LMFDB - Embedded newform 48.7.i.a.5.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,7,Mod(5,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("48.5");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	48.i (of order $4$, degree $2$, 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:	$11.0425960138$
Analytic rank:	$0$
Dimension:	$92$
Relative dimension:	$46$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.9
Character	$\chi$	$=$	48.5
Dual form			48.7.i.a.29.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.67919 - 4.40322i) q^{2} +(0.0252819 + 27.0000i) q^{3} +(25.2233 + 58.8200i) q^{4} +(-118.285 + 118.285i) q^{5} +(118.718 - 180.449i) q^{6} +448.417i q^{7} +(90.5262 - 503.934i) q^{8} +(-728.999 + 1.36522i) q^{9} +O(q^{10})$	\(q+(-6.67919 - 4.40322i) q^{2} +(0.0252819 + 27.0000i) q^{3} +(25.2233 + 58.8200i) q^{4} +(-118.285 + 118.285i) q^{5} +(118.718 - 180.449i) q^{6} +448.417i q^{7} +(90.5262 - 503.934i) q^{8} +(-728.999 + 1.36522i) q^{9} +(1310.88 - 269.213i) q^{10} +(1333.28 - 1333.28i) q^{11} +(-1587.50 + 682.515i) q^{12} +(-650.804 + 650.804i) q^{13} +(1974.48 - 2995.06i) q^{14} +(-3196.69 - 3190.70i) q^{15} +(-2823.57 + 2967.26i) q^{16} -1813.68i q^{17} +(4875.14 + 3200.82i) q^{18} +(-2078.53 + 2078.53i) q^{19} +(-9941.06 - 3973.99i) q^{20} +(-12107.3 + 11.3368i) q^{21} +(-14775.9 + 3034.50i) q^{22} -17242.9 q^{23} +(13608.5 + 2431.47i) q^{24} -12357.7i q^{25} +(7212.48 - 1481.21i) q^{26} +(-55.2914 - 19682.9i) q^{27} +(-26375.9 + 11310.5i) q^{28} +(-4951.67 - 4951.67i) q^{29} +(7301.90 + 35387.1i) q^{30} +49594.4 q^{31} +(31924.7 - 7386.10i) q^{32} +(36032.2 + 35964.7i) q^{33} +(-7986.02 + 12113.9i) q^{34} +(-53041.0 - 53041.0i) q^{35} +(-18468.0 - 42845.2i) q^{36} +(7538.79 + 7538.79i) q^{37} +(23035.2 - 4730.68i) q^{38} +(-17588.1 - 17555.2i) q^{39} +(48899.9 + 70315.7i) q^{40} +36323.3 q^{41} +(80916.6 + 53235.2i) q^{42} +(-103736. - 103736. i) q^{43} +(112053. + 44793.7i) q^{44} +(86068.2 - 86391.1i) q^{45} +(115169. + 75924.2i) q^{46} +52604.6i q^{47} +(-80187.4 - 76161.4i) q^{48} -83428.7 q^{49} +(-54413.7 + 82539.5i) q^{50} +(48969.3 - 45.8532i) q^{51} +(-54695.6 - 21864.8i) q^{52} +(-66047.6 + 66047.6i) q^{53} +(-86299.0 + 131710. i) q^{54} +315413. i q^{55} +(225972. + 40593.5i) q^{56} +(-56172.9 - 56067.8i) q^{57} +(11269.9 + 54876.5i) q^{58} +(-230346. + 230346. i) q^{59} +(107046. - 268509. i) q^{60} +(241134. - 241134. i) q^{61} +(-331251. - 218375. i) q^{62} +(-612.188 - 326895. i) q^{63} +(-245754. - 91238.4i) q^{64} -153961. i q^{65} +(-82305.0 - 398873. i) q^{66} +(-203131. + 203131. i) q^{67} +(106680. - 45746.9i) q^{68} +(-435.932 - 465557. i) q^{69} +(120720. + 587823. i) q^{70} +68204.8 q^{71} +(-65305.5 + 367490. i) q^{72} +347282. i q^{73} +(-17158.1 - 83548.0i) q^{74} +(333658. - 312.426i) q^{75} +(-174687. - 69831.8i) q^{76} +(597864. + 597864. i) q^{77} +(40175.0 + 194699. i) q^{78} -494609. q^{79} +(-16996.3 - 684969. i) q^{80} +(531437. - 1990.49i) q^{81} +(-242611. - 159940. i) q^{82} +(-544140. - 544140. i) q^{83} +(-306051. - 711862. i) q^{84} +(214531. + 214531. i) q^{85} +(236100. + 1.14964e6i) q^{86} +(133570. - 133820. i) q^{87} +(-551186. - 792579. i) q^{88} +227378. q^{89} +(-955265. + 198046. i) q^{90} +(-291831. - 291831. i) q^{91} +(-434922. - 1.01423e6i) q^{92} +(1253.84 + 1.33905e6i) q^{93} +(231630. - 351356. i) q^{94} -491719. i q^{95} +(200232. + 861780. i) q^{96} +828870. q^{97} +(557237. + 367355. i) q^{98} +(-970137. + 973777. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6}+O(q^{10}) $ 92 * q - 2 * q^3 - 4 * q^4 + 508 * q^6	$ 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6} + 1496 q^{10} + 4288 q^{12} - 4 q^{13} - 4 q^{15} + 10352 q^{16} + 10020 q^{18} - 3940 q^{19} + 1456 q^{21} - 42088 q^{22} + 66376 q^{24} - 34322 q^{27} + 27000 q^{28} - 127836 q^{30} - 8 q^{31} - 4 q^{33} + 128424 q^{34} + 172420 q^{36} - 4 q^{37} - 164392 q^{40} + 221560 q^{42} - 195268 q^{43} - 31252 q^{45} + 150712 q^{46} - 188048 q^{48} - 1142884 q^{49} + 385056 q^{51} - 122368 q^{52} + 151912 q^{54} - 181960 q^{58} + 242304 q^{60} - 326500 q^{61} + 470592 q^{63} - 251752 q^{64} + 489172 q^{66} + 1207676 q^{67} - 1460 q^{69} + 346392 q^{70} - 903480 q^{72} + 1413778 q^{75} - 359992 q^{76} + 1478252 q^{78} + 860920 q^{79} - 4 q^{81} - 2412800 q^{82} - 730640 q^{84} + 434496 q^{85} + 1259360 q^{88} - 291792 q^{90} + 2320992 q^{91} - 1176260 q^{93} - 1412496 q^{94} + 1956200 q^{96} - 8 q^{97} - 4048228 q^{99}+O(q^{100}) $ 92 * q - 2 * q^3 - 4 * q^4 + 508 * q^6 + 1496 * q^10 + 4288 * q^12 - 4 * q^13 - 4 * q^15 + 10352 * q^16 + 10020 * q^18 - 3940 * q^19 + 1456 * q^21 - 42088 * q^22 + 66376 * q^24 - 34322 * q^27 + 27000 * q^28 - 127836 * q^30 - 8 * q^31 - 4 * q^33 + 128424 * q^34 + 172420 * q^36 - 4 * q^37 - 164392 * q^40 + 221560 * q^42 - 195268 * q^43 - 31252 * q^45 + 150712 * q^46 - 188048 * q^48 - 1142884 * q^49 + 385056 * q^51 - 122368 * q^52 + 151912 * q^54 - 181960 * q^58 + 242304 * q^60 - 326500 * q^61 + 470592 * q^63 - 251752 * q^64 + 489172 * q^66 + 1207676 * q^67 - 1460 * q^69 + 346392 * q^70 - 903480 * q^72 + 1413778 * q^75 - 359992 * q^76 + 1478252 * q^78 + 860920 * q^79 - 4 * q^81 - 2412800 * q^82 - 730640 * q^84 + 434496 * q^85 + 1259360 * q^88 - 291792 * q^90 + 2320992 * q^91 - 1176260 * q^93 - 1412496 * q^94 + 1956200 * q^96 - 8 * q^97 - 4048228 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−6.67919	−	4.40322i	−0.834899	−	0.550403i
$2$	−6.67919	−	4.40322i	−0.834899	−	0.550403i
$3$	0.0252819	+	27.0000i	0.000936366	+	1.00000i
$3$	0.0252819	+	27.0000i	0.000936366	+	1.00000i
$4$	25.2233	+	58.8200i	0.394114	+	0.919062i
$5$	−118.285	+	118.285i	−0.946280	+	0.946280i	−0.998629	−	0.0523484i	$-0.983329\pi$
$5$	−118.285	+	118.285i	−0.946280	+	0.946280i	0.0523484	+	0.998629i	$0.483329\pi$
$6$	118.718	−	180.449i	0.549621	−	0.835414i
$7$			448.417i			1.30734i	0.756781	+	0.653669i	$0.226771\pi$
$7$			448.417i			1.30734i	−0.756781	+	0.653669i	$0.773229\pi$
$8$	90.5262	−	503.934i	0.176809	−	0.984245i
$9$	−728.999	+	1.36522i	−0.999998	+	0.00187273i
$10$	1310.88	−	269.213i	1.31088	−	0.269213i
$11$	1333.28	−	1333.28i	1.00171	−	1.00171i	0.00171193	−	0.999999i	$-0.499455\pi$
$11$	1333.28	−	1333.28i	1.00171	−	1.00171i	0.999999	−	0.00171193i	$-0.000544924\pi$
$12$	−1587.50	+	682.515i	−0.918692	+	0.394974i
$13$	−650.804	+	650.804i	−0.296224	+	0.296224i	−0.839533	−	0.543309i	$-0.817171\pi$
$13$	−650.804	+	650.804i	−0.296224	+	0.296224i	0.543309	+	0.839533i	$0.317171\pi$
$14$	1974.48	−	2995.06i	0.719562	−	1.09150i
$15$	−3196.69	−	3190.70i	−0.947166	−	0.945394i
$16$	−2823.57	+	2967.26i	−0.689349	+	0.724429i
$17$		−	1813.68i		−	0.369159i	−0.982818	−	0.184579i	$-0.940908\pi$
$17$		−	1813.68i		−	0.369159i	0.982818	−	0.184579i	$-0.0590923\pi$
$18$	4875.14	+	3200.82i	0.835929	+	0.548838i
$19$	−2078.53	+	2078.53i	−0.303037	+	0.303037i	−0.842201	−	0.539164i	$-0.818740\pi$
$19$	−2078.53	+	2078.53i	−0.303037	+	0.303037i	0.539164	+	0.842201i	$0.318740\pi$
$20$	−9941.06	−	3973.99i	−1.24263	−	0.496748i
$21$	−12107.3	+	11.3368i	−1.30734	+	0.00122415i
$22$	−14775.9	+	3034.50i	−1.38767	+	0.284983i
$23$	−17242.9			−1.41718			−0.708592	−	0.705618i	$-0.750669\pi$
$23$	−17242.9			−1.41718			−0.708592	+	0.705618i	$0.750669\pi$
$24$	13608.5	+	2431.47i	0.984410	+	0.175887i
$25$		−	12357.7i		−	0.790893i
$26$	7212.48	−	1481.21i	0.410359	−	0.0842746i
$27$	−55.2914	−	19682.9i	−0.00280909	−	0.999996i
$28$	−26375.9	+	11310.5i	−1.20152	+	0.515240i
$29$	−4951.67	−	4951.67i	−0.203029	−	0.203029i	0.598268	−	0.801296i	$-0.295856\pi$
$29$	−4951.67	−	4951.67i	−0.203029	−	0.203029i	−0.801296	+	0.598268i	$0.795856\pi$
$30$	7301.90	+	35387.1i	0.270441	+	1.31063i
$31$	49594.4			1.66475			0.832373	−	0.554216i	$-0.186982\pi$
$31$	49594.4			1.66475			0.832373	+	0.554216i	$0.186982\pi$
$32$	31924.7	−	7386.10i	0.974265	−	0.225406i
$33$	36032.2	+	35964.7i	1.00265	+	1.00077i
$34$	−7986.02	+	12113.9i	−0.203186	+	0.308210i
$35$	−53041.0	−	53041.0i	−1.23711	−	1.23711i
$36$	−18468.0	−	42845.2i	−0.395834	−	0.918322i
$37$	7538.79	+	7538.79i	0.148832	+	0.148832i	0.777596	−	0.628764i	$-0.216439\pi$
$37$	7538.79	+	7538.79i	0.148832	+	0.148832i	−0.628764	+	0.777596i	$0.716439\pi$
$38$	23035.2	−	4730.68i	0.419798	−	0.0862131i
$39$	−17588.1	−	17555.2i	−0.296501	−	0.295946i
$40$	48899.9	+	70315.7i	0.764061	+	1.09868i
$41$	36323.3			0.527029			0.263514	−	0.964655i	$-0.415118\pi$
$41$	36323.3			0.527029			0.263514	+	0.964655i	$0.415118\pi$
$42$	80916.6	+	53235.2i	1.09217	+	0.718540i
$43$	−103736.	−	103736.i	−1.30474	−	1.30474i	−0.925159	−	0.379580i	$-0.876068\pi$
$43$	−103736.	−	103736.i	−1.30474	−	1.30474i	−0.379580	−	0.925159i	$-0.623932\pi$
$44$	112053.	+	44793.7i	1.31542	+	0.525846i
$45$	86068.2	−	86391.1i	0.944507	−	0.948051i
$46$	115169.	+	75924.2i	1.18321	+	0.780022i
$47$			52604.6i			0.506676i	0.967378	+	0.253338i	$0.0815285\pi$
$47$			52604.6i			0.506676i	−0.967378	+	0.253338i	$0.918472\pi$
$48$	−80187.4	−	76161.4i	−0.725075	−	0.688670i
$49$	−83428.7			−0.709132
$50$	−54413.7	+	82539.5i	−0.435310	+	0.660316i
$51$	48969.3	−	45.8532i	0.369159	−	0.000345668i
$52$	−54695.6	−	21864.8i	−0.388994	−	0.155502i
$53$	−66047.6	+	66047.6i	−0.443639	+	0.443639i	−0.893233	−	0.449594i	$-0.851569\pi$
$53$	−66047.6	+	66047.6i	−0.443639	+	0.443639i	0.449594	+	0.893233i	$0.351569\pi$
$54$	−86299.0	+	131710.i	−0.548055	+	0.836442i
$55$			315413.i			1.89580i
$56$	225972.	+	40593.5i	1.28674	+	0.231149i
$57$	−56172.9	−	56067.8i	−0.303321	−	0.302753i
$58$	11269.9	+	54876.5i	0.0577610	+	0.281256i
$59$	−230346.	+	230346.i	−1.12157	+	1.12157i	−0.130060	+	0.991506i	$0.541517\pi$
