LMFDB - Embedded newform 31.6.c.a.25.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [31,6,Mod(5,31)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(31, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("31.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	31.c (of order $3$, 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:	$4.97189841420$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.8
Character	$\chi$	$=$	31.25
Dual form			31.6.c.a.5.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.80839 q^{2} +(1.76382 + 3.05503i) q^{3} -24.1129 q^{4} +(-42.4669 + 73.5549i) q^{5} +(4.95350 + 8.57972i) q^{6} +(87.7771 + 152.034i) q^{7} -157.587 q^{8} +(115.278 - 199.667i) q^{9} +O(q^{10})$	\(q+2.80839 q^{2} +(1.76382 + 3.05503i) q^{3} -24.1129 q^{4} +(-42.4669 + 73.5549i) q^{5} +(4.95350 + 8.57972i) q^{6} +(87.7771 + 152.034i) q^{7} -157.587 q^{8} +(115.278 - 199.667i) q^{9} +(-119.264 + 206.571i) q^{10} +(-48.8124 + 84.5455i) q^{11} +(-42.5309 - 73.6656i) q^{12} +(-187.194 + 324.230i) q^{13} +(246.513 + 426.972i) q^{14} -299.616 q^{15} +329.047 q^{16} +(-276.497 - 478.907i) q^{17} +(323.746 - 560.744i) q^{18} +(200.076 + 346.542i) q^{19} +(1024.00 - 1773.62i) q^{20} +(-309.646 + 536.322i) q^{21} +(-137.084 + 237.437i) q^{22} +326.731 q^{23} +(-277.956 - 481.433i) q^{24} +(-2044.38 - 3540.98i) q^{25} +(-525.715 + 910.565i) q^{26} +1670.53 q^{27} +(-2116.56 - 3665.99i) q^{28} +8220.01 q^{29} -841.441 q^{30} +(-47.0326 + 5350.41i) q^{31} +5966.88 q^{32} -344.385 q^{33} +(-776.512 - 1344.96i) q^{34} -14910.5 q^{35} +(-2779.69 + 4814.56i) q^{36} +(-363.153 - 629.000i) q^{37} +(561.892 + 973.225i) q^{38} -1320.71 q^{39} +(6692.25 - 11591.3i) q^{40} +(-8522.72 + 14761.8i) q^{41} +(-869.608 + 1506.20i) q^{42} +(6685.31 + 11579.3i) q^{43} +(1177.01 - 2038.64i) q^{44} +(9791.00 + 16958.5i) q^{45} +917.589 q^{46} -13881.8 q^{47} +(580.379 + 1005.25i) q^{48} +(-7006.12 + 12135.0i) q^{49} +(-5741.43 - 9944.46i) q^{50} +(975.381 - 1689.41i) q^{51} +(4513.80 - 7818.13i) q^{52} +(12957.6 - 22443.2i) q^{53} +4691.52 q^{54} +(-4145.82 - 7180.78i) q^{55} +(-13832.5 - 23958.7i) q^{56} +(-705.796 + 1222.47i) q^{57} +23085.0 q^{58} +(-7988.25 - 13836.1i) q^{59} +7224.62 q^{60} -4952.51 q^{61} +(-132.086 + 15026.1i) q^{62} +40475.0 q^{63} +6227.87 q^{64} +(-15899.1 - 27538.1i) q^{65} -967.169 q^{66} +(20004.0 - 34647.9i) q^{67} +(6667.15 + 11547.8i) q^{68} +(576.295 + 998.171i) q^{69} -41874.5 q^{70} +(16221.2 - 28095.9i) q^{71} +(-18166.3 + 31465.0i) q^{72} +(-42746.7 + 74039.5i) q^{73} +(-1019.88 - 1766.48i) q^{74} +(7211.85 - 12491.3i) q^{75} +(-4824.41 - 8356.13i) q^{76} -17138.4 q^{77} -3709.07 q^{78} +(54223.0 + 93916.9i) q^{79} +(-13973.6 + 24203.0i) q^{80} +(-25066.0 - 43415.6i) q^{81} +(-23935.2 + 41456.9i) q^{82} +(52098.6 - 90237.5i) q^{83} +(7466.47 - 12932.3i) q^{84} +46967.9 q^{85} +(18775.0 + 32519.2i) q^{86} +(14498.6 + 25112.3i) q^{87} +(7692.20 - 13323.3i) q^{88} -106477. q^{89} +(27497.0 + 47626.2i) q^{90} -65725.4 q^{91} -7878.44 q^{92} +(-16428.6 + 9293.48i) q^{93} -38985.5 q^{94} -33986.4 q^{95} +(10524.5 + 18229.0i) q^{96} +18007.7 q^{97} +(-19676.0 + 34079.7i) q^{98} +(11254.0 + 19492.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 10 q^{3} + 336 q^{4} + 28 q^{5} + 72 q^{6} - 134 q^{7} - 804 q^{8} - 668 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 + 10 * q^3 + 336 * q^4 + 28 * q^5 + 72 * q^6 - 134 * q^7 - 804 * q^8 - 668 * q^9	\( 24 q - 4 q^{2} + 10 q^{3} + 336 q^{4} + 28 q^{5} + 72 q^{6} - 134 q^{7} - 804 q^{8} - 668 q^{9} - 746 q^{10} + 394 q^{11} - 646 q^{12} - 664 q^{13} + 432 q^{14} - 1596 q^{15} + 4040 q^{16} + 432 q^{17} + 1208 q^{18} - 694 q^{19} + 5692 q^{20} - 1712 q^{21} + 616 q^{22} - 1920 q^{23} + 8432 q^{24} + 88 q^{25} + 10798 q^{26} - 3284 q^{27} - 6570 q^{28} - 21496 q^{29} + 20760 q^{30} - 284 q^{31} - 24412 q^{32} - 51144 q^{33} + 16026 q^{34} + 25172 q^{35} - 3252 q^{36} - 2116 q^{37} - 14516 q^{38} + 19116 q^{39} - 43746 q^{40} + 12416 q^{41} + 32978 q^{42} + 38354 q^{43} + 28734 q^{44} + 21396 q^{45} - 44232 q^{46} + 80256 q^{47} - 32098 q^{48} + 8876 q^{49} + 14432 q^{50} + 29346 q^{51} - 64628 q^{52} + 14152 q^{53} + 36872 q^{54} - 2202 q^{55} + 13296 q^{56} - 26440 q^{57} - 41224 q^{58} - 66074 q^{59} - 252956 q^{60} - 93928 q^{61} - 210172 q^{62} + 86656 q^{63} - 21872 q^{64} + 103544 q^{65} + 313820 q^{66} + 8434 q^{67} - 116388 q^{68} - 3768 q^{69} + 241720 q^{70} - 46854 q^{71} + 177728 q^{72} + 105776 q^{73} + 241354 q^{74} + 2800 q^{75} + 208806 q^{76} - 336920 q^{77} + 120424 q^{78} - 42030 q^{79} + 204912 q^{80} + 63960 q^{81} + 54870 q^{82} + 7174 q^{83} - 266196 q^{84} - 316144 q^{85} - 41552 q^{86} - 13808 q^{87} - 232624 q^{88} - 285000 q^{89} - 169776 q^{90} - 86900 q^{91} - 282936 q^{92} - 552372 q^{93} + 137000 q^{94} - 80860 q^{95} + 317764 q^{96} + 165384 q^{97} - 192032 q^{98} - 27496 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 + 10 * q^3 + 336 * q^4 + 28 * q^5 + 72 * q^6 - 134 * q^7 - 804 * q^8 - 668 * q^9 - 746 * q^10 + 394 * q^11 - 646 * q^12 - 664 * q^13 + 432 * q^14 - 1596 * q^15 + 4040 * q^16 + 432 * q^17 + 1208 * q^18 - 694 * q^19 + 5692 * q^20 - 1712 * q^21 + 616 * q^22 - 1920 * q^23 + 8432 * q^24 + 88 * q^25 + 10798 * q^26 - 3284 * q^27 - 6570 * q^28 - 21496 * q^29 + 20760 * q^30 - 284 * q^31 - 24412 * q^32 - 51144 * q^33 + 16026 * q^34 + 25172 * q^35 - 3252 * q^36 - 2116 * q^37 - 14516 * q^38 + 19116 * q^39 - 43746 * q^40 + 12416 * q^41 + 32978 * q^42 + 38354 * q^43 + 28734 * q^44 + 21396 * q^45 - 44232 * q^46 + 80256 * q^47 - 32098 * q^48 + 8876 * q^49 + 14432 * q^50 + 29346 * q^51 - 64628 * q^52 + 14152 * q^53 + 36872 * q^54 - 2202 * q^55 + 13296 * q^56 - 26440 * q^57 - 41224 * q^58 - 66074 * q^59 - 252956 * q^60 - 93928 * q^61 - 210172 * q^62 + 86656 * q^63 - 21872 * q^64 + 103544 * q^65 + 313820 * q^66 + 8434 * q^67 - 116388 * q^68 - 3768 * q^69 + 241720 * q^70 - 46854 * q^71 + 177728 * q^72 + 105776 * q^73 + 241354 * q^74 + 2800 * q^75 + 208806 * q^76 - 336920 * q^77 + 120424 * q^78 - 42030 * q^79 + 204912 * q^80 + 63960 * q^81 + 54870 * q^82 + 7174 * q^83 - 266196 * q^84 - 316144 * q^85 - 41552 * q^86 - 13808 * q^87 - 232624 * q^88 - 285000 * q^89 - 169776 * q^90 - 86900 * q^91 - 282936 * q^92 - 552372 * q^93 + 137000 * q^94 - 80860 * q^95 + 317764 * q^96 + 165384 * q^97 - 192032 * q^98 - 27496 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

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

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 $

$2$	2.80839			0.496459			0.248229	−	0.968701i	$-0.420151\pi$
$2$	2.80839			0.496459			0.248229	+	0.968701i	$0.420151\pi$
$3$	1.76382	+	3.05503i	0.113149	+	0.195980i	0.917038	−	0.398799i	$-0.130573\pi$
$3$	1.76382	+	3.05503i	0.113149	+	0.195980i	−0.803889	+	0.594779i	$0.797240\pi$
$4$	−24.1129			−0.753529
$5$	−42.4669	+	73.5549i	−0.759672	+	1.31579i	0.183346	+	0.983048i	$0.441307\pi$
$5$	−42.4669	+	73.5549i	−0.759672	+	1.31579i	−0.943018	+	0.332742i	$0.892026\pi$
$6$	4.95350	+	8.57972i	0.0561739	+	0.0972960i
$7$	87.7771	+	152.034i	0.677074	+	1.17273i	0.975858	+	0.218405i	$0.0700855\pi$
$7$	87.7771	+	152.034i	0.677074	+	1.17273i	−0.298785	+	0.954321i	$0.596581\pi$
$8$	−157.587			−0.870555
$9$	115.278	−	199.667i	0.474395	−	0.821675i
$10$	−119.264	+	206.571i	−0.377146	+	0.653235i
$11$	−48.8124	+	84.5455i	−0.121632	+	0.210673i	−0.920411	−	0.390951i	$-0.872146\pi$
$11$	−48.8124	+	84.5455i	−0.121632	+	0.210673i	0.798779	+	0.601624i	$0.205479\pi$
$12$	−42.5309	−	73.6656i	−0.0852611	−	0.147677i
$13$	−187.194	+	324.230i	−0.307209	+	0.532101i	−0.977751	−	0.209770i	$-0.932728\pi$
$13$	−187.194	+	324.230i	−0.307209	+	0.532101i	0.670542	+	0.741872i	$0.266062\pi$
$14$	246.513	+	426.972i	0.336139	+	0.582210i
$15$	−299.616			−0.343825
$16$	329.047			0.321335
$17$	−276.497	−	478.907i	−0.232043	−	0.401910i	0.726366	−	0.687308i	$-0.241208\pi$
$17$	−276.497	−	478.907i	−0.232043	−	0.401910i	−0.958409	+	0.285398i	$0.907874\pi$
$18$	323.746	−	560.744i	0.235517	−	0.407928i
$19$	200.076	+	346.542i	0.127148	+	0.220227i	0.922571	−	0.385828i	$-0.126084\pi$
$19$	200.076	+	346.542i	0.127148	+	0.220227i	−0.795422	+	0.606056i	$0.792751\pi$
$20$	1024.00	−	1773.62i	0.572435	−	0.991486i
$21$	−309.646	+	536.322i	−0.153221	+	0.265386i
$22$	−137.084	+	237.437i	−0.0603853	+	0.104590i
$23$	326.731			0.128787			0.0643933	−	0.997925i	$-0.479489\pi$
$23$	326.731			0.128787			0.0643933	+	0.997925i	$0.479489\pi$
$24$	−277.956	−	481.433i	−0.0985025	−	0.170611i
$25$	−2044.38	−	3540.98i	−0.654203	−	1.13311i
$26$	−525.715	+	910.565i	−0.152517	+	0.264166i
$27$	1670.53			0.441008
$28$	−2116.56	−	3665.99i	−0.510194	−	0.883683i
$29$	8220.01			1.81500			0.907502	−	0.420049i	$-0.137987\pi$
$29$	8220.01			1.81500			0.907502	+	0.420049i	$0.137987\pi$
$30$	−841.441			−0.170695
$31$	−47.0326	+	5350.41i	−0.00879011	+	0.999961i
$31$	−47.0326	+	5350.41i	−0.00879011	+	0.999961i
$32$	5966.88			1.03008
$33$	−344.385			−0.0550503
$34$	−776.512	−	1344.96i	−0.115200	−	0.199532i
$35$	−14910.5			−2.05742
$36$	−2779.69	+	4814.56i	−0.357470	+	0.619156i
$37$	−363.153	−	629.000i	−0.0436100	−	0.0755347i	0.843397	−	0.537292i	$-0.180553\pi$
$37$	−363.153	−	629.000i	−0.0436100	−	0.0755347i	−0.887006	+	0.461757i	$0.847219\pi$
$38$	561.892	+	973.225i	0.0631239	+	0.109334i
$39$	−1320.71			−0.139042
$40$	6692.25	−	11591.3i	0.661336	−	1.14547i
