LMFDB - Embedded newform 354.7.d.a.235.1

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			235.1
Character	$\chi$	$=$	354.235
Dual form			354.7.d.a.235.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.65685i q^{2} -15.5885 q^{3} -32.0000 q^{4} -92.5158 q^{5} +88.1816i q^{6} +505.471 q^{7} +181.019i q^{8} +243.000 q^{9} +O(q^{10})$	\(q-5.65685i q^{2} -15.5885 q^{3} -32.0000 q^{4} -92.5158 q^{5} +88.1816i q^{6} +505.471 q^{7} +181.019i q^{8} +243.000 q^{9} +523.348i q^{10} +2499.89i q^{11} +498.831 q^{12} +1947.22i q^{13} -2859.38i q^{14} +1442.18 q^{15} +1024.00 q^{16} +894.582 q^{17} -1374.62i q^{18} +1989.65 q^{19} +2960.50 q^{20} -7879.52 q^{21} +14141.5 q^{22} +11570.3i q^{23} -2821.81i q^{24} -7065.84 q^{25} +11015.1 q^{26} -3788.00 q^{27} -16175.1 q^{28} -12830.8 q^{29} -8158.19i q^{30} -33718.0i q^{31} -5792.62i q^{32} -38969.4i q^{33} -5060.52i q^{34} -46764.1 q^{35} -7776.00 q^{36} -44162.7i q^{37} -11255.2i q^{38} -30354.1i q^{39} -16747.1i q^{40} +88360.7 q^{41} +44573.3i q^{42} +1495.65i q^{43} -79996.5i q^{44} -22481.3 q^{45} +65451.3 q^{46} -774.757i q^{47} -15962.6 q^{48} +137852. q^{49} +39970.4i q^{50} -13945.2 q^{51} -62310.9i q^{52} +7209.13 q^{53} +21428.1i q^{54} -231279. i q^{55} +91500.1i q^{56} -31015.7 q^{57} +72581.8i q^{58} +(-184827. + 89551.6i) q^{59} -46149.7 q^{60} +45521.2i q^{61} -190738. q^{62} +122830. q^{63} -32768.0 q^{64} -180148. i q^{65} -220444. q^{66} +302695. i q^{67} -28626.6 q^{68} -180362. i q^{69} +264537. i q^{70} -532292. q^{71} +43987.7i q^{72} -206553. i q^{73} -249822. q^{74} +110145. q^{75} -63669.0 q^{76} +1.26362e6i q^{77} -171709. q^{78} -875330. q^{79} -94736.1 q^{80} +59049.0 q^{81} -499843. i q^{82} +166279. i q^{83} +252145. q^{84} -82763.0 q^{85} +8460.68 q^{86} +200012. q^{87} -452528. q^{88} +721149. i q^{89} +127174. i q^{90} +984262. i q^{91} -370248. i q^{92} +525612. i q^{93} -4382.69 q^{94} -184074. q^{95} +90298.0i q^{96} -1.08466e6i q^{97} -779810. i q^{98} +607473. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−92.5158			−0.740126			−0.370063	−	0.929007i	$-0.620664\pi$
$5$	−92.5158			−0.740126			−0.370063	+	0.929007i	$0.620664\pi$
$6$			88.1816i			0.408248i
$7$	505.471			1.47368			0.736839	−	0.676069i	$-0.236318\pi$
$7$	505.471			1.47368			0.736839	+	0.676069i	$0.236318\pi$
$8$			181.019i			0.353553i
$9$	243.000			0.333333
$10$			523.348i			0.523348i
$11$			2499.89i			1.87820i	0.343638	+	0.939102i	$0.388341\pi$
$11$			2499.89i			1.87820i	−0.343638	+	0.939102i	$0.611659\pi$
$12$	498.831			0.288675
$13$			1947.22i			0.886307i	0.896446	+	0.443153i	$0.146140\pi$
$13$			1947.22i			0.886307i	−0.896446	+	0.443153i	$0.853860\pi$
$14$		−	2859.38i		−	1.04205i
$15$	1442.18			0.427312
$16$	1024.00			0.250000
$17$	894.582			0.182085			0.0910424	−	0.995847i	$-0.470980\pi$
$17$	894.582			0.182085			0.0910424	+	0.995847i	$0.470980\pi$
$18$		−	1374.62i		−	0.235702i
$19$	1989.65			0.290079			0.145040	−	0.989426i	$-0.453669\pi$
$19$	1989.65			0.290079			0.145040	+	0.989426i	$0.453669\pi$
$20$	2960.50			0.370063
$21$	−7879.52			−0.850828
$22$	14141.5			1.32809
$23$			11570.3i			0.950954i	0.879728	+	0.475477i	$0.157725\pi$
$23$			11570.3i			0.950954i	−0.879728	+	0.475477i	$0.842275\pi$
$24$		−	2821.81i		−	0.204124i
$25$	−7065.84			−0.452213
$26$	11015.1			0.626714
$27$	−3788.00			−0.192450
$28$	−16175.1			−0.736839
$29$	−12830.8			−0.526089			−0.263044	−	0.964784i	$-0.584727\pi$
$29$	−12830.8			−0.526089			−0.263044	+	0.964784i	$0.584727\pi$
$30$		−	8158.19i		−	0.302155i
$31$		−	33718.0i		−	1.13182i	−0.824467	−	0.565910i	$-0.808525\pi$
$31$		−	33718.0i		−	1.13182i	0.824467	−	0.565910i	$-0.191475\pi$
$32$		−	5792.62i		−	0.176777i
$33$		−	38969.4i		−	1.08438i
$34$		−	5060.52i		−	0.128753i
$35$	−46764.1			−1.09071
$36$	−7776.00			−0.166667
$37$		−	44162.7i		−	0.871866i	−0.899979	−	0.435933i	$-0.856418\pi$
$37$		−	44162.7i		−	0.871866i	0.899979	−	0.435933i	$-0.143582\pi$
$38$		−	11255.2i		−	0.205117i
$39$		−	30354.1i		−	0.511710i
$40$		−	16747.1i		−	0.261674i
$41$	88360.7			1.28206			0.641029	−	0.767517i	$-0.278508\pi$
$41$	88360.7			1.28206			0.641029	+	0.767517i	$0.278508\pi$
$42$			44573.3i			0.601626i
$43$			1495.65i			0.0188116i	0.999956	+	0.00940578i	$0.00299400\pi$
$43$			1495.65i			0.0188116i	−0.999956	+	0.00940578i	$0.997006\pi$
$44$		−	79996.5i		−	0.939102i
$45$	−22481.3			−0.246709
$46$	65451.3			0.672426
$47$		−	774.757i		−	0.00746229i	−0.999993	−	0.00373114i	$-0.998812\pi$
$47$		−	774.757i		−	0.00746229i	0.999993	−	0.00373114i	$-0.00118766\pi$
$48$	−15962.6			−0.144338
$49$	137852.			1.17172
$50$			39970.4i			0.319763i
$51$	−13945.2			−0.105127
$52$		−	62310.9i		−	0.443153i
$53$	7209.13			0.0484234			0.0242117	−	0.999707i	$-0.492292\pi$
$53$	7209.13			0.0484234			0.0242117	+	0.999707i	$0.492292\pi$
$54$			21428.1i			0.136083i
$55$		−	231279.i		−	1.39011i
$56$			91500.1i			0.521024i
$57$	−31015.7			−0.167477
$58$			72581.8i			0.372001i
$59$	−184827.	+	89551.6i	−0.899932	+	0.436031i
$59$	−184827.	+	89551.6i	−0.899932	+	0.436031i
$60$	−46149.7			−0.213656
$61$			45521.2i			0.200551i	0.994960	+	0.100275i	$0.0319724\pi$
$61$			45521.2i			0.200551i	−0.994960	+	0.100275i	$0.968028\pi$
$62$	−190738.			−0.800317
$63$	122830.			0.491226
$64$	−32768.0			−0.125000
$65$		−	180148.i		−	0.655979i
$66$	−220444.			−0.766774
$67$			302695.i			1.00642i	0.864163	+	0.503212i	$0.167849\pi$
$67$			302695.i			1.00642i	−0.864163	+	0.503212i	$0.832151\pi$
$68$	−28626.6			−0.0910424
$69$		−	180362.i		−	0.549034i
$70$			264537.i			0.771246i
$71$	−532292.			−1.48722			−0.743610	−	0.668614i	$-0.766888\pi$
$71$	−532292.			−1.48722			−0.743610	+	0.668614i	$0.766888\pi$
$72$			43987.7i			0.117851i
$73$		−	206553.i		−	0.530962i	−0.964116	−	0.265481i	$-0.914469\pi$
$73$		−	206553.i		−	0.530962i	0.964116	−	0.265481i	$-0.0855308\pi$
$74$	−249822.			−0.616503
$75$	110145.			0.261086
$76$	−63669.0			−0.145040
$77$			1.26362e6i			2.76787i
$78$	−171709.			−0.361833
$79$	−875330.			−1.77538			−0.887688	−	0.460445i	$-0.847690\pi$
$79$	−875330.			−1.77538			−0.887688	+	0.460445i	$0.847690\pi$
$80$	−94736.1			−0.185032
$81$	59049.0			0.111111
$82$		−	499843.i		−	0.906551i
$83$			166279.i			0.290806i	0.989373	+	0.145403i	$0.0464479\pi$
$83$			166279.i			0.290806i	−0.989373	+	0.145403i	$0.953552\pi$
$84$	252145.			0.425414
$85$	−82763.0			−0.134766
$86$	8460.68			0.0133018
$87$	200012.			0.303737
$88$	−452528.			−0.664046
$89$			721149.i			1.02295i	0.859298	+	0.511476i	$0.170901\pi$
