LMFDB - Embedded newform 354.7.d.a.235.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,7,Mod(235,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("354.235");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	354.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:	$81.4391456014$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			235.17
Character	$\chi$	$=$	354.235
Dual form			354.7.d.a.235.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.65685i q^{2} +15.5885 q^{3} -32.0000 q^{4} -16.5609 q^{5} -88.1816i q^{6} +303.476 q^{7} +181.019i q^{8} +243.000 q^{9} +O(q^{10})$	\(q-5.65685i q^{2} +15.5885 q^{3} -32.0000 q^{4} -16.5609 q^{5} -88.1816i q^{6} +303.476 q^{7} +181.019i q^{8} +243.000 q^{9} +93.6824i q^{10} +1270.52i q^{11} -498.831 q^{12} -254.528i q^{13} -1716.72i q^{14} -258.158 q^{15} +1024.00 q^{16} +2446.12 q^{17} -1374.62i q^{18} -1529.68 q^{19} +529.948 q^{20} +4730.72 q^{21} +7187.14 q^{22} +5763.23i q^{23} +2821.81i q^{24} -15350.7 q^{25} -1439.83 q^{26} +3788.00 q^{27} -9711.23 q^{28} +5933.62 q^{29} +1460.36i q^{30} +49160.9i q^{31} -5792.62i q^{32} +19805.4i q^{33} -13837.4i q^{34} -5025.82 q^{35} -7776.00 q^{36} -28763.3i q^{37} +8653.17i q^{38} -3967.70i q^{39} -2997.84i q^{40} -110854. q^{41} -26761.0i q^{42} +99580.5i q^{43} -40656.6i q^{44} -4024.29 q^{45} +32601.7 q^{46} -107078. i q^{47} +15962.6 q^{48} -25551.4 q^{49} +86836.9i q^{50} +38131.3 q^{51} +8144.89i q^{52} +52704.6 q^{53} -21428.1i q^{54} -21040.9i q^{55} +54935.0i q^{56} -23845.3 q^{57} -33565.6i q^{58} +(136415. + 153530. i) q^{59} +8261.07 q^{60} +168873. i q^{61} +278096. q^{62} +73744.6 q^{63} -32768.0 q^{64} +4215.20i q^{65} +112036. q^{66} +107071. i q^{67} -78276.0 q^{68} +89839.8i q^{69} +28430.4i q^{70} -388354. q^{71} +43987.7i q^{72} +448694. i q^{73} -162710. q^{74} -239294. q^{75} +48949.7 q^{76} +385572. i q^{77} -22444.7 q^{78} +889491. q^{79} -16958.3 q^{80} +59049.0 q^{81} +627085. i q^{82} +610324. i q^{83} -151383. q^{84} -40509.9 q^{85} +563312. q^{86} +92495.9 q^{87} -229988. q^{88} -402623. i q^{89} +22764.8i q^{90} -77243.1i q^{91} -184423. i q^{92} +766342. i q^{93} -605724. q^{94} +25332.8 q^{95} -90298.0i q^{96} -1.49863e6i q^{97} +144540. i q^{98} +308736. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 1920 q^{4} + 408 q^{7} + 14580 q^{9}+O(q^{10}) $ 60 * q - 1920 * q^4 + 408 * q^7 + 14580 * q^9	$ 60 q - 1920 q^{4} + 408 q^{7} + 14580 q^{9} + 4536 q^{15} + 61440 q^{16} - 15840 q^{17} - 5616 q^{19} - 17472 q^{22} + 226260 q^{25} - 34048 q^{26} - 13056 q^{28} - 75392 q^{29} + 278000 q^{35} - 466560 q^{36} + 67376 q^{41} + 209856 q^{46} + 269100 q^{49} - 206064 q^{51} + 490000 q^{53} - 373248 q^{57} - 863472 q^{59} - 145152 q^{60} - 155072 q^{62} + 99144 q^{63} - 1966080 q^{64} - 404352 q^{66} + 506880 q^{68} - 2041856 q^{71} - 2146176 q^{74} + 808704 q^{75} + 179712 q^{76} + 228096 q^{78} + 670248 q^{79} + 3542940 q^{81} + 873408 q^{85} + 1832576 q^{86} - 2568024 q^{87} + 559104 q^{88} + 1049472 q^{94} - 245856 q^{95}+O(q^{100}) $ 60 * q - 1920 * q^4 + 408 * q^7 + 14580 * q^9 + 4536 * q^15 + 61440 * q^16 - 15840 * q^17 - 5616 * q^19 - 17472 * q^22 + 226260 * q^25 - 34048 * q^26 - 13056 * q^28 - 75392 * q^29 + 278000 * q^35 - 466560 * q^36 + 67376 * q^41 + 209856 * q^46 + 269100 * q^49 - 206064 * q^51 + 490000 * q^53 - 373248 * q^57 - 863472 * q^59 - 145152 * q^60 - 155072 * q^62 + 99144 * q^63 - 1966080 * q^64 - 404352 * q^66 + 506880 * q^68 - 2041856 * q^71 - 2146176 * q^74 + 808704 * q^75 + 179712 * q^76 + 228096 * q^78 + 670248 * q^79 + 3542940 * q^81 + 873408 * q^85 + 1832576 * q^86 - 2568024 * q^87 + 559104 * q^88 + 1049472 * q^94 - 245856 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	5.65685i		−	0.707107i
$2$		−	5.65685i		−	0.707107i
$3$	15.5885			0.577350
$3$	15.5885			0.577350
$4$	−32.0000			−0.500000
$5$	−16.5609			−0.132487			−0.0662435	−	0.997803i	$-0.521101\pi$
$5$	−16.5609			−0.132487			−0.0662435	+	0.997803i	$0.521101\pi$
$6$		−	88.1816i		−	0.408248i
$7$	303.476			0.884769			0.442385	−	0.896825i	$-0.354133\pi$
$7$	303.476			0.884769			0.442385	+	0.896825i	$0.354133\pi$
$8$			181.019i			0.353553i
$9$	243.000			0.333333
$10$			93.6824i			0.0936824i
$11$			1270.52i			0.954559i	0.878751	+	0.477280i	$0.158377\pi$
$11$			1270.52i			0.954559i	−0.878751	+	0.477280i	$0.841623\pi$
$12$	−498.831			−0.288675
$13$		−	254.528i		−	0.115852i	−0.998321	−	0.0579262i	$-0.981551\pi$
$13$		−	254.528i		−	0.115852i	0.998321	−	0.0579262i	$-0.0184488\pi$
$14$		−	1716.72i		−	0.625626i
$15$	−258.158			−0.0764914
$16$	1024.00			0.250000
$17$	2446.12			0.497888			0.248944	−	0.968518i	$-0.419916\pi$
$17$	2446.12			0.497888			0.248944	+	0.968518i	$0.419916\pi$
$18$		−	1374.62i		−	0.235702i
$19$	−1529.68			−0.223018			−0.111509	−	0.993763i	$-0.535568\pi$
$19$	−1529.68			−0.223018			−0.111509	+	0.993763i	$0.535568\pi$
$20$	529.948			0.0662435
$21$	4730.72			0.510822
$22$	7187.14			0.674975
$23$			5763.23i			0.473677i	0.971549	+	0.236838i	$0.0761112\pi$
$23$			5763.23i			0.473677i	−0.971549	+	0.236838i	$0.923889\pi$
$24$			2821.81i			0.204124i
$25$	−15350.7			−0.982447
$26$	−1439.83			−0.0819201
$27$	3788.00			0.192450
$28$	−9711.23			−0.442385
$29$	5933.62			0.243291			0.121645	−	0.992574i	$-0.461183\pi$
$29$	5933.62			0.243291			0.121645	+	0.992574i	$0.461183\pi$
$30$			1460.36i			0.0540876i
$31$			49160.9i			1.65019i	0.564992	+	0.825096i	$0.308879\pi$
$31$			49160.9i			1.65019i	−0.564992	+	0.825096i	$0.691121\pi$
$32$		−	5792.62i		−	0.176777i
$33$			19805.4i			0.551115i
$34$		−	13837.4i		−	0.352060i
$35$	−5025.82			−0.117220
$36$	−7776.00			−0.166667
$37$		−	28763.3i		−	0.567850i	−0.958846	−	0.283925i	$-0.908363\pi$
$37$		−	28763.3i		−	0.567850i	0.958846	−	0.283925i	$-0.0916367\pi$
$38$			8653.17i			0.157697i
$39$		−	3967.70i		−	0.0668875i
$40$		−	2997.84i		−	0.0468412i
$41$	−110854.			−1.60842			−0.804211	−	0.594344i	$-0.797412\pi$
$41$	−110854.			−1.60842			−0.804211	+	0.594344i	$0.797412\pi$
$42$		−	26761.0i		−	0.361206i
$43$			99580.5i			1.25247i	0.779632	+	0.626237i	$0.215406\pi$
$43$			99580.5i			1.25247i	−0.779632	+	0.626237i	$0.784594\pi$
$44$		−	40656.6i		−	0.477280i
$45$	−4024.29			−0.0441623
$46$	32601.7			0.334940
$47$		−	107078.i		−	1.03135i	−0.856784	−	0.515675i	$-0.827541\pi$
$47$		−	107078.i		−	1.03135i	0.856784	−	0.515675i	$-0.172459\pi$
$48$	15962.6			0.144338
$49$	−25551.4			−0.217183
$50$			86836.9i			0.694695i
$51$	38131.3			0.287456
$52$			8144.89i			0.0579262i
$53$	52704.6			0.354014			0.177007	−	0.984210i	$-0.443358\pi$
$53$	52704.6			0.354014			0.177007	+	0.984210i	$0.443358\pi$
$54$		−	21428.1i		−	0.136083i
$55$		−	21040.9i		−	0.126467i
$56$			54935.0i			0.312813i
$57$	−23845.3			−0.128759
$58$		−	33565.6i		−	0.172033i
$59$	136415.	+	153530.i	0.664211	+	0.747545i
$59$	136415.	+	153530.i	0.664211	+	0.747545i
$60$	8261.07			0.0382457
