LMFDB - Embedded newform 51.6.e.a.4.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [51,6,Mod(4,51)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(51, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("51.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	51.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:	$8.17957481046$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			4.5
Character	$\chi$	$=$	51.4
Dual form			51.6.e.a.13.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.57214i q^{2} +(6.36396 - 6.36396i) q^{3} +0.951217 q^{4} +(-32.5739 + 32.5739i) q^{5} +(-35.4609 - 35.4609i) q^{6} +(-135.342 - 135.342i) q^{7} -183.609i q^{8} -81.0000i q^{9} +O(q^{10})$	\(q-5.57214i q^{2} +(6.36396 - 6.36396i) q^{3} +0.951217 q^{4} +(-32.5739 + 32.5739i) q^{5} +(-35.4609 - 35.4609i) q^{6} +(-135.342 - 135.342i) q^{7} -183.609i q^{8} -81.0000i q^{9} +(181.507 + 181.507i) q^{10} +(-173.891 - 173.891i) q^{11} +(6.05351 - 6.05351i) q^{12} -132.026 q^{13} +(-754.145 + 754.145i) q^{14} +414.598i q^{15} -992.656 q^{16} +(204.474 + 1173.90i) q^{17} -451.344 q^{18} -2925.79i q^{19} +(-30.9849 + 30.9849i) q^{20} -1722.62 q^{21} +(-968.947 + 968.947i) q^{22} +(1989.82 + 1989.82i) q^{23} +(-1168.48 - 1168.48i) q^{24} +1002.88i q^{25} +735.668i q^{26} +(-515.481 - 515.481i) q^{27} +(-128.740 - 128.740i) q^{28} +(1095.52 - 1095.52i) q^{29} +2310.20 q^{30} +(2617.25 - 2617.25i) q^{31} -344.262i q^{32} -2213.27 q^{33} +(6541.15 - 1139.36i) q^{34} +8817.24 q^{35} -77.0486i q^{36} +(8717.02 - 8717.02i) q^{37} -16302.9 q^{38} +(-840.209 + 840.209i) q^{39} +(5980.86 + 5980.86i) q^{40} +(6902.05 + 6902.05i) q^{41} +9598.70i q^{42} -17260.4i q^{43} +(-165.408 - 165.408i) q^{44} +(2638.49 + 2638.49i) q^{45} +(11087.6 - 11087.6i) q^{46} -12612.4 q^{47} +(-6317.23 + 6317.23i) q^{48} +19827.9i q^{49} +5588.19 q^{50} +(8771.94 + 6169.40i) q^{51} -125.586 q^{52} +9212.04i q^{53} +(-2872.33 + 2872.33i) q^{54} +11328.6 q^{55} +(-24850.0 + 24850.0i) q^{56} +(-18619.6 - 18619.6i) q^{57} +(-6104.39 - 6104.39i) q^{58} -45973.7i q^{59} +394.373i q^{60} +(26116.4 + 26116.4i) q^{61} +(-14583.7 - 14583.7i) q^{62} +(-10962.7 + 10962.7i) q^{63} -33683.3 q^{64} +(4300.61 - 4300.61i) q^{65} +12332.7i q^{66} -21833.2 q^{67} +(194.499 + 1116.64i) q^{68} +25326.3 q^{69} -49130.9i q^{70} +(-16109.8 + 16109.8i) q^{71} -14872.3 q^{72} +(11623.0 - 11623.0i) q^{73} +(-48572.5 - 48572.5i) q^{74} +(6382.29 + 6382.29i) q^{75} -2783.06i q^{76} +47069.6i q^{77} +(4681.76 + 4681.76i) q^{78} +(13773.4 + 13773.4i) q^{79} +(32334.7 - 32334.7i) q^{80} -6561.00 q^{81} +(38459.2 - 38459.2i) q^{82} +35262.8i q^{83} -1638.59 q^{84} +(-44899.1 - 31578.1i) q^{85} -96177.5 q^{86} -13943.7i q^{87} +(-31928.0 + 31928.0i) q^{88} +90709.7 q^{89} +(14702.0 - 14702.0i) q^{90} +(17868.7 + 17868.7i) q^{91} +(1892.75 + 1892.75i) q^{92} -33312.2i q^{93} +70278.2i q^{94} +(95304.3 + 95304.3i) q^{95} +(-2190.87 - 2190.87i) q^{96} +(-94849.7 + 94849.7i) q^{97} +110484. q^{98} +(-14085.2 + 14085.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 576 q^{4} + 76 q^{5} - 180 q^{6} + 236 q^{7}+O(q^{10}) $ 32 * q - 576 * q^4 + 76 * q^5 - 180 * q^6 + 236 * q^7	\( 32 q - 576 q^{4} + 76 q^{5} - 180 q^{6} + 236 q^{7} + 724 q^{10} - 672 q^{11} - 2684 q^{13} + 2832 q^{14} + 8824 q^{16} - 4868 q^{17} + 1296 q^{18} + 4464 q^{20} - 3528 q^{21} - 1628 q^{22} + 5584 q^{23} + 10872 q^{24} - 36792 q^{28} + 4820 q^{29} - 1728 q^{30} + 13880 q^{31} + 7236 q^{33} + 5068 q^{34} - 12152 q^{35} - 33328 q^{37} - 29256 q^{38} - 11160 q^{39} - 43288 q^{40} - 50932 q^{41} + 116000 q^{44} - 6156 q^{45} + 47596 q^{46} - 16552 q^{47} + 27360 q^{48} + 139080 q^{50} + 12924 q^{51} + 186888 q^{52} - 14580 q^{54} - 129428 q^{55} - 117024 q^{56} + 19440 q^{57} - 212912 q^{58} + 118952 q^{61} - 219736 q^{62} + 19116 q^{63} - 143848 q^{64} + 220976 q^{65} + 98632 q^{67} + 367680 q^{68} + 156060 q^{69} - 205512 q^{71} - 62208 q^{72} - 40924 q^{73} - 178760 q^{74} - 58896 q^{75} + 87012 q^{78} - 309916 q^{79} - 664992 q^{80} - 209952 q^{81} + 350116 q^{82} + 6264 q^{84} + 335336 q^{85} + 1139576 q^{86} - 307696 q^{88} - 62680 q^{89} + 58644 q^{90} + 174460 q^{91} - 94256 q^{92} + 367240 q^{95} - 508824 q^{96} - 299020 q^{97} - 1191536 q^{98} - 54432 q^{99}+O(q^{100}) \) 32 * q - 576 * q^4 + 76 * q^5 - 180 * q^6 + 236 * q^7 + 724 * q^10 - 672 * q^11 - 2684 * q^13 + 2832 * q^14 + 8824 * q^16 - 4868 * q^17 + 1296 * q^18 + 4464 * q^20 - 3528 * q^21 - 1628 * q^22 + 5584 * q^23 + 10872 * q^24 - 36792 * q^28 + 4820 * q^29 - 1728 * q^30 + 13880 * q^31 + 7236 * q^33 + 5068 * q^34 - 12152 * q^35 - 33328 * q^37 - 29256 * q^38 - 11160 * q^39 - 43288 * q^40 - 50932 * q^41 + 116000 * q^44 - 6156 * q^45 + 47596 * q^46 - 16552 * q^47 + 27360 * q^48 + 139080 * q^50 + 12924 * q^51 + 186888 * q^52 - 14580 * q^54 - 129428 * q^55 - 117024 * q^56 + 19440 * q^57 - 212912 * q^58 + 118952 * q^61 - 219736 * q^62 + 19116 * q^63 - 143848 * q^64 + 220976 * q^65 + 98632 * q^67 + 367680 * q^68 + 156060 * q^69 - 205512 * q^71 - 62208 * q^72 - 40924 * q^73 - 178760 * q^74 - 58896 * q^75 + 87012 * q^78 - 309916 * q^79 - 664992 * q^80 - 209952 * q^81 + 350116 * q^82 + 6264 * q^84 + 335336 * q^85 + 1139576 * q^86 - 307696 * q^88 - 62680 * q^89 + 58644 * q^90 + 174460 * q^91 - 94256 * q^92 + 367240 * q^95 - 508824 * q^96 - 299020 * q^97 - 1191536 * q^98 - 54432 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		−	5.57214i		−	0.985025i	−0.870305	−	0.492513i	$-0.836079\pi$
$2$		−	5.57214i		−	0.985025i	0.870305	−	0.492513i	$-0.163921\pi$
$3$	6.36396	−	6.36396i	0.408248	−	0.408248i
$3$	6.36396	−	6.36396i	0.408248	−	0.408248i
$4$	0.951217			0.0297255
$5$	−32.5739	+	32.5739i	−0.582700	+	0.582700i	−0.935644	−	0.352944i	$-0.885180\pi$
$5$	−32.5739	+	32.5739i	−0.582700	+	0.582700i	0.352944	+	0.935644i	$0.385180\pi$
$6$	−35.4609	−	35.4609i	−0.402135	−	0.402135i
$7$	−135.342	−	135.342i	−1.04397	−	1.04397i	−0.998988	−	0.0449810i	$-0.985677\pi$
$7$	−135.342	−	135.342i	−1.04397	−	1.04397i	−0.0449810	−	0.998988i	$-0.514323\pi$
$8$		−	183.609i		−	1.01431i
$9$		−	81.0000i		−	0.333333i
$10$	181.507	+	181.507i	0.573974	+	0.573974i
$11$	−173.891	−	173.891i	−0.433307	−	0.433307i	0.456445	−	0.889752i	$-0.349123\pi$
$11$	−173.891	−	173.891i	−0.433307	−	0.433307i	−0.889752	+	0.456445i	$0.849123\pi$
$12$	6.05351	−	6.05351i	0.0121354	−	0.0121354i
$13$	−132.026			−0.216671			−0.108336	−	0.994114i	$-0.534552\pi$
$13$	−132.026			−0.216671			−0.108336	+	0.994114i	$0.534552\pi$
$14$	−754.145	+	754.145i	−1.02834	+	1.02834i
$15$			414.598i			0.475772i
$16$	−992.656			−0.969391
$17$	204.474	+	1173.90i	0.171600	+	0.985167i
$17$	204.474	+	1173.90i	0.171600	+	0.985167i
$18$	−451.344			−0.328342
$19$		−	2925.79i		−	1.85934i	−0.368394	−	0.929670i	$-0.620092\pi$
$19$		−	2925.79i		−	1.85934i	0.368394	−	0.929670i	$-0.379908\pi$
$20$	−30.9849	+	30.9849i	−0.0173211	+	0.0173211i
$21$	−1722.62			−0.852397
$22$	−968.947	+	968.947i	−0.426819	+	0.426819i
$23$	1989.82	+	1989.82i	0.784322	+	0.784322i	0.980557	−	0.196235i	$-0.0628716\pi$
$23$	1989.82	+	1989.82i	0.784322	+	0.784322i	−0.196235	+	0.980557i	$0.562872\pi$
$24$	−1168.48	−	1168.48i	−0.414088	−	0.414088i
$25$			1002.88i			0.320922i
$26$			735.668i			0.213427i
$27$	−515.481	−	515.481i	−0.136083	−	0.136083i
$28$	−128.740	−	128.740i	−0.0310325	−	0.0310325i
$29$	1095.52	−	1095.52i	0.241894	−	0.241894i	−0.575739	−	0.817633i	$-0.695286\pi$
$29$	1095.52	−	1095.52i	0.241894	−	0.241894i	0.817633	+	0.575739i	$0.195286\pi$
$30$	2310.20			0.468648
$31$	2617.25	−	2617.25i	0.489149	−	0.489149i	−0.418889	−	0.908038i	$-0.637580\pi$
$31$	2617.25	−	2617.25i	0.489149	−	0.489149i	0.908038	+	0.418889i	$0.137580\pi$
$32$		−	344.262i		−	0.0594312i
$33$	−2213.27			−0.353794
$34$	6541.15	−	1139.36i	0.970414	−	0.169030i
$35$	8817.24			1.21664
$36$		−	77.0486i		−	0.00990851i
$37$	8717.02	−	8717.02i	1.04680	−	1.04680i	0.0479503	−	0.998850i	$-0.484731\pi$
$37$	8717.02	−	8717.02i	1.04680	−	1.04680i	0.998850	−	0.0479503i	$-0.0152689\pi$
$38$	−16302.9			−1.83150
$39$	−840.209	+	840.209i	−0.0884557	+	0.0884557i
$40$	5980.86	+	5980.86i	0.591036	+	0.591036i
$41$	6902.05	+	6902.05i	0.641237	+	0.641237i	0.950860	−	0.309623i	$-0.100203\pi$
$41$	6902.05	+	6902.05i	0.641237	+	0.641237i	−0.309623	+	0.950860i	$0.600203\pi$
$42$			9598.70i			0.839632i
$43$		−	17260.4i		−	1.42357i	−0.702395	−	0.711787i	$-0.747886\pi$
$43$		−	17260.4i		−	1.42357i	0.702395	−	0.711787i	$-0.252114\pi$
$44$	−165.408	−	165.408i	−0.0128803	−	0.0128803i
$45$	2638.49	+	2638.49i	0.194233	+	0.194233i
$46$	11087.6	−	11087.6i	0.772576	−	0.772576i
$47$	−12612.4			−0.832824			−0.416412	−	0.909176i	$-0.636713\pi$
$47$	−12612.4			−0.832824			−0.416412	+	0.909176i	$0.636713\pi$
$48$	−6317.23	+	6317.23i	−0.395752	+	0.395752i
