$0.437626\pi$
$282$	−1.81442e6	−	468480.i	−0.0809076	−	0.0208903i
$283$	1.27350e7			0.561873			0.280937	−	0.959726i	$-0.409355\pi$
$283$	1.27350e7			0.561873			0.280937	+	0.959726i	$0.409355\pi$
$284$	1.64909e7	−	2.98055e7i	0.719928	−	1.30119i
$285$		0			0
$286$	1.09070e7	+	2.81619e6i	0.466239	+	0.120382i
$287$	9.09748e6			0.384836
$288$	2.29033e6	+	7.21459e6i	0.0958783	+	0.302019i
$289$	1.42281e6			0.0589460
$290$		0			0
$291$		−	4.51462e7i		−	1.83207i
$292$	8.94275e6	−	1.61631e7i	0.359189	−	0.649195i
$293$			4.45415e7i			1.77077i	0.464859	+	0.885385i	$0.346105\pi$
$293$			4.45415e7i			1.77077i	−0.464859	+	0.885385i	$0.653895\pi$
$294$	−5.19576e6	−	1.34154e6i	−0.204459	−	0.0527912i
$295$		0			0
$296$	−701888.	+	741382.i	−0.0270640	+	0.0285869i
$297$		−	1.48205e7i		−	0.565709i
$298$	2.53623e7	+	6.54852e6i	0.958386	+	0.247454i
$299$		−	1.53528e7i		−	0.574345i
$300$		0			0
$301$	6.67200e6			0.244656
$302$	−1.11870e7	+	4.33272e7i	−0.406157	+	1.57304i
$303$	−1.98036e7			−0.711895
$304$	−2.61274e7	+	1.63833e7i	−0.929983	+	0.583150i
$305$		0			0
$306$	2.20189e6	−	8.52789e6i	0.0768479	−	0.297630i
$307$	−4.89051e7			−1.69020			−0.845102	−	0.534606i	$-0.820460\pi$
$307$	−4.89051e7			−1.69020			−0.845102	+	0.534606i	$0.820460\pi$
$308$	−9.22080e6	+	1.66656e7i	−0.315585	+	0.570386i
$309$	−4.30406e7			−1.45883
$310$		0			0
$311$		−	5.00220e7i		−	1.66295i	−0.555559	−	0.831477i	$-0.687496\pi$
$311$		−	5.00220e7i		−	1.66295i	0.555559	−	0.831477i	$-0.312504\pi$
$312$	1.59887e7	−	1.68883e7i	0.526440	−	0.556061i
$313$		−	1.12719e6i		−	0.0367589i	−0.999831	−	0.0183795i	$-0.994149\pi$
$313$		−	1.12719e6i		−	0.0367589i	0.999831	−	0.0183795i	$-0.00585069\pi$
$314$	−1.63359e6	+	6.32686e6i	−0.0527659	+	0.204362i
$315$		0			0
$316$	9.62688e6	−	1.73995e7i	0.305087	−	0.551413i
$317$			3.44882e7i			1.08266i	0.840810	+	0.541330i	$0.182079\pi$
$317$			3.44882e7i			1.08266i	−0.840810	+	0.541330i	$0.817921\pi$
$318$	−1.19507e7	+	4.62850e7i	−0.371632	+	1.43932i
$319$		−	2.44908e7i		−	0.754452i
$320$		0			0
$321$	−3.56112e7			−1.07664
$322$	2.51341e7	+	6.48960e6i	0.752828	+	0.194379i
$323$	3.58836e7			1.06485
$324$	−3.62028e7	−	2.00304e7i	−1.06441	−	0.588918i
$325$		0			0
$326$	1.42985e7	+	3.69185e6i	0.412702	+	0.106559i
$327$	−4.75831e7			−1.36085
$328$	1.09170e7	+	1.03354e7i	0.309372	+	0.292891i
$329$	−2.34240e6			−0.0657769
$330$		0			0
$331$		−	4.02696e7i		−	1.11044i	−0.831705	−	0.555218i	$-0.812635\pi$
$331$		−	4.02696e7i		−	1.11044i	0.831705	−	0.555218i	$-0.187365\pi$
$332$	1.14326e7	+	6.32544e6i	0.312413	+	0.172853i
$333$			460614.i			0.0124740i
$334$	6.16978e7	+	1.59303e7i	1.65588	+	0.427547i
$335$		0			0
$336$	2.08896e7	+	3.33139e7i	0.550696	+	0.878228i
$337$		−	3.42531e7i		−	0.894973i	−0.894291	−	0.447487i	$-0.852319\pi$
$337$		−	3.42531e7i		−	0.894973i	0.894291	−	0.447487i	$-0.147681\pi$
$338$	2.07410e7	+	5.35531e6i	0.537131	+	0.138687i
$339$			1.86428e7i			0.478533i
$340$		0			0
$341$	4.02355e7			1.01472
$342$	−3.47843e6	+	1.34719e7i	−0.0869572	+	0.336784i
$343$	−4.31599e7			−1.06954
$344$	8.00640e6	+	7.57989e6i	0.196681	+	0.186203i
$345$		0			0
$346$	−1.02531e7	+	3.97100e7i	−0.247529	+	0.958674i
$347$	5.45496e7			1.30558			0.652790	−	0.757539i	$-0.273599\pi$
$347$	5.45496e7			1.30558			0.652790	+	0.757539i	$0.273599\pi$
$348$	−4.42415e7	−	2.44781e7i	−1.04976	−	0.580817i
$349$	−4.70009e7			−1.10568			−0.552840	−	0.833287i	$-0.686456\pi$
$349$	−4.70009e7			−1.10568			−0.552840	+	0.833287i	$0.686456\pi$
$350$		0			0
$351$			2.26203e7i			0.523091i
$352$	−2.99983e7	+	9.52320e6i	−0.687811	+	0.218351i
$353$			1.27231e7i			0.289248i	0.989487	+	0.144624i	$0.0461972\pi$
$353$			1.27231e7i			0.289248i	−0.989487	+	0.144624i	$0.953803\pi$
$354$	4.85952e6	−	1.88208e7i	0.109543	−	0.424257i
$355$		0			0
$356$	−1.74013e7	−	9.62786e6i	−0.385685	−	0.213393i
$357$		−	4.57536e7i		−	1.00559i
$358$	4.66822e6	−	1.80799e7i	0.101742	−	0.394046i
$359$		−	2.02153e7i		−	0.436915i	−0.975846	−	0.218457i	$-0.929898\pi$
$359$		−	2.02153e7i		−	0.436915i	0.975846	−	0.218457i	$-0.0701025\pi$
$360$		0			0
$361$	−9.64116e6			−0.204931
$362$	7.50705e7	+	1.93831e7i	1.58250	+	0.408600i
$363$	2.63053e7			0.549951
$364$	1.40736e7	−	2.54365e7i	0.291811	−	0.527416i
$365$		0			0
$366$	−2.62032e6	−	676564.i	−0.0534455	−	0.0137996i
$367$	−1.11057e7			−0.224672			−0.112336	−	0.993670i	$-0.535833\pi$
$367$	−1.11057e7			−0.224672			−0.112336	+	0.993670i	$0.535833\pi$
$368$	2.27883e7	+	3.63418e7i	0.457265	+	0.729227i
$369$	6.78262e6			0.134995
$370$		0			0
$371$			5.97536e7i			1.17015i
$372$	4.02146e7	−	7.26835e7i	0.781186	−	1.41191i
$373$		−	687146.i		−	0.0132411i	−0.999978	−	0.00662053i	$-0.997893\pi$
$373$		−	687146.i		−	0.0132411i	0.999978	−	0.00662053i	$-0.00210739\pi$
$374$	3.54590e7	+	9.15548e6i	0.677817	+	0.175011i
$375$		0			0
$376$	−2.81088e6	−	2.66114e6i	−0.0528785	−	0.0500616i
$377$			3.73801e7i			0.697615i
$378$	−3.70319e7	−	9.56160e6i	−0.685647	−	0.177033i
$379$			1.48499e7i			0.272775i	0.990656	+	0.136388i	$0.0435492\pi$
$379$			1.48499e7i			0.272775i	−0.990656	+	0.136388i	$0.956451\pi$
$380$		0			0
$381$	5.18861e7			0.938158
$382$	−2.28329e7	+	8.84314e7i	−0.409610	+	1.58641i
