LMFDB - Embedded newform 15.8.e.a.8.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,8,Mod(2,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("15.2");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	15.e (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:	$4.68577538226$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.8
Character	$\chi$	$=$	15.8
Dual form			15.8.e.a.2.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.42850 + 5.42850i) q^{2} +(44.8885 + 13.1156i) q^{3} -69.0629i q^{4} +(275.850 + 45.0737i) q^{5} +(172.479 + 314.875i) q^{6} +(-775.470 + 775.470i) q^{7} +(1069.75 - 1069.75i) q^{8} +(1842.96 + 1177.48i) q^{9} +O(q^{10})$	\(q+(5.42850 + 5.42850i) q^{2} +(44.8885 + 13.1156i) q^{3} -69.0629i q^{4} +(275.850 + 45.0737i) q^{5} +(172.479 + 314.875i) q^{6} +(-775.470 + 775.470i) q^{7} +(1069.75 - 1069.75i) q^{8} +(1842.96 + 1177.48i) q^{9} +(1252.77 + 1742.13i) q^{10} +1977.76i q^{11} +(905.801 - 3100.13i) q^{12} +(-6601.06 - 6601.06i) q^{13} -8419.28 q^{14} +(11791.3 + 5641.23i) q^{15} +2774.28 q^{16} +(-23341.3 - 23341.3i) q^{17} +(3612.56 + 16396.5i) q^{18} -9983.78i q^{19} +(3112.92 - 19051.0i) q^{20} +(-44980.5 + 24639.0i) q^{21} +(-10736.3 + 10736.3i) q^{22} +(-24556.6 + 24556.6i) q^{23} +(62050.2 - 33989.3i) q^{24} +(74061.7 + 24867.2i) q^{25} -71667.6i q^{26} +(67284.5 + 77026.9i) q^{27} +(53556.2 + 53556.2i) q^{28} +135024. q^{29} +(33385.9 + 94632.7i) q^{30} -128063. q^{31} +(-121868. - 121868. i) q^{32} +(-25939.6 + 88778.9i) q^{33} -253416. i q^{34} +(-248867. + 178960. i) q^{35} +(81320.2 - 127280. i) q^{36} +(-274562. + 274562. i) q^{37} +(54196.9 - 54196.9i) q^{38} +(-209735. - 382889. i) q^{39} +(343310. - 246874. i) q^{40} +21856.1i q^{41} +(-377929. - 110424. i) q^{42} +(82226.5 + 82226.5i) q^{43} +136590. q^{44} +(455308. + 407877. i) q^{45} -266611. q^{46} +(400763. + 400763. i) q^{47} +(124533. + 36386.3i) q^{48} -379166. i q^{49} +(267052. + 537035. i) q^{50} +(-741620. - 1.35389e6i) q^{51} +(-455888. + 455888. i) q^{52} +(540245. - 540245. i) q^{53} +(-52886.8 + 783394. i) q^{54} +(-89145.0 + 545566. i) q^{55} +1.65913e6i q^{56} +(130943. - 448157. i) q^{57} +(732976. + 732976. i) q^{58} +1.84639e6 q^{59} +(389600. - 814344. i) q^{60} +1.57816e6 q^{61} +(-695188. - 695188. i) q^{62} +(-2.34226e6 + 516061. i) q^{63} -1.67823e6i q^{64} +(-1.52337e6 - 2.11844e6i) q^{65} +(-622749. + 341123. i) q^{66} +(781256. - 781256. i) q^{67} +(-1.61201e6 + 1.61201e6i) q^{68} +(-1.42439e6 + 780237. i) q^{69} +(-2.32246e6 - 379488. i) q^{70} -766664. i q^{71} +(3.23113e6 - 711902. i) q^{72} +(-853564. - 853564. i) q^{73} -2.98092e6 q^{74} +(2.99837e6 + 2.08762e6i) q^{75} -689509. q^{76} +(-1.53370e6 - 1.53370e6i) q^{77} +(939964. - 3.21706e6i) q^{78} +6.22014e6i q^{79} +(765285. + 125047. i) q^{80} +(2.01005e6 + 4.34010e6i) q^{81} +(-118646. + 118646. i) q^{82} +(4.42311e6 - 4.42311e6i) q^{83} +(1.70164e6 + 3.10648e6i) q^{84} +(-5.38661e6 - 7.49077e6i) q^{85} +892732. i q^{86} +(6.06102e6 + 1.77092e6i) q^{87} +(2.11572e6 + 2.11572e6i) q^{88} -1.97693e6 q^{89} +(257478. + 4.68580e6i) q^{90} +1.02378e7 q^{91} +(1.69595e6 + 1.69595e6i) q^{92} +(-5.74855e6 - 1.67962e6i) q^{93} +4.35108e6i q^{94} +(450006. - 2.75403e6i) q^{95} +(-3.87212e6 - 7.06888e6i) q^{96} +(-7.15589e6 + 7.15589e6i) q^{97} +(2.05830e6 - 2.05830e6i) q^{98} +(-2.32878e6 + 3.64494e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{3} + 924 q^{6} + 1344 q^{7}+O(q^{10}) $ 24 * q + 24 * q^3 + 924 * q^6 + 1344 * q^7	$ 24 q + 24 q^{3} + 924 q^{6} + 1344 q^{7} - 3180 q^{10} - 2028 q^{12} + 16848 q^{13} + 37560 q^{15} - 68868 q^{16} - 106560 q^{18} + 84144 q^{21} + 166020 q^{22} - 275760 q^{25} - 264168 q^{27} + 602028 q^{28} + 892380 q^{30} - 208992 q^{31} - 877800 q^{33} - 256212 q^{36} - 635616 q^{37} - 1574040 q^{40} + 1219380 q^{42} + 1397328 q^{43} + 570240 q^{45} + 2787168 q^{46} - 476796 q^{48} - 4028016 q^{51} - 6426336 q^{52} + 2324880 q^{55} + 8457264 q^{57} + 986340 q^{58} + 2037900 q^{60} + 12157968 q^{61} - 1973952 q^{63} - 25406040 q^{66} - 16720176 q^{67} - 13165860 q^{70} + 36245880 q^{72} + 4059528 q^{73} + 11226120 q^{75} + 37968816 q^{76} - 26156280 q^{78} - 31289976 q^{81} - 53633520 q^{82} - 34181760 q^{85} + 44480160 q^{87} + 74717340 q^{88} + 71623080 q^{90} + 67599648 q^{91} - 58742592 q^{93} - 103105308 q^{96} - 75148056 q^{97}+O(q^{100}) $ 24 * q + 24 * q^3 + 924 * q^6 + 1344 * q^7 - 3180 * q^10 - 2028 * q^12 + 16848 * q^13 + 37560 * q^15 - 68868 * q^16 - 106560 * q^18 + 84144 * q^21 + 166020 * q^22 - 275760 * q^25 - 264168 * q^27 + 602028 * q^28 + 892380 * q^30 - 208992 * q^31 - 877800 * q^33 - 256212 * q^36 - 635616 * q^37 - 1574040 * q^40 + 1219380 * q^42 + 1397328 * q^43 + 570240 * q^45 + 2787168 * q^46 - 476796 * q^48 - 4028016 * q^51 - 6426336 * q^52 + 2324880 * q^55 + 8457264 * q^57 + 986340 * q^58 + 2037900 * q^60 + 12157968 * q^61 - 1973952 * q^63 - 25406040 * q^66 - 16720176 * q^67 - 13165860 * q^70 + 36245880 * q^72 + 4059528 * q^73 + 11226120 * q^75 + 37968816 * q^76 - 26156280 * q^78 - 31289976 * q^81 - 53633520 * q^82 - 34181760 * q^85 + 44480160 * q^87 + 74717340 * q^88 + 71623080 * q^90 + 67599648 * q^91 - 58742592 * q^93 - 103105308 * q^96 - 75148056 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	5.42850	+	5.42850i	0.479816	+	0.479816i	0.905073	−	0.425257i	$-0.139816\pi$
$2$	5.42850	+	5.42850i	0.479816	+	0.479816i	−0.425257	+	0.905073i	$0.639816\pi$
$3$	44.8885	+	13.1156i	0.959867	+	0.280455i
$3$	44.8885	+	13.1156i	0.959867	+	0.280455i
$4$		−	69.0629i		−	0.539554i
$5$	275.850	+	45.0737i	0.986912	+	0.161260i
$5$	275.850	+	45.0737i	0.986912	+	0.161260i
$6$	172.479	+	314.875i	0.325992	+	0.595126i
$7$	−775.470	+	775.470i	−0.854520	+	0.854520i	−0.990686	−	0.136166i	$-0.956522\pi$
$7$	−775.470	+	775.470i	−0.854520	+	0.854520i	0.136166	+	0.990686i	$0.456522\pi$
$8$	1069.75	−	1069.75i	0.738702	−	0.738702i
$9$	1842.96	+	1177.48i	0.842689	+	0.538400i
$10$	1252.77	+	1742.13i	0.396161	+	0.550911i
$11$			1977.76i			0.448023i	0.974587	+	0.224011i	$0.0719152\pi$
$11$			1977.76i			0.448023i	−0.974587	+	0.224011i	$0.928085\pi$
$12$	905.801	−	3100.13i	0.151321	−	0.517900i
$13$	−6601.06	−	6601.06i	−0.833320	−	0.833320i	0.154649	−	0.987969i	$-0.450575\pi$
$13$	−6601.06	−	6601.06i	−0.833320	−	0.833320i	−0.987969	+	0.154649i	$0.950575\pi$
$14$	−8419.28			−0.820024
$15$	11791.3	+	5641.23i	0.902078	+	0.431573i
$16$	2774.28			0.169328
$17$	−23341.3	−	23341.3i	−1.15227	−	1.15227i	−0.986097	−	0.166169i	$-0.946860\pi$
$17$	−23341.3	−	23341.3i	−1.15227	−	1.15227i	−0.166169	−	0.986097i	$-0.553140\pi$
$18$	3612.56	+	16396.5i	0.146003	+	0.662669i
$19$		−	9983.78i		−	0.333932i	−0.985963	−	0.166966i	$-0.946603\pi$
$19$		−	9983.78i		−	0.333932i	0.985963	−	0.166966i	$-0.0533970\pi$
$20$	3112.92	−	19051.0i	0.0870087	−	0.532492i
$21$	−44980.5	+	24639.0i	−1.05988	+	0.580571i
$22$	−10736.3	+	10736.3i	−0.214968	+	0.214968i
$23$	−24556.6	+	24556.6i	−0.420844	+	0.420844i	−0.885494	−	0.464650i	$-0.846180\pi$
$23$	−24556.6	+	24556.6i	−0.420844	+	0.420844i	0.464650	+	0.885494i	$0.346180\pi$
$24$	62050.2	−	33989.3i	0.916229	−	0.501883i
$25$	74061.7	+	24867.2i	0.947990	+	0.318300i
$26$		−	71667.6i		−	0.799680i
$27$	67284.5	+	77026.9i	0.657873	+	0.753129i
$28$	53556.2	+	53556.2i	0.461059	+	0.461059i
$29$	135024.			1.02806			0.514028	−	0.857773i	$-0.328153\pi$
$29$	135024.			1.02806			0.514028	+	0.857773i	$0.328153\pi$
$30$	33385.9	+	94632.7i	0.225755	+	0.639907i
$31$	−128063.			−0.772071			−0.386035	−	0.922484i	$-0.626156\pi$
$31$	−128063.			−0.772071			−0.386035	+	0.922484i	$0.626156\pi$
$32$	−121868.	−	121868.i	−0.657456	−	0.657456i
$33$	−25939.6	+	88778.9i	−0.125650	+	0.430042i
$34$		−	253416.i		−	1.10575i
$35$	−248867.	+	178960.i	−0.981136	+	0.705535i
$36$	81320.2	−	127280.i	0.290496	−	0.454676i
$37$	−274562.	+	274562.i	−0.891116	+	0.891116i	−0.994628	−	0.103512i	$-0.966992\pi$
$37$	−274562.	+	274562.i	−0.891116	+	0.891116i	0.103512	+	0.994628i	$0.466992\pi$
$38$	54196.9	−	54196.9i	0.160226	−	0.160226i
$39$	−209735.	−	382889.i	−0.566167	−	1.03359i
$40$	343310.	−	246874.i	0.848157	−	0.609910i
$41$			21856.1i			0.0495256i	0.999693	+	0.0247628i	$0.00788305\pi$
$41$			21856.1i			0.0495256i	−0.999693	+	0.0247628i	$0.992117\pi$
$42$	−377929.	−	110424.i	−0.787114	−	0.229980i
$43$	82226.5	+	82226.5i	0.157715	+	0.157715i	0.781553	−	0.623839i	$-0.214428\pi$
$43$	82226.5	+	82226.5i	0.157715	+	0.157715i	−0.623839	+	0.781553i	$0.714428\pi$
$44$	136590.			0.241732
$45$	455308.	+	407877.i	0.744838	+	0.667246i
$46$	−266611.			−0.403856
$47$	400763.	+	400763.i	0.563048	+	0.563048i	0.930172	−	0.367124i	$-0.119658\pi$
$47$	400763.	+	400763.i	0.563048	+	0.563048i	−0.367124	+	0.930172i	$0.619658\pi$
$48$	124533.	+	36386.3i	0.162533	+	0.0474891i
$49$		−	379166.i		−	0.460408i
$50$	267052.	+	537035.i	0.302135	+	0.607586i
$51$	−741620.	−	1.35389e6i	−0.782863	−	1.42918i
$52$	−455888.	+	455888.i	−0.449621	+	0.449621i
$53$	540245.	−	540245.i	0.498454	−	0.498454i	−0.412503	−	0.910956i	$-0.635345\pi$
$53$	540245.	−	540245.i	0.498454	−	0.498454i	0.910956	+	0.412503i	$0.135345\pi$
$54$	−52886.8	+	783394.i	−0.0457056	+	0.677021i
$55$	−89145.0	+	545566.i	−0.0722483	+	0.442159i
$56$			1.65913e6i			1.26247i
$57$	130943.	−	448157.i	0.0936529	−	0.320530i
$58$	732976.	+	732976.i	0.493278	+	0.493278i
$59$	1.84639e6			1.17042			0.585210	−	0.810882i	$-0.301012\pi$
$59$	1.84639e6			1.17042			0.585210	+	0.810882i	$0.301012\pi$