$61$			168873.i			0.743998i	0.928233	+	0.371999i	$0.121327\pi$
$61$			168873.i			0.743998i	−0.928233	+	0.371999i	$0.878673\pi$
$62$	278096.			1.16686
$63$	73744.6			0.294923
$64$	−32768.0			−0.125000
$65$			4215.20i			0.0153489i
$66$	112036.			0.389697
$67$			107071.i			0.355997i	0.984031	+	0.177998i	$0.0569622\pi$
$67$			107071.i			0.355997i	−0.984031	+	0.177998i	$0.943038\pi$
$68$	−78276.0			−0.248944
$69$			89839.8i			0.273478i
$70$			28430.4i			0.0828873i
$71$	−388354.			−1.08506			−0.542529	−	0.840037i	$-0.682533\pi$
$71$	−388354.			−1.08506			−0.542529	+	0.840037i	$0.682533\pi$
$72$			43987.7i			0.117851i
$73$			448694.i			1.15341i	0.816954	+	0.576703i	$0.195661\pi$
$73$			448694.i			1.15341i	−0.816954	+	0.576703i	$0.804339\pi$
$74$	−162710.			−0.401531
$75$	−239294.			−0.567216
$76$	48949.7			0.111509
$77$			385572.i			0.844565i
$78$	−22444.7			−0.0472966
$79$	889491.			1.80410			0.902049	−	0.431634i	$-0.142063\pi$
$79$	889491.			1.80410			0.902049	+	0.431634i	$0.142063\pi$
$80$	−16958.3			−0.0331217
$81$	59049.0			0.111111
$82$			627085.i			1.13733i
$83$			610324.i			1.06740i	0.845675	+	0.533699i	$0.179198\pi$
$83$			610324.i			1.06740i	−0.845675	+	0.533699i	$0.820802\pi$
$84$	−151383.			−0.255411
$85$	−40509.9			−0.0659637
$86$	563312.			0.885633
$87$	92495.9			0.140464
$88$	−229988.			−0.337488
$89$		−	402623.i		−	0.571122i	−0.958361	−	0.285561i	$-0.907820\pi$
$89$		−	402623.i		−	0.571122i	0.958361	−	0.285561i	$-0.0921800\pi$
$90$			22764.8i			0.0312275i
$91$		−	77243.1i		−	0.102503i
$92$		−	184423.i		−	0.236838i
$93$			766342.i			0.952739i
$94$	−605724.			−0.729275
$95$	25332.8			0.0295470
$96$		−	90298.0i		−	0.102062i
$97$		−	1.49863e6i		−	1.64202i	−0.570911	−	0.821012i	$-0.693410\pi$
$97$		−	1.49863e6i		−	1.64202i	0.570911	−	0.821012i	$-0.306590\pi$
$98$			144540.i			0.153572i
$99$			308736.i			0.318186i
$100$	491224.			0.491224
$101$			939089.i			0.911471i	0.890115	+	0.455735i	$0.150624\pi$
$101$			939089.i			0.911471i	−0.890115	+	0.455735i	$0.849376\pi$
$102$		−	215703.i		−	0.203262i
$103$			1.53844e6i			1.40789i	0.710255	+	0.703944i	$0.248580\pi$
$103$			1.53844e6i			1.40789i	−0.710255	+	0.703944i	$0.751420\pi$
$104$	46074.5			0.0409600
$105$	−78344.9			−0.0676772
$106$		−	298142.i		−	0.250326i
$107$	−653308.			−0.533294			−0.266647	−	0.963794i	$-0.585916\pi$
$107$	−653308.			−0.533294			−0.266647	+	0.963794i	$0.585916\pi$
$108$	−121216.			−0.0962250
$109$		−	1.09097e6i		−	0.842428i	−0.906961	−	0.421214i	$-0.861604\pi$
$109$		−	1.09097e6i		−	0.842428i	0.906961	−	0.421214i	$-0.138396\pi$
$110$	−119025.			−0.0894254
$111$		−	448376.i		−	0.327849i
$112$	310759.			0.221192
$113$			1.09148e6i			0.756450i	0.925714	+	0.378225i	$0.123465\pi$
$113$			1.09148e6i			0.756450i	−0.925714	+	0.378225i	$0.876535\pi$
$114$			134890.i			0.0910467i
$115$		−	95444.1i		−	0.0627560i
$116$	−189876.			−0.121645
$117$		−	61850.3i		−	0.0386175i
$118$	868498.	−	771679.i	0.528594	−	0.469668i
$119$	742340.			0.440516
$120$		−	46731.7i		−	0.0270438i
$121$	157344.			0.0888167
$122$	955292.			0.526086
$123$	−1.72804e6			−0.928623
$124$		−	1.57315e6i		−	0.825096i
$125$	512985.			0.262648
$126$		−	417163.i		−	0.208542i
$127$	3.37863e6			1.64942			0.824708	−	0.565559i	$-0.191340\pi$
$127$	3.37863e6			1.64942			0.824708	+	0.565559i	$0.191340\pi$
$128$			185364.i			0.0883883i
$129$			1.55231e6i			0.723117i
$130$	23844.8			0.0108533
$131$			3.19893e6i			1.42296i	0.702709	+	0.711478i	$0.251974\pi$
$131$			3.19893e6i			1.42296i	−0.702709	+	0.711478i	$0.748026\pi$
$132$		−	633773.i		−	0.275558i
$133$	−464221.			−0.197319
$134$	605683.			0.251728
$135$	−62732.5			−0.0254971
$136$			442796.i			0.176030i
$137$	938199.			0.364866			0.182433	−	0.983218i	$-0.441603\pi$
$137$	938199.			0.364866			0.182433	+	0.983218i	$0.441603\pi$
$138$	508211.			0.193378
$139$	−2.42404e6			−0.902601			−0.451301	−	0.892372i	$-0.649040\pi$
$139$	−2.42404e6			−0.902601			−0.451301	+	0.892372i	$0.649040\pi$
$140$	160826.			0.0586102
$141$		−	1.66918e6i		−	0.595451i
$142$			2.19686e6i			0.767252i
$143$	323382.			0.110588
$144$	248832.			0.0833333
$145$	−98265.9			−0.0322329
$146$	2.53820e6			0.815581
$147$	−398307.			−0.125391
$148$			920426.i			0.283925i
$149$		−	1.60775e6i		−	0.486026i	−0.970023	−	0.243013i	$-0.921864\pi$
$149$		−	1.60775e6i		−	0.486026i	0.970023	−	0.243013i	$-0.0781357\pi$
$150$			1.35365e6i			0.401082i
$151$			3.79859e6i			1.10330i	0.834077	+	0.551648i	$0.186001\pi$
$151$			3.79859e6i			1.10330i	−0.834077	+	0.551648i	$0.813999\pi$
$152$		−	276902.i		−	0.0788487i
$153$	594408.			0.165963
$154$	2.18112e6			0.597197
$155$		−	814147.i		−	0.218629i
$156$			126966.i			0.0334437i
$157$		−	2.52351e6i		−	0.652087i	−0.945355	−	0.326044i	$-0.894284\pi$
$157$		−	2.52351e6i		−	0.652087i	0.945355	−	0.326044i	$-0.105716\pi$
$158$		−	5.03172e6i		−	1.27569i
$159$	821583.			0.204390
$160$			95930.8i			0.0234206i
$161$			1.74900e6i			0.419095i
$162$		−	334032.i		−	0.0785674i
$163$	4.31015e6			0.995245			0.497623	−	0.867394i	$-0.334206\pi$
$163$	4.31015e6			0.995245			0.497623	+	0.867394i	$0.334206\pi$
$164$	3.54733e6			0.804211
$165$		−	327995.i		−	0.0730156i
$166$	3.45251e6			0.754764
$167$	6.33519e6			1.36022			0.680112	−	0.733109i	$-0.261931\pi$
$167$	6.33519e6			1.36022			0.680112	+	0.733109i	$0.261931\pi$
$168$			856352.i			0.180603i
$169$	4.76202e6			0.986578
$170$			229159.i			0.0466434i
$171$	−371712.			−0.0743393
$172$		−	3.18658e6i		−	0.626237i
$173$			3.23939e6i			0.625640i	0.949812	+	0.312820i	$0.101274\pi$
$173$			3.23939e6i			0.625640i	−0.949812	+	0.312820i	$0.898726\pi$
$174$		−	523236.i		−	0.0993230i
$175$	−4.65858e6			−0.869239
$176$			1.30101e6i			0.238640i
$177$	2.12650e6	+	2.39330e6i	0.383482	+	0.431596i
$178$	−2.27758e6			−0.403844
$179$			1.11451e7i			1.94323i	0.236573	+	0.971614i	$0.423976\pi$
$179$			1.11451e7i			1.94323i	−0.236573	+	0.971614i	$0.576024\pi$
$180$	128777.			0.0220812
$181$	1.09849e7			1.85252			0.926259	−	0.376889i	$-0.123006\pi$
$181$	1.09849e7			1.85252			0.926259	+	0.376889i	$0.123006\pi$
$182$	−436953.			−0.0724804
$183$			2.63247e6i			0.429547i
$184$	−1.04326e6			−0.167470
$185$			476346.i			0.0752328i
$186$	4.33509e6			0.673688
$187$			3.10784e6i			0.475264i
$188$			3.42649e6i			0.515675i
$189$	1.14957e6			0.170274
$190$		−	143304.i		−	0.0208929i
$191$		−	2.95275e6i		−	0.423767i	−0.977295	−	0.211883i	$-0.932040\pi$
$191$		−	2.95275e6i		−	0.423767i	0.977295	−	0.211883i	$-0.0679597\pi$
$192$	−510803.			−0.0721688
$193$	1.12025e7			1.55827			0.779136	−	0.626854i	$-0.215658\pi$
$193$	1.12025e7			1.55827			0.779136	+	0.626854i	$0.215658\pi$
$194$	−8.47754e6			−1.16109
$195$			65708.5i			0.00886172i
$196$	817644.			0.108592
$197$	−1.04191e7			−1.36279			−0.681397	−	0.731914i	$-0.738627\pi$
$197$	−1.04191e7			−1.36279			−0.681397	+	0.731914i	$0.738627\pi$
$198$	1.74647e6			0.224992