$49$			19827.9i			1.17974i
$50$	5588.19			0.316116
$51$	8771.94	+	6169.40i	0.472248	+	0.332137i
$52$	−125.586			−0.00644067
$53$			9212.04i			0.450470i	0.974304	+	0.225235i	$0.0723150\pi$
$53$			9212.04i			0.450470i	−0.974304	+	0.225235i	$0.927685\pi$
$54$	−2872.33	+	2872.33i	−0.134045	+	0.134045i
$55$	11328.6			0.504976
$56$	−24850.0	+	24850.0i	−1.05890	+	1.05890i
$57$	−18619.6	−	18619.6i	−0.759072	−	0.759072i
$58$	−6104.39	−	6104.39i	−0.238271	−	0.238271i
$59$		−	45973.7i		−	1.71941i	−0.510790	−	0.859706i	$-0.670647\pi$
$59$		−	45973.7i		−	1.71941i	0.510790	−	0.859706i	$-0.329353\pi$
$60$			394.373i			0.0141426i
$61$	26116.4	+	26116.4i	0.898645	+	0.898645i	0.995316	−	0.0966714i	$-0.0308196\pi$
$61$	26116.4	+	26116.4i	0.898645	+	0.898645i	−0.0966714	+	0.995316i	$0.530820\pi$
$62$	−14583.7	−	14583.7i	−0.481824	−	0.481824i
$63$	−10962.7	+	10962.7i	−0.347990	+	0.347990i
$64$	−33683.3			−1.02793
$65$	4300.61	−	4300.61i	0.126254	−	0.126254i
$66$			12332.7i			0.348496i
$67$	−21833.2			−0.594198			−0.297099	−	0.954847i	$-0.596019\pi$
$67$	−21833.2			−0.594198			−0.297099	+	0.954847i	$0.596019\pi$
$68$	194.499	+	1116.64i	0.00510089	+	0.0292846i
$69$	25326.3			0.640396
$70$		−	49130.9i		−	1.19842i
$71$	−16109.8	+	16109.8i	−0.379267	+	0.379267i	−0.870838	−	0.491571i	$-0.836423\pi$
$71$	−16109.8	+	16109.8i	−0.379267	+	0.379267i	0.491571	+	0.870838i	$0.336423\pi$
$72$	−14872.3			−0.338102
$73$	11623.0	−	11623.0i	0.255276	−	0.255276i	−0.567854	−	0.823129i	$-0.692226\pi$
$73$	11623.0	−	11623.0i	0.255276	−	0.255276i	0.823129	+	0.567854i	$0.192226\pi$
$74$	−48572.5	−	48572.5i	−1.03112	−	1.03112i
$75$	6382.29	+	6382.29i	0.131016	+	0.131016i
$76$		−	2783.06i		−	0.0552699i
$77$			47069.6i			0.904719i
$78$	4681.76	+	4681.76i	0.0871311	+	0.0871311i
$79$	13773.4	+	13773.4i	0.248299	+	0.248299i	0.820272	−	0.571973i	$-0.193822\pi$
$79$	13773.4	+	13773.4i	0.248299	+	0.248299i	−0.571973	+	0.820272i	$0.693822\pi$
$80$	32334.7	−	32334.7i	0.564864	−	0.564864i
$81$	−6561.00			−0.111111
$82$	38459.2	−	38459.2i	0.631635	−	0.631635i
$83$			35262.8i			0.561852i	0.959729	+	0.280926i	$0.0906415\pi$
$83$			35262.8i			0.561852i	−0.959729	+	0.280926i	$0.909359\pi$
$84$	−1638.59			−0.0253380
$85$	−44899.1	−	31578.1i	−0.674048	−	0.474065i
$86$	−96177.5			−1.40226
$87$		−	13943.7i		−	0.197505i
$88$	−31928.0	+	31928.0i	−0.439506	+	0.439506i
$89$	90709.7			1.21389			0.606944	−	0.794744i	$-0.292395\pi$
$89$	90709.7			1.21389			0.606944	+	0.794744i	$0.292395\pi$
$90$	14702.0	−	14702.0i	0.191325	−	0.191325i
$91$	17868.7	+	17868.7i	0.226198	+	0.226198i
$92$	1892.75	+	1892.75i	0.0233144	+	0.0233144i
$93$		−	33312.2i		−	0.399389i
$94$			70278.2i			0.820353i
$95$	95304.3	+	95304.3i	1.08344	+	1.08344i
$96$	−2190.87	−	2190.87i	−0.0242627	−	0.0242627i
$97$	−94849.7	+	94849.7i	−1.02354	+	1.02354i	−0.0238280	+	0.999716i	$0.507585\pi$
$97$	−94849.7	+	94849.7i	−1.02354	+	1.02354i	−0.999716	+	0.0238280i	$0.992415\pi$
$98$	110484.			1.16208
$99$	−14085.2	+	14085.2i	−0.144436	+	0.144436i
$100$			953.957i			0.00953957i
$101$	188984.			1.84341			0.921705	−	0.387892i	$-0.126797\pi$
$101$	188984.			1.84341			0.921705	+	0.387892i	$0.126797\pi$
$102$	34376.8	−	48878.5i	0.327164	−	0.465176i
$103$	57126.6			0.530573			0.265287	−	0.964170i	$-0.414533\pi$
$103$	57126.6			0.530573			0.265287	+	0.964170i	$0.414533\pi$
$104$			24241.2i			0.219771i
$105$	56112.6	−	56112.6i	0.496692	−	0.496692i
$106$	51330.8			0.443724
$107$	−86259.4	+	86259.4i	−0.728361	+	0.728361i	−0.970293	−	0.241932i	$-0.922219\pi$
$107$	−86259.4	+	86259.4i	−0.728361	+	0.728361i	0.241932	+	0.970293i	$0.422219\pi$
$108$	−490.334	−	490.334i	−0.00404513	−	0.00404513i
$109$	−17063.5	−	17063.5i	−0.137563	−	0.137563i	0.634972	−	0.772535i	$-0.281012\pi$
$109$	−17063.5	−	17063.5i	−0.137563	−	0.137563i	−0.772535	+	0.634972i	$0.781012\pi$
$110$		−	63124.8i		−	0.497414i
$111$		−	110950.i		−	0.854709i
$112$	134348.	+	134348.i	1.01201	+	1.01201i
$113$	−59718.8	−	59718.8i	−0.439962	−	0.439962i	0.452037	−	0.891999i	$-0.350697\pi$
$113$	−59718.8	−	59718.8i	−0.439962	−	0.439962i	−0.891999	+	0.452037i	$0.850697\pi$
$114$	−103751.	+	103751.i	−0.747705	+	0.747705i
$115$	−129632.			−0.914048
$116$	1042.08	−	1042.08i	0.00719043	−	0.00719043i
$117$			10694.1i			0.0722238i
$118$	−256172.			−1.69366
$119$	131204.	−	186552.i	0.849339	−	1.20763i
$120$	76123.9			0.482579
$121$		−	100575.i		−	0.624490i
$122$	145524.	−	145524.i	0.885188	−	0.885188i
$123$	87848.8			0.523568
$124$	2489.58	−	2489.58i	0.0145402	−	0.0145402i
$125$	−134461.	−	134461.i	−0.769701	−	0.769701i
$126$	61085.8	+	61085.8i	0.342778	+	0.342778i
$127$		−	323818.i		−	1.78152i	−0.454472	−	0.890761i	$-0.650172\pi$
$127$		−	323818.i		−	1.78152i	0.454472	−	0.890761i	$-0.349828\pi$
$128$			176672.i			0.953108i
$129$	−109845.	−	109845.i	−0.581172	−	0.581172i
$130$	−23963.6	−	23963.6i	−0.124364	−	0.124364i
$131$	−25094.4	+	25094.4i	−0.127761	+	0.127761i	−0.768096	−	0.640335i	$-0.778796\pi$
$131$	−25094.4	+	25094.4i	−0.127761	+	0.127761i	0.640335	+	0.768096i	$0.278796\pi$
$132$	−2105.30			−0.0105167
$133$	−395982.	+	395982.i	−1.94109	+	1.94109i
$134$			121658.i			0.585300i
$135$	33582.5			0.158591
$136$	215539.	−	37543.3i	0.999260	−	0.174054i
$137$	−231056.			−1.05176			−0.525879	−	0.850559i	$-0.676264\pi$
$137$	−231056.			−1.05176			−0.525879	+	0.850559i	$0.676264\pi$
$138$		−	141122.i		−	0.630806i
$139$	−77164.4	+	77164.4i	−0.338750	+	0.338750i	−0.855897	−	0.517146i	$-0.826994\pi$
$139$	−77164.4	+	77164.4i	−0.338750	+	0.338750i	0.517146	+	0.855897i	$0.326994\pi$
$140$	8387.11			0.0361653
$141$	−80264.9	+	80264.9i	−0.339999	+	0.339999i
$142$	89766.2	+	89766.2i	0.373587	+	0.373587i
$143$	22958.2	+	22958.2i	0.0938853	+	0.0938853i
$144$			80405.2i			0.323130i
$145$			71370.7i			0.281903i
$146$	−64764.8	−	64764.8i	−0.251453	−	0.251453i
$147$	126184.	+	126184.i	0.481628	+	0.481628i
$148$	8291.78	−	8291.78i	0.0311167	−	0.0311167i
$149$	−129096.			−0.476372			−0.238186	−	0.971220i	$-0.576553\pi$
$149$	−129096.			−0.476372			−0.238186	+	0.971220i	$0.576553\pi$
$150$	35563.0	−	35563.0i	0.129054	−	0.129054i
$151$			150361.i			0.536654i	0.963328	+	0.268327i	$0.0864707\pi$
$151$			150361.i			0.536654i	−0.963328	+	0.268327i	$0.913529\pi$
$152$	−537201.			−1.88594
$153$	95086.1	−	16562.4i	0.328389	−	0.0571999i
$154$	262278.			0.891170
$155$			170508.i			0.570054i
$156$	−799.221	+	799.221i	−0.00262939	+	0.00262939i
$157$	−260720.			−0.844159			−0.422080	−	0.906559i	$-0.638700\pi$
$157$	−260720.			−0.844159			−0.422080	+	0.906559i	$0.638700\pi$
$158$	76747.6	−	76747.6i	0.244580	−	0.244580i
$159$	58625.0	+	58625.0i	0.183904	+	0.183904i
$160$	11214.0	+	11214.0i	0.0346305	+	0.0346305i
$161$		−	538612.i		−	1.63761i
$162$			36558.8i			0.109447i
$163$	154665.	+	154665.i	0.455956	+	0.455956i	0.897325	−	0.441369i	$-0.145507\pi$
$163$	154665.	+	154665.i	0.455956	+	0.455956i	−0.441369	+	0.897325i	$0.645507\pi$
$164$	6565.35	+	6565.35i	0.0190611	+	0.0190611i
$165$	72095.0	−	72095.0i	0.206156	−	0.206156i
$166$	196489.			0.553438
$167$	86361.1	−	86361.1i	0.239622	−	0.239622i	−0.577071	−	0.816694i	$-0.695805\pi$
$167$	86361.1	−	86361.1i	0.239622	−	0.239622i	0.816694	+	0.577071i	$0.195805\pi$
$168$			316289.i			0.864591i
$169$	−353862.			−0.953054
$170$	−175958.	+	250184.i	−0.466966	+	0.663954i
$171$	−236989.			−0.619780
$172$		−	16418.4i		−	0.0423165i
$173$	304865.	−	304865.i	0.774448	−	0.774448i	−0.204433	−	0.978881i	$-0.565535\pi$
$173$	304865.	−	304865.i	0.774448	−	0.774448i	0.978881	+	0.204433i	$0.0655349\pi$
$174$	−77696.2			−0.194548
$175$	135732.	−	135732.i	0.335032	−	0.335032i
$176$	172614.	+	172614.i	0.420044	+	0.420044i
$177$	−292575.	−	292575.i	−0.701947	−	0.701947i
$178$		−	505448.i		−	1.19571i
$179$		−	178112.i		−	0.415490i	−0.978183	−	0.207745i	$-0.933388\pi$
$179$		−	178112.i		−	0.415490i	0.978183	−	0.207745i	$-0.0666124\pi$
$180$	2509.77	+	2509.77i	0.00577369	+	0.00577369i
$181$	418382.	+	418382.i	0.949241	+	0.949241i	0.998773	−	0.0495316i	$-0.0157729\pi$
$181$	418382.	+	418382.i	0.949241	+	0.949241i	−0.0495316	+	0.998773i	$0.515773\pi$
$182$	99566.8	−	99566.8i	0.222811	−	0.222811i
$183$	332407.			0.733741
$184$	365349.	−	365349.i	0.795542	−	0.795542i
$185$			567895.i			1.21994i
$186$	−185620.			−0.393408
$187$	168575.	−	239688.i	0.352525	−	0.501235i
$188$	−11997.1			−0.0247562
$189$			139532.i			0.284132i
$190$	531049.	−	531049.i	1.06721	−	1.06721i
$191$	3149.43			0.00624667			0.00312333	−	0.999995i	$-0.499006\pi$
$191$	3149.43			0.00624667			0.00312333	+	0.999995i	$0.499006\pi$
$192$	−214359.	+	214359.i	−0.419652	+	0.419652i
$193$	−192923.	−	192923.i	−0.372812	−	0.372812i	0.495688	−	0.868501i	$-0.334916\pi$
$193$	−192923.	−	192923.i	−0.372812	−	0.372812i	−0.868501	+	0.495688i	$0.834916\pi$