$41$	−8522.72	+	14761.8i	−0.791806	+	1.37145i	0.133042	+	0.991110i	$0.457525\pi$
$41$	−8522.72	+	14761.8i	−0.791806	+	1.37145i	−0.924848	+	0.380337i	$0.875808\pi$
$42$	−869.608	+	1506.20i	−0.0760677	+	0.131753i
$43$	6685.31	+	11579.3i	0.551379	+	0.955017i	0.998175	+	0.0603810i	$0.0192316\pi$
$43$	6685.31	+	11579.3i	0.551379	+	0.955017i	−0.446796	+	0.894636i	$0.647435\pi$
$44$	1177.01	−	2038.64i	0.0916533	−	0.158748i
$45$	9791.00	+	16958.5i	0.720768	+	1.24841i
$46$	917.589			0.0639372
$47$	−13881.8			−0.916644			−0.458322	−	0.888786i	$-0.651549\pi$
$47$	−13881.8			−0.916644			−0.458322	+	0.888786i	$0.651549\pi$
$48$	580.379	+	1005.25i	0.0363587	+	0.0629751i
$49$	−7006.12	+	12135.0i	−0.416857	+	0.722018i
$50$	−5741.43	−	9944.46i	−0.324785	−	0.562543i
$51$	975.381	−	1689.41i	0.0525108	−	0.0909515i
$52$	4513.80	−	7818.13i	0.231491	−	0.400954i
$53$	12957.6	−	22443.2i	0.633627	−	1.09747i	−0.353177	−	0.935556i	$-0.614899\pi$
$53$	12957.6	−	22443.2i	0.633627	−	1.09747i	0.986804	−	0.161918i	$-0.0517679\pi$
$54$	4691.52			0.218942
$55$	−4145.82	−	7180.78i	−0.184801	−	0.320085i
$56$	−13832.5	−	23958.7i	−0.589430	−	1.02092i
$57$	−705.796	+	1222.47i	−0.0287735	+	0.0498371i
$58$	23085.0			0.901074
$59$	−7988.25	−	13836.1i	−0.298760	−	0.517467i	0.677093	−	0.735898i	$-0.263240\pi$
$59$	−7988.25	−	13836.1i	−0.298760	−	0.517467i	−0.975852	+	0.218431i	$0.929906\pi$
$60$	7224.62			0.259082
$61$	−4952.51			−0.170412			−0.0852061	−	0.996363i	$-0.527155\pi$
$61$	−4952.51			−0.170412			−0.0852061	+	0.996363i	$0.527155\pi$
$62$	−132.086	+	15026.1i	−0.00436393	+	0.496439i
$63$	40475.0			1.28480
$64$	6227.87			0.190059
$65$	−15899.1	−	27538.1i	−0.466756	−	0.808445i
$66$	−967.169			−0.0273302
$67$	20004.0	−	34647.9i	0.544414	−	0.942953i	−0.454229	−	0.890885i	$-0.650085\pi$
$67$	20004.0	−	34647.9i	0.544414	−	0.942953i	0.998644	−	0.0520685i	$-0.0165814\pi$
$68$	6667.15	+	11547.8i	0.174851	+	0.302851i
$69$	576.295	+	998.171i	0.0145721	+	0.0252396i
$70$	−41874.5			−1.02142
$71$	16221.2	−	28095.9i	0.381888	−	0.661449i	−0.609444	−	0.792829i	$-0.708607\pi$
$71$	16221.2	−	28095.9i	0.381888	−	0.661449i	0.991332	+	0.131380i	$0.0419407\pi$
$72$	−18166.3	+	31465.0i	−0.412986	+	0.715313i
$73$	−42746.7	+	74039.5i	−0.938849	+	1.62613i	−0.171228	+	0.985231i	$0.554773\pi$
$73$	−42746.7	+	74039.5i	−0.938849	+	1.62613i	−0.767622	+	0.640903i	$0.778560\pi$
$74$	−1019.88	−	1766.48i	−0.0216505	−	0.0374998i
$75$	7211.85	−	12491.3i	0.148045	−	0.256421i
$76$	−4824.41	−	8356.13i	−0.0958100	−	0.165948i
$77$	−17138.4			−0.329416
$78$	−3709.07			−0.0690284
$79$	54223.0	+	93916.9i	0.977497	+	1.69307i	0.671435	+	0.741063i	$0.265678\pi$
$79$	54223.0	+	93916.9i	0.977497	+	1.69307i	0.306062	+	0.952012i	$0.400989\pi$
$80$	−13973.6	+	24203.0i	−0.244109	+	0.422809i
$81$	−25066.0	−	43415.6i	−0.424495	−	0.735247i
$82$	−23935.2	+	41456.9i	−0.393099	+	0.680867i
$83$	52098.6	−	90237.5i	0.830101	−	1.43778i	−0.0678562	−	0.997695i	$-0.521616\pi$
$83$	52098.6	−	90237.5i	0.830101	−	1.43778i	0.897957	−	0.440082i	$-0.145051\pi$
$84$	7466.47	−	12932.3i	0.115456	−	0.199976i
$85$	46967.9			0.705105
$86$	18775.0	+	32519.2i	0.273737	+	0.474126i
$87$	14498.6	+	25112.3i	0.205366	+	0.355704i
$88$	7692.20	−	13323.3i	0.105887	−	0.183402i
$89$	−106477.			−1.42489			−0.712444	−	0.701729i	$-0.752412\pi$
$89$	−106477.			−1.42489			−0.712444	+	0.701729i	$0.752412\pi$
$90$	27497.0	+	47626.2i	0.357832	+	0.619783i
$91$	−65725.4			−0.832012
$92$	−7878.44			−0.0970444
$93$	−16428.6	+	9293.48i	−0.196967	+	0.111422i
$94$	−38985.5			−0.455076
$95$	−33986.4			−0.386364
$96$	10524.5	+	18229.0i	0.116553	+	0.201876i
$97$	18007.7			0.194325			0.0971625	−	0.995269i	$-0.469023\pi$
$97$	18007.7			0.194325			0.0971625	+	0.995269i	$0.469023\pi$
$98$	−19676.0	+	34079.7i	−0.206952	+	0.358452i
$99$	11254.0	+	19492.5i	0.115403	+	0.199884i
$100$	49296.1	+	85383.3i	0.492961	+	0.853833i
$101$	5879.34			0.0573489			0.0286745	−	0.999589i	$-0.490871\pi$
$101$	5879.34			0.0573489			0.0286745	+	0.999589i	$0.490871\pi$
$102$	2739.26	−	4744.53i	0.0260695	−	0.0451536i
$103$	71858.0	−	124462.i	0.667394	−	1.15596i	−0.311236	−	0.950333i	$-0.600743\pi$
$103$	71858.0	−	124462.i	0.667394	−	1.15596i	0.978630	−	0.205628i	$-0.0659236\pi$
$104$	29499.4	−	51094.5i	0.267442	−	0.463223i
$105$	−26299.4	−	45552.0i	−0.232795	−	0.403212i
$106$	36389.9	−	63029.2i	0.314570	−	0.544851i
$107$	−60050.0	−	104010.i	−0.507054	−	0.878243i	−0.999967	−	0.00816398i	$-0.997401\pi$
$107$	−60050.0	−	104010.i	−0.507054	−	0.878243i	0.492913	−	0.870079i	$-0.335932\pi$
$108$	−40281.5			−0.332312
$109$	189700.			1.52933			0.764664	−	0.644429i	$-0.222905\pi$
$109$	189700.			1.52933			0.764664	+	0.644429i	$0.222905\pi$
$110$	−11643.1	−	20166.5i	−0.0917460	−	0.158909i
$111$	1281.07	−	2218.89i	0.00986886	−	0.0170934i
$112$	28882.7	+	50026.4i	0.217567	+	0.376837i
$113$	2812.71	−	4871.76i	0.0207219	−	0.0358914i	−0.855479	−	0.517838i	$-0.826737\pi$
$113$	2812.71	−	4871.76i	0.0207219	−	0.0358914i	0.876200	+	0.481947i	$0.160070\pi$
$114$	−1982.15	+	3433.19i	−0.0142848	+	0.0247420i
$115$	−13875.3	+	24032.7i	−0.0978355	+	0.169456i
$116$	−198208.			−1.36766
$117$	43158.7	+	74753.0i	0.291476	+	0.504852i
$118$	−22434.2	−	38857.1i	−0.148322	−	0.256901i
$119$	48540.2	−	84074.0i	0.314220	−	0.544245i
$120$	47215.7			0.299318
$121$	75760.2	+	131221.i	0.470411	+	0.814776i
$122$	−13908.6			−0.0846026
$123$	−60130.2			−0.358368
$124$	1134.09	−	129014.i	0.00662360	−	0.753500i
$125$	81856.5			0.468574
$126$	113670.			0.637850
$127$	−97750.9	−	169309.i	−0.537788	−	0.931477i	−0.999023	−	0.0441984i	$-0.985927\pi$
$127$	−97750.9	−	169309.i	−0.537788	−	0.931477i	0.461234	−	0.887278i	$-0.347407\pi$
$128$	−173450.			−0.935727
$129$	−23583.4	+	40847.6i	−0.124776	+	0.216119i
$130$	−44651.0	−	77337.8i	−0.231725	−	0.401360i
$131$	−17875.4	−	30961.1i	−0.0910077	−	0.157630i	0.816928	−	0.576740i	$-0.195675\pi$
$131$	−17875.4	−	30961.1i	−0.0910077	−	0.157630i	−0.907935	+	0.419110i	$0.862342\pi$
$132$	8304.13			0.0414820
$133$	−35124.1	+	60836.8i	−0.172178	+	0.298220i
$134$	56179.1	−	97305.0i	0.270279	−	0.468137i
$135$	−70942.5	+	122876.i	−0.335021	+	0.580273i
$136$	43572.4	+	75469.5i	0.202006	+	0.349884i
$137$	10226.2	−	17712.3i	0.0465492	−	0.0806255i	−0.841812	−	0.539771i	$-0.818511\pi$
$137$	10226.2	−	17712.3i	0.0465492	−	0.0806255i	0.888361	+	0.459145i	$0.151844\pi$
$138$	1618.46	+	2803.26i	0.00723444	+	0.0125304i
$139$	247955.			1.08852			0.544258	−	0.838918i	$-0.316811\pi$
$139$	247955.			1.08852			0.544258	+	0.838918i	$0.316811\pi$
$140$	359536.			1.55032
$141$	−24485.0	−	42409.2i	−0.103718	−	0.179644i
$142$	45555.4	−	78904.3i	0.189592	−	0.328382i
$143$	−18274.8	−	31652.8i	−0.0747329	−	0.129441i
$144$	37931.8	−	65699.8i	0.152439	−	0.264033i
$145$	−349079.	+	604622.i	−1.37881	+	2.38816i
$146$	−120050.	+	207932.i	−0.466100	+	0.807309i
$147$	−49430.2			−0.188668
$148$	8756.69	+	15167.0i	0.0328614	+	0.0569176i
$149$	147846.	+	256077.i	0.545561	+	0.944940i	0.998571	+	0.0534346i	$0.0170169\pi$
$149$	147846.	+	256077.i	0.545561	+	0.944940i	−0.453010	+	0.891505i	$0.649650\pi$
$150$	20253.7	−	35080.5i	0.0734982	−	0.127303i
$151$	−308716.			−1.10184			−0.550918	−	0.834559i	$-0.685722\pi$
$151$	−308716.			−1.10184			−0.550918	+	0.834559i	$0.685722\pi$
$152$	−31529.4	−	54610.5i	−0.110690	−	0.191720i
$153$	−127496.			−0.440319
$154$	−48131.4			−0.163541
$155$	−391552.	−	230675.i	−1.30906	−	0.771208i
$156$	31846.1			0.104772
$157$	−290256.			−0.939792			−0.469896	−	0.882722i	$-0.655709\pi$
$157$	−290256.			−0.939792			−0.469896	+	0.882722i	$0.655709\pi$
$158$	152279.	+	263756.i	0.485287	+	0.840542i
$159$	91419.3			0.286777
$160$	−253395.	+	438894.i	−0.782526	+	1.35537i
$161$	28679.5	+	49674.3i	0.0871980	+	0.151031i
$162$	−70395.2	−	121928.i	−0.210744	−	0.365020i
$163$	460361.			1.35716			0.678578	−	0.734528i	$-0.262597\pi$
$163$	460361.			1.35716			0.678578	+	0.734528i	$0.262597\pi$
$164$	205508.	−	355950.i	0.596648	−	1.03343i
$165$	14625.0	−	25331.2i	0.0418201	−	0.0724346i
$166$	146313.	−	253422.i	0.412111	−	0.713797i
$167$	168973.	+	292670.i	0.468842	+	0.812057i	0.999366	−	0.0356125i	$-0.0113382\pi$
$167$	168973.	+	292670.i	0.468842	+	0.812057i	−0.530524	+	0.847670i	$0.678005\pi$
$168$	48796.2	−	84517.5i	0.133387	−	0.231033i
$169$	115563.	+	200161.i	0.311245	+	0.539093i
$170$	131904.			0.350056
$171$	92257.3			0.241274
$172$	−161202.	−	279211.i	−0.415480	−	0.719633i
$173$	41432.4	−	71763.0i	0.105251	−	0.182299i	−0.808590	−	0.588373i	$-0.799769\pi$
$173$	41432.4	−	71763.0i	0.105251	−	0.182299i	0.913841	+	0.406073i	$0.133102\pi$
$174$	40717.8	+	70525.4i	0.101956	+	0.176593i
$175$	358900.	−	621633.i	0.885887	−	1.53440i
$176$	−16061.5	+	27819.4i	−0.0390846	+	0.0676965i
$177$	28179.7	−	48808.6i	0.0676088	−	0.117102i
$178$	−299029.			−0.707398
$179$	−104263.	−	180590.i	−0.243220	−	0.421270i	0.718410	−	0.695620i	$-0.244870\pi$
$179$	−104263.	−	180590.i	−0.243220	−	0.421270i	−0.961630	+	0.274351i	$0.911537\pi$
$180$	−236090.	−	408919.i	−0.543120	−	0.940711i
$181$	−3875.74	+	6712.98i	−0.00879343	+	0.0152307i	−0.870389	−	0.492365i	$-0.836132\pi$
$181$	−3875.74	+	6712.98i	−0.00879343	+	0.0152307i	0.861595	+	0.507596i	$0.169466\pi$
$182$	−184583.			−0.413060
$183$	−8735.33	−	15130.0i	−0.0192820	−	0.0333974i
$184$	−51488.6			−0.112116
$185$	61688.1			0.132517
$186$	−46138.0	+	26099.8i	−0.0977860	+	0.0553164i