$89$			721149.i			1.02295i	−0.859298	+	0.511476i	$0.829099\pi$
$90$			127174.i			0.174449i
$91$			984262.i			1.30613i
$92$		−	370248.i		−	0.475477i
$93$			525612.i			0.653456i
$94$	−4382.69			−0.00527663
$95$	−184074.			−0.214695
$96$			90298.0i			0.102062i
$97$		−	1.08466e6i		−	1.18845i	−0.804300	−	0.594224i	$-0.797459\pi$
$97$		−	1.08466e6i		−	1.18845i	0.804300	−	0.594224i	$-0.202541\pi$
$98$		−	779810.i		−	0.828534i
$99$			607473.i			0.626068i
$100$	226107.			0.226107
$101$			899342.i			0.872892i	0.899730	+	0.436446i	$0.143763\pi$
$101$			899342.i			0.872892i	−0.899730	+	0.436446i	$0.856237\pi$
$102$			78885.7i			0.0743358i
$103$			616368.i			0.564064i	0.959405	+	0.282032i	$0.0910084\pi$
$103$			616368.i			0.564064i	−0.959405	+	0.282032i	$0.908992\pi$
$104$	−352484.			−0.313357
$105$	728980.			0.629720
$106$		−	40781.0i		−	0.0342405i
$107$	1.80593e6			1.47418			0.737090	−	0.675795i	$-0.236199\pi$
$107$	1.80593e6			1.47418			0.737090	+	0.675795i	$0.236199\pi$
$108$	121216.			0.0962250
$109$		−	564156.i		−	0.435632i	−0.975990	−	0.217816i	$-0.930107\pi$
$109$		−	564156.i		−	0.435632i	0.975990	−	0.217816i	$-0.0698933\pi$
$110$	−1.30831e6			−0.982955
$111$			688428.i			0.503372i
$112$	517603.			0.368419
$113$		−	414716.i		−	0.287419i	−0.989620	−	0.143709i	$-0.954097\pi$
$113$		−	414716.i		−	0.287419i	0.989620	−	0.143709i	$-0.0459031\pi$
$114$			175451.i			0.118424i
$115$		−	1.07043e6i		−	0.703826i
$116$	410585.			0.263044
$117$			473174.i			0.295436i
$118$	506580.	+	1.04554e6i	0.308320	+	0.636348i
$119$	452186.			0.268334
$120$			261062.i			0.151078i
$121$	−4.47789e6			−2.52765
$122$	257507.			0.141811
$123$	−1.37741e6			−0.740196
$124$			1.07898e6i			0.565910i
$125$	2.09926e6			1.07482
$126$		−	694829.i		−	0.347349i
$127$	−3.31037e6			−1.61609			−0.808045	−	0.589121i	$-0.799474\pi$
$127$	−3.31037e6			−1.61609			−0.808045	+	0.589121i	$0.799474\pi$
$128$			185364.i			0.0883883i
$129$		−	23314.9i		−	0.0108609i
$130$	−1.01907e6			−0.463847
$131$			80538.0i			0.0358251i	0.999840	+	0.0179125i	$0.00570204\pi$
$131$			80538.0i			0.0358251i	−0.999840	+	0.0179125i	$0.994298\pi$
$132$			1.24702e6i			0.542191i
$133$	1.00571e6			0.427483
$134$	1.71230e6			0.711650
$135$	350449.			0.142437
$136$			161937.i			0.0643767i
$137$	63538.0			0.0247100			0.0123550	−	0.999924i	$-0.496067\pi$
$137$	63538.0			0.0247100			0.0123550	+	0.999924i	$0.496067\pi$
$138$	−1.02028e6			−0.388225
$139$	284120.			0.105793			0.0528965	−	0.998600i	$-0.483155\pi$
$139$	284120.			0.105793			0.0528965	+	0.998600i	$0.483155\pi$
$140$	1.49645e6			0.545353
$141$			12077.3i			0.00430835i
$142$			3.01110e6i			1.05162i
$143$	−4.86783e6			−1.66467
$144$	248832.			0.0833333
$145$	1.18705e6			0.389372
$146$	−1.16844e6			−0.375447
$147$	−2.14890e6			−0.676496
$148$			1.41320e6i			0.435933i
$149$		−	6.19006e6i		−	1.87127i	−0.352970	−	0.935635i	$-0.614828\pi$
$149$		−	6.19006e6i		−	1.87127i	0.352970	−	0.935635i	$-0.385172\pi$
$150$		−	623077.i		−	0.184615i
$151$			3.41295e6i			0.991286i	0.868526	+	0.495643i	$0.165068\pi$
$151$			3.41295e6i			0.991286i	−0.868526	+	0.495643i	$0.834932\pi$
$152$			360166.i			0.102559i
$153$	217384.			0.0606949
$154$	7.14813e6			1.95718
$155$			3.11945e6i			0.837689i
$156$			971331.i			0.255855i
$157$			4.52915e6i			1.17036i	0.810905	+	0.585178i	$0.198975\pi$
$157$			4.52915e6i			1.17036i	−0.810905	+	0.585178i	$0.801025\pi$
$158$			4.95161e6i			1.25538i
$159$	−112379.			−0.0279573
$160$			535908.i			0.130837i
$161$			5.84843e6i			1.40140i
$162$		−	334032.i		−	0.0785674i
$163$	−3.56590e6			−0.823390			−0.411695	−	0.911322i	$-0.635063\pi$
$163$	−3.56590e6			−0.823390			−0.411695	+	0.911322i	$0.635063\pi$
$164$	−2.82754e6			−0.641029
$165$			3.60529e6i			0.802579i
$166$	940617.			0.205631
$167$	3.83080e6			0.822509			0.411254	−	0.911521i	$-0.365091\pi$
$167$	3.83080e6			0.822509			0.411254	+	0.911521i	$0.365091\pi$
$168$		−	1.42635e6i		−	0.300813i
$169$	1.03516e6			0.214460
$170$			468178.i			0.0952937i
$171$	483486.			0.0966932
$172$		−	47860.8i		−	0.00940578i
$173$			7.43789e6i			1.43652i	0.695775	+	0.718260i	$0.255061\pi$
$173$			7.43789e6i			1.43652i	−0.695775	+	0.718260i	$0.744939\pi$
$174$		−	1.13144e6i		−	0.214775i
$175$	−3.57158e6			−0.666417
$176$			2.55989e6i			0.469551i
$177$	2.88117e6	−	1.39597e6i	0.519576	−	0.251742i
$178$	4.07943e6			0.723336
$179$		−	1.00375e6i		−	0.175011i	−0.996164	−	0.0875055i	$-0.972110\pi$
$179$		−	1.00375e6i		−	0.175011i	0.996164	−	0.0875055i	$-0.0278895\pi$
$180$	719403.			0.123354
$181$	328151.			0.0553399			0.0276700	−	0.999617i	$-0.491191\pi$
$181$	328151.			0.0553399			0.0276700	+	0.999617i	$0.491191\pi$
$182$	5.56783e6			0.923574
$183$		−	709606.i		−	0.115788i
$184$	−2.09444e6			−0.336213
$185$			4.08574e6i			0.645291i
$186$	2.97331e6			0.462063
$187$			2.23636e6i			0.341992i
$188$			24792.2i			0.00373114i
$189$	−1.91472e6			−0.283609
$190$			1.04128e6i			0.151813i
$191$		−	1.30448e7i		−	1.87213i	−0.351826	−	0.936065i	$-0.614439\pi$
$191$		−	1.30448e7i		−	1.87213i	0.351826	−	0.936065i	$-0.385561\pi$
$192$	510803.			0.0721688
$193$	−1.63775e6			−0.227811			−0.113906	−	0.993492i	$-0.536336\pi$
$193$	−1.63775e6			−0.227811			−0.113906	+	0.993492i	$0.536336\pi$
$194$	−6.13578e6			−0.840359
$195$			2.80823e6i			0.378730i
$196$	−4.41127e6			−0.585862
$197$	5.29151e6			0.692119			0.346060	−	0.938213i	$-0.387519\pi$
$197$	5.29151e6			0.692119			0.346060	+	0.938213i	$0.387519\pi$
$198$	3.43639e6			0.442697
$199$	−6.67399e6			−0.846889			−0.423444	−	0.905922i	$-0.639179\pi$
$199$	−6.67399e6			−0.846889			−0.423444	+	0.905922i	$0.639179\pi$
$200$		−	1.27905e6i		−	0.159882i
$201$		−	4.71855e6i		−	0.581060i
$202$	5.08745e6			0.617228
$203$	−6.48559e6			−0.775285
$204$	446245.			0.0525633
$205$	−8.17475e6			−0.948884
$206$	3.48670e6			0.398853
$207$			2.81157e6i			0.316985i
$208$			1.99395e6i			0.221577i
$209$			4.97392e6i			0.544829i
$210$		−	4.12373e6i		−	0.445279i
$211$			3.99485e6i			0.425258i	0.977133	+	0.212629i	$0.0682026\pi$
$211$			3.99485e6i			0.425258i	−0.977133	+	0.212629i	$0.931797\pi$
$212$	−230692.			−0.0242117
$213$	8.29761e6			0.858647
$214$		−	1.02159e7i		−	1.04240i
$215$		−	138371.i		−	0.0139229i
$216$		−	685700.i		−	0.0680414i
$217$		−	1.70435e7i		−	1.66794i
$218$	−3.19135e6			−0.308038
$219$			3.21985e6i			0.306551i
$220$			7.40094e6i			0.695054i
$221$			1.74195e6i			0.161383i
$222$	3.89433e6			0.355938
$223$	−1.38972e7			−1.25317			−0.626587	−	0.779351i	$-0.715549\pi$