$194$	528516.	+	528516.i	1.00822	+	1.00822i
$195$		−	54737.8i		−	0.103086i
$196$			18860.7i			0.0350685i
$197$	347504.	+	347504.i	0.637962	+	0.637962i	0.950052	−	0.312091i	$-0.101029\pi$
$197$	347504.	+	347504.i	0.637962	+	0.637962i	−0.312091	+	0.950052i	$0.601029\pi$
$198$	78484.7	+	78484.7i	0.142273	+	0.142273i
$199$	140439.	−	140439.i	0.251394	−	0.251394i	−0.570148	−	0.821542i	$-0.693114\pi$
$199$	140439.	−	140439.i	0.251394	−	0.251394i	0.821542	+	0.570148i	$0.193114\pi$
$200$	184138.			0.325513
$201$	−138946.	+	138946.i	−0.242580	+	0.242580i
$202$		−	1.05305e6i		−	1.81581i
$203$	−296539.			−0.505059
$204$	8344.02	+	5868.44i	0.0140378	+	0.00987296i
$205$	−449654.			−0.747298
$206$		−	318318.i		−	0.522628i
$207$	161175.	−	161175.i	0.261441	−	0.261441i
$208$	131057.			0.210039
$209$	−508769.	+	508769.i	−0.805665	+	0.805665i
$210$	−312667.	−	312667.i	−0.489254	−	0.489254i
$211$	686130.	+	686130.i	1.06096	+	1.06096i	0.998017	+	0.0629462i	$0.0200496\pi$
$211$	686130.	+	686130.i	1.06096	+	1.06096i	0.0629462	+	0.998017i	$0.479950\pi$
$212$			8762.65i			0.0133905i
$213$			205044.i			0.309670i
$214$	480650.	+	480650.i	0.717454	+	0.717454i
$215$	562239.	+	562239.i	0.829517	+	0.829517i
$216$	−94646.9	+	94646.9i	−0.138029	+	0.138029i
$217$	−708448.			−1.02131
$218$	−95080.5	+	95080.5i	−0.135503	+	0.135503i
$219$		−	147936.i		−	0.208432i
$220$	10776.0			0.0150107
$221$	−26995.9	−	154986.i	−0.0371807	−	0.213457i
$222$	−618227.			−0.841909
$223$			1.04266e6i			1.40404i	0.712155	+	0.702022i	$0.247719\pi$
$223$			1.04266e6i			1.40404i	−0.712155	+	0.702022i	$0.752281\pi$
$224$	−46593.1	+	46593.1i	−0.0620443	+	0.0620443i
$225$	81233.3			0.106974
$226$	−332762.	+	332762.i	−0.433374	+	0.433374i
$227$	−981737.	−	981737.i	−1.26453	−	1.26453i	−0.948871	−	0.315663i	$-0.897773\pi$
$227$	−981737.	−	981737.i	−1.26453	−	1.26453i	−0.315663	−	0.948871i	$-0.602227\pi$
$228$	−17711.3	−	17711.3i	−0.0225638	−	0.0225638i
$229$		−	131723.i		−	0.165986i	−0.996550	−	0.0829931i	$-0.973552\pi$
$229$		−	131723.i		−	0.165986i	0.996550	−	0.0829931i	$-0.0264480\pi$
$230$			722331.i			0.900360i
$231$	299549.	+	299549.i	0.369350	+	0.369350i
$232$	−201147.	−	201147.i	−0.245354	−	0.245354i
$233$	−516478.	+	516478.i	−0.623250	+	0.623250i	−0.946361	−	0.323111i	$-0.895271\pi$
$233$	−516478.	+	516478.i	−0.623250	+	0.623250i	0.323111	+	0.946361i	$0.395271\pi$
$234$	59589.1			0.0711422
$235$	410836.	−	410836.i	0.485287	−	0.485287i
$236$		−	43731.0i		−	0.0511104i
$237$	175307.			0.202735
$238$	−1.03950e6	−	731090.i	−1.18954	−	0.836620i
$239$	444985.			0.503907			0.251954	−	0.967739i	$-0.418927\pi$
$239$	444985.			0.503907			0.251954	+	0.967739i	$0.418927\pi$
$240$		−	411554.i		−	0.461209i
$241$	1.04636e6	−	1.04636e6i	1.16048	−	1.16048i	0.176109	−	0.984371i	$-0.443649\pi$
$241$	1.04636e6	−	1.04636e6i	1.16048	−	1.16048i	0.984371	−	0.176109i	$-0.0563510\pi$
$242$	−560417.			−0.615138
$243$	−41753.9	+	41753.9i	−0.0453609	+	0.0453609i
$244$	24842.3	+	24842.3i	0.0267127	+	0.0267127i
$245$	−645873.	−	645873.i	−0.687435	−	0.687435i
$246$		−	489506.i		−	0.515727i
$247$			386280.i			0.402866i
$248$	−480551.	−	480551.i	−0.496147	−	0.496147i
$249$	224411.	+	224411.i	0.229375	+	0.229375i
$250$	−749237.	+	749237.i	−0.758175	+	0.758175i
$251$	1.68578e6			1.68895			0.844475	−	0.535595i	$-0.179913\pi$
$251$	1.68578e6			1.68895			0.844475	+	0.535595i	$0.179913\pi$
$252$	−10427.9	+	10427.9i	−0.0103442	+	0.0103442i
$253$		−	692024.i		−	0.679704i
$254$	−1.80436e6			−1.75484
$255$	−486698.	+	84774.7i	−0.468715	+	0.0816424i
$256$	−93425.0			−0.0890971
$257$		−	928224.i		−	0.876637i	−0.898820	−	0.438319i	$-0.855574\pi$
$257$		−	928224.i		−	0.876637i	0.898820	−	0.438319i	$-0.144426\pi$
$258$	−612070.	+	612070.i	−0.572469	+	0.572469i
$259$	−2.35956e6			−2.18565
$260$	4090.81	−	4090.81i	0.00375298	−	0.00375298i
$261$	−88737.0	−	88737.0i	−0.0806313	−	0.0806313i
$262$	139829.	+	139829.i	0.125848	+	0.125848i
$263$			498692.i			0.444573i	0.974981	+	0.222287i	$0.0713520\pi$
$263$			498692.i			0.444573i	−0.974981	+	0.222287i	$0.928648\pi$
$264$			406377.i			0.358855i
$265$	−300072.	−	300072.i	−0.262489	−	0.262489i
$266$	2.20647e6	+	2.20647e6i	1.91202	+	1.91202i
$267$	577273.	−	577273.i	0.495568	−	0.495568i
$268$	−20768.1			−0.0176628
$269$	659670.	−	659670.i	0.555835	−	0.555835i	−0.372284	−	0.928119i	$-0.621425\pi$
$269$	659670.	−	659670.i	0.555835	−	0.555835i	0.928119	+	0.372284i	$0.121425\pi$
$270$		−	187126.i		−	0.156216i
$271$	1.51896e6			1.25639			0.628193	−	0.778058i	$-0.283795\pi$
$271$	1.51896e6			1.25639			0.628193	+	0.778058i	$0.283795\pi$
$272$	−202973.	−	1.16528e6i	−0.166347	−	0.955012i
$273$	227431.			0.184690
$274$			1.28748e6i			1.03601i
$275$	174392.	−	174392.i	0.139058	−	0.139058i
$276$	24090.8			0.0190361
$277$	160028.	−	160028.i	0.125313	−	0.125313i	−0.641669	−	0.766982i	$-0.721758\pi$
$277$	160028.	−	160028.i	0.125313	−	0.125313i	0.766982	+	0.641669i	$0.221758\pi$
$278$	429971.	+	429971.i	0.333678	+	0.333678i
$279$	−211997.	−	211997.i	−0.163050	−	0.163050i
$280$		−	1.61892e6i		−	1.23405i
$281$		−	672360.i		−	0.507968i	−0.967208	−	0.253984i	$-0.918259\pi$
$281$		−	672360.i		−	0.507968i	0.967208	−	0.253984i	$-0.0817411\pi$
$282$	447248.	+	447248.i	0.334908	+	0.334908i
$283$	1.10245e6	+	1.10245e6i	0.818260	+	0.818260i	0.985856	−	0.167596i	$-0.0536004\pi$
$283$	1.10245e6	+	1.10245e6i	0.818260	+	0.818260i	−0.167596	+	0.985856i	$0.553600\pi$
$284$	−15323.9	+	15323.9i	−0.0112739	+	0.0112739i
$285$	1.21303e6			0.884623
$286$	127926.	−	127926.i	0.0924793	−	0.0924793i
$287$		−	1.86828e6i		−	1.33886i
$288$	−27885.2			−0.0198104
$289$	−1.33624e6	+	480066.i	−0.941107	+	0.338109i
$290$	397688.			0.277682
$291$			1.20724e6i			0.835720i
$292$	11056.0	−	11056.0i	0.00758821	−	0.00758821i
$293$	−644762.			−0.438763			−0.219382	−	0.975639i	$-0.570404\pi$
$293$	−644762.			−0.438763			−0.219382	+	0.975639i	$0.570404\pi$
$294$	703116.	−	703116.i	0.474415	−	0.474415i
$295$	1.49754e6	+	1.49754e6i	1.00190	+	1.00190i
$296$	−1.60052e6	−	1.60052e6i	−1.06178	−	1.06178i
$297$			179275.i			0.117931i
$298$			719340.i			0.469239i
$299$	−262708.	−	262708.i	−0.169940	−	0.169940i
$300$	6070.95	+	6070.95i	0.00389451	+	0.00389451i
$301$	−2.33606e6	+	2.33606e6i	−1.48617	+	1.48617i
$302$	837836.			0.528617
$303$	1.20269e6	−	1.20269e6i	0.752569	−	0.752569i
$304$			2.90430e6i			1.80243i
$305$	−1.70142e6			−1.04728
$306$	−92288.2	−	529833.i	−0.0563433	−	0.323471i
$307$	1.41071e6			0.854264			0.427132	−	0.904189i	$-0.359524\pi$
$307$	1.41071e6			0.854264			0.427132	+	0.904189i	$0.359524\pi$
$308$			44773.4i			0.0268933i
$309$	363551.	−	363551.i	0.216606	−	0.216606i
$310$	950096.			0.561518
$311$	−525362.	+	525362.i	−0.308005	+	0.308005i	−0.844135	−	0.536130i	$-0.819886\pi$
$311$	−525362.	+	525362.i	−0.308005	+	0.308005i	0.536130	+	0.844135i	$0.319886\pi$
$312$	154270.	+	154270.i	0.0897211	+	0.0897211i
$313$	247427.	+	247427.i	0.142753	+	0.142753i	0.774872	−	0.632118i	$-0.217814\pi$
$313$	247427.	+	247427.i	0.142753	+	0.142753i	−0.632118	+	0.774872i	$0.717814\pi$
$314$			1.45277e6i			0.831518i
$315$		−	714196.i		−	0.405547i
$316$	13101.5	+	13101.5i	0.00738081	+	0.00738081i
$317$	611885.	+	611885.i	0.341997	+	0.341997i	0.857118	−	0.515121i	$-0.172253\pi$
$317$	611885.	+	611885.i	0.341997	+	0.341997i	−0.515121	+	0.857118i	$0.672253\pi$
$318$	326667.	−	326667.i	0.181150	−	0.181150i
$319$	−381002.			−0.209629
$320$	1.09720e6	−	1.09720e6i	0.598976	−	0.598976i
$321$			1.09790e6i			0.594704i
$322$	−3.00123e6			−1.61309
$323$	3.43459e6	−	598248.i	1.83176	−	0.319062i
$324$	−6240.94			−0.00330284
$325$		−	132406.i		−	0.0695345i
$326$	861815.	−	861815.i	0.449128	−	0.449128i
$327$	−217183.			−0.112320
$328$	1.26728e6	−	1.26728e6i	0.650410	−	0.650410i
$329$	1.70699e6	+	1.70699e6i	0.869443	+	0.869443i
$330$	−401724.	−	401724.i	−0.203069	−	0.203069i
$331$		−	2.97513e6i		−	1.49257i	−0.665625	−	0.746287i	$-0.731835\pi$
$331$		−	2.97513e6i		−	1.49257i	0.665625	−	0.746287i	$-0.268165\pi$
$332$			33542.6i			0.0167013i
$333$	−706079.	−	706079.i	−0.348933	−	0.348933i
$334$	−481216.	−	481216.i	−0.236034	−	0.236034i
$335$	711194.	−	711194.i	0.346239	−	0.346239i
$336$	1.70997e6			0.826306
$337$	1.18080e6	−	1.18080e6i	0.566370	−	0.566370i	−0.364739	−	0.931110i	$-0.618842\pi$
$337$	1.18080e6	−	1.18080e6i	0.566370	−	0.566370i	0.931110	+	0.364739i	$0.118842\pi$
$338$			1.97177e6i			0.938782i
$339$	−760097.			−0.359228
$340$	−42708.8	−	30037.6i	−0.0200364	−	0.0140919i
$341$	−910234.			−0.423904
$342$			1.32054e6i			0.610499i
$343$	408857.	−	408857.i	0.187645	−	0.187645i
$344$	−3.16917e6			−1.44394
$345$	−824976.	+	824976.i	−0.373159	+	0.373159i
$346$	−1.69875e6	−	1.69875e6i	−0.762851	−	0.762851i
$347$	1.01350e6	+	1.01350e6i	0.451858	+	0.451858i	0.895971	−	0.444113i	$-0.146481\pi$