$187$	53985.9			0.112895
$188$	334731.			0.690718
$189$	146635.	+	253979.i	0.298595	+	0.517181i
$190$	−95447.3			−0.191814
$191$	64337.2	−	111435.i	0.127608	−	0.221024i	−0.795141	−	0.606424i	$-0.792603\pi$
$191$	64337.2	−	111435.i	0.127608	−	0.221024i	0.922749	+	0.385400i	$0.125937\pi$
$192$	10984.8	+	19026.3i	0.0215051	+	0.0372479i
$193$	−334946.	−	580144.i	−0.647264	−	1.12109i	−0.983774	−	0.179415i	$-0.942580\pi$
$193$	−334946.	−	580144.i	−0.647264	−	1.12109i	0.336509	−	0.941680i	$-0.390754\pi$
$194$	50572.7			0.0964743
$195$	56086.4	−	97144.5i	0.105626	−	0.182950i
$196$	168938.	−	292609.i	0.314114	−	0.544061i
$197$	−434569.	+	752695.i	−0.797798	+	1.38183i	0.123249	+	0.992376i	$0.460669\pi$
$197$	−434569.	+	752695.i	−0.797798	+	1.38183i	−0.921047	+	0.389451i	$0.872665\pi$
$198$	31605.6	+	54742.5i	0.0572929	+	0.0992342i
$199$	403997.	−	699743.i	0.723179	−	1.25258i	−0.236541	−	0.971622i	$-0.576014\pi$
$199$	403997.	−	699743.i	0.723179	−	1.25258i	0.959719	−	0.280960i	$-0.0906530\pi$
$200$	322169.	+	558012.i	0.569519	+	0.986436i
$201$	141134.			0.246400
$202$	16511.5			0.0284714
$203$	721528.	+	1.24972e6i	1.22889	+	2.12850i
$204$	−23519.3	+	40736.6i	−0.0395684	+	0.0685345i
$205$	−723868.	−	1.25378e6i	−1.20302	−	2.08370i
$206$	201806.	−	349538.i	0.331334	−	0.573886i
$207$	37664.8	−	65237.4i	0.0610956	−	0.105821i
$208$	−61595.6	+	106687.i	−0.0987168	+	0.170983i
$209$	−39064.7			−0.0618613
$210$	−73859.2	−	127928.i	−0.115573	−	0.200178i
$211$	386025.	+	668614.i	0.596910	+	1.03388i	0.993274	+	0.115785i	$0.0369384\pi$
$211$	386025.	+	668614.i	0.596910	+	1.03388i	−0.396364	+	0.918093i	$0.629728\pi$
$212$	−312445.	+	541170.i	−0.477456	+	0.826978i
$213$	114445.			0.172841
$214$	−168644.	−	292100.i	−0.251731	−	0.436011i
$215$	−1.13562e6			−1.67547
$216$	−263255.			−0.383921
$217$	−817575.	+	462493.i	−1.17863	+	0.666739i
$218$	532752.			0.759249
$219$	−301590.			−0.424920
$220$	99967.9	+	173150.i	0.139253	+	0.241193i
$221$	207034.			0.285142
$222$	3597.76	−	6231.51i	0.00489948	−	0.00848615i
$223$	−1140.57	−	1975.53i	−0.00153589	−	0.00266025i	0.865256	−	0.501330i	$-0.167156\pi$
$223$	−1140.57	−	1975.53i	−0.00153589	−	0.00266025i	−0.866792	+	0.498669i	$0.833822\pi$
$224$	523755.	+	907171.i	0.697443	+	1.20801i
$225$	−942689.			−1.24140
$226$	7899.21	−	13681.8i	0.0102876	−	0.0178186i
$227$	−124225.	+	215164.i	−0.160009	+	0.277143i	−0.934872	−	0.354986i	$-0.884486\pi$
$227$	−124225.	+	215164.i	−0.160009	+	0.277143i	0.774863	+	0.632130i	$0.217819\pi$
$228$	17018.8	−	29477.4i	0.0216816	−	0.0375537i
$229$	757731.	+	1.31243e6i	0.954830	+	1.65381i	0.734757	+	0.678331i	$0.237296\pi$
$229$	757731.	+	1.31243e6i	0.954830	+	1.65381i	0.220073	+	0.975483i	$0.429370\pi$
$230$	−38967.2	+	67493.2i	−0.0485713	+	0.0841279i
$231$	−30229.1	−	52358.3i	−0.0372731	−	0.0645589i
$232$	−1.29537e6			−1.58006
$233$	808105.			0.975165			0.487582	−	0.873077i	$-0.337879\pi$
$233$	808105.			0.975165			0.487582	+	0.873077i	$0.337879\pi$
$234$	121207.	+	209936.i	0.144706	+	0.250638i
$235$	589517.	−	1.02107e6i	0.696349	−	1.20611i
$236$	192620.	+	333628.i	0.225124	+	0.389926i
$237$	−191279.	+	331305.i	−0.221206	+	0.383140i
$238$	136320.	−	236113.i	0.155997	−	0.270195i
$239$	409320.	−	708962.i	0.463519	−	0.802839i	−0.535614	−	0.844463i	$-0.679920\pi$
$239$	409320.	−	708962.i	0.463519	−	0.802839i	0.999133	+	0.0416239i	$0.0132531\pi$
$240$	−98587.7			−0.110483
$241$	374990.	+	649501.i	0.415888	+	0.720340i	0.995521	−	0.0945380i	$-0.0301374\pi$
$241$	374990.	+	649501.i	0.415888	+	0.720340i	−0.579633	+	0.814878i	$0.696804\pi$
$242$	212765.	+	368519.i	0.233540	+	0.404503i
$243$	291394.	−	504709.i	0.316566	−	0.548309i
$244$	119419.			0.128410
$245$	−595057.	−	1.03067e6i	−0.633350	−	1.09699i
$246$	−168869.			−0.177915
$247$	−149812.			−0.156244
$248$	7411.73	−	843157.i	0.00765227	−	0.870521i
$249$	367570.			0.375701
$250$	229885.			0.232627
$251$	−140853.	−	243965.i	−0.141118	−	0.244423i	0.786800	−	0.617208i	$-0.211736\pi$
$251$	−140853.	−	243965.i	−0.141118	−	0.244423i	−0.927918	+	0.372785i	$0.878403\pi$
$252$	−975971.			−0.968134
$253$	−15948.5	+	27623.6i	−0.0156646	+	0.0271318i
$254$	−274523.	−	475488.i	−0.266990	−	0.462440i
$255$	82842.9	+	143488.i	0.0797820	+	0.138187i
$256$	−686408.			−0.654609
$257$	484037.	−	838377.i	0.457136	−	0.791784i	−0.541672	−	0.840590i	$-0.682208\pi$
$257$	484037.	−	838377.i	0.457136	−	0.791784i	0.998808	+	0.0488065i	$0.0155418\pi$
$258$	−66231.4	+	114716.i	−0.0619462	+	0.107294i
$259$	63753.1	−	110424.i	0.0590543	−	0.102285i
$260$	383374.	+	664024.i	0.351714	+	0.609187i
$261$	947585.	−	1.64127e6i	0.861028	−	1.49134i
$262$	−50201.2	−	86951.1i	−0.0451816	−	0.0782568i
$263$	−1.10641e6			−0.986337			−0.493168	−	0.869934i	$-0.664161\pi$
$263$	−1.10641e6			−0.986337			−0.493168	+	0.869934i	$0.664161\pi$
$264$	54270.7			0.0479242
$265$	1.10054e6	+	1.90618e6i	0.962697	+	1.66744i
$266$	−98642.4	+	170854.i	−0.0854791	+	0.148054i
$267$	−187806.	−	325290.i	−0.161225	−	0.279249i
$268$	−482355.	+	835463.i	−0.410232	+	0.710543i
$269$	1.05567e6	−	1.82848e6i	0.889504	−	1.54067i	0.0490417	−	0.998797i	$-0.484383\pi$
$269$	1.05567e6	−	1.82848e6i	0.889504	−	1.54067i	0.840462	−	0.541870i	$-0.182283\pi$
$270$	−199235.	+	345084.i	−0.166324	+	0.288082i
$271$	−497048.			−0.411126			−0.205563	−	0.978644i	$-0.565903\pi$
$271$	−497048.			−0.411126			−0.205563	+	0.978644i	$0.565903\pi$
$272$	−90980.3	−	157583.i	−0.0745633	−	0.129147i
$273$	−115928.	−	200793.i	−0.0941415	−	0.163058i
$274$	28719.1	−	49743.0i	0.0231097	−	0.0400272i
$275$	399165.			0.318288
$276$	−13896.1	−	24068.8i	−0.0109805	−	0.0190188i
$277$	−1.10874e6			−0.868220			−0.434110	−	0.900860i	$-0.642937\pi$
$277$	−1.10874e6			−0.868220			−0.434110	+	0.900860i	$0.642937\pi$
$278$	696354.			0.540404
$279$	1.06288e6	+	626175.i	0.817474	+	0.481599i
$280$	2.34970e6			1.79109
$281$	468121.			0.353665			0.176833	−	0.984241i	$-0.443415\pi$
$281$	468121.			0.353665			0.176833	+	0.984241i	$0.443415\pi$
$282$	−68763.5	−	119102.i	−0.0514915	−	0.0891858i
$283$	−818274.			−0.607341			−0.303670	−	0.952777i	$-0.598212\pi$
$283$	−818274.			−0.607341			−0.303670	+	0.952777i	$0.598212\pi$
$284$	−391139.	+	677473.i	−0.287764	+	0.498421i
$285$	−59946.0	−	103829.i	−0.0437168	−	0.0757197i
$286$	−51322.8	−	88893.7i	−0.0371018	−	0.0642622i
$287$	−2.99240e6			−2.14444
$288$	687850.	−	1.19139e6i	0.488666	−	0.846395i
$289$	557028.	−	964800.i	0.392312	−	0.679505i
$290$	−980351.	+	1.69802e6i	−0.684521	+	1.18562i
$291$	31762.3	+	55014.0i	0.0219877	+	0.0380838i
$292$	1.03075e6	−	1.78531e6i	0.707450	−	1.22534i
$293$	−310330.	−	537508.i	−0.211181	−	0.365776i	0.740903	−	0.671612i	$-0.234398\pi$
$293$	−310330.	−	537508.i	−0.211181	−	0.365776i	−0.952084	+	0.305835i	$0.901064\pi$
$294$	−138819.			−0.0936659
$295$	1.35695e6			0.907837
$296$	57228.3	+	99122.4i	0.0379649	+	0.0657571i
$297$	−81542.7	+	141236.i	−0.0536407	+	0.0929084i
$298$	415210.	+	719164.i	0.270849	+	0.469124i
$299$	−61162.1	+	105936.i	−0.0395644	+	0.0685275i
$300$	−173899.	+	301201.i	−0.111556	+	0.193221i
$301$	−1.17363e6	+	2.03279e6i	−0.746649	+	1.29323i
$302$	−866997.			−0.547016
$303$	10370.1	+	17961.6i	0.00648898	+	0.0112392i
$304$	65834.3	+	114028.i	0.0408572	+	0.0707667i
$305$	210318.	−	364281.i	0.129457	−	0.224227i
$306$	−358059.			−0.218600
$307$	−492200.	−	852515.i	−0.298054	−	0.516245i	0.677636	−	0.735397i	$-0.263004\pi$
$307$	−492200.	−	852515.i	−0.298054	−	0.516245i	−0.975691	+	0.219152i	$0.929671\pi$
$308$	413257.			0.248224
$309$	506979.			0.302060
$310$	−1.09963e6	−	647827.i	−0.649895	−	0.382873i
$311$	994648.			0.583134			0.291567	−	0.956550i	$-0.405823\pi$
$311$	994648.			0.583134			0.291567	+	0.956550i	$0.405823\pi$
$312$	208127.			0.121043
$313$	954713.	+	1.65361e6i	0.550823	+	0.954054i	0.998215	+	0.0597158i	$0.0190194\pi$
$313$	954713.	+	1.65361e6i	0.550823	+	0.954054i	−0.447392	+	0.894338i	$0.647647\pi$
$314$	−815153.			−0.466568
$315$	−1.71885e6	+	2.97714e6i	−0.976027	+	1.69053i
$316$	−1.30747e6	−	2.26461e6i	−0.736572	−	1.27578i
$317$	159827.	+	276829.i	0.0893311	+	0.154726i	0.907229	−	0.420638i	$-0.138194\pi$
$317$	159827.	+	276829.i	0.0893311	+	0.154726i	−0.817897	+	0.575364i	$0.804860\pi$
$318$	256741.			0.142373
$319$	−401238.	+	694965.i	−0.220763	+	0.382372i
$320$	−264479.	+	458090.i	−0.144383	+	0.250078i
$321$	211835.	−	366909.i	0.114745	−	0.198745i
$322$	80543.3	+	139505.i	0.0432902	+	0.0749808i
$323$	110641.	−	191635.i	0.0590077	−	0.102204i
$324$	604415.	+	1.04688e6i	0.319869	+	0.554030i
$325$	1.53079e6			0.803908
$326$	1.29288e6			0.673772
$327$	334597.	+	579538.i	0.173042	+	0.299718i
$328$	1.34307e6	−	2.32627e6i	0.689310	−	1.19392i
$329$	−1.21850e6	−	2.11051e6i	−0.620636	−	1.07497i
$330$	41072.7	−	71140.0i	0.0207620	−	0.0359608i
$331$	−1.28457e6	+	2.22495e6i	−0.644450	+	1.11622i	0.339979	+	0.940433i	$0.389580\pi$
$331$	−1.28457e6	+	2.22495e6i	−0.644450	+	1.11622i	−0.984428	+	0.175786i	$0.943753\pi$
$332$	−1.25625e6	+	2.17589e6i	−0.625505	+	1.08341i
$333$	−167454.			−0.0827533
$334$	474543.	+	821932.i	0.232760	+	0.403153i
$335$	1.69902e6	+	2.94278e6i	0.827153	+	1.43267i
$336$	−101888.	+	176475.i	−0.0492351	+	0.0852776i
$337$	−1.08623e6			−0.521013			−0.260506	−	0.965472i	$-0.583890\pi$
$337$	−1.08623e6			−0.521013			−0.260506	+	0.965472i	$0.583890\pi$
$338$	324547.	+	562132.i	0.154520	+	0.267637i
$339$	19844.5			0.00937866