$199$	−1.50745e7			−1.91286			−0.956430	−	0.291960i	$-0.905692\pi$
$199$	−1.50745e7			−1.91286			−0.956430	+	0.291960i	$0.905692\pi$
$200$		−	2.77878e6i		−	0.347348i
$201$			1.66907e6i			0.205535i
$202$	5.31229e6			0.644507
$203$	1.80071e6			0.215256
$204$	−1.22020e6			−0.143728
$205$	1.83584e6			0.213095
$206$	8.70272e6			0.995528
$207$			1.40046e6i			0.157892i
$208$		−	260637.i		−	0.0289631i
$209$		−	1.94349e6i		−	0.212884i
$210$			443185.i			0.0478550i
$211$		−	1.17931e7i		−	1.25540i	−0.778456	−	0.627700i	$-0.783997\pi$
$211$		−	1.17931e7i		−	1.25540i	0.778456	−	0.627700i	$-0.216003\pi$
$212$	−1.68655e6			−0.177007
$213$	−6.05384e6			−0.626459
$214$			3.69567e6i			0.377096i
$215$		−	1.64914e6i		−	0.165937i
$216$			685700.i			0.0680414i
$217$			1.49191e7i			1.46004i
$218$	−6.17145e6			−0.595687
$219$			6.99445e6i			0.665919i
$220$			673308.i			0.0632333i
$221$		−	622607.i		−	0.0576816i
$222$	−2.53640e6			−0.231824
$223$	1.10370e7			0.995258			0.497629	−	0.867390i	$-0.334204\pi$
$223$	1.10370e7			0.995258			0.497629	+	0.867390i	$0.334204\pi$
$224$		−	1.75792e6i		−	0.156407i
$225$	−3.73023e6			−0.327482
$226$	6.17434e6			0.534891
$227$			199181.i			0.0170282i	0.999964	+	0.00851412i	$0.00271016\pi$
$227$			199181.i			0.0170282i	−0.999964	+	0.00851412i	$0.997290\pi$
$228$	763051.			0.0643797
$229$		−	8.23982e6i		−	0.686137i	−0.939310	−	0.343069i	$-0.888534\pi$
$229$		−	8.23982e6i		−	0.686137i	0.939310	−	0.343069i	$-0.111466\pi$
$230$	−539913.			−0.0443752
$231$			6.01047e6i			0.487610i
$232$			1.07410e6i			0.0860163i
$233$		−	1.18013e7i		−	0.932960i	−0.884532	−	0.466480i	$-0.845522\pi$
$233$		−	1.18013e7i		−	0.932960i	0.884532	−	0.466480i	$-0.154478\pi$
$234$	−349878.			−0.0273067
$235$			1.77330e6i			0.136641i
$236$	−4.36528e6	−	4.91296e6i	−0.332105	−	0.373773i
$237$	1.38658e7			1.04160
$238$		−	4.19931e6i		−	0.311492i
$239$	1.26503e6			0.0926634			0.0463317	−	0.998926i	$-0.485247\pi$
$239$	1.26503e6			0.0926634			0.0463317	+	0.998926i	$0.485247\pi$
$240$	−264354.			−0.0191228
$241$	4.68733e6			0.334869			0.167434	−	0.985883i	$-0.446452\pi$
$241$	4.68733e6			0.334869			0.167434	+	0.985883i	$0.446452\pi$
$242$		−	890073.i		−	0.0628029i
$243$	920483.			0.0641500
$244$		−	5.40395e6i		−	0.371999i
$245$	423153.			0.0287739
$246$			9.77529e6i			0.656636i
$247$			389346.i			0.0258372i
$248$	−8.89907e6			−0.583431
$249$			9.51401e6i			0.616262i
$250$		−	2.90188e6i		−	0.185720i
$251$	−2.30745e7			−1.45919			−0.729595	−	0.683879i	$-0.760292\pi$
$251$	−2.30745e7			−1.45919			−0.729595	+	0.683879i	$0.760292\pi$
$252$	−2.35983e6			−0.147462
$253$	−7.32229e6			−0.452153
$254$		−	1.91124e7i		−	1.16631i
$255$	−631487.			−0.0380841
$256$	1.04858e6			0.0625000
$257$	−1.19294e7			−0.702778			−0.351389	−	0.936230i	$-0.614291\pi$
$257$	−1.19294e7			−0.702778			−0.351389	+	0.936230i	$0.614291\pi$
$258$	8.78117e6			0.511321
$259$		−	8.72898e6i		−	0.502417i
$260$		−	134887.i		−	0.00767447i
$261$	1.44187e6			0.0810969
$262$	1.80959e7			1.00618
$263$	−2.96762e7			−1.63133			−0.815664	−	0.578526i	$-0.803628\pi$
$263$	−2.96762e7			−1.63133			−0.815664	+	0.578526i	$0.803628\pi$
$264$	−3.58516e6			−0.194849
$265$	−872833.			−0.0469022
$266$			2.62603e6i			0.139526i
$267$		−	6.27628e6i		−	0.329738i
$268$		−	3.42626e6i		−	0.177998i
$269$		−	2.49719e6i		−	0.128290i	−0.997941	−	0.0641452i	$-0.979568\pi$
$269$		−	2.49719e6i		−	0.128290i	0.997941	−	0.0641452i	$-0.0204321\pi$
$270$			354869.i			0.0180292i
$271$	5.90215e6			0.296553			0.148276	−	0.988946i	$-0.452627\pi$
$271$	5.90215e6			0.296553			0.148276	+	0.988946i	$0.452627\pi$
$272$	2.50483e6			0.124472
$273$		−	1.20410e6i		−	0.0591800i
$274$		−	5.30725e6i		−	0.257999i
$275$		−	1.95034e7i		−	0.937804i
$276$		−	2.87487e6i		−	0.136739i
$277$	−3.67923e6			−0.173108			−0.0865541	−	0.996247i	$-0.527586\pi$
$277$	−3.67923e6			−0.173108			−0.0865541	+	0.996247i	$0.527586\pi$
$278$			1.37125e7i			0.638236i
$279$			1.19461e7i			0.550064i
$280$		−	909771.i		−	0.0414437i
$281$	−3.75734e7			−1.69341			−0.846704	−	0.532065i	$-0.821416\pi$
$281$	−3.75734e7			−1.69341			−0.846704	+	0.532065i	$0.821416\pi$
$282$	−9.44231e6			−0.421047
$283$			3.10484e7i			1.36987i	0.728604	+	0.684935i	$0.240169\pi$
$283$			3.10484e7i			1.36987i	−0.728604	+	0.684935i	$0.759831\pi$
$284$	1.24273e7			0.542529
$285$	394900.			0.0170589
$286$		−	1.82933e6i		−	0.0781976i
$287$	−3.36415e7			−1.42308
$288$		−	1.40761e6i		−	0.0589256i
$289$	−1.81540e7			−0.752108
$290$			555876.i			0.0227921i
$291$		−	2.33613e7i		−	0.948023i
$292$		−	1.43582e7i		−	0.576703i
$293$	−3.13992e7			−1.24829			−0.624146	−	0.781308i	$-0.714553\pi$
$293$	−3.13992e7			−1.24829			−0.624146	+	0.781308i	$0.714553\pi$
$294$			2.25316e6i			0.0886647i
$295$	−2.25915e6	−	2.54259e6i	−0.0879993	−	0.0990400i
$296$	5.20672e6			0.200765
$297$			4.81272e6i			0.183705i
$298$	−9.09480e6			−0.343672
$299$	1.46690e6			0.0548767
$300$	7.65742e6			0.283608
$301$			3.02203e7i			1.10815i
$302$	2.14881e7			0.780148
$303$			1.46390e7i			0.526238i
$304$	−1.56639e6			−0.0557545
$305$		−	2.79669e6i		−	0.0985700i
$306$		−	3.36248e6i		−	0.117353i
$307$	−3.36534e7			−1.16309			−0.581546	−	0.813513i	$-0.697552\pi$
$307$	−3.36534e7			−1.16309			−0.581546	+	0.813513i	$0.697552\pi$
$308$		−	1.23383e7i		−	0.422282i
$309$			2.39819e7i			0.812845i
$310$	−4.60551e6			−0.154594
$311$	−3.45011e6			−0.114697			−0.0573484	−	0.998354i	$-0.518265\pi$
$311$	−3.45011e6			−0.114697			−0.0573484	+	0.998354i	$0.518265\pi$
$312$	718230.			0.0236483
$313$			4.37174e6i			0.142568i	0.997456	+	0.0712838i	$0.0227096\pi$
$313$			4.37174e6i			0.142568i	−0.997456	+	0.0712838i	$0.977290\pi$
$314$	−1.42751e7			−0.461095
$315$	−1.22128e6			−0.0390735
$316$	−2.84637e7			−0.902049
$317$	4.33359e7			1.36041			0.680205	−	0.733022i	$-0.261891\pi$
$317$	4.33359e7			1.36041			0.680205	+	0.733022i	$0.261891\pi$
$318$		−	4.64757e6i		−	0.144526i
$319$			7.53877e6i			0.232235i
$320$	542667.			0.0165609
$321$	−1.01841e7			−0.307897
$322$	9.89384e6			0.296345
$323$	−3.74178e6			−0.111038
$324$	−1.88957e6			−0.0555556
$325$			3.90719e6i			0.113819i
$326$		−	2.43819e7i		−	0.703745i
$327$		−	1.70065e7i		−	0.486376i
$328$		−	2.00667e7i		−	0.568663i
$329$		−	3.24956e7i		−	0.912507i
$330$	−1.85542e6			−0.0516298
$331$	2.79905e6			0.0771838			0.0385919	−	0.999255i	$-0.487713\pi$
$331$	2.79905e6			0.0771838			0.0385919	+	0.999255i	$0.487713\pi$
$332$		−	1.95304e7i		−	0.533699i
$333$		−	6.98949e6i		−	0.189283i
$334$		−	3.58372e7i		−	0.961823i
$335$		−	1.77318e6i		−	0.0471649i
$336$	4.84426e6			0.127705
$337$		−	5.64401e7i		−	1.47468i	−0.675521	−	0.737341i	$-0.736081\pi$
$337$		−	5.64401e7i		−	1.47468i	0.675521	−	0.737341i	$-0.263919\pi$
$338$		−	2.69381e7i		−	0.697616i
$339$			1.70145e7i			0.436737i
$340$	1.29632e6			0.0329818
$341$	−6.24598e7			−1.57521
$342$			2.10272e6i			0.0525658i
$343$	−4.34579e7			−1.07693