$59$	−230346.	+	230346.i	−1.12157	+	1.12157i	−0.991506	+	0.130060i	$0.958483\pi$
$60$	107046.	−	268509.i	0.495584	−	1.24310i
$61$	241134.	−	241134.i	1.06235	−	1.06235i	0.0644289	−	0.997922i	$-0.479477\pi$
$61$	241134.	−	241134.i	1.06235	−	1.06235i	0.997922	−	0.0644289i	$-0.0205226\pi$
$62$	−331251.	−	218375.i	−1.38989	−	0.916281i
$63$	−612.188	−	326895.i	−0.00244829	−	1.30734i
$64$	−245754.	−	91238.4i	−0.937477	−	0.348047i
$65$		−	153961.i		−	0.560622i
$66$	−82305.0	−	398873.i	−0.286282	−	1.38740i
$67$	−203131.	+	203131.i	−0.675386	+	0.675386i	−0.958953	−	0.283567i	$-0.908482\pi$
$67$	−203131.	+	203131.i	−0.675386	+	0.675386i	0.283567	+	0.958953i	$0.408482\pi$
$68$	106680.	−	45746.9i	0.339280	−	0.145490i
$69$	−435.932	−	465557.i	−0.00132700	−	1.41718i
$70$	120720.	+	587823.i	0.351953	+	1.71377i
$71$	68204.8			0.190564			0.0952818	−	0.995450i	$-0.469625\pi$
$71$	68204.8			0.190564			0.0952818	+	0.995450i	$0.469625\pi$
$72$	−65305.5	+	367490.i	−0.174965	+	0.984575i
$73$			347282.i			0.892717i	0.894854	+	0.446358i	$0.147279\pi$
$73$			347282.i			0.892717i	−0.894854	+	0.446358i	$0.852721\pi$
$74$	−17158.1	−	83548.0i	−0.0423422	−	0.206177i
$75$	333658.	−	312.426i	0.790893	−	0.000740565i
$76$	−174687.	−	69831.8i	−0.397941	−	0.159079i
$77$	597864.	+	597864.i	1.30957	+	1.30957i
$78$	40175.0	+	194699.i	0.0846588	+	0.410280i
$79$	−494609.			−1.00319			−0.501593	−	0.865104i	$-0.667252\pi$
$79$	−494609.			−1.00319			−0.501593	+	0.865104i	$0.667252\pi$
$80$	−16996.3	−	684969.i	−0.0331960	−	1.33783i
$81$	531437.	−	1990.49i	0.999993	−	0.00374545i
$82$	−242611.	−	159940.i	−0.440016	−	0.290078i
$83$	−544140.	−	544140.i	−0.951648	−	0.951648i	0.0472360	−	0.998884i	$-0.484959\pi$
$83$	−544140.	−	544140.i	−0.951648	−	0.951648i	−0.998884	+	0.0472360i	$0.984959\pi$
$84$	−306051.	−	711862.i	−0.516364	−	1.20104i
$85$	214531.	+	214531.i	0.349328	+	0.349328i
$86$	236100.	+	1.14964e6i	0.371194	+	1.80746i
$87$	133570.	−	133820.i	0.202839	−	0.203219i
$88$	−551186.	−	792579.i	−0.808817	−	1.16304i
$89$	227378.			0.322536			0.161268	−	0.986911i	$-0.448442\pi$
$89$	227378.			0.322536			0.161268	+	0.986911i	$0.448442\pi$
$90$	−955265.	+	198046.i	−1.31038	+	0.271668i
$91$	−291831.	−	291831.i	−0.387265	−	0.387265i
$92$	−434922.	−	1.01423e6i	−0.558531	−	1.30248i
$93$	1253.84	+	1.33905e6i	0.00155881	+	1.66474i
$94$	231630.	−	351356.i	0.278876	−	0.423023i
$95$		−	491719.i		−	0.573517i
$96$	200232.	+	861780.i	0.226318	+	0.974053i
$97$	828870.			0.908179			0.454090	−	0.890956i	$-0.349965\pi$
$97$	828870.			0.908179			0.454090	+	0.890956i	$0.349965\pi$
$98$	557237.	+	367355.i	0.592054	+	0.390308i
$99$	−970137.	+	973777.i	−0.999833	+	1.00358i
$100$	726880.	−	311702.i	0.726880	−	0.311702i
$101$	−1.24116e6	+	1.24116e6i	−1.20465	+	1.20465i	−0.231919	+	0.972735i	$0.574500\pi$
$101$	−1.24116e6	+	1.24116e6i	−1.20465	+	1.20465i	−0.972735	+	0.231919i	$0.925500\pi$
$102$	−327277.	−	215316.i	−0.308401	−	0.202897i
$103$			1.77781e6i			1.62695i	0.581600	+	0.813475i	$0.302427\pi$
$103$			1.77781e6i			1.62695i	−0.581600	+	0.813475i	$0.697573\pi$
$104$	269047.	+	386877.i	0.239182	+	0.343932i
$105$	1.43077e6	−	1.43345e6i	1.23595	−	1.23827i
$106$	731967.	−	150323.i	0.614574	−	0.126214i
$107$	−69418.1	+	69418.1i	−0.0566658	+	0.0566658i	−0.734872	−	0.678206i	$-0.762758\pi$
$107$	−69418.1	+	69418.1i	−0.0566658	+	0.0566658i	0.678206	+	0.734872i	$0.262758\pi$
$108$	1.15635e6	−	499720.i	0.917951	−	0.396694i
$109$	−649777.	+	649777.i	−0.501747	+	0.501747i	−0.911981	−	0.410233i	$-0.865447\pi$
$109$	−649777.	+	649777.i	−0.501747	+	0.501747i	0.410233	+	0.911981i	$0.365447\pi$
$110$	1.38884e6	−	2.10671e6i	1.04345	−	1.58280i
$111$	−203357.	+	203738.i	−0.148693	+	0.148971i
$112$	−1.33057e6	−	1.26614e6i	−0.947074	−	0.901212i
$113$			1.12036e6i			0.776467i	0.921561	+	0.388234i	$0.126915\pi$
$113$			1.12036e6i			0.776467i	−0.921561	+	0.388234i	$0.873085\pi$
$114$	128311.	+	621830.i	0.0866061	+	0.419717i
$115$	2.03957e6	−	2.03957e6i	1.34105	−	1.34105i
$116$	166360.	−	416154.i	0.106580	−	0.266612i
$117$	473547.	−	475324.i	0.295669	−	0.296778i
$118$	2.55279e6	−	524261.i	1.55371	−	0.319082i
$119$	813284.			0.482615
$120$	−1.89729e6	+	1.32207e6i	−1.09797	+	0.765090i
$121$		−	1.78369e6i		−	1.00685i
$122$	−2.67234e6	+	548813.i	−1.47168	+	0.302235i
$123$	918.322	+	980730.i	0.000493492	+	0.527028i
$124$	1.25093e6	+	2.91714e6i	0.656099	+	1.53000i
$125$	−386472.	−	386472.i	−0.197874	−	0.197874i
$126$	−1.43530e6	+	2.18609e6i	−0.717517	+	1.09284i
$127$	775740.			0.378709			0.189354	−	0.981909i	$-0.439361\pi$
$127$	775740.			0.378709			0.189354	+	0.981909i	$0.439361\pi$
$128$	1.23970e6	+	1.69151e6i	0.591133	+	0.806574i
$129$	2.79824e6	−	2.80349e6i	1.30352	−	1.30596i
$130$	−677923.	+	1.02833e6i	−0.308568	+	0.468063i
$131$	−748805.	−	748805.i	−0.333085	−	0.333085i	0.520672	−	0.853757i	$-0.325681\pi$
$131$	−748805.	−	748805.i	−0.333085	−	0.333085i	−0.853757	+	0.520672i	$0.825681\pi$
$132$	−1.20660e6	+	3.02656e6i	−0.524614	+	1.31591i
$133$	−932049.	−	932049.i	−0.396172	−	0.396172i
$134$	2.25118e6	−	462321.i	0.935613	−	0.192145i
$135$	2.33474e6	+	2.32166e6i	0.948935	+	0.943619i
$136$	−913973.	−	164185.i	−0.363343	−	0.0652706i
$137$	−4.43261e6			−1.72384			−0.861922	−	0.507041i	$-0.830739\pi$
$137$	−4.43261e6			−1.72384			−0.861922	+	0.507041i	$0.830739\pi$
$138$	−2.04704e6	+	3.11147e6i	−0.778914	+	1.18394i
$139$	−2.87972e6	−	2.87972e6i	−1.07227	−	1.07227i	−0.997176	−	0.0750980i	$-0.976073\pi$
$139$	−2.87972e6	−	2.87972e6i	−1.07227	−	1.07227i	−0.0750980	−	0.997176i	$-0.523927\pi$
$140$	1.78200e6	−	4.45774e6i	0.649418	−	1.62454i
$141$	−1.42032e6	+	1329.94i	−0.506676	+	0.000474434i
$142$	−455553.	−	300321.i	−0.159101	−	0.104887i
$143$			1.73540e6i			0.593461i
$144$	2.05433e6	−	2.16699e6i	0.687991	−	0.725719i
$145$	1.17142e6			0.384244
$146$	1.52916e6	−	2.31956e6i	0.491354	−	0.745329i
$147$	−2109.23	−	2.25257e6i	−0.000664007	−	0.709132i
$148$	−253278.	+	633584.i	−0.0781291	+	0.195443i
$149$	977145.	−	977145.i	0.295393	−	0.295393i	−0.543813	−	0.839206i	$-0.683020\pi$
$149$	977145.	−	977145.i	0.295393	−	0.295393i	0.839206	+	0.543813i	$0.183020\pi$
$150$	−2.22994e6	−	1.46708e6i	−0.660724	−	0.434691i
$151$		−	4.80593e6i		−	1.39587i	−0.716159	−	0.697937i	$-0.754101\pi$
$151$		−	4.80593e6i		−	1.39587i	0.716159	−	0.697937i	$-0.245899\pi$
$152$	859281.	+	1.23560e6i	0.244683	+	0.351843i
$153$	2476.07	+	1.32217e6i	0.000691335	+	0.369158i
$154$	−1.36072e6	−	6.62578e6i	−0.372569	−	1.81416i
$155$	−5.86628e6	+	5.86628e6i	−1.57532	+	1.57532i
$156$	588968.	−	1.47733e6i	0.155138	−	0.389139i
$157$	−4.44246e6	+	4.44246e6i	−1.14795	+	1.14795i	−0.160998	+	0.986955i	$0.551471\pi$
$157$	−4.44246e6	+	4.44246e6i	−1.14795	+	1.14795i	−0.986955	+	0.160998i	$0.948529\pi$
$158$	3.30359e6	+	2.17788e6i	0.837559	+	0.552156i
$159$	−1.78495e6	−	1.78162e6i	−0.444054	−	0.443223i
$160$	−2.90255e6	+	4.64988e6i	−0.708631	+	1.13523i
$161$		−	7.73200e6i		−	1.85274i
$162$	−3.55834e6	−	2.32674e6i	−0.836955	−	0.547272i
$163$	2.66050e6	−	2.66050e6i	0.614329	−	0.614329i	−0.329742	−	0.944071i	$-0.606962\pi$
$163$	2.66050e6	−	2.66050e6i	0.614329	−	0.614329i	0.944071	+	0.329742i	$0.106962\pi$
$164$	916193.	+	2.13654e6i	0.207709	+	0.484372i
$165$	−8.51616e6	+	7974.24i	−1.89580	+	0.00177516i
$166$	1.23845e6	+	6.03038e6i	0.270740	+	1.31832i
$167$	−255814.			−0.0549255			−0.0274628	−	0.999623i	$-0.508743\pi$
$167$	−255814.			−0.0549255			−0.0274628	+	0.999623i	$0.508743\pi$
$168$	−1.09031e6	+	6.10228e6i	−0.229944	+	1.28696i
$169$			3.97972e6i			0.824503i
$170$	−488266.	−	2.37752e6i	−0.0993825	−	0.483924i
$171$	1.51241e6	−	1.51809e6i	0.302469	−	0.303604i
$172$	3.48518e6	−	8.71830e6i	0.684920	−	1.71335i
$173$	1.64869e6	+	1.64869e6i	0.318420	+	0.318420i	0.848160	−	0.529740i	$-0.177711\pi$
$173$	1.64869e6	+	1.64869e6i	0.318420	+	0.318420i	−0.529740	+	0.848160i	$0.677711\pi$
$174$	−1.48138e6	+	305673.i	−0.281202	+	0.0580243i
$175$	5.54141e6			1.03396
$176$	191578.	+	7.72079e6i	0.0351405	+	1.41620i
$177$	−6.22517e6	−	6.21352e6i	−1.12262	−	1.12052i
$178$	−1.51870e6	−	1.00120e6i	−0.269285	−	0.177525i
$179$	2.56261e6	+	2.56261e6i	0.446810	+	0.446810i	0.894293	−	0.447482i	$-0.147679\pi$
$179$	2.56261e6	+	2.56261e6i	0.446810	+	0.446810i	−0.447482	+	0.894293i	$0.647679\pi$
$180$	7.25244e6	+	2.88346e6i	1.24356	+	0.494420i
$181$	1.79377e6	+	1.79377e6i	0.302504	+	0.302504i	0.841993	−	0.539489i	$-0.181383\pi$
$181$	1.79377e6	+	1.79377e6i	0.302504	+	0.302504i	−0.539489	+	0.841993i	$0.681383\pi$
$182$	664200.	+	3.23420e6i	0.110175	+	0.536478i
$183$	6.51670e6	+	6.50451e6i	1.06335	+	1.06136i
$184$	−1.56093e6	+	8.68926e6i	−0.250571	+	1.39486i
$185$	−1.78345e6			−0.281674
$186$	5.88776e6	−	8.94929e6i	0.914979	−	1.39075i
$187$	−2.41813e6	−	2.41813e6i	−0.369790	−	0.369790i
$188$	−3.09420e6	+	1.32686e6i	−0.465666	+	0.199688i
$189$	8.82616e6	−	24793.6i	1.30733	−	0.00367244i
$190$	−2.16515e6	+	3.28428e6i	−0.315665	+	0.478829i
$191$			764453.i			0.109711i	0.998494	+	0.0548555i	$0.0174698\pi$
$191$			764453.i			0.109711i	−0.998494	+	0.0548555i	$0.982530\pi$
$192$	2.45722e6	−	6.63766e6i	0.347169	−	0.937803i
$193$	6.78754e6			0.944149			0.472075	−	0.881559i	$-0.343505\pi$
$193$	6.78754e6			0.944149			0.472075	+	0.881559i	$0.343505\pi$
$194$	−5.53619e6	−	3.64970e6i	−0.758238	−	0.499864i
$195$	4.15694e6	−	3892.41i	0.560621	−	0.000524947i
$196$	−2.10435e6	−	4.90727e6i	−0.279479	−	0.651737i
$197$	−1.28809e6	+	1.28809e6i	−0.168479	+	0.168479i	−0.786311	−	0.617831i	$-0.788011\pi$
$197$	−1.28809e6	+	1.28809e6i	−0.168479	+	0.168479i	0.617831	+	0.786311i	$0.288011\pi$
$198$	1.07675e7	−	2.23232e6i	1.38714	−	0.287581i
$199$			2.11914e6i			0.268905i	0.990920	+	0.134453i	$0.0429276\pi$