$340$	−1.13253e6			−0.531317
$341$	−450058.	−	265143.i	−0.209596	−	0.123479i
$342$	259095.			0.119783
$343$	490631.			0.225175
$344$	−1.05352e6	−	1.82475e6i	−0.480006	−	0.831394i
$345$	−97893.9			−0.0442800
$346$	116358.	−	201539.i	0.0522526	−	0.0905041i
$347$	−1.08802e6	−	1.88450e6i	−0.485079	−	0.840181i	0.514774	−	0.857326i	$-0.327876\pi$
$347$	−1.08802e6	−	1.88450e6i	−0.485079	−	0.840181i	−0.999853	+	0.0171444i	$0.994542\pi$
$348$	−349604.	−	605532.i	−0.154749	−	0.268033i
$349$	−1.24421e6			−0.546802			−0.273401	−	0.961900i	$-0.588149\pi$
$349$	−1.24421e6			−0.546802			−0.273401	+	0.961900i	$0.588149\pi$
$350$	1.00793e6	−	1.74579e6i	0.439806	−	0.761767i
$351$	−312714.	+	541637.i	−0.135481	+	0.234661i
$352$	−291258.	+	504473.i	−0.125291	+	0.217011i
$353$	−87359.1	−	151310.i	−0.0373140	−	0.0646297i	0.846765	−	0.531967i	$-0.178547\pi$
$353$	−87359.1	−	151310.i	−0.0373140	−	0.0646297i	−0.884079	+	0.467337i	$0.845213\pi$
$354$	79139.7	−	137074.i	0.0335650	−	0.0581362i
$355$	1.37773e6	+	2.38629e6i	0.580219	+	1.00497i
$356$	2.56747e6			1.07369
$357$	342464.			0.142215
$358$	−292813.	−	507167.i	−0.120749	−	0.209143i
$359$	322140.	−	557963.i	0.131919	−	0.228491i	−0.792497	−	0.609876i	$-0.791219\pi$
$359$	322140.	−	557963.i	0.131919	−	0.228491i	0.924416	+	0.381385i	$0.124553\pi$
$360$	−1.54294e6	−	2.67244e6i	−0.627468	−	1.08681i
$361$	1.15799e6	−	2.00570e6i	0.467667	−	0.810022i
$362$	−10884.6	+	18852.7i	−0.00436557	+	0.00756140i
$363$	−267255.	+	462899.i	−0.106453	+	0.184382i
$364$	1.58483e6			0.626945
$365$	−3.63065e6	−	6.28847e6i	−1.42643	−	2.47066i
$366$	−24532.3	−	42491.1i	−0.00957271	−	0.0165804i
$367$	894574.	−	1.54945e6i	0.346698	−	0.600498i	−0.638963	−	0.769238i	$-0.720636\pi$
$367$	894574.	−	1.54945e6i	0.346698	−	0.600498i	0.985661	+	0.168739i	$0.0539696\pi$
$368$	107510.			0.0413836
$369$	1.96496e6	+	3.40341e6i	0.751256	+	1.30121i
$370$	173244.			0.0657892
$371$	4.54951e6			1.71605
$372$	396142.	−	224093.i	0.148420	−	0.0839597i
$373$	−1.67534e6			−0.623493			−0.311746	−	0.950165i	$-0.600914\pi$
$373$	−1.67534e6			−0.623493			−0.311746	+	0.950165i	$0.600914\pi$
$374$	151614.			0.0560479
$375$	144380.	+	250074.i	0.0530187	+	0.0918311i
$376$	2.18759e6			0.797989
$377$	−1.53874e6	+	2.66517e6i	−0.557585	+	0.965766i
$378$	411808.	+	713272.i	0.148240	+	0.256759i
$379$	−1.44793e6	−	2.50789e6i	−0.517785	−	0.896831i	−0.999787	−	0.0206601i	$-0.993423\pi$
$379$	−1.44793e6	−	2.50789e6i	−0.517785	−	0.896831i	0.482001	−	0.876171i	$-0.339910\pi$
$380$	819513.			0.291136
$381$	344830.	−	597263.i	0.121701	−	0.210792i
$382$	180684.	−	312954.i	0.0633522	−	0.109729i
$383$	−1.56663e6	+	2.71348e6i	−0.545719	+	0.945213i	0.452842	+	0.891591i	$0.350410\pi$
$383$	−1.56663e6	+	2.71348e6i	−0.545719	+	0.945213i	−0.998561	+	0.0536223i	$0.982923\pi$
$384$	−305935.	−	529894.i	−0.105877	−	0.183384i
$385$	727816.	−	1.26062e6i	0.250248	−	0.433442i
$386$	−940661.	−	1.62927e6i	−0.321340	−	0.556577i
$387$	3.08267e6			1.04629
$388$	−434218.			−0.146429
$389$	397550.	+	688576.i	0.133204	+	0.230716i	0.924910	−	0.380186i	$-0.124140\pi$
$389$	397550.	+	688576.i	0.133204	+	0.230716i	−0.791706	+	0.610902i	$0.790807\pi$
$390$	157513.	−	272820.i	0.0524390	−	0.0908270i
$391$	−90340.0	−	156474.i	−0.0298840	−	0.0517606i
$392$	1.10408e6	−	1.91231e6i	0.362897	−	0.628556i
$393$	63058.1	−	109220.i	0.0205949	−	0.0356714i
$394$	−1.22044e6	+	2.11387e6i	−0.396074	+	0.686020i
$395$	−9.21073e6			−2.97031
$396$	−271366.	−	470020.i	−0.0869596	−	0.150619i
$397$	1.01992e6	+	1.76655e6i	0.324780	+	0.562536i	0.981468	−	0.191627i	$-0.0613763\pi$
$397$	1.01992e6	+	1.76655e6i	0.324780	+	0.562536i	−0.656688	+	0.754163i	$0.728043\pi$
$398$	1.13458e6	−	1.96516e6i	0.359028	−	0.621855i
$399$	−247811.			−0.0779270
$400$	−672697.	−	1.16515e6i	−0.210218	−	0.364108i
$401$	−2.56139e6			−0.795454			−0.397727	−	0.917504i	$-0.630201\pi$
$401$	−2.56139e6			−0.795454			−0.397727	+	0.917504i	$0.630201\pi$
$402$	396359.			0.122327
$403$	−1.72596e6	−	1.01682e6i	−0.529381	−	0.311874i
$404$	−141768.			−0.0432141
$405$	4.25791e6			1.28991
$406$	2.02634e6	+	3.50972e6i	0.610093	+	1.05671i
$407$	70905.5			0.0212175
$408$	−153708.	+	266229.i	−0.0457136	+	0.0791782i
$409$	331233.	+	573712.i	0.0979095	+	0.169584i	0.910819	−	0.412806i	$-0.135451\pi$
$409$	331233.	+	573712.i	0.0979095	+	0.169584i	−0.812910	+	0.582390i	$0.802118\pi$
$410$	−2.03291e6	−	3.52110e6i	−0.597252	−	1.03447i
$411$	72148.6			0.0210680
$412$	−1.73271e6	+	3.00114e6i	−0.502901	+	0.871049i
$413$	1.40237e6	−	2.42898e6i	0.404564	−	0.700726i
$414$	105778.	−	183212.i	0.0303315	−	0.0525356i
$415$	4.42494e6	+	7.66422e6i	1.26121	+	2.18448i
$416$	−1.11697e6	+	1.93464e6i	−0.316451	+	0.548109i
$417$	437347.	+	757508.i	0.123165	+	0.213328i
$418$	−109709.			−0.0307116
$419$	4.39971e6			1.22430			0.612151	−	0.790741i	$-0.290304\pi$
$419$	4.39971e6			1.22430			0.612151	+	0.790741i	$0.290304\pi$
$420$	634156.	+	1.09839e6i	0.175418	+	0.303832i
$421$	1.56721e6	−	2.71449e6i	0.430945	−	0.746418i	−0.566010	−	0.824398i	$-0.691514\pi$
$421$	1.56721e6	−	2.71449e6i	0.430945	−	0.746418i	0.996955	+	0.0779799i	$0.0248470\pi$
$422$	1.08411e6	+	1.87773e6i	0.296341	+	0.513278i
$423$	−1.60026e6	+	2.77174e6i	−0.434851	+	0.753184i
$424$	−2.04195e6	+	3.53675e6i	−0.551607	+	0.955411i
$425$	−1.13053e6	+	1.95814e6i	−0.303606	+	0.525861i
$426$	321406.			0.0858085
$427$	−434716.	−	752951.i	−0.115382	−	0.199847i
$428$	1.44798e6	+	2.50798e6i	0.382079	+	0.661781i
$429$	64466.8	−	111660.i	0.0169119	−	0.0292923i
$430$	−3.18926e6			−0.831801
$431$	−1.71840e6	−	2.97635e6i	−0.445585	−	0.771775i	0.552508	−	0.833508i	$-0.313671\pi$
$431$	−1.71840e6	−	2.97635e6i	−0.445585	−	0.771775i	−0.998093	+	0.0617322i	$0.980338\pi$
$432$	549684.			0.141711
$433$	−5.32586e6			−1.36512			−0.682559	−	0.730830i	$-0.739133\pi$
$433$	−5.32586e6			−1.36512			−0.682559	+	0.730830i	$0.739133\pi$
$434$	−2.29607e6	+	1.29886e6i	−0.585142	+	0.331008i
$435$	−2.46285e6			−0.624043
$436$	−4.57422e6			−1.15239
$437$	65371.0	+	113226.i	0.0163750	+	0.0283623i
$438$	−846984.			−0.210955
$439$	−368648.	+	638517.i	−0.0912957	+	0.158129i	−0.908057	−	0.418848i	$-0.862434\pi$
$439$	−368648.	+	638517.i	−0.0912957	+	0.158129i	0.816761	+	0.576976i	$0.195768\pi$
$440$	653329.	+	1.13160e6i	0.160879	+	0.278651i
$441$	1.61530e6	+	2.79778e6i	0.395510	+	0.685043i
$442$	581434.			0.141561
$443$	753002.	−	1.30424e6i	0.182300	−	0.315753i	−0.760363	−	0.649498i	$-0.774979\pi$
$443$	753002.	−	1.30424e6i	0.182300	−	0.315753i	0.942663	+	0.333745i	$0.108312\pi$
$444$	−30890.4	+	53503.8i	−0.00743647	+	0.0128803i
$445$	4.52175e6	−	7.83190e6i	1.08245	−	1.87485i
$446$	−3203.18	−	5548.07i	−0.000762508	−	0.00132070i
$447$	−521547.	+	903346.i	−0.123460	+	0.213838i
$448$	546664.	+	946850.i	0.128684	+	0.222888i
$449$	−1.64888e6			−0.385986			−0.192993	−	0.981200i	$-0.561820\pi$
$449$	−1.64888e6			−0.385986			−0.192993	+	0.981200i	$0.561820\pi$
$450$	−2.64744e6			−0.616304
$451$	−832028.	−	1.44112e6i	−0.192618	−	0.333624i
$452$	−67822.7	+	117472.i	−0.0156145	+	0.0270452i
$453$	−544520.	−	943136.i	−0.124672	−	0.215938i
$454$	−348872.	+	604265.i	−0.0794378	+	0.137590i
$455$	2.79116e6	−	4.83443e6i	0.632056	−	1.09475i
$456$	111224.	−	192646.i	0.0250489	−	0.0433859i
$457$	4.71036e6			1.05503			0.527514	−	0.849547i	$-0.323124\pi$
$457$	4.71036e6			1.05503			0.527514	+	0.849547i	$0.323124\pi$
$458$	2.12801e6	+	3.68581e6i	0.474034	+	0.821050i
$459$	−461897.	−	800030.i	−0.102333	−	0.177245i
$460$	334573.	−	579498.i	0.0737219	−	0.127690i
$461$	2.24696e6			0.492429			0.246215	−	0.969215i	$-0.420813\pi$
$461$	2.24696e6			0.492429			0.246215	+	0.969215i	$0.420813\pi$
$462$	−84895.2	−	147043.i	−0.0185045	−	0.0320508i
$463$	−2.31382e6			−0.501623			−0.250811	−	0.968036i	$-0.580697\pi$
$463$	−2.31382e6			−0.501623			−0.250811	+	0.968036i	$0.580697\pi$
$464$	2.70477e6			0.583223
$465$	14091.7	−	1.60307e6i	0.00302226	−	0.343812i
$466$	2.26948e6			0.484129
$467$	1.10058e6			0.233524			0.116762	−	0.993160i	$-0.462749\pi$
$467$	1.10058e6			0.233524			0.116762	+	0.993160i	$0.462749\pi$
$468$	−1.04068e6	−	1.80251e6i	−0.219636	−	0.380421i
$469$	7.02356e6			1.47443
$470$	1.65560e6	−	2.86758e6i	0.345708	−	0.598785i
$471$	−511959.	−	886739.i	−0.106337	−	0.184180i
$472$	1.25885e6	+	2.18039e6i	0.260086	+	0.450483i
$473$	−1.30530e6			−0.268262
$474$	−537187.	+	930435.i	−0.109820	+	0.190213i
$475$	818064.	−	1.41693e6i	0.166362	−	0.288147i
$476$	−1.17044e6	+	2.02727e6i	−0.236774	+	0.410104i
$477$	−2.98744e6	−	5.17440e6i	−0.601178	−	1.04127i
$478$	1.14953e6	−	1.99105e6i	0.230118	−	0.398576i
$479$	−1.96143e6	−	3.39730e6i	−0.390602	−	0.676542i	0.601927	−	0.798551i	$-0.294400\pi$
$479$	−1.96143e6	−	3.39730e6i	−0.390602	−	0.676542i	−0.992529	+	0.122009i	$0.961066\pi$
$480$	−1.78778e6			−0.354168
$481$	271921.			0.0535895
$482$	1.05312e6	+	1.82406e6i	0.206471	+	0.357619i
$483$	−101171.	+	175233.i	−0.0197328	+	0.0341781i
$484$	−1.82680e6	−	3.16411e6i	−0.354468	−	0.613957i
$485$	−764731.	+	1.32455e6i	−0.147623	+	0.255691i
$486$	818349.	−	1.41742e6i	0.157162	−	0.272213i
$487$	2.76653e6	−	4.79177e6i	0.528583	−	0.915533i	−0.470862	−	0.882207i	$-0.656057\pi$
$487$	2.76653e6	−	4.79177e6i	0.528583	−	0.915533i	0.999445	−	0.0333254i	$-0.0106098\pi$
$488$	780452.			0.148353
$489$	811994.	+	1.40642e6i	0.153561	+	0.265975i
$490$	−1.67116e6	−	2.89453e6i	−0.314432	−	0.544612i
