LMFDB - Embedded newform 354.7.d.a.235.16

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			235.16
Character	$\chi$	$=$	354.235
Dual form			354.7.d.a.235.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.65685i q^{2} -15.5885 q^{3} -32.0000 q^{4} +65.2792 q^{5} -88.1816i q^{6} -409.923 q^{7} -181.019i q^{8} +243.000 q^{9} +O(q^{10})$	\(q+5.65685i q^{2} -15.5885 q^{3} -32.0000 q^{4} +65.2792 q^{5} -88.1816i q^{6} -409.923 q^{7} -181.019i q^{8} +243.000 q^{9} +369.275i q^{10} +1272.88i q^{11} +498.831 q^{12} -1180.61i q^{13} -2318.88i q^{14} -1017.60 q^{15} +1024.00 q^{16} +3176.91 q^{17} +1374.62i q^{18} +276.395 q^{19} -2088.94 q^{20} +6390.07 q^{21} -7200.50 q^{22} -20069.3i q^{23} +2821.81i q^{24} -11363.6 q^{25} +6678.55 q^{26} -3788.00 q^{27} +13117.5 q^{28} +16324.0 q^{29} -5756.43i q^{30} -14639.5i q^{31} +5792.62i q^{32} -19842.2i q^{33} +17971.3i q^{34} -26759.5 q^{35} -7776.00 q^{36} +1906.40i q^{37} +1563.53i q^{38} +18403.9i q^{39} -11816.8i q^{40} -1127.08 q^{41} +36147.7i q^{42} +23408.4i q^{43} -40732.2i q^{44} +15862.9 q^{45} +113529. q^{46} -16.9213i q^{47} -15962.6 q^{48} +50388.0 q^{49} -64282.4i q^{50} -49523.1 q^{51} +37779.6i q^{52} +195285. q^{53} -21428.1i q^{54} +83092.7i q^{55} +74204.0i q^{56} -4308.57 q^{57} +92342.5i q^{58} +(185162. - 88857.5i) q^{59} +32563.3 q^{60} +268173. i q^{61} +82813.5 q^{62} -99611.3 q^{63} -32768.0 q^{64} -77069.5i q^{65} +112245. q^{66} +77405.3i q^{67} -101661. q^{68} +312850. i q^{69} -151374. i q^{70} +274736. q^{71} -43987.7i q^{72} -59202.5i q^{73} -10784.2 q^{74} +177141. q^{75} -8844.63 q^{76} -521783. i q^{77} -104108. q^{78} -939144. q^{79} +66845.9 q^{80} +59049.0 q^{81} -6375.74i q^{82} -569060. i q^{83} -204482. q^{84} +207386. q^{85} -132418. q^{86} -254466. q^{87} +230416. q^{88} +767427. i q^{89} +89733.8i q^{90} +483960. i q^{91} +642219. i q^{92} +228207. i q^{93} +95.7214 q^{94} +18042.8 q^{95} -90298.0i q^{96} +1.50550e6i q^{97} +285037. i q^{98} +309310. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	65.2792			0.522234			0.261117	−	0.965307i	$-0.415909\pi$
$5$	65.2792			0.522234			0.261117	+	0.965307i	$0.415909\pi$
$6$		−	88.1816i		−	0.408248i
$7$	−409.923			−1.19511			−0.597556	−	0.801828i	$-0.703861\pi$
$7$	−409.923			−1.19511			−0.597556	+	0.801828i	$0.703861\pi$
$8$		−	181.019i		−	0.353553i
$9$	243.000			0.333333
$10$			369.275i			0.369275i
$11$			1272.88i			0.956334i	0.878269	+	0.478167i	$0.158699\pi$
$11$			1272.88i			0.956334i	−0.878269	+	0.478167i	$0.841301\pi$
$12$	498.831			0.288675
$13$		−	1180.61i		−	0.537375i	−0.963227	−	0.268687i	$-0.913410\pi$
$13$		−	1180.61i		−	0.537375i	0.963227	−	0.268687i	$-0.0865899\pi$
$14$		−	2318.88i		−	0.845071i
$15$	−1017.60			−0.301512
$16$	1024.00			0.250000
$17$	3176.91			0.646633			0.323317	−	0.946291i	$-0.395202\pi$
$17$	3176.91			0.646633			0.323317	+	0.946291i	$0.395202\pi$
$18$			1374.62i			0.235702i
$19$	276.395			0.0402967			0.0201483	−	0.999797i	$-0.493586\pi$
$19$	276.395			0.0402967			0.0201483	+	0.999797i	$0.493586\pi$
$20$	−2088.94			−0.261117
$21$	6390.07			0.689998
$22$	−7200.50			−0.676230
$23$		−	20069.3i		−	1.64949i	−0.565506	−	0.824744i	$-0.691319\pi$
$23$		−	20069.3i		−	1.64949i	0.565506	−	0.824744i	$-0.308681\pi$
$24$			2821.81i			0.204124i
$25$	−11363.6			−0.727272
$26$	6678.55			0.379981
$27$	−3788.00			−0.192450
$28$	13117.5			0.597556
$29$	16324.0			0.669318			0.334659	−	0.942339i	$-0.391379\pi$
$29$	16324.0			0.669318			0.334659	+	0.942339i	$0.391379\pi$
$30$		−	5756.43i		−	0.213201i
$31$		−	14639.5i		−	0.491406i	−0.969345	−	0.245703i	$-0.920981\pi$
$31$		−	14639.5i		−	0.491406i	0.969345	−	0.245703i	$-0.0790189\pi$
$32$			5792.62i			0.176777i
$33$		−	19842.2i		−	0.552140i
$34$			17971.3i			0.457239i
$35$	−26759.5			−0.624127
$36$	−7776.00			−0.166667
$37$			1906.40i			0.0376365i	0.999823	+	0.0188182i	$0.00599039\pi$
$37$			1906.40i			0.0376365i	−0.999823	+	0.0188182i	$0.994010\pi$
$38$			1563.53i			0.0284940i
$39$			18403.9i			0.310254i
$40$		−	11816.8i		−	0.184638i
$41$	−1127.08			−0.0163532			−0.00817662	−	0.999967i	$-0.502603\pi$
$41$	−1127.08			−0.0163532			−0.00817662	+	0.999967i	$0.502603\pi$
$42$			36147.7i			0.487902i
$43$			23408.4i			0.294419i	0.989105	+	0.147210i	$0.0470292\pi$
$43$			23408.4i			0.294419i	−0.989105	+	0.147210i	$0.952971\pi$
$44$		−	40732.2i		−	0.478167i
$45$	15862.9			0.174078
$46$	113529.			1.16636
$47$		−	16.9213i		−	0.000162982i	−1.00000		8.14912e-5i	$-0.999974\pi$
$47$		−	16.9213i		−	0.000162982i	1.00000		8.14912e-5i	$-2.59395e-5\pi$
$48$	−15962.6			−0.144338
$49$	50388.0			0.428291
$50$		−	64282.4i		−	0.514259i
$51$	−49523.1			−0.373334
$52$			37779.6i			0.268687i
$53$	195285.			1.31172			0.655861	−	0.754881i	$-0.272306\pi$
$53$	195285.			1.31172			0.655861	+	0.754881i	$0.272306\pi$
$54$		−	21428.1i		−	0.136083i
$55$			83092.7i			0.499430i
$56$			74204.0i			0.422536i
$57$	−4308.57			−0.0232653
$58$			92342.5i			0.473279i
$59$	185162.	−	88857.5i	0.901561	−	0.432651i
$59$	185162.	−	88857.5i	0.901561	−	0.432651i
$60$	32563.3			0.150756
$61$			268173.i			1.18148i	0.806863	+	0.590739i	$0.201164\pi$
$61$			268173.i			1.18148i	−0.806863	+	0.590739i	$0.798836\pi$
$62$	82813.5			0.347477
$63$	−99611.3			−0.398370
$64$	−32768.0			−0.125000
$65$		−	77069.5i		−	0.280635i
$66$	112245.			0.390422
$67$			77405.3i			0.257363i	0.991686	+	0.128682i	$0.0410745\pi$
$67$			77405.3i			0.257363i	−0.991686	+	0.128682i	$0.958925\pi$
$68$	−101661.			−0.323317
$69$			312850.i			0.952333i
$70$		−	151374.i		−	0.441325i
$71$	274736.			0.767611			0.383805	−	0.923414i	$-0.374613\pi$
$71$	274736.			0.767611			0.383805	+	0.923414i	$0.374613\pi$
$72$		−	43987.7i		−	0.117851i
$73$		−	59202.5i		−	0.152185i	−0.997101	−	0.0760924i	$-0.975756\pi$
$73$		−	59202.5i		−	0.152185i	0.997101	−	0.0760924i	$-0.0242444\pi$
$74$	−10784.2			−0.0266130
$75$	177141.			0.419891
$76$	−8844.63			−0.0201483
$77$		−	521783.i		−	1.14293i
$78$	−104108.			−0.219382
$79$	−939144.			−1.90481			−0.952403	−	0.304841i	$-0.901397\pi$
$79$	−939144.			−1.90481			−0.952403	+	0.304841i	$0.901397\pi$
$80$	66845.9			0.130558
$81$	59049.0			0.111111
$82$		−	6375.74i		−	0.0115635i
$83$		−	569060.i		−	0.995230i	−0.867398	−	0.497615i	$-0.834209\pi$
$83$		−	569060.i		−	0.995230i	0.867398	−	0.497615i	$-0.165791\pi$
$84$	−204482.			−0.344999
$85$	207386.			0.337694
$86$	−132418.			−0.208186
$87$	−254466.			−0.386431
$88$	230416.			0.338115
$89$			767427.i			1.08860i	0.838892	+	0.544299i	$0.183204\pi$