$383$	3.35885e7			0.597853			0.298926	−	0.954276i	$-0.403372\pi$
$383$	3.35885e7			0.597853			0.298926	+	0.954276i	$0.403372\pi$
$384$	−1.27795e7	+	6.37088e7i	−0.225694	+	1.12514i
$385$		0			0
$386$	−4.86067e6	+	1.88253e7i	−0.0845150	+	0.327325i
$387$	4.97430e6			0.0858222
$388$	4.51462e7	−	8.15968e7i	0.772904	−	1.39694i
$389$	1.01122e8			1.71789			0.858946	−	0.512066i	$-0.171120\pi$
$389$	1.01122e8			1.71789			0.858946	+	0.512066i	$0.171120\pi$
$390$		0			0
$391$		−	4.99122e7i		−	0.834980i
$392$	−8.04924e6	−	7.62045e6i	−0.133628	−	0.126509i
$393$		−	8.81347e7i		−	1.45201i
$394$	4.46129e6	−	1.72785e7i	0.0729410	−	0.282499i
$395$		0			0
$396$	−6.87456e6	+	1.24250e7i	−0.110703	+	0.200084i
$397$		−	3.48266e7i		−	0.556595i	−0.960495	−	0.278297i	$-0.910230\pi$
$397$		−	3.48266e7i		−	0.556595i	0.960495	−	0.278297i	$-0.0897701\pi$
$398$	−9.79152e6	+	3.79224e7i	−0.155311	+	0.601515i
$399$			7.22792e7i			1.13787i
$400$		0			0
$401$	−6.88398e7			−1.06760			−0.533798	−	0.845612i	$-0.679236\pi$
$401$	−6.88398e7			−1.06760			−0.533798	+	0.845612i	$0.679236\pi$
$402$	−9.45950e7	−	2.44243e7i	−1.45610	−	0.375962i
$403$	−6.14110e7			−0.938277
$404$	−3.57928e7	−	1.98036e7i	−0.542815	−	0.300331i
$405$		0			0
$406$	−6.11952e7	−	1.58005e7i	−0.914406	−	0.236099i
$407$	−1.91524e6			−0.0284079
$408$	5.19795e7	−	5.49043e7i	0.765335	−	0.808399i
$409$	−4.59959e7			−0.672278			−0.336139	−	0.941812i	$-0.609121\pi$
$409$	−4.59959e7			−0.672278			−0.336139	+	0.941812i	$0.609121\pi$
$410$		0			0
$411$			1.18050e8i			1.70035i
$412$	−7.77913e7	−	4.30406e7i	−1.11234	−	0.615442i
$413$		−	2.42976e7i		−	0.344916i
$414$	1.87387e7	+	4.83832e6i	0.264082	+	0.0681857i
$415$		0			0
$416$	4.57861e7	−	1.45352e7i	0.635995	−	0.201902i
$417$			4.30176e6i			0.0593250i
$418$	−5.60164e7	−	1.44634e7i	−0.766983	−	0.198034i
$419$			2.71153e7i			0.368615i	0.982869	+	0.184307i	$0.0590042\pi$
$419$			2.71153e7i			0.368615i	−0.982869	+	0.184307i	$0.940996\pi$
$420$		0			0
$421$	−9.42078e7			−1.26253			−0.631263	−	0.775569i	$-0.717463\pi$
$421$	−9.42078e7			−1.26253			−0.631263	+	0.775569i	$0.717463\pi$
$422$	7.81903e6	−	3.02830e7i	0.104044	−	0.402959i
$423$	−1.74637e6			−0.0230737
$424$	−6.78846e7	+	7.17044e7i	−0.890582	+	0.940693i
$425$		0			0
$426$	3.29818e7	−	1.27738e8i	0.426624	−	1.65231i
$427$	−3.38282e6			−0.0434505
$428$	−6.43634e7	−	3.56112e7i	−0.820933	−	0.454209i
$429$	4.36282e7			0.552580
$430$		0			0
$431$			5.19187e7i			0.648473i	0.945976	+	0.324236i	$0.105107\pi$
$431$			5.19187e7i			0.648473i	−0.945976	+	0.324236i	$0.894893\pi$
$432$	−3.35756e7	−	5.35450e7i	−0.416459	−	0.664152i
$433$		−	8.40210e7i		−	1.03496i	−0.855695	−	0.517481i	$-0.826870\pi$
$433$		−	8.40210e7i		−	1.03496i	0.855695	−	0.517481i	$-0.173130\pi$
$434$	2.59584e7	−	1.00536e8i	0.317548	−	1.22986i
$435$		0			0
$436$	−8.60013e7	−	4.75831e7i	−1.03764	−	0.574108i
$437$			7.88486e7i			0.944822i
$438$	1.78855e7	−	6.92702e7i	0.212852	−	0.824374i
$439$		−	1.48115e8i		−	1.75068i	−0.483512	−	0.875338i	$-0.660639\pi$
$439$		−	1.48115e8i		−	1.75068i	0.483512	−	0.875338i	$-0.339361\pi$
$440$		0			0
$441$	−5.00092e6			−0.0583088
$442$	−5.41207e7	−	1.39739e7i	−0.626754	−	0.161827i
$443$	−8.03735e7			−0.924489			−0.462245	−	0.886752i	$-0.652956\pi$
$443$	−8.03735e7			−0.924489			−0.462245	+	0.886752i	$0.652956\pi$
$444$	−1.91424e6	+	3.45978e6i	−0.0218699	+	0.0395275i
$445$		0			0
$446$	−2.58029e7	−	6.66227e6i	−0.290846	−	0.0750962i
$447$	1.01449e8			1.13586
$448$	4.44185e6	+	8.11008e7i	0.0494003	+	0.901968i
$449$	8.80925e7			0.973196			0.486598	−	0.873626i	$-0.338238\pi$
$449$	8.80925e7			0.973196			0.486598	+	0.873626i	$0.338238\pi$
$450$		0			0
$451$			2.82022e7i			0.307435i
$452$	−1.86428e7	+	3.36949e7i	−0.201881	+	0.364879i
$453$			1.73309e8i			1.86434i
$454$	−1.04596e8	−	2.70066e7i	−1.11776	−	0.288604i
$455$		0			0
$456$	−8.21146e7	+	8.67350e7i	−0.866015	+	0.914745i
$457$		−	3.75423e7i		−	0.393344i	−0.980469	−	0.196672i	$-0.936987\pi$
$457$		−	3.75423e7i		−	0.393344i	0.980469	−	0.196672i	$-0.0630133\pi$
$458$	−1.23624e7	−	3.19196e6i	−0.128679	−	0.0332247i
$459$			7.35392e7i			0.760468i
$460$		0			0
$461$	1.15260e8			1.17646			0.588228	−	0.808695i	$-0.299826\pi$
$461$	1.15260e8			1.17646			0.588228	+	0.808695i	$0.299826\pi$
$462$	−1.84416e7	+	7.14240e7i	−0.187013	+	0.724300i
$463$	1.03415e7			0.104194			0.0520970	−	0.998642i	$-0.483410\pi$
$463$	1.03415e7			0.104194			0.0520970	+	0.998642i	$0.483410\pi$
$464$	−5.54836e7	−	8.84830e7i	−0.555407	−	0.885739i
$465$		0			0
$466$	1.60877e7	−	6.23072e7i	0.158977	−	0.615716i
$467$	1.64223e8			1.61243			0.806217	−	0.591620i	$-0.201511\pi$
$467$	1.64223e8			1.61243			0.806217	+	0.591620i	$0.201511\pi$
$468$	1.04926e7	−	1.89642e7i	0.102363	−	0.185011i
$469$	−1.22122e8			−1.18379
$470$		0			0
$471$			2.53074e7i			0.242206i
$472$	2.76039e7	−	2.91571e7i	0.262509	−	0.277280i
$473$			2.06832e7i			0.195449i
$474$	1.92538e7	−	7.45695e7i	0.180793	−	0.700207i
$475$		0			0
$476$	4.57536e7	−	8.26947e7i	0.424233	−	0.766755i
$477$			4.45493e7i			0.410474i
$478$	−2.25064e7	+	8.71670e7i	−0.206074	+	0.798121i
$479$			7.76230e7i			0.706291i	0.935568	+	0.353146i	$0.114888\pi$