$60$	389600.	−	814344.i	0.232857	−	0.486719i
$61$	1.57816e6			0.890220			0.445110	−	0.895476i	$-0.353165\pi$
$61$	1.57816e6			0.890220			0.445110	+	0.895476i	$0.353165\pi$
$62$	−695188.	−	695188.i	−0.370452	−	0.370452i
$63$	−2.34226e6	+	516061.i	−1.18017	+	0.260021i
$64$		−	1.67823e6i		−	0.800244i
$65$	−1.52337e6	−	2.11844e6i	−0.688032	−	0.956795i
$66$	−622749.	+	341123.i	−0.266630	+	0.146052i
$67$	781256.	−	781256.i	0.317345	−	0.317345i	−0.530402	−	0.847746i	$-0.677959\pi$
$67$	781256.	−	781256.i	0.317345	−	0.317345i	0.847746	+	0.530402i	$0.177959\pi$
$68$	−1.61201e6	+	1.61201e6i	−0.621710	+	0.621710i
$69$	−1.42439e6	+	780237.i	−0.521983	+	0.285927i
$70$	−2.32246e6	−	379488.i	−0.809292	−	0.132237i
$71$		−	766664.i		−	0.254215i	−0.991889	−	0.127107i	$-0.959431\pi$
$71$		−	766664.i		−	0.254215i	0.991889	−	0.127107i	$-0.0405693\pi$
$72$	3.23113e6	−	711902.i	1.02021	−	0.224779i
$73$	−853564.	−	853564.i	−0.256806	−	0.256806i	0.566947	−	0.823754i	$-0.308124\pi$
$73$	−853564.	−	853564.i	−0.256806	−	0.256806i	−0.823754	+	0.566947i	$0.808124\pi$
$74$	−2.98092e6			−0.855143
$75$	2.99837e6	+	2.08762e6i	0.820676	+	0.571394i
$76$	−689509.			−0.180174
$77$	−1.53370e6	−	1.53370e6i	−0.382844	−	0.382844i
$78$	939964.	−	3.21706e6i	0.224275	−	0.767587i
$79$			6.22014e6i			1.41940i	0.704503	+	0.709701i	$0.251170\pi$
$79$			6.22014e6i			1.41940i	−0.704503	+	0.709701i	$0.748830\pi$
$80$	765285.	+	125047.i	0.167112	+	0.0273060i
$81$	2.01005e6	+	4.34010e6i	0.420251	+	0.907408i
$82$	−118646.	+	118646.i	−0.0237632	+	0.0237632i
$83$	4.42311e6	−	4.42311e6i	0.849092	−	0.849092i	−0.140928	−	0.990020i	$-0.545009\pi$
$83$	4.42311e6	−	4.42311e6i	0.849092	−	0.849092i	0.990020	+	0.140928i	$0.0450085\pi$
$84$	1.70164e6	+	3.10648e6i	0.313249	+	0.571862i
$85$	−5.38661e6	−	7.49077e6i	−0.951371	−	1.32300i
$86$			892732.i			0.151348i
$87$	6.06102e6	+	1.77092e6i	0.986798	+	0.288324i
$88$	2.11572e6	+	2.11572e6i	0.330955	+	0.330955i
$89$	−1.97693e6			−0.297252			−0.148626	−	0.988893i	$-0.547485\pi$
$89$	−1.97693e6			−0.297252			−0.148626	+	0.988893i	$0.547485\pi$
$90$	257478.	+	4.68580e6i	0.0372298	+	0.677540i
$91$	1.02378e7			1.42418
$92$	1.69595e6	+	1.69595e6i	0.227068	+	0.227068i
$93$	−5.74855e6	−	1.67962e6i	−0.741085	−	0.216531i
$94$			4.35108e6i			0.540319i
$95$	450006.	−	2.75403e6i	0.0538500	−	0.329561i
$96$	−3.87212e6	−	7.06888e6i	−0.446683	−	0.815457i
$97$	−7.15589e6	+	7.15589e6i	−0.796090	+	0.796090i	−0.982477	−	0.186386i	$-0.940322\pi$
$97$	−7.15589e6	+	7.15589e6i	−0.796090	+	0.796090i	0.186386	+	0.982477i	$0.440322\pi$
$98$	2.05830e6	−	2.05830e6i	0.220911	−	0.220911i
$99$	−2.32878e6	+	3.64494e6i	−0.241215	+	0.377544i
$100$	1.71740e6	−	5.11491e6i	0.171740	−	0.511491i
$101$			950035.i			0.0917518i	0.998947	+	0.0458759i	$0.0146079\pi$
$101$			950035.i			0.0917518i	−0.998947	+	0.0458759i	$0.985392\pi$
$102$	3.32370e6	−	1.13755e7i	0.310114	−	1.06137i
$103$	−952905.	−	952905.i	−0.0859250	−	0.0859250i	0.662838	−	0.748763i	$-0.269352\pi$
$103$	−952905.	−	952905.i	−0.0859250	−	0.0859250i	−0.748763	+	0.662838i	$0.769352\pi$
$104$	−1.41230e7			−1.23115
$105$	−1.35185e7	+	4.76923e6i	−1.13963	+	0.402055i
$106$	5.86543e6			0.478332
$107$	7.24408e6	+	7.24408e6i	0.571663	+	0.571663i	0.932593	−	0.360930i	$-0.117541\pi$
$107$	7.24408e6	+	7.24408e6i	0.571663	+	0.571663i	−0.360930	+	0.932593i	$0.617541\pi$
$108$	5.31970e6	−	4.64686e6i	0.406354	−	0.354958i
$109$		−	2.46975e7i		−	1.82667i	−0.407210	−	0.913334i	$-0.633498\pi$
$109$		−	2.46975e7i		−	1.82667i	0.407210	−	0.913334i	$-0.366502\pi$
$110$	−3.44553e6	+	2.47768e6i	−0.246821	+	0.177489i
$111$	−1.59257e7	+	8.72363e6i	−1.10527	+	0.605434i
$112$	−2.15137e6	+	2.15137e6i	−0.144694	+	0.144694i
$113$	−1.27851e7	+	1.27851e7i	−0.833546	+	0.833546i	−0.988000	−	0.154454i	$-0.950638\pi$
$113$	−1.27851e7	+	1.27851e7i	−0.833546	+	0.833546i	0.154454	+	0.988000i	$0.450638\pi$
$114$	3.14365e6	−	1.72200e6i	0.198732	−	0.108859i
$115$	−7.88081e6	+	5.66710e6i	−0.483202	+	0.347471i
$116$		−	9.32512e6i		−	0.554692i
$117$	−4.39288e6	−	1.99381e7i	−0.253571	−	1.15089i
$118$	1.00231e7	+	1.00231e7i	0.561586	+	0.561586i
$119$	3.62009e7			1.96927
$120$	1.86486e7	−	6.57911e6i	0.985171	−	0.347563i
$121$	1.55756e7			0.799276
$122$	8.56705e6	+	8.56705e6i	0.427142	+	0.427142i
$123$	−286656.	+	981090.i	−0.0138897	+	0.0475380i
$124$			8.84438e6i			0.416573i
$125$	1.93091e7	+	1.01978e7i	0.884254	+	0.467007i
$126$	−1.55164e7	−	9.91353e6i	−0.691026	−	0.441501i
$127$	−2.89367e7	+	2.89367e7i	−1.25353	+	1.25353i	−0.299410	+	0.954124i	$0.596790\pi$
$127$	−2.89367e7	+	2.89367e7i	−1.25353	+	1.25353i	−0.954124	+	0.299410i	$0.903210\pi$
$128$	−6.48889e6	+	6.48889e6i	−0.273486	+	0.273486i
$129$	2.61258e6	+	4.76948e6i	0.107153	+	0.195617i
$130$	3.23032e6	−	1.97695e7i	0.128957	−	0.789214i
$131$			539893.i			0.0209826i	0.999945	+	0.0104913i	$0.00333954\pi$
$131$			539893.i			0.0209826i	−0.999945	+	0.0104913i	$0.996660\pi$
$132$	6.13132e6	+	1.79146e6i	0.232031	+	0.0677951i
$133$	7.74213e6	+	7.74213e6i	0.285351	+	0.285351i
$134$	8.48209e6			0.304534
$135$	1.50886e7	+	2.42807e7i	0.527812	+	0.849361i
$136$	−4.99388e7			−1.70236
$137$	−3.23862e7	−	3.23862e7i	−1.07606	−	1.07606i	−0.996858	−	0.0792063i	$-0.974761\pi$
$137$	−3.23862e7	−	3.23862e7i	−1.07606	−	1.07606i	−0.0792063	−	0.996858i	$-0.525239\pi$
$138$	−1.19678e7	−	3.49677e6i	−0.387648	−	0.113263i
$139$		−	4.39095e7i		−	1.38678i	−0.720565	−	0.693388i	$-0.756117\pi$
$139$		−	4.39095e7i		−	1.38678i	0.720565	−	0.693388i	$-0.243883\pi$
$140$	1.23595e7	+	1.71875e7i	0.380674	+	0.529375i
$141$	1.27334e7	+	2.32459e7i	0.382541	+	0.698361i
$142$	4.16183e6	−	4.16183e6i	0.121976	−	0.121976i
$143$	1.30553e7	−	1.30553e7i	0.373346	−	0.373346i
$144$	5.11288e6	+	3.26666e6i	0.142691	+	0.0911664i
$145$	3.72463e7	+	6.08602e6i	1.01460	+	0.165785i
$146$		−	9.26714e6i		−	0.246440i
$147$	4.97299e6	−	1.70202e7i	0.129124	−	0.441930i
$148$	1.89620e7	+	1.89620e7i	0.480805	+	0.480805i
$149$	−5.80020e7			−1.43645			−0.718226	−	0.695810i	$-0.755046\pi$
$149$	−5.80020e7			−1.43645			−0.718226	+	0.695810i	$0.755046\pi$
$150$	4.94406e6	+	2.76093e7i	0.119609	+	0.667937i
$151$	2.54246e7			0.600944			0.300472	−	0.953791i	$-0.402856\pi$
$151$	2.54246e7			0.600944			0.300472	+	0.953791i	$0.402856\pi$
$152$	−1.06802e7	−	1.06802e7i	−0.246676	−	0.246676i
$153$	−1.55332e7	−	7.05009e7i	−0.350623	−	1.59138i
$154$		−	1.66513e7i		−	0.367389i
$155$	−3.53262e7	−	5.77226e6i	−0.761966	−	0.124504i
$156$	−2.64434e7	+	1.44849e7i	−0.557675	+	0.305478i
$157$	−2.28986e7	+	2.28986e7i	−0.472238	+	0.472238i	−0.902638	−	0.430401i	$-0.858372\pi$
$157$	−2.28986e7	+	2.28986e7i	−0.472238	+	0.472238i	0.430401	+	0.902638i	$0.358372\pi$
$158$	−3.37660e7	+	3.37660e7i	−0.681051	+	0.681051i
$159$	3.13364e7	−	1.71652e7i	0.618243	−	0.338655i
$160$	−2.81244e7	−	3.91105e7i	−0.542829	−	0.754872i
$161$		−	3.80859e7i		−	0.719240i
$162$	−1.26487e7	+	3.44718e7i	−0.233745	+	0.637032i
$163$	1.57411e7	+	1.57411e7i	0.284695	+	0.284695i	0.834978	−	0.550283i	$-0.185480\pi$
$163$	1.57411e7	+	1.57411e7i	0.284695	+	0.284695i	−0.550283	+	0.834978i	$0.685480\pi$
$164$	1.50945e6			0.0267217
$165$	−1.11570e7	+	2.33205e7i	−0.193355	+	0.404151i
$166$	4.80217e7			0.814816
$167$	2.07930e7	+	2.07930e7i	0.345469	+	0.345469i	0.858419	−	0.512950i	$-0.171447\pi$
$167$	2.07930e7	+	2.07930e7i	0.345469	+	0.345469i	−0.512950	+	0.858419i	$0.671447\pi$
$168$	−2.17604e7	+	7.44758e7i	−0.354067	+	1.21180i
$169$			2.43994e7i			0.388844i
$170$	1.14224e7	−	6.99048e7i	0.178314	−	1.09128i
$171$	1.17557e7	−	1.83997e7i	0.179789	−	0.281401i
$172$	5.67880e6	−	5.67880e6i	0.0850955	−	0.0850955i
$173$	5.85025e7	−	5.85025e7i	0.859040	−	0.859040i	−0.132185	−	0.991225i	$-0.542199\pi$
$173$	5.85025e7	−	5.85025e7i	0.859040	−	0.859040i	0.991225	+	0.132185i	$0.0421993\pi$
$174$	2.32888e7	+	4.25156e7i	0.335139	+	0.611824i
$175$	−7.67164e7	+	3.81489e7i	−1.08207	+	0.538083i
$176$			5.48686e6i			0.0758629i
$177$	8.28818e7	+	2.42165e7i	1.12345	+	0.328251i
$178$	−1.07317e7	−	1.07317e7i	−0.142626	−	0.142626i
$179$	5.82083e7			0.758576			0.379288	−	0.925279i	$-0.376169\pi$
$179$	5.82083e7			0.758576			0.379288	+	0.925279i	$0.376169\pi$
$180$	2.81692e7	−	3.14449e7i	0.360015	−	0.401880i
$181$	1.25289e7			0.157050			0.0785248	−	0.996912i	$-0.474979\pi$
$181$	1.25289e7			0.157050			0.0785248	+	0.996912i	$0.474979\pi$
$182$	5.55761e7	+	5.55761e7i	0.683342	+	0.683342i
$183$	7.08414e7	+	2.06986e7i	0.854493	+	0.249667i
$184$			5.25392e7i			0.621757i
$185$	−8.81135e7	+	6.33624e7i	−1.02315	+	0.735751i
$186$	−2.20882e7	−	4.03238e7i	−0.251689	−	0.459480i
$187$	4.61635e7	−	4.61635e7i	0.516241	−	0.516241i
$188$	2.76779e7	−	2.76779e7i	0.303795	−	0.303795i
$189$	−1.11909e8	−	7.55497e6i	−1.20573	−	0.0813985i
$190$	1.73931e7	−	1.25074e7i	0.183967	−	0.132291i
$191$			1.09118e8i			1.13312i	0.824019	+	0.566562i	$0.191727\pi$
$191$			1.09118e8i			1.13312i	−0.824019	+	0.566562i	$0.808273\pi$
$192$	2.20110e7	−	7.53334e7i	0.224433	−	0.768128i
$193$	−8.69441e7	−	8.69441e7i	−0.870542	−	0.870542i	0.121990	−	0.992531i	$-0.461072\pi$
$193$	−8.69441e7	−	8.69441e7i	−0.870542	−	0.870542i	−0.992531	+	0.121990i	$0.961072\pi$
$194$	−7.76914e7			−0.763953
$195$	−4.05972e7	−	1.15073e8i	−0.392081	−	1.11136i
$196$	−2.61863e7			−0.248415
$197$	−3.32439e7	−	3.32439e7i	−0.309800	−	0.309800i	0.535032	−	0.844832i	$-0.320299\pi$
$197$	−3.32439e7	−	3.32439e7i	−0.309800	−	0.309800i	−0.844832	+	0.535032i	$0.820299\pi$
$198$	−3.24283e7	+	7.14479e6i	−0.296890	+	0.0654126i