$199$			2.11914e6i			0.268905i	−0.990920	+	0.134453i	$0.957072\pi$
$200$	−6.22746e6	−	1.11870e6i	−0.778433	−	0.139837i
$201$	−5.48967e6	−	5.47940e6i	−0.676018	−	0.674753i
$202$	1.37550e7	−	2.82484e6i	1.66881	−	0.342720i
$203$	2.22041e6	−	2.22041e6i	0.265427	−	0.265427i
$204$	1.23786e6	+	2.87921e6i	0.145808	+	0.339143i
$205$	−4.29651e6	+	4.29651e6i	−0.498717	+	0.498717i
$206$	7.82810e6	−	1.18743e7i	0.895478	−	1.35834i
$207$	1.25700e7	−	23540.3i	1.41718	−	0.00265400i
$208$	−93513.7	−	3.76870e6i	−0.0103917	−	0.418795i
$209$			5.54252e6i			0.607111i
$210$	−1.58682e7	+	3.27430e6i	−1.71344	+	0.353558i
$211$	2.12658e6	−	2.12658e6i	0.226378	−	0.226378i	−0.584800	−	0.811178i	$-0.698827\pi$
$211$	2.12658e6	−	2.12658e6i	0.226378	−	0.226378i	0.811178	+	0.584800i	$0.198827\pi$
$212$	−5.55085e6	−	2.21898e6i	−0.582576	−	0.232887i
$213$	1724.35	+	1.84153e6i	0.000178437	+	0.190564i
$214$	769320.	−	157994.i	0.0784993	−	0.0161212i
$215$	2.45408e7			2.46930
$216$	−9.92389e6	−	1.75396e6i	−0.984738	−	0.174043i
$217$			2.22390e7i			2.17638i
$218$	7.20110e6	−	1.47888e6i	0.695072	−	0.142745i
$219$	−9.37661e6	+	8779.94i	−0.892716	+	0.000835909i
$220$	−1.85526e7	+	7.95576e6i	−1.74236	+	0.747160i
$221$	1.18035e6	+	1.18035e6i	0.109354	+	0.109354i
$222$	2.25536e6	−	465380.i	0.206138	−	0.0425353i
$223$	−5.51305e6			−0.497139			−0.248569	−	0.968614i	$-0.579960\pi$
$223$	−5.51305e6			−0.497139			−0.248569	+	0.968614i	$0.579960\pi$
$224$	3.31205e6	+	1.43156e7i	0.294682	+	1.27369i
$225$	16871.0	+	9.00875e6i	0.00148113	+	0.790892i
$226$	4.93320e6	−	7.48312e6i	0.427370	−	0.648272i
$227$	−8.18710e6	−	8.18710e6i	−0.699927	−	0.699927i	0.264468	−	0.964394i	$-0.414804\pi$
$227$	−8.18710e6	−	8.18710e6i	−0.699927	−	0.699927i	−0.964394	+	0.264468i	$0.914804\pi$
$228$	1.88104e6	−	4.71830e6i	0.158706	−	0.398090i
$229$	−4.34668e6	−	4.34668e6i	−0.361952	−	0.361952i	0.502579	−	0.864531i	$-0.332385\pi$
$229$	−4.34668e6	−	4.34668e6i	−0.361952	−	0.361952i	−0.864531	+	0.502579i	$0.832385\pi$
$230$	−2.26034e7	+	4.64201e6i	−1.85776	+	0.381525i
$231$	−1.61272e7	+	1.61574e7i	−1.30835	+	1.31080i
$232$	−2.94357e6	+	2.04706e6i	−0.235727	+	0.163933i
$233$	8.92984e6			0.705953			0.352977	−	0.935632i	$-0.385170\pi$
$233$	8.92984e6			0.705953			0.352977	+	0.935632i	$0.385170\pi$
$234$	−5.25586e6	+	1.08965e6i	−0.410201	+	0.0850430i
$235$	−6.22234e6	−	6.22234e6i	−0.479457	−	0.479457i
$236$	−1.93590e7	−	7.73886e6i	−1.47281	−	0.588764i
$237$	−12504.7	−	1.33544e7i	−0.000939348	−	1.00318i
$238$	−5.43208e6	−	3.58107e6i	−0.402935	−	0.265633i
$239$		−	1.51557e6i		−	0.111015i	−0.998458	−	0.0555076i	$-0.982322\pi$
$239$		−	1.51557e6i		−	0.111015i	0.998458	−	0.0555076i	$-0.0176777\pi$
$240$	1.84937e7	−	476218.i	1.33780	−	0.0344486i
$241$	−5.69357e6			−0.406756			−0.203378	−	0.979100i	$-0.565192\pi$
$241$	−5.69357e6			−0.406756			−0.203378	+	0.979100i	$0.565192\pi$
$242$	−7.85399e6	+	1.19136e7i	−0.554172	+	0.840616i
$243$	67178.9	+	1.43487e7i	0.00468181	+	0.999989i
$244$	2.02656e7	+	8.10129e6i	1.39505	+	0.557679i
$245$	9.86837e6	−	9.86837e6i	0.671038	−	0.671038i
$246$	4.31224e6	−	6.55453e6i	0.289666	−	0.440287i
$247$		−	2.70543e6i		−	0.179534i
$248$	4.48960e6	−	2.49923e7i	0.294342	−	1.63852i
$249$	1.46780e7	−	1.47055e7i	0.950756	−	0.952538i
$250$	879599.	+	4.28304e6i	0.0562943	+	0.274115i
$251$	6.97458e6	−	6.97458e6i	0.441059	−	0.441059i	−0.451309	−	0.892368i	$-0.649043\pi$
$251$	6.97458e6	−	6.97458e6i	0.441059	−	0.441059i	0.892368	+	0.451309i	$0.149043\pi$
$252$	1.92125e7	−	8.28138e6i	1.20056	−	0.517489i
$253$	−2.29895e7	+	2.29895e7i	−1.41961	+	1.41961i
$254$	−5.18132e6	−	3.41576e6i	−0.316184	−	0.208442i
$255$	−5.78691e6	+	5.79776e6i	−0.349001	+	0.349655i
$256$	−832083.	−	1.67566e7i	−0.0495960	−	0.998769i
$257$		−	1.34367e7i		−	0.791574i	−0.918342	−	0.395787i	$-0.870472\pi$
$257$		−	1.34367e7i		−	0.791574i	0.918342	−	0.395787i	$-0.129528\pi$
$258$	−3.10344e7	+	6.40376e6i	−1.80711	+	0.372886i
$259$	−3.38052e6	+	3.38052e6i	−0.194574	+	0.194574i
$260$	9.05596e6	−	3.88339e6i	0.515246	−	0.220949i
$261$	3.61652e6	+	3.60300e6i	0.203409	+	0.202648i
$262$	1.70426e6	+	8.29856e6i	0.0947614	+	0.461423i
$263$	−8.65258e6			−0.475640			−0.237820	−	0.971309i	$-0.576433\pi$
$263$	−8.65258e6			−0.475640			−0.237820	+	0.971309i	$0.576433\pi$
$264$	2.13857e7	−	1.49021e7i	1.16228	−	0.809906i
$265$		−	1.56249e7i		−	0.839614i
$266$	2.12132e6	+	1.03294e7i	0.112710	+	0.548818i
$267$	5748.54	+	6.13920e6i	0.000302012	+	0.322536i
$268$	−1.70718e7	−	6.82453e6i	−0.886900	−	0.354543i
$269$	−4.43140e6	−	4.43140e6i	−0.227659	−	0.227659i	0.584055	−	0.811714i	$-0.301465\pi$
$269$	−4.43140e6	−	4.43140e6i	−0.227659	−	0.227659i	−0.811714	+	0.584055i	$0.801465\pi$
$270$	−5.37139e6	−	2.57871e7i	−0.272895	−	1.31012i
$271$	−6.55662e6			−0.329437			−0.164719	−	0.986341i	$-0.552672\pi$
$271$	−6.55662e6			−0.329437			−0.164719	+	0.986341i	$0.552672\pi$
$272$	5.38166e6	+	5.12105e6i	0.267429	+	0.254479i
$273$	7.87207e6	−	7.88682e6i	0.386902	−	0.387627i
$274$	2.96063e7	+	1.95178e7i	1.43924	+	0.948808i
$275$	−1.64762e7	−	1.64762e7i	−0.792246	−	0.792246i
$276$	2.73731e7	−	1.17685e7i	1.30196	−	0.559751i
$277$	1.44417e7	+	1.44417e7i	0.679483	+	0.679483i	0.959883	−	0.280401i	$-0.0904673\pi$
$277$	1.44417e7	+	1.44417e7i	0.679483	+	0.679483i	−0.280401	+	0.959883i	$0.590467\pi$
$278$	6.55416e6	+	3.19143e7i	0.305058	+	1.48542i
$279$	−3.61543e7	+	67707.3i	−1.66474	+	0.00311762i
$280$	−3.15308e7	+	2.19275e7i	−1.43635	+	0.998886i
$281$	4.51668e6			0.203564			0.101782	−	0.994807i	$-0.467546\pi$
$281$	4.51668e6			0.203564			0.101782	+	0.994807i	$0.467546\pi$
$282$	9.49247e6	+	6.24512e6i	0.423284	+	0.278480i
$283$	2.02953e7	+	2.02953e7i	0.895441	+	0.895441i	0.995029	−	0.0995874i	$-0.0317523\pi$
$283$	2.02953e7	+	2.02953e7i	0.895441	+	0.895441i	−0.0995874	+	0.995029i	$0.531752\pi$
$284$	1.72035e6	+	4.01181e6i	0.0751037	+	0.175140i
$285$	1.32764e7	−	12431.6i	0.573516	−	0.000537021i
$286$	7.64136e6	−	1.15911e7i	0.326643	−	0.495480i
$287$			1.62880e7i			0.689005i
$288$	−2.32630e7	+	5.42805e6i	−0.973841	+	0.227230i
$289$	2.08481e7			0.863722
$290$	−7.82412e6	−	5.15801e6i	−0.320805	−	0.211489i
$291$	20955.4	+	2.23795e7i	0.000850388	+	0.908179i
$292$	−2.04271e7	+	8.75959e6i	−0.820462	+	0.351832i
$293$	−4.23640e6	+	4.23640e6i	−0.168420	+	0.168420i	−0.786285	−	0.617865i	$-0.787998\pi$
$293$	−4.23640e6	+	4.23640e6i	−0.168420	+	0.168420i	0.617865	+	0.786285i	$0.287998\pi$
$294$	−9.90450e6	+	1.50547e7i	−0.389754	+	0.592419i
$295$		−	5.44930e7i		−	2.12263i
$296$	4.48151e6	−	3.11659e6i	0.172802	−	0.120172i
$297$	−2.63165e7	−	2.61691e7i	−1.00452	−	0.998893i
$298$	−1.08291e7	+	2.22396e6i	−0.409209	+	0.0840383i
$299$	1.12217e7	−	1.12217e7i	0.419804	−	0.419804i
$300$	8.43432e6	+	1.96179e7i	0.312382	+	0.726588i
$301$	4.65169e7	−	4.65169e7i	1.70573	−	1.70573i
$302$	−2.11616e7	+	3.20997e7i	−0.768293	+	1.16541i
$303$	−3.35426e7	−	3.34798e7i	−1.20578	−	1.20353i
$304$	−298664.	−	1.20364e7i	−0.0106307	−	0.428428i
$305$			5.70450e7i			2.01056i
$306$	5.80526e6	−	8.84192e6i	0.202608	−	0.308590i
$307$	7.78173e6	−	7.78173e6i	0.268943	−	0.268943i	−0.559731	−	0.828674i	$-0.689096\pi$
$307$	7.78173e6	−	7.78173e6i	0.268943	−	0.268943i	0.828674	+	0.559731i	$0.189096\pi$
$308$	−2.00862e7	+	5.02464e7i	−0.687459	+	1.71970i
$309$	−4.80009e7	+	44946.4i	−1.62695	+	0.00152342i
$310$	6.50126e7	−	1.33515e7i	2.18229	−	0.448172i
$311$	1.08251e7			0.359874			0.179937	−	0.983678i	$-0.442411\pi$
$311$	1.08251e7			0.359874			0.179937	+	0.983678i	$0.442411\pi$
$312$	−1.04389e7	+	7.27405e6i	−0.343708	+	0.239504i
$313$		−	1.85485e7i		−	0.604889i	−0.953167	−	0.302444i	$-0.902197\pi$
$313$		−	1.85485e7i		−	0.604889i	0.953167	−	0.302444i	$-0.0978027\pi$
$314$	4.92331e7	−	1.01109e7i	1.59026	−	0.326589i
$315$	3.87392e7	+	3.85944e7i	1.23942	+	1.23479i
$316$	−1.24757e7	−	2.90929e7i	−0.395369	−	0.921989i
$317$	1.63028e7	+	1.63028e7i	0.511782	+	0.511782i	0.915072	−	0.403290i	$-0.132133\pi$
$317$	1.63028e7	+	1.63028e7i	0.511782	+	0.511782i	−0.403290	+	0.915072i	$0.632133\pi$
$318$	4.07721e6	+	1.97593e7i	0.126789	+	0.614455i
$319$	−1.32039e7			−0.406752
$320$	3.98612e7	−	1.82769e7i	1.21647	−	0.557766i
$321$	−1.87604e6	−	1.87253e6i	−0.0567189	−	0.0566127i
$322$	−3.40457e7	+	5.16435e7i	−1.01975	+	1.54685i
$323$	3.76979e6	+	3.76979e6i	0.111869	+	0.111869i
$324$	1.35217e7	+	3.12089e7i	0.397553	+	0.917579i
$325$	8.04244e6	+	8.04244e6i	0.234281	+	0.234281i
$326$	−2.94848e7	+	6.05523e6i	−0.851032	+	0.174775i
$327$	−1.75604e7	−	1.75276e7i	−0.502217	−	0.501277i
$328$	3.28821e6	−	1.83046e7i	0.0931834	−	0.518725i
$329$	−2.35888e7			−0.662397
$330$	5.69162e7	+	3.74453e7i	1.58378	+	1.04197i
$331$	−9.16542e6	−	9.16542e6i	−0.252737	−	0.252737i	0.569355	−	0.822092i	$-0.307193\pi$
$331$	−9.16542e6	−	9.16542e6i	−0.252737	−	0.252737i	−0.822092	+	0.569355i	$0.807193\pi$
$332$	1.82813e7	−	4.57313e7i	0.499566	−	1.24968i
$333$	−5.50606e6	−	5.48548e6i	−0.149111	−	0.148553i
$334$	1.70863e6	+	1.12640e6i	0.0458573	+	0.0302312i
$335$		−	4.80547e7i		−	1.27821i
$336$	3.41521e7	−	3.59574e7i	0.900325	−	0.947918i
$337$	−3.33363e7			−0.871020			−0.435510	−	0.900184i	$-0.643432\pi$
$337$	−3.33363e7			−0.871020			−0.435510	+	0.900184i	$0.643432\pi$
$338$	1.75236e7	−	2.65813e7i	0.453809	−	0.688377i
$339$	−3.02498e7	+	28324.9i	−0.776467	+	0.000727057i
$340$	−7.20753e6	+	1.80299e7i	−0.183379	+	0.458729i
$341$	6.61231e7	−	6.61231e7i	1.66759	−	1.66759i
$342$	−1.67861e7	+	3.48011e6i	−0.419636	+	0.0869991i
$343$			1.53449e7i			0.380262i
$344$	−6.16668e7	+	4.28852e7i	−1.51487	+	1.05349i
$345$	5.51201e7	+	5.50169e7i	1.34231	+	1.33980i
$346$	−3.75237e6	−	1.82714e7i	−0.0905893	−	0.441108i
$347$	−1.84654e7	+	1.84654e7i	−0.441948	+	0.441948i	−0.892666	−	0.450718i	$-0.851168\pi$