$479$			7.76230e7i			0.706291i	−0.935568	+	0.353146i	$0.885112\pi$
$480$		0			0
$481$	2.92320e6			0.0262678
$482$	3.91252e7	+	1.01021e7i	0.349394	+	0.0902132i
$483$	1.00536e8			0.892241
$484$	4.75441e7	+	2.63053e7i	0.419334	+	0.232011i
$485$		0			0
$486$	−6.80249e7	−	1.75639e7i	−0.592596	−	0.153008i
$487$	−1.08071e7			−0.0935670			−0.0467835	−	0.998905i	$-0.514897\pi$
$487$	−1.08071e7			−0.0935670			−0.0467835	+	0.998905i	$0.514897\pi$
$488$	−4.05938e6	−	3.84314e6i	−0.0349302	−	0.0330694i
$489$	5.71939e7			0.489129
$490$		0			0
$491$			1.85067e8i			1.56345i	0.623624	+	0.781724i	$0.285660\pi$
$491$			1.85067e8i			1.56345i	−0.623624	+	0.781724i	$0.714340\pi$
$492$	5.09459e7	+	2.81875e7i	0.427774	+	0.236680i
$493$			1.21523e8i			1.01419i
$494$	8.54971e7	+	2.20753e7i	0.709203	+	0.183115i
$495$		0			0
$496$	1.45367e8	−	9.11530e7i	1.19130	−	0.747010i
$497$		−	1.64909e8i		−	1.34331i
$498$	4.89966e7	+	1.26509e7i	0.396715	+	0.102431i
$499$		−	6.83704e7i		−	0.550258i	−0.961407	−	0.275129i	$-0.911279\pi$
$499$		−	6.83704e7i		−	0.550258i	0.961407	−	0.275129i	$-0.0887206\pi$
$500$		0			0
$501$	2.46791e8			1.96253
$502$	9.43180e6	−	3.65292e7i	0.0745561	−	0.288755i
$503$	−1.31562e7			−0.103377			−0.0516887	−	0.998663i	$-0.516460\pi$
$503$	−1.31562e7			−0.103377			−0.0516887	+	0.998663i	$0.516460\pi$
$504$	2.66112e7	+	2.51936e7i	0.207861	+	0.196788i
$505$		0			0
$506$	−2.01178e7	+	7.79157e7i	−0.155284	+	0.601414i
$507$	8.29640e7			0.636599
$508$	9.37785e7	+	5.18861e7i	0.715339	+	0.395785i
$509$	−1.34186e8			−1.01755			−0.508775	−	0.860900i	$-0.669901\pi$
$509$	−1.34186e8			−1.01755			−0.508775	+	0.860900i	$0.669901\pi$
$510$		0			0
$511$		−	8.94275e7i		−	0.670206i
$512$	−8.68064e7	+	1.02367e8i	−0.646758	+	0.762695i
$513$		−	1.16173e8i		−	0.860508i
$514$	−4.69105e7	+	1.81683e8i	−0.345446	+	1.33791i
$515$		0			0
$516$	3.73632e7	+	2.06724e7i	0.271954	+	0.150467i
$517$		−	7.26144e6i		−	0.0525474i
$518$	−1.23564e6	+	4.78560e6i	−0.00888999	+	0.0344308i
$519$			1.58840e8i			1.13621i
$520$		0			0
$521$	−1.98565e8			−1.40407			−0.702036	−	0.712142i	$-0.747725\pi$
$521$	−1.98565e8			−1.40407			−0.702036	+	0.712142i	$0.747725\pi$
$522$	−4.56240e7	−	1.17801e7i	−0.320761	−	0.0828203i
$523$	−2.15512e8			−1.50649			−0.753245	−	0.657740i	$-0.771513\pi$
$523$	−2.15512e8			−1.50649			−0.753245	+	0.657740i	$0.771513\pi$
$524$	8.81347e7	−	1.59294e8i	0.612566	−	1.10715i
$525$		0			0
$526$	1.68082e8	+	4.33986e7i	1.15495	+	0.298207i
$527$	−1.99649e8			−1.36406
$528$	−1.03273e8	+	6.47578e7i	−0.701592	+	0.439937i
$529$	−3.83616e7			−0.259137
$530$		0			0
$531$		−	1.81151e7i		−	0.120992i
$532$	−7.22792e7	+	1.30637e8i	−0.480041	+	0.867622i
$533$		−	4.30447e7i		−	0.284275i
$534$	−7.45771e7	−	1.92557e7i	−0.489758	−	0.126455i
$535$		0			0
$536$	−1.46546e8	−	1.38739e8i	−0.951655	−	0.900959i
$537$		−	7.23197e7i		−	0.467018i
$538$	2.27947e8	+	5.88556e7i	1.46382	+	0.377956i
$539$		−	2.07939e7i		−	0.132791i
$540$		0			0
$541$	1.44188e7			0.0910623			0.0455311	−	0.998963i	$-0.485502\pi$
$541$	1.44188e7			0.0910623			0.0455311	+	0.998963i	$0.485502\pi$
$542$	−1.70295e7	+	6.59549e7i	−0.106956	+	0.414237i
$543$	3.00282e8			1.87556
$544$	1.48852e8	−	4.72541e7i	0.924607	−	0.293524i
$545$		0			0
$546$	2.81472e7	−	1.09014e8i	0.172925	−	0.669735i
$547$	4.24129e7			0.259141			0.129571	−	0.991570i	$-0.458640\pi$
$547$	4.24129e7			0.259141			0.129571	+	0.991570i	$0.458640\pi$
$548$	−1.18050e8	+	2.13362e8i	−0.717336	+	1.29651i
$549$	−2.52206e6			−0.0152419
$550$		0			0
$551$		−	1.91976e8i		−	1.14761i
$552$	1.20644e8	+	1.14217e8i	0.717278	+	0.679068i
$553$		−	9.62688e7i		−	0.569259i
$554$	−5.52453e7	+	2.13964e8i	−0.324912	+	1.25838i
$555$		0			0
$556$	−4.30176e6	+	7.77497e6i	−0.0250277	+	0.0452350i
$557$			8.90848e7i			0.515511i	0.966210	+	0.257756i	$0.0829829\pi$
$557$			8.90848e7i			0.515511i	−0.966210	+	0.257756i	$0.917017\pi$
$558$	1.93533e7	−	7.49549e7i	0.111391	−	0.431417i
$559$		−	3.15685e7i		−	0.180725i
$560$		0			0
$561$	1.41836e8			0.803338
$562$	6.69258e7	+	1.72802e7i	0.377037	+	0.0973507i
$563$	2.41576e8			1.35372			0.676860	−	0.736112i	$-0.263340\pi$
$563$	2.41576e8			1.35372			0.676860	+	0.736112i	$0.263340\pi$
$564$	−1.31174e7	−	7.25766e6i	−0.0731159	−	0.0404538i
$565$		0			0
$566$	9.86446e7	+	2.54699e7i	0.544031	+	0.140468i
$567$	−2.00304e8			−1.09886
$568$	1.87349e8	−	1.97891e8i	1.02236	−	1.07989i
$569$	2.56141e7			0.139041			0.0695203	−	0.997581i	$-0.477853\pi$
$569$	2.56141e7			0.139041			0.0695203	+	0.997581i	$0.477853\pi$
$570$		0			0
$571$		−	1.10781e8i		−	0.595057i	−0.954713	−	0.297528i	$-0.903838\pi$
$571$		−	1.10781e8i		−	0.595057i	0.954713	−	0.297528i	$-0.0961623\pi$
$572$	7.88532e7	+	4.36282e7i	0.421339	+	0.233120i
$573$			3.53725e8i			1.88019i
$574$	7.04688e7	+	1.81950e7i	0.372616	+	0.0962090i
$575$		0			0
$576$	3.31162e6	+	6.04646e7i	0.0173290	+	0.316398i
$577$			1.07272e8i			0.558415i	0.960231	+	0.279208i	$0.0900717\pi$
$577$			1.07272e8i			0.558415i	−0.960231	+	0.279208i	$0.909928\pi$
$578$	1.10211e7	+	2.84563e6i	0.0570742	+	0.0147365i
$579$			7.53011e7i			0.387941i
$580$		0			0
$581$	6.32544e7			0.322524
$582$	9.02923e7	−	3.49701e8i	0.458017	−	1.77389i