$223$	−1.38972e7			−1.25317			−0.626587	+	0.779351i	$0.715549\pi$
$224$		−	2.92800e6i		−	0.260512i
$225$	−1.71700e6			−0.150738
$226$	−2.34599e6			−0.203236
$227$			5.56143e6i			0.475454i	0.971332	+	0.237727i	$0.0764024\pi$
$227$			5.56143e6i			0.475454i	−0.971332	+	0.237727i	$0.923598\pi$
$228$	992501.			0.0837387
$229$		−	1.61185e7i		−	1.34221i	−0.741364	−	0.671103i	$-0.765821\pi$
$229$		−	1.61185e7i		−	1.34221i	0.741364	−	0.671103i	$-0.234179\pi$
$230$	−6.05527e6			−0.497680
$231$		−	1.96979e7i		−	1.59803i
$232$		−	2.32262e6i		−	0.186000i
$233$			2.01514e7i			1.59308i	0.604585	+	0.796540i	$0.293339\pi$
$233$			2.01514e7i			1.59308i	−0.604585	+	0.796540i	$0.706661\pi$
$234$	2.67667e6			0.208905
$235$			71677.2i			0.00552303i
$236$	5.91447e6	−	2.86565e6i	0.449966	−	0.218015i
$237$	1.36450e7			1.02501
$238$		−	2.55795e6i		−	0.189741i
$239$	2.40887e7			1.76449			0.882246	−	0.470789i	$-0.156031\pi$
$239$	2.40887e7			1.76449			0.882246	+	0.470789i	$0.156031\pi$
$240$	1.47679e6			0.106828
$241$	1.70570e7			1.21857			0.609286	−	0.792951i	$-0.291456\pi$
$241$	1.70570e7			1.21857			0.609286	+	0.792951i	$0.291456\pi$
$242$			2.53308e7i			1.78732i
$243$	−920483.			−0.0641500
$244$		−	1.45668e6i		−	0.100275i
$245$	−1.27535e7			−0.867224
$246$			7.79179e6i			0.523398i
$247$			3.87429e6i			0.257099i
$248$	6.10362e6			0.400159
$249$		−	2.59203e6i		−	0.167897i
$250$		−	1.18752e7i		−	0.760013i
$251$	−1.40114e7			−0.886053			−0.443027	−	0.896508i	$-0.646095\pi$
$251$	−1.40114e7			−0.886053			−0.443027	+	0.896508i	$0.646095\pi$
$252$	−3.93054e6			−0.245613
$253$	−2.89244e7			−1.78609
$254$			1.87263e7i			1.14275i
$255$	1.29015e6			0.0778070
$256$	1.04858e6			0.0625000
$257$	−1.42333e7			−0.838504			−0.419252	−	0.907870i	$-0.637708\pi$
$257$	−1.42333e7			−0.838504			−0.419252	+	0.907870i	$0.637708\pi$
$258$	−131889.			−0.00767979
$259$		−	2.23230e7i		−	1.28485i
$260$			5.76474e6i			0.327989i
$261$	−3.11788e6			−0.175363
$262$	455592.			0.0253321
$263$	−3.06767e7			−1.68633			−0.843164	−	0.537656i	$-0.819310\pi$
$263$	−3.06767e7			−1.68633			−0.843164	+	0.537656i	$0.819310\pi$
$264$	7.05422e6			0.383387
$265$	−666958.			−0.0358394
$266$		−	5.68917e6i		−	0.302276i
$267$		−	1.12416e7i		−	0.590601i
$268$		−	9.68625e6i		−	0.503212i
$269$			3.27868e7i			1.68439i	0.539175	+	0.842194i	$0.318736\pi$
$269$			3.27868e7i			1.68439i	−0.539175	+	0.842194i	$0.681264\pi$
$270$		−	1.98244e6i		−	0.100718i
$271$	−3.73596e6			−0.187713			−0.0938566	−	0.995586i	$-0.529920\pi$
$271$	−3.73596e6			−0.187713			−0.0938566	+	0.995586i	$0.529920\pi$
$272$	916052.			0.0455212
$273$		−	1.53431e7i		−	0.754095i
$274$		−	359425.i		−	0.0174726i
$275$		−	1.76638e7i		−	0.849349i
$276$			5.77160e6i			0.274517i
$277$	2.26107e7			1.06384			0.531918	−	0.846796i	$-0.321471\pi$
$277$	2.26107e7			1.06384			0.531918	+	0.846796i	$0.321471\pi$
$278$		−	1.60722e6i		−	0.0748070i
$279$		−	8.19348e6i		−	0.377273i
$280$		−	8.46520e6i		−	0.385623i
$281$	−1.21090e7			−0.545742			−0.272871	−	0.962051i	$-0.587973\pi$
$281$	−1.21090e7			−0.545742			−0.272871	+	0.962051i	$0.587973\pi$
$282$	68319.3			0.00304647
$283$		−	1.55712e7i		−	0.687008i	−0.939151	−	0.343504i	$-0.888386\pi$
$283$		−	1.55712e7i		−	0.687008i	0.939151	−	0.343504i	$-0.111614\pi$
$284$	1.70333e7			0.743610
$285$	2.86944e6			0.123954
$286$			2.75366e7i			1.17710i
$287$	4.46638e7			1.88934
$288$		−	1.40761e6i		−	0.0589256i
$289$	−2.33373e7			−0.966845
$290$		−	6.71496e6i		−	0.275328i
$291$			1.69082e7i			0.686150i
$292$			6.60971e6i			0.265481i
$293$	−4.80370e7			−1.90974			−0.954868	−	0.297031i	$-0.904003\pi$
$293$	−4.80370e7			−1.90974			−0.954868	+	0.297031i	$0.904003\pi$
$294$			1.21560e7i			0.478355i
$295$	1.70994e7	−	8.28493e6i	0.666063	−	0.322718i
$296$	7.99429e6			0.308251
$297$		−	9.46957e6i		−	0.361461i
$298$	−3.50163e7			−1.32319
$299$	−2.25298e7			−0.842837
$300$	−3.52465e6			−0.130543
$301$			756008.i			0.0277222i
$302$	1.93066e7			0.700945
$303$		−	1.40194e7i		−	0.503965i
$304$	2.03741e6			0.0725199
$305$		−	4.21143e6i		−	0.148433i
$306$		−	1.22971e6i		−	0.0429178i
$307$	1.36841e7			0.472934			0.236467	−	0.971639i	$-0.424010\pi$
$307$	1.36841e7			0.472934			0.236467	+	0.971639i	$0.424010\pi$
$308$		−	4.04359e7i		−	1.38393i
$309$		−	9.60823e6i		−	0.325663i
$310$	1.76463e7			0.592336
$311$	−3.24244e7			−1.07793			−0.538965	−	0.842328i	$-0.681184\pi$
$311$	−3.24244e7			−1.07793			−0.538965	+	0.842328i	$0.681184\pi$
$312$	5.49468e6			0.180917
$313$		−	1.60654e7i		−	0.523912i	−0.965080	−	0.261956i	$-0.915633\pi$
$313$		−	1.60654e7i		−	0.523912i	0.965080	−	0.261956i	$-0.0843675\pi$
$314$	2.56208e7			0.827567
$315$	−1.13637e7			−0.363569
$316$	2.80105e7			0.887688
$317$	−2.46535e7			−0.773928			−0.386964	−	0.922095i	$-0.626476\pi$
$317$	−2.46535e7			−0.773928			−0.386964	+	0.922095i	$0.626476\pi$
$318$			635713.i			0.0197688i
$319$		−	3.20755e7i		−	0.988102i
$320$	3.03156e6			0.0925158
$321$	−2.81517e7			−0.851118
$322$	3.30837e7			0.990939
$323$	1.77991e6			0.0528191
$324$	−1.88957e6			−0.0555556
$325$		−	1.37587e7i		−	0.400800i
$326$			2.01718e7i			0.582225i
$327$			8.79432e6i			0.251512i
$328$			1.59950e7i			0.453276i
$329$		−	391617.i		−	0.0109970i
$330$	2.03946e7			0.567509
$331$	1.20391e6			0.0331979			0.0165990	−	0.999862i	$-0.494716\pi$
$331$	1.20391e6			0.0331979			0.0165990	+	0.999862i	$0.494716\pi$
$332$		−	5.32093e6i		−	0.145403i
$333$		−	1.07315e7i		−	0.290622i
$334$		−	2.16703e7i		−	0.581602i
$335$		−	2.80041e7i		−	0.744881i
$336$	−8.06863e6			−0.212707
$337$		−	5.64806e7i		−	1.47574i	−0.674943	−	0.737870i	$-0.735832\pi$
$337$		−	5.64806e7i		−	1.47574i	0.674943	−	0.737870i	$-0.264168\pi$
$338$		−	5.85574e6i		−	0.151646i
$339$			6.46478e6i			0.165941i
$340$	2.64842e6			0.0673828
$341$	8.42914e7			2.12579
$342$		−	2.73501e6i		−	0.0683724i
$343$	1.02122e7			0.253067
$344$	−270742.			−0.00665089
$345$			1.66864e7i			0.406354i
$346$	4.20751e7			1.01577
$347$			2.51187e7i			0.601185i	0.953753	+	0.300593i	$0.0971845\pi$
$347$			2.51187e7i			0.601185i	−0.953753	+	0.300593i	$0.902816\pi$
$348$	−6.40039e6			−0.151869
$349$		−	2.06837e7i		−	0.486577i	−0.969954	−	0.243288i	$-0.921774\pi$
$349$		−	2.06837e7i		−	0.486577i	0.969954	−	0.243288i	$-0.0782262\pi$
$350$			2.02039e7i			0.471228i
$351$		−	7.37605e6i		−	0.170570i
$352$	1.44809e7			0.332023
$353$		−	4.58427e7i		−	1.04219i	−0.853499	−	0.521094i	$-0.825524\pi$
$353$		−	4.58427e7i		−	1.04219i	0.853499	−	0.521094i	$-0.174476\pi$