$89$			767427.i			1.08860i	−0.838892	+	0.544299i	$0.816796\pi$
$90$			89733.8i			0.123092i
$91$			483960.i			0.642223i
$92$			642219.i			0.824744i
$93$			228207.i			0.283714i
$94$	95.7214			0.000115246
$95$	18042.8			0.0210443
$96$		−	90298.0i		−	0.102062i
$97$			1.50550e6i			1.64955i	0.565464	+	0.824773i	$0.308697\pi$
$97$			1.50550e6i			1.64955i	−0.565464	+	0.824773i	$0.691303\pi$
$98$			285037.i			0.302847i
$99$			309310.i			0.318778i
$100$	363636.			0.363636
$101$			374850.i			0.363826i	0.983315	+	0.181913i	$0.0582289\pi$
$101$			374850.i			0.363826i	−0.983315	+	0.181913i	$0.941771\pi$
$102$		−	280145.i		−	0.263987i
$103$			130573.i			0.119493i	0.998214	+	0.0597463i	$0.0190292\pi$
$103$			130573.i			0.119493i	−0.998214	+	0.0597463i	$0.980971\pi$
$104$	−213714.			−0.189991
$105$	417139.			0.360340
$106$			1.10470e6i			0.927528i
$107$	793873.			0.648036			0.324018	−	0.946051i	$-0.394966\pi$
$107$	793873.			0.648036			0.324018	+	0.946051i	$0.394966\pi$
$108$	121216.			0.0962250
$109$			2.44420e6i			1.88737i	0.330842	+	0.943686i	$0.392667\pi$
$109$			2.44420e6i			1.88737i	−0.330842	+	0.943686i	$0.607333\pi$
$110$	−470043.			−0.353150
$111$		−	29717.8i		−	0.0217294i
$112$	−419761.			−0.298778
$113$			2.71847e6i			1.88404i	0.335563	+	0.942018i	$0.391073\pi$
$113$			2.71847e6i			1.88404i	−0.335563	+	0.942018i	$0.608927\pi$
$114$		−	24372.9i		−	0.0164510i
$115$		−	1.31011e6i		−	0.861419i
$116$	−522368.			−0.334659
$117$		−	286889.i		−	0.179125i
$118$	502654.	+	1.04743e6i	0.305931	+	0.637500i
$119$	−1.30229e6			−0.772799
$120$			184206.i			0.106601i
$121$	151336.			0.0854253
$122$	−1.51702e6			−0.835431
$123$	17569.5			0.00944155
$124$			468464.i			0.245703i
$125$	−1.76180e6			−0.902040
$126$		−	563487.i		−	0.281690i
$127$	−1.26432e6			−0.617226			−0.308613	−	0.951188i	$-0.599865\pi$
$127$	−1.26432e6			−0.617226			−0.308613	+	0.951188i	$0.599865\pi$
$128$		−	185364.i		−	0.0883883i
$129$		−	364901.i		−	0.169983i
$130$	435971.			0.198439
$131$			1.66446e6i			0.740389i	0.928954	+	0.370195i	$0.120709\pi$
$131$			1.66446e6i			0.740389i	−0.928954	+	0.370195i	$0.879291\pi$
$132$			634952.i			0.276070i
$133$	−113301.			−0.0481590
$134$	−437871.			−0.181983
$135$	−247277.			−0.100504
$136$		−	575082.i		−	0.228619i
$137$	−2.16349e6			−0.841384			−0.420692	−	0.907204i	$-0.638213\pi$
$137$	−2.16349e6			−0.841384			−0.420692	+	0.907204i	$0.638213\pi$
$138$	−1.76975e6			−0.673401
$139$	−2.96019e6			−1.10224			−0.551119	−	0.834427i	$-0.685799\pi$
$139$	−2.96019e6			−1.10224			−0.551119	+	0.834427i	$0.685799\pi$
$140$	856303.			0.312064
$141$			263.777i			9.40979e-5i
$142$			1.55414e6i			0.542783i
$143$	1.50278e6			0.513910
$144$	248832.			0.0833333
$145$	1.06562e6			0.349541
$146$	334900.			0.107611
$147$	−785471.			−0.247274
$148$		−	61004.8i		−	0.0188182i
$149$		−	1.51648e6i		−	0.458436i	−0.973375	−	0.229218i	$-0.926383\pi$
$149$		−	1.51648e6i		−	0.458436i	0.973375	−	0.229218i	$-0.0736169\pi$
$150$			1.00206e6i			0.296907i
$151$		−	100776.i		−	0.0292702i	−0.999893	−	0.0146351i	$-0.995341\pi$
$151$		−	100776.i		−	0.0292702i	0.999893	−	0.0146351i	$-0.00465866\pi$
$152$		−	50032.8i		−	0.0142470i
$153$	771989.			0.215544
$154$	2.95165e6			0.808170
$155$		−	955655.i		−	0.256629i
$156$		−	588926.i		−	0.155127i
$157$		−	4.05994e6i		−	1.04911i	−0.851377	−	0.524555i	$-0.824232\pi$
$157$		−	4.05994e6i		−	1.04911i	0.851377	−	0.524555i	$-0.175768\pi$
$158$		−	5.31260e6i		−	1.34690i
$159$	−3.04420e6			−0.757323
$160$			378138.i			0.0923188i
$161$			8.22688e6i			1.97132i
$162$			334032.i			0.0785674i
$163$	−710583.			−0.164079			−0.0820393	−	0.996629i	$-0.526143\pi$
$163$	−710583.			−0.164079			−0.0820393	+	0.996629i	$0.526143\pi$
$164$	36066.6			0.00817662
$165$		−	1.29529e6i		−	0.288346i
$166$	3.21909e6			0.703734
$167$	−8.36818e6			−1.79672			−0.898362	−	0.439256i	$-0.855242\pi$
$167$	−8.36818e6			−1.79672			−0.898362	+	0.439256i	$0.855242\pi$
$168$		−	1.15673e6i		−	0.243951i
$169$	3.43296e6			0.711228
$170$			1.17315e6i			0.238786i
$171$	67163.9			0.0134322
$172$		−	749069.i		−	0.147210i
$173$			1.11082e6i			0.214539i	0.994230	+	0.107269i	$0.0342108\pi$
$173$			1.11082e6i			0.214539i	−0.994230	+	0.107269i	$0.965789\pi$
$174$		−	1.43948e6i		−	0.273248i
$175$	4.65821e6			0.869171
$176$			1.30343e6i			0.239084i
$177$	−2.88639e6	+	1.38515e6i	−0.520517	+	0.249791i
$178$	−4.34122e6			−0.769754
$179$			3.22136e6i			0.561669i	0.959756	+	0.280834i	$0.0906112\pi$
$179$			3.22136e6i			0.561669i	−0.959756	+	0.280834i	$0.909389\pi$
$180$	−507611.			−0.0870390
$181$	7.18502e6			1.21169			0.605846	−	0.795582i	$-0.292835\pi$
$181$	7.18502e6			1.21169			0.605846	+	0.795582i	$0.292835\pi$
$182$	−2.73769e6			−0.454120
$183$		−	4.18041e6i		−	0.682127i
$184$	−3.63294e6			−0.583182
$185$			124448.i			0.0196550i
$186$	−1.29093e6			−0.200616
$187$			4.04383e6i			0.618397i
$188$			541.482i			8.14912e-5i
$189$	1.55279e6			0.229999
$190$			102066.i			0.0148806i
$191$			4.01597e6i			0.576355i	0.957577	+	0.288178i	$0.0930493\pi$
$191$			4.01597e6i			0.576355i	−0.957577	+	0.288178i	$0.906951\pi$
$192$	510803.			0.0721688
$193$	739443.			0.102857			0.0514283	−	0.998677i	$-0.483623\pi$
$193$	739443.			0.102857			0.0514283	+	0.998677i	$0.483623\pi$
$194$	−8.51637e6			−1.16640
$195$			1.20139e6i			0.162025i
$196$	−1.61241e6			−0.214145
$197$	1.30582e7			1.70799			0.853994	−	0.520283i	$-0.174174\pi$
$197$	1.30582e7			1.70799			0.853994	+	0.520283i	$0.174174\pi$
$198$	−1.74972e6			−0.225410
$199$	−6.20558e6			−0.787450			−0.393725	−	0.919228i	$-0.628814\pi$
$199$	−6.20558e6			−0.787450			−0.393725	+	0.919228i	$0.628814\pi$
$200$			2.05704e6i			0.257129i
$201$		−	1.20663e6i		−	0.148589i
$202$	−2.12047e6			−0.257264
$203$	−6.69158e6			−0.799909
$204$	1.58474e6			0.186667
$205$	−73575.0			−0.00854021
$206$	−738631.			−0.0844940
$207$		−	4.87685e6i		−	0.549830i
$208$		−	1.20895e6i		−	0.134344i
$209$			351818.i			0.0385371i
$210$			2.35969e6i			0.254799i
$211$			6.41941e6i			0.683357i	0.939817	+	0.341678i	$0.110995\pi$
$211$			6.41941e6i			0.683357i	−0.939817	+	0.341678i	$0.889005\pi$
$212$	−6.24913e6			−0.655861
$213$	−4.28272e6			−0.443180
$214$			4.49082e6i			0.458231i
$215$			1.52808e6i			0.153756i
$216$			685700.i			0.0680414i
$217$			6.00106e6i			0.587285i
$218$	−1.38265e7			−1.33457
$219$			922875.i			0.0878639i
$220$		−	2.65897e6i		−	0.249715i
$221$		−	3.75070e6i		−	0.347484i
$222$	168110.			0.0153650