$583$	−1.85236e8			−0.934803
$584$	1.01596e8	−	1.07313e8i	0.510082	−	0.538783i
$585$		0			0
$586$	−8.90830e7	+	3.45017e8i	−0.442692	+	1.71454i
$587$	2.16397e7			0.106988			0.0534941	−	0.998568i	$-0.482964\pi$
$587$	2.16397e7			0.106988			0.0534941	+	0.998568i	$0.482964\pi$
$588$	−3.75631e7	−	2.07830e7i	−0.184769	−	0.102230i
$589$	3.15395e8			1.54351
$590$		0			0
$591$		−	6.91140e7i		−	0.334814i
$592$	−6.91956e6	+	4.33894e6i	−0.0333514	+	0.0209131i
$593$		−	2.00341e8i		−	0.960738i	−0.877066	−	0.480369i	$-0.840503\pi$
$593$		−	2.00341e8i		−	0.960738i	0.877066	−	0.480369i	$-0.159497\pi$
$594$	2.96410e7	−	1.14799e8i	0.141427	−	0.547745i
$595$		0			0
$596$	1.83359e8	+	1.01449e8i	0.866089	+	0.479193i
$597$			1.51690e8i			0.712907i
$598$	3.07055e7	−	1.18922e8i	0.143586	−	0.556107i
$599$		−	1.37592e8i		−	0.640197i	−0.947384	−	0.320098i	$-0.896284\pi$
$599$		−	1.37592e8i		−	0.640197i	0.947384	−	0.320098i	$-0.103716\pi$
$600$		0			0
$601$	−1.90306e8			−0.876655			−0.438327	−	0.898815i	$-0.644429\pi$
$601$	−1.90306e8			−0.876655			−0.438327	+	0.898815i	$0.644429\pi$
$602$	5.16811e7	+	1.33440e7i	0.236888	+	0.0611641i
$603$	−9.10477e7			−0.415257
$604$	−1.73309e8	+	3.13237e8i	−0.786520	+	1.42155i
$605$		0			0
$606$	−1.53398e8	−	3.96072e7i	−0.689289	−	0.177974i
$607$	1.25461e8			0.560974			0.280487	−	0.959858i	$-0.409504\pi$
$607$	1.25461e8			0.560974			0.280487	+	0.959858i	$0.409504\pi$
$608$	−2.35148e8	+	7.46496e7i	−1.04624	+	0.332137i
$609$	−2.44781e8			−1.08374
$610$		0			0
$611$			1.10831e7i			0.0485888i
$612$	3.41116e7	−	6.16530e7i	0.148815	−	0.268967i
$613$			9.91111e7i			0.430270i	0.976584	+	0.215135i	$0.0690191\pi$
$613$			9.91111e7i			0.430270i	−0.976584	+	0.215135i	$0.930981\pi$
$614$	−3.78817e8	−	9.78102e7i	−1.63653	−	0.422551i
$615$		0			0
$616$	−1.04755e8	+	1.10650e8i	−0.448160	+	0.473378i
$617$			3.70827e7i			0.157876i	0.996880	+	0.0789379i	$0.0251529\pi$
$617$			3.70827e7i			0.157876i	−0.996880	+	0.0789379i	$0.974847\pi$
$618$	−3.33391e8	−	8.60813e7i	−1.41250	−	0.364706i
$619$		−	4.05274e8i		−	1.70874i	−0.519662	−	0.854372i	$-0.673942\pi$
$619$		−	4.05274e8i		−	1.70874i	0.519662	−	0.854372i	$-0.326058\pi$
$620$		0			0
$621$	−1.61591e8			−0.674749
$622$	1.00044e8	−	3.87469e8i	0.415738	−	1.61015i
$623$	−9.62786e7			−0.398168
$624$	1.57624e8	−	9.88390e7i	0.648738	−	0.406794i
$625$		0			0
$626$	2.25437e6	−	8.73115e6i	0.00918973	−	0.0355917i
$627$	−2.24065e8			−0.909017
$628$	−2.53074e7	+	4.57405e7i	−0.102181	+	0.184681i
$629$	9.50340e6			0.0381880
$630$		0			0
$631$			2.52648e7i			0.100561i	0.998735	+	0.0502803i	$0.0160115\pi$
$631$			2.52648e7i			0.100561i	−0.998735	+	0.0502803i	$0.983989\pi$
$632$	1.09369e8	−	1.15523e8i	0.433253	−	0.457631i
$633$		−	1.21132e8i		−	0.477581i
$634$	−6.89763e7	+	2.67144e8i	−0.270665	+	1.04828i
$635$		0			0
$636$	−1.85140e8	+	3.34620e8i	−0.719662	+	1.30071i
$637$			3.17374e7i			0.122787i
$638$	4.89817e7	−	1.89705e8i	0.188613	−	0.730495i
$639$		−	1.22948e8i		−	0.471213i
$640$		0			0
$641$	−4.21293e8			−1.59959			−0.799797	−	0.600270i	$-0.795060\pi$
$641$	−4.21293e8			−1.59959			−0.799797	+	0.600270i	$0.795060\pi$
$642$	−2.75843e8	−	7.12224e7i	−1.04245	−	0.269161i
$643$	−8.17706e7			−0.307584			−0.153792	−	0.988103i	$-0.549149\pi$
$643$	−8.17706e7			−0.307584			−0.153792	+	0.988103i	$0.549149\pi$
$644$	1.81709e8	+	1.00536e8i	0.680328	+	0.376414i
$645$		0			0
$646$	2.77953e8	+	7.17672e7i	1.03104	+	0.266212i
$647$	−1.84284e8			−0.680416			−0.340208	−	0.940350i	$-0.610497\pi$
$647$	−1.84284e8			−0.680416			−0.340208	+	0.940350i	$0.610497\pi$
$648$	−2.40365e8	−	2.27561e8i	−0.883377	−	0.836319i
$649$	7.53226e7			0.275544
$650$		0			0
$651$		−	4.02146e8i		−	1.45761i
$652$	1.03372e8	+	5.71939e7i	0.372958	+	0.206351i
$653$		−	6.43842e7i		−	0.231228i	−0.993294	−	0.115614i	$-0.963117\pi$
$653$		−	6.43842e7i		−	0.231228i	0.993294	−	0.115614i	$-0.0368835\pi$
$654$	−3.68577e8	−	9.51662e7i	−1.31764	−	0.340212i
$655$		0			0
$656$	6.38917e7	+	1.01892e8i	0.226325	+	0.360934i
$657$		−	6.66726e7i		−	0.235099i
$658$	−1.81442e7	−	4.68480e6i	−0.0636882	−	0.0164442i
$659$			5.38099e8i			1.88021i	0.340889	+	0.940103i	$0.389272\pi$
$659$			5.38099e8i			1.88021i	−0.340889	+	0.940103i	$0.610728\pi$
$660$		0			0
$661$	2.83897e8			0.983008			0.491504	−	0.870875i	$-0.336447\pi$
$661$	2.83897e8			0.983008			0.491504	+	0.870875i	$0.336447\pi$
$662$	8.05393e7	−	3.11927e8i	0.277609	−	1.07518i
$663$	−2.16483e8			−0.742819
$664$	7.59053e7	+	7.18617e7i	0.259279	+	0.245467i
$665$		0			0
$666$	−921228.	+	3.56790e6i	−0.00311849	+	0.0120779i
$667$	−2.67029e8			−0.899872
$668$	4.46048e8	+	2.46791e8i	1.49642	+	0.827942i
$669$	−1.03212e8			−0.344707
$670$		0			0
$671$		−	1.04867e7i		−	0.0347115i
$672$	9.51824e7	+	2.99827e8i	0.313653	+	0.988014i
$673$		−	2.77693e8i		−	0.911002i	−0.890235	−	0.455501i	$-0.849460\pi$
$673$		−	2.77693e8i		−	0.911002i	0.890235	−	0.455501i	$-0.150540\pi$
$674$	6.85062e7	−	2.65323e8i	0.223743	−	0.866554i
$675$		0			0
$676$	1.49949e8	+	8.29640e7i	0.485403	+	0.268565i
$677$		−	9.23026e7i		−	0.297473i	−0.988877	−	0.148737i	$-0.952479\pi$
$677$		−	9.23026e7i		−	0.297473i	0.988877	−	0.148737i	$-0.0475207\pi$