$347$	−1.84654e7	+	1.84654e7i	−0.441948	+	0.441948i	0.450718	+	0.892666i	$0.351168\pi$
$348$	1.12404e7	+	4.48119e6i	0.266712	+	0.106330i
$349$	2.16758e7	−	2.16758e7i	0.509917	−	0.509917i	−0.404584	−	0.914501i	$-0.632584\pi$
$349$	2.16758e7	−	2.16758e7i	0.509917	−	0.509917i	0.914501	+	0.404584i	$0.132584\pi$
$350$	−3.70121e7	−	2.44000e7i	−0.863257	−	0.569097i
$351$	1.28457e7	+	1.27737e7i	0.297055	+	0.295390i
$352$	3.27168e7	−	5.24122e7i	0.750140	−	1.20172i
$353$			6.25095e7i			1.42109i	0.703652	+	0.710545i	$0.251552\pi$
$353$			6.25095e7i			1.42109i	−0.703652	+	0.710545i	$0.748448\pi$
$354$	1.42196e7	+	6.89121e7i	0.320536	+	1.55341i
$355$	−8.06761e6	+	8.06761e6i	−0.180327	+	0.180327i
$356$	5.73521e6	+	1.33744e7i	0.127116	+	0.296430i
$357$	20561.3	+	2.19586e7i	0.000451904	+	0.482615i
$358$	−5.83243e6	−	2.83999e7i	−0.127116	−	0.618967i
$359$	−5.35732e7			−1.15788			−0.578940	−	0.815370i	$-0.696534\pi$
$359$	−5.35732e7			−1.15788			−0.578940	+	0.815370i	$0.696534\pi$
$360$	−3.57440e7	−	5.11933e7i	−0.766117	−	1.09725i
$361$			3.84053e7i			0.816337i
$362$	−4.08257e6	−	1.98793e7i	−0.0860613	−	0.419059i
$363$	4.81597e7	−	45095.1i	1.00685	−	0.000942778i
$364$	9.80457e6	−	2.45264e7i	0.203294	−	0.508546i
$365$	−4.10783e7	−	4.10783e7i	−0.844760	−	0.844760i
$366$	−1.48855e7	−	7.21393e7i	−0.303613	−	1.47139i
$367$	−1.02590e7			−0.207543			−0.103771	−	0.994601i	$-0.533091\pi$
$367$	−1.02590e7			−0.207543			−0.103771	+	0.994601i	$0.533091\pi$
$368$	4.86865e7	−	5.11641e7i	0.976934	−	1.02665i
$369$	−2.64797e7	+	49589.4i	−0.527028	+	0.000986983i
$370$	1.19120e7	+	7.85294e6i	0.235169	+	0.155034i
$371$	−2.96169e7	−	2.96169e7i	−0.579986	−	0.579986i
$372$	−7.87312e7	+	3.38489e7i	−1.52939	+	0.657531i
$373$	5.33382e7	+	5.33382e7i	1.02781	+	1.02781i	0.999602	+	0.0282064i	$0.00897956\pi$
$373$	5.33382e7	+	5.33382e7i	1.02781	+	1.02781i	0.0282064	+	0.999602i	$0.491020\pi$
$374$	5.50360e6	+	2.67988e7i	0.105204	+	0.512271i
$375$	1.04250e7	−	1.04445e7i	0.197688	−	0.198059i
$376$	2.65092e7	+	4.76210e6i	0.498693	+	0.0895848i
$377$	6.44513e6			0.120284
$378$	−5.90608e7	−	3.86979e7i	−1.09351	−	0.716493i
$379$	−5.45339e7	−	5.45339e7i	−1.00173	−	1.00173i	−0.999999	−	0.00172715i	$-0.999450\pi$
$379$	−5.45339e7	−	5.45339e7i	−1.00173	−	1.00173i	−0.00172715	−	0.999999i	$-0.500550\pi$
$380$	2.89229e7	−	1.24028e7i	0.527097	−	0.226031i
$381$	19612.2	+	2.09450e7i	0.000354610	+	0.378708i
$382$	3.36605e6	−	5.10593e6i	0.0603853	−	0.0915977i
$383$			8.89001e7i			1.58236i	0.611582	+	0.791181i	$0.290534\pi$
$383$			8.89001e7i			1.58236i	−0.611582	+	0.791181i	$0.709466\pi$
$384$	−4.56394e7	+	3.35145e7i	−0.806020	+	0.591888i
$385$	−1.41437e8			−2.47845
$386$	−4.53353e7	−	2.98871e7i	−0.788269	−	0.519662i
$387$	7.57649e7	+	7.54817e7i	1.30718	+	1.30229i
$388$	2.09068e7	+	4.87541e7i	0.357926	+	0.834673i
$389$	3.23995e7	−	3.23995e7i	0.550414	−	0.550414i	−0.376146	−	0.926560i	$-0.622751\pi$
$389$	3.23995e7	−	3.23995e7i	0.550414	−	0.550414i	0.926560	+	0.376146i	$0.122751\pi$
$390$	−2.77821e7	−	1.82779e7i	−0.468351	−	0.308129i
$391$			3.12730e7i			0.523166i
$392$	−7.55249e6	+	4.20425e7i	−0.125381	+	0.697960i
$393$	2.01988e7	−	2.02366e7i	0.332773	−	0.333396i
$394$	1.42751e7	−	2.93165e6i	0.233395	−	0.0479318i
$395$	5.85049e7	−	5.85049e7i	0.949295	−	0.949295i
$396$	−8.17475e7	−	3.25016e7i	−1.31640	−	0.523382i
$397$	7.19489e6	−	7.19489e6i	0.114988	−	0.114988i	−0.647271	−	0.762260i	$-0.724090\pi$
$397$	7.19489e6	−	7.19489e6i	0.114988	−	0.114988i	0.762260	+	0.647271i	$0.224090\pi$
$398$	9.33102e6	−	1.41541e7i	0.148006	−	0.224509i
$399$	2.51418e7	−	2.51889e7i	0.395801	−	0.396543i
$400$	3.66686e7	+	3.48929e7i	0.572946	+	0.545202i
$401$		−	20452.6i		−	0.000317187i	−1.00000		0.000158594i	$-0.999950\pi$
$401$		−	20452.6i		−	0.000317187i	1.00000		0.000158594i	$-5.04820e-5\pi$
$402$	1.25396e7	+	6.07702e7i	0.193021	+	0.935433i
$403$	−3.22762e7	+	3.22762e7i	−0.493137	+	0.493137i
$404$	−1.04311e8	−	4.16987e7i	−1.58192	−	0.632381i
$405$	−6.26256e7	+	6.30965e7i	−0.942730	+	0.949818i
$406$	−2.46075e7	+	5.05360e6i	−0.367697	+	0.0755131i
$407$	2.01026e7			0.298173
$408$	4.40989e6	−	2.46814e7i	0.0649303	−	0.363404i
$409$			1.76402e7i			0.257830i	0.991656	+	0.128915i	$0.0411494\pi$
$409$			1.76402e7i			0.257830i	−0.991656	+	0.128915i	$0.958851\pi$
$410$	4.76157e7	−	9.77873e6i	0.690874	−	0.141883i
$411$	−112065.	−	1.19680e8i	−0.00161415	−	1.72384i
$412$	−1.04571e8	+	4.48422e7i	−1.49527	+	0.641203i
$413$	−1.03291e8	−	1.03291e8i	−1.46627	−	1.46627i
$414$	−8.40614e7	−	5.51914e7i	−1.18466	−	0.777805i
$415$	1.28727e8			1.80105
$416$	−1.59698e7	+	2.55836e7i	−0.221830	+	0.355371i
$417$	7.76796e7	−	7.78252e7i	1.07127	−	1.07328i
$418$	2.44049e7	−	3.70196e7i	0.334156	−	0.506877i
$419$	8.23838e7	+	8.23838e7i	1.11995	+	1.11995i	0.991748	+	0.128205i	$0.0409214\pi$
$419$	8.23838e7	+	8.23838e7i	1.11995	+	1.11995i	0.128205	+	0.991748i	$0.459079\pi$
$420$	1.20404e8	+	4.80013e7i	1.62515	+	0.647896i
$421$	−4.84347e7	−	4.84347e7i	−0.649098	−	0.649098i	0.303677	−	0.952775i	$-0.401786\pi$
$421$	−4.84347e7	−	4.84347e7i	−0.649098	−	0.649098i	−0.952775	+	0.303677i	$0.901786\pi$
$422$	−2.35676e7	+	4.84003e6i	−0.313602	+	0.0644037i
$423$	−71816.9	−	3.83487e7i	−0.000948867	−	0.506675i
$424$	2.73046e7	+	3.92626e7i	0.358210	+	0.515089i
$425$	−2.24129e7			−0.291965
$426$	8.09715e6	−	1.23075e7i	0.104738	−	0.159200i
$427$	1.08128e8	+	1.08128e8i	1.38885	+	1.38885i
$428$	−5.83412e6	−	2.33222e6i	−0.0744122	−	0.0297466i
$429$	−4.68558e7	+	43874.2i	−0.593461	+	0.000555696i
$430$	−1.63913e8	−	1.08059e8i	−2.06162	−	1.35911i
$431$			1.33649e8i			1.66930i	0.550781	+	0.834650i	$0.314330\pi$
$431$			1.33649e8i			1.66930i	−0.550781	+	0.834650i	$0.685670\pi$
$432$	5.85605e7	+	5.54121e7i	0.726363	+	0.687311i
$433$	6.96887e7			0.858418			0.429209	−	0.903205i	$-0.358792\pi$
$433$	6.96887e7			0.858418			0.429209	+	0.903205i	$0.358792\pi$
$434$	9.79232e7	−	1.48538e8i	1.19789	−	1.81706i
$435$	29615.6	+	3.16282e7i	0.000359793	+	0.384244i
$436$	−5.46094e7	−	2.18304e7i	−0.658882	−	0.263391i
$437$	3.58399e7	−	3.58399e7i	0.429460	−	0.429460i
$438$	6.26669e7	+	4.12287e7i	0.745788	+	0.490656i
$439$		−	7.33798e6i		−	0.0867327i	−0.999059	−	0.0433664i	$-0.986192\pi$
$439$		−	7.33798e6i		−	0.0867327i	0.999059	−	0.0433664i	$-0.0138083\pi$
$440$	1.58947e8	+	2.85532e7i	1.86593	+	0.335194i
$441$	6.08194e7	−	113899.i	0.709131	−	0.00132801i
$442$	−2.68644e6	−	1.30811e7i	−0.0311107	−	0.151488i
$443$	−8.72146e7	+	8.72146e7i	−1.00318	+	1.00318i	−0.00318286	+	0.999995i	$0.501013\pi$
$443$	−8.72146e7	+	8.72146e7i	−1.00318	+	1.00318i	−0.999995	+	0.00318286i	$0.998987\pi$
$444$	−1.71132e7	−	6.82250e6i	−0.195516	−	0.0779461i
$445$	−2.68954e7	+	2.68954e7i	−0.305209	+	0.305209i
$446$	3.68228e7	+	2.42752e7i	0.415061	+	0.273627i
$447$	2.64076e7	+	2.63582e7i	0.295670	+	0.295116i
$448$	4.09128e7	−	1.10200e8i	0.455015	−	1.22560i
$449$			1.19978e8i			1.32545i	0.748865	+	0.662723i	$0.230599\pi$
$449$			1.19978e8i			1.32545i	−0.748865	+	0.662723i	$0.769401\pi$
$450$	3.95549e7	−	6.02455e7i	0.434073	−	0.661130i
$451$	4.84291e7	−	4.84291e7i	0.527930	−	0.527930i
$452$	−6.58997e7	+	2.82592e7i	−0.713621	+	0.306016i
$453$	1.29760e8	−	121503.i	1.39587	−	0.00130705i
$454$	1.86336e7	+	9.07328e7i	0.199127	+	0.969610i
$455$	6.90386e7			0.732922
$456$	−3.33396e7	+	2.32318e7i	−0.351613	+	0.245013i
$457$			1.33655e8i			1.40035i	0.713973	+	0.700174i	$0.246894\pi$
$457$			1.33655e8i			1.40035i	−0.713973	+	0.700174i	$0.753106\pi$
$458$	9.89292e6	+	4.81717e7i	0.102974	+	0.501413i
$459$	−3.56985e7	+	100281.i	−0.369157	+	0.00103700i
$460$	1.71412e8	+	6.85229e7i	1.76104	+	0.703984i
$461$	1.16177e8	+	1.16177e8i	1.18582	+	1.18582i	0.978213	+	0.207603i	$0.0665661\pi$
$461$	1.16177e8	+	1.16177e8i	1.18582	+	1.18582i	0.207603	+	0.978213i	$0.433434\pi$
$462$	1.78861e8	−	3.69070e7i	1.81381	−	0.374268i
$463$	−7.83192e7			−0.789088			−0.394544	−	0.918877i	$-0.629097\pi$
$463$	−7.83192e7			−0.789088			−0.394544	+	0.918877i	$0.629097\pi$
$464$	2.86743e7	−	711503.i	0.287038	−	0.00712234i
$465$	−1.58538e8	−	1.58241e8i	−1.57679	−	1.57384i
$466$	−5.96441e7	−	3.93201e7i	−0.589400	−	0.388559i
$467$	−9.37862e7	−	9.37862e7i	−0.920849	−	0.920849i	0.0762408	−	0.997089i	$-0.475708\pi$
$467$	−9.37862e7	−	9.37862e7i	−0.920849	−	0.920849i	−0.997089	+	0.0762408i	$0.975708\pi$
$468$	3.99029e7	+	1.58648e7i	0.389284	+	0.154773i
$469$	−9.10874e7	−	9.10874e7i	−0.882957	−	0.882957i
$470$	1.41619e7	+	6.89585e7i	0.136404	+	0.664193i
$471$	−1.20059e8	−	1.19834e8i	−1.14903	−	1.14688i
$472$	9.52268e7	+	1.36931e8i	0.905593	+	1.30220i
$473$	−2.76617e8			−2.61394
$474$	−5.87191e7	+	8.92520e7i	−0.551371	+	0.838075i
$475$	2.56859e7	+	2.56859e7i	0.239670	+	0.239670i
$476$	2.05137e7	+	4.78373e7i	0.190205	+	0.443553i
$477$	4.80585e7	−	4.82388e7i	0.442807	−	0.444469i
$478$	−6.67340e6	+	1.01228e7i	−0.0611031	+	0.0926866i
$479$		−	4.09155e7i		−	0.372290i	−0.982522	−	0.186145i	$-0.940401\pi$
$479$		−	4.09155e7i		−	0.372290i	0.982522	−	0.186145i	$-0.0595994\pi$
$480$	−1.25620e8	−	7.82513e7i	−1.13589	−	0.707567i
$481$	−9.81255e6			−0.0881752
$482$	3.80285e7	+	2.50701e7i	0.339600	+	0.223879i
$483$	2.08764e8	−	195479.i	1.85274	−	0.00173484i
$484$	1.04917e8	−	4.49905e7i	0.925355	−	0.396812i
$485$	−9.80430e7	+	9.80430e7i	−0.859392	+	0.859392i
$486$	6.27320e7	−	9.61339e7i	0.546488	−	0.837467i
$487$			6.40980e6i			0.0554955i	0.999615	+	0.0277477i	$0.00883351\pi$
$487$			6.40980e6i			0.0554955i	−0.999615	+	0.0277477i	$0.991166\pi$
$488$	−9.96864e7	−	1.43344e8i	−0.857781	−	1.23345i
$489$	7.19009e7	+	7.17663e7i	0.614904	+	0.613754i
$490$	−1.09365e8	+	2.24601e7i	−0.929591	+	0.190908i