$491$	−3.64692e6	+	6.31665e6i	−0.682688	+	1.18245i	0.291470	+	0.956580i	$0.405856\pi$
$491$	−3.64692e6	+	6.31665e6i	−0.682688	+	1.18245i	−0.974157	+	0.225870i	$0.927478\pi$
$492$	1.44991e6			0.270041
$493$	−2.27281e6	−	3.93662e6i	−0.421158	−	0.729467i
$494$	−420731.			−0.0775689
$495$	−1.91169e6			−0.350674
$496$	−15475.9	+	1.76054e6i	−0.00282457	+	0.321322i
$497$	5.69538e6			1.03426
$498$	1.03228e6			0.186520
$499$	−1.07936e6	−	1.86951e6i	−0.194051	−	0.336106i	0.752538	−	0.658549i	$-0.228829\pi$
$499$	−1.07936e6	−	1.86951e6i	−0.194051	−	0.336106i	−0.946589	+	0.322443i	$0.895496\pi$
$500$	−1.97380e6			−0.353084
$501$	−596076.	+	1.03243e6i	−0.106098	+	0.183767i
$502$	−395571.	−	685149.i	−0.0700592	−	0.121346i
$503$	3.42022e6	+	5.92399e6i	0.602745	+	1.04398i	0.992404	+	0.123026i	$0.0392597\pi$
$503$	3.42022e6	+	5.92399e6i	0.602745	+	1.04398i	−0.389659	+	0.920959i	$0.627407\pi$
$504$	−6.37834e6			−1.11849
$505$	−249678.	+	432455.i	−0.0435664	+	0.0754592i
$506$	−44789.7	+	77578.0i	−0.00777682	+	0.0134698i
$507$	−407666.	+	706097.i	−0.0704343	+	0.121996i
$508$	2.35706e6	+	4.08255e6i	0.405239	+	0.701895i
$509$	1.13853e6	−	1.97199e6i	0.194783	−	0.337374i	−0.752047	−	0.659110i	$-0.770933\pi$
$509$	1.13853e6	−	1.97199e6i	0.194783	−	0.337374i	0.946829	+	0.321736i	$0.104266\pi$
$510$	232656.	+	402971.i	0.0396085	+	0.0686039i
$511$	−1.50087e7			−2.54268
$512$	3.62269e6			0.610741
$513$	334234.	+	578910.i	0.0560734	+	0.0971220i
$514$	1.35937e6	−	2.35449e6i	0.226949	−	0.393088i
$515$	6.10318e6	+	1.05710e7i	1.01400	+	1.75630i
$516$	568664.	−	984955.i	0.0940224	−	0.162852i
$517$	677603.	−	1.17364e6i	0.111493	−	0.193112i
$518$	179044.	−	310113.i	0.0293180	−	0.0507803i
$519$	292317.			0.0476361
$520$	2.50550e6	+	4.33965e6i	0.406337	+	0.703795i
$521$	−4.86765e6	−	8.43101e6i	−0.785642	−	1.36077i	−0.928615	−	0.371045i	$-0.879000\pi$
$521$	−4.86765e6	−	8.43101e6i	−0.785642	−	1.36077i	0.142973	−	0.989727i	$-0.454334\pi$
$522$	2.66119e6	−	4.60932e6i	0.427465	−	0.740390i
$523$	5.39663e6			0.862717			0.431359	−	0.902181i	$-0.358034\pi$
$523$	5.39663e6			0.862717			0.431359	+	0.902181i	$0.358034\pi$
$524$	431029.	+	746564.i	0.0685769	+	0.118779i
$525$	2.53214e6			0.400949
$526$	−3.10722e6			−0.489675
$527$	2.57535e6	−	1.45685e6i	0.403934	−	0.228501i
$528$	−113319.			−0.0176895
$529$	−6.32959e6			−0.983414
$530$	3.09074e6	+	5.35332e6i	0.477939	+	0.827815i
$531$	−3.68348e6			−0.566920
$532$	846946.	−	1.46695e6i	0.129741	−	0.224718i
$533$	−3.19081e6	−	5.52664e6i	−0.486499	−	0.842642i
$534$	−527434.	−	913542.i	−0.0800414	−	0.138636i
$535$	1.02006e7			1.54078
$536$	−3.15237e6	+	5.46007e6i	−0.473942	+	0.820892i
$537$	367804.	−	637055.i	0.0550403	−	0.0953326i
$538$	2.96474e6	−	5.13508e6i	0.441602	−	0.764877i
$539$	−683971.	−	1.18467e6i	−0.101406	−	0.175641i
$540$	1.71063e6	−	2.96290e6i	0.252448	−	0.437253i
$541$	4.16349e6	+	7.21138e6i	0.611596	+	1.05932i	0.990972	+	0.134073i	$0.0428055\pi$
$541$	4.16349e6	+	7.21138e6i	0.611596	+	1.05932i	−0.379376	+	0.925243i	$0.623861\pi$
$542$	−1.39591e6			−0.204107
$543$	−27344.4			−0.00397988
$544$	−1.64982e6	−	2.85758e6i	−0.239023	−	0.414001i
$545$	−8.05598e6	+	1.39534e7i	−1.16179	+	2.01228i
$546$	−325571.	−	563905.i	−0.0467373	−	0.0809514i
$547$	−967565.	+	1.67587e6i	−0.138265	+	0.239482i	−0.926840	−	0.375457i	$-0.877486\pi$
$547$	−967565.	+	1.67587e6i	−0.138265	+	0.239482i	0.788575	+	0.614939i	$0.210819\pi$
$548$	−246583.	+	427094.i	−0.0350762	+	0.0607537i
$549$	−570915.	+	988853.i	−0.0808426	+	0.140023i
$550$	1.12101e6			0.158017
$551$	1.64463e6	+	2.84858e6i	0.230775	+	0.399713i
$552$	−90816.6	−	157299.i	−0.0126858	−	0.0219724i
$553$	−9.51906e6	+	1.64875e7i	−1.32368	+	2.29267i
$554$	−3.11378e6			−0.431036
$555$	108807.	+	188459.i	0.0149942	+	0.0259707i
$556$	−5.97891e6			−0.820229
$557$	3.33985e6			0.456130			0.228065	−	0.973646i	$-0.426760\pi$
$557$	3.33985e6			0.456130			0.228065	+	0.973646i	$0.426760\pi$
$558$	2.98499e6	+	1.75855e6i	0.405842	+	0.239094i
$559$	−5.00580e6			−0.677554
$560$	−4.90625e6			−0.661118
$561$	95221.3	+	164928.i	0.0127740	+	0.0221252i
$562$	1.31467e6			0.175580
$563$	6.50772e6	−	1.12717e7i	0.865282	−	1.49871i	−0.00148512	−	0.999999i	$-0.500473\pi$
$563$	6.50772e6	−	1.12717e7i	0.865282	−	1.49871i	0.866767	−	0.498713i	$-0.166194\pi$
$564$	590405.	+	1.02261e6i	0.0781541	+	0.135367i
$565$	238895.	+	413778.i	0.0314837	+	0.0545313i
$566$	−2.29803e6			−0.301520
$567$	4.40044e6	−	7.62178e6i	0.574829	−	0.995632i
$568$	−2.55625e6	+	4.42755e6i	−0.332454	+	0.575828i
$569$	−6.19703e6	+	1.07336e7i	−0.802423	+	1.38984i	0.115595	+	0.993296i	$0.463123\pi$
$569$	−6.19703e6	+	1.07336e7i	−0.802423	+	1.38984i	−0.918017	+	0.396540i	$0.870211\pi$
$570$	−168352.	−	291594.i	−0.0217036	−	0.0375917i
$571$	−1.29900e6	+	2.24993e6i	−0.166732	+	0.288787i	−0.937269	−	0.348607i	$-0.886655\pi$
$571$	−1.29900e6	+	2.24993e6i	−0.166732	+	0.288787i	0.770537	+	0.637395i	$0.219988\pi$
$572$	440658.	+	763242.i	0.0563134	+	0.0975377i
$573$	453917.			0.0577550
$574$	−8.40383e6			−1.06463
$575$	−667963.	−	1.15695e6i	−0.0842525	−	0.145930i
$576$	717936.	−	1.24350e6i	0.0901632	−	0.156167i
$577$	−810279.	−	1.40344e6i	−0.101320	−	0.175491i	0.810909	−	0.585173i	$-0.198973\pi$
$577$	−810279.	−	1.40344e6i	−0.101320	−	0.175491i	−0.912229	+	0.409681i	$0.865640\pi$
$578$	1.56435e6	−	2.70954e6i	0.194767	−	0.337346i
$579$	1.18157e6	−	2.04654e6i	0.146475	−	0.253702i
$580$	8.41731e6	−	1.45792e7i	1.03897	−	1.79955i
$581$	1.82923e7			2.24816
$582$	89201.1	+	154501.i	0.0109160	+	0.0189070i
$583$	1.26498e6	+	2.19101e6i	0.154139	+	0.266976i
$584$	6.73634e6	−	1.16677e7i	0.817320	−	1.41564i
$585$	−7.33127e6			−0.885706
$586$	−871530.	−	1.50953e6i	−0.104843	−	0.181593i
$587$	1.31134e7			1.57080			0.785398	−	0.618991i	$-0.212458\pi$
$587$	1.31134e7			1.57080			0.785398	+	0.618991i	$0.212458\pi$
$588$	1.19191e6			0.142167
$589$	−1.86355e6	+	1.05419e6i	−0.221337	+	0.125208i
$590$	3.81084e6			0.450703
$591$	−3.06601e6			−0.361081
$592$	−119494.	−	206970.i	−0.0140134	−	0.0242719i
$593$	−8.92880e6			−1.04269			−0.521346	−	0.853345i	$-0.674570\pi$
$593$	−8.92880e6			−1.04269			−0.521346	+	0.853345i	$0.674570\pi$
$594$	−229004.	+	396647.i	−0.0266304	+	0.0461252i
$595$	4.12270e6	+	7.14073e6i	0.477408	+	0.826895i
$596$	−3.56500e6	−	6.17476e6i	−0.411096	−	0.712040i
$597$	2.85031e6			0.327308
$598$	−171767.	+	297510.i	−0.0196421	+	0.0340211i
$599$	−3.96664e6	+	6.87042e6i	−0.451706	+	0.782377i	−0.998492	−	0.0548948i	$-0.982518\pi$
$599$	−3.96664e6	+	6.87042e6i	−0.451706	+	0.782377i	0.546786	+	0.837272i	$0.315851\pi$
$600$	−1.13650e6	+	1.96847e6i	−0.128881	+	0.223229i
$601$	−1.37617e6	−	2.38359e6i	−0.155412	−	0.269182i	0.777797	−	0.628516i	$-0.216337\pi$
$601$	−1.37617e6	−	2.38359e6i	−0.155412	−	0.269182i	−0.933209	+	0.359334i	$0.883004\pi$
$602$	−3.29603e6	+	5.70888e6i	−0.370680	+	0.642037i
$603$	−4.61203e6	−	7.98828e6i	−0.516534	−	0.894664i
$604$	7.44405e6			0.830265
$605$	−1.28692e7			−1.42943
$606$	29123.3	+	50443.1i	0.00322151	+	0.00557982i
$607$	−660814.	+	1.14456e6i	−0.0727960	+	0.126086i	−0.900126	−	0.435630i	$-0.856526\pi$
$607$	−660814.	+	1.14456e6i	−0.0727960	+	0.126086i	0.827330	+	0.561717i	$0.189859\pi$
$608$	1.19383e6	+	2.06777e6i	0.130973	+	0.226853i
$609$	−2.54529e6	+	4.40858e6i	−0.278096	+	0.481676i
$610$	590655.	−	1.02305e6i	0.0642702	−	0.111319i
$611$	2.59859e6	−	4.50089e6i	0.281601	−	0.487748i
$612$	3.07430e6			0.331793
$613$	150336.	+	260390.i	0.0161589	+	0.0279881i	0.873992	−	0.485941i	$-0.161523\pi$
$613$	150336.	+	260390.i	0.0161589	+	0.0279881i	−0.857833	+	0.513929i	$0.828190\pi$
$614$	−1.38229e6	−	2.39420e6i	−0.147972	−	0.256294i
$615$	2.55355e6	−	4.42287e6i	0.272242	−	0.471538i
$616$	2.70080e6			0.286774
$617$	4.45977e6	+	7.72455e6i	0.471628	+	0.816883i	0.999473	−	0.0324572i	$-0.0103333\pi$
$617$	4.45977e6	+	7.72455e6i	0.471628	+	0.816883i	−0.527845	+	0.849341i	$0.677000\pi$
$618$	1.42380e6			0.149960
$619$	−1.01769e7			−1.06755			−0.533777	−	0.845625i	$-0.679228\pi$
$619$	−1.01769e7			−1.06755			−0.533777	+	0.845625i	$0.679228\pi$
$620$	9.44146e6	+	5.56225e6i	0.986416	+	0.581128i
$621$	545815.			0.0567958
$622$	2.79336e6			0.289502
$623$	−9.34623e6	−	1.61881e7i	−0.964753	−	1.67100i
$624$	−434574.			−0.0446789
$625$	2.91250e6	−	5.04461e6i	0.298240	−	0.516568i
$626$	2.68121e6	+	4.64399e6i	0.273461	+	0.473648i
$627$	−68903.1	−	119344.i	−0.00699955	−	0.0121236i
$628$	6.99891e6			0.708160
$629$	−200821.	+	347833.i	−0.0202387	+	0.0350545i
$630$	−4.82721e6	+	8.36097e6i	−0.484557	+	0.839277i
$631$	6.78664e6	−	1.17548e7i	0.678550	−	1.17528i	−0.296868	−	0.954919i	$-0.595942\pi$
$631$	6.78664e6	−	1.17548e7i	0.678550	−	1.17528i	0.975418	−	0.220364i	$-0.0707245\pi$
$632$	−8.54484e6	−	1.48001e7i	−0.850965	−	1.47391i
$633$	−1.36176e6	+	2.35863e6i	−0.135080	+	0.233965i
$634$	448858.	+	777445.i	0.0443492	+	0.0768150i
$635$	1.66047e7			1.63417
$636$	−2.20439e6			−0.216095
$637$	−2.62301e6	−	4.54319e6i	−0.256125	−	0.443621i
$638$	−1.12683e6	+	1.95174e6i	−0.109600	+	0.189832i
$639$	−3.73988e6	−	6.47766e6i	−0.362331	−	0.627576i
$640$	7.36589e6	−	1.27581e7i	0.710846	−	1.23122i
$641$	−7.08250e6	+	1.22673e7i	−0.680835	+	1.17924i	0.293892	+	0.955839i	$0.405049\pi$
$641$	−7.08250e6	+	1.22673e7i	−0.680835	+	1.17924i	−0.974727	+	0.223401i	$0.928284\pi$
$642$	594916.	−	1.03042e6i	0.0569663	−	0.0986685i
$643$	−1.82858e7			−1.74416			−0.872081	−	0.489361i	$-0.837230\pi$