$344$	−1.80260e7			−0.442817
$345$		−	1.48783e6i		−	0.0362322i
$346$	1.83247e7			0.442394
$347$			4.53238e7i			1.08477i	0.840130	+	0.542385i	$0.182478\pi$
$347$			4.53238e7i			1.08477i	−0.840130	+	0.542385i	$0.817522\pi$
$348$	−2.95987e6			−0.0702320
$349$			1.67993e7i			0.395199i	0.980283	+	0.197599i	$0.0633145\pi$
$349$			1.67993e7i			0.395199i	−0.980283	+	0.197599i	$0.936686\pi$
$350$			2.63529e7i			0.614645i
$351$		−	964151.i		−	0.0222958i
$352$	7.35963e6			0.168744
$353$		−	1.75640e7i		−	0.399301i	−0.979867	−	0.199650i	$-0.936019\pi$
$353$		−	1.75640e7i		−	0.399301i	0.979867	−	0.199650i	$-0.0639806\pi$
$354$	1.35385e7	−	1.20293e7i	0.305184	−	0.271163i
$355$	6.43148e6			0.143756
$356$			1.28840e7i			0.285561i
$357$	1.15719e7			0.254332
$358$	6.30460e7			1.37407
$359$	−2.23505e7			−0.483064			−0.241532	−	0.970393i	$-0.577650\pi$
$359$	−2.23505e7			−0.483064			−0.241532	+	0.970393i	$0.577650\pi$
$360$		−	728475.i		−	0.0156137i
$361$	−4.47060e7			−0.950263
$362$		−	6.21402e7i		−	1.30993i
$363$	2.45275e6			0.0512783
$364$			2.47178e6i			0.0512514i
$365$		−	7.43077e6i		−	0.152811i
$366$	1.48915e7			0.303736
$367$			2.76276e7i			0.558914i	0.960158	+	0.279457i	$0.0901544\pi$
$367$			2.76276e7i			0.558914i	−0.960158	+	0.279457i	$0.909846\pi$
$368$			5.90155e6i			0.118419i
$369$	−2.69375e7			−0.536141
$370$	2.69462e6			0.0531976
$371$	1.59946e7			0.313221
$372$		−	2.45230e7i		−	0.476370i
$373$	8.06850e7			1.55477			0.777385	−	0.629025i	$-0.216546\pi$
$373$	8.06850e7			1.55477			0.777385	+	0.629025i	$0.216546\pi$
$374$	1.75806e7			0.336062
$375$	7.99665e6			0.151640
$376$	1.93832e7			0.364638
$377$		−	1.51027e6i		−	0.0281858i
$378$		−	6.50292e6i		−	0.120402i
$379$	4.73157e7			0.869135			0.434568	−	0.900639i	$-0.356901\pi$
$379$	4.73157e7			0.869135			0.434568	+	0.900639i	$0.356901\pi$
$380$	−810650.			−0.0147735
$381$	5.26677e7			0.952290
$382$	−1.67033e7			−0.299648
$383$	−1.95412e7			−0.347820			−0.173910	−	0.984762i	$-0.555640\pi$
$383$	−1.95412e7			−0.347820			−0.173910	+	0.984762i	$0.555640\pi$
$384$			2.88954e6i			0.0510310i
$385$		−	6.38540e6i		−	0.111894i
$386$		−	6.33710e7i		−	1.10187i
$387$			2.41981e7i			0.417492i
$388$			4.79562e7i			0.821012i
$389$	−3.60095e7			−0.611742			−0.305871	−	0.952073i	$-0.598948\pi$
$389$	−3.60095e7			−0.611742			−0.305871	+	0.952073i	$0.598948\pi$
$390$	371704.			0.00626618
$391$			1.40976e7i			0.235838i
$392$		−	4.62529e6i		−	0.0767858i
$393$			4.98664e7i			0.821544i
$394$			5.89391e7i			0.963641i
$395$	−1.47307e7			−0.239019
$396$		−	9.87955e6i		−	0.159093i
$397$		−	8.84660e7i		−	1.41385i	−0.707286	−	0.706927i	$-0.750081\pi$
$397$		−	8.84660e7i		−	1.41385i	0.707286	−	0.706927i	$-0.249919\pi$
$398$			8.52742e7i			1.35260i
$399$	−7.23649e6			−0.113922
$400$	−1.57192e7			−0.245612
$401$		−	3.69209e7i		−	0.572585i	−0.958142	−	0.286292i	$-0.907577\pi$
$401$		−	3.69209e7i		−	0.572585i	0.958142	−	0.286292i	$-0.0924228\pi$
$402$	9.44167e6			0.145335
$403$	1.25128e7			0.191179
$404$		−	3.00509e7i		−	0.455735i
$405$	−977903.			−0.0147208
$406$		−	1.01864e7i		−	0.152209i
$407$	3.65443e7			0.542047
$408$			6.90250e6i			0.101631i
$409$		−	8.94448e6i		−	0.130733i	−0.997861	−	0.0653665i	$-0.979178\pi$
$409$		−	8.94448e6i		−	0.130733i	0.997861	−	0.0653665i	$-0.0208217\pi$
$410$		−	1.03851e7i		−	0.150681i
$411$	1.46251e7			0.210655
$412$		−	4.92300e7i		−	0.703944i
$413$	4.13986e7	+	4.65927e7i	0.587673	+	0.661405i
$414$	7.92222e6			0.111647
$415$		−	1.01075e7i		−	0.141416i
$416$	−1.47438e6			−0.0204800
$417$	−3.77871e7			−0.521117
$418$	−1.09940e7			−0.150532
$419$		−	7.75423e7i		−	1.05414i	−0.849823	−	0.527068i	$-0.823291\pi$
$419$		−	7.75423e7i		−	1.05414i	0.849823	−	0.527068i	$-0.176709\pi$
$420$	2.50704e6			0.0338386
$421$			5.55958e7i			0.745067i	0.928019	+	0.372534i	$0.121511\pi$
$421$			5.55958e7i			0.745067i	−0.928019	+	0.372534i	$0.878489\pi$
$422$	−6.67120e7			−0.887701
$423$		−	2.60199e7i		−	0.343784i
$424$			9.54054e6i			0.125163i
$425$	−3.75498e7			−0.489149
$426$			3.42457e7i			0.442973i
$427$			5.12490e7i			0.658266i
$428$	2.09058e7			0.266647
$429$	5.04103e6			0.0638480
$430$	−9.32894e6			−0.117335
$431$			3.71760e6i			0.0464335i	0.999730	+	0.0232167i	$0.00739078\pi$
$431$			3.71760e6i			0.0464335i	−0.999730	+	0.0232167i	$0.992609\pi$
$432$	3.87891e6			0.0481125
$433$	−4.09319e7			−0.504194			−0.252097	−	0.967702i	$-0.581120\pi$
$433$	−4.09319e7			−0.504194			−0.252097	+	0.967702i	$0.581120\pi$
$434$	8.43954e7			1.03240
$435$	−1.53181e6			−0.0186096
$436$			3.49110e7i			0.421214i
$437$		−	8.81589e6i		−	0.105638i
$438$	3.95666e7			0.470876
$439$	6.41798e7			0.758586			0.379293	−	0.925277i	$-0.376167\pi$
$439$	6.41798e7			0.758586			0.379293	+	0.925277i	$0.376167\pi$
$440$	3.80881e6			0.0447127
$441$	−6.20899e6			−0.0723944
$442$	−3.52200e6			−0.0407870
$443$		−	1.46998e8i		−	1.69083i	−0.534111	−	0.845414i	$-0.679354\pi$
$443$		−	1.46998e8i		−	1.69083i	0.534111	−	0.845414i	$-0.320646\pi$
$444$			1.43480e7i			0.163924i
$445$			6.66779e6i			0.0756662i
$446$		−	6.24346e7i		−	0.703754i
$447$		−	2.50623e7i		−	0.280607i
$448$	−9.94430e6			−0.110596
$449$	−5.12847e7			−0.566563			−0.283282	−	0.959037i	$-0.591423\pi$
$449$	−5.12847e7			−0.566563			−0.283282	+	0.959037i	$0.591423\pi$
$450$			2.11014e7i			0.231565i
$451$		−	1.40842e8i		−	1.53533i
$452$		−	3.49274e7i		−	0.378225i
$453$			5.92142e7i			0.636988i
$454$	1.12674e6			0.0120408
$455$			1.27921e6i			0.0135803i
$456$		−	4.31647e6i		−	0.0455233i
$457$			6.56816e7i			0.688169i	0.938939	+	0.344085i	$0.111811\pi$
$457$			6.56816e7i			0.688169i	−0.938939	+	0.344085i	$0.888189\pi$
$458$	−4.66114e7			−0.485172
$459$	9.26590e6			0.0958186
$460$			3.05421e6i			0.0313780i
$461$	3.15830e7			0.322367			0.161184	−	0.986924i	$-0.448469\pi$
$461$	3.15830e7			0.322367			0.161184	+	0.986924i	$0.448469\pi$
$462$	3.40003e7			0.344792
$463$			9.84904e7i			0.992318i	0.868232	+	0.496159i	$0.165257\pi$
$463$			9.84904e7i			0.992318i	−0.868232	+	0.496159i	$0.834743\pi$
$464$	6.07602e6			0.0608227
$465$		−	1.26913e7i		−	0.126226i
$466$	−6.67584e7			−0.659702
$467$			3.52831e7i			0.346431i	0.984884	+	0.173215i	$0.0554156\pi$
$467$			3.52831e7i			0.346431i	−0.984884	+	0.173215i	$0.944584\pi$
$468$			1.97921e6i			0.0193087i
$469$			3.24934e7i			0.314975i
$470$	1.00313e7			0.0966194
$471$		−	3.93376e7i		−	0.376483i
$472$	−2.77919e7	+	2.46937e7i	−0.264297	+	0.234834i
$473$	−1.26519e8			−1.19556
$474$		−	7.84367e7i		−	0.736520i
$475$	2.34817e7			0.219103
$476$	−2.37549e7			−0.220258
$477$	1.28072e7			0.118005
$478$		−	7.15610e6i		−	0.0655229i
$479$	−2.32698e7			−0.211732			−0.105866	−	0.994380i	$-0.533761\pi$
$479$	−2.32698e7			−0.211732			−0.105866	+	0.994380i	$0.533761\pi$
$480$			1.49541e6i			0.0135219i
$481$	−7.32107e6			−0.0657869
$482$		−	2.65155e7i		−	0.236788i
$483$			2.72642e7i			0.241965i
$484$	−5.03501e6			−0.0444083