$223$	6.27616e6			0.565951			0.282976	−	0.959127i	$-0.408678\pi$
$223$	6.27616e6			0.565951			0.282976	+	0.959127i	$0.408678\pi$
$224$		−	2.37453e6i		−	0.211268i
$225$	−2.76136e6			−0.242424
$226$	−1.53780e7			−1.33221
$227$			1.34741e7i			1.15192i	0.817478	+	0.575960i	$0.195372\pi$
$227$			1.34741e7i			1.15192i	−0.817478	+	0.575960i	$0.804628\pi$
$228$	137874.			0.0116326
$229$			4.94116e6i			0.411455i	0.978609	+	0.205728i	$0.0659561\pi$
$229$			4.94116e6i			0.411455i	−0.978609	+	0.205728i	$0.934044\pi$
$230$	7.41110e6			0.609115
$231$			8.13379e6i			0.659868i
$232$		−	2.95496e6i		−	0.236640i
$233$			9.57163e6i			0.756690i	0.925665	+	0.378345i	$0.123507\pi$
$233$			9.57163e6i			0.756690i	−0.925665	+	0.378345i	$0.876493\pi$
$234$	1.62289e6			0.126660
$235$		−	1104.61i		−	8.51149e-5i
$236$	−5.92518e6	+	2.84344e6i	−0.450781	+	0.216326i
$237$	1.46398e7			1.09974
$238$		−	7.36686e6i		−	0.546451i
$239$	1.12079e7			0.820978			0.410489	−	0.911866i	$-0.365358\pi$
$239$	1.12079e7			0.820978			0.410489	+	0.911866i	$0.365358\pi$
$240$	−1.04202e6			−0.0753780
$241$	5.83049e6			0.416537			0.208269	−	0.978072i	$-0.433217\pi$
$241$	5.83049e6			0.416537			0.208269	+	0.978072i	$0.433217\pi$
$242$			856086.i			0.0604048i
$243$	−920483.			−0.0641500
$244$		−	8.58154e6i		−	0.590739i
$245$	3.28929e6			0.223668
$246$			99387.9i			0.00667618i
$247$		−	326315.i		−	0.0216544i
$248$	−2.65003e6			−0.173738
$249$			8.87076e6i			0.574596i
$250$		−	9.96623e6i		−	0.637838i
$251$	1.71292e7			1.08322			0.541610	−	0.840630i	$-0.317815\pi$
$251$	1.71292e7			1.08322			0.541610	+	0.840630i	$0.317815\pi$
$252$	3.18756e6			0.199185
$253$	2.55459e7			1.57746
$254$		−	7.15205e6i		−	0.436445i
$255$	−3.23283e6			−0.194968
$256$	1.04858e6			0.0625000
$257$	2.38745e7			1.40648			0.703242	−	0.710951i	$-0.251735\pi$
$257$	2.38745e7			1.40648			0.703242	+	0.710951i	$0.251735\pi$
$258$	2.06419e6			0.120196
$259$		−	781478.i		−	0.0449798i
$260$			2.46622e6i			0.140318i
$261$	3.96673e6			0.223106
$262$	−9.41562e6			−0.523534
$263$	−2.76769e7			−1.52142			−0.760712	−	0.649089i	$-0.775150\pi$
$263$	−2.76769e7			−1.52142			−0.760712	+	0.649089i	$0.775150\pi$
$264$	−3.59183e6			−0.195211
$265$	1.27481e7			0.685026
$266$		−	640925.i		−	0.0340535i
$267$		−	1.19630e7i		−	0.628502i
$268$		−	2.47697e6i		−	0.128682i
$269$			1.13057e6i			0.0580818i	0.999578	+	0.0290409i	$0.00924531\pi$
$269$			1.13057e6i			0.0580818i	−0.999578	+	0.0290409i	$0.990755\pi$
$270$		−	1.39881e6i		−	0.0710670i
$271$	2.86835e7			1.44120			0.720601	−	0.693350i	$-0.243866\pi$
$271$	2.86835e7			1.44120			0.720601	+	0.693350i	$0.243866\pi$
$272$	3.25315e6			0.161658
$273$		−	7.54420e6i		−	0.370787i
$274$		−	1.22386e7i		−	0.594948i
$275$		−	1.44645e7i		−	0.695515i
$276$		−	1.00112e7i		−	0.476166i
$277$	3.84939e7			1.81114			0.905571	−	0.424195i	$-0.139443\pi$
$277$	3.84939e7			1.81114			0.905571	+	0.424195i	$0.139443\pi$
$278$		−	1.67454e7i		−	0.779399i
$279$		−	3.55740e6i		−	0.163802i
$280$			4.84398e6i			0.220662i
$281$	−7.05182e6			−0.317821			−0.158910	−	0.987293i	$-0.550798\pi$
$281$	−7.05182e6			−0.317821			−0.158910	+	0.987293i	$0.550798\pi$
$282$	−1492.15			−6.65373e−5
$283$		−	8.66667e6i		−	0.382378i	−0.981553	−	0.191189i	$-0.938766\pi$
$283$		−	8.66667e6i		−	0.382378i	0.981553	−	0.191189i	$-0.0612344\pi$
$284$	−8.79156e6			−0.383805
$285$	−281260.			−0.0121499
$286$			8.50100e6i			0.363389i
$287$	462017.			0.0195439
$288$			1.40761e6i			0.0589256i
$289$	−1.40448e7			−0.581865
$290$			6.02805e6i			0.247162i
$291$		−	2.34684e7i		−	0.952365i
$292$			1.89448e6i			0.0760924i
$293$	−1.39186e7			−0.553341			−0.276670	−	0.960965i	$-0.589231\pi$
$293$	−1.39186e7			−0.553341			−0.276670	+	0.960965i	$0.589231\pi$
$294$		−	4.44329e6i		−	0.174849i
$295$	1.20872e7	−	5.80055e6i	0.470826	−	0.225945i
$296$	345095.			0.0133065
$297$		−	4.82167e6i		−	0.184047i
$298$	8.57853e6			0.324163
$299$	−2.36941e7			−0.886394
$300$	−5.66852e6			−0.209945
$301$		−	9.59564e6i		−	0.351864i
$302$	570074.			0.0206971
$303$		−	5.84333e6i		−	0.210055i
$304$	283028.			0.0100742
$305$			1.75061e7i			0.617008i
$306$			4.36703e6i			0.152413i
$307$	2.60059e7			0.898787			0.449394	−	0.893334i	$-0.351640\pi$
$307$	2.60059e7			0.898787			0.449394	+	0.893334i	$0.351640\pi$
$308$			1.66971e7i			0.571463i
$309$		−	2.03543e6i		−	0.0689891i
$310$	5.40600e6			0.181464
$311$	−1.64054e7			−0.545387			−0.272693	−	0.962101i	$-0.587914\pi$
$311$	−1.64054e7			−0.545387			−0.272693	+	0.962101i	$0.587914\pi$
$312$	3.33147e6			0.109691
$313$			8.64633e6i			0.281967i	0.990012	+	0.140984i	$0.0450265\pi$
$313$			8.64633e6i			0.281967i	−0.990012	+	0.140984i	$0.954973\pi$
$314$	2.29665e7			0.741833
$315$	−6.50255e6			−0.208042
$316$	3.00526e7			0.952403
$317$	−4.03635e6			−0.126710			−0.0633550	−	0.997991i	$-0.520180\pi$
$317$	−4.03635e6			−0.126710			−0.0633550	+	0.997991i	$0.520180\pi$
$318$		−	1.72206e7i		−	0.535509i
$319$			2.07785e7i			0.640092i
$320$	−2.13907e6			−0.0652792
$321$	−1.23752e7			−0.374144
$322$	−4.65383e7			−1.39394
$323$	878081.			0.0260572
$324$	−1.88957e6			−0.0555556
$325$			1.34160e7i			0.390818i
$326$		−	4.01966e6i		−	0.116021i
$327$		−	3.81013e7i		−	1.08967i
$328$			204024.i			0.00578174i
$329$			6936.44i			0.000194782i
$330$	7.32725e6			0.203891
$331$	3.16465e7			0.872653			0.436327	−	0.899788i	$-0.356279\pi$
$331$	3.16465e7			0.872653			0.436327	+	0.899788i	$0.356279\pi$
$332$			1.82099e7i			0.497615i
$333$			463255.i			0.0125455i
$334$		−	4.73376e7i		−	1.27048i
$335$			5.05296e6i			0.134404i
$336$	6.54343e6			0.172499
$337$		−	4.10046e7i		−	1.07138i	−0.844416	−	0.535689i	$-0.820052\pi$
$337$		−	4.10046e7i		−	1.07138i	0.844416	−	0.535689i	$-0.179948\pi$
$338$			1.94198e7i			0.502914i
$339$		−	4.23767e7i		−	1.08775i
$340$	−6.63636e6			−0.168847
$341$	1.86343e7			0.469949
$342$			379937.i			0.00949801i
$343$	2.75719e7			0.683256
$344$	4.23737e6			0.104093
$345$			2.04226e7i			0.497340i
$346$	−6.28376e6			−0.151702
$347$			6.29927e7i			1.50765i	0.657073	+	0.753827i	$0.271794\pi$
$347$			6.29927e7i			1.50765i	−0.657073	+	0.753827i	$0.728206\pi$
$348$	8.14291e6			0.193215
$349$		−	2.05330e7i		−	0.483031i	−0.970397	−	0.241516i	$-0.922355\pi$
$349$		−	2.05330e7i		−	0.483031i	0.970397	−	0.241516i	$-0.0776445\pi$
$350$			2.63508e7i			0.614596i
$351$			4.47215e6i			0.103418i
$352$	−7.37331e6			−0.169058
$353$		−	6.50173e7i		−	1.47810i	−0.673649	−	0.739051i	$-0.735274\pi$
$353$		−	6.50173e7i		−	1.47810i	0.673649	−	0.739051i	$-0.264726\pi$