$347$	1.01350e6	+	1.01350e6i	0.451858	+	0.451858i	−0.444113	+	0.895971i	$0.646481\pi$
$348$		−	13263.5i		−	0.00587096i
$349$			3.04994e6i			1.34038i	0.742191	+	0.670189i	$0.233787\pi$
$349$			3.04994e6i			1.34038i	−0.742191	+	0.670189i	$0.766213\pi$
$350$	−756317.	−	756317.i	−0.330015	−	0.330015i
$351$	68056.9	+	68056.9i	0.0294852	+	0.0294852i
$352$	−59864.2	+	59864.2i	−0.0257520	+	0.0257520i
$353$	−1.27414e6			−0.544226			−0.272113	−	0.962265i	$-0.587722\pi$
$353$	−1.27414e6			−0.544226			−0.272113	+	0.962265i	$0.587722\pi$
$354$	−1.63027e6	+	1.63027e6i	−0.691435	+	0.691435i
$355$		−	1.04952e6i		−	0.441997i
$356$	86284.7			0.0360835
$357$	−352232.	−	2.02219e6i	−0.146271	−	0.839753i
$358$	−992465.			−0.409268
$359$			2.54146e6i			1.04075i	0.853938	+	0.520375i	$0.174208\pi$
$359$			2.54146e6i			1.04075i	−0.853938	+	0.520375i	$0.825792\pi$
$360$	484450.	−	484450.i	0.197012	−	0.197012i
$361$	−6.08413e6			−2.45714
$362$	2.33128e6	−	2.33128e6i	0.935026	−	0.935026i
$363$	−640053.	−	640053.i	−0.254947	−	0.254947i
$364$	16997.0	+	16997.0i	0.00672386	+	0.00672386i
$365$			757211.i			0.297498i
$366$		−	1.85222e6i		−	0.722753i
$367$	−2.41958e6	−	2.41958e6i	−0.937722	−	0.937722i	0.0604494	−	0.998171i	$-0.480747\pi$
$367$	−2.41958e6	−	2.41958e6i	−0.937722	−	0.937722i	−0.998171	+	0.0604494i	$0.980747\pi$
$368$	−1.97521e6	−	1.97521e6i	−0.760314	−	0.760314i
$369$	559066.	−	559066.i	0.213746	−	0.213746i
$370$	3.16439e6			1.20167
$371$	1.24678e6	−	1.24678e6i	0.470277	−	0.470277i
$372$		−	31687.1i		−	0.0118720i
$373$	2.51785e6			0.937039			0.468520	−	0.883453i	$-0.344788\pi$
$373$	2.51785e6			0.937039			0.468520	+	0.883453i	$0.344788\pi$
$374$	−1.33557e6	−	939325.i	−0.493729	−	0.347246i
$375$	−1.71141e6			−0.628458
$376$			2.31575e6i			0.844738i
$377$	−144637.	+	144637.i	−0.0524115	+	0.0524115i
$378$	777495.			0.279877
$379$	77448.3	−	77448.3i	0.0276958	−	0.0276958i	−0.693123	−	0.720819i	$-0.743766\pi$
$379$	77448.3	−	77448.3i	0.0276958	−	0.0276958i	0.720819	+	0.693123i	$0.243766\pi$
$380$	90655.1	+	90655.1i	0.0322058	+	0.0322058i
$381$	−2.06076e6	−	2.06076e6i	−0.727303	−	0.727303i
$382$		−	17549.1i		−	0.00615312i
$383$			5.64441e6i			1.96617i	0.183141	+	0.983087i	$0.441374\pi$
$383$			5.64441e6i			1.96617i	−0.183141	+	0.983087i	$0.558626\pi$
$384$	1.12433e6	+	1.12433e6i	0.389105	+	0.389105i
$385$	−1.53324e6	−	1.53324e6i	−0.527179	−	0.527179i
$386$	−1.07499e6	+	1.07499e6i	−0.367229	+	0.367229i
$387$	−1.39809e6			−0.474525
$388$	−90222.7	+	90222.7i	−0.0304254	+	0.0304254i
$389$		−	2.08078e6i		−	0.697193i	−0.937273	−	0.348596i	$-0.886658\pi$
$389$		−	2.08078e6i		−	0.697193i	0.937273	−	0.348596i	$-0.113342\pi$
$390$	−305007.			−0.101543
$391$	−1.92899e6	+	2.74272e6i	−0.638098	+	0.907277i
$392$	3.64058e6			1.19662
$393$			319399.i			0.104316i
$394$	1.93634e6	−	1.93634e6i	0.628408	−	0.628408i
$395$	−897309.			−0.289367
$396$	−13398.1	+	13398.1i	−0.00429343	+	0.00429343i
$397$	1.70919e6	+	1.70919e6i	0.544270	+	0.544270i	0.924778	−	0.380507i	$-0.124251\pi$
$397$	1.70919e6	+	1.70919e6i	0.544270	+	0.544270i	−0.380507	+	0.924778i	$0.624251\pi$
$398$	−782545.	−	782545.i	−0.247629	−	0.247629i
$399$			5.04003e6i			1.58490i
$400$		−	995515.i		−	0.311098i
$401$	201521.	+	201521.i	0.0625835	+	0.0625835i	0.737706	−	0.675122i	$-0.235909\pi$
$401$	201521.	+	201521.i	0.0625835	+	0.0625835i	−0.675122	+	0.737706i	$0.735909\pi$
$402$	774226.	+	774226.i	0.238948	+	0.238948i
$403$	−345545.	+	345545.i	−0.105985	+	0.105985i
$404$	179765.			0.0547964
$405$	213717.	−	213717.i	0.0647444	−	0.0647444i
$406$			1.65236e6i			0.497496i
$407$	−3.03163e6			−0.907172
$408$	1.13276e6	−	1.61061e6i	0.336889	−	0.479004i
$409$	3.84970e6			1.13794			0.568970	−	0.822359i	$-0.307342\pi$
$409$	3.84970e6			1.13794			0.568970	+	0.822359i	$0.307342\pi$
$410$			2.50554e6i			0.736107i
$411$	−1.47043e6	+	1.47043e6i	−0.429379	+	0.429379i
$412$	54339.8			0.0157716
$413$	−6.22218e6	+	6.22218e6i	−1.79501	+	1.79501i
$414$	−898092.	−	898092.i	−0.257525	−	0.257525i
$415$	−1.14865e6	−	1.14865e6i	−0.327391	−	0.327391i
$416$			45451.6i			0.0128770i
$417$			982142.i			0.276589i
$418$	2.83493e6	+	2.83493e6i	0.793601	+	0.793601i
$419$	1.80899e6	+	1.80899e6i	0.503386	+	0.503386i	0.912488	−	0.409102i	$-0.134158\pi$
$419$	1.80899e6	+	1.80899e6i	0.503386	+	0.503386i	−0.409102	+	0.912488i	$0.634158\pi$
$420$	53375.2	−	53375.2i	0.0147644	−	0.0147644i
$421$	3.93452e6			1.08190			0.540950	−	0.841055i	$-0.318065\pi$
$421$	3.93452e6			1.08190			0.540950	+	0.841055i	$0.318065\pi$
$422$	3.82321e6	−	3.82321e6i	1.04508	−	1.04508i
$423$			1.02161e6i			0.277608i
$424$	1.69141e6			0.456914
$425$	−1.17728e6	+	205063.i	−0.316161	+	0.0550700i
$426$	1.14254e6			0.305033
$427$		−	7.06928e6i		−	1.87631i
$428$	−82051.4	+	82051.4i	−0.0216509	+	0.0216509i
$429$	292210.			0.0766570
$430$	3.13288e6	−	3.13288e6i	0.817095	−	0.817095i
$431$	−4.35684e6	−	4.35684e6i	−1.12974	−	1.12974i	−0.990219	−	0.139522i	$-0.955443\pi$
$431$	−4.35684e6	−	4.35684e6i	−1.12974	−	1.12974i	−0.139522	−	0.990219i	$-0.544557\pi$
$432$	511695.	+	511695.i	0.131917	+	0.131917i
$433$		−	5.36002e6i		−	1.37387i	−0.726717	−	0.686937i	$-0.758955\pi$
$433$		−	5.36002e6i		−	1.37387i	0.726717	−	0.686937i	$-0.241045\pi$
$434$			3.94757e6i			1.00602i
$435$	454200.	+	454200.i	0.115086	+	0.115086i
$436$	−16231.1	−	16231.1i	−0.00408915	−	0.00408915i
$437$	5.82179e6	−	5.82179e6i	1.45832	−	1.45832i
$438$	−824321.			−0.205311
$439$	5.41406e6	−	5.41406e6i	1.34079	−	1.34079i	0.445522	−	0.895271i	$-0.353018\pi$
$439$	5.41406e6	−	5.41406e6i	1.34079	−	1.34079i	0.895271	−	0.445522i	$-0.146982\pi$
$440$		−	2.08004e6i		−	0.512200i
$441$	1.60606e6			0.393247
$442$	−863603.	+	150425.i	−0.210261	+	0.0366239i
$443$	−6.46209e6			−1.56446			−0.782229	−	0.622992i	$-0.785917\pi$
$443$	−6.46209e6			−1.56446			−0.782229	+	0.622992i	$0.785917\pi$
$444$		−	105537.i		−	0.0254067i
$445$	−2.95477e6	+	2.95477e6i	−0.707333	+	0.707333i
$446$	5.80985e6			1.38302
$447$	−821561.	+	821561.i	−0.194478	+	0.194478i
$448$	4.55876e6	+	4.55876e6i	1.07313	+	1.07313i
$449$	4.92069e6	+	4.92069e6i	1.15189	+	1.15189i	0.986174	+	0.165713i	$0.0529925\pi$
$449$	4.92069e6	+	4.92069e6i	1.15189	+	1.15189i	0.165713	+	0.986174i	$0.447007\pi$
$450$		−	452644.i		−	0.105372i
$451$		−	2.40041e6i		−	0.555705i
$452$	−56805.6	−	56805.6i	−0.0130781	−	0.0130781i
$453$	956895.	+	956895.i	0.219088	+	0.219088i
$454$	−5.47038e6	+	5.47038e6i	−1.24560	+	1.24560i
$455$	−1.16411e6			−0.263611
$456$	−3.41872e6	+	3.41872e6i	−0.769931	+	0.769931i
$457$		−	5.02743e6i		−	1.12605i	−0.826442	−	0.563023i	$-0.809638\pi$
$457$		−	5.02743e6i		−	1.12605i	0.826442	−	0.563023i	$-0.190362\pi$
$458$	−733978.			−0.163501
$459$	499722.	−	710527.i	0.110712	−	0.157416i
$460$	−123309.			−0.0271706
$461$		−	7.06992e6i		−	1.54939i	−0.632332	−	0.774697i	$-0.717902\pi$
$461$		−	7.06992e6i		−	1.54939i	0.632332	−	0.774697i	$-0.282098\pi$
$462$	1.66913e6	−	1.66913e6i	0.363819	−	0.363819i
$463$	6.28004e6			1.36148			0.680738	−	0.732527i	$-0.261659\pi$
$463$	6.28004e6			1.36148			0.680738	+	0.732527i	$0.261659\pi$
$464$	−1.08747e6	+	1.08747e6i	−0.234490	+	0.234490i
$465$	1.08511e6	+	1.08511e6i	0.232724	+	0.232724i
$466$	2.87789e6	+	2.87789e6i	0.613917	+	0.613917i
$467$		−	969512.i		−	0.205713i	−0.994696	−	0.102856i	$-0.967202\pi$
$467$		−	969512.i		−	0.205713i	0.994696	−	0.102856i	$-0.0327982\pi$
$468$			10172.4i			0.00214689i
$469$	2.95495e6	+	2.95495e6i	0.620324	+	0.620324i
$470$	−2.28923e6	−	2.28923e6i	−0.478020	−	0.478020i
$471$	−1.65921e6	+	1.65921e6i	−0.344627	+	0.344627i
$472$	−8.44119e6			−1.74401
$473$	−3.00144e6	+	3.00144e6i	−0.616845	+	0.616845i
$474$		−	976837.i		−	0.199699i
$475$	2.93421e6			0.596702
$476$	124804.	−	177452.i	0.0252471	−	0.0358974i
$477$	746175.			0.150157
$478$		−	2.47952e6i		−	0.496361i
$479$	−1.86689e6	+	1.86689e6i	−0.371775	+	0.371775i	−0.868123	−	0.496348i	$-0.834674\pi$
$479$	−1.86689e6	+	1.86689e6i	−0.371775	+	0.371775i	0.496348	+	0.868123i	$0.334674\pi$
$480$	142731.			0.0282757
$481$	−1.15087e6	+	1.15087e6i	−0.226812	+	0.226812i
$482$	−5.83045e6	−	5.83045e6i	−1.14310	−	1.14310i
$483$	−3.42771e6	−	3.42771e6i	−0.668553	−	0.668553i
$484$		−	95668.4i		−	0.0185633i
$485$		−	6.17925e6i		−	1.19284i
$486$	232659.	+	232659.i	0.0446816	+	0.0446816i
$487$	3.30528e6	+	3.30528e6i	0.631519	+	0.631519i	0.948449	−	0.316930i	$-0.102652\pi$
$487$	3.30528e6	+	3.30528e6i	0.631519	+	0.631519i	−0.316930	+	0.948449i	$0.602652\pi$
$488$	4.79520e6	−	4.79520e6i	0.911501	−	0.911501i
$489$	1.96856e6			0.372286
$490$	−3.59890e6	+	3.59890e6i	−0.677141	+	0.677141i
$491$			1.00575e7i			1.88272i	0.337403	+	0.941360i	$0.390451\pi$
$491$			1.00575e7i			1.88272i	−0.337403	+	0.941360i	$0.609549\pi$
$492$	83563.3			0.0155633