$354$	−7.89680e6	−	1.62984e7i	−0.178009	−	0.367396i
$355$	4.92454e7			1.10073
$356$		−	2.30768e7i		−	0.511476i
$357$	−7.04888e6			−0.154923
$358$	−5.67805e6			−0.123751
$359$	−2.01976e7			−0.436533			−0.218266	−	0.975889i	$-0.570040\pi$
$359$	−2.01976e7			−0.436533			−0.218266	+	0.975889i	$0.570040\pi$
$360$		−	4.06956e6i		−	0.0872247i
$361$	−4.30872e7			−0.915854
$362$		−	1.85630e6i		−	0.0391312i
$363$	6.98034e7			1.45934
$364$		−	3.14964e7i		−	0.653065i
$365$			1.91094e7i			0.392979i
$366$	−4.01414e6			−0.0818745
$367$			3.42332e7i			0.692546i	0.938134	+	0.346273i	$0.112553\pi$
$367$			3.42332e7i			0.692546i	−0.938134	+	0.346273i	$0.887447\pi$
$368$			1.18479e7i			0.237739i
$369$	2.14716e7			0.427352
$370$	2.31124e7			0.456290
$371$	3.64401e6			0.0713605
$372$		−	1.68196e7i		−	0.326728i
$373$	−4.79762e6			−0.0924484			−0.0462242	−	0.998931i	$-0.514719\pi$
$373$	−4.79762e6			−0.0924484			−0.0462242	+	0.998931i	$0.514719\pi$
$374$	1.26508e7			0.241825
$375$	−3.27242e7			−0.620548
$376$	140246.			0.00263832
$377$		−	2.49843e7i		−	0.466276i
$378$			1.08313e7i			0.200542i
$379$	1.10489e7			0.202956			0.101478	−	0.994838i	$-0.467643\pi$
$379$	1.10489e7			0.202956			0.101478	+	0.994838i	$0.467643\pi$
$380$	5.89038e6			0.107348
$381$	5.16036e7			0.933050
$382$	−7.37923e7			−1.32380
$383$	−2.59500e7			−0.461892			−0.230946	−	0.972967i	$-0.574182\pi$
$383$	−2.59500e7			−0.461892			−0.230946	+	0.972967i	$0.574182\pi$
$384$		−	2.88954e6i		−	0.0510310i
$385$		−	1.16905e8i		−	2.04857i
$386$			9.26451e6i			0.161087i
$387$			363443.i			0.00627052i
$388$			3.47092e7i			0.594224i
$389$	−7.45960e7			−1.26726			−0.633632	−	0.773635i	$-0.718437\pi$
$389$	−7.45960e7			−1.26726			−0.633632	+	0.773635i	$0.718437\pi$
$390$	1.58858e7			0.267802
$391$			1.03506e7i			0.173154i
$392$			2.49539e7i			0.414267i
$393$		−	1.25546e6i		−	0.0206836i
$394$		−	2.99333e7i		−	0.489402i
$395$	8.09818e7			1.31400
$396$		−	1.94391e7i		−	0.313034i
$397$			9.13444e7i			1.45986i	0.683524	+	0.729928i	$0.260447\pi$
$397$			9.13444e7i			1.45986i	−0.683524	+	0.729928i	$0.739553\pi$
$398$			3.77538e7i			0.598841i
$399$	−1.56775e7			−0.246808
$400$	−7.23542e6			−0.113053
$401$		−	9.76307e6i		−	0.151410i	−0.997130	−	0.0757048i	$-0.975879\pi$
$401$		−	9.76307e6i		−	0.151410i	0.997130	−	0.0757048i	$-0.0241207\pi$
$402$	−2.66922e7			−0.410871
$403$	6.56563e7			1.00314
$404$		−	2.87789e7i		−	0.436446i
$405$	−5.46296e6			−0.0822362
$406$			3.66880e7i			0.548209i
$407$	1.10402e8			1.63754
$408$		−	2.52434e6i		−	0.0371679i
$409$		−	7.68708e7i		−	1.12355i	−0.827291	−	0.561773i	$-0.810119\pi$
$409$		−	7.68708e7i		−	1.12355i	0.827291	−	0.561773i	$-0.189881\pi$
$410$			4.62434e7i			0.670962i
$411$	−990460.			−0.0142663
$412$		−	1.97238e7i		−	0.282032i
$413$	−9.34248e7	+	4.52657e7i	−1.32621	+	0.642569i
$414$	1.59047e7			0.224142
$415$		−	1.53834e7i		−	0.215233i
$416$	1.12795e7			0.156678
$417$	−4.42899e6			−0.0610796
$418$	2.81367e7			0.385252
$419$			6.95728e7i			0.945795i	0.881117	+	0.472898i	$0.156792\pi$
$419$			6.95728e7i			0.945795i	−0.881117	+	0.472898i	$0.843208\pi$
$420$	−2.33273e7			−0.314860
$421$		−	9.15314e7i		−	1.22666i	−0.789827	−	0.613329i	$-0.789830\pi$
$421$		−	9.15314e7i		−	1.22666i	0.789827	−	0.613329i	$-0.210170\pi$
$422$	2.25983e7			0.300703
$423$		−	188266.i		−	0.00248743i
$424$			1.30499e6i			0.0171203i
$425$	−6.32097e6			−0.0823412
$426$		−	4.69384e7i		−	0.607155i
$427$			2.30097e7i			0.295547i
$428$	−5.77899e7			−0.737090
$429$	7.58819e7			0.961095
$430$	−782746.			−0.00984499
$431$			6.32748e7i			0.790313i	0.918614	+	0.395157i	$0.129310\pi$
$431$			6.32748e7i			0.790313i	−0.918614	+	0.395157i	$0.870690\pi$
$432$	−3.87891e6			−0.0481125
$433$	−1.28784e8			−1.58635			−0.793175	−	0.608994i	$-0.791573\pi$
$433$	−1.28784e8			−1.58635			−0.793175	+	0.608994i	$0.791573\pi$
$434$	−9.64126e7			−1.17941
$435$	−1.85043e7			−0.224804
$436$			1.80530e7i			0.217816i
$437$			2.30208e7i			0.275852i
$438$	1.82142e7			0.216764
$439$	2.58275e7			0.305273			0.152637	−	0.988282i	$-0.451224\pi$
$439$	2.58275e7			0.305273			0.152637	+	0.988282i	$0.451224\pi$
$440$	4.18660e7			0.491477
$441$	3.34981e7			0.390575
$442$	9.85393e6			0.114115
$443$			3.15231e7i			0.362591i	0.983429	+	0.181296i	$0.0580291\pi$
$443$			3.15231e7i			0.362591i	−0.983429	+	0.181296i	$0.941971\pi$
$444$		−	2.20297e7i		−	0.251686i
$445$		−	6.67176e7i		−	0.757113i
$446$			7.86142e7i			0.886128i
$447$			9.64935e7i			1.08038i
$448$	−1.65633e7			−0.184210
$449$	1.45251e8			1.60465			0.802325	−	0.596887i	$-0.203596\pi$
$449$	1.45251e8			1.60465			0.802325	+	0.596887i	$0.203596\pi$
$450$			9.71281e6i			0.106588i
$451$			2.20892e8i			2.40797i
$452$			1.32709e7i			0.143709i
$453$		−	5.32026e7i		−	0.572319i
$454$	3.14602e7			0.336197
$455$		−	9.10597e7i		−	0.966701i
$456$		−	5.61443e6i		−	0.0592122i
$457$		−	3.92708e7i		−	0.411454i	−0.978609	−	0.205727i	$-0.934044\pi$
$457$		−	3.92708e7i		−	0.411454i	0.978609	−	0.205727i	$-0.0659559\pi$
$458$	−9.11802e7			−0.949082
$459$	−3.38867e6			−0.0350422
$460$			3.42538e7i			0.351913i
$461$	−7.08498e7			−0.723162			−0.361581	−	0.932341i	$-0.617763\pi$
$461$	−7.08498e7			−0.723162			−0.361581	+	0.932341i	$0.617763\pi$
$462$	−1.11428e8			−1.12998
$463$			1.17049e8i			1.17930i	0.807659	+	0.589650i	$0.200734\pi$
$463$			1.17049e8i			1.17930i	−0.807659	+	0.589650i	$0.799266\pi$
$464$	−1.31387e7			−0.131522
$465$		−	4.86274e7i		−	0.483640i
$466$	1.13994e8			1.12648
$467$			1.43180e7i			0.140583i	0.997526	+	0.0702915i	$0.0223930\pi$
$467$			1.43180e7i			0.140583i	−0.997526	+	0.0702915i	$0.977607\pi$
$468$		−	1.51416e7i		−	0.147718i
$469$			1.53004e8i			1.48315i
$470$	405468.			0.00390537
$471$		−	7.06025e7i		−	0.675706i
$472$	−1.62106e7	−	3.34573e7i	−0.154160	−	0.318174i
$473$	−3.73896e6			−0.0353320
$474$		−	7.71880e7i		−	0.724794i
$475$	−1.40586e7			−0.131178
$476$	−1.44699e7			−0.134167
$477$	1.75182e6			0.0161411
$478$		−	1.36266e8i		−	1.24768i
$479$	5.83797e7			0.531197			0.265598	−	0.964084i	$-0.414430\pi$
$479$	5.83797e7			0.531197			0.265598	+	0.964084i	$0.414430\pi$
$480$		−	8.35399e6i		−	0.0755388i
$481$	8.59942e7			0.772741
$482$		−	9.64888e7i		−	0.861660i
$483$		−	9.11681e7i		−	0.809098i
$484$	1.43292e8			1.26383
$485$			1.00348e8i			0.879601i
$486$			5.20704e6i			0.0453609i
$487$	1.40174e8			1.21361			0.606807	−	0.794849i	$-0.292450\pi$
$487$	1.40174e8			1.21361			0.606807	+	0.794849i	$0.292450\pi$
$488$	−8.24022e6			−0.0709054