$491$	1.10821e7	−	1.10821e7i	0.0936221	−	0.0936221i	−0.658745	−	0.752367i	$-0.728912\pi$
$491$	1.10821e7	−	1.10821e7i	0.0936221	−	0.0936221i	0.752367	+	0.658745i	$0.228912\pi$
$492$	−5.76633e7	+	2.47912e7i	−0.484177	+	0.208163i
$493$	−8.98073e6	+	8.98073e6i	−0.0749499	+	0.0749499i
$494$	−1.19126e7	+	1.80701e7i	−0.0988158	+	0.149893i
$495$	−430609.	−	2.29936e8i	−0.00355032	−	1.89579i
$496$	−1.40034e8	+	1.47160e8i	−1.14759	+	1.20599i
$497$			3.05842e7i			0.249131i
$498$	−1.62789e8	+	3.35905e7i	−1.31807	+	0.271975i
$499$	5.75907e6	−	5.75907e6i	0.0463501	−	0.0463501i	−0.683552	−	0.729902i	$-0.739566\pi$
$499$	5.75907e6	−	5.75907e6i	0.0463501	−	0.0463501i	0.729902	+	0.683552i	$0.239566\pi$
$500$	1.29842e7	−	3.24803e7i	0.103873	−	0.259843i
$501$	−6467.45	−	6.90696e6i	−5.14304e−5	−	0.0549255i
$502$	−7.72952e7	+	1.58739e7i	−0.611000	+	0.125480i
$503$	1.95748e8			1.53813			0.769064	−	0.639172i	$-0.220723\pi$
$503$	1.95748e8			1.53813			0.769064	+	0.639172i	$0.220723\pi$
$504$	−1.64789e8	−	2.92841e7i	−1.28717	−	0.228739i
$505$		−	2.93620e8i		−	2.27988i
$506$	2.54779e8	−	5.23235e7i	1.96659	−	0.403873i
$507$	−1.07452e8	+	100615.i	−0.824503	+	0.000772036i
$508$	1.95667e7	+	4.56290e7i	0.149254	+	0.348057i
$509$	−8.49016e7	−	8.49016e7i	−0.643817	−	0.643817i	0.307675	−	0.951492i	$-0.400449\pi$
$509$	−8.49016e7	−	8.49016e7i	−0.643817	−	0.643817i	−0.951492	+	0.307675i	$0.900449\pi$
$510$	6.41807e7	−	1.32433e7i	0.483831	−	0.0998356i
$511$	−1.55727e8			−1.16708
$512$	−6.82253e7	+	1.15584e8i	−0.508318	+	0.861170i
$513$	4.10265e7	+	4.07967e7i	0.303887	+	0.302185i
$514$	−5.91646e7	+	8.97460e7i	−0.435685	+	0.660885i
$515$	−2.10289e8	−	2.10289e8i	−1.53955	−	1.53955i
$516$	2.35482e8	+	9.38794e7i	1.71399	+	0.683316i
$517$	7.01365e7	+	7.01365e7i	0.507543	+	0.507543i
$518$	3.74644e7	−	7.69397e6i	0.269544	−	0.0553556i
$519$	−4.44729e7	+	4.45562e7i	−0.318122	+	0.318718i
$520$	−7.75860e7	−	1.39375e7i	−0.551789	−	0.0991229i
$521$	3.75963e7			0.265847			0.132924	−	0.991126i	$-0.457564\pi$
$521$	3.75963e7			0.265847			0.132924	+	0.991126i	$0.457564\pi$
$522$	−8.29063e6	−	3.99895e7i	−0.0582876	−	0.281148i
$523$	−7.03365e6	−	7.03365e6i	−0.0491673	−	0.0491673i	0.682096	−	0.731263i	$-0.261069\pi$
$523$	−7.03365e6	−	7.03365e6i	−0.0491673	−	0.0491673i	−0.731263	+	0.682096i	$0.761069\pi$
$524$	2.51573e7	−	6.29319e7i	0.174852	−	0.437398i
$525$	140097.	+	1.49618e8i	0.000968169	+	1.03396i
$526$	5.77923e7	+	3.80992e7i	0.397112	+	0.261794i
$527$		−	8.99483e7i		−	0.614555i
$528$	−2.08456e8	+	5.36780e6i	−1.41616	+	0.0364665i
$529$	1.49281e8			1.00841
$530$	−6.87999e7	+	1.04362e8i	−0.462126	+	0.700993i
$531$	1.67608e8	−	1.68236e8i	1.11946	−	1.12366i
$532$	3.13138e7	−	7.83324e7i	0.207970	−	0.520243i
$533$	−2.36394e7	+	2.36394e7i	−0.156118	+	0.156118i
$534$	2.69939e7	−	4.10302e7i	0.177272	−	0.269451i
$535$		−	1.64222e7i		−	0.107244i
$536$	8.39759e7	+	1.20753e8i	0.545331	+	0.784159i
$537$	−6.91256e7	+	6.92552e7i	−0.446392	+	0.447229i
$538$	1.00857e7	+	4.91106e7i	0.0647681	+	0.315376i
$539$	−1.11234e8	+	1.11234e8i	−0.710345	+	0.710345i
$540$	−7.76700e7	+	1.95889e8i	−0.493256	+	1.24402i
$541$	−2.54407e7	+	2.54407e7i	−0.160671	+	0.160671i	−0.782864	−	0.622193i	$-0.786242\pi$
$541$	−2.54407e7	+	2.54407e7i	−0.160671	+	0.160671i	0.622193	+	0.782864i	$0.286242\pi$
$542$	4.37930e7	+	2.88703e7i	0.275047	+	0.181323i
$543$	−4.83864e7	+	4.84771e7i	−0.302220	+	0.302787i
$544$	−1.33960e7	−	5.79011e7i	−0.0832106	−	0.359658i
$545$		−	1.53718e8i		−	0.949587i
$546$	−8.73065e7	+	1.80152e7i	−0.536375	+	0.110678i
$547$	−1.67498e8	+	1.67498e8i	−1.02341	+	1.02341i	−0.0236865	+	0.999719i	$0.507540\pi$
$547$	−1.67498e8	+	1.67498e8i	−1.02341	+	1.02341i	−0.999719	+	0.0236865i	$0.992460\pi$
$548$	−1.11805e8	−	2.60726e8i	−0.679390	−	1.58432i
$549$	−1.75457e8	+	1.76115e8i	−1.06036	+	1.06434i
$550$	3.74995e7	+	1.82597e8i	0.225391	+	1.09750i
$551$	2.05844e7			0.123051
$552$	−2.34649e8	−	4.19255e7i	−1.39509	−	0.249265i
$553$		−	2.21791e8i		−	1.31150i
$554$	−3.28689e7	−	1.60049e8i	−0.193310	−	0.941289i
$555$	−45089.0	−	4.81532e7i	−0.000263750	−	0.281674i
$556$	9.67490e7	−	2.42021e8i	0.562888	−	1.40808i
$557$	5.35727e7	+	5.35727e7i	0.310012	+	0.310012i	0.844914	−	0.534902i	$-0.179652\pi$
$557$	5.35727e7	+	5.35727e7i	0.310012	+	0.310012i	−0.534902	+	0.844914i	$0.679652\pi$
$558$	2.41780e8	+	1.58743e8i	1.39161	+	0.913676i
$559$	1.35023e8			0.772989
$560$	3.07152e8	−	7.62144e6i	1.74900	−	0.0433983i
$561$	6.52284e7	−	6.53507e7i	0.369444	−	0.370136i
$562$	−3.01678e7	−	1.98880e7i	−0.169955	−	0.112042i
$563$	−1.00531e8	−	1.00531e8i	−0.563346	−	0.563346i	0.366910	−	0.930256i	$-0.380416\pi$
$563$	−1.00531e8	−	1.00531e8i	−0.563346	−	0.563346i	−0.930256	+	0.366910i	$0.880416\pi$
$564$	−3.59034e7	−	8.35098e7i	−0.200124	−	0.465479i
$565$	−1.32522e8	−	1.32522e8i	−0.734756	−	0.734756i
$566$	−4.61916e7	−	2.24921e8i	−0.254750	−	1.24046i
$567$	892569.	+	2.38305e8i	0.00489658	+	1.30733i
$568$	6.17432e6	−	3.43707e7i	0.0336934	−	0.187561i
$569$	1.59387e8			0.865197			0.432599	−	0.901587i	$-0.357597\pi$
$569$	1.59387e8			0.865197			0.432599	+	0.901587i	$0.357597\pi$
$570$	−8.87304e7	−	5.83759e7i	−0.479124	−	0.315217i
$571$	8.61343e7	+	8.61343e7i	0.462666	+	0.462666i	0.899528	−	0.436862i	$-0.143910\pi$
$571$	8.61343e7	+	8.61343e7i	0.462666	+	0.462666i	−0.436862	+	0.899528i	$0.643910\pi$
$572$	−1.02076e8	+	4.37725e7i	−0.545427	+	0.233891i
$573$	−2.06402e7	+	19326.8i	−0.109711	+	0.000102730i
$574$	7.17197e7	−	1.08791e8i	0.379230	−	0.575249i
$575$			2.13082e8i			1.12084i
$576$	1.79279e8	+	6.61772e7i	0.938127	+	0.346291i
$577$	3.01278e8			1.56834			0.784169	−	0.620547i	$-0.213089\pi$
$577$	3.01278e8			1.56834			0.784169	+	0.620547i	$0.213089\pi$
$578$	−1.39249e8	−	9.17990e7i	−0.721121	−	0.475395i
$579$	171602.	+	1.83264e8i	0.000884069	+	0.944149i
$580$	2.95470e7	+	6.89027e7i	0.151436	+	0.353144i
$581$	2.44001e8	−	2.44001e8i	1.24413	−	1.24413i
$582$	9.84019e7	−	1.49569e8i	0.499154	−	0.758706i
$583$			1.76119e8i			0.888795i
$584$	1.75007e8	+	3.14381e7i	0.878652	+	0.157840i
$585$	210190.	+	1.12237e8i	0.00104989	+	0.560621i
$586$	4.69495e7	−	9.64192e6i	0.233313	−	0.0479149i
$587$	−2.25529e7	+	2.25529e7i	−0.111503	+	0.111503i	−0.760657	−	0.649154i	$-0.775123\pi$
$587$	−2.25529e7	+	2.25529e7i	−0.111503	+	0.111503i	0.649154	+	0.760657i	$0.275123\pi$
$588$	1.32443e8	−	5.69414e7i	0.651475	−	0.280089i
$589$	−1.03084e8	+	1.03084e8i	−0.504480	+	0.504480i
$590$	−2.39945e8	+	3.63969e8i	−1.16830	+	1.77218i
$591$	−3.48109e7	−	3.47458e7i	−0.168637	−	0.168322i
$592$	−4.36559e7	+	1.08325e6i	−0.210416	+	0.00522110i
$593$		−	7.85579e7i		−	0.376726i	−0.982099	−	0.188363i	$-0.939682\pi$
$593$		−	7.85579e7i		−	0.376726i	0.982099	−	0.188363i	$-0.0603182\pi$
$594$	6.05448e7	+	2.90666e8i	0.288880	+	1.38687i
$595$	−9.61993e7	+	9.61993e7i	−0.456689	+	0.456689i
$596$	8.21225e7	+	3.28288e7i	0.387903	+	0.155066i
$597$	−5.72166e7	+	53575.7i	−0.268905	+	0.000251794i
$598$	−1.24364e8	+	2.55403e7i	−0.581555	+	0.119433i
$599$	2.69838e8			1.25552			0.627758	−	0.778408i	$-0.283973\pi$
$599$	2.69838e8			1.25552			0.627758	+	0.778408i	$0.283973\pi$
$600$	3.00473e7	−	1.68170e8i	0.139108	−	0.778564i
$601$		−	3.26623e8i		−	1.50461i	−0.658817	−	0.752303i	$-0.728943\pi$
$601$		−	3.26623e8i		−	1.50461i	0.658817	−	0.752303i	$-0.271057\pi$
$602$	−5.15520e8	+	1.05871e8i	−2.36296	+	0.485276i
$603$	1.47805e8	−	1.48360e8i	0.674120	−	0.676649i
$604$	2.82684e8	−	1.21221e8i	1.28290	−	0.550133i
$605$	2.10984e8	+	2.10984e8i	0.952760	+	0.952760i
$606$	7.66183e7	+	3.71314e8i	0.344282	+	1.66849i
$607$	−3.26301e7			−0.145899			−0.0729495	−	0.997336i	$-0.523241\pi$
$607$	−3.26301e7			−0.145899			−0.0729495	+	0.997336i	$0.523241\pi$
$608$	−5.10043e7	+	8.17088e7i	−0.226932	+	0.363545i
$609$	6.00072e7	+	5.98950e7i	0.265676	+	0.265179i
$610$	2.51182e8	−	3.81015e8i	1.10662	−	1.67862i
$611$	−3.42353e7	−	3.42353e7i	−0.150089	−	0.150089i
$612$	−7.77074e7	+	3.34951e7i	−0.339007	+	0.146126i
$613$	−1.74443e8	−	1.74443e8i	−0.757306	−	0.757306i	0.218526	−	0.975831i	$-0.429875\pi$
$613$	−1.74443e8	−	1.74443e8i	−0.757306	−	0.757306i	−0.975831	+	0.218526i	$0.929875\pi$
$614$	−8.62404e7	+	1.77110e7i	−0.372568	+	0.0765135i
$615$	−1.16114e8	−	1.15897e8i	−0.499184	−	0.498250i
$616$	3.55406e8	−	2.47161e8i	1.52049	−	1.05740i
$617$	1.04096e8			0.443179			0.221589	−	0.975140i	$-0.428876\pi$
$617$	1.04096e8			0.443179			0.221589	+	0.975140i	$0.428876\pi$
$618$	3.20805e8	+	2.11058e8i	1.35918	+	0.894205i
$619$	−2.38291e8	−	2.38291e8i	−1.00470	−	1.00470i	−0.999989	−	0.00470978i	$-0.998501\pi$
$619$	−2.38291e8	−	2.38291e8i	−1.00470	−	1.00470i	−0.00470978	−	0.999989i	$-0.501499\pi$
$620$	−4.93021e8	−	1.97088e8i	−2.06867	−	0.826959i
$621$	953383.	+	3.39390e8i	0.00398100	+	1.41718i
$622$	−7.23029e7	−	4.76653e7i	−0.300458	−	0.198076i
$623$			1.01960e8i			0.421663i
$624$	1.01752e8	−	2.62015e6i	0.418785	−	0.0107838i
$625$	2.84517e8			1.16538
$626$	−8.16731e7	+	1.23889e8i	−0.332933	+	0.505021i
$627$	−1.49648e8	+	140125.i	−0.607111	+	0.000568478i
$628$	−3.73358e8	−	1.49252e8i	−1.50746	−	0.602616i
$629$	1.36729e7	−	1.36729e7i	0.0549427	−	0.0549427i
$630$	−8.88071e7	−	4.28357e8i	−0.355162	−	1.71311i
$631$			3.98378e8i			1.58565i	0.609450	+	0.792824i	$0.291390\pi$
$631$			3.98378e8i			1.58565i	−0.609450	+	0.792824i	$0.708610\pi$
$632$	−4.47751e7	+	2.49250e8i	−0.177372	+	0.987380i
$633$	5.74714e7	+	5.73638e7i	0.226590	+	0.226166i
$634$	−3.71048e7	−	1.80675e8i	−0.145600	−	0.708973i
$635$	−9.17585e7	+	9.17585e7i	−0.358365	+	0.358365i
$636$	5.97721e7	−	1.49929e8i	0.232342	−	0.582793i
$637$	5.42957e7	−	5.42957e7i	0.210062	−	0.210062i
$638$	8.81913e7	+	5.81397e7i	0.339597	+	0.223878i
$639$	−4.97212e7	+	93114.6i	−0.190563	+	0.000356874i
