LMFDB - Embedded newform 115.7.d.a.91.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,7,Mod(91,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, 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("115.91");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	115.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:	$26.4562196163$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.25
Character	$\chi$	$=$	115.91
Dual form			115.7.d.a.91.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.576987 q^{2} +45.3261 q^{3} -63.6671 q^{4} +55.9017i q^{5} -26.1526 q^{6} -580.802i q^{7} +73.6623 q^{8} +1325.46 q^{9} +O(q^{10})$	\(q-0.576987 q^{2} +45.3261 q^{3} -63.6671 q^{4} +55.9017i q^{5} -26.1526 q^{6} -580.802i q^{7} +73.6623 q^{8} +1325.46 q^{9} -32.2546i q^{10} +355.332i q^{11} -2885.78 q^{12} -3005.26 q^{13} +335.115i q^{14} +2533.81i q^{15} +4032.19 q^{16} -2913.04i q^{17} -764.771 q^{18} -9730.86i q^{19} -3559.10i q^{20} -26325.5i q^{21} -205.022i q^{22} +(-11956.2 - 2254.92i) q^{23} +3338.82 q^{24} -3125.00 q^{25} +1734.00 q^{26} +27035.0 q^{27} +36977.9i q^{28} +27905.9 q^{29} -1461.97i q^{30} -27704.9 q^{31} -7040.91 q^{32} +16105.8i q^{33} +1680.79i q^{34} +32467.8 q^{35} -84387.9 q^{36} -77661.1i q^{37} +5614.58i q^{38} -136217. q^{39} +4117.85i q^{40} +105635. q^{41} +15189.5i q^{42} -97228.0i q^{43} -22622.9i q^{44} +74095.3i q^{45} +(6898.59 + 1301.06i) q^{46} +65291.8 q^{47} +182764. q^{48} -219682. q^{49} +1803.09 q^{50} -132037. i q^{51} +191336. q^{52} +121989. i q^{53} -15598.9 q^{54} -19863.7 q^{55} -42783.2i q^{56} -441062. i q^{57} -16101.3 q^{58} -169145. q^{59} -161320. i q^{60} -221422. i q^{61} +15985.4 q^{62} -769827. i q^{63} -253998. q^{64} -167999. i q^{65} -9292.85i q^{66} +481948. i q^{67} +185465. i q^{68} +(-541929. - 102207. i) q^{69} -18733.5 q^{70} +463486. q^{71} +97636.1 q^{72} -338686. q^{73} +44809.5i q^{74} -141644. q^{75} +619536. i q^{76} +206377. q^{77} +78595.3 q^{78} -701834. i q^{79} +225406. i q^{80} +259136. q^{81} -60950.1 q^{82} +281512. i q^{83} +1.67607e6i q^{84} +162844. q^{85} +56099.4i q^{86} +1.26486e6 q^{87} +26174.6i q^{88} +40235.0i q^{89} -42752.0i q^{90} +1.74546e6i q^{91} +(761218. + 143564. i) q^{92} -1.25576e6 q^{93} -37672.5 q^{94} +543972. q^{95} -319137. q^{96} +208192. i q^{97} +126753. q^{98} +470977. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 20 q^{2} + 1584 q^{4} + 410 q^{6} - 1210 q^{8} + 12896 q^{9}+O(q^{10}) $ 48 * q - 20 * q^2 + 1584 * q^4 + 410 * q^6 - 1210 * q^8 + 12896 * q^9	$ 48 q - 20 q^{2} + 1584 q^{4} + 410 q^{6} - 1210 q^{8} + 12896 q^{9} + 4290 q^{12} - 1440 q^{13} + 65400 q^{16} + 4610 q^{18} + 26600 q^{23} + 14940 q^{24} - 150000 q^{25} + 47594 q^{26} + 16080 q^{27} + 131800 q^{29} - 1392 q^{31} - 225040 q^{32} + 5000 q^{35} + 658786 q^{36} - 236320 q^{39} - 351496 q^{41} + 382692 q^{46} + 395680 q^{47} + 1042550 q^{48} - 637848 q^{49} + 62500 q^{50} + 523890 q^{52} - 241250 q^{54} - 402000 q^{55} - 479130 q^{58} - 466312 q^{59} - 1124330 q^{62} + 837582 q^{64} + 1021060 q^{69} - 396000 q^{70} - 114336 q^{71} - 1960750 q^{72} - 498720 q^{73} + 3610400 q^{77} - 1104610 q^{78} + 972888 q^{81} + 124950 q^{82} - 246000 q^{85} - 2090960 q^{87} + 4913480 q^{92} + 3234320 q^{93} - 5550378 q^{94} - 1664000 q^{95} - 776990 q^{96} + 9993220 q^{98}+O(q^{100}) $ 48 * q - 20 * q^2 + 1584 * q^4 + 410 * q^6 - 1210 * q^8 + 12896 * q^9 + 4290 * q^12 - 1440 * q^13 + 65400 * q^16 + 4610 * q^18 + 26600 * q^23 + 14940 * q^24 - 150000 * q^25 + 47594 * q^26 + 16080 * q^27 + 131800 * q^29 - 1392 * q^31 - 225040 * q^32 + 5000 * q^35 + 658786 * q^36 - 236320 * q^39 - 351496 * q^41 + 382692 * q^46 + 395680 * q^47 + 1042550 * q^48 - 637848 * q^49 + 62500 * q^50 + 523890 * q^52 - 241250 * q^54 - 402000 * q^55 - 479130 * q^58 - 466312 * q^59 - 1124330 * q^62 + 837582 * q^64 + 1021060 * q^69 - 396000 * q^70 - 114336 * q^71 - 1960750 * q^72 - 498720 * q^73 + 3610400 * q^77 - 1104610 * q^78 + 972888 * q^81 + 124950 * q^82 - 246000 * q^85 - 2090960 * q^87 + 4913480 * q^92 + 3234320 * q^93 - 5550378 * q^94 - 1664000 * q^95 - 776990 * q^96 + 9993220 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$-1$

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 $

$2$	−0.576987			−0.0721234			−0.0360617	−	0.999350i	$-0.511481\pi$
$2$	−0.576987			−0.0721234			−0.0360617	+	0.999350i	$0.511481\pi$
$3$	45.3261			1.67874			0.839372	−	0.543557i	$-0.182923\pi$
$3$	45.3261			1.67874			0.839372	+	0.543557i	$0.182923\pi$
$4$	−63.6671			−0.994798
$5$			55.9017i			0.447214i
$5$			55.9017i			0.447214i
$6$	−26.1526			−0.121077
$7$		−	580.802i		−	1.69330i	−0.532151	−	0.846650i	$-0.678616\pi$
$7$		−	580.802i		−	1.69330i	0.532151	−	0.846650i	$-0.321384\pi$
$8$	73.6623			0.143872
$9$	1325.46			1.81818
$10$		−	32.2546i		−	0.0322546i
$11$			355.332i			0.266966i	0.991051	+	0.133483i	$0.0426162\pi$
$11$			355.332i			0.266966i	−0.991051	+	0.133483i	$0.957384\pi$
$12$	−2885.78			−1.67001
$13$	−3005.26			−1.36789			−0.683946	−	0.729533i	$-0.739738\pi$
$13$	−3005.26			−1.36789			−0.683946	+	0.729533i	$0.739738\pi$
$14$			335.115i			0.122127i
$15$			2533.81i			0.750757i
$16$	4032.19			0.984422
$17$		−	2913.04i		−	0.592924i	−0.955045	−	0.296462i	$-0.904193\pi$
$17$		−	2913.04i		−	0.592924i	0.955045	−	0.296462i	$-0.0958069\pi$
$18$	−764.771			−0.131134
$19$		−	9730.86i		−	1.41870i	−0.704857	−	0.709350i	$-0.748989\pi$
$19$		−	9730.86i		−	1.41870i	0.704857	−	0.709350i	$-0.251011\pi$
$20$		−	3559.10i		−	0.444887i
$21$		−	26325.5i		−	2.84262i
$22$		−	205.022i		−	0.0192545i
$23$	−11956.2	−	2254.92i	−0.982676	−	0.185331i
$23$	−11956.2	−	2254.92i	−0.982676	−	0.185331i
$24$	3338.82			0.241524
$25$	−3125.00			−0.200000
$26$	1734.00			0.0986570
$27$	27035.0			1.37352
$28$			36977.9i			1.68449i
$29$	27905.9			1.14420			0.572100	−	0.820184i	$-0.306129\pi$
$29$	27905.9			1.14420			0.572100	+	0.820184i	$0.306129\pi$
$30$		−	1461.97i		−	0.0541472i
$31$	−27704.9			−0.929976			−0.464988	−	0.885317i	$-0.653941\pi$
$31$	−27704.9			−0.929976			−0.464988	+	0.885317i	$0.653941\pi$
$32$	−7040.91			−0.214872
$33$			16105.8i			0.448168i
$34$			1680.79i			0.0427637i
$35$	32467.8			0.757266
$36$	−84387.9			−1.80873
$37$		−	77661.1i		−	1.53320i	−0.642126	−	0.766599i	$-0.721947\pi$
$37$		−	77661.1i		−	1.53320i	0.642126	−	0.766599i	$-0.278053\pi$
$38$			5614.58i			0.102321i
$39$	−136217.			−2.29634
$40$			4117.85i			0.0643414i
$41$	105635.			1.53270			0.766349	−	0.642425i	$-0.222072\pi$
$41$	105635.			1.53270			0.766349	+	0.642425i	$0.222072\pi$
$42$			15189.5i			0.205019i
$43$		−	97228.0i		−	1.22289i	−0.791288	−	0.611443i	$-0.790589\pi$
$43$		−	97228.0i		−	1.22289i	0.791288	−	0.611443i	$-0.209411\pi$
$44$		−	22622.9i		−	0.265577i
$45$			74095.3i			0.813117i
$46$	6898.59	+	1301.06i	0.0708740	+	0.0133667i
$47$	65291.8			0.628876			0.314438	−	0.949278i	$-0.398184\pi$
$47$	65291.8			0.628876			0.314438	+	0.949278i	$0.398184\pi$
$48$	182764.			1.65259
$49$	−219682.			−1.86726
$50$	1803.09			0.0144247
$51$		−	132037.i		−	0.995369i
$52$	191336.			1.36078