$643$	−1.82858e7			−1.74416			−0.872081	+	0.489361i	$0.837230\pi$
$644$	−691546.	−	1.19779e6i	−0.0657062	−	0.113806i
$645$	−2.00303e6	−	3.46934e6i	−0.189578	−	0.328358i
$646$	310723.	−	538187.i	0.0292949	−	0.0507402i
$647$	1.25091e7			1.17480			0.587401	−	0.809296i	$-0.300151\pi$
$647$	1.25091e7			1.17480			0.587401	+	0.809296i	$0.300151\pi$
$648$	3.95008e6	+	6.84174e6i	0.369546	+	0.640072i
$649$	1.55970e6			0.145355
$650$	4.29905e6			0.399107
$651$	−2.85498e6	−	1.68196e6i	−0.264029	−	0.155547i
$652$	−1.11007e7			−1.02266
$653$	1.51626e7			1.39153			0.695763	−	0.718272i	$-0.255066\pi$
$653$	1.51626e7			1.39153			0.695763	+	0.718272i	$0.255066\pi$
$654$	939679.	+	1.62757e6i	0.0859083	+	0.148798i
$655$	3.03646e6			0.276544
$656$	−2.80437e6	+	4.85731e6i	−0.254434	+	0.440693i
$657$	9.85551e6	+	1.70702e7i	0.890770	+	1.54286i
$658$	−3.42204e6	−	5.92714e6i	−0.308120	−	0.533679i
$659$	5.20858e6			0.467204			0.233602	−	0.972332i	$-0.424949\pi$
$659$	5.20858e6			0.467204			0.233602	+	0.972332i	$0.424949\pi$
$660$	−352651.	+	610809.i	−0.0315127	+	0.0545816i
$661$	8.02055e6	−	1.38920e7i	0.714003	−	1.23669i	−0.249339	−	0.968416i	$-0.580213\pi$
$661$	8.02055e6	−	1.38920e7i	0.714003	−	1.23669i	0.963343	−	0.268274i	$-0.0864532\pi$
$662$	−3.60759e6	+	6.24853e6i	−0.319943	+	0.554157i
$663$	365171.	+	632495.i	0.0322636	+	0.0558822i
$664$	−8.21008e6	+	1.42203e7i	−0.722648	+	1.25166i
$665$	−2.98323e6	−	5.16711e6i	−0.261597	−	0.453099i
$666$	−470277.			−0.0410836
$667$	2.68573e6			0.233748
$668$	−4.07443e6	−	7.05712e6i	−0.353286	−	0.611909i
$669$	4023.54	−	6968.97i	0.000347570	−	0.000602009i
$670$	4.77151e6	+	8.26449e6i	0.410647	+	0.711262i
$671$	241744.	−	418712.i	0.0207276	−	0.0359012i
$672$	−1.84762e6	+	3.20017e6i	−0.157830	+	0.273370i
$673$	−649376.	+	1.12475e6i	−0.0552660	+	0.0957236i	−0.892335	−	0.451374i	$-0.850934\pi$
$673$	−649376.	+	1.12475e6i	−0.0552660	+	0.0957236i	0.837069	+	0.547098i	$0.184267\pi$
$674$	−3.05057e6			−0.258661
$675$	−3.41521e6	−	5.91532e6i	−0.288508	−	0.499711i
$676$	−2.78657e6	−	4.82648e6i	−0.234532	−	0.406222i
$677$	−5.70845e6	+	9.88733e6i	−0.478681	+	0.829101i	−0.999701	−	0.0244440i	$-0.992218\pi$
$677$	−5.70845e6	+	9.88733e6i	−0.478681	+	0.829101i	0.521020	+	0.853545i	$0.325552\pi$
$678$	55731.1			0.00465611
$679$	1.58066e6	+	2.73779e6i	0.131572	+	0.227890i
$680$	−7.40154e6			−0.613832
$681$	−876442.			−0.0724194
$682$	−1.26394e6	−	744625.i	−0.104056	−	0.0613023i
$683$	−1.65959e7			−1.36129			−0.680644	−	0.732614i	$-0.738300\pi$
$683$	−1.65959e7			−1.36129			−0.680644	+	0.732614i	$0.738300\pi$
$684$	−2.22459e6			−0.181807
$685$	868549.	+	1.50437e6i	0.0707242	+	0.122498i
$686$	1.37789e6			0.111790
$687$	−2.67300e6	+	4.62977e6i	−0.216076	+	0.374255i
$688$	2.19978e6	+	3.81013e6i	0.177177	+	0.306880i
$689$	4.85116e6	+	8.40245e6i	0.389312	+	0.674308i
$690$	−274925.			−0.0219832
$691$	−4.94994e6	+	8.57355e6i	−0.394371	+	0.683070i	−0.993021	−	0.117941i	$-0.962371\pi$
$691$	−4.94994e6	+	8.57355e6i	−0.394371	+	0.683070i	0.598650	+	0.801011i	$0.295704\pi$
$692$	−999056.	+	1.73042e6i	−0.0793094	+	0.137368i
$693$	−1.97568e6	+	3.42198e6i	−0.156273	+	0.270673i
$694$	−3.05558e6	−	5.29243e6i	−0.240822	−	0.417115i
$695$	−1.05299e7	+	1.82383e7i	−0.826916	+	1.43226i
$696$	−2.28480e6	−	3.95738e6i	−0.178782	−	0.309660i
$697$	9.42602e6			0.734931
$698$	−3.49423e6			−0.271465
$699$	1.42535e6	+	2.46878e6i	0.110339	+	0.191113i
$700$	−8.65412e6	+	1.49894e7i	−0.667541	+	1.15622i
$701$	−2.44763e6	−	4.23941e6i	−0.188127	−	0.325845i	0.756499	−	0.653995i	$-0.226908\pi$
$701$	−2.44763e6	−	4.23941e6i	−0.188127	−	0.325845i	−0.944626	+	0.328150i	$0.893575\pi$
$702$	−878225.	+	1.52113e6i	−0.0672609	+	0.116499i
$703$	145316.	−	251695.i	0.0110899	−	0.0192082i
$704$	−303997.	+	526538.i	−0.0231173	+	0.0400404i
$705$	4.15921e6			0.315165
$706$	−245339.	−	424939.i	−0.0185248	−	0.0320860i
$707$	516071.	+	893862.i	0.0388295	+	0.0672546i
$708$	−679495.	+	1.17692e6i	−0.0509452	+	0.0882396i
$709$	−9.90219e6			−0.739803			−0.369901	−	0.929071i	$-0.620609\pi$
$709$	−9.90219e6			−0.739803			−0.369901	+	0.929071i	$0.620609\pi$
$710$	3.86920e6	+	6.70165e6i	0.288055	+	0.498925i
$711$	2.50028e7			1.85488
$712$	1.67794e7			1.24044
$713$	−15367.0	+	1.74815e6i	−0.00113205	+	0.128782i
$714$	961775.			0.0706038
$715$	3.10430e6			0.227090
$716$	2.51410e6	+	4.35454e6i	0.183273	+	0.317439i
$717$	2.88787e6			0.209787
$718$	904697.	−	1.56698e6i	0.0654925	−	0.113436i
$719$	3.72880e6	+	6.45848e6i	0.268997	+	0.465916i	0.968603	−	0.248612i	$-0.0799745\pi$
$719$	3.72880e6	+	6.45848e6i	0.268997	+	0.465916i	−0.699606	+	0.714529i	$0.746641\pi$
$720$	3.22169e6	+	5.58014e6i	0.231608	+	0.401156i
$721$	2.52299e7			1.80750
$722$	3.25209e6	−	5.63278e6i	0.232177	−	0.402143i
$723$	−1.32283e6	+	2.29121e6i	−0.0941148	+	0.163012i
$724$	93455.5	−	161870.i	0.00662610	−	0.0114767i
$725$	−1.68049e7	−	2.91069e7i	−1.18738	−	2.05660i
$726$	−750557.	+	1.30000e6i	−0.0528496	+	0.0915383i
$727$	−1.32906e7	−	2.30201e7i	−0.932631	−	1.61536i	−0.778804	−	0.627267i	$-0.784174\pi$
$727$	−1.32906e7	−	2.30201e7i	−0.932631	−	1.61536i	−0.153827	−	0.988098i	$-0.549160\pi$
$728$	1.03575e7			0.724312
$729$	−1.01262e7			−0.705713
$730$	−1.01963e7	−	1.76605e7i	−0.708166	−	1.22658i
$731$	3.69693e6	−	6.40328e6i	0.255887	−	0.443209i
$732$	210634.	+	364829.i	0.0145295	+	0.0251659i
$733$	−9.15283e6	+	1.58532e7i	−0.629210	+	1.08982i	0.358501	+	0.933529i	$0.383288\pi$
$733$	−9.15283e6	+	1.58532e7i	−0.629210	+	1.08982i	−0.987711	+	0.156294i	$0.950045\pi$
$734$	2.51232e6	−	4.35146e6i	0.172121	−	0.298123i
$735$	2.09915e6	−	3.63583e6i	0.143326	−	0.248248i
$736$	1.94956e6			0.132661
$737$	1.95288e6	+	3.38249e6i	0.132437	+	0.229387i
$738$	5.51839e6	+	9.55813e6i	0.372968	+	0.645999i
$739$	7.15393e6	−	1.23910e7i	0.481874	−	0.834631i	−0.517909	−	0.855436i	$-0.673290\pi$
$739$	7.15393e6	−	1.23910e7i	0.481874	−	0.834631i	0.999784	+	0.0208049i	$0.00662288\pi$
$740$	−1.48748e6			−0.0998554
$741$	−264242.	−	457680.i	−0.0176789	−	0.0306208i
$742$	1.27768e7			0.851947
$743$	−2.53840e7			−1.68689			−0.843446	−	0.537213i	$-0.819477\pi$
$743$	−2.53840e7			−1.68689			−0.843446	+	0.537213i	$0.819477\pi$
$744$	2.58894e6	−	1.46453e6i	0.171471	−	0.0969990i
$745$	−2.51143e7			−1.65779
$746$	−4.70502e6			−0.309538
$747$	−1.20116e7	−	2.08048e7i	−0.787591	−	1.36415i
$748$	−1.30176e6			−0.0850699
$749$	1.05420e7	−	1.82593e7i	0.686625	−	1.18927i
$750$	405476.	+	702305.i	0.0263216	+	0.0455903i
$751$	4.64003e6	+	8.03676e6i	0.300207	+	0.519974i	0.976183	−	0.216950i	$-0.0696109\pi$
$751$	4.64003e6	+	8.03676e6i	0.300207	+	0.519974i	−0.675976	+	0.736924i	$0.736278\pi$
$752$	−4.56776e6			−0.294550
$753$	496879.	−	860620.i	0.0319347	−	0.0553126i
$754$	−4.32138e6	+	7.48485e6i	−0.276818	+	0.479463i
$755$	1.31102e7	−	2.27076e7i	0.837034	−	1.44979i
$756$	−3.53579e6	−	6.12417e6i	−0.225000	−	0.389711i
$757$	−1.15862e6	+	2.00679e6i	−0.0734855	+	0.127281i	−0.900427	−	0.435008i	$-0.856746\pi$
$757$	−1.15862e6	+	2.00679e6i	−0.0734855	+	0.127281i	0.826941	+	0.562288i	$0.190079\pi$
$758$	−4.06636e6	−	7.04314e6i	−0.257059	−	0.445239i
$759$	−112521.			−0.00708973
$760$	5.35583e6			0.336351
$761$	−2.30890e6	−	3.99913e6i	−0.144525	−	0.250325i	0.784671	−	0.619913i	$-0.212832\pi$
$761$	−2.30890e6	−	3.99913e6i	−0.144525	−	0.250325i	−0.929196	+	0.369588i	$0.879499\pi$
$762$	968418.	−	1.67735e6i	0.0604193	−	0.104649i
$763$	1.66513e7	+	2.88409e7i	1.03547	+	1.79348i
$764$	−1.55136e6	+	2.68703e6i	−0.0961565	+	0.166548i
$765$	5.41436e6	−	9.37795e6i	0.334498	−	0.579368i
$766$	−4.39971e6	+	7.62052e6i	−0.270927	+	0.469259i
$767$	5.98142e6			0.367126
$768$	−1.21070e6	−	2.09699e6i	−0.0740685	−	0.128290i
$769$	1.98319e6	+	3.43499e6i	0.120934	+	0.209464i	0.920136	−	0.391598i	$-0.128078\pi$
$769$	1.98319e6	+	3.43499e6i	0.120934	+	0.209464i	−0.799202	+	0.601062i	$0.794744\pi$
$770$	2.04400e6	−	3.54030e6i	0.124238	−	0.215186i
$771$	3.41502e6			0.206898
$772$	8.07653e6	+	1.39890e7i	0.487732	+	0.844777i
$773$	9.33285e6			0.561779			0.280890	−	0.959740i	$-0.409371\pi$
$773$	9.33285e6			0.561779			0.280890	+	0.959740i	$0.409371\pi$
$774$	8.65736e6			0.519437
$775$	1.90418e7	−	1.07718e7i	1.13882	−	0.644217i
$776$	−2.83778e6			−0.169170
$777$	449796.			0.0267278
$778$	1.11648e6	+	1.93379e6i	0.0661303	+	0.114541i
$779$	−6.82076e6			−0.402707
$780$	−1.35241e6	+	2.34244e6i	−0.0795923	+	0.137858i
$781$	1.58359e6	+	2.74285e6i	0.0928996	+	0.160907i
$782$	−253710.	−	439439.i	−0.0148362	−	0.0256970i
$783$	1.37318e7			0.800430
$784$	−2.30534e6	+	3.99297e6i	−0.133951	+	0.232009i
$785$	1.23263e7	−	2.13497e7i	0.713933	−	1.23657i
$786$	177092.	−	306732.i	0.0102245	−	0.0177094i
$787$	2.10564e6	+	3.64707e6i	0.121184	+	0.209898i	0.920235	−	0.391366i	$-0.127997\pi$
$787$	2.10564e6	+	3.64707e6i	0.121184	+	0.209898i	−0.799051	+	0.601264i	$0.794664\pi$
$788$	1.04787e7	−	1.81497e7i	0.601164	−	1.04125i
$789$	−1.95150e6	−	3.38010e6i	−0.111603	−	0.193302i
$790$	−2.58674e7			−1.47464
$791$	987567.			0.0561210
$792$	−1.77348e6	−	3.07176e6i	−0.100465	−	0.174010i
$793$	927080.	−	1.60575e6i	0.0523521	−	0.0906765i
$794$	2.86434e6	+	4.96117e6i	0.161240	+	0.279276i
$795$	−3.88230e6	+	6.72434e6i	−0.217857	+	0.377339i
$796$	−9.74155e6	+	1.68729e7i	−0.544936	+	0.943857i
$797$	−5.18445e6	+	8.97974e6i	−0.289106	+	0.500746i	−0.973597	−	0.228275i	$-0.926691\pi$
$797$	−5.18445e6	+	8.97974e6i	−0.289106	+	0.500746i	0.684491	+	0.729022i	$0.260025\pi$