$640$	−3.46718e8	−	5.34427e7i	−1.32262	−	0.203868i
$641$			2.16255e8i			0.821093i	0.911840	+	0.410546i	$0.134662\pi$
$641$			2.16255e8i			0.821093i	−0.911840	+	0.410546i	$0.865338\pi$
$642$	4.28527e6	+	2.07676e7i	0.0161947	+	0.0784841i
$643$	2.96172e8	−	2.96172e8i	1.11407	−	1.11407i	0.121472	−	0.992595i	$-0.461239\pi$
$643$	2.96172e8	−	2.96172e8i	1.11407	−	1.11407i	0.992595	−	0.121472i	$-0.0387615\pi$
$644$	4.54796e8	−	1.95026e8i	1.70278	−	0.730189i
$645$	620438.	+	6.62602e8i	0.00231217	+	2.46930i
$646$	−8.57993e6	−	4.17784e7i	−0.0318263	−	0.154972i
$647$	−2.63319e8			−0.972230			−0.486115	−	0.873895i	$-0.661586\pi$
$647$	−2.63319e8			−0.972230			−0.486115	+	0.873895i	$0.661586\pi$
$648$	4.71059e7	−	2.67989e8i	0.173121	−	0.984901i
$649$			6.14230e8i			2.24697i
$650$	−1.83044e7	−	8.91297e7i	−0.0666522	−	0.324551i
$651$	−6.00452e8	+	562243.i	−2.17638	+	0.00203789i
$652$	2.23597e8	+	8.93841e7i	0.806722	+	0.322491i
$653$	1.43432e8	+	1.43432e8i	0.515119	+	0.515119i	0.916090	−	0.400972i	$-0.131327\pi$
$653$	1.43432e8	+	1.43432e8i	0.515119	+	0.515119i	−0.400972	+	0.916090i	$0.631327\pi$
$654$	4.01117e7	+	1.94392e8i	0.143396	+	0.694938i
$655$	1.77145e8			0.630383
$656$	−1.02562e8	+	1.07781e8i	−0.363307	+	0.381795i
$657$	−474117.	−	2.53168e8i	−0.00167182	−	0.892715i
$658$	1.57554e8	+	1.03867e8i	0.553034	+	0.364585i
$659$	2.15652e8	+	2.15652e8i	0.753525	+	0.753525i	0.975135	−	0.221610i	$-0.0711313\pi$
$659$	2.15652e8	+	2.15652e8i	0.753525	+	0.753525i	−0.221610	+	0.975135i	$0.571131\pi$
$660$	−2.15274e8	−	5.00719e8i	−0.748791	−	1.74166i
$661$	1.46563e8	+	1.46563e8i	0.507481	+	0.507481i	0.913753	−	0.406271i	$-0.133171\pi$
$661$	1.46563e8	+	1.46563e8i	0.507481	+	0.507481i	−0.406271	+	0.913753i	$0.633171\pi$
$662$	2.08602e7	+	1.01575e8i	0.0719027	+	0.350117i
$663$	−3.18395e7	+	3.18992e7i	−0.109251	+	0.109456i
$664$	−3.23469e8	+	2.24951e8i	−1.10491	+	0.768395i
$665$	2.20495e8			0.749780
$666$	1.26223e7	+	6.08830e7i	0.0427283	+	0.206098i
$667$	8.53810e7	+	8.53810e7i	0.287729	+	0.287729i
$668$	−6.45245e6	−	1.50469e7i	−0.0216469	−	0.0504799i
$669$	−139380.	−	1.48852e8i	−0.000465504	−	0.497139i
$670$	−2.11596e8	+	3.20967e8i	−0.703530	+	1.06718i
$671$		−	6.42995e8i		−	2.12834i
$672$	−3.86437e8	+	8.97873e7i	−1.27342	+	0.295874i
$673$	−3.68120e8			−1.20766			−0.603829	−	0.797114i	$-0.706359\pi$
$673$	−3.68120e8			−1.20766			−0.603829	+	0.797114i	$0.706359\pi$
$674$	2.22660e8	+	1.46787e8i	0.727214	+	0.479412i
$675$	−2.43236e8	+	683275.i	−0.790890	+	0.00222169i
$676$	−2.34087e8	+	1.00382e8i	−0.757769	+	0.324948i
$677$	1.96548e8	−	1.96548e8i	0.633435	−	0.633435i	−0.315493	−	0.948928i	$-0.602170\pi$
$677$	1.96548e8	−	1.96548e8i	0.633435	−	0.633435i	0.948928	+	0.315493i	$0.102170\pi$
$678$	2.02169e8	+	1.33007e8i	0.648672	+	0.426763i
$679$			3.71680e8i			1.18730i
$680$	1.27530e8	−	8.86887e7i	0.405588	−	0.282060i
$681$	2.20845e8	−	2.21259e8i	0.699271	−	0.700582i
$682$	−7.32804e8	+	1.50494e8i	−2.31012	+	0.474424i
$683$	3.50145e8	−	3.50145e8i	1.09897	−	1.09897i	0.104438	−	0.994531i	$-0.466696\pi$
$683$	3.50145e8	−	3.50145e8i	1.09897	−	1.09897i	0.994531	−	0.104438i	$-0.0333043\pi$
$684$	1.27442e8	+	5.06688e7i	0.398238	+	0.158333i
$685$	5.24312e8	−	5.24312e8i	1.63124	−	1.63124i
$686$	6.75672e7	−	1.02492e8i	0.209297	−	0.317481i
$687$	1.17250e8	−	1.17470e8i	0.361613	−	0.362291i
$688$	6.00717e8	−	1.49058e7i	1.84461	−	0.0457708i
$689$		−	8.59681e7i		−	0.262833i
$690$	−1.25906e8	−	6.10175e8i	−0.383264	−	1.85741i
$691$	−3.41455e6	+	3.41455e6i	−0.0103490	+	0.0103490i	−0.712262	−	0.701913i	$-0.752329\pi$
$691$	−3.41455e6	+	3.41455e6i	−0.0103490	+	0.0103490i	0.701913	+	0.712262i	$0.252329\pi$
$692$	−5.53904e7	+	1.38561e8i	−0.167154	+	0.418141i
$693$	−4.36658e8	−	4.35026e8i	−1.31202	−	1.30712i
$694$	2.04642e8	−	4.20268e7i	0.612231	−	0.125733i
$695$	6.81256e8			2.02934
$696$	−5.53449e7	−	7.94246e7i	−0.164153	−	0.235574i
$697$		−	6.58788e7i		−	0.194557i
$698$	−2.40221e8	+	4.93336e7i	−0.706390	+	0.145070i
$699$	225763.	+	2.41106e8i	0.000661030	+	0.705953i
$700$	1.39772e8	+	3.25945e8i	0.407500	+	0.950278i
$701$	−1.84445e8	−	1.84445e8i	−0.535442	−	0.535442i	0.386745	−	0.922187i	$-0.373599\pi$
$701$	−1.84445e8	−	1.84445e8i	−0.535442	−	0.535442i	−0.922187	+	0.386745i	$0.873599\pi$
$702$	−2.95533e7	−	1.41881e8i	−0.0854270	−	0.410121i
$703$	−3.13393e7			−0.0902034
$704$	−4.49304e8	+	2.06012e8i	−1.28772	+	0.590439i
$705$	1.67846e8	−	1.68160e8i	0.479008	−	0.479906i
$706$	2.75243e8	−	4.17513e8i	0.782172	−	1.18647i
$707$	−5.56555e8	−	5.56555e8i	−1.57489	−	1.57489i
$708$	2.08460e8	−	5.22889e8i	0.587385	−	1.47336i
$709$	−1.22955e8	−	1.22955e8i	−0.344992	−	0.344992i	0.513248	−	0.858240i	$-0.328442\pi$
$709$	−1.22955e8	−	1.22955e8i	−0.344992	−	0.344992i	−0.858240	+	0.513248i	$0.828442\pi$
$710$	8.94086e7	−	1.83617e7i	0.249807	−	0.0513023i
$711$	3.60570e8	−	675251.i	1.00318	−	0.00187870i
$712$	2.05836e7	−	1.14583e8i	0.0570272	−	0.317454i
$713$	−8.55151e8			−2.35925
$714$	9.65515e7	−	1.46757e8i	0.265255	−	0.403184i
$715$	−2.05272e8	−	2.05272e8i	−0.561580	−	0.561580i
$716$	−8.60952e7	+	2.15370e8i	−0.234552	+	0.586740i
$717$	4.09204e7	−	38316.5i	0.111015	−	0.000103951i
$718$	3.57826e8	+	2.35895e8i	0.966714	+	0.637301i
$719$			3.10806e8i			0.836186i	0.908404	+	0.418093i	$0.137301\pi$
$719$			3.10806e8i			0.836186i	−0.908404	+	0.418093i	$0.862699\pi$
$720$	1.33254e7	+	4.99319e8i	0.0357013	+	1.33777i
$721$	−7.97201e8			−2.12697
$722$	1.69107e8	−	2.56516e8i	0.449314	−	0.681559i
$723$	−143944.	−	1.53726e8i	−0.000380872	−	0.406755i
$724$	−6.02647e7	+	1.50754e8i	−0.158799	+	0.397241i
$725$	−6.11913e7	+	6.11913e7i	−0.160574	+	0.160574i
$726$	−3.21866e8	−	2.11757e8i	−0.841135	−	0.553384i
$727$		−	2.30904e8i		−	0.600936i	−0.953792	−	0.300468i	$-0.902857\pi$
$727$		−	2.30904e8i		−	0.600936i	0.953792	−	0.300468i	$-0.0971429\pi$
$728$	−1.73482e8	+	1.20645e8i	−0.449635	+	0.312691i
$729$	−3.87414e8	+	2.17659e6i	−0.999984	+	0.00561817i
$730$	9.34930e7	+	4.55247e8i	0.240331	+	1.17025i
$731$	−1.88143e8	+	1.88143e8i	−0.481656	+	0.481656i
$732$	−2.18222e8	+	5.47377e8i	−0.556373	+	1.39557i
$733$	−3.49497e8	+	3.49497e8i	−0.887425	+	0.887425i	−0.994275	−	0.106850i	$-0.965923\pi$
$733$	−3.49497e8	+	3.49497e8i	−0.887425	+	0.887425i	0.106850	+	0.994275i	$0.465923\pi$
$734$	6.85220e7	+	4.51728e7i	0.173277	+	0.114232i
$735$	2.66695e8	+	2.66196e8i	0.671666	+	0.670410i
$736$	−5.50474e8	+	1.27358e8i	−1.38071	+	0.319442i
$737$			5.41660e8i			1.35308i
$738$	1.77081e8	+	1.16265e8i	0.440558	+	0.289253i
$739$	−2.53799e8	+	2.53799e8i	−0.628863	+	0.628863i	−0.947782	−	0.318919i	$-0.896680\pi$
$739$	−2.53799e8	+	2.53799e8i	−0.628863	+	0.628863i	0.318919	+	0.947782i	$0.396680\pi$
$740$	−4.49845e7	−	1.04903e8i	−0.111011	−	0.258876i
$741$	7.30467e7	−	68398.4i	0.179534	−	0.000168109i
$742$	6.74072e7	+	3.28226e8i	0.165004	+	0.803456i
$743$	−2.17226e8			−0.529598			−0.264799	−	0.964304i	$-0.585306\pi$
$743$	−2.17226e8			−0.529598			−0.264799	+	0.964304i	$0.585306\pi$
$744$	6.74905e8	+	1.20587e8i	1.63879	+	0.292808i
$745$			2.31163e8i			0.559050i
$746$	−1.21396e8	−	5.91117e8i	−0.292408	−	1.42383i
$747$	3.97420e8	+	3.95934e8i	0.953428	+	0.949864i
$748$	8.12413e7	−	2.03228e8i	0.194121	−	0.485599i
$749$	−3.11282e7	−	3.11282e7i	−0.0740814	−	0.0740814i
$750$	−1.15620e8	+	2.38574e7i	−0.274062	+	0.0565510i
$751$	−3.05378e8			−0.720970			−0.360485	−	0.932765i	$-0.617389\pi$
$751$	−3.05378e8			−0.720970			−0.360485	+	0.932765i	$0.617389\pi$
$752$	−1.56092e8	−	1.48533e8i	−0.367051	−	0.349276i
$753$	1.88490e8	+	1.88137e8i	0.441472	+	0.440646i
$754$	−4.30483e7	−	2.83793e7i	−0.100425	−	0.0662046i
$755$	5.68470e8	+	5.68470e8i	1.32089	+	1.32089i
$756$	2.24083e8	+	5.18529e8i	0.518613	+	1.20007i
$757$	3.18654e7	+	3.18654e7i	0.0734568	+	0.0734568i	0.742881	−	0.669424i	$-0.233459\pi$
$757$	3.18654e7	+	3.18654e7i	0.0734568	+	0.0734568i	−0.669424	+	0.742881i	$0.733459\pi$
$758$	1.24118e8	+	6.04367e8i	0.284987	+	1.38769i
$759$	−6.21298e8	−	6.20136e8i	−1.42094	−	1.41828i
$760$	−2.47794e8	−	4.45134e7i	−0.564481	−	0.101403i
$761$	1.65435e8			0.375382			0.187691	−	0.982228i	$-0.439900\pi$
$761$	1.65435e8			0.375382			0.187691	+	0.982228i	$0.439900\pi$
$762$	9.20944e7	−	1.39982e8i	0.208146	−	0.316379i
$763$	−2.91371e8	−	2.91371e8i	−0.655953	−	0.655953i
$764$	−4.49651e7	+	1.92820e7i	−0.100831	+	0.0432386i
$765$	−1.56686e8	−	1.56100e8i	−0.349981	−	0.348673i
$766$	3.91447e8	−	5.93781e8i	0.870937	−	1.32111i
$767$		−	2.99820e8i		−	0.664469i
$768$	4.52406e8	−	2.28899e7i	0.998722	−	0.0505312i
$769$	2.03053e8			0.446509			0.223255	−	0.974760i	$-0.428332\pi$
$769$	2.03053e8			0.446509			0.223255	+	0.974760i	$0.428332\pi$
$770$	9.44683e8	+	6.22777e8i	2.06926	+	1.36415i
$771$	3.62789e8	−	339704.i	0.791574	−	0.000741203i
$772$	1.71204e8	+	3.99243e8i	0.372102	+	0.867731i
$773$	−1.78083e8	+	1.78083e8i	−0.385552	+	0.385552i	−0.873098	−	0.487545i	$-0.837892\pi$
$773$	−1.78083e8	+	1.78083e8i	−0.385552	+	0.385552i	0.487545	+	0.873098i	$0.337892\pi$
$774$	−1.73686e8	−	8.37767e8i	−0.374578	−	1.80676i
$775$		−	6.12874e8i		−	1.31664i
$776$	7.50345e7	−	4.17696e8i	0.160574	−	0.893871i
$777$	−9.13595e7	−	9.11886e7i	−0.194756	−	0.194392i
$778$	−3.59065e8	+	7.37403e7i	−0.762489	+	0.156591i
$779$	−7.54993e7	+	7.54993e7i	−0.159709	+	0.159709i
$780$	1.05080e8	+	2.44413e8i	0.221431	+	0.515039i
$781$	9.09359e7	−	9.09359e7i	0.190890	−	0.190890i
$782$	1.37702e8	−	2.08879e8i	0.287952	−	0.436791i
$783$	−9.71895e7	+	9.77371e7i	−0.202458	+	0.203598i
$784$	2.35567e8	−	2.47555e8i	0.488840	−	0.513716i
$785$		−	1.05095e9i		−	2.17257i
$786$	−2.24018e8	+	4.62248e7i	−0.461334	+	0.0951934i
$787$	6.59037e8	−	6.59037e8i	1.35203	−	1.35203i	0.468635	−	0.883392i	$-0.344746\pi$