$53$			121989.i			0.819393i	0.912222	+	0.409697i	$0.134365\pi$
$53$			121989.i			0.819393i	−0.912222	+	0.409697i	$0.865635\pi$
$54$	−15598.9			−0.0990631
$55$	−19863.7			−0.119391
$56$		−	42783.2i		−	0.243618i
$57$		−	441062.i		−	2.38163i
$58$	−16101.3			−0.0825235
$59$	−169145.			−0.823573			−0.411787	−	0.911280i	$-0.635095\pi$
$59$	−169145.			−0.823573			−0.411787	+	0.911280i	$0.635095\pi$
$60$		−	161320.i		−	0.746852i
$61$		−	221422.i		−	0.975510i	−0.872980	−	0.487755i	$-0.837816\pi$
$61$		−	221422.i		−	0.975510i	0.872980	−	0.487755i	$-0.162184\pi$
$62$	15985.4			0.0670730
$63$		−	769827.i		−	3.07873i
$64$	−253998.			−0.968924
$65$		−	167999.i		−	0.611740i
$66$		−	9292.85i		−	0.0323234i
$67$			481948.i			1.60242i	0.598385	+	0.801209i	$0.295809\pi$
$67$			481948.i			1.60242i	−0.598385	+	0.801209i	$0.704191\pi$
$68$			185465.i			0.589840i
$69$	−541929.	−	102207.i	−1.64966	−	0.311123i
$70$	−18733.5			−0.0546166
$71$	463486.			1.29498			0.647488	−	0.762076i	$-0.275820\pi$
$71$	463486.			1.29498			0.647488	+	0.762076i	$0.275820\pi$
$72$	97636.1			0.261585
$73$	−338686.			−0.870620			−0.435310	−	0.900281i	$-0.643361\pi$
$73$	−338686.			−0.870620			−0.435310	+	0.900281i	$0.643361\pi$
$74$			44809.5i			0.110580i
$75$	−141644.			−0.335749
$76$			619536.i			1.41132i
$77$	206377.			0.452054
$78$	78595.3			0.165620
$79$		−	701834.i		−	1.42349i	−0.702440	−	0.711743i	$-0.747906\pi$
$79$		−	701834.i		−	1.42349i	0.702440	−	0.711743i	$-0.252094\pi$
$80$			225406.i			0.440247i
$81$	259136.			0.487609
$82$	−60950.1			−0.110543
$83$			281512.i			0.492338i	0.969227	+	0.246169i	$0.0791718\pi$
$83$			281512.i			0.492338i	−0.969227	+	0.246169i	$0.920828\pi$
$84$			1.67607e6i			2.82783i
$85$	162844.			0.265164
$86$			56099.4i			0.0881988i
$87$	1.26486e6			1.92082
$88$			26174.6i			0.0384089i
$89$			40235.0i			0.0570735i	0.999593	+	0.0285367i	$0.00908476\pi$
$89$			40235.0i			0.0570735i	−0.999593	+	0.0285367i	$0.990915\pi$
$90$		−	42752.0i		−	0.0586447i
$91$			1.74546e6i			2.31625i
$92$	761218.	+	143564.i	0.977565	+	0.184367i
$93$	−1.25576e6			−1.56119
$94$	−37672.5			−0.0453567
$95$	543972.			0.634462
$96$	−319137.			−0.360714
$97$			208192.i			0.228112i	0.993474	+	0.114056i	$0.0363844\pi$
$97$			208192.i			0.228112i	−0.993474	+	0.114056i	$0.963616\pi$
$98$	126753.			0.134673
$99$			470977.i			0.485394i
$100$	198960.			0.198960
$101$	−103833.			−0.100779			−0.0503895	−	0.998730i	$-0.516046\pi$
$101$	−103833.			−0.100779			−0.0503895	+	0.998730i	$0.516046\pi$
$102$			76183.5i			0.0717894i
$103$			184649.i			0.168980i	0.996424	+	0.0844900i	$0.0269261\pi$
$103$			184649.i			0.168980i	−0.996424	+	0.0844900i	$0.973074\pi$
$104$	−221374.			−0.196801
$105$	1.47164e6			1.27126
$106$		−	70386.0i		−	0.0590975i
$107$			1.82391e6i			1.48885i	0.667704	+	0.744427i	$0.267277\pi$
$107$			1.82391e6i			1.48885i	−0.667704	+	0.744427i	$0.732723\pi$
$108$	−1.72124e6			−1.36638
$109$			396614.i			0.306259i	0.988206	+	0.153129i	$0.0489352\pi$
$109$			396614.i			0.306259i	−0.988206	+	0.153129i	$0.951065\pi$
$110$	11461.1			0.00861088
$111$		−	3.52008e6i		−	2.57385i
$112$		−	2.34190e6i		−	1.66692i
$113$			2.73411e6i			1.89488i	0.319938	+	0.947439i	$0.396338\pi$
$113$			2.73411e6i			1.89488i	−0.319938	+	0.947439i	$0.603662\pi$
$114$			254487.i			0.171772i
$115$	126054.	−	668373.i	0.0828825	−	0.439466i
$116$	−1.77669e6			−1.13825
$117$	−3.98334e6			−2.48708
$118$	97594.3			0.0593989
$119$	−1.69190e6			−1.00400
$120$			186646.i			0.108013i
$121$	1.64530e6			0.928729
$122$			127758.i			0.0703571i
$123$	4.78802e6			2.57301
$124$	1.76389e6			0.925138
$125$		−	174693.i		−	0.0894427i
$126$			444180.i			0.222048i
$127$	2.55759e6			1.24859			0.624295	−	0.781189i	$-0.285386\pi$
$127$	2.55759e6			1.24859			0.624295	+	0.781189i	$0.285386\pi$
$128$	597172.			0.284754
$129$		−	4.40697e6i		−	2.05291i
$130$			96933.3i			0.0441208i
$131$	1.28466e6			0.571443			0.285722	−	0.958313i	$-0.407767\pi$
$131$	1.28466e6			0.571443			0.285722	+	0.958313i	$0.407767\pi$
$132$		−	1.02541e6i		−	0.445837i
$133$	−5.65170e6			−2.40228
$134$		−	278078.i		−	0.115572i
$135$			1.51130e6i			0.614258i
$136$		−	214581.i		−	0.0853050i
$137$			1.45748e6i			0.566816i	0.958999	+	0.283408i	$0.0914651\pi$
$137$			1.45748e6i			0.566816i	−0.958999	+	0.283408i	$0.908535\pi$
$138$	312686.	+	58972.0i	0.118979	+	0.0224393i
$139$	−20377.0			−0.00758746			−0.00379373	−	0.999993i	$-0.501208\pi$
$139$	−20377.0			−0.00758746			−0.00379373	+	0.999993i	$0.501208\pi$
$140$	−2.06713e6			−0.753327
$141$	2.95942e6			1.05572
$142$	−267426.			−0.0933981
$143$		−	1.06786e6i		−	0.365181i
$144$	5.34449e6			1.78986
$145$			1.55999e6i			0.511701i
$146$	195418.			0.0627921
$147$	−9.95731e6			−3.13466
$148$			4.94446e6i			1.52522i
$149$			1.73619e6i			0.524855i	0.964952	+	0.262427i	$0.0845230\pi$
$149$			1.73619e6i			0.524855i	−0.964952	+	0.262427i	$0.915477\pi$
$150$	81726.8			0.0242154
$151$	−1.23583e6			−0.358946			−0.179473	−	0.983763i	$-0.557439\pi$
$151$	−1.23583e6			−0.358946			−0.179473	+	0.983763i	$0.557439\pi$
$152$		−	716798.i		−	0.204111i
$153$		−	3.86110e6i		−	1.07805i
$154$	−119077.			−0.0326036
$155$		−	1.54875e6i		−	0.415898i
$156$	8.67252e6			2.28440
$157$		−	1940.43i		−	0.000501418i	−1.00000		0.000250709i	$-0.999920\pi$
$157$		−	1940.43i		−	0.000501418i	1.00000		0.000250709i	$-7.98031e-5\pi$
$158$			404949.i			0.102667i
$159$			5.52928e6i			1.37555i
$160$		−	393599.i		−	0.0960935i
$161$	−1.30966e6	+	6.94419e6i	−0.313821	+	1.66396i
$162$	−149518.			−0.0351680
$163$	1.13179e6			0.261338			0.130669	−	0.991426i	$-0.458287\pi$
$163$	1.13179e6			0.261338			0.130669	+	0.991426i	$0.458287\pi$
$164$	−6.72547e6			−1.52472
$165$	−900342.			−0.200427
$166$		−	162429.i		−	0.0355091i
$167$	−539630.			−0.115863			−0.0579317	−	0.998321i	$-0.518451\pi$
$167$	−539630.			−0.115863			−0.0579317	+	0.998321i	$0.518451\pi$
$168$		−	1.93919e6i		−	0.408972i
$169$	4.20477e6			0.871128
$170$	−93958.8			−0.0191245
$171$		−	1.28978e7i		−	2.57946i
$172$			6.19023e6i			1.21653i
$173$	4.35676e6			0.841445			0.420722	−	0.907189i	$-0.361777\pi$
$173$	4.35676e6			0.841445			0.420722	+	0.907189i	$0.361777\pi$
$174$	−729811.			−0.138536
$175$			1.81501e6i			0.338660i
$176$			1.43277e6i			0.262807i
$177$	−7.66667e6			−1.38257
$178$		−	23215.1i		−	0.00411633i
$179$	6.21397e6			1.08345			0.541727	−	0.840555i	$-0.317771\pi$
$179$	6.21397e6			1.08345			0.541727	+	0.840555i	$0.317771\pi$
$180$		−	4.71743e6i		−	0.808887i
$181$		−	1.63857e6i		−	0.276331i	−0.990409	−	0.138166i	$-0.955879\pi$
$181$		−	1.63857e6i		−	0.276331i	0.990409	−	0.138166i	$-0.0441206\pi$
$182$		−	1.00711e6i		−	0.167056i
$183$		−	1.00362e7i		−	1.63763i
$184$	−880723.	−	166103.i	−0.141379	−	0.0266639i
$185$	4.34139e6			0.685667
$186$	724555.			0.112598
$187$	1.03510e6			0.158291
$188$	−4.15694e6			−0.625605
$189$		−	1.57020e7i		−	2.32578i
$190$	−313865.			−0.0457596
$191$		−	1.37107e7i		−	1.96771i	−0.178978	−	0.983853i	$-0.557279\pi$
$191$		−	1.37107e7i		−	1.96771i	0.178978	−	0.983853i	$-0.442721\pi$
$192$	−1.15127e7			−1.62658