$485$			2.48186e7i			0.217547i
$486$		−	5.20704e6i		−	0.0453609i
$487$	1.04581e8			0.905449			0.452725	−	0.891650i	$-0.350452\pi$
$487$	1.04581e8			0.905449			0.452725	+	0.891650i	$0.350452\pi$
$488$	−3.05693e7			−0.263043
$489$	6.71887e7			0.574605
$490$		−	2.39372e6i		−	0.0203462i
$491$	9.71491e7			0.820719			0.410359	−	0.911924i	$-0.365403\pi$
$491$	9.71491e7			0.820719			0.410359	+	0.911924i	$0.365403\pi$
$492$	5.52974e7			0.464312
$493$	1.45144e7			0.121132
$494$	2.20247e6			0.0182696
$495$		−	5.11294e6i		−	0.0421556i
$496$			5.03407e7i			0.412548i
$497$	−1.17856e8			−0.960026
$498$	5.38194e7			0.435763
$499$	−1.96549e8			−1.58187			−0.790934	−	0.611901i	$-0.790405\pi$
$499$	−1.96549e8			−1.58187			−0.790934	+	0.611901i	$0.790405\pi$
$500$	−1.64155e7			−0.131324
$501$	9.87558e7			0.785325
$502$			1.30529e8i			1.03180i
$503$		−	4.09770e7i		−	0.321985i	−0.986956	−	0.160993i	$-0.948530\pi$
$503$		−	4.09770e7i		−	0.321985i	0.986956	−	0.160993i	$-0.0514695\pi$
$504$			1.33492e7i			0.104271i
$505$		−	1.55521e7i		−	0.120758i
$506$			4.14211e7i			0.319720i
$507$	7.42326e7			0.569601
$508$	−1.08116e8			−0.824708
$509$		−	2.47809e8i		−	1.87916i	−0.342326	−	0.939581i	$-0.611215\pi$
$509$		−	2.47809e8i		−	1.87916i	0.342326	−	0.939581i	$-0.388785\pi$
$510$			3.57223e6i			0.0269296i
$511$			1.36168e8i			1.02050i
$512$		−	5.93164e6i		−	0.0441942i
$513$	−5.79442e6			−0.0429198
$514$			6.74827e7i			0.496939i
$515$		−	2.54779e7i		−	0.186527i
$516$		−	4.96738e7i		−	0.361558i
$517$	1.36044e8			0.984485
$518$	−4.93785e7			−0.355262
$519$			5.04970e7i			0.361213i
$520$	−763033.			−0.00542667
$521$	2.05392e7			0.145235			0.0726174	−	0.997360i	$-0.476865\pi$
$521$	2.05392e7			0.145235			0.0726174	+	0.997360i	$0.476865\pi$
$522$		−	8.15644e6i		−	0.0573442i
$523$	5.57388e7			0.389630			0.194815	−	0.980840i	$-0.437589\pi$
$523$	5.57388e7			0.389630			0.194815	+	0.980840i	$0.437589\pi$
$524$		−	1.02366e8i		−	0.711478i
$525$	−7.26201e7			−0.501855
$526$			1.67874e8i			1.15352i
$527$			1.20254e8i			0.821611i
$528$			2.02808e7i			0.137779i
$529$	1.14821e8			0.775630
$530$			4.93749e6i			0.0331649i
$531$	3.31488e7	+	3.73078e7i	0.221404	+	0.249182i
$532$	1.48551e7			0.0986597
$533$			2.82155e7i			0.186340i
$534$	−3.55040e7			−0.233160
$535$	1.08193e7			0.0706545
$536$	−1.93819e7			−0.125864
$537$			1.73734e8i			1.12192i
$538$	−1.41262e7			−0.0907150
$539$		−	3.24635e7i		−	0.207314i
$540$	2.00744e6			0.0127486
$541$			6.58267e7i			0.415729i	0.978158	+	0.207865i	$0.0666513\pi$
$541$			6.58267e7i			0.415729i	−0.978158	+	0.207865i	$0.933349\pi$
$542$		−	3.33876e7i		−	0.209694i
$543$	1.71238e8			1.06955
$544$		−	1.41695e7i		−	0.0880150i
$545$			1.80674e7i			0.111611i
$546$	−6.81142e6			−0.0418466
$547$	−1.42663e8			−0.871666			−0.435833	−	0.900028i	$-0.643546\pi$
$547$	−1.42663e8			−0.871666			−0.435833	+	0.900028i	$0.643546\pi$
$548$	−3.00224e7			−0.182433
$549$			4.10362e7i			0.247999i
$550$	−1.10328e8			−0.663128
$551$	−9.07653e6			−0.0542582
$552$	−1.62627e7			−0.0966889
$553$	2.69939e8			1.59621
$554$			2.08129e7i			0.122406i
$555$			7.42549e6i			0.0434357i
$556$	7.75694e7			0.451301
$557$	−7.30823e7			−0.422909			−0.211454	−	0.977388i	$-0.567820\pi$
$557$	−7.30823e7			−0.422909			−0.211454	+	0.977388i	$0.567820\pi$
$558$	6.75773e7			0.388954
$559$	2.53460e7			0.145102
$560$	−5.14644e6			−0.0293051
$561$			4.84465e7i			0.274394i
$562$			2.12547e8i			1.19742i
$563$			3.65091e7i			0.204586i	0.994754	+	0.102293i	$0.0326180\pi$
$563$			3.65091e7i			0.204586i	−0.994754	+	0.102293i	$0.967382\pi$
$564$			5.34137e7i			0.297725i
$565$		−	1.80759e7i		−	0.100220i
$566$	1.75636e8			0.968645
$567$	1.79199e7			0.0983077
$568$		−	7.02996e7i		−	0.383626i
$569$			2.44852e8i			1.32913i	0.747231	+	0.664565i	$0.231383\pi$
$569$			2.44852e8i			1.32913i	−0.747231	+	0.664565i	$0.768617\pi$
$570$		−	2.23389e6i		−	0.0120625i
$571$			5.81938e7i			0.312585i	0.987711	+	0.156293i	$0.0499543\pi$
$571$			5.81938e7i			0.312585i	−0.987711	+	0.156293i	$0.950046\pi$
$572$	−1.03482e7			−0.0552940
$573$		−	4.60288e7i		−	0.244662i
$574$			1.90305e8i			1.00627i
$575$		−	8.84698e7i		−	0.465363i
$576$	−7.96262e6			−0.0416667
$577$	1.94553e8			1.01277			0.506385	−	0.862307i	$-0.330981\pi$
$577$	1.94553e8			1.01277			0.506385	+	0.862307i	$0.330981\pi$
$578$			1.02695e8i			0.531820i
$579$	1.74630e8			0.899669
$580$	3.14451e6			0.0161164
$581$			1.85219e8i			0.944401i
$582$	−1.32152e8			−0.670353
$583$			6.69621e7i			0.337927i
$584$	−8.12223e7			−0.407790
$585$			1.02429e6i			0.00511631i
$586$			1.77621e8i			0.882676i
$587$		−	9.36081e7i		−	0.462806i	−0.972858	−	0.231403i	$-0.925668\pi$
$587$		−	9.36081e7i		−	0.462806i	0.972858	−	0.231403i	$-0.0743316\pi$
$588$	1.27458e7			0.0626954
$589$		−	7.52004e7i		−	0.368022i
$590$	−1.43831e7	+	1.27797e7i	−0.0700319	+	0.0622249i
$591$	−1.62417e8			−0.786809
$592$		−	2.94536e7i		−	0.141963i
$593$	3.76932e8			1.80759			0.903793	−	0.427970i	$-0.140771\pi$
$593$	3.76932e8			1.80759			0.903793	+	0.427970i	$0.140771\pi$
$594$	2.72248e7			0.129899
$595$	−1.22938e7			−0.0583626
$596$			5.14479e7i			0.243013i
$597$	−2.34988e8			−1.10439
$598$		−	8.29805e6i		−	0.0388037i
$599$	−2.68359e8			−1.24864			−0.624318	−	0.781170i	$-0.714623\pi$
$599$	−2.68359e8			−1.24864			−0.624318	+	0.781170i	$0.714623\pi$
$600$		−	4.33169e7i		−	0.200541i
$601$			208011.i			0.000958216i	1.00000		0.000479108i	$0.000152505\pi$
$601$			208011.i			0.000958216i	−1.00000		0.000479108i	$0.999847\pi$
$602$	1.70952e8			0.783581
$603$			2.60182e7i			0.118666i
$604$		−	1.21555e8i		−	0.551648i
$605$	−2.60576e6			−0.0117671
$606$	8.28104e7			0.372106
$607$	2.37666e8			1.06268			0.531338	−	0.847160i	$-0.321689\pi$
$607$	2.37666e8			1.06268			0.531338	+	0.847160i	$0.321689\pi$
$608$			8.86085e6i			0.0394244i
$609$	2.80703e7			0.124278
$610$	−1.58205e7			−0.0696995
$611$	−2.72543e7			−0.119485
$612$	−1.90211e7			−0.0829813
$613$		−	7.12793e6i		−	0.0309444i	−0.999880	−	0.0154722i	$-0.995075\pi$
$613$		−	7.12793e6i		−	0.0309444i	0.999880	−	0.0154722i	$-0.00492515\pi$
$614$			1.90373e8i			0.822431i
$615$	2.86179e7			0.123030
$616$	−6.97959e7			−0.298599
$617$	6.41284e7			0.273020			0.136510	−	0.990639i	$-0.456411\pi$
$617$	6.41284e7			0.273020			0.136510	+	0.990639i	$0.456411\pi$
$618$	1.35662e8			0.574768
$619$	3.28898e8			1.38672			0.693361	−	0.720590i	$-0.256129\pi$
$619$	3.28898e8			1.38672			0.693361	+	0.720590i	$0.256129\pi$
$620$			2.60527e7i			0.109314i
$621$			2.18311e7i			0.0911592i
$622$			1.95168e7i			0.0811029i
$623$		−	1.22187e8i		−	0.505311i
$624$		−	4.06292e6i		−	0.0167219i
$625$	2.31360e8			0.947650
$626$	2.47303e7			0.100811
$627$		−	3.02959e7i		−	0.122908i
$628$			8.07523e7i			0.326044i
$629$		−	7.03586e7i		−	0.282726i
$630$			6.90858e6i			0.0276291i
$631$	−2.27446e8			−0.905297			−0.452648	−	0.891689i	$-0.649521\pi$
$631$	−2.27446e8			−0.905297			−0.452648	+	0.891689i	$0.649521\pi$