$354$	−7.83560e6	−	1.63279e7i	−0.176629	−	0.368061i
$355$	1.79346e7			0.400872
$356$		−	2.45577e7i		−	0.544299i
$357$	2.03007e7			0.446175
$358$	−1.82228e7			−0.397160
$359$	1.45686e7			0.314873			0.157437	−	0.987529i	$-0.449677\pi$
$359$	1.45686e7			0.314873			0.157437	+	0.987529i	$0.449677\pi$
$360$		−	2.87148e6i		−	0.0615458i
$361$	−4.69695e7			−0.998376
$362$			4.06446e7i			0.856796i
$363$	−2.35910e6			−0.0493203
$364$		−	1.54867e7i		−	0.321111i
$365$		−	3.86469e6i		−	0.0794760i
$366$	2.36479e7			0.482337
$367$		−	3.46611e7i		−	0.701204i	−0.936525	−	0.350602i	$-0.885977\pi$
$367$		−	3.46611e7i		−	0.701204i	0.936525	−	0.350602i	$-0.114023\pi$
$368$		−	2.05510e7i		−	0.412372i
$369$	−273881.			−0.00545108
$370$	−703986.			−0.0138982
$371$	−8.00520e7			−1.56765
$372$		−	7.30263e6i		−	0.141857i
$373$	−3.99236e7			−0.769314			−0.384657	−	0.923060i	$-0.625680\pi$
$373$	−3.99236e7			−0.769314			−0.384657	+	0.923060i	$0.625680\pi$
$374$	−2.28753e7			−0.437273
$375$	2.74637e7			0.520793
$376$	−3063.09			−5.76230e−5
$377$		−	1.92723e7i		−	0.359675i
$378$			8.78389e6i			0.162634i
$379$	7.48190e6			0.137434			0.0687170	−	0.997636i	$-0.478109\pi$
$379$	7.48190e6			0.137434			0.0687170	+	0.997636i	$0.478109\pi$
$380$	−577371.			−0.0105221
$381$	1.97087e7			0.356356
$382$	−2.27177e7			−0.407545
$383$	1.09186e8			1.94343			0.971717	−	0.236147i	$-0.0758847\pi$
$383$	1.09186e8			1.94343			0.971717	+	0.236147i	$0.0758847\pi$
$384$			2.88954e6i			0.0510310i
$385$		−	3.40616e7i		−	0.596874i
$386$			4.18292e6i			0.0727307i
$387$			5.68824e6i			0.0981398i
$388$		−	4.81759e7i		−	0.824773i
$389$	6.98125e7			1.18600			0.592999	−	0.805203i	$-0.297944\pi$
$389$	6.98125e7			1.18600			0.592999	+	0.805203i	$0.297944\pi$
$390$	−6.79611e6			−0.114569
$391$		−	6.37584e7i		−	1.06661i
$392$		−	9.12120e6i		−	0.151424i
$393$		−	2.59464e7i		−	0.427464i
$394$			7.38683e7i			1.20773i
$395$	−6.13066e7			−0.994754
$396$		−	9.89792e6i		−	0.159389i
$397$		−	6.40226e7i		−	1.02320i	−0.859223	−	0.511602i	$-0.829052\pi$
$397$		−	6.40226e7i		−	1.02320i	0.859223	−	0.511602i	$-0.170948\pi$
$398$		−	3.51041e7i		−	0.556812i
$399$	1.76618e6			0.0278046
$400$	−1.16363e7			−0.181818
$401$			8.10967e7i			1.25768i	0.777535	+	0.628840i	$0.216470\pi$
$401$			8.10967e7i			1.25768i	−0.777535	+	0.628840i	$0.783530\pi$
$402$	6.82573e6			0.105068
$403$	−1.72836e7			−0.264069
$404$		−	1.19952e7i		−	0.181913i
$405$	3.85467e6			0.0580260
$406$		−	3.78533e7i		−	0.565621i
$407$	−2.42662e6			−0.0359931
$408$			8.96464e6i			0.131993i
$409$			5.60506e7i			0.819238i	0.912257	+	0.409619i	$0.134338\pi$
$409$			5.60506e7i			0.819238i	−0.912257	+	0.409619i	$0.865662\pi$
$410$		−	416203.i		−	0.00603884i
$411$	3.37255e7			0.485773
$412$		−	4.17833e6i		−	0.0597463i
$413$	−7.59021e7	+	3.64247e7i	−1.07747	+	0.517066i
$414$	2.75876e7			0.388788
$415$		−	3.71478e7i		−	0.519743i
$416$	6.83884e6			0.0949954
$417$	4.61448e7			0.636377
$418$	−1.99018e6			−0.0272498
$419$			1.00766e8i			1.36984i	0.728618	+	0.684921i	$0.240163\pi$
$419$			1.00766e8i			1.36984i	−0.728618	+	0.684921i	$0.759837\pi$
$420$	−1.33484e7			−0.180170
$421$			4.14760e7i			0.555841i	0.960604	+	0.277921i	$0.0896453\pi$
$421$			4.14760e7i			0.555841i	−0.960604	+	0.277921i	$0.910355\pi$
$422$	−3.63136e7			−0.483206
$423$		−	4111.88i		−	5.43275e-5i
$424$		−	3.53504e7i		−	0.463764i
$425$	−3.61012e7			−0.470278
$426$		−	2.42267e7i		−	0.313376i
$427$		−	1.09930e8i		−	1.41200i
$428$	−2.54039e7			−0.324018
$429$	−2.34260e7			−0.296706
$430$	−8.64414e6			−0.108722
$431$		−	5.33073e7i		−	0.665817i	−0.942959	−	0.332908i	$-0.891970\pi$
$431$		−	5.33073e7i		−	0.665817i	0.942959	−	0.332908i	$-0.108030\pi$
$432$	−3.87891e6			−0.0481125
$433$	8.40987e6			0.103592			0.0517959	−	0.998658i	$-0.483505\pi$
$433$	8.40987e6			0.103592			0.0517959	+	0.998658i	$0.483505\pi$
$434$	−3.39471e7			−0.415273
$435$	−1.66113e7			−0.201807
$436$		−	7.82145e7i		−	0.943686i
$437$		−	5.54706e6i		−	0.0664689i
$438$	−5.22057e6			−0.0621292
$439$	−3.51328e6			−0.0415259			−0.0207630	−	0.999784i	$-0.506610\pi$
$439$	−3.51328e6			−0.0415259			−0.0207630	+	0.999784i	$0.506610\pi$
$440$	1.50414e7			0.176575
$441$	1.22443e7			0.142764
$442$	2.12172e7			0.245709
$443$			2.20013e7i			0.253067i	0.991962	+	0.126534i	$0.0403852\pi$
$443$			2.20013e7i			0.253067i	−0.991962	+	0.126534i	$0.959615\pi$
$444$			950971.i			0.0108647i
$445$			5.00971e7i			0.568502i
$446$			3.55033e7i			0.400188i
$447$			2.36396e7i			0.264678i
$448$	1.34324e7			0.149389
$449$	3.50146e7			0.386821			0.193410	−	0.981118i	$-0.438045\pi$
$449$	3.50146e7			0.386821			0.193410	+	0.981118i	$0.438045\pi$
$450$		−	1.56206e7i		−	0.171420i
$451$		−	1.43464e6i		−	0.0156392i
$452$		−	8.69910e7i		−	0.942018i
$453$			1.57094e6i			0.0168991i
$454$	−7.62211e7			−0.814531
$455$			3.15926e7i			0.335390i
$456$			779934.i			0.00822552i
$457$		−	2.11066e7i		−	0.221141i	−0.993868	−	0.110570i	$-0.964732\pi$
$457$		−	2.11066e7i		−	0.221141i	0.993868	−	0.110570i	$-0.0352678\pi$
$458$	−2.79514e7			−0.290943
$459$	−1.20341e7			−0.124445
$460$			4.19235e7i			0.430709i
$461$	8.99525e7			0.918143			0.459071	−	0.888399i	$-0.348182\pi$
$461$	8.99525e7			0.918143			0.459071	+	0.888399i	$0.348182\pi$
$462$	−4.60117e7			−0.466597
$463$			1.18652e8i			1.19546i	0.801699	+	0.597728i	$0.203930\pi$
$463$			1.18652e8i			1.19546i	−0.801699	+	0.597728i	$0.796070\pi$
$464$	1.67158e7			0.167330
$465$			1.48972e7i			0.148165i
$466$	−5.41453e7			−0.535061
$467$			4.46059e7i			0.437967i	0.975729	+	0.218984i	$0.0702741\pi$
$467$			4.46059e7i			0.437967i	−0.975729	+	0.218984i	$0.929726\pi$
$468$			9.18044e6i			0.0895625i
$469$		−	3.17302e7i		−	0.307578i
$470$	6248.62			6.01853e−5
$471$			6.32883e7i			0.605704i
$472$	−1.60849e7	−	3.35179e7i	−0.152965	−	0.318750i
$473$	−2.97961e7			−0.281563
$474$			8.28152e7i			0.777634i
$475$	−3.14085e6			−0.0293066
$476$	4.16732e7			0.386399
$477$	4.74543e7			0.437241
$478$			6.34016e7i			0.580519i
$479$	−1.55925e8			−1.41876			−0.709378	−	0.704828i	$-0.751024\pi$
$479$	−1.55925e8			−1.41876			−0.709378	+	0.704828i	$0.751024\pi$
$480$		−	5.89458e6i		−	0.0533003i
$481$	2.25072e6			0.0202249
$482$			3.29822e7i			0.294536i
$483$		−	1.28244e8i		−	1.13814i
$484$	−4.84275e6			−0.0427126
$485$			9.82776e7i			0.861448i
$486$		−	5.20704e6i		−	0.0453609i
$487$	2.63703e7			0.228312			0.114156	−	0.993463i	$-0.463584\pi$
$487$	2.63703e7			0.228312			0.114156	+	0.993463i	$0.463584\pi$
$488$	4.85445e7			0.417716