$193$	−1.60892e6			−0.223802			−0.111901	−	0.993719i	$-0.535694\pi$
$193$	−1.60892e6			−0.223802			−0.111901	+	0.993719i	$0.535694\pi$
$194$		−	120124.i		−	0.0164523i
$195$		−	7.61474e6i		−	1.02696i
$196$	1.39865e7			1.85755
$197$	−9.07541e6			−1.18705			−0.593523	−	0.804817i	$-0.702263\pi$
$197$	−9.07541e6			−1.18705			−0.593523	+	0.804817i	$0.702263\pi$
$198$		−	271748.i		−	0.0350082i
$199$		−	1.07507e7i		−	1.36420i	−0.731258	−	0.682101i	$-0.761066\pi$
$199$		−	1.07507e7i		−	1.36420i	0.731258	−	0.682101i	$-0.238934\pi$
$200$	−230195.			−0.0287743
$201$			2.18448e7i			2.69005i
$202$	59910.1			0.00726852
$203$		−	1.62078e7i		−	1.93747i
$204$			8.40639e6i			0.990191i
$205$			5.90518e6i			0.685443i
$206$		−	106540.i		−	0.0121874i
$207$	−1.58474e7	−	2.98880e6i	−1.78669	−	0.336966i
$208$	−1.21178e7			−1.34658
$209$	3.45769e6			0.378745
$210$	−849117.			−0.0916874
$211$	2.86707e6			0.305204			0.152602	−	0.988288i	$-0.451235\pi$
$211$	2.86707e6			0.305204			0.152602	+	0.988288i	$0.451235\pi$
$212$		−	7.76667e6i		−	0.815131i
$213$	2.10080e7			2.17393
$214$		−	1.05237e6i		−	0.107381i
$215$	5.43521e6			0.546892
$216$	1.99146e6			0.197611
$217$			1.60911e7i			1.57473i
$218$		−	228841.i		−	0.0220884i
$219$	−1.53513e7			−1.46155
$220$	1.26466e6			0.118770
$221$			8.75443e6i			0.811057i
$222$			2.03104e6i			0.185635i
$223$	3.97731e6			0.358653			0.179327	−	0.983790i	$-0.442608\pi$
$223$	3.97731e6			0.358653			0.179327	+	0.983790i	$0.442608\pi$
$224$			4.08937e6i			0.363842i
$225$	−4.14205e6			−0.363637
$226$		−	1.57755e6i		−	0.136665i
$227$		−	9.22006e6i		−	0.788236i	−0.919060	−	0.394118i	$-0.871050\pi$
$227$		−	9.22006e6i		−	0.788236i	0.919060	−	0.394118i	$-0.128950\pi$
$228$			2.80811e7i			2.36925i
$229$			1.10745e7i			0.922183i	0.887353	+	0.461091i	$0.152542\pi$
$229$			1.10745e7i			0.922183i	−0.887353	+	0.461091i	$0.847458\pi$
$230$	−72731.5	+	385643.i	−0.00597777	+	0.0316958i
$231$	9.35428e6			0.758883
$232$	2.05561e6			0.164618
$233$	7.89689e6			0.624293			0.312146	−	0.950034i	$-0.398952\pi$
$233$	7.89689e6			0.624293			0.312146	+	0.950034i	$0.398952\pi$
$234$	2.29834e6			0.179377
$235$			3.64992e6i			0.281242i
$236$	1.07689e7			0.819289
$237$		−	3.18114e7i		−	2.38967i
$238$	976203.			0.0724118
$239$	3.76156e6			0.275534			0.137767	−	0.990465i	$-0.456008\pi$
$239$	3.76156e6			0.275534			0.137767	+	0.990465i	$0.456008\pi$
$240$			1.02168e7i			0.739062i
$241$		−	1.73098e7i		−	1.23663i	−0.785929	−	0.618317i	$-0.787815\pi$
$241$		−	1.73098e7i		−	1.23663i	0.785929	−	0.618317i	$-0.212185\pi$
$242$	−949317.			−0.0669831
$243$	−7.96294e6			−0.554951
$244$			1.40973e7i			0.970436i
$245$		−	1.22806e7i		−	0.835065i
$246$	−2.76263e6			−0.185574
$247$			2.92438e7i			1.94063i
$248$	−2.04081e6			−0.133797
$249$			1.27599e7i			0.826509i
$250$			100796.i			0.00645091i
$251$		−	1.44438e7i		−	0.913399i	−0.889621	−	0.456700i	$-0.849031\pi$
$251$		−	1.44438e7i		−	0.913399i	0.889621	−	0.456700i	$-0.150969\pi$
$252$			4.90126e7i			3.06271i
$253$	801245.	−	4.24843e6i	0.0494771	−	0.262341i
$254$	−1.47570e6			−0.0900526
$255$	7.38107e6			0.445142
$256$	1.59113e7			0.948387
$257$	−442067.			−0.0260429			−0.0130214	−	0.999915i	$-0.504145\pi$
$257$	−442067.			−0.0260429			−0.0130214	+	0.999915i	$0.504145\pi$
$258$			2.54277e6i			0.148063i
$259$	−4.51057e7			−2.59616
$260$			1.06960e7i			0.608558i
$261$	3.69880e7			2.08036
$262$	−741230.			−0.0412144
$263$			2.68355e7i			1.47517i	0.675255	+	0.737585i	$0.264034\pi$
$263$			2.68355e7i			1.47517i	−0.675255	+	0.737585i	$0.735966\pi$
$264$			1.18639e6i			0.0644787i
$265$	−6.81938e6			−0.366444
$266$	3.26096e6			0.173261
$267$			1.82370e6i			0.0958118i
$268$		−	3.06842e7i		−	1.59408i
$269$	−1.99974e7			−1.02735			−0.513674	−	0.857985i	$-0.671716\pi$
$269$	−1.99974e7			−1.02735			−0.513674	+	0.857985i	$0.671716\pi$
$270$		−	872004.i		−	0.0443024i
$271$	−2.27057e7			−1.14085			−0.570423	−	0.821351i	$-0.693221\pi$
$271$	−2.27057e7			−1.14085			−0.570423	+	0.821351i	$0.693221\pi$
$272$		−	1.17459e7i		−	0.583688i
$273$			7.91149e7i			3.88839i
$274$		−	840950.i		−	0.0408807i
$275$		−	1.11041e6i		−	0.0533932i
$276$	3.45030e7	+	6.50721e6i	1.64108	+	0.309505i
$277$	1.41302e7			0.664827			0.332414	−	0.943134i	$-0.392137\pi$
$277$	1.41302e7			0.664827			0.332414	+	0.943134i	$0.392137\pi$
$278$	11757.3			0.000547233
$279$	−3.67216e7			−1.69087
$280$	2.39165e6			0.108949
$281$		−	2.39579e7i		−	1.07976i	−0.841741	−	0.539882i	$-0.818469\pi$
$281$		−	2.39579e7i		−	1.07976i	0.841741	−	0.539882i	$-0.181531\pi$
$282$	−1.70755e6			−0.0761423
$283$		−	4.15614e6i		−	0.183371i	−0.995788	−	0.0916855i	$-0.970775\pi$
$283$		−	4.15614e6i		−	0.183371i	0.995788	−	0.0916855i	$-0.0292254\pi$
$284$	−2.95088e7			−1.28824
$285$	2.46561e7			1.06510
$286$			616144.i			0.0263381i
$287$		−	6.13530e7i		−	2.59532i
$288$	−9.33242e6			−0.390676
$289$	1.56518e7			0.648441
$290$		−	900092.i		−	0.0369056i
$291$			9.43654e6i			0.382943i
$292$	2.15632e7			0.866092
$293$		−	3.72998e7i		−	1.48287i	−0.671024	−	0.741436i	$-0.734145\pi$
$293$		−	3.72998e7i		−	1.48287i	0.671024	−	0.741436i	$-0.265855\pi$
$294$	5.74524e6			0.226082
$295$		−	9.45547e6i		−	0.368313i
$296$		−	5.72070e6i		−	0.220584i
$297$			9.60641e6i			0.366684i
$298$		−	1.00176e6i		−	0.0378543i
$299$	3.59315e7	+	6.77662e6i	1.34419	+	0.253513i
$300$	9.01807e6			0.334002
$301$	−5.64702e7			−2.07071
$302$	713061.			0.0258884
$303$	−4.70633e6			−0.169182
$304$		−	3.92367e7i		−	1.39660i
$305$	1.23779e7			0.436262
$306$			2.22781e6i			0.0777523i
$307$	2.53278e7			0.875352			0.437676	−	0.899133i	$-0.355802\pi$
$307$	2.53278e7			0.875352			0.437676	+	0.899133i	$0.355802\pi$
$308$	−1.31394e7			−0.449702
$309$			8.36943e6i			0.283674i
$310$			893610.i			0.0299960i
$311$	8.58163e6			0.285291			0.142646	−	0.989774i	$-0.454439\pi$
$311$	8.58163e6			0.285291			0.142646	+	0.989774i	$0.454439\pi$
$312$	−1.00340e7			−0.330378
$313$		−	1.57232e7i		−	0.512754i	−0.966577	−	0.256377i	$-0.917471\pi$
$313$		−	1.57232e7i		−	0.512754i	0.966577	−	0.256377i	$-0.0825288\pi$
$314$			1119.60i			3.61639e-5i
$315$	4.30346e7			1.37685
$316$			4.46837e7i			1.41608i
$317$	−3.29046e7			−1.03295			−0.516475	−	0.856302i	$-0.672756\pi$
$317$	−3.29046e7			−1.03295			−0.516475	+	0.856302i	$0.672756\pi$
$318$		−	3.19032e6i		−	0.0992095i
$319$			9.91585e6i			0.305462i
$320$		−	1.41989e7i		−	0.433316i
$321$			8.26708e7i			2.49941i
$322$	755658.	−	4.00671e6i	0.0226338	−	0.120011i
$323$	−2.83464e7			−0.841182
$324$	−1.64984e7			−0.485073
$325$	9.39143e6			0.273578
$326$	−653028.			−0.0188486
$327$			1.79770e7i			0.514131i
$328$	7.78132e6			0.220512
$329$		−	3.79216e7i		−	1.06488i
$330$	519486.			0.0144555
$331$	4.21415e7			1.16205			0.581027	−	0.813885i	$-0.302651\pi$
$331$	4.21415e7			1.16205			0.581027	+	0.813885i	$0.302651\pi$
$332$		−	1.79231e7i		−	0.489777i
$333$		−	1.02936e8i		−	2.78764i
$334$	311359.			0.00835646
$335$	−2.69417e7			−0.716623
$336$		−	1.06149e8i		−	2.79833i
$337$			5.69768e7i			1.48870i	0.667788	+	0.744351i	$0.267241\pi$
$337$			5.69768e7i			1.48870i	−0.667788	+	0.744351i	$0.732759\pi$
$338$	−2.42610e6			−0.0628287