$493$	1.51004e6	+	1.06203e6i	0.279815	+	0.196797i
$494$	2.15241e6			0.396833
$495$		−	917620.i		−	0.168325i
$496$	−2.59803e6	+	2.59803e6i	−0.474177	+	0.474177i
$497$	4.36067e6			0.791885
$498$	1.25045e6	−	1.25045e6i	0.225940	−	0.225940i
$499$	−13766.8	−	13766.8i	−0.00247504	−	0.00247504i	0.705868	−	0.708343i	$-0.250557\pi$
$499$	−13766.8	−	13766.8i	−0.00247504	−	0.00247504i	−0.708343	+	0.705868i	$0.750557\pi$
$500$	−127902.	−	127902.i	−0.0228798	−	0.0228798i
$501$		−	1.09920e6i		−	0.195651i
$502$		−	9.39341e6i		−	1.66366i
$503$	−533830.	−	533830.i	−0.0940769	−	0.0940769i	0.658502	−	0.752579i	$-0.271190\pi$
$503$	−533830.	−	533830.i	−0.0940769	−	0.0940769i	−0.752579	+	0.658502i	$0.771190\pi$
$504$	2.01285e6	+	2.01285e6i	0.352968	+	0.352968i
$505$	−6.15595e6	+	6.15595e6i	−1.07415	+	1.07415i
$506$	−3.85606e6			−0.669526
$507$	−2.25196e6	+	2.25196e6i	−0.389082	+	0.389082i
$508$		−	308021.i		−	0.0529567i
$509$	2.49970e6			0.427655			0.213828	−	0.976871i	$-0.431407\pi$
$509$	2.49970e6			0.427655			0.213828	+	0.976871i	$0.431407\pi$
$510$	472377.	+	2.71195e6i	0.0804198	+	0.461696i
$511$	−3.14615e6			−0.533000
$512$			6.17407e6i			1.04087i
$513$	−1.50819e6	+	1.50819e6i	−0.253024	+	0.253024i
$514$	−5.17220e6			−0.863510
$515$	−1.86084e6	+	1.86084e6i	−0.309165	+	0.309165i
$516$	−104486.	−	104486.i	−0.0172756	−	0.0172756i
$517$	2.19319e6	+	2.19319e6i	0.360869	+	0.360869i
$518$			1.31478e7i			2.15292i
$519$		−	3.88030e6i		−	0.632334i
$520$	−789630.	−	789630.i	−0.128060	−	0.128060i
$521$	−2.63994e6	−	2.63994e6i	−0.426089	−	0.426089i	0.461205	−	0.887294i	$-0.347417\pi$
$521$	−2.63994e6	−	2.63994e6i	−0.426089	−	0.426089i	−0.887294	+	0.461205i	$0.847417\pi$
$522$	−494455.	+	494455.i	−0.0794238	+	0.0794238i
$523$	−6.89081e6			−1.10158			−0.550790	−	0.834644i	$-0.685673\pi$
$523$	−6.89081e6			−1.10158			−0.550790	+	0.834644i	$0.685673\pi$
$524$	−23870.2	+	23870.2i	−0.00379776	+	0.00379776i
$525$		−	1.72758e6i		−	0.273553i
$526$	2.77878e6			0.437916
$527$	3.60756e6	+	2.53724e6i	0.565831	+	0.397956i
$528$	2.19702e6			0.342965
$529$			1.48242e6i			0.230321i
$530$	−1.67204e6	+	1.67204e6i	−0.258558	+	0.258558i
$531$	−3.72387e6			−0.573137
$532$	−376665.	+	376665.i	−0.0577000	+	0.0577000i
$533$	−911251.	−	911251.i	−0.138938	−	0.138938i
$534$	−3.21665e6	−	3.21665e6i	−0.488147	−	0.488147i
$535$		−	5.61961e6i		−	0.848832i
$536$			4.00877e6i			0.602698i
$537$	−1.13350e6	−	1.13350e6i	−0.169623	−	0.169623i
$538$	−3.67578e6	−	3.67578e6i	−0.547512	−	0.547512i
$539$	3.44790e6	−	3.44790e6i	0.511191	−	0.511191i
$540$	31944.2			0.00471420
$541$	−9.50077e6	+	9.50077e6i	−1.39562	+	1.39562i	−0.583507	+	0.812108i	$0.698320\pi$
$541$	−9.50077e6	+	9.50077e6i	−1.39562	+	1.39562i	−0.812108	+	0.583507i	$0.801680\pi$
$542$		−	8.46386e6i		−	1.23757i
$543$	5.32513e6			0.775052
$544$	404130.	−	70392.8i	0.0585496	−	0.0101984i
$545$	1.11165e6			0.160316
$546$		−	1.26728e6i		−	0.181924i
$547$	5.82821e6	−	5.82821e6i	0.832851	−	0.832851i	−0.155055	−	0.987906i	$-0.549555\pi$
$547$	5.82821e6	−	5.82821e6i	0.832851	−	0.832851i	0.987906	+	0.155055i	$0.0495555\pi$
$548$	−219785.			−0.0312641
$549$	2.11543e6	−	2.11543e6i	0.299548	−	0.299548i
$550$	−971738.	−	971738.i	−0.136975	−	0.136975i
$551$	−3.20525e6	−	3.20525e6i	−0.449763	−	0.449763i
$552$		−	4.65013e6i		−	0.649557i
$553$		−	3.72825e6i		−	0.518432i
$554$	−891701.	−	891701.i	−0.123437	−	0.123437i
$555$	3.61406e6	+	3.61406e6i	0.498039	+	0.498039i
$556$	−73400.1	+	73400.1i	−0.0100695	+	0.0100695i
$557$	6.52180e6			0.890696			0.445348	−	0.895358i	$-0.353080\pi$
$557$	6.52180e6			0.890696			0.445348	+	0.895358i	$0.353080\pi$
$558$	−1.18128e6	+	1.18128e6i	−0.160608	+	0.160608i
$559$			2.27883e6i			0.308448i
$560$	−8.75249e6			−1.17940
$561$	−452558.	−	2.59817e6i	−0.0607109	−	0.348546i
$562$	−3.74649e6			−0.500361
$563$		−	5.93241e6i		−	0.788788i	−0.918942	−	0.394394i	$-0.870955\pi$
$563$		−	5.93241e6i		−	0.788788i	0.918942	−	0.394394i	$-0.129045\pi$
$564$	−76349.4	+	76349.4i	−0.0101067	+	0.0101067i
$565$	3.89055e6			0.512732
$566$	6.14299e6	−	6.14299e6i	0.806006	−	0.806006i
$567$	887979.	+	887979.i	0.115997	+	0.115997i
$568$	2.95790e6	+	2.95790e6i	0.384692	+	0.384692i
$569$		−	479552.i		−	0.0620947i	−0.999518	−	0.0310474i	$-0.990116\pi$
$569$		−	479552.i		−	0.0620947i	0.999518	−	0.0310474i	$-0.00988427\pi$
$570$		−	6.75916e6i		−	0.871376i
$571$	−1.08129e6	−	1.08129e6i	−0.138788	−	0.138788i	0.634299	−	0.773087i	$-0.281289\pi$
$571$	−1.08129e6	−	1.08129e6i	−0.138788	−	0.138788i	−0.773087	+	0.634299i	$0.781289\pi$
$572$	21838.2	+	21838.2i	0.00279079	+	0.00279079i
$573$	20042.8	−	20042.8i	0.00255019	−	0.00255019i
$574$	−1.04103e7			−1.31881
$575$	−1.99555e6	+	1.99555e6i	−0.251706	+	0.251706i
$576$			2.72835e6i			0.342644i
$577$	3.57871e6			0.447493			0.223747	−	0.974647i	$-0.428171\pi$
$577$	3.57871e6			0.447493			0.223747	+	0.974647i	$0.428171\pi$
$578$	2.67500e6	+	7.44571e6i	0.333045	+	0.927014i
$579$	−2.45551e6			−0.304400
$580$			67889.0i			0.00837972i
$581$	4.77254e6	−	4.77254e6i	0.586556	−	0.586556i
$582$	6.72691e6			0.823205
$583$	1.60189e6	−	1.60189e6i	0.195192	−	0.195192i
$584$	−2.13408e6	−	2.13408e6i	−0.258928	−	0.258928i
$585$	−348349.	−	348349.i	−0.0420848	−	0.0420848i
$586$			3.59271e6i			0.432193i
$587$			5.11292e6i			0.612455i	0.951958	+	0.306227i	$0.0990668\pi$
$587$			5.11292e6i			0.612455i	−0.951958	+	0.306227i	$0.900933\pi$
$588$	120029.	+	120029.i	0.0143166	+	0.0143166i
$589$	−7.65752e6	−	7.65752e6i	−0.909494	−	0.909494i
$590$	8.34453e6	−	8.34453e6i	0.986898	−	0.986898i
$591$	4.42301e6			0.520894
$592$	−8.65300e6	+	8.65300e6i	−1.01476	+	1.01476i
$593$		−	670277.i		−	0.0782740i	−0.999234	−	0.0391370i	$-0.987539\pi$
$593$		−	670277.i		−	0.0782740i	0.999234	−	0.0391370i	$-0.0124609\pi$
$594$	998947.			0.116165
$595$	1.80290e6	+	1.03506e7i	0.208775	+	1.19859i
$596$	−122798.			−0.0141604
$597$		−	1.78749e6i		−	0.205262i
$598$	−1.46385e6	+	1.46385e6i	−0.167395	+	0.167395i
$599$	1.34679e7			1.53367			0.766835	−	0.641845i	$-0.221831\pi$
$599$	1.34679e7			1.53367			0.766835	+	0.641845i	$0.221831\pi$
$600$	1.17185e6	−	1.17185e6i	0.132890	−	0.132890i
$601$	9.76028e6	+	9.76028e6i	1.10224	+	1.10224i	0.994140	+	0.108100i	$0.0344765\pi$
$601$	9.76028e6	+	9.76028e6i	1.10224	+	1.10224i	0.108100	+	0.994140i	$0.465523\pi$
$602$	1.30169e7	+	1.30169e7i	1.46391	+	1.46391i
$603$			1.76849e6i			0.198066i
$604$			143026.i			0.0159523i
$605$	3.27611e6	+	3.27611e6i	0.363890	+	0.363890i
$606$	−6.70155e6	−	6.70155e6i	−0.741299	−	0.741299i
$607$	7.38649e6	−	7.38649e6i	0.813704	−	0.813704i	−0.171483	−	0.985187i	$-0.554856\pi$
$607$	7.38649e6	−	7.38649e6i	0.813704	−	0.813704i	0.985187	+	0.171483i	$0.0548560\pi$
$608$	−1.00724e6			−0.110503
$609$	−1.88717e6	+	1.88717e6i	−0.206190	+	0.206190i
$610$			9.48058e6i			1.03160i
$611$	1.66517e6			0.180449
$612$	90447.6	−	15754.5i	0.00976154	−	0.00170030i
$613$	2.98265e6			0.320591			0.160295	−	0.987069i	$-0.448755\pi$
$613$	2.98265e6			0.320591			0.160295	+	0.987069i	$0.448755\pi$
$614$		−	7.86068e6i		−	0.841472i
$615$	−2.86158e6	+	2.86158e6i	−0.305083	+	0.305083i
$616$	8.64239e6			0.917661
$617$	−5.31704e6	+	5.31704e6i	−0.562286	+	0.562286i	−0.929956	−	0.367670i	$-0.880155\pi$
$617$	−5.31704e6	+	5.31704e6i	−0.562286	+	0.562286i	0.367670	+	0.929956i	$0.380155\pi$
$618$	−2.02576e6	−	2.02576e6i	−0.213362	−	0.213362i
$619$	−4.67722e6	−	4.67722e6i	−0.490638	−	0.490638i	0.417869	−	0.908507i	$-0.362777\pi$
$619$	−4.67722e6	−	4.67722e6i	−0.490638	−	0.490638i	−0.908507	+	0.417869i	$0.862777\pi$
$620$			162190.i			0.0169452i
$621$		−	2.05143e6i		−	0.213465i
$622$	2.92739e6	+	2.92739e6i	0.303393	+	0.303393i
$623$	−1.22768e7	−	1.22768e7i	−1.26726	−	1.26726i
$624$	834039.	−	834039.i	0.0857481	−	0.0857481i
$625$	5.62586e6			0.576088
$626$	1.37870e6	−	1.37870e6i	0.140616	−	0.140616i
$627$			6.47557e6i			0.657823i
$628$	−248001.			−0.0250931
$629$	1.20153e7	+	8.45053e6i	1.21090	+	0.851642i
$630$	−3.97960e6			−0.399474
$631$			1.16028e7i			1.16009i	0.814585	+	0.580044i	$0.196964\pi$
$631$			1.16028e7i			1.16009i	−0.814585	+	0.580044i	$0.803036\pi$
$632$	2.52893e6	−	2.52893e6i	0.251851	−	0.251851i
$633$	8.73301e6			0.866273
$634$	3.40951e6	−	3.40951e6i	0.336875	−	0.336875i
$635$	1.05480e7	+	1.05480e7i	1.03809	+	1.03809i
$636$	55765.2	+	55765.2i	0.00546664	+	0.00546664i
$637$		−	2.61780e6i		−	0.255616i
$638$			2.12300e6i			0.206490i
$639$	1.30489e6	+	1.30489e6i	0.126422	+	0.126422i
$640$	−5.75489e6	−	5.75489e6i	−0.555376	−	0.555376i
$641$	−3.92544e6	+	3.92544e6i	−0.377349	+	0.377349i	−0.870145	−	0.492796i	$-0.835975\pi$
$641$	−3.92544e6	+	3.92544e6i	−0.377349	+	0.377349i	0.492796	+	0.870145i	$0.335975\pi$
$642$	6.11767e6			0.585799
$643$	−1.34489e7	+	1.34489e7i	−1.28280	+	1.28280i	−0.343735	+	0.939067i	$0.611692\pi$