$199$			4.95740e7i			0.445932i	0.974826	+	0.222966i	$0.0715738\pi$
$199$			4.95740e7i			0.445932i	−0.974826	+	0.222966i	$0.928426\pi$
$200$	1.05830e8	−	5.26261e7i	0.935411	−	0.465154i
$201$	4.53161e7	−	2.48228e7i	0.393610	−	0.215608i
$202$	−5.15726e6	+	5.15726e6i	−0.0440240	+	0.0440240i
$203$	−1.04707e8	+	1.04707e8i	−0.878495	+	0.878495i
$204$	−9.35035e7	+	5.12184e7i	−0.771120	+	0.422397i
$205$	−985136.	+	6.02902e6i	−0.00798653	+	0.0488774i
$206$		−	1.03457e7i		−	0.0824563i
$207$	−7.41719e7	+	1.63420e7i	−0.581224	+	0.128059i
$208$	−1.83132e7	−	1.83132e7i	−0.141105	−	0.141105i
$209$	1.97456e7			0.149609
$210$	−9.92746e7	−	4.74951e7i	−0.739726	−	0.353901i
$211$	8.59084e7			0.629574			0.314787	−	0.949162i	$-0.398067\pi$
$211$	8.59084e7			0.629574			0.314787	+	0.949162i	$0.398067\pi$
$212$	−3.73108e7	−	3.73108e7i	−0.268943	−	0.268943i
$213$	1.00553e7	−	3.44144e7i	0.0712959	−	0.244012i
$214$			7.86489e7i			0.548586i
$215$	1.89759e7	+	2.63884e7i	0.130217	+	0.181084i
$216$	1.54378e8	+	1.04220e7i	1.04231	+	0.0703661i
$217$	9.93089e7	−	9.93089e7i	0.659750	−	0.659750i
$218$	1.34070e8	−	1.34070e8i	0.876465	−	0.876465i
$219$	−2.71202e7	−	4.95102e7i	−0.174477	−	0.318523i
$220$	3.76784e7	+	6.15661e6i	0.238568	+	0.0389818i
$221$			3.08154e8i			1.92041i
$222$	−1.33809e8	−	3.90965e7i	−0.820823	−	0.239829i
$223$	−1.10872e8	−	1.10872e8i	−0.669505	−	0.669505i	0.288096	−	0.957602i	$-0.406978\pi$
$223$	−1.10872e8	−	1.10872e8i	−0.669505	−	0.669505i	−0.957602	+	0.288096i	$0.906978\pi$
$224$	1.89011e8			1.12362
$225$	1.07212e8	+	1.33035e8i	0.627489	+	0.778626i
$226$	−1.38808e8			−0.799897
$227$	2.67846e7	+	2.67846e7i	0.151983	+	0.151983i	0.779003	−	0.627020i	$-0.215726\pi$
$227$	2.67846e7	+	2.67846e7i	0.151983	+	0.151983i	−0.627020	+	0.779003i	$0.715726\pi$
$228$	−3.09510e7	−	9.04332e6i	−0.172943	−	0.0505308i
$229$			1.75133e8i			0.963706i	0.876252	+	0.481853i	$0.160036\pi$
$229$			1.75133e8i			0.963706i	−0.876252	+	0.481853i	$0.839964\pi$
$230$	−7.35448e7	−	1.20172e7i	−0.398570	−	0.0651259i
$231$	−4.87300e7	−	8.89608e7i	−0.260109	−	0.474850i
$232$	1.44442e8	−	1.44442e8i	0.759428	−	0.759428i
$233$	6.39936e7	−	6.39936e7i	0.331429	−	0.331429i	−0.521700	−	0.853129i	$-0.674702\pi$
$233$	6.39936e7	−	6.39936e7i	0.331429	−	0.331429i	0.853129	+	0.521700i	$0.174702\pi$
$234$	8.43872e7	−	1.32081e8i	0.430548	−	0.673882i
$235$	9.24868e7	+	1.28615e8i	0.464881	+	0.646476i
$236$		−	1.27517e8i		−	0.631504i
$237$	−8.15809e7	+	2.79213e8i	−0.398079	+	1.36244i
$238$	1.96516e8	+	1.96516e8i	0.944886	+	0.944886i
$239$	−5.77148e7			−0.273460			−0.136730	−	0.990608i	$-0.543659\pi$
$239$	−5.77148e7			−0.273460			−0.136730	+	0.990608i	$0.543659\pi$
$240$	3.27124e7	+	1.56503e7i	0.152747	+	0.0730776i
$241$	−1.54291e8			−0.710036			−0.355018	−	0.934859i	$-0.615525\pi$
$241$	−1.54291e8			−0.710036			−0.355018	+	0.934859i	$0.615525\pi$
$242$	8.45522e7	+	8.45522e7i	0.383505	+	0.383505i
$243$	3.33051e7	+	2.21184e8i	0.148898	+	0.988853i
$244$		−	1.08992e8i		−	0.480321i
$245$	1.70904e7	−	1.04593e8i	0.0742456	−	0.454382i
$246$	−6.88196e6	+	3.76973e6i	−0.0294740	+	0.0161450i
$247$	−6.59035e7	+	6.59035e7i	−0.278272	+	0.278272i
$248$	−1.36996e8	+	1.36996e8i	−0.570330	+	0.570330i
$249$	2.56559e8	−	1.40535e8i	1.05315	−	0.576883i
$250$	4.94603e7	+	1.60178e8i	0.200201	+	0.648356i
$251$		−	4.48473e8i		−	1.79010i	−0.445964	−	0.895051i	$-0.647139\pi$
$251$		−	4.48473e8i		−	1.79010i	0.445964	−	0.895051i	$-0.352861\pi$
$252$	3.56407e7	+	1.61763e8i	0.140296	+	0.636764i
$253$	−4.85672e7	−	4.85672e7i	−0.188548	−	0.188548i
$254$	−3.14166e8			−1.20293
$255$	−1.43551e8	−	4.06898e8i	−0.542146	−	1.53672i
$256$	−2.85264e8			−1.06269
$257$	−1.93996e8	−	1.93996e8i	−0.712896	−	0.712896i	0.254244	−	0.967140i	$-0.418173\pi$
$257$	−1.93996e8	−	1.93996e8i	−0.712896	−	0.712896i	−0.967140	+	0.254244i	$0.918173\pi$
$258$	−1.17087e7	+	4.00734e7i	−0.0424464	+	0.145274i
$259$		−	4.25829e8i		−	1.52295i
$260$	−1.46305e8	+	1.05208e8i	−0.516242	+	0.371230i
$261$	2.48844e8	+	1.58988e8i	0.866333	+	0.553506i
$262$	−2.93081e6	+	2.93081e6i	−0.0100678	+	0.0100678i
$263$	−2.34274e8	+	2.34274e8i	−0.794106	+	0.794106i	−0.982159	−	0.188053i	$-0.939782\pi$
$263$	−2.34274e8	+	2.34274e8i	−0.794106	+	0.794106i	0.188053	+	0.982159i	$0.439782\pi$
$264$	6.72227e7	+	1.22721e8i	0.224855	+	0.410491i
$265$	1.73377e8	−	1.24676e8i	0.572311	−	0.411549i
$266$			8.40562e7i			0.273832i
$267$	−8.87413e7	−	2.59286e7i	−0.285323	−	0.0833660i
$268$	−5.39557e7	−	5.39557e7i	−0.171225	−	0.171225i
$269$	2.68002e8			0.839469			0.419735	−	0.907647i	$-0.362123\pi$
$269$	2.68002e8			0.839469			0.419735	+	0.907647i	$0.362123\pi$
$270$	−4.98993e7	+	2.13716e8i	−0.154284	+	0.660790i
$271$	−6.56166e7			−0.200273			−0.100136	−	0.994974i	$-0.531928\pi$
$271$	−6.56166e7			−0.200273			−0.100136	+	0.994974i	$0.531928\pi$
$272$	−6.47551e7	−	6.47551e7i	−0.195111	−	0.195111i
$273$	4.59562e8	+	1.34276e8i	1.36702	+	0.399418i
$274$		−	3.51617e8i		−	1.03263i
$275$	−4.91814e7	+	1.46477e8i	−0.142605	+	0.424721i
$276$	5.38854e7	+	9.83722e7i	0.154273	+	0.281638i
$277$	−5.37520e7	+	5.37520e7i	−0.151955	+	0.151955i	−0.778991	−	0.627036i	$-0.784268\pi$
$277$	−5.37520e7	+	5.37520e7i	−0.151955	+	0.151955i	0.627036	+	0.778991i	$0.284268\pi$
$278$	2.38362e8	−	2.38362e8i	0.665397	−	0.665397i
$279$	−2.36015e8	−	1.50791e8i	−0.650616	−	0.415683i
$280$	−7.47829e7	+	4.57671e8i	−0.203587	+	1.24595i
$281$		−	6.23605e8i		−	1.67663i	−0.545185	−	0.838315i	$-0.683541\pi$
$281$		−	6.23605e8i		−	1.67663i	0.545185	−	0.838315i	$-0.316459\pi$
$282$	−5.70671e7	+	1.95314e8i	−0.151535	+	0.518634i
$283$	2.80653e7	+	2.80653e7i	0.0736067	+	0.0736067i	0.742952	−	0.669345i	$-0.233425\pi$
$283$	2.80653e7	+	2.80653e7i	0.0736067	+	0.0736067i	−0.669345	+	0.742952i	$0.733425\pi$
$284$	−5.29480e7			−0.137162
$285$	5.63209e7	−	1.17722e8i	0.144116	−	0.301232i
$286$	1.41742e8			0.358275
$287$	−1.69488e7	−	1.69488e7i	−0.0423206	−	0.0423206i
$288$	−8.11012e7	−	3.68097e8i	−0.200057	−	0.908005i
$289$			6.79290e8i			1.65544i
$290$	1.69154e8	+	2.35229e8i	0.407276	+	0.566368i
$291$	−4.15071e8	+	2.27364e8i	−0.987409	+	0.540873i
$292$	−5.89496e7	+	5.89496e7i	−0.138561	+	0.138561i
$293$	3.23279e7	−	3.23279e7i	0.0750829	−	0.0750829i	−0.668568	−	0.743651i	$-0.733092\pi$
$293$	3.23279e7	−	3.23279e7i	0.0750829	−	0.0750829i	0.743651	+	0.668568i	$0.233092\pi$
$294$	1.19390e8	−	6.53982e7i	0.274001	−	0.150090i
$295$	5.09328e8	+	8.32237e7i	1.15510	+	0.188743i
$296$			5.87428e8i			1.31654i
$297$	−1.52341e8	+	1.33073e8i	−0.337419	+	0.294742i
$298$	−3.14864e8	−	3.14864e8i	−0.689232	−	0.689232i
$299$	3.24200e8			0.701396
$300$	1.44177e8	−	2.07076e8i	0.308298	−	0.442798i
$301$	−1.27528e8			−0.269541
$302$	1.38017e8	+	1.38017e8i	0.288342	+	0.288342i
$303$	−1.24603e7	+	4.26457e7i	−0.0257323	+	0.0880696i
$304$		−	2.76978e7i		−	0.0565441i
$305$	4.35337e8	+	7.11336e7i	0.878569	+	0.143557i
$306$	2.98392e8	−	4.67036e8i	0.595336	−	0.931805i
$307$	2.80567e8	−	2.80567e8i	0.553416	−	0.553416i	−0.374009	−	0.927425i	$-0.622017\pi$
$307$	2.80567e8	−	2.80567e8i	0.553416	−	0.553416i	0.927425	+	0.374009i	$0.122017\pi$
$308$	−1.05921e8	+	1.05921e8i	−0.206565	+	0.206565i
$309$	−3.02766e7	−	5.52724e7i	−0.0583784	−	0.106575i
$310$	−1.60433e8	−	2.23103e8i	−0.305864	−	0.425342i
$311$			2.08937e8i			0.393871i	0.980416	+	0.196936i	$0.0630990\pi$
$311$			2.08937e8i			0.393871i	−0.980416	+	0.196936i	$0.936901\pi$
$312$	−6.33962e8	−	1.85232e8i	−1.18174	−	0.345283i
$313$	2.05330e8	+	2.05330e8i	0.378484	+	0.378484i	0.870555	−	0.492071i	$-0.163760\pi$
$313$	2.05330e8	+	2.05330e8i	0.378484	+	0.378484i	−0.492071	+	0.870555i	$0.663760\pi$
$314$	−2.48610e8			−0.453174
$315$	−6.69375e8	+	3.67812e7i	−1.20665	+	0.0663038i
$316$	4.29581e8			0.765843
$317$	3.73944e8	+	3.73944e8i	0.659325	+	0.659325i	0.955220	−	0.295895i	$-0.0956179\pi$
$317$	3.73944e8	+	3.73944e8i	0.659325	+	0.659325i	−0.295895	+	0.955220i	$0.595618\pi$
$318$	2.63291e8	+	7.69287e7i	0.459135	+	0.134151i
$319$			2.67045e8i			0.460593i
$320$	7.56441e7	−	4.62941e8i	0.129048	−	0.789770i
$321$	2.30166e8	+	4.20186e8i	0.388394	+	0.709046i
$322$	2.06749e8	−	2.06749e8i	0.345103	−	0.345103i
$323$	−2.33034e8	+	2.33034e8i	−0.384778	+	0.384778i
$324$	2.99740e8	−	1.38820e8i	0.489595	−	0.226748i
$325$	−3.24736e8	−	6.53035e8i	−0.524734	−	1.05522i
$326$			1.70901e8i			0.273202i
$327$	3.23922e8	−	1.10863e9i	0.512299	−	1.75336i
$328$	2.33807e7	+	2.33807e7i	0.0365847	+	0.0365847i
$329$	−6.21560e8			−0.962271
$330$	−1.87161e8	+	6.60293e7i	−0.286693	+	0.101144i
$331$	−8.42634e8			−1.27715			−0.638573	−	0.769561i	$-0.720475\pi$
$331$	−8.42634e8			−1.27715			−0.638573	+	0.769561i	$0.720475\pi$
$332$	−3.05473e8	−	3.05473e8i	−0.458131	−	0.458131i
$333$	−8.29298e8	+	1.82716e8i	−1.23071	+	0.271157i
$334$			2.25749e8i			0.331523i
$335$	2.50724e8	−	1.80296e8i	0.364367	−	0.262016i
$336$	−1.24788e8	+	6.83553e7i	−0.179468	+	0.0983071i
$337$	7.03986e7	−	7.03986e7i	0.100198	−	0.100198i	−0.655231	−	0.755429i	$-0.727429\pi$
$337$	7.03986e7	−	7.03986e7i	0.100198	−	0.100198i	0.755429	+	0.655231i	$0.227429\pi$
$338$	−1.32452e8	+	1.32452e8i	−0.186574	+	0.186574i
$339$	−7.41589e8	+	4.06220e8i	−1.03387	+	0.566321i
$340$	−5.17334e8	+	3.72015e8i	−0.713830	+	0.513315i
$341$		−	2.53278e8i		−	0.345905i
$342$	1.63699e8	−	3.60670e7i	0.221286	−	0.0487550i
$343$	−3.44601e8	−	3.44601e8i	−0.461092	−	0.461092i
$344$	1.75924e8			0.233008
$345$	−4.28086e8	+	1.51026e8i	−0.561260	+	0.198009i
$346$	6.35162e8			0.824362
$347$	6.56662e8	+	6.56662e8i	0.843701	+	0.843701i	0.989338	−	0.145637i	$-0.0465231\pi$