$339$			1.23927e8i			3.18102i
$340$	−1.03678e7			−0.263785
$341$		−	9.84444e6i		−	0.248272i
$342$			7.44188e6i			0.186039i
$343$			5.92607e7i			1.46853i
$344$		−	7.16204e6i		−	0.175939i
$345$	5.71353e6	−	3.02948e7i	0.139139	−	0.737752i
$346$	−2.51380e6			−0.0606879
$347$	4.85873e7			1.16288			0.581439	−	0.813590i	$-0.302490\pi$
$347$	4.85873e7			1.16288			0.581439	+	0.813590i	$0.302490\pi$
$348$	−8.05302e7			−1.91083
$349$	5.14514e7			1.21038			0.605189	−	0.796082i	$-0.293097\pi$
$349$	5.14514e7			1.21038			0.605189	+	0.796082i	$0.293097\pi$
$350$		−	1.04723e6i		−	0.0244253i
$351$	−8.12473e7			−1.87883
$352$		−	2.50186e6i		−	0.0573634i
$353$	−6.17276e7			−1.40332			−0.701658	−	0.712514i	$-0.747556\pi$
$353$	−6.17276e7			−1.40332			−0.701658	+	0.712514i	$0.747556\pi$
$354$	4.42357e6			0.0997156
$355$			2.59097e7i			0.579131i
$356$		−	2.56165e6i		−	0.0567766i
$357$	−7.66871e7			−1.68546
$358$	−3.58538e6			−0.0781423
$359$		−	5.81096e7i		−	1.25593i	−0.778243	−	0.627963i	$-0.783889\pi$
$359$		−	5.81096e7i		−	1.25593i	0.778243	−	0.627963i	$-0.216111\pi$
$360$			5.45803e6i			0.116984i
$361$	−4.76438e7			−1.01271
$362$			945436.i			0.0199300i
$363$	7.45751e7			1.55910
$364$		−	1.11128e8i		−	2.30420i
$365$		−	1.89331e7i		−	0.389353i
$366$			5.79077e6i			0.118112i
$367$			3.05855e6i			0.0618753i	0.999521	+	0.0309377i	$0.00984934\pi$
$367$			3.05855e6i			0.0618753i	−0.999521	+	0.0309377i	$0.990151\pi$
$368$	−4.82098e7	−	9.09227e6i	−0.967368	−	0.182444i
$369$	1.40015e8			2.78673
$370$	−2.50493e6			−0.0494527
$371$	7.08513e7			1.38748
$372$	7.99503e7			1.55307
$373$		−	1.49408e7i		−	0.287904i	−0.989585	−	0.143952i	$-0.954019\pi$
$373$		−	1.49408e7i		−	0.287904i	0.989585	−	0.143952i	$-0.0459811\pi$
$374$	−597237.			−0.0114165
$375$		−	7.91815e6i		−	0.150151i
$376$	4.80954e6			0.0904775
$377$	−8.38644e7			−1.56514
$378$			9.05985e6i			0.167743i
$379$		−	3.09976e7i		−	0.569390i	−0.958618	−	0.284695i	$-0.908108\pi$
$379$		−	3.09976e7i		−	0.569390i	0.958618	−	0.284695i	$-0.0918924\pi$
$380$	−3.46331e7			−0.631161
$381$	1.15926e8			2.09606
$382$			7.91091e6i			0.141918i
$383$			5.57008e6i			0.0991437i	0.998771	+	0.0495718i	$0.0157857\pi$
$383$			5.57008e6i			0.0991437i	−0.998771	+	0.0495718i	$0.984214\pi$
$384$	2.70675e7			0.478029
$385$			1.15368e7i			0.202165i
$386$	928328.			0.0161413
$387$		−	1.28872e8i		−	2.22343i
$388$		−	1.32550e7i		−	0.226926i
$389$			9.86429e7i			1.67578i	0.545839	+	0.837890i	$0.316211\pi$
$389$			9.86429e7i			1.67578i	−0.545839	+	0.837890i	$0.683789\pi$
$390$			4.39361e6i			0.0740675i
$391$	−6.56867e6	+	3.48289e7i	−0.109887	+	0.582653i
$392$	−1.61822e7			−0.268646
$393$	5.82285e7			0.959307
$394$	5.23640e6			0.0856138
$395$	3.92337e7			0.636602
$396$		−	2.99857e7i		−	0.482869i
$397$	−1.31294e7			−0.209833			−0.104916	−	0.994481i	$-0.533457\pi$
$397$	−1.31294e7			−0.209833			−0.104916	+	0.994481i	$0.533457\pi$
$398$			6.20304e6i			0.0983909i
$399$	−2.56170e8			−4.03282
$400$	−1.26006e7			−0.196884
$401$		−	7.72164e6i		−	0.119750i	−0.998206	−	0.0598751i	$-0.980930\pi$
$401$		−	7.72164e6i		−	0.119750i	0.998206	−	0.0598751i	$-0.0190703\pi$
$402$		−	1.26042e7i		−	0.194016i
$403$	8.32604e7			1.27211
$404$	6.61072e6			0.100255
$405$			1.44861e7i			0.218065i
$406$			9.35168e6i			0.139737i
$407$	2.75955e7			0.409312
$408$		−	9.72612e6i		−	0.143205i
$409$	−7.85865e7			−1.14862			−0.574312	−	0.818637i	$-0.694730\pi$
$409$	−7.85865e7			−1.14862			−0.574312	+	0.818637i	$0.694730\pi$
$410$		−	3.40721e6i		−	0.0494365i
$411$			6.60621e7i			0.951540i
$412$		−	1.17561e7i		−	0.168101i
$413$			9.82395e7i			1.39456i
$414$	9.14378e6	+	1.72450e6i	0.128862	+	0.0243031i
$415$	−1.57370e7			−0.220180
$416$	2.11598e7			0.293921
$417$	−923611.			−0.0127374
$418$	−1.99504e6			−0.0273164
$419$		−	8.60330e7i		−	1.16956i	−0.811191	−	0.584781i	$-0.801180\pi$
$419$		−	8.60330e7i		−	1.16956i	0.811191	−	0.584781i	$-0.198820\pi$
$420$	−9.36950e7			−1.26464
$421$		−	1.42116e8i		−	1.90457i	−0.305209	−	0.952285i	$-0.598726\pi$
$421$		−	1.42116e8i		−	1.90457i	0.305209	−	0.952285i	$-0.401274\pi$
$422$	−1.65426e6			−0.0220124
$423$	8.65414e7			1.14341
$424$			8.98598e6i			0.117887i
$425$			9.10324e6i			0.118585i
$426$	−1.21214e7			−0.156791
$427$	−1.28602e8			−1.65183
$428$		−	1.16123e8i		−	1.48111i
$429$		−	4.84021e7i		−	0.613045i
$430$	−3.13605e6			−0.0394437
$431$		−	6.34595e7i		−	0.792620i	−0.918117	−	0.396310i	$-0.870291\pi$
$431$		−	6.34595e7i		−	0.792620i	0.918117	−	0.396310i	$-0.129709\pi$
$432$	1.09010e8			1.35213
$433$		−	3.10326e7i		−	0.382256i	−0.981565	−	0.191128i	$-0.938786\pi$
$433$		−	3.10326e7i		−	0.382256i	0.981565	−	0.191128i	$-0.0612145\pi$
$434$		−	9.28433e6i		−	0.113575i
$435$			7.07081e7i			0.859016i
$436$		−	2.52513e7i		−	0.304666i
$437$	−2.19423e7	+	1.16344e8i	−0.262929	+	1.39412i
$438$	8.85752e6			0.105412
$439$	8.84096e7			1.04498			0.522488	−	0.852647i	$-0.325004\pi$
$439$	8.84096e7			1.04498			0.522488	+	0.852647i	$0.325004\pi$
$440$	−1.46320e6			−0.0171770
$441$	−2.91178e8			−3.39503
$442$		−	5.05120e6i		−	0.0584962i
$443$	1.49677e8			1.72164			0.860821	−	0.508907i	$-0.169950\pi$
$443$	1.49677e8			1.72164			0.860821	+	0.508907i	$0.169950\pi$
$444$			2.24113e8i			2.56046i
$445$	−2.24921e6			−0.0255240
$446$	−2.29486e6			−0.0258673
$447$			7.86949e7i			0.881097i
$448$			1.47522e8i			1.64068i
$449$	7.96625e7			0.880065			0.440032	−	0.897982i	$-0.354967\pi$
$449$	7.96625e7			0.880065			0.440032	+	0.897982i	$0.354967\pi$
$450$	2.38991e6			0.0262267
$451$			3.75355e7i			0.409178i
$452$		−	1.74073e8i		−	1.88502i
$453$	−5.60156e7			−0.602579
$454$			5.31986e6i			0.0568503i
$455$	−9.75741e7			−1.03586
$456$		−	3.24896e7i		−	0.342650i
$457$			1.49523e7i			0.156660i	0.996927	+	0.0783300i	$0.0249588\pi$
$457$			1.49523e7i			0.156660i	−0.996927	+	0.0783300i	$0.975041\pi$
$458$		−	6.38984e6i		−	0.0665110i
$459$		−	7.87541e7i		−	0.814395i
$460$	−8.02548e6	+	4.25534e7i	−0.0824513	+	0.437180i
$461$	−3.17716e7			−0.324292			−0.162146	−	0.986767i	$-0.551842\pi$
$461$	−3.17716e7			−0.324292			−0.162146	+	0.986767i	$0.551842\pi$
$462$	−5.39730e6			−0.0547332
$463$	−2.91314e7			−0.293507			−0.146754	−	0.989173i	$-0.546882\pi$
$463$	−2.91314e7			−0.293507			−0.146754	+	0.989173i	$0.546882\pi$
$464$	1.12522e8			1.12637
$465$		−	7.01989e7i		−	0.698186i
$466$	−4.55640e6			−0.0450261
$467$			1.49924e8i			1.47205i	0.676956	+	0.736023i	$0.263299\pi$
$467$			1.49924e8i			1.47205i	−0.676956	+	0.736023i	$0.736701\pi$
$468$	2.53608e8			2.47414
$469$	2.79916e8			2.71337
$470$		−	2.10596e6i		−	0.0202841i
$471$		−	87952.2i		−	0.000841752i
$472$	−1.24596e7			−0.118489
$473$	3.45482e7			0.326469
$474$			1.83548e7i			0.172351i
$475$			3.04089e7i			0.283740i
$476$	1.07718e8			0.998776
$477$			1.61691e8i			1.48981i
$478$	−2.17037e6			−0.0198724
$479$			6.26479e7i			0.570033i	0.958523	+	0.285016i	$0.0919990\pi$
$479$			6.26479e7i			0.570033i	−0.958523	+	0.285016i	$0.908001\pi$
$480$		−	1.78403e7i		−	0.161316i
$481$			2.33392e8i			2.09725i
$482$			9.98754e6i			0.0891903i
$483$	−5.93619e7	+	3.14753e8i	−0.526825	+	2.79337i