$643$	−1.34489e7	+	1.34489e7i	−1.28280	+	1.28280i	−0.939067	+	0.343735i	$0.888308\pi$
$644$		−	512337.i		−	0.0486790i
$645$	7.15614e6			0.677298
$646$	−3.33353e6	−	1.91380e7i	−0.314284	−	1.80433i
$647$	−1.93830e7			−1.82037			−0.910184	−	0.414203i	$-0.864060\pi$
$647$	−1.93830e7			−1.82037			−0.910184	+	0.414203i	$0.864060\pi$
$648$			1.20466e6i			0.112701i
$649$	−7.99443e6	+	7.99443e6i	−0.745033	+	0.745033i
$650$	−737787.			−0.0684932
$651$	−4.50854e6	+	4.50854e6i	−0.416949	+	0.416949i
$652$	147120.	+	147120.i	0.0135535	+	0.0135535i
$653$	7.45657e6	+	7.45657e6i	0.684315	+	0.684315i	0.960969	−	0.276655i	$-0.0892258\pi$
$653$	7.45657e6	+	7.45657e6i	0.684315	+	0.684315i	−0.276655	+	0.960969i	$0.589226\pi$
$654$			1.21018e6i			0.110638i
$655$		−	1.63484e6i		−	0.148893i
$656$	−6.85137e6	−	6.85137e6i	−0.621609	−	0.621609i
$657$	−941460.	−	941460.i	−0.0850919	−	0.0850919i
$658$	9.51159e6	−	9.51159e6i	0.856423	−	0.856423i
$659$	−2.08553e7			−1.87069			−0.935346	−	0.353735i	$-0.884912\pi$
$659$	−2.08553e7			−1.87069			−0.935346	+	0.353735i	$0.884912\pi$
$660$	68578.0	−	68578.0i	0.00612809	−	0.00612809i
$661$		−	1.30188e7i		−	1.15895i	−0.814989	−	0.579476i	$-0.803257\pi$
$661$		−	1.30188e7i		−	1.15895i	0.814989	−	0.579476i	$-0.196743\pi$
$662$	−1.65778e7			−1.47022
$663$	−1.15812e6	−	814522.i	−0.102323	−	0.0719646i
$664$	6.47457e6			0.569889
$665$		−	2.57974e7i		−	2.26215i
$666$	−3.93437e6	+	3.93437e6i	−0.343708	+	0.343708i
$667$	4.35977e6			0.379445
$668$	82148.2	−	82148.2i	0.00712290	−	0.00712290i
$669$	6.63545e6	+	6.63545e6i	0.573199	+	0.573199i
$670$	−3.96287e6	−	3.96287e6i	−0.341054	−	0.341054i
$671$		−	9.08281e6i		−	0.778779i
$672$			593034.i			0.0506590i
$673$	−2.87572e6	−	2.87572e6i	−0.244742	−	0.244742i	0.574066	−	0.818809i	$-0.305365\pi$
$673$	−2.87572e6	−	2.87572e6i	−0.244742	−	0.244742i	−0.818809	+	0.574066i	$0.805365\pi$
$674$	−6.57957e6	−	6.57957e6i	−0.557889	−	0.557889i
$675$	516965.	−	516965.i	0.0436719	−	0.0436719i
$676$	−336600.			−0.0283300
$677$	7.93160e6	−	7.93160e6i	0.665103	−	0.665103i	−0.291475	−	0.956578i	$-0.594146\pi$
$677$	7.93160e6	−	7.93160e6i	0.665103	−	0.665103i	0.956578	+	0.291475i	$0.0941461\pi$
$678$			4.23537e6i			0.353848i
$679$	2.56743e7			2.13710
$680$	−5.79802e6	+	8.24388e6i	−0.480847	+	0.683690i
$681$	−1.24955e7			−1.03249
$682$			5.07196e6i			0.417556i
$683$	−1.49962e7	+	1.49962e7i	−1.23007	+	1.23007i	−0.266137	+	0.963935i	$0.585747\pi$
$683$	−1.49962e7	+	1.49962e7i	−1.23007	+	1.23007i	−0.963935	+	0.266137i	$0.914253\pi$
$684$	−225428.			−0.0184233
$685$	7.52640e6	−	7.52640e6i	0.612860	−	0.612860i
$686$	−2.27821e6	−	2.27821e6i	−0.184835	−	0.184835i
$687$	−838279.	−	838279.i	−0.0677636	−	0.0677636i
$688$			1.71337e7i			1.38000i
$689$		−	1.21623e6i		−	0.0976039i
$690$	4.59688e6	+	4.59688e6i	0.367571	+	0.367571i
$691$	6.89556e6	+	6.89556e6i	0.549382	+	0.549382i	0.926262	−	0.376880i	$-0.123003\pi$
$691$	6.89556e6	+	6.89556e6i	0.549382	+	0.549382i	−0.376880	+	0.926262i	$0.623003\pi$
$692$	289993.	−	289993.i	0.0230209	−	0.0230209i
$693$	3.81264e6			0.301573
$694$	5.64739e6	−	5.64739e6i	0.445091	−	0.445091i
$695$		−	5.02709e6i		−	0.394780i
$696$	−2.56018e6			−0.200331
$697$	−6.69104e6	+	9.51363e6i	−0.521689	+	0.741761i
$698$	1.69947e7			1.32031
$699$			6.57369e6i			0.508881i
$700$	129110.	−	129110.i	0.00995901	−	0.00995901i
$701$	−3.83244e6			−0.294564			−0.147282	−	0.989095i	$-0.547053\pi$
$701$	−3.83244e6			−0.294564			−0.147282	+	0.989095i	$0.547053\pi$
$702$	379223.	−	379223.i	0.0290437	−	0.0290437i
$703$	−2.55041e7	−	2.55041e7i	−1.94636	−	1.94636i
$704$	5.85723e6	+	5.85723e6i	0.445410	+	0.445410i
$705$		−	5.22908e6i		−	0.396235i
$706$			7.09967e6i			0.536076i
$707$	−2.55775e7	−	2.55775e7i	−1.92446	−	1.92446i
$708$	−278303.	−	278303.i	−0.0208657	−	0.0208657i
$709$	−8.96539e6	+	8.96539e6i	−0.669813	+	0.669813i	−0.957673	−	0.287859i	$-0.907056\pi$
$709$	−8.96539e6	+	8.96539e6i	−0.669813	+	0.669813i	0.287859	+	0.957673i	$0.407056\pi$
$710$	−5.84807e6			−0.435378
$711$	1.11565e6	−	1.11565e6i	0.0827662	−	0.0827662i
$712$		−	1.66551e7i		−	1.23125i
$713$	1.04157e7			0.767300
$714$	−1.12679e7	+	1.96269e6i	−0.827178	+	0.144081i
$715$	−1.49568e6			−0.109414
$716$		−	169423.i		−	0.0123507i
$717$	2.83187e6	−	2.83187e6i	0.205719	−	0.205719i
$718$	1.41614e7			1.02517
$719$	−9.14954e6	+	9.14954e6i	−0.660050	+	0.660050i	−0.955392	−	0.295341i	$-0.904567\pi$
$719$	−9.14954e6	+	9.14954e6i	−0.660050	+	0.660050i	0.295341	+	0.955392i	$0.404567\pi$
$720$	−2.61911e6	−	2.61911e6i	−0.188288	−	0.188288i
$721$	−7.73163e6	−	7.73163e6i	−0.553902	−	0.553902i
$722$			3.39017e7i			2.42035i
$723$		−	1.33180e7i		−	0.947527i
$724$	397972.	+	397972.i	0.0282167	+	0.0282167i
$725$	1.09867e6	+	1.09867e6i	0.0776290	+	0.0776290i
$726$	−3.56647e6	+	3.56647e6i	−0.251129	+	0.251129i
$727$	3.30616e6			0.232000			0.116000	−	0.993249i	$-0.462993\pi$
$727$	3.30616e6			0.232000			0.116000	+	0.993249i	$0.462993\pi$
$728$	3.28085e6	−	3.28085e6i	0.229434	−	0.229434i
$729$			531441.i			0.0370370i
$730$	4.21929e6			0.293043
$731$	2.02620e7	−	3.52931e6i	1.40246	−	0.244285i
$732$	316191.			0.0218108
$733$			5.49280e6i			0.377601i	0.982015	+	0.188801i	$0.0604600\pi$
$733$			5.49280e6i			0.377601i	−0.982015	+	0.188801i	$0.939540\pi$
$734$	−1.34822e7	+	1.34822e7i	−0.923680	+	0.923680i
$735$	−8.22062e6			−0.561289
$736$	685020.	−	685020.i	0.0466132	−	0.0466132i
$737$	3.79661e6	+	3.79661e6i	0.257470	+	0.257470i
$738$	−3.11520e6	−	3.11520e6i	−0.210545	−	0.210545i
$739$		−	878317.i		−	0.0591617i	−0.999562	−	0.0295808i	$-0.990583\pi$
$739$		−	878317.i		−	0.0591617i	0.999562	−	0.0295808i	$-0.00941724\pi$
$740$			540192.i			0.0362634i
$741$	2.45827e6	+	2.45827e6i	0.164469	+	0.164469i
$742$	−6.94721e6	−	6.94721e6i	−0.463234	−	0.463234i
$743$	−1.24848e7	+	1.24848e7i	−0.829678	+	0.829678i	−0.987472	−	0.157794i	$-0.949562\pi$
$743$	−1.24848e7	+	1.24848e7i	−0.829678	+	0.829678i	0.157794	+	0.987472i	$0.449562\pi$
$744$	−6.11641e6			−0.405102
$745$	4.20516e6	−	4.20516e6i	0.277582	−	0.277582i
$746$		−	1.40298e7i		−	0.923007i
$747$	2.85629e6			0.187284
$748$	160352.	−	227995.i	0.0104790	−	0.0148995i
$749$	2.33490e7			1.52077
$750$			9.53623e6i			0.619047i
$751$	−6.10587e6	+	6.10587e6i	−0.395046	+	0.395046i	−0.876482	−	0.481435i	$-0.840116\pi$
$751$	−6.10587e6	+	6.10587e6i	−0.395046	+	0.395046i	0.481435	+	0.876482i	$0.340116\pi$
$752$	1.25198e7			0.807332
$753$	1.07282e7	−	1.07282e7i	0.689511	−	0.689511i
$754$	805938.	+	805938.i	0.0516266	+	0.0516266i
$755$	−4.89786e6	−	4.89786e6i	−0.312708	−	0.312708i
$756$			132726.i			0.00844599i
$757$			8.73487e6i			0.554009i	0.960869	+	0.277005i	$0.0893417\pi$
$757$			8.73487e6i			0.554009i	−0.960869	+	0.277005i	$0.910658\pi$
$758$	−431553.	−	431553.i	−0.0272810	−	0.0272810i
$759$	−4.40402e6	−	4.40402e6i	−0.277488	−	0.277488i
$760$	1.74987e7	−	1.74987e7i	1.09894	−	1.09894i
$761$	−1.47206e7			−0.921436			−0.460718	−	0.887547i	$-0.652408\pi$
$761$	−1.47206e7			−0.921436			−0.460718	+	0.887547i	$0.652408\pi$
$762$	−1.14829e7	+	1.14829e7i	−0.716412	+	0.716412i
$763$			4.61883e6i			0.287224i
$764$	2995.79			0.000185686
$765$	−2.55782e6	+	3.63683e6i	−0.158022	+	0.224683i
$766$	3.14515e7			1.93673
$767$			6.06973e6i			0.372547i
$768$	−594553.	+	594553.i	−0.0363737	+	0.0363737i
$769$	−1.43806e7			−0.876923			−0.438462	−	0.898750i	$-0.644476\pi$
$769$	−1.43806e7			−0.876923			−0.438462	+	0.898750i	$0.644476\pi$
$770$	−8.54344e6	+	8.54344e6i	−0.519285	+	0.519285i
$771$	−5.90718e6	−	5.90718e6i	−0.357886	−	0.357886i
$772$	−183511.	−	183511.i	−0.0110820	−	0.0110820i
$773$			2.24125e7i			1.34909i	0.738232	+	0.674547i	$0.235661\pi$
$773$			2.24125e7i			1.34909i	−0.738232	+	0.674547i	$0.764339\pi$
$774$			7.79038e6i			0.467419i
$775$	2.62479e6	+	2.62479e6i	0.156979	+	0.156979i
$776$	1.74152e7	+	1.74152e7i	1.03819	+	1.03819i
$777$	−1.50161e7	+	1.50161e7i	−0.892289	+	0.892289i
$778$	−1.15944e7			−0.686752
$779$	2.01939e7	−	2.01939e7i	1.19228	−	1.19228i
$780$		−	52067.5i		−	0.00306429i
$781$	5.60271e6			0.328678
$782$	1.52828e7	+	1.07486e7i	0.893690	+	0.628543i
$783$	−1.12944e6			−0.0658352
$784$		−	1.96823e7i		−	1.14363i
$785$	8.49266e6	−	8.49266e6i	0.491892	−	0.491892i
$786$	1.77974e6			0.102754
$787$	8.93245e6	−	8.93245e6i	0.514084	−	0.514084i	−0.401691	−	0.915775i	$-0.631578\pi$
$787$	8.93245e6	−	8.93245e6i	0.514084	−	0.514084i	0.915775	+	0.401691i	$0.131578\pi$
$788$	330552.	+	330552.i	0.0189638	+	0.0189638i
$789$	3.17366e6	+	3.17366e6i	0.181496	+	0.181496i
$790$			4.99994e6i			0.285034i
$791$			1.61649e7i			0.918614i
$792$	2.58617e6	+	2.58617e6i	0.146502	+	0.146502i
$793$	−3.44804e6	−	3.44804e6i	−0.194711	−	0.194711i
$794$	9.52387e6	−	9.52387e6i	0.536120	−	0.536120i
$795$	−3.81929e6			−0.214321
$796$	133588.	−	133588.i	0.00747282	−	0.00747282i