$632$			1.61015e8i			0.637845i
$633$		−	1.83837e8i		−	0.724805i
$634$		−	2.45145e8i		−	0.961955i
$635$	−5.59531e7			−0.218526
$636$	−2.62906e7			−0.102195
$637$			6.50354e6i			0.0251612i
$638$	4.26457e7			0.164215
$639$	−9.43701e7			−0.361686
$640$		−	3.06979e6i		−	0.0117103i
$641$	−3.31239e8			−1.25767			−0.628836	−	0.777538i	$-0.716468\pi$
$641$	−3.31239e8			−1.25767			−0.628836	+	0.777538i	$0.716468\pi$
$642$			5.76097e7i			0.217716i
$643$	2.85654e8			1.07450			0.537251	−	0.843422i	$-0.319463\pi$
$643$	2.85654e8			1.07450			0.537251	+	0.843422i	$0.319463\pi$
$644$		−	5.59680e7i		−	0.209547i
$645$		−	2.57075e7i		−	0.0958035i
$646$			2.11667e7i			0.0785156i
$647$	2.18186e8			0.805590			0.402795	−	0.915290i	$-0.368039\pi$
$647$	2.18186e8			0.805590			0.402795	+	0.915290i	$0.368039\pi$
$648$			1.06890e7i			0.0392837i
$649$	−1.95063e8	+	1.73318e8i	−0.713576	+	0.634028i
$650$	2.21024e7			0.0804822
$651$			2.32566e8i			0.842954i
$652$	−1.37925e8			−0.497623
$653$	1.73314e8			0.622434			0.311217	−	0.950339i	$-0.399263\pi$
$653$	1.73314e8			0.622434			0.311217	+	0.950339i	$0.399263\pi$
$654$	−9.62034e7			−0.343920
$655$		−	5.29771e7i		−	0.188523i
$656$	−1.13515e8			−0.402106
$657$			1.09033e8i			0.384468i
$658$	−1.83823e8			−0.645240
$659$		−	1.07268e8i		−	0.374813i	−0.982282	−	0.187406i	$-0.939992\pi$
$659$		−	1.07268e8i		−	0.374813i	0.982282	−	0.187406i	$-0.0600081\pi$
$660$			1.04958e7i			0.0365078i
$661$	−1.64278e8			−0.568820			−0.284410	−	0.958703i	$-0.591798\pi$
$661$	−1.64278e8			−0.568820			−0.284410	+	0.958703i	$0.591798\pi$
$662$		−	1.58338e7i		−	0.0545772i
$663$		−	9.70548e6i		−	0.0333025i
$664$	−1.10480e8			−0.377382
$665$	7.68790e6			0.0261422
$666$	−3.95385e7			−0.133844
$667$			3.41968e7i			0.115241i
$668$	−2.02726e8			−0.680112
$669$	1.72050e8			0.574613
$670$	−1.00306e7			−0.0333506
$671$	−2.14557e8			−0.710190
$672$		−	2.74033e7i		−	0.0903014i
$673$		−	4.74204e8i		−	1.55568i	−0.628462	−	0.777840i	$-0.716315\pi$
$673$		−	4.74204e8i		−	1.55568i	0.628462	−	0.777840i	$-0.283685\pi$
$674$	−3.19274e8			−1.04276
$675$	−5.81485e7			−0.189072
$676$	−1.52385e8			−0.493289
$677$	4.97418e8			1.60308			0.801540	−	0.597941i	$-0.204014\pi$
$677$	4.97418e8			1.60308			0.801540	+	0.597941i	$0.204014\pi$
$678$	9.62485e7			0.308820
$679$		−	4.54798e8i		−	1.45281i
$680$		−	7.33308e6i		−	0.0233217i
$681$			3.10492e6i			0.00983126i
$682$			3.53326e8i			1.11384i
$683$		−	1.56666e7i		−	0.0491714i	−0.999698	−	0.0245857i	$-0.992173\pi$
$683$		−	1.56666e7i		−	0.0491714i	0.999698	−	0.0245857i	$-0.00782667\pi$
$684$	1.18948e7			0.0371696
$685$	−1.55374e7			−0.0483400
$686$			2.45835e8i			0.761502i
$687$		−	1.28446e8i		−	0.396142i
$688$			1.01970e8i			0.313119i
$689$		−	1.34148e7i		−	0.0410134i
$690$	−8.41641e6			−0.0256200
$691$		−	1.58330e8i		−	0.479877i	−0.970788	−	0.239939i	$-0.922873\pi$
$691$		−	1.58330e8i		−	0.479877i	0.970788	−	0.239939i	$-0.0771273\pi$
$692$		−	1.03660e8i		−	0.312820i
$693$			9.36939e7i			0.281522i
$694$	2.56390e8			0.767048
$695$	4.01443e7			0.119583
$696$			1.67436e7i			0.0496615i
$697$	−2.71163e8			−0.800814
$698$	9.50313e7			0.279448
$699$		−	1.83964e8i		−	0.538645i
$700$	1.49075e8			0.434620
$701$		−	5.20203e8i		−	1.51015i	−0.655641	−	0.755073i	$-0.727602\pi$
$701$		−	5.20203e8i		−	1.51015i	0.655641	−	0.755073i	$-0.272398\pi$
$702$	−5.45406e6			−0.0157655
$703$			4.39987e7i			0.126641i
$704$		−	4.16323e7i		−	0.119320i
$705$			2.76431e7i			0.0788894i
$706$	−9.93571e7			−0.282348
$707$			2.84991e8i			0.806441i
$708$	−6.80479e7	−	7.65855e7i	−0.191741	−	0.215798i
$709$	1.26776e8			0.355710			0.177855	−	0.984057i	$-0.443084\pi$
$709$	1.26776e8			0.355710			0.177855	+	0.984057i	$0.443084\pi$
$710$		−	3.63820e7i		−	0.101651i
$711$	2.16146e8			0.601366
$712$	7.28826e7			0.201922
$713$	−2.83325e8			−0.781658
$714$		−	6.54607e7i		−	0.179840i
$715$	−5.35549e6			−0.0146515
$716$		−	3.56642e8i		−	0.971614i
$717$	1.97199e7			0.0534992
$718$			1.26434e8i			0.341578i
$719$		−	6.08235e8i		−	1.63638i	−0.574946	−	0.818192i	$-0.694977\pi$
$719$		−	6.08235e8i		−	1.63638i	0.574946	−	0.818192i	$-0.305023\pi$
$720$	−4.12087e6			−0.0110406
$721$			4.66879e8i			1.24566i
$722$			2.52895e8i			0.671937i
$723$	7.30682e7			0.193336
$724$	−3.51518e8			−0.926259
$725$	−9.10854e7			−0.239020
$726$		−	1.38749e7i		−	0.0362593i
$727$	3.55324e8			0.924744			0.462372	−	0.886686i	$-0.346998\pi$
$727$	3.55324e8			0.924744			0.462372	+	0.886686i	$0.346998\pi$
$728$	1.39825e7			0.0362402
$729$	1.43489e7			0.0370370
$730$	−4.20348e7			−0.108054
$731$			2.43586e8i			0.623592i
$732$		−	8.42392e7i		−	0.214774i
$733$	2.17504e8			0.552274			0.276137	−	0.961118i	$-0.410946\pi$
$733$	2.17504e8			0.552274			0.276137	+	0.961118i	$0.410946\pi$
$734$	1.56285e8			0.395212
$735$	6.59630e6			0.0166126
$736$	3.33842e7			0.0837350
$737$	−1.36035e8			−0.339820
$738$			1.52382e8i			0.379109i
$739$		−	6.12327e8i		−	1.51723i	−0.651541	−	0.758613i	$-0.725877\pi$
$739$		−	6.12327e8i		−	1.51723i	0.651541	−	0.758613i	$-0.274123\pi$
$740$		−	1.52431e7i		−	0.0376164i
$741$			6.06931e6i			0.0149171i
$742$		−	9.04789e7i		−	0.221481i
$743$	6.43088e8			1.56785			0.783925	−	0.620856i	$-0.213215\pi$
$743$	6.43088e8			1.56785			0.783925	+	0.620856i	$0.213215\pi$
$744$	−1.38723e8			−0.336844
$745$			2.66257e7i			0.0643921i
$746$		−	4.56423e8i		−	1.09939i
$747$			1.48309e8i			0.355799i
$748$		−	9.94510e7i		−	0.237632i
$749$	−1.98263e8			−0.471842
$750$		−	4.52359e7i		−	0.107226i
$751$			6.28393e8i			1.48358i	0.670632	+	0.741790i	$0.266023\pi$
$751$			6.28393e8i			1.48358i	−0.670632	+	0.741790i	$0.733977\pi$
$752$		−	1.09648e8i		−	0.257838i
$753$	−3.59697e8			−0.842464
$754$	−8.54339e6			−0.0199304
$755$		−	6.29080e7i		−	0.146172i
$756$	−3.67861e7			−0.0851370
$757$	−4.23443e8			−0.976129			−0.488064	−	0.872808i	$-0.662297\pi$
$757$	−4.23443e8			−0.976129			−0.488064	+	0.872808i	$0.662297\pi$
$758$		−	2.67658e8i		−	0.614571i
$759$	−1.14143e8			−0.261050
$760$			4.58573e6i			0.0104464i
$761$	−4.89607e8			−1.11095			−0.555474	−	0.831534i	$-0.687463\pi$
$761$	−4.89607e8			−1.11095			−0.555474	+	0.831534i	$0.687463\pi$
$762$		−	2.97933e8i		−	0.673371i
$763$		−	3.31083e8i		−	0.745355i
$764$			9.44880e7i			0.211883i
$765$	−9.84391e6			−0.0219879
$766$			1.10542e8i			0.245946i
$767$	3.90777e7	−	3.47214e7i	0.0866050	−	0.0769505i
$768$	1.63457e7			0.0360844
$769$		−	6.31788e8i		−	1.38929i	−0.719354	−	0.694644i	$-0.755562\pi$
$769$		−	6.31788e8i		−	1.38929i	0.719354	−	0.694644i	$-0.244438\pi$
$770$	−3.61213e7			−0.0791209
$771$	−1.85960e8			−0.405749
$772$	−3.58480e8			−0.779136
$773$		−	8.04891e7i		−	0.174260i	−0.996197	−	0.0871301i	$-0.972230\pi$
$773$		−	8.04891e7i		−	0.174260i	0.996197	−	0.0871301i	$-0.0277696\pi$
$774$	1.36885e8			0.295211
$775$		−	7.54656e8i		−	1.62123i
$776$	2.71281e8			0.580543
$777$		−	1.36071e8i		−	0.290070i