$484$	−1.04751e8			−0.923898
$485$	−1.16383e7			−0.102015
$486$	4.59451e6			0.0400249
$487$	1.07573e8			0.931362			0.465681	−	0.884953i	$-0.345809\pi$
$487$	1.07573e8			0.931362			0.465681	+	0.884953i	$0.345809\pi$
$488$		−	1.63105e7i		−	0.140348i
$489$	5.12996e7			0.438720
$490$			7.08573e6i			0.0602277i
$491$	1.91370e7			0.161670			0.0808351	−	0.996727i	$-0.474241\pi$
$491$	1.91370e7			0.161670			0.0808351	+	0.996727i	$0.474241\pi$
$492$	−3.04840e8			−2.55962
$493$		−	8.12909e7i		−	0.678424i
$494$		−	1.68733e7i		−	0.139965i
$495$	−2.63284e7			−0.217075
$496$	−1.11711e8			−0.915488
$497$		−	2.69193e8i		−	2.19278i
$498$		−	7.36228e6i		−	0.0596107i
$499$	3.23092e6			0.0260030			0.0130015	−	0.999915i	$-0.495861\pi$
$499$	3.23092e6			0.0260030			0.0130015	+	0.999915i	$0.495861\pi$
$500$			1.11222e7i			0.0889775i
$501$	−2.44593e7			−0.194505
$502$			8.33390e6i			0.0658775i
$503$		−	7.54249e7i		−	0.592667i	−0.955085	−	0.296334i	$-0.904236\pi$
$503$		−	7.54249e7i		−	0.592667i	0.955085	−	0.296334i	$-0.0957640\pi$
$504$		−	5.67072e7i		−	0.442942i
$505$		−	5.80442e6i		−	0.0450697i
$506$	−462308.	+	2.45129e6i	−0.00356845	+	0.0189209i
$507$	1.90586e8			1.46240
$508$	−1.62834e8			−1.24209
$509$	−1.32412e8			−1.00409			−0.502047	−	0.864840i	$-0.667419\pi$
$509$	−1.32412e8			−1.00409			−0.502047	+	0.864840i	$0.667419\pi$
$510$	−4.25879e6			−0.0321052
$511$			1.96709e8i			1.47422i
$512$	−4.73996e7			−0.353155
$513$		−	2.63074e8i		−	1.94862i
$514$	255067.			0.00187830
$515$	−1.03222e7			−0.0755702
$516$			2.80579e8i			2.04224i
$517$			2.32003e7i			0.167889i
$518$	2.60254e7			0.187244
$519$	1.97475e8			1.41257
$520$		−	1.23752e7i		−	0.0880120i
$521$		−	2.36908e7i		−	0.167520i	−0.996486	−	0.0837599i	$-0.973307\pi$
$521$		−	2.36908e7i		−	0.167520i	0.996486	−	0.0837599i	$-0.0266929\pi$
$522$	−2.13416e7			−0.150043
$523$			1.90311e8i			1.33033i	0.746698	+	0.665163i	$0.231638\pi$
$523$			1.90311e8i			1.33033i	−0.746698	+	0.665163i	$0.768362\pi$
$524$	−8.17903e7			−0.568471
$525$			8.22671e7i			0.568523i
$526$		−	1.54837e7i		−	0.106394i
$527$			8.07054e7i			0.551405i
$528$			6.49417e7i			0.441186i
$529$	1.37867e8	+	5.39206e7i	0.931305	+	0.364240i
$530$	3.93470e6			0.0264292
$531$	−2.24194e8			−1.49741
$532$	3.59827e8			2.38979
$533$	−3.17461e8			−2.09656
$534$		−	1.05225e6i		−	0.00691027i
$535$	−1.01960e8			−0.665836
$536$			3.55014e7i			0.230542i
$537$	2.81655e8			1.81884
$538$	1.15383e7			0.0740958
$539$		−	7.80599e7i		−	0.498496i
$540$		−	9.62204e7i		−	0.611063i
$541$	−2.62524e7			−0.165797			−0.0828986	−	0.996558i	$-0.526418\pi$
$541$	−2.62524e7			−0.165797			−0.0828986	+	0.996558i	$0.526418\pi$
$542$	1.31009e7			0.0822817
$543$		−	7.42702e7i		−	0.463890i
$544$			2.05104e7i			0.127403i
$545$	−2.21714e7			−0.136963
$546$		−	4.56483e7i		−	0.280444i
$547$	1.96747e8			1.20211			0.601057	−	0.799206i	$-0.294746\pi$
$547$	1.96747e8			1.20211			0.601057	+	0.799206i	$0.294746\pi$
$548$		−	9.27938e7i		−	0.563868i
$549$		−	2.93486e8i		−	1.77366i
$550$			640694.i			0.00385090i
$551$		−	2.71548e8i		−	1.62327i
$552$	−3.99197e7	−	7.52878e6i	−0.237340	−	0.0447618i
$553$	−4.07626e8			−2.41039
$554$	−8.15294e6			−0.0479496
$555$	1.96778e8			1.15106
$556$	1.29735e6			0.00754799
$557$			8.39555e7i			0.485829i	0.970048	+	0.242915i	$0.0781035\pi$
$557$			8.39555e7i			0.485829i	−0.970048	+	0.242915i	$0.921897\pi$
$558$	2.11879e7			0.121951
$559$			2.92195e8i			1.67278i
$560$	1.30916e8			0.745470
$561$	4.69168e7			0.265730
$562$			1.38234e7i			0.0778763i
$563$		−	8.96190e7i		−	0.502198i	−0.967961	−	0.251099i	$-0.919208\pi$
$563$		−	8.96190e7i		−	0.502198i	0.967961	−	0.251099i	$-0.0807920\pi$
$564$	−1.88418e8			−1.05023
$565$	−1.52842e8			−0.847415
$566$			2.39804e6i			0.0132253i
$567$		−	1.50506e8i		−	0.825668i
$568$	3.41414e7			0.186310
$569$			4.43571e6i			0.0240783i	0.999928	+	0.0120392i	$0.00383227\pi$
$569$			4.43571e6i			0.0240783i	−0.999928	+	0.0120392i	$0.996168\pi$
$570$	−1.42263e7			−0.0768186
$571$		−	1.77550e8i		−	0.953701i	−0.878984	−	0.476851i	$-0.841778\pi$
$571$		−	1.77550e8i		−	0.953701i	0.878984	−	0.476851i	$-0.158222\pi$
$572$			6.79878e7i			0.363281i
$573$		−	6.21454e8i		−	3.30328i
$574$			3.53999e7i			0.187183i
$575$	3.73632e7	+	7.04663e6i	0.196535	+	0.0370662i
$576$	−3.36663e8			−1.76168
$577$	3.74782e8			1.95097			0.975486	−	0.220063i	$-0.0706263\pi$
$577$	3.74782e8			1.95097			0.975486	+	0.220063i	$0.0706263\pi$
$578$	−9.03088e6			−0.0467677
$579$	−7.29262e7			−0.375706
$580$		−	9.93197e7i		−	0.509040i
$581$	1.63503e8			0.833675
$582$		−	5.44476e6i		−	0.0276191i
$583$	−4.33465e7			−0.218750
$584$	−2.49484e7			−0.125258
$585$		−	2.22675e8i		−	1.11226i
$586$			2.15215e7i			0.106950i
$587$	1.13937e8			0.563316			0.281658	−	0.959515i	$-0.409116\pi$
$587$	1.13937e8			0.563316			0.281658	+	0.959515i	$0.409116\pi$
$588$	6.33953e8			3.11835
$589$			2.69593e8i			1.31936i
$590$			5.45569e6i			0.0265640i
$591$	−4.11353e8			−1.99275
$592$		−	3.13144e8i		−	1.50931i
$593$	−2.76272e7			−0.132487			−0.0662435	−	0.997803i	$-0.521101\pi$
$593$	−2.76272e7			−0.132487			−0.0662435	+	0.997803i	$0.521101\pi$
$594$		−	5.54278e6i		−	0.0264465i
$595$		−	9.45799e7i		−	0.449002i
$596$		−	1.10538e8i		−	0.522125i
$597$		−	4.87289e8i		−	2.29015i
$598$	−2.07320e7	−	3.91002e6i	−0.0969479	−	0.0182842i
$599$	−2.02569e8			−0.942523			−0.471262	−	0.881993i	$-0.656201\pi$
$599$	−2.02569e8			−0.942523			−0.471262	+	0.881993i	$0.656201\pi$
$600$	−1.04338e7			−0.0483048
$601$	−7.01973e7			−0.323368			−0.161684	−	0.986843i	$-0.551693\pi$
$601$	−7.01973e7			−0.323368			−0.161684	+	0.986843i	$0.551693\pi$
$602$	3.25826e7			0.149347
$603$			6.38801e8i			2.91349i
$604$	7.86820e7			0.357079
$605$			9.19751e7i			0.415340i
$606$	2.71549e6			0.0122020
$607$	−2.83839e8			−1.26913			−0.634566	−	0.772869i	$-0.718821\pi$
$607$	−2.83839e8			−1.26913			−0.634566	+	0.772869i	$0.718821\pi$
$608$			6.85141e7i			0.304838i
$609$		−	7.34635e8i		−	3.25252i
$610$	−7.14188e6			−0.0314647
$611$	−1.96219e8			−0.860235
$612$			2.45825e8i			1.07244i
$613$		−	1.46667e8i		−	0.636723i	−0.947969	−	0.318362i	$-0.896867\pi$
$613$		−	1.46667e8i		−	0.636723i	0.947969	−	0.318362i	$-0.103133\pi$
$614$	−1.46138e7			−0.0631334
$615$			2.67659e8i			1.15068i
$616$	1.52022e7			0.0650377
$617$			7.51441e7i			0.319919i	0.987124	+	0.159959i	$0.0511363\pi$
$617$			7.51441e7i			0.319919i	−0.987124	+	0.159959i	$0.948864\pi$
$618$		−	4.82905e6i		−	0.0204596i
$619$			1.66214e8i			0.700803i	0.936600	+	0.350401i	$0.113955\pi$
$619$			1.66214e8i			0.700803i	−0.936600	+	0.350401i	$0.886045\pi$
$620$			9.86045e7i			0.413734i
$621$	−3.23237e8	−	6.09618e7i	−1.34973	−	0.254556i
$622$	−4.95149e6			−0.0205762
$623$	2.33686e7			0.0966425
$624$	−5.49252e8			−2.26057
$625$	9.76562e6			0.0400000
$626$			9.07210e6i			0.0369815i
$627$	1.56723e8			0.635816
$628$			123542.i			0.000498809i
$629$	−2.26230e8			−0.909071
$630$	−2.48304e7			−0.0993031
$631$			1.73512e7i			0.0690625i	0.999404	+	0.0345312i	$0.0109938\pi$
$631$			1.73512e7i			0.0690625i	−0.999404	+	0.0345312i	$0.989006\pi$