$797$			1.04110e7i			0.580562i	0.956941	+	0.290281i	$0.0937488\pi$
$797$			1.04110e7i			0.580562i	−0.956941	+	0.290281i	$0.906251\pi$
$798$	2.80838e7			1.56116
$799$	−2.57891e6	−	1.48057e7i	−0.142912	−	0.820471i
$800$	345254.			0.0190728
$801$		−	7.34749e6i		−	0.404630i
$802$	1.12290e6	−	1.12290e6i	0.0616463	−	0.0616463i
$803$	−4.04226e6			−0.221226
$804$	−132168.	+	132168.i	−0.00721083	+	0.00721083i
$805$	1.75447e7	+	1.75447e7i	0.954238	+	0.954238i
$806$	1.92543e6	+	1.92543e6i	0.104397	+	0.104397i
$807$		−	8.39623e6i		−	0.453838i
$808$		−	3.46992e7i		−	1.86978i
$809$	−6.46151e6	−	6.46151e6i	−0.347106	−	0.347106i	0.511924	−	0.859031i	$-0.328933\pi$
$809$	−6.46151e6	−	6.46151e6i	−0.347106	−	0.347106i	−0.859031	+	0.511924i	$0.828933\pi$
$810$	−1.19086e6	−	1.19086e6i	−0.0637749	−	0.0637749i
$811$	3.85951e6	−	3.85951e6i	0.206054	−	0.206054i	−0.596534	−	0.802588i	$-0.703456\pi$
$811$	3.85951e6	−	3.85951e6i	0.206054	−	0.206054i	0.802588	+	0.596534i	$0.203456\pi$
$812$	−282073.			−0.0150132
$813$	9.66660e6	−	9.66660e6i	0.512917	−	0.512917i
$814$			1.68927e7i			0.893587i
$815$	−1.00761e7			−0.531371
$816$	−8.70752e6	−	6.12410e6i	−0.457793	−	0.321971i
$817$	−5.05003e7			−2.64691
$818$		−	2.14511e7i		−	1.12090i
$819$	1.44736e6	−	1.44736e6i	0.0753994	−	0.0753994i
$820$	−427718.			−0.0222138
$821$	7.37094e6	−	7.37094e6i	0.381650	−	0.381650i	−0.490047	−	0.871696i	$-0.663020\pi$
$821$	7.37094e6	−	7.37094e6i	0.381650	−	0.381650i	0.871696	+	0.490047i	$0.163020\pi$
$822$	8.19346e6	+	8.19346e6i	0.422949	+	0.422949i
$823$	−1.09332e7	−	1.09332e7i	−0.562661	−	0.562661i	0.367402	−	0.930062i	$-0.380247\pi$
$823$	−1.09332e7	−	1.09332e7i	−0.562661	−	0.562661i	−0.930062	+	0.367402i	$0.880247\pi$
$824$		−	1.04890e7i		−	0.538163i
$825$		−	2.21965e6i		−	0.113540i
$826$	3.46709e7	+	3.46709e7i	1.76813	+	1.76813i
$827$	1.44315e7	+	1.44315e7i	0.733747	+	0.733747i	0.971360	−	0.237613i	$-0.0763649\pi$
$827$	1.44315e7	+	1.44315e7i	0.733747	+	0.733747i	−0.237613	+	0.971360i	$0.576365\pi$
$828$	153313.	−	153313.i	0.00777146	−	0.00777146i
$829$	3.19431e7			1.61432			0.807162	−	0.590331i	$-0.201003\pi$
$829$	3.19431e7			1.61432			0.807162	+	0.590331i	$0.201003\pi$
$830$	−6.40043e6	+	6.40043e6i	−0.322488	+	0.322488i
$831$		−	2.03683e6i		−	0.102318i
$832$	4.44707e6			0.222723
$833$	−2.32760e7	+	4.05430e6i	−1.16224	+	0.202443i
$834$	5.47264e6			0.272447
$835$			5.62624e6i			0.279256i
$836$	−483950.	+	483950.i	−0.0239488	+	0.0239488i
$837$	−2.69829e6			−0.133130
$838$	1.00800e7	−	1.00800e7i	0.495848	−	0.495848i
$839$	−9.09225e6	−	9.09225e6i	−0.445930	−	0.445930i	0.448069	−	0.893999i	$-0.352112\pi$
$839$	−9.09225e6	−	9.09225e6i	−0.445930	−	0.445930i	−0.893999	+	0.448069i	$0.852112\pi$
$840$	−1.03028e7	−	1.03028e7i	−0.503797	−	0.503797i
$841$			1.81108e7i			0.882975i
$842$		−	2.19237e7i		−	1.06570i
$843$	−4.27888e6	−	4.27888e6i	−0.207377	−	0.207377i
$844$	652659.	+	652659.i	0.0315377	+	0.0315377i
$845$	1.15267e7	−	1.15267e7i	0.555344	−	0.555344i
$846$	5.69253e6			0.273451
$847$	−1.36120e7	+	1.36120e7i	−0.651948	+	0.651948i
$848$		−	9.14439e6i		−	0.436682i
$849$	1.40318e7			0.668106
$850$	1.14264e6	+	6.55999e6i	0.0542454	+	0.311427i
$851$	3.46906e7			1.64206
$852$			195042.i			0.00920510i
$853$	−1.11278e7	+	1.11278e7i	−0.523646	+	0.523646i	−0.918670	−	0.395025i	$-0.870736\pi$
$853$	−1.11278e7	+	1.11278e7i	−0.523646	+	0.523646i	0.395025	+	0.918670i	$0.370736\pi$
$854$	−3.93911e7			−1.84822
$855$	7.71965e6	−	7.71965e6i	0.361146	−	0.361146i
$856$	1.58380e7	+	1.58380e7i	0.738781	+	0.738781i
$857$	6.48335e6	+	6.48335e6i	0.301542	+	0.301542i	0.841617	−	0.540075i	$-0.181604\pi$
$857$	6.48335e6	+	6.48335e6i	0.301542	+	0.301542i	−0.540075	+	0.841617i	$0.681604\pi$
$858$		−	1.62824e6i		−	0.0755091i
$859$		−	3.92008e7i		−	1.81264i	−0.422588	−	0.906322i	$-0.638878\pi$
$859$		−	3.92008e7i		−	1.81264i	0.422588	−	0.906322i	$-0.361122\pi$
$860$	534812.	+	534812.i	0.0246578	+	0.0246578i
$861$	−1.18896e7	−	1.18896e7i	−0.546589	−	0.546589i
$862$	−2.42770e7	+	2.42770e7i	−1.11282	+	1.11282i
$863$	2.21435e7			1.01209			0.506045	−	0.862507i	$-0.331107\pi$
$863$	2.21435e7			1.01209			0.506045	+	0.862507i	$0.331107\pi$
$864$	−177461.	+	177461.i	−0.00808756	+	0.00808756i
$865$			1.98613e7i			0.902542i
$866$	−2.98668e7			−1.35330
$867$	−5.44864e6	+	1.15589e7i	−0.246173	+	0.522238i
$868$	−673888.			−0.0303591
$869$		−	4.79016e6i		−	0.215179i
$870$	2.53087e6	−	2.53087e6i	0.113363	−	0.113363i
$871$	2.88256e6			0.128746
$872$	−3.13302e6	+	3.13302e6i	−0.139531	+	0.139531i
$873$	7.68282e6	+	7.68282e6i	0.341181	+	0.341181i
$874$	−3.24398e7	−	3.24398e7i	−1.43648	−	1.43648i
$875$			3.63965e7i			1.60709i
$876$		−	140719.i		−	0.00619575i
$877$	−3.03987e7	−	3.03987e7i	−1.33461	−	1.33461i	−0.901191	−	0.433423i	$-0.857306\pi$
$877$	−3.03987e7	−	3.03987e7i	−1.33461	−	1.33461i	−0.433423	−	0.901191i	$-0.642694\pi$
$878$	−3.01679e7	−	3.01679e7i	−1.32071	−	1.32071i
$879$	−4.10324e6	+	4.10324e6i	−0.179124	+	0.179124i
$880$	−1.12454e7			−0.489519
$881$	2.50867e7	−	2.50867e7i	1.08894	−	1.08894i	0.0933007	−	0.995638i	$-0.470258\pi$
$881$	2.50867e7	−	2.50867e7i	1.08894	−	1.08894i	0.995638	−	0.0933007i	$-0.0297418\pi$
$882$		−	8.94921e6i		−	0.387358i
$883$	−1.59143e6			−0.0686886			−0.0343443	−	0.999410i	$-0.510934\pi$
$883$	−1.59143e6			−0.0686886			−0.0343443	+	0.999410i	$0.510934\pi$
$884$	−25679.0	−	147425.i	−0.00110522	−	0.00634514i
$885$	1.90606e7			0.818049
$886$			3.60077e7i			1.54103i
$887$	5.53077e6	−	5.53077e6i	0.236035	−	0.236035i	−0.579171	−	0.815206i	$-0.696624\pi$
$887$	5.53077e6	−	5.53077e6i	0.236035	−	0.236035i	0.815206	+	0.579171i	$0.196624\pi$
$888$	−2.03713e7			−0.866936
$889$	−4.38261e7	+	4.38261e7i	−1.85985	+	1.85985i
$890$	1.64644e7	+	1.64644e7i	0.696741	+	0.696741i
$891$	1.14090e6	+	1.14090e6i	0.0481453	+	0.0481453i
$892$			991797.i			0.0417360i
$893$			3.69012e7i			1.54850i
$894$	4.57785e6	+	4.57785e6i	0.191566	+	0.191566i
$895$	5.80180e6	+	5.80180e6i	0.242106	+	0.242106i
$896$	2.39111e7	−	2.39111e7i	0.995015	−	0.995015i
$897$	−3.34373e6			−0.138755
$898$	2.74188e7	−	2.74188e7i	1.13464	−	1.13464i
$899$		−	5.73450e6i		−	0.236644i
$900$	77270.5			0.00317986
$901$	−1.08140e7	+	1.88362e6i	−0.443788	+	0.0773005i
$902$	−1.33754e7			−0.547384
$903$			2.97332e7i			1.21345i
$904$	−1.09649e7	+	1.09649e7i	−0.446256	+	0.446256i
$905$	−2.72567e7			−1.10625
$906$	5.33195e6	−	5.33195e6i	0.215807	−	0.215807i
$907$	−6.59910e6	−	6.59910e6i	−0.266359	−	0.266359i	0.561272	−	0.827631i	$-0.310312\pi$
$907$	−6.59910e6	−	6.59910e6i	−0.266359	−	0.266359i	−0.827631	+	0.561272i	$0.810312\pi$
$908$	−933846.	−	933846.i	−0.0375890	−	0.0375890i
$909$		−	1.53077e7i		−	0.614470i
$910$			6.48656e6i			0.259664i
$911$	−1.23771e7	−	1.23771e7i	−0.494109	−	0.494109i	0.415489	−	0.909598i	$-0.363610\pi$
$911$	−1.23771e7	−	1.23771e7i	−0.494109	−	0.494109i	−0.909598	+	0.415489i	$0.863610\pi$
$912$	1.84829e7	+	1.84829e7i	0.735838	+	0.735838i
$913$	6.13189e6	−	6.13189e6i	0.243454	−	0.243454i
$914$	−2.80136e7			−1.10918
$915$	−1.08278e7	+	1.08278e7i	−0.427551	+	0.427551i
$916$		−	125297.i		−	0.00493403i
$917$	6.79264e6			0.266757
$918$	−3.95916e6	−	2.78452e6i	−0.155059	−	0.109055i
$919$	−1.02716e7			−0.401189			−0.200595	−	0.979674i	$-0.564287\pi$
$919$	−1.02716e7			−0.401189			−0.200595	+	0.979674i	$0.564287\pi$
$920$			2.38017e7i			0.927124i
$921$	8.97771e6	−	8.97771e6i	0.348752	−	0.348752i
$922$	−3.93946e7			−1.52619
$923$	2.12692e6	−	2.12692e6i	0.0821762	−	0.0821762i
$924$	284936.	+	284936.i	0.0109791	+	0.0109791i
$925$	8.74213e6	+	8.74213e6i	0.335941	+	0.335941i
$926$		−	3.49933e7i		−	1.34109i
$927$		−	4.62725e6i		−	0.176858i
$928$	−377146.	−	377146.i	−0.0143760	−	0.0143760i
$929$	−2.79039e7	−	2.79039e7i	−1.06078	−	1.06078i	−0.998029	−	0.0627523i	$-0.980012\pi$
$929$	−2.79039e7	−	2.79039e7i	−1.06078	−	1.06078i	−0.0627523	−	0.998029i	$-0.519988\pi$
$930$	6.04638e6	−	6.04638e6i	0.229239	−	0.229239i
$931$	5.80123e7			2.19354
$932$	−491283.	+	491283.i	−0.0185264	+	0.0185264i
$933$			6.68676e6i			0.251485i
$934$	−5.40226e6			−0.202632
$935$	2.31641e6	+	1.32987e7i	0.0866537	+	0.497486i
$936$	1.96353e6			0.0732570
$937$			4.67172e6i			0.173831i	0.996216	+	0.0869156i	$0.0277010\pi$
$937$			4.67172e6i			0.173831i	−0.996216	+	0.0869156i	$0.972299\pi$
$938$	1.64654e7	−	1.64654e7i	0.611034	−	0.611034i
$939$	3.14923e6			0.116558
$940$	390794.	−	390794.i	0.0144254	−	0.0144254i
$941$	−2.47112e7	−	2.47112e7i	−0.909744	−	0.909744i	0.0865069	−	0.996251i	$-0.472430\pi$
$941$	−2.47112e7	−	2.47112e7i	−0.909744	−	0.909744i	−0.996251	+	0.0865069i	$0.972430\pi$
$942$	9.24535e6	+	9.24535e6i	0.339466	+	0.339466i
$943$			2.74677e7i			1.00587i
$944$			4.56361e7i			1.66678i
$945$	−4.54512e6	−	4.54512e6i	−0.165564	−	0.165564i