$347$	6.56662e8	+	6.56662e8i	0.843701	+	0.843701i	−0.145637	+	0.989338i	$0.546523\pi$
$348$	1.22305e8	−	4.18591e8i	0.155566	−	0.532430i
$349$			6.73524e8i			0.848133i	0.905631	+	0.424067i	$0.139398\pi$
$349$			6.73524e8i			0.848133i	−0.905631	+	0.424067i	$0.860602\pi$
$350$	−6.23546e8	−	2.09364e8i	−0.777375	−	0.261014i
$351$	6.43104e7	−	9.52608e8i	0.0793791	−	1.17582i
$352$	2.41027e8	−	2.41027e8i	0.294555	−	0.294555i
$353$	3.36761e8	−	3.36761e8i	0.407484	−	0.407484i	−0.473377	−	0.880860i	$-0.656965\pi$
$353$	3.36761e8	−	3.36761e8i	0.407484	−	0.407484i	0.880860	+	0.473377i	$0.156965\pi$
$354$	3.18464e8	+	5.81383e8i	0.381548	+	0.696548i
$355$	3.45564e7	−	2.11484e8i	0.0409948	−	0.250888i
$356$			1.36532e8i			0.160384i
$357$	1.62501e9	+	4.74797e8i	1.89024	+	0.552292i
$358$	3.15983e8	+	3.15983e8i	0.363977	+	0.363977i
$359$	3.70610e8			0.422753			0.211377	−	0.977405i	$-0.432205\pi$
$359$	3.70610e8			0.422753			0.211377	+	0.977405i	$0.432205\pi$
$360$	9.23397e8	−	5.07393e7i	1.04311	−	0.0573173i
$361$	7.94196e8			0.888490
$362$	6.80129e7	+	6.80129e7i	0.0753548	+	0.0753548i
$363$	6.99167e8	+	2.04284e8i	0.767199	+	0.224161i
$364$		−	7.07055e8i		−	0.768420i
$365$	−1.96983e8	−	2.73929e8i	−0.212033	−	0.294858i
$366$	2.72200e8	+	4.96924e8i	0.290205	+	0.529793i
$367$	−1.07938e9	+	1.07938e9i	−1.13984	+	1.13984i	−0.151363	+	0.988478i	$0.548366\pi$
$367$	−1.07938e9	+	1.07938e9i	−1.13984	+	1.13984i	−0.988478	+	0.151363i	$0.951634\pi$
$368$	−6.81269e7	+	6.81269e7i	−0.0712609	+	0.0712609i
$369$	−2.57352e7	+	4.02800e7i	−0.0266646	+	0.0417347i
$370$	−8.22286e8	−	1.34361e8i	−0.843951	−	0.137901i
$371$			8.37887e8i			0.851877i
$372$	−1.15999e8	+	3.97011e8i	−0.116830	+	0.399855i
$373$	−3.15571e8	−	3.15571e8i	−0.314859	−	0.314859i	0.531930	−	0.846789i	$-0.321467\pi$
$373$	−3.15571e8	−	3.15571e8i	−0.314859	−	0.314859i	−0.846789	+	0.531930i	$0.821467\pi$
$374$	5.01196e8			0.495402
$375$	7.33006e8	+	7.11017e8i	0.717791	+	0.696259i
$376$	8.57437e8			0.831850
$377$	−8.91299e8	−	8.91299e8i	−0.856700	−	0.856700i
$378$	−5.66487e8	−	6.48511e8i	−0.539472	−	0.617584i
$379$		−	1.14690e8i		−	0.108215i	−0.998535	−	0.0541076i	$-0.982769\pi$
$379$		−	1.14690e8i		−	0.108215i	0.998535	−	0.0541076i	$-0.0172314\pi$
$380$	−1.90201e8	−	3.10787e7i	−0.177816	−	0.0290549i
$381$	−1.67845e9	+	9.19405e8i	−1.55479	+	0.851666i
$382$	−5.92344e8	+	5.92344e8i	−0.543691	+	0.543691i
$383$	1.45747e9	−	1.45747e9i	1.32557	−	1.32557i	0.416381	−	0.909190i	$-0.363298\pi$
$383$	1.45747e9	−	1.45747e9i	1.32557	−	1.32557i	0.909190	−	0.416381i	$-0.136702\pi$
$384$	−3.76382e8	+	2.06171e8i	−0.339211	+	0.185810i
$385$	−3.53941e8	−	4.92200e8i	−0.316096	−	0.439571i
$386$		−	9.43951e8i		−	0.835399i
$387$	5.47202e7	+	2.48360e8i	0.0479909	+	0.217818i
$388$	4.94206e8	+	4.94206e8i	0.429533	+	0.429533i
$389$	−2.18691e9			−1.88368			−0.941841	−	0.336058i	$-0.890906\pi$
$389$	−2.18691e9			−1.88368			−0.941841	+	0.336058i	$0.890906\pi$
$390$	4.04294e8	−	8.45058e8i	0.345121	−	0.721374i
$391$	1.14637e9			0.969850
$392$	−4.05614e8	−	4.05614e8i	−0.340104	−	0.340104i
$393$	−7.08102e6	+	2.42350e7i	−0.00588467	+	0.0201405i
$394$		−	3.60929e8i		−	0.297293i
$395$	−2.80365e8	+	1.71583e9i	−0.228893	+	1.40082i
$396$	2.51730e8	+	1.60832e8i	0.203705	+	0.130149i
$397$	4.61752e8	−	4.61752e8i	0.370375	−	0.370375i	−0.497239	−	0.867614i	$-0.665653\pi$
$397$	4.61752e8	−	4.61752e8i	0.370375	−	0.370375i	0.867614	+	0.497239i	$0.165653\pi$
$398$	−2.69112e8	+	2.69112e8i	−0.213965	+	0.213965i
$399$	2.45990e8	+	4.49076e8i	0.193871	+	0.353927i
$400$	2.05468e8	+	6.89884e7i	0.160522	+	0.0538972i
$401$		−	1.64048e9i		−	1.27047i	−0.772318	−	0.635236i	$-0.780903\pi$
$401$		−	1.64048e9i		−	1.27047i	0.772318	−	0.635236i	$-0.219097\pi$
$402$	3.80748e8	+	1.11248e8i	0.292312	+	0.0854082i
$403$	8.45350e8	+	8.45350e8i	0.643382	+	0.643382i
$404$	6.56121e7			0.0495050
$405$	3.58848e8	+	1.28782e9i	0.268422	+	0.963301i
$406$	−1.13680e9			−0.843031
$407$	−5.43018e8	−	5.43018e8i	−0.399240	−	0.399240i
$408$	−2.24168e9	−	6.54978e8i	−1.63404	−	0.477437i
$409$		−	9.26505e8i		−	0.669601i	−0.942289	−	0.334800i	$-0.891331\pi$
$409$		−	9.26505e8i		−	0.669601i	0.942289	−	0.334800i	$-0.108669\pi$
$410$	−3.80763e7	+	2.73807e7i	−0.0272842	+	0.0196201i
$411$	−1.02901e9	−	1.87854e9i	−0.731091	−	1.33467i
$412$	−6.58103e7	+	6.58103e7i	−0.0463611	+	0.0463611i
$413$	−1.43182e9	+	1.43182e9i	−1.00015	+	1.00015i
$414$	−4.91354e8	−	3.13930e8i	−0.340325	−	0.217436i
$415$	1.41948e9	−	1.02075e9i	0.974904	−	0.701054i
$416$			1.60892e9i			1.09574i
$417$	5.75899e8	−	1.97103e9i	0.388929	−	1.33112i
$418$	1.07189e8	+	1.07189e8i	0.0717847	+	0.0717847i
$419$	2.35565e9			1.56445			0.782226	−	0.622995i	$-0.214084\pi$
$419$	2.35565e9			1.56445			0.782226	+	0.622995i	$0.214084\pi$
$420$	3.29377e8	+	9.33623e8i	0.216930	+	0.614892i
$421$	−7.12264e8			−0.465215			−0.232608	−	0.972571i	$-0.574726\pi$
$421$	−7.12264e8			−0.465215			−0.232608	+	0.972571i	$0.574726\pi$
$422$	4.66354e8	+	4.66354e8i	0.302080	+	0.302080i
$423$	2.66701e8	+	1.21048e9i	0.171330	+	0.777620i
$424$		−	1.15586e9i		−	0.736418i
$425$	−1.14826e9	−	2.30912e9i	−0.725571	−	1.45910i
$426$	2.41403e8	−	1.32234e8i	0.151290	−	0.0828721i
$427$	−1.22382e9	+	1.22382e9i	−0.760711	+	0.760711i
$428$	5.00297e8	−	5.00297e8i	0.308443	−	0.308443i
$429$	7.57263e8	−	4.14806e8i	0.463070	−	0.253656i
$430$	−4.02387e7	+	2.46260e8i	−0.0244065	+	0.149367i
$431$			1.94254e9i			1.16869i	0.811505	+	0.584346i	$0.198649\pi$
$431$			1.94254e9i			1.16869i	−0.811505	+	0.584346i	$0.801351\pi$
$432$	1.86666e8	+	2.13694e8i	0.111397	+	0.127526i
$433$	8.06092e8	+	8.06092e8i	0.477174	+	0.477174i	0.904227	−	0.427053i	$-0.140448\pi$
$433$	8.06092e8	+	8.06092e8i	0.477174	+	0.477174i	−0.427053	+	0.904227i	$0.640448\pi$
$434$	1.07820e9			0.633117
$435$	1.59211e9	+	7.61700e8i	0.927387	+	0.443682i
$436$	−1.70568e9			−0.985586
$437$	2.45168e8	+	2.45168e8i	0.140533	+	0.140533i
$438$	1.21544e8	−	4.15988e8i	0.0691153	−	0.236549i
$439$		−	1.31334e9i		−	0.740886i	−0.928855	−	0.370443i	$-0.879206\pi$
$439$		−	1.31334e9i		−	0.740886i	0.928855	−	0.370443i	$-0.120794\pi$
$440$	4.88259e8	+	6.78986e8i	0.273254	+	0.379994i
$441$	4.46460e8	−	6.98788e8i	0.247884	−	0.387981i
$442$	−1.67281e9	+	1.67281e9i	−0.921445	+	0.921445i
$443$	6.81104e7	−	6.81104e7i	0.0372221	−	0.0372221i	−0.688251	−	0.725473i	$-0.741621\pi$
$443$	6.81104e7	−	6.81104e7i	0.0372221	−	0.0372221i	0.725473	+	0.688251i	$0.241621\pi$
$444$	6.02479e8	+	1.09988e9i	0.326664	+	0.596353i
$445$	−5.45335e8	−	8.91073e7i	−0.293362	−	0.0479351i
$446$		−	1.20373e9i		−	0.642479i
$447$	−2.60363e9	−	7.60731e8i	−1.37880	−	0.402861i
$448$	1.30142e9	+	1.30142e9i	0.683824	+	0.683824i
$449$	1.41987e9			0.740263			0.370131	−	0.928979i	$-0.379313\pi$
$449$	1.41987e9			0.740263			0.370131	+	0.928979i	$0.379313\pi$
$450$	−1.40181e8	+	1.30418e9i	−0.0725179	+	0.674676i
$451$	−4.32263e7			−0.0221886
$452$	8.82975e8	+	8.82975e8i	0.449743	+	0.449743i
$453$	1.14127e9	+	3.33458e8i	0.576826	+	0.168538i
$454$			2.90800e8i			0.145848i
$455$	2.82411e9	+	4.61458e8i	1.40554	+	0.229663i
$456$	−3.39341e8	−	6.19496e8i	−0.167595	−	0.305958i
$457$	2.19576e8	−	2.19576e8i	0.107616	−	0.107616i	−0.651248	−	0.758865i	$-0.725754\pi$
$457$	2.19576e8	−	2.19576e8i	0.107616	−	0.107616i	0.758865	+	0.651248i	$0.225754\pi$
$458$	−9.50710e8	+	9.50710e8i	−0.462401	+	0.462401i
$459$	2.27401e8	−	3.36841e9i	0.109761	−	1.62585i
$460$	3.91386e8	+	5.44272e8i	0.187479	+	0.260713i
$461$			2.01606e9i			0.958407i	0.877704	+	0.479203i	$0.159074\pi$
$461$			2.01606e9i			0.958407i	−0.877704	+	0.479203i	$0.840926\pi$
$462$	2.18392e8	−	7.47454e8i	0.103036	−	0.352645i
$463$	−1.31234e9	−	1.31234e9i	−0.614490	−	0.614490i	0.329623	−	0.944113i	$-0.393078\pi$
$463$	−1.31234e9	−	1.31234e9i	−0.614490	−	0.614490i	−0.944113	+	0.329623i	$0.893078\pi$
$464$	3.74593e8			0.174079
$465$	−1.51003e9	−	7.22432e8i	−0.696468	−	0.333205i
$466$	6.94778e8			0.318050
$467$	−3.60458e8	−	3.60458e8i	−0.163774	−	0.163774i	0.620462	−	0.784236i	$-0.286945\pi$
$467$	−3.60458e8	−	3.60458e8i	−0.163774	−	0.163774i	−0.784236	+	0.620462i	$0.786945\pi$
$468$	−1.37698e9	+	3.03385e8i	−0.620966	+	0.136815i
$469$			1.21168e9i			0.542355i
$470$	−1.96119e8	+	1.20025e9i	−0.0871321	+	0.533247i
$471$	−1.32821e9	+	7.27556e8i	−0.585727	+	0.320844i
$472$	1.97519e9	−	1.97519e9i	0.864592	−	0.864592i
$473$	−1.62624e8	+	1.62624e8i	−0.0706597	+	0.0706597i
$474$	−1.95857e9	+	1.07285e9i	−0.844723	+	0.462714i
$475$	2.48268e8	−	7.39416e8i	0.106290	−	0.316564i
$476$		−	2.50014e9i		−	1.06253i
$477$	1.63178e9	−	3.59523e8i	0.688409	−	0.151674i
$478$	−3.13304e8	−	3.13304e8i	−0.131211	−	0.131211i
$479$	−2.41427e9			−1.00372			−0.501859	−	0.864950i	$-0.667350\pi$
$479$	−2.41427e9			−1.00372			−0.501859	+	0.864950i	$0.667350\pi$
$480$	−7.49505e8	−	2.12448e9i	−0.309336	−	0.876817i
$481$	3.62480e9			1.48517
$482$	−8.37567e8	−	8.37567e8i	−0.340687	−	0.340687i
$483$	4.99520e8	−	1.70962e9i	0.201715	−	0.690374i
$484$		−	1.07570e9i		−	0.431252i
$485$	−2.29650e9	+	1.65141e9i	−0.914049	+	0.657293i
$486$	−1.01990e9	+	1.38149e9i	−0.403024	+	0.545911i
$487$	−2.64870e9	+	2.64870e9i	−1.03916	+	1.03916i	−0.0399577	+	0.999201i	$0.512722\pi$
$487$	−2.64870e9	+	2.64870e9i	−1.03916	+	1.03916i	−0.999201	+	0.0399577i	$0.987278\pi$
$488$	1.68825e9	−	1.68825e9i	0.657608	−	0.657608i
$489$	5.00142e8	+	9.13051e8i	0.193425	+	0.353113i
$490$	6.60558e8	−	4.75007e8i	0.253644	−	0.182395i