$778$			2.03700e8i			0.432567i
$779$	1.69571e8			0.358707
$780$		−	2.10267e6i		−	0.00443086i
$781$		−	4.93411e8i		−	1.03575i
$782$	7.97479e7			0.166763
$783$	2.24765e7			0.0468213
$784$	−2.61646e7			−0.0542958
$785$			4.17915e7i			0.0863931i
$786$	2.82087e8			0.580919
$787$	3.99600e8			0.819788			0.409894	−	0.912133i	$-0.365566\pi$
$787$	3.99600e8			0.819788			0.409894	+	0.912133i	$0.365566\pi$
$788$	3.33410e8			0.681397
$789$	−4.62606e8			−0.941848
$790$			8.33296e7i			0.169012i
$791$			3.31238e8i			0.669284i
$792$	−5.58872e7			−0.112496
$793$	4.29830e7			0.0861940
$794$	−5.00439e8			−0.999746
$795$	−1.36061e7			−0.0270790
$796$	4.82384e8			0.956430
$797$			6.31266e8i			1.24692i	0.781857	+	0.623458i	$0.214273\pi$
$797$			6.31266e8i			1.24692i	−0.781857	+	0.623458i	$0.785727\pi$
$798$			4.09357e7i			0.0805553i
$799$		−	2.61926e8i		−	0.513497i
$800$			8.89210e7i			0.173674i
$801$		−	9.78375e7i		−	0.190374i
$802$	−2.08856e8			−0.404878
$803$	−5.70074e8			−1.10099
$804$		−	5.34101e7i		−	0.102767i
$805$		−	2.89650e7i		−	0.0555246i
$806$		−	7.07832e7i		−	0.135184i
$807$		−	3.89273e7i		−	0.0740685i
$808$	−1.69993e8			−0.322254
$809$			7.35948e8i			1.38996i	0.719030	+	0.694979i	$0.244586\pi$
$809$			7.35948e8i			1.38996i	−0.719030	+	0.694979i	$0.755414\pi$
$810$			5.53185e6i			0.0104092i
$811$		−	9.33100e8i		−	1.74930i	−0.484750	−	0.874652i	$-0.661090\pi$
$811$		−	9.33100e8i		−	1.74930i	0.484750	−	0.874652i	$-0.338910\pi$
$812$	−5.76227e7			−0.107628
$813$	9.20053e7			0.171215
$814$		−	2.06726e8i		−	0.383285i
$815$	−7.13799e7			−0.131857
$816$	3.90464e7			0.0718639
$817$		−	1.52326e8i		−	0.279324i
$818$	−5.05976e7			−0.0924422
$819$		−	1.87701e7i		−	0.0341676i
$820$	−5.87469e7			−0.106547
$821$		−	7.42121e8i		−	1.34105i	−0.741886	−	0.670526i	$-0.766069\pi$
$821$		−	7.42121e8i		−	1.34105i	0.741886	−	0.670526i	$-0.233931\pi$
$822$		−	8.27319e7i		−	0.148956i
$823$			1.29181e8i			0.231740i	0.993264	+	0.115870i	$0.0369655\pi$
$823$			1.29181e8i			0.231740i	−0.993264	+	0.115870i	$0.963034\pi$
$824$	−2.78487e8			−0.497764
$825$		−	3.04028e8i		−	0.541441i
$826$	2.63568e8	−	2.34186e8i	0.467684	−	0.415548i
$827$	−2.07745e8			−0.367294			−0.183647	−	0.982992i	$-0.558790\pi$
$827$	−2.07745e8			−0.367294			−0.183647	+	0.982992i	$0.558790\pi$
$828$		−	4.48149e7i		−	0.0789462i
$829$	−3.57968e8			−0.628319			−0.314160	−	0.949370i	$-0.601723\pi$
$829$	−3.57968e8			−0.628319			−0.314160	+	0.949370i	$0.601723\pi$
$830$	−5.71766e7			−0.0999964
$831$	−5.73535e7			−0.0999440
$832$			8.34037e6i			0.0144816i
$833$	−6.25018e7			−0.108133
$834$			2.13756e8i			0.368485i
$835$	−1.04916e8			−0.180212
$836$			6.21915e7i			0.106442i
$837$			1.86221e8i			0.317580i
$838$	−4.38646e8			−0.745387
$839$			1.30657e7i			0.0221231i	0.999939	+	0.0110616i	$0.00352107\pi$
$839$			1.30657e7i			0.0221231i	−0.999939	+	0.0110616i	$0.996479\pi$
$840$		−	1.41819e7i		−	0.0239275i
$841$	−5.59615e8			−0.940810
$842$	3.14497e8			0.526842
$843$	−5.85711e8			−0.977689
$844$			3.77380e8i			0.627700i
$845$	−7.88633e7			−0.130709
$846$	−1.47191e8			−0.243092
$847$	4.77502e7			0.0785823
$848$	5.39695e7			0.0885035
$849$			4.83996e8i			0.790895i
$850$			2.12414e8i			0.345880i
$851$	1.65770e8			0.268978
$852$	1.93723e8			0.313229
$853$	−9.15045e8			−1.47433			−0.737166	−	0.675711i	$-0.763837\pi$
$853$	−9.15045e8			−1.47433			−0.737166	+	0.675711i	$0.763837\pi$
$854$	2.89908e8			0.465465
$855$	6.15588e6			0.00984899
$856$		−	1.18261e8i		−	0.188548i
$857$			6.79589e8i			1.07970i	0.841761	+	0.539851i	$0.181519\pi$
$857$			6.79589e8i			1.07970i	−0.841761	+	0.539851i	$0.818481\pi$
$858$		−	2.85164e7i		−	0.0451474i
$859$		−	1.07416e8i		−	0.169468i	−0.996404	−	0.0847341i	$-0.972996\pi$
$859$		−	1.07416e8i		−	0.169468i	0.996404	−	0.0847341i	$-0.0270041\pi$
$860$			5.27725e7i			0.0829683i
$861$	−5.24420e8			−0.821617
$862$	2.10299e7			0.0328334
$863$		−	8.02305e8i		−	1.24827i	−0.781318	−	0.624133i	$-0.785452\pi$
$863$		−	8.02305e8i		−	1.24827i	0.781318	−	0.624133i	$-0.214548\pi$
$864$		−	2.19424e7i		−	0.0340207i
$865$		−	5.36470e7i		−	0.0828891i
$866$			2.31546e8i			0.356519i
$867$	−2.82994e8			−0.434230
$868$		−	4.77413e8i		−	0.730020i
$869$			1.13011e9i			1.72212i
$870$			8.66525e6i			0.0131590i
$871$	2.72525e7			0.0412431
$872$	1.97487e8			0.297843
$873$		−	3.64167e8i		−	0.547341i
$874$	−4.98702e7			−0.0746976
$875$	1.55679e8			0.232383
$876$		−	2.23822e8i		−	0.332959i
$877$	7.78448e8			1.15407			0.577033	−	0.816721i	$-0.304210\pi$
$877$	7.78448e8			1.15407			0.577033	+	0.816721i	$0.304210\pi$
$878$		−	3.63056e8i		−	0.536402i
$879$	−4.89466e8			−0.720702
$880$		−	2.15459e7i		−	0.0316167i
$881$			4.50656e8i			0.659048i	0.944147	+	0.329524i	$0.106888\pi$
$881$			4.50656e8i			0.659048i	−0.944147	+	0.329524i	$0.893112\pi$
$882$			3.51233e7i			0.0511906i
$883$	5.13839e8			0.746355			0.373177	−	0.927760i	$-0.378268\pi$
$883$	5.13839e8			0.746355			0.373177	+	0.927760i	$0.378268\pi$
$884$			1.99234e7i			0.0288408i
$885$	−3.52167e7	−	3.96351e7i	−0.0508064	−	0.0571808i
$886$	−8.31545e8			−1.19560
$887$		−	6.72464e8i		−	0.963603i	−0.876280	−	0.481801i	$-0.839983\pi$
$887$		−	6.72464e8i		−	0.963603i	0.876280	−	0.481801i	$-0.160017\pi$
$888$	8.11647e7			0.115912
$889$	1.02533e9			1.45935
$890$	3.77187e7			0.0535041
$891$			7.50228e7i			0.106062i
$892$	−3.53183e8			−0.497629
$893$			1.63795e8i			0.230010i
$894$	−1.41774e8			−0.198419
$895$		−	1.84572e8i		−	0.257452i
$896$			5.62534e7i			0.0782033i
$897$	2.28667e7			0.0316831
$898$			2.90110e8i			0.400621i
$899$			2.91702e8i			0.401477i
$900$	1.19367e8			0.163741
$901$	1.28922e8			0.176259
$902$	−7.96723e8			−1.08565
$903$			4.71088e8i			0.639791i
$904$	−1.97579e8			−0.267446
$905$	−1.81920e8			−0.245434
$906$	3.34966e8			0.450418
$907$	9.79282e8			1.31246			0.656230	−	0.754561i	$-0.272150\pi$
$907$	9.79282e8			1.31246			0.656230	+	0.754561i	$0.272150\pi$
$908$		−	6.37379e6i		−	0.00851412i
$909$			2.28199e8i			0.303824i
$910$	7.23632e6			0.00960270
$911$	3.70575e8			0.490141			0.245071	−	0.969505i	$-0.421189\pi$
$911$	3.70575e8			0.490141			0.245071	+	0.969505i	$0.421189\pi$
$912$	−2.44176e7			−0.0321899
$913$	−7.75428e8			−1.01889
$914$	3.71551e8			0.486609
$915$		−	4.35961e7i		−	0.0569094i
$916$			2.63674e8i			0.343069i
$917$			9.70799e8i			1.25899i
$918$		−	5.24159e7i		−	0.0677540i
$919$		−	9.63406e8i		−	1.24126i	−0.784104	−	0.620630i	$-0.786877\pi$
$919$		−	9.63406e8i		−	1.24126i	0.784104	−	0.620630i	$-0.213123\pi$
$920$	1.72772e7			0.0221876
$921$	−5.24605e8			−0.671512
$922$		−	1.78661e8i		−	0.227948i
$923$			9.88470e7i			0.125707i
$924$		−	1.92335e8i		−	0.243805i
$925$			4.41538e8i			0.557883i
$926$	5.57146e8			0.701675
$927$			3.73840e8i			0.469296i
$928$		−	3.43712e7i		−	0.0430081i
$929$			1.02523e9i			1.27871i	0.768911	+	0.639356i	$0.220799\pi$
$929$			1.02523e9i			1.27871i	−0.768911	+	0.639356i	$0.779201\pi$