$678$	−3.72856e7	+	1.44407e8i	−0.119633	+	0.463338i
$679$		−	4.51462e8i		−	1.44215i
$680$		0			0
$681$	−4.18384e8			−1.32475
$682$	3.11663e8	+	8.04710e7i	0.982499	+	0.253680i
$683$	2.70862e8			0.850132			0.425066	−	0.905162i	$-0.360251\pi$
$683$	2.70862e8			0.850132			0.425066	+	0.905162i	$0.360251\pi$
$684$	−5.38877e7	+	9.73962e7i	−0.168392	+	0.304350i
$685$		0			0
$686$	−3.34315e8	−	8.63198e7i	−1.03558	−	0.267386i
$687$	−4.94496e7			−0.152508
$688$	4.68575e7	+	7.47264e7i	0.143884	+	0.229461i
$689$	2.82724e8			0.864380
$690$		0			0
$691$			1.92568e7i			0.0583645i	0.999574	+	0.0291823i	$0.00929032\pi$
$691$			1.92568e7i			0.0583645i	−0.999574	+	0.0291823i	$0.990710\pi$
$692$	−1.58840e8	+	2.87086e8i	−0.479337	+	0.866350i
$693$			6.87456e7i			0.206560i
$694$	4.22539e8	+	1.09099e8i	1.26412	+	0.326395i
$695$		0			0
$696$	−2.93737e8	−	2.78089e8i	−0.871226	−	0.824815i
$697$		−	1.39939e8i		−	0.413277i
$698$	−3.64067e8	−	9.40017e7i	−1.07057	−	0.276420i
$699$		−	2.49229e8i		−	0.729738i
$700$		0			0
$701$	3.52234e8			1.02253			0.511266	−	0.859423i	$-0.329177\pi$
$701$	3.52234e8			1.02253			0.511266	+	0.859423i	$0.329177\pi$
$702$	−4.52407e7	+	1.75216e8i	−0.130773	+	0.506481i
$703$	−1.50130e7			−0.0432117
$704$	−2.51412e8	+	1.37697e7i	−0.720558	+	0.0394646i
$705$		0			0
$706$	−2.54463e7	+	9.85530e7i	−0.0723119	+	0.280063i
$707$	−1.98036e8			−0.560384
$708$	7.52834e7	−	1.36067e8i	0.212129	−	0.383400i
$709$	−4.62733e8			−1.29835			−0.649175	−	0.760639i	$-0.724886\pi$
$709$	−4.62733e8			−1.29835			−0.649175	+	0.760639i	$0.724886\pi$
$710$		0			0
$711$		−	7.17731e7i		−	0.199689i
$712$	−1.15534e8	−	1.09380e8i	−0.320089	−	0.303038i
$713$		−	4.38697e8i		−	1.21031i
$714$	9.15072e7	−	3.54406e8i	0.251397	−	0.973658i
$715$		0			0
$716$	7.23197e7	−	1.30710e8i	0.197023	−	0.356098i
$717$			3.48668e8i			0.945921i
$718$	4.04306e7	−	1.56587e8i	0.109229	−	0.423041i
$719$			4.60385e8i			1.23861i	0.785150	+	0.619305i	$0.212586\pi$
$719$			4.60385e8i			1.23861i	−0.785150	+	0.619305i	$0.787414\pi$
$720$		0			0
$721$	−4.30406e8			−1.14835
$722$	−7.46801e7	−	1.92823e7i	−0.198424	−	0.0512327i
$723$	1.56501e8			0.414097
$724$	5.42727e8	+	3.00282e8i	1.43010	+	0.791250i
$725$		0			0
$726$	2.03760e8	+	5.26107e7i	0.532488	+	0.137488i
$727$	4.82173e8			1.25487			0.627437	−	0.778668i	$-0.284104\pi$
$727$	4.82173e8			1.25487			0.627437	+	0.778668i	$0.284104\pi$
$728$	1.59887e8	−	1.68883e8i	0.414398	−	0.437716i
$729$	1.99184e8			0.514128
$730$		0			0
$731$		−	1.02630e8i		−	0.262738i
$732$	−1.89438e7	−	1.04813e7i	−0.0482985	−	0.0267227i
$733$			5.08270e8i			1.29057i	0.763941	+	0.645287i	$0.223262\pi$
$733$			5.08270e8i			1.29057i	−0.763941	+	0.645287i	$0.776738\pi$
$734$	−8.60246e7	−	2.22115e7i	−0.217538	−	0.0561680i
$735$		0			0
$736$	1.03834e8	+	3.27079e8i	0.260438	+	0.820387i
$737$		−	3.78577e8i		−	0.945696i
$738$	5.25380e7	+	1.35652e7i	0.130709	+	0.0337488i
$739$			1.27767e8i			0.316582i	0.987392	+	0.158291i	$0.0505984\pi$
$739$			1.27767e8i			0.316582i	−0.987392	+	0.158291i	$0.949402\pi$
$740$		0			0
$741$	3.41988e8			0.840537
$742$	−1.19507e8	+	4.62850e8i	−0.292538	+	1.13300i
$743$	2.83312e8			0.690716			0.345358	−	0.938471i	$-0.387758\pi$
$743$	2.83312e8			0.690716			0.345358	+	0.938471i	$0.387758\pi$
$744$	4.56868e8	−	4.82575e8i	1.10936	−	1.17178i
$745$		0			0
$746$	1.37429e6	−	5.32261e6i	0.00331026	−	0.0128206i
$747$	4.71593e7			0.113137
$748$	2.56354e8	+	1.41836e8i	0.612540	+	0.338908i
$749$	−3.56112e8			−0.847503
$750$		0			0
$751$			2.15309e8i			0.508325i	0.967161	+	0.254163i	$0.0817999\pi$
$751$			2.15309e8i			0.508325i	−0.967161	+	0.254163i	$0.918200\pi$
$752$	−1.64507e7	−	2.62349e7i	−0.0386839	−	0.0616915i
$753$		−	1.46117e8i		−	0.342228i
$754$	−7.47601e7	+	2.89545e8i	−0.174404	+	0.675463i
$755$		0			0
$756$	−2.67725e8	−	1.48128e8i	−0.619617	−	0.342824i
$757$		−	3.03985e8i		−	0.700753i	−0.936609	−	0.350377i	$-0.886054\pi$
$757$		−	3.03985e8i		−	0.700753i	0.936609	−	0.350377i	$-0.113946\pi$
$758$	−2.96997e7	+	1.15026e8i	−0.0681938	+	0.264113i
$759$			3.11663e8i			0.712787i
$760$		0			0
$761$	8.63611e8			1.95959			0.979793	−	0.200014i	$-0.0640988\pi$
$761$	8.63611e8			1.95959			0.979793	+	0.200014i	$0.0640988\pi$
$762$	4.01908e8	+	1.03772e8i	0.908367	+	0.234539i
$763$	−4.75831e8			−1.07122
$764$	−3.53725e8	+	6.39321e8i	−0.793206	+	1.43364i
$765$		0			0
$766$	2.60175e8	+	6.71770e7i	0.578868	+	0.149463i
$767$	−1.14964e8			−0.254786
$768$	−2.26407e8	+	4.67927e8i	−0.499812	+	1.03299i
$769$	1.97898e7			0.0435174			0.0217587	−	0.999763i	$-0.493073\pi$
$769$	1.97898e7			0.0435174			0.0217587	+	0.999763i	$0.493073\pi$
$770$		0			0
$771$			7.26734e8i			1.58567i
$772$	−7.53011e7	+	1.36099e8i	−0.163663	+	0.295803i
$773$			5.64048e8i			1.22117i	0.791949	+	0.610587i	$0.209067\pi$
$773$			5.64048e8i			1.22117i	−0.791949	+	0.610587i	$0.790933\pi$
$774$	3.85308e7	+	9.94861e6i	0.0830970	+	0.0214555i
$775$		0			0
$776$	5.12894e8	−	5.41754e8i	1.09760	−	1.15936i
$777$			1.91424e7i			0.0408069i
$778$	7.83286e8	+	2.02244e8i	1.66334	+	0.429473i
$779$			2.21069e8i			0.467644i
$780$		0			0
$781$	5.11217e8			1.07313
$782$	9.98243e7	−	3.86618e8i	0.208745	−	0.808466i