$632$		−	5.16987e7i		−	0.204799i
$633$	1.29953e8			0.512360
$634$	1.89855e7			0.0744998
$635$			1.42974e8i			0.558386i
$636$		−	3.52033e8i		−	1.36840i
$637$	6.60200e8			2.55421
$638$		−	5.72132e6i		−	0.0220310i
$639$	6.14330e8			2.35450
$640$			3.33829e7i			0.127346i
$641$			2.73588e8i			1.03878i	0.854538	+	0.519389i	$0.173841\pi$
$641$			2.73588e8i			1.03878i	−0.854538	+	0.519389i	$0.826159\pi$
$642$		−	4.77000e7i		−	0.180266i
$643$			4.93648e8i			1.85688i	0.371481	+	0.928441i	$0.378850\pi$
$643$			4.93648e8i			1.85688i	−0.371481	+	0.928441i	$0.621150\pi$
$644$	8.33823e7	−	4.42117e8i	0.312188	−	1.65531i
$645$	2.46357e8			0.918091
$646$	1.63555e7			0.0606689
$647$	3.76723e8			1.39094			0.695472	−	0.718553i	$-0.255195\pi$
$647$	3.76723e8			1.39094			0.695472	+	0.718553i	$0.255195\pi$
$648$	1.90885e7			0.0701531
$649$		−	6.01025e7i		−	0.219866i
$650$	−5.41874e6			−0.0197314
$651$			7.29345e8i			2.64357i
$652$	−7.20577e7			−0.259979
$653$	−4.21390e8			−1.51337			−0.756684	−	0.653781i	$-0.773182\pi$
$653$	−4.21390e8			−1.51337			−0.756684	+	0.653781i	$0.773182\pi$
$654$		−	1.03725e7i		−	0.0370809i
$655$			7.18145e7i			0.255557i
$656$	4.25941e8			1.50882
$657$	−4.48914e8			−1.58295
$658$			2.18803e7i			0.0768025i
$659$			4.68612e8i			1.63741i	0.574215	+	0.818705i	$0.305307\pi$
$659$			4.68612e8i			1.63741i	−0.574215	+	0.818705i	$0.694693\pi$
$660$	5.73222e7			0.199384
$661$		−	2.20641e8i		−	0.763980i	−0.924166	−	0.381990i	$-0.875239\pi$
$661$		−	2.20641e8i		−	0.763980i	0.924166	−	0.381990i	$-0.124761\pi$
$662$	−2.43151e7			−0.0838112
$663$			3.96804e8i			1.36156i
$664$			2.07368e7i			0.0708334i
$665$		−	3.15940e8i		−	1.07433i
$666$			5.93930e7i			0.201054i
$667$	−3.33649e8	−	6.29255e7i	−1.12438	−	0.212055i
$668$	3.43566e7			0.115261
$669$	1.80276e8			0.602088
$670$	1.55450e7			0.0516853
$671$	7.86784e7			0.260428
$672$			1.85355e8i			0.610797i
$673$	1.00753e6			0.00330533			0.00165266	−	0.999999i	$-0.499474\pi$
$673$	1.00753e6			0.00330533			0.00165266	+	0.999999i	$0.499474\pi$
$674$		−	3.28749e7i		−	0.107370i
$675$	−8.44845e7			−0.274704
$676$	−2.67705e8			−0.866597
$677$		−	4.61044e8i		−	1.48586i	−0.669371	−	0.742928i	$-0.733436\pi$
$677$		−	4.61044e8i		−	1.48586i	0.669371	−	0.742928i	$-0.266564\pi$
$678$		−	7.15041e7i		−	0.229426i
$679$	1.20918e8			0.386263
$680$	1.19954e7			0.0381496
$681$		−	4.17910e8i		−	1.32325i
$682$			5.68012e6i			0.0179062i
$683$	−6.23238e8			−1.95610			−0.978052	−	0.208362i	$-0.933187\pi$
$683$	−6.23238e8			−1.95610			−0.978052	+	0.208362i	$0.933187\pi$
$684$			8.21167e8i			2.56604i
$685$	−8.14759e7			−0.253488
$686$		−	3.41927e7i		−	0.105916i
$687$			5.01963e8i			1.54811i
$688$		−	3.92042e8i		−	1.20384i
$689$		−	3.66608e8i		−	1.12084i
$690$	−3.29664e6	+	1.74797e7i	−0.0100351	+	0.0532092i
$691$	5.35897e8			1.62423			0.812114	−	0.583498i	$-0.198316\pi$
$691$	5.35897e8			1.62423			0.812114	+	0.583498i	$0.198316\pi$
$692$	−2.77382e8			−0.837068
$693$	2.73544e8			0.821917
$694$	−2.80343e7			−0.0838708
$695$		−	1.13911e6i		−	0.00339321i
$696$	9.31728e7			0.276351
$697$		−	3.07719e8i		−	0.908774i
$698$	−2.96868e7			−0.0872966
$699$	3.57935e8			1.04803
$700$		−	1.15556e8i		−	0.336898i
$701$		−	7.52640e7i		−	0.218491i	−0.994015	−	0.109245i	$-0.965157\pi$
$701$		−	7.52640e7i		−	0.218491i	0.994015	−	0.109245i	$-0.0348434\pi$
$702$	4.68786e7			0.135508
$703$	−7.55710e8			−2.17515
$704$		−	9.02535e7i		−	0.258670i
$705$			1.65437e8i			0.472134i
$706$	3.56160e7			0.101212
$707$			6.03062e7i			0.170649i
$708$	4.88114e8			1.37538
$709$		−	9.19942e7i		−	0.258120i	−0.991637	−	0.129060i	$-0.958804\pi$
$709$		−	9.19942e7i		−	0.258120i	0.991637	−	0.129060i	$-0.0411960\pi$
$710$		−	1.49495e7i		−	0.0417689i
$711$		−	9.30250e8i		−	2.58816i
$712$			2.96380e6i			0.00821125i
$713$	3.31246e8	+	6.24724e7i	0.913865	+	0.172353i
$714$	4.42475e7			0.121561
$715$	5.96954e7			0.163314
$716$	−3.95625e8			−1.07782
$717$	1.70497e8			0.462551
$718$			3.35285e7i			0.0905817i
$719$	−2.08673e8			−0.561408			−0.280704	−	0.959794i	$-0.590568\pi$
$719$	−2.08673e8			−0.561408			−0.280704	+	0.959794i	$0.590568\pi$
$720$			2.98766e8i			0.800450i
$721$	1.07245e8			0.286134
$722$	2.74899e7			0.0730400
$723$		−	7.84586e8i		−	2.07599i
$724$			1.04323e8i			0.274894i
$725$	−8.72058e7			−0.228840
$726$	−4.30289e7			−0.112448
$727$			1.61033e7i			0.0419094i	0.999780	+	0.0209547i	$0.00667057\pi$
$727$			1.61033e7i			0.0419094i	−0.999780	+	0.0209547i	$0.993329\pi$
$728$			1.28575e8i			0.333243i
$729$	−5.49839e8			−1.41923
$730$			1.09242e7i			0.0280815i
$731$	−2.83229e8			−0.725079
$732$			6.38976e8i			1.62911i
$733$			3.14921e8i			0.799631i	0.916596	+	0.399816i	$0.130926\pi$
$733$			3.14921e8i			0.799631i	−0.916596	+	0.399816i	$0.869074\pi$
$734$		−	1.76475e6i		−	0.00446266i
$735$		−	5.56631e8i		−	1.40186i
$736$	8.41827e7	+	1.58767e7i	0.211149	+	0.0398223i
$737$	−1.71251e8			−0.427791
$738$	−8.07866e7			−0.200988
$739$	−2.69480e8			−0.667718			−0.333859	−	0.942623i	$-0.608351\pi$
$739$	−2.69480e8			−0.667718			−0.333859	+	0.942623i	$0.608351\pi$
$740$	−2.76404e8			−0.682101
$741$			1.32551e9i			3.25782i
$742$	−4.08803e7			−0.100070
$743$			1.96083e8i			0.478051i	0.971013	+	0.239025i	$0.0768279\pi$
$743$			1.96083e8i			0.478051i	−0.971013	+	0.239025i	$0.923172\pi$
$744$	−9.25018e7			−0.224611
$745$	−9.70562e7			−0.234722
$746$			8.62066e6i			0.0207646i
$747$			3.73132e8i			0.895161i
$748$	−6.59015e7			−0.157467
$749$	1.05933e9			2.52108
$750$			4.56867e6i			0.0108294i
$751$		−	4.40140e8i		−	1.03913i	−0.854430	−	0.519566i	$-0.826094\pi$
$751$		−	4.40140e8i		−	1.03913i	0.854430	−	0.519566i	$-0.173906\pi$
$752$	2.63269e8			0.619079
$753$		−	6.54682e8i		−	1.53336i
$754$	4.83887e7			0.112883
$755$		−	6.90853e7i		−	0.160526i
$756$			9.99700e8i			2.31369i
$757$		−	2.75963e8i		−	0.636155i	−0.948065	−	0.318078i	$-0.896963\pi$
$757$		−	2.75963e8i		−	0.636155i	0.948065	−	0.318078i	$-0.103037\pi$
$758$			1.78852e7i			0.0410664i
$759$	3.63173e7	−	1.92565e8i	0.0830593	−	0.440404i
$760$	4.00702e7			0.0912811
$761$	5.76242e8			1.30753			0.653763	−	0.756699i	$-0.273189\pi$
$761$	5.76242e8			1.30753			0.653763	+	0.756699i	$0.273189\pi$
$762$	−6.68876e7			−0.151175
$763$	2.30354e8			0.518588
$764$			8.72922e8i			1.95747i
$765$	2.15842e8			0.482117
$766$		−	3.21386e6i		−	0.00715058i
$767$	5.08323e8			1.12656
$768$	7.21197e8			1.59210
$769$		−	4.29792e8i		−	0.945104i	−0.881303	−	0.472552i	$-0.843333\pi$
$769$		−	4.29792e8i		−	0.945104i	0.881303	−	0.472552i	$-0.156667\pi$
$770$		−	6.65661e6i		−	0.0145808i
$771$	−2.00372e7			−0.0437193
$772$	1.02435e8			0.222637
$773$		−	1.84981e8i		−	0.400488i	−0.979746	−	0.200244i	$-0.935827\pi$
$773$		−	1.84981e8i		−	0.400488i	0.979746	−	0.200244i	$-0.0641734\pi$
$774$			7.43572e7i			0.160362i
$775$	8.65778e7			0.185995
$776$			1.53359e7i			0.0328189i
$777$	−2.04447e9			−4.35830
$778$		−	5.69157e7i		−	0.120863i
$779$		−	1.02792e9i		−	2.17444i
$780$			4.84809e8i			1.02161i
$781$			1.64691e8i			0.345715i
$782$	3.79004e6	−	2.00958e7i	0.00792544	−	0.0420229i
$783$	7.54436e8			1.57158
$784$	−8.85798e8			−1.83817