$489$	5.55868e7			0.475385
$490$			7.21447e7i			0.613220i
$491$	−8.71788e7			−0.736490			−0.368245	−	0.929729i	$-0.620041\pi$
$491$	−8.71788e7			−0.736490			−0.368245	+	0.929729i	$0.620041\pi$
$492$	4.40770e7			0.370098
$493$	−1.14782e7			−0.0957928
$494$	2.19163e7			0.181797
$495$		−	5.62009e7i		−	0.463369i
$496$		−	3.45273e7i		−	0.282955i
$497$	−2.69058e8			−2.19168
$498$	−1.46628e7			−0.118721
$499$	5.81686e7			0.468152			0.234076	−	0.972218i	$-0.424794\pi$
$499$	5.81686e7			0.468152			0.234076	+	0.972218i	$0.424794\pi$
$500$	−6.71763e7			−0.537410
$501$	−5.97163e7			−0.474876
$502$			7.92603e7i			0.626534i
$503$			2.45531e8i			1.92931i	0.263513	+	0.964656i	$0.415119\pi$
$503$			2.45531e8i			1.92931i	−0.263513	+	0.964656i	$0.584881\pi$
$504$			2.22345e7i			0.173675i
$505$		−	8.32033e7i		−	0.646050i
$506$			1.63621e8i			1.26295i
$507$	−1.61365e7			−0.123819
$508$	1.05932e8			0.808045
$509$			5.42962e7i			0.411734i	0.978580	+	0.205867i	$0.0660014\pi$
$509$			5.42962e7i			0.411734i	−0.978580	+	0.205867i	$0.933999\pi$
$510$		−	7.29817e6i		−	0.0550179i
$511$		−	1.04407e8i		−	0.782467i
$512$		−	5.93164e6i		−	0.0441942i
$513$	−7.53680e6			−0.0558258
$514$			8.05155e7i			0.592912i
$515$		−	5.70237e7i		−	0.417478i
$516$			746076.i			0.00543043i
$517$	1.93681e6			0.0140157
$518$	−1.26278e8			−0.908526
$519$		−	1.15945e8i		−	0.829375i
$520$	3.26103e7			0.231924
$521$	−2.40969e8			−1.70392			−0.851958	−	0.523610i	$-0.824585\pi$
$521$	−2.40969e8			−1.70392			−0.851958	+	0.523610i	$0.824585\pi$
$522$			1.76374e7i			0.124000i
$523$	9.01311e7			0.630042			0.315021	−	0.949085i	$-0.397988\pi$
$523$	9.01311e7			0.630042			0.315021	+	0.949085i	$0.397988\pi$
$524$		−	2.57722e6i		−	0.0179125i
$525$	5.56754e7			0.384756
$526$			1.73534e8i			1.19241i
$527$		−	3.01636e7i		−	0.206087i
$528$		−	3.99047e7i		−	0.271095i
$529$	1.41650e7			0.0956863
$530$			3.77289e6i			0.0253423i
$531$	−4.49130e7	+	2.17610e7i	−0.299977	+	0.145344i
$532$	−3.21828e7			−0.213742
$533$			1.72057e8i			1.13630i
$534$	−6.35921e7			−0.417618
$535$	−1.67077e8			−1.09108
$536$	−5.47937e7			−0.355825
$537$			1.56469e7i			0.101043i
$538$	1.85470e8			1.19104
$539$			3.44615e8i			2.20074i
$540$	−1.12144e7			−0.0712187
$541$			2.07502e8i			1.31048i	0.755420	+	0.655241i	$0.227433\pi$
$541$			2.07502e8i			1.31048i	−0.755420	+	0.655241i	$0.772567\pi$
$542$			2.11338e7i			0.132733i
$543$	−5.11537e6			−0.0319505
$544$		−	5.18198e6i		−	0.0321883i
$545$			5.21933e7i			0.322423i
$546$	−8.67938e7			−0.533225
$547$	−8.08634e7			−0.494072			−0.247036	−	0.969006i	$-0.579457\pi$
$547$	−8.08634e7			−0.494072			−0.247036	+	0.969006i	$0.579457\pi$
$548$	−2.03322e6			−0.0123550
$549$			1.10617e7i			0.0668503i
$550$	−9.99216e7			−0.600581
$551$	−2.55288e7			−0.152608
$552$	3.26491e7			0.194113
$553$	−4.42454e8			−2.61633
$554$		−	1.27905e8i		−	0.752246i
$555$		−	6.36904e7i		−	0.372559i
$556$	−9.09183e6			−0.0528965
$557$	−3.25045e8			−1.88095			−0.940476	−	0.339860i	$-0.889620\pi$
$557$	−3.25045e8			−1.88095			−0.940476	+	0.339860i	$0.889620\pi$
$558$	−4.63493e7			−0.266772
$559$	−2.91235e6			−0.0166728
$560$	−4.78864e7			−0.272677
$561$		−	3.48614e7i		−	0.197449i
$562$			6.84986e7i			0.385898i
$563$			3.12840e7i			0.175306i	0.996151	+	0.0876530i	$0.0279367\pi$
$563$			3.12840e7i			0.175306i	−0.996151	+	0.0876530i	$0.972063\pi$
$564$		−	386473.i		−	0.00215418i
$565$			3.83677e7i			0.212726i
$566$	−8.80839e7			−0.485788
$567$	2.98476e7			0.163742
$568$		−	9.63552e7i		−	0.525811i
$569$		−	1.37099e8i		−	0.744214i	−0.928190	−	0.372107i	$-0.878635\pi$
$569$		−	1.37099e8i		−	0.744214i	0.928190	−	0.372107i	$-0.121365\pi$
$570$		−	1.62320e7i		−	0.0876490i
$571$		−	2.65047e8i		−	1.42369i	−0.702338	−	0.711843i	$-0.747861\pi$
$571$		−	2.65047e8i		−	1.42369i	0.702338	−	0.711843i	$-0.252139\pi$
$572$	1.55770e8			0.832333
$573$			2.03348e8i			1.08088i
$574$		−	2.52657e8i		−	1.33596i
$575$		−	8.17535e7i		−	0.430034i
$576$	−7.96262e6			−0.0416667
$577$	−1.46699e8			−0.763659			−0.381829	−	0.924233i	$-0.624706\pi$
$577$	−1.46699e8			−0.763659			−0.381829	+	0.924233i	$0.624706\pi$
$578$			1.32016e8i			0.683663i
$579$	2.55300e7			0.131527
$580$	−3.79856e7			−0.194686
$581$			8.40493e7i			0.428554i
$582$	9.56474e7			0.485182
$583$			1.80220e7i			0.0909491i
$584$	3.73902e7			0.187724
$585$		−	4.37760e7i		−	0.218660i
$586$			2.71738e8i			1.35039i
$587$			1.14363e7i			0.0565422i	0.999600	+	0.0282711i	$0.00900018\pi$
$587$			1.14363e7i			0.0565422i	−0.999600	+	0.0282711i	$0.991000\pi$
$588$	6.87649e7			0.338248
$589$		−	6.70873e7i		−	0.328318i
$590$	−4.68666e7	−	9.67289e7i	−0.228196	−	0.470978i
$591$	−8.24865e7			−0.399595
$592$		−	4.52226e7i		−	0.217967i
$593$	−9.11841e7			−0.437275			−0.218638	−	0.975806i	$-0.570161\pi$
$593$	−9.11841e7			−0.437275			−0.218638	+	0.975806i	$0.570161\pi$
$594$	−5.35680e7			−0.255591
$595$	−4.18343e7			−0.198601
$596$			1.98082e8i			0.935635i
$597$	1.04037e8			0.488951
$598$			1.27448e8i			0.595976i
$599$	1.36332e8			0.634333			0.317166	−	0.948370i	$-0.397269\pi$
$599$	1.36332e8			0.634333			0.317166	+	0.948370i	$0.397269\pi$
$600$			1.99385e7i			0.0923077i
$601$		−	1.13531e8i		−	0.522986i	−0.965205	−	0.261493i	$-0.915785\pi$
$601$		−	1.13531e8i		−	0.522986i	0.965205	−	0.261493i	$-0.0842148\pi$
$602$	4.27663e6			0.0196025
$603$			7.35550e7i			0.335475i
$604$		−	1.09214e8i		−	0.495643i
$605$	4.14275e8			1.87078
$606$	−7.93054e7			−0.356357
$607$	−1.70023e8			−0.760225			−0.380113	−	0.924940i	$-0.624115\pi$
$607$	−1.70023e8			−0.760225			−0.380113	+	0.924940i	$0.624115\pi$
$608$		−	1.15253e7i		−	0.0512793i
$609$	1.01100e8			0.447611
$610$	−2.38235e7			−0.104958
$611$	1.50862e6			0.00661388
$612$	−6.95627e6			−0.0303475
$613$			5.64840e7i			0.245213i	0.992455	+	0.122607i	$0.0391254\pi$
$613$			5.64840e7i			0.245213i	−0.992455	+	0.122607i	$0.960875\pi$
$614$		−	7.74089e7i		−	0.334415i
$615$	1.27432e8			0.547838
$616$	−2.28740e8			−0.978589
$617$	4.48998e8			1.91157			0.955783	−	0.294074i	$-0.0950112\pi$
$617$	4.48998e8			1.91157			0.955783	+	0.294074i	$0.0950112\pi$
$618$	−5.43523e7			−0.230278
$619$	−1.78041e8			−0.750670			−0.375335	−	0.926889i	$-0.622472\pi$
$619$	−1.78041e8			−0.750670			−0.375335	+	0.926889i	$0.622472\pi$
$620$		−	9.98224e7i		−	0.418845i
$621$		−	4.38281e7i		−	0.183011i
$622$			1.83420e8i			0.762211i
$623$			3.64520e8i			1.50750i
$624$		−	3.10826e7i		−	0.127927i
$625$	−8.38109e7			−0.343290
$626$	−9.08795e7			−0.370461