$798$	−695950.			−0.0386875
$799$	3.83827e6	+	6.64808e6i	0.212701	+	0.368408i
$800$	−1.21986e7	−	2.11286e7i	−0.673884	−	1.16720i
$801$	−1.22744e7	+	2.12599e7i	−0.675959	+	1.17079i
$802$	−7.19340e6			−0.394910
$803$	−4.17314e6	−	7.22809e6i	−0.228388	−	0.395580i
$804$	−3.40315e6			−0.185670
$805$	−4.87172e6			−0.264967
$806$	−4.84717e6	−	2.85562e6i	−0.262816	−	0.154833i
$807$	7.44806e6			0.402586
$808$	−926509.			−0.0499254
$809$	788574.	+	1.36585e6i	0.0423615	+	0.0733722i	0.886429	−	0.462865i	$-0.153179\pi$
$809$	788574.	+	1.36585e6i	0.0423615	+	0.0733722i	−0.844067	+	0.536237i	$0.819845\pi$
$810$	1.19579e7			0.640386
$811$	7.18659e6	−	1.24475e7i	0.383681	−	0.664556i	−0.607904	−	0.794011i	$-0.707989\pi$
$811$	7.18659e6	−	1.24475e7i	0.383681	−	0.664556i	0.991585	+	0.129455i	$0.0413227\pi$
$812$	−1.73982e7	−	3.01345e7i	−0.926005	−	1.60389i
$813$	−876704.	−	1.51850e6i	−0.0465186	−	0.0805725i
$814$	199131.			0.0105336
$815$	−1.95501e7	+	3.38618e7i	−1.03099	+	1.78573i
$816$	320946.	−	555895.i	0.0168735	−	0.0292258i
$817$	−2.67514e6	+	4.63348e6i	−0.140214	+	0.242858i
$818$	930232.	+	1.61121e6i	0.0486080	+	0.0841916i
$819$	−7.57668e6	+	1.31232e7i	−0.394702	+	0.683644i
$820$	1.74546e7	+	3.02322e7i	0.906514	+	1.57013i
$821$	−8.51716e6			−0.440998			−0.220499	−	0.975387i	$-0.570769\pi$
$821$	−8.51716e6			−0.440998			−0.220499	+	0.975387i	$0.570769\pi$
$822$	202622.			0.0104594
$823$	−6.68037e6	−	1.15707e7i	−0.343796	−	0.595472i	0.641338	−	0.767258i	$-0.278380\pi$
$823$	−6.68037e6	−	1.15707e7i	−0.343796	−	0.595472i	−0.985134	+	0.171786i	$0.945046\pi$
$824$	−1.13239e7	+	1.96136e7i	−0.581003	+	1.00633i
$825$	704055.	+	1.21946e6i	0.0360140	+	0.0623781i
$826$	3.93841e6	−	6.82153e6i	0.200849	−	0.347882i
$827$	3.72339e6	−	6.44910e6i	0.189311	−	0.327896i	−0.755710	−	0.654906i	$-0.772708\pi$
$827$	3.72339e6	−	6.44910e6i	0.189311	−	0.327896i	0.945021	+	0.327011i	$0.106041\pi$
$828$	−908209.	+	1.57306e6i	−0.0460373	+	0.0797390i
$829$	1.57553e7			0.796234			0.398117	−	0.917335i	$-0.369664\pi$
$829$	1.57553e7			0.796234			0.398117	+	0.917335i	$0.369664\pi$
$830$	1.24270e7	+	2.15241e7i	0.626138	+	1.08450i
$831$	−1.95562e6	−	3.38723e6i	−0.0982384	−	0.170154i
$832$	−1.16582e6	+	2.01926e6i	−0.0583880	+	0.101131i
$833$	7.74868e6			0.386915
$834$	1.22824e6	+	2.12738e6i	0.0611462	+	0.105908i
$835$	−2.87031e7			−1.42466
$836$	941964.			0.0466143
$837$	−78569.5	+	8.93805e6i	−0.00387651	+	0.440991i
$838$	1.23561e7			0.607815
$839$	−5.41751e6			−0.265702			−0.132851	−	0.991136i	$-0.542413\pi$
$839$	−5.41751e6			−0.265702			−0.132851	+	0.991136i	$0.542413\pi$
$840$	4.14445e6	+	7.17840e6i	0.202660	+	0.351018i
$841$	4.70574e7			2.29424
$842$	4.40134e6	−	7.62335e6i	0.213946	−	0.370566i
$843$	825681.	+	1.43012e6i	0.0400169	+	0.0693113i
$844$	−9.30818e6	−	1.61222e7i	−0.449789	−	0.779057i
$845$	−1.96305e7			−0.945777
$846$	−4.49417e6	+	7.78413e6i	−0.215886	+	0.373925i
$847$	−1.33000e7	+	2.30363e7i	−0.637006	+	1.10333i
$848$	4.26364e6	−	7.38484e6i	0.203606	−	0.352656i
$849$	−1.44329e6	−	2.49985e6i	−0.0687201	−	0.119027i
$850$	−3.17498e6	+	5.49922e6i	−0.150728	+	0.261068i
$851$	−118653.	−	205514.i	−0.00561638	−	0.00972785i
$852$	−2.75960e6			−0.130241
$853$	−2.85425e7			−1.34314			−0.671568	−	0.740943i	$-0.734379\pi$
$853$	−2.85425e7			−1.34314			−0.671568	+	0.740943i	$0.734379\pi$
$854$	−1.22086e6	−	2.11458e6i	−0.0572822	−	0.0992156i
$855$	−3.91789e6	+	6.78598e6i	−0.183289	+	0.317466i
$856$	9.46312e6	+	1.63906e7i	0.441418	+	0.764558i
$857$	−1.24802e7	+	2.16164e7i	−0.580458	+	1.00538i	0.414967	+	0.909836i	$0.363793\pi$
$857$	−1.24802e7	+	2.16164e7i	−0.580458	+	1.00538i	−0.995425	+	0.0955459i	$0.969540\pi$
$858$	181048.	−	313585.i	0.00839607	−	0.0145424i
$859$	1.64864e7	−	2.85553e7i	0.762331	−	1.32040i	−0.179316	−	0.983792i	$-0.557388\pi$
$859$	1.64864e7	−	2.85553e7i	0.762331	−	1.32040i	0.941646	−	0.336604i	$-0.109278\pi$
$860$	2.73831e7			1.26251
$861$	−5.27805e6	−	9.14185e6i	−0.242642	−	0.420268i
$862$	−4.82594e6	−	8.35877e6i	−0.221214	−	0.383155i
$863$	7.68893e6	−	1.33176e7i	0.351430	−	0.608695i	−0.635070	−	0.772454i	$-0.719029\pi$
$863$	7.68893e6	−	1.33176e7i	0.351430	−	0.608695i	0.986500	+	0.163760i	$0.0523622\pi$
$864$	9.96788e6			0.454275
$865$	3.51901e6	+	6.09511e6i	0.159912	+	0.276976i
$866$	−1.49571e7			−0.677725
$867$	3.92999e6			0.177559
$868$	1.97141e7	−	1.11521e7i	0.888133	−	0.502407i
$869$	−1.05870e7			−0.475580
$870$	−6.91665e6			−0.309812
$871$	7.48926e6	+	1.29718e7i	0.334498	+	0.579367i
$872$	−2.98943e7			−1.33136
$873$	2.07589e6	−	3.59554e6i	0.0921867	−	0.159672i
$874$	183587.	+	317983.i	0.00812951	+	0.0140807i
$875$	7.18512e6	+	1.24450e7i	0.317259	+	0.549508i
$876$	7.27222e6			0.320189
$877$	2.34570e6	−	4.06288e6i	0.102985	−	0.178375i	−0.809928	−	0.586529i	$-0.800494\pi$
$877$	2.34570e6	−	4.06288e6i	0.102985	−	0.178375i	0.912913	+	0.408154i	$0.133827\pi$
$878$	−1.03531e6	+	1.79321e6i	−0.0453245	+	0.0785044i
$879$	1.09473e6	−	1.89613e6i	0.0477899	−	0.0827746i
$880$	−1.36417e6	−	2.36281e6i	−0.0593829	−	0.102854i
$881$	−6.44728e6	+	1.11670e7i	−0.279857	+	0.484727i	−0.971349	−	0.237657i	$-0.923620\pi$
$881$	−6.44728e6	+	1.11670e7i	−0.279857	+	0.484727i	0.691492	+	0.722384i	$0.256954\pi$
$882$	4.53640e6	+	7.85728e6i	0.196354	+	0.340095i
$883$	−1.28876e7			−0.556252			−0.278126	−	0.960545i	$-0.589713\pi$
$883$	−1.28876e7			−0.556252			−0.278126	+	0.960545i	$0.589713\pi$
$884$	−4.99220e6			−0.214863
$885$	2.39341e6	+	4.14551e6i	0.102721	+	0.177918i
$886$	2.11473e6	−	3.66281e6i	0.0905044	−	0.156758i
$887$	−9.83945e6	−	1.70424e7i	−0.419915	−	0.727314i	0.576015	−	0.817439i	$-0.304607\pi$
$887$	−9.83945e6	−	1.70424e7i	−0.419915	−	0.727314i	−0.995931	+	0.0901244i	$0.971274\pi$
$888$	−201881.	+	349668.i	−0.00859138	+	0.0148807i
$889$	1.71606e7	−	2.97230e7i	0.728245	−	1.26136i
$890$	1.26989e7	−	2.19951e7i	0.537390	−	0.930787i
$891$	4.89412e6			0.206529
$892$	27502.6	+	47635.9i	0.00115734	+	0.00200457i
$893$	−2.77741e6	−	4.81062e6i	−0.116550	−	0.201870i
$894$	−1.46471e6	+	2.53695e6i	−0.0612926	+	0.106162i
$895$	1.77110e7			0.739070
$896$	−1.52249e7	−	2.63703e7i	−0.633556	−	1.09735i
$897$	−431516.			−0.0179067
$898$	−4.63069e6			−0.191626
$899$	−386608.	+	4.39805e7i	−0.0159541	+	1.81493i
$900$	2.27310e7			0.935431
$901$	−1.43309e7			−0.588114
$902$	−2.33666e6	−	4.04722e6i	−0.0956268	−	0.165631i
$903$	−8.28031e6			−0.337931
$904$	−443248.	+	767728.i	−0.0180395	+	0.0312454i
$905$	−329182.	−	570160.i	−0.0133602	−	0.0231406i
$906$	−1.52923e6	−	2.64870e6i	−0.0618944	−	0.107204i
$907$	−3.23622e7			−1.30623			−0.653116	−	0.757258i	$-0.726538\pi$
$907$	−3.23622e7			−1.30623			−0.653116	+	0.757258i	$0.726538\pi$
$908$	2.99543e6	−	5.18823e6i	0.120571	−	0.208836i
$909$	677758.	−	1.17391e6i	0.0272060	−	0.0471222i
$910$	7.83867e6	−	1.35770e7i	0.313790	−	0.543500i
$911$	1.75632e7	+	3.04204e7i	0.701145	+	1.21442i	0.968065	+	0.250700i	$0.0806607\pi$
$911$	1.75632e7	+	3.04204e7i	0.701145	+	1.21442i	−0.266920	+	0.963719i	$0.586006\pi$
$912$	−232240.	+	402251.i	−0.00924590	+	0.0160144i
$913$	5.08611e6	+	8.80941e6i	0.201934	+	0.349760i
$914$	1.32285e7			0.523777
$915$	1.48385e6			0.0585919
$916$	−1.82711e7	−	3.16465e7i	−0.719492	−	1.24620i
$917$	3.13810e6	−	5.43536e6i	0.123238	−	0.213454i
$918$	−1.29719e6	−	2.24680e6i	−0.0508039	−	0.0879949i
$919$	7.93476e6	−	1.37434e7i	0.309917	−	0.536792i	−0.668427	−	0.743778i	$-0.733032\pi$
$919$	7.93476e6	−	1.37434e7i	0.309917	−	0.536792i	0.978344	+	0.206986i	$0.0663654\pi$
$920$	2.18656e6	−	3.78724e6i	0.0851712	−	0.147521i
$921$	1.73630e6	−	3.00737e6i	0.0674492	−	0.116825i
$922$	6.31036e6			0.244471
$923$	6.07301e6	+	1.05188e7i	0.234639	+	0.406406i
$924$	728912.	+	1.26251e6i	0.0280863	+	0.0486470i
$925$	−1.48485e6	+	2.57183e6i	−0.0570595	+	0.0988300i
$926$	−6.49812e6			−0.249035
$927$	−1.65673e7	−	2.86954e7i	−0.633216	−	1.09676i
$928$	4.90478e7			1.86961
$929$	3.23917e7			1.23139			0.615694	−	0.787986i	$-0.288876\pi$
$929$	3.23917e7			1.23139			0.615694	+	0.787986i	$0.288876\pi$
$930$	39575.1	−	4.50206e6i	0.00150043	−	0.170688i
$931$	−5.60702e6			−0.212011
$932$	−1.94858e7			−0.734815
$933$	1.75438e6	+	3.03868e6i	0.0659811	+	0.114283i
$934$	3.09087e6			0.115935
$935$	−2.29261e6	+	3.97092e6i	−0.0857634	+	0.148547i
$936$	−6.80126e6	−	1.17801e7i	−0.253746	−	0.439501i
$937$	−4.22569e6	−	7.31910e6i	−0.157235	−	0.272338i	0.776636	−	0.629950i	$-0.216925\pi$
$937$	−4.22569e6	−	7.31910e6i	−0.157235	−	0.272338i	−0.933870	+	0.357611i	$0.883591\pi$
$938$	1.97249e7			0.731996
$939$	−3.36789e6	+	5.83335e6i	−0.124650	+	0.215901i
$940$	−1.42150e7	+	2.46211e7i	−0.524719	+	0.908840i
$941$	9.41748e6	−	1.63116e7i	0.346706	−	0.600512i	−0.638957	−	0.769243i	$-0.720634\pi$
$941$	9.41748e6	−	1.63116e7i	0.346706	−	0.600512i	0.985662	+	0.168731i	$0.0539670\pi$
$942$	−1.43778e6	−	2.49031e6i	−0.0527917	−	0.0914380i
$943$	−2.78464e6	+	4.82313e6i	−0.101974	+	0.176624i
$944$	−2.62851e6	−	4.55271e6i	−0.0960018	−	0.166280i
$945$	−2.49085e7			−0.907336
$946$	−3.66581e6			−0.133181
$947$	1.96913e7	+	3.41064e7i	0.713510	+	1.23584i	0.963531	+	0.267595i	$0.0862289\pi$
$947$	1.96913e7	+	3.41064e7i	0.713510	+	1.23584i	−0.250022	+	0.968240i	$0.580438\pi$
$948$	4.61230e6	−	7.98874e6i	0.166685	−	0.288707i
$949$	−1.60039e7	−	2.77195e7i	−0.576846	−	0.999126i
$950$	2.29745e6	−	3.97929e6i	0.0825916	−	0.143053i