$785$	108473.			0.000224241
$786$	−3.35971e7			−0.0691885
$787$		−	9.58287e7i		−	0.196594i	−0.995157	−	0.0982972i	$-0.968660\pi$
$787$		−	9.58287e7i		−	0.196594i	0.995157	−	0.0982972i	$-0.0313396\pi$
$788$	5.77805e8			1.18087
$789$			1.21635e9i			2.47643i
$790$	−2.26374e7			−0.0459139
$791$	1.58798e9			3.20859
$792$			3.46932e7i			0.0698344i
$793$			6.65431e8i			1.33439i
$794$	7.57549e6			0.0151338
$795$	−3.09096e8			−0.615166
$796$			6.84468e8i			1.35711i
$797$			3.35333e8i			0.662372i	0.943566	+	0.331186i	$0.107449\pi$
$797$			3.35333e8i			0.662372i	−0.943566	+	0.331186i	$0.892551\pi$
$798$	1.47807e8			0.290861
$799$		−	1.90198e8i		−	0.372876i
$800$	2.20028e7			0.0429743
$801$			5.33298e7i			0.103770i
$802$			4.45529e6i			0.00863680i
$803$		−	1.20346e8i		−	0.232426i
$804$		−	1.39080e9i		−	2.67606i
$805$	−3.88192e8	−	7.32123e7i	−0.744148	−	0.140345i
$806$	−4.80402e7			−0.0917486
$807$	−9.06406e8			−1.72466
$808$	−7.64855e6			−0.0144992
$809$	−6.82405e8			−1.28883			−0.644416	−	0.764675i	$-0.722900\pi$
$809$	−6.82405e8			−1.28883			−0.644416	+	0.764675i	$0.722900\pi$
$810$		−	8.35830e6i		−	0.0157276i
$811$	−2.89838e8			−0.543367			−0.271684	−	0.962387i	$-0.587580\pi$
$811$	−2.89838e8			−0.543367			−0.271684	+	0.962387i	$0.587580\pi$
$812$			1.03190e9i			1.92739i
$813$	−1.02916e9			−1.91519
$814$	−1.59222e7			−0.0295210
$815$			6.32690e7i			0.116874i
$816$		−	5.32397e8i		−	0.979863i
$817$	−9.46113e8			−1.73491
$818$	4.53434e7			0.0828427
$819$			2.31353e9i			4.21137i
$820$		−	3.75965e8i		−	0.681878i
$821$	4.90960e8			0.887189			0.443595	−	0.896228i	$-0.353703\pi$
$821$	4.90960e8			0.887189			0.443595	+	0.896228i	$0.353703\pi$
$822$		−	3.81170e7i		−	0.0686283i
$823$	2.16640e8			0.388632			0.194316	−	0.980939i	$-0.437751\pi$
$823$	2.16640e8			0.388632			0.194316	+	0.980939i	$0.437751\pi$
$824$			1.36017e7i			0.0243114i
$825$		−	5.03307e7i		−	0.0896336i
$826$		−	5.66829e7i		−	0.100580i
$827$			4.37721e8i			0.773894i	0.922102	+	0.386947i	$0.126470\pi$
$827$			4.37721e8i			0.773894i	−0.922102	+	0.386947i	$0.873530\pi$
$828$	1.00896e9	+	1.90288e8i	1.77739	+	0.335213i
$829$	8.98543e8			1.57716			0.788579	−	0.614933i	$-0.210817\pi$
$829$	8.98543e8			1.57716			0.788579	+	0.614933i	$0.210817\pi$
$830$	9.08006e6			0.0158801
$831$	6.40467e8			1.11608
$832$	7.63329e8			1.32538
$833$			6.39941e8i			1.10715i
$834$	532912.			0.000918665
$835$		−	3.01662e7i		−	0.0518157i
$836$	−2.20141e8			−0.376775
$837$	−7.49003e8			−1.27734
$838$			4.96400e7i			0.0843528i
$839$			5.85794e8i			0.991880i	0.868357	+	0.495940i	$0.165176\pi$
$839$			5.85794e8i			0.991880i	−0.868357	+	0.495940i	$0.834824\pi$
$840$	1.08404e8			0.182898
$841$	1.83914e8			0.309191
$842$			8.19992e7i			0.137364i
$843$		−	1.08592e9i		−	1.81265i
$844$	−1.82538e8			−0.303616
$845$			2.35054e8i			0.389580i
$846$	−4.99333e7			−0.0824668
$847$		−	9.55593e8i		−	1.57262i
$848$			4.91882e8i			0.806629i
$849$		−	1.88381e8i		−	0.307833i
$850$		−	5.25246e6i		−	0.00855275i
$851$	−1.75120e8	+	9.28534e8i	−0.284149	+	1.50664i
$852$	−1.33752e9			−2.16263
$853$	3.49395e8			0.562950			0.281475	−	0.959569i	$-0.409176\pi$
$853$	3.49395e8			0.562950			0.281475	+	0.959569i	$0.409176\pi$
$854$	7.42020e7			0.119136
$855$	7.21011e8			1.15357
$856$			1.34353e8i			0.214204i
$857$	−7.06417e8			−1.12233			−0.561163	−	0.827706i	$-0.689646\pi$
$857$	−7.06417e8			−1.12233			−0.561163	+	0.827706i	$0.689646\pi$
$858$			2.79274e7i			0.0442149i
$859$	9.85705e8			1.55513			0.777567	−	0.628801i	$-0.216454\pi$
$859$	9.85705e8			1.55513			0.777567	+	0.628801i	$0.216454\pi$
$860$	−3.46044e8			−0.544047
$861$		−	2.78089e9i		−	4.35687i
$862$			3.66154e7i			0.0571665i
$863$	−4.73633e8			−0.736902			−0.368451	−	0.929647i	$-0.620112\pi$
$863$	−4.73633e8			−0.736902			−0.368451	+	0.929647i	$0.620112\pi$
$864$	−1.90351e8			−0.295131
$865$			2.43550e8i			0.376306i
$866$			1.79054e7i			0.0275696i
$867$	7.09434e8			1.08857
$868$		−	1.02447e9i		−	1.56654i
$869$	2.49384e8			0.380023
$870$		−	4.07977e7i		−	0.0619552i
$871$		−	1.44838e9i		−	2.19193i
$872$			2.92155e7i			0.0440620i
$873$			2.75950e8i			0.414750i
$874$	1.26604e7	−	6.71292e7i	0.0189633	−	0.100549i
$875$	−1.01462e8			−0.151453
$876$	9.77374e8			1.45395
$877$	−3.46318e8			−0.513424			−0.256712	−	0.966488i	$-0.582639\pi$
$877$	−3.46318e8			−0.513424			−0.256712	+	0.966488i	$0.582639\pi$
$878$	−5.10112e7			−0.0753672
$879$		−	1.69065e9i		−	2.48936i
$880$	−8.00941e7			−0.117531
$881$		−	4.10351e8i		−	0.600106i	−0.953923	−	0.300053i	$-0.902996\pi$
$881$		−	4.10351e8i		−	0.600106i	0.953923	−	0.300053i	$-0.0970043\pi$
$882$	1.68006e8			0.244861
$883$	−3.17497e8			−0.461166			−0.230583	−	0.973053i	$-0.574063\pi$
$883$	−3.17497e8			−0.461166			−0.230583	+	0.973053i	$0.574063\pi$
$884$		−	5.57369e8i		−	0.806838i
$885$		−	4.28580e8i		−	0.618304i
$886$	−8.63616e7			−0.124171
$887$	−4.84423e8			−0.694151			−0.347076	−	0.937837i	$-0.612825\pi$
$887$	−4.84423e8			−0.694151			−0.347076	+	0.937837i	$0.612825\pi$
$888$		−	2.59297e8i		−	0.370304i
$889$		−	1.48545e9i		−	2.11424i
$890$	1.29776e6			0.00184088
$891$			9.20791e7i			0.130175i
$892$	−2.53224e8			−0.356788
$893$		−	6.35346e8i		−	0.892186i
$894$		−	4.54060e7i		−	0.0635478i
$895$			3.47372e8i			0.484535i
$896$		−	3.46838e8i		−	0.482173i
$897$	1.62864e9	+	3.07158e8i	2.25656	+	0.425583i
$898$	−4.59642e7			−0.0634733
$899$	−7.73130e8			−1.06408
$900$	2.63712e8			0.361745
$901$	3.55358e8			0.485838
$902$		−	2.16575e7i		−	0.0295113i
$903$	−2.55957e9			−3.47620
$904$			2.01401e8i			0.272619i
$905$	9.15990e7			0.123579
$906$	3.23203e7			0.0434601
$907$		−	1.43932e9i		−	1.92901i	−0.264057	−	0.964507i	$-0.585061\pi$
$907$		−	1.43932e9i		−	1.92901i	0.264057	−	0.964507i	$-0.414939\pi$
$908$			5.87014e8i			0.784136i
$909$	−1.37626e8			−0.183235
$910$	5.62990e7			0.0747097
$911$			2.13084e8i			0.281835i	0.990021	+	0.140918i	$0.0450053\pi$
$911$			2.13084e8i			0.281835i	−0.990021	+	0.140918i	$0.954995\pi$
$912$		−	1.77845e9i		−	2.34453i
$913$	−1.00030e8			−0.131437
$914$		−	8.62726e6i		−	0.0112988i
$915$	5.61041e8			0.732372
$916$		−	7.05080e8i		−	0.917386i
$917$		−	7.46130e8i		−	0.967624i
$918$			4.54401e7i			0.0587369i
$919$			7.30122e8i			0.940695i	0.882481	+	0.470347i	$0.155871\pi$
$919$			7.30122e8i			0.940695i	−0.882481	+	0.470347i	$0.844129\pi$
$920$	9.28542e6	−	4.92339e7i	0.0119244	−	0.0632267i
$921$	1.14801e9			1.46949
$922$	1.83318e7			0.0233890
$923$	−1.39290e9			−1.77139
$924$	−5.95560e8			−0.754935
$925$			2.42691e8i			0.306640i
$926$	1.68085e7			0.0211688
$927$			2.44744e8i			0.307237i
$928$	−1.96483e8			−0.245856
$929$	5.33249e8			0.665093			0.332547	−	0.943087i	$-0.392092\pi$
$929$	5.33249e8			0.665093			0.332547	+	0.943087i	$0.392092\pi$
$930$			4.05039e7i			0.0503556i
$931$			2.13769e9i			2.64908i
$932$	−5.02772e8			−0.621045
$933$	3.88972e8			0.478931
$934$		−	8.65045e7i		−	0.106169i
$935$			5.78636e7i			0.0707898i
$936$	−2.93422e8			−0.357820
$937$			6.22322e8i			0.756479i	0.925708	+	0.378239i	$0.123470\pi$
$937$			6.22322e8i			0.756479i	−0.925708	+	0.378239i	$0.876530\pi$