$627$		−	7.75357e7i		−	0.314557i
$628$		−	1.44933e8i		−	0.585178i
$629$		−	3.95071e7i		−	0.158754i
$630$			6.42826e7i			0.257082i
$631$	4.68824e8			1.86604			0.933022	−	0.359819i	$-0.117162\pi$
$631$	4.68824e8			1.86604			0.933022	+	0.359819i	$0.117162\pi$
$632$		−	1.58452e8i		−	0.627690i
$633$		−	6.22735e7i		−	0.245523i
$634$			1.39461e8i			0.547249i
$635$	3.06261e8			1.19611
$636$	3.59614e6			0.0139786
$637$			2.68428e8i			1.03851i
$638$	−1.81447e8			−0.698694
$639$	−1.29347e8			−0.495740
$640$		−	1.71491e7i		−	0.0654185i
$641$	6.16366e7			0.234026			0.117013	−	0.993130i	$-0.462668\pi$
$641$	6.16366e7			0.234026			0.117013	+	0.993130i	$0.462668\pi$
$642$			1.59250e8i			0.601831i
$643$	5.18490e8			1.95033			0.975163	−	0.221487i	$-0.0710909\pi$
$643$	5.18490e8			1.95033			0.975163	+	0.221487i	$0.0710909\pi$
$644$		−	1.87150e8i		−	0.700700i
$645$			2.15699e6i			0.00803840i
$646$		−	1.00687e7i		−	0.0373487i
$647$	−2.09484e8			−0.773459			−0.386730	−	0.922193i	$-0.626395\pi$
$647$	−2.09484e8			−0.773459			−0.386730	+	0.922193i	$0.626395\pi$
$648$			1.06890e7i			0.0392837i
$649$	−2.23869e8	−	4.62047e8i	−0.818955	−	1.69026i
$650$	−7.78310e7			−0.283408
$651$			2.65682e8i			0.962984i
$652$	1.14109e8			0.411695
$653$	1.80486e8			0.648191			0.324095	−	0.946024i	$-0.394940\pi$
$653$	1.80486e8			0.648191			0.324095	+	0.946024i	$0.394940\pi$
$654$	4.97482e7			0.177846
$655$		−	7.45103e6i		−	0.0265151i
$656$	9.04813e7			0.320514
$657$		−	5.01925e7i		−	0.176987i
$658$	−2.21532e6			−0.00777606
$659$			2.05293e8i			0.717330i	0.933466	+	0.358665i	$0.116768\pi$
$659$			2.05293e8i			0.717330i	−0.933466	+	0.358665i	$0.883232\pi$
$660$		−	1.15369e8i		−	0.401290i
$661$	2.53384e8			0.877354			0.438677	−	0.898645i	$-0.355447\pi$
$661$	2.53384e8			0.877354			0.438677	+	0.898645i	$0.355447\pi$
$662$		−	6.81036e6i		−	0.0234745i
$663$		−	2.71542e7i		−	0.0931745i
$664$	−3.00997e7			−0.102815
$665$	−9.30443e7			−0.316392
$666$	−6.07067e7			−0.205501
$667$		−	1.48455e8i		−	0.500286i
$668$	−1.22586e8			−0.411254
$669$	2.16635e8			0.723521
$670$	−1.58415e8			−0.526711
$671$	−1.13798e8			−0.376676
$672$			4.56430e7i			0.150407i
$673$			5.20083e8i			1.70619i	0.521755	+	0.853095i	$0.325277\pi$
$673$			5.20083e8i			1.70619i	−0.521755	+	0.853095i	$0.674723\pi$
$674$	−3.19503e8			−1.04351
$675$	2.67653e7			0.0870285
$676$	−3.31251e7			−0.107230
$677$	1.00165e8			0.322814			0.161407	−	0.986888i	$-0.448397\pi$
$677$	1.00165e8			0.322814			0.161407	+	0.986888i	$0.448397\pi$
$678$	3.65703e7			0.117338
$679$		−	5.48266e8i		−	1.75139i
$680$		−	1.49817e7i		−	0.0476469i
$681$		−	8.66941e7i		−	0.274504i
$682$		−	4.76824e8i		−	1.50316i
$683$		−	3.19388e8i		−	1.00244i	−0.865321	−	0.501218i	$-0.832885\pi$
$683$		−	3.19388e8i		−	1.00244i	0.865321	−	0.501218i	$-0.167115\pi$
$684$	−1.54716e7			−0.0483466
$685$	−5.87827e6			−0.0182885
$686$		−	5.77687e7i		−	0.178945i
$687$			2.51263e8i			0.774923i
$688$			1.53155e6i			0.00470289i
$689$			1.40377e7i			0.0429180i
$690$	9.43924e7			0.287336
$691$		−	3.18204e8i		−	0.964433i	−0.876052	−	0.482217i	$-0.839832\pi$
$691$		−	3.18204e8i		−	0.964433i	0.876052	−	0.482217i	$-0.160168\pi$
$692$		−	2.38013e8i		−	0.718260i
$693$			3.07060e8i			0.922622i
$694$	1.42093e8			0.425102
$695$	−2.62856e7			−0.0783002
$696$			3.62060e7i			0.107387i
$697$	7.90459e7			0.233443
$698$	−1.17005e8			−0.344062
$699$		−	3.14130e8i		−	0.919766i
$700$	1.14290e8			0.333208
$701$			2.47527e8i			0.718569i	0.933228	+	0.359285i	$0.116979\pi$
$701$			2.47527e8i			0.718569i	−0.933228	+	0.359285i	$0.883021\pi$
$702$	−4.17252e7			−0.120611
$703$		−	8.78684e7i		−	0.252911i
$704$		−	8.19164e7i		−	0.234776i
$705$		−	1.11734e6i		−	0.00318872i
$706$	−2.59325e8			−0.736938
$707$			4.54591e8i			1.28636i
$708$	−9.21974e7	+	4.46711e7i	−0.259788	+	0.125871i
$709$	1.78904e7			0.0501975			0.0250987	−	0.999685i	$-0.492010\pi$
$709$	1.78904e7			0.0501975			0.0250987	+	0.999685i	$0.492010\pi$
$710$		−	2.78574e8i		−	0.778334i
$711$	−2.12705e8			−0.591792
$712$	−1.30542e8			−0.361668
$713$	3.90126e8			1.07631
$714$			3.98745e7i			0.109547i
$715$	4.50351e8			1.23206
$716$			3.21199e7i			0.0875055i
$717$	−3.75506e8			−1.01873
$718$			1.14255e8i			0.308675i
$719$			3.47160e8i			0.933991i	0.884260	+	0.466995i	$0.154664\pi$
$719$			3.47160e8i			0.933991i	−0.884260	+	0.466995i	$0.845336\pi$
$720$	−2.30209e7			−0.0616772
$721$			3.11556e8i			0.831248i
$722$			2.43738e8i			0.647607i
$723$	−2.65892e8			−0.703542
$724$	−1.05008e7			−0.0276700
$725$	9.06602e7			0.237904
$726$		−	3.94868e8i		−	1.03191i
$727$	2.44699e8			0.636837			0.318419	−	0.947950i	$-0.396848\pi$
$727$	2.44699e8			0.636837			0.318419	+	0.947950i	$0.396848\pi$
$728$	−1.78170e8			−0.461787
$729$	1.43489e7			0.0370370
$730$	1.08099e8			0.277878
$731$			1.33798e6i			0.00342530i
$732$			2.27074e7i			0.0578940i
$733$	5.22414e7			0.132649			0.0663243	−	0.997798i	$-0.478873\pi$
$733$	5.22414e7			0.132649			0.0663243	+	0.997798i	$0.478873\pi$
$734$	1.93652e8			0.489704
$735$	1.98807e8			0.500692
$736$	6.70221e7			0.168107
$737$	−7.56705e8			−1.89027
$738$		−	1.21462e8i		−	0.302184i
$739$			4.82927e8i			1.19660i	0.801273	+	0.598299i	$0.204157\pi$
$739$			4.82927e8i			1.19660i	−0.801273	+	0.598299i	$0.795843\pi$
$740$		−	1.30744e8i		−	0.322646i
$741$		−	6.03942e7i		−	0.148436i
$742$		−	2.06136e7i		−	0.0504595i
$743$	−1.03419e8			−0.252136			−0.126068	−	0.992022i	$-0.540236\pi$
$743$	−1.03419e8			−0.252136			−0.126068	+	0.992022i	$0.540236\pi$
$744$	−9.51460e7			−0.231032
$745$			5.72678e8i			1.38498i
$746$			2.71395e7i			0.0653709i
$747$			4.04058e7i			0.0969353i
$748$		−	7.15635e7i		−	0.170996i
$749$	9.12848e8			2.17247
$750$			1.85116e8i			0.438794i
$751$			3.89130e8i			0.918701i	0.888255	+	0.459351i	$0.151918\pi$
$751$			3.89130e8i			0.918701i	−0.888255	+	0.459351i	$0.848082\pi$
$752$		−	793351.i		−	0.00186557i
$753$	2.18416e8			0.511563
$754$	−1.41333e8			−0.329707
$755$		−	3.15752e8i		−	0.733677i
$756$	6.12711e7			0.141805
$757$	2.67012e8			0.615521			0.307761	−	0.951464i	$-0.400420\pi$
$757$	2.67012e8			0.615521			0.307761	+	0.951464i	$0.400420\pi$
$758$		−	6.25020e7i		−	0.143511i
$759$	4.50886e8			1.03120
$760$		−	3.33210e7i		−	0.0759063i
$761$	2.62491e8			0.595608			0.297804	−	0.954627i	$-0.403746\pi$
$761$	2.62491e8			0.595608			0.297804	+	0.954627i	$0.403746\pi$
$762$		−	2.91914e8i		−	0.659766i
$763$		−	2.85165e8i		−	0.641981i
$764$			4.17432e8i			0.936065i
$765$	−2.01114e7			−0.0449219