$491$		−	9.53317e8i		−	0.363456i	−0.983349	−	0.181728i	$-0.941831\pi$
$491$		−	9.53317e8i		−	0.363456i	0.983349	−	0.181728i	$-0.0581691\pi$
$492$	6.77569e7	+	1.97973e7i	0.0256493	+	0.00749425i
$493$	−3.15162e9	−	3.15162e9i	−1.18460	−	1.18460i
$494$	−7.15514e8			−0.267039
$495$	−8.06685e8	+	9.00492e8i	−0.298941	+	0.333704i
$496$	−3.55282e8			−0.130733
$497$	5.94525e8	+	5.94525e8i	0.217232	+	0.217232i
$498$	2.15562e9	+	6.29834e8i	0.782115	+	0.228519i
$499$			3.28649e9i			1.18408i	0.805910	+	0.592038i	$0.201677\pi$
$499$			3.28649e9i			1.18408i	−0.805910	+	0.592038i	$0.798323\pi$
$500$	7.04293e8	−	1.33354e9i	0.251975	−	0.477102i
$501$	6.60653e8	+	1.20608e9i	0.234715	+	0.428492i
$502$	2.43453e9	−	2.43453e9i	0.858919	−	0.858919i
$503$	−1.80566e9	+	1.80566e9i	−0.632628	+	0.632628i	−0.948727	−	0.316098i	$-0.897627\pi$
$503$	−1.80566e9	+	1.80566e9i	−0.632628	+	0.632628i	0.316098	+	0.948727i	$0.397627\pi$
$504$	−1.95359e9	+	3.05771e9i	−0.679714	+	1.06387i
$505$	−4.28216e7	+	2.62067e8i	−0.0147959	+	0.0905510i
$506$		−	5.27294e8i		−	0.180936i
$507$	−3.20013e8	+	1.09525e9i	−0.109053	+	0.373239i
$508$	1.99845e9	+	1.99845e9i	0.676349	+	0.676349i
$509$	−3.91111e9			−1.31458			−0.657291	−	0.753637i	$-0.728298\pi$
$509$	−3.91111e9			−1.31458			−0.657291	+	0.753637i	$0.728298\pi$
$510$	1.42958e9	−	2.98811e9i	0.477213	−	0.997474i
$511$	1.32383e9			0.438892
$512$	−7.17975e8	−	7.17975e8i	−0.236409	−	0.236409i
$513$	7.69020e8	−	6.71754e8i	0.251494	−	0.219685i
$514$		−	2.10621e9i		−	0.684117i
$515$	−2.19908e8	−	3.05810e8i	−0.0709441	−	0.0986567i
$516$	3.29394e8	−	1.80432e8i	0.105546	−	0.0578149i
$517$	−7.92615e8	+	7.92615e8i	−0.252258	+	0.252258i
$518$	2.31161e9	−	2.31161e9i	0.730736	−	0.730736i
$519$	3.39339e9	−	1.85880e9i	1.06549	−	0.583642i
$520$	−3.89584e9	−	6.36577e8i	−1.21504	−	0.198536i
$521$		−	3.38976e8i		−	0.105011i	−0.998621	−	0.0525057i	$-0.983279\pi$
$521$		−	3.38976e8i		−	0.105011i	0.998621	−	0.0525057i	$-0.0167208\pi$
$522$	4.87782e8	+	2.21391e9i	0.150099	+	0.681261i
$523$	1.40483e8	+	1.40483e8i	0.0429405	+	0.0429405i	0.728251	−	0.685311i	$-0.240334\pi$
$523$	1.40483e8	+	1.40483e8i	0.0429405	+	0.0429405i	−0.685311	+	0.728251i	$0.740334\pi$
$524$	3.72866e7			0.0113212
$525$	−3.94403e9	+	7.06267e8i	−1.18955	+	0.213016i
$526$	−2.54351e9			−0.762049
$527$	2.98915e9	+	2.98915e9i	0.889631	+	0.889631i
$528$	−7.19635e7	+	2.46297e8i	−0.0212762	+	0.0728183i
$529$			2.19877e9i			0.645780i
$530$	1.61798e9	+	2.64377e8i	0.472072	+	0.0771361i
$531$	3.40283e9	+	2.17409e9i	0.986301	+	0.630154i
$532$	5.34694e8	−	5.34694e8i	0.153962	−	0.153962i
$533$	1.44274e8	−	1.44274e8i	0.0412707	−	0.0412707i
$534$	−3.40979e8	−	6.22485e8i	−0.0969020	−	0.176903i
$535$	1.67176e9	+	2.32480e9i	0.471994	+	0.656367i
$536$		−	1.67150e9i		−	0.468847i
$537$	2.61288e9	+	7.63436e8i	0.728132	+	0.212747i
$538$	1.45485e9	+	1.45485e9i	0.402791	+	0.402791i
$539$	7.49900e8			0.206273
$540$	1.67689e9	−	1.04206e9i	0.458276	−	0.284783i
$541$	1.95221e9			0.530074			0.265037	−	0.964238i	$-0.414616\pi$
$541$	1.95221e9			0.530074			0.265037	+	0.964238i	$0.414616\pi$
$542$	−3.56200e8	−	3.56200e8i	−0.0960939	−	0.0960939i
$543$	5.62402e8	+	1.64324e8i	0.150747	+	0.0440454i
$544$			5.68913e9i			1.51513i
$545$	1.11321e9	−	6.81280e9i	0.294570	−	1.80276i
$546$	1.76582e9	+	3.22365e9i	0.464271	+	0.847565i
$547$	4.20016e9	−	4.20016e9i	1.09726	−	1.09726i	0.102533	−	0.994730i	$-0.467305\pi$
$547$	4.20016e9	−	4.20016e9i	1.09726	−	1.09726i	0.994730	−	0.102533i	$-0.0326946\pi$
$548$	−2.23669e9	+	2.23669e9i	−0.580594	+	0.580594i
$549$	2.90849e9	+	1.85826e9i	0.750179	+	0.479294i
$550$	−1.06213e9	+	5.28166e8i	−0.272212	+	0.135363i
$551$		−	1.34805e9i		−	0.343301i
$552$	−6.89083e8	+	2.35841e9i	−0.174375	+	0.596804i
$553$	−4.82353e9	−	4.82353e9i	−1.21291	−	1.21291i
$554$	−5.83585e8			−0.145821
$555$	−4.78632e9	+	1.68859e9i	−1.18844	+	0.419274i
$556$	−3.03251e9			−0.748240
$557$	−7.58882e6	−	7.58882e6i	−0.00186072	−	0.00186072i	0.706176	−	0.708037i	$-0.250419\pi$
$557$	−7.58882e6	−	7.58882e6i	−0.00186072	−	0.00186072i	−0.708037	+	0.706176i	$0.750419\pi$
$558$	−4.62635e8	−	2.09978e9i	−0.112725	−	0.511627i
$559$		−	1.08556e9i		−	0.262854i
$560$	−6.90426e8	+	4.96486e8i	−0.166134	+	0.119467i
$561$	2.67767e9	−	1.46675e9i	0.640306	−	0.350740i
$562$	3.38524e9	−	3.38524e9i	0.804474	−	0.804474i
$563$	−1.08634e8	+	1.08634e8i	−0.0256558	+	0.0256558i	−0.719818	−	0.694163i	$-0.755775\pi$
$563$	−1.08634e8	+	1.08634e8i	−0.0256558	+	0.0256558i	0.694163	+	0.719818i	$0.255775\pi$
$564$	1.60543e9	−	8.79407e8i	0.376803	−	0.206402i
$565$	−4.10304e9	+	2.95050e9i	−0.957054	+	0.688218i
$566$			3.04705e8i			0.0706353i
$567$	−4.92435e9	−	1.80689e9i	−1.13451	−	0.416285i
$568$	−8.20142e8	−	8.20142e8i	−0.187789	−	0.187789i
$569$	−2.06965e9			−0.470982			−0.235491	−	0.971877i	$-0.575670\pi$
$569$	−2.06965e9			−0.470982			−0.235491	+	0.971877i	$0.575670\pi$
$570$	9.44792e8	−	3.33317e8i	0.213685	−	0.0753869i
$571$	−5.59476e9			−1.25764			−0.628818	−	0.777553i	$-0.716461\pi$
$571$	−5.59476e9			−1.25764			−0.628818	+	0.777553i	$0.716461\pi$
$572$	−9.01638e8	−	9.01638e8i	−0.201440	−	0.201440i
$573$	−1.43114e9	+	4.89813e9i	−0.317791	+	1.08765i
$574$		−	1.84013e8i		−	0.0406122i
$575$	−2.42936e9	+	1.20805e9i	−0.532911	+	0.265002i
$576$	1.97609e9	−	3.09292e9i	0.430851	−	0.674357i
$577$	1.90691e9	−	1.90691e9i	0.413252	−	0.413252i	−0.469618	−	0.882870i	$-0.655608\pi$
$577$	1.90691e9	−	1.90691e9i	0.413252	−	0.413252i	0.882870	+	0.469618i	$0.155608\pi$
$578$	−3.68752e9	+	3.68752e9i	−0.794305	+	0.794305i
$579$	−2.76247e9	−	5.04312e9i	−0.591456	−	1.07975i
$580$	4.20318e8	−	2.57234e9i	0.0894499	−	0.547432i
$581$			6.85999e9i			1.45113i
$582$	−3.48745e9	−	1.01897e9i	−0.733294	−	0.214255i
$583$	1.06848e9	+	1.06848e9i	0.223319	+	0.223319i
$584$	−1.82621e9			−0.379407
$585$	−3.13093e8	−	5.69794e9i	−0.0646589	−	1.17672i
$586$	3.50984e8			0.0720519
$587$	−2.35423e9	−	2.35423e9i	−0.480413	−	0.480413i	0.424850	−	0.905264i	$-0.360327\pi$
$587$	−2.35423e9	−	2.35423e9i	−0.480413	−	0.480413i	−0.905264	+	0.424850i	$0.860327\pi$
$588$	−1.17546e9	−	3.43449e8i	−0.238445	−	0.0696693i
$589$			1.27855e9i			0.257819i
$590$	2.31310e9	+	3.21666e9i	0.463674	+	0.644798i
$591$	−1.05626e9	−	1.92829e9i	−0.210481	−	0.384251i
$592$	−7.61710e8	+	7.61710e8i	−0.150891	+	0.150891i
$593$	5.72337e9	−	5.72337e9i	1.12709	−	1.12709i	0.136448	−	0.990647i	$-0.456431\pi$
$593$	5.72337e9	−	5.72337e9i	1.12709	−	1.12709i	0.990647	−	0.136448i	$-0.0435685\pi$
$594$	−1.54937e9	−	1.04598e8i	−0.303321	−	0.0204771i
$595$	9.98603e9	+	1.63171e9i	1.94350	+	0.317565i
$596$			4.00578e9i			0.775043i
$597$	−6.50193e8	+	2.22530e9i	−0.125064	+	0.428035i
$598$	1.75992e9	+	1.75992e9i	0.336541	+	0.336541i
$599$	5.51876e9			1.04917			0.524587	−	0.851357i	$-0.324220\pi$
$599$	5.51876e9			1.04917			0.524587	+	0.851357i	$0.324220\pi$
$600$	5.44076e9	−	9.74290e8i	1.02833	−	0.184144i
$601$	2.18409e9			0.410403			0.205201	−	0.978720i	$-0.434215\pi$
$601$	2.18409e9			0.410403			0.205201	+	0.978720i	$0.434215\pi$
$602$	−6.92287e8	−	6.92287e8i	−0.129330	−	0.129330i
$603$	2.35974e9	−	5.19911e8i	0.438282	−	0.0965647i
$604$		−	1.75589e9i		−	0.324241i
$605$	4.29654e9	+	7.02051e8i	0.788815	+	0.128892i
$606$	−2.99143e8	+	1.63861e8i	−0.0546039	+	0.0299104i
$607$	−1.38773e9	+	1.38773e9i	−0.251852	+	0.251852i	−0.821730	−	0.569878i	$-0.806991\pi$
$607$	−1.38773e9	+	1.38773e9i	−0.251852	+	0.251852i	0.569878	+	0.821730i	$0.306991\pi$
$608$	−1.21671e9	+	1.21671e9i	−0.219545	+	0.219545i
$609$	−6.07343e9	+	3.32685e9i	−1.08962	+	0.596860i
$610$	1.97707e9	+	2.74937e9i	0.352670	+	0.490432i
$611$		−	5.29092e9i		−	0.938398i
$612$	−4.86899e9	+	1.07277e9i	−0.858636	+	0.189180i
$613$	−5.81285e8	−	5.81285e8i	−0.101924	−	0.101924i	0.654306	−	0.756230i	$-0.272961\pi$
$613$	−5.81285e8	−	5.81285e8i	−0.101924	−	0.101924i	−0.756230	+	0.654306i	$0.772961\pi$
$614$	3.04611e9			0.531075
$615$	−1.23296e8	+	2.57713e8i	−0.0213739	+	0.0446760i
$616$	−3.28136e9			−0.565615
$617$	1.83711e9	+	1.83711e9i	0.314874	+	0.314874i	0.846794	−	0.531920i	$-0.178529\pi$
$617$	1.83711e9	+	1.83711e9i	0.314874	+	0.314874i	−0.531920	+	0.846794i	$0.678529\pi$
$618$	1.35690e8	−	4.64403e8i	0.0231253	−	0.0791471i
$619$		−	7.14479e9i		−	1.21080i	−0.795922	−	0.605399i	$-0.793013\pi$
$619$		−	7.14479e9i		−	1.21080i	0.795922	−	0.605399i	$-0.206987\pi$
$620$	−3.98649e8	+	2.43973e9i	−0.0671768	+	0.411121i
$621$	−3.54380e9	−	2.39242e8i	−0.593812	−	0.0400881i
$622$	−1.13421e9	+	1.13421e9i	−0.188986	+	0.188986i
$623$	1.53305e9	−	1.53305e9i	0.254008	−	0.254008i
$624$	−5.81863e8	−	1.06224e9i	−0.0958682	−	0.175015i
$625$	4.86676e9	+	3.68341e9i	0.797371	+	0.603490i
$626$			2.22926e9i			0.363205i
$627$	8.86349e8	+	2.58975e8i	0.143605	+	0.0419586i
$628$	1.58144e9	+	1.58144e9i	0.254797	+	0.254797i
$629$	1.28172e10			2.05361
$630$	−3.83337e9	−	3.43403e9i	−0.610785	−	0.547158i
$631$	−4.24240e9			−0.672216			−0.336108	−	0.941823i	$-0.609111\pi$
$631$	−4.24240e9			−0.672216			−0.336108	+	0.941823i	$0.609111\pi$
$632$	6.65403e9	+	6.65403e9i	1.04852	+	1.04852i
$633$	3.85630e9	+	1.12674e9i	0.604308	+	0.176568i
$634$			4.05991e9i			0.632709i
$635$	−9.28649e9	+	6.67792e9i	−1.43927	+	1.03498i
$636$	−1.18547e9	−	2.16418e9i	−0.182723	−	0.333575i
$637$	−2.50289e9	+	2.50289e9i	−0.383667	+	0.383667i
$638$	−1.44965e9	+	1.44965e9i	−0.221000	+	0.221000i
$639$	9.02732e8	−	1.41293e9i	0.136869	−	0.214224i
$640$	−2.08244e9	+	1.49748e9i	−0.314009	+	0.225804i
$641$		−	4.48952e9i		−	0.673281i	−0.941633	−	0.336641i	$-0.890709\pi$