$938$	−1.61508e8			−0.195698
$939$		−	7.12673e8i		−	0.860782i
$940$		−	2.32380e8i		−	0.279779i
$941$		−	1.74017e8i		−	0.208844i	−0.994533	−	0.104422i	$-0.966701\pi$
$941$		−	1.74017e8i		−	0.208844i	0.994533	−	0.104422i	$-0.0332993\pi$
$942$			50747.3i			6.07100e-5i
$943$	−1.26300e9	−	2.38199e8i	−1.50615	−	0.284056i
$944$	−6.82024e8			−0.810743
$945$	8.77768e8			1.04012
$946$	−1.99339e7			−0.0235461
$947$	6.32205e8			0.744403			0.372202	−	0.928152i	$-0.378603\pi$
$947$	6.32205e8			0.744403			0.372202	+	0.928152i	$0.378603\pi$
$948$			2.02534e9i			2.37724i
$949$	1.01784e9			1.19091
$950$		−	1.75456e7i		−	0.0204643i
$951$	−1.49144e9			−1.73406
$952$	−1.24629e8			−0.144447
$953$			7.22486e8i			0.834739i	0.908737	+	0.417370i	$0.137048\pi$
$953$			7.22486e8i			0.834739i	−0.908737	+	0.417370i	$0.862952\pi$
$954$		−	9.32936e7i		−	0.107450i
$955$	7.66453e8			0.879985
$956$	−2.39488e8			−0.274100
$957$			4.49447e8i			0.512793i
$958$		−	3.61470e7i		−	0.0411127i
$959$	8.46509e8			0.959789
$960$		−	6.43581e8i		−	0.727427i
$961$	−1.19942e8			−0.135145
$962$		−	1.34664e8i		−	0.151261i
$963$			2.41751e9i			2.70701i
$964$			1.10207e9i			1.23020i
$965$		−	8.99415e7i		−	0.100087i
$966$	3.42510e7	−	1.81609e8i	0.0379964	−	0.201468i
$967$	−1.60090e8			−0.177046			−0.0885230	−	0.996074i	$-0.528215\pi$
$967$	−1.60090e8			−0.177046			−0.0885230	+	0.996074i	$0.528215\pi$
$968$	1.21197e8			0.133618
$969$	−1.28483e9			−1.41213
$970$	6.71515e6			0.00735767
$971$		−	1.53965e8i		−	0.168176i	−0.996458	−	0.0840880i	$-0.973202\pi$
$971$		−	1.53965e8i		−	0.168176i	0.996458	−	0.0840880i	$-0.0267977\pi$
$972$	5.06977e8			0.552064
$973$			1.18350e7i			0.0128478i
$974$	−6.20685e7			−0.0671730
$975$	4.25677e8			0.459268
$976$		−	8.92817e8i		−	0.960314i
$977$			1.64047e9i			1.75907i	0.475831	+	0.879537i	$0.342147\pi$
$977$			1.64047e9i			1.75907i	−0.475831	+	0.879537i	$0.657853\pi$
$978$	−2.95992e7			−0.0316420
$979$	−1.42968e7			−0.0152367
$980$			7.81868e8i			0.830721i
$981$			5.25695e8i			0.556835i
$982$	−1.10418e7			−0.0116602
$983$		−	5.29564e8i		−	0.557516i	−0.960361	−	0.278758i	$-0.910077\pi$
$983$		−	5.29564e8i		−	0.557516i	0.960361	−	0.278758i	$-0.0899228\pi$
$984$	3.52697e8			0.370183
$985$		−	5.07331e8i		−	0.530863i
$986$			4.69038e7i			0.0489302i
$987$		−	1.71884e9i		−	1.78765i
$988$		−	1.86186e9i		−	1.93053i
$989$	−2.19241e8	+	1.16248e9i	−0.226639	+	1.20170i
$990$	1.51912e7			0.0156562
$991$	1.14738e9			1.17892			0.589462	−	0.807796i	$-0.299340\pi$
$991$	1.14738e9			1.17892			0.589462	+	0.807796i	$0.299340\pi$
$992$	1.95068e8			0.199825
$993$	1.91011e9			1.95079
$994$			1.55321e8i			0.158151i
$995$	6.00984e8			0.610090
$996$		−	8.12383e8i		−	0.822210i
$997$	−6.96255e8			−0.702559			−0.351280	−	0.936271i	$-0.614253\pi$
$997$	−6.96255e8			−0.702559			−0.351280	+	0.936271i	$0.614253\pi$
$998$	−1.86420e6			−0.00187543
$999$		−	2.09957e9i		−	2.10588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.7.d.a.91.25	✓	48
23.22	odd	2	inner	115.7.d.a.91.26	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.7.d.a.91.25	✓	48	1.1	even	1	trivial
115.7.d.a.91.26	yes	48	23.22	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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	115.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.576987 q^{2} +45.3261 q^{3} -63.6671 q^{4} +55.9017i q^{5} -26.1526 q^{6} -580.802i q^{7} +73.6623 q^{8} +1325.46 q^{9} +O(q^{10})\)	\(q-0.576987 q^{2} +45.3261 q^{3} -63.6671 q^{4} +55.9017i q^{5} -26.1526 q^{6} -580.802i q^{7} +73.6623 q^{8} +1325.46 q^{9} -32.2546i q^{10} +355.332i q^{11} -2885.78 q^{12} -3005.26 q^{13} +335.115i q^{14} +2533.81i q^{15} +4032.19 q^{16} -2913.04i q^{17} -764.771 q^{18} -9730.86i q^{19} -3559.10i q^{20} -26325.5i q^{21} -205.022i q^{22} +(-11956.2 - 2254.92i) q^{23} +3338.82 q^{24} -3125.00 q^{25} +1734.00 q^{26} +27035.0 q^{27} +36977.9i q^{28} +27905.9 q^{29} -1461.97i q^{30} -27704.9 q^{31} -7040.91 q^{32} +16105.8i q^{33} +1680.79i q^{34} +32467.8 q^{35} -84387.9 q^{36} -77661.1i q^{37} +5614.58i q^{38} -136217. q^{39} +4117.85i q^{40} +105635. q^{41} +15189.5i q^{42} -97228.0i q^{43} -22622.9i q^{44} +74095.3i q^{45} +(6898.59 + 1301.06i) q^{46} +65291.8 q^{47} +182764. q^{48} -219682. q^{49} +1803.09 q^{50} -132037. i q^{51} +191336. q^{52} +121989. i q^{53} -15598.9 q^{54} -19863.7 q^{55} -42783.2i q^{56} -441062. i q^{57} -16101.3 q^{58} -169145. q^{59} -161320. i q^{60} -221422. i q^{61} +15985.4 q^{62} -769827. i q^{63} -253998. q^{64} -167999. i q^{65} -9292.85i q^{66} +481948. i q^{67} +185465. i q^{68} +(-541929. - 102207. i) q^{69} -18733.5 q^{70} +463486. q^{71} +97636.1 q^{72} -338686. q^{73} +44809.5i q^{74} -141644. q^{75} +619536. i q^{76} +206377. q^{77} +78595.3 q^{78} -701834. i q^{79} +225406. i q^{80} +259136. q^{81} -60950.1 q^{82} +281512. i q^{83} +1.67607e6i q^{84} +162844. q^{85} +56099.4i q^{86} +1.26486e6 q^{87} +26174.6i q^{88} +40235.0i q^{89} -42752.0i q^{90} +1.74546e6i q^{91} +(761218. + 143564. i) q^{92} -1.25576e6 q^{93} -37672.5 q^{94} +543972. q^{95} -319137. q^{96} +208192. i q^{97} +126753. q^{98} +470977. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 20 q^{2} + 1584 q^{4} + 410 q^{6} - 1210 q^{8} + 12896 q^{9}+O(q^{10}) \) 48 * q - 20 * q^2 + 1584 * q^4 + 410 * q^6 - 1210 * q^8 + 12896 * q^9	\( 48 q - 20 q^{2} + 1584 q^{4} + 410 q^{6} - 1210 q^{8} + 12896 q^{9} + 4290 q^{12} - 1440 q^{13} + 65400 q^{16} + 4610 q^{18} + 26600 q^{23} + 14940 q^{24} - 150000 q^{25} + 47594 q^{26} + 16080 q^{27} + 131800 q^{29} - 1392 q^{31} - 225040 q^{32} + 5000 q^{35} + 658786 q^{36} - 236320 q^{39} - 351496 q^{41} + 382692 q^{46} + 395680 q^{47} + 1042550 q^{48} - 637848 q^{49} + 62500 q^{50} + 523890 q^{52} - 241250 q^{54} - 402000 q^{55} - 479130 q^{58} - 466312 q^{59} - 1124330 q^{62} + 837582 q^{64} + 1021060 q^{69} - 396000 q^{70} - 114336 q^{71} - 1960750 q^{72} - 498720 q^{73} + 3610400 q^{77} - 1104610 q^{78} + 972888 q^{81} + 124950 q^{82} - 246000 q^{85} - 2090960 q^{87} + 4913480 q^{92} + 3234320 q^{93} - 5550378 q^{94} - 1664000 q^{95} - 776990 q^{96} + 9993220 q^{98}+O(q^{100}) \) 48 * q - 20 * q^2 + 1584 * q^4 + 410 * q^6 - 1210 * q^8 + 12896 * q^9 + 4290 * q^12 - 1440 * q^13 + 65400 * q^16 + 4610 * q^18 + 26600 * q^23 + 14940 * q^24 - 150000 * q^25 + 47594 * q^26 + 16080 * q^27 + 131800 * q^29 - 1392 * q^31 - 225040 * q^32 + 5000 * q^35 + 658786 * q^36 - 236320 * q^39 - 351496 * q^41 + 382692 * q^46 + 395680 * q^47 + 1042550 * q^48 - 637848 * q^49 + 62500 * q^50 + 523890 * q^52 - 241250 * q^54 - 402000 * q^55 - 479130 * q^58 - 466312 * q^59 - 1124330 * q^62 + 837582 * q^64 + 1021060 * q^69 - 396000 * q^70 - 114336 * q^71 - 1960750 * q^72 - 498720 * q^73 + 3610400 * q^77 - 1104610 * q^78 + 972888 * q^81 + 124950 * q^82 - 246000 * q^85 - 2090960 * q^87 + 4913480 * q^92 + 3234320 * q^93 - 5550378 * q^94 - 1664000 * q^95 - 776990 * q^96 + 9993220 * q^98

Introduction

L-functions

Modular forms

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Database

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