$766$			1.46795e8i			0.326607i
$767$	−1.74376e8	−	3.59898e8i	−0.386457	−	0.797616i
$768$	−1.63457e7			−0.0360844
$769$			6.77674e7i			0.149019i	0.997220	+	0.0745095i	$0.0237391\pi$
$769$			6.77674e7i			0.149019i	−0.997220	+	0.0745095i	$0.976261\pi$
$770$	−6.61315e8			−1.44856
$771$	2.21875e8			0.484111
$772$	5.24080e7			0.113906
$773$		−	5.17218e8i		−	1.11979i	−0.828565	−	0.559893i	$-0.810842\pi$
$773$		−	5.17218e8i		−	1.11979i	0.828565	−	0.559893i	$-0.189158\pi$
$774$	2.05594e6			0.00443393
$775$			2.38246e8i			0.511824i
$776$	1.96345e8			0.420180
$777$			3.47980e8i			0.741808i
$778$			4.21979e8i			0.896091i
$779$	1.75807e8			0.371899
$780$		−	8.98634e7i		−	0.189365i
$781$		−	1.33067e9i		−	2.79330i
$782$	5.85516e7			0.122439
$783$	4.86029e7			0.101246
$784$	1.41161e8			0.292931
$785$		−	4.19018e8i		−	0.866211i
$786$	−7.10197e6			−0.0146255
$787$	−9.49104e7			−0.194711			−0.0973553	−	0.995250i	$-0.531038\pi$
$787$	−9.49104e7			−0.194711			−0.0973553	+	0.995250i	$0.531038\pi$
$788$	−1.69328e8			−0.346060
$789$	4.78203e8			0.973602
$790$		−	4.58102e8i		−	0.929140i
$791$		−	2.09627e8i		−	0.423563i
$792$	−1.09964e8			−0.221349
$793$	−8.86397e7			−0.177750
$794$	5.16722e8			1.03227
$795$	1.03968e7			0.0206919
$796$	2.13568e8			0.423444
$797$		−	2.49058e8i		−	0.491955i	−0.969276	−	0.245978i	$-0.920891\pi$
$797$		−	2.49058e8i		−	0.491955i	0.969276	−	0.245978i	$-0.0791089\pi$
$798$			8.86855e7i			0.174519i
$799$		−	693084.i		−	0.00135877i
$800$			4.09297e7i			0.0799408i
$801$			1.75239e8i			0.340984i
$802$	−5.52283e7			−0.107063
$803$	5.16361e8			0.997256
$804$			1.50994e8i			0.290530i
$805$		−	5.41072e8i		−	1.03721i
$806$		−	3.71408e8i		−	0.709327i
$807$		−	5.11095e8i		−	0.972481i
$808$	−1.62798e8			−0.308614
$809$			4.06901e8i			0.768499i	0.923229	+	0.384250i	$0.125540\pi$
$809$			4.06901e8i			0.768499i	−0.923229	+	0.384250i	$0.874460\pi$
$810$			3.09032e7i			0.0581498i
$811$			7.06402e8i			1.32431i	0.749367	+	0.662155i	$0.230358\pi$
$811$			7.06402e8i			1.32431i	−0.749367	+	0.662155i	$0.769642\pi$
$812$	2.07539e8			0.387643
$813$	5.82379e7			0.108376
$814$		−	6.24527e8i		−	1.15792i
$815$	3.29902e8			0.609413
$816$	−1.42798e7			−0.0262817
$817$			2.97583e6i			0.00545685i
$818$	−4.34847e8			−0.794468
$819$			2.39176e8i			0.435377i
$820$	2.61592e8			0.474442
$821$		−	4.14466e8i		−	0.748962i	−0.927235	−	0.374481i	$-0.877821\pi$
$821$		−	4.14466e8i		−	0.748962i	0.927235	−	0.374481i	$-0.122179\pi$
$822$			5.60289e6i			0.0100878i
$823$		−	5.64848e8i		−	1.01329i	−0.862156	−	0.506643i	$-0.830886\pi$
$823$		−	5.64848e8i		−	1.01329i	0.862156	−	0.506643i	$-0.169114\pi$
$824$	−1.11575e8			−0.199427
$825$			2.75352e8i			0.490372i
$826$	2.56062e8	+	5.28490e8i	0.454365	+	0.937771i
$827$	9.40153e8			1.66220			0.831098	−	0.556127i	$-0.187713\pi$
$827$	9.40153e8			1.66220			0.831098	+	0.556127i	$0.187713\pi$
$828$		−	8.99703e7i		−	0.158492i
$829$	−9.85614e8			−1.72999			−0.864994	−	0.501782i	$-0.832678\pi$
$829$	−9.85614e8			−1.72999			−0.864994	+	0.501782i	$0.832678\pi$
$830$	−8.70219e7			−0.152193
$831$	−3.52466e8			−0.614206
$832$		−	6.38064e7i		−	0.110788i
$833$	1.23320e8			0.213353
$834$			2.50541e7i			0.0431898i
$835$	−3.54410e8			−0.608760
$836$		−	1.59165e8i		−	0.272414i
$837$			1.27724e8i			0.217819i
$838$	3.93563e8			0.668778
$839$		−	9.73677e7i		−	0.164865i	−0.996597	−	0.0824326i	$-0.973731\pi$
$839$		−	9.73677e7i		−	0.164865i	0.996597	−	0.0824326i	$-0.0262689\pi$
$840$			1.31959e8i			0.222640i
$841$	−4.30194e8			−0.723231
$842$	−5.17780e8			−0.867378
$843$	1.88760e8			0.315084
$844$		−	1.27835e8i		−	0.212629i
$845$	−9.57684e7			−0.158728
$846$	−1.06499e6			−0.00175888
$847$	−2.26345e9			−3.72494
$848$	7.38215e6			0.0121059
$849$			2.42731e8i			0.396644i
$850$			3.57568e7i			0.0582240i
$851$	5.10973e8			0.829105
$852$	−2.65524e8			−0.429323
$853$	1.11405e9			1.79496			0.897482	−	0.441050i	$-0.145394\pi$
$853$	1.11405e9			1.79496			0.897482	+	0.441050i	$0.145394\pi$
$854$	1.30162e8			0.208983
$855$	−4.47301e7			−0.0715651
$856$			3.26909e8i			0.521201i
$857$		−	3.12919e8i		−	0.497152i	−0.968612	−	0.248576i	$-0.920037\pi$
$857$		−	3.12919e8i		−	0.497152i	0.968612	−	0.248576i	$-0.0799625\pi$
$858$		−	4.29253e8i		−	0.679597i
$859$		−	6.89904e8i		−	1.08845i	−0.838939	−	0.544226i	$-0.816823\pi$
$859$		−	6.89904e8i		−	1.08845i	0.838939	−	0.544226i	$-0.183177\pi$
$860$			4.42788e6i			0.00696146i
$861$	−6.96240e8			−1.09081
$862$	3.57937e8			0.558836
$863$			7.37676e8i			1.14771i	0.818956	+	0.573857i	$0.194553\pi$
$863$			7.37676e8i			1.14771i	−0.818956	+	0.573857i	$0.805447\pi$
$864$			2.19424e7i			0.0340207i
$865$		−	6.88122e8i		−	1.06321i
$866$			7.28513e8i			1.12172i
$867$	3.63792e8			0.558208
$868$			5.45392e8i			0.833968i
$869$		−	2.18823e9i		−	3.33452i
$870$			1.04676e8i			0.158960i
$871$	−5.89413e8			−0.892001
$872$	1.02123e8			0.154019
$873$		−	2.63573e8i		−	0.396149i
$874$	1.30225e8			0.195057
$875$	1.06112e9			1.58394
$876$		−	1.03035e8i		−	0.153276i
$877$	5.19147e7			0.0769646			0.0384823	−	0.999259i	$-0.487748\pi$
$877$	5.19147e7			0.0769646			0.0384823	+	0.999259i	$0.487748\pi$
$878$		−	1.46102e8i		−	0.215861i
$879$	7.48823e8			1.10259
$880$		−	2.36830e8i		−	0.347527i
$881$		−	9.01871e8i		−	1.31891i	−0.751742	−	0.659457i	$-0.770786\pi$
$881$		−	9.01871e8i		−	1.31891i	0.751742	−	0.659457i	$-0.229214\pi$
$882$		−	1.89494e8i		−	0.276178i
$883$	3.65770e8			0.531283			0.265642	−	0.964072i	$-0.414416\pi$
$883$	3.65770e8			0.531283			0.265642	+	0.964072i	$0.414416\pi$
$884$		−	5.57423e7i		−	0.0806915i
$885$	−2.66554e8	+	1.29149e8i	−0.384552	+	0.186321i
$886$	1.78321e8			0.256391
$887$			8.93869e8i			1.28086i	0.768015	+	0.640432i	$0.221245\pi$
$887$			8.93869e8i			1.28086i	−0.768015	+	0.640432i	$0.778755\pi$
$888$	−1.24619e8			−0.177969
$889$	−1.67330e9			−2.38159
$890$	−3.77412e8			−0.535360
$891$			1.47616e8i			0.208689i
$892$	4.44709e8			0.626587
$893$		−	1.54150e6i		−	0.00216466i
$894$	5.45850e8			0.763943
$895$			9.28625e7i			0.129530i
$896$			9.36961e7i			0.130256i
$897$	3.51205e8			0.486612
$898$		−	8.21664e8i		−	1.13466i
$899$			4.32629e8i			0.595437i
$900$	5.49439e7			0.0753689
$901$	6.44916e6			0.00881716
$902$	1.24955e9			1.70269
$903$		−	1.17850e7i		−	0.0160054i
$904$	7.50716e7			0.101618
$905$	−3.03592e7			−0.0409585
$906$	−3.00959e8			−0.404691
$907$	−1.33678e9			−1.79158			−0.895791	−	0.444476i	$-0.853390\pi$
$907$	−1.33678e9			−1.79158			−0.895791	+	0.444476i	$0.853390\pi$
$908$		−	1.77966e8i		−	0.237727i