$787$	6.59037e8	−	6.59037e8i	1.35203	−	1.35203i	0.883392	−	0.468635i	$-0.155254\pi$
$788$	−1.08255e8	−	4.32755e7i	−0.221243	−	0.0884429i
$789$	−218753.	−	2.33620e8i	−0.000445373	−	0.475640i
$790$	−6.48376e8	+	1.33156e8i	−1.31506	+	0.270071i
$791$	−5.02389e8			−1.01511
$792$	4.02896e8	+	5.77037e8i	0.810994	+	1.16152i
$793$			3.13861e8i			0.629387i
$794$	−7.97368e7	+	1.63754e7i	−0.159293	+	0.0327137i
$795$	4.21872e8	−	395027.i	0.839613	−	0.000786185i
$796$	−1.24647e8	+	5.34515e7i	−0.247141	+	0.105979i
$797$	−3.01211e8	−	3.01211e8i	−0.594972	−	0.594972i	0.343998	−	0.938970i	$-0.388219\pi$
$797$	−3.01211e8	−	3.01211e8i	−0.594972	−	0.594972i	−0.938970	+	0.343998i	$0.888219\pi$
$798$	−2.78839e8	+	5.75367e7i	−0.548712	+	0.113223i
$799$	9.54078e7			0.187044
$800$	−9.12753e7	−	3.94516e8i	−0.178272	−	0.770540i
$801$	−1.65758e8	+	310421.i	−0.322535	+	0.000604023i
$802$	−90057.5	+	136607.i	−0.000174581	+	0.000264820i
$803$	4.63023e8	+	4.63023e8i	0.894244	+	0.894244i
$804$	1.83831e8	−	4.61111e8i	0.353712	−	0.887232i
$805$	9.14580e8	+	9.14580e8i	1.75321	+	1.75321i
$806$	3.57699e8	−	7.34598e7i	0.683144	−	0.140296i
$807$	1.19536e8	−	1.19760e8i	0.227445	−	0.227872i
$808$	5.13103e8	+	7.37817e8i	0.972681	+	1.39867i
$809$	4.11778e7			0.0777710			0.0388855	−	0.999244i	$-0.487619\pi$
$809$	4.11778e7			0.0777710			0.0388855	+	0.999244i	$0.487619\pi$
$810$	6.96117e8	−	1.45679e8i	1.30987	−	0.274121i
$811$	5.79494e8	+	5.79494e8i	1.08639	+	1.08639i	0.995897	+	0.0904956i	$0.0288451\pi$
$811$	5.79494e8	+	5.79494e8i	1.08639	+	1.08639i	0.0904956	+	0.995897i	$0.471155\pi$
$812$	1.86611e8	+	7.45985e7i	0.348553	+	0.139336i
$813$	−165764.	−	1.77029e8i	−0.000308474	−	0.329437i
$814$	−1.34269e8	−	8.85162e7i	−0.248945	−	0.164115i
$815$			6.29396e8i			1.16266i
$816$	−1.38132e8	+	1.45434e8i	−0.254229	+	0.267668i
$817$	4.31237e8			0.790769
$818$	7.76736e7	−	1.17822e8i	0.141910	−	0.215262i
$819$	2.13143e8	+	2.12346e8i	0.387989	+	0.386539i
$820$	−3.61092e8	−	1.44348e8i	−0.654903	−	0.261801i
$821$	1.11012e8	−	1.11012e8i	0.200605	−	0.200605i	−0.599654	−	0.800259i	$-0.704695\pi$
$821$	1.11012e8	−	1.11012e8i	0.200605	−	0.200605i	0.800259	+	0.599654i	$0.204695\pi$
$822$	−5.26231e8	+	7.99862e8i	−0.947460	+	1.44012i
$823$		−	6.47399e8i		−	1.16138i	−0.814126	−	0.580688i	$-0.802784\pi$
$823$		−	6.47399e8i		−	1.16138i	0.814126	−	0.580688i	$-0.197216\pi$
$824$	8.95899e8	+	1.60939e8i	1.60132	+	0.287659i
$825$	4.44442e8	−	4.45275e8i	0.791504	−	0.792988i
$826$	2.35088e8	+	1.14471e9i	0.417147	+	2.03122i
$827$	4.04114e8	−	4.04114e8i	0.714476	−	0.714476i	−0.252993	−	0.967468i	$-0.581415\pi$
$827$	4.04114e8	−	4.04114e8i	0.714476	−	0.714476i	0.967468	+	0.252993i	$0.0814148\pi$
$828$	3.18442e8	+	7.38775e8i	0.560970	+	1.30143i
$829$	−6.68540e8	+	6.68540e8i	−1.17345	+	1.17345i	−0.192065	+	0.981382i	$0.561518\pi$
$829$	−6.68540e8	+	6.68540e8i	−1.17345	+	1.17345i	−0.981382	+	0.192065i	$0.938482\pi$
$830$	−8.59794e8	−	5.66815e8i	−1.50370	−	0.991304i
$831$	−3.89560e8	+	3.90290e8i	−0.678846	+	0.680119i
$832$	2.19316e8	−	1.00559e8i	0.380803	−	0.174603i
$833$			1.51313e8i			0.261782i
$834$	−8.61519e8	+	1.77769e8i	−1.48514	+	0.306449i
$835$	3.02589e7	−	3.02589e7i	0.0519749	−	0.0519749i
$836$	−3.26011e8	+	1.39800e8i	−0.557973	+	0.239271i
$837$	−2.74215e6	−	9.76163e8i	−0.00467643	−	1.66474i
$838$	−1.87503e8	−	9.13011e8i	−0.318623	−	1.55147i
$839$	−8.90033e7			−0.150702			−0.0753512	−	0.997157i	$-0.524008\pi$
$839$	−8.90033e7			−0.150702			−0.0753512	+	0.997157i	$0.524008\pi$
$840$	−5.92841e8	−	8.50776e8i	−1.00023	−	1.43541i
$841$		−	5.45785e8i		−	0.917559i
$842$	1.10236e8	+	5.36773e8i	0.184666	+	0.899196i
$843$	114190.	+	1.21950e8i	0.000190610	+	0.203564i
$844$	1.78725e8	+	7.14460e7i	0.297274	+	0.118837i
$845$	−4.70741e8	−	4.70741e8i	−0.780211	−	0.780211i
$846$	−1.68378e8	+	2.56455e8i	−0.278083	+	0.423545i
$847$	7.99838e8			1.31629
$848$	−9.49035e6	−	3.82471e8i	−0.0155631	−	0.627207i
$849$	−5.47461e8	+	5.48487e8i	−0.894603	+	0.896279i
$850$	1.49700e8	+	9.86890e7i	0.243762	+	0.160698i
$851$	−1.29990e8	−	1.29990e8i	−0.210922	−	0.210922i
$852$	−1.08275e8	+	4.65508e7i	−0.175069	+	0.0752677i
$853$	−1.77409e8	−	1.77409e8i	−0.285844	−	0.285844i	0.549590	−	0.835434i	$-0.314784\pi$
$853$	−1.77409e8	−	1.77409e8i	−0.285844	−	0.285844i	−0.835434	+	0.549590i	$0.814784\pi$
$854$	−2.46097e8	−	1.19832e9i	−0.395124	−	1.92398i
$855$	671305.	+	3.58462e8i	0.00107404	+	0.573516i
$856$	2.86979e7	+	4.12662e7i	0.0457540	+	0.0657921i
$857$	7.40303e8			1.17616			0.588081	−	0.808802i	$-0.299884\pi$
$857$	7.40303e8			1.17616			0.588081	+	0.808802i	$0.299884\pi$
$858$	3.13152e8	+	2.06024e8i	0.495786	+	0.326178i
$859$	8.58230e7	+	8.58230e7i	0.135402	+	0.135402i	0.771559	−	0.636157i	$-0.219477\pi$
$859$	8.58230e7	+	8.58230e7i	0.135402	+	0.135402i	−0.636157	+	0.771559i	$0.719477\pi$
$860$	6.18999e8	+	1.44349e9i	0.973184	+	2.26944i
$861$	−4.39776e8	+	411791.i	−0.689004	+	0.000645160i
$862$	5.88487e8	−	8.92668e8i	0.918787	−	1.39370i
$863$			4.24089e8i			0.659819i	0.944013	+	0.329910i	$0.107018\pi$
$863$			4.24089e8i			0.659819i	−0.944013	+	0.329910i	$0.892982\pi$
$864$	−1.47145e8	−	6.27963e8i	−0.228142	−	0.973628i
$865$	−3.90030e8			−0.602629
$866$	−4.65465e8	−	3.06855e8i	−0.716693	−	0.472476i
$867$	527080.	+	5.62900e8i	0.000808759	+	0.863721i
$868$	−1.30810e9	+	5.60940e8i	−2.00023	+	0.857743i
$869$	−6.59451e8	+	6.59451e8i	−1.00490	+	1.00490i
$870$	1.39068e8	−	2.11382e8i	0.211189	−	0.321003i
$871$		−	2.64397e8i		−	0.400131i
$872$	2.68623e8	+	3.86266e8i	0.405129	+	0.582556i
$873$	−6.04246e8	+	1.13159e6i	−0.908177	+	0.00170077i
$874$	−3.97193e8	+	8.15706e7i	−0.594931	+	0.122180i
$875$	1.73300e8	−	1.73300e8i	0.258688	−	0.258688i
$876$	−2.37025e8	−	5.51310e8i	−0.352600	−	0.820132i
$877$	−2.96677e8	+	2.96677e8i	−0.439830	+	0.439830i	−0.891955	−	0.452125i	$-0.850666\pi$
$877$	−2.96677e8	+	2.96677e8i	−0.439830	+	0.439830i	0.452125	+	0.891955i	$0.350666\pi$
$878$	−3.23108e7	+	4.90118e7i	−0.0477379	+	0.0724131i
$879$	−1.14490e8	−	1.14276e8i	−0.168578	−	0.168262i
$880$	−9.35914e8	−	8.90593e8i	−1.37337	−	1.30687i
$881$			5.69345e8i			0.832622i	0.909222	+	0.416311i	$0.136677\pi$
$881$			5.69345e8i			0.832622i	−0.909222	+	0.416311i	$0.863323\pi$
$882$	−4.06726e8	−	2.67041e8i	−0.592784	−	0.389199i
$883$	−7.55435e8	+	7.55435e8i	−1.09727	+	1.09727i	−0.102546	+	0.994728i	$0.532699\pi$
$883$	−7.55435e8	+	7.55435e8i	−1.09727	+	1.09727i	−0.994728	+	0.102546i	$0.967301\pi$
$884$	−3.96558e7	+	9.92002e7i	−0.0574050	+	0.143600i
$885$	1.47131e9	−	1.37769e6i	2.12263	−	0.00198756i
$886$	9.66548e8	−	1.98498e8i	1.38970	−	0.285401i
$887$	−9.76593e8			−1.39940			−0.699701	−	0.714436i	$-0.746683\pi$
$887$	−9.76593e8			−1.39940			−0.699701	+	0.714436i	$0.746683\pi$
$888$	8.42613e7	+	1.20922e8i	0.120334	+	0.172690i
$889$			3.47855e8i			0.495100i
$890$	2.98066e8	−	6.12132e7i	0.422807	−	0.0868310i
$891$	7.05899e8	−	7.11207e8i	0.997952	−	1.00546i
$892$	−1.39057e8	−	3.24278e8i	−0.195929	−	0.456901i
$893$	−1.09340e8	−	1.09340e8i	−0.153542	−	0.153542i
$894$	−6.03206e7	−	2.92330e8i	−0.0844215	−	0.409130i
$895$	−6.06237e8			−0.845616
$896$	−7.58501e8	+	5.55901e8i	−1.05446	+	0.772811i
$897$	3.03270e8	+	3.02703e8i	0.420196	+	0.419410i
$898$	5.28289e8	−	8.01355e8i	0.729529	−	1.10661i
$899$	−2.45575e8	−	2.45575e8i	−0.337991	−	0.337991i
$900$	−5.29469e8	+	2.28223e8i	−0.726295	+	0.313063i
$901$	1.19789e8	+	1.19789e8i	0.163773	+	0.163773i
$902$	−5.36711e8	+	1.10223e8i	−0.731343	+	0.150194i
$903$	1.25713e9	+	1.25478e9i	1.70733	+	1.70414i
$904$	5.64588e8	+	1.01422e8i	0.764234	+	0.137286i
$905$	−4.24352e8			−0.572507
$906$	−8.67227e8	−	5.70551e8i	−1.16613	−	0.767202i
$907$	1.17693e8	+	1.17693e8i	0.157735	+	0.157735i	0.781562	−	0.623827i	$-0.214423\pi$
$907$	1.17693e8	+	1.17693e8i	0.157735	+	0.157735i	−0.623827	+	0.781562i	$0.714423\pi$
$908$	2.75059e8	−	6.88070e8i	0.367425	−	0.919126i
$909$	9.03107e8	−	9.06496e8i	1.20240	−	1.20691i
$910$	−4.61122e8	−	3.03992e8i	−0.611916	−	0.403402i
$911$			5.92190e8i			0.783261i	0.920123	+	0.391630i	$0.128089\pi$
$911$			5.92190e8i			0.783261i	−0.920123	+	0.391630i	$0.871911\pi$
$912$	3.24976e8	−	8.36822e6i	0.428417	−	0.0110318i
$913$	−1.45098e9			−1.90655
$914$	5.88511e8	−	8.92706e8i	0.770755	−	1.16915i
$915$	−1.54021e9	+	1.44220e6i	−2.01056	+	0.00188262i
$916$	1.46034e8	−	3.65309e8i	0.190006	−	0.475307i
$917$	3.35777e8	−	3.35777e8i	0.435454	−	0.435454i
$918$	2.38879e8	+	1.56518e8i	0.308780	+	0.202319i
$919$		−	8.80139e8i		−	1.13398i	−0.823725	−	0.566989i	$-0.808108\pi$
$919$		−	8.80139e8i		−	1.13398i	0.823725	−	0.566989i	$-0.191892\pi$
$920$	−8.43175e8	−	1.21244e9i	−1.08282	−	1.55704i
$921$	2.10303e8	+	2.09910e8i	0.269195	+	0.268692i
$922$	−2.64416e8	−	1.28752e9i	−0.337360	−	1.64271i
$923$	−4.43880e7	+	4.43880e7i	−0.0564495	+	0.0564495i
$924$	−1.35716e9	−	5.41058e8i	−1.72034	−	0.685848i
$925$	9.31622e7	−	9.31622e7i	0.117710	−	0.117710i
$926$	5.23109e8	+	3.44857e8i	0.658809	+	0.434316i
$927$	−2.42711e6	−	1.29602e9i	−0.00304684	−	1.62695i
$928$	−1.94654e8	−	1.21507e8i	−0.243568	−	0.152040i
$929$			6.66937e8i			0.831836i	0.909402	+	0.415918i	$0.136540\pi$
$929$			6.66937e8i			0.831836i	−0.909402	+	0.415918i	$0.863460\pi$
$930$	3.62134e8	+	1.75500e9i	0.450215	+	2.18187i
$931$	1.73409e8	−	1.73409e8i	0.214894	−	0.214894i
$932$	2.25240e8	+	5.25253e8i	0.278226	+	0.648815i
$933$	273679.	+	2.92277e8i	0.000336974	+	0.359874i
$934$	2.13455e8	+	1.03938e9i	0.261978	+	1.27565i
$935$	5.72058e8			0.699851
$936$	−1.96663e8	−	2.81665e8i	−0.239825	−	0.343483i
$937$			1.10098e9i			1.33833i	0.743115	+	0.669164i	$0.233348\pi$
$937$			1.10098e9i			1.33833i	−0.743115	+	0.669164i	$0.766652\pi$
$938$	2.07312e8	+	1.00947e9i	0.251198	+	1.22316i