$951$	−563813.	+	976553.i	−0.0202155	+	0.0350142i
$952$	−7.64931e6	+	1.32490e7i	−0.273546	+	0.473795i
$953$	9.83652e6			0.350840			0.175420	−	0.984494i	$-0.443872\pi$
$953$	9.83652e6			0.350840			0.175420	+	0.984494i	$0.443872\pi$
$954$	−8.38991e6	−	1.45318e7i	−0.298460	−	0.516948i
$955$	5.46441e6	+	9.46463e6i	0.193881	+	0.335811i
$956$	−9.86989e6	+	1.70952e7i	−0.349275	+	0.604962i
$957$	−2.83085e6			−0.0999164
$958$	−5.50847e6	−	9.54095e6i	−0.193918	−	0.335875i
$959$	3.59050e6			0.126069
$960$	−1.86597e6			−0.0653472
$961$	−2.86247e7	−	503287.i	−0.999845	−	0.0175795i
$962$	763660.			0.0266050
$963$	−2.76898e7			−0.962174
$964$	−9.04210e6	−	1.56614e7i	−0.313384	−	0.542797i
$965$	5.68966e7			1.96683
$966$	−284128.	+	492124.i	−0.00979649	+	0.0169680i
$967$	1.72363e7	+	2.98542e7i	0.592759	+	1.02669i	0.993859	+	0.110654i	$0.0352946\pi$
$967$	1.72363e7	+	2.98542e7i	0.592759	+	1.02669i	−0.401100	+	0.916034i	$0.631372\pi$
$968$	−1.19388e7	−	2.06787e7i	−0.409519	−	0.709307i
$969$	780601.			0.0267067
$970$	−2.14767e6	+	3.71987e6i	−0.0732888	+	0.126940i
$971$	1.54124e7	−	2.66951e7i	0.524593	−	0.908622i	−0.474997	−	0.879987i	$-0.657551\pi$
$971$	1.54124e7	−	2.66951e7i	0.524593	−	0.908622i	0.999590	−	0.0286342i	$-0.00911580\pi$
$972$	−7.02636e6	+	1.21700e7i	−0.238542	+	0.413166i
$973$	2.17647e7	+	3.76976e7i	0.737006	+	1.27653i
$974$	7.76951e6	−	1.34572e7i	0.262420	−	0.454524i
$975$	2.70003e6	+	4.67659e6i	0.0909614	+	0.157550i
$976$	−1.62961e6			−0.0547593
$977$	−4.07909e7			−1.36718			−0.683592	−	0.729865i	$-0.739583\pi$
$977$	−4.07909e7			−1.36718			−0.683592	+	0.729865i	$0.739583\pi$
$978$	2.28040e6	+	3.94977e6i	0.0762367	+	0.132046i
$979$	5.19739e6	−	9.00214e6i	0.173312	−	0.300185i
$980$	1.43486e7	+	2.48524e7i	0.477247	+	0.826616i
$981$	2.18682e7	−	3.78768e7i	0.725505	−	1.25661i
$982$	−1.02420e7	+	1.77396e7i	−0.338926	+	0.587037i
$983$	−6.53301e6	+	1.13155e7i	−0.215640	+	0.373500i	−0.953470	−	0.301487i	$-0.902517\pi$
$983$	−6.53301e6	+	1.13155e7i	−0.215640	+	0.373500i	0.737830	+	0.674986i	$0.235850\pi$
$984$	9.47575e6			0.311979
$985$	−3.69096e7	−	6.39294e7i	−1.21213	−	2.09947i
$986$	−6.38294e6	−	1.10556e7i	−0.209088	−	0.362150i
$987$	4.29844e6	−	7.44512e6i	0.140449	−	0.243264i
$988$	3.61241e6			0.117735
$989$	2.18430e6	+	3.78331e6i	0.0710102	+	0.122993i
$990$	−5.36877e6			−0.174095
$991$	−7.14733e6			−0.231185			−0.115593	−	0.993297i	$-0.536877\pi$
$991$	−7.14733e6			−0.231185			−0.115593	+	0.993297i	$0.536877\pi$
$992$	−280638.	+	3.19253e7i	−0.00905455	+	1.03004i
$993$	−9.06303e6			−0.291676
$994$	1.59949e7			0.513470
$995$	3.43130e7	+	5.94319e7i	1.09876	+	1.90310i
$996$	−8.86320e6			−0.283101
$997$	4.52128e6	−	7.83109e6i	0.144053	−	0.249508i	−0.784966	−	0.619539i	$-0.787320\pi$
$997$	4.52128e6	−	7.83109e6i	0.144053	−	0.249508i	0.929019	+	0.370031i	$0.120653\pi$
$998$	−3.03127e6	−	5.25031e6i	−0.0963381	−	0.166863i
$999$	−606660.	−	1.05077e6i	−0.0192323	−	0.0333114i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.6.c.a.25.8	yes	24
31.5	even	3	inner	31.6.c.a.5.8	✓	24
31.6	odd	6		961.6.a.f.1.8		12
31.25	even	3		961.6.a.e.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.6.c.a.5.8	✓	24	31.5	even	3	inner
31.6.c.a.25.8	yes	24	1.1	even	1	trivial
961.6.a.e.1.8		12	31.25	even	3
961.6.a.f.1.8		12	31.6	odd	6

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:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	31.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.80839 q^{2} +(1.76382 + 3.05503i) q^{3} -24.1129 q^{4} +(-42.4669 + 73.5549i) q^{5} +(4.95350 + 8.57972i) q^{6} +(87.7771 + 152.034i) q^{7} -157.587 q^{8} +(115.278 - 199.667i) q^{9} +O(q^{10})\)	\(q+2.80839 q^{2} +(1.76382 + 3.05503i) q^{3} -24.1129 q^{4} +(-42.4669 + 73.5549i) q^{5} +(4.95350 + 8.57972i) q^{6} +(87.7771 + 152.034i) q^{7} -157.587 q^{8} +(115.278 - 199.667i) q^{9} +(-119.264 + 206.571i) q^{10} +(-48.8124 + 84.5455i) q^{11} +(-42.5309 - 73.6656i) q^{12} +(-187.194 + 324.230i) q^{13} +(246.513 + 426.972i) q^{14} -299.616 q^{15} +329.047 q^{16} +(-276.497 - 478.907i) q^{17} +(323.746 - 560.744i) q^{18} +(200.076 + 346.542i) q^{19} +(1024.00 - 1773.62i) q^{20} +(-309.646 + 536.322i) q^{21} +(-137.084 + 237.437i) q^{22} +326.731 q^{23} +(-277.956 - 481.433i) q^{24} +(-2044.38 - 3540.98i) q^{25} +(-525.715 + 910.565i) q^{26} +1670.53 q^{27} +(-2116.56 - 3665.99i) q^{28} +8220.01 q^{29} -841.441 q^{30} +(-47.0326 + 5350.41i) q^{31} +5966.88 q^{32} -344.385 q^{33} +(-776.512 - 1344.96i) q^{34} -14910.5 q^{35} +(-2779.69 + 4814.56i) q^{36} +(-363.153 - 629.000i) q^{37} +(561.892 + 973.225i) q^{38} -1320.71 q^{39} +(6692.25 - 11591.3i) q^{40} +(-8522.72 + 14761.8i) q^{41} +(-869.608 + 1506.20i) q^{42} +(6685.31 + 11579.3i) q^{43} +(1177.01 - 2038.64i) q^{44} +(9791.00 + 16958.5i) q^{45} +917.589 q^{46} -13881.8 q^{47} +(580.379 + 1005.25i) q^{48} +(-7006.12 + 12135.0i) q^{49} +(-5741.43 - 9944.46i) q^{50} +(975.381 - 1689.41i) q^{51} +(4513.80 - 7818.13i) q^{52} +(12957.6 - 22443.2i) q^{53} +4691.52 q^{54} +(-4145.82 - 7180.78i) q^{55} +(-13832.5 - 23958.7i) q^{56} +(-705.796 + 1222.47i) q^{57} +23085.0 q^{58} +(-7988.25 - 13836.1i) q^{59} +7224.62 q^{60} -4952.51 q^{61} +(-132.086 + 15026.1i) q^{62} +40475.0 q^{63} +6227.87 q^{64} +(-15899.1 - 27538.1i) q^{65} -967.169 q^{66} +(20004.0 - 34647.9i) q^{67} +(6667.15 + 11547.8i) q^{68} +(576.295 + 998.171i) q^{69} -41874.5 q^{70} +(16221.2 - 28095.9i) q^{71} +(-18166.3 + 31465.0i) q^{72} +(-42746.7 + 74039.5i) q^{73} +(-1019.88 - 1766.48i) q^{74} +(7211.85 - 12491.3i) q^{75} +(-4824.41 - 8356.13i) q^{76} -17138.4 q^{77} -3709.07 q^{78} +(54223.0 + 93916.9i) q^{79} +(-13973.6 + 24203.0i) q^{80} +(-25066.0 - 43415.6i) q^{81} +(-23935.2 + 41456.9i) q^{82} +(52098.6 - 90237.5i) q^{83} +(7466.47 - 12932.3i) q^{84} +46967.9 q^{85} +(18775.0 + 32519.2i) q^{86} +(14498.6 + 25112.3i) q^{87} +(7692.20 - 13323.3i) q^{88} -106477. q^{89} +(27497.0 + 47626.2i) q^{90} -65725.4 q^{91} -7878.44 q^{92} +(-16428.6 + 9293.48i) q^{93} -38985.5 q^{94} -33986.4 q^{95} +(10524.5 + 18229.0i) q^{96} +18007.7 q^{97} +(-19676.0 + 34079.7i) q^{98} +(11254.0 + 19492.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 10 q^{3} + 336 q^{4} + 28 q^{5} + 72 q^{6} - 134 q^{7} - 804 q^{8} - 668 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 + 10 * q^3 + 336 * q^4 + 28 * q^5 + 72 * q^6 - 134 * q^7 - 804 * q^8 - 668 * q^9	\( 24 q - 4 q^{2} + 10 q^{3} + 336 q^{4} + 28 q^{5} + 72 q^{6} - 134 q^{7} - 804 q^{8} - 668 q^{9} - 746 q^{10} + 394 q^{11} - 646 q^{12} - 664 q^{13} + 432 q^{14} - 1596 q^{15} + 4040 q^{16} + 432 q^{17} + 1208 q^{18} - 694 q^{19} + 5692 q^{20} - 1712 q^{21} + 616 q^{22} - 1920 q^{23} + 8432 q^{24} + 88 q^{25} + 10798 q^{26} - 3284 q^{27} - 6570 q^{28} - 21496 q^{29} + 20760 q^{30} - 284 q^{31} - 24412 q^{32} - 51144 q^{33} + 16026 q^{34} + 25172 q^{35} - 3252 q^{36} - 2116 q^{37} - 14516 q^{38} + 19116 q^{39} - 43746 q^{40} + 12416 q^{41} + 32978 q^{42} + 38354 q^{43} + 28734 q^{44} + 21396 q^{45} - 44232 q^{46} + 80256 q^{47} - 32098 q^{48} + 8876 q^{49} + 14432 q^{50} + 29346 q^{51} - 64628 q^{52} + 14152 q^{53} + 36872 q^{54} - 2202 q^{55} + 13296 q^{56} - 26440 q^{57} - 41224 q^{58} - 66074 q^{59} - 252956 q^{60} - 93928 q^{61} - 210172 q^{62} + 86656 q^{63} - 21872 q^{64} + 103544 q^{65} + 313820 q^{66} + 8434 q^{67} - 116388 q^{68} - 3768 q^{69} + 241720 q^{70} - 46854 q^{71} + 177728 q^{72} + 105776 q^{73} + 241354 q^{74} + 2800 q^{75} + 208806 q^{76} - 336920 q^{77} + 120424 q^{78} - 42030 q^{79} + 204912 q^{80} + 63960 q^{81} + 54870 q^{82} + 7174 q^{83} - 266196 q^{84} - 316144 q^{85} - 41552 q^{86} - 13808 q^{87} - 232624 q^{88} - 285000 q^{89} - 169776 q^{90} - 86900 q^{91} - 282936 q^{92} - 552372 q^{93} + 137000 q^{94} - 80860 q^{95} + 317764 q^{96} + 165384 q^{97} - 192032 q^{98} - 27496 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 + 10 * q^3 + 336 * q^4 + 28 * q^5 + 72 * q^6 - 134 * q^7 - 804 * q^8 - 668 * q^9 - 746 * q^10 + 394 * q^11 - 646 * q^12 - 664 * q^13 + 432 * q^14 - 1596 * q^15 + 4040 * q^16 + 432 * q^17 + 1208 * q^18 - 694 * q^19 + 5692 * q^20 - 1712 * q^21 + 616 * q^22 - 1920 * q^23 + 8432 * q^24 + 88 * q^25 + 10798 * q^26 - 3284 * q^27 - 6570 * q^28 - 21496 * q^29 + 20760 * q^30 - 284 * q^31 - 24412 * q^32 - 51144 * q^33 + 16026 * q^34 + 25172 * q^35 - 3252 * q^36 - 2116 * q^37 - 14516 * q^38 + 19116 * q^39 - 43746 * q^40 + 12416 * q^41 + 32978 * q^42 + 38354 * q^43 + 28734 * q^44 + 21396 * q^45 - 44232 * q^46 + 80256 * q^47 - 32098 * q^48 + 8876 * q^49 + 14432 * q^50 + 29346 * q^51 - 64628 * q^52 + 14152 * q^53 + 36872 * q^54 - 2202 * q^55 + 13296 * q^56 - 26440 * q^57 - 41224 * q^58 - 66074 * q^59 - 252956 * q^60 - 93928 * q^61 - 210172 * q^62 + 86656 * q^63 - 21872 * q^64 + 103544 * q^65 + 313820 * q^66 + 8434 * q^67 - 116388 * q^68 - 3768 * q^69 + 241720 * q^70 - 46854 * q^71 + 177728 * q^72 + 105776 * q^73 + 241354 * q^74 + 2800 * q^75 + 208806 * q^76 - 336920 * q^77 + 120424 * q^78 - 42030 * q^79 + 204912 * q^80 + 63960 * q^81 + 54870 * q^82 + 7174 * q^83 - 266196 * q^84 - 316144 * q^85 - 41552 * q^86 - 13808 * q^87 - 232624 * q^88 - 285000 * q^89 - 169776 * q^90 - 86900 * q^91 - 282936 * q^92 - 552372 * q^93 + 137000 * q^94 - 80860 * q^95 + 317764 * q^96 + 165384 * q^97 - 192032 * q^98 - 27496 * q^99

Introduction

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