$783$	3.93433e8			0.819570
$784$	−4.71082e7	−	7.51262e7i	−0.0977572	−	0.155899i
$785$		0			0
$786$	1.76269e8	−	6.82689e8i	0.363002	−	1.40590i
$787$	4.04198e8			0.829220			0.414610	−	0.909999i	$-0.363918\pi$
$787$	4.04198e8			0.829220			0.414610	+	0.909999i	$0.363918\pi$
$788$	6.91140e7	−	1.24916e8i	0.141250	−	0.255294i
$789$	6.72328e8			1.36883
$790$		0			0
$791$			1.86428e8i			0.376688i
$792$	−7.81002e7	+	8.24947e7i	−0.157209	+	0.166054i
$793$			1.60058e7i			0.0320965i
$794$	6.96531e7	−	2.69765e8i	0.139149	−	0.538921i
$795$		0			0
$796$	−1.51690e8	+	2.74163e8i	−0.300758	+	0.543587i
$797$		−	2.15998e7i		−	0.0426654i	−0.999772	−	0.0213327i	$-0.993209\pi$
$797$		−	2.15998e7i		−	0.0426654i	0.999772	−	0.0213327i	$-0.00679092\pi$
$798$	−1.44558e8	+	5.59872e8i	−0.284469	+	1.10174i
$799$			3.60313e7i			0.0706381i
$800$		0			0
$801$	−7.17805e7			−0.139672
$802$	−5.33231e8	−	1.37680e8i	−1.03369	−	0.266899i
$803$	2.77225e8			0.535410
$804$	−6.83881e8	−	3.78380e8i	−1.31587	−	0.728048i
$805$		0			0
$806$	−4.75688e8	−	1.22822e8i	−0.908483	−	0.234569i
$807$	9.11786e8			1.73489
$808$	−2.37643e8	−	2.24984e8i	−0.450496	−	0.426498i
$809$	−6.51310e8			−1.23011			−0.615053	−	0.788486i	$-0.710865\pi$
$809$	−6.51310e8			−1.23011			−0.615053	+	0.788486i	$0.710865\pi$
$810$		0			0
$811$		−	5.52891e8i		−	1.03652i	−0.855223	−	0.518259i	$-0.826580\pi$
$811$		−	5.52891e8i		−	1.03652i	0.855223	−	0.518259i	$-0.173420\pi$
$812$	−4.42415e8	−	2.44781e8i	−0.826346	−	0.457203i
$813$			2.63820e8i			0.490948i
$814$	−1.48354e7	−	3.83047e6i	−0.0275058	−	0.00710198i
$815$		0			0
$816$	5.12440e8	−	3.21328e8i	0.943133	−	0.591396i
$817$			1.62130e8i			0.297301i
$818$	−3.56282e8	−	9.19917e7i	−0.650930	−	0.168069i
$819$		−	1.04926e8i		−	0.190998i
$820$		0			0
$821$	−8.94865e8			−1.61707			−0.808534	−	0.588450i	$-0.799738\pi$
$821$	−8.94865e8			−1.61707			−0.808534	+	0.588450i	$0.799738\pi$
$822$	−2.36099e8	+	9.14408e8i	−0.425088	+	1.64636i
$823$	−8.44482e8			−1.51492			−0.757462	−	0.652879i	$-0.773561\pi$
$823$	−8.44482e8			−1.51492			−0.757462	+	0.652879i	$0.773561\pi$
$824$	−5.16488e8	−	4.88974e8i	−0.923163	−	0.873985i
$825$		0			0
$826$	4.85952e7	−	1.88208e8i	0.0862290	−	0.333963i
$827$	−3.11099e7			−0.0550024			−0.0275012	−	0.999622i	$-0.508755\pi$
$827$	−3.11099e7			−0.0550024			−0.0275012	+	0.999622i	$0.508755\pi$
$828$	1.35473e8	+	7.49549e7i	0.238650	+	0.132041i
$829$	4.05444e7			0.0711652			0.0355826	−	0.999367i	$-0.488671\pi$
$829$	4.05444e7			0.0711652			0.0355826	+	0.999367i	$0.488671\pi$
$830$		0			0
$831$			8.55856e8i			1.49141i
$832$	3.83728e8	−	2.10166e7i	0.666275	−	0.0364915i
$833$			1.03179e8i			0.178508i
$834$	−8.60352e6	+	3.33213e7i	−0.0148313	+	0.0574412i
$835$		0			0
$836$	−4.04974e8	−	2.24065e8i	−0.693120	−	0.383492i
$837$			6.46364e8i			1.10230i
$838$	−5.42306e7	+	2.10034e8i	−0.0921537	+	0.356910i
$839$		−	4.17820e8i		−	0.707463i	−0.935347	−	0.353731i	$-0.884913\pi$
$839$		−	4.17820e8i		−	0.707463i	0.935347	−	0.353731i	$-0.115087\pi$
$840$		0			0
$841$	5.53247e7			0.0930103
$842$	−7.29730e8	−	1.88416e8i	−1.22244	−	0.315632i
$843$	2.67703e8			0.446859
$844$	1.21132e8	−	2.18933e8i	0.201480	−	0.364153i
$845$		0			0
$846$	−1.35274e7	−	3.49275e6i	−0.0223410	−	0.00576841i
$847$	2.63053e8			0.432906
$848$	−6.69241e8	+	4.19650e8i	−1.09748	+	0.688177i
$849$	3.94578e8			0.644778
$850$		0			0
$851$			2.08823e7i			0.0338835i
$852$	5.10951e8	−	9.23489e8i	0.826153	−	1.49318i
$853$			4.28994e8i			0.691201i	0.938382	+	0.345601i	$0.112325\pi$
$853$			4.28994e8i			0.691201i	−0.938382	+	0.345601i	$0.887675\pi$
$854$	−2.62032e7	−	6.76564e6i	−0.0420708	−	0.0108626i
$855$		0			0
$856$	−4.27334e8	−	4.04570e8i	−0.681313	−	0.645019i
$857$			2.20598e8i			0.350476i	0.984526	+	0.175238i	$0.0560695\pi$
$857$			2.20598e8i			0.350476i	−0.984526	+	0.175238i	$0.943930\pi$
$858$	3.37942e8	+	8.72563e7i	0.535033	+	0.138145i
$859$		−	1.14768e9i		−	1.81068i	−0.424689	−	0.905339i	$-0.639617\pi$
$859$		−	1.14768e9i		−	1.81068i	0.424689	−	0.905339i	$-0.360383\pi$
$860$		0			0
$861$	2.81875e8			0.441619
$862$	−1.03837e8	+	4.02160e8i	−0.162118	+	0.627881i
$863$	−6.44987e7			−0.100350			−0.0501752	−	0.998740i	$-0.515978\pi$
$863$	−6.44987e7			−0.100350			−0.0501752	+	0.998740i	$0.515978\pi$
$864$	−1.52986e8	−	4.81909e8i	−0.237197	−	0.747177i
$865$		0			0
$866$	1.68042e8	−	6.50824e8i	0.258740	−	1.00210i
$867$	4.40842e7			0.0676435
$868$	4.02146e8	−	7.26835e8i	0.614928	−	1.11142i
$869$	2.98433e8			0.454766
$870$		0			0
$871$			5.77818e8i			0.874453i
$872$	−5.70997e8	−	5.40580e8i	−0.861161	−	0.815287i
$873$		−	3.36587e8i		−	0.505888i
$874$	−1.57697e8	+	6.10759e8i	−0.236205	+	0.914820i
$875$		0			0
$876$	2.77081e8	−	5.00794e8i	0.412187	−	0.744984i
$877$			5.15252e8i			0.763873i	0.924189	+	0.381937i	$0.124743\pi$
$877$			5.15252e8i			0.763873i	−0.924189	+	0.381937i	$0.875257\pi$
$878$	2.96230e8	−	1.14729e9i	0.437669	−	1.69508i
$879$			1.38007e9i			2.03205i
$880$		0			0
$881$	−1.18519e8			−0.173324			−0.0866622	−	0.996238i	$-0.527620\pi$
$881$	−1.18519e8			−0.173324			−0.0866622	+	0.996238i	$0.527620\pi$
$882$	−3.87370e7	−	1.00018e7i	−0.0564572	−	0.0145772i