$930$	−7.17928e7			−0.0892549
$931$	3.90854e7			0.0484357
$932$			3.77642e8i			0.466480i
$933$	−5.37818e7			−0.0662202
$934$	1.99591e8			0.244963
$935$		−	5.14686e7i		−	0.0629662i
$936$	1.11961e7			0.0136533
$937$		−	7.10175e8i		−	0.863270i	−0.902048	−	0.431635i	$-0.857937\pi$
$937$		−	7.10175e8i		−	0.863270i	0.902048	−	0.431635i	$-0.142063\pi$
$938$	1.83810e8			0.222721
$939$			6.81486e7i			0.0823115i
$940$		−	5.67457e7i		−	0.0683203i
$941$		−	2.04115e8i		−	0.244966i	−0.992471	−	0.122483i	$-0.960914\pi$
$941$		−	2.04115e8i		−	0.244966i	0.992471	−	0.122483i	$-0.0390858\pi$
$942$	−2.22527e8			−0.266214
$943$		−	6.38877e8i		−	0.761873i
$944$	1.39689e8	+	1.57215e8i	0.166053	+	0.186886i
$945$	−1.90378e7			−0.0225591
$946$			7.15699e8i			0.845389i
$947$	1.01600e9			1.19631			0.598155	−	0.801380i	$-0.295901\pi$
$947$	1.01600e9			1.19631			0.598155	+	0.801380i	$0.295901\pi$
$948$	−4.43705e8			−0.520798
$949$	1.14205e8			0.133625
$950$		−	1.32833e8i		−	0.154929i
$951$	6.75540e8			0.785433
$952$			1.34378e8i			0.155746i
$953$	2.34249e7			0.0270644			0.0135322	−	0.999908i	$-0.495692\pi$
$953$	2.34249e7			0.0270644			0.0135322	+	0.999908i	$0.495692\pi$
$954$		−	7.24485e7i		−	0.0834419i
$955$			4.89001e7i			0.0561435i
$956$	−4.04810e7			−0.0463317
$957$			1.17518e8i			0.134081i
$958$			1.31634e8i			0.149717i
$959$	2.84721e8			0.322822
$960$	8.45933e6			0.00956142
$961$	−1.52929e9			−1.72314
$962$			4.14142e7i			0.0465183i
$963$	−1.58754e8			−0.177765
$964$	−1.49995e8			−0.167434
$965$	−1.85523e8			−0.206451
$966$	1.54230e8			0.171095
$967$			5.09787e8i			0.563780i	0.959447	+	0.281890i	$0.0909613\pi$
$967$			5.09787e8i			0.563780i	−0.959447	+	0.281890i	$0.909039\pi$
$968$			2.84823e7i			0.0314014i
$969$	−5.83286e7			−0.0641078
$970$	1.40395e8			0.153829
$971$	7.24248e8			0.791097			0.395549	−	0.918445i	$-0.370554\pi$
$971$	7.24248e8			0.791097			0.395549	+	0.918445i	$0.370554\pi$
$972$	−2.94555e7			−0.0320750
$973$	−7.35639e8			−0.798594
$974$		−	5.91597e8i		−	0.640249i
$975$			6.09071e7i			0.0657134i
$976$			1.72926e8i			0.185999i
$977$			1.13010e9i			1.21181i	0.795538	+	0.605903i	$0.207188\pi$
$977$			1.13010e9i			1.21181i	−0.795538	+	0.605903i	$0.792812\pi$
$978$		−	3.80076e8i		−	0.406307i
$979$	5.11540e8			0.545170
$980$	−1.35409e7			−0.0143870
$981$		−	2.65106e8i		−	0.280809i
$982$		−	5.49558e8i		−	0.580336i
$983$			1.73854e9i			1.83031i	0.403104	+	0.915154i	$0.367931\pi$
$983$			1.73854e9i			1.83031i	−0.403104	+	0.915154i	$0.632069\pi$
$984$		−	3.12809e8i		−	0.328318i
$985$	1.72549e8			0.180552
$986$		−	8.21056e7i		−	0.0856529i
$987$		−	5.06556e8i		−	0.526836i
$988$		−	1.24591e7i		−	0.0129186i
$989$	−5.73905e8			−0.593268
$990$	−2.89231e7			−0.0298085
$991$		−	9.80593e8i		−	1.00755i	−0.863834	−	0.503777i	$-0.831944\pi$
$991$		−	9.80593e8i		−	1.00755i	0.863834	−	0.503777i	$-0.168056\pi$
$992$	2.84770e8			0.291716
$993$	4.36328e7			0.0445621
$994$			6.66695e8i			0.678841i
$995$	2.49647e8			0.253429
$996$		−	3.04448e8i		−	0.308131i
$997$	−7.25134e8			−0.731700			−0.365850	−	0.930674i	$-0.619222\pi$
$997$	−7.25134e8			−0.731700			−0.365850	+	0.930674i	$0.619222\pi$
$998$			1.11185e9i			1.11855i
$999$		−	1.08955e8i		−	0.109283i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.7.d.a.235.17	✓	60
59.58	odd	2	inner	354.7.d.a.235.18	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.7.d.a.235.17	✓	60	1.1	even	1	trivial
354.7.d.a.235.18	yes	60	59.58	odd	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	354.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.65685i q^{2} +15.5885 q^{3} -32.0000 q^{4} -16.5609 q^{5} -88.1816i q^{6} +303.476 q^{7} +181.019i q^{8} +243.000 q^{9} +O(q^{10})\)	\(q-5.65685i q^{2} +15.5885 q^{3} -32.0000 q^{4} -16.5609 q^{5} -88.1816i q^{6} +303.476 q^{7} +181.019i q^{8} +243.000 q^{9} +93.6824i q^{10} +1270.52i q^{11} -498.831 q^{12} -254.528i q^{13} -1716.72i q^{14} -258.158 q^{15} +1024.00 q^{16} +2446.12 q^{17} -1374.62i q^{18} -1529.68 q^{19} +529.948 q^{20} +4730.72 q^{21} +7187.14 q^{22} +5763.23i q^{23} +2821.81i q^{24} -15350.7 q^{25} -1439.83 q^{26} +3788.00 q^{27} -9711.23 q^{28} +5933.62 q^{29} +1460.36i q^{30} +49160.9i q^{31} -5792.62i q^{32} +19805.4i q^{33} -13837.4i q^{34} -5025.82 q^{35} -7776.00 q^{36} -28763.3i q^{37} +8653.17i q^{38} -3967.70i q^{39} -2997.84i q^{40} -110854. q^{41} -26761.0i q^{42} +99580.5i q^{43} -40656.6i q^{44} -4024.29 q^{45} +32601.7 q^{46} -107078. i q^{47} +15962.6 q^{48} -25551.4 q^{49} +86836.9i q^{50} +38131.3 q^{51} +8144.89i q^{52} +52704.6 q^{53} -21428.1i q^{54} -21040.9i q^{55} +54935.0i q^{56} -23845.3 q^{57} -33565.6i q^{58} +(136415. + 153530. i) q^{59} +8261.07 q^{60} +168873. i q^{61} +278096. q^{62} +73744.6 q^{63} -32768.0 q^{64} +4215.20i q^{65} +112036. q^{66} +107071. i q^{67} -78276.0 q^{68} +89839.8i q^{69} +28430.4i q^{70} -388354. q^{71} +43987.7i q^{72} +448694. i q^{73} -162710. q^{74} -239294. q^{75} +48949.7 q^{76} +385572. i q^{77} -22444.7 q^{78} +889491. q^{79} -16958.3 q^{80} +59049.0 q^{81} +627085. i q^{82} +610324. i q^{83} -151383. q^{84} -40509.9 q^{85} +563312. q^{86} +92495.9 q^{87} -229988. q^{88} -402623. i q^{89} +22764.8i q^{90} -77243.1i q^{91} -184423. i q^{92} +766342. i q^{93} -605724. q^{94} +25332.8 q^{95} -90298.0i q^{96} -1.49863e6i q^{97} +144540. i q^{98} +308736. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 1920 q^{4} + 408 q^{7} + 14580 q^{9}+O(q^{10}) \) 60 * q - 1920 * q^4 + 408 * q^7 + 14580 * q^9	\( 60 q - 1920 q^{4} + 408 q^{7} + 14580 q^{9} + 4536 q^{15} + 61440 q^{16} - 15840 q^{17} - 5616 q^{19} - 17472 q^{22} + 226260 q^{25} - 34048 q^{26} - 13056 q^{28} - 75392 q^{29} + 278000 q^{35} - 466560 q^{36} + 67376 q^{41} + 209856 q^{46} + 269100 q^{49} - 206064 q^{51} + 490000 q^{53} - 373248 q^{57} - 863472 q^{59} - 145152 q^{60} - 155072 q^{62} + 99144 q^{63} - 1966080 q^{64} - 404352 q^{66} + 506880 q^{68} - 2041856 q^{71} - 2146176 q^{74} + 808704 q^{75} + 179712 q^{76} + 228096 q^{78} + 670248 q^{79} + 3542940 q^{81} + 873408 q^{85} + 1832576 q^{86} - 2568024 q^{87} + 559104 q^{88} + 1049472 q^{94} - 245856 q^{95}+O(q^{100}) \) 60 * q - 1920 * q^4 + 408 * q^7 + 14580 * q^9 + 4536 * q^15 + 61440 * q^16 - 15840 * q^17 - 5616 * q^19 - 17472 * q^22 + 226260 * q^25 - 34048 * q^26 - 13056 * q^28 - 75392 * q^29 + 278000 * q^35 - 466560 * q^36 + 67376 * q^41 + 209856 * q^46 + 269100 * q^49 - 206064 * q^51 + 490000 * q^53 - 373248 * q^57 - 863472 * q^59 - 145152 * q^60 - 155072 * q^62 + 99144 * q^63 - 1966080 * q^64 - 404352 * q^66 + 506880 * q^68 - 2041856 * q^71 - 2146176 * q^74 + 808704 * q^75 + 179712 * q^76 + 228096 * q^78 + 670248 * q^79 + 3542940 * q^81 + 873408 * q^85 + 1832576 * q^86 - 2568024 * q^87 + 559104 * q^88 + 1049472 * q^94 - 245856 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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