$939$	5.00809e8	−	468941.i	0.604889	−	0.000566397i
$940$	2.09050e8	−	5.22945e8i	0.251690	−	0.629612i
$941$	1.55883e8	+	1.55883e8i	0.187081	+	0.187081i	0.794433	−	0.607352i	$-0.207768\pi$
$941$	1.55883e8	+	1.55883e8i	0.187081	+	0.187081i	−0.607352	+	0.794433i	$0.707768\pi$
$942$	2.74239e8	+	1.32904e9i	0.328078	+	1.58996i
$943$	−6.26319e8			−0.746897
$944$	−3.30983e7	−	1.33390e9i	−0.0393451	−	1.58565i
$945$	−1.04107e9	+	1.04693e9i	−1.23363	+	1.24058i
$946$	1.84758e9	+	1.21801e9i	2.18238	+	1.43872i
$947$	9.53506e8	+	9.53506e8i	1.12273	+	1.12273i	0.991330	+	0.131396i	$0.0419458\pi$
$947$	9.53506e8	+	9.53506e8i	1.12273	+	1.12273i	0.131396	+	0.991330i	$0.458054\pi$
$948$	7.85193e8	−	3.37578e8i	0.921619	−	0.396232i
$949$	−2.26012e8	−	2.26012e8i	−0.264444	−	0.264444i
$950$	−5.84604e7	−	2.84662e8i	−0.0681853	−	0.332016i
$951$	−4.39764e8	+	4.40588e8i	−0.511303	+	0.512261i
$952$	7.36235e7	−	4.09841e8i	0.0853307	−	0.475012i
$953$	1.38226e9			1.59702			0.798509	−	0.601983i	$-0.205622\pi$
$953$	1.38226e9			1.59702			0.798509	+	0.601983i	$0.205622\pi$
$954$	−5.33398e8	+	1.10584e8i	−0.614336	+	0.127364i
$955$	−9.04233e7	−	9.04233e7i	−0.103817	−	0.103817i
$956$	8.91458e7	−	3.82277e7i	0.102030	−	0.0437526i
$957$	−333819.	−	3.56505e8i	−0.000380869	−	0.406752i
$958$	−1.80160e8	+	2.73283e8i	−0.204910	+	0.310825i
$959$		−	1.98766e9i		−	2.25365i
$960$	4.94484e8	+	1.07579e9i	0.558905	+	1.21594i
$961$	1.57210e9			1.77138
$962$	6.55399e7	+	4.32068e7i	0.0736174	+	0.0485319i
$963$	5.05109e7	−	5.07005e7i	0.0565596	−	0.0567718i
$964$	−1.43610e8	−	3.34895e8i	−0.160308	−	0.373833i
$965$	−8.02865e8	+	8.02865e8i	−0.893430	+	0.893430i
$966$	−1.39523e9	−	9.17928e8i	−1.54780	−	1.01830i
$967$		−	8.46803e8i		−	0.936490i	−0.883599	−	0.468245i	$-0.844887\pi$
$967$		−	8.46803e8i		−	0.936490i	0.883599	−	0.468245i	$-0.155113\pi$
$968$	−8.98862e8	−	1.61471e8i	−0.990985	−	0.178020i
$969$	−1.01689e8	+	1.01880e8i	−0.111764	+	0.111974i
$970$	1.08655e9	−	2.23143e8i	1.19052	−	0.244494i
$971$	−9.70767e8	+	9.70767e8i	−1.06037	+	1.06037i	−0.0623133	+	0.998057i	$0.519848\pi$
$971$	−9.70767e8	+	9.70767e8i	−1.06037	+	1.06037i	−0.998057	+	0.0623133i	$0.980152\pi$
$972$	−8.42298e8	+	3.65874e8i	−0.917207	+	0.398412i
$973$	1.29132e9	−	1.29132e9i	1.40182	−	1.40182i
$974$	2.82238e7	−	4.28123e7i	0.0305449	−	0.0463331i
$975$	−2.16943e8	+	2.17349e8i	−0.234062	+	0.234501i
$976$	3.46484e7	+	1.39636e9i	0.0372678	+	1.50193i
$977$		−	7.40123e8i		−	0.793634i	−0.917898	−	0.396817i	$-0.870115\pi$
$977$		−	7.40123e8i		−	0.793634i	0.917898	−	0.396817i	$-0.129885\pi$
$978$	−1.64237e8	−	7.95937e8i	−0.175571	−	0.850868i
$979$	3.03158e8	−	3.03158e8i	0.323088	−	0.323088i
$980$	8.29370e8	+	3.31545e8i	0.881191	+	0.352260i
$981$	4.72800e8	−	4.74574e8i	0.500807	−	0.502686i
$982$	−1.22817e8	+	2.52226e7i	−0.129695	+	0.0266352i
$983$	−1.78534e9			−1.87958			−0.939790	−	0.341752i	$-0.888980\pi$
$983$	−1.78534e9			−1.87958			−0.939790	+	0.341752i	$0.888980\pi$
$984$	4.94306e8	+	8.83190e7i	0.518812	+	0.0926976i
$985$		−	3.04723e8i		−	0.318857i
$986$	9.95282e7	−	2.04399e7i	0.103828	−	0.0213230i
$987$	−596369.	−	6.36897e8i	−0.000620245	−	0.662396i
$988$	1.59133e8	−	6.82399e7i	0.165003	−	0.0707567i
$989$	1.78870e9	+	1.78870e9i	1.84906	+	1.84906i
$990$	−1.00958e9	+	1.53768e9i	−1.04049	+	1.58475i
$991$	5.28716e8			0.543252			0.271626	−	0.962403i	$-0.412439\pi$
$991$	5.28716e8			0.543252			0.271626	+	0.962403i	$0.412439\pi$
$992$	1.58329e9	−	3.66310e8i	1.62190	−	0.375244i
$993$	2.47235e8	−	2.47698e8i	0.252500	−	0.252973i
$994$	1.34669e8	−	2.04278e8i	0.137122	−	0.207999i
$995$	−2.50662e8	−	2.50662e8i	−0.254460	−	0.254460i
$996$	1.23521e9	+	4.92439e8i	1.25015	+	0.498395i
$997$	1.77505e8	+	1.77505e8i	0.179112	+	0.179112i	0.790969	−	0.611857i	$-0.209577\pi$
$997$	1.77505e8	+	1.77505e8i	0.179112	+	0.179112i	−0.611857	+	0.790969i	$0.709577\pi$
$998$	−6.38244e7	+	1.31075e7i	−0.0642089	+	0.0131864i
$999$	1.47969e8	−	1.48802e8i	0.148413	−	0.149250i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.7.i.a.5.9	✓	92
3.2	odd	2	inner	48.7.i.a.5.38	yes	92
4.3	odd	2		192.7.i.a.113.24		92
12.11	even	2		192.7.i.a.113.46		92
16.3	odd	4		192.7.i.a.17.46		92
16.13	even	4	inner	48.7.i.a.29.38	yes	92
48.29	odd	4	inner	48.7.i.a.29.9	yes	92
48.35	even	4		192.7.i.a.17.24		92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.i.a.5.9	✓	92	1.1	even	1	trivial
48.7.i.a.5.38	yes	92	3.2	odd	2	inner
48.7.i.a.29.9	yes	92	48.29	odd	4	inner
48.7.i.a.29.38	yes	92	16.13	even	4	inner
192.7.i.a.17.24		92	48.35	even	4
192.7.i.a.17.46		92	16.3	odd	4
192.7.i.a.113.24		92	4.3	odd	2
192.7.i.a.113.46		92	12.11	even	2

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	48.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.67919 - 4.40322i) q^{2} +(0.0252819 + 27.0000i) q^{3} +(25.2233 + 58.8200i) q^{4} +(-118.285 + 118.285i) q^{5} +(118.718 - 180.449i) q^{6} +448.417i q^{7} +(90.5262 - 503.934i) q^{8} +(-728.999 + 1.36522i) q^{9} +O(q^{10})\)	\(q+(-6.67919 - 4.40322i) q^{2} +(0.0252819 + 27.0000i) q^{3} +(25.2233 + 58.8200i) q^{4} +(-118.285 + 118.285i) q^{5} +(118.718 - 180.449i) q^{6} +448.417i q^{7} +(90.5262 - 503.934i) q^{8} +(-728.999 + 1.36522i) q^{9} +(1310.88 - 269.213i) q^{10} +(1333.28 - 1333.28i) q^{11} +(-1587.50 + 682.515i) q^{12} +(-650.804 + 650.804i) q^{13} +(1974.48 - 2995.06i) q^{14} +(-3196.69 - 3190.70i) q^{15} +(-2823.57 + 2967.26i) q^{16} -1813.68i q^{17} +(4875.14 + 3200.82i) q^{18} +(-2078.53 + 2078.53i) q^{19} +(-9941.06 - 3973.99i) q^{20} +(-12107.3 + 11.3368i) q^{21} +(-14775.9 + 3034.50i) q^{22} -17242.9 q^{23} +(13608.5 + 2431.47i) q^{24} -12357.7i q^{25} +(7212.48 - 1481.21i) q^{26} +(-55.2914 - 19682.9i) q^{27} +(-26375.9 + 11310.5i) q^{28} +(-4951.67 - 4951.67i) q^{29} +(7301.90 + 35387.1i) q^{30} +49594.4 q^{31} +(31924.7 - 7386.10i) q^{32} +(36032.2 + 35964.7i) q^{33} +(-7986.02 + 12113.9i) q^{34} +(-53041.0 - 53041.0i) q^{35} +(-18468.0 - 42845.2i) q^{36} +(7538.79 + 7538.79i) q^{37} +(23035.2 - 4730.68i) q^{38} +(-17588.1 - 17555.2i) q^{39} +(48899.9 + 70315.7i) q^{40} +36323.3 q^{41} +(80916.6 + 53235.2i) q^{42} +(-103736. - 103736. i) q^{43} +(112053. + 44793.7i) q^{44} +(86068.2 - 86391.1i) q^{45} +(115169. + 75924.2i) q^{46} +52604.6i q^{47} +(-80187.4 - 76161.4i) q^{48} -83428.7 q^{49} +(-54413.7 + 82539.5i) q^{50} +(48969.3 - 45.8532i) q^{51} +(-54695.6 - 21864.8i) q^{52} +(-66047.6 + 66047.6i) q^{53} +(-86299.0 + 131710. i) q^{54} +315413. i q^{55} +(225972. + 40593.5i) q^{56} +(-56172.9 - 56067.8i) q^{57} +(11269.9 + 54876.5i) q^{58} +(-230346. + 230346. i) q^{59} +(107046. - 268509. i) q^{60} +(241134. - 241134. i) q^{61} +(-331251. - 218375. i) q^{62} +(-612.188 - 326895. i) q^{63} +(-245754. - 91238.4i) q^{64} -153961. i q^{65} +(-82305.0 - 398873. i) q^{66} +(-203131. + 203131. i) q^{67} +(106680. - 45746.9i) q^{68} +(-435.932 - 465557. i) q^{69} +(120720. + 587823. i) q^{70} +68204.8 q^{71} +(-65305.5 + 367490. i) q^{72} +347282. i q^{73} +(-17158.1 - 83548.0i) q^{74} +(333658. - 312.426i) q^{75} +(-174687. - 69831.8i) q^{76} +(597864. + 597864. i) q^{77} +(40175.0 + 194699. i) q^{78} -494609. q^{79} +(-16996.3 - 684969. i) q^{80} +(531437. - 1990.49i) q^{81} +(-242611. - 159940. i) q^{82} +(-544140. - 544140. i) q^{83} +(-306051. - 711862. i) q^{84} +(214531. + 214531. i) q^{85} +(236100. + 1.14964e6i) q^{86} +(133570. - 133820. i) q^{87} +(-551186. - 792579. i) q^{88} +227378. q^{89} +(-955265. + 198046. i) q^{90} +(-291831. - 291831. i) q^{91} +(-434922. - 1.01423e6i) q^{92} +(1253.84 + 1.33905e6i) q^{93} +(231630. - 351356. i) q^{94} -491719. i q^{95} +(200232. + 861780. i) q^{96} +828870. q^{97} +(557237. + 367355. i) q^{98} +(-970137. + 973777. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6}+O(q^{10}) \) 92 * q - 2 * q^3 - 4 * q^4 + 508 * q^6	\( 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6} + 1496 q^{10} + 4288 q^{12} - 4 q^{13} - 4 q^{15} + 10352 q^{16} + 10020 q^{18} - 3940 q^{19} + 1456 q^{21} - 42088 q^{22} + 66376 q^{24} - 34322 q^{27} + 27000 q^{28} - 127836 q^{30} - 8 q^{31} - 4 q^{33} + 128424 q^{34} + 172420 q^{36} - 4 q^{37} - 164392 q^{40} + 221560 q^{42} - 195268 q^{43} - 31252 q^{45} + 150712 q^{46} - 188048 q^{48} - 1142884 q^{49} + 385056 q^{51} - 122368 q^{52} + 151912 q^{54} - 181960 q^{58} + 242304 q^{60} - 326500 q^{61} + 470592 q^{63} - 251752 q^{64} + 489172 q^{66} + 1207676 q^{67} - 1460 q^{69} + 346392 q^{70} - 903480 q^{72} + 1413778 q^{75} - 359992 q^{76} + 1478252 q^{78} + 860920 q^{79} - 4 q^{81} - 2412800 q^{82} - 730640 q^{84} + 434496 q^{85} + 1259360 q^{88} - 291792 q^{90} + 2320992 q^{91} - 1176260 q^{93} - 1412496 q^{94} + 1956200 q^{96} - 8 q^{97} - 4048228 q^{99}+O(q^{100}) \) 92 * q - 2 * q^3 - 4 * q^4 + 508 * q^6 + 1496 * q^10 + 4288 * q^12 - 4 * q^13 - 4 * q^15 + 10352 * q^16 + 10020 * q^18 - 3940 * q^19 + 1456 * q^21 - 42088 * q^22 + 66376 * q^24 - 34322 * q^27 + 27000 * q^28 - 127836 * q^30 - 8 * q^31 - 4 * q^33 + 128424 * q^34 + 172420 * q^36 - 4 * q^37 - 164392 * q^40 + 221560 * q^42 - 195268 * q^43 - 31252 * q^45 + 150712 * q^46 - 188048 * q^48 - 1142884 * q^49 + 385056 * q^51 - 122368 * q^52 + 151912 * q^54 - 181960 * q^58 + 242304 * q^60 - 326500 * q^61 + 470592 * q^63 - 251752 * q^64 + 489172 * q^66 + 1207676 * q^67 - 1460 * q^69 + 346392 * q^70 - 903480 * q^72 + 1413778 * q^75 - 359992 * q^76 + 1478252 * q^78 + 860920 * q^79 - 4 * q^81 - 2412800 * q^82 - 730640 * q^84 + 434496 * q^85 + 1259360 * q^88 - 291792 * q^90 + 2320992 * q^91 - 1176260 * q^93 - 1412496 * q^94 + 1956200 * q^96 - 8 * q^97 - 4048228 * q^99

Introduction

L-functions

Modular forms

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