$883$	1.28669e8			0.186893			0.0934466	−	0.995624i	$-0.470212\pi$
$883$	1.28669e8			0.186893			0.0934466	+	0.995624i	$0.470212\pi$
$884$	−3.91270e8	−	2.16483e8i	−0.566395	−	0.313377i
$885$		0			0
$886$	−6.22571e8	−	1.60747e8i	−0.895133	−	0.231122i
$887$	5.09948e8			0.730727			0.365363	−	0.930865i	$-0.380945\pi$
$887$	5.09948e8			0.730727			0.365363	+	0.930865i	$0.380945\pi$
$888$	−2.17472e7	+	2.29709e7i	−0.0310574	+	0.0328049i
$889$	5.18861e8			0.738492
$890$		0			0
$891$		−	6.20943e8i		−	0.877847i
$892$	−1.86544e8	−	1.03212e8i	−0.262837	−	0.145423i
$893$		−	5.69203e7i		−	0.0799306i
$894$	7.85823e8	+	2.02899e8i	1.09980	+	0.283966i
$895$		0			0
$896$	−1.27795e8	+	6.37088e8i	−0.177660	+	0.885677i
$897$		−	4.75688e8i		−	0.659090i
$898$	6.82362e8	+	1.76185e8i	0.942293	+	0.243299i
$899$			1.06812e9i			1.47007i
$900$		0			0
$901$	9.19142e8			1.25663
$902$	−5.64044e7	+	2.18453e8i	−0.0768588	+	0.297673i
$903$	2.06724e8			0.280756
$904$	−2.11796e8	+	2.23714e8i	−0.286690	+	0.302822i
$905$		0			0
$906$	−3.46618e8	+	1.34244e9i	−0.466086	+	1.80514i
$907$	−5.43212e8			−0.728027			−0.364014	−	0.931394i	$-0.618594\pi$
$907$	−5.43212e8			−0.728027			−0.364014	+	0.931394i	$0.618594\pi$
$908$	−7.56185e8	−	4.18384e8i	−1.01011	−	0.558879i
$909$	−1.47645e8			−0.196575
$910$		0			0
$911$			5.99585e8i			0.793041i	0.918026	+	0.396520i	$0.129782\pi$
$911$			5.99585e8i			0.793041i	−0.918026	+	0.396520i	$0.870218\pi$
$912$	−8.09527e8	+	5.07617e8i	−1.06720	+	0.669194i
$913$			1.96089e8i			0.257656i
$914$	7.50846e7	−	2.90801e8i	0.0983359	−	0.380853i
$915$		0			0
$916$	−8.93748e7	−	4.94496e7i	−0.116286	−	0.0643393i
$917$		−	8.81347e8i		−	1.14298i
$918$	−1.47078e8	+	5.69632e8i	−0.190117	+	0.736320i
$919$		−	9.66486e8i		−	1.24523i	−0.782529	−	0.622614i	$-0.786071\pi$
$919$		−	9.66486e8i		−	1.24523i	0.782529	−	0.622614i	$-0.213929\pi$
$920$		0			0
$921$	−1.51527e9			−1.93959
$922$	8.92800e8	+	2.30520e8i	1.13910	+	0.294114i
$923$	−7.80265e8			−0.992286
$924$	−2.85696e8	+	5.16365e8i	−0.362150	+	0.654547i
$925$		0			0
$926$	8.01053e7	+	2.06831e7i	0.100885	+	0.0260485i
$927$	−3.20889e8			−0.402825
$928$	−2.52809e8	−	7.96354e8i	−0.316335	−	0.996465i
$929$	−7.22626e8			−0.901295			−0.450647	−	0.892702i	$-0.648807\pi$
$929$	−7.22626e8			−0.901295			−0.450647	+	0.892702i	$0.648807\pi$
$930$		0			0
$931$		−	1.62997e8i		−	0.201990i
$932$	2.49229e8	−	4.50454e8i	0.307858	−	0.556420i
$933$		−	1.54988e9i		−	1.90832i
$934$	1.27206e9	+	3.28445e8i	1.56123	+	0.403109i
$935$		0			0
$936$	1.19203e8	−	1.25911e8i	0.145365	−	0.153545i
$937$		−	4.12016e8i		−	0.500836i	−0.968138	−	0.250418i	$-0.919432\pi$
$937$		−	4.12016e8i		−	0.500836i	0.968138	−	0.250418i	$-0.0805680\pi$
$938$	−9.45950e8	−	2.44243e8i	−1.14620	−	0.295947i
$939$		−	3.49246e7i		−	0.0421827i
$940$		0			0
$941$	7.87666e8			0.945308			0.472654	−	0.881248i	$-0.343296\pi$
$941$	7.87666e8			0.945308			0.472654	+	0.881248i	$0.343296\pi$
$942$	−5.06149e7	+	1.96031e8i	−0.0605516	+	0.234515i
$943$	3.07495e8			0.366693
$944$	2.72133e8	−	1.70642e8i	0.323493	−	0.202848i
$945$		0			0
$946$	−4.13664e7	+	1.60211e8i	−0.0488623	+	0.189243i
$947$	−5.29504e8			−0.623475			−0.311738	−	0.950168i	$-0.600911\pi$
$947$	−5.29504e8			−0.623475			−0.311738	+	0.950168i	$0.600911\pi$
$948$	2.98278e8	−	5.39105e8i	0.350103	−	0.632774i
$949$	−4.23126e8			−0.495075
$950$		0			0
$951$			1.06858e9i			1.24241i
$952$	5.19795e8	−	5.49043e8i	0.602451	−	0.636349i
$953$		−	1.18323e9i		−	1.36706i	−0.729920	−	0.683532i	$-0.760443\pi$
$953$		−	1.18323e9i		−	1.36706i	0.729920	−	0.683532i	$-0.239557\pi$
$954$	−8.90985e7	+	3.45077e8i	−0.102618	+	0.397440i
$955$		0			0
$956$	−3.48668e8	+	6.30180e8i	−0.399060	+	0.721259i
$957$		−	7.58820e8i		−	0.865771i
$958$	−1.55246e8	+	6.01265e8i	−0.176573	+	0.683864i
$959$			1.18050e9i			1.33847i
$960$		0			0
$961$	−8.67284e8			−0.977218
$962$	2.26430e7	+	5.84641e6i	0.0254337	+	0.00656695i
$963$	−2.65499e8			−0.297293
$964$	2.82858e8	+	1.56501e8i	0.315746	+	0.174697i
$965$		0			0
$966$	7.78752e8	+	2.01073e8i	0.863909	+	0.223060i
$967$	4.78688e8			0.529387			0.264693	−	0.964333i	$-0.414729\pi$
$967$	4.78688e8			0.529387			0.264693	+	0.964333i	$0.414729\pi$
$968$	3.15664e8	+	2.98848e8i	0.348016	+	0.329477i
$969$	1.11181e9			1.22197
$970$		0			0
$971$			7.02914e8i			0.767793i	0.923376	+	0.383897i	$0.125418\pi$
$971$			7.02914e8i			0.767793i	−0.923376	+	0.383897i	$0.874582\pi$
$972$	−4.91791e8	−	2.72100e8i	−0.535527	−	0.296298i
$973$			4.30176e7i			0.0466990i
$974$	−8.37115e7	−	2.16142e7i	−0.0905959	−	0.0233918i
$975$		0			0
$976$	−2.37576e7	−	3.78876e7i	−0.0255536	−	0.0407518i
$977$		−	9.21323e8i		−	0.987934i	−0.869481	−	0.493967i	$-0.835546\pi$
$977$		−	9.21323e8i		−	0.987934i	0.869481	−	0.493967i	$-0.164454\pi$
$978$	4.43022e8	+	1.14388e8i	0.473597	+	0.122282i
$979$		−	2.98464e8i		−	0.318085i
$980$		0			0
$981$	−3.54755e8			−0.375770
$982$	−3.70133e8	+	1.43352e9i	−0.390862	+	1.51380i
$983$	−2.44410e8			−0.257311			−0.128655	−	0.991689i	$-0.541066\pi$
$983$	−2.44410e8			−0.257311			−0.128655	+	0.991689i	$0.541066\pi$
$984$	3.38250e8	+	3.20231e8i	0.355020	+	0.336108i
$985$		0			0
$986$	−2.43047e8	+	9.41317e8i	−0.253548	+	0.981985i