$489$	1.10769e7			0.0947308
$490$			1.86070e7i			0.158157i
$491$	−5.70938e7			−0.482330			−0.241165	−	0.970484i	$-0.577530\pi$
$491$	−5.70938e7			−0.482330			−0.241165	+	0.970484i	$0.577530\pi$
$492$	−562223.			−0.00472077
$493$	5.18599e7			0.432803
$494$	1.84592e6			0.0153120
$495$			2.01915e7i			0.166477i
$496$		−	1.49908e7i		−	0.122852i
$497$	−1.12621e8			−0.917380
$498$	−5.01806e7			−0.406301
$499$	−1.20022e8			−0.965959			−0.482979	−	0.875632i	$-0.660445\pi$
$499$	−1.20022e8			−0.965959			−0.482979	+	0.875632i	$0.660445\pi$
$500$	5.63775e7			0.451020
$501$	1.30447e8			1.03734
$502$			9.68976e7i			0.765953i
$503$		−	1.19727e7i		−	0.0940782i	−0.998893	−	0.0470391i	$-0.985021\pi$
$503$		−	1.19727e7i		−	0.0940782i	0.998893	−	0.0470391i	$-0.0149785\pi$
$504$			1.80316e7i			0.140845i
$505$			2.44699e7i			0.190002i
$506$			1.44509e8i			1.11543i
$507$	−5.35146e7			−0.410628
$508$	4.04581e7			0.308613
$509$			1.46317e8i			1.10954i	0.832005	+	0.554769i	$0.187193\pi$
$509$			1.46317e8i			1.10954i	−0.832005	+	0.554769i	$0.812807\pi$
$510$		−	1.82877e7i		−	0.137863i
$511$			2.42685e7i			0.181878i
$512$			5.93164e6i			0.0441942i
$513$	−1.04698e6			−0.00775510
$514$			1.35054e8i			0.994534i
$515$			8.52369e6i			0.0624031i
$516$			1.16768e7i			0.0849915i
$517$	21538.8			0.000155866
$518$	4.42071e6			0.0318055
$519$		−	1.73160e7i		−	0.123864i
$520$	−1.39511e7			−0.0992196
$521$	−6.07882e6			−0.0429839			−0.0214920	−	0.999769i	$-0.506842\pi$
$521$	−6.07882e6			−0.0429839			−0.0214920	+	0.999769i	$0.506842\pi$
$522$			2.24392e7i			0.157760i
$523$	7.23650e7			0.505852			0.252926	−	0.967486i	$-0.418607\pi$
$523$	7.23650e7			0.505852			0.252926	+	0.967486i	$0.418607\pi$
$524$		−	5.32628e7i		−	0.370195i
$525$	−7.26143e7			−0.501816
$526$		−	1.56564e8i		−	1.07581i
$527$		−	4.65083e7i		−	0.317760i
$528$		−	2.03185e7i		−	0.138035i
$529$	−2.54742e8			−1.72081
$530$			7.21140e7i			0.484386i
$531$	4.49943e7	−	2.15924e7i	0.300520	−	0.144217i
$532$	3.62562e6			0.0240795
$533$			1.33065e6i			0.00878782i
$534$	6.76730e7			0.444418
$535$	5.18234e7			0.338427
$536$	1.40119e7			0.0909916
$537$		−	5.02160e7i		−	0.324280i
$538$	−6.39546e6			−0.0410701
$539$			6.41379e7i			0.409589i
$540$	7.91288e6			0.0502520
$541$		−	1.59390e8i		−	1.00663i	−0.864104	−	0.503313i	$-0.832114\pi$
$541$		−	1.59390e8i		−	1.00663i	0.864104	−	0.503313i	$-0.167886\pi$
$542$			1.62259e8i			1.01908i
$543$	−1.12003e8			−0.699571
$544$			1.84026e7i			0.114310i
$545$			1.59556e8i			0.985650i
$546$	4.26764e7			0.262186
$547$	−1.29800e8			−0.793075			−0.396538	−	0.918019i	$-0.629788\pi$
$547$	−1.29800e8			−0.793075			−0.396538	+	0.918019i	$0.629788\pi$
$548$	6.92318e7			0.420692
$549$			6.51661e7i			0.393826i
$550$	8.18238e7			0.491803
$551$	4.51187e6			0.0269713
$552$	5.66319e7			0.336700
$553$	3.84977e8			2.27646
$554$			2.17754e8i			1.28067i
$555$		−	1.93996e6i		−	0.0113478i
$556$	9.47261e7			0.551119
$557$	−1.74795e7			−0.101150			−0.0505748	−	0.998720i	$-0.516105\pi$
$557$	−1.74795e7			−0.101150			−0.0505748	+	0.998720i	$0.516105\pi$
$558$	2.01237e7			0.115826
$559$	2.76363e7			0.158214
$560$	−2.74017e7			−0.156032
$561$		−	6.30370e7i		−	0.357032i
$562$		−	3.98911e7i		−	0.224733i
$563$		−	7.60210e7i		−	0.425999i	−0.977052	−	0.212999i	$-0.931677\pi$
$563$		−	7.60210e7i		−	0.425999i	0.977052	−	0.212999i	$-0.0683232\pi$
$564$		−	8440.87i		−	4.70490e-5i
$565$			1.77460e8i			0.983907i
$566$	4.90261e7			0.270382
$567$	−2.42056e7			−0.132790
$568$		−	4.97326e7i		−	0.271391i
$569$			1.54110e8i			0.836555i	0.908319	+	0.418277i	$0.137366\pi$
$569$			1.54110e8i			0.836555i	−0.908319	+	0.418277i	$0.862634\pi$
$570$		−	1.59105e6i		−	0.00859129i
$571$			4.23716e7i			0.227597i	0.993504	+	0.113799i	$0.0363019\pi$
$571$			4.23716e7i			0.227597i	−0.993504	+	0.113799i	$0.963698\pi$
$572$	−4.80889e7			−0.256955
$573$		−	6.26028e7i		−	0.332759i
$574$			2.61356e6i			0.0138196i
$575$			2.28060e8i			1.19963i
$576$	−7.96262e6			−0.0416667
$577$	−1.36051e8			−0.708228			−0.354114	−	0.935202i	$-0.615218\pi$
$577$	−1.36051e8			−0.708228			−0.354114	+	0.935202i	$0.615218\pi$
$578$		−	7.94495e7i		−	0.411441i
$579$	−1.15268e7			−0.0593843
$580$	−3.40998e7			−0.174770
$581$			2.33271e8i			1.18941i
$582$	1.32757e8			0.673424
$583$			2.48575e8i			1.25444i
$584$	−1.07168e7			−0.0538055
$585$		−	1.87279e7i		−	0.0935451i
$586$		−	7.87355e7i		−	0.391271i
$587$			1.73632e8i			0.858450i	0.903198	+	0.429225i	$0.141213\pi$
$587$			1.73632e8i			0.858450i	−0.903198	+	0.429225i	$0.858787\pi$
$588$	2.51351e7			0.123637
$589$		−	4.04628e6i		−	0.0198020i
$590$	3.28129e7	+	6.83756e7i	0.159767	+	0.332924i
$591$	−2.03557e8			−0.986107
$592$			1.95215e6i			0.00940912i
$593$	8.48406e7			0.406855			0.203428	−	0.979090i	$-0.434792\pi$
$593$	8.48406e7			0.406855			0.203428	+	0.979090i	$0.434792\pi$
$594$	2.72755e7			0.130141
$595$	−8.50124e7			−0.403582
$596$			4.85275e7i			0.229218i
$597$	9.67354e7			0.454635
$598$		−	1.34034e8i		−	0.626775i
$599$	−1.10579e8			−0.514510			−0.257255	−	0.966344i	$-0.582818\pi$
$599$	−1.10579e8			−0.514510			−0.257255	+	0.966344i	$0.582818\pi$
$600$		−	3.20660e7i		−	0.148454i
$601$			9.86921e7i			0.454631i	0.973821	+	0.227316i	$0.0729949\pi$
$601$			9.86921e7i			0.454631i	−0.973821	+	0.227316i	$0.927005\pi$
$602$	5.42812e7			0.248805
$603$			1.88095e7i			0.0857877i
$604$			3.22482e6i			0.0146351i
$605$	9.87910e6			0.0446120
$606$	3.30549e7			0.148531
$607$	−2.15368e8			−0.962973			−0.481487	−	0.876453i	$-0.659903\pi$
$607$	−2.15368e8			−0.962973			−0.481487	+	0.876453i	$0.659903\pi$
$608$			1.60105e6i			0.00712351i
$609$	1.04311e8			0.461828
$610$	−9.90297e7			−0.436290
$611$	−19977.5			−8.75826e−5
$612$	−2.47036e7			−0.107772
$613$		−	3.80371e8i		−	1.65130i	−0.564182	−	0.825650i	$-0.690808\pi$
$613$		−	3.80371e8i		−	1.65130i	0.564182	−	0.825650i	$-0.309192\pi$
$614$			1.47112e8i			0.635538i
$615$	1.14692e6			0.00493069
$616$	−9.44528e7			−0.404085
$617$	−1.65981e8			−0.706649			−0.353325	−	0.935501i	$-0.614949\pi$
$617$	−1.65981e8			−0.706649			−0.353325	+	0.935501i	$0.614949\pi$
$618$	1.15141e7			0.0487826
$619$	2.78433e8			1.17395			0.586975	−	0.809605i	$-0.300319\pi$
$619$	2.78433e8			1.17395			0.586975	+	0.809605i	$0.300319\pi$
$620$			3.05809e7i			0.128315i
$621$			7.60225e7i			0.317444i
$622$		−	9.28028e7i		−	0.385647i
$623$		−	3.14586e8i		−	1.30099i
$624$			1.88456e7i			0.0775634i
$625$	6.25479e7			0.256196
$626$	−4.89110e7			−0.199381
$627$		−	5.48429e6i		−	0.0222494i