$641$		−	4.48952e9i		−	0.673281i	0.941633	−	0.336641i	$-0.109291\pi$
$642$	−1.03153e9	+	3.53043e9i	−0.153854	+	0.526569i
$643$	−6.37305e9	−	6.37305e9i	−0.945385	−	0.945385i	0.0531986	−	0.998584i	$-0.483058\pi$
$643$	−6.37305e9	−	6.37305e9i	−0.945385	−	0.945385i	−0.998584	+	0.0531986i	$0.983058\pi$
$644$	−2.63032e9			−0.388068
$645$	5.05702e8	+	1.43342e9i	0.0742054	+	0.210336i
$646$	−2.53005e9			−0.369245
$647$	−5.82867e9	−	5.82867e9i	−0.846066	−	0.846066i	0.143573	−	0.989640i	$-0.454141\pi$
$647$	−5.82867e9	−	5.82867e9i	−0.846066	−	0.846066i	−0.989640	+	0.143573i	$0.954141\pi$
$648$	6.79311e9	+	2.49259e9i	0.980745	+	0.359864i
$649$			3.65172e9i			0.524375i
$650$	1.78217e9	−	5.30783e9i	0.254538	−	0.758089i
$651$	5.76033e9	−	3.15534e9i	0.818302	−	0.448242i
$652$	1.08713e9	−	1.08713e9i	0.153608	−	0.153608i
$653$	6.81743e8	−	6.81743e8i	0.0958130	−	0.0958130i	−0.657576	−	0.753389i	$-0.728418\pi$
$653$	6.81743e8	−	6.81743e8i	0.0958130	−	0.0958130i	0.753389	+	0.657576i	$0.228418\pi$
$654$	7.77662e9	−	4.25980e9i	1.08710	−	0.595480i
$655$	−2.43350e7	+	1.48930e8i	−0.00338366	+	0.0207079i
$656$			6.06350e7i			0.00838609i
$657$	−5.68031e8	−	2.57814e9i	−0.0781435	−	0.354673i
$658$	−3.37414e9	−	3.37414e9i	−0.461713	−	0.461713i
$659$	−8.04668e9			−1.09526			−0.547631	−	0.836720i	$-0.684470\pi$
$659$	−8.04668e9			−1.09526			−0.547631	+	0.836720i	$0.684470\pi$
$660$	1.61058e9	+	7.70536e8i	0.218061	+	0.104325i
$661$	9.13587e9			1.23040			0.615198	−	0.788373i	$-0.289076\pi$
$661$	9.13587e9			1.23040			0.615198	+	0.788373i	$0.289076\pi$
$662$	−4.57423e9	−	4.57423e9i	−0.612795	−	0.612795i
$663$	−4.04162e9	+	1.38326e10i	−0.538590	+	1.84334i
$664$		−	9.46330e9i		−	1.25445i
$665$	1.78670e9	+	2.48463e9i	0.235601	+	0.327632i
$666$	−5.49371e9	−	3.50997e9i	−0.720620	−	0.460409i
$667$	−3.31573e9	+	3.31573e9i	−0.432652	+	0.432652i
$668$	1.43602e9	−	1.43602e9i	0.186399	−	0.186399i
$669$	−3.52272e9	−	6.43102e9i	−0.454870	−	0.830403i
$670$	2.33979e9	+	3.82319e8i	0.300548	+	0.0491093i
$671$			3.12123e9i			0.398839i
$672$	8.48442e9	+	2.47899e9i	1.07852	+	0.315125i
$673$	7.87916e9	+	7.87916e9i	0.996385	+	0.996385i	0.999993	−	0.00360834i	$-0.00114857\pi$
$673$	7.87916e9	+	7.87916e9i	0.996385	+	0.996385i	−0.00360834	+	0.999993i	$0.501149\pi$
$674$	7.64317e8			0.0961533
$675$	3.06776e9	+	7.37792e9i	0.383936	+	0.923360i
$676$	1.68509e9			0.209802
$677$	2.63665e9	+	2.63665e9i	0.326582	+	0.326582i	0.851285	−	0.524703i	$-0.175824\pi$
$677$	2.63665e9	+	2.63665e9i	0.326582	+	0.326582i	−0.524703	+	0.851285i	$0.675824\pi$
$678$	−6.23087e9	−	1.82055e9i	−0.767795	−	0.224335i
$679$		−	1.10984e10i		−	1.36055i
$680$	−1.37756e10	−	2.25093e9i	−1.68008	−	0.274524i
$681$	8.51025e8	+	1.55362e9i	0.103259	+	0.188508i
$682$	1.37492e9	−	1.37492e9i	0.165971	−	0.165971i
$683$	−1.13380e9	+	1.13380e9i	−0.136164	+	0.136164i	−0.771904	−	0.635739i	$-0.780695\pi$
$683$	−1.13380e9	+	1.13380e9i	−0.136164	+	0.136164i	0.635739	+	0.771904i	$0.280695\pi$
$684$	−1.27074e9	−	8.11883e8i	−0.151831	−	0.0970057i
$685$	−7.47398e9	−	1.03935e10i	−0.888454	−	1.23551i
$686$		−	3.74133e9i		−	0.442479i
$687$	−2.29698e9	+	7.86148e9i	−0.270277	+	0.925029i
$688$	2.28119e8	+	2.28119e8i	0.0267056	+	0.0267056i
$689$	−7.13237e9			−0.830743
$690$	−3.14371e9	−	1.50402e9i	−0.364309	−	0.174293i
$691$	−1.43668e10			−1.65648			−0.828242	−	0.560371i	$-0.810659\pi$
$691$	−1.43668e10			−1.65648			−0.828242	+	0.560371i	$0.810659\pi$
$692$	−4.04035e9	−	4.04035e9i	−0.463498	−	0.463498i
$693$	−1.02065e9	−	4.63244e9i	−0.116495	−	0.528742i
$694$			7.12938e9i			0.809643i
$695$	1.97916e9	−	1.21124e10i	0.223632	−	1.36863i
$696$	8.37825e9	−	4.58936e9i	0.941935	−	0.515964i
$697$	5.10150e8	−	5.10150e8i	0.0570667	−	0.0570667i
$698$	−3.65622e9	+	3.65622e9i	−0.406948	+	0.406948i
$699$	3.71189e9	−	2.03326e9i	0.411079	−	0.225177i
$700$	2.63467e9	+	5.29826e9i	0.290325	+	0.583835i
$701$			5.26911e9i			0.577729i	0.957370	+	0.288864i	$0.0932777\pi$
$701$			5.26911e9i			0.577729i	−0.957370	+	0.288864i	$0.906722\pi$
$702$	5.52034e9	−	4.82212e9i	0.602262	−	0.526088i
$703$	2.74117e9	+	2.74117e9i	0.297572	+	0.297572i
$704$	3.31915e9			0.358527
$705$	2.46474e9	+	6.98634e9i	0.264917	+	0.750910i
$706$	3.65621e9			0.391034
$707$	−7.36724e8	−	7.36724e8i	−0.0784038	−	0.0784038i
$708$	1.67246e9	−	5.72406e9i	0.177109	−	0.606160i
$709$			1.58617e10i			1.67143i	0.549163	+	0.835715i	$0.314947\pi$
$709$			1.58617e10i			1.67143i	−0.549163	+	0.835715i	$0.685053\pi$
$710$	1.33563e9	−	9.60453e8i	0.140050	−	0.100710i
$711$	−7.32409e9	+	1.14635e10i	−0.764206	+	1.19611i
$712$	−2.11483e9	+	2.11483e9i	−0.219581	+	0.219581i
$713$	3.14479e9	−	3.14479e9i	0.324922	−	0.324922i
$714$	6.24391e9	+	1.13988e10i	0.641967	+	1.17196i
$715$	4.18977e9	−	3.01286e9i	0.428666	−	0.308254i
$716$		−	4.02003e9i		−	0.409292i
$717$	−2.59073e9	−	7.56964e8i	−0.262486	−	0.0766934i
$718$	2.01186e9	+	2.01186e9i	0.202844	+	0.202844i
$719$	9.04698e9			0.907722			0.453861	−	0.891073i	$-0.350046\pi$
$719$	9.04698e9			0.907722			0.453861	+	0.891073i	$0.350046\pi$
$720$	1.26315e9	+	1.13156e9i	0.126122	+	0.112984i
$721$	1.47790e9			0.146849
$722$	4.31129e9	+	4.31129e9i	0.426311	+	0.426311i
$723$	−6.92589e9	−	2.02362e9i	−0.681540	−	0.199134i
$724$		−	8.65279e8i		−	0.0847366i
$725$	1.00001e10	+	3.35766e9i	0.974588	+	0.327230i
$726$	2.68647e9	+	4.90438e9i	0.260558	+	0.475670i
$727$	7.53789e9	−	7.53789e9i	0.727578	−	0.727578i	−0.242559	−	0.970137i	$-0.577987\pi$
$727$	7.53789e9	−	7.53789e9i	0.727578	−	0.727578i	0.970137	+	0.242559i	$0.0779868\pi$
$728$	1.09520e10	−	1.09520e10i	1.05204	−	1.05204i
$729$	−1.40595e9	+	1.03654e10i	−0.134407	+	0.990926i
$730$	4.17704e8	−	2.55634e9i	0.0397410	−	0.243214i
$731$		−	3.83854e9i		−	0.363459i
$732$	1.42950e9	−	4.89251e9i	0.134709	−	0.461045i
$733$	−7.21731e9	−	7.21731e9i	−0.676879	−	0.676879i	0.282413	−	0.959293i	$-0.408865\pi$
$733$	−7.21731e9	−	7.21731e9i	−0.676879	−	0.676879i	−0.959293	+	0.282413i	$0.908865\pi$
$734$	−1.17189e10			−1.09383
$735$	2.13896e9	−	4.47087e9i	0.198700	−	0.415324i
$736$	5.98536e9			0.553373
$737$	1.54514e9	+	1.54514e9i	0.142178	+	0.142178i
$738$	−3.58363e8	+	7.89567e7i	−0.0328191	+	0.00723089i
$739$			8.81910e9i			0.803839i	0.915675	+	0.401919i	$0.131657\pi$
$739$			8.81910e9i			0.803839i	−0.915675	+	0.401919i	$0.868343\pi$
$740$	4.37599e9	+	6.08537e9i	0.396977	+	0.552047i
$741$	−3.82268e9	+	2.09395e9i	−0.345147	+	0.189061i
$742$	−4.54847e9	+	4.54847e9i	−0.408744	+	0.408744i
$743$	−1.01325e10	+	1.01325e10i	−0.906265	+	0.906265i	−0.995969	−	0.0897031i	$-0.971408\pi$
$743$	−1.01325e10	+	1.01325e10i	−0.906265	+	0.906265i	0.0897031	+	0.995969i	$0.471408\pi$
$744$	−7.94632e9	+	4.35276e9i	−0.707393	+	0.387489i
$745$	−1.59999e10	−	2.61436e9i	−1.41765	−	0.231643i
$746$		−	3.42615e9i		−	0.302149i
$747$	1.33598e10	−	2.94350e9i	1.17267	−	0.258370i
$748$	−3.18818e9	−	3.18818e9i	−0.278540	−	0.278540i
$749$	−1.12351e10			−0.976994
$750$	1.19367e8	+	7.83887e9i	0.0103317	+	0.678483i
$751$	8.87279e9			0.764400			0.382200	−	0.924080i	$-0.375167\pi$
$751$	8.87279e9			0.764400			0.382200	+	0.924080i	$0.375167\pi$
$752$	1.11183e9	+	1.11183e9i	0.0953400	+	0.0953400i
$753$	5.88199e9	−	2.01313e10i	0.502044	−	1.71826i
$754$		−	9.67683e9i		−	0.822117i
$755$	7.01337e9	+	1.14598e9i	0.593079	+	0.0969085i
$756$	−5.21768e8	+	7.72877e9i	−0.0439189	+	0.650555i
$757$	9.30542e9	−	9.30542e9i	0.779651	−	0.779651i	−0.200120	−	0.979771i	$-0.564133\pi$
$757$	9.30542e9	−	9.30542e9i	0.779651	−	0.779651i	0.979771	+	0.200120i	$0.0641333\pi$
$758$	6.22594e8	−	6.22594e8i	0.0519233	−	0.0519233i
$759$	−1.54312e9	−	2.81710e9i	−0.128102	−	0.233860i
$760$	−2.46474e9	−	3.42753e9i	−0.203668	−	0.283227i
$761$			1.59794e10i			1.31436i	0.753735	+	0.657179i	$0.228250\pi$
$761$			1.59794e10i			1.31436i	−0.753735	+	0.657179i	$0.771750\pi$
$762$	−1.41024e10	−	4.12047e9i	−1.15465	−	0.337369i
$763$	1.91522e10	+	1.91522e10i	1.56092	+	1.56092i
$764$	7.53597e9			0.611382
$765$	−1.10709e9	−	2.01478e10i	−0.0894065	−	1.62710i
$766$	1.58237e10			1.27206
$767$	−1.21881e10	−	1.21881e10i	−0.975334	−	0.975334i
$768$	−1.28051e10	−	3.74140e9i	−1.02004	−	0.298037i
$769$			7.53248e9i			0.597305i	0.954362	+	0.298652i	$0.0965371\pi$
$769$			7.53248e9i			0.597305i	−0.954362	+	0.298652i	$0.903463\pi$
$770$	7.50537e8	−	4.59327e9i	0.0592454	−	0.362581i
$771$	−6.16381e9	−	1.12526e10i	−0.484350	−	0.884221i
$772$	−6.00461e9	+	6.00461e9i	−0.469704	+	0.469704i
$773$	−4.16161e9	+	4.16161e9i	−0.324066	+	0.324066i	−0.850325	−	0.526259i	$-0.823594\pi$
$773$	−4.16161e9	+	4.16161e9i	−0.324066	+	0.324066i	0.526259	+	0.850325i	$0.323594\pi$
$774$	−1.05117e9	+	1.64527e9i	−0.0814857	+	0.127539i
$775$	−9.48455e9	−	3.18456e9i	−0.731915	−	0.245750i
$776$			1.53101e10i			1.17615i
$777$	5.58501e9	−	1.91148e10i	0.427120	−	1.46183i
$778$	−1.18716e10	−	1.18716e10i	−0.903821	−	0.903821i
$779$	2.18207e8			0.0165382
$780$	−7.94730e9	+	2.80376e9i	−0.599637	+	0.211549i
$781$	1.51628e9			0.113894
$782$	6.22304e9	+	6.22304e9i	0.465349	+	0.465349i
$783$	9.08500e9	+	1.04005e10i	0.676330	+	0.774260i
$784$		−	1.05191e9i		−	0.0779601i
$785$	−7.34871e9	+	5.28446e9i	−0.542210	+	0.389904i
$786$	−1.69999e8	+	9.31204e7i	−0.0124873	+	0.00684015i
$787$	−1.76320e10	+	1.76320e10i	−1.28941	+	1.28941i	−0.354262	+	0.935146i	$0.615268\pi$
$787$	−1.76320e10	+	1.76320e10i	−1.28941	+	1.28941i	−0.935146	+	0.354262i	$0.884732\pi$
$788$	−2.29592e9	+	2.29592e9i	−0.167153	+	0.167153i
$789$	−1.35888e10	+	7.44357e9i	−0.984948	+	0.539525i