$946$	1.67244e7	+	1.67244e7i	0.607608	+	0.607608i
$947$	−2.75731e6	+	2.75731e6i	−0.0999103	+	0.0999103i	−0.755295	−	0.655385i	$-0.772506\pi$
$947$	−2.75731e6	+	2.75731e6i	−0.0999103	+	0.0999103i	0.655385	+	0.755295i	$0.272506\pi$
$948$	166755.			0.00602641
$949$	−1.53453e6	+	1.53453e6i	−0.0553109	+	0.0553109i
$950$		−	1.63499e7i		−	0.587767i
$951$	7.78803e6			0.279239
$952$	−3.42527e7	−	2.40903e7i	−1.22490	−	0.861489i
$953$	6.42342e6			0.229105			0.114552	−	0.993417i	$-0.463457\pi$
$953$	6.42342e6			0.229105			0.114552	+	0.993417i	$0.463457\pi$
$954$		−	4.15779e6i		−	0.147908i
$955$	−102589.	+	102589.i	−0.00363993	+	0.00363993i
$956$	423278.			0.0149789
$957$	−2.42468e6	+	2.42468e6i	−0.0855806	+	0.0855806i
$958$	1.04026e7	+	1.04026e7i	0.366208	+	0.366208i
$959$	3.12716e7	+	3.12716e7i	1.09800	+	1.09800i
$960$		−	1.39650e7i		−	0.489062i
$961$			1.49291e7i			0.521466i
$962$	6.41284e6	+	6.41284e6i	0.223415	+	0.223415i
$963$	6.98701e6	+	6.98701e6i	0.242787	+	0.242787i
$964$	995313.	−	995313.i	0.0344959	−	0.0344959i
$965$	1.25685e7			0.434475
$966$	−1.90997e7	+	1.90997e7i	−0.658542	+	0.658542i
$967$			2.32902e7i			0.800952i	0.916307	+	0.400476i	$0.131155\pi$
$967$			2.32902e7i			0.800952i	−0.916307	+	0.400476i	$0.868845\pi$
$968$	−1.84664e7			−0.633423
$969$	1.80504e7	−	2.56648e7i	0.617556	−	0.878069i
$970$	−3.44317e7			−1.17498
$971$			2.42531e7i			0.825502i	0.910844	+	0.412751i	$0.135432\pi$
$971$			2.42531e7i			0.825502i	−0.910844	+	0.412751i	$0.864568\pi$
$972$	−39717.1	+	39717.1i	−0.00134838	+	0.00134838i
$973$	2.08872e7			0.707290
$974$	1.84175e7	−	1.84175e7i	0.622062	−	0.622062i
$975$	−842629.	−	842629.i	−0.0283873	−	0.0283873i
$976$	−2.59246e7	−	2.59246e7i	−0.871138	−	0.871138i
$977$		−	2.47323e7i		−	0.828951i	−0.910061	−	0.414475i	$-0.863965\pi$
$977$		−	2.47323e7i		−	0.828951i	0.910061	−	0.414475i	$-0.136035\pi$
$978$		−	1.09691e7i		−	0.366712i
$979$	−1.57736e7	−	1.57736e7i	−0.525987	−	0.525987i
$980$	−614366.	−	614366.i	−0.0204344	−	0.0204344i
$981$	−1.38215e6	+	1.38215e6i	−0.0458545	+	0.0458545i
$982$	5.60418e7			1.85453
$983$	2.38725e7	−	2.38725e7i	0.787977	−	0.787977i	−0.193185	−	0.981162i	$-0.561882\pi$
$983$	2.38725e7	−	2.38725e7i	0.787977	−	0.787977i	0.981162	+	0.193185i	$0.0618818\pi$
$984$		−	1.61298e7i		−	0.531058i
$985$	−2.26392e7			−0.743481
$986$	5.91777e6	−	8.41415e6i	0.193850	−	0.275624i
$987$	2.17264e7			0.709897
$988$			367436.i			0.0119754i
$989$	3.43451e7	−	3.43451e7i	1.11654	−	1.11654i
$990$	−5.11311e6			−0.165805
$991$	1.20388e7	−	1.20388e7i	0.389403	−	0.389403i	−0.485072	−	0.874474i	$-0.661206\pi$
$991$	1.20388e7	−	1.20388e7i	0.389403	−	0.389403i	0.874474	+	0.485072i	$0.161206\pi$
$992$	−901021.	−	901021.i	−0.0290707	−	0.0290707i
$993$	−1.89336e7	−	1.89336e7i	−0.609341	−	0.609341i
$994$		−	2.42983e7i		−	0.780026i
$995$			9.14929e6i			0.292974i
$996$	213464.	+	213464.i	0.00681830	+	0.00681830i
$997$	4.23483e7	+	4.23483e7i	1.34927	+	1.34927i	0.886456	+	0.462813i	$0.153160\pi$
$997$	4.23483e7	+	4.23483e7i	1.34927	+	1.34927i	0.462813	+	0.886456i	$0.346840\pi$
$998$	−76710.6	+	76710.6i	−0.00243798	+	0.00243798i
$999$	−8.98691e6			−0.284903

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.6.e.a.4.5	✓	32
3.2	odd	2		153.6.f.c.55.12		32
17.8	even	8		867.6.a.n.1.5		16
17.9	even	8		867.6.a.o.1.5		16
17.13	even	4	inner	51.6.e.a.13.12	yes	32
51.47	odd	4		153.6.f.c.64.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.6.e.a.4.5	✓	32	1.1	even	1	trivial
51.6.e.a.13.12	yes	32	17.13	even	4	inner
153.6.f.c.55.12		32	3.2	odd	2
153.6.f.c.64.5		32	51.47	odd	4
867.6.a.n.1.5		16	17.8	even	8
867.6.a.o.1.5		16	17.9	even	8

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:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	51.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-5.57214i q^{2} +(6.36396 - 6.36396i) q^{3} +0.951217 q^{4} +(-32.5739 + 32.5739i) q^{5} +(-35.4609 - 35.4609i) q^{6} +(-135.342 - 135.342i) q^{7} -183.609i q^{8} -81.0000i q^{9} +O(q^{10})\)	\(q-5.57214i q^{2} +(6.36396 - 6.36396i) q^{3} +0.951217 q^{4} +(-32.5739 + 32.5739i) q^{5} +(-35.4609 - 35.4609i) q^{6} +(-135.342 - 135.342i) q^{7} -183.609i q^{8} -81.0000i q^{9} +(181.507 + 181.507i) q^{10} +(-173.891 - 173.891i) q^{11} +(6.05351 - 6.05351i) q^{12} -132.026 q^{13} +(-754.145 + 754.145i) q^{14} +414.598i q^{15} -992.656 q^{16} +(204.474 + 1173.90i) q^{17} -451.344 q^{18} -2925.79i q^{19} +(-30.9849 + 30.9849i) q^{20} -1722.62 q^{21} +(-968.947 + 968.947i) q^{22} +(1989.82 + 1989.82i) q^{23} +(-1168.48 - 1168.48i) q^{24} +1002.88i q^{25} +735.668i q^{26} +(-515.481 - 515.481i) q^{27} +(-128.740 - 128.740i) q^{28} +(1095.52 - 1095.52i) q^{29} +2310.20 q^{30} +(2617.25 - 2617.25i) q^{31} -344.262i q^{32} -2213.27 q^{33} +(6541.15 - 1139.36i) q^{34} +8817.24 q^{35} -77.0486i q^{36} +(8717.02 - 8717.02i) q^{37} -16302.9 q^{38} +(-840.209 + 840.209i) q^{39} +(5980.86 + 5980.86i) q^{40} +(6902.05 + 6902.05i) q^{41} +9598.70i q^{42} -17260.4i q^{43} +(-165.408 - 165.408i) q^{44} +(2638.49 + 2638.49i) q^{45} +(11087.6 - 11087.6i) q^{46} -12612.4 q^{47} +(-6317.23 + 6317.23i) q^{48} +19827.9i q^{49} +5588.19 q^{50} +(8771.94 + 6169.40i) q^{51} -125.586 q^{52} +9212.04i q^{53} +(-2872.33 + 2872.33i) q^{54} +11328.6 q^{55} +(-24850.0 + 24850.0i) q^{56} +(-18619.6 - 18619.6i) q^{57} +(-6104.39 - 6104.39i) q^{58} -45973.7i q^{59} +394.373i q^{60} +(26116.4 + 26116.4i) q^{61} +(-14583.7 - 14583.7i) q^{62} +(-10962.7 + 10962.7i) q^{63} -33683.3 q^{64} +(4300.61 - 4300.61i) q^{65} +12332.7i q^{66} -21833.2 q^{67} +(194.499 + 1116.64i) q^{68} +25326.3 q^{69} -49130.9i q^{70} +(-16109.8 + 16109.8i) q^{71} -14872.3 q^{72} +(11623.0 - 11623.0i) q^{73} +(-48572.5 - 48572.5i) q^{74} +(6382.29 + 6382.29i) q^{75} -2783.06i q^{76} +47069.6i q^{77} +(4681.76 + 4681.76i) q^{78} +(13773.4 + 13773.4i) q^{79} +(32334.7 - 32334.7i) q^{80} -6561.00 q^{81} +(38459.2 - 38459.2i) q^{82} +35262.8i q^{83} -1638.59 q^{84} +(-44899.1 - 31578.1i) q^{85} -96177.5 q^{86} -13943.7i q^{87} +(-31928.0 + 31928.0i) q^{88} +90709.7 q^{89} +(14702.0 - 14702.0i) q^{90} +(17868.7 + 17868.7i) q^{91} +(1892.75 + 1892.75i) q^{92} -33312.2i q^{93} +70278.2i q^{94} +(95304.3 + 95304.3i) q^{95} +(-2190.87 - 2190.87i) q^{96} +(-94849.7 + 94849.7i) q^{97} +110484. q^{98} +(-14085.2 + 14085.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 576 q^{4} + 76 q^{5} - 180 q^{6} + 236 q^{7}+O(q^{10}) \) 32 * q - 576 * q^4 + 76 * q^5 - 180 * q^6 + 236 * q^7	\( 32 q - 576 q^{4} + 76 q^{5} - 180 q^{6} + 236 q^{7} + 724 q^{10} - 672 q^{11} - 2684 q^{13} + 2832 q^{14} + 8824 q^{16} - 4868 q^{17} + 1296 q^{18} + 4464 q^{20} - 3528 q^{21} - 1628 q^{22} + 5584 q^{23} + 10872 q^{24} - 36792 q^{28} + 4820 q^{29} - 1728 q^{30} + 13880 q^{31} + 7236 q^{33} + 5068 q^{34} - 12152 q^{35} - 33328 q^{37} - 29256 q^{38} - 11160 q^{39} - 43288 q^{40} - 50932 q^{41} + 116000 q^{44} - 6156 q^{45} + 47596 q^{46} - 16552 q^{47} + 27360 q^{48} + 139080 q^{50} + 12924 q^{51} + 186888 q^{52} - 14580 q^{54} - 129428 q^{55} - 117024 q^{56} + 19440 q^{57} - 212912 q^{58} + 118952 q^{61} - 219736 q^{62} + 19116 q^{63} - 143848 q^{64} + 220976 q^{65} + 98632 q^{67} + 367680 q^{68} + 156060 q^{69} - 205512 q^{71} - 62208 q^{72} - 40924 q^{73} - 178760 q^{74} - 58896 q^{75} + 87012 q^{78} - 309916 q^{79} - 664992 q^{80} - 209952 q^{81} + 350116 q^{82} + 6264 q^{84} + 335336 q^{85} + 1139576 q^{86} - 307696 q^{88} - 62680 q^{89} + 58644 q^{90} + 174460 q^{91} - 94256 q^{92} + 367240 q^{95} - 508824 q^{96} - 299020 q^{97} - 1191536 q^{98} - 54432 q^{99}+O(q^{100}) \) 32 * q - 576 * q^4 + 76 * q^5 - 180 * q^6 + 236 * q^7 + 724 * q^10 - 672 * q^11 - 2684 * q^13 + 2832 * q^14 + 8824 * q^16 - 4868 * q^17 + 1296 * q^18 + 4464 * q^20 - 3528 * q^21 - 1628 * q^22 + 5584 * q^23 + 10872 * q^24 - 36792 * q^28 + 4820 * q^29 - 1728 * q^30 + 13880 * q^31 + 7236 * q^33 + 5068 * q^34 - 12152 * q^35 - 33328 * q^37 - 29256 * q^38 - 11160 * q^39 - 43288 * q^40 - 50932 * q^41 + 116000 * q^44 - 6156 * q^45 + 47596 * q^46 - 16552 * q^47 + 27360 * q^48 + 139080 * q^50 + 12924 * q^51 + 186888 * q^52 - 14580 * q^54 - 129428 * q^55 - 117024 * q^56 + 19440 * q^57 - 212912 * q^58 + 118952 * q^61 - 219736 * q^62 + 19116 * q^63 - 143848 * q^64 + 220976 * q^65 + 98632 * q^67 + 367680 * q^68 + 156060 * q^69 - 205512 * q^71 - 62208 * q^72 - 40924 * q^73 - 178760 * q^74 - 58896 * q^75 + 87012 * q^78 - 309916 * q^79 - 664992 * q^80 - 209952 * q^81 + 350116 * q^82 + 6264 * q^84 + 335336 * q^85 + 1139576 * q^86 - 307696 * q^88 - 62680 * q^89 + 58644 * q^90 + 174460 * q^91 - 94256 * q^92 + 367240 * q^95 - 508824 * q^96 - 299020 * q^97 - 1191536 * q^98 - 54432 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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