$909$			2.18540e8i			0.290964i
$910$	−5.15112e8			−0.683561
$911$	1.95630e8			0.258750			0.129375	−	0.991596i	$-0.458703\pi$
$911$	1.95630e8			0.258750			0.129375	+	0.991596i	$0.458703\pi$
$912$	−3.17600e7			−0.0418694
$913$	−4.15679e8			−0.546193
$914$	−2.22149e8			−0.290942
$915$			6.56497e7i			0.0856978i
$916$			5.15793e8i			0.671103i
$917$			4.07097e7i			0.0527946i
$918$			1.91692e7i			0.0247786i
$919$			7.40085e7i			0.0953531i	0.998863	+	0.0476766i	$0.0151817\pi$
$919$			7.40085e7i			0.0953531i	−0.998863	+	0.0476766i	$0.984818\pi$
$920$	1.93769e8			0.248840
$921$	−2.13314e8			−0.273049
$922$			4.00787e8i			0.511353i
$923$		−	1.03649e9i		−	1.31813i
$924$			6.30334e8i			0.799014i
$925$			3.12046e8i			0.394270i
$926$	6.62129e8			0.833891
$927$			1.49777e8i			0.188021i
$928$			7.43238e7i			0.0930002i
$929$		−	3.65693e8i		−	0.456109i	−0.973648	−	0.228055i	$-0.926764\pi$
$929$		−	3.65693e8i		−	0.456109i	0.973648	−	0.228055i	$-0.0732365\pi$
$930$	−2.75078e8			−0.341985
$931$	2.74278e8			0.339893
$932$		−	6.44845e8i		−	0.796540i
$933$	5.05446e8			0.622343
$934$	8.09951e7			0.0994072
$935$		−	2.06898e8i		−	0.253118i
$936$	−8.56536e7			−0.104452
$937$			5.98694e8i			0.727756i	0.931447	+	0.363878i	$0.118548\pi$
$937$			5.98694e8i			0.727756i	−0.931447	+	0.363878i	$0.881452\pi$
$938$	8.65520e8			1.04874
$939$			2.50435e8i			0.302481i
$940$		−	2.29367e6i		−	0.00276152i
$941$			3.08634e8i			0.370404i	0.982700	+	0.185202i	$0.0592939\pi$
$941$			3.08634e8i			0.370404i	−0.982700	+	0.185202i	$0.940706\pi$
$942$	−3.99388e8			−0.477796
$943$			1.02236e9i			1.21918i
$944$	−1.89263e8	+	9.17008e7i	−0.224983	+	0.109008i
$945$	1.77142e8			0.209907
$946$			2.11508e7i			0.0249835i
$947$	5.66673e7			0.0667241			0.0333621	−	0.999443i	$-0.489379\pi$
$947$	5.66673e7			0.0667241			0.0333621	+	0.999443i	$0.489379\pi$
$948$	−4.36641e8			−0.512507
$949$	4.02204e8			0.470596
$950$			7.95273e7i			0.0927567i
$951$	3.84310e8			0.446827
$952$			8.18544e7i			0.0948705i
$953$	−8.86801e8			−1.02458			−0.512292	−	0.858811i	$-0.671203\pi$
$953$	−8.86801e8			−1.02458			−0.512292	+	0.858811i	$0.671203\pi$
$954$		−	9.90978e6i		−	0.0114135i
$955$			1.20685e9i			1.38561i
$956$	−7.70838e8			−0.882246
$957$			5.00008e8i			0.570481i
$958$		−	3.30246e8i		−	0.375613i
$959$	3.21167e7			0.0364145
$960$	−4.72573e7			−0.0534140
$961$	−2.49402e8			−0.281015
$962$		−	4.86457e8i		−	0.546411i
$963$	4.38842e8			0.491393
$964$	−5.45823e8			−0.609286
$965$	1.51518e8			0.168609
$966$	−5.15724e8			−0.572119
$967$		−	1.26135e9i		−	1.39494i	−0.716613	−	0.697471i	$-0.754309\pi$
$967$		−	1.26135e9i		−	1.39494i	0.716613	−	0.697471i	$-0.245691\pi$
$968$		−	8.10585e8i		−	0.893660i
$969$	−2.77461e7			−0.0304951
$970$	5.67657e8			0.621972
$971$	1.87775e8			0.205107			0.102553	−	0.994727i	$-0.467299\pi$
$971$	1.87775e8			0.205107			0.102553	+	0.994727i	$0.467299\pi$
$972$	2.94555e7			0.0320750
$973$	1.43614e8			0.155905
$974$		−	7.92944e8i		−	0.858155i
$975$			2.14477e8i			0.231402i
$976$			4.66137e7i			0.0501377i
$977$		−	8.91138e8i		−	0.955568i	−0.878477	−	0.477784i	$-0.841440\pi$
$977$		−	8.91138e8i		−	0.955568i	0.878477	−	0.477784i	$-0.158560\pi$
$978$		−	3.14446e8i		−	0.336148i
$979$	−1.80279e9			−1.92131
$980$	4.08112e8			0.433612
$981$		−	1.37090e8i		−	0.145211i
$982$			4.93158e8i			0.520777i
$983$		−	5.65644e8i		−	0.595501i	−0.954644	−	0.297750i	$-0.903764\pi$
$983$		−	5.65644e8i		−	0.595501i	0.954644	−	0.297750i	$-0.0962363\pi$
$984$		−	2.49337e8i		−	0.261699i
$985$	−4.89548e8			−0.512256
$986$			6.49304e7i			0.0677357i
$987$			6.10471e6i			0.00634912i
$988$		−	1.23977e8i		−	0.128550i
$989$	−1.73051e7			−0.0178889
$990$	−3.17920e8			−0.327652
$991$		−	7.03293e7i		−	0.0722629i	−0.999347	−	0.0361314i	$-0.988497\pi$
$991$		−	7.03293e7i		−	0.0722629i	0.999347	−	0.0361314i	$-0.0115035\pi$
$992$	−1.95316e8			−0.200079
$993$	−1.87671e7			−0.0191668
$994$			1.52202e9i			1.54975i
$995$	6.17449e8			0.626804
$996$			8.29451e7i			0.0839485i
$997$	−1.15623e9			−1.16670			−0.583348	−	0.812222i	$-0.698258\pi$
$997$	−1.15623e9			−1.16670			−0.583348	+	0.812222i	$0.698258\pi$
$998$		−	3.29051e8i		−	0.331034i
$999$			1.67288e8i			0.167791i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.7.d.a.235.1	✓	60
59.58	odd	2	inner	354.7.d.a.235.2	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.7.d.a.235.1	✓	60	1.1	even	1	trivial
354.7.d.a.235.2	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)

\(f(q)\)	\(=\)	\(q-5.65685i q^{2} -15.5885 q^{3} -32.0000 q^{4} -92.5158 q^{5} +88.1816i q^{6} +505.471 q^{7} +181.019i q^{8} +243.000 q^{9} +O(q^{10})\)	\(q-5.65685i q^{2} -15.5885 q^{3} -32.0000 q^{4} -92.5158 q^{5} +88.1816i q^{6} +505.471 q^{7} +181.019i q^{8} +243.000 q^{9} +523.348i q^{10} +2499.89i q^{11} +498.831 q^{12} +1947.22i q^{13} -2859.38i q^{14} +1442.18 q^{15} +1024.00 q^{16} +894.582 q^{17} -1374.62i q^{18} +1989.65 q^{19} +2960.50 q^{20} -7879.52 q^{21} +14141.5 q^{22} +11570.3i q^{23} -2821.81i q^{24} -7065.84 q^{25} +11015.1 q^{26} -3788.00 q^{27} -16175.1 q^{28} -12830.8 q^{29} -8158.19i q^{30} -33718.0i q^{31} -5792.62i q^{32} -38969.4i q^{33} -5060.52i q^{34} -46764.1 q^{35} -7776.00 q^{36} -44162.7i q^{37} -11255.2i q^{38} -30354.1i q^{39} -16747.1i q^{40} +88360.7 q^{41} +44573.3i q^{42} +1495.65i q^{43} -79996.5i q^{44} -22481.3 q^{45} +65451.3 q^{46} -774.757i q^{47} -15962.6 q^{48} +137852. q^{49} +39970.4i q^{50} -13945.2 q^{51} -62310.9i q^{52} +7209.13 q^{53} +21428.1i q^{54} -231279. i q^{55} +91500.1i q^{56} -31015.7 q^{57} +72581.8i q^{58} +(-184827. + 89551.6i) q^{59} -46149.7 q^{60} +45521.2i q^{61} -190738. q^{62} +122830. q^{63} -32768.0 q^{64} -180148. i q^{65} -220444. q^{66} +302695. i q^{67} -28626.6 q^{68} -180362. i q^{69} +264537. i q^{70} -532292. q^{71} +43987.7i q^{72} -206553. i q^{73} -249822. q^{74} +110145. q^{75} -63669.0 q^{76} +1.26362e6i q^{77} -171709. q^{78} -875330. q^{79} -94736.1 q^{80} +59049.0 q^{81} -499843. i q^{82} +166279. i q^{83} +252145. q^{84} -82763.0 q^{85} +8460.68 q^{86} +200012. q^{87} -452528. q^{88} +721149. i q^{89} +127174. i q^{90} +984262. i q^{91} -370248. i q^{92} +525612. i q^{93} -4382.69 q^{94} -184074. q^{95} +90298.0i q^{96} -1.08466e6i q^{97} -779810. i q^{98} +607473. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 1920 q^{4} + 408 q^{7} + 14580 q^{9}+O(q^{10}) \) 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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