$790$	−1.08363e10	+	7.79240e9i	−0.781964	+	0.562311i
$791$		−	1.98289e10i		−	1.42456i
$792$	1.40797e9	+	6.39042e9i	0.100706	+	0.457079i
$793$	−1.04175e10	−	1.04175e10i	−0.741838	−	0.741838i
$794$	5.01324e9			0.355424
$795$	9.41786e9	−	3.32257e9i	0.664764	−	0.234525i
$796$	3.42372e9			0.240604
$797$	1.12595e10	+	1.12595e10i	0.787798	+	0.787798i	0.981133	−	0.193335i	$-0.0619303\pi$
$797$	1.12595e10	+	1.12595e10i	0.787798	+	0.787798i	−0.193335	+	0.981133i	$0.561930\pi$
$798$	−1.10245e9	+	3.77316e9i	−0.0767977	+	0.262842i
$799$		−	1.87086e10i		−	1.29756i
$800$	−5.99527e9	−	1.20563e10i	−0.413994	−	0.832530i
$801$	−3.64340e9	−	2.32779e9i	−0.250491	−	0.160041i
$802$	8.90533e9	−	8.90533e9i	0.609592	−	0.609592i
$803$	1.68815e9	−	1.68815e9i	0.115055	−	0.115055i
$804$	−1.71433e9	−	3.12966e9i	−0.116332	−	0.212374i
$805$	1.71667e9	−	1.05060e10i	0.115985	−	0.709826i
$806$			9.17796e9i			0.617410i
$807$	1.20302e10	+	3.51501e9i	0.805779	+	0.235434i
$808$	1.01630e9	+	1.01630e9i	0.0677773	+	0.0677773i
$809$	−4.39207e9			−0.291642			−0.145821	−	0.989311i	$-0.546582\pi$
$809$	−4.39207e9			−0.291642			−0.145821	+	0.989311i	$0.546582\pi$
$810$	−5.04292e9	+	8.93892e9i	−0.333414	+	0.591000i
$811$	1.75494e9			0.115529			0.0577643	−	0.998330i	$-0.481603\pi$
$811$	1.75494e9			0.115529			0.0577643	+	0.998330i	$0.481603\pi$
$812$	7.23136e9	+	7.23136e9i	0.473995	+	0.473995i
$813$	−2.94543e9	−	8.60602e8i	−0.192235	−	0.0561675i
$814$		−	5.89554e9i		−	0.383123i
$815$	3.63269e9	+	5.05171e9i	0.235059	+	0.326879i
$816$	−2.05746e9	−	3.75606e9i	−0.132561	−	0.242001i
$817$	8.20931e8	−	8.20931e8i	0.0526659	−	0.0526659i
$818$	5.02953e9	−	5.02953e9i	0.321285	−	0.321285i
$819$	1.88680e10	+	1.20549e10i	1.20014	+	0.766777i
$820$	4.16381e8	+	6.80363e7i	0.0263720	+	0.00430916i
$821$		−	2.30379e10i		−	1.45292i	−0.687208	−	0.726461i	$-0.741164\pi$
$821$		−	2.30379e10i		−	1.45292i	0.687208	−	0.726461i	$-0.258836\pi$
$822$	4.61167e9	−	1.57836e10i	0.289605	−	0.991183i
$823$	1.88740e10	+	1.88740e10i	1.18022	+	1.18022i	0.979686	+	0.200538i	$0.0642691\pi$
$823$	1.88740e10	+	1.88740e10i	1.18022	+	1.18022i	0.200538	+	0.979686i	$0.435731\pi$
$824$	−2.03875e9			−0.126946
$825$	−4.12881e9	+	5.93007e9i	−0.255998	+	0.367681i
$826$	−1.55453e10			−0.959773
$827$	2.14819e10	+	2.14819e10i	1.32070	+	1.32070i	0.913211	+	0.407488i	$0.133595\pi$
$827$	2.14819e10	+	2.14819e10i	1.32070	+	1.32070i	0.407488	+	0.913211i	$0.366405\pi$
$828$	1.12862e9	+	5.12252e9i	0.0690945	+	0.313601i
$829$			5.85259e9i			0.356786i	0.983959	+	0.178393i	$0.0570898\pi$
$829$			5.85259e9i			0.356786i	−0.983959	+	0.178393i	$0.942910\pi$
$830$	1.32468e10	+	2.16452e9i	0.804151	+	0.131398i
$831$	−3.11784e9	+	1.70786e9i	−0.188473	+	0.103240i
$832$	−1.10781e10	+	1.10781e10i	−0.666859	+	0.666859i
$833$	−8.85020e9	+	8.85020e9i	−0.530513	+	0.530513i
$834$	1.38260e10	−	7.57347e9i	0.825307	−	0.452078i
$835$	4.79853e9	+	6.67296e9i	0.285237	+	0.396657i
$836$		−	1.36368e9i		−	0.0807220i
$837$	−8.61664e9	−	9.86429e9i	−0.507924	−	0.581469i
$838$	1.27876e10	+	1.27876e10i	0.750648	+	0.750648i
$839$	1.34315e10			0.785159			0.392579	−	0.919718i	$-0.371583\pi$
$839$	1.34315e10			0.785159			0.392579	+	0.919718i	$0.371583\pi$
$840$	−9.35952e9	+	1.95633e10i	−0.544849	+	1.13885i
$841$	9.81530e8			0.0569007
$842$	−3.86653e9	−	3.86653e9i	−0.223218	−	0.223218i
$843$	8.17896e9	−	2.79927e10i	0.470220	−	1.60934i
$844$		−	5.93308e9i		−	0.339689i
$845$	−1.09977e9	+	6.73058e9i	−0.0627052	+	0.383755i
$846$	−5.12332e9	+	8.01888e9i	−0.290908	+	0.455321i
$847$	−1.20784e10	+	1.20784e10i	−0.682997	+	0.682997i
$848$	1.49879e9	−	1.49879e9i	0.0844024	−	0.0844024i
$849$	8.91717e8	+	1.62790e9i	0.0500092	+	0.0912960i
$850$	6.30173e9	−	1.87684e10i	0.351960	−	1.04824i
$851$		−	1.34846e10i		−	0.750042i
$852$	−2.37676e9	−	6.94445e8i	−0.131658	−	0.0384680i
$853$	9.75541e9	+	9.75541e9i	0.538176	+	0.538176i	0.922993	−	0.384817i	$-0.125736\pi$
$853$	9.75541e9	+	9.75541e9i	0.538176	+	0.538176i	−0.384817	+	0.922993i	$0.625736\pi$
$854$	−1.32870e10			−0.730002
$855$	4.07216e9	−	4.54570e9i	0.222814	−	0.248725i
$856$	1.54988e10			0.844577
$857$	−1.08940e10	−	1.08940e10i	−0.591228	−	0.591228i	0.346735	−	0.937963i	$-0.387290\pi$
$857$	−1.08940e10	−	1.08940e10i	−0.591228	−	0.591228i	−0.937963	+	0.346735i	$0.887290\pi$
$858$	6.36257e9	+	1.85903e9i	0.343896	+	0.100480i
$859$			6.30235e9i			0.339255i	0.985508	+	0.169628i	$0.0542565\pi$
$859$			6.30235e9i			0.339255i	−0.985508	+	0.169628i	$0.945744\pi$
$860$	1.82246e9	−	1.31053e9i	0.0977043	−	0.0702592i
$861$	−5.38513e8	−	9.83100e8i	−0.0287531	−	0.0524912i
$862$	−1.05451e10	+	1.05451e10i	−0.560757	+	0.560757i
$863$	−3.14203e9	+	3.14203e9i	−0.166407	+	0.166407i	−0.785398	−	0.618991i	$-0.787542\pi$
$863$	−3.14203e9	+	3.14203e9i	−0.166407	+	0.166407i	0.618991	+	0.785398i	$0.287542\pi$
$864$	1.18730e9	−	1.75870e10i	0.0626269	−	0.927671i
$865$	1.87749e10	−	1.35010e10i	0.986326	−	0.709268i
$866$			8.75173e9i			0.457911i
$867$	−8.90929e9	+	3.04923e10i	−0.464276	+	1.58900i
$868$	−6.85856e9	−	6.85856e9i	−0.355970	−	0.355970i
$869$	−1.23020e10			−0.635924
$870$	4.50788e9	+	1.27777e10i	0.232089	+	0.657861i
$871$	−1.03142e10			−0.528899
$872$	−2.64202e10	−	2.64202e10i	−1.34936	−	1.34936i
$873$	−2.16139e10	+	4.76211e9i	−1.09947	+	0.242242i
$874$			2.66179e9i			0.134860i
$875$	−2.28818e10	+	7.06550e9i	−1.15468	+	0.356545i
$876$	−3.41932e9	+	1.87300e9i	−0.171860	+	0.0941399i
$877$	6.86769e9	−	6.86769e9i	0.343805	−	0.343805i	−0.513991	−	0.857796i	$-0.671833\pi$
$877$	6.86769e9	−	6.86769e9i	0.343805	−	0.343805i	0.857796	+	0.513991i	$0.171833\pi$
$878$	7.12946e9	−	7.12946e9i	0.355489	−	0.355489i
$879$	1.87515e9	−	1.02715e9i	0.0931270	−	0.0510122i
$880$	−2.47313e8	+	1.51355e9i	−0.0122337	+	0.0748700i
$881$			5.44693e9i			0.268371i	0.990956	+	0.134186i	$0.0428419\pi$
$881$			5.44693e9i			0.268371i	−0.990956	+	0.134186i	$0.957158\pi$
$882$	6.21698e9	−	1.36976e9i	0.305098	−	0.0672209i
$883$	−2.22634e10	−	2.22634e10i	−1.08825	−	1.08825i	−0.995709	−	0.0925395i	$-0.970502\pi$
$883$	−2.22634e10	−	2.22634e10i	−1.08825	−	1.08825i	−0.0925395	−	0.995709i	$-0.529498\pi$
$884$	2.12820e10			1.03617
$885$	2.17714e10	+	1.04159e10i	1.05581	+	0.505122i
$886$	7.39475e8			0.0357195
$887$	−2.08485e10	−	2.08485e10i	−1.00310	−	1.00310i	−0.999995	−	0.00310193i	$-0.999013\pi$
$887$	−2.08485e10	−	2.08485e10i	−1.00310	−	1.00310i	−0.00310193	−	0.999995i	$-0.500987\pi$
$888$	−7.70447e9	+	2.63688e10i	−0.369230	+	1.26370i
$889$		−	4.48792e10i		−	2.14234i
$890$	−2.47663e9	−	3.44407e9i	−0.117760	−	0.163760i
$891$	−8.58370e9	+	3.97540e9i	−0.406539	+	0.188282i
$892$	−7.65712e9	+	7.65712e9i	−0.361234	+	0.361234i
$893$	4.00113e9	−	4.00113e9i	0.188020	−	0.188020i
$894$	−1.00041e10	−	1.82634e10i	−0.468272	−	0.854870i
$895$	1.60568e10	+	2.62366e9i	0.748647	+	0.122328i
$896$		−	1.00639e10i		−	0.467399i
$897$	1.45528e10	+	4.25207e9i	0.673247	+	0.196710i
$898$	7.70775e9	+	7.70775e9i	0.355190	+	0.355190i
$899$	−1.72915e10			−0.793732
$900$	9.18781e9	−	7.40439e9i	0.420110	−	0.338564i
$901$	−2.52200e10			−1.14870
$902$	−2.34654e8	−	2.34654e8i	−0.0106464	−	0.0106464i
$903$	−5.72456e9	−	1.67261e9i	−0.258723	−	0.0755941i
$904$			2.73538e10i			1.23148i
$905$	3.45609e9	+	5.64722e8i	0.154994	+	0.0253259i
$906$	4.38521e9	+	8.00556e9i	0.195903	+	0.357638i
$907$	2.57911e10	−	2.57911e10i	1.14774	−	1.14774i	0.160746	−	0.986996i	$-0.448610\pi$
$907$	2.57911e10	−	2.57911e10i	1.14774	−	1.14774i	0.986996	−	0.160746i	$-0.0513901\pi$
$908$	1.84982e9	−	1.84982e9i	0.0820029	−	0.0820029i
$909$	−1.11865e9	+	1.75088e9i	−0.0493992	+	0.0773183i
$910$	1.28257e10	+	1.78357e10i	0.564203	+	0.784595i
$911$			1.51512e10i			0.663945i	0.943289	+	0.331973i	$0.107714\pi$
$911$			1.51512e10i			0.663945i	−0.943289	+	0.331973i	$0.892286\pi$
$912$	3.63273e8	−	1.24331e9i	0.0158581	−	0.0542748i
$913$	8.74787e9	+	8.74787e9i	0.380412	+	0.380412i
$914$	2.38393e9			0.103272
$915$	1.86087e10	+	8.90279e9i	0.803048	+	0.384195i
$916$	1.20952e10			0.519971
$917$	−4.18671e8	−	4.18671e8i	−0.0179300	−	0.0179300i
$918$	1.95198e10	−	1.70510e10i	0.832774	−	0.727444i
$919$		−	7.99993e9i		−	0.340002i	−0.985444	−	0.170001i	$-0.945623\pi$
$919$		−	7.99993e9i		−	0.340002i	0.985444	−	0.170001i	$-0.0543772\pi$
$920$	−2.36813e9	+	1.44929e10i	−0.100265	+	0.613620i
$921$	1.62740e10	−	8.91442e9i	0.686414	−	0.375997i
$922$	−1.09442e10	+	1.09442e10i	−0.459859	+	0.459859i
$923$	−5.06079e9	+	5.06079e9i	−0.211842	+	0.211842i
$924$	−6.14388e9	+	3.36544e9i	−0.256207	+	0.140343i
$925$	−2.71621e10	+	1.35069e10i	−1.12841	+	0.561127i
$926$		−	1.42481e10i		−	0.589684i
$927$	−6.34141e8	−	2.87819e9i	−0.0261461	−	0.118670i
$928$	−1.64551e10	−	1.64551e10i	−0.675902	−	0.675902i
$929$	2.66946e10			1.09236			0.546182	−	0.837666i	$-0.316081\pi$
$929$	2.66946e10			1.09236			0.546182	+	0.837666i	$0.316081\pi$
$930$	−4.27549e9	−	1.21189e10i	−0.174299	−	0.494053i
$931$	−3.78551e9			−0.153745
$932$	−4.41958e9	−	4.41958e9i	−0.178824	−	0.178824i
$933$	−2.74034e9	+	9.37888e9i	−0.110463	+	0.378064i
$934$		−	3.91349e9i		−	0.157163i
$935$	1.48150e10	−	1.06534e10i	0.592734	−	0.426235i
$936$	−2.60282e10	−	1.66296e10i	−1.03748	−	0.662851i
$937$	−2.94294e10	+	2.94294e10i	−1.16867	+	1.16867i	−0.186153	+	0.982521i	$0.559602\pi$
$937$	−2.94294e10	+	2.94294e10i	−1.16867	+	1.16867i	−0.982521	+	0.186153i	$0.940398\pi$
$938$	−6.57761e9	+	6.57761e9i	−0.260230	+	0.260230i
$939$	6.52393e9	+	1.19100e10i	0.257146	+	0.469442i
$940$	8.88249e9	−	6.38740e9i	0.348809	−	0.250828i