$628$			1.29918e8i			0.524555i
$629$			6.05646e6i			0.0243370i
$630$		−	3.67840e7i		−	0.147108i
$631$	−1.10201e8			−0.438630			−0.219315	−	0.975654i	$-0.570382\pi$
$631$	−1.10201e8			−0.438630			−0.219315	+	0.975654i	$0.570382\pi$
$632$			1.70003e8i			0.673451i
$633$		−	1.00069e8i		−	0.394536i
$634$		−	2.28331e7i		−	0.0895976i
$635$	−8.25335e7			−0.322336
$636$	9.74143e7			0.378662
$637$		−	5.94887e7i		−	0.230153i
$638$	−1.17541e8			−0.452613
$639$	6.67609e7			0.255870
$640$		−	1.21004e7i		−	0.0461594i
$641$	−2.19321e8			−0.832735			−0.416367	−	0.909196i	$-0.636697\pi$
$641$	−2.19321e8			−0.832735			−0.416367	+	0.909196i	$0.636697\pi$
$642$		−	7.00050e7i		−	0.264560i
$643$	−1.20872e6			−0.00454667			−0.00227333	−	0.999997i	$-0.500724\pi$
$643$	−1.20872e6			−0.00454667			−0.00227333	+	0.999997i	$0.500724\pi$
$644$		−	2.63260e8i		−	0.985661i
$645$		−	2.38204e7i		−	0.0887709i
$646$			4.96718e6i			0.0184252i
$647$	−3.30143e8			−1.21896			−0.609480	−	0.792801i	$-0.708622\pi$
$647$	−3.30143e8			−1.21896			−0.609480	+	0.792801i	$0.708622\pi$
$648$		−	1.06890e7i		−	0.0392837i
$649$	1.13105e8	+	2.35689e8i	0.413759	+	0.862194i
$650$	−7.58926e7			−0.276350
$651$		−	9.35473e7i		−	0.339069i
$652$	2.27386e7			0.0820393
$653$	4.09092e8			1.46920			0.734602	−	0.678499i	$-0.237369\pi$
$653$	4.09092e8			1.46920			0.734602	+	0.678499i	$0.237369\pi$
$654$	2.15534e8			0.770517
$655$			1.08655e8i			0.386656i
$656$	−1.15413e6			−0.00408831
$657$		−	1.43862e7i		−	0.0507283i
$658$	−39238.4			−0.000137732
$659$			6.30114e7i			0.220172i	0.993922	+	0.110086i	$0.0351127\pi$
$659$			6.30114e7i			0.220172i	−0.993922	+	0.110086i	$0.964887\pi$
$660$			4.14492e7i			0.144173i
$661$	7.21556e7			0.249842			0.124921	−	0.992167i	$-0.460132\pi$
$661$	7.21556e7			0.249842			0.124921	+	0.992167i	$0.460132\pi$
$662$			1.79020e8i			0.617059i
$663$			5.84676e7i			0.200620i
$664$	−1.03011e8			−0.351867
$665$	−7.39618e6			−0.0251503
$666$	−2.62057e6			−0.00887100
$667$		−	3.27612e8i		−	1.10403i
$668$	2.67782e8			0.898362
$669$	−9.78356e7			−0.326752
$670$	−2.85839e7			−0.0950378
$671$	−3.41352e8			−1.12989
$672$			3.70152e7i			0.121976i
$673$		−	1.25604e7i		−	0.0412057i	−0.999788	−	0.0206028i	$-0.993441\pi$
$673$		−	1.25604e7i		−	0.0412057i	0.999788	−	0.0206028i	$-0.00655855\pi$
$674$	2.31957e8			0.757578
$675$	4.30453e7			0.139964
$676$	−1.09855e8			−0.355614
$677$	1.93944e8			0.625044			0.312522	−	0.949911i	$-0.398826\pi$
$677$	1.93944e8			0.625044			0.312522	+	0.949911i	$0.398826\pi$
$678$	2.39719e8			0.769154
$679$		−	6.17137e8i		−	1.97139i
$680$		−	3.75409e7i		−	0.119393i
$681$		−	2.10041e8i		−	0.665062i
$682$			1.05412e8i			0.332304i
$683$			5.43095e7i			0.170457i	0.996361	+	0.0852283i	$0.0271620\pi$
$683$			5.43095e7i			0.170457i	−0.996361	+	0.0852283i	$0.972838\pi$
$684$	−2.14925e6			−0.00671611
$685$	−1.41231e8			−0.439399
$686$			1.55970e8i			0.483135i
$687$		−	7.70251e7i		−	0.237554i
$688$			2.39702e7i			0.0736048i
$689$		−	2.30556e8i		−	0.704887i
$690$	−1.15528e8			−0.351673
$691$			5.12040e8i			1.55192i	0.630781	+	0.775961i	$0.282735\pi$
$691$			5.12040e8i			1.55192i	−0.630781	+	0.775961i	$0.717265\pi$
$692$		−	3.55463e7i		−	0.107269i
$693$		−	1.26793e8i		−	0.380975i
$694$	−3.56341e8			−1.06607
$695$	−1.93239e8			−0.575626
$696$			4.60633e7i			0.136624i
$697$	−3.58064e6			−0.0105745
$698$	1.16152e8			0.341555
$699$		−	1.49207e8i		−	0.436875i
$700$	−1.49063e8			−0.434585
$701$		−	2.67372e8i		−	0.776180i	−0.921621	−	0.388090i	$-0.873135\pi$
$701$		−	2.67372e8i		−	0.776180i	0.921621	−	0.388090i	$-0.126865\pi$
$702$	−2.52983e7			−0.0731275
$703$			526919.i			0.00151662i
$704$		−	4.17098e7i		−	0.119542i
$705$			17219.2i			4.91411e-5i
$706$	3.67793e8			1.04518
$707$		−	1.53660e8i		−	0.434812i
$708$	9.23644e7	−	4.43248e7i	0.260258	−	0.124896i
$709$	−2.66641e8			−0.748150			−0.374075	−	0.927399i	$-0.622040\pi$
$709$	−2.66641e8			−0.748150			−0.374075	+	0.927399i	$0.622040\pi$
$710$			1.01453e8i			0.283459i
$711$	−2.28212e8			−0.634935
$712$	1.38919e8			0.384877
$713$	−2.93805e8			−0.810569
$714$			1.14838e8i			0.315494i
$715$	9.81002e7			0.268381
$716$		−	1.03084e8i		−	0.280834i
$717$	−1.74714e8			−0.473992
$718$			8.24126e7i			0.222649i
$719$		−	6.39340e8i		−	1.72007i	−0.510237	−	0.860034i	$-0.670442\pi$
$719$		−	6.39340e8i		−	1.72007i	0.510237	−	0.860034i	$-0.329558\pi$
$720$	1.62436e7			0.0435195
$721$		−	5.35248e7i		−	0.142807i
$722$		−	2.65700e8i		−	0.705959i
$723$	−9.08883e7			−0.240488
$724$	−2.29921e8			−0.605846
$725$	−1.85500e8			−0.486776
$726$		−	1.33451e7i		−	0.0348747i
$727$	1.61561e8			0.420468			0.210234	−	0.977651i	$-0.432577\pi$
$727$	1.61561e8			0.420468			0.210234	+	0.977651i	$0.432577\pi$
$728$	8.76062e7			0.227060
$729$	1.43489e7			0.0370370
$730$	2.18620e7			0.0561981
$731$			7.43664e7i			0.190381i
$732$			1.33773e8i			0.341063i
$733$	7.71651e8			1.95934			0.979668	−	0.200627i	$-0.0642979\pi$
$733$	7.71651e8			1.95934			0.979668	+	0.200627i	$0.0642979\pi$
$734$	1.96073e8			0.495826
$735$	−5.12749e7			−0.129135
$736$	1.16254e8			0.291591
$737$	−9.85277e7			−0.246125
$738$		−	1.54930e6i		−	0.00385449i
$739$			4.70271e8i			1.16524i	0.812745	+	0.582620i	$0.197972\pi$
$739$			4.70271e8i			1.16524i	−0.812745	+	0.582620i	$0.802028\pi$
$740$		−	3.98235e6i		−	0.00982752i
$741$			5.08675e6i			0.0125022i
$742$		−	4.52842e8i		−	1.10850i
$743$	5.80553e8			1.41539			0.707694	−	0.706520i	$-0.249736\pi$
$743$	5.80553e8			1.41539			0.707694	+	0.706520i	$0.249736\pi$
$744$	4.13099e7			0.100308
$745$		−	9.89949e7i		−	0.239411i
$746$		−	2.25842e8i		−	0.543987i
$747$		−	1.38281e8i		−	0.331743i
$748$		−	1.29402e8i		−	0.309199i
$749$	−3.25427e8			−0.774476
$750$			1.55358e8i			0.368256i
$751$			4.19872e7i			0.0991281i	0.998771	+	0.0495641i	$0.0157832\pi$
$751$			4.19872e7i			0.0991281i	−0.998771	+	0.0495641i	$0.984217\pi$
$752$		−	17327.4i		−	4.07456e-5i
$753$	−2.67018e8			−0.625398
$754$	1.09021e8			0.254328
$755$		−	6.57856e6i		−	0.0152859i
$756$	−4.96892e7			−0.115000
$757$	4.12578e8			0.951082			0.475541	−	0.879693i	$-0.342252\pi$
$757$	4.12578e8			0.951082			0.475541	+	0.879693i	$0.342252\pi$
$758$			4.23240e7i			0.0971806i
$759$	−3.98221e8			−0.910748
$760$		−	3.26610e6i		−	0.00744028i
$761$	−3.78013e8			−0.857733			−0.428867	−	0.903368i	$-0.641087\pi$
$761$	−3.78013e8			−0.857733			−0.428867	+	0.903368i	$0.641087\pi$
$762$			1.11489e8i			0.251982i
$763$		−	1.00193e9i		−	2.25562i
$764$		−	1.28511e8i		−	0.288178i
$765$	5.03948e7			0.112565