$987$	−7.25766e7			−0.0754823
$988$	6.18107e8	+	3.41988e8i	0.640904	+	0.354602i
$989$	2.25514e8			0.233122
$990$		0			0
$991$		−	1.78184e9i		−	1.83083i	−0.402516	−	0.915413i	$-0.631864\pi$
$991$		−	1.78184e9i		−	1.83083i	0.402516	−	0.915413i	$-0.368136\pi$
$992$	1.30831e9	−	4.15334e8i	1.34022	−	0.425464i
$993$		−	1.24771e9i		−	1.27428i
$994$	3.29818e8	−	1.27738e9i	0.335826	−	1.30065i
$995$		0			0
$996$	3.54225e8	+	1.95987e8i	0.358510	+	0.198357i
$997$			1.36790e9i			1.38029i	0.723673	+	0.690143i	$0.242452\pi$
$997$			1.36790e9i			1.38029i	−0.723673	+	0.690143i	$0.757548\pi$
$998$	1.36741e8	−	5.29595e8i	0.137565	−	0.532785i
$999$		−	3.07674e7i		−	0.0308598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.7.d.a.99.4		4
4.3	odd	2	inner	100.7.d.a.99.2		4
5.2	odd	4		100.7.b.c.51.2		2
5.3	odd	4		4.7.b.a.3.1	✓	2
5.4	even	2	inner	100.7.d.a.99.1		4
15.8	even	4		36.7.d.c.19.2		2
20.3	even	4		4.7.b.a.3.2	yes	2
20.7	even	4		100.7.b.c.51.1		2
20.19	odd	2	inner	100.7.d.a.99.3		4
40.3	even	4		64.7.c.c.63.2		2
40.13	odd	4		64.7.c.c.63.1		2
60.23	odd	4		36.7.d.c.19.1		2
80.3	even	4		256.7.d.f.127.3		4
80.13	odd	4		256.7.d.f.127.1		4
80.43	even	4		256.7.d.f.127.2		4
80.53	odd	4		256.7.d.f.127.4		4
120.53	even	4		576.7.g.h.127.1		2
120.83	odd	4		576.7.g.h.127.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.7.b.a.3.1	✓	2	5.3	odd	4
4.7.b.a.3.2	yes	2	20.3	even	4
36.7.d.c.19.1		2	60.23	odd	4
36.7.d.c.19.2		2	15.8	even	4
64.7.c.c.63.1		2	40.13	odd	4
64.7.c.c.63.2		2	40.3	even	4
100.7.b.c.51.1		2	20.7	even	4
100.7.b.c.51.2		2	5.2	odd	4
100.7.d.a.99.1		4	5.4	even	2	inner
100.7.d.a.99.2		4	4.3	odd	2	inner
100.7.d.a.99.3		4	20.19	odd	2	inner
100.7.d.a.99.4		4	1.1	even	1	trivial
256.7.d.f.127.1		4	80.13	odd	4
256.7.d.f.127.2		4	80.43	even	4
256.7.d.f.127.3		4	80.3	even	4
256.7.d.f.127.4		4	80.53	odd	4
576.7.g.h.127.1		2	120.53	even	4
576.7.g.h.127.2		2	120.83	odd	4

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	100.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(7.74597 + 2.00000i) q^{2} +30.9839 q^{3} +(56.0000 + 30.9839i) q^{4} +(240.000 + 61.9677i) q^{6} +309.839 q^{7} +(371.806 + 352.000i) q^{8} +231.000 q^{9} +O(q^{10})\)	\(q+(7.74597 + 2.00000i) q^{2} +30.9839 q^{3} +(56.0000 + 30.9839i) q^{4} +(240.000 + 61.9677i) q^{6} +309.839 q^{7} +(371.806 + 352.000i) q^{8} +231.000 q^{9} +960.500i q^{11} +(1735.10 + 960.000i) q^{12} -1466.00i q^{13} +(2400.00 + 619.677i) q^{14} +(2176.00 + 3470.19i) q^{16} -4766.00i q^{17} +(1789.32 + 462.000i) q^{18} +7529.08i q^{19} +9600.00 q^{21} +(-1921.00 + 7440.00i) q^{22} +10472.5 q^{23} +(11520.0 + 10906.3i) q^{24} +(2932.00 - 11355.6i) q^{26} -15430.0 q^{27} +(17351.0 + 9600.00i) q^{28} -25498.0 q^{29} -41890.2i q^{31} +(9914.84 + 31232.0i) q^{32} +29760.0i q^{33} +(9532.00 - 36917.3i) q^{34} +(12936.0 + 7157.27i) q^{36} +1994.00i q^{37} +(-15058.2 + 58320.0i) q^{38} -45422.3i q^{39} +29362.0 q^{41} +(74361.3 + 19200.0i) q^{42} +21533.8 q^{43} +(-29760.0 + 53788.0i) q^{44} +(81120.0 + 20945.1i) q^{46} -7560.06 q^{47} +(67420.9 + 107520. i) q^{48} -21649.0 q^{49} -147669. i q^{51} +(45422.3 - 82096.0i) q^{52} +192854. i q^{53} +(-119520. - 30859.9i) q^{54} +(115200. + 109063. i) q^{56} +233280. i q^{57} +(-197507. - 50996.0i) q^{58} -78420.2i q^{59} -10918.0 q^{61} +(83780.4 - 324480. i) q^{62} +71572.7 q^{63} +(14336.0 + 261752. i) q^{64} +(-59520.0 + 230520. i) q^{66} -394146. q^{67} +(147669. - 266896. i) q^{68} +324480. q^{69} -532241. i q^{71} +(85887.3 + 81312.0i) q^{72} -288626. i q^{73} +(-3988.00 + 15445.5i) q^{74} +(-233280. + 421628. i) q^{76} +297600. i q^{77} +(90844.7 - 351840. i) q^{78} -310706. i q^{79} -646479. q^{81} +(227437. + 58724.0i) q^{82} +204153. q^{83} +(537600. + 297445. i) q^{84} +(166800. + 43067.6i) q^{86} -790027. q^{87} +(-338096. + 357120. i) q^{88} -310738. q^{89} -454223. i q^{91} +(586463. + 324480. i) q^{92} -1.29792e6i q^{93} +(-58560.0 - 15120.1i) q^{94} +(307200. + 967688. i) q^{96} -1.45709e6i q^{97} +(-167692. - 43298.0i) q^{98} +221875. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 224 q^{4} + 960 q^{6} + 924 q^{9}+O(q^{10}) \) 4 * q + 224 * q^4 + 960 * q^6 + 924 * q^9	\( 4 q + 224 q^{4} + 960 q^{6} + 924 q^{9} + 9600 q^{14} + 8704 q^{16} + 38400 q^{21} + 46080 q^{24} + 11728 q^{26} - 101992 q^{29} + 38128 q^{34} + 51744 q^{36} + 117448 q^{41} - 119040 q^{44} + 324480 q^{46} - 86596 q^{49} - 478080 q^{54} + 460800 q^{56} - 43672 q^{61} + 57344 q^{64} - 238080 q^{66} + 1297920 q^{69} - 15952 q^{74} - 933120 q^{76} - 2585916 q^{81} + 2150400 q^{84} + 667200 q^{86} - 1242952 q^{89} - 234240 q^{94} + 1228800 q^{96}+O(q^{100}) \) 4 * q + 224 * q^4 + 960 * q^6 + 924 * q^9 + 9600 * q^14 + 8704 * q^16 + 38400 * q^21 + 46080 * q^24 + 11728 * q^26 - 101992 * q^29 + 38128 * q^34 + 51744 * q^36 + 117448 * q^41 - 119040 * q^44 + 324480 * q^46 - 86596 * q^49 - 478080 * q^54 + 460800 * q^56 - 43672 * q^61 + 57344 * q^64 - 238080 * q^66 + 1297920 * q^69 - 15952 * q^74 - 933120 * q^76 - 2585916 * q^81 + 2150400 * q^84 + 667200 * q^86 - 1242952 * q^89 - 234240 * q^94 + 1228800 * q^96

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