$941$			1.31946e10i			0.516217i	0.966116	+	0.258109i	$0.0830993\pi$
$941$			1.31946e10i			0.516217i	−0.966116	+	0.258109i	$0.916901\pi$
$942$	−1.11597e10	−	3.26067e9i	−0.434987	−	0.127095i
$943$	−5.36713e8	−	5.36713e8i	−0.0208426	−	0.0208426i
$944$	5.12240e9			0.198185
$945$	−3.05297e10	−	7.12820e9i	−1.17682	−	0.274770i
$946$	−1.76561e9			−0.0678073
$947$	−3.41874e9	−	3.41874e9i	−0.130810	−	0.130810i	0.638670	−	0.769480i	$-0.279485\pi$
$947$	−3.41874e9	−	3.41874e9i	−0.130810	−	0.130810i	−0.769480	+	0.638670i	$0.779485\pi$
$948$	1.92832e10	+	5.63421e9i	0.735108	+	0.214785i
$949$			1.12688e10i			0.428004i
$950$	5.36164e9	−	2.66619e9i	0.202892	−	0.100893i
$951$	1.18813e10	+	2.16903e10i	0.447953	+	0.817776i
$952$	3.87261e10	−	3.87261e10i	1.45470	−	1.45470i
$953$	−1.51190e10	+	1.51190e10i	−0.565847	+	0.565847i	−0.930962	−	0.365116i	$-0.881029\pi$
$953$	−1.51190e10	+	1.51190e10i	−0.565847	+	0.565847i	0.365116	+	0.930962i	$0.381029\pi$
$954$	1.08098e10	+	6.90643e9i	0.403085	+	0.257534i
$955$	−4.91833e9	+	3.01001e10i	−0.182728	+	1.11829i
$956$			3.98595e9i			0.147547i
$957$	−3.50246e9	+	1.19873e10i	−0.129176	+	0.442108i
$958$	−1.31058e10	−	1.31058e10i	−0.481599	−	0.481599i
$959$	5.02291e10			1.83904
$960$	9.46730e9	−	1.97886e10i	0.345364	−	0.721882i
$961$	−1.11125e10			−0.403907
$962$	1.96772e10	+	1.96772e10i	0.712608	+	0.712608i
$963$	4.82080e9	+	2.18803e10i	0.173951	+	0.789517i
$964$			1.06558e10i			0.383103i
$965$	−2.00647e10	−	2.79024e10i	−0.718764	−	0.999532i
$966$	1.19923e10	−	6.56903e9i	0.428038	−	0.234467i
$967$	−1.79878e9	+	1.79878e9i	−0.0639713	+	0.0639713i	−0.738369	−	0.674397i	$-0.764404\pi$
$967$	−1.79878e9	+	1.79878e9i	−0.0639713	+	0.0639713i	0.674397	+	0.738369i	$0.264404\pi$
$968$	1.66621e10	−	1.66621e10i	0.590427	−	0.590427i
$969$	−1.35169e10	+	7.40418e9i	−0.477249	+	0.261423i
$970$	−2.14312e10	−	3.50184e9i	−0.753955	−	0.123196i
$971$			3.66968e10i			1.28636i	0.765717	+	0.643178i	$0.222384\pi$
$971$			3.66968e10i			1.28636i	−0.765717	+	0.643178i	$0.777616\pi$
$972$	1.52756e10	−	2.30014e9i	0.533539	−	0.0803383i
$973$	3.40505e10	+	3.40505e10i	1.18503	+	1.18503i
$974$	−2.87570e10			−0.997210
$975$	−6.01198e9	−	3.35729e10i	−0.207731	−	1.16004i
$976$	4.37826e9			0.150740
$977$	3.64228e10	+	3.64228e10i	1.24952	+	1.24952i	0.955933	+	0.293586i	$0.0948488\pi$
$977$	3.64228e10	+	3.64228e10i	1.24952	+	1.24952i	0.293586	+	0.955933i	$0.405151\pi$
$978$	−2.24148e9	+	7.67152e9i	−0.0766210	+	0.262238i
$979$		−	3.90989e9i		−	0.133176i
$980$	−7.22349e9	−	1.18031e9i	−0.245163	−	0.0400595i
$981$	2.90808e10	−	4.55165e10i	0.983478	−	1.53931i
$982$	5.17508e9	−	5.17508e9i	0.174392	−	0.174392i
$983$	1.31199e10	−	1.31199e10i	0.440549	−	0.440549i	−0.451647	−	0.892196i	$-0.649164\pi$
$983$	1.31199e10	−	1.31199e10i	0.440549	−	0.440549i	0.892196	+	0.451647i	$0.149164\pi$
$984$	7.42874e8	+	1.35618e9i	0.0248561	+	0.0453768i
$985$	−7.67192e9	−	1.06688e10i	−0.255786	−	0.355703i
$986$		−	3.42171e10i		−	1.13678i
$987$	−2.79009e10	−	8.15214e9i	−0.923652	−	0.269874i
$988$	4.55149e9	+	4.55149e9i	0.150143	+	0.150143i
$989$	−4.03841e9			−0.132747
$990$	−9.26740e9	+	5.09230e8i	−0.303553	+	0.0166798i
$991$	5.97561e9			0.195040			0.0975201	−	0.995234i	$-0.468909\pi$
$991$	5.97561e9			0.195040			0.0975201	+	0.995234i	$0.468909\pi$
$992$	1.56068e10	+	1.56068e10i	0.507602	+	0.507602i
$993$	−3.78246e10	−	1.10516e10i	−1.22589	−	0.358183i
$994$			6.45475e9i			0.208462i
$995$	−2.23448e9	+	1.36750e10i	−0.0719112	+	0.440095i
$996$	−9.70577e9	−	1.77187e10i	−0.311259	−	0.568230i
$997$	3.81056e10	−	3.81056e10i	1.21774	−	1.21774i	0.249323	−	0.968420i	$-0.419792\pi$
$997$	3.81056e10	−	3.81056e10i	1.21774	−	1.21774i	0.968420	−	0.249323i	$-0.0802082\pi$
$998$	−1.78407e10	+	1.78407e10i	−0.568139	+	0.568139i
$999$	−3.96224e10	−	2.67490e9i	−1.25737	−	0.0848845i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.8.e.a.8.8	yes	24
3.2	odd	2	inner	15.8.e.a.8.5	yes	24
5.2	odd	4	inner	15.8.e.a.2.5	✓	24
5.3	odd	4		75.8.e.d.32.8		24
5.4	even	2		75.8.e.d.68.5		24
15.2	even	4	inner	15.8.e.a.2.8	yes	24
15.8	even	4		75.8.e.d.32.5		24
15.14	odd	2		75.8.e.d.68.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.8.e.a.2.5	✓	24	5.2	odd	4	inner
15.8.e.a.2.8	yes	24	15.2	even	4	inner
15.8.e.a.8.5	yes	24	3.2	odd	2	inner
15.8.e.a.8.8	yes	24	1.1	even	1	trivial
75.8.e.d.32.5		24	15.8	even	4
75.8.e.d.32.8		24	5.3	odd	4
75.8.e.d.68.5		24	5.4	even	2
75.8.e.d.68.8		24	15.14	odd	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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	15.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(5.42850 + 5.42850i) q^{2} +(44.8885 + 13.1156i) q^{3} -69.0629i q^{4} +(275.850 + 45.0737i) q^{5} +(172.479 + 314.875i) q^{6} +(-775.470 + 775.470i) q^{7} +(1069.75 - 1069.75i) q^{8} +(1842.96 + 1177.48i) q^{9} +O(q^{10})\)	\(q+(5.42850 + 5.42850i) q^{2} +(44.8885 + 13.1156i) q^{3} -69.0629i q^{4} +(275.850 + 45.0737i) q^{5} +(172.479 + 314.875i) q^{6} +(-775.470 + 775.470i) q^{7} +(1069.75 - 1069.75i) q^{8} +(1842.96 + 1177.48i) q^{9} +(1252.77 + 1742.13i) q^{10} +1977.76i q^{11} +(905.801 - 3100.13i) q^{12} +(-6601.06 - 6601.06i) q^{13} -8419.28 q^{14} +(11791.3 + 5641.23i) q^{15} +2774.28 q^{16} +(-23341.3 - 23341.3i) q^{17} +(3612.56 + 16396.5i) q^{18} -9983.78i q^{19} +(3112.92 - 19051.0i) q^{20} +(-44980.5 + 24639.0i) q^{21} +(-10736.3 + 10736.3i) q^{22} +(-24556.6 + 24556.6i) q^{23} +(62050.2 - 33989.3i) q^{24} +(74061.7 + 24867.2i) q^{25} -71667.6i q^{26} +(67284.5 + 77026.9i) q^{27} +(53556.2 + 53556.2i) q^{28} +135024. q^{29} +(33385.9 + 94632.7i) q^{30} -128063. q^{31} +(-121868. - 121868. i) q^{32} +(-25939.6 + 88778.9i) q^{33} -253416. i q^{34} +(-248867. + 178960. i) q^{35} +(81320.2 - 127280. i) q^{36} +(-274562. + 274562. i) q^{37} +(54196.9 - 54196.9i) q^{38} +(-209735. - 382889. i) q^{39} +(343310. - 246874. i) q^{40} +21856.1i q^{41} +(-377929. - 110424. i) q^{42} +(82226.5 + 82226.5i) q^{43} +136590. q^{44} +(455308. + 407877. i) q^{45} -266611. q^{46} +(400763. + 400763. i) q^{47} +(124533. + 36386.3i) q^{48} -379166. i q^{49} +(267052. + 537035. i) q^{50} +(-741620. - 1.35389e6i) q^{51} +(-455888. + 455888. i) q^{52} +(540245. - 540245. i) q^{53} +(-52886.8 + 783394. i) q^{54} +(-89145.0 + 545566. i) q^{55} +1.65913e6i q^{56} +(130943. - 448157. i) q^{57} +(732976. + 732976. i) q^{58} +1.84639e6 q^{59} +(389600. - 814344. i) q^{60} +1.57816e6 q^{61} +(-695188. - 695188. i) q^{62} +(-2.34226e6 + 516061. i) q^{63} -1.67823e6i q^{64} +(-1.52337e6 - 2.11844e6i) q^{65} +(-622749. + 341123. i) q^{66} +(781256. - 781256. i) q^{67} +(-1.61201e6 + 1.61201e6i) q^{68} +(-1.42439e6 + 780237. i) q^{69} +(-2.32246e6 - 379488. i) q^{70} -766664. i q^{71} +(3.23113e6 - 711902. i) q^{72} +(-853564. - 853564. i) q^{73} -2.98092e6 q^{74} +(2.99837e6 + 2.08762e6i) q^{75} -689509. q^{76} +(-1.53370e6 - 1.53370e6i) q^{77} +(939964. - 3.21706e6i) q^{78} +6.22014e6i q^{79} +(765285. + 125047. i) q^{80} +(2.01005e6 + 4.34010e6i) q^{81} +(-118646. + 118646. i) q^{82} +(4.42311e6 - 4.42311e6i) q^{83} +(1.70164e6 + 3.10648e6i) q^{84} +(-5.38661e6 - 7.49077e6i) q^{85} +892732. i q^{86} +(6.06102e6 + 1.77092e6i) q^{87} +(2.11572e6 + 2.11572e6i) q^{88} -1.97693e6 q^{89} +(257478. + 4.68580e6i) q^{90} +1.02378e7 q^{91} +(1.69595e6 + 1.69595e6i) q^{92} +(-5.74855e6 - 1.67962e6i) q^{93} +4.35108e6i q^{94} +(450006. - 2.75403e6i) q^{95} +(-3.87212e6 - 7.06888e6i) q^{96} +(-7.15589e6 + 7.15589e6i) q^{97} +(2.05830e6 - 2.05830e6i) q^{98} +(-2.32878e6 + 3.64494e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{3} + 924 q^{6} + 1344 q^{7}+O(q^{10}) \) 24 * q + 24 * q^3 + 924 * q^6 + 1344 * q^7	\( 24 q + 24 q^{3} + 924 q^{6} + 1344 q^{7} - 3180 q^{10} - 2028 q^{12} + 16848 q^{13} + 37560 q^{15} - 68868 q^{16} - 106560 q^{18} + 84144 q^{21} + 166020 q^{22} - 275760 q^{25} - 264168 q^{27} + 602028 q^{28} + 892380 q^{30} - 208992 q^{31} - 877800 q^{33} - 256212 q^{36} - 635616 q^{37} - 1574040 q^{40} + 1219380 q^{42} + 1397328 q^{43} + 570240 q^{45} + 2787168 q^{46} - 476796 q^{48} - 4028016 q^{51} - 6426336 q^{52} + 2324880 q^{55} + 8457264 q^{57} + 986340 q^{58} + 2037900 q^{60} + 12157968 q^{61} - 1973952 q^{63} - 25406040 q^{66} - 16720176 q^{67} - 13165860 q^{70} + 36245880 q^{72} + 4059528 q^{73} + 11226120 q^{75} + 37968816 q^{76} - 26156280 q^{78} - 31289976 q^{81} - 53633520 q^{82} - 34181760 q^{85} + 44480160 q^{87} + 74717340 q^{88} + 71623080 q^{90} + 67599648 q^{91} - 58742592 q^{93} - 103105308 q^{96} - 75148056 q^{97}+O(q^{100}) \) 24 * q + 24 * q^3 + 924 * q^6 + 1344 * q^7 - 3180 * q^10 - 2028 * q^12 + 16848 * q^13 + 37560 * q^15 - 68868 * q^16 - 106560 * q^18 + 84144 * q^21 + 166020 * q^22 - 275760 * q^25 - 264168 * q^27 + 602028 * q^28 + 892380 * q^30 - 208992 * q^31 - 877800 * q^33 - 256212 * q^36 - 635616 * q^37 - 1574040 * q^40 + 1219380 * q^42 + 1397328 * q^43 + 570240 * q^45 + 2787168 * q^46 - 476796 * q^48 - 4028016 * q^51 - 6426336 * q^52 + 2324880 * q^55 + 8457264 * q^57 + 986340 * q^58 + 2037900 * q^60 + 12157968 * q^61 - 1973952 * q^63 - 25406040 * q^66 - 16720176 * q^67 - 13165860 * q^70 + 36245880 * q^72 + 4059528 * q^73 + 11226120 * q^75 + 37968816 * q^76 - 26156280 * q^78 - 31289976 * q^81 - 53633520 * q^82 - 34181760 * q^85 + 44480160 * q^87 + 74717340 * q^88 + 71623080 * q^90 + 67599648 * q^91 - 58742592 * q^93 - 103105308 * q^96 - 75148056 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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