$766$			6.17648e8i			1.37422i
$767$	−1.04906e8	−	2.18604e8i	−0.232496	−	0.484476i
$768$	−1.63457e7			−0.0360844
$769$			3.08742e8i			0.678916i	0.940621	+	0.339458i	$0.110244\pi$
$769$			3.08742e8i			0.678916i	−0.940621	+	0.339458i	$0.889756\pi$
$770$	1.92682e8			0.422054
$771$	−3.72166e8			−0.812034
$772$	−2.36622e7			−0.0514283
$773$			2.39861e8i			0.519303i	0.965702	+	0.259652i	$0.0836078\pi$
$773$			2.39861e8i			0.519303i	−0.965702	+	0.259652i	$0.916392\pi$
$774$	−3.21776e7			−0.0693953
$775$			1.66358e8i			0.357386i
$776$	2.72524e8			0.583202
$777$			1.21820e7i			0.0259691i
$778$			3.94919e8i			0.838628i
$779$	−311519.			−0.000658981
$780$		−	3.84446e7i		−	0.0810124i
$781$			3.49707e8i			0.734092i
$782$	3.60672e8			0.754210
$783$	−6.18352e7			−0.128810
$784$	5.15973e7			0.107073
$785$		−	2.65030e8i		−	0.547881i
$786$	1.46775e8			0.302263
$787$	2.37582e8			0.487404			0.243702	−	0.969850i	$-0.421638\pi$
$787$	2.37582e8			0.487404			0.243702	+	0.969850i	$0.421638\pi$
$788$	−4.17862e8			−0.853994
$789$	4.31440e8			0.878395
$790$		−	3.46802e8i		−	0.703397i
$791$		−	1.11436e9i		−	2.25163i
$792$	5.59911e7			0.112705
$793$	3.16609e8			0.634897
$794$	3.62167e8			0.723514
$795$	−1.98723e8			−0.395500
$796$	1.98579e8			0.393725
$797$			3.79075e8i			0.748773i	0.927273	+	0.374387i	$0.122147\pi$
$797$			3.79075e8i			0.748773i	−0.927273	+	0.374387i	$0.877853\pi$
$798$			9.99103e6i			0.0196608i
$799$		−	53757.5i		−	0.000105390i
$800$		−	6.58251e7i		−	0.128565i
$801$			1.86485e8i			0.362866i
$802$	−4.58752e8			−0.889314
$803$	7.53577e7			0.145540
$804$			3.86121e7i			0.0742943i
$805$			5.37045e8i			1.02949i
$806$		−	9.77706e7i		−	0.186725i
$807$		−	1.76238e7i		−	0.0335336i
$808$	6.78551e7			0.128632
$809$		−	5.75323e8i		−	1.08659i	−0.839541	−	0.543296i	$-0.817176\pi$
$809$		−	5.75323e8i		−	1.08659i	0.839541	−	0.543296i	$-0.182824\pi$
$810$			2.18053e7i			0.0410306i
$811$			5.32801e7i			0.0998855i	0.998752	+	0.0499428i	$0.0159039\pi$
$811$			5.32801e7i			0.0998855i	−0.998752	+	0.0499428i	$0.984096\pi$
$812$	2.14131e8			0.399955
$813$	−4.47132e8			−0.832078
$814$		−	1.37270e7i		−	0.0254509i
$815$	−4.63863e7			−0.0856874
$816$	−5.07117e7			−0.0933335
$817$			6.46996e6i			0.0118641i
$818$	−3.17070e8			−0.579289
$819$			1.17602e8i			0.214074i
$820$	2.35440e6			0.00427011
$821$		−	5.46346e8i		−	0.987275i	−0.869668	−	0.493637i	$-0.835667\pi$
$821$		−	5.46346e8i		−	0.987275i	0.869668	−	0.493637i	$-0.164333\pi$
$822$			1.90780e8i			0.343494i
$823$			7.65920e8i			1.37399i	0.726661	+	0.686996i	$0.241071\pi$
$823$			7.65920e8i			1.37399i	−0.726661	+	0.686996i	$0.758929\pi$
$824$	2.36362e7			0.0422470
$825$			2.25480e8i			0.401556i
$826$	−2.06049e8	−	4.29367e8i	−0.365621	−	0.761883i
$827$	−4.69914e8			−0.830810			−0.415405	−	0.909636i	$-0.636360\pi$
$827$	−4.69914e8			−0.830810			−0.415405	+	0.909636i	$0.636360\pi$
$828$			1.56059e8i			0.274915i
$829$	−6.54418e7			−0.114866			−0.0574330	−	0.998349i	$-0.518292\pi$
$829$	−6.54418e7			−0.114866			−0.0574330	+	0.998349i	$0.518292\pi$
$830$	2.10140e8			0.367514
$831$	−6.00060e8			−1.04566
$832$			3.86863e7i			0.0671719i
$833$	1.60078e8			0.276947
$834$			2.61034e8i			0.449987i
$835$	−5.46268e8			−0.938310
$836$		−	1.12582e7i		−	0.0192685i
$837$			5.54543e7i			0.0945712i
$838$	−5.70016e8			−0.968624
$839$		−	5.63272e8i		−	0.953745i	−0.878972	−	0.476872i	$-0.841770\pi$
$839$		−	5.63272e8i		−	0.953745i	0.878972	−	0.476872i	$-0.158230\pi$
$840$		−	7.55102e7i		−	0.127399i
$841$	−3.28350e8			−0.552013
$842$	−2.34624e8			−0.393039
$843$	1.09927e8			0.183494
$844$		−	2.05421e8i		−	0.341678i
$845$	2.24101e8			0.371427
$846$	23260.3			3.84153e−5
$847$	−6.20362e7			−0.102093
$848$	1.99972e8			0.327931
$849$			1.35100e8i			0.220766i
$850$		−	2.04219e8i		−	0.332537i
$851$	3.82602e7			0.0620810
$852$	1.37047e8			0.221590
$853$	1.91596e7			0.0308702			0.0154351	−	0.999881i	$-0.495087\pi$
$853$	1.91596e7			0.0308702			0.0154351	+	0.999881i	$0.495087\pi$
$854$	6.21860e8			0.998433
$855$	4.38441e6			0.00701476
$856$		−	1.43706e8i		−	0.229115i
$857$			6.46184e8i			1.02663i	0.858201	+	0.513314i	$0.171583\pi$
$857$			6.46184e8i			1.02663i	−0.858201	+	0.513314i	$0.828417\pi$
$858$		−	1.32517e8i		−	0.209803i
$859$		−	9.00210e8i		−	1.42025i	−0.704076	−	0.710124i	$-0.748639\pi$
$859$		−	9.00210e8i		−	1.42025i	0.704076	−	0.710124i	$-0.251361\pi$
$860$		−	4.88986e7i		−	0.0768779i
$861$	−7.20213e6			−0.0112837
$862$	3.01551e8			0.470803
$863$			4.48341e8i			0.697551i	0.937206	+	0.348775i	$0.113402\pi$
$863$			4.48341e8i			0.697551i	−0.937206	+	0.348775i	$0.886598\pi$
$864$		−	2.19424e7i		−	0.0340207i
$865$			7.25136e7i			0.112039i
$866$			4.75734e7i			0.0732505i
$867$	2.18937e8			0.335940
$868$		−	1.92034e8i		−	0.293643i
$869$		−	1.19542e9i		−	1.82163i
$870$		−	9.39679e7i		−	0.142699i
$871$	9.13857e7			0.138300
$872$	4.42448e8			0.667287
$873$			3.65835e8i			0.549848i
$874$	3.13789e7			0.0470006
$875$	7.22201e8			1.07804
$876$		−	2.95320e7i		−	0.0439320i
$877$	−7.15352e8			−1.06053			−0.530263	−	0.847833i	$-0.677907\pi$
$877$	−7.15352e8			−1.06053			−0.530263	+	0.847833i	$0.677907\pi$
$878$		−	1.98741e7i		−	0.0293633i
$879$	2.16969e8			0.319471
$880$			8.50869e7i			0.124857i
$881$		−	7.56579e8i		−	1.10644i	−0.833036	−	0.553218i	$-0.813400\pi$
$881$		−	7.56579e8i		−	1.10644i	0.833036	−	0.553218i	$-0.186600\pi$
$882$			6.92641e7i			0.100949i
$883$	6.78185e8			0.985068			0.492534	−	0.870293i	$-0.336071\pi$
$883$	6.78185e8			0.985068			0.492534	+	0.870293i	$0.336071\pi$
$884$			1.20022e8i			0.173742i
$885$	−1.88421e8	+	9.04216e7i	−0.271831	+	0.130449i
$886$	−1.24458e8			−0.178946
$887$			2.08113e8i			0.298214i	0.988821	+	0.149107i	$0.0476399\pi$
$887$			2.08113e8i			0.298214i	−0.988821	+	0.149107i	$0.952360\pi$
$888$	−5.37951e6			−0.00768252
$889$	5.18272e8			0.737654
$890$	−2.83392e8			−0.401992
$891$			7.51623e7i			0.106259i
$892$	−2.00837e8			−0.282976
$893$		−	4676.96i		−	6.56765e-6i
$894$	−1.33726e8			−0.187156
$895$			2.10288e8i			0.293322i
$896$			7.59849e7i			0.105634i
$897$	3.69355e8			0.511760
$898$			1.98072e8i			0.273523i
$899$		−	2.38975e8i		−	0.328907i
$900$	8.83635e7			0.121212
$901$	6.20404e8			0.848203
$902$	8.11555e6			0.0110586
$903$			1.49581e8i			0.203149i
$904$	4.92095e8			0.666107
$905$	4.69033e8			0.632787
$906$	−8.88657e6			−0.0119495
$907$	1.20266e9			1.61183			0.805916	−	0.592030i	$-0.201673\pi$
$907$	1.20266e9			1.61183			0.805916	+	0.592030i	$0.201673\pi$
$908$		−	4.31172e8i		−	0.575960i
$909$			9.10886e7i			0.121275i
$910$	−1.78715e8			−0.237157
$911$	2.92030e8			0.386254			0.193127	−	0.981174i	$-0.438137\pi$
$911$	2.92030e8			0.386254			0.193127	+	0.981174i	$0.438137\pi$
$912$	−4.41197e6			−0.00581632
$913$	7.24345e8			0.951772
$914$	1.19397e8			0.156370
$915$		−	2.72894e8i		−	0.356230i
$916$		−	1.58117e8i		−	0.205728i
$917$		−	6.82302e8i		−	0.884847i
$918$		−	6.80752e7i		−	0.0879956i
$919$			7.98782e7i			0.102916i	0.998675	+	0.0514578i	$0.0163868\pi$
$919$			7.98782e7i			0.102916i	−0.998675	+	0.0514578i	$0.983613\pi$
$920$	−2.37155e8			−0.304558
$921$	−4.05392e8			−0.518915
$922$			5.08848e8i			0.649225i
$923$		−	3.24357e8i		−	0.412495i
$924$		−	2.60281e8i		−	0.329934i
$925$		−	2.16636e7i		−	0.0273720i
$926$	−6.71200e8			−0.845315
$927$			3.17292e7i			0.0398309i
$928$			9.45587e7i			0.118320i
$929$		−	8.28461e8i		−	1.03330i	−0.856198	−	0.516648i	$-0.827180\pi$
$929$		−	8.28461e8i		−	1.03330i	0.856198	−	0.516648i	$-0.172820\pi$
$930$	−8.42712e7			−0.104768
$931$	1.39270e7			0.0172587
$932$		−	3.06292e8i		−	0.378345i
$933$	2.55734e8			0.314879
$934$	−2.52329e8			−0.309689
$935$			2.63978e8i			0.322948i
$936$	−5.19324e7			−0.0633302
$937$			2.74675e8i			0.333887i	0.985966	+	0.166944i	$0.0533898\pi$
$937$			2.74675e8i			0.333887i	−0.985966	+	0.166944i	$0.946610\pi$
$938$	1.79493e8			0.217490
$939$		−	1.34783e8i		−	0.162794i
$940$			35347.5i			4.25575e-5i
$941$		−	3.00870e7i		−	0.0361085i	−0.999837	−	0.0180543i	$-0.994253\pi$
$941$		−	3.00870e7i		−	0.0361085i	0.999837	−	0.0180543i	$-0.00574716\pi$
$942$	−3.58012e8			−0.428297
$943$			2.26198e7i			0.0269745i
$944$	1.89606e8	−	9.09901e7i	0.225390	−	0.108163i
$945$	1.01365e8			0.120113
$946$		−	1.68552e8i		−	0.199095i
$947$	5.22300e8			0.614993			0.307496	−	0.951549i	$-0.400509\pi$
$947$	5.22300e8			0.614993			0.307496	+	0.951549i	$0.400509\pi$
$948$	−4.68474e8			−0.549870
$949$	−6.98952e7			−0.0817803
$950$		−	1.77673e7i		−	0.0207229i
$951$	6.29205e7			0.0731561
$952$			2.35739e8i			0.273226i
$953$	1.00812e9			1.16475			0.582377	−	0.812919i	$-0.302123\pi$
$953$	1.00812e9			1.16475			0.582377	+	0.812919i	$0.302123\pi$
$954$			2.68442e8i			0.309176i
$955$			2.62159e8i			0.300992i
$956$	−3.58653e8			−0.410489
$957$		−	3.23905e8i		−	0.369557i
$958$		−	8.82043e8i		−	1.00321i
$959$	8.86867e8			1.00555
$960$	3.33448e7			0.0376890
$961$	6.73189e8			0.758520
$962$			1.27320e7i			0.0143012i
$963$	1.92911e8			0.216012
$964$	−1.86576e8			−0.208269
$965$	4.82702e7			0.0537152
$966$	7.25460e8			0.804789
$967$		−	5.74079e8i		−	0.634880i	−0.948278	−	0.317440i	$-0.897177\pi$
$967$		−	5.74079e8i		−	0.634880i	0.948278	−	0.317440i	$-0.102823\pi$
$968$		−	2.73948e7i		−	0.0302024i
$969$	−1.36879e7			−0.0150441
$970$	−5.55942e8			−0.609136
$971$	−6.88573e8			−0.752129			−0.376064	−	0.926594i	$-0.622723\pi$
$971$	−6.88573e8			−0.752129			−0.376064	+	0.926594i	$0.622723\pi$
$972$	2.94555e7			0.0320750
$973$	1.21345e9			1.31730
$974$			1.49173e8i			0.161441i
$975$		−	2.09135e8i		−	0.225639i
$976$			2.74609e8i			0.295370i
$977$		−	6.17420e8i		−	0.662060i	−0.943620	−	0.331030i	$-0.892604\pi$
$977$		−	6.17420e8i		−	0.662060i	0.943620	−	0.331030i	$-0.107396\pi$
$978$			6.26603e7i			0.0669848i
$979$	−9.76843e8			−1.04106
$980$	−1.05257e8			−0.111834
$981$			5.93941e8i			0.629124i
$982$		−	3.22971e8i		−	0.341059i
$983$		−	1.40428e8i		−	0.147841i	−0.997264	−	0.0739204i	$-0.976449\pi$
$983$		−	1.40428e8i		−	0.147841i	0.997264	−	0.0739204i	$-0.0235511\pi$
$984$		−	3.18041e6i		−	0.00333809i
$985$	8.52429e8			0.891969
$986$			2.93364e8i			0.306038i
$987$		−	108128.i		−	0.000112457i
$988$			1.04421e7i			0.0108272i
$989$	4.69791e8			0.485641
$990$	−1.14220e8			−0.117717
$991$			1.52293e9i			1.56480i	0.622778	+	0.782399i	$0.286004\pi$
$991$			1.52293e9i			1.56480i	−0.622778	+	0.782399i	$0.713996\pi$
$992$	8.48010e7			0.0868692
$993$	−4.93320e8			−0.503827
$994$		−	6.37079e8i		−	0.648686i
$995$	−4.05096e8			−0.411233
$996$		−	2.83864e8i		−	0.287298i
$997$	1.47192e9			1.48524			0.742622	−	0.669711i	$-0.233582\pi$
$997$	1.47192e9			1.48524			0.742622	+	0.669711i	$0.233582\pi$
$998$		−	6.78946e8i		−	0.683036i
$999$		−	7.22144e6i		−	0.00724314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.7.d.a.235.16	yes	60
59.58	odd	2	inner	354.7.d.a.235.15	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.7.d.a.235.15	✓	60	59.58	odd	2	inner
354.7.d.a.235.16	yes	60	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+5.65685i q^{2} -15.5885 q^{3} -32.0000 q^{4} +65.2792 q^{5} -88.1816i q^{6} -409.923 q^{7} -181.019i q^{8} +243.000 q^{9} +O(q^{10})\)	\(q+5.65685i q^{2} -15.5885 q^{3} -32.0000 q^{4} +65.2792 q^{5} -88.1816i q^{6} -409.923 q^{7} -181.019i q^{8} +243.000 q^{9} +369.275i q^{10} +1272.88i q^{11} +498.831 q^{12} -1180.61i q^{13} -2318.88i q^{14} -1017.60 q^{15} +1024.00 q^{16} +3176.91 q^{17} +1374.62i q^{18} +276.395 q^{19} -2088.94 q^{20} +6390.07 q^{21} -7200.50 q^{22} -20069.3i q^{23} +2821.81i q^{24} -11363.6 q^{25} +6678.55 q^{26} -3788.00 q^{27} +13117.5 q^{28} +16324.0 q^{29} -5756.43i q^{30} -14639.5i q^{31} +5792.62i q^{32} -19842.2i q^{33} +17971.3i q^{34} -26759.5 q^{35} -7776.00 q^{36} +1906.40i q^{37} +1563.53i q^{38} +18403.9i q^{39} -11816.8i q^{40} -1127.08 q^{41} +36147.7i q^{42} +23408.4i q^{43} -40732.2i q^{44} +15862.9 q^{45} +113529. q^{46} -16.9213i q^{47} -15962.6 q^{48} +50388.0 q^{49} -64282.4i q^{50} -49523.1 q^{51} +37779.6i q^{52} +195285. q^{53} -21428.1i q^{54} +83092.7i q^{55} +74204.0i q^{56} -4308.57 q^{57} +92342.5i q^{58} +(185162. - 88857.5i) q^{59} +32563.3 q^{60} +268173. i q^{61} +82813.5 q^{62} -99611.3 q^{63} -32768.0 q^{64} -77069.5i q^{65} +112245. q^{66} +77405.3i q^{67} -101661. q^{68} +312850. i q^{69} -151374. i q^{70} +274736. q^{71} -43987.7i q^{72} -59202.5i q^{73} -10784.2 q^{74} +177141. q^{75} -8844.63 q^{76} -521783. i q^{77} -104108. q^{78} -939144. q^{79} +66845.9 q^{80} +59049.0 q^{81} -6375.74i q^{82} -569060. i q^{83} -204482. q^{84} +207386. q^{85} -132418. q^{86} -254466. q^{87} +230416. q^{88} +767427. i q^{89} +89733.8i q^{90} +483960. i q^{91} +642219. i q^{92} +228207. i q^{93} +95.7214 q^{94} +18042.8 q^{95} -90298.0i q^{96} +1.50550e6i q^{97} +285037. i q^{98} +309310. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 1920 q^{4} + 408 q^{7} + 14580 q^{9}+O(q^{10}) \) 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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